LMFDB - Embedded newform 1274.2.h.p.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(263,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("1274.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1274.373
Dual form			1274.2.h.p.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +1.73205 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.133975 - 0.232051i) q^{5} +(-0.866025 - 1.50000i) q^{6} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +1.73205 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.133975 - 0.232051i) q^{5} +(-0.866025 - 1.50000i) q^{6} +1.00000 q^{8} -0.267949 q^{10} -5.46410 q^{11} +(-0.866025 + 1.50000i) q^{12} +(-1.59808 + 3.23205i) q^{13} +(0.232051 - 0.401924i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 + 3.00000i) q^{17} -3.46410 q^{19} +(0.133975 + 0.232051i) q^{20} +(2.73205 + 4.73205i) q^{22} +(-4.23205 - 7.33013i) q^{23} +1.73205 q^{24} +(2.46410 + 4.26795i) q^{25} +(3.59808 - 0.232051i) q^{26} -5.19615 q^{27} +(-4.46410 + 7.73205i) q^{29} -0.464102 q^{30} +(0.267949 + 0.464102i) q^{31} +(-0.500000 + 0.866025i) q^{32} -9.46410 q^{33} +3.46410 q^{34} +(1.26795 + 2.19615i) q^{37} +(1.73205 + 3.00000i) q^{38} +(-2.76795 + 5.59808i) q^{39} +(0.133975 - 0.232051i) q^{40} +(4.73205 - 8.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-4.23205 + 7.33013i) q^{46} +(2.46410 - 4.26795i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(2.46410 - 4.26795i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-2.00000 - 3.00000i) q^{52} +(3.46410 + 6.00000i) q^{53} +(2.59808 + 4.50000i) q^{54} +(-0.732051 + 1.26795i) q^{55} -6.00000 q^{57} +8.92820 q^{58} +(1.40192 - 2.42820i) q^{59} +(0.232051 + 0.401924i) q^{60} -3.19615 q^{61} +(0.267949 - 0.464102i) q^{62} +1.00000 q^{64} +(0.535898 + 0.803848i) q^{65} +(4.73205 + 8.19615i) q^{66} +4.92820 q^{67} +(-1.73205 - 3.00000i) q^{68} +(-7.33013 - 12.6962i) q^{69} +(1.23205 + 2.13397i) q^{71} +(-0.267949 - 0.464102i) q^{73} +(1.26795 - 2.19615i) q^{74} +(4.26795 + 7.39230i) q^{75} +(1.73205 - 3.00000i) q^{76} +(6.23205 - 0.401924i) q^{78} +(-0.535898 + 0.928203i) q^{79} -0.267949 q^{80} -9.00000 q^{81} -9.46410 q^{82} -10.3923 q^{83} +(0.464102 + 0.803848i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-7.73205 + 13.3923i) q^{87} -5.46410 q^{88} +(-4.26795 - 7.39230i) q^{89} +8.46410 q^{92} +(0.464102 + 0.803848i) q^{93} -4.92820 q^{94} +(-0.464102 + 0.803848i) q^{95} +(-0.866025 + 1.50000i) q^{96} +(-1.53590 - 2.66025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 8 q^{10} - 8 q^{11} + 4 q^{13} - 6 q^{15} - 2 q^{16} + 4 q^{20} + 4 q^{22} - 10 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{31} - 2 q^{32} - 24 q^{33} + 12 q^{37} - 18 q^{39} + 4 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} - 10 q^{46} - 4 q^{47} - 4 q^{50} - 12 q^{51} - 8 q^{52} + 4 q^{55} - 24 q^{57} + 8 q^{58} + 16 q^{59} - 6 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{65} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 2 q^{71} - 8 q^{73} + 12 q^{74} + 24 q^{75} + 18 q^{78} - 16 q^{79} - 8 q^{80} - 36 q^{81} - 24 q^{82} - 12 q^{85} - 8 q^{86} - 24 q^{87} - 8 q^{88} - 24 q^{89} + 20 q^{92} - 12 q^{93} + 8 q^{94} + 12 q^{95} - 20 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 8 * q^10 - 8 * q^11 + 4 * q^13 - 6 * q^15 - 2 * q^16 + 4 * q^20 + 4 * q^22 - 10 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^29 + 12 * q^30 + 8 * q^31 - 2 * q^32 - 24 * q^33 + 12 * q^37 - 18 * q^39 + 4 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 - 10 * q^46 - 4 * q^47 - 4 * q^50 - 12 * q^51 - 8 * q^52 + 4 * q^55 - 24 * q^57 + 8 * q^58 + 16 * q^59 - 6 * q^60 + 8 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^65 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 2 * q^71 - 8 * q^73 + 12 * q^74 + 24 * q^75 + 18 * q^78 - 16 * q^79 - 8 * q^80 - 36 * q^81 - 24 * q^82 - 12 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 + 20 * q^92 - 12 * q^93 + 8 * q^94 + 12 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.73205			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.73205			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.133975	−	0.232051i	0.0599153	−	0.103776i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	0.133975	−	0.232051i	0.0599153	−	0.103776i	0.894427	+	0.447214i	$0.147584\pi$
$6$	−0.866025	−	1.50000i	−0.353553	−	0.612372i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.267949			−0.0847330
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$	−0.866025	+	1.50000i	−0.250000	+	0.433013i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$		0			0
$15$	0.232051	−	0.401924i	0.0599153	−	0.103776i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	−0.995947	−	0.0899392i	$-0.971333\pi$
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	0.575863	+	0.817546i	$0.304666\pi$
$18$		0			0
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$	0.133975	+	0.232051i	0.0299576	+	0.0518881i
$21$		0			0
$22$	2.73205	+	4.73205i	0.582475	+	1.00888i
$23$	−4.23205	−	7.33013i	−0.882444	−	1.52844i	−0.848616	−	0.529009i	$-0.822564\pi$
$23$	−4.23205	−	7.33013i	−0.882444	−	1.52844i	−0.0338277	−	0.999428i	$-0.510770\pi$
$24$	1.73205			0.353553
$25$	2.46410	+	4.26795i	0.492820	+	0.853590i
$26$	3.59808	−	0.232051i	0.705641	−	0.0455089i
$27$	−5.19615			−1.00000
$28$		0			0
$29$	−4.46410	+	7.73205i	−0.828963	+	1.43581i	0.0698897	+	0.997555i	$0.477735\pi$
$29$	−4.46410	+	7.73205i	−0.828963	+	1.43581i	−0.898853	+	0.438251i	$0.855598\pi$
$30$	−0.464102			−0.0847330
$31$	0.267949	+	0.464102i	0.0481251	+	0.0833551i	0.889085	−	0.457743i	$-0.151342\pi$
$31$	0.267949	+	0.464102i	0.0481251	+	0.0833551i	−0.840959	+	0.541098i	$0.818009\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−9.46410			−1.64749
$34$	3.46410			0.594089
$35$		0			0
$36$		0			0
$37$	1.26795	+	2.19615i	0.208450	+	0.361045i	0.951226	−	0.308494i	$-0.0998250\pi$
$37$	1.26795	+	2.19615i	0.208450	+	0.361045i	−0.742777	+	0.669539i	$0.766492\pi$
$38$	1.73205	+	3.00000i	0.280976	+	0.486664i
$39$	−2.76795	+	5.59808i	−0.443227	+	0.896410i
$40$	0.133975	−	0.232051i	0.0211832	−	0.0366905i
$41$	4.73205	−	8.19615i	0.739022	−	1.28002i	−0.213914	−	0.976853i	$-0.568621\pi$
$41$	4.73205	−	8.19615i	0.739022	−	1.28002i	0.952936	−	0.303171i	$-0.0980455\pi$
$42$		0			0
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$	2.73205	−	4.73205i	0.411872	−	0.713384i
$45$		0			0
$46$	−4.23205	+	7.33013i	−0.623982	+	1.08077i
$47$	2.46410	−	4.26795i	0.359426	−	0.622544i	−0.628439	−	0.777859i	$-0.716306\pi$
$47$	2.46410	−	4.26795i	0.359426	−	0.622544i	0.987865	+	0.155315i	$0.0496391\pi$
$48$	−0.866025	−	1.50000i	−0.125000	−	0.216506i
$49$		0			0
$50$	2.46410	−	4.26795i	0.348477	−	0.603579i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	3.46410	+	6.00000i	0.475831	+	0.824163i	0.999617	−	0.0276867i	$-0.00881407\pi$
$53$	3.46410	+	6.00000i	0.475831	+	0.824163i	−0.523786	+	0.851850i	$0.675481\pi$
$54$	2.59808	+	4.50000i	0.353553	+	0.612372i
$55$	−0.732051	+	1.26795i	−0.0987097	+	0.170970i
$56$		0			0
$57$	−6.00000			−0.794719
$58$	8.92820			1.17233
$59$	1.40192	−	2.42820i	0.182515	−	0.316125i	−0.760221	−	0.649664i	$-0.774910\pi$
$59$	1.40192	−	2.42820i	0.182515	−	0.316125i	0.942736	+	0.333539i	$0.108243\pi$
$60$	0.232051	+	0.401924i	0.0299576	+	0.0518881i
$61$	−3.19615			−0.409225			−0.204613	−	0.978843i	$-0.565593\pi$
$61$	−3.19615			−0.409225			−0.204613	+	0.978843i	$0.565593\pi$
$62$	0.267949	−	0.464102i	0.0340296	−	0.0589410i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.535898	+	0.803848i	0.0664700	+	0.0997050i
$66$	4.73205	+	8.19615i	0.582475	+	1.00888i
$67$	4.92820			0.602076			0.301038	−	0.953612i	$-0.402667\pi$
$67$	4.92820			0.602076			0.301038	+	0.953612i	$0.402667\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$	−7.33013	−	12.6962i	−0.882444	−	1.52844i
$70$		0			0
$71$	1.23205	+	2.13397i	0.146218	+	0.253256i	0.929827	−	0.367998i	$-0.119957\pi$
$71$	1.23205	+	2.13397i	0.146218	+	0.253256i	−0.783609	+	0.621254i	$0.786623\pi$
$72$		0			0
$73$	−0.267949	−	0.464102i	−0.0313611	−	0.0543190i	0.849919	−	0.526914i	$-0.176651\pi$
$73$	−0.267949	−	0.464102i	−0.0313611	−	0.0543190i	−0.881280	+	0.472595i	$0.843318\pi$
$74$	1.26795	−	2.19615i	0.147396	−	0.255298i
$75$	4.26795	+	7.39230i	0.492820	+	0.853590i
$76$	1.73205	−	3.00000i	0.198680	−	0.344124i
$77$		0			0
$78$	6.23205	−	0.401924i	0.705641	−	0.0455089i
$79$	−0.535898	+	0.928203i	−0.0602933	+	0.104431i	−0.894596	−	0.446875i	$-0.852537\pi$
$79$	−0.535898	+	0.928203i	−0.0602933	+	0.104431i	0.834303	+	0.551306i	$0.185870\pi$
$80$	−0.267949			−0.0299576
$81$	−9.00000			−1.00000
$82$	−9.46410			−1.04514
$83$	−10.3923			−1.14070			−0.570352	−	0.821401i	$-0.693193\pi$
$83$	−10.3923			−1.14070			−0.570352	+	0.821401i	$0.693193\pi$
$84$		0			0
$85$	0.464102	+	0.803848i	0.0503389	+	0.0871895i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−7.73205	+	13.3923i	−0.828963	+	1.43581i
$88$	−5.46410			−0.582475
$89$	−4.26795	−	7.39230i	−0.452402	−	0.783583i	0.546133	−	0.837699i	$-0.316099\pi$
$89$	−4.26795	−	7.39230i	−0.452402	−	0.783583i	−0.998535	+	0.0541158i	$0.982766\pi$
$90$		0			0
$91$		0			0
$92$	8.46410			0.882444
$93$	0.464102	+	0.803848i	0.0481251	+	0.0833551i
$94$	−4.92820			−0.508305
$95$	−0.464102	+	0.803848i	−0.0476158	+	0.0824730i
$96$	−0.866025	+	1.50000i	−0.0883883	+	0.153093i
$97$	−1.53590	−	2.66025i	−0.155947	−	0.270108i	0.777457	−	0.628937i	$-0.216510\pi$
$97$	−1.53590	−	2.66025i	−0.155947	−	0.270108i	−0.933403	+	0.358829i	$0.883176\pi$
$98$		0			0
$99$		0			0
$100$	−4.92820			−0.492820
$101$	−16.0000			−1.59206			−0.796030	−	0.605257i	$-0.793070\pi$
$101$	−16.0000			−1.59206			−0.796030	+	0.605257i	$0.793070\pi$
$102$	6.00000			0.594089
$103$	8.46410	−	14.6603i	0.833993	−	1.44452i	−0.0608552	−	0.998147i	$-0.519383\pi$
$103$	8.46410	−	14.6603i	0.833993	−	1.44452i	0.894848	−	0.446371i	$-0.147284\pi$
$104$	−1.59808	+	3.23205i	−0.156704	+	0.316929i
$105$		0			0
$106$	3.46410	−	6.00000i	0.336463	−	0.582772i
$107$	7.19615	+	12.4641i	0.695678	+	1.20495i	0.969951	+	0.243298i	$0.0782294\pi$
$107$	7.19615	+	12.4641i	0.695678	+	1.20495i	−0.274273	+	0.961652i	$0.588437\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	8.73205	+	15.1244i	0.836379	+	1.44865i	0.892903	+	0.450249i	$0.148665\pi$
$109$	8.73205	+	15.1244i	0.836379	+	1.44865i	−0.0565241	+	0.998401i	$0.518002\pi$
$110$	1.46410			0.139597
$111$	2.19615	+	3.80385i	0.208450	+	0.361045i
$112$		0			0
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	0.815149	−	0.579252i	$-0.196655\pi$
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	−0.909221	+	0.416314i	$0.863322\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−2.26795			−0.211487
$116$	−4.46410	−	7.73205i	−0.414481	−	0.717903i
$117$		0			0
$118$	−2.80385			−0.258115
$119$		0			0
$120$	0.232051	−	0.401924i	0.0211832	−	0.0366905i
$121$	18.8564			1.71422
$122$	1.59808	+	2.76795i	0.144683	+	0.250598i
$123$	8.19615	−	14.1962i	0.739022	−	1.28002i
$124$	−0.535898			−0.0481251
$125$	2.66025			0.237940
$126$		0			0
$127$	−5.69615	+	9.86603i	−0.505452	+	0.875468i	0.494528	+	0.869162i	$0.335341\pi$
$127$	−5.69615	+	9.86603i	−0.505452	+	0.875468i	−0.999980	+	0.00630667i	$0.997993\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.46410	−	6.00000i	−0.304997	−	0.528271i
$130$	0.428203	−	0.866025i	0.0375559	−	0.0759555i
$131$	−4.59808	+	7.96410i	−0.401736	+	0.695827i	−0.993936	−	0.109964i	$-0.964926\pi$
$131$	−4.59808	+	7.96410i	−0.401736	+	0.695827i	0.592200	+	0.805791i	$0.298260\pi$
$132$	4.73205	−	8.19615i	0.411872	−	0.713384i
$133$		0			0
$134$	−2.46410	−	4.26795i	−0.212866	−	0.368695i
$135$	−0.696152	+	1.20577i	−0.0599153	+	0.103776i
$136$	−1.73205	+	3.00000i	−0.148522	+	0.257248i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	−7.33013	+	12.6962i	−0.623982	+	1.08077i
$139$	9.73205	+	16.8564i	0.825462	+	1.42974i	0.901566	+	0.432642i	$0.142419\pi$
$139$	9.73205	+	16.8564i	0.825462	+	1.42974i	−0.0761041	+	0.997100i	$0.524248\pi$
$140$		0			0
$141$	4.26795	−	7.39230i	0.359426	−	0.622544i
$142$	1.23205	−	2.13397i	0.103391	−	0.179079i
$143$	8.73205	−	17.6603i	0.730211	−	1.47682i
$144$		0			0
$145$	1.19615	+	2.07180i	0.0993351	+	0.172053i
$146$	−0.267949	+	0.464102i	−0.0221756	+	0.0384093i
$147$		0			0
$148$	−2.53590			−0.208450
$149$	−4.39230			−0.359832			−0.179916	−	0.983682i	$-0.557583\pi$
$149$	−4.39230			−0.359832			−0.179916	+	0.983682i	$0.557583\pi$
$150$	4.26795	−	7.39230i	0.348477	−	0.603579i
$151$	−3.69615	−	6.40192i	−0.300789	−	0.520981i	0.675526	−	0.737336i	$-0.263917\pi$
$151$	−3.69615	−	6.40192i	−0.300789	−	0.520981i	−0.976315	+	0.216355i	$0.930583\pi$
$152$	−3.46410			−0.280976
$153$		0			0
$154$		0			0
$155$	0.143594			0.0115337
$156$	−3.46410	−	5.19615i	−0.277350	−	0.416025i
$157$	4.92820	+	8.53590i	0.393313	+	0.681239i	0.992884	−	0.119083i	$-0.0379954\pi$
$157$	4.92820	+	8.53590i	0.393313	+	0.681239i	−0.599571	+	0.800322i	$0.704662\pi$
$158$	1.07180			0.0852676
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$	0.133975	+	0.232051i	0.0105916	+	0.0183452i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	0.392305			0.0307277			0.0153638	−	0.999882i	$-0.495109\pi$
$163$	0.392305			0.0307277			0.0153638	+	0.999882i	$0.495109\pi$
$164$	4.73205	+	8.19615i	0.369511	+	0.640012i
$165$	−1.26795	+	2.19615i	−0.0987097	+	0.170970i
$166$	5.19615	+	9.00000i	0.403300	+	0.698535i
$167$	2.19615	−	3.80385i	0.169943	−	0.294351i	−0.768456	−	0.639902i	$-0.778975\pi$
$167$	2.19615	−	3.80385i	0.169943	−	0.294351i	0.938400	+	0.345552i	$0.112308\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	0.464102	−	0.803848i	0.0355950	−	0.0616523i
$171$		0			0
$172$	4.00000			0.304997
$173$	15.1962			1.15534			0.577671	−	0.816270i	$-0.303962\pi$
$173$	15.1962			1.15534			0.577671	+	0.816270i	$0.303962\pi$
$174$	15.4641			1.17233
$175$		0			0
$176$	2.73205	+	4.73205i	0.205936	+	0.356692i
$177$	2.42820	−	4.20577i	0.182515	−	0.316125i
$178$	−4.26795	+	7.39230i	−0.319896	+	0.554077i
$179$	−3.46410			−0.258919			−0.129460	−	0.991585i	$-0.541324\pi$
$179$	−3.46410			−0.258919			−0.129460	+	0.991585i	$0.541324\pi$
$180$		0			0
$181$	−25.0526			−1.86214			−0.931071	−	0.364838i	$-0.881124\pi$
$181$	−25.0526			−1.86214			−0.931071	+	0.364838i	$0.881124\pi$
$182$		0			0
$183$	−5.53590			−0.409225
$184$	−4.23205	−	7.33013i	−0.311991	−	0.540384i
$185$	0.679492			0.0499572
$186$	0.464102	−	0.803848i	0.0340296	−	0.0589410i
$187$	9.46410	−	16.3923i	0.692084	−	1.19872i
$188$	2.46410	+	4.26795i	0.179713	+	0.311272i
$189$		0			0
$190$	0.928203			0.0673389
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	1.73205			0.125000
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	−1.53590	+	2.66025i	−0.110271	+	0.190995i
$195$	0.928203	+	1.39230i	0.0664700	+	0.0997050i
$196$		0			0
$197$	10.3923	−	18.0000i	0.740421	−	1.28245i	−0.211883	−	0.977295i	$-0.567959\pi$
$197$	10.3923	−	18.0000i	0.740421	−	1.28245i	0.952304	−	0.305152i	$-0.0987072\pi$
$198$		0			0
$199$	5.73205	−	9.92820i	0.406334	−	0.703792i	−0.588141	−	0.808758i	$-0.700140\pi$
$199$	5.73205	−	9.92820i	0.406334	−	0.703792i	0.994476	+	0.104966i	$0.0334735\pi$
$200$	2.46410	+	4.26795i	0.174238	+	0.301790i
$201$	8.53590			0.602076
$202$	8.00000	+	13.8564i	0.562878	+	0.974933i
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	−1.26795	−	2.19615i	−0.0885574	−	0.153386i
$206$	−16.9282			−1.17944
$207$		0			0
$208$	3.59808	−	0.232051i	0.249482	−	0.0160898i
$209$	18.9282			1.30929
$210$		0			0
$211$	−13.4641	+	23.3205i	−0.926907	+	1.60545i	−0.138442	+	0.990371i	$0.544209\pi$
$211$	−13.4641	+	23.3205i	−0.926907	+	1.60545i	−0.788465	+	0.615079i	$0.789124\pi$
$212$	−6.92820			−0.475831
$213$	2.13397	+	3.69615i	0.146218	+	0.253256i
$214$	7.19615	−	12.4641i	0.491919	−	0.852028i
$215$	−1.07180			−0.0730959
$216$	−5.19615			−0.353553
$217$		0			0
$218$	8.73205	−	15.1244i	0.591409	−	1.02435i
$219$	−0.464102	−	0.803848i	−0.0313611	−	0.0543190i
$220$	−0.732051	−	1.26795i	−0.0493549	−	0.0854851i
$221$	−6.92820	−	10.3923i	−0.466041	−	0.699062i
$222$	2.19615	−	3.80385i	0.147396	−	0.255298i
$223$	−11.6603	+	20.1962i	−0.780828	+	1.35243i	0.150631	+	0.988590i	$0.451869\pi$
$223$	−11.6603	+	20.1962i	−0.780828	+	1.35243i	−0.931460	+	0.363844i	$0.881464\pi$
$224$		0			0
$225$		0			0
$226$	−1.00000	+	1.73205i	−0.0665190	+	0.115214i
$227$	12.8660	−	22.2846i	0.853948	−	1.47908i	−0.0236694	−	0.999720i	$-0.507535\pi$
$227$	12.8660	−	22.2846i	0.853948	−	1.47908i	0.877617	−	0.479362i	$-0.159132\pi$
$228$	3.00000	−	5.19615i	0.198680	−	0.344124i
$229$	−6.00000	+	10.3923i	−0.396491	+	0.686743i	−0.993290	−	0.115648i	$-0.963106\pi$
$229$	−6.00000	+	10.3923i	−0.396491	+	0.686743i	0.596799	+	0.802391i	$0.296439\pi$
$230$	1.13397	+	1.96410i	0.0747721	+	0.129509i
$231$		0			0
$232$	−4.46410	+	7.73205i	−0.293083	+	0.507634i
$233$	−13.4282	+	23.2583i	−0.879711	+	1.52370i	−0.0280525	+	0.999606i	$0.508931\pi$
$233$	−13.4282	+	23.2583i	−0.879711	+	1.52370i	−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−0.660254	−	1.14359i	−0.0430702	−	0.0745998i
$236$	1.40192	+	2.42820i	0.0912575	+	0.158063i
$237$	−0.928203	+	1.60770i	−0.0602933	+	0.104431i
$238$		0			0
$239$	−14.3205			−0.926317			−0.463158	−	0.886276i	$-0.653284\pi$
$239$	−14.3205			−0.926317			−0.463158	+	0.886276i	$0.653284\pi$
$240$	−0.464102			−0.0299576
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	−0.991975	−	0.126432i	$-0.959647\pi$
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	0.605481	+	0.795860i	$0.292981\pi$
$242$	−9.42820	−	16.3301i	−0.606068	−	1.04974i
$243$		0			0
$244$	1.59808	−	2.76795i	0.102306	−	0.177200i
$245$		0			0
$246$	−16.3923			−1.04514
$247$	5.53590	−	11.1962i	0.352241	−	0.712394i
$248$	0.267949	+	0.464102i	0.0170148	+	0.0294705i
$249$	−18.0000			−1.14070
$250$	−1.33013	−	2.30385i	−0.0841246	−	0.145708i
$251$	12.0622	+	20.8923i	0.761358	+	1.31871i	0.942151	+	0.335189i	$0.108800\pi$
$251$	12.0622	+	20.8923i	0.761358	+	1.31871i	−0.180793	+	0.983521i	$0.557866\pi$
$252$		0			0
$253$	23.1244	+	40.0526i	1.45382	+	2.51808i
$254$	11.3923			0.714817
$255$	0.803848	+	1.39230i	0.0503389	+	0.0871895i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.92820	−	6.80385i	−0.245035	−	0.424412i	0.717107	−	0.696963i	$-0.245466\pi$
$257$	−3.92820	−	6.80385i	−0.245035	−	0.424412i	−0.962141	+	0.272551i	$0.912133\pi$
$258$	−3.46410	+	6.00000i	−0.215666	+	0.373544i
$259$		0			0
$260$	−0.964102	+	0.0621778i	−0.0597910	+	0.00385611i
$261$		0			0
$262$	9.19615			0.568140
$263$	5.53590			0.341358			0.170679	−	0.985327i	$-0.445404\pi$
$263$	5.53590			0.341358			0.170679	+	0.985327i	$0.445404\pi$
$264$	−9.46410			−0.582475
$265$	1.85641			0.114038
$266$		0			0
$267$	−7.39230	−	12.8038i	−0.452402	−	0.783583i
$268$	−2.46410	+	4.26795i	−0.150519	+	0.260706i
$269$	6.52628	−	11.3038i	0.397914	−	0.689208i	−0.595554	−	0.803315i	$-0.703067\pi$
$269$	6.52628	−	11.3038i	0.397914	−	0.689208i	0.993468	+	0.114107i	$0.0364008\pi$
$270$	1.39230			0.0847330
$271$	−11.3923	−	19.7321i	−0.692033	−	1.19864i	−0.971171	−	0.238386i	$-0.923382\pi$
$271$	−11.3923	−	19.7321i	−0.692033	−	1.19864i	0.279137	−	0.960251i	$-0.409952\pi$
$272$	3.46410			0.210042
$273$		0			0
$274$	3.00000			0.181237
$275$	−13.4641	−	23.3205i	−0.811916	−	1.40628i
$276$	14.6603			0.882444
$277$	4.26795	−	7.39230i	0.256436	−	0.444161i	−0.708848	−	0.705361i	$-0.750785\pi$
$277$	4.26795	−	7.39230i	0.256436	−	0.444161i	0.965285	+	0.261200i	$0.0841183\pi$
$278$	9.73205	−	16.8564i	0.583690	−	1.01098i
$279$		0			0
$280$		0			0
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$	−8.53590			−0.508305
$283$	−12.6603			−0.752574			−0.376287	−	0.926503i	$-0.622799\pi$
$283$	−12.6603			−0.752574			−0.376287	+	0.926503i	$0.622799\pi$
$284$	−2.46410			−0.146218
$285$	−0.803848	+	1.39230i	−0.0476158	+	0.0824730i
$286$	−19.6603	+	1.26795i	−1.16254	+	0.0749754i
$287$		0			0
$288$		0			0
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	1.19615	−	2.07180i	0.0702405	−	0.121660i
$291$	−2.66025	−	4.60770i	−0.155947	−	0.270108i
$292$	0.535898			0.0313611
$293$	−10.9282	−	18.9282i	−0.638432	−	1.10580i	−0.985777	−	0.168060i	$-0.946250\pi$
$293$	−10.9282	−	18.9282i	−0.638432	−	1.10580i	0.347344	−	0.937738i	$-0.387084\pi$
$294$		0			0
$295$	−0.375644	−	0.650635i	−0.0218709	−	0.0378814i
$296$	1.26795	+	2.19615i	0.0736980	+	0.127649i
$297$	28.3923			1.64749
$298$	2.19615	+	3.80385i	0.127220	+	0.220351i
$299$	30.4545	−	1.96410i	1.76123	−	0.113587i
$300$	−8.53590			−0.492820
$301$		0			0
$302$	−3.69615	+	6.40192i	−0.212690	+	0.368389i
$303$	−27.7128			−1.59206
$304$	1.73205	+	3.00000i	0.0993399	+	0.172062i
$305$	−0.428203	+	0.741670i	−0.0245188	+	0.0424679i
$306$		0			0
$307$	−2.80385			−0.160024			−0.0800120	−	0.996794i	$-0.525496\pi$
$307$	−2.80385			−0.160024			−0.0800120	+	0.996794i	$0.525496\pi$
$308$		0			0
$309$	14.6603	−	25.3923i	0.833993	−	1.44452i
$310$	−0.0717968	−	0.124356i	−0.00407778	−	0.00706293i
$311$	−9.92820	−	17.1962i	−0.562977	−	0.975104i	−0.997235	−	0.0743158i	$-0.976323\pi$
$311$	−9.92820	−	17.1962i	−0.562977	−	0.975104i	0.434258	−	0.900789i	$-0.357011\pi$
$312$	−2.76795	+	5.59808i	−0.156704	+	0.316929i
$313$	6.53590	−	11.3205i	0.369431	−	0.639873i	−0.620046	−	0.784566i	$-0.712886\pi$
$313$	6.53590	−	11.3205i	0.369431	−	0.639873i	0.989477	+	0.144693i	$0.0462193\pi$
$314$	4.92820	−	8.53590i	0.278115	−	0.481709i
$315$		0			0
$316$	−0.535898	−	0.928203i	−0.0301466	−	0.0522155i
$317$	2.53590	−	4.39230i	0.142430	−	0.246696i	−0.785981	−	0.618251i	$-0.787842\pi$
$317$	2.53590	−	4.39230i	0.142430	−	0.246696i	0.928411	+	0.371554i	$0.121175\pi$
$318$	6.00000	−	10.3923i	0.336463	−	0.582772i
$319$	24.3923	−	42.2487i	1.36571	−	2.36547i
$320$	0.133975	−	0.232051i	0.00748941	−	0.0129720i
$321$	12.4641	+	21.5885i	0.695678	+	1.20495i
$322$		0			0
$323$	6.00000	−	10.3923i	0.333849	−	0.578243i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−17.7321	+	1.14359i	−0.983597	+	0.0634352i
$326$	−0.196152	−	0.339746i	−0.0108639	−	0.0188168i
$327$	15.1244	+	26.1962i	0.836379	+	1.44865i
$328$	4.73205	−	8.19615i	0.261284	−	0.452557i
$329$		0			0
$330$	2.53590			0.139597
$331$	15.8564			0.871547			0.435773	−	0.900056i	$-0.356475\pi$
$331$	15.8564			0.871547			0.435773	+	0.900056i	$0.356475\pi$
$332$	5.19615	−	9.00000i	0.285176	−	0.493939i
$333$		0			0
$334$	−4.39230			−0.240336
$335$	0.660254	−	1.14359i	0.0360735	−	0.0624812i
$336$		0			0
$337$	−11.8564			−0.645860			−0.322930	−	0.946423i	$-0.604668\pi$
$337$	−11.8564			−0.645860			−0.322930	+	0.946423i	$0.604668\pi$
$338$	−5.00000	+	12.0000i	−0.271964	+	0.652714i
$339$	−1.73205	−	3.00000i	−0.0940721	−	0.162938i
$340$	−0.928203			−0.0503389
$341$	−1.46410	−	2.53590i	−0.0792855	−	0.137327i
$342$		0			0
$343$		0			0
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$	−3.92820			−0.211487
$346$	−7.59808	−	13.1603i	−0.408475	−	0.707500i
$347$	9.12436	−	15.8038i	0.489821	−	0.848395i	−0.510110	−	0.860109i	$-0.670395\pi$
$347$	9.12436	−	15.8038i	0.489821	−	0.848395i	0.999931	+	0.0117140i	$0.00372877\pi$
$348$	−7.73205	−	13.3923i	−0.414481	−	0.717903i
$349$	11.8660	−	20.5526i	0.635174	−	1.10015i	−0.351305	−	0.936261i	$-0.614262\pi$
$349$	11.8660	−	20.5526i	0.635174	−	1.10015i	0.986478	−	0.163892i	$-0.0524049\pi$
$350$		0			0
$351$	8.30385	−	16.7942i	0.443227	−	0.896410i
$352$	2.73205	−	4.73205i	0.145619	−	0.252219i
$353$	−0.535898			−0.0285230			−0.0142615	−	0.999898i	$-0.504540\pi$
$353$	−0.535898			−0.0285230			−0.0142615	+	0.999898i	$0.504540\pi$
$354$	−4.85641			−0.258115
$355$	0.660254			0.0350426
$356$	8.53590			0.452402
$357$		0			0
$358$	1.73205	+	3.00000i	0.0915417	+	0.158555i
$359$	5.76795	−	9.99038i	0.304421	−	0.527272i	−0.672711	−	0.739905i	$-0.734870\pi$
$359$	5.76795	−	9.99038i	0.304421	−	0.527272i	0.977132	+	0.212633i	$0.0682038\pi$
$360$		0			0
$361$	−7.00000			−0.368421
$362$	12.5263	+	21.6962i	0.658367	+	1.14032i
$363$	32.6603			1.71422
$364$		0			0
$365$	−0.143594			−0.00751603
$366$	2.76795	+	4.79423i	0.144683	+	0.250598i
$367$	16.9282			0.883645			0.441823	−	0.897102i	$-0.354332\pi$
$367$	16.9282			0.883645			0.441823	+	0.897102i	$0.354332\pi$
$368$	−4.23205	+	7.33013i	−0.220611	+	0.382109i
$369$		0			0
$370$	−0.339746	−	0.588457i	−0.0176626	−	0.0305924i
$371$		0			0
$372$	−0.928203			−0.0481251
$373$	−10.9282			−0.565841			−0.282920	−	0.959143i	$-0.591303\pi$
$373$	−10.9282			−0.565841			−0.282920	+	0.959143i	$0.591303\pi$
$374$	−18.9282			−0.978754
$375$	4.60770			0.237940
$376$	2.46410	−	4.26795i	0.127076	−	0.220103i
$377$	−17.8564	−	26.7846i	−0.919652	−	1.37948i
$378$		0			0
$379$	0.535898	−	0.928203i	0.0275273	−	0.0476786i	−0.851934	−	0.523650i	$-0.824570\pi$
$379$	0.535898	−	0.928203i	0.0275273	−	0.0476786i	0.879461	+	0.475971i	$0.157903\pi$
$380$	−0.464102	−	0.803848i	−0.0238079	−	0.0412365i
$381$	−9.86603	+	17.0885i	−0.505452	+	0.875468i
$382$	4.00000	+	6.92820i	0.204658	+	0.354478i
$383$	−29.3205			−1.49821			−0.749104	−	0.662452i	$-0.769516\pi$
$383$	−29.3205			−1.49821			−0.749104	+	0.662452i	$0.769516\pi$
$384$	−0.866025	−	1.50000i	−0.0441942	−	0.0765466i
$385$		0			0
$386$	−5.50000	−	9.52628i	−0.279943	−	0.484875i
$387$		0			0
$388$	3.07180			0.155947
$389$	−6.46410	−	11.1962i	−0.327743	−	0.567667i	0.654321	−	0.756217i	$-0.272955\pi$
$389$	−6.46410	−	11.1962i	−0.327743	−	0.567667i	−0.982064	+	0.188550i	$0.939621\pi$
$390$	0.741670	−	1.50000i	0.0375559	−	0.0759555i
$391$	29.3205			1.48280
$392$		0			0
$393$	−7.96410	+	13.7942i	−0.401736	+	0.695827i
$394$	−20.7846			−1.04711
$395$	0.143594	+	0.248711i	0.00722498	+	0.0125140i
$396$		0			0
$397$	−26.1244			−1.31114			−0.655572	−	0.755133i	$-0.727572\pi$
$397$	−26.1244			−1.31114			−0.655572	+	0.755133i	$0.727572\pi$
$398$	−11.4641			−0.574643
$399$		0			0
$400$	2.46410	−	4.26795i	0.123205	−	0.213397i
$401$	−3.92820	−	6.80385i	−0.196165	−	0.339768i	0.751117	−	0.660169i	$-0.229516\pi$
$401$	−3.92820	−	6.80385i	−0.196165	−	0.339768i	−0.947282	+	0.320401i	$0.896182\pi$
$402$	−4.26795	−	7.39230i	−0.212866	−	0.368695i
$403$	−1.92820	+	0.124356i	−0.0960506	+	0.00619460i
$404$	8.00000	−	13.8564i	0.398015	−	0.689382i
$405$	−1.20577	+	2.08846i	−0.0599153	+	0.103776i
$406$		0			0
$407$	−6.92820	−	12.0000i	−0.343418	−	0.594818i
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	7.53590	−	13.0526i	0.372626	−	0.645407i	−0.617342	−	0.786695i	$-0.711791\pi$
$409$	7.53590	−	13.0526i	0.372626	−	0.645407i	0.989969	+	0.141287i	$0.0451240\pi$
$410$	−1.26795	+	2.19615i	−0.0626195	+	0.108460i
$411$	−2.59808	+	4.50000i	−0.128154	+	0.221969i
$412$	8.46410	+	14.6603i	0.416996	+	0.722259i
$413$		0			0
$414$		0			0
$415$	−1.39230	+	2.41154i	−0.0683456	+	0.118378i
$416$	−2.00000	−	3.00000i	−0.0980581	−	0.147087i
$417$	16.8564	+	29.1962i	0.825462	+	1.42974i
$418$	−9.46410	−	16.3923i	−0.462904	−	0.801774i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$	11.8564			0.577846			0.288923	−	0.957352i	$-0.406703\pi$
$421$	11.8564			0.577846			0.288923	+	0.957352i	$0.406703\pi$
$422$	26.9282			1.31084
$423$		0			0
$424$	3.46410	+	6.00000i	0.168232	+	0.291386i
$425$	−17.0718			−0.828104
$426$	2.13397	−	3.69615i	0.103391	−	0.179079i
$427$		0			0
$428$	−14.3923			−0.695678
$429$	15.1244	−	30.5885i	0.730211	−	1.47682i
$430$	0.535898	+	0.928203i	0.0258433	+	0.0447619i
$431$	−6.46410			−0.311365			−0.155682	−	0.987807i	$-0.549758\pi$
$431$	−6.46410			−0.311365			−0.155682	+	0.987807i	$0.549758\pi$
$432$	2.59808	+	4.50000i	0.125000	+	0.216506i
$433$	−4.00000	−	6.92820i	−0.192228	−	0.332948i	0.753760	−	0.657149i	$-0.228238\pi$
$433$	−4.00000	−	6.92820i	−0.192228	−	0.332948i	−0.945988	+	0.324201i	$0.894905\pi$
$434$		0			0
$435$	2.07180	+	3.58846i	0.0993351	+	0.172053i
$436$	−17.4641			−0.836379
$437$	14.6603	+	25.3923i	0.701295	+	1.21468i
$438$	−0.464102	+	0.803848i	−0.0221756	+	0.0384093i
$439$	7.92820	+	13.7321i	0.378392	+	0.655395i	0.990829	−	0.135125i	$-0.0431436\pi$
$439$	7.92820	+	13.7321i	0.378392	+	0.655395i	−0.612436	+	0.790520i	$0.709810\pi$
$440$	−0.732051	+	1.26795i	−0.0348992	+	0.0604471i
$441$		0			0
$442$	−5.53590	+	11.1962i	−0.263316	+	0.532547i
$443$	−1.73205	+	3.00000i	−0.0822922	+	0.142534i	−0.904234	−	0.427037i	$-0.859557\pi$
$443$	−1.73205	+	3.00000i	−0.0822922	+	0.142534i	0.821942	+	0.569571i	$0.192891\pi$
$444$	−4.39230			−0.208450
$445$	−2.28719			−0.108423
$446$	23.3205			1.10426
$447$	−7.60770			−0.359832
$448$		0			0
$449$	8.96410	+	15.5263i	0.423042	+	0.732730i	0.996235	−	0.0866898i	$-0.0276289\pi$
$449$	8.96410	+	15.5263i	0.423042	+	0.732730i	−0.573193	+	0.819420i	$0.694296\pi$
$450$		0			0
$451$	−25.8564	+	44.7846i	−1.21753	+	2.10882i
$452$	2.00000			0.0940721
$453$	−6.40192	−	11.0885i	−0.300789	−	0.520981i
$454$	−25.7321			−1.20766
$455$		0			0
$456$	−6.00000			−0.280976
$457$	14.5000	+	25.1147i	0.678281	+	1.17482i	0.975498	+	0.220008i	$0.0706083\pi$
$457$	14.5000	+	25.1147i	0.678281	+	1.17482i	−0.297217	+	0.954810i	$0.596058\pi$
$458$	12.0000			0.560723
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$	1.13397	−	1.96410i	0.0528718	−	0.0915767i
$461$	8.13397	+	14.0885i	0.378837	+	0.656165i	0.990893	−	0.134649i	$-0.0429908\pi$
$461$	8.13397	+	14.0885i	0.378837	+	0.656165i	−0.612056	+	0.790814i	$0.709657\pi$
$462$		0			0
$463$	−0.607695			−0.0282420			−0.0141210	−	0.999900i	$-0.504495\pi$
$463$	−0.607695			−0.0282420			−0.0141210	+	0.999900i	$0.504495\pi$
$464$	8.92820			0.414481
$465$	0.248711			0.0115337
$466$	26.8564			1.24410
$467$	−17.5263	+	30.3564i	−0.811019	+	1.40473i	0.101132	+	0.994873i	$0.467754\pi$
$467$	−17.5263	+	30.3564i	−0.811019	+	1.40473i	−0.912151	+	0.409854i	$0.865580\pi$
$468$		0			0
$469$		0			0
$470$	−0.660254	+	1.14359i	−0.0304552	+	0.0527500i
$471$	8.53590	+	14.7846i	0.393313	+	0.681239i
$472$	1.40192	−	2.42820i	0.0645288	−	0.111767i
$473$	10.9282	+	18.9282i	0.502479	+	0.870320i
$474$	1.85641			0.0852676
$475$	−8.53590	−	14.7846i	−0.391654	−	0.678364i
$476$		0			0
$477$		0			0
$478$	7.16025	+	12.4019i	0.327502	+	0.567251i
$479$	31.1769			1.42451			0.712255	−	0.701921i	$-0.247674\pi$
$479$	31.1769			1.42451			0.712255	+	0.701921i	$0.247674\pi$
$480$	0.232051	+	0.401924i	0.0105916	+	0.0183452i
$481$	−9.12436	+	0.588457i	−0.416035	+	0.0268313i
$482$	12.0000			0.546585
$483$		0			0
$484$	−9.42820	+	16.3301i	−0.428555	+	0.742279i
$485$	−0.823085			−0.0373744
$486$		0			0
$487$	−1.69615	+	2.93782i	−0.0768600	+	0.133125i	−0.901894	−	0.431958i	$-0.857823\pi$
$487$	−1.69615	+	2.93782i	−0.0768600	+	0.133125i	0.825034	+	0.565084i	$0.191156\pi$
$488$	−3.19615			−0.144683
$489$	0.679492			0.0307277
$490$		0			0
$491$	16.9282	−	29.3205i	0.763959	−	1.32322i	−0.176836	−	0.984240i	$-0.556586\pi$
$491$	16.9282	−	29.3205i	0.763959	−	1.32322i	0.940795	−	0.338976i	$-0.110080\pi$
$492$	8.19615	+	14.1962i	0.369511	+	0.640012i
$493$	−15.4641	−	26.7846i	−0.696468	−	1.20632i
$494$	−12.4641	+	0.803848i	−0.560786	+	0.0361668i
$495$		0			0
$496$	0.267949	−	0.464102i	0.0120313	−	0.0208388i
$497$		0			0
$498$	9.00000	+	15.5885i	0.403300	+	0.698535i
$499$	−19.1962	+	33.2487i	−0.859338	+	1.48842i	0.0132238	+	0.999913i	$0.495791\pi$
$499$	−19.1962	+	33.2487i	−0.859338	+	1.48842i	−0.872562	+	0.488504i	$0.837543\pi$
$500$	−1.33013	+	2.30385i	−0.0594851	+	0.103031i
$501$	3.80385	−	6.58846i	0.169943	−	0.294351i
$502$	12.0622	−	20.8923i	0.538361	−	0.932469i
$503$	−3.53590	−	6.12436i	−0.157658	−	0.273072i	0.776366	−	0.630283i	$-0.217061\pi$
$503$	−3.53590	−	6.12436i	−0.157658	−	0.273072i	−0.934024	+	0.357211i	$0.883728\pi$
$504$		0			0
$505$	−2.14359	+	3.71281i	−0.0953887	+	0.165218i
$506$	23.1244	−	40.0526i	1.02800	−	1.78055i
$507$	−13.6699	−	17.8923i	−0.607100	−	0.794625i
$508$	−5.69615	−	9.86603i	−0.252726	−	0.437734i
$509$	0.669873	+	1.16025i	0.0296916	+	0.0514274i	0.880489	−	0.474066i	$-0.157214\pi$
$509$	0.669873	+	1.16025i	0.0296916	+	0.0514274i	−0.850798	+	0.525493i	$0.823881\pi$
$510$	0.803848	−	1.39230i	0.0355950	−	0.0616523i
$511$		0			0
$512$	1.00000			0.0441942
$513$	18.0000			0.794719
$514$	−3.92820	+	6.80385i	−0.173266	+	0.300105i
$515$	−2.26795	−	3.92820i	−0.0999378	−	0.173097i
$516$	6.92820			0.304997
$517$	−13.4641	+	23.3205i	−0.592151	+	1.02563i
$518$		0			0
$519$	26.3205			1.15534
$520$	0.535898	+	0.803848i	0.0235007	+	0.0352510i
$521$	16.7321	+	28.9808i	0.733044	+	1.26967i	0.955576	+	0.294745i	$0.0952346\pi$
$521$	16.7321	+	28.9808i	0.733044	+	1.26967i	−0.222532	+	0.974925i	$0.571432\pi$
$522$		0			0
$523$	3.40192	+	5.89230i	0.148756	+	0.257653i	0.930768	−	0.365611i	$-0.119140\pi$
$523$	3.40192	+	5.89230i	0.148756	+	0.257653i	−0.782012	+	0.623263i	$0.785807\pi$
$524$	−4.59808	−	7.96410i	−0.200868	−	0.347913i
$525$		0			0
$526$	−2.76795	−	4.79423i	−0.120688	−	0.209038i
$527$	−1.85641			−0.0808663
$528$	4.73205	+	8.19615i	0.205936	+	0.356692i
$529$	−24.3205	+	42.1244i	−1.05741	+	1.83149i
$530$	−0.928203	−	1.60770i	−0.0403186	−	0.0698338i
$531$		0			0
$532$		0			0
$533$	18.9282	+	28.3923i	0.819871	+	1.22981i
$534$	−7.39230	+	12.8038i	−0.319896	+	0.554077i
$535$	3.85641			0.166727
$536$	4.92820			0.212866
$537$	−6.00000			−0.258919
$538$	−13.0526			−0.562736
$539$		0			0
$540$	−0.696152	−	1.20577i	−0.0299576	−	0.0518881i
$541$	−4.80385	+	8.32051i	−0.206534	+	0.357727i	−0.950620	−	0.310356i	$-0.899552\pi$
$541$	−4.80385	+	8.32051i	−0.206534	+	0.357727i	0.744087	+	0.668083i	$0.232885\pi$
$542$	−11.3923	+	19.7321i	−0.489341	+	0.847564i
$543$	−43.3923			−1.86214
$544$	−1.73205	−	3.00000i	−0.0742611	−	0.128624i
$545$	4.67949			0.200447
$546$		0			0
$547$	−3.60770			−0.154254			−0.0771270	−	0.997021i	$-0.524575\pi$
$547$	−3.60770			−0.154254			−0.0771270	+	0.997021i	$0.524575\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$		0			0
$550$	−13.4641	+	23.3205i	−0.574111	+	0.994390i
$551$	15.4641	−	26.7846i	0.658793	−	1.14106i
$552$	−7.33013	−	12.6962i	−0.311991	−	0.540384i
$553$		0			0
$554$	−8.53590			−0.362656
$555$	1.17691			0.0499572
$556$	−19.4641			−0.825462
$557$	−5.07180			−0.214899			−0.107449	−	0.994211i	$-0.534268\pi$
$557$	−5.07180			−0.214899			−0.107449	+	0.994211i	$0.534268\pi$
$558$		0			0
$559$	14.3923	−	0.928203i	0.608730	−	0.0392588i
$560$		0			0
$561$	16.3923	−	28.3923i	0.692084	−	1.19872i
$562$	7.00000	+	12.1244i	0.295277	+	0.511435i
$563$	−7.19615	+	12.4641i	−0.303282	+	0.525299i	−0.976877	−	0.213801i	$-0.931416\pi$
$563$	−7.19615	+	12.4641i	−0.303282	+	0.525299i	0.673596	+	0.739100i	$0.264749\pi$
$564$	4.26795	+	7.39230i	0.179713	+	0.311272i
$565$	−0.535898			−0.0225454
$566$	6.33013	+	10.9641i	0.266075	+	0.460856i
$567$		0			0
$568$	1.23205	+	2.13397i	0.0516957	+	0.0895396i
$569$	−13.4282	−	23.2583i	−0.562940	−	0.975040i	−0.997238	−	0.0742709i	$-0.976337\pi$
$569$	−13.4282	−	23.2583i	−0.562940	−	0.975040i	0.434299	−	0.900769i	$-0.356996\pi$
$570$	1.60770			0.0673389
$571$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$571$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$572$	10.9282	+	16.3923i	0.456931	+	0.685397i
$573$	−13.8564			−0.578860
$574$		0			0
$575$	20.8564	−	36.1244i	0.869772	−	1.50649i
$576$		0			0
$577$	15.4641	+	26.7846i	0.643779	+	1.11506i	0.984582	+	0.174923i	$0.0559677\pi$
$577$	15.4641	+	26.7846i	0.643779	+	1.11506i	−0.340803	+	0.940135i	$0.610699\pi$
$578$	2.50000	−	4.33013i	0.103986	−	0.180110i
$579$	19.0526			0.791797
$580$	−2.39230			−0.0993351
$581$		0			0
$582$	−2.66025	+	4.60770i	−0.110271	+	0.190995i
$583$	−18.9282	−	32.7846i	−0.783926	−	1.35780i
$584$	−0.267949	−	0.464102i	−0.0110878	−	0.0192047i
$585$		0			0
$586$	−10.9282	+	18.9282i	−0.451440	+	0.781917i
$587$	−2.86603	+	4.96410i	−0.118294	+	0.204890i	−0.919092	−	0.394044i	$-0.871076\pi$
$587$	−2.86603	+	4.96410i	−0.118294	+	0.204890i	0.800798	+	0.598935i	$0.204409\pi$
$588$		0			0
$589$	−0.928203	−	1.60770i	−0.0382459	−	0.0662439i
$590$	−0.375644	+	0.650635i	−0.0154650	+	0.0267862i
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	1.26795	−	2.19615i	0.0521124	−	0.0902613i
$593$	−16.1962	+	28.0526i	−0.665096	+	1.15198i	0.314163	+	0.949369i	$0.398276\pi$
$593$	−16.1962	+	28.0526i	−0.665096	+	1.15198i	−0.979259	+	0.202611i	$0.935057\pi$
$594$	−14.1962	−	24.5885i	−0.582475	−	1.00888i
$595$		0			0
$596$	2.19615	−	3.80385i	0.0899579	−	0.155812i
$597$	9.92820	−	17.1962i	0.406334	−	0.703792i
$598$	−16.9282	−	25.3923i	−0.692246	−	1.03837i
$599$	−2.69615	−	4.66987i	−0.110162	−	0.190806i	0.805674	−	0.592360i	$-0.201804\pi$
$599$	−2.69615	−	4.66987i	−0.110162	−	0.190806i	−0.915835	+	0.401554i	$0.868470\pi$
$600$	4.26795	+	7.39230i	0.174238	+	0.301790i
$601$	−23.3923	+	40.5167i	−0.954192	+	1.65271i	−0.217986	+	0.975952i	$0.569949\pi$
$601$	−23.3923	+	40.5167i	−0.954192	+	1.65271i	−0.736206	+	0.676757i	$0.763385\pi$
$602$		0			0
$603$		0			0
$604$	7.39230			0.300789
$605$	2.52628	−	4.37564i	0.102708	−	0.177895i
$606$	13.8564	+	24.0000i	0.562878	+	0.974933i
$607$	−10.3923			−0.421811			−0.210905	−	0.977506i	$-0.567641\pi$
$607$	−10.3923			−0.421811			−0.210905	+	0.977506i	$0.567641\pi$
$608$	1.73205	−	3.00000i	0.0702439	−	0.121666i
$609$		0			0
$610$	0.856406			0.0346749
$611$	9.85641	+	14.7846i	0.398748	+	0.598121i
$612$		0			0
$613$	−24.5359			−0.990996			−0.495498	−	0.868609i	$-0.665014\pi$
$613$	−24.5359			−0.990996			−0.495498	+	0.868609i	$0.665014\pi$
$614$	1.40192	+	2.42820i	0.0565770	+	0.0979943i
$615$	−2.19615	−	3.80385i	−0.0885574	−	0.153386i
$616$		0			0
$617$	11.9641	+	20.7224i	0.481657	+	0.834254i	0.999778	−	0.0210532i	$-0.00670193\pi$
$617$	11.9641	+	20.7224i	0.481657	+	0.834254i	−0.518122	+	0.855307i	$0.673369\pi$
$618$	−29.3205			−1.17944
$619$	9.79423	+	16.9641i	0.393663	+	0.681845i	0.992930	−	0.118705i	$-0.0378743\pi$
$619$	9.79423	+	16.9641i	0.393663	+	0.681845i	−0.599266	+	0.800550i	$0.704541\pi$
$620$	−0.0717968	+	0.124356i	−0.00288343	+	0.00499424i
$621$	21.9904	+	38.0885i	0.882444	+	1.52844i
$622$	−9.92820	+	17.1962i	−0.398085	+	0.689503i
$623$		0			0
$624$	6.23205	−	0.401924i	0.249482	−	0.0160898i
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	−13.0718			−0.522454
$627$	32.7846			1.30929
$628$	−9.85641			−0.393313
$629$	−8.78461			−0.350265
$630$		0			0
$631$	17.6244	+	30.5263i	0.701615	+	1.21523i	0.967899	+	0.251338i	$0.0808705\pi$
$631$	17.6244	+	30.5263i	0.701615	+	1.21523i	−0.266285	+	0.963894i	$0.585796\pi$
$632$	−0.535898	+	0.928203i	−0.0213169	+	0.0369219i
$633$	−23.3205	+	40.3923i	−0.926907	+	1.60545i
$634$	−5.07180			−0.201427
$635$	1.52628	+	2.64359i	0.0605686	+	0.104908i
$636$	−12.0000			−0.475831
$637$		0			0
$638$	−48.7846			−1.93140
$639$		0			0
$640$	−0.267949			−0.0105916
$641$	3.89230	−	6.74167i	0.153737	−	0.266280i	−0.778862	−	0.627196i	$-0.784203\pi$
$641$	3.89230	−	6.74167i	0.153737	−	0.266280i	0.932598	+	0.360916i	$0.117536\pi$
$642$	12.4641	−	21.5885i	0.491919	−	0.852028i
$643$	−13.2583	−	22.9641i	−0.522858	−	0.905616i	−0.999646	−	0.0265978i	$-0.991533\pi$
$643$	−13.2583	−	22.9641i	−0.522858	−	0.905616i	0.476789	−	0.879018i	$-0.341801\pi$
$644$		0			0
$645$	−1.85641			−0.0730959
$646$	−12.0000			−0.472134
$647$	−10.9282			−0.429632			−0.214816	−	0.976655i	$-0.568915\pi$
$647$	−10.9282			−0.429632			−0.214816	+	0.976655i	$0.568915\pi$
$648$	−9.00000			−0.353553
$649$	−7.66025	+	13.2679i	−0.300691	+	0.520813i
$650$	9.85641	+	14.7846i	0.386600	+	0.579900i
$651$		0			0
$652$	−0.196152	+	0.339746i	−0.00768192	+	0.0133055i
$653$	6.12436	+	10.6077i	0.239665	+	0.415111i	0.960618	−	0.277872i	$-0.0896292\pi$
$653$	6.12436	+	10.6077i	0.239665	+	0.415111i	−0.720953	+	0.692983i	$0.756296\pi$
$654$	15.1244	−	26.1962i	0.591409	−	1.02435i
$655$	1.23205	+	2.13397i	0.0481402	+	0.0833813i
$656$	−9.46410			−0.369511
$657$		0			0
$658$		0			0
$659$	−10.8564	−	18.8038i	−0.422906	−	0.732494i	0.573317	−	0.819334i	$-0.305656\pi$
$659$	−10.8564	−	18.8038i	−0.422906	−	0.732494i	−0.996222	+	0.0868399i	$0.972323\pi$
$660$	−1.26795	−	2.19615i	−0.0493549	−	0.0854851i
$661$	−31.4449			−1.22306			−0.611532	−	0.791220i	$-0.709446\pi$
$661$	−31.4449			−1.22306			−0.611532	+	0.791220i	$0.709446\pi$
$662$	−7.92820	−	13.7321i	−0.308138	−	0.533711i
$663$	−12.0000	−	18.0000i	−0.466041	−	0.699062i
$664$	−10.3923			−0.403300
$665$		0			0
$666$		0			0
$667$	75.5692			2.92605
$668$	2.19615	+	3.80385i	0.0849717	+	0.147175i
$669$	−20.1962	+	34.9808i	−0.780828	+	1.35243i
$670$	−1.32051			−0.0510157
$671$	17.4641			0.674194
$672$		0			0
$673$	−22.3205	+	38.6603i	−0.860392	+	1.49024i	0.0111583	+	0.999938i	$0.496448\pi$
$673$	−22.3205	+	38.6603i	−0.860392	+	1.49024i	−0.871551	+	0.490306i	$0.836885\pi$
$674$	5.92820	+	10.2679i	0.228346	+	0.395507i
$675$	−12.8038	−	22.1769i	−0.492820	−	0.853590i
$676$	12.8923	−	1.66987i	0.495858	−	0.0642259i
$677$	−1.33013	+	2.30385i	−0.0511209	+	0.0885441i	−0.890454	−	0.455074i	$-0.849613\pi$
$677$	−1.33013	+	2.30385i	−0.0511209	+	0.0885441i	0.839333	+	0.543618i	$0.182946\pi$
$678$	−1.73205	+	3.00000i	−0.0665190	+	0.115214i
$679$		0			0
$680$	0.464102	+	0.803848i	0.0177975	+	0.0308261i
$681$	22.2846	−	38.5981i	0.853948	−	1.47908i
$682$	−1.46410	+	2.53590i	−0.0560633	+	0.0971046i
$683$	−14.5885	+	25.2679i	−0.558212	+	0.966851i	0.439434	+	0.898275i	$0.355179\pi$
$683$	−14.5885	+	25.2679i	−0.558212	+	0.966851i	−0.997646	+	0.0685764i	$0.978154\pi$
$684$		0			0
$685$	0.401924	+	0.696152i	0.0153567	+	0.0265986i
$686$		0			0
$687$	−10.3923	+	18.0000i	−0.396491	+	0.686743i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−24.9282	+	1.60770i	−0.949689	+	0.0612483i
$690$	1.96410	+	3.40192i	0.0747721	+	0.129509i
$691$	−7.52628	−	13.0359i	−0.286313	−	0.495909i	0.686614	−	0.727023i	$-0.259096\pi$
$691$	−7.52628	−	13.0359i	−0.286313	−	0.495909i	−0.972927	+	0.231114i	$0.925763\pi$
$692$	−7.59808	+	13.1603i	−0.288836	+	0.500278i
$693$		0			0
$694$	−18.2487			−0.692712
$695$	5.21539			0.197831
$696$	−7.73205	+	13.3923i	−0.293083	+	0.507634i
$697$	16.3923	+	28.3923i	0.620903	+	1.07544i
$698$	−23.7321			−0.898271
$699$	−23.2583	+	40.2846i	−0.879711	+	1.52370i
$700$		0			0
$701$	2.53590			0.0957796			0.0478898	−	0.998853i	$-0.484750\pi$
$701$	2.53590			0.0957796			0.0478898	+	0.998853i	$0.484750\pi$
$702$	−18.6962	+	1.20577i	−0.705641	+	0.0455089i
$703$	−4.39230	−	7.60770i	−0.165659	−	0.286930i
$704$	−5.46410			−0.205936
$705$	−1.14359	−	1.98076i	−0.0430702	−	0.0745998i
$706$	0.267949	+	0.464102i	0.0100844	+	0.0174667i
$707$		0			0
$708$	2.42820	+	4.20577i	0.0912575	+	0.158063i
$709$	40.5359			1.52236			0.761179	−	0.648542i	$-0.224621\pi$
$709$	40.5359			1.52236			0.761179	+	0.648542i	$0.224621\pi$
$710$	−0.330127	−	0.571797i	−0.0123894	−	0.0214592i
$711$		0			0
$712$	−4.26795	−	7.39230i	−0.159948	−	0.277038i
$713$	2.26795	−	3.92820i	0.0849354	−	0.147112i
$714$		0			0
$715$	−2.92820	−	4.39230i	−0.109509	−	0.164263i
$716$	1.73205	−	3.00000i	0.0647298	−	0.112115i
$717$	−24.8038			−0.926317
$718$	−11.5359			−0.430516
$719$	−5.46410			−0.203777			−0.101888	−	0.994796i	$-0.532488\pi$
$719$	−5.46410			−0.203777			−0.101888	+	0.994796i	$0.532488\pi$
$720$		0			0
$721$		0			0
$722$	3.50000	+	6.06218i	0.130257	+	0.225611i
$723$	−10.3923	+	18.0000i	−0.386494	+	0.669427i
$724$	12.5263	−	21.6962i	0.465536	−	0.806331i
$725$	−44.0000			−1.63412
$726$	−16.3301	−	28.2846i	−0.606068	−	1.04974i
$727$	19.3205			0.716558			0.358279	−	0.933615i	$-0.383364\pi$
$727$	19.3205			0.716558			0.358279	+	0.933615i	$0.383364\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	0.0717968	+	0.124356i	0.00265732	+	0.00460261i
$731$	13.8564			0.512498
$732$	2.76795	−	4.79423i	0.102306	−	0.177200i
$733$	−12.9186	+	22.3756i	−0.477159	+	0.826463i	−0.999657	−	0.0261769i	$-0.991667\pi$
$733$	−12.9186	+	22.3756i	−0.477159	+	0.826463i	0.522499	+	0.852640i	$0.325000\pi$
$734$	−8.46410	−	14.6603i	−0.312416	−	0.541120i
$735$		0			0
$736$	8.46410			0.311991
$737$	−26.9282			−0.991913
$738$		0			0
$739$	47.3205			1.74071			0.870357	−	0.492422i	$-0.163888\pi$
$739$	47.3205			1.74071			0.870357	+	0.492422i	$0.163888\pi$
$740$	−0.339746	+	0.588457i	−0.0124893	+	0.0216321i
$741$	9.58846	−	19.3923i	0.352241	−	0.712394i
$742$		0			0
$743$	−20.0000	+	34.6410i	−0.733729	+	1.27086i	0.221550	+	0.975149i	$0.428888\pi$
$743$	−20.0000	+	34.6410i	−0.733729	+	1.27086i	−0.955279	+	0.295707i	$0.904445\pi$
$744$	0.464102	+	0.803848i	0.0170148	+	0.0294705i
$745$	−0.588457	+	1.01924i	−0.0215594	+	0.0373420i
$746$	5.46410	+	9.46410i	0.200055	+	0.346505i
$747$		0			0
$748$	9.46410	+	16.3923i	0.346042	+	0.599362i
$749$		0			0
$750$	−2.30385	−	3.99038i	−0.0841246	−	0.145708i
$751$	−17.7679	−	30.7750i	−0.648362	−	1.12300i	−0.983514	−	0.180831i	$-0.942121\pi$
$751$	−17.7679	−	30.7750i	−0.648362	−	1.12300i	0.335152	−	0.942164i	$-0.391212\pi$
$752$	−4.92820			−0.179713
$753$	20.8923	+	36.1865i	0.761358	+	1.31871i
$754$	−14.2679	+	28.8564i	−0.519608	+	1.05089i
$755$	−1.98076			−0.0720873
$756$		0			0
$757$	−13.2679	+	22.9808i	−0.482232	+	0.835250i	−0.999792	−	0.0203968i	$-0.993507\pi$
$757$	−13.2679	+	22.9808i	−0.482232	+	0.835250i	0.517560	+	0.855647i	$0.326840\pi$
$758$	−1.07180			−0.0389294
$759$	40.0526	+	69.3731i	1.45382	+	2.51808i
$760$	−0.464102	+	0.803848i	−0.0168347	+	0.0291586i
$761$	37.8564			1.37229			0.686147	−	0.727463i	$-0.259301\pi$
$761$	37.8564			1.37229			0.686147	+	0.727463i	$0.259301\pi$
$762$	19.7321			0.714817
$763$		0			0
$764$	4.00000	−	6.92820i	0.144715	−	0.250654i
$765$		0			0
$766$	14.6603	+	25.3923i	0.529697	+	0.917461i
$767$	5.60770	+	8.41154i	0.202482	+	0.303723i
$768$	−0.866025	+	1.50000i	−0.0312500	+	0.0541266i
$769$	2.66025	−	4.60770i	0.0959312	−	0.166158i	−0.814066	−	0.580773i	$-0.802750\pi$
$769$	2.66025	−	4.60770i	0.0959312	−	0.166158i	0.909997	+	0.414615i	$0.136084\pi$
$770$		0			0
$771$	−6.80385	−	11.7846i	−0.245035	−	0.424412i
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	25.4641	−	44.1051i	0.915880	−	1.58635i	0.110272	−	0.993901i	$-0.464828\pi$
$773$	25.4641	−	44.1051i	0.915880	−	1.58635i	0.805608	−	0.592449i	$-0.201839\pi$
$774$		0			0
$775$	−1.32051	+	2.28719i	−0.0474341	+	0.0821582i
$776$	−1.53590	−	2.66025i	−0.0551355	−	0.0954976i
$777$		0			0
$778$	−6.46410	+	11.1962i	−0.231749	+	0.401402i
$779$	−16.3923	+	28.3923i	−0.587315	+	1.01726i
$780$	−1.66987	+	0.107695i	−0.0597910	+	0.00385611i
$781$	−6.73205	−	11.6603i	−0.240892	−	0.417237i
$782$	−14.6603	−	25.3923i	−0.524250	−	0.908027i
$783$	23.1962	−	40.1769i	0.828963	−	1.43581i
$784$		0			0
$785$	2.64102			0.0942619
$786$	15.9282			0.568140
$787$	13.4019	−	23.2128i	0.477727	−	0.827447i	−0.521947	−	0.852978i	$-0.674794\pi$
$787$	13.4019	−	23.2128i	0.477727	−	0.827447i	0.999674	+	0.0255305i	$0.00812748\pi$
$788$	10.3923	+	18.0000i	0.370211	+	0.641223i
$789$	9.58846			0.341358
$790$	0.143594	−	0.248711i	0.00510883	−	0.00884875i
$791$		0			0
$792$		0			0
$793$	5.10770	−	10.3301i	0.181380	−	0.366834i
$794$	13.0622	+	22.6244i	0.463559	+	0.802908i
$795$	3.21539			0.114038
$796$	5.73205	+	9.92820i	0.203167	+	0.351896i
$797$	−14.1340	−	24.4808i	−0.500651	−	0.867153i	−1.00000		0.000751950i	$-0.999761\pi$
$797$	−14.1340	−	24.4808i	−0.500651	−	0.867153i	0.499349	−	0.866401i	$-0.333573\pi$
$798$		0			0
$799$	8.53590	+	14.7846i	0.301978	+	0.523042i
$800$	−4.92820			−0.174238
$801$		0			0
$802$	−3.92820	+	6.80385i	−0.138710	+	0.240252i
$803$	1.46410	+	2.53590i	0.0516670	+	0.0894899i
$804$	−4.26795	+	7.39230i	−0.150519	+	0.260706i
$805$		0			0
$806$	1.07180	+	1.60770i	0.0377524	+	0.0566286i
$807$	11.3038	−	19.5788i	0.397914	−	0.689208i
$808$	−16.0000			−0.562878
$809$	−9.71281			−0.341484			−0.170742	−	0.985316i	$-0.554617\pi$
$809$	−9.71281			−0.341484			−0.170742	+	0.985316i	$0.554617\pi$
$810$	2.41154			0.0847330
$811$	−26.8038			−0.941210			−0.470605	−	0.882344i	$-0.655964\pi$
$811$	−26.8038			−0.941210			−0.470605	+	0.882344i	$0.655964\pi$
$812$		0			0
$813$	−19.7321	−	34.1769i	−0.692033	−	1.19864i
$814$	−6.92820	+	12.0000i	−0.242833	+	0.420600i
$815$	0.0525589	−	0.0910347i	0.00184106	−	0.00318880i
$816$	6.00000			0.210042
$817$	6.92820	+	12.0000i	0.242387	+	0.419827i
$818$	−15.0718			−0.526973
$819$		0			0
$820$	2.53590			0.0885574
$821$	−7.12436	−	12.3397i	−0.248642	−	0.430660i	0.714507	−	0.699628i	$-0.246651\pi$
$821$	−7.12436	−	12.3397i	−0.248642	−	0.430660i	−0.963149	+	0.268968i	$0.913318\pi$
$822$	5.19615			0.181237
$823$	−4.83975	+	8.38269i	−0.168703	+	0.292202i	−0.937964	−	0.346732i	$-0.887291\pi$
$823$	−4.83975	+	8.38269i	−0.168703	+	0.292202i	0.769261	+	0.638935i	$0.220625\pi$
$824$	8.46410	−	14.6603i	0.294861	−	0.510714i
$825$	−23.3205	−	40.3923i	−0.811916	−	1.40628i
$826$		0			0
$827$	47.3205			1.64550			0.822748	−	0.568407i	$-0.192440\pi$
$827$	47.3205			1.64550			0.822748	+	0.568407i	$0.192440\pi$
$828$		0			0
$829$	−20.2679			−0.703935			−0.351967	−	0.936012i	$-0.614487\pi$
$829$	−20.2679			−0.703935			−0.351967	+	0.936012i	$0.614487\pi$
$830$	2.78461			0.0966552
$831$	7.39230	−	12.8038i	0.256436	−	0.444161i
$832$	−1.59808	+	3.23205i	−0.0554033	+	0.112051i
$833$		0			0
$834$	16.8564	−	29.1962i	0.583690	−	1.01098i
$835$	−0.588457	−	1.01924i	−0.0203644	−	0.0352722i
$836$	−9.46410	+	16.3923i	−0.327323	+	0.566940i
$837$	−1.39230	−	2.41154i	−0.0481251	−	0.0833551i
$838$	−17.3205			−0.598327
$839$	−20.4641	−	35.4449i	−0.706499	−	1.22369i	−0.966148	−	0.257989i	$-0.916940\pi$
$839$	−20.4641	−	35.4449i	−0.706499	−	1.22369i	0.259649	−	0.965703i	$-0.416393\pi$
$840$		0			0
$841$	−25.3564	−	43.9186i	−0.874359	−	1.51443i
$842$	−5.92820	−	10.2679i	−0.204299	−	0.353857i
$843$	−24.2487			−0.835170
$844$	−13.4641	−	23.3205i	−0.463453	−	0.802725i
$845$	−3.45448	+	0.447441i	−0.118838	+	0.0153924i
$846$		0			0
$847$		0			0
$848$	3.46410	−	6.00000i	0.118958	−	0.206041i
$849$	−21.9282			−0.752574
$850$	8.53590	+	14.7846i	0.292779	+	0.507108i
$851$	10.7321	−	18.5885i	0.367890	−	0.637204i
$852$	−4.26795			−0.146218
$853$	45.0526			1.54257			0.771285	−	0.636490i	$-0.219614\pi$
$853$	45.0526			1.54257			0.771285	+	0.636490i	$0.219614\pi$
$854$		0			0
$855$		0			0
$856$	7.19615	+	12.4641i	0.245959	+	0.426014i
$857$	18.8564	+	32.6603i	0.644123	+	1.11565i	0.984503	+	0.175365i	$0.0561107\pi$
$857$	18.8564	+	32.6603i	0.644123	+	1.11565i	−0.340381	+	0.940288i	$0.610556\pi$
$858$	−34.0526	+	2.19615i	−1.16254	+	0.0749754i
$859$	23.0526	−	39.9282i	0.786543	−	1.36233i	−0.141530	−	0.989934i	$-0.545202\pi$
$859$	23.0526	−	39.9282i	0.786543	−	1.36233i	0.928073	−	0.372399i	$-0.121465\pi$
$860$	0.535898	−	0.928203i	0.0182740	−	0.0316515i
$861$		0			0
$862$	3.23205	+	5.59808i	0.110084	+	0.190671i
$863$	−22.5526	+	39.0622i	−0.767698	+	1.32969i	0.171110	+	0.985252i	$0.445265\pi$
$863$	−22.5526	+	39.0622i	−0.767698	+	1.32969i	−0.938808	+	0.344440i	$0.888069\pi$
$864$	2.59808	−	4.50000i	0.0883883	−	0.153093i
$865$	2.03590	−	3.52628i	0.0692226	−	0.119897i
$866$	−4.00000	+	6.92820i	−0.135926	+	0.235430i
$867$	4.33013	+	7.50000i	0.147059	+	0.254713i
$868$		0			0
$869$	2.92820	−	5.07180i	0.0993325	−	0.172049i
$870$	2.07180	−	3.58846i	0.0702405	−	0.121660i
$871$	−7.87564	+	15.9282i	−0.266856	+	0.539707i
$872$	8.73205	+	15.1244i	0.295705	+	0.512175i
$873$		0			0
$874$	14.6603	−	25.3923i	0.495890	−	0.858908i
$875$		0			0
$876$	0.928203			0.0313611
$877$	−31.8564			−1.07571			−0.537857	−	0.843036i	$-0.680766\pi$
$877$	−31.8564			−1.07571			−0.537857	+	0.843036i	$0.680766\pi$
$878$	7.92820	−	13.7321i	0.267564	−	0.463434i
$879$	−18.9282	−	32.7846i	−0.638432	−	1.10580i
$880$	1.46410			0.0493549
$881$	−10.2679	+	17.7846i	−0.345936	+	0.599179i	−0.985523	−	0.169540i	$-0.945772\pi$
$881$	−10.2679	+	17.7846i	−0.345936	+	0.599179i	0.639587	+	0.768718i	$0.279105\pi$
$882$		0			0
$883$	43.0333			1.44819			0.724093	−	0.689702i	$-0.242258\pi$
$883$	43.0333			1.44819			0.724093	+	0.689702i	$0.242258\pi$
$884$	12.4641	−	0.803848i	0.419213	−	0.0270363i
$885$	−0.650635	−	1.12693i	−0.0218709	−	0.0378814i
$886$	3.46410			0.116379
$887$	6.73205	+	11.6603i	0.226040	+	0.391513i	0.956631	−	0.291302i	$-0.0940886\pi$
$887$	6.73205	+	11.6603i	0.226040	+	0.391513i	−0.730591	+	0.682816i	$0.760755\pi$
$888$	2.19615	+	3.80385i	0.0736980	+	0.127649i
$889$		0			0
$890$	1.14359	+	1.98076i	0.0383333	+	0.0663953i
$891$	49.1769			1.64749
$892$	−11.6603	−	20.1962i	−0.390414	−	0.676217i
$893$	−8.53590	+	14.7846i	−0.285643	+	0.494748i
$894$	3.80385	+	6.58846i	0.127220	+	0.220351i
$895$	−0.464102	+	0.803848i	−0.0155132	+	0.0268697i
$896$		0			0
$897$	52.7487	−	3.40192i	1.76123	−	0.113587i
$898$	8.96410	−	15.5263i	0.299136	−	0.518119i
$899$	−4.78461			−0.159576
$900$		0			0
$901$	−24.0000			−0.799556
$902$	51.7128			1.72185
$903$		0			0
$904$	−1.00000	−	1.73205i	−0.0332595	−	0.0576072i
$905$	−3.35641	+	5.81347i	−0.111571	+	0.193246i
$906$	−6.40192	+	11.0885i	−0.212690	+	0.368389i
$907$	−16.1436			−0.536039			−0.268020	−	0.963413i	$-0.586369\pi$
$907$	−16.1436			−0.536039			−0.268020	+	0.963413i	$0.586369\pi$
$908$	12.8660	+	22.2846i	0.426974	+	0.739541i
$909$		0			0
$910$		0			0
$911$	−28.1769			−0.933543			−0.466771	−	0.884378i	$-0.654583\pi$
$911$	−28.1769			−0.933543			−0.466771	+	0.884378i	$0.654583\pi$
$912$	3.00000	+	5.19615i	0.0993399	+	0.172062i
$913$	56.7846			1.87930
$914$	14.5000	−	25.1147i	0.479617	−	0.830722i
$915$	−0.741670	+	1.28461i	−0.0245188	+	0.0424679i
$916$	−6.00000	−	10.3923i	−0.198246	−	0.343371i
$917$		0			0
$918$	−18.0000			−0.594089
$919$	2.32051			0.0765465			0.0382732	−	0.999267i	$-0.487814\pi$
$919$	2.32051			0.0765465			0.0382732	+	0.999267i	$0.487814\pi$
$920$	−2.26795			−0.0747721
$921$	−4.85641			−0.160024
$922$	8.13397	−	14.0885i	0.267878	−	0.463979i
$923$	−8.86603	+	0.571797i	−0.291829	+	0.0188209i
$924$		0			0
$925$	−6.24871	+	10.8231i	−0.205456	+	0.355861i
$926$	0.303848	+	0.526279i	0.00998505	+	0.0172946i
$927$		0			0
$928$	−4.46410	−	7.73205i	−0.146541	−	0.253817i
$929$	−29.3205			−0.961975			−0.480987	−	0.876728i	$-0.659722\pi$
$929$	−29.3205			−0.961975			−0.480987	+	0.876728i	$0.659722\pi$
$930$	−0.124356	−	0.215390i	−0.00407778	−	0.00706293i
$931$		0			0
$932$	−13.4282	−	23.2583i	−0.439855	−	0.761852i
$933$	−17.1962	−	29.7846i	−0.562977	−	0.975104i
$934$	35.0526			1.14695
$935$	−2.53590	−	4.39230i	−0.0829327	−	0.143644i
$936$		0			0
$937$	18.9282			0.618357			0.309179	−	0.951004i	$-0.399946\pi$
$937$	18.9282			0.618357			0.309179	+	0.951004i	$0.399946\pi$
$938$		0			0
$939$	11.3205	−	19.6077i	0.369431	−	0.639873i
$940$	1.32051			0.0430702
$941$	−9.47372	−	16.4090i	−0.308834	−	0.534917i	0.669273	−	0.743016i	$-0.266606\pi$
$941$	−9.47372	−	16.4090i	−0.308834	−	0.534917i	−0.978108	+	0.208099i	$0.933272\pi$
$942$	8.53590	−	14.7846i	0.278115	−	0.481709i
$943$	−80.1051			−2.60858
$944$	−2.80385			−0.0912575
$945$		0			0
$946$	10.9282	−	18.9282i	0.355307	−	0.615409i
$947$	6.46410	+	11.1962i	0.210055	+	0.363826i	0.951732	−	0.306932i	$-0.0993023\pi$
$947$	6.46410	+	11.1962i	0.210055	+	0.363826i	−0.741676	+	0.670758i	$0.765969\pi$
$948$	−0.928203	−	1.60770i	−0.0301466	−	0.0522155i
$949$	1.92820	−	0.124356i	0.0625921	−	0.00403676i
$950$	−8.53590	+	14.7846i	−0.276941	+	0.479676i
$951$	4.39230	−	7.60770i	0.142430	−	0.246696i
$952$		0			0
$953$	12.9641	+	22.4545i	0.419948	+	0.727372i	0.995934	−	0.0900880i	$-0.0287148\pi$
$953$	12.9641	+	22.4545i	0.419948	+	0.727372i	−0.575985	+	0.817460i	$0.695381\pi$
$954$		0			0
$955$	−1.07180	+	1.85641i	−0.0346825	+	0.0600719i
$956$	7.16025	−	12.4019i	0.231579	−	0.401107i
$957$	42.2487	−	73.1769i	1.36571	−	2.36547i
$958$	−15.5885	−	27.0000i	−0.503640	−	0.872330i
$959$		0			0
$960$	0.232051	−	0.401924i	0.00748941	−	0.0129720i
$961$	15.3564	−	26.5981i	0.495368	−	0.858002i
$962$	5.07180	+	7.60770i	0.163521	+	0.245282i
$963$		0			0
$964$	−6.00000	−	10.3923i	−0.193247	−	0.334714i
$965$	1.47372	−	2.55256i	0.0474407	−	0.0821698i
$966$		0			0
$967$	−48.7846			−1.56881			−0.784404	−	0.620251i	$-0.787031\pi$
$967$	−48.7846			−1.56881			−0.784404	+	0.620251i	$0.787031\pi$
$968$	18.8564			0.606068
$969$	10.3923	−	18.0000i	0.333849	−	0.578243i
$970$	0.411543	+	0.712813i	0.0132138	+	0.0228870i
$971$	37.9808			1.21886			0.609430	−	0.792840i	$-0.291398\pi$
$971$	37.9808			1.21886			0.609430	+	0.792840i	$0.291398\pi$
$972$		0			0
$973$		0			0
$974$	3.39230			0.108696
$975$	−30.7128	+	1.98076i	−0.983597	+	0.0634352i
$976$	1.59808	+	2.76795i	0.0511532	+	0.0885999i
$977$	23.7846			0.760937			0.380469	−	0.924794i	$-0.375763\pi$
$977$	23.7846			0.760937			0.380469	+	0.924794i	$0.375763\pi$
$978$	−0.339746	−	0.588457i	−0.0108639	−	0.0188168i
$979$	23.3205	+	40.3923i	0.745327	+	1.29094i
$980$		0			0
$981$		0			0
$982$	−33.8564			−1.08040
$983$	−19.7846	−	34.2679i	−0.631031	−	1.09298i	−0.987341	−	0.158610i	$-0.949299\pi$
$983$	−19.7846	−	34.2679i	−0.631031	−	1.09298i	0.356310	−	0.934368i	$-0.384035\pi$
$984$	8.19615	−	14.1962i	0.261284	−	0.452557i
$985$	−2.78461	−	4.82309i	−0.0887250	−	0.153676i
$986$	−15.4641	+	26.7846i	−0.492477	+	0.852996i
$987$		0			0
$988$	6.92820	+	10.3923i	0.220416	+	0.330623i
$989$	−16.9282	+	29.3205i	−0.538286	+	0.932338i
$990$		0			0
$991$	−10.1769			−0.323280			−0.161640	−	0.986850i	$-0.551678\pi$
$991$	−10.1769			−0.323280			−0.161640	+	0.986850i	$0.551678\pi$
$992$	−0.535898			−0.0170148
$993$	27.4641			0.871547
$994$		0			0
$995$	−1.53590	−	2.66025i	−0.0486913	−	0.0843357i
$996$	9.00000	−	15.5885i	0.285176	−	0.493939i
$997$	16.5263	−	28.6244i	0.523393	−	0.906542i	−0.476237	−	0.879317i	$-0.657999\pi$
$997$	16.5263	−	28.6244i	0.523393	−	0.906542i	0.999629	−	0.0272254i	$-0.00866717\pi$
$998$	38.3923			1.21529
$999$	−6.58846	−	11.4115i	−0.208450	−	0.361045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.h.p.373.2		4
7.2	even	3		1274.2.g.l.295.1		4
7.3	odd	6		1274.2.e.o.165.2		4
7.4	even	3		1274.2.e.p.165.1		4
7.5	odd	6		182.2.g.e.113.2	yes	4
7.6	odd	2		1274.2.h.o.373.1		4
13.3	even	3		1274.2.e.p.471.1		4
21.5	even	6		1638.2.r.v.1387.2		4
28.19	even	6		1456.2.s.l.113.1		4
91.3	odd	6		1274.2.h.o.263.1		4
91.16	even	3		1274.2.g.l.393.1		4
91.19	even	12		2366.2.d.l.337.1		4
91.33	even	12		2366.2.d.l.337.3		4
91.55	odd	6		1274.2.e.o.471.2		4
91.61	odd	6		2366.2.a.t.1.1		2
91.68	odd	6		182.2.g.e.29.2	✓	4
91.81	even	3	inner	1274.2.h.p.263.2		4
91.82	odd	6		2366.2.a.r.1.1		2
273.68	even	6		1638.2.r.v.757.2		4
364.159	even	6		1456.2.s.l.1121.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.e.29.2	✓	4	91.68	odd	6
182.2.g.e.113.2	yes	4	7.5	odd	6
1274.2.e.o.165.2		4	7.3	odd	6
1274.2.e.o.471.2		4	91.55	odd	6
1274.2.e.p.165.1		4	7.4	even	3
1274.2.e.p.471.1		4	13.3	even	3
1274.2.g.l.295.1		4	7.2	even	3
1274.2.g.l.393.1		4	91.16	even	3
1274.2.h.o.263.1		4	91.3	odd	6
1274.2.h.o.373.1		4	7.6	odd	2
1274.2.h.p.263.2		4	91.81	even	3	inner
1274.2.h.p.373.2		4	1.1	even	1	trivial
1456.2.s.l.113.1		4	28.19	even	6
1456.2.s.l.1121.1		4	364.159	even	6
1638.2.r.v.757.2		4	273.68	even	6
1638.2.r.v.1387.2		4	21.5	even	6
2366.2.a.r.1.1		2	91.82	odd	6
2366.2.a.t.1.1		2	91.61	odd	6
2366.2.d.l.337.1		4	91.19	even	12
2366.2.d.l.337.3		4	91.33	even	12

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.73205 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.133975 - 0.232051i) q^{5} +(-0.866025 - 1.50000i) q^{6} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.73205 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.133975 - 0.232051i) q^{5} +(-0.866025 - 1.50000i) q^{6} +1.00000 q^{8} -0.267949 q^{10} -5.46410 q^{11} +(-0.866025 + 1.50000i) q^{12} +(-1.59808 + 3.23205i) q^{13} +(0.232051 - 0.401924i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 + 3.00000i) q^{17} -3.46410 q^{19} +(0.133975 + 0.232051i) q^{20} +(2.73205 + 4.73205i) q^{22} +(-4.23205 - 7.33013i) q^{23} +1.73205 q^{24} +(2.46410 + 4.26795i) q^{25} +(3.59808 - 0.232051i) q^{26} -5.19615 q^{27} +(-4.46410 + 7.73205i) q^{29} -0.464102 q^{30} +(0.267949 + 0.464102i) q^{31} +(-0.500000 + 0.866025i) q^{32} -9.46410 q^{33} +3.46410 q^{34} +(1.26795 + 2.19615i) q^{37} +(1.73205 + 3.00000i) q^{38} +(-2.76795 + 5.59808i) q^{39} +(0.133975 - 0.232051i) q^{40} +(4.73205 - 8.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-4.23205 + 7.33013i) q^{46} +(2.46410 - 4.26795i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(2.46410 - 4.26795i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-2.00000 - 3.00000i) q^{52} +(3.46410 + 6.00000i) q^{53} +(2.59808 + 4.50000i) q^{54} +(-0.732051 + 1.26795i) q^{55} -6.00000 q^{57} +8.92820 q^{58} +(1.40192 - 2.42820i) q^{59} +(0.232051 + 0.401924i) q^{60} -3.19615 q^{61} +(0.267949 - 0.464102i) q^{62} +1.00000 q^{64} +(0.535898 + 0.803848i) q^{65} +(4.73205 + 8.19615i) q^{66} +4.92820 q^{67} +(-1.73205 - 3.00000i) q^{68} +(-7.33013 - 12.6962i) q^{69} +(1.23205 + 2.13397i) q^{71} +(-0.267949 - 0.464102i) q^{73} +(1.26795 - 2.19615i) q^{74} +(4.26795 + 7.39230i) q^{75} +(1.73205 - 3.00000i) q^{76} +(6.23205 - 0.401924i) q^{78} +(-0.535898 + 0.928203i) q^{79} -0.267949 q^{80} -9.00000 q^{81} -9.46410 q^{82} -10.3923 q^{83} +(0.464102 + 0.803848i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-7.73205 + 13.3923i) q^{87} -5.46410 q^{88} +(-4.26795 - 7.39230i) q^{89} +8.46410 q^{92} +(0.464102 + 0.803848i) q^{93} -4.92820 q^{94} +(-0.464102 + 0.803848i) q^{95} +(-0.866025 + 1.50000i) q^{96} +(-1.53590 - 2.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 8 q^{10} - 8 q^{11} + 4 q^{13} - 6 q^{15} - 2 q^{16} + 4 q^{20} + 4 q^{22} - 10 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{31} - 2 q^{32} - 24 q^{33} + 12 q^{37} - 18 q^{39} + 4 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} - 10 q^{46} - 4 q^{47} - 4 q^{50} - 12 q^{51} - 8 q^{52} + 4 q^{55} - 24 q^{57} + 8 q^{58} + 16 q^{59} - 6 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{65} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 2 q^{71} - 8 q^{73} + 12 q^{74} + 24 q^{75} + 18 q^{78} - 16 q^{79} - 8 q^{80} - 36 q^{81} - 24 q^{82} - 12 q^{85} - 8 q^{86} - 24 q^{87} - 8 q^{88} - 24 q^{89} + 20 q^{92} - 12 q^{93} + 8 q^{94} + 12 q^{95} - 20 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 8 * q^10 - 8 * q^11 + 4 * q^13 - 6 * q^15 - 2 * q^16 + 4 * q^20 + 4 * q^22 - 10 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^29 + 12 * q^30 + 8 * q^31 - 2 * q^32 - 24 * q^33 + 12 * q^37 - 18 * q^39 + 4 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 - 10 * q^46 - 4 * q^47 - 4 * q^50 - 12 * q^51 - 8 * q^52 + 4 * q^55 - 24 * q^57 + 8 * q^58 + 16 * q^59 - 6 * q^60 + 8 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^65 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 2 * q^71 - 8 * q^73 + 12 * q^74 + 24 * q^75 + 18 * q^78 - 16 * q^79 - 8 * q^80 - 36 * q^81 - 24 * q^82 - 12 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 + 20 * q^92 - 12 * q^93 + 8 * q^94 + 12 * q^95 - 20 * q^97

Introduction

L-functions

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