LMFDB - Embedded newform 48.2.j.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$0.500000 + 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	48.13
Dual form			48.2.j.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +(-0.665096 - 0.0793096i) q^{10} +(-2.47363 + 2.47363i) q^{11} +(1.70711 - 1.04201i) q^{12} +(-0.0594122 - 0.0594122i) q^{13} +(5.06524 - 3.98593i) q^{14} +0.473626 q^{15} +(-3.55765 - 1.82843i) q^{16} +3.61706 q^{17} +(-1.11137 + 0.874559i) q^{18} +(2.55765 + 2.55765i) q^{19} +(-0.493523 - 0.808530i) q^{20} +(-3.22274 + 3.22274i) q^{21} +(-4.91245 - 0.585786i) q^{22} +2.82843i q^{23} +(2.65103 + 0.985930i) q^{24} +4.77568i q^{25} +(0.0140696 - 0.117988i) q^{26} +(0.707107 - 0.707107i) q^{27} +(8.85970 + 2.14343i) q^{28} +(-5.16333 - 5.16333i) q^{29} +(0.414214 + 0.526374i) q^{30} -0.557647 q^{31} +(-1.07931 - 5.55294i) q^{32} +3.49824 q^{33} +(3.16333 + 4.01990i) q^{34} +(1.52637 + 1.52637i) q^{35} +(-1.94392 - 0.470294i) q^{36} +(4.38607 - 4.38607i) q^{37} +(-0.605684 + 5.07931i) q^{38} +0.0840215i q^{39} +(0.466962 - 1.25559i) q^{40} -9.27391i q^{41} +(-6.40014 - 0.763187i) q^{42} +(-1.61040 + 1.61040i) q^{43} +(-3.64520 - 5.97186i) q^{44} +(-0.334904 - 0.334904i) q^{45} +(-3.14343 + 2.47363i) q^{46} +2.82843 q^{47} +(1.22274 + 3.80853i) q^{48} -13.7721 q^{49} +(-5.30755 + 4.17661i) q^{50} +(-2.55765 - 2.55765i) q^{51} +(0.143434 - 0.0875513i) q^{52} +(-0.493523 + 0.493523i) q^{53} +(1.40426 + 0.167452i) q^{54} -1.65685i q^{55} +(5.36618 + 11.7210i) q^{56} -3.61706i q^{57} +(1.22274 - 10.2540i) q^{58} +(4.00000 - 4.00000i) q^{59} +(-0.222743 + 0.920690i) q^{60} +(2.72922 + 2.72922i) q^{61} +(-0.487695 - 0.619753i) q^{62} +4.55765 q^{63} +(5.22746 - 6.05588i) q^{64} +0.0397948 q^{65} +(3.05941 + 3.88784i) q^{66} +(3.77568 + 3.77568i) q^{67} +(-1.70108 + 7.03127i) q^{68} +(2.00000 - 2.00000i) q^{69} +(-0.361465 + 3.03127i) q^{70} +9.11529i q^{71} +(-1.17740 - 2.57172i) q^{72} -0.541560i q^{73} +(8.71044 + 1.03868i) q^{74} +(3.37691 - 3.37691i) q^{75} +(-6.17471 + 3.76901i) q^{76} +(11.2739 + 11.2739i) q^{77} +(-0.0933792 + 0.0734818i) q^{78} -10.9937 q^{79} +(1.80382 - 0.579123i) q^{80} -1.00000 q^{81} +(10.3068 - 8.11058i) q^{82} +(-10.6417 - 10.6417i) q^{83} +(-4.74912 - 7.78039i) q^{84} +(-1.21137 + 1.21137i) q^{85} +(-3.19813 - 0.381362i) q^{86} +7.30205i q^{87} +(3.44902 - 9.27391i) q^{88} +14.6533i q^{89} +(0.0793096 - 0.665096i) q^{90} +(-0.270780 + 0.270780i) q^{91} +(-5.49824 - 1.33019i) q^{92} +(0.394316 + 0.394316i) q^{93} +(2.47363 + 3.14343i) q^{94} -1.71313 q^{95} +(-3.16333 + 4.68971i) q^{96} +4.31724 q^{97} +(-12.0446 - 15.3060i) q^{98} +(-2.47363 - 2.47363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 - 12 * q^8	$ 8 q - 4 q^{4} - 12 q^{8} - 8 q^{10} - 8 q^{11} + 8 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{18} - 8 q^{19} + 16 q^{20} + 4 q^{24} + 20 q^{26} + 8 q^{28} - 16 q^{29} - 8 q^{30} + 24 q^{31} + 24 q^{35} - 4 q^{36} - 16 q^{37} - 8 q^{38} + 16 q^{40} - 20 q^{42} - 8 q^{43} - 40 q^{44} - 8 q^{46} - 16 q^{48} - 8 q^{49} - 36 q^{50} + 8 q^{51} - 16 q^{52} + 16 q^{53} + 4 q^{54} - 16 q^{58} + 32 q^{59} + 24 q^{60} + 16 q^{61} - 12 q^{62} + 8 q^{63} + 8 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{67} + 32 q^{68} + 16 q^{69} + 32 q^{70} - 4 q^{72} + 52 q^{74} + 16 q^{75} + 8 q^{76} + 16 q^{77} - 12 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 40 q^{82} - 40 q^{83} - 24 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{88} - 8 q^{90} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 48 q^{95} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 12 * q^8 - 8 * q^10 - 8 * q^11 + 8 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^18 - 8 * q^19 + 16 * q^20 + 4 * q^24 + 20 * q^26 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 24 * q^35 - 4 * q^36 - 16 * q^37 - 8 * q^38 + 16 * q^40 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 8 * q^46 - 16 * q^48 - 8 * q^49 - 36 * q^50 + 8 * q^51 - 16 * q^52 + 16 * q^53 + 4 * q^54 - 16 * q^58 + 32 * q^59 + 24 * q^60 + 16 * q^61 - 12 * q^62 + 8 * q^63 + 8 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^67 + 32 * q^68 + 16 * q^69 + 32 * q^70 - 4 * q^72 + 52 * q^74 + 16 * q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 40 * q^82 - 40 * q^83 - 24 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^88 - 8 * q^90 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 48 * q^95 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.874559	+	1.11137i	0.618406	+	0.785858i
$2$	0.874559	+	1.11137i	0.618406	+	0.785858i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.470294	+	1.94392i	−0.235147	+	0.971960i
$5$	−0.334904	+	0.334904i	−0.149774	+	0.149774i	−0.778017	−	0.628243i	$-0.783774\pi$
$5$	−0.334904	+	0.334904i	−0.149774	+	0.149774i	0.628243	+	0.778017i	$0.283774\pi$
$6$	0.167452	−	1.40426i	0.0683620	−	0.573289i
$7$		−	4.55765i		−	1.72263i	−0.508072	−	0.861314i	$-0.669642\pi$
$7$		−	4.55765i		−	1.72263i	0.508072	−	0.861314i	$-0.330358\pi$
$8$	−2.57172	+	1.17740i	−0.909239	+	0.416274i
$9$			1.00000i			0.333333i
$10$	−0.665096	−	0.0793096i	−0.210322	−	0.0250799i
$11$	−2.47363	+	2.47363i	−0.745826	+	0.745826i	−0.973692	−	0.227866i	$-0.926825\pi$
$11$	−2.47363	+	2.47363i	−0.745826	+	0.745826i	0.227866	+	0.973692i	$0.426825\pi$
$12$	1.70711	−	1.04201i	0.492799	−	0.300803i
$13$	−0.0594122	−	0.0594122i	−0.0164780	−	0.0164780i	0.698820	−	0.715298i	$-0.253709\pi$
$13$	−0.0594122	−	0.0594122i	−0.0164780	−	0.0164780i	−0.715298	+	0.698820i	$0.753709\pi$
$14$	5.06524	−	3.98593i	1.35374	−	1.06528i
$15$	0.473626			0.122290
$16$	−3.55765	−	1.82843i	−0.889412	−	0.457107i
$17$	3.61706			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$17$	3.61706			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$18$	−1.11137	+	0.874559i	−0.261953	+	0.206135i
$19$	2.55765	+	2.55765i	0.586765	+	0.586765i	0.936754	−	0.349989i	$-0.113815\pi$
$19$	2.55765	+	2.55765i	0.586765	+	0.586765i	−0.349989	+	0.936754i	$0.613815\pi$
$20$	−0.493523	−	0.808530i	−0.110355	−	0.180793i
$21$	−3.22274	+	3.22274i	−0.703260	+	0.703260i
$22$	−4.91245	−	0.585786i	−1.04734	−	0.124890i
$23$			2.82843i			0.589768i	0.955533	+	0.294884i	$0.0952810\pi$
$23$			2.82843i			0.589768i	−0.955533	+	0.294884i	$0.904719\pi$
$24$	2.65103	+	0.985930i	0.541139	+	0.201252i
$25$			4.77568i			0.955136i
$26$	0.0140696	−	0.117988i	0.00275927	−	0.0231394i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	8.85970	+	2.14343i	1.67433	+	0.405071i
$29$	−5.16333	−	5.16333i	−0.958807	−	0.958807i	0.0403780	−	0.999184i	$-0.487144\pi$
$29$	−5.16333	−	5.16333i	−0.958807	−	0.958807i	−0.999184	+	0.0403780i	$0.987144\pi$
$30$	0.414214	+	0.526374i	0.0756247	+	0.0961023i
$31$	−0.557647			−0.100156			−0.0500782	−	0.998745i	$-0.515947\pi$
$31$	−0.557647			−0.100156			−0.0500782	+	0.998745i	$0.515947\pi$
$32$	−1.07931	−	5.55294i	−0.190797	−	0.981630i
$33$	3.49824			0.608965
$34$	3.16333	+	4.01990i	0.542507	+	0.689407i
$35$	1.52637	+	1.52637i	0.258004	+	0.258004i
$36$	−1.94392	−	0.470294i	−0.323987	−	0.0783823i
$37$	4.38607	−	4.38607i	0.721066	−	0.721066i	−0.247756	−	0.968822i	$-0.579693\pi$
$37$	4.38607	−	4.38607i	0.721066	−	0.721066i	0.968822	+	0.247756i	$0.0796932\pi$
$38$	−0.605684	+	5.07931i	−0.0982549	+	0.823973i
$39$			0.0840215i			0.0134542i
$40$	0.466962	−	1.25559i	0.0738332	−	0.198527i
$41$		−	9.27391i		−	1.44834i	−0.689620	−	0.724171i	$-0.742223\pi$
$41$		−	9.27391i		−	1.44834i	0.689620	−	0.724171i	$-0.257777\pi$
$42$	−6.40014	−	0.763187i	−0.987564	−	0.117762i
$43$	−1.61040	+	1.61040i	−0.245583	+	0.245583i	−0.819155	−	0.573572i	$-0.805557\pi$
$43$	−1.61040	+	1.61040i	−0.245583	+	0.245583i	0.573572	+	0.819155i	$0.305557\pi$
$44$	−3.64520	−	5.97186i	−0.549534	−	0.900292i
$45$	−0.334904	−	0.334904i	−0.0499245	−	0.0499245i
$46$	−3.14343	+	2.47363i	−0.463474	+	0.364716i
$47$	2.82843			0.412568			0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843			0.412568			0.206284	+	0.978492i	$0.433863\pi$
$48$	1.22274	+	3.80853i	0.176488	+	0.549714i
$49$	−13.7721			−1.96745
$50$	−5.30755	+	4.17661i	−0.750601	+	0.590662i
$51$	−2.55765	−	2.55765i	−0.358142	−	0.358142i
$52$	0.143434	−	0.0875513i	0.0198907	−	0.0121412i
$53$	−0.493523	+	0.493523i	−0.0677906	+	0.0677906i	−0.740189	−	0.672399i	$-0.765264\pi$
$53$	−0.493523	+	0.493523i	−0.0677906	+	0.0677906i	0.672399	+	0.740189i	$0.265264\pi$
$54$	1.40426	+	0.167452i	0.191096	+	0.0227873i
$55$		−	1.65685i		−	0.223410i
$56$	5.36618	+	11.7210i	0.717086	+	1.56628i
$57$		−	3.61706i		−	0.479091i
$58$	1.22274	−	10.2540i	0.160554	−	1.34642i
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	−0.397044	−	0.917800i	$-0.629964\pi$
$59$	4.00000	−	4.00000i	0.520756	−	0.520756i	0.917800	+	0.397044i	$0.129964\pi$
$60$	−0.222743	+	0.920690i	−0.0287560	+	0.118861i
$61$	2.72922	+	2.72922i	0.349441	+	0.349441i	0.859901	−	0.510460i	$-0.170525\pi$
$61$	2.72922	+	2.72922i	0.349441	+	0.349441i	−0.510460	+	0.859901i	$0.670525\pi$
$62$	−0.487695	−	0.619753i	−0.0619374	−	0.0787088i
$63$	4.55765			0.574210
$64$	5.22746	−	6.05588i	0.653432	−	0.756985i
$65$	0.0397948			0.00493593
$66$	3.05941	+	3.88784i	0.376588	+	0.478560i
$67$	3.77568	+	3.77568i	0.461273	+	0.461273i	0.899072	−	0.437800i	$-0.144242\pi$
$67$	3.77568	+	3.77568i	0.461273	+	0.461273i	−0.437800	+	0.899072i	$0.644242\pi$
$68$	−1.70108	+	7.03127i	−0.206286	+	0.852667i
$69$	2.00000	−	2.00000i	0.240772	−	0.240772i
$70$	−0.361465	+	3.03127i	−0.0432033	+	0.362306i
$71$			9.11529i			1.08179i	0.841091	+	0.540893i	$0.181914\pi$
$71$			9.11529i			1.08179i	−0.841091	+	0.540893i	$0.818086\pi$
$72$	−1.17740	−	2.57172i	−0.138758	−	0.303080i
$73$		−	0.541560i		−	0.0633848i	−0.999498	−	0.0316924i	$-0.989910\pi$
$73$		−	0.541560i		−	0.0633848i	0.999498	−	0.0316924i	$-0.0100897\pi$
$74$	8.71044	+	1.03868i	1.01257	+	0.120744i
$75$	3.37691	−	3.37691i	0.389933	−	0.389933i
$76$	−6.17471	+	3.76901i	−0.708287	+	0.432336i
$77$	11.2739	+	11.2739i	1.28478	+	1.28478i
$78$	−0.0933792	+	0.0734818i	−0.0105731	+	0.00832017i
$79$	−10.9937			−1.23689			−0.618445	−	0.785828i	$-0.712237\pi$
$79$	−10.9937			−1.23689			−0.618445	+	0.785828i	$0.712237\pi$
$80$	1.80382	−	0.579123i	0.201673	−	0.0647479i
$81$	−1.00000			−0.111111
$82$	10.3068	−	8.11058i	1.13819	−	0.895664i
$83$	−10.6417	−	10.6417i	−1.16807	−	1.16807i	−0.982660	−	0.185415i	$-0.940637\pi$
$83$	−10.6417	−	10.6417i	−1.16807	−	1.16807i	−0.185415	−	0.982660i	$-0.559363\pi$
$84$	−4.74912	−	7.78039i	−0.518171	−	0.848910i
$85$	−1.21137	+	1.21137i	−0.131391	+	0.131391i
$86$	−3.19813	−	0.381362i	−0.344864	−	0.0411234i
$87$			7.30205i			0.782862i
$88$	3.44902	−	9.27391i	0.367666	−	0.988603i
$89$			14.6533i			1.55325i	0.629964	+	0.776625i	$0.283070\pi$
$89$			14.6533i			1.55325i	−0.629964	+	0.776625i	$0.716930\pi$
$90$	0.0793096	−	0.665096i	0.00835996	−	0.0701073i
$91$	−0.270780	+	0.270780i	−0.0283854	+	0.0283854i
$92$	−5.49824	−	1.33019i	−0.573231	−	0.138682i
$93$	0.394316	+	0.394316i	0.0408887	+	0.0408887i
$94$	2.47363	+	3.14343i	0.255135	+	0.324220i
$95$	−1.71313			−0.175764
$96$	−3.16333	+	4.68971i	−0.322856	+	0.478641i
$97$	4.31724			0.438349			0.219175	−	0.975686i	$-0.429664\pi$
$97$	4.31724			0.438349			0.219175	+	0.975686i	$0.429664\pi$
$98$	−12.0446	−	15.3060i	−1.21668	−	1.54614i
$99$	−2.47363	−	2.47363i	−0.248609	−	0.248609i
$100$	−9.28354	−	2.24597i	−0.928354	−	0.224597i
$101$	−0.453728	+	0.453728i	−0.0451477	+	0.0451477i	−0.729320	−	0.684173i	$-0.760164\pi$
$101$	−0.453728	+	0.453728i	−0.0451477	+	0.0451477i	0.684173	+	0.729320i	$0.260164\pi$
$102$	0.605684	−	5.07931i	0.0599716	−	0.502927i
$103$			1.33686i			0.131724i	0.997829	+	0.0658622i	$0.0209798\pi$
$103$			1.33686i			0.131724i	−0.997829	+	0.0658622i	$0.979020\pi$
$104$	0.222743	+	0.0828394i	0.0218418	+	0.00812307i
$105$		−	2.15862i		−	0.210660i
$106$	−0.980103	−	0.116873i	−0.0951960	−	0.0113517i
$107$	6.06255	−	6.06255i	0.586088	−	0.586088i	−0.350481	−	0.936570i	$-0.613982\pi$
$107$	6.06255	−	6.06255i	0.586088	−	0.586088i	0.936570	+	0.350481i	$0.113982\pi$
$108$	1.04201	+	1.70711i	0.100268	+	0.164266i
$109$	5.71627	+	5.71627i	0.547519	+	0.547519i	0.925722	−	0.378203i	$-0.123458\pi$
$109$	5.71627	+	5.71627i	0.547519	+	0.547519i	−0.378203	+	0.925722i	$0.623458\pi$
$110$	1.84138	−	1.44902i	0.175569	−	0.138158i
$111$	−6.20285			−0.588748
$112$	−8.33333	+	16.2145i	−0.787425	+	1.53213i
$113$	−9.55136			−0.898516			−0.449258	−	0.893402i	$-0.648312\pi$
$113$	−9.55136			−0.898516			−0.449258	+	0.893402i	$0.648312\pi$
$114$	4.01990	−	3.16333i	0.376498	−	0.296273i
$115$	−0.947252	−	0.947252i	−0.0883317	−	0.0883317i
$116$	12.4654	−	7.60882i	1.15738	−	0.706461i
$117$	0.0594122	−	0.0594122i	0.00549266	−	0.00549266i
$118$	7.94372	+	0.947252i	0.731279	+	0.0872016i
$119$		−	16.4853i		−	1.51120i
$120$	−1.21803	+	0.557647i	−0.111191	+	0.0509060i
$121$		−	1.23765i		−	0.112514i
$122$	−0.646314	+	5.42004i	−0.0585146	+	0.490707i
$123$	−6.55765	+	6.55765i	−0.591283	+	0.591283i
$124$	0.262258	−	1.08402i	0.0235515	−	0.0973480i
$125$	−3.27391	−	3.27391i	−0.292828	−	0.292828i
$126$	3.98593	+	5.06524i	0.355095	+	0.451247i
$127$	5.09921			0.452481			0.226241	−	0.974071i	$-0.427356\pi$
$127$	5.09921			0.452481			0.226241	+	0.974071i	$0.427356\pi$
$128$	11.3021	+	0.513421i	0.998970	+	0.0453804i
$129$	2.27744			0.200518
$130$	0.0348029	+	0.0442268i	0.00305241	+	0.00387894i
$131$	2.11882	+	2.11882i	0.185123	+	0.185123i	0.793584	−	0.608461i	$-0.208213\pi$
$131$	2.11882	+	2.11882i	0.185123	+	0.185123i	−0.608461	+	0.793584i	$0.708213\pi$
$132$	−1.64520	+	6.80029i	−0.143196	+	0.591889i
$133$	11.6569	−	11.6569i	1.01078	−	1.01078i
$134$	−0.894129	+	7.49824i	−0.0772410	+	0.647749i
$135$			0.473626i			0.0407632i
$136$	−9.30205	+	4.25873i	−0.797644	+	0.365183i
$137$		−	3.37941i		−	0.288723i	−0.989525	−	0.144361i	$-0.953887\pi$
$137$		−	3.37941i		−	0.288723i	0.989525	−	0.144361i	$-0.0461127\pi$
$138$	3.97186	+	0.473626i	0.338107	+	0.0403177i
$139$	5.88118	−	5.88118i	0.498835	−	0.498835i	−0.412240	−	0.911075i	$-0.635254\pi$
$139$	5.88118	−	5.88118i	0.498835	−	0.498835i	0.911075	+	0.412240i	$0.135254\pi$
$140$	−3.68499	+	2.24930i	−0.311439	+	0.190101i
$141$	−2.00000	−	2.00000i	−0.168430	−	0.168430i
$142$	−10.1305	+	7.97186i	−0.850131	+	0.668984i
$143$	0.293927			0.0245794
$144$	1.82843	−	3.55765i	0.152369	−	0.296471i
$145$	3.45844			0.287208
$146$	0.601874	−	0.473626i	0.0498115	−	0.0391975i
$147$	9.73838	+	9.73838i	0.803208	+	0.803208i
$148$	6.46343	+	10.5889i	0.531291	+	0.870404i
$149$	−9.99176	+	9.99176i	−0.818557	+	0.818557i	−0.985899	−	0.167342i	$-0.946482\pi$
$149$	−9.99176	+	9.99176i	−0.818557	+	0.818557i	0.167342	+	0.985899i	$0.446482\pi$
$150$	6.70632	+	0.799697i	0.547569	+	0.0652950i
$151$			9.97685i			0.811905i	0.913894	+	0.405952i	$0.133060\pi$
$151$			9.97685i			0.811905i	−0.913894	+	0.405952i	$0.866940\pi$
$152$	−9.58892	−	3.56617i	−0.777764	−	0.289255i
$153$			3.61706i			0.292422i
$154$	−2.66981	+	22.3892i	−0.215139	+	1.80417i
$155$	0.186758	−	0.186758i	0.0150008	−	0.0150008i
$156$	−0.163331	−	0.0395148i	−0.0130770	−	0.00316372i
$157$	−16.1618	−	16.1618i	−1.28985	−	1.28985i	−0.934877	−	0.354971i	$-0.884491\pi$
$157$	−16.1618	−	16.1618i	−1.28985	−	1.28985i	−0.354971	−	0.934877i	$-0.615509\pi$
$158$	−9.61465	−	12.2181i	−0.764900	−	0.972020i
$159$	0.697947			0.0553508
$160$	2.22117	+	1.49824i	0.175599	+	0.118446i
$161$	12.8910			1.01595
$162$	−0.874559	−	1.11137i	−0.0687118	−	0.0873176i
$163$	−7.50490	−	7.50490i	−0.587829	−	0.587829i	0.349214	−	0.937043i	$-0.386449\pi$
$163$	−7.50490	−	7.50490i	−0.587829	−	0.587829i	−0.937043	+	0.349214i	$0.886449\pi$
$164$	18.0277	+	4.36147i	1.40773	+	0.340573i
$165$	−1.17157	+	1.17157i	−0.0912068	+	0.0912068i
$166$	2.52008	−	21.1336i	0.195596	−	1.64029i
$167$		−	5.83822i		−	0.451775i	−0.974153	−	0.225888i	$-0.927472\pi$
$167$		−	5.83822i		−	0.451775i	0.974153	−	0.225888i	$-0.0725282\pi$
$168$	4.49352	−	12.0824i	0.346683	−	0.932181i
$169$		−	12.9929i		−	0.999457i
$170$	−2.40569	−	0.286867i	−0.184508	−	0.0220017i
$171$	−2.55765	+	2.55765i	−0.195588	+	0.195588i
$172$	−2.37312	−	3.88784i	−0.180949	−	0.296445i
$173$	−3.62530	−	3.62530i	−0.275627	−	0.275627i	0.555734	−	0.831360i	$-0.312437\pi$
$173$	−3.62530	−	3.62530i	−0.275627	−	0.275627i	−0.831360	+	0.555734i	$0.812437\pi$
$174$	−8.11529	+	6.38607i	−0.615219	+	0.484127i
$175$	21.7659			1.64534
$176$	13.3231	−	4.27744i	1.00427	−	0.322424i
$177$	−5.65685			−0.425195
$178$	−16.2853	+	12.8152i	−1.22063	+	0.960539i
$179$	9.28334	+	9.28334i	0.693869	+	0.693869i	0.963081	−	0.269212i	$-0.0867632\pi$
$179$	9.28334	+	9.28334i	0.693869	+	0.693869i	−0.269212	+	0.963081i	$0.586763\pi$
$180$	0.808530	−	0.493523i	0.0602642	−	0.0367850i
$181$	−10.8316	+	10.8316i	−0.805104	+	0.805104i	−0.983888	−	0.178785i	$-0.942783\pi$
$181$	−10.8316	+	10.8316i	−0.805104	+	0.805104i	0.178785	+	0.983888i	$0.442783\pi$
$182$	−0.537750	−	0.0641242i	−0.0398607	−	0.00475320i
$183$		−	3.85970i		−	0.285317i
$184$	−3.33019	−	7.27391i	−0.245505	−	0.536240i
$185$			2.93783i			0.215993i
$186$	−0.0933792	+	0.783085i	−0.00684689	+	0.0574185i
$187$	−8.94725	+	8.94725i	−0.654288	+	0.654288i
$188$	−1.33019	+	5.49824i	−0.0970142	+	0.401000i
$189$	−3.22274	−	3.22274i	−0.234420	−	0.234420i
$190$	−1.49824	−	1.90393i	−0.108693	−	0.138125i
$191$	−8.63001			−0.624446			−0.312223	−	0.950009i	$-0.601074\pi$
$191$	−8.63001			−0.624446			−0.312223	+	0.950009i	$0.601074\pi$
$192$	−7.97852	+	0.585786i	−0.575800	+	0.0422755i
$193$	11.4514			0.824288			0.412144	−	0.911119i	$-0.364780\pi$
$193$	11.4514			0.824288			0.412144	+	0.911119i	$0.364780\pi$
$194$	3.77568	+	4.79806i	0.271078	+	0.344480i
$195$	−0.0281391	−	0.0281391i	−0.00201509	−	0.00201509i
$196$	6.47696	−	26.7720i	0.462640	−	1.91228i
$197$	7.48999	−	7.48999i	0.533640	−	0.533640i	−0.388014	−	0.921654i	$-0.626839\pi$
$197$	7.48999	−	7.48999i	0.533640	−	0.533640i	0.921654	+	0.388014i	$0.126839\pi$
$198$	0.585786	−	4.91245i	0.0416300	−	0.349113i
$199$		−	3.68000i		−	0.260868i	−0.991457	−	0.130434i	$-0.958363\pi$
$199$		−	3.68000i		−	0.260868i	0.991457	−	0.130434i	$-0.0416371\pi$
$200$	−5.62289	−	12.2817i	−0.397598	−	0.868447i
$201$		−	5.33962i		−	0.376627i
$202$	−0.901073	−	0.107449i	−0.0633993	−	0.00756007i
$203$	−23.5326	+	23.5326i	−1.65167	+	1.65167i
$204$	6.17471	−	3.76901i	0.432316	−	0.263884i
$205$	3.10587	+	3.10587i	0.216923	+	0.216923i
$206$	−1.48574	+	1.16916i	−0.103517	+	0.0814592i
$207$	−2.82843			−0.196589
$208$	0.102737	+	0.319999i	0.00712351	+	0.0221879i
$209$	−12.6533			−0.875249
$210$	2.39903	−	1.88784i	0.165549	−	0.130273i
$211$	10.1188	+	10.1188i	0.696609	+	0.696609i	0.963677	−	0.267069i	$-0.0860551\pi$
$211$	10.1188	+	10.1188i	0.696609	+	0.696609i	−0.267069	+	0.963677i	$0.586055\pi$
$212$	−0.727268	−	1.19147i	−0.0499490	−	0.0818305i
$213$	6.44549	−	6.44549i	0.441637	−	0.441637i
$214$	12.0398	+	1.43569i	0.823023	+	0.0981417i
$215$		−	1.07866i		−	0.0735637i
$216$	−0.985930	+	2.65103i	−0.0670841	+	0.180380i
$217$			2.54156i			0.172532i
$218$	−1.35369	+	11.3521i	−0.0916832	+	0.768862i
$219$	−0.382941	+	0.382941i	−0.0258767	+	0.0258767i
$220$	3.22079	+	0.779208i	0.217146	+	0.0525342i
$221$	−0.214897	−	0.214897i	−0.0144556	−	0.0144556i
$222$	−5.42475	−	6.89367i	−0.364086	−	0.462673i
$223$	−4.86156			−0.325554			−0.162777	−	0.986663i	$-0.552045\pi$
$223$	−4.86156			−0.325554			−0.162777	+	0.986663i	$0.552045\pi$
$224$	−25.3083	+	4.91911i	−1.69098	+	0.328672i
$225$	−4.77568			−0.318379
$226$	−8.35322	−	10.6151i	−0.555648	−	0.706106i
$227$	10.6417	+	10.6417i	0.706312	+	0.706312i	0.965758	−	0.259445i	$-0.0835398\pi$
$227$	10.6417	+	10.6417i	0.706312	+	0.706312i	−0.259445	+	0.965758i	$0.583540\pi$
$228$	7.03127	+	1.70108i	0.465657	+	0.112657i
$229$	−20.1712	+	20.1712i	−1.33295	+	1.33295i	−0.430229	+	0.902720i	$0.641567\pi$
$229$	−20.1712	+	20.1712i	−1.33295	+	1.33295i	−0.902720	+	0.430229i	$0.858433\pi$
$230$	0.224321	−	1.88118i	0.0147913	−	0.124041i
$231$		−	15.9437i		−	1.04902i
$232$	19.3579	+	7.19932i	1.27091	+	0.472658i
$233$			13.5702i			0.889014i	0.895775	+	0.444507i	$0.146621\pi$
$233$			13.5702i			0.889014i	−0.895775	+	0.444507i	$0.853379\pi$
$234$	0.117988	+	0.0140696i	0.00771315	+	0.000919757i
$235$	−0.947252	+	0.947252i	−0.0617919	+	0.0617919i
$236$	5.89450	+	9.65685i	0.383699	+	0.628608i
$237$	7.77373	+	7.77373i	0.504958	+	0.504958i
$238$	18.3213	−	14.4173i	1.18759	−	0.934538i
$239$	29.3629			1.89933			0.949665	−	0.313267i	$-0.101424\pi$
$239$	29.3629			1.89933			0.949665	+	0.313267i	$0.101424\pi$
$240$	−1.68499	−	0.865990i	−0.108766	−	0.0558994i
$241$	24.0063			1.54638			0.773190	−	0.634175i	$-0.218660\pi$
$241$	24.0063			1.54638			0.773190	+	0.634175i	$0.218660\pi$
$242$	1.37549	−	1.08240i	0.0884197	−	0.0695791i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−6.58892	+	4.02185i	−0.421812	+	0.257473i
$245$	4.61235	−	4.61235i	0.294672	−	0.294672i
$246$	−13.0230	−	1.55294i	−0.830318	−	0.0990115i
$247$		−	0.303911i		−	0.0193374i
$248$	1.43411	−	0.656574i	0.0910661	−	0.0416925i
$249$			15.0496i			0.953729i
$250$	0.775305	−	6.50176i	0.0490346	−	0.411208i
$251$	15.7570	−	15.7570i	0.994571	−	0.994571i	−0.00541463	−	0.999985i	$-0.501724\pi$
$251$	15.7570	−	15.7570i	0.994571	−	0.994571i	0.999985	+	0.00541463i	$0.00172354\pi$
$252$	−2.14343	+	8.85970i	−0.135024	+	0.558109i
$253$	−6.99647	−	6.99647i	−0.439864	−	0.439864i
$254$	4.45956	+	5.66711i	0.279817	+	0.355586i
$255$	1.71313			0.107281
$256$	9.31371	+	13.0098i	0.582107	+	0.813112i
$257$	8.66038			0.540220			0.270110	−	0.962829i	$-0.412940\pi$
$257$	8.66038			0.540220			0.270110	+	0.962829i	$0.412940\pi$
$258$	1.99176	+	2.53109i	0.124001	+	0.157579i
$259$	−19.9902	−	19.9902i	−1.24213	−	1.24213i
$260$	−0.0187152	+	0.0773578i	−0.00116067	+	0.00479753i
$261$	5.16333	−	5.16333i	0.319602	−	0.319602i
$262$	−0.501765	+	4.20784i	−0.0309991	+	0.259961i
$263$			13.3208i			0.821394i	0.911772	+	0.410697i	$0.134715\pi$
$263$			13.3208i			0.821394i	−0.911772	+	0.410697i	$0.865285\pi$
$264$	−8.99647	+	4.11882i	−0.553694	+	0.253496i
$265$		−	0.330566i		−	0.0203065i
$266$	23.1497	+	2.76049i	1.41940	+	0.169257i
$267$	10.3615	−	10.3615i	0.634111	−	0.634111i
$268$	−9.11529	+	5.56394i	−0.556805	+	0.339872i
$269$	−11.6714	−	11.6714i	−0.711616	−	0.711616i	0.255257	−	0.966873i	$-0.417840\pi$
$269$	−11.6714	−	11.6714i	−0.711616	−	0.711616i	−0.966873	+	0.255257i	$0.917840\pi$
$270$	−0.526374	+	0.414214i	−0.0320341	+	0.0252082i
$271$	−21.9769			−1.33500			−0.667499	−	0.744610i	$-0.732635\pi$
$271$	−21.9769			−1.33500			−0.667499	+	0.744610i	$0.732635\pi$
$272$	−12.8682	−	6.61353i	−0.780251	−	0.401004i
$273$	0.382941			0.0231766
$274$	3.75578	−	2.95549i	0.226895	−	0.178548i
$275$	−11.8132	−	11.8132i	−0.712365	−	0.712365i
$276$	2.94725	+	4.82843i	0.177404	+	0.290637i
$277$	−10.9504	+	10.9504i	−0.657945	+	0.657945i	−0.954893	−	0.296949i	$-0.904031\pi$
$277$	−10.9504	+	10.9504i	−0.657945	+	0.657945i	0.296949	+	0.954893i	$0.404031\pi$
$278$	11.6796	+	1.39274i	0.700496	+	0.0835309i
$279$		−	0.557647i		−	0.0333855i
$280$	−5.72256	−	2.12825i	−0.341988	−	0.127187i
$281$		−	22.8910i		−	1.36556i	−0.730624	−	0.682780i	$-0.760771\pi$
$281$		−	22.8910i		−	1.36556i	0.730624	−	0.682780i	$-0.239229\pi$
$282$	0.473626	−	3.97186i	0.0282040	−	0.236521i
$283$	4.48528	−	4.48528i	0.266622	−	0.266622i	−0.561115	−	0.827738i	$-0.689628\pi$
$283$	4.48528	−	4.48528i	0.266622	−	0.266622i	0.827738	+	0.561115i	$0.189628\pi$
$284$	−17.7194	−	4.28687i	−1.05145	−	0.254379i
$285$	1.21137	+	1.21137i	0.0717552	+	0.0717552i
$286$	0.257057	+	0.326662i	0.0152001	+	0.0193159i
$287$	−42.2672			−2.49496
$288$	5.55294	−	1.07931i	0.327210	−	0.0635989i
$289$	−3.91688			−0.230405
$290$	3.02461	+	3.84361i	0.177611	+	0.225705i
$291$	−3.05275	−	3.05275i	−0.178955	−	0.178955i
$292$	1.05275	+	0.254692i	0.0616074	+	0.0149047i
$293$	21.6221	−	21.6221i	1.26318	−	1.26318i	0.313636	−	0.949543i	$-0.398453\pi$
$293$	21.6221	−	21.6221i	1.26318	−	1.26318i	0.949543	−	0.313636i	$-0.101547\pi$
$294$	−2.30617	+	19.3397i	−0.134499	+	1.12792i
$295$			2.67923i			0.155991i
$296$	−6.11557	+	16.4439i	−0.355461	+	0.955783i
$297$			3.49824i			0.202988i
$298$	−19.8429	−	2.36618i	−1.14947	−	0.137069i
$299$	0.168043	−	0.168043i	0.00971818	−	0.00971818i
$300$	4.97631	+	8.15259i	0.287307	+	0.470690i
$301$	7.33962	+	7.33962i	0.423048	+	0.423048i
$302$	−11.0880	+	8.72534i	−0.638042	+	0.502087i
$303$	0.641669			0.0368629
$304$	−4.42274	−	13.7757i	−0.253661	−	0.790089i
$305$	−1.82805			−0.104674
$306$	−4.01990	+	3.16333i	−0.229802	+	0.180836i
$307$	−12.1118	−	12.1118i	−0.691255	−	0.691255i	0.271253	−	0.962508i	$-0.412562\pi$
$307$	−12.1118	−	12.1118i	−0.691255	−	0.691255i	−0.962508	+	0.271253i	$0.912562\pi$
$308$	−27.2176	+	16.6135i	−1.55087	+	0.946644i
$309$	0.945300	−	0.945300i	0.0537762	−	0.0537762i
$310$	0.370889	+	0.0442268i	0.0210651	+	0.00251191i
$311$		−	26.8651i		−	1.52338i	−0.647943	−	0.761689i	$-0.724370\pi$
$311$		−	26.8651i		−	1.52338i	0.647943	−	0.761689i	$-0.275630\pi$
$312$	−0.0989270	−	0.216080i	−0.00560064	−	0.0122331i
$313$			19.6890i			1.11289i	0.830885	+	0.556445i	$0.187835\pi$
$313$			19.6890i			1.11289i	−0.830885	+	0.556445i	$0.812165\pi$
$314$	3.82731	−	32.0961i	0.215988	−	1.81129i
$315$	−1.52637	+	1.52637i	−0.0860014	+	0.0860014i
$316$	5.17027	−	21.3709i	0.290851	−	1.20221i
$317$	21.3447	+	21.3447i	1.19884	+	1.19884i	0.974515	+	0.224323i	$0.0720171\pi$
$317$	21.3447	+	21.3447i	1.19884	+	1.19884i	0.224323	+	0.974515i	$0.427983\pi$
$318$	0.610396	+	0.775679i	0.0342293	+	0.0434979i
$319$	25.5443			1.43021
$320$	0.277444	+	3.77883i	0.0155096	+	0.211243i
$321$	−8.57373			−0.478539
$322$	11.2739	+	14.3267i	0.628271	+	0.798394i
$323$	9.25116	+	9.25116i	0.514748	+	0.514748i
$324$	0.470294	−	1.94392i	0.0261274	−	0.107996i
$325$	0.283734	−	0.283734i	0.0157387	−	0.0157387i
$326$	1.77726	−	14.9042i	0.0984331	−	0.825468i
$327$		−	8.08402i		−	0.447047i
$328$	10.9191	+	23.8499i	0.602907	+	1.31689i
$329$		−	12.8910i		−	0.710702i
$330$	−2.32666	−	0.277444i	−0.128079	−	0.0152728i
$331$	14.6926	−	14.6926i	0.807576	−	0.807576i	−0.176690	−	0.984266i	$-0.556539\pi$
$331$	14.6926	−	14.6926i	0.807576	−	0.807576i	0.984266	+	0.176690i	$0.0565391\pi$
$332$	25.6913	−	15.6818i	1.40999	−	0.860653i
$333$	4.38607	+	4.38607i	0.240355	+	0.240355i
$334$	6.48844	−	5.10587i	0.355032	−	0.279381i
$335$	−2.52898			−0.138173
$336$	17.3579	−	5.57283i	0.946953	−	0.304023i
$337$	−23.0098			−1.25342			−0.626712	−	0.779251i	$-0.715600\pi$
$337$	−23.0098			−1.25342			−0.626712	+	0.779251i	$0.715600\pi$
$338$	14.4400	−	11.3631i	0.785432	−	0.618071i
$339$	6.75383	+	6.75383i	0.366818	+	0.366818i
$340$	−1.78510	−	2.92450i	−0.0968108	−	0.158603i
$341$	1.37941	−	1.37941i	0.0746993	−	0.0746993i
$342$	−5.07931	−	0.605684i	−0.274658	−	0.0327516i
$343$			30.8651i			1.66656i
$344$	2.24540	−	6.03756i	0.121064	−	0.325524i
$345$			1.33962i			0.0721225i
$346$	0.858518	−	7.19960i	0.0461542	−	0.387053i
$347$	−10.9026	+	10.9026i	−0.585284	+	0.585284i	−0.936350	−	0.351067i	$-0.885819\pi$
$347$	−10.9026	+	10.9026i	−0.585284	+	0.585284i	0.351067	+	0.936350i	$0.385819\pi$
$348$	−14.1946	−	3.43411i	−0.760911	−	0.184088i
$349$	20.0563	+	20.0563i	1.07359	+	1.07359i	0.997068	+	0.0765186i	$0.0243805\pi$
$349$	20.0563	+	20.0563i	1.07359	+	1.07359i	0.0765186	+	0.997068i	$0.475620\pi$
$350$	19.0355	+	24.1900i	1.01749	+	1.29301i
$351$	−0.0840215			−0.00448474
$352$	16.4057	+	11.0661i	0.874426	+	0.589824i
$353$	−12.2117			−0.649965			−0.324983	−	0.945720i	$-0.605358\pi$
$353$	−12.2117			−0.649965			−0.324983	+	0.945720i	$0.605358\pi$
$354$	−4.94725	−	6.28687i	−0.262943	−	0.334143i
$355$	−3.05275	−	3.05275i	−0.162023	−	0.162023i
$356$	−28.4849	−	6.89137i	−1.50970	−	0.365242i
$357$	−11.6569	+	11.6569i	−0.616946	+	0.616946i
$358$	−2.19841	+	18.4361i	−0.116190	+	0.974376i
$359$			33.4780i			1.76690i	0.468522	+	0.883452i	$0.344786\pi$
$359$			33.4780i			1.76690i	−0.468522	+	0.883452i	$0.655214\pi$
$360$	1.25559	+	0.466962i	0.0661756	+	0.0246111i
$361$		−	5.91688i		−	0.311415i
$362$	−21.5107	−	2.56505i	−1.13058	−	0.134816i
$363$	−0.875150	+	0.875150i	−0.0459335	+	0.0459335i
$364$	−0.399028	−	0.653720i	−0.0209148	−	0.0342643i
$365$	0.181370	+	0.181370i	0.00949337	+	0.00949337i
$366$	4.28956	−	3.37553i	0.224219	−	0.176442i
$367$	−0.702379			−0.0366639			−0.0183319	−	0.999832i	$-0.505836\pi$
$367$	−0.702379			−0.0366639			−0.0183319	+	0.999832i	$0.505836\pi$
$368$	5.17157	−	10.0625i	0.269587	−	0.524546i
$369$	9.27391			0.482781
$370$	−3.26502	+	2.56930i	−0.169740	+	0.133572i
$371$	2.24930	+	2.24930i	0.116778	+	0.116778i
$372$	−0.951963	+	0.581074i	−0.0493570	+	0.0301273i
$373$	18.9598	−	18.9598i	0.981702	−	0.981702i	−0.0181339	−	0.999836i	$-0.505773\pi$
$373$	18.9598	−	18.9598i	0.981702	−	0.981702i	0.999836	+	0.0181339i	$0.00577250\pi$
$374$	−17.7686	−	2.11882i	−0.918793	−	0.109562i
$375$			4.63001i			0.239093i
$376$	−7.27391	+	3.33019i	−0.375123	+	0.171742i
$377$			0.613530i			0.0315984i
$378$	0.763187	−	6.40014i	0.0392541	−	0.329188i
$379$	−1.77844	+	1.77844i	−0.0913523	+	0.0913523i	−0.751306	−	0.659954i	$-0.770576\pi$
$379$	−1.77844	+	1.77844i	−0.0913523	+	0.0913523i	0.659954	+	0.751306i	$0.270576\pi$
$380$	0.805676	−	3.33019i	0.0413303	−	0.170835i
$381$	−3.60568	−	3.60568i	−0.184725	−	0.184725i
$382$	−7.54745	−	9.59115i	−0.386161	−	0.490726i
$383$	25.4880			1.30238			0.651188	−	0.758916i	$-0.274271\pi$
$383$	25.4880			1.30238			0.651188	+	0.758916i	$0.274271\pi$
$384$	−7.62872	−	8.35480i	−0.389301	−	0.426354i
$385$	−7.55136			−0.384853
$386$	10.0149	+	12.7267i	0.509745	+	0.647774i
$387$	−1.61040	−	1.61040i	−0.0818610	−	0.0818610i
$388$	−2.03037	+	8.39236i	−0.103076	+	0.426058i
$389$	−11.7049	+	11.7049i	−0.593462	+	0.593462i	−0.938565	−	0.345103i	$-0.887844\pi$
$389$	−11.7049	+	11.7049i	−0.593462	+	0.593462i	0.345103	+	0.938565i	$0.387844\pi$
$390$	0.00666371	−	0.0558824i	0.000337430	−	0.00282971i
$391$			10.2306i			0.517383i
$392$	35.4181	−	16.2153i	1.78888	−	0.818998i
$393$		−	2.99647i		−	0.151152i
$394$	14.8746	+	1.77373i	0.749372	+	0.0893591i
$395$	3.68184	−	3.68184i	0.185253	−	0.185253i
$396$	5.97186	−	3.64520i	0.300097	−	0.183178i
$397$	−9.04646	−	9.04646i	−0.454029	−	0.454029i	0.442661	−	0.896689i	$-0.354035\pi$
$397$	−9.04646	−	9.04646i	−0.454029	−	0.454029i	−0.896689	+	0.442661i	$0.854035\pi$
$398$	4.08985	−	3.21838i	0.205006	−	0.161323i
$399$	−16.4853			−0.825296
$400$	8.73198	−	16.9902i	0.436599	−	0.849509i
$401$	−18.0853			−0.903137			−0.451568	−	0.892237i	$-0.649135\pi$
$401$	−18.0853			−0.903137			−0.451568	+	0.892237i	$0.649135\pi$
$402$	5.93430	−	4.66981i	0.295976	−	0.232909i
$403$	0.0331311	+	0.0331311i	0.00165038	+	0.00165038i
$404$	−0.668626	−	1.09540i	−0.0332654	−	0.0544980i
$405$	0.334904	−	0.334904i	0.0166415	−	0.0166415i
$406$	−46.7342	−	5.57283i	−2.31938	−	0.276575i
$407$			21.6990i			1.07558i
$408$	9.58892	+	3.56617i	0.474722	+	0.176552i
$409$		−	25.2271i		−	1.24740i	−0.781665	−	0.623699i	$-0.785629\pi$
$409$		−	25.2271i		−	1.24740i	0.781665	−	0.623699i	$-0.214371\pi$
$410$	−0.735510	+	6.16804i	−0.0363243	+	0.304618i
$411$	−2.38960	+	2.38960i	−0.117870	+	0.117870i
$412$	−2.59874	−	0.628715i	−0.128031	−	0.0309746i
$413$	−18.2306	−	18.2306i	−0.897069	−	0.897069i
$414$	−2.47363	−	3.14343i	−0.121572	−	0.154491i
$415$	7.12787			0.349894
$416$	−0.265788	+	0.394036i	−0.0130313	+	0.0193192i
$417$	−8.31724			−0.407297
$418$	−11.0661	−	14.0625i	−0.541259	−	0.687822i
$419$	7.25283	+	7.25283i	0.354324	+	0.354324i	0.861716	−	0.507392i	$-0.169390\pi$
$419$	7.25283	+	7.25283i	0.354324	+	0.354324i	−0.507392	+	0.861716i	$0.669390\pi$
$420$	4.19618	+	1.01519i	0.204753	+	0.0495360i
$421$	2.39550	−	2.39550i	0.116749	−	0.116749i	−0.646318	−	0.763068i	$-0.723692\pi$
$421$	2.39550	−	2.39550i	0.116749	−	0.116749i	0.763068	+	0.646318i	$0.223692\pi$
$422$	−2.39627	+	20.0953i	−0.116648	+	0.978223i
$423$			2.82843i			0.137523i
$424$	0.688127	−	1.85028i	0.0334184	−	0.0898574i
$425$			17.2739i			0.837908i
$426$	12.8003	+	1.52637i	0.620176	+	0.0739531i
$427$	12.4388	−	12.4388i	0.601957	−	0.601957i
$428$	8.93392	+	14.6363i	0.431838	+	0.707471i
$429$	−0.207838	−	0.207838i	−0.0100345	−	0.0100345i
$430$	1.19879	−	0.943348i	0.0578107	−	0.0454923i
$431$	−4.42454			−0.213123			−0.106561	−	0.994306i	$-0.533984\pi$
$431$	−4.42454			−0.213123			−0.106561	+	0.994306i	$0.533984\pi$
$432$	−3.80853	+	1.22274i	−0.183238	+	0.0588293i
$433$	7.31371			0.351474			0.175737	−	0.984437i	$-0.443769\pi$
$433$	7.31371			0.351474			0.175737	+	0.984437i	$0.443769\pi$
$434$	−2.82462	+	2.22274i	−0.135586	+	0.106695i
$435$	−2.44549	−	2.44549i	−0.117252	−	0.117252i
$436$	−13.8003	+	8.42364i	−0.660914	+	0.403419i
$437$	−7.23412	+	7.23412i	−0.346055	+	0.346055i
$438$	−0.760493	−	0.0906852i	−0.0363378	−	0.00433311i
$439$		−	29.6533i		−	1.41527i	−0.706576	−	0.707637i	$-0.749761\pi$
$439$		−	29.6533i		−	1.41527i	0.706576	−	0.707637i	$-0.250239\pi$
$440$	1.95078	+	4.26096i	0.0929999	+	0.203133i
$441$		−	13.7721i		−	0.655817i
$442$	0.0508905	−	0.426771i	0.00242061	−	0.0202994i
$443$	10.3056	−	10.3056i	0.489633	−	0.489633i	−0.418557	−	0.908190i	$-0.637464\pi$
$443$	10.3056	−	10.3056i	0.489633	−	0.489633i	0.908190	+	0.418557i	$0.137464\pi$
$444$	2.91716	−	12.0578i	0.138442	−	0.572239i
$445$	−4.90746	−	4.90746i	−0.232636	−	0.232636i
$446$	−4.25172	−	5.40300i	−0.201325	−	0.255839i
$447$	14.1305			0.668349
$448$	−27.6006	−	23.8249i	−1.30400	−	1.12562i
$449$	−6.48844			−0.306208			−0.153104	−	0.988210i	$-0.548927\pi$
$449$	−6.48844			−0.306208			−0.153104	+	0.988210i	$0.548927\pi$
$450$	−4.17661	−	5.30755i	−0.196887	−	0.250200i
$451$	22.9402	+	22.9402i	1.08021	+	1.08021i
$452$	4.49195	−	18.5671i	0.211283	−	0.873322i
$453$	7.05470	−	7.05470i	0.331459	−	0.331459i
$454$	−2.52008	+	21.1336i	−0.118273	+	0.991850i
$455$		−	0.181370i		−	0.00850278i
$456$	4.25873	+	9.30205i	0.199433	+	0.435609i
$457$		−	9.00353i		−	0.421167i	−0.977576	−	0.210584i	$-0.932464\pi$
$457$		−	9.00353i		−	0.421167i	0.977576	−	0.210584i	$-0.0675364\pi$
$458$	−40.0586	−	4.77679i	−1.87181	−	0.223205i
$459$	2.55765	−	2.55765i	0.119381	−	0.119381i
$460$	2.28687	−	1.39589i	0.106626	−	0.0650839i
$461$	14.6218	+	14.6218i	0.681004	+	0.681004i	0.960226	−	0.279223i	$-0.0900767\pi$
$461$	14.6218	+	14.6218i	0.681004	+	0.681004i	−0.279223	+	0.960226i	$0.590077\pi$
$462$	17.7194	−	13.9437i	0.824381	−	0.648721i
$463$	−18.6435			−0.866437			−0.433219	−	0.901289i	$-0.642622\pi$
$463$	−18.6435			−0.866437			−0.433219	+	0.901289i	$0.642622\pi$
$464$	8.92854	+	27.8101i	0.414497	+	1.29105i
$465$	−0.264116			−0.0122481
$466$	−15.0815	+	11.8679i	−0.698639	+	0.549772i
$467$	−23.5138	−	23.5138i	−1.08809	−	1.08809i	−0.995725	−	0.0923633i	$-0.970558\pi$
$467$	−23.5138	−	23.5138i	−1.08809	−	1.08809i	−0.0923633	−	0.995725i	$-0.529442\pi$
$468$	0.0875513	+	0.143434i	0.00404706	+	0.00663023i
$469$	17.2082	−	17.2082i	0.794601	−	0.794601i
$470$	−1.88118	−	0.224321i	−0.0867722	−	0.0103472i
$471$			22.8562i			1.05316i
$472$	−5.57726	+	14.9965i	−0.256714	+	0.690268i
$473$		−	7.96703i		−	0.366325i
$474$	−1.84092	+	15.4381i	−0.0845562	+	0.709095i
$475$	−12.2145	+	12.2145i	−0.560440	+	0.560440i
$476$	32.0461	+	7.75293i	1.46883	+	0.355355i
$477$	−0.493523	−	0.493523i	−0.0225969	−	0.0225969i
$478$	25.6796	+	32.6331i	1.17456	+	1.49260i
$479$	−1.08864			−0.0497412			−0.0248706	−	0.999691i	$-0.507917\pi$
$479$	−1.08864			−0.0497412			−0.0248706	+	0.999691i	$0.507917\pi$
$480$	−0.511189	−	2.63001i	−0.0233325	−	0.120043i
$481$	−0.521173			−0.0237634
$482$	20.9949	+	26.6799i	0.956291	+	1.21524i
$483$	−9.11529	−	9.11529i	−0.414760	−	0.414760i
$484$	2.40589	+	0.582059i	0.109359	+	0.0264572i
$485$	−1.44586	+	1.44586i	−0.0656531	+	0.0656531i
$486$	−0.167452	+	1.40426i	−0.00759578	+	0.0636987i
$487$		−	35.3298i		−	1.60095i	−0.599369	−	0.800473i	$-0.704582\pi$
$487$		−	35.3298i		−	1.60095i	0.599369	−	0.800473i	$-0.295418\pi$
$488$	−10.2322	−	3.80540i	−0.463188	−	0.172262i
$489$			10.6135i			0.479960i
$490$	9.15980	+	1.09226i	0.413798	+	0.0493434i
$491$	−12.8910	+	12.8910i	−0.581761	+	0.581761i	−0.935387	−	0.353626i	$-0.884949\pi$
$491$	−12.8910	+	12.8910i	−0.581761	+	0.581761i	0.353626	+	0.935387i	$0.384949\pi$
$492$	−9.66352	−	15.8316i	−0.435665	−	0.713742i
$493$	−18.6761	−	18.6761i	−0.841128	−	0.841128i
$494$	0.337758	−	0.265788i	0.0151964	−	0.0119584i
$495$	1.65685			0.0744701
$496$	1.98391	+	1.01962i	0.0890803	+	0.0457822i
$497$	41.5443			1.86352
$498$	−16.7257	+	13.1618i	−0.749496	+	0.589792i
$499$	14.3798	+	14.3798i	0.643728	+	0.643728i	0.951470	−	0.307742i	$-0.0995734\pi$
$499$	14.3798	+	14.3798i	0.643728	+	0.643728i	−0.307742	+	0.951470i	$0.599573\pi$
$500$	7.90393	−	4.82452i	0.353474	−	0.215759i
$501$	−4.12825	+	4.12825i	−0.184437	+	0.184437i
$502$	31.2922	+	3.73145i	1.39664	+	0.166543i
$503$		−	30.2969i		−	1.35087i	−0.737420	−	0.675435i	$-0.763956\pi$
$503$		−	30.2969i		−	1.35087i	0.737420	−	0.675435i	$-0.236044\pi$
$504$	−11.7210	+	5.36618i	−0.522094	+	0.239029i
$505$		−	0.303911i		−	0.0135239i
$506$	1.65685	−	13.8945i	0.0736562	−	0.617686i
$507$	−9.18740	+	9.18740i	−0.408027	+	0.408027i
$508$	−2.39813	+	9.91245i	−0.106400	+	0.439794i
$509$	10.5825	+	10.5825i	0.469063	+	0.469063i	0.901611	−	0.432548i	$-0.142385\pi$
$509$	10.5825	+	10.5825i	0.469063	+	0.469063i	−0.432548	+	0.901611i	$0.642385\pi$
$510$	1.49824	+	1.90393i	0.0663430	+	0.0843073i
$511$	−2.46824			−0.109188
$512$	−6.31333	+	21.7288i	−0.279013	+	0.960287i
$513$	3.61706			0.159697
$514$	7.57401	+	9.62491i	0.334075	+	0.424536i
$515$	−0.447718	−	0.447718i	−0.0197288	−	0.0197288i
$516$	−1.07107	+	4.42717i	−0.0471511	+	0.194895i
$517$	−6.99647	+	6.99647i	−0.307704	+	0.307704i
$518$	4.73393	−	39.6991i	0.207997	−	1.74428i
$519$			5.12695i			0.225048i
$520$	−0.102341	+	0.0468544i	−0.00448794	+	0.00205470i
$521$			24.9049i			1.09110i	0.838078	+	0.545551i	$0.183680\pi$
$521$			24.9049i			1.09110i	−0.838078	+	0.545551i	$0.816320\pi$
$522$	10.2540	+	1.22274i	0.448806	+	0.0535180i
$523$	−12.9008	+	12.9008i	−0.564112	+	0.564112i	−0.930473	−	0.366361i	$-0.880604\pi$
$523$	−12.9008	+	12.9008i	−0.564112	+	0.564112i	0.366361	+	0.930473i	$0.380604\pi$
$524$	−5.11529	+	3.12235i	−0.223463	+	0.136401i
$525$	−15.3908	−	15.3908i	−0.671709	−	0.671709i
$526$	−14.8043	+	11.6498i	−0.645499	+	0.507955i
$527$	−2.01704			−0.0878638
$528$	−12.4455	−	6.39627i	−0.541620	−	0.278362i
$529$	15.0000			0.652174
$530$	0.367381	−	0.289099i	0.0159580	−	0.0125577i
$531$	4.00000	+	4.00000i	0.173585	+	0.173585i
$532$	17.1778	+	28.1421i	0.744754	+	1.22012i
$533$	−0.550984	+	0.550984i	−0.0238657	+	0.0238657i
$534$	20.5771	+	2.45373i	0.890460	+	0.106183i
$535$			4.06074i			0.175561i
$536$	−14.1555	−	5.26449i	−0.611423	−	0.227391i
$537$		−	13.1286i		−	0.566542i
$538$	2.76393	−	23.1785i	0.119161	−	0.999297i
$539$	34.0671	−	34.0671i	1.46738	−	1.46738i
$540$	−0.920690	−	0.222743i	−0.0396202	−	0.00958535i
$541$	18.2767	+	18.2767i	0.785776	+	0.785776i	0.980799	−	0.195023i	$-0.0624782\pi$
$541$	18.2767	+	18.2767i	0.785776	+	0.785776i	−0.195023	+	0.980799i	$0.562478\pi$
$542$	−19.2200	−	24.4245i	−0.825572	−	1.04912i
$543$	15.3181			0.657364
$544$	−3.90393	−	20.0853i	−0.167379	−	0.861150i
$545$	−3.82880			−0.164008
$546$	0.334904	+	0.425589i	0.0143326	+	0.0182135i
$547$	13.7355	+	13.7355i	0.587287	+	0.587287i	0.936896	−	0.349609i	$-0.113685\pi$
$547$	13.7355	+	13.7355i	0.587287	+	0.587287i	−0.349609	+	0.936896i	$0.613685\pi$
$548$	6.56930	+	1.58932i	0.280627	+	0.0678922i
$549$	−2.72922	+	2.72922i	−0.116480	+	0.116480i
$550$	2.79753	−	23.4603i	0.119287	−	1.00035i
$551$		−	26.4120i		−	1.12519i
$552$	−2.78863	+	7.49824i	−0.118692	+	0.319146i
$553$			50.1055i			2.13070i
$554$	−21.7467	−	2.59319i	−0.923929	−	0.110174i
$555$	2.07736	−	2.07736i	0.0881789	−	0.0881789i
$556$	8.66665	+	14.1984i	0.367548	+	0.602147i
$557$	−27.5525	−	27.5525i	−1.16744	−	1.16744i	−0.982808	−	0.184631i	$-0.940891\pi$
$557$	−27.5525	−	27.5525i	−1.16744	−	1.16744i	−0.184631	−	0.982808i	$-0.559109\pi$
$558$	0.619753	−	0.487695i	0.0262363	−	0.0206458i
$559$	0.191354			0.00809342
$560$	−2.63944	−	8.22117i	−0.111537	−	0.347408i
$561$	12.6533			0.534224
$562$	25.4404	−	20.0195i	1.07314	−	0.844472i
$563$	−19.8928	−	19.8928i	−0.838383	−	0.838383i	0.150263	−	0.988646i	$-0.451988\pi$
$563$	−19.8928	−	19.8928i	−0.838383	−	0.838383i	−0.988646	+	0.150263i	$0.951988\pi$
$564$	4.82843	−	2.94725i	0.203313	−	0.124102i
$565$	3.19879	−	3.19879i	0.134574	−	0.134574i
$566$	8.90746	+	1.06217i	0.374408	+	0.0446464i
$567$			4.55765i			0.191403i
$568$	−10.7324	−	23.4420i	−0.450320	−	0.983603i
$569$			13.4849i			0.565317i	0.959221	+	0.282658i	$0.0912163\pi$
$569$			13.4849i			0.565317i	−0.959221	+	0.282658i	$0.908784\pi$
$570$	−0.286867	+	2.40569i	−0.0120156	+	0.100763i
$571$	−14.8284	+	14.8284i	−0.620550	+	0.620550i	−0.945672	−	0.325122i	$-0.894595\pi$
$571$	−14.8284	+	14.8284i	−0.620550	+	0.620550i	0.325122	+	0.945672i	$0.394595\pi$
$572$	−0.138232	+	0.571371i	−0.00577977	+	0.0238902i
$573$	6.10234	+	6.10234i	0.254929	+	0.254929i
$574$	−36.9652	−	46.9746i	−1.54290	−	1.96068i
$575$	−13.5077			−0.563308
$576$	6.05588	+	5.22746i	0.252328	+	0.217811i
$577$	−11.6176			−0.483648			−0.241824	−	0.970320i	$-0.577746\pi$
$577$	−11.6176			−0.483648			−0.241824	+	0.970320i	$0.577746\pi$
$578$	−3.42554	−	4.35311i	−0.142484	−	0.181066i
$579$	−8.09735	−	8.09735i	−0.336514	−	0.336514i
$580$	−1.62648	+	6.72293i	−0.0675360	+	0.279154i
$581$	−48.5010	+	48.5010i	−2.01216	+	2.01216i
$582$	0.722930	−	6.06255i	0.0299664	−	0.251301i
$583$		−	2.44158i		−	0.101120i
$584$	0.637633	+	1.39274i	0.0263854	+	0.0576319i
$585$			0.0397948i			0.00164531i
$586$	42.9401	+	5.12040i	1.77384	+	0.211522i
$587$	−17.0268	+	17.0268i	−0.702773	+	0.702773i	−0.965005	−	0.262232i	$-0.915541\pi$
$587$	−17.0268	+	17.0268i	−0.702773	+	0.702773i	0.262232	+	0.965005i	$0.415541\pi$
$588$	−23.5105	+	14.3507i	−0.969558	+	0.591814i
$589$	−1.42627	−	1.42627i	−0.0587682	−	0.0587682i
$590$	−2.97762	+	2.34315i	−0.122587	+	0.0964658i
$591$	−10.5925			−0.435715
$592$	−23.6237	+	7.58449i	−0.970929	+	0.311721i
$593$	41.5372			1.70573			0.852865	−	0.522132i	$-0.174863\pi$
$593$	41.5372			1.70573			0.852865	+	0.522132i	$0.174863\pi$
$594$	−3.88784	+	3.05941i	−0.159520	+	0.125529i
$595$	5.52099	+	5.52099i	0.226338	+	0.226338i
$596$	−14.7241	−	24.1222i	−0.603123	−	0.988085i
$597$	−2.60215	+	2.60215i	−0.106499	+	0.106499i
$598$	0.333722	+	0.0397948i	0.0136469	+	0.00162733i
$599$		−	6.43160i		−	0.262788i	−0.991330	−	0.131394i	$-0.958055\pi$
$599$		−	6.43160i		−	0.262788i	0.991330	−	0.131394i	$-0.0419453\pi$
$600$	−4.70849	+	12.6605i	−0.192223	+	0.516861i
$601$			3.45844i			0.141073i	0.997509	+	0.0705364i	$0.0224711\pi$
$601$			3.45844i			0.141073i	−0.997509	+	0.0705364i	$0.977529\pi$
$602$	−1.73812	+	14.5760i	−0.0708403	+	0.594072i
$603$	−3.77568	+	3.77568i	−0.153758	+	0.153758i
$604$	−19.3942	−	4.69205i	−0.789139	−	0.190917i
$605$	0.414494	+	0.414494i	0.0168516	+	0.0168516i
$606$	0.561177	+	0.713133i	0.0227963	+	0.0289690i
$607$	−30.1019			−1.22180			−0.610900	−	0.791708i	$-0.709192\pi$
$607$	−30.1019			−1.22180			−0.610900	+	0.791708i	$0.709192\pi$
$608$	11.4420	−	16.9629i	0.464033	−	0.687938i
$609$	33.2802			1.34858
$610$	−1.59874	−	2.03165i	−0.0647311	−	0.0822590i
$611$	−0.168043	−	0.168043i	−0.00679829	−	0.00679829i
$612$	−7.03127	−	1.70108i	−0.284222	−	0.0687621i
$613$	2.50490	−	2.50490i	0.101172	−	0.101172i	−0.654709	−	0.755881i	$-0.727209\pi$
$613$	2.50490	−	2.50490i	0.101172	−	0.101172i	0.755881	+	0.654709i	$0.227209\pi$
$614$	2.86822	−	24.0531i	0.115752	−	0.970705i
$615$		−	4.39236i		−	0.177117i
$616$	−42.2672	−	15.7194i	−1.70300	−	0.633353i
$617$		−	22.9098i		−	0.922315i	−0.887318	−	0.461157i	$-0.847434\pi$
$617$		−	22.9098i		−	0.922315i	0.887318	−	0.461157i	$-0.152566\pi$
$618$	1.87730	+	0.223859i	0.0755161	+	0.00900494i
$619$	−28.6104	+	28.6104i	−1.14995	+	1.14995i	−0.163386	+	0.986562i	$0.552242\pi$
$619$	−28.6104	+	28.6104i	−1.14995	+	1.14995i	−0.986562	+	0.163386i	$0.947758\pi$
$620$	0.275212	+	0.450874i	0.0110528	+	0.0181076i
$621$	2.00000	+	2.00000i	0.0802572	+	0.0802572i
$622$	29.8571	−	23.4951i	1.19716	−	0.942067i
$623$	66.7847			2.67567
$624$	0.153627	−	0.298919i	0.00615001	−	0.0119663i
$625$	−21.6855			−0.867420
$626$	−21.8818	+	17.2192i	−0.874574	+	0.688218i
$627$	8.94725	+	8.94725i	0.357319	+	0.357319i
$628$	39.0179	−	23.8164i	1.55698	−	0.950377i
$629$	15.8647	−	15.8647i	0.632567	−	0.632567i
$630$	−3.03127	−	0.361465i	−0.120769	−	0.0144011i
$631$		−	11.1851i		−	0.445270i	−0.974902	−	0.222635i	$-0.928534\pi$
$631$		−	11.1851i		−	0.445270i	0.974902	−	0.222635i	$-0.0714659\pi$
$632$	28.2727	−	12.9440i	1.12463	−	0.514885i
$633$		−	14.3102i		−	0.568779i
$634$	−5.05470	+	42.3891i	−0.200748	+	1.68349i
$635$	−1.70774	+	1.70774i	−0.0677698	+	0.0677698i
$636$	−0.328240	+	1.35675i	−0.0130156	+	0.0537988i
$637$	0.818234	+	0.818234i	0.0324196	+	0.0324196i
$638$	22.3400	+	28.3892i	0.884449	+	1.12394i
$639$	−9.11529			−0.360595
$640$	−3.95705	+	3.61316i	−0.156416	+	0.142823i
$641$	−6.69312			−0.264362			−0.132181	−	0.991226i	$-0.542198\pi$
$641$	−6.69312			−0.264362			−0.132181	+	0.991226i	$0.542198\pi$
$642$	−7.49824	−	9.52861i	−0.295932	−	0.376064i
$643$	−17.9410	−	17.9410i	−0.707522	−	0.707522i	0.258491	−	0.966014i	$-0.416775\pi$
$643$	−17.9410	−	17.9410i	−0.707522	−	0.707522i	−0.966014	+	0.258491i	$0.916775\pi$
$644$	−6.06255	+	25.0590i	−0.238898	+	0.987464i
$645$	−0.762725	+	0.762725i	−0.0300323	+	0.0300323i
$646$	−2.19079	+	18.3722i	−0.0861957	+	0.722843i
$647$		−	6.72999i		−	0.264583i	−0.991211	−	0.132292i	$-0.957766\pi$
$647$		−	6.72999i		−	0.264583i	0.991211	−	0.132292i	$-0.0422335\pi$
$648$	2.57172	−	1.17740i	0.101027	−	0.0462527i
$649$			19.7890i			0.776786i
$650$	0.563475	+	0.0671918i	0.0221013	+	0.00263548i
$651$	1.79715	−	1.79715i	0.0704360	−	0.0704360i
$652$	18.1184	−	11.0594i	0.709572	−	0.433120i
$653$	26.1731	+	26.1731i	1.02423	+	1.02423i	0.999699	+	0.0245347i	$0.00781042\pi$
$653$	26.1731	+	26.1731i	1.02423	+	1.02423i	0.0245347	+	0.999699i	$0.492190\pi$
$654$	8.98435	−	7.06995i	0.351316	−	0.276457i
$655$	−1.41921			−0.0554529
$656$	−16.9567	+	32.9933i	−0.662047	+	1.28817i
$657$	0.541560			0.0211283
$658$	14.3267	−	11.2739i	0.558511	−	0.439503i
$659$	13.9741	+	13.9741i	0.544353	+	0.544353i	0.924802	−	0.380449i	$-0.124230\pi$
$659$	13.9741	+	13.9741i	0.544353	+	0.544353i	−0.380449	+	0.924802i	$0.624230\pi$
$660$	−1.72646	−	2.82843i	−0.0672024	−	0.110096i
$661$	11.9241	−	11.9241i	0.463794	−	0.463794i	−0.436103	−	0.899897i	$-0.643642\pi$
$661$	11.9241	−	11.9241i	0.463794	−	0.463794i	0.899897	+	0.436103i	$0.143642\pi$
$662$	29.1784	+	3.47939i	1.13405	+	0.135230i
$663$			0.303911i			0.0118029i
$664$	39.8969	+	14.8379i	1.54830	+	0.575820i
$665$			7.80785i			0.302776i
$666$	−1.03868	+	8.71044i	−0.0402480	+	0.337523i
$667$	14.6041	−	14.6041i	0.565473	−	0.565473i
$668$	11.3490	+	2.74568i	0.439108	+	0.106234i
$669$	3.43764	+	3.43764i	0.132907	+	0.132907i
$670$	−2.21174	−	2.81064i	−0.0854470	−	0.108584i
$671$	−13.5021			−0.521244
$672$	21.3740	+	14.4173i	0.824521	+	0.556161i
$673$	−37.3066			−1.43807			−0.719033	−	0.694976i	$-0.755415\pi$
$673$	−37.3066			−1.43807			−0.719033	+	0.694976i	$0.755415\pi$
$674$	−20.1234	−	25.5724i	−0.775125	−	0.985013i
$675$	3.37691	+	3.37691i	0.129978	+	0.129978i
$676$	25.2572	+	6.11050i	0.971432	+	0.235019i
$677$	0.447461	−	0.447461i	0.0171973	−	0.0171973i	−0.698456	−	0.715653i	$-0.746129\pi$
$677$	0.447461	−	0.447461i	0.0171973	−	0.0171973i	0.715653	+	0.698456i	$0.246129\pi$
$678$	−1.59939	+	13.4126i	−0.0614243	+	0.515109i
$679$		−	19.6764i		−	0.755113i
$680$	1.68903	−	4.54156i	0.0647713	−	0.174161i
$681$		−	15.0496i		−	0.576702i
$682$	2.73941	+	0.326662i	0.104898	+	0.0125085i
$683$	−4.27521	+	4.27521i	−0.163586	+	0.163586i	−0.784153	−	0.620567i	$-0.786902\pi$
$683$	−4.27521	+	4.27521i	−0.163586	+	0.163586i	0.620567	+	0.784153i	$0.286902\pi$
$684$	−3.76901	−	6.17471i	−0.144112	−	0.236096i
$685$	1.13178	+	1.13178i	0.0432430	+	0.0432430i
$686$	−34.3026	+	26.9933i	−1.30968	+	1.03061i
$687$	28.5264			1.08835
$688$	8.67371	−	2.78473i	0.330682	−	0.106167i
$689$	0.0586426			0.00223410
$690$	−1.48881	+	1.17157i	−0.0566781	+	0.0446010i
$691$	20.0786	+	20.0786i	0.763827	+	0.763827i	0.977012	−	0.213185i	$-0.0683836\pi$
$691$	20.0786	+	20.0786i	0.763827	+	0.763827i	−0.213185	+	0.977012i	$0.568384\pi$
$692$	8.75225	−	5.34234i	0.332711	−	0.203085i
$693$	−11.2739	+	11.2739i	−0.428261	+	0.428261i
$694$	−21.6519	−	2.58188i	−0.821893	−	0.0980069i
$695$			3.93926i			0.149425i
$696$	−8.59744	−	18.7788i	−0.325885	−	0.711809i
$697$		−	33.5443i		−	1.27058i
$698$	−4.74958	+	39.8303i	−0.179774	+	1.50760i
$699$	9.59558	−	9.59558i	0.362938	−	0.362938i
$700$	−10.2364	+	42.3111i	−0.386898	+	1.59921i
$701$	−10.4467	−	10.4467i	−0.394565	−	0.394565i	0.481746	−	0.876311i	$-0.340003\pi$
$701$	−10.4467	−	10.4467i	−0.394565	−	0.394565i	−0.876311	+	0.481746i	$0.840003\pi$
$702$	−0.0734818	−	0.0933792i	−0.00277339	−	0.00352437i
$703$	22.4361			0.846192
$704$	2.04922	+	27.9108i	0.0772328	+	1.05193i
$705$	1.33962			0.0504529
$706$	−10.6799	−	13.5718i	−0.401943	−	0.510781i
$707$	2.06793	+	2.06793i	0.0777727	+	0.0777727i
$708$	2.66038	−	10.9965i	0.0999834	−	0.413273i
$709$	16.0916	−	16.0916i	0.604332	−	0.604332i	−0.337127	−	0.941459i	$-0.609455\pi$
$709$	16.0916	−	16.0916i	0.604332	−	0.604332i	0.941459	+	0.337127i	$0.109455\pi$
$710$	0.722930	−	6.06255i	0.0271311	−	0.227523i
$711$		−	10.9937i		−	0.412296i
$712$	−17.2528	−	37.6842i	−0.646577	−	1.41228i
$713$		−	1.57726i		−	0.0590690i
$714$	−23.1497	−	2.76049i	−0.866356	−	0.103309i
$715$	−0.0984373	+	0.0984373i	−0.00368135	+	0.00368135i
$716$	−22.4120	+	13.6802i	−0.837574	+	0.511252i
$717$	−20.7627	−	20.7627i	−0.775398	−	0.775398i
$718$	−37.2065	+	29.2785i	−1.38854	+	1.09266i
$719$	−30.9957			−1.15594			−0.577972	−	0.816057i	$-0.696156\pi$
$719$	−30.9957			−1.15594			−0.577972	+	0.816057i	$0.696156\pi$
$720$	0.579123	+	1.80382i	0.0215826	+	0.0672243i
$721$	6.09292			0.226912
$722$	6.57585	−	5.17466i	0.244728	−	0.192581i
$723$	−16.9750	−	16.9750i	−0.631307	−	0.631307i
$724$	−15.9617	−	26.1497i	−0.593211	−	0.971846i
$725$	24.6584	−	24.6584i	0.915790	−	0.915790i
$726$	−1.73799	−	0.207247i	−0.0645027	−	0.00769165i
$727$			41.1117i			1.52475i	0.647135	+	0.762375i	$0.275967\pi$
$727$			41.1117i			1.52475i	−0.647135	+	0.762375i	$0.724033\pi$
$728$	0.377553	−	1.01519i	0.0139930	−	0.0376253i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.0429509	+	0.360189i	−0.00158968	+	0.0133312i
$731$	−5.82490	+	5.82490i	−0.215442	+	0.215442i
$732$	7.50295	+	1.81519i	0.277317	+	0.0670915i
$733$	0.146061	+	0.146061i	0.00539490	+	0.00539490i	0.709799	−	0.704404i	$-0.248786\pi$
$733$	0.146061	+	0.146061i	0.00539490	+	0.00539490i	−0.704404	+	0.709799i	$0.748786\pi$
$734$	−0.614272	−	0.780604i	−0.0226732	−	0.0288126i
$735$	−6.52284			−0.240599
$736$	15.7061	−	3.05275i	0.578934	−	0.112526i
$737$	−18.6792			−0.688058
$738$	8.11058	+	10.3068i	0.298555	+	0.379397i
$739$	−1.50766	−	1.50766i	−0.0554601	−	0.0554601i	0.678833	−	0.734293i	$-0.262486\pi$
$739$	−1.50766	−	1.50766i	−0.0554601	−	0.0554601i	−0.734293	+	0.678833i	$0.762486\pi$
$740$	−5.71090	−	1.38164i	−0.209937	−	0.0507902i
$741$	−0.214897	+	0.214897i	−0.00789445	+	0.00789445i
$742$	−0.532664	+	4.46696i	−0.0195547	+	0.163987i
$743$			40.5175i			1.48644i	0.669046	+	0.743221i	$0.266703\pi$
$743$			40.5175i			1.48644i	−0.669046	+	0.743221i	$0.733297\pi$
$744$	−1.47834	−	0.549801i	−0.0541985	−	0.0201567i
$745$		−	6.69256i		−	0.245196i
$746$	37.6529	+	4.48993i	1.37857	+	0.164388i
$747$	10.6417	−	10.6417i	0.389358	−	0.389358i
$748$	−13.1849	−	21.6006i	−0.482088	−	0.789795i
$749$	−27.6309	−	27.6309i	−1.00961	−	1.00961i
$750$	−5.14567	+	4.04922i	−0.187893	+	0.147857i
$751$	−12.5843			−0.459208			−0.229604	−	0.973284i	$-0.573743\pi$
$751$	−12.5843			−0.459208			−0.229604	+	0.973284i	$0.573743\pi$
$752$	−10.0625	−	5.17157i	−0.366943	−	0.188588i
$753$	−22.2837			−0.812064
$754$	−0.681859	+	0.536568i	−0.0248319	+	0.0195406i
$755$	−3.34129	−	3.34129i	−0.121602	−	0.121602i
$756$	7.78039	−	4.74912i	0.282970	−	0.172724i
$757$	−7.49900	+	7.49900i	−0.272556	+	0.272556i	−0.830128	−	0.557572i	$-0.811733\pi$
$757$	−7.49900	+	7.49900i	−0.272556	+	0.272556i	0.557572	+	0.830128i	$0.311733\pi$
$758$	−3.53186	−	0.421157i	−0.128283	−	0.0152971i
$759$			9.89450i			0.359148i
$760$	4.40569	−	2.01704i	0.159811	−	0.0731659i
$761$		−	42.8182i		−	1.55216i	−0.630635	−	0.776079i	$-0.717206\pi$
$761$		−	42.8182i		−	1.55216i	0.630635	−	0.776079i	$-0.282794\pi$
$762$	0.853872	−	7.16064i	0.0309325	−	0.259403i
$763$	26.0527	−	26.0527i	0.943172	−	0.943172i
$764$	4.05864	−	16.7761i	0.146837	−	0.606936i
$765$	−1.21137	−	1.21137i	−0.0437971	−	0.0437971i
$766$	22.2908	+	28.3267i	0.805398	+	1.02348i
$767$	−0.475298			−0.0171620
$768$	2.61353

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +(-0.665096 - 0.0793096i) q^{10} +(-2.47363 + 2.47363i) q^{11} +(1.70711 - 1.04201i) q^{12} +(-0.0594122 - 0.0594122i) q^{13} +(5.06524 - 3.98593i) q^{14} +0.473626 q^{15} +(-3.55765 - 1.82843i) q^{16} +3.61706 q^{17} +(-1.11137 + 0.874559i) q^{18} +(2.55765 + 2.55765i) q^{19} +(-0.493523 - 0.808530i) q^{20} +(-3.22274 + 3.22274i) q^{21} +(-4.91245 - 0.585786i) q^{22} +2.82843i q^{23} +(2.65103 + 0.985930i) q^{24} +4.77568i q^{25} +(0.0140696 - 0.117988i) q^{26} +(0.707107 - 0.707107i) q^{27} +(8.85970 + 2.14343i) q^{28} +(-5.16333 - 5.16333i) q^{29} +(0.414214 + 0.526374i) q^{30} -0.557647 q^{31} +(-1.07931 - 5.55294i) q^{32} +3.49824 q^{33} +(3.16333 + 4.01990i) q^{34} +(1.52637 + 1.52637i) q^{35} +(-1.94392 - 0.470294i) q^{36} +(4.38607 - 4.38607i) q^{37} +(-0.605684 + 5.07931i) q^{38} +0.0840215i q^{39} +(0.466962 - 1.25559i) q^{40} -9.27391i q^{41} +(-6.40014 - 0.763187i) q^{42} +(-1.61040 + 1.61040i) q^{43} +(-3.64520 - 5.97186i) q^{44} +(-0.334904 - 0.334904i) q^{45} +(-3.14343 + 2.47363i) q^{46} +2.82843 q^{47} +(1.22274 + 3.80853i) q^{48} -13.7721 q^{49} +(-5.30755 + 4.17661i) q^{50} +(-2.55765 - 2.55765i) q^{51} +(0.143434 - 0.0875513i) q^{52} +(-0.493523 + 0.493523i) q^{53} +(1.40426 + 0.167452i) q^{54} -1.65685i q^{55} +(5.36618 + 11.7210i) q^{56} -3.61706i q^{57} +(1.22274 - 10.2540i) q^{58} +(4.00000 - 4.00000i) q^{59} +(-0.222743 + 0.920690i) q^{60} +(2.72922 + 2.72922i) q^{61} +(-0.487695 - 0.619753i) q^{62} +4.55765 q^{63} +(5.22746 - 6.05588i) q^{64} +0.0397948 q^{65} +(3.05941 + 3.88784i) q^{66} +(3.77568 + 3.77568i) q^{67} +(-1.70108 + 7.03127i) q^{68} +(2.00000 - 2.00000i) q^{69} +(-0.361465 + 3.03127i) q^{70} +9.11529i q^{71} +(-1.17740 - 2.57172i) q^{72} -0.541560i q^{73} +(8.71044 + 1.03868i) q^{74} +(3.37691 - 3.37691i) q^{75} +(-6.17471 + 3.76901i) q^{76} +(11.2739 + 11.2739i) q^{77} +(-0.0933792 + 0.0734818i) q^{78} -10.9937 q^{79} +(1.80382 - 0.579123i) q^{80} -1.00000 q^{81} +(10.3068 - 8.11058i) q^{82} +(-10.6417 - 10.6417i) q^{83} +(-4.74912 - 7.78039i) q^{84} +(-1.21137 + 1.21137i) q^{85} +(-3.19813 - 0.381362i) q^{86} +7.30205i q^{87} +(3.44902 - 9.27391i) q^{88} +14.6533i q^{89} +(0.0793096 - 0.665096i) q^{90} +(-0.270780 + 0.270780i) q^{91} +(-5.49824 - 1.33019i) q^{92} +(0.394316 + 0.394316i) q^{93} +(2.47363 + 3.14343i) q^{94} -1.71313 q^{95} +(-3.16333 + 4.68971i) q^{96} +4.31724 q^{97} +(-12.0446 - 15.3060i) q^{98} +(-2.47363 - 2.47363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 - 12 * q^8	\( 8 q - 4 q^{4} - 12 q^{8} - 8 q^{10} - 8 q^{11} + 8 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{18} - 8 q^{19} + 16 q^{20} + 4 q^{24} + 20 q^{26} + 8 q^{28} - 16 q^{29} - 8 q^{30} + 24 q^{31} + 24 q^{35} - 4 q^{36} - 16 q^{37} - 8 q^{38} + 16 q^{40} - 20 q^{42} - 8 q^{43} - 40 q^{44} - 8 q^{46} - 16 q^{48} - 8 q^{49} - 36 q^{50} + 8 q^{51} - 16 q^{52} + 16 q^{53} + 4 q^{54} - 16 q^{58} + 32 q^{59} + 24 q^{60} + 16 q^{61} - 12 q^{62} + 8 q^{63} + 8 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{67} + 32 q^{68} + 16 q^{69} + 32 q^{70} - 4 q^{72} + 52 q^{74} + 16 q^{75} + 8 q^{76} + 16 q^{77} - 12 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 40 q^{82} - 40 q^{83} - 24 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{88} - 8 q^{90} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 48 q^{95} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 12 * q^8 - 8 * q^10 - 8 * q^11 + 8 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^18 - 8 * q^19 + 16 * q^20 + 4 * q^24 + 20 * q^26 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 24 * q^35 - 4 * q^36 - 16 * q^37 - 8 * q^38 + 16 * q^40 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 8 * q^46 - 16 * q^48 - 8 * q^49 - 36 * q^50 + 8 * q^51 - 16 * q^52 + 16 * q^53 + 4 * q^54 - 16 * q^58 + 32 * q^59 + 24 * q^60 + 16 * q^61 - 12 * q^62 + 8 * q^63 + 8 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^67 + 32 * q^68 + 16 * q^69 + 32 * q^70 - 4 * q^72 + 52 * q^74 + 16 * q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 40 * q^82 - 40 * q^83 - 24 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^88 - 8 * q^90 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 48 * q^95 - 40 * q^98 - 8 * q^99

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