LMFDB - Embedded newform 48.2.j.a.37.4

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			37.4
Root			$0.500000 - 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	48.37
Dual form			48.2.j.a.13.4

$q$-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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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	0.628243	−	0.778017i	$-0.283774\pi$
$5$	−0.334904	−	0.334904i	−0.149774	−	0.149774i	−0.778017	+	0.628243i	$0.783774\pi$
$6$	0.167452	+	1.40426i	0.0683620	+	0.573289i
$7$			4.55765i			1.72263i	0.508072	+	0.861314i	$0.330358\pi$
$7$			4.55765i			1.72263i	−0.508072	+	0.861314i	$0.669642\pi$
$8$	−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	0.227866	−	0.973692i	$-0.426825\pi$
$11$	−2.47363	−	2.47363i	−0.745826	−	0.745826i	−0.973692	+	0.227866i	$0.926825\pi$
$12$	1.70711	+	1.04201i	0.492799	+	0.300803i
$13$	−0.0594122	+	0.0594122i	−0.0164780	+	0.0164780i	−0.715298	−	0.698820i	$-0.753709\pi$
$13$	−0.0594122	+	0.0594122i	−0.0164780	+	0.0164780i	0.698820	+	0.715298i	$0.253709\pi$
$14$	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	−0.349989	−	0.936754i	$-0.613815\pi$
$19$	2.55765	−	2.55765i	0.586765	−	0.586765i	0.936754	+	0.349989i	$0.113815\pi$
$20$	−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	$-0.904719\pi$
$23$		−	2.82843i		−	0.589768i	0.955533	−	0.294884i	$-0.0952810\pi$
$24$	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	−0.999184	−	0.0403780i	$-0.987144\pi$
$29$	−5.16333	+	5.16333i	−0.958807	+	0.958807i	0.0403780	+	0.999184i	$0.487144\pi$
$30$	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	0.968822	−	0.247756i	$-0.0796932\pi$
$37$	4.38607	+	4.38607i	0.721066	+	0.721066i	−0.247756	+	0.968822i	$0.579693\pi$
$38$	−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	$0.257777\pi$
$41$			9.27391i			1.44834i	−0.689620	+	0.724171i	$0.742223\pi$
$42$	−6.40014	+	0.763187i	−0.987564	+	0.117762i
$43$	−1.61040	−	1.61040i	−0.245583	−	0.245583i	0.573572	−	0.819155i	$-0.305557\pi$
$43$	−1.61040	−	1.61040i	−0.245583	−	0.245583i	−0.819155	+	0.573572i	$0.805557\pi$
$44$	−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	0.672399	−	0.740189i	$-0.265264\pi$
$53$	−0.493523	−	0.493523i	−0.0677906	−	0.0677906i	−0.740189	+	0.672399i	$0.765264\pi$
$54$	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	0.917800	−	0.397044i	$-0.129964\pi$
$59$	4.00000	+	4.00000i	0.520756	+	0.520756i	−0.397044	+	0.917800i	$0.629964\pi$
$60$	−0.222743	−	0.920690i	−0.0287560	−	0.118861i
$61$	2.72922	−	2.72922i	0.349441	−	0.349441i	−0.510460	−	0.859901i	$-0.670525\pi$
$61$	2.72922	−	2.72922i	0.349441	−	0.349441i	0.859901	+	0.510460i	$0.170525\pi$
$62$	−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	−0.437800	−	0.899072i	$-0.644242\pi$
$67$	3.77568	−	3.77568i	0.461273	−	0.461273i	0.899072	+	0.437800i	$0.144242\pi$
$68$	−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	$-0.818086\pi$
$71$		−	9.11529i		−	1.08179i	0.841091	−	0.540893i	$-0.181914\pi$
$72$	−1.17740	+	2.57172i	−0.138758	+	0.303080i
$73$			0.541560i			0.0633848i	0.999498	+	0.0316924i	$0.0100897\pi$
$73$			0.541560i			0.0633848i	−0.999498	+	0.0316924i	$0.989910\pi$
$74$	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	−0.185415	+	0.982660i	$0.559363\pi$
$83$	−10.6417	+	10.6417i	−1.16807	+	1.16807i	−0.982660	+	0.185415i	$0.940637\pi$
$84$	−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	$-0.716930\pi$
$89$		−	14.6533i		−	1.55325i	0.629964	−	0.776625i	$-0.283070\pi$
$90$	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	0.684173	−	0.729320i	$-0.260164\pi$
$101$	−0.453728	−	0.453728i	−0.0451477	−	0.0451477i	−0.729320	+	0.684173i	$0.760164\pi$
$102$	0.605684	+	5.07931i	0.0599716	+	0.502927i
$103$		−	1.33686i		−	0.131724i	−0.997829	−	0.0658622i	$-0.979020\pi$
$103$		−	1.33686i		−	0.131724i	0.997829	−	0.0658622i	$-0.0209798\pi$
$104$	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	0.936570	−	0.350481i	$-0.113982\pi$
$107$	6.06255	+	6.06255i	0.586088	+	0.586088i	−0.350481	+	0.936570i	$0.613982\pi$
$108$	1.04201	−	1.70711i	0.100268	−	0.164266i
$109$	5.71627	−	5.71627i	0.547519	−	0.547519i	−0.378203	−	0.925722i	$-0.623458\pi$
$109$	5.71627	−	5.71627i	0.547519	−	0.547519i	0.925722	+	0.378203i	$0.123458\pi$
$110$	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	−0.608461	−	0.793584i	$-0.708213\pi$
$131$	2.11882	−	2.11882i	0.185123	−	0.185123i	0.793584	+	0.608461i	$0.208213\pi$
$132$	−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	$0.0461127\pi$
$137$			3.37941i			0.288723i	−0.989525	+	0.144361i	$0.953887\pi$
$138$	3.97186	−	0.473626i	0.338107	−	0.0403177i
$139$	5.88118	+	5.88118i	0.498835	+	0.498835i	0.911075	−	0.412240i	$-0.135254\pi$
$139$	5.88118	+	5.88118i	0.498835	+	0.498835i	−0.412240	+	0.911075i	$0.635254\pi$
$140$	−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	0.167342	−	0.985899i	$-0.446482\pi$
$149$	−9.99176	−	9.99176i	−0.818557	−	0.818557i	−0.985899	+	0.167342i	$0.946482\pi$
$150$	6.70632	−	0.799697i	0.547569	−	0.0652950i
$151$		−	9.97685i		−	0.811905i	−0.913894	−	0.405952i	$-0.866940\pi$
$151$		−	9.97685i		−	0.811905i	0.913894	−	0.405952i	$-0.133060\pi$
$152$	−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	−0.354971	+	0.934877i	$0.615509\pi$
$157$	−16.1618	+	16.1618i	−1.28985	+	1.28985i	−0.934877	+	0.354971i	$0.884491\pi$
$158$	−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	−0.937043	−	0.349214i	$-0.886449\pi$
$163$	−7.50490	+	7.50490i	−0.587829	+	0.587829i	0.349214	+	0.937043i	$0.386449\pi$
$164$	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	$0.0725282\pi$
$167$			5.83822i			0.451775i	−0.974153	+	0.225888i	$0.927472\pi$
$168$	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	−0.831360	−	0.555734i	$-0.812437\pi$
$173$	−3.62530	+	3.62530i	−0.275627	+	0.275627i	0.555734	+	0.831360i	$0.312437\pi$
$174$	−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	−0.269212	−	0.963081i	$-0.586763\pi$
$179$	9.28334	−	9.28334i	0.693869	−	0.693869i	0.963081	+	0.269212i	$0.0867632\pi$
$180$	0.808530	+	0.493523i	0.0602642	+	0.0367850i
$181$	−10.8316	−	10.8316i	−0.805104	−	0.805104i	0.178785	−	0.983888i	$-0.442783\pi$
$181$	−10.8316	−	10.8316i	−0.805104	−	0.805104i	−0.983888	+	0.178785i	$0.942783\pi$
$182$	−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	0.921654	−	0.388014i	$-0.126839\pi$
$197$	7.48999	+	7.48999i	0.533640	+	0.533640i	−0.388014	+	0.921654i	$0.626839\pi$
$198$	0.585786	+	4.91245i	0.0416300	+	0.349113i
$199$			3.68000i			0.260868i	0.991457	+	0.130434i	$0.0416371\pi$
$199$			3.68000i			0.260868i	−0.991457	+	0.130434i	$0.958363\pi$
$200$	−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	−0.267069	−	0.963677i	$-0.586055\pi$
$211$	10.1188	−	10.1188i	0.696609	−	0.696609i	0.963677	+	0.267069i	$0.0860551\pi$
$212$	−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	−0.259445	−	0.965758i	$-0.583540\pi$
$227$	10.6417	−	10.6417i	0.706312	−	0.706312i	0.965758	+	0.259445i	$0.0835398\pi$
$228$	7.03127	−	1.70108i	0.465657	−	0.112657i
$229$	−20.1712	−	20.1712i	−1.33295	−	1.33295i	−0.902720	−	0.430229i	$-0.858433\pi$
$229$	−20.1712	−	20.1712i	−1.33295	−	1.33295i	−0.430229	−	0.902720i	$-0.641567\pi$
$230$	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	$-0.853379\pi$
$233$		−	13.5702i		−	0.889014i	0.895775	−	0.444507i	$-0.146621\pi$
$234$	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	0.999985	−	0.00541463i	$-0.00172354\pi$
$251$	15.7570	+	15.7570i	0.994571	+	0.994571i	−0.00541463	+	0.999985i	$0.501724\pi$
$252$	−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	$-0.865285\pi$
$263$		−	13.3208i		−	0.821394i	0.911772	−	0.410697i	$-0.134715\pi$
$264$	−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	−0.966873	−	0.255257i	$-0.917840\pi$
$269$	−11.6714	+	11.6714i	−0.711616	+	0.711616i	0.255257	+	0.966873i	$0.417840\pi$
$270$	−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	0.296949	−	0.954893i	$-0.404031\pi$
$277$	−10.9504	−	10.9504i	−0.657945	−	0.657945i	−0.954893	+	0.296949i	$0.904031\pi$
$278$	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	$0.239229\pi$
$281$			22.8910i			1.36556i	−0.730624	+	0.682780i	$0.760771\pi$
$282$	0.473626	+	3.97186i	0.0282040	+	0.236521i
$283$	4.48528	+	4.48528i	0.266622	+	0.266622i	0.827738	−	0.561115i	$-0.189628\pi$
$283$	4.48528	+	4.48528i	0.266622	+	0.266622i	−0.561115	+	0.827738i	$0.689628\pi$
$284$	−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	0.949543	+	0.313636i	$0.101547\pi$
$293$	21.6221	+	21.6221i	1.26318	+	1.26318i	0.313636	+	0.949543i	$0.398453\pi$
$294$	−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	−0.962508	−	0.271253i	$-0.912562\pi$
$307$	−12.1118	+	12.1118i	−0.691255	+	0.691255i	0.271253	+	0.962508i	$0.412562\pi$
$308$	−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	$0.275630\pi$
$311$			26.8651i			1.52338i	−0.647943	+	0.761689i	$0.724370\pi$
$312$	−0.0989270	+	0.216080i	−0.00560064	+	0.0122331i
$313$		−	19.6890i		−	1.11289i	−0.830885	−	0.556445i	$-0.812165\pi$
$313$		−	19.6890i		−	1.11289i	0.830885	−	0.556445i	$-0.187835\pi$
$314$	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	0.224323	−	0.974515i	$-0.427983\pi$
$317$	21.3447	−	21.3447i	1.19884	−	1.19884i	0.974515	−	0.224323i	$-0.0720171\pi$
$318$	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	0.984266	−	0.176690i	$-0.0565391\pi$
$331$	14.6926	+	14.6926i	0.807576	+	0.807576i	−0.176690	+	0.984266i	$0.556539\pi$
$332$	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	0.351067	−	0.936350i	$-0.385819\pi$
$347$	−10.9026	−	10.9026i	−0.585284	−	0.585284i	−0.936350	+	0.351067i	$0.885819\pi$
$348$	−14.1946	+	3.43411i	−0.760911	+	0.184088i
$349$	20.0563	−	20.0563i	1.07359	−	1.07359i	0.0765186	−	0.997068i	$-0.475620\pi$
$349$	20.0563	−	20.0563i	1.07359	−	1.07359i	0.997068	−	0.0765186i	$-0.0243805\pi$
$350$	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	$-0.655214\pi$
$359$		−	33.4780i		−	1.76690i	0.468522	−	0.883452i	$-0.344786\pi$
$360$	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	0.999836	−	0.0181339i	$-0.00577250\pi$
$373$	18.9598	+	18.9598i	0.981702	+	0.981702i	−0.0181339	+	0.999836i	$0.505773\pi$
$374$	−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	0.659954	−	0.751306i	$-0.270576\pi$
$379$	−1.77844	−	1.77844i	−0.0913523	−	0.0913523i	−0.751306	+	0.659954i	$0.770576\pi$
$380$	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	0.345103	−	0.938565i	$-0.387844\pi$
$389$	−11.7049	−	11.7049i	−0.593462	−	0.593462i	−0.938565	+	0.345103i	$0.887844\pi$
$390$	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	−0.896689	−	0.442661i	$-0.854035\pi$
$397$	−9.04646	+	9.04646i	−0.454029	+	0.454029i	0.442661	+	0.896689i	$0.354035\pi$
$398$	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	$0.214371\pi$
$409$			25.2271i			1.24740i	−0.781665	+	0.623699i	$0.785629\pi$
$410$	−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	−0.507392	−	0.861716i	$-0.669390\pi$
$419$	7.25283	−	7.25283i	0.354324	−	0.354324i	0.861716	+	0.507392i	$0.169390\pi$
$420$	4.19618	−	1.01519i	0.204753	−	0.0495360i
$421$	2.39550	+	2.39550i	0.116749	+	0.116749i	0.763068	−	0.646318i	$-0.223692\pi$
$421$	2.39550	+	2.39550i	0.116749	+	0.116749i	−0.646318	+	0.763068i	$0.723692\pi$
$422$	−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	$0.250239\pi$
$439$			29.6533i			1.41527i	−0.706576	+	0.707637i	$0.749761\pi$
$440$	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	0.908190	−	0.418557i	$-0.137464\pi$
$443$	10.3056	+	10.3056i	0.489633	+	0.489633i	−0.418557	+	0.908190i	$0.637464\pi$
$444$	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	$0.0675364\pi$
$457$			9.00353i			0.421167i	−0.977576	+	0.210584i	$0.932464\pi$
$458$	−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	−0.279223	−	0.960226i	$-0.590077\pi$
$461$	14.6218	−	14.6218i	0.681004	−	0.681004i	0.960226	+	0.279223i	$0.0900767\pi$
$462$	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	−0.0923633	+	0.995725i	$0.529442\pi$
$467$	−23.5138	+	23.5138i	−1.08809	+	1.08809i	−0.995725	+	0.0923633i	$0.970558\pi$
$468$	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	$0.295418\pi$
$487$			35.3298i			1.60095i	−0.599369	+	0.800473i	$0.704582\pi$
$488$	−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	0.353626	−	0.935387i	$-0.384949\pi$
$491$	−12.8910	−	12.8910i	−0.581761	−	0.581761i	−0.935387	+	0.353626i	$0.884949\pi$
$492$	−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	−0.307742	−	0.951470i	$-0.599573\pi$
$499$	14.3798	−	14.3798i	0.643728	−	0.643728i	0.951470	+	0.307742i	$0.0995734\pi$
$500$	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	$0.236044\pi$
$503$			30.2969i			1.35087i	−0.737420	+	0.675435i	$0.763956\pi$
$504$	−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	−0.432548	−	0.901611i	$-0.642385\pi$
$509$	10.5825	−	10.5825i	0.469063	−	0.469063i	0.901611	+	0.432548i	$0.142385\pi$
$510$	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	$-0.816320\pi$
$521$		−	24.9049i		−	1.09110i	0.838078	−	0.545551i	$-0.183680\pi$
$522$	10.2540	−	1.22274i	0.448806	−	0.0535180i
$523$	−12.9008	−	12.9008i	−0.564112	−	0.564112i	0.366361	−	0.930473i	$-0.380604\pi$
$523$	−12.9008	−	12.9008i	−0.564112	−	0.564112i	−0.930473	+	0.366361i	$0.880604\pi$
$524$	−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	−0.195023	−	0.980799i	$-0.562478\pi$
$541$	18.2767	−	18.2767i	0.785776	−	0.785776i	0.980799	+	0.195023i	$0.0624782\pi$
$542$	−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	−0.349609	−	0.936896i	$-0.613685\pi$
$547$	13.7355	−	13.7355i	0.587287	−	0.587287i	0.936896	+	0.349609i	$0.113685\pi$
$548$	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	−0.184631	+	0.982808i	$0.559109\pi$
$557$	−27.5525	+	27.5525i	−1.16744	+	1.16744i	−0.982808	+	0.184631i	$0.940891\pi$
$558$	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	−0.988646	−	0.150263i	$-0.951988\pi$
$563$	−19.8928	+	19.8928i	−0.838383	+	0.838383i	0.150263	+	0.988646i	$0.451988\pi$
$564$	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	$-0.908784\pi$
$569$		−	13.4849i		−	0.565317i	0.959221	−	0.282658i	$-0.0912163\pi$
$570$	−0.286867	−	2.40569i	−0.0120156	−	0.100763i
$571$	−14.8284	−	14.8284i	−0.620550	−	0.620550i	0.325122	−	0.945672i	$-0.394595\pi$
$571$	−14.8284	−	14.8284i	−0.620550	−	0.620550i	−0.945672	+	0.325122i	$0.894595\pi$
$572$	−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	0.262232	−	0.965005i	$-0.415541\pi$
$587$	−17.0268	−	17.0268i	−0.702773	−	0.702773i	−0.965005	+	0.262232i	$0.915541\pi$
$588$	−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	$0.0419453\pi$
$599$			6.43160i			0.262788i	−0.991330	+	0.131394i	$0.958055\pi$
$600$	−4.70849	−	12.6605i	−0.192223	−	0.516861i
$601$		−	3.45844i		−	0.141073i	−0.997509	−	0.0705364i	$-0.977529\pi$
$601$		−	3.45844i		−	0.141073i	0.997509	−	0.0705364i	$-0.0224711\pi$
$602$	−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	0.755881	−	0.654709i	$-0.227209\pi$
$613$	2.50490	+	2.50490i	0.101172	+	0.101172i	−0.654709	+	0.755881i	$0.727209\pi$
$614$	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	$0.152566\pi$
$617$			22.9098i			0.922315i	−0.887318	+	0.461157i	$0.847434\pi$
$618$	1.87730	−	0.223859i	0.0755161	−	0.00900494i
$619$	−28.6104	−	28.6104i	−1.14995	−	1.14995i	−0.986562	−	0.163386i	$-0.947758\pi$
$619$	−28.6104	−	28.6104i	−1.14995	−	1.14995i	−0.163386	−	0.986562i	$-0.552242\pi$
$620$	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	$0.0714659\pi$
$631$			11.1851i			0.445270i	−0.974902	+	0.222635i	$0.928534\pi$
$632$	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	−0.966014	−	0.258491i	$-0.916775\pi$
$643$	−17.9410	+	17.9410i	−0.707522	+	0.707522i	0.258491	+	0.966014i	$0.416775\pi$
$644$	−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	$0.0422335\pi$
$647$			6.72999i			0.264583i	−0.991211	+	0.132292i	$0.957766\pi$
$648$	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	0.0245347	−	0.999699i	$-0.492190\pi$
$653$	26.1731	−	26.1731i	1.02423	−	1.02423i	0.999699	−	0.0245347i	$-0.00781042\pi$
$654$	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	−0.380449	−	0.924802i	$-0.624230\pi$
$659$	13.9741	−	13.9741i	0.544353	−	0.544353i	0.924802	+	0.380449i	$0.124230\pi$
$660$	−1.72646	+	2.82843i	−0.0672024	+	0.110096i
$661$	11.9241	+	11.9241i	0.463794	+	0.463794i	0.899897	−	0.436103i	$-0.143642\pi$
$661$	11.9241	+	11.9241i	0.463794	+	0.463794i	−0.436103	+	0.899897i	$0.643642\pi$
$662$	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	0.715653	−	0.698456i	$-0.246129\pi$
$677$	0.447461	+	0.447461i	0.0171973	+	0.0171973i	−0.698456	+	0.715653i	$0.746129\pi$
$678$	−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	0.620567	−	0.784153i	$-0.286902\pi$
$683$	−4.27521	−	4.27521i	−0.163586	−	0.163586i	−0.784153	+	0.620567i	$0.786902\pi$
$684$	−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	−0.213185	−	0.977012i	$-0.568384\pi$
$691$	20.0786	−	20.0786i	0.763827	−	0.763827i	0.977012	+	0.213185i	$0.0683836\pi$
$692$	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	−0.876311	−	0.481746i	$-0.840003\pi$
$701$	−10.4467	+	10.4467i	−0.394565	+	0.394565i	0.481746	+	0.876311i	$0.340003\pi$
$702$	−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	0.941459	−	0.337127i	$-0.109455\pi$
$709$	16.0916	+	16.0916i	0.604332	+	0.604332i	−0.337127	+	0.941459i	$0.609455\pi$
$710$	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	$-0.724033\pi$
$727$		−	41.1117i		−	1.52475i	0.647135	−	0.762375i	$-0.275967\pi$
$728$	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	−0.704404	−	0.709799i	$-0.748786\pi$
$733$	0.146061	−	0.146061i	0.00539490	−	0.00539490i	0.709799	+	0.704404i	$0.248786\pi$
$734$	−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	−0.734293	−	0.678833i	$-0.762486\pi$
$739$	−1.50766	+	1.50766i	−0.0554601	+	0.0554601i	0.678833	+	0.734293i	$0.262486\pi$
$740$	−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	$-0.733297\pi$
$743$		−	40.5175i		−	1.48644i	0.669046	−	0.743221i	$-0.266703\pi$
$744$	−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	0.557572	−	0.830128i	$-0.311733\pi$
$757$	−7.49900	−	7.49900i	−0.272556	−	0.272556i	−0.830128	+	0.557572i	$0.811733\pi$
$758$	−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	$0.282794\pi$
$761$			42.8182i			1.55216i	−0.630635	+	0.776079i	$0.717206\pi$
$762$	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	+	15.7851i	0.0943076	+	0.569596i
$769$	12.7455			0.459614			0.229807	−	0.973236i	$-0.426190\pi$
$769$	12.7455			0.459614			0.229807	+	0.973236i	$0.426190\pi$
$770$	−6.60411	+	8.39236i	−0.237995	+	0.302440i
$771$	−6.12382	+	6.12382i	−0.220544	+	0.220544i
$772$	−5.38551	−	22.2606i	−0.193829	−	0.801175i
$773$	−22.8765	−	22.8765i	−0.822809	−	0.822809i	0.163701	−	0.986510i	$-0.447657\pi$
$773$	−22.8765	−	22.8765i	−0.822809	−	0.822809i	−0.986510	+	0.163701i	$0.947657\pi$
$774$	0.381362	+	3.19813i	0.0137078	+	0.114955i
$775$			2.66314i			0.0956630i
$776$	−11.1027	−	5.08312i	−0.398564	−	0.182473i
$777$		−	28.2704i		−	1.01419i
$778$	−23.2451	+	2.77187i	−0.833377	+	0.0993763i
$779$	23.7194	+	23.7194i	0.849836	+	0.849836i
$780$	0.0679339	+	0.0414666i	0.00243242	+	0.00148474i
$781$	−22.5478	+	22.5478i	−0.806825	+	0.806825i
$782$	−11.3700	−	8.94725i	−0.406590	−	0.319953i
$783$	−7.30205			−0.260954
$784$	48.9964	−	25.1814i	1.74987	−	0.899335i
$785$	10.8253			0.386370
$786$	3.33019	+	2.62059i	0.118784	+	0.0934733i
$787$	5.20470	−	5.20470i	0.185528	−	0.185528i	−0.608232	−	0.793759i	$-0.708121\pi$
$787$	5.20470	−	5.20470i	0.185528	−	0.185528i	0.793759	+	0.608232i	$0.208121\pi$
$788$	11.0374	−	18.0824i	0.393193	−	0.644160i
$789$	9.41921	+	9.41921i	0.335333	+	0.335333i
$790$	7.31187	−	0.871906i	0.260145	−	0.0310210i
$791$		−	43.5317i		−	1.54781i
$792$	9.27391	−	3.44902i	0.329534	−	0.122555i
$793$			0.324298i			0.0115162i
$794$	2.14232	+	17.9656i	0.0760280	+	0.637577i
$795$	−0.233745	−	0.233745i	−0.00829009	−	0.00829009i
$796$	7.15363	−	1.73068i	0.253554	−	0.0613424i
$797$	17.0149	−	17.0149i	0.602698	−	0.602698i	−0.338330	−	0.941028i	$-0.609862\pi$
$797$	17.0149	−	17.0149i	0.602698	−	0.602698i	0.941028	+	0.338330i	$0.109862\pi$
$798$	−14.4173	+	18.3213i	−0.510369	+	0.648566i
$799$	10.2306			0.361932
$800$	26.5190	+	5.15444i	0.937589	+	0.182237i
$801$	−14.6533			−0.517750
$802$	−15.8167	+	20.0995i	−0.558506	+	0.709738i
$803$	1.33962	−	1.33962i	0.0472740	−	0.0472740i
$804$	10.3798	−	2.51119i	0.366067	−	0.0885628i
$805$	−4.31724	−	4.31724i	−0.152163	−	0.152163i
$806$	−0.00784586	−	0.0657960i	−0.000276359	−	0.00231756i
$807$		−	16.5058i		−	0.581032i
$808$	0.632641	+	1.70108i	0.0222562	+	0.0598438i
$809$			7.83586i			0.275494i	0.990467	+	0.137747i	$0.0439861\pi$
$809$			7.83586i			0.275494i	−0.990467	+	0.137747i	$0.956014\pi$
$810$	0.665096	−	0.0793096i	0.0233691	−	0.00278665i
$811$	32.3396	+	32.3396i	1.13560	+	1.13560i	0.989230	+	0.146366i	$0.0467578\pi$
$811$	32.3396	+	32.3396i	1.13560	+	1.13560i	0.146366	+	0.989230i	$0.453242\pi$
$812$	−34.6783	+	56.8128i	−1.21697	+	1.99374i
$813$	15.5400	−	15.5400i	0.545011	−	0.545011i
$814$	−24.1157	−	18.9771i	−0.845254	−	0.665146i
$815$	5.02684			0.176083
$816$	4.42274	−	13.7757i	0.154827	−	0.482245i
$817$	−8.23765			−0.288199
$818$	28.0366	+	22.0625i	0.980278	+	0.771399i
$819$	−0.270780	+	0.270780i	−0.00946181	+	0.00946181i
$820$	−7.49824	−	4.57689i	−0.261850	−	0.159832i
$821$	19.3541	+	19.3541i	0.675464	+	0.675464i	0.958970	−	0.283507i	$-0.0914978\pi$
$821$	19.3541	+	19.3541i	0.675464	+	0.675464i	−0.283507	+	0.958970i	$0.591498\pi$
$822$	−4.74559	+	0.565889i	−0.165521	+	0.0197376i
$823$			28.8560i			1.00586i	0.864328	+	0.502929i	$0.167744\pi$
$823$			28.8560i			1.00586i	−0.864328	+	0.502929i	$0.832256\pi$
$824$	−1.57401	+	3.43801i	−0.0548334	+	0.119769i
$825$		−	16.7064i		−	0.581644i
$826$	4.31724	+	36.2047i	0.150216	+	1.25972i
$827$	−10.1984	−	10.1984i	−0.354634	−	0.354634i	0.507197	−	0.861830i	$-0.330682\pi$
$827$	−10.1984	−	10.1984i	−0.354634	−	0.354634i	−0.861830	+	0.507197i	$0.830682\pi$
$828$	1.33019	+	5.49824i	0.0462274	+	0.191077i
$829$	15.3794	−	15.3794i	0.534148	−	0.534148i	−0.387656	−	0.921804i	$-0.626715\pi$
$829$	15.3794	−	15.3794i	0.534148	−	0.534148i	0.921804	+	0.387656i	$0.126715\pi$
$830$	6.23375	−	7.92172i	0.216376	−	0.274967i
$831$	15.4862			0.537210
$832$	−0.670368	−	0.0492187i	−0.0232408	−	0.00170635i
$833$	−49.8147			−1.72598
$834$	−7.27391	+	9.24354i	−0.251875	+	0.320078i
$835$	1.95524	−	1.95524i	0.0676640	−	0.0676640i
$836$	5.95078	+	24.5970i	0.205812	+	0.850707i
$837$	−0.394316	−	0.394316i	−0.0136296	−	0.0136296i
$838$	−1.71756	−	14.4036i	−0.0593323	−	0.497565i
$839$		−	44.4557i		−	1.53478i	−0.641181	−	0.767390i	$-0.721555\pi$
$839$		−	44.4557i		−	1.53478i	0.641181	−	0.767390i	$-0.278445\pi$
$840$	2.54156	−	5.55136i	0.0876921	−	0.191540i
$841$		−	24.3200i		−	0.838620i
$842$	4.75729	−	0.567285i	0.163947	−	0.0195499i
$843$	−16.1864	−	16.1864i	−0.557488	−	0.557488i
$844$	−24.4290	−	14.9114i	−0.840881	−	0.513270i
$845$	4.35139	−	4.35139i	0.149692	−	0.149692i
$846$	−3.14343	−	2.47363i	−0.108073	−	0.0850450i
$847$	−5.64077			−0.193819
$848$	2.65815	+	0.853410i	0.0912813	+	0.0293062i
$849$	−6.34315			−0.217696
$850$	−19.1977	−	15.1071i	−0.658477	−	0.518168i
$851$	12.4057	−	12.4057i	0.425262	−	0.425262i
$852$	9.49824	−	15.5608i	0.325404	−	0.533104i
$853$	−11.7131	−	11.7131i	−0.401049	−	0.401049i	0.477553	−	0.878603i	$-0.341524\pi$
$853$	−11.7131	−	11.7131i	−0.401049	−	0.401049i	−0.878603	+	0.477553i	$0.841524\pi$
$854$	24.7026	−	2.94567i	0.845307	−	0.100799i
$855$			1.71313i			0.0585879i
$856$	−8.45311	−	22.7292i	−0.288921	−	0.776868i
$857$		−	19.0888i		−	0.652062i	−0.945359	−	0.326031i	$-0.894289\pi$
$857$		−	19.0888i		−	0.652062i	0.945359	−	0.326031i	$-0.105711\pi$
$858$	0.0492187	+	0.412751i	0.00168030	+	0.0140911i
$859$	−38.1323	−	38.1323i	−1.30106	−	1.30106i	−0.927679	−	0.373379i	$-0.878199\pi$
$859$	−38.1323	−	38.1323i	−1.30106	−	1.30106i	−0.373379	−	0.927679i	$-0.621801\pi$
$860$	2.09682	−	0.507285i	0.0715010	−	0.0172983i
$861$	29.8874	−	29.8874i	1.01856	−	1.01856i
$862$	−3.86952	+	4.91731i	−0.131796	+	0.167484i
$863$	3.64533			0.124089			0.0620443	−	0.998073i	$-0.480238\pi$
$863$	3.64533			0.124089			0.0620443	+	0.998073i	$0.480238\pi$
$864$	−4.68971	+	3.16333i	−0.159547	+	0.107619i
$865$	2.42826			0.0825632
$866$	6.39627	−	8.12825i	0.217354	−	0.276209i
$867$	2.76965	−	2.76965i	0.0940623	−	0.0940623i
$868$	−4.94059	+	1.19528i	−0.167694	+	0.0405704i
$869$	27.1943	+	27.1943i	0.922504	+	0.922504i
$870$	0.579123	+	4.85657i	0.0196341	+	0.164653i
$871$			0.448643i			0.0152017i
$872$	−21.4310	+	7.97028i	−0.725744	+	0.269908i
$873$		−	4.31724i		−	0.146116i
$874$	−14.3665	+	1.71313i	−0.485953	+	0.0579476i
$875$	−14.9213	−	14.9213i	−0.504433	−	0.504433i
$876$	−0.564311	+	0.924500i	−0.0190663	+	0.0312360i
$877$	40.0563	−	40.0563i	1.35260	−	1.35260i	0.469866	−	0.882738i	$-0.344302\pi$
$877$	40.0563	−	40.0563i	1.35260	−	1.35260i	0.882738	−	0.469866i	$-0.155698\pi$
$878$	32.9558	+	25.9336i	1.11221	+	0.875215i
$879$	−30.5783			−1.03138
$880$	−3.02944	−	5.89450i	−0.102122	−	0.198704i
$881$	−20.0118			−0.674214			−0.337107	−	0.941466i	$-0.609448\pi$
$881$	−20.0118			−0.674214			−0.337107	+	0.941466i	$0.609448\pi$
$882$	15.3060	+	12.0446i	0.515379	+	0.405561i
$883$	−10.6273	+	10.6273i	−0.357636	+	0.357636i	−0.862941	−	0.505305i	$-0.831380\pi$
$883$	−10.6273	+	10.6273i	−0.357636	+	0.357636i	0.505305	+	0.862941i	$0.331380\pi$
$884$	0.518808	+	0.316678i	0.0174494	+	0.0106510i
$885$	1.89450	+	1.89450i	0.0636830	+	0.0636830i
$886$	20.4662	−	2.44049i	0.687574	−	0.0819900i
$887$			26.1180i			0.876958i	0.898742	+	0.438479i	$0.144483\pi$
$887$			26.1180i			0.876958i	−0.898742	+	0.438479i	$0.855517\pi$
$888$	15.9520	+	7.30324i	0.535313	+	0.245081i
$889$			23.2404i			0.779458i
$890$	1.16215	+	9.74587i	0.0389553	+	0.326682i
$891$	2.47363	+	2.47363i	0.0828696	+	0.0828696i
$892$	2.28636	+	9.45048i	0.0765530	+	0.316425i
$893$	7.23412	−	7.23412i	0.242081	−	0.242081i
$894$	12.3579	−	15.7042i	0.413311	−	0.525228i
$895$	−6.21805			−0.207847
$896$	2.33999	+	51.5108i	0.0781736	+	1.72085i
$897$	−0.237649			−0.00793486
$898$	−5.67452	+	7.21107i	−0.189361	+	0.240636i
$899$	2.87932	−	2.87932i	0.0960306	−	0.0960306i
$900$	2.24597	+	9.28354i	0.0748658	+	0.309451i
$901$	−1.78510	−	1.78510i	−0.0594704	−	0.0594704i
$902$	−5.43253	−	45.5576i	−0.180884	−	1.51690i
$903$			10.3798i			0.345418i
$904$	24.5634	+	11.2458i	0.816966	+	0.374029i
$905$			7.25507i			0.241167i
$906$	14.0101	−	1.67064i	0.465456	−	0.0555034i
$907$	36.2378	+	36.2378i	1.20326	+	1.20326i	0.973170	+	0.230087i	$0.0739010\pi$
$907$	36.2378	+	36.2378i	1.20326	+	1.20326i	0.230087	+	0.973170i	$0.426099\pi$
$908$	−25.6913	−	15.6818i	−0.852594	−	0.520420i
$909$	−0.453728	+	0.453728i	−0.0150492	+	0.0150492i
$910$	0.201570	+	0.158619i	0.00668198	+	0.00525817i
$911$	−21.0535			−0.697533			−0.348767	−	0.937210i	$-0.613399\pi$
$911$	−21.0535			−0.697533			−0.348767	+	0.937210i	$0.613399\pi$
$912$	−6.61353	−	12.8682i	−0.218996	−	0.426109i
$913$	52.6470			1.74236
$914$	10.0063	+	7.87412i	0.330978	+	0.260453i
$915$	1.29263	−	1.29263i	0.0427330	−	0.0427330i
$916$	−29.7248	+	48.6975i	−0.982134	+	1.60901i
$917$	9.65685	+	9.65685i	0.318897	+	0.318897i
$918$	5.07931	−	0.605684i	0.167642	−	0.0199905i
$919$		−	17.8839i		−	0.589937i	−0.955507	−	0.294968i	$-0.904691\pi$
$919$		−	17.8839i		−	0.589937i	0.955507	−	0.294968i	$-0.0953091\pi$
$920$	3.55136	−	1.32077i	0.117085	−	0.0435444i
$921$		−	17.1286i		−	0.564407i
$922$	−3.46262	−	29.0378i	−0.114035	−	0.956310i
$923$	0.541560	+	0.541560i	0.0178257	+	0.0178257i
$924$	30.9933	−	7.49824i	1.01961	−	0.246674i
$925$	20.9465	−	20.9465i	0.688716	−	0.688716i
$926$	−16.3048	+	20.7199i	−0.535810	+	0.680897i
$927$	−1.33686			−0.0439081
$928$	−23.0988	−	34.2445i	−0.758256	−	1.12413i
$929$	10.2774			0.337192			0.168596	−	0.985685i	$-0.446077\pi$
$929$	10.2774			0.337192			0.168596	+	0.985685i	$0.446077\pi$
$930$	−0.230985	+	0.293531i	−0.00757430	+	0.00962527i
$931$	−35.2243	+	35.2243i	−1.15443	+	1.15443i
$932$	−26.3794	+	6.38198i	−0.864086	+	0.209049i
$933$	−18.9965	−	18.9965i	−0.621917	−	0.621917i
$934$	5.56837	+	46.6968i	0.182203	+	1.52796i
$935$			5.99294i			0.195990i
$936$	−0.0828394	−	0.222743i	−0.00270769	−	0.00728059i
$937$			13.5780i			0.443574i	0.975095	+	0.221787i	$0.0711890\pi$
$937$			13.5780i			0.443574i	−0.975095	+	0.221787i	$0.928811\pi$
$938$	34.1743	−	4.07513i	1.11583	−	0.133058i
$939$	13.9222	+	13.9222i	0.454335	+	0.454335i
$940$	−1.39589	+	2.28687i	−0.0455290	+	0.0745894i
$941$	−3.95902	+	3.95902i	−0.129060	+	0.129060i	−0.768686	−	0.639626i	$-0.779089\pi$
$941$	−3.95902	+	3.95902i	−0.129060	+	0.129060i	0.639626	+	0.768686i	$0.279089\pi$
$942$	−25.4017	−	19.9891i	−0.827632	−	0.651279i
$943$	26.2306			0.854186
$944$	−21.5443	−	6.91688i	−0.701207	−	0.225125i
$945$	2.15862			0.0702199
$946$	8.85433	+	6.96764i	0.287879	+	0.226537i
$947$	−33.1708	+	33.1708i	−1.07791	+	1.07791i	−0.0812084	+	0.996697i	$0.525878\pi$
$947$	−33.1708	+	33.1708i	−1.07791	+	1.07791i	−0.996697	+	0.0812084i	$0.974122\pi$
$948$	−18.7674	−	11.4556i	−0.609538	−	0.372059i
$949$	−0.0321752	−	0.0321752i	−0.00104445	−	0.00104445i
$950$	−24.2572	+	2.89255i	−0.787006	+	0.0938468i
$951$			30.1860i			0.978847i
$952$	19.4098	−	42.3955i	0.629075	−	1.37405i
$953$			5.59115i			0.181115i	0.995891	+	0.0905576i	$0.0288649\pi$
$953$			5.59115i			0.181115i	−0.995891	+	0.0905576i	$0.971135\pi$
$954$	0.116873	+	0.980103i	0.00378389	+	0.0317320i
$955$	2.89023	+	2.89023i	0.0935255	+	0.0935255i
$956$	−13.8092	−	57.0792i	−0.446622	−	1.84607i
$957$	−18.0625	+	18.0625i	−0.583879	+	0.583879i
$958$	−0.952079	+	1.20988i	−0.0307603	+	0.0390896i
$959$	−15.4022			−0.497362
$960$	2.47586	+	2.86822i	0.0799080	+	0.0925715i
$961$	−30.6890			−0.989969
$962$	−0.455796	+	0.579216i	−0.0146955	+	0.0186747i
$963$	6.06255	−	6.06255i	0.195363	−	0.195363i
$964$	−11.2900	−	46.6663i	−0.363626	−	1.50302i
$965$	−3.83511	−	3.83511i	−0.123457	−	0.123457i
$966$	2.15862	+	18.1023i	0.0694524	+	0.582433i
$967$		−	30.7561i		−	0.989048i	−0.869164	−	0.494524i	$-0.835342\pi$
$967$		−	30.7561i		−	0.989048i	0.869164	−	0.494524i	$-0.164658\pi$
$968$	1.45721	−	3.18288i	0.0468365	−	0.102302i
$969$			13.0831i			0.420290i
$970$	−2.87138	+	0.342398i	−0.0921944	+	0.0109937i
$971$	8.03756	+	8.03756i	0.257938	+	0.257938i	0.824215	−	0.566277i	$-0.191617\pi$
$971$	8.03756	+	8.03756i	0.257938	+	0.257938i	−0.566277	+	0.824215i	$0.691617\pi$
$972$	−1.70711	−	1.04201i	−0.0547555	−	0.0334225i
$973$	−26.8043	+	26.8043i	−0.859307	+	0.859307i
$974$	39.2645	+	30.8980i	1.25812	+	0.990035i
$975$	−0.401260			−0.0128506
$976$	−4.71942	+	14.6998i	−0.151065	+	0.470529i
$977$	22.8323			0.730471			0.365235	−	0.930915i	$-0.380988\pi$
$977$	22.8323			0.730471			0.365235	+	0.930915i	$0.380988\pi$
$978$	−11.7956	−	9.28216i	−0.377181	−	0.296811i
$979$	−36.2468	+	36.2468i	−1.15845	+	1.15845i
$980$	6.79687	−	11.1352i	0.217118	−	0.355701i
$981$	−5.71627	−	5.71627i	−0.182506	−	0.182506i
$982$	−25.6006	+	3.05275i	−0.816947	+	0.0974171i
$983$			46.3557i			1.47852i	0.673422	+	0.739258i	$0.264824\pi$
$983$			46.3557i			1.47852i	−0.673422	+	0.739258i	$0.735176\pi$
$984$	9.14343	+	24.5854i	0.291482	+	0.783754i
$985$		−	5.01686i		−	0.159850i
$986$	4.42274	+	37.0894i	0.140849	+	1.18117i
$987$	−9.11529	−	9.11529i	−0.290143	−	0.290143i
$988$	0.590778	−	0.142927i	0.0187952	−	0.00454713i
$989$	−4.55489	+	4.55489i	−0.144837	+	0.144837i
$990$	1.44902	−	1.84138i	0.0460528	−	0.0585229i
$991$	3.43683			0.109175			0.0545873	−	0.998509i	$-0.482616\pi$
$991$	3.43683			0.109175			0.0545873	+	0.998509i	$0.482616\pi$
$992$	0.601874	−	3.09658i	0.0191095	−	0.0983165i
$993$	−20.7784			−0.659383
$994$	36.3329	−	46.1712i	1.15241	−	1.46446i
$995$	1.23245	−	1.23245i	0.0390712	−	0.0390712i
$996$	−29.2552	+	7.07773i	−0.926986	+	0.224267i
$997$	−21.9430	−	21.9430i	−0.694940	−	0.694940i	0.268374	−	0.963315i	$-0.413514\pi$
$997$	−21.9430	−	21.9430i	−0.694940	−	0.694940i	−0.963315	+	0.268374i	$0.913514\pi$
$998$	−3.40532	−	28.5573i	−0.107793	−	0.903964i
$999$			6.20285i			0.196249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.2.j.a.37.4	yes	8
3.2	odd	2		144.2.k.b.37.1		8
4.3	odd	2		192.2.j.a.49.3		8
8.3	odd	2		384.2.j.a.97.2		8
8.5	even	2		384.2.j.b.97.4		8
12.11	even	2		576.2.k.b.433.3		8
16.3	odd	4		192.2.j.a.145.3		8
16.5	even	4		384.2.j.b.289.4		8
16.11	odd	4		384.2.j.a.289.2		8
16.13	even	4	inner	48.2.j.a.13.4	✓	8
24.5	odd	2		1152.2.k.c.865.2		8
24.11	even	2		1152.2.k.f.865.2		8
32.3	odd	8		3072.2.a.o.1.3		4
32.5	even	8		3072.2.d.f.1537.2		8
32.11	odd	8		3072.2.d.i.1537.3		8
32.13	even	8		3072.2.a.t.1.2		4
32.19	odd	8		3072.2.a.n.1.2		4
32.21	even	8		3072.2.d.f.1537.7		8
32.27	odd	8		3072.2.d.i.1537.6		8
32.29	even	8		3072.2.a.i.1.3		4
48.5	odd	4		1152.2.k.c.289.2		8
48.11	even	4		1152.2.k.f.289.2		8
48.29	odd	4		144.2.k.b.109.1		8
48.35	even	4		576.2.k.b.145.3		8
96.29	odd	8		9216.2.a.bo.1.2		4
96.35	even	8		9216.2.a.bn.1.2		4
96.77	odd	8		9216.2.a.y.1.3		4
96.83	even	8		9216.2.a.x.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.4	✓	8	16.13	even	4	inner
48.2.j.a.37.4	yes	8	1.1	even	1	trivial
144.2.k.b.37.1		8	3.2	odd	2
144.2.k.b.109.1		8	48.29	odd	4
192.2.j.a.49.3		8	4.3	odd	2
192.2.j.a.145.3		8	16.3	odd	4
384.2.j.a.97.2		8	8.3	odd	2
384.2.j.a.289.2		8	16.11	odd	4
384.2.j.b.97.4		8	8.5	even	2
384.2.j.b.289.4		8	16.5	even	4
576.2.k.b.145.3		8	48.35	even	4
576.2.k.b.433.3		8	12.11	even	2
1152.2.k.c.289.2		8	48.5	odd	4
1152.2.k.c.865.2		8	24.5	odd	2
1152.2.k.f.289.2		8	48.11	even	4
1152.2.k.f.865.2		8	24.11	even	2
3072.2.a.i.1.3		4	32.29	even	8
3072.2.a.n.1.2		4	32.19	odd	8
3072.2.a.o.1.3		4	32.3	odd	8
3072.2.a.t.1.2		4	32.13	even	8
3072.2.d.f.1537.2		8	32.5	even	8
3072.2.d.f.1537.7		8	32.21	even	8
3072.2.d.i.1537.3		8	32.11	odd	8
3072.2.d.i.1537.6		8	32.27	odd	8
9216.2.a.x.1.3		4	96.83	even	8
9216.2.a.y.1.3		4	96.77	odd	8
9216.2.a.bn.1.2		4	96.35	even	8
9216.2.a.bo.1.2		4	96.29	odd	8

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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