LMFDB - Embedded newform 104.2.b.b.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(53,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("104.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.b (of order $2$, degree $1$, 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:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.4
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	104.53
Dual form			104.2.b.b.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +2.00000i q^{3} +(1.73205 + 1.00000i) q^{4} -3.46410i q^{5} +(-0.732051 + 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +2.00000i q^{3} +(1.73205 + 1.00000i) q^{4} -3.46410i q^{5} +(-0.732051 + 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(1.26795 - 4.73205i) q^{10} -1.26795i q^{11} +(-2.00000 + 3.46410i) q^{12} +1.00000i q^{13} +(-6.46410 - 1.73205i) q^{14} +6.92820 q^{15} +(2.00000 + 3.46410i) q^{16} -1.46410 q^{17} +(-1.36603 - 0.366025i) q^{18} -2.73205i q^{19} +(3.46410 - 6.00000i) q^{20} -9.46410i q^{21} +(0.464102 - 1.73205i) q^{22} +4.00000 q^{23} +(-4.00000 + 4.00000i) q^{24} -7.00000 q^{25} +(-0.366025 + 1.36603i) q^{26} +4.00000i q^{27} +(-8.19615 - 4.73205i) q^{28} +2.00000i q^{29} +(9.46410 + 2.53590i) q^{30} -3.26795 q^{31} +(1.46410 + 5.46410i) q^{32} +2.53590 q^{33} +(-2.00000 - 0.535898i) q^{34} +16.3923i q^{35} +(-1.73205 - 1.00000i) q^{36} +4.92820i q^{37} +(1.00000 - 3.73205i) q^{38} -2.00000 q^{39} +(6.92820 - 6.92820i) q^{40} -4.92820 q^{41} +(3.46410 - 12.9282i) q^{42} -7.46410i q^{43} +(1.26795 - 2.19615i) q^{44} +3.46410i q^{45} +(5.46410 + 1.46410i) q^{46} +3.26795 q^{47} +(-6.92820 + 4.00000i) q^{48} +15.3923 q^{49} +(-9.56218 - 2.56218i) q^{50} -2.92820i q^{51} +(-1.00000 + 1.73205i) q^{52} +10.9282i q^{53} +(-1.46410 + 5.46410i) q^{54} -4.39230 q^{55} +(-9.46410 - 9.46410i) q^{56} +5.46410 q^{57} +(-0.732051 + 2.73205i) q^{58} +0.196152i q^{59} +(12.0000 + 6.92820i) q^{60} -10.9282i q^{61} +(-4.46410 - 1.19615i) q^{62} +4.73205 q^{63} +8.00000i q^{64} +3.46410 q^{65} +(3.46410 + 0.928203i) q^{66} -2.73205i q^{67} +(-2.53590 - 1.46410i) q^{68} +8.00000i q^{69} +(-6.00000 + 22.3923i) q^{70} +2.19615 q^{71} +(-2.00000 - 2.00000i) q^{72} -0.535898 q^{73} +(-1.80385 + 6.73205i) q^{74} -14.0000i q^{75} +(2.73205 - 4.73205i) q^{76} +6.00000i q^{77} +(-2.73205 - 0.732051i) q^{78} -1.46410 q^{79} +(12.0000 - 6.92820i) q^{80} -11.0000 q^{81} +(-6.73205 - 1.80385i) q^{82} +6.73205i q^{83} +(9.46410 - 16.3923i) q^{84} +5.07180i q^{85} +(2.73205 - 10.1962i) q^{86} -4.00000 q^{87} +(2.53590 - 2.53590i) q^{88} +17.3205 q^{89} +(-1.26795 + 4.73205i) q^{90} -4.73205i q^{91} +(6.92820 + 4.00000i) q^{92} -6.53590i q^{93} +(4.46410 + 1.19615i) q^{94} -9.46410 q^{95} +(-10.9282 + 2.92820i) q^{96} -14.3923 q^{97} +(21.0263 + 5.63397i) q^{98} +1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^6 - 12 * q^7 + 8 * q^8 - 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9} + 12 q^{10} - 8 q^{12} - 12 q^{14} + 8 q^{16} + 8 q^{17} - 2 q^{18} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 28 q^{25} + 2 q^{26} - 12 q^{28} + 24 q^{30} - 20 q^{31} - 8 q^{32} + 24 q^{33} - 8 q^{34} + 4 q^{38} - 8 q^{39} + 8 q^{41} + 12 q^{44} + 8 q^{46} + 20 q^{47} + 20 q^{49} - 14 q^{50} - 4 q^{52} + 8 q^{54} + 24 q^{55} - 24 q^{56} + 8 q^{57} + 4 q^{58} + 48 q^{60} - 4 q^{62} + 12 q^{63} - 24 q^{68} - 24 q^{70} - 12 q^{71} - 8 q^{72} - 16 q^{73} - 28 q^{74} + 4 q^{76} - 4 q^{78} + 8 q^{79} + 48 q^{80} - 44 q^{81} - 20 q^{82} + 24 q^{84} + 4 q^{86} - 16 q^{87} + 24 q^{88} - 12 q^{90} + 4 q^{94} - 24 q^{95} - 16 q^{96} - 16 q^{97} + 46 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^6 - 12 * q^7 + 8 * q^8 - 4 * q^9 + 12 * q^10 - 8 * q^12 - 12 * q^14 + 8 * q^16 + 8 * q^17 - 2 * q^18 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 28 * q^25 + 2 * q^26 - 12 * q^28 + 24 * q^30 - 20 * q^31 - 8 * q^32 + 24 * q^33 - 8 * q^34 + 4 * q^38 - 8 * q^39 + 8 * q^41 + 12 * q^44 + 8 * q^46 + 20 * q^47 + 20 * q^49 - 14 * q^50 - 4 * q^52 + 8 * q^54 + 24 * q^55 - 24 * q^56 + 8 * q^57 + 4 * q^58 + 48 * q^60 - 4 * q^62 + 12 * q^63 - 24 * q^68 - 24 * q^70 - 12 * q^71 - 8 * q^72 - 16 * q^73 - 28 * q^74 + 4 * q^76 - 4 * q^78 + 8 * q^79 + 48 * q^80 - 44 * q^81 - 20 * q^82 + 24 * q^84 + 4 * q^86 - 16 * q^87 + 24 * q^88 - 12 * q^90 + 4 * q^94 - 24 * q^95 - 16 * q^96 - 16 * q^97 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$			2.00000i			1.15470i	0.816497	+	0.577350i	$0.195913\pi$
$3$			2.00000i			1.15470i	−0.816497	+	0.577350i	$0.804087\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$		−	3.46410i		−	1.54919i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$	−0.732051	+	2.73205i	−0.298858	+	1.11536i
$7$	−4.73205			−1.78855			−0.894274	−	0.447521i	$-0.852307\pi$
$7$	−4.73205			−1.78855			−0.894274	+	0.447521i	$0.852307\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.00000			−0.333333
$10$	1.26795	−	4.73205i	0.400961	−	1.49641i
$11$		−	1.26795i		−	0.382301i	−0.981561	−	0.191151i	$-0.938778\pi$
$11$		−	1.26795i		−	0.382301i	0.981561	−	0.191151i	$-0.0612219\pi$
$12$	−2.00000	+	3.46410i	−0.577350	+	1.00000i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−6.46410	−	1.73205i	−1.72760	−	0.462910i
$15$	6.92820			1.78885
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.46410			−0.355097			−0.177548	−	0.984112i	$-0.556817\pi$
$17$	−1.46410			−0.355097			−0.177548	+	0.984112i	$0.556817\pi$
$18$	−1.36603	−	0.366025i	−0.321975	−	0.0862730i
$19$		−	2.73205i		−	0.626775i	−0.949625	−	0.313388i	$-0.898536\pi$
$19$		−	2.73205i		−	0.626775i	0.949625	−	0.313388i	$-0.101464\pi$
$20$	3.46410	−	6.00000i	0.774597	−	1.34164i
$21$		−	9.46410i		−	2.06524i
$22$	0.464102	−	1.73205i	0.0989468	−	0.369274i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	−4.00000	+	4.00000i	−0.816497	+	0.816497i
$25$	−7.00000			−1.40000
$26$	−0.366025	+	1.36603i	−0.0717835	+	0.267900i
$27$			4.00000i			0.769800i
$28$	−8.19615	−	4.73205i	−1.54893	−	0.894274i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$	9.46410	+	2.53590i	1.72790	+	0.462990i
$31$	−3.26795			−0.586941			−0.293471	−	0.955968i	$-0.594810\pi$
$31$	−3.26795			−0.586941			−0.293471	+	0.955968i	$0.594810\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$	2.53590			0.441443
$34$	−2.00000	−	0.535898i	−0.342997	−	0.0919058i
$35$			16.3923i			2.77081i
$36$	−1.73205	−	1.00000i	−0.288675	−	0.166667i
$37$			4.92820i			0.810192i	0.914274	+	0.405096i	$0.132762\pi$
$37$			4.92820i			0.810192i	−0.914274	+	0.405096i	$0.867238\pi$
$38$	1.00000	−	3.73205i	0.162221	−	0.605419i
$39$	−2.00000			−0.320256
$40$	6.92820	−	6.92820i	1.09545	−	1.09545i
$41$	−4.92820			−0.769656			−0.384828	−	0.922988i	$-0.625739\pi$
$41$	−4.92820			−0.769656			−0.384828	+	0.922988i	$0.625739\pi$
$42$	3.46410	−	12.9282i	0.534522	−	1.99487i
$43$		−	7.46410i		−	1.13826i	−0.822246	−	0.569132i	$-0.807279\pi$
$43$		−	7.46410i		−	1.13826i	0.822246	−	0.569132i	$-0.192721\pi$
$44$	1.26795	−	2.19615i	0.191151	−	0.331082i
$45$			3.46410i			0.516398i
$46$	5.46410	+	1.46410i	0.805638	+	0.215870i
$47$	3.26795			0.476679			0.238340	−	0.971182i	$-0.423397\pi$
$47$	3.26795			0.476679			0.238340	+	0.971182i	$0.423397\pi$
$48$	−6.92820	+	4.00000i	−1.00000	+	0.577350i
$49$	15.3923			2.19890
$50$	−9.56218	−	2.56218i	−1.35230	−	0.362347i
$51$		−	2.92820i		−	0.410030i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$			10.9282i			1.50110i	0.660811	+	0.750552i	$0.270212\pi$
$53$			10.9282i			1.50110i	−0.660811	+	0.750552i	$0.729788\pi$
$54$	−1.46410	+	5.46410i	−0.199239	+	0.743570i
$55$	−4.39230			−0.592258
$56$	−9.46410	−	9.46410i	−1.26469	−	1.26469i
$57$	5.46410			0.723738
$58$	−0.732051	+	2.73205i	−0.0961230	+	0.358736i
$59$			0.196152i			0.0255369i	0.999918	+	0.0127684i	$0.00406443\pi$
$59$			0.196152i			0.0255369i	−0.999918	+	0.0127684i	$0.995936\pi$
$60$	12.0000	+	6.92820i	1.54919	+	0.894427i
$61$		−	10.9282i		−	1.39921i	−0.714528	−	0.699607i	$-0.753359\pi$
$61$		−	10.9282i		−	1.39921i	0.714528	−	0.699607i	$-0.246641\pi$
$62$	−4.46410	−	1.19615i	−0.566941	−	0.151912i
$63$	4.73205			0.596182
$64$			8.00000i			1.00000i
$65$	3.46410			0.429669
$66$	3.46410	+	0.928203i	0.426401	+	0.114254i
$67$		−	2.73205i		−	0.333773i	−0.985976	−	0.166887i	$-0.946629\pi$
$67$		−	2.73205i		−	0.333773i	0.985976	−	0.166887i	$-0.0533714\pi$
$68$	−2.53590	−	1.46410i	−0.307523	−	0.177548i
$69$			8.00000i			0.963087i
$70$	−6.00000	+	22.3923i	−0.717137	+	2.67639i
$71$	2.19615			0.260635			0.130318	−	0.991472i	$-0.458400\pi$
$71$	2.19615			0.260635			0.130318	+	0.991472i	$0.458400\pi$
$72$	−2.00000	−	2.00000i	−0.235702	−	0.235702i
$73$	−0.535898			−0.0627222			−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898			−0.0627222			−0.0313611	+	0.999508i	$0.509984\pi$
$74$	−1.80385	+	6.73205i	−0.209693	+	0.782585i
$75$		−	14.0000i		−	1.61658i
$76$	2.73205	−	4.73205i	0.313388	−	0.542803i
$77$			6.00000i			0.683763i
$78$	−2.73205	−	0.732051i	−0.309344	−	0.0828884i
$79$	−1.46410			−0.164724			−0.0823622	−	0.996602i	$-0.526246\pi$
$79$	−1.46410			−0.164724			−0.0823622	+	0.996602i	$0.526246\pi$
$80$	12.0000	−	6.92820i	1.34164	−	0.774597i
$81$	−11.0000			−1.22222
$82$	−6.73205	−	1.80385i	−0.743431	−	0.199202i
$83$			6.73205i			0.738939i	0.929243	+	0.369469i	$0.120461\pi$
$83$			6.73205i			0.738939i	−0.929243	+	0.369469i	$0.879539\pi$
$84$	9.46410	−	16.3923i	1.03262	−	1.78855i
$85$			5.07180i			0.550114i
$86$	2.73205	−	10.1962i	0.294605	−	1.09948i
$87$	−4.00000			−0.428845
$88$	2.53590	−	2.53590i	0.270328	−	0.270328i
$89$	17.3205			1.83597			0.917985	−	0.396615i	$-0.129815\pi$
$89$	17.3205			1.83597			0.917985	+	0.396615i	$0.129815\pi$
$90$	−1.26795	+	4.73205i	−0.133654	+	0.498802i
$91$		−	4.73205i		−	0.496054i
$92$	6.92820	+	4.00000i	0.722315	+	0.417029i
$93$		−	6.53590i		−	0.677741i
$94$	4.46410	+	1.19615i	0.460437	+	0.123374i
$95$	−9.46410			−0.970996
$96$	−10.9282	+	2.92820i	−1.11536	+	0.298858i
$97$	−14.3923			−1.46132			−0.730659	−	0.682743i	$-0.760787\pi$
$97$	−14.3923			−1.46132			−0.730659	+	0.682743i	$0.760787\pi$
$98$	21.0263	+	5.63397i	2.12397	+	0.569117i
$99$			1.26795i			0.127434i
$100$	−12.1244	−	7.00000i	−1.21244	−	0.700000i
$101$		−	12.0000i		−	1.19404i	−0.802225	−	0.597022i	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$	1.07180	−	4.00000i	0.106124	−	0.396059i
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$	−2.00000	+	2.00000i	−0.196116	+	0.196116i
$105$	−32.7846			−3.19945
$106$	−4.00000	+	14.9282i	−0.388514	+	1.44996i
$107$		−	8.92820i		−	0.863122i	−0.902084	−	0.431561i	$-0.857963\pi$
$107$		−	8.92820i		−	0.863122i	0.902084	−	0.431561i	$-0.142037\pi$
$108$	−4.00000	+	6.92820i	−0.384900	+	0.666667i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	−6.00000	−	1.60770i	−0.572078	−	0.153288i
$111$	−9.85641			−0.935529
$112$	−9.46410	−	16.3923i	−0.894274	−	1.54893i
$113$	9.46410			0.890308			0.445154	−	0.895454i	$-0.353149\pi$
$113$	9.46410			0.890308			0.445154	+	0.895454i	$0.353149\pi$
$114$	7.46410	+	2.00000i	0.699077	+	0.187317i
$115$		−	13.8564i		−	1.29212i
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		−	1.00000i		−	0.0924500i
$118$	−0.0717968	+	0.267949i	−0.00660943	+	0.0246667i
$119$	6.92820			0.635107
$120$	13.8564	+	13.8564i	1.26491	+	1.26491i
$121$	9.39230			0.853846
$122$	4.00000	−	14.9282i	0.362143	−	1.35154i
$123$		−	9.85641i		−	0.888722i
$124$	−5.66025	−	3.26795i	−0.508306	−	0.293471i
$125$			6.92820i			0.619677i
$126$	6.46410	+	1.73205i	0.575868	+	0.154303i
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	14.9282			1.31436
$130$	4.73205	+	1.26795i	0.415028	+	0.111207i
$131$		−	7.85641i		−	0.686417i	−0.939259	−	0.343209i	$-0.888486\pi$
$131$		−	7.85641i		−	0.686417i	0.939259	−	0.343209i	$-0.111514\pi$
$132$	4.39230	+	2.53590i	0.382301	+	0.220722i
$133$			12.9282i			1.12102i
$134$	1.00000	−	3.73205i	0.0863868	−	0.322400i
$135$	13.8564			1.19257
$136$	−2.92820	−	2.92820i	−0.251091	−	0.251091i
$137$	−0.928203			−0.0793018			−0.0396509	−	0.999214i	$-0.512625\pi$
$137$	−0.928203			−0.0793018			−0.0396509	+	0.999214i	$0.512625\pi$
$138$	−2.92820	+	10.9282i	−0.249265	+	0.930270i
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$	−16.3923	+	28.3923i	−1.38540	+	2.39959i
$141$			6.53590i			0.550422i
$142$	3.00000	+	0.803848i	0.251754	+	0.0674574i
$143$	1.26795			0.106031
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	6.92820			0.575356
$146$	−0.732051	−	0.196152i	−0.0605850	−	0.0162337i
$147$			30.7846i			2.53907i
$148$	−4.92820	+	8.53590i	−0.405096	+	0.701647i
$149$			0.928203i			0.0760414i	0.999277	+	0.0380207i	$0.0121053\pi$
$149$			0.928203i			0.0760414i	−0.999277	+	0.0380207i	$0.987895\pi$
$150$	5.12436	−	19.1244i	0.418402	−	1.56150i
$151$	17.1244			1.39356			0.696780	−	0.717285i	$-0.254615\pi$
$151$	17.1244			1.39356			0.696780	+	0.717285i	$0.254615\pi$
$152$	5.46410	−	5.46410i	0.443197	−	0.443197i
$153$	1.46410			0.118366
$154$	−2.19615	+	8.19615i	−0.176971	+	0.660465i
$155$			11.3205i			0.909285i
$156$	−3.46410	−	2.00000i	−0.277350	−	0.160128i
$157$		−	3.07180i		−	0.245156i	−0.992459	−	0.122578i	$-0.960884\pi$
$157$		−	3.07180i		−	0.245156i	0.992459	−	0.122578i	$-0.0391162\pi$
$158$	−2.00000	−	0.535898i	−0.159111	−	0.0426338i
$159$	−21.8564			−1.73333
$160$	18.9282	−	5.07180i	1.49641	−	0.400961i
$161$	−18.9282			−1.49175
$162$	−15.0263	−	4.02628i	−1.18058	−	0.316334i
$163$			13.2679i			1.03923i	0.854402	+	0.519613i	$0.173924\pi$
$163$			13.2679i			1.03923i	−0.854402	+	0.519613i	$0.826076\pi$
$164$	−8.53590	−	4.92820i	−0.666542	−	0.384828i
$165$		−	8.78461i		−	0.683881i
$166$	−2.46410	+	9.19615i	−0.191251	+	0.713760i
$167$	11.6603			0.902298			0.451149	−	0.892449i	$-0.351014\pi$
$167$	11.6603			0.902298			0.451149	+	0.892449i	$0.351014\pi$
$168$	18.9282	−	18.9282i	1.46034	−	1.46034i
$169$	−1.00000			−0.0769231
$170$	−1.85641	+	6.92820i	−0.142380	+	0.531369i
$171$			2.73205i			0.208925i
$172$	7.46410	−	12.9282i	0.569132	−	0.985766i
$173$		−	6.92820i		−	0.526742i	−0.964695	−	0.263371i	$-0.915166\pi$
$173$		−	6.92820i		−	0.526742i	0.964695	−	0.263371i	$-0.0848343\pi$
$174$	−5.46410	−	1.46410i	−0.414232	−	0.110993i
$175$	33.1244			2.50397
$176$	4.39230	−	2.53590i	0.331082	−	0.191151i
$177$	−0.392305			−0.0294874
$178$	23.6603	+	6.33975i	1.77341	+	0.475184i
$179$			10.3923i			0.776757i	0.921500	+	0.388379i	$0.126965\pi$
$179$			10.3923i			0.776757i	−0.921500	+	0.388379i	$0.873035\pi$
$180$	−3.46410	+	6.00000i	−0.258199	+	0.447214i
$181$			4.92820i			0.366310i	0.983084	+	0.183155i	$0.0586311\pi$
$181$			4.92820i			0.366310i	−0.983084	+	0.183155i	$0.941369\pi$
$182$	1.73205	−	6.46410i	0.128388	−	0.479151i
$183$	21.8564			1.61567
$184$	8.00000	+	8.00000i	0.589768	+	0.589768i
$185$	17.0718			1.25514
$186$	2.39230	−	8.92820i	0.175412	−	0.654648i
$187$			1.85641i			0.135754i
$188$	5.66025	+	3.26795i	0.412816	+	0.238340i
$189$		−	18.9282i		−	1.37682i
$190$	−12.9282	−	3.46410i	−0.937910	−	0.251312i
$191$	−21.4641			−1.55309			−0.776544	−	0.630063i	$-0.783029\pi$
$191$	−21.4641			−1.55309			−0.776544	+	0.630063i	$0.783029\pi$
$192$	−16.0000			−1.15470
$193$	−22.3923			−1.61183			−0.805917	−	0.592029i	$-0.798327\pi$
$193$	−22.3923			−1.61183			−0.805917	+	0.592029i	$0.798327\pi$
$194$	−19.6603	−	5.26795i	−1.41152	−	0.378217i
$195$			6.92820i			0.496139i
$196$	26.6603	+	15.3923i	1.90430	+	1.09945i
$197$		−	16.9282i		−	1.20608i	−0.797709	−	0.603042i	$-0.793955\pi$
$197$		−	16.9282i		−	1.20608i	0.797709	−	0.603042i	$-0.206045\pi$
$198$	−0.464102	+	1.73205i	−0.0329823	+	0.123091i
$199$	−24.7846			−1.75693			−0.878467	−	0.477803i	$-0.841433\pi$
$199$	−24.7846			−1.75693			−0.878467	+	0.477803i	$0.841433\pi$
$200$	−14.0000	−	14.0000i	−0.989949	−	0.989949i
$201$	5.46410			0.385408
$202$	4.39230	−	16.3923i	0.309041	−	1.15336i
$203$		−	9.46410i		−	0.664250i
$204$	2.92820	−	5.07180i	0.205015	−	0.355097i
$205$			17.0718i			1.19235i
$206$	−9.46410	−	2.53590i	−0.659395	−	0.176684i
$207$	−4.00000			−0.278019
$208$	−3.46410	+	2.00000i	−0.240192	+	0.138675i
$209$	−3.46410			−0.239617
$210$	−44.7846	−	12.0000i	−3.09043	−	0.828079i
$211$			19.8564i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$211$			19.8564i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$212$	−10.9282	+	18.9282i	−0.750552	+	1.29999i
$213$			4.39230i			0.300956i
$214$	3.26795	−	12.1962i	0.223392	−	0.833712i
$215$	−25.8564			−1.76339
$216$	−8.00000	+	8.00000i	−0.544331	+	0.544331i
$217$	15.4641			1.04977
$218$	0.732051	−	2.73205i	0.0495807	−	0.185038i
$219$		−	1.07180i		−	0.0724253i
$220$	−7.60770	−	4.39230i	−0.512911	−	0.296129i
$221$		−	1.46410i		−	0.0984861i
$222$	−13.4641	−	3.60770i	−0.903651	−	0.242133i
$223$	10.1962			0.682785			0.341392	−	0.939921i	$-0.389101\pi$
$223$	10.1962			0.682785			0.341392	+	0.939921i	$0.389101\pi$
$224$	−6.92820	−	25.8564i	−0.462910	−	1.72760i
$225$	7.00000			0.466667
$226$	12.9282	+	3.46410i	0.859971	+	0.230429i
$227$			27.1244i			1.80031i	0.435573	+	0.900153i	$0.356546\pi$
$227$			27.1244i			1.80031i	−0.435573	+	0.900153i	$0.643454\pi$
$228$	9.46410	+	5.46410i	0.626775	+	0.361869i
$229$			29.3205i			1.93755i	0.247934	+	0.968777i	$0.420248\pi$
$229$			29.3205i			1.93755i	−0.247934	+	0.968777i	$0.579752\pi$
$230$	5.07180	−	18.9282i	0.334424	−	1.24809i
$231$	−12.0000			−0.789542
$232$	−4.00000	+	4.00000i	−0.262613	+	0.262613i
$233$	3.07180			0.201240			0.100620	−	0.994925i	$-0.467917\pi$
$233$	3.07180			0.201240			0.100620	+	0.994925i	$0.467917\pi$
$234$	0.366025	−	1.36603i	0.0239278	−	0.0892999i
$235$		−	11.3205i		−	0.738469i
$236$	−0.196152	+	0.339746i	−0.0127684	+	0.0221156i
$237$		−	2.92820i		−	0.190207i
$238$	9.46410	+	2.53590i	0.613467	+	0.164378i
$239$	15.2679			0.987602			0.493801	−	0.869575i	$-0.335607\pi$
$239$	15.2679			0.987602			0.493801	+	0.869575i	$0.335607\pi$
$240$	13.8564	+	24.0000i	0.894427	+	1.54919i
$241$	−9.60770			−0.618886			−0.309443	−	0.950918i	$-0.600143\pi$
$241$	−9.60770			−0.618886			−0.309443	+	0.950918i	$0.600143\pi$
$242$	12.8301	+	3.43782i	0.824752	+	0.220992i
$243$		−	10.0000i		−	0.641500i
$244$	10.9282	−	18.9282i	0.699607	−	1.21175i
$245$		−	53.3205i		−	3.40652i
$246$	3.60770	−	13.4641i	0.230018	−	0.858440i
$247$	2.73205			0.173836
$248$	−6.53590	−	6.53590i	−0.415030	−	0.415030i
$249$	−13.4641			−0.853253
$250$	−2.53590	+	9.46410i	−0.160384	+	0.598562i
$251$		−	14.3923i		−	0.908434i	−0.890891	−	0.454217i	$-0.849919\pi$
$251$		−	14.3923i		−	0.908434i	0.890891	−	0.454217i	$-0.150081\pi$
$252$	8.19615	+	4.73205i	0.516309	+	0.298091i
$253$		−	5.07180i		−	0.318861i
$254$	−5.46410	−	1.46410i	−0.342848	−	0.0918659i
$255$	−10.1436			−0.635216
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	3.85641			0.240556			0.120278	−	0.992740i	$-0.461621\pi$
$257$	3.85641			0.240556			0.120278	+	0.992740i	$0.461621\pi$
$258$	20.3923	+	5.46410i	1.26957	+	0.340180i
$259$		−	23.3205i		−	1.44907i
$260$	6.00000	+	3.46410i	0.372104	+	0.214834i
$261$		−	2.00000i		−	0.123797i
$262$	2.87564	−	10.7321i	0.177658	−	0.663028i
$263$	7.32051			0.451402			0.225701	−	0.974197i	$-0.427533\pi$
$263$	7.32051			0.451402			0.225701	+	0.974197i	$0.427533\pi$
$264$	5.07180	+	5.07180i	0.312148	+	0.312148i
$265$	37.8564			2.32550
$266$	−4.73205	+	17.6603i	−0.290141	+	1.08282i
$267$			34.6410i			2.12000i
$268$	2.73205	−	4.73205i	0.166887	−	0.289056i
$269$			19.8564i			1.21067i	0.795972	+	0.605333i	$0.206960\pi$
$269$			19.8564i			1.21067i	−0.795972	+	0.605333i	$0.793040\pi$
$270$	18.9282	+	5.07180i	1.15193	+	0.308660i
$271$	−9.80385			−0.595541			−0.297771	−	0.954637i	$-0.596243\pi$
$271$	−9.80385			−0.595541			−0.297771	+	0.954637i	$0.596243\pi$
$272$	−2.92820	−	5.07180i	−0.177548	−	0.307523i
$273$	9.46410			0.572793
$274$	−1.26795	−	0.339746i	−0.0765996	−	0.0205248i
$275$			8.87564i			0.535221i
$276$	−8.00000	+	13.8564i	−0.481543	+	0.834058i
$277$		−	25.8564i		−	1.55356i	−0.629771	−	0.776780i	$-0.716851\pi$
$277$		−	25.8564i		−	1.55356i	0.629771	−	0.776780i	$-0.283149\pi$
$278$	3.66025	−	13.6603i	0.219527	−	0.819288i
$279$	3.26795			0.195647
$280$	−32.7846	+	32.7846i	−1.95926	+	1.95926i
$281$	−25.3205			−1.51049			−0.755247	−	0.655440i	$-0.772483\pi$
$281$	−25.3205			−1.51049			−0.755247	+	0.655440i	$0.772483\pi$
$282$	−2.39230	+	8.92820i	−0.142460	+	0.531667i
$283$			12.5359i			0.745182i	0.927996	+	0.372591i	$0.121531\pi$
$283$			12.5359i			0.745182i	−0.927996	+	0.372591i	$0.878469\pi$
$284$	3.80385	+	2.19615i	0.225717	+	0.130318i
$285$		−	18.9282i		−	1.12121i
$286$	1.73205	+	0.464102i	0.102418	+	0.0274429i
$287$	23.3205			1.37657
$288$	−1.46410	−	5.46410i	−0.0862730	−	0.321975i
$289$	−14.8564			−0.873906
$290$	9.46410	+	2.53590i	0.555751	+	0.148913i
$291$		−	28.7846i		−	1.68738i
$292$	−0.928203	−	0.535898i	−0.0543190	−	0.0313611i
$293$			19.0718i			1.11419i	0.830450	+	0.557093i	$0.188083\pi$
$293$			19.0718i			1.11419i	−0.830450	+	0.557093i	$0.811917\pi$
$294$	−11.2679	+	42.0526i	−0.657160	+	2.45256i
$295$	0.679492			0.0395615
$296$	−9.85641	+	9.85641i	−0.572892	+	0.572892i
$297$	5.07180			0.294295
$298$	−0.339746	+	1.26795i	−0.0196810	+	0.0734503i
$299$			4.00000i			0.231326i
$300$	14.0000	−	24.2487i	0.808290	−	1.40000i
$301$			35.3205i			2.03584i
$302$	23.3923	+	6.26795i	1.34608	+	0.360680i
$303$	24.0000			1.37876
$304$	9.46410	−	5.46410i	0.542803	−	0.313388i
$305$	−37.8564			−2.16765
$306$	2.00000	+	0.535898i	0.114332	+	0.0306353i
$307$		−	2.73205i		−	0.155926i	−0.996956	−	0.0779632i	$-0.975158\pi$
$307$		−	2.73205i		−	0.155926i	0.996956	−	0.0779632i	$-0.0248417\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$		−	13.8564i		−	0.788263i
$310$	−4.14359	+	15.4641i	−0.235340	+	0.878302i
$311$	14.9282			0.846501			0.423250	−	0.906013i	$-0.360889\pi$
$311$	14.9282			0.846501			0.423250	+	0.906013i	$0.360889\pi$
$312$	−4.00000	−	4.00000i	−0.226455	−	0.226455i
$313$	−20.3923			−1.15264			−0.576321	−	0.817224i	$-0.695512\pi$
$313$	−20.3923			−1.15264			−0.576321	+	0.817224i	$0.695512\pi$
$314$	1.12436	−	4.19615i	0.0634511	−	0.236803i
$315$		−	16.3923i		−	0.923602i
$316$	−2.53590	−	1.46410i	−0.142655	−	0.0823622i
$317$		−	3.46410i		−	0.194563i	−0.995257	−	0.0972817i	$-0.968985\pi$
$317$		−	3.46410i		−	0.194563i	0.995257	−	0.0972817i	$-0.0310148\pi$
$318$	−29.8564	−	8.00000i	−1.67426	−	0.448618i
$319$	2.53590			0.141983
$320$	27.7128			1.54919
$321$	17.8564			0.996647
$322$	−25.8564	−	6.92820i	−1.44092	−	0.386094i
$323$			4.00000i			0.222566i
$324$	−19.0526	−	11.0000i	−1.05848	−	0.611111i
$325$		−	7.00000i		−	0.388290i
$326$	−4.85641	+	18.1244i	−0.268971	+	1.00382i
$327$	4.00000			0.221201
$328$	−9.85641	−	9.85641i	−0.544229	−	0.544229i
$329$	−15.4641			−0.852564
$330$	3.21539	−	12.0000i	0.177001	−	0.660578i
$331$		−	27.5167i		−	1.51245i	−0.654310	−	0.756226i	$-0.727041\pi$
$331$		−	27.5167i		−	1.51245i	0.654310	−	0.756226i	$-0.272959\pi$
$332$	−6.73205	+	11.6603i	−0.369469	+	0.639940i
$333$		−	4.92820i		−	0.270064i
$334$	15.9282	+	4.26795i	0.871553	+	0.233532i
$335$	−9.46410			−0.517079
$336$	32.7846	−	18.9282i	1.78855	−	1.03262i
$337$	−5.46410			−0.297649			−0.148824	−	0.988864i	$-0.547549\pi$
$337$	−5.46410			−0.297649			−0.148824	+	0.988864i	$0.547549\pi$
$338$	−1.36603	−	0.366025i	−0.0743020	−	0.0199092i
$339$			18.9282i			1.02804i
$340$	−5.07180	+	8.78461i	−0.275057	+	0.476412i
$341$			4.14359i			0.224388i
$342$	−1.00000	+	3.73205i	−0.0540738	+	0.201806i
$343$	−39.7128			−2.14429
$344$	14.9282	−	14.9282i	0.804875	−	0.804875i
$345$	27.7128			1.49201
$346$	2.53590	−	9.46410i	0.136331	−	0.508793i
$347$		−	20.9282i		−	1.12348i	−0.827312	−	0.561742i	$-0.810131\pi$
$347$		−	20.9282i		−	1.12348i	0.827312	−	0.561742i	$-0.189869\pi$
$348$	−6.92820	−	4.00000i	−0.371391	−	0.214423i
$349$			30.3923i			1.62686i	0.581661	+	0.813431i	$0.302403\pi$
$349$			30.3923i			1.62686i	−0.581661	+	0.813431i	$0.697597\pi$
$350$	45.2487	+	12.1244i	2.41865	+	0.648074i
$351$	−4.00000			−0.213504
$352$	6.92820	−	1.85641i	0.369274	−	0.0989468i
$353$	−24.9282			−1.32679			−0.663397	−	0.748267i	$-0.730886\pi$
$353$	−24.9282			−1.32679			−0.663397	+	0.748267i	$0.730886\pi$
$354$	−0.535898	−	0.143594i	−0.0284827	−	0.00763191i
$355$		−	7.60770i		−	0.403775i
$356$	30.0000	+	17.3205i	1.59000	+	0.917985i
$357$			13.8564i			0.733359i
$358$	−3.80385	+	14.1962i	−0.201040	+	0.750290i
$359$	−13.5167			−0.713382			−0.356691	−	0.934222i	$-0.616095\pi$
$359$	−13.5167			−0.713382			−0.356691	+	0.934222i	$0.616095\pi$
$360$	−6.92820	+	6.92820i	−0.365148	+	0.365148i
$361$	11.5359			0.607153
$362$	−1.80385	+	6.73205i	−0.0948081	+	0.353829i
$363$			18.7846i			0.985936i
$364$	4.73205	−	8.19615i	0.248027	−	0.429595i
$365$			1.85641i			0.0971688i
$366$	29.8564	+	8.00000i	1.56062	+	0.418167i
$367$	26.2487			1.37017			0.685086	−	0.728462i	$-0.259765\pi$
$367$	26.2487			1.37017			0.685086	+	0.728462i	$0.259765\pi$
$368$	8.00000	+	13.8564i	0.417029	+	0.722315i
$369$	4.92820			0.256552
$370$	23.3205	+	6.24871i	1.21238	+	0.324855i
$371$		−	51.7128i		−	2.68480i
$372$	6.53590	−	11.3205i	0.338871	−	0.586941i
$373$			26.7846i			1.38685i	0.720527	+	0.693427i	$0.243900\pi$
$373$			26.7846i			1.38685i	−0.720527	+	0.693427i	$0.756100\pi$
$374$	−0.679492	+	2.53590i	−0.0351357	+	0.131128i
$375$	−13.8564			−0.715542
$376$	6.53590	+	6.53590i	0.337063	+	0.337063i
$377$	−2.00000			−0.103005
$378$	6.92820	−	25.8564i	0.356348	−	1.32991i
$379$		−	16.5885i		−	0.852092i	−0.904702	−	0.426046i	$-0.859906\pi$
$379$		−	16.5885i		−	0.852092i	0.904702	−	0.426046i	$-0.140094\pi$
$380$	−16.3923	−	9.46410i	−0.840907	−	0.485498i
$381$		−	8.00000i		−	0.409852i
$382$	−29.3205	−	7.85641i	−1.50017	−	0.401969i
$383$	−27.6603			−1.41337			−0.706686	−	0.707527i	$-0.749811\pi$
$383$	−27.6603			−1.41337			−0.706686	+	0.707527i	$0.749811\pi$
$384$	−21.8564	−	5.85641i	−1.11536	−	0.298858i
$385$	20.7846			1.05928
$386$	−30.5885	−	8.19615i	−1.55691	−	0.417173i
$387$			7.46410i			0.379422i
$388$	−24.9282	−	14.3923i	−1.26554	−	0.730659i
$389$			2.00000i			0.101404i	0.998714	+	0.0507020i	$0.0161459\pi$
$389$			2.00000i			0.101404i	−0.998714	+	0.0507020i	$0.983854\pi$
$390$	−2.53590	+	9.46410i	−0.128410	+	0.479233i
$391$	−5.85641			−0.296171
$392$	30.7846	+	30.7846i	1.55486	+	1.55486i
$393$	15.7128			0.792607
$394$	6.19615	−	23.1244i	0.312158	−	1.16499i
$395$			5.07180i			0.255190i
$396$	−1.26795	+	2.19615i	−0.0637168	+	0.110361i
$397$		−	11.4641i		−	0.575367i	−0.957726	−	0.287683i	$-0.907115\pi$
$397$		−	11.4641i		−	0.575367i	0.957726	−	0.287683i	$-0.0928851\pi$
$398$	−33.8564	−	9.07180i	−1.69707	−	0.454728i
$399$	−25.8564			−1.29444
$400$	−14.0000	−	24.2487i	−0.700000	−	1.21244i
$401$	11.4641			0.572490			0.286245	−	0.958156i	$-0.407593\pi$
$401$	11.4641			0.572490			0.286245	+	0.958156i	$0.407593\pi$
$402$	7.46410	+	2.00000i	0.372276	+	0.0997509i
$403$		−	3.26795i		−	0.162788i
$404$	12.0000	−	20.7846i	0.597022	−	1.03407i
$405$			38.1051i			1.89346i
$406$	3.46410	−	12.9282i	0.171920	−	0.641616i
$407$	6.24871			0.309737
$408$	5.85641	−	5.85641i	0.289935	−	0.289935i
$409$	−0.928203			−0.0458967			−0.0229483	−	0.999737i	$-0.507305\pi$
$409$	−0.928203			−0.0458967			−0.0229483	+	0.999737i	$0.507305\pi$
$410$	−6.24871	+	23.3205i	−0.308602	+	1.15172i
$411$		−	1.85641i		−	0.0915698i
$412$	−12.0000	−	6.92820i	−0.591198	−	0.341328i
$413$		−	0.928203i		−	0.0456739i
$414$	−5.46410	−	1.46410i	−0.268546	−	0.0719567i
$415$	23.3205			1.14476
$416$	−5.46410	+	1.46410i	−0.267900	+	0.0717835i
$417$	20.0000			0.979404
$418$	−4.73205	−	1.26795i	−0.231452	−	0.0620174i
$419$			10.7846i			0.526863i	0.964678	+	0.263431i	$0.0848542\pi$
$419$			10.7846i			0.526863i	−0.964678	+	0.263431i	$0.915146\pi$
$420$	−56.7846	−	32.7846i	−2.77081	−	1.59973i
$421$		−	24.2487i		−	1.18181i	−0.806741	−	0.590905i	$-0.798771\pi$
$421$		−	24.2487i		−	1.18181i	0.806741	−	0.590905i	$-0.201229\pi$
$422$	−7.26795	+	27.1244i	−0.353798	+	1.32039i
$423$	−3.26795			−0.158893
$424$	−21.8564	+	21.8564i	−1.06144	+	1.06144i
$425$	10.2487			0.497136
$426$	−1.60770	+	6.00000i	−0.0778931	+	0.290701i
$427$			51.7128i			2.50256i
$428$	8.92820	−	15.4641i	0.431561	−	0.747486i
$429$			2.53590i			0.122434i
$430$	−35.3205	−	9.46410i	−1.70331	−	0.456400i
$431$	14.8756			0.716535			0.358267	−	0.933619i	$-0.383368\pi$
$431$	14.8756			0.716535			0.358267	+	0.933619i	$0.383368\pi$
$432$	−13.8564	+	8.00000i	−0.666667	+	0.384900i
$433$	34.7846			1.67164			0.835821	−	0.549002i	$-0.184992\pi$
$433$	34.7846			1.67164			0.835821	+	0.549002i	$0.184992\pi$
$434$	21.1244	+	5.66025i	1.01400	+	0.271701i
$435$			13.8564i			0.664364i
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$		−	10.9282i		−	0.522767i
$438$	0.392305	−	1.46410i	0.0187451	−	0.0699575i
$439$	−10.9282			−0.521575			−0.260787	−	0.965396i	$-0.583982\pi$
$439$	−10.9282			−0.521575			−0.260787	+	0.965396i	$0.583982\pi$
$440$	−8.78461	−	8.78461i	−0.418790	−	0.418790i
$441$	−15.3923			−0.732967
$442$	0.535898	−	2.00000i	0.0254901	−	0.0951303i
$443$		−	30.0000i		−	1.42534i	−0.701498	−	0.712672i	$-0.747485\pi$
$443$		−	30.0000i		−	1.42534i	0.701498	−	0.712672i	$-0.252515\pi$
$444$	−17.0718	−	9.85641i	−0.810192	−	0.467764i
$445$		−	60.0000i		−	2.84427i
$446$	13.9282	+	3.73205i	0.659520	+	0.176718i
$447$	−1.85641			−0.0878050
$448$		−	37.8564i		−	1.78855i
$449$	38.3923			1.81184			0.905922	−	0.423444i	$-0.139179\pi$
$449$	38.3923			1.81184			0.905922	+	0.423444i	$0.139179\pi$
$450$	9.56218	+	2.56218i	0.450765	+	0.120782i
$451$			6.24871i			0.294240i
$452$	16.3923	+	9.46410i	0.771029	+	0.445154i
$453$			34.2487i			1.60914i
$454$	−9.92820	+	37.0526i	−0.465954	+	1.73896i
$455$	−16.3923			−0.768483
$456$	10.9282	+	10.9282i	0.511760	+	0.511760i
$457$	−14.0000			−0.654892			−0.327446	−	0.944870i	$-0.606188\pi$
$457$	−14.0000			−0.654892			−0.327446	+	0.944870i	$0.606188\pi$
$458$	−10.7321	+	40.0526i	−0.501476	+	1.87153i
$459$		−	5.85641i		−	0.273354i
$460$	13.8564	−	24.0000i	0.646058	−	1.11901i
$461$			7.07180i			0.329366i	0.986347	+	0.164683i	$0.0526602\pi$
$461$			7.07180i			0.329366i	−0.986347	+	0.164683i	$0.947340\pi$
$462$	−16.3923	−	4.39230i	−0.762639	−	0.204349i
$463$	−15.6603			−0.727794			−0.363897	−	0.931439i	$-0.618554\pi$
$463$	−15.6603			−0.727794			−0.363897	+	0.931439i	$0.618554\pi$
$464$	−6.92820	+	4.00000i	−0.321634	+	0.185695i
$465$	−22.6410			−1.04995
$466$	4.19615	+	1.12436i	0.194383	+	0.0520848i
$467$		−	12.2487i		−	0.566803i	−0.959001	−	0.283401i	$-0.908537\pi$
$467$		−	12.2487i		−	0.566803i	0.959001	−	0.283401i	$-0.0914629\pi$
$468$	1.00000	−	1.73205i	0.0462250	−	0.0800641i
$469$			12.9282i			0.596969i
$470$	4.14359	−	15.4641i	0.191130	−	0.713306i
$471$	6.14359			0.283082
$472$	−0.392305	+	0.392305i	−0.0180573	+	0.0180573i
$473$	−9.46410			−0.435160
$474$	1.07180	−	4.00000i	0.0492293	−	0.183726i
$475$			19.1244i			0.877486i
$476$	12.0000	+	6.92820i	0.550019	+	0.317554i
$477$		−	10.9282i		−	0.500368i
$478$	20.8564	+	5.58846i	0.953950	+	0.255610i
$479$	24.7321			1.13004			0.565018	−	0.825078i	$-0.308869\pi$
$479$	24.7321			1.13004			0.565018	+	0.825078i	$0.308869\pi$
$480$	10.1436	+	37.8564i	0.462990	+	1.72790i
$481$	−4.92820			−0.224707
$482$	−13.1244	−	3.51666i	−0.597798	−	0.160179i
$483$		−	37.8564i		−	1.72253i
$484$	16.2679	+	9.39230i	0.739452	+	0.426923i
$485$			49.8564i			2.26386i
$486$	3.66025	−	13.6603i	0.166032	−	0.619642i
$487$	16.4449			0.745188			0.372594	−	0.927994i	$-0.378468\pi$
$487$	16.4449			0.745188			0.372594	+	0.927994i	$0.378468\pi$
$488$	21.8564	−	21.8564i	0.989393	−	0.989393i
$489$	−26.5359			−1.19999
$490$	19.5167	−	72.8372i	0.881673	−	3.29045i
$491$			24.2487i			1.09433i	0.837025	+	0.547165i	$0.184293\pi$
$491$			24.2487i			1.09433i	−0.837025	+	0.547165i	$0.815707\pi$
$492$	9.85641	−	17.0718i	0.444361	−	0.769656i
$493$		−	2.92820i		−	0.131880i
$494$	3.73205	+	1.00000i	0.167913	+	0.0449921i
$495$	4.39230			0.197419
$496$	−6.53590	−	11.3205i	−0.293471	−	0.508306i
$497$	−10.3923			−0.466159
$498$	−18.3923	−	4.92820i	−0.824179	−	0.220838i
$499$		−	10.7321i		−	0.480433i	−0.970719	−	0.240216i	$-0.922782\pi$
$499$		−	10.7321i		−	0.480433i	0.970719	−	0.240216i	$-0.0772184\pi$
$500$	−6.92820	+	12.0000i	−0.309839	+	0.536656i
$501$			23.3205i			1.04188i
$502$	5.26795	−	19.6603i	0.235120	−	0.877480i
$503$	37.4641			1.67044			0.835221	−	0.549915i	$-0.185340\pi$
$503$	37.4641			1.67044			0.835221	+	0.549915i	$0.185340\pi$
$504$	9.46410	+	9.46410i	0.421565	+	0.421565i
$505$	−41.5692			−1.84981
$506$	1.85641	−	6.92820i	0.0825273	−	0.307996i
$507$		−	2.00000i		−	0.0888231i
$508$	−6.92820	−	4.00000i	−0.307389	−	0.177471i
$509$		−	6.39230i		−	0.283334i	−0.989914	−	0.141667i	$-0.954754\pi$
$509$		−	6.39230i		−	0.283334i	0.989914	−	0.141667i	$-0.0452462\pi$
$510$	−13.8564	−	3.71281i	−0.613572	−	0.164406i
$511$	2.53590			0.112182
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	10.9282			0.482492
$514$	5.26795	+	1.41154i	0.232359	+	0.0622605i
$515$			24.0000i			1.05757i
$516$	25.8564	+	14.9282i	1.13826	+	0.657178i
$517$		−	4.14359i		−	0.182235i
$518$	8.53590	−	31.8564i	0.375046	−	1.39969i
$519$	13.8564			0.608229
$520$	6.92820	+	6.92820i	0.303822	+	0.303822i
$521$	37.1769			1.62875			0.814375	−	0.580339i	$-0.197080\pi$
$521$	37.1769			1.62875			0.814375	+	0.580339i	$0.197080\pi$
$522$	0.732051	−	2.73205i	0.0320410	−	0.119579i
$523$			14.0000i			0.612177i	0.952003	+	0.306089i	$0.0990204\pi$
$523$			14.0000i			0.612177i	−0.952003	+	0.306089i	$0.900980\pi$
$524$	7.85641	−	13.6077i	0.343209	−	0.594455i
$525$			66.2487i			2.89133i
$526$	10.0000	+	2.67949i	0.436021	+	0.116831i
$527$	4.78461			0.208421
$528$	5.07180	+	8.78461i	0.220722	+	0.382301i
$529$	−7.00000			−0.304348
$530$	51.7128	+	13.8564i	2.24626	+	0.601884i
$531$		−	0.196152i		−	0.00851229i
$532$	−12.9282	+	22.3923i	−0.560509	+	0.970830i
$533$		−	4.92820i		−	0.213464i
$534$	−12.6795	+	47.3205i	−0.548695	+	2.04776i
$535$	−30.9282			−1.33714
$536$	5.46410	−	5.46410i	0.236013	−	0.236013i
$537$	−20.7846			−0.896922
$538$	−7.26795	+	27.1244i	−0.313344	+	1.16941i
$539$		−	19.5167i		−	0.840642i
$540$	24.0000	+	13.8564i	1.03280	+	0.596285i
$541$		−	16.9282i		−	0.727800i	−0.931438	−	0.363900i	$-0.881445\pi$
$541$		−	16.9282i		−	0.727800i	0.931438	−	0.363900i	$-0.118555\pi$
$542$	−13.3923	−	3.58846i	−0.575249	−	0.154137i
$543$	−9.85641			−0.422979
$544$	−2.14359	−	8.00000i	−0.0919058	−	0.342997i
$545$	−6.92820			−0.296772
$546$	12.9282	+	3.46410i	0.553276	+	0.148250i
$547$			15.8564i			0.677971i	0.940792	+	0.338985i	$0.110084\pi$
$547$			15.8564i			0.677971i	−0.940792	+	0.338985i	$0.889916\pi$
$548$	−1.60770	−	0.928203i	−0.0686773	−	0.0396509i
$549$			10.9282i			0.466404i
$550$	−3.24871	+	12.1244i	−0.138526	+	0.516984i
$551$	5.46410			0.232779
$552$	−16.0000	+	16.0000i	−0.681005	+	0.681005i
$553$	6.92820			0.294617
$554$	9.46410	−	35.3205i	0.402091	−	1.50062i
$555$			34.1436i			1.44931i
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$		−	6.78461i		−	0.287473i	−0.989616	−	0.143737i	$-0.954088\pi$
$557$		−	6.78461i		−	0.287473i	0.989616	−	0.143737i	$-0.0459118\pi$
$558$	4.46410	+	1.19615i	0.188980	+	0.0506372i
$559$	7.46410			0.315698
$560$	−56.7846	+	32.7846i	−2.39959	+	1.38540i
$561$	−3.71281			−0.156755
$562$	−34.5885	−	9.26795i	−1.45903	−	0.390945i
$563$		−	0.535898i		−	0.0225854i	−0.999936	−	0.0112927i	$-0.996405\pi$
$563$		−	0.535898i		−	0.0225854i	0.999936	−	0.0112927i	$-0.00359466\pi$
$564$	−6.53590	+	11.3205i	−0.275211	+	0.476679i
$565$		−	32.7846i		−	1.37926i
$566$	−4.58846	+	17.1244i	−0.192867	+	0.719790i
$567$	52.0526			2.18600
$568$	4.39230	+	4.39230i	0.184297	+	0.184297i
$569$	−14.0000			−0.586911			−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000			−0.586911			−0.293455	+	0.955973i	$0.594805\pi$
$570$	6.92820	−	25.8564i	0.290191	−	1.08301i
$571$			37.3205i			1.56181i	0.624647	+	0.780907i	$0.285243\pi$
$571$			37.3205i			1.56181i	−0.624647	+	0.780907i	$0.714757\pi$
$572$	2.19615	+	1.26795i	0.0918257	+	0.0530156i
$573$		−	42.9282i		−	1.79335i
$574$	31.8564	+	8.53590i	1.32966	+	0.356282i
$575$	−28.0000			−1.16768
$576$		−	8.00000i		−	0.333333i
$577$	−20.9282			−0.871253			−0.435626	−	0.900128i	$-0.643473\pi$
$577$	−20.9282			−0.871253			−0.435626	+	0.900128i	$0.643473\pi$
$578$	−20.2942	−	5.43782i	−0.844129	−	0.226184i
$579$		−	44.7846i		−	1.86118i
$580$	12.0000	+	6.92820i	0.498273	+	0.287678i
$581$		−	31.8564i		−	1.32163i
$582$	10.5359	−	39.3205i	0.436727	−	1.62989i
$583$	13.8564			0.573874
$584$	−1.07180	−	1.07180i	−0.0443513	−	0.0443513i
$585$	−3.46410			−0.143223
$586$	−6.98076	+	26.0526i	−0.288373	+	1.07622i
$587$		−	21.6603i		−	0.894014i	−0.894530	−	0.447007i	$-0.852490\pi$
$587$		−	21.6603i		−	0.894014i	0.894530	−	0.447007i	$-0.147510\pi$
$588$	−30.7846	+	53.3205i	−1.26954	+	2.19890i
$589$			8.92820i			0.367880i
$590$	0.928203	+	0.248711i	0.0382135	+	0.0102393i
$591$	33.8564			1.39267
$592$	−17.0718	+	9.85641i	−0.701647	+	0.405096i
$593$	19.8564			0.815405			0.407702	−	0.913115i	$-0.366330\pi$
$593$	19.8564			0.815405			0.407702	+	0.913115i	$0.366330\pi$
$594$	6.92820	+	1.85641i	0.284268	+	0.0761693i
$595$		−	24.0000i		−	0.983904i
$596$	−0.928203	+	1.60770i	−0.0380207	+	0.0658538i
$597$		−	49.5692i		−	2.02873i
$598$	−1.46410	+	5.46410i	−0.0598716	+	0.223444i
$599$	17.1769			0.701830			0.350915	−	0.936407i	$-0.385871\pi$
$599$	17.1769			0.701830			0.350915	+	0.936407i	$0.385871\pi$
$600$	28.0000	−	28.0000i	1.14310	−	1.14310i
$601$	16.3923			0.668656			0.334328	−	0.942457i	$-0.391491\pi$
$601$	16.3923			0.668656			0.334328	+	0.942457i	$0.391491\pi$
$602$	−12.9282	+	48.2487i	−0.526914	+	1.96647i
$603$			2.73205i			0.111258i
$604$	29.6603	+	17.1244i	1.20686	+	0.696780i
$605$		−	32.5359i		−	1.32277i
$606$	32.7846	+	8.78461i	1.33178	+	0.356850i
$607$	−27.3205			−1.10891			−0.554453	−	0.832215i	$-0.687072\pi$
$607$	−27.3205			−1.10891			−0.554453	+	0.832215i	$0.687072\pi$
$608$	14.9282	−	4.00000i	0.605419	−	0.162221i
$609$	18.9282			0.767010
$610$	−51.7128	−	13.8564i	−2.09379	−	0.561029i
$611$			3.26795i			0.132207i
$612$	2.53590	+	1.46410i	0.102508	+	0.0591828i
$613$		−	44.6410i		−	1.80303i	−0.432744	−	0.901517i	$-0.642455\pi$
$613$		−	44.6410i		−	1.80303i	0.432744	−	0.901517i	$-0.357545\pi$
$614$	1.00000	−	3.73205i	0.0403567	−	0.150613i
$615$	−34.1436			−1.37680
$616$	−12.0000	+	12.0000i	−0.483494	+	0.483494i
$617$	6.67949			0.268906			0.134453	−	0.990920i	$-0.457072\pi$
$617$	6.67949			0.268906			0.134453	+	0.990920i	$0.457072\pi$
$618$	5.07180	−	18.9282i	0.204018	−	0.761404i
$619$			12.5885i			0.505973i	0.967470	+	0.252986i	$0.0814128\pi$
$619$			12.5885i			0.505973i	−0.967470	+	0.252986i	$0.918587\pi$
$620$	−11.3205	+	19.6077i	−0.454643	+	0.787464i
$621$			16.0000i			0.642058i
$622$	20.3923	+	5.46410i	0.817657	+	0.219091i
$623$	−81.9615			−3.28372
$624$	−4.00000	−	6.92820i	−0.160128	−	0.277350i
$625$	−11.0000			−0.440000
$626$	−27.8564	−	7.46410i	−1.11337	−	0.298325i
$627$		−	6.92820i		−	0.276686i
$628$	3.07180	−	5.32051i	0.122578	−	0.212311i
$629$		−	7.21539i		−	0.287696i
$630$	6.00000	−	22.3923i	0.239046	−	0.892131i
$631$	−3.94744			−0.157145			−0.0785726	−	0.996908i	$-0.525036\pi$
$631$	−3.94744			−0.157145			−0.0785726	+	0.996908i	$0.525036\pi$
$632$	−2.92820	−	2.92820i	−0.116478	−	0.116478i
$633$	−39.7128			−1.57844
$634$	1.26795	−	4.73205i	0.0503567	−	0.187934i
$635$			13.8564i			0.549875i
$636$	−37.8564	−	21.8564i	−1.50110	−	0.866663i
$637$			15.3923i			0.609865i
$638$	3.46410	+	0.928203i	0.137145	+	0.0367479i
$639$	−2.19615			−0.0868784
$640$	37.8564	+	10.1436i	1.49641	+	0.400961i
$641$	26.2487			1.03676			0.518381	−	0.855150i	$-0.326535\pi$
$641$	26.2487			1.03676			0.518381	+	0.855150i	$0.326535\pi$
$642$	24.3923	+	6.53590i	0.962687	+	0.257951i
$643$		−	9.26795i		−	0.365492i	−0.983160	−	0.182746i	$-0.941501\pi$
$643$		−	9.26795i		−	0.365492i	0.983160	−	0.182746i	$-0.0584986\pi$
$644$	−32.7846	−	18.9282i	−1.29189	−	0.745876i
$645$		−	51.7128i		−	2.03619i
$646$	−1.46410	+	5.46410i	−0.0576043	+	0.214982i
$647$	10.1436			0.398786			0.199393	−	0.979920i	$-0.436103\pi$
$647$	10.1436			0.398786			0.199393	+	0.979920i	$0.436103\pi$
$648$	−22.0000	−	22.0000i	−0.864242	−	0.864242i
$649$	0.248711			0.00976277
$650$	2.56218	−	9.56218i	0.100497	−	0.375059i
$651$			30.9282i			1.21217i
$652$	−13.2679	+	22.9808i	−0.519613	+	0.899996i
$653$		−	16.9282i		−	0.662452i	−0.943551	−	0.331226i	$-0.892538\pi$
$653$		−	16.9282i		−	0.662452i	0.943551	−	0.331226i	$-0.107462\pi$
$654$	5.46410	+	1.46410i	0.213663	+	0.0572509i
$655$	−27.2154			−1.06339
$656$	−9.85641	−	17.0718i	−0.384828	−	0.666542i
$657$	0.535898			0.0209074
$658$	−21.1244	−	5.66025i	−0.823513	−	0.220660i
$659$			14.0000i			0.545363i	0.962104	+	0.272681i	$0.0879105\pi$
$659$			14.0000i			0.545363i	−0.962104	+	0.272681i	$0.912090\pi$
$660$	8.78461	−	15.2154i	0.341940	−	0.592258i
$661$		−	17.3205i		−	0.673690i	−0.941560	−	0.336845i	$-0.890640\pi$
$661$		−	17.3205i		−	0.673690i	0.941560	−	0.336845i	$-0.109360\pi$
$662$	10.0718	−	37.5885i	0.391451	−	1.46092i
$663$	2.92820			0.113722
$664$	−13.4641	+	13.4641i	−0.522508	+	0.522508i
$665$	44.7846			1.73667
$666$	1.80385	−	6.73205i	0.0698977	−	0.260862i
$667$			8.00000i			0.309761i
$668$	20.1962	+	11.6603i	0.781413	+	0.451149i
$669$			20.3923i			0.788412i
$670$	−12.9282	−	3.46410i	−0.499460	−	0.133830i
$671$	−13.8564			−0.534921
$672$	51.7128	−	13.8564i	1.99487	−	0.534522i
$673$	−29.1769			−1.12469			−0.562344	−	0.826904i	$-0.690100\pi$
$673$	−29.1769			−1.12469			−0.562344	+	0.826904i	$0.690100\pi$
$674$	−7.46410	−	2.00000i	−0.287506	−	0.0770371i
$675$		−	28.0000i		−	1.07772i
$676$	−1.73205	−	1.00000i	−0.0666173	−	0.0384615i
$677$			34.9282i			1.34240i	0.741276	+	0.671200i	$0.234221\pi$
$677$			34.9282i			1.34240i	−0.741276	+	0.671200i	$0.765779\pi$
$678$	−6.92820	+	25.8564i	−0.266076	+	0.993009i
$679$	68.1051			2.61363
$680$	−10.1436	+	10.1436i	−0.388989	+	0.388989i
$681$	−54.2487			−2.07882
$682$	−1.51666	+	5.66025i	−0.0580759	+	0.216742i
$683$		−	28.1962i		−	1.07890i	−0.842019	−	0.539448i	$-0.818633\pi$
$683$		−	28.1962i		−	1.07890i	0.842019	−	0.539448i	$-0.181367\pi$
$684$	−2.73205	+	4.73205i	−0.104463	+	0.180934i
$685$			3.21539i			0.122854i
$686$	−54.2487	−	14.5359i	−2.07123	−	0.554983i
$687$	−58.6410			−2.23729
$688$	25.8564	−	14.9282i	0.985766	−	0.569132i
$689$	−10.9282			−0.416331
$690$	37.8564	+	10.1436i	1.44117	+	0.386160i
$691$			46.8372i			1.78177i	0.454229	+	0.890885i	$0.349915\pi$
$691$			46.8372i			1.78177i	−0.454229	+	0.890885i	$0.650085\pi$
$692$	6.92820	−	12.0000i	0.263371	−	0.456172i
$693$		−	6.00000i		−	0.227921i
$694$	7.66025	−	28.5885i	0.290779	−	1.08520i
$695$	−34.6410			−1.31401
$696$	−8.00000	−	8.00000i	−0.303239	−	0.303239i
$697$	7.21539			0.273302
$698$	−11.1244	+	41.5167i	−0.421063	+	1.57143i
$699$			6.14359i			0.232372i
$700$	57.3731	+	33.1244i	2.16850	+	1.25198i
$701$			28.6410i			1.08176i	0.841101	+	0.540878i	$0.181908\pi$
$701$			28.6410i			1.08176i	−0.841101	+	0.540878i	$0.818092\pi$
$702$	−5.46410	−	1.46410i	−0.206229	−	0.0552590i
$703$	13.4641			0.507808
$704$	10.1436			0.382301
$705$	22.6410			0.852710
$706$	−34.0526	−	9.12436i	−1.28158	−	0.343400i
$707$			56.7846i			2.13561i
$708$	−0.679492	−	0.392305i	−0.0255369	−	0.0147437i
$709$		−	5.32051i		−	0.199816i	−0.994997	−	0.0999079i	$-0.968145\pi$
$709$		−	5.32051i		−	0.199816i	0.994997	−	0.0999079i	$-0.0318548\pi$
$710$	2.78461	−	10.3923i	0.104505	−	0.390016i
$711$	1.46410			0.0549081
$712$	34.6410	+	34.6410i	1.29823	+	1.29823i
$713$	−13.0718			−0.489543
$714$	−5.07180	+	18.9282i	−0.189807	+	0.708370i
$715$		−	4.39230i		−	0.164263i
$716$	−10.3923	+	18.0000i	−0.388379	+	0.672692i
$717$			30.5359i			1.14038i
$718$	−18.4641	−	4.94744i	−0.689074	−	0.184637i
$719$	17.0718			0.636671			0.318335	−	0.947978i	$-0.396876\pi$
$719$	17.0718			0.636671			0.318335	+	0.947978i	$0.396876\pi$
$720$	−12.0000	+	6.92820i	−0.447214	+	0.258199i
$721$	32.7846			1.22096
$722$	15.7583	+	4.22243i	0.586464	+	0.157143i
$723$		−	19.2154i		−	0.714628i
$724$	−4.92820	+	8.53590i	−0.183155	+	0.317234i
$725$		−	14.0000i		−	0.519947i
$726$	−6.87564	+	25.6603i	−0.255179	+	0.952341i
$727$	−9.07180			−0.336454			−0.168227	−	0.985748i	$-0.553804\pi$
$727$	−9.07180			−0.336454			−0.168227	+	0.985748i	$0.553804\pi$
$728$	9.46410	−	9.46410i	0.350763	−	0.350763i
$729$	−13.0000			−0.481481
$730$	−0.679492	+	2.53590i	−0.0251491	+	0.0938578i
$731$			10.9282i			0.404194i
$732$	37.8564	+	21.8564i	1.39921	+	0.807836i
$733$			2.67949i			0.0989693i	0.998775	+	0.0494846i	$0.0157579\pi$
$733$			2.67949i			0.0989693i	−0.998775	+	0.0494846i	$0.984242\pi$
$734$	35.8564	+	9.60770i	1.32348	+	0.354626i
$735$	106.641			3.93351
$736$	5.85641	+	21.8564i	0.215870	+	0.805638i
$737$	−3.46410			−0.127602
$738$	6.73205	+	1.80385i	0.247810	+	0.0664005i
$739$		−	53.7654i		−	1.97779i	−0.148612	−	0.988896i	$-0.547481\pi$
$739$		−	53.7654i		−	1.97779i	0.148612	−	0.988896i	$-0.452519\pi$
$740$	29.5692	+	17.0718i	1.08699	+	0.627572i
$741$			5.46410i			0.200729i
$742$	18.9282	−	70.6410i	0.694876	−	2.59331i
$743$	−21.8038			−0.799906			−0.399953	−	0.916536i	$-0.630973\pi$
$743$	−21.8038			−0.799906			−0.399953	+	0.916536i	$0.630973\pi$
$744$	13.0718	−	13.0718i	0.479235	−	0.479235i
$745$	3.21539			0.117803
$746$	−9.80385	+	36.5885i	−0.358944	+	1.33960i
$747$		−	6.73205i		−	0.246313i
$748$	−1.85641	+	3.21539i	−0.0678769	+	0.117566i
$749$			42.2487i			1.54373i
$750$	−18.9282	−	5.07180i	−0.691160	−	0.185196i
$751$	14.9282			0.544738			0.272369	−	0.962193i	$-0.412193\pi$
$751$	14.9282			0.544738			0.272369	+	0.962193i	$0.412193\pi$
$752$	6.53590	+	11.3205i	0.238340	+	0.412816i
$753$	28.7846			1.04897
$754$	−2.73205	−	0.732051i	−0.0994954	−	0.0266597i
$755$		−	59.3205i		−	2.15889i
$756$	18.9282	−	32.7846i	0.688412	−	1.19236i
$757$		−	0.784610i		−	0.0285171i	−0.999898	−	0.0142586i	$-0.995461\pi$
$757$		−	0.784610i		−	0.0285171i	0.999898	−	0.0142586i	$-0.00453880\pi$
$758$	6.07180	−	22.6603i	0.220538	−	0.823057i
$759$	10.1436			0.368189
$760$	−18.9282	−	18.9282i	−0.686598	−	0.686598i
$761$	−22.7846			−0.825941			−0.412971	−	0.910744i	$-0.635509\pi$
$761$	−22.7846			−0.825941			−0.412971	+	0.910744i	$0.635509\pi$
$762$	2.92820	−	10.9282i	0.106078	−	0.395887i
$763$			9.46410i			0.342623i
$764$	−37.1769	−	21.4641i	−1.34501	−	0.776544i
$765$		−	5.07180i		−	0.183371i
$766$	−37.7846	−	10.1244i	−1.36521	−	0.365808i
$767$	−0.196152			−0.00708265
$768$	−27.7128	−	16.0000i	−1.00000	−	0.577350i
$769$	24.5359			0.884787			0.442394	−	0.896821i	$-0.354129\pi$
$769$	24.5359			0.884787			0.442394	+	0.896821i	$0.354129\pi$
$770$	28.3923	+	7.60770i	1.02319	+	0.274162i
$771$			7.71281i			0.277770i
$772$	−38.7846	−	22.3923i	−1.39589	−	0.805917i
$773$			20.5359i			0.738625i

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +2.00000i q^{3} +(1.73205 + 1.00000i) q^{4} -3.46410i q^{5} +(-0.732051 + 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +2.00000i q^{3} +(1.73205 + 1.00000i) q^{4} -3.46410i q^{5} +(-0.732051 + 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(1.26795 - 4.73205i) q^{10} -1.26795i q^{11} +(-2.00000 + 3.46410i) q^{12} +1.00000i q^{13} +(-6.46410 - 1.73205i) q^{14} +6.92820 q^{15} +(2.00000 + 3.46410i) q^{16} -1.46410 q^{17} +(-1.36603 - 0.366025i) q^{18} -2.73205i q^{19} +(3.46410 - 6.00000i) q^{20} -9.46410i q^{21} +(0.464102 - 1.73205i) q^{22} +4.00000 q^{23} +(-4.00000 + 4.00000i) q^{24} -7.00000 q^{25} +(-0.366025 + 1.36603i) q^{26} +4.00000i q^{27} +(-8.19615 - 4.73205i) q^{28} +2.00000i q^{29} +(9.46410 + 2.53590i) q^{30} -3.26795 q^{31} +(1.46410 + 5.46410i) q^{32} +2.53590 q^{33} +(-2.00000 - 0.535898i) q^{34} +16.3923i q^{35} +(-1.73205 - 1.00000i) q^{36} +4.92820i q^{37} +(1.00000 - 3.73205i) q^{38} -2.00000 q^{39} +(6.92820 - 6.92820i) q^{40} -4.92820 q^{41} +(3.46410 - 12.9282i) q^{42} -7.46410i q^{43} +(1.26795 - 2.19615i) q^{44} +3.46410i q^{45} +(5.46410 + 1.46410i) q^{46} +3.26795 q^{47} +(-6.92820 + 4.00000i) q^{48} +15.3923 q^{49} +(-9.56218 - 2.56218i) q^{50} -2.92820i q^{51} +(-1.00000 + 1.73205i) q^{52} +10.9282i q^{53} +(-1.46410 + 5.46410i) q^{54} -4.39230 q^{55} +(-9.46410 - 9.46410i) q^{56} +5.46410 q^{57} +(-0.732051 + 2.73205i) q^{58} +0.196152i q^{59} +(12.0000 + 6.92820i) q^{60} -10.9282i q^{61} +(-4.46410 - 1.19615i) q^{62} +4.73205 q^{63} +8.00000i q^{64} +3.46410 q^{65} +(3.46410 + 0.928203i) q^{66} -2.73205i q^{67} +(-2.53590 - 1.46410i) q^{68} +8.00000i q^{69} +(-6.00000 + 22.3923i) q^{70} +2.19615 q^{71} +(-2.00000 - 2.00000i) q^{72} -0.535898 q^{73} +(-1.80385 + 6.73205i) q^{74} -14.0000i q^{75} +(2.73205 - 4.73205i) q^{76} +6.00000i q^{77} +(-2.73205 - 0.732051i) q^{78} -1.46410 q^{79} +(12.0000 - 6.92820i) q^{80} -11.0000 q^{81} +(-6.73205 - 1.80385i) q^{82} +6.73205i q^{83} +(9.46410 - 16.3923i) q^{84} +5.07180i q^{85} +(2.73205 - 10.1962i) q^{86} -4.00000 q^{87} +(2.53590 - 2.53590i) q^{88} +17.3205 q^{89} +(-1.26795 + 4.73205i) q^{90} -4.73205i q^{91} +(6.92820 + 4.00000i) q^{92} -6.53590i q^{93} +(4.46410 + 1.19615i) q^{94} -9.46410 q^{95} +(-10.9282 + 2.92820i) q^{96} -14.3923 q^{97} +(21.0263 + 5.63397i) q^{98} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^6 - 12 * q^7 + 8 * q^8 - 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9} + 12 q^{10} - 8 q^{12} - 12 q^{14} + 8 q^{16} + 8 q^{17} - 2 q^{18} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 28 q^{25} + 2 q^{26} - 12 q^{28} + 24 q^{30} - 20 q^{31} - 8 q^{32} + 24 q^{33} - 8 q^{34} + 4 q^{38} - 8 q^{39} + 8 q^{41} + 12 q^{44} + 8 q^{46} + 20 q^{47} + 20 q^{49} - 14 q^{50} - 4 q^{52} + 8 q^{54} + 24 q^{55} - 24 q^{56} + 8 q^{57} + 4 q^{58} + 48 q^{60} - 4 q^{62} + 12 q^{63} - 24 q^{68} - 24 q^{70} - 12 q^{71} - 8 q^{72} - 16 q^{73} - 28 q^{74} + 4 q^{76} - 4 q^{78} + 8 q^{79} + 48 q^{80} - 44 q^{81} - 20 q^{82} + 24 q^{84} + 4 q^{86} - 16 q^{87} + 24 q^{88} - 12 q^{90} + 4 q^{94} - 24 q^{95} - 16 q^{96} - 16 q^{97} + 46 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^6 - 12 * q^7 + 8 * q^8 - 4 * q^9 + 12 * q^10 - 8 * q^12 - 12 * q^14 + 8 * q^16 + 8 * q^17 - 2 * q^18 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 28 * q^25 + 2 * q^26 - 12 * q^28 + 24 * q^30 - 20 * q^31 - 8 * q^32 + 24 * q^33 - 8 * q^34 + 4 * q^38 - 8 * q^39 + 8 * q^41 + 12 * q^44 + 8 * q^46 + 20 * q^47 + 20 * q^49 - 14 * q^50 - 4 * q^52 + 8 * q^54 + 24 * q^55 - 24 * q^56 + 8 * q^57 + 4 * q^58 + 48 * q^60 - 4 * q^62 + 12 * q^63 - 24 * q^68 - 24 * q^70 - 12 * q^71 - 8 * q^72 - 16 * q^73 - 28 * q^74 + 4 * q^76 - 4 * q^78 + 8 * q^79 + 48 * q^80 - 44 * q^81 - 20 * q^82 + 24 * q^84 + 4 * q^86 - 16 * q^87 + 24 * q^88 - 12 * q^90 + 4 * q^94 - 24 * q^95 - 16 * q^96 - 16 * q^97 + 46 * q^98

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