LMFDB - Embedded newform 238.2.p.b.181.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [238,2,Mod(27,238)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(238, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("238.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 238 = 2 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	238.p (of order $16$, degree $8$, 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:	$1.90043956811$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			181.4
Character	$\chi$	$=$	238.181
Dual form			238.2.p.b.167.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{2} +(0.596251 - 0.118602i) q^{3} +(0.707107 + 0.707107i) q^{4} +(1.74990 - 2.61891i) q^{5} +(-0.596251 - 0.118602i) q^{6} +(2.56001 - 0.668077i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-2.43019 + 1.00662i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{2} +(0.596251 - 0.118602i) q^{3} +(0.707107 + 0.707107i) q^{4} +(1.74990 - 2.61891i) q^{5} +(-0.596251 - 0.118602i) q^{6} +(2.56001 - 0.668077i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-2.43019 + 1.00662i) q^{9} +(-2.61891 + 1.74990i) q^{10} +(-3.66064 - 0.728148i) q^{11} +(0.505478 + 0.337749i) q^{12} +(2.81055 + 2.81055i) q^{13} +(-2.62081 - 0.362452i) q^{14} +(0.732773 - 1.76907i) q^{15} +1.00000i q^{16} +(2.54704 - 3.24231i) q^{17} +2.63042 q^{18} +(2.08896 - 5.04320i) q^{19} +(3.08922 - 0.614483i) q^{20} +(1.44718 - 0.701964i) q^{21} +(3.10334 + 2.07359i) q^{22} +(0.0421562 - 0.211933i) q^{23} +(-0.337749 - 0.505478i) q^{24} +(-1.88313 - 4.54627i) q^{25} +(-1.52106 - 3.67216i) q^{26} +(-2.84605 + 1.90167i) q^{27} +(2.28261 + 1.33780i) q^{28} +(-1.71924 + 2.57302i) q^{29} +(-1.35399 + 1.35399i) q^{30} +(0.521615 + 2.62233i) q^{31} +(0.382683 - 0.923880i) q^{32} -2.26902 q^{33} +(-3.59394 + 2.02079i) q^{34} +(2.73013 - 7.87352i) q^{35} +(-2.43019 - 1.00662i) q^{36} +(0.603404 + 3.03352i) q^{37} +(-3.85990 + 3.85990i) q^{38} +(2.00913 + 1.34246i) q^{39} +(-3.08922 - 0.614483i) q^{40} +(4.30003 + 6.43545i) q^{41} +(-1.60565 + 0.0947197i) q^{42} +(-3.97341 + 1.64584i) q^{43} +(-2.07359 - 3.10334i) q^{44} +(-1.61635 + 8.12593i) q^{45} +(-0.120051 + 0.179668i) q^{46} +(-3.26587 - 3.26587i) q^{47} +(0.118602 + 0.596251i) q^{48} +(6.10735 - 3.42057i) q^{49} +4.92084i q^{50} +(1.13413 - 2.23532i) q^{51} +3.97471i q^{52} +(3.59356 + 1.48850i) q^{53} +(3.35714 - 0.667778i) q^{54} +(-8.31272 + 8.31272i) q^{55} +(-1.59690 - 2.10948i) q^{56} +(0.647414 - 3.25477i) q^{57} +(2.57302 - 1.71924i) q^{58} +(-7.33351 + 3.03764i) q^{59} +(1.76907 - 0.732773i) q^{60} +(-1.63428 + 1.09199i) q^{61} +(0.521615 - 2.62233i) q^{62} +(-5.54882 + 4.20051i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(12.2787 - 2.44239i) q^{65} +(2.09631 + 0.868318i) q^{66} +15.5597i q^{67} +(4.09369 - 0.491629i) q^{68} -0.131365i q^{69} +(-5.53538 + 6.22940i) q^{70} +(1.58501 + 7.96838i) q^{71} +(1.85999 + 1.85999i) q^{72} +(-6.68332 + 10.0023i) q^{73} +(0.603404 - 3.03352i) q^{74} +(-1.66201 - 2.48738i) q^{75} +(5.04320 - 2.08896i) q^{76} +(-9.85776 + 0.581525i) q^{77} +(-1.34246 - 2.00913i) q^{78} +(0.195993 + 0.0389854i) q^{79} +(2.61891 + 1.74990i) q^{80} +(4.10854 - 4.10854i) q^{81} +(-1.50997 - 7.59113i) q^{82} +(-13.2346 - 5.48194i) q^{83} +(1.51967 + 0.526945i) q^{84} +(-4.03425 - 12.3442i) q^{85} +4.30078 q^{86} +(-0.719933 + 1.73807i) q^{87} +(0.728148 + 3.66064i) q^{88} +(7.68024 - 7.68024i) q^{89} +(4.60297 - 6.88883i) q^{90} +(9.07270 + 5.31738i) q^{91} +(0.179668 - 0.120051i) q^{92} +(0.622027 + 1.50171i) q^{93} +(1.76748 + 4.26707i) q^{94} +(-9.55221 - 14.2959i) q^{95} +(0.118602 - 0.596251i) q^{96} +(0.729748 + 0.487602i) q^{97} +(-6.95145 + 0.823018i) q^{98} +(9.62903 - 1.91533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 16 q^{11} - 8 q^{14} + 64 q^{15} - 80 q^{18} - 48 q^{21} + 16 q^{22} - 16 q^{25} + 8 q^{28} + 32 q^{29} + 16 q^{39} - 24 q^{42} - 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 32 q^{51} - 48 q^{53} + 64 q^{57} + 16 q^{58} + 32 q^{60} - 104 q^{63} - 48 q^{65} + 16 q^{70} - 112 q^{71} - 16 q^{72} - 40 q^{77} - 64 q^{78} + 32 q^{79} + 112 q^{81} - 176 q^{85} + 32 q^{86} + 16 q^{88} + 80 q^{91} - 32 q^{93} - 32 q^{95} - 96 q^{99}+O(q^{100}) $ 48 * q - 16 * q^11 - 8 * q^14 + 64 * q^15 - 80 * q^18 - 48 * q^21 + 16 * q^22 - 16 * q^25 + 8 * q^28 + 32 * q^29 + 16 * q^39 - 24 * q^42 - 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 32 * q^51 - 48 * q^53 + 64 * q^57 + 16 * q^58 + 32 * q^60 - 104 * q^63 - 48 * q^65 + 16 * q^70 - 112 * q^71 - 16 * q^72 - 40 * q^77 - 64 * q^78 + 32 * q^79 + 112 * q^81 - 176 * q^85 + 32 * q^86 + 16 * q^88 + 80 * q^91 - 32 * q^93 - 32 * q^95 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/238\mathbb{Z}\right)^\times$.

$n$	$71$	$171$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	0.596251	−	0.118602i	0.344246	−	0.0684748i	−0.0199396	−	0.999801i	$-0.506347\pi$
$3$	0.596251	−	0.118602i	0.344246	−	0.0684748i	0.364186	+	0.931326i	$0.381347\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	1.74990	−	2.61891i	0.782579	−	1.17121i	−0.198971	−	0.980005i	$-0.563760\pi$
$5$	1.74990	−	2.61891i	0.782579	−	1.17121i	0.981550	−	0.191207i	$-0.0612402\pi$
$6$	−0.596251	−	0.118602i	−0.243419	−	0.0484190i
$7$	2.56001	−	0.668077i	0.967594	−	0.252509i
$7$	2.56001	−	0.668077i	0.967594	−	0.252509i
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	−2.43019	+	1.00662i	−0.810063	+	0.335539i
$10$	−2.61891	+	1.74990i	−0.828172	+	0.553367i
$11$	−3.66064	−	0.728148i	−1.10373	−	0.219545i	−0.390586	−	0.920566i	$-0.627728\pi$
$11$	−3.66064	−	0.728148i	−1.10373	−	0.219545i	−0.713140	+	0.701022i	$0.752728\pi$
$12$	0.505478	+	0.337749i	0.145919	+	0.0974998i
$13$	2.81055	+	2.81055i	0.779506	+	0.779506i	0.979747	−	0.200241i	$-0.0641725\pi$
$13$	2.81055	+	2.81055i	0.779506	+	0.779506i	−0.200241	+	0.979747i	$0.564173\pi$
$14$	−2.62081	−	0.362452i	−0.700440	−	0.0968694i
$15$	0.732773	−	1.76907i	0.189201	−	0.456772i
$16$			1.00000i			0.250000i
$17$	2.54704	−	3.24231i	0.617748	−	0.786376i
$17$	2.54704	−	3.24231i	0.617748	−	0.786376i
$18$	2.63042			0.619995
$19$	2.08896	−	5.04320i	0.479240	−	1.15699i	−0.480725	−	0.876871i	$-0.659627\pi$
$19$	2.08896	−	5.04320i	0.479240	−	1.15699i	0.959966	−	0.280118i	$-0.0903735\pi$
$20$	3.08922	−	0.614483i	0.690770	−	0.137403i
$21$	1.44718	−	0.701964i	0.315800	−	0.153181i
$22$	3.10334	+	2.07359i	0.661635	+	0.442091i
$23$	0.0421562	−	0.211933i	0.00879017	−	0.0441912i	−0.976141	−	0.217136i	$-0.930328\pi$
$23$	0.0421562	−	0.211933i	0.00879017	−	0.0441912i	0.984931	+	0.172945i	$0.0553284\pi$
$24$	−0.337749	−	0.505478i	−0.0689428	−	0.103180i
$25$	−1.88313	−	4.54627i	−0.376625	−	0.909253i
$26$	−1.52106	−	3.67216i	−0.298304	−	0.720169i
$27$	−2.84605	+	1.90167i	−0.547723	+	0.365977i
$28$	2.28261	+	1.33780i	0.431372	+	0.252821i
$29$	−1.71924	+	2.57302i	−0.319254	+	0.477798i	−0.956037	−	0.293245i	$-0.905265\pi$
$29$	−1.71924	+	2.57302i	−0.319254	+	0.477798i	0.636783	+	0.771043i	$0.280265\pi$
$30$	−1.35399	+	1.35399i	−0.247203	+	0.247203i
$31$	0.521615	+	2.62233i	0.0936847	+	0.470985i	0.998936	+	0.0461092i	$0.0146822\pi$
$31$	0.521615	+	2.62233i	0.0936847	+	0.470985i	−0.905252	+	0.424876i	$0.860318\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	−2.26902			−0.394986
$34$	−3.59394	+	2.02079i	−0.616355	+	0.346563i
$35$	2.73013	−	7.87352i	0.461477	−	1.33087i
$36$	−2.43019	−	1.00662i	−0.405032	−	0.167770i
$37$	0.603404	+	3.03352i	0.0991990	+	0.498707i	0.998158	+	0.0606736i	$0.0193249\pi$
$37$	0.603404	+	3.03352i	0.0991990	+	0.498707i	−0.898959	+	0.438034i	$0.855675\pi$
$38$	−3.85990	+	3.85990i	−0.626158	+	0.626158i
$39$	2.00913	+	1.34246i	0.321718	+	0.214965i
$40$	−3.08922	−	0.614483i	−0.488448	−	0.0971583i
$41$	4.30003	+	6.43545i	0.671552	+	1.00505i	0.998204	+	0.0599042i	$0.0190795\pi$
$41$	4.30003	+	6.43545i	0.671552	+	1.00505i	−0.326652	+	0.945145i	$0.605920\pi$
$42$	−1.60565	+	0.0947197i	−0.247757	+	0.0146156i
$43$	−3.97341	+	1.64584i	−0.605939	+	0.250988i	−0.664491	−	0.747296i	$-0.731352\pi$
$43$	−3.97341	+	1.64584i	−0.605939	+	0.250988i	0.0585521	+	0.998284i	$0.481352\pi$
$44$	−2.07359	−	3.10334i	−0.312605	−	0.467847i
$45$	−1.61635	+	8.12593i	−0.240951	+	1.21134i
$46$	−0.120051	+	0.179668i	−0.0177005	+	0.0264907i
$47$	−3.26587	−	3.26587i	−0.476377	−	0.476377i	0.427594	−	0.903971i	$-0.359361\pi$
$47$	−3.26587	−	3.26587i	−0.476377	−	0.476377i	−0.903971	+	0.427594i	$0.859361\pi$
$48$	0.118602	+	0.596251i	0.0171187	+	0.0860615i
$49$	6.10735	−	3.42057i	0.872478	−	0.488653i
$50$			4.92084i			0.695912i
$51$	1.13413	−	2.23532i	0.158810	−	0.313007i
$52$			3.97471i			0.551194i
$53$	3.59356	+	1.48850i	0.493614	+	0.204462i	0.615583	−	0.788072i	$-0.288921\pi$
$53$	3.59356	+	1.48850i	0.493614	+	0.204462i	−0.121969	+	0.992534i	$0.538921\pi$
$54$	3.35714	−	0.667778i	0.456850	−	0.0908730i
$55$	−8.31272	+	8.31272i	−1.12089	+	1.12089i
$56$	−1.59690	−	2.10948i	−0.213394	−	0.281891i
$57$	0.647414	−	3.25477i	0.0857520	−	0.431105i
$58$	2.57302	−	1.71924i	0.337854	−	0.225747i
$59$	−7.33351	+	3.03764i	−0.954741	+	0.395467i	−0.805011	−	0.593260i	$-0.797841\pi$
$59$	−7.33351	+	3.03764i	−0.954741	+	0.395467i	−0.149730	+	0.988727i	$0.547841\pi$
$60$	1.76907	−	0.732773i	0.228386	−	0.0946006i
$61$	−1.63428	+	1.09199i	−0.209248	+	0.139815i	−0.655779	−	0.754953i	$-0.727659\pi$
$61$	−1.63428	+	1.09199i	−0.209248	+	0.139815i	0.446530	+	0.894768i	$0.352659\pi$
$62$	0.521615	−	2.62233i	0.0662451	−	0.333037i
$63$	−5.54882	+	4.20051i	−0.699086	+	0.529214i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	12.2787	−	2.44239i	1.52299	−	0.302942i
$66$	2.09631	+	0.868318i	0.258037	+	0.106883i
$67$			15.5597i			1.90092i	0.310849	+	0.950459i	$0.399387\pi$
$67$			15.5597i			1.90092i	−0.310849	+	0.950459i	$0.600613\pi$
$68$	4.09369	−	0.491629i	0.496433	−	0.0596188i
$69$		−	0.131365i		−	0.0158145i
$70$	−5.53538	+	6.22940i	−0.661604	+	0.744556i
$71$	1.58501	+	7.96838i	0.188106	+	0.945673i	0.953335	+	0.301915i	$0.0976258\pi$
$71$	1.58501	+	7.96838i	0.188106	+	0.945673i	−0.765229	+	0.643758i	$0.777374\pi$
$72$	1.85999	+	1.85999i	0.219201	+	0.219201i
$73$	−6.68332	+	10.0023i	−0.782224	+	1.17068i	0.199412	+	0.979916i	$0.436097\pi$
$73$	−6.68332	+	10.0023i	−0.782224	+	1.17068i	−0.981636	+	0.190765i	$0.938903\pi$
$74$	0.603404	−	3.03352i	0.0701443	−	0.352639i
$75$	−1.66201	−	2.48738i	−0.191913	−	0.287217i
$76$	5.04320	−	2.08896i	0.578494	−	0.239620i
$77$	−9.85776	+	0.581525i	−1.12340	+	0.0662709i
$78$	−1.34246	−	2.00913i	−0.152003	−	0.227489i
$79$	0.195993	+	0.0389854i	0.0220509	+	0.00438620i	0.206103	−	0.978530i	$-0.433922\pi$
$79$	0.195993	+	0.0389854i	0.0220509	+	0.00438620i	−0.184053	+	0.982916i	$0.558922\pi$
$80$	2.61891	+	1.74990i	0.292803	+	0.195645i
$81$	4.10854	−	4.10854i	0.456504	−	0.456504i
$82$	−1.50997	−	7.59113i	−0.166748	−	0.838301i
$83$	−13.2346	−	5.48194i	−1.45268	−	0.601721i	−0.489847	−	0.871809i	$-0.662947\pi$
$83$	−13.2346	−	5.48194i	−1.45268	−	0.601721i	−0.962836	+	0.270088i	$0.912947\pi$
$84$	1.51967	+	0.526945i	0.165810	+	0.0574944i
$85$	−4.03425	−	12.3442i	−0.437576	−	1.33892i
$86$	4.30078			0.463766
$87$	−0.719933	+	1.73807i	−0.0771849	+	0.186341i
$88$	0.728148	+	3.66064i	0.0776208	+	0.390226i
$89$	7.68024	−	7.68024i	0.814104	−	0.814104i	−0.171142	−	0.985246i	$-0.554746\pi$
$89$	7.68024	−	7.68024i	0.814104	−	0.814104i	0.985246	+	0.171142i	$0.0547457\pi$
$90$	4.60297	−	6.88883i	0.485195	−	0.726146i
$91$	9.07270	+	5.31738i	0.951078	+	0.557413i
$92$	0.179668	−	0.120051i	0.0187317	−	0.0125161i
$93$	0.622027	+	1.50171i	0.0645012	+	0.155720i
$94$	1.76748	+	4.26707i	0.182301	+	0.440115i
$95$	−9.55221	−	14.2959i	−0.980036	−	1.46673i
$96$	0.118602	−	0.596251i	0.0121047	−	0.0608547i
$97$	0.729748	+	0.487602i	0.0740947	+	0.0495085i	0.592066	−	0.805890i	$-0.298313\pi$
$97$	0.729748	+	0.487602i	0.0740947	+	0.0495085i	−0.517971	+	0.855398i	$0.673313\pi$
$98$	−6.95145	+	0.823018i	−0.702202	+	0.0831374i
$99$	9.62903	−	1.91533i	0.967753	−	0.192498i
$100$	1.88313	−	4.54627i	0.188313	−	0.454627i
$101$	16.6365			1.65540			0.827698	−	0.561174i	$-0.189650\pi$
$101$	16.6365			1.65540			0.827698	+	0.561174i	$0.189650\pi$
$102$	−1.90322	+	1.63115i	−0.188447	+	0.161508i
$103$		−	7.17378i		−	0.706853i	−0.935462	−	0.353427i	$-0.885016\pi$
$103$		−	7.17378i		−	0.706853i	0.935462	−	0.353427i	$-0.114984\pi$
$104$	1.52106	−	3.67216i	0.149152	−	0.360085i
$105$	0.694034	−	5.01839i	0.0677308	−	0.489745i
$106$	−2.75039	−	2.75039i	−0.267142	−	0.267142i
$107$	−12.6355	−	8.44275i	−1.22152	−	0.816192i	−0.233776	−	0.972291i	$-0.575108\pi$
$107$	−12.6355	−	8.44275i	−1.22152	−	0.816192i	−0.987741	+	0.156099i	$0.950108\pi$
$108$	−3.35714	−	0.667778i	−0.323041	−	0.0642569i
$109$	−8.50537	+	5.68310i	−0.814666	+	0.544343i	−0.891669	−	0.452688i	$-0.850465\pi$
$109$	−8.50537	+	5.68310i	−0.814666	+	0.544343i	0.0770024	+	0.997031i	$0.475465\pi$
$110$	10.8611	−	4.49881i	1.03556	−	0.428945i
$111$	0.719561	+	1.73717i	0.0682977	+	0.164885i
$112$	0.668077	+	2.56001i	0.0631274	+	0.241899i
$113$	−5.00798	−	0.996149i	−0.471111	−	0.0937098i	−0.0461753	−	0.998933i	$-0.514703\pi$
$113$	−5.00798	−	0.996149i	−0.471111	−	0.0937098i	−0.424936	+	0.905224i	$0.639703\pi$
$114$	−1.84368	+	2.75926i	−0.172676	+	0.258428i
$115$	−0.481266	−	0.481266i	−0.0448782	−	0.0448782i
$116$	−3.03508	+	0.603716i	−0.281800	+	0.0560536i
$117$	−9.65931	−	4.00102i	−0.893003	−	0.369894i
$118$	7.93773			0.730727
$119$	4.35435	−	10.0020i	0.399163	−	0.916880i
$120$	−1.91483			−0.174799
$121$	2.70745	+	1.12146i	0.246132	+	0.101951i
$122$	1.92777	−	0.383456i	0.174532	−	0.0347165i
$123$	3.32716	+	3.32716i	0.300000	+	0.300000i
$124$	−1.48543	+	2.22311i	−0.133396	+	0.199641i
$125$	0.244533	+	0.0486406i	0.0218717	+	0.00435055i
$126$	6.73391	−	1.75732i	0.599904	−	0.156555i
$127$	4.03649	+	9.74494i	0.358180	+	0.864724i	0.995556	+	0.0941707i	$0.0300199\pi$
$127$	4.03649	+	9.74494i	0.358180	+	0.864724i	−0.637376	+	0.770553i	$0.719980\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	−2.17395	+	1.45259i	−0.191406	+	0.127893i
$130$	−12.2787	−	2.44239i	−1.07692	−	0.214212i
$131$	14.6753	+	9.80572i	1.28219	+	0.856730i	0.994876	−	0.101107i	$-0.0322386\pi$
$131$	14.6753	+	9.80572i	1.28219	+	0.856730i	0.287311	+	0.957837i	$0.407239\pi$
$132$	−1.60444	−	1.60444i	−0.139649	−	0.139649i
$133$	1.97852	−	14.3062i	0.171560	−	1.24051i
$134$	5.95444	−	14.3753i	0.514385	−	1.24183i
$135$			10.7813i			0.927905i
$136$	−3.97022	−	1.11238i	−0.340443	−	0.0953859i
$137$	21.0575			1.79906			0.899530	−	0.436859i	$-0.143909\pi$
$137$	21.0575			1.79906			0.899530	+	0.436859i	$0.143909\pi$
$138$	−0.0502714	+	0.121366i	−0.00427938	+	0.0103313i
$139$	−8.87296	+	1.76494i	−0.752595	+	0.149700i	−0.556457	−	0.830876i	$-0.687840\pi$
$139$	−8.87296	+	1.76494i	−0.752595	+	0.149700i	−0.196137	+	0.980576i	$0.562840\pi$
$140$	7.49791	−	3.63692i	0.633689	−	0.307376i
$141$	−2.33462	−	1.55994i	−0.196611	−	0.131371i
$142$	1.58501	−	7.96838i	0.133011	−	0.668692i
$143$	−8.24192	−	12.3349i	−0.689224	−	1.03150i
$144$	−1.00662	−	2.43019i	−0.0838848	−	0.202516i
$145$	3.73001	+	9.00505i	0.309761	+	0.747829i
$146$	10.0023	−	6.68332i	0.827796	−	0.553116i
$147$	3.23583	−	2.76386i	0.266887	−	0.227960i
$148$	−1.71835	+	2.57169i	−0.141247	+	0.211392i
$149$	−14.5770	+	14.5770i	−1.19419	+	1.19419i	−0.218315	+	0.975878i	$0.570056\pi$
$149$	−14.5770	+	14.5770i	−1.19419	+	1.19419i	−0.975878	+	0.218315i	$0.929944\pi$
$150$	0.583621	+	2.93406i	0.0476524	+	0.239565i
$151$	5.98858	−	14.4577i	0.487344	−	1.17655i	−0.468708	−	0.883353i	$-0.655280\pi$
$151$	5.98858	−	14.4577i	0.487344	−	1.17655i	0.956052	−	0.293198i	$-0.0947196\pi$
$152$	−5.45872			−0.442760
$153$	−2.92603	+	10.4433i	−0.236555	+	0.844293i
$154$	9.32992	+	3.23514i	0.751827	+	0.260695i
$155$	7.78043	+	3.22276i	0.624939	+	0.258858i
$156$	0.471408	+	2.36993i	0.0377429	+	0.189746i
$157$	13.4815	−	13.4815i	1.07594	−	1.07594i	0.0790759	−	0.996869i	$-0.474803\pi$
$157$	13.4815	−	13.4815i	1.07594	−	1.07594i	0.996869	−	0.0790759i	$-0.0251969\pi$
$158$	−0.166155	−	0.111021i	−0.0132186	−	0.00883236i
$159$	2.31921	+	0.461319i	0.183925	+	0.0365850i
$160$	−1.74990	−	2.61891i	−0.138342	−	0.207043i
$161$	−0.0336675	−	0.570716i	−0.00265337	−	0.0449787i
$162$	−5.36806	+	2.22353i	−0.421755	+	0.174697i
$163$	−8.55679	−	12.8061i	−0.670219	−	1.00305i	−0.998293	−	0.0584020i	$-0.981399\pi$
$163$	−8.55679	−	12.8061i	−0.670219	−	1.00305i	0.328074	−	0.944652i	$-0.393601\pi$
$164$	−1.50997	+	7.59113i	−0.117909	+	0.592768i
$165$	−3.97057	+	5.94237i	−0.309108	+	0.462613i
$166$	10.1293	+	10.1293i	0.786186	+	0.786186i
$167$	2.42364	+	12.1845i	0.187547	+	0.942862i	0.953827	+	0.300356i	$0.0971054\pi$
$167$	2.42364	+	12.1845i	0.187547	+	0.942862i	−0.766280	+	0.642506i	$0.777895\pi$
$168$	−1.20234	−	1.06839i	−0.0927626	−	0.0824279i
$169$			2.79835i			0.215258i
$170$	−0.996755	+	12.9484i	−0.0764476	+	0.993096i
$171$			14.3587i			1.09804i
$172$	−3.97341	−	1.64584i	−0.302969	−	0.125494i
$173$	−12.3092	+	2.44846i	−0.935854	+	0.186153i	−0.639383	−	0.768889i	$-0.720810\pi$
$173$	−12.3092	+	2.44846i	−0.935854	+	0.186153i	−0.296472	+	0.955042i	$0.595810\pi$
$174$	1.33026	−	1.33026i	0.100847	−	0.100847i
$175$	−7.85808	−	10.3804i	−0.594015	−	0.784687i
$176$	0.728148	−	3.66064i	0.0548862	−	0.275931i
$177$	−4.01235	+	2.68096i	−0.301586	+	0.201514i
$178$	−10.0347	+	4.15652i	−0.752134	+	0.311544i
$179$	0.444478	−	0.184109i	0.0332219	−	0.0137610i	−0.366011	−	0.930611i	$-0.619277\pi$
$179$	0.444478	−	0.184109i	0.0332219	−	0.0137610i	0.399233	+	0.916850i	$0.369277\pi$
$180$	−6.88883	+	4.60297i	−0.513463	+	0.343085i
$181$	3.41862	−	17.1866i	0.254104	−	1.27747i	−0.617231	−	0.786782i	$-0.711746\pi$
$181$	3.41862	−	17.1866i	0.254104	−	1.27747i	0.871336	−	0.490687i	$-0.163254\pi$
$182$	−6.34721	−	8.38459i	−0.470487	−	0.621507i
$183$	−0.844930	+	0.844930i	−0.0624590	+	0.0624590i
$184$	−0.211933	+	0.0421562i	−0.0156239	+	0.00310779i
$185$	9.00041	+	3.72809i	0.661723	+	0.274095i
$186$		−	1.62543i		−	0.119183i
$187$	−11.6847	+	10.0143i	−0.854470	+	0.732320i
$188$		−	4.61864i		−	0.336849i
$189$	−6.01547	+	6.76968i	−0.437561	+	0.492422i
$190$	3.35429	+	16.8632i	0.243346	+	1.22338i
$191$	−13.2893	−	13.2893i	−0.961579	−	0.961579i	0.0377102	−	0.999289i	$-0.487994\pi$
$191$	−13.2893	−	13.2893i	−0.961579	−	0.961579i	−0.999289	+	0.0377102i	$0.987994\pi$
$192$	−0.337749	+	0.505478i	−0.0243750	+	0.0364797i
$193$	−2.83654	+	14.2603i	−0.204179	+	1.02648i	0.733689	+	0.679485i	$0.237797\pi$
$193$	−2.83654	+	14.2603i	−0.204179	+	1.02648i	−0.937868	+	0.346991i	$0.887203\pi$
$194$	−0.487602	−	0.729748i	−0.0350078	−	0.0523929i
$195$	7.03155	−	2.91256i	0.503540	−	0.208573i
$196$	6.73726	+	1.89983i	0.481233	+	0.135702i
$197$	−8.44857	−	12.6442i	−0.601935	−	0.900860i	0.397927	−	0.917417i	$-0.369730\pi$
$197$	−8.44857	−	12.6442i	−0.601935	−	0.900860i	−0.999863	+	0.0165568i	$0.994730\pi$
$198$	−9.62903	−	1.91533i	−0.684305	−	0.136117i
$199$	−13.9819	−	9.34243i	−0.991154	−	0.662268i	−0.0494729	−	0.998775i	$-0.515754\pi$
$199$	−13.9819	−	9.34243i	−0.991154	−	0.662268i	−0.941681	+	0.336508i	$0.890754\pi$
$200$	−3.47956	+	3.47956i	−0.246042	+	0.246042i
$201$	1.84541	+	9.27749i	0.130165	+	0.654384i
$202$	−15.3701	−	6.36652i	−1.08144	−	0.447947i
$203$	−2.68229	+	7.73555i	−0.188260	+	0.542929i
$204$	2.38256	−	0.778654i	0.166813	−	0.0545167i
$205$	24.3785			1.70267
$206$	−2.74529	+	6.62771i	−0.191273	+	0.461774i
$207$	0.110888	+	0.557473i	0.00770727	+	0.0387471i
$208$	−2.81055	+	2.81055i	−0.194876	+	0.194876i
$209$	−11.3191	+	16.9403i	−0.782961	+	1.17178i
$210$	−2.56166	+	4.37080i	−0.176771	+	0.301614i
$211$	15.6561	−	10.4610i	1.07781	−	0.720168i	0.115823	−	0.993270i	$-0.463050\pi$
$211$	15.6561	−	10.4610i	1.07781	−	0.720168i	0.961985	+	0.273102i	$0.0880495\pi$
$212$	1.48850	+	3.59356i	0.102231	+	0.246807i
$213$	1.89013	+	4.56317i	0.129509	+	0.312664i
$214$	8.44275	+	12.6355i	0.577135	+	0.863743i
$215$	−2.64276	+	13.2861i	−0.180235	+	0.906101i
$216$	2.84605	+	1.90167i	0.193649	+	0.129392i
$217$	3.08726	+	6.36473i	0.209577	+	0.432066i
$218$	10.0328	−	1.99564i	0.679505	−	0.135162i
$219$	−2.79865	+	6.75654i	−0.189115	+	0.456565i
$220$	−11.7560			−0.792586
$221$	16.2712	−	1.95409i	1.09452	−	0.131446i
$222$		−	1.88030i		−	0.126198i
$223$	4.92790	−	11.8970i	0.329997	−	0.796682i	−0.668595	−	0.743627i	$-0.733104\pi$
$223$	4.92790	−	11.8970i	0.329997	−	0.796682i	0.998592	−	0.0530556i	$-0.0168961\pi$
$224$	0.362452	−	2.62081i	0.0242174	−	0.175110i
$225$	9.15270	+	9.15270i	0.610180	+	0.610180i
$226$	4.24556	+	2.83679i	0.282410	+	0.188701i
$227$	0.891910	+	0.177412i	0.0591981	+	0.0117752i	0.224601	−	0.974451i	$-0.427892\pi$
$227$	0.891910	+	0.177412i	0.0591981	+	0.0117752i	−0.165402	+	0.986226i	$0.552892\pi$
$228$	2.75926	−	1.84368i	0.182736	−	0.122101i
$229$	0.861960	−	0.357036i	0.0569599	−	0.0235936i	−0.354022	−	0.935237i	$-0.615186\pi$
$229$	0.861960	−	0.357036i	0.0569599	−	0.0235936i	0.410982	+	0.911644i	$0.365186\pi$
$230$	0.260459	+	0.628804i	0.0171742	+	0.0414621i
$231$	−5.80874	+	1.51588i	−0.382187	+	0.0997378i
$232$	3.03508	+	0.603716i	0.199263	+	0.0396359i
$233$	−1.78716	+	2.67468i	−0.117081	+	0.175224i	−0.885381	−	0.464865i	$-0.846103\pi$
$233$	−1.78716	+	2.67468i	−0.117081	+	0.175224i	0.768300	+	0.640089i	$0.221103\pi$
$234$	7.39291	+	7.39291i	0.483290	+	0.483290i
$235$	−14.2680	+	2.83808i	−0.930741	+	0.185136i
$236$	−7.33351	−	3.03764i	−0.477371	−	0.197733i
$237$	0.121485			0.00789129
$238$	−7.85049	+	7.57429i	−0.508871	+	0.490968i
$239$	−12.1337			−0.784861			−0.392431	−	0.919782i	$-0.628366\pi$
$239$	−12.1337			−0.784861			−0.392431	+	0.919782i	$0.628366\pi$
$240$	1.76907	+	0.732773i	0.114193	+	0.0473003i
$241$	22.1209	−	4.40012i	1.42493	−	0.283437i	0.578391	−	0.815759i	$-0.303681\pi$
$241$	22.1209	−	4.40012i	1.42493	−	0.283437i	0.846542	+	0.532323i	$0.178681\pi$
$242$	−2.07219	−	2.07219i	−0.133205	−	0.133205i
$243$	7.66745	−	11.4752i	0.491867	−	0.736131i
$244$	−1.92777	−	0.383456i	−0.123413	−	0.0245483i
$245$	1.72907	−	21.9803i	0.110466	−	1.40427i
$246$	−1.80064	−	4.34714i	−0.114805	−	0.277164i
$247$	20.0453	−	8.30302i	1.27545	−	0.528309i
$248$	2.22311	−	1.48543i	0.141167	−	0.0943251i
$249$	−8.54130	−	1.69897i	−0.541283	−	0.107668i
$250$	−0.207305	−	0.138517i	−0.0131111	−	0.00876057i
$251$	2.97932	+	2.97932i	0.188053	+	0.188053i	0.794854	−	0.606801i	$-0.207547\pi$
$251$	2.97932	+	2.97932i	0.188053	+	0.188053i	−0.606801	+	0.794854i	$0.707547\pi$
$252$	−6.89382	−	0.953401i	−0.434270	−	0.0600586i
$253$	−0.308638	+	0.745117i	−0.0194039	+	0.0468451i
$254$		−	10.5479i		−	0.661831i
$255$	−3.86947	−	6.88177i	−0.242316	−	0.430953i
$256$	−1.00000			−0.0625000
$257$	−7.63050	+	18.4217i	−0.475978	+	1.14911i	0.485502	+	0.874236i	$0.338637\pi$
$257$	−7.63050	+	18.4217i	−0.475978	+	1.14911i	−0.961480	+	0.274876i	$0.911363\pi$
$258$	2.56435	−	0.510081i	0.159649	−	0.0317562i
$259$	3.57135	+	7.36273i	0.221913	+	0.457498i
$260$	10.4094	+	6.95535i	0.645565	+	0.431353i
$261$	1.58802	−	7.98354i	0.0982962	−	0.494168i
$262$	−9.80572	−	14.6753i	−0.605800	−	0.906643i
$263$	−1.16578	−	2.81444i	−0.0718850	−	0.173546i	0.883853	−	0.467765i	$-0.154941\pi$
$263$	−1.16578	−	2.81444i	−0.0718850	−	0.173546i	−0.955738	+	0.294219i	$0.904941\pi$
$264$	0.868318	+	2.09631i	0.0534413	+	0.129019i
$265$	10.1866	−	6.80649i	0.625760	−	0.418119i
$266$	−7.30268	+	12.4601i	−0.447756	+	0.763978i
$267$	3.66847	−	5.49025i	0.224506	−	0.335998i
$268$	−11.0024	+	11.0024i	−0.672076	+	0.672076i
$269$	−5.85556	−	29.4379i	−0.357020	−	1.79486i	−0.574187	−	0.818725i	$-0.694682\pi$
$269$	−5.85556	−	29.4379i	−0.357020	−	1.79486i	0.217167	−	0.976134i	$-0.430318\pi$
$270$	4.12582	−	9.96061i	0.251089	−	0.606183i
$271$	10.8364			0.658267			0.329134	−	0.944283i	$-0.393243\pi$
$271$	10.8364			0.658267			0.329134	+	0.944283i	$0.393243\pi$
$272$	3.24231	+	2.54704i	0.196594	+	0.154437i
$273$	6.04026	+	2.09446i	0.365573	+	0.126762i
$274$	−19.4546	−	8.05834i	−1.17529	−	0.486822i
$275$	3.58310	+	18.0135i	0.216069	+	1.08625i
$276$	0.0928894	−	0.0928894i	0.00559128	−	0.00559128i
$277$	−14.1929	−	9.48337i	−0.852766	−	0.569800i	0.0505762	−	0.998720i	$-0.483894\pi$
$277$	−14.1929	−	9.48337i	−0.852766	−	0.569800i	−0.903342	+	0.428920i	$0.858894\pi$
$278$	8.87296	+	1.76494i	0.532165	+	0.105854i
$279$	−3.90731	−	5.84770i	−0.233924	−	0.350093i
$280$	−8.31896	+	0.490749i	−0.497153	+	0.0293278i
$281$	−17.3050	+	7.16796i	−1.03233	+	0.427605i	−0.833553	−	0.552440i	$-0.813697\pi$
$281$	−17.3050	+	7.16796i	−1.03233	+	0.427605i	−0.198776	+	0.980045i	$0.563697\pi$
$282$	1.55994	+	2.33462i	0.0928933	+	0.139025i
$283$	1.42129	−	7.14528i	0.0844866	−	0.424743i	−0.915273	−	0.402833i	$-0.868025\pi$
$283$	1.42129	−	7.14528i	0.0844866	−	0.424743i	0.999760	−	0.0219096i	$-0.00697460\pi$
$284$	−4.51373	+	6.75527i	−0.267840	+	0.400851i
$285$	−7.39104	−	7.39104i	−0.437807	−	0.437807i
$286$	2.89418	+	14.5500i	0.171136	+	0.860361i
$287$	15.3075	+	13.6021i	0.903574	+	0.802906i
$288$			2.63042i			0.154999i
$289$	−4.02516	−	16.5166i	−0.236774	−	0.971565i
$290$		−	9.74700i		−	0.572363i
$291$	0.492944	+	0.204184i	0.0288969	+	0.0119695i
$292$	−11.7985	+	2.34687i	−0.690456	+	0.137340i
$293$	−19.1482	+	19.1482i	−1.11865	+	1.11865i	−0.126707	+	0.991940i	$0.540441\pi$
$293$	−19.1482	+	19.1482i	−1.11865	+	1.11865i	−0.991940	+	0.126707i	$0.959559\pi$
$294$	−4.04720	+	1.31518i	−0.236038	+	0.0767029i
$295$	−4.87760	+	24.5214i	−0.283985	+	1.42769i
$296$	2.57169	−	1.71835i	0.149477	−	0.0998770i
$297$	11.8031	−	4.88899i	0.684884	−	0.283688i
$298$	19.0458	−	7.88901i	1.10329	−	0.456998i
$299$	0.714131	−	0.477167i	0.0412992	−	0.0275953i
$300$	0.583621	−	2.93406i	0.0336954	−	0.169398i
$301$	−9.07243	+	6.86791i	−0.522926	+	0.395860i
$302$	−11.0654	+	11.0654i	−0.636745	+	0.636745i
$303$	9.91955	−	1.97312i	0.569863	−	0.113353i
$304$	5.04320	+	2.08896i	0.289247	+	0.119810i
$305$			6.19091i			0.354490i
$306$	6.69978	−	8.52863i	0.383001	−	0.487549i
$307$		−	21.6619i		−	1.23631i	−0.786057	−	0.618154i	$-0.787881\pi$
$307$		−	21.6619i		−	1.23631i	0.786057	−	0.618154i	$-0.212119\pi$
$308$	−7.38169	−	6.55929i	−0.420611	−	0.373750i
$309$	−0.850823	−	4.27737i	−0.0484016	−	0.243331i
$310$	−5.95488	−	5.95488i	−0.338215	−	0.338215i
$311$	3.28727	−	4.91974i	0.186404	−	0.278973i	−0.726484	−	0.687183i	$-0.758847\pi$
$311$	3.28727	−	4.91974i	0.186404	−	0.278973i	0.912888	+	0.408210i	$0.133847\pi$
$312$	0.471408	−	2.36993i	0.0266882	−	0.134171i
$313$	16.6705	+	24.9491i	0.942271	+	1.41021i	0.911783	+	0.410672i	$0.134706\pi$
$313$	16.6705	+	24.9491i	0.942271	+	1.41021i	0.0304877	+	0.999535i	$0.490294\pi$
$314$	−17.6145	+	7.29616i	−0.994043	+	0.411746i
$315$	1.29087	+	21.8823i	0.0727325	+	1.23293i
$316$	0.111021	+	0.166155i	0.00624542	+	0.00934694i
$317$	0.956736	+	0.190307i	0.0537357	+	0.0106887i	0.221885	−	0.975073i	$-0.428779\pi$
$317$	0.956736	+	0.190307i	0.0537357	+	0.0106887i	−0.168149	+	0.985762i	$0.553779\pi$
$318$	−1.96613	−	1.31372i	−0.110255	−	0.0736700i
$319$	8.16705	−	8.16705i	0.457267	−	0.457267i
$320$	0.614483	+	3.08922i	0.0343507	+	0.172692i
$321$	−8.53524	−	3.53541i	−0.476391	−	0.197328i
$322$	−0.187299	+	0.540157i	−0.0104378	+	0.0301018i
$323$	−11.0309	−	19.6183i	−0.613778	−	1.09159i
$324$	5.81035			0.322797
$325$	7.48488	−	18.0701i	0.415187	−	1.00235i
$326$	3.00474	+	15.1059i	0.166417	+	0.836637i
$327$	−4.39731	+	4.39731i	−0.243172	+	0.243172i
$328$	4.30003	−	6.43545i	0.237430	−	0.355338i
$329$	−10.5425	−	6.17883i	−0.581229	−	0.340650i
$330$	5.94237	−	3.97057i	0.327117	−	0.218572i
$331$	1.06832	+	2.57915i	0.0587200	+	0.141763i	0.950516	−	0.310674i	$-0.100555\pi$
$331$	1.06832	+	2.57915i	0.0587200	+	0.141763i	−0.891796	+	0.452437i	$0.850555\pi$
$332$	−5.48194	−	13.2346i	−0.300860	−	0.726341i
$333$	−4.51998	−	6.76462i	−0.247693	−	0.370699i
$334$	2.42364	−	12.1845i	0.132616	−	0.666704i
$335$	40.7494	+	27.2279i	2.22638	+	1.48762i
$336$	0.701964	+	1.44718i	0.0382953	+	0.0789500i
$337$	−15.7999	+	3.14280i	−0.860676	+	0.171199i	−0.605646	−	0.795734i	$-0.707085\pi$
$337$	−15.7999	+	3.14280i	−0.860676	+	0.171199i	−0.255030	+	0.966933i	$0.582085\pi$
$338$	1.07088	−	2.58534i	0.0582483	−	0.140624i
$339$	−3.10416			−0.168595
$340$	5.87602	−	11.5813i	0.318672	−	0.628085i
$341$		−	9.97924i		−	0.540406i
$342$	5.49484	−	13.2657i	0.297127	−	0.717328i
$343$	13.3497	−	12.8369i	0.720815	−	0.693127i
$344$	3.04111	+	3.04111i	0.163966	+	0.163966i
$345$	−0.344034	−	0.229876i	−0.0185222	−	0.0123761i
$346$	12.3092	+	2.44846i	0.661749	+	0.131630i
$347$	15.8256	−	10.5743i	0.849564	−	0.567661i	−0.0528145	−	0.998604i	$-0.516819\pi$
$347$	15.8256	−	10.5743i	0.849564	−	0.567661i	0.902379	+	0.430944i	$0.141819\pi$
$348$	−1.73807	+	0.719933i	−0.0931704	+	0.0385924i
$349$	−8.46260	−	20.4305i	−0.452992	−	1.09362i	−0.971179	−	0.238353i	$-0.923393\pi$
$349$	−8.46260	−	20.4305i	−0.452992	−	1.09362i	0.518186	−	0.855268i	$-0.326607\pi$
$350$	3.28750	+	12.5974i	0.175724	+	0.673361i
$351$	−13.3437	−	2.65423i	−0.712234	−	0.141672i
$352$	−2.07359	+	3.10334i	−0.110523	+	0.165409i
$353$	−8.08913	−	8.08913i	−0.430541	−	0.430541i	0.458271	−	0.888812i	$-0.348469\pi$
$353$	−8.08913	−	8.08913i	−0.430541	−	0.430541i	−0.888812	+	0.458271i	$0.848469\pi$
$354$	4.73288	−	0.941429i	0.251550	−	0.0500364i
$355$	23.6421	+	9.79287i	1.25479	+	0.519752i
$356$	10.8615			0.575659
$357$	1.41003	−	6.48013i	0.0746269	−	0.342965i
$358$	−0.481100			−0.0254269
$359$	34.2758	+	14.1975i	1.80901	+	0.749314i	0.982468	+	0.186433i	$0.0596926\pi$
$359$	34.2758	+	14.1975i	1.80901	+	0.749314i	0.826537	+	0.562882i	$0.190307\pi$
$360$	8.12593	−	1.61635i	0.428274	−	0.0851890i
$361$	−7.63506	−	7.63506i	−0.401845	−	0.401845i
$362$	−9.73542	+	14.5701i	−0.511682	+	0.765787i
$363$	1.74733	+	0.347565i	0.0917109	+	0.0182424i
$364$	2.65542	+	10.1753i	0.139182	+	0.533332i
$365$	14.5000	+	35.0060i	0.758963	+	1.83230i
$366$	1.10395	−	0.457273i	0.0577046	−	0.0239020i
$367$	−9.13686	+	6.10505i	−0.476940	+	0.318681i	−0.770700	−	0.637198i	$-0.780093\pi$
$367$	−9.13686	+	6.10505i	−0.476940	+	0.318681i	0.293760	+	0.955879i	$0.405093\pi$
$368$	0.211933	+	0.0421562i	0.0110478	+	0.00219754i
$369$	−16.9279	−	11.3109i	−0.881233	−	0.588821i
$370$	−6.88861	−	6.88861i	−0.358122	−	0.358122i
$371$	10.1940	+	1.40981i	0.529246	+	0.0731937i
$372$	−0.622027	+	1.50171i	−0.0322506	+	0.0778598i
$373$		−	20.7863i		−	1.07628i	−0.842857	−	0.538138i	$-0.819128\pi$
$373$		−	20.7863i		−	1.07628i	0.842857	−	0.538138i	$-0.180872\pi$
$374$	14.6276	−	4.78049i	0.756374	−	0.247193i
$375$	0.151572			0.00782715
$376$	−1.76748	+	4.26707i	−0.0911507	+	0.220057i
$377$	−12.0636	+	2.39960i	−0.621306	+	0.123586i
$378$	8.14821	−	3.95235i	0.419099	−	0.203287i
$379$	−7.17539	−	4.79444i	−0.368575	−	0.246274i	0.357465	−	0.933927i	$-0.383641\pi$
$379$	−7.17539	−	4.79444i	−0.368575	−	0.246274i	−0.726040	+	0.687653i	$0.758641\pi$
$380$	3.35429	−	16.8632i	0.172071	−	0.865062i
$381$	3.56253	+	5.33170i	0.182514	+	0.273151i
$382$	7.19211	+	17.3633i	0.367980	+	0.888383i
$383$	−4.19194	−	10.1202i	−0.214198	−	0.517120i	0.779862	−	0.625951i	$-0.215289\pi$
$383$	−4.19194	−	10.1202i	−0.214198	−	0.517120i	−0.994060	+	0.108832i	$0.965289\pi$
$384$	0.505478	−	0.337749i	0.0257950	−	0.0172357i
$385$	−15.7271	+	26.8342i	−0.801529	+	1.36760i
$386$	8.07779	−	12.0893i	0.411149	−	0.615328i
$387$	7.99940	−	7.99940i	0.406632	−	0.406632i
$388$	0.171223	+	0.860797i	0.00869254	+	0.0437003i
$389$	−4.63464	+	11.1890i	−0.234985	+	0.567305i	−0.996751	−	0.0805482i	$-0.974333\pi$
$389$	−4.63464	+	11.1890i	−0.234985	+	0.567305i	0.761765	+	0.647853i	$0.224333\pi$
$390$	−7.61089			−0.385393
$391$	−0.579780	−	0.676487i	−0.0293208	−	0.0342114i
$392$	−5.49738	−	4.33345i	−0.277660	−	0.218873i
$393$	9.91315	+	4.10616i	0.500052	+	0.207128i
$394$	2.96674	+	14.9148i	0.149462	+	0.751398i
$395$	0.445067	−	0.445067i	0.0223938	−	0.0223938i
$396$	8.16309	+	5.45440i	0.410211	+	0.274094i
$397$	−34.8966	−	6.94136i	−1.75141	−	0.348377i	−0.787848	−	0.615869i	$-0.788805\pi$
$397$	−34.8966	−	6.94136i	−1.75141	−	0.348377i	−0.963560	+	0.267493i	$0.913805\pi$
$398$	9.34243	+	13.9819i	0.468294	+	0.700851i
$399$	−0.517048	−	8.76478i	−0.0258848	−	0.438788i
$400$	4.54627	−	1.88313i	0.227313	−	0.0941563i
$401$	−5.90196	−	8.83291i	−0.294730	−	0.441094i	0.654321	−	0.756217i	$-0.272954\pi$
$401$	−5.90196	−	8.83291i	−0.294730	−	0.441094i	−0.949051	+	0.315122i	$0.897954\pi$
$402$	1.84541	−	9.27749i	0.0920405	−	0.462719i
$403$	−5.90417	+	8.83621i	−0.294108	+	0.440163i
$404$	11.7638	+	11.7638i	0.585271	+	0.585271i
$405$	−3.57036	−	17.9494i	−0.177413	−	0.891914i
$406$	5.43838	−	6.12024i	0.269902	−	0.303743i
$407$		−	11.5440i		−	0.572215i
$408$	−2.49918	−	0.192384i	−0.123728	−	0.00952444i
$409$		−	9.65626i		−	0.477471i	−0.971085	−	0.238736i	$-0.923267\pi$
$409$		−	9.65626i		−	0.477471i	0.971085	−	0.238736i	$-0.0767330\pi$
$410$	−22.5228	−	9.32925i	−1.11232	−	0.460739i
$411$	12.5555	−	2.49745i	0.619319	−	0.123190i
$412$	5.07263	−	5.07263i	0.249910	−	0.249910i
$413$	−16.7445	+	12.6757i	−0.823943	+	0.623733i
$414$	0.110888	−	0.557473i	0.00544987	−	0.0273983i
$415$	−37.5159	+	25.0673i	−1.84158	+	1.23051i
$416$	3.67216	−	1.52106i	0.180042	−	0.0745760i
$417$	−5.08119	+	2.10470i	−0.248827	+	0.103067i
$418$	16.9403	−	11.3191i	0.828576	−	0.553637i
$419$	−1.38439	+	6.95978i	−0.0676317	+	0.340008i	−0.999755	−	0.0221335i	$-0.992954\pi$
$419$	−1.38439	+	6.95978i	−0.0676317	+	0.340008i	0.932123	+	0.362141i	$0.117954\pi$
$420$	4.03930	−	3.05779i	0.197098	−	0.149205i
$421$	5.97230	−	5.97230i	0.291072	−	0.291072i	−0.546432	−	0.837504i	$-0.684014\pi$
$421$	5.97230	−	5.97230i	0.291072	−	0.291072i	0.837504	+	0.546432i	$0.184014\pi$
$422$	−18.4676	+	3.67343i	−0.898988	+	0.178820i
$423$	11.2242	+	4.64921i	0.545738	+	0.226052i
$424$		−	3.88964i		−	0.188898i
$425$	−19.5368	−	5.47385i	−0.947674	−	0.265521i
$426$		−	4.93914i		−	0.239302i
$427$	−3.45425	+	3.88734i	−0.167163	+	0.188121i
$428$	−2.96470	−	14.9046i	−0.143304	−	0.720439i
$429$	−6.37720	−	6.37720i	−0.307894	−	0.307894i
$430$	7.52594	−	11.2634i	0.362933	−	0.543168i
$431$	−5.51141	+	27.7077i	−0.265475	+	1.33463i	0.586030	+	0.810289i	$0.300690\pi$
$431$	−5.51141	+	27.7077i	−0.265475	+	1.33463i	−0.851505	+	0.524346i	$0.824310\pi$
$432$	−1.90167	−	2.84605i	−0.0914941	−	0.136931i
$433$	30.8461	−	12.7769i	1.48237	−	0.614017i	0.512728	−	0.858551i	$-0.328635\pi$
$433$	30.8461	−	12.7769i	1.48237	−	0.614017i	0.969641	+	0.244534i	$0.0786348\pi$
$434$	−0.416580	−	7.06169i	−0.0199965	−	0.338972i
$435$	3.29204	+	4.92689i	0.157841	+	0.236226i
$436$	−10.0328	−	1.99564i	−0.480482	−	0.0955739i
$437$	−0.980759	−	0.655323i	−0.0469161	−	0.0313483i
$438$	5.17123	−	5.17123i	0.247091	−	0.247091i
$439$	2.46874	+	12.4112i	0.117827	+	0.592354i	0.993910	+	0.110195i	$0.0351474\pi$
$439$	2.46874	+	12.4112i	0.117827	+	0.592354i	−0.876083	+	0.482160i	$0.839853\pi$
$440$	10.8611	+	4.49881i	0.517782	+	0.214472i
$441$	−11.3988	+	14.4604i	−0.542800	+	0.688591i
$442$	−15.7805	−	4.42140i	−0.750600	−	0.210304i
$443$	2.27487			0.108082			0.0540411	−	0.998539i	$-0.482790\pi$
$443$	2.27487			0.108082			0.0540411	+	0.998539i	$0.482790\pi$
$444$	−0.719561	+	1.73717i	−0.0341489	+	0.0824426i
$445$	−6.67421	−	33.5535i	−0.316388	−	1.59059i
$446$	−9.10557	+	9.10557i	−0.431161	+	0.431161i
$447$	−6.96270	+	10.4204i	−0.329324	+	0.492868i
$448$	−1.33780	+	2.28261i	−0.0632052	+	0.107843i
$449$	11.7252	−	7.83452i	0.553346	−	0.369734i	−0.247238	−	0.968955i	$-0.579523\pi$
$449$	11.7252	−	7.83452i	0.553346	−	0.369734i	0.800584	+	0.599221i	$0.204523\pi$
$450$	−4.95341	−	11.9586i	−0.233506	−	0.563733i
$451$	−11.0549	−	26.6890i	−0.520556	−	1.25673i
$452$	−2.83679	−	4.24556i	−0.133431	−	0.199694i
$453$	1.85599	−	9.33068i	0.0872019	−	0.438394i
$454$	−0.756124	−	0.505226i	−0.0354867	−	0.0237114i
$455$	29.8021	−	14.4557i	1.39714	−	0.677694i
$456$	−3.25477	+	0.647414i	−0.152419	+	0.0303179i
$457$	−15.3173	+	36.9793i	−0.716514	+	1.72982i	−0.0334716	+	0.999440i	$0.510656\pi$
$457$	−15.3173	+	36.9793i	−0.716514	+	1.72982i	−0.683043	+	0.730379i	$0.739344\pi$
$458$	−0.932979			−0.0435952
$459$	−1.08320	+	14.0714i	−0.0505596	+	0.656797i
$460$		−	0.680612i		−	0.0317337i
$461$	2.98973	−	7.21784i	0.139245	−	0.336168i	−0.838838	−	0.544381i	$-0.816765\pi$
$461$	2.98973	−	7.21784i	0.139245	−	0.336168i	0.978084	+	0.208213i	$0.0667646\pi$
$462$	5.94668	+	0.822413i	0.276664	+	0.0382621i
$463$	20.2431	+	20.2431i	0.940778	+	0.940778i	0.998342	−	0.0575637i	$-0.0183332\pi$
$463$	20.2431	+	20.2431i	0.940778	+	0.940778i	−0.0575637	+	0.998342i	$0.518333\pi$
$464$	−2.57302	−	1.71924i	−0.119449	−	0.0798135i
$465$	5.02132	+	0.998802i	0.232858	+	0.0463183i
$466$	2.67468	−	1.78716i	0.123902	−	0.0827888i
$467$	−13.0901	+	5.42209i	−0.605737	+	0.250905i	−0.664405	−	0.747373i	$-0.731315\pi$
$467$	−13.0901	+	5.42209i	−0.605737	+	0.250905i	0.0586675	+	0.998278i	$0.481315\pi$
$468$	−4.00102	−	9.65931i	−0.184947	−	0.446502i
$469$	10.3951	+	39.8330i	0.480000	+	1.83932i
$470$	14.2680	+	2.83808i	0.658133	+	0.130911i
$471$	6.43946	−	9.63733i	0.296714	−	0.444065i
$472$	5.61282	+	5.61282i	0.258351	+	0.258351i
$473$	15.7436	−	3.13161i	0.723894	−	0.143991i
$474$	−0.112237	−	0.0464902i	−0.00515523	−	0.00213537i
$475$	−26.8615			−1.23249
$476$	10.1515	−	3.99348i	0.465291	−	0.183041i
$477$	−10.2314			−0.468463
$478$	11.2100	+	4.64335i	0.512735	+	0.212382i
$479$	−0.0603537	+	0.0120051i	−0.00275763	+	0.000548527i	−0.196469	−	0.980510i	$-0.562947\pi$
$479$	−0.0603537	+	0.0120051i	−0.00275763	+	0.000548527i	0.193711	+	0.981059i	$0.437947\pi$
$480$	−1.35399	−	1.35399i	−0.0618008	−	0.0618008i
$481$	−6.82995	+	10.2217i	−0.311419	+	0.466071i
$482$	−22.1209	−	4.40012i	−1.00758	−	0.200420i
$483$	−0.0877622	−	0.336297i	−0.00399332	−	0.0153021i
$484$	1.12146	+	2.70745i	0.0509755	+	0.123066i
$485$	2.55397	−	1.05789i	0.115970	−	0.0480363i
$486$	−11.4752	+	7.66745i	−0.520523	+	0.347803i
$487$	−1.66871	−	0.331927i	−0.0756166	−	0.0150411i	0.157137	−	0.987577i	$-0.449774\pi$
$487$	−1.66871	−	0.331927i	−0.0756166	−	0.0150411i	−0.232754	+	0.972536i	$0.574774\pi$
$488$	1.63428	+	1.09199i	0.0739804	+	0.0494321i
$489$	−6.62083	−	6.62083i	−0.299404	−	0.299404i
$490$	−10.0089	+	19.6454i	−0.452157	+	0.887490i
$491$	11.6022	−	28.0101i	0.523598	−	1.26408i	−0.412056	−	0.911158i	$-0.635189\pi$
$491$	11.6022	−	28.0101i	0.523598	−	1.26408i	0.935654	−	0.352919i	$-0.114811\pi$
$492$			4.70531i			0.212132i
$493$	3.96356	+	12.1279i	0.178510	+	0.546212i
$494$	−21.6968			−0.976187
$495$	11.8337	−	28.5692i	0.531887	−	1.28409i
$496$	−2.62233	+	0.521615i	−0.117746	+	0.0234212i
$497$	9.38114	+	19.3403i	0.420802	+	0.867529i
$498$	7.24096	+	4.83826i	0.324475	+	0.216807i
$499$	0.475451	−	2.39025i	0.0212841	−	0.107002i	−0.968683	−	0.248301i	$-0.920128\pi$
$499$	0.475451	−	2.39025i	0.0212841	−	0.107002i	0.989967	+	0.141299i	$0.0451278\pi$
$500$	0.138517	+	0.207305i	0.00619466	+	0.00927097i
$501$	2.89020	+	6.97756i	0.129125	+	0.311734i
$502$	−1.61240	−	3.89267i	−0.0719648	−	0.173739i
$503$	−8.94594	+	5.97749i	−0.398880	+	0.266523i	−0.738791	−	0.673935i	$-0.764603\pi$
$503$	−8.94594	+	5.97749i	−0.398880	+	0.266523i	0.339911	+	0.940458i	$0.389603\pi$
$504$	6.00421	+	3.51898i	0.267449	+	0.156748i
$505$	29.1122	−	43.5696i	1.29548	−	1.93882i
$506$	0.570288	−	0.570288i	0.0253524	−	0.0253524i
$507$	0.331889	+	1.66852i	0.0147397	+	0.0741016i
$508$	−4.03649	+	9.74494i	−0.179090	+	0.432362i
$509$	8.62286			0.382201			0.191101	−	0.981570i	$-0.438794\pi$
$509$	8.62286			0.382201			0.191101	+	0.981570i	$0.438794\pi$
$510$	0.941386	+	7.83871i	0.0416853	+	0.347104i
$511$	−10.4271	+	30.0710i	−0.461267	+	1.33026i
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	3.64521	+	18.3257i	0.160940	+	0.809100i
$514$	14.0993	−	14.0993i	0.621895	−	0.621895i
$515$	−18.7875	−	12.5534i	−0.827875	−	0.553169i
$516$	−2.56435	−	0.510081i	−0.112889	−	0.0224551i
$517$	9.57717	+	14.3332i	0.421203	+	0.630375i
$518$	−0.481901	−	8.16897i	−0.0211735	−	0.358924i
$519$	−7.04901	+	2.91980i	−0.309417	+	0.128165i
$520$	−6.95535	−	10.4094i	−0.305012	−	0.456483i
$521$	−0.543951	+	2.73462i	−0.0238309	+	0.119806i	−0.990870	−	0.134823i	$-0.956953\pi$
$521$	−0.543951	+	2.73462i	−0.0238309	+	0.119806i	0.967039	+	0.254629i	$0.0819534\pi$
$522$	−4.52231	+	6.76811i	−0.197936	+	0.296232i
$523$	2.93806	+	2.93806i	0.128472	+	0.128472i	0.768419	−	0.639947i	$-0.221044\pi$
$523$	2.93806	+	2.93806i	0.128472	+	0.128472i	−0.639947	+	0.768419i	$0.721044\pi$
$524$	3.44331	+	17.3107i	0.150422	+	0.756221i
$525$	−5.91653	−	5.25737i	−0.258219	−	0.229450i
$526$			3.04633i			0.132826i
$527$	9.83099	+	4.98796i	0.428245	+	0.217279i
$528$		−	2.26902i		−	0.0987466i
$529$	21.2061	+	8.78385i	0.922004	+	0.381907i
$530$	−12.0159	+	2.39012i	−0.521940	+	0.103820i
$531$	14.7641	−	14.7641i	0.640706	−	0.640706i
$532$	11.5151	−	8.71701i	0.499242	−	0.377931i
$533$	−6.00170	+	30.1726i	−0.259963	+	1.30692i
$534$	−5.49025	+	3.66847i	−0.237586	+	0.158750i
$535$	−44.2216	+	18.3172i	−1.91187	+	0.791922i
$536$	14.3753	−	5.95444i	0.620917	−	0.257192i
$537$	0.243185	−	0.162491i	0.0104942	−	0.00701201i
$538$	−5.85556	+	29.4379i	−0.252451	+	1.26916i
$539$	−24.8475	+	8.07446i	−1.07026	+	0.347792i
$540$	−7.62352	+	7.62352i	−0.328064	+	0.328064i
$541$	−33.4596	+	6.65552i	−1.43854	+	0.286143i	−0.851900	−	0.523705i	$-0.824550\pi$
$541$	−33.4596	+	6.65552i	−1.43854	+	0.286143i	−0.586640	+	0.809848i	$0.699550\pi$
$542$	−10.0116	−	4.14693i	−0.430034	−	0.178126i
$543$		−	10.6530i		−	0.457163i
$544$	−2.02079	−	3.59394i	−0.0866408	−	0.154089i
$545$			32.2197i			1.38014i
$546$	−4.77896	−	4.24653i	−0.204521	−	0.181735i
$547$	−4.25286	−	21.3806i	−0.181839	−	0.914167i	−0.958684	−	0.284474i	$-0.908181\pi$
$547$	−4.25286	−	21.3806i	−0.181839	−	0.914167i	0.776845	−	0.629692i	$-0.216819\pi$
$548$	14.8899	+	14.8899i	0.636064	+	0.636064i
$549$	2.87239	−	4.29884i	0.122591	−	0.183470i
$550$	3.58310	−	18.0135i	0.152784	−	0.768096i
$551$	9.38483	+	14.0454i	0.399807	+	0.598353i
$552$	−0.121366	+	0.0502714i	−0.00516567	+	0.00213969i
$553$	0.527790	−	0.0311352i	0.0224439	−	0.00132400i
$554$	9.48337	+	14.1929i	0.402910	+	0.602997i
$555$	5.80866	+	1.15542i	0.246564	+	0.0490446i
$556$	−7.52213	−	5.02613i	−0.319009	−	0.213155i
$557$	−7.25726	+	7.25726i	−0.307500	+	0.307500i	−0.843939	−	0.536439i	$-0.819769\pi$
$557$	−7.25726	+	7.25726i	−0.307500	+	0.307500i	0.536439	+	0.843939i	$0.319769\pi$
$558$	1.37206	+	6.89783i	0.0580841	+	0.292009i
$559$	−15.7932	−	6.54174i	−0.667979	−	0.276686i
$560$	7.87352	+	2.73013i	0.332717	+	0.115369i
$561$	−5.77930	+	7.35688i	−0.244002	+	0.310608i
$562$	18.7308			0.790110
$563$	−6.54943	+	15.8117i	−0.276025	+	0.666384i	−0.999718	−	0.0237379i	$-0.992443\pi$
$563$	−6.54943	+	15.8117i	−0.276025	+	0.666384i	0.723693	+	0.690122i	$0.242443\pi$
$564$	−0.547779	−	2.75387i	−0.0230657	−	0.115959i
$565$	−11.3723	+	11.3723i	−0.478436	+	0.478436i
$566$	−4.04748	+	6.05748i	−0.170128	+	0.254615i
$567$	7.77310	−	13.2627i	0.326439	−	0.556983i
$568$	6.75527	−	4.51373i	0.283445	−	0.189392i
$569$	−3.35289	−	8.09459i	−0.140560	−	0.339343i	0.837886	−	0.545846i	$-0.183792\pi$
$569$	−3.35289	−	8.09459i	−0.140560	−	0.339343i	−0.978446	+	0.206503i	$0.933792\pi$
$570$	4.00000	+	9.65686i	0.167542	+	0.404481i
$571$	22.6797	+	33.9426i	0.949117	+	1.42045i	0.906900	+	0.421346i	$0.138442\pi$
$571$	22.6797	+	33.9426i	0.949117	+	1.42045i	0.0422175	+	0.999108i	$0.486558\pi$
$572$	2.89418	−	14.5500i	0.121012	−	0.608367i
$573$	−9.49988	−	6.34762i	−0.396863	−	0.265176i
$574$	−8.93701	−	18.4246i	−0.373024	−	0.769029i
$575$	−1.04289	+	0.207444i	−0.0434916	+	0.00865101i
$576$	1.00662	−	2.43019i	0.0419424	−	0.101258i
$577$	−3.96500			−0.165065			−0.0825325	−	0.996588i	$-0.526301\pi$
$577$	−3.96500			−0.165065			−0.0825325	+	0.996588i	$0.526301\pi$
$578$	−2.60187	+	16.7997i	−0.108223	+	0.698776i
$579$			8.83912i			0.367341i
$580$	−3.73001	+	9.00505i	−0.154880	+	0.373914i
$581$	−37.5430	−	5.19212i	−1.55755	−	0.215406i
$582$	−0.377283	−	0.377283i	−0.0156389	−	0.0156389i
$583$	−12.0709	−	8.06552i	−0.499926	−	0.334040i
$584$	11.7985	+	2.34687i	0.488226	+	0.0971142i
$585$	−27.3811	+	18.2955i	−1.13207	+	0.756425i
$586$	25.0183	−	10.3629i	1.03350	−	0.428088i
$587$	11.4909	+	27.7414i	0.474280	+	1.14501i	0.962254	+	0.272154i	$0.0877360\pi$
$587$	11.4909	+	27.7414i	0.474280	+	1.14501i	−0.487974	+	0.872858i	$0.662264\pi$
$588$	4.24242	+	0.333728i	0.174955	+	0.0137627i
$589$	14.3146	+	2.84735i	0.589822	+	0.117323i
$590$	13.8902	−	20.7882i	0.571852	−	0.855837i
$591$	−6.53709	−	6.53709i	−0.268900	−	0.268900i
$592$	−3.03352	+	0.603404i	−0.124677	+	0.0247998i
$593$	−10.3704	−	4.29556i	−0.425861	−	0.176397i	0.159450	−	0.987206i	$-0.449028\pi$
$593$	−10.3704	−	4.29556i	−0.425861	−	0.176397i	−0.585312	+	0.810808i	$0.699028\pi$
$594$	−12.7756			−0.524187
$595$	−18.5746	−	28.9061i	−0.761485	−	1.18504i
$596$	−20.6150			−0.844422
$597$	−9.44478	−	3.91216i	−0.386549	−	0.160114i
$598$	−0.842375	+	0.167559i	−0.0344473	+	0.00685199i
$599$	−8.91841	−	8.91841i	−0.364396	−	0.364396i	0.501032	−	0.865429i	$-0.332954\pi$
$599$	−8.91841	−	8.91841i	−0.364396	−	0.364396i	−0.865429	+	0.501032i	$0.832954\pi$
$600$	−1.66201	+	2.48738i	−0.0678513	+	0.101547i
$601$	24.4908	+	4.87152i	0.999000	+	0.198713i	0.667394	−	0.744705i	$-0.267410\pi$
$601$	24.4908	+	4.87152i	0.999000	+	0.198713i	0.331606	+	0.943418i	$0.392410\pi$
$602$	11.0101	−	2.87326i	0.448737	−	0.117105i
$603$	−15.6627	−	37.8130i	−0.637832	−	1.53986i
$604$	14.4577	−	5.98858i	0.588276	−	0.243672i
$605$	7.67477	−	5.12812i	0.312024	−	0.208488i
$606$	−9.91955	−	1.97312i	−0.402954	−	0.0801526i
$607$	−25.1429	−	16.7999i	−1.02052	−	0.681888i	−0.0716074	−	0.997433i	$-0.522813\pi$
$607$	−25.1429	−	16.7999i	−1.02052	−	0.681888i	−0.948911	+	0.315544i	$0.897813\pi$
$608$	−3.85990	−	3.85990i	−0.156539	−	0.156539i
$609$	−0.681872	+	4.93046i	−0.0276308	+	0.199792i
$610$	2.36916	−	5.71965i	0.0959244	−	0.231582i
$611$		−	18.3578i		−	0.742677i
$612$	−9.45356	+	5.31553i	−0.382137	+	0.214868i
$613$	7.35484			0.297059			0.148530	−	0.988908i	$-0.452546\pi$
$613$	7.35484			0.297059			0.148530	+	0.988908i	$0.452546\pi$
$614$	−8.28964	+	20.0130i	−0.334543	+	0.807657i
$615$	14.5357	−	2.89133i	0.586137	−	0.116590i
$616$	4.30966	+	8.88484i	0.173641	+	0.357981i
$617$	27.4442	+	18.3376i	1.10486	+	0.738245i	0.967650	−	0.252297i	$-0.0811860\pi$
$617$	27.4442	+	18.3376i	1.10486	+	0.738245i	0.137212	+	0.990542i	$0.456186\pi$
$618$	−0.850823	+	4.27737i	−0.0342251	+	0.172061i
$619$	5.00571	+	7.49157i	0.201196	+	0.301112i	0.918324	−	0.395831i	$-0.129543\pi$
$619$	5.00571	+	7.49157i	0.201196	+	0.301112i	−0.717127	+	0.696942i	$0.754543\pi$
$620$	3.22276	+	7.78043i	0.129429	+	0.312470i
$621$	0.283049	+	0.683340i	0.0113584	+	0.0274215i
$622$	−4.91974	+	3.28727i	−0.197264	+	0.131807i
$623$	14.5305	−	24.7925i	0.582154	−	0.993292i
$624$	−1.34246	+	2.00913i	−0.0537413	+	0.0804295i
$625$	17.9531	−	17.9531i	0.718124	−	0.718124i
$626$	−5.85389	−	29.4295i	−0.233969	−	1.17624i
$627$	−4.73990	+	11.4431i	−0.189294	+	0.456995i
$628$	19.0658			0.760808
$629$	11.3725	+	5.77007i	0.453451	+	0.230068i
$630$	7.18140	−	20.7106i	0.286114	−	0.825132i
$631$	20.2424	+	8.38467i	0.805837	+	0.333789i	0.747292	−	0.664496i	$-0.231354\pi$
$631$	20.2424	+	8.38467i	0.805837	+	0.333789i	0.0585452	+	0.998285i	$0.481354\pi$
$632$	−0.0389854	−	0.195993i	−0.00155076	−	0.00779618i
$633$	8.09425	−	8.09425i	0.321718	−	0.321718i
$634$	−0.811082	−	0.541948i	−0.0322122	−	0.0215235i
$635$	32.5846	+	6.48148i	1.29308	+	0.257210i
$636$	1.31372	+	1.96613i	0.0520926	+	0.0779620i
$637$	26.7787	+	7.55130i	1.06101	+	0.299193i
$638$	−10.6708	+	4.41998i	−0.422460	+	0.174989i
$639$	−11.8730	−	17.7692i	−0.469688	−	0.702938i
$640$	0.614483	−	3.08922i	0.0242896	−	0.122112i
$641$	4.63227	−	6.93269i	0.182964	−	0.273825i	−0.728638	−	0.684899i	$-0.759846\pi$
$641$	4.63227	−	6.93269i	0.182964	−	0.273825i	0.911602	+	0.411074i	$0.134846\pi$
$642$	6.53259	+	6.53259i	0.257821	+	0.257821i
$643$	−5.16712	−	25.9769i	−0.203771	−	1.02443i	−0.938293	−	0.345842i	$-0.887593\pi$
$643$	−5.16712	−	25.9769i	−0.203771	−	1.02443i	0.734521	−	0.678586i	$-0.237407\pi$
$644$	0.379751	−	0.427364i	0.0149643	−	0.0168405i
$645$			8.23526i			0.324263i
$646$	2.68367	+	22.3463i	0.105587	+	0.879203i
$647$			1.67274i			0.0657624i	0.999459	+	0.0328812i	$0.0104683\pi$
$647$			1.67274i			0.0657624i	−0.999459	+	0.0328812i	$0.989532\pi$
$648$	−5.36806	−	2.22353i	−0.210877	−	0.0873483i
$649$	29.0572	−	5.77984i	1.14060	−	0.226879i
$650$	−13.8303	+	13.8303i	−0.542467	+	0.542467i
$651$	2.59565	+	3.42883i	0.101732	+	0.134386i
$652$	3.00474	−	15.1059i	0.117675	−	0.591592i
$653$	−31.9784	+	21.3673i	−1.25141	+	0.836167i	−0.991581	−	0.129487i	$-0.958667\pi$
$653$	−31.9784	+	21.3673i	−1.25141	+	0.836167i	−0.259831	+	0.965654i	$0.583667\pi$
$654$	5.74536	−	2.37981i	0.224662	−	0.0930579i
$655$	51.3606	−	21.2743i	2.00683	−	0.831254i
$656$	−6.43545	+	4.30003i	−0.251262	+	0.167888i
$657$	6.17325	−	31.0350i	0.240841	−	1.21079i
$658$	7.37550	+	9.74295i	0.287527	+	0.379820i
$659$	−22.1758	+	22.1758i	−0.863846	+	0.863846i	−0.991782	−	0.127936i	$-0.959165\pi$
$659$	−22.1758	+	22.1758i	−0.863846	+	0.863846i	0.127936	+	0.991782i	$0.459165\pi$
$660$	−7.00951	+	1.39428i	−0.272845	+	0.0542722i
$661$	−12.6432	−	5.23699i	−0.491764	−	0.203695i	0.123000	−	0.992407i	$-0.460749\pi$
$661$	−12.6432	−	5.23699i	−0.491764	−	0.203695i	−0.614764	+	0.788711i	$0.710749\pi$
$662$		−	2.79165i		−	0.108500i
$663$	9.47000	−	3.09493i	0.367784	−	0.120197i
$664$			14.3250i			0.555917i
$665$	−34.0046	−	30.2161i	−1.31864	−	1.17173i
$666$	1.58720	+	7.97942i	0.0615029	+	0.309196i
$667$	0.472832	+	0.472832i	0.0183081	+	0.0183081i
$668$	−6.90195	+	10.3295i	−0.267044	+	0.399660i
$669$	1.52726	−	7.67807i	0.0590474	−	0.296851i
$670$	−27.2279	−	40.7494i	−1.05191	−	1.57429i
$671$	6.77765	−	2.80739i	0.261648	−	0.108378i
$672$	−0.0947197	−	1.60565i	−0.00365389	−	0.0619392i
$673$	1.25085	+	1.87203i	0.0482168	+	0.0721616i	0.854795	−	0.518966i	$-0.173683\pi$
$673$	1.25085	+	1.87203i	0.0482168	+	0.0721616i	−0.806578	+	0.591128i	$0.798683\pi$
$674$	15.7999	+	3.14280i	0.608590	+	0.121056i
$675$	14.0050	+	9.35782i	0.539051	+	0.360183i
$676$	−1.97873	+	1.97873i	−0.0761051	+	0.0761051i
$677$	−0.377823	−	1.89945i	−0.0145209	−	0.0730016i	0.972845	−	0.231456i	$-0.0743489\pi$
$677$	−0.377823	−	1.89945i	−0.0145209	−	0.0730016i	−0.987366	+	0.158454i	$0.949349\pi$
$678$	2.86787	+	1.18791i	0.110140	+	0.0456214i
$679$	2.19392	+	0.760740i	0.0841950	+	0.0291945i
$680$	−9.86071	+	8.45108i	−0.378141	+	0.324084i
$681$	0.552844			0.0211850
$682$	−3.81889	+	9.21962i	−0.146233	+	0.353037i
$683$	0.00577370	+	0.0290263i	0.000220924	+	0.00111066i	0.980896	−	0.194535i	$-0.0623198\pi$
$683$	0.00577370	+	0.0290263i	0.000220924	+	0.00111066i	−0.980675	+	0.195646i	$0.937320\pi$
$684$	−10.1531	+	10.1531i	−0.388215	+	0.388215i
$685$	36.8484	−	55.1476i	1.40791	−	2.10708i
$686$	−17.2460	+	6.75104i	−0.658454	+	0.257756i
$687$	0.471600	−	0.315113i	0.0179927	−	0.0120223i
$688$	−1.64584	−	3.97341i	−0.0627470	−	0.151485i
$689$	5.91637	+	14.2834i	0.225396	+	0.544154i
$690$	0.229876	+	0.344034i	0.00875124	+	0.0130972i
$691$	−4.03578	+	20.2892i	−0.153528	+	0.771839i	0.824904	+	0.565273i	$0.191229\pi$
$691$	−4.03578	+	20.2892i	−0.153528	+	0.771839i	−0.978433	+	0.206567i	$0.933771\pi$
$692$	−10.4353	−	6.97262i	−0.396689	−	0.265059i
$693$	23.3709	−	11.3362i	0.887785	−	0.430627i
$694$	−18.6676	+	3.71322i	−0.708613	+	0.140952i
$695$	−10.9046	+	26.3260i	−0.413634	+	0.998600i
$696$	1.88127			0.0713095
$697$	31.8181	+	2.44933i	1.20520	+	0.0927749i
$698$			22.1138i			0.837021i
$699$	−0.748378	+	1.80674i	−0.0283062	+	0.0683373i
$700$	1.78357	−	12.8966i	0.0674126	−	0.487445i
$701$	−10.7736	−	10.7736i	−0.406912	−	0.406912i	0.473748	−	0.880660i	$-0.342901\pi$
$701$	−10.7736	−	10.7736i	−0.406912	−	0.406912i	−0.880660	+	0.473748i	$0.842901\pi$
$702$	11.3122	+	7.55859i	0.426953	+	0.285281i
$703$	16.5591	+	3.29381i	0.624539	+	0.124229i
$704$	3.10334	−	2.07359i	0.116962	−	0.0781513i
$705$	−8.17071	+	3.38442i	−0.307727	+	0.127465i
$706$	4.37781	+	10.5690i	0.164761	+	0.397768i
$707$	42.5897	−	11.1145i	1.60175	−	0.418003i
$708$	−4.73288	−	0.941429i	−0.177873	−	0.0353811i
$709$	11.5365	−	17.2656i	0.433262	−	0.648423i	−0.549024	−	0.835806i	$-0.685001\pi$
$709$	11.5365	−	17.2656i	0.433262	−	0.648423i	0.982287	+	0.187383i	$0.0600006\pi$
$710$	−18.0949	−	18.0949i	−0.679088	−	0.679088i
$711$	−0.515543	+	0.102548i	−0.0193344	+	0.00384585i
$712$	−10.0347	−	4.15652i	−0.376067	−	0.155772i
$713$	0.577749			0.0216369
$714$	−3.78254	+	5.44726i	−0.141558	+	0.203859i
$715$	−46.7266			−1.74747
$716$	0.444478	+	0.184109i	0.0166109	+	0.00688048i
$717$	−7.23471	+	1.43907i	−0.270185	+	0.0537432i
$718$	−26.2335	−	26.2335i	−0.979027	−	0.979027i
$719$	16.3123	−	24.4131i	0.608347	−	0.910455i	−0.391606	−	0.920133i	$-0.628081\pi$
$719$	16.3123	−	24.4131i	0.608347	−	0.910455i	0.999953	+	0.00967761i	$0.00308053\pi$
$720$	−8.12593	−	1.61635i	−0.302835	−	0.0602377i
$721$	−4.79264	−	18.3650i	−0.178487	−	0.683947i
$722$	4.13206	+	9.97568i	0.153779	+	0.371256i
$723$	12.6678	−	5.24716i	0.471119	−	0.195144i
$724$	14.5701	−	9.73542i	0.541493	−	0.361814i
$725$	14.9352	+	2.97079i	0.554678	+	0.110332i
$726$	−1.48131	−	0.989781i	−0.0549767	−	0.0367342i
$727$	5.90078	+	5.90078i	0.218848	+	0.218848i	0.808013	−	0.589165i	$-0.200543\pi$
$727$	5.90078	+	5.90078i	0.218848	+	0.218848i	−0.589165	+	0.808013i	$0.700543\pi$
$728$	1.44064	−	10.4170i	0.0533938	−	0.386078i
$729$	−3.45982	+	8.35274i	−0.128141	+	0.309361i
$730$		−	37.8903i		−	1.40238i
$731$	−4.78411	+	17.0750i	−0.176947	+	0.631543i
$732$	−1.19491			−0.0441652
$733$	4.05508	−	9.78982i	0.149778	−	0.361595i	−0.831128	−	0.556082i	$-0.812304\pi$
$733$	4.05508	−	9.78982i	0.149778	−	0.361595i	0.980905	+	0.194487i	$0.0623041\pi$
$734$	10.7777	−	2.14381i	0.397811	−	0.0791294i
$735$	−1.57594	−	13.3108i	−0.0581294	−	0.490977i
$736$	−0.179668	−	0.120051i	−0.00662267	−	0.00442513i
$737$	11.3297	−	56.9585i	0.417337	−	2.09809i
$738$	11.3109	+	16.9279i	0.416359	+	0.623126i
$739$	−9.84272	−	23.7624i	−0.362070	−	0.874115i	−0.994997	−	0.0999033i	$-0.968147\pi$
$739$	−9.84272	−	23.7624i	−0.362070	−	0.874115i	0.632927	−	0.774212i	$-0.281853\pi$
$740$	3.72809	+	9.00041i	0.137047	+	0.330862i
$741$	10.9673	−	7.32809i	0.402893	−	0.269204i
$742$	−8.87852	−	5.20357i	−0.325941	−	0.191029i
$743$	−7.72336	+	11.5588i	−0.283343	+	0.424052i	−0.945653	−	0.325177i	$-0.894576\pi$
$743$	−7.72336	+	11.5588i	−0.283343	+	0.424052i	0.662310	+	0.749230i	$0.269576\pi$
$744$	1.14936	−	1.14936i	0.0421374	−	0.0421374i
$745$	12.6676	+	63.6841i	0.464103	+	2.33321i
$746$	−7.95459	+	19.2041i	−0.291238	+	0.703111i
$747$	37.6807			1.37867
$748$	−15.3435	−	1.18113i	−0.561015	−	0.0431864i
$749$	−37.9874	−	13.1721i	−1.38803	−	0.481298i
$750$	−0.140034	−	0.0580041i	−0.00511333	−	0.00211801i
$751$	9.33936	+	46.9521i	0.340798	+	1.71331i	0.647980	+	0.761657i	$0.275614\pi$
$751$	9.33936	+	46.9521i	0.340798	+	1.71331i	−0.307182	+	0.951651i	$0.599386\pi$
$752$	3.26587	−	3.26587i	0.119094	−	0.119094i
$753$	2.12978	+	1.42307i	0.0776135	+	0.0518597i
$754$	12.0636	+	2.39960i	0.439330	+	0.0873881i
$755$	−27.3840	−	40.9831i	−0.996607	−	1.49153i
$756$	−9.04047	+	0.533312i	−0.328799	+	0.0193964i
$757$	−32.9799	+	13.6607i	−1.19868	+	0.496508i	−0.890571	−	0.454844i	$-0.849695\pi$
$757$	−32.9799	+	13.6607i	−1.19868	+	0.496508i	−0.308105	+	0.951352i	$0.599695\pi$
$758$	4.79444	+	7.17539i	0.174142	+	0.260622i
$759$	−0.0956534	+	0.480882i	−0.00347200	+	0.0174549i
$760$	−9.55221	+	14.2959i	−0.346495	+	0.518567i
$761$	−25.1209	−	25.1209i	−0.910630	−	0.910630i	0.0856914	−	0.996322i	$-0.472690\pi$
$761$	−25.1209	−	25.1209i	−0.910630	−	0.910630i	−0.996322	+	0.0856914i	$0.972690\pi$
$762$	−1.25099	−	6.28917i	−0.0453187	−	0.227833i
$763$	−17.9771	+	20.2311i	−0.650815	+	0.732414i
$764$		−	18.7939i		−	0.679939i
$765$	22.2299	+	25.9378i	0.803723	+	0.937782i
$766$			10.9541i			0.395786i
$767$	−29.1486	−	12.0737i	−1.05249	−	0.435958i
$768$	−0.596251	+	0.118602i	−0.0215154	+	0.00427967i
$769$	20.5717	−	20.5717i	0.741833	−	0.741833i	−0.231098	−	0.972931i	$-0.574232\pi$
$769$	20.5717	−	20.5717i	0.741833	−	0.741833i	0.972931	+	0.231098i	$0.0742317\pi$
$770$	24.7990	−	18.7731i	0.893693	−	0.676534i
$771$	−2.36486	+	11.8889i	−0.0851682	+	0.428170i
$772$	−12.0893	+	8.07779i	−0.435102	+	0.290726i
$773$	7.82740	−	3.24222i	0.281532	−	0.116614i	−0.237449	−	0.971400i	$-0.576311\pi$
$773$	7.82740	−	3.24222i	0.281532	−	0.116614i	0.518981	+	0.854786i	$0.326311\pi$
$774$	−10.4517	+	4.32924i	−0.375679	+	0.155611i
$775$	10.9396	−	7.30958i	0.392961	−	0.262568i
$776$	0.171223	−	0.860797i	0.00614655	−	0.0309008i
$777$	3.00265	+	3.96647i	0.107720	+	0.142296i
$778$	8.56369	−	8.56369i	0.307023	−	0.307023i
$779$	41.4379	−	8.24250i	1.48467	−	0.295318i
$780$	7.03155	+	2.91256i	0.251770	+	0.104286i
$781$		−	30.3235i		−	1.08506i
$782$	0.276767	+	0.846865i	0.00989717	+	0.0302838i
$783$		−	10.5924i		−	0.378540i
$784$	3.42057	+	6.10735i	0.122163	+	0.218119i
$785$	−11.7156	−	58.8983i	−0.418148	−	2.10217i
$786$	−7.58719	−	7.58719i	−0.270626	−	0.270626i
$787$	−13.6832	+	20.4783i	−0.487753	+	0.729974i	−0.990955	−	0.134195i	$-0.957155\pi$
$787$	−13.6832	+	20.4783i	−0.487753	+	0.729974i	0.503202	+	0.864169i	$0.332155\pi$
$788$	2.96674	−	14.9148i	0.105686	−	0.531318i
$789$	−1.02889	−	1.53985i	−0.0366296	−	0.0548201i
$790$	−0.581509	+	0.240869i	−0.0206891	+	0.00856972i
$791$	−13.4860	+	0.795561i	−0.479507	+	0.0282869i
$792$	−5.45440	−	8.16309i	−0.193814	−	0.290063i
$793$	−7.66231	−	1.52413i	−0.272097	−	0.0541234i
$794$	29.5839	+	19.7673i	1.04989	+	0.701516i
$795$	5.26653	−	5.26653i	0.186785	−	0.186785i
$796$	−3.28063	−	16.4928i	−0.116279	−	0.584573i
$797$	50.5039	+	20.9194i	1.78894	+	0.741003i	0.990257	+	0.139249i	$0.0444689\pi$
$797$	50.5039	+	20.9194i	1.78894	+	0.741003i	0.798682	+	0.601754i	$0.205531\pi$
$798$	−2.87644	+	8.29546i	−0.101825	+	0.293656i
$799$	−18.9073	+	2.27066i	−0.668892	+	0.0803302i
$800$	−4.92084			−0.173978
$801$	−10.9334	+	26.3955i	−0.386312	+	0.932640i
$802$	2.07249	+	10.4191i	0.0731822	+	0.367912i
$803$	31.7484	−	31.7484i	1.12038	−	1.12038i
$804$	−5.25527	+	7.86507i	−0.185339	+	0.277380i
$805$	−1.55357	−	0.910524i	−0.0547561	−	0.0320918i
$806$	8.83621	−	5.90417i	0.311242	−	0.207965i
$807$	−6.98277	−	16.8579i	−0.245805	−	0.593426i
$808$	−6.36652	−	15.3701i	−0.223973	−	0.540720i
$809$	−10.1006	−	15.1167i	−0.355119	−	0.531473i	0.610302	−	0.792169i	$-0.291048\pi$
$809$	−10.1006	−	15.1167i	−0.355119	−	0.531473i	−0.965421	+	0.260696i	$0.916048\pi$
$810$	−3.57036	+	17.9494i	−0.125450	+	0.630679i
$811$	−30.3949	−	20.3092i	−1.06731	−	0.713153i	−0.107613	−	0.994193i	$-0.534321\pi$
$811$	−30.3949	−	20.3092i	−1.06731	−	0.713153i	−0.959696	+	0.281040i	$0.909321\pi$
$812$	−7.36653	+	3.57319i	−0.258514	+	0.125394i
$813$	6.46125	−	1.28522i	0.226606	−	0.0450747i
$814$	−4.41770	+	10.6653i	−0.154840	+	0.373817i
$815$	−48.5117			−1.69929
$816$	2.23532	+	1.13413i	0.0782517	+	0.0397026i
$817$			23.4768i			0.821348i
$818$	−3.69529	+	8.92122i	−0.129203	+	0.311923i
$819$	−27.4010	−	3.78950i	−0.957467	−	0.132416i
$820$	17.2382	+	17.2382i	0.601984	+	0.601984i
$821$	18.7123	+	12.5032i	0.653063	+	0.436363i	0.837467	−	0.546488i	$-0.184035\pi$
$821$	18.7123	+	12.5032i	0.653063	+	0.436363i	−0.184404	+	0.982851i	$0.559035\pi$
$822$	−12.5555	−	2.49745i	−0.437925	−	0.0871086i
$823$	−8.56470	+	5.72275i	−0.298547	+	0.199483i	−0.695817	−	0.718219i	$-0.744958\pi$
$823$	−8.56470	+	5.72275i	−0.298547	+	0.199483i	0.397270	+	0.917702i	$0.369958\pi$
$824$	−6.62771	+	2.74529i	−0.230887	+	0.0956365i
$825$	4.27286	+	10.3156i	0.148762	+	0.359143i
$826$	20.3207	−	5.30302i	0.707048	−	0.184516i
$827$	53.9329	+	10.7279i	1.87543	+	0.373046i	0.994894	−	0.100930i	$-0.0321819\pi$
$827$	53.9329	+	10.7279i	1.87543	+	0.373046i	0.880537	+	0.473977i	$0.157182\pi$
$828$	−0.315783	+	0.472603i	−0.0109742	+	0.0164241i
$829$	14.2597	+	14.2597i	0.495261	+	0.495261i	0.909959	−	0.414698i	$-0.136113\pi$
$829$	14.2597	+	14.2597i	0.495261	+	0.495261i	−0.414698	+	0.909959i	$0.636113\pi$
$830$	44.2530	−	8.80247i	1.53604	−	0.305538i
$831$	−9.58726	−	3.97117i	−0.332578	−	0.137758i
$832$	−3.97471			−0.137798
$833$	4.46510	−	28.5143i	0.154707	−	0.987960i
$834$	5.49984			0.190444
$835$	36.1512	+	14.9743i	1.25106	+	0.518207i
$836$	−19.9824	+	3.97475i	−0.691107	+	0.137470i
$837$	−6.47135	−	6.47135i	−0.223683	−	0.223683i
$838$	3.94240	−	5.90022i	0.136188	−	0.203820i
$839$	9.99504	+	1.98814i	0.345067	+	0.0686381i	0.364582	−	0.931171i	$-0.381212\pi$
$839$	9.99504	+	1.98814i	0.345067	+	0.0686381i	−0.0195144	+	0.999810i	$0.506212\pi$
$840$	−4.90199	+	1.27925i	−0.169135	+	0.0441384i
$841$	7.43317	+	17.9453i	0.256316	+	0.618802i
$842$	−7.80319	+	3.23219i	−0.268916	+	0.111389i
$843$	−9.46799	+	6.32631i	−0.326095	+	0.217890i
$844$	18.4676	+	3.67343i	0.635681	+	0.126445i
$845$	7.32863	+	4.89684i	0.252113	+	0.168456i
$846$	−8.59061	−	8.59061i	−0.295351	−	0.295351i
$847$	7.68033	+	1.06217i	0.263899	+	0.0364967i
$848$	−1.48850	+	3.59356i	−0.0511154	+	0.123403i
$849$		−	4.42895i		−	0.152001i
$850$	15.9549	+	12.5336i	0.547249	+	0.429899i
$851$	0.668341			0.0229104
$852$	−1.89013	+	4.56317i	−0.0647547	+	0.156332i
$853$	−46.1843	+	9.18663i	−1.58132	+	0.314544i	−0.906097	−	0.423070i	$-0.860953\pi$
$853$	−46.1843	+	9.18663i	−1.58132	+	0.314544i	−0.675223	+	0.737614i	$0.735953\pi$
$854$	4.67893	−	2.26955i	0.160110	−	0.0776624i
$855$	37.6042	+	25.1263i	1.28604	+	0.859302i
$856$	−2.96470	+	14.9046i	−0.101331	+	0.509427i
$857$	−2.25105	−	3.36893i	−0.0768944	−	0.115081i	0.791029	−	0.611779i	$-0.209546\pi$
$857$	−2.25105	−	3.36893i	−0.0768944	−	0.115081i	−0.867923	+	0.496698i	$0.834546\pi$
$858$	3.45132	+	8.33221i	0.117826	+	0.284457i
$859$	2.48840	+	6.00754i	0.0849033	+	0.204975i	0.960629	−	0.277834i	$-0.0896166\pi$
$859$	2.48840	+	6.00754i	0.0849033	+	0.204975i	−0.875726	+	0.482809i	$0.839617\pi$
$860$	−11.2634	+	7.52594i	−0.384078	+	0.256633i
$861$	10.7404	+	6.29477i	0.366031	+	0.214525i
$862$	15.6952	−	23.4895i	0.534580	−	0.800055i
$863$	−6.63245	+	6.63245i	−0.225771	+	0.225771i	−0.810923	−	0.585152i	$-0.801035\pi$
$863$	−6.63245	+	6.63245i	−0.225771	+	0.225771i	0.585152	+	0.810923i	$0.301035\pi$
$864$	0.667778	+	3.35714i	0.0227183	+	0.114212i
$865$	−15.1276	+	36.5214i	−0.514355	+	1.24176i
$866$	−33.3876			−1.13456
$867$	−4.35890	−	9.37066i	−0.148036	−	0.318244i
$868$	−2.31752	+	6.68357i	−0.0786618	+	0.226855i
$869$	−0.689073	−	0.285424i	−0.0233752	−	0.00968233i
$870$	−1.15601	−	5.81166i	−0.0391925	−	0.197034i
$871$	−43.7312	+	43.7312i	−1.48178	+	1.48178i
$872$	8.50537	+	5.68310i	0.288028	+	0.192454i
$873$	−2.26426	−	0.450388i	−0.0766334	−	0.0152433i
$874$	0.655323	+	0.980759i	0.0221666	+	0.0331747i
$875$	0.658504	−	0.0388462i	0.0222615	−	0.00131324i
$876$	−6.75654	+	2.79865i	−0.228282	+	0.0945576i
$877$	−2.70145	−	4.04301i	−0.0912215	−	0.136523i	0.783052	−	0.621956i	$-0.213662\pi$
$877$	−2.70145	−	4.04301i	−0.0912215	−	0.136523i	−0.874274	+	0.485434i	$0.838662\pi$
$878$	2.46874	−	12.4112i	0.0833160	−	0.418858i
$879$	−9.14611	+	13.6881i	−0.308491	+	0.461689i
$880$	−8.31272	−	8.31272i	−0.280222	−	0.280222i
$881$	1.82698	+	9.18483i	0.0615524	+	0.309445i	0.999281	−	0.0379251i	$-0.0120748\pi$
$881$	1.82698	+	9.18483i	0.0615524	+	0.309445i	−0.937728	+	0.347370i	$0.887075\pi$
$882$	16.0649	−	8.99754i	0.540932	−	0.302963i
$883$		−	31.9578i		−	1.07547i	−0.843115	−	0.537733i	$-0.819281\pi$
$883$		−	31.9578i		−	1.07547i	0.843115	−	0.537733i	$-0.180719\pi$
$884$	12.8873	+	10.1238i	0.433445	+	0.340499i
$885$			15.1994i			0.510922i
$886$	−2.10170	−	0.870553i	−0.0706080	−	0.0292468i
$887$	−28.6490	+	5.69864i	−0.961940	+	0.191342i	−0.650991	−	0.759085i	$-0.725647\pi$
$887$	−28.6490	+	5.69864i	−0.961940	+	0.191342i	−0.310948	+	0.950427i	$0.600647\pi$
$888$	1.32958	−	1.32958i	0.0446176	−	0.0446176i
$889$	16.8438	+	22.2505i	0.564924	+	0.746258i
$890$	−6.67421	+	33.5535i	−0.223720	+	1.12472i
$891$	−18.0315	+	12.0483i	−0.604079	+	0.403633i
$892$	11.8970	−	4.92790i	0.398341	−	0.164998i
$893$	−23.2927	+	9.64817i	−0.779462	+	0.322864i
$894$	10.4204	−	6.96270i	0.348511	−	0.232867i
$895$	0.295628	−	1.48622i	0.00988175	−	0.0496789i
$896$	2.10948	−	1.59690i	0.0704729	−	0.0533486i
$897$	0.369209	−	0.369209i	0.0123275	−	0.0123275i
$898$	−13.8308	+	2.75112i	−0.461540	+	0.0918060i
$899$	−7.64409	−	3.16629i	−0.254945	−	0.105602i
$900$			12.9439i			0.431462i
$901$	13.9791	−	7.86017i	0.465713	−	0.261860i
$902$			28.8879i			0.961863i
$903$	−4.59490	+	5.17101i	−0.152909	+	0.172080i
$904$	0.996149	+	5.00798i	0.0331314	+	0.166563i
$905$	−39.0279	−	39.0279i	−1.29733	−	1.29733i
$906$	−5.28541	+	7.91017i	−0.175596	+	0.262798i
$907$	4.31523	−	21.6941i	0.143285	−	0.720342i	−0.840617	−	0.541631i	$-0.817807\pi$
$907$	4.31523	−	21.6941i	0.143285	−	0.720342i	0.983902	−	0.178712i	$-0.0571929\pi$
$908$	0.505226	+	0.756124i	0.0167665	+	0.0250929i
$909$	−40.4299	+	16.7466i	−1.34097	+	0.555450i
$910$	−33.0655	+	1.95059i	−1.09611	+	0.0646613i
$911$	5.73283	+	8.57979i	0.189937	+	0.284261i	0.914200	−	0.405263i	$-0.132820\pi$
$911$	5.73283	+	8.57979i	0.189937	+	0.284261i	−0.724263	+	0.689524i	$0.757820\pi$
$912$	3.25477	+	0.647414i	0.107776	+	0.0214380i
$913$	44.4554	+	29.7041i	1.47126	+	0.983064i
$914$	28.3027	−	28.3027i	0.936171	−	0.936171i
$915$	0.734253	+	3.69134i	0.0242737	+	0.122032i
$916$	0.861960	+	0.357036i	0.0284800	+	0.0117968i
$917$	44.1200	+	15.2986i	1.45697	+	0.505203i
$918$	6.38565	−	12.5858i	0.210758	−	0.415392i
$919$	−50.9276			−1.67995			−0.839974	−	0.542627i	$-0.817430\pi$
$919$	−50.9276			−1.67995			−0.839974	+	0.542627i	$0.817430\pi$
$920$	−0.260459	+	0.628804i	−0.00858708	+	0.0207310i
$921$	−2.56914	−	12.9159i	−0.0846559	−	0.425594i
$922$	−5.52429	+	5.52429i	−0.181933	+	0.181933i
$923$	−17.9408	+	26.8503i	−0.590528	+	0.883787i
$924$	−5.17929	−	3.03550i	−0.170386	−	0.0998608i
$925$	12.6549	−	8.45573i	0.416090	−	0.278023i
$926$	−10.9555	−	26.4489i	−0.360020	−	0.869166i
$927$	7.22125	+	17.4336i	0.237177	+	0.572596i
$928$	1.71924	+	2.57302i	0.0564367	+	0.0844635i
$929$	4.67301	−	23.4928i	0.153316	−	0.770774i	−0.825238	−	0.564785i	$-0.808959\pi$
$929$	4.67301	−	23.4928i	0.153316	−	0.770774i	0.978554	−	0.205989i	$-0.0660410\pi$
$930$	−4.25687	−	2.84435i	−0.139588	−	0.0932698i
$931$	−4.49263	−	37.9460i	−0.147240	−	1.24363i
$932$	−3.15500	+	0.627569i	−0.103345	+	0.0205567i
$933$	1.37655	−	3.32328i	0.0450662	−	0.108799i
$934$	14.1686			0.463611
$935$	5.77957	+	48.1252i	0.189012	+	1.57386i
$936$			10.4552i			0.341738i
$937$	−12.1736	+	29.3896i	−0.397694	+	0.960118i	0.590518	+	0.807024i	$0.298923\pi$
$937$	−12.1736	+	29.3896i	−0.397694	+	0.960118i	−0.988212	+	0.153093i	$0.951077\pi$
$938$	5.63964	−	40.7789i	0.184141	−	1.33148i
$939$	12.8988	+	12.8988i	0.420936	+	0.420936i
$940$	−12.0958	−	8.08216i	−0.394522	−	0.263611i
$941$	−0.528276	−	0.105081i	−0.0172213	−	0.00342553i	0.186472	−	0.982460i	$-0.440295\pi$
$941$	−0.528276	−	0.105081i	−0.0172213	−	0.00342553i	−0.203693	+	0.979035i	$0.565295\pi$
$942$	−9.63733	+	6.43946i	−0.314001	+	0.209809i
$943$	1.54516	−	0.640026i	0.0503173	−	0.0208421i
$944$	−3.03764	−	7.33351i	−0.0988667	−	0.238685i
$945$	7.20273	+	27.6002i	0.234305	+	0.897836i
$946$	−15.7436	−	3.13161i	−0.511870	−	0.101817i
$947$	−19.7874	+	29.6139i	−0.643004	+	0.962324i	0.356602	+	0.934257i	$0.383935\pi$
$947$	−19.7874	+	29.6139i	−0.643004	+	0.962324i	−0.999606	+	0.0280675i	$0.991065\pi$
$948$	0.0859027	+	0.0859027i	0.00278999	+	0.00278999i
$949$	−46.8957	+	9.32814i	−1.52230	+	0.302804i
$950$	24.8168	+	10.2794i	0.805163	+	0.333509i
$951$	0.593026			0.0192302
$952$	−10.9070	−	0.195301i	−0.353497	−	0.00632975i
$953$	−7.00541			−0.226927			−0.113464	−	0.993542i	$-0.536195\pi$
$953$	−7.00541			−0.226927			−0.113464	+	0.993542i	$0.536195\pi$
$954$	9.45257	+	3.91538i	0.306038	+	0.126765i
$955$	−58.0583	+	11.5485i	−1.87872	+	0.373701i
$956$	−8.57979	−	8.57979i	−0.277490	−	0.277490i
$957$	3.90099	−	5.83824i	0.126101	−	0.188724i
$958$	0.0603537	+	0.0120051i	0.00194994	+	0.000387867i
$959$	53.9074	−	14.0680i	1.74076	−	0.454280i
$960$	0.732773	+	1.76907i	0.0236501	+	0.0570965i
$961$	22.0357	−	9.12749i	0.710830	−	0.294435i
$962$	10.2217	−	6.82995i	0.329562	−	0.220206i
$963$	39.2052	+	7.79840i	1.26337	+	0.251300i
$964$	18.7532	+	12.5305i	0.604000	+	0.403580i
$965$	32.3827	+	32.3827i	1.04244	+	1.04244i
$966$	−0.0476137	+	0.344283i	−0.00153195	+	0.0110771i
$967$	−5.14961	+	12.4323i	−0.165600	+	0.399794i	−0.984795	−	0.173721i	$-0.944421\pi$
$967$	−5.14961	+	12.4323i	−0.165600	+	0.399794i	0.819195	+	0.573516i	$0.194421\pi$
$968$		−	2.93052i		−	0.0941905i
$969$	−8.90398	−	10.3891i	−0.286037	−	0.333748i
$970$	−2.76440			−0.0887596
$971$	2.27867	−	5.50120i	0.0731261	−	0.176542i	−0.883090	−	0.469204i	$-0.844541\pi$
$971$	2.27867	−	5.50120i	0.0731261	−	0.176542i	0.956216	+	0.292662i	$0.0945410\pi$
$972$	13.5359	−	2.69245i	0.434163	−	0.0863604i
$973$	−21.5358	+	10.4461i	−0.690406	+	0.334886i
$974$	1.41467	+	0.945249i	0.0453288	+	0.0302877i
$975$	2.31973	−	11.6620i	0.0742907	−	0.373484i
$976$	−1.09199	−	1.63428i	−0.0349538	−	0.0523120i
$977$	−2.54352	−	6.14059i	−0.0813743	−	0.196455i	0.877956	−	0.478742i	$-0.158907\pi$
$977$	−2.54352	−	6.14059i	−0.0813743	−	0.196455i	−0.959330	+	0.282287i	$0.908907\pi$
$978$	3.58317	+	8.65053i	0.114577	+	0.276613i
$979$	−33.7070	+	22.5223i	−1.07728	+	0.719816i
$980$	16.7650	−	14.3198i	0.535539	−	0.457428i
$981$	14.9489	−	22.3727i	0.477283	−	0.714304i
$982$	−21.4380	+	21.4380i	−0.684114	+	0.684114i
$983$	−1.11993	−	5.63026i	−0.0357202	−	0.179577i	0.958807	−	0.284060i	$-0.0916814\pi$
$983$	−1.11993	−	5.63026i	−0.0357202	−	0.179577i	−0.994527	+	0.104482i	$0.966681\pi$
$984$	1.80064	−	4.34714i	0.0574024	−	0.138582i
$985$	−47.8981			−1.52616
$986$	0.979288	−	12.7215i	0.0311869	−	0.405135i
$987$	−7.01882	−	2.43377i	−0.223412	−	0.0774678i
$988$	20.0453	+	8.30302i	0.637725	+	0.264154i
$989$	0.181305	+	0.911480i	0.00576515	+	0.0289834i
$990$	−21.8659	+	21.8659i	−0.694944	+	0.694944i
$991$	−3.87351	−	2.58819i	−0.123046	−	0.0822167i	0.492524	−	0.870299i	$-0.336074\pi$
$991$	−3.87351	−	2.58819i	−0.123046	−	0.0822167i	−0.615570	+	0.788082i	$0.711074\pi$
$992$	2.62233	+	0.521615i	0.0832592	+	0.0165613i
$993$	0.942877	+	1.41111i	0.0299213	+	0.0447804i
$994$	−1.26585	−	21.4581i	−0.0401502	−	0.680609i
$995$	−48.9340	+	20.2691i	−1.55131	+	0.642575i
$996$	−4.83826	−	7.24096i	−0.153306	−	0.229439i
$997$	−6.37941	+	32.0715i	−0.202038	+	1.01571i	0.738041	+	0.674756i	$0.235751\pi$
$997$	−6.37941	+	32.0715i	−0.202038	+	1.01571i	−0.940079	+	0.340958i	$0.889249\pi$
$998$	−1.35397	+	2.02636i	−0.0428591	+	0.0641433i
$999$	−7.48607	−	7.48607i	−0.236849	−	0.236849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	238.2.p.b.181.4	yes	48
7.6	odd	2	inner	238.2.p.b.181.3	yes	48
17.14	odd	16	inner	238.2.p.b.167.3	✓	48
119.48	even	16	inner	238.2.p.b.167.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.p.b.167.3	✓	48	17.14	odd	16	inner
238.2.p.b.167.4	yes	48	119.48	even	16	inner
238.2.p.b.181.3	yes	48	7.6	odd	2	inner
238.2.p.b.181.4	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 238 = 2 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	238.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{2} +(0.596251 - 0.118602i) q^{3} +(0.707107 + 0.707107i) q^{4} +(1.74990 - 2.61891i) q^{5} +(-0.596251 - 0.118602i) q^{6} +(2.56001 - 0.668077i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-2.43019 + 1.00662i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{2} +(0.596251 - 0.118602i) q^{3} +(0.707107 + 0.707107i) q^{4} +(1.74990 - 2.61891i) q^{5} +(-0.596251 - 0.118602i) q^{6} +(2.56001 - 0.668077i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-2.43019 + 1.00662i) q^{9} +(-2.61891 + 1.74990i) q^{10} +(-3.66064 - 0.728148i) q^{11} +(0.505478 + 0.337749i) q^{12} +(2.81055 + 2.81055i) q^{13} +(-2.62081 - 0.362452i) q^{14} +(0.732773 - 1.76907i) q^{15} +1.00000i q^{16} +(2.54704 - 3.24231i) q^{17} +2.63042 q^{18} +(2.08896 - 5.04320i) q^{19} +(3.08922 - 0.614483i) q^{20} +(1.44718 - 0.701964i) q^{21} +(3.10334 + 2.07359i) q^{22} +(0.0421562 - 0.211933i) q^{23} +(-0.337749 - 0.505478i) q^{24} +(-1.88313 - 4.54627i) q^{25} +(-1.52106 - 3.67216i) q^{26} +(-2.84605 + 1.90167i) q^{27} +(2.28261 + 1.33780i) q^{28} +(-1.71924 + 2.57302i) q^{29} +(-1.35399 + 1.35399i) q^{30} +(0.521615 + 2.62233i) q^{31} +(0.382683 - 0.923880i) q^{32} -2.26902 q^{33} +(-3.59394 + 2.02079i) q^{34} +(2.73013 - 7.87352i) q^{35} +(-2.43019 - 1.00662i) q^{36} +(0.603404 + 3.03352i) q^{37} +(-3.85990 + 3.85990i) q^{38} +(2.00913 + 1.34246i) q^{39} +(-3.08922 - 0.614483i) q^{40} +(4.30003 + 6.43545i) q^{41} +(-1.60565 + 0.0947197i) q^{42} +(-3.97341 + 1.64584i) q^{43} +(-2.07359 - 3.10334i) q^{44} +(-1.61635 + 8.12593i) q^{45} +(-0.120051 + 0.179668i) q^{46} +(-3.26587 - 3.26587i) q^{47} +(0.118602 + 0.596251i) q^{48} +(6.10735 - 3.42057i) q^{49} +4.92084i q^{50} +(1.13413 - 2.23532i) q^{51} +3.97471i q^{52} +(3.59356 + 1.48850i) q^{53} +(3.35714 - 0.667778i) q^{54} +(-8.31272 + 8.31272i) q^{55} +(-1.59690 - 2.10948i) q^{56} +(0.647414 - 3.25477i) q^{57} +(2.57302 - 1.71924i) q^{58} +(-7.33351 + 3.03764i) q^{59} +(1.76907 - 0.732773i) q^{60} +(-1.63428 + 1.09199i) q^{61} +(0.521615 - 2.62233i) q^{62} +(-5.54882 + 4.20051i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(12.2787 - 2.44239i) q^{65} +(2.09631 + 0.868318i) q^{66} +15.5597i q^{67} +(4.09369 - 0.491629i) q^{68} -0.131365i q^{69} +(-5.53538 + 6.22940i) q^{70} +(1.58501 + 7.96838i) q^{71} +(1.85999 + 1.85999i) q^{72} +(-6.68332 + 10.0023i) q^{73} +(0.603404 - 3.03352i) q^{74} +(-1.66201 - 2.48738i) q^{75} +(5.04320 - 2.08896i) q^{76} +(-9.85776 + 0.581525i) q^{77} +(-1.34246 - 2.00913i) q^{78} +(0.195993 + 0.0389854i) q^{79} +(2.61891 + 1.74990i) q^{80} +(4.10854 - 4.10854i) q^{81} +(-1.50997 - 7.59113i) q^{82} +(-13.2346 - 5.48194i) q^{83} +(1.51967 + 0.526945i) q^{84} +(-4.03425 - 12.3442i) q^{85} +4.30078 q^{86} +(-0.719933 + 1.73807i) q^{87} +(0.728148 + 3.66064i) q^{88} +(7.68024 - 7.68024i) q^{89} +(4.60297 - 6.88883i) q^{90} +(9.07270 + 5.31738i) q^{91} +(0.179668 - 0.120051i) q^{92} +(0.622027 + 1.50171i) q^{93} +(1.76748 + 4.26707i) q^{94} +(-9.55221 - 14.2959i) q^{95} +(0.118602 - 0.596251i) q^{96} +(0.729748 + 0.487602i) q^{97} +(-6.95145 + 0.823018i) q^{98} +(9.62903 - 1.91533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 16 q^{11} - 8 q^{14} + 64 q^{15} - 80 q^{18} - 48 q^{21} + 16 q^{22} - 16 q^{25} + 8 q^{28} + 32 q^{29} + 16 q^{39} - 24 q^{42} - 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 32 q^{51} - 48 q^{53} + 64 q^{57} + 16 q^{58} + 32 q^{60} - 104 q^{63} - 48 q^{65} + 16 q^{70} - 112 q^{71} - 16 q^{72} - 40 q^{77} - 64 q^{78} + 32 q^{79} + 112 q^{81} - 176 q^{85} + 32 q^{86} + 16 q^{88} + 80 q^{91} - 32 q^{93} - 32 q^{95} - 96 q^{99}+O(q^{100}) \) 48 * q - 16 * q^11 - 8 * q^14 + 64 * q^15 - 80 * q^18 - 48 * q^21 + 16 * q^22 - 16 * q^25 + 8 * q^28 + 32 * q^29 + 16 * q^39 - 24 * q^42 - 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 32 * q^51 - 48 * q^53 + 64 * q^57 + 16 * q^58 + 32 * q^60 - 104 * q^63 - 48 * q^65 + 16 * q^70 - 112 * q^71 - 16 * q^72 - 40 * q^77 - 64 * q^78 + 32 * q^79 + 112 * q^81 - 176 * q^85 + 32 * q^86 + 16 * q^88 + 80 * q^91 - 32 * q^93 - 32 * q^95 - 96 * q^99

Introduction

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