LMFDB - Embedded newform 238.2.p.b.167.3

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			167.3
Character	$\chi$	$=$	238.167
Dual form			238.2.p.b.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 + 0.382683i) q^{2} +(-0.596251 - 0.118602i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.74990 - 2.61891i) q^{5} +(0.596251 - 0.118602i) q^{6} +(1.59690 + 2.10948i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.43019 - 1.00662i) q^{9} +O(q^{10})$	\(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} +(1.59690 + 2.10948i) 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} +(-2.28261 - 1.33780i) 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} +(-0.701964 - 1.44718i) 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} +(2.62081 + 0.362452i) 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} +(1.20234 + 1.06839i) 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} +(-1.89983 + 6.73726i) 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} +(-2.56001 + 0.668077i) 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} +(-1.75732 - 6.73391i) 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} +(0.490749 + 8.31896i) 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} +(-7.38169 - 6.55929i) 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} +(-10.4170 - 1.44064i) 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} +(-0.823018 - 6.95145i) 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 $\left(\mathbb{Z}/238\mathbb{Z}\right)^\times$.

$n$	$71$	$171$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$-1$

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	$-0.493653\pi$
$3$	−0.596251	−	0.118602i	−0.344246	−	0.0684748i	−0.364186	+	0.931326i	$0.618653\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	−1.74990	−	2.61891i	−0.782579	−	1.17121i	−0.981550	−	0.191207i	$-0.938760\pi$
$5$	−1.74990	−	2.61891i	−0.782579	−	1.17121i	0.198971	−	0.980005i	$-0.436240\pi$
$6$	0.596251	−	0.118602i	0.243419	−	0.0484190i
$7$	1.59690	+	2.10948i	0.603571	+	0.797310i
$7$	1.59690	+	2.10948i	0.603571	+	0.797310i
$8$	−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	−0.713140	−	0.701022i	$-0.752728\pi$
$11$	−3.66064	+	0.728148i	−1.10373	+	0.219545i	−0.390586	+	0.920566i	$0.627728\pi$
$12$	−0.505478	+	0.337749i	−0.145919	+	0.0974998i
$13$	−2.81055	+	2.81055i	−0.779506	+	0.779506i	−0.979747	−	0.200241i	$-0.935827\pi$
$13$	−2.81055	+	2.81055i	−0.779506	+	0.779506i	0.200241	+	0.979747i	$0.435827\pi$
$14$	−2.28261	−	1.33780i	−0.610052	−	0.357542i
$15$	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	−0.959966	−	0.280118i	$-0.909627\pi$
$19$	−2.08896	−	5.04320i	−0.479240	−	1.15699i	0.480725	−	0.876871i	$-0.340373\pi$
$20$	−3.08922	−	0.614483i	−0.690770	−	0.137403i
$21$	−0.701964	−	1.44718i	−0.153181	−	0.315800i
$22$	3.10334	−	2.07359i	0.661635	−	0.442091i
$23$	0.0421562	+	0.211933i	0.00879017	+	0.0441912i	0.984931	−	0.172945i	$-0.0553284\pi$
$23$	0.0421562	+	0.211933i	0.00879017	+	0.0441912i	−0.976141	+	0.217136i	$0.930328\pi$
$24$	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
$28$	2.62081	+	0.362452i	0.495286	+	0.0684970i
$29$	−1.71924	−	2.57302i	−0.319254	−	0.477798i	0.636783	−	0.771043i	$-0.280265\pi$
$29$	−1.71924	−	2.57302i	−0.319254	−	0.477798i	−0.956037	+	0.293245i	$0.905265\pi$
$30$	−1.35399	−	1.35399i	−0.247203	−	0.247203i
$31$	−0.521615	+	2.62233i	−0.0936847	+	0.470985i	0.905252	+	0.424876i	$0.139682\pi$
$31$	−0.521615	+	2.62233i	−0.0936847	+	0.470985i	−0.998936	+	0.0461092i	$0.985318\pi$
$32$	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	−0.898959	−	0.438034i	$-0.855675\pi$
$37$	0.603404	−	3.03352i	0.0991990	−	0.498707i	0.998158	−	0.0606736i	$-0.0193249\pi$
$38$	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	0.326652	+	0.945145i	$0.394080\pi$
$41$	−4.30003	+	6.43545i	−0.671552	+	1.00505i	−0.998204	+	0.0599042i	$0.980920\pi$
$42$	1.20234	+	1.06839i	0.185525	+	0.164856i
$43$	−3.97341	−	1.64584i	−0.605939	−	0.250988i	0.0585521	−	0.998284i	$-0.481352\pi$
$43$	−3.97341	−	1.64584i	−0.605939	−	0.250988i	−0.664491	+	0.747296i	$0.731352\pi$
$44$	−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	$-0.640639\pi$
$47$	3.26587	−	3.26587i	0.476377	−	0.476377i	0.903971	+	0.427594i	$0.140639\pi$
$48$	−0.118602	+	0.596251i	−0.0171187	+	0.0860615i
$49$	−1.89983	+	6.73726i	−0.271405	+	0.962465i
$50$		−	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	−0.121969	−	0.992534i	$-0.538921\pi$
$53$	3.59356	−	1.48850i	0.493614	−	0.204462i	0.615583	+	0.788072i	$0.288921\pi$
$54$	−3.35714	−	0.667778i	−0.456850	−	0.0908730i
$55$	8.31272	+	8.31272i	1.12089	+	1.12089i
$56$	−2.56001	+	0.668077i	−0.342096	+	0.0892756i
$57$	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	$-0.202159\pi$
$59$	7.33351	+	3.03764i	0.954741	+	0.395467i	0.149730	+	0.988727i	$0.452159\pi$
$60$	1.76907	+	0.732773i	0.228386	+	0.0946006i
$61$	1.63428	+	1.09199i	0.209248	+	0.139815i	0.655779	−	0.754953i	$-0.272341\pi$
$61$	1.63428	+	1.09199i	0.209248	+	0.139815i	−0.446530	+	0.894768i	$0.647341\pi$
$62$	−0.521615	−	2.62233i	−0.0662451	−	0.333037i
$63$	−1.75732	−	6.73391i	−0.221402	−	0.848393i
$64$	−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	$-0.600613\pi$
$67$		−	15.5597i		−	1.90092i	0.310849	−	0.950459i	$-0.399387\pi$
$68$	−4.09369	−	0.491629i	−0.496433	−	0.0596188i
$69$		−	0.131365i		−	0.0158145i
$70$	0.490749	+	8.31896i	0.0586557	+	0.994306i
$71$	1.58501	−	7.96838i	0.188106	−	0.945673i	−0.765229	−	0.643758i	$-0.777374\pi$
$71$	1.58501	−	7.96838i	0.188106	−	0.945673i	0.953335	−	0.301915i	$-0.0976258\pi$
$72$	1.85999	−	1.85999i	0.219201	−	0.219201i
$73$	6.68332	+	10.0023i	0.782224	+	1.17068i	0.981636	+	0.190765i	$0.0610967\pi$
$73$	6.68332	+	10.0023i	0.782224	+	1.17068i	−0.199412	+	0.979916i	$0.563903\pi$
$74$	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
$77$	−7.38169	−	6.55929i	−0.841222	−	0.747500i
$78$	−1.34246	+	2.00913i	−0.152003	+	0.227489i
$79$	0.195993	−	0.0389854i	0.0220509	−	0.00438620i	−0.184053	−	0.982916i	$-0.558922\pi$
$79$	0.195993	−	0.0389854i	0.0220509	−	0.00438620i	0.206103	+	0.978530i	$0.433922\pi$
$80$	−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	$-0.337053\pi$
$83$	13.2346	−	5.48194i	1.45268	−	0.601721i	0.962836	+	0.270088i	$0.0870528\pi$
$84$	−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	$-0.445254\pi$
$89$	−7.68024	−	7.68024i	−0.814104	−	0.814104i	−0.985246	+	0.171142i	$0.945254\pi$
$90$	−4.60297	−	6.88883i	−0.485195	−	0.726146i
$91$	−10.4170	−	1.44064i	−1.09199	−	0.151021i
$92$	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	$-0.701687\pi$
$97$	−0.729748	+	0.487602i	−0.0740947	+	0.0495085i	0.517971	+	0.855398i	$0.326687\pi$
$98$	−0.823018	−	6.95145i	−0.0831374	−	0.702202i
$99$	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	$-0.810350\pi$
$101$	−16.6365			−1.65540			−0.827698	+	0.561174i	$0.810350\pi$
$102$	−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
$105$	−2.56166	+	4.37080i	−0.249992	+	0.426546i
$106$	−2.75039	+	2.75039i	−0.267142	+	0.267142i
$107$	−12.6355	+	8.44275i	−1.22152	+	0.816192i	−0.987741	−	0.156099i	$-0.950108\pi$
$107$	−12.6355	+	8.44275i	−1.22152	+	0.816192i	−0.233776	+	0.972291i	$0.575108\pi$
$108$	3.35714	−	0.667778i	0.323041	−	0.0642569i
$109$	−8.50537	−	5.68310i	−0.814666	−	0.544343i	0.0770024	−	0.997031i	$-0.475465\pi$
$109$	−8.50537	−	5.68310i	−0.814666	−	0.544343i	−0.891669	+	0.452688i	$0.850465\pi$
$110$	−10.8611	−	4.49881i	−1.03556	−	0.428945i
$111$	−0.719561	+	1.73717i	−0.0682977	+	0.164885i
$112$	2.10948	−	1.59690i	0.199327	−	0.150893i
$113$	−5.00798	+	0.996149i	−0.471111	+	0.0937098i	−0.424936	−	0.905224i	$-0.639703\pi$
$113$	−5.00798	+	0.996149i	−0.471111	+	0.0937098i	−0.0461753	+	0.998933i	$0.514703\pi$
$114$	−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
$119$	2.77223	−	10.5506i	0.254130	−	0.967170i
$120$	−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
$126$	4.20051	+	5.54882i	0.374211	+	0.494328i
$127$	4.03649	−	9.74494i	0.358180	−	0.864724i	−0.637376	−	0.770553i	$-0.719980\pi$
$127$	4.03649	−	9.74494i	0.358180	−	0.864724i	0.995556	−	0.0941707i	$-0.0300199\pi$
$128$	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	$-0.967761\pi$
$131$	−14.6753	+	9.80572i	−1.28219	+	0.856730i	−0.287311	+	0.957837i	$0.592761\pi$
$132$	1.60444	−	1.60444i	0.139649	−	0.139649i
$133$	7.30268	−	12.4601i	0.633223	−	1.08043i
$134$	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	$-0.312160\pi$
$139$	8.87296	+	1.76494i	0.752595	+	0.149700i	0.196137	+	0.980576i	$0.437160\pi$
$140$	−3.63692	−	7.49791i	−0.307376	−	0.633689i
$141$	−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
$147$	1.93183	−	3.79178i	0.159335	−	0.312740i
$148$	−1.71835	−	2.57169i	−0.141247	−	0.211392i
$149$	−14.5770	−	14.5770i	−1.19419	−	1.19419i	−0.975878	−	0.218315i	$-0.929944\pi$
$149$	−14.5770	−	14.5770i	−1.19419	−	1.19419i	−0.218315	−	0.975878i	$-0.570056\pi$
$150$	−0.583621	+	2.93406i	−0.0476524	+	0.239565i
$151$	5.98858	+	14.4577i	0.487344	+	1.17655i	0.956052	+	0.293198i	$0.0947196\pi$
$151$	5.98858	+	14.4577i	0.487344	+	1.17655i	−0.468708	+	0.883353i	$0.655280\pi$
$152$	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	−0.996869	−	0.0790759i	$-0.974803\pi$
$157$	−13.4815	−	13.4815i	−1.07594	−	1.07594i	−0.0790759	−	0.996869i	$-0.525197\pi$
$158$	−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
$161$	−0.379751	+	0.427364i	−0.0299286	+	0.0336810i
$162$	−5.36806	−	2.22353i	−0.421755	−	0.174697i
$163$	−8.55679	+	12.8061i	−0.670219	+	1.00305i	0.328074	+	0.944652i	$0.393601\pi$
$163$	−8.55679	+	12.8061i	−0.670219	+	1.00305i	−0.998293	+	0.0584020i	$0.981399\pi$
$164$	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	0.766280	+	0.642506i	$0.222105\pi$
$167$	−2.42364	+	12.1845i	−0.187547	+	0.942862i	−0.953827	+	0.300356i	$0.902895\pi$
$168$	1.60565	−	0.0947197i	0.123878	−	0.00730779i
$169$		−	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	$-0.279190\pi$
$173$	12.3092	+	2.44846i	0.935854	+	0.186153i	0.296472	+	0.955042i	$0.404190\pi$
$174$	−1.33026	−	1.33026i	−0.100847	−	0.100847i
$175$	−12.5974	+	3.28750i	−0.952276	+	0.248512i
$176$	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	0.399233	−	0.916850i	$-0.369277\pi$
$179$	0.444478	+	0.184109i	0.0332219	+	0.0137610i	−0.366011	+	0.930611i	$0.619277\pi$
$180$	6.88883	+	4.60297i	0.513463	+	0.343085i
$181$	−3.41862	−	17.1866i	−0.254104	−	1.27747i	−0.871336	−	0.490687i	$-0.836746\pi$
$181$	−3.41862	−	17.1866i	−0.254104	−	1.27747i	0.617231	−	0.786782i	$-0.288254\pi$
$182$	10.1753	−	2.65542i	0.754245	−	0.196833i
$183$	−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
$189$	0.533312	+	9.04047i	0.0387927	+	0.657597i
$190$	3.35429	−	16.8632i	0.243346	−	1.22338i
$191$	−13.2893	+	13.2893i	−0.961579	+	0.961579i	−0.999289	−	0.0377102i	$-0.987994\pi$
$191$	−13.2893	+	13.2893i	−0.961579	+	0.961579i	0.0377102	+	0.999289i	$0.487994\pi$
$192$	0.337749	+	0.505478i	0.0243750	+	0.0364797i
$193$	−2.83654	−	14.2603i	−0.204179	−	1.02648i	−0.937868	−	0.346991i	$-0.887203\pi$
$193$	−2.83654	−	14.2603i	−0.204179	−	1.02648i	0.733689	−	0.679485i	$-0.237797\pi$
$194$	0.487602	−	0.729748i	0.0350078	−	0.0523929i
$195$	−7.03155	−	2.91256i	−0.503540	−	0.208573i
$196$	3.42057	+	6.10735i	0.244327	+	0.436239i
$197$	−8.44857	+	12.6442i	−0.601935	+	0.900860i	−0.999863	−	0.0165568i	$-0.994730\pi$
$197$	−8.44857	+	12.6442i	−0.601935	+	0.900860i	0.397927	+	0.917417i	$0.369730\pi$
$198$	−9.62903	+	1.91533i	−0.684305	+	0.136117i
$199$	13.9819	−	9.34243i	0.991154	−	0.662268i	0.0494729	−	0.998775i	$-0.484246\pi$
$199$	13.9819	−	9.34243i	0.991154	−	0.662268i	0.941681	+	0.336508i	$0.109246\pi$
$200$	−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
$210$	0.694034	−	5.01839i	0.0478929	−	0.346302i
$211$	15.6561	+	10.4610i	1.07781	+	0.720168i	0.961985	−	0.273102i	$-0.0880495\pi$
$211$	15.6561	+	10.4610i	1.07781	+	0.720168i	0.115823	+	0.993270i	$0.463050\pi$
$212$	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
$217$	−6.36473	+	3.08726i	−0.432066	+	0.209577i
$218$	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	−0.998592	−	0.0530556i	$-0.983104\pi$
$223$	−4.92790	−	11.8970i	−0.329997	−	0.796682i	0.668595	−	0.743627i	$-0.266896\pi$
$224$	−1.33780	+	2.28261i	−0.0893856	+	0.152513i
$225$	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	$-0.572108\pi$
$227$	−0.891910	+	0.177412i	−0.0591981	+	0.0117752i	0.165402	+	0.986226i	$0.447108\pi$
$228$	2.75926	+	1.84368i	0.182736	+	0.122101i
$229$	−0.861960	−	0.357036i	−0.0569599	−	0.0235936i	0.354022	−	0.935237i	$-0.384814\pi$
$229$	−0.861960	−	0.357036i	−0.0569599	−	0.0235936i	−0.410982	+	0.911644i	$0.634814\pi$
$230$	−0.260459	+	0.628804i	−0.0171742	+	0.0414621i
$231$	3.62340	+	4.78647i	0.238402	+	0.314926i
$232$	3.03508	−	0.603716i	0.199263	−	0.0396359i
$233$	−1.78716	−	2.67468i	−0.117081	−	0.175224i	0.768300	−	0.640089i	$-0.221103\pi$
$233$	−1.78716	−	2.67468i	−0.117081	−	0.175224i	−0.885381	+	0.464865i	$0.846103\pi$
$234$	−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
$238$	1.47632	+	10.8084i	0.0956958	+	0.700601i
$239$	−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	$-0.696319\pi$
$241$	−22.1209	−	4.40012i	−1.42493	−	0.283437i	−0.846542	+	0.532323i	$0.821319\pi$
$242$	−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
$245$	20.9688	−	6.81403i	1.33965	−	0.435332i
$246$	−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	$-0.792453\pi$
$251$	−2.97932	+	2.97932i	−0.188053	+	0.188053i	0.606801	+	0.794854i	$0.292453\pi$
$252$	−6.00421	−	3.51898i	−0.378229	−	0.221675i
$253$	−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	0.961480	+	0.274876i	$0.0886369\pi$
$257$	7.63050	+	18.4217i	0.475978	+	1.14911i	−0.485502	+	0.874236i	$0.661363\pi$
$258$	−2.56435	−	0.510081i	−0.159649	−	0.0317562i
$259$	7.36273	−	3.57135i	0.457498	−	0.221913i
$260$	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	−0.955738	−	0.294219i	$-0.904941\pi$
$263$	−1.16578	+	2.81444i	−0.0718850	+	0.173546i	0.883853	+	0.467765i	$0.154941\pi$
$264$	−0.868318	+	2.09631i	−0.0534413	+	0.129019i
$265$	−10.1866	−	6.80649i	−0.625760	−	0.418119i
$266$	−1.97852	+	14.3062i	−0.121311	+	0.877172i
$267$	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	−0.217167	−	0.976134i	$-0.569682\pi$
$269$	5.85556	−	29.4379i	0.357020	−	1.79486i	0.574187	−	0.818725i	$-0.305318\pi$
$270$	4.12582	+	9.96061i	0.251089	+	0.606183i
$271$	−10.8364			−0.658267			−0.329134	−	0.944283i	$-0.606757\pi$
$271$	−10.8364			−0.658267			−0.329134	+	0.944283i	$0.606757\pi$
$272$	−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	−0.903342	−	0.428920i	$-0.858894\pi$
$277$	−14.1929	+	9.48337i	−0.852766	+	0.569800i	0.0505762	+	0.998720i	$0.483894\pi$
$278$	−8.87296	+	1.76494i	−0.532165	+	0.105854i
$279$	3.90731	−	5.84770i	0.233924	−	0.350093i
$280$	6.22940	+	5.53538i	0.372278	+	0.330802i
$281$	−17.3050	−	7.16796i	−1.03233	−	0.427605i	−0.198776	−	0.980045i	$-0.563697\pi$
$281$	−17.3050	−	7.16796i	−1.03233	−	0.427605i	−0.833553	+	0.552440i	$0.813697\pi$
$282$	1.55994	−	2.33462i	0.0928933	−	0.139025i
$283$	−1.42129	−	7.14528i	−0.0844866	−	0.424743i	−0.999760	−	0.0219096i	$-0.993025\pi$
$283$	−1.42129	−	7.14528i	−0.0844866	−	0.424743i	0.915273	−	0.402833i	$-0.131975\pi$
$284$	−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
$287$	−20.4422	+	1.20592i	−1.20666	+	0.0711831i
$288$		−	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	0.991940	+	0.126707i	$0.0404408\pi$
$293$	19.1482	+	19.1482i	1.11865	+	1.11865i	0.126707	+	0.991940i	$0.459559\pi$
$294$	−0.333728	+	4.24242i	−0.0194634	+	0.247423i
$295$	−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
$301$	−2.87326	−	11.0101i	−0.165612	−	0.634610i
$302$	−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	$-0.212119\pi$
$308$	−9.85776	+	0.581525i	−0.561698	+	0.0331355i
$309$	−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	$-0.241153\pi$
$311$	−3.28727	−	4.91974i	−0.186404	−	0.278973i	−0.912888	+	0.408210i	$0.866153\pi$
$312$	0.471408	+	2.36993i	0.0266882	+	0.134171i
$313$	−16.6705	+	24.9491i	−0.942271	+	1.41021i	−0.0304877	+	0.999535i	$0.509706\pi$
$313$	−16.6705	+	24.9491i	−0.942271	+	1.41021i	−0.911783	+	0.410672i	$0.865294\pi$
$314$	17.6145	+	7.29616i	0.994043	+	0.411746i
$315$	−14.5604	+	16.3859i	−0.820383	+	0.923243i
$316$	0.111021	−	0.166155i	0.00624542	−	0.00934694i
$317$	0.956736	−	0.190307i	0.0537357	−	0.0106887i	−0.168149	−	0.985762i	$-0.553779\pi$
$317$	0.956736	−	0.190307i	0.0537357	−	0.0106887i	0.221885	+	0.975073i	$0.428779\pi$
$318$	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
$329$	12.1046	+	1.67404i	0.667347	+	0.0922927i
$330$	5.94237	+	3.97057i	0.327117	+	0.218572i
$331$	1.06832	−	2.57915i	0.0587200	−	0.141763i	−0.891796	−	0.452437i	$-0.850555\pi$
$331$	1.06832	−	2.57915i	0.0587200	−	0.141763i	0.950516	+	0.310674i	$0.100555\pi$
$332$	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
$336$	−1.44718	+	0.701964i	−0.0789500	+	0.0382953i
$337$	−15.7999	−	3.14280i	−0.860676	−	0.171199i	−0.255030	−	0.966933i	$-0.582085\pi$
$337$	−15.7999	−	3.14280i	−0.860676	−	0.171199i	−0.605646	+	0.795734i	$0.707085\pi$
$338$	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
$343$	−17.2460	+	6.75104i	−0.931195	+	0.364522i
$344$	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	0.902379	−	0.430944i	$-0.141819\pi$
$347$	15.8256	+	10.5743i	0.849564	+	0.567661i	−0.0528145	+	0.998604i	$0.516819\pi$
$348$	1.73807	+	0.719933i	0.0931704	+	0.0385924i
$349$	8.46260	−	20.4305i	0.452992	−	1.09362i	−0.518186	−	0.855268i	$-0.673393\pi$
$349$	8.46260	−	20.4305i	0.452992	−	1.09362i	0.971179	−	0.238353i	$-0.0766074\pi$
$350$	10.3804	−	7.85808i	0.554857	−	0.420032i
$351$	−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	$-0.651531\pi$
$353$	8.08913	−	8.08913i	0.430541	−	0.430541i	0.888812	+	0.458271i	$0.151531\pi$
$354$	4.73288	+	0.941429i	0.251550	+	0.0500364i
$355$	−23.6421	+	9.79287i	−1.25479	+	0.519752i
$356$	−10.8615			−0.575659
$357$	−2.90427	+	5.96201i	−0.153710	+	0.315543i
$358$	−0.481100			−0.0254269
$359$	34.2758	−	14.1975i	1.80901	−	0.749314i	0.826537	−	0.562882i	$-0.190307\pi$
$359$	34.2758	−	14.1975i	1.80901	−	0.749314i	0.982468	−	0.186433i	$-0.0596926\pi$
$360$	−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
$364$	−8.38459	+	6.34721i	−0.439472	+	0.332684i
$365$	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	$-0.219907\pi$
$367$	9.13686	+	6.10505i	0.476940	+	0.318681i	−0.293760	+	0.955879i	$0.594907\pi$
$368$	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
$371$	8.87852	+	5.20357i	0.460950	+	0.270156i
$372$	−0.622027	−	1.50171i	−0.0322506	−	0.0778598i
$373$			20.7863i			1.07628i	0.842857	+	0.538138i	$0.180872\pi$
$373$			20.7863i			1.07628i	−0.842857	+	0.538138i	$0.819128\pi$
$374$	−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
$378$	−3.95235	−	8.14821i	−0.203287	−	0.419099i
$379$	−7.17539	+	4.79444i	−0.368575	+	0.246274i	−0.726040	−	0.687653i	$-0.758641\pi$
$379$	−7.17539	+	4.79444i	−0.368575	+	0.246274i	0.357465	+	0.933927i	$0.383641\pi$
$380$	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	$-0.784711\pi$
$383$	4.19194	−	10.1202i	0.214198	−	0.517120i	0.994060	+	0.108832i	$0.0347109\pi$
$384$	−0.505478	−	0.337749i	−0.0257950	−	0.0172357i
$385$	−4.26097	+	30.8101i	−0.217159	+	1.57023i
$386$	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	0.761765	−	0.647853i	$-0.224333\pi$
$389$	−4.63464	−	11.1890i	−0.234985	−	0.567305i	−0.996751	+	0.0805482i	$0.974333\pi$
$390$	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	$-0.211195\pi$
$397$	34.8966	−	6.94136i	1.75141	−	0.348377i	0.963560	+	0.267493i	$0.0861951\pi$
$398$	−9.34243	+	13.9819i	−0.468294	+	0.700851i
$399$	−5.83202	+	6.56324i	−0.291966	+	0.328573i
$400$	4.54627	+	1.88313i	0.227313	+	0.0941563i
$401$	−5.90196	+	8.83291i	−0.294730	+	0.441094i	−0.949051	−	0.315122i	$-0.897954\pi$
$401$	−5.90196	+	8.83291i	−0.294730	+	0.441094i	0.654321	+	0.756217i	$0.272954\pi$
$402$	−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
$406$	0.482149	+	8.17318i	0.0239287	+	0.405628i
$407$			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
$413$	5.30302	+	20.3207i	0.260944	+	0.999916i
$414$	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	$-0.00704588\pi$
$419$	1.38439	+	6.95978i	0.0676317	+	0.340008i	−0.932123	+	0.362141i	$0.882046\pi$
$420$	1.27925	+	4.90199i	0.0624212	+	0.239192i
$421$	5.97230	+	5.97230i	0.291072	+	0.291072i	0.837504	−	0.546432i	$-0.184014\pi$
$421$	5.97230	+	5.97230i	0.291072	+	0.291072i	−0.546432	+	0.837504i	$0.684014\pi$
$422$	−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
$427$	0.306242	+	5.19128i	0.0148201	+	0.251224i
$428$	−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	−0.851505	−	0.524346i	$-0.824310\pi$
$431$	−5.51141	−	27.7077i	−0.265475	−	1.33463i	0.586030	−	0.810289i	$-0.300690\pi$
$432$	1.90167	−	2.84605i	0.0914941	−	0.136931i
$433$	−30.8461	−	12.7769i	−1.48237	−	0.614017i	−0.512728	−	0.858551i	$-0.671365\pi$
$433$	−30.8461	−	12.7769i	−1.48237	−	0.614017i	−0.969641	+	0.244534i	$0.921365\pi$
$434$	4.69880	−	5.28794i	0.225550	−	0.253829i
$435$	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	0.876083	+	0.482160i	$0.160147\pi$
$439$	−2.46874	+	12.4112i	−0.117827	+	0.592354i	−0.993910	+	0.110195i	$0.964853\pi$
$440$	−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
$448$	0.362452	−	2.62081i	0.0171243	−	0.123821i
$449$	11.7252	+	7.83452i	0.553346	+	0.369734i	0.800584	−	0.599221i	$-0.204523\pi$
$449$	11.7252	+	7.83452i	0.553346	+	0.369734i	−0.247238	+	0.968955i	$0.579523\pi$
$450$	−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
$455$	14.4557	+	29.8021i	0.677694	+	1.39714i
$456$	−3.25477	−	0.647414i	−0.152419	−	0.0303179i
$457$	−15.3173	−	36.9793i	−0.716514	−	1.72982i	−0.683043	−	0.730379i	$-0.739344\pi$
$457$	−15.3173	−	36.9793i	−0.716514	−	1.72982i	−0.0334716	−	0.999440i	$-0.510656\pi$
$458$	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	$-0.183235\pi$
$461$	−2.98973	−	7.21784i	−0.139245	−	0.336168i	−0.978084	+	0.208213i	$0.933235\pi$
$462$	−5.17929	−	3.03550i	−0.240962	−	0.141224i
$463$	20.2431	−	20.2431i	0.940778	−	0.940778i	−0.0575637	−	0.998342i	$-0.518333\pi$
$463$	20.2431	−	20.2431i	0.940778	−	0.940778i	0.998342	+	0.0575637i	$0.0183332\pi$
$464$	−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	$-0.268685\pi$
$467$	13.0901	+	5.42209i	0.605737	+	0.250905i	−0.0586675	+	0.998278i	$0.518685\pi$
$468$	4.00102	−	9.65931i	0.184947	−	0.446502i
$469$	32.8229	−	24.8472i	1.51562	−	1.14734i
$470$	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
$476$	−5.50012	−	9.42065i	−0.252098	−	0.431795i
$477$	−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	$-0.437053\pi$
$479$	0.0603537	+	0.0120051i	0.00275763	+	0.000548527i	−0.193711	+	0.981059i	$0.562053\pi$
$480$	−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
$483$	0.277113	−	0.209777i	0.0126091	−	0.00954519i
$484$	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	−0.232754	−	0.972536i	$-0.574774\pi$
$487$	−1.66871	+	0.331927i	−0.0756166	+	0.0150411i	0.157137	+	0.987577i	$0.449774\pi$
$488$	−1.63428	+	1.09199i	−0.0739804	+	0.0494321i
$489$	6.62083	−	6.62083i	0.299404	−	0.299404i
$490$	−16.7650	+	14.3198i	−0.757367	+	0.646900i
$491$	11.6022	+	28.0101i	0.523598	+	1.26408i	0.935654	+	0.352919i	$0.114811\pi$
$491$	11.6022	+	28.0101i	0.523598	+	1.26408i	−0.412056	+	0.911158i	$0.635189\pi$
$492$		−	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
$497$	19.3403	−	9.38114i	0.867529	−	0.420802i
$498$	7.24096	−	4.83826i	0.324475	−	0.216807i
$499$	0.475451	+	2.39025i	0.0212841	+	0.107002i	0.989967	−	0.141299i	$-0.0451278\pi$
$499$	0.475451	+	2.39025i	0.0212841	+	0.107002i	−0.968683	+	0.248301i	$0.920128\pi$
$500$	−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	$-0.235397\pi$
$503$	8.94594	+	5.97749i	0.398880	+	0.266523i	−0.339911	+	0.940458i	$0.610397\pi$
$504$	6.89382	+	0.953401i	0.307075	+	0.0424678i
$505$	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	$-0.561206\pi$
$509$	−8.62286			−0.382201			−0.191101	+	0.981570i	$0.561206\pi$
$510$	−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
$518$	−5.43558	+	6.11709i	−0.238826	+	0.268769i
$519$	−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	$-0.0430466\pi$
$521$	0.543951	+	2.73462i	0.0238309	+	0.119806i	−0.967039	+	0.254629i	$0.918047\pi$
$522$	−4.52231	−	6.76811i	−0.197936	−	0.296232i
$523$	−2.93806	+	2.93806i	−0.128472	+	0.128472i	−0.768419	−	0.639947i	$-0.778956\pi$
$523$	−2.93806	+	2.93806i	−0.128472	+	0.128472i	0.639947	+	0.768419i	$0.278956\pi$
$524$	−3.44331	+	17.3107i	−0.150422	+	0.756221i
$525$	7.90114	−	0.466101i	0.344834	−	0.0203423i
$526$		−	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
$532$	−3.64684	−	13.9744i	−0.158111	−	0.605867i
$533$	−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
$539$	2.04890	−	26.0461i	0.0882525	−	1.12188i
$540$	−7.62352	−	7.62352i	−0.328064	−	0.328064i
$541$	−33.4596	−	6.65552i	−1.43854	−	0.286143i	−0.586640	−	0.809848i	$-0.699550\pi$
$541$	−33.4596	−	6.65552i	−1.43854	−	0.286143i	−0.851900	+	0.523705i	$0.824550\pi$
$542$	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
$546$	−6.38199	+	0.376484i	−0.273124	+	0.0161120i
$547$	−4.25286	+	21.3806i	−0.181839	+	0.914167i	0.776845	+	0.629692i	$0.216819\pi$
$547$	−4.25286	+	21.3806i	−0.181839	+	0.914167i	−0.958684	+	0.284474i	$0.908181\pi$
$548$	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
$553$	0.395220	+	0.351188i	0.0168065	+	0.0149340i
$554$	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	0.536439	−	0.843939i	$-0.319769\pi$
$557$	−7.25726	−	7.25726i	−0.307500	−	0.307500i	−0.843939	+	0.536439i	$0.819769\pi$
$558$	−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	$-0.00755670\pi$
$563$	6.54943	+	15.8117i	0.276025	+	0.666384i	−0.723693	+	0.690122i	$0.757557\pi$
$564$	−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
$567$	−2.10597	+	15.2278i	−0.0884426	+	0.639508i
$568$	6.75527	+	4.51373i	0.283445	+	0.189392i
$569$	−3.35289	+	8.09459i	−0.140560	+	0.339343i	−0.978446	−	0.206503i	$-0.933792\pi$
$569$	−3.35289	+	8.09459i	−0.140560	+	0.339343i	0.837886	+	0.545846i	$0.183792\pi$
$570$	−4.00000	+	9.65686i	−0.167542	+	0.404481i
$571$	22.6797	−	33.9426i	0.949117	−	1.42045i	0.0422175	−	0.999108i	$-0.486558\pi$
$571$	22.6797	−	33.9426i	0.949117	−	1.42045i	0.906900	−	0.421346i	$-0.138442\pi$
$572$	−2.89418	−	14.5500i	−0.121012	−	0.608367i
$573$	9.49988	−	6.34762i	0.396863	−	0.265176i
$574$	18.4246	−	8.93701i	0.769029	−	0.373024i
$575$	−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	$-0.473699\pi$
$577$	3.96500			0.165065			0.0825325	+	0.996588i	$0.473699\pi$
$578$	−2.60187	−	16.7997i	−0.108223	−	0.698776i
$579$			8.83912i			0.367341i
$580$	3.73001	+	9.00505i	0.154880	+	0.373914i
$581$	32.6983	+	19.1640i	1.35655	+	0.795056i
$582$	−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	0.487974	+	0.872858i	$0.337736\pi$
$587$	−11.4909	+	27.7414i	−0.474280	+	1.14501i	−0.962254	+	0.272154i	$0.912264\pi$
$588$	−1.31518	−	4.04720i	−0.0542371	−	0.166904i
$589$	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	$-0.550972\pi$
$593$	10.3704	−	4.29556i	0.425861	−	0.176397i	0.585312	+	0.810808i	$0.300972\pi$
$594$	12.7756			0.524187
$595$	−32.4822	+	11.2022i	−1.33164	+	0.459247i
$596$	−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	−0.865429	−	0.501032i	$-0.832954\pi$
$599$	−8.91841	+	8.91841i	−0.364396	+	0.364396i	0.501032	+	0.865429i	$0.332954\pi$
$600$	1.66201	+	2.48738i	0.0678513	+	0.101547i
$601$	−24.4908	+	4.87152i	−0.999000	+	0.198713i	−0.667394	−	0.744705i	$-0.732590\pi$
$601$	−24.4908	+	4.87152i	−0.999000	+	0.198713i	−0.331606	+	0.943418i	$0.607590\pi$
$602$	6.86791	+	9.07243i	0.279915	+	0.369765i
$603$	−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	$-0.477187\pi$
$607$	25.1429	−	16.7999i	1.02052	−	0.681888i	0.948911	+	0.315544i	$0.102187\pi$
$608$	3.85990	−	3.85990i	0.156539	−	0.156539i
$609$	−2.51677	+	4.29421i	−0.101985	+	0.174010i
$610$	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
$616$	8.88484	−	4.30966i	0.357981	−	0.173641i
$617$	27.4442	−	18.3376i	1.10486	−	0.738245i	0.137212	−	0.990542i	$-0.456186\pi$
$617$	27.4442	−	18.3376i	1.10486	−	0.738245i	0.967650	+	0.252297i	$0.0811860\pi$
$618$	−0.850823	−	4.27737i	−0.0342251	−	0.172061i
$619$	−5.00571	+	7.49157i	−0.201196	+	0.301112i	−0.918324	−	0.395831i	$-0.870457\pi$
$619$	−5.00571	+	7.49157i	−0.201196	+	0.301112i	0.717127	+	0.696942i	$0.245457\pi$
$620$	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
$623$	3.93678	−	28.4659i	0.157724	−	1.14046i
$624$	−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	0.0585452	−	0.998285i	$-0.481354\pi$
$631$	20.2424	−	8.38467i	0.805837	−	0.333789i	0.747292	+	0.664496i	$0.231354\pi$
$632$	−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
$637$	−13.5958	−	24.2750i	−0.538685	−	0.961809i
$638$	−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	0.911602	−	0.411074i	$-0.134846\pi$
$641$	4.63227	+	6.93269i	0.182964	+	0.273825i	−0.728638	+	0.684899i	$0.759846\pi$
$642$	−6.53259	+	6.53259i	−0.257821	+	0.257821i
$643$	5.16712	−	25.9769i	0.203771	−	1.02443i	−0.734521	−	0.678586i	$-0.762593\pi$
$643$	5.16712	−	25.9769i	0.203771	−	1.02443i	0.938293	−	0.345842i	$-0.112407\pi$
$644$	0.0336675	+	0.570716i	0.00132668	+	0.0224894i
$645$		−	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
$651$	4.16114	−	1.08592i	0.163088	−	0.0425604i
$652$	3.00474	+	15.1059i	0.117675	+	0.591592i
$653$	−31.9784	−	21.3673i	−1.25141	−	0.836167i	−0.259831	−	0.965654i	$-0.583667\pi$
$653$	−31.9784	−	21.3673i	−1.25141	−	0.836167i	−0.991581	+	0.129487i	$0.958667\pi$
$654$	−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
$658$	−11.8238	+	3.08561i	−0.460939	+	0.120290i
$659$	−22.1758	−	22.1758i	−0.863846	−	0.863846i	0.127936	−	0.991782i	$-0.459165\pi$
$659$	−22.1758	−	22.1758i	−0.863846	−	0.863846i	−0.991782	+	0.127936i	$0.959165\pi$
$660$	−7.00951	−	1.39428i	−0.272845	−	0.0542722i
$661$	12.6432	−	5.23699i	0.491764	−	0.203695i	−0.123000	−	0.992407i	$-0.539251\pi$
$661$	12.6432	−	5.23699i	0.491764	−	0.203695i	0.614764	+	0.788711i	$0.289251\pi$
$662$			2.79165i			0.108500i
$663$	−9.47000	−	3.09493i	−0.367784	−	0.120197i
$664$			14.3250i			0.555917i
$665$	−45.4108	+	2.67886i	−1.76096	+	0.103882i
$666$	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
$672$	1.06839	−	1.20234i	0.0412139	−	0.0463813i
$673$	1.25085	−	1.87203i	0.0482168	−	0.0721616i	−0.806578	−	0.591128i	$-0.798683\pi$
$673$	1.25085	−	1.87203i	0.0482168	−	0.0721616i	0.854795	+	0.518966i	$0.173683\pi$
$674$	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	$-0.925651\pi$
$677$	0.377823	−	1.89945i	0.0145209	−	0.0730016i	0.987366	+	0.158454i	$0.0506511\pi$
$678$	−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	−0.980675	−	0.195646i	$-0.937320\pi$
$683$	0.00577370	−	0.0290263i	0.000220924	−	0.00111066i	0.980896	+	0.194535i	$0.0623198\pi$
$684$	10.1531	+	10.1531i	0.388215	+	0.388215i
$685$	−36.8484	−	55.1476i	−1.40791	−	2.10708i
$686$	13.3497	−	12.8369i	0.509693	−	0.490115i
$687$	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	0.978433	+	0.206567i	$0.0662290\pi$
$691$	4.03578	+	20.2892i	0.153528	+	0.771839i	−0.824904	+	0.565273i	$0.808771\pi$
$692$	10.4353	−	6.97262i	0.396689	−	0.265059i
$693$	11.3362	+	23.3709i	0.430627	+	0.887785i
$694$	−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
$700$	−6.58311	+	11.2323i	−0.248818	+	0.424543i
$701$	−10.7736	+	10.7736i	−0.406912	+	0.406912i	−0.880660	−	0.473748i	$-0.842901\pi$
$701$	−10.7736	+	10.7736i	−0.406912	+	0.406912i	0.473748	+	0.880660i	$0.342901\pi$
$702$	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
$707$	−26.5668	−	35.0944i	−0.999148	−	1.31986i
$708$	−4.73288	+	0.941429i	−0.177873	+	0.0353811i
$709$	11.5365	+	17.2656i	0.433262	+	0.648423i	0.982287	−	0.187383i	$-0.0600006\pi$
$709$	11.5365	+	17.2656i	0.433262	+	0.648423i	−0.549024	+	0.835806i	$0.685001\pi$
$710$	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
$714$	0.401630	−	6.61959i	0.0150306	−	0.247732i
$715$	−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	$-0.371919\pi$
$719$	−16.3123	−	24.4131i	−0.608347	−	0.910455i	−0.999953	+	0.00967761i	$0.996919\pi$
$720$	8.12593	−	1.61635i	0.302835	−	0.0602377i
$721$	15.1330	−	11.4558i	0.563581	−	0.426636i
$722$	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	$-0.799457\pi$
$727$	−5.90078	+	5.90078i	−0.218848	+	0.218848i	0.589165	+	0.808013i	$0.299457\pi$
$728$	5.31738	−	9.07270i	0.197075	−	0.336257i
$729$	−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	$-0.187696\pi$
$733$	−4.05508	−	9.78982i	−0.149778	−	0.361595i	−0.980905	+	0.194487i	$0.937696\pi$
$734$	−10.7777	−	2.14381i	−0.397811	−	0.0791294i
$735$	−13.3108	+	1.57594i	−0.490977	+	0.0581294i
$736$	−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	0.632927	+	0.774212i	$0.281853\pi$
$739$	−9.84272	+	23.7624i	−0.362070	+	0.874115i	−0.994997	+	0.0999033i	$0.968147\pi$
$740$	−3.72809	+	9.00041i	−0.137047	+	0.330862i
$741$	−10.9673	−	7.32809i	−0.402893	−	0.269204i
$742$	−10.1940	−	1.40981i	−0.374234	−	0.0517558i
$743$	−7.72336	−	11.5588i	−0.283343	−	0.424052i	0.662310	−	0.749230i	$-0.269576\pi$
$743$	−7.72336	−	11.5588i	−0.283343	−	0.424052i	−0.945653	+	0.325177i	$0.894576\pi$
$744$	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	−0.307182	−	0.951651i	$-0.599386\pi$
$751$	9.33936	−	46.9521i	0.340798	−	1.71331i	0.647980	−	0.761657i	$-0.275614\pi$
$752$	−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
$756$	6.76968	+	6.01547i	0.246211	+	0.218780i
$757$	−32.9799	−	13.6607i	−1.19868	−	0.496508i	−0.308105	−	0.951352i	$-0.599695\pi$
$757$	−32.9799	−	13.6607i	−1.19868	−	0.496508i	−0.890571	+	0.454844i	$0.849695\pi$
$758$	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	$-0.527310\pi$
$761$	25.1209	−	25.1209i	0.910630	−	0.910630i	0.996322	+	0.0856914i	$0.0273099\pi$
$762$	1.25099	−	6.28917i	0.0453187	−	0.227833i
$763$	−1.59379	−	27.0173i	−0.0576991	−	0.978091i
$764$			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	$-0.425768\pi$
$769$	−20.5717	−	20.5717i	−0.741833	−	0.741833i	−0.972931	+	0.231098i	$0.925768\pi$
$770$	−7.85389	−	30.0954i	−0.283034	−	1.08456i
$771$	−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	$-0.423689\pi$
$773$	−7.82740	−	3.24222i	−0.281532	−	0.116614i	−0.518981	+	0.854786i	$0.673689\pi$
$774$	−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
$777$	−4.81361	+	1.25619i	−0.172687	+	0.0450655i
$778$	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
$784$	6.73726	+	1.89983i	0.240616	+	0.0678512i
$785$	−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	$-0.0428448\pi$
$787$	13.6832	+	20.4783i	0.487753	+	0.729974i	−0.503202	+	0.864169i	$0.667845\pi$
$788$	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
$791$	−10.0986	−	8.97350i	−0.359065	−	0.319061i
$792$	−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	−0.798682	+	0.601754i	$0.794469\pi$
$797$	−50.5039	+	20.9194i	−1.78894	+	0.741003i	−0.990257	+	0.139249i	$0.955531\pi$
$798$	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
$805$	1.78375	+	0.246689i	0.0628690	+	0.00869466i
$806$	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	−0.965421	−	0.260696i	$-0.916048\pi$
$809$	−10.1006	+	15.1167i	−0.355119	+	0.531473i	0.610302	+	0.792169i	$0.291048\pi$
$810$	3.57036	+	17.9494i	0.125450	+	0.630679i
$811$	30.3949	−	20.3092i	1.06731	−	0.713153i	0.107613	−	0.994193i	$-0.465679\pi$
$811$	30.3949	−	20.3092i	1.06731	−	0.713153i	0.959696	+	0.281040i	$0.0906793\pi$
$812$	−3.57319	−	7.36653i	−0.125394	−	0.258514i
$813$	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
$819$	23.8650	+	13.9869i	0.833911	+	0.488743i
$820$	17.2382	−	17.2382i	0.601984	−	0.601984i
$821$	18.7123	−	12.5032i	0.653063	−	0.436363i	−0.184404	−	0.982851i	$-0.559035\pi$
$821$	18.7123	−	12.5032i	0.653063	−	0.436363i	0.837467	+	0.546488i	$0.184035\pi$
$822$	12.5555	−	2.49745i	0.437925	−	0.0871086i
$823$	−8.56470	−	5.72275i	−0.298547	−	0.199483i	0.397270	−	0.917702i	$-0.369958\pi$
$823$	−8.56470	−	5.72275i	−0.298547	−	0.199483i	−0.695817	+	0.718219i	$0.744958\pi$
$824$	6.62771	+	2.74529i	0.230887	+	0.0956365i
$825$	−4.27286	+	10.3156i	−0.148762	+	0.359143i
$826$	−12.6757	−	16.7445i	−0.441046	−	0.582616i
$827$	53.9329	−	10.7279i	1.87543	−	0.373046i	0.880537	−	0.473977i	$-0.157182\pi$
$827$	53.9329	−	10.7279i	1.87543	−	0.373046i	0.994894	+	0.100930i	$0.0321819\pi$
$828$	−0.315783	−	0.472603i	−0.0109742	−	0.0164241i
$829$	−14.2597	+	14.2597i	−0.495261	+	0.495261i	−0.909959	−	0.414698i	$-0.863887\pi$
$829$	−14.2597	+	14.2597i	−0.495261	+	0.495261i	0.414698	+	0.909959i	$0.363887\pi$
$830$	44.2530	+	8.80247i	1.53604	+	0.305538i
$831$	9.58726	−	3.97117i	0.332578	−	0.137758i
$832$	3.97471			0.137798
$833$	26.6832	−	11.0002i	0.924519	−	0.381135i
$834$	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	$-0.618788\pi$
$839$	−9.99504	+	1.98814i	−0.345067	+	0.0686381i	0.0195144	+	0.999810i	$0.493788\pi$
$840$	−3.05779	−	4.03930i	−0.105504	−	0.139369i
$841$	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
$847$	6.68922	+	3.92045i	0.229844	+	0.134708i
$848$	−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	$-0.139047\pi$
$853$	46.1843	+	9.18663i	1.58132	+	0.314544i	0.675223	+	0.737614i	$0.264047\pi$
$854$	−2.26955	−	4.67893i	−0.0776624	−	0.160110i
$855$	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	$-0.790454\pi$
$857$	2.25105	−	3.36893i	0.0768944	−	0.115081i	0.867923	+	0.496698i	$0.165454\pi$
$858$	3.45132	−	8.33221i	0.117826	−	0.284457i
$859$	−2.48840	+	6.00754i	−0.0849033	+	0.204975i	−0.960629	−	0.277834i	$-0.910383\pi$
$859$	−2.48840	+	6.00754i	−0.0849033	+	0.204975i	0.875726	+	0.482809i	$0.160383\pi$
$860$	11.2634	+	7.52594i	0.384078	+	0.256633i
$861$	12.3317	+	1.70545i	0.420264	+	0.0581216i
$862$	15.6952	+	23.4895i	0.534580	+	0.800055i
$863$	−6.63245	−	6.63245i	−0.225771	−	0.225771i	0.585152	−	0.810923i	$-0.301035\pi$
$863$	−6.63245	−	6.63245i	−0.225771	−	0.225771i	−0.810923	+	0.585152i	$0.801035\pi$
$864$	−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
$875$	−0.493101	−	0.438164i	−0.0166699	−	0.0148126i
$876$	−6.75654	−	2.79865i	−0.228282	−	0.0945576i
$877$	−2.70145	+	4.04301i	−0.0912215	+	0.136523i	−0.874274	−	0.485434i	$-0.838662\pi$
$877$	−2.70145	+	4.04301i	−0.0912215	+	0.136523i	0.783052	+	0.621956i	$0.213662\pi$
$878$	−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	$-0.987925\pi$
$881$	−1.82698	+	9.18483i	−0.0615524	+	0.309445i	0.937728	+	0.347370i	$0.112925\pi$
$882$	−4.99736	+	17.7218i	−0.168270	+	0.596724i
$883$			31.9578i			1.07547i	0.843115	+	0.537733i	$0.180719\pi$
$883$			31.9578i			1.07547i	−0.843115	+	0.537733i	$0.819281\pi$
$884$	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	$-0.274353\pi$
$887$	28.6490	+	5.69864i	0.961940	+	0.191342i	0.310948	+	0.950427i	$0.399353\pi$
$888$	−1.32958	−	1.32958i	−0.0446176	−	0.0446176i
$889$	27.0026	−	7.04678i	0.905640	−	0.236341i
$890$	−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
$896$	0.668077	+	2.56001i	0.0223189	+	0.0855241i
$897$	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
$903$	0.407369	+	6.90554i	0.0135564	+	0.229802i
$904$	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	0.983902	+	0.178712i	$0.0571929\pi$
$907$	4.31523	+	21.6941i	0.143285	+	0.720342i	−0.840617	+	0.541631i	$0.817807\pi$
$908$	−0.505226	+	0.756124i	−0.0167665	+	0.0250929i
$909$	40.4299	+	16.7466i	1.34097	+	0.555450i
$910$	−24.7601	−	22.0016i	−0.820789	−	0.729344i
$911$	5.73283	−	8.57979i	0.189937	−	0.284261i	−0.724263	−	0.689524i	$-0.757820\pi$
$911$	5.73283	−	8.57979i	0.189937	−	0.284261i	0.914200	+	0.405263i	$0.132820\pi$
$912$	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
$924$	5.94668	+	0.822413i	0.195631	+	0.0270554i
$925$	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	−0.978554	−	0.205989i	$-0.933959\pi$
$929$	−4.67301	−	23.4928i	−0.153316	−	0.770774i	0.825238	−	0.564785i	$-0.191041\pi$
$930$	4.25687	−	2.84435i	0.139588	−	0.0932698i
$931$	37.9460	−	4.49263i	1.24363	−	0.147240i
$932$	−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	0.988212	+	0.153093i	$0.0489234\pi$
$937$	12.1736	+	29.3896i	0.397694	+	0.960118i	−0.590518	+	0.807024i	$0.701077\pi$
$938$	−20.8158	+	35.5166i	−0.679659	+	1.15966i
$939$	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	$-0.559705\pi$
$941$	0.528276	−	0.105081i	0.0172213	−	0.00342553i	0.203693	+	0.979035i	$0.434705\pi$
$942$	−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
$945$	22.7429	−	17.2166i	0.739828	−	0.560056i
$946$	−15.7436	+	3.13161i	−0.511870	+	0.101817i
$947$	−19.7874	−	29.6139i	−0.643004	−	0.962324i	−0.999606	−	0.0280675i	$-0.991065\pi$
$947$	−19.7874	−	29.6139i	−0.643004	−	0.962324i	0.356602	−	0.934257i	$-0.383935\pi$
$948$	−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
$952$	8.68658	+	6.59874i	0.281534	+	0.213866i
$953$	−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
$959$	33.6266	+	44.4203i	1.08586	+	1.43441i
$960$	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
$966$	−0.175741	+	0.299855i	−0.00565437	+	0.00964769i
$967$	−5.14961	−	12.4323i	−0.165600	−	0.399794i	0.819195	−	0.573516i	$-0.194421\pi$
$967$	−5.14961	−	12.4323i	−0.165600	−	0.399794i	−0.984795	+	0.173721i	$0.944421\pi$
$968$			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	$-0.155459\pi$
$971$	−2.27867	−	5.50120i	−0.0731261	−	0.176542i	−0.956216	+	0.292662i	$0.905459\pi$
$972$	−13.5359	−	2.69245i	−0.434163	−	0.0863604i
$973$	10.4461	+	21.5358i	0.334886	+	0.690406i
$974$	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	−0.959330	−	0.282287i	$-0.908907\pi$
$977$	−2.54352	+	6.14059i	−0.0813743	+	0.196455i	0.877956	+	0.478742i	$0.158907\pi$
$978$	−3.58317	+	8.65053i	−0.114577	+	0.276613i
$979$	33.7070	+	22.5223i	1.07728	+	0.719816i
$980$	10.0089	−	19.6454i	0.319724	−	0.627550i
$981$	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	$-0.908319\pi$
$983$	1.11993	−	5.63026i	0.0357202	−	0.179577i	0.994527	+	0.104482i	$0.0333186\pi$
$984$	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	−0.615570	−	0.788082i	$-0.711074\pi$
$991$	−3.87351	+	2.58819i	−0.123046	+	0.0822167i	0.492524	+	0.870299i	$0.336074\pi$
$992$	−2.62233	+	0.521615i	−0.0832592	+	0.0165613i
$993$	−0.942877	+	1.41111i	−0.0299213	+	0.0447804i
$994$	−14.2781	+	16.0682i	−0.452873	+	0.509654i
$995$	−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	0.940079	+	0.340958i	$0.110751\pi$
$997$	6.37941	+	32.0715i	0.202038	+	1.01571i	−0.738041	+	0.674756i	$0.764249\pi$
$998$	−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.167.3	✓	48
7.6	odd	2	inner	238.2.p.b.167.4	yes	48
17.11	odd	16	inner	238.2.p.b.181.4	yes	48
119.62	even	16	inner	238.2.p.b.181.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.p.b.167.3	✓	48	1.1	even	1	trivial
238.2.p.b.167.4	yes	48	7.6	odd	2	inner
238.2.p.b.181.3	yes	48	119.62	even	16	inner
238.2.p.b.181.4	yes	48	17.11	odd	16	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(-0.596251 - 0.118602i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.74990 - 2.61891i) q^{5} +(0.596251 - 0.118602i) q^{6} +(1.59690 + 2.10948i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-2.43019 - 1.00662i) q^{9} +O(q^{10})\)	\(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} +(1.59690 + 2.10948i) 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} +(-2.28261 - 1.33780i) 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} +(-0.701964 - 1.44718i) 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} +(2.62081 + 0.362452i) 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} +(1.20234 + 1.06839i) 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} +(-1.89983 + 6.73726i) 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} +(-2.56001 + 0.668077i) 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} +(-1.75732 - 6.73391i) 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} +(0.490749 + 8.31896i) 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} +(-7.38169 - 6.55929i) 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} +(-10.4170 - 1.44064i) 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} +(-0.823018 - 6.95145i) 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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