LMFDB - Embedded newform 231.2.j.d.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.d.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +0.236068 q^{10} +(0.309017 - 3.30220i) q^{11} -1.61803 q^{12} +(0.809017 + 0.587785i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(3.42705 - 2.48990i) q^{17} +(-0.190983 - 0.587785i) q^{18} +(-0.500000 - 0.363271i) q^{20} +1.00000 q^{21} +(1.35410 - 1.53884i) q^{22} -3.23607 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-1.50000 + 4.61653i) q^{25} +(0.190983 + 0.587785i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.30902 - 0.951057i) q^{28} +(2.07295 + 6.37988i) q^{29} +(0.0729490 - 0.224514i) q^{30} +(8.28115 + 6.01661i) q^{31} -5.61803 q^{32} +(-3.04508 - 1.31433i) q^{33} +2.61803 q^{34} +(0.309017 + 0.224514i) q^{35} +(-0.500000 + 1.53884i) q^{36} +(2.14590 + 6.60440i) q^{37} +(0.809017 - 0.587785i) q^{39} +(-0.263932 - 0.812299i) q^{40} +(1.57295 - 4.84104i) q^{41} +(0.500000 + 0.363271i) q^{42} -1.00000 q^{43} +(-5.23607 + 1.17557i) q^{44} -0.381966 q^{45} +(-1.61803 - 1.17557i) q^{46} +(-2.26393 + 6.96767i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-2.42705 + 1.76336i) q^{50} +(-1.30902 - 4.02874i) q^{51} +(0.500000 - 1.53884i) q^{52} +(-6.16312 - 4.47777i) q^{53} -0.618034 q^{54} +(-0.645898 - 1.08981i) q^{55} +2.23607 q^{56} +(-1.28115 + 3.94298i) q^{58} +(-1.28115 - 3.94298i) q^{59} +(-0.500000 + 0.363271i) q^{60} +(4.66312 - 3.38795i) q^{61} +(1.95492 + 6.01661i) q^{62} +(0.309017 - 0.951057i) q^{63} +(0.190983 + 0.138757i) q^{64} +0.381966 q^{65} +(-1.04508 - 1.76336i) q^{66} -9.23607 q^{67} +(-5.54508 - 4.02874i) q^{68} +(-1.00000 + 3.07768i) q^{69} +(0.0729490 + 0.224514i) q^{70} +(6.04508 - 4.39201i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(3.57295 + 10.9964i) q^{73} +(-1.32624 + 4.08174i) q^{74} +(3.92705 + 2.85317i) q^{75} +(3.23607 - 0.726543i) q^{77} +0.618034 q^{78} +(-8.78115 - 6.37988i) q^{79} +(-0.218847 + 0.673542i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.54508 - 1.84911i) q^{82} +(4.85410 - 3.52671i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(0.500000 - 1.53884i) q^{85} +(-0.500000 - 0.363271i) q^{86} +6.70820 q^{87} +(-6.80902 - 2.93893i) q^{88} -6.38197 q^{89} +(-0.190983 - 0.138757i) q^{90} +(-0.309017 + 0.951057i) q^{91} +(1.61803 + 4.97980i) q^{92} +(8.28115 - 6.01661i) q^{93} +(-3.66312 + 2.66141i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(13.7533 + 9.99235i) q^{97} -0.618034 q^{98} +(-2.19098 + 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} + q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{20} + 4 q^{21} - 8 q^{22} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 3 q^{26} - q^{27} + 3 q^{28} + 15 q^{29} + 7 q^{30} + 13 q^{31} - 18 q^{32} - q^{33} + 6 q^{34} - q^{35} - 2 q^{36} + 22 q^{37} + q^{39} - 10 q^{40} + 13 q^{41} + 2 q^{42} - 4 q^{43} - 12 q^{44} - 6 q^{45} - 2 q^{46} - 18 q^{47} + 9 q^{48} - q^{49} - 3 q^{50} - 3 q^{51} + 2 q^{52} - 9 q^{53} + 2 q^{54} - 16 q^{55} + 15 q^{58} + 15 q^{59} - 2 q^{60} + 3 q^{61} + 19 q^{62} - q^{63} + 3 q^{64} + 6 q^{65} + 7 q^{66} - 28 q^{67} - 11 q^{68} - 4 q^{69} + 7 q^{70} + 13 q^{71} - 5 q^{72} + 21 q^{73} + 26 q^{74} + 9 q^{75} + 4 q^{77} - 2 q^{78} - 15 q^{79} - 21 q^{80} - q^{81} - q^{82} + 6 q^{83} - 2 q^{84} + 2 q^{85} - 2 q^{86} - 25 q^{88} - 30 q^{89} - 3 q^{90} + q^{91} + 2 q^{92} + 13 q^{93} + q^{94} + 2 q^{96} + 17 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 + q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^20 + 4 * q^21 - 8 * q^22 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 3 * q^26 - q^27 + 3 * q^28 + 15 * q^29 + 7 * q^30 + 13 * q^31 - 18 * q^32 - q^33 + 6 * q^34 - q^35 - 2 * q^36 + 22 * q^37 + q^39 - 10 * q^40 + 13 * q^41 + 2 * q^42 - 4 * q^43 - 12 * q^44 - 6 * q^45 - 2 * q^46 - 18 * q^47 + 9 * q^48 - q^49 - 3 * q^50 - 3 * q^51 + 2 * q^52 - 9 * q^53 + 2 * q^54 - 16 * q^55 + 15 * q^58 + 15 * q^59 - 2 * q^60 + 3 * q^61 + 19 * q^62 - q^63 + 3 * q^64 + 6 * q^65 + 7 * q^66 - 28 * q^67 - 11 * q^68 - 4 * q^69 + 7 * q^70 + 13 * q^71 - 5 * q^72 + 21 * q^73 + 26 * q^74 + 9 * q^75 + 4 * q^77 - 2 * q^78 - 15 * q^79 - 21 * q^80 - q^81 - q^82 + 6 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 - 25 * q^88 - 30 * q^89 - 3 * q^90 + q^91 + 2 * q^92 + 13 * q^93 + q^94 + 2 * q^96 + 17 * q^97 + 2 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	−0.516539	−	0.856264i	$-0.672780\pi$
$5$	0.309017	−	0.224514i	0.138197	−	0.100406i	0.654736	+	0.755858i	$0.272780\pi$
$6$	0.500000	−	0.363271i	0.204124	−	0.148305i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.236068			0.0746512
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−1.61803			−0.467086
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i	0.694297	−	0.719689i	$-0.255716\pi$
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i	−0.469916	+	0.882711i	$0.655716\pi$
$14$	−0.190983	+	0.587785i	−0.0510424	+	0.157092i
$15$	−0.118034	−	0.363271i	−0.0304762	−	0.0937962i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	3.42705	−	2.48990i	0.831182	−	0.603889i	−0.0887115	−	0.996057i	$-0.528275\pi$
$17$	3.42705	−	2.48990i	0.831182	−	0.603889i	0.919893	+	0.392168i	$0.128275\pi$
$18$	−0.190983	−	0.587785i	−0.0450151	−	0.138542i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−0.500000	−	0.363271i	−0.111803	−	0.0812299i
$21$	1.00000			0.218218
$22$	1.35410	−	1.53884i	0.288696	−	0.328082i
$23$	−3.23607			−0.674767			−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607			−0.674767			−0.337383	+	0.941367i	$0.609542\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$	−1.50000	+	4.61653i	−0.300000	+	0.923305i
$26$	0.190983	+	0.587785i	0.0374548	+	0.115274i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.30902	−	0.951057i	0.247381	−	0.179733i
$29$	2.07295	+	6.37988i	0.384937	+	1.18471i	0.936526	+	0.350598i	$0.114022\pi$
$29$	2.07295	+	6.37988i	0.384937	+	1.18471i	−0.551589	+	0.834116i	$0.685978\pi$
$30$	0.0729490	−	0.224514i	0.0133186	−	0.0409905i
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.975098	+	0.221773i	$0.0711844\pi$
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.512241	+	0.858842i	$0.328816\pi$
$32$	−5.61803			−0.993137
$33$	−3.04508	−	1.31433i	−0.530081	−	0.228795i
$34$	2.61803			0.448989
$35$	0.309017	+	0.224514i	0.0522334	+	0.0379498i
$36$	−0.500000	+	1.53884i	−0.0833333	+	0.256474i
$37$	2.14590	+	6.60440i	0.352783	+	1.08576i	0.957284	+	0.289151i	$0.0933729\pi$
$37$	2.14590	+	6.60440i	0.352783	+	1.08576i	−0.604500	+	0.796605i	$0.706627\pi$
$38$		0			0
$39$	0.809017	−	0.587785i	0.129546	−	0.0941210i
$40$	−0.263932	−	0.812299i	−0.0417313	−	0.128436i
$41$	1.57295	−	4.84104i	0.245653	−	0.756043i	−0.749875	−	0.661580i	$-0.769886\pi$
$41$	1.57295	−	4.84104i	0.245653	−	0.756043i	0.995528	−	0.0944637i	$-0.0301136\pi$
$42$	0.500000	+	0.363271i	0.0771517	+	0.0560540i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−5.23607	+	1.17557i	−0.789367	+	0.177224i
$45$	−0.381966			−0.0569401
$46$	−1.61803	−	1.17557i	−0.238566	−	0.173328i
$47$	−2.26393	+	6.96767i	−0.330228	+	1.01634i	0.638797	+	0.769376i	$0.279433\pi$
$47$	−2.26393	+	6.96767i	−0.330228	+	1.01634i	−0.969025	+	0.246963i	$0.920567\pi$
$48$	0.572949	+	1.76336i	0.0826981	+	0.254518i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−2.42705	+	1.76336i	−0.343237	+	0.249376i
$51$	−1.30902	−	4.02874i	−0.183299	−	0.564136i
$52$	0.500000	−	1.53884i	0.0693375	−	0.213399i
$53$	−6.16312	−	4.47777i	−0.846569	−	0.615069i	0.0776285	−	0.996982i	$-0.475265\pi$
$53$	−6.16312	−	4.47777i	−0.846569	−	0.615069i	−0.924198	+	0.381914i	$0.875265\pi$
$54$	−0.618034			−0.0841038
$55$	−0.645898	−	1.08981i	−0.0870929	−	0.146950i
$56$	2.23607			0.298807
$57$		0			0
$58$	−1.28115	+	3.94298i	−0.168224	+	0.517739i
$59$	−1.28115	−	3.94298i	−0.166792	−	0.513333i	0.832372	−	0.554217i	$-0.186982\pi$
$59$	−1.28115	−	3.94298i	−0.166792	−	0.513333i	−0.999164	+	0.0408847i	$0.986982\pi$
$60$	−0.500000	+	0.363271i	−0.0645497	+	0.0468981i
$61$	4.66312	−	3.38795i	0.597051	−	0.433783i	−0.247780	−	0.968816i	$-0.579701\pi$
$61$	4.66312	−	3.38795i	0.597051	−	0.433783i	0.844831	+	0.535033i	$0.179701\pi$
$62$	1.95492	+	6.01661i	0.248274	+	0.764110i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	0.381966			0.0473771
$66$	−1.04508	−	1.76336i	−0.128641	−	0.217054i
$67$	−9.23607			−1.12837			−0.564183	−	0.825650i	$-0.690809\pi$
$67$	−9.23607			−1.12837			−0.564183	+	0.825650i	$0.690809\pi$
$68$	−5.54508	−	4.02874i	−0.672440	−	0.488556i
$69$	−1.00000	+	3.07768i	−0.120386	+	0.370510i
$70$	0.0729490	+	0.224514i	0.00871908	+	0.0268346i
$71$	6.04508	−	4.39201i	0.717420	−	0.521236i	−0.168139	−	0.985763i	$-0.553776\pi$
$71$	6.04508	−	4.39201i	0.717420	−	0.521236i	0.885559	+	0.464527i	$0.153776\pi$
$72$	−1.80902	+	1.31433i	−0.213195	+	0.154895i
$73$	3.57295	+	10.9964i	0.418182	+	1.28703i	0.909374	+	0.415980i	$0.136562\pi$
$73$	3.57295	+	10.9964i	0.418182	+	1.28703i	−0.491192	+	0.871052i	$0.663438\pi$
$74$	−1.32624	+	4.08174i	−0.154172	+	0.474493i
$75$	3.92705	+	2.85317i	0.453457	+	0.329456i
$76$		0			0
$77$	3.23607	−	0.726543i	0.368784	−	0.0827972i
$78$	0.618034			0.0699786
$79$	−8.78115	−	6.37988i	−0.987957	−	0.717793i	−0.0284842	−	0.999594i	$-0.509068\pi$
$79$	−8.78115	−	6.37988i	−0.987957	−	0.717793i	−0.959473	+	0.281802i	$0.909068\pi$
$80$	−0.218847	+	0.673542i	−0.0244678	+	0.0753043i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.54508	−	1.84911i	0.281058	−	0.204200i
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	−0.288600	−	0.957450i	$-0.593190\pi$
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	0.821407	+	0.570343i	$0.193190\pi$
$84$	−0.500000	−	1.53884i	−0.0545545	−	0.167901i
$85$	0.500000	−	1.53884i	0.0542326	−	0.166911i
$86$	−0.500000	−	0.363271i	−0.0539164	−	0.0391725i
$87$	6.70820			0.719195
$88$	−6.80902	−	2.93893i	−0.725844	−	0.313291i
$89$	−6.38197			−0.676487			−0.338244	−	0.941059i	$-0.609833\pi$
$89$	−6.38197			−0.676487			−0.338244	+	0.941059i	$0.609833\pi$
$90$	−0.190983	−	0.138757i	−0.0201314	−	0.0146263i
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$	1.61803	+	4.97980i	0.168692	+	0.519180i
$93$	8.28115	−	6.01661i	0.858716	−	0.623893i
$94$	−3.66312	+	2.66141i	−0.377822	+	0.274504i
$95$		0			0
$96$	−1.73607	+	5.34307i	−0.177187	+	0.545325i
$97$	13.7533	+	9.99235i	1.39643	+	1.01457i	0.995124	+	0.0986273i	$0.0314452\pi$
$97$	13.7533	+	9.99235i	1.39643	+	1.01457i	0.401310	+	0.915942i	$0.368555\pi$
$98$	−0.618034			−0.0624309
$99$	−2.19098	+	2.48990i	−0.220202	+	0.250244i
$100$	7.85410			0.785410
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	0.743191	−	0.669079i	$-0.233311\pi$
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	−0.406673	+	0.913574i	$0.633311\pi$
$102$	0.809017	−	2.48990i	0.0801046	−	0.246537i
$103$	−3.92705	−	12.0862i	−0.386944	−	1.19089i	−0.935060	−	0.354489i	$-0.884655\pi$
$103$	−3.92705	−	12.0862i	−0.386944	−	1.19089i	0.548116	−	0.836402i	$-0.315345\pi$
$104$	1.80902	−	1.31433i	0.177389	−	0.128880i
$105$	0.309017	−	0.224514i	0.0301570	−	0.0219103i
$106$	−1.45492	−	4.47777i	−0.141314	−	0.434919i
$107$	4.87132	−	14.9924i	0.470929	−	1.44937i	−0.380442	−	0.924805i	$-0.624228\pi$
$107$	4.87132	−	14.9924i	0.470929	−	1.44937i	0.851371	−	0.524564i	$-0.175772\pi$
$108$	1.30902	+	0.951057i	0.125960	+	0.0915155i
$109$	−7.56231			−0.724338			−0.362169	−	0.932113i	$-0.617964\pi$
$109$	−7.56231			−0.724338			−0.362169	+	0.932113i	$0.617964\pi$
$110$	0.0729490	−	0.779543i	0.00695542	−	0.0743265i
$111$	6.94427			0.659121
$112$	−1.50000	−	1.08981i	−0.141737	−	0.102978i
$113$	−3.60081	+	11.0822i	−0.338736	+	1.04252i	0.626116	+	0.779730i	$0.284643\pi$
$113$	−3.60081	+	11.0822i	−0.338736	+	1.04252i	−0.964852	+	0.262793i	$0.915357\pi$
$114$		0			0
$115$	−1.00000	+	0.726543i	−0.0932505	+	0.0677504i
$116$	8.78115	−	6.37988i	0.815310	−	0.592357i
$117$	−0.309017	−	0.951057i	−0.0285686	−	0.0879252i
$118$	0.791796	−	2.43690i	0.0728907	−	0.224335i
$119$	3.42705	+	2.48990i	0.314157	+	0.228249i
$120$	−0.854102			−0.0779685
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	3.56231			0.322516
$123$	−4.11803	−	2.99193i	−0.371311	−	0.269773i
$124$	5.11803	−	15.7517i	0.459613	−	1.41454i
$125$	1.16312	+	3.57971i	0.104033	+	0.320179i
$126$	0.500000	−	0.363271i	0.0445435	−	0.0323628i
$127$	5.92705	−	4.30625i	0.525941	−	0.382118i	−0.292896	−	0.956144i	$-0.594619\pi$
$127$	5.92705	−	4.30625i	0.525941	−	0.382118i	0.818837	+	0.574026i	$0.194619\pi$
$128$	3.51722	+	10.8249i	0.310881	+	0.956794i
$129$	−0.309017	+	0.951057i	−0.0272074	+	0.0837359i
$130$	0.190983	+	0.138757i	0.0167503	+	0.0121698i
$131$	−3.32624			−0.290615			−0.145307	−	0.989387i	$-0.546417\pi$
$131$	−3.32624			−0.290615			−0.145307	+	0.989387i	$0.546417\pi$
$132$	−0.500000	+	5.34307i	−0.0435194	+	0.465054i
$133$		0			0
$134$	−4.61803	−	3.35520i	−0.398937	−	0.289845i
$135$	−0.118034	+	0.363271i	−0.0101587	+	0.0312654i
$136$	−2.92705	−	9.00854i	−0.250993	−	0.772476i
$137$	2.47214	−	1.79611i	0.211209	−	0.153452i	−0.477152	−	0.878821i	$-0.658331\pi$
$137$	2.47214	−	1.79611i	0.211209	−	0.153452i	0.688360	+	0.725369i	$0.258331\pi$
$138$	−1.61803	+	1.17557i	−0.137736	+	0.100071i
$139$	−5.42705	−	16.7027i	−0.460316	−	1.41671i	−0.864778	−	0.502154i	$-0.832541\pi$
$139$	−5.42705	−	16.7027i	−0.460316	−	1.41671i	0.404462	−	0.914555i	$-0.367459\pi$
$140$	0.190983	−	0.587785i	0.0161410	−	0.0496769i
$141$	5.92705	+	4.30625i	0.499148	+	0.362652i
$142$	4.61803			0.387537
$143$	2.19098	−	2.48990i	0.183219	−	0.208216i
$144$	1.85410			0.154508
$145$	2.07295	+	1.50609i	0.172149	+	0.125074i
$146$	−2.20820	+	6.79615i	−0.182752	+	0.562454i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	9.09017	−	6.60440i	0.747207	−	0.542878i
$149$	10.5902	−	7.69421i	0.867581	−	0.630334i	−0.0623561	−	0.998054i	$-0.519861\pi$
$149$	10.5902	−	7.69421i	0.867581	−	0.630334i	0.929937	+	0.367720i	$0.119861\pi$
$150$	0.927051	+	2.85317i	0.0756934	+	0.232960i
$151$	−6.51722	+	20.0579i	−0.530364	+	1.63229i	0.223095	+	0.974797i	$0.428384\pi$
$151$	−6.51722	+	20.0579i	−0.530364	+	1.63229i	−0.753458	+	0.657495i	$0.771616\pi$
$152$		0			0
$153$	−4.23607			−0.342466
$154$	1.88197	+	0.812299i	0.151653	+	0.0654569i
$155$	3.90983			0.314045
$156$	−1.30902	−	0.951057i	−0.104805	−	0.0761455i
$157$	−0.517221	+	1.59184i	−0.0412787	+	0.127043i	−0.969572	−	0.244806i	$-0.921276\pi$
$157$	−0.517221	+	1.59184i	−0.0412787	+	0.127043i	0.928293	+	0.371848i	$0.121276\pi$
$158$	−2.07295	−	6.37988i	−0.164915	−	0.507556i
$159$	−6.16312	+	4.47777i	−0.488767	+	0.355110i
$160$	−1.73607	+	1.26133i	−0.137248	+	0.0997167i
$161$	−1.00000	−	3.07768i	−0.0788110	−	0.242555i
$162$	−0.190983	+	0.587785i	−0.0150050	+	0.0461808i
$163$	−4.88197	−	3.54696i	−0.382385	−	0.277819i	0.379943	−	0.925010i	$-0.375944\pi$
$163$	−4.88197	−	3.54696i	−0.382385	−	0.277819i	−0.762328	+	0.647191i	$0.775944\pi$
$164$	−8.23607			−0.643129
$165$	−1.23607	+	0.277515i	−0.0962278	+	0.0216045i
$166$	3.70820			0.287812
$167$	−7.59017	−	5.51458i	−0.587345	−	0.426731i	0.254020	−	0.967199i	$-0.418247\pi$
$167$	−7.59017	−	5.51458i	−0.587345	−	0.426731i	−0.841365	+	0.540468i	$0.818247\pi$
$168$	0.690983	−	2.12663i	0.0533105	−	0.164073i
$169$	−3.70820	−	11.4127i	−0.285246	−	0.877898i
$170$	0.809017	−	0.587785i	0.0620488	−	0.0450811i
$171$		0			0
$172$	0.500000	+	1.53884i	0.0381246	+	0.117336i
$173$	−4.51722	+	13.9026i	−0.343438	+	1.05699i	0.618977	+	0.785409i	$0.287547\pi$
$173$	−4.51722	+	13.9026i	−0.343438	+	1.05699i	−0.962415	+	0.271584i	$0.912453\pi$
$174$	3.35410	+	2.43690i	0.254274	+	0.184741i
$175$	−4.85410			−0.366936
$176$	3.13525	+	5.29007i	0.236329	+	0.398754i
$177$	−4.14590			−0.311625
$178$	−3.19098	−	2.31838i	−0.239174	−	0.173770i
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$	0.190983	+	0.587785i	0.0142350	+	0.0438109i
$181$	0.190983	−	0.138757i	0.0141957	−	0.0103137i	−0.580665	−	0.814143i	$-0.697207\pi$
$181$	0.190983	−	0.138757i	0.0141957	−	0.0103137i	0.594860	+	0.803829i	$0.297207\pi$
$182$	−0.500000	+	0.363271i	−0.0370625	+	0.0269275i
$183$	−1.78115	−	5.48183i	−0.131667	−	0.405228i
$184$	−2.23607	+	6.88191i	−0.164845	+	0.507341i
$185$	2.14590	+	1.55909i	0.157770	+	0.114626i
$186$	6.32624			0.463862
$187$	−7.16312	−	12.0862i	−0.523819	−	0.883832i
$188$	11.8541			0.864549
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$		0			0
$191$	3.01722	+	9.28605i	0.218318	+	0.671915i	0.998901	+	0.0468628i	$0.0149224\pi$
$191$	3.01722	+	9.28605i	0.218318	+	0.671915i	−0.780583	+	0.625052i	$0.785078\pi$
$192$	0.190983	−	0.138757i	0.0137830	−	0.0100139i
$193$	−4.09017	+	2.97168i	−0.294417	+	0.213906i	−0.725181	−	0.688558i	$-0.758244\pi$
$193$	−4.09017	+	2.97168i	−0.294417	+	0.213906i	0.430764	+	0.902464i	$0.358244\pi$
$194$	3.24671	+	9.99235i	0.233100	+	0.717409i
$195$	0.118034	−	0.363271i	0.00845259	−	0.0260144i
$196$	1.30902	+	0.951057i	0.0935012	+	0.0679326i
$197$	−9.23607			−0.658043			−0.329021	−	0.944323i	$-0.606719\pi$
$197$	−9.23607			−0.658043			−0.329021	+	0.944323i	$0.606719\pi$
$198$	−2.00000	+	0.449028i	−0.142134	+	0.0319110i
$199$	−7.56231			−0.536078			−0.268039	−	0.963408i	$-0.586376\pi$
$199$	−7.56231			−0.536078			−0.268039	+	0.963408i	$0.586376\pi$
$200$	8.78115	+	6.37988i	0.620921	+	0.451126i
$201$	−2.85410	+	8.78402i	−0.201313	+	0.619577i
$202$	0.798374	+	2.45714i	0.0561734	+	0.172884i
$203$	−5.42705	+	3.94298i	−0.380904	+	0.276743i
$204$	−5.54508	+	4.02874i	−0.388234	+	0.282068i
$205$	−0.600813	−	1.84911i	−0.0419626	−	0.129148i
$206$	2.42705	−	7.46969i	0.169101	−	0.520438i
$207$	2.61803	+	1.90211i	0.181966	+	0.132206i
$208$	−1.85410			−0.128559
$209$		0			0
$210$	0.236068			0.0162902
$211$	−4.28115	−	3.11044i	−0.294727	−	0.214131i	0.430589	−	0.902548i	$-0.358306\pi$
$211$	−4.28115	−	3.11044i	−0.294727	−	0.214131i	−0.725315	+	0.688417i	$0.758306\pi$
$212$	−3.80902	+	11.7229i	−0.261604	+	0.805135i
$213$	−2.30902	−	7.10642i	−0.158211	−	0.486924i
$214$	7.88197	−	5.72658i	0.538800	−	0.391461i
$215$	−0.309017	+	0.224514i	−0.0210748	+	0.0153117i
$216$	0.690983	+	2.12663i	0.0470154	+	0.144699i
$217$	−3.16312	+	9.73508i	−0.214727	+	0.660860i
$218$	−3.78115	−	2.74717i	−0.256092	−	0.186062i
$219$	11.5623			0.781308
$220$	−1.35410	+	1.53884i	−0.0912935	+	0.103749i
$221$	4.23607			0.284949
$222$	3.47214	+	2.52265i	0.233035	+	0.169309i
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	0.729178	+	0.684324i	$0.239903\pi$
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	−0.992153	+	0.125029i	$0.960097\pi$
$224$	−1.73607	−	5.34307i	−0.115996	−	0.356999i
$225$	3.92705	−	2.85317i	0.261803	−	0.190211i
$226$	−5.82624	+	4.23301i	−0.387556	+	0.281576i
$227$	5.86475	+	18.0498i	0.389257	+	1.19801i	0.933345	+	0.358981i	$0.116876\pi$
$227$	5.86475	+	18.0498i	0.389257	+	1.19801i	−0.544088	+	0.839028i	$0.683124\pi$
$228$		0			0
$229$	9.47214	+	6.88191i	0.625936	+	0.454769i	0.854990	−	0.518644i	$-0.173563\pi$
$229$	9.47214	+	6.88191i	0.625936	+	0.454769i	−0.229054	+	0.973414i	$0.573563\pi$
$230$	−0.763932			−0.0503722
$231$	0.309017	−	3.30220i	0.0203318	−	0.217269i
$232$	15.0000			0.984798
$233$	−5.04508	−	3.66547i	−0.330515	−	0.240133i	0.410134	−	0.912025i	$-0.365482\pi$
$233$	−5.04508	−	3.66547i	−0.330515	−	0.240133i	−0.740649	+	0.671892i	$0.765482\pi$
$234$	0.190983	−	0.587785i	0.0124849	−	0.0384247i
$235$	0.864745	+	2.66141i	0.0564097	+	0.173611i
$236$	−5.42705	+	3.94298i	−0.353271	+	0.256666i
$237$	−8.78115	+	6.37988i	−0.570397	+	0.414418i
$238$	0.809017	+	2.48990i	0.0524408	+	0.161396i
$239$	5.91641	−	18.2088i	0.382701	−	1.17783i	−0.555434	−	0.831561i	$-0.687448\pi$
$239$	5.91641	−	18.2088i	0.382701	−	1.17783i	0.938135	−	0.346271i	$-0.112552\pi$
$240$	0.572949	+	0.416272i	0.0369837	+	0.0268702i
$241$	−24.7082			−1.59160			−0.795798	−	0.605563i	$-0.792948\pi$
$241$	−24.7082			−1.59160			−0.795798	+	0.605563i	$0.792948\pi$
$242$	−4.66312	−	4.94704i	−0.299757	−	0.318008i
$243$	1.00000			0.0641500
$244$	−7.54508	−	5.48183i	−0.483025	−	0.350938i
$245$	−0.118034	+	0.363271i	−0.00754091	+	0.0232085i
$246$	−0.972136	−	2.99193i	−0.0619811	−	0.190758i
$247$		0			0
$248$	18.5172	−	13.4535i	1.17584	−	0.854301i
$249$	−1.85410	−	5.70634i	−0.117499	−	0.361625i
$250$	−0.718847	+	2.21238i	−0.0454639	+	0.139923i
$251$	−21.5172	−	15.6332i	−1.35815	−	0.986757i	−0.998560	−	0.0536489i	$-0.982915\pi$
$251$	−21.5172	−	15.6332i	−1.35815	−	0.986757i	−0.359595	−	0.933108i	$-0.617085\pi$
$252$	−1.61803			−0.101927
$253$	−1.00000	+	10.6861i	−0.0628695	+	0.671832i
$254$	4.52786			0.284103
$255$	−1.30902	−	0.951057i	−0.0819738	−	0.0595575i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	8.32624	+	25.6255i	0.519376	+	1.59848i	0.775175	+	0.631746i	$0.217662\pi$
$257$	8.32624	+	25.6255i	0.519376	+	1.59848i	−0.255799	+	0.966730i	$0.582338\pi$
$258$	−0.500000	+	0.363271i	−0.0311286	+	0.0226163i
$259$	−5.61803	+	4.08174i	−0.349088	+	0.253627i
$260$	−0.190983	−	0.587785i	−0.0118443	−	0.0364529i
$261$	2.07295	−	6.37988i	0.128312	−	0.394905i
$262$	−1.66312	−	1.20833i	−0.102748	−	0.0746507i
$263$	0.708204			0.0436697			0.0218349	−	0.999762i	$-0.493049\pi$
$263$	0.708204			0.0436697			0.0218349	+	0.999762i	$0.493049\pi$
$264$	−4.89919	+	5.56758i	−0.301524	+	0.342661i
$265$	−2.90983			−0.178749
$266$		0			0
$267$	−1.97214	+	6.06961i	−0.120693	+	0.371454i
$268$	4.61803	+	14.2128i	0.282091	+	0.868188i
$269$	−19.3713	+	14.0741i	−1.18109	+	0.858112i	−0.992294	−	0.123904i	$-0.960459\pi$
$269$	−19.3713	+	14.0741i	−1.18109	+	0.858112i	−0.188796	+	0.982016i	$0.560459\pi$
$270$	−0.190983	+	0.138757i	−0.0116229	+	0.00844450i
$271$	−1.98278	−	6.10237i	−0.120445	−	0.370692i	0.872599	−	0.488438i	$-0.162433\pi$
$271$	−1.98278	−	6.10237i	−0.120445	−	0.370692i	−0.993044	+	0.117746i	$0.962433\pi$
$272$	−2.42705	+	7.46969i	−0.147162	+	0.452917i
$273$	0.809017	+	0.587785i	0.0489639	+	0.0355744i
$274$	1.88854			0.114091
$275$	14.7812	+	6.37988i	0.891337	+	0.384721i
$276$	5.23607			0.315174
$277$	20.5623	+	14.9394i	1.23547	+	0.897621i	0.997288	−	0.0735998i	$-0.0234487\pi$
$277$	20.5623	+	14.9394i	1.23547	+	0.897621i	0.238181	+	0.971221i	$0.423449\pi$
$278$	3.35410	−	10.3229i	0.201166	−	0.619124i
$279$	−3.16312	−	9.73508i	−0.189371	−	0.582824i
$280$	0.690983	−	0.502029i	0.0412941	−	0.0300019i
$281$	−12.6353	+	9.18005i	−0.753756	+	0.547636i	−0.896989	−	0.442053i	$-0.854250\pi$
$281$	−12.6353	+	9.18005i	−0.753756	+	0.547636i	0.143233	+	0.989689i	$0.454250\pi$
$282$	1.39919	+	4.30625i	0.0833204	+	0.256434i
$283$	2.25329	−	6.93491i	0.133944	−	0.412238i	−0.861480	−	0.507791i	$-0.830462\pi$
$283$	2.25329	−	6.93491i	0.133944	−	0.412238i	0.995424	+	0.0955536i	$0.0304621\pi$
$284$	−9.78115	−	7.10642i	−0.580405	−	0.421689i
$285$		0			0
$286$	2.00000	−	0.449028i	0.118262	−	0.0265516i
$287$	5.09017			0.300463
$288$	4.54508	+	3.30220i	0.267822	+	0.194584i
$289$	0.291796	−	0.898056i	0.0171645	−	0.0528268i
$290$	0.489357	+	1.50609i	0.0287360	+	0.0884404i
$291$	13.7533	−	9.99235i	0.806232	−	0.585762i
$292$	15.1353	−	10.9964i	0.885724	−	0.643516i
$293$	−4.09017	−	12.5882i	−0.238950	−	0.735413i	−0.996573	−	0.0827204i	$-0.973639\pi$
$293$	−4.09017	−	12.5882i	−0.238950	−	0.735413i	0.757623	−	0.652693i	$-0.226361\pi$
$294$	−0.190983	+	0.587785i	−0.0111384	+	0.0342803i
$295$	−1.28115	−	0.930812i	−0.0745916	−	0.0541940i
$296$	15.5279			0.902539
$297$	1.69098	+	2.85317i	0.0981208	+	0.165558i
$298$	8.09017			0.468651
$299$	−2.61803	−	1.90211i	−0.151405	−	0.110002i
$300$	2.42705	−	7.46969i	0.140126	−	0.431263i
$301$	−0.309017	−	0.951057i	−0.0178114	−	0.0548180i
$302$	−10.5451	+	7.66145i	−0.606801	+	0.440867i
$303$	3.38197	−	2.45714i	0.194289	−	0.141159i
$304$		0			0
$305$	0.680340	−	2.09387i	0.0389561	−	0.119895i
$306$	−2.11803	−	1.53884i	−0.121080	−	0.0879697i
$307$	19.1803			1.09468			0.547340	−	0.836910i	$-0.315640\pi$
$307$	19.1803			1.09468			0.547340	+	0.836910i	$0.315640\pi$
$308$	−2.73607	−	4.61653i	−0.155902	−	0.263051i
$309$	−12.7082			−0.722944
$310$	1.95492	+	1.42033i	0.111032	+	0.0806693i
$311$	5.19098	−	15.9762i	0.294354	−	0.905927i	−0.689084	−	0.724681i	$-0.741987\pi$
$311$	5.19098	−	15.9762i	0.294354	−	0.905927i	0.983438	−	0.181246i	$-0.0580130\pi$
$312$	−0.690983	−	2.12663i	−0.0391192	−	0.120397i
$313$	12.7812	−	9.28605i	0.722433	−	0.524879i	−0.164727	−	0.986339i	$-0.552674\pi$
$313$	12.7812	−	9.28605i	0.722433	−	0.524879i	0.887161	+	0.461461i	$0.152674\pi$
$314$	−0.836881	+	0.608030i	−0.0472279	+	0.0343131i
$315$	−0.118034	−	0.363271i	−0.00665046	−	0.0204680i
$316$	−5.42705	+	16.7027i	−0.305295	+	0.939603i
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.163569	−	0.986532i	$-0.552301\pi$
$317$	−20.5172	−	14.9066i	−1.15236	−	0.837240i	−0.988793	+	0.149292i	$0.952301\pi$
$318$	−4.70820			−0.264023
$319$	21.7082	−	4.87380i	1.21543	−	0.272880i
$320$	0.0901699			0.00504065
$321$	−12.7533	−	9.26581i	−0.711819	−	0.517167i
$322$	0.618034	−	1.90211i	0.0344417	−	0.106001i
$323$		0			0
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$	−3.92705	+	2.85317i	−0.217834	+	0.158265i
$326$	−1.15248	−	3.54696i	−0.0638297	−	0.196448i
$327$	−2.33688	+	7.19218i	−0.129230	+	0.397728i
$328$	−9.20820	−	6.69015i	−0.508438	−	0.369402i
$329$	−7.32624			−0.403909
$330$	−0.718847	−	0.310271i	−0.0395712	−	0.0170798i
$331$	−14.7082			−0.808436			−0.404218	−	0.914663i	$-0.632456\pi$
$331$	−14.7082			−0.808436			−0.404218	+	0.914663i	$0.632456\pi$
$332$	−7.85410	−	5.70634i	−0.431050	−	0.313176i
$333$	2.14590	−	6.60440i	0.117594	−	0.361919i
$334$	−1.79180	−	5.51458i	−0.0980427	−	0.301744i
$335$	−2.85410	+	2.07363i	−0.155936	+	0.113294i
$336$	−1.50000	+	1.08981i	−0.0818317	+	0.0594542i
$337$	0.399187	+	1.22857i	0.0217451	+	0.0669245i	0.961340	−	0.275363i	$-0.0887982\pi$
$337$	0.399187	+	1.22857i	0.0217451	+	0.0669245i	−0.939595	+	0.342288i	$0.888798\pi$
$338$	2.29180	−	7.05342i	0.124657	−	0.383656i
$339$	9.42705	+	6.84915i	0.512007	+	0.371995i
$340$	−2.61803			−0.141983
$341$	22.4271	−	25.4868i	1.21449	−	1.38019i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−0.690983	+	2.12663i	−0.0372553	+	0.114660i
$345$	0.381966	+	1.17557i	0.0205644	+	0.0632906i
$346$	−7.30902	+	5.31031i	−0.392935	+	0.285484i
$347$	20.5623	−	14.9394i	1.10384	−	0.801988i	0.122159	−	0.992510i	$-0.461018\pi$
$347$	20.5623	−	14.9394i	1.10384	−	0.801988i	0.981683	+	0.190522i	$0.0610181\pi$
$348$	−3.35410	−	10.3229i	−0.179799	−	0.553364i
$349$	10.7918	−	33.2137i	0.577672	−	1.77789i	−0.0492248	−	0.998788i	$-0.515675\pi$
$349$	10.7918	−	33.2137i	0.577672	−	1.77789i	0.626896	−	0.779103i	$-0.284325\pi$
$350$	−2.42705	−	1.76336i	−0.129731	−	0.0942553i
$351$	−1.00000			−0.0533761
$352$	−1.73607	+	18.5519i	−0.0925327	+	0.988817i
$353$	−25.4721			−1.35574			−0.677872	−	0.735179i	$-0.737098\pi$
$353$	−25.4721			−1.35574			−0.677872	+	0.735179i	$0.737098\pi$
$354$	−2.07295	−	1.50609i	−0.110176	−	0.0800475i
$355$	0.881966	−	2.71441i	0.0468099	−	0.144066i
$356$	3.19098	+	9.82084i	0.169122	+	0.520503i
$357$	3.42705	−	2.48990i	0.181379	−	0.131779i
$358$	−1.11803	+	0.812299i	−0.0590899	+	0.0429313i
$359$	−10.2639	−	31.5891i	−0.541710	−	1.66721i	−0.728687	−	0.684847i	$-0.759869\pi$
$359$	−10.2639	−	31.5891i	−0.541710	−	1.66721i	0.186978	−	0.982364i	$-0.440131\pi$
$360$	−0.263932	+	0.812299i	−0.0139104	+	0.0428119i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$	0.145898			0.00766823
$363$	−5.28115	+	9.64932i	−0.277189	+	0.506458i
$364$	1.61803			0.0848080
$365$	3.57295	+	2.59590i	0.187017	+	0.135876i
$366$	1.10081	−	3.38795i	0.0575404	−	0.177091i
$367$	3.48936	+	10.7391i	0.182143	+	0.560578i	0.999887	−	0.0150030i	$-0.00477579\pi$
$367$	3.48936	+	10.7391i	0.182143	+	0.560578i	−0.817745	+	0.575581i	$0.804776\pi$
$368$	4.85410	−	3.52671i	0.253038	−	0.183843i
$369$	−4.11803	+	2.99193i	−0.214376	+	0.155753i
$370$	0.506578	+	1.55909i	0.0263357	+	0.0810530i
$371$	2.35410	−	7.24518i	0.122219	−	0.376151i
$372$	−13.3992	−	9.73508i	−0.694715	−	0.504740i
$373$	30.1803			1.56268			0.781339	−	0.624106i	$-0.214537\pi$
$373$	30.1803			1.56268			0.781339	+	0.624106i	$0.214537\pi$
$374$	0.809017	−	8.64527i	0.0418333	−	0.447036i
$375$	3.76393			0.194369
$376$	13.2533	+	9.62908i	0.683486	+	0.496582i
$377$	−2.07295	+	6.37988i	−0.106762	+	0.328581i
$378$	−0.190983	−	0.587785i	−0.00982311	−	0.0302324i
$379$	8.78115	−	6.37988i	0.451058	−	0.327712i	−0.338956	−	0.940802i	$-0.610074\pi$
$379$	8.78115	−	6.37988i	0.451058	−	0.327712i	0.790013	+	0.613090i	$0.210074\pi$
$380$		0			0
$381$	−2.26393	−	6.96767i	−0.115985	−	0.356964i
$382$	−1.86475	+	5.73910i	−0.0954087	+	0.293638i
$383$	6.39919	+	4.64928i	0.326983	+	0.237567i	0.739149	−	0.673541i	$-0.235228\pi$
$383$	6.39919	+	4.64928i	0.326983	+	0.237567i	−0.412166	+	0.911109i	$0.635228\pi$
$384$	11.3820			0.580834
$385$	0.836881	−	0.951057i	0.0426514	−	0.0484703i
$386$	−3.12461			−0.159039
$387$	0.809017	+	0.587785i	0.0411246	+	0.0298788i
$388$	8.50000	−	26.1603i	0.431522	−	1.32809i
$389$	6.38197	+	19.6417i	0.323579	+	0.995872i	0.972078	+	0.234657i	$0.0753968\pi$
$389$	6.38197	+	19.6417i	0.323579	+	0.995872i	−0.648500	+	0.761215i	$0.724603\pi$
$390$	0.190983	−	0.138757i	0.00967080	−	0.00702625i
$391$	−11.0902	+	8.05748i	−0.560854	+	0.407484i
$392$	0.690983	+	2.12663i	0.0348999	+	0.107411i
$393$	−1.02786	+	3.16344i	−0.0518489	+	0.159574i
$394$	−4.61803	−	3.35520i	−0.232653	−	0.169032i
$395$	−4.14590			−0.208603
$396$	4.92705	+	2.12663i	0.247594	+	0.106867i
$397$	25.6869			1.28919			0.644595	−	0.764524i	$-0.277026\pi$
$397$	25.6869			1.28919			0.644595	+	0.764524i	$0.277026\pi$
$398$	−3.78115	−	2.74717i	−0.189532	−	0.137703i
$399$		0			0
$400$	−2.78115	−	8.55951i	−0.139058	−	0.427975i
$401$	−9.44427	+	6.86167i	−0.471624	+	0.342655i	−0.798074	−	0.602559i	$-0.794148\pi$
$401$	−9.44427	+	6.86167i	−0.471624	+	0.342655i	0.326450	+	0.945215i	$0.394148\pi$
$402$	−4.61803	+	3.35520i	−0.230327	+	0.167342i
$403$	3.16312	+	9.73508i	0.157566	+	0.484939i
$404$	2.09017	−	6.43288i	0.103990	−	0.320048i
$405$	0.309017	+	0.224514i	0.0153552	+	0.0111562i
$406$	−4.14590			−0.205757
$407$	22.4721	−	5.04531i	1.11390	−	0.250087i
$408$	−9.47214			−0.468941
$409$	21.3435	+	15.5069i	1.05537	+	0.766768i	0.973226	−	0.229852i	$-0.0738243\pi$
$409$	21.3435	+	15.5069i	1.05537	+	0.766768i	0.0821406	+	0.996621i	$0.473824\pi$
$410$	0.371323	−	1.14281i	0.0183383	−	0.0564396i
$411$	−0.944272	−	2.90617i	−0.0465775	−	0.143351i
$412$	−16.6353	+	12.0862i	−0.819560	+	0.595445i
$413$	3.35410	−	2.43690i	0.165045	−	0.119912i
$414$	0.618034	+	1.90211i	0.0303747	+	0.0934838i
$415$	0.708204	−	2.17963i	0.0347644	−	0.106994i
$416$	−4.54508	−	3.30220i	−0.222841	−	0.161904i
$417$	−17.5623			−0.860030
$418$		0			0
$419$	−15.3262			−0.748736			−0.374368	−	0.927280i	$-0.622140\pi$
$419$	−15.3262			−0.748736			−0.374368	+	0.927280i	$0.622140\pi$
$420$	−0.500000	−	0.363271i	−0.0243975	−	0.0177258i
$421$	0.843459	−	2.59590i	0.0411077	−	0.126516i	−0.928397	−	0.371591i	$-0.878812\pi$
$421$	0.843459	−	2.59590i	0.0411077	−	0.126516i	0.969504	+	0.245074i	$0.0788124\pi$
$422$	−1.01064	−	3.11044i	−0.0491973	−	0.151414i
$423$	5.92705	−	4.30625i	0.288183	−	0.209377i
$424$	−13.7812	+	10.0126i	−0.669272	+	0.486255i
$425$	6.35410	+	19.5559i	0.308219	+	0.948601i
$426$	1.42705	−	4.39201i	0.0691408	−	0.212794i
$427$	4.66312	+	3.38795i	0.225664	+	0.163955i
$428$	−25.5066			−1.23291
$429$	−1.69098	−	2.85317i	−0.0816414	−	0.137752i
$430$	−0.236068			−0.0113842
$431$	30.5795	+	22.2173i	1.47296	+	1.07017i	0.979741	+	0.200268i	$0.0641813\pi$
$431$	30.5795	+	22.2173i	1.47296	+	1.07017i	0.493223	+	0.869903i	$0.335819\pi$
$432$	0.572949	−	1.76336i	0.0275660	−	0.0848395i
$433$	−0.798374	−	2.45714i	−0.0383674	−	0.118083i	0.930038	−	0.367462i	$-0.119773\pi$
$433$	−0.798374	−	2.45714i	−0.0383674	−	0.118083i	−0.968406	+	0.249380i	$0.919773\pi$
$434$	−5.11803	+	3.71847i	−0.245673	+	0.178492i
$435$	2.07295	−	1.50609i	0.0993903	−	0.0722113i
$436$	3.78115	+	11.6372i	0.181084	+	0.557320i
$437$		0			0
$438$	5.78115	+	4.20025i	0.276234	+	0.200696i
$439$	0.527864			0.0251936			0.0125968	−	0.999921i	$-0.495990\pi$
$439$	0.527864			0.0251936			0.0125968	+	0.999921i	$0.495990\pi$
$440$	−2.76393	+	0.620541i	−0.131765	+	0.0295832i
$441$	1.00000			0.0476190
$442$	2.11803	+	1.53884i	0.100745	+	0.0731952i
$443$	−11.3262	+	34.8586i	−0.538126	+	1.65618i	0.198671	+	0.980066i	$0.436338\pi$
$443$	−11.3262	+	34.8586i	−0.538126	+	1.65618i	−0.736796	+	0.676115i	$0.763662\pi$
$444$	−3.47214	−	10.6861i	−0.164780	−	0.507142i
$445$	−1.97214	+	1.43284i	−0.0934882	+	0.0679232i
$446$	−6.35410	+	4.61653i	−0.300875	+	0.218599i
$447$	−4.04508	−	12.4495i	−0.191326	−	0.588841i
$448$	−0.0729490	+	0.224514i	−0.00344652	+	0.0106073i
$449$	−12.6631	−	9.20029i	−0.597610	−	0.434189i	0.247420	−	0.968908i	$-0.420417\pi$
$449$	−12.6631	−	9.20029i	−0.597610	−	0.434189i	−0.845030	+	0.534720i	$0.820417\pi$
$450$	3.00000			0.141421
$451$	−15.5000	−	6.69015i	−0.729866	−	0.315027i
$452$	18.8541			0.886822
$453$	17.0623	+	12.3965i	0.801657	+	0.582438i
$454$	−3.62461	+	11.1554i	−0.170111	+	0.523549i
$455$	0.118034	+	0.363271i	0.00553352	+	0.0170304i
$456$		0			0
$457$	−9.92705	+	7.21242i	−0.464368	+	0.337383i	−0.795242	−	0.606292i	$-0.792656\pi$
$457$	−9.92705	+	7.21242i	−0.464368	+	0.337383i	0.330874	+	0.943675i	$0.392656\pi$
$458$	2.23607	+	6.88191i	0.104485	+	0.321571i
$459$	−1.30902	+	4.02874i	−0.0610997	+	0.188045i
$460$	1.61803	+	1.17557i	0.0754412	+	0.0548113i
$461$	23.1803			1.07962			0.539808	−	0.841788i	$-0.318497\pi$
$461$	23.1803			1.07962			0.539808	+	0.841788i	$0.318497\pi$
$462$	1.35410	−	1.53884i	0.0629985	−	0.0715934i
$463$	−35.9230			−1.66948			−0.834741	−	0.550642i	$-0.814383\pi$
$463$	−35.9230			−1.66948			−0.834741	+	0.550642i	$0.814383\pi$
$464$	−10.0623	−	7.31069i	−0.467131	−	0.339390i
$465$	1.20820	−	3.71847i	0.0560291	−	0.172440i
$466$	−1.19098	−	3.66547i	−0.0551712	−	0.169800i
$467$	−25.8435	+	18.7764i	−1.19589	+	0.868867i	−0.993874	−	0.110515i	$-0.964750\pi$
$467$	−25.8435	+	18.7764i	−1.19589	+	0.868867i	−0.202018	+	0.979382i	$0.564750\pi$
$468$	−1.30902	+	0.951057i	−0.0605093	+	0.0439626i
$469$	−2.85410	−	8.78402i	−0.131790	−	0.405608i
$470$	−0.534442	+	1.64484i	−0.0246520	+	0.0758709i
$471$	1.35410	+	0.983813i	0.0623937	+	0.0453317i
$472$	−9.27051			−0.426710
$473$	−0.309017	+	3.30220i	−0.0142086	+	0.151835i
$474$	−6.70820			−0.308118
$475$		0			0
$476$	2.11803	−	6.51864i	0.0970799	−	0.298781i
$477$	2.35410	+	7.24518i	0.107787	+	0.331734i
$478$	9.57295	−	6.95515i	0.437856	−	0.318121i
$479$	−17.3992	+	12.6412i	−0.794989	+	0.577593i	−0.909440	−	0.415836i	$-0.863489\pi$
$479$	−17.3992	+	12.6412i	−0.794989	+	0.577593i	0.114451	+	0.993429i	$0.463489\pi$
$480$	0.663119	+	2.04087i	0.0302671	+	0.0931526i
$481$	−2.14590	+	6.60440i	−0.0978445	+	0.301134i
$482$	−12.3541	−	8.97578i	−0.562714	−	0.408836i
$483$	−3.23607			−0.147246
$484$	2.26393	+	17.6538i	0.102906	+	0.802446i
$485$	6.49342			0.294851
$486$	0.500000	+	0.363271i	0.0226805	+	0.0164783i
$487$	5.13525	−	15.8047i	0.232701	−	0.716179i	−0.764717	−	0.644366i	$-0.777121\pi$
$487$	5.13525	−	15.8047i	0.232701	−	0.716179i	0.997418	−	0.0718131i	$-0.0228785\pi$
$488$	−3.98278	−	12.2577i	−0.180292	−	0.554882i
$489$	−4.88197	+	3.54696i	−0.220770	+	0.160399i
$490$	−0.190983	+	0.138757i	−0.00862773	+	0.00626841i
$491$	1.14590	+	3.52671i	0.0517137	+	0.159158i	0.973578	−	0.228354i	$-0.0733344\pi$
$491$	1.14590	+	3.52671i	0.0517137	+	0.159158i	−0.921864	+	0.387512i	$0.873334\pi$
$492$	−2.54508	+	7.83297i	−0.114741	+	0.353137i
$493$	22.9894	+	16.7027i	1.03539	+	0.752254i
$494$		0			0
$495$	−0.118034	+	1.26133i	−0.00530523	+	0.0566924i
$496$	−18.9787			−0.852169
$497$	6.04508	+	4.39201i	0.271159	+	0.197009i
$498$	1.14590	−	3.52671i	0.0513489	−	0.158036i
$499$	−1.54508	−	4.75528i	−0.0691675	−	0.212876i	0.910498	−	0.413514i	$-0.135699\pi$
$499$	−1.54508	−	4.75528i	−0.0691675	−	0.212876i	−0.979665	+	0.200638i	$0.935699\pi$
$500$	4.92705	−	3.57971i	0.220344	−	0.160090i
$501$	−7.59017	+	5.51458i	−0.339104	+	0.246373i
$502$	−5.07953	−	15.6332i	−0.226710	−	0.697743i
$503$	−9.98278	+	30.7238i	−0.445110	+	1.36991i	0.437253	+	0.899339i	$0.355951\pi$
$503$	−9.98278	+	30.7238i	−0.445110	+	1.36991i	−0.882363	+	0.470569i	$0.844049\pi$
$504$	−1.80902	−	1.31433i	−0.0805800	−	0.0585448i
$505$	1.59675			0.0710543
$506$	−4.38197	+	4.97980i	−0.194802	+	0.221379i
$507$	−12.0000			−0.532939
$508$	−9.59017	−	6.96767i	−0.425495	−	0.309140i
$509$	12.9271	−	39.7854i	0.572981	−	1.76346i	−0.0699705	−	0.997549i	$-0.522291\pi$
$509$	12.9271	−	39.7854i	0.572981	−	1.76346i	0.642952	−	0.765907i	$-0.277709\pi$
$510$	−0.309017	−	0.951057i	−0.0136835	−	0.0421135i
$511$	−9.35410	+	6.79615i	−0.413801	+	0.300644i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$		0			0
$514$	−5.14590	+	15.8374i	−0.226976	+	0.698560i
$515$	−3.92705	−	2.85317i	−0.173047	−	0.125726i
$516$	1.61803			0.0712300
$517$	22.3090	+	9.62908i	0.981149	+	0.423486i
$518$	−4.29180			−0.188571
$519$	11.8262	+	8.59226i	0.519114	+	0.377159i
$520$	0.263932	−	0.812299i	0.0115742	−	0.0356217i
$521$	−5.92705	−	18.2416i	−0.259669	−	0.799178i	−0.992874	−	0.119171i	$-0.961976\pi$
$521$	−5.92705	−	18.2416i	−0.259669	−	0.799178i	0.733205	−	0.680008i	$-0.238024\pi$
$522$	3.35410	−	2.43690i	0.146805	−	0.106660i
$523$	−16.4271	+	11.9350i	−0.718305	+	0.521879i	−0.885842	−	0.463987i	$-0.846419\pi$
$523$	−16.4271	+	11.9350i	−0.718305	+	0.521879i	0.167537	+	0.985866i	$0.446419\pi$
$524$	1.66312	+	5.11855i	0.0726537	+	0.223605i
$525$	−1.50000	+	4.61653i	−0.0654654	+	0.201482i
$526$	0.354102	+	0.257270i	0.0154396	+	0.0112175i
$527$	43.3607			1.88882
$528$	6.00000	−	1.34708i	0.261116	−	0.0586243i
$529$	−12.5279			−0.544690
$530$	−1.45492	−	1.05706i	−0.0631975	−	0.0459156i
$531$	−1.28115	+	3.94298i	−0.0555973	+	0.171111i
$532$		0			0
$533$	4.11803	−	2.99193i	0.178372	−	0.129595i
$534$	−3.19098	+	2.31838i	−0.138087	+	0.100326i
$535$	−1.86068	−	5.72658i	−0.0804442	−	0.247582i
$536$	−6.38197	+	19.6417i	−0.275659	+	0.848391i
$537$	1.80902	+	1.31433i	0.0780648	+	0.0567174i
$538$	−14.7984			−0.638003
$539$	1.69098	+	2.85317i	0.0728358	+	0.122895i
$540$	0.618034			0.0265959
$541$	−16.2533	−	11.8087i	−0.698783	−	0.507696i	0.180752	−	0.983529i	$-0.442147\pi$
$541$	−16.2533	−	11.8087i	−0.698783	−	0.507696i	−0.879536	+	0.475833i	$0.842147\pi$
$542$	1.22542	−	3.77147i	0.0526365	−	0.161999i
$543$	−0.0729490	−	0.224514i	−0.00313054	−	0.00963482i
$544$	−19.2533	+	13.9883i	−0.825478	+	0.599745i
$545$	−2.33688	+	1.69784i	−0.100101	+	0.0727276i
$546$	0.190983	+	0.587785i	0.00817332	+	0.0251549i
$547$	6.98278	−	21.4908i	0.298562	−	0.918880i	−0.683440	−	0.730007i	$-0.739517\pi$
$547$	6.98278	−	21.4908i	0.298562	−	0.918880i	0.982002	−	0.188872i	$-0.0604833\pi$
$548$	−4.00000	−	2.90617i	−0.170872	−	0.124145i
$549$	−5.76393			−0.245999
$550$	5.07295	+	8.55951i	0.216311	+	0.364979i
$551$		0			0
$552$	5.85410	+	4.25325i	0.249167	+	0.181031i
$553$	3.35410	−	10.3229i	0.142631	−	0.438973i
$554$	4.85410	+	14.9394i	0.206231	+	0.634714i
$555$	2.14590	−	1.55909i	0.0910883	−	0.0661795i
$556$	−22.9894	+	16.7027i	−0.974966	+	0.708354i
$557$	0.236068	+	0.726543i	0.0100025	+	0.0307846i	0.955933	−	0.293584i	$-0.0948481\pi$
$557$	0.236068	+	0.726543i	0.0100025	+	0.0307846i	−0.945931	+	0.324369i	$0.894848\pi$
$558$	1.95492	−	6.01661i	0.0827582	−	0.254703i
$559$	−0.809017	−	0.587785i	−0.0342178	−	0.0248607i
$560$	−0.708204			−0.0299271
$561$	−13.7082	+	3.07768i	−0.578761	+	0.129940i
$562$	−9.65248			−0.407165
$563$	36.4615	+	26.4908i	1.53667	+	1.11646i	0.952382	+	0.304908i	$0.0986257\pi$
$563$	36.4615	+	26.4908i	1.53667	+	1.11646i	0.584287	+	0.811547i	$0.301374\pi$
$564$	3.66312	−	11.2739i	0.154245	−	0.474718i
$565$	1.37539	+	4.23301i	0.0578630	+	0.178084i
$566$	3.64590	−	2.64890i	0.153249	−	0.111342i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	−5.16312	−	15.8904i	−0.216640	−	0.666748i
$569$	12.0729	−	37.1567i	0.506124	−	1.55769i	−0.292748	−	0.956190i	$-0.594570\pi$
$569$	12.0729	−	37.1567i	0.506124	−	1.55769i	0.798872	−	0.601501i	$-0.205430\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$	−4.92705	−	2.12663i	−0.206010	−	0.0889187i
$573$	9.76393			0.407894
$574$	2.54508	+	1.84911i	0.106230	+	0.0771805i
$575$	4.85410	−	14.9394i	0.202430	−	0.623016i
$576$	−0.0729490	−	0.224514i	−0.00303954	−	0.00935475i
$577$	7.63525	−	5.54734i	0.317860	−	0.230939i	−0.417402	−	0.908722i	$-0.637059\pi$
$577$	7.63525	−	5.54734i	0.317860	−	0.230939i	0.735262	+	0.677783i	$0.237059\pi$
$578$	0.472136	−	0.343027i	0.0196383	−	0.0142680i
$579$	1.56231	+	4.80828i	0.0649272	+	0.199825i
$580$	1.28115	−	3.94298i	0.0531970	−	0.163723i
$581$	4.85410	+	3.52671i	0.201382	+	0.146313i
$582$	10.5066			0.435512
$583$	−16.6910	+	18.9681i	−0.691270	+	0.785580i
$584$	25.8541			1.06985
$585$	−0.309017	−	0.224514i	−0.0127763	−	0.00928251i
$586$	2.52786	−	7.77997i	0.104425	−	0.321387i
$587$	11.0902	+	34.1320i	0.457740	+	1.40878i	0.867888	+	0.496761i	$0.165477\pi$
$587$	11.0902	+	34.1320i	0.457740	+	1.40878i	−0.410147	+	0.912019i	$0.634523\pi$
$588$	1.30902	−	0.951057i	0.0539830	−	0.0392209i
$589$		0			0
$590$	−0.302439	−	0.930812i	−0.0124512	−	0.0383209i
$591$	−2.85410	+	8.78402i	−0.117402	+	0.361326i
$592$	−10.4164	−	7.56796i	−0.428112	−	0.311041i
$593$	−23.8885			−0.980985			−0.490492	−	0.871445i	$-0.663183\pi$
$593$	−23.8885			−0.980985			−0.490492	+	0.871445i	$0.663183\pi$
$594$	−0.190983	+	2.04087i	−0.00783613	+	0.0837379i
$595$	1.61803			0.0663329
$596$	−17.1353	−	12.4495i	−0.701887	−	0.509951i
$597$	−2.33688	+	7.19218i	−0.0956422	+	0.294356i
$598$	−0.618034	−	1.90211i	−0.0252733	−	0.0777832i
$599$	−25.4894	+	18.5191i	−1.04147	+	0.756670i	−0.970571	−	0.240814i	$-0.922586\pi$
$599$	−25.4894	+	18.5191i	−1.04147	+	0.756670i	−0.0708955	+	0.997484i	$0.522586\pi$
$600$	8.78115	−	6.37988i	0.358489	−	0.260458i
$601$	−4.58359	−	14.1068i	−0.186969	−	0.575430i	0.813008	−	0.582252i	$-0.197828\pi$
$601$	−4.58359	−	14.1068i	−0.186969	−	0.575430i	−0.999977	+	0.00682211i	$0.997828\pi$
$602$	0.190983	−	0.587785i	0.00778389	−	0.0239563i
$603$	7.47214	+	5.42882i	0.304289	+	0.221079i
$604$	34.1246			1.38851
$605$	−3.79837	+	1.79611i	−0.154426	+	0.0730223i
$606$	2.58359			0.104951
$607$	13.0623	+	9.49032i	0.530183	+	0.385200i	0.820426	−	0.571753i	$-0.193736\pi$
$607$	13.0623	+	9.49032i	0.530183	+	0.385200i	−0.290243	+	0.956953i	$0.593736\pi$
$608$		0			0
$609$	2.07295	+	6.37988i	0.0840001	+	0.258526i
$610$	1.10081	−	0.799788i	0.0445706	−	0.0323824i
$611$	−5.92705	+	4.30625i	−0.239783	+	0.174212i
$612$	2.11803	+	6.51864i	0.0856164	+	0.263500i
$613$	10.6459	−	32.7647i	0.429984	−	1.32335i	−0.468157	−	0.883645i	$-0.655082\pi$
$613$	10.6459	−	32.7647i	0.429984	−	1.32335i	0.898141	−	0.439709i	$-0.144918\pi$
$614$	9.59017	+	6.96767i	0.387028	+	0.281192i
$615$	−1.94427			−0.0784006
$616$	0.690983	−	7.38394i	0.0278405	−	0.297507i
$617$	−10.0902			−0.406215			−0.203107	−	0.979156i	$-0.565104\pi$
$617$	−10.0902			−0.406215			−0.203107	+	0.979156i	$0.565104\pi$
$618$	−6.35410	−	4.61653i	−0.255599	−	0.185704i
$619$	10.8541	−	33.4055i	0.436263	−	1.34268i	−0.455523	−	0.890224i	$-0.650548\pi$
$619$	10.8541	−	33.4055i	0.436263	−	1.34268i	0.891787	−	0.452456i	$-0.149452\pi$
$620$	−1.95492	−	6.01661i	−0.0785113	−	0.241633i
$621$	2.61803	−	1.90211i	0.105058	−	0.0763292i
$622$	8.39919	−	6.10237i	0.336777	−	0.244683i
$623$	−1.97214	−	6.06961i	−0.0790120	−	0.243174i
$624$	−0.572949	+	1.76336i	−0.0229363	+	0.0705907i
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	9.76393			0.390245
$627$		0			0
$628$	2.70820			0.108069
$629$	23.7984	+	17.2905i	0.948903	+	0.689419i
$630$	0.0729490	−	0.224514i	0.00290636	−	0.00894485i
$631$	−2.83688	−	8.73102i	−0.112934	−	0.347577i	0.878576	−	0.477602i	$-0.158494\pi$
$631$	−2.83688	−	8.73102i	−0.112934	−	0.347577i	−0.991511	+	0.130026i	$0.958494\pi$
$632$	−19.6353	+	14.2658i	−0.781049	+	0.567465i
$633$	−4.28115	+	3.11044i	−0.170161	+	0.123629i
$634$	−4.84346	−	14.9066i	−0.192358	−	0.592018i
$635$	0.864745	−	2.66141i	0.0343164	−	0.105615i
$636$	9.97214	+	7.24518i	0.395421	+	0.287290i
$637$	−1.00000			−0.0396214
$638$	12.6246	+	5.44907i	0.499813	+	0.215731i
$639$	−7.47214			−0.295593
$640$	3.51722	+	2.55541i	0.139030	+	0.101011i
$641$	8.64590	−	26.6093i	0.341492	−	1.05101i	−0.621942	−	0.783063i	$-0.713656\pi$
$641$	8.64590	−	26.6093i	0.341492	−	1.05101i	0.963435	−	0.267943i	$-0.0863438\pi$
$642$	−3.01064	−	9.26581i	−0.118821	−	0.365692i
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	−0.302530	−	0.953140i	$-0.597831\pi$
$643$	12.9443	−	9.40456i	0.510472	−	0.370880i	0.813003	+	0.582260i	$0.197831\pi$
$644$	−4.23607	+	3.07768i	−0.166924	+	0.121278i
$645$	0.118034	+	0.363271i	0.00464758	+	0.0143038i
$646$		0			0
$647$	−1.89919	−	1.37984i	−0.0746647	−	0.0542471i	0.549827	−	0.835279i	$-0.314694\pi$
$647$	−1.89919	−	1.37984i	−0.0746647	−	0.0542471i	−0.624491	+	0.781032i	$0.714694\pi$
$648$	2.23607			0.0878410
$649$	−13.4164	+	3.01217i	−0.526640	+	0.118238i
$650$	−3.00000			−0.117670
$651$	8.28115	+	6.01661i	0.324564	+	0.235810i
$652$	−3.01722	+	9.28605i	−0.118163	+	0.363670i
$653$	0.218847	+	0.673542i	0.00856415	+	0.0263577i	0.955247	−	0.295808i	$-0.0955890\pi$
$653$	0.218847	+	0.673542i	0.00856415	+	0.0263577i	−0.946683	+	0.322166i	$0.895589\pi$
$654$	−3.78115	+	2.74717i	−0.147855	+	0.107423i
$655$	−1.02786	+	0.746787i	−0.0401620	+	0.0291794i
$656$	2.91641	+	8.97578i	0.113867	+	0.350445i
$657$	3.57295	−	10.9964i	0.139394	−	0.429011i
$658$	−3.66312	−	2.66141i	−0.142803	−	0.103753i
$659$	41.8328			1.62958			0.814788	−	0.579760i	$-0.196854\pi$
$659$	41.8328			1.62958			0.814788	+	0.579760i	$0.196854\pi$
$660$	1.04508	+	1.76336i	0.0406799	+	0.0686385i
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$	−7.35410	−	5.34307i	−0.285825	−	0.207664i
$663$	1.30902	−	4.02874i	0.0508380	−	0.156463i
$664$	−4.14590	−	12.7598i	−0.160892	−	0.495175i
$665$		0			0
$666$	3.47214	−	2.52265i	0.134543	−	0.0977509i
$667$	−6.70820	−	20.6457i	−0.259743	−	0.799406i
$668$	−4.69098	+	14.4374i	−0.181500	+	0.558598i
$669$	10.2812	+	7.46969i	0.397492	+	0.288795i
$670$	−2.18034			−0.0842339
$671$	−9.74671	−	16.4455i	−0.376268	−	0.634871i
$672$	−5.61803			−0.216720
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	0.699721	−	0.714416i	$-0.253308\pi$
$673$	6.13525	+	4.45752i	0.236497	+	0.171825i	−0.463224	+	0.886241i	$0.653308\pi$
$674$	−0.246711	+	0.759299i	−0.00950296	+	0.0292471i
$675$	−1.50000	−	4.61653i	−0.0577350	−	0.177690i
$676$	−15.7082	+	11.4127i	−0.604162	+	0.438949i
$677$	−18.9721	+	13.7841i	−0.729158	+	0.529765i	−0.889297	−	0.457330i	$-0.848806\pi$
$677$	−18.9721	+	13.7841i	−0.729158	+	0.529765i	0.160139	+	0.987095i	$0.448806\pi$
$678$	2.22542	+	6.84915i	0.0854669	+	0.263040i
$679$	−5.25329	+	16.1680i	−0.201603	+	0.620469i
$680$	−2.92705	−	2.12663i	−0.112247	−	0.0815524i
$681$	18.9787			0.727266
$682$	20.4721	−	4.59628i	0.783919	−	0.176001i
$683$	−32.3050			−1.23611			−0.618057	−	0.786133i	$-0.712080\pi$
$683$	−32.3050			−1.23611			−0.618057	+	0.786133i	$0.712080\pi$
$684$		0			0
$685$	0.360680	−	1.11006i	0.0137809	−	0.0424131i
$686$	−0.190983	−	0.587785i	−0.00729177	−	0.0224417i
$687$	9.47214	−	6.88191i	0.361385	−	0.262561i
$688$	1.50000	−	1.08981i	0.0571870	−	0.0415488i
$689$	−2.35410	−	7.24518i	−0.0896841	−	0.276019i
$690$	−0.236068	+	0.726543i	−0.00898695	+	0.0276590i
$691$	−11.7812	−	8.55951i	−0.448176	−	0.325619i	0.340699	−	0.940172i	$-0.389336\pi$
$691$	−11.7812	−	8.55951i	−0.448176	−	0.325619i	−0.788875	+	0.614553i	$0.789336\pi$
$692$	23.6525			0.899132
$693$	−3.04508	−	1.31433i	−0.115673	−	0.0499272i
$694$	15.7082			0.596275
$695$	−5.42705	−	3.94298i	−0.205860	−	0.149566i
$696$	4.63525	−	14.2658i	0.175699	−	0.540746i
$697$	−6.66312	−	20.5070i	−0.252384	−	0.776757i
$698$	17.4615	−	12.6865i	0.660927	−	0.480192i
$699$	−5.04508	+	3.66547i	−0.190823	+	0.138641i
$700$	2.42705	+	7.46969i	0.0917339	+	0.282328i
$701$	8.34346	−	25.6785i	0.315128	−	0.969865i	−0.660574	−	0.750761i	$-0.729687\pi$
$701$	8.34346	−	25.6785i	0.315128	−	0.969865i	0.975702	−	0.219103i	$-0.0703132\pi$
$702$	−0.500000	−	0.363271i	−0.0188713	−	0.0137108i
$703$		0			0
$704$	0.517221	−	0.587785i	0.0194935	−	0.0221530i
$705$	2.79837			0.105393
$706$	−12.7361	−	9.25330i	−0.479328	−	0.348252i
$707$	−1.29180	+	3.97574i	−0.0485830	+	0.149523i
$708$	2.07295	+	6.37988i	0.0779062	+	0.239771i
$709$	40.9787	−	29.7728i	1.53899	−	1.11814i	0.588022	−	0.808845i	$-0.299907\pi$
$709$	40.9787	−	29.7728i	1.53899	−	1.11814i	0.950966	−	0.309295i	$-0.100093\pi$
$710$	1.42705	−	1.03681i	0.0535563	−	0.0389109i
$711$	3.35410	+	10.3229i	0.125789	+	0.387138i
$712$	−4.40983	+	13.5721i	−0.165265	+	0.508635i
$713$	−26.7984	−	19.4702i	−1.00361	−	0.729163i
$714$	2.61803			0.0979775
$715$	0.118034	−	1.26133i	0.00441422	−	0.0471710i
$716$	3.61803			0.135212
$717$	−15.4894	−	11.2537i	−0.578461	−	0.420276i
$718$	6.34346	−	19.5232i	0.236736	−	0.728598i
$719$	−2.66312	−	8.19624i	−0.0993176	−	0.305668i	0.889037	−	0.457835i	$-0.151375\pi$
$719$	−2.66312	−	8.19624i	−0.0993176	−	0.305668i	−0.988355	+	0.152167i	$0.951375\pi$
$720$	0.572949	−	0.416272i	0.0213525	−	0.0155135i
$721$	10.2812	−	7.46969i	0.382890	−	0.278186i
$722$	3.62868	+	11.1679i	0.135045	+	0.415627i
$723$	−7.63525	+	23.4989i	−0.283958	+	0.873933i
$724$	−0.309017	−	0.224514i	−0.0114845	−	0.00834400i
$725$	−32.5623			−1.20933
$726$	−6.14590	+	2.90617i	−0.228096	+	0.107858i
$727$	22.1459			0.821346			0.410673	−	0.911783i	$-0.365294\pi$
$727$	22.1459			0.821346			0.410673	+	0.911783i	$0.365294\pi$
$728$	1.80902	+	1.31433i	0.0670466	+	0.0487122i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.843459	+	2.59590i	0.0312178	+	0.0960785i
$731$	−3.42705	+	2.48990i	−0.126754	+	0.0920922i
$732$	−7.54508	+	5.48183i	−0.278874	+	0.202614i
$733$	1.27458	+	3.92274i	0.0470775	+	0.144890i	0.971832	−	0.235674i	$-0.0757299\pi$
$733$	1.27458	+	3.92274i	0.0470775	+	0.144890i	−0.924755	+	0.380564i	$0.875730\pi$
$734$	−2.15654	+	6.63715i	−0.0795994	+	0.244982i
$735$	0.309017	+	0.224514i	0.0113983	+	0.00828132i
$736$	18.1803			0.670136
$737$	−2.85410	+	30.4993i	−0.105132	+	1.12346i
$738$	−3.14590			−0.115802
$739$	−34.5344	−	25.0907i	−1.27037	−	0.922978i	−0.271153	−	0.962536i	$-0.587405\pi$
$739$	−34.5344	−	25.0907i	−1.27037	−	0.922978i	−0.999217	+	0.0395585i	$0.987405\pi$
$740$	1.32624	−	4.08174i	0.0487535	−	0.150048i
$741$		0			0
$742$	3.80902	−	2.76741i	0.139833	−	0.101595i
$743$	−20.9615	+	15.2294i	−0.769003	+	0.558713i	−0.901658	−	0.432449i	$-0.857650\pi$
$743$	−20.9615	+	15.2294i	−0.769003	+	0.558713i	0.132656	+	0.991162i	$0.457650\pi$
$744$	−7.07295	−	21.7683i	−0.259307	−	0.798065i
$745$	1.54508	−	4.75528i	0.0566075	−	0.174220i
$746$	15.0902	+	10.9637i	0.552490	+	0.401408i
$747$	−6.00000			−0.219529
$748$	−15.0172	+	17.0660i	−0.549084	+	0.623995i
$749$	15.7639			0.576002
$750$	1.88197	+	1.36733i	0.0687197	+	0.0499278i
$751$	−8.91641	+	27.4419i	−0.325364	+	1.00137i	0.645912	+	0.763412i	$0.276477\pi$
$751$	−8.91641	+	27.4419i	−0.325364	+	1.00137i	−0.971276	+	0.237956i	$0.923523\pi$
$752$	−4.19756	−	12.9188i	−0.153069	−	0.471099i
$753$	−21.5172	+	15.6332i	−0.784131	+	0.569705i
$754$	−3.35410	+	2.43690i	−0.122149	+	0.0887466i
$755$	2.48936	+	7.66145i	0.0905970	+	0.278829i
$756$	−0.500000	+	1.53884i	−0.0181848	+	0.0559671i
$757$	−36.5967	−	26.5891i	−1.33013	−	0.966397i	−0.999746	−	0.0225510i	$-0.992821\pi$
$757$	−36.5967	−	26.5891i	−1.33013	−	0.966397i	−0.330386	−	0.943846i	$-0.607179\pi$
$758$	6.70820			0.243653
$759$	9.85410	+	4.25325i	0.357681	+	0.154383i
$760$		0			0
$761$	−0.0729490	−	0.0530006i	−0.00264440	−	0.00192127i	0.586462	−	0.809977i	$-0.300520\pi$
$761$	−0.0729490	−	0.0530006i	−0.00264440	−	0.00192127i	−0.589107	+	0.808055i	$0.700520\pi$
$762$	1.39919	−	4.30625i	0.0506872	−	0.155999i
$763$	−2.33688	−	7.19218i	−0.0846008	−	0.260374i
$764$	12.7812	−	9.28605i	0.462406	−	0.335958i
$765$	−1.30902	+	0.951057i	−0.0473276	+	0.0343855i
$766$	1.51064	+	4.64928i	0.0545818	+	0.167985i
$767$	1.28115	−	3.94298i	0.0462598	−	0.142373i
$768$	5.30902	+	3.85723i	0.191573	+	0.139186i
$769$	44.4721			1.60371			0.801853	−	0.597521i	$-0.203848\pi$
$769$	44.4721			1.60371			0.801853	+	0.597521i	$0.203848\pi$
$770$	0.763932	−	0.171513i	0.0275302	−	0.00618091i
$771$	26.9443			0.970374
$772$	6.61803	+	4.80828i	0.238188	+	0.173054i
$773$	3.27051	−	10.0656i	0.117632	−	0.362034i	−0.874855	−	0.484385i	$-0.839043\pi$
$773$	3.27051	−	10.0656i	0.117632	−	0.362034i	0.992487	+	0.122351i	$0.0390433\pi$
$774$	0.190983	+	0.587785i	0.00686474	+	0.0211275i
$775$	−40.1976	+	29.2052i	−1.44394	+	1.04908i
$776$	30.7533	−	22.3436i	1.10398	−	0.802088i
$777$	2.14590	+	6.60440i	0.0769837	+	0.236931i
$778$	−3.94427	+	12.1392i	−0.141409	+	0.435212i
$779$		0			0
$780$	−0.618034			−0.0221292
$781$	−12.6353	−	21.3193i	−0.452125	−	0.762863i
$782$	−8.47214			−0.302963
$783$	−5.42705	−	3.94298i	−0.193947	−	0.140911i
$784$	0.572949	−	1.76336i	0.0204625	−	0.0629770i
$785$	0.197561	+	0.608030i	0.00705125	+	0.0217015i
$786$	−1.66312	+	1.20833i	−0.0593215	+	0.0430996i
$787$	26.5795	−	19.3112i	0.947458	−	0.688368i	−0.00274643	−	0.999996i	$-0.500874\pi$
$787$	26.5795	−	19.3112i	0.947458	−	0.688368i	0.950204	+	0.311628i	$0.100874\pi$
$788$	4.61803	+	14.2128i	0.164511	+	0.506312i
$789$	0.218847	−	0.673542i	0.00779116	−	0.0239787i
$790$	−2.07295	−	1.50609i	−0.0737522	−	0.0535841i
$791$	−11.6525			−0.414314
$792$	3.78115	+	6.37988i	0.134357	+	0.226699i
$793$	5.76393			0.204683
$794$	12.8435	+	9.33132i	0.455797	+	0.331156i
$795$	−0.899187	+	2.76741i	−0.0318909	+	0.0981500i
$796$	3.78115	+	11.6372i	0.134019	+	0.412469i
$797$	26.2533	−	19.0741i	0.929939	−	0.675640i	−0.0160387	−	0.999871i	$-0.505106\pi$
$797$	26.2533	−	19.0741i	0.929939	−	0.675640i	0.945978	+	0.324231i	$0.105106\pi$
$798$		0			0
$799$	9.59017	+	29.5155i	0.339276	+	1.04418i
$800$	8.42705	−	25.9358i	0.297941	−	0.916969i
$801$	5.16312	+	3.75123i	0.182430	+	0.132543i
$802$	−7.21478			−0.254763
$803$	37.4164	−	8.40051i	1.32040	−	0.296447i
$804$	14.9443			0.527044
$805$	−1.00000	−	0.726543i	−0.0352454	−	0.0256073i
$806$	−1.95492	+	6.01661i	−0.0688589	+	0.211926i
$807$	7.39919	+	22.7724i	0.260464	+	0.801625i
$808$	7.56231	−	5.49434i	0.266041	−	0.193290i
$809$	−25.0623	+	18.2088i	−0.881144	+	0.640188i	−0.933554	−	0.358437i	$-0.883310\pi$
$809$	−25.0623	+	18.2088i	−0.881144	+	0.640188i	0.0524101	+	0.998626i	$0.483310\pi$
$810$	0.0729490	+	0.224514i	0.00256317	+	0.00788862i
$811$	−7.14590	+	21.9928i	−0.250926	+	0.772272i	0.743679	+	0.668537i	$0.233079\pi$
$811$	−7.14590	+	21.9928i	−0.250926	+	0.772272i	−0.994605	+	0.103735i	$0.966921\pi$
$812$	8.78115	+	6.37988i	0.308158	+	0.223890i
$813$	−6.41641			−0.225033
$814$	13.0689	+	5.64083i	0.458064	+	0.197711i
$815$	−2.30495			−0.0807389
$816$	6.35410	+	4.61653i	0.222438	+	0.161611i
$817$		0			0
$818$	5.03851	+	15.5069i	0.176167	+	0.542187i
$819$	0.809017	−	0.587785i	0.0282693	−	0.0205389i
$820$	−2.54508	+	1.84911i	−0.0888782	+	0.0645738i
$821$	1.79837	+	5.53483i	0.0627637	+	0.193167i	0.977521	−	0.210836i	$-0.0676186\pi$
$821$	1.79837	+	5.53483i	0.0627637	+	0.193167i	−0.914758	+	0.404003i	$0.867619\pi$
$822$	0.583592	−	1.79611i	0.0203551	−	0.0626466i
$823$	21.2361	+	15.4289i	0.740243	+	0.537818i	0.892787	−	0.450479i	$-0.148747\pi$
$823$	21.2361	+	15.4289i	0.740243	+	0.537818i	−0.152544	+	0.988297i	$0.548747\pi$
$824$	−28.4164			−0.989932
$825$	10.6353	−	12.0862i	0.370272	−	0.420788i
$826$	2.56231			0.0891540
$827$	−4.13525	−	3.00444i	−0.143797	−	0.104475i	0.513561	−	0.858053i	$-0.328326\pi$
$827$	−4.13525	−	3.00444i	−0.143797	−	0.104475i	−0.657358	+	0.753579i	$0.728326\pi$
$828$	1.61803	−	4.97980i	0.0562306	−	0.173060i
$829$	11.6459	+	35.8424i	0.404479	+	1.24486i	0.921330	+	0.388782i	$0.127104\pi$
$829$	11.6459	+	35.8424i	0.404479	+	1.24486i	−0.516851	+	0.856075i	$0.672896\pi$
$830$	1.14590	−	0.832544i	0.0397747	−	0.0288980i
$831$	20.5623	−	14.9394i	0.713298	−	0.518242i
$832$	0.0729490	+	0.224514i	0.00252905	+	0.00778362i
$833$	−1.30902	+	4.02874i	−0.0453548	+	0.139588i
$834$	−8.78115	−	6.37988i	−0.304066	−	0.220917i
$835$	−3.58359			−0.124015
$836$		0			0
$837$	−10.2361			−0.353810
$838$	−7.66312	−	5.56758i	−0.264718	−	0.192329i
$839$	8.98278	−	27.6462i	0.310120	−	0.954451i	−0.667597	−	0.744523i	$-0.732677\pi$
$839$	8.98278	−	27.6462i	0.310120	−	0.954451i	0.977717	−	0.209928i	$-0.0673230\pi$
$840$	−0.263932	−	0.812299i	−0.00910652	−	0.0280270i
$841$	−12.9443	+	9.40456i	−0.446354	+	0.324295i
$842$	1.36475	−	0.991545i	0.0470322	−	0.0341709i
$843$	4.82624	+	14.8536i	0.166224	+	0.511586i
$844$	−2.64590	+	8.14324i	−0.0910756	+	0.280302i
$845$	−3.70820	−	2.69417i	−0.127566	−	0.0926822i
$846$	4.52786			0.155671
$847$	−1.39919	−	10.9106i	−0.0480766	−	0.374894i
$848$	14.1246			0.485041
$849$	−5.89919	−	4.28601i	−0.202460	−	0.147095i
$850$	−3.92705	+	12.0862i	−0.134697	+	0.414554i
$851$	−6.94427	−	21.3723i	−0.238047	−	0.732632i
$852$	−9.78115	+	7.10642i	−0.335097	+	0.243462i
$853$	−7.44427	+	5.40858i	−0.254887	+	0.185186i	−0.707890	−	0.706323i	$-0.750353\pi$
$853$	−7.44427	+	5.40858i	−0.254887	+	0.185186i	0.453003	+	0.891509i	$0.350353\pi$
$854$	1.10081	+	3.38795i	0.0376690	+	0.115933i
$855$		0			0
$856$	−28.5172	−	20.7190i	−0.974699	−	0.708160i
$857$	−54.2361			−1.85267			−0.926334	−	0.376702i	$-0.877058\pi$
$857$	−54.2361			−1.85267			−0.926334	+	0.376702i	$0.877058\pi$
$858$	0.190983	−	2.04087i	0.00652005	−	0.0696742i
$859$	−41.8328			−1.42732			−0.713659	−	0.700494i	$-0.752963\pi$
$859$	−41.8328			−1.42732			−0.713659	+	0.700494i	$0.752963\pi$
$860$	0.500000	+	0.363271i	0.0170499	+	0.0123874i
$861$	1.57295	−	4.84104i	0.0536060	−	0.164982i
$862$	7.21885	+	22.2173i	0.245875	+	0.756725i
$863$	−25.3713	+	18.4333i	−0.863650	+	0.627478i	−0.928875	−	0.370392i	$-0.879223\pi$
$863$	−25.3713	+	18.4333i	−0.863650	+	0.627478i	0.0652256	+	0.997871i	$0.479223\pi$
$864$	4.54508	−	3.30220i	0.154627	−	0.112343i
$865$	1.72542	+	5.31031i	0.0586662	+	0.180556i
$866$	0.493422	−	1.51860i	0.0167672	−	0.0516040i
$867$	−0.763932	−	0.555029i	−0.0259445	−	0.0188498i
$868$	16.5623			0.562161
$869$	−23.7812	+	27.0256i	−0.806720	+	0.916781i
$870$	1.58359			0.0536888
$871$	−7.47214	−	5.42882i	−0.253184	−	0.183949i
$872$	−5.22542	+	16.0822i	−0.176955	+	0.544612i
$873$	−5.25329	−	16.1680i	−0.177797	−	0.547203i
$874$		0			0
$875$	−3.04508	+	2.21238i	−0.102943	+	0.0747922i
$876$	−5.78115	−	17.7926i	−0.195327	−	0.601155i
$877$	12.8992	−	39.6996i	0.435575	−	1.34056i	−0.456922	−	0.889507i	$-0.651048\pi$
$877$	12.8992	−	39.6996i	0.435575	−	1.34056i	0.892497	−	0.451054i	$-0.148952\pi$
$878$	0.263932	+	0.191758i	0.00890727	+	0.00647151i
$879$	−13.2361			−0.446441
$880$	2.15654	+	0.930812i	0.0726970	+	0.0313777i
$881$	−11.9443			−0.402413			−0.201206	−	0.979549i	$-0.564486\pi$
$881$	−11.9443			−0.402413			−0.201206	+	0.979549i	$0.564486\pi$
$882$	0.500000	+	0.363271i	0.0168359	+	0.0122320i
$883$	−10.2082	+	31.4176i	−0.343533	+	1.05729i	0.618831	+	0.785524i	$0.287607\pi$
$883$	−10.2082	+	31.4176i	−0.343533	+	1.05729i	−0.962364	+	0.271763i	$0.912393\pi$
$884$	−2.11803	−	6.51864i	−0.0712372	−	0.219246i
$885$	−1.28115	+	0.930812i	−0.0430655	+	0.0312889i
$886$	−18.3262	+	13.3148i	−0.615682	+	0.447319i
$887$	−6.63525	−	20.4212i	−0.222790	−	0.685677i	−0.998508	−	0.0545980i	$-0.982612\pi$
$887$	−6.63525	−	20.4212i	−0.222790	−	0.685677i	0.775718	−	0.631079i	$-0.217388\pi$
$888$	4.79837	−	14.7679i	0.161023	−	0.495577i
$889$	5.92705	+	4.30625i	0.198787	+	0.144427i
$890$	−1.50658			−0.0505006
$891$	3.23607	−	0.726543i	0.108412	−	0.0243401i
$892$	20.5623			0.688477
$893$		0			0
$894$	2.50000	−	7.69421i	0.0836125	−	0.257333i
$895$	0.263932	+	0.812299i	0.00882227	+	0.0271522i
$896$	−9.20820	+	6.69015i	−0.307625	+	0.223502i
$897$	−2.61803	+	1.90211i	−0.0874136	+	0.0635097i
$898$	−2.98936	−	9.20029i	−0.0997561	−	0.307018i
$899$	−21.2188	+	65.3049i	−0.707688	+	2.17804i
$900$	−6.35410	−	4.61653i	−0.211803	−	0.153884i
$901$	−32.2705			−1.07509
$902$	−5.31966	−	8.97578i	−0.177125	−	0.298861i
$903$	−1.00000			−0.0332779
$904$	21.0795	+	15.3152i	0.701095	+	0.509375i
$905$	0.0278640	−	0.0857567i	0.000926232	−	0.00285065i
$906$	4.02786	+	12.3965i	0.133817	+	0.411846i
$907$	−15.3541	+	11.1554i	−0.509825	+	0.370409i	−0.812757	−	0.582603i	$-0.802034\pi$
$907$	−15.3541	+	11.1554i	−0.509825	+	0.370409i	0.302932	+	0.953012i	$0.402034\pi$
$908$	24.8435	−	18.0498i	0.824459	−	0.599005i
$909$	−1.29180	−	3.97574i	−0.0428462	−	0.131867i
$910$	−0.0729490	+	0.224514i	−0.00241824	+	0.00744257i
$911$	26.4336	+	19.2052i	0.875785	+	0.636295i	0.932133	−	0.362116i	$-0.117946\pi$
$911$	26.4336	+	19.2052i	0.875785	+	0.636295i	−0.0563478	+	0.998411i	$0.517946\pi$
$912$		0			0
$913$	−10.1459	−	17.1190i	−0.335780	−	0.566557i
$914$	−7.58359			−0.250843
$915$	−1.78115	−	1.29408i	−0.0588831	−	0.0427811i
$916$	5.85410	−	18.0171i	0.193425	−	0.595301i
$917$	−1.02786	−	3.16344i	−0.0339431	−	0.104466i
$918$	−2.11803	+	1.53884i	−0.0699055	+	0.0507893i
$919$	13.4164	−	9.74759i	0.442566	−	0.321543i	−0.344087	−	0.938938i	$-0.611812\pi$
$919$	13.4164	−	9.74759i	0.442566	−	0.321543i	0.786654	+	0.617394i	$0.211812\pi$
$920$	0.854102	+	2.62866i	0.0281589	+	0.0866642i
$921$	5.92705	−	18.2416i	0.195303	−	0.601081i
$922$	11.5902	+	8.42075i	0.381702	+	0.277323i
$923$	7.47214			0.245948
$924$	−5.23607	+	1.17557i	−0.172254	+	0.0386734i
$925$	−33.7082			−1.10832
$926$	−17.9615	−	13.0498i	−0.590251	−	0.428843i
$927$	−3.92705	+	12.0862i	−0.128981	+	0.396964i
$928$	−11.6459	−	35.8424i	−0.382295	−	1.17658i
$929$	12.7639	−	9.27354i	0.418771	−	0.304255i	−0.358372	−	0.933579i	$-0.616668\pi$
$929$	12.7639	−	9.27354i	0.418771	−	0.304255i	0.777143	+	0.629324i	$0.216668\pi$
$930$	1.95492	−	1.42033i	0.0641042	−	0.0465744i
$931$		0			0
$932$	−3.11803	+	9.59632i	−0.102135	+	0.314338i
$933$	−13.5902	−	9.87384i	−0.444922	−	0.323255i
$934$	−19.7426			−0.645999
$935$	−4.92705	−	2.12663i	−0.161132	−	0.0695481i
$936$	−2.23607			−0.0730882
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	0.676433	−	0.736504i	$-0.263525\pi$
$937$	5.66312	+	4.11450i	0.185006	+	0.134415i	−0.491427	+	0.870919i	$0.663525\pi$
$938$	1.76393	−	5.42882i	0.0575944	−	0.177257i
$939$	−4.88197	−	15.0251i	−0.159317	−	0.490327i
$940$	3.66312	−	2.66141i	0.119478	−	0.0868057i
$941$	43.8328	−	31.8464i	1.42891	−	1.03816i	0.438690	−	0.898638i	$-0.355442\pi$
$941$	43.8328	−	31.8464i	1.42891	−	1.03816i	0.990219	−	0.139525i	$-0.0445575\pi$
$942$	0.319660	+	0.983813i	0.0104151	+	0.0320543i
$943$	−5.09017	+	15.6659i	−0.165759	+	0.510153i
$944$	6.21885	+	4.51826i	0.202406	+	0.147057i
$945$	−0.381966			−0.0124254
$946$	−1.35410	+	1.53884i	−0.0440257	+	0.0500321i
$947$	−0.618034			−0.0200834			−0.0100417	−	0.999950i	$-0.503196\pi$
$947$	−0.618034			−0.0200834			−0.0100417	+	0.999950i	$0.503196\pi$
$948$	14.2082	+	10.3229i	0.461461	+	0.335271i
$949$	−3.57295	+	10.9964i	−0.115983	+	0.356958i
$950$		0			0
$951$	−20.5172	+	14.9066i	−0.665316	+	0.483381i
$952$	7.66312	−	5.56758i	0.248363	−	0.180446i
$953$	5.93363	+	18.2618i	0.192209	+	0.591559i	0.999998	+	0.00208665i	$0.000664201\pi$
$953$	5.93363	+	18.2618i	0.192209	+	0.591559i	−0.807789	+	0.589472i	$0.799336\pi$
$954$	−1.45492	+	4.47777i	−0.0471046	+	0.144973i
$955$	3.01722	+	2.19214i	0.0976350	+	0.0709360i
$956$	−30.9787			−1.00192
$957$	2.07295	−	22.1518i	0.0670089	−	0.716066i
$958$	−13.2918			−0.429438
$959$	2.47214	+	1.79611i	0.0798294	+	0.0579995i
$960$	0.0278640	−	0.0857567i	0.000899308	−	0.00276779i
$961$	22.7984	+	70.1662i	0.735431	+	2.26343i
$962$	−3.47214	+	2.52265i	−0.111946	+	0.0813336i
$963$	−12.7533	+	9.26581i	−0.410969	+	0.298586i
$964$	12.3541	+	38.0220i	0.397899	+	1.22461i
$965$	−0.596748	+	1.83660i	−0.0192100	+	0.0591223i
$966$	−1.61803	−	1.17557i	−0.0520594	−	0.0378234i
$967$	36.2918			1.16707			0.583533	−	0.812090i	$-0.301670\pi$
$967$	36.2918			1.16707			0.583533	+	0.812090i	$0.301670\pi$
$968$	−11.8090	+	21.5765i	−0.379556	+	0.693496i
$969$		0			0
$970$	3.24671	+	2.35887i	0.104246	+	0.0757389i
$971$	−7.63525	+	23.4989i	−0.245027	+	0.754116i	0.750605	+	0.660751i	$0.229762\pi$
$971$	−7.63525	+	23.4989i	−0.245027	+	0.754116i	−0.995632	+	0.0933644i	$0.970238\pi$
$972$	−0.500000	−	1.53884i	−0.0160375	−	0.0493584i
$973$	14.2082	−	10.3229i	0.455494	−	0.330936i
$974$	8.30902	−	6.03685i	0.266238	−	0.193433i
$975$	1.50000	+	4.61653i	0.0480384	+	0.147847i
$976$	−3.30244	+	10.1639i	−0.105709	+	0.325337i
$977$	−26.6976	−	19.3969i	−0.854131	−	0.620562i	0.0721512	−	0.997394i	$-0.477014\pi$
$977$	−26.6976	−	19.3969i	−0.854131	−	0.620562i	−0.926282	+	0.376831i	$0.877014\pi$
$978$	−3.72949			−0.119256
$979$	−1.97214	+	21.0745i	−0.0630297	+	0.673544i
$980$	0.618034			0.0197424
$981$	6.11803	+	4.44501i	0.195334	+	0.141918i
$982$	−0.708204	+	2.17963i	−0.0225997	+	0.0695547i
$983$	−9.25329	−	28.4787i	−0.295134	−	0.908329i	−0.983176	−	0.182659i	$-0.941530\pi$
$983$	−9.25329	−	28.4787i	−0.295134	−	0.908329i	0.688042	−	0.725671i	$-0.258470\pi$
$984$	−9.20820	+	6.69015i	−0.293547	+	0.213274i
$985$	−2.85410	+	2.07363i	−0.0909393	+	0.0660712i
$986$	5.42705	+	16.7027i	0.172833	+	0.531924i
$987$	−2.26393	+	6.96767i	−0.0720618	+	0.221783i
$988$		0			0
$989$	3.23607			0.102901
$990$	−0.517221	+	0.587785i	−0.0164384	+	0.0186810i
$991$	33.6312			1.06833			0.534165	−	0.845380i	$-0.320626\pi$
$991$	33.6312			1.06833			0.534165	+	0.845380i	$0.320626\pi$
$992$	−46.5238	−	33.8015i	−1.47713	−	1.07320i
$993$	−4.54508	+	13.9883i	−0.144234	+	0.443906i
$994$	1.42705	+	4.39201i	0.0452633	+	0.139306i
$995$	−2.33688	+	1.69784i	−0.0740841	+	0.0538253i
$996$	−7.85410	+	5.70634i	−0.248867	+	0.180812i
$997$	0.437694	+	1.34708i	0.0138619	+	0.0426626i	0.957748	−	0.287608i	$-0.0928600\pi$
$997$	0.437694	+	1.34708i	0.0138619	+	0.0426626i	−0.943886	+	0.330271i	$0.892860\pi$
$998$	0.954915	−	2.93893i	0.0302273	−	0.0930301i
$999$	−5.61803	−	4.08174i	−0.177747	−	0.129141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.d.169.1	✓	4
3.2	odd	2		693.2.m.b.631.1		4
11.3	even	5	inner	231.2.j.d.190.1	yes	4
11.5	even	5		2541.2.a.bb.1.1		2
11.6	odd	10		2541.2.a.s.1.2		2
33.5	odd	10		7623.2.a.ba.1.2		2
33.14	odd	10		693.2.m.b.190.1		4
33.17	even	10		7623.2.a.bp.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.d.169.1	✓	4	1.1	even	1	trivial
231.2.j.d.190.1	yes	4	11.3	even	5	inner
693.2.m.b.190.1		4	33.14	odd	10
693.2.m.b.631.1		4	3.2	odd	2
2541.2.a.s.1.2		2	11.6	odd	10
2541.2.a.bb.1.1		2	11.5	even	5
7623.2.a.ba.1.2		2	33.5	odd	10
7623.2.a.bp.1.1		2	33.17	even	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.363271i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.309017 - 0.224514i) q^{5} +(0.500000 - 0.363271i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +0.236068 q^{10} +(0.309017 - 3.30220i) q^{11} -1.61803 q^{12} +(0.809017 + 0.587785i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(3.42705 - 2.48990i) q^{17} +(-0.190983 - 0.587785i) q^{18} +(-0.500000 - 0.363271i) q^{20} +1.00000 q^{21} +(1.35410 - 1.53884i) q^{22} -3.23607 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-1.50000 + 4.61653i) q^{25} +(0.190983 + 0.587785i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.30902 - 0.951057i) q^{28} +(2.07295 + 6.37988i) q^{29} +(0.0729490 - 0.224514i) q^{30} +(8.28115 + 6.01661i) q^{31} -5.61803 q^{32} +(-3.04508 - 1.31433i) q^{33} +2.61803 q^{34} +(0.309017 + 0.224514i) q^{35} +(-0.500000 + 1.53884i) q^{36} +(2.14590 + 6.60440i) q^{37} +(0.809017 - 0.587785i) q^{39} +(-0.263932 - 0.812299i) q^{40} +(1.57295 - 4.84104i) q^{41} +(0.500000 + 0.363271i) q^{42} -1.00000 q^{43} +(-5.23607 + 1.17557i) q^{44} -0.381966 q^{45} +(-1.61803 - 1.17557i) q^{46} +(-2.26393 + 6.96767i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-2.42705 + 1.76336i) q^{50} +(-1.30902 - 4.02874i) q^{51} +(0.500000 - 1.53884i) q^{52} +(-6.16312 - 4.47777i) q^{53} -0.618034 q^{54} +(-0.645898 - 1.08981i) q^{55} +2.23607 q^{56} +(-1.28115 + 3.94298i) q^{58} +(-1.28115 - 3.94298i) q^{59} +(-0.500000 + 0.363271i) q^{60} +(4.66312 - 3.38795i) q^{61} +(1.95492 + 6.01661i) q^{62} +(0.309017 - 0.951057i) q^{63} +(0.190983 + 0.138757i) q^{64} +0.381966 q^{65} +(-1.04508 - 1.76336i) q^{66} -9.23607 q^{67} +(-5.54508 - 4.02874i) q^{68} +(-1.00000 + 3.07768i) q^{69} +(0.0729490 + 0.224514i) q^{70} +(6.04508 - 4.39201i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(3.57295 + 10.9964i) q^{73} +(-1.32624 + 4.08174i) q^{74} +(3.92705 + 2.85317i) q^{75} +(3.23607 - 0.726543i) q^{77} +0.618034 q^{78} +(-8.78115 - 6.37988i) q^{79} +(-0.218847 + 0.673542i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.54508 - 1.84911i) q^{82} +(4.85410 - 3.52671i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(0.500000 - 1.53884i) q^{85} +(-0.500000 - 0.363271i) q^{86} +6.70820 q^{87} +(-6.80902 - 2.93893i) q^{88} -6.38197 q^{89} +(-0.190983 - 0.138757i) q^{90} +(-0.309017 + 0.951057i) q^{91} +(1.61803 + 4.97980i) q^{92} +(8.28115 - 6.01661i) q^{93} +(-3.66312 + 2.66141i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(13.7533 + 9.99235i) q^{97} -0.618034 q^{98} +(-2.19098 + 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} - 8 q^{10} - q^{11} - 2 q^{12} + q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{20} + 4 q^{21} - 8 q^{22} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 3 q^{26} - q^{27} + 3 q^{28} + 15 q^{29} + 7 q^{30} + 13 q^{31} - 18 q^{32} - q^{33} + 6 q^{34} - q^{35} - 2 q^{36} + 22 q^{37} + q^{39} - 10 q^{40} + 13 q^{41} + 2 q^{42} - 4 q^{43} - 12 q^{44} - 6 q^{45} - 2 q^{46} - 18 q^{47} + 9 q^{48} - q^{49} - 3 q^{50} - 3 q^{51} + 2 q^{52} - 9 q^{53} + 2 q^{54} - 16 q^{55} + 15 q^{58} + 15 q^{59} - 2 q^{60} + 3 q^{61} + 19 q^{62} - q^{63} + 3 q^{64} + 6 q^{65} + 7 q^{66} - 28 q^{67} - 11 q^{68} - 4 q^{69} + 7 q^{70} + 13 q^{71} - 5 q^{72} + 21 q^{73} + 26 q^{74} + 9 q^{75} + 4 q^{77} - 2 q^{78} - 15 q^{79} - 21 q^{80} - q^{81} - q^{82} + 6 q^{83} - 2 q^{84} + 2 q^{85} - 2 q^{86} - 25 q^{88} - 30 q^{89} - 3 q^{90} + q^{91} + 2 q^{92} + 13 q^{93} + q^{94} + 2 q^{96} + 17 q^{97} + 2 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 - 8 * q^10 - q^11 - 2 * q^12 + q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^20 + 4 * q^21 - 8 * q^22 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 3 * q^26 - q^27 + 3 * q^28 + 15 * q^29 + 7 * q^30 + 13 * q^31 - 18 * q^32 - q^33 + 6 * q^34 - q^35 - 2 * q^36 + 22 * q^37 + q^39 - 10 * q^40 + 13 * q^41 + 2 * q^42 - 4 * q^43 - 12 * q^44 - 6 * q^45 - 2 * q^46 - 18 * q^47 + 9 * q^48 - q^49 - 3 * q^50 - 3 * q^51 + 2 * q^52 - 9 * q^53 + 2 * q^54 - 16 * q^55 + 15 * q^58 + 15 * q^59 - 2 * q^60 + 3 * q^61 + 19 * q^62 - q^63 + 3 * q^64 + 6 * q^65 + 7 * q^66 - 28 * q^67 - 11 * q^68 - 4 * q^69 + 7 * q^70 + 13 * q^71 - 5 * q^72 + 21 * q^73 + 26 * q^74 + 9 * q^75 + 4 * q^77 - 2 * q^78 - 15 * q^79 - 21 * q^80 - q^81 - q^82 + 6 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 - 25 * q^88 - 30 * q^89 - 3 * q^90 + q^91 + 2 * q^92 + 13 * q^93 + q^94 + 2 * q^96 + 17 * q^97 + 2 * q^98 - 11 * q^99

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