LMFDB - Embedded newform 231.2.j.a.64.1

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	231.64
Dual form			231.2.j.a.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.118034 - 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.118034 - 0.363271i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.19098 - 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.118034 - 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.118034 - 0.363271i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.19098 - 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.236068 q^{10} +(3.04508 - 1.31433i) q^{11} +1.85410 q^{12} +(-1.07295 + 3.30220i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.927051 - 2.85317i) q^{17} +(-0.309017 - 0.224514i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(0.354102 - 1.08981i) q^{20} -1.00000 q^{21} +(-0.118034 - 1.26133i) q^{22} -2.76393 q^{23} +(0.454915 - 1.40008i) q^{24} +(3.73607 - 2.71441i) q^{25} +(1.07295 + 0.779543i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(-2.42705 - 1.76336i) q^{29} +(-0.190983 + 0.138757i) q^{30} +(-1.30902 + 4.02874i) q^{31} +4.14590 q^{32} +(1.69098 - 2.85317i) q^{33} -1.14590 q^{34} +(-0.190983 + 0.587785i) q^{35} +(1.50000 - 1.08981i) q^{36} +(-0.381966 - 0.277515i) q^{37} +(0.472136 + 1.45309i) q^{38} +(1.07295 + 3.30220i) q^{39} +(-0.736068 - 0.534785i) q^{40} +(-6.54508 + 4.75528i) q^{41} +(-0.118034 + 0.363271i) q^{42} -9.00000 q^{43} +(6.00000 + 1.34708i) q^{44} -0.618034 q^{45} +(-0.326238 + 1.00406i) q^{46} +(0.881966 - 0.640786i) q^{47} +(2.54508 + 1.84911i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.545085 - 1.67760i) q^{50} +(-2.42705 - 1.76336i) q^{51} +(-5.20820 + 3.78398i) q^{52} +(-2.19098 + 6.74315i) q^{53} -0.381966 q^{54} +(-1.35410 - 1.53884i) q^{55} -1.47214 q^{56} +(-1.23607 + 3.80423i) q^{57} +(-0.927051 + 0.673542i) q^{58} +(-8.39919 - 6.10237i) q^{59} +(-0.354102 - 1.08981i) q^{60} +(2.07295 + 6.37988i) q^{61} +(1.30902 + 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-1.45492 + 4.47777i) q^{64} +2.14590 q^{65} +(-0.836881 - 0.951057i) q^{66} +9.70820 q^{67} +(1.71885 - 5.29007i) q^{68} +(-2.23607 + 1.62460i) q^{69} +(0.190983 + 0.138757i) q^{70} +(2.39919 + 7.38394i) q^{71} +(-0.454915 - 1.40008i) q^{72} +(-2.30902 - 1.67760i) q^{73} +(-0.145898 + 0.106001i) q^{74} +(1.42705 - 4.39201i) q^{75} -7.41641 q^{76} +(-3.23607 - 0.726543i) q^{77} +1.32624 q^{78} +(0.0450850 - 0.138757i) q^{79} +(1.57295 - 1.14281i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.954915 + 2.93893i) q^{82} +(-4.61803 - 14.2128i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(-1.50000 + 1.08981i) q^{85} +(-1.06231 + 3.26944i) q^{86} -3.00000 q^{87} +(2.48936 - 4.20025i) q^{88} +18.3262 q^{89} +(-0.0729490 + 0.224514i) q^{90} +(2.80902 - 2.04087i) q^{91} +(-4.14590 - 3.01217i) q^{92} +(1.30902 + 4.02874i) q^{93} +(-0.128677 - 0.396027i) q^{94} +(2.00000 + 1.45309i) q^{95} +(3.35410 - 2.43690i) q^{96} +(3.21885 - 9.90659i) q^{97} +0.381966 q^{98} +(-0.309017 - 3.30220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 6 * q^4 - 3 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9	\( 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9} + 8 q^{10} + q^{11} - 6 q^{12} - 11 q^{13} + q^{14} - 2 q^{15} - 14 q^{16} + 3 q^{17} + q^{18} - 4 q^{19} - 12 q^{20} - 4 q^{21} + 4 q^{22} - 20 q^{23} + 13 q^{24} + 6 q^{25} + 11 q^{26} + q^{27} - 9 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 30 q^{32} + 9 q^{33} - 18 q^{34} - 3 q^{35} + 6 q^{36} - 6 q^{37} - 16 q^{38} + 11 q^{39} + 6 q^{40} - 15 q^{41} + 4 q^{42} - 36 q^{43} + 24 q^{44} + 2 q^{45} + 30 q^{46} + 8 q^{47} - q^{48} - q^{49} + 9 q^{50} - 3 q^{51} + 6 q^{52} - 11 q^{53} - 6 q^{54} + 8 q^{55} + 12 q^{56} + 4 q^{57} + 3 q^{58} - 9 q^{59} + 12 q^{60} + 15 q^{61} + 3 q^{62} - q^{63} - 17 q^{64} + 22 q^{65} - 19 q^{66} + 12 q^{67} + 27 q^{68} + 3 q^{70} - 15 q^{71} - 13 q^{72} - 7 q^{73} - 14 q^{74} - q^{75} + 24 q^{76} - 4 q^{77} - 26 q^{78} - 11 q^{79} + 13 q^{80} - q^{81} + 15 q^{82} - 14 q^{83} - 6 q^{84} - 6 q^{85} + 36 q^{86} - 12 q^{87} - 37 q^{88} + 42 q^{89} - 7 q^{90} + 9 q^{91} - 30 q^{92} + 3 q^{93} - 43 q^{94} + 8 q^{95} + 33 q^{97} + 6 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 6 * q^4 - 3 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9 + 8 * q^10 + q^11 - 6 * q^12 - 11 * q^13 + q^14 - 2 * q^15 - 14 * q^16 + 3 * q^17 + q^18 - 4 * q^19 - 12 * q^20 - 4 * q^21 + 4 * q^22 - 20 * q^23 + 13 * q^24 + 6 * q^25 + 11 * q^26 + q^27 - 9 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 30 * q^32 + 9 * q^33 - 18 * q^34 - 3 * q^35 + 6 * q^36 - 6 * q^37 - 16 * q^38 + 11 * q^39 + 6 * q^40 - 15 * q^41 + 4 * q^42 - 36 * q^43 + 24 * q^44 + 2 * q^45 + 30 * q^46 + 8 * q^47 - q^48 - q^49 + 9 * q^50 - 3 * q^51 + 6 * q^52 - 11 * q^53 - 6 * q^54 + 8 * q^55 + 12 * q^56 + 4 * q^57 + 3 * q^58 - 9 * q^59 + 12 * q^60 + 15 * q^61 + 3 * q^62 - q^63 - 17 * q^64 + 22 * q^65 - 19 * q^66 + 12 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 - 13 * q^72 - 7 * q^73 - 14 * q^74 - q^75 + 24 * q^76 - 4 * q^77 - 26 * q^78 - 11 * q^79 + 13 * q^80 - q^81 + 15 * q^82 - 14 * q^83 - 6 * q^84 - 6 * q^85 + 36 * q^86 - 12 * q^87 - 37 * q^88 + 42 * q^89 - 7 * q^90 + 9 * q^91 - 30 * q^92 + 3 * q^93 - 43 * q^94 + 8 * q^95 + 33 * q^97 + 6 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.118034	−	0.363271i	0.0834626	−	0.256872i	−0.900613	−	0.434622i	$-0.856882\pi$
$2$	0.118034	−	0.363271i	0.0834626	−	0.256872i	0.984076	+	0.177750i	$0.0568820\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	0.899226	−	0.437485i	$-0.144131\pi$
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	−0.984636	+	0.174619i	$0.944131\pi$
$6$	−0.118034	−	0.363271i	−0.0481872	−	0.148305i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	1.19098	−	0.865300i	0.421076	−	0.305930i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.236068			−0.0746512
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	1.85410			0.535233
$13$	−1.07295	+	3.30220i	−0.297583	+	0.915865i	0.684759	+	0.728769i	$0.259907\pi$
$13$	−1.07295	+	3.30220i	−0.297583	+	0.915865i	−0.982342	+	0.187095i	$0.940093\pi$
$14$	−0.309017	+	0.224514i	−0.0825883	+	0.0600039i
$15$	−0.500000	−	0.363271i	−0.129099	−	0.0937962i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	−0.927051	−	2.85317i	−0.224843	−	0.691995i	−0.998308	−	0.0581558i	$-0.981478\pi$
$17$	−0.927051	−	2.85317i	−0.224843	−	0.691995i	0.773465	−	0.633839i	$-0.218522\pi$
$18$	−0.309017	−	0.224514i	−0.0728360	−	0.0529185i
$19$	−3.23607	+	2.35114i	−0.742405	+	0.539389i	−0.893463	−	0.449136i	$-0.851732\pi$
$19$	−3.23607	+	2.35114i	−0.742405	+	0.539389i	0.151058	+	0.988525i	$0.451732\pi$
$20$	0.354102	−	1.08981i	0.0791796	−	0.243690i
$21$	−1.00000			−0.218218
$22$	−0.118034	−	1.26133i	−0.0251649	−	0.268916i
$23$	−2.76393			−0.576320			−0.288160	−	0.957582i	$-0.593043\pi$
$23$	−2.76393			−0.576320			−0.288160	+	0.957582i	$0.593043\pi$
$24$	0.454915	−	1.40008i	0.0928591	−	0.285791i
$25$	3.73607	−	2.71441i	0.747214	−	0.542882i
$26$	1.07295	+	0.779543i	0.210423	+	0.152881i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.572949	−	1.76336i	−0.108277	−	0.333243i
$29$	−2.42705	−	1.76336i	−0.450692	−	0.327447i	0.339177	−	0.940723i	$-0.389851\pi$
$29$	−2.42705	−	1.76336i	−0.450692	−	0.327447i	−0.789869	+	0.613276i	$0.789851\pi$
$30$	−0.190983	+	0.138757i	−0.0348686	+	0.0253335i
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	0.762001	+	0.647576i	$0.224217\pi$
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	−0.997107	+	0.0760071i	$0.975783\pi$
$32$	4.14590			0.732898
$33$	1.69098	−	2.85317i	0.294362	−	0.496673i
$34$	−1.14590			−0.196520
$35$	−0.190983	+	0.587785i	−0.0322820	+	0.0993538i
$36$	1.50000	−	1.08981i	0.250000	−	0.181636i
$37$	−0.381966	−	0.277515i	−0.0627948	−	0.0456231i	0.555945	−	0.831219i	$-0.312356\pi$
$37$	−0.381966	−	0.277515i	−0.0627948	−	0.0456231i	−0.618740	+	0.785596i	$0.712356\pi$
$38$	0.472136	+	1.45309i	0.0765906	+	0.235722i
$39$	1.07295	+	3.30220i	0.171809	+	0.528775i
$40$	−0.736068	−	0.534785i	−0.116383	−	0.0845569i
$41$	−6.54508	+	4.75528i	−1.02217	+	0.742650i	−0.966727	−	0.255811i	$-0.917657\pi$
$41$	−6.54508	+	4.75528i	−1.02217	+	0.742650i	−0.0554438	+	0.998462i	$0.517657\pi$
$42$	−0.118034	+	0.363271i	−0.0182130	+	0.0560540i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$	6.00000	+	1.34708i	0.904534	+	0.203081i
$45$	−0.618034			−0.0921311
$46$	−0.326238	+	1.00406i	−0.0481012	+	0.148040i
$47$	0.881966	−	0.640786i	0.128648	−	0.0934682i	−0.521600	−	0.853190i	$-0.674665\pi$
$47$	0.881966	−	0.640786i	0.128648	−	0.0934682i	0.650248	+	0.759722i	$0.274665\pi$
$48$	2.54508	+	1.84911i	0.367351	+	0.266896i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.545085	−	1.67760i	−0.0770867	−	0.237248i
$51$	−2.42705	−	1.76336i	−0.339855	−	0.246919i
$52$	−5.20820	+	3.78398i	−0.722248	+	0.524744i
$53$	−2.19098	+	6.74315i	−0.300955	+	0.926243i	0.680201	+	0.733025i	$0.261892\pi$
$53$	−2.19098	+	6.74315i	−0.300955	+	0.926243i	−0.981156	+	0.193218i	$0.938108\pi$
$54$	−0.381966			−0.0519790
$55$	−1.35410	−	1.53884i	−0.182587	−	0.207497i
$56$	−1.47214			−0.196722
$57$	−1.23607	+	3.80423i	−0.163721	+	0.503882i
$58$	−0.927051	+	0.673542i	−0.121728	+	0.0884404i
$59$	−8.39919	−	6.10237i	−1.09348	−	0.794460i	−0.113497	−	0.993538i	$-0.536205\pi$
$59$	−8.39919	−	6.10237i	−1.09348	−	0.794460i	−0.979984	+	0.199078i	$0.936205\pi$
$60$	−0.354102	−	1.08981i	−0.0457144	−	0.140694i
$61$	2.07295	+	6.37988i	0.265414	+	0.816860i	0.991598	+	0.129359i	$0.0412921\pi$
$61$	2.07295	+	6.37988i	0.265414	+	0.816860i	−0.726184	+	0.687501i	$0.758708\pi$
$62$	1.30902	+	0.951057i	0.166245	+	0.120784i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	2.14590			0.266166
$66$	−0.836881	−	0.951057i	−0.103013	−	0.117067i
$67$	9.70820			1.18605			0.593023	−	0.805186i	$-0.297934\pi$
$67$	9.70820			1.18605			0.593023	+	0.805186i	$0.297934\pi$
$68$	1.71885	−	5.29007i	0.208441	−	0.641515i
$69$	−2.23607	+	1.62460i	−0.269191	+	0.195579i
$70$	0.190983	+	0.138757i	0.0228268	+	0.0165847i
$71$	2.39919	+	7.38394i	0.284731	+	0.876312i	0.986479	+	0.163887i	$0.0524032\pi$
$71$	2.39919	+	7.38394i	0.284731	+	0.876312i	−0.701748	+	0.712425i	$0.747597\pi$
$72$	−0.454915	−	1.40008i	−0.0536123	−	0.165002i
$73$	−2.30902	−	1.67760i	−0.270250	−	0.196348i	0.444404	−	0.895827i	$-0.353416\pi$
$73$	−2.30902	−	1.67760i	−0.270250	−	0.196348i	−0.714654	+	0.699479i	$0.753416\pi$
$74$	−0.145898	+	0.106001i	−0.0169603	+	0.0123224i
$75$	1.42705	−	4.39201i	0.164782	−	0.507146i
$76$	−7.41641			−0.850720
$77$	−3.23607	−	0.726543i	−0.368784	−	0.0827972i
$78$	1.32624			0.150167
$79$	0.0450850	−	0.138757i	0.00507246	−	0.0156114i	−0.948488	−	0.316812i	$-0.897387\pi$
$79$	0.0450850	−	0.138757i	0.00507246	−	0.0156114i	0.953561	+	0.301201i	$0.0973875\pi$
$80$	1.57295	−	1.14281i	0.175861	−	0.127771i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.954915	+	2.93893i	0.105453	+	0.324550i
$83$	−4.61803	−	14.2128i	−0.506895	−	1.56006i	−0.797561	−	0.603238i	$-0.793877\pi$
$83$	−4.61803	−	14.2128i	−0.506895	−	1.56006i	0.290666	−	0.956825i	$-0.406123\pi$
$84$	−1.50000	−	1.08981i	−0.163663	−	0.118908i
$85$	−1.50000	+	1.08981i	−0.162698	+	0.118207i
$86$	−1.06231	+	3.26944i	−0.114551	+	0.352553i
$87$	−3.00000			−0.321634
$88$	2.48936	−	4.20025i	0.265366	−	0.447749i
$89$	18.3262			1.94258			0.971289	−	0.237904i	$-0.0764604\pi$
$89$	18.3262			1.94258			0.971289	+	0.237904i	$0.0764604\pi$
$90$	−0.0729490	+	0.224514i	−0.00768950	+	0.0236659i
$91$	2.80902	−	2.04087i	0.294465	−	0.213941i
$92$	−4.14590	−	3.01217i	−0.432240	−	0.314041i
$93$	1.30902	+	4.02874i	0.135739	+	0.417761i
$94$	−0.128677	−	0.396027i	−0.0132720	−	0.0408471i
$95$	2.00000	+	1.45309i	0.205196	+	0.149083i
$96$	3.35410	−	2.43690i	0.342327	−	0.248715i
$97$	3.21885	−	9.90659i	0.326824	−	1.00586i	−0.643786	−	0.765206i	$-0.722637\pi$
$97$	3.21885	−	9.90659i	0.326824	−	1.00586i	0.970610	−	0.240656i	$-0.0773627\pi$
$98$	0.381966			0.0385844
$99$	−0.309017	−	3.30220i	−0.0310574	−	0.331883i
$100$	8.56231			0.856231
$101$	−0.381966	+	1.17557i	−0.0380070	+	0.116974i	−0.968260	−	0.249945i	$-0.919587\pi$
$101$	−0.381966	+	1.17557i	−0.0380070	+	0.116974i	0.930253	+	0.366919i	$0.119587\pi$
$102$	−0.927051	+	0.673542i	−0.0917917	+	0.0666906i
$103$	−6.28115	−	4.56352i	−0.618900	−	0.449657i	0.233637	−	0.972324i	$-0.424937\pi$
$103$	−6.28115	−	4.56352i	−0.618900	−	0.449657i	−0.852537	+	0.522666i	$0.824937\pi$
$104$	1.57953	+	4.86128i	0.154885	+	0.476688i
$105$	0.190983	+	0.587785i	0.0186380	+	0.0573620i
$106$	2.19098	+	1.59184i	0.212807	+	0.154613i
$107$	−1.57295	+	1.14281i	−0.152063	+	0.110480i	−0.661215	−	0.750196i	$-0.729959\pi$
$107$	−1.57295	+	1.14281i	−0.152063	+	0.110480i	0.509152	+	0.860676i	$0.329959\pi$
$108$	0.572949	−	1.76336i	0.0551320	−	0.169679i
$109$	20.5623			1.96951			0.984756	−	0.173942i	$-0.0556506\pi$
$109$	20.5623			1.96951			0.984756	+	0.173942i	$0.0556506\pi$
$110$	−0.718847	+	0.310271i	−0.0685394	+	0.0295832i
$111$	−0.472136			−0.0448132
$112$	0.972136	−	2.99193i	0.0918582	−	0.282711i
$113$	−6.04508	+	4.39201i	−0.568674	+	0.413166i	−0.834623	−	0.550821i	$-0.814315\pi$
$113$	−6.04508	+	4.39201i	−0.568674	+	0.413166i	0.265949	+	0.963987i	$0.414315\pi$
$114$	1.23607	+	0.898056i	0.115768	+	0.0841106i
$115$	0.527864	+	1.62460i	0.0492236	+	0.151495i
$116$	−1.71885	−	5.29007i	−0.159591	−	0.491170i
$117$	2.80902	+	2.04087i	0.259694	+	0.188679i
$118$	−3.20820	+	2.33090i	−0.295339	+	0.214576i
$119$	−0.927051	+	2.85317i	−0.0849826	+	0.261550i
$120$	−0.909830			−0.0830557
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	2.56231			0.231980
$123$	−2.50000	+	7.69421i	−0.225417	+	0.693763i
$124$	−6.35410	+	4.61653i	−0.570615	+	0.414576i
$125$	−4.80902	−	3.49396i	−0.430132	−	0.312509i
$126$	0.118034	+	0.363271i	0.0105153	+	0.0323628i
$127$	−4.19098	−	12.8985i	−0.371890	−	1.14456i	−0.945553	−	0.325468i	$-0.894478\pi$
$127$	−4.19098	−	12.8985i	−0.371890	−	1.14456i	0.573664	−	0.819091i	$-0.305522\pi$
$128$	8.16312	+	5.93085i	0.721525	+	0.524218i
$129$	−7.28115	+	5.29007i	−0.641070	+	0.465764i
$130$	0.253289	−	0.779543i	0.0222149	−	0.0683705i
$131$	14.3262			1.25169			0.625845	−	0.779948i	$-0.284754\pi$
$131$	14.3262			1.25169			0.625845	+	0.779948i	$0.284754\pi$
$132$	5.64590	−	2.43690i	0.491412	−	0.212105i
$133$	4.00000			0.346844
$134$	1.14590	−	3.52671i	0.0989905	−	0.304661i
$135$	−0.500000	+	0.363271i	−0.0430331	+	0.0312654i
$136$	−3.57295	−	2.59590i	−0.306378	−	0.222597i
$137$	−0.472136	−	1.45309i	−0.0403373	−	0.124145i	0.928860	−	0.370431i	$-0.120790\pi$
$137$	−0.472136	−	1.45309i	−0.0403373	−	0.124145i	−0.969197	+	0.246285i	$0.920790\pi$
$138$	0.326238	+	1.00406i	0.0277712	+	0.0854710i
$139$	−2.07295	−	1.50609i	−0.175825	−	0.127745i	0.496392	−	0.868099i	$-0.334658\pi$
$139$	−2.07295	−	1.50609i	−0.175825	−	0.127745i	−0.672217	+	0.740354i	$0.734658\pi$
$140$	−0.927051	+	0.673542i	−0.0783501	+	0.0569247i
$141$	0.336881	−	1.03681i	0.0283705	−	0.0873154i
$142$	2.96556			0.248864
$143$	1.07295	+	11.4657i	0.0897245	+	0.958808i
$144$	3.14590			0.262158
$145$	−0.572949	+	1.76336i	−0.0475808	+	0.146439i
$146$	−0.881966	+	0.640786i	−0.0729920	+	0.0530318i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	−0.270510	−	0.832544i	−0.0222358	−	0.0684347i
$149$	−1.44427	−	4.44501i	−0.118319	−	0.364150i	0.874306	−	0.485376i	$-0.161317\pi$
$149$	−1.44427	−	4.44501i	−0.118319	−	0.364150i	−0.992625	+	0.121226i	$0.961317\pi$
$150$	−1.42705	−	1.03681i	−0.116518	−	0.0846554i
$151$	6.78115	−	4.92680i	0.551842	−	0.400937i	−0.276622	−	0.960979i	$-0.589215\pi$
$151$	6.78115	−	4.92680i	0.551842	−	0.400937i	0.828464	+	0.560042i	$0.189215\pi$
$152$	−1.81966	+	5.60034i	−0.147594	+	0.454247i
$153$	−3.00000			−0.242536
$154$	−0.645898	+	1.08981i	−0.0520479	+	0.0878197i
$155$	2.61803			0.210286
$156$	−1.98936	+	6.12261i	−0.159276	+	0.490201i
$157$	18.4894	−	13.4333i	1.47561	−	1.07209i	0.496673	−	0.867938i	$-0.334555\pi$
$157$	18.4894	−	13.4333i	1.47561	−	1.07209i	0.978938	−	0.204157i	$-0.0654452\pi$
$158$	−0.0450850	−	0.0327561i	−0.00358677	−	0.00260594i
$159$	2.19098	+	6.74315i	0.173756	+	0.534767i
$160$	−0.791796	−	2.43690i	−0.0625970	−	0.192654i
$161$	2.23607	+	1.62460i	0.176227	+	0.128036i
$162$	−0.309017	+	0.224514i	−0.0242787	+	0.0176395i
$163$	5.82624	−	17.9313i	0.456346	−	1.40449i	−0.413201	−	0.910640i	$-0.635589\pi$
$163$	5.82624	−	17.9313i	0.456346	−	1.40449i	0.869547	−	0.493849i	$-0.164411\pi$
$164$	−15.0000			−1.17130
$165$	−2.00000	−	0.449028i	−0.155700	−	0.0349568i
$166$	−5.70820			−0.443043
$167$	1.20820	−	3.71847i	0.0934936	−	0.287744i	−0.893365	−	0.449333i	$-0.851662\pi$
$167$	1.20820	−	3.71847i	0.0934936	−	0.287744i	0.986858	+	0.161589i	$0.0516618\pi$
$168$	−1.19098	+	0.865300i	−0.0918863	+	0.0667593i
$169$	0.763932	+	0.555029i	0.0587640	+	0.0426945i
$170$	0.218847	+	0.673542i	0.0167848	+	0.0516583i
$171$	1.23607	+	3.80423i	0.0945245	+	0.290916i
$172$	−13.5000	−	9.80832i	−1.02937	−	0.747878i
$173$	−8.39919	+	6.10237i	−0.638578	+	0.463954i	−0.859361	−	0.511369i	$-0.829139\pi$
$173$	−8.39919	+	6.10237i	−0.638578	+	0.463954i	0.220783	+	0.975323i	$0.429139\pi$
$174$	−0.354102	+	1.08981i	−0.0268444	+	0.0826186i
$175$	−4.61803			−0.349091
$176$	6.89261	+	7.83297i	0.519550	+	0.590432i
$177$	−10.3820			−0.780356
$178$	2.16312	−	6.65740i	0.162133	−	0.498993i
$179$	−17.3713	+	12.6210i	−1.29839	+	0.943338i	−0.999939	−	0.0110855i	$-0.996471\pi$
$179$	−17.3713	+	12.6210i	−1.29839	+	0.943338i	−0.298455	+	0.954424i	$0.596471\pi$
$180$	−0.927051	−	0.673542i	−0.0690983	−	0.0502029i
$181$	3.78115	+	11.6372i	0.281051	+	0.864986i	0.987555	+	0.157276i	$0.0502713\pi$
$181$	3.78115	+	11.6372i	0.281051	+	0.864986i	−0.706504	+	0.707709i	$0.749729\pi$
$182$	−0.409830	−	1.26133i	−0.0303786	−	0.0934958i
$183$	5.42705	+	3.94298i	0.401179	+	0.291474i
$184$	−3.29180	+	2.39163i	−0.242674	+	0.176313i
$185$	−0.0901699	+	0.277515i	−0.00662943	+	0.0204033i
$186$	1.61803			0.118640
$187$	−6.57295	−	7.46969i	−0.480662	−	0.546238i
$188$	2.02129			0.147417
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	0.763932	−	0.555029i	0.0554215	−	0.0402660i
$191$	−20.6074	−	14.9721i	−1.49110	−	1.08335i	−0.973763	−	0.227564i	$-0.926924\pi$
$191$	−20.6074	−	14.9721i	−1.49110	−	1.08335i	−0.517335	−	0.855783i	$-0.673076\pi$
$192$	1.45492	+	4.47777i	0.104999	+	0.323155i
$193$	1.67376	+	5.15131i	0.120480	+	0.370799i	0.993051	−	0.117689i	$-0.0375485\pi$
$193$	1.67376	+	5.15131i	0.120480	+	0.370799i	−0.872570	+	0.488488i	$0.837549\pi$
$194$	−3.21885	−	2.33863i	−0.231100	−	0.167904i
$195$	1.73607	−	1.26133i	0.124322	−	0.0903255i
$196$	−0.572949	+	1.76336i	−0.0409249	+	0.125954i
$197$	20.1803			1.43779			0.718895	−	0.695119i	$-0.244648\pi$
$197$	20.1803			1.43779			0.718895	+	0.695119i	$0.244648\pi$
$198$	−1.23607	−	0.277515i	−0.0878435	−	0.0197221i
$199$	8.56231			0.606966			0.303483	−	0.952837i	$-0.401850\pi$
$199$	8.56231			0.606966			0.303483	+	0.952837i	$0.401850\pi$
$200$	2.10081	−	6.46564i	0.148550	−	0.457190i
$201$	7.85410	−	5.70634i	0.553986	−	0.402494i
$202$	0.381966	+	0.277515i	0.0268750	+	0.0195259i
$203$	0.927051	+	2.85317i	0.0650662	+	0.200253i
$204$	−1.71885	−	5.29007i	−0.120343	−	0.370379i
$205$	4.04508	+	2.93893i	0.282521	+	0.205264i
$206$	−2.39919	+	1.74311i	−0.167159	+	0.121448i
$207$	−0.854102	+	2.62866i	−0.0593642	+	0.182704i
$208$	−10.9230			−0.757373
$209$	−6.76393	+	11.4127i	−0.467871	+	0.789431i
$210$	0.236068			0.0162902
$211$	−5.45492	+	16.7885i	−0.375532	+	1.15577i	0.567587	+	0.823313i	$0.307877\pi$
$211$	−5.45492	+	16.7885i	−0.375532	+	1.15577i	−0.943119	+	0.332455i	$0.892123\pi$
$212$	−10.6353	+	7.72696i	−0.730432	+	0.530690i
$213$	6.28115	+	4.56352i	0.430378	+	0.312688i
$214$	0.229490	+	0.706298i	0.0156876	+	0.0482815i
$215$	1.71885	+	5.29007i	0.117224	+	0.360780i
$216$	−1.19098	−	0.865300i	−0.0810361	−	0.0588762i
$217$	3.42705	−	2.48990i	0.232643	−	0.169025i
$218$	2.42705	−	7.46969i	0.164381	−	0.505912i
$219$	−2.85410			−0.192862
$220$	−0.354102	−	3.78398i	−0.0238735	−	0.255116i
$221$	10.4164			0.700683
$222$	−0.0557281	+	0.171513i	−0.00374022	+	0.0115112i
$223$	−5.80902	+	4.22050i	−0.389001	+	0.282625i	−0.765046	−	0.643976i	$-0.777284\pi$
$223$	−5.80902	+	4.22050i	−0.389001	+	0.282625i	0.376045	+	0.926601i	$0.377284\pi$
$224$	−3.35410	−	2.43690i	−0.224105	−	0.162822i
$225$	−1.42705	−	4.39201i	−0.0951367	−	0.292801i
$226$	0.881966	+	2.71441i	0.0586675	+	0.180560i
$227$	−1.30902	−	0.951057i	−0.0868825	−	0.0631238i	0.543496	−	0.839412i	$-0.317100\pi$
$227$	−1.30902	−	0.951057i	−0.0868825	−	0.0631238i	−0.630379	+	0.776288i	$0.717100\pi$
$228$	−6.00000	+	4.35926i	−0.397360	+	0.288699i
$229$	−9.29180	+	28.5972i	−0.614019	+	1.88976i	−0.198781	+	0.980044i	$0.563698\pi$
$229$	−9.29180	+	28.5972i	−0.614019	+	1.88976i	−0.415238	+	0.909713i	$0.636302\pi$
$230$	0.652476			0.0430230
$231$	−3.04508	+	1.31433i	−0.200352	+	0.0864764i
$232$	−4.41641			−0.289951
$233$	−6.92705	+	21.3193i	−0.453806	+	1.39667i	0.418725	+	0.908113i	$0.362477\pi$
$233$	−6.92705	+	21.3193i	−0.453806	+	1.39667i	−0.872531	+	0.488559i	$0.837523\pi$
$234$	1.07295	−	0.779543i	0.0701409	−	0.0509603i
$235$	−0.545085	−	0.396027i	−0.0355574	−	0.0258340i
$236$	−5.94834	−	18.3071i	−0.387204	−	1.19169i
$237$	−0.0450850	−	0.138757i	−0.00292858	−	0.00901325i
$238$	0.927051	+	0.673542i	0.0600918	+	0.0436592i
$239$	2.11803	−	1.53884i	0.137004	−	0.0995394i	−0.517172	−	0.855881i	$-0.673015\pi$
$239$	2.11803	−	1.53884i	0.137004	−	0.0995394i	0.654176	+	0.756342i	$0.273015\pi$
$240$	0.600813	−	1.84911i	0.0387823	−	0.119360i
$241$	12.7082			0.818607			0.409304	−	0.912398i	$-0.365772\pi$
$241$	12.7082			0.818607			0.409304	+	0.912398i	$0.365772\pi$
$242$	−2.01722	−	3.68571i	−0.129672	−	0.236927i
$243$	−1.00000			−0.0641500
$244$	−3.84346	+	11.8290i	−0.246052	+	0.757271i
$245$	0.500000	−	0.363271i	0.0319438	−	0.0232085i
$246$	2.50000	+	1.81636i	0.159394	+	0.115807i
$247$	−4.29180	−	13.2088i	−0.273080	−	0.840455i
$248$	1.92705	+	5.93085i	0.122368	+	0.376610i
$249$	−12.0902	−	8.78402i	−0.766183	−	0.556665i
$250$	−1.83688	+	1.33457i	−0.116175	+	0.0844058i
$251$	5.07295	−	15.6129i	0.320202	−	0.985480i	−0.653358	−	0.757049i	$-0.726641\pi$
$251$	5.07295	−	15.6129i	0.320202	−	0.985480i	0.973560	−	0.228431i	$-0.0733595\pi$
$252$	−1.85410			−0.116797
$253$	−8.41641	+	3.63271i	−0.529135	+	0.228387i
$254$	−5.18034			−0.325043
$255$	−0.572949	+	1.76336i	−0.0358795	+	0.110426i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	−6.85410	−	4.97980i	−0.427547	−	0.310631i	0.353120	−	0.935578i	$-0.385121\pi$
$257$	−6.85410	−	4.97980i	−0.427547	−	0.310631i	−0.780667	+	0.624947i	$0.785121\pi$
$258$	1.06231	+	3.26944i	0.0661363	+	0.203547i
$259$	0.145898	+	0.449028i	0.00906566	+	0.0279012i
$260$	3.21885	+	2.33863i	0.199624	+	0.145036i
$261$	−2.42705	+	1.76336i	−0.150231	+	0.109149i
$262$	1.69098	−	5.20431i	0.104469	−	0.321523i
$263$	−15.0000			−0.924940			−0.462470	−	0.886635i	$-0.653037\pi$
$263$	−15.0000			−0.924940			−0.462470	+	0.886635i	$0.653037\pi$
$264$	−0.454915	−	4.86128i	−0.0279981	−	0.299191i
$265$	4.38197			0.269182
$266$	0.472136	−	1.45309i	0.0289485	−	0.0890944i
$267$	14.8262	−	10.7719i	0.907351	−	0.659229i
$268$	14.5623	+	10.5801i	0.889534	+	0.646285i
$269$	6.21885	+	19.1396i	0.379170	+	1.16696i	0.940622	+	0.339456i	$0.110243\pi$
$269$	6.21885	+	19.1396i	0.379170	+	1.16696i	−0.561452	+	0.827509i	$0.689757\pi$
$270$	0.0729490	+	0.224514i	0.00443954	+	0.0136635i
$271$	−15.2812	−	11.1024i	−0.928264	−	0.674423i	0.0173032	−	0.999850i	$-0.494492\pi$
$271$	−15.2812	−	11.1024i	−0.928264	−	0.674423i	−0.945567	+	0.325427i	$0.894492\pi$
$272$	7.63525	−	5.54734i	0.462955	−	0.336357i
$273$	1.07295	−	3.30220i	0.0649378	−	0.199858i
$274$	−0.583592			−0.0352561
$275$	7.80902	−	13.1760i	0.470901	−	0.794545i
$276$	−5.12461			−0.308465
$277$	−1.09017	+	3.35520i	−0.0655020	+	0.201594i	−0.978451	−	0.206479i	$-0.933799\pi$
$277$	−1.09017	+	3.35520i	−0.0655020	+	0.201594i	0.912949	+	0.408074i	$0.133799\pi$
$278$	−0.791796	+	0.575274i	−0.0474888	+	0.0345026i
$279$	3.42705	+	2.48990i	0.205172	+	0.149066i
$280$	0.281153	+	0.865300i	0.0168021	+	0.0517116i
$281$	−8.19098	−	25.2093i	−0.488633	−	1.50386i	−0.826649	−	0.562718i	$-0.809756\pi$
$281$	−8.19098	−	25.2093i	−0.488633	−	1.50386i	0.338016	−	0.941140i	$-0.390244\pi$
$282$	−0.336881	−	0.244758i	−0.0200610	−	0.0145752i
$283$	5.89919	−	4.28601i	0.350670	−	0.254777i	−0.398480	−	0.917177i	$-0.630462\pi$
$283$	5.89919	−	4.28601i	0.350670	−	0.254777i	0.749150	+	0.662400i	$0.230462\pi$
$284$	−4.44834	+	13.6906i	−0.263960	+	0.812386i
$285$	2.47214			0.146437
$286$	4.29180	+	0.963568i	0.253779	+	0.0569770i
$287$	8.09017			0.477548
$288$	1.28115	−	3.94298i	0.0754927	−	0.232343i
$289$	6.47214	−	4.70228i	0.380714	−	0.276605i
$290$	0.572949	+	0.416272i	0.0336447	+	0.0244443i
$291$	−3.21885	−	9.90659i	−0.188692	−	0.580735i
$292$	−1.63525	−	5.03280i	−0.0956961	−	0.294522i
$293$	24.7984	+	18.0171i	1.44874	+	1.05257i	0.986124	+	0.166008i	$0.0530877\pi$
$293$	24.7984	+	18.0171i	1.44874	+	1.05257i	0.462612	+	0.886561i	$0.346912\pi$
$294$	0.309017	−	0.224514i	0.0180222	−	0.0130939i
$295$	−1.98278	+	6.10237i	−0.115442	+	0.355294i
$296$	−0.695048			−0.0403989
$297$	−2.19098	−	2.48990i	−0.127134	−	0.144479i
$298$	−1.78522			−0.103415
$299$	2.96556	−	9.12705i	0.171503	−	0.527831i
$300$	6.92705	−	5.03280i	0.399933	−	0.290569i
$301$	7.28115	+	5.29007i	0.419679	+	0.304914i
$302$	−0.989357	−	3.04493i	−0.0569311	−	0.175216i
$303$	0.381966	+	1.17557i	0.0219434	+	0.0675348i
$304$	−10.1803	−	7.39645i	−0.583883	−	0.424215i
$305$	3.35410	−	2.43690i	0.192055	−	0.139536i
$306$	−0.354102	+	1.08981i	−0.0202427	+	0.0623005i
$307$	6.70820			0.382857			0.191429	−	0.981507i	$-0.438688\pi$
$307$	6.70820			0.382857			0.191429	+	0.981507i	$0.438688\pi$
$308$	−4.06231	−	4.61653i	−0.231471	−	0.263051i
$309$	−7.76393			−0.441675
$310$	0.309017	−	0.951057i	0.0175510	−	0.0540164i
$311$	4.07295	−	2.95917i	0.230956	−	0.167799i	−0.466289	−	0.884633i	$-0.654409\pi$
$311$	4.07295	−	2.95917i	0.230956	−	0.167799i	0.697244	+	0.716833i	$0.254409\pi$
$312$	4.13525	+	3.00444i	0.234113	+	0.170093i
$313$	4.42705	+	13.6251i	0.250232	+	0.770134i	0.994732	+	0.102512i	$0.0326879\pi$
$313$	4.42705	+	13.6251i	0.250232	+	0.770134i	−0.744500	+	0.667622i	$0.767312\pi$
$314$	−2.69756	−	8.30224i	−0.152232	−	0.468522i
$315$	0.500000	+	0.363271i	0.0281718	+	0.0204680i
$316$	0.218847	−	0.159002i	0.0123111	−	0.00894454i
$317$	3.01722	−	9.28605i	0.169464	−	0.521557i	−0.829873	−	0.557952i	$-0.811587\pi$
$317$	3.01722	−	9.28605i	0.169464	−	0.521557i	0.999337	+	0.0363950i	$0.0115875\pi$
$318$	2.70820			0.151869
$319$	−9.70820	−	2.17963i	−0.543555	−	0.122036i
$320$	2.90983			0.162664
$321$	−0.600813	+	1.84911i	−0.0335341	+	0.103207i
$322$	0.854102	−	0.620541i	0.0475972	−	0.0345814i
$323$	9.70820	+	7.05342i	0.540179	+	0.392463i
$324$	−0.572949	−	1.76336i	−0.0318305	−	0.0979642i
$325$	4.95492	+	15.2497i	0.274849	+	0.845899i
$326$	−5.82624	−	4.23301i	−0.322685	−	0.234445i
$327$	16.6353	−	12.0862i	0.919932	−	0.668370i
$328$	−3.68034	+	11.3269i	−0.203213	+	0.625425i
$329$	−1.09017			−0.0601030
$330$	−0.399187	+	0.673542i	−0.0219745	+	0.0370773i
$331$	−35.5410			−1.95351			−0.976756	−	0.214356i	$-0.931235\pi$
$331$	−35.5410			−1.95351			−0.976756	+	0.214356i	$0.931235\pi$
$332$	8.56231	−	26.3521i	0.469918	−	1.44626i
$333$	−0.381966	+	0.277515i	−0.0209316	+	0.0152077i
$334$	−1.20820	−	0.877812i	−0.0661100	−	0.0480317i
$335$	−1.85410	−	5.70634i	−0.101300	−	0.311771i
$336$	−0.972136	−	2.99193i	−0.0530344	−	0.163223i
$337$	−3.42705	−	2.48990i	−0.186683	−	0.135633i	0.490518	−	0.871431i	$-0.336808\pi$
$337$	−3.42705	−	2.48990i	−0.186683	−	0.135633i	−0.677202	+	0.735798i	$0.736808\pi$
$338$	0.291796	−	0.212002i	0.0158716	−	0.0115314i
$339$	−2.30902	+	7.10642i	−0.125409	+	0.385968i
$340$	−3.43769			−0.186435
$341$	1.30902	+	13.9883i	0.0708872	+	0.757511i
$342$	1.52786			0.0826174
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−10.7188	+	7.78770i	−0.577922	+	0.419885i
$345$	1.38197	+	1.00406i	0.0744025	+	0.0540566i
$346$	1.22542	+	3.77147i	0.0658792	+	0.202755i
$347$	3.67376	+	11.3067i	0.197218	+	0.606974i	0.999944	+	0.0106257i	$0.00338234\pi$
$347$	3.67376	+	11.3067i	0.197218	+	0.606974i	−0.802726	+	0.596348i	$0.796618\pi$
$348$	−4.50000	−	3.26944i	−0.241225	−	0.175260i
$349$	14.2082	−	10.3229i	0.760548	−	0.552570i	−0.138531	−	0.990358i	$-0.544238\pi$
$349$	14.2082	−	10.3229i	0.760548	−	0.552570i	0.899078	+	0.437788i	$0.144238\pi$
$350$	−0.545085	+	1.67760i	−0.0291360	+	0.0896714i
$351$	3.47214			0.185329
$352$	12.6246	−	5.44907i	0.672894	−	0.290436i
$353$	11.2918			0.601002			0.300501	−	0.953782i	$-0.402846\pi$
$353$	11.2918			0.601002			0.300501	+	0.953782i	$0.402846\pi$
$354$	−1.22542	+	3.77147i	−0.0651306	+	0.200451i
$355$	3.88197	−	2.82041i	0.206033	−	0.149692i
$356$	27.4894	+	19.9722i	1.45693	+	1.05852i
$357$	0.927051	+	2.85317i	0.0490647	+	0.151006i
$358$	2.53444	+	7.80021i	0.133949	+	0.412254i
$359$	25.0623	+	18.2088i	1.32274	+	0.961025i	0.999894	+	0.0145732i	$0.00463896\pi$
$359$	25.0623	+	18.2088i	1.32274	+	0.961025i	0.322844	+	0.946452i	$0.395361\pi$
$360$	−0.736068	+	0.534785i	−0.0387942	+	0.0281856i
$361$	−0.927051	+	2.85317i	−0.0487922	+	0.150167i
$362$	4.67376			0.245647
$363$	1.39919	−	10.9106i	0.0734383	−	0.572661i
$364$	6.43769			0.337427
$365$	−0.545085	+	1.67760i	−0.0285311	+	0.0878095i
$366$	2.07295	−	1.50609i	0.108355	−	0.0787244i
$367$	9.13525	+	6.63715i	0.476856	+	0.346456i	0.800107	−	0.599857i	$-0.204776\pi$
$367$	9.13525	+	6.63715i	0.476856	+	0.346456i	−0.323251	+	0.946313i	$0.604776\pi$
$368$	−2.68692	−	8.26948i	−0.140065	−	0.431077i
$369$	2.50000	+	7.69421i	0.130145	+	0.400545i
$370$	0.0901699	+	0.0655123i	0.00468771	+	0.00340582i
$371$	5.73607	−	4.16750i	0.297802	−	0.216366i
$372$	−2.42705	+	7.46969i	−0.125837	+	0.387286i
$373$	−11.8197			−0.611999			−0.305999	−	0.952032i	$-0.598991\pi$
$373$	−11.8197			−0.611999			−0.305999	+	0.952032i	$0.598991\pi$
$374$	−3.48936	+	1.50609i	−0.180430	+	0.0778778i
$375$	−5.94427			−0.306961
$376$	0.495935	−	1.52633i	0.0255759	−	0.0787145i
$377$	8.42705	−	6.12261i	0.434015	−	0.315331i
$378$	0.309017	+	0.224514i	0.0158941	+	0.0115478i
$379$	3.95492	+	12.1720i	0.203150	+	0.625232i	0.999784	+	0.0207704i	$0.00661190\pi$
$379$	3.95492	+	12.1720i	0.203150	+	0.625232i	−0.796634	+	0.604462i	$0.793388\pi$
$380$	1.41641	+	4.35926i	0.0726602	+	0.223625i
$381$	−10.9721	−	7.97172i	−0.562120	−	0.408404i
$382$	−7.87132	+	5.71885i	−0.402732	+	0.292602i
$383$	8.42705	−	25.9358i	0.430602	−	1.32526i	−0.466925	−	0.884297i	$-0.654638\pi$
$383$	8.42705	−	25.9358i	0.430602	−	1.32526i	0.897527	−	0.440960i	$-0.145362\pi$
$384$	10.0902			0.514912
$385$	0.190983	+	2.04087i	0.00973340	+	0.104012i
$386$	2.06888			0.105303
$387$	−2.78115	+	8.55951i	−0.141374	+	0.435104i
$388$	15.6246	−	11.3519i	0.793219	−	0.576308i
$389$	−24.3262	−	17.6740i	−1.23339	−	0.896110i	−0.236250	−	0.971692i	$-0.575918\pi$
$389$	−24.3262	−	17.6740i	−1.23339	−	0.896110i	−0.997140	+	0.0755827i	$0.975918\pi$
$390$	−0.253289	−	0.779543i	−0.0128258	−	0.0394737i
$391$	2.56231	+	7.88597i	0.129581	+	0.398810i
$392$	1.19098	+	0.865300i	0.0601537	+	0.0437042i
$393$	11.5902	−	8.42075i	0.584647	−	0.424771i
$394$	2.38197	−	7.33094i	0.120002	−	0.369327i
$395$	−0.0901699			−0.00453694
$396$	3.13525	−	5.29007i	0.157552	−	0.265836i
$397$	−15.2705			−0.766405			−0.383202	−	0.923664i	$-0.625179\pi$
$397$	−15.2705			−0.766405			−0.383202	+	0.923664i	$0.625179\pi$
$398$	1.01064	−	3.11044i	0.0506590	−	0.155912i
$399$	3.23607	−	2.35114i	0.162006	−	0.117704i
$400$	11.7533	+	8.53926i	0.587664	+	0.426963i
$401$	−9.35410	−	28.7890i	−0.467122	−	1.43765i	−0.856295	−	0.516488i	$-0.827239\pi$
$401$	−9.35410	−	28.7890i	−0.467122	−	1.43765i	0.389173	−	0.921165i	$-0.372761\pi$
$402$	−1.14590	−	3.52671i	−0.0571522	−	0.175896i
$403$	−11.8992	−	8.64527i	−0.592741	−	0.430651i
$404$	−1.85410	+	1.34708i	−0.0922450	+	0.0670199i
$405$	−0.190983	+	0.587785i	−0.00949002	+	0.0292073i
$406$	1.14590			0.0568700
$407$	−1.52786	−	0.343027i	−0.0757334	−	0.0170032i
$408$	−4.41641			−0.218645
$409$	2.28115	−	7.02067i	0.112796	−	0.347150i	−0.878685	−	0.477402i	$-0.841579\pi$
$409$	2.28115	−	7.02067i	0.112796	−	0.347150i	0.991481	+	0.130252i	$0.0415787\pi$
$410$	1.54508	−	1.12257i	0.0763063	−	0.0554398i
$411$	−1.23607	−	0.898056i	−0.0609707	−	0.0442978i
$412$	−4.44834	−	13.6906i	−0.219154	−	0.674486i
$413$	3.20820	+	9.87384i	0.157865	+	0.485860i
$414$	0.854102	+	0.620541i	0.0419768	+	0.0304979i
$415$	−7.47214	+	5.42882i	−0.366793	+	0.266491i
$416$	−4.44834	+	13.6906i	−0.218098	+	0.671236i
$417$	−2.56231			−0.125477
$418$	3.34752	+	3.80423i	0.163733	+	0.186071i
$419$	2.32624			0.113644			0.0568221	−	0.998384i	$-0.481903\pi$
$419$	2.32624			0.113644			0.0568221	+	0.998384i	$0.481903\pi$
$420$	−0.354102	+	1.08981i	−0.0172784	+	0.0531775i
$421$	−1.92705	+	1.40008i	−0.0939187	+	0.0682359i	−0.633754	−	0.773535i	$-0.718487\pi$
$421$	−1.92705	+	1.40008i	−0.0939187	+	0.0682359i	0.539835	+	0.841771i	$0.318487\pi$
$422$	5.45492	+	3.96323i	0.265541	+	0.192927i
$423$	−0.336881	−	1.03681i	−0.0163797	−	0.0504116i
$424$	3.22542	+	9.92684i	0.156640	+	0.482090i
$425$	−11.2082	−	8.14324i	−0.543678	−	0.395005i
$426$	2.39919	−	1.74311i	0.116241	−	0.0844540i
$427$	2.07295	−	6.37988i	0.100317	−	0.308744i
$428$	−3.60488			−0.174248
$429$	7.60739	+	8.64527i	0.367288	+	0.417397i
$430$	2.12461			0.102458
$431$	5.37132	−	16.5312i	0.258728	−	0.796281i	−0.734345	−	0.678777i	$-0.762510\pi$
$431$	5.37132	−	16.5312i	0.258728	−	0.796281i	0.993072	−	0.117505i	$-0.0374895\pi$
$432$	2.54508	−	1.84911i	0.122450	−	0.0889655i
$433$	−0.854102	−	0.620541i	−0.0410455	−	0.0298213i	0.567073	−	0.823667i	$-0.308076\pi$
$433$	−0.854102	−	0.620541i	−0.0410455	−	0.0298213i	−0.608119	+	0.793846i	$0.708076\pi$
$434$	−0.500000	−	1.53884i	−0.0240008	−	0.0738668i
$435$	0.572949	+	1.76336i	0.0274708	+	0.0845464i
$436$	30.8435	+	22.4091i	1.47713	+	1.07320i
$437$	8.94427	−	6.49839i	0.427863	−	0.310860i
$438$	−0.336881	+	1.03681i	−0.0160968	+	0.0495409i
$439$	−23.8328			−1.13748			−0.568739	−	0.822518i	$-0.692569\pi$
$439$	−23.8328			−1.13748			−0.568739	+	0.822518i	$0.692569\pi$
$440$	−2.94427	−	0.661030i	−0.140363	−	0.0315134i
$441$	1.00000			0.0476190
$442$	1.22949	−	3.78398i	0.0584809	−	0.179986i
$443$	−31.2705	+	22.7194i	−1.48571	+	1.07943i	−0.510045	+	0.860148i	$0.670371\pi$
$443$	−31.2705	+	22.7194i	−1.48571	+	1.07943i	−0.975662	+	0.219281i	$0.929629\pi$
$444$	−0.708204	−	0.514540i	−0.0336099	−	0.0244190i
$445$	−3.50000	−	10.7719i	−0.165916	−	0.510637i
$446$	0.847524	+	2.60841i	0.0401314	+	0.123512i
$447$	−3.78115	−	2.74717i	−0.178842	−	0.129937i
$448$	3.80902	−	2.76741i	0.179959	−	0.130748i
$449$	1.39919	−	4.30625i	0.0660317	−	0.203225i	−0.912597	−	0.408861i	$-0.865926\pi$
$449$	1.39919	−	4.30625i	0.0660317	−	0.203225i	0.978629	+	0.205636i	$0.0659262\pi$
$450$	−1.76393			−0.0831526
$451$	−13.6803	+	23.0826i	−0.644182	+	1.08692i
$452$	−13.8541			−0.651642
$453$	2.59017	−	7.97172i	0.121697	−	0.374544i
$454$	−0.500000	+	0.363271i	−0.0234662	+	0.0170492i
$455$	−1.73607	−	1.26133i	−0.0813881	−	0.0591319i
$456$	1.81966	+	5.60034i	0.0852134	+	0.262260i
$457$	−5.51722	−	16.9803i	−0.258085	−	0.794303i	−0.993206	−	0.116368i	$-0.962875\pi$
$457$	−5.51722	−	16.9803i	−0.258085	−	0.794303i	0.735121	−	0.677935i	$-0.237125\pi$
$458$	9.29180	+	6.75089i	0.434177	+	0.315448i
$459$	−2.42705	+	1.76336i	−0.113285	+	0.0823064i
$460$	−0.978714	+	3.01217i	−0.0456328	+	0.140443i
$461$	−22.4164			−1.04404			−0.522018	−	0.852934i	$-0.674821\pi$
$461$	−22.4164			−1.04404			−0.522018	+	0.852934i	$0.674821\pi$
$462$	0.118034	+	1.26133i	0.00549144	+	0.0586823i
$463$	−29.6869			−1.37967			−0.689834	−	0.723968i	$-0.742317\pi$
$463$	−29.6869			−1.37967			−0.689834	+	0.723968i	$0.742317\pi$
$464$	2.91641	−	8.97578i	0.135391	−	0.416690i
$465$	2.11803	−	1.53884i	0.0982215	−	0.0713621i
$466$	6.92705	+	5.03280i	0.320889	+	0.233140i
$467$	−1.12868	−	3.47371i	−0.0522289	−	0.160744i	0.921540	−	0.388284i	$-0.126932\pi$
$467$	−1.12868	−	3.47371i	−0.0522289	−	0.160744i	−0.973769	+	0.227539i	$0.926932\pi$
$468$	1.98936	+	6.12261i	0.0919581	+	0.283018i
$469$	−7.85410	−	5.70634i	−0.362669	−	0.263494i
$470$	−0.208204	+	0.151269i	−0.00960373	+	0.00697752i
$471$	7.06231	−	21.7355i	0.325414	−	1.00152i
$472$	−15.2837			−0.703488
$473$	−27.4058	+	11.8290i	−1.26012	+	0.543896i
$474$	−0.0557281			−0.00255968
$475$	−5.70820	+	17.5680i	−0.261910	+	0.806077i
$476$	−4.50000	+	3.26944i	−0.206257	+	0.149855i
$477$	5.73607	+	4.16750i	0.262637	+	0.190817i
$478$	−0.309017	−	0.951057i	−0.0141341	−	0.0435003i
$479$	6.28115	+	19.3314i	0.286993	+	0.883274i	0.985794	+	0.167958i	$0.0537173\pi$
$479$	6.28115	+	19.3314i	0.286993	+	0.883274i	−0.698801	+	0.715316i	$0.746283\pi$
$480$	−2.07295	−	1.50609i	−0.0946167	−	0.0687431i
$481$	1.32624	−	0.963568i	0.0604712	−	0.0439349i
$482$	1.50000	−	4.61653i	0.0683231	−	0.210277i
$483$	2.76393			0.125763
$484$	20.0410	−	3.78398i	0.910955	−	0.171999i
$485$	−6.43769			−0.292321
$486$	−0.118034	+	0.363271i	−0.00535413	+	0.0164783i
$487$	−9.92705	+	7.21242i	−0.449838	+	0.326826i	−0.789532	−	0.613710i	$-0.789676\pi$
$487$	−9.92705	+	7.21242i	−0.449838	+	0.326826i	0.339694	+	0.940536i	$0.389676\pi$
$488$	7.98936	+	5.80461i	0.361661	+	0.262762i
$489$	−5.82624	−	17.9313i	−0.263472	−	0.810882i
$490$	−0.0729490	−	0.224514i	−0.00329550	−	0.0101425i
$491$	7.56231	+	5.49434i	0.341282	+	0.247956i	0.745203	−	0.666838i	$-0.232353\pi$
$491$	7.56231	+	5.49434i	0.341282	+	0.247956i	−0.403920	+	0.914794i	$0.632353\pi$
$492$	−12.1353	+	8.81678i	−0.547100	+	0.397491i
$493$	−2.78115	+	8.55951i	−0.125257	+	0.385501i
$494$	−5.30495			−0.238681
$495$	−1.88197	+	0.812299i	−0.0845881	+	0.0365101i
$496$	−13.3262			−0.598366
$497$	2.39919	−	7.38394i	0.107618	−	0.331215i
$498$	−4.61803	+	3.35520i	−0.206939	+	0.150350i
$499$	4.04508	+	2.93893i	0.181083	+	0.131564i	0.674634	−	0.738152i	$-0.264301\pi$
$499$	4.04508	+	2.93893i	0.181083	+	0.131564i	−0.493551	+	0.869717i	$0.664301\pi$
$500$	−3.40576	−	10.4819i	−0.152310	−	0.468763i
$501$	−1.20820	−	3.71847i	−0.0539786	−	0.166129i
$502$	−5.07295	−	3.68571i	−0.226417	−	0.164501i
$503$	−22.8435	+	16.5967i	−1.01854	+	0.740012i	−0.965983	−	0.258606i	$-0.916737\pi$
$503$	−22.8435	+	16.5967i	−1.01854	+	0.740012i	−0.0525565	+	0.998618i	$0.516737\pi$
$504$	−0.454915	+	1.40008i	−0.0202635	+	0.0623647i
$505$	0.763932			0.0339945
$506$	0.326238	+	3.48622i	0.0145030	+	0.154982i
$507$	0.944272			0.0419366
$508$	7.77051	−	23.9152i	0.344761	−	1.06106i
$509$	−21.9894	+	15.9762i	−0.974661	+	0.708133i	−0.956509	−	0.291702i	$-0.905778\pi$
$509$	−21.9894	+	15.9762i	−0.974661	+	0.708133i	−0.0181520	+	0.999835i	$0.505778\pi$
$510$	0.572949	+	0.416272i	0.0253706	+	0.0184328i
$511$	0.881966	+	2.71441i	0.0390159	+	0.120079i
$512$	6.89261	+	21.2133i	0.304613	+	0.937503i
$513$	3.23607	+	2.35114i	0.142876	+	0.103805i
$514$	−2.61803	+	1.90211i	−0.115477	+	0.0838986i
$515$	−1.48278	+	4.56352i	−0.0653391	+	0.201093i
$516$	−16.6869			−0.734601
$517$	1.84346	−	3.11044i	0.0810752	−	0.136797i
$518$	0.180340			0.00792368
$519$	−3.20820	+	9.87384i	−0.140825	+	0.433413i
$520$	2.55573	−	1.85685i	0.112076	−	0.0814280i
$521$	−15.6631	−	11.3799i	−0.686214	−	0.498563i	0.189200	−	0.981939i	$-0.439411\pi$
$521$	−15.6631	−	11.3799i	−0.686214	−	0.498563i	−0.875413	+	0.483375i	$0.839411\pi$
$522$	0.354102	+	1.08981i	0.0154986	+	0.0476999i
$523$	10.6353	+	32.7319i	0.465047	+	1.43127i	0.858923	+	0.512105i	$0.171134\pi$
$523$	10.6353	+	32.7319i	0.465047	+	1.43127i	−0.393876	+	0.919164i	$0.628866\pi$
$524$	21.4894	+	15.6129i	0.938767	+	0.682054i
$525$	−3.73607	+	2.71441i	−0.163055	+	0.118467i
$526$	−1.77051	+	5.44907i	−0.0771979	+	0.237591i
$527$	12.7082			0.553578
$528$	10.1803	+	2.28563i	0.443042	+	0.0994692i
$529$	−15.3607			−0.667856
$530$	0.517221	−	1.59184i	0.0224666	−	0.0691452i
$531$	−8.39919	+	6.10237i	−0.364494	+	0.264820i
$532$	6.00000	+	4.35926i	0.260133	+	0.188998i
$533$	−8.68034	−	26.7153i	−0.375987	−	1.15717i
$534$	−2.16312	−	6.65740i	−0.0936073	−	0.288094i
$535$	0.972136	+	0.706298i	0.0420291	+	0.0305359i
$536$	11.5623	−	8.40051i	0.499416	−	0.362847i
$537$	−6.63525	+	20.4212i	−0.286332	+	0.881240i
$538$	7.68692			0.331407
$539$	2.19098	+	2.48990i	0.0943723	+	0.107248i
$540$	−1.14590			−0.0493116
$541$	−12.1910	+	37.5200i	−0.524131	+	1.61311i	0.241896	+	0.970302i	$0.422231\pi$
$541$	−12.1910	+	37.5200i	−0.524131	+	1.61311i	−0.766027	+	0.642808i	$0.777769\pi$
$542$	−5.83688	+	4.24074i	−0.250716	+	0.182155i
$543$	9.89919	+	7.19218i	0.424815	+	0.308646i
$544$	−3.84346	−	11.8290i	−0.164787	−	0.507162i
$545$	−3.92705	−	12.0862i	−0.168216	−	0.517717i
$546$	−1.07295	−	0.779543i	−0.0459180	−	0.0333614i
$547$	21.5172	−	15.6332i	0.920010	−	0.668426i	−0.0235166	−	0.999723i	$-0.507486\pi$
$547$	21.5172	−	15.6332i	0.920010	−	0.668426i	0.943526	+	0.331297i	$0.107486\pi$
$548$	0.875388	−	2.69417i	0.0373947	−	0.115089i
$549$	6.70820			0.286299
$550$	−3.86475	−	4.39201i	−0.164793	−	0.187276i
$551$	12.0000			0.511217
$552$	−1.25735	+	3.86974i	−0.0535165	+	0.164707i
$553$	−0.118034	+	0.0857567i	−0.00501932	+	0.00364675i
$554$	1.09017	+	0.792055i	0.0463169	+	0.0336512i
$555$	0.0901699	+	0.277515i	0.00382750	+	0.0117798i
$556$	−1.46807	−	4.51826i	−0.0622601	−	0.191617i
$557$	11.4721	+	8.33499i	0.486090	+	0.353165i	0.803679	−	0.595064i	$-0.202873\pi$
$557$	11.4721	+	8.33499i	0.486090	+	0.353165i	−0.317589	+	0.948229i	$0.602873\pi$
$558$	1.30902	−	0.951057i	0.0554151	−	0.0402614i
$559$	9.65654	−	29.7198i	0.408428	−	1.25701i
$560$	−1.94427			−0.0821605
$561$	−9.70820	−	2.17963i	−0.409881	−	0.0920239i
$562$	−10.1246			−0.427081
$563$	13.6910	−	42.1365i	0.577006	−	1.77584i	−0.0522381	−	0.998635i	$-0.516635\pi$
$563$	13.6910	−	42.1365i	0.577006	−	1.77584i	0.629244	−	0.777208i	$-0.283365\pi$
$564$	1.63525	−	1.18808i	0.0688567	−	0.0500273i
$565$	3.73607	+	2.71441i	0.157178	+	0.114196i
$566$	−0.860680	−	2.64890i	−0.0361771	−	0.111342i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	9.24671	+	6.71813i	0.387983	+	0.281886i
$569$	2.04508	−	1.48584i	0.0857344	−	0.0622897i	−0.544092	−	0.839025i	$-0.683126\pi$
$569$	2.04508	−	1.48584i	0.0857344	−	0.0622897i	0.629827	+	0.776736i	$0.283126\pi$
$570$	0.291796	−	0.898056i	0.0122220	−	0.0376154i
$571$	12.8885			0.539369			0.269684	−	0.962949i	$-0.413081\pi$
$571$	12.8885			0.539369			0.269684	+	0.962949i	$0.413081\pi$
$572$	−10.8860	+	18.3678i	−0.455168	+	0.767998i
$573$	−25.4721			−1.06411
$574$	0.954915	−	2.93893i	0.0398574	−	0.122668i
$575$	−10.3262	+	7.50245i	−0.430634	+	0.312874i
$576$	3.80902	+	2.76741i	0.158709	+	0.115309i
$577$	−5.60739	−	17.2578i	−0.233439	−	0.718451i	−0.997325	−	0.0730993i	$-0.976711\pi$
$577$	−5.60739	−	17.2578i	−0.233439	−	0.718451i	0.763886	−	0.645351i	$-0.223289\pi$
$578$	−0.944272	−	2.90617i	−0.0392765	−	0.120881i
$579$	4.38197	+	3.18368i	0.182108	+	0.132309i
$580$	−2.78115	+	2.02063i	−0.115481	+	0.0839019i
$581$	−4.61803	+	14.2128i	−0.191588	+	0.589648i
$582$	−3.97871			−0.164923
$583$	2.19098	+	23.4131i	0.0907412	+	0.969673i
$584$	−4.20163			−0.173865
$585$	0.663119	−	2.04087i	0.0274166	−	0.0843796i
$586$	9.47214	−	6.88191i	0.391290	−	0.284289i
$587$	−4.85410	−	3.52671i	−0.200350	−	0.145563i	0.483087	−	0.875573i	$-0.339516\pi$
$587$	−4.85410	−	3.52671i	−0.200350	−	0.145563i	−0.683437	+	0.730010i	$0.739516\pi$
$588$	0.572949	+	1.76336i	0.0236280	+	0.0727196i
$589$	−5.23607	−	16.1150i	−0.215748	−	0.664005i
$590$	1.98278	+	1.44057i	0.0816297	+	0.0593075i
$591$	16.3262	−	11.8617i	0.671572	−	0.487925i
$592$	0.458980	−	1.41260i	0.0188640	−	0.0580573i
$593$	18.3607			0.753983			0.376991	−	0.926217i	$-0.376959\pi$
$593$	18.3607			0.753983			0.376991	+	0.926217i	$0.376959\pi$
$594$	−1.16312	+	0.502029i	−0.0477233	+	0.0205985i
$595$	1.85410			0.0760108
$596$	2.67783	−	8.24151i	0.109688	−	0.337585i
$597$	6.92705	−	5.03280i	0.283505	−	0.205979i
$598$	−2.96556	−	2.15460i	−0.121271	−	0.0881083i
$599$	12.6074	+	38.8016i	0.515124	+	1.58539i	0.783056	+	0.621951i	$0.213660\pi$
$599$	12.6074	+	38.8016i	0.515124	+	1.58539i	−0.267932	+	0.963438i	$0.586340\pi$
$600$	−2.10081	−	6.46564i	−0.0857653	−	0.263959i
$601$	17.7082	+	12.8658i	0.722333	+	0.524805i	0.887129	−	0.461522i	$-0.152697\pi$
$601$	17.7082	+	12.8658i	0.722333	+	0.524805i	−0.164796	+	0.986328i	$0.552697\pi$
$602$	2.78115	−	2.02063i	0.113351	−	0.0823546i
$603$	3.00000	−	9.23305i	0.122169	−	0.375999i
$604$	15.5410			0.632355
$605$	−6.14590	−	2.90617i	−0.249866	−	0.118153i
$606$	0.472136			0.0191792
$607$	9.00658	−	27.7194i	0.365566	−	1.12510i	−0.584060	−	0.811710i	$-0.698537\pi$
$607$	9.00658	−	27.7194i	0.365566	−	1.12510i	0.949626	−	0.313385i	$-0.101463\pi$
$608$	−13.4164	+	9.74759i	−0.544107	+	0.395317i
$609$	2.42705	+	1.76336i	0.0983491	+	0.0714548i
$610$	−0.489357	−	1.50609i	−0.0198135	−	0.0609796i
$611$	1.16970	+	3.59996i	0.0473209	+	0.145639i
$612$	−4.50000	−	3.26944i	−0.181902	−	0.132159i
$613$	25.0623	−	18.2088i	1.01226	−	0.735448i	0.0475757	−	0.998868i	$-0.484850\pi$
$613$	25.0623	−	18.2088i	1.01226	−	0.735448i	0.964681	+	0.263420i	$0.0848505\pi$
$614$	0.791796	−	2.43690i	0.0319543	−	0.0983452i
$615$	5.00000			0.201619
$616$	−4.48278	+	1.93487i	−0.180616	+	0.0779581i
$617$	−10.7984			−0.434726			−0.217363	−	0.976091i	$-0.569746\pi$
$617$	−10.7984			−0.434726			−0.217363	+	0.976091i	$0.569746\pi$
$618$	−0.916408	+	2.82041i	−0.0368633	+	0.113454i
$619$	−14.7984	+	10.7516i	−0.594797	+	0.432145i	−0.844028	−	0.536299i	$-0.819822\pi$
$619$	−14.7984	+	10.7516i	−0.594797	+	0.432145i	0.249231	+	0.968444i	$0.419822\pi$
$620$	3.92705	+	2.85317i	0.157714	+	0.114586i
$621$	0.854102	+	2.62866i	0.0342739	+	0.105484i
$622$	−0.594235	−	1.82887i	−0.0238267	−	0.0733309i
$623$	−14.8262	−	10.7719i	−0.594001	−	0.431567i
$624$	−8.83688	+	6.42037i	−0.353758	+	0.257020i
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$	5.47214			0.218711
$627$	1.23607	+	13.2088i	0.0493638	+	0.527508i
$628$	42.3738			1.69090
$629$	−0.437694	+	1.34708i	−0.0174520	+	0.0537118i
$630$	0.190983	−	0.138757i	0.00760895	−	0.00552822i
$631$	−6.19098	−	4.49801i	−0.246459	−	0.179063i	0.457697	−	0.889108i	$-0.348674\pi$
$631$	−6.19098	−	4.49801i	−0.246459	−	0.179063i	−0.704156	+	0.710045i	$0.748674\pi$
$632$	−0.0663712	−	0.204270i	−0.00264010	−	0.00812541i
$633$	5.45492	+	16.7885i	0.216813	+	0.667283i
$634$	−3.01722	−	2.19214i	−0.119829	−	0.0870610i
$635$	−6.78115	+	4.92680i	−0.269102	+	0.195514i
$636$	−4.06231	+	12.5025i	−0.161081	+	0.495756i
$637$	−3.47214			−0.137571
$638$	−1.93769	+	3.26944i	−0.0767140	+	0.129438i
$639$	7.76393			0.307136
$640$	1.92705	−	5.93085i	0.0761734	−	0.234438i
$641$	31.1525	−	22.6336i	1.23045	−	0.893973i	0.233525	−	0.972351i	$-0.424974\pi$
$641$	31.1525	−	22.6336i	1.23045	−	0.893973i	0.996924	+	0.0783774i	$0.0249739\pi$
$642$	0.600813	+	0.436516i	0.0237122	+	0.0172279i
$643$	−9.88854	−	30.4338i	−0.389966	−	1.20019i	−0.932813	−	0.360361i	$-0.882654\pi$
$643$	−9.88854	−	30.4338i	−0.389966	−	1.20019i	0.542847	−	0.839832i	$-0.317346\pi$
$644$	1.58359	+	4.87380i	0.0624023	+	0.192054i
$645$	4.50000	+	3.26944i	0.177187	+	0.128734i
$646$	3.70820	−	2.69417i	0.145897	−	0.106001i
$647$	−6.78115	+	20.8702i	−0.266595	+	0.820494i	0.724727	+	0.689036i	$0.241966\pi$
$647$	−6.78115	+	20.8702i	−0.266595	+	0.820494i	−0.991322	+	0.131458i	$0.958034\pi$
$648$	−1.47214			−0.0578310
$649$	−33.5967	−	7.54294i	−1.31879	−	0.296086i
$650$	6.12461			0.240227
$651$	1.30902	−	4.02874i	0.0513044	−	0.157899i
$652$	28.2812	−	20.5475i	1.10758	−	0.804701i
$653$	−18.2254	−	13.2415i	−0.713216	−	0.518182i	0.170994	−	0.985272i	$-0.445302\pi$
$653$	−18.2254	−	13.2415i	−0.713216	−	0.518182i	−0.884210	+	0.467090i	$0.845302\pi$
$654$	−2.42705	−	7.46969i	−0.0949052	−	0.292088i
$655$	−2.73607	−	8.42075i	−0.106907	−	0.329026i
$656$	−20.5902	−	14.9596i	−0.803911	−	0.584076i
$657$	−2.30902	+	1.67760i	−0.0900833	+	0.0654494i
$658$	−0.128677	+	0.396027i	−0.00501636	+	0.0154388i
$659$	32.1246			1.25140			0.625699	−	0.780065i	$-0.284814\pi$
$659$	32.1246			1.25140			0.625699	+	0.780065i	$0.284814\pi$
$660$	−2.51064	−	2.85317i	−0.0977267	−	0.111059i
$661$	8.41641			0.327360			0.163680	−	0.986513i	$-0.447663\pi$
$661$	8.41641			0.327360			0.163680	+	0.986513i	$0.447663\pi$
$662$	−4.19505	+	12.9110i	−0.163045	+	0.501801i
$663$	8.42705	−	6.12261i	0.327280	−	0.237783i
$664$	−17.7984	−	12.9313i	−0.690711	−	0.501831i
$665$	−0.763932	−	2.35114i	−0.0296240	−	0.0911733i
$666$	0.0557281	+	0.171513i	0.00215942	+	0.00664601i
$667$	6.70820	+	4.87380i	0.259743	+	0.188714i
$668$	5.86475	−	4.26099i	0.226914	−	0.164863i
$669$	−2.21885	+	6.82891i	−0.0857856	+	0.264021i
$670$	−2.29180			−0.0885398
$671$	14.6976	+	16.7027i	0.567393	+	0.644802i
$672$	−4.14590			−0.159931
$673$	5.07295	−	15.6129i	0.195548	−	0.601834i	−0.804422	−	0.594058i	$-0.797525\pi$
$673$	5.07295	−	15.6129i	0.195548	−	0.601834i	0.999970	−	0.00777594i	$-0.00247518\pi$
$674$	−1.30902	+	0.951057i	−0.0504215	+	0.0366333i
$675$	−3.73607	−	2.71441i	−0.143801	−	0.104478i
$676$	0.541020	+	1.66509i	0.0208084	+	0.0640418i
$677$	10.5344	+	32.4217i	0.404871	+	1.24607i	0.921002	+	0.389557i	$0.127372\pi$
$677$	10.5344	+	32.4217i	0.404871	+	1.24607i	−0.516131	+	0.856510i	$0.672628\pi$
$678$	2.30902	+	1.67760i	0.0886773	+	0.0644278i
$679$	−8.42705	+	6.12261i	−0.323401	+	0.234964i
$680$	−0.843459	+	2.59590i	−0.0323452	+	0.0995482i
$681$	−1.61803			−0.0620032
$682$	5.23607	+	1.17557i	0.200499	+	0.0450149i
$683$	31.6525			1.21115			0.605574	−	0.795789i	$-0.292944\pi$
$683$	31.6525			1.21115			0.605574	+	0.795789i	$0.292944\pi$
$684$	−2.29180	+	7.05342i	−0.0876290	+	0.269694i
$685$	−0.763932	+	0.555029i	−0.0291883	+	0.0212066i
$686$	−0.309017	−	0.224514i	−0.0117983	−	0.00857198i
$687$	9.29180	+	28.5972i	0.354504	+	1.09105i
$688$	−8.74922	−	26.9273i	−0.333561	−	1.02660i
$689$	−19.9164	−	14.4701i	−0.758755	−	0.551268i
$690$	0.527864	−	0.383516i	0.0200954	−	0.0146002i
$691$	6.28115	−	19.3314i	0.238946	−	0.735401i	−0.757627	−	0.652688i	$-0.773641\pi$
$691$	6.28115	−	19.3314i	0.238946	−	0.735401i	0.996573	−	0.0827134i	$-0.0263586\pi$
$692$	−19.2492			−0.731746
$693$	−1.69098	+	2.85317i	−0.0642351	+	0.108383i
$694$	4.54102			0.172375
$695$	−0.489357	+	1.50609i	−0.0185624	+	0.0571291i
$696$	−3.57295	+	2.59590i	−0.135432	+	0.0983973i
$697$	19.6353	+	14.2658i	0.743738	+	0.540358i
$698$	−2.07295	−	6.37988i	−0.0784623	−	0.241482i
$699$	6.92705	+	21.3193i	0.262005	+	0.806369i
$700$	−6.92705	−	5.03280i	−0.261818	−	0.190222i
$701$	−9.04508	+	6.57164i	−0.341628	+	0.248207i	−0.745348	−	0.666675i	$-0.767717\pi$
$701$	−9.04508	+	6.57164i	−0.341628	+	0.248207i	0.403720	+	0.914882i	$0.367717\pi$
$702$	0.409830	−	1.26133i	0.0154680	−	0.0476057i
$703$	1.88854			0.0712278
$704$	1.45492	+	15.5474i	0.0548342	+	0.585965i
$705$	−0.673762			−0.0253753
$706$	1.33282	−	4.10199i	0.0501612	−	0.154380i
$707$	1.00000	−	0.726543i	0.0376089	−	0.0273244i
$708$	−15.5729	−	11.3144i	−0.585267	−	0.425222i
$709$	−5.61803	−	17.2905i	−0.210990	−	0.649360i	−0.999414	−	0.0342278i	$-0.989103\pi$
$709$	−5.61803	−	17.2905i	−0.210990	−	0.649360i	0.788424	−	0.615132i	$-0.210897\pi$
$710$	−0.566371	−	1.74311i	−0.0212555	−	0.0654178i
$711$	−0.118034	−	0.0857567i	−0.00442662	−	0.00321613i
$712$	21.8262	−	15.8577i	0.817973	−	0.594292i
$713$	3.61803	−	11.1352i	0.135496	−	0.417015i
$714$	1.14590			0.0428842
$715$	6.53444	−	2.82041i	0.244374	−	0.105477i
$716$	−39.8115			−1.48783
$717$	0.809017	−	2.48990i	0.0302133	−	0.0929870i
$718$	9.57295	−	6.95515i	0.357259	−	0.259564i
$719$	14.6353	+	10.6331i	0.545803	+	0.396549i	0.826236	−	0.563325i	$-0.190478\pi$
$719$	14.6353	+	10.6331i	0.545803	+	0.396549i	−0.280433	+	0.959874i	$0.590478\pi$
$720$	−0.600813	−	1.84911i	−0.0223910	−	0.0689124i
$721$	2.39919	+	7.38394i	0.0893504	+	0.274992i
$722$	0.927051	+	0.673542i	0.0345013	+	0.0250666i
$723$	10.2812	−	7.46969i	0.382360	−	0.277801i
$724$	−7.01064	+	21.5765i	−0.260548	+	0.801886i
$725$	−13.8541			−0.514528
$726$	−3.79837	−	1.79611i	−0.140971	−	0.0666600i
$727$	−37.3951			−1.38691			−0.693454	−	0.720501i	$-0.743912\pi$
$727$	−37.3951			−1.38691			−0.693454	+	0.720501i	$0.743912\pi$
$728$	1.57953	−	4.86128i	0.0585412	−	0.180171i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.545085	+	0.396027i	0.0201745	+	0.0146576i
$731$	8.34346	+	25.6785i	0.308594	+	0.949755i
$732$	3.84346	+	11.8290i	0.142058	+	0.437211i
$733$	26.7533	+	19.4374i	0.988155	+	0.717937i	0.959516	−	0.281653i	$-0.0908827\pi$
$733$	26.7533	+	19.4374i	0.988155	+	0.717937i	0.0286389	+	0.999590i	$0.490883\pi$
$734$	3.48936	−	2.53517i	0.128795	−	0.0935747i
$735$	0.190983	−	0.587785i	0.00704451	−	0.0216808i
$736$	−11.4590			−0.422384
$737$	29.5623	−	12.7598i	1.08894	−	0.470012i
$738$	3.09017			0.113751
$739$	2.64590	−	8.14324i	0.0973309	−	0.299554i	−0.890523	−	0.454938i	$-0.849661\pi$
$739$	2.64590	−	8.14324i	0.0973309	−	0.299554i	0.987854	+	0.155384i	$0.0496615\pi$
$740$	−0.437694	+	0.318003i	−0.0160900	+	0.0116900i
$741$	−11.2361	−	8.16348i	−0.412767	−	0.299893i
$742$	−0.836881	−	2.57565i	−0.0307229	−	0.0945553i
$743$	4.66312	+	14.3516i	0.171073	+	0.526509i	0.999432	−	0.0336881i	$-0.0107253\pi$
$743$	4.66312	+	14.3516i	0.171073	+	0.526509i	−0.828359	+	0.560197i	$0.810725\pi$
$744$	5.04508	+	3.66547i	0.184962	+	0.134383i
$745$	−2.33688	+	1.69784i	−0.0856167	+	0.0622042i
$746$	−1.39512	+	4.29374i	−0.0510790	+	0.157205i
$747$	−14.9443			−0.546782
$748$	−1.71885	−	18.3678i	−0.0628473	−	0.671594i
$749$	1.94427			0.0710421
$750$	−0.701626	+	2.15938i	−0.0256198	+	0.0788495i
$751$	−5.20820	+	3.78398i	−0.190050	+	0.138079i	−0.678742	−	0.734377i	$-0.737474\pi$
$751$	−5.20820	+	3.78398i	−0.190050	+	0.138079i	0.488692	+	0.872457i	$0.337474\pi$
$752$	2.77458	+	2.01585i	0.101178	+	0.0735104i
$753$	−5.07295	−	15.6129i	−0.184869	−	0.568967i
$754$	−1.22949	−	3.78398i	−0.0447754	−	0.137804i
$755$	−4.19098	−	3.04493i	−0.152525	−	0.110816i
$756$	−1.50000	+	1.08981i	−0.0545545	+	0.0396361i
$757$	7.76393	−	23.8949i	0.282185	−	0.868476i	−0.705043	−	0.709164i	$-0.749073\pi$
$757$	7.76393	−	23.8949i	0.282185	−	0.868476i	0.987228	−	0.159312i	$-0.0509275\pi$
$758$	4.88854			0.177560
$759$	−4.67376	+	7.88597i	−0.169647	+	0.286242i
$760$	3.63932			0.132012
$761$	7.01064	−	21.5765i	0.254136	−	0.782149i	−0.739863	−	0.672757i	$-0.765110\pi$
$761$	7.01064	−	21.5765i	0.254136	−	0.782149i	0.993999	−	0.109392i	$-0.0348902\pi$
$762$	−4.19098	+	3.04493i	−0.151823	+	0.110306i
$763$	−16.6353	−	12.0862i	−0.602237	−	0.437551i
$764$	−14.5942	−	44.9164i	−0.528001	−	1.62502i
$765$	0.572949	+	1.76336i	0.0207150	+	0.0637543i
$766$	−8.42705	−	6.12261i	−0.304482	−	0.221219i
$767$	29.1631	−	21.1882i	1.05302	−	0.765063i
$768$	−1.71885	+	5.29007i	−0.0620236	+	0.190889i
$769$	32.4721			1.17098			0.585488	−	0.810681i	$-0.300903\pi$
$769$	32.4721			1.17098			0.585488	+	0.810681i	$0.300903\pi$
$770$	0.763932	+	0.171513i	0.0275302	+	0.00618091i
$771$	−8.47214			−0.305117
$772$	−3.10333	+	9.55105i	−0.111691	+	0.343750i
$773$	−0.854102	+	0.620541i	−0.0307199	+	0.0223193i	−0.603039	−	0.797712i	$-0.706044\pi$
$773$	−0.854102	+	0.620541i	−0.0307199	+	0.0223193i	0.572319	+	0.820031i	$0.306044\pi$
$774$	2.78115	+	2.02063i	0.0999665	+	0.0726299i
$775$	6.04508	+	18.6049i	0.217146	+	0.668306i
$776$	−4.73858	−	14.5839i	−0.170105	−	0.523530i
$777$	0.381966	+	0.277515i	0.0137030	+	0.00995578i
$778$	−9.29180	+	6.75089i	−0.333127	+	0.242031i
$779$	10.0000	−	30.7768i	0.358287	−	1.10269i
$780$	3.97871			0.142461
$781$	17.0106	+	19.3314i	0.608689	+	0.691732i
$782$	3.16718			0.113258
$783$	−0.927051	+	2.85317i	−0.0331301	+	0.101964i
$784$	−2.54508	+	1.84911i	−0.0908959	+	0.0660397i
$785$	−11.4271	−	8.30224i	−0.407849	−	0.296320i
$786$	−1.69098	−	5.20431i	−0.0603154	−	0.185632i
$787$	12.5729	+	38.6956i	0.448177	+	1.37935i	0.878961	+	0.476893i	$0.158237\pi$
$787$	12.5729	+	38.6956i	0.448177	+	1.37935i	−0.430784	+	0.902455i	$0.641763\pi$
$788$	30.2705	+	21.9928i	1.07834	+	0.783462i
$789$	−12.1353	+	8.81678i	−0.432027	+	0.313886i
$790$	−0.0106431	+	0.0327561i	−0.000378665	+	0.00116541i
$791$	7.47214			0.265679
$792$	−3.22542	−	3.66547i	−0.114610	−	0.130247i
$793$	−23.2918			−0.827116
$794$	−1.80244	+	5.54734i	−0.0639662	+	0.196868i
$795$	3.54508	−	2.57565i	0.125731	−	0.0913491i
$796$	12.8435	+	9.33132i	0.455224	+	0.330740i
$797$	12.4058	+	38.1810i	0.439435	+	1.35244i	0.888473	+	0.458929i	$0.151767\pi$
$797$	12.4058	+	38.1810i	0.439435	+	1.35244i	−0.449038	+	0.893512i	$0.648233\pi$
$798$	−0.472136	−	1.45309i	−0.0167134	−	0.0514387i
$799$	−2.64590	−	1.92236i	−0.0936051	−	0.0680081i
$800$	15.4894	−	11.2537i	0.547631	−	0.397878i
$801$	5.66312	−	17.4293i	0.200096	−	0.615834i
$802$	−11.5623			−0.408279
$803$	−9.23607	−	2.07363i	−0.325934	−	0.0731767i
$804$	18.0000			0.634811
$805$	0.527864	−	1.62460i	0.0186048	−	0.0572596i
$806$	−4.54508	+	3.30220i	−0.160094	+	0.116315i
$807$	16.2812	+	11.8290i	0.573124	+	0.416399i
$808$	0.562306	+	1.73060i	0.0197819	+	0.0608823i
$809$	−8.26393	−	25.4338i	−0.290544	−	0.894204i	−0.984682	−	0.174361i	$-0.944214\pi$
$809$	−8.26393	−	25.4338i	−0.290544	−	0.894204i	0.694137	−	0.719843i	$-0.255786\pi$
$810$	0.190983	+	0.138757i	0.00671046	+	0.00487543i
$811$	18.0344	−	13.1028i	0.633275	−	0.460101i	−0.224258	−	0.974530i	$-0.571996\pi$
$811$	18.0344	−	13.1028i	0.633275	−	0.460101i	0.857533	+	0.514429i	$0.171996\pi$
$812$	−1.71885	+	5.29007i	−0.0603197	+	0.185645i
$813$	−18.8885			−0.662450
$814$	−0.304952	+	0.514540i	−0.0106886	+	0.0180346i
$815$	−11.6525			−0.408168
$816$	2.91641	−	8.97578i	0.102095	−	0.314215i
$817$	29.1246	−	21.1603i	1.01894	−	0.740304i
$818$	−2.28115	−	1.65735i	−0.0797586	−	0.0579480i
$819$	−1.07295	−	3.30220i	−0.0374919	−	0.115388i
$820$	2.86475	+	8.81678i	0.100041	+	0.307895i
$821$	37.2705	+	27.0786i	1.30075	+	0.945050i	0.999963	−	0.00864129i	$-0.00275064\pi$
$821$	37.2705	+	27.0786i	1.30075	+	0.945050i	0.300787	+	0.953691i	$0.402751\pi$
$822$	−0.472136	+	0.343027i	−0.0164676	+	0.0119644i
$823$	−2.11146	+	6.49839i	−0.0736007	+	0.226520i	−0.981089	−	0.193558i	$-0.937997\pi$
$823$	−2.11146	+	6.49839i	−0.0736007	+	0.226520i	0.907488	+	0.420078i	$0.137997\pi$
$824$	−11.4296			−0.398168
$825$	−1.42705	−	15.2497i	−0.0496835	−	0.530925i
$826$	3.96556			0.137979
$827$	−14.3647	+	44.2101i	−0.499511	+	1.53734i	0.310295	+	0.950640i	$0.399572\pi$
$827$	−14.3647	+	44.2101i	−0.499511	+	1.53734i	−0.809807	+	0.586697i	$0.800428\pi$
$828$	−4.14590	+	3.01217i	−0.144080	+	0.104680i
$829$	−22.2984	−	16.2007i	−0.774455	−	0.562674i	0.128855	−	0.991663i	$-0.458870\pi$
$829$	−22.2984	−	16.2007i	−0.774455	−	0.562674i	−0.903310	+	0.428989i	$0.858870\pi$
$830$	1.09017	+	3.35520i	0.0378404	+	0.116461i
$831$	1.09017	+	3.35520i	0.0378176	+	0.116391i
$832$	−13.2254	−	9.60883i	−0.458509	−	0.333126i
$833$	2.42705	−	1.76336i	0.0840923	−	0.0610967i
$834$	−0.302439	+	0.930812i	−0.0104726	+	0.0322314i
$835$	−2.41641			−0.0836232
$836$	−22.5836	+	9.74759i	−0.781070	+	0.337127i
$837$	4.23607			0.146420
$838$	0.274575	−	0.845055i	0.00948504	−	0.0291920i
$839$	12.1353	−	8.81678i	0.418956	−	0.304389i	−0.358262	−	0.933621i	$-0.616631\pi$
$839$	12.1353	−	8.81678i	0.418956	−	0.304389i	0.777217	+	0.629232i	$0.216631\pi$
$840$	0.736068	+	0.534785i	0.0253968	+	0.0184518i
$841$	−6.18034	−	19.0211i	−0.213115	−	0.655901i
$842$	0.281153	+	0.865300i	0.00968917	+	0.0298202i
$843$	−21.4443	−	15.5802i	−0.738580	−	0.536610i
$844$	−26.4787	+	19.2379i	−0.911435	+	0.662196i
$845$	0.180340	−	0.555029i	0.00620388	−	0.0190936i
$846$	−0.416408			−0.0143164
$847$	−10.8090	+	2.04087i	−0.371402	+	0.0701251i
$848$	−22.3050			−0.765955
$849$	2.25329	−	6.93491i	0.0773327	−	0.238006i
$850$	−4.28115	+	3.11044i	−0.146842	+	0.106687i
$851$	1.05573	+	0.767031i	0.0361899	+	0.0262935i
$852$	4.44834	+	13.6906i	0.152398	+	0.469031i
$853$	12.4443	+	38.2995i	0.426084	+	1.31135i	0.901953	+	0.431835i	$0.142134\pi$
$853$	12.4443	+	38.2995i	0.426084	+	1.31135i	−0.475869	+	0.879516i	$0.657866\pi$
$854$	−2.07295	−	1.50609i	−0.0709349	−	0.0515372i
$855$	2.00000	−	1.45309i	0.0683986	−	0.0496945i
$856$	−0.884479	+	2.72214i	−0.0302309	+	0.0930410i
$857$	6.05573			0.206860			0.103430	−	0.994637i	$-0.467018\pi$
$857$	6.05573			0.206860			0.103430	+	0.994637i	$0.467018\pi$
$858$	4.03851	−	1.74311i	0.137872	−	0.0595088i
$859$	13.5836			0.463466			0.231733	−	0.972779i	$-0.425560\pi$
$859$	13.5836			0.463466			0.231733	+	0.972779i	$0.425560\pi$
$860$	−3.18692	+	9.80832i	−0.108673	+	0.334461i
$861$	6.54508	−	4.75528i	0.223056	−	0.162060i
$862$	−5.37132	−	3.90249i	−0.182948	−	0.132919i
$863$	0.690983	+	2.12663i	0.0235213	+	0.0723912i	0.962128	−	0.272598i	$-0.0878827\pi$
$863$	0.690983	+	2.12663i	0.0235213	+	0.0723912i	−0.938607	+	0.344989i	$0.887883\pi$
$864$	−1.28115	−	3.94298i	−0.0435857	−	0.134143i
$865$	5.19098	+	3.77147i	0.176499	+	0.128234i
$866$	−0.326238	+	0.237026i	−0.0110860	+	0.00805446i
$867$	2.47214	−	7.60845i	0.0839581	−	0.258397i
$868$	7.85410			0.266586
$869$	−0.0450850	−	0.481784i	−0.00152940	−	0.0163434i
$870$	0.708204			0.0240104
$871$	−10.4164	+	32.0584i	−0.352947	+	1.08626i
$872$	24.4894	−	17.7926i	0.829314	−	0.602532i
$873$	−8.42705	−	6.12261i	−0.285212	−	0.207219i
$874$	−1.30495	−	4.01623i	−0.0441406	−	0.135851i
$875$	1.83688	+	5.65334i	0.0620979	+	0.191118i
$876$	−4.28115	−	3.11044i	−0.144647	−	0.105092i
$877$	−37.5795	+	27.3031i	−1.26897	+	0.921961i	−0.999161	−	0.0409528i	$-0.986961\pi$
$877$	−37.5795	+	27.3031i	−1.26897	+	0.921961i	−0.269809	+	0.962914i	$0.586961\pi$
$878$	−2.81308	+	8.65778i	−0.0949369	+	0.292186i
$879$	30.6525			1.03388
$880$	3.28773	−	5.54734i	0.110829	−	0.187001i
$881$	−57.0689			−1.92270			−0.961350	−	0.275330i	$-0.911213\pi$
$881$	−57.0689			−1.92270			−0.961350	+	0.275330i	$0.911213\pi$
$882$	0.118034	−	0.363271i	0.00397441	−	0.0122320i
$883$	−41.6246	+	30.2421i	−1.40078	+	1.01773i	−0.406196	+	0.913786i	$0.633145\pi$
$883$	−41.6246	+	30.2421i	−1.40078	+	1.01773i	−0.994584	+	0.103940i	$0.966855\pi$
$884$	15.6246	+	11.3519i	0.525513	+	0.381807i
$885$	1.98278	+	6.10237i	0.0666504	+	0.205129i
$886$	4.56231	+	14.0413i	0.153274	+	0.471728i
$887$	−43.0238	−	31.2586i	−1.44460	−	1.04956i	−0.987056	−	0.160373i	$-0.948730\pi$
$887$	−43.0238	−	31.2586i	−1.44460	−	1.04956i	−0.457541	−	0.889188i	$-0.651270\pi$
$888$	−0.562306	+	0.408539i	−0.0188698	+	0.0137097i
$889$	−4.19098	+	12.8985i	−0.140561	+	0.432602i
$890$	−4.32624			−0.145016
$891$	−3.23607	−	0.726543i	−0.108412	−	0.0243401i
$892$	−13.3131			−0.445755
$893$	−1.34752	+	4.14725i	−0.0450932	+	0.138783i
$894$	−1.44427	+	1.04932i	−0.0483037	+	0.0350947i
$895$	10.7361	+	7.80021i	0.358867	+	0.260732i
$896$	−3.11803	−	9.59632i	−0.104166	−	0.320591i
$897$	−2.96556	−	9.12705i	−0.0990171	−	0.304743i
$898$	−1.39919	−	1.01657i	−0.0466915	−	0.0339233i
$899$	10.2812	−	7.46969i	0.342896	−	0.249128i
$900$	2.64590	−	8.14324i	0.0881966	−	0.271441i
$901$	21.2705			0.708623
$902$	6.77051	+	7.69421i	0.225433	+	0.256189i
$903$	9.00000			0.299501
$904$	−3.39919	+	10.4616i	−0.113055	+	0.347948i
$905$	6.11803	−	4.44501i	0.203370	−	0.147757i
$906$	−2.59017	−	1.88187i	−0.0860526	−	0.0625209i
$907$	17.8262	+	54.8635i	0.591911	+	1.82171i	0.569540	+	0.821963i	$0.307121\pi$
$907$	17.8262	+	54.8635i	0.591911	+	1.82171i	0.0223703	+	0.999750i	$0.492879\pi$
$908$	−0.927051	−	2.85317i	−0.0307653	−	0.0946858i
$909$	1.00000	+	0.726543i	0.0331679	+	0.0240979i
$910$	−0.663119	+	0.481784i	−0.0219822	+	0.0159710i
$911$	−8.71885	+	26.8339i	−0.288868	+	0.889045i	0.696344	+	0.717708i	$0.254809\pi$
$911$	−8.71885	+	26.8339i	−0.288868	+	0.889045i	−0.985212	+	0.171337i	$0.945191\pi$
$912$	−12.5836			−0.416684
$913$	−32.7426	−	37.2097i	−1.08362	−	1.23146i
$914$	−6.81966			−0.225574
$915$	1.28115	−	3.94298i	0.0423536	−	0.130351i
$916$	−45.1033	+	32.7695i	−1.49026	+	1.08273i
$917$	−11.5902	−	8.42075i	−0.382741	−	0.278078i
$918$	0.354102	+	1.08981i	0.0116871	+	0.0359692i
$919$	−9.41641	−	28.9807i	−0.310619	−	0.955986i	−0.977521	−	0.210840i	$-0.932380\pi$
$919$	−9.41641	−	28.9807i	−0.310619	−	0.955986i	0.666902	−	0.745146i	$-0.267620\pi$
$920$	2.03444	+	1.47811i	0.0670736	+	0.0487318i
$921$	5.42705	−	3.94298i	0.178827	−	0.129926i
$922$	−2.64590	+	8.14324i	−0.0871380	+	0.268183i
$923$	−26.9574			−0.887315
$924$	−6.00000	−	1.34708i	−0.197386	−	0.0443158i
$925$	−2.18034			−0.0716891
$926$	−3.50407	+	10.7844i	−0.115151	+	0.354398i
$927$	−6.28115	+	4.56352i	−0.206300	+	0.149886i
$928$	−10.0623	−	7.31069i	−0.330311	−	0.239985i
$929$	11.1246	+	34.2380i	0.364987	+	1.12331i	0.949989	+	0.312282i	$0.101093\pi$
$929$	11.1246	+	34.2380i	0.364987	+	1.12331i	−0.585003	+	0.811031i	$0.698907\pi$
$930$	−0.309017	−	0.951057i	−0.0101331	−	0.0311864i
$931$	−3.23607	−	2.35114i	−0.106058	−	0.0770555i
$932$	−33.6246	+	24.4297i	−1.10141	+	0.800222i
$933$	1.55573	−	4.78804i	0.0509323	−	0.156753i
$934$	−1.39512			−0.0456498
$935$	−3.13525	+	5.29007i	−0.102534	+	0.173004i
$936$	5.11146			0.167073
$937$	−9.10739	+	28.0297i	−0.297525	+	0.915689i	0.684836	+	0.728697i	$0.259874\pi$
$937$	−9.10739	+	28.0297i	−0.297525	+	0.915689i	−0.982361	+	0.186992i	$0.940126\pi$
$938$	−3.00000	+	2.17963i	−0.0979535	+	0.0711674i
$939$	11.5902	+	8.42075i	0.378231	+	0.274801i
$940$	−0.386031	−	1.18808i	−0.0125910	−	0.0387510i
$941$	−18.2361	−	56.1248i	−0.594479	−	1.82962i	−0.557303	−	0.830309i	$-0.688164\pi$
$941$	−18.2361	−	56.1248i	−0.594479	−	1.82962i	−0.0371754	−	0.999309i	$-0.511836\pi$
$942$	−7.06231	−	5.13107i	−0.230102	−	0.167179i
$943$	18.0902	−	13.1433i	0.589097	−	0.428004i
$944$	10.0927	−	31.0621i	0.328489	−	1.01098i
$945$	0.618034			0.0201046
$946$	1.06231	+	11.3519i	0.0345385	+	0.369084i
$947$	−8.56231			−0.278238			−0.139119	−	0.990276i	$-0.544427\pi$
$947$	−8.56231			−0.278238			−0.139119	+	0.990276i	$0.544427\pi$
$948$	0.0835921	−	0.257270i	0.00271495	−	0.00835575i
$949$	8.01722	−	5.82485i	0.260250	−	0.189083i
$950$	5.70820	+	4.14725i	0.185199	+	0.134555i
$951$	−3.01722	−	9.28605i	−0.0978401	−	0.301121i
$952$	1.36475	+	4.20025i	0.0442316	+	0.136131i
$953$	−33.6697	−	24.4625i	−1.09067	−	0.792417i	−0.111156	−	0.993803i	$-0.535455\pi$
$953$	−33.6697	−	24.4625i	−1.09067	−	0.792417i	−0.979512	+	0.201386i	$0.935455\pi$
$954$	2.19098	−	1.59184i	0.0709357	−	0.0515378i
$955$	−4.86475	+	14.9721i	−0.157419	+	0.484487i
$956$	4.85410			0.156993
$957$	−9.13525	+	3.94298i	−0.295301	+	0.127459i
$958$	7.76393			0.250841
$959$	−0.472136	+	1.45309i	−0.0152461	+	0.0469226i
$960$	2.35410	−	1.71036i	0.0759783	−	0.0552015i
$961$	10.5623	+	7.67396i	0.340720	+	0.247547i
$962$	−0.193496	−	0.595518i	−0.00623855	−	0.0192003i
$963$	0.600813	+	1.84911i	0.0193609	+	0.0595868i
$964$	19.0623	+	13.8496i	0.613956	+	0.446065i
$965$	2.70820	−	1.96763i	0.0871802	−	0.0633401i
$966$	0.326238	−	1.00406i	0.0104965	−	0.0323050i
$967$	−1.34752			−0.0433335			−0.0216667	−	0.999765i	$-0.506897\pi$
$967$	−1.34752			−0.0433335			−0.0216667	+	0.999765i	$0.506897\pi$
$968$	2.05979	−	16.0620i	0.0662043	−	0.516251i
$969$	12.0000			0.385496
$970$	−0.759867	+	2.33863i	−0.0243978	+	0.0750889i
$971$	10.9894	−	7.98424i	0.352665	−	0.256226i	−0.397321	−	0.917680i	$-0.630060\pi$
$971$	10.9894	−	7.98424i	0.352665	−	0.256226i	0.749986	+	0.661453i	$0.230060\pi$
$972$	−1.50000	−	1.08981i	−0.0481125	−	0.0349558i
$973$	0.791796	+	2.43690i	0.0253838	+	0.0781234i
$974$	1.44834	+	4.45752i	0.0464077	+	0.142828i
$975$	12.9721	+	9.42481i	0.415441	+	0.301835i
$976$	−17.0729	+	12.4042i	−0.546492	+	0.397050i
$977$	1.66970	−	5.13880i	0.0534183	−	0.164405i	−0.920788	−	0.390063i	$-0.872453\pi$
$977$	1.66970	−	5.13880i	0.0534183	−	0.164405i	0.974207	+	0.225658i	$0.0724533\pi$
$978$	−7.20163			−0.230283
$979$	55.8050	−	24.0867i	1.78353	−	0.769814i
$980$	1.14590			0.0366044
$981$	6.35410	−	19.5559i	0.202871	−	0.624372i
$982$	2.88854	−	2.09865i	0.0921771	−	0.0669706i
$983$	31.1353	+	22.6211i	0.993060	+	0.721501i	0.960589	−	0.277972i	$-0.0896623\pi$
$983$	31.1353	+	22.6211i	0.993060	+	0.721501i	0.0324712	+	0.999473i	$0.489662\pi$
$984$	3.68034	+	11.3269i	0.117325	+	0.361089i
$985$	−3.85410	−	11.8617i	−0.122802	−	0.377945i
$986$	2.78115	+	2.02063i	0.0885700	+	0.0643498i
$987$	−0.881966	+	0.640786i	−0.0280733	+	0.0203964i
$988$	7.95743	−	24.4904i	0.253159	−	0.779145i
$989$	24.8754			0.790991
$990$	0.0729490	+	0.779543i	0.00231847	+	0.0247755i
$991$	18.2016			0.578194			0.289097	−	0.957300i	$-0.406645\pi$
$991$	18.2016			0.578194			0.289097	+	0.957300i	$0.406645\pi$
$992$	−5.42705	+	16.7027i	−0.172309	+	0.530313i
$993$	−28.7533	+	20.8905i	−0.912458	+	0.662940i
$994$	−2.39919	−	1.74311i	−0.0760976	−	0.0552881i
$995$	−1.63525	−	5.03280i	−0.0518411	−	0.159550i
$996$	−8.56231	−	26.3521i	−0.271307	−	0.834997i
$997$	−44.4508	−	32.2954i	−1.40777	−	1.02281i	−0.993642	−	0.112589i	$-0.964086\pi$
$997$	−44.4508	−	32.2954i	−1.40777	−	1.02281i	−0.414131	−	0.910217i	$-0.635914\pi$
$998$	1.54508	−	1.12257i	0.0489088	−	0.0355343i
$999$	−0.145898	+	0.449028i	−0.00461601	+	0.0142066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.a.64.1	✓	4
3.2	odd	2		693.2.m.e.64.1		4
11.4	even	5		2541.2.a.bf.1.1		2
11.5	even	5	inner	231.2.j.a.148.1	yes	4
11.7	odd	10		2541.2.a.m.1.2		2
33.5	odd	10		693.2.m.e.379.1		4
33.26	odd	10		7623.2.a.u.1.2		2
33.29	even	10		7623.2.a.by.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.a.64.1	✓	4	1.1	even	1	trivial
231.2.j.a.148.1	yes	4	11.5	even	5	inner
693.2.m.e.64.1		4	3.2	odd	2
693.2.m.e.379.1		4	33.5	odd	10
2541.2.a.m.1.2		2	11.7	odd	10
2541.2.a.bf.1.1		2	11.4	even	5
7623.2.a.u.1.2		2	33.26	odd	10
7623.2.a.by.1.1		2	33.29	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)

\(f(q)\)	\(=\)	\(q+(0.118034 - 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.118034 - 0.363271i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.19098 - 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.118034 - 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.118034 - 0.363271i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.19098 - 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.236068 q^{10} +(3.04508 - 1.31433i) q^{11} +1.85410 q^{12} +(-1.07295 + 3.30220i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.927051 - 2.85317i) q^{17} +(-0.309017 - 0.224514i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(0.354102 - 1.08981i) q^{20} -1.00000 q^{21} +(-0.118034 - 1.26133i) q^{22} -2.76393 q^{23} +(0.454915 - 1.40008i) q^{24} +(3.73607 - 2.71441i) q^{25} +(1.07295 + 0.779543i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(-2.42705 - 1.76336i) q^{29} +(-0.190983 + 0.138757i) q^{30} +(-1.30902 + 4.02874i) q^{31} +4.14590 q^{32} +(1.69098 - 2.85317i) q^{33} -1.14590 q^{34} +(-0.190983 + 0.587785i) q^{35} +(1.50000 - 1.08981i) q^{36} +(-0.381966 - 0.277515i) q^{37} +(0.472136 + 1.45309i) q^{38} +(1.07295 + 3.30220i) q^{39} +(-0.736068 - 0.534785i) q^{40} +(-6.54508 + 4.75528i) q^{41} +(-0.118034 + 0.363271i) q^{42} -9.00000 q^{43} +(6.00000 + 1.34708i) q^{44} -0.618034 q^{45} +(-0.326238 + 1.00406i) q^{46} +(0.881966 - 0.640786i) q^{47} +(2.54508 + 1.84911i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.545085 - 1.67760i) q^{50} +(-2.42705 - 1.76336i) q^{51} +(-5.20820 + 3.78398i) q^{52} +(-2.19098 + 6.74315i) q^{53} -0.381966 q^{54} +(-1.35410 - 1.53884i) q^{55} -1.47214 q^{56} +(-1.23607 + 3.80423i) q^{57} +(-0.927051 + 0.673542i) q^{58} +(-8.39919 - 6.10237i) q^{59} +(-0.354102 - 1.08981i) q^{60} +(2.07295 + 6.37988i) q^{61} +(1.30902 + 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-1.45492 + 4.47777i) q^{64} +2.14590 q^{65} +(-0.836881 - 0.951057i) q^{66} +9.70820 q^{67} +(1.71885 - 5.29007i) q^{68} +(-2.23607 + 1.62460i) q^{69} +(0.190983 + 0.138757i) q^{70} +(2.39919 + 7.38394i) q^{71} +(-0.454915 - 1.40008i) q^{72} +(-2.30902 - 1.67760i) q^{73} +(-0.145898 + 0.106001i) q^{74} +(1.42705 - 4.39201i) q^{75} -7.41641 q^{76} +(-3.23607 - 0.726543i) q^{77} +1.32624 q^{78} +(0.0450850 - 0.138757i) q^{79} +(1.57295 - 1.14281i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.954915 + 2.93893i) q^{82} +(-4.61803 - 14.2128i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(-1.50000 + 1.08981i) q^{85} +(-1.06231 + 3.26944i) q^{86} -3.00000 q^{87} +(2.48936 - 4.20025i) q^{88} +18.3262 q^{89} +(-0.0729490 + 0.224514i) q^{90} +(2.80902 - 2.04087i) q^{91} +(-4.14590 - 3.01217i) q^{92} +(1.30902 + 4.02874i) q^{93} +(-0.128677 - 0.396027i) q^{94} +(2.00000 + 1.45309i) q^{95} +(3.35410 - 2.43690i) q^{96} +(3.21885 - 9.90659i) q^{97} +0.381966 q^{98} +(-0.309017 - 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 6 * q^4 - 3 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9	\( 4 q - 4 q^{2} + q^{3} + 6 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + 7 q^{8} - q^{9} + 8 q^{10} + q^{11} - 6 q^{12} - 11 q^{13} + q^{14} - 2 q^{15} - 14 q^{16} + 3 q^{17} + q^{18} - 4 q^{19} - 12 q^{20} - 4 q^{21} + 4 q^{22} - 20 q^{23} + 13 q^{24} + 6 q^{25} + 11 q^{26} + q^{27} - 9 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 30 q^{32} + 9 q^{33} - 18 q^{34} - 3 q^{35} + 6 q^{36} - 6 q^{37} - 16 q^{38} + 11 q^{39} + 6 q^{40} - 15 q^{41} + 4 q^{42} - 36 q^{43} + 24 q^{44} + 2 q^{45} + 30 q^{46} + 8 q^{47} - q^{48} - q^{49} + 9 q^{50} - 3 q^{51} + 6 q^{52} - 11 q^{53} - 6 q^{54} + 8 q^{55} + 12 q^{56} + 4 q^{57} + 3 q^{58} - 9 q^{59} + 12 q^{60} + 15 q^{61} + 3 q^{62} - q^{63} - 17 q^{64} + 22 q^{65} - 19 q^{66} + 12 q^{67} + 27 q^{68} + 3 q^{70} - 15 q^{71} - 13 q^{72} - 7 q^{73} - 14 q^{74} - q^{75} + 24 q^{76} - 4 q^{77} - 26 q^{78} - 11 q^{79} + 13 q^{80} - q^{81} + 15 q^{82} - 14 q^{83} - 6 q^{84} - 6 q^{85} + 36 q^{86} - 12 q^{87} - 37 q^{88} + 42 q^{89} - 7 q^{90} + 9 q^{91} - 30 q^{92} + 3 q^{93} - 43 q^{94} + 8 q^{95} + 33 q^{97} + 6 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 6 * q^4 - 3 * q^5 + 4 * q^6 - q^7 + 7 * q^8 - q^9 + 8 * q^10 + q^11 - 6 * q^12 - 11 * q^13 + q^14 - 2 * q^15 - 14 * q^16 + 3 * q^17 + q^18 - 4 * q^19 - 12 * q^20 - 4 * q^21 + 4 * q^22 - 20 * q^23 + 13 * q^24 + 6 * q^25 + 11 * q^26 + q^27 - 9 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 30 * q^32 + 9 * q^33 - 18 * q^34 - 3 * q^35 + 6 * q^36 - 6 * q^37 - 16 * q^38 + 11 * q^39 + 6 * q^40 - 15 * q^41 + 4 * q^42 - 36 * q^43 + 24 * q^44 + 2 * q^45 + 30 * q^46 + 8 * q^47 - q^48 - q^49 + 9 * q^50 - 3 * q^51 + 6 * q^52 - 11 * q^53 - 6 * q^54 + 8 * q^55 + 12 * q^56 + 4 * q^57 + 3 * q^58 - 9 * q^59 + 12 * q^60 + 15 * q^61 + 3 * q^62 - q^63 - 17 * q^64 + 22 * q^65 - 19 * q^66 + 12 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 - 13 * q^72 - 7 * q^73 - 14 * q^74 - q^75 + 24 * q^76 - 4 * q^77 - 26 * q^78 - 11 * q^79 + 13 * q^80 - q^81 + 15 * q^82 - 14 * q^83 - 6 * q^84 - 6 * q^85 + 36 * q^86 - 12 * q^87 - 37 * q^88 + 42 * q^89 - 7 * q^90 + 9 * q^91 - 30 * q^92 + 3 * q^93 - 43 * q^94 + 8 * q^95 + 33 * q^97 + 6 * q^98 + q^99

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