LMFDB - Embedded newform 231.2.j.c.190.1

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			190.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	231.190
Dual form			231.2.j.c.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.30902 + 1.67760i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.30902 + 1.67760i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.85410 q^{10} +(3.04508 - 1.31433i) q^{11} +1.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.881966 - 2.71441i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.35410 - 4.61653i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.809017 + 2.48990i) q^{19} +(-2.30902 + 1.67760i) q^{20} -1.00000 q^{21} +(1.69098 - 2.85317i) q^{22} -3.09017 q^{23} +(2.42705 - 1.76336i) q^{24} +(0.972136 + 2.99193i) q^{25} +(0.381966 - 1.17557i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-0.618034 + 1.90211i) q^{29} +(-0.881966 - 2.71441i) q^{30} +(5.92705 - 4.30625i) q^{31} -5.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -7.85410 q^{34} +(2.30902 - 1.67760i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(-3.73607 + 11.4984i) q^{37} +(2.11803 + 1.53884i) q^{38} +(-1.00000 - 0.726543i) q^{39} +(-2.64590 + 8.14324i) q^{40} +(-3.35410 - 10.3229i) q^{41} +(-0.809017 + 0.587785i) q^{42} -1.23607 q^{43} +(0.309017 + 3.30220i) q^{44} -2.85410 q^{45} +(-2.50000 + 1.81636i) q^{46} +(0.618034 + 1.90211i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.54508 + 1.84911i) q^{50} +(-2.42705 + 7.46969i) q^{51} +(0.381966 + 1.17557i) q^{52} +(-9.85410 + 7.15942i) q^{53} +1.00000 q^{54} +(9.23607 + 2.07363i) q^{55} +3.00000 q^{56} +(2.11803 - 1.53884i) q^{57} +(0.618034 + 1.90211i) q^{58} +(2.09017 - 6.43288i) q^{59} +(2.30902 + 1.67760i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(2.26393 - 6.96767i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-5.66312 + 4.11450i) q^{64} +3.52786 q^{65} +(-3.23607 - 0.726543i) q^{66} +8.00000 q^{67} +(6.35410 - 4.61653i) q^{68} +(0.954915 + 2.93893i) q^{69} +(0.881966 - 2.71441i) q^{70} +(-7.23607 - 5.25731i) q^{71} +(-2.42705 - 1.76336i) q^{72} +(-1.61803 + 4.97980i) q^{73} +(3.73607 + 11.4984i) q^{74} +(2.54508 - 1.84911i) q^{75} -2.61803 q^{76} +(-0.309017 - 3.30220i) q^{77} -1.23607 q^{78} +(11.3262 - 8.22899i) q^{79} +(0.881966 + 2.71441i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.78115 - 6.37988i) q^{82} +(-2.38197 - 1.73060i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-6.92705 - 21.3193i) q^{85} +(-1.00000 + 0.726543i) q^{86} +2.00000 q^{87} +(6.57295 + 7.46969i) q^{88} +1.09017 q^{89} +(-2.30902 + 1.67760i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(0.954915 - 2.93893i) q^{92} +(-5.92705 - 4.30625i) q^{93} +(1.61803 + 1.17557i) q^{94} +(-2.30902 + 7.10642i) q^{95} +(1.54508 + 4.75528i) q^{96} +(2.85410 - 2.07363i) q^{97} -1.00000 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9} - 2 q^{10} + q^{11} + 4 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + q^{16} - 12 q^{17} + q^{18} + q^{19} - 7 q^{20} - 4 q^{21} + 9 q^{22} + 10 q^{23} + 3 q^{24} - 14 q^{25} + 6 q^{26} + q^{27} + q^{28} + 2 q^{29} - 8 q^{30} + 17 q^{31} - 20 q^{32} - 11 q^{33} - 18 q^{34} + 7 q^{35} + q^{36} - 6 q^{37} + 4 q^{38} - 4 q^{39} - 24 q^{40} - q^{42} + 4 q^{43} - q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 3 q^{51} + 6 q^{52} - 26 q^{53} + 4 q^{54} + 28 q^{55} + 12 q^{56} + 4 q^{57} - 2 q^{58} - 14 q^{59} + 7 q^{60} - 20 q^{61} + 18 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} - 4 q^{66} + 32 q^{67} + 12 q^{68} + 15 q^{69} + 8 q^{70} - 20 q^{71} - 3 q^{72} - 2 q^{73} + 6 q^{74} - q^{75} - 6 q^{76} + q^{77} + 4 q^{78} + 14 q^{79} + 8 q^{80} - q^{81} - 15 q^{82} - 14 q^{83} - q^{84} - 21 q^{85} - 4 q^{86} + 8 q^{87} + 33 q^{88} - 18 q^{89} - 7 q^{90} - 6 q^{91} + 15 q^{92} - 17 q^{93} + 2 q^{94} - 7 q^{95} - 5 q^{96} - 2 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9 - 2 * q^10 + q^11 + 4 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + q^16 - 12 * q^17 + q^18 + q^19 - 7 * q^20 - 4 * q^21 + 9 * q^22 + 10 * q^23 + 3 * q^24 - 14 * q^25 + 6 * q^26 + q^27 + q^28 + 2 * q^29 - 8 * q^30 + 17 * q^31 - 20 * q^32 - 11 * q^33 - 18 * q^34 + 7 * q^35 + q^36 - 6 * q^37 + 4 * q^38 - 4 * q^39 - 24 * q^40 - q^42 + 4 * q^43 - q^44 + 2 * q^45 - 10 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 3 * q^51 + 6 * q^52 - 26 * q^53 + 4 * q^54 + 28 * q^55 + 12 * q^56 + 4 * q^57 - 2 * q^58 - 14 * q^59 + 7 * q^60 - 20 * q^61 + 18 * q^62 - q^63 - 7 * q^64 + 32 * q^65 - 4 * q^66 + 32 * q^67 + 12 * q^68 + 15 * q^69 + 8 * q^70 - 20 * q^71 - 3 * q^72 - 2 * q^73 + 6 * q^74 - q^75 - 6 * q^76 + q^77 + 4 * q^78 + 14 * q^79 + 8 * q^80 - q^81 - 15 * q^82 - 14 * q^83 - q^84 - 21 * q^85 - 4 * q^86 + 8 * q^87 + 33 * q^88 - 18 * q^89 - 7 * q^90 - 6 * q^91 + 15 * q^92 - 17 * q^93 + 2 * q^94 - 7 * q^95 - 5 * q^96 - 2 * q^97 - 4 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	−0.263792	−	0.964580i	$-0.584973\pi$
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	0.835853	+	0.548953i	$0.184973\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.30902	+	1.67760i	1.03262	+	0.750245i	0.968832	−	0.247718i	$-0.0796807\pi$
$5$	2.30902	+	1.67760i	1.03262	+	0.750245i	0.0637916	+	0.997963i	$0.479681\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.927051	+	2.85317i	0.327762	+	1.00875i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	2.85410			0.902546
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	1.00000			0.288675
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.881966	−	2.71441i	0.227723	−	0.700858i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.949644	−	0.313332i	$-0.898555\pi$
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.591452	−	0.806340i	$-0.701445\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	0.809017	+	2.48990i	0.185601	+	0.571222i	0.999958	−	0.00914245i	$-0.00291017\pi$
$19$	0.809017	+	2.48990i	0.185601	+	0.571222i	−0.814357	+	0.580364i	$0.802910\pi$
$20$	−2.30902	+	1.67760i	−0.516312	+	0.375123i
$21$	−1.00000			−0.218218
$22$	1.69098	−	2.85317i	0.360519	−	0.608298i
$23$	−3.09017			−0.644345			−0.322172	−	0.946681i	$-0.604413\pi$
$23$	−3.09017			−0.644345			−0.322172	+	0.946681i	$0.604413\pi$
$24$	2.42705	−	1.76336i	0.495420	−	0.359943i
$25$	0.972136	+	2.99193i	0.194427	+	0.598385i
$26$	0.381966	−	1.17557i	0.0749097	−	0.230548i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−0.618034	+	1.90211i	−0.114766	+	0.353214i	−0.991898	−	0.127036i	$-0.959454\pi$
$29$	−0.618034	+	1.90211i	−0.114766	+	0.353214i	0.877132	+	0.480249i	$0.159454\pi$
$30$	−0.881966	−	2.71441i	−0.161024	−	0.495582i
$31$	5.92705	−	4.30625i	1.06453	−	0.773426i	0.0896087	−	0.995977i	$-0.471438\pi$
$31$	5.92705	−	4.30625i	1.06453	−	0.773426i	0.974921	+	0.222551i	$0.0714384\pi$
$32$	−5.00000			−0.883883
$33$	−2.19098	−	2.48990i	−0.381401	−	0.433436i
$34$	−7.85410			−1.34697
$35$	2.30902	−	1.67760i	0.390295	−	0.283566i
$36$	−0.309017	−	0.951057i	−0.0515028	−	0.158509i
$37$	−3.73607	+	11.4984i	−0.614206	+	1.89033i	−0.201412	+	0.979507i	$0.564553\pi$
$37$	−3.73607	+	11.4984i	−0.614206	+	1.89033i	−0.412794	+	0.910824i	$0.635447\pi$
$38$	2.11803	+	1.53884i	0.343590	+	0.249633i
$39$	−1.00000	−	0.726543i	−0.160128	−	0.116340i
$40$	−2.64590	+	8.14324i	−0.418353	+	1.28756i
$41$	−3.35410	−	10.3229i	−0.523823	−	1.61216i	−0.766632	−	0.642087i	$-0.778069\pi$
$41$	−3.35410	−	10.3229i	−0.523823	−	1.61216i	0.242809	−	0.970074i	$-0.421931\pi$
$42$	−0.809017	+	0.587785i	−0.124834	+	0.0906972i
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	0.309017	+	3.30220i	0.0465861	+	0.497825i
$45$	−2.85410			−0.425464
$46$	−2.50000	+	1.81636i	−0.368605	+	0.267807i
$47$	0.618034	+	1.90211i	0.0901495	+	0.277452i	0.985959	−	0.166986i	$-0.0534035\pi$
$47$	0.618034	+	1.90211i	0.0901495	+	0.277452i	−0.895810	+	0.444438i	$0.853403\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	2.54508	+	1.84911i	0.359929	+	0.261504i
$51$	−2.42705	+	7.46969i	−0.339855	+	1.04597i
$52$	0.381966	+	1.17557i	0.0529692	+	0.163022i
$53$	−9.85410	+	7.15942i	−1.35357	+	0.983423i	−0.354740	+	0.934965i	$0.615431\pi$
$53$	−9.85410	+	7.15942i	−1.35357	+	0.983423i	−0.998825	+	0.0484575i	$0.984569\pi$
$54$	1.00000			0.136083
$55$	9.23607	+	2.07363i	1.24539	+	0.279608i
$56$	3.00000			0.400892
$57$	2.11803	−	1.53884i	0.280540	−	0.203825i
$58$	0.618034	+	1.90211i	0.0811518	+	0.249760i
$59$	2.09017	−	6.43288i	0.272117	−	0.837490i	−0.717851	−	0.696197i	$-0.754874\pi$
$59$	2.09017	−	6.43288i	0.272117	−	0.837490i	0.989968	−	0.141293i	$-0.0451260\pi$
$60$	2.30902	+	1.67760i	0.298093	+	0.216577i
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	0.0186458	−	0.999826i	$-0.494065\pi$
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	−0.945129	+	0.326696i	$0.894065\pi$
$62$	2.26393	−	6.96767i	0.287520	−	0.884895i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−5.66312	+	4.11450i	−0.707890	+	0.514312i
$65$	3.52786			0.437578
$66$	−3.23607	−	0.726543i	−0.398332	−	0.0894312i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	6.35410	−	4.61653i	0.770548	−	0.559836i
$69$	0.954915	+	2.93893i	0.114958	+	0.353805i
$70$	0.881966	−	2.71441i	0.105415	−	0.324434i
$71$	−7.23607	−	5.25731i	−0.858763	−	0.623928i	0.0687850	−	0.997632i	$-0.478088\pi$
$71$	−7.23607	−	5.25731i	−0.858763	−	0.623928i	−0.927548	+	0.373703i	$0.878088\pi$
$72$	−2.42705	−	1.76336i	−0.286031	−	0.207813i
$73$	−1.61803	+	4.97980i	−0.189377	+	0.582841i	−0.999996	−	0.00273185i	$-0.999130\pi$
$73$	−1.61803	+	4.97980i	−0.189377	+	0.582841i	0.810620	+	0.585573i	$0.199130\pi$
$74$	3.73607	+	11.4984i	0.434309	+	1.33667i
$75$	2.54508	−	1.84911i	0.293881	−	0.213517i
$76$	−2.61803			−0.300309
$77$	−0.309017	−	3.30220i	−0.0352158	−	0.376320i
$78$	−1.23607			−0.139957
$79$	11.3262	−	8.22899i	1.27430	−	0.925834i	0.274936	−	0.961462i	$-0.411343\pi$
$79$	11.3262	−	8.22899i	1.27430	−	0.925834i	0.999365	+	0.0356284i	$0.0113433\pi$
$80$	0.881966	+	2.71441i	0.0986068	+	0.303481i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−8.78115	−	6.37988i	−0.969716	−	0.704540i
$83$	−2.38197	−	1.73060i	−0.261455	−	0.189958i	0.449333	−	0.893364i	$-0.351662\pi$
$83$	−2.38197	−	1.73060i	−0.261455	−	0.189958i	−0.710788	+	0.703406i	$0.751662\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	−6.92705	−	21.3193i	−0.751344	−	2.31240i
$86$	−1.00000	+	0.726543i	−0.107833	+	0.0783451i
$87$	2.00000			0.214423
$88$	6.57295	+	7.46969i	0.700679	+	0.796272i
$89$	1.09017			0.115558			0.0577789	−	0.998329i	$-0.481598\pi$
$89$	1.09017			0.115558			0.0577789	+	0.998329i	$0.481598\pi$
$90$	−2.30902	+	1.67760i	−0.243392	+	0.176834i
$91$	−0.381966	−	1.17557i	−0.0400409	−	0.123233i
$92$	0.954915	−	2.93893i	0.0995568	−	0.306404i
$93$	−5.92705	−	4.30625i	−0.614607	−	0.446538i
$94$	1.61803	+	1.17557i	0.166887	+	0.121251i
$95$	−2.30902	+	7.10642i	−0.236900	+	0.729104i
$96$	1.54508	+	4.75528i	0.157695	+	0.485334i
$97$	2.85410	−	2.07363i	0.289790	−	0.210545i	−0.433386	−	0.901208i	$-0.642681\pi$
$97$	2.85410	−	2.07363i	0.289790	−	0.210545i	0.723176	+	0.690663i	$0.242681\pi$
$98$	−1.00000			−0.101015
$99$	−1.69098	+	2.85317i	−0.169950	+	0.286754i
$100$	−3.14590			−0.314590
$101$	1.69098	−	1.22857i	0.168259	−	0.122247i	−0.500469	−	0.865754i	$-0.666839\pi$
$101$	1.69098	−	1.22857i	0.168259	−	0.122247i	0.668728	+	0.743507i	$0.266839\pi$
$102$	2.42705	+	7.46969i	0.240314	+	0.739610i
$103$	−3.19098	+	9.82084i	−0.314417	+	0.967676i	0.661577	+	0.749877i	$0.269888\pi$
$103$	−3.19098	+	9.82084i	−0.314417	+	0.967676i	−0.975994	+	0.217798i	$0.930112\pi$
$104$	3.00000	+	2.17963i	0.294174	+	0.213730i
$105$	−2.30902	−	1.67760i	−0.225337	−	0.163717i
$106$	−3.76393	+	11.5842i	−0.365585	+	1.12516i
$107$	1.51722	+	4.66953i	0.146675	+	0.451420i	0.997223	−	0.0744784i	$-0.0237292\pi$
$107$	1.51722	+	4.66953i	0.146675	+	0.451420i	−0.850547	+	0.525898i	$0.823729\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	10.5623			1.01169			0.505843	−	0.862626i	$-0.331182\pi$
$109$	10.5623			1.01169			0.505843	+	0.862626i	$0.331182\pi$
$110$	8.69098	−	3.75123i	0.828653	−	0.357665i
$111$	12.0902			1.14755
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	0.236068	+	0.726543i	0.0222074	+	0.0683474i	0.961546	−	0.274644i	$-0.0885599\pi$
$113$	0.236068	+	0.726543i	0.0222074	+	0.0683474i	−0.939339	+	0.342991i	$0.888560\pi$
$114$	0.809017	−	2.48990i	0.0757714	−	0.233200i
$115$	−7.13525	−	5.18407i	−0.665366	−	0.483417i
$116$	−1.61803	−	1.17557i	−0.150231	−	0.109149i
$117$	−0.381966	+	1.17557i	−0.0353128	+	0.108682i
$118$	−2.09017	−	6.43288i	−0.192416	−	0.592195i
$119$	−6.35410	+	4.61653i	−0.582480	+	0.423196i
$120$	8.56231			0.781628
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	−8.94427			−0.809776
$123$	−8.78115	+	6.37988i	−0.791770	+	0.575255i
$124$	2.26393	+	6.96767i	0.203307	+	0.625715i
$125$	1.63525	−	5.03280i	0.146262	−	0.450147i
$126$	0.809017	+	0.587785i	0.0720730	+	0.0523641i
$127$	2.61803	+	1.90211i	0.232313	+	0.168785i	0.697852	−	0.716242i	$-0.254139\pi$
$127$	2.61803	+	1.90211i	0.232313	+	0.168785i	−0.465539	+	0.885027i	$0.654139\pi$
$128$	0.927051	−	2.85317i	0.0819405	−	0.252187i
$129$	0.381966	+	1.17557i	0.0336302	+	0.103503i
$130$	2.85410	−	2.07363i	0.250321	−	0.181869i
$131$	2.29180			0.200235			0.100118	−	0.994976i	$-0.468078\pi$
$131$	2.29180			0.200235			0.100118	+	0.994976i	$0.468078\pi$
$132$	3.04508	−	1.31433i	0.265041	−	0.114398i
$133$	2.61803			0.227012
$134$	6.47214	−	4.70228i	0.559107	−	0.406215i
$135$	0.881966	+	2.71441i	0.0759075	+	0.233619i
$136$	7.28115	−	22.4091i	0.624354	−	1.92156i
$137$	−5.47214	−	3.97574i	−0.467516	−	0.339670i	0.328956	−	0.944345i	$-0.393303\pi$
$137$	−5.47214	−	3.97574i	−0.467516	−	0.339670i	−0.796472	+	0.604675i	$0.793303\pi$
$138$	2.50000	+	1.81636i	0.212814	+	0.154619i
$139$	1.48278	−	4.56352i	0.125768	−	0.387073i	−0.868272	−	0.496088i	$-0.834769\pi$
$139$	1.48278	−	4.56352i	0.125768	−	0.387073i	0.994040	+	0.109014i	$0.0347695\pi$
$140$	0.881966	+	2.71441i	0.0745397	+	0.229410i
$141$	1.61803	−	1.17557i	0.136263	−	0.0990009i
$142$	−8.94427			−0.750587
$143$	2.09017	−	3.52671i	0.174789	−	0.294918i
$144$	−1.00000			−0.0833333
$145$	−4.61803	+	3.35520i	−0.383507	+	0.278634i
$146$	1.61803	+	4.97980i	0.133909	+	0.412131i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	−9.78115	−	7.10642i	−0.804006	−	0.584144i
$149$	16.1803	+	11.7557i	1.32555	+	0.963065i	0.999845	+	0.0175917i	$0.00559989\pi$
$149$	16.1803	+	11.7557i	1.32555	+	0.963065i	0.325700	+	0.945473i	$0.394400\pi$
$150$	0.972136	−	2.99193i	0.0793746	−	0.244290i
$151$	−0.618034	−	1.90211i	−0.0502949	−	0.154792i	0.922755	−	0.385388i	$-0.125932\pi$
$151$	−0.618034	−	1.90211i	−0.0502949	−	0.154792i	−0.973050	+	0.230596i	$0.925932\pi$
$152$	−6.35410	+	4.61653i	−0.515386	+	0.374450i
$153$	7.85410			0.634967
$154$	−2.19098	−	2.48990i	−0.176554	−	0.200642i
$155$	20.9098			1.67952
$156$	1.00000	−	0.726543i	0.0800641	−	0.0581700i
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$	4.32624	−	13.3148i	0.344177	−	1.05927i
$159$	9.85410	+	7.15942i	0.781481	+	0.567779i
$160$	−11.5451	−	8.38800i	−0.912719	−	0.663129i
$161$	−0.954915	+	2.93893i	−0.0752578	+	0.231620i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	4.38197	−	3.18368i	0.343222	−	0.249365i	−0.402798	−	0.915289i	$-0.631962\pi$
$163$	4.38197	−	3.18368i	0.343222	−	0.249365i	0.746020	+	0.665923i	$0.231962\pi$
$164$	10.8541			0.847563
$165$	−0.881966	−	9.42481i	−0.0686610	−	0.733720i
$166$	−2.94427			−0.228520
$167$	−6.61803	+	4.80828i	−0.512119	+	0.372076i	−0.813627	−	0.581388i	$-0.802510\pi$
$167$	−6.61803	+	4.80828i	−0.512119	+	0.372076i	0.301508	+	0.953464i	$0.402510\pi$
$168$	−0.927051	−	2.85317i	−0.0715235	−	0.220127i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	−18.1353	−	13.1760i	−1.39091	−	1.01056i
$171$	−2.11803	−	1.53884i	−0.161970	−	0.117678i
$172$	0.381966	−	1.17557i	0.0291246	−	0.0896364i
$173$	6.13525	+	18.8824i	0.466455	+	1.43560i	0.857144	+	0.515077i	$0.172237\pi$
$173$	6.13525	+	18.8824i	0.466455	+	1.43560i	−0.390689	+	0.920523i	$0.627763\pi$
$174$	1.61803	−	1.17557i	0.122663	−	0.0891198i
$175$	3.14590			0.237808
$176$	3.23607	+	0.726543i	0.243928	+	0.0547652i
$177$	−6.76393			−0.508408
$178$	0.881966	−	0.640786i	0.0661061	−	0.0480289i
$179$	2.59017	+	7.97172i	0.193598	+	0.595835i	0.999990	+	0.00445278i	$0.00141737\pi$
$179$	2.59017	+	7.97172i	0.193598	+	0.595835i	−0.806392	+	0.591382i	$0.798583\pi$
$180$	0.881966	−	2.71441i	0.0657379	−	0.202320i
$181$	15.3262	+	11.1352i	1.13919	+	0.827670i	0.987006	−	0.160682i	$-0.0513693\pi$
$181$	15.3262	+	11.1352i	1.13919	+	0.827670i	0.152184	+	0.988352i	$0.451369\pi$
$182$	−1.00000	−	0.726543i	−0.0741249	−	0.0538549i
$183$	−2.76393	+	8.50651i	−0.204316	+	0.628819i
$184$	−2.86475	−	8.81678i	−0.211192	−	0.649982i
$185$	−27.9164	+	20.2825i	−2.05246	+	1.49120i
$186$	−7.32624			−0.537186
$187$	−25.4164	−	5.70634i	−1.85863	−	0.417289i
$188$	−2.00000			−0.145865
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	2.30902	+	7.10642i	0.167514	+	0.515554i
$191$	−5.64590	+	17.3763i	−0.408523	+	1.25730i	0.509395	+	0.860533i	$0.329869\pi$
$191$	−5.64590	+	17.3763i	−0.408523	+	1.25730i	−0.917918	+	0.396771i	$0.870131\pi$
$192$	5.66312	+	4.11450i	0.408700	+	0.296938i
$193$	−14.8713	−	10.8046i	−1.07046	−	0.777736i	−0.0944661	−	0.995528i	$-0.530114\pi$
$193$	−14.8713	−	10.8046i	−1.07046	−	0.777736i	−0.975995	+	0.217792i	$0.930114\pi$
$194$	1.09017	−	3.35520i	0.0782696	−	0.240889i
$195$	−1.09017	−	3.35520i	−0.0780687	−	0.240271i
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$	0.309017	+	3.30220i	0.0219609	+	0.234677i
$199$	−2.61803			−0.185588			−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803			−0.185588			−0.0927938	+	0.995685i	$0.529580\pi$
$200$	−7.63525	+	5.54734i	−0.539894	+	0.392256i
$201$	−2.47214	−	7.60845i	−0.174371	−	0.536659i
$202$	0.645898	−	1.98787i	0.0454452	−	0.139866i
$203$	1.61803	+	1.17557i	0.113564	+	0.0825089i
$204$	−6.35410	−	4.61653i	−0.444876	−	0.323221i
$205$	9.57295	−	29.4625i	0.668604	−	2.05775i
$206$	3.19098	+	9.82084i	0.222326	+	0.684250i
$207$	2.50000	−	1.81636i	0.173762	−	0.126245i
$208$	1.23607			0.0857059
$209$	5.73607	+	6.51864i	0.396772	+	0.450904i
$210$	−2.85410			−0.196952
$211$	1.61803	−	1.17557i	0.111390	−	0.0809296i	−0.530696	−	0.847562i	$-0.678069\pi$
$211$	1.61803	−	1.17557i	0.111390	−	0.0809296i	0.642086	+	0.766633i	$0.278069\pi$
$212$	−3.76393	−	11.5842i	−0.258508	−	0.795606i
$213$	−2.76393	+	8.50651i	−0.189382	+	0.582856i
$214$	3.97214	+	2.88593i	0.271530	+	0.197278i
$215$	−2.85410	−	2.07363i	−0.194648	−	0.141420i
$216$	−0.927051	+	2.85317i	−0.0630778	+	0.194134i
$217$	−2.26393	−	6.96767i	−0.153686	−	0.472996i
$218$	8.54508	−	6.20837i	0.578746	−	0.420484i
$219$	5.23607			0.353821
$220$	−4.82624	+	8.14324i	−0.325385	+	0.549017i
$221$	−9.70820			−0.653044
$222$	9.78115	−	7.10642i	0.656468	−	0.476952i
$223$	6.42705	+	19.7804i	0.430387	+	1.32460i	0.897740	+	0.440525i	$0.145208\pi$
$223$	6.42705	+	19.7804i	0.430387	+	1.32460i	−0.467353	+	0.884071i	$0.654792\pi$
$224$	−1.54508	+	4.75528i	−0.103235	+	0.317726i
$225$	−2.54508	−	1.84911i	−0.169672	−	0.123274i
$226$	0.618034	+	0.449028i	0.0411110	+	0.0298689i
$227$	6.61803	−	20.3682i	0.439254	−	1.35189i	−0.449409	−	0.893326i	$-0.648365\pi$
$227$	6.61803	−	20.3682i	0.439254	−	1.35189i	0.888664	−	0.458560i	$-0.151635\pi$
$228$	0.809017	+	2.48990i	0.0535785	+	0.164898i
$229$	−17.1803	+	12.4822i	−1.13531	+	0.824850i	−0.986459	−	0.164010i	$-0.947557\pi$
$229$	−17.1803	+	12.4822i	−1.13531	+	0.824850i	−0.148850	+	0.988860i	$0.547557\pi$
$230$	−8.81966			−0.581551
$231$	−3.04508	+	1.31433i	−0.200352	+	0.0864764i
$232$	−6.00000			−0.393919
$233$	4.61803	−	3.35520i	0.302537	−	0.219806i	−0.426150	−	0.904652i	$-0.640131\pi$
$233$	4.61803	−	3.35520i	0.302537	−	0.219806i	0.728688	+	0.684846i	$0.240131\pi$
$234$	0.381966	+	1.17557i	0.0249699	+	0.0768494i
$235$	−1.76393	+	5.42882i	−0.115066	+	0.354137i
$236$	5.47214	+	3.97574i	0.356206	+	0.258799i
$237$	−11.3262	−	8.22899i	−0.735718	−	0.534531i
$238$	−2.42705	+	7.46969i	−0.157322	+	0.484188i
$239$	−0.482779	−	1.48584i	−0.0312284	−	0.0961111i	0.934227	−	0.356678i	$-0.116091\pi$
$239$	−0.482779	−	1.48584i	−0.0312284	−	0.0961111i	−0.965456	+	0.260567i	$0.916091\pi$
$240$	2.30902	−	1.67760i	0.149046	−	0.108289i
$241$	4.94427			0.318489			0.159244	−	0.987239i	$-0.449094\pi$
$241$	4.94427			0.318489			0.159244	+	0.987239i	$0.449094\pi$
$242$	1.39919	−	10.9106i	0.0899431	−	0.701363i
$243$	−1.00000			−0.0641500
$244$	7.23607	−	5.25731i	0.463242	−	0.336565i
$245$	−0.881966	−	2.71441i	−0.0563467	−	0.173417i
$246$	−3.35410	+	10.3229i	−0.213850	+	0.658162i
$247$	2.61803	+	1.90211i	0.166582	+	0.121029i
$248$	17.7812	+	12.9188i	1.12910	+	0.820342i
$249$	−0.909830	+	2.80017i	−0.0576581	+	0.177453i
$250$	−1.63525	−	5.03280i	−0.103423	−	0.318302i
$251$	−19.5623	+	14.2128i	−1.23476	+	0.897107i	−0.997238	−	0.0742747i	$-0.976336\pi$
$251$	−19.5623	+	14.2128i	−1.23476	+	0.897107i	−0.237524	+	0.971382i	$0.576336\pi$
$252$	−1.00000			−0.0629941
$253$	−9.40983	+	4.06150i	−0.591591	+	0.255344i
$254$	3.23607			0.203049
$255$	−18.1353	+	13.1760i	−1.13567	+	0.825115i
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	0.809017	−	2.48990i	0.0504651	−	0.155316i	−0.922648	−	0.385643i	$-0.873980\pi$
$257$	0.809017	−	2.48990i	0.0504651	−	0.155316i	0.973113	+	0.230327i	$0.0739797\pi$
$258$	1.00000	+	0.726543i	0.0622573	+	0.0452326i
$259$	9.78115	+	7.10642i	0.607771	+	0.441572i
$260$	−1.09017	+	3.35520i	−0.0676095	+	0.208081i
$261$	−0.618034	−	1.90211i	−0.0382553	−	0.117738i
$262$	1.85410	−	1.34708i	0.114547	−	0.0832231i
$263$	2.43769			0.150315			0.0751573	−	0.997172i	$-0.476054\pi$
$263$	2.43769			0.150315			0.0751573	+	0.997172i	$0.476054\pi$
$264$	5.07295	−	8.55951i	0.312218	−	0.526801i
$265$	−34.7639			−2.13553
$266$	2.11803	−	1.53884i	0.129865	−	0.0943524i
$267$	−0.336881	−	1.03681i	−0.0206168	−	0.0634519i
$268$	−2.47214	+	7.60845i	−0.151010	+	0.464760i
$269$	−22.5623	−	16.3925i	−1.37565	−	0.999467i	−0.997272	−	0.0738149i	$-0.976483\pi$
$269$	−22.5623	−	16.3925i	−1.37565	−	0.999467i	−0.378376	−	0.925652i	$-0.623517\pi$
$270$	2.30902	+	1.67760i	0.140522	+	0.102095i
$271$	7.44427	−	22.9111i	0.452207	−	1.39175i	−0.422175	−	0.906514i	$-0.638733\pi$
$271$	7.44427	−	22.9111i	0.452207	−	1.39175i	0.874383	−	0.485237i	$-0.161267\pi$
$272$	−2.42705	−	7.46969i	−0.147162	−	0.452917i
$273$	−1.00000	+	0.726543i	−0.0605228	+	0.0439724i
$274$	−6.76393			−0.408624
$275$	6.89261	+	7.83297i	0.415640	+	0.472346i
$276$	−3.09017			−0.186006
$277$	8.44427	−	6.13512i	0.507367	−	0.368624i	−0.304457	−	0.952526i	$-0.598475\pi$
$277$	8.44427	−	6.13512i	0.507367	−	0.368624i	0.811824	+	0.583902i	$0.198475\pi$
$278$	−1.48278	−	4.56352i	−0.0889312	−	0.273702i
$279$	−2.26393	+	6.96767i	−0.135538	+	0.417143i
$280$	6.92705	+	5.03280i	0.413970	+	0.300767i
$281$	−0.854102	−	0.620541i	−0.0509515	−	0.0370184i	0.562018	−	0.827125i	$-0.310025\pi$
$281$	−0.854102	−	0.620541i	−0.0509515	−	0.0370184i	−0.612969	+	0.790107i	$0.710025\pi$
$282$	0.618034	−	1.90211i	0.0368034	−	0.113269i
$283$	4.15248	+	12.7800i	0.246839	+	0.759693i	0.995329	+	0.0965459i	$0.0307794\pi$
$283$	4.15248	+	12.7800i	0.246839	+	0.759693i	−0.748489	+	0.663147i	$0.769221\pi$
$284$	7.23607	−	5.25731i	0.429382	−	0.311964i
$285$	7.47214			0.442611
$286$	−0.381966	−	4.08174i	−0.0225861	−	0.241358i
$287$	−10.8541			−0.640697
$288$	4.04508	−	2.93893i	0.238359	−	0.173178i
$289$	13.8090	+	42.4998i	0.812295	+	2.49999i
$290$	−1.76393	+	5.42882i	−0.103582	+	0.318792i
$291$	−2.85410	−	2.07363i	−0.167310	−	0.121558i
$292$	−4.23607	−	3.07768i	−0.247897	−	0.180108i
$293$	6.11803	−	18.8294i	0.357419	−	1.10002i	−0.597174	−	0.802112i	$-0.703710\pi$
$293$	6.11803	−	18.8294i	0.357419	−	1.10002i	0.954593	−	0.297912i	$-0.0962902\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	15.6180	−	11.3472i	0.909317	−	0.660658i
$296$	−36.2705			−2.10818
$297$	3.23607	+	0.726543i	0.187776	+	0.0421583i
$298$	20.0000			1.15857
$299$	−3.09017	+	2.24514i	−0.178709	+	0.129840i
$300$	0.972136	+	2.99193i	0.0561263	+	0.172739i
$301$	−0.381966	+	1.17557i	−0.0220162	+	0.0677588i
$302$	−1.61803	−	1.17557i	−0.0931074	−	0.0676465i
$303$	−1.69098	−	1.22857i	−0.0971444	−	0.0705796i
$304$	−0.809017	+	2.48990i	−0.0464003	+	0.142805i
$305$	−7.88854	−	24.2784i	−0.451697	−	1.39018i
$306$	6.35410	−	4.61653i	0.363240	−	0.263909i
$307$	−24.2705			−1.38519			−0.692596	−	0.721326i	$-0.743533\pi$
$307$	−24.2705			−1.38519			−0.692596	+	0.721326i	$0.743533\pi$
$308$	3.23607	+	0.726543i	0.184392	+	0.0413986i
$309$	10.3262			0.587439
$310$	16.9164	−	12.2905i	0.960787	−	0.698053i
$311$	−0.236068	−	0.726543i	−0.0133862	−	0.0411984i	0.944140	−	0.329544i	$-0.106895\pi$
$311$	−0.236068	−	0.726543i	−0.0133862	−	0.0411984i	−0.957527	+	0.288345i	$0.906895\pi$
$312$	1.14590	−	3.52671i	0.0648737	−	0.199661i
$313$	7.94427	+	5.77185i	0.449037	+	0.326244i	0.789215	−	0.614117i	$-0.210488\pi$
$313$	7.94427	+	5.77185i	0.449037	+	0.326244i	−0.340179	+	0.940361i	$0.610488\pi$
$314$	7.85410	+	5.70634i	0.443233	+	0.322027i
$315$	−0.881966	+	2.71441i	−0.0496932	+	0.152940i
$316$	4.32624	+	13.3148i	0.243370	+	0.749016i
$317$	22.3262	−	16.2210i	1.25397	−	0.911060i	0.255521	−	0.966803i	$-0.417753\pi$
$317$	22.3262	−	16.2210i	1.25397	−	0.911060i	0.998445	+	0.0557435i	$0.0177529\pi$
$318$	12.1803			0.683040
$319$	0.618034	+	6.60440i	0.0346033	+	0.369775i
$320$	−19.9787			−1.11684
$321$	3.97214	−	2.88593i	0.221703	−	0.161077i
$322$	0.954915	+	2.93893i	0.0532153	+	0.163780i
$323$	6.35410	−	19.5559i	0.353552	−	1.08812i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	3.14590	+	2.28563i	0.174503	+	0.126784i
$326$	1.67376	−	5.15131i	0.0927011	−	0.285305i
$327$	−3.26393	−	10.0453i	−0.180496	−	0.555509i
$328$	26.3435	−	19.1396i	1.45457	−	1.05681i
$329$	2.00000			0.110264
$330$	−6.25329	−	7.10642i	−0.344232	−	0.391196i
$331$	30.3607			1.66877			0.834387	−	0.551179i	$-0.185822\pi$
$331$	30.3607			1.66877			0.834387	+	0.551179i	$0.185822\pi$
$332$	2.38197	−	1.73060i	0.130727	−	0.0949790i
$333$	−3.73607	−	11.4984i	−0.204735	−	0.630110i
$334$	−2.52786	+	7.77997i	−0.138319	+	0.425701i
$335$	18.4721	+	13.4208i	1.00924	+	0.733256i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	−8.38854	+	25.8173i	−0.456953	+	1.40636i	0.411874	+	0.911241i	$0.364874\pi$
$337$	−8.38854	+	25.8173i	−0.456953	+	1.40636i	−0.868827	+	0.495116i	$0.835126\pi$
$338$	3.54508	+	10.9106i	0.192827	+	0.593461i
$339$	0.618034	−	0.449028i	0.0335670	−	0.0243879i
$340$	22.4164			1.21570
$341$	12.3885	−	20.9030i	0.670877	−	1.13196i
$342$	−2.61803			−0.141567
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−1.14590	−	3.52671i	−0.0617827	−	0.190148i
$345$	−2.72542	+	8.38800i	−0.146732	+	0.451594i
$346$	16.0623	+	11.6699i	0.863515	+	0.627380i
$347$	10.0172	+	7.27794i	0.537753	+	0.390700i	0.823250	−	0.567679i	$-0.192159\pi$
$347$	10.0172	+	7.27794i	0.537753	+	0.390700i	−0.285497	+	0.958380i	$0.592159\pi$
$348$	−0.618034	+	1.90211i	−0.0331301	+	0.101964i
$349$	7.03444	+	21.6498i	0.376545	+	1.15889i	0.942430	+	0.334403i	$0.108534\pi$
$349$	7.03444	+	21.6498i	0.376545	+	1.15889i	−0.565885	+	0.824484i	$0.691466\pi$
$350$	2.54508	−	1.84911i	0.136041	−	0.0988392i
$351$	1.23607			0.0659764
$352$	−15.2254	+	6.57164i	−0.811518	+	0.350270i
$353$	12.4721			0.663825			0.331912	−	0.943310i	$-0.392306\pi$
$353$	12.4721			0.663825			0.331912	+	0.943310i	$0.392306\pi$
$354$	−5.47214	+	3.97574i	−0.290841	+	0.211308i
$355$	−7.88854	−	24.2784i	−0.418680	−	1.28857i
$356$	−0.336881	+	1.03681i	−0.0178547	+	0.0549510i
$357$	6.35410	+	4.61653i	0.336295	+	0.244332i
$358$	6.78115	+	4.92680i	0.358395	+	0.260389i
$359$	2.17376	−	6.69015i	0.114727	−	0.353093i	−0.877163	−	0.480192i	$-0.840567\pi$
$359$	2.17376	−	6.69015i	0.114727	−	0.353093i	0.991890	+	0.127100i	$0.0405668\pi$
$360$	−2.64590	−	8.14324i	−0.139451	−	0.429186i
$361$	9.82624	−	7.13918i	0.517170	−	0.375746i
$362$	18.9443			0.995689
$363$	−9.94427	−	4.70228i	−0.521939	−	0.246806i
$364$	1.23607			0.0647876
$365$	−12.0902	+	8.78402i	−0.632828	+	0.459777i
$366$	2.76393	+	8.50651i	0.144473	+	0.444642i
$367$	5.02786	−	15.4742i	0.262452	−	0.807745i	−0.729817	−	0.683643i	$-0.760395\pi$
$367$	5.02786	−	15.4742i	0.262452	−	0.807745i	0.992269	−	0.124103i	$-0.0396053\pi$
$368$	−2.50000	−	1.81636i	−0.130322	−	0.0946841i
$369$	8.78115	+	6.37988i	0.457129	+	0.332123i
$370$	−10.6631	+	32.8177i	−0.554349	+	1.70611i
$371$	3.76393	+	11.5842i	0.195414	+	0.601421i
$372$	5.92705	−	4.30625i	0.307303	−	0.223269i
$373$	−23.3262			−1.20779			−0.603893	−	0.797065i	$-0.706385\pi$
$373$	−23.3262			−1.20779			−0.603893	+	0.797065i	$0.706385\pi$
$374$	−23.9164	+	10.3229i	−1.23669	+	0.533783i
$375$	−5.29180			−0.273267
$376$	−4.85410	+	3.52671i	−0.250331	+	0.181876i
$377$	0.763932	+	2.35114i	0.0393445	+	0.121090i
$378$	0.309017	−	0.951057i	0.0158941	−	0.0489171i
$379$	−2.00000	−	1.45309i	−0.102733	−	0.0746400i	0.535233	−	0.844705i	$-0.320224\pi$
$379$	−2.00000	−	1.45309i	−0.102733	−	0.0746400i	−0.637966	+	0.770065i	$0.720224\pi$
$380$	−6.04508	−	4.39201i	−0.310106	−	0.225305i
$381$	1.00000	−	3.07768i	0.0512316	−	0.157675i
$382$	5.64590	+	17.3763i	0.288869	+	0.889048i
$383$	10.5623	−	7.67396i	0.539709	−	0.392121i	−0.284268	−	0.958745i	$-0.591751\pi$
$383$	10.5623	−	7.67396i	0.539709	−	0.392121i	0.823977	+	0.566624i	$0.191751\pi$
$384$	−3.00000			−0.153093
$385$	4.82624	−	8.14324i	0.245968	−	0.415018i
$386$	−18.3820			−0.935617
$387$	1.00000	−	0.726543i	0.0508329	−	0.0369322i
$388$	1.09017	+	3.35520i	0.0553450	+	0.170334i
$389$	6.85410	−	21.0948i	0.347517	−	1.06955i	−0.612706	−	0.790311i	$-0.709919\pi$
$389$	6.85410	−	21.0948i	0.347517	−	1.06955i	0.960223	−	0.279236i	$-0.0900810\pi$
$390$	−2.85410	−	2.07363i	−0.144523	−	0.105002i
$391$	19.6353	+	14.2658i	0.992998	+	0.721455i
$392$	0.927051	−	2.85317i	0.0468231	−	0.144107i
$393$	−0.708204	−	2.17963i	−0.0357242	−	0.109948i
$394$	3.23607	−	2.35114i	0.163031	−	0.118449i
$395$	39.9574			2.01048
$396$	−2.19098	−	2.48990i	−0.110101	−	0.125122i
$397$	14.6525			0.735387			0.367693	−	0.929947i	$-0.380148\pi$
$397$	14.6525			0.735387			0.367693	+	0.929947i	$0.380148\pi$
$398$	−2.11803	+	1.53884i	−0.106167	+	0.0771352i
$399$	−0.809017	−	2.48990i	−0.0405015	−	0.124651i
$400$	−0.972136	+	2.99193i	−0.0486068	+	0.149596i
$401$	−14.9443	−	10.8576i	−0.746281	−	0.542205i	0.148391	−	0.988929i	$-0.452591\pi$
$401$	−14.9443	−	10.8576i	−0.746281	−	0.542205i	−0.894672	+	0.446724i	$0.852591\pi$
$402$	−6.47214	−	4.70228i	−0.322801	−	0.234529i
$403$	2.79837	−	8.61251i	0.139397	−	0.429020i
$404$	0.645898	+	1.98787i	0.0321346	+	0.0989002i
$405$	2.30902	−	1.67760i	0.114736	−	0.0833606i
$406$	2.00000			0.0992583
$407$	3.73607	+	39.9241i	0.185190	+	1.97897i
$408$	−23.5623			−1.16651
$409$	−23.2705	+	16.9070i	−1.15065	+	0.835998i	−0.988568	−	0.150779i	$-0.951822\pi$
$409$	−23.2705	+	16.9070i	−1.15065	+	0.835998i	−0.162085	+	0.986777i	$0.551822\pi$
$410$	−9.57295	−	29.4625i	−0.472774	−	1.45505i
$411$	−2.09017	+	6.43288i	−0.103100	+	0.317311i
$412$	−8.35410	−	6.06961i	−0.411577	−	0.299028i
$413$	−5.47214	−	3.97574i	−0.269266	−	0.195633i
$414$	0.954915	−	2.93893i	0.0469315	−	0.144440i
$415$	−2.59675	−	7.99197i	−0.127469	−	0.392310i
$416$	−5.00000	+	3.63271i	−0.245145	+	0.178108i
$417$	−4.79837			−0.234977
$418$	8.47214	+	1.90211i	0.414386	+	0.0930354i
$419$	14.7639			0.721265			0.360633	−	0.932708i	$-0.382561\pi$
$419$	14.7639			0.721265			0.360633	+	0.932708i	$0.382561\pi$
$420$	2.30902	−	1.67760i	0.112668	−	0.0818585i
$421$	−1.33688	−	4.11450i	−0.0651556	−	0.200528i	0.913179	−	0.407559i	$-0.133620\pi$
$421$	−1.33688	−	4.11450i	−0.0651556	−	0.200528i	−0.978334	+	0.207031i	$0.933620\pi$
$422$	0.618034	−	1.90211i	0.0300854	−	0.0925934i
$423$	−1.61803	−	1.17557i	−0.0786715	−	0.0571582i
$424$	−29.5623	−	21.4783i	−1.43567	−	1.04308i
$425$	7.63525	−	23.4989i	0.370364	−	1.13986i
$426$	2.76393	+	8.50651i	0.133913	+	0.412142i
$427$	−7.23607	+	5.25731i	−0.350178	+	0.254419i
$428$	−4.90983			−0.237326
$429$	−4.00000	−	0.898056i	−0.193122	−	0.0433585i
$430$	−3.52786			−0.170129
$431$	1.69098	−	1.22857i	0.0814518	−	0.0591782i	−0.546314	−	0.837580i	$-0.683970\pi$
$431$	1.69098	−	1.22857i	0.0814518	−	0.0591782i	0.627766	+	0.778402i	$0.283970\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−5.32624	+	16.3925i	−0.255963	+	0.787772i	0.737676	+	0.675155i	$0.235923\pi$
$433$	−5.32624	+	16.3925i	−0.255963	+	0.787772i	−0.993638	+	0.112617i	$0.964077\pi$
$434$	−5.92705	−	4.30625i	−0.284508	−	0.206707i
$435$	4.61803	+	3.35520i	0.221418	+	0.160869i
$436$	−3.26393	+	10.0453i	−0.156314	+	0.481085i
$437$	−2.50000	−	7.69421i	−0.119591	−	0.368064i
$438$	4.23607	−	3.07768i	0.202407	−	0.147057i
$439$	−21.7984			−1.04038			−0.520190	−	0.854051i	$-0.674139\pi$
$439$	−21.7984			−1.04038			−0.520190	+	0.854051i	$0.674139\pi$
$440$	2.64590	+	28.2744i	0.126138	+	1.34793i
$441$	1.00000			0.0476190
$442$	−7.85410	+	5.70634i	−0.373582	+	0.271423i
$443$	1.51722	+	4.66953i	0.0720853	+	0.221856i	0.980608	−	0.195980i	$-0.0627887\pi$
$443$	1.51722	+	4.66953i	0.0720853	+	0.221856i	−0.908523	+	0.417836i	$0.862789\pi$
$444$	−3.73607	+	11.4984i	−0.177306	+	0.545692i
$445$	2.51722	+	1.82887i	0.119328	+	0.0866967i
$446$	16.8262	+	12.2250i	0.796745	+	0.578869i
$447$	6.18034	−	19.0211i	0.292320	−	0.899669i
$448$	2.16312	+	6.65740i	0.102198	+	0.314532i
$449$	−33.8885	+	24.6215i	−1.59930	+	1.16196i	−0.710462	+	0.703735i	$0.751514\pi$
$449$	−33.8885	+	24.6215i	−1.59930	+	1.16196i	−0.888837	+	0.458224i	$0.848486\pi$
$450$	−3.14590			−0.148299
$451$	−23.7812	−	27.0256i	−1.11981	−	1.27259i
$452$	−0.763932			−0.0359323
$453$	−1.61803	+	1.17557i	−0.0760219	+	0.0552331i
$454$	−6.61803	−	20.3682i	−0.310600	−	0.955928i
$455$	1.09017	−	3.35520i	0.0511080	−	0.157294i
$456$	6.35410	+	4.61653i	0.297558	+	0.216189i
$457$	−10.0902	−	7.33094i	−0.471998	−	0.342927i	0.326221	−	0.945293i	$-0.394225\pi$
$457$	−10.0902	−	7.33094i	−0.471998	−	0.342927i	−0.798220	+	0.602367i	$0.794225\pi$
$458$	−6.56231	+	20.1967i	−0.306636	+	0.943730i
$459$	−2.42705	−	7.46969i	−0.113285	−	0.348655i
$460$	7.13525	−	5.18407i	0.332683	−	0.241708i
$461$	−6.36068			−0.296246			−0.148123	−	0.988969i	$-0.547323\pi$
$461$	−6.36068			−0.296246			−0.148123	+	0.988969i	$0.547323\pi$
$462$	−1.69098	+	2.85317i	−0.0786716	+	0.132741i
$463$	11.4164			0.530565			0.265283	−	0.964171i	$-0.414535\pi$
$463$	11.4164			0.530565			0.265283	+	0.964171i	$0.414535\pi$
$464$	−1.61803	+	1.17557i	−0.0751153	+	0.0545745i
$465$	−6.46149	−	19.8864i	−0.299645	−	0.922211i
$466$	1.76393	−	5.42882i	0.0817126	−	0.251485i
$467$	−15.5623	−	11.3067i	−0.720138	−	0.523211i	0.166291	−	0.986077i	$-0.446821\pi$
$467$	−15.5623	−	11.3067i	−0.720138	−	0.523211i	−0.886428	+	0.462866i	$0.846821\pi$
$468$	−1.00000	−	0.726543i	−0.0462250	−	0.0335844i
$469$	2.47214	−	7.60845i	0.114153	−	0.351326i
$470$	1.76393	+	5.42882i	0.0813641	+	0.250413i
$471$	7.85410	−	5.70634i	0.361898	−	0.262934i
$472$	20.2918			0.934006
$473$	−3.76393	+	1.62460i	−0.173066	+	0.0746991i
$474$	−14.0000			−0.643041
$475$	−6.66312	+	4.84104i	−0.305725	+	0.222122i
$476$	−2.42705	−	7.46969i	−0.111244	−	0.342373i
$477$	3.76393	−	11.5842i	0.172339	−	0.530404i
$478$	−1.26393	−	0.918300i	−0.0578109	−	0.0420021i
$479$	8.94427	+	6.49839i	0.408674	+	0.296919i	0.773065	−	0.634327i	$-0.218723\pi$
$479$	8.94427	+	6.49839i	0.408674	+	0.296919i	−0.364391	+	0.931246i	$0.618723\pi$
$480$	−4.40983	+	13.5721i	−0.201280	+	0.619477i
$481$	4.61803	+	14.2128i	0.210564	+	0.648050i
$482$	4.00000	−	2.90617i	0.182195	−	0.132372i
$483$	3.09017			0.140608
$484$	5.28115	+	9.64932i	0.240052	+	0.438606i
$485$	10.0689			0.457204
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−12.1246	−	37.3157i	−0.549419	−	1.69094i	−0.710246	−	0.703954i	$-0.751416\pi$
$487$	−12.1246	−	37.3157i	−0.549419	−	1.69094i	0.160827	−	0.986983i	$-0.448584\pi$
$488$	8.29180	−	25.5195i	0.375352	−	1.15521i
$489$	−4.38197	−	3.18368i	−0.198159	−	0.143971i
$490$	−2.30902	−	1.67760i	−0.104311	−	0.0757862i
$491$	−0.100813	+	0.310271i	−0.00454963	+	0.0140023i	−0.953306	−	0.302007i	$-0.902343\pi$
$491$	−0.100813	+	0.310271i	−0.00454963	+	0.0140023i	0.948756	+	0.316010i	$0.102343\pi$
$492$	−3.35410	−	10.3229i	−0.151215	−	0.465391i
$493$	12.7082	−	9.23305i	0.572349	−	0.415836i
$494$	3.23607			0.145598
$495$	−8.69098	+	3.75123i	−0.390631	+	0.168605i
$496$	7.32624			0.328958
$497$	−7.23607	+	5.25731i	−0.324582	+	0.235823i
$498$	0.909830	+	2.80017i	0.0407705	+	0.125479i
$499$	8.09017	−	24.8990i	0.362166	−	1.11463i	−0.589571	−	0.807716i	$-0.700703\pi$
$499$	8.09017	−	24.8990i	0.362166	−	1.11463i	0.951737	−	0.306915i	$-0.0992968\pi$
$500$	4.28115	+	3.11044i	0.191459	+	0.139103i
$501$	6.61803	+	4.80828i	0.295672	+	0.214818i
$502$	−7.47214	+	22.9969i	−0.333498	+	1.02640i
$503$	−0.180340	−	0.555029i	−0.00804096	−	0.0247475i	0.946956	−	0.321365i	$-0.104142\pi$
$503$	−0.180340	−	0.555029i	−0.00804096	−	0.0247475i	−0.954996	+	0.296617i	$0.904142\pi$
$504$	−2.42705	+	1.76336i	−0.108109	+	0.0785461i
$505$	5.96556			0.265464
$506$	−5.22542	+	8.81678i	−0.232298	+	0.391954i
$507$	11.4721			0.509495
$508$	−2.61803	+	1.90211i	−0.116156	+	0.0843926i
$509$	−1.82624	−	5.62058i	−0.0809466	−	0.249128i	0.902391	−	0.430919i	$-0.141811\pi$
$509$	−1.82624	−	5.62058i	−0.0809466	−	0.249128i	−0.983337	+	0.181791i	$0.941811\pi$
$510$	−6.92705	+	21.3193i	−0.306735	+	0.944033i
$511$	4.23607	+	3.07768i	0.187393	+	0.136149i
$512$	−8.89919	−	6.46564i	−0.393292	−	0.285744i
$513$	−0.809017	+	2.48990i	−0.0357190	+	0.109932i
$514$	−0.809017	−	2.48990i	−0.0356842	−	0.109825i
$515$	−23.8435	+	17.3233i	−1.05067	+	0.763355i
$516$	−1.23607			−0.0544149
$517$	4.38197	+	4.97980i	0.192719	+	0.219011i
$518$	12.0902			0.531212
$519$	16.0623	−	11.6699i	0.705057	−	0.512254i
$520$	3.27051	+	10.0656i	0.143421	+	0.441406i
$521$	−3.59017	+	11.0494i	−0.157288	+	0.484083i	−0.998386	−	0.0568005i	$-0.981910\pi$
$521$	−3.59017	+	11.0494i	−0.157288	+	0.484083i	0.841097	+	0.540884i	$0.181910\pi$
$522$	−1.61803	−	1.17557i	−0.0708194	−	0.0514533i
$523$	−2.35410	−	1.71036i	−0.102938	−	0.0747886i	0.535126	−	0.844772i	$-0.320264\pi$
$523$	−2.35410	−	1.71036i	−0.102938	−	0.0747886i	−0.638063	+	0.769984i	$0.720264\pi$
$524$	−0.708204	+	2.17963i	−0.0309380	+	0.0952175i
$525$	−0.972136	−	2.99193i	−0.0424275	−	0.130578i
$526$	1.97214	−	1.43284i	0.0859892	−	0.0624748i
$527$	−57.5410			−2.50653
$528$	−0.309017	−	3.30220i	−0.0134482	−	0.143710i
$529$	−13.4508			−0.584820
$530$	−28.1246	+	20.4337i	−1.22166	+	0.887584i
$531$	2.09017	+	6.43288i	0.0907056	+	0.279163i
$532$	−0.809017	+	2.48990i	−0.0350753	+	0.107951i
$533$	−10.8541	−	7.88597i	−0.470143	−	0.341579i
$534$	−0.881966	−	0.640786i	−0.0381664	−	0.0277295i
$535$	−4.33030	+	13.3273i	−0.187215	+	0.576190i
$536$	7.41641	+	22.8254i	0.320340	+	0.985905i
$537$	6.78115	−	4.92680i	0.292628	−	0.212607i
$538$	−27.8885			−1.20236
$539$	−3.23607	−	0.726543i	−0.139387	−	0.0312944i
$540$	−2.85410			−0.122821
$541$	−13.6353	+	9.90659i	−0.586225	+	0.425918i	−0.840963	−	0.541093i	$-0.818011\pi$
$541$	−13.6353	+	9.90659i	−0.586225	+	0.425918i	0.254738	+	0.967010i	$0.418011\pi$
$542$	−7.44427	−	22.9111i	−0.319759	−	0.984117i
$543$	5.85410	−	18.0171i	0.251224	−	0.773187i
$544$	31.7705	+	23.0826i	1.36215	+	0.989659i
$545$	24.3885	+	17.7193i	1.04469	+	0.759012i
$546$	−0.381966	+	1.17557i	−0.0163466	+	0.0503098i
$547$	−11.2705	−	34.6871i	−0.481892	−	1.48311i	−0.836432	−	0.548071i	$-0.815362\pi$
$547$	−11.2705	−	34.6871i	−0.481892	−	1.48311i	0.354540	−	0.935041i	$-0.384638\pi$
$548$	5.47214	−	3.97574i	0.233758	−	0.169835i
$549$	8.94427			0.381732
$550$	10.1803	+	2.28563i	0.434091	+	0.0974595i
$551$	−5.23607			−0.223064
$552$	−7.50000	+	5.44907i	−0.319221	+	0.231928i
$553$	−4.32624	−	13.3148i	−0.183970	−	0.566203i
$554$	3.22542	−	9.92684i	0.137035	−	0.421751i
$555$	27.9164	+	20.2825i	1.18499	+	0.860942i
$556$	3.88197	+	2.82041i	0.164632	+	0.119612i
$557$	−6.61803	+	20.3682i	−0.280415	+	0.863029i	0.707320	+	0.706893i	$0.249904\pi$
$557$	−6.61803	+	20.3682i	−0.280415	+	0.863029i	−0.987736	+	0.156136i	$0.950096\pi$
$558$	2.26393	+	6.96767i	0.0958399	+	0.294965i
$559$	−1.23607	+	0.898056i	−0.0522801	+	0.0379837i
$560$	2.85410			0.120608
$561$	2.42705	+	25.9358i	0.102470	+	1.09501i
$562$	−1.05573			−0.0445332
$563$	−32.6525	+	23.7234i	−1.37614	+	0.999823i	−0.378908	+	0.925434i	$0.623700\pi$
$563$	−32.6525	+	23.7234i	−1.37614	+	0.999823i	−0.997229	+	0.0743885i	$0.976300\pi$
$564$	0.618034	+	1.90211i	0.0260239	+	0.0800934i
$565$	−0.673762	+	2.07363i	−0.0283454	+	0.0872381i
$566$	10.8713	+	7.89848i	0.456956	+	0.331998i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	8.29180	−	25.5195i	0.347916	−	1.07078i
$569$	−5.61803	−	17.2905i	−0.235520	−	0.724857i	−0.997052	−	0.0767291i	$-0.975552\pi$
$569$	−5.61803	−	17.2905i	−0.235520	−	0.724857i	0.761532	−	0.648128i	$-0.224448\pi$
$570$	6.04508	−	4.39201i	0.253201	−	0.183961i
$571$	28.5410			1.19440			0.597202	−	0.802091i	$-0.296279\pi$
$571$	28.5410			1.19440			0.597202	+	0.802091i	$0.296279\pi$
$572$	2.70820	+	3.07768i	0.113236	+	0.128684i
$573$	18.2705			0.763261
$574$	−8.78115	+	6.37988i	−0.366518	+	0.266291i
$575$	−3.00407	−	9.24556i	−0.125278	−	0.385567i
$576$	2.16312	−	6.65740i	0.0901300	−	0.277391i
$577$	11.8541	+	8.61251i	0.493493	+	0.358543i	0.806526	−	0.591199i	$-0.201345\pi$
$577$	11.8541	+	8.61251i	0.493493	+	0.358543i	−0.313033	+	0.949742i	$0.601345\pi$
$578$	36.1525	+	26.2663i	1.50374	+	1.09253i
$579$	−5.68034	+	17.4823i	−0.236067	+	0.726539i
$580$	−1.76393	−	5.42882i	−0.0732433	−	0.225420i
$581$	−2.38197	+	1.73060i	−0.0988206	+	0.0717974i
$582$	−3.52786			−0.146235
$583$	−20.5967	+	34.7526i	−0.853030	+	1.43930i
$584$	−15.7082			−0.650010
$585$	−2.85410	+	2.07363i	−0.118003	+	0.0857339i
$586$	−6.11803	−	18.8294i	−0.252734	−	0.777834i
$587$	1.20163	−	3.69822i	0.0495964	−	0.152642i	−0.923191	−	0.384341i	$-0.874429\pi$
$587$	1.20163	−	3.69822i	0.0495964	−	0.152642i	0.972787	+	0.231699i	$0.0744286\pi$
$588$	−0.809017	−	0.587785i	−0.0333633	−	0.0242399i
$589$	15.5172	+	11.2739i	0.639376	+	0.464534i
$590$	5.96556	−	18.3601i	0.245598	−	0.755873i
$591$	−1.23607	−	3.80423i	−0.0508450	−	0.156485i
$592$	−9.78115	+	7.10642i	−0.402003	+	0.292072i
$593$	3.43769			0.141169			0.0705846	−	0.997506i	$-0.477514\pi$
$593$	3.43769			0.141169			0.0705846	+	0.997506i	$0.477514\pi$
$594$	3.04508	−	1.31433i	0.124941	−	0.0539275i
$595$	−22.4164			−0.918983
$596$	−16.1803	+	11.7557i	−0.662773	+	0.481532i
$597$	0.809017	+	2.48990i	0.0331109	+	0.101905i
$598$	−1.18034	+	3.63271i	−0.0482677	+	0.148553i
$599$	1.26393	+	0.918300i	0.0516429	+	0.0375207i	0.613307	−	0.789844i	$-0.289839\pi$
$599$	1.26393	+	0.918300i	0.0516429	+	0.0375207i	−0.561664	+	0.827365i	$0.689839\pi$
$600$	7.63525	+	5.54734i	0.311708	+	0.226469i
$601$	1.85410	−	5.70634i	0.0756304	−	0.232766i	−0.906093	−	0.423078i	$-0.860950\pi$
$601$	1.85410	−	5.70634i	0.0756304	−	0.232766i	0.981724	+	0.190311i	$0.0609497\pi$
$602$	0.381966	+	1.17557i	0.0155678	+	0.0479127i
$603$	−6.47214	+	4.70228i	−0.263566	+	0.191492i
$604$	2.00000			0.0813788
$605$	30.8500	−	5.82485i	1.25423	−	0.236814i
$606$	−2.09017			−0.0849073
$607$	8.35410	−	6.06961i	0.339083	−	0.246358i	−0.405192	−	0.914232i	$-0.632795\pi$
$607$	8.35410	−	6.06961i	0.339083	−	0.246358i	0.744275	+	0.667874i	$0.232795\pi$
$608$	−4.04508	−	12.4495i	−0.164050	−	0.504894i
$609$	0.618034	−	1.90211i	0.0250440	−	0.0770775i
$610$	−20.6525	−	15.0049i	−0.836194	−	0.607531i
$611$	2.00000	+	1.45309i	0.0809113	+	0.0587855i
$612$	−2.42705	+	7.46969i	−0.0981077	+	0.301945i
$613$	−1.80902	−	5.56758i	−0.0730655	−	0.224873i	0.907854	−	0.419286i	$-0.137720\pi$
$613$	−1.80902	−	5.56758i	−0.0730655	−	0.224873i	−0.980920	+	0.194414i	$0.937720\pi$
$614$	−19.6353	+	14.2658i	−0.792414	+	0.575723i
$615$	−30.9787			−1.24918
$616$	9.13525	−	3.94298i	0.368070	−	0.158867i
$617$	44.6525			1.79764			0.898820	−	0.438317i	$-0.144425\pi$
$617$	44.6525			1.79764			0.898820	+	0.438317i	$0.144425\pi$
$618$	8.35410	−	6.06961i	0.336051	−	0.244156i
$619$	−3.55573	−	10.9434i	−0.142917	−	0.439853i	0.853820	−	0.520568i	$-0.174280\pi$
$619$	−3.55573	−	10.9434i	−0.142917	−	0.439853i	−0.996737	+	0.0807150i	$0.974280\pi$
$620$	−6.46149	+	19.8864i	−0.259500	+	0.798658i
$621$	−2.50000	−	1.81636i	−0.100322	−	0.0728879i
$622$	−0.618034	−	0.449028i	−0.0247809	−	0.0180044i
$623$	0.336881	−	1.03681i	0.0134969	−	0.0415390i
$624$	−0.381966	−	1.17557i	−0.0152909	−	0.0470605i
$625$	24.9443	−	18.1231i	0.997771	−	0.724923i
$626$	9.81966			0.392473
$627$	4.42705	−	7.46969i	0.176799	−	0.298311i
$628$	−9.70820			−0.387400
$629$	76.8222	−	55.8146i	3.06310	−	2.22547i
$630$	0.881966	+	2.71441i	0.0351384	+	0.108145i
$631$	9.23607	−	28.4257i	0.367682	−	1.13161i	−0.580602	−	0.814187i	$-0.697183\pi$
$631$	9.23607	−	28.4257i	0.367682	−	1.13161i	0.948284	−	0.317422i	$-0.102817\pi$
$632$	33.9787	+	24.6870i	1.35160	+	0.981995i
$633$	−1.61803	−	1.17557i	−0.0643111	−	0.0467247i
$634$	8.52786	−	26.2461i	0.338685	−	1.04236i
$635$	2.85410	+	8.78402i	0.113262	+	0.348583i
$636$	−9.85410	+	7.15942i	−0.390741	+	0.283890i
$637$	−1.23607			−0.0489748
$638$	4.38197	+	4.97980i	0.173484	+	0.197152i
$639$	8.94427			0.353830
$640$	6.92705	−	5.03280i	0.273816	−	0.198939i
$641$	2.67376	+	8.22899i	0.105607	+	0.325026i	0.989872	−	0.141959i	$-0.0453402\pi$
$641$	2.67376	+	8.22899i	0.105607	+	0.325026i	−0.884265	+	0.466985i	$0.845340\pi$
$642$	1.51722	−	4.66953i	0.0598799	−	0.184291i
$643$	−38.7705	−	28.1684i	−1.52896	−	1.11085i	−0.956813	−	0.290703i	$-0.906111\pi$
$643$	−38.7705	−	28.1684i	−1.52896	−	1.11085i	−0.572146	−	0.820152i	$-0.693889\pi$
$644$	−2.50000	−	1.81636i	−0.0985138	−	0.0715745i
$645$	−1.09017	+	3.35520i	−0.0429254	+	0.132111i
$646$	−6.35410	−	19.5559i	−0.249999	−	0.769417i
$647$	24.5623	−	17.8456i	0.965644	−	0.701581i	0.0111892	−	0.999937i	$-0.496438\pi$
$647$	24.5623	−	17.8456i	0.965644	−	0.701581i	0.954455	+	0.298356i	$0.0964383\pi$
$648$	3.00000			0.117851
$649$	−2.09017	−	22.3358i	−0.0820463	−	0.876758i
$650$	3.88854			0.152521
$651$	−5.92705	+	4.30625i	−0.232299	+	0.168775i
$652$	1.67376	+	5.15131i	0.0655496	+	0.201741i
$653$	−8.00000	+	24.6215i	−0.313064	+	0.963513i	0.663480	+	0.748194i	$0.269079\pi$
$653$	−8.00000	+	24.6215i	−0.313064	+	0.963513i	−0.976544	+	0.215318i	$0.930921\pi$
$654$	−8.54508	−	6.20837i	−0.334139	−	0.242766i
$655$	5.29180	+	3.84471i	0.206768	+	0.150225i
$656$	3.35410	−	10.3229i	0.130956	−	0.403040i
$657$	−1.61803	−	4.97980i	−0.0631255	−	0.194280i
$658$	1.61803	−	1.17557i	0.0630775	−	0.0458285i
$659$	−35.0344			−1.36475			−0.682374	−	0.731003i	$-0.739052\pi$
$659$	−35.0344			−1.36475			−0.682374	+	0.731003i	$0.739052\pi$
$660$	9.23607	+	2.07363i	0.359513	+	0.0807158i
$661$	8.29180			0.322513			0.161257	−	0.986912i	$-0.448445\pi$
$661$	8.29180			0.322513			0.161257	+	0.986912i	$0.448445\pi$
$662$	24.5623	−	17.8456i	0.954641	−	0.693587i
$663$	3.00000	+	9.23305i	0.116510	+	0.358582i
$664$	2.72949	−	8.40051i	0.105925	−	0.326003i
$665$	6.04508	+	4.39201i	0.234418	+	0.170315i
$666$	−9.78115	−	7.10642i	−0.379012	−	0.275368i
$667$	1.90983	−	5.87785i	0.0739489	−	0.227591i
$668$	−2.52786	−	7.77997i	−0.0978060	−	0.301016i
$669$	16.8262	−	12.2250i	0.650540	−	0.472645i
$670$	22.8328			0.882109
$671$	−28.9443	−	6.49839i	−1.11738	−	0.250868i
$672$	5.00000			0.192879
$673$	−29.0344	+	21.0948i	−1.11920	+	0.813143i	−0.984087	−	0.177688i	$-0.943138\pi$
$673$	−29.0344	+	21.0948i	−1.11920	+	0.813143i	−0.135109	+	0.990831i	$0.543138\pi$
$674$	8.38854	+	25.8173i	0.323115	+	0.994445i
$675$	−0.972136	+	2.99193i	−0.0374175	+	0.115159i
$676$	−9.28115	−	6.74315i	−0.356967	−	0.259352i
$677$	−19.3262	−	14.0413i	−0.742768	−	0.539652i	0.150809	−	0.988563i	$-0.451812\pi$
$677$	−19.3262	−	14.0413i	−0.742768	−	0.539652i	−0.893577	+	0.448911i	$0.851812\pi$
$678$	0.236068	−	0.726543i	0.00906614	−	0.0279027i
$679$	−1.09017	−	3.35520i	−0.0418369	−	0.128761i
$680$	54.4058	−	39.5281i	2.08637	−	1.51583i
$681$	−21.4164			−0.820679
$682$	−2.26393	−	24.1927i	−0.0866904	−	0.926386i
$683$	40.9230			1.56587			0.782937	−	0.622101i	$-0.213721\pi$
$683$	40.9230			1.56587			0.782937	+	0.622101i	$0.213721\pi$
$684$	2.11803	−	1.53884i	0.0809851	−	0.0588391i
$685$	−5.96556	−	18.3601i	−0.227932	−	0.701503i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	17.1803	+	12.4822i	0.655471	+	0.476227i
$688$	−1.00000	−	0.726543i	−0.0381246	−	0.0276992i
$689$	−4.65248	+	14.3188i	−0.177245	+	0.545505i
$690$	2.72542	+	8.38800i	0.103755	+	0.319326i
$691$	−32.2984	+	23.4661i	−1.22869	+	0.892694i	−0.996791	−	0.0800463i	$-0.974493\pi$
$691$	−32.2984	+	23.4661i	−1.22869	+	0.892694i	−0.231897	+	0.972740i	$0.574493\pi$
$692$	−19.8541			−0.754740
$693$	2.19098	+	2.48990i	0.0832286	+	0.0945834i
$694$	12.3820			0.470013
$695$	11.0795	−	8.04975i	0.420270	−	0.305344i
$696$	1.85410	+	5.70634i	0.0702796	+	0.216298i
$697$	−26.3435	+	81.0768i	−0.997830	+	3.07100i
$698$	18.4164	+	13.3803i	0.697071	+	0.506452i
$699$	−4.61803	−	3.35520i	−0.174670	−	0.126905i
$700$	−0.972136	+	2.99193i	−0.0367433	+	0.113084i
$701$	7.43769	+	22.8909i	0.280918	+	0.864576i	0.987593	+	0.157038i	$0.0501944\pi$
$701$	7.43769	+	22.8909i	0.280918	+	0.864576i	−0.706675	+	0.707539i	$0.749806\pi$
$702$	1.00000	−	0.726543i	0.0377426	−	0.0274216i
$703$	−31.6525			−1.19380
$704$	−11.8369	+	19.9722i	−0.446119	+	0.752730i
$705$	5.70820			0.214983
$706$	10.0902	−	7.33094i	0.379749	−	0.275903i
$707$	−0.645898	−	1.98787i	−0.0242915	−	0.0747615i
$708$	2.09017	−	6.43288i	0.0785534	−	0.241762i
$709$	15.9271	+	11.5717i	0.598153	+	0.434584i	0.845223	−	0.534414i	$-0.179468\pi$
$709$	15.9271	+	11.5717i	0.598153	+	0.434584i	−0.247070	+	0.968998i	$0.579468\pi$
$710$	−20.6525	−	15.0049i	−0.775074	−	0.563124i
$711$	−4.32624	+	13.3148i	−0.162247	+	0.499344i
$712$	1.01064	+	3.11044i	0.0378755	+	0.116569i
$713$	−18.3156	+	13.3071i	−0.685924	+	0.498353i
$714$	7.85410			0.293932
$715$	10.7426	−	4.63677i	0.401752	−	0.173405i
$716$	−8.38197			−0.313249
$717$	−1.26393	+	0.918300i	−0.0472024	+	0.0342946i
$718$	−2.17376	−	6.69015i	−0.0811241	−	0.249674i
$719$	1.50658	−	4.63677i	0.0561859	−	0.172922i	−0.919025	−	0.394199i	$-0.871022\pi$
$719$	1.50658	−	4.63677i	0.0561859	−	0.172922i	0.975211	+	0.221276i	$0.0710222\pi$
$720$	−2.30902	−	1.67760i	−0.0860520	−	0.0625204i
$721$	8.35410	+	6.06961i	0.311123	+	0.226044i
$722$	3.75329	−	11.5514i	0.139683	−	0.429900i
$723$	−1.52786	−	4.70228i	−0.0568219	−	0.174880i
$724$	−15.3262	+	11.1352i	−0.569595	+	0.413835i
$725$	−6.29180			−0.233671
$726$	−10.8090	+	2.04087i	−0.401160	+	0.0757438i
$727$	25.7426			0.954742			0.477371	−	0.878702i	$-0.341590\pi$
$727$	25.7426			0.954742			0.477371	+	0.878702i	$0.341590\pi$
$728$	3.00000	−	2.17963i	0.111187	−	0.0807824i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−4.61803	+	14.2128i	−0.170921	+	0.526041i
$731$	7.85410	+	5.70634i	0.290494	+	0.211057i
$732$	−7.23607	−	5.25731i	−0.267453	−	0.194316i
$733$	9.61803	−	29.6013i	0.355250	−	1.09335i	−0.600614	−	0.799539i	$-0.705077\pi$
$733$	9.61803	−	29.6013i	0.355250	−	1.09335i	0.955864	−	0.293809i	$-0.0949228\pi$
$734$	−5.02786	−	15.4742i	−0.185582	−	0.571162i
$735$	−2.30902	+	1.67760i	−0.0851694	+	0.0618792i
$736$	15.4508			0.569526
$737$	24.3607	−	10.5146i	0.897337	−	0.387311i
$738$	10.8541			0.399545
$739$	−39.6525	+	28.8092i	−1.45864	+	1.05976i	−0.474925	+	0.880026i	$0.657525\pi$
$739$	−39.6525	+	28.8092i	−1.45864	+	1.05976i	−0.983715	+	0.179738i	$0.942475\pi$
$740$	−10.6631	−	32.8177i	−0.391984	−	1.20640i
$741$	1.00000	−	3.07768i	0.0367359	−	0.113062i
$742$	9.85410	+	7.15942i	0.361755	+	0.262831i
$743$	−14.0172	−	10.1841i	−0.514242	−	0.373619i	0.300188	−	0.953880i	$-0.402950\pi$
$743$	−14.0172	−	10.1841i	−0.514242	−	0.373619i	−0.814430	+	0.580261i	$0.802950\pi$
$744$	6.79180	−	20.9030i	0.248999	−	0.766341i
$745$	17.6393	+	54.2882i	0.646255	+	1.98897i
$746$	−18.8713	+	13.7108i	−0.690928	+	0.501989i
$747$	2.94427			0.107725
$748$	13.2812	−	22.4091i	0.485607	−	0.819357i
$749$	4.90983			0.179401
$750$	−4.28115	+	3.11044i	−0.156326	+	0.113577i
$751$	−3.23607	−	9.95959i	−0.118086	−	0.363431i	0.874492	−	0.485039i	$-0.161195\pi$
$751$	−3.23607	−	9.95959i	−0.118086	−	0.363431i	−0.992578	+	0.121609i	$0.961195\pi$
$752$	−0.618034	+	1.90211i	−0.0225374	+	0.0693629i
$753$	19.5623	+	14.2128i	0.712890	+	0.517945i
$754$	2.00000	+	1.45309i	0.0728357	+	0.0529182i
$755$	1.76393	−	5.42882i	0.0641961	−	0.197575i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	−0.263932	+	0.191758i	−0.00959277	+	0.00696956i	−0.592571	−	0.805518i	$-0.701887\pi$
$757$	−0.263932	+	0.191758i	−0.00959277	+	0.00696956i	0.582979	+	0.812488i	$0.301887\pi$
$758$	−2.47214			−0.0897920
$759$	6.77051	+	7.69421i	0.245754	+	0.279282i
$760$	−22.4164			−0.813129
$761$	−37.0344	+	26.9071i	−1.34250	+	0.975382i	−0.343149	+	0.939281i	$0.611494\pi$
$761$	−37.0344	+	26.9071i	−1.34250	+	0.975382i	−0.999348	+	0.0361006i	$0.988506\pi$
$762$	−1.00000	−	3.07768i	−0.0362262	−	0.111493i
$763$	3.26393	−	10.0453i	0.118162	−	0.363666i
$764$	−14.7812	−	10.7391i	−0.534763	−	0.388528i
$765$	18.1353	+	13.1760i	0.655682	+	0.476381i
$766$	4.03444	−	12.4167i	0.145770	−	0.448635i
$767$	−2.58359	−	7.95148i	−0.0932881	−	0.287111i
$768$	−13.7533	+	9.99235i	−0.496279	+	0.360568i
$769$	14.5836			0.525898			0.262949	−	0.964810i	$-0.415305\pi$
$769$	14.5836			0.525898			0.262949	+	0.964810i	$0.415305\pi$
$770$	−0.881966	−	9.42481i	−0.0317838	−	0.339647i
$771$	−2.61803			−0.0942862
$772$	14.8713	−	10.8046i	0.535231	−	0.388868i
$773$	−12.0344	−	37.0382i	−0.432849	−	1.33217i	−0.895275	−	0.445514i	$-0.853021\pi$
$773$	−12.0344	−	37.0382i	−0.432849	−	1.33217i	0.462426	−	0.886658i	$-0.346979\pi$
$774$	0.381966	−	1.17557i	0.0137295	−	0.0422550i
$775$	18.6459	+	13.5470i	0.669780	+	0.486624i
$776$	8.56231	+	6.22088i	0.307369	+	0.223317i
$777$	3.73607	−	11.4984i	0.134031	−	0.412504i
$778$	−6.85410	−	21.0948i	−0.245731	−	0.756284i
$779$	22.9894	−	16.7027i	0.823679	−	0.598438i
$780$	3.52786			0.126318
$781$	−28.9443	−	6.49839i	−1.03571	−	0.232531i
$782$	24.2705			0.867912
$783$	−1.61803	+	1.17557i	−0.0578238	+	0.0420115i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−8.56231	+	26.3521i	−0.305602	+	0.940546i
$786$	−1.85410	−	1.34708i	−0.0661336	−	0.0480489i
$787$	−9.92705	−	7.21242i	−0.353861	−	0.257095i	0.396626	−	0.917980i	$-0.370181\pi$
$787$	−9.92705	−	7.21242i	−0.353861	−	0.257095i	−0.750487	+	0.660885i	$0.770181\pi$
$788$	−1.23607	+	3.80423i	−0.0440331	+	0.135520i
$789$	−0.753289	−	2.31838i	−0.0268178	−	0.0825367i
$790$	32.3262	−	23.4864i	1.15012	−	0.835608i
$791$	0.763932			0.0271623
$792$	−9.70820	−	2.17963i	−0.344966	−	0.0774497i
$793$	−11.0557			−0.392600
$794$	11.8541	−	8.61251i	0.420686	−	0.305647i
$795$	10.7426	+	33.0625i	0.381002	+	1.17260i
$796$	0.809017	−	2.48990i	0.0286748	−	0.0882521i
$797$	−8.30902	−	6.03685i	−0.294320	−	0.213836i	0.430819	−	0.902438i	$-0.358225\pi$
$797$	−8.30902	−	6.03685i	−0.294320	−	0.213836i	−0.725139	+	0.688602i	$0.758225\pi$
$798$	−2.11803	−	1.53884i	−0.0749776	−	0.0544744i
$799$	4.85410	−	14.9394i	0.171726	−	0.528518i
$800$	−4.86068	−	14.9596i	−0.171851	−	0.528903i
$801$	−0.881966	+	0.640786i	−0.0311627	+	0.0226411i
$802$	−18.4721			−0.652274
$803$	1.61803	+	17.2905i	0.0570992	+	0.610170i
$804$	8.00000			0.282138
$805$	−7.13525	+	5.18407i	−0.251485	+	0.182714i
$806$	−2.79837	−	8.61251i	−0.0985685	−	0.303363i
$807$	−8.61803	+	26.5236i	−0.303369	+	0.933674i
$808$	5.07295	+	3.68571i	0.178466	+	0.129663i
$809$	23.1803	+	16.8415i	0.814977	+	0.592116i	0.915269	−	0.402842i	$-0.131978\pi$
$809$	23.1803	+	16.8415i	0.814977	+	0.592116i	−0.100292	+	0.994958i	$0.531978\pi$
$810$	0.881966	−	2.71441i	0.0309891	−	0.0953747i
$811$	−5.05573	−	15.5599i	−0.177531	−	0.546383i	0.822209	−	0.569185i	$-0.192741\pi$
$811$	−5.05573	−	15.5599i	−0.177531	−	0.546383i	−0.999740	+	0.0228021i	$0.992741\pi$
$812$	−1.61803	+	1.17557i	−0.0567819	+	0.0412544i
$813$	−24.0902			−0.844879
$814$	26.4894	+	30.1033i	0.928451	+	1.05512i
$815$	15.4590			0.541504
$816$	−6.35410	+	4.61653i	−0.222438	+	0.161611i
$817$	−1.00000	−	3.07768i	−0.0349856	−	0.107675i
$818$	−8.88854	+	27.3561i	−0.310781	+	0.956484i
$819$	1.00000	+	0.726543i	0.0349428	+	0.0253875i
$820$	25.0623	+	18.2088i	0.875214	+	0.635880i
$821$	9.38197	−	28.8747i	0.327433	−	1.00773i	−0.642898	−	0.765952i	$-0.722268\pi$
$821$	9.38197	−	28.8747i	0.327433	−	1.00773i	0.970330	−	0.241783i	$-0.0777321\pi$
$822$	2.09017	+	6.43288i	0.0729030	+	0.224373i
$823$	−19.7984	+	14.3844i	−0.690128	+	0.501407i	−0.876702	−	0.481034i	$-0.840262\pi$
$823$	−19.7984	+	14.3844i	−0.690128	+	0.501407i	0.186574	+	0.982441i	$0.440262\pi$
$824$	−30.9787			−1.07919
$825$	5.31966	−	8.97578i	0.185207	−	0.312497i
$826$	−6.76393			−0.235347
$827$	3.50000	−	2.54290i	0.121707	−	0.0884253i	−0.525267	−	0.850938i	$-0.676034\pi$
$827$	3.50000	−	2.54290i	0.121707	−	0.0884253i	0.646974	+	0.762512i	$0.276034\pi$
$828$	0.954915	+	2.93893i	0.0331856	+	0.102135i
$829$	8.94427	−	27.5276i	0.310647	−	0.956074i	−0.666862	−	0.745181i	$-0.732363\pi$
$829$	8.94427	−	27.5276i	0.310647	−	0.956074i	0.977509	−	0.210893i	$-0.0676371\pi$
$830$	−6.79837	−	4.93931i	−0.235975	−	0.171446i
$831$	−8.44427	−	6.13512i	−0.292929	−	0.212825i
$832$	−2.67376	+	8.22899i	−0.0926960	+	0.285289i
$833$	2.42705	+	7.46969i	0.0840923	+	0.258810i
$834$	−3.88197	+	2.82041i	−0.134421	+	0.0976629i
$835$	−23.3475			−0.807974
$836$	−7.97214	+	3.44095i	−0.275722	+	0.119008i
$837$	7.32624			0.253232
$838$	11.9443	−	8.67802i	0.412608	−	0.299777i
$839$	10.3262	+	31.7809i	0.356501	+	1.09720i	0.955134	+	0.296174i	$0.0957110\pi$
$839$	10.3262	+	31.7809i	0.356501	+	1.09720i	−0.598633	+	0.801024i	$0.704289\pi$
$840$	2.64590	−	8.14324i	0.0912922	−	0.280968i
$841$	20.2254	+	14.6946i	0.697428	+	0.506711i
$842$	−3.50000	−	2.54290i	−0.120618	−	0.0876341i
$843$	−0.326238	+	1.00406i	−0.0112362	+	0.0345816i
$844$	0.618034	+	1.90211i	0.0212736	+	0.0654734i
$845$	−26.4894	+	19.2456i	−0.911262	+	0.662070i
$846$	−2.00000			−0.0687614
$847$	−5.28115	−	9.64932i	−0.181463	−	0.331555i
$848$	−12.1803			−0.418275
$849$	10.8713	−	7.89848i	0.373103	−	0.271075i
$850$	−7.63525	−	23.4989i	−0.261887	−	0.806006i
$851$	11.5451	−	35.5321i	0.395760	−	1.21803i
$852$	−7.23607	−	5.25731i	−0.247904	−	0.180113i
$853$	12.7082	+	9.23305i	0.435121	+	0.316134i	0.783693	−	0.621148i	$-0.213333\pi$
$853$	12.7082	+	9.23305i	0.435121	+	0.316134i	−0.348573	+	0.937282i	$0.613333\pi$
$854$	−2.76393	+	8.50651i	−0.0945798	+	0.291087i
$855$	−2.30902	−	7.10642i	−0.0789667	−	0.243035i
$856$	−11.9164	+	8.65778i	−0.407294	+	0.295917i
$857$	−18.9443			−0.647124			−0.323562	−	0.946207i	$-0.604880\pi$
$857$	−18.9443			−0.647124			−0.323562	+	0.946207i	$0.604880\pi$
$858$	−3.76393	+	1.62460i	−0.128499	+	0.0554629i
$859$	−5.88854			−0.200915			−0.100457	−	0.994941i	$-0.532031\pi$
$859$	−5.88854			−0.200915			−0.100457	+	0.994941i	$0.532031\pi$
$860$	2.85410	−	2.07363i	0.0973241	−	0.0707101i
$861$	3.35410	+	10.3229i	0.114307	+	0.351802i
$862$	0.645898	−	1.98787i	0.0219994	−	0.0677071i
$863$	−30.4894	−	22.1518i	−1.03787	−	0.754057i	−0.0680012	−	0.997685i	$-0.521662\pi$
$863$	−30.4894	−	22.1518i	−1.03787	−	0.754057i	−0.969869	+	0.243629i	$0.921662\pi$
$864$	−4.04508	−	2.93893i	−0.137617	−	0.0999843i
$865$	−17.5106	+	53.8922i	−0.595380	+	1.83239i
$866$	5.32624	+	16.3925i	0.180993	+	0.557039i
$867$	36.1525	−	26.2663i	1.22780	−	0.892051i
$868$	7.32624			0.248669
$869$	23.6738	−	39.9444i	0.803077	−	1.35502i
$870$	5.70820			0.193526
$871$	8.00000	−	5.81234i	0.271070	−	0.196944i
$872$	9.79180	+	30.1360i	0.331592	+	1.02054i
$873$	−1.09017	+	3.35520i	−0.0368967	+	0.113556i
$874$	−6.54508	−	4.75528i	−0.221391	−	0.160850i
$875$	−4.28115	−	3.11044i	−0.144729	−	0.105152i
$876$	−1.61803	+	4.97980i	−0.0546683	+	0.168252i
$877$	−14.3262	−	44.0916i	−0.483763	−	1.48887i	−0.833765	−	0.552120i	$-0.813819\pi$
$877$	−14.3262	−	44.0916i	−0.483763	−	1.48887i	0.350002	−	0.936749i	$-0.386181\pi$
$878$	−17.6353	+	12.8128i	−0.595161	+	0.432410i
$879$	−19.7984			−0.667783
$880$	6.25329	+	7.10642i	0.210798	+	0.239557i
$881$	−33.4508			−1.12699			−0.563494	−	0.826120i	$-0.690543\pi$
$881$	−33.4508			−1.12699			−0.563494	+	0.826120i	$0.690543\pi$
$882$	0.809017	−	0.587785i	0.0272410	−	0.0197918i
$883$	2.38197	+	7.33094i	0.0801595	+	0.246706i	0.983103	−	0.183054i	$-0.0585983\pi$
$883$	2.38197	+	7.33094i	0.0801595	+	0.246706i	−0.902943	+	0.429760i	$0.858598\pi$
$884$	3.00000	−	9.23305i	0.100901	−	0.310541i
$885$	−15.6180	−	11.3472i	−0.524994	−	0.381431i
$886$	3.97214	+	2.88593i	0.133447	+	0.0969546i
$887$	−14.3820	+	44.2631i	−0.482899	+	1.48621i	0.352101	+	0.935962i	$0.385467\pi$
$887$	−14.3820	+	44.2631i	−0.482899	+	1.48621i	−0.835001	+	0.550249i	$0.814533\pi$
$888$	11.2082	+	34.4953i	0.376123	+	1.15759i
$889$	2.61803	−	1.90211i	0.0878060	−	0.0637948i
$890$	3.11146			0.104296
$891$	−0.309017	−	3.30220i	−0.0103525	−	0.110628i
$892$	−20.7984			−0.696381
$893$	−4.23607	+	3.07768i	−0.141755	+	0.102991i
$894$	−6.18034	−	19.0211i	−0.206701	−	0.636162i
$895$	−7.39261	+	22.7521i	−0.247108	+	0.760519i
$896$	−2.42705	−	1.76336i	−0.0810821	−	0.0589096i
$897$	3.09017	+	2.24514i	0.103178	+	0.0749630i
$898$	−12.9443	+	39.8384i	−0.431956	+	1.32942i
$899$	4.52786	+	13.9353i	0.151013	+	0.464769i
$900$	2.54508	−	1.84911i	0.0848362	−	0.0616371i
$901$	95.6656			3.18708
$902$	−35.1246	−	7.88597i	−1.16952	−	0.262574i
$903$	1.23607			0.0411338
$904$	−1.85410	+	1.34708i	−0.0616665	+	0.0448033i
$905$	16.7082	+	51.4226i	0.555399	+	1.70934i
$906$	−0.618034	+	1.90211i	−0.0205328	+	0.0631935i
$907$	38.2148	+	27.7647i	1.26890	+	0.921911i	0.999158	−	0.0410219i	$-0.0130613\pi$
$907$	38.2148	+	27.7647i	1.26890	+	0.921911i	0.269743	+	0.962932i	$0.413061\pi$
$908$	17.3262	+	12.5882i	0.574991	+	0.417756i
$909$	−0.645898	+	1.98787i	−0.0214231	+	0.0659335i
$910$	−1.09017	−	3.35520i	−0.0361388	−	0.111224i
$911$	8.94427	−	6.49839i	0.296337	−	0.215301i	−0.429675	−	0.902984i	$-0.641372\pi$
$911$	8.94427	−	6.49839i	0.296337	−	0.215301i	0.726012	+	0.687682i	$0.241372\pi$
$912$	2.61803			0.0866918
$913$	−9.52786	−	2.13914i	−0.315326	−	0.0707952i
$914$	−12.4721			−0.412542
$915$	−20.6525	+	15.0049i	−0.682750	+	0.496047i
$916$	−6.56231	−	20.1967i	−0.216825	−	0.667318i
$917$	0.708204	−	2.17963i	0.0233870	−	0.0719776i
$918$	−6.35410	−	4.61653i	−0.209717	−	0.152368i
$919$	−6.00000	−	4.35926i	−0.197922	−	0.143799i	0.484410	−	0.874841i	$-0.339034\pi$
$919$	−6.00000	−	4.35926i	−0.197922	−	0.143799i	−0.682332	+	0.731042i	$0.739034\pi$
$920$	8.17627	−	25.1640i	0.269564	−	0.829632i
$921$	7.50000	+	23.0826i	0.247133	+	0.760598i
$922$	−5.14590	+	3.73871i	−0.169471	+	0.123128i
$923$	−11.0557			−0.363904
$924$	−0.309017	−	3.30220i	−0.0101659	−	0.108634i
$925$	−38.0344			−1.25056
$926$	9.23607	−	6.71040i	0.303516	−	0.220517i
$927$	−3.19098	−	9.82084i	−0.104806	−	0.322559i
$928$	3.09017	−	9.51057i	0.101440	−	0.312200i
$929$	23.2984	+	16.9273i	0.764395	+	0.555365i	0.900255	−	0.435363i	$-0.143380\pi$
$929$	23.2984	+	16.9273i	0.764395	+	0.555365i	−0.135860	+	0.990728i	$0.543380\pi$
$930$	−16.9164	−	12.2905i	−0.554711	−	0.403021i
$931$	0.809017	−	2.48990i	0.0265145	−	0.0816031i
$932$	1.76393	+	5.42882i	0.0577795	+	0.177827i
$933$	−0.618034	+	0.449028i	−0.0202335	+	0.0147005i
$934$	−19.2361			−0.629423
$935$	−49.1140	−	55.8146i	−1.60620	−	1.82533i
$936$	−3.70820			−0.121206
$937$	−9.47214	+	6.88191i	−0.309441	+	0.224822i	−0.731657	−	0.681673i	$-0.761253\pi$
$937$	−9.47214	+	6.88191i	−0.309441	+	0.224822i	0.422215	+	0.906495i	$0.361253\pi$
$938$	−2.47214	−	7.60845i	−0.0807181	−	0.248425i
$939$	3.03444	−	9.33905i	0.0990253	−	0.304768i
$940$	−4.61803	−	3.35520i	−0.150624	−	0.109434i
$941$	9.59017	+	6.96767i	0.312631	+	0.227139i	0.733024	−	0.680202i	$-0.238108\pi$
$941$	9.59017	+	6.96767i	0.312631	+	0.227139i	−0.420394	+	0.907342i	$0.638108\pi$
$942$	3.00000	−	9.23305i	0.0977453	−	0.300829i
$943$	10.3647	+	31.8994i	0.337523	+	1.03879i
$944$	5.47214	−	3.97574i	0.178103	−	0.129399i
$945$	2.85410			0.0928439
$946$	−2.09017	+	3.52671i	−0.0679573	+	0.114663i
$947$	−23.4377			−0.761623			−0.380811	−	0.924653i	$-0.624355\pi$
$947$	−23.4377			−0.761623			−0.380811	+	0.924653i	$0.624355\pi$
$948$	11.3262	−	8.22899i	0.367859	−	0.267265i
$949$	2.00000	+	6.15537i	0.0649227	+	0.199812i
$950$	−2.54508	+	7.83297i	−0.0825735	+	0.254135i
$951$	−22.3262	−	16.2210i	−0.723978	−	0.526001i
$952$	−19.0623	−	13.8496i	−0.617813	−	0.448867i
$953$	1.49342	−	4.59628i	0.0483767	−	0.148888i	−0.923950	−	0.382513i	$-0.875059\pi$
$953$	1.49342	−	4.59628i	0.0483767	−	0.148888i	0.972327	+	0.233625i	$0.0750587\pi$
$954$	−3.76393	−	11.5842i	−0.121862	−	0.375052i
$955$	−42.1869	+	30.6506i	−1.36514	+	0.991830i
$956$	1.56231			0.0505286
$957$	6.09017	−	2.62866i	0.196867	−	0.0849724i
$958$	11.0557			0.357194
$959$	−5.47214	+	3.97574i	−0.176704	+	0.128383i
$960$	6.17376	+	19.0009i	0.199257	+	0.613251i
$961$	7.00658	−	21.5640i	0.226019	−	0.695614i
$962$	12.0902	+	8.78402i	0.389803	+	0.283208i
$963$	−3.97214	−	2.88593i	−0.128000	−	0.0929977i
$964$	−1.52786	+	4.70228i	−0.0492092	+	0.151450i
$965$	−16.2123	−	49.8962i	−0.521891	−	1.60622i
$966$	2.50000	−	1.81636i	0.0804362	−	0.0584403i
$967$	49.3050			1.58554			0.792770	−	0.609521i	$-0.208638\pi$
$967$	49.3050			1.58554			0.792770	+	0.609521i	$0.208638\pi$
$968$	29.8328	+	14.1068i	0.958863	+	0.453411i
$969$	−20.5623			−0.660556
$970$	8.14590	−	5.91834i	0.261549	−	0.190026i
$971$	13.0000	+	40.0099i	0.417190	+	1.28398i	0.910277	+	0.413999i	$0.135868\pi$
$971$	13.0000	+	40.0099i	0.417190	+	1.28398i	−0.493088	+	0.869980i	$0.664132\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−3.88197	−	2.82041i	−0.124450	−	0.0904183i
$974$	−31.7426	−	23.0624i	−1.01710	−	0.738966i
$975$	1.20163	−	3.69822i	0.0384828	−	0.118438i
$976$	−2.76393	−	8.50651i	−0.0884713	−	0.272287i
$977$	21.5066	−	15.6254i	0.688056	−	0.499902i	−0.187964	−	0.982176i	$-0.560189\pi$
$977$	21.5066	−	15.6254i	0.688056	−	0.499902i	0.876021	+	0.482274i	$0.160189\pi$
$978$	−5.41641			−0.173198
$979$	3.31966	−	1.43284i	0.106097	−	0.0457938i
$980$	2.85410			0.0911709
$981$	−8.54508	+	6.20837i	−0.272824	+	0.198218i
$982$	0.100813	+	0.310271i	0.00321707	+	0.00990114i
$983$	14.9787	−	46.0997i	0.477747	−	1.47035i	−0.364470	−	0.931215i	$-0.618750\pi$
$983$	14.9787	−	46.0997i	0.477747	−	1.47035i	0.842217	−	0.539138i	$-0.181250\pi$
$984$	−26.3435	−	19.1396i	−0.839799	−	0.610150i
$985$	9.23607	+	6.71040i	0.294286	+	0.213811i
$986$	4.85410	−	14.9394i	0.154586	−	0.475767i
$987$	−0.618034	−	1.90211i	−0.0196722	−	0.0605449i
$988$	−2.61803	+	1.90211i	−0.0832908	+	0.0605143i
$989$	3.81966			0.121458
$990$	−4.82624	+	8.14324i	−0.153388	+	0.258809i
$991$	18.6525			0.592515			0.296258	−	0.955108i	$-0.404261\pi$
$991$	18.6525			0.592515			0.296258	+	0.955108i	$0.404261\pi$
$992$	−29.6353	+	21.5313i	−0.940920	+	0.683619i
$993$	−9.38197	−	28.8747i	−0.297728	−	0.916312i
$994$	−2.76393	+	8.50651i	−0.0876666	+	0.269810i
$995$	−6.04508	−	4.39201i	−0.191642	−	0.139236i
$996$	−2.38197	−	1.73060i	−0.0754755	−	0.0548361i
$997$	−16.2361	+	49.9695i	−0.514201	+	1.58255i	0.270529	+	0.962712i	$0.412801\pi$
$997$	−16.2361	+	49.9695i	−0.514201	+	1.58255i	−0.784730	+	0.619837i	$0.787199\pi$
$998$	−8.09017	−	24.8990i	−0.256090	−	0.788164i
$999$	−9.78115	+	7.10642i	−0.309462	+	0.224837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.c.190.1	yes	4
3.2	odd	2		693.2.m.c.190.1		4
11.2	odd	10		2541.2.a.bd.1.1		2
11.4	even	5	inner	231.2.j.c.169.1	✓	4
11.9	even	5		2541.2.a.n.1.1		2
33.2	even	10		7623.2.a.w.1.2		2
33.20	odd	10		7623.2.a.bu.1.2		2
33.26	odd	10		693.2.m.c.631.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.169.1	✓	4	11.4	even	5	inner
231.2.j.c.190.1	yes	4	1.1	even	1	trivial
693.2.m.c.190.1		4	3.2	odd	2
693.2.m.c.631.1		4	33.26	odd	10
2541.2.a.n.1.1		2	11.9	even	5
2541.2.a.bd.1.1		2	11.2	odd	10
7623.2.a.w.1.2		2	33.2	even	10
7623.2.a.bu.1.2		2	33.20	odd	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.30902 + 1.67760i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.30902 + 1.67760i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.85410 q^{10} +(3.04508 - 1.31433i) q^{11} +1.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.881966 - 2.71441i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.35410 - 4.61653i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.809017 + 2.48990i) q^{19} +(-2.30902 + 1.67760i) q^{20} -1.00000 q^{21} +(1.69098 - 2.85317i) q^{22} -3.09017 q^{23} +(2.42705 - 1.76336i) q^{24} +(0.972136 + 2.99193i) q^{25} +(0.381966 - 1.17557i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-0.618034 + 1.90211i) q^{29} +(-0.881966 - 2.71441i) q^{30} +(5.92705 - 4.30625i) q^{31} -5.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -7.85410 q^{34} +(2.30902 - 1.67760i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(-3.73607 + 11.4984i) q^{37} +(2.11803 + 1.53884i) q^{38} +(-1.00000 - 0.726543i) q^{39} +(-2.64590 + 8.14324i) q^{40} +(-3.35410 - 10.3229i) q^{41} +(-0.809017 + 0.587785i) q^{42} -1.23607 q^{43} +(0.309017 + 3.30220i) q^{44} -2.85410 q^{45} +(-2.50000 + 1.81636i) q^{46} +(0.618034 + 1.90211i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.54508 + 1.84911i) q^{50} +(-2.42705 + 7.46969i) q^{51} +(0.381966 + 1.17557i) q^{52} +(-9.85410 + 7.15942i) q^{53} +1.00000 q^{54} +(9.23607 + 2.07363i) q^{55} +3.00000 q^{56} +(2.11803 - 1.53884i) q^{57} +(0.618034 + 1.90211i) q^{58} +(2.09017 - 6.43288i) q^{59} +(2.30902 + 1.67760i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(2.26393 - 6.96767i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-5.66312 + 4.11450i) q^{64} +3.52786 q^{65} +(-3.23607 - 0.726543i) q^{66} +8.00000 q^{67} +(6.35410 - 4.61653i) q^{68} +(0.954915 + 2.93893i) q^{69} +(0.881966 - 2.71441i) q^{70} +(-7.23607 - 5.25731i) q^{71} +(-2.42705 - 1.76336i) q^{72} +(-1.61803 + 4.97980i) q^{73} +(3.73607 + 11.4984i) q^{74} +(2.54508 - 1.84911i) q^{75} -2.61803 q^{76} +(-0.309017 - 3.30220i) q^{77} -1.23607 q^{78} +(11.3262 - 8.22899i) q^{79} +(0.881966 + 2.71441i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.78115 - 6.37988i) q^{82} +(-2.38197 - 1.73060i) q^{83} +(0.309017 - 0.951057i) q^{84} +(-6.92705 - 21.3193i) q^{85} +(-1.00000 + 0.726543i) q^{86} +2.00000 q^{87} +(6.57295 + 7.46969i) q^{88} +1.09017 q^{89} +(-2.30902 + 1.67760i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(0.954915 - 2.93893i) q^{92} +(-5.92705 - 4.30625i) q^{93} +(1.61803 + 1.17557i) q^{94} +(-2.30902 + 7.10642i) q^{95} +(1.54508 + 4.75528i) q^{96} +(2.85410 - 2.07363i) q^{97} -1.00000 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9} - 2 q^{10} + q^{11} + 4 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + q^{16} - 12 q^{17} + q^{18} + q^{19} - 7 q^{20} - 4 q^{21} + 9 q^{22} + 10 q^{23} + 3 q^{24} - 14 q^{25} + 6 q^{26} + q^{27} + q^{28} + 2 q^{29} - 8 q^{30} + 17 q^{31} - 20 q^{32} - 11 q^{33} - 18 q^{34} + 7 q^{35} + q^{36} - 6 q^{37} + 4 q^{38} - 4 q^{39} - 24 q^{40} - q^{42} + 4 q^{43} - q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 3 q^{51} + 6 q^{52} - 26 q^{53} + 4 q^{54} + 28 q^{55} + 12 q^{56} + 4 q^{57} - 2 q^{58} - 14 q^{59} + 7 q^{60} - 20 q^{61} + 18 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} - 4 q^{66} + 32 q^{67} + 12 q^{68} + 15 q^{69} + 8 q^{70} - 20 q^{71} - 3 q^{72} - 2 q^{73} + 6 q^{74} - q^{75} - 6 q^{76} + q^{77} + 4 q^{78} + 14 q^{79} + 8 q^{80} - q^{81} - 15 q^{82} - 14 q^{83} - q^{84} - 21 q^{85} - 4 q^{86} + 8 q^{87} + 33 q^{88} - 18 q^{89} - 7 q^{90} - 6 q^{91} + 15 q^{92} - 17 q^{93} + 2 q^{94} - 7 q^{95} - 5 q^{96} - 2 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9 - 2 * q^10 + q^11 + 4 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + q^16 - 12 * q^17 + q^18 + q^19 - 7 * q^20 - 4 * q^21 + 9 * q^22 + 10 * q^23 + 3 * q^24 - 14 * q^25 + 6 * q^26 + q^27 + q^28 + 2 * q^29 - 8 * q^30 + 17 * q^31 - 20 * q^32 - 11 * q^33 - 18 * q^34 + 7 * q^35 + q^36 - 6 * q^37 + 4 * q^38 - 4 * q^39 - 24 * q^40 - q^42 + 4 * q^43 - q^44 + 2 * q^45 - 10 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 3 * q^51 + 6 * q^52 - 26 * q^53 + 4 * q^54 + 28 * q^55 + 12 * q^56 + 4 * q^57 - 2 * q^58 - 14 * q^59 + 7 * q^60 - 20 * q^61 + 18 * q^62 - q^63 - 7 * q^64 + 32 * q^65 - 4 * q^66 + 32 * q^67 + 12 * q^68 + 15 * q^69 + 8 * q^70 - 20 * q^71 - 3 * q^72 - 2 * q^73 + 6 * q^74 - q^75 - 6 * q^76 + q^77 + 4 * q^78 + 14 * q^79 + 8 * q^80 - q^81 - 15 * q^82 - 14 * q^83 - q^84 - 21 * q^85 - 4 * q^86 + 8 * q^87 + 33 * q^88 - 18 * q^89 - 7 * q^90 - 6 * q^91 + 15 * q^92 - 17 * q^93 + 2 * q^94 - 7 * q^95 - 5 * q^96 - 2 * q^97 - 4 * q^98 - 9 * q^99

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