LMFDB - Embedded newform 231.2.j.e.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:	$\Z[a_1, a_2, a_3]$
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.e.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 - 1.31433i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.80902 - 1.31433i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.61803 q^{10} +(0.809017 + 3.21644i) q^{11} -3.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.690983 - 2.12663i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.50000 + 1.08981i) q^{17} +(-0.690983 + 2.12663i) q^{18} +(-1.19098 - 3.66547i) q^{19} +(-3.92705 + 2.85317i) q^{20} -1.00000 q^{21} +(5.69098 + 4.75528i) q^{22} +6.61803 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(0.854102 - 2.62866i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.42705 - 1.76336i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(1.11803 + 3.44095i) q^{30} +(-6.54508 + 4.75528i) q^{31} +6.70820 q^{32} +(2.80902 - 1.76336i) q^{33} +4.14590 q^{34} +(-1.30902 + 0.951057i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.736068 - 2.26538i) q^{37} +(-6.97214 - 5.06555i) q^{38} +(-1.00000 - 0.726543i) q^{39} +(-1.11803 + 3.44095i) q^{40} +(2.97214 + 9.14729i) q^{41} +(-1.80902 + 1.31433i) q^{42} -3.70820 q^{43} +(9.92705 + 0.673542i) q^{44} +1.61803 q^{45} +(11.9721 - 8.69827i) q^{46} +(-1.38197 - 4.25325i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-4.30902 - 3.13068i) q^{50} +(0.572949 - 1.76336i) q^{51} +(-1.14590 - 3.52671i) q^{52} +(-9.09017 + 6.60440i) q^{53} +2.23607 q^{54} +(2.00000 - 4.97980i) q^{55} -2.23607 q^{56} +(-3.11803 + 2.26538i) q^{57} +(4.14590 + 12.7598i) q^{58} +(-0.381966 + 1.17557i) q^{59} +(3.92705 + 2.85317i) q^{60} +(-5.59017 + 17.2048i) q^{62} +(0.309017 + 0.951057i) q^{63} +(10.5172 - 7.64121i) q^{64} -2.00000 q^{65} +(2.76393 - 6.88191i) q^{66} +(4.50000 - 3.26944i) q^{68} +(-2.04508 - 6.29412i) q^{69} +(-1.11803 + 3.44095i) q^{70} +(-10.4721 - 7.60845i) q^{71} +(1.80902 + 1.31433i) q^{72} +(0.0901699 - 0.277515i) q^{73} +(-1.64590 - 5.06555i) q^{74} +(-1.92705 + 1.40008i) q^{75} -11.5623 q^{76} +(3.30902 + 0.224514i) q^{77} -2.76393 q^{78} +(8.09017 - 5.87785i) q^{79} +(-0.500000 - 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(17.3992 + 12.6412i) q^{82} +(-6.09017 - 4.42477i) q^{83} +(-0.927051 + 2.85317i) q^{84} +(-0.927051 - 2.85317i) q^{85} +(-6.70820 + 4.87380i) q^{86} +6.00000 q^{87} +(6.28115 - 3.94298i) q^{88} +3.38197 q^{89} +(2.92705 - 2.12663i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(6.13525 - 18.8824i) q^{92} +(6.54508 + 4.75528i) q^{93} +(-8.09017 - 5.87785i) q^{94} +(-1.92705 + 5.93085i) q^{95} +(-2.07295 - 6.37988i) q^{96} +(4.85410 - 3.52671i) q^{97} -2.23607 q^{98} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9	$ 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9} - 10 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - 5 q^{18} - 7 q^{19} - 9 q^{20} - 4 q^{21} + 25 q^{22} + 22 q^{23} - 5 q^{24} + 6 q^{25} - 10 q^{26} + q^{27} - 3 q^{28} + 6 q^{29} - 15 q^{31} + 9 q^{33} + 30 q^{34} - 3 q^{35} - 3 q^{36} - 6 q^{37} - 10 q^{38} - 4 q^{39} - 6 q^{41} - 5 q^{42} + 12 q^{43} + 33 q^{44} + 2 q^{45} + 30 q^{46} - 10 q^{47} - q^{48} - q^{49} - 15 q^{50} + 9 q^{51} - 18 q^{52} - 14 q^{53} + 8 q^{55} - 8 q^{57} + 30 q^{58} - 6 q^{59} + 9 q^{60} - q^{63} + 13 q^{64} - 8 q^{65} + 20 q^{66} + 18 q^{68} + 3 q^{69} - 24 q^{71} + 5 q^{72} - 22 q^{73} - 20 q^{74} - q^{75} - 6 q^{76} + 11 q^{77} - 20 q^{78} + 10 q^{79} - 2 q^{80} - q^{81} + 45 q^{82} - 2 q^{83} + 3 q^{84} + 3 q^{85} + 24 q^{87} + 5 q^{88} + 18 q^{89} + 5 q^{90} - 6 q^{91} - 9 q^{92} + 15 q^{93} - 10 q^{94} - q^{95} - 15 q^{96} + 6 q^{97} + q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9 - 10 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 + q^16 + 6 * q^17 - 5 * q^18 - 7 * q^19 - 9 * q^20 - 4 * q^21 + 25 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 - 10 * q^26 + q^27 - 3 * q^28 + 6 * q^29 - 15 * q^31 + 9 * q^33 + 30 * q^34 - 3 * q^35 - 3 * q^36 - 6 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^41 - 5 * q^42 + 12 * q^43 + 33 * q^44 + 2 * q^45 + 30 * q^46 - 10 * q^47 - q^48 - q^49 - 15 * q^50 + 9 * q^51 - 18 * q^52 - 14 * q^53 + 8 * q^55 - 8 * q^57 + 30 * q^58 - 6 * q^59 + 9 * q^60 - q^63 + 13 * q^64 - 8 * q^65 + 20 * q^66 + 18 * q^68 + 3 * q^69 - 24 * q^71 + 5 * q^72 - 22 * q^73 - 20 * q^74 - q^75 - 6 * q^76 + 11 * q^77 - 20 * q^78 + 10 * q^79 - 2 * q^80 - q^81 + 45 * q^82 - 2 * q^83 + 3 * q^84 + 3 * q^85 + 24 * q^87 + 5 * q^88 + 18 * q^89 + 5 * q^90 - 6 * q^91 - 9 * q^92 + 15 * q^93 - 10 * q^94 - q^95 - 15 * q^96 + 6 * q^97 + 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 $

$2$	1.80902	−	1.31433i	1.27917	−	0.929370i	0.279641	−	0.960105i	$-0.409785\pi$
$2$	1.80902	−	1.31433i	1.27917	−	0.929370i	0.999528	+	0.0307347i	$0.00978469\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.927051	−	2.85317i	0.463525	−	1.42658i
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	0.255260	−	0.966872i	$-0.417839\pi$
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	−0.840670	+	0.541547i	$0.817839\pi$
$6$	−1.80902	−	1.31433i	−0.738528	−	0.536572i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−3.61803			−1.14412
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$11$	0.809017	+	3.21644i	0.243928	+	0.969793i
$12$	−3.00000			−0.866025
$13$	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	$0.245167\pi$
$14$	−0.690983	−	2.12663i	−0.184673	−	0.568365i
$15$	−0.500000	+	1.53884i	−0.129099	+	0.397327i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	0.754637	−	0.656143i	$-0.227813\pi$
$17$	1.50000	+	1.08981i	0.363803	+	0.264319i	−0.390833	+	0.920461i	$0.627813\pi$
$18$	−0.690983	+	2.12663i	−0.162866	+	0.501251i
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	−0.989682	−	0.143280i	$-0.954235\pi$
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	0.716452	−	0.697636i	$-0.245765\pi$
$20$	−3.92705	+	2.85317i	−0.878115	+	0.637988i
$21$	−1.00000			−0.218218
$22$	5.69098	+	4.75528i	1.21332	+	1.01383i
$23$	6.61803			1.37996			0.689978	−	0.723831i	$-0.257620\pi$
$23$	6.61803			1.37996			0.689978	+	0.723831i	$0.257620\pi$
$24$	−1.80902	+	1.31433i	−0.369264	+	0.268286i
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$	0.854102	−	2.62866i	0.167503	−	0.515522i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.42705	−	1.76336i	−0.458670	−	0.333243i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$	1.11803	+	3.44095i	0.204124	+	0.628230i
$31$	−6.54508	+	4.75528i	−1.17553	+	0.854074i	−0.991661	−	0.128876i	$-0.958863\pi$
$31$	−6.54508	+	4.75528i	−1.17553	+	0.854074i	−0.183871	+	0.982950i	$0.558863\pi$
$32$	6.70820			1.18585
$33$	2.80902	−	1.76336i	0.488987	−	0.306961i
$34$	4.14590			0.711016
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$	0.927051	+	2.85317i	0.154508	+	0.475528i
$37$	0.736068	−	2.26538i	0.121009	−	0.372427i	−0.872144	−	0.489249i	$-0.837271\pi$
$37$	0.736068	−	2.26538i	0.121009	−	0.372427i	0.993153	+	0.116822i	$0.0372708\pi$
$38$	−6.97214	−	5.06555i	−1.13103	−	0.821741i
$39$	−1.00000	−	0.726543i	−0.160128	−	0.116340i
$40$	−1.11803	+	3.44095i	−0.176777	+	0.544063i
$41$	2.97214	+	9.14729i	0.464170	+	1.42857i	0.860024	+	0.510254i	$0.170449\pi$
$41$	2.97214	+	9.14729i	0.464170	+	1.42857i	−0.395854	+	0.918313i	$0.629551\pi$
$42$	−1.80902	+	1.31433i	−0.279137	+	0.202805i
$43$	−3.70820			−0.565496			−0.282748	−	0.959194i	$-0.591246\pi$
$43$	−3.70820			−0.565496			−0.282748	+	0.959194i	$0.591246\pi$
$44$	9.92705	+	0.673542i	1.49656	+	0.101540i
$45$	1.61803			0.241202
$46$	11.9721	−	8.69827i	1.76520	−	1.28249i
$47$	−1.38197	−	4.25325i	−0.201580	−	0.620401i	−0.999836	−	0.0180826i	$-0.994244\pi$
$47$	−1.38197	−	4.25325i	−0.201580	−	0.620401i	0.798256	−	0.602318i	$-0.205756\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−4.30902	−	3.13068i	−0.609387	−	0.442746i
$51$	0.572949	−	1.76336i	0.0802289	−	0.246919i
$52$	−1.14590	−	3.52671i	−0.158907	−	0.489067i
$53$	−9.09017	+	6.60440i	−1.24863	+	0.907183i	−0.998142	−	0.0609360i	$-0.980591\pi$
$53$	−9.09017	+	6.60440i	−1.24863	+	0.907183i	−0.250489	+	0.968119i	$0.580591\pi$
$54$	2.23607			0.304290
$55$	2.00000	−	4.97980i	0.269680	−	0.671476i
$56$	−2.23607			−0.298807
$57$	−3.11803	+	2.26538i	−0.412994	+	0.300057i
$58$	4.14590	+	12.7598i	0.544383	+	1.67544i
$59$	−0.381966	+	1.17557i	−0.0497277	+	0.153046i	−0.972837	−	0.231492i	$-0.925639\pi$
$59$	−0.381966	+	1.17557i	−0.0497277	+	0.153046i	0.923109	+	0.384538i	$0.125639\pi$
$60$	3.92705	+	2.85317i	0.506980	+	0.368343i
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	−5.59017	+	17.2048i	−0.709952	+	2.18501i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	10.5172	−	7.64121i	1.31465	−	0.955151i
$65$	−2.00000			−0.248069
$66$	2.76393	−	6.88191i	0.340217	−	0.847105i
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	4.50000	−	3.26944i	0.545705	−	0.396478i
$69$	−2.04508	−	6.29412i	−0.246199	−	0.757724i
$70$	−1.11803	+	3.44095i	−0.133631	+	0.411273i
$71$	−10.4721	−	7.60845i	−1.24281	−	0.902957i	−0.245031	−	0.969515i	$-0.578798\pi$
$71$	−10.4721	−	7.60845i	−1.24281	−	0.902957i	−0.997783	+	0.0665580i	$0.978798\pi$
$72$	1.80902	+	1.31433i	0.213195	+	0.154895i
$73$	0.0901699	−	0.277515i	0.0105536	−	0.0324806i	−0.945641	−	0.325212i	$-0.894564\pi$
$73$	0.0901699	−	0.277515i	0.0105536	−	0.0324806i	0.956195	+	0.292732i	$0.0945643\pi$
$74$	−1.64590	−	5.06555i	−0.191332	−	0.588859i
$75$	−1.92705	+	1.40008i	−0.222517	+	0.161668i
$76$	−11.5623			−1.32629
$77$	3.30902	+	0.224514i	0.377097	+	0.0255857i
$78$	−2.76393			−0.312954
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	0.941069	+	0.338214i	$0.109823\pi$
$80$	−0.500000	−	1.53884i	−0.0559017	−	0.172048i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	17.3992	+	12.6412i	1.92142	+	1.39599i
$83$	−6.09017	−	4.42477i	−0.668483	−	0.485681i	0.201034	−	0.979584i	$-0.435570\pi$
$83$	−6.09017	−	4.42477i	−0.668483	−	0.485681i	−0.869517	+	0.493903i	$0.835570\pi$
$84$	−0.927051	+	2.85317i	−0.101150	+	0.311306i
$85$	−0.927051	−	2.85317i	−0.100553	−	0.309470i
$86$	−6.70820	+	4.87380i	−0.723364	+	0.525555i
$87$	6.00000			0.643268
$88$	6.28115	−	3.94298i	0.669573	−	0.420323i
$89$	3.38197			0.358488			0.179244	−	0.983805i	$-0.442635\pi$
$89$	3.38197			0.358488			0.179244	+	0.983805i	$0.442635\pi$
$90$	2.92705	−	2.12663i	0.308538	−	0.224166i
$91$	−0.381966	−	1.17557i	−0.0400409	−	0.123233i
$92$	6.13525	−	18.8824i	0.639645	−	1.96862i
$93$	6.54508	+	4.75528i	0.678694	+	0.493100i
$94$	−8.09017	−	5.87785i	−0.834437	−	0.606254i
$95$	−1.92705	+	5.93085i	−0.197711	+	0.608493i
$96$	−2.07295	−	6.37988i	−0.211569	−	0.651144i
$97$	4.85410	−	3.52671i	0.492859	−	0.358083i	−0.313423	−	0.949613i	$-0.601476\pi$
$97$	4.85410	−	3.52671i	0.492859	−	0.358083i	0.806283	+	0.591530i	$0.201476\pi$
$98$	−2.23607			−0.225877
$99$	−2.54508	−	2.12663i	−0.255791	−	0.213734i
$100$	−7.14590			−0.714590
$101$	−14.3992	+	10.4616i	−1.43277	+	1.04097i	−0.443281	+	0.896383i	$0.646185\pi$
$101$	−14.3992	+	10.4616i	−1.43277	+	1.04097i	−0.989492	+	0.144587i	$0.953815\pi$
$102$	−1.28115	−	3.94298i	−0.126853	−	0.390414i
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	0.455631	+	0.890169i	$0.349414\pi$
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	−0.891841	+	0.452348i	$0.850586\pi$
$104$	−2.23607	−	1.62460i	−0.219265	−	0.159305i
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$	−7.76393	+	23.8949i	−0.754100	+	2.32088i
$107$	−2.71885	−	8.36775i	−0.262841	−	0.808941i	−0.992183	−	0.124792i	$-0.960174\pi$
$107$	−2.71885	−	8.36775i	−0.262841	−	0.808941i	0.729342	−	0.684149i	$-0.239826\pi$
$108$	2.42705	−	1.76336i	0.233543	−	0.169679i
$109$	2.56231			0.245424			0.122712	−	0.992442i	$-0.460841\pi$
$109$	2.56231			0.245424			0.122712	+	0.992442i	$0.460841\pi$
$110$	−2.92705	−	11.6372i	−0.279083	−	1.10956i
$111$	−2.38197			−0.226086
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	−0.236068	−	0.726543i	−0.0222074	−	0.0683474i	0.939339	−	0.342991i	$-0.111440\pi$
$113$	−0.236068	−	0.726543i	−0.0222074	−	0.0683474i	−0.961546	+	0.274644i	$0.911440\pi$
$114$	−2.66312	+	8.19624i	−0.249424	+	0.767648i
$115$	−8.66312	−	6.29412i	−0.807840	−	0.586930i
$116$	14.5623	+	10.5801i	1.35208	+	0.982341i
$117$	−0.381966	+	1.17557i	−0.0353128	+	0.108682i
$118$	0.854102	+	2.62866i	0.0786265	+	0.241987i
$119$	1.50000	−	1.08981i	0.137505	−	0.0999031i
$120$	3.61803			0.330280
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$		0			0
$123$	7.78115	−	5.65334i	0.701603	−	0.509744i
$124$	7.50000	+	23.0826i	0.673520	+	2.07288i
$125$	−3.69098	+	11.3597i	−0.330132	+	1.01604i
$126$	1.80902	+	1.31433i	0.161160	+	0.117090i
$127$	−11.0902	−	8.05748i	−0.984093	−	0.714986i	−0.0254737	−	0.999675i	$-0.508109\pi$
$127$	−11.0902	−	8.05748i	−0.984093	−	0.714986i	−0.958620	+	0.284690i	$0.908109\pi$
$128$	4.83688	−	14.8864i	0.427524	−	1.31578i
$129$	1.14590	+	3.52671i	0.100891	+	0.310510i
$130$	−3.61803	+	2.62866i	−0.317323	+	0.230548i
$131$	14.6525			1.28019			0.640096	−	0.768295i	$-0.278894\pi$
$131$	14.6525			1.28019			0.640096	+	0.768295i	$0.278894\pi$
$132$	−2.42705	−	9.64932i	−0.211248	−	0.839866i
$133$	−3.85410			−0.334193
$134$		0			0
$135$	−0.500000	−	1.53884i	−0.0430331	−	0.132442i
$136$	1.28115	−	3.94298i	0.109858	−	0.338108i
$137$	11.4721	+	8.33499i	0.980131	+	0.712107i	0.957738	−	0.287643i	$-0.0928715\pi$
$137$	11.4721	+	8.33499i	0.980131	+	0.712107i	0.0223929	+	0.999749i	$0.492872\pi$
$138$	−11.9721	−	8.69827i	−1.01914	−	0.740446i
$139$	6.13525	−	18.8824i	0.520386	−	1.60158i	−0.252879	−	0.967498i	$-0.581377\pi$
$139$	6.13525	−	18.8824i	0.520386	−	1.60158i	0.773264	−	0.634084i	$-0.218623\pi$
$140$	1.50000	+	4.61653i	0.126773	+	0.390168i
$141$	−3.61803	+	2.62866i	−0.304693	+	0.221373i
$142$	−28.9443			−2.42895
$143$	3.14590	+	2.62866i	0.263073	+	0.219819i
$144$	−1.00000			−0.0833333
$145$	7.85410	−	5.70634i	0.652248	−	0.473886i
$146$	−0.201626	−	0.620541i	−0.0166867	−	0.0513564i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	−5.78115	−	4.20025i	−0.475208	−	0.345259i
$149$	−10.4721	−	7.60845i	−0.857911	−	0.623309i	0.0694050	−	0.997589i	$-0.477890\pi$
$149$	−10.4721	−	7.60845i	−0.857911	−	0.623309i	−0.927316	+	0.374280i	$0.877890\pi$
$150$	−1.64590	+	5.06555i	−0.134387	+	0.413601i
$151$	−7.56231	−	23.2744i	−0.615412	−	1.89404i	−0.395223	−	0.918585i	$-0.629333\pi$
$151$	−7.56231	−	23.2744i	−0.615412	−	1.89404i	−0.220189	−	0.975457i	$-0.570667\pi$
$152$	−6.97214	+	5.06555i	−0.565515	+	0.410871i
$153$	−1.85410			−0.149895
$154$	6.28115	−	3.94298i	0.506150	−	0.317735i
$155$	13.0902			1.05143
$156$	−3.00000	+	2.17963i	−0.240192	+	0.174510i
$157$	5.29180	+	16.2865i	0.422331	+	1.29980i	0.905527	+	0.424290i	$0.139476\pi$
$157$	5.29180	+	16.2865i	0.422331	+	1.29980i	−0.483195	+	0.875513i	$0.660524\pi$
$158$	6.90983	−	21.2663i	0.549717	−	1.69185i
$159$	9.09017	+	6.60440i	0.720897	+	0.523763i
$160$	−8.78115	−	6.37988i	−0.694211	−	0.504374i
$161$	2.04508	−	6.29412i	0.161175	−	0.496046i
$162$	−0.690983	−	2.12663i	−0.0542888	−	0.167084i
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	−0.223999	−	0.974589i	$-0.571911\pi$
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	0.857670	+	0.514200i	$0.171911\pi$
$164$	28.8541			2.25313
$165$	−5.35410	−	0.363271i	−0.416816	−	0.0282806i
$166$	−16.8328			−1.30648
$167$	13.5623	−	9.85359i	1.04948	−	0.762494i	0.0773687	−	0.997003i	$-0.475348\pi$
$167$	13.5623	−	9.85359i	1.04948	−	0.762494i	0.972114	+	0.234509i	$0.0753481\pi$
$168$	0.690983	+	2.12663i	0.0533105	+	0.164073i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	−5.42705	−	3.94298i	−0.416236	−	0.302413i
$171$	3.11803	+	2.26538i	0.238442	+	0.173238i
$172$	−3.43769	+	10.5801i	−0.262122	+	0.806728i
$173$	−3.51722	−	10.8249i	−0.267409	−	0.823001i	−0.991129	−	0.132907i	$-0.957569\pi$
$173$	−3.51722	−	10.8249i	−0.267409	−	0.823001i	0.723719	−	0.690095i	$-0.242431\pi$
$174$	10.8541	−	7.88597i	0.822847	−	0.597834i
$175$	−2.38197			−0.180060
$176$	−1.23607	+	3.07768i	−0.0931721	+	0.231989i
$177$	1.23607			0.0929086
$178$	6.11803	−	4.44501i	0.458566	−	0.333168i
$179$	3.02786	+	9.31881i	0.226313	+	0.696520i	0.998156	+	0.0607066i	$0.0193354\pi$
$179$	3.02786	+	9.31881i	0.226313	+	0.696520i	−0.771842	+	0.635814i	$0.780665\pi$
$180$	1.50000	−	4.61653i	0.111803	−	0.344095i
$181$	−12.8541	−	9.33905i	−0.955438	−	0.694166i	−0.00335114	−	0.999994i	$-0.501067\pi$
$181$	−12.8541	−	9.33905i	−0.955438	−	0.694166i	−0.952087	+	0.305828i	$0.901067\pi$
$182$	−2.23607	−	1.62460i	−0.165748	−	0.120423i
$183$		0			0
$184$	−4.57295	−	14.0741i	−0.337122	−	1.03756i
$185$	−3.11803	+	2.26538i	−0.229242	+	0.166554i
$186$	18.0902			1.32644
$187$	−2.29180	+	5.70634i	−0.167593	+	0.417289i
$188$	−13.4164			−0.978492
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	4.30902	+	13.2618i	0.312609	+	0.962111i
$191$	4.97214	−	15.3027i	0.359771	−	1.10726i	−0.593420	−	0.804893i	$-0.702223\pi$
$191$	4.97214	−	15.3027i	0.359771	−	1.10726i	0.953191	−	0.302369i	$-0.0977774\pi$
$192$	−10.5172	−	7.64121i	−0.759015	−	0.551457i
$193$	12.2533	+	8.90254i	0.882011	+	0.640819i	0.933783	−	0.357840i	$-0.116487\pi$
$193$	12.2533	+	8.90254i	0.882011	+	0.640819i	−0.0517717	+	0.998659i	$0.516487\pi$
$194$	4.14590	−	12.7598i	0.297658	−	0.916098i
$195$	0.618034	+	1.90211i	0.0442583	+	0.136213i
$196$	−2.42705	+	1.76336i	−0.173361	+	0.125954i
$197$	13.5279			0.963820			0.481910	−	0.876221i	$-0.339943\pi$
$197$	13.5279			0.963820			0.481910	+	0.876221i	$0.339943\pi$
$198$	−7.39919	−	0.502029i	−0.525837	−	0.0356776i
$199$	19.8541			1.40742			0.703710	−	0.710487i	$-0.251525\pi$
$199$	19.8541			1.40742			0.703710	+	0.710487i	$0.251525\pi$
$200$	−4.30902	+	3.13068i	−0.304694	+	0.221373i
$201$		0			0
$202$	−12.2984	+	37.8505i	−0.865311	+	2.66315i
$203$	4.85410	+	3.52671i	0.340691	+	0.247527i
$204$	−4.50000	−	3.26944i	−0.315063	−	0.228907i
$205$	4.80902	−	14.8006i	0.335876	−	1.03372i
$206$	9.89919	+	30.4666i	0.689709	+	2.12271i
$207$	−5.35410	+	3.88998i	−0.372136	+	0.270372i
$208$	1.23607			0.0857059
$209$	10.8262	−	6.79615i	0.748867	−	0.470100i
$210$	3.61803			0.249668
$211$	−21.3262	+	15.4944i	−1.46816	+	1.06668i	−0.487017	+	0.873393i	$0.661915\pi$
$211$	−21.3262	+	15.4944i	−1.46816	+	1.06668i	−0.981142	+	0.193287i	$0.938085\pi$
$212$	10.4164	+	32.0584i	0.715402	+	2.20178i
$213$	−4.00000	+	12.3107i	−0.274075	+	0.843518i
$214$	−15.9164	−	11.5639i	−1.08802	−	0.790495i
$215$	4.85410	+	3.52671i	0.331047	+	0.240520i
$216$	0.690983	−	2.12663i	0.0470154	−	0.144699i
$217$	2.50000	+	7.69421i	0.169711	+	0.522317i
$218$	4.63525	−	3.36771i	0.313939	−	0.228090i
$219$	−0.291796			−0.0197178
$220$	−12.3541	−	10.3229i	−0.832913	−	0.695967i
$221$	2.29180			0.154163
$222$	−4.30902	+	3.13068i	−0.289202	+	0.210118i
$223$	5.37132	+	16.5312i	0.359690	+	1.10701i	0.953240	+	0.302216i	$0.0977262\pi$
$223$	5.37132	+	16.5312i	0.359690	+	1.10701i	−0.593549	+	0.804798i	$0.702274\pi$
$224$	2.07295	−	6.37988i	0.138505	−	0.426274i
$225$	1.92705	+	1.40008i	0.128470	+	0.0933390i
$226$	−1.38197	−	1.00406i	−0.0919270	−	0.0667889i
$227$	1.09017	−	3.35520i	0.0723571	−	0.222692i	−0.908337	−	0.418238i	$-0.862648\pi$
$227$	1.09017	−	3.35520i	0.0723571	−	0.222692i	0.980695	+	0.195546i	$0.0626478\pi$
$228$	3.57295	+	10.9964i	0.236624	+	0.728255i
$229$	5.00000	−	3.63271i	0.330409	−	0.240056i	−0.410195	−	0.911998i	$-0.634539\pi$
$229$	5.00000	−	3.63271i	0.330409	−	0.240056i	0.740604	+	0.671941i	$0.234539\pi$
$230$	−23.9443			−1.57884
$231$	−0.809017	−	3.21644i	−0.0532294	−	0.211626i
$232$	13.4164			0.880830
$233$	1.85410	−	1.34708i	0.121466	−	0.0882504i	−0.525394	−	0.850859i	$-0.676082\pi$
$233$	1.85410	−	1.34708i	0.121466	−	0.0882504i	0.646860	+	0.762609i	$0.276082\pi$
$234$	0.854102	+	2.62866i	0.0558344	+	0.171841i
$235$	−2.23607	+	6.88191i	−0.145865	+	0.448926i
$236$	3.00000	+	2.17963i	0.195283	+	0.141882i
$237$	−8.09017	−	5.87785i	−0.525513	−	0.381808i
$238$	1.28115	−	3.94298i	0.0830448	−	0.255586i
$239$	3.10081	+	9.54332i	0.200575	+	0.617306i	0.999866	+	0.0163622i	$0.00520850\pi$
$239$	3.10081	+	9.54332i	0.200575	+	0.617306i	−0.799291	+	0.600944i	$0.794792\pi$
$240$	−1.30902	+	0.951057i	−0.0844967	+	0.0613904i
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$	−10.6910	+	22.1518i	−0.687242	+	1.42397i
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.500000	+	1.53884i	0.0319438	+	0.0983130i
$246$	6.64590	−	20.4540i	0.423727	−	1.30410i
$247$	−3.85410	−	2.80017i	−0.245231	−	0.178170i
$248$	14.6353	+	10.6331i	0.929340	+	0.675205i
$249$	−2.32624	+	7.15942i	−0.147419	+	0.453710i
$250$	8.25329	+	25.4010i	0.521984	+	1.60650i
$251$	−11.5623	+	8.40051i	−0.729806	+	0.530235i	−0.889502	−	0.456931i	$-0.848949\pi$
$251$	−11.5623	+	8.40051i	−0.729806	+	0.530235i	0.159696	+	0.987166i	$0.448949\pi$
$252$	3.00000			0.188982
$253$	5.35410	+	21.2865i	0.336610	+	1.33827i
$254$	−30.6525			−1.92331
$255$	−2.42705	+	1.76336i	−0.151988	+	0.110426i
$256$	−2.78115	−	8.55951i	−0.173822	−	0.534969i
$257$	−9.71885	+	29.9115i	−0.606245	+	1.86583i	−0.118250	+	0.992984i	$0.537728\pi$
$257$	−9.71885	+	29.9115i	−0.606245	+	1.86583i	−0.487995	+	0.872846i	$0.662272\pi$
$258$	6.70820	+	4.87380i	0.417635	+	0.303429i
$259$	−1.92705	−	1.40008i	−0.119741	−	0.0869970i
$260$	−1.85410	+	5.70634i	−0.114987	+	0.353892i
$261$	−1.85410	−	5.70634i	−0.114766	−	0.353214i
$262$	26.5066	−	19.2582i	1.63758	−	1.18977i
$263$	4.14590			0.255647			0.127824	−	0.991797i	$-0.459201\pi$
$263$	4.14590			0.255647			0.127824	+	0.991797i	$0.459201\pi$
$264$	−5.69098	−	4.75528i	−0.350256	−	0.292667i
$265$	18.1803			1.11681
$266$	−6.97214	+	5.06555i	−0.427489	+	0.310589i
$267$	−1.04508	−	3.21644i	−0.0639582	−	0.196843i
$268$		0			0
$269$	−10.8541	−	7.88597i	−0.661786	−	0.480816i	0.205479	−	0.978661i	$-0.434125\pi$
$269$	−10.8541	−	7.88597i	−0.661786	−	0.480816i	−0.867266	+	0.497846i	$0.834125\pi$
$270$	−2.92705	−	2.12663i	−0.178135	−	0.129422i
$271$	4.79180	−	14.7476i	0.291081	−	0.895855i	−0.693429	−	0.720525i	$-0.743901\pi$
$271$	4.79180	−	14.7476i	0.291081	−	0.895855i	0.984510	−	0.175330i	$-0.0560992\pi$
$272$	0.572949	+	1.76336i	0.0347401	+	0.106919i
$273$	−1.00000	+	0.726543i	−0.0605228	+	0.0439724i
$274$	31.7082			1.91556
$275$	6.69098	−	4.20025i	0.403481	−	0.253285i
$276$	−19.8541			−1.19508
$277$	−8.97214	+	6.51864i	−0.539083	+	0.391667i	−0.823744	−	0.566961i	$-0.808119\pi$
$277$	−8.97214	+	6.51864i	−0.539083	+	0.391667i	0.284661	+	0.958628i	$0.408119\pi$
$278$	−13.7188	−	42.2223i	−0.822802	−	2.53232i
$279$	2.50000	−	7.69421i	0.149671	−	0.460640i
$280$	2.92705	+	2.12663i	0.174925	+	0.127090i
$281$	7.32624	+	5.32282i	0.437047	+	0.317533i	0.784460	−	0.620179i	$-0.212940\pi$
$281$	7.32624	+	5.32282i	0.437047	+	0.317533i	−0.347414	+	0.937712i	$0.612940\pi$
$282$	−3.09017	+	9.51057i	−0.184017	+	0.566346i
$283$	5.02786	+	15.4742i	0.298875	+	0.919844i	0.981892	+	0.189441i	$0.0606677\pi$
$283$	5.02786	+	15.4742i	0.298875	+	0.919844i	−0.683017	+	0.730403i	$0.739332\pi$
$284$	−31.4164	+	22.8254i	−1.86422	+	1.35444i
$285$	6.23607			0.369393
$286$	9.14590	+	0.620541i	0.540808	+	0.0366934i
$287$	9.61803			0.567735
$288$	−5.42705	+	3.94298i	−0.319792	+	0.232343i
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$	6.70820	−	20.6457i	0.393919	−	1.21236i
$291$	−4.85410	−	3.52671i	−0.284552	−	0.206739i
$292$	−0.708204	−	0.514540i	−0.0414445	−	0.0301112i
$293$	10.2639	−	31.5891i	0.599625	−	1.84546i	0.0694203	−	0.997588i	$-0.477885\pi$
$293$	10.2639	−	31.5891i	0.599625	−	1.84546i	0.530205	−	0.847869i	$-0.322115\pi$
$294$	0.690983	+	2.12663i	0.0402989	+	0.124027i
$295$	1.61803	−	1.17557i	0.0942056	−	0.0684444i
$296$	−5.32624			−0.309581
$297$	−1.23607	+	3.07768i	−0.0717239	+	0.178585i
$298$	−28.9443			−1.67670
$299$	6.61803	−	4.80828i	0.382731	−	0.278070i
$300$	2.20820	+	6.79615i	0.127491	+	0.392376i
$301$	−1.14590	+	3.52671i	−0.0660485	+	0.203276i
$302$	−44.2705	−	32.1644i	−2.54748	−	1.85085i
$303$	14.3992	+	10.4616i	0.827212	+	0.601004i
$304$	1.19098	−	3.66547i	0.0683076	−	0.210229i
$305$		0			0
$306$	−3.35410	+	2.43690i	−0.191741	+	0.139308i
$307$	2.56231			0.146239			0.0731193	−	0.997323i	$-0.476705\pi$
$307$	2.56231			0.146239			0.0731193	+	0.997323i	$0.476705\pi$
$308$	3.70820	−	9.23305i	0.211295	−	0.526102i
$309$	14.3262			0.814991
$310$	23.6803	−	17.2048i	1.34495	−	0.977166i
$311$	−3.29180	−	10.1311i	−0.186661	−	0.574482i	0.813312	−	0.581827i	$-0.197662\pi$
$311$	−3.29180	−	10.1311i	−0.186661	−	0.574482i	−0.999973	+	0.00734490i	$0.997662\pi$
$312$	−0.854102	+	2.62866i	−0.0483540	+	0.148818i
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.996871	+	0.0790445i	$0.0251869\pi$
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.383226	+	0.923655i	$0.374813\pi$
$314$	30.9787	+	22.5074i	1.74823	+	1.27016i
$315$	0.500000	−	1.53884i	0.0281718	−	0.0867039i
$316$	−9.27051	−	28.5317i	−0.521507	−	1.60503i
$317$	−9.09017	+	6.60440i	−0.510555	+	0.370940i	−0.813034	−	0.582216i	$-0.802186\pi$
$317$	−9.09017	+	6.60440i	−0.510555	+	0.370940i	0.302479	+	0.953156i	$0.402186\pi$
$318$	25.1246			1.40892
$319$	−19.8541	−	1.34708i	−1.11162	−	0.0754222i
$320$	−21.0344			−1.17586
$321$	−7.11803	+	5.17155i	−0.397290	+	0.288648i
$322$	−4.57295	−	14.0741i	−0.254840	−	0.784318i
$323$	2.20820	−	6.79615i	0.122868	−	0.378148i
$324$	−2.42705	−	1.76336i	−0.134836	−	0.0979642i
$325$	−2.38197	−	1.73060i	−0.132128	−	0.0959964i
$326$	6.90983	−	21.2663i	0.382700	−	1.17783i
$327$	−0.791796	−	2.43690i	−0.0437864	−	0.134761i
$328$	17.3992	−	12.6412i	0.960709	−	0.697996i
$329$	−4.47214			−0.246557
$330$	−10.1631	+	6.37988i	−0.559461	+	0.351201i
$331$	−9.41641			−0.517573			−0.258786	−	0.965935i	$-0.583323\pi$
$331$	−9.41641			−0.517573			−0.258786	+	0.965935i	$0.583323\pi$
$332$	−18.2705	+	13.2743i	−1.00272	+	0.728522i
$333$	0.736068	+	2.26538i	0.0403363	+	0.124142i
$334$	11.5836	−	35.6506i	0.633826	−	1.95072i
$335$		0			0
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	4.91641	−	15.1311i	0.267814	−	0.824246i	−0.723218	−	0.690620i	$-0.757338\pi$
$337$	4.91641	−	15.1311i	0.267814	−	0.824246i	0.991032	−	0.133626i	$-0.0426622\pi$
$338$	7.92705	+	24.3970i	0.431175	+	1.32702i
$339$	−0.618034	+	0.449028i	−0.0335670	+	0.0243879i
$340$	−9.00000			−0.488094
$341$	−20.5902	−	17.2048i	−1.11502	−	0.931691i
$342$	8.61803			0.466010
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	2.56231	+	7.88597i	0.138150	+	0.425183i
$345$	−3.30902	+	10.1841i	−0.178151	+	0.548294i
$346$	−20.5902	−	14.9596i	−1.10693	−	0.804235i
$347$	−19.0172	−	13.8168i	−1.02090	−	0.741726i	−0.0544312	−	0.998518i	$-0.517335\pi$
$347$	−19.0172	−	13.8168i	−1.02090	−	0.741726i	−0.966467	+	0.256792i	$0.917335\pi$
$348$	5.56231	−	17.1190i	0.298171	−	0.917676i
$349$	−2.56231	−	7.88597i	−0.137157	−	0.422126i	0.858762	−	0.512374i	$-0.171234\pi$
$349$	−2.56231	−	7.88597i	−0.137157	−	0.422126i	−0.995919	+	0.0902482i	$0.971234\pi$
$350$	−4.30902	+	3.13068i	−0.230327	+	0.167342i
$351$	1.23607			0.0659764
$352$	5.42705	+	21.5765i	0.289263	+	1.15003i
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$	2.23607	−	1.62460i	0.118846	−	0.0863464i
$355$	6.47214	+	19.9192i	0.343505	+	1.05720i
$356$	3.13525	−	9.64932i	0.166168	−	0.511413i
$357$	−1.50000	−	1.08981i	−0.0793884	−	0.0576791i
$358$	17.7254	+	12.8783i	0.936818	+	0.680638i
$359$	8.20820	−	25.2623i	0.433212	−	1.33329i	−0.461695	−	0.887039i	$-0.652759\pi$
$359$	8.20820	−	25.2623i	0.433212	−	1.33329i	0.894907	−	0.446252i	$-0.147241\pi$
$360$	−1.11803	−	3.44095i	−0.0589256	−	0.181354i
$361$	3.35410	−	2.43690i	0.176532	−	0.128258i
$362$	−35.5279			−1.86730
$363$	7.94427	+	7.60845i	0.416966	+	0.399340i
$364$	−3.70820			−0.194363
$365$	−0.381966	+	0.277515i	−0.0199930	+	0.0145258i
$366$		0			0
$367$	11.2082	−	34.4953i	0.585063	−	1.80064i	−0.0139518	−	0.999903i	$-0.504441\pi$
$367$	11.2082	−	34.4953i	0.585063	−	1.80064i	0.599015	−	0.800738i	$-0.295559\pi$
$368$	5.35410	+	3.88998i	0.279102	+	0.202779i
$369$	−7.78115	−	5.65334i	−0.405071	−	0.294301i
$370$	−2.66312	+	8.19624i	−0.138449	+	0.426102i
$371$	3.47214	+	10.6861i	0.180264	+	0.554797i
$372$	19.6353	−	14.2658i	1.01804	−	0.739650i
$373$	0.673762			0.0348861			0.0174430	−	0.999848i	$-0.494447\pi$
$373$	0.673762			0.0348861			0.0174430	+	0.999848i	$0.494447\pi$
$374$	3.35410	+	13.3350i	0.173436	+	0.689538i
$375$	11.9443			0.616800
$376$	−8.09017	+	5.87785i	−0.417219	+	0.303127i
$377$	2.29180	+	7.05342i	0.118034	+	0.363270i
$378$	0.690983	−	2.12663i	0.0355403	−	0.109382i
$379$	−24.6525	−	17.9111i	−1.26631	−	0.920030i	−0.267263	−	0.963624i	$-0.586119\pi$
$379$	−24.6525	−	17.9111i	−1.26631	−	0.920030i	−0.999049	+	0.0435936i	$0.986119\pi$
$380$	15.1353	+	10.9964i	0.776422	+	0.564104i
$381$	−4.23607	+	13.0373i	−0.217020	+	0.667920i
$382$	−11.1180	−	34.2178i	−0.568848	−	1.75073i
$383$	−26.5623	+	19.2986i	−1.35727	+	0.986115i	−0.358657	+	0.933469i	$0.616765\pi$
$383$	−26.5623	+	19.2986i	−1.35727	+	0.986115i	−0.998613	+	0.0526453i	$0.983235\pi$
$384$	−15.6525			−0.798762
$385$	−4.11803	−	3.44095i	−0.209874	−	0.175367i
$386$	33.8673			1.72380
$387$	3.00000	−	2.17963i	0.152499	−	0.110797i
$388$	−5.56231	−	17.1190i	−0.282383	−	0.869086i
$389$	3.32624	−	10.2371i	0.168647	−	0.519042i	−0.830640	−	0.556810i	$-0.812025\pi$
$389$	3.32624	−	10.2371i	0.168647	−	0.519042i	0.999287	+	0.0377685i	$0.0120250\pi$
$390$	3.61803	+	2.62866i	0.183206	+	0.133107i
$391$	9.92705	+	7.21242i	0.502033	+	0.364748i
$392$	−0.690983	+	2.12663i	−0.0348999	+	0.107411i
$393$	−4.52786	−	13.9353i	−0.228401	−	0.702945i
$394$	24.4721	−	17.7800i	1.23289	−	0.895746i
$395$	−16.1803			−0.814121
$396$	−8.42705	+	5.29007i	−0.423475	+	0.265836i
$397$	−36.5410			−1.83394			−0.916971	−	0.398955i	$-0.869373\pi$
$397$	−36.5410			−1.83394			−0.916971	+	0.398955i	$0.869373\pi$
$398$	35.9164	−	26.0948i	1.80033	−	1.30801i
$399$	1.19098	+	3.66547i	0.0596237	+	0.183503i
$400$	0.736068	−	2.26538i	0.0368034	−	0.113269i
$401$	15.7082	+	11.4127i	0.784430	+	0.569922i	0.906305	−	0.422623i	$-0.138891\pi$
$401$	15.7082	+	11.4127i	0.784430	+	0.569922i	−0.121875	+	0.992545i	$0.538891\pi$
$402$		0			0
$403$	−3.09017	+	9.51057i	−0.153932	+	0.473755i
$404$	16.5000	+	50.7818i	0.820906	+	2.52649i
$405$	−1.30902	+	0.951057i	−0.0650456	+	0.0472584i
$406$	13.4164			0.665845
$407$	7.88197	+	0.534785i	0.390695	+	0.0265083i
$408$	−4.14590			−0.205253
$409$	−0.145898	+	0.106001i	−0.00721419	+	0.00524142i	−0.591387	−	0.806388i	$-0.701419\pi$
$409$	−0.145898	+	0.106001i	−0.00721419	+	0.00524142i	0.584172	+	0.811630i	$0.301419\pi$
$410$	−10.7533	−	33.0952i	−0.531067	−	1.63446i
$411$	4.38197	−	13.4863i	0.216146	−	0.665230i
$412$	34.7705	+	25.2623i	1.71302	+	1.24458i
$413$	1.00000	+	0.726543i	0.0492068	+	0.0357508i
$414$	−4.57295	+	14.0741i	−0.224748	+	0.691704i
$415$	3.76393	+	11.5842i	0.184764	+	0.568646i
$416$	6.70820	−	4.87380i	0.328897	−	0.238957i
$417$	−19.8541			−0.972260
$418$	10.6525	−	26.5236i	0.521030	−	1.29731i
$419$	1.23607			0.0603859			0.0301929	−	0.999544i	$-0.490388\pi$
$419$	1.23607			0.0603859			0.0301929	+	0.999544i	$0.490388\pi$
$420$	3.92705	−	2.85317i	0.191620	−	0.139220i
$421$	−4.57295	−	14.0741i	−0.222872	−	0.685929i	−0.998501	−	0.0547398i	$-0.982567\pi$
$421$	−4.57295	−	14.0741i	−0.222872	−	0.685929i	0.775629	−	0.631189i	$-0.217433\pi$
$422$	−18.2148	+	56.0593i	−0.886682	+	2.72893i
$423$	3.61803	+	2.62866i	0.175915	+	0.127810i
$424$	20.3262	+	14.7679i	0.987129	+	0.717191i
$425$	1.36475	−	4.20025i	0.0661999	−	0.203742i
$426$	8.94427	+	27.5276i	0.433351	+	1.33372i
$427$		0			0
$428$	−26.3951			−1.27586
$429$	1.52786	−	3.80423i	0.0737660	−	0.183670i
$430$	13.4164			0.646997
$431$	−3.16312	+	2.29814i	−0.152362	+	0.110698i	−0.661355	−	0.750073i	$-0.730018\pi$
$431$	−3.16312	+	2.29814i	−0.152362	+	0.110698i	0.508992	+	0.860771i	$0.330018\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−8.27051	+	25.4540i	−0.397455	+	1.22324i	0.529577	+	0.848262i	$0.322350\pi$
$433$	−8.27051	+	25.4540i	−0.397455	+	1.22324i	−0.927033	+	0.374980i	$0.877650\pi$
$434$	14.6353	+	10.6331i	0.702515	+	0.510407i
$435$	−7.85410	−	5.70634i	−0.376575	−	0.273598i
$436$	2.37539	−	7.31069i	0.113760	−	0.350119i
$437$	−7.88197	−	24.2582i	−0.377046	−	1.16043i
$438$	−0.527864	+	0.383516i	−0.0252223	+	0.0183251i
$439$	−4.85410			−0.231674			−0.115837	−	0.993268i	$-0.536955\pi$
$439$	−4.85410			−0.231674			−0.115837	+	0.993268i	$0.536955\pi$
$440$	−11.9721	−	0.812299i	−0.570749	−	0.0387248i
$441$	1.00000			0.0476190
$442$	4.14590	−	3.01217i	0.197200	−	0.143274i
$443$	6.98936	+	21.5110i	0.332074	+	1.02202i	0.968145	+	0.250389i	$0.0805586\pi$
$443$	6.98936	+	21.5110i	0.332074	+	1.02202i	−0.636071	+	0.771631i	$0.719441\pi$
$444$	−2.20820	+	6.79615i	−0.104797	+	0.322531i
$445$	−4.42705	−	3.21644i	−0.209862	−	0.152474i
$446$	31.4443	+	22.8456i	1.48893	+	1.08177i
$447$	−4.00000	+	12.3107i	−0.189194	+	0.582278i
$448$	−4.01722	−	12.3637i	−0.189796	−	0.584132i
$449$	4.94427	−	3.59222i	0.233335	−	0.169528i	−0.464974	−	0.885324i	$-0.653936\pi$
$449$	4.94427	−	3.59222i	0.233335	−	0.169528i	0.698309	+	0.715797i	$0.253936\pi$
$450$	5.32624			0.251081
$451$	−27.0172	+	16.9600i	−1.27219	+	0.798616i
$452$	−2.29180			−0.107797
$453$	−19.7984	+	14.3844i	−0.930209	+	0.675836i
$454$	−2.43769	−	7.50245i	−0.114407	−	0.352107i
$455$	−0.618034	+	1.90211i	−0.0289739	+	0.0891724i
$456$	6.97214	+	5.06555i	0.326500	+	0.237216i
$457$	4.38197	+	3.18368i	0.204980	+	0.148926i	0.685539	−	0.728036i	$-0.259566\pi$
$457$	4.38197	+	3.18368i	0.204980	+	0.148926i	−0.480560	+	0.876962i	$0.659566\pi$
$458$	4.27051	−	13.1433i	0.199548	−	0.614145i
$459$	0.572949	+	1.76336i	0.0267430	+	0.0823064i
$460$	−25.9894	+	18.8824i	−1.21176	+	0.880395i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$	−5.69098	−	4.75528i	−0.264768	−	0.221236i
$463$	3.41641			0.158774			0.0793870	−	0.996844i	$-0.474704\pi$
$463$	3.41641			0.158774			0.0793870	+	0.996844i	$0.474704\pi$
$464$	−4.85410	+	3.52671i	−0.225346	+	0.163723i
$465$	−4.04508	−	12.4495i	−0.187586	−	0.577331i
$466$	1.58359	−	4.87380i	0.0733585	−	0.225774i
$467$	−3.09017	−	2.24514i	−0.142996	−	0.103893i	0.513987	−	0.857798i	$-0.328168\pi$
$467$	−3.09017	−	2.24514i	−0.142996	−	0.103893i	−0.656983	+	0.753905i	$0.728168\pi$
$468$	3.00000	+	2.17963i	0.138675	+	0.100753i
$469$		0			0
$470$	5.00000	+	15.3884i	0.230633	+	0.709815i
$471$	13.8541	−	10.0656i	0.638363	−	0.463798i
$472$	2.76393			0.127220
$473$	−3.00000	−	11.9272i	−0.137940	−	0.548414i
$474$	−22.3607			−1.02706
$475$	−7.42705	+	5.39607i	−0.340776	+	0.247589i
$476$	−1.71885	−	5.29007i	−0.0787832	−	0.242470i
$477$	3.47214	−	10.6861i	0.158978	−	0.489285i
$478$	18.1525	+	13.1885i	0.830275	+	0.603230i
$479$	−13.7082	−	9.95959i	−0.626344	−	0.455065i	0.228788	−	0.973476i	$-0.426524\pi$
$479$	−13.7082	−	9.95959i	−0.626344	−	0.455065i	−0.855132	+	0.518411i	$0.826524\pi$
$480$	−3.35410	+	10.3229i	−0.153093	+	0.471172i
$481$	−0.909830	−	2.80017i	−0.0414847	−	0.127677i
$482$	21.7082	−	15.7719i	0.988782	−	0.718392i
$483$	−6.61803			−0.301131
$484$	5.86475	+	32.4747i	0.266579	+	1.47612i
$485$	−9.70820			−0.440827
$486$	−1.80902	+	1.31433i	−0.0820587	+	0.0596191i
$487$	4.41641	+	13.5923i	0.200127	+	0.615926i	0.999878	+	0.0155954i	$0.00496438\pi$
$487$	4.41641	+	13.5923i	0.200127	+	0.615926i	−0.799752	+	0.600331i	$0.795036\pi$
$488$		0			0
$489$	−8.09017	−	5.87785i	−0.365850	−	0.265806i
$490$	2.92705	+	2.12663i	0.132231	+	0.0960712i
$491$	−11.2812	+	34.7198i	−0.509111	+	1.56688i	0.284636	+	0.958636i	$0.408127\pi$
$491$	−11.2812	+	34.7198i	−0.509111	+	1.56688i	−0.793747	+	0.608248i	$0.791873\pi$
$492$	−8.91641	−	27.4419i	−0.401983	−	1.23718i
$493$	−9.00000	+	6.53888i	−0.405340	+	0.294496i
$494$	−10.6525			−0.479278
$495$	1.30902	+	5.20431i	0.0588359	+	0.233916i
$496$	−8.09017			−0.363259
$497$	−10.4721	+	7.60845i	−0.469739	+	0.341286i
$498$	5.20163	+	16.0090i	0.233090	+	0.717379i
$499$	−5.90983	+	18.1886i	−0.264560	+	0.814233i	0.727234	+	0.686390i	$0.240805\pi$
$499$	−5.90983	+	18.1886i	−0.264560	+	0.814233i	−0.991794	+	0.127843i	$0.959195\pi$
$500$	28.9894	+	21.0620i	1.29644	+	0.941921i
$501$	−13.5623	−	9.85359i	−0.605919	−	0.440226i
$502$	−9.87539	+	30.3933i	−0.440760	+	1.35652i
$503$	−1.70820	−	5.25731i	−0.0761650	−	0.234412i	0.905724	−	0.423867i	$-0.139328\pi$
$503$	−1.70820	−	5.25731i	−0.0761650	−	0.234412i	−0.981889	+	0.189455i	$0.939328\pi$
$504$	1.80902	−	1.31433i	0.0805800	−	0.0585448i
$505$	28.7984			1.28151
$506$	37.6631	+	31.4706i	1.67433	+	1.39904i
$507$	11.4721			0.509495
$508$	−33.2705	+	24.1724i	−1.47614	+	1.07248i
$509$	−4.91641	−	15.1311i	−0.217916	−	0.670676i	−0.998934	−	0.0461675i	$-0.985299\pi$
$509$	−4.91641	−	15.1311i	−0.217916	−	0.670676i	0.781018	−	0.624509i	$-0.214701\pi$
$510$	−2.07295	+	6.37988i	−0.0917917	+	0.282506i
$511$	−0.236068	−	0.171513i	−0.0104430	−	0.00758731i
$512$	9.04508	+	6.57164i	0.399740	+	0.290428i
$513$	1.19098	−	3.66547i	0.0525832	−	0.161834i
$514$	21.7320	+	66.8842i	0.958558	+	2.95014i
$515$	18.7533	−	13.6251i	0.826369	−	0.600392i
$516$	11.1246			0.489734
$517$	12.5623	−	7.88597i	0.552490	−	0.346824i
$518$	−5.32624			−0.234021
$519$	−9.20820	+	6.69015i	−0.404195	+	0.293665i
$520$	1.38197	+	4.25325i	0.0606032	+	0.186518i
$521$	1.02786	−	3.16344i	0.0450315	−	0.138593i	−0.926013	−	0.377492i	$-0.876787\pi$
$521$	1.02786	−	3.16344i	0.0450315	−	0.138593i	0.971044	+	0.238899i	$0.0767866\pi$
$522$	−10.8541	−	7.88597i	−0.475071	−	0.345159i
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	0.178343	−	0.983968i	$-0.442926\pi$
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	−0.880699	+	0.473677i	$0.842926\pi$
$524$	13.5836	−	41.8060i	0.593402	−	1.82630i
$525$	0.736068	+	2.26538i	0.0321246	+	0.0988695i
$526$	7.50000	−	5.44907i	0.327016	−	0.237591i
$527$	−15.0000			−0.653410
$528$	3.30902	+	0.224514i	0.144006	+	0.00977072i
$529$	20.7984			0.904277
$530$	32.8885	−	23.8949i	1.42859	−	1.03793i
$531$	−0.381966	−	1.17557i	−0.0165759	−	0.0510154i
$532$	−3.57295	+	10.9964i	−0.154907	+	0.476755i
$533$	9.61803	+	6.98791i	0.416603	+	0.302680i
$534$	−6.11803	−	4.44501i	−0.264753	−	0.192354i
$535$	−4.39919	+	13.5393i	−0.190193	+	0.585355i
$536$		0			0
$537$	7.92705	−	5.75934i	0.342077	−	0.248534i
$538$	−30.0000			−1.29339
$539$	1.23607	−	3.07768i	0.0532412	−	0.132565i
$540$	−4.85410			−0.208887
$541$	0.545085	−	0.396027i	0.0234350	−	0.0170265i	−0.576006	−	0.817445i	$-0.695390\pi$
$541$	0.545085	−	0.396027i	0.0234350	−	0.0170265i	0.599441	+	0.800419i	$0.295390\pi$
$542$	−10.7148	−	32.9767i	−0.460239	−	1.41647i
$543$	−4.90983	+	15.1109i	−0.210701	+	0.648471i
$544$	10.0623	+	7.31069i	0.431418	+	0.313443i
$545$	−3.35410	−	2.43690i	−0.143674	−	0.104385i
$546$	−0.854102	+	2.62866i	−0.0365522	+	0.112496i
$547$	−8.50658	−	26.1806i	−0.363715	−	1.11940i	−0.950782	−	0.309861i	$-0.899717\pi$
$547$	−8.50658	−	26.1806i	−0.363715	−	1.11940i	0.587067	−	0.809538i	$-0.300283\pi$
$548$	34.4164	−	25.0050i	1.47020	−	1.06816i
$549$		0			0
$550$	6.58359	−	16.3925i	0.280725	−	0.698977i
$551$	23.1246			0.985142
$552$	−11.9721	+	8.69827i	−0.509568	+	0.370223i
$553$	−3.09017	−	9.51057i	−0.131407	−	0.404430i
$554$	−7.66312	+	23.5847i	−0.325575	+	1.00202i
$555$	3.11803	+	2.26538i	0.132353	+	0.0961602i
$556$	−48.1869	−	35.0098i	−2.04358	−	1.48475i
$557$	−6.90983	+	21.2663i	−0.292779	+	0.901081i	0.691180	+	0.722683i	$0.257091\pi$
$557$	−6.90983	+	21.2663i	−0.292779	+	0.901081i	−0.983958	+	0.178398i	$0.942909\pi$
$558$	−5.59017	−	17.2048i	−0.236651	−	0.728336i
$559$	−3.70820	+	2.69417i	−0.156840	+	0.113951i
$560$	−1.61803			−0.0683744
$561$	6.13525	+	0.416272i	0.259031	+	0.0175750i
$562$	20.2492			0.854162
$563$	14.9443	−	10.8576i	0.629826	−	0.457595i	−0.226514	−	0.974008i	$-0.572733\pi$
$563$	14.9443	−	10.8576i	0.629826	−	0.457595i	0.856340	+	0.516413i	$0.172733\pi$
$564$	4.14590	+	12.7598i	0.174574	+	0.537283i
$565$	−0.381966	+	1.17557i	−0.0160694	+	0.0494566i
$566$	29.4336	+	21.3848i	1.23719	+	0.898869i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	−8.94427	+	27.5276i	−0.375293	+	1.15503i
$569$	−11.6180	−	35.7566i	−0.487053	−	1.49900i	−0.828985	−	0.559271i	$-0.811081\pi$
$569$	−11.6180	−	35.7566i	−0.487053	−	1.49900i	0.341931	−	0.939725i	$-0.388919\pi$
$570$	11.2812	−	8.19624i	0.472516	−	0.343303i
$571$	46.6525			1.95235			0.976173	−	0.216995i	$-0.0696256\pi$
$571$	46.6525			1.95235			0.976173	+	0.216995i	$0.0696256\pi$
$572$	10.4164	−	6.53888i	0.435532	−	0.273404i
$573$	−16.0902			−0.672176
$574$	17.3992	−	12.6412i	0.726228	−	0.527636i
$575$	−4.87132	−	14.9924i	−0.203148	−	0.625226i
$576$	−4.01722	+	12.3637i	−0.167384	+	0.515156i
$577$	18.0344	+	13.1028i	0.750784	+	0.545476i	0.896070	−	0.443913i	$-0.146410\pi$
$577$	18.0344	+	13.1028i	0.750784	+	0.545476i	−0.145286	+	0.989390i	$0.546410\pi$
$578$	−24.5344	−	17.8253i	−1.02050	−	0.741435i
$579$	4.68034	−	14.4046i	0.194508	−	0.598635i
$580$	−9.00000	−	27.6992i	−0.373705	−	1.15014i
$581$	−6.09017	+	4.42477i	−0.252663	+	0.183570i
$582$	−13.4164			−0.556128
$583$	−28.5967	−	23.8949i	−1.18436	−	0.989627i
$584$	−0.652476			−0.0269996
$585$	1.61803	−	1.17557i	0.0668975	−	0.0486039i
$586$	−22.9508	−	70.6355i	−0.948091	−	2.91792i
$587$	7.85410	−	24.1724i	0.324173	−	0.997703i	−0.647639	−	0.761947i	$-0.724243\pi$
$587$	7.85410	−	24.1724i	0.324173	−	0.997703i	0.971812	−	0.235756i	$-0.0757566\pi$
$588$	2.42705	+	1.76336i	0.100090	+	0.0727196i
$589$	25.2254	+	18.3273i	1.03940	+	0.755165i
$590$	1.38197	−	4.25325i	0.0568946	−	0.175104i
$591$	−4.18034	−	12.8658i	−0.171956	−	0.529227i
$592$	1.92705	−	1.40008i	0.0792013	−	0.0575431i
$593$	−15.5066			−0.636779			−0.318389	−	0.947960i	$-0.603142\pi$
$593$	−15.5066			−0.636779			−0.318389	+	0.947960i	$0.603142\pi$
$594$	1.80902	+	7.19218i	0.0742249	+	0.295099i
$595$	−3.00000			−0.122988
$596$	−31.4164	+	22.8254i	−1.28687	+	0.934963i
$597$	−6.13525	−	18.8824i	−0.251099	−	0.772804i
$598$	5.65248	−	17.3965i	0.231147	−	0.711397i
$599$	17.2984	+	12.5680i	0.706792	+	0.513515i	0.882137	−	0.470992i	$-0.156104\pi$
$599$	17.2984	+	12.5680i	0.706792	+	0.513515i	−0.175345	+	0.984507i	$0.556104\pi$
$600$	4.30902	+	3.13068i	0.175915	+	0.127810i
$601$	3.85410	−	11.8617i	0.157212	−	0.483849i	−0.841166	−	0.540777i	$-0.818130\pi$
$601$	3.85410	−	11.8617i	0.157212	−	0.483849i	0.998378	+	0.0569276i	$0.0181304\pi$
$602$	2.56231	+	7.88597i	0.104432	+	0.321408i
$603$		0			0
$604$	−73.4164			−2.98727
$605$	17.6353	+	2.40414i	0.716975	+	0.0977423i
$606$	39.7984			1.61670
$607$	−28.2984	+	20.5600i	−1.14860	+	0.834504i	−0.988294	−	0.152564i	$-0.951247\pi$
$607$	−28.2984	+	20.5600i	−1.14860	+	0.834504i	−0.160302	+	0.987068i	$0.551247\pi$
$608$	−7.98936	−	24.5887i	−0.324011	−	0.997204i
$609$	1.85410	−	5.70634i	0.0751320	−	0.231233i
$610$		0			0
$611$	−4.47214	−	3.24920i	−0.180923	−	0.131448i
$612$	−1.71885	+	5.29007i	−0.0694803	+	0.213838i
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	0.977067	+	0.212932i	$0.0683012\pi$
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	−0.665306	+	0.746571i	$0.731699\pi$
$614$	4.63525	−	3.36771i	0.187064	−	0.135910i
$615$	−15.5623			−0.627533
$616$	−1.80902	−	7.19218i	−0.0728874	−	0.289781i
$617$	44.0689			1.77415			0.887073	−	0.461629i	$-0.152735\pi$
$617$	44.0689			1.77415			0.887073	+	0.461629i	$0.152735\pi$
$618$	25.9164	−	18.8294i	1.04251	−	0.757428i
$619$	7.31966	+	22.5276i	0.294202	+	0.905461i	0.983488	+	0.180972i	$0.0579242\pi$
$619$	7.31966	+	22.5276i	0.294202	+	0.905461i	−0.689286	+	0.724489i	$0.742076\pi$
$620$	12.1353	−	37.3485i	0.487364	−	1.49995i
$621$	5.35410	+	3.88998i	0.214853	+	0.156100i
$622$	−19.2705	−	14.0008i	−0.772677	−	0.561383i
$623$	1.04508	−	3.21644i	0.0418704	−	0.128864i
$624$	−0.381966	−	1.17557i	−0.0152909	−	0.0470605i
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$	67.4853			2.69725
$627$	−9.80902	−	8.19624i	−0.391734	−	0.327326i
$628$	51.3738			2.05004
$629$	3.57295	−	2.59590i	0.142463	−	0.103505i
$630$	−1.11803	−	3.44095i	−0.0445435	−	0.137091i
$631$	5.34752	−	16.4580i	0.212882	−	0.655182i	−0.786416	−	0.617698i	$-0.788066\pi$
$631$	5.34752	−	16.4580i	0.212882	−	0.655182i	0.999297	−	0.0374844i	$-0.0119345\pi$
$632$	−18.0902	−	13.1433i	−0.719588	−	0.522812i
$633$	21.3262	+	15.4944i	0.847642	+	0.615848i
$634$	−7.76393	+	23.8949i	−0.308345	+	0.948989i
$635$	6.85410	+	21.0948i	0.271997	+	0.837120i
$636$	27.2705	−	19.8132i	1.08135	−	0.785644i
$637$	−1.23607			−0.0489748
$638$	−37.6869	+	23.6579i	−1.49204	+	0.936625i
$639$	12.9443			0.512067
$640$	−20.4894	+	14.8864i	−0.809913	+	0.588436i
$641$	5.32624	+	16.3925i	0.210374	+	0.647464i	0.999450	+	0.0331683i	$0.0105597\pi$
$641$	5.32624	+	16.3925i	0.210374	+	0.647464i	−0.789076	+	0.614296i	$0.789440\pi$
$642$	−6.07953	+	18.7109i	−0.239940	+	0.738459i
$643$	18.8262	+	13.6781i	0.742434	+	0.539410i	0.893473	−	0.449118i	$-0.148262\pi$
$643$	18.8262	+	13.6781i	0.742434	+	0.539410i	−0.151038	+	0.988528i	$0.548262\pi$
$644$	−16.0623	−	11.6699i	−0.632944	−	0.459860i
$645$	1.85410	−	5.70634i	0.0730052	−	0.224687i
$646$	−4.93769	−	15.1967i	−0.194271	−	0.597905i
$647$	−22.2705	+	16.1805i	−0.875544	+	0.636120i	−0.932069	−	0.362281i	$-0.881998\pi$
$647$	−22.2705	+	16.1805i	−0.875544	+	0.636120i	0.0565248	+	0.998401i	$0.481998\pi$
$648$	−2.23607			−0.0878410
$649$	−4.09017	−	0.277515i	−0.160553	−	0.0108934i
$650$	−6.58359			−0.258230
$651$	6.54508	−	4.75528i	0.256522	−	0.186374i
$652$	−9.27051	−	28.5317i	−0.363061	−	1.11739i
$653$	−8.76393	+	26.9726i	−0.342959	+	1.05552i	0.619708	+	0.784832i	$0.287251\pi$
$653$	−8.76393	+	26.9726i	−0.342959	+	1.05552i	−0.962667	+	0.270687i	$0.912749\pi$
$654$	−4.63525	−	3.36771i	−0.181253	−	0.131688i
$655$	−19.1803	−	13.9353i	−0.749438	−	0.544499i
$656$	−2.97214	+	9.14729i	−0.116042	+	0.357142i
$657$	0.0901699	+	0.277515i	0.00351786	+	0.0108269i
$658$	−8.09017	+	5.87785i	−0.315388	+	0.229143i
$659$	−19.1459			−0.745818			−0.372909	−	0.927868i	$-0.621640\pi$
$659$	−19.1459			−0.745818			−0.372909	+	0.927868i	$0.621640\pi$
$660$	−6.00000	+	14.9394i	−0.233550	+	0.581515i
$661$	34.5410			1.34349			0.671745	−	0.740782i	$-0.265545\pi$
$661$	34.5410			1.34349			0.671745	+	0.740782i	$0.265545\pi$
$662$	−17.0344	+	12.3762i	−0.662062	+	0.481016i
$663$	−0.708204	−	2.17963i	−0.0275044	−	0.0846497i
$664$	−5.20163	+	16.0090i	−0.201862	+	0.621268i
$665$	5.04508	+	3.66547i	0.195640	+	0.142141i
$666$	4.30902	+	3.13068i	0.166971	+	0.121312i
$667$	−12.2705	+	37.7647i	−0.475116	+	1.46226i
$668$	−15.5410	−	47.8303i	−0.601300	−	1.85061i
$669$	14.0623	−	10.2169i	0.543680	−	0.395007i
$670$		0			0
$671$		0			0
$672$	−6.70820			−0.258775
$673$	−7.14590	+	5.19180i	−0.275454	+	0.200129i	−0.716932	−	0.697143i	$-0.754454\pi$
$673$	−7.14590	+	5.19180i	−0.275454	+	0.200129i	0.441478	+	0.897272i	$0.354454\pi$
$674$	−10.9934	−	33.8343i	−0.423451	−	1.30325i
$675$	0.736068	−	2.26538i	0.0283313	−	0.0871947i
$676$	27.8435	+	20.2295i	1.07090	+	0.778056i
$677$	8.38197	+	6.08985i	0.322145	+	0.234052i	0.737090	−	0.675794i	$-0.236199\pi$
$677$	8.38197	+	6.08985i	0.322145	+	0.234052i	−0.414945	+	0.909846i	$0.636199\pi$
$678$	−0.527864	+	1.62460i	−0.0202725	+	0.0623923i
$679$	−1.85410	−	5.70634i	−0.0711539	−	0.218989i
$680$	−5.42705	+	3.94298i	−0.208118	+	0.151207i
$681$	−3.52786			−0.135188
$682$	−59.8607	−	4.06150i	−2.29218	−	0.155523i
$683$	2.20163			0.0842429			0.0421214	−	0.999112i	$-0.486588\pi$
$683$	2.20163			0.0842429			0.0421214	+	0.999112i	$0.486588\pi$
$684$	9.35410	−	6.79615i	0.357663	−	0.259857i
$685$	−7.09017	−	21.8213i	−0.270901	−	0.833749i
$686$	−0.690983	+	2.12663i	−0.0263819	+	0.0811950i
$687$	−5.00000	−	3.63271i	−0.190762	−	0.138597i
$688$	−3.00000	−	2.17963i	−0.114374	−	0.0830975i
$689$	−4.29180	+	13.2088i	−0.163504	+	0.503215i
$690$	7.39919	+	22.7724i	0.281682	+	0.866929i
$691$	−5.06231	+	3.67798i	−0.192579	+	0.139917i	−0.679897	−	0.733308i	$-0.737975\pi$
$691$	−5.06231	+	3.67798i	−0.192579	+	0.139917i	0.487318	+	0.873225i	$0.337975\pi$
$692$	−34.1459			−1.29803
$693$	−2.80902	+	1.76336i	−0.106706	+	0.0669843i
$694$	−52.5623			−1.99524
$695$	−25.9894	+	18.8824i	−0.985832	+	0.716249i
$696$	−4.14590	−	12.7598i	−0.157150	−	0.483658i
$697$	−5.51064	+	16.9600i	−0.208730	+	0.642406i
$698$	−15.0000	−	10.8981i	−0.567758	−	0.412501i
$699$	−1.85410	−	1.34708i	−0.0701286	−	0.0509514i
$700$	−2.20820	+	6.79615i	−0.0834623	+	0.256870i
$701$	−2.96556	−	9.12705i	−0.112008	−	0.344724i	0.879304	−	0.476262i	$-0.158009\pi$
$701$	−2.96556	−	9.12705i	−0.112008	−	0.344724i	−0.991311	+	0.131538i	$0.958009\pi$
$702$	2.23607	−	1.62460i	0.0843949	−	0.0613165i
$703$	−9.18034			−0.346243
$704$	33.0861	+	27.6462i	1.24698	+	1.04195i
$705$	7.23607			0.272526
$706$	−32.5623	+	23.6579i	−1.22550	+	0.890377i
$707$	5.50000	+	16.9273i	0.206849	+	0.636615i
$708$	1.14590	−	3.52671i	0.0430655	−	0.132542i
$709$	−17.0172	−	12.3637i	−0.639095	−	0.464330i	0.220444	−	0.975400i	$-0.429249\pi$
$709$	−17.0172	−	12.3637i	−0.639095	−	0.464330i	−0.859539	+	0.511070i	$0.829249\pi$
$710$	37.8885	+	27.5276i	1.42193	+	1.03309i
$711$	−3.09017	+	9.51057i	−0.115890	+	0.356674i
$712$	−2.33688	−	7.19218i	−0.0875783	−	0.269538i
$713$	−43.3156	+	31.4706i	−1.62218	+	1.17858i
$714$	−4.14590			−0.155156
$715$	−1.61803	−	6.43288i	−0.0605110	−	0.240576i
$716$	29.3951			1.09855
$717$	8.11803	−	5.89810i	0.303174	−	0.220268i
$718$	−18.3541	−	56.4881i	−0.684969	−	2.10812i
$719$	−11.4377	+	35.2016i	−0.426554	+	1.31280i	0.474944	+	0.880016i	$0.342468\pi$
$719$	−11.4377	+	35.2016i	−0.426554	+	1.31280i	−0.901498	+	0.432782i	$0.857532\pi$
$720$	1.30902	+	0.951057i	0.0487842	+	0.0354438i
$721$	11.5902	+	8.42075i	0.431640	+	0.313605i
$722$	2.86475	−	8.81678i	0.106615	−	0.328127i
$723$	−3.70820	−	11.4127i	−0.137910	−	0.424442i
$724$	−38.5623	+	28.0172i	−1.43316	+	1.04125i
$725$	14.2918			0.530784
$726$	24.3713	+	3.32244i	0.904505	+	0.123307i
$727$	−12.1459			−0.450466			−0.225233	−	0.974305i	$-0.572314\pi$
$727$	−12.1459			−0.450466			−0.225233	+	0.974305i	$0.572314\pi$
$728$	−2.23607	+	1.62460i	−0.0828742	+	0.0602116i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.326238	+	1.00406i	−0.0120746	+	0.0371618i
$731$	−5.56231	−	4.04125i	−0.205729	−	0.149471i
$732$		0			0
$733$	12.3820	−	38.1078i	0.457338	−	1.40754i	−0.411029	−	0.911622i	$-0.634831\pi$
$733$	12.3820	−	38.1078i	0.457338	−	1.40754i	0.868368	−	0.495921i	$-0.165169\pi$
$734$	−25.0623	−	77.1338i	−0.925067	−	2.84706i
$735$	1.30902	−	0.951057i	0.0482838	−	0.0350802i
$736$	44.3951			1.63643
$737$		0			0
$738$	−21.5066			−0.791668
$739$	−0.708204	+	0.514540i	−0.0260517	+	0.0189277i	−0.600735	−	0.799448i	$-0.705125\pi$
$739$	−0.708204	+	0.514540i	−0.0260517	+	0.0189277i	0.574683	+	0.818376i	$0.305125\pi$
$740$	3.57295	+	10.9964i	0.131344	+	0.404236i
$741$	−1.47214	+	4.53077i	−0.0540803	+	0.166442i
$742$	20.3262	+	14.7679i	0.746200	+	0.542146i
$743$	0.545085	+	0.396027i	0.0199972	+	0.0145288i	0.597739	−	0.801691i	$-0.296066\pi$
$743$	0.545085	+	0.396027i	0.0199972	+	0.0145288i	−0.577742	+	0.816220i	$0.696066\pi$
$744$	5.59017	−	17.2048i	0.204946	−	0.630758i
$745$	6.47214	+	19.9192i	0.237121	+	0.729783i
$746$	1.21885	−	0.885544i	0.0446252	−	0.0324221i
$747$	7.52786			0.275430
$748$	14.1565	+	11.8290i	0.517614	+	0.432509i
$749$	−8.79837			−0.321486
$750$	21.6074	−	15.6987i	0.788990	−	0.573235i
$751$	7.41641	+	22.8254i	0.270629	+	0.832909i	0.990343	+	0.138639i	$0.0442727\pi$
$751$	7.41641	+	22.8254i	0.270629	+	0.832909i	−0.719714	+	0.694270i	$0.755727\pi$
$752$	1.38197	−	4.25325i	0.0503951	−	0.155100i
$753$	11.5623	+	8.40051i	0.421354	+	0.306131i
$754$	13.4164	+	9.74759i	0.488597	+	0.354986i
$755$	−12.2361	+	37.6587i	−0.445316	+	1.37054i
$756$	−0.927051	−	2.85317i	−0.0337165	−	0.103769i
$757$	7.73607	−	5.62058i	0.281172	−	0.204284i	−0.438256	−	0.898850i	$-0.644404\pi$
$757$	7.73607	−	5.62058i	0.281172	−	0.204284i	0.719429	+	0.694566i	$0.244404\pi$
$758$	−68.1378			−2.47488
$759$	18.5902	−	11.6699i	0.674780	−	0.423592i
$760$	13.9443			0.505812
$761$	20.5623	−	14.9394i	0.745383	−	0.541552i	−0.149009	−	0.988836i	$-0.547608\pi$
$761$	20.5623	−	14.9394i	0.745383	−	0.541552i	0.894392	+	0.447283i	$0.147608\pi$
$762$	9.47214	+	29.1522i	0.343139	+	1.05607i
$763$	0.791796	−	2.43690i	0.0286649	−	0.0882216i
$764$	−39.0517	−	28.3727i	−1.41284	−	1.02649i
$765$	2.42705	+	1.76336i	0.0877502	+	0.0637543i
$766$	−22.6869	+	69.8232i	−0.819712	+	2.52281i
$767$	0.472136	+	1.45309i	0.0170478	+	0.0524679i
$768$	−7.28115	+	5.29007i	−0.262736	+	0.190889i
$769$	18.9443			0.683148			0.341574	−	0.939855i	$-0.389040\pi$
$769$	18.9443			0.683148			0.341574	+	0.939855i	$0.389040\pi$
$770$	−11.9721	−	0.812299i	−0.431446	−	0.0292732i
$771$	31.4508			1.13267
$772$	36.7599	−	26.7076i	1.32302	−	0.961228i
$773$	−0.145898	−	0.449028i	−0.00524759	−	0.0161504i	0.948398	−	0.317081i	$-0.102703\pi$
$773$	−0.145898	−	0.449028i	−0.00524759	−	0.0161504i	−0.953646	+	0.300931i	$0.902703\pi$
$774$	2.56231	−	7.88597i	0.0921002	−	0.283455i
$775$	15.5902	+	11.3269i	0.560015	+	0.406875i
$776$	−10.8541	−	7.88597i	−0.389640	−	0.283090i
$777$	−0.736068	+	2.26538i	−0.0264063	+	0.0812702i
$778$	−7.43769	−	22.8909i	−0.266654	−	0.820677i
$779$	29.9894	−	21.7885i	1.07448	−	0.780656i
$780$	6.00000			0.214834
$781$	16.0000	−	39.8384i	0.572525	−	1.42553i
$782$	27.4377			0.981170
$783$	−4.85410	+	3.52671i	−0.173471	+	0.126034i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	8.56231	−	26.3521i	0.305602	−	0.940546i
$786$	−26.5066	−	19.2582i	−0.945458	−	0.686916i
$787$	15.4894	+	11.2537i	0.552136	+	0.401150i	0.828572	−	0.559882i	$-0.189154\pi$
$787$	15.4894	+	11.2537i	0.552136	+	0.401150i	−0.276436	+	0.961032i	$0.589154\pi$
$788$	12.5410	−	38.5973i	0.446755	−	1.37497i
$789$	−1.28115	−	3.94298i	−0.0456103	−	0.140374i
$790$	−29.2705	+	21.2663i	−1.04140	+	0.756620i
$791$	−0.763932			−0.0271623
$792$	−2.76393	+	6.88191i	−0.0982120	+	0.244538i
$793$		0			0
$794$	−66.1033	+	48.0269i	−2.34592	+	1.70441i
$795$	−5.61803	−	17.2905i	−0.199251	−	0.613232i
$796$	18.4058	−	56.6471i	0.652375	−	2.00780i
$797$	−17.3435	−	12.6008i	−0.614337	−	0.446342i	0.236602	−	0.971607i	$-0.423966\pi$
$797$	−17.3435	−	12.6008i	−0.614337	−	0.446342i	−0.850939	+	0.525265i	$0.823966\pi$
$798$	6.97214	+	5.06555i	0.246811	+	0.179319i
$799$	2.56231	−	7.88597i	0.0906479	−	0.278985i
$800$	−4.93769	−	15.1967i	−0.174574	−	0.537283i
$801$	−2.73607	+	1.98787i	−0.0966742	+	0.0702379i
$802$	43.4164			1.53309
$803$	0.965558	+	0.0655123i	0.0340738	+	0.00231188i
$804$		0			0
$805$	−8.66312	+	6.29412i	−0.305335	+	0.221839i
$806$	6.90983	+	21.2663i	0.243388	+	0.749072i
$807$	−4.14590	+	12.7598i	−0.145943	+	0.449165i
$808$	32.1976	+	23.3929i	1.13271	+	0.822959i
$809$	−2.23607	−	1.62460i	−0.0786160	−	0.0571178i	0.547783	−	0.836620i	$-0.315472\pi$
$809$	−2.23607	−	1.62460i	−0.0786160	−	0.0571178i	−0.626399	+	0.779503i	$0.715472\pi$
$810$	−1.11803	+	3.44095i	−0.0392837	+	0.120903i
$811$	10.9443	+	33.6830i	0.384305	+	1.18277i	0.936983	+	0.349375i	$0.113606\pi$
$811$	10.9443	+	33.6830i	0.384305	+	1.18277i	−0.552678	+	0.833395i	$0.686394\pi$
$812$	14.5623	−	10.5801i	0.511037	−	0.371290i
$813$	−15.5066			−0.543839
$814$	14.9615	−	9.39205i	0.524400	−	0.329191i
$815$	−16.1803			−0.566773
$816$	1.50000	−	1.08981i	0.0525105	−	0.0381511i
$817$	4.41641	+	13.5923i	0.154511	+	0.475535i
$818$	−0.124612	+	0.383516i	−0.00435695	+	0.0134093i
$819$	1.00000	+	0.726543i	0.0349428	+	0.0253875i
$820$	−37.7705	−	27.4419i	−1.31900	−	0.958312i
$821$	2.14590	−	6.60440i	0.0748924	−	0.230495i	−0.906602	−	0.421987i	$-0.861333\pi$
$821$	2.14590	−	6.60440i	0.0748924	−	0.230495i	0.981494	+	0.191492i	$0.0613327\pi$
$822$	−9.79837	−	30.1563i	−0.341758	−	1.05182i
$823$	39.5066	−	28.7032i	1.37711	−	1.00053i	0.379969	−	0.924999i	$-0.375935\pi$
$823$	39.5066	−	28.7032i	1.37711	−	1.00053i	0.997143	−	0.0755319i	$-0.0240655\pi$
$824$	32.0344			1.11597
$825$	−6.06231	−	5.06555i	−0.211062	−	0.176360i
$826$	2.76393			0.0961695
$827$	42.7705	−	31.0746i	1.48728	−	1.08057i	0.512156	−	0.858892i	$-0.328847\pi$
$827$	42.7705	−	31.0746i	1.48728	−	1.08057i	0.975120	−	0.221677i	$-0.0711531\pi$
$828$	6.13525	+	18.8824i	0.213215	+	0.656208i
$829$	15.5279	−	47.7899i	0.539305	−	1.65981i	−0.194854	−	0.980832i	$-0.562423\pi$
$829$	15.5279	−	47.7899i	0.539305	−	1.65981i	0.734159	−	0.678978i	$-0.237577\pi$
$830$	22.0344	+	16.0090i	0.764827	+	0.555679i
$831$	8.97214	+	6.51864i	0.311240	+	0.226129i
$832$	4.96556	−	15.2824i	0.172150	−	0.529822i
$833$	−0.572949	−	1.76336i	−0.0198515	−	0.0610967i
$834$	−35.9164	+	26.0948i	−1.24368	+	0.903589i
$835$	−27.1246			−0.938686
$836$	−9.35410	−	37.1895i	−0.323518	−	1.28622i
$837$	−8.09017			−0.279637
$838$	2.23607	−	1.62460i	0.0772437	−	0.0561208i
$839$	12.4377	+	38.2793i	0.429397	+	1.32155i	0.898721	+	0.438522i	$0.144498\pi$
$839$	12.4377	+	38.2793i	0.429397	+	1.32155i	−0.469324	+	0.883026i	$0.655502\pi$
$840$	1.11803	−	3.44095i	0.0385758	−	0.118724i
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	−26.7705	−	19.4499i	−0.922573	−	0.670288i
$843$	2.79837	−	8.61251i	0.0963811	−	0.296631i
$844$	24.4377	+	75.2115i	0.841180	+	2.58889i
$845$	15.0172	−	10.9106i	0.516608	−	0.375338i
$846$	10.0000			0.343807
$847$	1.95492	+	10.8249i	0.0671717	+	0.371948i
$848$	−11.2361			−0.385848
$849$	13.1631	−	9.56357i	0.451757	−	0.328221i
$850$	−3.05166	−	9.39205i	−0.104671	−	0.322145i
$851$	4.87132	−	14.9924i	0.166987	−	0.513933i
$852$	31.4164	+	22.8254i	1.07631	+	0.781984i
$853$	22.8885	+	16.6295i	0.783689	+	0.569383i	0.906084	−	0.423098i	$-0.139057\pi$
$853$	22.8885	+	16.6295i	0.783689	+	0.569383i	−0.122395	+	0.992481i	$0.539057\pi$
$854$		0			0
$855$	−1.92705	−	5.93085i	−0.0659038	−	0.202831i
$856$	−15.9164	+	11.5639i	−0.544012	+	0.395248i
$857$	10.3607			0.353914			0.176957	−	0.984219i	$-0.443375\pi$
$857$	10.3607			0.353914			0.176957	+	0.984219i	$0.443375\pi$
$858$	−2.23607	−	8.89002i	−0.0763381	−	0.303500i
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$	14.5623	−	10.5801i	0.496571	−	0.360780i
$861$	−2.97214	−	9.14729i	−0.101290	−	0.311739i
$862$	−2.70163	+	8.31475i	−0.0920178	+	0.283202i
$863$	−2.69098	−	1.95511i	−0.0916021	−	0.0665528i	0.541041	−	0.840996i	$-0.318030\pi$
$863$	−2.69098	−	1.95511i	−0.0916021	−	0.0665528i	−0.632644	+	0.774443i	$0.718030\pi$
$864$	5.42705	+	3.94298i	0.184632	+	0.134143i
$865$	−5.69098	+	17.5150i	−0.193499	+	0.595529i
$866$	18.4934	+	56.9169i	0.628432	+	1.93412i
$867$	−10.9721	+	7.97172i	−0.372633	+	0.270734i
$868$	24.2705			0.823795
$869$	25.4508	+	21.2663i	0.863361	+	0.721409i
$870$	−21.7082			−0.735977
$871$		0			0
$872$	−1.77051	−	5.44907i	−0.0599570	−	0.184529i
$873$	−1.85410	+	5.70634i	−0.0627518	+	0.193130i
$874$	−46.1418	−	33.5240i	−1.56077	−	1.13397i
$875$	9.66312	+	7.02067i	0.326673	+	0.237342i
$876$	−0.270510	+	0.832544i	−0.00913968	+	0.0281290i
$877$	1.09017	+	3.35520i	0.0368124	+	0.113297i	0.967774	−	0.251820i	$-0.0810290\pi$
$877$	1.09017	+	3.35520i	0.0368124	+	0.113297i	−0.930962	+	0.365117i	$0.881029\pi$
$878$	−8.78115	+	6.37988i	−0.296350	+	0.215311i
$879$	−33.2148			−1.12031
$880$	4.54508	−	2.85317i	0.153215	−	0.0961803i
$881$	−4.32624			−0.145755			−0.0728773	−	0.997341i	$-0.523218\pi$
$881$	−4.32624			−0.145755			−0.0728773	+	0.997341i	$0.523218\pi$
$882$	1.80902	−	1.31433i	0.0609128	−	0.0442557i
$883$	−9.14590	−	28.1482i	−0.307784	−	0.947262i	−0.978624	−	0.205659i	$-0.934066\pi$
$883$	−9.14590	−	28.1482i	−0.307784	−	0.947262i	0.670840	−	0.741602i	$-0.265934\pi$
$884$	2.12461	−	6.53888i	0.0714584	−	0.219926i
$885$	−1.61803	−	1.17557i	−0.0543896	−	0.0395164i
$886$	40.9164	+	29.7275i	1.37461	+	0.998715i
$887$	−6.67376	+	20.5397i	−0.224083	+	0.689657i	0.774300	+	0.632818i	$0.218102\pi$
$887$	−6.67376	+	20.5397i	−0.224083	+	0.689657i	−0.998383	+	0.0568383i	$0.981898\pi$
$888$	1.64590	+	5.06555i	0.0552327	+	0.169989i
$889$	−11.0902	+	8.05748i	−0.371952	+	0.270239i
$890$	−12.2361			−0.410154
$891$	3.30902	+	0.224514i	0.110856	+	0.00752150i
$892$	52.1459			1.74597
$893$	−13.9443	+	10.1311i	−0.466627	+	0.339025i
$894$	8.94427	+	27.5276i	0.299141	+	0.920662i
$895$	4.89919	−	15.0781i	0.163762	−	0.504007i
$896$	−12.6631	−	9.20029i	−0.423045	−	0.307360i
$897$	−6.61803	−	4.80828i	−0.220970	−	0.160544i
$898$	4.22291	−	12.9968i	0.140920	−	0.433708i
$899$	−15.0000	−	46.1653i	−0.500278	−	1.53970i
$900$	5.78115	−	4.20025i	0.192705	−	0.140008i
$901$	−20.8328			−0.694042
$902$	−26.5836	+	66.1904i	−0.885137	+	2.20390i
$903$	3.70820			0.123401
$904$	−1.38197	+	1.00406i	−0.0459635	+	0.0333944i
$905$	7.94427	+	24.4500i	0.264077	+	0.812744i
$906$	−16.9098	+	52.0431i	−0.561791	+	1.72902i
$907$	−24.0344	−	17.4620i	−0.798051	−	0.579818i	0.112291	−	0.993675i	$-0.464181\pi$
$907$	−24.0344	−	17.4620i	−0.798051	−	0.579818i	−0.910342	+	0.413858i	$0.864181\pi$
$908$	−8.56231	−	6.22088i	−0.284150	−	0.206447i
$909$	5.50000	−	16.9273i	0.182423	−	0.561442i
$910$	1.38197	+	4.25325i	0.0458117	+	0.140994i
$911$	−13.7082	+	9.95959i	−0.454173	+	0.329976i	−0.791241	−	0.611504i	$-0.790565\pi$
$911$	−13.7082	+	9.95959i	−0.454173	+	0.329976i	0.337068	+	0.941480i	$0.390565\pi$
$912$	−3.85410			−0.127622
$913$	9.30495	−	23.1684i	0.307949	−	0.766762i
$914$	12.1115			0.400611
$915$		0			0
$916$	−5.72949	−	17.6336i	−0.189308	−	0.582629i
$917$	4.52786	−	13.9353i	0.149523	−	0.460185i
$918$	3.35410	+	2.43690i	0.110702	+	0.0804296i
$919$	17.4164	+	12.6538i	0.574514	+	0.417409i	0.836742	−	0.547597i	$-0.184457\pi$
$919$	17.4164	+	12.6538i	0.574514	+	0.417409i	−0.262228	+	0.965006i	$0.584457\pi$
$920$	−7.39919	+	22.7724i	−0.243944	+	0.750782i
$921$	−0.791796	−	2.43690i	−0.0260906	−	0.0802985i
$922$	−10.8541	+	7.88597i	−0.357461	+	0.259710i
$923$	−16.0000			−0.526646
$924$	−9.92705	−	0.673542i	−0.326576	−	0.0221579i
$925$	−5.67376			−0.186552
$926$	6.18034	−	4.49028i	0.203099	−	0.147560i
$927$	−4.42705	−	13.6251i	−0.145403	−	0.447506i
$928$	−12.4377	+	38.2793i	−0.408287	+	1.25658i
$929$	−46.3328	−	33.6628i	−1.52013	−	1.10444i	−0.961423	−	0.275075i	$-0.911297\pi$
$929$	−46.3328	−	33.6628i	−1.52013	−	1.10444i	−0.558707	−	0.829365i	$-0.688703\pi$
$930$	−23.6803	−	17.2048i	−0.776509	−	0.564167i
$931$	−1.19098	+	3.66547i	−0.0390329	+	0.120131i
$932$	−2.12461	−	6.53888i	−0.0695940	−	0.214188i
$933$	−8.61803	+	6.26137i	−0.282142	+	0.204988i
$934$	−8.54102			−0.279471
$935$	8.42705	−	5.29007i	0.275594	−	0.173004i
$936$	2.76393			0.0903419
$937$	19.4721	−	14.1473i	0.636127	−	0.462173i	−0.222390	−	0.974958i	$-0.571386\pi$
$937$	19.4721	−	14.1473i	0.636127	−	0.462173i	0.858517	+	0.512784i	$0.171386\pi$
$938$		0			0
$939$	9.32624	−	28.7032i	0.304350	−	0.936694i
$940$	17.5623	+	12.7598i	0.572819	+	0.416178i
$941$	31.1525	+	22.6336i	1.01554	+	0.737834i	0.965364	−	0.260906i	$-0.0840213\pi$
$941$	31.1525	+	22.6336i	1.01554	+	0.737834i	0.0501775	+	0.998740i	$0.484021\pi$
$942$	11.8328	−	36.4177i	0.385534	−	1.18655i
$943$	19.6697	+	60.5371i	0.640533	+	1.97136i
$944$	−1.00000	+	0.726543i	−0.0325472	+	0.0236469i
$945$	−1.61803			−0.0526346
$946$	−21.1033	−	17.6336i	−0.686128	−	0.573316i
$947$	7.14590			0.232210			0.116105	−	0.993237i	$-0.462959\pi$
$947$	7.14590			0.232210			0.116105	+	0.993237i	$0.462959\pi$
$948$	−24.2705	+	17.6336i	−0.788270	+	0.572711i
$949$	−0.111456	−	0.343027i	−0.00361802	−	0.0111351i
$950$	−6.34346	+	19.5232i	−0.205809	+	0.633415i
$951$	9.09017	+	6.60440i	0.294769	+	0.214162i
$952$	−3.35410	−	2.43690i	−0.108707	−	0.0789803i
$953$	−7.38197	+	22.7194i	−0.239125	+	0.735952i	0.757422	+	0.652926i	$0.226459\pi$
$953$	−7.38197	+	22.7194i	−0.239125	+	0.735952i	−0.996547	+	0.0830265i	$0.973541\pi$
$954$	−7.76393	−	23.8949i	−0.251367	−	0.773627i
$955$	−21.0623	+	15.3027i	−0.681560	+	0.495182i
$956$	30.1033			0.973611
$957$	4.85410	+	19.2986i	0.156911	+	0.623837i
$958$	−37.8885			−1.22412
$959$	11.4721	−	8.33499i	0.370455	−	0.269151i
$960$	6.50000	+	20.0049i	0.209787	+	0.645657i
$961$	10.6459	−	32.7647i	0.343416	−	1.05693i
$962$	−5.32624	−	3.86974i	−0.171725	−	0.124765i
$963$	7.11803	+	5.17155i	0.229375	+	0.166651i
$964$	11.1246	−	34.2380i	0.358300	−	1.10273i
$965$	−7.57295	−	23.3071i	−0.243782	−	0.750283i
$966$	−11.9721	+	8.69827i	−0.385197	+	0.279862i
$967$	−48.3607			−1.55517			−0.777587	−	0.628775i	$-0.783557\pi$
$967$	−48.3607			−1.55517			−0.777587	+	0.628775i	$0.783557\pi$
$968$	17.7639	+	17.0130i	0.570954	+	0.546819i
$969$	−7.14590			−0.229559
$970$	−17.5623	+	12.7598i	−0.563892	+	0.409691i
$971$	−3.87539	−	11.9272i	−0.124367	−	0.382763i	0.869418	−	0.494077i	$-0.164494\pi$
$971$	−3.87539	−	11.9272i	−0.124367	−	0.382763i	−0.993785	+	0.111314i	$0.964494\pi$
$972$	−0.927051	+	2.85317i	−0.0297352	+	0.0915155i
$973$	−16.0623	−	11.6699i	−0.514934	−	0.374121i
$974$	25.8541	+	18.7841i	0.828419	+	0.601882i
$975$	−0.909830	+	2.80017i	−0.0291379	+	0.0896772i
$976$		0			0
$977$	47.2148	−	34.3035i	1.51053	−	1.09747i	0.544595	−	0.838699i	$-0.316683\pi$
$977$	47.2148	−	34.3035i	1.51053	−	1.09747i	0.965939	−	0.258769i	$-0.0833168\pi$
$978$	−22.3607			−0.715016
$979$	2.73607	+	10.8779i	0.0874451	+	0.347659i
$980$	4.85410			0.155059
$981$	−2.07295	+	1.50609i	−0.0661842	+	0.0480856i
$982$	25.2254	+	77.6359i	0.804976	+	2.47746i
$983$	2.14590	−	6.60440i	0.0684435	−	0.210647i	−0.910985	−	0.412440i	$-0.864677\pi$
$983$	2.14590	−	6.60440i	0.0684435	−	0.210647i	0.979428	+	0.201792i	$0.0646767\pi$
$984$	−17.3992	−	12.6412i	−0.554666	−	0.402988i
$985$	−17.7082	−	12.8658i	−0.564230	−	0.409937i
$986$	−7.68692	+	23.6579i	−0.244801	+	0.753421i
$987$	1.38197	+	4.25325i	0.0439885	+	0.135383i
$988$	−11.5623	+	8.40051i	−0.367846	+	0.267256i
$989$	−24.5410			−0.780359
$990$	9.20820	+	7.69421i	0.292656	+	0.244538i
$991$	−28.7639			−0.913716			−0.456858	−	0.889540i	$-0.651025\pi$
$991$	−28.7639			−0.913716			−0.456858	+	0.889540i	$0.651025\pi$
$992$	−43.9058	+	31.8994i	−1.39401	+	1.01281i
$993$	2.90983	+	8.95554i	0.0923407	+	0.284195i
$994$	−8.94427	+	27.5276i	−0.283695	+	0.873124i
$995$	−25.9894	−	18.8824i	−0.823918	−	0.598611i
$996$	18.2705	+	13.2743i	0.578923	+	0.420612i
$997$	18.0557	−	55.5698i	0.571831	−	1.75991i	−0.0748954	−	0.997191i	$-0.523862\pi$
$997$	18.0557	−	55.5698i	0.571831	−	1.75991i	0.646726	−	0.762722i	$-0.276138\pi$
$998$	13.2148	+	40.6709i	0.418307	+	1.28742i
$999$	1.92705	−	1.40008i	0.0609692	−	0.0442967i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.80902 - 1.31433i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.80902 - 1.31433i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.61803 q^{10} +(0.809017 + 3.21644i) q^{11} -3.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.690983 - 2.12663i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.50000 + 1.08981i) q^{17} +(-0.690983 + 2.12663i) q^{18} +(-1.19098 - 3.66547i) q^{19} +(-3.92705 + 2.85317i) q^{20} -1.00000 q^{21} +(5.69098 + 4.75528i) q^{22} +6.61803 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(0.854102 - 2.62866i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.42705 - 1.76336i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(1.11803 + 3.44095i) q^{30} +(-6.54508 + 4.75528i) q^{31} +6.70820 q^{32} +(2.80902 - 1.76336i) q^{33} +4.14590 q^{34} +(-1.30902 + 0.951057i) q^{35} +(0.927051 + 2.85317i) q^{36} +(0.736068 - 2.26538i) q^{37} +(-6.97214 - 5.06555i) q^{38} +(-1.00000 - 0.726543i) q^{39} +(-1.11803 + 3.44095i) q^{40} +(2.97214 + 9.14729i) q^{41} +(-1.80902 + 1.31433i) q^{42} -3.70820 q^{43} +(9.92705 + 0.673542i) q^{44} +1.61803 q^{45} +(11.9721 - 8.69827i) q^{46} +(-1.38197 - 4.25325i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-4.30902 - 3.13068i) q^{50} +(0.572949 - 1.76336i) q^{51} +(-1.14590 - 3.52671i) q^{52} +(-9.09017 + 6.60440i) q^{53} +2.23607 q^{54} +(2.00000 - 4.97980i) q^{55} -2.23607 q^{56} +(-3.11803 + 2.26538i) q^{57} +(4.14590 + 12.7598i) q^{58} +(-0.381966 + 1.17557i) q^{59} +(3.92705 + 2.85317i) q^{60} +(-5.59017 + 17.2048i) q^{62} +(0.309017 + 0.951057i) q^{63} +(10.5172 - 7.64121i) q^{64} -2.00000 q^{65} +(2.76393 - 6.88191i) q^{66} +(4.50000 - 3.26944i) q^{68} +(-2.04508 - 6.29412i) q^{69} +(-1.11803 + 3.44095i) q^{70} +(-10.4721 - 7.60845i) q^{71} +(1.80902 + 1.31433i) q^{72} +(0.0901699 - 0.277515i) q^{73} +(-1.64590 - 5.06555i) q^{74} +(-1.92705 + 1.40008i) q^{75} -11.5623 q^{76} +(3.30902 + 0.224514i) q^{77} -2.76393 q^{78} +(8.09017 - 5.87785i) q^{79} +(-0.500000 - 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(17.3992 + 12.6412i) q^{82} +(-6.09017 - 4.42477i) q^{83} +(-0.927051 + 2.85317i) q^{84} +(-0.927051 - 2.85317i) q^{85} +(-6.70820 + 4.87380i) q^{86} +6.00000 q^{87} +(6.28115 - 3.94298i) q^{88} +3.38197 q^{89} +(2.92705 - 2.12663i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(6.13525 - 18.8824i) q^{92} +(6.54508 + 4.75528i) q^{93} +(-8.09017 - 5.87785i) q^{94} +(-1.92705 + 5.93085i) q^{95} +(-2.07295 - 6.37988i) q^{96} +(4.85410 - 3.52671i) q^{97} -2.23607 q^{98} +(-2.54508 - 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9	\( 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9} - 10 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - 5 q^{18} - 7 q^{19} - 9 q^{20} - 4 q^{21} + 25 q^{22} + 22 q^{23} - 5 q^{24} + 6 q^{25} - 10 q^{26} + q^{27} - 3 q^{28} + 6 q^{29} - 15 q^{31} + 9 q^{33} + 30 q^{34} - 3 q^{35} - 3 q^{36} - 6 q^{37} - 10 q^{38} - 4 q^{39} - 6 q^{41} - 5 q^{42} + 12 q^{43} + 33 q^{44} + 2 q^{45} + 30 q^{46} - 10 q^{47} - q^{48} - q^{49} - 15 q^{50} + 9 q^{51} - 18 q^{52} - 14 q^{53} + 8 q^{55} - 8 q^{57} + 30 q^{58} - 6 q^{59} + 9 q^{60} - q^{63} + 13 q^{64} - 8 q^{65} + 20 q^{66} + 18 q^{68} + 3 q^{69} - 24 q^{71} + 5 q^{72} - 22 q^{73} - 20 q^{74} - q^{75} - 6 q^{76} + 11 q^{77} - 20 q^{78} + 10 q^{79} - 2 q^{80} - q^{81} + 45 q^{82} - 2 q^{83} + 3 q^{84} + 3 q^{85} + 24 q^{87} + 5 q^{88} + 18 q^{89} + 5 q^{90} - 6 q^{91} - 9 q^{92} + 15 q^{93} - 10 q^{94} - q^{95} - 15 q^{96} + 6 q^{97} + q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9 - 10 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 + q^16 + 6 * q^17 - 5 * q^18 - 7 * q^19 - 9 * q^20 - 4 * q^21 + 25 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 - 10 * q^26 + q^27 - 3 * q^28 + 6 * q^29 - 15 * q^31 + 9 * q^33 + 30 * q^34 - 3 * q^35 - 3 * q^36 - 6 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^41 - 5 * q^42 + 12 * q^43 + 33 * q^44 + 2 * q^45 + 30 * q^46 - 10 * q^47 - q^48 - q^49 - 15 * q^50 + 9 * q^51 - 18 * q^52 - 14 * q^53 + 8 * q^55 - 8 * q^57 + 30 * q^58 - 6 * q^59 + 9 * q^60 - q^63 + 13 * q^64 - 8 * q^65 + 20 * q^66 + 18 * q^68 + 3 * q^69 - 24 * q^71 + 5 * q^72 - 22 * q^73 - 20 * q^74 - q^75 - 6 * q^76 + 11 * q^77 - 20 * q^78 + 10 * q^79 - 2 * q^80 - q^81 + 45 * q^82 - 2 * q^83 + 3 * q^84 + 3 * q^85 + 24 * q^87 + 5 * q^88 + 18 * q^89 + 5 * q^90 - 6 * q^91 - 9 * q^92 + 15 * q^93 - 10 * q^94 - q^95 - 15 * q^96 + 6 * q^97 + q^99

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