LMFDB - Embedded newform 231.2.j.b.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.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +(1.69098 + 2.85317i) q^{11} +1.61803 q^{12} +(-3.42705 + 2.48990i) q^{13} +(-0.190983 - 0.587785i) q^{14} +(0.500000 - 1.53884i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(2.80902 + 2.04087i) q^{17} +(0.190983 - 0.587785i) q^{18} +(2.00000 + 6.15537i) q^{19} +(-2.11803 + 1.53884i) q^{20} +1.00000 q^{21} +(-1.88197 - 0.812299i) q^{22} +5.70820 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(0.809017 - 2.48990i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.30902 - 0.951057i) q^{28} +(-0.0729490 + 0.224514i) q^{29} +(0.309017 + 0.951057i) q^{30} +(-2.42705 + 1.76336i) q^{31} +5.61803 q^{32} +(2.19098 - 2.48990i) q^{33} -2.14590 q^{34} +(-1.30902 + 0.951057i) q^{35} +(-0.500000 - 1.53884i) q^{36} +(1.85410 - 5.70634i) q^{37} +(-3.23607 - 2.35114i) q^{38} +(3.42705 + 2.48990i) q^{39} +(1.11803 - 3.44095i) q^{40} +(-3.04508 - 9.37181i) q^{41} +(-0.500000 + 0.363271i) q^{42} -11.4721 q^{43} +(-5.23607 + 1.17557i) q^{44} -1.61803 q^{45} +(-2.85410 + 2.07363i) q^{46} +(-1.59017 - 4.89404i) q^{47} +(-0.572949 + 1.76336i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.19098 + 0.865300i) q^{50} +(1.07295 - 3.30220i) q^{51} +(-2.11803 - 6.51864i) q^{52} +(10.1631 - 7.38394i) q^{53} -0.618034 q^{54} +(-0.500000 + 5.34307i) q^{55} +2.23607 q^{56} +(5.23607 - 3.80423i) q^{57} +(-0.0450850 - 0.138757i) q^{58} +(-1.42705 + 4.39201i) q^{59} +(2.11803 + 1.53884i) q^{60} +(6.42705 + 4.66953i) q^{61} +(0.572949 - 1.76336i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(0.190983 - 0.138757i) q^{64} -6.85410 q^{65} +(-0.190983 + 2.04087i) q^{66} +13.2361 q^{67} +(-4.54508 + 3.30220i) q^{68} +(-1.76393 - 5.42882i) q^{69} +(0.309017 - 0.951057i) q^{70} +(3.66312 + 2.66141i) q^{71} +(1.80902 + 1.31433i) q^{72} +(2.28115 - 7.02067i) q^{73} +(1.14590 + 3.52671i) q^{74} +(-1.92705 + 1.40008i) q^{75} -10.4721 q^{76} +(-3.23607 + 0.726543i) q^{77} -2.61803 q^{78} +(4.92705 - 3.57971i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.92705 + 3.57971i) q^{82} +(-6.85410 - 4.97980i) q^{83} +(-0.500000 + 1.53884i) q^{84} +(1.73607 + 5.34307i) q^{85} +(5.73607 - 4.16750i) q^{86} +0.236068 q^{87} +(4.89919 - 5.56758i) q^{88} +1.32624 q^{89} +(0.809017 - 0.587785i) q^{90} +(-1.30902 - 4.02874i) q^{91} +(-2.85410 + 8.78402i) q^{92} +(2.42705 + 1.76336i) q^{93} +(2.57295 + 1.86936i) q^{94} +(-3.23607 + 9.95959i) q^{95} +(-1.73607 - 5.34307i) q^{96} +(4.28115 - 3.11044i) q^{97} +0.618034 q^{98} +(-3.04508 - 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} - 4 q^{10} + 9 q^{11} + 2 q^{12} - 7 q^{13} - 3 q^{14} + 2 q^{15} - 6 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} - 5 q^{24} + 6 q^{25} + q^{26} + q^{27} - 3 q^{28} - 7 q^{29} - q^{30} - 3 q^{31} + 18 q^{32} + 11 q^{33} - 22 q^{34} - 3 q^{35} - 2 q^{36} - 6 q^{37} - 4 q^{38} + 7 q^{39} - q^{41} - 2 q^{42} - 28 q^{43} - 12 q^{44} - 2 q^{45} + 2 q^{46} + 16 q^{47} - 9 q^{48} - q^{49} + 7 q^{50} + 11 q^{51} - 4 q^{52} + 25 q^{53} + 2 q^{54} - 2 q^{55} + 12 q^{57} + 11 q^{58} + q^{59} + 4 q^{60} + 19 q^{61} + 9 q^{62} + q^{63} + 3 q^{64} - 14 q^{65} - 3 q^{66} + 44 q^{67} - 7 q^{68} - 16 q^{69} - q^{70} - q^{71} + 5 q^{72} - 11 q^{73} + 18 q^{74} - q^{75} - 24 q^{76} - 4 q^{77} - 6 q^{78} + 13 q^{79} + 3 q^{80} - q^{81} + 13 q^{82} - 14 q^{83} - 2 q^{84} - 2 q^{85} + 14 q^{86} - 8 q^{87} - 5 q^{88} - 26 q^{89} + q^{90} - 3 q^{91} + 2 q^{92} + 3 q^{93} + 17 q^{94} - 4 q^{95} + 2 q^{96} - 3 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 - 4 * q^10 + 9 * q^11 + 2 * q^12 - 7 * q^13 - 3 * q^14 + 2 * q^15 - 6 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 - 5 * q^24 + 6 * q^25 + q^26 + q^27 - 3 * q^28 - 7 * q^29 - q^30 - 3 * q^31 + 18 * q^32 + 11 * q^33 - 22 * q^34 - 3 * q^35 - 2 * q^36 - 6 * q^37 - 4 * q^38 + 7 * q^39 - q^41 - 2 * q^42 - 28 * q^43 - 12 * q^44 - 2 * q^45 + 2 * q^46 + 16 * q^47 - 9 * q^48 - q^49 + 7 * q^50 + 11 * q^51 - 4 * q^52 + 25 * q^53 + 2 * q^54 - 2 * q^55 + 12 * q^57 + 11 * q^58 + q^59 + 4 * q^60 + 19 * q^61 + 9 * q^62 + q^63 + 3 * q^64 - 14 * q^65 - 3 * q^66 + 44 * q^67 - 7 * q^68 - 16 * q^69 - q^70 - q^71 + 5 * q^72 - 11 * q^73 + 18 * q^74 - q^75 - 24 * q^76 - 4 * q^77 - 6 * q^78 + 13 * q^79 + 3 * q^80 - q^81 + 13 * q^82 - 14 * q^83 - 2 * q^84 - 2 * q^85 + 14 * q^86 - 8 * q^87 - 5 * q^88 - 26 * q^89 + q^90 - 3 * q^91 + 2 * q^92 + 3 * q^93 + 17 * q^94 - 4 * q^95 + 2 * q^96 - 3 * q^97 - 2 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	−0.750358	−	0.661031i	$-0.770119\pi$
$2$	−0.500000	+	0.363271i	−0.353553	+	0.256872i	0.396805	+	0.917903i	$0.370119\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	0.840670	−	0.541547i	$-0.182161\pi$
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	−0.255260	+	0.966872i	$0.582161\pi$
$6$	0.500000	+	0.363271i	0.204124	+	0.148305i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.00000			−0.316228
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$12$	1.61803			0.467086
$13$	−3.42705	+	2.48990i	−0.950493	+	0.690574i	−0.950923	−	0.309426i	$-0.899863\pi$
$13$	−3.42705	+	2.48990i	−0.950493	+	0.690574i	0.000430477		1.00000i	$0.499863\pi$
$14$	−0.190983	−	0.587785i	−0.0510424	−	0.157092i
$15$	0.500000	−	1.53884i	0.129099	−	0.397327i
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	2.80902	+	2.04087i	0.681287	+	0.494984i	0.873784	−	0.486314i	$-0.161659\pi$
$17$	2.80902	+	2.04087i	0.681287	+	0.494984i	−0.192498	+	0.981297i	$0.561659\pi$
$18$	0.190983	−	0.587785i	0.0450151	−	0.138542i
$19$	2.00000	+	6.15537i	0.458831	+	1.41214i	0.866577	+	0.499043i	$0.166315\pi$
$19$	2.00000	+	6.15537i	0.458831	+	1.41214i	−0.407746	+	0.913095i	$0.633685\pi$
$20$	−2.11803	+	1.53884i	−0.473607	+	0.344095i
$21$	1.00000			0.218218
$22$	−1.88197	−	0.812299i	−0.401237	−	0.173183i
$23$	5.70820			1.19024			0.595121	−	0.803636i	$-0.297104\pi$
$23$	5.70820			1.19024			0.595121	+	0.803636i	$0.297104\pi$
$24$	−1.80902	+	1.31433i	−0.369264	+	0.268286i
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$	0.809017	−	2.48990i	0.158661	−	0.488309i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.30902	−	0.951057i	−0.247381	−	0.179733i
$29$	−0.0729490	+	0.224514i	−0.0135463	+	0.0416912i	−0.957601	−	0.288097i	$-0.906977\pi$
$29$	−0.0729490	+	0.224514i	−0.0135463	+	0.0416912i	0.944055	+	0.329788i	$0.106977\pi$
$30$	0.309017	+	0.951057i	0.0564185	+	0.173638i
$31$	−2.42705	+	1.76336i	−0.435911	+	0.316708i	−0.784008	−	0.620750i	$-0.786828\pi$
$31$	−2.42705	+	1.76336i	−0.435911	+	0.316708i	0.348097	+	0.937459i	$0.386828\pi$
$32$	5.61803			0.993137
$33$	2.19098	−	2.48990i	0.381401	−	0.433436i
$34$	−2.14590			−0.368018
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$	−0.500000	−	1.53884i	−0.0833333	−	0.256474i
$37$	1.85410	−	5.70634i	0.304812	−	0.938116i	−0.674935	−	0.737878i	$-0.735828\pi$
$37$	1.85410	−	5.70634i	0.304812	−	0.938116i	0.979747	−	0.200239i	$-0.0641718\pi$
$38$	−3.23607	−	2.35114i	−0.524960	−	0.381405i
$39$	3.42705	+	2.48990i	0.548767	+	0.398703i
$40$	1.11803	−	3.44095i	0.176777	−	0.544063i
$41$	−3.04508	−	9.37181i	−0.475562	−	1.46363i	−0.845198	−	0.534454i	$-0.820517\pi$
$41$	−3.04508	−	9.37181i	−0.475562	−	1.46363i	0.369635	−	0.929177i	$-0.379483\pi$
$42$	−0.500000	+	0.363271i	−0.0771517	+	0.0560540i
$43$	−11.4721			−1.74948			−0.874742	−	0.484589i	$-0.838969\pi$
$43$	−11.4721			−1.74948			−0.874742	+	0.484589i	$0.838969\pi$
$44$	−5.23607	+	1.17557i	−0.789367	+	0.177224i
$45$	−1.61803			−0.241202
$46$	−2.85410	+	2.07363i	−0.420814	+	0.305740i
$47$	−1.59017	−	4.89404i	−0.231950	−	0.713869i	−0.997511	−	0.0705060i	$-0.977539\pi$
$47$	−1.59017	−	4.89404i	−0.231950	−	0.713869i	0.765561	−	0.643363i	$-0.222461\pi$
$48$	−0.572949	+	1.76336i	−0.0826981	+	0.254518i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.19098	+	0.865300i	0.168430	+	0.122372i
$51$	1.07295	−	3.30220i	0.150243	−	0.462400i
$52$	−2.11803	−	6.51864i	−0.293718	−	0.903972i
$53$	10.1631	−	7.38394i	1.39601	−	1.01426i	0.400836	−	0.916150i	$-0.368720\pi$
$53$	10.1631	−	7.38394i	1.39601	−	1.01426i	0.995175	−	0.0981123i	$-0.0312804\pi$
$54$	−0.618034			−0.0841038
$55$	−0.500000	+	5.34307i	−0.0674200	+	0.720459i
$56$	2.23607			0.298807
$57$	5.23607	−	3.80423i	0.693534	−	0.503882i
$58$	−0.0450850	−	0.138757i	−0.00591995	−	0.0182197i
$59$	−1.42705	+	4.39201i	−0.185786	+	0.571791i	−0.999961	−	0.00882865i	$-0.997190\pi$
$59$	−1.42705	+	4.39201i	−0.185786	+	0.571791i	0.814175	+	0.580620i	$0.197190\pi$
$60$	2.11803	+	1.53884i	0.273437	+	0.198664i
$61$	6.42705	+	4.66953i	0.822900	+	0.597872i	0.917542	−	0.397640i	$-0.130171\pi$
$61$	6.42705	+	4.66953i	0.822900	+	0.597872i	−0.0946420	+	0.995511i	$0.530171\pi$
$62$	0.572949	−	1.76336i	0.0727646	−	0.223946i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	−6.85410			−0.850147
$66$	−0.190983	+	2.04087i	−0.0235084	+	0.251214i
$67$	13.2361			1.61704			0.808522	−	0.588467i	$-0.200268\pi$
$67$	13.2361			1.61704			0.808522	+	0.588467i	$0.200268\pi$
$68$	−4.54508	+	3.30220i	−0.551173	+	0.400450i
$69$	−1.76393	−	5.42882i	−0.212352	−	0.653554i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	3.66312	+	2.66141i	0.434732	+	0.315851i	0.783538	−	0.621343i	$-0.213413\pi$
$71$	3.66312	+	2.66141i	0.434732	+	0.315851i	−0.348806	+	0.937195i	$0.613413\pi$
$72$	1.80902	+	1.31433i	0.213195	+	0.154895i
$73$	2.28115	−	7.02067i	0.266989	−	0.821707i	−0.724240	−	0.689548i	$-0.757809\pi$
$73$	2.28115	−	7.02067i	0.266989	−	0.821707i	0.991229	−	0.132159i	$-0.0421909\pi$
$74$	1.14590	+	3.52671i	0.133208	+	0.409972i
$75$	−1.92705	+	1.40008i	−0.222517	+	0.161668i
$76$	−10.4721			−1.20124
$77$	−3.23607	+	0.726543i	−0.368784	+	0.0827972i
$78$	−2.61803			−0.296434
$79$	4.92705	−	3.57971i	0.554337	−	0.402749i	−0.275045	−	0.961431i	$-0.588693\pi$
$79$	4.92705	−	3.57971i	0.554337	−	0.402749i	0.829382	+	0.558682i	$0.188693\pi$
$80$	−0.927051	−	2.85317i	−0.103647	−	0.318994i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	4.92705	+	3.57971i	0.544102	+	0.395313i
$83$	−6.85410	−	4.97980i	−0.752335	−	0.546604i	0.144214	−	0.989546i	$-0.453934\pi$
$83$	−6.85410	−	4.97980i	−0.752335	−	0.546604i	−0.896550	+	0.442943i	$0.853934\pi$
$84$	−0.500000	+	1.53884i	−0.0545545	+	0.167901i
$85$	1.73607	+	5.34307i	0.188303	+	0.579537i
$86$	5.73607	−	4.16750i	0.618536	−	0.449393i
$87$	0.236068			0.0253091
$88$	4.89919	−	5.56758i	0.522255	−	0.593506i
$89$	1.32624			0.140581			0.0702905	−	0.997527i	$-0.477607\pi$
$89$	1.32624			0.140581			0.0702905	+	0.997527i	$0.477607\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−1.30902	−	4.02874i	−0.137222	−	0.422327i
$92$	−2.85410	+	8.78402i	−0.297561	+	0.915798i
$93$	2.42705	+	1.76336i	0.251673	+	0.182851i
$94$	2.57295	+	1.86936i	0.265379	+	0.192809i
$95$	−3.23607	+	9.95959i	−0.332014	+	1.02183i
$96$	−1.73607	−	5.34307i	−0.177187	−	0.545325i
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	−0.348834	−	0.937184i	$-0.613422\pi$
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	0.783520	+	0.621367i	$0.213422\pi$
$98$	0.618034			0.0624309
$99$	−3.04508	−	1.31433i	−0.306043	−	0.132095i
$100$	3.85410			0.385410
$101$	−9.09017	+	6.60440i	−0.904506	+	0.657162i	−0.939619	−	0.342221i	$-0.888821\pi$
$101$	−9.09017	+	6.60440i	−0.904506	+	0.657162i	0.0351136	+	0.999383i	$0.488821\pi$
$102$	0.663119	+	2.04087i	0.0656586	+	0.202076i
$103$	−4.78115	+	14.7149i	−0.471101	+	1.44990i	0.380044	+	0.924969i	$0.375909\pi$
$103$	−4.78115	+	14.7149i	−0.471101	+	1.44990i	−0.851145	+	0.524931i	$0.824091\pi$
$104$	7.66312	+	5.56758i	0.751431	+	0.545946i
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$	−2.39919	+	7.38394i	−0.233030	+	0.717191i
$107$	1.78115	+	5.48183i	0.172191	+	0.529948i	0.999494	−	0.0318072i	$-0.0101263\pi$
$107$	1.78115	+	5.48183i	0.172191	+	0.529948i	−0.827303	+	0.561755i	$0.810126\pi$
$108$	−1.30902	+	0.951057i	−0.125960	+	0.0915155i
$109$	−4.14590			−0.397105			−0.198553	−	0.980090i	$-0.563624\pi$
$109$	−4.14590			−0.397105			−0.198553	+	0.980090i	$0.563624\pi$
$110$	−1.69098	−	2.85317i	−0.161229	−	0.272039i
$111$	−6.00000			−0.569495
$112$	1.50000	−	1.08981i	0.141737	−	0.102978i
$113$	−3.45492	−	10.6331i	−0.325011	−	1.00028i	−0.971436	−	0.237303i	$-0.923736\pi$
$113$	−3.45492	−	10.6331i	−0.325011	−	1.00028i	0.646425	−	0.762978i	$-0.276264\pi$
$114$	−1.23607	+	3.80423i	−0.115768	+	0.356298i
$115$	7.47214	+	5.42882i	0.696780	+	0.506240i
$116$	−0.309017	−	0.224514i	−0.0286915	−	0.0208456i
$117$	1.30902	−	4.02874i	0.121019	−	0.372457i
$118$	−0.881966	−	2.71441i	−0.0811916	−	0.249882i
$119$	−2.80902	+	2.04087i	−0.257502	+	0.187086i
$120$	−3.61803			−0.330280
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	−4.90983			−0.444515
$123$	−7.97214	+	5.79210i	−0.718823	+	0.522256i
$124$	−1.50000	−	4.61653i	−0.134704	−	0.414576i
$125$	3.69098	−	11.3597i	0.330132	−	1.01604i
$126$	0.500000	+	0.363271i	0.0445435	+	0.0323628i
$127$	5.92705	+	4.30625i	0.525941	+	0.382118i	0.818837	−	0.574026i	$-0.194619\pi$
$127$	5.92705	+	4.30625i	0.525941	+	0.382118i	−0.292896	+	0.956144i	$0.594619\pi$
$128$	−3.51722	+	10.8249i	−0.310881	+	0.956794i
$129$	3.54508	+	10.9106i	0.312127	+	0.960629i
$130$	3.42705	−	2.48990i	0.300572	−	0.218379i
$131$	6.85410			0.598846			0.299423	−	0.954121i	$-0.403206\pi$
$131$	6.85410			0.598846			0.299423	+	0.954121i	$0.403206\pi$
$132$	2.73607	+	4.61653i	0.238144	+	0.401817i
$133$	−6.47214			−0.561205
$134$	−6.61803	+	4.80828i	−0.571711	+	0.415372i
$135$	0.500000	+	1.53884i	0.0430331	+	0.132442i
$136$	2.39919	−	7.38394i	0.205729	−	0.633167i
$137$	8.47214	+	6.15537i	0.723823	+	0.525888i	0.887603	−	0.460608i	$-0.152369\pi$
$137$	8.47214	+	6.15537i	0.723823	+	0.525888i	−0.163780	+	0.986497i	$0.552369\pi$
$138$	2.85410	+	2.07363i	0.242957	+	0.176519i
$139$	0.809017	−	2.48990i	0.0686199	−	0.211190i	−0.910866	−	0.412702i	$-0.864585\pi$
$139$	0.809017	−	2.48990i	0.0686199	−	0.211190i	0.979486	+	0.201511i	$0.0645852\pi$
$140$	−0.809017	−	2.48990i	−0.0683744	−	0.210435i
$141$	−4.16312	+	3.02468i	−0.350598	+	0.254724i
$142$	−2.79837			−0.234834
$143$	−12.8992	−	5.56758i	−1.07868	−	0.465585i
$144$	1.85410			0.154508
$145$	−0.309017	+	0.224514i	−0.0256625	+	0.0186449i
$146$	1.40983	+	4.33901i	0.116678	+	0.359099i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	7.85410	+	5.70634i	0.645603	+	0.469058i
$149$	1.11803	+	0.812299i	0.0915929	+	0.0665461i	0.632639	−	0.774447i	$-0.281972\pi$
$149$	1.11803	+	0.812299i	0.0915929	+	0.0665461i	−0.541046	+	0.840993i	$0.681972\pi$
$150$	0.454915	−	1.40008i	0.0371437	−	0.114316i
$151$	1.95492	+	6.01661i	0.159089	+	0.489625i	0.998552	−	0.0537914i	$-0.0171306\pi$
$151$	1.95492	+	6.01661i	0.159089	+	0.489625i	−0.839463	+	0.543416i	$0.817131\pi$
$152$	11.7082	−	8.50651i	0.949661	−	0.689969i
$153$	−3.47214			−0.280706
$154$	1.35410	−	1.53884i	0.109117	−	0.124003i
$155$	−4.85410			−0.389891
$156$	−5.54508	+	4.02874i	−0.443962	+	0.322557i
$157$	−2.10081	−	6.46564i	−0.167663	−	0.516014i	0.831560	−	0.555436i	$-0.187448\pi$
$157$	−2.10081	−	6.46564i	−0.167663	−	0.516014i	−0.999223	+	0.0394216i	$0.987448\pi$
$158$	−1.16312	+	3.57971i	−0.0925328	+	0.284787i
$159$	−10.1631	−	7.38394i	−0.805988	−	0.585584i
$160$	7.35410	+	5.34307i	0.581393	+	0.422407i
$161$	−1.76393	+	5.42882i	−0.139017	+	0.427851i
$162$	0.190983	+	0.587785i	0.0150050	+	0.0461808i
$163$	14.8262	−	10.7719i	1.16128	−	0.843720i	0.171341	−	0.985212i	$-0.445190\pi$
$163$	14.8262	−	10.7719i	1.16128	−	0.843720i	0.989939	+	0.141492i	$0.0451900\pi$
$164$	15.9443			1.24504
$165$	5.23607	−	1.17557i	0.407627	−	0.0915180i
$166$	5.23607			0.406398
$167$	1.73607	−	1.26133i	0.134341	−	0.0976044i	−0.518585	−	0.855026i	$-0.673541\pi$
$167$	1.73607	−	1.26133i	0.134341	−	0.0976044i	0.652926	+	0.757421i	$0.273541\pi$
$168$	−0.690983	−	2.12663i	−0.0533105	−	0.164073i
$169$	1.52786	−	4.70228i	0.117528	−	0.361714i
$170$	−2.80902	−	2.04087i	−0.215442	−	0.156528i
$171$	−5.23607	−	3.80423i	−0.400412	−	0.290916i
$172$	5.73607	−	17.6538i	0.437371	−	1.34609i
$173$	3.33688	+	10.2699i	0.253698	+	0.780803i	0.994083	+	0.108620i	$0.0346432\pi$
$173$	3.33688	+	10.2699i	0.253698	+	0.780803i	−0.740385	+	0.672183i	$0.765357\pi$
$174$	−0.118034	+	0.0857567i	−0.00894813	+	0.00650120i
$175$	2.38197			0.180060
$176$	0.572949	−	6.12261i	0.0431877	−	0.461509i
$177$	4.61803			0.347113
$178$	−0.663119	+	0.481784i	−0.0497029	+	0.0361112i
$179$	−5.78115	−	17.7926i	−0.432104	−	1.32988i	−0.896026	−	0.444002i	$-0.853558\pi$
$179$	−5.78115	−	17.7926i	−0.432104	−	1.32988i	0.463922	−	0.885876i	$-0.346442\pi$
$180$	0.809017	−	2.48990i	0.0603006	−	0.185586i
$181$	0.427051	+	0.310271i	0.0317424	+	0.0230622i	0.603543	−	0.797330i	$-0.293755\pi$
$181$	0.427051	+	0.310271i	0.0317424	+	0.0230622i	−0.571801	+	0.820392i	$0.693755\pi$
$182$	2.11803	+	1.53884i	0.156999	+	0.114067i
$183$	2.45492	−	7.55545i	0.181473	−	0.558515i
$184$	−3.94427	−	12.1392i	−0.290776	−	0.894915i
$185$	7.85410	−	5.70634i	0.577445	−	0.419538i
$186$	−1.85410			−0.135949
$187$	−1.07295	+	11.4657i	−0.0784618	+	0.838453i
$188$	8.32624			0.607253
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	−2.00000	−	6.15537i	−0.145095	−	0.446557i
$191$	−5.01722	+	15.4414i	−0.363033	+	1.11730i	0.588170	+	0.808737i	$0.299849\pi$
$191$	−5.01722	+	15.4414i	−0.363033	+	1.11730i	−0.951203	+	0.308565i	$0.900151\pi$
$192$	−0.190983	−	0.138757i	−0.0137830	−	0.0100139i
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.0491400	−	0.998792i	$-0.515648\pi$
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.965093	+	0.261909i	$0.915648\pi$
$194$	−1.01064	+	3.11044i	−0.0725599	+	0.223317i
$195$	2.11803	+	6.51864i	0.151676	+	0.466809i
$196$	1.30902	−	0.951057i	0.0935012	−	0.0679326i
$197$	4.65248			0.331475			0.165738	−	0.986170i	$-0.447000\pi$
$197$	4.65248			0.331475			0.165738	+	0.986170i	$0.447000\pi$
$198$	2.00000	−	0.449028i	0.142134	−	0.0319110i
$199$	−26.2148			−1.85832			−0.929158	−	0.369682i	$-0.879467\pi$
$199$	−26.2148			−1.85832			−0.929158	+	0.369682i	$0.879467\pi$
$200$	−4.30902	+	3.13068i	−0.304694	+	0.221373i
$201$	−4.09017	−	12.5882i	−0.288498	−	0.887907i
$202$	2.14590	−	6.60440i	0.150985	−	0.464684i
$203$	−0.190983	−	0.138757i	−0.0134044	−	0.00973885i
$204$	4.54508	+	3.30220i	0.318220	+	0.231200i
$205$	4.92705	−	15.1639i	0.344120	−	1.05909i
$206$	−2.95492	−	9.09429i	−0.205879	−	0.633629i
$207$	−4.61803	+	3.35520i	−0.320976	+	0.233202i
$208$	7.85410			0.544584
$209$	−14.1803	+	16.1150i	−0.980875	+	1.11470i
$210$	−1.00000			−0.0690066
$211$	15.1353	−	10.9964i	1.04195	−	0.757024i	0.0712879	−	0.997456i	$-0.477289\pi$
$211$	15.1353	−	10.9964i	1.04195	−	0.757024i	0.970666	+	0.240432i	$0.0772891\pi$
$212$	6.28115	+	19.3314i	0.431391	+	1.32769i
$213$	1.39919	−	4.30625i	0.0958707	−	0.295060i
$214$	−2.88197	−	2.09387i	−0.197007	−	0.143134i
$215$	−15.0172	−	10.9106i	−1.02417	−	0.744100i
$216$	0.690983	−	2.12663i	0.0470154	−	0.144699i
$217$	−0.927051	−	2.85317i	−0.0629323	−	0.193686i
$218$	2.07295	−	1.50609i	0.140398	−	0.102005i
$219$	−7.38197			−0.498827
$220$	−7.97214	−	3.44095i	−0.537481	−	0.231989i
$221$	−14.7082			−0.989381
$222$	3.00000	−	2.17963i	0.201347	−	0.146287i
$223$	6.16312	+	18.9681i	0.412713	+	1.27020i	0.914281	+	0.405081i	$0.132757\pi$
$223$	6.16312	+	18.9681i	0.412713	+	1.27020i	−0.501568	+	0.865118i	$0.667243\pi$
$224$	−1.73607	+	5.34307i	−0.115996	+	0.356999i
$225$	1.92705	+	1.40008i	0.128470	+	0.0933390i
$226$	5.59017	+	4.06150i	0.371853	+	0.270167i
$227$	−0.281153	+	0.865300i	−0.0186608	+	0.0574320i	−0.959953	−	0.280160i	$-0.909612\pi$
$227$	−0.281153	+	0.865300i	−0.0186608	+	0.0574320i	0.941293	+	0.337592i	$0.109612\pi$
$228$	3.23607	+	9.95959i	0.214314	+	0.659590i
$229$	−12.2361	+	8.89002i	−0.808582	+	0.587469i	−0.913419	−	0.407020i	$-0.866568\pi$
$229$	−12.2361	+	8.89002i	−0.808582	+	0.587469i	0.104837	+	0.994489i	$0.466568\pi$
$230$	−5.70820			−0.376388
$231$	1.69098	+	2.85317i	0.111259	+	0.187725i
$232$	0.527864			0.0346560
$233$	12.7533	−	9.26581i	0.835496	−	0.607023i	−0.0856131	−	0.996328i	$-0.527285\pi$
$233$	12.7533	−	9.26581i	0.835496	−	0.607023i	0.921109	+	0.389305i	$0.127285\pi$
$234$	0.809017	+	2.48990i	0.0528871	+	0.162770i
$235$	2.57295	−	7.91872i	0.167841	−	0.516561i
$236$	−6.04508	−	4.39201i	−0.393502	−	0.285896i
$237$	−4.92705	−	3.57971i	−0.320046	−	0.232527i
$238$	0.663119	−	2.04087i	0.0429836	−	0.132290i
$239$	−6.68034	−	20.5600i	−0.432115	−	1.32991i	−0.896014	−	0.444026i	$-0.853550\pi$
$239$	−6.68034	−	20.5600i	−0.432115	−	1.32991i	0.463899	−	0.885888i	$-0.346450\pi$
$240$	−2.42705	+	1.76336i	−0.156665	+	0.113824i
$241$	10.4164			0.670980			0.335490	−	0.942044i	$-0.391098\pi$
$241$	10.4164			0.670980			0.335490	+	0.942044i	$0.391098\pi$
$242$	−0.864745	−	6.74315i	−0.0555879	−	0.433466i
$243$	−1.00000			−0.0641500
$244$	−10.3992	+	7.55545i	−0.665740	+	0.483688i
$245$	−0.500000	−	1.53884i	−0.0319438	−	0.0983130i
$246$	1.88197	−	5.79210i	0.119990	−	0.369291i
$247$	−22.1803	−	16.1150i	−1.41130	−	1.02537i
$248$	5.42705	+	3.94298i	0.344618	+	0.250380i
$249$	−2.61803	+	8.05748i	−0.165911	+	0.510622i
$250$	2.28115	+	7.02067i	0.144273	+	0.444026i
$251$	11.2812	−	8.19624i	0.712060	−	0.517342i	−0.171778	−	0.985136i	$-0.554951\pi$
$251$	11.2812	−	8.19624i	0.712060	−	0.517342i	0.883838	+	0.467794i	$0.154951\pi$
$252$	1.61803			0.101927
$253$	9.65248	+	16.2865i	0.606846	+	1.02392i
$254$	−4.52786			−0.284103
$255$	4.54508	−	3.30220i	0.284624	−	0.206792i
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	7.38197	−	22.7194i	0.460474	−	1.41719i	−0.404112	−	0.914710i	$-0.632419\pi$
$257$	7.38197	−	22.7194i	0.460474	−	1.41719i	0.864586	−	0.502485i	$-0.167581\pi$
$258$	−5.73607	−	4.16750i	−0.357112	−	0.259457i
$259$	4.85410	+	3.52671i	0.301619	+	0.219139i
$260$	3.42705	−	10.5474i	0.212537	−	0.654121i
$261$	−0.0729490	−	0.224514i	−0.00451543	−	0.0138971i
$262$	−3.42705	+	2.48990i	−0.211724	+	0.153826i
$263$	−9.29180			−0.572957			−0.286478	−	0.958087i	$-0.592485\pi$
$263$	−9.29180			−0.572957			−0.286478	+	0.958087i	$0.592485\pi$
$264$	−6.80902	−	2.93893i	−0.419066	−	0.180878i
$265$	20.3262			1.24863
$266$	3.23607	−	2.35114i	0.198416	−	0.144158i
$267$	−0.409830	−	1.26133i	−0.0250812	−	0.0771920i
$268$	−6.61803	+	20.3682i	−0.404261	+	1.24419i
$269$	23.6074	+	17.1518i	1.43937	+	1.04576i	0.988174	+	0.153336i	$0.0490017\pi$
$269$	23.6074	+	17.1518i	1.43937	+	1.04576i	0.451194	+	0.892426i	$0.350998\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−6.83688	+	21.0418i	−0.415311	+	1.27820i	0.496662	+	0.867944i	$0.334559\pi$
$271$	−6.83688	+	21.0418i	−0.415311	+	1.27820i	−0.911972	+	0.410251i	$0.865441\pi$
$272$	−1.98936	−	6.12261i	−0.120622	−	0.371238i
$273$	−3.42705	+	2.48990i	−0.207415	+	0.150695i
$274$	−6.47214			−0.390996
$275$	5.21885	−	5.93085i	0.314708	−	0.357644i
$276$	9.23607			0.555946
$277$	−6.85410	+	4.97980i	−0.411823	+	0.299207i	−0.774339	−	0.632770i	$-0.781918\pi$
$277$	−6.85410	+	4.97980i	−0.411823	+	0.299207i	0.362516	+	0.931977i	$0.381918\pi$
$278$	0.500000	+	1.53884i	0.0299880	+	0.0922936i
$279$	0.927051	−	2.85317i	0.0555011	−	0.170815i
$280$	2.92705	+	2.12663i	0.174925	+	0.127090i
$281$	−8.78115	−	6.37988i	−0.523840	−	0.380592i	0.294209	−	0.955741i	$-0.404944\pi$
$281$	−8.78115	−	6.37988i	−0.523840	−	0.380592i	−0.818048	+	0.575149i	$0.804944\pi$
$282$	0.982779	−	3.02468i	0.0585236	−	0.180117i
$283$	3.98278	+	12.2577i	0.236752	+	0.728647i	0.996884	+	0.0788786i	$0.0251340\pi$
$283$	3.98278	+	12.2577i	0.236752	+	0.728647i	−0.760133	+	0.649768i	$0.774866\pi$
$284$	−5.92705	+	4.30625i	−0.351706	+	0.255529i
$285$	10.4721			0.620316
$286$	8.47214	−	1.90211i	0.500968	−	0.112474i
$287$	9.85410			0.581669
$288$	−4.54508	+	3.30220i	−0.267822	+	0.194584i
$289$	−1.52786	−	4.70228i	−0.0898744	−	0.276605i
$290$	0.0729490	−	0.224514i	0.00428371	−	0.0131839i
$291$	−4.28115	−	3.11044i	−0.250966	−	0.182337i
$292$	9.66312	+	7.02067i	0.565491	+	0.410853i
$293$	−2.38197	+	7.33094i	−0.139156	+	0.428278i	−0.996213	−	0.0869431i	$-0.972290\pi$
$293$	−2.38197	+	7.33094i	−0.139156	+	0.428278i	0.857057	+	0.515221i	$0.172290\pi$
$294$	−0.190983	−	0.587785i	−0.0111384	−	0.0342803i
$295$	−6.04508	+	4.39201i	−0.351958	+	0.255713i
$296$	−13.4164			−0.779813
$297$	−0.309017	+	3.30220i	−0.0179310	+	0.191613i
$298$	−0.854102			−0.0494768
$299$	−19.5623	+	14.2128i	−1.13132	+	0.821950i
$300$	−1.19098	−	3.66547i	−0.0687614	−	0.211626i
$301$	3.54508	−	10.9106i	0.204335	−	0.628879i
$302$	−3.16312	−	2.29814i	−0.182017	−	0.132243i
$303$	9.09017	+	6.60440i	0.522217	+	0.379413i
$304$	3.70820	−	11.4127i	0.212680	−	0.654562i
$305$	3.97214	+	12.2250i	0.227444	+	0.700000i
$306$	1.73607	−	1.26133i	0.0992444	−	0.0721053i
$307$	8.05573			0.459765			0.229882	−	0.973218i	$-0.426166\pi$
$307$	8.05573			0.459765			0.229882	+	0.973218i	$0.426166\pi$
$308$	0.500000	−	5.34307i	0.0284901	−	0.304450i
$309$	15.4721			0.880179
$310$	2.42705	−	1.76336i	0.137847	−	0.100152i
$311$	2.10081	+	6.46564i	0.119126	+	0.366633i	0.992785	−	0.119906i	$-0.0382593\pi$
$311$	2.10081	+	6.46564i	0.119126	+	0.366633i	−0.873659	+	0.486539i	$0.838259\pi$
$312$	2.92705	−	9.00854i	0.165712	−	0.510008i
$313$	−25.9615	−	18.8621i	−1.46743	−	1.06615i	−0.981348	−	0.192237i	$-0.938426\pi$
$313$	−25.9615	−	18.8621i	−1.46743	−	1.06615i	−0.486082	−	0.873913i	$-0.661574\pi$
$314$	3.39919	+	2.46965i	0.191827	+	0.139371i
$315$	0.500000	−	1.53884i	0.0281718	−	0.0867039i
$316$	3.04508	+	9.37181i	0.171299	+	0.527205i
$317$	28.2254	−	20.5070i	1.58530	−	1.15179i	0.675011	−	0.737807i	$-0.264139\pi$
$317$	28.2254	−	20.5070i	1.58530	−	1.15179i	0.910286	−	0.413979i	$-0.135861\pi$
$318$	7.76393			0.435380
$319$	−0.763932	+	0.171513i	−0.0427720	+	0.00960291i
$320$	0.381966			0.0213525
$321$	4.66312	−	3.38795i	0.260270	−	0.189097i
$322$	−1.09017	−	3.35520i	−0.0607528	−	0.186978i
$323$	−6.94427	+	21.3723i	−0.386390	+	1.18918i
$324$	1.30902	+	0.951057i	0.0727232	+	0.0528365i
$325$	8.16312	+	5.93085i	0.452808	+	0.328985i
$326$	−3.50000	+	10.7719i	−0.193847	+	0.596600i
$327$	1.28115	+	3.94298i	0.0708479	+	0.218047i
$328$	−17.8262	+	12.9515i	−0.984289	+	0.715128i
$329$	5.14590			0.283703
$330$	−2.19098	+	2.48990i	−0.120610	+	0.137064i
$331$	−19.2918			−1.06037			−0.530187	−	0.847881i	$-0.677878\pi$
$331$	−19.2918			−1.06037			−0.530187	+	0.847881i	$0.677878\pi$
$332$	11.0902	−	8.05748i	0.608652	−	0.442212i
$333$	1.85410	+	5.70634i	0.101604	+	0.312705i
$334$	−0.409830	+	1.26133i	−0.0224249	+	0.0690168i
$335$	17.3262	+	12.5882i	0.946634	+	0.687769i
$336$	−1.50000	−	1.08981i	−0.0818317	−	0.0594542i
$337$	−1.30902	+	4.02874i	−0.0713067	+	0.219459i	−0.980359	−	0.197224i	$-0.936808\pi$
$337$	−1.30902	+	4.02874i	−0.0713067	+	0.219459i	0.909052	+	0.416683i	$0.136808\pi$
$338$	0.944272	+	2.90617i	0.0513616	+	0.158075i
$339$	−9.04508	+	6.57164i	−0.491262	+	0.356922i
$340$	−9.09017			−0.492984
$341$	−9.13525	−	3.94298i	−0.494702	−	0.213525i
$342$	4.00000			0.216295
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	7.92705	+	24.3970i	0.427398	+	1.31540i
$345$	2.85410	−	8.78402i	0.153660	−	0.472916i
$346$	−5.39919	−	3.92274i	−0.290262	−	0.210888i
$347$	0.381966	+	0.277515i	0.0205050	+	0.0148978i	0.597991	−	0.801503i	$-0.295966\pi$
$347$	0.381966	+	0.277515i	0.0205050	+	0.0148978i	−0.577486	+	0.816401i	$0.695966\pi$
$348$	−0.118034	+	0.363271i	−0.00632729	+	0.0194734i
$349$	−5.35410	−	16.4782i	−0.286599	−	0.882060i	−0.985915	−	0.167247i	$-0.946512\pi$
$349$	−5.35410	−	16.4782i	−0.286599	−	0.882060i	0.699316	−	0.714812i	$-0.253488\pi$
$350$	−1.19098	+	0.865300i	−0.0636607	+	0.0462522i
$351$	−4.23607			−0.226105
$352$	9.50000	+	16.0292i	0.506352	+	0.854359i
$353$	−4.12461			−0.219531			−0.109765	−	0.993958i	$-0.535010\pi$
$353$	−4.12461			−0.219531			−0.109765	+	0.993958i	$0.535010\pi$
$354$	−2.30902	+	1.67760i	−0.122723	+	0.0891634i
$355$	2.26393	+	6.96767i	0.120157	+	0.369805i
$356$	−0.663119	+	2.04087i	−0.0351452	+	0.108166i
$357$	2.80902	+	2.04087i	0.148669	+	0.108014i
$358$	9.35410	+	6.79615i	0.494380	+	0.359188i
$359$	3.20820	−	9.87384i	0.169323	−	0.521121i	−0.830006	−	0.557754i	$-0.811663\pi$
$359$	3.20820	−	9.87384i	0.169323	−	0.521121i	0.999329	+	0.0366329i	$0.0116632\pi$
$360$	1.11803	+	3.44095i	0.0589256	+	0.181354i
$361$	−18.5172	+	13.4535i	−0.974591	+	0.708082i
$362$	−0.326238			−0.0171467
$363$	10.8090	+	2.04087i	0.567326	+	0.107118i
$364$	6.85410			0.359253
$365$	9.66312	−	7.02067i	0.505791	−	0.367478i
$366$	1.51722	+	4.66953i	0.0793064	+	0.244080i
$367$	−1.54508	+	4.75528i	−0.0806528	+	0.248224i	−0.983250	−	0.182263i	$-0.941658\pi$
$367$	−1.54508	+	4.75528i	−0.0806528	+	0.248224i	0.902597	+	0.430486i	$0.141658\pi$
$368$	−8.56231	−	6.22088i	−0.446341	−	0.324286i
$369$	7.97214	+	5.79210i	0.415013	+	0.301524i
$370$	−1.85410	+	5.70634i	−0.0963902	+	0.296658i
$371$	3.88197	+	11.9475i	0.201542	+	0.620281i
$372$	−3.92705	+	2.85317i	−0.203608	+	0.147930i
$373$	−20.2918			−1.05067			−0.525335	−	0.850896i	$-0.676060\pi$
$373$	−20.2918			−1.05067			−0.525335	+	0.850896i	$0.676060\pi$
$374$	−3.62868	−	6.12261i	−0.187634	−	0.316593i
$375$	−11.9443			−0.616800
$376$	−9.30902	+	6.76340i	−0.480076	+	0.348796i
$377$	−0.309017	−	0.951057i	−0.0159152	−	0.0489819i
$378$	0.190983	−	0.587785i	0.00982311	−	0.0302324i
$379$	1.54508	+	1.12257i	0.0793657	+	0.0576625i	0.626761	−	0.779212i	$-0.284380\pi$
$379$	1.54508	+	1.12257i	0.0793657	+	0.0576625i	−0.547395	+	0.836874i	$0.684380\pi$
$380$	−13.7082	−	9.95959i	−0.703216	−	0.510916i
$381$	2.26393	−	6.96767i	0.115985	−	0.356964i
$382$	−3.10081	−	9.54332i	−0.158651	−	0.488279i
$383$	2.16312	−	1.57160i	0.110530	−	0.0803049i	−0.531147	−	0.847280i	$-0.678239\pi$
$383$	2.16312	−	1.57160i	0.110530	−	0.0803049i	0.641677	+	0.766975i	$0.278239\pi$
$384$	11.3820			0.580834
$385$	−4.92705	−	2.12663i	−0.251106	−	0.108383i
$386$	10.7639			0.547870
$387$	9.28115	−	6.74315i	0.471788	−	0.342774i
$388$	2.64590	+	8.14324i	0.134325	+	0.413410i
$389$	−5.32624	+	16.3925i	−0.270051	+	0.831131i	0.720436	+	0.693522i	$0.243942\pi$
$389$	−5.32624	+	16.3925i	−0.270051	+	0.831131i	−0.990487	+	0.137610i	$0.956058\pi$
$390$	−3.42705	−	2.48990i	−0.173535	−	0.126081i
$391$	16.0344	+	11.6497i	0.810897	+	0.589151i
$392$	−0.690983	+	2.12663i	−0.0348999	+	0.107411i
$393$	−2.11803	−	6.51864i	−0.106841	−	0.328822i
$394$	−2.32624	+	1.69011i	−0.117194	+	0.0851466i
$395$	9.85410			0.495814
$396$	3.54508	−	4.02874i	0.178147	−	0.202452i
$397$	−10.5623			−0.530107			−0.265053	−	0.964234i	$-0.585390\pi$
$397$	−10.5623			−0.530107			−0.265053	+	0.964234i	$0.585390\pi$
$398$	13.1074	−	9.52308i	0.657014	−	0.477349i
$399$	2.00000	+	6.15537i	0.100125	+	0.308154i
$400$	−1.36475	+	4.20025i	−0.0682373	+	0.210013i
$401$	−22.4443	−	16.3067i	−1.12081	−	0.814319i	−0.136481	−	0.990643i	$-0.543579\pi$
$401$	−22.4443	−	16.3067i	−1.12081	−	0.814319i	−0.984332	+	0.176324i	$0.943579\pi$
$402$	6.61803	+	4.80828i	0.330078	+	0.239815i
$403$	3.92705	−	12.0862i	0.195620	−	0.602058i
$404$	−5.61803	−	17.2905i	−0.279508	−	0.860236i
$405$	1.30902	−	0.951057i	0.0650456	−	0.0472584i
$406$	0.145898			0.00724080
$407$	19.4164	−	4.35926i	0.962436	−	0.216080i
$408$	−7.76393			−0.384372
$409$	−6.63525	+	4.82079i	−0.328092	+	0.238373i	−0.739621	−	0.673024i	$-0.764995\pi$
$409$	−6.63525	+	4.82079i	−0.328092	+	0.238373i	0.411528	+	0.911397i	$0.364995\pi$
$410$	3.04508	+	9.37181i	0.150386	+	0.462841i
$411$	3.23607	−	9.95959i	0.159623	−	0.491271i
$412$	−20.2533	−	14.7149i	−0.997808	−	0.724950i
$413$	−3.73607	−	2.71441i	−0.183840	−	0.133567i
$414$	1.09017	−	3.35520i	0.0535789	−	0.164899i
$415$	−4.23607	−	13.0373i	−0.207940	−	0.639975i
$416$	−19.2533	+	13.9883i	−0.943970	+	0.685834i
$417$	−2.61803			−0.128206
$418$	1.23607	−	13.2088i	0.0604581	−	0.646063i
$419$	−35.6180			−1.74005			−0.870027	−	0.493003i	$-0.835899\pi$
$419$	−35.6180			−1.74005			−0.870027	+	0.493003i	$0.835899\pi$
$420$	−2.11803	+	1.53884i	−0.103349	+	0.0750878i
$421$	5.60739	+	17.2578i	0.273288	+	0.841092i	0.989667	+	0.143382i	$0.0457978\pi$
$421$	5.60739	+	17.2578i	0.273288	+	0.841092i	−0.716380	+	0.697710i	$0.754202\pi$
$422$	−3.57295	+	10.9964i	−0.173928	+	0.535297i
$423$	4.16312	+	3.02468i	0.202418	+	0.147065i
$424$	−22.7254	−	16.5110i	−1.10364	−	0.801844i
$425$	2.55573	−	7.86572i	0.123971	−	0.381544i
$426$	0.864745	+	2.66141i	0.0418970	+	0.128946i
$427$	−6.42705	+	4.66953i	−0.311027	+	0.225974i
$428$	−9.32624			−0.450801
$429$	−1.30902	+	13.9883i	−0.0631999	+	0.675363i
$430$	11.4721			0.553236
$431$	5.78115	−	4.20025i	0.278468	−	0.202319i	−0.439781	−	0.898105i	$-0.644944\pi$
$431$	5.78115	−	4.20025i	0.278468	−	0.202319i	0.718249	+	0.695786i	$0.244944\pi$
$432$	−0.572949	−	1.76336i	−0.0275660	−	0.0848395i
$433$	−2.14590	+	6.60440i	−0.103125	+	0.317387i	−0.989286	−	0.145991i	$-0.953363\pi$
$433$	−2.14590	+	6.60440i	−0.103125	+	0.317387i	0.886161	+	0.463378i	$0.153363\pi$
$434$	1.50000	+	1.08981i	0.0720023	+	0.0523127i
$435$	0.309017	+	0.224514i	0.0148162	+	0.0107646i
$436$	2.07295	−	6.37988i	0.0992763	−	0.305541i
$437$	11.4164	+	35.1361i	0.546121	+	1.68079i
$438$	3.69098	−	2.68166i	0.176362	−	0.128134i
$439$	35.6525			1.70160			0.850800	−	0.525490i	$-0.176118\pi$
$439$	35.6525			1.70160			0.850800	+	0.525490i	$0.176118\pi$
$440$	11.7082	−	2.62866i	0.558167	−	0.125316i
$441$	1.00000			0.0476190
$442$	7.35410	−	5.34307i	0.349799	−	0.254144i
$443$	7.61803	+	23.4459i	0.361944	+	1.11395i	0.951873	+	0.306493i	$0.0991557\pi$
$443$	7.61803	+	23.4459i	0.361944	+	1.11395i	−0.589929	+	0.807455i	$0.700844\pi$
$444$	3.00000	−	9.23305i	0.142374	−	0.438181i
$445$	1.73607	+	1.26133i	0.0822975	+	0.0597926i
$446$	−9.97214	−	7.24518i	−0.472194	−	0.343069i
$447$	0.427051	−	1.31433i	0.0201988	−	0.0621656i
$448$	0.0729490	+	0.224514i	0.00344652	+	0.0106073i
$449$	16.6631	−	12.1065i	0.786381	−	0.571339i	−0.120506	−	0.992713i	$-0.538452\pi$
$449$	16.6631	−	12.1065i	0.786381	−	0.571339i	0.906887	+	0.421373i	$0.138452\pi$
$450$	−1.47214			−0.0693972
$451$	21.5902	−	24.5357i	1.01664	−	1.15534i
$452$	18.0902			0.850890
$453$	5.11803	−	3.71847i	0.240466	−	0.174709i
$454$	−0.173762	−	0.534785i	−0.00815506	−	0.0250987i
$455$	2.11803	−	6.51864i	0.0992950	−	0.305598i
$456$	−11.7082	−	8.50651i	−0.548287	−	0.398354i
$457$	−15.1631	−	11.0167i	−0.709301	−	0.515337i	0.173647	−	0.984808i	$-0.444445\pi$
$457$	−15.1631	−	11.0167i	−0.709301	−	0.515337i	−0.882948	+	0.469471i	$0.844445\pi$
$458$	2.88854	−	8.89002i	0.134973	−	0.415404i
$459$	1.07295	+	3.30220i	0.0500810	+	0.154133i
$460$	−12.0902	+	8.78402i	−0.563707	+	0.409557i
$461$	28.3050			1.31829			0.659147	−	0.752015i	$-0.270918\pi$
$461$	28.3050			1.31829			0.659147	+	0.752015i	$0.270918\pi$
$462$	−1.88197	−	0.812299i	−0.0875570	−	0.0377916i
$463$	−14.9787			−0.696120			−0.348060	−	0.937472i	$-0.613159\pi$
$463$	−14.9787			−0.696120			−0.348060	+	0.937472i	$0.613159\pi$
$464$	0.354102	−	0.257270i	0.0164388	−	0.0119435i
$465$	1.50000	+	4.61653i	0.0695608	+	0.214086i
$466$	−3.01064	+	9.26581i	−0.139465	+	0.429230i
$467$	21.6074	+	15.6987i	0.999871	+	0.726449i	0.962060	−	0.272836i	$-0.0879617\pi$
$467$	21.6074	+	15.6987i	0.999871	+	0.726449i	0.0378103	+	0.999285i	$0.487962\pi$
$468$	5.54508	+	4.02874i	0.256322	+	0.186229i
$469$	−4.09017	+	12.5882i	−0.188866	+	0.581271i
$470$	1.59017	+	4.89404i	0.0733491	+	0.225745i
$471$	−5.50000	+	3.99598i	−0.253427	+	0.184125i
$472$	10.3262			0.475304
$473$	−19.3992	−	32.7319i	−0.891976	−	1.50502i
$474$	3.76393			0.172883
$475$	12.4721	−	9.06154i	0.572261	−	0.415772i
$476$	−1.73607	−	5.34307i	−0.0795725	−	0.244899i
$477$	−3.88197	+	11.9475i	−0.177743	+	0.547037i
$478$	10.8090	+	7.85321i	0.494393	+	0.359197i
$479$	−24.5795	−	17.8581i	−1.12307	−	0.815956i	−0.138396	−	0.990377i	$-0.544195\pi$
$479$	−24.5795	−	17.8581i	−1.12307	−	0.815956i	−0.984671	+	0.174421i	$0.944195\pi$
$480$	2.80902	−	8.64527i	0.128213	−	0.394601i
$481$	7.85410	+	24.1724i	0.358116	+	1.10217i
$482$	−5.20820	+	3.78398i	−0.237227	+	0.172356i
$483$	5.70820			0.259732
$484$	−12.2082	−	12.9515i	−0.554918	−	0.588705i
$485$	8.56231			0.388794
$486$	0.500000	−	0.363271i	0.0226805	−	0.0164783i
$487$	−4.75329	−	14.6291i	−0.215392	−	0.662909i	−0.999126	−	0.0418113i	$-0.986687\pi$
$487$	−4.75329	−	14.6291i	−0.215392	−	0.662909i	0.783733	−	0.621097i	$-0.213313\pi$
$488$	5.48936	−	16.8945i	0.248492	−	0.764778i
$489$	−14.8262	−	10.7719i	−0.670466	−	0.487122i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	−2.56231	+	7.88597i	−0.115635	+	0.355889i	−0.992079	−	0.125616i	$-0.959909\pi$
$491$	−2.56231	+	7.88597i	−0.115635	+	0.355889i	0.876444	+	0.481504i	$0.159909\pi$
$492$	−4.92705	−	15.1639i	−0.222129	−	0.683642i
$493$	−0.663119	+	0.481784i	−0.0298654	+	0.0216985i
$494$	16.9443			0.762359
$495$	−2.73607	−	4.61653i	−0.122977	−	0.207497i
$496$	5.56231			0.249755
$497$	−3.66312	+	2.66141i	−0.164313	+	0.119381i
$498$	−1.61803	−	4.97980i	−0.0725058	−	0.223150i
$499$	2.16312	−	6.65740i	0.0968345	−	0.298026i	−0.890893	−	0.454213i	$-0.849920\pi$
$499$	2.16312	−	6.65740i	0.0968345	−	0.298026i	0.987727	+	0.156187i	$0.0499204\pi$
$500$	15.6353	+	11.3597i	0.699230	+	0.508020i
$501$	−1.73607	−	1.26133i	−0.0775618	−	0.0563519i
$502$	−2.66312	+	8.19624i	−0.118861	+	0.365816i
$503$	−12.9828	−	39.9569i	−0.578874	−	1.78159i	−0.622593	−	0.782546i	$-0.713921\pi$
$503$	−12.9828	−	39.9569i	−0.578874	−	1.78159i	0.0437197	−	0.999044i	$-0.486079\pi$
$504$	−1.80902	+	1.31433i	−0.0805800	+	0.0585448i
$505$	−18.1803			−0.809015
$506$	−10.7426	−	4.63677i	−0.477569	−	0.206130i
$507$	−4.94427			−0.219583
$508$	−9.59017	+	6.96767i	−0.425495	+	0.309140i
$509$	3.74671	+	11.5312i	0.166070	+	0.511111i	0.999114	−	0.0420964i	$-0.0134037\pi$
$509$	3.74671	+	11.5312i	0.166070	+	0.511111i	−0.833044	+	0.553207i	$0.813404\pi$
$510$	−1.07295	+	3.30220i	−0.0475110	+	0.146224i
$511$	5.97214	+	4.33901i	0.264192	+	0.191947i
$512$	−15.1353	−	10.9964i	−0.668890	−	0.485977i
$513$	−2.00000	+	6.15537i	−0.0883022	+	0.271766i
$514$	4.56231	+	14.0413i	0.201235	+	0.619337i
$515$	−20.2533	+	14.7149i	−0.892467	+	0.648415i
$516$	−18.5623			−0.817160
$517$	11.2746	−	12.8128i	0.495855	−	0.563505i
$518$	−3.70820			−0.162929
$519$	8.73607	−	6.34712i	0.383471	−	0.278608i
$520$	4.73607	+	14.5761i	0.207690	+	0.639205i
$521$	2.60081	−	8.00448i	0.113944	−	0.350683i	−0.877782	−	0.479061i	$-0.840977\pi$
$521$	2.60081	−	8.00448i	0.113944	−	0.350683i	0.991725	+	0.128378i	$0.0409772\pi$
$522$	0.118034	+	0.0857567i	0.00516621	+	0.00375347i
$523$	−23.8992	−	17.3638i	−1.04504	−	0.759265i	−0.0737758	−	0.997275i	$-0.523505\pi$
$523$	−23.8992	−	17.3638i	−1.04504	−	0.759265i	−0.971263	+	0.238010i	$0.923505\pi$
$524$	−3.42705	+	10.5474i	−0.149711	+	0.460764i
$525$	−0.736068	−	2.26538i	−0.0321246	−	0.0988695i
$526$	4.64590	−	3.37544i	0.202571	−	0.147176i
$527$	−10.4164			−0.453746
$528$	−6.00000	+	1.34708i	−0.261116	+	0.0586243i
$529$	9.58359			0.416678
$530$	−10.1631	+	7.38394i	−0.441458	+	0.320738i
$531$	−1.42705	−	4.39201i	−0.0619287	−	0.190597i
$532$	3.23607	−	9.95959i	0.140301	−	0.431803i
$533$	33.7705	+	24.5357i	1.46276	+	1.06276i
$534$	0.663119	+	0.481784i	0.0286960	+	0.0208488i
$535$	−2.88197	+	8.86978i	−0.124598	+	0.383474i
$536$	−9.14590	−	28.1482i	−0.395043	−	1.21582i
$537$	−15.1353	+	10.9964i	−0.653134	+	0.474530i
$538$	−18.0344			−0.777520
$539$	0.309017	−	3.30220i	0.0133103	−	0.142236i
$540$	−2.61803			−0.112662
$541$	8.87132	−	6.44539i	0.381408	−	0.277109i	−0.380518	−	0.924774i	$-0.624254\pi$
$541$	8.87132	−	6.44539i	0.381408	−	0.277109i	0.761926	+	0.647665i	$0.224254\pi$
$542$	−4.22542	−	13.0045i	−0.181498	−	0.558592i
$543$	0.163119	−	0.502029i	0.00700010	−	0.0215441i
$544$	15.7812	+	11.4657i	0.676611	+	0.491587i
$545$	−5.42705	−	3.94298i	−0.232469	−	0.168899i
$546$	0.809017	−	2.48990i	0.0346227	−	0.106558i
$547$	−5.89261	−	18.1356i	−0.251950	−	0.775422i	−0.994415	−	0.105537i	$-0.966344\pi$
$547$	−5.89261	−	18.1356i	−0.251950	−	0.775422i	0.742466	−	0.669884i	$-0.233656\pi$
$548$	−13.7082	+	9.95959i	−0.585585	+	0.425453i
$549$	−7.94427			−0.339053
$550$	−0.454915	+	4.86128i	−0.0193976	+	0.207286i
$551$	−1.52786			−0.0650892
$552$	−10.3262	+	7.50245i	−0.439514	+	0.319326i
$553$	1.88197	+	5.79210i	0.0800293	+	0.246305i
$554$	1.61803	−	4.97980i	0.0687437	−	0.211571i
$555$	−7.85410	−	5.70634i	−0.333388	−	0.242221i
$556$	3.42705	+	2.48990i	0.145339	+	0.105595i
$557$	−6.34752	+	19.5357i	−0.268953	+	0.827753i	0.721803	+	0.692099i	$0.243314\pi$
$557$	−6.34752	+	19.5357i	−0.268953	+	0.827753i	−0.990756	+	0.135654i	$0.956686\pi$
$558$	0.572949	+	1.76336i	0.0242549	+	0.0746488i
$559$	39.3156	−	28.5645i	1.66287	−	1.20815i
$560$	3.00000			0.126773
$561$	11.2361	−	2.52265i	0.474387	−	0.106507i
$562$	6.70820			0.282969
$563$	22.6074	−	16.4252i	0.952788	−	0.692241i	0.00132332	−	0.999999i	$-0.499579\pi$
$563$	22.6074	−	16.4252i	0.952788	−	0.692241i	0.951465	+	0.307758i	$0.0995788\pi$
$564$	−2.57295	−	7.91872i	−0.108341	−	0.333438i
$565$	5.59017	−	17.2048i	0.235180	−	0.723810i
$566$	−6.44427	−	4.68204i	−0.270873	−	0.196801i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	3.12868	−	9.62908i	0.131276	−	0.404027i
$569$	−11.9615	−	36.8137i	−0.501452	−	1.54331i	−0.806655	−	0.591023i	$-0.798724\pi$
$569$	−11.9615	−	36.8137i	−0.501452	−	1.54331i	0.305203	−	0.952287i	$-0.401276\pi$
$570$	−5.23607	+	3.80423i	−0.219315	+	0.159341i
$571$	35.9443			1.50422			0.752110	−	0.659037i	$-0.229036\pi$
$571$	35.9443			1.50422			0.752110	+	0.659037i	$0.229036\pi$
$572$	15.0172	−	17.0660i	0.627902	−	0.713566i
$573$	16.2361			0.678271
$574$	−4.92705	+	3.57971i	−0.205651	+	0.149414i
$575$	−4.20163	−	12.9313i	−0.175220	−	0.539271i
$576$	−0.0729490	+	0.224514i	−0.00303954	+	0.00935475i
$577$	−30.0517	−	21.8338i	−1.25107	−	0.908953i	−0.252784	−	0.967523i	$-0.581346\pi$
$577$	−30.0517	−	21.8338i	−1.25107	−	0.908953i	−0.998283	+	0.0585694i	$0.981346\pi$
$578$	2.47214	+	1.79611i	0.102827	+	0.0747084i
$579$	−5.38197	+	16.5640i	−0.223667	+	0.688376i
$580$	−0.190983	−	0.587785i	−0.00793014	−	0.0244065i
$581$	6.85410	−	4.97980i	0.284356	−	0.206597i
$582$	3.27051			0.135567
$583$	38.2533	+	16.5110i	1.58429	+	0.683815i
$584$	−16.5066			−0.683047
$585$	5.54508	−	4.02874i	0.229261	−	0.166568i
$586$	−1.47214	−	4.53077i	−0.0608134	−	0.187164i
$587$	−9.96556	+	30.6708i	−0.411323	+	1.26592i	0.504176	+	0.863601i	$0.331796\pi$
$587$	−9.96556	+	30.6708i	−0.411323	+	1.26592i	−0.915499	+	0.402320i	$0.868204\pi$
$588$	−1.30902	−	0.951057i	−0.0539830	−	0.0392209i
$589$	−15.7082	−	11.4127i	−0.647245	−	0.470251i
$590$	1.42705	−	4.39201i	0.0587508	−	0.180816i
$591$	−1.43769	−	4.42477i	−0.0591388	−	0.182011i
$592$	−9.00000	+	6.53888i	−0.369898	+	0.268746i
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$	−1.04508	−	1.76336i	−0.0428804	−	0.0723514i
$595$	−5.61803			−0.230317
$596$	−1.80902	+	1.31433i	−0.0741002	+	0.0538370i
$597$	8.10081	+	24.9317i	0.331544	+	1.02039i
$598$	4.61803	−	14.2128i	0.188845	−	0.581207i
$599$	11.7812	+	8.55951i	0.481365	+	0.349732i	0.801854	−	0.597520i	$-0.203847\pi$
$599$	11.7812	+	8.55951i	0.481365	+	0.349732i	−0.320489	+	0.947252i	$0.603847\pi$
$600$	4.30902	+	3.13068i	0.175915	+	0.127810i
$601$	−1.41641	+	4.35926i	−0.0577765	+	0.177818i	−0.975780	−	0.218755i	$-0.929800\pi$
$601$	−1.41641	+	4.35926i	−0.0577765	+	0.177818i	0.918003	+	0.396573i	$0.129800\pi$
$602$	2.19098	+	6.74315i	0.0892978	+	0.274830i
$603$	−10.7082	+	7.77997i	−0.436072	+	0.316825i
$604$	−10.2361			−0.416500
$605$	−16.0902	+	7.60845i	−0.654158	+	0.309328i
$606$	−6.94427			−0.282092
$607$	18.7361	−	13.6126i	0.760474	−	0.552516i	−0.138582	−	0.990351i	$-0.544254\pi$
$607$	18.7361	−	13.6126i	0.760474	−	0.552516i	0.899056	+	0.437835i	$0.144254\pi$
$608$	11.2361	+	34.5811i	0.455683	+	1.40245i
$609$	−0.0729490	+	0.224514i	−0.00295604	+	0.00909777i
$610$	−6.42705	−	4.66953i	−0.260224	−	0.189064i
$611$	17.6353	+	12.8128i	0.713446	+	0.518349i
$612$	1.73607	−	5.34307i	0.0701764	−	0.215981i
$613$	7.59017	+	23.3601i	0.306564	+	0.943507i	0.979089	+	0.203433i	$0.0652098\pi$
$613$	7.59017	+	23.3601i	0.306564	+	0.943507i	−0.672525	+	0.740075i	$0.734790\pi$
$614$	−4.02786	+	2.92641i	−0.162551	+	0.118100i
$615$	−15.9443			−0.642935
$616$	3.78115	+	6.37988i	0.152347	+	0.257053i
$617$	−1.32624			−0.0533923			−0.0266962	−	0.999644i	$-0.508499\pi$
$617$	−1.32624			−0.0533923			−0.0266962	+	0.999644i	$0.508499\pi$
$618$	−7.73607	+	5.62058i	−0.311190	+	0.226093i
$619$	−6.85410	−	21.0948i	−0.275490	−	0.847870i	−0.989089	−	0.147316i	$-0.952936\pi$
$619$	−6.85410	−	21.0948i	−0.275490	−	0.847870i	0.713600	−	0.700554i	$-0.247064\pi$
$620$	2.42705	−	7.46969i	0.0974727	−	0.299990i
$621$	4.61803	+	3.35520i	0.185315	+	0.134639i
$622$	−3.39919	−	2.46965i	−0.136295	−	0.0990241i
$623$	−0.409830	+	1.26133i	−0.0164195	+	0.0505340i
$624$	−2.42705	−	7.46969i	−0.0971598	−	0.299027i
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$	19.8328			0.792679
$627$	19.7082	+	8.50651i	0.787070	+	0.339717i
$628$	11.0000			0.438948
$629$	16.8541	−	12.2452i	0.672017	−	0.488249i
$630$	0.309017	+	0.951057i	0.0123115	+	0.0378910i
$631$	0.218847	−	0.673542i	0.00871216	−	0.0268133i	−0.946606	−	0.322393i	$-0.895513\pi$
$631$	0.218847	−	0.673542i	0.00871216	−	0.0268133i	0.955318	+	0.295580i	$0.0955128\pi$
$632$	−11.0172	−	8.00448i	−0.438242	−	0.318401i
$633$	−15.1353	−	10.9964i	−0.601572	−	0.437068i
$634$	−6.66312	+	20.5070i	−0.264626	+	0.814436i
$635$	3.66312	+	11.2739i	0.145366	+	0.447392i
$636$	16.4443	−	11.9475i	0.652058	−	0.473748i
$637$	4.23607			0.167839
$638$	0.319660	−	0.363271i	0.0126555	−	0.0143820i
$639$	−4.52786			−0.179120
$640$	−14.8992	+	10.8249i	−0.588942	+	0.427891i
$641$	2.88197	+	8.86978i	0.113831	+	0.350335i	0.991701	−	0.128563i	$-0.0410364\pi$
$641$	2.88197	+	8.86978i	0.113831	+	0.350335i	−0.877871	+	0.478898i	$0.841036\pi$
$642$	−1.10081	+	3.38795i	−0.0434456	+	0.133712i
$643$	−4.76393	−	3.46120i	−0.187871	−	0.136496i	0.489874	−	0.871793i	$-0.337043\pi$
$643$	−4.76393	−	3.46120i	−0.187871	−	0.136496i	−0.677745	+	0.735297i	$0.737043\pi$
$644$	−7.47214	−	5.42882i	−0.294443	−	0.213926i
$645$	−5.73607	+	17.6538i	−0.225857	+	0.695118i
$646$	−4.29180	−	13.2088i	−0.168858	−	0.519693i
$647$	−12.0451	+	8.75127i	−0.473541	+	0.344048i	−0.798820	−	0.601570i	$-0.794542\pi$
$647$	−12.0451	+	8.75127i	−0.473541	+	0.344048i	0.325279	+	0.945618i	$0.394542\pi$
$648$	−2.23607			−0.0878410
$649$	−14.9443	+	3.35520i	−0.586614	+	0.131703i
$650$	−6.23607			−0.244599
$651$	−2.42705	+	1.76336i	−0.0951236	+	0.0691114i
$652$	9.16312	+	28.2012i	0.358855	+	1.10444i
$653$	−9.63525	+	29.6543i	−0.377057	+	1.16046i	0.565024	+	0.825075i	$0.308867\pi$
$653$	−9.63525	+	29.6543i	−0.377057	+	1.16046i	−0.942081	+	0.335387i	$0.891133\pi$
$654$	−2.07295	−	1.50609i	−0.0810587	−	0.0588926i
$655$	8.97214	+	6.51864i	0.350570	+	0.254704i
$656$	−5.64590	+	17.3763i	−0.220435	+	0.678430i
$657$	2.28115	+	7.02067i	0.0889963	+	0.273902i
$658$	−2.57295	+	1.86936i	−0.100304	+	0.0728751i
$659$	−20.8885			−0.813702			−0.406851	−	0.913495i	$-0.633373\pi$
$659$	−20.8885			−0.813702			−0.406851	+	0.913495i	$0.633373\pi$
$660$	−0.809017	+	8.64527i	−0.0314909	+	0.336516i
$661$	18.5967			0.723330			0.361665	−	0.932308i	$-0.382208\pi$
$661$	18.5967			0.723330			0.361665	+	0.932308i	$0.382208\pi$
$662$	9.64590	−	7.00816i	0.374898	−	0.272380i
$663$	4.54508	+	13.9883i	0.176516	+	0.543262i
$664$	−5.85410	+	18.0171i	−0.227183	+	0.699198i
$665$	−8.47214	−	6.15537i	−0.328535	−	0.238695i
$666$	−3.00000	−	2.17963i	−0.116248	−	0.0844589i
$667$	−0.416408	+	1.28157i	−0.0161234	+	0.0496227i
$668$	1.07295	+	3.30220i	0.0415136	+	0.127766i
$669$	16.1353	−	11.7229i	0.623825	−	0.453235i
$670$	−13.2361			−0.511354
$671$	−2.45492	+	26.2336i	−0.0947709	+	1.01274i
$672$	5.61803			0.216720
$673$	14.6074	−	10.6129i	0.563074	−	0.409097i	−0.269509	−	0.962998i	$-0.586861\pi$
$673$	14.6074	−	10.6129i	0.563074	−	0.409097i	0.832583	+	0.553901i	$0.186861\pi$
$674$	−0.809017	−	2.48990i	−0.0311622	−	0.0959073i
$675$	0.736068	−	2.26538i	0.0283313	−	0.0871947i
$676$	6.47214	+	4.70228i	0.248928	+	0.180857i
$677$	−11.0623	−	8.03724i	−0.425159	−	0.308896i	0.354551	−	0.935037i	$-0.384634\pi$
$677$	−11.0623	−	8.03724i	−0.425159	−	0.308896i	−0.779710	+	0.626141i	$0.784634\pi$
$678$	2.13525	−	6.57164i	0.0820040	−	0.252382i
$679$	1.63525	+	5.03280i	0.0627553	+	0.193141i
$680$	10.1631	−	7.38394i	0.389738	−	0.283161i
$681$	0.909830			0.0348648
$682$	6.00000	−	1.34708i	0.229752	−	0.0515825i
$683$	−15.4721			−0.592025			−0.296012	−	0.955184i	$-0.595657\pi$
$683$	−15.4721			−0.592025			−0.296012	+	0.955184i	$0.595657\pi$
$684$	8.47214	−	6.15537i	0.323940	−	0.235356i
$685$	5.23607	+	16.1150i	0.200060	+	0.615721i
$686$	−0.190983	+	0.587785i	−0.00729177	+	0.0224417i
$687$	12.2361	+	8.89002i	0.466835	+	0.339176i
$688$	17.2082	+	12.5025i	0.656057	+	0.476653i
$689$	−16.4443	+	50.6103i	−0.626477	+	1.92810i
$690$	1.76393	+	5.42882i	0.0671517	+	0.206672i
$691$	0.781153	−	0.567541i	0.0297165	−	0.0215903i	−0.572828	−	0.819676i	$-0.694154\pi$
$691$	0.781153	−	0.567541i	0.0297165	−	0.0215903i	0.602544	+	0.798085i	$0.294154\pi$
$692$	−17.4721			−0.664191
$693$	2.19098	−	2.48990i	0.0832286	−	0.0945834i
$694$	−0.291796			−0.0110764
$695$	3.42705	−	2.48990i	0.129995	−	0.0944472i
$696$	−0.163119	−	0.502029i	−0.00618301	−	0.0190293i
$697$	10.5729	−	32.5402i	0.400479	−	1.23255i
$698$	8.66312	+	6.29412i	0.327904	+	0.238236i
$699$	−12.7533	−	9.26581i	−0.482374	−	0.350465i
$700$	−1.19098	+	3.66547i	−0.0450149	+	0.138542i
$701$	10.4894	+	32.2829i	0.396178	+	1.21931i	0.928041	+	0.372479i	$0.121492\pi$
$701$	10.4894	+	32.2829i	0.396178	+	1.21931i	−0.531863	+	0.846830i	$0.678508\pi$
$702$	2.11803	−	1.53884i	0.0799400	−	0.0580798i
$703$	38.8328			1.46461
$704$	0.718847	+	0.310271i	0.0270926	+	0.0116938i
$705$	−8.32624			−0.313584
$706$	2.06231	−	1.49835i	0.0776159	−	0.0563913i
$707$	−3.47214	−	10.6861i	−0.130583	−	0.401893i
$708$	−2.30902	+	7.10642i	−0.0867782	+	0.267076i
$709$	4.61803	+	3.35520i	0.173434	+	0.126007i	0.671116	−	0.741353i	$-0.265815\pi$
$709$	4.61803	+	3.35520i	0.173434	+	0.126007i	−0.497682	+	0.867360i	$0.665815\pi$
$710$	−3.66312	−	2.66141i	−0.137474	−	0.0998810i
$711$	−1.88197	+	5.79210i	−0.0705792	+	0.217221i
$712$	−0.916408	−	2.82041i	−0.0343438	−	0.105699i
$713$	−13.8541	+	10.0656i	−0.518840	+	0.376959i
$714$	−2.14590			−0.0803082
$715$	−11.5902	−	19.5559i	−0.433448	−	0.731350i
$716$	30.2705			1.13126
$717$	−17.4894	+	12.7068i	−0.653152	+	0.474543i
$718$	1.98278	+	6.10237i	0.0739967	+	0.227738i
$719$	−10.3369	+	31.8136i	−0.385501	+	1.18645i	0.550616	+	0.834759i	$0.314393\pi$
$719$	−10.3369	+	31.8136i	−0.385501	+	1.18645i	−0.936116	+	0.351690i	$0.885607\pi$
$720$	2.42705	+	1.76336i	0.0904508	+	0.0657164i
$721$	−12.5172	−	9.09429i	−0.466166	−	0.338689i
$722$	4.37132	−	13.4535i	0.162684	−	0.500689i
$723$	−3.21885	−	9.90659i	−0.119710	−	0.368430i
$724$	−0.690983	+	0.502029i	−0.0256802	+	0.0186577i
$725$	0.562306			0.0208835
$726$	−6.14590	+	2.90617i	−0.228096	+	0.107858i
$727$	−2.03444			−0.0754533			−0.0377266	−	0.999288i	$-0.512012\pi$
$727$	−2.03444			−0.0754533			−0.0377266	+	0.999288i	$0.512012\pi$
$728$	−7.66312	+	5.56758i	−0.284014	+	0.206348i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−2.28115	+	7.02067i	−0.0844293	+	0.259847i
$731$	−32.2254	−	23.4131i	−1.19190	−	0.865966i
$732$	10.3992	+	7.55545i	0.384365	+	0.279258i
$733$	5.43363	−	16.7230i	0.200696	−	0.617678i	−0.799167	−	0.601109i	$-0.794726\pi$
$733$	5.43363	−	16.7230i	0.200696	−	0.617678i	0.999863	−	0.0165688i	$-0.00527424\pi$
$734$	−0.954915	−	2.93893i	−0.0352466	−	0.108478i
$735$	−1.30902	+	0.951057i	−0.0482838	+	0.0350802i
$736$	32.0689			1.18207
$737$	22.3820	+	37.7647i	0.824450	+	1.39108i
$738$	−6.09017			−0.224182
$739$	32.4787	−	23.5972i	1.19475	−	0.868036i	0.200991	−	0.979593i	$-0.435584\pi$
$739$	32.4787	−	23.5972i	1.19475	−	0.868036i	0.993758	+	0.111557i	$0.0355839\pi$
$740$	4.85410	+	14.9394i	0.178440	+	0.549183i
$741$	−8.47214	+	26.0746i	−0.311232	+	0.957873i
$742$	−6.28115	−	4.56352i	−0.230588	−	0.167532i
$743$	−30.8156	−	22.3888i	−1.13051	−	0.821367i	−0.144745	−	0.989469i	$-0.546236\pi$
$743$	−30.8156	−	22.3888i	−1.13051	−	0.821367i	−0.985770	+	0.168102i	$0.946236\pi$
$744$	2.07295	−	6.37988i	0.0759980	−	0.233898i
$745$	0.690983	+	2.12663i	0.0253157	+	0.0779136i
$746$	10.1459	−	7.37143i	0.371468	−	0.269887i
$747$	8.47214			0.309979
$748$	−17.1074	−	7.38394i	−0.625508	−	0.269984i
$749$	−5.76393			−0.210609
$750$	5.97214	−	4.33901i	0.218072	−	0.158438i
$751$	15.6246	+	48.0876i	0.570150	+	1.75474i	0.652129	+	0.758108i	$0.273876\pi$
$751$	15.6246	+	48.0876i	0.570150	+	1.75474i	−0.0819791	+	0.996634i	$0.526124\pi$
$752$	−2.94834	+	9.07405i	−0.107515	+	0.330897i
$753$	−11.2812	−	8.19624i	−0.411108	−	0.298687i
$754$	0.500000	+	0.363271i	0.0182089	+	0.0132296i
$755$	−3.16312	+	9.73508i	−0.115118	+	0.354296i
$756$	−0.500000	−	1.53884i	−0.0181848	−	0.0559671i
$757$	−41.3607	+	30.0503i	−1.50328	+	1.09220i	−0.534227	+	0.845341i	$0.679397\pi$
$757$	−41.3607	+	30.0503i	−1.50328	+	1.09220i	−0.969052	+	0.246856i	$0.920603\pi$
$758$	−1.18034			−0.0428719
$759$	12.5066	−	14.2128i	0.453960	−	0.515894i
$760$	23.4164			0.849402
$761$	−24.9615	+	18.1356i	−0.904853	+	0.657414i	−0.939708	−	0.341978i	$-0.888903\pi$
$761$	−24.9615	+	18.1356i	−0.904853	+	0.657414i	0.0348546	+	0.999392i	$0.488903\pi$
$762$	1.39919	+	4.30625i	0.0506872	+	0.155999i
$763$	1.28115	−	3.94298i	0.0463809	−	0.142746i
$764$	−21.2533	−	15.4414i	−0.768917	−	0.558651i
$765$	−4.54508	−	3.30220i	−0.164328	−	0.119391i
$766$	−0.510643	+	1.57160i	−0.0184503	+	0.0567841i
$767$	−6.04508	−	18.6049i	−0.218275	−	0.671783i
$768$	−5.30902	+	3.85723i	−0.191573	+	0.139186i
$769$	−53.7771			−1.93925			−0.969626	−	0.244594i	$-0.921345\pi$
$769$	−53.7771			−1.93925			−0.969626	+	0.244594i	$0.921345\pi$
$770$	3.23607	−	0.726543i	0.116620	−	0.0261828i
$771$	−23.8885			−0.860325
$772$	22.7984	−	16.5640i	0.820531	−	0.596151i
$773$	−9.56231	−	29.4298i	−0.343932	−	1.05851i	−0.962153	−	0.272510i	$-0.912146\pi$
$773$	−9.56231	−	29.4298i	−0.343932	−	1.05851i	0.618221	−	0.786005i	$-0.287854\pi$
$774$	−2.19098	+	6.74315i	−0.0787533	+	0.242378i
$775$	5.78115	+	4.20025i	0.207665	+	0.150878i
$776$	−9.57295	−	6.95515i	−0.343649	−	0.249675i
$777$	1.85410	−	5.70634i	0.0665155	−	0.204714i
$778$	−3.29180	−	10.1311i	−0.118017	−	0.363218i
$779$	51.5967	−	37.4872i	1.84865	−	1.34312i
$780$	−11.0902			−0.397092
$781$	−1.39919	+	14.9519i	−0.0500668	+	0.535021i
$782$	−12.2492			−0.438031
$783$	−0.190983	+	0.138757i	−0.00682518	+	0.00495878i
$784$	0.572949	+	1.76336i	0.0204625	+	0.0629770i
$785$	3.39919	−	10.4616i	0.121322	−	0.373391i
$786$	3.42705	+	2.48990i	0.122239	+	0.0888117i
$787$	−0.454915	−	0.330515i	−0.0162160	−	0.0117816i	0.579648	−	0.814867i	$-0.303190\pi$
$787$	−0.454915	−	0.330515i	−0.0162160	−	0.0117816i	−0.595864	+	0.803086i	$0.703190\pi$
$788$	−2.32624	+	7.15942i	−0.0828688	+	0.255044i
$789$	2.87132	+	8.83702i	0.102222	+	0.314606i
$790$	−4.92705	+	3.57971i	−0.175297	+	0.127360i
$791$	11.1803			0.397527
$792$	−0.690983	+	7.38394i	−0.0245530	+	0.262377i
$793$	−33.6525			−1.19503
$794$	5.28115	−	3.83698i	0.187421	−	0.136169i
$795$	−6.28115	−	19.3314i	−0.222770	−	0.685614i
$796$	13.1074	−	40.3404i	0.464579	−	1.42983i
$797$	−30.0517	−	21.8338i	−1.06448	−	0.773393i	−0.0895717	−	0.995980i	$-0.528550\pi$
$797$	−30.0517	−	21.8338i	−1.06448	−	0.773393i	−0.974913	+	0.222587i	$0.928550\pi$
$798$	−3.23607	−	2.35114i	−0.114556	−	0.0832295i
$799$	5.52129	−	16.9928i	0.195329	−	0.601161i
$800$	−4.13525	−	12.7270i	−0.146203	−	0.449968i
$801$	−1.07295	+	0.779543i	−0.0379108	+	0.0275438i
$802$	17.1459			0.605443
$803$	23.8885	−	5.36331i	0.843008	−	0.189267i
$804$	21.4164			0.755298
$805$	−7.47214	+	5.42882i	−0.263358	+	0.191341i
$806$	2.42705	+	7.46969i	0.0854892	+	0.263109i
$807$	9.01722	−	27.7522i	0.317421	−	0.976922i
$808$	20.3262	+	14.7679i	0.715075	+	0.519532i
$809$	44.0066	+	31.9727i	1.54719	+	1.12410i	0.945618	+	0.325279i	$0.105458\pi$
$809$	44.0066	+	31.9727i	1.54719	+	1.12410i	0.601571	+	0.798819i	$0.294542\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	14.7426	+	45.3732i	0.517684	+	1.59327i	0.778344	+	0.627838i	$0.216060\pi$
$811$	14.7426	+	45.3732i	0.517684	+	1.59327i	−0.260660	+	0.965431i	$0.583940\pi$
$812$	0.309017	−	0.224514i	0.0108444	−	0.00787890i
$813$	22.1246			0.775944
$814$	−8.12461	+	9.23305i	−0.284767	+	0.323618i
$815$	29.6525			1.03868
$816$	−5.20820	+	3.78398i	−0.182324	+	0.132466i
$817$	−22.9443	−	70.6152i	−0.802718	−	2.47051i
$818$	1.56637	−	4.82079i	0.0547669	−	0.168555i
$819$	3.42705	+	2.48990i	0.119751	+	0.0870041i
$820$	20.8713	+	15.1639i	0.728858	+	0.529546i
$821$	−4.27051	+	13.1433i	−0.149042	+	0.458704i	−0.997509	−	0.0705451i	$-0.977526\pi$
$821$	−4.27051	+	13.1433i	−0.149042	+	0.458704i	0.848467	+	0.529249i	$0.177526\pi$
$822$	2.00000	+	6.15537i	0.0697580	+	0.214693i
$823$	−18.1803	+	13.2088i	−0.633727	+	0.460429i	−0.857689	−	0.514168i	$-0.828101\pi$
$823$	−18.1803	+	13.2088i	−0.633727	+	0.460429i	0.223963	+	0.974598i	$0.428101\pi$
$824$	34.5967			1.20523
$825$	−7.25329	−	3.13068i	−0.252527	−	0.108996i
$826$	2.85410			0.0993069
$827$	−33.9336	+	24.6542i	−1.17999	+	0.857311i	−0.992170	−	0.124893i	$-0.960141\pi$
$827$	−33.9336	+	24.6542i	−1.17999	+	0.857311i	−0.187818	+	0.982204i	$0.560141\pi$
$828$	−2.85410	−	8.78402i	−0.0991869	−	0.305266i
$829$	−0.208204	+	0.640786i	−0.00723122	+	0.0222554i	−0.954607	−	0.297868i	$-0.903724\pi$
$829$	−0.208204	+	0.640786i	−0.00723122	+	0.0222554i	0.947376	+	0.320124i	$0.103724\pi$
$830$	6.85410	+	4.97980i	0.237909	+	0.172851i
$831$	6.85410	+	4.97980i	0.237766	+	0.172747i
$832$	−0.309017	+	0.951057i	−0.0107132	+	0.0329720i
$833$	−1.07295	−	3.30220i	−0.0371755	−	0.114414i
$834$	1.30902	−	0.951057i	0.0453276	−	0.0329324i
$835$	3.47214			0.120158
$836$	−17.7082	−	29.8788i	−0.612451	−	1.03338i
$837$	−3.00000			−0.103695
$838$	17.8090	−	12.9390i	0.615202	−	0.446971i
$839$	−4.48936	−	13.8168i	−0.154990	−	0.477010i	0.843170	−	0.537647i	$-0.180687\pi$
$839$	−4.48936	−	13.8168i	−0.154990	−	0.477010i	−0.998160	+	0.0606374i	$0.980687\pi$
$840$	1.11803	−	3.44095i	0.0385758	−	0.118724i
$841$	23.4164	+	17.0130i	0.807462	+	0.586656i
$842$	−9.07295	−	6.59188i	−0.312674	−	0.227171i
$843$	−3.35410	+	10.3229i	−0.115521	+	0.355538i
$844$	9.35410	+	28.7890i	0.321981	+	0.990957i
$845$	6.47214	−	4.70228i	0.222648	−	0.161763i
$846$	−3.18034			−0.109342
$847$	−7.54508	−	8.00448i	−0.259252	−	0.275037i
$848$	−23.2918			−0.799844
$849$	10.4271	−	7.57570i	0.357855	−	0.259997i
$850$	1.57953	+	4.86128i	0.0541773	+	0.166741i
$851$	10.5836	−	32.5729i	0.362801	−	1.11659i
$852$	5.92705	+	4.30625i	0.203057	+	0.147530i
$853$	−20.0623	−	14.5761i	−0.686920	−	0.499077i	0.188726	−	0.982030i	$-0.439564\pi$
$853$	−20.0623	−	14.5761i	−0.686920	−	0.499077i	−0.875646	+	0.482953i	$0.839564\pi$
$854$	1.51722	−	4.66953i	0.0519182	−	0.159788i
$855$	−3.23607	−	9.95959i	−0.110671	−	0.340611i
$856$	10.4271	−	7.57570i	0.356389	−	0.258932i
$857$	−31.9443			−1.09120			−0.545598	−	0.838047i	$-0.683697\pi$
$857$	−31.9443			−1.09120			−0.545598	+	0.838047i	$0.683697\pi$
$858$	−4.42705	−	7.46969i	−0.151137	−	0.255011i
$859$	1.65248			0.0563817			0.0281909	−	0.999603i	$-0.491025\pi$
$859$	1.65248			0.0563817			0.0281909	+	0.999603i	$0.491025\pi$
$860$	24.2984	−	17.6538i	0.828568	−	0.601990i
$861$	−3.04508	−	9.37181i	−0.103776	−	0.319390i
$862$	−1.36475	+	4.20025i	−0.0464834	+	0.143061i
$863$	−25.2812	−	18.3678i	−0.860580	−	0.625248i	0.0674624	−	0.997722i	$-0.478510\pi$
$863$	−25.2812	−	18.3678i	−0.860580	−	0.625248i	−0.928043	+	0.372474i	$0.878510\pi$
$864$	4.54508	+	3.30220i	0.154627	+	0.112343i
$865$	−5.39919	+	16.6170i	−0.183578	+	0.564995i
$866$	−1.32624	−	4.08174i	−0.0450674	−	0.138703i
$867$	−4.00000	+	2.90617i	−0.135847	+	0.0986987i
$868$	4.85410			0.164759
$869$	18.5451	+	8.00448i	0.629099	+	0.271533i
$870$	−0.236068			−0.00800345
$871$	−45.3607	+	32.9565i	−1.53699	+	1.11669i
$872$	2.86475	+	8.81678i	0.0970125	+	0.298574i
$873$	−1.63525	+	5.03280i	−0.0553450	+	0.170334i
$874$	−18.4721	−	13.4208i	−0.624829	−	0.453965i
$875$	9.66312	+	7.02067i	0.326673	+	0.237342i
$876$	3.69098	−	11.3597i	0.124707	−	0.383808i
$877$	−3.75329	−	11.5514i	−0.126740	−	0.390064i	0.867474	−	0.497482i	$-0.165742\pi$
$877$	−3.75329	−	11.5514i	−0.126740	−	0.390064i	−0.994214	+	0.107417i	$0.965742\pi$
$878$	−17.8262	+	12.9515i	−0.601606	+	0.437093i
$879$	7.70820			0.259991
$880$	6.57295	−	7.46969i	0.221574	−	0.251803i
$881$	−5.29180			−0.178285			−0.0891426	−	0.996019i	$-0.528413\pi$
$881$	−5.29180			−0.178285			−0.0891426	+	0.996019i	$0.528413\pi$
$882$	−0.500000	+	0.363271i	−0.0168359	+	0.0122320i
$883$	−13.6246	−	41.9322i	−0.458505	−	1.41113i	−0.866971	−	0.498359i	$-0.833936\pi$
$883$	−13.6246	−	41.9322i	−0.458505	−	1.41113i	0.408466	−	0.912773i	$-0.366064\pi$
$884$	7.35410	−	22.6336i	0.247345	−	0.761250i
$885$	6.04508	+	4.39201i	0.203203	+	0.147636i
$886$	−12.3262	−	8.95554i	−0.414108	−	0.300867i
$887$	11.9615	−	36.8137i	0.401628	−	1.23608i	−0.522051	−	0.852914i	$-0.674833\pi$
$887$	11.9615	−	36.8137i	0.401628	−	1.23608i	0.923679	−	0.383168i	$-0.125167\pi$
$888$	4.14590	+	12.7598i	0.139127	+	0.428190i
$889$	−5.92705	+	4.30625i	−0.198787	+	0.144427i
$890$	−1.32624			−0.0444556
$891$	3.23607	−	0.726543i	0.108412	−	0.0243401i
$892$	−32.2705			−1.08050
$893$	26.9443	−	19.5762i	0.901656	−	0.655091i
$894$	0.263932	+	0.812299i	0.00882721	+	0.0271674i
$895$	9.35410	−	28.7890i	0.312673	−	0.962309i
$896$	−9.20820	−	6.69015i	−0.307625	−	0.223502i
$897$	19.5623	+	14.2128i	0.653166	+	0.474553i
$898$	−3.93363	+	12.1065i	−0.131267	+	0.403998i
$899$	−0.218847	−	0.673542i	−0.00729896	−	0.0224639i
$900$	−3.11803	+	2.26538i	−0.103934	+	0.0755128i
$901$	43.6180			1.45313
$902$	−1.88197	+	20.1109i	−0.0626626	+	0.669621i
$903$	−11.4721			−0.381769
$904$	−20.2254	+	14.6946i	−0.672688	+	0.488736i
$905$	0.263932	+	0.812299i	0.00877340	+	0.0270017i
$906$	−1.20820	+	3.71847i	−0.0401399	+	0.123538i
$907$	9.29837	+	6.75566i	0.308747	+	0.224318i	0.731359	−	0.681993i	$-0.238886\pi$
$907$	9.29837	+	6.75566i	0.308747	+	0.224318i	−0.422611	+	0.906311i	$0.638886\pi$
$908$	−1.19098	−	0.865300i	−0.0395242	−	0.0287160i
$909$	3.47214	−	10.6861i	0.115163	−	0.354437i
$910$	1.30902	+	4.02874i	0.0433935	+	0.133551i
$911$	25.8156	−	18.7561i	0.855309	−	0.621418i	−0.0712958	−	0.997455i	$-0.522713\pi$
$911$	25.8156	−	18.7561i	0.855309	−	0.621418i	0.926605	+	0.376037i	$0.122713\pi$
$912$	−12.0000			−0.397360
$913$	2.61803	−	27.9767i	0.0866443	−	0.925893i
$914$	11.5836			0.383151
$915$	10.3992	−	7.55545i	0.343787	−	0.249776i
$916$	−7.56231	−	23.2744i	−0.249866	−	0.769007i
$917$	−2.11803	+	6.51864i	−0.0699436	+	0.215264i
$918$	−1.73607	−	1.26133i	−0.0572988	−	0.0416300i
$919$	3.23607	+	2.35114i	0.106748	+	0.0775570i	0.639879	−	0.768476i	$-0.278985\pi$
$919$	3.23607	+	2.35114i	0.106748	+	0.0775570i	−0.533131	+	0.846033i	$0.678985\pi$
$920$	6.38197	−	19.6417i	0.210407	−	0.647567i
$921$	−2.48936	−	7.66145i	−0.0820271	−	0.252453i
$922$	−14.1525	+	10.2824i	−0.466087	+	0.338632i
$923$	−19.1803			−0.631329
$924$	−5.23607	+	1.17557i	−0.172254	+	0.0386734i
$925$	−14.2918			−0.469911
$926$	7.48936	−	5.44134i	0.246116	−	0.178813i
$927$	−4.78115	−	14.7149i	−0.157034	−	0.483300i
$928$	−0.409830	+	1.26133i	−0.0134533	+	0.0414051i
$929$	8.00000	+	5.81234i	0.262471	+	0.190697i	0.711236	−	0.702953i	$-0.248136\pi$
$929$	8.00000	+	5.81234i	0.262471	+	0.190697i	−0.448764	+	0.893650i	$0.648136\pi$
$930$	−2.42705	−	1.76336i	−0.0795861	−	0.0578227i
$931$	2.00000	−	6.15537i	0.0655474	−	0.201734i
$932$	7.88197	+	24.2582i	0.258182	+	0.794604i
$933$	5.50000	−	3.99598i	0.180062	−	0.130823i
$934$	−16.5066			−0.540112
$935$	−12.3090	+	13.9883i	−0.402548	+	0.457467i
$936$	−9.47214			−0.309606
$937$	17.8992	−	13.0045i	0.584741	−	0.424839i	−0.255689	−	0.966759i	$-0.582302\pi$
$937$	17.8992	−	13.0045i	0.584741	−	0.424839i	0.840430	+	0.541920i	$0.182302\pi$
$938$	−2.52786	−	7.77997i	−0.0825377	−	0.254025i
$939$	−9.91641	+	30.5196i	−0.323610	+	0.995968i
$940$	10.8992	+	7.91872i	0.355492	+	0.258280i
$941$	1.94427	+	1.41260i	0.0633815	+	0.0460493i	0.619025	−	0.785371i	$-0.287528\pi$
$941$	1.94427	+	1.41260i	0.0633815	+	0.0460493i	−0.555643	+	0.831421i	$0.687528\pi$
$942$	1.29837	−	3.99598i	0.0423033	−	0.130196i
$943$	−17.3820	−	53.4962i	−0.566035	−	1.74208i
$944$	6.92705	−	5.03280i	0.225456	−	0.163804i
$945$	−1.61803			−0.0526346
$946$	21.5902	+	9.31881i	0.701957	+	0.302981i
$947$	4.97871			0.161786			0.0808932	−	0.996723i	$-0.474223\pi$
$947$	4.97871			0.161786			0.0808932	+	0.996723i	$0.474223\pi$
$948$	7.97214	−	5.79210i	0.258923	−	0.188119i
$949$	9.66312	+	29.7400i	0.313678	+	0.965402i
$950$	−2.94427	+	9.06154i	−0.0955248	+	0.293995i
$951$	−28.2254	−	20.5070i	−0.915272	−	0.664984i
$952$	6.28115	+	4.56352i	0.203573	+	0.147905i
$953$	−3.10081	+	9.54332i	−0.100445	+	0.309139i	−0.988634	−	0.150339i	$-0.951963\pi$
$953$	−3.10081	+	9.54332i	−0.100445	+	0.309139i	0.888189	+	0.459478i	$0.151963\pi$
$954$	−2.39919	−	7.38394i	−0.0776765	−	0.239064i
$955$	−21.2533	+	15.4414i	−0.687740	+	0.499673i
$956$	34.9787			1.13129
$957$	0.399187	+	0.673542i	0.0129039	+	0.0217725i
$958$	18.7771			0.606660
$959$	−8.47214	+	6.15537i	−0.273580	+	0.198767i
$960$	−0.118034	−	0.363271i	−0.00380953	−	0.0117245i
$961$	−6.79837	+	20.9232i	−0.219302	+	0.674943i
$962$	−12.7082	−	9.23305i	−0.409729	−	0.297685i
$963$	−4.66312	−	3.38795i	−0.150267	−	0.109175i
$964$	−5.20820	+	16.0292i	−0.167745	+	0.516266i
$965$	−8.70820	−	26.8011i	−0.280327	−	0.862758i
$966$	−2.85410	+	2.07363i	−0.0918292	+	0.0667178i
$967$	−48.6525			−1.56456			−0.782279	−	0.622928i	$-0.785943\pi$
$967$	−48.6525			−1.56456			−0.782279	+	0.622928i	$0.785943\pi$
$968$	24.1697	+	4.56352i	0.776843	+	0.146677i
$969$	22.4721			0.721909
$970$	−4.28115	+	3.11044i	−0.137460	+	0.0998702i
$971$	−3.21885	−	9.90659i	−0.103298	−	0.317918i	0.886029	−	0.463629i	$-0.153453\pi$
$971$	−3.21885	−	9.90659i	−0.103298	−	0.317918i	−0.989327	+	0.145711i	$0.953453\pi$
$972$	0.500000	−	1.53884i	0.0160375	−	0.0493584i
$973$	2.11803	+	1.53884i	0.0679011	+	0.0493330i
$974$	7.69098	+	5.58783i	0.246435	+	0.179046i
$975$	3.11803	−	9.59632i	0.0998570	−	0.307328i
$976$	−4.55166	−	14.0086i	−0.145695	−	0.448404i
$977$	−34.6074	+	25.1437i	−1.10719	+	0.804420i	−0.982219	−	0.187741i	$-0.939883\pi$
$977$	−34.6074	+	25.1437i	−1.10719	+	0.804420i	−0.124970	+	0.992161i	$0.539883\pi$
$978$	11.3262			0.362173
$979$	2.24265	+	3.78398i	0.0716753	+	0.120937i
$980$	2.61803			0.0836300
$981$	3.35410	−	2.43690i	0.107088	−	0.0778042i
$982$	−1.58359	−	4.87380i	−0.0505345	−	0.155529i
$983$	15.6353	−	48.1204i	0.498687	−	1.53480i	−0.312443	−	0.949936i	$-0.601147\pi$
$983$	15.6353	−	48.1204i	0.498687	−	1.53480i	0.811131	−	0.584865i	$-0.198853\pi$
$984$	17.8262	+	12.9515i	0.568280	+	0.412879i
$985$	6.09017	+	4.42477i	0.194049	+	0.140985i
$986$	0.156541	−	0.481784i	0.00498529	−	0.0153431i
$987$	−1.59017	−	4.89404i	−0.0506157	−	0.155779i
$988$	35.8885	−	26.0746i	1.14177	−	0.829542i
$989$	−65.4853			−2.08231
$990$	3.04508	+	1.31433i	0.0967792	+	0.0417721i
$991$	−28.6180			−0.909082			−0.454541	−	0.890726i	$-0.650197\pi$
$991$	−28.6180			−0.909082			−0.454541	+	0.890726i	$0.650197\pi$
$992$	−13.6353	+	9.90659i	−0.432920	+	0.314535i
$993$	5.96149	+	18.3476i	0.189182	+	0.582243i
$994$	0.864745	−	2.66141i	0.0274280	−	0.0844149i
$995$	−34.3156	−	24.9317i	−1.08788	−	0.790389i
$996$	−11.0902	−	8.05748i	−0.351405	−	0.255311i
$997$	−12.7295	+	39.1773i	−0.403147	+	1.24076i	0.519286	+	0.854601i	$0.326198\pi$
$997$	−12.7295	+	39.1773i	−0.403147	+	1.24076i	−0.922433	+	0.386158i	$0.873802\pi$
$998$	1.33688	+	4.11450i	0.0423182	+	0.130242i
$999$	4.85410	−	3.52671i	0.153577	−	0.111580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.b.190.1	yes	4
3.2	odd	2		693.2.m.d.190.1		4
11.2	odd	10		2541.2.a.x.1.1		2
11.4	even	5	inner	231.2.j.b.169.1	✓	4
11.9	even	5		2541.2.a.p.1.2		2
33.2	even	10		7623.2.a.z.1.2		2
33.20	odd	10		7623.2.a.bo.1.1		2
33.26	odd	10		693.2.m.d.631.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.b.169.1	✓	4	11.4	even	5	inner
231.2.j.b.190.1	yes	4	1.1	even	1	trivial
693.2.m.d.190.1		4	3.2	odd	2
693.2.m.d.631.1		4	33.26	odd	10
2541.2.a.p.1.2		2	11.9	even	5
2541.2.a.x.1.1		2	11.2	odd	10
7623.2.a.z.1.2		2	33.2	even	10
7623.2.a.bo.1.1		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.500000 + 0.363271i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +(1.69098 + 2.85317i) q^{11} +1.61803 q^{12} +(-3.42705 + 2.48990i) q^{13} +(-0.190983 - 0.587785i) q^{14} +(0.500000 - 1.53884i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(2.80902 + 2.04087i) q^{17} +(0.190983 - 0.587785i) q^{18} +(2.00000 + 6.15537i) q^{19} +(-2.11803 + 1.53884i) q^{20} +1.00000 q^{21} +(-1.88197 - 0.812299i) q^{22} +5.70820 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(0.809017 - 2.48990i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.30902 - 0.951057i) q^{28} +(-0.0729490 + 0.224514i) q^{29} +(0.309017 + 0.951057i) q^{30} +(-2.42705 + 1.76336i) q^{31} +5.61803 q^{32} +(2.19098 - 2.48990i) q^{33} -2.14590 q^{34} +(-1.30902 + 0.951057i) q^{35} +(-0.500000 - 1.53884i) q^{36} +(1.85410 - 5.70634i) q^{37} +(-3.23607 - 2.35114i) q^{38} +(3.42705 + 2.48990i) q^{39} +(1.11803 - 3.44095i) q^{40} +(-3.04508 - 9.37181i) q^{41} +(-0.500000 + 0.363271i) q^{42} -11.4721 q^{43} +(-5.23607 + 1.17557i) q^{44} -1.61803 q^{45} +(-2.85410 + 2.07363i) q^{46} +(-1.59017 - 4.89404i) q^{47} +(-0.572949 + 1.76336i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.19098 + 0.865300i) q^{50} +(1.07295 - 3.30220i) q^{51} +(-2.11803 - 6.51864i) q^{52} +(10.1631 - 7.38394i) q^{53} -0.618034 q^{54} +(-0.500000 + 5.34307i) q^{55} +2.23607 q^{56} +(5.23607 - 3.80423i) q^{57} +(-0.0450850 - 0.138757i) q^{58} +(-1.42705 + 4.39201i) q^{59} +(2.11803 + 1.53884i) q^{60} +(6.42705 + 4.66953i) q^{61} +(0.572949 - 1.76336i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(0.190983 - 0.138757i) q^{64} -6.85410 q^{65} +(-0.190983 + 2.04087i) q^{66} +13.2361 q^{67} +(-4.54508 + 3.30220i) q^{68} +(-1.76393 - 5.42882i) q^{69} +(0.309017 - 0.951057i) q^{70} +(3.66312 + 2.66141i) q^{71} +(1.80902 + 1.31433i) q^{72} +(2.28115 - 7.02067i) q^{73} +(1.14590 + 3.52671i) q^{74} +(-1.92705 + 1.40008i) q^{75} -10.4721 q^{76} +(-3.23607 + 0.726543i) q^{77} -2.61803 q^{78} +(4.92705 - 3.57971i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.92705 + 3.57971i) q^{82} +(-6.85410 - 4.97980i) q^{83} +(-0.500000 + 1.53884i) q^{84} +(1.73607 + 5.34307i) q^{85} +(5.73607 - 4.16750i) q^{86} +0.236068 q^{87} +(4.89919 - 5.56758i) q^{88} +1.32624 q^{89} +(0.809017 - 0.587785i) q^{90} +(-1.30902 - 4.02874i) q^{91} +(-2.85410 + 8.78402i) q^{92} +(2.42705 + 1.76336i) q^{93} +(2.57295 + 1.86936i) q^{94} +(-3.23607 + 9.95959i) q^{95} +(-1.73607 - 5.34307i) q^{96} +(4.28115 - 3.11044i) q^{97} +0.618034 q^{98} +(-3.04508 - 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} - 4 q^{10} + 9 q^{11} + 2 q^{12} - 7 q^{13} - 3 q^{14} + 2 q^{15} - 6 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} - 5 q^{24} + 6 q^{25} + q^{26} + q^{27} - 3 q^{28} - 7 q^{29} - q^{30} - 3 q^{31} + 18 q^{32} + 11 q^{33} - 22 q^{34} - 3 q^{35} - 2 q^{36} - 6 q^{37} - 4 q^{38} + 7 q^{39} - q^{41} - 2 q^{42} - 28 q^{43} - 12 q^{44} - 2 q^{45} + 2 q^{46} + 16 q^{47} - 9 q^{48} - q^{49} + 7 q^{50} + 11 q^{51} - 4 q^{52} + 25 q^{53} + 2 q^{54} - 2 q^{55} + 12 q^{57} + 11 q^{58} + q^{59} + 4 q^{60} + 19 q^{61} + 9 q^{62} + q^{63} + 3 q^{64} - 14 q^{65} - 3 q^{66} + 44 q^{67} - 7 q^{68} - 16 q^{69} - q^{70} - q^{71} + 5 q^{72} - 11 q^{73} + 18 q^{74} - q^{75} - 24 q^{76} - 4 q^{77} - 6 q^{78} + 13 q^{79} + 3 q^{80} - q^{81} + 13 q^{82} - 14 q^{83} - 2 q^{84} - 2 q^{85} + 14 q^{86} - 8 q^{87} - 5 q^{88} - 26 q^{89} + q^{90} - 3 q^{91} + 2 q^{92} + 3 q^{93} + 17 q^{94} - 4 q^{95} + 2 q^{96} - 3 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 - 4 * q^10 + 9 * q^11 + 2 * q^12 - 7 * q^13 - 3 * q^14 + 2 * q^15 - 6 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 - 5 * q^24 + 6 * q^25 + q^26 + q^27 - 3 * q^28 - 7 * q^29 - q^30 - 3 * q^31 + 18 * q^32 + 11 * q^33 - 22 * q^34 - 3 * q^35 - 2 * q^36 - 6 * q^37 - 4 * q^38 + 7 * q^39 - q^41 - 2 * q^42 - 28 * q^43 - 12 * q^44 - 2 * q^45 + 2 * q^46 + 16 * q^47 - 9 * q^48 - q^49 + 7 * q^50 + 11 * q^51 - 4 * q^52 + 25 * q^53 + 2 * q^54 - 2 * q^55 + 12 * q^57 + 11 * q^58 + q^59 + 4 * q^60 + 19 * q^61 + 9 * q^62 + q^63 + 3 * q^64 - 14 * q^65 - 3 * q^66 + 44 * q^67 - 7 * q^68 - 16 * q^69 - q^70 - q^71 + 5 * q^72 - 11 * q^73 + 18 * q^74 - q^75 - 24 * q^76 - 4 * q^77 - 6 * q^78 + 13 * q^79 + 3 * q^80 - q^81 + 13 * q^82 - 14 * q^83 - 2 * q^84 - 2 * q^85 + 14 * q^86 - 8 * q^87 - 5 * q^88 - 26 * q^89 + q^90 - 3 * q^91 + 2 * q^92 + 3 * q^93 + 17 * q^94 - 4 * q^95 + 2 * q^96 - 3 * q^97 - 2 * q^98 - q^99

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