LMFDB - Embedded newform 231.2.j.b.148.1

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			148.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	231.148
Dual form			231.2.j.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(2.80902 - 1.76336i) q^{11} -0.618034 q^{12} +(-0.0729490 - 0.224514i) q^{13} +(-1.30902 - 0.951057i) q^{14} +(0.500000 - 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(1.69098 - 5.20431i) q^{17} +(1.30902 - 0.951057i) q^{18} +(2.00000 + 1.45309i) q^{19} +(0.118034 + 0.363271i) q^{20} +1.00000 q^{21} +(-4.11803 - 3.44095i) q^{22} -7.70820 q^{23} +(-0.690983 - 2.12663i) q^{24} +(3.73607 + 2.71441i) q^{25} +(-0.309017 + 0.224514i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.190983 + 0.587785i) q^{28} +(-3.42705 + 2.48990i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(0.927051 + 2.85317i) q^{31} +3.38197 q^{32} +(3.30902 + 0.224514i) q^{33} -8.85410 q^{34} +(-0.190983 - 0.587785i) q^{35} +(-0.500000 - 0.363271i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(1.23607 - 3.80423i) q^{38} +(0.0729490 - 0.224514i) q^{39} +(-1.11803 + 0.812299i) q^{40} +(2.54508 + 1.84911i) q^{41} +(-0.500000 - 1.53884i) q^{42} -2.52786 q^{43} +(-0.763932 + 1.90211i) q^{44} +0.618034 q^{45} +(3.85410 + 11.8617i) q^{46} +(9.59017 + 6.96767i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.30902 - 7.10642i) q^{50} +(4.42705 - 3.21644i) q^{51} +(0.118034 + 0.0857567i) q^{52} +(2.33688 + 7.19218i) q^{53} +1.61803 q^{54} +(-0.500000 - 1.98787i) q^{55} -2.23607 q^{56} +(0.763932 + 2.35114i) q^{57} +(5.54508 + 4.02874i) q^{58} +(1.92705 - 1.40008i) q^{59} +(-0.118034 + 0.363271i) q^{60} +(3.07295 - 9.45756i) q^{61} +(3.92705 - 2.85317i) q^{62} +(0.809017 + 0.587785i) q^{63} +(1.30902 + 4.02874i) q^{64} -0.145898 q^{65} +(-1.30902 - 5.20431i) q^{66} +8.76393 q^{67} +(1.04508 + 3.21644i) q^{68} +(-6.23607 - 4.53077i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-4.16312 + 12.8128i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-7.78115 + 5.65334i) q^{73} +(7.85410 + 5.70634i) q^{74} +(1.42705 + 4.39201i) q^{75} -1.52786 q^{76} +(1.23607 - 3.07768i) q^{77} -0.381966 q^{78} +(1.57295 + 4.84104i) q^{79} +(2.42705 + 1.76336i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.57295 - 4.84104i) q^{82} +(-0.145898 + 0.449028i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(-2.73607 - 1.98787i) q^{85} +(1.26393 + 3.88998i) q^{86} -4.23607 q^{87} +(-7.39919 - 0.502029i) q^{88} -14.3262 q^{89} +(-0.309017 - 0.951057i) q^{90} +(-0.190983 - 0.138757i) q^{91} +(3.85410 - 2.80017i) q^{92} +(-0.927051 + 2.85317i) q^{93} +(5.92705 - 18.2416i) q^{94} +(1.23607 - 0.898056i) q^{95} +(2.73607 + 1.98787i) q^{96} +(-5.78115 - 17.7926i) q^{97} -1.61803 q^{98} +(2.54508 + 2.12663i) 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 $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	−0.899226	−	0.437485i	$-0.855869\pi$
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	0.984636	+	0.174619i	$0.0558694\pi$
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.00000			−0.316228
$11$	2.80902	−	1.76336i	0.846950	−	0.531672i
$11$	2.80902	−	1.76336i	0.846950	−	0.531672i
$12$	−0.618034			−0.178411
$13$	−0.0729490	−	0.224514i	−0.0202324	−	0.0622690i	0.940431	−	0.339986i	$-0.110422\pi$
$13$	−0.0729490	−	0.224514i	−0.0202324	−	0.0622690i	−0.960663	+	0.277717i	$0.910422\pi$
$14$	−1.30902	−	0.951057i	−0.349850	−	0.254181i
$15$	0.500000	−	0.363271i	0.129099	−	0.0937962i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	1.69098	−	5.20431i	0.410124	−	1.26223i	−0.506417	−	0.862289i	$-0.669030\pi$
$17$	1.69098	−	5.20431i	0.410124	−	1.26223i	0.916540	−	0.399942i	$-0.130970\pi$
$18$	1.30902	−	0.951057i	0.308538	−	0.224166i
$19$	2.00000	+	1.45309i	0.458831	+	0.333361i	0.793073	−	0.609127i	$-0.208480\pi$
$19$	2.00000	+	1.45309i	0.458831	+	0.333361i	−0.334241	+	0.942488i	$0.608480\pi$
$20$	0.118034	+	0.363271i	0.0263932	+	0.0812299i
$21$	1.00000			0.218218
$22$	−4.11803	−	3.44095i	−0.877968	−	0.733614i
$23$	−7.70820			−1.60727			−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−7.70820			−1.60727			−0.803636	+	0.595121i	$0.797104\pi$
$24$	−0.690983	−	2.12663i	−0.141046	−	0.434096i
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$	−0.309017	+	0.224514i	−0.0606032	+	0.0440308i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.190983	+	0.587785i	−0.0360924	+	0.111081i
$29$	−3.42705	+	2.48990i	−0.636387	+	0.462363i	−0.858607	−	0.512634i	$-0.828670\pi$
$29$	−3.42705	+	2.48990i	−0.636387	+	0.462363i	0.222220	+	0.974997i	$0.428670\pi$
$30$	−0.809017	−	0.587785i	−0.147706	−	0.107314i
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	0.999144	−	0.0413693i	$-0.0131720\pi$
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	−0.832641	+	0.553814i	$0.813172\pi$
$32$	3.38197			0.597853
$33$	3.30902	+	0.224514i	0.576026	+	0.0390829i
$34$	−8.85410			−1.51847
$35$	−0.190983	−	0.587785i	−0.0322820	−	0.0993538i
$36$	−0.500000	−	0.363271i	−0.0833333	−	0.0605452i
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	−0.910330	−	0.413884i	$-0.864172\pi$
$37$	−4.85410	+	3.52671i	−0.798009	+	0.579788i	0.112320	+	0.993672i	$0.464172\pi$
$38$	1.23607	−	3.80423i	0.200517	−	0.617127i
$39$	0.0729490	−	0.224514i	0.0116812	−	0.0359510i
$40$	−1.11803	+	0.812299i	−0.176777	+	0.128436i
$41$	2.54508	+	1.84911i	0.397475	+	0.288783i	0.768512	−	0.639835i	$-0.220998\pi$
$41$	2.54508	+	1.84911i	0.397475	+	0.288783i	−0.371036	+	0.928618i	$0.620998\pi$
$42$	−0.500000	−	1.53884i	−0.0771517	−	0.237448i
$43$	−2.52786			−0.385496			−0.192748	−	0.981248i	$-0.561740\pi$
$43$	−2.52786			−0.385496			−0.192748	+	0.981248i	$0.561740\pi$
$44$	−0.763932	+	1.90211i	−0.115167	+	0.286754i
$45$	0.618034			0.0921311
$46$	3.85410	+	11.8617i	0.568256	+	1.74891i
$47$	9.59017	+	6.96767i	1.39887	+	1.01634i	0.994825	+	0.101599i	$0.0323960\pi$
$47$	9.59017	+	6.96767i	1.39887	+	1.01634i	0.404045	+	0.914739i	$0.367604\pi$
$48$	−3.92705	+	2.85317i	−0.566821	+	0.411820i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	2.30902	−	7.10642i	0.326544	−	1.00500i
$51$	4.42705	−	3.21644i	0.619911	−	0.450392i
$52$	0.118034	+	0.0857567i	0.0163684	+	0.0118923i
$53$	2.33688	+	7.19218i	0.320995	+	0.987922i	0.973216	+	0.229893i	$0.0738376\pi$
$53$	2.33688	+	7.19218i	0.320995	+	0.987922i	−0.652221	+	0.758029i	$0.726162\pi$
$54$	1.61803			0.220187
$55$	−0.500000	−	1.98787i	−0.0674200	−	0.268044i
$56$	−2.23607			−0.298807
$57$	0.763932	+	2.35114i	0.101185	+	0.311416i
$58$	5.54508	+	4.02874i	0.728105	+	0.528999i
$59$	1.92705	−	1.40008i	0.250881	−	0.182275i	−0.455236	−	0.890371i	$-0.650445\pi$
$59$	1.92705	−	1.40008i	0.250881	−	0.182275i	0.706117	+	0.708095i	$0.250445\pi$
$60$	−0.118034	+	0.363271i	−0.0152381	+	0.0468981i
$61$	3.07295	−	9.45756i	0.393451	−	1.21092i	−0.536711	−	0.843766i	$-0.680333\pi$
$61$	3.07295	−	9.45756i	0.393451	−	1.21092i	0.930161	−	0.367151i	$-0.119667\pi$
$62$	3.92705	−	2.85317i	0.498736	−	0.362353i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	−0.145898			−0.0180964
$66$	−1.30902	−	5.20431i	−0.161129	−	0.640606i
$67$	8.76393			1.07068			0.535342	−	0.844635i	$-0.320183\pi$
$67$	8.76393			1.07068			0.535342	+	0.844635i	$0.320183\pi$
$68$	1.04508	+	3.21644i	0.126735	+	0.390051i
$69$	−6.23607	−	4.53077i	−0.750734	−	0.545440i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	−4.16312	+	12.8128i	−0.494071	+	1.52060i	0.324328	+	0.945945i	$0.394862\pi$
$71$	−4.16312	+	12.8128i	−0.494071	+	1.52060i	−0.818399	+	0.574650i	$0.805138\pi$
$72$	0.690983	−	2.12663i	0.0814331	−	0.250625i
$73$	−7.78115	+	5.65334i	−0.910715	+	0.661673i	−0.941196	−	0.337862i	$-0.890296\pi$
$73$	−7.78115	+	5.65334i	−0.910715	+	0.661673i	0.0304805	+	0.999535i	$0.490296\pi$
$74$	7.85410	+	5.70634i	0.913021	+	0.663348i
$75$	1.42705	+	4.39201i	0.164782	+	0.507146i
$76$	−1.52786			−0.175258
$77$	1.23607	−	3.07768i	0.140863	−	0.350735i
$78$	−0.381966			−0.0432491
$79$	1.57295	+	4.84104i	0.176971	+	0.544659i	0.999718	−	0.0237477i	$-0.00755984\pi$
$79$	1.57295	+	4.84104i	0.176971	+	0.544659i	−0.822747	+	0.568407i	$0.807560\pi$
$80$	2.42705	+	1.76336i	0.271353	+	0.197149i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.57295	−	4.84104i	0.173703	−	0.534603i
$83$	−0.145898	+	0.449028i	−0.0160144	+	0.0492872i	−0.958744	−	0.284270i	$-0.908249\pi$
$83$	−0.145898	+	0.449028i	−0.0160144	+	0.0492872i	0.942730	+	0.333557i	$0.108249\pi$
$84$	−0.500000	+	0.363271i	−0.0545545	+	0.0396361i
$85$	−2.73607	−	1.98787i	−0.296768	−	0.215615i
$86$	1.26393	+	3.88998i	0.136293	+	0.419468i
$87$	−4.23607			−0.454154
$88$	−7.39919	−	0.502029i	−0.788756	−	0.0535164i
$89$	−14.3262			−1.51858			−0.759289	−	0.650753i	$-0.774453\pi$
$89$	−14.3262			−1.51858			−0.759289	+	0.650753i	$0.774453\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	−0.190983	−	0.138757i	−0.0200205	−	0.0145457i
$92$	3.85410	−	2.80017i	0.401818	−	0.291938i
$93$	−0.927051	+	2.85317i	−0.0961307	+	0.295860i
$94$	5.92705	−	18.2416i	0.611329	−	1.88148i
$95$	1.23607	−	0.898056i	0.126818	−	0.0921386i
$96$	2.73607	+	1.98787i	0.279249	+	0.202886i
$97$	−5.78115	−	17.7926i	−0.586987	−	1.80656i	−0.591140	−	0.806569i	$-0.701322\pi$
$97$	−5.78115	−	17.7926i	−0.586987	−	1.80656i	0.00415240	−	0.999991i	$-0.498678\pi$
$98$	−1.61803			−0.163446
$99$	2.54508	+	2.12663i	0.255791	+	0.213734i
$100$	−2.85410			−0.285410
$101$	2.09017	+	6.43288i	0.207980	+	0.640096i	0.999578	+	0.0290536i	$0.00924936\pi$
$101$	2.09017	+	6.43288i	0.207980	+	0.640096i	−0.791598	+	0.611042i	$0.790751\pi$
$102$	−7.16312	−	5.20431i	−0.709254	−	0.515304i
$103$	5.28115	−	3.83698i	0.520367	−	0.378069i	−0.296375	−	0.955072i	$-0.595778\pi$
$103$	5.28115	−	3.83698i	0.520367	−	0.378069i	0.816742	+	0.577003i	$0.195778\pi$
$104$	−0.163119	+	0.502029i	−0.0159951	+	0.0492279i
$105$	0.190983	−	0.587785i	0.0186380	−	0.0573620i
$106$	9.89919	−	7.19218i	0.961494	−	0.698566i
$107$	−8.28115	−	6.01661i	−0.800569	−	0.581648i	0.110512	−	0.993875i	$-0.464751\pi$
$107$	−8.28115	−	6.01661i	−0.800569	−	0.581648i	−0.911081	+	0.412227i	$0.864751\pi$
$108$	−0.190983	−	0.587785i	−0.0183773	−	0.0565597i
$109$	−10.8541			−1.03963			−0.519817	−	0.854278i	$-0.674000\pi$
$109$	−10.8541			−1.03963			−0.519817	+	0.854278i	$0.674000\pi$
$110$	−2.80902	+	1.76336i	−0.267829	+	0.168129i
$111$	−6.00000			−0.569495
$112$	1.50000	+	4.61653i	0.141737	+	0.436221i
$113$	−9.04508	−	6.57164i	−0.850890	−	0.618208i	0.0745013	−	0.997221i	$-0.476264\pi$
$113$	−9.04508	−	6.57164i	−0.850890	−	0.618208i	−0.925391	+	0.379013i	$0.876264\pi$
$114$	3.23607	−	2.35114i	0.303086	−	0.220205i
$115$	−1.47214	+	4.53077i	−0.137277	+	0.422496i
$116$	0.809017	−	2.48990i	0.0751153	−	0.231181i
$117$	0.190983	−	0.138757i	0.0176564	−	0.0128281i
$118$	−3.11803	−	2.26538i	−0.287038	−	0.208546i
$119$	−1.69098	−	5.20431i	−0.155012	−	0.477078i
$120$	−1.38197			−0.126156
$121$	4.78115	−	9.90659i	0.434650	−	0.900599i
$122$	−16.0902			−1.45674
$123$	0.972136	+	2.99193i	0.0876545	+	0.269773i
$124$	−1.50000	−	1.08981i	−0.134704	−	0.0978682i
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$	0.500000	−	1.53884i	0.0445435	−	0.137091i
$127$	2.57295	−	7.91872i	0.228312	−	0.702673i	−0.769626	−	0.638495i	$-0.779557\pi$
$127$	2.57295	−	7.91872i	0.228312	−	0.702673i	0.997938	−	0.0641782i	$-0.0204426\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	−2.04508	−	1.48584i	−0.180060	−	0.130821i
$130$	0.0729490	+	0.224514i	0.00639805	+	0.0196912i
$131$	0.145898			0.0127472			0.00637359	−	0.999980i	$-0.497971\pi$
$131$	0.145898			0.0127472			0.00637359	+	0.999980i	$0.497971\pi$
$132$	−1.73607	+	1.08981i	−0.151105	+	0.0948561i
$133$	2.47214			0.214361
$134$	−4.38197	−	13.4863i	−0.378544	−	1.16504i
$135$	0.500000	+	0.363271i	0.0430331	+	0.0312654i
$136$	−9.89919	+	7.19218i	−0.848848	+	0.616724i
$137$	−0.472136	+	1.45309i	−0.0403373	+	0.124145i	−0.969197	−	0.246285i	$-0.920790\pi$
$137$	−0.472136	+	1.45309i	−0.0403373	+	0.124145i	0.928860	+	0.370431i	$0.120790\pi$
$138$	−3.85410	+	11.8617i	−0.328083	+	1.00974i
$139$	−0.309017	+	0.224514i	−0.0262105	+	0.0190430i	−0.600813	−	0.799389i	$-0.705157\pi$
$139$	−0.309017	+	0.224514i	−0.0262105	+	0.0190430i	0.574603	+	0.818432i	$0.305157\pi$
$140$	0.309017	+	0.224514i	0.0261167	+	0.0189749i
$141$	3.66312	+	11.2739i	0.308490	+	0.949435i
$142$	21.7984			1.82928
$143$	−0.600813	−	0.502029i	−0.0502425	−	0.0419817i
$144$	−4.85410			−0.404508
$145$	0.809017	+	2.48990i	0.0671852	+	0.206775i
$146$	12.5902	+	9.14729i	1.04197	+	0.757035i
$147$	0.809017	−	0.587785i	0.0667266	−	0.0484797i
$148$	1.14590	−	3.52671i	0.0941922	−	0.289894i
$149$	−1.11803	+	3.44095i	−0.0915929	+	0.281894i	−0.986351	−	0.164658i	$-0.947348\pi$
$149$	−1.11803	+	3.44095i	−0.0915929	+	0.281894i	0.894758	+	0.446552i	$0.147348\pi$
$150$	6.04508	−	4.39201i	0.493579	−	0.358606i
$151$	7.54508	+	5.48183i	0.614010	+	0.446105i	0.850824	−	0.525450i	$-0.176103\pi$
$151$	7.54508	+	5.48183i	0.614010	+	0.446105i	−0.236814	+	0.971555i	$0.576103\pi$
$152$	−1.70820	−	5.25731i	−0.138554	−	0.426424i
$153$	5.47214			0.442396
$154$	−5.35410	−	0.363271i	−0.431446	−	0.0292732i
$155$	1.85410			0.148925
$156$	0.0450850	+	0.138757i	0.00360969	+	0.0111095i
$157$	−14.3992	−	10.4616i	−1.14918	−	0.834928i	−0.160809	−	0.986986i	$-0.551410\pi$
$157$	−14.3992	−	10.4616i	−1.14918	−	0.834928i	−0.988372	+	0.152057i	$0.951410\pi$
$158$	6.66312	−	4.84104i	0.530089	−	0.385132i
$159$	−2.33688	+	7.19218i	−0.185327	+	0.570377i
$160$	0.645898	−	1.98787i	0.0510627	−	0.157155i
$161$	−6.23607	+	4.53077i	−0.491471	+	0.357075i
$162$	1.30902	+	0.951057i	0.102846	+	0.0747221i
$163$	−0.826238	−	2.54290i	−0.0647159	−	0.199175i	0.913470	−	0.406906i	$-0.133392\pi$
$163$	−0.826238	−	2.54290i	−0.0647159	−	0.199175i	−0.978186	+	0.207731i	$0.933392\pi$
$164$	−1.94427			−0.151822
$165$	0.763932	−	1.90211i	0.0594720	−	0.148079i
$166$	0.763932			0.0592926
$167$	−2.73607	−	8.42075i	−0.211723	−	0.651617i	−0.999370	−	0.0354902i	$-0.988701\pi$
$167$	−2.73607	−	8.42075i	−0.211723	−	0.651617i	0.787647	−	0.616127i	$-0.211299\pi$
$168$	−1.80902	−	1.31433i	−0.139569	−	0.101403i
$169$	10.4721	−	7.60845i	0.805549	−	0.585266i
$170$	−1.69098	+	5.20431i	−0.129692	+	0.399152i
$171$	−0.763932	+	2.35114i	−0.0584193	+	0.179796i
$172$	1.26393	−	0.918300i	0.0963739	−	0.0700197i
$173$	11.1631	+	8.11048i	0.848716	+	0.616628i	0.924792	−	0.380474i	$-0.124239\pi$
$173$	11.1631	+	8.11048i	0.848716	+	0.616628i	−0.0760756	+	0.997102i	$0.524239\pi$
$174$	2.11803	+	6.51864i	0.160568	+	0.494177i
$175$	4.61803			0.349091
$176$	3.92705	+	15.6129i	0.296013	+	1.17687i
$177$	2.38197			0.179040
$178$	7.16312	+	22.0458i	0.536898	+	1.65240i
$179$	4.28115	+	3.11044i	0.319988	+	0.232485i	0.736171	−	0.676796i	$-0.236632\pi$
$179$	4.28115	+	3.11044i	0.319988	+	0.232485i	−0.416182	+	0.909281i	$0.636632\pi$
$180$	−0.309017	+	0.224514i	−0.0230328	+	0.0167343i
$181$	−2.92705	+	9.00854i	−0.217566	+	0.669599i	0.781395	+	0.624036i	$0.214508\pi$
$181$	−2.92705	+	9.00854i	−0.217566	+	0.669599i	−0.998961	+	0.0455631i	$0.985492\pi$
$182$	−0.118034	+	0.363271i	−0.00874926	+	0.0269275i
$183$	8.04508	−	5.84510i	0.594710	−	0.432082i
$184$	13.9443	+	10.1311i	1.02799	+	0.746875i
$185$	1.14590	+	3.52671i	0.0842481	+	0.259289i
$186$	4.85410			0.355920
$187$	−4.42705	−	17.6008i	−0.323738	−	1.28710i
$188$	−7.32624			−0.534321
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	−2.00000	−	1.45309i	−0.145095	−	0.105418i
$191$	9.51722	−	6.91467i	0.688642	−	0.500328i	−0.187571	−	0.982251i	$-0.560062\pi$
$191$	9.51722	−	6.91467i	0.688642	−	0.500328i	0.876213	+	0.481923i	$0.160062\pi$
$192$	−1.30902	+	4.02874i	−0.0944702	+	0.290749i
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	0.790047	+	0.613046i	$0.210056\pi$
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	−0.999501	+	0.0315871i	$0.989944\pi$
$194$	−24.4894	+	17.7926i	−1.75823	+	1.27743i
$195$	−0.118034	−	0.0857567i	−0.00845259	−	0.00614117i
$196$	0.190983	+	0.587785i	0.0136416	+	0.0419847i
$197$	−26.6525			−1.89891			−0.949455	−	0.313903i	$-0.898363\pi$
$197$	−26.6525			−1.89891			−0.949455	+	0.313903i	$0.898363\pi$
$198$	2.00000	−	4.97980i	0.142134	−	0.353899i
$199$	25.2148			1.78743			0.893714	−	0.448637i	$-0.148090\pi$
$199$	25.2148			1.78743			0.893714	+	0.448637i	$0.148090\pi$
$200$	−3.19098	−	9.82084i	−0.225637	−	0.694438i
$201$	7.09017	+	5.15131i	0.500102	+	0.363345i
$202$	8.85410	−	6.43288i	0.622972	−	0.452616i
$203$	−1.30902	+	4.02874i	−0.0918750	+	0.282762i
$204$	−1.04508	+	3.21644i	−0.0731706	+	0.225196i
$205$	1.57295	−	1.14281i	0.109860	−	0.0798176i
$206$	−8.54508	−	6.20837i	−0.595364	−	0.432557i
$207$	−2.38197	−	7.33094i	−0.165558	−	0.509535i
$208$	1.14590			0.0794537
$209$	8.18034	+	0.555029i	0.565846	+	0.0383922i
$210$	−1.00000			−0.0690066
$211$	−1.63525	−	5.03280i	−0.112576	−	0.346472i	0.878858	−	0.477083i	$-0.158306\pi$
$211$	−1.63525	−	5.03280i	−0.112576	−	0.346472i	−0.991434	+	0.130611i	$0.958306\pi$
$212$	−3.78115	−	2.74717i	−0.259691	−	0.188676i
$213$	−10.8992	+	7.91872i	−0.746800	+	0.542582i
$214$	−5.11803	+	15.7517i	−0.349862	+	1.07676i
$215$	−0.482779	+	1.48584i	−0.0329253	+	0.101334i
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	2.42705	+	1.76336i	0.164759	+	0.119704i
$218$	5.42705	+	16.7027i	0.367566	+	1.13125i
$219$	−9.61803			−0.649927
$220$	0.972136	+	0.812299i	0.0655414	+	0.0547652i
$221$	−1.29180			−0.0868956
$222$	3.00000	+	9.23305i	0.201347	+	0.619682i
$223$	−1.66312	−	1.20833i	−0.111371	−	0.0809155i	0.530706	−	0.847556i	$-0.321927\pi$
$223$	−1.66312	−	1.20833i	−0.111371	−	0.0809155i	−0.642077	+	0.766641i	$0.721927\pi$
$224$	2.73607	−	1.98787i	0.182811	−	0.132820i
$225$	−1.42705	+	4.39201i	−0.0951367	+	0.292801i
$226$	−5.59017	+	17.2048i	−0.371853	+	1.14444i
$227$	9.78115	−	7.10642i	0.649198	−	0.471670i	−0.213800	−	0.976877i	$-0.568584\pi$
$227$	9.78115	−	7.10642i	0.649198	−	0.471670i	0.862998	+	0.505208i	$0.168584\pi$
$228$	−1.23607	−	0.898056i	−0.0818606	−	0.0594752i
$229$	−7.76393	−	23.8949i	−0.513055	−	1.57902i	−0.786793	−	0.617217i	$-0.788260\pi$
$229$	−7.76393	−	23.8949i	−0.513055	−	1.57902i	0.273738	−	0.961804i	$-0.411740\pi$
$230$	7.70820			0.508264
$231$	2.80902	−	1.76336i	0.184820	−	0.116020i
$232$	9.47214			0.621876
$233$	−6.25329	−	19.2456i	−0.409667	−	1.26082i	−0.916935	−	0.399036i	$-0.869345\pi$
$233$	−6.25329	−	19.2456i	−0.409667	−	1.26082i	0.507269	−	0.861788i	$-0.330655\pi$
$234$	−0.309017	−	0.224514i	−0.0202011	−	0.0146769i
$235$	5.92705	−	4.30625i	0.386638	−	0.280909i
$236$	−0.454915	+	1.40008i	−0.0296124	+	0.0911377i
$237$	−1.57295	+	4.84104i	−0.102174	+	0.314459i
$238$	−7.16312	+	5.20431i	−0.464316	+	0.337345i
$239$	15.6803	+	11.3924i	1.01428	+	0.736915i	0.965102	−	0.261875i	$-0.0843408\pi$
$239$	15.6803	+	11.3924i	1.01428	+	0.736915i	0.0491750	+	0.998790i	$0.484341\pi$
$240$	0.927051	+	2.85317i	0.0598409	+	0.184171i
$241$	−16.4164			−1.05747			−0.528737	−	0.848786i	$-0.677334\pi$
$241$	−16.4164			−1.05747			−0.528737	+	0.848786i	$0.677334\pi$
$242$	−17.6353	−	2.40414i	−1.13364	−	0.154544i
$243$	−1.00000			−0.0641500
$244$	1.89919	+	5.84510i	0.121583	+	0.374194i
$245$	−0.500000	−	0.363271i	−0.0319438	−	0.0232085i
$246$	4.11803	−	2.99193i	0.262556	−	0.190758i
$247$	0.180340	−	0.555029i	0.0114748	−	0.0353157i
$248$	2.07295	−	6.37988i	0.131632	−	0.405123i
$249$	−0.381966	+	0.277515i	−0.0242061	+	0.0175868i
$250$	−7.78115	−	5.65334i	−0.492123	−	0.357549i
$251$	1.21885	+	3.75123i	0.0769329	+	0.236775i	0.982126	−	0.188226i	$-0.0602737\pi$
$251$	1.21885	+	3.75123i	0.0769329	+	0.236775i	−0.905193	+	0.425001i	$0.860274\pi$
$252$	−0.618034			−0.0389325
$253$	−21.6525	+	13.5923i	−1.36128	+	0.854541i
$254$	−13.4721			−0.845317
$255$	−1.04508	−	3.21644i	−0.0654458	−	0.201421i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	9.61803	−	6.98791i	0.599956	−	0.435894i	−0.245907	−	0.969293i	$-0.579086\pi$
$257$	9.61803	−	6.98791i	0.599956	−	0.435894i	0.845863	+	0.533400i	$0.179086\pi$
$258$	−1.26393	+	3.88998i	−0.0786890	+	0.242180i
$259$	−1.85410	+	5.70634i	−0.115208	+	0.354575i
$260$	0.0729490	−	0.0530006i	0.00452411	−	0.00328696i
$261$	−3.42705	−	2.48990i	−0.212129	−	0.154121i
$262$	−0.0729490	−	0.224514i	−0.00450681	−	0.0138705i
$263$	−22.7082			−1.40025			−0.700124	−	0.714021i	$-0.746872\pi$
$263$	−22.7082			−1.40025			−0.700124	+	0.714021i	$0.746872\pi$
$264$	−5.69098	−	4.75528i	−0.350256	−	0.292667i
$265$	4.67376			0.287107
$266$	−1.23607	−	3.80423i	−0.0757882	−	0.233252i
$267$	−11.5902	−	8.42075i	−0.709307	−	0.515342i
$268$	−4.38197	+	3.18368i	−0.267671	+	0.194474i
$269$	−2.10739	+	6.48588i	−0.128490	+	0.395451i	−0.994521	−	0.104539i	$-0.966663\pi$
$269$	−2.10739	+	6.48588i	−0.128490	+	0.395451i	0.866031	+	0.499991i	$0.166663\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−14.6631	+	10.6534i	−0.890721	+	0.647147i	−0.936066	−	0.351825i	$-0.885561\pi$
$271$	−14.6631	+	10.6534i	−0.890721	+	0.647147i	0.0453449	+	0.998971i	$0.485561\pi$
$272$	21.4894	+	15.6129i	1.30298	+	0.946673i
$273$	−0.0729490	−	0.224514i	−0.00441508	−	0.0135882i
$274$	2.47214			0.149347
$275$	15.2812	+	1.03681i	0.921488	+	0.0625222i
$276$	4.76393			0.286755
$277$	−0.145898	−	0.449028i	−0.00876616	−	0.0269795i	0.946578	−	0.322476i	$-0.104515\pi$
$277$	−0.145898	−	0.449028i	−0.00876616	−	0.0269795i	−0.955344	+	0.295496i	$0.904515\pi$
$278$	0.500000	+	0.363271i	0.0299880	+	0.0217876i
$279$	−2.42705	+	1.76336i	−0.145304	+	0.105569i
$280$	−0.427051	+	1.31433i	−0.0255212	+	0.0785461i
$281$	1.28115	−	3.94298i	0.0764272	−	0.235219i	−0.905543	−	0.424254i	$-0.860536\pi$
$281$	1.28115	−	3.94298i	0.0764272	−	0.235219i	0.981970	+	0.189036i	$0.0605362\pi$
$282$	15.5172	−	11.2739i	0.924037	−	0.671352i
$283$	18.5172	+	13.4535i	1.10073	+	0.799730i	0.981180	−	0.193097i	$-0.0618533\pi$
$283$	18.5172	+	13.4535i	1.10073	+	0.799730i	0.119555	+	0.992828i	$0.461853\pi$
$284$	−2.57295	−	7.91872i	−0.152676	−	0.469890i
$285$	1.52786			0.0905029
$286$	−0.472136	+	1.17557i	−0.0279180	+	0.0695129i
$287$	3.14590			0.185696
$288$	1.04508	+	3.21644i	0.0615822	+	0.189531i
$289$	−10.4721	−	7.60845i	−0.616008	−	0.447556i
$290$	3.42705	−	2.48990i	0.201243	−	0.146212i
$291$	5.78115	−	17.7926i	0.338897	−	1.04302i
$292$	1.83688	−	5.65334i	0.107495	−	0.330837i
$293$	−4.61803	+	3.35520i	−0.269788	+	0.196013i	−0.714451	−	0.699685i	$-0.753324\pi$
$293$	−4.61803	+	3.35520i	−0.269788	+	0.196013i	0.444663	+	0.895698i	$0.353324\pi$
$294$	−1.30902	−	0.951057i	−0.0763434	−	0.0554667i
$295$	−0.454915	−	1.40008i	−0.0264862	−	0.0815161i
$296$	13.4164			0.779813
$297$	0.809017	+	3.21644i	0.0469439	+	0.186637i
$298$	5.85410			0.339119
$299$	0.562306	+	1.73060i	0.0325190	+	0.100083i
$300$	−2.30902	−	1.67760i	−0.133311	−	0.0968562i
$301$	−2.04508	+	1.48584i	−0.117877	+	0.0856425i
$302$	4.66312	−	14.3516i	0.268332	−	0.825842i
$303$	−2.09017	+	6.43288i	−0.120077	+	0.369559i
$304$	−9.70820	+	7.05342i	−0.556804	+	0.404542i
$305$	−4.97214	−	3.61247i	−0.284704	−	0.206849i
$306$	−2.73607	−	8.42075i	−0.156411	−	0.481382i
$307$	25.9443			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$307$	25.9443			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$308$	0.500000	+	1.98787i	0.0284901	+	0.113269i
$309$	6.52786			0.371357
$310$	−0.927051	−	2.85317i	−0.0526530	−	0.162049i
$311$	14.3992	+	10.4616i	0.816503	+	0.593224i	0.915709	−	0.401843i	$-0.131630\pi$
$311$	14.3992	+	10.4616i	0.816503	+	0.593224i	−0.0992057	+	0.995067i	$0.531630\pi$
$312$	−0.427051	+	0.310271i	−0.0241770	+	0.0175656i
$313$	6.46149	−	19.8864i	0.365225	−	1.12405i	−0.584615	−	0.811311i	$-0.698754\pi$
$313$	6.46149	−	19.8864i	0.365225	−	1.12405i	0.949840	−	0.312736i	$-0.101246\pi$
$314$	−8.89919	+	27.3889i	−0.502210	+	1.54564i
$315$	0.500000	−	0.363271i	0.0281718	−	0.0204680i
$316$	−2.54508	−	1.84911i	−0.143172	−	0.104021i
$317$	0.274575	+	0.845055i	0.0154217	+	0.0474630i	0.958471	−	0.285189i	$-0.0920565\pi$
$317$	0.274575	+	0.845055i	0.0154217	+	0.0474630i	−0.943050	+	0.332652i	$0.892056\pi$
$318$	12.2361			0.686165
$319$	−5.23607	+	13.0373i	−0.293164	+	0.729947i
$320$	2.61803			0.146353
$321$	−3.16312	−	9.73508i	−0.176548	−	0.543359i
$322$	10.0902	+	7.33094i	0.562303	+	0.408537i
$323$	10.9443	−	7.95148i	0.608956	−	0.442432i
$324$	0.190983	−	0.587785i	0.0106102	−	0.0326547i
$325$	0.336881	−	1.03681i	0.0186868	−	0.0575121i
$326$	−3.50000	+	2.54290i	−0.193847	+	0.140838i
$327$	−8.78115	−	6.37988i	−0.485599	−	0.352808i
$328$	−2.17376	−	6.69015i	−0.120026	−	0.369402i
$329$	11.8541			0.653538
$330$	−3.30902	−	0.224514i	−0.182155	−	0.0123591i
$331$	−32.7082			−1.79781			−0.898903	−	0.438148i	$-0.855635\pi$
$331$	−32.7082			−1.79781			−0.898903	+	0.438148i	$0.855635\pi$
$332$	−0.0901699	−	0.277515i	−0.00494872	−	0.0152306i
$333$	−4.85410	−	3.52671i	−0.266003	−	0.193263i
$334$	−11.5902	+	8.42075i	−0.634186	+	0.460763i
$335$	1.67376	−	5.15131i	0.0914474	−	0.281446i
$336$	−1.50000	+	4.61653i	−0.0818317	+	0.251852i
$337$	−0.190983	+	0.138757i	−0.0104035	+	0.00755859i	−0.592975	−	0.805221i	$-0.702047\pi$
$337$	−0.190983	+	0.138757i	−0.0104035	+	0.00755859i	0.582571	+	0.812780i	$0.302047\pi$
$338$	−16.9443	−	12.3107i	−0.921647	−	0.669616i
$339$	−3.45492	−	10.6331i	−0.187645	−	0.577513i
$340$	2.09017			0.113355
$341$	7.63525	+	6.37988i	0.413472	+	0.345490i
$342$	4.00000			0.216295
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	4.57295	+	3.32244i	0.246557	+	0.179134i
$345$	−3.85410	+	2.80017i	−0.207498	+	0.150756i
$346$	6.89919	−	21.2335i	0.370903	−	1.14152i
$347$	2.61803	−	8.05748i	0.140543	−	0.432548i	−0.855868	−	0.517195i	$-0.826976\pi$
$347$	2.61803	−	8.05748i	0.140543	−	0.432548i	0.996411	+	0.0846468i	$0.0269762\pi$
$348$	2.11803	−	1.53884i	0.113539	−	0.0824906i
$349$	1.35410	+	0.983813i	0.0724834	+	0.0526623i	0.623437	−	0.781874i	$-0.285736\pi$
$349$	1.35410	+	0.983813i	0.0724834	+	0.0526623i	−0.550953	+	0.834536i	$0.685736\pi$
$350$	−2.30902	−	7.10642i	−0.123422	−	0.379854i
$351$	0.236068			0.0126004
$352$	9.50000	−	5.96361i	0.506352	−	0.317861i
$353$	36.1246			1.92272			0.961360	−	0.275296i	$-0.0887758\pi$
$353$	36.1246			1.92272			0.961360	+	0.275296i	$0.0887758\pi$
$354$	−1.19098	−	3.66547i	−0.0633000	−	0.194817i
$355$	6.73607	+	4.89404i	0.357513	+	0.259749i
$356$	7.16312	−	5.20431i	0.379645	−	0.275828i
$357$	1.69098	−	5.20431i	0.0894963	−	0.275441i
$358$	2.64590	−	8.14324i	0.139840	−	0.430383i
$359$	−10.2082	+	7.41669i	−0.538768	+	0.391438i	−0.823627	−	0.567131i	$-0.808053\pi$
$359$	−10.2082	+	7.41669i	−0.538768	+	0.391438i	0.284859	+	0.958569i	$0.408053\pi$
$360$	−1.11803	−	0.812299i	−0.0589256	−	0.0428119i
$361$	−3.98278	−	12.2577i	−0.209620	−	0.645144i
$362$	15.3262			0.805529
$363$	9.69098	−	5.20431i	0.508645	−	0.273155i
$364$	0.145898			0.00764713
$365$	1.83688	+	5.65334i	0.0961467	+	0.295909i
$366$	−13.0172	−	9.45756i	−0.680421	−	0.494355i
$367$	4.04508	−	2.93893i	0.211152	−	0.153411i	−0.477183	−	0.878804i	$-0.658342\pi$
$367$	4.04508	−	2.93893i	0.211152	−	0.153411i	0.688335	+	0.725393i	$0.258342\pi$
$368$	11.5623	−	35.5851i	0.602727	−	1.85500i
$369$	−0.972136	+	2.99193i	−0.0506074	+	0.155753i
$370$	4.85410	−	3.52671i	0.252353	−	0.183345i
$371$	6.11803	+	4.44501i	0.317632	+	0.230774i
$372$	−0.572949	−	1.76336i	−0.0297060	−	0.0914257i
$373$	−33.7082			−1.74534			−0.872672	−	0.488306i	$-0.837615\pi$
$373$	−33.7082			−1.74534			−0.872672	+	0.488306i	$0.837615\pi$
$374$	−24.8713	+	15.6129i	−1.28607	+	0.807325i
$375$	5.94427			0.306961
$376$	−8.19098	−	25.2093i	−0.422418	−	1.30007i
$377$	0.809017	+	0.587785i	0.0416665	+	0.0302725i
$378$	1.30902	−	0.951057i	0.0673286	−	0.0489171i
$379$	−4.04508	+	12.4495i	−0.207782	+	0.639487i	0.791806	+	0.610773i	$0.209141\pi$
$379$	−4.04508	+	12.4495i	−0.207782	+	0.639487i	−0.999588	+	0.0287142i	$0.990859\pi$
$380$	−0.291796	+	0.898056i	−0.0149688	+	0.0460693i
$381$	6.73607	−	4.89404i	0.345099	−	0.250729i
$382$	−15.3992	−	11.1882i	−0.787891	−	0.572436i
$383$	−5.66312	−	17.4293i	−0.289372	−	0.890595i	−0.985054	−	0.172245i	$-0.944898\pi$
$383$	−5.66312	−	17.4293i	−0.289372	−	0.890595i	0.695682	−	0.718350i	$-0.255102\pi$
$384$	13.6180			0.694942
$385$	−1.57295	−	1.31433i	−0.0801649	−	0.0669843i
$386$	15.2361			0.775495
$387$	−0.781153	−	2.40414i	−0.0397082	−	0.122209i
$388$	9.35410	+	6.79615i	0.474883	+	0.345022i
$389$	10.3262	−	7.50245i	0.523561	−	0.380389i	−0.294383	−	0.955688i	$-0.595114\pi$
$389$	10.3262	−	7.50245i	0.523561	−	0.380389i	0.817944	+	0.575298i	$0.195114\pi$
$390$	−0.0729490	+	0.224514i	−0.00369392	+	0.0113687i
$391$	−13.0344	+	40.1159i	−0.659180	+	2.02875i
$392$	−1.80902	+	1.31433i	−0.0913692	+	0.0663836i
$393$	0.118034	+	0.0857567i	0.00595403	+	0.00432585i
$394$	13.3262	+	41.0139i	0.671366	+	2.06625i
$395$	3.14590			0.158287
$396$	−2.04508	−	0.138757i	−0.102769	−	0.00697282i
$397$	9.56231			0.479918			0.239959	−	0.970783i	$-0.422866\pi$
$397$	9.56231			0.479918			0.239959	+	0.970783i	$0.422866\pi$
$398$	−12.6074	−	38.8016i	−0.631951	−	1.94495i
$399$	2.00000	+	1.45309i	0.100125	+	0.0727452i
$400$	−18.1353	+	13.1760i	−0.906763	+	0.658802i
$401$	−4.55573	+	14.0211i	−0.227502	+	0.700180i	0.770526	+	0.637409i	$0.219994\pi$
$401$	−4.55573	+	14.0211i	−0.227502	+	0.700180i	−0.998028	+	0.0627709i	$0.980006\pi$
$402$	4.38197	−	13.4863i	0.218553	−	0.672636i
$403$	0.572949	−	0.416272i	0.0285406	−	0.0207360i
$404$	−3.38197	−	2.45714i	−0.168259	−	0.122247i
$405$	0.190983	+	0.587785i	0.00949002	+	0.0292073i
$406$	6.85410			0.340163
$407$	−7.41641	+	18.4661i	−0.367618	+	0.915331i
$408$	−12.2361			−0.605776
$409$	10.1353	+	31.1931i	0.501156	+	1.54240i	0.807138	+	0.590363i	$0.201015\pi$
$409$	10.1353	+	31.1931i	0.501156	+	1.54240i	−0.305982	+	0.952037i	$0.598985\pi$
$410$	−2.54508	−	1.84911i	−0.125693	−	0.0913212i
$411$	−1.23607	+	0.898056i	−0.0609707	+	0.0442978i
$412$	−1.24671	+	3.83698i	−0.0614210	+	0.189035i
$413$	0.736068	−	2.26538i	0.0362195	−	0.111472i
$414$	−10.0902	+	7.33094i	−0.495905	+	0.360296i
$415$	0.236068	+	0.171513i	0.0115881	+	0.00841926i
$416$	−0.246711	−	0.759299i	−0.0120960	−	0.0372277i
$417$	−0.381966			−0.0187050
$418$	−3.23607	−	12.8658i	−0.158281	−	0.629285i
$419$	−33.3820			−1.63082			−0.815408	−	0.578887i	$-0.803487\pi$
$419$	−33.3820			−1.63082			−0.815408	+	0.578887i	$0.803487\pi$
$420$	0.118034	+	0.363271i	0.00575947	+	0.0177258i
$421$	−20.1074	−	14.6089i	−0.979974	−	0.711993i	−0.0222714	−	0.999752i	$-0.507090\pi$
$421$	−20.1074	−	14.6089i	−0.979974	−	0.711993i	−0.957703	+	0.287759i	$0.907090\pi$
$422$	−6.92705	+	5.03280i	−0.337204	+	0.244993i
$423$	−3.66312	+	11.2739i	−0.178107	+	0.548157i
$424$	5.22542	−	16.0822i	0.253769	−	0.781021i
$425$	20.4443	−	14.8536i	0.991693	−	0.720507i
$426$	17.6353	+	12.8128i	0.854431	+	0.620780i
$427$	−3.07295	−	9.45756i	−0.148710	−	0.457684i
$428$	6.32624			0.305790
$429$	−0.190983	−	0.759299i	−0.00922075	−	0.0366593i
$430$	2.52786			0.121904
$431$	−4.28115	−	13.1760i	−0.206216	−	0.634667i	−0.999661	−	0.0260258i	$-0.991715\pi$
$431$	−4.28115	−	13.1760i	−0.206216	−	0.634667i	0.793445	−	0.608641i	$-0.208285\pi$
$432$	−3.92705	−	2.85317i	−0.188940	−	0.137273i
$433$	−8.85410	+	6.43288i	−0.425501	+	0.309145i	−0.779847	−	0.625970i	$-0.784703\pi$
$433$	−8.85410	+	6.43288i	−0.425501	+	0.309145i	0.354346	+	0.935114i	$0.384703\pi$
$434$	1.50000	−	4.61653i	0.0720023	−	0.221600i
$435$	−0.809017	+	2.48990i	−0.0387894	+	0.119381i
$436$	5.42705	−	3.94298i	0.259909	−	0.188835i
$437$	−15.4164	−	11.2007i	−0.737467	−	0.535801i
$438$	4.80902	+	14.8006i	0.229784	+	0.707202i
$439$	4.34752			0.207496			0.103748	−	0.994604i	$-0.466916\pi$
$439$	4.34752			0.207496			0.103748	+	0.994604i	$0.466916\pi$
$440$	−1.70820	+	4.25325i	−0.0814354	+	0.202766i
$441$	1.00000			0.0476190
$442$	0.645898	+	1.98787i	0.0307222	+	0.0945533i
$443$	5.38197	+	3.91023i	0.255705	+	0.185781i	0.708251	−	0.705960i	$-0.249484\pi$
$443$	5.38197	+	3.91023i	0.255705	+	0.185781i	−0.452546	+	0.891741i	$0.649484\pi$
$444$	3.00000	−	2.17963i	0.142374	−	0.103441i
$445$	−2.73607	+	8.42075i	−0.129702	+	0.399182i
$446$	−1.02786	+	3.16344i	−0.0486708	+	0.149793i
$447$	−2.92705	+	2.12663i	−0.138445	+	0.100586i
$448$	3.42705	+	2.48990i	0.161913	+	0.117637i
$449$	8.83688	+	27.1971i	0.417038	+	1.28351i	0.910415	+	0.413696i	$0.135762\pi$
$449$	8.83688	+	27.1971i	0.417038	+	1.28351i	−0.493377	+	0.869816i	$0.664238\pi$
$450$	7.47214			0.352240
$451$	10.4098	+	0.706298i	0.490180	+	0.0332583i
$452$	6.90983			0.325011
$453$	2.88197	+	8.86978i	0.135407	+	0.416739i
$454$	−15.8262	−	11.4984i	−0.742762	−	0.539648i
$455$	−0.118034	+	0.0857567i	−0.00553352	+	0.00402034i
$456$	1.70820	−	5.25731i	0.0799940	−	0.246196i
$457$	−7.33688	+	22.5806i	−0.343205	+	1.05628i	0.619333	+	0.785128i	$0.287403\pi$
$457$	−7.33688	+	22.5806i	−0.343205	+	1.05628i	−0.962538	+	0.271147i	$0.912597\pi$
$458$	−32.8885	+	23.8949i	−1.53678	+	1.11654i
$459$	4.42705	+	3.21644i	0.206637	+	0.150131i
$460$	−0.909830	−	2.80017i	−0.0424210	−	0.130559i
$461$	−34.3050			−1.59774			−0.798870	−	0.601503i	$-0.794569\pi$
$461$	−34.3050			−1.59774			−0.798870	+	0.601503i	$0.794569\pi$
$462$	−4.11803	−	3.44095i	−0.191588	−	0.160088i
$463$	31.9787			1.48618			0.743088	−	0.669193i	$-0.233360\pi$
$463$	31.9787			1.48618			0.743088	+	0.669193i	$0.233360\pi$
$464$	−6.35410	−	19.5559i	−0.294982	−	0.907861i
$465$	1.50000	+	1.08981i	0.0695608	+	0.0505389i
$466$	−26.4894	+	19.2456i	−1.22710	+	0.891537i
$467$	−4.10739	+	12.6412i	−0.190067	+	0.584967i	−0.999999	−	0.00155736i	$-0.999504\pi$
$467$	−4.10739	+	12.6412i	−0.190067	+	0.584967i	0.809931	+	0.586525i	$0.199504\pi$
$468$	−0.0450850	+	0.138757i	−0.00208405	+	0.00641406i
$469$	7.09017	−	5.15131i	0.327394	−	0.237865i
$470$	−9.59017	−	6.96767i	−0.442362	−	0.321394i
$471$	−5.50000	−	16.9273i	−0.253427	−	0.779967i
$472$	−5.32624			−0.245160
$473$	−7.10081	+	4.45752i	−0.326496	+	0.204957i
$474$	8.23607			0.378295
$475$	3.52786	+	10.8576i	0.161870	+	0.498183i
$476$	2.73607	+	1.98787i	0.125407	+	0.0911139i
$477$	−6.11803	+	4.44501i	−0.280126	+	0.203523i
$478$	9.69098	−	29.8258i	0.443255	−	1.36420i
$479$	10.0795	−	31.0216i	0.460545	−	1.41741i	−0.403954	−	0.914779i	$-0.632364\pi$
$479$	10.0795	−	31.0216i	0.460545	−	1.41741i	0.864500	−	0.502634i	$-0.167636\pi$
$480$	1.69098	−	1.22857i	0.0771825	−	0.0560763i
$481$	1.14590	+	0.832544i	0.0522485	+	0.0379607i
$482$	8.20820	+	25.2623i	0.373873	+	1.15066i
$483$	−7.70820			−0.350735
$484$	1.20820	+	6.69015i	0.0549184	+	0.304098i
$485$	−11.5623			−0.525017
$486$	0.500000	+	1.53884i	0.0226805	+	0.0698033i
$487$	14.2533	+	10.3556i	0.645878	+	0.469258i	0.861865	−	0.507138i	$-0.169297\pi$
$487$	14.2533	+	10.3556i	0.645878	+	0.469258i	−0.215986	+	0.976396i	$0.569297\pi$
$488$	−17.9894	+	13.0700i	−0.814340	+	0.591653i
$489$	0.826238	−	2.54290i	0.0373638	−	0.114994i
$490$	−0.309017	+	0.951057i	−0.0139600	+	0.0429644i
$491$	17.5623	−	12.7598i	0.792576	−	0.575840i	−0.116151	−	0.993232i	$-0.537056\pi$
$491$	17.5623	−	12.7598i	0.792576	−	0.575840i	0.908727	+	0.417392i	$0.137056\pi$
$492$	−1.57295	−	1.14281i	−0.0709140	−	0.0515221i
$493$	7.16312	+	22.0458i	0.322611	+	0.992893i
$494$	−0.944272			−0.0424848
$495$	1.73607	−	1.08981i	0.0780305	−	0.0489835i
$496$	−14.5623			−0.653867
$497$	4.16312	+	12.8128i	0.186741	+	0.574731i
$498$	0.618034	+	0.449028i	0.0276948	+	0.0201214i
$499$	−5.66312	+	4.11450i	−0.253516	+	0.184190i	−0.707284	−	0.706930i	$-0.750080\pi$
$499$	−5.66312	+	4.11450i	−0.253516	+	0.184190i	0.453768	+	0.891120i	$0.350080\pi$
$500$	−1.13525	+	3.49396i	−0.0507701	+	0.156254i
$501$	2.73607	−	8.42075i	0.122239	−	0.376211i
$502$	5.16312	−	3.75123i	0.230441	−	0.167425i
$503$	−27.5172	−	19.9924i	−1.22693	−	0.891418i	−0.230276	−	0.973125i	$-0.573963\pi$
$503$	−27.5172	−	19.9924i	−1.22693	−	0.891418i	−0.996656	+	0.0817069i	$0.973963\pi$
$504$	−0.690983	−	2.12663i	−0.0307788	−	0.0947275i
$505$	4.18034			0.186023
$506$	31.7426	+	26.5236i	1.41113	+	1.17912i
$507$	12.9443			0.574875
$508$	1.59017	+	4.89404i	0.0705524	+	0.217138i
$509$	22.7533	+	16.5312i	1.00852	+	0.732734i	0.963899	−	0.266270i	$-0.0857912\pi$
$509$	22.7533	+	16.5312i	1.00852	+	0.732734i	0.0446233	+	0.999004i	$0.485791\pi$
$510$	−4.42705	+	3.21644i	−0.196033	+	0.142426i
$511$	−2.97214	+	9.14729i	−0.131480	+	0.404652i
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	−2.00000	+	1.45309i	−0.0883022	+	0.0641553i
$514$	−15.5623	−	11.3067i	−0.686424	−	0.498716i
$515$	−1.24671	−	3.83698i	−0.0549367	−	0.169078i
$516$	1.56231			0.0687767
$517$	39.2254	+	2.66141i	1.72513	+	0.117049i
$518$	9.70820			0.426554
$519$	4.26393	+	13.1230i	0.187166	+	0.576037i
$520$	0.263932	+	0.191758i	0.0115742	+	0.00840914i
$521$	14.8992	−	10.8249i	0.652745	−	0.474247i	−0.211460	−	0.977387i	$-0.567822\pi$
$521$	14.8992	−	10.8249i	0.652745	−	0.474247i	0.864205	+	0.503139i	$0.167822\pi$
$522$	−2.11803	+	6.51864i	−0.0927038	+	0.285313i
$523$	−11.6008	+	35.7036i	−0.507268	+	1.56121i	0.289656	+	0.957131i	$0.406459\pi$
$523$	−11.6008	+	35.7036i	−0.507268	+	1.56121i	−0.796924	+	0.604080i	$0.793541\pi$
$524$	−0.0729490	+	0.0530006i	−0.00318679	+	0.00231534i
$525$	3.73607	+	2.71441i	0.163055	+	0.118467i
$526$	11.3541	+	34.9443i	0.495062	+	1.52365i
$527$	16.4164			0.715110
$528$	−6.00000	+	14.9394i	−0.261116	+	0.650153i
$529$	36.4164			1.58332
$530$	−2.33688	−	7.19218i	−0.101508	−	0.312408i
$531$	1.92705	+	1.40008i	0.0836269	+	0.0607585i
$532$	−1.23607	+	0.898056i	−0.0535903	+	0.0389357i
$533$	0.229490	−	0.706298i	0.00994032	−	0.0305932i
$534$	−7.16312	+	22.0458i	−0.309978	+	0.954016i
$535$	−5.11803	+	3.71847i	−0.221272	+	0.160763i
$536$	−15.8541	−	11.5187i	−0.684793	−	0.497531i
$537$	1.63525	+	5.03280i	0.0705665	+	0.217181i
$538$	11.0344			0.475729
$539$	−0.809017	−	3.21644i	−0.0348468	−	0.138542i
$540$	−0.381966			−0.0164372
$541$	−12.3713	−	38.0750i	−0.531885	−	1.63697i	−0.750286	−	0.661114i	$-0.770084\pi$
$541$	−12.3713	−	38.0750i	−0.531885	−	1.63697i	0.218401	−	0.975859i	$-0.429916\pi$
$542$	23.7254	+	17.2375i	1.01909	+	0.740415i
$543$	−7.66312	+	5.56758i	−0.328856	+	0.238928i
$544$	5.71885	−	17.6008i	0.245194	−	0.754628i
$545$	−2.07295	+	6.37988i	−0.0887954	+	0.273284i
$546$	−0.309017	+	0.224514i	−0.0132247	+	0.00960831i
$547$	−31.6074	−	22.9641i	−1.35143	−	0.981875i	−0.998939	−	0.0460612i	$-0.985333\pi$
$547$	−31.6074	−	22.9641i	−1.35143	−	0.981875i	−0.352496	−	0.935813i	$-0.614667\pi$
$548$	−0.291796	−	0.898056i	−0.0124649	−	0.0383630i
$549$	9.94427			0.424411
$550$	−6.04508	−	24.0337i	−0.257763	−	1.02480i
$551$	−10.4721			−0.446128
$552$	5.32624	+	16.3925i	0.226700	+	0.697710i
$553$	4.11803	+	2.99193i	0.175117	+	0.127230i
$554$	−0.618034	+	0.449028i	−0.0262577	+	0.0190774i
$555$	−1.14590	+	3.52671i	−0.0486407	+	0.149701i
$556$	0.0729490	−	0.224514i	0.00309373	−	0.00952151i
$557$	−37.6525	+	27.3561i	−1.59539	+	1.15912i	−0.699694	+	0.714443i	$0.746680\pi$
$557$	−37.6525	+	27.3561i	−1.59539	+	1.15912i	−0.895693	+	0.444673i	$0.853320\pi$
$558$	3.92705	+	2.85317i	0.166245	+	0.120784i
$559$	0.184405	+	0.567541i	0.00779951	+	0.0240044i
$560$	3.00000			0.126773
$561$	6.76393	−	16.8415i	0.285573	−	0.711049i
$562$	−6.70820			−0.282969
$563$	−3.10739	−	9.56357i	−0.130961	−	0.403056i	0.863979	−	0.503528i	$-0.167965\pi$
$563$	−3.10739	−	9.56357i	−0.130961	−	0.403056i	−0.994940	+	0.100472i	$0.967965\pi$
$564$	−5.92705	−	4.30625i	−0.249574	−	0.181326i
$565$	−5.59017	+	4.06150i	−0.235180	+	0.170868i
$566$	11.4443	−	35.2218i	0.481039	−	1.48048i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	24.3713	−	17.7068i	1.02260	−	0.742961i
$569$	20.4615	+	14.8661i	0.857790	+	0.623221i	0.927283	−	0.374361i	$-0.122138\pi$
$569$	20.4615	+	14.8661i	0.857790	+	0.623221i	−0.0694925	+	0.997582i	$0.522138\pi$
$570$	−0.763932	−	2.35114i	−0.0319976	−	0.0984785i
$571$	18.0557			0.755609			0.377804	−	0.925885i	$-0.376679\pi$
$571$	18.0557			0.755609			0.377804	+	0.925885i	$0.376679\pi$
$572$	0.482779	+	0.0327561i	0.0201860	+	0.00136960i
$573$	11.7639			0.491445
$574$	−1.57295	−	4.84104i	−0.0656536	−	0.202061i
$575$	−28.7984	−	20.9232i	−1.20098	−	0.872560i
$576$	−3.42705	+	2.48990i	−0.142794	+	0.103746i
$577$	13.5517	−	41.7077i	0.564163	−	1.73632i	−0.106262	−	0.994338i	$-0.533888\pi$
$577$	13.5517	−	41.7077i	0.564163	−	1.73632i	0.670425	−	0.741977i	$-0.266112\pi$
$578$	−6.47214	+	19.9192i	−0.269205	+	0.828529i
$579$	−7.61803	+	5.53483i	−0.316595	+	0.230020i
$580$	−1.30902	−	0.951057i	−0.0543540	−	0.0394905i
$581$	0.145898	+	0.449028i	0.00605287	+	0.0186288i
$582$	−30.2705			−1.25475
$583$	19.2467	+	16.0822i	0.797117	+	0.666057i
$584$	21.5066			0.889949
$585$	−0.0450850	−	0.138757i	−0.00186403	−	0.00573691i
$586$	7.47214	+	5.42882i	0.308671	+	0.224263i
$587$	−39.0344	+	28.3602i	−1.61112	+	1.17055i	−0.751297	+	0.659964i	$0.770571\pi$
$587$	−39.0344	+	28.3602i	−1.61112	+	1.17055i	−0.859827	+	0.510586i	$0.829429\pi$
$588$	−0.190983	+	0.587785i	−0.00787601	+	0.0242399i
$589$	−2.29180	+	7.05342i	−0.0944318	+	0.290631i
$590$	−1.92705	+	1.40008i	−0.0793354	+	0.0576406i
$591$	−21.5623	−	15.6659i	−0.886955	−	0.644410i
$592$	−9.00000	−	27.6992i	−0.369898	−	1.13843i
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$	4.54508	−	2.85317i	0.186487	−	0.117067i
$595$	−3.38197			−0.138647
$596$	−0.690983	−	2.12663i	−0.0283038	−	0.0871100i
$597$	20.3992	+	14.8209i	0.834883	+	0.606578i
$598$	2.38197	−	1.73060i	0.0974058	−	0.0707695i
$599$	1.71885	−	5.29007i	0.0702302	−	0.216146i	−0.909781	−	0.415089i	$-0.863751\pi$
$599$	1.71885	−	5.29007i	0.0702302	−	0.216146i	0.980011	+	0.198942i	$0.0637506\pi$
$600$	3.19098	−	9.82084i	0.130271	−	0.400934i
$601$	25.4164	−	18.4661i	1.03676	−	0.753248i	0.0671071	−	0.997746i	$-0.478623\pi$
$601$	25.4164	−	18.4661i	1.03676	−	0.753248i	0.969650	+	0.244498i	$0.0786231\pi$
$602$	3.30902	+	2.40414i	0.134865	+	0.0979855i
$603$	2.70820	+	8.33499i	0.110287	+	0.339427i
$604$	−5.76393			−0.234531
$605$	−4.90983	−	4.70228i	−0.199613	−	0.191175i
$606$	10.9443			0.444581
$607$	14.2639	+	43.8999i	0.578955	+	1.78184i	0.622298	+	0.782780i	$0.286199\pi$
$607$	14.2639	+	43.8999i	0.578955	+	1.78184i	−0.0433428	+	0.999060i	$0.513801\pi$
$608$	6.76393	+	4.91428i	0.274314	+	0.199301i
$609$	−3.42705	+	2.48990i	−0.138871	+	0.100896i
$610$	−3.07295	+	9.45756i	−0.124420	+	0.382926i
$611$	0.864745	−	2.66141i	0.0349838	−	0.107669i
$612$	−2.73607	+	1.98787i	−0.110599	+	0.0803549i
$613$	−3.59017	−	2.60841i	−0.145006	−	0.105353i	0.512917	−	0.858438i	$-0.328565\pi$
$613$	−3.59017	−	2.60841i	−0.145006	−	0.105353i	−0.657923	+	0.753085i	$0.728565\pi$
$614$	−12.9721	−	39.9241i	−0.523513	−	1.61121i
$615$	1.94427			0.0784006
$616$	−6.28115	+	3.94298i	−0.253075	+	0.158867i
$617$	14.3262			0.576753			0.288376	−	0.957517i	$-0.406885\pi$
$617$	14.3262			0.576753			0.288376	+	0.957517i	$0.406885\pi$
$618$	−3.26393	−	10.0453i	−0.131295	−	0.404083i
$619$	−0.145898	−	0.106001i	−0.00586414	−	0.00426054i	0.584849	−	0.811142i	$-0.301154\pi$
$619$	−0.145898	−	0.106001i	−0.00586414	−	0.00426054i	−0.590713	+	0.806881i	$0.701154\pi$
$620$	−0.927051	+	0.673542i	−0.0372313	+	0.0270501i
$621$	2.38197	−	7.33094i	0.0955850	−	0.294180i
$622$	8.89919	−	27.3889i	0.356825	−	1.09819i
$623$	−11.5902	+	8.42075i	−0.464350	+	0.337370i
$624$	0.927051	+	0.673542i	0.0371117	+	0.0269633i
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$	−33.8328			−1.35223
$627$	6.29180	+	5.25731i	0.251270	+	0.209957i
$628$	11.0000			0.438948
$629$	10.1459	+	31.2259i	0.404543	+	1.24506i
$630$	−0.809017	−	0.587785i	−0.0322320	−	0.0234179i
$631$	10.2812	−	7.46969i	0.409286	−	0.297364i	−0.364027	−	0.931389i	$-0.618598\pi$
$631$	10.2812	−	7.46969i	0.409286	−	0.297364i	0.773313	+	0.634025i	$0.218598\pi$
$632$	3.51722	−	10.8249i	0.139908	−	0.430591i
$633$	1.63525	−	5.03280i	0.0649955	−	0.200036i
$634$	1.16312	−	0.845055i	0.0461934	−	0.0335614i
$635$	−4.16312	−	3.02468i	−0.165208	−	0.120031i
$636$	−1.44427	−	4.44501i	−0.0572691	−	0.176256i
$637$	−0.236068			−0.00935335
$638$	22.6803	+	1.53884i	0.897923	+	0.0609233i
$639$	−13.4721			−0.532949
$640$	−2.60081	−	8.00448i	−0.102806	−	0.316405i
$641$	5.11803	+	3.71847i	0.202150	+	0.146871i	0.684255	−	0.729243i	$-0.260128\pi$
$641$	5.11803	+	3.71847i	0.202150	+	0.146871i	−0.482105	+	0.876114i	$0.660128\pi$
$642$	−13.3992	+	9.73508i	−0.528824	+	0.384213i
$643$	−9.23607	+	28.4257i	−0.364235	+	1.12100i	0.586224	+	0.810149i	$0.300614\pi$
$643$	−9.23607	+	28.4257i	−0.364235	+	1.12100i	−0.950459	+	0.310851i	$0.899386\pi$
$644$	1.47214	−	4.53077i	0.0580103	−	0.178537i
$645$	−1.26393	+	0.918300i	−0.0497673	+	0.0361580i
$646$	−17.7082	−	12.8658i	−0.696720	−	0.506197i
$647$	−6.45492	−	19.8662i	−0.253769	−	0.781020i	−0.994070	−	0.108745i	$-0.965317\pi$
$647$	−6.45492	−	19.8662i	−0.253769	−	0.781020i	0.740301	−	0.672276i	$-0.234683\pi$
$648$	2.23607			0.0878410
$649$	2.94427	−	7.33094i	0.115573	−	0.287764i
$650$	−1.76393			−0.0691871
$651$	0.927051	+	2.85317i	0.0363340	+	0.111825i
$652$	1.33688	+	0.971301i	0.0523563	+	0.0380391i
$653$	7.13525	−	5.18407i	0.279224	−	0.202868i	−0.439355	−	0.898314i	$-0.644793\pi$
$653$	7.13525	−	5.18407i	0.279224	−	0.202868i	0.718579	+	0.695445i	$0.244793\pi$
$654$	−5.42705	+	16.7027i	−0.212214	+	0.653129i
$655$	0.0278640	−	0.0857567i	0.00108874	−	0.00335079i
$656$	−12.3541	+	8.97578i	−0.482347	+	0.350445i
$657$	−7.78115	−	5.65334i	−0.303572	−	0.220558i
$658$	−5.92705	−	18.2416i	−0.231061	−	0.711131i
$659$	14.8885			0.579975			0.289988	−	0.957030i	$-0.406349\pi$
$659$	14.8885			0.579975			0.289988	+	0.957030i	$0.406349\pi$
$660$	0.309017	+	1.22857i	0.0120285	+	0.0478221i
$661$	−30.5967			−1.19008			−0.595038	−	0.803698i	$-0.702863\pi$
$661$	−30.5967			−1.19008			−0.595038	+	0.803698i	$0.702863\pi$
$662$	16.3541	+	50.3328i	0.635620	+	1.95624i
$663$	−1.04508	−	0.759299i	−0.0405877	−	0.0294887i
$664$	0.854102	−	0.620541i	0.0331456	−	0.0240817i
$665$	0.472136	−	1.45309i	0.0183086	−	0.0563482i
$666$	−3.00000	+	9.23305i	−0.116248	+	0.357773i
$667$	26.4164	−	19.1926i	1.02285	−	0.743142i
$668$	4.42705	+	3.21644i	0.171288	+	0.124448i
$669$	−0.635255	−	1.95511i	−0.0245604	−	0.0755891i
$670$	−8.76393			−0.338580
$671$	−8.04508	−	31.9852i	−0.310577	−	1.23477i
$672$	3.38197			0.130462
$673$	−11.1074	−	34.1850i	−0.428158	−	1.31774i	−0.899937	−	0.436019i	$-0.856388\pi$
$673$	−11.1074	−	34.1850i	−0.428158	−	1.31774i	0.471779	−	0.881717i	$-0.343612\pi$
$674$	0.309017	+	0.224514i	0.0119029	+	0.00864796i
$675$	−3.73607	+	2.71441i	−0.143801	+	0.104478i
$676$	−2.47214	+	7.60845i	−0.0950822	+	0.292633i
$677$	9.06231	−	27.8909i	0.348293	−	1.07193i	−0.611505	−	0.791241i	$-0.709435\pi$
$677$	9.06231	−	27.8909i	0.348293	−	1.07193i	0.959797	−	0.280694i	$-0.0905646\pi$
$678$	−14.6353	+	10.6331i	−0.562064	+	0.408363i
$679$	−15.1353	−	10.9964i	−0.580838	−	0.422003i
$680$	2.33688	+	7.19218i	0.0896153	+	0.275808i
$681$	12.0902			0.463296
$682$	6.00000	−	14.9394i	0.229752	−	0.572059i
$683$	−6.52786			−0.249782			−0.124891	−	0.992170i	$-0.539858\pi$
$683$	−6.52786			−0.249782			−0.124891	+	0.992170i	$0.539858\pi$
$684$	−0.472136	−	1.45309i	−0.0180526	−	0.0555601i
$685$	0.763932	+	0.555029i	0.0291883	+	0.0212066i
$686$	−1.30902	+	0.951057i	−0.0499785	+	0.0363115i
$687$	7.76393	−	23.8949i	0.296212	−	0.911648i
$688$	3.79180	−	11.6699i	0.144561	−	0.444913i
$689$	1.44427	−	1.04932i	0.0550224	−	0.0399761i
$690$	6.23607	+	4.53077i	0.237403	+	0.172483i
$691$	−9.28115	−	28.5645i	−0.353072	−	1.08664i	−0.957119	−	0.289695i	$-0.906446\pi$
$691$	−9.28115	−	28.5645i	−0.353072	−	1.08664i	0.604047	−	0.796948i	$-0.293554\pi$
$692$	−8.52786			−0.324181
$693$	3.30902	+	0.224514i	0.125699	+	0.00852858i
$694$	−13.7082			−0.520356
$695$	0.0729490	+	0.224514i	0.00276711	+	0.00851630i
$696$	7.66312	+	5.56758i	0.290470	+	0.211039i
$697$	13.9271	−	10.1186i	0.527525	−	0.383269i
$698$	0.836881	−	2.57565i	0.0316764	−	0.0974900i
$699$	6.25329	−	19.2456i	0.236521	−	0.727937i
$700$	−2.30902	+	1.67760i	−0.0872726	+	0.0634073i
$701$	−12.9894	−	9.43732i	−0.490601	−	0.356443i	0.314814	−	0.949153i	$-0.398058\pi$
$701$	−12.9894	−	9.43732i	−0.490601	−	0.356443i	−0.805415	+	0.592711i	$0.798058\pi$
$702$	−0.118034	−	0.363271i	−0.00445491	−	0.0137108i
$703$	−14.8328			−0.559430
$704$	10.7812	+	9.00854i	0.406330	+	0.339522i
$705$	7.32624			0.275922
$706$	−18.0623	−	55.5901i	−0.679784	−	2.09216i
$707$	5.47214	+	3.97574i	0.205801	+	0.149523i
$708$	−1.19098	+	0.865300i	−0.0447599	+	0.0325200i
$709$	2.38197	−	7.33094i	0.0894566	−	0.275319i	−0.896313	−	0.443422i	$-0.853764\pi$
$709$	2.38197	−	7.33094i	0.0894566	−	0.275319i	0.985769	+	0.168103i	$0.0537642\pi$
$710$	4.16312	−	12.8128i	0.156239	−	0.480854i
$711$	−4.11803	+	2.99193i	−0.154438	+	0.112206i
$712$	25.9164	+	18.8294i	0.971258	+	0.705661i
$713$	−7.14590	−	21.9928i	−0.267616	−	0.823637i
$714$	−8.85410			−0.331356
$715$	−0.409830	+	0.257270i	−0.0153268	+	0.00962136i
$716$	−3.27051			−0.122225
$717$	5.98936	+	18.4333i	0.223677	+	0.688406i
$718$	16.5172	+	12.0005i	0.616417	+	0.447853i
$719$	−18.1631	+	13.1963i	−0.677370	+	0.492138i	−0.872484	−	0.488642i	$-0.837492\pi$
$719$	−18.1631	+	13.1963i	−0.677370	+	0.492138i	0.195114	+	0.980781i	$0.437492\pi$
$720$	−0.927051	+	2.85317i	−0.0345492	+	0.106331i
$721$	2.01722	−	6.20837i	0.0751252	−	0.231212i
$722$	−16.8713	+	12.2577i	−0.627886	+	0.456186i
$723$	−13.2812	−	9.64932i	−0.493931	−	0.358862i
$724$	−1.80902	−	5.56758i	−0.0672316	−	0.206918i
$725$	−19.5623			−0.726526
$726$	−12.8541	−	12.3107i	−0.477060	−	0.456894i
$727$	27.0344			1.00265			0.501326	−	0.865258i	$-0.332846\pi$
$727$	27.0344			1.00265			0.501326	+	0.865258i	$0.332846\pi$
$728$	0.163119	+	0.502029i	0.00604559	+	0.0186064i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	7.78115	−	5.65334i	0.287993	−	0.209239i
$731$	−4.27458	+	13.1558i	−0.158101	+	0.486584i
$732$	−1.89919	+	5.84510i	−0.0701960	+	0.216041i
$733$	−35.9336	+	26.1073i	−1.32724	+	0.964295i	−0.327427	+	0.944876i	$0.606182\pi$
$733$	−35.9336	+	26.1073i	−1.32724	+	0.964295i	−0.999811	+	0.0194191i	$0.993818\pi$
$734$	−6.54508	−	4.75528i	−0.241583	−	0.175521i
$735$	−0.190983	−	0.587785i	−0.00704451	−	0.0216808i
$736$	−26.0689			−0.960912
$737$	24.6180	−	15.4539i	0.906817	−	0.569253i
$738$	5.09017			0.187372
$739$	−14.4787	−	44.5609i	−0.532608	−	1.63920i	−0.748761	−	0.662840i	$-0.769351\pi$
$739$	−14.4787	−	44.5609i	−0.532608	−	1.63920i	0.216153	−	0.976359i	$-0.430649\pi$
$740$	−1.85410	−	1.34708i	−0.0681581	−	0.0495198i
$741$	0.472136	−	0.343027i	0.0173443	−	0.0126014i
$742$	3.78115	−	11.6372i	0.138810	−	0.427215i
$743$	8.31559	−	25.5928i	0.305070	−	0.938908i	−0.674582	−	0.738200i	$-0.735676\pi$
$743$	8.31559	−	25.5928i	0.305070	−	0.938908i	0.979651	−	0.200707i	$-0.0643240\pi$
$744$	5.42705	−	3.94298i	0.198965	−	0.144557i
$745$	1.80902	+	1.31433i	0.0662773	+	0.0481532i
$746$	16.8541	+	51.8716i	0.617073	+	1.89915i
$747$	−0.472136			−0.0172746
$748$	8.60739	+	7.19218i	0.314717	+	0.262972i
$749$	−10.2361			−0.374018
$750$	−2.97214	−	9.14729i	−0.108527	−	0.334012i
$751$	−24.6246	−	17.8908i	−0.898565	−	0.652846i	0.0395321	−	0.999218i	$-0.487413\pi$
$751$	−24.6246	−	17.8908i	−0.898565	−	0.652846i	−0.938097	+	0.346373i	$0.887413\pi$
$752$	−46.5517	+	33.8218i	−1.69756	+	1.23335i
$753$	−1.21885	+	3.75123i	−0.0444173	+	0.136702i
$754$	0.500000	−	1.53884i	0.0182089	−	0.0560413i
$755$	4.66312	−	3.38795i	0.169708	−	0.123300i
$756$	−0.500000	−	0.363271i	−0.0181848	−	0.0132120i
$757$	3.36068	+	10.3431i	0.122146	+	0.375927i	0.993370	−	0.114958i	$-0.0366735\pi$
$757$	3.36068	+	10.3431i	0.122146	+	0.375927i	−0.871224	+	0.490885i	$0.836673\pi$
$758$	21.1803			0.769305
$759$	−25.5066	−	1.73060i	−0.925830	−	0.0628168i
$760$	−3.41641			−0.123926
$761$	7.46149	+	22.9641i	0.270479	+	0.832448i	0.990380	+	0.138372i	$0.0441870\pi$
$761$	7.46149	+	22.9641i	0.270479	+	0.832448i	−0.719901	+	0.694076i	$0.755813\pi$
$762$	−10.8992	−	7.91872i	−0.394836	−	0.286865i
$763$	−8.78115	+	6.37988i	−0.317899	+	0.230967i
$764$	−2.24671	+	6.91467i	−0.0812832	+	0.250164i
$765$	1.04508	−	3.21644i	0.0377851	−	0.116291i
$766$	−23.9894	+	17.4293i	−0.866771	+	0.629746i
$767$	−0.454915	−	0.330515i	−0.0164260	−	0.0119342i
$768$	−4.19098	−	12.8985i	−0.151229	−	0.465435i
$769$	17.7771			0.641058			0.320529	−	0.947239i	$-0.396139\pi$
$769$	17.7771			0.641058			0.320529	+	0.947239i	$0.396139\pi$
$770$	−1.23607	+	3.07768i	−0.0445448	+	0.110912i
$771$	11.8885			0.428155
$772$	−1.79837	−	5.53483i	−0.0647249	−	0.199203i
$773$	10.5623	+	7.67396i	0.379900	+	0.276013i	0.761304	−	0.648395i	$-0.224559\pi$
$773$	10.5623	+	7.67396i	0.379900	+	0.276013i	−0.381404	+	0.924408i	$0.624559\pi$
$774$	−3.30902	+	2.40414i	−0.118940	+	0.0864151i
$775$	−4.28115	+	13.1760i	−0.153784	+	0.473297i
$776$	−12.9271	+	39.7854i	−0.464054	+	1.42821i
$777$	−4.85410	+	3.52671i	−0.174140	+	0.126520i
$778$	−16.7082	−	12.1392i	−0.599018	−	0.435212i
$779$	2.40325	+	7.39645i	0.0861054	+	0.265005i
$780$	0.0901699			0.00322860
$781$	10.8992	+	43.3323i	0.390004	+	1.55055i
$782$	68.2492			2.44059
$783$	−1.30902	−	4.02874i	−0.0467805	−	0.143975i
$784$	3.92705	+	2.85317i	0.140252	+	0.101899i
$785$	−8.89919	+	6.46564i	−0.317626	+	0.230769i
$786$	0.0729490	−	0.224514i	0.00260201	−	0.00800815i
$787$	−6.04508	+	18.6049i	−0.215484	+	0.663192i	0.783635	+	0.621222i	$0.213363\pi$
$787$	−6.04508	+	18.6049i	−0.215484	+	0.663192i	−0.999119	+	0.0419699i	$0.986637\pi$
$788$	13.3262	−	9.68208i	0.474728	−	0.344910i
$789$	−18.3713	−	13.3475i	−0.654036	−	0.475185i
$790$	−1.57295	−	4.84104i	−0.0559630	−	0.172236i
$791$	−11.1803			−0.397527
$792$	−1.80902	−	7.19218i	−0.0642806	−	0.255563i
$793$	−2.34752			−0.0833630
$794$	−4.78115	−	14.7149i	−0.169677	−	0.522211i
$795$	3.78115	+	2.74717i	0.134104	+	0.0974320i
$796$	−12.6074	+	9.15981i	−0.446857	+	0.324661i
$797$	13.5517	−	41.7077i	0.480025	−	1.47736i	−0.359035	−	0.933324i	$-0.616894\pi$
$797$	13.5517	−	41.7077i	0.480025	−	1.47736i	0.839060	−	0.544040i	$-0.183106\pi$
$798$	1.23607	−	3.80423i	0.0437563	−	0.134668i
$799$	52.4787	−	38.1280i	1.85656	−	1.34887i
$800$	12.6353	+	9.18005i	0.446724	+	0.324564i
$801$	−4.42705	−	13.6251i	−0.156422	−	0.481418i
$802$	23.8541			0.842318
$803$	−11.8885	+	29.6013i	−0.419538	+	1.04461i
$804$	−5.41641			−0.191022
$805$	1.47214	+	4.53077i	0.0518860	+	0.159689i
$806$	−0.927051	−	0.673542i	−0.0326540	−	0.0237245i
$807$	−5.51722	+	4.00850i	−0.194215	+	0.141106i
$808$	4.67376	−	14.3844i	0.164422	−	0.506040i
$809$	5.99342	−	18.4459i	0.210718	−	0.648522i	−0.788712	−	0.614762i	$-0.789252\pi$
$809$	5.99342	−	18.4459i	0.210718	−	0.648522i	0.999430	−	0.0337595i	$-0.0107480\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	−27.7426	−	20.1562i	−0.974176	−	0.707780i	−0.0177766	−	0.999842i	$-0.505659\pi$
$811$	−27.7426	−	20.1562i	−0.974176	−	0.707780i	−0.956399	+	0.292062i	$0.905659\pi$
$812$	−0.809017	−	2.48990i	−0.0283909	−	0.0873783i
$813$	−18.1246			−0.635658
$814$	32.1246	+	2.17963i	1.12597	+	0.0763959i
$815$	−1.65248			−0.0578837
$816$	8.20820	+	25.2623i	0.287345	+	0.884356i
$817$	−5.05573	−	3.67320i	−0.176878	−	0.128509i
$818$	42.9336	−	31.1931i	1.50114	−	1.09064i
$819$	0.0729490	−	0.224514i	0.00254904	−	0.00784515i
$820$	−0.371323	+	1.14281i	−0.0129672	+	0.0399088i
$821$	29.2705	−	21.2663i	1.02155	−	0.742198i	0.0549482	−	0.998489i	$-0.482501\pi$
$821$	29.2705	−	21.2663i	1.02155	−	0.742198i	0.966600	+	0.256291i	$0.0825006\pi$
$822$	2.00000	+	1.45309i	0.0697580	+	0.0506822i
$823$	4.18034	+	12.8658i	0.145717	+	0.448472i	0.997103	−	0.0760689i	$-0.0242369\pi$
$823$	4.18034	+	12.8658i	0.145717	+	0.448472i	−0.851385	+	0.524541i	$0.824237\pi$
$824$	−14.5967			−0.508502
$825$	11.7533	+	9.82084i	0.409197	+	0.341918i
$826$	−3.85410			−0.134101
$827$	7.43363	+	22.8784i	0.258493	+	0.795558i	0.993121	+	0.117089i	$0.0373563\pi$
$827$	7.43363	+	22.8784i	0.258493	+	0.795558i	−0.734629	+	0.678469i	$0.762644\pi$
$828$	3.85410	+	2.80017i	0.133939	+	0.0973126i
$829$	13.2082	−	9.59632i	0.458740	−	0.333294i	−0.334297	−	0.942468i	$-0.608499\pi$
$829$	13.2082	−	9.59632i	0.458740	−	0.333294i	0.793037	+	0.609174i	$0.208499\pi$
$830$	0.145898	−	0.449028i	0.00506419	−	0.0155860i
$831$	0.145898	−	0.449028i	0.00506115	−	0.0155766i
$832$	0.809017	−	0.587785i	0.0280476	−	0.0203778i
$833$	−4.42705	−	3.21644i	−0.153388	−	0.111443i
$834$	0.190983	+	0.587785i	0.00661320	+	0.0203533i
$835$	−5.47214			−0.189371
$836$	−4.29180	+	2.69417i	−0.148435	+	0.0931797i
$837$	−3.00000			−0.103695
$838$	16.6910	+	51.3696i	0.576580	+	1.77453i
$839$	18.9894	+	13.7966i	0.655585	+	0.476311i	0.865169	−	0.501480i	$-0.167211\pi$
$839$	18.9894	+	13.7966i	0.655585	+	0.476311i	−0.209584	+	0.977791i	$0.567211\pi$
$840$	−1.11803	+	0.812299i	−0.0385758	+	0.0280270i
$841$	−3.41641	+	10.5146i	−0.117807	+	0.362573i
$842$	−12.4271	+	38.2465i	−0.428264	+	1.31806i
$843$	3.35410	−	2.43690i	0.115521	−	0.0839312i
$844$	2.64590	+	1.92236i	0.0910756	+	0.0661703i
$845$	−2.47214	−	7.60845i	−0.0850441	−	0.261739i
$846$	19.1803			0.659434
$847$	−1.95492	−	10.8249i	−0.0671717	−	0.371948i
$848$	−36.7082			−1.26056
$849$	7.07295	+	21.7683i	0.242743	+	0.747086i
$850$	−33.0795	−	24.0337i	−1.13462	−	0.824349i
$851$	37.4164	−	27.1846i	1.28262	−	0.931876i
$852$	2.57295	−	7.91872i	0.0881478	−	0.271291i
$853$	0.0623059	−	0.191758i	0.00213331	−	0.00656566i	−0.949984	−	0.312298i	$-0.898901\pi$
$853$	0.0623059	−	0.191758i	0.00213331	−	0.00656566i	0.952118	+	0.305732i	$0.0989013\pi$
$854$	−13.0172	+	9.45756i	−0.445440	+	0.323631i
$855$	1.23607	+	0.898056i	0.0422726	+	0.0307129i
$856$	7.07295	+	21.7683i	0.241748	+	0.744025i
$857$	−14.0557			−0.480135			−0.240067	−	0.970756i	$-0.577170\pi$
$857$	−14.0557			−0.480135			−0.240067	+	0.970756i	$0.577170\pi$
$858$	−1.07295	+	0.673542i	−0.0366299	+	0.0229943i
$859$	−29.6525			−1.01173			−0.505865	−	0.862613i	$-0.668827\pi$
$859$	−29.6525			−1.01173			−0.505865	+	0.862613i	$0.668827\pi$
$860$	−0.298374	−	0.918300i	−0.0101745	−	0.0313138i
$861$	2.54508	+	1.84911i	0.0867363	+	0.0630176i
$862$	−18.1353	+	13.1760i	−0.617689	+	0.448777i
$863$	−15.2188	+	46.8388i	−0.518056	+	1.59441i	0.259597	+	0.965717i	$0.416410\pi$
$863$	−15.2188	+	46.8388i	−0.518056	+	1.59441i	−0.777653	+	0.628694i	$0.783590\pi$
$864$	−1.04508	+	3.21644i	−0.0355545	+	0.109426i
$865$	6.89919	−	5.01255i	0.234579	−	0.170432i
$866$	14.3262	+	10.4086i	0.486825	+	0.353699i
$867$	−4.00000	−	12.3107i	−0.135847	−	0.418094i
$868$	−1.85410			−0.0629323
$869$	12.9549	+	10.8249i	0.439465	+	0.367209i
$870$	4.23607			0.143616
$871$	−0.639320	−	1.96763i	−0.0216625	−	0.0666704i
$872$	19.6353	+	14.2658i	0.664934	+	0.483103i
$873$	15.1353	−	10.9964i	0.512251	−	0.372172i
$874$	−9.52786	+	29.3238i	−0.322285	+	0.991891i
$875$	1.83688	−	5.65334i	0.0620979	−	0.191118i
$876$	4.80902	−	3.49396i	0.162482	−	0.118050i
$877$	15.2533	+	11.0822i	0.515067	+	0.374218i	0.814742	−	0.579823i	$-0.196878\pi$
$877$	15.2533	+	11.0822i	0.515067	+	0.374218i	−0.299675	+	0.954041i	$0.596878\pi$
$878$	−2.17376	−	6.69015i	−0.0733609	−	0.225782i
$879$	−5.70820			−0.192533
$880$	9.92705	+	0.673542i	0.334641	+	0.0227051i
$881$	−18.7082			−0.630295			−0.315148	−	0.949043i	$-0.602054\pi$
$881$	−18.7082			−0.630295			−0.315148	+	0.949043i	$0.602054\pi$
$882$	−0.500000	−	1.53884i	−0.0168359	−	0.0518155i
$883$	26.6246	+	19.3439i	0.895990	+	0.650974i	0.937433	−	0.348166i	$-0.113196\pi$
$883$	26.6246	+	19.3439i	0.895990	+	0.650974i	−0.0414432	+	0.999141i	$0.513196\pi$
$884$	0.645898	−	0.469272i	0.0217239	−	0.0157833i
$885$	0.454915	−	1.40008i	0.0152918	−	0.0470633i
$886$	3.32624	−	10.2371i	0.111747	−	0.343922i
$887$	−20.4615	+	14.8661i	−0.687030	+	0.499156i	−0.875682	−	0.482888i	$-0.839588\pi$
$887$	−20.4615	+	14.8661i	−0.687030	+	0.499156i	0.188653	+	0.982044i	$0.439588\pi$
$888$	10.8541	+	7.88597i	0.364240	+	0.264636i
$889$	−2.57295	−	7.91872i	−0.0862939	−	0.265585i
$890$	14.3262			0.480217
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$	1.27051			0.0425398
$893$	9.05573	+	27.8707i	0.303038	+	0.932656i
$894$	4.73607	+	3.44095i	0.158398	+	0.115083i
$895$	2.64590	−	1.92236i	0.0884426	−	0.0642573i
$896$	4.20820	−	12.9515i	0.140586	−	0.432680i
$897$	−0.562306	+	1.73060i	−0.0187748	+	0.0577830i
$898$	37.4336	−	27.1971i	1.24918	−	0.907580i
$899$	−10.2812	−	7.46969i	−0.342896	−	0.249128i
$900$	−0.881966	−	2.71441i	−0.0293989	−	0.0904804i
$901$	41.3820			1.37863
$902$	−4.11803	−	16.3722i	−0.137116	−	0.545136i
$903$	−2.52786			−0.0841220
$904$	7.72542	+	23.7764i	0.256944	+	0.790792i
$905$	4.73607	+	3.44095i	0.157432	+	0.114381i
$906$	12.2082	−	8.86978i	0.405590	−	0.294679i
$907$	−15.2984	+	47.0836i	−0.507974	+	1.56338i	0.287738	+	0.957709i	$0.407097\pi$
$907$	−15.2984	+	47.0836i	−0.507974	+	1.56338i	−0.795712	+	0.605675i	$0.792903\pi$
$908$	−2.30902	+	7.10642i	−0.0766274	+	0.235835i
$909$	−5.47214	+	3.97574i	−0.181499	+	0.131867i
$910$	0.190983	+	0.138757i	0.00633102	+	0.00459976i
$911$	−13.3156	−	40.9812i	−0.441165	−	1.35777i	−0.886635	−	0.462470i	$-0.846963\pi$
$911$	−13.3156	−	40.9812i	−0.441165	−	1.35777i	0.445469	−	0.895297i	$-0.353037\pi$
$912$	−12.0000			−0.397360
$913$	0.381966	+	1.51860i	0.0126412	+	0.0502582i
$914$	38.4164			1.27070
$915$	−1.89919	−	5.84510i	−0.0627852	−	0.193233i
$916$	12.5623	+	9.12705i	0.415070	+	0.301566i
$917$	0.118034	−	0.0857567i	0.00389783	−	0.00283194i
$918$	2.73607	−	8.42075i	0.0903037	−	0.277926i
$919$	−1.23607	+	3.80423i	−0.0407741	+	0.125490i	−0.969372	−	0.245599i	$-0.921015\pi$
$919$	−1.23607	+	3.80423i	−0.0407741	+	0.125490i	0.928597	+	0.371089i	$0.121015\pi$
$920$	8.61803	−	6.26137i	0.284128	−	0.206431i
$921$	20.9894	+	15.2497i	0.691623	+	0.502493i
$922$	17.1525	+	52.7899i	0.564887	+	1.73854i
$923$	3.18034			0.104682
$924$	−0.763932	+	1.90211i	−0.0251315	+	0.0625749i
$925$	−27.7082			−0.911040
$926$	−15.9894	−	49.2102i	−0.525443	−	1.61715i
$927$	5.28115	+	3.83698i	0.173456	+	0.126023i
$928$	−11.5902	+	8.42075i	−0.380466	+	0.276425i
$929$	8.00000	−	24.6215i	0.262471	−	0.807804i	−0.729794	−	0.683667i	$-0.760384\pi$
$929$	8.00000	−	24.6215i	0.262471	−	0.807804i	0.992265	−	0.124137i	$-0.0396161\pi$
$930$	0.927051	−	2.85317i	0.0303992	−	0.0935591i
$931$	2.00000	−	1.45309i	0.0655474	−	0.0476229i
$932$	10.1180	+	7.35118i	0.331427	+	0.240796i
$933$	5.50000	+	16.9273i	0.180062	+	0.554174i
$934$	21.5066			0.703717
$935$	−11.1910	−	0.759299i	−0.365984	−	0.0248317i
$936$	−0.527864			−0.0172538
$937$	5.60081	+	17.2375i	0.182971	+	0.563126i	0.999907	−	0.0136015i	$-0.00432962\pi$
$937$	5.60081	+	17.2375i	0.182971	+	0.563126i	−0.816937	+	0.576727i	$0.804330\pi$
$938$	−11.4721	−	8.33499i	−0.374579	−	0.272147i
$939$	16.9164	−	12.2905i	0.552046	−	0.401085i
$940$	−1.39919	+	4.30625i	−0.0456364	+	0.140455i
$941$	−15.9443	+	49.0714i	−0.519768	+	1.59968i	0.254666	+	0.967029i	$0.418034\pi$
$941$	−15.9443	+	49.0714i	−0.519768	+	1.59968i	−0.774435	+	0.632654i	$0.781966\pi$
$942$	−23.2984	+	16.9273i	−0.759102	+	0.551520i
$943$	−19.6180	−	14.2533i	−0.638851	−	0.464152i
$944$	3.57295	+	10.9964i	0.116290	+	0.357903i
$945$	0.618034			0.0201046
$946$	10.4098	+	8.69827i	0.338453	+	0.282805i
$947$	−41.9787			−1.36412			−0.682062	−	0.731294i	$-0.738917\pi$
$947$	−41.9787			−1.36412			−0.682062	+	0.731294i	$0.738917\pi$
$948$	−0.972136	−	2.99193i	−0.0315735	−	0.0971733i
$949$	1.83688	+	1.33457i	0.0596277	+	0.0433220i
$950$	14.9443	−	10.8576i	0.484856	−	0.352269i
$951$	−0.274575	+	0.845055i	−0.00890371	+	0.0274028i
$952$	−3.78115	+	11.6372i	−0.122548	+	0.377164i
$953$	−15.3992	+	11.1882i	−0.498829	+	0.362420i	−0.808569	−	0.588401i	$-0.799758\pi$
$953$	−15.3992	+	11.1882i	−0.498829	+	0.362420i	0.309741	+	0.950821i	$0.399758\pi$
$954$	9.89919	+	7.19218i	0.320498	+	0.232855i
$955$	−2.24671	−	6.91467i	−0.0727019	−	0.223753i
$956$	−11.9787			−0.387419
$957$	−11.8992	+	7.46969i	−0.384646	+	0.241461i
$958$	−52.7771			−1.70515
$959$	0.472136	+	1.45309i	0.0152461	+	0.0469226i
$960$	2.11803	+	1.53884i	0.0683593	+	0.0496659i
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$	0.708204	−	2.17963i	0.0228334	−	0.0702740i
$963$	3.16312	−	9.73508i	0.101930	−	0.313709i
$964$	8.20820	−	5.96361i	0.264368	−	0.192075i
$965$	4.70820	+	3.42071i	0.151562	+	0.110117i
$966$	3.85410	+	11.8617i	0.124004	+	0.381644i
$967$	−17.3475			−0.557859			−0.278929	−	0.960312i	$-0.589980\pi$
$967$	−17.3475			−0.557859			−0.278929	+	0.960312i	$0.589980\pi$
$968$	−21.6697	+	11.6372i	−0.696490	+	0.374034i
$969$	13.5279			0.434578
$970$	5.78115	+	17.7926i	0.185622	+	0.571285i
$971$	−13.2812	−	9.64932i	−0.426212	−	0.309661i	0.353920	−	0.935276i	$-0.384848\pi$
$971$	−13.2812	−	9.64932i	−0.426212	−	0.309661i	−0.780133	+	0.625614i	$0.784848\pi$
$972$	0.500000	−	0.363271i	0.0160375	−	0.0116519i
$973$	−0.118034	+	0.363271i	−0.00378400	+	0.0116459i
$974$	8.80902	−	27.1114i	0.282259	−	0.868704i
$975$	0.881966	−	0.640786i	0.0282455	−	0.0205216i
$976$	39.0517	+	28.3727i	1.25001	+	0.908188i
$977$	−8.89261	−	27.3686i	−0.284500	−	0.875600i	−0.986548	−	0.163471i	$-0.947731\pi$
$977$	−8.89261	−	27.3686i	−0.284500	−	0.875600i	0.702048	−	0.712129i	$-0.252269\pi$
$978$	−4.32624			−0.138338
$979$	−40.2426	+	25.2623i	−1.28616	+	0.807385i
$980$	0.381966			0.0122015
$981$	−3.35410	−	10.3229i	−0.107088	−	0.329584i
$982$	−28.4164	−	20.6457i	−0.906804	−	0.658832i
$983$	−1.13525	+	0.824811i	−0.0362090	+	0.0263074i	−0.605743	−	0.795661i	$-0.707124\pi$
$983$	−1.13525	+	0.824811i	−0.0362090	+	0.0263074i	0.569534	+	0.821968i	$0.307124\pi$
$984$	2.17376	−	6.69015i	0.0692970	−	0.213274i
$985$	−5.09017	+	15.6659i	−0.162186	+	0.499158i
$986$	30.3435	−	22.0458i	0.966333	−	0.702082i
$987$	9.59017	+	6.96767i	0.305258	+	0.221783i
$988$	0.111456	+	0.343027i	0.00354589	+	0.0109131i
$989$	19.4853			0.619596
$990$	−2.54508	−	2.12663i	−0.0808881	−	0.0675886i
$991$	−26.3820			−0.838051			−0.419025	−	0.907975i	$-0.637628\pi$
$991$	−26.3820			−0.838051			−0.419025	+	0.907975i	$0.637628\pi$
$992$	3.13525	+	9.64932i	0.0995444	+	0.306366i
$993$	−26.4615	−	19.2254i	−0.839730	−	0.610100i
$994$	17.6353	−	12.8128i	0.559356	−	0.406396i
$995$	4.81559	−	14.8209i	0.152665	−	0.469853i
$996$	0.0901699	−	0.277515i	0.00285714	−	0.00879339i
$997$	−46.2705	+	33.6175i	−1.46540	+	1.06468i	−0.483487	+	0.875351i	$0.660630\pi$
$997$	−46.2705	+	33.6175i	−1.46540	+	1.06468i	−0.981914	+	0.189325i	$0.939370\pi$
$998$	9.16312	+	6.65740i	0.290053	+	0.210736i
$999$	−1.85410	−	5.70634i	−0.0586612	−	0.180541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.b.148.1	yes	4
3.2	odd	2		693.2.m.d.379.1		4
11.3	even	5		2541.2.a.p.1.1		2
11.8	odd	10		2541.2.a.x.1.2		2
11.9	even	5	inner	231.2.j.b.64.1	✓	4
33.8	even	10		7623.2.a.z.1.1		2
33.14	odd	10		7623.2.a.bo.1.2		2
33.20	odd	10		693.2.m.d.64.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.b.64.1	✓	4	11.9	even	5	inner
231.2.j.b.148.1	yes	4	1.1	even	1	trivial
693.2.m.d.64.1		4	33.20	odd	10
693.2.m.d.379.1		4	3.2	odd	2
2541.2.a.p.1.1		2	11.3	even	5
2541.2.a.x.1.2		2	11.8	odd	10
7623.2.a.z.1.1		2	33.8	even	10
7623.2.a.bo.1.2		2	33.14	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 1.53884i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.500000 - 1.53884i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(2.80902 - 1.76336i) q^{11} -0.618034 q^{12} +(-0.0729490 - 0.224514i) q^{13} +(-1.30902 - 0.951057i) q^{14} +(0.500000 - 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(1.69098 - 5.20431i) q^{17} +(1.30902 - 0.951057i) q^{18} +(2.00000 + 1.45309i) q^{19} +(0.118034 + 0.363271i) q^{20} +1.00000 q^{21} +(-4.11803 - 3.44095i) q^{22} -7.70820 q^{23} +(-0.690983 - 2.12663i) q^{24} +(3.73607 + 2.71441i) q^{25} +(-0.309017 + 0.224514i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.190983 + 0.587785i) q^{28} +(-3.42705 + 2.48990i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(0.927051 + 2.85317i) q^{31} +3.38197 q^{32} +(3.30902 + 0.224514i) q^{33} -8.85410 q^{34} +(-0.190983 - 0.587785i) q^{35} +(-0.500000 - 0.363271i) q^{36} +(-4.85410 + 3.52671i) q^{37} +(1.23607 - 3.80423i) q^{38} +(0.0729490 - 0.224514i) q^{39} +(-1.11803 + 0.812299i) q^{40} +(2.54508 + 1.84911i) q^{41} +(-0.500000 - 1.53884i) q^{42} -2.52786 q^{43} +(-0.763932 + 1.90211i) q^{44} +0.618034 q^{45} +(3.85410 + 11.8617i) q^{46} +(9.59017 + 6.96767i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.30902 - 7.10642i) q^{50} +(4.42705 - 3.21644i) q^{51} +(0.118034 + 0.0857567i) q^{52} +(2.33688 + 7.19218i) q^{53} +1.61803 q^{54} +(-0.500000 - 1.98787i) q^{55} -2.23607 q^{56} +(0.763932 + 2.35114i) q^{57} +(5.54508 + 4.02874i) q^{58} +(1.92705 - 1.40008i) q^{59} +(-0.118034 + 0.363271i) q^{60} +(3.07295 - 9.45756i) q^{61} +(3.92705 - 2.85317i) q^{62} +(0.809017 + 0.587785i) q^{63} +(1.30902 + 4.02874i) q^{64} -0.145898 q^{65} +(-1.30902 - 5.20431i) q^{66} +8.76393 q^{67} +(1.04508 + 3.21644i) q^{68} +(-6.23607 - 4.53077i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-4.16312 + 12.8128i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-7.78115 + 5.65334i) q^{73} +(7.85410 + 5.70634i) q^{74} +(1.42705 + 4.39201i) q^{75} -1.52786 q^{76} +(1.23607 - 3.07768i) q^{77} -0.381966 q^{78} +(1.57295 + 4.84104i) q^{79} +(2.42705 + 1.76336i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.57295 - 4.84104i) q^{82} +(-0.145898 + 0.449028i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(-2.73607 - 1.98787i) q^{85} +(1.26393 + 3.88998i) q^{86} -4.23607 q^{87} +(-7.39919 - 0.502029i) q^{88} -14.3262 q^{89} +(-0.309017 - 0.951057i) q^{90} +(-0.190983 - 0.138757i) q^{91} +(3.85410 - 2.80017i) q^{92} +(-0.927051 + 2.85317i) q^{93} +(5.92705 - 18.2416i) q^{94} +(1.23607 - 0.898056i) q^{95} +(2.73607 + 1.98787i) q^{96} +(-5.78115 - 17.7926i) q^{97} -1.61803 q^{98} +(2.54508 + 2.12663i) 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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