LMFDB - Embedded newform 731.2.e.a.681.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.13
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.546292 q^{2} +(0.344032 + 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 + 1.16347i) q^{5} +(-0.187942 - 0.325525i) q^{6} +(0.618902 - 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 - 2.18807i) q^{9} +O(q^{10})$	\(q-0.546292 q^{2} +(0.344032 + 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 + 1.16347i) q^{5} +(-0.187942 - 0.325525i) q^{6} +(0.618902 - 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 - 2.18807i) q^{9} +(-0.366962 - 0.635597i) q^{10} -0.376735 q^{11} +(-0.585392 - 1.01393i) q^{12} +(-0.470269 + 0.814530i) q^{13} +(-0.338101 + 0.585609i) q^{14} +(-0.462195 + 0.800545i) q^{15} +2.29845 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.690122 + 1.19533i) q^{18} +(-2.39780 - 4.15311i) q^{19} +(-1.14300 - 1.97973i) q^{20} +0.851688 q^{21} +0.205807 q^{22} +(3.55543 + 6.15818i) q^{23} +(0.695679 + 1.20495i) q^{24} +(1.59755 - 2.76704i) q^{25} +(0.256904 - 0.444971i) q^{26} +3.80263 q^{27} +(-1.05310 + 1.82403i) q^{28} +(1.90315 - 3.29634i) q^{29} +(0.252493 - 0.437331i) q^{30} +(-1.39144 - 2.41005i) q^{31} -5.29990 q^{32} +(-0.129609 - 0.224489i) q^{33} +(-0.273146 + 0.473103i) q^{34} +1.66295 q^{35} +(-2.14956 + 3.72315i) q^{36} +(4.86114 + 8.41974i) q^{37} +(1.30990 + 2.26881i) q^{38} -0.647150 q^{39} +(1.35833 + 2.35270i) q^{40} +6.95562 q^{41} -0.465271 q^{42} +(6.12810 - 2.33375i) q^{43} +0.641038 q^{44} +3.39436 q^{45} +(-1.94230 - 3.36417i) q^{46} +6.61167 q^{47} +(0.790741 + 1.36960i) q^{48} +(2.73392 + 4.73529i) q^{49} +(-0.872730 + 1.51161i) q^{50} +0.688064 q^{51} +(0.800193 - 1.38597i) q^{52} +(3.05510 + 5.29158i) q^{53} -2.07735 q^{54} +(-0.253065 - 0.438321i) q^{55} +(1.25150 - 2.16767i) q^{56} +(1.64984 - 2.85760i) q^{57} +(-1.03967 + 1.80077i) q^{58} +0.791761 q^{59} +(0.786454 - 1.36218i) q^{60} +(-1.45666 + 2.52301i) q^{61} +(0.760134 + 1.31659i) q^{62} +(-1.56370 - 2.70840i) q^{63} -1.70161 q^{64} -1.26358 q^{65} +(0.0708042 + 0.122637i) q^{66} +(-5.93843 - 10.2857i) q^{67} +(-0.850782 + 1.47360i) q^{68} +(-2.44636 + 4.23722i) q^{69} -0.908454 q^{70} +(-3.31931 + 5.74921i) q^{71} +(2.55453 - 4.42458i) q^{72} +(2.39725 - 4.15217i) q^{73} +(-2.65560 - 4.59964i) q^{74} +2.19843 q^{75} +(4.08001 + 7.06679i) q^{76} +(-0.233162 + 0.403848i) q^{77} +0.353533 q^{78} +(2.59411 - 4.49313i) q^{79} +(1.54394 + 2.67419i) q^{80} +(-2.48163 - 4.29830i) q^{81} -3.79980 q^{82} +(3.70861 + 6.42350i) q^{83} -1.44920 q^{84} +1.34346 q^{85} +(-3.34773 + 1.27491i) q^{86} +2.61897 q^{87} -0.761809 q^{88} +(-7.18187 - 12.4394i) q^{89} -1.85431 q^{90} +(0.582101 + 1.00823i) q^{91} +(-6.04979 - 10.4785i) q^{92} +(0.957400 - 1.65827i) q^{93} -3.61190 q^{94} +(3.22136 - 5.57956i) q^{95} +(-1.82333 - 3.15811i) q^{96} +9.03956 q^{97} +(-1.49352 - 2.58685i) q^{98} +(-0.475923 + 0.824323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.546292			−0.386287			−0.193143	−	0.981171i	$-0.561868\pi$
$2$	−0.546292			−0.386287			−0.193143	+	0.981171i	$0.561868\pi$
$3$	0.344032	+	0.595881i	0.198627	+	0.344032i	0.948083	−	0.318022i	$-0.103018\pi$
$3$	0.344032	+	0.595881i	0.198627	+	0.344032i	−0.749457	+	0.662054i	$0.769685\pi$
$4$	−1.70156			−0.850782
$5$	0.671732	+	1.16347i	0.300408	+	0.520322i	0.976228	−	0.216745i	$-0.0695439\pi$
$5$	0.671732	+	1.16347i	0.300408	+	0.520322i	−0.675821	+	0.737066i	$0.736211\pi$
$6$	−0.187942	−	0.325525i	−0.0767270	−	0.132895i
$7$	0.618902	−	1.07197i	0.233923	−	0.405166i	−0.725036	−	0.688711i	$-0.758177\pi$
$7$	0.618902	−	1.07197i	0.233923	−	0.405166i	0.958959	+	0.283544i	$0.0915103\pi$
$8$	2.02214			0.714933
$9$	1.26328	−	2.18807i	0.421095	−	0.729357i
$10$	−0.366962	−	0.635597i	−0.116044	−	0.200993i
$11$	−0.376735			−0.113590			−0.0567949	−	0.998386i	$-0.518088\pi$
$11$	−0.376735			−0.113590			−0.0567949	+	0.998386i	$0.518088\pi$
$12$	−0.585392	−	1.01393i	−0.168988	−	0.292696i
$13$	−0.470269	+	0.814530i	−0.130429	+	0.225910i	−0.923842	−	0.382774i	$-0.874969\pi$
$13$	−0.470269	+	0.814530i	−0.130429	+	0.225910i	0.793413	+	0.608684i	$0.208302\pi$
$14$	−0.338101	+	0.585609i	−0.0903614	+	0.156511i
$15$	−0.462195	+	0.800545i	−0.119338	+	0.206700i
$16$	2.29845			0.574613
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	−0.690122	+	1.19533i	−0.162663	+	0.281741i
$19$	−2.39780	−	4.15311i	−0.550093	−	0.952789i	−0.998267	−	0.0588427i	$-0.981259\pi$
$19$	−2.39780	−	4.15311i	−0.550093	−	0.952789i	0.448174	−	0.893946i	$-0.352074\pi$
$20$	−1.14300	−	1.97973i	−0.255582	−	0.442680i
$21$	0.851688			0.185854
$22$	0.205807			0.0438782
$23$	3.55543	+	6.15818i	0.741358	+	1.28407i	0.951877	+	0.306480i	$0.0991513\pi$
$23$	3.55543	+	6.15818i	0.741358	+	1.28407i	−0.210519	+	0.977590i	$0.567515\pi$
$24$	0.695679	+	1.20495i	0.142005	+	0.245960i
$25$	1.59755	−	2.76704i	0.319510	−	0.553408i
$26$	0.256904	−	0.444971i	0.0503831	−	0.0872660i
$27$	3.80263			0.731817
$28$	−1.05310	+	1.82403i	−0.199018	+	0.344708i
$29$	1.90315	−	3.29634i	0.353405	−	0.612116i	−0.633438	−	0.773793i	$-0.718357\pi$
$29$	1.90315	−	3.29634i	0.353405	−	0.612116i	0.986844	+	0.161677i	$0.0516904\pi$
$30$	0.252493	−	0.437331i	0.0460988	−	0.0798454i
$31$	−1.39144	−	2.41005i	−0.249910	−	0.432857i	0.713590	−	0.700563i	$-0.247068\pi$
$31$	−1.39144	−	2.41005i	−0.249910	−	0.432857i	−0.963501	+	0.267706i	$0.913734\pi$
$32$	−5.29990			−0.936899
$33$	−0.129609	−	0.224489i	−0.0225620	−	0.0390785i
$34$	−0.273146	+	0.473103i	−0.0468442	+	0.0811365i
$35$	1.66295			0.281089
$36$	−2.14956	+	3.72315i	−0.358260	+	0.620524i
$37$	4.86114	+	8.41974i	0.799167	+	1.38420i	0.920159	+	0.391544i	$0.128059\pi$
$37$	4.86114	+	8.41974i	0.799167	+	1.38420i	−0.120993	+	0.992653i	$0.538608\pi$
$38$	1.30990	+	2.26881i	0.212494	+	0.368050i
$39$	−0.647150			−0.103627
$40$	1.35833	+	2.35270i	0.214771	+	0.371995i
$41$	6.95562			1.08629			0.543143	−	0.839640i	$-0.317234\pi$
$41$	6.95562			1.08629			0.543143	+	0.839640i	$0.317234\pi$
$42$	−0.465271			−0.0717928
$43$	6.12810	−	2.33375i	0.934526	−	0.355894i
$43$	6.12810	−	2.33375i	0.934526	−	0.355894i
$44$	0.641038			0.0966402
$45$	3.39436			0.506001
$46$	−1.94230	−	3.36417i	−0.286377	−	0.496019i
$47$	6.61167			0.964411			0.482205	−	0.876058i	$-0.339836\pi$
$47$	6.61167			0.964411			0.482205	+	0.876058i	$0.339836\pi$
$48$	0.790741	+	1.36960i	0.114134	+	0.197685i
$49$	2.73392	+	4.73529i	0.390560	+	0.676470i
$50$	−0.872730	+	1.51161i	−0.123423	+	0.213774i
$51$	0.688064			0.0963482
$52$	0.800193	−	1.38597i	0.110967	−	0.192200i
$53$	3.05510	+	5.29158i	0.419650	+	0.726855i	0.995904	−	0.0904156i	$-0.0288195\pi$
$53$	3.05510	+	5.29158i	0.419650	+	0.726855i	−0.576254	+	0.817270i	$0.695486\pi$
$54$	−2.07735			−0.282691
$55$	−0.253065	−	0.438321i	−0.0341233	−	0.0591032i
$56$	1.25150	−	2.16767i	0.167239	−	0.289667i
$57$	1.64984	−	2.85760i	0.218526	−	0.378499i
$58$	−1.03967	+	1.80077i	−0.136516	+	0.236452i
$59$	0.791761			0.103079			0.0515393	−	0.998671i	$-0.483587\pi$
$59$	0.791761			0.103079			0.0515393	+	0.998671i	$0.483587\pi$
$60$	0.786454	−	1.36218i	0.101531	−	0.175856i
$61$	−1.45666	+	2.52301i	−0.186507	+	0.323039i	−0.944083	−	0.329707i	$-0.893050\pi$
$61$	−1.45666	+	2.52301i	−0.186507	+	0.323039i	0.757577	+	0.652746i	$0.226383\pi$
$62$	0.760134	+	1.31659i	0.0965371	+	0.167207i
$63$	−1.56370	−	2.70840i	−0.197007	−	0.341227i
$64$	−1.70161			−0.212701
$65$	−1.26358			−0.156728
$66$	0.0708042	+	0.122637i	0.00871540	+	0.0150955i
$67$	−5.93843	−	10.2857i	−0.725494	−	1.25659i	−0.958770	−	0.284182i	$-0.908278\pi$
$67$	−5.93843	−	10.2857i	−0.725494	−	1.25659i	0.233276	−	0.972411i	$-0.425055\pi$
$68$	−0.850782	+	1.47360i	−0.103173	+	0.178700i
$69$	−2.44636	+	4.23722i	−0.294507	+	0.510102i
$70$	−0.908454			−0.108581
$71$	−3.31931	+	5.74921i	−0.393929	+	0.682306i	−0.992964	−	0.118418i	$-0.962218\pi$
$71$	−3.31931	+	5.74921i	−0.393929	+	0.682306i	0.599035	+	0.800723i	$0.295551\pi$
$72$	2.55453	−	4.42458i	0.301055	−	0.521442i
$73$	2.39725	−	4.15217i	0.280577	−	0.485974i	−0.690950	−	0.722903i	$-0.742807\pi$
$73$	2.39725	−	4.15217i	0.280577	−	0.485974i	0.971527	+	0.236929i	$0.0761407\pi$
$74$	−2.65560	−	4.59964i	−0.308708	−	0.534697i
$75$	2.19843			0.253853
$76$	4.08001	+	7.06679i	0.468009	+	0.810616i
$77$	−0.233162	+	0.403848i	−0.0265713	+	0.0460228i
$78$	0.353533			0.0400297
$79$	2.59411	−	4.49313i	0.291860	−	0.505517i	−0.682389	−	0.730989i	$-0.739059\pi$
$79$	2.59411	−	4.49313i	0.291860	−	0.505517i	0.974250	+	0.225472i	$0.0723924\pi$
$80$	1.54394	+	2.67419i	0.172618	+	0.298984i
$81$	−2.48163	−	4.29830i	−0.275736	−	0.477589i
$82$	−3.79980			−0.419618
$83$	3.70861	+	6.42350i	0.407073	+	0.705071i	0.994560	−	0.104163i	$-0.0332162\pi$
$83$	3.70861	+	6.42350i	0.407073	+	0.705071i	−0.587488	+	0.809233i	$0.699883\pi$
$84$	−1.44920			−0.158121
$85$	1.34346			0.145719
$86$	−3.34773	+	1.27491i	−0.360995	+	0.137477i
$87$	2.61897			0.280783
$88$	−0.761809			−0.0812091
$89$	−7.18187	−	12.4394i	−0.761276	−	1.31857i	−0.942193	−	0.335071i	$-0.891240\pi$
$89$	−7.18187	−	12.4394i	−0.761276	−	1.31857i	0.180917	−	0.983498i	$-0.442094\pi$
$90$	−1.85431			−0.195461
$91$	0.582101	+	1.00823i	0.0610207	+	0.105691i
$92$	−6.04979	−	10.4785i	−0.630734	−	1.09246i
$93$	0.957400	−	1.65827i	0.0992778	−	0.171954i
$94$	−3.61190			−0.372539
$95$	3.22136	−	5.57956i	0.330504	−	0.572450i
$96$	−1.82333	−	3.15811i	−0.186093	−	0.322323i
$97$	9.03956			0.917828			0.458914	−	0.888481i	$-0.348239\pi$
$97$	9.03956			0.917828			0.458914	+	0.888481i	$0.348239\pi$
$98$	−1.49352	−	2.58685i	−0.150868	−	0.261312i
$99$	−0.475923	+	0.824323i	−0.0478321	+	0.0828476i
$100$	−2.71834	+	4.70830i	−0.271834	+	0.470830i
$101$	7.14481	−	12.3752i	0.710936	−	1.23138i	−0.253571	−	0.967317i	$-0.581605\pi$
$101$	7.14481	−	12.3752i	0.710936	−	1.23138i	0.964506	−	0.264060i	$-0.0850616\pi$
$102$	−0.375884			−0.0372180
$103$	−7.07308	+	12.2509i	−0.696931	+	1.20712i	0.272594	+	0.962129i	$0.412118\pi$
$103$	−7.07308	+	12.2509i	−0.696931	+	1.20712i	−0.969525	+	0.244991i	$0.921215\pi$
$104$	−0.950948	+	1.64709i	−0.0932481	+	0.161510i
$105$	0.572106	+	0.990917i	0.0558319	+	0.0967036i
$106$	−1.66898	−	2.89075i	−0.162105	−	0.280775i
$107$	−14.2119			−1.37391			−0.686956	−	0.726699i	$-0.741054\pi$
$107$	−14.2119			−1.37391			−0.686956	+	0.726699i	$0.741054\pi$
$108$	−6.47042			−0.622617
$109$	3.34958	+	5.80164i	0.320831	+	0.555696i	0.980660	−	0.195720i	$-0.0627044\pi$
$109$	3.34958	+	5.80164i	0.320831	+	0.555696i	−0.659828	+	0.751416i	$0.729371\pi$
$110$	0.138247	+	0.239451i	0.0131814	+	0.0228308i
$111$	−3.34478	+	5.79332i	−0.317472	+	0.549878i
$112$	1.42252	−	2.46387i	0.134415	−	0.232814i
$113$	−11.8684			−1.11649			−0.558243	−	0.829678i	$-0.688524\pi$
$113$	−11.8684			−1.11649			−0.558243	+	0.829678i	$0.688524\pi$
$114$	−0.901294	+	1.56109i	−0.0844139	+	0.146209i
$115$	−4.77659	+	8.27330i	−0.445420	+	0.771489i
$116$	−3.23833	+	5.60894i	−0.300671	+	0.520777i
$117$	1.18817	+	2.05796i	0.109846	+	0.190259i
$118$	−0.432533			−0.0398179
$119$	−0.618902	−	1.07197i	−0.0567347	−	0.0982673i
$120$	−0.934620	+	1.61881i	−0.0853188	+	0.147776i
$121$	−10.8581			−0.987097
$122$	0.795764	−	1.37830i	0.0720451	−	0.124786i
$123$	2.39296	+	4.14472i	0.215766	+	0.373717i
$124$	2.36763	+	4.10085i	0.212619	+	0.368267i
$125$	11.0098			0.984749
$126$	0.854236	+	1.47958i	0.0761014	+	0.131812i
$127$	−10.2894			−0.913040			−0.456520	−	0.889713i	$-0.650904\pi$
$127$	−10.2894			−0.913040			−0.456520	+	0.889713i	$0.650904\pi$
$128$	11.5294			1.01906
$129$	3.49890	+	2.84873i	0.308061	+	0.250817i
$130$	0.690283			0.0605419
$131$	20.9025			1.82626			0.913128	−	0.407673i	$-0.133660\pi$
$131$	20.9025			1.82626			0.913128	+	0.407673i	$0.133660\pi$
$132$	0.220538	+	0.381982i	0.0191953	+	0.0332473i
$133$	−5.93601			−0.514717
$134$	3.24412	+	5.61897i	0.280249	+	0.485405i
$135$	2.55435	+	4.42426i	0.219843	+	0.380780i
$136$	1.01107	−	1.75122i	0.0866984	−	0.150166i
$137$	−4.25668			−0.363672			−0.181836	−	0.983329i	$-0.558204\pi$
$137$	−4.25668			−0.363672			−0.181836	+	0.983329i	$0.558204\pi$
$138$	1.33643	−	2.31476i	0.113764	−	0.197046i
$139$	−8.55711	−	14.8214i	−0.725805	−	1.25713i	−0.958642	−	0.284615i	$-0.908134\pi$
$139$	−8.55711	−	14.8214i	−0.725805	−	1.25713i	0.232837	−	0.972516i	$-0.425199\pi$
$140$	−2.82961			−0.239146
$141$	2.27462	+	3.93977i	0.191558	+	0.331788i
$142$	1.81331	−	3.14075i	0.152170	−	0.263566i
$143$	0.177167	−	0.306862i	0.0148154	−	0.0256611i
$144$	2.90360	−	5.02918i	0.241967	−	0.419098i
$145$	5.11362			0.424663
$146$	−1.30960	+	2.26830i	−0.108383	+	0.187726i
$147$	−1.88111	+	3.25818i	−0.155151	+	0.268730i
$148$	−8.27155	−	14.3267i	−0.679917	−	1.17765i
$149$	−1.75004	−	3.03115i	−0.143368	−	0.248322i	0.785395	−	0.618995i	$-0.212460\pi$
$149$	−1.75004	−	3.03115i	−0.143368	−	0.248322i	−0.928763	+	0.370674i	$0.879127\pi$
$150$	−1.20099			−0.0980602
$151$	−1.07338			−0.0873505			−0.0436752	−	0.999046i	$-0.513907\pi$
$151$	−1.07338			−0.0873505			−0.0436752	+	0.999046i	$0.513907\pi$
$152$	−4.84868	−	8.39815i	−0.393280	−	0.681180i
$153$	−1.26328	−	2.18807i	−0.102130	−	0.176895i
$154$	0.127375	−	0.220619i	0.0102641	−	0.0177780i
$155$	1.86935	−	3.23781i	0.150150	−	0.260067i
$156$	1.10117			0.0881640
$157$	9.73171	−	16.8558i	0.776675	−	1.34524i	−0.157173	−	0.987571i	$-0.550238\pi$
$157$	9.73171	−	16.8558i	0.776675	−	1.34524i	0.933848	−	0.357669i	$-0.116428\pi$
$158$	−1.41714	+	2.45456i	−0.112742	+	0.195275i
$159$	−2.10210	+	3.64095i	−0.166707	+	0.288746i
$160$	−3.56011	−	6.16630i	−0.281452	−	0.487489i
$161$	8.80185			0.693683
$162$	1.35569	+	2.34813i	0.106513	+	0.184486i
$163$	−9.69133	+	16.7859i	−0.759084	+	1.31477i	0.184234	+	0.982882i	$0.441019\pi$
$163$	−9.69133	+	16.7859i	−0.759084	+	1.31477i	−0.943318	+	0.331890i	$0.892314\pi$
$164$	−11.8354			−0.924193
$165$	0.174125	−	0.301593i	0.0135556	−	0.0234790i
$166$	−2.02598	−	3.50911i	−0.157247	−	0.272360i
$167$	2.62914	+	4.55381i	0.203449	+	0.352384i	0.949638	−	0.313351i	$-0.101451\pi$
$167$	2.62914	+	4.55381i	0.203449	+	0.352384i	−0.746188	+	0.665735i	$0.768118\pi$
$168$	1.72223			0.132873
$169$	6.05769	+	10.4922i	0.465976	+	0.807095i
$170$	−0.733924			−0.0562894
$171$	−12.1164			−0.926565
$172$	−10.4274	+	3.97103i	−0.795078	+	0.302789i
$173$	−10.7383			−0.816420			−0.408210	−	0.912888i	$-0.633847\pi$
$173$	−10.7383			−0.816420			−0.408210	+	0.912888i	$0.633847\pi$
$174$	−1.43072			−0.108463
$175$	−1.97746	−	3.42505i	−0.149482	−	0.258910i
$176$	−0.865907			−0.0652702
$177$	0.272391	+	0.471795i	0.0204742	+	0.0354623i
$178$	3.92340	+	6.79552i	0.294071	+	0.509346i
$179$	10.5108	−	18.2052i	0.785613	−	1.36072i	−0.143020	−	0.989720i	$-0.545681\pi$
$179$	10.5108	−	18.2052i	0.785613	−	1.36072i	0.928632	−	0.371001i	$-0.120985\pi$
$180$	−5.77572			−0.430496
$181$	−11.8457	+	20.5173i	−0.880482	+	1.52504i	−0.0296752	+	0.999560i	$0.509447\pi$
$181$	−11.8457	+	20.5173i	−0.880482	+	1.52504i	−0.850806	+	0.525479i	$0.823886\pi$
$182$	−0.317997	−	0.550787i	−0.0235715	−	0.0408271i
$183$	−2.00455			−0.148181
$184$	7.18956	+	12.4527i	0.530021	+	0.918024i
$185$	−6.53077	+	11.3116i	−0.480152	+	0.831647i
$186$	−0.523020	+	0.905898i	−0.0383497	+	0.0664237i
$187$	−0.188367	+	0.326262i	−0.0137748	+	0.0238586i
$188$	−11.2502			−0.820504
$189$	2.35346	−	4.07631i	0.171189	−	0.296508i
$190$	−1.75980	+	3.04807i	−0.127670	+	0.221130i
$191$	−6.48004	−	11.2238i	−0.468880	−	0.812123i	0.530488	−	0.847693i	$-0.322009\pi$
$191$	−6.48004	−	11.2238i	−0.468880	−	0.812123i	−0.999367	+	0.0355695i	$0.988675\pi$
$192$	−0.585408	−	1.01396i	−0.0422482	−	0.0731761i
$193$	1.13960			0.0820302			0.0410151	−	0.999159i	$-0.486941\pi$
$193$	1.13960			0.0820302			0.0410151	+	0.999159i	$0.486941\pi$
$194$	−4.93824			−0.354545
$195$	−0.434711	−	0.752942i	−0.0311303	−	0.0539193i
$196$	−4.65194	−	8.05740i	−0.332282	−	0.575529i
$197$	0.807859	−	1.39925i	0.0575576	−	0.0996926i	−0.835811	−	0.549017i	$-0.815002\pi$
$197$	0.807859	−	1.39925i	0.0575576	−	0.0996926i	0.893368	+	0.449325i	$0.148335\pi$
$198$	0.259993	−	0.450321i	0.0184769	−	0.0320029i
$199$	−13.2722			−0.940838			−0.470419	−	0.882443i	$-0.655897\pi$
$199$	−13.2722			−0.940838			−0.470419	+	0.882443i	$0.655897\pi$
$200$	3.23047	−	5.59533i	0.228428	−	0.395650i
$201$	4.08601	−	7.07719i	0.288205	−	0.499186i
$202$	−3.90316	+	6.76047i	−0.274625	+	0.475665i
$203$	−2.35572	−	4.08023i	−0.165339	−	0.286376i
$204$	−1.17078			−0.0819713
$205$	4.67232	+	8.09269i	0.326329	+	0.565218i
$206$	3.86397	−	6.69259i	0.269215	−	0.466295i
$207$	17.9661			1.24873
$208$	−1.08089	+	1.87216i	−0.0749463	+	0.129811i
$209$	0.903334	+	1.56462i	0.0624849	+	0.108227i
$210$	−0.312537	−	0.541330i	−0.0215671	−	0.0373553i
$211$	−6.07480			−0.418206			−0.209103	−	0.977894i	$-0.567054\pi$
$211$	−6.07480			−0.418206			−0.209103	+	0.977894i	$0.567054\pi$
$212$	−5.19845	−	9.00397i	−0.357031	−	0.618395i
$213$	−4.56779			−0.312980
$214$	7.76383			0.530724
$215$	6.83171	+	5.56223i	0.465918	+	0.379341i
$216$	7.68944			0.523200
$217$	−3.44466			−0.233839
$218$	−1.82985	−	3.16939i	−0.123933	−	0.214658i
$219$	3.29893			0.222921
$220$	0.430606	+	0.745832i	0.0290315	+	0.0502840i
$221$	0.470269	+	0.814530i	0.0316337	+	0.0547912i
$222$	1.82722	−	3.16485i	0.122635	−	0.212411i
$223$	−17.6313			−1.18068			−0.590340	−	0.807155i	$-0.701006\pi$
$223$	−17.6313			−1.18068			−0.590340	+	0.807155i	$0.701006\pi$
$224$	−3.28012	+	5.68133i	−0.219162	+	0.379600i
$225$	−4.03632	−	6.99112i	−0.269088	−	0.466074i
$226$	6.48362			0.431284
$227$	2.01775	+	3.49484i	0.133922	+	0.231961i	0.925185	−	0.379516i	$-0.123909\pi$
$227$	2.01775	+	3.49484i	0.133922	+	0.231961i	−0.791263	+	0.611476i	$0.790576\pi$
$228$	−2.80731	+	4.86240i	−0.185918	+	0.322020i
$229$	−7.81344	+	13.5333i	−0.516326	+	0.894303i	0.483494	+	0.875348i	$0.339368\pi$
$229$	−7.81344	+	13.5333i	−0.516326	+	0.894303i	−0.999820	+	0.0189558i	$0.993966\pi$
$230$	2.60942	−	4.51964i	0.172060	−	0.298016i
$231$	−0.320860			−0.0211111
$232$	3.84842	−	6.66566i	0.252661	−	0.437622i
$233$	7.47200	−	12.9419i	0.489507	−	0.847851i	−0.510420	−	0.859925i	$-0.670510\pi$
$233$	7.47200	−	12.9419i	0.489507	−	0.847851i	0.999927	+	0.0120745i	$0.00384351\pi$
$234$	−0.649086	−	1.12425i	−0.0424321	−	0.0734945i
$235$	4.44127	+	7.69251i	0.289717	+	0.501804i
$236$	−1.34723			−0.0876974
$237$	3.56983			0.231885
$238$	0.338101	+	0.585609i	0.0219159	+	0.0379594i
$239$	−5.60195	−	9.70286i	−0.362360	−	0.627626i	0.625989	−	0.779832i	$-0.284696\pi$
$239$	−5.60195	−	9.70286i	−0.362360	−	0.627626i	−0.988349	+	0.152206i	$0.951362\pi$
$240$	−1.06233	+	1.84001i	−0.0685733	+	0.118772i
$241$	−5.56837	+	9.64469i	−0.358690	+	0.621269i	−0.987742	−	0.156094i	$-0.950110\pi$
$241$	−5.56837	+	9.64469i	−0.358690	+	0.621269i	0.629052	+	0.777363i	$0.283443\pi$
$242$	5.93168			0.381303
$243$	7.41146	−	12.8370i	0.475446	−	0.823496i
$244$	2.47861	−	4.29307i	0.158677	−	0.274836i
$245$	−3.67293	+	6.36169i	−0.234655	+	0.406434i
$246$	−1.30725	−	2.26423i	−0.0833474	−	0.144362i
$247$	4.51044			0.286993
$248$	−2.81368	−	4.87344i	−0.178669	−	0.309464i
$249$	−2.55176	+	4.41978i	−0.161711	+	0.280092i
$250$	−6.01458			−0.380396
$251$	−10.7536	+	18.6257i	−0.678759	+	1.17565i	0.296595	+	0.955003i	$0.404149\pi$
$251$	−10.7536	+	18.6257i	−0.678759	+	1.17565i	−0.975355	+	0.220643i	$0.929185\pi$
$252$	2.66073	+	4.60853i	0.167610	+	0.290310i
$253$	−1.33945	−	2.32000i	−0.0842107	−	0.145857i
$254$	5.62104			0.352696
$255$	0.462195	+	0.800545i	0.0289437	+	0.0501320i
$256$	−2.89519			−0.180949
$257$	20.1238			1.25529			0.627643	−	0.778501i	$-0.284020\pi$
$257$	20.1238			1.25529			0.627643	+	0.778501i	$0.284020\pi$
$258$	−1.91142	−	1.55624i	−0.119000	−	0.0968872i
$259$	12.0343			0.747774
$260$	2.15006			0.133341
$261$	−4.80843	−	8.32844i	−0.297634	−	0.515517i
$262$	−11.4189			−0.705459
$263$	−10.6698	−	18.4806i	−0.657925	−	1.13956i	−0.981152	−	0.193238i	$-0.938101\pi$
$263$	−10.6698	−	18.4806i	−0.657925	−	1.13956i	0.323227	−	0.946322i	$-0.395232\pi$
$264$	−0.262086	−	0.453947i	−0.0161303	−	0.0279385i
$265$	−4.10441	+	7.10905i	−0.252132	+	0.436706i
$266$	3.24280			0.198829
$267$	4.94158	−	8.55907i	0.302420	−	0.523807i
$268$	10.1046	+	17.5017i	0.617238	+	1.06909i
$269$	−7.60229			−0.463520			−0.231760	−	0.972773i	$-0.574448\pi$
$269$	−7.60229			−0.463520			−0.231760	+	0.972773i	$0.574448\pi$
$270$	−1.39542	−	2.41694i	−0.0849227	−	0.147090i
$271$	2.28993	−	3.96628i	0.139104	−	0.240934i	−0.788054	−	0.615606i	$-0.788911\pi$
$271$	2.28993	−	3.96628i	0.139104	−	0.240934i	0.927158	+	0.374672i	$0.122245\pi$
$272$	1.14923	−	1.99052i	0.0696821	−	0.120693i
$273$	−0.400522	+	0.693725i	−0.0242407	+	0.0419861i
$274$	2.32539			0.140482
$275$	−0.601853	+	1.04244i	−0.0362931	+	0.0628615i
$276$	4.16264	−	7.20991i	0.250562	−	0.433985i
$277$	10.6591	+	18.4622i	0.640445	+	1.10928i	0.985333	+	0.170640i	$0.0545834\pi$
$277$	10.6591	+	18.4622i	0.640445	+	1.10928i	−0.344888	+	0.938644i	$0.612083\pi$
$278$	4.67468	+	8.09679i	0.280369	+	0.485613i
$279$	−7.03114			−0.420944
$280$	3.36270			0.200960
$281$	−12.3112	−	21.3236i	−0.734425	−	1.27206i	−0.954975	−	0.296685i	$-0.904119\pi$
$281$	−12.3112	−	21.3236i	−0.734425	−	1.27206i	0.220551	−	0.975376i	$-0.429215\pi$
$282$	−1.24261	−	2.15226i	−0.0739963	−	0.128165i
$283$	−15.0663	+	26.0956i	−0.895600	+	1.55122i	−0.0625400	+	0.998042i	$0.519920\pi$
$283$	−15.0663	+	26.0956i	−0.895600	+	1.55122i	−0.833060	+	0.553182i	$0.813413\pi$
$284$	5.64802	−	9.78265i	0.335148	−	0.580494i
$285$	4.43300			0.262588
$286$	−0.0967847	+	0.167636i	−0.00572300	+	0.00991253i
$287$	4.30485	−	7.45622i	0.254107	−	0.440127i
$288$	−6.69528	+	11.5966i	−0.394523	+	0.683334i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.79353			−0.164042
$291$	3.10990	+	5.38650i	0.182305	+	0.315762i
$292$	−4.07908	+	7.06518i	−0.238710	+	0.413458i
$293$	17.2906			1.01013			0.505064	−	0.863082i	$-0.331469\pi$
$293$	17.2906			1.01013			0.505064	+	0.863082i	$0.331469\pi$
$294$	1.02764	−	1.77992i	0.0599330	−	0.103807i
$295$	0.531852	+	0.921194i	0.0309656	+	0.0536340i
$296$	9.82989	+	17.0259i	0.571351	+	0.989609i
$297$	−1.43258			−0.0831269
$298$	0.956031	+	1.65589i	0.0553814	+	0.0959234i
$299$	−6.68803			−0.386779
$300$	−3.74078			−0.215974
$301$	1.29098	−	8.01350i	0.0744107	−	0.461891i
$302$	0.586380			0.0337424
$303$	9.83218			0.564844
$304$	−5.51123	−	9.54573i	−0.316091	−	0.547485i
$305$	−3.91395			−0.224112
$306$	0.690122	+	1.19533i	0.0394517	+	0.0683323i
$307$	6.13975	+	10.6344i	0.350414	+	0.606935i	0.986322	−	0.164830i	$-0.0527075\pi$
$307$	6.13975	+	10.6344i	0.350414	+	0.606935i	−0.635908	+	0.771765i	$0.719374\pi$
$308$	0.396740	−	0.687174i	0.0226064	−	0.0391554i
$309$	−9.73346			−0.553717
$310$	−1.02121	+	1.76879i	−0.0580010	+	0.100461i
$311$	−3.98889	−	6.90895i	−0.226189	−	0.391771i	0.730486	−	0.682927i	$-0.239293\pi$
$311$	−3.98889	−	6.90895i	−0.226189	−	0.391771i	−0.956676	+	0.291156i	$0.905960\pi$
$312$	−1.30863			−0.0740863
$313$	7.48489	+	12.9642i	0.423071	+	0.732781i	0.996238	−	0.0866578i	$-0.0276187\pi$
$313$	7.48489	+	12.9642i	0.423071	+	0.732781i	−0.573167	+	0.819439i	$0.694285\pi$
$314$	−5.31636	+	9.20820i	−0.300019	+	0.519649i
$315$	2.10077	−	3.63865i	0.118365	−	0.205014i
$316$	−4.41405	+	7.64536i	−0.248310	+	0.430085i
$317$	23.9652			1.34602			0.673011	−	0.739632i	$-0.265001\pi$
$317$	23.9652			1.34602			0.673011	+	0.739632i	$0.265001\pi$
$318$	1.14836	−	1.98902i	0.0643969	−	0.111539i
$319$	−0.716981	+	1.24185i	−0.0401432	+	0.0695301i
$320$	−1.14303	−	1.97978i	−0.0638972	−	0.110673i
$321$	−4.88933	−	8.46857i	−0.272896	−	0.472670i
$322$	−4.80838			−0.267961
$323$	−4.79560			−0.266834
$324$	4.22265	+	7.31384i	0.234592	+	0.406325i
$325$	1.50256	+	2.60251i	0.0833469	+	0.144361i
$326$	5.29430	−	9.17000i	0.293224	−	0.507879i
$327$	−2.30472	+	3.99190i	−0.127452	+	0.220752i
$328$	14.0652			0.776622
$329$	4.09197	−	7.08751i	0.225598	−	0.390747i
$330$	−0.0951230	+	0.164758i	−0.00523635	+	0.00906962i
$331$	1.77176	−	3.06877i	0.0973845	−	0.168675i	−0.813217	−	0.581961i	$-0.802286\pi$
$331$	1.77176	−	3.06877i	0.0973845	−	0.168675i	0.910601	+	0.413286i	$0.135619\pi$
$332$	−6.31044	−	10.9300i	−0.346330	−	0.599862i
$333$	24.5640			1.34610
$334$	−1.43628	−	2.48771i	−0.0785898	−	0.136121i
$335$	7.97806	−	13.8184i	0.435888	−	0.754981i
$336$	1.95756			0.106794
$337$	12.7887	−	22.1507i	0.696646	−	1.20663i	−0.272977	−	0.962021i	$-0.588008\pi$
$337$	12.7887	−	22.1507i	0.696646	−	1.20663i	0.969623	−	0.244605i	$-0.0786584\pi$
$338$	−3.30927	−	5.73183i	−0.180001	−	0.311770i
$339$	−4.08311	−	7.07215i	−0.221764	−	0.384107i
$340$	−2.28599			−0.123975
$341$	0.524204	+	0.907948i	0.0283873	+	0.0491682i
$342$	6.61910			0.357920
$343$	15.4327			0.833290
$344$	12.3918	−	4.71917i	0.668124	−	0.254441i
$345$	−6.57320			−0.353889
$346$	5.86627			0.315372
$347$	−4.93211	−	8.54267i	−0.264770	−	0.458594i	0.702734	−	0.711453i	$-0.251963\pi$
$347$	−4.93211	−	8.54267i	−0.264770	−	0.458594i	−0.967503	+	0.252859i	$0.918629\pi$
$348$	−4.45635			−0.238885
$349$	15.7639	+	27.3039i	0.843822	+	1.46154i	0.886640	+	0.462460i	$0.153033\pi$
$349$	15.7639	+	27.3039i	0.843822	+	1.46154i	−0.0428181	+	0.999083i	$0.513634\pi$
$350$	1.08027	+	1.87108i	0.0577428	+	0.100013i
$351$	−1.78826	+	3.09736i	−0.0954502	+	0.165325i
$352$	1.99666			0.106422
$353$	1.52728	−	2.64532i	0.0812887	−	0.140796i	−0.822515	−	0.568743i	$-0.807430\pi$
$353$	1.52728	−	2.64532i	0.0812887	−	0.140796i	0.903804	+	0.427947i	$0.140763\pi$
$354$	−0.148805	−	0.257738i	−0.00790890	−	0.0136986i
$355$	−8.91875			−0.473358
$356$	12.2204	+	21.1664i	0.647681	+	1.12182i
$357$	0.425844	−	0.737583i	0.0225381	−	0.0390371i
$358$	−5.74196	+	9.94536i	−0.303472	+	0.525629i
$359$	−9.29311	+	16.0961i	−0.490472	+	0.849522i	−0.999940	−	0.0109678i	$-0.996509\pi$
$359$	−9.29311	+	16.0961i	−0.490472	+	0.849522i	0.509468	+	0.860489i	$0.329842\pi$
$360$	6.86385			0.361757
$361$	−1.99889	+	3.46217i	−0.105204	+	0.182220i
$362$	6.47120	−	11.2084i	0.340119	−	0.589103i
$363$	−3.73552	−	6.47011i	−0.196064	−	0.339593i
$364$	−0.990482	−	1.71557i	−0.0519154	−	0.0899200i
$365$	6.44125			0.337151
$366$	1.09507			0.0572403
$367$	−14.6450	−	25.3658i	−0.764460	−	1.32408i	−0.940531	−	0.339707i	$-0.889672\pi$
$367$	−14.6450	−	25.3658i	−0.764460	−	1.32408i	0.176071	−	0.984377i	$-0.443661\pi$
$368$	8.17198	+	14.1543i	0.425994	+	0.737843i
$369$	8.78693	−	15.2194i	0.457429	−	0.792291i
$370$	3.56771	−	6.17945i	0.185476	−	0.321255i
$371$	7.56322			0.392663
$372$	−1.62908	+	2.82165i	−0.0844638	+	0.146296i
$373$	−3.93588	+	6.81714i	−0.203792	+	0.352978i	−0.949747	−	0.313018i	$-0.898660\pi$
$373$	−3.93588	+	6.81714i	−0.203792	+	0.352978i	0.745955	+	0.665996i	$0.231993\pi$
$374$	0.102904	−	0.178234i	0.00532102	−	0.00921628i
$375$	3.78773	+	6.56054i	0.195598	+	0.338785i
$376$	13.3697			0.689489
$377$	1.78998	+	3.10034i	0.0921887	+	0.159675i
$378$	−1.28567	+	2.22685i	−0.0661280	+	0.114537i
$379$	23.8755			1.22640			0.613201	−	0.789927i	$-0.289882\pi$
$379$	23.8755			1.22640			0.613201	+	0.789927i	$0.289882\pi$
$380$	−5.48135	+	9.49398i	−0.281187	+	0.487031i
$381$	−3.53990	−	6.13128i	−0.181354	−	0.314115i
$382$	3.54000	+	6.13146i	0.181122	+	0.313713i
$383$	−10.4601			−0.534486			−0.267243	−	0.963629i	$-0.586113\pi$
$383$	−10.4601			−0.534486			−0.267243	+	0.963629i	$0.586113\pi$
$384$	3.96647	+	6.87013i	0.202413	+	0.350590i
$385$	−0.626489			−0.0319289
$386$	−0.622555			−0.0316872
$387$	2.63511	−	16.3569i	0.133950	−	0.831469i
$388$	−15.3814			−0.780872
$389$	27.1136			1.37471			0.687356	−	0.726320i	$-0.258771\pi$
$389$	27.1136			1.37471			0.687356	+	0.726320i	$0.258771\pi$
$390$	0.237479	+	0.411327i	0.0120252	+	0.0208283i
$391$	7.11086			0.359612
$392$	5.52836	+	9.57540i	0.279224	+	0.483631i
$393$	7.19111	+	12.4554i	0.362744	+	0.628290i
$394$	−0.441327	+	0.764401i	−0.0222337	+	0.0385100i
$395$	6.97020			0.350709
$396$	0.809814	−	1.40264i	0.0406947	−	0.0704852i
$397$	−3.05135	−	5.28509i	−0.153143	−	0.265251i	0.779238	−	0.626728i	$-0.215606\pi$
$397$	−3.05135	−	5.28509i	−0.153143	−	0.265251i	−0.932381	+	0.361477i	$0.882273\pi$
$398$	7.25048			0.363434
$399$	−2.04218	−	3.53715i	−0.102237	−	0.177079i
$400$	3.67190	−	6.35991i	0.183595	−	0.317996i
$401$	−6.41013	+	11.1027i	−0.320107	+	0.554441i	−0.980510	−	0.196470i	$-0.937052\pi$
$401$	−6.41013	+	11.1027i	−0.320107	+	0.554441i	0.660403	+	0.750911i	$0.270385\pi$
$402$	−2.23216	+	3.86621i	−0.111330	+	0.192829i
$403$	2.61741			0.130382
$404$	−12.1574	+	21.0572i	−0.604852	+	1.04763i
$405$	3.33398	−	5.77462i	0.165667	−	0.286943i
$406$	1.28691	+	2.22900i	0.0638684	+	0.110623i
$407$	−1.83136	−	3.17201i	−0.0907772	−	0.157231i
$408$	1.39136			0.0688825
$409$	−15.6258			−0.772647			−0.386323	−	0.922363i	$-0.626255\pi$
$409$	−15.6258			−0.772647			−0.386323	+	0.922363i	$0.626255\pi$
$410$	−2.55245	−	4.42097i	−0.126057	−	0.218336i
$411$	−1.46443	−	2.53647i	−0.0722351	−	0.125115i
$412$	12.0353	−	20.8458i	0.592937	−	1.02700i
$413$	0.490023	−	0.848744i	0.0241124	−	0.0417640i
$414$	−9.81472			−0.482367
$415$	−4.98238	+	8.62974i	−0.244576	+	0.423617i
$416$	2.49238	−	4.31692i	0.122199	−	0.211655i
$417$	5.88784	−	10.1980i	0.288329	−	0.499400i
$418$	−0.493484	−	0.854740i	−0.0241371	−	0.0418067i
$419$	−2.35015			−0.114813			−0.0574063	−	0.998351i	$-0.518283\pi$
$419$	−2.35015			−0.114813			−0.0574063	+	0.998351i	$0.518283\pi$
$420$	−0.973476	−	1.68611i	−0.0475008	−	0.0822737i
$421$	−7.42873	+	12.8669i	−0.362054	+	0.627096i	−0.988299	−	0.152530i	$-0.951258\pi$
$421$	−7.42873	+	12.8669i	−0.362054	+	0.627096i	0.626244	+	0.779627i	$0.284591\pi$
$422$	3.31861			0.161548
$423$	8.35242	−	14.4668i	0.406108	−	0.703400i
$424$	6.17782	+	10.7003i	0.300022	+	0.519653i
$425$	−1.59755	−	2.76704i	−0.0774926	−	0.134221i
$426$	2.49535			0.120900
$427$	1.80306	+	3.12300i	0.0872563	+	0.151132i
$428$	24.1824			1.16890
$429$	0.243804			0.0117710
$430$	−3.73211	−	3.03860i	−0.179978	−	0.146534i
$431$	27.4875			1.32402			0.662012	−	0.749493i	$-0.269703\pi$
$431$	27.4875			1.32402			0.662012	+	0.749493i	$0.269703\pi$
$432$	8.74017			0.420511
$433$	0.257536	+	0.446066i	0.0123764	+	0.0214366i	0.872147	−	0.489243i	$-0.162727\pi$
$433$	0.257536	+	0.446066i	0.0123764	+	0.0214366i	−0.859771	+	0.510680i	$0.829394\pi$
$434$	1.88179			0.0903289
$435$	1.75925	+	3.04711i	0.0843494	+	0.146098i
$436$	−5.69953	−	9.87187i	−0.272958	−	0.472777i
$437$	17.0504	−	29.5322i	0.815632	−	1.41272i
$438$	−1.80218			−0.0861114
$439$	−11.0511	+	19.1410i	−0.527439	+	0.913551i	0.472049	+	0.881572i	$0.343514\pi$
$439$	−11.0511	+	19.1410i	−0.527439	+	0.913551i	−0.999489	+	0.0319793i	$0.989819\pi$
$440$	−0.511732	−	0.886345i	−0.0243958	−	0.0422548i
$441$	13.8149			0.657851
$442$	−0.256904	−	0.444971i	−0.0122197	−	0.0211651i
$443$	−15.1477	+	26.2367i	−0.719691	+	1.24654i	0.241431	+	0.970418i	$0.422383\pi$
$443$	−15.1477	+	26.2367i	−0.719691	+	1.24654i	−0.961122	+	0.276123i	$0.910950\pi$
$444$	5.69135	−	9.85771i	0.270100	−	0.467826i
$445$	9.64858	−	16.7118i	0.457387	−	0.792217i
$446$	9.63184			0.456081
$447$	1.20414	−	2.08562i	0.0569537	−	0.0986467i
$448$	−1.05313	+	1.82408i	−0.0497557	+	0.0861795i
$449$	−9.49782	−	16.4507i	−0.448230	−	0.776357i	0.550041	−	0.835138i	$-0.314612\pi$
$449$	−9.49782	−	16.4507i	−0.448230	−	0.776357i	−0.998271	+	0.0587805i	$0.981279\pi$
$450$	2.20501	+	3.81919i	0.103945	+	0.180038i
$451$	−2.62042			−0.123391
$452$	20.1949			0.949886
$453$	−0.369277	−	0.639607i	−0.0173502	−	0.0300513i
$454$	−1.10228	−	1.90920i	−0.0517325	−	0.0896033i
$455$	−0.782032	+	1.35452i	−0.0366622	+	0.0635008i
$456$	3.33620	−	5.77847i	0.156232	−	0.270601i
$457$	−2.66102			−0.124477			−0.0622385	−	0.998061i	$-0.519824\pi$
$457$	−2.66102			−0.124477			−0.0622385	+	0.998061i	$0.519824\pi$
$458$	4.26842	−	7.39312i	0.199450	−	0.345458i
$459$	1.90132	−	3.29318i	0.0887458	−	0.153712i
$460$	8.12768	−	14.0776i	0.378955	−	0.656369i
$461$	5.87858	+	10.1820i	0.273793	+	0.474223i	0.969830	−	0.243783i	$-0.0783884\pi$
$461$	5.87858	+	10.1820i	0.273793	+	0.474223i	−0.696037	+	0.718006i	$0.745055\pi$
$462$	0.175284			0.00815493
$463$	−9.36180	−	16.2151i	−0.435080	−	0.753580i	0.562222	−	0.826986i	$-0.309946\pi$
$463$	−9.36180	−	16.2151i	−0.435080	−	0.753580i	−0.997302	+	0.0734059i	$0.976613\pi$
$464$	4.37429	−	7.57649i	0.203071	−	0.351730i
$465$	2.57247			0.119295
$466$	−4.08189	+	7.07005i	−0.189090	+	0.327514i
$467$	9.89136	+	17.1323i	0.457717	+	0.792790i	0.998840	−	0.0481541i	$-0.0153338\pi$
$467$	9.89136	+	17.1323i	0.457717	+	0.792790i	−0.541123	+	0.840944i	$0.682001\pi$
$468$	−2.02174	−	3.50176i	−0.0934551	−	0.161869i
$469$	−14.7012			−0.678839
$470$	−2.42623	−	4.20236i	−0.111914	−	0.193840i
$471$	13.3921			0.617074
$472$	1.60105			0.0736942
$473$	−2.30867	+	0.879206i	−0.106153	+	0.0404260i
$474$	−1.95017			−0.0895743
$475$	−15.3224			−0.703041
$476$	1.05310	+	1.82403i	0.0482688	+	0.0836041i
$477$	15.4378			0.706849
$478$	3.06030	+	5.30060i	0.139975	+	0.242444i
$479$	−11.9155	−	20.6382i	−0.544431	−	0.942983i	−0.998642	−	0.0520888i	$-0.983412\pi$
$479$	−11.9155	−	20.6382i	−0.544431	−	0.942983i	0.454211	−	0.890894i	$-0.349921\pi$
$480$	2.44958	−	4.24281i	0.111808	−	0.193657i
$481$	−9.14417			−0.416938
$482$	3.04195	−	5.26882i	0.138557	−	0.239988i
$483$	3.02812	+	5.24485i	0.137784	+	0.238649i
$484$	18.4757			0.839805
$485$	6.07217	+	10.5173i	0.275723	+	0.477566i
$486$	−4.04882	+	7.01277i	−0.183658	+	0.318106i
$487$	−13.5209	+	23.4189i	−0.612691	+	1.06121i	0.378093	+	0.925767i	$0.376580\pi$
$487$	−13.5209	+	23.4189i	−0.612691	+	1.06121i	−0.990785	+	0.135445i	$0.956754\pi$
$488$	−2.94557	+	5.10188i	−0.133340	+	0.230951i
$489$	−13.3365			−0.603098
$490$	2.00649	−	3.47534i	0.0906440	−	0.157000i
$491$	−13.5858	+	23.5314i	−0.613120	+	1.06196i	0.377591	+	0.925972i	$0.376753\pi$
$491$	−13.5858	+	23.5314i	−0.613120	+	1.06196i	−0.990711	+	0.135983i	$0.956581\pi$
$492$	−4.07177	−	7.05251i	−0.183570	−	0.317952i
$493$	−1.90315	−	3.29634i	−0.0857134	−	0.148460i
$494$	−2.46402			−0.110861
$495$	−1.27877			−0.0574765
$496$	−3.19816	−	5.53938i	−0.143602	−	0.248725i
$497$	4.10865	+	7.11639i	0.184298	+	0.319214i
$498$	1.39401	−	2.41449i	0.0624669	−	0.108196i
$499$	−16.2616	+	28.1659i	−0.727969	+	1.26088i	0.229771	+	0.973245i	$0.426202\pi$
$499$	−16.2616	+	28.1659i	−0.727969	+	1.26088i	−0.957740	+	0.287634i	$0.907131\pi$
$500$	−18.7339			−0.837807
$501$	−1.80902	+	3.13331i	−0.0808209	+	0.139986i
$502$	5.87459	−	10.1751i	0.262196	−	0.454137i
$503$	6.57606	−	11.3901i	0.293212	−	0.507858i	−0.681355	−	0.731953i	$-0.738609\pi$
$503$	6.57606	−	11.3901i	0.293212	−	0.507858i	0.974567	+	0.224095i	$0.0719424\pi$
$504$	−3.16201	−	5.47676i	−0.140847	−	0.243954i
$505$	19.1976			0.854283
$506$	0.731733	+	1.26740i	0.0325295	+	0.0563427i
$507$	−4.16808	+	7.21933i	−0.185111	+	0.320622i
$508$	17.5082			0.776799
$509$	−16.7077	+	28.9385i	−0.740554	+	1.28268i	0.211690	+	0.977337i	$0.432103\pi$
$509$	−16.7077	+	28.9385i	−0.740554	+	1.28268i	−0.952244	+	0.305340i	$0.901230\pi$
$510$	−0.252493	−	0.437331i	−0.0111806	−	0.0193654i
$511$	−2.96733	−	5.13957i	−0.131267	−	0.227361i
$512$	−21.4771			−0.949164
$513$	−9.11795	−	15.7927i	−0.402567	−	0.697267i
$514$	−10.9935			−0.484900
$515$	−19.0049			−0.837455
$516$	−5.95361	−	4.84730i	−0.262093	−	0.213390i
$517$	−2.49084			−0.109547
$518$	−6.57423			−0.288855
$519$	−3.69433	−	6.39876i	−0.162163	−	0.280875i
$520$	−2.55513			−0.112050
$521$	8.83174	+	15.2970i	0.386926	+	0.670175i	0.992034	−	0.125968i	$-0.0402037\pi$
$521$	8.83174	+	15.2970i	0.386926	+	0.670175i	−0.605109	+	0.796143i	$0.706870\pi$
$522$	2.62681	+	4.54976i	0.114972	+	0.199138i
$523$	−13.0218	+	22.5544i	−0.569402	+	0.986234i	0.427223	+	0.904146i	$0.359492\pi$
$523$	−13.0218	+	22.5544i	−0.569402	+	0.986234i	−0.996625	+	0.0820873i	$0.973841\pi$
$524$	−35.5669			−1.55375
$525$	1.36062	−	2.35665i	0.0593821	−	0.102853i
$526$	5.82880	+	10.0958i	0.254148	+	0.440197i
$527$	−2.78288			−0.121224
$528$	−0.297899	−	0.515977i	−0.0129644	−	0.0224550i
$529$	−13.7821	+	23.8714i	−0.599224	+	1.03789i
$530$	2.24221	−	3.88362i	0.0973954	−	0.168694i
$531$	1.00022	−	1.73243i	0.0434058	−	0.0751811i
$532$	10.1005			0.437913
$533$	−3.27101	+	5.66556i	−0.141683	+	0.245403i
$534$	−2.69955	+	4.67575i	−0.116821	+	0.202340i
$535$	−9.54656	−	16.5351i	−0.412734	−	0.714876i
$536$	−12.0083	−	20.7990i	−0.518680	−	0.898380i
$537$	14.4642			0.624175
$538$	4.15307			0.179052
$539$	−1.02996	−	1.78395i	−0.0443636	−	0.0768401i
$540$	−4.34639	−	7.52817i	−0.187039	−	0.323961i
$541$	3.28029	−	5.68163i	0.141031	−	0.244272i	−0.786854	−	0.617139i	$-0.788292\pi$
$541$	3.28029	−	5.68163i	0.141031	−	0.244272i	0.927885	+	0.372867i	$0.121625\pi$
$542$	−1.25097	+	2.16675i	−0.0537339	+	0.0930698i
$543$	−16.3011			−0.699549
$544$	−2.64995	+	4.58985i	−0.113616	+	0.196788i
$545$	−4.50004	+	7.79430i	−0.192761	+	0.333871i
$546$	0.218802	−	0.378977i	0.00936387	−	0.0162187i
$547$	−21.7129	−	37.6079i	−0.928377	−	1.60800i	−0.786037	−	0.618179i	$-0.787871\pi$
$547$	−21.7129	−	37.6079i	−0.928377	−	1.60800i	−0.142340	−	0.989818i	$-0.545463\pi$
$548$	7.24301			0.309406
$549$	3.68036	+	6.37457i	0.157074	+	0.272060i
$550$	0.328788	−	0.569477i	0.0140196	−	0.0242826i
$551$	−18.2534			−0.777623
$552$	−4.94688	+	8.56824i	−0.210553	+	0.364689i
$553$	−3.21100	−	5.56162i	−0.136546	−	0.236504i
$554$	−5.82300	−	10.0857i	−0.247396	−	0.428502i
$555$	−8.98717			−0.381484
$556$	14.5605	+	25.2195i	0.617502	+	1.06954i
$557$	−15.1135			−0.640382			−0.320191	−	0.947353i	$-0.603747\pi$
$557$	−15.1135			−0.640382			−0.320191	+	0.947353i	$0.603747\pi$
$558$	3.84106			0.162605
$559$	−0.980942	+	6.08901i	−0.0414894	+	0.257538i
$560$	3.82220			0.161517
$561$	−0.259217			−0.0109442
$562$	6.72551	+	11.6489i	0.283699	+	0.491381i
$563$	−27.4256			−1.15585			−0.577926	−	0.816089i	$-0.696138\pi$
$563$	−27.4256			−1.15585			−0.577926	+	0.816089i	$0.696138\pi$
$564$	−3.87042	−	6.70377i	−0.162974	−	0.282279i
$565$	−7.97239	−	13.8086i	−0.335401	−	0.580932i
$566$	8.23062	−	14.2558i	0.345959	−	0.599218i
$567$	−6.14353			−0.258004
$568$	−6.71209	+	11.6257i	−0.281633	+	0.487803i
$569$	17.4906	+	30.2946i	0.733244	+	1.27002i	0.955489	+	0.295026i	$0.0953282\pi$
$569$	17.4906	+	30.2946i	0.733244	+	1.27002i	−0.222245	+	0.974991i	$0.571338\pi$
$570$	−2.42171			−0.101434
$571$	−12.1379	−	21.0235i	−0.507956	−	0.879806i	−0.999958	−	0.00921123i	$-0.997068\pi$
$571$	−12.1379	−	21.0235i	−0.507956	−	0.879806i	0.492002	−	0.870594i	$-0.336265\pi$
$572$	−0.301460	+	0.522145i	−0.0126047	+	0.0218320i
$573$	4.45868	−	7.72267i	0.186264	−	0.322619i
$574$	−2.35171	+	4.07327i	−0.0981583	+	0.170015i
$575$	22.7199			0.947486
$576$	−2.14962	+	3.72325i	−0.0895674	+	0.155135i
$577$	5.25256	−	9.09769i	0.218667	−	0.378742i	−0.735734	−	0.677271i	$-0.763163\pi$
$577$	5.25256	−	9.09769i	0.218667	−	0.378742i	0.954401	+	0.298529i	$0.0964959\pi$
$578$	0.273146	+	0.473103i	0.0113614	+	0.0196785i
$579$	0.392059	+	0.679065i	0.0162934	+	0.0282210i
$580$	−8.70115			−0.361296
$581$	9.18106			0.380895
$582$	−1.69891	−	2.94260i	−0.0704222	−	0.121975i
$583$	−1.15096	−	1.99352i	−0.0476679	−	0.0825633i
$584$	4.84758	−	8.39625i	0.200594	−	0.347439i
$585$	−1.59626	+	2.76480i	−0.0659972	+	0.114311i
$586$	−9.44572			−0.390199
$587$	11.4848	−	19.8922i	0.474028	−	0.821040i	−0.525530	−	0.850775i	$-0.676133\pi$
$587$	11.4848	−	19.8922i	0.474028	−	0.821040i	0.999558	+	0.0297348i	$0.00946629\pi$
$588$	3.20083	−	5.54401i	0.132000	−	0.228631i
$589$	−6.67280	+	11.5576i	−0.274948	+	0.476223i
$590$	−0.290546	−	0.503241i	−0.0119616	−	0.0207181i
$591$	1.11172			0.0457299
$592$	11.1731	+	19.3524i	0.459212	+	0.795378i
$593$	−19.9373	+	34.5325i	−0.818728	+	1.41808i	0.0878919	+	0.996130i	$0.471987\pi$
$593$	−19.9373	+	34.5325i	−0.818728	+	1.41808i	−0.906620	+	0.421948i	$0.861346\pi$
$594$	0.782609			0.0321108
$595$	0.831473	−	1.44015i	0.0340871	−	0.0590405i
$596$	2.97780	+	5.15770i	0.121975	+	0.211268i
$597$	−4.56604	−	7.90862i	−0.186876	−	0.323678i
$598$	3.65362			0.149408
$599$	−5.81260	−	10.0677i	−0.237496	−	0.411356i	0.722499	−	0.691372i	$-0.242993\pi$
$599$	−5.81260	−	10.0677i	−0.237496	−	0.411356i	−0.959995	+	0.280016i	$0.909660\pi$
$600$	4.44553			0.181488
$601$	−16.4549			−0.671209			−0.335605	−	0.942003i	$-0.608941\pi$
$601$	−16.4549			−0.671209			−0.335605	+	0.942003i	$0.608941\pi$
$602$	−0.705251	+	4.37771i	−0.0287439	+	0.178422i
$603$	−30.0077			−1.22201
$604$	1.82643			0.0743163
$605$	−7.29372	−	12.6331i	−0.296532	−	0.513608i
$606$	−5.37124			−0.218192
$607$	−4.83907	−	8.38152i	−0.196412	−	0.340195i	0.750951	−	0.660358i	$-0.229596\pi$
$607$	−4.83907	−	8.38152i	−0.196412	−	0.340195i	−0.947362	+	0.320163i	$0.896262\pi$
$608$	12.7081	+	22.0111i	0.515381	+	0.892667i
$609$	1.62089	−	2.80746i	0.0656816	−	0.113764i
$610$	2.13816			0.0865716
$611$	−3.10926	+	5.38540i	−0.125787	+	0.217870i
$612$	2.14956	+	3.72315i	0.0868908	+	0.150499i
$613$	−15.3447			−0.619767			−0.309884	−	0.950775i	$-0.600290\pi$
$613$	−15.3447			−0.619767			−0.309884	+	0.950775i	$0.600290\pi$
$614$	−3.35410	−	5.80947i	−0.135360	−	0.234451i
$615$	−3.21485	+	5.56829i	−0.129635	+	0.224535i
$616$	−0.471485	+	0.816636i	−0.0189967	+	0.0329032i
$617$	19.7210	−	34.1578i	0.793938	−	1.37514i	−0.129573	−	0.991570i	$-0.541361\pi$
$617$	19.7210	−	34.1578i	0.793938	−	1.37514i	0.923511	−	0.383571i	$-0.125306\pi$
$618$	5.31731			0.213894
$619$	−10.4125	+	18.0349i	−0.418513	+	0.724885i	−0.995790	−	0.0916631i	$-0.970782\pi$
$619$	−10.4125	+	18.0349i	−0.418513	+	0.724885i	0.577278	+	0.816548i	$0.304115\pi$
$620$	−3.18082	+	5.50935i	−0.127745	+	0.221261i
$621$	13.5200	+	23.4173i	0.542538	+	0.939704i
$622$	2.17910	+	3.77431i	0.0873739	+	0.151336i
$623$	−17.7795			−0.712320
$624$	−1.48744			−0.0595454
$625$	−0.592099	−	1.02554i	−0.0236839	−	0.0410218i
$626$	−4.08894	−	7.08225i	−0.163427	−	0.283064i
$627$	−0.621552	+	1.07656i	−0.0248224	+	0.0429936i
$628$	−16.5591	+	28.6813i	−0.660781	+	1.14451i
$629$	9.72228			0.387653
$630$	−1.14764	+	1.98776i	−0.0457229	+	0.0791944i
$631$	16.1240	−	27.9275i	0.641885	−	1.11178i	−0.343127	−	0.939289i	$-0.611486\pi$
$631$	16.1240	−	27.9275i	0.641885	−	1.11178i	0.985012	−	0.172488i	$-0.0551806\pi$
$632$	5.24565	−	9.08573i	0.208661	−	0.361411i
$633$	−2.08992	−	3.61985i	−0.0830670	−	0.143876i
$634$	−13.0920			−0.519951
$635$	−6.91175	−	11.9715i	−0.274284	−	0.475075i
$636$	3.57686	−	6.19531i	0.141832	−	0.245660i
$637$	−5.14271			−0.203762
$638$	0.391681	−	0.678412i	0.0155068	−	0.0268586i
$639$	8.38646	+	14.5258i	0.331763	+	0.574631i
$640$	7.74465	+	13.4141i	0.306134	+	0.530240i
$641$	−34.9428			−1.38016			−0.690079	−	0.723734i	$-0.742424\pi$
$641$	−34.9428			−1.38016			−0.690079	+	0.723734i	$0.742424\pi$
$642$	2.67100	+	4.62632i	0.105416	+	0.182586i
$643$	0.854278			0.0336894			0.0168447	−	0.999858i	$-0.494638\pi$
$643$	0.854278			0.0336894			0.0168447	+	0.999858i	$0.494638\pi$
$644$	−14.9769			−0.590173
$645$	−0.964099	+	5.98446i	−0.0379614	+	0.235638i
$646$	2.61980			0.103075
$647$	25.9415			1.01987			0.509933	−	0.860214i	$-0.329670\pi$
$647$	25.9415			1.01987			0.509933	+	0.860214i	$0.329670\pi$
$648$	−5.01819	−	8.69175i	−0.197133	−	0.341444i
$649$	−0.298284			−0.0117087
$650$	−0.820835	−	1.42173i	−0.0321958	−	0.0557648i
$651$	−1.18507	−	2.05261i	−0.0464467	−	0.0804481i
$652$	16.4904	−	28.5623i	0.645815	−	1.11858i
$653$	26.9885			1.05614			0.528071	−	0.849200i	$-0.322916\pi$
$653$	26.9885			1.05614			0.528071	+	0.849200i	$0.322916\pi$
$654$	1.25905	−	2.18074i	0.0492329	−	0.0852738i
$655$	14.0409	+	24.3195i	0.548622	+	0.950241i
$656$	15.9872			0.624194
$657$	−6.05683	−	10.4907i	−0.236299	−	0.409282i
$658$	−2.23541	+	3.87185i	−0.0871455	+	0.150940i
$659$	−10.3459	+	17.9196i	−0.403019	+	0.698049i	−0.994089	−	0.108571i	$-0.965372\pi$
$659$	−10.3459	+	17.9196i	−0.403019	+	0.698049i	0.591070	+	0.806620i	$0.298706\pi$
$660$	−0.296285	+	0.513180i	−0.0115329	+	0.0199755i
$661$	−35.1486			−1.36712			−0.683561	−	0.729894i	$-0.739570\pi$
$661$	−35.1486			−1.36712			−0.683561	+	0.729894i	$0.739570\pi$
$662$	−0.967897	+	1.67645i	−0.0376184	+	0.0651569i
$663$	−0.323575	+	0.560448i	−0.0125666	+	0.0217660i
$664$	7.49931	+	12.9892i	0.291030	+	0.504078i
$665$	−3.98741	−	6.90640i	−0.154625	−	0.267819i
$666$	−13.4191			−0.519981
$667$	27.0660			1.04800
$668$	−4.47366	−	7.74860i	−0.173091	−	0.299802i
$669$	−6.06573	−	10.5061i	−0.234515	−	0.406191i
$670$	−4.35835	+	7.54889i	−0.168378	+	0.291639i
$671$	0.548775	−	0.950507i	0.0211852	−	0.0366939i
$672$	−4.51386			−0.174126
$673$	4.76512	−	8.25342i	0.183682	−	0.318146i	−0.759450	−	0.650566i	$-0.774532\pi$
$673$	4.76512	−	8.25342i	0.183682	−	0.318146i	0.943131	+	0.332420i	$0.107865\pi$
$674$	−6.98638	+	12.1008i	−0.269105	+	0.466104i
$675$	6.07490	−	10.5220i	0.233823	−	0.404993i
$676$	−10.3076	−	17.8532i	−0.396445	−	0.686662i
$677$	−25.7719			−0.990493			−0.495247	−	0.868752i	$-0.664922\pi$
$677$	−25.7719			−0.990493			−0.495247	+	0.868752i	$0.664922\pi$
$678$	2.23057	+	3.86346i	0.0856646	+	0.148375i
$679$	5.59460	−	9.69014i	0.214701	−	0.371873i
$680$	2.71667			0.104179
$681$	−1.38834	+	2.40467i	−0.0532012	+	0.0921472i
$682$	−0.286369	−	0.496005i	−0.0109656	−	0.0189930i
$683$	16.7822	+	29.0677i	0.642155	+	1.11224i	0.984951	+	0.172835i	$0.0552926\pi$
$683$	16.7822	+	29.0677i	0.642155	+	1.11224i	−0.342796	+	0.939410i	$0.611374\pi$
$684$	20.6169			0.788305
$685$	−2.85935	−	4.95253i	−0.109250	−	0.189227i
$686$	−8.43079			−0.321889
$687$	−10.7523			−0.410225
$688$	14.0851	−	5.36402i	0.536991	−	0.204501i
$689$	−5.74687			−0.218938
$690$	3.59089			0.136703
$691$	−11.7008	−	20.2663i	−0.445118	−	0.770966i	0.552943	−	0.833219i	$-0.313505\pi$
$691$	−11.7008	−	20.2663i	−0.445118	−	0.770966i	−0.998060	+	0.0622529i	$0.980171\pi$
$692$	18.2720			0.694596
$693$	0.589099	+	1.02035i	0.0223780	+	0.0387599i
$694$	2.69437	+	4.66679i	0.102277	+	0.177149i
$695$	11.4962	−	19.9120i	0.436075	−	0.755304i
$696$	5.29591			0.200741
$697$	3.47781	−	6.02375i	0.131731	−	0.228166i
$698$	−8.61169	−	14.9159i	−0.325957	−	0.564575i
$699$	10.2824			0.388917
$700$	3.36477	+	5.82795i	0.127176	+	0.220276i
$701$	−23.9234	+	41.4365i	−0.903573	+	1.56503i	−0.0807523	+	0.996734i	$0.525732\pi$
$701$	−23.9234	+	41.4365i	−0.903573	+	1.56503i	−0.822821	+	0.568301i	$0.807601\pi$
$702$	0.976912	−	1.69206i	0.0368712	−	0.0638627i
$703$	23.3121	−	40.3777i	0.879232	−	1.52287i
$704$	0.641056			0.0241607
$705$	−3.05588	+	5.29294i	−0.115091	+	0.199343i
$706$	−0.834339	+	1.44512i	−0.0314008	+	0.0543877i
$707$	−8.84388	−	15.3181i	−0.332608	−	0.576095i
$708$	−0.463491	−	0.802790i	−0.0174191	−	0.0301707i
$709$	26.9650			1.01269			0.506345	−	0.862331i	$-0.330996\pi$
$709$	26.9650			1.01269			0.506345	+	0.862331i	$0.330996\pi$
$710$	4.87224			0.182852
$711$	−6.55420	−	11.3522i	−0.245802	−	0.425741i
$712$	−14.5227	−	25.1541i	−0.544262	−	0.942689i
$713$	9.89434	−	17.1375i	0.370546	−	0.641804i
$714$	−0.232635	+	0.402936i	−0.00870616	+	0.0150795i
$715$	0.476034			0.0178027
$716$	−17.8848	+	30.9773i	−0.668385	+	1.15768i
$717$	3.85450	−	6.67619i	0.143949	−	0.249327i
$718$	5.07675	−	8.79319i	0.189463	−	0.328159i
$719$	−0.0144280	−	0.0249901i	−0.000538075	−	0.000931974i	0.865756	−	0.500466i	$-0.166838\pi$
$719$	−0.0144280	−	0.0249901i	−0.000538075	−	0.000931974i	−0.866294	+	0.499534i	$0.833505\pi$
$720$	7.80176			0.290755
$721$	8.75509	+	15.1643i	0.326057	+	0.564746i
$722$	1.09198	−	1.89136i	0.0406391	−	0.0703890i
$723$	−7.66278			−0.284982
$724$	20.1562	−	34.9115i	0.749098	−	1.29748i
$725$	−6.08075	−	10.5322i	−0.225833	−	0.391155i
$726$	2.04069	+	3.53457i	0.0757370	+	0.131180i
$727$	−49.0678			−1.81983			−0.909913	−	0.414800i	$-0.863852\pi$
$727$	−49.0678			−1.81983			−0.909913	+	0.414800i	$0.863852\pi$
$728$	1.17709	+	2.03877i	0.0436257	+	0.0755620i
$729$	−4.69064			−0.173727
$730$	−3.51881			−0.130237
$731$	1.04296	−	6.47397i	0.0385752	−	0.239448i
$732$	3.41088			0.126070
$733$	9.49167			0.350583			0.175291	−	0.984517i	$-0.443913\pi$
$733$	9.49167			0.350583			0.175291	+	0.984517i	$0.443913\pi$
$734$	8.00042	+	13.8571i	0.295301	+	0.511476i
$735$	−5.05441			−0.186435
$736$	−18.8434	−	32.6377i	−0.694577	−	1.20304i
$737$	2.23721	+	3.87496i	0.0824087	+	0.142736i
$738$	−4.80023	+	8.31424i	−0.176699	+	0.306052i
$739$	2.68129			0.0986327			0.0493164	−	0.998783i	$-0.484296\pi$
$739$	2.68129			0.0986327			0.0493164	+	0.998783i	$0.484296\pi$
$740$	11.1125	−	19.2475i	0.408505	−	0.707551i
$741$	1.55174	+	2.68768i	0.0570044	+	0.0987346i
$742$	−4.13173			−0.151681
$743$	−16.8294	−	29.1494i	−0.617412	−	1.06939i	−0.989956	−	0.141374i	$-0.954848\pi$
$743$	−16.8294	−	29.1494i	−0.617412	−	1.06939i	0.372545	−	0.928014i	$-0.378485\pi$
$744$	1.93599	−	3.35324i	0.0709770	−	0.122936i
$745$	2.35111	−	4.07224i	0.0861380	−	0.149195i
$746$	2.15014	−	3.72415i	0.0787222	−	0.136351i
$747$	18.7401			0.685665
$748$	0.320519	−	0.555156i	0.0117193	−	0.0202985i
$749$	−8.79575	+	15.2347i	−0.321390	+	0.556663i
$750$	−2.06921	−	3.58397i	−0.0755568	−	0.130868i
$751$	6.68818	+	11.5843i	0.244055	+	0.422716i	0.961866	−	0.273523i	$-0.0881888\pi$
$751$	6.68818	+	11.5843i	0.244055	+	0.422716i	−0.717810	+	0.696239i	$0.754855\pi$
$752$	15.1966			0.554163
$753$	−14.7983			−0.539280
$754$	−0.977852	−	1.69369i	−0.0356113	−	0.0616805i
$755$	−0.721024	−	1.24885i	−0.0262408	−	0.0454503i
$756$	−4.00456	+	6.93610i	−0.145644	+	0.252263i
$757$	10.2019	−	17.6702i	0.370794	−	0.642234i	−0.618894	−	0.785475i	$-0.712419\pi$
$757$	10.2019	−	17.6702i	0.370794	−	0.642234i	0.989688	+	0.143241i	$0.0457523\pi$
$758$	−13.0430			−0.473743
$759$	0.921629	−	1.59631i	0.0334530	−	0.0579423i
$760$	6.51403	−	11.2826i	0.236289	−	0.409264i
$761$	−9.41279	+	16.3034i	−0.341213	+	0.590999i	−0.984658	−	0.174493i	$-0.944171\pi$
$761$	−9.41279	+	16.3034i	−0.341213	+	0.590999i	0.643445	+	0.765492i	$0.277505\pi$
$762$	1.93382	+	3.34947i	0.0700548	+	0.121338i
$763$	8.29224			0.300199
$764$	11.0262	+	19.0980i	0.398914	+	0.690940i
$765$	1.69718	−	2.93960i	0.0613616	−	0.106281i
$766$	5.71427			0.206465
$767$	−0.372341	+	0.644913i	−0.0134444	+	0.0232865i
$768$	−0.996036	−	1.72519i	−0.0359414	−	0.0622523i
$769$	22.2328	+	38.5083i	0.801734	+	1.38864i	0.918474	+	0.395481i	$0.129422\pi$
$769$	22.2328	+	38.5083i	0.801734	+	1.38864i	−0.116740	+	0.993162i	$0.537245\pi$
$770$	0.342246			0.0123337
$771$	6.92321	+	11.9914i	0.249333	+	0.431858i
$772$	−1.93910			−0.0697898
$773$	−14.8666			−0.534715			−0.267358	−	0.963597i	$-0.586151\pi$
$773$	−14.8666			−0.534715			−0.267358	+	0.963597i	$0.586151\pi$
$774$	−1.43954	+	8.93566i	−0.0517431	+	0.321186i
$775$	−8.89160			−0.319396
$776$	18.2792			0.656186
$777$	4.14018	+	7.17100i	0.148528	+	0.257258i
$778$	−14.8119			−0.531034
$779$	−16.6782	−	28.8875i	−0.597558	−	1.03500i
$780$	0.739690	+	1.28118i	0.0264851	+	0.0458736i
$781$	1.25050	−	2.16593i	0.0447464	−	0.0775030i
$782$	−3.88461			−0.138913
$783$	7.23696	−	12.5348i	0.258628	−	0.447957i
$784$	6.28379	+	10.8838i	0.224421	+	0.388708i
$785$	26.1484			0.933277
$786$	−3.92845	−	6.80427i	−0.140123	−	0.242700i
$787$	−23.5542	+	40.7971i	−0.839618	+	1.45426i	0.0505965	+	0.998719i	$0.483888\pi$
$787$	−23.5542	+	40.7971i	−0.839618	+	1.45426i	−0.890214	+	0.455542i	$0.849446\pi$
$788$	−1.37462	+	2.38092i	−0.0489690	+	0.0848167i
$789$	7.34147	−	12.7158i	0.261363	−	0.452694i
$790$	−3.80776			−0.135474
$791$	−7.34538	+	12.7226i	−0.261172	+	0.452363i
$792$	−0.962381	+	1.66689i	−0.0341967	+	0.0592305i
$793$	−1.37005	−	2.37299i	−0.0486518	−	0.0842673i
$794$	1.66693	+	2.88720i	0.0591570	+	0.102463i
$795$	−5.64820			−0.200321
$796$	22.5834			0.800449
$797$	−6.02268	−	10.4316i	−0.213334	−	0.369506i	0.739422	−	0.673242i	$-0.235099\pi$
$797$	−6.02268	−	10.4316i	−0.213334	−	0.369506i	−0.952756	+	0.303737i	$0.901766\pi$
$798$	1.11563	+	1.93232i	0.0394927	+	0.0684034i
$799$	3.30583	−	5.72587i	0.116952	−	0.202567i
$800$	−8.46686	+	14.6650i	−0.299349	+	0.518487i
$801$	−36.2910			−1.28228
$802$	3.50181	−	6.06531i	0.123653	−	0.214173i
$803$	−0.903129	+	1.56427i	−0.0318707	+	0.0552017i
$804$	−6.95262	+	12.0423i	−0.245200	+	0.424699i
$805$	5.91249	+	10.2407i	0.208388	+	0.360938i
$806$	−1.42987			−0.0503650
$807$	−2.61543	−	4.53006i	−0.0920675	−	0.159466i
$808$	14.4478	−	25.0243i	0.508271	−	0.880352i
$809$	35.5485			1.24982			0.624909	−	0.780698i	$-0.285136\pi$
$809$	35.5485			1.24982			0.624909	+	0.780698i	$0.285136\pi$
$810$	−1.82133	+	3.15463i	−0.0639949	+	0.110842i
$811$	−6.12630	−	10.6111i	−0.215123	−	0.372605i	0.738187	−	0.674596i	$-0.235682\pi$
$811$	−6.12630	−	10.6111i	−0.215123	−	0.372605i	−0.953311	+	0.301991i	$0.902349\pi$
$812$	4.00841	+	6.94277i	0.140668	+	0.243644i
$813$	3.15124			0.110519
$814$	1.00046	+	1.73284i	0.0350660	+	0.0607362i
$815$	−26.0399			−0.912139
$816$	1.58148			0.0553629
$817$	−24.3863	−	19.8548i	−0.853168	−	0.694631i
$818$	8.53626			0.298463
$819$	2.94143			0.102782
$820$	−7.95025	−	13.7702i	−0.277635	−	0.480877i
$821$	49.2115			1.71749			0.858746	−	0.512402i	$-0.171244\pi$
$821$	49.2115			1.71749			0.858746	+	0.512402i	$0.171244\pi$
$822$	0.800008	+	1.38565i	0.0279035	+	0.0483302i
$823$	15.4875	+	26.8251i	0.539860	+	0.935066i	0.998911	+	0.0466555i	$0.0148563\pi$
$823$	15.4875	+	26.8251i	0.539860	+	0.935066i	−0.459051	+	0.888410i	$0.651810\pi$
$824$	−14.3027	+	24.7731i	−0.498259	+	0.863010i
$825$	−0.828226			−0.0288351
$826$	−0.267696	+	0.463662i	−0.00931432	+	0.0161329i
$827$	10.8126	+	18.7280i	0.375992	+	0.651238i	0.990475	−	0.137692i	$-0.0439685\pi$
$827$	10.8126	+	18.7280i	0.375992	+	0.651238i	−0.614483	+	0.788930i	$0.710635\pi$
$828$	−30.5704			−1.06240
$829$	21.6710	+	37.5353i	0.752666	+	1.30366i	0.946526	+	0.322627i	$0.104566\pi$
$829$	21.6710	+	37.5353i	0.752666	+	1.30366i	−0.193860	+	0.981029i	$0.562101\pi$
$830$	2.72184	−	4.71436i	0.0944764	−	0.163638i
$831$	−7.33416	+	12.7031i	−0.254419	+	0.440667i
$832$	0.800215	−	1.38601i	0.0277425	−	0.0480513i
$833$	5.46784			0.189449
$834$	−3.21648	+	5.57111i	−0.111378	+	0.192912i
$835$	−3.53216	+	6.11788i	−0.122235	+	0.211718i
$836$	−1.53708	−	2.66230i	−0.0531611	−	0.0920777i
$837$	−5.29114	−	9.16452i	−0.182888	−	0.316772i
$838$	1.28387			0.0443506
$839$	−20.2822			−0.700218			−0.350109	−	0.936709i	$-0.613855\pi$
$839$	−20.2822			−0.700218			−0.350109	+	0.936709i	$0.613855\pi$
$840$	1.15688	+	2.00377i	0.0399160	+	0.0691366i
$841$	7.25607	+	12.5679i	0.250209	+	0.433376i
$842$	4.05826	−	7.02911i	0.139857	−	0.242239i
$843$	8.47089	−	14.6720i	0.291753	−	0.505331i
$844$	10.3367			0.355802
$845$	−8.13830	+	14.0959i	−0.279966	+	0.484915i
$846$	−4.56286	+	7.90311i	−0.156874	+	0.271714i
$847$	−6.72008	+	11.6395i	−0.230905	+	0.399939i
$848$	7.02199	+	12.1625i	0.241136	+	0.417660i
$849$	−20.7332			−0.711561
$850$	0.872730	+	1.51161i	0.0299344	+	0.0518479i
$851$	−34.5669	+	59.8716i	−1.18494	+	2.05237i
$852$	7.77239			0.266278
$853$	22.0371	−	38.1693i	0.754535	−	1.30689i	−0.191070	−	0.981576i	$-0.561196\pi$
$853$	22.0371	−	38.1693i	0.754535	−	1.30689i	0.945605	−	0.325316i	$-0.105471\pi$
$854$	−0.984999	−	1.70607i	−0.0337060	−	0.0583805i
$855$	−8.13898	−	14.0971i	−0.278347	−	0.482112i
$856$	−28.7383			−0.982255
$857$	1.40458	+	2.43280i	0.0479795	+	0.0831029i	0.889018	−	0.457873i	$-0.151388\pi$
$857$	1.40458	+	2.43280i	0.0479795	+	0.0831029i	−0.841038	+	0.540976i	$0.818055\pi$
$858$	−0.133188			−0.00454697
$859$	−35.3762			−1.20702			−0.603509	−	0.797356i	$-0.706231\pi$
$859$	−35.3762			−1.20702			−0.603509	+	0.797356i	$0.706231\pi$
$860$	−11.6246	−	9.46449i	−0.396395	−	0.322736i
$861$	5.92402			0.201890
$862$	−15.0162			−0.511453
$863$	8.94661	+	15.4960i	0.304546	+	0.527489i	0.977160	−	0.212504i	$-0.0681619\pi$
$863$	8.94661	+	15.4960i	0.304546	+	0.527489i	−0.672614	+	0.739994i	$0.734829\pi$
$864$	−20.1536			−0.685638
$865$	−7.21328	−	12.4938i	−0.245259	−	0.424801i
$866$	−0.140690	−	0.243682i	−0.00478084	−	0.00828066i
$867$	0.344032	−	0.595881i	0.0116839	−	0.0202372i
$868$	5.86132			0.198946
$869$	−0.977292	+	1.69272i	−0.0331524	+	0.0574216i
$870$	−0.961063	−	1.66461i	−0.0325831	−	0.0564356i
$871$	11.1706			0.378502
$872$	6.77330	+	11.7317i	0.229373	+	0.397286i
$873$	11.4195	−	19.7792i	0.386493	−	0.669425i
$874$	−9.31451	+	16.1332i	−0.315068	+	0.545714i
$875$	6.81401	−	11.8022i	0.230355	−	0.398987i
$876$	−5.61334			−0.189657
$877$	26.4607	−	45.8312i	0.893513	−	1.54761i	0.0578798	−	0.998324i	$-0.481566\pi$
$877$	26.4607	−	45.8312i	0.893513	−	1.54761i	0.835634	−	0.549287i	$-0.185101\pi$
$878$	6.03712	−	10.4566i	0.203743	−	0.352893i
$879$	5.94852	+	10.3031i	0.200639	+	0.347516i
$880$	−0.581658	−	1.00746i	−0.0196077	−	0.0339615i
$881$	8.30633			0.279847			0.139924	−	0.990162i	$-0.455314\pi$
$881$	8.30633			0.279847			0.139924	+	0.990162i	$0.455314\pi$
$882$	−7.54696			−0.254119
$883$	−8.18909	−	14.1839i	−0.275585	−	0.477327i	0.694698	−	0.719302i	$-0.255538\pi$
$883$	−8.18909	−	14.1839i	−0.275585	−	0.477327i	−0.970283	+	0.241975i	$0.922205\pi$
$884$	−0.800193	−	1.38597i	−0.0269134	−	0.0466154i
$885$	−0.365948	+	0.633840i	−0.0123012	+	0.0213063i
$886$	8.27509	−	14.3329i	0.278007	−	0.481523i
$887$	7.06099			0.237085			0.118542	−	0.992949i	$-0.462178\pi$
$887$	7.06099			0.237085			0.118542	+	0.992949i	$0.462178\pi$
$888$	−6.76359	+	11.7149i	−0.226971	+	0.393126i
$889$	−6.36816	+	11.0300i	−0.213581	+	0.369933i
$890$	−5.27095	+	9.12955i	−0.176683	+	0.306023i
$891$	0.934915	+	1.61932i	0.0313208	+	0.0542493i
$892$	30.0008			1.00450
$893$	−15.8535	−	27.4590i	−0.530516	−	0.918880i
$894$	−0.657810	+	1.13936i	−0.0220005	+	0.0381059i
$895$	28.2417			0.944017
$896$	7.13555	−	12.3591i	0.238382	−	0.412890i
$897$	−2.30090	−	3.98527i	−0.0768247	−	0.133064i
$898$	5.18859	+	8.98690i	0.173145	+	0.299897i
$899$	−10.5925			−0.353278
$900$	6.86807	+	11.8958i	0.228936	+	0.396528i
$901$	6.11019			0.203560
$902$	1.43152			0.0476643
$903$	5.21923	−	1.98763i	0.173685	−	0.0661442i
$904$	−23.9995			−0.798213
$905$	−31.8285			−1.05801
$906$	0.201733	+	0.349412i	0.00670214	+	0.0116084i
$907$	14.2998			0.474817			0.237409	−	0.971410i	$-0.423702\pi$
$907$	14.2998			0.474817			0.237409	+	0.971410i	$0.423702\pi$
$908$	−3.43332	−	5.94669i	−0.113939	−	0.197348i
$909$	−18.0519	−	31.2667i	−0.598743	−	1.03705i
$910$	0.427218	−	0.739963i	0.0141621	−	0.0245295i
$911$	−43.3383			−1.43586			−0.717931	−	0.696114i	$-0.754911\pi$
$911$	−43.3383			−1.43586			−0.717931	+	0.696114i	$0.754911\pi$
$912$	3.79208	−	6.56807i	0.125568	−	0.217490i
$913$	−1.39716	−	2.41995i	−0.0462393	−	0.0800888i
$914$	1.45369			0.0480839
$915$	−1.34652	−	2.33225i	−0.0445147	−	0.0771017i
$916$	13.2951	−	23.0277i	0.439281	−	0.760858i
$917$	12.9366	−	22.4068i	0.427203	−	0.739938i
$918$	−1.03867	+	1.79904i	−0.0342813	+	0.0593770i
$919$	−11.3446			−0.374225			−0.187112	−	0.982339i	$-0.559913\pi$
$919$	−11.3446			−0.374225			−0.187112	+	0.982339i	$0.559913\pi$
$920$	−9.65892	+	16.7297i	−0.318445	+	0.551563i
$921$	−4.22454	+	7.31712i	−0.139203	+	0.241107i
$922$	−3.21142	−	5.56235i	−0.105763	−	0.183186i
$923$	−3.12193	−	5.40735i	−0.102760	−	0.177985i
$924$	0.545965			0.0179609
$925$	31.0637			1.02137
$926$	5.11428	+	8.85819i	0.168066	+	0.291098i
$927$	17.8706	+	30.9528i	0.586948	+	1.01662i
$928$	−10.0865	+	17.4703i	−0.331105	+	0.573490i
$929$	−14.1496	+	24.5079i	−0.464234	+	0.804077i	−0.999167	−	0.0408176i	$-0.987004\pi$
$929$	−14.1496	+	24.5079i	−0.464234	+	0.804077i	0.534932	+	0.844895i	$0.320337\pi$
$930$	−1.40532			−0.0460822
$931$	13.1108	−	22.7086i	0.429689	−	0.744243i
$932$	−12.7141	+	22.0214i	−0.416464	+	0.721336i
$933$	2.74461	−	4.75380i	0.0898544	−	0.155632i
$934$	−5.40357	−	9.35926i	−0.176810	−	0.306244i
$935$	−0.506130			−0.0165522
$936$	2.40263	+	4.16148i	0.0785326	+	0.136022i
$937$	−8.40604	+	14.5597i	−0.274613	+	0.475644i	−0.970038	−	0.242955i	$-0.921883\pi$
$937$	−8.40604	+	14.5597i	−0.274613	+	0.475644i	0.695424	+	0.718600i	$0.255217\pi$
$938$	8.03116			0.262227
$939$	−5.15008	+	8.92021i	−0.168067	+	0.291100i
$940$	−7.55711	−	13.0893i	−0.246486	−	0.426926i
$941$	17.1005	+	29.6190i	0.557461	+	0.965552i	0.997707	+	0.0676744i	$0.0215579\pi$
$941$	17.1005	+	29.6190i	0.557461	+	0.965552i	−0.440246	+	0.897877i	$0.645109\pi$
$942$	−7.31598			−0.238368
$943$	24.7302	+	42.8340i	0.805327	+	1.39487i
$944$	1.81983			0.0592303
$945$	6.32357			0.205706
$946$	1.26121	−	0.480304i	0.0410054	−	0.0156160i
$947$	−7.51284			−0.244134			−0.122067	−	0.992522i	$-0.538952\pi$
$947$	−7.51284			−0.244134			−0.122067	+	0.992522i	$0.538952\pi$
$948$	−6.07430			−0.197284
$949$	2.25471	+	3.90527i	0.0731909	+	0.126770i
$950$	8.37053			0.271576
$951$	8.24481	+	14.2804i	0.267356	+	0.463075i
$952$	−1.25150	−	2.16767i	−0.0405615	−	0.0702545i
$953$	23.8770	−	41.3561i	0.773451	−	1.33966i	−0.162210	−	0.986756i	$-0.551862\pi$
$953$	23.8770	−	41.3561i	0.773451	−	1.33966i	0.935661	−	0.352900i	$-0.114805\pi$
$954$	−8.43356			−0.273047
$955$	8.70571	−	15.0787i	0.281710	−	0.487936i
$956$	9.53208	+	16.5100i	0.308289	+	0.533973i
$957$	−0.986657			−0.0318941
$958$	6.50933	+	11.2745i	0.210307	+	0.364262i
$959$	−2.63447	+	4.56303i	−0.0850713	+	0.147348i
$960$	0.786475	−	1.36222i	0.0253834	−	0.0439653i
$961$	11.6278	−	20.1399i	0.375090	−	0.649674i
$962$	4.99539			0.161058
$963$	−17.9536	+	31.0966i	−0.578547	+	1.00207i
$964$	9.47493	−	16.4111i	0.305167	−	0.528565i
$965$	0.765506	+	1.32590i	0.0246425	+	0.0426821i
$966$	−1.65424	−	2.86522i	−0.0532242	−	0.0921870i
$967$	−6.16763			−0.198338			−0.0991689	−	0.995071i	$-0.531618\pi$
$967$	−6.16763			−0.198338			−0.0991689	+	0.995071i	$0.531618\pi$
$968$	−21.9565			−0.705709
$969$	−1.64984	−	2.85760i	−0.0530005	−	0.0917995i
$970$	−3.31718	−	5.74552i	−0.106508	−	0.184477i
$971$	−12.3364	+	21.3672i	−0.395893	+	0.685706i	−0.993215	−	0.116295i	$-0.962898\pi$
$971$	−12.3364	+	21.3672i	−0.395893	+	0.685706i	0.597322	+	0.802002i	$0.296231\pi$
$972$	−12.6111	+	21.8430i	−0.404501	+	0.700616i
$973$	−21.1841			−0.679130
$974$	7.38637	−	12.7936i	0.236675	−	0.409933i
$975$	−1.03386	+	1.79069i	−0.0331099	+	0.0573480i
$976$	−3.34807	+	5.79903i	−0.107169	+	0.185622i
$977$	−11.2066	−	19.4104i	−0.358531	−	0.620994i	0.629184	−	0.777256i	$-0.283389\pi$
$977$	−11.2066	−	19.4104i	−0.358531	−	0.620994i	−0.987716	+	0.156262i	$0.950056\pi$
$978$	7.28563			0.232969
$979$	2.70566	+	4.68634i	0.0864732	+	0.149776i
$980$	6.24972	−	10.8248i	0.199640	−	0.345787i
$981$	16.9259			0.540402
$982$	7.42184	−	12.8550i	0.236840	−	0.410219i
$983$	−7.72775	−	13.3849i	−0.246477	−	0.426911i	0.716069	−	0.698030i	$-0.245940\pi$
$983$	−7.72775	−	13.3849i	−0.246477	−	0.426911i	−0.962546	+	0.271119i	$0.912606\pi$
$984$	4.83888	+	8.38119i	0.154258	+	0.267183i
$985$	2.17066			0.0691630
$986$	1.03967	+	1.80077i	0.0331100	+	0.0573481i
$987$	5.63108			0.179239
$988$	−7.67481			−0.244168
$989$	36.1597	+	29.4405i	1.14981	+	0.936152i
$990$	0.698583			0.0222024
$991$	−17.1022			−0.543268			−0.271634	−	0.962401i	$-0.587564\pi$
$991$	−17.1022			−0.543268			−0.271634	+	0.962401i	$0.587564\pi$
$992$	7.37450	+	12.7730i	0.234141	+	0.405543i
$993$	2.43816			0.0773728
$994$	−2.24452	−	3.88763i	−0.0711920	−	0.123308i
$995$	−8.91534	−	15.4418i	−0.282635	−	0.489538i
$996$	4.34198	−	7.52054i	0.137581	−	0.238297i
$997$	0.563709			0.0178529			0.00892643	−	0.999960i	$-0.497159\pi$
$997$	0.563709			0.0178529			0.00892643	+	0.999960i	$0.497159\pi$
$998$	8.88358	−	15.3868i	0.281205	−	0.487061i
$999$	18.4851	+	32.0172i	0.584844	+	1.01298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.13	yes	58
43.6	even	3	inner	731.2.e.a.307.13	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.13	✓	58	43.6	even	3	inner
731.2.e.a.681.13	yes	58	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.546292 q^{2} +(0.344032 + 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 + 1.16347i) q^{5} +(-0.187942 - 0.325525i) q^{6} +(0.618902 - 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 - 2.18807i) q^{9} +O(q^{10})\)	\(q-0.546292 q^{2} +(0.344032 + 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 + 1.16347i) q^{5} +(-0.187942 - 0.325525i) q^{6} +(0.618902 - 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 - 2.18807i) q^{9} +(-0.366962 - 0.635597i) q^{10} -0.376735 q^{11} +(-0.585392 - 1.01393i) q^{12} +(-0.470269 + 0.814530i) q^{13} +(-0.338101 + 0.585609i) q^{14} +(-0.462195 + 0.800545i) q^{15} +2.29845 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.690122 + 1.19533i) q^{18} +(-2.39780 - 4.15311i) q^{19} +(-1.14300 - 1.97973i) q^{20} +0.851688 q^{21} +0.205807 q^{22} +(3.55543 + 6.15818i) q^{23} +(0.695679 + 1.20495i) q^{24} +(1.59755 - 2.76704i) q^{25} +(0.256904 - 0.444971i) q^{26} +3.80263 q^{27} +(-1.05310 + 1.82403i) q^{28} +(1.90315 - 3.29634i) q^{29} +(0.252493 - 0.437331i) q^{30} +(-1.39144 - 2.41005i) q^{31} -5.29990 q^{32} +(-0.129609 - 0.224489i) q^{33} +(-0.273146 + 0.473103i) q^{34} +1.66295 q^{35} +(-2.14956 + 3.72315i) q^{36} +(4.86114 + 8.41974i) q^{37} +(1.30990 + 2.26881i) q^{38} -0.647150 q^{39} +(1.35833 + 2.35270i) q^{40} +6.95562 q^{41} -0.465271 q^{42} +(6.12810 - 2.33375i) q^{43} +0.641038 q^{44} +3.39436 q^{45} +(-1.94230 - 3.36417i) q^{46} +6.61167 q^{47} +(0.790741 + 1.36960i) q^{48} +(2.73392 + 4.73529i) q^{49} +(-0.872730 + 1.51161i) q^{50} +0.688064 q^{51} +(0.800193 - 1.38597i) q^{52} +(3.05510 + 5.29158i) q^{53} -2.07735 q^{54} +(-0.253065 - 0.438321i) q^{55} +(1.25150 - 2.16767i) q^{56} +(1.64984 - 2.85760i) q^{57} +(-1.03967 + 1.80077i) q^{58} +0.791761 q^{59} +(0.786454 - 1.36218i) q^{60} +(-1.45666 + 2.52301i) q^{61} +(0.760134 + 1.31659i) q^{62} +(-1.56370 - 2.70840i) q^{63} -1.70161 q^{64} -1.26358 q^{65} +(0.0708042 + 0.122637i) q^{66} +(-5.93843 - 10.2857i) q^{67} +(-0.850782 + 1.47360i) q^{68} +(-2.44636 + 4.23722i) q^{69} -0.908454 q^{70} +(-3.31931 + 5.74921i) q^{71} +(2.55453 - 4.42458i) q^{72} +(2.39725 - 4.15217i) q^{73} +(-2.65560 - 4.59964i) q^{74} +2.19843 q^{75} +(4.08001 + 7.06679i) q^{76} +(-0.233162 + 0.403848i) q^{77} +0.353533 q^{78} +(2.59411 - 4.49313i) q^{79} +(1.54394 + 2.67419i) q^{80} +(-2.48163 - 4.29830i) q^{81} -3.79980 q^{82} +(3.70861 + 6.42350i) q^{83} -1.44920 q^{84} +1.34346 q^{85} +(-3.34773 + 1.27491i) q^{86} +2.61897 q^{87} -0.761809 q^{88} +(-7.18187 - 12.4394i) q^{89} -1.85431 q^{90} +(0.582101 + 1.00823i) q^{91} +(-6.04979 - 10.4785i) q^{92} +(0.957400 - 1.65827i) q^{93} -3.61190 q^{94} +(3.22136 - 5.57956i) q^{95} +(-1.82333 - 3.15811i) q^{96} +9.03956 q^{97} +(-1.49352 - 2.58685i) q^{98} +(-0.475923 + 0.824323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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