LMFDB - Embedded newform 1338.2.e.h.931.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-14,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 21 x^{12} - 26 x^{11} + 217 x^{10} - 335 x^{9} + 1058 x^{8} - 1539 x^{7} + 3657 x^{6} + \cdots + 64 $ x^14 - 3x^13 + 21x^12 - 26x^11 + 217x^10 - 335x^9 + 1058x^8 - 1539x^7 + 3657x^6 - 4850x^5 + 6077x^4 - 4079x^3 + 2145x^2 - 424*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			931.5
Root			$-1.35878 - 2.35347i$ of defining polynomial
Character	$\chi$	$=$	1338.931
Dual form			1338.2.e.h.1075.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.158723 + 0.274916i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.33321 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.158723 - 0.274916i) q^{10} +(1.24487 + 2.15618i) q^{11} +(-0.500000 + 0.866025i) q^{12} +6.11204 q^{13} -3.33321 q^{14} -0.317445 q^{15} +1.00000 q^{16} +0.481807 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.81125 + 6.60128i) q^{19} +(0.158723 + 0.274916i) q^{20} +(-1.66660 + 2.88664i) q^{21} +(-1.24487 - 2.15618i) q^{22} +(-1.21640 + 2.10687i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.44961 - 4.24286i) q^{25} -6.11204 q^{26} +1.00000 q^{27} +3.33321 q^{28} +(-5.17524 - 8.96378i) q^{29} +0.317445 q^{30} +(3.61153 - 6.25535i) q^{31} -1.00000 q^{32} -2.48974 q^{33} -0.481807 q^{34} +(0.529055 + 0.916351i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.06556 + 3.57765i) q^{37} +(3.81125 - 6.60128i) q^{38} +(-3.05602 + 5.29318i) q^{39} +(-0.158723 - 0.274916i) q^{40} +11.4607 q^{41} +(1.66660 - 2.88664i) q^{42} +(1.13846 - 1.97188i) q^{43} +(1.24487 + 2.15618i) q^{44} +(0.158723 - 0.274916i) q^{45} +(1.21640 - 2.10687i) q^{46} +(0.338188 + 0.585760i) q^{47} +(-0.500000 + 0.866025i) q^{48} +4.11026 q^{49} +(-2.44961 + 4.24286i) q^{50} +(-0.240904 + 0.417257i) q^{51} +6.11204 q^{52} +(3.03581 + 5.25818i) q^{53} -1.00000 q^{54} +(-0.395178 + 0.684469i) q^{55} -3.33321 q^{56} +(-3.81125 - 6.60128i) q^{57} +(5.17524 + 8.96378i) q^{58} -10.4971 q^{59} -0.317445 q^{60} +(-4.31593 + 7.47540i) q^{61} +(-3.61153 + 6.25535i) q^{62} +(-1.66660 - 2.88664i) q^{63} +1.00000 q^{64} +(0.970120 + 1.68030i) q^{65} +2.48974 q^{66} +(2.08306 - 3.60796i) q^{67} +0.481807 q^{68} +(-1.21640 - 2.10687i) q^{69} +(-0.529055 - 0.916351i) q^{70} +(-0.623014 + 1.07909i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-2.95216 - 5.11330i) q^{73} +(-2.06556 - 3.57765i) q^{74} +(2.44961 + 4.24286i) q^{75} +(-3.81125 + 6.60128i) q^{76} +(4.14941 + 7.18698i) q^{77} +(3.05602 - 5.29318i) q^{78} +(4.00598 + 6.93857i) q^{79} +(0.158723 + 0.274916i) q^{80} +(-0.500000 + 0.866025i) q^{81} -11.4607 q^{82} +(-0.899848 - 1.55858i) q^{83} +(-1.66660 + 2.88664i) q^{84} +(0.0764738 + 0.132456i) q^{85} +(-1.13846 + 1.97188i) q^{86} +10.3505 q^{87} +(-1.24487 - 2.15618i) q^{88} +(-5.53862 + 9.59317i) q^{89} +(-0.158723 + 0.274916i) q^{90} +20.3727 q^{91} +(-1.21640 + 2.10687i) q^{92} +(3.61153 + 6.25535i) q^{93} +(-0.338188 - 0.585760i) q^{94} -2.41973 q^{95} +(0.500000 - 0.866025i) q^{96} +(-0.704230 - 1.21976i) q^{97} -4.11026 q^{98} +(1.24487 - 2.15618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) $ 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.158723	+	0.274916i	0.0709830	+	0.122946i	0.899332	−	0.437266i	$-0.144053\pi$
$5$	0.158723	+	0.274916i	0.0709830	+	0.122946i	−0.828349	+	0.560212i	$0.810720\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	3.33321			1.25983			0.629917	−	0.776663i	$-0.283089\pi$
$7$	3.33321			1.25983			0.629917	+	0.776663i	$0.283089\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.158723	−	0.274916i	−0.0501925	−	0.0869360i
$11$	1.24487	+	2.15618i	0.375342	+	0.650112i	0.990378	−	0.138387i	$-0.0441918\pi$
$11$	1.24487	+	2.15618i	0.375342	+	0.650112i	−0.615036	+	0.788499i	$0.710858\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	6.11204			1.69518			0.847588	−	0.530655i	$-0.178054\pi$
$13$	6.11204			1.69518			0.847588	+	0.530655i	$0.178054\pi$
$14$	−3.33321			−0.890837
$15$	−0.317445			−0.0819641
$16$	1.00000			0.250000
$17$	0.481807			0.116855			0.0584277	−	0.998292i	$-0.481391\pi$
$17$	0.481807			0.116855			0.0584277	+	0.998292i	$0.481391\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.81125	+	6.60128i	−0.874361	+	1.51444i	−0.0169197	+	0.999857i	$0.505386\pi$
$19$	−3.81125	+	6.60128i	−0.874361	+	1.51444i	−0.857442	+	0.514581i	$0.827947\pi$
$20$	0.158723	+	0.274916i	0.0354915	+	0.0614731i
$21$	−1.66660	+	2.88664i	−0.363682	+	0.629917i
$22$	−1.24487	−	2.15618i	−0.265407	−	0.459699i
$23$	−1.21640	+	2.10687i	−0.253637	+	0.439312i	−0.964524	−	0.263994i	$-0.914960\pi$
$23$	−1.21640	+	2.10687i	−0.253637	+	0.439312i	0.710887	+	0.703306i	$0.248294\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.44961	−	4.24286i	0.489923	−	0.848571i
$26$	−6.11204			−1.19867
$27$	1.00000			0.192450
$28$	3.33321			0.629917
$29$	−5.17524	−	8.96378i	−0.961018	−	1.66453i	−0.719953	−	0.694022i	$-0.755837\pi$
$29$	−5.17524	−	8.96378i	−0.961018	−	1.66453i	−0.241064	−	0.970509i	$-0.577496\pi$
$30$	0.317445			0.0579574
$31$	3.61153	−	6.25535i	0.648650	−	1.12349i	−0.334796	−	0.942291i	$-0.608667\pi$
$31$	3.61153	−	6.25535i	0.648650	−	1.12349i	0.983446	−	0.181203i	$-0.0579992\pi$
$32$	−1.00000			−0.176777
$33$	−2.48974			−0.433408
$34$	−0.481807			−0.0826292
$35$	0.529055	+	0.916351i	0.0894267	+	0.154892i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.06556	+	3.57765i	0.339576	+	0.588162i	0.984353	−	0.176208i	$-0.0563832\pi$
$37$	2.06556	+	3.57765i	0.339576	+	0.588162i	−0.644777	+	0.764371i	$0.723050\pi$
$38$	3.81125	−	6.60128i	0.618267	−	1.07087i
$39$	−3.05602	+	5.29318i	−0.489355	+	0.847588i
$40$	−0.158723	−	0.274916i	−0.0250963	−	0.0434680i
$41$	11.4607			1.78987			0.894933	−	0.446201i	$-0.147223\pi$
$41$	11.4607			1.78987			0.894933	+	0.446201i	$0.147223\pi$
$42$	1.66660	−	2.88664i	0.257162	−	0.445418i
$43$	1.13846	−	1.97188i	0.173614	−	0.300708i	−0.766067	−	0.642761i	$-0.777789\pi$
$43$	1.13846	−	1.97188i	0.173614	−	0.300708i	0.939681	+	0.342053i	$0.111122\pi$
$44$	1.24487	+	2.15618i	0.187671	+	0.325056i
$45$	0.158723	−	0.274916i	0.0236610	−	0.0409820i
$46$	1.21640	−	2.10687i	0.179349	−	0.310641i
$47$	0.338188	+	0.585760i	0.0493299	+	0.0854418i	0.889636	−	0.456670i	$-0.150958\pi$
$47$	0.338188	+	0.585760i	0.0493299	+	0.0854418i	−0.840306	+	0.542112i	$0.817625\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	4.11026			0.587179
$50$	−2.44961	+	4.24286i	−0.346428	+	0.600030i
$51$	−0.240904	+	0.417257i	−0.0337332	+	0.0584277i
$52$	6.11204			0.847588
$53$	3.03581	+	5.25818i	0.417001	+	0.722266i	0.995636	−	0.0933200i	$-0.0297480\pi$
$53$	3.03581	+	5.25818i	0.417001	+	0.722266i	−0.578636	+	0.815586i	$0.696415\pi$
$54$	−1.00000			−0.136083
$55$	−0.395178	+	0.684469i	−0.0532858	+	0.0922938i
$56$	−3.33321			−0.445418
$57$	−3.81125	−	6.60128i	−0.504813	−	0.874361i
$58$	5.17524	+	8.96378i	0.679542	+	1.17700i
$59$	−10.4971			−1.36661			−0.683306	−	0.730132i	$-0.739459\pi$
$59$	−10.4971			−1.36661			−0.683306	+	0.730132i	$0.739459\pi$
$60$	−0.317445			−0.0409820
$61$	−4.31593	+	7.47540i	−0.552598	+	0.957127i	0.445488	+	0.895288i	$0.353030\pi$
$61$	−4.31593	+	7.47540i	−0.552598	+	0.957127i	−0.998086	+	0.0618396i	$0.980303\pi$
$62$	−3.61153	+	6.25535i	−0.458664	+	0.794430i
$63$	−1.66660	−	2.88664i	−0.209972	−	0.363682i
$64$	1.00000			0.125000
$65$	0.970120	+	1.68030i	0.120329	+	0.208415i
$66$	2.48974			0.306466
$67$	2.08306	−	3.60796i	0.254486	−	0.440783i	−0.710270	−	0.703930i	$-0.751427\pi$
$67$	2.08306	−	3.60796i	0.254486	−	0.440783i	0.964756	+	0.263147i	$0.0847604\pi$
$68$	0.481807			0.0584277
$69$	−1.21640	−	2.10687i	−0.146437	−	0.253637i
$70$	−0.529055	−	0.916351i	−0.0632342	−	0.109525i
$71$	−0.623014	+	1.07909i	−0.0739382	+	0.128065i	−0.900624	−	0.434599i	$-0.856890\pi$
$71$	−0.623014	+	1.07909i	−0.0739382	+	0.128065i	0.826686	+	0.562664i	$0.190223\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−2.95216	−	5.11330i	−0.345525	−	0.598466i	0.639924	−	0.768438i	$-0.278966\pi$
$73$	−2.95216	−	5.11330i	−0.345525	−	0.598466i	−0.985449	+	0.169972i	$0.945632\pi$
$74$	−2.06556	−	3.57765i	−0.240116	−	0.415894i
$75$	2.44961	+	4.24286i	0.282857	+	0.489923i
$76$	−3.81125	+	6.60128i	−0.437181	+	0.757219i
$77$	4.14941	+	7.18698i	0.472869	+	0.819033i
$78$	3.05602	−	5.29318i	0.346026	−	0.599335i
$79$	4.00598	+	6.93857i	0.450708	+	0.780650i	0.998430	−	0.0560106i	$-0.0178381\pi$
$79$	4.00598	+	6.93857i	0.450708	+	0.780650i	−0.547722	+	0.836661i	$0.684505\pi$
$80$	0.158723	+	0.274916i	0.0177457	+	0.0307365i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−11.4607			−1.26563
$83$	−0.899848	−	1.55858i	−0.0987712	−	0.171077i	0.812405	−	0.583093i	$-0.198158\pi$
$83$	−0.899848	−	1.55858i	−0.0987712	−	0.171077i	−0.911176	+	0.412017i	$0.864825\pi$
$84$	−1.66660	+	2.88664i	−0.181841	+	0.314958i
$85$	0.0764738	+	0.132456i	0.00829474	+	0.0143669i
$86$	−1.13846	+	1.97188i	−0.122764	+	0.212633i
$87$	10.3505			1.10969
$88$	−1.24487	−	2.15618i	−0.132704	−	0.229849i
$89$	−5.53862	+	9.59317i	−0.587093	+	1.01687i	0.407518	+	0.913197i	$0.366394\pi$
$89$	−5.53862	+	9.59317i	−0.587093	+	1.01687i	−0.994611	+	0.103677i	$0.966939\pi$
$90$	−0.158723	+	0.274916i	−0.0167308	+	0.0289787i
$91$	20.3727			2.13564
$92$	−1.21640	+	2.10687i	−0.126819	+	0.219656i
$93$	3.61153	+	6.25535i	0.374498	+	0.648650i
$94$	−0.338188	−	0.585760i	−0.0348815	−	0.0604165i
$95$	−2.41973			−0.248259
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−0.704230	−	1.21976i	−0.0715037	−	0.123848i	0.828057	−	0.560644i	$-0.189446\pi$
$97$	−0.704230	−	1.21976i	−0.0715037	−	0.123848i	−0.899561	+	0.436796i	$0.856113\pi$
$98$	−4.11026			−0.415199
$99$	1.24487	−	2.15618i	0.125114	−	0.216704i
$100$	2.44961	−	4.24286i	0.244961	−	0.424286i
$101$	3.32729	−	5.76303i	0.331078	−	0.573443i	−0.651646	−	0.758523i	$-0.725921\pi$
$101$	3.32729	−	5.76303i	0.331078	−	0.573443i	0.982723	+	0.185080i	$0.0592545\pi$
$102$	0.240904	−	0.417257i	0.0238530	−	0.0413146i
$103$	1.36349			0.134349			0.0671744	−	0.997741i	$-0.478602\pi$
$103$	1.36349			0.134349			0.0671744	+	0.997741i	$0.478602\pi$
$104$	−6.11204			−0.599335
$105$	−1.05811			−0.103261
$106$	−3.03581	−	5.25818i	−0.294864	−	0.510719i
$107$	7.47456	+	12.9463i	0.722593	+	1.25157i	0.959957	+	0.280148i	$0.0903834\pi$
$107$	7.47456	+	12.9463i	0.722593	+	1.25157i	−0.237364	+	0.971421i	$0.576283\pi$
$108$	1.00000			0.0962250
$109$	6.24230	+	10.8120i	0.597903	+	1.03560i	0.993130	+	0.117016i	$0.0373327\pi$
$109$	6.24230	+	10.8120i	0.597903	+	1.03560i	−0.395227	+	0.918584i	$0.629334\pi$
$110$	0.395178	−	0.684469i	0.0376788	−	0.0652616i
$111$	−4.13112			−0.392108
$112$	3.33321			0.314958
$113$	−0.514881	+	0.891800i	−0.0484359	+	0.0838935i	−0.889227	−	0.457466i	$-0.848757\pi$
$113$	−0.514881	+	0.891800i	−0.0484359	+	0.0838935i	0.840791	+	0.541360i	$0.182090\pi$
$114$	3.81125	+	6.60128i	0.356957	+	0.618267i
$115$	−0.772282			−0.0720157
$116$	−5.17524	−	8.96378i	−0.480509	−	0.832266i
$117$	−3.05602	−	5.29318i	−0.282529	−	0.489355i
$118$	10.4971			0.966341
$119$	1.60596			0.147218
$120$	0.317445			0.0289787
$121$	2.40060	−	4.15796i	0.218236	−	0.377996i
$122$	4.31593	−	7.47540i	0.390746	−	0.676791i
$123$	−5.73037	+	9.92529i	−0.516690	+	0.894933i
$124$	3.61153	−	6.25535i	0.324325	−	0.561747i
$125$	3.14247			0.281071
$126$	1.66660	+	2.88664i	0.148473	+	0.257162i
$127$	−3.07874	+	5.33254i	−0.273194	+	0.473186i	−0.969678	−	0.244386i	$-0.921414\pi$
$127$	−3.07874	+	5.33254i	−0.273194	+	0.473186i	0.696484	+	0.717573i	$0.254747\pi$
$128$	−1.00000			−0.0883883
$129$	1.13846	+	1.97188i	0.100236	+	0.173614i
$130$	−0.970120	−	1.68030i	−0.0850852	−	0.147372i
$131$	−5.59778	+	9.69565i	−0.489081	+	0.847112i	−0.999921	−	0.0125631i	$-0.996001\pi$
$131$	−5.59778	+	9.69565i	−0.489081	+	0.847112i	0.510840	+	0.859676i	$0.329334\pi$
$132$	−2.48974			−0.216704
$133$	−12.7037	+	22.0034i	−1.10155	+	1.90794i
$134$	−2.08306	+	3.60796i	−0.179949	+	0.311681i
$135$	0.158723	+	0.274916i	0.0136607	+	0.0236610i
$136$	−0.481807			−0.0413146
$137$	3.93682	−	6.81877i	0.336345	−	0.582567i	−0.647397	−	0.762153i	$-0.724143\pi$
$137$	3.93682	−	6.81877i	0.336345	−	0.582567i	0.983742	+	0.179586i	$0.0574759\pi$
$138$	1.21640	+	2.10687i	0.103547	+	0.179349i
$139$	−2.32804	+	4.03228i	−0.197461	+	0.342013i	−0.947705	−	0.319149i	$-0.896603\pi$
$139$	−2.32804	+	4.03228i	−0.197461	+	0.342013i	0.750243	+	0.661162i	$0.229936\pi$
$140$	0.529055	+	0.916351i	0.0447133	+	0.0774458i
$141$	−0.676377			−0.0569612
$142$	0.623014	−	1.07909i	0.0522822	−	0.0905554i
$143$	7.60870	+	13.1787i	0.636271	+	1.10205i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.64286	−	2.84551i	0.136432	−	0.236307i
$146$	2.95216	+	5.11330i	0.244323	+	0.423180i
$147$	−2.05513	+	3.55959i	−0.169504	+	0.293590i
$148$	2.06556	+	3.57765i	0.169788	+	0.294081i
$149$	7.18795	+	12.4499i	0.588860	+	1.01993i	0.994382	+	0.105850i	$0.0337563\pi$
$149$	7.18795	+	12.4499i	0.588860	+	1.01993i	−0.405522	+	0.914085i	$0.632910\pi$
$150$	−2.44961	−	4.24286i	−0.200010	−	0.346428i
$151$	2.67314	+	4.63001i	0.217537	+	0.376785i	0.954054	−	0.299634i	$-0.0968644\pi$
$151$	2.67314	+	4.63001i	0.217537	+	0.376785i	−0.736517	+	0.676419i	$0.763531\pi$
$152$	3.81125	−	6.60128i	0.309133	−	0.535435i
$153$	−0.240904	−	0.417257i	−0.0194759	−	0.0337332i
$154$	−4.14941	−	7.18698i	−0.334369	−	0.579144i
$155$	2.29293			0.184172
$156$	−3.05602	+	5.29318i	−0.244677	+	0.423794i
$157$	−21.2688			−1.69744			−0.848719	−	0.528844i	$-0.822626\pi$
$157$	−21.2688			−1.69744			−0.848719	+	0.528844i	$0.822626\pi$
$158$	−4.00598	−	6.93857i	−0.318699	−	0.552003i
$159$	−6.07162			−0.481511
$160$	−0.158723	−	0.274916i	−0.0125481	−	0.0217340i
$161$	−4.05451	+	7.02262i	−0.319540	+	0.553460i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	13.3427			1.04508			0.522539	−	0.852616i	$-0.324985\pi$
$163$	13.3427			1.04508			0.522539	+	0.852616i	$0.324985\pi$
$164$	11.4607			0.894933
$165$	−0.395178	−	0.684469i	−0.0307646	−	0.0532858i
$166$	0.899848	+	1.55858i	0.0698418	+	0.120969i
$167$	2.05239			0.158819			0.0794093	−	0.996842i	$-0.474697\pi$
$167$	2.05239			0.158819			0.0794093	+	0.996842i	$0.474697\pi$
$168$	1.66660	−	2.88664i	0.128581	−	0.222709i
$169$	24.3571			1.87362
$170$	−0.0764738	−	0.132456i	−0.00586527	−	0.0101589i
$171$	7.62251			0.582908
$172$	1.13846	−	1.97188i	0.0868070	−	0.150354i
$173$	−0.748011	+	1.29559i	−0.0568702	+	0.0985021i	−0.893059	−	0.449940i	$-0.851445\pi$
$173$	−0.748011	+	1.29559i	−0.0568702	+	0.0985021i	0.836189	+	0.548442i	$0.184779\pi$
$174$	−10.3505			−0.784668
$175$	8.16507	−	14.1423i	0.617221	−	1.06906i
$176$	1.24487	+	2.15618i	0.0938356	+	0.162528i
$177$	5.24857	−	9.09080i	0.394507	−	0.683306i
$178$	5.53862	−	9.59317i	0.415137	−	0.719039i
$179$	−12.1097	−	20.9746i	−0.905121	−	1.56772i	−0.820755	−	0.571281i	$-0.806447\pi$
$179$	−12.1097	−	20.9746i	−0.905121	−	1.56772i	−0.0843666	−	0.996435i	$-0.526887\pi$
$180$	0.158723	−	0.274916i	0.0118305	−	0.0204910i
$181$	1.69523	−	2.93622i	0.126005	−	0.218247i	−0.796120	−	0.605138i	$-0.793118\pi$
$181$	1.69523	−	2.93622i	0.126005	−	0.218247i	0.922125	+	0.386891i	$0.126451\pi$
$182$	−20.3727			−1.51012
$183$	−4.31593	−	7.47540i	−0.319042	−	0.552598i
$184$	1.21640	−	2.10687i	0.0896743	−	0.155320i
$185$	−0.655702	+	1.13571i	−0.0482082	+	0.0834990i
$186$	−3.61153	−	6.25535i	−0.264810	−	0.458664i
$187$	0.599787	+	1.03886i	0.0438608	+	0.0759691i
$188$	0.338188	+	0.585760i	0.0246649	+	0.0427209i
$189$	3.33321			0.242455
$190$	2.41973			0.175546
$191$	8.72580			0.631377			0.315688	−	0.948863i	$-0.397765\pi$
$191$	8.72580			0.631377			0.315688	+	0.948863i	$0.397765\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	12.2142			0.879196			0.439598	−	0.898195i	$-0.355121\pi$
$193$	12.2142			0.879196			0.439598	+	0.898195i	$0.355121\pi$
$194$	0.704230	+	1.21976i	0.0505608	+	0.0875738i
$195$	−1.94024			−0.138943
$196$	4.11026			0.293590
$197$	−0.344699			−0.0245588			−0.0122794	−	0.999925i	$-0.503909\pi$
$197$	−0.344699			−0.0245588			−0.0122794	+	0.999925i	$0.503909\pi$
$198$	−1.24487	+	2.15618i	−0.0884691	+	0.153233i
$199$	−0.512952	+	0.888459i	−0.0363622	+	0.0629812i	−0.883634	−	0.468179i	$-0.844910\pi$
$199$	−0.512952	+	0.888459i	−0.0363622	+	0.0629812i	0.847272	+	0.531160i	$0.178244\pi$
$200$	−2.44961	+	4.24286i	−0.173214	+	0.300015i
$201$	2.08306	+	3.60796i	0.146928	+	0.254486i
$202$	−3.32729	+	5.76303i	−0.234107	+	0.405486i
$203$	−17.2501	−	29.8781i	−1.21072	−	2.09703i
$204$	−0.240904	+	0.417257i	−0.0168666	+	0.0292138i
$205$	1.81908	+	3.15074i	0.127050	+	0.220057i
$206$	−1.36349			−0.0949989
$207$	2.43280			0.169091
$208$	6.11204			0.423794
$209$	−18.9781			−1.31274
$210$	1.05811			0.0730166
$211$	−0.327413	+	0.567096i	−0.0225401	+	0.0390405i	−0.877075	−	0.480353i	$-0.840509\pi$
$211$	−0.327413	+	0.567096i	−0.0225401	+	0.0390405i	0.854535	+	0.519393i	$0.173842\pi$
$212$	3.03581	+	5.25818i	0.208500	+	0.361133i
$213$	−0.623014	−	1.07909i	−0.0426882	−	0.0739382i
$214$	−7.47456	−	12.9463i	−0.510951	−	0.884993i
$215$	0.722800			0.0492946
$216$	−1.00000			−0.0680414
$217$	12.0380	−	20.8504i	0.817190	−	1.41541i
$218$	−6.24230	−	10.8120i	−0.422782	−	0.732279i
$219$	5.90433			0.398978
$220$	−0.395178	+	0.684469i	−0.0266429	+	0.0461469i
$221$	2.94483			0.198090
$222$	4.13112			0.277262
$223$	7.09104	+	13.1422i	0.474851	+	0.880066i
$223$	7.09104	+	13.1422i	0.474851	+	0.880066i
$224$	−3.33321			−0.222709
$225$	−4.89923			−0.326615
$226$	0.514881	−	0.891800i	0.0342494	−	0.0593216i
$227$	−22.0684			−1.46473			−0.732366	−	0.680911i	$-0.761584\pi$
$227$	−22.0684			−1.46473			−0.732366	+	0.680911i	$0.761584\pi$
$228$	−3.81125	−	6.60128i	−0.252406	−	0.437181i
$229$	12.3111	−	21.3234i	0.813538	−	1.40909i	−0.0968354	−	0.995300i	$-0.530872\pi$
$229$	12.3111	−	21.3234i	0.813538	−	1.40909i	0.910373	−	0.413788i	$-0.135795\pi$
$230$	0.772282			0.0509228
$231$	−8.29881			−0.546022
$232$	5.17524	+	8.96378i	0.339771	+	0.588501i
$233$	−14.0993	−	24.4206i	−0.923673	−	1.59985i	−0.793681	−	0.608334i	$-0.791838\pi$
$233$	−14.0993	−	24.4206i	−0.923673	−	1.59985i	−0.129992	−	0.991515i	$-0.541495\pi$
$234$	3.05602	+	5.29318i	0.199778	+	0.346026i
$235$	−0.107356	+	0.185947i	−0.00700316	+	0.0121298i
$236$	−10.4971			−0.683306
$237$	−8.01197			−0.520433
$238$	−1.60596			−0.104099
$239$	−1.06849			−0.0691151			−0.0345575	−	0.999403i	$-0.511002\pi$
$239$	−1.06849			−0.0691151			−0.0345575	+	0.999403i	$0.511002\pi$
$240$	−0.317445			−0.0204910
$241$	−12.0709	−	20.9074i	−0.777553	−	1.34676i	−0.933349	−	0.358972i	$-0.883128\pi$
$241$	−12.0709	−	20.9074i	−0.777553	−	1.34676i	0.155796	−	0.987789i	$-0.450206\pi$
$242$	−2.40060	+	4.15796i	−0.154316	+	0.267284i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.31593	+	7.47540i	−0.276299	+	0.478564i
$245$	0.652391	+	1.12997i	0.0416797	+	0.0721914i
$246$	5.73037	−	9.92529i	0.365355	−	0.632813i
$247$	−23.2945	+	40.3473i	−1.48220	+	2.56724i
$248$	−3.61153	+	6.25535i	−0.229332	+	0.397215i
$249$	1.79970			0.114051
$250$	−3.14247			−0.198747
$251$	8.71182			0.549885			0.274943	−	0.961461i	$-0.411341\pi$
$251$	8.71182			0.549885			0.274943	+	0.961461i	$0.411341\pi$
$252$	−1.66660	−	2.88664i	−0.104986	−	0.181841i
$253$	−6.05704			−0.380803
$254$	3.07874	−	5.33254i	0.193177	−	0.334593i
$255$	−0.152948			−0.00957794
$256$	1.00000			0.0625000
$257$	4.14474			0.258542			0.129271	−	0.991609i	$-0.458736\pi$
$257$	4.14474			0.258542			0.129271	+	0.991609i	$0.458736\pi$
$258$	−1.13846	−	1.97188i	−0.0708776	−	0.122764i
$259$	6.88493	+	11.9250i	0.427809	+	0.740986i
$260$	0.970120	+	1.68030i	0.0601643	+	0.104208i
$261$	−5.17524	+	8.96378i	−0.320339	+	0.554844i
$262$	5.59778	−	9.69565i	0.345832	−	0.598999i
$263$	10.5375	+	18.2516i	0.649773	+	1.12544i	0.983177	+	0.182656i	$0.0584694\pi$
$263$	10.5375	+	18.2516i	0.649773	+	1.12544i	−0.333404	+	0.942784i	$0.608197\pi$
$264$	2.48974			0.153233
$265$	−0.963704	+	1.66918i	−0.0591999	+	0.102537i
$266$	12.7037	−	22.0034i	0.778913	−	1.34912i
$267$	−5.53862	−	9.59317i	−0.338958	−	0.587093i
$268$	2.08306	−	3.60796i	0.127243	−	0.220391i
$269$	0.765600	−	1.32606i	0.0466795	−	0.0808512i	−0.841742	−	0.539881i	$-0.818469\pi$
$269$	0.765600	−	1.32606i	0.0466795	−	0.0808512i	0.888421	+	0.459029i	$0.151803\pi$
$270$	−0.158723	−	0.274916i	−0.00965956	−	0.0167308i
$271$	9.18460	−	15.9082i	0.557925	−	0.966354i	−0.439745	−	0.898123i	$-0.644931\pi$
$271$	9.18460	−	15.9082i	0.557925	−	0.966354i	0.997670	−	0.0682313i	$-0.0217356\pi$
$272$	0.481807			0.0292138
$273$	−10.1863	+	17.6433i	−0.616506	+	1.06782i
$274$	−3.93682	+	6.81877i	−0.237832	+	0.411937i
$275$	12.1978			0.735555
$276$	−1.21640	−	2.10687i	−0.0732187	−	0.126819i
$277$	−24.6709			−1.48233			−0.741165	−	0.671323i	$-0.765726\pi$
$277$	−24.6709			−1.48233			−0.741165	+	0.671323i	$0.765726\pi$
$278$	2.32804	−	4.03228i	0.139626	−	0.241840i
$279$	−7.22306			−0.432433
$280$	−0.529055	−	0.916351i	−0.0316171	−	0.0547624i
$281$	−7.67302	−	13.2901i	−0.457734	−	0.792818i	0.541107	−	0.840954i	$-0.318005\pi$
$281$	−7.67302	−	13.2901i	−0.457734	−	0.792818i	−0.998841	+	0.0481354i	$0.984672\pi$
$282$	0.676377			0.0402777
$283$	−16.4101			−0.975477			−0.487738	−	0.872990i	$-0.662178\pi$
$283$	−16.4101			−0.975477			−0.487738	+	0.872990i	$0.662178\pi$
$284$	−0.623014	+	1.07909i	−0.0369691	+	0.0640324i
$285$	1.20986	−	2.09555i	0.0716662	−	0.124130i
$286$	−7.60870	−	13.1787i	−0.449912	−	0.779270i
$287$	38.2010			2.25493
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−16.7679			−0.986345
$290$	−1.64286	+	2.84551i	−0.0964718	+	0.167094i
$291$	1.40846			0.0825654
$292$	−2.95216	−	5.11330i	−0.172762	−	0.299233i
$293$	−12.2124	−	21.1525i	−0.713455	−	1.23574i	−0.963553	−	0.267519i	$-0.913796\pi$
$293$	−12.2124	−	21.1525i	−0.713455	−	1.23574i	0.250098	−	0.968221i	$-0.419537\pi$
$294$	2.05513	−	3.55959i	0.119858	−	0.207599i
$295$	−1.66614	−	2.88583i	−0.0970062	−	0.168020i
$296$	−2.06556	−	3.57765i	−0.120058	−	0.207947i
$297$	1.24487	+	2.15618i	0.0722347	+	0.125114i
$298$	−7.18795	−	12.4499i	−0.416387	−	0.721203i
$299$	−7.43469	+	12.8773i	−0.429959	+	0.744712i
$300$	2.44961	+	4.24286i	0.141429	+	0.244961i
$301$	3.79473	−	6.57267i	0.218725	−	0.378842i
$302$	−2.67314	−	4.63001i	−0.153822	−	0.266427i
$303$	3.32729	+	5.76303i	0.191148	+	0.331078i
$304$	−3.81125	+	6.60128i	−0.218590	+	0.378610i
$305$	−2.74014			−0.156900
$306$	0.240904	+	0.417257i	0.0137715	+	0.0238530i
$307$	−10.3706	+	17.9624i	−0.591880	+	1.02517i	0.402099	+	0.915596i	$0.368281\pi$
$307$	−10.3706	+	17.9624i	−0.591880	+	1.02517i	−0.993979	+	0.109571i	$0.965052\pi$
$308$	4.14941	+	7.18698i	0.236434	+	0.409516i
$309$	−0.681745	+	1.18082i	−0.0387831	+	0.0671744i
$310$	−2.29293			−0.130229
$311$	11.2169	+	19.4283i	0.636055	+	1.10168i	0.986291	+	0.165018i	$0.0527681\pi$
$311$	11.2169	+	19.4283i	0.636055	+	1.10168i	−0.350236	+	0.936662i	$0.613899\pi$
$312$	3.05602	−	5.29318i	0.173013	−	0.299667i
$313$	0.621989	−	1.07732i	0.0351569	−	0.0608935i	−0.847912	−	0.530138i	$-0.822140\pi$
$313$	0.621989	−	1.07732i	0.0351569	−	0.0608935i	0.883068	+	0.469244i	$0.155474\pi$
$314$	21.2688			1.20027
$315$	0.529055	−	0.916351i	0.0298089	−	0.0516305i
$316$	4.00598	+	6.93857i	0.225354	+	0.390325i
$317$	−11.4277	−	19.7934i	−0.641844	−	1.11171i	−0.985021	−	0.172436i	$-0.944836\pi$
$317$	−11.4277	−	19.7934i	−0.641844	−	1.11171i	0.343177	−	0.939271i	$-0.388497\pi$
$318$	6.07162			0.340480
$319$	12.8850	−	22.3175i	0.721421	−	1.24954i
$320$	0.158723	+	0.274916i	0.00887287	+	0.0153683i
$321$	−14.9491			−0.834379
$322$	4.05451	−	7.02262i	0.225949	−	0.391356i
$323$	−1.83629	+	3.18055i	−0.102174	+	0.176970i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	14.9721	−	25.9325i	0.830505	−	1.43848i
$326$	−13.3427			−0.738981
$327$	−12.4846			−0.690399
$328$	−11.4607			−0.632813
$329$	1.12725	+	1.95246i	0.0621474	+	0.107642i
$330$	0.395178	+	0.684469i	0.0217539	+	0.0376788i
$331$	12.7162			0.698948			0.349474	−	0.936946i	$-0.386360\pi$
$331$	12.7162			0.698948			0.349474	+	0.936946i	$0.386360\pi$
$332$	−0.899848	−	1.55858i	−0.0493856	−	0.0855383i
$333$	2.06556	−	3.57765i	0.113192	−	0.196054i
$334$	−2.05239			−0.112302
$335$	1.32252			0.0722567
$336$	−1.66660	+	2.88664i	−0.0909206	+	0.157479i
$337$	−5.08368	−	8.80519i	−0.276926	−	0.479649i	0.693694	−	0.720270i	$-0.255982\pi$
$337$	−5.08368	−	8.80519i	−0.276926	−	0.479649i	−0.970619	+	0.240621i	$0.922649\pi$
$338$	−24.3571			−1.32485
$339$	−0.514881	−	0.891800i	−0.0279645	−	0.0484359i
$340$	0.0764738	+	0.132456i	0.00414737	+	0.00718346i
$341$	17.9835			0.973863
$342$	−7.62251			−0.412178
$343$	−9.63211			−0.520085
$344$	−1.13846	+	1.97188i	−0.0613818	+	0.106316i
$345$	0.386141	−	0.668816i	0.0207891	−	0.0360078i
$346$	0.748011	−	1.29559i	0.0402133	−	0.0696515i
$347$	1.36218	−	2.35936i	0.0731254	−	0.126657i	−0.827144	−	0.561990i	$-0.810036\pi$
$347$	1.36218	−	2.35936i	0.0731254	−	0.126657i	0.900270	+	0.435333i	$0.143369\pi$
$348$	10.3505			0.554844
$349$	4.07814	+	7.06354i	0.218298	+	0.378103i	0.954288	−	0.298890i	$-0.0966163\pi$
$349$	4.07814	+	7.06354i	0.218298	+	0.378103i	−0.735990	+	0.676992i	$0.763283\pi$
$350$	−8.16507	+	14.1423i	−0.436441	+	0.755938i
$351$	6.11204			0.326237
$352$	−1.24487	−	2.15618i	−0.0663518	−	0.114925i
$353$	6.34205	+	10.9847i	0.337553	+	0.584659i	0.983972	−	0.178324i	$-0.0570674\pi$
$353$	6.34205	+	10.9847i	0.337553	+	0.584659i	−0.646419	+	0.762983i	$0.723734\pi$
$354$	−5.24857	+	9.09080i	−0.278959	+	0.483170i
$355$	−0.395546			−0.0209934
$356$	−5.53862	+	9.59317i	−0.293546	+	0.508437i
$357$	−0.802981	+	1.39080i	−0.0424983	+	0.0736092i
$358$	12.1097	+	20.9746i	0.640017	+	1.10854i
$359$	28.4555			1.50183			0.750913	−	0.660401i	$-0.229614\pi$
$359$	28.4555			1.50183			0.750913	+	0.660401i	$0.229614\pi$
$360$	−0.158723	+	0.274916i	−0.00836542	+	0.0144893i
$361$	−19.5513	−	33.8638i	−1.02902	−	1.78231i
$362$	−1.69523	+	2.93622i	−0.0890991	+	0.154324i
$363$	2.40060	+	4.15796i	0.125999	+	0.218236i
$364$	20.3727			1.06782
$365$	0.937151	−	1.62319i	0.0490527	−	0.0849618i
$366$	4.31593	+	7.47540i	0.225597	+	0.390746i
$367$	−12.6326	−	21.8803i	−0.659417	−	1.14214i	−0.980767	−	0.195183i	$-0.937470\pi$
$367$	−12.6326	−	21.8803i	−0.659417	−	1.14214i	0.321350	−	0.946960i	$-0.395863\pi$
$368$	−1.21640	+	2.10687i	−0.0634093	+	0.109828i
$369$	−5.73037	−	9.92529i	−0.298311	−	0.516690i
$370$	0.655702	−	1.13571i	0.0340883	−	0.0590427i
$371$	10.1190	+	17.5266i	0.525351	+	0.909935i
$372$	3.61153	+	6.25535i	0.187249	+	0.324325i
$373$	−0.641700	−	1.11146i	−0.0332260	−	0.0575491i	0.848934	−	0.528498i	$-0.177245\pi$
$373$	−0.641700	−	1.11146i	−0.0332260	−	0.0575491i	−0.882160	+	0.470949i	$0.843911\pi$
$374$	−0.599787	−	1.03886i	−0.0310143	−	0.0537183i
$375$	−1.57123	+	2.72145i	−0.0811381	+	0.140535i
$376$	−0.338188	−	0.585760i	−0.0174407	−	0.0302082i
$377$	−31.6313	−	54.7870i	−1.62909	−	2.82167i
$378$	−3.33321			−0.171442
$379$	2.09075	−	3.62128i	0.107395	−	0.186013i	−0.807319	−	0.590115i	$-0.799083\pi$
$379$	2.09075	−	3.62128i	0.107395	−	0.186013i	0.914714	+	0.404102i	$0.132416\pi$
$380$	−2.41973			−0.124130
$381$	−3.07874	−	5.33254i	−0.157729	−	0.273194i
$382$	−8.72580			−0.446451
$383$	−3.76289	−	6.51751i	−0.192275	−	0.333029i	0.753729	−	0.657185i	$-0.228253\pi$
$383$	−3.76289	−	6.51751i	−0.192275	−	0.333029i	−0.946004	+	0.324156i	$0.894920\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−1.31721	+	2.28148i	−0.0671313	+	0.116275i
$386$	−12.2142			−0.621685
$387$	−2.27693			−0.115743
$388$	−0.704230	−	1.21976i	−0.0357519	−	0.0619241i
$389$	1.28543	+	2.22642i	0.0651737	+	0.112884i	0.896771	−	0.442495i	$-0.145907\pi$
$389$	1.28543	+	2.22642i	0.0651737	+	0.112884i	−0.831597	+	0.555379i	$0.812573\pi$
$390$	1.94024			0.0982479
$391$	−0.586071	+	1.01510i	−0.0296389	+	0.0513360i
$392$	−4.11026			−0.207599
$393$	−5.59778	−	9.69565i	−0.282371	−	0.489081i
$394$	0.344699			0.0173657
$395$	−1.27168	+	2.20262i	−0.0639852	+	0.110826i
$396$	1.24487	−	2.15618i	0.0625571	−	0.108352i
$397$	−0.563474			−0.0282799			−0.0141400	−	0.999900i	$-0.504501\pi$
$397$	−0.563474			−0.0282799			−0.0141400	+	0.999900i	$0.504501\pi$
$398$	0.512952	−	0.888459i	0.0257120	−	0.0445344i
$399$	−12.7037	−	22.0034i	−0.635980	−	1.10155i
$400$	2.44961	−	4.24286i	0.122481	−	0.212143i
$401$	6.71838	−	11.6366i	0.335500	−	0.581103i	−0.648081	−	0.761572i	$-0.724428\pi$
$401$	6.71838	−	11.6366i	0.335500	−	0.581103i	0.983581	+	0.180469i	$0.0577615\pi$
$402$	−2.08306	−	3.60796i	−0.103894	−	0.179949i
$403$	22.0738	−	38.2330i	1.09957	−	1.90452i
$404$	3.32729	−	5.76303i	0.165539	−	0.286722i
$405$	−0.317445			−0.0157740
$406$	17.2501	+	29.8781i	0.856110	+	1.48283i
$407$	−5.14270	+	8.90742i	−0.254914	+	0.441525i
$408$	0.240904	−	0.417257i	0.0119265	−	0.0206573i
$409$	13.2735	+	22.9903i	0.656331	+	1.13680i	0.981558	+	0.191162i	$0.0612257\pi$
$409$	13.2735	+	22.9903i	0.656331	+	1.13680i	−0.325228	+	0.945636i	$0.605441\pi$
$410$	−1.81908	−	3.15074i	−0.0898379	−	0.155604i
$411$	3.93682	+	6.81877i	0.194189	+	0.336345i
$412$	1.36349			0.0671744
$413$	−34.9892			−1.72170
$414$	−2.43280			−0.119566
$415$	0.285653	−	0.494765i	0.0140221	−	0.0242871i
$416$	−6.11204			−0.299667
$417$	−2.32804	−	4.03228i	−0.114004	−	0.197461i
$418$	18.9781			0.928247
$419$	4.44546			0.217175			0.108587	−	0.994087i	$-0.465367\pi$
$419$	4.44546			0.217175			0.108587	+	0.994087i	$0.465367\pi$
$420$	−1.05811			−0.0516305
$421$	−8.30460	+	14.3840i	−0.404741	+	0.701033i	−0.994291	−	0.106699i	$-0.965972\pi$
$421$	−8.30460	+	14.3840i	−0.404741	+	0.701033i	0.589550	+	0.807732i	$0.299305\pi$
$422$	0.327413	−	0.567096i	0.0159382	−	0.0276058i
$423$	0.338188	−	0.585760i	0.0164433	−	0.0284806i
$424$	−3.03581	−	5.25818i	−0.147432	−	0.255360i
$425$	1.18024	−	2.04424i	0.0572501	−	0.0991601i
$426$	0.623014	+	1.07909i	0.0301851	+	0.0522822i
$427$	−14.3859	+	24.9171i	−0.696181	+	1.20582i
$428$	7.47456	+	12.9463i	0.361297	+	0.625784i
$429$	−15.2174			−0.734703
$430$	−0.722800			−0.0348565
$431$	−24.7175			−1.19060			−0.595301	−	0.803503i	$-0.702967\pi$
$431$	−24.7175			−1.19060			−0.595301	+	0.803503i	$0.702967\pi$
$432$	1.00000			0.0481125
$433$	−39.1940			−1.88354			−0.941772	−	0.336253i	$-0.890840\pi$
$433$	−39.1940			−1.88354			−0.941772	+	0.336253i	$0.890840\pi$
$434$	−12.0380	+	20.8504i	−0.577841	+	1.00085i
$435$	1.64286	+	2.84551i	0.0787689	+	0.136432i
$436$	6.24230	+	10.8120i	0.298952	+	0.517800i
$437$	−9.27202	−	16.0596i	−0.443541	−	0.768236i
$438$	−5.90433			−0.282120
$439$	−21.2037			−1.01200			−0.505999	−	0.862534i	$-0.668876\pi$
$439$	−21.2037			−1.01200			−0.505999	+	0.862534i	$0.668876\pi$
$440$	0.395178	−	0.684469i	0.0188394	−	0.0326308i
$441$	−2.05513	−	3.55959i	−0.0978632	−	0.169504i
$442$	−2.94483			−0.140071
$443$	−3.68286	+	6.37890i	−0.174978	+	0.303071i	−0.940154	−	0.340751i	$-0.889319\pi$
$443$	−3.68286	+	6.37890i	−0.174978	+	0.303071i	0.765176	+	0.643822i	$0.222652\pi$
$444$	−4.13112			−0.196054
$445$	−3.51642			−0.166694
$446$	−7.09104	−	13.1422i	−0.335770	−	0.622301i
$447$	−14.3759			−0.679957
$448$	3.33321			0.157479
$449$	4.81711	−	8.34347i	0.227333	−	0.393753i	−0.729684	−	0.683785i	$-0.760333\pi$
$449$	4.81711	−	8.34347i	0.227333	−	0.393753i	0.957017	+	0.290032i	$0.0936660\pi$
$450$	4.89923			0.230952
$451$	14.2671	+	24.7114i	0.671813	+	1.16361i
$452$	−0.514881	+	0.891800i	−0.0242180	+	0.0419467i
$453$	−5.34628			−0.251190
$454$	22.0684			1.03572
$455$	3.23361	+	5.60078i	0.151594	+	0.262568i
$456$	3.81125	+	6.60128i	0.178478	+	0.309133i
$457$	−19.6936	−	34.1103i	−0.921228	−	1.59561i	−0.797517	−	0.603296i	$-0.793854\pi$
$457$	−19.6936	−	34.1103i	−0.921228	−	1.59561i	−0.123711	−	0.992318i	$-0.539480\pi$
$458$	−12.3111	+	21.3234i	−0.575258	+	0.996376i
$459$	0.481807			0.0224888
$460$	−0.772282			−0.0360078
$461$	20.6899			0.963626			0.481813	−	0.876274i	$-0.339978\pi$
$461$	20.6899			0.963626			0.481813	+	0.876274i	$0.339978\pi$
$462$	8.29881			0.386096
$463$	7.94253			0.369121			0.184560	−	0.982821i	$-0.440914\pi$
$463$	7.94253			0.369121			0.184560	+	0.982821i	$0.440914\pi$
$464$	−5.17524	−	8.96378i	−0.240254	−	0.416133i
$465$	−1.14646	+	1.98573i	−0.0531660	+	0.0920861i
$466$	14.0993	+	24.4206i	0.653136	+	1.13126i
$467$	0.995744	−	1.72468i	0.0460775	−	0.0798086i	−0.842067	−	0.539373i	$-0.818661\pi$
$467$	0.995744	−	1.72468i	0.0460775	−	0.0798086i	0.888144	+	0.459565i	$0.151995\pi$
$468$	−3.05602	−	5.29318i	−0.141265	−	0.244677i
$469$	6.94326	−	12.0261i	0.320610	−	0.555313i
$470$	0.107356	−	0.185947i	0.00495198	−	0.00857708i
$471$	10.6344	−	18.4194i	0.490008	−	0.848719i
$472$	10.4971			0.483170
$473$	5.66896			0.260659
$474$	8.01197			0.368002
$475$	18.6722	+	32.3412i	0.856739	+	1.48392i
$476$	1.60596			0.0736092
$477$	3.03581	−	5.25818i	0.139000	−	0.240755i
$478$	1.06849			0.0488717
$479$	27.5409			1.25838			0.629188	−	0.777253i	$-0.283388\pi$
$479$	27.5409			1.25838			0.629188	+	0.777253i	$0.283388\pi$
$480$	0.317445			0.0144893
$481$	12.6248	+	21.8668i	0.575640	+	0.997038i
$482$	12.0709	+	20.9074i	0.549813	+	0.952304i
$483$	−4.05451	−	7.02262i	−0.184487	−	0.319540i
$484$	2.40060	−	4.15796i	0.109118	−	0.188998i
$485$	0.223555	−	0.387208i	0.0101511	−	0.0175822i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−24.4289			−1.10698			−0.553490	−	0.832856i	$-0.686704\pi$
$487$	−24.4289			−1.10698			−0.553490	+	0.832856i	$0.686704\pi$
$488$	4.31593	−	7.47540i	0.195373	−	0.338396i
$489$	−6.67133	+	11.5551i	−0.301688	+	0.522539i
$490$	−0.652391	−	1.12997i	−0.0294720	−	0.0510471i
$491$	−4.40001	+	7.62104i	−0.198570	+	0.343933i	−0.948065	−	0.318077i	$-0.896963\pi$
$491$	−4.40001	+	7.62104i	−0.198570	+	0.343933i	0.749495	+	0.662010i	$0.230296\pi$
$492$	−5.73037	+	9.92529i	−0.258345	+	0.447466i
$493$	−2.49347	−	4.31881i	−0.112300	−	0.194509i
$494$	23.2945	−	40.3473i	1.04807	−	1.81531i
$495$	0.790357			0.0355239
$496$	3.61153	−	6.25535i	0.162162	−	0.280873i
$497$	−2.07663	+	3.59684i	−0.0931498	+	0.161340i
$498$	−1.79970			−0.0806463
$499$	−8.72858	−	15.1183i	−0.390745	−	0.676790i	0.601803	−	0.798644i	$-0.294449\pi$
$499$	−8.72858	−	15.1183i	−0.390745	−	0.676790i	−0.992548	+	0.121855i	$0.961116\pi$
$500$	3.14247			0.140535
$501$	−1.02619	+	1.77742i	−0.0458470	+	0.0794093i
$502$	−8.71182			−0.388827
$503$	−17.6188	−	30.5167i	−0.785585	−	1.36067i	−0.928649	−	0.370960i	$-0.879029\pi$
$503$	−17.6188	−	30.5167i	−0.785585	−	1.36067i	0.143064	−	0.989713i	$-0.454305\pi$
$504$	1.66660	+	2.88664i	0.0742364	+	0.128581i
$505$	2.11247			0.0940035
$506$	6.05704			0.269268
$507$	−12.1785	+	21.0938i	−0.540867	+	0.936810i
$508$	−3.07874	+	5.33254i	−0.136597	+	0.236593i
$509$	3.85406	+	6.67542i	0.170828	+	0.295883i	0.938710	−	0.344709i	$-0.112022\pi$
$509$	3.85406	+	6.67542i	0.170828	+	0.295883i	−0.767881	+	0.640592i	$0.778689\pi$
$510$	0.152948			0.00677263
$511$	−9.84017	−	17.0437i	−0.435303	−	0.753968i
$512$	−1.00000			−0.0441942
$513$	−3.81125	+	6.60128i	−0.168271	+	0.291454i
$514$	−4.14474			−0.182817
$515$	0.216417	+	0.374845i	0.00953647	+	0.0165177i
$516$	1.13846	+	1.97188i	0.0501181	+	0.0868070i
$517$	−0.842001	+	1.45839i	−0.0370312	+	0.0641399i
$518$	−6.88493	−	11.9250i	−0.302506	−	0.523956i
$519$	−0.748011	−	1.29559i	−0.0328340	−	0.0568702i
$520$	−0.970120	−	1.68030i	−0.0425426	−	0.0736859i
$521$	12.0088	+	20.7999i	0.526117	+	0.911262i	0.999537	+	0.0304249i	$0.00968604\pi$
$521$	12.0088	+	20.7999i	0.526117	+	0.911262i	−0.473420	+	0.880837i	$0.656981\pi$
$522$	5.17524	−	8.96378i	0.226514	−	0.392334i
$523$	−4.38324	−	7.59200i	−0.191666	−	0.331975i	0.754137	−	0.656718i	$-0.228056\pi$
$523$	−4.38324	−	7.59200i	−0.191666	−	0.331975i	−0.945802	+	0.324743i	$0.894722\pi$
$524$	−5.59778	+	9.69565i	−0.244540	+	0.423556i
$525$	8.16507	+	14.1423i	0.356353	+	0.617221i
$526$	−10.5375	−	18.2516i	−0.459459	−	0.795806i
$527$	1.74006	−	3.01387i	0.0757982	−	0.131286i
$528$	−2.48974			−0.108352
$529$	8.54074	+	14.7930i	0.371336	+	0.643174i
$530$	0.963704	−	1.66918i	0.0418606	−	0.0725048i
$531$	5.24857	+	9.09080i	0.227769	+	0.394507i
$532$	−12.7037	+	22.0034i	−0.550775	+	0.953970i
$533$	70.0485			3.03414
$534$	5.53862	+	9.59317i	0.239680	+	0.415137i
$535$	−2.37277	+	4.10975i	−0.102584	+	0.177680i
$536$	−2.08306	+	3.60796i	−0.0899744	+	0.155840i
$537$	24.2194			1.04514
$538$	−0.765600	+	1.32606i	−0.0330074	+	0.0571704i
$539$	5.11674	+	8.86245i	0.220393	+	0.381733i
$540$	0.158723	+	0.274916i	0.00683034	+	0.0118305i
$541$	−29.1676			−1.25401			−0.627006	−	0.779015i	$-0.715720\pi$
$541$	−29.1676			−1.25401			−0.627006	+	0.779015i	$0.715720\pi$
$542$	−9.18460	+	15.9082i	−0.394512	+	0.683316i
$543$	1.69523	+	2.93622i	0.0727491	+	0.126005i
$544$	−0.481807			−0.0206573
$545$	−1.98159	+	3.43221i	−0.0848819	+	0.147020i
$546$	10.1863	−	17.6433i	0.435935	−	0.755062i
$547$	4.91342	−	8.51030i	0.210083	−	0.363874i	−0.741657	−	0.670779i	$-0.765960\pi$
$547$	4.91342	−	8.51030i	0.210083	−	0.363874i	0.951740	+	0.306905i	$0.0992933\pi$
$548$	3.93682	−	6.81877i	0.168172	−	0.291283i
$549$	8.63185			0.368398
$550$	−12.1978			−0.520116
$551$	78.8966			3.36111
$552$	1.21640	+	2.10687i	0.0517735	+	0.0896743i
$553$	13.3528	+	23.1277i	0.567817	+	0.983489i
$554$	24.6709			1.04817
$555$	−0.655702	−	1.13571i	−0.0278330	−	0.0482082i
$556$	−2.32804	+	4.03228i	−0.0987307	+	0.171007i
$557$	−14.0735			−0.596313			−0.298156	−	0.954517i	$-0.596372\pi$
$557$	−14.0735			−0.596313			−0.298156	+	0.954517i	$0.596372\pi$
$558$	7.22306			0.305776
$559$	6.95834	−	12.0522i	0.294306	−	0.509753i
$560$	0.529055	+	0.916351i	0.0223567	+	0.0387229i
$561$	−1.19957			−0.0506461
$562$	7.67302	+	13.2901i	0.323667	+	0.560607i
$563$	3.65190	+	6.32527i	0.153909	+	0.266579i	0.932661	−	0.360753i	$-0.117480\pi$
$563$	3.65190	+	6.32527i	0.153909	+	0.266579i	−0.778752	+	0.627332i	$0.784147\pi$
$564$	−0.676377			−0.0284806
$565$	−0.326893			−0.0137525
$566$	16.4101			0.689766
$567$	−1.66660	+	2.88664i	−0.0699907	+	0.121227i
$568$	0.623014	−	1.07909i	0.0261411	−	0.0452777i
$569$	−8.59100	+	14.8801i	−0.360154	+	0.623804i	−0.987986	−	0.154544i	$-0.950609\pi$
$569$	−8.59100	+	14.8801i	−0.360154	+	0.623804i	0.627832	+	0.778349i	$0.283942\pi$
$570$	−1.20986	+	2.09555i	−0.0506757	+	0.0877728i
$571$	41.6488			1.74295			0.871473	−	0.490443i	$-0.163165\pi$
$571$	41.6488			1.74295			0.871473	+	0.490443i	$0.163165\pi$
$572$	7.60870	+	13.1787i	0.318136	+	0.551027i
$573$	−4.36290	+	7.55677i	−0.182263	+	0.315688i
$574$	−38.2010			−1.59448
$575$	5.95943	+	10.3220i	0.248525	+	0.430458i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−10.1443	+	17.5705i	−0.422314	+	0.731470i	−0.996165	−	0.0874898i	$-0.972115\pi$
$577$	−10.1443	+	17.5705i	−0.422314	+	0.731470i	0.573851	+	0.818960i	$0.305449\pi$
$578$	16.7679			0.697451
$579$	−6.10709	+	10.5778i	−0.253802	+	0.439598i
$580$	1.64286	−	2.84551i	0.0682159	−	0.118153i
$581$	−2.99938	−	5.19508i	−0.124435	−	0.215528i
$582$	−1.40846			−0.0583826
$583$	−7.55838	+	13.0915i	−0.313036	+	0.542194i
$584$	2.95216	+	5.11330i	0.122161	+	0.211590i
$585$	0.970120	−	1.68030i	0.0401095	−	0.0694717i
$586$	12.2124	+	21.1525i	0.504489	+	0.873800i
$587$	14.9715			0.617941			0.308970	−	0.951072i	$-0.400016\pi$
$587$	14.9715			0.617941			0.308970	+	0.951072i	$0.400016\pi$
$588$	−2.05513	+	3.55959i	−0.0847521	+	0.146795i
$589$	27.5289	+	47.6814i	1.13431	+	1.96468i
$590$	1.66614	+	2.88583i	0.0685938	+	0.118808i
$591$	0.172350	−	0.298518i	0.00708952	−	0.0122794i
$592$	2.06556	+	3.57765i	0.0848939	+	0.147041i
$593$	2.02707	−	3.51098i	0.0832416	−	0.144179i	−0.821399	−	0.570354i	$-0.806806\pi$
$593$	2.02707	−	3.51098i	0.0832416	−	0.144179i	0.904641	+	0.426175i	$0.140139\pi$
$594$	−1.24487	−	2.15618i	−0.0510776	−	0.0884691i
$595$	0.254903	+	0.441504i	0.0104500	+	0.0180999i
$596$	7.18795	+	12.4499i	0.294430	+	0.509967i
$597$	−0.512952	−	0.888459i	−0.0209937	−	0.0363622i
$598$	7.43469	−	12.8773i	0.304027	−	0.526591i
$599$	−23.2687	−	40.3025i	−0.950732	−	1.64672i	−0.743846	−	0.668351i	$-0.767000\pi$
$599$	−23.2687	−	40.3025i	−0.950732	−	1.64672i	−0.206886	−	0.978365i	$-0.566333\pi$
$600$	−2.44961	−	4.24286i	−0.100005	−	0.173214i
$601$	17.0109			0.693890			0.346945	−	0.937885i	$-0.387219\pi$
$601$	17.0109			0.693890			0.346945	+	0.937885i	$0.387219\pi$
$602$	−3.79473	+	6.57267i	−0.154662	+	0.267882i
$603$	−4.16612			−0.169657
$604$	2.67314	+	4.63001i	0.108768	+	0.188393i
$605$	1.52412			0.0619642
$606$	−3.32729	−	5.76303i	−0.135162	−	0.234107i
$607$	−17.1751	+	29.7481i	−0.697114	+	1.20744i	0.272349	+	0.962199i	$0.412200\pi$
$607$	−17.1751	+	29.7481i	−0.697114	+	1.20744i	−0.969463	+	0.245238i	$0.921134\pi$
$608$	3.81125	−	6.60128i	0.154567	−	0.267717i
$609$	34.5003			1.39802
$610$	2.74014			0.110945
$611$	2.06702	+	3.58019i	0.0836227	+	0.144839i
$612$	−0.240904	−	0.417257i	−0.00973795	−	0.0168666i
$613$	−41.0387			−1.65754			−0.828769	−	0.559590i	$-0.810959\pi$
$613$	−41.0387			−1.65754			−0.828769	+	0.559590i	$0.810959\pi$
$614$	10.3706	−	17.9624i	0.418523	−	0.724903i
$615$	−3.63816			−0.146705
$616$	−4.14941	−	7.18698i	−0.167184	−	0.289572i
$617$	15.1746			0.610905			0.305453	−	0.952207i	$-0.401192\pi$
$617$	15.1746			0.610905			0.305453	+	0.952207i	$0.401192\pi$
$618$	0.681745	−	1.18082i	0.0274238	−	0.0474994i
$619$	5.53570	−	9.58812i	0.222499	−	0.385379i	−0.733067	−	0.680156i	$-0.761912\pi$
$619$	5.53570	−	9.58812i	0.222499	−	0.385379i	0.955566	+	0.294777i	$0.0952454\pi$
$620$	2.29293			0.0920861
$621$	−1.21640	+	2.10687i	−0.0488125	+	0.0845457i
$622$	−11.2169	−	19.4283i	−0.449759	−	0.779005i
$623$	−18.4614	+	31.9760i	−0.739639	+	1.28109i
$624$	−3.05602	+	5.29318i	−0.122339	+	0.211897i
$625$	−11.7493	−	20.3504i	−0.469972	−	0.814015i
$626$	−0.621989	+	1.07732i	−0.0248597	+	0.0430582i
$627$	9.48903	−	16.4355i	0.378955	−	0.656370i
$628$	−21.2688			−0.848719
$629$	0.995201	+	1.72374i	0.0396812	+	0.0687299i
$630$	−0.529055	+	0.916351i	−0.0210781	+	0.0365083i
$631$	−22.1404	+	38.3482i	−0.881394	+	1.52662i	−0.0316018	+	0.999501i	$0.510061\pi$
$631$	−22.1404	+	38.3482i	−0.881394	+	1.52662i	−0.849792	+	0.527118i	$0.823272\pi$
$632$	−4.00598	−	6.93857i	−0.159349	−	0.276001i
$633$	−0.327413	−	0.567096i	−0.0130135	−	0.0225401i
$634$	11.4277	+	19.7934i	0.453852	+	0.786095i
$635$	−1.95467			−0.0775686
$636$	−6.07162			−0.240755
$637$	25.1221			0.995372
$638$	−12.8850	+	22.3175i	−0.510122	+	0.883557i
$639$	1.24603			0.0492921
$640$	−0.158723	−	0.274916i	−0.00627407	−	0.0108670i
$641$	21.0479			0.831343			0.415672	−	0.909515i	$-0.363547\pi$
$641$	21.0479			0.831343			0.415672	+	0.909515i	$0.363547\pi$
$642$	14.9491			0.589995
$643$	−30.5915			−1.20641			−0.603206	−	0.797585i	$-0.706110\pi$
$643$	−30.5915			−1.20641			−0.603206	+	0.797585i	$0.706110\pi$
$644$	−4.05451	+	7.02262i	−0.159770	+	0.276730i
$645$	−0.361400	+	0.625963i	−0.0142301	+	0.0246473i
$646$	1.83629	−	3.18055i	0.0722478	−	0.125137i
$647$	−17.3926	−	30.1249i	−0.683775	−	1.18433i	−0.973820	−	0.227320i	$-0.927004\pi$
$647$	−17.3926	−	30.1249i	−0.683775	−	1.18433i	0.290045	−	0.957013i	$-0.406330\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−13.0676	−	22.6337i	−0.512948	−	0.888451i
$650$	−14.9721	+	25.9325i	−0.587256	+	1.01716i
$651$	12.0380	+	20.8504i	0.471805	+	0.817190i
$652$	13.3427			0.522539
$653$	44.9841			1.76037			0.880183	−	0.474635i	$-0.157420\pi$
$653$	44.9841			1.76037			0.880183	+	0.474635i	$0.157420\pi$
$654$	12.4846			0.488186
$655$	−3.55398			−0.138866
$656$	11.4607			0.447466
$657$	−2.95216	+	5.11330i	−0.115175	+	0.199489i
$658$	−1.12725	−	1.95246i	−0.0439448	−	0.0761147i
$659$	−0.930295	−	1.61132i	−0.0362392	−	0.0627681i	0.847337	−	0.531056i	$-0.178204\pi$
$659$	−0.930295	−	1.61132i	−0.0362392	−	0.0627681i	−0.883576	+	0.468288i	$0.844871\pi$
$660$	−0.395178	−	0.684469i	−0.0153823	−	0.0266429i
$661$	5.48374			0.213293			0.106646	−	0.994297i	$-0.465989\pi$
$661$	5.48374			0.213293			0.106646	+	0.994297i	$0.465989\pi$
$662$	−12.7162			−0.494231
$663$	−1.47241	+	2.55029i	−0.0571838	+	0.0990452i
$664$	0.899848	+	1.55858i	0.0349209	+	0.0604847i
$665$	−8.06546			−0.312765
$666$	−2.06556	+	3.57765i	−0.0800387	+	0.138631i
$667$	25.1807			0.974999
$668$	2.05239			0.0794093
$669$	−14.9270	−	0.430076i	−0.577111	−	0.0166277i
$670$	−1.32252			−0.0510932
$671$	−21.4911			−0.829654
$672$	1.66660	−	2.88664i	0.0642906	−	0.111355i
$673$	−48.2853			−1.86126			−0.930632	−	0.365957i	$-0.880742\pi$
$673$	−48.2853			−1.86126			−0.930632	+	0.365957i	$0.880742\pi$
$674$	5.08368	+	8.80519i	0.195816	+	0.339163i
$675$	2.44961	−	4.24286i	0.0942857	−	0.163308i
$676$	24.3571			0.936810
$677$	16.8521			0.647678			0.323839	−	0.946112i	$-0.395026\pi$
$677$	16.8521			0.647678			0.323839	+	0.946112i	$0.395026\pi$
$678$	0.514881	+	0.891800i	0.0197739	+	0.0342494i
$679$	−2.34734	−	4.06572i	−0.0900828	−	0.156028i
$680$	−0.0764738	−	0.132456i	−0.00293263	−	0.00507947i
$681$	11.0342	−	19.1118i	0.422832	−	0.732366i
$682$	−17.9835			−0.688625
$683$	37.6035			1.43886			0.719428	−	0.694567i	$-0.244404\pi$
$683$	37.6035			1.43886			0.719428	+	0.694567i	$0.244404\pi$
$684$	7.62251			0.291454
$685$	2.49945			0.0954991
$686$	9.63211			0.367756
$687$	12.3111	+	21.3234i	0.469696	+	0.813538i
$688$	1.13846	−	1.97188i	0.0434035	−	0.0751771i
$689$	18.5550	+	32.1382i	0.706889	+	1.22437i
$690$	−0.386141	+	0.668816i	−0.0147001	+	0.0254614i
$691$	−20.1926	−	34.9746i	−0.768163	−	1.33050i	−0.938558	−	0.345121i	$-0.887838\pi$
$691$	−20.1926	−	34.9746i	−0.768163	−	1.33050i	0.170396	−	0.985376i	$-0.445495\pi$
$692$	−0.748011	+	1.29559i	−0.0284351	+	0.0492510i
$693$	4.14941	−	7.18698i	0.157623	−	0.273011i
$694$	−1.36218	+	2.35936i	−0.0517075	+	0.0895600i
$695$	−1.47805			−0.0560656
$696$	−10.3505			−0.392334
$697$	5.52186			0.209155
$698$	−4.07814	−	7.06354i	−0.154360	−	0.267359i
$699$	28.1985			1.06657
$700$	8.16507	−	14.1423i	0.308611	−	0.534529i
$701$	−23.0771			−0.871610			−0.435805	−	0.900041i	$-0.643536\pi$
$701$	−23.0771			−0.871610			−0.435805	+	0.900041i	$0.643536\pi$
$702$	−6.11204			−0.230684
$703$	−31.4895			−1.18765
$704$	1.24487	+	2.15618i	0.0469178	+	0.0812640i
$705$	−0.107356	−	0.185947i	−0.00404328	−	0.00700316i
$706$	−6.34205	−	10.9847i	−0.238686	−	0.413417i
$707$	11.0905	−	19.2094i	0.417102	−	0.722443i
$708$	5.24857	−	9.09080i	0.197254	−	0.341653i
$709$	−6.80452	−	11.7858i	−0.255549	−	0.442624i	0.709495	−	0.704710i	$-0.248923\pi$
$709$	−6.80452	−	11.7858i	−0.255549	−	0.442624i	−0.965045	+	0.262086i	$0.915590\pi$
$710$	0.395546			0.0148446
$711$	4.00598	−	6.93857i	0.150236	−	0.260217i
$712$	5.53862	−	9.59317i	0.207569	−	0.359519i
$713$	8.78613	+	15.2180i	0.329043	+	0.569920i
$714$	0.802981	−	1.39080i	0.0300508	−	0.0520495i
$715$	−2.41535	+	4.18350i	−0.0903288	+	0.156454i
$716$	−12.1097	−	20.9746i	−0.452561	−	0.783858i
$717$	0.534247	−	0.925342i	0.0199518	−	0.0345575i
$718$	−28.4555			−1.06195
$719$	6.18329	−	10.7098i	0.230598	−	0.399407i	−0.727386	−	0.686228i	$-0.759265\pi$
$719$	6.18329	−	10.7098i	0.230598	−	0.399407i	0.957984	+	0.286821i	$0.0925985\pi$
$720$	0.158723	−	0.274916i	0.00591525	−	0.0102455i
$721$	4.54479			0.169257
$722$	19.5513	+	33.8638i	0.727624	+	1.26028i
$723$	24.1417			0.897841
$724$	1.69523	−	2.93622i	0.0630026	−	0.109124i
$725$	−50.7094			−1.88330
$726$	−2.40060	−	4.15796i	−0.0890945	−	0.154316i
$727$	−6.48532	−	11.2329i	−0.240527	−	0.416605i	0.720337	−	0.693624i	$-0.243987\pi$
$727$	−6.48532	−	11.2329i	−0.240527	−	0.416605i	−0.960865	+	0.277019i	$0.910654\pi$
$728$	−20.3727			−0.755062
$729$	1.00000			0.0370370
$730$	−0.937151	+	1.62319i	−0.0346855	+	0.0600771i
$731$	0.548520	−	0.950064i	0.0202877	−	0.0351394i
$732$	−4.31593	−	7.47540i	−0.159521	−	0.276299i
$733$	21.2661			0.785482			0.392741	−	0.919649i	$-0.371527\pi$
$733$	21.2661			0.785482			0.392741	+	0.919649i	$0.371527\pi$
$734$	12.6326	+	21.8803i	0.466278	+	0.807617i
$735$	−1.30478			−0.0481276
$736$	1.21640	−	2.10687i	0.0448371	−	0.0776602i
$737$	10.3725			0.382078
$738$	5.73037	+	9.92529i	0.210938	+	0.365355i
$739$	10.2190	+	17.6998i	0.375911	+	0.651097i	0.990463	−	0.137780i	$-0.0439966\pi$
$739$	10.2190	+	17.6998i	0.375911	+	0.651097i	−0.614552	+	0.788876i	$0.710663\pi$
$740$	−0.655702	+	1.13571i	−0.0241041	+	0.0417495i
$741$	−23.2945	−	40.3473i	−0.855746	−	1.48220i
$742$	−10.1190	−	17.5266i	−0.371479	−	0.643421i
$743$	−16.0453	−	27.7914i	−0.588647	−	1.01957i	−0.994410	−	0.105588i	$-0.966328\pi$
$743$	−16.0453	−	27.7914i	−0.588647	−	1.01957i	0.405763	−	0.913978i	$-0.367006\pi$
$744$	−3.61153	−	6.25535i	−0.132405	−	0.229332i
$745$	−2.28178	+	3.95216i	−0.0835980	+	0.144796i
$746$	0.641700	+	1.11146i	0.0234943	+	0.0406934i
$747$	−0.899848	+	1.55858i	−0.0329237	+	0.0570256i
$748$	0.599787	+	1.03886i	0.0219304	+	0.0379846i
$749$	24.9143	+	43.1528i	0.910347	+	1.57677i
$750$	1.57123	−	2.72145i	0.0573733	−	0.0993735i
$751$	19.5420			0.713100			0.356550	−	0.934276i	$-0.383953\pi$
$751$	19.5420			0.713100			0.356550	+	0.934276i	$0.383953\pi$
$752$	0.338188	+	0.585760i	0.0123325	+	0.0213605i
$753$	−4.35591	+	7.54466i	−0.158738	+	0.274943i
$754$	31.6313	+	54.7870i	1.15194	+	1.99522i
$755$	−0.848576	+	1.46978i	−0.0308828	+	0.0534906i
$756$	3.33321			0.121227
$757$	−16.0647	−	27.8249i	−0.583882	−	1.01131i	−0.995014	−	0.0997368i	$-0.968200\pi$
$757$	−16.0647	−	27.8249i	−0.583882	−	1.01131i	0.411132	−	0.911576i	$-0.365133\pi$
$758$	−2.09075	+	3.62128i	−0.0759394	+	0.131531i
$759$	3.02852	−	5.24555i	0.109928	−	0.190402i
$760$	2.41973			0.0877728
$761$	21.1550	−	36.6416i	0.766870	−	1.32826i	−0.172383	−	0.985030i	$-0.555147\pi$
$761$	21.1550	−	36.6416i	0.766870	−	1.32826i	0.939252	−	0.343227i	$-0.111520\pi$
$762$	3.07874	+	5.33254i	0.111531	+	0.193177i
$763$	20.8069	+	36.0385i	0.753259	+	1.30468i
$764$	8.72580			0.315688
$765$	0.0764738	−	0.132456i	0.00276491	−	0.00478897i
$766$	3.76289	+	6.51751i	0.135959	+	0.235487i
$767$	−64.1590			−2.31665
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	16.2661	−	28.1736i	0.586569	−	1.01597i	−0.408109	−	0.912933i	$-0.633812\pi$
$769$	16.2661	−	28.1736i	0.586569	−	1.01597i	0.994678	−	0.103034i	$-0.0328551\pi$
$770$	1.31721	−	2.28148i	0.0474690	−	0.0822187i
$771$	−2.07237	+	3.58945i	−0.0746345	+	0.129271i
$772$	12.2142			0.439598
$773$	12.3628			0.444658			0.222329	−	0.974972i	$-0.428634\pi$
$773$	12.3628			0.444658			0.222329	+	0.974972i	$0.428634\pi$
$774$	2.27693			0.0818424
$775$	−17.6937	−	30.6464i	−0.635576	−	1.10085i
$776$	0.704230	+	1.21976i	0.0252804	+	0.0437869i
$777$	−13.7699			−0.493991
$778$	−1.28543	−	2.22642i	−0.0460847	−	0.0798211i
$779$	−43.6798	+	75.6555i	−1.56499	+	2.71064i
$780$	−1.94024			−0.0694717
$781$	−3.10229			−0.111009
$782$	0.586071	−	1.01510i	0.0209578	−	0.0363001i
$783$	−5.17524	−	8.96378i	−0.184948	−	0.320339i
$784$	4.11026			0.146795
$785$	−3.37585	−	5.84714i	−0.120489	−	0.208693i
$786$	5.59778	+	9.69565i	0.199666	+	0.345832i
$787$	48.8683			1.74197			0.870984	−	0.491311i	$-0.163482\pi$
$787$	48.8683			1.74197			0.870984	+	0.491311i	$0.163482\pi$
$788$	−0.344699			−0.0122794
$789$	−21.0751			−0.750293
$790$	1.27168	−	2.20262i	0.0452444	−	0.0783656i
$791$	−1.71620	+	2.97255i	−0.0610212	+	0.105692i
$792$	−1.24487	+	2.15618i	−0.0442345	+	0.0766165i
$793$	−26.3791	+	45.6900i	−0.936750	+	1.62250i
$794$	0.563474			0.0199969
$795$	−0.963704	−	1.66918i	−0.0341791	−	0.0591999i
$796$	−0.512952	+	0.888459i	−0.0181811	+	0.0314906i
$797$	22.8668			0.809982			0.404991	−	0.914321i	$-0.367275\pi$
$797$	22.8668			0.809982			0.404991	+	0.914321i	$0.367275\pi$
$798$	12.7037	+	22.0034i	0.449706	+	0.778913i
$799$	0.162942	+	0.282223i	0.00576446	+	0.00998434i
$800$	−2.44961	+	4.24286i	−0.0866069	+	0.150008i
$801$	11.0772			0.391395
$802$	−6.71838	+	11.6366i	−0.237234	+	0.410902i
$803$	7.35012	−	12.7308i	0.259380	−	0.449260i
$804$	2.08306	+	3.60796i	0.0734638	+	0.127243i
$805$	−2.57417			−0.0907277
$806$	−22.0738	+	38.2330i	−0.777517	+	1.34670i
$807$	0.765600	+	1.32606i	0.0269504	+	0.0466795i
$808$	−3.32729	+	5.76303i	−0.117054	+	0.202743i
$809$	−22.3195	−	38.6585i	−0.784713	−	1.35916i	−0.929171	−	0.369651i	$-0.879477\pi$
$809$	−22.3195	−	38.6585i	−0.784713	−	1.35916i	0.144458	−	0.989511i	$-0.453856\pi$
$810$	0.317445			0.0111539
$811$	10.1394	−	17.5620i	0.356043	−	0.616685i	−0.631253	−	0.775577i	$-0.717459\pi$
$811$	10.1394	−	17.5620i	0.356043	−	0.616685i	0.987296	+	0.158892i	$0.0507923\pi$
$812$	−17.2501	−	29.8781i	−0.605361	−	1.04852i
$813$	9.18460	+	15.9082i	0.322118	+	0.557925i
$814$	5.14270	−	8.90742i	0.180252	−	0.312205i
$815$	2.11778	+	3.66811i	0.0741827	+	0.128488i
$816$	−0.240904	+	0.417257i	−0.00843331	+	0.0146069i
$817$	8.67794	+	15.0306i	0.303603	+	0.525856i
$818$	−13.2735	−	22.9903i	−0.464096	−	0.803838i
$819$	−10.1863	−	17.6433i	−0.355940	−	0.616506i
$820$	1.81908	+	3.15074i	0.0635250	+	0.110029i
$821$	6.23263	−	10.7952i	0.217520	−	0.376756i	−0.736529	−	0.676406i	$-0.763536\pi$
$821$	6.23263	−	10.7952i	0.217520	−	0.376756i	0.954049	+	0.299650i	$0.0968698\pi$
$822$	−3.93682	−	6.81877i	−0.137312	−	0.237832i
$823$	21.2426	+	36.7932i	0.740469	+	1.28253i	0.952282	+	0.305220i	$0.0987301\pi$
$823$	21.2426	+	36.7932i	0.740469	+	1.28253i	−0.211812	+	0.977310i	$0.567937\pi$
$824$	−1.36349			−0.0474994
$825$	−6.09890	+	10.5636i	−0.212337	+	0.367778i
$826$	34.9892			1.21743
$827$	23.6350	+	40.9371i	0.821871	+	1.42352i	0.904288	+	0.426924i	$0.140403\pi$
$827$	23.6350	+	40.9371i	0.821871	+	1.42352i	−0.0824168	+	0.996598i	$0.526264\pi$
$828$	2.43280			0.0845457
$829$	−20.0565	−	34.7389i	−0.696592	−	1.20653i	−0.969641	−	0.244532i	$-0.921366\pi$
$829$	−20.0565	−	34.7389i	−0.696592	−	1.20653i	0.273050	−	0.962000i	$-0.411968\pi$
$830$	−0.285653	+	0.494765i	−0.00991515	+	0.0171735i
$831$	12.3354	−	21.3656i	0.427912	−	0.741165i
$832$	6.11204			0.211897
$833$	1.98035			0.0686151
$834$	2.32804	+	4.03228i	0.0806133	+	0.139626i
$835$	0.325761	+	0.564234i	0.0112734	+	0.0195261i
$836$	−18.9781			−0.656370
$837$	3.61153	−	6.25535i	0.124833	−	0.216217i
$838$	−4.44546			−0.153566
$839$	−10.0241	−	17.3622i	−0.346070	−	0.599410i	0.639478	−	0.768809i	$-0.279151\pi$
$839$	−10.0241	−	17.3622i	−0.346070	−	0.599410i	−0.985547	+	0.169399i	$0.945817\pi$
$840$	1.05811			0.0365083
$841$	−39.0662	+	67.6646i	−1.34711	+	2.33326i
$842$	8.30460	−	14.3840i	0.286195	−	0.495705i
$843$	15.3460			0.528546
$844$	−0.327413	+	0.567096i	−0.0112700	+	0.0195203i
$845$	3.86602	+	6.69614i	0.132995	+	0.230354i
$846$	−0.338188	+	0.585760i	−0.0116272	+	0.0201388i
$847$	8.00168	−	13.8593i	0.274941	−	0.476212i
$848$	3.03581	+	5.25818i	0.104250	+	0.180567i
$849$	8.20503	−	14.2115i	0.281596	−	0.487738i
$850$	−1.18024	+	2.04424i	−0.0404820	+	0.0701168i
$851$	−10.0502			−0.344516
$852$	−0.623014	−	1.07909i	−0.0213441	−	0.0369691i
$853$	−12.4703	+	21.5991i	−0.426974	+	0.739541i	−0.996603	−	0.0823617i	$-0.973754\pi$
$853$	−12.4703	+	21.5991i	−0.426974	+	0.739541i	0.569629	+	0.821902i	$0.307087\pi$
$854$	14.3859	−	24.9171i	0.492274	−	0.852644i
$855$	1.20986	+	2.09555i	0.0413765	+	0.0716662i
$856$	−7.47456	−	12.9463i	−0.255475	−	0.442496i
$857$	−3.22089	−	5.57875i	−0.110024	−	0.190567i	0.805756	−	0.592248i	$-0.201759\pi$
$857$	−3.22089	−	5.57875i	−0.110024	−	0.190567i	−0.915780	+	0.401681i	$0.868426\pi$
$858$	15.2174			0.519513
$859$	−40.3276			−1.37596			−0.687979	−	0.725730i	$-0.741502\pi$
$859$	−40.3276			−1.37596			−0.687979	+	0.725730i	$0.741502\pi$
$860$	0.722800			0.0246473
$861$	−19.1005	+	33.0830i	−0.650943	+	1.12747i
$862$	24.7175			0.841883
$863$	−21.7769	−	37.7187i	−0.741295	−	1.28396i	−0.951906	−	0.306391i	$-0.900879\pi$
$863$	−21.7769	−	37.7187i	−0.741295	−	1.28396i	0.210611	−	0.977570i	$-0.432455\pi$
$864$	−1.00000			−0.0340207
$865$	−0.474905			−0.0161473
$866$	39.1940			1.33187
$867$	8.38393	−	14.5214i	0.284733	−	0.493172i
$868$	12.0380	−	20.8504i	0.408595	−	0.707707i
$869$	−9.97386	+	17.2752i	−0.338340	+	0.586022i
$870$	−1.64286	−	2.84551i	−0.0556980	−	0.0964718i
$871$	12.7317	−	22.0520i	0.431399	−	0.747204i
$872$	−6.24230	−	10.8120i	−0.211391	−	0.366140i
$873$	−0.704230	+	1.21976i	−0.0238346	+	0.0412827i
$874$	9.27202	+	16.0596i	0.313631	+	0.543225i
$875$	10.4745			0.354102
$876$	5.90433			0.199489
$877$	2.38144			0.0804156			0.0402078	−	0.999191i	$-0.487198\pi$
$877$	2.38144			0.0804156			0.0402078	+	0.999191i	$0.487198\pi$
$878$	21.2037			0.715591
$879$	24.4248			0.823826
$880$	−0.395178	+	0.684469i	−0.0133215	+	0.0230734i
$881$	2.42137	+	4.19393i	0.0815780	+	0.141297i	0.903928	−	0.427685i	$-0.140671\pi$
$881$	2.42137	+	4.19393i	0.0815780	+	0.141297i	−0.822350	+	0.568982i	$0.807337\pi$
$882$	2.05513	+	3.55959i	0.0691998	+	0.119858i
$883$	−0.135575	−	0.234823i	−0.00456247	−	0.00790244i	0.863735	−	0.503946i	$-0.168119\pi$
$883$	−0.135575	−	0.234823i	−0.00456247	−	0.00790244i	−0.868298	+	0.496044i	$0.834786\pi$
$884$	2.94483			0.0990452
$885$	3.33227			0.112013
$886$	3.68286	−	6.37890i	0.123728	−	0.214303i
$887$	4.19900	+	7.27288i	0.140989	+	0.244199i	0.927869	−	0.372906i	$-0.121639\pi$
$887$	4.19900	+	7.27288i	0.140989	+	0.244199i	−0.786881	+	0.617105i	$0.788305\pi$
$888$	4.13112			0.138631
$889$	−10.2621	+	17.7744i	−0.344179	+	0.596136i
$890$	3.51642			0.117871
$891$	−2.48974			−0.0834094
$892$	7.09104	+	13.1422i	0.237426	+	0.440033i
$893$	−5.15569			−0.172528
$894$	14.3759			0.480802
$895$	3.84417	−	6.65829i	0.128496	−	0.222562i
$896$	−3.33321			−0.111355
$897$	−7.43469	−	12.8773i	−0.248237	−	0.429959i
$898$	−4.81711	+	8.34347i	−0.160749	+	0.278425i
$899$	−74.7621			−2.49345
$900$	−4.89923			−0.163308
$901$	1.46268	+	2.53343i	0.0487288	+	0.0844007i
$902$	−14.2671	−	24.7114i	−0.475043	−	0.822799i
$903$	3.79473	+	6.57267i	0.126281	+	0.218725i
$904$	0.514881	−	0.891800i	0.0171247	−	0.0296608i
$905$	1.07628			0.0357769
$906$	5.34628			0.177618
$907$	43.5298			1.44538			0.722691	−	0.691171i	$-0.242905\pi$
$907$	43.5298			1.44538			0.722691	+	0.691171i	$0.242905\pi$
$908$	−22.0684			−0.732366
$909$	−6.65458			−0.220718
$910$	−3.23361	−	5.60078i	−0.107193	−	0.185664i
$911$	13.2304	−	22.9157i	0.438343	−	0.759232i	−0.559219	−	0.829020i	$-0.688899\pi$
$911$	13.2304	−	22.9157i	0.438343	−	0.759232i	0.997562	+	0.0697882i	$0.0222323\pi$
$912$	−3.81125	−	6.60128i	−0.126203	−	0.218590i
$913$	2.24039	−	3.88047i	0.0741460	−	0.128425i
$914$	19.6936	+	34.1103i	0.651407	+	1.12827i
$915$	1.37007	−	2.37303i	0.0452932	−	0.0784501i
$916$	12.3111	−	21.3234i	0.406769	−	0.704544i
$917$	−18.6586	+	32.3176i	−0.616160	+	1.06722i
$918$	−0.481807			−0.0159020
$919$	21.9412			0.723774			0.361887	−	0.932222i	$-0.382133\pi$
$919$	21.9412			0.723774			0.361887	+	0.932222i	$0.382133\pi$
$920$	0.772282			0.0254614
$921$	−10.3706	−	17.9624i	−0.341722	−	0.591880i
$922$	−20.6899			−0.681387
$923$	−3.80789	+	6.59546i	−0.125338	+	0.217092i
$924$	−8.29881			−0.273011
$925$	20.2393			0.665463
$926$	−7.94253			−0.261008
$927$	−0.681745	−	1.18082i	−0.0223915	−	0.0387831i
$928$	5.17524	+	8.96378i	0.169886	+	0.294250i
$929$	22.4389	+	38.8653i	0.736196	+	1.27513i	0.954197	+	0.299181i	$0.0967133\pi$
$929$	22.4389	+	38.8653i	0.736196	+	1.27513i	−0.218000	+	0.975949i	$0.569953\pi$
$930$	1.14646	−	1.98573i	0.0375940	−	0.0651147i
$931$	−15.6652	+	27.1330i	−0.513407	+	0.889247i
$932$	−14.0993	−	24.4206i	−0.461837	−	0.799925i
$933$	−22.4339			−0.734453
$934$	−0.995744	+	1.72468i	−0.0325817	+	0.0564332i
$935$	−0.190400	+	0.329782i	−0.00622674	+	0.0107850i
$936$	3.05602	+	5.29318i	0.0998892	+	0.173013i
$937$	20.0763	−	34.7731i	0.655864	−	1.13599i	−0.325813	−	0.945434i	$-0.605638\pi$
$937$	20.0763	−	34.7731i	0.655864	−	1.13599i	0.981677	−	0.190555i	$-0.0610287\pi$
$938$	−6.94326	+	12.0261i	−0.226706	+	0.392665i
$939$	0.621989	+	1.07732i	0.0202978	+	0.0351569i
$940$	−0.107356	+	0.185947i	−0.00350158	+	0.00606491i
$941$	53.7174			1.75114			0.875568	−	0.483094i	$-0.160487\pi$
$941$	53.7174			1.75114			0.875568	+	0.483094i	$0.160487\pi$
$942$	−10.6344	+	18.4194i	−0.346488	+	0.600135i
$943$	−13.9408	+	24.1463i	−0.453976	+	0.786310i
$944$	−10.4971			−0.341653
$945$	0.529055	+	0.916351i	0.0172102	+	0.0298089i
$946$	−5.66896			−0.184314
$947$	17.0801	−	29.5835i	0.555027	−	0.961336i	−0.442874	−	0.896584i	$-0.646041\pi$
$947$	17.0801	−	29.5835i	0.555027	−	0.961336i	0.997901	−	0.0647518i	$-0.0206256\pi$
$948$	−8.01197			−0.260217
$949$	−18.0438	−	31.2527i	−0.585725	−	1.01451i
$950$	−18.6722	−	32.3412i	−0.605806	−	1.04929i
$951$	22.8554			0.741138
$952$	−1.60596			−0.0520495
$953$	−4.26587	+	7.38870i	−0.138185	+	0.239344i	−0.926810	−	0.375531i	$-0.877460\pi$
$953$	−4.26587	+	7.38870i	−0.138185	+	0.239344i	0.788625	+	0.614875i	$0.210794\pi$
$954$	−3.03581	+	5.25818i	−0.0982880	+	0.170240i
$955$	1.38498	+	2.39886i	0.0448170	+	0.0776253i
$956$	−1.06849			−0.0345575
$957$	12.8850	+	22.3175i	0.416513	+	0.721421i
$958$	−27.5409			−0.889806
$959$	13.1222	−	22.7283i	0.423739	−	0.733937i
$960$	−0.317445			−0.0102455
$961$	−10.5863	−	18.3359i	−0.341492	−	0.591482i
$962$	−12.6248	−	21.8668i	−0.407039	−	0.705012i
$963$	7.47456	−	12.9463i	0.240864	−	0.417189i
$964$	−12.0709	−	20.9074i	−0.388776	−	0.673380i
$965$	1.93867	+	3.35787i	0.0624079	+	0.108094i
$966$	4.05451	+	7.02262i	0.130452	+	0.225949i
$967$	−19.5270	−	33.8218i	−0.627947	−	1.08764i	−0.987963	−	0.154690i	$-0.950562\pi$
$967$	−19.5270	−	33.8218i	−0.627947	−	1.08764i	0.360016	−	0.932946i	$-0.382771\pi$
$968$	−2.40060	+	4.15796i	−0.0771581	+	0.133642i
$969$	−1.83629	−	3.18055i	−0.0589901	−	0.102174i
$970$	−0.223555	+	0.387208i	−0.00717791	+	0.0124325i
$971$	−0.153652	−	0.266133i	−0.00493092	−	0.00854061i	0.863549	−	0.504264i	$-0.168236\pi$
$971$	−0.153652	−	0.266133i	−0.00493092	−	0.00854061i	−0.868480	+	0.495724i	$0.834903\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−7.75982	+	13.4404i	−0.248768	+	0.430879i
$974$	24.4289			0.782753
$975$	14.9721	+	25.9325i	0.479492	+	0.830505i
$976$	−4.31593	+	7.47540i	−0.138149	+	0.239282i
$977$	5.30320	+	9.18541i	0.169664	+	0.293867i	0.938302	−	0.345817i	$-0.112398\pi$
$977$	5.30320	+	9.18541i	0.169664	+	0.293867i	−0.768637	+	0.639685i	$0.779065\pi$
$978$	6.67133	−	11.5551i	0.213325	−	0.369491i
$979$	−27.5795			−0.881443
$980$	0.652391	+	1.12997i	0.0208399	+	0.0360957i
$981$	6.24230	−	10.8120i	0.199301	−	0.345200i
$982$	4.40001	−	7.62104i	0.140410	−	0.243197i
$983$	−46.0507			−1.46879			−0.734395	−	0.678722i	$-0.762534\pi$
$983$	−46.0507			−1.46879			−0.734395	+	0.678722i	$0.762534\pi$
$984$	5.73037	−	9.92529i	0.182677	−	0.316407i
$985$	−0.0547116	−	0.0947633i	−0.00174326	−	0.00301941i
$986$	2.49347	+	4.31881i	0.0794082	+	0.137539i
$987$	−2.25450			−0.0717616
$988$	−23.2945	+	40.3473i	−0.741098	+	1.28362i
$989$	2.76966	+	4.79719i	0.0880699	+	0.152542i
$990$	−0.790357			−0.0251192
$991$	11.0012	−	19.0547i	0.349466	−	0.605292i	−0.636689	−	0.771121i	$-0.719696\pi$
$991$	11.0012	−	19.0547i	0.349466	−	0.605292i	0.986155	+	0.165828i	$0.0530298\pi$
$992$	−3.61153	+	6.25535i	−0.114666	+	0.198608i
$993$	−6.35812	+	11.0126i	−0.201769	+	0.349474i
$994$	2.07663	−	3.59684i	0.0658669	−	0.114085i
$995$	−0.325669			−0.0103244
$996$	1.79970			0.0570256
$997$	−9.10641			−0.288403			−0.144201	−	0.989548i	$-0.546061\pi$
$997$	−9.10641			−0.288403			−0.144201	+	0.989548i	$0.546061\pi$
$998$	8.72858	+	15.1183i	0.276298	+	0.478563i
$999$	2.06556	+	3.57765i	0.0653514	+	0.113192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.h.931.5	✓	14
223.183	even	3	inner	1338.2.e.h.1075.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.h.931.5	✓	14	1.1	even	1	trivial
1338.2.e.h.1075.5	yes	14	223.183	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.158723 + 0.274916i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.33321 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.158723 - 0.274916i) q^{10} +(1.24487 + 2.15618i) q^{11} +(-0.500000 + 0.866025i) q^{12} +6.11204 q^{13} -3.33321 q^{14} -0.317445 q^{15} +1.00000 q^{16} +0.481807 q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.81125 + 6.60128i) q^{19} +(0.158723 + 0.274916i) q^{20} +(-1.66660 + 2.88664i) q^{21} +(-1.24487 - 2.15618i) q^{22} +(-1.21640 + 2.10687i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.44961 - 4.24286i) q^{25} -6.11204 q^{26} +1.00000 q^{27} +3.33321 q^{28} +(-5.17524 - 8.96378i) q^{29} +0.317445 q^{30} +(3.61153 - 6.25535i) q^{31} -1.00000 q^{32} -2.48974 q^{33} -0.481807 q^{34} +(0.529055 + 0.916351i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.06556 + 3.57765i) q^{37} +(3.81125 - 6.60128i) q^{38} +(-3.05602 + 5.29318i) q^{39} +(-0.158723 - 0.274916i) q^{40} +11.4607 q^{41} +(1.66660 - 2.88664i) q^{42} +(1.13846 - 1.97188i) q^{43} +(1.24487 + 2.15618i) q^{44} +(0.158723 - 0.274916i) q^{45} +(1.21640 - 2.10687i) q^{46} +(0.338188 + 0.585760i) q^{47} +(-0.500000 + 0.866025i) q^{48} +4.11026 q^{49} +(-2.44961 + 4.24286i) q^{50} +(-0.240904 + 0.417257i) q^{51} +6.11204 q^{52} +(3.03581 + 5.25818i) q^{53} -1.00000 q^{54} +(-0.395178 + 0.684469i) q^{55} -3.33321 q^{56} +(-3.81125 - 6.60128i) q^{57} +(5.17524 + 8.96378i) q^{58} -10.4971 q^{59} -0.317445 q^{60} +(-4.31593 + 7.47540i) q^{61} +(-3.61153 + 6.25535i) q^{62} +(-1.66660 - 2.88664i) q^{63} +1.00000 q^{64} +(0.970120 + 1.68030i) q^{65} +2.48974 q^{66} +(2.08306 - 3.60796i) q^{67} +0.481807 q^{68} +(-1.21640 - 2.10687i) q^{69} +(-0.529055 - 0.916351i) q^{70} +(-0.623014 + 1.07909i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-2.95216 - 5.11330i) q^{73} +(-2.06556 - 3.57765i) q^{74} +(2.44961 + 4.24286i) q^{75} +(-3.81125 + 6.60128i) q^{76} +(4.14941 + 7.18698i) q^{77} +(3.05602 - 5.29318i) q^{78} +(4.00598 + 6.93857i) q^{79} +(0.158723 + 0.274916i) q^{80} +(-0.500000 + 0.866025i) q^{81} -11.4607 q^{82} +(-0.899848 - 1.55858i) q^{83} +(-1.66660 + 2.88664i) q^{84} +(0.0764738 + 0.132456i) q^{85} +(-1.13846 + 1.97188i) q^{86} +10.3505 q^{87} +(-1.24487 - 2.15618i) q^{88} +(-5.53862 + 9.59317i) q^{89} +(-0.158723 + 0.274916i) q^{90} +20.3727 q^{91} +(-1.21640 + 2.10687i) q^{92} +(3.61153 + 6.25535i) q^{93} +(-0.338188 - 0.585760i) q^{94} -2.41973 q^{95} +(0.500000 - 0.866025i) q^{96} +(-0.704230 - 1.21976i) q^{97} -4.11026 q^{98} +(1.24487 - 2.15618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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