LMFDB - Embedded newform 57.2.e.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(7,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("57.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	57.7
Dual form			57.2.e.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.285997 + 0.495361i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.836412 - 1.44871i) q^{4} +(1.33641 + 2.31473i) q^{5} +(0.285997 - 0.495361i) q^{6} -3.67282 q^{7} +2.10083 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.285997 + 0.495361i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.836412 - 1.44871i) q^{4} +(1.33641 + 2.31473i) q^{5} +(0.285997 - 0.495361i) q^{6} -3.67282 q^{7} +2.10083 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.764419 + 1.32401i) q^{10} -3.81681 q^{11} -1.67282 q^{12} +(-0.0719933 + 0.124696i) q^{13} +(-1.05042 - 1.81937i) q^{14} +(1.33641 - 2.31473i) q^{15} +(-1.07199 - 1.85675i) q^{16} -0.571993 q^{18} +(4.24482 - 0.990721i) q^{19} +4.47116 q^{20} +(1.83641 + 3.18076i) q^{21} +(-1.09159 - 1.89070i) q^{22} +(-3.76442 + 6.52016i) q^{23} +(-1.05042 - 1.81937i) q^{24} +(-1.07199 + 1.85675i) q^{25} -0.0823593 q^{26} +1.00000 q^{27} +(-3.07199 + 5.32085i) q^{28} +(2.67282 - 4.62947i) q^{29} +1.52884 q^{30} +8.81681 q^{31} +(2.71400 - 4.70079i) q^{32} +(1.90841 + 3.30545i) q^{33} +(-4.90841 - 8.50161i) q^{35} +(0.836412 + 1.44871i) q^{36} -1.00000 q^{37} +(1.70477 + 1.81937i) q^{38} +0.143987 q^{39} +(2.80757 + 4.86286i) q^{40} +(-2.67282 - 4.62947i) q^{41} +(-1.05042 + 1.81937i) q^{42} +(-1.40841 - 2.43943i) q^{43} +(-3.19243 + 5.52944i) q^{44} -2.67282 q^{45} -4.30644 q^{46} +(3.00000 - 5.19615i) q^{47} +(-1.07199 + 1.85675i) q^{48} +6.48963 q^{49} -1.22635 q^{50} +(0.120432 + 0.208594i) q^{52} +(-4.00924 + 6.94420i) q^{53} +(0.285997 + 0.495361i) q^{54} +(-5.10083 - 8.83490i) q^{55} -7.71598 q^{56} +(-2.98040 - 3.18076i) q^{57} +3.05767 q^{58} +(-1.90841 - 3.30545i) q^{59} +(-2.23558 - 3.87214i) q^{60} +(-5.74482 + 9.95031i) q^{61} +(2.52158 + 4.36750i) q^{62} +(1.83641 - 3.18076i) q^{63} -1.18319 q^{64} -0.384851 q^{65} +(-1.09159 + 1.89070i) q^{66} +(-2.69243 + 4.66342i) q^{67} +7.52884 q^{69} +(2.80757 - 4.86286i) q^{70} +(6.81681 + 11.8071i) q^{71} +(-1.05042 + 1.81937i) q^{72} +(0.172824 + 0.299339i) q^{73} +(-0.285997 - 0.495361i) q^{74} +2.14399 q^{75} +(2.11515 - 6.97815i) q^{76} +14.0185 q^{77} +(0.0411797 + 0.0713253i) q^{78} +(-3.26442 - 5.65414i) q^{79} +(2.86525 - 4.96276i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.52884 - 2.64802i) q^{82} -2.28797 q^{83} +6.14399 q^{84} +(0.805598 - 1.39534i) q^{86} -5.34565 q^{87} -8.01847 q^{88} +(4.33641 - 7.51089i) q^{89} +(-0.764419 - 1.32401i) q^{90} +(0.264419 - 0.457986i) q^{91} +(6.29721 + 10.9071i) q^{92} +(-4.40841 - 7.63558i) q^{93} +3.43196 q^{94} +(7.96608 + 8.50161i) q^{95} -5.42801 q^{96} +(2.95684 + 5.12140i) q^{97} +(1.85601 + 3.21471i) q^{98} +(1.90841 - 3.30545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9} + 4 q^{10} + 10 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} - 5 q^{16} - 2 q^{18} + 4 q^{19} + 44 q^{20} + q^{21} - 18 q^{22} - 14 q^{23} + 3 q^{24} - 5 q^{25} - 42 q^{26} + 6 q^{27} - 17 q^{28} - 4 q^{29} - 8 q^{30} + 30 q^{31} + 17 q^{32} - 18 q^{35} - 5 q^{36} - 6 q^{37} + 41 q^{38} - 2 q^{39} + 24 q^{40} + 4 q^{41} + 3 q^{42} + 3 q^{43} - 12 q^{44} + 4 q^{45} + 40 q^{46} + 18 q^{47} - 5 q^{48} - 4 q^{49} - 46 q^{50} - 5 q^{52} + 6 q^{53} + q^{54} - 12 q^{55} - 42 q^{56} - 5 q^{57} - 16 q^{58} - 22 q^{60} - 13 q^{61} + 23 q^{62} + q^{63} - 30 q^{64} + 12 q^{65} - 18 q^{66} - 9 q^{67} + 28 q^{69} + 24 q^{70} + 18 q^{71} + 3 q^{72} - 19 q^{73} - q^{74} + 10 q^{75} + 27 q^{76} + 24 q^{77} + 21 q^{78} - 11 q^{79} - 10 q^{80} - 3 q^{81} - 8 q^{82} - 8 q^{83} + 34 q^{84} + 17 q^{86} + 8 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} - 7 q^{91} + 2 q^{92} - 15 q^{93} + 12 q^{94} + 2 q^{95} - 34 q^{96} + 2 q^{97} + 14 q^{98}+O(q^{100}) $ 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9 + 4 * q^10 + 10 * q^12 + q^13 + 3 * q^14 - 2 * q^15 - 5 * q^16 - 2 * q^18 + 4 * q^19 + 44 * q^20 + q^21 - 18 * q^22 - 14 * q^23 + 3 * q^24 - 5 * q^25 - 42 * q^26 + 6 * q^27 - 17 * q^28 - 4 * q^29 - 8 * q^30 + 30 * q^31 + 17 * q^32 - 18 * q^35 - 5 * q^36 - 6 * q^37 + 41 * q^38 - 2 * q^39 + 24 * q^40 + 4 * q^41 + 3 * q^42 + 3 * q^43 - 12 * q^44 + 4 * q^45 + 40 * q^46 + 18 * q^47 - 5 * q^48 - 4 * q^49 - 46 * q^50 - 5 * q^52 + 6 * q^53 + q^54 - 12 * q^55 - 42 * q^56 - 5 * q^57 - 16 * q^58 - 22 * q^60 - 13 * q^61 + 23 * q^62 + q^63 - 30 * q^64 + 12 * q^65 - 18 * q^66 - 9 * q^67 + 28 * q^69 + 24 * q^70 + 18 * q^71 + 3 * q^72 - 19 * q^73 - q^74 + 10 * q^75 + 27 * q^76 + 24 * q^77 + 21 * q^78 - 11 * q^79 - 10 * q^80 - 3 * q^81 - 8 * q^82 - 8 * q^83 + 34 * q^84 + 17 * q^86 + 8 * q^87 + 12 * q^88 + 16 * q^89 + 4 * q^90 - 7 * q^91 + 2 * q^92 - 15 * q^93 + 12 * q^94 + 2 * q^95 - 34 * q^96 + 2 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.285997	+	0.495361i	0.202230	+	0.350273i	0.949247	−	0.314533i	$-0.101848\pi$
$2$	0.285997	+	0.495361i	0.202230	+	0.350273i	−0.747017	+	0.664805i	$0.768514\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.836412	−	1.44871i	0.418206	−	0.724354i
$5$	1.33641	+	2.31473i	0.597662	+	1.03518i	0.993165	+	0.116716i	$0.0372367\pi$
$5$	1.33641	+	2.31473i	0.597662	+	1.03518i	−0.395504	+	0.918464i	$0.629430\pi$
$6$	0.285997	−	0.495361i	0.116758	−	0.202230i
$7$	−3.67282			−1.38820			−0.694098	−	0.719880i	$-0.744197\pi$
$7$	−3.67282			−1.38820			−0.694098	+	0.719880i	$0.744197\pi$
$8$	2.10083			0.742756
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.764419	+	1.32401i	−0.241730	+	0.418689i
$11$	−3.81681			−1.15081			−0.575406	−	0.817868i	$-0.695156\pi$
$11$	−3.81681			−1.15081			−0.575406	+	0.817868i	$0.695156\pi$
$12$	−1.67282			−0.482903
$13$	−0.0719933	+	0.124696i	−0.0199673	+	0.0345844i	−0.875836	−	0.482608i	$-0.839690\pi$
$13$	−0.0719933	+	0.124696i	−0.0199673	+	0.0345844i	0.855869	+	0.517193i	$0.173023\pi$
$14$	−1.05042	−	1.81937i	−0.280735	−	0.486248i
$15$	1.33641	−	2.31473i	0.345060	−	0.597662i
$16$	−1.07199	−	1.85675i	−0.267998	−	0.464187i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−0.571993			−0.134820
$19$	4.24482	−	0.990721i	0.973828	−	0.227287i
$19$	4.24482	−	0.990721i	0.973828	−	0.227287i
$20$	4.47116			0.999782
$21$	1.83641	+	3.18076i	0.400738	+	0.694098i
$22$	−1.09159	−	1.89070i	−0.232729	−	0.403098i
$23$	−3.76442	+	6.52016i	−0.784936	+	1.35955i	0.144102	+	0.989563i	$0.453971\pi$
$23$	−3.76442	+	6.52016i	−0.784936	+	1.35955i	−0.929038	+	0.369985i	$0.879363\pi$
$24$	−1.05042	−	1.81937i	−0.214415	−	0.371378i
$25$	−1.07199	+	1.85675i	−0.214399	+	0.371349i
$26$	−0.0823593			−0.0161520
$27$	1.00000			0.192450
$28$	−3.07199	+	5.32085i	−0.580552	+	1.00555i
$29$	2.67282	−	4.62947i	0.496331	−	0.859670i	−0.503660	−	0.863902i	$-0.668014\pi$
$29$	2.67282	−	4.62947i	0.496331	−	0.859670i	0.999991	+	0.00423154i	$0.00134695\pi$
$30$	1.52884			0.279126
$31$	8.81681			1.58355			0.791773	−	0.610816i	$-0.209158\pi$
$31$	8.81681			1.58355			0.791773	+	0.610816i	$0.209158\pi$
$32$	2.71400	−	4.70079i	0.479773	−	0.830990i
$33$	1.90841	+	3.30545i	0.332211	+	0.575406i
$34$		0			0
$35$	−4.90841	−	8.50161i	−0.829672	−	1.43703i
$36$	0.836412	+	1.44871i	0.139402	+	0.241451i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	1.70477	+	1.81937i	0.276550	+	0.295141i
$39$	0.143987			0.0230563
$40$	2.80757	+	4.86286i	0.443917	+	0.768886i
$41$	−2.67282	−	4.62947i	−0.417425	−	0.723001i	0.578255	−	0.815856i	$-0.303734\pi$
$41$	−2.67282	−	4.62947i	−0.417425	−	0.723001i	−0.995680	+	0.0928551i	$0.970401\pi$
$42$	−1.05042	+	1.81937i	−0.162083	+	0.280735i
$43$	−1.40841	−	2.43943i	−0.214780	−	0.372009i	0.738425	−	0.674336i	$-0.235570\pi$
$43$	−1.40841	−	2.43943i	−0.214780	−	0.372009i	−0.953204	+	0.302327i	$0.902237\pi$
$44$	−3.19243	+	5.52944i	−0.481276	+	0.833595i
$45$	−2.67282			−0.398441
$46$	−4.30644			−0.634951
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	−1.07199	+	1.85675i	−0.154729	+	0.267998i
$49$	6.48963			0.927091
$50$	−1.22635			−0.173431
$51$		0			0
$52$	0.120432	+	0.208594i	0.0167009	+	0.0289268i
$53$	−4.00924	+	6.94420i	−0.550711	+	0.953859i	0.447513	+	0.894278i	$0.352310\pi$
$53$	−4.00924	+	6.94420i	−0.550711	+	0.953859i	−0.998223	+	0.0595815i	$0.981023\pi$
$54$	0.285997	+	0.495361i	0.0389192	+	0.0674101i
$55$	−5.10083	−	8.83490i	−0.687796	−	1.19130i
$56$	−7.71598			−1.03109
$57$	−2.98040	−	3.18076i	−0.394763	−	0.421302i
$58$	3.05767			0.401492
$59$	−1.90841	−	3.30545i	−0.248453	−	0.430334i	0.714644	−	0.699489i	$-0.246589\pi$
$59$	−1.90841	−	3.30545i	−0.248453	−	0.430334i	−0.963097	+	0.269155i	$0.913256\pi$
$60$	−2.23558	−	3.87214i	−0.288612	−	0.499891i
$61$	−5.74482	+	9.95031i	−0.735548	+	1.27401i	0.218934	+	0.975740i	$0.429742\pi$
$61$	−5.74482	+	9.95031i	−0.735548	+	1.27401i	−0.954482	+	0.298268i	$0.903591\pi$
$62$	2.52158	+	4.36750i	0.320241	+	0.554673i
$63$	1.83641	−	3.18076i	0.231366	−	0.400738i
$64$	−1.18319			−0.147899
$65$	−0.384851			−0.0477348
$66$	−1.09159	+	1.89070i	−0.134366	+	0.232729i
$67$	−2.69243	+	4.66342i	−0.328932	+	0.569727i	−0.982300	−	0.187313i	$-0.940022\pi$
$67$	−2.69243	+	4.66342i	−0.328932	+	0.569727i	0.653368	+	0.757040i	$0.273355\pi$
$68$		0			0
$69$	7.52884			0.906365
$70$	2.80757	−	4.86286i	0.335569	−	0.581223i
$71$	6.81681	+	11.8071i	0.809007	+	1.40124i	0.913553	+	0.406720i	$0.133328\pi$
$71$	6.81681	+	11.8071i	0.809007	+	1.40124i	−0.104546	+	0.994520i	$0.533339\pi$
$72$	−1.05042	+	1.81937i	−0.123793	+	0.214415i
$73$	0.172824	+	0.299339i	0.0202275	+	0.0350350i	0.875962	−	0.482380i	$-0.160228\pi$
$73$	0.172824	+	0.299339i	0.0202275	+	0.0350350i	−0.855734	+	0.517415i	$0.826894\pi$
$74$	−0.285997	−	0.495361i	−0.0332464	−	0.0575845i
$75$	2.14399			0.247566
$76$	2.11515	−	6.97815i	0.242624	−	0.800449i
$77$	14.0185			1.59755
$78$	0.0411797	+	0.0713253i	0.00466268	+	0.00807600i
$79$	−3.26442	−	5.65414i	−0.367276	−	0.636140i	0.621863	−	0.783126i	$-0.286376\pi$
$79$	−3.26442	−	5.65414i	−0.367276	−	0.636140i	−0.989139	+	0.146986i	$0.953043\pi$
$80$	2.86525	−	4.96276i	0.320345	−	0.554853i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.52884	−	2.64802i	0.168832	−	0.292425i
$83$	−2.28797			−0.251138			−0.125569	−	0.992085i	$-0.540076\pi$
$83$	−2.28797			−0.251138			−0.125569	+	0.992085i	$0.540076\pi$
$84$	6.14399			0.670364
$85$		0			0
$86$	0.805598	−	1.39534i	0.0868699	−	0.150463i
$87$	−5.34565			−0.573114
$88$	−8.01847			−0.854772
$89$	4.33641	−	7.51089i	0.459659	−	0.796152i	−0.539284	−	0.842124i	$-0.681305\pi$
$89$	4.33641	−	7.51089i	0.459659	−	0.796152i	0.998943	+	0.0459717i	$0.0146384\pi$
$90$	−0.764419	−	1.32401i	−0.0805768	−	0.139563i
$91$	0.264419	−	0.457986i	0.0277186	−	0.0480100i
$92$	6.29721	+	10.9071i	0.656529	+	1.13714i
$93$	−4.40841	−	7.63558i	−0.457130	−	0.791773i
$94$	3.43196			0.353980
$95$	7.96608	+	8.50161i	0.817303	+	0.872246i
$96$	−5.42801			−0.553994
$97$	2.95684	+	5.12140i	0.300222	+	0.520000i	0.976186	−	0.216935i	$-0.0696059\pi$
$97$	2.95684	+	5.12140i	0.300222	+	0.520000i	−0.675964	+	0.736935i	$0.736273\pi$
$98$	1.85601	+	3.21471i	0.187486	+	0.324735i
$99$	1.90841	−	3.30545i	0.191802	−	0.332211i
$100$	1.79326	+	3.10601i	0.179326	+	0.310601i
$101$	−4.14399	+	7.17760i	−0.412342	+	0.714197i	−0.995145	−	0.0984158i	$-0.968622\pi$
$101$	−4.14399	+	7.17760i	−0.412342	+	0.714197i	0.582803	+	0.812613i	$0.301956\pi$
$102$		0			0
$103$	14.6521			1.44371			0.721857	−	0.692043i	$-0.243289\pi$
$103$	14.6521			1.44371			0.721857	+	0.692043i	$0.243289\pi$
$104$	−0.151246	+	0.261965i	−0.0148309	+	0.0256878i
$105$	−4.90841	+	8.50161i	−0.479011	+	0.829672i
$106$	−4.58651			−0.445481
$107$	−16.6913			−1.61361			−0.806804	−	0.590819i	$-0.798805\pi$
$107$	−16.6913			−1.61361			−0.806804	+	0.590819i	$0.798805\pi$
$108$	0.836412	−	1.44871i	0.0804838	−	0.139402i
$109$	−3.91764	−	6.78555i	−0.375242	−	0.649938i	0.615121	−	0.788432i	$-0.289107\pi$
$109$	−3.91764	−	6.78555i	−0.375242	−	0.649938i	−0.990363	+	0.138494i	$0.955774\pi$
$110$	2.91764	−	5.05350i	0.278186	−	0.481832i
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$	3.93724	+	6.81950i	0.372034	+	0.644383i
$113$	−6.38485			−0.600636			−0.300318	−	0.953839i	$-0.597093\pi$
$113$	−6.38485			−0.600636			−0.300318	+	0.953839i	$0.597093\pi$
$114$	0.723239	−	2.38606i	0.0677375	−	0.223475i
$115$	−20.1233			−1.87650
$116$	−4.47116	−	7.74428i	−0.415137	−	0.719038i
$117$	−0.0719933	−	0.124696i	−0.00665578	−	0.0115281i
$118$	1.09159	−	1.89070i	0.100489	−	0.174053i
$119$		0			0
$120$	2.80757	−	4.86286i	0.256295	−	0.443917i
$121$	3.56804			0.324367
$122$	−6.57199			−0.595000
$123$	−2.67282	+	4.62947i	−0.241000	+	0.417425i
$124$	7.37448	−	12.7730i	0.662248	−	1.14705i
$125$	7.63362			0.682772
$126$	2.10083			0.187157
$127$	−1.32718	+	2.29874i	−0.117768	+	0.203980i	−0.918883	−	0.394531i	$-0.870907\pi$
$127$	−1.32718	+	2.29874i	−0.117768	+	0.203980i	0.801115	+	0.598511i	$0.204241\pi$
$128$	−5.76640	−	9.98769i	−0.509682	−	0.882795i
$129$	−1.40841	+	2.43943i	−0.124003	+	0.214780i
$130$	−0.110066	−	0.190640i	−0.00965343	−	0.0167202i
$131$	5.67282	+	9.82562i	0.495637	+	0.858468i	0.999987	−	0.00503076i	$-0.00160135\pi$
$131$	5.67282	+	9.82562i	0.495637	+	0.858468i	−0.504350	+	0.863499i	$0.668268\pi$
$132$	6.38485			0.555730
$133$	−15.5905	+	3.63875i	−1.35186	+	0.315519i
$134$	−3.08010			−0.266080
$135$	1.33641	+	2.31473i	0.115020	+	0.199221i
$136$		0			0
$137$	0.816810	−	1.41476i	0.0697848	−	0.120871i	−0.829022	−	0.559216i	$-0.811102\pi$
$137$	0.816810	−	1.41476i	0.0697848	−	0.120871i	0.898806	+	0.438346i	$0.144435\pi$
$138$	2.15322	+	3.72949i	0.183294	+	0.317475i
$139$	−3.75405	+	6.50221i	−0.318415	+	0.551510i	−0.980157	−	0.198221i	$-0.936484\pi$
$139$	−3.75405	+	6.50221i	−0.318415	+	0.551510i	0.661743	+	0.749731i	$0.269817\pi$
$140$	−16.4218			−1.38789
$141$	−6.00000			−0.505291
$142$	−3.89917	+	6.75356i	−0.327211	+	0.566746i
$143$	0.274785	−	0.475941i	0.0229786	−	0.0398002i
$144$	2.14399			0.178666
$145$	14.2880			1.18655
$146$	−0.0988540	+	0.171220i	−0.00818121	+	0.0141703i
$147$	−3.24482	−	5.62019i	−0.267628	−	0.463545i
$148$	−0.836412	+	1.44871i	−0.0687526	+	0.119083i
$149$	−7.00924	−	12.1404i	−0.574219	−	0.994576i	−0.996126	−	0.0879373i	$-0.971972\pi$
$149$	−7.00924	−	12.1404i	−0.574219	−	0.994576i	0.421907	−	0.906639i	$-0.361361\pi$
$150$	0.613173	+	1.06205i	0.0500654	+	0.0867157i
$151$	11.0577			0.899861			0.449930	−	0.893064i	$-0.351449\pi$
$151$	11.0577			0.899861			0.449930	+	0.893064i	$0.351449\pi$
$152$	8.91764	−	2.08134i	0.723316	−	0.168819i
$153$		0			0
$154$	4.00924	+	6.94420i	0.323073	+	0.559580i
$155$	11.7829	+	20.4086i	0.946424	+	1.63926i
$156$	0.120432	−	0.208594i	0.00964228	−	0.0167009i
$157$	−7.02884	−	12.1743i	−0.560962	−	0.971615i	−0.997413	−	0.0718869i	$-0.977098\pi$
$157$	−7.02884	−	12.1743i	−0.560962	−	0.971615i	0.436451	−	0.899728i	$-0.356235\pi$
$158$	1.86723	−	3.23413i	0.148548	−	0.257294i
$159$	8.01847			0.635906
$160$	14.5081			1.14697
$161$	13.8260	−	23.9474i	1.08965	−	1.88732i
$162$	0.285997	−	0.495361i	0.0224700	−	0.0389192i
$163$	4.61515			0.361486			0.180743	−	0.983530i	$-0.442150\pi$
$163$	4.61515			0.361486			0.180743	+	0.983530i	$0.442150\pi$
$164$	−8.94233			−0.698278
$165$	−5.10083	+	8.83490i	−0.397099	+	0.687796i
$166$	−0.654353	−	1.13337i	−0.0507876	−	0.0879667i
$167$	6.11007	−	10.5829i	0.472811	−	0.818933i	−0.526705	−	0.850048i	$-0.676573\pi$
$167$	6.11007	−	10.5829i	0.472811	−	0.818933i	0.999516	+	0.0311155i	$0.00990596\pi$
$168$	3.85799	+	6.68223i	0.297650	+	0.515546i
$169$	6.48963	+	11.2404i	0.499203	+	0.864644i
$170$		0			0
$171$	−1.26442	+	4.17148i	−0.0966925	+	0.319001i
$172$	−4.71203			−0.359289
$173$	−7.52884	−	13.0403i	−0.572407	−	0.991438i	−0.996318	−	0.0857340i	$-0.972676\pi$
$173$	−7.52884	−	13.0403i	−0.572407	−	0.991438i	0.423911	−	0.905704i	$-0.360657\pi$
$174$	−1.52884	−	2.64802i	−0.115901	−	0.200746i
$175$	3.93724	−	6.81950i	0.297628	−	0.515506i
$176$	4.09159	+	7.08685i	0.308416	+	0.534191i
$177$	−1.90841	+	3.30545i	−0.143445	+	0.248453i
$178$	4.96080			0.371827
$179$	−15.1625			−1.13330			−0.566648	−	0.823960i	$-0.691760\pi$
$179$	−15.1625			−1.13330			−0.566648	+	0.823960i	$0.691760\pi$
$180$	−2.23558	+	3.87214i	−0.166630	+	0.288612i
$181$	−6.10083	+	10.5669i	−0.453471	+	0.785435i	−0.998599	−	0.0529179i	$-0.983148\pi$
$181$	−6.10083	+	10.5669i	−0.453471	+	0.785435i	0.545128	+	0.838353i	$0.316481\pi$
$182$	0.302491			0.0224221
$183$	11.4896			0.849338
$184$	−7.90841	+	13.6978i	−0.583015	+	1.00981i
$185$	−1.33641	−	2.31473i	−0.0982550	−	0.170183i
$186$	2.52158	−	4.36750i	0.184891	−	0.320241i
$187$		0			0
$188$	−5.01847	−	8.69225i	−0.366010	−	0.633947i
$189$	−3.67282			−0.267159
$190$	−1.93309	+	6.37751i	−0.140241	+	0.462673i
$191$	5.45043			0.394379			0.197190	−	0.980365i	$-0.436819\pi$
$191$	5.45043			0.394379			0.197190	+	0.980365i	$0.436819\pi$
$192$	0.591595	+	1.02467i	0.0426947	+	0.0739494i
$193$	0.255183	+	0.441990i	0.0183685	+	0.0318151i	0.875064	−	0.484008i	$-0.160819\pi$
$193$	0.255183	+	0.441990i	0.0183685	+	0.0318151i	−0.856695	+	0.515823i	$0.827486\pi$
$194$	−1.69129	+	2.92941i	−0.121428	+	0.210319i
$195$	0.192425	+	0.333290i	0.0137799	+	0.0238674i
$196$	5.42801	−	9.40158i	0.387715	−	0.671542i
$197$	22.9608			1.63589			0.817945	−	0.575297i	$-0.195114\pi$
$197$	22.9608			1.63589			0.817945	+	0.575297i	$0.195114\pi$
$198$	2.18319			0.155153
$199$	0.0627577	−	0.108700i	0.00444878	−	0.00770551i	−0.863792	−	0.503848i	$-0.831917\pi$
$199$	0.0627577	−	0.108700i	0.00444878	−	0.00770551i	0.868241	+	0.496142i	$0.165251\pi$
$200$	−2.25208	+	3.90071i	−0.159246	+	0.275822i
$201$	5.38485			0.379818
$202$	−4.74066			−0.333552
$203$	−9.81681	+	17.0032i	−0.689005	+	1.19339i
$204$		0			0
$205$	7.14399	−	12.3737i	0.498958	−	0.864220i
$206$	4.19045	+	7.25807i	0.291962	+	0.505694i
$207$	−3.76442	−	6.52016i	−0.261645	−	0.453183i
$208$	0.308705			0.0214049
$209$	−16.2017	+	3.78140i	−1.12069	+	0.261565i
$210$	−5.61515			−0.387482
$211$	−12.4269	−	21.5240i	−0.855501	−	1.48177i	−0.876179	−	0.481986i	$-0.839916\pi$
$211$	−12.4269	−	21.5240i	−0.855501	−	1.48177i	0.0206776	−	0.999786i	$-0.493418\pi$
$212$	6.70674	+	11.6164i	0.460621	+	0.797819i
$213$	6.81681	−	11.8071i	0.467080	−	0.809007i
$214$	−4.77365	−	8.26821i	−0.326320	−	0.565203i
$215$	3.76442	−	6.52016i	0.256731	−	0.444672i
$216$	2.10083			0.142943
$217$	−32.3826			−2.19827
$218$	2.24086	−	3.88129i	0.151770	−	0.262874i
$219$	0.172824	−	0.299339i	0.0116783	−	0.0202275i
$220$	−17.0656			−1.15056
$221$		0			0
$222$	−0.285997	+	0.495361i	−0.0191948	+	0.0332464i
$223$	11.8980	+	20.6080i	0.796752	+	1.38001i	0.921721	+	0.387854i	$0.126783\pi$
$223$	11.8980	+	20.6080i	0.796752	+	1.38001i	−0.124969	+	0.992161i	$0.539883\pi$
$224$	−9.96806	+	17.2652i	−0.666019	+	1.15358i
$225$	−1.07199	−	1.85675i	−0.0714662	−	0.123783i
$226$	−1.82605	−	3.16280i	−0.121467	−	0.210387i
$227$	9.81681			0.651565			0.325782	−	0.945445i	$-0.394372\pi$
$227$	9.81681			0.651565			0.325782	+	0.945445i	$0.394372\pi$
$228$	−7.10083	+	1.65730i	−0.470264	+	0.109758i
$229$	0.143987			0.00951490			0.00475745	−	0.999989i	$-0.498486\pi$
$229$	0.143987			0.00951490			0.00475745	+	0.999989i	$0.498486\pi$
$230$	−5.75518	−	9.96827i	−0.379486	−	0.657288i
$231$	−7.00924	−	12.1404i	−0.461174	−	0.798777i
$232$	5.61515	−	9.72572i	0.368653	−	0.638525i
$233$	−5.28797	−	9.15904i	−0.346427	−	0.600029i	0.639185	−	0.769053i	$-0.279272\pi$
$233$	−5.28797	−	9.15904i	−0.346427	−	0.600029i	−0.985612	+	0.169024i	$0.945938\pi$
$234$	0.0411797	−	0.0713253i	0.00269200	−	0.00466268i
$235$	16.0369			1.04613
$236$	−6.38485			−0.415618
$237$	−3.26442	+	5.65414i	−0.212047	+	0.367276i
$238$		0			0
$239$	−9.81681			−0.634997			−0.317498	−	0.948259i	$-0.602843\pi$
$239$	−9.81681			−0.634997			−0.317498	+	0.948259i	$0.602843\pi$
$240$	−5.73050			−0.369902
$241$	−0.971163	+	1.68210i	−0.0625581	+	0.108354i	−0.895608	−	0.444844i	$-0.853259\pi$
$241$	−0.971163	+	1.68210i	−0.0625581	+	0.108354i	0.833050	+	0.553198i	$0.186593\pi$
$242$	1.02045	+	1.76747i	0.0655969	+	0.113617i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	9.61007	+	16.6451i	0.615221	+	1.06559i
$245$	8.67282	+	15.0218i	0.554086	+	0.959706i
$246$	−3.05767			−0.194950
$247$	−0.182059	+	0.600637i	−0.0115842	+	0.0382176i
$248$	18.5226			1.17619
$249$	1.14399	+	1.98144i	0.0724972	+	0.125569i
$250$	2.18319	+	3.78140i	0.138077	+	0.239156i
$251$	−6.81681	+	11.8071i	−0.430273	+	0.745255i	−0.996897	−	0.0787218i	$-0.974916\pi$
$251$	−6.81681	+	11.8071i	−0.430273	+	0.745255i	0.566623	+	0.823977i	$0.308249\pi$
$252$	−3.07199	−	5.32085i	−0.193517	−	0.335182i
$253$	14.3681	−	24.8862i	0.903313	−	1.56458i
$254$	−1.51827			−0.0952648
$255$		0			0
$256$	2.11515	−	3.66355i	0.132197	−	0.228972i
$257$	6.29721	−	10.9071i	0.392809	−	0.680365i	−0.600010	−	0.799993i	$-0.704837\pi$
$257$	6.29721	−	10.9071i	0.392809	−	0.680365i	0.992819	+	0.119627i	$0.0381700\pi$
$258$	−1.61120			−0.100309
$259$	3.67282			0.228218
$260$	−0.321894	+	0.557536i	−0.0199630	+	0.0345769i
$261$	2.67282	+	4.62947i	0.165444	+	0.286557i
$262$	−3.24482	+	5.62019i	−0.200465	+	0.347216i
$263$	0.816810	+	1.41476i	0.0503667	+	0.0872376i	0.890110	−	0.455747i	$-0.150628\pi$
$263$	0.816810	+	1.41476i	0.0503667	+	0.0872376i	−0.839743	+	0.542984i	$0.817294\pi$
$264$	4.00924	+	6.94420i	0.246751	+	0.427386i
$265$	−21.4320			−1.31655
$266$	−6.26131	−	6.68223i	−0.383906	−	0.409714i
$267$	−8.67282			−0.530768
$268$	4.50395	+	7.80108i	0.275123	+	0.476527i
$269$	10.8260	+	18.7513i	0.660076	+	1.14328i	0.980595	+	0.196043i	$0.0628091\pi$
$269$	10.8260	+	18.7513i	0.660076	+	1.14328i	−0.320520	+	0.947242i	$0.603858\pi$
$270$	−0.764419	+	1.32401i	−0.0465210	+	0.0805768i
$271$	10.7776	+	18.6674i	0.654693	+	1.13396i	0.981971	+	0.189033i	$0.0605354\pi$
$271$	10.7776	+	18.6674i	0.654693	+	1.13396i	−0.327278	+	0.944928i	$0.606131\pi$
$272$		0			0
$273$	−0.528837			−0.0320067
$274$	0.934420			0.0564504
$275$	4.09159	−	7.08685i	0.246732	−	0.427353i
$276$	6.29721	−	10.9071i	0.379047	−	0.656529i
$277$	7.62571			0.458185			0.229092	−	0.973405i	$-0.426424\pi$
$277$	7.62571			0.458185			0.229092	+	0.973405i	$0.426424\pi$
$278$	−4.29459			−0.257572
$279$	−4.40841	+	7.63558i	−0.263924	+	0.457130i
$280$	−10.3117	−	17.8604i	−0.616244	−	1.06737i
$281$	0.846778	−	1.46666i	0.0505145	−	0.0874937i	−0.839663	−	0.543109i	$-0.817247\pi$
$281$	0.846778	−	1.46666i	0.0505145	−	0.0874937i	0.890177	+	0.455615i	$0.150581\pi$
$282$	−1.71598	−	2.97216i	−0.102185	−	0.176990i
$283$	−5.14399	−	8.90965i	−0.305778	−	0.529623i	0.671656	−	0.740863i	$-0.265583\pi$
$283$	−5.14399	−	8.90965i	−0.305778	−	0.529623i	−0.977434	+	0.211240i	$0.932250\pi$
$284$	22.8066			1.35333
$285$	3.37957	−	11.1496i	0.200188	−	0.660447i
$286$	0.314350			0.0185879
$287$	9.81681	+	17.0032i	0.579468	+	1.00367i
$288$	2.71400	+	4.70079i	0.159924	+	0.276997i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	4.08631	+	7.07770i	0.239957	+	0.415617i
$291$	2.95684	−	5.12140i	0.173333	−	0.300222i
$292$	0.578207			0.0338370
$293$	12.1153			0.707786			0.353893	−	0.935286i	$-0.384858\pi$
$293$	12.1153			0.707786			0.353893	+	0.935286i	$0.384858\pi$
$294$	1.85601	−	3.21471i	0.108245	−	0.187486i
$295$	5.10083	−	8.83490i	0.296982	−	0.514388i
$296$	−2.10083			−0.122108
$297$	−3.81681			−0.221474
$298$	4.00924	−	6.94420i	0.232249	−	0.402267i
$299$	−0.542026	−	0.938816i	−0.0313461	−	0.0542931i
$300$	1.79326	−	3.10601i	0.103534	−	0.179326i
$301$	5.17282	+	8.95959i	0.298157	+	0.516422i
$302$	3.16246	+	5.47754i	0.181979	+	0.315197i
$303$	8.28797			0.476132
$304$	−6.38993	−	6.81950i	−0.366488	−	0.391125i
$305$	−30.7098			−1.75844
$306$		0			0
$307$	2.24482	+	3.88814i	0.128118	+	0.221908i	0.922948	−	0.384926i	$-0.125773\pi$
$307$	2.24482	+	3.88814i	0.128118	+	0.221908i	−0.794829	+	0.606833i	$0.792440\pi$
$308$	11.7252	−	20.3087i	0.668106	−	1.15719i
$309$	−7.32605	−	12.6891i	−0.416764	−	0.721857i
$310$	−6.73973	+	11.6736i	−0.382791	+	0.663014i
$311$	0.759136			0.0430466			0.0215233	−	0.999768i	$-0.493148\pi$
$311$	0.759136			0.0430466			0.0215233	+	0.999768i	$0.493148\pi$
$312$	0.302491			0.0171252
$313$	−5.71598	+	9.90037i	−0.323086	+	0.559602i	−0.981123	−	0.193384i	$-0.938054\pi$
$313$	−5.71598	+	9.90037i	−0.323086	+	0.559602i	0.658037	+	0.752986i	$0.271387\pi$
$314$	4.02045	−	6.96362i	0.226887	−	0.392980i
$315$	9.81681			0.553115
$316$	−10.9216			−0.614388
$317$	5.80757	−	10.0590i	0.326186	−	0.564971i	−0.655566	−	0.755138i	$-0.727570\pi$
$317$	5.80757	−	10.0590i	0.326186	−	0.564971i	0.981752	+	0.190168i	$0.0609031\pi$
$318$	2.29326	+	3.97204i	0.128599	+	0.222741i
$319$	−10.2017	+	17.6698i	−0.571183	+	0.989319i
$320$	−1.58123	−	2.73877i	−0.0883934	−	0.153102i
$321$	8.34565	+	14.4551i	0.465809	+	0.806804i
$322$	15.8168			0.881436
$323$		0			0
$324$	−1.67282			−0.0929347
$325$	−0.154353	−	0.267347i	−0.00856194	−	0.0148297i
$326$	1.31992	+	2.28616i	0.0731035	+	0.126619i
$327$	−3.91764	+	6.78555i	−0.216646	+	0.375242i
$328$	−5.61515	−	9.72572i	−0.310045	−	0.537013i
$329$	−11.0185	+	19.0846i	−0.607468	+	1.05217i
$330$	−5.83528			−0.321222
$331$	−11.4712			−0.630512			−0.315256	−	0.949007i	$-0.602090\pi$
$331$	−11.4712			−0.630512			−0.315256	+	0.949007i	$0.602090\pi$
$332$	−1.91369	+	3.31460i	−0.105027	+	0.181913i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$	6.98983			0.382467
$335$	−14.3928			−0.786360
$336$	3.93724	−	6.81950i	0.214794	−	0.372034i
$337$	−3.78402	−	6.55412i	−0.206129	−	0.357025i	0.744363	−	0.667775i	$-0.232753\pi$
$337$	−3.78402	−	6.55412i	−0.206129	−	0.357025i	−0.950492	+	0.310750i	$0.899420\pi$
$338$	−3.71203	+	6.42942i	−0.201908	+	0.349714i
$339$	3.19243	+	5.52944i	0.173389	+	0.300318i
$340$		0			0
$341$	−33.6521			−1.82236
$342$	−2.42801	+	0.566686i	−0.131292	+	0.0306429i
$343$	1.87448			0.101213
$344$	−2.95882	−	5.12483i	−0.159529	−	0.276312i
$345$	10.0616	+	17.4272i	0.541700	+	0.938252i
$346$	4.30644	−	7.45898i	0.231516	−	0.400997i
$347$	−10.9084	−	18.8939i	−0.585594	−	1.01428i	−0.994801	−	0.101837i	$-0.967528\pi$
$347$	−10.9084	−	18.8939i	−0.585594	−	1.01428i	0.409207	−	0.912441i	$-0.365805\pi$
$348$	−4.47116	+	7.74428i	−0.239679	+	0.415137i
$349$	−4.54731			−0.243412			−0.121706	−	0.992566i	$-0.538836\pi$
$349$	−4.54731			−0.243412			−0.121706	+	0.992566i	$0.538836\pi$
$350$	4.50415			0.240757
$351$	−0.0719933	+	0.124696i	−0.00384272	+	0.00665578i
$352$	−10.3588	+	17.9420i	−0.552128	+	0.956313i
$353$	−8.99774			−0.478901			−0.239451	−	0.970909i	$-0.576967\pi$
$353$	−8.99774			−0.478901			−0.239451	+	0.970909i	$0.576967\pi$
$354$	−2.18319			−0.116035
$355$	−18.2201	+	31.5582i	−0.967024	+	1.67494i
$356$	−7.25405	−	12.5644i	−0.384464	−	0.665911i
$357$		0			0
$358$	−4.33641	−	7.51089i	−0.229186	−	0.396963i
$359$	−6.48963	−	11.2404i	−0.342510	−	0.593244i	0.642388	−	0.766379i	$-0.277944\pi$
$359$	−6.48963	−	11.2404i	−0.342510	−	0.593244i	−0.984898	+	0.173135i	$0.944610\pi$
$360$	−5.61515			−0.295944
$361$	17.0369	−	8.41086i	0.896681	−	0.442677i
$362$	−6.97927			−0.366822
$363$	−1.78402	−	3.09001i	−0.0936368	−	0.162184i
$364$	−0.442326	−	0.766131i	−0.0231842	−	0.0401562i
$365$	−0.461927	+	0.800082i	−0.0241784	+	0.0418782i
$366$	3.28600	+	5.69151i	0.171762	+	0.297500i
$367$	2.02355	−	3.50490i	0.105629	−	0.182954i	−0.808366	−	0.588680i	$-0.799648\pi$
$367$	2.02355	−	3.50490i	0.105629	−	0.182954i	0.913995	+	0.405726i	$0.132981\pi$
$368$	16.1417			0.841446
$369$	5.34565			0.278283
$370$	0.764419	−	1.32401i	0.0397402	−	0.0688321i
$371$	14.7252	−	25.5048i	0.764495	−	1.32414i
$372$	−14.7490			−0.764698
$373$	3.79834			0.196671			0.0983353	−	0.995153i	$-0.468648\pi$
$373$	3.79834			0.196671			0.0983353	+	0.995153i	$0.468648\pi$
$374$		0			0
$375$	−3.81681	−	6.61091i	−0.197099	−	0.341386i
$376$	6.30249	−	10.9162i	0.325026	−	0.562962i
$377$	0.384851	+	0.666581i	0.0198208	+	0.0343307i
$378$	−1.05042	−	1.81937i	−0.0540275	−	0.0935784i
$379$	4.89522			0.251450			0.125725	−	0.992065i	$-0.459874\pi$
$379$	4.89522			0.251450			0.125725	+	0.992065i	$0.459874\pi$
$380$	18.9793	−	4.42968i	0.973616	−	0.227238i
$381$	2.65435			0.135987
$382$	1.55880	+	2.69993i	0.0797554	+	0.138140i
$383$	−17.0709	−	29.5676i	−0.872280	−	1.51083i	−0.859632	−	0.510914i	$-0.829307\pi$
$383$	−17.0709	−	29.5676i	−0.872280	−	1.51083i	−0.0126484	−	0.999920i	$-0.504026\pi$
$384$	−5.76640	+	9.98769i	−0.294265	+	0.509682i
$385$	18.7345	+	32.4490i	0.954796	+	1.65376i
$386$	−0.145963	+	0.252815i	−0.00742932	+	0.0128680i
$387$	2.81681			0.143187
$388$	9.89256			0.502218
$389$	−13.4412	+	23.2808i	−0.681496	+	1.18039i	0.293029	+	0.956104i	$0.405337\pi$
$389$	−13.4412	+	23.2808i	−0.681496	+	1.18039i	−0.974524	+	0.224281i	$0.927997\pi$
$390$	−0.110066	+	0.190640i	−0.00557341	+	0.00965343i
$391$		0			0
$392$	13.6336			0.688602
$393$	5.67282	−	9.82562i	0.286156	−	0.495637i
$394$	6.56671	+	11.3739i	0.330826	+	0.573008i
$395$	8.72522	−	15.1125i	0.439013	−	0.760393i
$396$	−3.19243	−	5.52944i	−0.160425	−	0.277865i
$397$	−12.6193	−	21.8573i	−0.633345	−	1.09699i	−0.986863	−	0.161558i	$-0.948348\pi$
$397$	−12.6193	−	21.8573i	−0.633345	−	1.09699i	0.353519	−	0.935427i	$-0.384985\pi$
$398$	0.0717940			0.00359871
$399$	10.9465	+	11.6824i	0.548009	+	0.584850i
$400$	4.59668			0.229834
$401$	1.66359	+	2.88142i	0.0830756	+	0.143891i	0.904570	−	0.426326i	$-0.140192\pi$
$401$	1.66359	+	2.88142i	0.0830756	+	0.143891i	−0.821494	+	0.570217i	$0.806859\pi$
$402$	1.54005	+	2.66744i	0.0768107	+	0.133040i
$403$	−0.634751	+	1.09942i	−0.0316192	+	0.0547661i
$404$	6.93216	+	12.0069i	0.344888	+	0.597363i
$405$	1.33641	−	2.31473i	0.0664068	−	0.115020i
$406$	−11.2303			−0.557350
$407$	3.81681			0.189192
$408$		0			0
$409$	−17.0616	+	29.5516i	−0.843643	+	1.46123i	0.0431512	+	0.999069i	$0.486260\pi$
$409$	−17.0616	+	29.5516i	−0.843643	+	1.46123i	−0.886794	+	0.462164i	$0.847073\pi$
$410$	8.17262			0.403617
$411$	−1.63362			−0.0805806
$412$	12.2552	−	21.2266i	0.603770	−	1.04576i
$413$	7.00924	+	12.1404i	0.344902	+	0.597388i
$414$	2.15322	−	3.72949i	0.105825	−	0.183294i
$415$	−3.05767	−	5.29605i	−0.150095	−	0.259973i
$416$	0.390780	+	0.676851i	0.0191596	+	0.0331853i
$417$	7.50811			0.367673
$418$	−6.50678	−	6.94420i	−0.318257	−	0.339652i
$419$	−9.16246			−0.447615			−0.223808	−	0.974633i	$-0.571849\pi$
$419$	−9.16246			−0.447615			−0.223808	+	0.974633i	$0.571849\pi$
$420$	8.21090	+	14.2217i	0.400651	+	0.693947i
$421$	7.91764	+	13.7138i	0.385882	+	0.668368i	0.991891	−	0.127090i	$-0.0405638\pi$
$421$	7.91764	+	13.7138i	0.385882	+	0.668368i	−0.606009	+	0.795458i	$0.707230\pi$
$422$	7.10809	−	12.3116i	0.346016	−	0.599318i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	−8.42272	+	14.5886i	−0.409044	+	0.708484i
$425$		0			0
$426$	7.79834			0.377831
$427$	21.0997	−	36.5458i	1.02109	−	1.76857i
$428$	−13.9608	+	24.1808i	−0.674821	+	1.16882i
$429$	−0.549569			−0.0265335
$430$	4.30644			0.207675
$431$	4.63362	−	8.02567i	0.223194	−	0.386583i	−0.732582	−	0.680678i	$-0.761685\pi$
$431$	4.63362	−	8.02567i	0.223194	−	0.386583i	0.955776	+	0.294096i	$0.0950184\pi$
$432$	−1.07199	−	1.85675i	−0.0515763	−	0.0893328i
$433$	9.90727	−	17.1599i	0.476113	−	0.824652i	−0.523512	−	0.852018i	$-0.675379\pi$
$433$	9.90727	−	17.1599i	0.476113	−	0.824652i	0.999625	+	0.0273658i	$0.00871190\pi$
$434$	−9.26131	−	16.0411i	−0.444557	−	0.769996i
$435$	−7.14399	−	12.3737i	−0.342528	−	0.593276i
$436$	−13.1070			−0.627714
$437$	−9.51960	+	31.4064i	−0.455384	+	1.50237i
$438$	0.197708			0.00944685
$439$	−3.45156	−	5.97828i	−0.164734	−	0.285328i	0.771827	−	0.635833i	$-0.219343\pi$
$439$	−3.45156	−	5.97828i	−0.164734	−	0.285328i	−0.936561	+	0.350505i	$0.886010\pi$
$440$	−10.7160	−	18.5606i	−0.510864	−	0.884843i
$441$	−3.24482	+	5.62019i	−0.154515	+	0.267628i
$442$		0			0
$443$	9.81681	−	17.0032i	0.466411	−	0.807847i	−0.532853	−	0.846208i	$-0.678880\pi$
$443$	9.81681	−	17.0032i	0.466411	−	0.807847i	0.999264	+	0.0383606i	$0.0122136\pi$
$444$	1.67282			0.0793887
$445$	23.1809			1.09888
$446$	−6.80560	+	11.7876i	−0.322254	+	0.558161i
$447$	−7.00924	+	12.1404i	−0.331525	+	0.574219i
$448$	4.34565			0.205313
$449$	29.0162			1.36936			0.684680	−	0.728844i	$-0.259942\pi$
$449$	29.0162			1.36936			0.684680	+	0.728844i	$0.259942\pi$
$450$	0.613173	−	1.06205i	0.0289052	−	0.0500654i
$451$	10.2017	+	17.6698i	0.480377	+	0.832038i
$452$	−5.34036	+	9.24978i	−0.251190	+	0.435073i
$453$	−5.52884	−	9.57623i	−0.259767	−	0.449930i
$454$	2.80757	+	4.86286i	0.131766	+	0.228225i
$455$	1.41349			0.0662654
$456$	−6.26131	−	6.68223i	−0.293213	−	0.312924i
$457$	32.5473			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$457$	32.5473			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$458$	0.0411797	+	0.0713253i	0.00192420	+	0.00333281i
$459$		0			0
$460$	−16.8313	+	29.1527i	−0.784765	+	1.35925i
$461$	4.82605	+	8.35896i	0.224771	+	0.389315i	0.956251	−	0.292548i	$-0.0945031\pi$
$461$	4.82605	+	8.35896i	0.224771	+	0.389315i	−0.731479	+	0.681863i	$0.761170\pi$
$462$	4.00924	−	6.94420i	0.186527	−	0.323073i
$463$	−31.0554			−1.44327			−0.721634	−	0.692275i	$-0.756608\pi$
$463$	−31.0554			−1.44327			−0.721634	+	0.692275i	$0.756608\pi$
$464$	−11.4610			−0.532063
$465$	11.7829	−	20.4086i	0.546418	−	0.946424i
$466$	3.02469	−	5.23891i	0.140116	−	0.242688i
$467$	8.61289			0.398557			0.199278	−	0.979943i	$-0.436140\pi$
$467$	8.61289			0.398557			0.199278	+	0.979943i	$0.436140\pi$
$468$	−0.240864			−0.0111339
$469$	9.88880	−	17.1279i	0.456623	−	0.790893i
$470$	4.58651	+	7.94407i	0.211560	+	0.366433i
$471$	−7.02884	+	12.1743i	−0.323872	+	0.560962i
$472$	−4.00924	−	6.94420i	−0.184540	−	0.319633i
$473$	5.37562	+	9.31084i	0.247171	+	0.428113i
$474$	−3.73445			−0.171529
$475$	−2.71090	+	8.94360i	−0.124384	+	0.410360i
$476$		0			0
$477$	−4.00924	−	6.94420i	−0.183570	−	0.317953i
$478$	−2.80757	−	4.86286i	−0.128415	−	0.222422i
$479$	−8.73050	+	15.1217i	−0.398907	+	0.690927i	−0.993591	−	0.113032i	$-0.963944\pi$
$479$	−8.73050	+	15.1217i	−0.398907	+	0.690927i	0.594685	+	0.803959i	$0.297277\pi$
$480$	−7.25405	−	12.5644i	−0.331101	−	0.573483i
$481$	0.0719933	−	0.124696i	0.00328261	−	0.00568565i
$482$	−1.11100			−0.0506045
$483$	−27.6521			−1.25821
$484$	2.98435	−	5.16905i	0.135652	−	0.234957i
$485$	−7.90312	+	13.6886i	−0.358862	+	0.621568i
$486$	−0.571993			−0.0259461
$487$	−11.6336			−0.527170			−0.263585	−	0.964636i	$-0.584905\pi$
$487$	−11.6336			−0.527170			−0.263585	+	0.964636i	$0.584905\pi$
$488$	−12.0689	+	20.9039i	−0.546333	+	0.946276i
$489$	−2.30757	−	3.99684i	−0.104352	−	0.180743i
$490$	−4.96080	+	8.59235i	−0.224106	+	0.388163i
$491$	12.1625	+	21.0660i	0.548884	+	0.950695i	0.998351	+	0.0573983i	$0.0182805\pi$
$491$	12.1625	+	21.0660i	0.548884	+	0.950695i	−0.449467	+	0.893297i	$0.648386\pi$
$492$	4.47116	+	7.74428i	0.201576	+	0.349139i
$493$		0			0
$494$	−0.349600	+	0.0815952i	−0.0157293	+	0.00367114i
$495$	10.2017			0.458531
$496$	−9.45156	−	16.3706i	−0.424388	−	0.735061i
$497$	−25.0369	−	43.3653i	−1.12306	−	1.94520i
$498$	−0.654353	+	1.13337i	−0.0293222	+	0.0507876i
$499$	−19.0565	−	33.0069i	−0.853088	−	1.47759i	−0.878407	−	0.477912i	$-0.841394\pi$
$499$	−19.0565	−	33.0069i	−0.853088	−	1.47759i	0.0253194	−	0.999679i	$-0.491940\pi$
$500$	6.38485	−	11.0589i	0.285539	−	0.494568i
$501$	−12.2201			−0.545955
$502$	−7.79834			−0.348057
$503$	−2.18319	+	3.78140i	−0.0973436	+	0.168604i	−0.910584	−	0.413323i	$-0.864368\pi$
$503$	−2.18319	+	3.78140i	−0.0973436	+	0.168604i	0.813241	+	0.581927i	$0.197701\pi$
$504$	3.85799	−	6.68223i	0.171849	−	0.297650i
$505$	−22.1523			−0.985764
$506$	16.4369			0.730708
$507$	6.48963	−	11.2404i	0.288215	−	0.499203i
$508$	2.22013	+	3.84538i	0.0985024	+	0.170611i
$509$	7.85601	−	13.6070i	0.348212	−	0.603120i	−0.637720	−	0.770268i	$-0.720122\pi$
$509$	7.85601	−	13.6070i	0.348212	−	0.603120i	0.985932	+	0.167148i	$0.0534557\pi$
$510$		0			0
$511$	−0.634751	−	1.09942i	−0.0280797	−	0.0486355i
$512$	−20.6459			−0.912428
$513$	4.24482	−	0.990721i	0.187413	−	0.0437414i
$514$	7.20392			0.317751
$515$	19.5812	+	33.9157i	0.862852	+	1.49450i
$516$	2.35601	+	4.08074i	0.103718	+	0.179644i
$517$	−11.4504	+	19.8327i	−0.503589	+	0.872242i
$518$	1.05042	+	1.81937i	0.0461526	+	0.0799386i
$519$	−7.52884	+	13.0403i	−0.330479	+	0.572407i
$520$	−0.808506			−0.0354553
$521$	33.4425			1.46514			0.732572	−	0.680690i	$-0.238320\pi$
$521$	33.4425			1.46514			0.732572	+	0.680690i	$0.238320\pi$
$522$	−1.52884	+	2.64802i	−0.0669154	+	0.115901i
$523$	14.7109	−	25.4800i	0.643263	−	1.11416i	−0.341437	−	0.939905i	$-0.610914\pi$
$523$	14.7109	−	25.4800i	0.643263	−	1.11416i	0.984700	−	0.174259i	$-0.0557530\pi$
$524$	18.9793			0.829113
$525$	−7.87448			−0.343671
$526$	−0.467210	+	0.809231i	−0.0203713	+	0.0352842i
$527$		0			0
$528$	4.09159	−	7.08685i	0.178064	−	0.308416i
$529$	−16.8417	−	29.1707i	−0.732248	−	1.26829i
$530$	−6.12947	−	10.6166i	−0.266247	−	0.461153i
$531$	3.81681			0.165635
$532$	−7.76857	+	25.6295i	−0.336810	+	1.11118i
$533$	0.769701			0.0333395
$534$	−2.48040	−	4.29618i	−0.107337	−	0.185914i
$535$	−22.3064	−	38.6359i	−0.964392	−	1.67038i
$536$	−5.65633	+	9.79705i	−0.244316	+	0.423168i
$537$	7.58123	+	13.1311i	0.327154	+	0.566648i
$538$	−6.19243	+	10.7256i	−0.266974	+	0.462413i
$539$	−24.7697			−1.06691
$540$	4.47116			0.192408
$541$	−13.0865	+	22.6665i	−0.562633	+	0.974509i	0.434632	+	0.900608i	$0.356878\pi$
$541$	−13.0865	+	22.6665i	−0.562633	+	0.974509i	−0.997266	+	0.0739012i	$0.976455\pi$
$542$	−6.16472	+	10.6776i	−0.264797	+	0.458642i
$543$	12.2017			0.523623
$544$		0			0
$545$	10.4712	−	18.1366i	0.448535	−	0.776886i
$546$	−0.151246	−	0.261965i	−0.00647272	−	0.0112111i
$547$	−10.9557	+	18.9759i	−0.468432	+	0.811349i	−0.999349	−	0.0360752i	$-0.988514\pi$
$547$	−10.9557	+	18.9759i	−0.468432	+	0.811349i	0.530917	+	0.847424i	$0.321848\pi$
$548$	−1.36638	−	2.36664i	−0.0583688	−	0.101098i
$549$	−5.74482	−	9.95031i	−0.245183	−	0.424669i
$550$	4.68073			0.199587
$551$	6.75914	−	22.2993i	0.287949	−	0.949980i
$552$	15.8168			0.673208
$553$	11.9896	+	20.7667i	0.509851	+	0.883088i
$554$	2.18093	+	3.77748i	0.0926588	+	0.160490i
$555$	−1.33641	+	2.31473i	−0.0567275	+	0.0982550i
$556$	6.27987	+	10.8771i	0.266326	+	0.461290i
$557$	−17.0185	+	29.4769i	−0.721096	+	1.24897i	0.239465	+	0.970905i	$0.423028\pi$
$557$	−17.0185	+	29.4769i	−0.721096	+	1.24897i	−0.960561	+	0.278070i	$0.910305\pi$
$558$	−5.04316			−0.213494
$559$	0.405583			0.0171543
$560$	−10.5236	+	18.2273i	−0.444701	+	0.770245i
$561$		0			0
$562$	0.968703			0.0408622
$563$	11.5552			0.486994			0.243497	−	0.969902i	$-0.421705\pi$
$563$	11.5552			0.486994			0.243497	+	0.969902i	$0.421705\pi$
$564$	−5.01847	+	8.69225i	−0.211316	+	0.366010i
$565$	−8.53279	−	14.7792i	−0.358977	−	0.621767i
$566$	2.94233	−	5.09626i	0.123675	−	0.214212i
$567$	1.83641	+	3.18076i	0.0771220	+	0.133579i
$568$	14.3210	+	24.8046i	0.600894	+	1.04078i
$569$	39.7075			1.66463			0.832313	−	0.554307i	$-0.187016\pi$
$569$	39.7075			1.66463			0.832313	+	0.554307i	$0.187016\pi$
$570$	6.48963	−	1.51465i	0.271821	−	0.0634418i
$571$	14.6521			0.613171			0.306585	−	0.951843i	$-0.400813\pi$
$571$	14.6521			0.613171			0.306585	+	0.951843i	$0.400813\pi$
$572$	−0.459666	−	0.796165i	−0.0192196	−	0.0332893i
$573$	−2.72522	−	4.72021i	−0.113848	−	0.197190i
$574$	−5.61515	+	9.72572i	−0.234372	+	0.405944i
$575$	−8.07086	−	13.9791i	−0.336578	−	0.582971i
$576$	0.591595	−	1.02467i	0.0246498	−	0.0426947i
$577$	20.8145			0.866521			0.433261	−	0.901269i	$-0.357363\pi$
$577$	20.8145			0.866521			0.433261	+	0.901269i	$0.357363\pi$
$578$	9.72389			0.404460
$579$	0.255183	−	0.441990i	0.0106050	−	0.0183685i
$580$	11.9506	−	20.6991i	0.496223	−	0.859483i
$581$	8.40332			0.348629
$582$	3.38259			0.140213
$583$	15.3025	−	26.5047i	0.633764	−	1.09771i
$584$	0.363073	+	0.628861i	0.0150241	+	0.0260225i
$585$	0.192425	−	0.333290i	0.00795581	−	0.0137799i
$586$	3.46495	+	6.00147i	0.143136	+	0.247918i
$587$	−9.82209	−	17.0124i	−0.405401	−	0.702175i	0.588967	−	0.808157i	$-0.299535\pi$
$587$	−9.82209	−	17.0124i	−0.405401	−	0.702175i	−0.994368	+	0.105982i	$0.966201\pi$
$588$	−10.8560			−0.447694
$589$	37.4257	−	8.73500i	1.54210	−	0.359920i
$590$	5.83528			0.240235
$591$	−11.4804	−	19.8846i	−0.472240	−	0.817945i
$592$	1.07199	+	1.85675i	0.0440587	+	0.0763118i
$593$	−10.8260	+	18.7513i	−0.444572	+	0.770022i	−0.998022	−	0.0628605i	$-0.979978\pi$
$593$	−10.8260	+	18.7513i	−0.444572	+	0.770022i	0.553450	+	0.832882i	$0.313311\pi$
$594$	−1.09159	−	1.89070i	−0.0447887	−	0.0775763i
$595$		0			0
$596$	−23.4504			−0.960567
$597$	−0.125515			−0.00513700
$598$	0.310035	−	0.536996i	0.0126783	−	0.0219594i
$599$	5.88993	−	10.2017i	0.240656	−	0.416829i	−0.720245	−	0.693720i	$-0.755971\pi$
$599$	5.88993	−	10.2017i	0.240656	−	0.416829i	0.960901	+	0.276891i	$0.0893040\pi$
$600$	4.50415			0.183881
$601$	−11.4112			−0.465474			−0.232737	−	0.972540i	$-0.574768\pi$
$601$	−11.4112			−0.465474			−0.232737	+	0.972540i	$0.574768\pi$
$602$	−2.95882	+	5.12483i	−0.120593	+	0.208872i
$603$	−2.69243	−	4.66342i	−0.109644	−	0.189909i
$604$	9.24877	−	16.0193i	0.376327	−	0.651818i
$605$	4.76837	+	8.25906i	0.193862	+	0.335779i
$606$	2.37033	+	4.10554i	0.0962882	+	0.166776i
$607$	−1.10478			−0.0448418			−0.0224209	−	0.999749i	$-0.507137\pi$
$607$	−1.10478			−0.0448418			−0.0224209	+	0.999749i	$0.507137\pi$
$608$	6.86327	−	22.6428i	0.278342	−	0.918288i
$609$	19.6336			0.795594
$610$	−8.78289	−	15.2124i	−0.355609	−	0.615933i
$611$	0.431960	+	0.748176i	0.0174752	+	0.0302680i
$612$		0			0
$613$	−2.38880	−	4.13753i	−0.0964829	−	0.167113i	0.813744	−	0.581224i	$-0.197426\pi$
$613$	−2.38880	−	4.13753i	−0.0964829	−	0.167113i	−0.910227	+	0.414111i	$0.864093\pi$
$614$	−1.28402	+	2.22399i	−0.0518188	+	0.0897529i
$615$	−14.2880			−0.576147
$616$	29.4504			1.18659
$617$	−18.7397	+	32.4582i	−0.754433	+	1.30672i	0.191222	+	0.981547i	$0.438755\pi$
$617$	−18.7397	+	32.4582i	−0.754433	+	1.30672i	−0.945656	+	0.325170i	$0.894578\pi$
$618$	4.19045	−	7.25807i	0.168565	−	0.291962i
$619$	−0.615149			−0.0247249			−0.0123625	−	0.999924i	$-0.503935\pi$
$619$	−0.615149			−0.0247249			−0.0123625	+	0.999924i	$0.503935\pi$
$620$	39.4214			1.58320
$621$	−3.76442	+	6.52016i	−0.151061	+	0.261645i
$622$	0.217110	+	0.376046i	0.00870533	+	0.0150781i
$623$	−15.9269	+	27.5862i	−0.638097	+	1.10522i
$624$	−0.154353	−	0.267347i	−0.00617905	−	0.0107024i
$625$	15.5616	+	26.9535i	0.622465	+	1.07814i
$626$	−6.53900			−0.261351
$627$	11.3756	+	12.1404i	0.454298	+	0.484839i
$628$	−23.5160			−0.938391
$629$		0			0
$630$	2.80757	+	4.86286i	0.111856	+	0.193741i
$631$	−10.6532	+	18.4519i	−0.424098	+	0.734559i	−0.996336	−	0.0855284i	$-0.972742\pi$
$631$	−10.6532	+	18.4519i	−0.424098	+	0.734559i	0.572238	+	0.820088i	$0.306075\pi$
$632$	−6.85799	−	11.8784i	−0.272796	−	0.472497i
$633$	−12.4269	+	21.5240i	−0.493924	+	0.855501i
$634$	6.64379			0.263858
$635$	−7.09462			−0.281541
$636$	6.70674	−	11.6164i	0.265940	−	0.460621i
$637$	−0.467210	+	0.809231i	−0.0185115	+	0.0320629i
$638$	−11.6706			−0.462042
$639$	−13.6336			−0.539338
$640$	15.4126	−	26.6953i	0.609235	−	1.05523i
$641$	−19.9608	−	34.5731i	−0.788404	−	1.36556i	−0.926944	−	0.375199i	$-0.877574\pi$
$641$	−19.9608	−	34.5731i	−0.788404	−	1.36556i	0.138540	−	0.990357i	$-0.455759\pi$
$642$	−4.77365	+	8.26821i	−0.188401	+	0.326320i
$643$	18.6924	+	32.3762i	0.737157	+	1.27679i	0.953770	+	0.300536i	$0.0971657\pi$
$643$	18.6924	+	32.3762i	0.737157	+	1.27679i	−0.216613	+	0.976258i	$0.569501\pi$
$644$	−23.1285	−	40.0598i	−0.911392	−	1.57858i
$645$	−7.52884			−0.296448
$646$		0			0
$647$	16.0369			0.630477			0.315239	−	0.949012i	$-0.397915\pi$
$647$	16.0369			0.630477			0.315239	+	0.949012i	$0.397915\pi$
$648$	−1.05042	−	1.81937i	−0.0412642	−	0.0714717i
$649$	7.28402	+	12.6163i	0.285923	+	0.495233i
$650$	0.0882886	−	0.152920i	0.00346297	−	0.00599803i
$651$	16.1913	+	28.0441i	0.634587	+	1.09914i
$652$	3.86017	−	6.68600i	0.151176	−	0.261844i
$653$	13.4241			0.525324			0.262662	−	0.964888i	$-0.415400\pi$
$653$	13.4241			0.525324			0.262662	+	0.964888i	$0.415400\pi$
$654$	−4.48173			−0.175249
$655$	−15.1625	+	26.2621i	−0.592446	+	1.02615i
$656$	−5.73050	+	9.92551i	−0.223738	+	0.387526i
$657$	−0.345647			−0.0134850
$658$	−12.6050			−0.491393
$659$	9.27252	−	16.0605i	0.361206	−	0.625628i	−0.626953	−	0.779057i	$-0.715698\pi$
$659$	9.27252	−	16.0605i	0.361206	−	0.625628i	0.988160	+	0.153429i	$0.0490317\pi$
$660$	8.53279	+	14.7792i	0.332138	+	0.575281i
$661$	−3.28797	+	5.69494i	−0.127887	+	0.221507i	−0.922858	−	0.385141i	$-0.874153\pi$
$661$	−3.28797	+	5.69494i	−0.127887	+	0.221507i	0.794971	+	0.606648i	$0.207486\pi$
$662$	−3.28071	−	5.68236i	−0.127509	−	0.220851i
$663$		0			0
$664$	−4.80664			−0.186534
$665$	−29.2580	−	31.2249i	−1.13458	−	1.21085i
$666$	0.571993			0.0221643
$667$	20.1233	+	34.8545i	0.779176	+	1.34957i
$668$	−10.2211	−	17.7034i	−0.395465	−	0.684965i
$669$	11.8980	−	20.6080i	0.460005	−	0.796752i
$670$	−4.11628	−	7.12961i	−0.159026	−	0.275441i
$671$	21.9269	−	37.9785i	0.846478	−	1.46614i
$672$	19.9361			0.769052
$673$	−39.2386			−1.51254			−0.756268	−	0.654261i	$-0.772980\pi$
$673$	−39.2386			−1.51254			−0.756268	+	0.654261i	$0.772980\pi$
$674$	2.16443	−	3.74891i	0.0833709	−	0.144403i
$675$	−1.07199	+	1.85675i	−0.0412610	+	0.0714662i
$676$	21.7120			0.835078
$677$	−25.8432			−0.993234			−0.496617	−	0.867970i	$-0.665425\pi$
$677$	−25.8432			−0.993234			−0.496617	+	0.867970i	$0.665425\pi$
$678$	−1.82605	+	3.16280i	−0.0701289	+	0.121467i
$679$	−10.8600	−	18.8100i	−0.416767	−	0.721862i
$680$		0			0
$681$	−4.90841	−	8.50161i	−0.188090	−	0.325782i
$682$	−9.62438	−	16.6699i	−0.368537	−	0.638324i
$683$	42.9898			1.64496			0.822480	−	0.568794i	$-0.192590\pi$
$683$	42.9898			1.64496			0.822480	+	0.568794i	$0.192590\pi$
$684$	4.98568	+	5.32085i	0.190632	+	0.203448i
$685$	4.36638			0.166831
$686$	0.536096	+	0.928546i	0.0204683	+	0.0354521i
$687$	−0.0719933	−	0.124696i	−0.00274671	−	0.00475745i
$688$	−3.01960	+	5.23010i	−0.115121	+	0.199396i
$689$	−0.577276	−	0.999871i	−0.0219925	−	0.0380921i
$690$	−5.75518	+	9.96827i	−0.219096	+	0.379486i
$691$	−48.4033			−1.84135			−0.920675	−	0.390331i	$-0.872361\pi$
$691$	−48.4033			−1.84135			−0.920675	+	0.390331i	$0.872361\pi$
$692$	−25.1888			−0.957536
$693$	−7.00924	+	12.1404i	−0.266259	+	0.461174i
$694$	6.23953	−	10.8072i	0.236849	−	0.410235i
$695$	−20.0678			−0.761217
$696$	−11.2303			−0.425683
$697$		0			0
$698$	−1.30051	−	2.25256i	−0.0492252	−	0.0852606i
$699$	−5.28797	+	9.15904i	−0.200010	+	0.346427i
$700$	−6.58631	−	11.4078i	−0.248939	−	0.431175i
$701$	1.60591	+	2.78152i	0.0606545	+	0.105057i	0.894758	−	0.446551i	$-0.147348\pi$
$701$	1.60591	+	2.78152i	0.0606545	+	0.105057i	−0.834104	+	0.551608i	$0.814015\pi$
$702$	−0.0823593			−0.00310845
$703$	−4.24482	+	0.990721i	−0.160096	+	0.0373658i
$704$	4.51601			0.170204
$705$	−8.01847	−	13.8884i	−0.301993	−	0.523067i
$706$	−2.57332	−	4.45713i	−0.0968483	−	0.167746i
$707$	15.2201	−	26.3620i	0.572412	−	0.991447i
$708$	3.19243	+	5.52944i	0.119979	+	0.207809i
$709$	−11.0328	+	19.1094i	−0.414345	+	0.717667i	−0.995359	−	0.0962265i	$-0.969323\pi$
$709$	−11.0328	+	19.1094i	−0.414345	+	0.717667i	0.581014	+	0.813893i	$0.302656\pi$
$710$	−20.8436			−0.782246
$711$	6.52884			0.244851
$712$	9.11007	−	15.7791i	0.341414	−	0.591347i
$713$	−33.1902	+	57.4871i	−1.24298	+	2.15291i
$714$		0			0
$715$	1.46890			0.0549338
$716$	−12.6821	+	21.9660i	−0.473951	+	0.820907i
$717$	4.90841	+	8.50161i	0.183308	+	0.317498i
$718$	3.71203	−	6.42942i	0.138532	−	0.239944i
$719$	−8.83000	−	15.2940i	−0.329303	−	0.570370i	0.653070	−	0.757297i	$-0.273481\pi$
$719$	−8.83000	−	15.2940i	−0.329303	−	0.570370i	−0.982374	+	0.186927i	$0.940147\pi$
$720$	2.86525	+	4.96276i	0.106782	+	0.184951i
$721$	−53.8145			−2.00416
$722$	9.03892	+	6.03395i	0.336394	+	0.224560i
$723$	1.94233			0.0722359
$724$	10.2056	+	17.6766i	0.379289	+	0.656947i
$725$	5.73050	+	9.92551i	0.212825	+	0.368624i
$726$	1.02045	−	1.76747i	0.0378724	−	0.0655969i
$727$	20.1966	+	34.9815i	0.749050	+	1.29739i	0.948279	+	0.317439i	$0.102823\pi$
$727$	20.1966	+	34.9815i	0.749050	+	1.29739i	−0.199229	+	0.979953i	$0.563844\pi$
$728$	0.555499	−	0.962152i	0.0205881	−	0.0356597i
$729$	1.00000			0.0370370
$730$	−0.528439			−0.0195584
$731$		0			0
$732$	9.61007	−	16.6451i	0.355198	−	0.615221i
$733$	−17.9137			−0.661657			−0.330829	−	0.943691i	$-0.607328\pi$
$733$	−17.9137			−0.661657			−0.330829	+	0.943691i	$0.607328\pi$
$734$	2.31492			0.0854452
$735$	8.67282	−	15.0218i	0.319902	−	0.554086i
$736$	20.4333	+	35.3915i	0.753181	+	1.30455i
$737$	10.2765	−	17.7994i	0.378539	−	0.655649i
$738$	1.52884	+	2.64802i	0.0562773	+	0.0974751i
$739$	8.48850	+	14.7025i	0.312255	+	0.540841i	0.978850	−	0.204579i	$-0.0655825\pi$
$739$	8.48850	+	14.7025i	0.312255	+	0.540841i	−0.666595	+	0.745420i	$0.732249\pi$
$740$	−4.47116			−0.164363
$741$	0.611196	−	0.142651i	0.0224529	−	0.00524040i
$742$	16.8454			0.618416
$743$	25.3588	+	43.9228i	0.930325	+	1.61137i	0.782765	+	0.622318i	$0.213809\pi$
$743$	25.3588	+	43.9228i	0.930325	+	1.61137i	0.147561	+	0.989053i	$0.452858\pi$
$744$	−9.26131	−	16.0411i	−0.339536	−	0.588094i
$745$	18.7345	−	32.4490i	0.686377	−	1.18884i
$746$	1.08631	+	1.88155i	0.0397727	+	0.0688884i
$747$	1.14399	−	1.98144i	0.0418563	−	0.0724972i
$748$		0			0
$749$	61.3042			2.24001
$750$	2.18319	−	3.78140i	0.0797188	−	0.138077i
$751$	12.7972	−	22.1654i	0.466977	−	0.808828i	−0.532312	−	0.846549i	$-0.678676\pi$
$751$	12.7972	−	22.1654i	0.466977	−	0.808828i	0.999288	+	0.0377210i	$0.0120098\pi$
$752$	−12.8639			−0.469099
$753$	13.6336			0.496837
$754$	−0.220132	+	0.381280i	−0.00801673	+	0.0138854i
$755$	14.7776	+	25.5956i	0.537812	+	0.931518i
$756$	−3.07199	+	5.32085i	−0.111727	+	0.193517i
$757$	−22.8681	−	39.6087i	−0.831154	−	1.43960i	−0.897124	−	0.441780i	$-0.854347\pi$
$757$	−22.8681	−	39.6087i	−0.831154	−	1.43960i	0.0659694	−	0.997822i	$-0.478986\pi$
$758$	1.40002	+	2.42490i	0.0508509	+	0.0880763i
$759$	−28.7361			−1.04306
$760$	16.7354	+	17.8604i	0.607056	+	0.647866i
$761$	−44.1338			−1.59985			−0.799925	−	0.600100i	$-0.795127\pi$
$761$	−44.1338			−1.59985			−0.799925	+	0.600100i	$0.795127\pi$
$762$	0.759136	+	1.31486i	0.0275006	+	0.0476324i
$763$	14.3888	+	24.9221i	0.520910	+	0.902242i
$764$	4.55880	−	7.89608i	0.164932	−	0.285670i
$765$		0			0
$766$	9.76442	−	16.9125i	0.352803	−	0.611072i
$767$	0.549569			0.0198438
$768$	−4.23030			−0.152648
$769$	22.0473	−	38.1871i	0.795046	−	1.37706i	−0.127764	−	0.991805i	$-0.540780\pi$
$769$	22.0473	−	38.1871i	0.795046	−	1.37706i	0.922810	−	0.385256i	$-0.125887\pi$
$770$	−10.7160	+	18.5606i	−0.386177	+	0.668878i
$771$	−12.5944			−0.453577
$772$	0.853752			0.0307272
$773$	−2.45043	+	4.24427i	−0.0881359	+	0.152656i	−0.906723	−	0.421726i	$-0.861424\pi$
$773$	−2.45043	+	4.24427i	−0.0881359	+	0.152656i	0.818587	+	0.574382i	$0.194758\pi$
$774$	0.805598	+	1.39534i	0.0289566	+	0.0501544i
$775$	−9.45156	+	16.3706i	−0.339510	+	0.588049i
$776$	6.21183	+	10.7592i	0.222992	+	0.386233i
$777$	−1.83641	−	3.18076i	−0.0658809	−	0.114109i
$778$	−15.3765			−0.551276
$779$	−15.9322	−	17.0032i	−0.570829	−	0.609203i
$780$	0.643787			0.0230513
$781$	−26.0185	−	45.0653i	−0.931014	−	1.61256i
$782$		0			0
$783$	2.67282	−	4.62947i	0.0955189	−	0.165444i
$784$	−6.95684	−	12.0496i	−0.248459	−	0.430343i
$785$	18.7868	−	32.5398i	0.670531	−	1.16139i
$786$	6.48963			0.231478
$787$	35.0554			1.24959			0.624795	−	0.780789i	$-0.285182\pi$
$787$	35.0554			1.24959			0.624795	+	0.780789i	$0.285182\pi$
$788$	19.2047	−	33.2635i	0.684138	−	1.18496i
$789$	0.816810	−	1.41476i	0.0290792	−	0.0503667i
$790$	9.98153			0.355127
$791$	23.4504			0.833801
$792$	4.00924	−	6.94420i	0.142462	−	0.246751i
$793$	−0.827176	−	1.43271i	−0.0293739	−	0.0508771i
$794$	7.21816	−	12.5022i	0.256163	−	0.443687i
$795$	10.7160	+	18.5606i	0.380057	+	0.658277i
$796$	−0.104983	−	0.181835i	−0.00372101	−	0.00644498i
$797$	−5.67056			−0.200862			−0.100431	−	0.994944i	$-0.532022\pi$
$797$	−5.67056			−0.200862			−0.100431	+	0.994944i	$0.532022\pi$
$798$	−2.65633	+	8.76357i	−0.0940330	+	0.310227i
$799$		0			0
$800$	5.81879	+	10.0784i	0.205725	+	0.356326i
$801$	4.33641	+	7.51089i	0.153220	+	0.265384i
$802$	−0.951561	+	1.64815i	−0.0336008	+	0.0581983i
$803$	−0.659635	−	1.14252i	−0.0232780	−	0.0403187i
$804$	4.50395	−	7.80108i	0.158842	−	0.275123i
$805$	73.9092			2.60496
$806$	−0.726147			−0.0255774
$807$	10.8260	−	18.7513i	0.381095	−	0.660076i
$808$	−8.70581	+	15.0789i	−0.306269	+	0.530474i
$809$	10.6359			0.373938			0.186969	−	0.982366i	$-0.440134\pi$
$809$	10.6359			0.373938			0.186969	+	0.982366i	$0.440134\pi$
$810$	1.52884			0.0537179
$811$	−13.6521	+	23.6461i	−0.479390	+	0.830327i	−0.999721	−	0.0236373i	$-0.992475\pi$
$811$	−13.6521	+	23.6461i	−0.479390	+	0.830327i	0.520331	+	0.853965i	$0.325809\pi$
$812$	16.4218	+	28.4434i	0.576292	+	0.998167i
$813$	10.7776	−	18.6674i	0.377987	−	0.654693i
$814$	1.09159	+	1.89070i	0.0382604	+	0.0662689i
$815$	6.16774	+	10.6828i	0.216047	+	0.374204i
$816$		0			0
$817$	−8.39522	−	8.95959i	−0.293711	−	0.313456i
$818$	−19.5183			−0.682440
$819$	0.264419	+	0.457986i	0.00923953	+	0.0160033i
$820$	−11.9506	−	20.6991i	−0.417334	−	0.722844i
$821$	−10.5865	+	18.3364i	−0.369472	+	0.639944i	−0.989483	−	0.144649i	$-0.953795\pi$
$821$	−10.5865	+	18.3364i	−0.369472	+	0.639944i	0.620011	+	0.784593i	$0.287128\pi$
$822$	−0.467210	−	0.809231i	−0.0162958	−	0.0282252i
$823$	−23.3641	+	40.4678i	−0.814422	+	1.41062i	0.0953202	+	0.995447i	$0.469612\pi$
$823$	−23.3641	+	40.4678i	−0.814422	+	1.41062i	−0.909742	+	0.415174i	$0.863721\pi$
$824$	30.7816			1.07233
$825$	−8.18319			−0.284902
$826$	−4.00924	+	6.94420i	−0.139499	+	0.241620i
$827$	2.83754	−	4.91477i	0.0986710	−	0.170903i	−0.812464	−	0.583012i	$-0.801874\pi$
$827$	2.83754	−	4.91477i	0.0986710	−	0.170903i	0.911135	+	0.412108i	$0.135208\pi$
$828$	−12.5944			−0.437686
$829$	−22.3377			−0.775822			−0.387911	−	0.921697i	$-0.626803\pi$
$829$	−22.3377			−0.775822			−0.387911	+	0.921697i	$0.626803\pi$
$830$	1.74897	−	3.02930i	0.0607076	−	0.105149i
$831$	−3.81286	−	6.60406i	−0.132267	−	0.229092i
$832$	0.0851817	−	0.147539i	0.00295314	−	0.00511500i
$833$		0			0
$834$	2.14729	+	3.71922i	0.0743547	+	0.128786i
$835$	32.6623			1.13032
$836$	−8.07312	+	26.6343i	−0.279215	+	0.921166i
$837$	8.81681			0.304754
$838$	−2.62043	−	4.53872i	−0.0905213	−	0.156788i
$839$	6.54203	+	11.3311i	0.225856	+	0.391194i	0.956576	−	0.291484i	$-0.0941488\pi$
$839$	6.54203	+	11.3311i	0.225856	+	0.391194i	−0.730720	+	0.682677i	$0.760816\pi$
$840$	−10.3117	+	17.8604i	−0.355788	+	0.616244i
$841$	0.212027	+	0.367241i	0.00731127	+	0.0126635i
$842$	−4.52884	+	7.84418i	−0.156074	+	0.270328i
$843$	−1.69356			−0.0583292
$844$	−41.5759			−1.43110
$845$	−17.3456	+	30.0435i	−0.596708	+	1.03353i
$846$	−1.71598	+	2.97216i	−0.0589966	+	0.102185i
$847$	−13.1048			−0.450286
$848$	17.1915			0.590358
$849$	−5.14399	+	8.90965i	−0.176541	+	0.305778i
$850$		0			0
$851$	3.76442	−	6.52016i	0.129043	−	0.223508i
$852$	−11.4033	−	19.7511i	−0.390671	−	0.676663i
$853$	−20.1129	−	34.8365i	−0.688652	−	1.19278i	−0.972274	−	0.233844i	$-0.924869\pi$
$853$	−20.1129	−	34.8365i	−0.688652	−	1.19278i	0.283622	−	0.958936i	$-0.408464\pi$
$854$	24.1378			0.825978
$855$	−11.3456	+	2.64802i	−0.388013	+	0.0905605i
$856$	−35.0656			−1.19852
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	0.912705	−	0.408619i	$-0.133990\pi$
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	−0.810227	+	0.586116i	$0.800656\pi$
$858$	−0.157175	−	0.272235i	−0.00536586	−	0.00929395i
$859$	10.9412	−	18.9507i	0.373309	−	0.646590i	−0.616764	−	0.787148i	$-0.711557\pi$
$859$	10.9412	−	18.9507i	0.373309	−	0.646590i	0.990072	+	0.140559i	$0.0448899\pi$
$860$	−6.29721	−	10.9071i	−0.214733	−	0.371929i
$861$	9.81681	−	17.0032i	0.334556	−	0.579468i
$862$	5.30080			0.180546
$863$	−10.5759			−0.360009			−0.180005	−	0.983666i	$-0.557611\pi$
$863$	−10.5759			−0.360009			−0.180005	+	0.983666i	$0.557611\pi$
$864$	2.71400	−	4.70079i	0.0923323	−	0.159924i
$865$	20.1233	−	34.8545i	0.684211	−	1.18509i
$866$	11.3338			0.385138
$867$	−17.0000			−0.577350
$868$	−27.0852	+	46.9129i	−0.919331	+	1.59233i
$869$	12.4597	+	21.5808i	0.422665	+	0.732078i
$870$	4.08631	−	7.07770i	0.138539	−	0.239957i
$871$	−0.387673	−	0.671469i	−0.0131358	−	0.0227519i
$872$	−8.23030	−	14.2553i	−0.278713	−	0.482745i
$873$	−5.91369			−0.200148
$874$	−18.2801	+	4.26649i	−0.618333	+	0.144316i
$875$	−28.0369			−0.947822
$876$	−0.289104	−	0.500742i	−0.00976790	−	0.0169185i
$877$	21.7672	+	37.7020i	0.735028	+	1.27310i	0.954711	+	0.297534i	$0.0961641\pi$
$877$	21.7672	+	37.7020i	0.735028	+	1.27310i	−0.219684	+	0.975571i	$0.570503\pi$
$878$	1.97427	−	3.41954i	0.0666284	−	0.115404i
$879$	−6.05767	−	10.4922i	−0.204320	−	0.353893i
$880$	−10.9361	+	18.9419i	−0.368656	+	0.638531i
$881$	4.96080			0.167133			0.0835667	−	0.996502i	$-0.473369\pi$
$881$	4.96080			0.167133			0.0835667	+	0.996502i	$0.473369\pi$
$882$	−3.71203			−0.124990
$883$	6.50528	−	11.2675i	0.218920	−	0.379181i	−0.735558	−	0.677462i	$-0.763080\pi$
$883$	6.50528	−	11.2675i	0.218920	−	0.379181i	0.954478	+	0.298281i	$0.0964132\pi$
$884$		0			0
$885$	−10.2017			−0.342925
$886$	11.2303			0.377289
$887$	−17.0709	+	29.5676i	−0.573183	+	0.992783i	0.423053	+	0.906105i	$0.360958\pi$
$887$	−17.0709	+	29.5676i	−0.573183	+	0.992783i	−0.996236	+	0.0866779i	$0.972375\pi$
$888$	1.05042	+	1.81937i	0.0352496	+	0.0610541i
$889$	4.87448	−	8.44285i	0.163485	−	0.283164i
$890$	6.62967	+	11.4829i	0.222227	+	0.384908i
$891$	1.90841	+	3.30545i	0.0639340	+	0.110737i
$892$	39.8066			1.33283
$893$	7.58651	−	25.0289i	0.253873	−	0.837560i
$894$	−8.01847			−0.268178
$895$	−20.2633	−	35.0970i	−0.677327	−	1.17316i
$896$	21.1790	+	36.6830i	0.707539	+	1.22549i
$897$	−0.542026	+	0.938816i	−0.0180977	+	0.0313461i
$898$	8.29854	+	14.3735i	0.276926	+	0.479650i
$899$	23.5658	−	40.8171i	0.785963	−	1.36133i
$900$	−3.58651			−0.119550
$901$		0			0
$902$	−5.83528	+	10.1070i	−0.194294	+	0.336526i
$903$	5.17282	−	8.95959i	0.172141	−	0.298157i
$904$	−13.4135			−0.446126
$905$	−32.6129			−1.08409
$906$	3.16246	−	5.47754i	0.105066	−	0.181979i
$907$	−23.7490	−	41.1344i	−0.788572	−	1.36585i	−0.926842	−	0.375452i	$-0.877488\pi$
$907$	−23.7490	−	41.1344i	−0.788572	−	1.36585i	0.138270	−	0.990395i	$-0.455846\pi$
$908$	8.21090	−	14.2217i	0.272488	−	0.471963i
$909$	−4.14399	−	7.17760i	−0.137447	−	0.238066i
$910$	0.404253	+	0.700187i	0.0134009	+	0.0232110i
$911$	−46.1523			−1.52909			−0.764547	−	0.644568i	$-0.777037\pi$
$911$	−46.1523			−1.52909			−0.764547	+	0.644568i	$0.777037\pi$
$912$	−2.71090	+	8.94360i	−0.0897668	+	0.296152i
$913$	8.73276			0.289012
$914$	9.30842	+	16.1227i	0.307895	+	0.533290i
$915$	15.3549	+	26.5954i	0.507617	+	0.879218i
$916$	0.120432	−	0.208594i	0.00397919	−	0.00689215i
$917$	−20.8353	−	36.0878i	−0.688042	−	1.19172i
$918$		0			0
$919$	−29.5160			−0.973643			−0.486822	−	0.873501i	$-0.661844\pi$
$919$	−29.5160			−0.973643			−0.486822	+	0.873501i	$0.661844\pi$
$920$	−42.2755			−1.39378
$921$	2.24482	−	3.88814i	0.0739692	−	0.128118i
$922$	−2.76047	+	4.78127i	−0.0909111	+	0.157463i
$923$	−1.96306			−0.0646148
$924$	−23.4504			−0.771463
$925$	1.07199	−	1.85675i	0.0352469	−	0.0610495i
$926$	−8.88174	−	15.3836i	−0.291872	−	0.505537i
$927$	−7.32605	+	12.6891i	−0.240619	+	0.416764i
$928$	−14.5081	−	25.1288i	−0.476252	−	0.824892i
$929$	19.7213	+	34.1582i	0.647034	+	1.12070i	0.983828	+	0.179117i	$0.0573240\pi$
$929$	19.7213	+	34.1582i	0.647034	+	1.12070i	−0.336794	+	0.941578i	$0.609343\pi$
$930$	13.4795			0.442009
$931$	27.5473	−	6.42942i	0.902827	−	0.210716i
$932$	−17.6917			−0.579511
$933$	−0.379568	−	0.657431i	−0.0124265	−	0.0215233i
$934$	2.46326	+	4.26649i	0.0806002	+	0.139604i
$935$		0			0
$936$	−0.151246	−	0.261965i	−0.00494362	−	0.00856260i
$937$	−13.8681	+	24.0202i	−0.453050	+	0.784706i	−0.998574	−	0.0533896i	$-0.982997\pi$
$937$	−13.8681	+	24.0202i	−0.453050	+	0.784706i	0.545524	+	0.838095i	$0.316331\pi$
$938$	11.3127			0.369371
$939$	11.4320			0.373068
$940$	13.4135	−	23.2328i	0.437500	−	0.757772i
$941$	8.12325	−	14.0699i	0.264811	−	0.458665i	−0.702703	−	0.711483i	$-0.748024\pi$
$941$	8.12325	−	14.0699i	0.264811	−	0.458665i	0.967514	+	0.252818i	$0.0813573\pi$
$942$	−8.04090			−0.261987
$943$	40.2465			1.31061
$944$	−4.09159	+	7.08685i	−0.133170	+	0.230657i
$945$	−4.90841	−	8.50161i	−0.159670	−	0.276557i
$946$	−3.07482	+	5.32574i	−0.0999709	+	0.173155i
$947$	7.96080	+	13.7885i	0.258691	+	0.448066i	0.965892	−	0.258947i	$-0.0833755\pi$
$947$	7.96080	+	13.7885i	0.258691	+	0.448066i	−0.707200	+	0.707013i	$0.750042\pi$
$948$	5.46080	+	9.45838i	0.177358	+	0.307194i
$949$	−0.0497686			−0.00161556
$950$	−5.20561	+	1.21497i	−0.168892	+	0.0394187i
$951$	−11.6151			−0.376647
$952$		0			0
$953$	−17.9700	−	31.1250i	−0.582106	−	1.00824i	−0.995229	−	0.0975627i	$-0.968895\pi$
$953$	−17.9700	−	31.1250i	−0.582106	−	1.00824i	0.413123	−	0.910675i	$-0.364438\pi$
$954$	2.29326	−	3.97204i	0.0742469	−	0.128599i
$955$	7.28402	+	12.6163i	0.235705	+	0.408254i
$956$	−8.21090	+	14.2217i	−0.265559	+	0.459962i
$957$	20.4033			0.659546
$958$	−9.98757			−0.322684
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$	−1.58123	+	2.73877i	−0.0510339	+	0.0883934i
$961$	46.7361			1.50762
$962$	0.0823593			0.00265537
$963$	8.34565	−	14.4551i	0.268935	−	0.465809i
$964$	1.62458	+	2.81386i	0.0523243	+	0.0906284i
$965$	−0.682059	+	1.18136i	−0.0219563	+	0.0380294i
$966$	−7.90841	−	13.6978i	−0.254449	−	0.440718i
$967$	−1.30362	−	2.25794i	−0.0419217	−	0.0726104i	0.844303	−	0.535866i	$-0.180015\pi$
$967$	−1.30362	−	2.25794i	−0.0419217	−	0.0726104i	−0.886225	+	0.463255i	$0.846681\pi$
$968$	7.49585			0.240926
$969$		0			0
$970$	−9.04107			−0.290291
$971$	−8.06558	−	13.9700i	−0.258837	−	0.448318i	0.707094	−	0.707120i	$-0.250006\pi$
$971$	−8.06558	−	13.9700i	−0.258837	−	0.448318i	−0.965931	+	0.258801i	$0.916673\pi$
$972$	0.836412	+	1.44871i	0.0268279	+	0.0464673i
$973$	13.7880	−	23.8815i	0.442022	−	0.765605i
$974$	−3.32718	−	5.76284i	−0.106610	−	0.184653i
$975$	−0.154353	+	0.267347i	−0.00494324	+	0.00856194i
$976$	24.6336			0.788503
$977$	−3.17302			−0.101514			−0.0507570	−	0.998711i	$-0.516163\pi$
$977$	−3.17302			−0.101514			−0.0507570	+	0.998711i	$0.516163\pi$
$978$	1.31992	−	2.28616i	0.0422063	−	0.0731035i
$979$	−16.5513	+	28.6676i	−0.528981	+	0.916221i
$980$	29.0162			0.926889
$981$	7.83528			0.250161
$982$	−6.95684	+	12.0496i	−0.222002	+	0.384518i
$983$	−10.4165	−	18.0419i	−0.332235	−	0.575448i	0.650715	−	0.759322i	$-0.274469\pi$
$983$	−10.4165	−	18.0419i	−0.332235	−	0.575448i	−0.982950	+	0.183874i	$0.941136\pi$
$984$	−5.61515	+	9.72572i	−0.179004	+	0.310045i
$985$	30.6851	+	53.1481i	0.977708	+	1.69344i
$986$		0			0
$987$	22.0369			0.701444
$988$	0.717871	+	0.766131i	0.0228385	+	0.0243739i
$989$	21.2073			0.674353
$990$	2.91764	+	5.05350i	0.0927287	+	0.160611i
$991$	22.9165	+	39.6926i	0.727967	+	1.26088i	0.957741	+	0.287632i	$0.0928679\pi$
$991$	22.9165	+	39.6926i	0.727967	+	1.26088i	−0.229774	+	0.973244i	$0.573799\pi$
$992$	23.9289	−	41.4460i	0.759742	−	1.31591i
$993$	5.73558	+	9.93432i	0.182013	+	0.315256i
$994$	14.3210	−	24.8046i	0.454233	−	0.786755i
$995$	0.335481			0.0106355
$996$	3.82738			0.121275
$997$	−27.3168	+	47.3141i	−0.865132	+	1.49845i	0.00178393	+	0.999998i	$0.499432\pi$
$997$	−27.3168	+	47.3141i	−0.865132	+	1.49845i	−0.866916	+	0.498454i	$0.833901\pi$
$998$	10.9002	−	18.8797i	0.345040	−	0.597627i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.e.b.7.2	✓	6
3.2	odd	2		171.2.f.b.64.2		6
4.3	odd	2		912.2.q.l.577.3		6
12.11	even	2		2736.2.s.z.577.1		6
19.7	even	3		1083.2.a.l.1.2		3
19.11	even	3	inner	57.2.e.b.49.2	yes	6
19.12	odd	6		1083.2.a.o.1.2		3
57.11	odd	6		171.2.f.b.163.2		6
57.26	odd	6		3249.2.a.y.1.2		3
57.50	even	6		3249.2.a.t.1.2		3
76.11	odd	6		912.2.q.l.49.3		6
228.11	even	6		2736.2.s.z.1873.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.2	✓	6	1.1	even	1	trivial
57.2.e.b.49.2	yes	6	19.11	even	3	inner
171.2.f.b.64.2		6	3.2	odd	2
171.2.f.b.163.2		6	57.11	odd	6
912.2.q.l.49.3		6	76.11	odd	6
912.2.q.l.577.3		6	4.3	odd	2
1083.2.a.l.1.2		3	19.7	even	3
1083.2.a.o.1.2		3	19.12	odd	6
2736.2.s.z.577.1		6	12.11	even	2
2736.2.s.z.1873.1		6	228.11	even	6
3249.2.a.t.1.2		3	57.50	even	6
3249.2.a.y.1.2		3	57.26	odd	6

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.285997 + 0.495361i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.836412 - 1.44871i) q^{4} +(1.33641 + 2.31473i) q^{5} +(0.285997 - 0.495361i) q^{6} -3.67282 q^{7} +2.10083 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.285997 + 0.495361i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.836412 - 1.44871i) q^{4} +(1.33641 + 2.31473i) q^{5} +(0.285997 - 0.495361i) q^{6} -3.67282 q^{7} +2.10083 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.764419 + 1.32401i) q^{10} -3.81681 q^{11} -1.67282 q^{12} +(-0.0719933 + 0.124696i) q^{13} +(-1.05042 - 1.81937i) q^{14} +(1.33641 - 2.31473i) q^{15} +(-1.07199 - 1.85675i) q^{16} -0.571993 q^{18} +(4.24482 - 0.990721i) q^{19} +4.47116 q^{20} +(1.83641 + 3.18076i) q^{21} +(-1.09159 - 1.89070i) q^{22} +(-3.76442 + 6.52016i) q^{23} +(-1.05042 - 1.81937i) q^{24} +(-1.07199 + 1.85675i) q^{25} -0.0823593 q^{26} +1.00000 q^{27} +(-3.07199 + 5.32085i) q^{28} +(2.67282 - 4.62947i) q^{29} +1.52884 q^{30} +8.81681 q^{31} +(2.71400 - 4.70079i) q^{32} +(1.90841 + 3.30545i) q^{33} +(-4.90841 - 8.50161i) q^{35} +(0.836412 + 1.44871i) q^{36} -1.00000 q^{37} +(1.70477 + 1.81937i) q^{38} +0.143987 q^{39} +(2.80757 + 4.86286i) q^{40} +(-2.67282 - 4.62947i) q^{41} +(-1.05042 + 1.81937i) q^{42} +(-1.40841 - 2.43943i) q^{43} +(-3.19243 + 5.52944i) q^{44} -2.67282 q^{45} -4.30644 q^{46} +(3.00000 - 5.19615i) q^{47} +(-1.07199 + 1.85675i) q^{48} +6.48963 q^{49} -1.22635 q^{50} +(0.120432 + 0.208594i) q^{52} +(-4.00924 + 6.94420i) q^{53} +(0.285997 + 0.495361i) q^{54} +(-5.10083 - 8.83490i) q^{55} -7.71598 q^{56} +(-2.98040 - 3.18076i) q^{57} +3.05767 q^{58} +(-1.90841 - 3.30545i) q^{59} +(-2.23558 - 3.87214i) q^{60} +(-5.74482 + 9.95031i) q^{61} +(2.52158 + 4.36750i) q^{62} +(1.83641 - 3.18076i) q^{63} -1.18319 q^{64} -0.384851 q^{65} +(-1.09159 + 1.89070i) q^{66} +(-2.69243 + 4.66342i) q^{67} +7.52884 q^{69} +(2.80757 - 4.86286i) q^{70} +(6.81681 + 11.8071i) q^{71} +(-1.05042 + 1.81937i) q^{72} +(0.172824 + 0.299339i) q^{73} +(-0.285997 - 0.495361i) q^{74} +2.14399 q^{75} +(2.11515 - 6.97815i) q^{76} +14.0185 q^{77} +(0.0411797 + 0.0713253i) q^{78} +(-3.26442 - 5.65414i) q^{79} +(2.86525 - 4.96276i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.52884 - 2.64802i) q^{82} -2.28797 q^{83} +6.14399 q^{84} +(0.805598 - 1.39534i) q^{86} -5.34565 q^{87} -8.01847 q^{88} +(4.33641 - 7.51089i) q^{89} +(-0.764419 - 1.32401i) q^{90} +(0.264419 - 0.457986i) q^{91} +(6.29721 + 10.9071i) q^{92} +(-4.40841 - 7.63558i) q^{93} +3.43196 q^{94} +(7.96608 + 8.50161i) q^{95} -5.42801 q^{96} +(2.95684 + 5.12140i) q^{97} +(1.85601 + 3.21471i) q^{98} +(1.90841 - 3.30545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + q^{2} - 3 q^{3} - 5 q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - 3 q^{9} + 4 q^{10} + 10 q^{12} + q^{13} + 3 q^{14} - 2 q^{15} - 5 q^{16} - 2 q^{18} + 4 q^{19} + 44 q^{20} + q^{21} - 18 q^{22} - 14 q^{23} + 3 q^{24} - 5 q^{25} - 42 q^{26} + 6 q^{27} - 17 q^{28} - 4 q^{29} - 8 q^{30} + 30 q^{31} + 17 q^{32} - 18 q^{35} - 5 q^{36} - 6 q^{37} + 41 q^{38} - 2 q^{39} + 24 q^{40} + 4 q^{41} + 3 q^{42} + 3 q^{43} - 12 q^{44} + 4 q^{45} + 40 q^{46} + 18 q^{47} - 5 q^{48} - 4 q^{49} - 46 q^{50} - 5 q^{52} + 6 q^{53} + q^{54} - 12 q^{55} - 42 q^{56} - 5 q^{57} - 16 q^{58} - 22 q^{60} - 13 q^{61} + 23 q^{62} + q^{63} - 30 q^{64} + 12 q^{65} - 18 q^{66} - 9 q^{67} + 28 q^{69} + 24 q^{70} + 18 q^{71} + 3 q^{72} - 19 q^{73} - q^{74} + 10 q^{75} + 27 q^{76} + 24 q^{77} + 21 q^{78} - 11 q^{79} - 10 q^{80} - 3 q^{81} - 8 q^{82} - 8 q^{83} + 34 q^{84} + 17 q^{86} + 8 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} - 7 q^{91} + 2 q^{92} - 15 q^{93} + 12 q^{94} + 2 q^{95} - 34 q^{96} + 2 q^{97} + 14 q^{98}+O(q^{100}) \) 6 * q + q^2 - 3 * q^3 - 5 * q^4 - 2 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - 3 * q^9 + 4 * q^10 + 10 * q^12 + q^13 + 3 * q^14 - 2 * q^15 - 5 * q^16 - 2 * q^18 + 4 * q^19 + 44 * q^20 + q^21 - 18 * q^22 - 14 * q^23 + 3 * q^24 - 5 * q^25 - 42 * q^26 + 6 * q^27 - 17 * q^28 - 4 * q^29 - 8 * q^30 + 30 * q^31 + 17 * q^32 - 18 * q^35 - 5 * q^36 - 6 * q^37 + 41 * q^38 - 2 * q^39 + 24 * q^40 + 4 * q^41 + 3 * q^42 + 3 * q^43 - 12 * q^44 + 4 * q^45 + 40 * q^46 + 18 * q^47 - 5 * q^48 - 4 * q^49 - 46 * q^50 - 5 * q^52 + 6 * q^53 + q^54 - 12 * q^55 - 42 * q^56 - 5 * q^57 - 16 * q^58 - 22 * q^60 - 13 * q^61 + 23 * q^62 + q^63 - 30 * q^64 + 12 * q^65 - 18 * q^66 - 9 * q^67 + 28 * q^69 + 24 * q^70 + 18 * q^71 + 3 * q^72 - 19 * q^73 - q^74 + 10 * q^75 + 27 * q^76 + 24 * q^77 + 21 * q^78 - 11 * q^79 - 10 * q^80 - 3 * q^81 - 8 * q^82 - 8 * q^83 + 34 * q^84 + 17 * q^86 + 8 * q^87 + 12 * q^88 + 16 * q^89 + 4 * q^90 - 7 * q^91 + 2 * q^92 - 15 * q^93 + 12 * q^94 + 2 * q^95 - 34 * q^96 + 2 * q^97 + 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more