LMFDB - Embedded newform 722.2.c.i.429.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.i.653.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.80902 - 3.13331i) q^{5} +(-0.618034 - 1.07047i) q^{6} -3.23607 q^{7} -1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.80902 - 3.13331i) q^{5} +(-0.618034 - 1.07047i) q^{6} -3.23607 q^{7} -1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +(-1.80902 - 3.13331i) q^{10} -3.23607 q^{11} -1.23607 q^{12} +(-0.690983 - 1.19682i) q^{13} +(-1.61803 + 2.80252i) q^{14} +(-2.23607 - 3.87298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.69098 - 2.92887i) q^{17} +1.47214 q^{18} -3.61803 q^{20} +(-2.00000 + 3.46410i) q^{21} +(-1.61803 + 2.80252i) q^{22} +(-2.61803 - 4.53457i) q^{23} +(-0.618034 + 1.07047i) q^{24} +(-4.04508 - 7.00629i) q^{25} -1.38197 q^{26} +5.52786 q^{27} +(1.61803 + 2.80252i) q^{28} +(4.54508 + 7.87232i) q^{29} -4.47214 q^{30} -1.23607 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} +(-1.69098 - 2.92887i) q^{34} +(-5.85410 + 10.1396i) q^{35} +(0.736068 - 1.27491i) q^{36} +8.38197 q^{37} -1.70820 q^{39} +(-1.80902 + 3.13331i) q^{40} +(-0.427051 + 0.739674i) q^{41} +(2.00000 + 3.46410i) q^{42} +(4.61803 - 7.99867i) q^{43} +(1.61803 + 2.80252i) q^{44} +5.32624 q^{45} -5.23607 q^{46} +(-2.23607 - 3.87298i) q^{47} +(0.618034 + 1.07047i) q^{48} +3.47214 q^{49} -8.09017 q^{50} +(-2.09017 - 3.62028i) q^{51} +(-0.690983 + 1.19682i) q^{52} +(3.04508 + 5.27424i) q^{53} +(2.76393 - 4.78727i) q^{54} +(-5.85410 + 10.1396i) q^{55} +3.23607 q^{56} +9.09017 q^{58} +(0.236068 - 0.408882i) q^{59} +(-2.23607 + 3.87298i) q^{60} +(-0.690983 - 1.19682i) q^{61} +(-0.618034 + 1.07047i) q^{62} +(-2.38197 - 4.12569i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(2.00000 + 3.46410i) q^{66} +(-5.85410 - 10.1396i) q^{67} -3.38197 q^{68} -6.47214 q^{69} +(5.85410 + 10.1396i) q^{70} +(-1.47214 + 2.54981i) q^{71} +(-0.736068 - 1.27491i) q^{72} +(2.80902 - 4.86536i) q^{73} +(4.19098 - 7.25900i) q^{74} -10.0000 q^{75} +10.4721 q^{77} +(-0.854102 + 1.47935i) q^{78} +(1.38197 - 2.39364i) q^{79} +(1.80902 + 3.13331i) q^{80} +(1.20820 - 2.09267i) q^{81} +(0.427051 + 0.739674i) q^{82} -0.472136 q^{83} +4.00000 q^{84} +(-6.11803 - 10.5967i) q^{85} +(-4.61803 - 7.99867i) q^{86} +11.2361 q^{87} +3.23607 q^{88} +(-4.42705 - 7.66788i) q^{89} +(2.66312 - 4.61266i) q^{90} +(2.23607 + 3.87298i) q^{91} +(-2.61803 + 4.53457i) q^{92} +(-0.763932 + 1.32317i) q^{93} -4.47214 q^{94} +1.23607 q^{96} +(-4.30902 + 7.46344i) q^{97} +(1.73607 - 3.00696i) q^{98} +(-2.38197 - 4.12569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 5 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 5 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 5 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 6 q^{9} - 5 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 2 q^{14} - 2 q^{16} + 9 q^{17} - 12 q^{18} - 10 q^{20} - 8 q^{21} - 2 q^{22} - 6 q^{23} + 2 q^{24} - 5 q^{25} - 10 q^{26} + 40 q^{27} + 2 q^{28} + 7 q^{29} + 4 q^{31} + 2 q^{32} - 8 q^{33} - 9 q^{34} - 10 q^{35} - 6 q^{36} + 38 q^{37} + 20 q^{39} - 5 q^{40} + 5 q^{41} + 8 q^{42} + 14 q^{43} + 2 q^{44} - 10 q^{45} - 12 q^{46} - 2 q^{48} - 4 q^{49} - 10 q^{50} + 14 q^{51} - 5 q^{52} + q^{53} + 20 q^{54} - 10 q^{55} + 4 q^{56} + 14 q^{58} - 8 q^{59} - 5 q^{61} + 2 q^{62} - 14 q^{63} + 4 q^{64} - 20 q^{65} + 8 q^{66} - 10 q^{67} - 18 q^{68} - 8 q^{69} + 10 q^{70} + 12 q^{71} + 6 q^{72} + 9 q^{73} + 19 q^{74} - 40 q^{75} + 24 q^{77} + 10 q^{78} + 10 q^{79} + 5 q^{80} - 22 q^{81} - 5 q^{82} + 16 q^{83} + 16 q^{84} - 20 q^{85} - 14 q^{86} + 36 q^{87} + 4 q^{88} - 11 q^{89} - 5 q^{90} - 6 q^{92} - 12 q^{93} - 4 q^{96} - 15 q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 5 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 6 * q^9 - 5 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 2 * q^14 - 2 * q^16 + 9 * q^17 - 12 * q^18 - 10 * q^20 - 8 * q^21 - 2 * q^22 - 6 * q^23 + 2 * q^24 - 5 * q^25 - 10 * q^26 + 40 * q^27 + 2 * q^28 + 7 * q^29 + 4 * q^31 + 2 * q^32 - 8 * q^33 - 9 * q^34 - 10 * q^35 - 6 * q^36 + 38 * q^37 + 20 * q^39 - 5 * q^40 + 5 * q^41 + 8 * q^42 + 14 * q^43 + 2 * q^44 - 10 * q^45 - 12 * q^46 - 2 * q^48 - 4 * q^49 - 10 * q^50 + 14 * q^51 - 5 * q^52 + q^53 + 20 * q^54 - 10 * q^55 + 4 * q^56 + 14 * q^58 - 8 * q^59 - 5 * q^61 + 2 * q^62 - 14 * q^63 + 4 * q^64 - 20 * q^65 + 8 * q^66 - 10 * q^67 - 18 * q^68 - 8 * q^69 + 10 * q^70 + 12 * q^71 + 6 * q^72 + 9 * q^73 + 19 * q^74 - 40 * q^75 + 24 * q^77 + 10 * q^78 + 10 * q^79 + 5 * q^80 - 22 * q^81 - 5 * q^82 + 16 * q^83 + 16 * q^84 - 20 * q^85 - 14 * q^86 + 36 * q^87 + 4 * q^88 - 11 * q^89 - 5 * q^90 - 6 * q^92 - 12 * q^93 - 4 * q^96 - 15 * q^97 - 2 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.618034	−	1.07047i	0.356822	−	0.618034i	−0.630606	−	0.776103i	$-0.717194\pi$
$3$	0.618034	−	1.07047i	0.356822	−	0.618034i	0.987428	+	0.158069i	$0.0505269\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.80902	−	3.13331i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$5$	1.80902	−	3.13331i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$6$	−0.618034	−	1.07047i	−0.252311	−	0.437016i
$7$	−3.23607			−1.22312			−0.611559	−	0.791199i	$-0.709457\pi$
$7$	−3.23607			−1.22312			−0.611559	+	0.791199i	$0.709457\pi$
$8$	−1.00000			−0.353553
$9$	0.736068	+	1.27491i	0.245356	+	0.424969i
$10$	−1.80902	−	3.13331i	−0.572061	−	0.990839i
$11$	−3.23607			−0.975711			−0.487856	−	0.872924i	$-0.662221\pi$
$11$	−3.23607			−0.975711			−0.487856	+	0.872924i	$0.662221\pi$
$12$	−1.23607			−0.356822
$13$	−0.690983	−	1.19682i	−0.191644	−	0.331937i	0.754151	−	0.656701i	$-0.228049\pi$
$13$	−0.690983	−	1.19682i	−0.191644	−	0.331937i	−0.945795	+	0.324763i	$0.894715\pi$
$14$	−1.61803	+	2.80252i	−0.432438	+	0.749004i
$15$	−2.23607	−	3.87298i	−0.577350	−	1.00000i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.69098	−	2.92887i	0.410124	−	0.710355i	−0.584779	−	0.811192i	$-0.698819\pi$
$17$	1.69098	−	2.92887i	0.410124	−	0.710355i	0.994903	+	0.100837i	$0.0321522\pi$
$18$	1.47214			0.346986
$19$		0			0
$19$		0			0
$20$	−3.61803			−0.809017
$21$	−2.00000	+	3.46410i	−0.436436	+	0.755929i
$22$	−1.61803	+	2.80252i	−0.344966	+	0.597499i
$23$	−2.61803	−	4.53457i	−0.545898	−	0.945523i	−0.998550	−	0.0538355i	$-0.982855\pi$
$23$	−2.61803	−	4.53457i	−0.545898	−	0.945523i	0.452652	−	0.891687i	$-0.350478\pi$
$24$	−0.618034	+	1.07047i	−0.126156	+	0.218508i
$25$	−4.04508	−	7.00629i	−0.809017	−	1.40126i
$26$	−1.38197			−0.271026
$27$	5.52786			1.06384
$28$	1.61803	+	2.80252i	0.305780	+	0.529626i
$29$	4.54508	+	7.87232i	0.844001	+	1.46185i	0.886486	+	0.462756i	$0.153139\pi$
$29$	4.54508	+	7.87232i	0.844001	+	1.46185i	−0.0424848	+	0.999097i	$0.513527\pi$
$30$	−4.47214			−0.816497
$31$	−1.23607			−0.222004			−0.111002	−	0.993820i	$-0.535406\pi$
$31$	−1.23607			−0.222004			−0.111002	+	0.993820i	$0.535406\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	−1.69098	−	2.92887i	−0.290001	−	0.502297i
$35$	−5.85410	+	10.1396i	−0.989524	+	1.71391i
$36$	0.736068	−	1.27491i	0.122678	−	0.212485i
$37$	8.38197			1.37799			0.688993	−	0.724768i	$-0.258053\pi$
$37$	8.38197			1.37799			0.688993	+	0.724768i	$0.258053\pi$
$38$		0			0
$39$	−1.70820			−0.273532
$40$	−1.80902	+	3.13331i	−0.286031	+	0.495420i
$41$	−0.427051	+	0.739674i	−0.0666942	+	0.115518i	−0.897444	−	0.441128i	$-0.854579\pi$
$41$	−0.427051	+	0.739674i	−0.0666942	+	0.115518i	0.830750	+	0.556646i	$0.187912\pi$
$42$	2.00000	+	3.46410i	0.308607	+	0.534522i
$43$	4.61803	−	7.99867i	0.704244	−	1.21979i	−0.262720	−	0.964872i	$-0.584620\pi$
$43$	4.61803	−	7.99867i	0.704244	−	1.21979i	0.966964	−	0.254914i	$-0.0820470\pi$
$44$	1.61803	+	2.80252i	0.243928	+	0.422495i
$45$	5.32624			0.793989
$46$	−5.23607			−0.772016
$47$	−2.23607	−	3.87298i	−0.326164	−	0.564933i	0.655583	−	0.755123i	$-0.272423\pi$
$47$	−2.23607	−	3.87298i	−0.326164	−	0.564933i	−0.981747	+	0.190190i	$0.939090\pi$
$48$	0.618034	+	1.07047i	0.0892055	+	0.154508i
$49$	3.47214			0.496019
$50$	−8.09017			−1.14412
$51$	−2.09017	−	3.62028i	−0.292682	−	0.506941i
$52$	−0.690983	+	1.19682i	−0.0958221	+	0.165969i
$53$	3.04508	+	5.27424i	0.418275	+	0.724473i	0.995766	−	0.0919239i	$-0.0293017\pi$
$53$	3.04508	+	5.27424i	0.418275	+	0.724473i	−0.577491	+	0.816397i	$0.695968\pi$
$54$	2.76393	−	4.78727i	0.376124	−	0.651465i
$55$	−5.85410	+	10.1396i	−0.789367	+	1.36722i
$56$	3.23607			0.432438
$57$		0			0
$58$	9.09017			1.19360
$59$	0.236068	−	0.408882i	0.0307334	−	0.0532319i	−0.850250	−	0.526380i	$-0.823549\pi$
$59$	0.236068	−	0.408882i	0.0307334	−	0.0532319i	0.880983	+	0.473148i	$0.156882\pi$
$60$	−2.23607	+	3.87298i	−0.288675	+	0.500000i
$61$	−0.690983	−	1.19682i	−0.0884713	−	0.153237i	0.818394	−	0.574658i	$-0.194865\pi$
$61$	−0.690983	−	1.19682i	−0.0884713	−	0.153237i	−0.906865	+	0.421421i	$0.861531\pi$
$62$	−0.618034	+	1.07047i	−0.0784904	+	0.135949i
$63$	−2.38197	−	4.12569i	−0.300100	−	0.519788i
$64$	1.00000			0.125000
$65$	−5.00000			−0.620174
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−5.85410	−	10.1396i	−0.715192	−	1.23875i	−0.962885	−	0.269911i	$-0.913006\pi$
$67$	−5.85410	−	10.1396i	−0.715192	−	1.23875i	0.247693	−	0.968839i	$-0.420328\pi$
$68$	−3.38197			−0.410124
$69$	−6.47214			−0.779154
$70$	5.85410	+	10.1396i	0.699699	+	1.21191i
$71$	−1.47214	+	2.54981i	−0.174710	+	0.302607i	−0.940061	−	0.341006i	$-0.889232\pi$
$71$	−1.47214	+	2.54981i	−0.174710	+	0.302607i	0.765351	+	0.643614i	$0.222566\pi$
$72$	−0.736068	−	1.27491i	−0.0867464	−	0.150249i
$73$	2.80902	−	4.86536i	0.328771	−	0.569447i	−0.653498	−	0.756929i	$-0.726699\pi$
$73$	2.80902	−	4.86536i	0.328771	−	0.569447i	0.982268	+	0.187481i	$0.0600324\pi$
$74$	4.19098	−	7.25900i	0.487192	−	0.843841i
$75$	−10.0000			−1.15470
$76$		0			0
$77$	10.4721			1.19341
$78$	−0.854102	+	1.47935i	−0.0967080	+	0.167503i
$79$	1.38197	−	2.39364i	0.155483	−	0.269305i	−0.777752	−	0.628572i	$-0.783640\pi$
$79$	1.38197	−	2.39364i	0.155483	−	0.269305i	0.933235	+	0.359267i	$0.116973\pi$
$80$	1.80902	+	3.13331i	0.202254	+	0.350315i
$81$	1.20820	−	2.09267i	0.134245	−	0.232519i
$82$	0.427051	+	0.739674i	0.0471599	+	0.0816833i
$83$	−0.472136			−0.0518237			−0.0259118	−	0.999664i	$-0.508249\pi$
$83$	−0.472136			−0.0518237			−0.0259118	+	0.999664i	$0.508249\pi$
$84$	4.00000			0.436436
$85$	−6.11803	−	10.5967i	−0.663594	−	1.14938i
$86$	−4.61803	−	7.99867i	−0.497975	−	0.862519i
$87$	11.2361			1.20463
$88$	3.23607			0.344966
$89$	−4.42705	−	7.66788i	−0.469266	−	0.812793i	0.530116	−	0.847925i	$-0.322148\pi$
$89$	−4.42705	−	7.66788i	−0.469266	−	0.812793i	−0.999383	+	0.0351316i	$0.988815\pi$
$90$	2.66312	−	4.61266i	0.280717	−	0.486217i
$91$	2.23607	+	3.87298i	0.234404	+	0.405999i
$92$	−2.61803	+	4.53457i	−0.272949	+	0.472761i
$93$	−0.763932	+	1.32317i	−0.0792161	+	0.137206i
$94$	−4.47214			−0.461266
$95$		0			0
$96$	1.23607			0.126156
$97$	−4.30902	+	7.46344i	−0.437514	+	0.757797i	−0.997497	−	0.0707071i	$-0.977474\pi$
$97$	−4.30902	+	7.46344i	−0.437514	+	0.757797i	0.559983	+	0.828504i	$0.310808\pi$
$98$	1.73607	−	3.00696i	0.175369	−	0.303749i
$99$	−2.38197	−	4.12569i	−0.239397	−	0.414647i
$100$	−4.04508	+	7.00629i	−0.404508	+	0.700629i
$101$	7.80902	+	13.5256i	0.777026	+	1.34585i	0.933649	+	0.358190i	$0.116606\pi$
$101$	7.80902	+	13.5256i	0.777026	+	1.34585i	−0.156622	+	0.987659i	$0.550061\pi$
$102$	−4.18034			−0.413915
$103$	14.6525			1.44375			0.721876	−	0.692023i	$-0.243280\pi$
$103$	14.6525			1.44375			0.721876	+	0.692023i	$0.243280\pi$
$104$	0.690983	+	1.19682i	0.0677565	+	0.117358i
$105$	7.23607	+	12.5332i	0.706168	+	1.22312i
$106$	6.09017			0.591530
$107$	9.41641			0.910319			0.455159	−	0.890410i	$-0.349582\pi$
$107$	9.41641			0.910319			0.455159	+	0.890410i	$0.349582\pi$
$108$	−2.76393	−	4.78727i	−0.265959	−	0.460655i
$109$	5.51722	−	9.55611i	0.528454	−	0.915309i	−0.470996	−	0.882136i	$-0.656105\pi$
$109$	5.51722	−	9.55611i	0.528454	−	0.915309i	0.999450	−	0.0331735i	$-0.0105614\pi$
$110$	5.85410	+	10.1396i	0.558167	+	0.966773i
$111$	5.18034	−	8.97261i	0.491696	−	0.851643i
$112$	1.61803	−	2.80252i	0.152890	−	0.264813i
$113$	−9.85410			−0.926996			−0.463498	−	0.886098i	$-0.653406\pi$
$113$	−9.85410			−0.926996			−0.463498	+	0.886098i	$0.653406\pi$
$114$		0			0
$115$	−18.9443			−1.76656
$116$	4.54508	−	7.87232i	0.422001	−	0.730926i
$117$	1.01722	−	1.76188i	0.0940421	−	0.162886i
$118$	−0.236068	−	0.408882i	−0.0217318	−	0.0376406i
$119$	−5.47214	+	9.47802i	−0.501630	+	0.868848i
$120$	2.23607	+	3.87298i	0.204124	+	0.353553i
$121$	−0.527864			−0.0479876
$122$	−1.38197			−0.125117
$123$	0.527864	+	0.914287i	0.0475959	+	0.0824385i
$124$	0.618034	+	1.07047i	0.0555011	+	0.0961307i
$125$	−11.1803			−1.00000
$126$	−4.76393			−0.424405
$127$	5.70820	+	9.88690i	0.506521	+	0.877320i	0.999972	+	0.00754646i	$0.00240214\pi$
$127$	5.70820	+	9.88690i	0.506521	+	0.877320i	−0.493450	+	0.869774i	$0.664265\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.70820	−	9.88690i	−0.502579	−	0.870493i
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	−2.23607	+	3.87298i	−0.195366	+	0.338384i	−0.947020	−	0.321173i	$-0.895923\pi$
$131$	−2.23607	+	3.87298i	−0.195366	+	0.338384i	0.751654	+	0.659557i	$0.229256\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	−11.7082			−1.01143
$135$	10.0000	−	17.3205i	0.860663	−	1.49071i
$136$	−1.69098	+	2.92887i	−0.145001	+	0.251148i
$137$	−1.19098	−	2.06284i	−0.101753	−	0.176241i	0.810654	−	0.585525i	$-0.199112\pi$
$137$	−1.19098	−	2.06284i	−0.101753	−	0.176241i	−0.912407	+	0.409285i	$0.865778\pi$
$138$	−3.23607	+	5.60503i	−0.275472	+	0.477132i
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	0.993724	+	0.111856i	$0.0356795\pi$
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	−0.399992	+	0.916519i	$0.630987\pi$
$140$	11.7082			0.989524
$141$	−5.52786			−0.465530
$142$	1.47214	+	2.54981i	0.123539	+	0.213976i
$143$	2.23607	+	3.87298i	0.186989	+	0.323875i
$144$	−1.47214			−0.122678
$145$	32.8885			2.73124
$146$	−2.80902	−	4.86536i	−0.232476	−	0.402660i
$147$	2.14590	−	3.71680i	0.176991	−	0.306557i
$148$	−4.19098	−	7.25900i	−0.344497	−	0.596686i
$149$	6.54508	−	11.3364i	0.536194	−	0.928716i	−0.462910	−	0.886405i	$-0.653195\pi$
$149$	6.54508	−	11.3364i	0.536194	−	0.928716i	0.999105	−	0.0423105i	$-0.0134719\pi$
$150$	−5.00000	+	8.66025i	−0.408248	+	0.707107i
$151$	14.4721			1.17773			0.588863	−	0.808233i	$-0.299576\pi$
$151$	14.4721			1.17773			0.588863	+	0.808233i	$0.299576\pi$
$152$		0			0
$153$	4.97871			0.402505
$154$	5.23607	−	9.06914i	0.421934	−	0.730812i
$155$	−2.23607	+	3.87298i	−0.179605	+	0.311086i
$156$	0.854102	+	1.47935i	0.0683829	+	0.118443i
$157$	−4.69098	+	8.12502i	−0.374381	+	0.648447i	−0.990234	−	0.139414i	$-0.955478\pi$
$157$	−4.69098	+	8.12502i	−0.374381	+	0.648447i	0.615853	+	0.787861i	$0.288812\pi$
$158$	−1.38197	−	2.39364i	−0.109943	−	0.190427i
$159$	7.52786			0.596998
$160$	3.61803			0.286031
$161$	8.47214	+	14.6742i	0.667698	+	1.15649i
$162$	−1.20820	−	2.09267i	−0.0949255	−	0.164416i
$163$	10.6525			0.834366			0.417183	−	0.908822i	$-0.363017\pi$
$163$	10.6525			0.834366			0.417183	+	0.908822i	$0.363017\pi$
$164$	0.854102			0.0666942
$165$	7.23607	+	12.5332i	0.563327	+	0.975711i
$166$	−0.236068	+	0.408882i	−0.0183224	+	0.0317354i
$167$	6.23607	+	10.8012i	0.482561	+	0.835821i	0.999800	−	0.0200206i	$-0.00637318\pi$
$167$	6.23607	+	10.8012i	0.482561	+	0.835821i	−0.517238	+	0.855842i	$0.673040\pi$
$168$	2.00000	−	3.46410i	0.154303	−	0.267261i
$169$	5.54508	−	9.60437i	0.426545	−	0.738798i
$170$	−12.2361			−0.938464
$171$		0			0
$172$	−9.23607			−0.704244
$173$	−0.663119	+	1.14856i	−0.0504160	+	0.0873231i	−0.890132	−	0.455703i	$-0.849388\pi$
$173$	−0.663119	+	1.14856i	−0.0504160	+	0.0873231i	0.839716	+	0.543026i	$0.182721\pi$
$174$	5.61803	−	9.73072i	0.425902	−	0.737684i
$175$	13.0902	+	22.6728i	0.989524	+	1.71391i
$176$	1.61803	−	2.80252i	0.121964	−	0.211248i
$177$	−0.291796	−	0.505406i	−0.0219327	−	0.0379886i
$178$	−8.85410			−0.663643
$179$	−23.4164			−1.75022			−0.875112	−	0.483920i	$-0.839213\pi$
$179$	−23.4164			−1.75022			−0.875112	+	0.483920i	$0.839213\pi$
$180$	−2.66312	−	4.61266i	−0.198497	−	0.343807i
$181$	−2.70820	−	4.69075i	−0.201299	−	0.348660i	0.747648	−	0.664095i	$-0.231183\pi$
$181$	−2.70820	−	4.69075i	−0.201299	−	0.348660i	−0.948947	+	0.315435i	$0.897850\pi$
$182$	4.47214			0.331497
$183$	−1.70820			−0.126274
$184$	2.61803	+	4.53457i	0.193004	+	0.334293i
$185$	15.1631	−	26.2633i	1.11481	−	1.93092i
$186$	0.763932	+	1.32317i	0.0560142	+	0.0970195i
$187$	−5.47214	+	9.47802i	−0.400162	+	0.693101i
$188$	−2.23607	+	3.87298i	−0.163082	+	0.282466i
$189$	−17.8885			−1.30120
$190$		0			0
$191$	3.52786			0.255267			0.127634	−	0.991821i	$-0.459262\pi$
$191$	3.52786			0.255267			0.127634	+	0.991821i	$0.459262\pi$
$192$	0.618034	−	1.07047i	0.0446028	−	0.0772542i
$193$	5.76393	−	9.98342i	0.414897	−	0.718623i	−0.580521	−	0.814245i	$-0.697151\pi$
$193$	5.76393	−	9.98342i	0.414897	−	0.718623i	0.995418	+	0.0956230i	$0.0304843\pi$
$194$	4.30902	+	7.46344i	0.309369	+	0.535844i
$195$	−3.09017	+	5.35233i	−0.221292	+	0.383288i
$196$	−1.73607	−	3.00696i	−0.124005	−	0.214783i
$197$	−4.14590			−0.295383			−0.147692	−	0.989033i	$-0.547184\pi$
$197$	−4.14590			−0.295383			−0.147692	+	0.989033i	$0.547184\pi$
$198$	−4.76393			−0.338558
$199$	−5.23607	−	9.06914i	−0.371175	−	0.642894i	0.618572	−	0.785728i	$-0.287712\pi$
$199$	−5.23607	−	9.06914i	−0.371175	−	0.642894i	−0.989747	+	0.142834i	$0.954378\pi$
$200$	4.04508	+	7.00629i	0.286031	+	0.495420i
$201$	−14.4721			−1.02079
$202$	15.6180			1.09888
$203$	−14.7082	−	25.4754i	−1.03231	−	1.78802i
$204$	−2.09017	+	3.62028i	−0.146341	+	0.253470i
$205$	1.54508	+	2.67617i	0.107913	+	0.186912i
$206$	7.32624	−	12.6894i	0.510443	−	0.884114i
$207$	3.85410	−	6.67550i	0.267879	−	0.463979i
$208$	1.38197			0.0958221
$209$		0			0
$210$	14.4721			0.998672
$211$	3.61803	−	6.26662i	0.249076	−	0.431412i	−0.714194	−	0.699948i	$-0.753207\pi$
$211$	3.61803	−	6.26662i	0.249076	−	0.431412i	0.963270	+	0.268536i	$0.0865399\pi$
$212$	3.04508	−	5.27424i	0.209137	−	0.362236i
$213$	1.81966	+	3.15174i	0.124681	+	0.215954i
$214$	4.70820	−	8.15485i	0.321846	−	0.557454i
$215$	−16.7082	−	28.9395i	−1.13949	−	1.97365i
$216$	−5.52786			−0.376124
$217$	4.00000			0.271538
$218$	−5.51722	−	9.55611i	−0.373673	−	0.647221i
$219$	−3.47214	−	6.01392i	−0.234625	−	0.406383i
$220$	11.7082			0.789367
$221$	−4.67376			−0.314391
$222$	−5.18034	−	8.97261i	−0.347682	−	0.602202i
$223$	−13.8541	+	23.9960i	−0.927739	+	1.60689i	−0.140644	+	0.990060i	$0.544917\pi$
$223$	−13.8541	+	23.9960i	−0.927739	+	1.60689i	−0.787095	+	0.616831i	$0.788416\pi$
$224$	−1.61803	−	2.80252i	−0.108109	−	0.187251i
$225$	5.95492	−	10.3142i	0.396994	−	0.687614i
$226$	−4.92705	+	8.53390i	−0.327743	+	0.567667i
$227$	−8.94427			−0.593652			−0.296826	−	0.954932i	$-0.595928\pi$
$227$	−8.94427			−0.593652			−0.296826	+	0.954932i	$0.595928\pi$
$228$		0			0
$229$	4.38197			0.289568			0.144784	−	0.989463i	$-0.453751\pi$
$229$	4.38197			0.289568			0.144784	+	0.989463i	$0.453751\pi$
$230$	−9.47214	+	16.4062i	−0.624574	+	1.08179i
$231$	6.47214	−	11.2101i	0.425835	−	0.737568i
$232$	−4.54508	−	7.87232i	−0.298399	−	0.516843i
$233$	−0.781153	+	1.35300i	−0.0511750	+	0.0886378i	−0.890478	−	0.455026i	$-0.849630\pi$
$233$	−0.781153	+	1.35300i	−0.0511750	+	0.0886378i	0.839303	+	0.543664i	$0.182963\pi$
$234$	−1.01722	−	1.76188i	−0.0664978	−	0.115178i
$235$	−16.1803			−1.05549
$236$	−0.472136			−0.0307334
$237$	−1.70820	−	2.95870i	−0.110960	−	0.192188i
$238$	5.47214	+	9.47802i	0.354706	+	0.614369i
$239$	30.1803			1.95220			0.976102	−	0.217313i	$-0.0697293\pi$
$239$	30.1803			1.95220			0.976102	+	0.217313i	$0.0697293\pi$
$240$	4.47214			0.288675
$241$	12.7082	+	22.0113i	0.818607	+	1.41787i	0.906708	+	0.421758i	$0.138587\pi$
$241$	12.7082	+	22.0113i	0.818607	+	1.41787i	−0.0881010	+	0.996112i	$0.528080\pi$
$242$	−0.263932	+	0.457144i	−0.0169662	+	0.0293863i
$243$	6.79837	+	11.7751i	0.436116	+	0.755375i
$244$	−0.690983	+	1.19682i	−0.0442357	+	0.0766184i
$245$	6.28115	−	10.8793i	0.401288	−	0.695051i
$246$	1.05573			0.0673108
$247$		0			0
$248$	1.23607			0.0784904
$249$	−0.291796	+	0.505406i	−0.0184918	+	0.0320288i
$250$	−5.59017	+	9.68246i	−0.353553	+	0.612372i
$251$	1.14590	+	1.98475i	0.0723284	+	0.125277i	0.899921	−	0.436052i	$-0.143624\pi$
$251$	1.14590	+	1.98475i	0.0723284	+	0.125277i	−0.827593	+	0.561329i	$0.810290\pi$
$252$	−2.38197	+	4.12569i	−0.150050	+	0.259894i
$253$	8.47214	+	14.6742i	0.532639	+	0.922557i
$254$	11.4164			0.716329
$255$	−15.1246			−0.947140
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.19098	−	15.9192i	−0.573318	−	0.993016i	−0.996222	−	0.0868412i	$-0.972323\pi$
$257$	−9.19098	−	15.9192i	−0.573318	−	0.993016i	0.422904	−	0.906174i	$-0.361011\pi$
$258$	−11.4164			−0.710755
$259$	−27.1246			−1.68544
$260$	2.50000	+	4.33013i	0.155043	+	0.268543i
$261$	−6.69098	+	11.5891i	−0.414161	+	0.717349i
$262$	2.23607	+	3.87298i	0.138145	+	0.239274i
$263$	−1.47214	+	2.54981i	−0.0907758	+	0.157228i	−0.907838	−	0.419322i	$-0.862268\pi$
$263$	−1.47214	+	2.54981i	−0.0907758	+	0.157228i	0.817062	+	0.576550i	$0.195601\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	22.0344			1.35357
$266$		0			0
$267$	−10.9443			−0.669779
$268$	−5.85410	+	10.1396i	−0.357596	+	0.619375i
$269$	−7.16312	+	12.4069i	−0.436743	+	0.756461i	−0.997436	−	0.0715625i	$-0.977201\pi$
$269$	−7.16312	+	12.4069i	−0.436743	+	0.756461i	0.560693	+	0.828024i	$0.310535\pi$
$270$	−10.0000	−	17.3205i	−0.608581	−	1.05409i
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	0.136461	+	0.990645i	$0.456427\pi$
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	−0.926155	+	0.377144i	$0.876906\pi$
$272$	1.69098	+	2.92887i	0.102531	+	0.177589i
$273$	5.52786			0.334562
$274$	−2.38197			−0.143900
$275$	13.0902	+	22.6728i	0.789367	+	1.36722i
$276$	3.23607	+	5.60503i	0.194788	+	0.337383i
$277$	−10.0902			−0.606260			−0.303130	−	0.952949i	$-0.598032\pi$
$277$	−10.0902			−0.606260			−0.303130	+	0.952949i	$0.598032\pi$
$278$	14.0000			0.839664
$279$	−0.909830	−	1.57587i	−0.0544701	−	0.0943450i
$280$	5.85410	−	10.1396i	0.349850	−	0.605957i
$281$	−10.4894	−	18.1681i	−0.625743	−	1.08382i	−0.988397	−	0.151894i	$-0.951463\pi$
$281$	−10.4894	−	18.1681i	−0.625743	−	1.08382i	0.362654	−	0.931924i	$-0.381871\pi$
$282$	−2.76393	+	4.78727i	−0.164590	+	0.285078i
$283$	−11.2361	+	19.4614i	−0.667915	+	1.15686i	0.310571	+	0.950550i	$0.399480\pi$
$283$	−11.2361	+	19.4614i	−0.667915	+	1.15686i	−0.978486	+	0.206312i	$0.933854\pi$
$284$	2.94427			0.174710
$285$		0			0
$286$	4.47214			0.264443
$287$	1.38197	−	2.39364i	0.0815749	−	0.141292i
$288$	−0.736068	+	1.27491i	−0.0433732	+	0.0751246i
$289$	2.78115	+	4.81710i	0.163597	+	0.283359i
$290$	16.4443	−	28.4823i	0.965641	−	1.67254i
$291$	5.32624	+	9.22531i	0.312230	+	0.540798i
$292$	−5.61803			−0.328771
$293$	22.9443			1.34042			0.670209	−	0.742172i	$-0.266204\pi$
$293$	22.9443			1.34042			0.670209	+	0.742172i	$0.266204\pi$
$294$	−2.14590	−	3.71680i	−0.125151	−	0.216768i
$295$	−0.854102	−	1.47935i	−0.0497277	−	0.0861310i
$296$	−8.38197			−0.487192
$297$	−17.8885			−1.03800
$298$	−6.54508	−	11.3364i	−0.379147	−	0.656701i
$299$	−3.61803	+	6.26662i	−0.209236	+	0.362408i
$300$	5.00000	+	8.66025i	0.288675	+	0.500000i
$301$	−14.9443	+	25.8842i	−0.861374	+	1.49194i
$302$	7.23607	−	12.5332i	0.416389	−	0.721207i
$303$	19.3050			1.10904
$304$		0			0
$305$	−5.00000			−0.286299
$306$	2.48936	−	4.31169i	0.142307	−	0.246483i
$307$	−5.85410	+	10.1396i	−0.334111	+	0.578698i	−0.983314	−	0.181918i	$-0.941769\pi$
$307$	−5.85410	+	10.1396i	−0.334111	+	0.578698i	0.649202	+	0.760616i	$0.275103\pi$
$308$	−5.23607	−	9.06914i	−0.298353	−	0.516762i
$309$	9.05573	−	15.6850i	0.515162	−	0.892287i
$310$	2.23607	+	3.87298i	0.127000	+	0.219971i
$311$	31.2361			1.77123			0.885617	−	0.464415i	$-0.153736\pi$
$311$	31.2361			1.77123			0.885617	+	0.464415i	$0.153736\pi$
$312$	1.70820			0.0967080
$313$	7.75329	+	13.4291i	0.438242	+	0.759057i	0.997554	−	0.0699000i	$-0.0222680\pi$
$313$	7.75329	+	13.4291i	0.438242	+	0.759057i	−0.559312	+	0.828957i	$0.688935\pi$
$314$	4.69098	+	8.12502i	0.264727	+	0.458521i
$315$	−17.2361			−0.971142
$316$	−2.76393			−0.155483
$317$	−0.663119	−	1.14856i	−0.0372445	−	0.0645093i	0.846802	−	0.531908i	$-0.178525\pi$
$317$	−0.663119	−	1.14856i	−0.0372445	−	0.0645093i	−0.884047	+	0.467398i	$0.845191\pi$
$318$	3.76393	−	6.51932i	0.211071	−	0.365585i
$319$	−14.7082	−	25.4754i	−0.823501	−	1.42635i
$320$	1.80902	−	3.13331i	0.101127	−	0.175157i
$321$	5.81966	−	10.0799i	0.324822	−	0.562608i
$322$	16.9443			0.944267
$323$		0			0
$324$	−2.41641			−0.134245
$325$	−5.59017	+	9.68246i	−0.310087	+	0.537086i
$326$	5.32624	−	9.22531i	0.294993	−	0.510943i
$327$	−6.81966	−	11.8120i	−0.377128	−	0.653205i
$328$	0.427051	−	0.739674i	0.0235799	−	0.0408417i
$329$	7.23607	+	12.5332i	0.398937	+	0.690980i
$330$	14.4721			0.796665
$331$	25.7082			1.41305			0.706525	−	0.707688i	$-0.250262\pi$
$331$	25.7082			1.41305			0.706525	+	0.707688i	$0.250262\pi$
$332$	0.236068	+	0.408882i	0.0129559	+	0.0224403i
$333$	6.16970	+	10.6862i	0.338097	+	0.585602i
$334$	12.4721			0.682445
$335$	−42.3607			−2.31441
$336$	−2.00000	−	3.46410i	−0.109109	−	0.188982i
$337$	−1.19098	+	2.06284i	−0.0648770	+	0.112370i	−0.896639	−	0.442762i	$-0.853999\pi$
$337$	−1.19098	+	2.06284i	−0.0648770	+	0.112370i	0.831762	+	0.555132i	$0.187332\pi$
$338$	−5.54508	−	9.60437i	−0.301613	−	0.522409i
$339$	−6.09017	+	10.5485i	−0.330773	+	0.572915i
$340$	−6.11803	+	10.5967i	−0.331797	+	0.574689i
$341$	4.00000			0.216612
$342$		0			0
$343$	11.4164			0.616428
$344$	−4.61803	+	7.99867i	−0.248988	+	0.431259i
$345$	−11.7082	+	20.2792i	−0.630349	+	1.09180i
$346$	0.663119	+	1.14856i	0.0356495	+	0.0617467i
$347$	1.32624	−	2.29711i	0.0711962	−	0.123315i	−0.828230	−	0.560389i	$-0.810652\pi$
$347$	1.32624	−	2.29711i	0.0711962	−	0.123315i	0.899426	+	0.437073i	$0.143985\pi$
$348$	−5.61803	−	9.73072i	−0.301158	−	0.521621i
$349$	−33.0902			−1.77128			−0.885638	−	0.464376i	$-0.846279\pi$
$349$	−33.0902			−1.77128			−0.885638	+	0.464376i	$0.846279\pi$
$350$	26.1803			1.39940
$351$	−3.81966	−	6.61585i	−0.203878	−	0.353128i
$352$	−1.61803	−	2.80252i	−0.0862415	−	0.149375i
$353$	−23.7426			−1.26369			−0.631847	−	0.775093i	$-0.717703\pi$
$353$	−23.7426			−1.26369			−0.631847	+	0.775093i	$0.717703\pi$
$354$	−0.583592			−0.0310176
$355$	5.32624	+	9.22531i	0.282687	+	0.489629i
$356$	−4.42705	+	7.66788i	−0.234633	+	0.406397i
$357$	6.76393	+	11.7155i	0.357985	+	0.620049i
$358$	−11.7082	+	20.2792i	−0.618798	+	1.07179i
$359$	−5.76393	+	9.98342i	−0.304209	+	0.526905i	−0.977085	−	0.212850i	$-0.931725\pi$
$359$	−5.76393	+	9.98342i	−0.304209	+	0.526905i	0.672876	+	0.739755i	$0.265059\pi$
$360$	−5.32624			−0.280717
$361$		0			0
$362$	−5.41641			−0.284680
$363$	−0.326238	+	0.565061i	−0.0171231	+	0.0296580i
$364$	2.23607	−	3.87298i	0.117202	−	0.202999i
$365$	−10.1631	−	17.6030i	−0.531962	−	0.921385i
$366$	−0.854102	+	1.47935i	−0.0446446	+	0.0773268i
$367$	−9.41641	−	16.3097i	−0.491532	−	0.851359i	0.508420	−	0.861109i	$-0.330230\pi$
$367$	−9.41641	−	16.3097i	−0.491532	−	0.851359i	−0.999952	+	0.00975000i	$0.996896\pi$
$368$	5.23607			0.272949
$369$	−1.25735			−0.0654552
$370$	−15.1631	−	26.2633i	−0.788293	−	1.36536i
$371$	−9.85410	−	17.0678i	−0.511599	−	0.886116i
$372$	1.52786			0.0792161
$373$	18.3262			0.948897			0.474448	−	0.880283i	$-0.342648\pi$
$373$	18.3262			0.948897			0.474448	+	0.880283i	$0.342648\pi$
$374$	5.47214	+	9.47802i	0.282957	+	0.490097i
$375$	−6.90983	+	11.9682i	−0.356822	+	0.618034i
$376$	2.23607	+	3.87298i	0.115316	+	0.199734i
$377$	6.28115	−	10.8793i	0.323496	−	0.560311i
$378$	−8.94427	+	15.4919i	−0.460044	+	0.796819i
$379$	−35.4164			−1.81922			−0.909609	−	0.415465i	$-0.863619\pi$
$379$	−35.4164			−1.81922			−0.909609	+	0.415465i	$0.863619\pi$
$380$		0			0
$381$	14.1115			0.722952
$382$	1.76393	−	3.05522i	0.0902506	−	0.156319i
$383$	−10.3820	+	17.9821i	−0.530494	+	0.918842i	0.468873	+	0.883265i	$0.344660\pi$
$383$	−10.3820	+	17.9821i	−0.530494	+	0.918842i	−0.999367	+	0.0355766i	$0.988673\pi$
$384$	−0.618034	−	1.07047i	−0.0315389	−	0.0546270i
$385$	18.9443	−	32.8124i	0.965489	−	1.67228i
$386$	−5.76393	−	9.98342i	−0.293376	−	0.508143i
$387$	13.5967			0.691162
$388$	8.61803			0.437514
$389$	−6.39919	−	11.0837i	−0.324452	−	0.561967i	0.656950	−	0.753935i	$-0.271846\pi$
$389$	−6.39919	−	11.0837i	−0.324452	−	0.561967i	−0.981401	+	0.191968i	$0.938513\pi$
$390$	3.09017	+	5.35233i	0.156477	+	0.271026i
$391$	−17.7082			−0.895542
$392$	−3.47214			−0.175369
$393$	2.76393	+	4.78727i	0.139422	+	0.241486i
$394$	−2.07295	+	3.59045i	−0.104434	+	0.180884i
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$	−2.38197	+	4.12569i	−0.119698	+	0.207324i
$397$	11.1803	−	19.3649i	0.561125	−	0.971897i	−0.436273	−	0.899814i	$-0.643702\pi$
$397$	11.1803	−	19.3649i	0.561125	−	0.971897i	0.997399	−	0.0720832i	$-0.0229647\pi$
$398$	−10.4721			−0.524921
$399$		0			0
$400$	8.09017			0.404508
$401$	−9.47214	+	16.4062i	−0.473016	+	0.819288i	−0.999523	−	0.0308832i	$-0.990168\pi$
$401$	−9.47214	+	16.4062i	−0.473016	+	0.819288i	0.526507	+	0.850171i	$0.323501\pi$
$402$	−7.23607	+	12.5332i	−0.360902	+	0.625101i
$403$	0.854102	+	1.47935i	0.0425458	+	0.0736916i
$404$	7.80902	−	13.5256i	0.388513	−	0.672924i
$405$	−4.37132	−	7.57135i	−0.217213	−	0.376224i
$406$	−29.4164			−1.45991
$407$	−27.1246			−1.34452
$408$	2.09017	+	3.62028i	0.103479	+	0.179231i
$409$	−8.13525	−	14.0907i	−0.402262	−	0.696739i	0.591736	−	0.806132i	$-0.298443\pi$
$409$	−8.13525	−	14.0907i	−0.402262	−	0.696739i	−0.993999	+	0.109393i	$0.965109\pi$
$410$	3.09017			0.152613
$411$	−2.94427			−0.145230
$412$	−7.32624	−	12.6894i	−0.360938	−	0.625163i
$413$	−0.763932	+	1.32317i	−0.0375906	+	0.0651089i
$414$	−3.85410	−	6.67550i	−0.189419	−	0.328083i
$415$	−0.854102	+	1.47935i	−0.0419262	+	0.0726183i
$416$	0.690983	−	1.19682i	0.0338782	−	0.0586788i
$417$	17.3050			0.847427
$418$		0			0
$419$	−6.47214			−0.316185			−0.158092	−	0.987424i	$-0.550534\pi$
$419$	−6.47214			−0.316185			−0.158092	+	0.987424i	$0.550534\pi$
$420$	7.23607	−	12.5332i	0.353084	−	0.611559i
$421$	−6.95492	+	12.0463i	−0.338962	+	0.587099i	−0.984238	−	0.176851i	$-0.943409\pi$
$421$	−6.95492	+	12.0463i	−0.338962	+	0.587099i	0.645276	+	0.763950i	$0.276742\pi$
$422$	−3.61803	−	6.26662i	−0.176123	−	0.305054i
$423$	3.29180	−	5.70156i	0.160053	−	0.277219i
$424$	−3.04508	−	5.27424i	−0.147882	−	0.256140i
$425$	−27.3607			−1.32719
$426$	3.63932			0.176326
$427$	2.23607	+	3.87298i	0.108211	+	0.187427i
$428$	−4.70820	−	8.15485i	−0.227580	−	0.394179i
$429$	5.52786			0.266888
$430$	−33.4164			−1.61148
$431$	−3.32624	−	5.76121i	−0.160219	−	0.277508i	0.774728	−	0.632295i	$-0.217887\pi$
$431$	−3.32624	−	5.76121i	−0.160219	−	0.277508i	−0.934947	+	0.354787i	$0.884553\pi$
$432$	−2.76393	+	4.78727i	−0.132980	+	0.230328i
$433$	12.5172	+	21.6805i	0.601539	+	1.04190i	0.992588	+	0.121527i	$0.0387790\pi$
$433$	12.5172	+	21.6805i	0.601539	+	1.04190i	−0.391049	+	0.920370i	$0.627888\pi$
$434$	2.00000	−	3.46410i	0.0960031	−	0.166282i
$435$	20.3262	−	35.2061i	0.974569	−	1.68800i
$436$	−11.0344			−0.528454
$437$		0			0
$438$	−6.94427			−0.331810
$439$	−14.6180	+	25.3192i	−0.697681	+	1.20842i	0.271588	+	0.962414i	$0.412451\pi$
$439$	−14.6180	+	25.3192i	−0.697681	+	1.20842i	−0.969269	+	0.246005i	$0.920882\pi$
$440$	5.85410	−	10.1396i	0.279083	−	0.483387i
$441$	2.55573	+	4.42665i	0.121701	+	0.210793i
$442$	−2.33688	+	4.04760i	−0.111154	+	0.192525i
$443$	−4.61803	−	7.99867i	−0.219409	−	0.380028i	0.735218	−	0.677831i	$-0.237080\pi$
$443$	−4.61803	−	7.99867i	−0.219409	−	0.380028i	−0.954628	+	0.297802i	$0.903746\pi$
$444$	−10.3607			−0.491696
$445$	−32.0344			−1.51858
$446$	13.8541	+	23.9960i	0.656011	+	1.13624i
$447$	−8.09017	−	14.0126i	−0.382652	−	0.662773i
$448$	−3.23607			−0.152890
$449$	−22.7984			−1.07592			−0.537961	−	0.842970i	$-0.680805\pi$
$449$	−22.7984			−1.07592			−0.537961	+	0.842970i	$0.680805\pi$
$450$	−5.95492	−	10.3142i	−0.280717	−	0.486217i
$451$	1.38197	−	2.39364i	0.0650742	−	0.112712i
$452$	4.92705	+	8.53390i	0.231749	+	0.401401i
$453$	8.94427	−	15.4919i	0.420239	−	0.727875i
$454$	−4.47214	+	7.74597i	−0.209888	+	0.363536i
$455$	16.1803			0.758546
$456$		0			0
$457$	25.2148			1.17950			0.589749	−	0.807587i	$-0.299227\pi$
$457$	25.2148			1.17950			0.589749	+	0.807587i	$0.299227\pi$
$458$	2.19098	−	3.79489i	0.102378	−	0.177324i
$459$	9.34752	−	16.1904i	0.436305	−	0.755703i
$460$	9.47214	+	16.4062i	0.441641	+	0.764944i
$461$	−10.7082	+	18.5472i	−0.498731	+	0.863827i	−0.999999	−	0.00146495i	$-0.999534\pi$
$461$	−10.7082	+	18.5472i	−0.498731	+	0.863827i	0.501268	+	0.865292i	$0.332867\pi$
$462$	−6.47214	−	11.2101i	−0.301111	−	0.521540i
$463$	−5.05573			−0.234960			−0.117480	−	0.993075i	$-0.537482\pi$
$463$	−5.05573			−0.234960			−0.117480	+	0.993075i	$0.537482\pi$
$464$	−9.09017			−0.422001
$465$	2.76393	+	4.78727i	0.128174	+	0.222004i
$466$	0.781153	+	1.35300i	0.0361862	+	0.0626764i
$467$	−33.3050			−1.54117			−0.770585	−	0.637338i	$-0.780036\pi$
$467$	−33.3050			−1.54117			−0.770585	+	0.637338i	$0.780036\pi$
$468$	−2.03444			−0.0940421
$469$	18.9443	+	32.8124i	0.874765	+	1.51514i
$470$	−8.09017	+	14.0126i	−0.373172	+	0.646352i
$471$	5.79837	+	10.0431i	0.267175	+	0.462761i
$472$	−0.236068	+	0.408882i	−0.0108659	+	0.0188203i
$473$	−14.9443	+	25.8842i	−0.687138	+	1.19016i
$474$	−3.41641			−0.156921
$475$		0			0
$476$	10.9443			0.501630
$477$	−4.48278	+	7.76440i	−0.205252	+	0.355508i
$478$	15.0902	−	26.1369i	0.690208	−	1.19548i
$479$	−3.85410	−	6.67550i	−0.176098	−	0.305011i	0.764442	−	0.644692i	$-0.223014\pi$
$479$	−3.85410	−	6.67550i	−0.176098	−	0.305011i	−0.940541	+	0.339681i	$0.889681\pi$
$480$	2.23607	−	3.87298i	0.102062	−	0.176777i
$481$	−5.79180	−	10.0317i	−0.264083	−	0.457405i
$482$	25.4164			1.15769
$483$	20.9443			0.952997
$484$	0.263932	+	0.457144i	0.0119969	+	0.0207793i
$485$	15.5902	+	27.0030i	0.707913	+	1.22614i
$486$	13.5967			0.616761
$487$	19.2361			0.871669			0.435835	−	0.900027i	$-0.356453\pi$
$487$	19.2361			0.871669			0.435835	+	0.900027i	$0.356453\pi$
$488$	0.690983	+	1.19682i	0.0312793	+	0.0541774i
$489$	6.58359	−	11.4031i	0.297720	−	0.515667i
$490$	−6.28115	−	10.8793i	−0.283754	−	0.491476i
$491$	0.763932	−	1.32317i	0.0344758	−	0.0597138i	−0.848273	−	0.529560i	$-0.822357\pi$
$491$	0.763932	−	1.32317i	0.0344758	−	0.0597138i	0.882748	+	0.469846i	$0.155691\pi$
$492$	0.527864	−	0.914287i	0.0237979	−	0.0412193i
$493$	30.7426			1.38458
$494$		0			0
$495$	−17.2361			−0.774704
$496$	0.618034	−	1.07047i	0.0277505	−	0.0480654i
$497$	4.76393	−	8.25137i	0.213692	−	0.370125i
$498$	0.291796	+	0.505406i	0.0130757	+	0.0226478i
$499$	17.6525	−	30.5750i	0.790233	−	1.36872i	−0.135589	−	0.990765i	$-0.543293\pi$
$499$	17.6525	−	30.5750i	0.790233	−	1.36872i	0.925822	−	0.377959i	$-0.123374\pi$
$500$	5.59017	+	9.68246i	0.250000	+	0.433013i
$501$	15.4164			0.688754
$502$	2.29180			0.102288
$503$	−3.38197	−	5.85774i	−0.150794	−	0.261184i	0.780725	−	0.624874i	$-0.214850\pi$
$503$	−3.38197	−	5.85774i	−0.150794	−	0.261184i	−0.931520	+	0.363691i	$0.881516\pi$
$504$	2.38197	+	4.12569i	0.106101	+	0.183773i
$505$	56.5066			2.51451
$506$	16.9443			0.753265
$507$	−6.85410	−	11.8717i	−0.304401	−	0.527239i
$508$	5.70820	−	9.88690i	0.253261	−	0.438660i
$509$	−21.3435	−	36.9680i	−0.946032	−	1.63858i	−0.753671	−	0.657252i	$-0.771719\pi$
$509$	−21.3435	−	36.9680i	−0.946032	−	1.63858i	−0.192361	−	0.981324i	$-0.561614\pi$
$510$	−7.56231	+	13.0983i	−0.334865	+	0.580002i
$511$	−9.09017	+	15.7446i	−0.402125	+	0.696502i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−18.3820			−0.810794
$515$	26.5066	−	45.9107i	1.16802	−	2.02307i
$516$	−5.70820	+	9.88690i	−0.251290	+	0.435246i
$517$	7.23607	+	12.5332i	0.318242	+	0.551211i
$518$	−13.5623	+	23.4906i	−0.595894	+	1.03212i
$519$	0.819660	+	1.41969i	0.0359791	+	0.0623176i
$520$	5.00000			0.219265
$521$	−5.27051			−0.230905			−0.115453	−	0.993313i	$-0.536832\pi$
$521$	−5.27051			−0.230905			−0.115453	+	0.993313i	$0.536832\pi$
$522$	6.69098	+	11.5891i	0.292856	+	0.507242i
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	4.47214			0.195366
$525$	32.3607			1.41234
$526$	1.47214	+	2.54981i	0.0641882	+	0.111177i
$527$	−2.09017	+	3.62028i	−0.0910492	+	0.157702i
$528$	−2.00000	−	3.46410i	−0.0870388	−	0.150756i
$529$	−2.20820	+	3.82472i	−0.0960089	+	0.166292i
$530$	11.0172	−	19.0824i	0.478557	−	0.828886i
$531$	0.695048			0.0301625
$532$		0			0
$533$	1.18034			0.0511262
$534$	−5.47214	+	9.47802i	−0.236802	+	0.410154i
$535$	17.0344	−	29.5045i	0.736463	−	1.27559i
$536$	5.85410	+	10.1396i	0.252859	+	0.437964i
$537$	−14.4721	+	25.0665i	−0.624519	+	1.08170i
$538$	7.16312	+	12.4069i	0.308824	+	0.534899i
$539$	−11.2361			−0.483972
$540$	−20.0000			−0.860663
$541$	13.3090	+	23.0519i	0.572199	+	0.991078i	0.996340	+	0.0854819i	$0.0272430\pi$
$541$	13.3090	+	23.0519i	0.572199	+	0.991078i	−0.424140	+	0.905596i	$0.639424\pi$
$542$	13.0000	+	22.5167i	0.558398	+	0.967173i
$543$	−6.69505			−0.287312
$544$	3.38197			0.145001
$545$	−19.9615	−	34.5743i	−0.855056	−	1.48100i
$546$	2.76393	−	4.78727i	0.118285	−	0.204876i
$547$	−2.52786	−	4.37839i	−0.108084	−	0.187206i	0.806910	−	0.590674i	$-0.201138\pi$
$547$	−2.52786	−	4.37839i	−0.108084	−	0.187206i	−0.914994	+	0.403468i	$0.867805\pi$
$548$	−1.19098	+	2.06284i	−0.0508763	+	0.0881203i
$549$	1.01722	−	1.76188i	0.0434139	−	0.0751951i
$550$	26.1803			1.11633
$551$		0			0
$552$	6.47214			0.275472
$553$	−4.47214	+	7.74597i	−0.190175	+	0.329392i
$554$	−5.04508	+	8.73834i	−0.214345	+	0.371257i
$555$	−18.7426	−	32.4632i	−0.795581	−	1.37799i
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−2.52786	−	4.37839i	−0.107109	−	0.185518i	0.807489	−	0.589883i	$-0.200826\pi$
$557$	−2.52786	−	4.37839i	−0.107109	−	0.185518i	−0.914598	+	0.404364i	$0.867493\pi$
$558$	−1.81966			−0.0770324
$559$	−12.7639			−0.539857
$560$	−5.85410	−	10.1396i	−0.247381	−	0.428476i
$561$	6.76393	+	11.7155i	0.285573	+	0.494628i
$562$	−20.9787			−0.884934
$563$	26.2918			1.10807			0.554034	−	0.832494i	$-0.313088\pi$
$563$	26.2918			1.10807			0.554034	+	0.832494i	$0.313088\pi$
$564$	2.76393	+	4.78727i	0.116383	+	0.201580i
$565$	−17.8262	+	30.8759i	−0.749955	+	1.29896i
$566$	11.2361	+	19.4614i	0.472287	+	0.818025i
$567$	−3.90983	+	6.77202i	−0.164197	+	0.284398i
$568$	1.47214	−	2.54981i	0.0617695	−	0.106988i
$569$	7.90983			0.331597			0.165799	−	0.986160i	$-0.446980\pi$
$569$	7.90983			0.331597			0.165799	+	0.986160i	$0.446980\pi$
$570$		0			0
$571$	−32.5410			−1.36180			−0.680900	−	0.732377i	$-0.738411\pi$
$571$	−32.5410			−1.36180			−0.680900	+	0.732377i	$0.738411\pi$
$572$	2.23607	−	3.87298i	0.0934947	−	0.161938i
$573$	2.18034	−	3.77646i	0.0910850	−	0.157764i
$574$	−1.38197	−	2.39364i	−0.0576821	−	0.0999084i
$575$	−21.1803	+	36.6854i	−0.883281	+	1.52989i
$576$	0.736068	+	1.27491i	0.0306695	+	0.0531211i
$577$	45.9230			1.91180			0.955899	−	0.293694i	$-0.0948847\pi$
$577$	45.9230			1.91180			0.955899	+	0.293694i	$0.0948847\pi$
$578$	5.56231			0.231361
$579$	−7.12461	−	12.3402i	−0.296089	−	0.512841i
$580$	−16.4443	−	28.4823i	−0.682811	−	1.18266i
$581$	1.52786			0.0633865
$582$	10.6525			0.441559
$583$	−9.85410	−	17.0678i	−0.408115	−	0.706876i
$584$	−2.80902	+	4.86536i	−0.116238	+	0.201330i
$585$	−3.68034	−	6.37454i	−0.152163	−	0.263555i
$586$	11.4721	−	19.8703i	0.473910	−	0.820835i
$587$	−1.43769	+	2.49016i	−0.0593400	+	0.102780i	−0.894169	−	0.447729i	$-0.852233\pi$
$587$	−1.43769	+	2.49016i	−0.0593400	+	0.102780i	0.834829	+	0.550509i	$0.185566\pi$
$588$	−4.29180			−0.176991
$589$		0			0
$590$	−1.70820			−0.0703256
$591$	−2.56231	+	4.43804i	−0.105399	+	0.182557i
$592$	−4.19098	+	7.25900i	−0.172248	+	0.298343i
$593$	17.4615	+	30.2442i	0.717058	+	1.24198i	0.962161	+	0.272483i	$0.0878449\pi$
$593$	17.4615	+	30.2442i	0.717058	+	1.24198i	−0.245103	+	0.969497i	$0.578822\pi$
$594$	−8.94427	+	15.4919i	−0.366988	+	0.635642i
$595$	19.7984	+	34.2918i	0.811654	+	1.40583i
$596$	−13.0902			−0.536194
$597$	−12.9443			−0.529774
$598$	3.61803	+	6.26662i	0.147952	+	0.256261i
$599$	19.5623	+	33.8829i	0.799294	+	1.38442i	0.920076	+	0.391739i	$0.128126\pi$
$599$	19.5623	+	33.8829i	0.799294	+	1.38442i	−0.120782	+	0.992679i	$0.538540\pi$
$600$	10.0000			0.408248
$601$	16.4721			0.671912			0.335956	−	0.941878i	$-0.390941\pi$
$601$	16.4721			0.671912			0.335956	+	0.941878i	$0.390941\pi$
$602$	14.9443	+	25.8842i	0.609083	+	1.05496i
$603$	8.61803	−	14.9269i	0.350953	−	0.607869i
$604$	−7.23607	−	12.5332i	−0.294431	−	0.509970i
$605$	−0.954915	+	1.65396i	−0.0388228	+	0.0672431i
$606$	9.65248	−	16.7186i	0.392105	−	0.679146i
$607$	−47.7771			−1.93921			−0.969606	−	0.244671i	$-0.921320\pi$
$607$	−47.7771			−1.93921			−0.969606	+	0.244671i	$0.921320\pi$
$608$		0			0
$609$	−36.3607			−1.47341
$610$	−2.50000	+	4.33013i	−0.101222	+	0.175322i
$611$	−3.09017	+	5.35233i	−0.125015	+	0.216532i
$612$	−2.48936	−	4.31169i	−0.100626	−	0.174290i
$613$	−4.19098	+	7.25900i	−0.169272	+	0.293188i	−0.938164	−	0.346191i	$-0.887475\pi$
$613$	−4.19098	+	7.25900i	−0.169272	+	0.293188i	0.768892	+	0.639379i	$0.220808\pi$
$614$	5.85410	+	10.1396i	0.236252	+	0.409201i
$615$	3.81966			0.154024
$616$	−10.4721			−0.421934
$617$	−21.4721	−	37.1908i	−0.864436	−	1.49725i	−0.867606	−	0.497251i	$-0.834343\pi$
$617$	−21.4721	−	37.1908i	−0.864436	−	1.49725i	0.00317081	−	0.999995i	$-0.498991\pi$
$618$	−9.05573	−	15.6850i	−0.364275	−	0.630942i
$619$	22.3607			0.898752			0.449376	−	0.893343i	$-0.351646\pi$
$619$	22.3607			0.898752			0.449376	+	0.893343i	$0.351646\pi$
$620$	4.47214			0.179605
$621$	−14.4721	−	25.0665i	−0.580747	−	1.00588i
$622$	15.6180	−	27.0512i	0.626226	−	1.08466i
$623$	14.3262	+	24.8138i	0.573969	+	0.994143i
$624$	0.854102	−	1.47935i	0.0341914	−	0.0592213i
$625$		0			0
$626$	15.5066			0.619767
$627$		0			0
$628$	9.38197			0.374381
$629$	14.1738	−	24.5497i	0.565145	−	0.978860i
$630$	−8.61803	+	14.9269i	−0.343351	+	0.594701i
$631$	15.5623	+	26.9547i	0.619526	+	1.07305i	0.989572	+	0.144037i	$0.0460083\pi$
$631$	15.5623	+	26.9547i	0.619526	+	1.07305i	−0.370047	+	0.929013i	$0.620658\pi$
$632$	−1.38197	+	2.39364i	−0.0549717	+	0.0952137i
$633$	−4.47214	−	7.74597i	−0.177751	−	0.307875i
$634$	−1.32624			−0.0526716
$635$	41.3050			1.63914
$636$	−3.76393	−	6.51932i	−0.149250	−	0.258508i
$637$	−2.39919	−	4.15551i	−0.0950592	−	0.164647i
$638$	−29.4164			−1.16461
$639$	−4.33437			−0.171465
$640$	−1.80902	−	3.13331i	−0.0715077	−	0.123855i
$641$	6.63525	−	11.4926i	0.262077	−	0.453930i	−0.704717	−	0.709489i	$-0.748926\pi$
$641$	6.63525	−	11.4926i	0.262077	−	0.453930i	0.966794	+	0.255558i	$0.0822593\pi$
$642$	−5.81966	−	10.0799i	−0.229684	−	0.397824i
$643$	19.4164	−	33.6302i	0.765708	−	1.32625i	−0.174163	−	0.984717i	$-0.555722\pi$
$643$	19.4164	−	33.6302i	0.765708	−	1.32625i	0.939871	−	0.341529i	$-0.110945\pi$
$644$	8.47214	−	14.6742i	0.333849	−	0.578243i
$645$	−41.3050			−1.62638
$646$		0			0
$647$	26.0689			1.02487			0.512437	−	0.858725i	$-0.328743\pi$
$647$	26.0689			1.02487			0.512437	+	0.858725i	$0.328743\pi$
$648$	−1.20820	+	2.09267i	−0.0474627	+	0.0822079i
$649$	−0.763932	+	1.32317i	−0.0299870	+	0.0519389i
$650$	5.59017	+	9.68246i	0.219265	+	0.379777i
$651$	2.47214	−	4.28187i	0.0968906	−	0.167820i
$652$	−5.32624	−	9.22531i	−0.208592	−	0.361291i
$653$	−35.3951			−1.38512			−0.692559	−	0.721361i	$-0.743517\pi$
$653$	−35.3951			−1.38512			−0.692559	+	0.721361i	$0.743517\pi$
$654$	−13.6393			−0.533340
$655$	8.09017	+	14.0126i	0.316109	+	0.547517i
$656$	−0.427051	−	0.739674i	−0.0166735	−	0.0288794i
$657$	8.27051			0.322663
$658$	14.4721			0.564183
$659$	24.2705	+	42.0378i	0.945445	+	1.63756i	0.754858	+	0.655888i	$0.227706\pi$
$659$	24.2705	+	42.0378i	0.945445	+	1.63756i	0.190587	+	0.981670i	$0.438961\pi$
$660$	7.23607	−	12.5332i	0.281664	−	0.487856i
$661$	10.7082	+	18.5472i	0.416501	+	0.721401i	0.995585	−	0.0938673i	$-0.0299230\pi$
$661$	10.7082	+	18.5472i	0.416501	+	0.721401i	−0.579084	+	0.815268i	$0.696590\pi$
$662$	12.8541	−	22.2640i	0.499589	−	0.865313i
$663$	−2.88854	+	5.00310i	−0.112182	+	0.194304i
$664$	0.472136			0.0183224
$665$		0			0
$666$	12.3394			0.478142
$667$	23.7984	−	41.2200i	0.921477	−	1.59604i
$668$	6.23607	−	10.8012i	0.241281	−	0.417910i
$669$	17.1246	+	29.6607i	0.662076	+	1.14675i
$670$	−21.1803	+	36.6854i	−0.818268	+	1.41728i
$671$	2.23607	+	3.87298i	0.0863224	+	0.149515i
$672$	−4.00000			−0.154303
$673$	30.3820			1.17114			0.585569	−	0.810622i	$-0.300871\pi$
$673$	30.3820			1.17114			0.585569	+	0.810622i	$0.300871\pi$
$674$	1.19098	+	2.06284i	0.0458750	+	0.0794577i
$675$	−22.3607	−	38.7298i	−0.860663	−	1.49071i
$676$	−11.0902			−0.426545
$677$	−6.61803			−0.254352			−0.127176	−	0.991880i	$-0.540591\pi$
$677$	−6.61803			−0.254352			−0.127176	+	0.991880i	$0.540591\pi$
$678$	6.09017	+	10.5485i	0.233892	+	0.405112i
$679$	13.9443	−	24.1522i	0.535132	−	0.926876i
$680$	6.11803	+	10.5967i	0.234616	+	0.406367i
$681$	−5.52786	+	9.57454i	−0.211828	+	0.366897i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−20.1803			−0.772179			−0.386090	−	0.922461i	$-0.626174\pi$
$683$	−20.1803			−0.772179			−0.386090	+	0.922461i	$0.626174\pi$
$684$		0			0
$685$	−8.61803			−0.329278
$686$	5.70820	−	9.88690i	0.217940	−	0.377484i
$687$	2.70820	−	4.69075i	0.103324	−	0.178963i
$688$	4.61803	+	7.99867i	0.176061	+	0.304946i
$689$	4.20820	−	7.28882i	0.160320	−	0.277682i
$690$	11.7082	+	20.2792i	0.445724	+	0.772016i
$691$	−22.3607			−0.850640			−0.425320	−	0.905043i	$-0.639839\pi$
$691$	−22.3607			−0.850640			−0.425320	+	0.905043i	$0.639839\pi$
$692$	1.32624			0.0504160
$693$	7.70820	+	13.3510i	0.292810	+	0.507163i
$694$	−1.32624	−	2.29711i	−0.0503433	−	0.0871972i
$695$	50.6525			1.92136
$696$	−11.2361			−0.425902
$697$	1.44427	+	2.50155i	0.0547057	+	0.0947531i
$698$	−16.5451	+	28.6569i	−0.626241	+	1.08468i
$699$	0.965558	+	1.67240i	0.0365208	+	0.0632558i
$700$	13.0902	−	22.6728i	0.494762	−	0.856953i
$701$	−19.3156	+	33.4556i	−0.729540	+	1.26360i	0.227538	+	0.973769i	$0.426932\pi$
$701$	−19.3156	+	33.4556i	−0.729540	+	1.26360i	−0.957078	+	0.289831i	$0.906401\pi$
$702$	−7.63932			−0.288328
$703$		0			0
$704$	−3.23607			−0.121964
$705$	−10.0000	+	17.3205i	−0.376622	+	0.652328i
$706$	−11.8713	+	20.5617i	−0.446783	+	0.773851i
$707$	−25.2705	−	43.7698i	−0.950395	−	1.64613i
$708$	−0.291796	+	0.505406i	−0.0109664	+	0.0189943i
$709$	−3.45492	−	5.98409i	−0.129752	−	0.224737i	0.793828	−	0.608142i	$-0.208085\pi$
$709$	−3.45492	−	5.98409i	−0.129752	−	0.224737i	−0.923580	+	0.383405i	$0.874751\pi$
$710$	10.6525			0.399780
$711$	4.06888			0.152595
$712$	4.42705	+	7.66788i	0.165911	+	0.287366i
$713$	3.23607	+	5.60503i	0.121192	+	0.209910i
$714$	13.5279			0.506268
$715$	16.1803			0.605110
$716$	11.7082	+	20.2792i	0.437556	+	0.757869i
$717$	18.6525	−	32.3070i	0.696589	−	1.20653i
$718$	5.76393	+	9.98342i	0.215108	+	0.372578i
$719$	−6.14590	+	10.6450i	−0.229203	+	0.396992i	−0.957572	−	0.288193i	$-0.906945\pi$
$719$	−6.14590	+	10.6450i	−0.229203	+	0.396992i	0.728369	+	0.685185i	$0.240279\pi$
$720$	−2.66312	+	4.61266i	−0.0992486	+	0.171904i
$721$	−47.4164			−1.76588
$722$		0			0
$723$	31.4164			1.16839
$724$	−2.70820	+	4.69075i	−0.100650	+	0.174330i
$725$	36.7705	−	63.6884i	1.36562	−	2.36533i
$726$	0.326238	+	0.565061i	0.0121078	+	0.0209714i
$727$	15.4721	−	26.7985i	0.573830	−	0.993902i	−0.422338	−	0.906438i	$-0.638790\pi$
$727$	15.4721	−	26.7985i	0.573830	−	0.993902i	0.996168	−	0.0874638i	$-0.0278762\pi$
$728$	−2.23607	−	3.87298i	−0.0828742	−	0.143542i
$729$	24.0557			0.890953
$730$	−20.3262			−0.752308
$731$	−15.6180	−	27.0512i	−0.577654	−	1.00053i
$732$	0.854102	+	1.47935i	0.0315685	+	0.0546783i
$733$	−1.09017			−0.0402663			−0.0201332	−	0.999797i	$-0.506409\pi$
$733$	−1.09017			−0.0402663			−0.0201332	+	0.999797i	$0.506409\pi$
$734$	−18.8328			−0.695132
$735$	−7.76393	−	13.4475i	−0.286377	−	0.496019i
$736$	2.61803	−	4.53457i	0.0965020	−	0.167146i
$737$	18.9443	+	32.8124i	0.697821	+	1.20866i
$738$	−0.628677	+	1.08890i	−0.0231419	+	0.0400830i
$739$	−4.56231	+	7.90215i	−0.167827	+	0.290685i	−0.937656	−	0.347566i	$-0.887008\pi$
$739$	−4.56231	+	7.90215i	−0.167827	+	0.290685i	0.769829	+	0.638251i	$0.220342\pi$
$740$	−30.3262			−1.11481
$741$		0			0
$742$	−19.7082			−0.723511
$743$	−3.05573	+	5.29268i	−0.112104	+	0.194169i	−0.916618	−	0.399764i	$-0.869092\pi$
$743$	−3.05573	+	5.29268i	−0.112104	+	0.194169i	0.804515	+	0.593933i	$0.202426\pi$
$744$	0.763932	−	1.32317i	0.0280071	−	0.0485097i
$745$	−23.6803	−	41.0156i	−0.867581	−	1.50269i
$746$	9.16312	−	15.8710i	0.335486	−	0.581078i
$747$	−0.347524	−	0.601929i	−0.0127152	−	0.0220234i
$748$	10.9443			0.400162
$749$	−30.4721			−1.11343
$750$	6.90983	+	11.9682i	0.252311	+	0.437016i
$751$	12.0344	+	20.8443i	0.439143	+	0.760618i	0.997624	−	0.0688996i	$-0.0219488\pi$
$751$	12.0344	+	20.8443i	0.439143	+	0.760618i	−0.558481	+	0.829518i	$0.688615\pi$
$752$	4.47214			0.163082
$753$	2.83282			0.103234
$754$	−6.28115	−	10.8793i	−0.228746	−	0.396200i
$755$	26.1803	−	45.3457i	0.952800	−	1.65030i
$756$	8.94427	+	15.4919i	0.325300	+	0.563436i
$757$	−2.21885	+	3.84316i	−0.0806454	+	0.139682i	−0.903527	−	0.428530i	$-0.859031\pi$
$757$	−2.21885	+	3.84316i	−0.0806454	+	0.139682i	0.822882	+	0.568212i	$0.192365\pi$
$758$	−17.7082	+	30.6715i	−0.643191	+	1.11404i
$759$	20.9443			0.760229
$760$		0			0
$761$	26.3607			0.955574			0.477787	−	0.878476i	$-0.341439\pi$
$761$	26.3607			0.955574			0.477787	+	0.878476i	$0.341439\pi$
$762$	7.05573	−	12.2209i	0.255602	−	0.442716i
$763$	−17.8541	+	30.9242i	−0.646362	+	1.11953i
$764$	−1.76393	−	3.05522i	−0.0638168	−	0.110534i
$765$	9.00658	−	15.5999i	0.325634	−	0.564014i
$766$	10.3820	+	17.9821i	0.375116	+	0.649719i
$767$	−0.652476			−0.0235595
$768$	−1.23607			−0.0446028
$769$	−19.3713	−	33.5521i	−0.698548	−	1.20992i	−0.968970	−	0.247178i	$-0.920497\pi$
$769$	−19.3713	−	33.5521i	−0.698548	−	1.20992i	0.270422	−	0.962742i	$-0.412837\pi$
$770$	−18.9443	−	32.8124i	−0.682704	−	1.18248i
$771$	−22.7214			−0.818290
$772$	−11.5279			−0.414897
$773$	4.07295	+	7.05455i	0.146494	+	0.253735i	0.929929	−	0.367738i	$-0.119868\pi$
$773$	4.07295	+	7.05455i	0.146494	+	0.253735i	−0.783435	+	0.621473i	$0.786534\pi$
$774$	6.79837	−	11.7751i	0.244363	−	0.423248i
$775$	5.00000	+	8.66025i	0.179605	+	0.311086i
$776$	4.30902	−	7.46344i	0.154685	−	0.267922i
$777$	−16.7639	+	29.0360i	−0.601403	+	1.04166i
$778$	−12.7984			−0.458844
$779$		0			0
$780$	6.18034			0.221292
$781$	4.76393	−	8.25137i	0.170467	−	0.295257i
$782$	−8.85410	+	15.3358i	−0.316622	+	0.548405i
$783$	25.1246	+	43.5171i	0.897880	+	1.55517i
$784$	−1.73607	+	3.00696i	−0.0620024	+	0.107391i
$785$	16.9721	+	29.3966i	0.605762	+	1.04921i
$786$	5.52786			0.197172
$787$	28.4721			1.01492			0.507461	−	0.861675i	$-0.330584\pi$
$787$	28.4721			1.01492			0.507461	+	0.861675i	$0.330584\pi$
$788$	2.07295	+	3.59045i	0.0738458	+	0.127905i
$789$	1.81966	+	3.15174i	0.0647816	+	0.112205i
$790$	−10.0000			−0.355784
$791$	31.8885			1.13383
$792$	2.38197	+	4.12569i	0.0846395	+	0.146600i
$793$	−0.954915	+	1.65396i	−0.0339100	+	0.0587339i
$794$	−11.1803	−	19.3649i	−0.396775	−	0.687235i
$795$	13.6180	−	23.5871i	0.482982	−	0.836549i
$796$	−5.23607	+	9.06914i	−0.185588	+	0.321447i
$797$	28.4377			1.00731			0.503657	−	0.863903i	$-0.331987\pi$
$797$	28.4377			1.00731			0.503657	+	0.863903i	$0.331987\pi$
$798$		0			0
$799$	−15.1246			−0.535070
$800$	4.04508	−	7.00629i	0.143015	−	0.247710i
$801$	6.51722	−	11.2882i	0.230275	−	0.398847i
$802$	9.47214	+	16.4062i	0.334473	+	0.579324i
$803$	−9.09017	+	15.7446i	−0.320785	+	0.555616i
$804$	7.23607	+	12.5332i	0.255196	+	0.442013i
$805$	61.3050			2.16072
$806$	1.70820			0.0601689
$807$	8.85410	+	15.3358i	0.311679	+	0.539844i
$808$	−7.80902	−	13.5256i	−0.274720	−	0.475829i
$809$	2.74265			0.0964263			0.0482131	−	0.998837i	$-0.484647\pi$
$809$	2.74265			0.0964263			0.0482131	+	0.998837i	$0.484647\pi$
$810$	−8.74265			−0.307185
$811$	−2.79837	−	4.84693i	−0.0982642	−	0.170199i	0.812702	−	0.582679i	$-0.197996\pi$
$811$	−2.79837	−	4.84693i	−0.0982642	−	0.170199i	−0.910966	+	0.412481i	$0.864662\pi$
$812$	−14.7082	+	25.4754i	−0.516157	+	0.894010i
$813$	16.0689	+	27.8321i	0.563560	+	0.976115i
$814$	−13.5623	+	23.4906i	−0.475359	+	0.823345i
$815$	19.2705	−	33.3775i	0.675017	−	1.16916i
$816$	4.18034			0.146341
$817$		0			0
$818$	−16.2705			−0.568885
$819$	−3.29180	+	5.70156i	−0.115025	+	0.199229i
$820$	1.54508	−	2.67617i	0.0539567	−	0.0934558i
$821$	−9.63525	−	16.6888i	−0.336273	−	0.582441i	0.647456	−	0.762103i	$-0.275833\pi$
$821$	−9.63525	−	16.6888i	−0.336273	−	0.582441i	−0.983728	+	0.179662i	$0.942500\pi$
$822$	−1.47214	+	2.54981i	−0.0513466	+	0.0889350i
$823$	10.4164	+	18.0417i	0.363093	+	0.628896i	0.988468	−	0.151429i	$-0.0483873\pi$
$823$	10.4164	+	18.0417i	0.363093	+	0.628896i	−0.625375	+	0.780324i	$0.715054\pi$
$824$	−14.6525			−0.510443
$825$	32.3607			1.12665
$826$	0.763932	+	1.32317i	0.0265806	+	0.0460389i
$827$	15.2705	+	26.4493i	0.531008	+	0.919732i	0.999345	+	0.0361826i	$0.0115198\pi$
$827$	15.2705	+	26.4493i	0.531008	+	0.919732i	−0.468338	+	0.883550i	$0.655147\pi$
$828$	−7.70820			−0.267879
$829$	−9.72949			−0.337919			−0.168960	−	0.985623i	$-0.554041\pi$
$829$	−9.72949			−0.337919			−0.168960	+	0.985623i	$0.554041\pi$
$830$	0.854102	+	1.47935i	0.0296463	+	0.0513489i
$831$	−6.23607	+	10.8012i	−0.216327	+	0.374689i
$832$	−0.690983	−	1.19682i	−0.0239555	−	0.0414922i
$833$	5.87132	−	10.1694i	0.203429	−	0.352350i
$834$	8.65248	−	14.9865i	0.299611	−	0.518941i
$835$	45.1246			1.56160
$836$		0			0
$837$	−6.83282			−0.236177
$838$	−3.23607	+	5.60503i	−0.111788	+	0.193623i
$839$	−11.0000	+	19.0526i	−0.379762	+	0.657767i	−0.991027	−	0.133658i	$-0.957328\pi$
$839$	−11.0000	+	19.0526i	−0.379762	+	0.657767i	0.611265	+	0.791426i	$0.290661\pi$
$840$	−7.23607	−	12.5332i	−0.249668	−	0.432438i
$841$	−26.8156	+	46.4460i	−0.924676	+	1.60159i
$842$	6.95492	+	12.0463i	0.239682	+	0.415142i
$843$	−25.9311			−0.893115
$844$	−7.23607			−0.249076
$845$	−20.0623	−	34.7489i	−0.690164	−	1.19540i
$846$	−3.29180	−	5.70156i	−0.113174	−	0.196024i
$847$	1.70820			0.0586946
$848$	−6.09017			−0.209137
$849$	13.8885	+	24.0557i	0.476654	+	0.825588i
$850$	−13.6803	+	23.6950i	−0.469232	+	0.812733i
$851$	−21.9443	−	38.0086i	−0.752240	−	1.30292i
$852$	1.81966	−	3.15174i	0.0623405	−	0.107977i
$853$	14.5451	−	25.1928i	0.498014	−	0.862586i	−0.501983	−	0.864877i	$-0.667396\pi$
$853$	14.5451	−	25.1928i	0.498014	−	0.862586i	0.999997	+	0.00229146i	$0.000729395\pi$
$854$	4.47214			0.153033
$855$		0			0
$856$	−9.41641			−0.321846
$857$	−2.78115	+	4.81710i	−0.0950024	+	0.164549i	−0.909610	−	0.415464i	$-0.863619\pi$
$857$	−2.78115	+	4.81710i	−0.0950024	+	0.164549i	0.814607	+	0.580013i	$0.196953\pi$
$858$	2.76393	−	4.78727i	0.0943591	−	0.163435i
$859$	−14.0344	−	24.3084i	−0.478849	−	0.829391i	0.520857	−	0.853644i	$-0.325613\pi$
$859$	−14.0344	−	24.3084i	−0.478849	−	0.829391i	−0.999706	+	0.0242533i	$0.992279\pi$
$860$	−16.7082	+	28.9395i	−0.569745	+	0.986827i
$861$	−1.70820	−	2.95870i	−0.0582154	−	0.100832i
$862$	−6.65248			−0.226584
$863$	−25.8885			−0.881256			−0.440628	−	0.897690i	$-0.645244\pi$
$863$	−25.8885			−0.881256			−0.440628	+	0.897690i	$0.645244\pi$
$864$	2.76393	+	4.78727i	0.0940309	+	0.162866i
$865$	2.39919	+	4.15551i	0.0815748	+	0.141292i
$866$	25.0344			0.850705
$867$	6.87539			0.233500
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−4.47214	+	7.74597i	−0.151707	+	0.262764i
$870$	−20.3262	−	35.2061i	−0.689124	−	1.19360i
$871$	−8.09017	+	14.0126i	−0.274125	+	0.474798i
$872$	−5.51722	+	9.55611i	−0.186837	+	0.323611i
$873$	−12.6869			−0.429387
$874$		0			0
$875$	36.1803			1.22312
$876$	−3.47214	+	6.01392i	−0.117313	+	0.203191i
$877$	−0.871323	+	1.50918i	−0.0294225	+	0.0509612i	−0.880362	−	0.474303i	$-0.842700\pi$
$877$	−0.871323	+	1.50918i	−0.0294225	+	0.0509612i	0.850939	+	0.525264i	$0.176033\pi$
$878$	14.6180	+	25.3192i	0.493335	+	0.854481i
$879$	14.1803	−	24.5611i	0.478291	−	0.828424i
$880$	−5.85410	−	10.1396i	−0.197342	−	0.341806i
$881$	5.21478			0.175690			0.0878452	−	0.996134i	$-0.472002\pi$
$881$	5.21478			0.175690			0.0878452	+	0.996134i	$0.472002\pi$
$882$	5.11146			0.172112
$883$	8.90983	+	15.4323i	0.299840	+	0.519338i	0.976099	−	0.217326i	$-0.0697335\pi$
$883$	8.90983	+	15.4323i	0.299840	+	0.519338i	−0.676259	+	0.736664i	$0.736400\pi$
$884$	2.33688	+	4.04760i	0.0785978	+	0.136135i
$885$	−2.11146			−0.0709758
$886$	−9.23607			−0.310292
$887$	−3.47214	−	6.01392i	−0.116583	−	0.201928i	0.801828	−	0.597554i	$-0.203861\pi$
$887$	−3.47214	−	6.01392i	−0.116583	−	0.201928i	−0.918411	+	0.395627i	$0.870527\pi$
$888$	−5.18034	+	8.97261i	−0.173841	+	0.301101i
$889$	−18.4721	−	31.9947i	−0.619536	−	1.07307i
$890$	−16.0172	+	27.7426i	−0.536898	+	0.929935i
$891$	−3.90983	+	6.77202i	−0.130984	+	0.226871i
$892$	27.7082			0.927739
$893$		0			0
$894$	−16.1803			−0.541152
$895$	−42.3607	+	73.3708i	−1.41596	+	2.45252i
$896$	−1.61803	+	2.80252i	−0.0540547	+	0.0936255i
$897$	4.47214	+	7.74597i	0.149320	+	0.258630i
$898$	−11.3992	+	19.7440i	−0.380396	+	0.658865i
$899$	−5.61803	−	9.73072i	−0.187372	−	0.324538i
$900$	−11.9098			−0.396994
$901$	20.5967			0.686177
$902$	−1.38197	−	2.39364i	−0.0460144	−	0.0796993i
$903$	18.4721	+	31.9947i	0.614714	+	1.06472i
$904$	9.85410			0.327743
$905$	−19.5967			−0.651418
$906$	−8.94427	−	15.4919i	−0.297154	−	0.514685i
$907$	0.145898	−	0.252703i	0.00484446	−	0.00839086i	−0.863593	−	0.504190i	$-0.831791\pi$
$907$	0.145898	−	0.252703i	0.00484446	−	0.00839086i	0.868437	+	0.495799i	$0.165125\pi$
$908$	4.47214	+	7.74597i	0.148413	+	0.257059i
$909$	−11.4959	+	19.9115i	−0.381296	+	0.660424i
$910$	8.09017	−	14.0126i	0.268187	−	0.464513i
$911$	12.0689			0.399860			0.199930	−	0.979810i	$-0.435929\pi$
$911$	12.0689			0.399860			0.199930	+	0.979810i	$0.435929\pi$
$912$		0			0
$913$	1.52786			0.0505649
$914$	12.6074	−	21.8366i	0.417015	−	0.722292i
$915$	−3.09017	+	5.35233i	−0.102158	+	0.176943i
$916$	−2.19098	−	3.79489i	−0.0723921	−	0.125387i
$917$	7.23607	−	12.5332i	0.238956	−	0.413884i
$918$	−9.34752	−	16.1904i	−0.308514	−	0.534362i
$919$	45.8885			1.51372			0.756862	−	0.653575i	$-0.226732\pi$
$919$	45.8885			1.51372			0.756862	+	0.653575i	$0.226732\pi$
$920$	18.9443			0.624574
$921$	7.23607	+	12.5332i	0.238437	+	0.412984i
$922$	10.7082	+	18.5472i	0.352656	+	0.610818i
$923$	4.06888			0.133929
$924$	−12.9443			−0.425835
$925$	−33.9058	−	58.7265i	−1.11481	−	1.93092i
$926$	−2.52786	+	4.37839i	−0.0830708	+	0.143883i
$927$	10.7852	+	18.6805i	0.354233	+	0.613550i
$928$	−4.54508	+	7.87232i	−0.149200	+	0.258422i
$929$	29.5795	−	51.2332i	0.970473	−	1.68091i	0.276342	−	0.961059i	$-0.410878\pi$
$929$	29.5795	−	51.2332i	0.970473	−	1.68091i	0.694131	−	0.719849i	$-0.255789\pi$
$930$	5.52786			0.181266
$931$		0			0
$932$	1.56231			0.0511750
$933$	19.3050	−	33.4372i	0.632016	−	1.09468i
$934$	−16.6525	+	28.8429i	−0.544886	+	0.943770i
$935$	19.7984	+	34.2918i	0.647476	+	1.12146i
$936$	−1.01722	+	1.76188i	−0.0332489	+	0.0575888i
$937$	−7.94427	−	13.7599i	−0.259528	−	0.449516i	0.706588	−	0.707626i	$-0.250234\pi$
$937$	−7.94427	−	13.7599i	−0.259528	−	0.449516i	−0.966116	+	0.258110i	$0.916900\pi$
$938$	37.8885			1.23710
$939$	19.1672			0.625497
$940$	8.09017	+	14.0126i	0.263872	+	0.457040i
$941$	−13.0000	−	22.5167i	−0.423788	−	0.734022i	0.572518	−	0.819892i	$-0.305966\pi$
$941$	−13.0000	−	22.5167i	−0.423788	−	0.734022i	−0.996306	+	0.0858697i	$0.972633\pi$
$942$	11.5967			0.377842
$943$	4.47214			0.145633
$944$	0.236068	+	0.408882i	0.00768336	+	0.0133080i
$945$	−32.3607	+	56.0503i	−1.05269	+	1.82332i
$946$	14.9443	+	25.8842i	0.485880	+	0.841569i
$947$	−4.09017	+	7.08438i	−0.132913	+	0.230211i	−0.924798	−	0.380458i	$-0.875766\pi$
$947$	−4.09017	+	7.08438i	−0.132913	+	0.230211i	0.791885	+	0.610670i	$0.209100\pi$
$948$	−1.70820	+	2.95870i	−0.0554799	+	0.0960940i
$949$	−7.76393			−0.252028
$950$		0			0
$951$	−1.63932			−0.0531586
$952$	5.47214	−	9.47802i	0.177353	−	0.307184i
$953$	−23.9058	+	41.4060i	−0.774384	+	1.34127i	0.160757	+	0.986994i	$0.448607\pi$
$953$	−23.9058	+	41.4060i	−0.774384	+	1.34127i	−0.935140	+	0.354278i	$0.884727\pi$
$954$	4.48278	+	7.76440i	0.145135	+	0.251382i
$955$	6.38197	−	11.0539i	0.206516	−	0.357695i
$956$	−15.0902	−	26.1369i	−0.488051	−	0.845329i
$957$	−36.3607			−1.17537
$958$	−7.70820			−0.249041
$959$	3.85410	+	6.67550i	0.124455	+	0.215563i
$960$	−2.23607	−	3.87298i	−0.0721688	−	0.125000i
$961$	−29.4721			−0.950714
$962$	−11.5836			−0.373470
$963$	6.93112	+	12.0050i	0.223352	+	0.386857i
$964$	12.7082	−	22.0113i	0.409304	−	0.708935i
$965$	−20.8541	−	36.1204i	−0.671317	−	1.16276i
$966$	10.4721	−	18.1383i	0.336935	−	0.583589i
$967$	−4.41641	+	7.64944i	−0.142022	+	0.245989i	−0.928258	−	0.371937i	$-0.878694\pi$
$967$	−4.41641	+	7.64944i	−0.142022	+	0.245989i	0.786236	+	0.617926i	$0.212027\pi$
$968$	0.527864			0.0169662
$969$		0			0
$970$	31.1803			1.00114
$971$	−30.2705	+	52.4301i	−0.971427	+	1.68256i	−0.280172	+	0.959950i	$0.590391\pi$
$971$	−30.2705	+	52.4301i	−0.971427	+	1.68256i	−0.691255	+	0.722611i	$0.742942\pi$
$972$	6.79837	−	11.7751i	0.218058	−	0.377687i
$973$	−22.6525	−	39.2352i	−0.726205	−	1.25782i
$974$	9.61803	−	16.6589i	0.308182	−	0.533786i
$975$	6.90983	+	11.9682i	0.221292	+	0.383288i
$976$	1.38197			0.0442357
$977$	−9.03444			−0.289037			−0.144519	−	0.989502i	$-0.546163\pi$
$977$	−9.03444			−0.289037			−0.144519	+	0.989502i	$0.546163\pi$
$978$	−6.58359	−	11.4031i	−0.210520	−	0.364631i
$979$	14.3262	+	24.8138i	0.457869	+	0.793052i
$980$	−12.5623			−0.401288
$981$	16.2442			0.518637
$982$	−0.763932	−	1.32317i	−0.0243781	−	0.0422240i
$983$	−9.79837	+	16.9713i	−0.312520	+	0.541300i	−0.978907	−	0.204306i	$-0.934506\pi$
$983$	−9.79837	+	16.9713i	−0.312520	+	0.541300i	0.666388	+	0.745606i	$0.267840\pi$
$984$	−0.527864	−	0.914287i	−0.0168277	−	0.0291464i
$985$	−7.50000	+	12.9904i	−0.238970	+	0.413908i
$986$	15.3713	−	26.6239i	0.489523	−	0.847878i
$987$	17.8885			0.569399
$988$		0			0
$989$	−48.3607			−1.53778
$990$	−8.61803	+	14.9269i	−0.273899	+	0.474407i
$991$	15.3262	−	26.5458i	0.486854	−	0.843256i	−0.513032	−	0.858370i	$-0.671478\pi$
$991$	15.3262	−	26.5458i	0.486854	−	0.843256i	0.999886	+	0.0151138i	$0.00481104\pi$
$992$	−0.618034	−	1.07047i	−0.0196226	−	0.0339873i
$993$	15.8885	−	27.5198i	0.504208	−	0.873313i
$994$	−4.76393	−	8.25137i	−0.151103	−	0.261718i
$995$	−37.8885			−1.20115
$996$	0.583592			0.0184918
$997$	6.75329	+	11.6970i	0.213879	+	0.370449i	0.952925	−	0.303206i	$-0.0980569\pi$
$997$	6.75329	+	11.6970i	0.213879	+	0.370449i	−0.739046	+	0.673655i	$0.764724\pi$
$998$	−17.6525	−	30.5750i	−0.558779	−	0.967834i
$999$	46.3344			1.46595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.i.429.2		4
19.2	odd	18		722.2.e.p.595.1		12
19.3	odd	18		722.2.e.p.99.2		12
19.4	even	9		722.2.e.q.423.1		12
19.5	even	9		722.2.e.q.389.1		12
19.6	even	9		722.2.e.q.415.2		12
19.7	even	3	inner	722.2.c.i.653.2		4
19.8	odd	6		722.2.a.i.1.2	yes	2
19.9	even	9		722.2.e.q.245.1		12
19.10	odd	18		722.2.e.p.245.2		12
19.11	even	3		722.2.a.h.1.1	✓	2
19.12	odd	6		722.2.c.h.653.1		4
19.13	odd	18		722.2.e.p.415.1		12
19.14	odd	18		722.2.e.p.389.2		12
19.15	odd	18		722.2.e.p.423.2		12
19.16	even	9		722.2.e.q.99.1		12
19.17	even	9		722.2.e.q.595.2		12
19.18	odd	2		722.2.c.h.429.1		4
57.8	even	6		6498.2.a.be.1.2		2
57.11	odd	6		6498.2.a.bk.1.2		2
76.11	odd	6		5776.2.a.t.1.2		2
76.27	even	6		5776.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.h.1.1	✓	2	19.11	even	3
722.2.a.i.1.2	yes	2	19.8	odd	6
722.2.c.h.429.1		4	19.18	odd	2
722.2.c.h.653.1		4	19.12	odd	6
722.2.c.i.429.2		4	1.1	even	1	trivial
722.2.c.i.653.2		4	19.7	even	3	inner
722.2.e.p.99.2		12	19.3	odd	18
722.2.e.p.245.2		12	19.10	odd	18
722.2.e.p.389.2		12	19.14	odd	18
722.2.e.p.415.1		12	19.13	odd	18
722.2.e.p.423.2		12	19.15	odd	18
722.2.e.p.595.1		12	19.2	odd	18
722.2.e.q.99.1		12	19.16	even	9
722.2.e.q.245.1		12	19.9	even	9
722.2.e.q.389.1		12	19.5	even	9
722.2.e.q.415.2		12	19.6	even	9
722.2.e.q.423.1		12	19.4	even	9
722.2.e.q.595.2		12	19.17	even	9
5776.2.a.t.1.2		2	76.11	odd	6
5776.2.a.be.1.1		2	76.27	even	6
6498.2.a.be.1.2		2	57.8	even	6
6498.2.a.bk.1.2		2	57.11	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.80902 - 3.13331i) q^{5} +(-0.618034 - 1.07047i) q^{6} -3.23607 q^{7} -1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.80902 - 3.13331i) q^{5} +(-0.618034 - 1.07047i) q^{6} -3.23607 q^{7} -1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +(-1.80902 - 3.13331i) q^{10} -3.23607 q^{11} -1.23607 q^{12} +(-0.690983 - 1.19682i) q^{13} +(-1.61803 + 2.80252i) q^{14} +(-2.23607 - 3.87298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.69098 - 2.92887i) q^{17} +1.47214 q^{18} -3.61803 q^{20} +(-2.00000 + 3.46410i) q^{21} +(-1.61803 + 2.80252i) q^{22} +(-2.61803 - 4.53457i) q^{23} +(-0.618034 + 1.07047i) q^{24} +(-4.04508 - 7.00629i) q^{25} -1.38197 q^{26} +5.52786 q^{27} +(1.61803 + 2.80252i) q^{28} +(4.54508 + 7.87232i) q^{29} -4.47214 q^{30} -1.23607 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} +(-1.69098 - 2.92887i) q^{34} +(-5.85410 + 10.1396i) q^{35} +(0.736068 - 1.27491i) q^{36} +8.38197 q^{37} -1.70820 q^{39} +(-1.80902 + 3.13331i) q^{40} +(-0.427051 + 0.739674i) q^{41} +(2.00000 + 3.46410i) q^{42} +(4.61803 - 7.99867i) q^{43} +(1.61803 + 2.80252i) q^{44} +5.32624 q^{45} -5.23607 q^{46} +(-2.23607 - 3.87298i) q^{47} +(0.618034 + 1.07047i) q^{48} +3.47214 q^{49} -8.09017 q^{50} +(-2.09017 - 3.62028i) q^{51} +(-0.690983 + 1.19682i) q^{52} +(3.04508 + 5.27424i) q^{53} +(2.76393 - 4.78727i) q^{54} +(-5.85410 + 10.1396i) q^{55} +3.23607 q^{56} +9.09017 q^{58} +(0.236068 - 0.408882i) q^{59} +(-2.23607 + 3.87298i) q^{60} +(-0.690983 - 1.19682i) q^{61} +(-0.618034 + 1.07047i) q^{62} +(-2.38197 - 4.12569i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(2.00000 + 3.46410i) q^{66} +(-5.85410 - 10.1396i) q^{67} -3.38197 q^{68} -6.47214 q^{69} +(5.85410 + 10.1396i) q^{70} +(-1.47214 + 2.54981i) q^{71} +(-0.736068 - 1.27491i) q^{72} +(2.80902 - 4.86536i) q^{73} +(4.19098 - 7.25900i) q^{74} -10.0000 q^{75} +10.4721 q^{77} +(-0.854102 + 1.47935i) q^{78} +(1.38197 - 2.39364i) q^{79} +(1.80902 + 3.13331i) q^{80} +(1.20820 - 2.09267i) q^{81} +(0.427051 + 0.739674i) q^{82} -0.472136 q^{83} +4.00000 q^{84} +(-6.11803 - 10.5967i) q^{85} +(-4.61803 - 7.99867i) q^{86} +11.2361 q^{87} +3.23607 q^{88} +(-4.42705 - 7.66788i) q^{89} +(2.66312 - 4.61266i) q^{90} +(2.23607 + 3.87298i) q^{91} +(-2.61803 + 4.53457i) q^{92} +(-0.763932 + 1.32317i) q^{93} -4.47214 q^{94} +1.23607 q^{96} +(-4.30902 + 7.46344i) q^{97} +(1.73607 - 3.00696i) q^{98} +(-2.38197 - 4.12569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 5 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 5 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 5 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 6 q^{9} - 5 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 2 q^{14} - 2 q^{16} + 9 q^{17} - 12 q^{18} - 10 q^{20} - 8 q^{21} - 2 q^{22} - 6 q^{23} + 2 q^{24} - 5 q^{25} - 10 q^{26} + 40 q^{27} + 2 q^{28} + 7 q^{29} + 4 q^{31} + 2 q^{32} - 8 q^{33} - 9 q^{34} - 10 q^{35} - 6 q^{36} + 38 q^{37} + 20 q^{39} - 5 q^{40} + 5 q^{41} + 8 q^{42} + 14 q^{43} + 2 q^{44} - 10 q^{45} - 12 q^{46} - 2 q^{48} - 4 q^{49} - 10 q^{50} + 14 q^{51} - 5 q^{52} + q^{53} + 20 q^{54} - 10 q^{55} + 4 q^{56} + 14 q^{58} - 8 q^{59} - 5 q^{61} + 2 q^{62} - 14 q^{63} + 4 q^{64} - 20 q^{65} + 8 q^{66} - 10 q^{67} - 18 q^{68} - 8 q^{69} + 10 q^{70} + 12 q^{71} + 6 q^{72} + 9 q^{73} + 19 q^{74} - 40 q^{75} + 24 q^{77} + 10 q^{78} + 10 q^{79} + 5 q^{80} - 22 q^{81} - 5 q^{82} + 16 q^{83} + 16 q^{84} - 20 q^{85} - 14 q^{86} + 36 q^{87} + 4 q^{88} - 11 q^{89} - 5 q^{90} - 6 q^{92} - 12 q^{93} - 4 q^{96} - 15 q^{97} - 2 q^{98} - 14 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 5 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 6 * q^9 - 5 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 2 * q^14 - 2 * q^16 + 9 * q^17 - 12 * q^18 - 10 * q^20 - 8 * q^21 - 2 * q^22 - 6 * q^23 + 2 * q^24 - 5 * q^25 - 10 * q^26 + 40 * q^27 + 2 * q^28 + 7 * q^29 + 4 * q^31 + 2 * q^32 - 8 * q^33 - 9 * q^34 - 10 * q^35 - 6 * q^36 + 38 * q^37 + 20 * q^39 - 5 * q^40 + 5 * q^41 + 8 * q^42 + 14 * q^43 + 2 * q^44 - 10 * q^45 - 12 * q^46 - 2 * q^48 - 4 * q^49 - 10 * q^50 + 14 * q^51 - 5 * q^52 + q^53 + 20 * q^54 - 10 * q^55 + 4 * q^56 + 14 * q^58 - 8 * q^59 - 5 * q^61 + 2 * q^62 - 14 * q^63 + 4 * q^64 - 20 * q^65 + 8 * q^66 - 10 * q^67 - 18 * q^68 - 8 * q^69 + 10 * q^70 + 12 * q^71 + 6 * q^72 + 9 * q^73 + 19 * q^74 - 40 * q^75 + 24 * q^77 + 10 * q^78 + 10 * q^79 + 5 * q^80 - 22 * q^81 - 5 * q^82 + 16 * q^83 + 16 * q^84 - 20 * q^85 - 14 * q^86 + 36 * q^87 + 4 * q^88 - 11 * q^89 - 5 * q^90 - 6 * q^92 - 12 * q^93 - 4 * q^96 - 15 * q^97 - 2 * q^98 - 14 * q^99

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