LMFDB - Embedded newform 722.2.c.h.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			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.h.653.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.690983 - 1.19682i) q^{5} +(1.61803 + 2.80252i) q^{6} +1.23607 q^{7} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.690983 - 1.19682i) q^{5} +(1.61803 + 2.80252i) q^{6} +1.23607 q^{7} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +(0.690983 + 1.19682i) q^{10} +1.23607 q^{11} -3.23607 q^{12} +(1.80902 + 3.13331i) q^{13} +(-0.618034 + 1.07047i) q^{14} +(-2.23607 - 3.87298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.80902 - 4.86536i) q^{17} +7.47214 q^{18} -1.38197 q^{20} +(2.00000 - 3.46410i) q^{21} +(-0.618034 + 1.07047i) q^{22} +(-0.381966 - 0.661585i) q^{23} +(1.61803 - 2.80252i) q^{24} +(1.54508 + 2.67617i) q^{25} -3.61803 q^{26} -14.4721 q^{27} +(-0.618034 - 1.07047i) q^{28} +(1.04508 + 1.81014i) q^{29} +4.47214 q^{30} -3.23607 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +(2.80902 + 4.86536i) q^{34} +(0.854102 - 1.47935i) q^{35} +(-3.73607 + 6.47106i) q^{36} -10.6180 q^{37} +11.7082 q^{39} +(0.690983 - 1.19682i) q^{40} +(-2.92705 + 5.06980i) q^{41} +(2.00000 + 3.46410i) q^{42} +(2.38197 - 4.12569i) q^{43} +(-0.618034 - 1.07047i) q^{44} -10.3262 q^{45} +0.763932 q^{46} +(2.23607 + 3.87298i) q^{47} +(1.61803 + 2.80252i) q^{48} -5.47214 q^{49} -3.09017 q^{50} +(-9.09017 - 15.7446i) q^{51} +(1.80902 - 3.13331i) q^{52} +(2.54508 + 4.40822i) q^{53} +(7.23607 - 12.5332i) q^{54} +(0.854102 - 1.47935i) q^{55} +1.23607 q^{56} -2.09017 q^{58} +(4.23607 - 7.33708i) q^{59} +(-2.23607 + 3.87298i) q^{60} +(-1.80902 - 3.13331i) q^{61} +(1.61803 - 2.80252i) q^{62} +(-4.61803 - 7.99867i) q^{63} +1.00000 q^{64} +5.00000 q^{65} +(2.00000 + 3.46410i) q^{66} +(-0.854102 - 1.47935i) q^{67} -5.61803 q^{68} -2.47214 q^{69} +(0.854102 + 1.47935i) q^{70} +(-7.47214 + 12.9421i) q^{71} +(-3.73607 - 6.47106i) q^{72} +(1.69098 - 2.92887i) q^{73} +(5.30902 - 9.19549i) q^{74} +10.0000 q^{75} +1.52786 q^{77} +(-5.85410 + 10.1396i) q^{78} +(-3.61803 + 6.26662i) q^{79} +(0.690983 + 1.19682i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-2.92705 - 5.06980i) q^{82} +8.47214 q^{83} -4.00000 q^{84} +(-3.88197 - 6.72376i) q^{85} +(2.38197 + 4.12569i) q^{86} +6.76393 q^{87} +1.23607 q^{88} +(1.07295 + 1.85840i) q^{89} +(5.16312 - 8.94278i) q^{90} +(2.23607 + 3.87298i) q^{91} +(-0.381966 + 0.661585i) q^{92} +(-5.23607 + 9.06914i) q^{93} -4.47214 q^{94} -3.23607 q^{96} +(3.19098 - 5.52694i) q^{97} +(2.73607 - 4.73901i) q^{98} +(-4.61803 - 7.99867i) 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
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.158069	−	0.987428i	$-0.449473\pi$
$3$	1.61803	−	2.80252i	0.934172	−	1.61803i	0.776103	−	0.630606i	$-0.217194\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.690983	−	1.19682i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$5$	0.690983	−	1.19682i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$6$	1.61803	+	2.80252i	0.660560	+	1.14412i
$7$	1.23607			0.467190			0.233595	−	0.972334i	$-0.424951\pi$
$7$	1.23607			0.467190			0.233595	+	0.972334i	$0.424951\pi$
$8$	1.00000			0.353553
$9$	−3.73607	−	6.47106i	−1.24536	−	2.15702i
$10$	0.690983	+	1.19682i	0.218508	+	0.378467i
$11$	1.23607			0.372689			0.186344	−	0.982485i	$-0.440336\pi$
$11$	1.23607			0.372689			0.186344	+	0.982485i	$0.440336\pi$
$12$	−3.23607			−0.934172
$13$	1.80902	+	3.13331i	0.501731	+	0.869024i	0.999998	+	0.00199999i	$0.000636617\pi$
$13$	1.80902	+	3.13331i	0.501731	+	0.869024i	−0.498267	+	0.867024i	$0.666030\pi$
$14$	−0.618034	+	1.07047i	−0.165177	+	0.286094i
$15$	−2.23607	−	3.87298i	−0.577350	−	1.00000i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.80902	−	4.86536i	0.681287	−	1.18002i	−0.293302	−	0.956020i	$-0.594754\pi$
$17$	2.80902	−	4.86536i	0.681287	−	1.18002i	0.974588	−	0.224003i	$-0.0719126\pi$
$18$	7.47214			1.76120
$19$		0			0
$19$		0			0
$20$	−1.38197			−0.309017
$21$	2.00000	−	3.46410i	0.436436	−	0.755929i
$22$	−0.618034	+	1.07047i	−0.131765	+	0.228224i
$23$	−0.381966	−	0.661585i	−0.0796454	−	0.137950i	0.823452	−	0.567387i	$-0.192045\pi$
$23$	−0.381966	−	0.661585i	−0.0796454	−	0.137950i	−0.903097	+	0.429437i	$0.858712\pi$
$24$	1.61803	−	2.80252i	0.330280	−	0.572061i
$25$	1.54508	+	2.67617i	0.309017	+	0.535233i
$26$	−3.61803			−0.709555
$27$	−14.4721			−2.78516
$28$	−0.618034	−	1.07047i	−0.116797	−	0.202299i
$29$	1.04508	+	1.81014i	0.194067	+	0.336135i	0.946594	−	0.322427i	$-0.104499\pi$
$29$	1.04508	+	1.81014i	0.194067	+	0.336135i	−0.752527	+	0.658561i	$0.771165\pi$
$30$	4.47214			0.816497
$31$	−3.23607			−0.581215			−0.290607	−	0.956842i	$-0.593857\pi$
$31$	−3.23607			−0.581215			−0.290607	+	0.956842i	$0.593857\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	2.80902	+	4.86536i	0.481742	+	0.834402i
$35$	0.854102	−	1.47935i	0.144370	−	0.250055i
$36$	−3.73607	+	6.47106i	−0.622678	+	1.07851i
$37$	−10.6180			−1.74559			−0.872797	−	0.488083i	$-0.837696\pi$
$37$	−10.6180			−1.74559			−0.872797	+	0.488083i	$0.837696\pi$
$38$		0			0
$39$	11.7082			1.87481
$40$	0.690983	−	1.19682i	0.109254	−	0.189233i
$41$	−2.92705	+	5.06980i	−0.457129	+	0.791770i	−0.998808	−	0.0488154i	$-0.984455\pi$
$41$	−2.92705	+	5.06980i	−0.457129	+	0.791770i	0.541679	+	0.840585i	$0.317789\pi$
$42$	2.00000	+	3.46410i	0.308607	+	0.534522i
$43$	2.38197	−	4.12569i	0.363246	−	0.629161i	−0.625247	−	0.780427i	$-0.715002\pi$
$43$	2.38197	−	4.12569i	0.363246	−	0.629161i	0.988493	+	0.151266i	$0.0483350\pi$
$44$	−0.618034	−	1.07047i	−0.0931721	−	0.161379i
$45$	−10.3262			−1.53934
$46$	0.763932			0.112636
$47$	2.23607	+	3.87298i	0.326164	+	0.564933i	0.981747	−	0.190190i	$-0.0609105\pi$
$47$	2.23607	+	3.87298i	0.326164	+	0.564933i	−0.655583	+	0.755123i	$0.727577\pi$
$48$	1.61803	+	2.80252i	0.233543	+	0.404508i
$49$	−5.47214			−0.781734
$50$	−3.09017			−0.437016
$51$	−9.09017	−	15.7446i	−1.27288	−	2.20469i
$52$	1.80902	−	3.13331i	0.250866	−	0.434512i
$53$	2.54508	+	4.40822i	0.349594	+	0.605515i	0.986177	−	0.165693i	$-0.0529861\pi$
$53$	2.54508	+	4.40822i	0.349594	+	0.605515i	−0.636583	+	0.771208i	$0.719653\pi$
$54$	7.23607	−	12.5332i	0.984704	−	1.70556i
$55$	0.854102	−	1.47935i	0.115167	−	0.199475i
$56$	1.23607			0.165177
$57$		0			0
$58$	−2.09017			−0.274453
$59$	4.23607	−	7.33708i	0.551489	−	0.955207i	−0.446678	−	0.894695i	$-0.647393\pi$
$59$	4.23607	−	7.33708i	0.551489	−	0.955207i	0.998167	−	0.0605125i	$-0.0192735\pi$
$60$	−2.23607	+	3.87298i	−0.288675	+	0.500000i
$61$	−1.80902	−	3.13331i	−0.231621	−	0.401179i	0.726664	−	0.686993i	$-0.241070\pi$
$61$	−1.80902	−	3.13331i	−0.231621	−	0.401179i	−0.958285	+	0.285813i	$0.907736\pi$
$62$	1.61803	−	2.80252i	0.205491	−	0.355920i
$63$	−4.61803	−	7.99867i	−0.581818	−	1.00774i
$64$	1.00000			0.125000
$65$	5.00000			0.620174
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−0.854102	−	1.47935i	−0.104345	−	0.180731i	0.809125	−	0.587636i	$-0.199941\pi$
$67$	−0.854102	−	1.47935i	−0.104345	−	0.180731i	−0.913470	+	0.406905i	$0.866608\pi$
$68$	−5.61803			−0.681287
$69$	−2.47214			−0.297610
$70$	0.854102	+	1.47935i	0.102085	+	0.176816i
$71$	−7.47214	+	12.9421i	−0.886779	+	1.53595i	−0.0431189	+	0.999070i	$0.513729\pi$
$71$	−7.47214	+	12.9421i	−0.886779	+	1.53595i	−0.843661	+	0.536877i	$0.819604\pi$
$72$	−3.73607	−	6.47106i	−0.440300	−	0.762622i
$73$	1.69098	−	2.92887i	0.197915	−	0.342798i	−0.749937	−	0.661509i	$-0.769916\pi$
$73$	1.69098	−	2.92887i	0.197915	−	0.342798i	0.947852	+	0.318711i	$0.103250\pi$
$74$	5.30902	−	9.19549i	0.617161	−	1.06895i
$75$	10.0000			1.15470
$76$		0			0
$77$	1.52786			0.174116
$78$	−5.85410	+	10.1396i	−0.662847	+	1.14808i
$79$	−3.61803	+	6.26662i	−0.407061	+	0.705050i	−0.994559	−	0.104176i	$-0.966780\pi$
$79$	−3.61803	+	6.26662i	−0.407061	+	0.705050i	0.587498	+	0.809225i	$0.300113\pi$
$80$	0.690983	+	1.19682i	0.0772542	+	0.133808i
$81$	−12.2082	+	21.1452i	−1.35647	+	2.34947i
$82$	−2.92705	−	5.06980i	−0.323239	−	0.559866i
$83$	8.47214			0.929938			0.464969	−	0.885327i	$-0.346066\pi$
$83$	8.47214			0.929938			0.464969	+	0.885327i	$0.346066\pi$
$84$	−4.00000			−0.436436
$85$	−3.88197	−	6.72376i	−0.421058	−	0.729294i
$86$	2.38197	+	4.12569i	0.256854	+	0.444884i
$87$	6.76393			0.725170
$88$	1.23607			0.131765
$89$	1.07295	+	1.85840i	0.113732	+	0.196990i	0.917272	−	0.398261i	$-0.130386\pi$
$89$	1.07295	+	1.85840i	0.113732	+	0.196990i	−0.803540	+	0.595251i	$0.797053\pi$
$90$	5.16312	−	8.94278i	0.544241	−	0.942652i
$91$	2.23607	+	3.87298i	0.234404	+	0.405999i
$92$	−0.381966	+	0.661585i	−0.0398227	+	0.0689750i
$93$	−5.23607	+	9.06914i	−0.542955	+	0.940426i
$94$	−4.47214			−0.461266
$95$		0			0
$96$	−3.23607			−0.330280
$97$	3.19098	−	5.52694i	0.323995	−	0.561176i	−0.657313	−	0.753617i	$-0.728307\pi$
$97$	3.19098	−	5.52694i	0.323995	−	0.561176i	0.981308	+	0.192441i	$0.0616405\pi$
$98$	2.73607	−	4.73901i	0.276385	−	0.478712i
$99$	−4.61803	−	7.99867i	−0.464130	−	0.803897i
$100$	1.54508	−	2.67617i	0.154508	−	0.267617i
$101$	6.69098	+	11.5891i	0.665778	+	1.15316i	0.979074	+	0.203505i	$0.0652334\pi$
$101$	6.69098	+	11.5891i	0.665778	+	1.15316i	−0.313296	+	0.949655i	$0.601433\pi$
$102$	18.1803			1.80012
$103$	16.6525			1.64082			0.820409	−	0.571778i	$-0.193746\pi$
$103$	16.6525			1.64082			0.820409	+	0.571778i	$0.193746\pi$
$104$	1.80902	+	3.13331i	0.177389	+	0.307246i
$105$	−2.76393	−	4.78727i	−0.269732	−	0.467190i
$106$	−5.09017			−0.494401
$107$	17.4164			1.68371			0.841854	−	0.539706i	$-0.181464\pi$
$107$	17.4164			1.68371			0.841854	+	0.539706i	$0.181464\pi$
$108$	7.23607	+	12.5332i	0.696291	+	1.20601i
$109$	9.01722	−	15.6183i	0.863693	−	1.49596i	−0.00464587	−	0.999989i	$-0.501479\pi$
$109$	9.01722	−	15.6183i	0.863693	−	1.49596i	0.868339	−	0.495971i	$-0.165188\pi$
$110$	0.854102	+	1.47935i	0.0814354	+	0.141050i
$111$	−17.1803	+	29.7572i	−1.63069	+	2.82443i
$112$	−0.618034	+	1.07047i	−0.0583987	+	0.101150i
$113$	3.14590			0.295941			0.147971	−	0.988992i	$-0.452726\pi$
$113$	3.14590			0.295941			0.147971	+	0.988992i	$0.452726\pi$
$114$		0			0
$115$	−1.05573			−0.0984472
$116$	1.04508	−	1.81014i	0.0970337	−	0.168067i
$117$	13.5172	−	23.4125i	1.24967	−	2.16449i
$118$	4.23607	+	7.33708i	0.389962	+	0.675433i
$119$	3.47214	−	6.01392i	0.318290	−	0.551295i
$120$	−2.23607	−	3.87298i	−0.204124	−	0.353553i
$121$	−9.47214			−0.861103
$122$	3.61803			0.327561
$123$	9.47214	+	16.4062i	0.854074	+	1.47930i
$124$	1.61803	+	2.80252i	0.145304	+	0.251673i
$125$	11.1803			1.00000
$126$	9.23607			0.822814
$127$	7.70820	+	13.3510i	0.683992	+	1.18471i	0.973752	+	0.227610i	$0.0730912\pi$
$127$	7.70820	+	13.3510i	0.683992	+	1.18471i	−0.289760	+	0.957099i	$0.593575\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−7.70820	−	13.3510i	−0.678670	−	1.17549i
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	2.23607	−	3.87298i	0.195366	−	0.338384i	−0.751654	−	0.659557i	$-0.770744\pi$
$131$	2.23607	−	3.87298i	0.195366	−	0.338384i	0.947020	+	0.321173i	$0.104077\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	1.70820			0.147566
$135$	−10.0000	+	17.3205i	−0.860663	+	1.49071i
$136$	2.80902	−	4.86536i	0.240871	−	0.417201i
$137$	−2.30902	−	3.99933i	−0.197273	−	0.341686i	0.750371	−	0.661017i	$-0.229875\pi$
$137$	−2.30902	−	3.99933i	−0.197273	−	0.341686i	−0.947643	+	0.319331i	$0.896542\pi$
$138$	1.23607	−	2.14093i	0.105221	−	0.182248i
$139$	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	$0.630987\pi$
$140$	−1.70820			−0.144370
$141$	14.4721			1.21877
$142$	−7.47214	−	12.9421i	−0.627048	−	1.08608i
$143$	2.23607	+	3.87298i	0.186989	+	0.323875i
$144$	7.47214			0.622678
$145$	2.88854			0.239881
$146$	1.69098	+	2.92887i	0.139947	+	0.242395i
$147$	−8.85410	+	15.3358i	−0.730274	+	1.26487i
$148$	5.30902	+	9.19549i	0.436399	+	0.755864i
$149$	0.954915	−	1.65396i	0.0782297	−	0.135498i	−0.824257	−	0.566217i	$-0.808407\pi$
$149$	0.954915	−	1.65396i	0.0782297	−	0.135498i	0.902486	+	0.430719i	$0.141740\pi$
$150$	−5.00000	+	8.66025i	−0.408248	+	0.707107i
$151$	−5.52786			−0.449851			−0.224926	−	0.974376i	$-0.572214\pi$
$151$	−5.52786			−0.449851			−0.224926	+	0.974376i	$0.572214\pi$
$152$		0			0
$153$	−41.9787			−3.39378
$154$	−0.763932	+	1.32317i	−0.0615594	+	0.106624i
$155$	−2.23607	+	3.87298i	−0.179605	+	0.311086i
$156$	−5.85410	−	10.1396i	−0.468703	−	0.811818i
$157$	−5.80902	+	10.0615i	−0.463610	+	0.802996i	−0.999138	−	0.0415216i	$-0.986779\pi$
$157$	−5.80902	+	10.0615i	−0.463610	+	0.802996i	0.535528	+	0.844518i	$0.320113\pi$
$158$	−3.61803	−	6.26662i	−0.287835	−	0.498545i
$159$	16.4721			1.30633
$160$	−1.38197			−0.109254
$161$	−0.472136	−	0.817763i	−0.0372095	−	0.0644488i
$162$	−12.2082	−	21.1452i	−0.959167	−	1.66133i
$163$	−20.6525			−1.61763			−0.808813	−	0.588065i	$-0.799890\pi$
$163$	−20.6525			−1.61763			−0.808813	+	0.588065i	$0.799890\pi$
$164$	5.85410			0.457129
$165$	−2.76393	−	4.78727i	−0.215172	−	0.372689i
$166$	−4.23607	+	7.33708i	−0.328783	+	0.569468i
$167$	−1.76393	−	3.05522i	−0.136497	−	0.236420i	0.789671	−	0.613530i	$-0.210251\pi$
$167$	−1.76393	−	3.05522i	−0.136497	−	0.236420i	−0.926168	+	0.377110i	$0.876918\pi$
$168$	2.00000	−	3.46410i	0.154303	−	0.267261i
$169$	−0.0450850	+	0.0780895i	−0.00346807	+	0.00600688i
$170$	7.76393			0.595466
$171$		0			0
$172$	−4.76393			−0.363246
$173$	−7.16312	+	12.4069i	−0.544602	+	0.943278i	0.454030	+	0.890986i	$0.349986\pi$
$173$	−7.16312	+	12.4069i	−0.544602	+	0.943278i	−0.998632	+	0.0522917i	$0.983347\pi$
$174$	−3.38197	+	5.85774i	−0.256386	+	0.444074i
$175$	1.90983	+	3.30792i	0.144370	+	0.250055i
$176$	−0.618034	+	1.07047i	−0.0465861	+	0.0806894i
$177$	−13.7082	−	23.7433i	−1.03037	−	1.78466i
$178$	−2.14590			−0.160842
$179$	−3.41641			−0.255354			−0.127677	−	0.991816i	$-0.540752\pi$
$179$	−3.41641			−0.255354			−0.127677	+	0.991816i	$0.540752\pi$
$180$	5.16312	+	8.94278i	0.384836	+	0.666556i
$181$	−10.7082	−	18.5472i	−0.795935	−	1.37860i	−0.922244	−	0.386608i	$-0.873647\pi$
$181$	−10.7082	−	18.5472i	−0.795935	−	1.37860i	0.126310	−	0.991991i	$-0.459687\pi$
$182$	−4.47214			−0.331497
$183$	−11.7082			−0.865495
$184$	−0.381966	−	0.661585i	−0.0281589	−	0.0487727i
$185$	−7.33688	+	12.7079i	−0.539418	+	0.934300i
$186$	−5.23607	−	9.06914i	−0.383927	−	0.664981i
$187$	3.47214	−	6.01392i	0.253908	−	0.439781i
$188$	2.23607	−	3.87298i	0.163082	−	0.282466i
$189$	−17.8885			−1.30120
$190$		0			0
$191$	12.4721			0.902452			0.451226	−	0.892410i	$-0.350987\pi$
$191$	12.4721			0.902452			0.451226	+	0.892410i	$0.350987\pi$
$192$	1.61803	−	2.80252i	0.116772	−	0.202254i
$193$	−10.2361	+	17.7294i	−0.736808	+	1.27619i	0.217117	+	0.976146i	$0.430335\pi$
$193$	−10.2361	+	17.7294i	−0.736808	+	1.27619i	−0.953925	+	0.300044i	$0.902999\pi$
$194$	3.19098	+	5.52694i	0.229099	+	0.396812i
$195$	8.09017	−	14.0126i	0.579349	−	1.00346i
$196$	2.73607	+	4.73901i	0.195433	+	0.338501i
$197$	−10.8541			−0.773323			−0.386661	−	0.922222i	$-0.626372\pi$
$197$	−10.8541			−0.773323			−0.386661	+	0.922222i	$0.626372\pi$
$198$	9.23607			0.656379
$199$	−0.763932	−	1.32317i	−0.0541537	−	0.0937970i	0.837678	−	0.546165i	$-0.183913\pi$
$199$	−0.763932	−	1.32317i	−0.0541537	−	0.0937970i	−0.891831	+	0.452368i	$0.850579\pi$
$200$	1.54508	+	2.67617i	0.109254	+	0.189233i
$201$	−5.52786			−0.389905
$202$	−13.3820			−0.941552
$203$	1.29180	+	2.23746i	0.0906663	+	0.157039i
$204$	−9.09017	+	15.7446i	−0.636439	+	1.10235i
$205$	4.04508	+	7.00629i	0.282521	+	0.489341i
$206$	−8.32624	+	14.4215i	−0.580116	+	1.00479i
$207$	−2.85410	+	4.94345i	−0.198374	+	0.343594i
$208$	−3.61803			−0.250866
$209$		0			0
$210$	5.52786			0.381459
$211$	−1.38197	+	2.39364i	−0.0951385	+	0.164785i	−0.909666	−	0.415340i	$-0.863663\pi$
$211$	−1.38197	+	2.39364i	−0.0951385	+	0.164785i	0.814528	+	0.580124i	$0.196996\pi$
$212$	2.54508	−	4.40822i	0.174797	−	0.302758i
$213$	24.1803	+	41.8816i	1.65681	+	2.86968i
$214$	−8.70820	+	15.0831i	−0.595281	+	1.03106i
$215$	−3.29180	−	5.70156i	−0.224499	−	0.388843i
$216$	−14.4721			−0.984704
$217$	−4.00000			−0.271538
$218$	9.01722	+	15.6183i	0.610723	+	1.05780i
$219$	−5.47214	−	9.47802i	−0.369773	−	0.640465i
$220$	−1.70820			−0.115167
$221$	20.3262			1.36729
$222$	−17.1803	−	29.7572i	−1.15307	−	1.99717i
$223$	7.14590	−	12.3771i	0.478525	−	0.828829i	−0.521172	−	0.853452i	$-0.674505\pi$
$223$	7.14590	−	12.3771i	0.478525	−	0.828829i	0.999697	+	0.0246225i	$0.00783837\pi$
$224$	−0.618034	−	1.07047i	−0.0412941	−	0.0715235i
$225$	11.5451	−	19.9967i	0.769672	−	1.33311i
$226$	−1.57295	+	2.72443i	−0.104631	+	0.181226i
$227$	−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
$229$	6.61803			0.437332			0.218666	−	0.975800i	$-0.429829\pi$
$229$	6.61803			0.437332			0.218666	+	0.975800i	$0.429829\pi$
$230$	0.527864	−	0.914287i	0.0348063	−	0.0602863i
$231$	2.47214	−	4.28187i	0.162655	−	0.281726i
$232$	1.04508	+	1.81014i	0.0686132	+	0.118842i
$233$	9.28115	−	16.0754i	0.608029	−	1.05314i	−0.383536	−	0.923526i	$-0.625294\pi$
$233$	9.28115	−	16.0754i	0.608029	−	1.05314i	0.991565	−	0.129611i	$-0.0413727\pi$
$234$	13.5172	+	23.4125i	0.883648	+	1.53052i
$235$	6.18034			0.403161
$236$	−8.47214			−0.551489
$237$	11.7082	+	20.2792i	0.760530	+	1.31728i
$238$	3.47214	+	6.01392i	0.225065	+	0.389824i
$239$	7.81966			0.505812			0.252906	−	0.967491i	$-0.418614\pi$
$239$	7.81966			0.505812			0.252906	+	0.967491i	$0.418614\pi$
$240$	4.47214			0.288675
$241$	0.708204	+	1.22665i	0.0456194	+	0.0790152i	0.887933	−	0.459972i	$-0.152141\pi$
$241$	0.708204	+	1.22665i	0.0456194	+	0.0790152i	−0.842314	+	0.538987i	$0.818807\pi$
$242$	4.73607	−	8.20311i	0.304446	−	0.527316i
$243$	17.7984	+	30.8277i	1.14177	+	1.97760i
$244$	−1.80902	+	3.13331i	−0.115810	+	0.200590i
$245$	−3.78115	+	6.54915i	−0.241569	+	0.418410i
$246$	−18.9443			−1.20784
$247$		0			0
$248$	−3.23607			−0.205491
$249$	13.7082	−	23.7433i	0.868722	−	1.50467i
$250$	−5.59017	+	9.68246i	−0.353553	+	0.612372i
$251$	7.85410	+	13.6037i	0.495747	+	0.858658i	0.999988	−	0.00490455i	$-0.00156117\pi$
$251$	7.85410	+	13.6037i	0.495747	+	0.858658i	−0.504241	+	0.863563i	$0.668228\pi$
$252$	−4.61803	+	7.99867i	−0.290909	+	0.503869i
$253$	−0.472136	−	0.817763i	−0.0296829	−	0.0514123i
$254$	−15.4164			−0.967311
$255$	−25.1246			−1.57336
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.3090	+	17.8557i	0.643059	+	1.11381i	0.984746	+	0.173997i	$0.0556683\pi$
$257$	10.3090	+	17.8557i	0.643059	+	1.11381i	−0.341687	+	0.939814i	$0.610998\pi$
$258$	15.4164			0.959784
$259$	−13.1246			−0.815524
$260$	−2.50000	−	4.33013i	−0.155043	−	0.268543i
$261$	7.80902	−	13.5256i	0.483366	−	0.837215i
$262$	2.23607	+	3.87298i	0.138145	+	0.239274i
$263$	7.47214	−	12.9421i	0.460752	−	0.798045i	−0.538247	−	0.842787i	$-0.680913\pi$
$263$	7.47214	−	12.9421i	0.460752	−	0.798045i	0.998999	+	0.0447419i	$0.0142466\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	7.03444			0.432122
$266$		0			0
$267$	6.94427			0.424983
$268$	−0.854102	+	1.47935i	−0.0521726	+	0.0903656i
$269$	−0.663119	+	1.14856i	−0.0404311	+	0.0700287i	−0.885533	−	0.464577i	$-0.846206\pi$
$269$	−0.663119	+	1.14856i	−0.0404311	+	0.0700287i	0.845102	+	0.534606i	$0.179540\pi$
$270$	−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	$0.876906\pi$
$272$	2.80902	+	4.86536i	0.170322	+	0.295006i
$273$	14.4721			0.875894
$274$	4.61803			0.278986
$275$	1.90983	+	3.30792i	0.115167	+	0.199475i
$276$	1.23607	+	2.14093i	0.0744025	+	0.128869i
$277$	1.09017			0.0655020			0.0327510	−	0.999464i	$-0.489573\pi$
$277$	1.09017			0.0655020			0.0327510	+	0.999464i	$0.489573\pi$
$278$	−14.0000			−0.839664
$279$	12.0902	+	20.9408i	0.723820	+	1.25369i
$280$	0.854102	−	1.47935i	0.0510424	−	0.0884080i
$281$	−12.9894	−	22.4982i	−0.774880	−	1.34213i	−0.934862	−	0.355012i	$-0.884477\pi$
$281$	−12.9894	−	22.4982i	−0.774880	−	1.34213i	0.159982	−	0.987120i	$-0.448856\pi$
$282$	−7.23607	+	12.5332i	−0.430902	+	0.746343i
$283$	−6.76393	+	11.7155i	−0.402074	+	0.696413i	−0.993976	−	0.109597i	$-0.965044\pi$
$283$	−6.76393	+	11.7155i	−0.402074	+	0.696413i	0.591902	+	0.806010i	$0.298377\pi$
$284$	14.9443			0.886779
$285$		0			0
$286$	−4.47214			−0.264443
$287$	−3.61803	+	6.26662i	−0.213566	+	0.369907i
$288$	−3.73607	+	6.47106i	−0.220150	+	0.381311i
$289$	−7.28115	−	12.6113i	−0.428303	−	0.741843i
$290$	−1.44427	+	2.50155i	−0.0848106	+	0.146896i
$291$	−10.3262	−	17.8856i	−0.605335	−	1.04847i
$292$	−3.38197			−0.197915
$293$	−5.05573			−0.295359			−0.147679	−	0.989035i	$-0.547180\pi$
$293$	−5.05573			−0.295359			−0.147679	+	0.989035i	$0.547180\pi$
$294$	−8.85410	−	15.3358i	−0.516382	−	0.894399i
$295$	−5.85410	−	10.1396i	−0.340839	−	0.590350i
$296$	−10.6180			−0.617161
$297$	−17.8885			−1.03800
$298$	0.954915	+	1.65396i	0.0553167	+	0.0958114i
$299$	1.38197	−	2.39364i	0.0799212	−	0.138428i
$300$	−5.00000	−	8.66025i	−0.288675	−	0.500000i
$301$	2.94427	−	5.09963i	0.169705	−	0.293938i
$302$	2.76393	−	4.78727i	0.159046	−	0.275476i
$303$	43.3050			2.48780
$304$		0			0
$305$	−5.00000			−0.286299
$306$	20.9894	−	36.3546i	1.19988	−	2.07826i
$307$	−0.854102	+	1.47935i	−0.0487462	+	0.0844308i	−0.889369	−	0.457190i	$-0.848856\pi$
$307$	−0.854102	+	1.47935i	−0.0487462	+	0.0844308i	0.840623	+	0.541621i	$0.182189\pi$
$308$	−0.763932	−	1.32317i	−0.0435291	−	0.0753946i
$309$	26.9443	−	46.6688i	1.53281	−	2.65490i
$310$	−2.23607	−	3.87298i	−0.127000	−	0.219971i
$311$	26.7639			1.51764			0.758822	−	0.651298i	$-0.225775\pi$
$311$	26.7639			1.51764			0.758822	+	0.651298i	$0.225775\pi$
$312$	11.7082			0.662847
$313$	−11.2533	−	19.4913i	−0.636073	−	1.10171i	−0.986287	−	0.165042i	$-0.947224\pi$
$313$	−11.2533	−	19.4913i	−0.636073	−	1.10171i	0.350213	−	0.936670i	$-0.386109\pi$
$314$	−5.80902	−	10.0615i	−0.327822	−	0.567804i
$315$	−12.7639			−0.719166
$316$	7.23607			0.407061
$317$	−7.16312	−	12.4069i	−0.402321	−	0.696840i	0.591685	−	0.806169i	$-0.298463\pi$
$317$	−7.16312	−	12.4069i	−0.402321	−	0.696840i	−0.994006	+	0.109329i	$0.965130\pi$
$318$	−8.23607	+	14.2653i	−0.461856	+	0.799958i
$319$	1.29180	+	2.23746i	0.0723267	+	0.125274i
$320$	0.690983	−	1.19682i	0.0386271	−	0.0669041i
$321$	28.1803	−	48.8098i	1.57287	−	2.72430i
$322$	0.944272			0.0526222
$323$		0			0
$324$	24.4164			1.35647
$325$	−5.59017	+	9.68246i	−0.310087	+	0.537086i
$326$	10.3262	−	17.8856i	0.571917	−	0.990590i
$327$	−29.1803	−	50.5418i	−1.61368	−	2.79497i
$328$	−2.92705	+	5.06980i	−0.161619	+	0.279933i
$329$	2.76393	+	4.78727i	0.152381	+	0.263931i
$330$	5.52786			0.304299
$331$	−12.2918			−0.675618			−0.337809	−	0.941215i	$-0.609686\pi$
$331$	−12.2918			−0.675618			−0.337809	+	0.941215i	$0.609686\pi$
$332$	−4.23607	−	7.33708i	−0.232484	−	0.402675i
$333$	39.6697	+	68.7099i	2.17389	+	3.76528i
$334$	3.52786			0.193036
$335$	−2.36068			−0.128978
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$	2.30902	−	3.99933i	0.125780	−	0.217858i	−0.796257	−	0.604958i	$-0.793190\pi$
$337$	2.30902	−	3.99933i	0.125780	−	0.217858i	0.922038	+	0.387100i	$0.126523\pi$
$338$	−0.0450850	−	0.0780895i	−0.00245230	−	0.00424751i
$339$	5.09017	−	8.81643i	0.276460	−	0.478843i
$340$	−3.88197	+	6.72376i	−0.210529	+	0.364647i
$341$	−4.00000			−0.216612
$342$		0			0
$343$	−15.4164			−0.832408
$344$	2.38197	−	4.12569i	0.128427	−	0.222442i
$345$	−1.70820	+	2.95870i	−0.0919666	+	0.159291i
$346$	−7.16312	−	12.4069i	−0.385092	−	0.666998i
$347$	−14.3262	+	24.8138i	−0.769073	+	1.33207i	0.168994	+	0.985617i	$0.445948\pi$
$347$	−14.3262	+	24.8138i	−0.769073	+	1.33207i	−0.938066	+	0.346456i	$0.887385\pi$
$348$	−3.38197	−	5.85774i	−0.181292	−	0.314008i
$349$	−21.9098			−1.17281			−0.586403	−	0.810019i	$-0.699457\pi$
$349$	−21.9098			−1.17281			−0.586403	+	0.810019i	$0.699457\pi$
$350$	−3.81966			−0.204169
$351$	−26.1803	−	45.3457i	−1.39740	−	2.42037i
$352$	−0.618034	−	1.07047i	−0.0329413	−	0.0570560i
$353$	18.7426			0.997570			0.498785	−	0.866726i	$-0.333780\pi$
$353$	18.7426			0.997570			0.498785	+	0.866726i	$0.333780\pi$
$354$	27.4164			1.45717
$355$	10.3262	+	17.8856i	0.548060	+	0.949267i
$356$	1.07295	−	1.85840i	0.0568662	−	0.0984951i
$357$	−11.2361	−	19.4614i	−0.594676	−	1.03001i
$358$	1.70820	−	2.95870i	0.0902814	−	0.156372i
$359$	−10.2361	+	17.7294i	−0.540239	+	0.935721i	0.458651	+	0.888617i	$0.348333\pi$
$359$	−10.2361	+	17.7294i	−0.540239	+	0.935721i	−0.998890	+	0.0471049i	$0.985000\pi$
$360$	−10.3262			−0.544241
$361$		0			0
$362$	21.4164			1.12562
$363$	−15.3262	+	26.5458i	−0.804419	+	1.39329i
$364$	2.23607	−	3.87298i	0.117202	−	0.202999i
$365$	−2.33688	−	4.04760i	−0.122318	−	0.211861i
$366$	5.85410	−	10.1396i	0.305999	−	0.530005i
$367$	17.4164	+	30.1661i	0.909129	+	1.57466i	0.815277	+	0.579072i	$0.196585\pi$
$367$	17.4164	+	30.1661i	0.909129	+	1.57466i	0.0938524	+	0.995586i	$0.470082\pi$
$368$	0.763932			0.0398227
$369$	43.7426			2.27715
$370$	−7.33688	−	12.7079i	−0.381426	−	0.660650i
$371$	3.14590	+	5.44886i	0.163327	+	0.282890i
$372$	10.4721			0.542955
$373$	−2.67376			−0.138442			−0.0692211	−	0.997601i	$-0.522051\pi$
$373$	−2.67376			−0.138442			−0.0692211	+	0.997601i	$0.522051\pi$
$374$	3.47214	+	6.01392i	0.179540	+	0.310972i
$375$	18.0902	−	31.3331i	0.934172	−	1.61803i
$376$	2.23607	+	3.87298i	0.115316	+	0.199734i
$377$	−3.78115	+	6.54915i	−0.194739	+	0.337298i
$378$	8.94427	−	15.4919i	0.460044	−	0.796819i
$379$	8.58359			0.440910			0.220455	−	0.975397i	$-0.429246\pi$
$379$	8.58359			0.440910			0.220455	+	0.975397i	$0.429246\pi$
$380$		0			0
$381$	49.8885			2.55587
$382$	−6.23607	+	10.8012i	−0.319065	+	0.552637i
$383$	12.6180	−	21.8551i	0.644751	−	1.11674i	−0.339607	−	0.940567i	$-0.610294\pi$
$383$	12.6180	−	21.8551i	0.644751	−	1.11674i	0.984359	−	0.176175i	$-0.0563724\pi$
$384$	1.61803	+	2.80252i	0.0825700	+	0.143015i
$385$	1.05573	−	1.82857i	0.0538049	−	0.0931928i
$386$	−10.2361	−	17.7294i	−0.521002	−	0.902402i
$387$	−35.5967			−1.80948
$388$	−6.38197			−0.323995
$389$	5.89919	+	10.2177i	0.299101	+	0.518058i	0.975930	−	0.218082i	$-0.0699800\pi$
$389$	5.89919	+	10.2177i	0.299101	+	0.518058i	−0.676830	+	0.736140i	$0.736647\pi$
$390$	8.09017	+	14.0126i	0.409662	+	0.709555i
$391$	−4.29180			−0.217045
$392$	−5.47214			−0.276385
$393$	−7.23607	−	12.5332i	−0.365011	−	0.632218i
$394$	5.42705	−	9.39993i	0.273411	−	0.473562i
$395$	5.00000	+	8.66025i	0.251577	+	0.435745i
$396$	−4.61803	+	7.99867i	−0.232065	+	0.401948i
$397$	−11.1803	+	19.3649i	−0.561125	+	0.971897i	0.436273	+	0.899814i	$0.356298\pi$
$397$	−11.1803	+	19.3649i	−0.561125	+	0.971897i	−0.997399	+	0.0720832i	$0.977035\pi$
$398$	1.52786			0.0765849
$399$		0			0
$400$	−3.09017			−0.154508
$401$	0.527864	−	0.914287i	0.0263603	−	0.0456573i	−0.852544	−	0.522655i	$-0.824942\pi$
$401$	0.527864	−	0.914287i	0.0263603	−	0.0456573i	0.878905	+	0.476998i	$0.158275\pi$
$402$	2.76393	−	4.78727i	0.137852	−	0.238767i
$403$	−5.85410	−	10.1396i	−0.291614	−	0.505090i
$404$	6.69098	−	11.5891i	0.332889	−	0.576580i
$405$	16.8713	+	29.2220i	0.838343	+	1.45205i
$406$	−2.58359			−0.128222
$407$	−13.1246			−0.650563
$408$	−9.09017	−	15.7446i	−0.450030	−	0.779476i
$409$	−8.63525	−	14.9567i	−0.426986	−	0.739561i	0.569618	−	0.821910i	$-0.307091\pi$
$409$	−8.63525	−	14.9567i	−0.426986	−	0.739561i	−0.996604	+	0.0823485i	$0.973758\pi$
$410$	−8.09017			−0.399545
$411$	−14.9443			−0.737147
$412$	−8.32624	−	14.4215i	−0.410204	−	0.710495i
$413$	5.23607	−	9.06914i	0.257650	−	0.446263i
$414$	−2.85410	−	4.94345i	−0.140271	−	0.242957i
$415$	5.85410	−	10.1396i	0.287367	−	0.497733i
$416$	1.80902	−	3.13331i	0.0886944	−	0.153623i
$417$	45.3050			2.21859
$418$		0			0
$419$	2.47214			0.120772			0.0603859	−	0.998175i	$-0.480767\pi$
$419$	2.47214			0.120772			0.0603859	+	0.998175i	$0.480767\pi$
$420$	−2.76393	+	4.78727i	−0.134866	+	0.233595i
$421$	12.5451	−	21.7287i	0.611410	−	1.05899i	−0.379593	−	0.925154i	$-0.623936\pi$
$421$	12.5451	−	21.7287i	0.611410	−	1.05899i	0.991003	−	0.133840i	$-0.0427307\pi$
$422$	−1.38197	−	2.39364i	−0.0672731	−	0.116520i
$423$	16.7082	−	28.9395i	0.812381	−	1.40708i
$424$	2.54508	+	4.40822i	0.123600	+	0.214082i
$425$	17.3607			0.842117
$426$	−48.3607			−2.34308
$427$	−2.23607	−	3.87298i	−0.108211	−	0.187427i
$428$	−8.70820	−	15.0831i	−0.420927	−	0.729067i
$429$	14.4721			0.698721
$430$	6.58359			0.317489
$431$	−12.3262	−	21.3497i	−0.593734	−	1.02838i	−0.993724	−	0.111858i	$-0.964320\pi$
$431$	−12.3262	−	21.3497i	−0.593734	−	1.02838i	0.399990	−	0.916519i	$-0.369014\pi$
$432$	7.23607	−	12.5332i	0.348145	−	0.603006i
$433$	2.01722	+	3.49393i	0.0969415	+	0.167908i	0.910417	−	0.413691i	$-0.135761\pi$
$433$	2.01722	+	3.49393i	0.0969415	+	0.167908i	−0.813476	+	0.581599i	$0.802427\pi$
$434$	2.00000	−	3.46410i	0.0960031	−	0.166282i
$435$	4.67376	−	8.09519i	0.224090	−	0.388135i
$436$	−18.0344			−0.863693
$437$		0			0
$438$	10.9443			0.522938
$439$	12.3820	−	21.4462i	0.590959	−	1.02357i	−0.403145	−	0.915136i	$-0.632083\pi$
$439$	12.3820	−	21.4462i	0.590959	−	1.02357i	0.994104	−	0.108435i	$-0.0345838\pi$
$440$	0.854102	−	1.47935i	0.0407177	−	0.0705251i
$441$	20.4443	+	35.4105i	0.973537	+	1.68622i
$442$	−10.1631	+	17.6030i	−0.483410	+	0.837291i
$443$	−2.38197	−	4.12569i	−0.113171	−	0.196017i	0.803876	−	0.594796i	$-0.202767\pi$
$443$	−2.38197	−	4.12569i	−0.113171	−	0.196017i	−0.917047	+	0.398779i	$0.869434\pi$
$444$	34.3607			1.63069
$445$	2.96556			0.140581
$446$	7.14590	+	12.3771i	0.338368	+	0.586071i
$447$	−3.09017	−	5.35233i	−0.146160	−	0.253157i
$448$	1.23607			0.0583987
$449$	−1.79837			−0.0848705			−0.0424353	−	0.999099i	$-0.513512\pi$
$449$	−1.79837			−0.0848705			−0.0424353	+	0.999099i	$0.513512\pi$
$450$	11.5451	+	19.9967i	0.544241	+	0.942652i
$451$	−3.61803	+	6.26662i	−0.170367	+	0.295084i
$452$	−1.57295	−	2.72443i	−0.0739853	−	0.128146i
$453$	−8.94427	+	15.4919i	−0.420239	+	0.727875i
$454$	4.47214	−	7.74597i	0.209888	−	0.363536i
$455$	6.18034			0.289739
$456$		0			0
$457$	−26.2148			−1.22628			−0.613138	−	0.789976i	$-0.710093\pi$
$457$	−26.2148			−1.22628			−0.613138	+	0.789976i	$0.710093\pi$
$458$	−3.30902	+	5.73139i	−0.154620	+	0.267810i
$459$	−40.6525	+	70.4122i	−1.89750	+	3.28656i
$460$	0.527864	+	0.914287i	0.0246118	+	0.0426289i
$461$	2.70820	−	4.69075i	0.126134	−	0.218470i	−0.796042	−	0.605242i	$-0.793077\pi$
$461$	2.70820	−	4.69075i	0.126134	−	0.218470i	0.922175	+	0.386772i	$0.126410\pi$
$462$	2.47214	+	4.28187i	0.115014	+	0.199210i
$463$	−22.9443			−1.06631			−0.533155	−	0.846017i	$-0.678994\pi$
$463$	−22.9443			−1.06631			−0.533155	+	0.846017i	$0.678994\pi$
$464$	−2.09017			−0.0970337
$465$	7.23607	+	12.5332i	0.335565	+	0.581215i
$466$	9.28115	+	16.0754i	0.429941	+	0.744680i
$467$	29.3050			1.35607			0.678036	−	0.735029i	$-0.262831\pi$
$467$	29.3050			1.35607			0.678036	+	0.735029i	$0.262831\pi$
$468$	−27.0344			−1.24967
$469$	−1.05573	−	1.82857i	−0.0487490	−	0.0844357i
$470$	−3.09017	+	5.35233i	−0.142539	+	0.246885i
$471$	18.7984	+	32.5597i	0.866183	+	1.50027i
$472$	4.23607	−	7.33708i	0.194981	−	0.337717i
$473$	2.94427	−	5.09963i	0.135378	−	0.234481i
$474$	−23.4164			−1.07555
$475$		0			0
$476$	−6.94427			−0.318290
$477$	19.0172	−	32.9388i	0.870739	−	1.50816i
$478$	−3.90983	+	6.77202i	−0.178831	+	0.309745i
$479$	2.85410	+	4.94345i	0.130407	+	0.225872i	0.923834	−	0.382794i	$-0.125038\pi$
$479$	2.85410	+	4.94345i	0.130407	+	0.225872i	−0.793426	+	0.608666i	$0.791705\pi$
$480$	−2.23607	+	3.87298i	−0.102062	+	0.176777i
$481$	−19.2082	−	33.2696i	−0.875819	−	1.51696i
$482$	−1.41641			−0.0645156
$483$	−3.05573			−0.139040
$484$	4.73607	+	8.20311i	0.215276	+	0.372869i
$485$	−4.40983	−	7.63805i	−0.200240	−	0.346826i
$486$	−35.5967			−1.61470
$487$	−14.7639			−0.669018			−0.334509	−	0.942393i	$-0.608570\pi$
$487$	−14.7639			−0.669018			−0.334509	+	0.942393i	$0.608570\pi$
$488$	−1.80902	−	3.13331i	−0.0818904	−	0.141838i
$489$	−33.4164	+	57.8789i	−1.51114	+	2.61738i
$490$	−3.78115	−	6.54915i	−0.170815	−	0.295860i
$491$	5.23607	−	9.06914i	0.236300	−	0.409284i	−0.723349	−	0.690482i	$-0.757398\pi$
$491$	5.23607	−	9.06914i	0.236300	−	0.409284i	0.959650	+	0.281198i	$0.0907317\pi$
$492$	9.47214	−	16.4062i	0.427037	−	0.739650i
$493$	11.7426			0.528862
$494$		0			0
$495$	−12.7639			−0.573696
$496$	1.61803	−	2.80252i	0.0726519	−	0.125837i
$497$	−9.23607	+	15.9973i	−0.414294	+	0.717579i
$498$	13.7082	+	23.7433i	0.614279	+	1.06396i
$499$	−13.6525	+	23.6468i	−0.611169	+	1.05858i	0.379875	+	0.925038i	$0.375967\pi$
$499$	−13.6525	+	23.6468i	−0.611169	+	1.05858i	−0.991044	+	0.133538i	$0.957366\pi$
$500$	−5.59017	−	9.68246i	−0.250000	−	0.433013i
$501$	−11.4164			−0.510047
$502$	−15.7082			−0.701091
$503$	−5.61803	−	9.73072i	−0.250496	−	0.433871i	0.713167	−	0.700995i	$-0.247260\pi$
$503$	−5.61803	−	9.73072i	−0.250496	−	0.433871i	−0.963662	+	0.267123i	$0.913927\pi$
$504$	−4.61803	−	7.99867i	−0.205704	−	0.356289i
$505$	18.4934			0.822946
$506$	0.944272			0.0419780
$507$	0.145898	+	0.252703i	0.00647956	+	0.0112229i
$508$	7.70820	−	13.3510i	0.341996	−	0.592355i
$509$	−8.84346	−	15.3173i	−0.391979	−	0.678928i	0.600731	−	0.799451i	$-0.294876\pi$
$509$	−8.84346	−	15.3173i	−0.391979	−	0.678928i	−0.992711	+	0.120523i	$0.961543\pi$
$510$	12.5623	−	21.7586i	0.556268	−	0.963485i
$511$	2.09017	−	3.62028i	0.0924637	−	0.160152i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−20.6180			−0.909422
$515$	11.5066	−	19.9300i	0.507040	−	0.878220i
$516$	−7.70820	+	13.3510i	−0.339335	+	0.587745i
$517$	2.76393	+	4.78727i	0.121558	+	0.210544i
$518$	6.56231	−	11.3662i	0.288331	−	0.499404i
$519$	23.1803	+	40.1495i	1.01750	+	1.76237i
$520$	5.00000			0.219265
$521$	−28.2705			−1.23855			−0.619277	−	0.785173i	$-0.712574\pi$
$521$	−28.2705			−1.23855			−0.619277	+	0.785173i	$0.712574\pi$
$522$	7.80902	+	13.5256i	0.341791	+	0.592000i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−4.47214			−0.195366
$525$	12.3607			0.539464
$526$	7.47214	+	12.9421i	0.325801	+	0.564303i
$527$	−9.09017	+	15.7446i	−0.395974	+	0.685847i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	11.2082	−	19.4132i	0.487313	−	0.844051i
$530$	−3.51722	+	6.09201i	−0.152778	+	0.264620i
$531$	−63.3050			−2.74720
$532$		0			0
$533$	−21.1803			−0.917422
$534$	−3.47214	+	6.01392i	−0.150254	+	0.260248i
$535$	12.0344	−	20.8443i	0.520294	−	0.901176i
$536$	−0.854102	−	1.47935i	−0.0368916	−	0.0638981i
$537$	−5.52786	+	9.57454i	−0.238545	+	0.413172i
$538$	−0.663119	−	1.14856i	−0.0285891	−	0.0495178i
$539$	−6.76393			−0.291343
$540$	20.0000			0.860663
$541$	12.1910	+	21.1154i	0.524131	+	0.907822i	0.999605	+	0.0280923i	$0.00894323\pi$
$541$	12.1910	+	21.1154i	0.524131	+	0.907822i	−0.475474	+	0.879730i	$0.657723\pi$
$542$	−13.0000	−	22.5167i	−0.558398	−	0.967173i
$543$	−69.3050			−2.97416
$544$	−5.61803			−0.240871
$545$	−12.4615	−	21.5839i	−0.533792	−	0.924554i
$546$	−7.23607	+	12.5332i	−0.309675	+	0.536373i
$547$	11.4721	+	19.8703i	0.490513	+	0.849594i	0.999940	−	0.0109201i	$-0.00347604\pi$
$547$	11.4721	+	19.8703i	0.490513	+	0.849594i	−0.509427	+	0.860514i	$0.670143\pi$
$548$	−2.30902	+	3.99933i	−0.0986363	+	0.170843i
$549$	−13.5172	+	23.4125i	−0.576901	+	0.999222i
$550$	−3.81966			−0.162871
$551$		0			0
$552$	−2.47214			−0.105221
$553$	−4.47214	+	7.74597i	−0.190175	+	0.329392i
$554$	−0.545085	+	0.944115i	−0.0231584	+	0.0401116i
$555$	23.7426	+	41.1235i	1.00782	+	1.74559i
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−11.4721	−	19.8703i	−0.486090	−	0.841933i	0.513782	−	0.857921i	$-0.328244\pi$
$557$	−11.4721	−	19.8703i	−0.486090	−	0.841933i	−0.999872	+	0.0159881i	$0.994911\pi$
$558$	−24.1803			−1.02364
$559$	17.2361			0.729008
$560$	0.854102	+	1.47935i	0.0360924	+	0.0625139i
$561$	−11.2361	−	19.4614i	−0.474387	−	0.821663i
$562$	25.9787			1.09585
$563$	−39.7082			−1.67350			−0.836751	−	0.547584i	$-0.815548\pi$
$563$	−39.7082			−1.67350			−0.836751	+	0.547584i	$0.815548\pi$
$564$	−7.23607	−	12.5332i	−0.304693	−	0.527744i
$565$	2.17376	−	3.76507i	0.0914509	−	0.158398i
$566$	−6.76393	−	11.7155i	−0.284309	−	0.492438i
$567$	−15.0902	+	26.1369i	−0.633728	+	1.09765i
$568$	−7.47214	+	12.9421i	−0.313524	+	0.543039i
$569$	−19.0902			−0.800302			−0.400151	−	0.916449i	$-0.631042\pi$
$569$	−19.0902			−0.800302			−0.400151	+	0.916449i	$0.631042\pi$
$570$		0			0
$571$	34.5410			1.44550			0.722748	−	0.691111i	$-0.242879\pi$
$571$	34.5410			1.44550			0.722748	+	0.691111i	$0.242879\pi$
$572$	2.23607	−	3.87298i	0.0934947	−	0.161938i
$573$	20.1803	−	34.9534i	0.843046	−	1.46020i
$574$	−3.61803	−	6.26662i	−0.151014	−	0.261564i
$575$	1.18034	−	2.04441i	0.0492236	−	0.0852577i
$576$	−3.73607	−	6.47106i	−0.155669	−	0.269627i
$577$	−18.9230			−0.787774			−0.393887	−	0.919159i	$-0.628870\pi$
$577$	−18.9230			−0.787774			−0.393887	+	0.919159i	$0.628870\pi$
$578$	14.5623			0.605712
$579$	33.1246	+	57.3735i	1.37661	+	2.38436i
$580$	−1.44427	−	2.50155i	−0.0599701	−	0.103871i
$581$	10.4721			0.434457
$582$	20.6525			0.856073
$583$	3.14590	+	5.44886i	0.130290	+	0.225669i
$584$	1.69098	−	2.92887i	0.0699734	−	0.121197i
$585$	−18.6803	−	32.3553i	−0.772337	−	1.33773i
$586$	2.52786	−	4.37839i	0.104425	−	0.180870i
$587$	−21.5623	+	37.3470i	−0.889972	+	1.54148i	−0.0500644	+	0.998746i	$0.515943\pi$
$587$	−21.5623	+	37.3470i	−0.889972	+	1.54148i	−0.839907	+	0.542730i	$0.817391\pi$
$588$	17.7082			0.730274
$589$		0			0
$590$	11.7082			0.482019
$591$	−17.5623	+	30.4188i	−0.722417	+	1.25126i
$592$	5.30902	−	9.19549i	0.218199	−	0.377932i
$593$	−14.9615	−	25.9141i	−0.614395	−	1.06416i	−0.990490	−	0.137582i	$-0.956067\pi$
$593$	−14.9615	−	25.9141i	−0.614395	−	1.06416i	0.376095	−	0.926581i	$-0.377266\pi$
$594$	8.94427	−	15.4919i	0.366988	−	0.635642i
$595$	−4.79837	−	8.31103i	−0.196714	−	0.340719i
$596$	−1.90983			−0.0782297
$597$	−4.94427			−0.202356
$598$	1.38197	+	2.39364i	0.0565128	+	0.0978830i
$599$	0.562306	+	0.973942i	0.0229752	+	0.0397942i	0.877284	−	0.479971i	$-0.159353\pi$
$599$	0.562306	+	0.973942i	0.0229752	+	0.0397942i	−0.854309	+	0.519765i	$0.826019\pi$
$600$	10.0000			0.408248
$601$	−7.52786			−0.307068			−0.153534	−	0.988143i	$-0.549065\pi$
$601$	−7.52786			−0.307068			−0.153534	+	0.988143i	$0.549065\pi$
$602$	2.94427	+	5.09963i	0.120000	+	0.207845i
$603$	−6.38197	+	11.0539i	−0.259894	+	0.450149i
$604$	2.76393	+	4.78727i	0.112463	+	0.194791i
$605$	−6.54508	+	11.3364i	−0.266096	+	0.460891i
$606$	−21.6525	+	37.5032i	−0.879572	+	1.52346i
$607$	−23.7771			−0.965082			−0.482541	−	0.875873i	$-0.660286\pi$
$607$	−23.7771			−0.965082			−0.482541	+	0.875873i	$0.660286\pi$
$608$		0			0
$609$	8.36068			0.338792
$610$	2.50000	−	4.33013i	0.101222	−	0.175322i
$611$	−8.09017	+	14.0126i	−0.327293	+	0.566889i
$612$	20.9894	+	36.3546i	0.848444	+	1.46955i
$613$	−5.30902	+	9.19549i	−0.214429	+	0.371402i	−0.953096	−	0.302669i	$-0.902122\pi$
$613$	−5.30902	+	9.19549i	−0.214429	+	0.371402i	0.738667	+	0.674071i	$0.235456\pi$
$614$	−0.854102	−	1.47935i	−0.0344688	−	0.0597016i
$615$	26.1803			1.05569
$616$	1.52786			0.0615594
$617$	−12.5279	−	21.6989i	−0.504353	−	0.873565i	−0.999987	−	0.00503351i	$-0.998398\pi$
$617$	−12.5279	−	21.6989i	−0.504353	−	0.873565i	0.495635	−	0.868531i	$-0.334936\pi$
$618$	26.9443	+	46.6688i	1.08386	+	1.87730i
$619$	−22.3607			−0.898752			−0.449376	−	0.893343i	$-0.648354\pi$
$619$	−22.3607			−0.898752			−0.449376	+	0.893343i	$0.648354\pi$
$620$	4.47214			0.179605
$621$	5.52786	+	9.57454i	0.221826	+	0.384213i
$622$	−13.3820	+	23.1782i	−0.536568	+	0.929363i
$623$	1.32624	+	2.29711i	0.0531346	+	0.0920318i
$624$	−5.85410	+	10.1396i	−0.234352	+	0.405909i
$625$		0			0
$626$	22.5066			0.899544
$627$		0			0
$628$	11.6180			0.463610
$629$	−29.8262	+	51.6606i	−1.18925	+	2.05984i
$630$	6.38197	−	11.0539i	0.254264	−	0.440397i
$631$	−4.56231	−	7.90215i	−0.181623	−	0.314579i	0.760811	−	0.648974i	$-0.224802\pi$
$631$	−4.56231	−	7.90215i	−0.181623	−	0.314579i	−0.942433	+	0.334394i	$0.891468\pi$
$632$	−3.61803	+	6.26662i	−0.143918	+	0.249273i
$633$	4.47214	+	7.74597i	0.177751	+	0.307875i
$634$	14.3262			0.568968
$635$	21.3050			0.845461
$636$	−8.23607	−	14.2653i	−0.326581	−	0.565655i
$637$	−9.89919	−	17.1459i	−0.392220	−	0.679345i
$638$	−2.58359			−0.102285
$639$	111.666			4.41742
$640$	0.690983	+	1.19682i	0.0273135	+	0.0473084i
$641$	10.1353	−	17.5548i	0.400319	−	0.693372i	−0.593446	−	0.804874i	$-0.702233\pi$
$641$	10.1353	−	17.5548i	0.400319	−	0.693372i	0.993764	+	0.111502i	$0.0355662\pi$
$642$	28.1803	+	48.8098i	1.11219	+	1.92637i
$643$	−7.41641	+	12.8456i	−0.292475	+	0.506581i	−0.974394	−	0.224846i	$-0.927812\pi$
$643$	−7.41641	+	12.8456i	−0.292475	+	0.506581i	0.681920	+	0.731427i	$0.261145\pi$
$644$	−0.472136	+	0.817763i	−0.0186048	+	0.0322244i
$645$	−21.3050			−0.838882
$646$		0			0
$647$	−32.0689			−1.26076			−0.630379	−	0.776288i	$-0.717100\pi$
$647$	−32.0689			−1.26076			−0.630379	+	0.776288i	$0.717100\pi$
$648$	−12.2082	+	21.1452i	−0.479584	+	0.830663i
$649$	5.23607	−	9.06914i	0.205534	−	0.355995i
$650$	−5.59017	−	9.68246i	−0.219265	−	0.379777i
$651$	−6.47214	+	11.2101i	−0.253663	+	0.439357i
$652$	10.3262	+	17.8856i	0.404407	+	0.700453i
$653$	38.3951			1.50252			0.751259	−	0.660008i	$-0.229447\pi$
$653$	38.3951			1.50252			0.751259	+	0.660008i	$0.229447\pi$
$654$	58.3607			2.28208
$655$	−3.09017	−	5.35233i	−0.120743	−	0.209133i
$656$	−2.92705	−	5.06980i	−0.114282	−	0.197942i
$657$	−25.2705			−0.985896
$658$	−5.52786			−0.215499
$659$	9.27051	+	16.0570i	0.361128	+	0.625492i	0.988147	−	0.153512i	$-0.0490585\pi$
$659$	9.27051	+	16.0570i	0.361128	+	0.625492i	−0.627019	+	0.779004i	$0.715725\pi$
$660$	−2.76393	+	4.78727i	−0.107586	+	0.186344i
$661$	2.70820	+	4.69075i	0.105337	+	0.182449i	0.913876	−	0.405994i	$-0.133075\pi$
$661$	2.70820	+	4.69075i	0.105337	+	0.182449i	−0.808539	+	0.588443i	$0.799741\pi$
$662$	6.14590	−	10.6450i	0.238867	−	0.413730i
$663$	32.8885	−	56.9646i	1.27729	−	2.21232i
$664$	8.47214			0.328783
$665$		0			0
$666$	−79.3394			−3.07434
$667$	0.798374	−	1.38282i	0.0309132	−	0.0535432i
$668$	−1.76393	+	3.05522i	−0.0682486	+	0.118210i
$669$	−23.1246	−	40.0530i	−0.894049	−	1.54854i
$670$	1.18034	−	2.04441i	0.0456005	−	0.0789824i
$671$	−2.23607	−	3.87298i	−0.0863224	−	0.149515i
$672$	−4.00000			−0.154303
$673$	−32.6180			−1.25733			−0.628666	−	0.777675i	$-0.716399\pi$
$673$	−32.6180			−1.25733			−0.628666	+	0.777675i	$0.716399\pi$
$674$	2.30902	+	3.99933i	0.0889400	+	0.154049i
$675$	−22.3607	−	38.7298i	−0.860663	−	1.49071i
$676$	0.0901699			0.00346807
$677$	4.38197			0.168413			0.0842063	−	0.996448i	$-0.473165\pi$
$677$	4.38197			0.168413			0.0842063	+	0.996448i	$0.473165\pi$
$678$	5.09017	+	8.81643i	0.195487	+	0.338593i
$679$	3.94427	−	6.83168i	0.151367	−	0.262176i
$680$	−3.88197	−	6.72376i	−0.148867	−	0.257845i
$681$	−14.4721	+	25.0665i	−0.554573	+	0.960549i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−2.18034			−0.0834284			−0.0417142	−	0.999130i	$-0.513282\pi$
$683$	−2.18034			−0.0834284			−0.0417142	+	0.999130i	$0.513282\pi$
$684$		0			0
$685$	−6.38197			−0.243842
$686$	7.70820	−	13.3510i	0.294301	−	0.509744i
$687$	10.7082	−	18.5472i	0.408543	−	0.707618i
$688$	2.38197	+	4.12569i	0.0908116	+	0.157290i
$689$	−9.20820	+	15.9491i	−0.350805	+	0.607611i
$690$	−1.70820	−	2.95870i	−0.0650302	−	0.112636i
$691$	22.3607			0.850640			0.425320	−	0.905043i	$-0.360161\pi$
$691$	22.3607			0.850640			0.425320	+	0.905043i	$0.360161\pi$
$692$	14.3262			0.544602
$693$	−5.70820	−	9.88690i	−0.216837	−	0.375572i
$694$	−14.3262	−	24.8138i	−0.543817	−	0.941918i
$695$	19.3475			0.733893
$696$	6.76393			0.256386
$697$	16.4443	+	28.4823i	0.622871	+	1.07884i
$698$	10.9549	−	18.9745i	0.414650	−	0.718194i
$699$	−30.0344	−	52.0212i	−1.13601	−	1.96762i
$700$	1.90983	−	3.30792i	0.0721848	−	0.125028i
$701$	19.8156	−	34.3216i	0.748425	−	1.29631i	−0.200153	−	0.979765i	$-0.564144\pi$
$701$	19.8156	−	34.3216i	0.748425	−	1.29631i	0.948578	−	0.316545i	$-0.102523\pi$
$702$	52.3607			1.97623
$703$		0			0
$704$	1.23607			0.0465861
$705$	10.0000	−	17.3205i	0.376622	−	0.652328i
$706$	−9.37132	+	16.2316i	−0.352694	+	0.610885i
$707$	8.27051	+	14.3249i	0.311045	+	0.538745i
$708$	−13.7082	+	23.7433i	−0.515186	+	0.892328i
$709$	−9.04508	−	15.6665i	−0.339695	−	0.588370i	0.644680	−	0.764453i	$-0.276991\pi$
$709$	−9.04508	−	15.6665i	−0.339695	−	0.588370i	−0.984375	+	0.176083i	$0.943657\pi$
$710$	−20.6525			−0.775074
$711$	54.0689			2.02774
$712$	1.07295	+	1.85840i	0.0402105	+	0.0696466i
$713$	1.23607	+	2.14093i	0.0462911	+	0.0801786i
$714$	22.4721			0.840999
$715$	6.18034			0.231132
$716$	1.70820	+	2.95870i	0.0638386	+	0.110572i
$717$	12.6525	−	21.9147i	0.472515	−	0.818421i
$718$	−10.2361	−	17.7294i	−0.382007	−	0.661655i
$719$	−12.8541	+	22.2640i	−0.479377	+	0.830306i	−0.999720	−	0.0236517i	$-0.992471\pi$
$719$	−12.8541	+	22.2640i	−0.479377	+	0.830306i	0.520343	+	0.853957i	$0.325804\pi$
$720$	5.16312	−	8.94278i	0.192418	−	0.333278i
$721$	20.5836			0.766573
$722$		0			0
$723$	4.58359			0.170466
$724$	−10.7082	+	18.5472i	−0.397967	+	0.689300i
$725$	−3.22949	+	5.59364i	−0.119940	+	0.207743i
$726$	−15.3262	−	26.5458i	−0.568810	−	0.985208i
$727$	6.52786	−	11.3066i	0.242105	−	0.419338i	−0.719209	−	0.694794i	$-0.755495\pi$
$727$	6.52786	−	11.3066i	0.242105	−	0.419338i	0.961314	+	0.275456i	$0.0888288\pi$
$728$	2.23607	+	3.87298i	0.0828742	+	0.143542i
$729$	41.9443			1.55349
$730$	4.67376			0.172984
$731$	−13.3820	−	23.1782i	−0.494950	−	0.857278i
$732$	5.85410	+	10.1396i	0.216374	+	0.374770i
$733$	10.0902			0.372689			0.186344	−	0.982484i	$-0.440336\pi$
$733$	10.0902			0.372689			0.186344	+	0.982484i	$0.440336\pi$
$734$	−34.8328			−1.28570
$735$	12.2361	+	21.1935i	0.451334	+	0.781734i
$736$	−0.381966	+	0.661585i	−0.0140795	+	0.0243863i
$737$	−1.05573	−	1.82857i	−0.0388882	−	0.0673564i
$738$	−21.8713	+	37.8822i	−0.805095	+	1.39446i
$739$	15.5623	−	26.9547i	0.572469	−	0.991545i	−0.423843	−	0.905736i	$-0.639319\pi$
$739$	15.5623	−	26.9547i	0.572469	−	0.991545i	0.996312	−	0.0858091i	$-0.0273475\pi$
$740$	14.6738			0.539418
$741$		0			0
$742$	−6.29180			−0.230979
$743$	20.9443	−	36.2765i	0.768371	−	1.33086i	−0.170075	−	0.985431i	$-0.554401\pi$
$743$	20.9443	−	36.2765i	0.768371	−	1.33086i	0.938446	−	0.345426i	$-0.112266\pi$
$744$	−5.23607	+	9.06914i	−0.191964	+	0.332491i
$745$	−1.31966	−	2.28572i	−0.0483486	−	0.0837422i
$746$	1.33688	−	2.31555i	0.0489467	−	0.0847782i
$747$	−31.6525	−	54.8237i	−1.15810	−	2.00589i
$748$	−6.94427			−0.253908
$749$	21.5279			0.786611
$750$	18.0902	+	31.3331i	0.660560	+	1.14412i
$751$	17.0344	+	29.5045i	0.621596	+	1.07664i	0.989189	+	0.146648i	$0.0468486\pi$
$751$	17.0344	+	29.5045i	0.621596	+	1.07664i	−0.367593	+	0.929987i	$0.619818\pi$
$752$	−4.47214			−0.163082
$753$	50.8328			1.85245
$754$	−3.78115	−	6.54915i	−0.137701	−	0.238506i
$755$	−3.81966	+	6.61585i	−0.139012	+	0.240775i
$756$	8.94427	+	15.4919i	0.325300	+	0.563436i
$757$	−12.2812	+	21.2716i	−0.446366	+	0.773129i	−0.998146	−	0.0608608i	$-0.980615\pi$
$757$	−12.2812	+	21.2716i	−0.446366	+	0.773129i	0.551780	+	0.833990i	$0.313949\pi$
$758$	−4.29180	+	7.43361i	−0.155885	+	0.270001i
$759$	−3.05573			−0.110916
$760$		0			0
$761$	−18.3607			−0.665574			−0.332787	−	0.943002i	$-0.607989\pi$
$761$	−18.3607			−0.665574			−0.332787	+	0.943002i	$0.607989\pi$
$762$	−24.9443	+	43.2047i	−0.903636	+	1.56514i
$763$	11.1459	−	19.3053i	0.403509	−	0.698897i
$764$	−6.23607	−	10.8012i	−0.225613	−	0.390773i
$765$	−29.0066	+	50.2409i	−1.04874	+	1.81646i
$766$	12.6180	+	21.8551i	0.455908	+	0.789656i
$767$	30.6525			1.10680
$768$	−3.23607			−0.116772
$769$	1.87132	+	3.24123i	0.0674816	+	0.116882i	0.897792	−	0.440419i	$-0.145170\pi$
$769$	1.87132	+	3.24123i	0.0674816	+	0.116882i	−0.830310	+	0.557301i	$0.811837\pi$
$770$	1.05573	+	1.82857i	0.0380458	+	0.0658973i
$771$	66.7214			2.40291
$772$	20.4721			0.736808
$773$	−7.42705	−	12.8640i	−0.267132	−	0.462687i	0.700988	−	0.713173i	$-0.252743\pi$
$773$	−7.42705	−	12.8640i	−0.267132	−	0.462687i	−0.968120	+	0.250486i	$0.919409\pi$
$774$	17.7984	−	30.8277i	0.639749	−	1.10808i
$775$	−5.00000	−	8.66025i	−0.179605	−	0.311086i
$776$	3.19098	−	5.52694i	0.114550	−	0.198406i
$777$	−21.2361	+	36.7819i	−0.761840	+	1.31955i
$778$	−11.7984			−0.422992
$779$		0			0
$780$	−16.1803			−0.579349
$781$	−9.23607	+	15.9973i	−0.330492	+	0.572430i
$782$	2.14590	−	3.71680i	0.0767372	−	0.132913i
$783$	−15.1246	−	26.1966i	−0.540510	−	0.936190i
$784$	2.73607	−	4.73901i	0.0977167	−	0.169250i
$785$	8.02786	+	13.9047i	0.286527	+	0.496279i
$786$	14.4721			0.516204
$787$	−19.5279			−0.696093			−0.348047	−	0.937477i	$-0.613155\pi$
$787$	−19.5279			−0.696093			−0.348047	+	0.937477i	$0.613155\pi$
$788$	5.42705	+	9.39993i	0.193331	+	0.334859i
$789$	−24.1803	−	41.8816i	−0.860843	−	1.49102i
$790$	−10.0000			−0.355784
$791$	3.88854			0.138261
$792$	−4.61803	−	7.99867i	−0.164095	−	0.284220i
$793$	6.54508	−	11.3364i	0.232423	−	0.402568i
$794$	−11.1803	−	19.3649i	−0.396775	−	0.687235i
$795$	11.3820	−	19.7141i	0.403677	−	0.699189i
$796$	−0.763932	+	1.32317i	−0.0270769	+	0.0468985i
$797$	−48.5623			−1.72017			−0.860083	−	0.510155i	$-0.829588\pi$
$797$	−48.5623			−1.72017			−0.860083	+	0.510155i	$0.829588\pi$
$798$		0			0
$799$	25.1246			0.888845
$800$	1.54508	−	2.67617i	0.0546270	−	0.0946167i
$801$	8.01722	−	13.8862i	0.283275	−	0.490646i
$802$	0.527864	+	0.914287i	0.0186395	+	0.0322846i
$803$	2.09017	−	3.62028i	0.0737605	−	0.127757i
$804$	2.76393	+	4.78727i	0.0974764	+	0.168834i
$805$	−1.30495			−0.0459935
$806$	11.7082			0.412404
$807$	2.14590	+	3.71680i	0.0755392	+	0.130838i
$808$	6.69098	+	11.5891i	0.235388	+	0.407704i
$809$	−39.7426			−1.39728			−0.698639	−	0.715475i	$-0.746210\pi$
$809$	−39.7426			−1.39728			−0.698639	+	0.715475i	$0.746210\pi$
$810$	−33.7426			−1.18560
$811$	−21.7984	−	37.7559i	−0.765444	−	1.32579i	−0.940011	−	0.341143i	$-0.889186\pi$
$811$	−21.7984	−	37.7559i	−0.765444	−	1.32579i	0.174567	−	0.984645i	$-0.444147\pi$
$812$	1.29180	−	2.23746i	0.0453332	−	0.0785193i
$813$	42.0689	+	72.8654i	1.47542	+	2.55550i
$814$	6.56231	−	11.3662i	0.230009	−	0.398387i
$815$	−14.2705	+	24.7172i	−0.499874	+	0.865807i
$816$	18.1803			0.636439
$817$		0			0
$818$	17.2705			0.603849
$819$	16.7082	−	28.9395i	0.583832	−	1.01123i
$820$	4.04508	−	7.00629i	0.141260	−	0.244670i
$821$	7.13525	+	12.3586i	0.249022	+	0.431319i	0.963255	−	0.268589i	$-0.0865575\pi$
$821$	7.13525	+	12.3586i	0.249022	+	0.431319i	−0.714233	+	0.699908i	$0.753224\pi$
$822$	7.47214	−	12.9421i	0.260621	−	0.451408i
$823$	−16.4164	−	28.4341i	−0.572240	−	0.991149i	−0.996335	−	0.0855313i	$-0.972741\pi$
$823$	−16.4164	−	28.4341i	−0.572240	−	0.991149i	0.424095	−	0.905617i	$-0.360592\pi$
$824$	16.6525			0.580116
$825$	12.3607			0.430344
$826$	5.23607	+	9.06914i	0.182186	+	0.315556i
$827$	18.2705	+	31.6455i	0.635328	+	1.10042i	0.986446	+	0.164089i	$0.0524684\pi$
$827$	18.2705	+	31.6455i	0.635328	+	1.10042i	−0.351118	+	0.936331i	$0.614198\pi$
$828$	5.70820			0.198374
$829$	43.2705			1.50285			0.751423	−	0.659820i	$-0.229368\pi$
$829$	43.2705			1.50285			0.751423	+	0.659820i	$0.229368\pi$
$830$	5.85410	+	10.1396i	0.203199	+	0.351951i
$831$	1.76393	−	3.05522i	0.0611901	−	0.105984i
$832$	1.80902	+	3.13331i	0.0627164	+	0.108628i
$833$	−15.3713	+	26.6239i	−0.532585	+	0.922464i
$834$	−22.6525	+	39.2352i	−0.784391	+	1.35861i
$835$	−4.87539			−0.168720
$836$		0			0
$837$	46.8328			1.61878
$838$	−1.23607	+	2.14093i	−0.0426993	+	0.0739573i
$839$	11.0000	−	19.0526i	0.379762	−	0.657767i	−0.611265	−	0.791426i	$-0.709339\pi$
$839$	11.0000	−	19.0526i	0.379762	−	0.657767i	0.991027	+	0.133658i	$0.0426725\pi$
$840$	−2.76393	−	4.78727i	−0.0953647	−	0.165177i
$841$	12.3156	−	21.3312i	0.424676	−	0.735560i
$842$	12.5451	+	21.7287i	0.432332	+	0.748821i
$843$	−84.0689			−2.89549
$844$	2.76393			0.0951385
$845$	0.0623059	+	0.107917i	0.00214339	+	0.00371246i
$846$	16.7082	+	28.9395i	0.574440	+	0.994959i
$847$	−11.7082			−0.402299
$848$	−5.09017			−0.174797
$849$	21.8885	+	37.9121i	0.751213	+	1.30114i
$850$	−8.68034	+	15.0348i	−0.297733	+	0.515689i
$851$	4.05573	+	7.02473i	0.139029	+	0.240805i
$852$	24.1803	−	41.8816i	0.828405	−	1.43484i
$853$	8.95492	−	15.5104i	0.306610	−	0.531065i	−0.671008	−	0.741450i	$-0.734138\pi$
$853$	8.95492	−	15.5104i	0.306610	−	0.531065i	0.977619	+	0.210385i	$0.0674718\pi$
$854$	4.47214			0.153033
$855$		0			0
$856$	17.4164			0.595281
$857$	−7.28115	+	12.6113i	−0.248719	+	0.430795i	−0.963171	−	0.268890i	$-0.913343\pi$
$857$	−7.28115	+	12.6113i	−0.248719	+	0.430795i	0.714451	+	0.699685i	$0.246676\pi$
$858$	−7.23607	+	12.5332i	−0.247035	+	0.427878i
$859$	15.0344	+	26.0404i	0.512969	+	0.888488i	0.999887	+	0.0150401i	$0.00478759\pi$
$859$	15.0344	+	26.0404i	0.512969	+	0.888488i	−0.486918	+	0.873447i	$0.661879\pi$
$860$	−3.29180	+	5.70156i	−0.112249	+	0.194422i
$861$	11.7082	+	20.2792i	0.399015	+	0.691113i
$862$	24.6525			0.839667
$863$	−9.88854			−0.336610			−0.168305	−	0.985735i	$-0.553829\pi$
$863$	−9.88854			−0.336610			−0.168305	+	0.985735i	$0.553829\pi$
$864$	7.23607	+	12.5332i	0.246176	+	0.426389i
$865$	9.89919	+	17.1459i	0.336582	+	0.582978i
$866$	−4.03444			−0.137096
$867$	−47.1246			−1.60044
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	−4.47214	+	7.74597i	−0.151707	+	0.262764i
$870$	4.67376	+	8.09519i	0.158455	+	0.274453i
$871$	3.09017	−	5.35233i	0.104706	−	0.181357i
$872$	9.01722	−	15.6183i	0.305362	−	0.528902i
$873$	−47.6869			−1.61396
$874$		0			0
$875$	13.8197			0.467190
$876$	−5.47214	+	9.47802i	−0.184886	+	0.320233i
$877$	−20.3713	+	35.2842i	−0.687891	+	1.19146i	0.284628	+	0.958638i	$0.408130\pi$
$877$	−20.3713	+	35.2842i	−0.687891	+	1.19146i	−0.972519	+	0.232824i	$0.925203\pi$
$878$	12.3820	+	21.4462i	0.417871	+	0.723774i
$879$	−8.18034	+	14.1688i	−0.275916	+	0.477901i
$880$	0.854102	+	1.47935i	0.0287918	+	0.0498688i
$881$	−46.2148			−1.55702			−0.778508	−	0.627635i	$-0.784023\pi$
$881$	−46.2148			−1.55702			−0.778508	+	0.627635i	$0.784023\pi$
$882$	−40.8885			−1.37679
$883$	20.0902	+	34.7972i	0.676088	+	1.17102i	0.976150	+	0.217099i	$0.0696594\pi$
$883$	20.0902	+	34.7972i	0.676088	+	1.17102i	−0.300062	+	0.953920i	$0.597007\pi$
$884$	−10.1631	−	17.6030i	−0.341823	−	0.592054i
$885$	−37.8885			−1.27361
$886$	4.76393			0.160047
$887$	−5.47214	−	9.47802i	−0.183736	−	0.318241i	0.759414	−	0.650608i	$-0.225486\pi$
$887$	−5.47214	−	9.47802i	−0.183736	−	0.318241i	−0.943150	+	0.332367i	$0.892153\pi$
$888$	−17.1803	+	29.7572i	−0.576534	+	0.998587i
$889$	9.52786	+	16.5027i	0.319554	+	0.553484i
$890$	−1.48278	+	2.56825i	−0.0497029	+	0.0860879i
$891$	−15.0902	+	26.1369i	−0.505540	+	0.875620i
$892$	−14.2918			−0.478525
$893$		0			0
$894$	6.18034			0.206701
$895$	−2.36068	+	4.08882i	−0.0789088	+	0.136674i
$896$	−0.618034	+	1.07047i	−0.0206471	+	0.0357618i
$897$	−4.47214	−	7.74597i	−0.149320	−	0.258630i
$898$	0.899187	−	1.55744i	0.0300063	−	0.0519724i
$899$	−3.38197	−	5.85774i	−0.112795	−	0.195366i
$900$	−23.0902			−0.769672
$901$	28.5967			0.952696
$902$	−3.61803	−	6.26662i	−0.120467	−	0.208656i
$903$	−9.52786	−	16.5027i	−0.317067	−	0.549177i
$904$	3.14590			0.104631
$905$	−29.5967			−0.983829
$906$	−8.94427	−	15.4919i	−0.297154	−	0.514685i
$907$	−6.85410	+	11.8717i	−0.227587	+	0.394192i	−0.957092	−	0.289783i	$-0.906417\pi$
$907$	−6.85410	+	11.8717i	−0.227587	+	0.394192i	0.729506	+	0.683975i	$0.239750\pi$
$908$	4.47214	+	7.74597i	0.148413	+	0.257059i
$909$	49.9959	−	86.5955i	1.65826	−	2.87219i
$910$	−3.09017	+	5.35233i	−0.102438	+	0.177428i
$911$	46.0689			1.52633			0.763165	−	0.646204i	$-0.223644\pi$
$911$	46.0689			1.52633			0.763165	+	0.646204i	$0.223644\pi$
$912$		0			0
$913$	10.4721			0.346577
$914$	13.1074	−	22.7027i	0.433554	−	0.750937i
$915$	−8.09017	+	14.0126i	−0.267453	+	0.463242i
$916$	−3.30902	−	5.73139i	−0.109333	−	0.189370i
$917$	2.76393	−	4.78727i	0.0912731	−	0.158090i
$918$	−40.6525	−	70.4122i	−1.34173	−	2.32395i
$919$	10.1115			0.333546			0.166773	−	0.985995i	$-0.446665\pi$
$919$	10.1115			0.333546			0.166773	+	0.985995i	$0.446665\pi$
$920$	−1.05573			−0.0348063
$921$	2.76393	+	4.78727i	0.0910747	+	0.157746i
$922$	2.70820	+	4.69075i	0.0891899	+	0.154482i
$923$	−54.0689			−1.77970
$924$	−4.94427			−0.162655
$925$	−16.4058	−	28.4156i	−0.539418	−	0.934300i
$926$	11.4721	−	19.8703i	0.376998	−	0.652979i
$927$	−62.2148	−	107.759i	−2.04340	−	3.53928i
$928$	1.04508	−	1.81014i	0.0343066	−	0.0594208i
$929$	−5.07953	+	8.79800i	−0.166654	+	0.288653i	−0.937241	−	0.348681i	$-0.886630\pi$
$929$	−5.07953	+	8.79800i	−0.166654	+	0.288653i	0.770588	+	0.637334i	$0.219963\pi$
$930$	−14.4721			−0.474560
$931$		0			0
$932$	−18.5623			−0.608029
$933$	43.3050	−	75.0064i	1.41774	−	2.45560i
$934$	−14.6525	+	25.3788i	−0.479444	+	0.830421i
$935$	−4.79837	−	8.31103i	−0.156924	−	0.271800i
$936$	13.5172	−	23.4125i	0.441824	−	0.765262i
$937$	9.94427	+	17.2240i	0.324865	+	0.562683i	0.981485	−	0.191539i	$-0.0613477\pi$
$937$	9.94427	+	17.2240i	0.324865	+	0.562683i	−0.656620	+	0.754222i	$0.728014\pi$
$938$	2.11146			0.0689415
$939$	−72.8328			−2.37681
$940$	−3.09017	−	5.35233i	−0.100790	−	0.174574i
$941$	13.0000	+	22.5167i	0.423788	+	0.734022i	0.996306	−	0.0858697i	$-0.0273669\pi$
$941$	13.0000	+	22.5167i	0.423788	+	0.734022i	−0.572518	+	0.819892i	$0.694034\pi$
$942$	−37.5967			−1.22497
$943$	4.47214			0.145633
$944$	4.23607	+	7.33708i	0.137872	+	0.238802i
$945$	−12.3607	+	21.4093i	−0.402093	+	0.696445i
$946$	2.94427	+	5.09963i	0.0957265	+	0.165803i
$947$	7.09017	−	12.2805i	0.230400	−	0.399064i	−0.727526	−	0.686080i	$-0.759330\pi$
$947$	7.09017	−	12.2805i	0.230400	−	0.399064i	0.957926	+	0.287016i	$0.0926634\pi$
$948$	11.7082	−	20.2792i	0.380265	−	0.658638i
$949$	12.2361			0.397200
$950$		0			0
$951$	−46.3607			−1.50335
$952$	3.47214	−	6.01392i	0.112533	−	0.194912i
$953$	−26.4058	+	45.7361i	−0.855367	+	1.48154i	0.0209379	+	0.999781i	$0.493335\pi$
$953$	−26.4058	+	45.7361i	−0.855367	+	1.48154i	−0.876304	+	0.481758i	$0.839999\pi$
$954$	19.0172	+	32.9388i	0.615705	+	1.06643i
$955$	8.61803	−	14.9269i	0.278873	−	0.483022i
$956$	−3.90983	−	6.77202i	−0.126453	−	0.219023i
$957$	8.36068			0.270262
$958$	−5.70820			−0.184424
$959$	−2.85410	−	4.94345i	−0.0921638	−	0.159632i
$960$	−2.23607	−	3.87298i	−0.0721688	−	0.125000i
$961$	−20.5279			−0.662189
$962$	38.4164			1.23859
$963$	−65.0689	−	112.703i	−2.09682	−	3.63179i
$964$	0.708204	−	1.22665i	0.0228097	−	0.0395076i
$965$	14.1459	+	24.5014i	0.455373	+	0.788728i
$966$	1.52786	−	2.64634i	0.0491582	−	0.0851445i
$967$	22.4164	−	38.8264i	0.720863	−	1.24857i	−0.239791	−	0.970824i	$-0.577079\pi$
$967$	22.4164	−	38.8264i	0.720863	−	1.24857i	0.960654	−	0.277747i	$-0.0895877\pi$
$968$	−9.47214			−0.304446
$969$		0			0
$970$	8.81966			0.283182
$971$	−3.27051	+	5.66469i	−0.104956	+	0.181789i	−0.913720	−	0.406344i	$-0.866803\pi$
$971$	−3.27051	+	5.66469i	−0.104956	+	0.181789i	0.808764	+	0.588133i	$0.200137\pi$
$972$	17.7984	−	30.8277i	0.570883	−	0.988799i
$973$	8.65248	+	14.9865i	0.277386	+	0.480446i
$974$	7.38197	−	12.7859i	0.236533	−	0.409688i
$975$	18.0902	+	31.3331i	0.579349	+	1.00346i
$976$	3.61803			0.115810
$977$	−20.0344			−0.640959			−0.320479	−	0.947256i	$-0.603844\pi$
$977$	−20.0344			−0.640959			−0.320479	+	0.947256i	$0.603844\pi$
$978$	−33.4164	−	57.8789i	−1.06854	−	1.85076i
$979$	1.32624	+	2.29711i	0.0423867	+	0.0734160i
$980$	7.56231			0.241569
$981$	−134.756			−4.30242
$982$	5.23607	+	9.06914i	0.167090	+	0.289408i
$983$	−14.7984	+	25.6315i	−0.471995	+	0.817519i	−0.999487	−	0.0320412i	$-0.989799\pi$
$983$	−14.7984	+	25.6315i	−0.471995	+	0.817519i	0.527492	+	0.849560i	$0.323133\pi$
$984$	9.47214	+	16.4062i	0.301961	+	0.523011i
$985$	−7.50000	+	12.9904i	−0.238970	+	0.413908i
$986$	−5.87132	+	10.1694i	−0.186981	+	0.323861i
$987$	17.8885			0.569399
$988$		0			0
$989$	−3.63932			−0.115724
$990$	6.38197	−	11.0539i	0.202832	−	0.351316i
$991$	0.326238	−	0.565061i	0.0103633	−	0.0179497i	−0.860797	−	0.508948i	$-0.830035\pi$
$991$	0.326238	−	0.565061i	0.0103633	−	0.0179497i	0.871161	+	0.490998i	$0.163368\pi$
$992$	1.61803	+	2.80252i	0.0513726	+	0.0889800i
$993$	−19.8885	+	34.4480i	−0.631144	+	1.09317i
$994$	−9.23607	−	15.9973i	−0.292950	−	0.507405i
$995$	−2.11146			−0.0669377
$996$	−27.4164			−0.868722
$997$	−12.2533	−	21.2233i	−0.388066	−	0.672149i	0.604124	−	0.796891i	$-0.293523\pi$
$997$	−12.2533	−	21.2233i	−0.388066	−	0.672149i	−0.992189	+	0.124741i	$0.960190\pi$
$998$	−13.6525	−	23.6468i	−0.432162	−	0.748526i
$999$	153.666			4.86177

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.690983 - 1.19682i) q^{5} +(1.61803 + 2.80252i) q^{6} +1.23607 q^{7} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.690983 - 1.19682i) q^{5} +(1.61803 + 2.80252i) q^{6} +1.23607 q^{7} +1.00000 q^{8} +(-3.73607 - 6.47106i) q^{9} +(0.690983 + 1.19682i) q^{10} +1.23607 q^{11} -3.23607 q^{12} +(1.80902 + 3.13331i) q^{13} +(-0.618034 + 1.07047i) q^{14} +(-2.23607 - 3.87298i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.80902 - 4.86536i) q^{17} +7.47214 q^{18} -1.38197 q^{20} +(2.00000 - 3.46410i) q^{21} +(-0.618034 + 1.07047i) q^{22} +(-0.381966 - 0.661585i) q^{23} +(1.61803 - 2.80252i) q^{24} +(1.54508 + 2.67617i) q^{25} -3.61803 q^{26} -14.4721 q^{27} +(-0.618034 - 1.07047i) q^{28} +(1.04508 + 1.81014i) q^{29} +4.47214 q^{30} -3.23607 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +(2.80902 + 4.86536i) q^{34} +(0.854102 - 1.47935i) q^{35} +(-3.73607 + 6.47106i) q^{36} -10.6180 q^{37} +11.7082 q^{39} +(0.690983 - 1.19682i) q^{40} +(-2.92705 + 5.06980i) q^{41} +(2.00000 + 3.46410i) q^{42} +(2.38197 - 4.12569i) q^{43} +(-0.618034 - 1.07047i) q^{44} -10.3262 q^{45} +0.763932 q^{46} +(2.23607 + 3.87298i) q^{47} +(1.61803 + 2.80252i) q^{48} -5.47214 q^{49} -3.09017 q^{50} +(-9.09017 - 15.7446i) q^{51} +(1.80902 - 3.13331i) q^{52} +(2.54508 + 4.40822i) q^{53} +(7.23607 - 12.5332i) q^{54} +(0.854102 - 1.47935i) q^{55} +1.23607 q^{56} -2.09017 q^{58} +(4.23607 - 7.33708i) q^{59} +(-2.23607 + 3.87298i) q^{60} +(-1.80902 - 3.13331i) q^{61} +(1.61803 - 2.80252i) q^{62} +(-4.61803 - 7.99867i) q^{63} +1.00000 q^{64} +5.00000 q^{65} +(2.00000 + 3.46410i) q^{66} +(-0.854102 - 1.47935i) q^{67} -5.61803 q^{68} -2.47214 q^{69} +(0.854102 + 1.47935i) q^{70} +(-7.47214 + 12.9421i) q^{71} +(-3.73607 - 6.47106i) q^{72} +(1.69098 - 2.92887i) q^{73} +(5.30902 - 9.19549i) q^{74} +10.0000 q^{75} +1.52786 q^{77} +(-5.85410 + 10.1396i) q^{78} +(-3.61803 + 6.26662i) q^{79} +(0.690983 + 1.19682i) q^{80} +(-12.2082 + 21.1452i) q^{81} +(-2.92705 - 5.06980i) q^{82} +8.47214 q^{83} -4.00000 q^{84} +(-3.88197 - 6.72376i) q^{85} +(2.38197 + 4.12569i) q^{86} +6.76393 q^{87} +1.23607 q^{88} +(1.07295 + 1.85840i) q^{89} +(5.16312 - 8.94278i) q^{90} +(2.23607 + 3.87298i) q^{91} +(-0.381966 + 0.661585i) q^{92} +(-5.23607 + 9.06914i) q^{93} -4.47214 q^{94} -3.23607 q^{96} +(3.19098 - 5.52694i) q^{97} +(2.73607 - 4.73901i) q^{98} +(-4.61803 - 7.99867i) 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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