LMFDB - Embedded newform 80.2.j.b.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$0.0376504 - 1.41371i$ of defining polynomial
Character	$\chi$	$=$	80.43
Dual form			80.2.j.b.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 - 1.45136i) q^{4} +(1.66635 + 1.49107i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 - 2.40368i) q^{7} +(2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +O(q^{10})$	\(q+(-0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 - 1.45136i) q^{4} +(1.66635 + 1.49107i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 - 2.40368i) q^{7} +(2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +(-2.86798 + 1.33217i) q^{10} +(-2.67707 + 2.67707i) q^{11} +(-3.70331 + 3.51117i) q^{12} -2.40164 q^{13} +(1.78040 + 4.46551i) q^{14} +(3.80462 - 4.25187i) q^{15} +(-0.212908 + 3.99433i) q^{16} +(-0.0750544 + 0.0750544i) q^{17} +(1.96087 - 4.56125i) q^{18} +(-2.67236 + 2.67236i) q^{19} +(-0.128922 - 4.47028i) q^{20} +(-6.13324 - 6.13324i) q^{21} +(-1.98291 - 4.97342i) q^{22} +(2.12375 + 2.12375i) q^{23} +(-2.49341 - 6.77263i) q^{24} +(0.553442 + 4.96928i) q^{25} +(1.34141 - 3.12031i) q^{26} +1.30310i q^{27} +(-6.79621 - 0.180999i) q^{28} +(3.95795 + 3.95795i) q^{29} +(3.39917 + 7.31797i) q^{30} -1.65367i q^{31} +(-5.07068 - 2.50762i) q^{32} +(6.83083 + 6.83083i) q^{33} +(-0.0555929 - 0.139435i) q^{34} +(7.58941 - 0.421324i) q^{35} +(4.83094 + 5.09530i) q^{36} -2.53082 q^{37} +(-1.97942 - 4.96467i) q^{38} +6.12803i q^{39} +(5.87998 + 2.32934i) q^{40} +1.70882i q^{41} +(11.3942 - 4.54289i) q^{42} -3.84601 q^{43} +(7.56921 + 0.201586i) q^{44} +(-5.85005 - 5.23469i) q^{45} +(-3.94547 + 1.57306i) q^{46} +(-2.15264 - 2.15264i) q^{47} +(10.1920 + 0.543256i) q^{48} -4.55532i q^{49} +(-6.76541 - 2.05649i) q^{50} +(0.191509 + 0.191509i) q^{51} +(3.30480 + 3.48565i) q^{52} -1.29475i q^{53} +(-1.69305 - 0.727839i) q^{54} +(-8.45262 + 0.469246i) q^{55} +(4.03113 - 8.72883i) q^{56} +(6.81881 + 6.81881i) q^{57} +(-7.35302 + 2.93166i) q^{58} +(-5.29614 - 5.29614i) q^{59} +(-11.4064 + 0.328959i) q^{60} +(10.2413 - 10.2413i) q^{61} +(2.14852 + 0.923645i) q^{62} +(-8.43858 + 8.43858i) q^{63} +(6.09020 - 5.18744i) q^{64} +(-4.00197 - 3.58100i) q^{65} +(-12.6902 + 5.05960i) q^{66} -10.6230 q^{67} +(0.212211 + 0.00565167i) q^{68} +(5.41898 - 5.41898i) q^{69} +(-3.69160 + 10.0958i) q^{70} +2.27322 q^{71} +(-9.31831 + 3.43062i) q^{72} +(9.99096 - 9.99096i) q^{73} +(1.41357 - 3.28815i) q^{74} +(12.6796 - 1.41217i) q^{75} +(7.55589 + 0.201231i) q^{76} +12.8696i q^{77} +(-7.96180 - 3.42276i) q^{78} +8.70617 q^{79} +(-6.31059 + 6.33849i) q^{80} -7.20709 q^{81} +(-2.22017 - 0.954448i) q^{82} +11.1310i q^{83} +(-0.461838 + 17.3413i) q^{84} +(-0.236978 + 0.0131558i) q^{85} +(2.14816 - 4.99689i) q^{86} +(10.0991 - 10.0991i) q^{87} +(-4.48963 + 9.72165i) q^{88} -15.6390 q^{89} +(10.0686 - 4.67685i) q^{90} +(-5.77276 + 5.77276i) q^{91} +(0.159920 - 6.00475i) q^{92} -4.21952 q^{93} +(3.99914 - 1.59446i) q^{94} +(-8.43775 + 0.468420i) q^{95} +(-6.39846 + 12.9384i) q^{96} +(5.00672 - 5.00672i) q^{97} +(5.91846 + 2.54434i) q^{98} +(9.39839 - 9.39839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.558542	+	1.29924i	−0.394949	+	0.918703i
$2$	−0.558542	+	1.29924i	−0.394949	+	0.918703i
$3$		−	2.55161i		−	1.47317i	−0.676344	−	0.736586i	$-0.736437\pi$
$3$		−	2.55161i		−	1.47317i	0.676344	−	0.736586i	$-0.263563\pi$
$4$	−1.37606	−	1.45136i	−0.688031	−	0.725681i
$5$	1.66635	+	1.49107i	0.745214	+	0.666825i
$5$	1.66635	+	1.49107i	0.745214	+	0.666825i
$6$	3.31516	+	1.42518i	1.35341	+	0.581827i
$7$	2.40368	−	2.40368i	0.908504	−	0.908504i	−0.0876474	−	0.996152i	$-0.527935\pi$
$7$	2.40368	−	2.40368i	0.908504	−	0.908504i	0.996152	+	0.0876474i	$0.0279349\pi$
$8$	2.65426	−	0.977191i	0.938423	−	0.345489i
$9$	−3.51070			−1.17023
$10$	−2.86798	+	1.33217i	−0.906936	+	0.421269i
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	−0.984204	−	0.177037i	$-0.943349\pi$
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	0.177037	+	0.984204i	$0.443349\pi$
$12$	−3.70331	+	3.51117i	−1.06905	+	1.01359i
$13$	−2.40164			−0.666094			−0.333047	−	0.942910i	$-0.608077\pi$
$13$	−2.40164			−0.666094			−0.333047	+	0.942910i	$0.608077\pi$
$14$	1.78040	+	4.46551i	0.475833	+	1.19346i
$15$	3.80462	−	4.25187i	0.982348	−	1.09783i
$16$	−0.212908	+	3.99433i	−0.0532269	+	0.998582i
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	−0.716150	−	0.697947i	$-0.754097\pi$
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	0.697947	+	0.716150i	$0.254097\pi$
$18$	1.96087	−	4.56125i	0.462182	−	1.07510i
$19$	−2.67236	+	2.67236i	−0.613081	+	0.613081i	−0.943748	−	0.330666i	$-0.892726\pi$
$19$	−2.67236	+	2.67236i	−0.613081	+	0.613081i	0.330666	+	0.943748i	$0.392726\pi$
$20$	−0.128922	−	4.47028i	−0.0288279	−	0.999584i
$21$	−6.13324	−	6.13324i	−1.33838	−	1.33838i
$22$	−1.98291	−	4.97342i	−0.422757	−	1.06034i
$23$	2.12375	+	2.12375i	0.442833	+	0.442833i	0.892963	−	0.450130i	$-0.148622\pi$
$23$	2.12375	+	2.12375i	0.442833	+	0.442833i	−0.450130	+	0.892963i	$0.648622\pi$
$24$	−2.49341	−	6.77263i	−0.508965	−	1.38246i
$25$	0.553442	+	4.96928i	0.110688	+	0.993855i
$26$	1.34141	−	3.12031i	0.263073	−	0.611943i
$27$			1.30310i			0.250783i
$28$	−6.79621	−	0.180999i	−1.28436	−	0.0342056i
$29$	3.95795	+	3.95795i	0.734974	+	0.734974i	0.971601	−	0.236627i	$-0.0760419\pi$
$29$	3.95795	+	3.95795i	0.734974	+	0.734974i	−0.236627	+	0.971601i	$0.576042\pi$
$30$	3.39917	+	7.31797i	0.620601	+	1.33607i
$31$		−	1.65367i		−	0.297008i	−0.988912	−	0.148504i	$-0.952554\pi$
$31$		−	1.65367i		−	0.297008i	0.988912	−	0.148504i	$-0.0474458\pi$
$32$	−5.07068	−	2.50762i	−0.896379	−	0.443289i
$33$	6.83083	+	6.83083i	1.18909	+	1.18909i
$34$	−0.0555929	−	0.139435i	−0.00953410	−	0.0239129i
$35$	7.58941	−	0.421324i	1.28284	−	0.0712168i
$36$	4.83094	+	5.09530i	0.805157	+	0.849216i
$37$	−2.53082			−0.416064			−0.208032	−	0.978122i	$-0.566706\pi$
$37$	−2.53082			−0.416064			−0.208032	+	0.978122i	$0.566706\pi$
$38$	−1.97942	−	4.96467i	−0.321104	−	0.805375i
$39$			6.12803i			0.981271i
$40$	5.87998	+	2.32934i	0.929707	+	0.368300i
$41$			1.70882i			0.266873i	0.991057	+	0.133436i	$0.0426012\pi$
$41$			1.70882i			0.266873i	−0.991057	+	0.133436i	$0.957399\pi$
$42$	11.3942	−	4.54289i	1.75817	−	0.700983i
$43$	−3.84601			−0.586510			−0.293255	−	0.956034i	$-0.594739\pi$
$43$	−3.84601			−0.586510			−0.293255	+	0.956034i	$0.594739\pi$
$44$	7.56921	+	0.201586i	1.14110	+	0.0303902i
$45$	−5.85005	−	5.23469i	−0.872074	−	0.780341i
$46$	−3.94547	+	1.57306i	−0.581728	+	0.231936i
$47$	−2.15264	−	2.15264i	−0.313995	−	0.313995i	0.532460	−	0.846455i	$-0.321268\pi$
$47$	−2.15264	−	2.15264i	−0.313995	−	0.313995i	−0.846455	+	0.532460i	$0.821268\pi$
$48$	10.1920	+	0.543256i	1.47108	+	0.0784123i
$49$		−	4.55532i		−	0.650760i
$50$	−6.76541	−	2.05649i	−0.956774	−	0.290832i
$51$	0.191509	+	0.191509i	0.0268167	+	0.0268167i
$52$	3.30480	+	3.48565i	0.458293	+	0.483372i
$53$		−	1.29475i		−	0.177848i	−0.996038	−	0.0889239i	$-0.971657\pi$
$53$		−	1.29475i		−	0.177848i	0.996038	−	0.0889239i	$-0.0283428\pi$
$54$	−1.69305	−	0.727839i	−0.230395	−	0.0990463i
$55$	−8.45262	+	0.469246i	−1.13975	+	0.0632731i
$56$	4.03113	−	8.72883i	0.538683	−	1.16644i
$57$	6.81881	+	6.81881i	0.903174	+	0.903174i
$58$	−7.35302	+	2.93166i	−0.965499	+	0.384946i
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	0.272622	−	0.962121i	$-0.412109\pi$
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	−0.962121	+	0.272622i	$0.912109\pi$
$60$	−11.4064	+	0.328959i	−1.47256	+	0.0424684i
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.390780	−	0.920484i	$-0.372205\pi$
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.920484	−	0.390780i	$-0.127795\pi$
$62$	2.14852	+	0.923645i	0.272862	+	0.117303i
$63$	−8.43858	+	8.43858i	−1.06316	+	1.06316i
$64$	6.09020	−	5.18744i	0.761274	−	0.648430i
$65$	−4.00197	−	3.58100i	−0.496383	−	0.444168i
$66$	−12.6902	+	5.05960i	−1.56206	+	0.622794i
$67$	−10.6230			−1.29780			−0.648901	−	0.760873i	$-0.724771\pi$
$67$	−10.6230			−1.29780			−0.648901	+	0.760873i	$0.724771\pi$
$68$	0.212211	+	0.00565167i	0.0257343	+	0.000685365i
$69$	5.41898	−	5.41898i	0.652369	−	0.652369i
$70$	−3.69160	+	10.0958i	−0.441230	+	1.20668i
$71$	2.27322			0.269781			0.134891	−	0.990860i	$-0.456932\pi$
$71$	2.27322			0.269781			0.134891	+	0.990860i	$0.456932\pi$
$72$	−9.31831	+	3.43062i	−1.09817	+	0.404303i
$73$	9.99096	−	9.99096i	1.16935	−	1.16935i	0.186992	−	0.982361i	$-0.440126\pi$
$73$	9.99096	−	9.99096i	1.16935	−	1.16935i	0.982361	−	0.186992i	$-0.0598739\pi$
$74$	1.41357	−	3.28815i	0.164324	−	0.382240i
$75$	12.6796	−	1.41217i	1.46412	−	0.163063i
$76$	7.55589	+	0.201231i	0.866720	+	0.0230828i
$77$			12.8696i			1.46663i
$78$	−7.96180	−	3.42276i	−0.901496	−	0.387552i
$79$	8.70617			0.979520			0.489760	−	0.871857i	$-0.337084\pi$
$79$	8.70617			0.979520			0.489760	+	0.871857i	$0.337084\pi$
$80$	−6.31059	+	6.33849i	−0.705545	+	0.708665i
$81$	−7.20709			−0.800787
$82$	−2.22017	−	0.954448i	−0.245177	−	0.105401i
$83$			11.1310i			1.22178i	0.791715	+	0.610890i	$0.209188\pi$
$83$			11.1310i			1.22178i	−0.791715	+	0.610890i	$0.790812\pi$
$84$	−0.461838	+	17.3413i	−0.0503907	+	1.89209i
$85$	−0.236978	+	0.0131558i	−0.0257039	+	0.00142695i
$86$	2.14816	−	4.99689i	0.231642	−	0.538829i
$87$	10.0991	−	10.0991i	1.08274	−	1.08274i
$88$	−4.48963	+	9.72165i	−0.478596	+	1.03633i
$89$	−15.6390			−1.65773			−0.828866	−	0.559447i	$-0.811014\pi$
$89$	−15.6390			−1.65773			−0.828866	+	0.559447i	$0.811014\pi$
$90$	10.0686	−	4.67685i	1.06133	−	0.492983i
$91$	−5.77276	+	5.77276i	−0.605149	+	0.605149i
$92$	0.159920	−	6.00475i	0.0166729	−	0.626038i
$93$	−4.21952			−0.437544
$94$	3.99914	−	1.59446i	0.412480	−	0.164456i
$95$	−8.43775	+	0.468420i	−0.865695	+	0.0480589i
$96$	−6.39846	+	12.9384i	−0.653040	+	1.32052i
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	−0.405666	−	0.914021i	$-0.632960\pi$
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	0.914021	+	0.405666i	$0.132960\pi$
$98$	5.91846	+	2.54434i	0.597855	+	0.257017i
$99$	9.39839	−	9.39839i	0.944573	−	0.944573i
$100$	6.45065	−	7.64128i	0.645065	−	0.764128i
$101$	6.37101	+	6.37101i	0.633939	+	0.633939i	0.949054	−	0.315115i	$-0.102043\pi$
$101$	6.37101	+	6.37101i	0.633939	+	0.633939i	−0.315115	+	0.949054i	$0.602043\pi$
$102$	−0.355783	+	0.141851i	−0.0352278	+	0.0140454i
$103$	−1.93695	−	1.93695i	−0.190854	−	0.190854i	0.605211	−	0.796065i	$-0.293089\pi$
$103$	−1.93695	−	1.93695i	−0.190854	−	0.190854i	−0.796065	+	0.605211i	$0.793089\pi$
$104$	−6.37457	+	2.34686i	−0.625078	+	0.230128i
$105$	−1.07505	−	19.3652i	−0.104915	−	1.88985i
$106$	1.68220	+	0.723173i	0.163389	+	0.0702408i
$107$		−	6.97778i		−	0.674568i	−0.941403	−	0.337284i	$-0.890492\pi$
$107$		−	6.97778i		−	0.674568i	0.941403	−	0.337284i	$-0.109508\pi$
$108$	1.89128	−	1.79315i	0.181988	−	0.172546i
$109$	−0.277748	−	0.277748i	−0.0266034	−	0.0266034i	0.693680	−	0.720283i	$-0.255988\pi$
$109$	−0.277748	−	0.277748i	−0.0266034	−	0.0266034i	−0.720283	+	0.693680i	$0.755988\pi$
$110$	4.11148	−	11.2441i	0.392014	−	1.07208i
$111$			6.45766i			0.612934i
$112$	9.08931	+	10.1128i	0.858859	+	0.955573i
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	0.162959	−	0.986633i	$-0.447896\pi$
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	−0.986633	+	0.162959i	$0.947896\pi$
$114$	−12.6679	+	5.05070i	−1.18646	+	0.473041i
$115$	0.372258	+	6.70557i	0.0347133	+	0.625298i
$116$	0.298037	−	11.1908i	0.0276721	−	1.03904i
$117$	8.43142			0.779485
$118$	9.83909	−	3.92286i	0.905762	−	0.361128i
$119$			0.360813i			0.0330757i
$120$	5.94355	−	15.0034i	0.542569	−	1.36962i
$121$		−	3.33340i		−	0.303036i
$122$	7.58574	+	19.0261i	0.686780	+	1.72254i
$123$	4.36024			0.393149
$124$	−2.40008	+	2.27555i	−0.215533	+	0.204351i
$125$	−6.48729	+	9.10577i	−0.580241	+	0.814445i
$126$	−6.25046	−	15.6771i	−0.556836	−	1.39662i
$127$	0.679502	+	0.679502i	0.0602961	+	0.0602961i	0.736612	−	0.676316i	$-0.236424\pi$
$127$	0.679502	+	0.679502i	0.0602961	+	0.0602961i	−0.676316	+	0.736612i	$0.736424\pi$
$128$	3.33811	+	10.8100i	0.295050	+	0.955482i
$129$			9.81350i			0.864030i
$130$	6.88785	−	3.19939i	0.604105	−	0.280605i
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	0.428412	−	0.903584i	$-0.359073\pi$
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	−0.903584	+	0.428412i	$0.859073\pi$
$132$	0.514367	−	19.3137i	0.0447699	−	1.68104i
$133$			12.8470i			1.11397i
$134$	5.93337	−	13.8018i	0.512565	−	1.19229i
$135$	−1.94302	+	2.17143i	−0.167228	+	0.186887i
$136$	−0.125871	+	0.272557i	−0.0107934	+	0.0233715i
$137$	7.47496	+	7.47496i	0.638629	+	0.638629i	0.950217	−	0.311588i	$-0.100861\pi$
$137$	7.47496	+	7.47496i	0.638629	+	0.638629i	−0.311588	+	0.950217i	$0.600861\pi$
$138$	4.01384	+	10.0673i	0.341681	+	0.856986i
$139$	11.5307	+	11.5307i	0.978023	+	0.978023i	0.999764	−	0.0217404i	$-0.00692074\pi$
$139$	11.5307	+	11.5307i	0.978023	+	0.978023i	−0.0217404	+	0.999764i	$0.506921\pi$
$140$	−11.0550	−	10.4352i	−0.934317	−	0.881936i
$141$	−5.49270	+	5.49270i	−0.462568	+	0.462568i
$142$	−1.26969	+	2.95346i	−0.106550	+	0.247849i
$143$	6.42935	−	6.42935i	0.537649	−	0.537649i
$144$	0.747455	−	14.0229i	0.0622879	−	1.16857i
$145$	0.693763	+	12.4969i	0.0576139	+	1.03781i
$146$	7.40031	+	18.5611i	0.612454	+	1.53612i
$147$	−11.6234			−0.958680
$148$	3.48257	+	3.67314i	0.286265	+	0.301930i
$149$	−5.51174	+	5.51174i	−0.451539	+	0.451539i	−0.895865	−	0.444326i	$-0.853443\pi$
$149$	−5.51174	+	5.51174i	−0.451539	+	0.451539i	0.444326	+	0.895865i	$0.353443\pi$
$150$	−5.24736	+	17.2627i	−0.428445	+	1.40949i
$151$	−4.13617			−0.336597			−0.168299	−	0.985736i	$-0.553827\pi$
$151$	−4.13617			−0.336597			−0.168299	+	0.985736i	$0.553827\pi$
$152$	−4.48173	+	9.70454i	−0.363516	+	0.787142i
$153$	0.263494	−	0.263494i	0.0213022	−	0.0213022i
$154$	−16.7207	−	7.18822i	−1.34740	−	0.579243i
$155$	2.46573	−	2.75559i	0.198052	−	0.221335i
$156$	8.89400	−	8.43255i	0.712090	−	0.675144i
$157$		−	20.2700i		−	1.61772i	−0.587999	−	0.808861i	$-0.700084\pi$
$157$		−	20.2700i		−	1.61772i	0.587999	−	0.808861i	$-0.299916\pi$
$158$	−4.86276	+	11.3114i	−0.386860	+	0.899889i
$159$	−3.30370			−0.262000
$160$	−4.71051	−	11.7393i	−0.372398	−	0.928073i
$161$	10.2096			0.804631
$162$	4.02546	−	9.36375i	0.316270	−	0.735686i
$163$		−	13.1835i		−	1.03262i	−0.856403	−	0.516308i	$-0.827306\pi$
$163$		−	13.1835i		−	1.03262i	0.856403	−	0.516308i	$-0.172694\pi$
$164$	2.48012	−	2.35144i	0.193665	−	0.183617i
$165$	1.19733	+	21.5678i	0.0932121	+	1.67905i
$166$	−14.4618	−	6.21710i	−1.12245	−	0.482541i
$167$	−11.8190	+	11.8190i	−0.914585	+	0.914585i	−0.996629	−	0.0820441i	$-0.973855\pi$
$167$	−11.8190	+	11.8190i	−0.914585	+	0.914585i	0.0820441	+	0.996629i	$0.473855\pi$
$168$	−22.2726	−	10.2859i	−1.71836	−	0.793572i
$169$	−7.23214			−0.556319
$170$	0.115270	−	0.315240i	0.00884078	−	0.0241778i
$171$	9.38185	−	9.38185i	0.717448	−	0.717448i
$172$	5.29234	+	5.58195i	0.403537	+	0.425620i
$173$	15.5763			1.18424			0.592120	−	0.805849i	$-0.298291\pi$
$173$	15.5763			1.18424			0.592120	+	0.805849i	$0.298291\pi$
$174$	7.48044	+	18.7620i	0.567091	+	1.42235i
$175$	13.2748	+	10.6142i	1.00348	+	0.802361i
$176$	−10.1231	−	11.2631i	−0.763060	−	0.848986i
$177$	−13.5137	+	13.5137i	−1.01575	+	1.01575i
$178$	8.73505	−	20.3189i	0.654719	−	1.52296i
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.182523	−	0.983202i	$-0.441574\pi$
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.983202	−	0.182523i	$-0.0584265\pi$
$180$	0.452607	+	15.6938i	0.0337353	+	1.16975i
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	0.809351	−	0.587325i	$-0.199819\pi$
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	−0.587325	+	0.809351i	$0.699819\pi$
$182$	−4.27588	−	10.7245i	−0.316950	−	0.794955i
$183$	−26.1318	−	26.1318i	−1.93172	−	1.93172i
$184$	7.71230	+	3.56168i	0.568559	+	0.262571i
$185$	−4.21723	−	3.77362i	−0.310057	−	0.277442i
$186$	2.35678	−	5.48218i	0.172807	−	0.401973i
$187$		−	0.401852i		−	0.0293863i
$188$	−0.162096	+	6.08643i	−0.0118221	+	0.443899i
$189$	3.13224	+	3.13224i	0.227837	+	0.227837i
$190$	4.10425	−	11.2243i	0.297753	−	0.814297i
$191$			6.47168i			0.468274i	0.972204	+	0.234137i	$0.0752264\pi$
$191$			6.47168i			0.468274i	−0.972204	+	0.234137i	$0.924774\pi$
$192$	−13.2363	−	15.5398i	−0.955248	−	1.12149i
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	0.183149	−	0.983085i	$-0.441371\pi$
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	−0.983085	+	0.183149i	$0.941371\pi$
$194$	3.70848	+	9.30141i	0.266253	+	0.667802i
$195$	−9.13730	+	10.2114i	−0.654336	+	0.731257i
$196$	−6.61142	+	6.26840i	−0.472244	+	0.447743i
$197$	−25.0927			−1.78778			−0.893889	−	0.448288i	$-0.852034\pi$
$197$	−25.0927			−1.78778			−0.893889	+	0.448288i	$0.852034\pi$
$198$	6.96139	+	17.4602i	0.494724	+	1.24084i
$199$			18.7579i			1.32972i	0.746970	+	0.664858i	$0.231508\pi$
$199$			18.7579i			1.32972i	−0.746970	+	0.664858i	$0.768492\pi$
$200$	6.32491	+	12.6489i	0.447239	+	0.894415i
$201$			27.1056i			1.91188i
$202$	−11.8360	+	4.71901i	−0.832775	+	0.332028i
$203$	19.0273			1.33545
$204$	0.0144208	−	0.541479i	0.00100966	−	0.0379111i
$205$	−2.54796	+	2.84749i	−0.177958	+	0.198877i
$206$	3.59844	−	1.43470i	0.250715	−	0.0999604i
$207$	−7.45586	−	7.45586i	−0.518218	−	0.518218i
$208$	0.511327	−	9.59293i	0.0354541	−	0.665150i
$209$		−	14.3082i		−	0.989718i
$210$	25.7605	+	9.41951i	1.77765	+	0.650008i
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	0.891948	−	0.452137i	$-0.149338\pi$
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	−0.452137	+	0.891948i	$0.649338\pi$
$212$	−1.87915	+	1.78166i	−0.129061	+	0.122365i
$213$		−	5.80036i		−	0.397434i
$214$	9.06583	+	3.89738i	0.619727	+	0.266420i
$215$	−6.40879	−	5.73465i	−0.437076	−	0.391100i
$216$	1.27338	+	3.45878i	0.0866427	+	0.235340i
$217$	−3.97489	−	3.97489i	−0.269833	−	0.269833i
$218$	0.515996	−	0.205728i	0.0349476	−	0.0139337i
$219$	−25.4930	−	25.4930i	−1.72266	−	1.72266i
$220$	12.3124	+	11.6221i	0.830100	+	0.783562i
$221$	0.180253	−	0.180253i	0.0121252	−	0.0121252i
$222$	−8.39006	−	3.60687i	−0.563104	−	0.242077i
$223$	4.29779	−	4.29779i	0.287801	−	0.287801i	−0.548409	−	0.836210i	$-0.684766\pi$
$223$	4.29779	−	4.29779i	0.287801	−	0.287801i	0.836210	+	0.548409i	$0.184766\pi$
$224$	−18.2158	+	6.16078i	−1.21709	+	0.411634i
$225$	−1.94297	−	17.4456i	−0.129531	−	1.16304i
$226$	16.2663	−	6.48541i	1.08202	−	0.431403i
$227$	29.1029			1.93163			0.965813	−	0.259241i	$-0.0834724\pi$
$227$	29.1029			1.93163			0.965813	+	0.259241i	$0.0834724\pi$
$228$	0.513462	−	19.2797i	0.0340049	−	1.27683i
$229$	18.3405	−	18.3405i	1.21198	−	1.21198i	0.241600	−	0.970376i	$-0.422328\pi$
$229$	18.3405	−	18.3405i	1.21198	−	1.21198i	0.970376	−	0.241600i	$-0.0776721\pi$
$230$	−8.92008	−	3.26169i	−0.588173	−	0.215069i
$231$	32.8382			2.16060
$232$	14.3731	+	6.63776i	0.943641	+	0.435790i
$233$	−1.46663	+	1.46663i	−0.0960824	+	0.0960824i	−0.753514	−	0.657432i	$-0.771643\pi$
$233$	−1.46663	+	1.46663i	−0.0960824	+	0.0960824i	0.657432	+	0.753514i	$0.271643\pi$
$234$	−4.70930	+	10.9545i	−0.307857	+	0.716116i
$235$	−0.377322	−	6.79678i	−0.0246138	−	0.443373i
$236$	−0.398804	+	14.9744i	−0.0259600	+	0.974754i
$237$		−	22.2147i		−	1.44300i
$238$	−0.468784	−	0.201529i	−0.0303867	−	0.0130632i
$239$	−12.5432			−0.811352			−0.405676	−	0.914017i	$-0.632964\pi$
$239$	−12.5432			−0.811352			−0.405676	+	0.914017i	$0.632964\pi$
$240$	16.1733	+	16.1021i	1.04398	+	1.03939i
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$	4.33089	+	1.86184i	0.278400	+	0.119684i
$243$			22.2990i			1.43048i
$244$	−28.9565	−	0.771179i	−1.85375	−	0.0493697i
$245$	6.79228	−	7.59075i	0.433943	−	0.484955i
$246$	−2.43538	+	5.66501i	−0.155274	+	0.361188i
$247$	6.41803	−	6.41803i	0.408370	−	0.408370i
$248$	−1.61595	−	4.38927i	−0.102613	−	0.278719i
$249$	28.4018			1.79989
$250$	−8.20718	−	13.5145i	−0.519068	−	0.854733i
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	−0.856319	−	0.516447i	$-0.827254\pi$
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	0.516447	+	0.856319i	$0.327254\pi$
$252$	23.8595	+	0.635433i	1.50300	+	0.0400285i
$253$	−11.3709			−0.714880
$254$	−1.26237	+	0.503308i	−0.0792081	+	0.0315803i
$255$	0.0335684	+	0.604675i	0.00210214	+	0.0378662i
$256$	−15.9093	−	1.70085i	−0.994334	−	0.106303i
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	−0.817858	−	0.575420i	$-0.804838\pi$
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	0.575420	+	0.817858i	$0.304838\pi$
$258$	−12.7501	−	5.48125i	−0.793787	−	0.341248i
$259$	−6.08327	+	6.08327i	−0.377996	+	0.377996i
$260$	0.309624	+	10.7360i	0.0192021	+	0.665817i
$261$	−13.8952	−	13.8952i	−0.860090	−	0.860090i
$262$	10.1037	−	4.02836i	0.624210	−	0.248873i
$263$	16.9658	+	16.9658i	1.04615	+	1.04615i	0.998882	+	0.0472716i	$0.0150526\pi$
$263$	16.9658	+	16.9658i	1.04615	+	1.04615i	0.0472716	+	0.998882i	$0.484947\pi$
$264$	24.8058	+	11.4558i	1.52669	+	0.705054i
$265$	1.93056	−	2.15751i	0.118593	−	0.132535i
$266$	−16.6913	−	7.17557i	−1.02341	−	0.439963i
$267$			39.9046i			2.44212i
$268$	14.6179	+	15.4178i	0.892928	+	0.941791i
$269$	−2.55482	−	2.55482i	−0.155770	−	0.155770i	0.624919	−	0.780689i	$-0.285132\pi$
$269$	−2.55482	−	2.55482i	−0.155770	−	0.155770i	−0.780689	+	0.624919i	$0.785132\pi$
$270$	−1.73596	−	3.73728i	−0.105647	−	0.227444i
$271$		−	3.33684i		−	0.202698i	−0.994851	−	0.101349i	$-0.967684\pi$
$271$		−	3.33684i		−	0.202698i	0.994851	−	0.101349i	$-0.0323159\pi$
$272$	−0.283813	−	0.315772i	−0.0172087	−	0.0191465i
$273$	14.7298	+	14.7298i	0.891488	+	0.891488i
$274$	−13.8869	+	5.53671i	−0.838937	+	0.334485i
$275$	−14.7847	−	11.8215i	−0.891551	−	0.712863i
$276$	−15.3218	−	0.408054i	−0.922262	−	0.0245620i
$277$	4.60736			0.276830			0.138415	−	0.990374i	$-0.455799\pi$
$277$	4.60736			0.276830			0.138415	+	0.990374i	$0.455799\pi$
$278$	−21.4216	+	8.54081i	−1.28478	+	0.512244i
$279$			5.80554i			0.347569i
$280$	19.7325	−	8.53460i	1.17924	−	0.510040i
$281$		−	22.1178i		−	1.31944i	−0.751513	−	0.659718i	$-0.770676\pi$
$281$		−	22.1178i		−	1.31944i	0.751513	−	0.659718i	$-0.229324\pi$
$282$	−4.06844	−	10.2042i	−0.242272	−	0.607654i
$283$	−10.8629			−0.645734			−0.322867	−	0.946444i	$-0.604647\pi$
$283$	−10.8629			−0.645734			−0.322867	+	0.946444i	$0.604647\pi$
$284$	−3.12809	−	3.29926i	−0.185618	−	0.195775i
$285$	1.19522	+	21.5298i	0.0707990	+	1.27532i
$286$	4.76222	+	11.9443i	0.281596	+	0.706284i
$287$	4.10745	+	4.10745i	0.242455	+	0.242455i
$288$	17.8017	+	8.80350i	1.04897	+	0.518751i
$289$			16.9887i			0.999337i
$290$	−16.6240	−	6.07868i	−0.976195	−	0.356952i
$291$	−12.7752	−	12.7752i	−0.748895	−	0.748895i
$292$	−28.2487	−	0.752328i	−1.65313	−	0.0440267i
$293$		−	18.4067i		−	1.07533i	−0.843159	−	0.537665i	$-0.819307\pi$
$293$		−	18.4067i		−	1.07533i	0.843159	−	0.537665i	$-0.180693\pi$
$294$	6.49214	−	15.1016i	0.378630	−	0.880743i
$295$	−0.928326	−	16.7221i	−0.0540492	−	0.973600i
$296$	−6.71746	+	2.47309i	−0.390444	+	0.143746i
$297$	−3.48850	−	3.48850i	−0.202423	−	0.202423i
$298$	−4.08255	−	10.2396i	−0.236496	−	0.593166i
$299$	−5.10048	−	5.10048i	−0.294968	−	0.294968i
$300$	−19.4975	−	16.4595i	−1.12569	−	0.950291i
$301$	−9.24455	+	9.24455i	−0.532847	+	0.532847i
$302$	2.31023	−	5.37389i	0.132939	−	0.309233i
$303$	16.2563	−	16.2563i	0.933900	−	0.933900i
$304$	−10.1053	−	11.2432i	−0.579580	−	0.644845i
$305$	32.3360	−	1.79513i	1.85156	−	0.102789i
$306$	0.195170	+	0.489514i	0.0111571	+	0.0279837i
$307$	−6.60872			−0.377180			−0.188590	−	0.982056i	$-0.560392\pi$
$307$	−6.60872			−0.377180			−0.188590	+	0.982056i	$0.560392\pi$
$308$	18.6785	−	17.7094i	1.06431	−	1.00909i
$309$	−4.94234	+	4.94234i	−0.281160	+	0.281160i
$310$	2.20297	+	4.74270i	0.125120	+	0.269367i
$311$	−0.606102			−0.0343689			−0.0171845	−	0.999852i	$-0.505470\pi$
$311$	−0.606102			−0.0343689			−0.0171845	+	0.999852i	$0.505470\pi$
$312$	5.98826	+	16.2654i	0.339018	+	0.920847i
$313$	−19.3708	+	19.3708i	−1.09490	+	1.09490i	−0.0999032	+	0.994997i	$0.531853\pi$
$313$	−19.3708	+	19.3708i	−1.09490	+	1.09490i	−0.994997	+	0.0999032i	$0.968147\pi$
$314$	26.3357	+	11.3216i	1.48621	+	0.638918i
$315$	−26.6441	+	1.47914i	−1.50123	+	0.0833403i
$316$	−11.9802	−	12.6358i	−0.673940	−	0.710820i
$317$			7.04328i			0.395590i	0.980243	+	0.197795i	$0.0633780\pi$
$317$			7.04328i			0.395590i	−0.980243	+	0.197795i	$0.936622\pi$
$318$	1.84525	−	4.29230i	0.103477	−	0.240700i
$319$	−21.1914			−1.18649
$320$	17.8832	+	0.436798i	0.999702	+	0.0244178i
$321$	−17.8046			−0.993753
$322$	−5.70250	+	13.2648i	−0.317788	+	0.739217i
$323$		−	0.401145i		−	0.0223203i
$324$	9.91740	+	10.4601i	0.550967	+	0.581117i
$325$	−1.32917	−	11.9344i	−0.0737290	−	0.662001i
$326$	17.1286	+	7.36356i	0.948667	+	0.407830i
$327$	−0.708703	+	0.708703i	−0.0391914	+	0.0391914i
$328$	1.66984	+	4.53565i	0.0922017	+	0.250440i
$329$	−10.3485			−0.570532
$330$	−28.6905	−	10.4909i	−1.57936	−	0.577504i
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	−0.970031	−	0.242983i	$-0.921874\pi$
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	0.242983	+	0.970031i	$0.421874\pi$
$332$	16.1550	−	15.3169i	0.886624	−	0.840623i
$333$	8.88495			0.486892
$334$	−8.75437	−	21.9572i	−0.479018	−	1.20145i
$335$	−17.7016	−	15.8395i	−0.967140	−	0.865407i
$336$	25.8040	−	23.1924i	1.40772	−	1.26525i
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	−0.464393	−	0.885629i	$-0.653727\pi$
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	0.885629	+	0.464393i	$0.153727\pi$
$338$	4.03945	−	9.39631i	0.219717	−	0.511092i
$339$	−22.3413	+	22.3413i	−1.21341	+	1.21341i
$340$	0.345190	+	0.325838i	0.0187206	+	0.0176710i
$341$	4.42699	+	4.42699i	0.239735	+	0.239735i
$342$	6.94914	+	17.4295i	0.375767	+	0.942477i
$343$	5.87623	+	5.87623i	0.317286	+	0.317286i
$344$	−10.2083	+	3.75828i	−0.550395	+	0.202633i
$345$	17.1100	−	0.949857i	0.921170	−	0.0511386i
$346$	−8.69999	+	20.2373i	−0.467714	+	1.08797i
$347$			11.3945i			0.611691i	0.952081	+	0.305845i	$0.0989391\pi$
$347$			11.3945i			0.611691i	−0.952081	+	0.305845i	$0.901061\pi$
$348$	−28.5546	−	0.760474i	−1.53069	−	0.0407657i
$349$	12.0508	+	12.0508i	0.645066	+	0.645066i	0.951796	−	0.306730i	$-0.0992350\pi$
$349$	12.0508	+	12.0508i	0.645066	+	0.645066i	−0.306730	+	0.951796i	$0.599235\pi$
$350$	−21.2050	+	11.3187i	−1.13346	+	0.605011i
$351$		−	3.12958i		−	0.167045i
$352$	20.2876	−	6.86150i	1.08134	−	0.365719i
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	0.513350	−	0.858179i	$-0.328404\pi$
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	−0.858179	+	0.513350i	$0.828404\pi$
$354$	−10.0096	−	25.1055i	−0.532004	−	1.33434i
$355$	3.78798	+	3.38952i	0.201045	+	0.179897i
$356$	21.5203	+	22.6979i	1.14057	+	1.20299i
$357$	0.920653			0.0487261
$358$	11.5522	+	28.9746i	0.610553	+	1.53136i
$359$			3.25098i			0.171580i	0.996313	+	0.0857902i	$0.0273415\pi$
$359$			3.25098i			0.171580i	−0.996313	+	0.0857902i	$0.972659\pi$
$360$	−20.6429	−	8.17760i	−1.08797	−	0.430997i
$361$			4.71699i			0.248263i
$362$	−5.54929	+	2.21251i	−0.291664	+	0.116287i
$363$	−8.50553			−0.446424
$364$	16.3220	+	0.434694i	0.855507	+	0.0227841i
$365$	31.5456	−	1.75125i	1.65117	−	0.0916646i
$366$	48.5472	−	19.3558i	2.53760	−	1.01174i
$367$	12.7038	+	12.7038i	0.663132	+	0.663132i	0.956117	−	0.292985i	$-0.0946487\pi$
$367$	12.7038	+	12.7038i	0.663132	+	0.663132i	−0.292985	+	0.956117i	$0.594649\pi$
$368$	−8.93513	+	8.03080i	−0.465776	+	0.418635i
$369$		−	5.99916i		−	0.312304i
$370$	7.25835	−	3.37148i	0.377344	−	0.175275i
$371$	−3.11216	−	3.11216i	−0.161575	−	0.161575i
$372$	5.80632	+	6.12405i	0.301044	+	0.317517i
$373$			21.9761i			1.13788i	0.822379	+	0.568939i	$0.192646\pi$
$373$			21.9761i			1.13788i	−0.822379	+	0.568939i	$0.807354\pi$
$374$	0.522103	+	0.224451i	0.0269973	+	0.0116061i
$375$	23.2343	+	16.5530i	1.19982	+	0.854794i
$376$	−7.81721	−	3.61013i	−0.403142	−	0.186178i
$377$	−9.50557	−	9.50557i	−0.489562	−	0.489562i
$378$	−5.81903	+	2.32005i	−0.299299	+	0.119331i
$379$	17.0642	+	17.0642i	0.876527	+	0.876527i	0.993174	−	0.116646i	$-0.0372144\pi$
$379$	17.0642	+	17.0642i	0.876527	+	0.876527i	−0.116646	+	0.993174i	$0.537214\pi$
$380$	12.2907	+	11.6017i	0.630500	+	0.595153i
$381$	1.73382	−	1.73382i	0.0888264	−	0.0888264i
$382$	−8.40828	−	3.61470i	−0.430205	−	0.184944i
$383$	0.228058	−	0.228058i	0.0116532	−	0.0116532i	−0.701256	−	0.712909i	$-0.747377\pi$
$383$	0.228058	−	0.228058i	0.0116532	−	0.0116532i	0.712909	+	0.701256i	$0.247377\pi$
$384$	27.5830	−	8.51755i	1.40759	−	0.434659i
$385$	−19.1894	+	21.4453i	−0.977985	+	1.09295i
$386$	20.6457	−	8.23145i	1.05084	−	0.418970i
$387$	13.5022			0.686354
$388$	−14.1561	−	0.377011i	−0.718668	−	0.0191398i
$389$	14.3036	−	14.3036i	0.725221	−	0.725221i	−0.244443	−	0.969664i	$-0.578605\pi$
$389$	14.3036	−	14.3036i	0.725221	−	0.725221i	0.969664	+	0.244443i	$0.0786050\pi$
$390$	−8.16358	−	17.5751i	−0.413379	−	0.889949i
$391$	−0.318794			−0.0161221
$392$	−4.45141	−	12.0910i	−0.224830	−	0.610688i
$393$	−13.8771	+	13.8771i	−0.700009	+	0.700009i
$394$	14.0153	−	32.6015i	0.706081	−	1.64244i
$395$	14.5075	+	12.9815i	0.729953	+	0.653169i
$396$	−26.5732	−	0.707707i	−1.33535	−	0.0355636i
$397$		−	5.11618i		−	0.256774i	−0.991724	−	0.128387i	$-0.959020\pi$
$397$		−	5.11618i		−	0.256774i	0.991724	−	0.128387i	$-0.0409799\pi$
$398$	−24.3711	−	10.4771i	−1.22161	−	0.525170i
$399$	32.7804			1.64107
$400$	−19.9668	+	1.15264i	−0.998338	+	0.0576318i
$401$	−16.2837			−0.813170			−0.406585	−	0.913613i	$-0.633281\pi$
$401$	−16.2837			−0.813170			−0.406585	+	0.913613i	$0.633281\pi$
$402$	−35.2168	−	15.1396i	−1.75645	−	0.755096i
$403$			3.97152i			0.197835i
$404$	0.479742	−	18.0135i	0.0238681	−	0.896207i
$405$	−12.0095	−	10.7462i	−0.596758	−	0.533985i
$406$	−10.6275	+	24.7210i	−0.527436	+	1.22688i
$407$	6.77518	−	6.77518i	0.335833	−	0.335833i
$408$	0.695457	+	0.321175i	0.0344303	+	0.0159005i
$409$	17.4256			0.861640			0.430820	−	0.902438i	$-0.358224\pi$
$409$	17.4256			0.861640			0.430820	+	0.902438i	$0.358224\pi$
$410$	−2.27644	−	4.90087i	−0.112425	−	0.242037i
$411$	19.0732	−	19.0732i	0.940810	−	0.940810i
$412$	−0.145854	+	5.47659i	−0.00718573	+	0.269812i
$413$	−25.4604			−1.25283
$414$	13.8514	−	5.52256i	0.680758	−	0.271419i
$415$	−16.5970	+	18.5481i	−0.814714	+	0.910488i
$416$	12.1779	+	6.02239i	0.597073	+	0.295272i
$417$	29.4219	−	29.4219i	1.44080	−	1.44080i
$418$	18.5898	+	7.99172i	0.909257	+	0.390888i
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	−0.360083	−	0.932920i	$-0.617252\pi$
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	0.932920	+	0.360083i	$0.117252\pi$
$420$	−26.6266	+	28.2080i	−1.29924	+	1.37641i
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.987082	−	0.160216i	$-0.948781\pi$
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.160216	−	0.987082i	$-0.551219\pi$
$422$	−11.8687	+	4.73206i	−0.577759	+	0.230353i
$423$	7.55728	+	7.55728i	0.367447	+	0.367447i
$424$	−1.26522	−	3.43661i	−0.0614445	−	0.166896i
$425$	−0.414505	−	0.331428i	−0.0201064	−	0.0160766i
$426$	7.53608	+	3.23974i	0.365124	+	0.156966i
$427$		−	49.2335i		−	2.38258i
$428$	−10.1273	+	9.60186i	−0.489521	+	0.464123i
$429$	−16.4052	−	16.4052i	−0.792049	−	0.792049i
$430$	11.0303	−	5.12353i	0.531927	−	0.247079i
$431$		−	35.0243i		−	1.68706i	−0.537079	−	0.843532i	$-0.680472\pi$
$431$		−	35.0243i		−	1.68706i	0.537079	−	0.843532i	$-0.319528\pi$
$432$	−5.20503	−	0.277441i	−0.250427	−	0.0133484i
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	0.906987	−	0.421159i	$-0.138376\pi$
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	−0.421159	+	0.906987i	$0.638376\pi$
$434$	7.38449	−	2.94420i	0.354467	−	0.141326i
$435$	31.8872	−	1.77021i	1.52887	−	0.0848752i
$436$	−0.0209147	+	0.785311i	−0.00100163	+	0.0376096i
$437$	−11.3509			−0.542985
$438$	47.3605	−	18.8827i	2.26297	−	0.902250i
$439$		−	22.6071i		−	1.07898i	−0.841993	−	0.539488i	$-0.818618\pi$
$439$		−	22.6071i		−	1.07898i	0.841993	−	0.539488i	$-0.181382\pi$
$440$	−21.9769	+	9.50533i	−1.04771	+	0.453149i
$441$			15.9923i			0.761540i
$442$	0.133514	+	0.334872i	0.00635061	+	0.0159282i
$443$	−10.9178			−0.518721			−0.259360	−	0.965781i	$-0.583512\pi$
$443$	−10.9178			−0.518721			−0.259360	+	0.965781i	$0.583512\pi$
$444$	9.37241	−	8.88614i	0.444795	−	0.421717i
$445$	−26.0601	−	23.3188i	−1.23537	−	1.10542i
$446$	3.18337	+	7.98436i	0.150737	+	0.378071i
$447$	14.0638	+	14.0638i	0.665195	+	0.665195i
$448$	2.16993	−	27.1078i	0.102520	−	1.28072i
$449$			28.8112i			1.35969i	0.733358	+	0.679843i	$0.237952\pi$
$449$			28.8112i			1.35969i	−0.733358	+	0.679843i	$0.762048\pi$
$450$	23.7513	+	7.21973i	1.11965	+	0.340341i
$451$	−4.57463	−	4.57463i	−0.215411	−	0.215411i
$452$	−0.659318	+	24.7563i	−0.0310117	+	1.16444i
$453$			10.5539i			0.495865i
$454$	−16.2552	+	37.8117i	−0.762893	+	1.77459i
$455$	−18.2270	+	1.01187i	−0.854495	+	0.0474371i
$456$	24.7622	+	11.4356i	1.15960	+	0.535522i
$457$	19.1653	+	19.1653i	0.896513	+	0.896513i	0.995126	−	0.0986128i	$-0.0314405\pi$
$457$	19.1653	+	19.1653i	0.896513	+	0.896513i	−0.0986128	+	0.995126i	$0.531441\pi$
$458$	13.5848	+	34.0727i	0.634778	+	1.59211i
$459$	−0.0978038	−	0.0978038i	−0.00456509	−	0.00456509i
$460$	9.21996	−	9.76756i	0.429883	−	0.455415i
$461$	4.43227	−	4.43227i	0.206431	−	0.206431i	−0.596317	−	0.802749i	$-0.703370\pi$
$461$	4.43227	−	4.43227i	0.206431	−	0.206431i	0.802749	+	0.596317i	$0.203370\pi$
$462$	−18.3415	+	42.6648i	−0.853324	+	1.98495i
$463$	−20.1518	+	20.1518i	−0.936534	+	0.936534i	−0.998103	−	0.0615691i	$-0.980390\pi$
$463$	−20.1518	+	20.1518i	−0.936534	+	0.936534i	0.0615691	+	0.998103i	$0.480390\pi$
$464$	−16.6521	+	14.9667i	−0.773052	+	0.694811i
$465$	−7.03120	−	6.29158i	−0.326064	−	0.291765i
$466$	−1.08634	−	2.72469i	−0.0503236	−	0.126219i
$467$	−3.89858			−0.180405			−0.0902025	−	0.995923i	$-0.528751\pi$
$467$	−3.89858			−0.180405			−0.0902025	+	0.995923i	$0.528751\pi$
$468$	−11.6022	−	12.2371i	−0.536310	−	0.565658i
$469$	−25.5342	+	25.5342i	−1.17906	+	1.17906i
$470$	9.04142	+	3.30606i	0.417050	+	0.152497i
$471$	−51.7211			−2.38318
$472$	−19.2327	−	8.88200i	−0.885256	−	0.408827i
$473$	10.2960	−	10.2960i	0.473412	−	0.473412i
$474$	28.8623	+	12.4079i	1.32569	+	0.569912i
$475$	−14.7587	−	11.8007i	−0.677175	−	0.541453i
$476$	0.523671	−	0.496501i	0.0240024	−	0.0227571i
$477$			4.54548i			0.208123i
$478$	7.00590	−	16.2967i	0.320443	−	0.745392i
$479$	−9.85299			−0.450194			−0.225097	−	0.974336i	$-0.572270\pi$
$479$	−9.85299			−0.450194			−0.225097	+	0.974336i	$0.572270\pi$
$480$	−29.9541	+	12.0194i	−1.36721	+	0.548606i
$481$	6.07811			0.277138
$482$	−8.31500	+	19.3418i	−0.378738	+	0.880994i
$483$		−	26.0510i		−	1.18536i
$484$	−4.83797	+	4.58696i	−0.219908	+	0.208498i
$485$	15.8083	−	0.877595i	0.717818	−	0.0398495i
$486$	−28.9718	−	12.4549i	−1.31419	−	0.564966i
$487$	−13.9164	+	13.9164i	−0.630611	+	0.630611i	−0.948221	−	0.317610i	$-0.897120\pi$
$487$	−13.9164	+	13.9164i	−0.630611	+	0.630611i	0.317610	+	0.948221i	$0.397120\pi$
$488$	17.1754	−	37.1908i	0.777492	−	1.68355i
$489$	−33.6392			−1.52122
$490$	6.06845	+	13.0646i	0.274145	+	0.590197i
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	−0.651066	−	0.759021i	$-0.725678\pi$
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	0.759021	+	0.651066i	$0.225678\pi$
$492$	−5.99996	−	6.32829i	−0.270499	−	0.285301i
$493$	−0.594124			−0.0267580
$494$	4.75384	+	11.9233i	0.213885	+	0.536456i
$495$	29.6746	−	1.64738i	1.33377	−	0.0740443i
$496$	6.60531	+	0.352079i	0.296587	+	0.0158088i
$497$	5.46408	−	5.46408i	0.245098	−	0.245098i
$498$	−15.8636	+	36.9008i	−0.710865	+	1.65357i
$499$	9.87034	−	9.87034i	0.441857	−	0.441857i	−0.450779	−	0.892636i	$-0.648854\pi$
$499$	9.87034	−	9.87034i	0.441857	−	0.441857i	0.892636	+	0.450779i	$0.148854\pi$
$500$	22.1427	−	3.11469i	0.990251	−	0.139293i
$501$	30.1575	+	30.1575i	1.34734	+	1.34734i
$502$	−3.98837	−	10.0034i	−0.178010	−	0.446474i
$503$	9.29035	+	9.29035i	0.414236	+	0.414236i	0.883211	−	0.468975i	$-0.155377\pi$
$503$	9.29035	+	9.29035i	0.414236	+	0.414236i	−0.468975	+	0.883211i	$0.655377\pi$
$504$	−14.1521	+	30.6443i	−0.630384	+	1.36501i
$505$	1.11673	+	20.1159i	0.0496939	+	0.895146i
$506$	6.35110	−	14.7735i	0.282341	−	0.656763i
$507$			18.4536i			0.819553i
$508$	0.0511671	−	1.92124i	0.00227017	−	0.0852413i
$509$	6.53818	+	6.53818i	0.289800	+	0.289800i	0.837001	−	0.547201i	$-0.184307\pi$
$509$	6.53818	+	6.53818i	0.289800	+	0.289800i	−0.547201	+	0.837001i	$0.684307\pi$
$510$	−0.804369	−	0.294123i	−0.0356181	−	0.0130240i
$511$		−	48.0301i		−	2.12473i
$512$	11.0958	−	19.7201i	0.490372	−	0.871513i
$513$	−3.48236	−	3.48236i	−0.153750	−	0.153750i
$514$	−2.87878	−	7.22040i	−0.126978	−	0.318478i
$515$	−0.339516	−	6.11577i	−0.0149608	−	0.269493i
$516$	14.2429	−	13.5040i	0.627011	−	0.594480i
$517$	11.5255			0.506893
$518$	−4.50588	−	11.3014i	−0.197977	−	0.496555i
$519$		−	39.7445i		−	1.74459i
$520$	−14.1216	−	5.59422i	−0.619272	−	0.245323i
$521$			14.2961i			0.626324i	0.949700	+	0.313162i	$0.101388\pi$
$521$			14.2961i			0.626324i	−0.949700	+	0.313162i	$0.898612\pi$
$522$	25.8143	−	10.2922i	1.12986	−	0.450476i
$523$	16.0319			0.701027			0.350513	−	0.936558i	$-0.386007\pi$
$523$	16.0319			0.701027			0.350513	+	0.936558i	$0.386007\pi$
$524$	−0.409530	+	15.3772i	−0.0178904	+	0.671756i
$525$	27.0834	−	33.8721i	1.18201	−	1.47830i
$526$	−31.5187	+	12.5665i	−1.37428	+	0.547928i
$527$	0.124115	+	0.124115i	0.00540655	+	0.00540655i
$528$	−28.7389	+	25.8302i	−1.25070	+	1.12412i
$529$		−	13.9794i		−	0.607798i
$530$	1.72483	+	3.71332i	0.0749217	+	0.161297i
$531$	18.5932	+	18.5932i	0.806875	+	0.806875i
$532$	18.6456	−	17.6782i	0.808390	−	0.766448i
$533$		−	4.10397i		−	0.177762i
$534$	−51.8458	−	22.2884i	−2.24359	−	0.964514i
$535$	10.4043	−	11.6274i	0.449819	−	0.502697i
$536$	−28.1961	+	10.3807i	−1.21789	+	0.448376i
$537$	−39.7957	−	39.7957i	−1.71731	−	1.71731i
$538$	4.74631	−	1.89236i	0.204628	−	0.0815854i
$539$	12.1949	+	12.1949i	0.525271	+	0.525271i
$540$	5.82524	−	0.167999i	0.250678	−	0.00722953i
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	−0.945220	−	0.326435i	$-0.894153\pi$
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	0.326435	+	0.945220i	$0.394153\pi$
$542$	4.33536	+	1.86376i	0.186220	+	0.0800555i
$543$	7.62178	−	7.62178i	0.327082	−	0.327082i
$544$	0.568785	−	0.192369i	0.0243865	−	0.00824777i
$545$	−0.0486846	−	0.876965i	−0.00208542	−	0.0375651i
$546$	−27.3648	+	10.9104i	−1.17111	+	0.466921i
$547$	−11.6741			−0.499148			−0.249574	−	0.968356i	$-0.580291\pi$
$547$	−11.6741			−0.499148			−0.249574	+	0.968356i	$0.580291\pi$
$548$	0.562871	−	21.1349i	0.0240447	−	0.902838i
$549$	−35.9541	+	35.9541i	−1.53448	+	1.53448i
$550$	23.6169	−	12.6061i	1.00703	−	0.537526i
$551$	−21.1541			−0.901197
$552$	9.08801	−	19.6788i	0.386811	−	0.837584i
$553$	20.9268	−	20.9268i	0.889898	−	0.889898i
$554$	−2.57340	+	5.98608i	−0.109333	+	0.254324i
$555$	−9.62880	+	10.7607i	−0.408720	+	0.456767i
$556$	0.868274	−	32.6023i	0.0368230	−	1.38264i
$557$			39.6712i			1.68092i	0.541873	+	0.840460i	$0.317715\pi$
$557$			39.6712i			1.68092i	−0.541873	+	0.840460i	$0.682285\pi$
$558$	−7.54281	−	3.24264i	−0.319313	−	0.137272i
$559$	9.23671			0.390671
$560$	0.0670669	+	30.4043i	0.00283409	+	1.28482i
$561$	−1.02537			−0.0432911
$562$	28.7364	+	12.3537i	1.21217	+	0.521110i
$563$		−	12.4534i		−	0.524850i	−0.964952	−	0.262425i	$-0.915478\pi$
$563$		−	12.4534i		−	0.524850i	0.964952	−	0.262425i	$-0.0845222\pi$
$564$	15.5302	+	0.413605i	0.653939	+	0.0174159i
$565$	−1.53474	−	27.6456i	−0.0645671	−	1.16306i
$566$	6.06740	−	14.1136i	0.255032	−	0.593238i
$567$	−17.3235	+	17.3235i	−0.727519	+	0.727519i
$568$	6.03371	−	2.22137i	0.253169	−	0.0932066i
$569$	5.62622			0.235863			0.117932	−	0.993022i	$-0.462374\pi$
$569$	5.62622			0.235863			0.117932	+	0.993022i	$0.462374\pi$
$570$	−28.6400	−	10.4724i	−1.19960	−	0.438641i
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	−0.0294797	−	0.999565i	$-0.509385\pi$
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	0.999565	+	0.0294797i	$0.00938505\pi$
$572$	−18.1785	−	0.484136i	−0.760081	−	0.0202427i
$573$	16.5132			0.689848
$574$	−7.63076	+	3.04239i	−0.318502	+	0.126987i
$575$	−9.37814	+	11.7289i	−0.391095	+	0.489128i
$576$	−21.3808	+	18.2115i	−0.890869	+	0.758814i
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.0694322	+	0.997587i	$0.522119\pi$
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.997587	+	0.0694322i	$0.977881\pi$
$578$	−22.0725	−	9.48892i	−0.918094	−	0.394687i
$579$	−28.3562	+	28.3562i	−1.17844	+	1.17844i
$580$	17.1829	−	18.2034i	0.713480	−	0.755856i
$581$	26.7552	+	26.7552i	1.10999	+	1.10999i
$582$	23.7335	−	9.46259i	0.983787	−	0.392237i
$583$	3.46614	+	3.46614i	0.143553	+	0.143553i
$584$	16.7555	−	36.2817i	0.693349	−	1.50135i
$585$	14.0497	+	12.5718i	0.580884	+	0.519780i
$586$	23.9147	+	10.2809i	0.987908	+	0.424700i
$587$		−	25.5579i		−	1.05489i	−0.849590	−	0.527444i	$-0.823151\pi$
$587$		−	25.5579i		−	1.05489i	0.849590	−	0.527444i	$-0.176849\pi$
$588$	15.9945	+	16.8697i	0.659602	+	0.695696i
$589$	4.41920	+	4.41920i	0.182090	+	0.182090i
$590$	22.2446	+	8.13389i	0.915796	+	0.334867i
$591$			64.0266i			2.63370i
$592$	0.538831	−	10.1089i	0.0221458	−	0.415474i
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	0.765380	−	0.643578i	$-0.222551\pi$
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	−0.643578	+	0.765380i	$0.722551\pi$
$594$	6.48088	−	2.58393i	0.265914	−	0.106020i
$595$	−0.537996	+	0.601241i	−0.0220557	+	0.0246485i
$596$	15.5840	+	0.415039i	0.638347	+	0.0170007i
$597$	47.8629			1.95890
$598$	9.47559	−	3.77793i	0.387486	−	0.154491i
$599$		−	5.14724i		−	0.210311i	−0.994456	−	0.105155i	$-0.966466\pi$
$599$		−	5.14724i		−	0.210311i	0.994456	−	0.105155i	$-0.0335340\pi$
$600$	32.2751	−	16.1387i	1.31763	−	0.658859i
$601$		−	33.5619i		−	1.36902i	−0.729005	−	0.684509i	$-0.760017\pi$
$601$		−	33.5619i		−	1.36902i	0.729005	−	0.684509i	$-0.239983\pi$
$602$	−6.84745	−	17.1744i	−0.279081	−	0.699976i
$603$	37.2940			1.51873
$604$	5.69163	+	6.00309i	0.231589	+	0.244262i
$605$	4.97032	−	5.55461i	0.202072	−	0.225827i
$606$	12.0411	+	30.2007i	0.489134	+	1.22682i
$607$	3.29572	+	3.29572i	0.133769	+	0.133769i	0.770821	−	0.637052i	$-0.219846\pi$
$607$	3.29572	+	3.29572i	0.133769	+	0.133769i	−0.637052	+	0.770821i	$0.719846\pi$
$608$	20.2519	−	6.84943i	0.821325	−	0.277781i
$609$		−	48.5501i		−	1.96735i
$610$	−15.7287	+	43.0150i	−0.636838	+	1.74163i
$611$	5.16986	+	5.16986i	0.209150	+	0.209150i
$612$	−0.745008	−	0.0198413i	−0.0301152	−	0.000802037i
$613$			0.261903i			0.0105781i	0.999986	+	0.00528907i	$0.00168357\pi$
$613$			0.261903i			0.0105781i	−0.999986	+	0.00528907i	$0.998316\pi$
$614$	3.69125	−	8.58633i	0.148967	−	0.346516i
$615$	7.26568	+	6.50140i	0.292981	+	0.262162i
$616$	12.5761	+	34.1593i	0.506704	+	1.37632i
$617$	−12.1529	−	12.1529i	−0.489259	−	0.489259i	0.418813	−	0.908072i	$-0.362446\pi$
$617$	−12.1529	−	12.1529i	−0.489259	−	0.489259i	−0.908072	+	0.418813i	$0.862446\pi$
$618$	−3.66080	−	9.18181i	−0.147259	−	0.369347i
$619$	12.1134	+	12.1134i	0.486877	+	0.486877i	0.907319	−	0.420442i	$-0.138125\pi$
$619$	12.1134	+	12.1134i	0.486877	+	0.486877i	−0.420442	+	0.907319i	$0.638125\pi$
$620$	−7.39237	+	0.213195i	−0.296885	+	0.00856211i
$621$	−2.76747	+	2.76747i	−0.111055	+	0.111055i
$622$	0.338534	−	0.787474i	0.0135740	−	0.0315748i
$623$	−37.5911	+	37.5911i	−1.50606	+	1.50606i
$624$	−24.4774	−	1.30470i	−0.979880	−	0.0522300i
$625$	−24.3874	+	5.50042i	−0.975496	+	0.220017i
$626$	−14.3479	−	35.9867i	−0.573459	−	1.43832i
$627$	−36.5089			−1.45802
$628$	−29.4191	+	27.8928i	−1.17395	+	1.11304i
$629$	0.189949	−	0.189949i	0.00757377	−	0.00757377i
$630$	12.9601	−	35.4433i	0.516342	−	1.41210i
$631$	49.8568			1.98477			0.992384	−	0.123179i	$-0.0393090\pi$
$631$	49.8568			1.98477			0.992384	+	0.123179i	$0.0393090\pi$
$632$	23.1084	−	8.50759i	0.919204	−	0.338414i
$633$	16.3013	−	16.3013i	0.647917	−	0.647917i
$634$	−9.15093	−	3.93397i	−0.363430	−	0.156238i
$635$	0.119105	+	2.14547i	0.00472656	+	0.0851404i
$636$	4.54609	+	4.79486i	0.180264	+	0.190129i
$637$			10.9402i			0.433467i
$638$	11.8363	−	27.5328i	0.468604	−	1.09003i
$639$	−7.98059			−0.315707
$640$	−10.5560	+	22.9907i	−0.417264	+	0.908785i
$641$	−4.10036			−0.161954			−0.0809772	−	0.996716i	$-0.525804\pi$
$641$	−4.10036			−0.161954			−0.0809772	+	0.996716i	$0.525804\pi$
$642$	9.94459	−	23.1324i	0.392482	−	0.912964i
$643$		−	18.7451i		−	0.739233i	−0.929184	−	0.369617i	$-0.879489\pi$
$643$		−	18.7451i		−	0.739233i	0.929184	−	0.369617i	$-0.120511\pi$
$644$	−14.0491	−	14.8179i	−0.553611	−	0.583906i
$645$	−14.6326	+	16.3527i	−0.576157	+	0.643888i
$646$	0.521184	+	0.224056i	0.0205057	+	0.00881537i
$647$	5.46529	−	5.46529i	0.214863	−	0.214863i	−0.591467	−	0.806330i	$-0.701451\pi$
$647$	5.46529	−	5.46529i	0.214863	−	0.214863i	0.806330	+	0.591467i	$0.201451\pi$
$648$	−19.1295	+	7.04270i	−0.751477	+	0.276663i
$649$	28.3563			1.11308
$650$	16.2481	+	4.93895i	0.637302	+	0.193721i
$651$	−10.1424	+	10.1424i	−0.397510	+	0.397510i
$652$	−19.1341	+	18.1414i	−0.749350	+	0.710471i
$653$	−33.9219			−1.32747			−0.663733	−	0.747970i	$-0.731029\pi$
$653$	−33.9219			−1.32747			−0.663733	+	0.747970i	$0.731029\pi$
$654$	−0.524937	−	1.31662i	−0.0205267	−	0.0514838i
$655$	−0.953294	−	17.1719i	−0.0372483	−	0.670961i
$656$	−6.82559	−	0.363821i	−0.266495	−	0.0142048i
$657$	−35.0753	+	35.0753i	−1.36842	+	1.36842i
$658$	5.78007	−	13.4452i	0.225331	−	0.524149i
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.0326746	+	0.999466i	$0.510402\pi$
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.999466	+	0.0326746i	$0.989598\pi$
$660$	29.6551	−	31.4163i	1.15432	−	1.22288i
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	0.883851	−	0.467769i	$-0.154942\pi$
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	−0.467769	+	0.883851i	$0.654942\pi$
$662$	−9.79759	−	24.5738i	−0.380794	−	0.955087i
$663$	−0.459936	−	0.459936i	−0.0178624	−	0.0178624i
$664$	10.8771	+	29.5444i	0.422112	+	1.14655i
$665$	−19.1557	+	21.4075i	−0.742826	+	0.830149i
$666$	−4.96262	+	11.5437i	−0.192297	+	0.447309i
$667$			16.8114i			0.650941i
$668$	33.4174	+	0.889984i	1.29296	+	0.0344345i
$669$	−10.9663	−	10.9663i	−0.423980	−	0.423980i
$670$	30.4665	−	14.1516i	1.17702	−	0.546723i
$671$			54.8333i			2.11682i
$672$	15.7199	+	46.4795i	0.606408	+	1.79299i
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	0.565887	−	0.824483i	$-0.308534\pi$
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	−0.824483	+	0.565887i	$0.808534\pi$
$674$	5.72774	+	14.3660i	0.220624	+	0.553358i
$675$	−6.47549	+	0.721194i	−0.249242	+	0.0277588i
$676$	9.95188	+	10.4965i	0.382764	+	0.403710i
$677$	13.1970			0.507200			0.253600	−	0.967309i	$-0.418385\pi$
$677$	13.1970			0.507200			0.253600	+	0.967309i	$0.418385\pi$
$678$	−16.5482	−	41.5053i	−0.635530	−	1.59400i
$679$		−	24.0691i		−	0.923686i
$680$	−0.616146	+	0.266492i	−0.0236281	+	0.0102195i
$681$		−	74.2591i		−	2.84561i
$682$	−8.22440	+	3.27908i	−0.314928	+	0.125562i
$683$	−37.9089			−1.45054			−0.725272	−	0.688462i	$-0.758286\pi$
$683$	−37.9089			−1.45054			−0.725272	+	0.688462i	$0.758286\pi$
$684$	−26.5265	−	0.706462i	−1.01427	−	0.0270122i
$685$	1.31024	+	23.6016i	0.0500616	+	0.901770i
$686$	−10.9168	+	4.35252i	−0.416804	+	0.166180i
$687$	−46.7978	−	46.7978i	−1.78545	−	1.78545i
$688$	0.818844	−	15.3622i	0.0312181	−	0.585679i
$689$			3.10952i			0.118463i
$690$	−8.32255	+	22.7605i	−0.316834	+	0.866479i
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	0.981873	−	0.189538i	$-0.0606991\pi$
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	−0.189538	+	0.981873i	$0.560699\pi$
$692$	−21.4339	−	22.6068i	−0.814794	−	0.859382i
$693$		−	45.1813i		−	1.71630i
$694$	−14.8043	−	6.36433i	−0.561962	−	0.241586i
$695$	2.02114	+	36.4073i	0.0766664	+	1.38101i
$696$	16.9370	−	36.6745i	0.641994	−	1.39015i
$697$	−0.128255	−	0.128255i	−0.00485799	−	0.00485799i
$698$	−22.3878	+	8.92605i	−0.847392	+	0.337856i
$699$	3.74227	+	3.74227i	0.141546	+	0.141546i
$700$	−2.86188	−	33.8724i	−0.108169	−	1.28026i
$701$	19.9053	−	19.9053i	0.751812	−	0.751812i	−0.223005	−	0.974817i	$-0.571587\pi$
$701$	19.9053	−	19.9053i	0.751812	−	0.751812i	0.974817	+	0.223005i	$0.0715868\pi$
$702$	4.06609	+	1.74800i	0.153465	+	0.0659741i
$703$	6.76326	−	6.76326i	0.255081	−	0.255081i
$704$	−2.41674	+	30.1910i	−0.0910844	+	1.13787i
$705$	−17.3427	+	0.962778i	−0.653165	+	0.0362603i
$706$	12.0361	−	4.79882i	0.452986	−	0.180606i
$707$	30.6277			1.15187
$708$	38.2089	+	1.01759i	1.43598	+	0.0382435i
$709$	8.57112	−	8.57112i	0.321895	−	0.321895i	−0.527599	−	0.849494i	$-0.676908\pi$
$709$	8.57112	−	8.57112i	0.321895	−	0.321895i	0.849494	+	0.527599i	$0.176908\pi$
$710$	−6.51955	+	3.02831i	−0.244674	+	0.113651i
$711$	−30.5647			−1.14627
$712$	−41.5100	+	15.2823i	−1.55565	+	0.572729i
$713$	3.51199	−	3.51199i	0.131525	−	0.131525i
$714$	−0.514224	+	1.19615i	−0.0192443	+	0.0447649i
$715$	20.3001	−	1.12696i	0.759182	−	0.0421458i
$716$	−44.0975	−	1.17442i	−1.64800	−	0.0438901i
$717$			32.0053i			1.19526i
$718$	−4.22382	−	1.81581i	−0.157631	−	0.0677655i
$719$	33.1900			1.23778			0.618889	−	0.785478i	$-0.287583\pi$
$719$	33.1900			1.23778			0.618889	+	0.785478i	$0.287583\pi$
$720$	22.1546	−	22.2525i	0.825653	−	0.829303i
$721$	−9.31162			−0.346783
$722$	−6.12852	−	2.63464i	−0.228080	−	0.0980511i
$723$		−	37.9857i		−	1.41270i
$724$	0.224927	−	8.44566i	0.00835936	−	0.313880i
$725$	−17.4777	+	21.8587i	−0.649104	+	0.811810i
$726$	4.75069	−	11.0507i	0.176315	−	0.410131i
$727$	5.06503	−	5.06503i	0.187852	−	0.187852i	−0.606915	−	0.794767i	$-0.707593\pi$
$727$	5.06503	−	5.06503i	0.187852	−	0.187852i	0.794767	+	0.606915i	$0.207593\pi$
$728$	−9.68131	+	20.9635i	−0.358813	+	0.776958i
$729$	35.2770			1.30655
$730$	−15.3443	+	41.9636i	−0.567916	+	1.55314i
$731$	0.288660	−	0.288660i	0.0106765	−	0.0106765i
$732$	−1.96775	+	73.8856i	−0.0727300	+	2.73089i
$733$	43.0744			1.59099			0.795494	−	0.605961i	$-0.207211\pi$
$733$	43.0744			1.59099			0.795494	+	0.605961i	$0.207211\pi$
$734$	−23.6009	+	9.40969i	−0.871124	+	0.347318i
$735$	−19.3686	−	17.3312i	−0.714422	−	0.639272i
$736$	−5.44332	−	16.0944i	−0.200643	−	0.593249i
$737$	28.4384	−	28.4384i	1.04754	−	1.04754i
$738$	7.79436	+	3.35078i	0.286914	+	0.123344i
$739$	−11.3838	+	11.3838i	−0.418762	+	0.418762i	−0.884777	−	0.466015i	$-0.845689\pi$
$739$	−11.3838	+	11.3838i	−0.418762	+	0.418762i	0.466015	+	0.884777i	$0.345689\pi$
$740$	0.326279	+	11.3135i	0.0119942	+	0.415891i
$741$	−16.3763	−	16.3763i	−0.601599	−	0.601599i
$742$	5.78173	−	2.30518i	0.212254	−	0.0846258i
$743$	1.54795	+	1.54795i	0.0567888	+	0.0567888i	0.734931	−	0.678142i	$-0.237215\pi$
$743$	1.54795	+	1.54795i	0.0567888	+	0.0567888i	−0.678142	+	0.734931i	$0.737215\pi$
$744$	−11.1997	+	4.12328i	−0.410601	+	0.151167i
$745$	−17.4029	+	0.966116i	−0.637591	+	0.0353958i
$746$	−28.5523	−	12.2746i	−1.04537	−	0.449404i
$747$		−	39.0774i		−	1.42977i
$748$	−0.583233	+	0.552973i	−0.0213251	+	0.0202187i
$749$	−16.7723	−	16.7723i	−0.612847	−	0.612847i
$750$	−34.4837	+	20.9415i	−1.25917	+	0.764675i
$751$			1.49244i			0.0544600i	0.999629	+	0.0272300i	$0.00866865\pi$
$751$			1.49244i			0.0544600i	−0.999629	+	0.0272300i	$0.991331\pi$
$752$	9.05667	−	8.14005i	0.330263	−	0.296837i
$753$	13.7394	+	13.7394i	0.500690	+	0.500690i
$754$	17.6593	−	7.04078i	0.643113	−	0.256410i
$755$	−6.89231	−	6.16731i	−0.250837	−	0.224451i
$756$	0.235861	−	8.85618i	0.00857817	−	0.322096i
$757$	−22.7030			−0.825154			−0.412577	−	0.910923i	$-0.635371\pi$
$757$	−22.7030			−0.825154			−0.412577	+	0.910923i	$0.635371\pi$
$758$	−31.7015	+	12.6394i	−1.15145	+	0.459085i
$759$			29.0140i			1.05314i
$760$	−21.9382	+	9.48860i	−0.795784	+	0.344188i
$761$			33.6599i			1.22017i	0.792335	+	0.610086i	$0.208865\pi$
$761$			33.6599i			1.22017i	−0.792335	+	0.610086i	$0.791135\pi$
$762$	1.28424	+	3.22107i	0.0465232	+	0.116687i
$763$	−1.33523			−0.0483386
$764$	9.39275	−	8.90543i	0.339818	−	0.322187i
$765$	0.831959	−	0.0461860i	0.0300795	−	0.00166986i
$766$	0.168923	+	0.423683i	0.00610343	+	0.0153083i
$767$	12.7194	+	12.7194i	0.459271	+	0.459271i
$768$	−4.33989	+	40.5944i	−0.156602	+	1.46482i
$769$		−	10.1943i		−	0.367615i	−0.982962	−	0.183808i	$-0.941158\pi$
$769$		−	10.1943i		−	0.367615i	0.982962	−	0.183808i	$-0.0588423\pi$
$770$	−17.1445	−	36.9098i	−0.617845	−	1.33014i
$771$	9.91699	+	9.91699i	0.357152	+	0.357152i
$772$	−0.836823	+	31.4213i	−0.0301179	+	1.13088i
$773$			7.34419i			0.264152i	0.991240	+	0.132076i	$0.0421643\pi$
$773$			7.34419i			0.264152i	−0.991240	+	0.132076i	$0.957836\pi$
$774$	−7.54153	+	17.5426i	−0.271075	+	0.630556i
$775$	8.21755	−	0.915212i	0.295183	−	0.0328754i
$776$	8.39662	−	18.1817i	0.301421	−	0.652684i
$777$	15.5221	+	15.5221i	0.556853	+	0.556853i
$778$	10.5947	+	26.5730i	0.379838	+	0.952688i
$779$	−4.56658	−	4.56658i	−0.163615	−	0.163615i
$780$	27.3940	−	0.790039i	0.980863	−	0.0282879i
$781$	−6.08556	+	6.08556i	−0.217759	+	0.217759i
$782$	0.178060	−	0.414191i	0.00636741	−	0.0148114i
$783$	−5.15763	+	5.15763i	−0.184319	+	0.184319i
$784$	18.1954	+	0.969861i	0.649837	+	0.0346379i
$785$	30.2239	−	33.7769i	1.07874	−	1.20555i
$786$	−10.2788	−	25.7807i	−0.366633	−	0.919568i
$787$	29.4359			1.04928			0.524638	−	0.851326i	$-0.324201\pi$
$787$	29.4359			1.04928			0.524638	+	0.851326i	$0.324201\pi$
$788$	34.5291	+	36.4186i	1.23005	+	1.29736i
$789$	43.2900	−	43.2900i	1.54116	−	1.54116i
$790$	−24.9691	+	11.5981i	−0.888362	+	0.412641i
$791$	−42.0921			−1.49662
$792$	15.7617	−	34.1298i	0.560069	−	1.21275i
$793$	−24.5959	+	24.5959i	−0.873425	+	0.873425i
$794$	6.64715	+	2.85760i	0.235899	+	0.101412i
$795$	−5.50511	−	4.92603i	−0.195246	−	0.174708i
$796$	27.2246	−	25.8121i	0.964950	−	0.914886i
$797$		−	50.3934i		−	1.78503i	−0.451022	−	0.892513i	$-0.648940\pi$
$797$		−	50.3934i		−	1.78503i	0.451022	−	0.892513i	$-0.351060\pi$
$798$	−18.3092	+	42.5897i	−0.648140	+	1.50766i
$799$	0.323131			0.0114315
$800$	9.65472	−	26.5855i	0.341346	−	0.939938i
$801$	54.9039			1.93993
$802$	9.09514	−	21.1565i	0.321161	−	0.747062i
$803$			53.4930i			1.88773i
$804$	39.3401	−	37.2990i	1.38742	−	1.31544i
$805$	17.0128	+	15.2232i	0.599623	+	0.536548i
$806$	−5.15996	−	2.21826i	−0.181752	−	0.0781348i
$807$	−6.51890	+	6.51890i	−0.229476	+	0.229476i
$808$	23.1360	+	10.6846i	0.813922	+	0.375884i
$809$	27.1588			0.954851			0.477426	−	0.878672i	$-0.341570\pi$
$809$	27.1588			0.954851			0.477426	+	0.878672i	$0.341570\pi$
$810$	20.6698	−	9.60106i	0.726263	−	0.337347i
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	−0.880089	−	0.474809i	$-0.842517\pi$
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	0.474809	+	0.880089i	$0.342517\pi$
$812$	−26.1827	−	27.6155i	−0.918833	−	0.969113i
$813$	−8.51429			−0.298609
$814$	5.01838	+	12.5868i	0.175894	+	0.441168i
$815$	19.6575	−	21.9684i	0.688574	−	0.769520i
$816$	−0.805726	+	0.724178i	−0.0282060	+	0.0253513i
$817$	10.2779	−	10.2779i	0.359579	−	0.359579i
$818$	−9.73292	+	22.6401i	−0.340304	+	0.791591i
$819$	20.2664	−	20.2664i	0.708166	−	0.708166i
$820$	7.63890	−	0.220305i	0.266762	−	0.00769338i
$821$	−20.2900	−	20.2900i	−0.708126	−	0.708126i	0.258015	−	0.966141i	$-0.416932\pi$
$821$	−20.2900	−	20.2900i	−0.708126	−	0.708126i	−0.966141	+	0.258015i	$0.916932\pi$
$822$	14.1275	+	35.4338i	0.492754	+	1.23590i
$823$	−31.4540	−	31.4540i	−1.09642	−	1.09642i	−0.994826	−	0.101592i	$-0.967606\pi$
$823$	−31.4540	−	31.4540i	−1.09642	−	1.09642i	−0.101592	−	0.994826i	$-0.532394\pi$
$824$	−7.03395	−	3.24840i	−0.245039	−	0.113164i
$825$	−30.1638	+	37.7247i	−1.05017	+	1.31341i
$826$	14.2207	−	33.0793i	0.494802	−	1.15098i
$827$		−	15.3304i		−	0.533090i	−0.963822	−	0.266545i	$-0.914118\pi$
$827$		−	15.3304i		−	0.533090i	0.963822	−	0.266545i	$-0.0858822\pi$
$828$	−0.561433	+	21.0809i	−0.0195111	+	0.732611i
$829$	0.896046	+	0.896046i	0.0311210	+	0.0311210i	0.722496	−	0.691375i	$-0.242995\pi$
$829$	0.896046	+	0.896046i	0.0311210	+	0.0311210i	−0.691375	+	0.722496i	$0.742995\pi$
$830$	−14.8283	−	31.9234i	−0.514698	−	1.10808i
$831$		−	11.7562i		−	0.407817i
$832$	−14.6264	+	12.4583i	−0.507080	+	0.431915i
$833$	0.341897	+	0.341897i	0.0118460	+	0.0118460i
$834$	21.7928	+	54.6595i	0.754623	+	1.89270i
$835$	−37.3176	+	2.07168i	−1.29143	+	0.0716935i
$836$	−20.7664	+	19.6889i	−0.718220	+	0.680956i
$837$	2.15491			0.0744845
$838$	8.68522	+	21.7838i	0.300026	+	0.752508i
$839$		−	48.1891i		−	1.66367i	−0.555021	−	0.831837i	$-0.687290\pi$
$839$		−	48.1891i		−	1.66367i	0.555021	−	0.831837i	$-0.312710\pi$
$840$	−21.7770	−	50.3497i	−0.751376	−	1.73723i
$841$			2.33080i			0.0803723i
$842$	43.7333	−	17.4365i	1.50715	−	0.600902i
$843$	−56.4359			−1.94376
$844$	0.481069	−	18.0634i	0.0165591	−	0.621767i
$845$	−12.0513	−	10.7836i	−0.414577	−	0.370967i
$846$	−14.0398	+	5.59768i	−0.482698	+	0.192452i
$847$	−8.01241	−	8.01241i	−0.275310	−	0.275310i
$848$	5.17166	+	0.275662i	0.177596	+	0.00946628i
$849$			27.7179i			0.951277i
$850$	0.662123	−	0.353426i	0.0227106	−	0.0121224i
$851$	−5.37484	−	5.37484i	−0.184247	−	0.184247i
$852$	−8.41843	+	7.98166i	−0.288411	+	0.273447i
$853$		−	13.7426i		−	0.470537i	−0.971930	−	0.235268i	$-0.924403\pi$
$853$		−	13.7426i		−	0.470537i	0.971930	−	0.235268i	$-0.0755969\pi$
$854$	63.9663	+	27.4990i	2.18888	+	0.940996i
$855$	29.6224	−	1.64448i	1.01306	−	0.0562401i
$856$	−6.81862	−	18.5208i	−0.233056	−	0.633029i
$857$	13.4366	+	13.4366i	0.458986	+	0.458986i	0.898323	−	0.439336i	$-0.144786\pi$
$857$	13.4366	+	13.4366i	0.458986	+	0.458986i	−0.439336	+	0.898323i	$0.644786\pi$
$858$	30.4773	−	12.1513i	1.04048	−	0.414839i
$859$	−7.00719	−	7.00719i	−0.239082	−	0.239082i	0.577388	−	0.816470i	$-0.304072\pi$
$859$	−7.00719	−	7.00719i	−0.239082	−	0.239082i	−0.816470	+	0.577388i	$0.804072\pi$
$860$	0.495835	+	17.1927i	0.0169078	+	0.586267i
$861$	10.4806	−	10.4806i	0.357178	−	0.357178i
$862$	45.5051	+	19.5626i	1.54991	+	0.666304i
$863$	41.4708	−	41.4708i	1.41168	−	1.41168i	0.663560	−	0.748123i	$-0.269045\pi$
$863$	41.4708	−	41.4708i	1.41168	−	1.41168i	0.748123	−	0.663560i	$-0.230955\pi$
$864$	3.26769	−	6.60763i	0.111169	−	0.224796i
$865$	25.9555	+	23.2252i	0.882513	+	0.789682i
$866$	−18.7811	+	7.48806i	−0.638209	+	0.254455i
$867$	43.3486			1.47219
$868$	−0.299313	+	11.2387i	−0.0101593	+	0.381466i
$869$	−23.3070	+	23.3070i	−0.790636	+	0.790636i
$870$	−15.5104	+	42.4179i	−0.525852	+	1.43810i
$871$	25.5125			0.864458
$872$	−1.00863	−	0.465802i	−0.0341564	−	0.0157741i
$873$	−17.5771	+	17.5771i	−0.594894	+	0.594894i
$874$	6.33993	−	14.7475i	0.214451	−	0.498842i
$875$	6.29398	+	37.4807i	0.212775	+	1.26708i
$876$	−1.91965	+	72.0796i	−0.0648588	+	2.43534i
$877$			5.34168i			0.180376i	0.995925	+	0.0901879i	$0.0287468\pi$
$877$			5.34168i			0.180376i	−0.995925	+	0.0901879i	$0.971253\pi$
$878$	29.3721	+	12.6270i	0.991259	+	0.426141i
$879$	−46.9666			−1.58414
$880$	−0.0746950	−	33.8625i	−0.00251797	−	1.14150i
$881$	−45.9723			−1.54885			−0.774423	−	0.632668i	$-0.781960\pi$
$881$	−45.9723			−1.54885			−0.774423	+	0.632668i	$0.781960\pi$
$882$	−20.7779	−	8.93240i	−0.699630	−	0.300769i
$883$			2.64739i			0.0890918i	0.999007	+	0.0445459i	$0.0141841\pi$
$883$			2.64739i			0.0890918i	−0.999007	+	0.0445459i	$0.985816\pi$
$884$	−0.509653	−	0.0135732i	−0.0171415	−	0.000456518i
$885$	−42.6683	+	2.36872i	−1.43428	+	0.0796238i
$886$	6.09806	−	14.1849i	0.204868	−	0.476551i
$887$	3.87171	−	3.87171i	0.129999	−	0.129999i	−0.639113	−	0.769113i	$-0.720699\pi$
$887$	3.87171	−	3.87171i	0.129999	−	0.129999i	0.769113	+	0.639113i	$0.220699\pi$
$888$	6.31037	+	17.1403i	0.211762	+	0.575191i
$889$	3.26661			0.109558
$890$	44.8524	−	20.8338i	1.50346	−	0.698351i
$891$	19.2939	−	19.2939i	0.646369	−	0.646369i
$892$	−12.1517	−	0.323627i	−0.406868	−	0.0108358i
$893$	11.5053			0.385009
$894$	−26.1275	+	10.4171i	−0.873834	+	0.348399i
$895$	49.2441	−	2.73378i	1.64605	−	0.0913801i
$896$	34.0076	+	17.9601i	1.13611	+	0.600005i
$897$	−13.0144	+	13.0144i	−0.434539	+	0.434539i
$898$	−37.4328	−	16.0923i	−1.24915	−	0.537006i
$899$	6.54516	−	6.54516i	0.218293	−	0.218293i
$900$	−22.6463	+	26.8262i	−0.754877	+	0.894208i
$901$	0.0971768	+	0.0971768i	0.00323743	+	0.00323743i
$902$	8.49868	−	3.38843i	0.282975	−	0.112822i
$903$	23.5885	+	23.5885i	0.784975	+	0.784975i
$904$	−31.7962	−	14.6840i	−1.05752	−	0.488384i
$905$	0.523580	+	9.43136i	0.0174044	+	0.313509i
$906$	−13.7121	−	5.89479i	−0.455553	−	0.195841i
$907$		−	26.2062i		−	0.870163i	−0.900391	−	0.435081i	$-0.856720\pi$
$907$		−	26.2062i		−	0.870163i	0.900391	−	0.435081i	$-0.143280\pi$
$908$	−40.0473	−	42.2388i	−1.32902	−	1.40174i
$909$	−22.3667	−	22.3667i	−0.741856	−	0.741856i
$910$	8.86588	−	24.2465i	0.293901	−	0.803762i
$911$			24.2898i			0.804757i	0.915473	+	0.402378i	$0.131816\pi$
$911$			24.2898i			0.804757i	−0.915473	+	0.402378i	$0.868184\pi$
$912$	−28.6884	+	25.7848i	−0.949966	+	0.853820i
$913$	−29.7983	−	29.7983i	−0.986181	−	0.986181i
$914$	−35.6049	+	14.1957i	−1.17771	+	0.469553i
$915$	−4.58047	−	82.5089i	−0.151426	−	2.72766i
$916$	−51.8564	−	1.38106i	−1.71339	−	0.0456314i
$917$	−26.1452			−0.863391
$918$	0.181698	−	0.0724433i	0.00599694	−	0.00239099i
$919$			41.1294i			1.35673i	0.734723	+	0.678367i	$0.237312\pi$
$919$			41.1294i			1.35673i	−0.734723	+	0.678367i	$0.762688\pi$
$920$	7.54069	+	17.4346i	0.248609	+	0.574800i
$921$			16.8629i			0.555650i
$922$	3.28298	+	8.23420i	0.108119	+	0.271179i
$923$	−5.45944			−0.179700
$924$	−45.1874	−	47.6601i	−1.48656	−	1.56790i
$925$	−1.40066	−	12.5763i	−0.0460535	−	0.413508i
$926$	−14.9265	−	37.4377i	−0.490514	−	1.23028i
$927$	6.80006	+	6.80006i	0.223343	+	0.223343i
$928$	−10.1445	−	29.9946i	−0.333009	−	0.984620i
$929$			43.4799i			1.42653i	0.700894	+	0.713265i	$0.252785\pi$
$929$			43.4799i			1.42653i	−0.700894	+	0.713265i	$0.747215\pi$
$930$	12.1015	−	5.62111i	0.396824	−	0.184324i
$931$	12.1734	+	12.1734i	0.398968	+	0.398968i
$932$	4.14680	+	0.110439i	0.135833	+	0.00361754i
$933$			1.54653i			0.0506313i
$934$	2.17752	−	5.06521i	0.0712507	−	0.165739i
$935$	0.599188	−	0.669626i	0.0195955	−	0.0218991i
$936$	22.3792	−	8.23911i	0.731487	−	0.269304i
$937$	−13.0565	−	13.0565i	−0.426537	−	0.426537i	0.460910	−	0.887447i	$-0.347523\pi$
$937$	−13.0565	−	13.0565i	−0.426537	−	0.426537i	−0.887447	+	0.460910i	$0.847523\pi$
$938$	−18.9132	−	47.4370i	−0.617537	−	1.54887i
$939$	49.4266	+	49.4266i	1.61298	+	1.61298i
$940$	−9.34538	+	9.90043i	−0.304813	+	0.322916i
$941$	−5.53494	+	5.53494i	−0.180434	+	0.180434i	−0.791545	−	0.611111i	$-0.790723\pi$
$941$	−5.53494	+	5.53494i	−0.180434	+	0.180434i	0.611111	+	0.791545i	$0.290723\pi$
$942$	28.8884	−	67.1982i	0.941235	−	2.18944i
$943$	−3.62911	+	3.62911i	−0.118180	+	0.118180i
$944$	22.2821	−	20.0270i	0.725222	−	0.651822i
$945$	0.549030	+	9.88979i	0.0178599	+	0.321715i
$946$	7.62627	+	19.1278i	0.247951	+	0.621898i
$947$	−31.6905			−1.02980			−0.514902	−	0.857249i	$-0.672172\pi$
$947$	−31.6905			−1.02980			−0.514902	+	0.857249i	$0.672172\pi$
$948$	−32.2416	+	30.5688i	−1.04716	+	0.992830i
$949$	−23.9947	+	23.9947i	−0.778900	+	0.778900i
$950$	23.5753	−	12.5839i	0.764884	−	0.408277i
$951$	17.9717			0.582772
$952$	0.352583	+	0.957692i	0.0114273	+	0.0310390i
$953$	−2.85543	+	2.85543i	−0.0924965	+	0.0924965i	−0.751841	−	0.659344i	$-0.770834\pi$
$953$	−2.85543	+	2.85543i	−0.0924965	+	0.0924965i	0.659344	+	0.751841i	$0.270834\pi$
$954$	−5.90568	−	2.53884i	−0.191204	−	0.0821981i
$955$	−9.64970	+	10.7841i	−0.312257	+	0.348964i
$956$	17.2602	+	18.2047i	0.558235	+	0.588783i
$957$			54.0722i			1.74791i
$958$	5.50331	−	12.8014i	0.177804	−	0.413595i
$959$	35.9348			1.16039
$960$	1.11454	−	45.6309i	0.0359716	−	1.47273i
$961$	28.2654			0.911786
$962$	−3.39488	+	7.89694i	−0.109455	+	0.254608i
$963$			24.4969i			0.789401i
$964$	−20.4854	−	21.6064i	−0.659790	−	0.695895i
$965$	−1.94793	−	35.0886i	−0.0627062	−	1.12954i
$966$	33.8465	+	14.5506i	1.08899	+	0.468156i
$967$	−40.1144	+	40.1144i	−1.28999	+	1.28999i	−0.355202	+	0.934790i	$0.615588\pi$
$967$	−40.1144	+	40.1144i	−1.28999	+	1.28999i	−0.934790	+	0.355202i	$0.884412\pi$
$968$	−3.25737	−	8.84771i	−0.104696	−	0.284376i
$969$	−1.02356			−0.0328816
$970$	−7.68939	+	21.0290i	−0.246891	+	0.675200i
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	−0.928335	−	0.371743i	$-0.878760\pi$
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	0.371743	+	0.928335i	$0.378760\pi$
$972$	32.3639	−	30.6848i	1.03807	−	0.984214i
$973$	55.4322			1.77708
$974$	−10.3079	−	25.8536i	−0.330285	−	0.828404i
$975$	−30.4519	+	3.39151i	−0.975241	+	0.108615i
$976$	38.7267	+	43.0876i	1.23961	+	1.37920i
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	−0.875065	−	0.484005i	$-0.839182\pi$
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	0.484005	+	0.875065i	$0.339182\pi$
$978$	18.7889	−	43.7055i	0.600804	−	1.39755i
$979$	41.8667	−	41.8667i	1.33807	−	1.33807i
$980$	−20.3635	+	0.587281i	−0.650489	+	0.0187600i
$981$	0.975089	+	0.975089i	0.0311322	+	0.0311322i
$982$	1.77185	+	4.44406i	0.0565421	+	0.141816i
$983$	13.6091	+	13.6091i	0.434063	+	0.434063i	0.890008	−	0.455945i	$-0.150699\pi$
$983$	13.6091	+	13.6091i	0.434063	+	0.434063i	−0.455945	+	0.890008i	$0.650699\pi$
$984$	11.5732	−	4.26079i	0.368940	−	0.135829i
$985$	−41.8132	−	37.4148i	−1.33228	−	1.19214i
$986$	0.331843	−	0.771911i	0.0105680	−	0.0245827i
$987$			26.4053i			0.840491i
$988$	−18.1465	−	0.483284i	−0.577317	−	0.0153753i
$989$	−8.16797	−	8.16797i	−0.259726	−	0.259726i
$990$	−14.4342	+	39.4746i	−0.458748	+	1.25459i
$991$		−	52.9400i		−	1.68169i	−0.541273	−	0.840847i	$-0.682058\pi$
$991$		−	52.9400i		−	1.68169i	0.541273	−	0.840847i	$-0.317942\pi$
$992$	−4.14678	+	8.38525i	−0.131660	+	0.266232i
$993$	33.7513	+	33.7513i	1.07107	+	1.07107i
$994$	4.04725	+	10.1511i	0.128371	+	0.321973i
$995$	−27.9693	+	31.2573i	−0.886688	+	0.990923i
$996$	−39.0827	−	41.2213i	−1.23838	−	1.30615i
$997$	3.67381			0.116351			0.0581754	−	0.998306i	$-0.481472\pi$
$997$	3.67381			0.116351			0.0581754	+	0.998306i	$0.481472\pi$
$998$	7.31097	+	18.3370i	0.231425	+	0.580446i
$999$		−	3.29792i		−	0.104342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.j.b.43.4	✓	18
3.2	odd	2		720.2.bd.g.523.6		18
4.3	odd	2		320.2.j.b.143.8		18
5.2	odd	4		80.2.s.b.27.2	yes	18
5.3	odd	4		400.2.s.d.107.8		18
5.4	even	2		400.2.j.d.43.6		18
8.3	odd	2		640.2.j.c.543.2		18
8.5	even	2		640.2.j.d.543.8		18
15.2	even	4		720.2.z.g.667.8		18
16.3	odd	4		80.2.s.b.3.2	yes	18
16.5	even	4		640.2.s.c.223.2		18
16.11	odd	4		640.2.s.d.223.8		18
16.13	even	4		320.2.s.b.303.8		18
20.3	even	4		1600.2.s.d.207.2		18
20.7	even	4		320.2.s.b.207.8		18
20.19	odd	2		1600.2.j.d.143.2		18
40.27	even	4		640.2.s.c.287.2		18
40.37	odd	4		640.2.s.d.287.8		18
48.35	even	4		720.2.z.g.163.8		18
80.3	even	4		400.2.j.d.307.6		18
80.13	odd	4		1600.2.j.d.1007.8		18
80.19	odd	4		400.2.s.d.243.8		18
80.27	even	4		640.2.j.d.607.2		18
80.29	even	4		1600.2.s.d.943.2		18
80.37	odd	4		640.2.j.c.607.8		18
80.67	even	4	inner	80.2.j.b.67.4	yes	18
80.77	odd	4		320.2.j.b.47.2		18
240.227	odd	4		720.2.bd.g.307.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	1.1	even	1	trivial
80.2.j.b.67.4	yes	18	80.67	even	4	inner
80.2.s.b.3.2	yes	18	16.3	odd	4
80.2.s.b.27.2	yes	18	5.2	odd	4
320.2.j.b.47.2		18	80.77	odd	4
320.2.j.b.143.8		18	4.3	odd	2
320.2.s.b.207.8		18	20.7	even	4
320.2.s.b.303.8		18	16.13	even	4
400.2.j.d.43.6		18	5.4	even	2
400.2.j.d.307.6		18	80.3	even	4
400.2.s.d.107.8		18	5.3	odd	4
400.2.s.d.243.8		18	80.19	odd	4
640.2.j.c.543.2		18	8.3	odd	2
640.2.j.c.607.8		18	80.37	odd	4
640.2.j.d.543.8		18	8.5	even	2
640.2.j.d.607.2		18	80.27	even	4
640.2.s.c.223.2		18	16.5	even	4
640.2.s.c.287.2		18	40.27	even	4
640.2.s.d.223.8		18	16.11	odd	4
640.2.s.d.287.8		18	40.37	odd	4
720.2.z.g.163.8		18	48.35	even	4
720.2.z.g.667.8		18	15.2	even	4
720.2.bd.g.307.6		18	240.227	odd	4
720.2.bd.g.523.6		18	3.2	odd	2
1600.2.j.d.143.2		18	20.19	odd	2
1600.2.j.d.1007.8		18	80.13	odd	4
1600.2.s.d.207.2		18	20.3	even	4
1600.2.s.d.943.2		18	80.29	even	4

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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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 - 1.45136i) q^{4} +(1.66635 + 1.49107i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 - 2.40368i) q^{7} +(2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +O(q^{10})\)	\(q+(-0.558542 + 1.29924i) q^{2} -2.55161i q^{3} +(-1.37606 - 1.45136i) q^{4} +(1.66635 + 1.49107i) q^{5} +(3.31516 + 1.42518i) q^{6} +(2.40368 - 2.40368i) q^{7} +(2.65426 - 0.977191i) q^{8} -3.51070 q^{9} +(-2.86798 + 1.33217i) q^{10} +(-2.67707 + 2.67707i) q^{11} +(-3.70331 + 3.51117i) q^{12} -2.40164 q^{13} +(1.78040 + 4.46551i) q^{14} +(3.80462 - 4.25187i) q^{15} +(-0.212908 + 3.99433i) q^{16} +(-0.0750544 + 0.0750544i) q^{17} +(1.96087 - 4.56125i) q^{18} +(-2.67236 + 2.67236i) q^{19} +(-0.128922 - 4.47028i) q^{20} +(-6.13324 - 6.13324i) q^{21} +(-1.98291 - 4.97342i) q^{22} +(2.12375 + 2.12375i) q^{23} +(-2.49341 - 6.77263i) q^{24} +(0.553442 + 4.96928i) q^{25} +(1.34141 - 3.12031i) q^{26} +1.30310i q^{27} +(-6.79621 - 0.180999i) q^{28} +(3.95795 + 3.95795i) q^{29} +(3.39917 + 7.31797i) q^{30} -1.65367i q^{31} +(-5.07068 - 2.50762i) q^{32} +(6.83083 + 6.83083i) q^{33} +(-0.0555929 - 0.139435i) q^{34} +(7.58941 - 0.421324i) q^{35} +(4.83094 + 5.09530i) q^{36} -2.53082 q^{37} +(-1.97942 - 4.96467i) q^{38} +6.12803i q^{39} +(5.87998 + 2.32934i) q^{40} +1.70882i q^{41} +(11.3942 - 4.54289i) q^{42} -3.84601 q^{43} +(7.56921 + 0.201586i) q^{44} +(-5.85005 - 5.23469i) q^{45} +(-3.94547 + 1.57306i) q^{46} +(-2.15264 - 2.15264i) q^{47} +(10.1920 + 0.543256i) q^{48} -4.55532i q^{49} +(-6.76541 - 2.05649i) q^{50} +(0.191509 + 0.191509i) q^{51} +(3.30480 + 3.48565i) q^{52} -1.29475i q^{53} +(-1.69305 - 0.727839i) q^{54} +(-8.45262 + 0.469246i) q^{55} +(4.03113 - 8.72883i) q^{56} +(6.81881 + 6.81881i) q^{57} +(-7.35302 + 2.93166i) q^{58} +(-5.29614 - 5.29614i) q^{59} +(-11.4064 + 0.328959i) q^{60} +(10.2413 - 10.2413i) q^{61} +(2.14852 + 0.923645i) q^{62} +(-8.43858 + 8.43858i) q^{63} +(6.09020 - 5.18744i) q^{64} +(-4.00197 - 3.58100i) q^{65} +(-12.6902 + 5.05960i) q^{66} -10.6230 q^{67} +(0.212211 + 0.00565167i) q^{68} +(5.41898 - 5.41898i) q^{69} +(-3.69160 + 10.0958i) q^{70} +2.27322 q^{71} +(-9.31831 + 3.43062i) q^{72} +(9.99096 - 9.99096i) q^{73} +(1.41357 - 3.28815i) q^{74} +(12.6796 - 1.41217i) q^{75} +(7.55589 + 0.201231i) q^{76} +12.8696i q^{77} +(-7.96180 - 3.42276i) q^{78} +8.70617 q^{79} +(-6.31059 + 6.33849i) q^{80} -7.20709 q^{81} +(-2.22017 - 0.954448i) q^{82} +11.1310i q^{83} +(-0.461838 + 17.3413i) q^{84} +(-0.236978 + 0.0131558i) q^{85} +(2.14816 - 4.99689i) q^{86} +(10.0991 - 10.0991i) q^{87} +(-4.48963 + 9.72165i) q^{88} -15.6390 q^{89} +(10.0686 - 4.67685i) q^{90} +(-5.77276 + 5.77276i) q^{91} +(0.159920 - 6.00475i) q^{92} -4.21952 q^{93} +(3.99914 - 1.59446i) q^{94} +(-8.43775 + 0.468420i) q^{95} +(-6.39846 + 12.9384i) q^{96} +(5.00672 - 5.00672i) q^{97} +(5.91846 + 2.54434i) q^{98} +(9.39839 - 9.39839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

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