LMFDB - Embedded newform 80.2.l.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(21,80)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.3
Root			$1.21331 + 0.726558i$ of defining polynomial
Character	$\chi$	$=$	80.61
Dual form			80.2.l.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +O(q^{10})$	\(q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +(-0.697313 - 1.23035i) q^{10} +(-1.64080 + 1.64080i) q^{11} +(-1.25807 - 5.01385i) q^{12} +(1.51857 + 1.51857i) q^{13} +(6.14687 + 1.69972i) q^{14} -2.58464 q^{15} +(1.88845 + 3.52615i) q^{16} +1.45616 q^{17} +(-5.01657 - 1.38717i) q^{18} +(-2.67964 - 2.67964i) q^{19} +(1.93986 - 0.486749i) q^{20} +(8.24183 - 8.24183i) q^{21} +(-1.61808 - 2.85495i) q^{22} -2.37423i q^{23} +(7.30837 + 0.174953i) q^{24} -1.00000i q^{25} +(-2.64228 + 1.49754i) q^{26} +(-1.24345 + 1.24345i) q^{27} +(-4.63366 + 7.73792i) q^{28} +(0.924966 + 0.924966i) q^{29} +(0.974182 - 3.52303i) q^{30} -7.20435 q^{31} +(-5.51814 + 1.24503i) q^{32} -5.99752 q^{33} +(-0.548843 + 1.98483i) q^{34} +(3.18877 + 3.18877i) q^{35} +(3.78161 - 6.31505i) q^{36} +(-5.21123 + 5.21123i) q^{37} +(4.66251 - 2.64253i) q^{38} +5.55074i q^{39} +(-0.0676894 + 2.82762i) q^{40} +6.41166i q^{41} +(8.12768 + 14.3406i) q^{42} +(7.65800 - 7.65800i) q^{43} +(4.50135 - 1.12947i) q^{44} +(-2.60241 - 2.60241i) q^{45} +(3.23622 + 0.894875i) q^{46} -2.51027 q^{47} +(-2.99308 + 9.89582i) q^{48} -13.3366 q^{49} +(1.36306 + 0.376912i) q^{50} +(2.66130 + 2.66130i) q^{51} +(-1.04534 - 4.16603i) q^{52} +(1.50312 - 1.50312i) q^{53} +(-1.22623 - 2.16357i) q^{54} -2.32045i q^{55} +(-8.80078 - 9.23248i) q^{56} -9.79472i q^{57} +(-1.60942 + 0.912155i) q^{58} +(-5.31807 + 5.31807i) q^{59} +(4.43492 + 2.65574i) q^{60} +(-1.02169 - 1.02169i) q^{61} +(2.71541 - 9.81998i) q^{62} +16.5970 q^{63} +(0.382800 - 7.99084i) q^{64} -2.14759 q^{65} +(2.26054 - 8.17499i) q^{66} +(5.22745 + 5.22745i) q^{67} +(-2.49859 - 1.49622i) q^{68} +(4.33918 - 4.33918i) q^{69} +(-5.54838 + 3.14461i) q^{70} +1.92097i q^{71} +(7.18247 + 7.53478i) q^{72} +1.39412i q^{73} +(-5.13905 - 9.06740i) q^{74} +(1.82762 - 1.82762i) q^{75} +(1.84458 + 7.35129i) q^{76} +(7.39938 + 7.39938i) q^{77} +(-7.56600 - 2.09214i) q^{78} +5.06317 q^{79} +(-3.82870 - 1.15803i) q^{80} +6.49599 q^{81} +(-8.73949 - 2.41663i) q^{82} +(-2.44974 - 2.44974i) q^{83} +(-22.6105 + 5.67340i) q^{84} +(-1.02966 + 1.02966i) q^{85} +(7.55194 + 13.3247i) q^{86} +3.38097i q^{87} +(-0.157070 + 6.56133i) q^{88} -9.36007i q^{89} +(4.52813 - 2.56637i) q^{90} +(6.84817 - 6.84817i) q^{91} +(-2.43954 + 4.07388i) q^{92} +(-13.1668 - 13.1668i) q^{93} +(0.946152 - 3.42166i) q^{94} +3.78959 q^{95} +(-12.3605 - 7.80961i) q^{96} +18.6313 q^{97} +(5.02671 - 18.1785i) q^{98} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.376912	+	1.36306i	−0.266517	+	0.963830i
$2$	−0.376912	+	1.36306i	−0.266517	+	0.963830i
$3$	1.82762	+	1.82762i	1.05518	+	1.05518i	0.998386	+	0.0567890i	$0.0180862\pi$
$3$	1.82762	+	1.82762i	1.05518	+	1.05518i	0.0567890	+	0.998386i	$0.481914\pi$
$4$	−1.71587	−	1.02751i	−0.857937	−	0.513754i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−3.18001	+	1.80230i	−1.29823	+	0.735788i
$7$		−	4.50961i		−	1.70447i	−0.523158	−	0.852236i	$-0.675246\pi$
$7$		−	4.50961i		−	1.70447i	0.523158	−	0.852236i	$-0.324754\pi$
$8$	2.04729	−	1.95156i	0.723827	−	0.689982i
$9$			3.68037i			1.22679i
$10$	−0.697313	−	1.23035i	−0.220510	−	0.389070i
$11$	−1.64080	+	1.64080i	−0.494721	+	0.494721i	−0.909790	−	0.415069i	$-0.863757\pi$
$11$	−1.64080	+	1.64080i	−0.494721	+	0.494721i	0.415069	+	0.909790i	$0.363757\pi$
$12$	−1.25807	−	5.01385i	−0.363174	−	1.44737i
$13$	1.51857	+	1.51857i	0.421176	+	0.421176i	0.885609	−	0.464432i	$-0.153742\pi$
$13$	1.51857	+	1.51857i	0.421176	+	0.421176i	−0.464432	+	0.885609i	$0.653742\pi$
$14$	6.14687	+	1.69972i	1.64282	+	0.454270i
$15$	−2.58464			−0.667351
$16$	1.88845	+	3.52615i	0.472113	+	0.881538i
$17$	1.45616			0.353170			0.176585	−	0.984285i	$-0.443495\pi$
$17$	1.45616			0.353170			0.176585	+	0.984285i	$0.443495\pi$
$18$	−5.01657	−	1.38717i	−1.18242	−	0.326960i
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	0.329428	−	0.944181i	$-0.393144\pi$
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	−0.944181	+	0.329428i	$0.893144\pi$
$20$	1.93986	−	0.486749i	0.433767	−	0.108840i
$21$	8.24183	−	8.24183i	1.79852	−	1.79852i
$22$	−1.61808	−	2.85495i	−0.344975	−	0.608678i
$23$		−	2.37423i		−	0.495061i	−0.968880	−	0.247530i	$-0.920381\pi$
$23$		−	2.37423i		−	0.495061i	0.968880	−	0.247530i	$-0.0796190\pi$
$24$	7.30837	+	0.174953i	1.49182	+	0.0357121i
$25$		−	1.00000i		−	0.200000i
$26$	−2.64228	+	1.49754i	−0.518193	+	0.293692i
$27$	−1.24345	+	1.24345i	−0.239303	+	0.239303i
$28$	−4.63366	+	7.73792i	−0.875679	+	1.46233i
$29$	0.924966	+	0.924966i	0.171762	+	0.171762i	0.787753	−	0.615991i	$-0.211244\pi$
$29$	0.924966	+	0.924966i	0.171762	+	0.171762i	−0.615991	+	0.787753i	$0.711244\pi$
$30$	0.974182	−	3.52303i	0.177860	−	0.643213i
$31$	−7.20435			−1.29394			−0.646970	−	0.762515i	$-0.723964\pi$
$31$	−7.20435			−1.29394			−0.646970	+	0.762515i	$0.723964\pi$
$32$	−5.51814	+	1.24503i	−0.975479	+	0.220092i
$33$	−5.99752			−1.04403
$34$	−0.548843	+	1.98483i	−0.0941259	+	0.340396i
$35$	3.18877	+	3.18877i	0.539001	+	0.539001i
$36$	3.78161	−	6.31505i	0.630268	−	1.05251i
$37$	−5.21123	+	5.21123i	−0.856720	+	0.856720i	−0.990950	−	0.134230i	$-0.957144\pi$
$37$	−5.21123	+	5.21123i	−0.856720	+	0.856720i	0.134230	+	0.990950i	$0.457144\pi$
$38$	4.66251	−	2.64253i	0.756359	−	0.428675i
$39$			5.55074i			0.888830i
$40$	−0.0676894	+	2.82762i	−0.0107026	+	0.447086i
$41$			6.41166i			1.00133i	0.865640	+	0.500667i	$0.166912\pi$
$41$			6.41166i			1.00133i	−0.865640	+	0.500667i	$0.833088\pi$
$42$	8.12768	+	14.3406i	1.25413	+	2.21280i
$43$	7.65800	−	7.65800i	1.16783	−	1.16783i	0.185118	−	0.982716i	$-0.440733\pi$
$43$	7.65800	−	7.65800i	1.16783	−	1.16783i	0.982716	−	0.185118i	$-0.0592669\pi$
$44$	4.50135	−	1.12947i	0.678604	−	0.170275i
$45$	−2.60241	−	2.60241i	−0.387945	−	0.387945i
$46$	3.23622	+	0.894875i	0.477155	+	0.131942i
$47$	−2.51027			−0.366161			−0.183081	−	0.983098i	$-0.558607\pi$
$47$	−2.51027			−0.366161			−0.183081	+	0.983098i	$0.558607\pi$
$48$	−2.99308	+	9.89582i	−0.432015	+	1.42834i
$49$	−13.3366			−1.90522
$50$	1.36306	+	0.376912i	0.192766	+	0.0533034i
$51$	2.66130	+	2.66130i	0.372657	+	0.372657i
$52$	−1.04534	−	4.16603i	−0.144962	−	0.577724i
$53$	1.50312	−	1.50312i	0.206470	−	0.206470i	−0.596295	−	0.802765i	$-0.703361\pi$
$53$	1.50312	−	1.50312i	0.206470	−	0.206470i	0.802765	+	0.596295i	$0.203361\pi$
$54$	−1.22623	−	2.16357i	−0.166869	−	0.294425i
$55$		−	2.32045i		−	0.312889i
$56$	−8.80078	−	9.23248i	−1.17605	−	1.23374i
$57$		−	9.79472i		−	1.29734i
$58$	−1.60942	+	0.912155i	−0.211327	+	0.119772i
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	−0.962749	−	0.270396i	$-0.912845\pi$
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	0.270396	+	0.962749i	$0.412845\pi$
$60$	4.43492	+	2.65574i	0.572546	+	0.342855i
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	0.638668	−	0.769483i	$-0.279486\pi$
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	−0.769483	+	0.638668i	$0.779486\pi$
$62$	2.71541	−	9.81998i	0.344857	−	1.24714i
$63$	16.5970			2.09103
$64$	0.382800	−	7.99084i	0.0478499	−	0.998855i
$65$	−2.14759			−0.266375
$66$	2.26054	−	8.17499i	0.278253	−	1.00627i
$67$	5.22745	+	5.22745i	0.638635	+	0.638635i	0.950219	−	0.311584i	$-0.100859\pi$
$67$	5.22745	+	5.22745i	0.638635	+	0.638635i	−0.311584	+	0.950219i	$0.600859\pi$
$68$	−2.49859	−	1.49622i	−0.302998	−	0.181443i
$69$	4.33918	−	4.33918i	0.522376	−	0.522376i
$70$	−5.54838	+	3.14461i	−0.663158	+	0.375853i
$71$			1.92097i			0.227978i	0.993482	+	0.113989i	$0.0363628\pi$
$71$			1.92097i			0.227978i	−0.993482	+	0.113989i	$0.963637\pi$
$72$	7.18247	+	7.53478i	0.846462	+	0.887983i
$73$			1.39412i			0.163169i	0.996666	+	0.0815847i	$0.0259981\pi$
$73$			1.39412i			0.163169i	−0.996666	+	0.0815847i	$0.974002\pi$
$74$	−5.13905	−	9.06740i	−0.597403	−	1.05406i
$75$	1.82762	−	1.82762i	0.211035	−	0.211035i
$76$	1.84458	+	7.35129i	0.211587	+	0.843250i
$77$	7.39938	+	7.39938i	0.843237	+	0.843237i
$78$	−7.56600	−	2.09214i	−0.856681	−	0.236888i
$79$	5.06317			0.569651			0.284825	−	0.958579i	$-0.408064\pi$
$79$	5.06317			0.569651			0.284825	+	0.958579i	$0.408064\pi$
$80$	−3.82870	−	1.15803i	−0.428062	−	0.129471i
$81$	6.49599			0.721777
$82$	−8.73949	−	2.41663i	−0.965115	−	0.266872i
$83$	−2.44974	−	2.44974i	−0.268894	−	0.268894i	0.559761	−	0.828654i	$-0.310893\pi$
$83$	−2.44974	−	2.44974i	−0.268894	−	0.268894i	−0.828654	+	0.559761i	$0.810893\pi$
$84$	−22.6105	+	5.67340i	−2.46701	+	0.619019i
$85$	−1.02966	+	1.02966i	−0.111682	+	0.111682i
$86$	7.55194	+	13.3247i	0.814347	+	1.43684i
$87$			3.38097i			0.362478i
$88$	−0.157070	+	6.56133i	−0.0167437	+	0.699440i
$89$		−	9.36007i		−	0.992165i	−0.868275	−	0.496083i	$-0.834771\pi$
$89$		−	9.36007i		−	0.992165i	0.868275	−	0.496083i	$-0.165229\pi$
$90$	4.52813	−	2.56637i	0.477307	−	0.270519i
$91$	6.84817	−	6.84817i	0.717883	−	0.717883i
$92$	−2.43954	+	4.07388i	−0.254340	+	0.424731i
$93$	−13.1668	−	13.1668i	−1.36533	−	1.36533i
$94$	0.946152	−	3.42166i	0.0975882	−	0.352917i
$95$	3.78959			0.388803
$96$	−12.3605	−	7.80961i	−1.26154	−	0.797065i
$97$	18.6313			1.89172			0.945859	−	0.324579i	$-0.105223\pi$
$97$	18.6313			1.89172			0.945859	+	0.324579i	$0.105223\pi$
$98$	5.02671	−	18.1785i	0.507774	−	1.83631i
$99$	−6.03876	−	6.03876i	−0.606918	−	0.606918i
$100$	−1.02751	+	1.71587i	−0.102751	+	0.171587i
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	−0.905676	−	0.423971i	$-0.860636\pi$
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	0.423971	+	0.905676i	$0.360636\pi$
$102$	−4.63059	+	2.62444i	−0.458497	+	0.259858i
$103$			9.12540i			0.899153i	0.893242	+	0.449576i	$0.148425\pi$
$103$			9.12540i			0.899153i	−0.893242	+	0.449576i	$0.851575\pi$
$104$	6.07255	+	0.145369i	0.595463	+	0.0142546i
$105$			11.6557i			1.13748i
$106$	1.48230	+	2.61539i	0.143974	+	0.254029i
$107$	−10.1505	+	10.1505i	−0.981290	+	0.981290i	−0.999828	−	0.0185385i	$-0.994099\pi$
$107$	−10.1505	+	10.1505i	−0.981290	+	0.981290i	0.0185385	+	0.999828i	$0.494099\pi$
$108$	3.41127	−	0.855951i	0.328249	−	0.0823639i
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	0.769011	−	0.639236i	$-0.220749\pi$
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	−0.639236	+	0.769011i	$0.720749\pi$
$110$	3.16291	+	0.874603i	0.301572	+	0.0833902i
$111$	−19.0483			−1.80798
$112$	15.9016	−	8.51618i	1.50256	−	0.804704i
$113$	−2.56039			−0.240861			−0.120431	−	0.992722i	$-0.538428\pi$
$113$	−2.56039			−0.240861			−0.120431	+	0.992722i	$0.538428\pi$
$114$	13.3508	+	3.69175i	1.25042	+	0.345764i
$115$	1.67883	+	1.67883i	0.156552	+	0.156552i
$116$	−0.636716	−	2.53754i	−0.0591176	−	0.235604i
$117$	−5.58891	+	5.58891i	−0.516695	+	0.516695i
$118$	−5.24441	−	9.25329i	−0.482787	−	0.851835i
$119$		−	6.56670i		−	0.601969i
$120$	−5.29151	+	5.04409i	−0.483047	+	0.460460i
$121$			5.61553i			0.510503i
$122$	1.77772	−	1.00754i	0.160947	−	0.0912188i
$123$	−11.7181	+	11.7181i	−1.05658	+	1.05658i
$124$	12.3618	+	7.40253i	1.11012	+	0.664767i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−6.25561	+	22.6228i	−0.557294	+	2.01540i
$127$	13.7354			1.21882			0.609409	−	0.792856i	$-0.291407\pi$
$127$	13.7354			1.21882			0.609409	+	0.792856i	$0.291407\pi$
$128$	10.7477	+	3.53362i	0.949973	+	0.312331i
$129$	27.9918			2.46454
$130$	0.809451	−	2.92729i	0.0709935	−	0.256741i
$131$	5.20726	+	5.20726i	0.454960	+	0.454960i	0.896997	−	0.442037i	$-0.145744\pi$
$131$	5.20726	+	5.20726i	0.454960	+	0.454960i	−0.442037	+	0.896997i	$0.645744\pi$
$132$	10.2910	+	6.16250i	0.895716	+	0.536377i
$133$	−12.0841	+	12.0841i	−1.04783	+	1.04783i
$134$	−9.09563	+	5.15505i	−0.785743	+	0.445329i
$135$		−	1.75851i		−	0.151348i
$136$	2.98118	−	2.84179i	0.255634	−	0.243681i
$137$		−	22.7563i		−	1.94420i	−0.234559	−	0.972102i	$-0.575365\pi$
$137$		−	22.7563i		−	1.94420i	0.234559	−	0.972102i	$-0.424635\pi$
$138$	4.27908	+	7.55006i	0.364260	+	0.642704i
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	−0.388651	−	0.921385i	$-0.627059\pi$
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	0.921385	+	0.388651i	$0.127059\pi$
$140$	−2.19505	−	8.74803i	−0.185515	−	0.739343i
$141$	−4.58782	−	4.58782i	−0.386364	−	0.386364i
$142$	−2.61841	−	0.724038i	−0.219732	−	0.0607599i
$143$	−4.98336			−0.416729
$144$	−12.9775	+	6.95020i	−1.08146	+	0.579184i
$145$	−1.30810			−0.108632
$146$	−1.90027	−	0.525460i	−0.157268	−	0.0434874i
$147$	−24.3741	−	24.3741i	−2.01034	−	2.01034i
$148$	14.2964	−	3.58723i	1.17516	−	0.294869i
$149$	−12.9574	+	12.9574i	−1.06151	+	1.06151i	−0.0635329	+	0.997980i	$0.520237\pi$
$149$	−12.9574	+	12.9574i	−1.06151	+	1.06151i	−0.997980	+	0.0635329i	$0.979763\pi$
$150$	1.80230	+	3.18001i	0.147158	+	0.259646i
$151$		−	14.3417i		−	1.16711i	−0.812073	−	0.583555i	$-0.801661\pi$
$151$		−	14.3417i		−	1.16711i	0.812073	−	0.583555i	$-0.198339\pi$
$152$	−10.7155	−	0.256515i	−0.869142	−	0.0208061i
$153$			5.35920i			0.433266i
$154$	−12.8747	+	7.29689i	−1.03747	+	0.588001i
$155$	5.09425	−	5.09425i	0.409180	−	0.409180i
$156$	5.70343	−	9.52438i	0.456640	−	0.762560i
$157$	−2.10564	−	2.10564i	−0.168049	−	0.168049i	0.618073	−	0.786121i	$-0.287914\pi$
$157$	−2.10564	−	2.10564i	−0.168049	−	0.168049i	−0.786121	+	0.618073i	$0.787914\pi$
$158$	−1.90837	+	6.90141i	−0.151822	+	0.549047i
$159$	5.49426			0.435723
$160$	3.02155	−	4.78229i	0.238874	−	0.378073i
$161$	−10.7068			−0.843817
$162$	−2.44842	+	8.85444i	−0.192366	+	0.695671i
$163$	−5.34004	−	5.34004i	−0.418265	−	0.418265i	0.466341	−	0.884605i	$-0.345572\pi$
$163$	−5.34004	−	5.34004i	−0.418265	−	0.418265i	−0.884605	+	0.466341i	$0.845572\pi$
$164$	6.58804	−	11.0016i	0.514439	−	0.859081i
$165$	4.24089	−	4.24089i	0.330153	−	0.330153i
$166$	4.26248	−	2.41581i	0.330833	−	0.187503i
$167$			16.0686i			1.24343i	0.783245	+	0.621714i	$0.213563\pi$
$167$			16.0686i			1.24343i	−0.783245	+	0.621714i	$0.786437\pi$
$168$	0.788969	−	32.9579i	0.0608702	−	2.54276i
$169$		−	8.38787i		−	0.645221i
$170$	−1.01540	−	1.79158i	−0.0778775	−	0.137408i
$171$	9.86207	−	9.86207i	0.754171	−	0.754171i
$172$	−21.0088	+	5.27151i	−1.60191	+	0.401949i
$173$	17.1133	+	17.1133i	1.30110	+	1.30110i	0.927649	+	0.373453i	$0.121826\pi$
$173$	17.1133	+	17.1133i	1.30110	+	1.30110i	0.373453	+	0.927649i	$0.378174\pi$
$174$	−4.60847	−	1.27433i	−0.349367	−	0.0966065i
$175$	−4.50961			−0.340894
$176$	−8.88430	−	2.68714i	−0.669679	−	0.202551i
$177$	−19.4388			−1.46111
$178$	12.7584	+	3.52792i	0.956279	+	0.264429i
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	0.745075	−	0.666981i	$-0.232414\pi$
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	−0.666981	+	0.745075i	$0.732414\pi$
$180$	1.79141	+	7.13942i	0.133524	+	0.532141i
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	−0.103523	−	0.994627i	$-0.533012\pi$
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	0.994627	+	0.103523i	$0.0330115\pi$
$182$	6.75332	+	11.9156i	0.500589	+	0.883245i
$183$		−	3.73453i		−	0.276065i
$184$	−4.63346	−	4.86074i	−0.341583	−	0.358338i
$185$		−	7.36979i		−	0.541838i
$186$	22.9099	−	12.9844i	1.67983	−	0.952065i
$187$	−2.38927	+	2.38927i	−0.174721	+	0.174721i
$188$	4.30732	+	2.57933i	0.314143	+	0.188117i
$189$	5.60748	+	5.60748i	0.407884	+	0.407884i
$190$	−1.42834	+	5.16544i	−0.103623	+	0.374741i
$191$	0.0667471			0.00482965			0.00241483	−	0.999997i	$-0.499231\pi$
$191$	0.0667471			0.00482965			0.00241483	+	0.999997i	$0.499231\pi$
$192$	15.3038	−	13.9046i	1.10446	−	1.00348i
$193$	−1.09895			−0.0791039			−0.0395520	−	0.999218i	$-0.512593\pi$
$193$	−1.09895			−0.0791039			−0.0395520	+	0.999218i	$0.512593\pi$
$194$	−7.02234	+	25.3956i	−0.504175	+	1.82329i
$195$	−3.92497	−	3.92497i	−0.281073	−	0.281073i
$196$	22.8839	+	13.7034i	1.63456	+	0.978816i
$197$	11.9289	−	11.9289i	0.849899	−	0.849899i	−0.140222	−	0.990120i	$-0.544782\pi$
$197$	11.9289	−	11.9289i	0.849899	−	0.849899i	0.990120	+	0.140222i	$0.0447815\pi$
$198$	10.5073	−	5.95512i	0.746720	−	0.423212i
$199$			11.0397i			0.782584i	0.920267	+	0.391292i	$0.127972\pi$
$199$			11.0397i			0.782584i	−0.920267	+	0.391292i	$0.872028\pi$
$200$	−1.95156	−	2.04729i	−0.137996	−	0.144765i
$201$			19.1076i			1.34774i
$202$	−4.77403	−	8.42334i	−0.335899	−	0.592664i
$203$	4.17123	−	4.17123i	0.292763	−	0.292763i
$204$	−1.83195	−	7.30097i	−0.128262	−	0.511170i
$205$	−4.53373	−	4.53373i	−0.316649	−	0.316649i
$206$	−12.4385	−	3.43947i	−0.866631	−	0.239639i
$207$	8.73803			0.607335
$208$	−2.48696	+	8.22247i	−0.172440	+	0.570126i
$209$	8.79353			0.608261
$210$	−15.8875	−	4.39318i	−1.09634	−	0.303158i
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	0.346268	−	0.938136i	$-0.387449\pi$
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	−0.938136	+	0.346268i	$0.887449\pi$
$212$	−4.12364	+	1.03470i	−0.283213	+	0.0710634i
$213$	−3.51080	+	3.51080i	−0.240556	+	0.240556i
$214$	−10.0100	−	17.6617i	−0.684266	−	1.20733i
$215$			10.8301i			0.738603i
$216$	−0.119032	+	4.97238i	−0.00809912	+	0.338328i
$217$			32.4888i			2.20548i
$218$	−2.35748	+	1.33613i	−0.159669	+	0.0904941i
$219$	−2.54792	+	2.54792i	−0.172172	+	0.172172i
$220$	−2.38428	+	3.98159i	−0.160748	+	0.268439i
$221$	2.21128	+	2.21128i	0.148747	+	0.148747i
$222$	7.17951	−	25.9639i	0.481857	−	1.74259i
$223$	−21.4238			−1.43465			−0.717323	−	0.696741i	$-0.754633\pi$
$223$	−21.4238			−1.43465			−0.717323	+	0.696741i	$0.754633\pi$
$224$	5.61460	+	24.8847i	0.375141	+	1.66268i
$225$	3.68037			0.245358
$226$	0.965041	−	3.48997i	0.0641936	−	0.232149i
$227$	−8.06331	−	8.06331i	−0.535181	−	0.535181i	0.386929	−	0.922110i	$-0.373536\pi$
$227$	−8.06331	−	8.06331i	−0.535181	−	0.535181i	−0.922110	+	0.386929i	$0.873536\pi$
$228$	−10.0642	+	16.8065i	−0.666515	+	1.11304i
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	−0.537313	−	0.843383i	$-0.680560\pi$
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	0.843383	+	0.537313i	$0.180560\pi$
$230$	−2.92112	+	1.65558i	−0.192613	+	0.109166i
$231$			27.0465i			1.77953i
$232$	3.69880	+	0.0885445i	0.242838	+	0.00581323i
$233$		−	26.0672i		−	1.70772i	−0.520502	−	0.853860i	$-0.674255\pi$
$233$		−	26.0672i		−	1.70772i	0.520502	−	0.853860i	$-0.325745\pi$
$234$	−5.51150	−	9.72455i	−0.360298	−	0.635714i
$235$	1.77503	−	1.77503i	0.115790	−	0.115790i
$236$	14.5895	−	3.66078i	0.949695	−	0.238296i
$237$	9.25353	+	9.25353i	0.601081	+	0.601081i
$238$	8.95082	+	2.47507i	0.580196	+	0.160435i
$239$	5.12209			0.331320			0.165660	−	0.986183i	$-0.447025\pi$
$239$	5.12209			0.331320			0.165660	+	0.986183i	$0.447025\pi$
$240$	−4.88097	−	9.11383i	−0.315066	−	0.588295i
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$	−7.65432	−	2.11656i	−0.492038	−	0.136058i
$243$	15.6025	+	15.6025i	1.00090	+	1.00090i
$244$	0.703301	+	2.80290i	0.0450242	+	0.179437i
$245$	9.43037	−	9.43037i	0.602484	−	0.602484i
$246$	−11.5558	−	20.3891i	−0.736769	−	1.29996i
$247$		−	8.13847i		−	0.517838i
$248$	−14.7494	+	14.0598i	−0.936588	+	0.892795i
$249$		−	8.95437i		−	0.567460i
$250$	−1.23035	+	0.697313i	−0.0778140	+	0.0441020i
$251$	−19.8270	+	19.8270i	−1.25147	+	1.25147i	−0.296408	+	0.955061i	$0.595789\pi$
$251$	−19.8270	+	19.8270i	−1.25147	+	1.25147i	−0.955061	+	0.296408i	$0.904211\pi$
$252$	−28.4784	−	17.0536i	−1.79397	−	1.07427i
$253$	3.89564	+	3.89564i	0.244917	+	0.244917i
$254$	−5.17703	+	18.7222i	−0.324836	+	1.17473i
$255$	−3.76365			−0.235689
$256$	−8.86749	+	13.3179i	−0.554218	+	0.832372i
$257$	−24.2494			−1.51264			−0.756319	−	0.654203i	$-0.773004\pi$
$257$	−24.2494			−1.51264			−0.756319	+	0.654203i	$0.773004\pi$
$258$	−10.5504	+	38.1545i	−0.656842	+	2.37540i
$259$	23.5006	+	23.5006i	1.46026	+	1.46026i
$260$	3.68499	+	2.20666i	0.228533	+	0.136851i
$261$	−3.40422	+	3.40422i	−0.210716	+	0.210716i
$262$	−9.06049	+	5.13514i	−0.559759	+	0.317250i
$263$		−	22.5680i		−	1.39160i	−0.718234	−	0.695802i	$-0.755049\pi$
$263$		−	22.5680i		−	1.39160i	0.718234	−	0.695802i	$-0.244951\pi$
$264$	−12.2787	+	11.7045i	−0.755700	+	0.720365i
$265$			2.12574i			0.130583i
$266$	−11.9168	−	21.0261i	−0.730664	−	1.28919i
$267$	17.1066	−	17.1066i	1.04691	−	1.04691i
$268$	−3.59840	−	14.3409i	−0.219807	−	0.876010i
$269$	−5.10558	−	5.10558i	−0.311293	−	0.311293i	0.534117	−	0.845410i	$-0.320644\pi$
$269$	−5.10558	−	5.10558i	−0.311293	−	0.311293i	−0.845410	+	0.534117i	$0.820644\pi$
$270$	2.39695	+	0.662802i	0.145874	+	0.0403369i
$271$	6.67920			0.405733			0.202866	−	0.979206i	$-0.434974\pi$
$271$	6.67920			0.405733			0.202866	+	0.979206i	$0.434974\pi$
$272$	2.74989	+	5.13464i	0.166736	+	0.311333i
$273$	25.0317			1.51498
$274$	31.0183	+	8.57713i	1.87388	+	0.518163i
$275$	1.64080	+	1.64080i	0.0989441	+	0.0989441i
$276$	−11.9040	+	2.98695i	−0.716539	+	0.179793i
$277$	−11.8524	+	11.8524i	−0.712141	+	0.712141i	−0.966983	−	0.254842i	$-0.917977\pi$
$277$	−11.8524	+	11.8524i	−0.712141	+	0.712141i	0.254842	+	0.966983i	$0.417977\pi$
$278$	6.19386	+	10.9285i	0.371483	+	0.655448i
$279$		−	26.5147i		−	1.58739i
$280$	12.7514	+	0.305253i	0.762044	+	0.0182423i
$281$		−	0.477460i		−	0.0284829i	−0.999899	−	0.0142414i	$-0.995467\pi$
$281$		−	0.477460i		−	0.0284829i	0.999899	−	0.0142414i	$-0.00453334\pi$
$282$	7.98269	−	4.52428i	0.475362	−	0.269417i
$283$	−0.482914	+	0.482914i	−0.0287063	+	0.0287063i	−0.721314	−	0.692608i	$-0.756462\pi$
$283$	−0.482914	+	0.482914i	−0.0287063	+	0.0287063i	0.692608	+	0.721314i	$0.256462\pi$
$284$	1.97382	−	3.29615i	0.117124	−	0.195591i
$285$	6.92591	+	6.92591i	0.410256	+	0.410256i
$286$	1.87829	−	6.79263i	0.111065	−	0.401656i
$287$	28.9141			1.70674
$288$	−4.58217	−	20.3088i	−0.270007	−	1.19671i
$289$	−14.8796			−0.875271
$290$	0.493038	−	1.78302i	0.0289522	−	0.104703i
$291$	34.0508	+	34.0508i	1.99609	+	1.99609i
$292$	1.43247	−	2.39214i	0.0838290	−	0.139989i
$293$	7.46638	−	7.46638i	0.436190	−	0.436190i	−0.454537	−	0.890728i	$-0.650195\pi$
$293$	7.46638	−	7.46638i	0.436190	−	0.436190i	0.890728	+	0.454537i	$0.150195\pi$
$294$	42.4103	−	24.0365i	2.47342	−	1.40184i
$295$		−	7.52088i		−	0.437883i
$296$	−0.498857	+	20.8389i	−0.0289955	+	1.21124i
$297$		−	4.08052i		−	0.236776i
$298$	−12.7780	−	22.5456i	−0.740207	−	1.30603i
$299$	3.60544	−	3.60544i	0.208508	−	0.208508i
$300$	−5.01385	+	1.25807i	−0.289475	+	0.0726347i
$301$	−34.5346	−	34.5346i	−1.99054	−	1.99054i
$302$	19.5486	+	5.40556i	1.12490	+	0.311055i
$303$	−17.6953			−1.01657
$304$	4.38845	−	14.5092i	0.251695	−	0.832160i
$305$	1.44489			0.0827344
$306$	−7.30492	−	2.01995i	−0.417595	−	0.115473i
$307$	2.39349	+	2.39349i	0.136604	+	0.136604i	0.772102	−	0.635498i	$-0.219205\pi$
$307$	2.39349	+	2.39349i	0.136604	+	0.136604i	−0.635498	+	0.772102i	$0.719205\pi$
$308$	−5.09348	−	20.2993i	−0.290228	−	1.15666i
$309$	−16.6777	+	16.6777i	−0.948764	+	0.948764i
$310$	5.02369	+	8.86386i	0.285327	+	0.503433i
$311$		−	20.4404i		−	1.15907i	−0.814948	−	0.579534i	$-0.803235\pi$
$311$		−	20.4404i		−	1.15907i	0.814948	−	0.579534i	$-0.196765\pi$
$312$	10.8326	+	11.3640i	0.613276	+	0.643359i
$313$			2.46975i			0.139598i	0.997561	+	0.0697992i	$0.0222359\pi$
$313$			2.46975i			0.139598i	−0.997561	+	0.0697992i	$0.977764\pi$
$314$	3.66376	−	2.07648i	0.206758	−	0.117182i
$315$	−11.7359	+	11.7359i	−0.661241	+	0.661241i
$316$	−8.68776	−	5.20245i	−0.488725	−	0.292660i
$317$	−16.2241	−	16.2241i	−0.911234	−	0.911234i	0.0851350	−	0.996369i	$-0.472868\pi$
$317$	−16.2241	−	16.2241i	−0.911234	−	0.911234i	−0.996369	+	0.0851350i	$0.972868\pi$
$318$	−2.07085	+	7.48902i	−0.116128	+	0.419963i
$319$	−3.03537			−0.169948
$320$	5.37969	+	5.92105i	0.300734	+	0.330997i
$321$	−37.1026			−2.07086
$322$	4.03553	−	14.5941i	0.224891	−	0.813296i
$323$	−3.90198	−	3.90198i	−0.217112	−	0.217112i
$324$	−11.1463	−	6.67469i	−0.619240	−	0.370816i
$325$	1.51857	−	1.51857i	0.0842353	−	0.0842353i
$326$	9.29154	−	5.26608i	0.514611	−	0.291661i
$327$			4.95246i			0.273871i
$328$	12.5128	+	13.1265i	0.690902	+	0.724792i
$329$			11.3204i			0.624111i
$330$	4.18215	+	7.37903i	0.230220	+	0.406202i
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	−0.606736	−	0.794903i	$-0.707521\pi$
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	0.794903	+	0.606736i	$0.207521\pi$
$332$	1.68632	+	6.72057i	0.0925487	+	0.368839i
$333$	−19.1792	−	19.1792i	−1.05102	−	1.05102i
$334$	−21.9025	−	6.05645i	−1.19845	−	0.331394i
$335$	−7.39273			−0.403908
$336$	44.6263	+	13.4976i	2.43456	+	0.736356i
$337$	−5.40017			−0.294166			−0.147083	−	0.989124i	$-0.546988\pi$
$337$	−5.40017			−0.294166			−0.147083	+	0.989124i	$0.546988\pi$
$338$	11.4332	+	3.16149i	0.621883	+	0.171962i
$339$	−4.67941	−	4.67941i	−0.254151	−	0.254151i
$340$	2.82475	−	0.708783i	0.153194	−	0.0384392i
$341$	11.8209	−	11.8209i	0.640139	−	0.640139i
$342$	9.72548	+	17.1597i	0.525894	+	0.927893i
$343$			28.5754i			1.54292i
$344$	0.733080	−	30.6232i	0.0395250	−	1.65109i
$345$			6.13653i			0.330379i
$346$	−29.7767	+	16.8763i	−1.60081	+	0.907276i
$347$	−4.07531	+	4.07531i	−0.218774	+	0.218774i	−0.807982	−	0.589208i	$-0.799440\pi$
$347$	−4.07531	+	4.07531i	−0.218774	+	0.218774i	0.589208	+	0.807982i	$0.299440\pi$
$348$	3.47397	−	5.80132i	0.186224	−	0.310983i
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	0.747545	−	0.664211i	$-0.231232\pi$
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	−0.664211	+	0.747545i	$0.731232\pi$
$350$	1.69972	−	6.14687i	0.0908541	−	0.328564i
$351$	−3.77655			−0.201577
$352$	7.01133	−	11.0970i	0.373705	−	0.591474i
$353$	1.34919			0.0718103			0.0359052	−	0.999355i	$-0.488569\pi$
$353$	1.34919			0.0718103			0.0359052	+	0.999355i	$0.488569\pi$
$354$	7.32670	−	26.4963i	0.389410	−	1.40826i
$355$	−1.35833	−	1.35833i	−0.0720929	−	0.0720929i
$356$	−9.61755	+	16.0607i	−0.509729	+	0.851216i
$357$	12.0014	−	12.0014i	0.635182	−	0.635182i
$358$	−1.81795	+	1.03035i	−0.0960819	+	0.0544555i
$359$		−	23.2192i		−	1.22546i	−0.790291	−	0.612732i	$-0.790071\pi$
$359$		−	23.2192i		−	1.22546i	0.790291	−	0.612732i	$-0.209929\pi$
$360$	−10.4067	−	0.249122i	−0.548480	−	0.0131299i
$361$		−	4.63903i		−	0.244159i
$362$	11.8225	+	20.8598i	0.621379	+	1.09637i
$363$	−10.2630	+	10.2630i	−0.538670	+	0.538670i
$364$	−18.7871	+	4.71405i	−0.984714	+	0.247083i
$365$	−0.985792	−	0.985792i	−0.0515987	−	0.0515987i
$366$	5.09040	+	1.40759i	0.266080	+	0.0735759i
$367$	−5.16452			−0.269586			−0.134793	−	0.990874i	$-0.543037\pi$
$367$	−5.16452			−0.269586			−0.134793	+	0.990874i	$0.543037\pi$
$368$	8.37189	−	4.48362i	0.436415	−	0.233725i
$369$	−23.5973			−1.22843
$370$	10.0455	+	2.77776i	0.522239	+	0.144409i
$371$	−6.77849	−	6.77849i	−0.351922	−	0.351922i
$372$	9.06359	+	36.1216i	0.469925	+	1.87282i
$373$	18.5056	−	18.5056i	0.958185	−	0.958185i	−0.0409750	−	0.999160i	$-0.513046\pi$
$373$	18.5056	−	18.5056i	0.958185	−	0.958185i	0.999160	+	0.0409750i	$0.0130464\pi$
$374$	−2.35618	−	4.15727i	−0.121835	−	0.214967i
$375$			2.58464i			0.133470i
$376$	−5.13926	+	4.89896i	−0.265037	+	0.252645i
$377$			2.80926i			0.144684i
$378$	−9.75687	+	5.52982i	−0.501839	+	0.284423i
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	−0.963274	−	0.268520i	$-0.913465\pi$
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	0.268520	+	0.963274i	$0.413465\pi$
$380$	−6.50246	−	3.89383i	−0.333569	−	0.199749i
$381$	25.1030	+	25.1030i	1.28607	+	1.28607i
$382$	−0.0251578	+	0.0909805i	−0.00128718	+	0.00465497i
$383$	21.9051			1.11930			0.559650	−	0.828729i	$-0.310936\pi$
$383$	21.9051			1.11930			0.559650	+	0.828729i	$0.310936\pi$
$384$	13.1846	+	26.1008i	0.672825	+	1.33195i
$385$	−10.4643			−0.533310
$386$	0.414206	−	1.49793i	0.0210825	−	0.0762427i
$387$	28.1843	+	28.1843i	1.43269	+	1.43269i
$388$	−31.9689	−	19.1438i	−1.62298	−	0.971878i
$389$	4.48844	−	4.48844i	0.227573	−	0.227573i	−0.584105	−	0.811678i	$-0.698554\pi$
$389$	4.48844	−	4.48844i	0.227573	−	0.227573i	0.811678	+	0.584105i	$0.198554\pi$
$390$	6.82934	−	3.87061i	0.345817	−	0.195996i
$391$		−	3.45725i		−	0.174841i
$392$	−27.3038	+	26.0271i	−1.37905	+	1.31457i
$393$			19.0337i			0.960126i
$394$	11.7637	+	20.7560i	0.592646	+	1.04567i
$395$	−3.58020	+	3.58020i	−0.180139	+	0.180139i
$396$	4.15688	+	16.5666i	0.208891	+	0.832504i
$397$	11.7892	+	11.7892i	0.591682	+	0.591682i	0.938086	−	0.346404i	$-0.112597\pi$
$397$	11.7892	+	11.7892i	0.591682	+	0.591682i	−0.346404	+	0.938086i	$0.612597\pi$
$398$	−15.0478	−	4.16100i	−0.754278	−	0.208572i
$399$	−44.1703			−2.21128
$400$	3.52615	−	1.88845i	0.176308	−	0.0944227i
$401$	24.9259			1.24474			0.622371	−	0.782722i	$-0.286170\pi$
$401$	24.9259			1.24474			0.622371	+	0.782722i	$0.286170\pi$
$402$	−26.0448	−	7.20187i	−1.29900	−	0.359196i
$403$	−10.9403	−	10.9403i	−0.544977	−	0.544977i
$404$	13.2809	−	3.33244i	0.660751	−	0.165795i
$405$	−4.59336	+	4.59336i	−0.228246	+	0.228246i
$406$	4.11346	+	7.25784i	0.204148	+	0.360200i
$407$		−	17.1012i		−	0.847675i
$408$	10.6422	+	0.254759i	0.526865	+	0.0126125i
$409$			21.5355i			1.06486i	0.846474	+	0.532430i	$0.178721\pi$
$409$			21.5355i			1.06486i	−0.846474	+	0.532430i	$0.821279\pi$
$410$	7.88857	−	4.47094i	0.389589	−	0.220804i
$411$	41.5898	−	41.5898i	2.05148	−	2.05148i
$412$	9.37643	−	15.6581i	0.461943	−	0.771417i
$413$	23.9824	+	23.9824i	1.18010	+	1.18010i
$414$	−3.29347	+	11.9105i	−0.161865	+	0.585368i
$415$	3.46445			0.170063
$416$	−10.2704	−	6.48903i	−0.503546	−	0.318151i
$417$	22.9580			1.12426
$418$	−3.31439	+	11.9861i	−0.162112	+	0.586261i
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	0.144452	−	0.989512i	$-0.453858\pi$
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	−0.989512	+	0.144452i	$0.953858\pi$
$420$	11.9763	−	19.9997i	0.584386	−	0.975888i
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	−0.998670	−	0.0515648i	$-0.983579\pi$
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	0.0515648	+	0.998670i	$0.483579\pi$
$422$	14.9592	−	8.47830i	0.728203	−	0.412717i
$423$		−	9.23874i		−	0.449203i
$424$	0.143890	−	6.01077i	0.00698791	−	0.291909i
$425$		−	1.45616i		−	0.0706341i
$426$	−3.46218	−	6.10871i	−0.167743	−	0.295968i
$427$	−4.60744	+	4.60744i	−0.222970	+	0.222970i
$428$	27.8468	−	6.98729i	1.34603	−	0.337744i
$429$	−9.10767	−	9.10767i	−0.439723	−	0.439723i
$430$	−14.7620	−	4.08198i	−0.711888	−	0.196850i
$431$	28.3769			1.36687			0.683433	−	0.730013i	$-0.260486\pi$
$431$	28.3769			1.36687			0.683433	+	0.730013i	$0.260486\pi$
$432$	−6.73280	−	2.03640i	−0.323932	−	0.0979763i
$433$	9.04007			0.434438			0.217219	−	0.976123i	$-0.430301\pi$
$433$	9.04007			0.434438			0.217219	+	0.976123i	$0.430301\pi$
$434$	−44.2842	−	12.2454i	−2.12571	−	0.587799i
$435$	−2.39071	−	2.39071i	−0.114626	−	0.114626i
$436$	−0.932664	−	3.71699i	−0.0446665	−	0.178012i
$437$	−6.36208	+	6.36208i	−0.304340	+	0.304340i
$438$	−2.51263	−	4.43331i	−0.120058	−	0.211832i
$439$			28.2949i			1.35044i	0.737615	+	0.675221i	$0.235952\pi$
$439$			28.2949i			1.35044i	−0.737615	+	0.675221i	$0.764048\pi$
$440$	−4.52850	−	4.75063i	−0.215888	−	0.226477i
$441$		−	49.0834i		−	2.33731i
$442$	−3.84757	+	2.18066i	−0.183010	+	0.103723i
$443$	−13.1232	+	13.1232i	−0.623504	+	0.623504i	−0.946426	−	0.322922i	$-0.895335\pi$
$443$	−13.1232	+	13.1232i	−0.623504	+	0.623504i	0.322922	+	0.946426i	$0.395335\pi$
$444$	32.6844	+	19.5722i	1.55113	+	0.928857i
$445$	6.61857	+	6.61857i	0.313750	+	0.313750i
$446$	8.07489	−	29.2020i	0.382357	−	1.38275i
$447$	−47.3624			−2.24016
$448$	−36.0355	−	1.72628i	−1.70252	−	0.0815588i
$449$	−14.3902			−0.679116			−0.339558	−	0.940585i	$-0.610277\pi$
$449$	−14.3902			−0.679116			−0.339558	+	0.940585i	$0.610277\pi$
$450$	−1.38717	+	5.01657i	−0.0653920	+	0.236483i
$451$	−10.5203	−	10.5203i	−0.495380	−	0.495380i
$452$	4.39331	+	2.63082i	0.206644	+	0.123743i
$453$	26.2111	−	26.2111i	1.23151	−	1.23151i
$454$	14.0299	−	7.95163i	0.658458	−	0.373189i
$455$			9.68477i			0.454029i
$456$	−19.1150	−	20.0526i	−0.895143	−	0.939051i
$457$		−	4.54538i		−	0.212624i	−0.994333	−	0.106312i	$-0.966096\pi$
$457$		−	4.54538i		−	0.212624i	0.994333	−	0.106312i	$-0.0339042\pi$
$458$	4.56754	+	8.05902i	0.213427	+	0.376573i
$459$	−1.81066	+	1.81066i	−0.0845146	+	0.0845146i
$460$	−1.15565	−	4.60568i	−0.0538826	−	0.214741i
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	0.997198	−	0.0748050i	$-0.0238334\pi$
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	−0.0748050	+	0.997198i	$0.523833\pi$
$462$	−36.8660	−	10.1941i	−1.71516	−	0.474274i
$463$	−14.5997			−0.678506			−0.339253	−	0.940695i	$-0.610174\pi$
$463$	−14.5997			−0.678506			−0.339253	+	0.940695i	$0.610174\pi$
$464$	−1.51481	+	5.00833i	−0.0703235	+	0.232506i
$465$	18.6207			0.863513
$466$	35.5312	+	9.82505i	1.64595	+	0.455137i
$467$	19.8105	+	19.8105i	0.916722	+	0.916722i	0.996789	−	0.0800671i	$-0.0255135\pi$
$467$	19.8105	+	19.8105i	0.916722	+	0.916722i	−0.0800671	+	0.996789i	$0.525513\pi$
$468$	15.3325	−	3.84722i	0.708746	−	0.177838i
$469$	23.5738	−	23.5738i	1.08853	−	1.08853i
$470$	1.75045	+	3.08851i	0.0807421	+	0.142462i
$471$		−	7.69661i		−	0.354641i
$472$	−0.509084	+	21.2662i	−0.0234325	+	0.978855i
$473$			25.1306i			1.15550i
$474$	−16.1009	+	9.12537i	−0.739539	+	0.419142i
$475$	−2.67964	+	2.67964i	−0.122950	+	0.122950i
$476$	−6.74734	+	11.2676i	−0.309264	+	0.516451i
$477$	5.53204	+	5.53204i	0.253295	+	0.253295i
$478$	−1.93058	+	6.98172i	−0.0883025	+	0.319337i
$479$	21.0378			0.961243			0.480621	−	0.876928i	$-0.340411\pi$
$479$	21.0378			0.961243			0.480621	+	0.876928i	$0.340411\pi$
$480$	14.2624	−	3.21796i	0.650987	−	0.146879i
$481$	−15.8273			−0.721661
$482$	−4.33399	+	15.6734i	−0.197408	+	0.713904i
$483$	−19.5680	−	19.5680i	−0.890375	−	0.890375i
$484$	5.77000	−	9.63555i	0.262273	−	0.437980i
$485$	−13.1743	+	13.1743i	−0.598214	+	0.598214i
$486$	−27.1480	+	15.3865i	−1.23146	+	0.697944i
$487$			10.2724i			0.465485i	0.972538	+	0.232743i	$0.0747699\pi$
$487$			10.2724i			0.465485i	−0.972538	+	0.232743i	$0.925230\pi$
$488$	−4.08561	−	0.0978041i	−0.184947	−	0.00442738i
$489$		−	19.5191i		−	0.882685i
$490$	9.29976	+	16.4086i	0.420120	+	0.741265i
$491$	−5.95681	+	5.95681i	−0.268827	+	0.268827i	−0.828627	−	0.559801i	$-0.810878\pi$
$491$	−5.95681	+	5.95681i	−0.268827	+	0.268827i	0.559801	+	0.828627i	$0.310878\pi$
$492$	32.1471	−	8.06632i	1.44930	−	0.363658i
$493$	1.34690	+	1.34690i	0.0606612	+	0.0606612i
$494$	11.0932	+	3.06748i	0.499108	+	0.138013i
$495$	8.54009			0.383849
$496$	−13.6051	−	25.4036i	−0.610886	−	1.14066i
$497$	8.66284			0.388581
$498$	12.2054	+	3.37501i	0.546935	+	0.151238i
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	0.641294	−	0.767295i	$-0.278398\pi$
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	−0.767295	+	0.641294i	$0.778398\pi$
$500$	−0.486749	−	1.93986i	−0.0217681	−	0.0867534i
$501$	−29.3673	+	29.3673i	−1.31203	+	1.31203i
$502$	−19.5524	−	34.4985i	−0.872666	−	1.53974i
$503$		−	5.49759i		−	0.245125i	−0.992461	−	0.122563i	$-0.960889\pi$
$503$		−	5.49759i		−	0.245125i	0.992461	−	0.122563i	$-0.0391113\pi$
$504$	33.9789	−	32.3901i	1.51354	−	1.44277i
$505$		−	6.84632i		−	0.304657i
$506$	−6.77831	+	3.84169i	−0.301333	+	0.170784i
$507$	15.3298	−	15.3298i	0.680821	−	0.680821i
$508$	−23.5682	−	14.1132i	−1.04567	−	0.626173i
$509$	−4.37578	−	4.37578i	−0.193953	−	0.193953i	0.603449	−	0.797402i	$-0.293793\pi$
$509$	−4.37578	−	4.37578i	−0.193953	−	0.193953i	−0.797402	+	0.603449i	$0.793793\pi$
$510$	1.41856	−	5.13008i	0.0628150	−	0.227164i
$511$	6.28693			0.278118
$512$	−14.8109	−	17.1066i	−0.654556	−	0.756013i
$513$	6.66402			0.294224
$514$	9.13990	−	33.0535i	0.403144	−	1.45793i
$515$	−6.45263	−	6.45263i	−0.284337	−	0.284337i
$516$	−48.0304	−	28.7618i	−2.11442	−	1.26617i
$517$	4.11887	−	4.11887i	0.181148	−	0.181148i
$518$	−40.8904	+	23.1751i	−1.79662	+	1.01826i
$519$			62.5532i			2.74578i
$520$	−4.39673	+	4.19115i	−0.192810	+	0.183794i
$521$			33.8729i			1.48400i	0.670401	+	0.741999i	$0.266122\pi$
$521$			33.8729i			1.48400i	−0.670401	+	0.741999i	$0.733878\pi$
$522$	−3.35707	−	5.92325i	−0.146935	−	0.259253i
$523$	27.8060	−	27.8060i	1.21587	−	1.21587i	0.246804	−	0.969065i	$-0.420620\pi$
$523$	27.8060	−	27.8060i	1.21587	−	1.21587i	0.969065	−	0.246804i	$-0.0793803\pi$
$524$	−3.58450	−	14.2855i	−0.156590	−	0.624065i
$525$	−8.24183	−	8.24183i	−0.359703	−	0.359703i
$526$	30.7616	+	8.50615i	1.34127	+	0.370886i
$527$	−10.4907			−0.456981
$528$	−11.3260	−	21.1482i	−0.492902	−	0.920356i
$529$	17.3630			0.754915
$530$	−2.89751	−	0.801215i	−0.125860	−	0.0348025i
$531$	−19.5724	−	19.5724i	−0.849372	−	0.849372i
$532$	33.1514	−	8.31832i	1.43730	−	0.360645i
$533$	−9.73658	+	9.73658i	−0.421738	+	0.421738i
$534$	16.8697	+	29.7651i	0.730023	+	1.28806i
$535$		−	14.3550i		−	0.620622i
$536$	20.9038	+	0.500410i	0.902907	+	0.0216144i
$537$			3.81905i			0.164804i
$538$	8.88358	−	5.03487i	0.382998	−	0.217069i
$539$	21.8827	−	21.8827i	0.942553	−	0.942553i
$540$	−1.80688	+	3.01738i	−0.0777558	+	0.129847i
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	0.769248	−	0.638950i	$-0.220631\pi$
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	−0.638950	+	0.769248i	$0.720631\pi$
$542$	−2.51747	+	9.10416i	−0.108135	+	0.391057i
$543$	43.8211			1.88054
$544$	−8.03529	+	1.81296i	−0.344510	+	0.0777301i
$545$	−1.91611			−0.0820771
$546$	−9.43473	+	34.1197i	−0.403769	+	1.46019i
$547$	−18.4783	−	18.4783i	−0.790074	−	0.790074i	0.191432	−	0.981506i	$-0.438687\pi$
$547$	−18.4783	−	18.4783i	−0.790074	−	0.790074i	−0.981506	+	0.191432i	$0.938687\pi$
$548$	−23.3823	+	39.0470i	−0.998843	+	1.66801i
$549$	3.76021	−	3.76021i	0.160482	−	0.160482i
$550$	−2.85495	+	1.61808i	−0.121736	+	0.0689951i
$551$		−	4.95716i		−	0.211182i
$552$	0.415378	−	17.3517i	0.0176797	−	0.738539i
$553$		−	22.8329i		−	0.970953i
$554$	−11.6882	−	20.6228i	−0.496585	−	0.876181i
$555$	13.4691	−	13.4691i	0.571734	−	0.571734i
$556$	−17.2308	+	4.32353i	−0.730747	+	0.183358i
$557$	−30.2060	−	30.2060i	−1.27987	−	1.27987i	−0.940741	−	0.339127i	$-0.889868\pi$
$557$	−30.2060	−	30.2060i	−1.27987	−	1.27987i	−0.339127	−	0.940741i	$-0.610132\pi$
$558$	36.1411	+	9.99370i	1.52998	+	0.423067i
$559$	23.2585			0.983729
$560$	−5.22225	+	17.2659i	−0.220680	+	0.729620i
$561$	−8.73334			−0.368722
$562$	0.650807	+	0.179960i	0.0274526	+	0.00759117i
$563$	2.86747	+	2.86747i	0.120850	+	0.120850i	0.764945	−	0.644095i	$-0.222766\pi$
$563$	2.86747	+	2.86747i	0.120850	+	0.120850i	−0.644095	+	0.764945i	$0.722766\pi$
$564$	3.15810	+	12.5862i	0.132980	+	0.529973i
$565$	1.81047	−	1.81047i	0.0761670	−	0.0761670i
$566$	−0.476226	−	0.840258i	−0.0200173	−	0.0353187i
$567$		−	29.2944i		−	1.23025i
$568$	3.74890	+	3.93279i	0.157300	+	0.165016i
$569$			35.8628i			1.50345i	0.659479	+	0.751723i	$0.270777\pi$
$569$			35.8628i			1.50345i	−0.659479	+	0.751723i	$0.729223\pi$
$570$	−12.0509	+	6.82999i	−0.504757	+	0.286077i
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	−0.972320	−	0.233653i	$-0.924932\pi$
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	0.233653	+	0.972320i	$0.424932\pi$
$572$	8.55082	+	5.12044i	0.357528	+	0.214096i
$573$	0.121988	+	0.121988i	0.00509613	+	0.00509613i
$574$	−10.8981	+	39.4117i	−0.454876	+	1.64501i
$575$	−2.37423			−0.0990122
$576$	29.4092	+	1.40884i	1.22538	+	0.0587018i
$577$	36.1387			1.50448			0.752238	−	0.658892i	$-0.228975\pi$
$577$	36.1387			1.50448			0.752238	+	0.658892i	$0.228975\pi$
$578$	5.60830	−	20.2818i	0.233274	−	0.843612i
$579$	−2.00845	−	2.00845i	−0.0834685	−	0.0834685i
$580$	2.24454	+	1.34408i	0.0931993	+	0.0558100i
$581$	−11.0474	+	11.0474i	−0.458322	+	0.458322i
$582$	−59.2475	+	33.5792i	−2.45589	+	1.39190i
$583$			4.93265i			0.204290i
$584$	2.72071	+	2.85417i	0.112584	+	0.118106i
$585$		−	7.90391i		−	0.326786i
$586$	7.36297	+	12.9913i	0.304161	+	0.536666i
$587$	−11.4005	+	11.4005i	−0.470550	+	0.470550i	−0.902093	−	0.431542i	$-0.857970\pi$
$587$	−11.4005	+	11.4005i	−0.470550	+	0.470550i	0.431542	+	0.902093i	$0.357970\pi$
$588$	16.7783	+	66.8675i	0.691927	+	2.75757i
$589$	19.3051	+	19.3051i	0.795453	+	0.795453i
$590$	10.2514	+	2.83471i	0.422045	+	0.116703i
$591$	43.6029			1.79358
$592$	−28.2167	−	8.53441i	−1.15970	−	0.350762i
$593$	−35.0454			−1.43914			−0.719572	−	0.694418i	$-0.755662\pi$
$593$	−35.0454			−1.43914			−0.719572	+	0.694418i	$0.755662\pi$
$594$	5.56200	+	1.53800i	0.228212	+	0.0631048i
$595$	4.64336	+	4.64336i	0.190359	+	0.190359i
$596$	35.5472	−	8.91945i	1.45607	−	0.365355i
$597$	−20.1764	+	20.1764i	−0.825764	+	0.825764i
$598$	3.55550	+	6.27337i	0.145395	+	0.256537i
$599$			18.2753i			0.746707i	0.927689	+	0.373354i	$0.121792\pi$
$599$			18.2753i			0.746707i	−0.927689	+	0.373354i	$0.878208\pi$
$600$	0.174953	−	7.30837i	0.00714242	−	0.298363i
$601$		−	0.480142i		−	0.0195854i	−0.999952	−	0.00979269i	$-0.996883\pi$
$601$		−	0.480142i		−	0.0195854i	0.999952	−	0.00979269i	$-0.00311716\pi$
$602$	60.0893	−	34.0563i	2.44906	−	1.38803i
$603$	−19.2389	+	19.2389i	−0.783470	+	0.783470i
$604$	−14.7362	+	24.6086i	−0.599608	+	1.00131i
$605$	−3.97078	−	3.97078i	−0.161435	−	0.161435i
$606$	6.66956	−	24.1197i	0.270932	−	0.979798i
$607$	−38.6107			−1.56716			−0.783581	−	0.621290i	$-0.786609\pi$
$607$	−38.6107			−1.56716			−0.783581	+	0.621290i	$0.786609\pi$
$608$	18.1229	+	11.4504i	0.734980	+	0.464376i
$609$	15.2468			0.617833
$610$	−0.544598	+	1.96948i	−0.0220501	+	0.0797419i
$611$	−3.81204	−	3.81204i	−0.154218	−	0.154218i
$612$	5.50662	−	9.19572i	0.222592	−	0.371715i
$613$	−5.53592	+	5.53592i	−0.223594	+	0.223594i	−0.810010	−	0.586416i	$-0.800538\pi$
$613$	−5.53592	+	5.53592i	−0.223594	+	0.223594i	0.586416	+	0.810010i	$0.300538\pi$
$614$	−4.16461	+	2.36034i	−0.168070	+	0.0952557i
$615$		−	16.5718i		−	0.668241i
$616$	29.5890	+	0.708322i	1.19218	+	0.0285391i
$617$		−	31.8836i		−	1.28358i	−0.766879	−	0.641792i	$-0.778191\pi$
$617$		−	31.8836i		−	1.28358i	0.766879	−	0.641792i	$-0.221809\pi$
$618$	−16.4468	−	29.0188i	−0.661586	−	1.16731i
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.202650	+	0.979251i	$0.564955\pi$
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.979251	+	0.202650i	$0.935045\pi$
$620$	−13.9755	+	3.50671i	−0.561269	+	0.140833i
$621$	2.95224	+	2.95224i	0.118469	+	0.118469i
$622$	27.8615	+	7.70422i	1.11714	+	0.308911i
$623$	−42.2102			−1.69112
$624$	−19.5728	+	10.4823i	−0.783537	+	0.419628i
$625$	−1.00000			−0.0400000
$626$	−3.36642	−	0.930878i	−0.134549	−	0.0372054i
$627$	16.0712	+	16.0712i	0.641822	+	0.641822i
$628$	1.44945	+	5.77658i	0.0578395	+	0.230511i
$629$	−7.58837	+	7.58837i	−0.302568	+	0.302568i
$630$	−11.5733	−	20.4201i	−0.461092	−	0.813556i
$631$			30.7381i			1.22367i	0.790987	+	0.611833i	$0.209568\pi$
$631$			30.7381i			1.22367i	−0.790987	+	0.611833i	$0.790432\pi$
$632$	10.3658	−	9.88109i	0.412328	−	0.393049i
$633$		−	31.4254i		−	1.24905i
$634$	28.2294	−	15.9994i	1.12113	−	0.635416i
$635$	−9.71239	+	9.71239i	−0.385424	+	0.385424i
$636$	−9.42747	−	5.64540i	−0.373823	−	0.223855i
$637$	−20.2525	−	20.2525i	−0.802435	−	0.802435i
$638$	1.14407	−	4.13740i	0.0452941	−	0.163801i
$639$	−7.06989			−0.279681
$640$	−10.0984	+	5.10114i	−0.399176	+	0.201640i
$641$	13.6348			0.538540			0.269270	−	0.963065i	$-0.413218\pi$
$641$	13.6348			0.538540			0.269270	+	0.963065i	$0.413218\pi$
$642$	13.9844	−	50.5731i	0.551921	−	1.99596i
$643$	14.9224	+	14.9224i	0.588480	+	0.588480i	0.937220	−	0.348740i	$-0.113390\pi$
$643$	14.9224	+	14.9224i	0.588480	+	0.588480i	−0.348740	+	0.937220i	$0.613390\pi$
$644$	18.3716	+	11.0014i	0.723942	+	0.433514i
$645$	−19.7932	+	19.7932i	−0.779356	+	0.779356i
$646$	6.78935	−	3.84794i	0.267123	−	0.151395i
$647$			4.87972i			0.191841i	0.995389	+	0.0959207i	$0.0305795\pi$
$647$			4.87972i			0.191841i	−0.995389	+	0.0959207i	$0.969420\pi$
$648$	13.2992	−	12.6773i	0.522442	−	0.498013i
$649$		−	17.4518i		−	0.685043i
$650$	1.49754	+	2.64228i	0.0587384	+	0.103639i
$651$	−59.3771	+	59.3771i	−2.32717	+	2.32717i
$652$	3.67591	+	14.6498i	0.143960	+	0.573730i
$653$	−10.2913	−	10.2913i	−0.402731	−	0.402731i	0.476463	−	0.879194i	$-0.341919\pi$
$653$	−10.2913	−	10.2913i	−0.402731	−	0.402731i	−0.879194	+	0.476463i	$0.841919\pi$
$654$	−6.75050	−	1.86664i	−0.263966	−	0.0729914i
$655$	−7.36417			−0.287742
$656$	−22.6085	+	12.1081i	−0.882713	+	0.472743i
$657$	−5.13088			−0.200174
$658$	−15.4303	−	4.26677i	−0.601537	−	0.166336i
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	0.137325	−	0.990526i	$-0.456149\pi$
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	−0.990526	+	0.137325i	$0.956149\pi$
$660$	−11.6344	+	2.91928i	−0.452867	+	0.113633i
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	−0.594114	−	0.804381i	$-0.702497\pi$
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	0.804381	+	0.594114i	$0.202497\pi$
$662$	3.37599	+	5.95663i	0.131212	+	0.231511i
$663$			8.08276i			0.313908i
$664$	−9.79615	−	0.234507i	−0.380164	−	0.00910063i
$665$		−	17.0895i		−	0.662704i
$666$	33.3714	−	18.9136i	1.29311	−	0.732887i
$667$	2.19608	−	2.19608i	0.0850326	−	0.0850326i
$668$	16.5106	−	27.5717i	0.638816	−	1.06678i
$669$	−39.1546	−	39.1546i	−1.51380	−	1.51380i
$670$	2.78641	−	10.0768i	0.107648	−	0.389299i
$671$	3.35280			0.129433
$672$	−35.2183	+	55.7410i	−1.35857	+	2.15025i
$673$	35.3820			1.36388			0.681938	−	0.731410i	$-0.261138\pi$
$673$	35.3820			1.36388			0.681938	+	0.731410i	$0.261138\pi$
$674$	2.03539	−	7.36076i	0.0784002	−	0.283526i
$675$	1.24345	+	1.24345i	0.0478605	+	0.0478605i
$676$	−8.61861	+	14.3925i	−0.331485	+	0.553559i
$677$	5.17061	−	5.17061i	0.198723	−	0.198723i	−0.600730	−	0.799452i	$-0.705123\pi$
$677$	5.17061	−	5.17061i	0.198723	−	0.198723i	0.799452	+	0.600730i	$0.205123\pi$
$678$	8.14205	−	4.61460i	0.312694	−	0.177223i
$679$		−	84.0196i		−	3.22438i
$680$	−0.0985665	+	4.11746i	−0.00377985	+	0.157897i
$681$		−	29.4733i		−	1.12942i
$682$	11.6572	+	20.5681i	0.446377	+	0.787593i
$683$	26.5989	−	26.5989i	1.01778	−	1.01778i	0.0179409	−	0.999839i	$-0.494289\pi$
$683$	26.5989	−	26.5989i	1.01778	−	1.01778i	0.999839	−	0.0179409i	$-0.00571108\pi$
$684$	−27.0554	+	6.78872i	−1.03449	+	0.259573i
$685$	16.0912	+	16.0912i	0.614811	+	0.614811i
$686$	−38.9500	−	10.7704i	−1.48712	−	0.411216i
$687$	16.9299			0.645916
$688$	41.4651	+	12.5415i	1.58084	+	0.478140i
$689$	4.56520			0.173920
$690$	−8.36447	−	2.31293i	−0.318430	−	0.0880517i
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	0.158146	−	0.987416i	$-0.449448\pi$
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	−0.987416	+	0.158146i	$0.949448\pi$
$692$	−11.7802	−	46.9484i	−0.447818	−	1.78471i
$693$	−27.2324	+	27.2324i	−1.03447	+	1.03447i
$694$	−4.01887	−	7.09093i	−0.152554	−	0.269168i
$695$			8.88246i			0.336931i
$696$	6.59817	+	6.92182i	0.250103	+	0.262371i
$697$			9.33640i			0.353641i
$698$	−2.70880	+	1.53524i	−0.102530	+	0.0581099i
$699$	47.6409	−	47.6409i	1.80194	−	1.80194i
$700$	7.73792	+	4.63366i	0.292466	+	0.175136i
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	0.358698	−	0.933454i	$-0.383221\pi$
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	−0.933454	+	0.358698i	$0.883221\pi$
$702$	1.42343	−	5.14767i	0.0537237	−	0.194286i
$703$	27.9285			1.05334
$704$	12.4833	+	13.7395i	0.470482	+	0.517826i
$705$	6.48816			0.244358
$706$	−0.508527	+	1.83903i	−0.0191387	+	0.0692130i
$707$	21.8313	+	21.8313i	0.821052	+	0.821052i
$708$	33.3545	+	19.9735i	1.25354	+	0.750650i
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	−0.609646	−	0.792674i	$-0.708688\pi$
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	0.792674	+	0.609646i	$0.208688\pi$
$710$	2.36346	−	1.33952i	0.0886992	−	0.0502713i
$711$			18.6343i			0.698842i
$712$	−18.2668	−	19.1628i	−0.684576	−	0.718156i
$713$			17.1048i			0.640579i
$714$	11.8352	+	20.8822i	0.442921	+	0.781495i
$715$	3.52377	−	3.52377i	0.131781	−	0.131781i
$716$	−0.719218	−	2.86633i	−0.0268784	−	0.107120i
$717$	9.36121	+	9.36121i	0.349601	+	0.349601i
$718$	31.6492	+	8.75160i	1.18114	+	0.326607i
$719$	9.27351			0.345843			0.172922	−	0.984936i	$-0.444679\pi$
$719$	9.27351			0.345843			0.172922	+	0.984936i	$0.444679\pi$
$720$	4.26197	−	14.0910i	0.158834	−	0.525142i
$721$	41.1520			1.53258
$722$	6.32328	+	1.74850i	0.235328	+	0.0650726i
$723$	21.0152	+	21.0152i	0.781563	+	0.781563i
$724$	−32.8893	+	8.25254i	−1.22232	+	0.306703i
$725$	0.924966	−	0.924966i	0.0343524	−	0.0343524i
$726$	−10.1209	−	17.8574i	−0.375622	−	0.662751i
$727$			10.6056i			0.393341i	0.980470	+	0.196670i	$0.0630129\pi$
$727$			10.6056i			0.393341i	−0.980470	+	0.196670i	$0.936987\pi$
$728$	0.655557	−	27.3848i	0.0242965	−	1.01495i
$729$			37.5430i			1.39048i
$730$	1.71525	−	0.972138i	0.0634843	−	0.0359805i
$731$	11.1513	−	11.1513i	0.412445	−	0.412445i
$732$	−3.83726	+	6.40799i	−0.141829	+	0.236846i
$733$	−29.6530	−	29.6530i	−1.09526	−	1.09526i	−0.994957	−	0.100301i	$-0.968019\pi$
$733$	−29.6530	−	29.6530i	−1.09526	−	1.09526i	−0.100301	−	0.994957i	$-0.531981\pi$
$734$	1.94657	−	7.03956i	0.0718492	−	0.259835i
$735$	34.4702			1.27145
$736$	2.95599	+	13.1013i	0.108959	+	0.482921i
$737$	−17.1544			−0.631892
$738$	8.89409	−	32.1645i	0.327396	−	1.18399i
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.989202	+	0.146559i	$0.0468197\pi$
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.146559	+	0.989202i	$0.453180\pi$
$740$	−7.57252	+	12.6456i	−0.278371	+	0.464863i
$741$	14.8740	−	14.8740i	0.546410	−	0.546410i
$742$	11.7944	−	6.68461i	0.432986	−	0.245400i
$743$			22.3956i			0.821617i	0.911722	+	0.410808i	$0.134753\pi$
$743$			22.3956i			0.821617i	−0.911722	+	0.410808i	$0.865247\pi$
$744$	−52.6521	−	1.26042i	−1.93032	−	0.0462093i
$745$		−	18.3245i		−	0.671360i
$746$	18.2493	+	32.1993i	0.668155	+	1.17890i
$747$	9.01594	−	9.01594i	0.329876	−	0.329876i
$748$	6.55468	−	1.64469i	0.239663	−	0.0601359i
$749$	45.7749	+	45.7749i	1.67258	+	1.67258i
$750$	−3.52303	−	0.974182i	−0.128643	−	0.0355721i
$751$	20.6448			0.753341			0.376670	−	0.926347i	$-0.377069\pi$
$751$	20.6448			0.753341			0.376670	+	0.926347i	$0.377069\pi$
$752$	−4.74054	−	8.85161i	−0.172870	−	0.322785i
$753$	−72.4724			−2.64104
$754$	−3.82919	−	1.05884i	−0.139451	−	0.0385608i
$755$	10.1411	+	10.1411i	0.369073	+	0.369073i
$756$	−3.86000	−	15.3835i	−0.140387	−	0.559491i
$757$	24.1323	−	24.1323i	0.877104	−	0.877104i	−0.116130	−	0.993234i	$-0.537049\pi$
$757$	24.1323	−	24.1323i	0.877104	−	0.877104i	0.993234	+	0.116130i	$0.0370490\pi$
$758$	−13.3381	−	23.5339i	−0.484461	−	0.854788i
$759$			14.2395i			0.516860i
$760$	7.75839	−	7.39562i	0.281426	−	0.268267i
$761$		−	50.1874i		−	1.81929i	−0.415383	−	0.909647i	$-0.636352\pi$
$761$		−	50.1874i		−	1.81929i	0.415383	−	0.909647i	$-0.363648\pi$
$762$	−43.6786	+	24.7554i	−1.58231	+	0.896792i
$763$	6.11004	−	6.11004i	0.221198	−	0.221198i
$764$	−0.114530	−	0.0685832i	−0.00414354	−	0.00248125i
$765$	−3.78953	−	3.78953i	−0.137011	−	0.137011i
$766$	−8.25631	+	29.8581i	−0.298312	+	1.07882i
$767$	−16.1517			−0.583206
$768$	−40.5465	+	8.13374i	−1.46309	+	0.293501i
$769$	−28.6887			−1.03454			−0.517270	−	0.855822i	$-0.673052\pi$
$769$	−28.6887			−1.03454			−0.517270	+	0.855822i	$0.673052\pi$
$770$	3.94412	−	14.2635i	0.142136	−	0.514020i
$771$	−44.3187	−	44.3187i	−1.59610	−	1.59610i
$772$	1.88565	+	1.12918i	0.0678662	+	0.0406400i
$773$	−37.5957	+	37.5957i	−1.35222	+	1.35222i	−0.469052	+	0.883171i	$0.655404\pi$
$773$	−37.5957	+	37.5957i	−1.35222	+	1.35222i	−0.883171	+	0.469052i	$0.844596\pi$
$774$	−49.0399	+	27.7939i	−1.76270	+	0.999032i
$775$			7.20435i			0.258788i
$776$	38.1436	−	36.3601i	1.36928	−	1.30525i
$777$			85.9001i			3.08165i
$778$	4.42628	+	7.80977i	0.158690	+	0.279994i
$779$	17.1810	−	17.1810i	0.615572	−	0.615572i
$780$	2.70182	+	10.7677i	0.0967405	+	0.385545i
$781$	−3.15194	−	3.15194i	−0.112785	−	0.112785i
$782$	4.71245	+	1.30308i	0.168517	+	0.0465980i
$783$	−2.30030			−0.0822061
$784$	−25.1855	−	47.0267i	−0.899481	−	1.67953i
$785$	2.97783			0.106283
$786$	−25.9442	−	7.17404i	−0.925398	−	0.255890i
$787$	−3.13285	−	3.13285i	−0.111674	−	0.111674i	0.649062	−	0.760736i	$-0.275162\pi$
$787$	−3.13285	−	3.13285i	−0.111674	−	0.111674i	−0.760736	+	0.649062i	$0.775162\pi$
$788$	−32.7255	+	8.21145i	−1.16580	+	0.292521i
$789$	41.2457	−	41.2457i	1.46839	−	1.46839i
$790$	−3.53061	−	6.22945i	−0.125614	−	0.221634i
$791$			11.5463i			0.410541i
$792$	−24.1481	−	0.578074i	−0.858066	−	0.0205410i
$793$		−	3.10304i		−	0.110192i
$794$	−20.5129	+	11.6259i	−0.727974	+	0.412588i
$795$	−3.88503	+	3.88503i	−0.137788	+	0.137788i
$796$	11.3434	−	18.9428i	0.402056	−	0.671408i
$797$	0.0562195	+	0.0562195i	0.00199140	+	0.00199140i	0.708102	−	0.706110i	$-0.249552\pi$
$797$	0.0562195	+	0.0562195i	0.00199140	+	0.00199140i	−0.706110	+	0.708102i	$0.749552\pi$
$798$	16.6483	−	60.2069i	0.589344	−	2.13130i
$799$	−3.65536			−0.129317
$800$	1.24503	+	5.51814i	0.0440185	+	0.195096i
$801$	34.4485			1.21718
$802$	−9.39488	+	33.9756i	−0.331745	+	1.19972i
$803$	−2.28748	−	2.28748i	−0.0807233	−	0.0807233i
$804$	19.6332	−	32.7862i	0.692409	−	1.15628i
$805$	7.57088	−	7.57088i	0.266838	−	0.266838i
$806$	19.0359	−	10.7888i	0.670511	−	0.380020i
$807$		−	18.6621i		−	0.656937i
$808$	−0.463423	+	19.3588i	−0.0163032	+	0.681039i
$809$			3.59856i			0.126518i	0.997997	+	0.0632592i	$0.0201495\pi$
$809$			3.59856i			0.126518i	−0.997997	+	0.0632592i	$0.979851\pi$
$810$	−4.52974	−	7.99233i	−0.159159	−	0.280822i
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	−0.824460	−	0.565920i	$-0.808521\pi$
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	0.565920	+	0.824460i	$0.308521\pi$
$812$	−11.4433	+	2.87134i	−0.401581	+	0.100764i
$813$	12.2070	+	12.2070i	0.428119	+	0.428119i
$814$	23.3100	+	6.44564i	0.817014	+	0.225920i
$815$	7.55196			0.264534
$816$	−4.35841	+	14.4099i	−0.152575	+	0.504447i
$817$	−41.0414			−1.43586
$818$	−29.3542	−	8.11697i	−1.02634	−	0.283803i
$819$	25.2038	+	25.2038i	0.880691	+	0.880691i
$820$	3.12087	+	12.4378i	0.108985	+	0.434345i
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	−0.400481	−	0.916305i	$-0.631157\pi$
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	0.916305	+	0.400481i	$0.131157\pi$
$822$	41.0138	+	72.3652i	1.43052	+	2.52403i
$823$			52.7544i			1.83890i	0.393203	+	0.919452i	$0.371367\pi$
$823$			52.7544i			1.83890i	−0.393203	+	0.919452i	$0.628633\pi$
$824$	17.8088	+	18.6824i	0.620399	+	0.650831i
$825$			5.99752i			0.208807i
$826$	−41.7287	+	23.6502i	−1.45193	+	0.822897i
$827$	16.8883	−	16.8883i	0.587265	−	0.587265i	−0.349625	−	0.936890i	$-0.613691\pi$
$827$	16.8883	−	16.8883i	0.587265	−	0.587265i	0.936890	+	0.349625i	$0.113691\pi$
$828$	−14.9934	−	8.97840i	−0.521056	−	0.312021i
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	0.542660	−	0.839952i	$-0.317417\pi$
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	−0.839952	+	0.542660i	$0.817417\pi$
$830$	−1.30579	+	4.72226i	−0.0453247	+	0.163912i
$831$	−43.3232			−1.50287
$832$	12.7160	−	11.5534i	0.440847	−	0.400541i
$833$	−19.4201			−0.672868
$834$	−8.65313	+	31.2931i	−0.299633	+	1.08359i
$835$	−11.3622	−	11.3622i	−0.393206	−	0.393206i
$836$	−15.0886	−	9.03543i	−0.521850	−	0.312497i
$837$	8.95827	−	8.95827i	0.309643	−	0.309643i
$838$	30.0980	−	17.0584i	1.03972	−	0.589271i
$839$			17.5407i			0.605572i	0.953059	+	0.302786i	$0.0979168\pi$
$839$			17.5407i			0.605572i	−0.953059	+	0.302786i	$0.902083\pi$
$840$	22.7469	+	23.8626i	0.784841	+	0.823339i
$841$		−	27.2889i		−	0.940996i
$842$	−19.1638	−	33.8129i	−0.660429	−	1.16527i
$843$	0.872614	−	0.872614i	0.0300544	−	0.0300544i
$844$	5.91814	+	23.5859i	0.203711	+	0.811860i
$845$	5.93112	+	5.93112i	0.204037	+	0.204037i
$846$	12.5930	+	3.48219i	0.432955	+	0.119720i
$847$	25.3238			0.870137
$848$	8.13881	+	2.46166i	0.279488	+	0.0845337i
$849$	−1.76516			−0.0605803
$850$	1.98483	+	0.548843i	0.0680793	+	0.0188252i
$851$	12.3726	+	12.3726i	0.424129	+	0.424129i
$852$	9.63148	−	2.41672i	0.329969	−	0.0827955i
$853$	−15.3577	+	15.3577i	−0.525839	+	0.525839i	−0.919329	−	0.393490i	$-0.871268\pi$
$853$	−15.3577	+	15.3577i	−0.525839	+	0.525839i	0.393490	+	0.919329i	$0.371268\pi$
$854$	−4.54363	−	8.01683i	−0.155480	−	0.274330i
$855$			13.9471i			0.476980i
$856$	−0.971684	+	40.5905i	−0.0332115	+	1.38736i
$857$			17.9553i			0.613341i	0.951816	+	0.306671i	$0.0992150\pi$
$857$			17.9553i			0.613341i	−0.951816	+	0.306671i	$0.900785\pi$
$858$	15.8471	−	8.98153i	0.541011	−	0.306624i
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.147245	+	0.989100i	$0.547040\pi$
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.989100	+	0.147245i	$0.952960\pi$
$860$	11.1280	−	18.5830i	0.379461	−	0.633676i
$861$	52.8439	+	52.8439i	1.80091	+	1.80091i
$862$	−10.6956	+	38.6795i	−0.364293	+	1.31743i
$863$	−32.3557			−1.10140			−0.550701	−	0.834703i	$-0.685639\pi$
$863$	−32.3557			−1.10140			−0.550701	+	0.834703i	$0.685639\pi$
$864$	5.31341	−	8.40968i	0.180766	−	0.286103i
$865$	−24.2019			−0.822889
$866$	−3.40731	+	12.3222i	−0.115785	+	0.418724i
$867$	−27.1942	−	27.1942i	−0.923564	−	0.923564i
$868$	33.3825	−	55.7467i	1.13308	−	1.89217i
$869$	−8.30766	+	8.30766i	−0.281818	+	0.281818i
$870$	4.15976	−	2.35759i	0.141029	−	0.0799299i
$871$			15.8765i			0.537956i
$872$	5.41803	+	0.129700i	0.183477	+	0.00439221i
$873$			68.5699i			2.32074i
$874$	−6.27397	−	11.0699i	−0.212220	−	0.374444i
$875$	3.18877	−	3.18877i	0.107800	−	0.107800i
$876$	6.98991	−	1.75390i	0.236167	−	0.0592588i
$877$	26.2297	+	26.2297i	0.885714	+	0.885714i	0.994108	−	0.108394i	$-0.0345707\pi$
$877$	26.2297	+	26.2297i	0.885714	+	0.885714i	−0.108394	+	0.994108i	$0.534571\pi$
$878$	−38.5677	−	10.6647i	−1.30160	−	0.359916i
$879$	27.2914			0.920515
$880$	8.18224	−	4.38205i	0.275823	−	0.147719i
$881$	−47.3359			−1.59479			−0.797394	−	0.603459i	$-0.793789\pi$
$881$	−47.3359			−1.59479			−0.797394	+	0.603459i	$0.793789\pi$
$882$	66.9037	+	18.5001i	2.25277	+	0.622932i
$883$	8.08371	+	8.08371i	0.272039	+	0.272039i	0.829920	−	0.557882i	$-0.188386\pi$
$883$	8.08371	+	8.08371i	0.272039	+	0.272039i	−0.557882	+	0.829920i	$0.688386\pi$
$884$	−1.52217	−	6.06640i	−0.0511962	−	0.204035i
$885$	13.7453	−	13.7453i	0.462043	−	0.462043i
$886$	−12.9415	−	22.8341i	−0.434778	−	0.767127i
$887$			12.9255i			0.433994i	0.976172	+	0.216997i	$0.0696263\pi$
$887$			12.9255i			0.433994i	−0.976172	+	0.216997i	$0.930374\pi$
$888$	−38.9973	+	37.1739i	−1.30866	+	1.24747i
$889$		−	61.9412i		−	2.07744i
$890$	−11.5161	+	6.52690i	−0.386022	+	0.218782i
$891$	−10.6586	+	10.6586i	−0.357078	+	0.357078i
$892$	36.7606	+	22.0132i	1.23084	+	0.737055i
$893$	6.72664	+	6.72664i	0.225098	+	0.225098i
$894$	17.8514	−	64.5578i	0.597042	−	2.15914i
$895$	−1.47760			−0.0493906
$896$	15.9352	−	48.4680i	0.532359	−	1.61920i
$897$	13.1787			0.440025
$898$	5.42384	−	19.6147i	0.180996	−	0.654553i
$899$	−6.66378	−	6.66378i	−0.222250	−	0.222250i
$900$	−6.31505	−	3.78161i	−0.210502	−	0.126054i
$901$	2.18878	−	2.18878i	0.0729190	−	0.0729190i
$902$	18.3050	−	10.3746i	0.609490	−	0.345435i
$903$		−	126.232i		−	4.20074i
$904$	−5.24186	+	4.99676i	−0.174342	+	0.166190i
$905$			16.9544i			0.563584i
$906$	25.8481	+	45.6067i	0.858746	+	1.51518i
$907$	16.4991	−	16.4991i	0.547844	−	0.547844i	−0.377973	−	0.925817i	$-0.623379\pi$
$907$	16.4991	−	16.4991i	0.547844	−	0.547844i	0.925817	+	0.377973i	$0.123379\pi$
$908$	5.55051	+	22.1207i	0.184200	+	0.734103i
$909$	−17.8169	−	17.8169i	−0.590951	−	0.590951i
$910$	−13.2009	−	3.65031i	−0.437607	−	0.121006i
$911$	−26.6745			−0.883765			−0.441883	−	0.897073i	$-0.645689\pi$
$911$	−26.6745			−0.883765			−0.441883	+	0.897073i	$0.645689\pi$
$912$	34.5377	−	18.4969i	1.14366	−	0.612493i
$913$	8.03908			0.266055
$914$	6.19563	+	1.71321i	0.204933	+	0.0566678i
$915$	2.64071	+	2.64071i	0.0872993	+	0.0872993i
$916$	−12.7065	+	3.18830i	−0.419834	+	0.105344i
$917$	23.4827	−	23.4827i	0.775467	−	0.775467i
$918$	−1.78559	−	3.15051i	−0.0589331	−	0.103982i
$919$		−	57.7425i		−	1.90475i	−0.304932	−	0.952374i	$-0.598634\pi$
$919$		−	57.7425i		−	1.90475i	0.304932	−	0.952374i	$-0.401366\pi$
$920$	6.71341	+	0.160710i	0.221334	+	0.00529846i
$921$			8.74878i			0.288282i
$922$	−34.4595	+	19.5303i	−1.13486	+	0.643197i
$923$	−2.91714	+	2.91714i	−0.0960188	+	0.0960188i
$924$	27.7905	−	46.4083i	0.914239	−	1.52672i
$925$	5.21123	+	5.21123i	0.171344	+	0.171344i
$926$	5.50280	−	19.9003i	0.180833	−	0.653965i
$927$	−33.5848			−1.10307
$928$	−6.25571	−	3.95248i	−0.205354	−	0.129747i
$929$	42.5386			1.39565			0.697823	−	0.716270i	$-0.254152\pi$
$929$	42.5386			1.39565			0.697823	+	0.716270i	$0.254152\pi$
$930$	−7.01835	+	25.3811i	−0.230141	+	0.832280i
$931$	35.7372	+	35.7372i	1.17124	+	1.17124i
$932$	−26.7843	+	44.7281i	−0.877349	+	1.46512i
$933$	37.3572	−	37.3572i	1.22302	−	1.22302i
$934$	−34.4698	+	19.5362i	−1.12789	+	0.639243i
$935$		−	3.37894i		−	0.110503i
$936$	−0.535011	+	22.3492i	−0.0174874	+	0.730507i
$937$			16.6795i			0.544894i	0.962171	+	0.272447i	$0.0878330\pi$
$937$			16.6795i			0.544894i	−0.962171	+	0.272447i	$0.912167\pi$
$938$	23.2473	+	41.0177i	0.759050	+	1.33928i
$939$	−4.51376	+	4.51376i	−0.147301	+	0.147301i
$940$	−4.86959	+	1.22187i	−0.158829	+	0.0398531i
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	0.846449	−	0.532470i	$-0.178736\pi$
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	−0.532470	+	0.846449i	$0.678736\pi$
$942$	10.4910	+	2.90094i	0.341814	+	0.0945179i
$943$	15.2227			0.495721
$944$	−28.7952	−	8.70938i	−0.937205	−	0.283466i
$945$	−7.93018			−0.257969
$946$	−34.2545	−	9.47200i	−1.11371	−	0.307961i
$947$	−3.44034	−	3.44034i	−0.111796	−	0.111796i	0.648996	−	0.760792i	$-0.275189\pi$
$947$	−3.44034	−	3.44034i	−0.111796	−	0.111796i	−0.760792	+	0.648996i	$0.775189\pi$
$948$	−6.36982	−	25.3860i	−0.206882	−	0.824498i
$949$	−2.11707	+	2.11707i	−0.0687231	+	0.0687231i
$950$	−2.64253	−	4.66251i	−0.0857350	−	0.151272i
$951$		−	59.3028i		−	1.92302i
$952$	−12.8153	−	13.4440i	−0.415347	−	0.435721i
$953$		−	17.6965i		−	0.573247i	−0.958043	−	0.286623i	$-0.907467\pi$
$953$		−	17.6965i		−	0.573247i	0.958043	−	0.286623i	$-0.0925328\pi$
$954$	−9.62561	+	5.45542i	−0.311641	+	0.176626i
$955$	−0.0471973	+	0.0471973i	−0.00152727	+	0.00152727i
$956$	−8.78886	−	5.26299i	−0.284252	−	0.170217i
$957$	−5.54750	−	5.54750i	−0.179325	−	0.179325i
$958$	−7.92940	+	28.6759i	−0.256187	+	0.926475i
$959$	−102.622			−3.31384
$960$	−0.989399	+	20.6534i	−0.0319327	+	0.666587i
$961$	20.9027			0.674281
$962$	5.96548	−	21.5735i	0.192335	−	0.695559i
$963$	−37.3577	−	37.3577i	−1.20384	−	1.20384i
$964$	−19.7303	−	11.8150i	−0.635470	−	0.380535i
$965$	0.777073	−	0.777073i	0.0250149	−	0.0250149i
$966$	34.0478	−	19.2970i	1.09547	−	0.620870i
$967$			15.0023i			0.482442i	0.970470	+	0.241221i	$0.0775479\pi$
$967$			15.0023i			0.482442i	−0.970470	+	0.241221i	$0.922452\pi$
$968$	10.9591	+	11.4966i	0.352238	+	0.369516i
$969$		−	14.2627i		−	0.458183i
$970$	−12.9918	−	22.9229i	−0.417142	−	0.736010i
$971$	−14.3135	+	14.3135i	−0.459340	+	0.459340i	−0.898439	−	0.439098i	$-0.855298\pi$
$971$	−14.3135	+	14.3135i	−0.459340	+	0.459340i	0.439098	+	0.898439i	$0.355298\pi$
$972$	−10.7403	−	42.8038i	−0.344494	−	1.37293i
$973$	−28.3241	−	28.3241i	−0.908030	−	0.908030i
$974$	−14.0019	−	3.87177i	−0.448649	−	0.124060i
$975$	5.55074			0.177766
$976$	1.67323	−	5.53207i	0.0535587	−	0.177077i
$977$	48.1433			1.54024			0.770120	−	0.637900i	$-0.220196\pi$
$977$	48.1433			1.54024			0.770120	+	0.637900i	$0.220196\pi$
$978$	26.6058	+	7.35698i	0.850758	+	0.235250i
$979$	15.3580	+	15.3580i	0.490845	+	0.490845i
$980$	−25.8711	+	6.49155i	−0.826422	+	0.207365i
$981$	−4.98651	+	4.98651i	−0.159207	+	0.159207i
$982$	−5.87430	−	10.3647i	−0.187457	−	0.330750i
$983$		−	0.791292i		−	0.0252383i	−0.999920	−	0.0126191i	$-0.995983\pi$
$983$		−	0.791292i		−	0.0252383i	0.999920	−	0.0126191i	$-0.00401690\pi$
$984$	−1.12174	+	46.8588i	−0.0357597	+	1.49380i
$985$			16.8700i			0.537523i
$986$	−2.34357	+	1.32824i	−0.0746343	+	0.0422999i
$987$	−20.6893	+	20.6893i	−0.658547	+	0.658547i
$988$	−8.36234	+	13.9646i	−0.266042	+	0.444273i
$989$	−18.1818	−	18.1818i	−0.578149	−	0.578149i
$990$	−3.21886	+	11.6407i	−0.102302	+	0.369965i
$991$	−60.2424			−1.91366			−0.956832	−	0.290643i	$-0.906131\pi$
$991$	−60.2424			−1.91366			−0.956832	+	0.290643i	$0.906131\pi$
$992$	39.7547	−	8.96964i	1.26221	−	0.284786i
$993$	12.5133			0.397099
$994$	−3.26513	+	11.8080i	−0.103563	+	0.374526i
$995$	−7.80625	−	7.80625i	−0.247475	−	0.247475i
$996$	−9.20069	+	15.3646i	−0.291535	+	0.486845i
$997$	1.15773	−	1.15773i	0.0366655	−	0.0366655i	−0.688536	−	0.725202i	$-0.741746\pi$
$997$	1.15773	−	1.15773i	0.0366655	−	0.0366655i	0.725202	+	0.688536i	$0.241746\pi$
$998$	4.89744	−	2.77568i	0.155026	−	0.0878626i
$999$		−	12.9598i		−	0.410031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.61.3	yes	16
3.2	odd	2		720.2.t.c.541.6		16
4.3	odd	2		320.2.l.a.81.1		16
5.2	odd	4		400.2.q.h.349.1		16
5.3	odd	4		400.2.q.g.349.8		16
5.4	even	2		400.2.l.h.301.6		16
8.3	odd	2		640.2.l.a.161.8		16
8.5	even	2		640.2.l.b.161.1		16
12.11	even	2		2880.2.t.c.721.8		16
16.3	odd	4		640.2.l.a.481.8		16
16.5	even	4	inner	80.2.l.a.21.3	✓	16
16.11	odd	4		320.2.l.a.241.1		16
16.13	even	4		640.2.l.b.481.1		16
20.3	even	4		1600.2.q.h.849.8		16
20.7	even	4		1600.2.q.g.849.1		16
20.19	odd	2		1600.2.l.i.401.8		16
32.5	even	8		5120.2.a.s.1.2		8
32.11	odd	8		5120.2.a.t.1.2		8
32.21	even	8		5120.2.a.v.1.7		8
32.27	odd	8		5120.2.a.u.1.7		8
48.5	odd	4		720.2.t.c.181.6		16
48.11	even	4		2880.2.t.c.2161.5		16
80.27	even	4		1600.2.q.h.49.8		16
80.37	odd	4		400.2.q.g.149.8		16
80.43	even	4		1600.2.q.g.49.1		16
80.53	odd	4		400.2.q.h.149.1		16
80.59	odd	4		1600.2.l.i.1201.8		16
80.69	even	4		400.2.l.h.101.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	16.5	even	4	inner
80.2.l.a.61.3	yes	16	1.1	even	1	trivial
320.2.l.a.81.1		16	4.3	odd	2
320.2.l.a.241.1		16	16.11	odd	4
400.2.l.h.101.6		16	80.69	even	4
400.2.l.h.301.6		16	5.4	even	2
400.2.q.g.149.8		16	80.37	odd	4
400.2.q.g.349.8		16	5.3	odd	4
400.2.q.h.149.1		16	80.53	odd	4
400.2.q.h.349.1		16	5.2	odd	4
640.2.l.a.161.8		16	8.3	odd	2
640.2.l.a.481.8		16	16.3	odd	4
640.2.l.b.161.1		16	8.5	even	2
640.2.l.b.481.1		16	16.13	even	4
720.2.t.c.181.6		16	48.5	odd	4
720.2.t.c.541.6		16	3.2	odd	2
1600.2.l.i.401.8		16	20.19	odd	2
1600.2.l.i.1201.8		16	80.59	odd	4
1600.2.q.g.49.1		16	80.43	even	4
1600.2.q.g.849.1		16	20.7	even	4
1600.2.q.h.49.8		16	80.27	even	4
1600.2.q.h.849.8		16	20.3	even	4
2880.2.t.c.721.8		16	12.11	even	2
2880.2.t.c.2161.5		16	48.11	even	4
5120.2.a.s.1.2		8	32.5	even	8
5120.2.a.t.1.2		8	32.11	odd	8
5120.2.a.u.1.7		8	32.27	odd	8
5120.2.a.v.1.7		8	32.21	even	8

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

\(f(q)\)	\(=\)	\(q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +O(q^{10})\)	\(q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +(-0.697313 - 1.23035i) q^{10} +(-1.64080 + 1.64080i) q^{11} +(-1.25807 - 5.01385i) q^{12} +(1.51857 + 1.51857i) q^{13} +(6.14687 + 1.69972i) q^{14} -2.58464 q^{15} +(1.88845 + 3.52615i) q^{16} +1.45616 q^{17} +(-5.01657 - 1.38717i) q^{18} +(-2.67964 - 2.67964i) q^{19} +(1.93986 - 0.486749i) q^{20} +(8.24183 - 8.24183i) q^{21} +(-1.61808 - 2.85495i) q^{22} -2.37423i q^{23} +(7.30837 + 0.174953i) q^{24} -1.00000i q^{25} +(-2.64228 + 1.49754i) q^{26} +(-1.24345 + 1.24345i) q^{27} +(-4.63366 + 7.73792i) q^{28} +(0.924966 + 0.924966i) q^{29} +(0.974182 - 3.52303i) q^{30} -7.20435 q^{31} +(-5.51814 + 1.24503i) q^{32} -5.99752 q^{33} +(-0.548843 + 1.98483i) q^{34} +(3.18877 + 3.18877i) q^{35} +(3.78161 - 6.31505i) q^{36} +(-5.21123 + 5.21123i) q^{37} +(4.66251 - 2.64253i) q^{38} +5.55074i q^{39} +(-0.0676894 + 2.82762i) q^{40} +6.41166i q^{41} +(8.12768 + 14.3406i) q^{42} +(7.65800 - 7.65800i) q^{43} +(4.50135 - 1.12947i) q^{44} +(-2.60241 - 2.60241i) q^{45} +(3.23622 + 0.894875i) q^{46} -2.51027 q^{47} +(-2.99308 + 9.89582i) q^{48} -13.3366 q^{49} +(1.36306 + 0.376912i) q^{50} +(2.66130 + 2.66130i) q^{51} +(-1.04534 - 4.16603i) q^{52} +(1.50312 - 1.50312i) q^{53} +(-1.22623 - 2.16357i) q^{54} -2.32045i q^{55} +(-8.80078 - 9.23248i) q^{56} -9.79472i q^{57} +(-1.60942 + 0.912155i) q^{58} +(-5.31807 + 5.31807i) q^{59} +(4.43492 + 2.65574i) q^{60} +(-1.02169 - 1.02169i) q^{61} +(2.71541 - 9.81998i) q^{62} +16.5970 q^{63} +(0.382800 - 7.99084i) q^{64} -2.14759 q^{65} +(2.26054 - 8.17499i) q^{66} +(5.22745 + 5.22745i) q^{67} +(-2.49859 - 1.49622i) q^{68} +(4.33918 - 4.33918i) q^{69} +(-5.54838 + 3.14461i) q^{70} +1.92097i q^{71} +(7.18247 + 7.53478i) q^{72} +1.39412i q^{73} +(-5.13905 - 9.06740i) q^{74} +(1.82762 - 1.82762i) q^{75} +(1.84458 + 7.35129i) q^{76} +(7.39938 + 7.39938i) q^{77} +(-7.56600 - 2.09214i) q^{78} +5.06317 q^{79} +(-3.82870 - 1.15803i) q^{80} +6.49599 q^{81} +(-8.73949 - 2.41663i) q^{82} +(-2.44974 - 2.44974i) q^{83} +(-22.6105 + 5.67340i) q^{84} +(-1.02966 + 1.02966i) q^{85} +(7.55194 + 13.3247i) q^{86} +3.38097i q^{87} +(-0.157070 + 6.56133i) q^{88} -9.36007i q^{89} +(4.52813 - 2.56637i) q^{90} +(6.84817 - 6.84817i) q^{91} +(-2.43954 + 4.07388i) q^{92} +(-13.1668 - 13.1668i) q^{93} +(0.946152 - 3.42166i) q^{94} +3.78959 q^{95} +(-12.3605 - 7.80961i) q^{96} +18.6313 q^{97} +(5.02671 - 18.1785i) q^{98} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Introduction

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