LMFDB - Embedded newform 80.2.l.a.21.6

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			21.6
Root			$-0.966675 - 1.03225i$ of defining polynomial
Character	$\chi$	$=$	80.21
Dual form			80.2.l.a.61.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.562546 - 1.29751i) q^{2} +(0.209571 - 0.209571i) q^{3} +(-1.36708 - 1.45982i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.154028 - 0.389815i) q^{6} -1.73696i q^{7} +(-2.66319 + 0.952595i) q^{8} +2.91216i q^{9} +O(q^{10})$	\(q+(0.562546 - 1.29751i) q^{2} +(0.209571 - 0.209571i) q^{3} +(-1.36708 - 1.45982i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.154028 - 0.389815i) q^{6} -1.73696i q^{7} +(-2.66319 + 0.952595i) q^{8} +2.91216i q^{9} +(1.31526 - 0.519701i) q^{10} +(0.505430 + 0.505430i) q^{11} +(-0.592438 - 0.0194351i) q^{12} +(-1.88750 + 1.88750i) q^{13} +(-2.25374 - 0.977122i) q^{14} +0.296378 q^{15} +(-0.262159 + 3.99140i) q^{16} +4.53524 q^{17} +(3.77857 + 1.63822i) q^{18} +(-3.22022 + 3.22022i) q^{19} +(0.0655751 - 1.99892i) q^{20} +(-0.364018 - 0.364018i) q^{21} +(0.940130 - 0.371475i) q^{22} -8.85045i q^{23} +(-0.358491 + 0.757764i) q^{24} +1.00000i q^{25} +(1.38725 + 3.51086i) q^{26} +(1.23902 + 1.23902i) q^{27} +(-2.53566 + 2.37458i) q^{28} +(-2.44059 + 2.44059i) q^{29} +(0.166726 - 0.384555i) q^{30} -5.70401 q^{31} +(5.03142 + 2.58550i) q^{32} +0.211847 q^{33} +(2.55128 - 5.88454i) q^{34} +(1.22822 - 1.22822i) q^{35} +(4.25123 - 3.98117i) q^{36} +(-5.35670 - 5.35670i) q^{37} +(2.36676 + 5.98979i) q^{38} +0.791130i q^{39} +(-2.55674 - 1.20957i) q^{40} -10.0343i q^{41} +(-0.677095 + 0.267541i) q^{42} +(-2.10564 - 2.10564i) q^{43} +(0.0468722 - 1.42880i) q^{44} +(-2.05921 + 2.05921i) q^{45} +(-11.4836 - 4.97878i) q^{46} +4.32303 q^{47} +(0.781541 + 0.891424i) q^{48} +3.98295 q^{49} +(1.29751 + 0.562546i) q^{50} +(0.950456 - 0.950456i) q^{51} +(5.33578 + 0.175041i) q^{52} +(-1.37458 - 1.37458i) q^{53} +(2.30465 - 0.910639i) q^{54} +0.714786i q^{55} +(1.65462 + 4.62586i) q^{56} +1.34973i q^{57} +(1.79375 + 4.53964i) q^{58} +(6.64140 + 6.64140i) q^{59} +(-0.405174 - 0.432660i) q^{60} +(5.26208 - 5.26208i) q^{61} +(-3.20877 + 7.40103i) q^{62} +5.05832 q^{63} +(6.18513 - 5.07388i) q^{64} -2.66933 q^{65} +(0.119174 - 0.274875i) q^{66} +(-10.5578 + 10.5578i) q^{67} +(-6.20006 - 6.62065i) q^{68} +(-1.85480 - 1.85480i) q^{69} +(-0.902702 - 2.28456i) q^{70} +14.0437i q^{71} +(-2.77411 - 7.75563i) q^{72} +6.63830i q^{73} +(-9.96378 + 3.93700i) q^{74} +(0.209571 + 0.209571i) q^{75} +(9.10325 + 0.298634i) q^{76} +(0.877914 - 0.877914i) q^{77} +(1.02650 + 0.445047i) q^{78} +4.27297 q^{79} +(-3.00772 + 2.63697i) q^{80} -8.21715 q^{81} +(-13.0196 - 5.64474i) q^{82} +(9.15483 - 9.15483i) q^{83} +(-0.0337580 + 1.02904i) q^{84} +(3.20690 + 3.20690i) q^{85} +(-3.91661 + 1.54758i) q^{86} +1.02295i q^{87} +(-1.82752 - 0.864585i) q^{88} -3.23826i q^{89} +(1.51345 + 3.83025i) q^{90} +(3.27852 + 3.27852i) q^{91} +(-12.9201 + 12.0993i) q^{92} +(-1.19540 + 1.19540i) q^{93} +(2.43190 - 5.60919i) q^{94} -4.55407 q^{95} +(1.59629 - 0.512594i) q^{96} +1.94129 q^{97} +(2.24059 - 5.16794i) q^{98} +(-1.47189 + 1.47189i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.562546	−	1.29751i	0.397780	−	0.917481i
$2$	0.562546	−	1.29751i	0.397780	−	0.917481i
$3$	0.209571	−	0.209571i	0.120996	−	0.120996i	−0.644016	−	0.765012i	$-0.722733\pi$
$3$	0.209571	−	0.209571i	0.120996	−	0.120996i	0.765012	+	0.644016i	$0.222733\pi$
$4$	−1.36708	−	1.45982i	−0.683542	−	0.729911i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−0.154028	−	0.389815i	−0.0628817	−	0.159141i
$7$		−	1.73696i		−	0.656511i	−0.944589	−	0.328255i	$-0.893539\pi$
$7$		−	1.73696i		−	0.656511i	0.944589	−	0.328255i	$-0.106461\pi$
$8$	−2.66319	+	0.952595i	−0.941579	+	0.336793i
$9$			2.91216i			0.970720i
$10$	1.31526	−	0.519701i	0.415922	−	0.164344i
$11$	0.505430	+	0.505430i	0.152393	+	0.152393i	0.779186	−	0.626793i	$-0.215633\pi$
$11$	0.505430	+	0.505430i	0.152393	+	0.152393i	−0.626793	+	0.779186i	$0.715633\pi$
$12$	−0.592438	−	0.0194351i	−0.171022	−	0.00561042i
$13$	−1.88750	+	1.88750i	−0.523498	+	0.523498i	−0.918626	−	0.395128i	$-0.870700\pi$
$13$	−1.88750	+	1.88750i	−0.523498	+	0.523498i	0.395128	+	0.918626i	$0.370700\pi$
$14$	−2.25374	−	0.977122i	−0.602336	−	0.261147i
$15$	0.296378			0.0765246
$16$	−0.262159	+	3.99140i	−0.0655399	+	0.997850i
$17$	4.53524			1.09996			0.549979	−	0.835178i	$-0.314636\pi$
$17$	4.53524			1.09996			0.549979	+	0.835178i	$0.314636\pi$
$18$	3.77857	+	1.63822i	0.890617	+	0.386133i
$19$	−3.22022	+	3.22022i	−0.738768	+	0.738768i	−0.972340	−	0.233571i	$-0.924959\pi$
$19$	−3.22022	+	3.22022i	−0.738768	+	0.738768i	0.233571	+	0.972340i	$0.424959\pi$
$20$	0.0655751	−	1.99892i	0.0146630	−	0.446973i
$21$	−0.364018	−	0.364018i	−0.0794352	−	0.0794352i
$22$	0.940130	−	0.371475i	0.200436	−	0.0791987i
$23$		−	8.85045i		−	1.84545i	−0.385463	−	0.922723i	$-0.625958\pi$
$23$		−	8.85045i		−	1.84545i	0.385463	−	0.922723i	$-0.374042\pi$
$24$	−0.358491	+	0.757764i	−0.0731766	+	0.154678i
$25$			1.00000i			0.200000i
$26$	1.38725	+	3.51086i	0.272062	+	0.688536i
$27$	1.23902	+	1.23902i	0.238449	+	0.238449i
$28$	−2.53566	+	2.37458i	−0.479195	+	0.448753i
$29$	−2.44059	+	2.44059i	−0.453205	+	0.453205i	−0.896417	−	0.443212i	$-0.853839\pi$
$29$	−2.44059	+	2.44059i	−0.453205	+	0.453205i	0.443212	+	0.896417i	$0.353839\pi$
$30$	0.166726	−	0.384555i	0.0304399	−	0.0702098i
$31$	−5.70401			−1.02447			−0.512235	−	0.858845i	$-0.671182\pi$
$31$	−5.70401			−1.02447			−0.512235	+	0.858845i	$0.671182\pi$
$32$	5.03142	+	2.58550i	0.889438	+	0.457056i
$33$	0.211847			0.0368779
$34$	2.55128	−	5.88454i	0.437541	−	1.00919i
$35$	1.22822	−	1.22822i	0.207607	−	0.207607i
$36$	4.25123	−	3.98117i	0.708539	−	0.663528i
$37$	−5.35670	−	5.35670i	−0.880636	−	0.880636i	0.112963	−	0.993599i	$-0.463966\pi$
$37$	−5.35670	−	5.35670i	−0.880636	−	0.880636i	−0.993599	+	0.112963i	$0.963966\pi$
$38$	2.36676	+	5.98979i	0.383939	+	0.971673i
$39$			0.791130i			0.126682i
$40$	−2.55674	−	1.20957i	−0.404257	−	0.191250i
$41$		−	10.0343i		−	1.56709i	−0.621335	−	0.783545i	$-0.713409\pi$
$41$		−	10.0343i		−	1.56709i	0.621335	−	0.783545i	$-0.286591\pi$
$42$	−0.677095	+	0.267541i	−0.104478	+	0.0412825i
$43$	−2.10564	−	2.10564i	−0.321107	−	0.321107i	0.528085	−	0.849192i	$-0.322910\pi$
$43$	−2.10564	−	2.10564i	−0.321107	−	0.321107i	−0.849192	+	0.528085i	$0.822910\pi$
$44$	0.0468722	−	1.42880i	0.00706625	−	0.215400i
$45$	−2.05921	+	2.05921i	−0.306969	+	0.306969i
$46$	−11.4836	−	4.97878i	−1.69316	−	0.734082i
$47$	4.32303			0.630578			0.315289	−	0.948996i	$-0.397899\pi$
$47$	4.32303			0.630578			0.315289	+	0.948996i	$0.397899\pi$
$48$	0.781541	+	0.891424i	0.112806	+	0.128666i
$49$	3.98295			0.568993
$50$	1.29751	+	0.562546i	0.183496	+	0.0795560i
$51$	0.950456	−	0.950456i	0.133091	−	0.133091i
$52$	5.33578	+	0.175041i	0.739940	+	0.0242739i
$53$	−1.37458	−	1.37458i	−0.188814	−	0.188814i	0.606369	−	0.795183i	$-0.292625\pi$
$53$	−1.37458	−	1.37458i	−0.188814	−	0.188814i	−0.795183	+	0.606369i	$0.792625\pi$
$54$	2.30465	−	0.910639i	0.313623	−	0.123922i
$55$			0.714786i			0.0963817i
$56$	1.65462	+	4.62586i	0.221108	+	0.618157i
$57$			1.34973i			0.178776i
$58$	1.79375	+	4.53964i	0.235531	+	0.596083i
$59$	6.64140	+	6.64140i	0.864637	+	0.864637i	0.991872	−	0.127236i	$-0.0406105\pi$
$59$	6.64140	+	6.64140i	0.864637	+	0.864637i	−0.127236	+	0.991872i	$0.540611\pi$
$60$	−0.405174	−	0.432660i	−0.0523078	−	0.0558561i
$61$	5.26208	−	5.26208i	0.673741	−	0.673741i	−0.284836	−	0.958576i	$-0.591939\pi$
$61$	5.26208	−	5.26208i	0.673741	−	0.673741i	0.958576	+	0.284836i	$0.0919391\pi$
$62$	−3.20877	+	7.40103i	−0.407514	+	0.939932i
$63$	5.05832			0.637288
$64$	6.18513	−	5.07388i	0.773141	−	0.634234i
$65$	−2.66933			−0.331089
$66$	0.119174	−	0.274875i	0.0146693	−	0.0338347i
$67$	−10.5578	+	10.5578i	−1.28984	+	1.28984i	−0.354954	+	0.934884i	$0.615503\pi$
$67$	−10.5578	+	10.5578i	−1.28984	+	1.28984i	−0.934884	+	0.354954i	$0.884497\pi$
$68$	−6.20006	−	6.62065i	−0.751868	−	0.802871i
$69$	−1.85480	−	1.85480i	−0.223292	−	0.223292i
$70$	−0.902702	−	2.28456i	−0.107894	−	0.273057i
$71$			14.0437i			1.66668i	0.552764	+	0.833338i	$0.313573\pi$
$71$			14.0437i			1.66668i	−0.552764	+	0.833338i	$0.686427\pi$
$72$	−2.77411	−	7.75563i	−0.326932	−	0.914009i
$73$			6.63830i			0.776954i	0.921458	+	0.388477i	$0.126999\pi$
$73$			6.63830i			0.776954i	−0.921458	+	0.388477i	$0.873001\pi$
$74$	−9.96378	+	3.93700i	−1.15827	+	0.457667i
$75$	0.209571	+	0.209571i	0.0241992	+	0.0241992i
$76$	9.10325	+	0.298634i	1.04421	+	0.0342557i
$77$	0.877914	−	0.877914i	0.100048	−	0.100048i
$78$	1.02650	+	0.445047i	0.116229	+	0.0503917i
$79$	4.27297			0.480746			0.240373	−	0.970681i	$-0.422730\pi$
$79$	4.27297			0.480746			0.240373	+	0.970681i	$0.422730\pi$
$80$	−3.00772	+	2.63697i	−0.336273	+	0.294822i
$81$	−8.21715			−0.913017
$82$	−13.0196	−	5.64474i	−1.43778	−	0.623357i
$83$	9.15483	−	9.15483i	1.00487	−	1.00487i	0.00488547	−	0.999988i	$-0.498445\pi$
$83$	9.15483	−	9.15483i	1.00487	−	1.00487i	0.999988	−	0.00488547i	$-0.00155510\pi$
$84$	−0.0337580	+	1.02904i	−0.00368330	+	0.112278i
$85$	3.20690	+	3.20690i	0.347837	+	0.347837i
$86$	−3.91661	+	1.54758i	−0.422339	+	0.166879i
$87$			1.02295i			0.109672i
$88$	−1.82752	−	0.864585i	−0.194815	−	0.0921650i
$89$		−	3.23826i		−	0.343255i	−0.985162	−	0.171627i	$-0.945097\pi$
$89$		−	3.23826i		−	0.343255i	0.985162	−	0.171627i	$-0.0549025\pi$
$90$	1.51345	+	3.83025i	0.159532	+	0.403744i
$91$	3.27852	+	3.27852i	0.343682	+	0.343682i
$92$	−12.9201	+	12.0993i	−1.34701	+	1.26144i
$93$	−1.19540	+	1.19540i	−0.123957	+	0.123957i
$94$	2.43190	−	5.60919i	0.250831	−	0.578543i
$95$	−4.55407			−0.467238
$96$	1.59629	−	0.512594i	0.162920	−	0.0523164i
$97$	1.94129			0.197108			0.0985541	−	0.995132i	$-0.468578\pi$
$97$	1.94129			0.197108			0.0985541	+	0.995132i	$0.468578\pi$
$98$	2.24059	−	5.16794i	0.226334	−	0.522041i
$99$	−1.47189	+	1.47189i	−0.147931	+	0.147931i
$100$	1.45982	−	1.36708i	0.145982	−	0.136708i
$101$	10.3395	+	10.3395i	1.02882	+	1.02882i	0.999572	+	0.0292464i	$0.00931074\pi$
$101$	10.3395	+	10.3395i	1.02882	+	1.02882i	0.0292464	+	0.999572i	$0.490689\pi$
$102$	−0.698555	−	1.76791i	−0.0691673	−	0.175049i
$103$			4.96401i			0.489118i	0.969634	+	0.244559i	$0.0786433\pi$
$103$			4.96401i			0.489118i	−0.969634	+	0.244559i	$0.921357\pi$
$104$	3.22874	−	6.82478i	0.316604	−	0.669225i
$105$		−	0.514799i		−	0.0502392i
$106$	−2.55681	+	1.01028i	−0.248339	+	0.0981266i
$107$	−2.74631	−	2.74631i	−0.265496	−	0.265496i	0.561787	−	0.827282i	$-0.310114\pi$
$107$	−2.74631	−	2.74631i	−0.265496	−	0.265496i	−0.827282	+	0.561787i	$0.810114\pi$
$108$	0.114903	−	3.50259i	0.0110566	−	0.337037i
$109$	6.99959	−	6.99959i	0.670439	−	0.670439i	−0.287378	−	0.957817i	$-0.592784\pi$
$109$	6.99959	−	6.99959i	0.670439	−	0.670439i	0.957817	+	0.287378i	$0.0927837\pi$
$110$	0.927445	+	0.402100i	0.0884284	+	0.0383387i
$111$	−2.24522			−0.213107
$112$	6.93292	+	0.455362i	0.655099	+	0.0430276i
$113$	−6.53194			−0.614474			−0.307237	−	0.951633i	$-0.599404\pi$
$113$	−6.53194			−0.614474			−0.307237	+	0.951633i	$0.599404\pi$
$114$	1.75129	+	0.759284i	0.164024	+	0.0711135i
$115$	6.25821	−	6.25821i	0.583582	−	0.583582i
$116$	6.89931	+	0.226333i	0.640585	+	0.0210145i
$117$	−5.49670	−	5.49670i	−0.508170	−	0.508170i
$118$	12.3534	−	4.88122i	1.13722	−	0.449353i
$119$		−	7.87756i		−	0.722134i
$120$	−0.789311	+	0.282329i	−0.0720539	+	0.0257730i
$121$		−	10.4891i		−	0.953553i
$122$	−3.86746	−	9.78779i	−0.350144	−	0.886145i
$123$	−2.10289	−	2.10289i	−0.189612	−	0.189612i
$124$	7.79786	+	8.32684i	0.700269	+	0.747772i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	2.84554	−	6.56324i	0.253500	−	0.584700i
$127$	−2.50861			−0.222603			−0.111302	−	0.993787i	$-0.535502\pi$
$127$	−2.50861			−0.222603			−0.111302	+	0.993787i	$0.535502\pi$
$128$	−3.10401	−	10.8796i	−0.274358	−	0.961628i
$129$	−0.882562			−0.0777053
$130$	−1.50162	+	3.46349i	−0.131701	+	0.303768i
$131$	8.55783	−	8.55783i	0.747701	−	0.747701i	−0.226346	−	0.974047i	$-0.572678\pi$
$131$	8.55783	−	8.55783i	0.747701	−	0.747701i	0.974047	+	0.226346i	$0.0726780\pi$
$132$	−0.289613	−	0.309259i	−0.0252076	−	0.0269176i
$133$	5.59340	+	5.59340i	0.485009	+	0.485009i
$134$	7.75963	+	19.6381i	0.670330	+	1.69647i
$135$			1.75224i			0.150809i
$136$	−12.0782	+	4.32025i	−1.03570	+	0.370458i
$137$			6.47131i			0.552881i	0.961031	+	0.276440i	$0.0891549\pi$
$137$			6.47131i			0.552881i	−0.961031	+	0.276440i	$0.910845\pi$
$138$	−3.45004	+	1.36322i	−0.293687	+	0.116045i
$139$	−16.4430	−	16.4430i	−1.39468	−	1.39468i	−0.814458	−	0.580223i	$-0.802965\pi$
$139$	−16.4430	−	16.4430i	−1.39468	−	1.39468i	−0.580223	−	0.814458i	$-0.697035\pi$
$140$	−3.47206	−	0.113902i	−0.293443	−	0.00962645i
$141$	0.905982	−	0.905982i	0.0762974	−	0.0762974i
$142$	18.2218	+	7.90020i	1.52914	+	0.662970i
$143$	−1.90800			−0.159555
$144$	−11.6236	−	0.763450i	−0.968633	−	0.0636209i
$145$	−3.45151			−0.286632
$146$	8.61329	+	3.73435i	0.712841	+	0.309057i
$147$	0.834712	−	0.834712i	0.0688459	−	0.0688459i
$148$	−0.496766	+	15.1429i	−0.0408339	+	1.24474i
$149$	−2.72803	−	2.72803i	−0.223489	−	0.223489i	0.586477	−	0.809966i	$-0.300514\pi$
$149$	−2.72803	−	2.72803i	−0.223489	−	0.223489i	−0.809966	+	0.586477i	$0.800514\pi$
$150$	0.389815	−	0.154028i	0.0318283	−	0.0125763i
$151$			11.5196i			0.937453i	0.883343	+	0.468726i	$0.155287\pi$
$151$			11.5196i			0.937453i	−0.883343	+	0.468726i	$0.844713\pi$
$152$	5.50848	−	11.6436i	0.446796	−	0.944420i
$153$			13.2074i			1.06775i
$154$	−0.645239	−	1.63297i	−0.0519948	−	0.131589i
$155$	−4.03334	−	4.03334i	−0.323966	−	0.323966i
$156$	1.15491	−	1.08154i	0.0924668	−	0.0865927i
$157$	3.28013	−	3.28013i	0.261783	−	0.261783i	−0.563995	−	0.825778i	$-0.690736\pi$
$157$	3.28013	−	3.28013i	0.261783	−	0.261783i	0.825778	+	0.563995i	$0.190736\pi$
$158$	2.40374	−	5.54423i	0.191231	−	0.441076i
$159$	−0.576147			−0.0456914
$160$	1.72953	+	5.38598i	0.136731	+	0.425799i
$161$	−15.3729			−1.21156
$162$	−4.62253	+	10.6619i	−0.363180	+	0.837676i
$163$	−9.27367	+	9.27367i	−0.726370	+	0.726370i	−0.969895	−	0.243525i	$-0.921696\pi$
$163$	−9.27367	+	9.27367i	−0.726370	+	0.726370i	0.243525	+	0.969895i	$0.421696\pi$
$164$	−14.6482	+	13.7177i	−1.14384	+	1.07117i
$165$	0.149799	+	0.149799i	0.0116618	+	0.0116618i
$166$	−6.72851	−	17.0285i	−0.522234	−	1.32167i
$167$		−	7.08065i		−	0.547917i	−0.961742	−	0.273958i	$-0.911667\pi$
$167$		−	7.08065i		−	0.547917i	0.961742	−	0.273958i	$-0.0883331\pi$
$168$	1.31621	+	0.622686i	0.101548	+	0.0480413i
$169$			5.87470i			0.451900i
$170$	5.96503	−	2.35697i	0.457497	−	0.180771i
$171$	−9.37778	−	9.37778i	−0.717137	−	0.717137i
$172$	−0.195271	+	5.95244i	−0.0148893	+	0.453869i
$173$	−5.21471	+	5.21471i	−0.396467	+	0.396467i	−0.876985	−	0.480518i	$-0.840449\pi$
$173$	−5.21471	+	5.21471i	−0.396467	+	0.396467i	0.480518	+	0.876985i	$0.340449\pi$
$174$	1.32730	+	0.575458i	0.100622	+	0.0436254i
$175$	1.73696			0.131302
$176$	−2.14988	+	1.88487i	−0.162053	+	0.142077i
$177$	2.78369			0.209235
$178$	−4.20169	−	1.82167i	−0.314930	−	0.136540i
$179$	6.32196	−	6.32196i	0.472525	−	0.472525i	−0.430206	−	0.902731i	$-0.641559\pi$
$179$	6.32196	−	6.32196i	0.472525	−	0.472525i	0.902731	+	0.430206i	$0.141559\pi$
$180$	5.82119	+	0.190965i	0.433886	+	0.0142337i
$181$	13.0695	+	13.0695i	0.971448	+	0.971448i	0.999604	−	0.0281553i	$-0.00896329\pi$
$181$	13.0695	+	13.0695i	0.971448	+	0.971448i	−0.0281553	+	0.999604i	$0.508963\pi$
$182$	6.09824	−	2.40961i	0.452031	−	0.178612i
$183$		−	2.20556i		−	0.163040i
$184$	8.43089	+	23.5704i	0.621534	+	1.73763i
$185$		−	7.57552i		−	0.556963i
$186$	0.878578	+	2.22351i	0.0644205	+	0.163035i
$187$	2.29225	+	2.29225i	0.167626	+	0.167626i
$188$	−5.90994	−	6.31085i	−0.431027	−	0.460266i
$189$	2.15213	−	2.15213i	0.156545	−	0.156545i
$190$	−2.56187	+	5.90897i	−0.185858	+	0.428682i
$191$	−22.1722			−1.60433			−0.802164	−	0.597104i	$-0.796318\pi$
$191$	−22.1722			−1.60433			−0.802164	+	0.597104i	$0.796318\pi$
$192$	0.232886	−	2.35956i	0.0168071	−	0.170287i
$193$	7.97695			0.574193			0.287097	−	0.957902i	$-0.407310\pi$
$193$	7.97695			0.574193			0.287097	+	0.957902i	$0.407310\pi$
$194$	1.09206	−	2.51885i	0.0784056	−	0.180843i
$195$	−0.559414	+	0.559414i	−0.0400604	+	0.0400604i
$196$	−5.44503	−	5.81440i	−0.388931	−	0.415314i
$197$	5.76327	+	5.76327i	0.410616	+	0.410616i	0.881953	−	0.471337i	$-0.156228\pi$
$197$	5.76327	+	5.76327i	0.410616	+	0.410616i	−0.471337	+	0.881953i	$0.656228\pi$
$198$	1.08179	+	2.73781i	0.0768798	+	0.194568i
$199$			5.38869i			0.381994i	0.981591	+	0.190997i	$0.0611721\pi$
$199$			5.38869i			0.381994i	−0.981591	+	0.190997i	$0.938828\pi$
$200$	−0.952595	−	2.66319i	−0.0673586	−	0.188316i
$201$			4.42521i			0.312130i
$202$	19.2321	−	7.59920i	1.35316	−	0.534678i
$203$	4.23921	+	4.23921i	0.297534	+	0.297534i
$204$	−2.68685	−	0.0881427i	−0.188117	−	0.00617122i
$205$	7.09530	−	7.09530i	0.495557	−	0.495557i
$206$	6.44087	+	2.79248i	0.448757	+	0.194561i
$207$	25.7739			1.79141
$208$	−7.03893	−	8.02858i	−0.488062	−	0.556682i
$209$	−3.25519			−0.225166
$210$	−0.667959	−	0.289598i	−0.0460935	−	0.0199842i
$211$	10.7547	−	10.7547i	0.740384	−	0.740384i	−0.232268	−	0.972652i	$-0.574615\pi$
$211$	10.7547	−	10.7547i	0.740384	−	0.740384i	0.972652	+	0.232268i	$0.0746147\pi$
$212$	−0.127475	+	3.88582i	−0.00875503	+	0.266879i
$213$	2.94315	+	2.94315i	0.201661	+	0.201661i
$214$	−5.10830	+	2.01845i	−0.349196	+	0.137978i
$215$		−	2.97782i		−	0.203086i
$216$	−4.48002	−	2.11946i	−0.304827	−	0.144211i
$217$			9.90766i			0.672576i
$218$	−5.14447	−	13.0197i	−0.348428	−	0.881802i
$219$	1.39120	+	1.39120i	0.0940084	+	0.0940084i
$220$	1.04346	−	0.977173i	0.0703501	−	0.0658810i
$221$	−8.56026	+	8.56026i	−0.575826	+	0.575826i
$222$	−1.26304	+	2.91320i	−0.0847696	+	0.195521i
$223$	−3.98714			−0.266998			−0.133499	−	0.991049i	$-0.542621\pi$
$223$	−3.98714			−0.266998			−0.133499	+	0.991049i	$0.542621\pi$
$224$	4.49092	−	8.73940i	0.300062	−	0.583926i
$225$	−2.91216			−0.194144
$226$	−3.67452	+	8.47529i	−0.244425	+	0.563768i
$227$	−3.82103	+	3.82103i	−0.253611	+	0.253611i	−0.822449	−	0.568839i	$-0.807393\pi$
$227$	−3.82103	+	3.82103i	−0.253611	+	0.253611i	0.568839	+	0.822449i	$0.307393\pi$
$228$	1.97036	−	1.84519i	0.130491	−	0.122201i
$229$	−8.80687	−	8.80687i	−0.581974	−	0.581974i	0.353471	−	0.935445i	$-0.385001\pi$
$229$	−8.80687	−	8.80687i	−0.581974	−	0.581974i	−0.935445	+	0.353471i	$0.885001\pi$
$230$	−4.59959	−	11.6407i	−0.303288	−	0.767562i
$231$		−	0.367971i		−	0.0242107i
$232$	4.17485	−	8.82463i	0.274092	−	0.579365i
$233$		−	16.6042i		−	1.08778i	−0.839157	−	0.543889i	$-0.816951\pi$
$233$		−	16.6042i		−	1.08778i	0.839157	−	0.543889i	$-0.183049\pi$
$234$	−10.2242	+	4.03990i	−0.668376	+	0.264096i
$235$	3.05684	+	3.05684i	0.199406	+	0.199406i
$236$	0.615905	−	18.7746i	0.0400920	−	1.22212i
$237$	0.895491	−	0.895491i	0.0581684	−	0.0581684i
$238$	−10.2212	−	4.43149i	−0.662545	−	0.287251i
$239$	3.81234			0.246600			0.123300	−	0.992369i	$-0.460652\pi$
$239$	3.81234			0.246600			0.123300	+	0.992369i	$0.460652\pi$
$240$	−0.0776984	+	1.18296i	−0.00501541	+	0.0763601i
$241$	9.54985			0.615160			0.307580	−	0.951522i	$-0.400481\pi$
$241$	9.54985			0.615160			0.307580	+	0.951522i	$0.400481\pi$
$242$	−13.6097	−	5.90059i	−0.874866	−	0.379304i
$243$	−5.43913	+	5.43913i	−0.348921	+	0.348921i
$244$	−14.8754	−	0.487991i	−0.952301	−	0.0312404i
$245$	2.81637	+	2.81637i	0.179932	+	0.179932i
$246$	−3.91151	+	1.54556i	−0.249389	+	0.0985413i
$247$		−	12.1563i		−	0.773487i
$248$	15.1908	−	5.43361i	0.964619	−	0.345034i
$249$		−	3.83718i		−	0.243171i
$250$	0.519701	+	1.31526i	0.0328688	+	0.0831844i
$251$	11.9933	+	11.9933i	0.757010	+	0.757010i	0.975777	−	0.218767i	$-0.0702034\pi$
$251$	11.9933	+	11.9933i	0.757010	+	0.757010i	−0.218767	+	0.975777i	$0.570203\pi$
$252$	−6.91515	−	7.38424i	−0.435613	−	0.465164i
$253$	4.47328	−	4.47328i	0.281233	−	0.281233i
$254$	−1.41121	+	3.25496i	−0.0885471	+	0.204234i
$255$	1.34415			0.0841738
$256$	−15.8625	−	2.09277i	−0.991409	−	0.130798i
$257$	18.8752			1.17740			0.588702	−	0.808350i	$-0.299639\pi$
$257$	18.8752			1.17740			0.588702	+	0.808350i	$0.299639\pi$
$258$	−0.496482	+	1.14514i	−0.0309096	+	0.0712931i
$259$	−9.30440	+	9.30440i	−0.578147	+	0.578147i
$260$	3.64919	+	3.89674i	0.226313	+	0.241666i
$261$	−7.10738	−	7.10738i	−0.439936	−	0.439936i
$262$	−6.28973	−	15.9181i	−0.388581	−	0.983422i
$263$			23.1398i			1.42686i	0.700727	+	0.713429i	$0.252859\pi$
$263$			23.1398i			1.42686i	−0.700727	+	0.713429i	$0.747141\pi$
$264$	−0.564189	+	0.201804i	−0.0347234	+	0.0124202i
$265$		−	1.94396i		−	0.119416i
$266$	10.4041	−	4.11097i	0.637914	−	0.252060i
$267$	−0.678646	−	0.678646i	−0.0415325	−	0.0415325i
$268$	29.8458	+	0.979099i	1.82313	+	0.0598080i
$269$	−10.6368	+	10.6368i	−0.648539	+	0.648539i	−0.952640	−	0.304101i	$-0.901644\pi$
$269$	−10.6368	+	10.6368i	−0.648539	+	0.648539i	0.304101	+	0.952640i	$0.401644\pi$
$270$	2.27355	+	0.985713i	0.138364	+	0.0599886i
$271$	19.9763			1.21348			0.606738	−	0.794902i	$-0.292478\pi$
$271$	19.9763			1.21348			0.606738	+	0.794902i	$0.292478\pi$
$272$	−1.18896	+	18.1020i	−0.0720911	+	1.09759i
$273$	1.37417			0.0831683
$274$	8.39661	+	3.64041i	0.507258	+	0.219925i
$275$	−0.505430	+	0.505430i	−0.0304786	+	0.0304786i
$276$	−0.172009	+	5.24335i	−0.0103537	+	0.315612i
$277$	−16.1534	−	16.1534i	−0.970563	−	0.970563i	0.0290160	−	0.999579i	$-0.490763\pi$
$277$	−16.1534	−	16.1534i	−0.970563	−	0.970563i	−0.999579	+	0.0290160i	$0.990763\pi$
$278$	−30.5850	+	12.0851i	−1.83437	+	0.724817i
$279$		−	16.6110i		−	0.994474i
$280$	−2.10098	+	4.44097i	−0.125558	+	0.265399i
$281$			9.43520i			0.562857i	0.959582	+	0.281429i	$0.0908082\pi$
$281$			9.43520i			0.562857i	−0.959582	+	0.281429i	$0.909192\pi$
$282$	−0.665868	−	1.68518i	−0.0396518	−	0.100351i
$283$	8.71287	+	8.71287i	0.517926	+	0.517926i	0.916943	−	0.399017i	$-0.130649\pi$
$283$	8.71287	+	8.71287i	0.517926	+	0.517926i	−0.399017	+	0.916943i	$0.630649\pi$
$284$	20.5012	−	19.1989i	1.21653	−	1.13924i
$285$	−0.954403	+	0.954403i	−0.0565339	+	0.0565339i
$286$	−1.07334	+	2.47565i	−0.0634676	+	0.146388i
$287$	−17.4292			−1.02881
$288$	−7.52939	+	14.6523i	−0.443674	+	0.863395i
$289$	3.56843			0.209908
$290$	−1.94163	+	4.47838i	−0.114017	+	0.262980i
$291$	0.406838	−	0.406838i	0.0238493	−	0.0238493i
$292$	9.69074	−	9.07512i	0.567107	−	0.531081i
$293$	−11.1045	−	11.1045i	−0.648729	−	0.648729i	0.303957	−	0.952686i	$-0.401692\pi$
$293$	−11.1045	−	11.1045i	−0.648729	−	0.648729i	−0.952686	+	0.303957i	$0.901692\pi$
$294$	−0.613487	−	1.55261i	−0.0357793	−	0.0905503i
$295$			9.39236i			0.546844i
$296$	19.3687	+	9.16313i	1.12578	+	0.532596i
$297$			1.25247i			0.0726759i
$298$	−5.07429	+	2.00501i	−0.293946	+	0.116147i
$299$	16.7052	+	16.7052i	0.966087	+	0.966087i
$300$	0.0194351	−	0.592438i	0.00112208	−	0.0342044i
$301$	−3.65742	+	3.65742i	−0.210810	+	0.210810i
$302$	14.9469	+	6.48031i	0.860095	+	0.372900i
$303$	4.33372			0.248966
$304$	−12.0090	−	13.6974i	−0.688761	−	0.785599i
$305$	7.44171			0.426111
$306$	17.1367	+	7.42974i	0.979641	+	0.424730i
$307$	−2.99854	+	2.99854i	−0.171136	+	0.171136i	−0.787478	−	0.616343i	$-0.788614\pi$
$307$	−2.99854	+	2.99854i	−0.171136	+	0.171136i	0.616343	+	0.787478i	$0.288614\pi$
$308$	−2.48178	−	0.0814153i	−0.141413	−	0.00463907i
$309$	1.04031	+	1.04031i	0.0591814	+	0.0591814i
$310$	−7.50226	+	2.96438i	−0.426100	+	0.168365i
$311$		−	9.06099i		−	0.513802i	−0.966438	−	0.256901i	$-0.917299\pi$
$311$		−	9.06099i		−	0.513802i	0.966438	−	0.256901i	$-0.0827014\pi$
$312$	−0.753627	−	2.10693i	−0.0426657	−	0.119281i
$313$		−	19.5699i		−	1.10616i	−0.833129	−	0.553078i	$-0.813453\pi$
$313$		−	19.5699i		−	1.10616i	0.833129	−	0.553078i	$-0.186547\pi$
$314$	−2.41079	−	6.10124i	−0.136049	−	0.344313i
$315$	3.57677	+	3.57677i	0.201528	+	0.201528i
$316$	−5.84151	−	6.23777i	−0.328610	−	0.350902i
$317$	−11.1019	+	11.1019i	−0.623546	+	0.623546i	−0.946436	−	0.322890i	$-0.895346\pi$
$317$	−11.1019	+	11.1019i	−0.623546	+	0.623546i	0.322890	+	0.946436i	$0.395346\pi$
$318$	−0.324109	+	0.747558i	−0.0181751	+	0.0419210i
$319$	−2.46709			−0.138131
$320$	7.96132	+	0.785774i	0.445051	+	0.0439261i
$321$	−1.15109			−0.0642478
$322$	−8.64797	+	19.9466i	−0.481933	+	1.11158i
$323$	−14.6045	+	14.6045i	−0.812614	+	0.812614i
$324$	11.2335	+	11.9956i	0.624086	+	0.666421i
$325$	−1.88750	−	1.88750i	−0.104700	−	0.104700i
$326$	6.81585	+	17.2496i	0.377495	+	0.955366i
$327$		−	2.93382i		−	0.162241i
$328$	9.55859	+	26.7231i	0.527785	+	1.47554i
$329$		−	7.50894i		−	0.413981i
$330$	0.278634	−	0.110097i	0.0153383	−	0.00606065i
$331$	−8.14718	−	8.14718i	−0.447810	−	0.447810i	0.446816	−	0.894626i	$-0.352558\pi$
$331$	−8.14718	−	8.14718i	−0.447810	−	0.447810i	−0.894626	+	0.446816i	$0.852558\pi$
$332$	−25.8799	−	0.848994i	−1.42034	−	0.0465946i
$333$	15.5996	−	15.5996i	0.854851	−	0.854851i
$334$	−9.18724	−	3.98319i	−0.502703	−	0.217950i
$335$	−14.9309			−0.815765
$336$	1.54837	−	1.35751i	0.0844706	−	0.0740582i
$337$	−25.1380			−1.36935			−0.684677	−	0.728847i	$-0.740057\pi$
$337$	−25.1380			−1.36935			−0.684677	+	0.728847i	$0.740057\pi$
$338$	7.62251	+	3.30479i	0.414610	+	0.179757i
$339$	−1.36891	+	1.36891i	−0.0743488	+	0.0743488i
$340$	0.297399	−	9.06561i	0.0161287	−	0.491652i
$341$	−2.88298	−	2.88298i	−0.156122	−	0.156122i
$342$	−17.4432	+	6.89237i	−0.943222	+	0.372697i
$343$		−	19.0770i		−	1.03006i
$344$	7.61353	+	3.60189i	0.410494	+	0.194201i
$345$		−	2.62308i		−	0.141222i
$346$	3.83265	+	9.69967i	0.206044	+	0.521458i
$347$	7.36719	+	7.36719i	0.395491	+	0.395491i	0.876639	−	0.481148i	$-0.159780\pi$
$347$	7.36719	+	7.36719i	0.395491	+	0.395491i	−0.481148	+	0.876639i	$0.659780\pi$
$348$	1.49333	−	1.39846i	0.0800509	−	0.0749655i
$349$	−3.25982	+	3.25982i	−0.174494	+	0.174494i	−0.788951	−	0.614457i	$-0.789375\pi$
$349$	−3.25982	+	3.25982i	−0.174494	+	0.174494i	0.614457	+	0.788951i	$0.289375\pi$
$350$	0.977122	−	2.25374i	0.0522294	−	0.120467i
$351$	−4.67729			−0.249655
$352$	1.23624	+	3.84982i	0.0658919	+	0.205196i
$353$	0.502832			0.0267630			0.0133815	−	0.999910i	$-0.495740\pi$
$353$	0.502832			0.0267630			0.0133815	+	0.999910i	$0.495740\pi$
$354$	1.56595	−	3.61188i	0.0832295	−	0.191969i
$355$	−9.93037	+	9.93037i	−0.527049	+	0.527049i
$356$	−4.72728	+	4.42697i	−0.250545	+	0.234629i
$357$	−1.65091	−	1.65091i	−0.0873754	−	0.0873754i
$358$	−4.64644	−	11.7592i	−0.245572	−	0.621494i
$359$			5.95161i			0.314114i	0.987590	+	0.157057i	$0.0502007\pi$
$359$			5.95161i			0.314114i	−0.987590	+	0.157057i	$0.949799\pi$
$360$	3.52246	−	7.44565i	0.185650	−	0.392420i
$361$		−	1.73958i		−	0.0915571i
$362$	24.3100	−	9.60567i	1.27771	−	0.504863i
$363$	−2.19821	−	2.19821i	−0.115376	−	0.115376i
$364$	0.304041	−	9.26806i	0.0159361	−	0.485778i
$365$	−4.69399	+	4.69399i	−0.245695	+	0.245695i
$366$	−2.86175	−	1.24073i	−0.149586	−	0.0648540i
$367$	1.95365			0.101980			0.0509898	−	0.998699i	$-0.483762\pi$
$367$	1.95365			0.101980			0.0509898	+	0.998699i	$0.483762\pi$
$368$	35.3257	+	2.32023i	1.84148	+	0.120950i
$369$	29.2214			1.52121
$370$	−9.82934	−	4.26157i	−0.511003	−	0.221549i
$371$	−2.38760	+	2.38760i	−0.123958	+	0.123958i
$372$	3.37927	+	0.110858i	0.175207	+	0.00574770i
$373$	−18.6509	−	18.6509i	−0.965708	−	0.965708i	0.0337233	−	0.999431i	$-0.489264\pi$
$373$	−18.6509	−	18.6509i	−0.965708	−	0.965708i	−0.999431	+	0.0337233i	$0.989264\pi$
$374$	4.26372	−	1.68473i	0.220472	−	0.0871153i
$375$			0.296378i			0.0153049i
$376$	−11.5130	+	4.11809i	−0.593739	+	0.212374i
$377$		−	9.21320i		−	0.474504i
$378$	−1.58175	−	4.00309i	−0.0813563	−	0.205897i
$379$	−3.85143	−	3.85143i	−0.197835	−	0.197835i	0.601236	−	0.799071i	$-0.294675\pi$
$379$	−3.85143	−	3.85143i	−0.197835	−	0.197835i	−0.799071	+	0.601236i	$0.794675\pi$
$380$	6.22580	+	6.64814i	0.319377	+	0.341042i
$381$	−0.525732	+	0.525732i	−0.0269341	+	0.0269341i
$382$	−12.4729	+	28.7688i	−0.638169	+	1.47194i
$383$	2.29258			0.117145			0.0585726	−	0.998283i	$-0.481345\pi$
$383$	2.29258			0.117145			0.0585726	+	0.998283i	$0.481345\pi$
$384$	−2.93056	−	1.62954i	−0.149549	−	0.0831569i
$385$	1.24156			0.0632757
$386$	4.48740	−	10.3502i	0.228403	−	0.526812i
$387$	6.13195	−	6.13195i	0.311705	−	0.311705i
$388$	−2.65391	−	2.83394i	−0.134732	−	0.143871i
$389$	4.90500	+	4.90500i	0.248693	+	0.248693i	0.820434	−	0.571741i	$-0.193732\pi$
$389$	4.90500	+	4.90500i	0.248693	+	0.248693i	−0.571741	+	0.820434i	$0.693732\pi$
$390$	0.411151	+	1.04054i	0.0208195	+	0.0526899i
$391$		−	40.1389i		−	2.02991i
$392$	−10.6073	+	3.79414i	−0.535752	+	0.191633i
$393$		−	3.58695i		−	0.180938i
$394$	10.7200	−	4.23582i	0.540067	−	0.213398i
$395$	3.02144	+	3.02144i	0.152025	+	0.152025i
$396$	4.16090	+	0.136499i	0.209093	+	0.00685935i
$397$	−10.8616	+	10.8616i	−0.545126	+	0.545126i	−0.925027	−	0.379901i	$-0.875958\pi$
$397$	−10.8616	+	10.8616i	−0.545126	+	0.545126i	0.379901	+	0.925027i	$0.375958\pi$
$398$	6.99190	+	3.03138i	0.350472	+	0.151950i
$399$	2.34443			0.117368
$400$	−3.99140	−	0.262159i	−0.199570	−	0.0131080i
$401$	−7.10783			−0.354948			−0.177474	−	0.984125i	$-0.556793\pi$
$401$	−7.10783			−0.354948			−0.177474	+	0.984125i	$0.556793\pi$
$402$	5.74177	+	2.48938i	0.286374	+	0.124159i
$403$	10.7663	−	10.7663i	0.536308	−	0.536308i
$404$	0.958857	−	29.2288i	0.0477049	−	1.45419i
$405$	−5.81041	−	5.81041i	−0.288721	−	0.288721i
$406$	7.88519	−	3.11569i	0.391335	−	0.154629i
$407$		−	5.41487i		−	0.268405i
$408$	−1.62584	+	3.43664i	−0.0804912	+	0.170139i
$409$			29.1697i			1.44235i	0.692752	+	0.721176i	$0.256398\pi$
$409$			29.1697i			1.44235i	−0.692752	+	0.721176i	$0.743602\pi$
$410$	−5.21482	−	13.1977i	−0.257542	−	0.651787i
$411$	1.35620	+	1.35620i	0.0668964	+	0.0668964i
$412$	7.24657	−	6.78622i	0.357013	−	0.334333i
$413$	11.5359	−	11.5359i	0.567643	−	0.567643i
$414$	14.4990	−	33.4420i	0.712588	−	1.64359i
$415$	12.9469			0.635538
$416$	−14.3769	+	4.61667i	−0.704887	+	0.226351i
$417$	−6.89198			−0.337502
$418$	−1.83119	+	4.22365i	−0.0895665	+	0.206586i
$419$	3.06616	−	3.06616i	0.149792	−	0.149792i	−0.628233	−	0.778025i	$-0.716222\pi$
$419$	3.06616	−	3.06616i	0.149792	−	0.149792i	0.778025	+	0.628233i	$0.216222\pi$
$420$	−0.751515	+	0.703774i	−0.0366702	+	0.0343406i
$421$	−0.532242	−	0.532242i	−0.0259399	−	0.0259399i	0.694018	−	0.719958i	$-0.255839\pi$
$421$	−0.532242	−	0.532242i	−0.0259399	−	0.0259399i	−0.719958	+	0.694018i	$0.755839\pi$
$422$	−7.90436	−	20.0044i	−0.384778	−	0.973798i
$423$			12.5893i			0.612115i
$424$	4.97020	+	2.35135i	0.241374	+	0.114192i
$425$			4.53524i			0.219992i
$426$	5.47443	−	2.16312i	0.265237	−	0.104803i
$427$	−9.14005	−	9.14005i	−0.442318	−	0.442318i
$428$	−0.254685	+	7.76356i	−0.0123107	+	0.375266i
$429$	−0.399861	+	0.399861i	−0.0193055	+	0.0193055i
$430$	−3.86376	−	1.67516i	−0.186327	−	0.0807834i
$431$	16.7237			0.805555			0.402777	−	0.915298i	$-0.368045\pi$
$431$	16.7237			0.805555			0.402777	+	0.915298i	$0.368045\pi$
$432$	−5.27024	+	4.62060i	−0.253564	+	0.222309i
$433$	28.3675			1.36326			0.681628	−	0.731699i	$-0.261272\pi$
$433$	28.3675			1.36326			0.681628	+	0.731699i	$0.261272\pi$
$434$	12.8553	+	5.57351i	0.617076	+	0.267537i
$435$	−0.723337	+	0.723337i	−0.0346814	+	0.0346814i
$436$	−19.7872	−	0.649122i	−0.947634	−	0.0310873i
$437$	28.5004	+	28.5004i	1.36336	+	1.36336i
$438$	2.58771	−	1.02249i	0.123645	−	0.0488562i
$439$			13.5018i			0.644405i	0.946671	+	0.322203i	$0.104423\pi$
$439$			13.5018i			0.644405i	−0.946671	+	0.322203i	$0.895577\pi$
$440$	−0.680901	−	1.90361i	−0.0324607	−	0.0907510i
$441$			11.5990i			0.552333i
$442$	6.29152	+	15.9226i	0.299257	+	0.757361i
$443$	−9.55246	−	9.55246i	−0.453851	−	0.453851i	0.442780	−	0.896630i	$-0.353992\pi$
$443$	−9.55246	−	9.55246i	−0.453851	−	0.453851i	−0.896630	+	0.442780i	$0.853992\pi$
$444$	3.06941	+	3.27762i	0.145668	+	0.155549i
$445$	2.28980	−	2.28980i	0.108547	−	0.108547i
$446$	−2.24295	+	5.17337i	−0.106207	+	0.244966i
$447$	−1.14343			−0.0540824
$448$	−8.81314	−	10.7433i	−0.416382	−	0.507575i
$449$	−9.35573			−0.441524			−0.220762	−	0.975328i	$-0.570854\pi$
$449$	−9.35573			−0.441524			−0.220762	+	0.975328i	$0.570854\pi$
$450$	−1.63822	+	3.77857i	−0.0772266	+	0.178123i
$451$	5.07162	−	5.07162i	0.238813	−	0.238813i
$452$	8.92972	+	9.53547i	0.420019	+	0.448511i
$453$	2.41418	+	2.41418i	0.113428	+	0.113428i
$454$	2.80833	+	7.10734i	0.131802	+	0.333564i
$455$			4.63652i			0.217364i
$456$	−1.28574	−	3.59458i	−0.0602105	−	0.168332i
$457$			6.84779i			0.320326i	0.987091	+	0.160163i	$0.0512020\pi$
$457$			6.84779i			0.320326i	−0.987091	+	0.160163i	$0.948798\pi$
$458$	−16.3813	+	6.47277i	−0.765448	+	0.302453i
$459$	5.61925	+	5.61925i	0.262284	+	0.262284i
$460$	−17.6914	−	0.580370i	−0.824865	−	0.0270599i
$461$	−11.7403	+	11.7403i	−0.546801	+	0.546801i	−0.925514	−	0.378713i	$-0.876367\pi$
$461$	−11.7403	+	11.7403i	−0.546801	+	0.546801i	0.378713	+	0.925514i	$0.376367\pi$
$462$	−0.477448	−	0.207001i	−0.0222129	−	0.00963054i
$463$	−26.6096			−1.23665			−0.618326	−	0.785922i	$-0.712189\pi$
$463$	−26.6096			−1.23665			−0.618326	+	0.785922i	$0.712189\pi$
$464$	−9.10153	−	10.3812i	−0.422528	−	0.481934i
$465$	−1.69055			−0.0783972
$466$	−21.5442	−	9.34063i	−0.998015	−	0.432696i
$467$	1.47583	−	1.47583i	0.0682933	−	0.0682933i	−0.672135	−	0.740428i	$-0.734623\pi$
$467$	1.47583	−	1.47583i	0.0682933	−	0.0682933i	0.740428	+	0.672135i	$0.234623\pi$
$468$	−0.509748	+	15.5386i	−0.0235631	+	0.718274i
$469$	18.3385	+	18.3385i	0.846792	+	0.846792i
$470$	5.68591	−	2.24668i	0.262271	−	0.103632i
$471$		−	1.37484i		−	0.0633494i
$472$	−24.0139	−	11.3607i	−1.10533	−	0.522920i
$473$		−	2.12851i		−	0.0978688i
$474$	−0.658157	−	1.66567i	−0.0302302	−	0.0765066i
$475$	−3.22022	−	3.22022i	−0.147754	−	0.147754i
$476$	−11.4998	+	10.7693i	−0.527094	+	0.493609i
$477$	4.00301	−	4.00301i	0.183285	−	0.183285i
$478$	2.14462	−	4.94656i	0.0980924	−	0.226251i
$479$	−2.78600			−0.127296			−0.0636479	−	0.997972i	$-0.520273\pi$
$479$	−2.78600			−0.127296			−0.0636479	+	0.997972i	$0.520273\pi$
$480$	1.49120	+	0.766287i	0.0680639	+	0.0349760i
$481$	20.2215			0.922022
$482$	5.37223	−	12.3911i	0.244698	−	0.564397i
$483$	−3.22172	+	3.22172i	−0.146593	+	0.146593i
$484$	−15.3122	+	14.3395i	−0.696009	+	0.651794i
$485$	1.37270	+	1.37270i	0.0623311	+	0.0623311i
$486$	3.99759	+	10.1171i	0.181334	+	0.458922i
$487$			16.9499i			0.768073i	0.923318	+	0.384036i	$0.125466\pi$
$487$			16.9499i			0.768073i	−0.923318	+	0.384036i	$0.874534\pi$
$488$	−9.00128	+	19.0265i	−0.407469	+	0.861291i
$489$			3.88699i			0.175776i
$490$	5.23862	−	2.06994i	0.236657	−	0.0935106i
$491$	−22.8390	−	22.8390i	−1.03071	−	1.03071i	−0.999513	−	0.0311972i	$-0.990068\pi$
$491$	−22.8390	−	22.8390i	−1.03071	−	1.03071i	−0.0311972	−	0.999513i	$-0.509932\pi$
$492$	−0.195017	+	5.94469i	−0.00879203	+	0.268007i
$493$	−11.0687	+	11.0687i	−0.498507	+	0.498507i
$494$	−15.7730	−	6.83848i	−0.709660	−	0.307678i
$495$	−2.08157			−0.0935597
$496$	1.49536	−	22.7670i	0.0671436	−	1.02227i
$497$	24.3933			1.09419
$498$	−4.97879	−	2.15859i	−0.223105	−	0.0967287i
$499$	2.33906	−	2.33906i	0.104711	−	0.104711i	−0.652811	−	0.757521i	$-0.726410\pi$
$499$	2.33906	−	2.33906i	0.104711	−	0.104711i	0.757521	+	0.652811i	$0.226410\pi$
$500$	1.99892	+	0.0655751i	0.0893946	+	0.00293261i
$501$	−1.48390	−	1.48390i	−0.0662958	−	0.0662958i
$502$	22.3083	−	8.81469i	0.995666	−	0.393419i
$503$		−	1.58801i		−	0.0708057i	−0.999373	−	0.0354029i	$-0.988729\pi$
$503$		−	1.58801i		−	0.0708057i	0.999373	−	0.0354029i	$-0.0112714\pi$
$504$	−13.4712	+	4.81853i	−0.600057	+	0.214634i
$505$			14.6223i			0.650682i
$506$	−3.28772	−	8.32058i	−0.146157	−	0.369895i
$507$	1.23117	+	1.23117i	0.0546781	+	0.0546781i
$508$	3.42948	+	3.66212i	0.152159	+	0.162480i
$509$	−3.61613	+	3.61613i	−0.160282	+	0.160282i	−0.782692	−	0.622410i	$-0.786154\pi$
$509$	−3.61613	+	3.61613i	−0.160282	+	0.160282i	0.622410	+	0.782692i	$0.286154\pi$
$510$	0.756145	−	1.74405i	0.0334827	−	0.0772279i
$511$	11.5305			0.510079
$512$	−11.6388	+	19.4046i	−0.514367	+	0.857570i
$513$	−7.97981			−0.352317
$514$	10.6182	−	24.4909i	0.468348	−	1.08025i
$515$	−3.51009	+	3.51009i	−0.154673	+	0.154673i
$516$	1.20654	+	1.28838i	0.0531148	+	0.0567179i
$517$	2.18499	+	2.18499i	0.0960956	+	0.0960956i
$518$	6.83844	+	17.3067i	0.300464	+	0.760414i
$519$			2.18571i			0.0959419i
$520$	7.10891	−	2.54279i	0.311746	−	0.111509i
$521$			8.93031i			0.391244i	0.980679	+	0.195622i	$0.0626725\pi$
$521$			8.93031i			0.391244i	−0.980679	+	0.195622i	$0.937327\pi$
$522$	−13.2201	+	5.22370i	−0.578630	+	0.228635i
$523$	15.0355	+	15.0355i	0.657455	+	0.657455i	0.954777	−	0.297323i	$-0.0960937\pi$
$523$	15.0355	+	15.0355i	0.657455	+	0.657455i	−0.297323	+	0.954777i	$0.596094\pi$
$524$	−24.1922	−	0.793629i	−1.05684	−	0.0346699i
$525$	0.364018	−	0.364018i	0.0158870	−	0.0158870i
$526$	30.0242	+	13.0172i	1.30912	+	0.567576i
$527$	−25.8691			−1.12687
$528$	−0.0555377	+	0.845567i	−0.00241697	+	0.0367986i
$529$	−55.3305			−2.40567
$530$	−2.52231	−	1.09356i	−0.109562	−	0.0475014i
$531$	−19.3408	+	19.3408i	−0.839320	+	0.839320i
$532$	0.518717	−	15.8120i	0.0224892	−	0.685538i
$533$	18.9397	+	18.9397i	0.820368	+	0.820368i
$534$	−1.26232	+	0.498783i	−0.0546260	+	0.0215845i
$535$		−	3.88387i		−	0.167914i
$536$	18.0600	−	38.1746i	0.780075	−	1.64889i
$537$		−	2.64980i		−	0.114347i
$538$	7.81773	+	19.7851i	0.337046	+	0.852998i
$539$	2.01310	+	2.01310i	0.0867106	+	0.0867106i
$540$	2.55795	−	2.39546i	0.110077	−	0.103084i
$541$	5.57591	−	5.57591i	0.239727	−	0.239727i	−0.577010	−	0.816737i	$-0.695781\pi$
$541$	5.57591	−	5.57591i	0.239727	−	0.239727i	0.816737	+	0.577010i	$0.195781\pi$
$542$	11.2376	−	25.9196i	0.482696	−	1.11334i
$543$	5.47798			0.235083
$544$	22.8187	+	11.7259i	0.978344	+	0.502743i
$545$	9.89891			0.424023
$546$	0.773031	−	1.78300i	0.0330827	−	0.0763053i
$547$	32.8366	−	32.8366i	1.40399	−	1.40399i	0.617136	−	0.786856i	$-0.288293\pi$
$547$	32.8366	−	32.8366i	1.40399	−	1.40399i	0.786856	−	0.617136i	$-0.211707\pi$
$548$	9.44695	−	8.84682i	0.403554	−	0.377918i
$549$	15.3240	+	15.3240i	0.654013	+	0.654013i
$550$	0.371475	+	0.940130i	0.0158397	+	0.0400873i
$551$		−	15.7184i		−	0.669628i
$552$	6.70655	+	3.17281i	0.285450	+	0.135044i
$553$		−	7.42199i		−	0.315615i
$554$	−30.0463	+	11.8722i	−1.27654	+	0.504402i
$555$	−1.58761	−	1.58761i	−0.0673903	−	0.0673903i
$556$	−1.52488	+	46.4829i	−0.0646694	+	1.97132i
$557$	24.2077	−	24.2077i	1.02571	−	1.02571i	0.0260537	−	0.999661i	$-0.491706\pi$
$557$	24.2077	−	24.2077i	1.02571	−	1.02571i	0.999661	−	0.0260537i	$-0.00829408\pi$
$558$	−21.5530	−	9.34444i	−0.912411	−	0.395582i
$559$	7.94877			0.336197
$560$	4.58033	+	5.22430i	0.193554	+	0.220767i
$561$	0.960778			0.0405641
$562$	12.2423	+	5.30773i	0.516411	+	0.223893i
$563$	22.3407	−	22.3407i	0.941547	−	0.941547i	−0.0568365	−	0.998384i	$-0.518101\pi$
$563$	22.3407	−	22.3407i	0.941547	−	0.941547i	0.998384	+	0.0568365i	$0.0181014\pi$
$564$	−2.56113	−	0.0840182i	−0.107843	−	0.00353781i
$565$	−4.61878	−	4.61878i	−0.194314	−	0.194314i
$566$	16.2065	−	6.40368i	0.681208	−	0.269167i
$567$			14.2729i			0.599406i
$568$	−13.3779	−	37.4009i	−0.561325	−	1.56931i
$569$		−	29.3339i		−	1.22974i	−0.788629	−	0.614870i	$-0.789209\pi$
$569$		−	29.3339i		−	1.22974i	0.788629	−	0.614870i	$-0.210791\pi$
$570$	0.701456	+	1.77525i	0.0293807	+	0.0743569i
$571$	23.9934	+	23.9934i	1.00409	+	1.00409i	0.999992	+	0.00410070i	$0.00130530\pi$
$571$	23.9934	+	23.9934i	1.00409	+	1.00409i	0.00410070	+	0.999992i	$0.498695\pi$
$572$	2.60839	+	2.78534i	0.109062	+	0.116461i
$573$	−4.64666	+	4.64666i	−0.194117	+	0.194117i
$574$	−9.80471	+	22.6146i	−0.409241	+	0.943915i
$575$	8.85045			0.369089
$576$	14.7759	+	18.0121i	0.615664	+	0.750503i
$577$	−31.9232			−1.32898			−0.664490	−	0.747297i	$-0.731351\pi$
$577$	−31.9232			−1.32898			−0.664490	+	0.747297i	$0.731351\pi$
$578$	2.00740	−	4.63009i	0.0834970	−	0.192586i
$579$	1.67174	−	1.67174i	0.0694751	−	0.0694751i
$580$	4.71851	+	5.03859i	0.195925	+	0.209216i
$581$	−15.9016	−	15.9016i	−0.659710	−	0.659710i
$582$	−0.299013	−	0.756744i	−0.0123945	−	0.0313680i
$583$		−	1.38951i		−	0.0575477i
$584$	−6.32361	−	17.6790i	−0.261673	−	0.731564i
$585$		−	7.77350i		−	0.321395i
$586$	−20.6549	+	8.16142i	−0.853248	+	0.337145i
$587$	−26.2847	−	26.2847i	−1.08488	−	1.08488i	−0.996046	−	0.0888379i	$-0.971685\pi$
$587$	−26.2847	−	26.2847i	−1.08488	−	1.08488i	−0.0888379	−	0.996046i	$-0.528315\pi$
$588$	−2.35965	−	0.0774089i	−0.0973105	−	0.00319229i
$589$	18.3681	−	18.3681i	0.756846	−	0.756846i
$590$	12.1867	+	5.28363i	0.501719	+	0.217524i
$591$	2.41563			0.0993658
$592$	22.7850	−	19.9764i	0.936459	−	0.821026i
$593$	−38.2085			−1.56904			−0.784518	−	0.620106i	$-0.787090\pi$
$593$	−38.2085			−1.56904			−0.784518	+	0.620106i	$0.787090\pi$
$594$	1.62510	+	0.704574i	0.0666788	+	0.0289090i
$595$	5.57027	−	5.57027i	0.228359	−	0.228359i
$596$	−0.252990	+	7.71187i	−0.0103629	+	0.315891i
$597$	1.12931	+	1.12931i	0.0462197	+	0.0462197i
$598$	31.0727	−	12.2778i	1.27066	−	0.502076i
$599$			25.1150i			1.02617i	0.858337	+	0.513086i	$0.171498\pi$
$599$			25.1150i			1.02617i	−0.858337	+	0.513086i	$0.828502\pi$
$600$	−0.757764	−	0.358491i	−0.0309356	−	0.0146353i
$601$			22.2022i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$601$			22.2022i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$602$	2.68809	+	6.80302i	0.109558	+	0.277270i
$603$	−30.7459	−	30.7459i	−1.25207	−	1.25207i
$604$	16.8166	−	15.7483i	0.684257	−	0.640789i
$605$	7.41690	−	7.41690i	0.301540	−	0.301540i
$606$	2.43792	−	5.62307i	0.0990336	−	0.228421i
$607$	12.9648			0.526226			0.263113	−	0.964765i	$-0.415251\pi$
$607$	12.9648			0.526226			0.263113	+	0.964765i	$0.415251\pi$
$608$	−24.5281	+	7.87639i	−0.994747	+	0.319430i
$609$	1.77683			0.0720009
$610$	4.18630	−	9.65572i	0.169498	−	0.390949i
$611$	−8.15970	+	8.15970i	−0.330106	+	0.330106i
$612$	19.2804	−	18.0556i	0.779363	−	0.729853i
$613$	7.42804	+	7.42804i	0.300016	+	0.300016i	0.841020	−	0.541004i	$-0.181956\pi$
$613$	7.42804	+	7.42804i	0.300016	+	0.300016i	−0.541004	+	0.841020i	$0.681956\pi$
$614$	2.20383	+	5.57746i	0.0889394	+	0.225088i
$615$		−	2.97394i		−	0.119921i
$616$	−1.50175	+	3.17435i	−0.0605074	+	0.127898i
$617$		−	23.2743i		−	0.936989i	−0.883467	−	0.468494i	$-0.844797\pi$
$617$		−	23.2743i		−	0.936989i	0.883467	−	0.468494i	$-0.155203\pi$
$618$	1.93505	−	0.764597i	0.0778389	−	0.0307566i
$619$	−31.6213	−	31.6213i	−1.27097	−	1.27097i	−0.945581	−	0.325386i	$-0.894506\pi$
$619$	−31.6213	−	31.6213i	−1.27097	−	1.27097i	−0.325386	−	0.945581i	$-0.605494\pi$
$620$	−0.374041	+	11.4019i	−0.0150219	+	0.457911i
$621$	10.9659	−	10.9659i	0.440045	−	0.440045i
$622$	−11.7568	−	5.09722i	−0.471403	−	0.204380i
$623$	−5.62474			−0.225351
$624$	−3.15772	−	0.207402i	−0.126410	−	0.00830274i
$625$	−1.00000			−0.0400000
$626$	−25.3922	−	11.0090i	−1.01488	−	0.440007i
$627$	−0.682194	+	0.682194i	−0.0272442	+	0.0272442i
$628$	−9.27262	−	0.304190i	−0.370018	−	0.0121385i
$629$	−24.2939	−	24.2939i	−0.968663	−	0.968663i
$630$	6.65301	−	2.62881i	0.265062	−	0.104734i
$631$			29.9258i			1.19133i	0.803234	+	0.595663i	$0.203111\pi$
$631$			29.9258i			1.19133i	−0.803234	+	0.595663i	$0.796889\pi$
$632$	−11.3797	+	4.07041i	−0.452661	+	0.161912i
$633$		−	4.50775i		−	0.179167i
$634$	8.15956	+	20.6502i	0.324058	+	0.820126i
$635$	−1.77386	−	1.77386i	−0.0703933	−	0.0703933i
$636$	0.787641	+	0.841071i	0.0312320	+	0.0333506i
$637$	−7.51782	+	7.51782i	−0.297867	+	0.297867i
$638$	−1.38785	+	3.20109i	−0.0549456	+	0.126732i
$639$	−40.8974			−1.61788
$640$	5.49816	−	9.88789i	0.217334	−	0.390853i
$641$	10.2240			0.403825			0.201912	−	0.979404i	$-0.435284\pi$
$641$	10.2240			0.403825			0.201912	+	0.979404i	$0.435284\pi$
$642$	−0.647543	+	1.49356i	−0.0255565	+	0.0589461i
$643$	−13.7202	+	13.7202i	−0.541074	+	0.541074i	−0.923844	−	0.382770i	$-0.874970\pi$
$643$	−13.7202	+	13.7202i	−0.541074	+	0.541074i	0.382770	+	0.923844i	$0.374970\pi$
$644$	21.0161	+	22.4417i	0.828150	+	0.884328i
$645$	−0.624066	−	0.624066i	−0.0245726	−	0.0245726i
$646$	10.7338	+	27.1652i	0.422316	+	1.06880i
$647$			18.6767i			0.734255i	0.930171	+	0.367128i	$0.119659\pi$
$647$			18.6767i			0.734255i	−0.930171	+	0.367128i	$0.880341\pi$
$648$	21.8838	−	7.82762i	0.859677	−	0.307498i
$649$			6.71353i			0.263529i
$650$	−3.51086	+	1.38725i	−0.137707	+	0.0544125i
$651$	2.07636	+	2.07636i	0.0813790	+	0.0813790i
$652$	26.2158	+	0.860014i	1.02669	+	0.0336808i
$653$	12.7935	−	12.7935i	0.500647	−	0.500647i	−0.410992	−	0.911639i	$-0.634817\pi$
$653$	12.7935	−	12.7935i	0.500647	−	0.500647i	0.911639	+	0.410992i	$0.134817\pi$
$654$	−3.80668	−	1.65041i	−0.148853	−	0.0645362i
$655$	12.1026			0.472888
$656$	40.0508	+	2.63058i	1.56372	+	0.102707i
$657$	−19.3318			−0.754205
$658$	−9.74296	−	4.22412i	−0.379820	−	0.164673i
$659$	12.3193	−	12.3193i	0.479893	−	0.479893i	−0.425204	−	0.905097i	$-0.639798\pi$
$659$	12.3193	−	12.3193i	0.479893	−	0.479893i	0.905097	+	0.425204i	$0.139798\pi$
$660$	0.0138919	−	0.423467i	0.000540742	−	0.0164834i
$661$	−24.0352	−	24.0352i	−0.934862	−	0.934862i	0.0631421	−	0.998005i	$-0.479888\pi$
$661$	−24.0352	−	24.0352i	−0.934862	−	0.934862i	−0.998005	+	0.0631421i	$0.979888\pi$
$662$	−15.1542	+	5.98792i	−0.588987	+	0.232727i
$663$			3.58797i			0.139345i
$664$	−15.6602	+	33.1019i	−0.607733	+	1.28460i
$665$			7.91026i			0.306747i
$666$	−11.4652	−	29.0161i	−0.444267	−	1.12435i
$667$	21.6003	+	21.6003i	0.836367	+	0.836367i
$668$	−10.3365	+	9.67984i	−0.399931	+	0.374524i
$669$	−0.835589	+	0.835589i	−0.0323057	+	0.0323057i
$670$	−8.39934	+	19.3731i	−0.324495	+	0.748449i
$671$	5.31923			0.205347
$672$	−0.890358	−	2.77269i	−0.0343463	−	0.106959i
$673$	−21.5360			−0.830150			−0.415075	−	0.909787i	$-0.636245\pi$
$673$	−21.5360			−0.830150			−0.415075	+	0.909787i	$0.636245\pi$
$674$	−14.1413	+	32.6169i	−0.544701	+	1.25636i
$675$	−1.23902	+	1.23902i	−0.0476898	+	0.0476898i
$676$	8.57602	−	8.03121i	0.329847	−	0.308893i
$677$	13.1852	+	13.1852i	0.506750	+	0.506750i	0.913527	−	0.406778i	$-0.133348\pi$
$677$	13.1852	+	13.1852i	0.506750	+	0.506750i	−0.406778	+	0.913527i	$0.633348\pi$
$678$	1.00610	+	2.54625i	0.0386392	+	0.0977881i
$679$		−	3.37195i		−	0.129404i
$680$	−11.5955	−	5.48570i	−0.444665	−	0.210367i
$681$			1.60156i			0.0613717i
$682$	−5.36251	+	2.11890i	−0.205341	+	0.0811367i
$683$	30.6011	+	30.6011i	1.17092	+	1.17092i	0.981991	+	0.188926i	$0.0605008\pi$
$683$	30.6011	+	30.6011i	1.17092	+	1.17092i	0.188926	+	0.981991i	$0.439499\pi$
$684$	−0.869670	+	26.5101i	−0.0332527	+	1.01364i
$685$	−4.57590	+	4.57590i	−0.174836	+	0.174836i
$686$	−24.7527	−	10.7317i	−0.945062	−	0.409738i
$687$	−3.69133			−0.140833
$688$	8.95645	−	7.85243i	0.341462	−	0.299371i
$689$	5.18905			0.197687
$690$	−3.40349	−	1.47560i	−0.129569	−	0.0561753i
$691$	−25.2675	+	25.2675i	−0.961220	+	0.961220i	−0.999276	−	0.0380558i	$-0.987884\pi$
$691$	−25.2675	+	25.2675i	−0.961220	+	0.961220i	0.0380558	+	0.999276i	$0.487884\pi$
$692$	14.7415	+	0.483598i	0.560388	+	0.0183836i
$693$	2.55663	+	2.55663i	0.0971182	+	0.0971182i
$694$	13.7034	−	5.41465i	0.520174	−	0.205537i
$695$		−	23.2540i		−	0.882074i
$696$	−0.974460	−	2.72432i	−0.0369368	−	0.103265i
$697$		−	45.5079i		−	1.72373i
$698$	2.39586	+	6.06345i	0.0906847	+	0.229505i
$699$	−3.47976	−	3.47976i	−0.131617	−	0.131617i
$700$	−2.37458	−	2.53566i	−0.0897506	−	0.0958389i
$701$	18.5583	−	18.5583i	0.700937	−	0.700937i	−0.263675	−	0.964612i	$-0.584935\pi$
$701$	18.5583	−	18.5583i	0.700937	−	0.700937i	0.964612	+	0.263675i	$0.0849345\pi$
$702$	−2.63119	+	6.06885i	−0.0993078	+	0.229054i
$703$	34.4995			1.30117
$704$	5.69064	+	0.561660i	0.214474	+	0.0211684i
$705$	1.28125			0.0482547
$706$	0.282866	−	0.652431i	0.0106458	−	0.0245546i
$707$	17.9593	−	17.9593i	0.675431	−	0.675431i
$708$	−3.80554	−	4.06369i	−0.143021	−	0.152723i
$709$	4.38093	+	4.38093i	0.164529	+	0.164529i	0.784570	−	0.620040i	$-0.212884\pi$
$709$	4.38093	+	4.38093i	0.164529	+	0.164529i	−0.620040	+	0.784570i	$0.712884\pi$
$710$	7.29850	+	18.4711i	0.273908	+	0.693207i
$711$			12.4436i			0.466670i
$712$	3.08475	+	8.62409i	0.115606	+	0.323201i
$713$			50.4831i			1.89061i
$714$	−3.07079	+	1.21337i	−0.114921	+	0.0454091i
$715$	−1.34916	−	1.34916i	−0.0504556	−	0.0504556i
$716$	−17.8716	−	0.586281i	−0.667892	−	0.0219103i
$717$	0.798957	−	0.798957i	0.0298376	−	0.0298376i
$718$	7.72230	+	3.34806i	0.288194	+	0.124948i
$719$	1.61691			0.0603007			0.0301503	−	0.999545i	$-0.490401\pi$
$719$	1.61691			0.0603007			0.0301503	+	0.999545i	$0.490401\pi$
$720$	−7.67928	−	8.75896i	−0.286190	−	0.326427i
$721$	8.62231			0.321112
$722$	−2.25713	−	0.978596i	−0.0840018	−	0.0364196i
$723$	2.00137	−	2.00137i	0.0744319	−	0.0744319i
$724$	1.21203	−	36.9463i	0.0450447	−	1.37310i
$725$	−2.44059	−	2.44059i	−0.0906411	−	0.0906411i
$726$	−4.08880	+	1.61561i	−0.151750	+	0.0599611i
$727$			39.3600i			1.45978i	0.683563	+	0.729891i	$0.260429\pi$
$727$			39.3600i			1.45978i	−0.683563	+	0.729891i	$0.739571\pi$
$728$	−11.8544	−	5.60821i	−0.439353	−	0.207854i
$729$		−	22.3717i		−	0.828581i
$730$	3.44993	+	8.73110i	0.127688	+	0.323152i
$731$	−9.54958	−	9.54958i	−0.353204	−	0.353204i
$732$	−3.21973	+	3.01519i	−0.119005	+	0.111445i
$733$	−34.0787	+	34.0787i	−1.25873	+	1.25873i	−0.307026	+	0.951701i	$0.599334\pi$
$733$	−34.0787	+	34.0787i	−1.25873	+	1.25873i	−0.951701	+	0.307026i	$0.900666\pi$
$734$	1.09902	−	2.53488i	0.0405654	−	0.0935643i
$735$	1.18046			0.0435420
$736$	22.8828	−	44.5303i	0.843473	−	1.64141i
$737$	−10.6724			−0.393124
$738$	16.4384	−	37.9152i	0.605105	−	1.39568i
$739$	15.4278	−	15.4278i	0.567520	−	0.567520i	−0.363913	−	0.931433i	$-0.618559\pi$
$739$	15.4278	−	15.4278i	0.567520	−	0.567520i	0.931433	+	0.363913i	$0.118559\pi$
$740$	−11.0589	+	10.3564i	−0.406533	+	0.380708i
$741$	−2.54761	−	2.54761i	−0.0935888	−	0.0935888i
$742$	1.75481	+	4.44109i	0.0644212	+	0.163037i
$743$			23.5004i			0.862147i	0.902317	+	0.431074i	$0.141865\pi$
$743$			23.5004i			0.862147i	−0.902317	+	0.431074i	$0.858135\pi$
$744$	2.04483	−	4.32229i	0.0749673	−	0.158463i
$745$		−	3.85801i		−	0.141347i
$746$	−34.6918	+	13.7078i	−1.27016	+	0.501879i
$747$	26.6603	+	26.6603i	0.975451	+	0.975451i
$748$	0.212577	−	6.47997i	0.00777258	−	0.236931i
$749$	−4.77024	+	4.77024i	−0.174301	+	0.174301i
$750$	0.384555	+	0.166726i	0.0140420	+	0.00608799i
$751$	10.8586			0.396236			0.198118	−	0.980178i	$-0.436517\pi$
$751$	10.8586			0.396236			0.198118	+	0.980178i	$0.436517\pi$
$752$	−1.13332	+	17.2549i	−0.0413280	+	0.629222i
$753$	5.02690			0.183190
$754$	−11.9543	−	5.18285i	−0.435348	−	0.188748i
$755$	−8.14560	+	8.14560i	−0.296449	+	0.296449i
$756$	−6.08387	−	0.199583i	−0.221268	−	0.00725875i
$757$	18.8434	+	18.8434i	0.684874	+	0.684874i	0.961094	−	0.276220i	$-0.0890819\pi$
$757$	18.8434	+	18.8434i	0.684874	+	0.684874i	−0.276220	+	0.961094i	$0.589082\pi$
$758$	−7.16389	+	2.83068i	−0.260204	+	0.102815i
$759$		−	1.87494i		−	0.0680561i
$760$	12.1283	−	4.33819i	0.439941	−	0.157363i
$761$		−	22.2837i		−	0.807783i	−0.914807	−	0.403891i	$-0.867657\pi$
$761$		−	22.2837i		−	0.807783i	0.914807	−	0.403891i	$-0.132343\pi$
$762$	0.386397	+	0.977894i	0.0139977	+	0.0354254i
$763$	−12.1580	−	12.1580i	−0.440151	−	0.440151i
$764$	30.3113	+	32.3675i	1.09663	+	1.17102i
$765$	−9.33901	+	9.33901i	−0.337653	+	0.337653i
$766$	1.28968	−	2.97465i	0.0465980	−	0.107478i
$767$	−25.0713			−0.905271
$768$	−3.76292	+	2.88575i	−0.135783	+	0.104130i
$769$	10.5399			0.380077			0.190039	−	0.981777i	$-0.439139\pi$
$769$	10.5399			0.380077			0.190039	+	0.981777i	$0.439139\pi$
$770$	0.698433	−	1.61094i	0.0251698	−	0.0580542i
$771$	3.95571	−	3.95571i	0.142461	−	0.142461i
$772$	−10.9052	−	11.6449i	−0.392486	−	0.419110i
$773$	4.07768	+	4.07768i	0.146664	+	0.146664i	0.776626	−	0.629962i	$-0.216930\pi$
$773$	4.07768	+	4.07768i	0.146664	+	0.146664i	−0.629962	+	0.776626i	$0.716930\pi$
$774$	−4.50679	−	11.4058i	−0.161993	−	0.409973i
$775$		−	5.70401i		−	0.204894i
$776$	−5.17002	+	1.84926i	−0.185593	+	0.0663846i
$777$			3.89987i			0.139907i
$778$	9.12358	−	3.60502i	0.327096	−	0.129246i
$779$	32.3125	+	32.3125i	1.15772	+	1.15772i
$780$	1.58141	+	0.0518785i	0.0566236	+	0.00185755i
$781$	−7.09809	+	7.09809i	−0.253990	+	0.253990i
$782$	−52.0808	−	22.5800i	−1.86241	−	0.807459i
$783$	−6.04786			−0.216133
$784$	−1.04417	+	15.8976i	−0.0372918	+	0.567770i
$785$	4.63881			0.165566
$786$	−4.65412	−	2.01782i	−0.166007	−	0.0719733i
$787$	−8.16669	+	8.16669i	−0.291111	+	0.291111i	−0.837519	−	0.546408i	$-0.815995\pi$
$787$	−8.16669	+	8.16669i	−0.291111	+	0.291111i	0.546408	+	0.837519i	$0.315995\pi$
$788$	0.534470	−	16.2922i	0.0190397	−	0.580387i
$789$	4.84943	+	4.84943i	0.172644	+	0.172644i
$790$	5.62007	−	2.22067i	0.199953	−	0.0790077i
$791$			11.3458i			0.403409i
$792$	2.51781	−	5.32204i	0.0894664	−	0.189111i
$793$			19.8643i			0.705403i
$794$	7.98290	+	20.2032i	0.283303	+	0.716983i
$795$	−0.407397	−	0.407397i	−0.0144489	−	0.0144489i
$796$	7.86653	−	7.36679i	0.278822	−	0.261109i
$797$	17.9971	−	17.9971i	0.637491	−	0.637491i	−0.312445	−	0.949936i	$-0.601148\pi$
$797$	17.9971	−	17.9971i	0.637491	−	0.637491i	0.949936	+	0.312445i	$0.101148\pi$
$798$	1.31885	−	3.04193i	0.0466868	−	0.107683i
$799$	19.6060			0.693609
$800$	−2.58550	+	5.03142i	−0.0914112	+	0.177888i
$801$	9.43033			0.333204
$802$	−3.99848	+	9.22250i	−0.141191	+	0.325658i
$803$	−3.35520	+	3.35520i	−0.118402	+	0.118402i
$804$	6.46002	−	6.04964i	0.227827	−	0.213354i
$805$	−10.8703	−	10.8703i	−0.383128	−	0.383128i
$806$	−7.91289	−	20.0260i	−0.278720	−	0.705385i
$807$			4.45835i			0.156941i
$808$	−37.3854	−	17.6867i	−1.31521	−	0.622215i
$809$		−	42.0296i		−	1.47768i	−0.673879	−	0.738841i	$-0.735373\pi$
$809$		−	42.0296i		−	1.47768i	0.673879	−	0.738841i	$-0.264627\pi$
$810$	−10.8077	+	4.27046i	−0.379744	+	0.150049i
$811$	18.7601	+	18.7601i	0.658757	+	0.658757i	0.955086	−	0.296329i	$-0.0957624\pi$
$811$	18.7601	+	18.7601i	0.658757	+	0.658757i	−0.296329	+	0.955086i	$0.595762\pi$
$812$	0.393133	−	11.9839i	0.0137963	−	0.420551i
$813$	4.18646	−	4.18646i	0.146826	−	0.146826i
$814$	−7.02587	−	3.04611i	−0.246257	−	0.106766i
$815$	−13.1149			−0.459397
$816$	3.54448	+	4.04282i	0.124082	+	0.141527i
$817$	13.5612			0.474447
$818$	37.8482	+	16.4093i	1.32333	+	0.573738i
$819$	−9.54757	+	9.54757i	−0.333619	+	0.333619i
$820$	−20.0578	−	0.657999i	−0.700447	−	0.0229783i
$821$	−21.4050	−	21.4050i	−0.747038	−	0.747038i	0.226884	−	0.973922i	$-0.427146\pi$
$821$	−21.4050	−	21.4050i	−0.747038	−	0.747038i	−0.973922	+	0.226884i	$0.927146\pi$
$822$	2.52261	−	0.996763i	0.0879862	−	0.0347661i
$823$		−	43.7323i		−	1.52441i	−0.647334	−	0.762206i	$-0.724116\pi$
$823$		−	43.7323i		−	1.52441i	0.647334	−	0.762206i	$-0.275884\pi$
$824$	−4.72869	−	13.2201i	−0.164732	−	0.460544i
$825$			0.211847i			0.00737557i
$826$	−8.47850	−	21.4574i	−0.295005	−	0.746599i
$827$	−19.9621	−	19.9621i	−0.694149	−	0.694149i	0.268993	−	0.963142i	$-0.413309\pi$
$827$	−19.9621	−	19.9621i	−0.694149	−	0.694149i	−0.963142	+	0.268993i	$0.913309\pi$
$828$	−35.2351	−	37.6253i	−1.22451	−	1.30757i
$829$	31.3869	−	31.3869i	1.09011	−	1.09011i	0.0945964	−	0.995516i	$-0.469844\pi$
$829$	31.3869	−	31.3869i	1.09011	−	1.09011i	0.995516	−	0.0945964i	$-0.0301561\pi$
$830$	7.28322	−	16.7988i	0.252804	−	0.583094i
$831$	−6.77057			−0.234868
$832$	−2.09749	+	21.2513i	−0.0727172	+	0.736758i
$833$	18.0637			0.625869
$834$	−3.87705	+	8.94244i	−0.134251	+	0.309651i
$835$	5.00677	−	5.00677i	0.173267	−	0.173267i
$836$	4.45012	+	4.75199i	0.153911	+	0.164351i
$837$	−7.06737	−	7.06737i	−0.244284	−	0.244284i
$838$	−2.25353	−	5.70324i	−0.0778469	−	0.197015i
$839$		−	54.5335i		−	1.88271i	−0.337423	−	0.941353i	$-0.609555\pi$
$839$		−	54.5335i		−	1.88271i	0.337423	−	0.941353i	$-0.390445\pi$
$840$	0.490395	+	1.37101i	0.0169202	+	0.0473042i
$841$			17.0871i			0.589210i
$842$	−0.990001	+	0.391181i	−0.0341177	+	0.0134810i
$843$	1.97735	+	1.97735i	0.0681035	+	0.0681035i
$844$	−30.4025	−	0.997361i	−1.04650	−	0.0343306i
$845$	−4.15404	+	4.15404i	−0.142903	+	0.142903i
$846$	16.3348	+	7.08208i	0.561603	+	0.243487i
$847$	−18.2192			−0.626018
$848$	5.84688	−	5.12615i	0.200783	−	0.176033i
$849$	3.65193			0.125334
$850$	5.88454	+	2.55128i	0.201838	+	0.0875082i
$851$	−47.4092	+	47.4092i	−1.62517	+	1.62517i
$852$	0.272939	−	8.32000i	0.00935075	−	0.285039i
$853$	21.5932	+	21.5932i	0.739336	+	0.739336i	0.972449	−	0.233114i	$-0.0748914\pi$
$853$	21.5932	+	21.5932i	0.739336	+	0.739336i	−0.233114	+	0.972449i	$0.574891\pi$
$854$	−17.0010	+	6.71765i	−0.581764	+	0.229873i
$855$		−	13.2622i		−	0.453557i
$856$	9.93005	+	4.69781i	0.339402	+	0.160568i
$857$			41.3609i			1.41286i	0.707782	+	0.706431i	$0.249696\pi$
$857$			41.3609i			1.41286i	−0.707782	+	0.706431i	$0.750304\pi$
$858$	0.293885	+	0.743766i	0.0100331	+	0.0253917i
$859$	−0.700596	−	0.700596i	−0.0239040	−	0.0239040i	0.695054	−	0.718958i	$-0.255381\pi$
$859$	−0.700596	−	0.700596i	−0.0239040	−	0.0239040i	−0.718958	+	0.695054i	$0.755381\pi$
$860$	−4.34709	+	4.07093i	−0.148234	+	0.138818i
$861$	−3.65265	+	3.65265i	−0.124482	+	0.124482i
$862$	9.40787	−	21.6993i	0.320433	−	0.739081i
$863$	55.0780			1.87488			0.937439	−	0.348150i	$-0.113190\pi$
$863$	55.0780			1.87488			0.937439	+	0.348150i	$0.113190\pi$
$864$	3.03054	+	9.43751i	0.103101	+	0.321070i
$865$	−7.37471			−0.250748
$866$	15.9580	−	36.8072i	0.542276	−	1.25076i
$867$	0.747840	−	0.747840i	0.0253980	−	0.0253980i
$868$	14.4634	−	13.5446i	0.490920	−	0.459734i
$869$	2.15969	+	2.15969i	0.0732623	+	0.0732623i
$870$	0.531630	+	1.34545i	0.0180239	+	0.0456150i
$871$		−	39.8556i		−	1.35045i
$872$	−11.9734	+	25.3090i	−0.405472	+	0.857070i
$873$			5.65335i			0.191337i
$874$	53.0124	−	20.9469i	1.79317	−	0.708538i
$875$	1.22822	+	1.22822i	0.0415214	+	0.0415214i
$876$	0.129016	−	3.93278i	0.00435904	−	0.132876i
$877$	−36.5100	+	36.5100i	−1.23285	+	1.23285i	−0.269992	+	0.962863i	$0.587021\pi$
$877$	−36.5100	+	36.5100i	−1.23285	+	1.23285i	−0.962863	+	0.269992i	$0.912979\pi$
$878$	17.5188	+	7.59537i	0.591229	+	0.256331i
$879$	−4.65435			−0.156987
$880$	−2.85300	−	0.187388i	−0.0961745	−	0.00631685i
$881$	54.3503			1.83111			0.915554	−	0.402196i	$-0.131753\pi$
$881$	54.3503			1.83111			0.915554	+	0.402196i	$0.131753\pi$
$882$	15.0499	+	6.52497i	0.506755	+	0.219707i
$883$	35.5476	−	35.5476i	1.19627	−	1.19627i	0.220999	−	0.975274i	$-0.429068\pi$
$883$	35.5476	−	35.5476i	1.19627	−	1.19627i	0.975274	−	0.220999i	$-0.0709319\pi$
$884$	24.1991	+	0.793855i	0.813902	+	0.0267002i
$885$	1.96837	+	1.96837i	0.0661660	+	0.0661660i
$886$	−17.7681	+	7.02075i	−0.596932	+	0.235867i
$887$			0.817003i			0.0274323i	0.999906	+	0.0137161i	$0.00436612\pi$
$887$			0.817003i			0.0274323i	−0.999906	+	0.0137161i	$0.995634\pi$
$888$	5.97944	−	2.13878i	0.200657	−	0.0717729i
$889$			4.35737i			0.146141i
$890$	−1.68293	−	4.25916i	−0.0564118	−	0.142767i
$891$	−4.15320	−	4.15320i	−0.139137	−	0.139137i
$892$	5.45075	+	5.82051i	0.182505	+	0.194885i
$893$	−13.9211	+	13.9211i	−0.465851	+	0.465851i
$894$	−0.643232	+	1.48362i	−0.0215129	+	0.0496196i
$895$	8.94060			0.298851
$896$	−18.8974	+	5.39155i	−0.631319	+	0.180119i
$897$	7.00186			0.233785
$898$	−5.26302	+	12.1392i	−0.175629	+	0.405090i
$899$	13.9211	−	13.9211i	0.464296	−	0.464296i
$900$	3.98117	+	4.25123i	0.132706	+	0.141708i
$901$	−6.23407	−	6.23407i	−0.207687	−	0.207687i
$902$	−3.72748	−	9.43352i	−0.124112	−	0.314102i
$903$			1.53298i			0.0510144i
$904$	17.3958	−	6.22230i	0.578575	−	0.206950i
$905$			18.4831i			0.614398i
$906$	4.49052	−	1.77434i	0.149187	−	0.0589487i
$907$	−3.36159	−	3.36159i	−0.111620	−	0.111620i	0.649091	−	0.760711i	$-0.275149\pi$
$907$	−3.36159	−	3.36159i	−0.111620	−	0.111620i	−0.760711	+	0.649091i	$0.775149\pi$
$908$	10.8017	+	0.354352i	0.358467	+	0.0117596i
$909$	−30.1103	+	30.1103i	−0.998695	+	0.998695i
$910$	6.01595	+	2.60826i	0.199427	+	0.0864629i
$911$	34.6568			1.14823			0.574116	−	0.818774i	$-0.305346\pi$
$911$	34.6568			1.14823			0.574116	+	0.818774i	$0.305346\pi$
$912$	−5.38731	−	0.353844i	−0.178392	−	0.0117170i
$913$	9.25426			0.306271
$914$	8.88510	+	3.85219i	0.293893	+	0.127419i
$915$	1.55957	−	1.55957i	0.0515577	−	0.0515577i
$916$	−0.816725	+	24.8962i	−0.0269853	+	0.822593i
$917$	−14.8646	−	14.8646i	−0.490874	−	0.490874i
$918$	10.4521	−	4.12997i	0.344972	−	0.136309i
$919$			24.3452i			0.803074i	0.915843	+	0.401537i	$0.131524\pi$
$919$			24.3452i			0.803074i	−0.915843	+	0.401537i	$0.868476\pi$
$920$	−10.7053	+	22.6283i	−0.352942	+	0.746034i
$921$			1.25681i			0.0414135i
$922$	8.62875	+	21.8377i	0.284173	+	0.719185i
$923$	−26.5074	−	26.5074i	−0.872501	−	0.872501i
$924$	−0.537172	+	0.503048i	−0.0176717	+	0.0165491i
$925$	5.35670	−	5.35670i	0.176127	−	0.176127i
$926$	−14.9691	+	34.5263i	−0.491915	+	1.13460i
$927$	−14.4560			−0.474797
$928$	−18.5898	+	5.96948i	−0.610238	+	0.195958i
$929$	3.16600			0.103873			0.0519366	−	0.998650i	$-0.483461\pi$
$929$	3.16600			0.103873			0.0519366	+	0.998650i	$0.483461\pi$
$930$	−0.951009	+	2.19351i	−0.0311848	+	0.0719279i
$931$	−12.8260	+	12.8260i	−0.420354	+	0.420354i
$932$	−24.2392	+	22.6994i	−0.793981	+	0.743542i
$933$	−1.89892	−	1.89892i	−0.0621680	−	0.0621680i
$934$	−1.08469	−	2.74513i	−0.0354921	−	0.0898235i
$935$			3.24173i			0.106016i
$936$	19.8749	+	9.40260i	0.649630	+	0.307334i
$937$		−	23.4847i		−	0.767211i	−0.923497	−	0.383606i	$-0.874682\pi$
$937$		−	23.4847i		−	0.767211i	0.923497	−	0.383606i	$-0.125318\pi$
$938$	34.1107	−	13.4782i	1.11375	−	0.440079i
$939$	−4.10129	−	4.10129i	−0.133840	−	0.133840i
$940$	0.283483	−	8.64140i	0.00924619	−	0.281851i
$941$	27.7583	−	27.7583i	0.904896	−	0.904896i	−0.0909585	−	0.995855i	$-0.528993\pi$
$941$	27.7583	−	27.7583i	0.904896	−	0.904896i	0.995855	+	0.0909585i	$0.0289931\pi$
$942$	−1.78388	−	0.773412i	−0.0581218	−	0.0251991i
$943$	−88.8078			−2.89198
$944$	−28.2496	+	24.7674i	−0.919446	+	0.806109i
$945$	3.04357			0.0990074
$946$	−2.76177	−	1.19738i	−0.0897927	−	0.0389302i
$947$	−27.2916	+	27.2916i	−0.886857	+	0.886857i	−0.994220	−	0.107363i	$-0.965759\pi$
$947$	−27.2916	+	27.2916i	−0.886857	+	0.886857i	0.107363	+	0.994220i	$0.465759\pi$
$948$	−2.53147	−	0.0830453i	−0.0822183	−	0.00269719i
$949$	−12.5298	−	12.5298i	−0.406734	−	0.406734i
$950$	−5.98979	+	2.36676i	−0.194335	+	0.0767877i
$951$			4.65329i			0.150893i
$952$	7.50412	+	20.9794i	0.243210	+	0.679946i
$953$			12.1516i			0.393630i	0.980441	+	0.196815i	$0.0630598\pi$
$953$			12.1516i			0.393630i	−0.980441	+	0.196815i	$0.936940\pi$
$954$	−2.94208	−	7.44584i	−0.0952535	−	0.241068i
$955$	−15.6781	−	15.6781i	−0.507333	−	0.507333i
$956$	−5.21179	−	5.56534i	−0.168561	−	0.179996i
$957$	−0.517031	+	0.517031i	−0.0167132	+	0.0167132i
$958$	−1.56725	+	3.61488i	−0.0506357	+	0.116791i
$959$	11.2404			0.362972
$960$	1.83314	−	1.50379i	0.0591643	−	0.0485345i
$961$	1.53571			0.0495392
$962$	11.3755	−	26.2377i	0.366762	−	0.845938i
$963$	7.99769	−	7.99769i	0.257722	−	0.257722i
$964$	−13.0554	−	13.9411i	−0.420488	−	0.449012i
$965$	5.64056	+	5.64056i	0.181576	+	0.181576i
$966$	2.36786	+	5.99259i	0.0761847	+	0.192809i
$967$		−	48.2694i		−	1.55224i	−0.630585	−	0.776120i	$-0.717185\pi$
$967$		−	48.2694i		−	1.55224i	0.630585	−	0.776120i	$-0.282815\pi$
$968$	9.99184	+	27.9344i	0.321150	+	0.897845i
$969$			6.12135i			0.196646i
$970$	2.55330	−	1.00889i	0.0819816	−	0.0323935i
$971$	5.92047	+	5.92047i	0.189997	+	0.189997i	0.795695	−	0.605698i	$-0.207106\pi$
$971$	5.92047	+	5.92047i	0.189997	+	0.189997i	−0.605698	+	0.795695i	$0.707106\pi$
$972$	15.3759	+	0.504410i	0.493183	+	0.0161790i
$973$	−28.5610	+	28.5610i	−0.915623	+	0.915623i
$974$	21.9927	+	9.53509i	0.704692	+	0.305524i
$975$	−0.791130			−0.0253365
$976$	19.6236	+	22.3826i	0.628135	+	0.716449i
$977$	−27.7522			−0.887872			−0.443936	−	0.896059i	$-0.646418\pi$
$977$	−27.7522			−0.887872			−0.443936	+	0.896059i	$0.646418\pi$
$978$	5.04342	+	2.18661i	0.161271	+	0.0699200i
$979$	1.63671	−	1.63671i	0.0523096	−	0.0523096i
$980$	0.261183	−	7.96162i	0.00834318	−	0.254325i
$981$	20.3839	+	20.3839i	0.650808	+	0.650808i
$982$	−42.4819	+	16.7859i	−1.35565	+	0.535661i
$983$		−	28.3604i		−	0.904556i	−0.891877	−	0.452278i	$-0.850611\pi$
$983$		−	28.3604i		−	0.904556i	0.891877	−	0.452278i	$-0.149389\pi$
$984$	7.60361	+	3.59719i	0.242394	+	0.114674i
$985$			8.15050i			0.259697i
$986$	8.13511	+	20.5884i	0.259075	+	0.655667i
$987$	−1.57366	−	1.57366i	−0.0500901	−	0.0500901i
$988$	−17.7460	+	16.6187i	−0.564577	+	0.528711i
$989$	−18.6358	+	18.6358i	−0.592585	+	0.592585i
$990$	−1.17098	+	2.70087i	−0.0372162	+	0.0858392i
$991$	−43.7506			−1.38979			−0.694893	−	0.719114i	$-0.744548\pi$
$991$	−43.7506			−1.38979			−0.694893	+	0.719114i	$0.744548\pi$
$992$	−28.6993	−	14.7477i	−0.911203	−	0.468240i
$993$	−3.41483			−0.108366
$994$	13.7224	−	31.6507i	0.435247	−	1.00390i
$995$	−3.81038	+	3.81038i	−0.120797	+	0.120797i
$996$	−5.60160	+	5.24575i	−0.177493	+	0.166218i
$997$	10.5572	+	10.5572i	0.334349	+	0.334349i	0.854235	−	0.519887i	$-0.174026\pi$
$997$	10.5572	+	10.5572i	0.334349	+	0.334349i	−0.519887	+	0.854235i	$0.674026\pi$
$998$	−1.71913	−	4.35079i	−0.0544183	−	0.137722i
$999$		−	13.2741i		−	0.419974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.21.6	✓	16
3.2	odd	2		720.2.t.c.181.3		16
4.3	odd	2		320.2.l.a.241.4		16
5.2	odd	4		400.2.q.g.149.7		16
5.3	odd	4		400.2.q.h.149.2		16
5.4	even	2		400.2.l.h.101.3		16
8.3	odd	2		640.2.l.a.481.5		16
8.5	even	2		640.2.l.b.481.4		16
12.11	even	2		2880.2.t.c.2161.4		16
16.3	odd	4		320.2.l.a.81.4		16
16.5	even	4		640.2.l.b.161.4		16
16.11	odd	4		640.2.l.a.161.5		16
16.13	even	4	inner	80.2.l.a.61.6	yes	16
20.3	even	4		1600.2.q.g.49.4		16
20.7	even	4		1600.2.q.h.49.5		16
20.19	odd	2		1600.2.l.i.1201.5		16
32.3	odd	8		5120.2.a.u.1.3		8
32.13	even	8		5120.2.a.v.1.3		8
32.19	odd	8		5120.2.a.t.1.6		8
32.29	even	8		5120.2.a.s.1.6		8
48.29	odd	4		720.2.t.c.541.3		16
48.35	even	4		2880.2.t.c.721.1		16
80.3	even	4		1600.2.q.h.849.5		16
80.13	odd	4		400.2.q.g.349.7		16
80.19	odd	4		1600.2.l.i.401.5		16
80.29	even	4		400.2.l.h.301.3		16
80.67	even	4		1600.2.q.g.849.4		16
80.77	odd	4		400.2.q.h.349.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.6	✓	16	1.1	even	1	trivial
80.2.l.a.61.6	yes	16	16.13	even	4	inner
320.2.l.a.81.4		16	16.3	odd	4
320.2.l.a.241.4		16	4.3	odd	2
400.2.l.h.101.3		16	5.4	even	2
400.2.l.h.301.3		16	80.29	even	4
400.2.q.g.149.7		16	5.2	odd	4
400.2.q.g.349.7		16	80.13	odd	4
400.2.q.h.149.2		16	5.3	odd	4
400.2.q.h.349.2		16	80.77	odd	4
640.2.l.a.161.5		16	16.11	odd	4
640.2.l.a.481.5		16	8.3	odd	2
640.2.l.b.161.4		16	16.5	even	4
640.2.l.b.481.4		16	8.5	even	2
720.2.t.c.181.3		16	3.2	odd	2
720.2.t.c.541.3		16	48.29	odd	4
1600.2.l.i.401.5		16	80.19	odd	4
1600.2.l.i.1201.5		16	20.19	odd	2
1600.2.q.g.49.4		16	20.3	even	4
1600.2.q.g.849.4		16	80.67	even	4
1600.2.q.h.49.5		16	20.7	even	4
1600.2.q.h.849.5		16	80.3	even	4
2880.2.t.c.721.1		16	48.35	even	4
2880.2.t.c.2161.4		16	12.11	even	2
5120.2.a.s.1.6		8	32.29	even	8
5120.2.a.t.1.6		8	32.19	odd	8
5120.2.a.u.1.3		8	32.3	odd	8
5120.2.a.v.1.3		8	32.13	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)

\(f(q)\)	\(=\)	\(q+(0.562546 - 1.29751i) q^{2} +(0.209571 - 0.209571i) q^{3} +(-1.36708 - 1.45982i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.154028 - 0.389815i) q^{6} -1.73696i q^{7} +(-2.66319 + 0.952595i) q^{8} +2.91216i q^{9} +O(q^{10})\)	\(q+(0.562546 - 1.29751i) q^{2} +(0.209571 - 0.209571i) q^{3} +(-1.36708 - 1.45982i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.154028 - 0.389815i) q^{6} -1.73696i q^{7} +(-2.66319 + 0.952595i) q^{8} +2.91216i q^{9} +(1.31526 - 0.519701i) q^{10} +(0.505430 + 0.505430i) q^{11} +(-0.592438 - 0.0194351i) q^{12} +(-1.88750 + 1.88750i) q^{13} +(-2.25374 - 0.977122i) q^{14} +0.296378 q^{15} +(-0.262159 + 3.99140i) q^{16} +4.53524 q^{17} +(3.77857 + 1.63822i) q^{18} +(-3.22022 + 3.22022i) q^{19} +(0.0655751 - 1.99892i) q^{20} +(-0.364018 - 0.364018i) q^{21} +(0.940130 - 0.371475i) q^{22} -8.85045i q^{23} +(-0.358491 + 0.757764i) q^{24} +1.00000i q^{25} +(1.38725 + 3.51086i) q^{26} +(1.23902 + 1.23902i) q^{27} +(-2.53566 + 2.37458i) q^{28} +(-2.44059 + 2.44059i) q^{29} +(0.166726 - 0.384555i) q^{30} -5.70401 q^{31} +(5.03142 + 2.58550i) q^{32} +0.211847 q^{33} +(2.55128 - 5.88454i) q^{34} +(1.22822 - 1.22822i) q^{35} +(4.25123 - 3.98117i) q^{36} +(-5.35670 - 5.35670i) q^{37} +(2.36676 + 5.98979i) q^{38} +0.791130i q^{39} +(-2.55674 - 1.20957i) q^{40} -10.0343i q^{41} +(-0.677095 + 0.267541i) q^{42} +(-2.10564 - 2.10564i) q^{43} +(0.0468722 - 1.42880i) q^{44} +(-2.05921 + 2.05921i) q^{45} +(-11.4836 - 4.97878i) q^{46} +4.32303 q^{47} +(0.781541 + 0.891424i) q^{48} +3.98295 q^{49} +(1.29751 + 0.562546i) q^{50} +(0.950456 - 0.950456i) q^{51} +(5.33578 + 0.175041i) q^{52} +(-1.37458 - 1.37458i) q^{53} +(2.30465 - 0.910639i) q^{54} +0.714786i q^{55} +(1.65462 + 4.62586i) q^{56} +1.34973i q^{57} +(1.79375 + 4.53964i) q^{58} +(6.64140 + 6.64140i) q^{59} +(-0.405174 - 0.432660i) q^{60} +(5.26208 - 5.26208i) q^{61} +(-3.20877 + 7.40103i) q^{62} +5.05832 q^{63} +(6.18513 - 5.07388i) q^{64} -2.66933 q^{65} +(0.119174 - 0.274875i) q^{66} +(-10.5578 + 10.5578i) q^{67} +(-6.20006 - 6.62065i) q^{68} +(-1.85480 - 1.85480i) q^{69} +(-0.902702 - 2.28456i) q^{70} +14.0437i q^{71} +(-2.77411 - 7.75563i) q^{72} +6.63830i q^{73} +(-9.96378 + 3.93700i) q^{74} +(0.209571 + 0.209571i) q^{75} +(9.10325 + 0.298634i) q^{76} +(0.877914 - 0.877914i) q^{77} +(1.02650 + 0.445047i) q^{78} +4.27297 q^{79} +(-3.00772 + 2.63697i) q^{80} -8.21715 q^{81} +(-13.0196 - 5.64474i) q^{82} +(9.15483 - 9.15483i) q^{83} +(-0.0337580 + 1.02904i) q^{84} +(3.20690 + 3.20690i) q^{85} +(-3.91661 + 1.54758i) q^{86} +1.02295i q^{87} +(-1.82752 - 0.864585i) q^{88} -3.23826i q^{89} +(1.51345 + 3.83025i) q^{90} +(3.27852 + 3.27852i) q^{91} +(-12.9201 + 12.0993i) q^{92} +(-1.19540 + 1.19540i) q^{93} +(2.43190 - 5.60919i) q^{94} -4.55407 q^{95} +(1.59629 - 0.512594i) q^{96} +1.94129 q^{97} +(2.24059 - 5.16794i) q^{98} +(-1.47189 + 1.47189i) 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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