LMFDB - Embedded newform 400.2.q.h.149.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.19401608085$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.2
Root			$-0.966675 + 1.03225i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.h.349.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29751 - 0.562546i) q^{2} +(0.209571 + 0.209571i) q^{3} +(1.36708 + 1.45982i) q^{4} +(-0.154028 - 0.389815i) q^{6} -1.73696 q^{7} +(-0.952595 - 2.66319i) q^{8} -2.91216i q^{9} +(0.505430 + 0.505430i) q^{11} +(-0.0194351 + 0.592438i) q^{12} +(-1.88750 - 1.88750i) q^{13} +(2.25374 + 0.977122i) q^{14} +(-0.262159 + 3.99140i) q^{16} -4.53524i q^{17} +(-1.63822 + 3.77857i) q^{18} +(3.22022 - 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +(-0.371475 - 0.940130i) q^{22} +8.85045 q^{23} +(0.358491 - 0.757764i) q^{24} +(1.38725 + 3.51086i) q^{26} +(1.23902 - 1.23902i) q^{27} +(-2.37458 - 2.53566i) q^{28} +(2.44059 - 2.44059i) q^{29} -5.70401 q^{31} +(2.58550 - 5.03142i) q^{32} +0.211847i q^{33} +(-2.55128 + 5.88454i) q^{34} +(4.25123 - 3.98117i) q^{36} +(-5.35670 + 5.35670i) q^{37} +(-5.98979 + 2.36676i) q^{38} -0.791130i q^{39} -10.0343i q^{41} +(0.267541 + 0.677095i) q^{42} +(2.10564 - 2.10564i) q^{43} +(-0.0468722 + 1.42880i) q^{44} +(-11.4836 - 4.97878i) q^{46} -4.32303i q^{47} +(-0.891424 + 0.781541i) q^{48} -3.98295 q^{49} +(0.950456 - 0.950456i) q^{51} +(0.175041 - 5.33578i) q^{52} +(1.37458 - 1.37458i) q^{53} +(-2.30465 + 0.910639i) q^{54} +(1.65462 + 4.62586i) q^{56} +1.34973 q^{57} +(-4.53964 + 1.79375i) q^{58} +(-6.64140 - 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +(7.40103 + 3.20877i) q^{62} +5.05832i q^{63} +(-6.18513 + 5.07388i) q^{64} +(0.119174 - 0.274875i) q^{66} +(10.5578 + 10.5578i) q^{67} +(6.62065 - 6.20006i) q^{68} +(1.85480 + 1.85480i) q^{69} +14.0437i q^{71} +(-7.75563 + 2.77411i) q^{72} -6.63830 q^{73} +(9.96378 - 3.93700i) q^{74} +(9.10325 + 0.298634i) q^{76} +(-0.877914 - 0.877914i) q^{77} +(-0.445047 + 1.02650i) q^{78} -4.27297 q^{79} -8.21715 q^{81} +(-5.64474 + 13.0196i) q^{82} +(9.15483 + 9.15483i) q^{83} +(0.0337580 - 1.02904i) q^{84} +(-3.91661 + 1.54758i) q^{86} +1.02295 q^{87} +(0.864585 - 1.82752i) q^{88} +3.23826i q^{89} +(3.27852 + 3.27852i) q^{91} +(12.0993 + 12.9201i) q^{92} +(-1.19540 - 1.19540i) q^{93} +(-2.43190 + 5.60919i) q^{94} +(1.59629 - 0.512594i) q^{96} -1.94129i q^{97} +(5.16794 + 2.24059i) q^{98} +(1.47189 - 1.47189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 4 q^{4} - 12 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} - 4 q^{14} + 16 q^{16} + 12 q^{18} + 8 q^{19} - 20 q^{22} + 24 q^{23} - 8 q^{24} - 16 q^{26} + 24 q^{27} + 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 4 * q^4 - 12 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 - 4 * q^14 + 16 * q^16 + 12 * q^18 + 8 * q^19 - 20 * q^22 + 24 * q^23 - 8 * q^24 - 16 * q^26 + 24 * q^27 + 20 * q^28 + 16 * q^29 + 24 * q^32 - 16 * q^34 - 4 * q^36 - 16 * q^37 - 20 * q^38 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 - 16 * q^52 - 16 * q^53 - 32 * q^54 + 16 * q^56 - 28 * q^58 + 8 * q^59 + 16 * q^61 + 48 * q^62 + 16 * q^64 - 40 * q^67 - 8 * q^68 - 16 * q^69 - 96 * q^72 + 72 * q^74 - 16 * q^77 + 24 * q^78 - 16 * q^79 - 16 * q^81 + 44 * q^82 + 40 * q^83 + 64 * q^84 + 28 * q^86 - 16 * q^88 + 32 * q^91 + 20 * q^92 - 48 * q^93 + 36 * q^94 + 8 * q^96 - 32 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.29751	−	0.562546i	−0.917481	−	0.397780i
$2$	−1.29751	−	0.562546i	−0.917481	−	0.397780i
$3$	0.209571	+	0.209571i	0.120996	+	0.120996i	0.765012	−	0.644016i	$-0.222733\pi$
$3$	0.209571	+	0.209571i	0.120996	+	0.120996i	−0.644016	+	0.765012i	$0.722733\pi$
$4$	1.36708	+	1.45982i	0.683542	+	0.729911i
$5$		0			0
$5$		0			0
$6$	−0.154028	−	0.389815i	−0.0628817	−	0.159141i
$7$	−1.73696			−0.656511			−0.328255	−	0.944589i	$-0.606461\pi$
$7$	−1.73696			−0.656511			−0.328255	+	0.944589i	$0.606461\pi$
$8$	−0.952595	−	2.66319i	−0.336793	−	0.941579i
$9$		−	2.91216i		−	0.970720i
$10$		0			0
$11$	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	$0.715633\pi$
$12$	−0.0194351	+	0.592438i	−0.00561042	+	0.171022i
$13$	−1.88750	−	1.88750i	−0.523498	−	0.523498i	0.395128	−	0.918626i	$-0.370700\pi$
$13$	−1.88750	−	1.88750i	−0.523498	−	0.523498i	−0.918626	+	0.395128i	$0.870700\pi$
$14$	2.25374	+	0.977122i	0.602336	+	0.261147i
$15$		0			0
$16$	−0.262159	+	3.99140i	−0.0655399	+	0.997850i
$17$		−	4.53524i		−	1.09996i	−0.835178	−	0.549979i	$-0.814636\pi$
$17$		−	4.53524i		−	1.09996i	0.835178	−	0.549979i	$-0.185364\pi$
$18$	−1.63822	+	3.77857i	−0.386133	+	0.890617i
$19$	3.22022	−	3.22022i	0.738768	−	0.738768i	−0.233571	−	0.972340i	$-0.575041\pi$
$19$	3.22022	−	3.22022i	0.738768	−	0.738768i	0.972340	+	0.233571i	$0.0750413\pi$
$20$		0			0
$21$	−0.364018	−	0.364018i	−0.0794352	−	0.0794352i
$22$	−0.371475	−	0.940130i	−0.0791987	−	0.200436i
$23$	8.85045			1.84545			0.922723	−	0.385463i	$-0.125958\pi$
$23$	8.85045			1.84545			0.922723	+	0.385463i	$0.125958\pi$
$24$	0.358491	−	0.757764i	0.0731766	−	0.154678i
$25$		0			0
$26$	1.38725	+	3.51086i	0.272062	+	0.688536i
$27$	1.23902	−	1.23902i	0.238449	−	0.238449i
$28$	−2.37458	−	2.53566i	−0.448753	−	0.479195i
$29$	2.44059	−	2.44059i	0.453205	−	0.453205i	−0.443212	−	0.896417i	$-0.646161\pi$
$29$	2.44059	−	2.44059i	0.453205	−	0.453205i	0.896417	+	0.443212i	$0.146161\pi$
$30$		0			0
$31$	−5.70401			−1.02447			−0.512235	−	0.858845i	$-0.671182\pi$
$31$	−5.70401			−1.02447			−0.512235	+	0.858845i	$0.671182\pi$
$32$	2.58550	−	5.03142i	0.457056	−	0.889438i
$33$			0.211847i			0.0368779i
$34$	−2.55128	+	5.88454i	−0.437541	+	1.00919i
$35$		0			0
$36$	4.25123	−	3.98117i	0.708539	−	0.663528i
$37$	−5.35670	+	5.35670i	−0.880636	+	0.880636i	−0.993599	−	0.112963i	$-0.963966\pi$
$37$	−5.35670	+	5.35670i	−0.880636	+	0.880636i	0.112963	+	0.993599i	$0.463966\pi$
$38$	−5.98979	+	2.36676i	−0.971673	+	0.383939i
$39$		−	0.791130i		−	0.126682i
$40$		0			0
$41$		−	10.0343i		−	1.56709i	−0.621335	−	0.783545i	$-0.713409\pi$
$41$		−	10.0343i		−	1.56709i	0.621335	−	0.783545i	$-0.286591\pi$
$42$	0.267541	+	0.677095i	0.0412825	+	0.104478i
$43$	2.10564	−	2.10564i	0.321107	−	0.321107i	−0.528085	−	0.849192i	$-0.677090\pi$
$43$	2.10564	−	2.10564i	0.321107	−	0.321107i	0.849192	+	0.528085i	$0.177090\pi$
$44$	−0.0468722	+	1.42880i	−0.00706625	+	0.215400i
$45$		0			0
$46$	−11.4836	−	4.97878i	−1.69316	−	0.734082i
$47$		−	4.32303i		−	0.630578i	−0.948996	−	0.315289i	$-0.897899\pi$
$47$		−	4.32303i		−	0.630578i	0.948996	−	0.315289i	$-0.102101\pi$
$48$	−0.891424	+	0.781541i	−0.128666	+	0.112806i
$49$	−3.98295			−0.568993
$50$		0			0
$51$	0.950456	−	0.950456i	0.133091	−	0.133091i
$52$	0.175041	−	5.33578i	0.0242739	−	0.739940i
$53$	1.37458	−	1.37458i	0.188814	−	0.188814i	−0.606369	−	0.795183i	$-0.707375\pi$
$53$	1.37458	−	1.37458i	0.188814	−	0.188814i	0.795183	+	0.606369i	$0.207375\pi$
$54$	−2.30465	+	0.910639i	−0.313623	+	0.123922i
$55$		0			0
$56$	1.65462	+	4.62586i	0.221108	+	0.618157i
$57$	1.34973			0.178776
$58$	−4.53964	+	1.79375i	−0.596083	+	0.235531i
$59$	−6.64140	−	6.64140i	−0.864637	−	0.864637i	0.127236	−	0.991872i	$-0.459389\pi$
$59$	−6.64140	−	6.64140i	−0.864637	−	0.864637i	−0.991872	+	0.127236i	$0.959389\pi$
$60$		0			0
$61$	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	$0.0919391\pi$
$62$	7.40103	+	3.20877i	0.939932	+	0.407514i
$63$			5.05832i			0.637288i
$64$	−6.18513	+	5.07388i	−0.773141	+	0.634234i
$65$		0			0
$66$	0.119174	−	0.274875i	0.0146693	−	0.0338347i
$67$	10.5578	+	10.5578i	1.28984	+	1.28984i	0.934884	+	0.354954i	$0.115503\pi$
$67$	10.5578	+	10.5578i	1.28984	+	1.28984i	0.354954	+	0.934884i	$0.384497\pi$
$68$	6.62065	−	6.20006i	0.802871	−	0.751868i
$69$	1.85480	+	1.85480i	0.223292	+	0.223292i
$70$		0			0
$71$			14.0437i			1.66668i	0.552764	+	0.833338i	$0.313573\pi$
$71$			14.0437i			1.66668i	−0.552764	+	0.833338i	$0.686427\pi$
$72$	−7.75563	+	2.77411i	−0.914009	+	0.326932i
$73$	−6.63830			−0.776954			−0.388477	−	0.921458i	$-0.626999\pi$
$73$	−6.63830			−0.776954			−0.388477	+	0.921458i	$0.626999\pi$
$74$	9.96378	−	3.93700i	1.15827	−	0.457667i
$75$		0			0
$76$	9.10325	+	0.298634i	1.04421	+	0.0342557i
$77$	−0.877914	−	0.877914i	−0.100048	−	0.100048i
$78$	−0.445047	+	1.02650i	−0.0503917	+	0.116229i
$79$	−4.27297			−0.480746			−0.240373	−	0.970681i	$-0.577270\pi$
$79$	−4.27297			−0.480746			−0.240373	+	0.970681i	$0.577270\pi$
$80$		0			0
$81$	−8.21715			−0.913017
$82$	−5.64474	+	13.0196i	−0.623357	+	1.43778i
$83$	9.15483	+	9.15483i	1.00487	+	1.00487i	0.999988	+	0.00488547i	$0.00155510\pi$
$83$	9.15483	+	9.15483i	1.00487	+	1.00487i	0.00488547	+	0.999988i	$0.498445\pi$
$84$	0.0337580	−	1.02904i	0.00368330	−	0.112278i
$85$		0			0
$86$	−3.91661	+	1.54758i	−0.422339	+	0.166879i
$87$	1.02295			0.109672
$88$	0.864585	−	1.82752i	0.0921650	−	0.194815i
$89$			3.23826i			0.343255i	0.985162	+	0.171627i	$0.0549025\pi$
$89$			3.23826i			0.343255i	−0.985162	+	0.171627i	$0.945097\pi$
$90$		0			0
$91$	3.27852	+	3.27852i	0.343682	+	0.343682i
$92$	12.0993	+	12.9201i	1.26144	+	1.34701i
$93$	−1.19540	−	1.19540i	−0.123957	−	0.123957i
$94$	−2.43190	+	5.60919i	−0.250831	+	0.578543i
$95$		0			0
$96$	1.59629	−	0.512594i	0.162920	−	0.0523164i
$97$		−	1.94129i		−	0.197108i	−0.995132	−	0.0985541i	$-0.968578\pi$
$97$		−	1.94129i		−	0.197108i	0.995132	−	0.0985541i	$-0.0314217\pi$
$98$	5.16794	+	2.24059i	0.522041	+	0.226334i
$99$	1.47189	−	1.47189i	0.147931	−	0.147931i
$100$		0			0
$101$	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	$0.490689\pi$
$102$	−1.76791	+	0.698555i	−0.175049	+	0.0691673i
$103$	−4.96401			−0.489118			−0.244559	−	0.969634i	$-0.578643\pi$
$103$	−4.96401			−0.489118			−0.244559	+	0.969634i	$0.578643\pi$
$104$	−3.22874	+	6.82478i	−0.316604	+	0.669225i
$105$		0			0
$106$	−2.55681	+	1.01028i	−0.248339	+	0.0981266i
$107$	−2.74631	+	2.74631i	−0.265496	+	0.265496i	−0.827282	−	0.561787i	$-0.810114\pi$
$107$	−2.74631	+	2.74631i	−0.265496	+	0.265496i	0.561787	+	0.827282i	$0.310114\pi$
$108$	3.50259	+	0.114903i	0.337037	+	0.0110566i
$109$	−6.99959	+	6.99959i	−0.670439	+	0.670439i	−0.957817	−	0.287378i	$-0.907216\pi$
$109$	−6.99959	+	6.99959i	−0.670439	+	0.670439i	0.287378	+	0.957817i	$0.407216\pi$
$110$		0			0
$111$	−2.24522			−0.213107
$112$	0.455362	−	6.93292i	0.0430276	−	0.655099i
$113$		−	6.53194i		−	0.614474i	−0.951633	−	0.307237i	$-0.900596\pi$
$113$		−	6.53194i		−	0.614474i	0.951633	−	0.307237i	$-0.0994044\pi$
$114$	−1.75129	−	0.759284i	−0.164024	−	0.0711135i
$115$		0			0
$116$	6.89931	+	0.226333i	0.640585	+	0.0210145i
$117$	−5.49670	+	5.49670i	−0.508170	+	0.508170i
$118$	4.88122	+	12.3534i	0.449353	+	1.13722i
$119$			7.87756i			0.722134i
$120$		0			0
$121$		−	10.4891i		−	0.953553i
$122$	−9.78779	+	3.86746i	−0.886145	+	0.350144i
$123$	2.10289	−	2.10289i	0.189612	−	0.189612i
$124$	−7.79786	−	8.32684i	−0.700269	−	0.747772i
$125$		0			0
$126$	2.84554	−	6.56324i	0.253500	−	0.584700i
$127$			2.50861i			0.222603i	0.993787	+	0.111302i	$0.0355020\pi$
$127$			2.50861i			0.222603i	−0.993787	+	0.111302i	$0.964498\pi$
$128$	10.8796	−	3.10401i	0.961628	−	0.274358i
$129$	0.882562			0.0777053
$130$		0			0
$131$	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	$0.0726780\pi$
$132$	−0.309259	+	0.289613i	−0.0269176	+	0.0252076i
$133$	−5.59340	+	5.59340i	−0.485009	+	0.485009i
$134$	−7.75963	−	19.6381i	−0.670330	−	1.69647i
$135$		0			0
$136$	−12.0782	+	4.32025i	−1.03570	+	0.370458i
$137$	6.47131			0.552881			0.276440	−	0.961031i	$-0.410845\pi$
$137$	6.47131			0.552881			0.276440	+	0.961031i	$0.410845\pi$
$138$	−1.36322	−	3.45004i	−0.116045	−	0.293687i
$139$	16.4430	+	16.4430i	1.39468	+	1.39468i	0.814458	+	0.580223i	$0.197035\pi$
$139$	16.4430	+	16.4430i	1.39468	+	1.39468i	0.580223	+	0.814458i	$0.302965\pi$
$140$		0			0
$141$	0.905982	−	0.905982i	0.0762974	−	0.0762974i
$142$	7.90020	−	18.2218i	0.662970	−	1.52914i
$143$		−	1.90800i		−	0.159555i
$144$	11.6236	+	0.763450i	0.968633	+	0.0636209i
$145$		0			0
$146$	8.61329	+	3.73435i	0.712841	+	0.309057i
$147$	−0.834712	−	0.834712i	−0.0688459	−	0.0688459i
$148$	−15.1429	−	0.496766i	−1.24474	−	0.0408339i
$149$	2.72803	+	2.72803i	0.223489	+	0.223489i	0.809966	−	0.586477i	$-0.199486\pi$
$149$	2.72803	+	2.72803i	0.223489	+	0.223489i	−0.586477	+	0.809966i	$0.699486\pi$
$150$		0			0
$151$			11.5196i			0.937453i	0.883343	+	0.468726i	$0.155287\pi$
$151$			11.5196i			0.937453i	−0.883343	+	0.468726i	$0.844713\pi$
$152$	−11.6436	−	5.50848i	−0.944420	−	0.446796i
$153$	−13.2074			−1.06775
$154$	0.645239	+	1.63297i	0.0519948	+	0.131589i
$155$		0			0
$156$	1.15491	−	1.08154i	0.0924668	−	0.0865927i
$157$	−3.28013	−	3.28013i	−0.261783	−	0.261783i	0.563995	−	0.825778i	$-0.309264\pi$
$157$	−3.28013	−	3.28013i	−0.261783	−	0.261783i	−0.825778	+	0.563995i	$0.809264\pi$
$158$	5.54423	+	2.40374i	0.441076	+	0.191231i
$159$	0.576147			0.0456914
$160$		0			0
$161$	−15.3729			−1.21156
$162$	10.6619	+	4.62253i	0.837676	+	0.363180i
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	0.243525	−	0.969895i	$-0.421696\pi$
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	−0.969895	+	0.243525i	$0.921696\pi$
$164$	14.6482	−	13.7177i	1.14384	−	1.07117i
$165$		0			0
$166$	−6.72851	−	17.0285i	−0.522234	−	1.32167i
$167$	−7.08065			−0.547917			−0.273958	−	0.961742i	$-0.588333\pi$
$167$	−7.08065			−0.547917			−0.273958	+	0.961742i	$0.588333\pi$
$168$	−0.622686	+	1.31621i	−0.0480413	+	0.101548i
$169$		−	5.87470i		−	0.451900i
$170$		0			0
$171$	−9.37778	−	9.37778i	−0.717137	−	0.717137i
$172$	5.95244	+	0.195271i	0.453869	+	0.0148893i
$173$	−5.21471	−	5.21471i	−0.396467	−	0.396467i	0.480518	−	0.876985i	$-0.340449\pi$
$173$	−5.21471	−	5.21471i	−0.396467	−	0.396467i	−0.876985	+	0.480518i	$0.840449\pi$
$174$	−1.32730	−	0.575458i	−0.100622	−	0.0436254i
$175$		0			0
$176$	−2.14988	+	1.88487i	−0.162053	+	0.142077i
$177$		−	2.78369i		−	0.209235i
$178$	1.82167	−	4.20169i	0.136540	−	0.314930i
$179$	−6.32196	+	6.32196i	−0.472525	+	0.472525i	−0.902731	−	0.430206i	$-0.858441\pi$
$179$	−6.32196	+	6.32196i	−0.472525	+	0.472525i	0.430206	+	0.902731i	$0.358441\pi$
$180$		0			0
$181$	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	$0.508963\pi$
$182$	−2.40961	−	6.09824i	−0.178612	−	0.452031i
$183$	2.20556			0.163040
$184$	−8.43089	−	23.5704i	−0.621534	−	1.73763i
$185$		0			0
$186$	0.878578	+	2.22351i	0.0644205	+	0.163035i
$187$	2.29225	−	2.29225i	0.167626	−	0.167626i
$188$	6.31085	−	5.90994i	0.460266	−	0.431027i
$189$	−2.15213	+	2.15213i	−0.156545	+	0.156545i
$190$		0			0
$191$	−22.1722			−1.60433			−0.802164	−	0.597104i	$-0.796318\pi$
$191$	−22.1722			−1.60433			−0.802164	+	0.597104i	$0.796318\pi$
$192$	−2.35956	−	0.232886i	−0.170287	−	0.0168071i
$193$			7.97695i			0.574193i	0.957902	+	0.287097i	$0.0926901\pi$
$193$			7.97695i			0.574193i	−0.957902	+	0.287097i	$0.907310\pi$
$194$	−1.09206	+	2.51885i	−0.0784056	+	0.180843i
$195$		0			0
$196$	−5.44503	−	5.81440i	−0.388931	−	0.415314i
$197$	5.76327	−	5.76327i	0.410616	−	0.410616i	−0.471337	−	0.881953i	$-0.656228\pi$
$197$	5.76327	−	5.76327i	0.410616	−	0.410616i	0.881953	+	0.471337i	$0.156228\pi$
$198$	−2.73781	+	1.08179i	−0.194568	+	0.0768798i
$199$		−	5.38869i		−	0.381994i	−0.981591	−	0.190997i	$-0.938828\pi$
$199$		−	5.38869i		−	0.381994i	0.981591	−	0.190997i	$-0.0611721\pi$
$200$		0			0
$201$			4.42521i			0.312130i
$202$	−7.59920	−	19.2321i	−0.534678	−	1.35316i
$203$	−4.23921	+	4.23921i	−0.297534	+	0.297534i
$204$	2.68685	+	0.0881427i	0.188117	+	0.00617122i
$205$		0			0
$206$	6.44087	+	2.79248i	0.448757	+	0.194561i
$207$		−	25.7739i		−	1.79141i
$208$	8.02858	−	7.03893i	0.556682	−	0.488062i
$209$	3.25519			0.225166
$210$		0			0
$211$	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	$0.0746147\pi$
$212$	3.88582	+	0.127475i	0.266879	+	0.00875503i
$213$	−2.94315	+	2.94315i	−0.201661	+	0.201661i
$214$	5.10830	−	2.01845i	0.349196	−	0.137978i
$215$		0			0
$216$	−4.48002	−	2.11946i	−0.304827	−	0.144211i
$217$	9.90766			0.672576
$218$	13.0197	−	5.14447i	0.881802	−	0.348428i
$219$	−1.39120	−	1.39120i	−0.0940084	−	0.0940084i
$220$		0			0
$221$	−8.56026	+	8.56026i	−0.575826	+	0.575826i
$222$	2.91320	+	1.26304i	0.195521	+	0.0847696i
$223$		−	3.98714i		−	0.266998i	−0.991049	−	0.133499i	$-0.957379\pi$
$223$		−	3.98714i		−	0.266998i	0.991049	−	0.133499i	$-0.0426214\pi$
$224$	−4.49092	+	8.73940i	−0.300062	+	0.583926i
$225$		0			0
$226$	−3.67452	+	8.47529i	−0.244425	+	0.563768i
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	0.822449	−	0.568839i	$-0.192607\pi$
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	−0.568839	+	0.822449i	$0.692607\pi$
$228$	1.84519	+	1.97036i	0.122201	+	0.130491i
$229$	8.80687	+	8.80687i	0.581974	+	0.581974i	0.935445	−	0.353471i	$-0.114999\pi$
$229$	8.80687	+	8.80687i	0.581974	+	0.581974i	−0.353471	+	0.935445i	$0.614999\pi$
$230$		0			0
$231$		−	0.367971i		−	0.0242107i
$232$	−8.82463	−	4.17485i	−0.579365	−	0.274092i
$233$	16.6042			1.08778			0.543889	−	0.839157i	$-0.316951\pi$
$233$	16.6042			1.08778			0.543889	+	0.839157i	$0.316951\pi$
$234$	10.2242	−	4.03990i	0.668376	−	0.264096i
$235$		0			0
$236$	0.615905	−	18.7746i	0.0400920	−	1.22212i
$237$	−0.895491	−	0.895491i	−0.0581684	−	0.0581684i
$238$	4.43149	−	10.2212i	0.287251	−	0.662545i
$239$	−3.81234			−0.246600			−0.123300	−	0.992369i	$-0.539348\pi$
$239$	−3.81234			−0.246600			−0.123300	+	0.992369i	$0.539348\pi$
$240$		0			0
$241$	9.54985			0.615160			0.307580	−	0.951522i	$-0.400481\pi$
$241$	9.54985			0.615160			0.307580	+	0.951522i	$0.400481\pi$
$242$	−5.90059	+	13.6097i	−0.379304	+	0.874866i
$243$	−5.43913	−	5.43913i	−0.348921	−	0.348921i
$244$	14.8754	+	0.487991i	0.952301	+	0.0312404i
$245$		0			0
$246$	−3.91151	+	1.54556i	−0.249389	+	0.0985413i
$247$	−12.1563			−0.773487
$248$	5.43361	+	15.1908i	0.345034	+	0.964619i
$249$			3.83718i			0.243171i
$250$		0			0
$251$	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	$0.570203\pi$
$252$	−7.38424	+	6.91515i	−0.465164	+	0.435613i
$253$	4.47328	+	4.47328i	0.281233	+	0.281233i
$254$	1.41121	−	3.25496i	0.0885471	−	0.204234i
$255$		0			0
$256$	−15.8625	−	2.09277i	−0.991409	−	0.130798i
$257$		−	18.8752i		−	1.17740i	−0.808350	−	0.588702i	$-0.799639\pi$
$257$		−	18.8752i		−	1.17740i	0.808350	−	0.588702i	$-0.200361\pi$
$258$	−1.14514	−	0.496482i	−0.0712931	−	0.0309096i
$259$	9.30440	−	9.30440i	0.578147	−	0.578147i
$260$		0			0
$261$	−7.10738	−	7.10738i	−0.439936	−	0.439936i
$262$	−15.9181	+	6.28973i	−0.983422	+	0.388581i
$263$	−23.1398			−1.42686			−0.713429	−	0.700727i	$-0.752859\pi$
$263$	−23.1398			−1.42686			−0.713429	+	0.700727i	$0.752859\pi$
$264$	0.564189	−	0.201804i	0.0347234	−	0.0124202i
$265$		0			0
$266$	10.4041	−	4.11097i	0.637914	−	0.252060i
$267$	−0.678646	+	0.678646i	−0.0415325	+	0.0415325i
$268$	−0.979099	+	29.8458i	−0.0598080	+	1.82313i
$269$	10.6368	−	10.6368i	0.648539	−	0.648539i	−0.304101	−	0.952640i	$-0.598356\pi$
$269$	10.6368	−	10.6368i	0.648539	−	0.648539i	0.952640	+	0.304101i	$0.0983560\pi$
$270$		0			0
$271$	19.9763			1.21348			0.606738	−	0.794902i	$-0.292478\pi$
$271$	19.9763			1.21348			0.606738	+	0.794902i	$0.292478\pi$
$272$	18.1020	+	1.18896i	1.09759	+	0.0720911i
$273$			1.37417i			0.0831683i
$274$	−8.39661	−	3.64041i	−0.507258	−	0.219925i
$275$		0			0
$276$	−0.172009	+	5.24335i	−0.0103537	+	0.315612i
$277$	−16.1534	+	16.1534i	−0.970563	+	0.970563i	−0.999579	−	0.0290160i	$-0.990763\pi$
$277$	−16.1534	+	16.1534i	−0.970563	+	0.970563i	0.0290160	+	0.999579i	$0.490763\pi$
$278$	−12.0851	−	30.5850i	−0.724817	−	1.83437i
$279$			16.6110i			0.994474i
$280$		0			0
$281$			9.43520i			0.562857i	0.959582	+	0.281429i	$0.0908082\pi$
$281$			9.43520i			0.562857i	−0.959582	+	0.281429i	$0.909192\pi$
$282$	−1.68518	+	0.665868i	−0.100351	+	0.0396518i
$283$	−8.71287	+	8.71287i	−0.517926	+	0.517926i	−0.916943	−	0.399017i	$-0.869351\pi$
$283$	−8.71287	+	8.71287i	−0.517926	+	0.517926i	0.399017	+	0.916943i	$0.369351\pi$
$284$	−20.5012	+	19.1989i	−1.21653	+	1.13924i
$285$		0			0
$286$	−1.07334	+	2.47565i	−0.0634676	+	0.146388i
$287$			17.4292i			1.02881i
$288$	−14.6523	−	7.52939i	−0.863395	−	0.443674i
$289$	−3.56843			−0.209908
$290$		0			0
$291$	0.406838	−	0.406838i	0.0238493	−	0.0238493i
$292$	−9.07512	−	9.69074i	−0.531081	−	0.567107i
$293$	11.1045	−	11.1045i	0.648729	−	0.648729i	−0.303957	−	0.952686i	$-0.598308\pi$
$293$	11.1045	−	11.1045i	0.648729	−	0.648729i	0.952686	+	0.303957i	$0.0983079\pi$
$294$	0.613487	+	1.55261i	0.0357793	+	0.0905503i
$295$		0			0
$296$	19.3687	+	9.16313i	1.12578	+	0.532596i
$297$	1.25247			0.0726759
$298$	−2.00501	−	5.07429i	−0.116147	−	0.293946i
$299$	−16.7052	−	16.7052i	−0.966087	−	0.966087i
$300$		0			0
$301$	−3.65742	+	3.65742i	−0.210810	+	0.210810i
$302$	6.48031	−	14.9469i	0.372900	−	0.860095i
$303$			4.33372i			0.248966i
$304$	12.0090	+	13.6974i	0.688761	+	0.785599i
$305$		0			0
$306$	17.1367	+	7.42974i	0.979641	+	0.424730i
$307$	2.99854	+	2.99854i	0.171136	+	0.171136i	0.787478	−	0.616343i	$-0.211386\pi$
$307$	2.99854	+	2.99854i	0.171136	+	0.171136i	−0.616343	+	0.787478i	$0.711386\pi$
$308$	0.0814153	−	2.48178i	0.00463907	−	0.141413i
$309$	−1.04031	−	1.04031i	−0.0591814	−	0.0591814i
$310$		0			0
$311$		−	9.06099i		−	0.513802i	−0.966438	−	0.256901i	$-0.917299\pi$
$311$		−	9.06099i		−	0.513802i	0.966438	−	0.256901i	$-0.0827014\pi$
$312$	−2.10693	+	0.753627i	−0.119281	+	0.0426657i
$313$	19.5699			1.10616			0.553078	−	0.833129i	$-0.313453\pi$
$313$	19.5699			1.10616			0.553078	+	0.833129i	$0.313453\pi$
$314$	2.41079	+	6.10124i	0.136049	+	0.344313i
$315$		0			0
$316$	−5.84151	−	6.23777i	−0.328610	−	0.350902i
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	0.946436	−	0.322890i	$-0.104654\pi$
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	−0.322890	+	0.946436i	$0.604654\pi$
$318$	−0.747558	−	0.324109i	−0.0419210	−	0.0181751i
$319$	2.46709			0.138131
$320$		0			0
$321$	−1.15109			−0.0642478
$322$	19.9466	+	8.64797i	1.11158	+	0.481933i
$323$	−14.6045	−	14.6045i	−0.812614	−	0.812614i
$324$	−11.2335	−	11.9956i	−0.624086	−	0.666421i
$325$		0			0
$326$	6.81585	+	17.2496i	0.377495	+	0.955366i
$327$	−2.93382			−0.162241
$328$	−26.7231	+	9.55859i	−1.47554	+	0.527785i
$329$			7.50894i			0.413981i
$330$		0			0
$331$	−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	$0.852558\pi$
$332$	−0.848994	+	25.8799i	−0.0465946	+	1.42034i
$333$	15.5996	+	15.5996i	0.854851	+	0.854851i
$334$	9.18724	+	3.98319i	0.502703	+	0.217950i
$335$		0			0
$336$	1.54837	−	1.35751i	0.0844706	−	0.0740582i
$337$			25.1380i			1.36935i	0.728847	+	0.684677i	$0.240057\pi$
$337$			25.1380i			1.36935i	−0.728847	+	0.684677i	$0.759943\pi$
$338$	−3.30479	+	7.62251i	−0.179757	+	0.414610i
$339$	1.36891	−	1.36891i	0.0743488	−	0.0743488i
$340$		0			0
$341$	−2.88298	−	2.88298i	−0.156122	−	0.156122i
$342$	6.89237	+	17.4432i	0.372697	+	0.943222i
$343$	19.0770			1.03006
$344$	−7.61353	−	3.60189i	−0.410494	−	0.194201i
$345$		0			0
$346$	3.83265	+	9.69967i	0.206044	+	0.521458i
$347$	7.36719	−	7.36719i	0.395491	−	0.395491i	−0.481148	−	0.876639i	$-0.659780\pi$
$347$	7.36719	−	7.36719i	0.395491	−	0.395491i	0.876639	+	0.481148i	$0.159780\pi$
$348$	1.39846	+	1.49333i	0.0749655	+	0.0800509i
$349$	3.25982	−	3.25982i	0.174494	−	0.174494i	−0.614457	−	0.788951i	$-0.710625\pi$
$349$	3.25982	−	3.25982i	0.174494	−	0.174494i	0.788951	+	0.614457i	$0.210625\pi$
$350$		0			0
$351$	−4.67729			−0.249655
$352$	3.84982	−	1.23624i	0.205196	−	0.0658919i
$353$			0.502832i			0.0267630i	0.999910	+	0.0133815i	$0.00425960\pi$
$353$			0.502832i			0.0267630i	−0.999910	+	0.0133815i	$0.995740\pi$
$354$	−1.56595	+	3.61188i	−0.0832295	+	0.191969i
$355$		0			0
$356$	−4.72728	+	4.42697i	−0.250545	+	0.234629i
$357$	−1.65091	+	1.65091i	−0.0873754	+	0.0873754i
$358$	11.7592	−	4.64644i	0.621494	−	0.245572i
$359$		−	5.95161i		−	0.314114i	−0.987590	−	0.157057i	$-0.949799\pi$
$359$		−	5.95161i		−	0.314114i	0.987590	−	0.157057i	$-0.0502007\pi$
$360$		0			0
$361$		−	1.73958i		−	0.0915571i
$362$	−9.60567	−	24.3100i	−0.504863	−	1.27771i
$363$	2.19821	−	2.19821i	0.115376	−	0.115376i
$364$	−0.304041	+	9.26806i	−0.0159361	+	0.485778i
$365$		0			0
$366$	−2.86175	−	1.24073i	−0.149586	−	0.0648540i
$367$		−	1.95365i		−	0.101980i	−0.998699	−	0.0509898i	$-0.983762\pi$
$367$		−	1.95365i		−	0.101980i	0.998699	−	0.0509898i	$-0.0162376\pi$
$368$	−2.32023	+	35.3257i	−0.120950	+	1.84148i
$369$	−29.2214			−1.52121
$370$		0			0
$371$	−2.38760	+	2.38760i	−0.123958	+	0.123958i
$372$	0.110858	−	3.37927i	0.00574770	−	0.175207i
$373$	18.6509	−	18.6509i	0.965708	−	0.965708i	−0.0337233	−	0.999431i	$-0.510736\pi$
$373$	18.6509	−	18.6509i	0.965708	−	0.965708i	0.999431	+	0.0337233i	$0.0107365\pi$
$374$	−4.26372	+	1.68473i	−0.220472	+	0.0871153i
$375$		0			0
$376$	−11.5130	+	4.11809i	−0.593739	+	0.212374i
$377$	−9.21320			−0.474504
$378$	4.00309	−	1.58175i	0.205897	−	0.0813563i
$379$	3.85143	+	3.85143i	0.197835	+	0.197835i	0.799071	−	0.601236i	$-0.205325\pi$
$379$	3.85143	+	3.85143i	0.197835	+	0.197835i	−0.601236	+	0.799071i	$0.705325\pi$
$380$		0			0
$381$	−0.525732	+	0.525732i	−0.0269341	+	0.0269341i
$382$	28.7688	+	12.4729i	1.47194	+	0.638169i
$383$			2.29258i			0.117145i	0.998283	+	0.0585726i	$0.0186549\pi$
$383$			2.29258i			0.117145i	−0.998283	+	0.0585726i	$0.981345\pi$
$384$	2.93056	+	1.62954i	0.149549	+	0.0831569i
$385$		0			0
$386$	4.48740	−	10.3502i	0.228403	−	0.526812i
$387$	−6.13195	−	6.13195i	−0.311705	−	0.311705i
$388$	2.83394	−	2.65391i	0.143871	−	0.134732i
$389$	−4.90500	−	4.90500i	−0.248693	−	0.248693i	0.571741	−	0.820434i	$-0.306268\pi$
$389$	−4.90500	−	4.90500i	−0.248693	−	0.248693i	−0.820434	+	0.571741i	$0.806268\pi$
$390$		0			0
$391$		−	40.1389i		−	2.02991i
$392$	3.79414	+	10.6073i	0.191633	+	0.535752i
$393$	3.58695			0.180938
$394$	−10.7200	+	4.23582i	−0.540067	+	0.213398i
$395$		0			0
$396$	4.16090	+	0.136499i	0.209093	+	0.00685935i
$397$	10.8616	+	10.8616i	0.545126	+	0.545126i	0.925027	−	0.379901i	$-0.124042\pi$
$397$	10.8616	+	10.8616i	0.545126	+	0.545126i	−0.379901	+	0.925027i	$0.624042\pi$
$398$	−3.03138	+	6.99190i	−0.151950	+	0.350472i
$399$	−2.34443			−0.117368
$400$		0			0
$401$	−7.10783			−0.354948			−0.177474	−	0.984125i	$-0.556793\pi$
$401$	−7.10783			−0.354948			−0.177474	+	0.984125i	$0.556793\pi$
$402$	2.48938	−	5.74177i	0.124159	−	0.286374i
$403$	10.7663	+	10.7663i	0.536308	+	0.536308i
$404$	−0.958857	+	29.2288i	−0.0477049	+	1.45419i
$405$		0			0
$406$	7.88519	−	3.11569i	0.391335	−	0.154629i
$407$	−5.41487			−0.268405
$408$	−3.43664	−	1.62584i	−0.170139	−	0.0804912i
$409$		−	29.1697i		−	1.44235i	−0.692752	−	0.721176i	$-0.743602\pi$
$409$		−	29.1697i		−	1.44235i	0.692752	−	0.721176i	$-0.256398\pi$
$410$		0			0
$411$	1.35620	+	1.35620i	0.0668964	+	0.0668964i
$412$	−6.78622	−	7.24657i	−0.334333	−	0.357013i
$413$	11.5359	+	11.5359i	0.567643	+	0.567643i
$414$	−14.4990	+	33.4420i	−0.712588	+	1.64359i
$415$		0			0
$416$	−14.3769	+	4.61667i	−0.704887	+	0.226351i
$417$			6.89198i			0.337502i
$418$	−4.22365	−	1.83119i	−0.206586	−	0.0895665i
$419$	−3.06616	+	3.06616i	−0.149792	+	0.149792i	−0.778025	−	0.628233i	$-0.783778\pi$
$419$	−3.06616	+	3.06616i	−0.149792	+	0.149792i	0.628233	+	0.778025i	$0.283778\pi$
$420$		0			0
$421$	−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	$0.755839\pi$
$422$	−20.0044	+	7.90436i	−0.973798	+	0.384778i
$423$	−12.5893			−0.612115
$424$	−4.97020	−	2.35135i	−0.241374	−	0.114192i
$425$		0			0
$426$	5.47443	−	2.16312i	0.265237	−	0.104803i
$427$	−9.14005	+	9.14005i	−0.442318	+	0.442318i
$428$	−7.76356	−	0.254685i	−0.375266	−	0.0123107i
$429$	0.399861	−	0.399861i	0.0193055	−	0.0193055i
$430$		0			0
$431$	16.7237			0.805555			0.402777	−	0.915298i	$-0.368045\pi$
$431$	16.7237			0.805555			0.402777	+	0.915298i	$0.368045\pi$
$432$	4.62060	+	5.27024i	0.222309	+	0.253564i
$433$			28.3675i			1.36326i	0.731699	+	0.681628i	$0.238728\pi$
$433$			28.3675i			1.36326i	−0.731699	+	0.681628i	$0.761272\pi$
$434$	−12.8553	−	5.57351i	−0.617076	−	0.267537i
$435$		0			0
$436$	−19.7872	−	0.649122i	−0.947634	−	0.0310873i
$437$	28.5004	−	28.5004i	1.36336	−	1.36336i
$438$	1.02249	+	2.58771i	0.0488562	+	0.123645i
$439$		−	13.5018i		−	0.644405i	−0.946671	−	0.322203i	$-0.895577\pi$
$439$		−	13.5018i		−	0.644405i	0.946671	−	0.322203i	$-0.104423\pi$
$440$		0			0
$441$			11.5990i			0.552333i
$442$	15.9226	−	6.29152i	0.757361	−	0.299257i
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	−0.442780	−	0.896630i	$-0.646008\pi$
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	0.896630	+	0.442780i	$0.146008\pi$
$444$	−3.06941	−	3.27762i	−0.145668	−	0.155549i
$445$		0			0
$446$	−2.24295	+	5.17337i	−0.106207	+	0.244966i
$447$			1.14343i			0.0540824i
$448$	10.7433	−	8.81314i	0.507575	−	0.416382i
$449$	9.35573			0.441524			0.220762	−	0.975328i	$-0.429146\pi$
$449$	9.35573			0.441524			0.220762	+	0.975328i	$0.429146\pi$
$450$		0			0
$451$	5.07162	−	5.07162i	0.238813	−	0.238813i
$452$	9.53547	−	8.92972i	0.448511	−	0.420019i
$453$	−2.41418	+	2.41418i	−0.113428	+	0.113428i
$454$	−2.80833	−	7.10734i	−0.131802	−	0.333564i
$455$		0			0
$456$	−1.28574	−	3.59458i	−0.0602105	−	0.168332i
$457$	6.84779			0.320326			0.160163	−	0.987091i	$-0.448798\pi$
$457$	6.84779			0.320326			0.160163	+	0.987091i	$0.448798\pi$
$458$	−6.47277	−	16.3813i	−0.302453	−	0.765448i
$459$	−5.61925	−	5.61925i	−0.262284	−	0.262284i
$460$		0			0
$461$	−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	$0.376367\pi$
$462$	−0.207001	+	0.477448i	−0.00963054	+	0.0222129i
$463$		−	26.6096i		−	1.23665i	−0.785922	−	0.618326i	$-0.787811\pi$
$463$		−	26.6096i		−	1.23665i	0.785922	−	0.618326i	$-0.212189\pi$
$464$	9.10153	+	10.3812i	0.422528	+	0.481934i
$465$		0			0
$466$	−21.5442	−	9.34063i	−0.998015	−	0.432696i
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	0.672135	−	0.740428i	$-0.265377\pi$
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	−0.740428	+	0.672135i	$0.765377\pi$
$468$	−15.5386	−	0.509748i	−0.718274	−	0.0235631i
$469$	−18.3385	−	18.3385i	−0.846792	−	0.846792i
$470$		0			0
$471$		−	1.37484i		−	0.0633494i
$472$	−11.3607	+	24.0139i	−0.522920	+	1.10533i
$473$	2.12851			0.0978688
$474$	0.658157	+	1.66567i	0.0302302	+	0.0765066i
$475$		0			0
$476$	−11.4998	+	10.7693i	−0.527094	+	0.493609i
$477$	−4.00301	−	4.00301i	−0.183285	−	0.183285i
$478$	4.94656	+	2.14462i	0.226251	+	0.0980924i
$479$	2.78600			0.127296			0.0636479	−	0.997972i	$-0.479727\pi$
$479$	2.78600			0.127296			0.0636479	+	0.997972i	$0.479727\pi$
$480$		0			0
$481$	20.2215			0.922022
$482$	−12.3911	−	5.37223i	−0.564397	−	0.244698i
$483$	−3.22172	−	3.22172i	−0.146593	−	0.146593i
$484$	15.3122	−	14.3395i	0.696009	−	0.651794i
$485$		0			0
$486$	3.99759	+	10.1171i	0.181334	+	0.458922i
$487$	16.9499			0.768073			0.384036	−	0.923318i	$-0.374534\pi$
$487$	16.9499			0.768073			0.384036	+	0.923318i	$0.374534\pi$
$488$	−19.0265	−	9.00128i	−0.861291	−	0.407469i
$489$		−	3.88699i		−	0.175776i
$490$		0			0
$491$	−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	$-0.509932\pi$
$492$	5.94469	+	0.195017i	0.268007	+	0.00879203i
$493$	−11.0687	−	11.0687i	−0.498507	−	0.498507i
$494$	15.7730	+	6.83848i	0.709660	+	0.307678i
$495$		0			0
$496$	1.49536	−	22.7670i	0.0671436	−	1.02227i
$497$		−	24.3933i		−	1.09419i
$498$	2.15859	−	4.97879i	0.0967287	−	0.223105i
$499$	−2.33906	+	2.33906i	−0.104711	+	0.104711i	−0.757521	−	0.652811i	$-0.773590\pi$
$499$	−2.33906	+	2.33906i	−0.104711	+	0.104711i	0.652811	+	0.757521i	$0.273590\pi$
$500$		0			0
$501$	−1.48390	−	1.48390i	−0.0662958	−	0.0662958i
$502$	−8.81469	−	22.3083i	−0.393419	−	0.995666i
$503$	1.58801			0.0708057			0.0354029	−	0.999373i	$-0.488729\pi$
$503$	1.58801			0.0708057			0.0354029	+	0.999373i	$0.488729\pi$
$504$	13.4712	−	4.81853i	0.600057	−	0.214634i
$505$		0			0
$506$	−3.28772	−	8.32058i	−0.146157	−	0.369895i
$507$	1.23117	−	1.23117i	0.0546781	−	0.0546781i
$508$	−3.66212	+	3.42948i	−0.162480	+	0.152159i
$509$	3.61613	−	3.61613i	0.160282	−	0.160282i	−0.622410	−	0.782692i	$-0.713846\pi$
$509$	3.61613	−	3.61613i	0.160282	−	0.160282i	0.782692	+	0.622410i	$0.213846\pi$
$510$		0			0
$511$	11.5305			0.510079
$512$	19.4046	+	11.6388i	0.857570	+	0.514367i
$513$		−	7.97981i		−	0.352317i
$514$	−10.6182	+	24.4909i	−0.468348	+	1.08025i
$515$		0			0
$516$	1.20654	+	1.28838i	0.0531148	+	0.0567179i
$517$	2.18499	−	2.18499i	0.0960956	−	0.0960956i
$518$	−17.3067	+	6.83844i	−0.760414	+	0.300464i
$519$		−	2.18571i		−	0.0959419i
$520$		0			0
$521$			8.93031i			0.391244i	0.980679	+	0.195622i	$0.0626725\pi$
$521$			8.93031i			0.391244i	−0.980679	+	0.195622i	$0.937327\pi$
$522$	5.22370	+	13.2201i	0.228635	+	0.578630i
$523$	−15.0355	+	15.0355i	−0.657455	+	0.657455i	−0.954777	−	0.297323i	$-0.903906\pi$
$523$	−15.0355	+	15.0355i	−0.657455	+	0.657455i	0.297323	+	0.954777i	$0.403906\pi$
$524$	24.1922	+	0.793629i	1.05684	+	0.0346699i
$525$		0			0
$526$	30.0242	+	13.0172i	1.30912	+	0.567576i
$527$			25.8691i			1.12687i
$528$	−0.845567	−	0.0555377i	−0.0367986	−	0.00241697i
$529$	55.3305			2.40567
$530$		0			0
$531$	−19.3408	+	19.3408i	−0.839320	+	0.839320i
$532$	−15.8120	−	0.518717i	−0.685538	−	0.0224892i
$533$	−18.9397	+	18.9397i	−0.820368	+	0.820368i
$534$	1.26232	−	0.498783i	0.0546260	−	0.0215845i
$535$		0			0
$536$	18.0600	−	38.1746i	0.780075	−	1.64889i
$537$	−2.64980			−0.114347
$538$	−19.7851	+	7.81773i	−0.852998	+	0.337046i
$539$	−2.01310	−	2.01310i	−0.0867106	−	0.0867106i
$540$		0			0
$541$	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	$0.195781\pi$
$542$	−25.9196	−	11.2376i	−1.11334	−	0.482696i
$543$			5.47798i			0.235083i
$544$	−22.8187	−	11.7259i	−0.978344	−	0.502743i
$545$		0			0
$546$	0.773031	−	1.78300i	0.0330827	−	0.0763053i
$547$	−32.8366	−	32.8366i	−1.40399	−	1.40399i	−0.786856	−	0.617136i	$-0.788293\pi$
$547$	−32.8366	−	32.8366i	−1.40399	−	1.40399i	−0.617136	−	0.786856i	$-0.711707\pi$
$548$	8.84682	+	9.44695i	0.377918	+	0.403554i
$549$	−15.3240	−	15.3240i	−0.654013	−	0.654013i
$550$		0			0
$551$		−	15.7184i		−	0.669628i
$552$	3.17281	−	6.70655i	0.135044	−	0.285450i
$553$	7.42199			0.315615
$554$	30.0463	−	11.8722i	1.27654	−	0.504402i
$555$		0			0
$556$	−1.52488	+	46.4829i	−0.0646694	+	1.97132i
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.999661	−	0.0260537i	$-0.991706\pi$
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.0260537	−	0.999661i	$-0.508294\pi$
$558$	9.34444	−	21.5530i	0.395582	−	0.912411i
$559$	−7.94877			−0.336197
$560$		0			0
$561$	0.960778			0.0405641
$562$	5.30773	−	12.2423i	0.223893	−	0.516411i
$563$	22.3407	+	22.3407i	0.941547	+	0.941547i	0.998384	−	0.0568365i	$-0.0181014\pi$
$563$	22.3407	+	22.3407i	0.941547	+	0.941547i	−0.0568365	+	0.998384i	$0.518101\pi$
$564$	2.56113	+	0.0840182i	0.107843	+	0.00353781i
$565$		0			0
$566$	16.2065	−	6.40368i	0.681208	−	0.269167i
$567$	14.2729			0.599406
$568$	37.4009	−	13.3779i	1.56931	−	0.561325i
$569$			29.3339i			1.22974i	0.788629	+	0.614870i	$0.210791\pi$
$569$			29.3339i			1.22974i	−0.788629	+	0.614870i	$0.789209\pi$
$570$		0			0
$571$	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	$0.498695\pi$
$572$	2.78534	−	2.60839i	0.116461	−	0.109062i
$573$	−4.64666	−	4.64666i	−0.194117	−	0.194117i
$574$	9.80471	−	22.6146i	0.409241	−	0.943915i
$575$		0			0
$576$	14.7759	+	18.0121i	0.615664	+	0.750503i
$577$			31.9232i			1.32898i	0.747297	+	0.664490i	$0.231351\pi$
$577$			31.9232i			1.32898i	−0.747297	+	0.664490i	$0.768649\pi$
$578$	4.63009	+	2.00740i	0.192586	+	0.0834970i
$579$	−1.67174	+	1.67174i	−0.0694751	+	0.0694751i
$580$		0			0
$581$	−15.9016	−	15.9016i	−0.659710	−	0.659710i
$582$	−0.756744	+	0.299013i	−0.0313680	+	0.0123945i
$583$	1.38951			0.0575477
$584$	6.32361	+	17.6790i	0.261673	+	0.731564i
$585$		0			0
$586$	−20.6549	+	8.16142i	−0.853248	+	0.337145i
$587$	−26.2847	+	26.2847i	−1.08488	+	1.08488i	−0.0888379	+	0.996046i	$0.528315\pi$
$587$	−26.2847	+	26.2847i	−1.08488	+	1.08488i	−0.996046	+	0.0888379i	$0.971685\pi$
$588$	0.0774089	−	2.35965i	0.00319229	−	0.0973105i
$589$	−18.3681	+	18.3681i	−0.756846	+	0.756846i
$590$		0			0
$591$	2.41563			0.0993658
$592$	−19.9764	−	22.7850i	−0.821026	−	0.936459i
$593$		−	38.2085i		−	1.56904i	−0.620106	−	0.784518i	$-0.712910\pi$
$593$		−	38.2085i		−	1.56904i	0.620106	−	0.784518i	$-0.287090\pi$
$594$	−1.62510	−	0.704574i	−0.0666788	−	0.0289090i
$595$		0			0
$596$	−0.252990	+	7.71187i	−0.0103629	+	0.315891i
$597$	1.12931	−	1.12931i	0.0462197	−	0.0462197i
$598$	12.2778	+	31.0727i	0.502076	+	1.27066i
$599$		−	25.1150i		−	1.02617i	−0.858337	−	0.513086i	$-0.828502\pi$
$599$		−	25.1150i		−	1.02617i	0.858337	−	0.513086i	$-0.171498\pi$
$600$		0			0
$601$			22.2022i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$601$			22.2022i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$602$	6.80302	−	2.68809i	0.277270	−	0.109558i
$603$	30.7459	−	30.7459i	1.25207	−	1.25207i
$604$	−16.8166	+	15.7483i	−0.684257	+	0.640789i
$605$		0			0
$606$	2.43792	−	5.62307i	0.0990336	−	0.228421i
$607$		−	12.9648i		−	0.526226i	−0.964765	−	0.263113i	$-0.915251\pi$
$607$		−	12.9648i		−	0.526226i	0.964765	−	0.263113i	$-0.0847492\pi$
$608$	−7.87639	−	24.5281i	−0.319430	−	0.994747i
$609$	−1.77683			−0.0720009
$610$		0			0
$611$	−8.15970	+	8.15970i	−0.330106	+	0.330106i
$612$	−18.0556	−	19.2804i	−0.729853	−	0.779363i
$613$	−7.42804	+	7.42804i	−0.300016	+	0.300016i	−0.841020	−	0.541004i	$-0.818044\pi$
$613$	−7.42804	+	7.42804i	−0.300016	+	0.300016i	0.541004	+	0.841020i	$0.318044\pi$
$614$	−2.20383	−	5.57746i	−0.0889394	−	0.225088i
$615$		0			0
$616$	−1.50175	+	3.17435i	−0.0605074	+	0.127898i
$617$	−23.2743			−0.936989			−0.468494	−	0.883467i	$-0.655203\pi$
$617$	−23.2743			−0.936989			−0.468494	+	0.883467i	$0.655203\pi$
$618$	0.764597	+	1.93505i	0.0307566	+	0.0778389i
$619$	31.6213	+	31.6213i	1.27097	+	1.27097i	0.945581	+	0.325386i	$0.105494\pi$
$619$	31.6213	+	31.6213i	1.27097	+	1.27097i	0.325386	+	0.945581i	$0.394506\pi$
$620$		0			0
$621$	10.9659	−	10.9659i	0.440045	−	0.440045i
$622$	−5.09722	+	11.7568i	−0.204380	+	0.471403i
$623$		−	5.62474i		−	0.225351i
$624$	3.15772	+	0.207402i	0.126410	+	0.00830274i
$625$		0			0
$626$	−25.3922	−	11.0090i	−1.01488	−	0.440007i
$627$	0.682194	+	0.682194i	0.0272442	+	0.0272442i
$628$	0.304190	−	9.27262i	0.0121385	−	0.370018i
$629$	24.2939	+	24.2939i	0.968663	+	0.968663i
$630$		0			0
$631$			29.9258i			1.19133i	0.803234	+	0.595663i	$0.203111\pi$
$631$			29.9258i			1.19133i	−0.803234	+	0.595663i	$0.796889\pi$
$632$	4.07041	+	11.3797i	0.161912	+	0.452661i
$633$	4.50775			0.179167
$634$	−8.15956	−	20.6502i	−0.324058	−	0.820126i
$635$		0			0
$636$	0.787641	+	0.841071i	0.0312320	+	0.0333506i
$637$	7.51782	+	7.51782i	0.297867	+	0.297867i
$638$	−3.20109	−	1.38785i	−0.126732	−	0.0549456i
$639$	40.8974			1.61788
$640$		0			0
$641$	10.2240			0.403825			0.201912	−	0.979404i	$-0.435284\pi$
$641$	10.2240			0.403825			0.201912	+	0.979404i	$0.435284\pi$
$642$	1.49356	+	0.647543i	0.0589461	+	0.0255565i
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	0.382770	−	0.923844i	$-0.374970\pi$
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	−0.923844	+	0.382770i	$0.874970\pi$
$644$	−21.0161	−	22.4417i	−0.828150	−	0.884328i
$645$		0			0
$646$	10.7338	+	27.1652i	0.422316	+	1.06880i
$647$	18.6767			0.734255			0.367128	−	0.930171i	$-0.380341\pi$
$647$	18.6767			0.734255			0.367128	+	0.930171i	$0.380341\pi$
$648$	7.82762	+	21.8838i	0.307498	+	0.859677i
$649$		−	6.71353i		−	0.263529i
$650$		0			0
$651$	2.07636	+	2.07636i	0.0813790	+	0.0813790i
$652$	0.860014	−	26.2158i	0.0336808	−	1.02669i
$653$	12.7935	+	12.7935i	0.500647	+	0.500647i	0.911639	−	0.410992i	$-0.134817\pi$
$653$	12.7935	+	12.7935i	0.500647	+	0.500647i	−0.410992	+	0.911639i	$0.634817\pi$
$654$	3.80668	+	1.65041i	0.148853	+	0.0645362i
$655$		0			0
$656$	40.0508	+	2.63058i	1.56372	+	0.102707i
$657$			19.3318i			0.754205i
$658$	4.22412	−	9.74296i	0.164673	−	0.379820i
$659$	−12.3193	+	12.3193i	−0.479893	+	0.479893i	−0.905097	−	0.425204i	$-0.860202\pi$
$659$	−12.3193	+	12.3193i	−0.479893	+	0.479893i	0.425204	+	0.905097i	$0.360202\pi$
$660$		0			0
$661$	−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	$0.979888\pi$
$662$	5.98792	+	15.1542i	0.232727	+	0.588987i
$663$	−3.58797			−0.139345
$664$	15.6602	−	33.1019i	0.607733	−	1.28460i
$665$		0			0
$666$	−11.4652	−	29.0161i	−0.444267	−	1.12435i
$667$	21.6003	−	21.6003i	0.836367	−	0.836367i
$668$	−9.67984	−	10.3365i	−0.374524	−	0.399931i
$669$	0.835589	−	0.835589i	0.0323057	−	0.0323057i
$670$		0			0
$671$	5.31923			0.205347
$672$	−2.77269	+	0.890358i	−0.106959	+	0.0343463i
$673$		−	21.5360i		−	0.830150i	−0.909787	−	0.415075i	$-0.863755\pi$
$673$		−	21.5360i		−	0.830150i	0.909787	−	0.415075i	$-0.136245\pi$
$674$	14.1413	−	32.6169i	0.544701	−	1.25636i
$675$		0			0
$676$	8.57602	−	8.03121i	0.329847	−	0.308893i
$677$	13.1852	−	13.1852i	0.506750	−	0.506750i	−0.406778	−	0.913527i	$-0.633348\pi$
$677$	13.1852	−	13.1852i	0.506750	−	0.506750i	0.913527	+	0.406778i	$0.133348\pi$
$678$	−2.54625	+	1.00610i	−0.0977881	+	0.0386392i
$679$			3.37195i			0.129404i
$680$		0			0
$681$			1.60156i			0.0613717i
$682$	2.11890	+	5.36251i	0.0811367	+	0.205341i
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.188926	+	0.981991i	$0.560501\pi$
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.981991	+	0.188926i	$0.939499\pi$
$684$	0.869670	−	26.5101i	0.0332527	−	1.01364i
$685$		0			0
$686$	−24.7527	−	10.7317i	−0.945062	−	0.409738i
$687$			3.69133i			0.140833i
$688$	7.85243	+	8.95645i	0.299371	+	0.341462i
$689$	−5.18905			−0.197687
$690$		0			0
$691$	−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	$0.487884\pi$
$692$	0.483598	−	14.7415i	0.0183836	−	0.560388i
$693$	−2.55663	+	2.55663i	−0.0971182	+	0.0971182i
$694$	−13.7034	+	5.41465i	−0.520174	+	0.205537i
$695$		0			0
$696$	−0.974460	−	2.72432i	−0.0369368	−	0.103265i
$697$	−45.5079			−1.72373
$698$	−6.06345	+	2.39586i	−0.229505	+	0.0906847i
$699$	3.47976	+	3.47976i	0.131617	+	0.131617i
$700$		0			0
$701$	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	$0.0849345\pi$
$702$	6.06885	+	2.63119i	0.229054	+	0.0993078i
$703$			34.4995i			1.30117i
$704$	−5.69064	−	0.561660i	−0.214474	−	0.0211684i
$705$		0			0
$706$	0.282866	−	0.652431i	0.0106458	−	0.0245546i
$707$	−17.9593	−	17.9593i	−0.675431	−	0.675431i
$708$	4.06369	−	3.80554i	0.152723	−	0.143021i
$709$	−4.38093	−	4.38093i	−0.164529	−	0.164529i	0.620040	−	0.784570i	$-0.287116\pi$
$709$	−4.38093	−	4.38093i	−0.164529	−	0.164529i	−0.784570	+	0.620040i	$0.787116\pi$
$710$		0			0
$711$			12.4436i			0.466670i
$712$	8.62409	−	3.08475i	0.323201	−	0.115606i
$713$	−50.4831			−1.89061
$714$	3.07079	−	1.21337i	0.114921	−	0.0454091i
$715$		0			0
$716$	−17.8716	−	0.586281i	−0.667892	−	0.0219103i
$717$	−0.798957	−	0.798957i	−0.0298376	−	0.0298376i
$718$	−3.34806	+	7.72230i	−0.124948	+	0.288194i
$719$	−1.61691			−0.0603007			−0.0301503	−	0.999545i	$-0.509599\pi$
$719$	−1.61691			−0.0603007			−0.0301503	+	0.999545i	$0.509599\pi$
$720$		0			0
$721$	8.62231			0.321112
$722$	−0.978596	+	2.25713i	−0.0364196	+	0.0840018i
$723$	2.00137	+	2.00137i	0.0744319	+	0.0744319i
$724$	−1.21203	+	36.9463i	−0.0450447	+	1.37310i
$725$		0			0
$726$	−4.08880	+	1.61561i	−0.151750	+	0.0599611i
$727$	39.3600			1.45978			0.729891	−	0.683563i	$-0.239571\pi$
$727$	39.3600			1.45978			0.729891	+	0.683563i	$0.239571\pi$
$728$	5.60821	−	11.8544i	0.207854	−	0.439353i
$729$			22.3717i			0.828581i
$730$		0			0
$731$	−9.54958	−	9.54958i	−0.353204	−	0.353204i
$732$	3.01519	+	3.21973i	0.111445	+	0.119005i
$733$	−34.0787	−	34.0787i	−1.25873	−	1.25873i	−0.951701	−	0.307026i	$-0.900666\pi$
$733$	−34.0787	−	34.0787i	−1.25873	−	1.25873i	−0.307026	−	0.951701i	$-0.599334\pi$
$734$	−1.09902	+	2.53488i	−0.0405654	+	0.0935643i
$735$		0			0
$736$	22.8828	−	44.5303i	0.843473	−	1.64141i
$737$			10.6724i			0.393124i
$738$	37.9152	+	16.4384i	1.39568	+	0.605105i
$739$	−15.4278	+	15.4278i	−0.567520	+	0.567520i	−0.931433	−	0.363913i	$-0.881441\pi$
$739$	−15.4278	+	15.4278i	−0.567520	+	0.567520i	0.363913	+	0.931433i	$0.381441\pi$
$740$		0			0
$741$	−2.54761	−	2.54761i	−0.0935888	−	0.0935888i
$742$	4.44109	−	1.75481i	0.163037	−	0.0644212i
$743$	−23.5004			−0.862147			−0.431074	−	0.902317i	$-0.641865\pi$
$743$	−23.5004			−0.862147			−0.431074	+	0.902317i	$0.641865\pi$
$744$	−2.04483	+	4.32229i	−0.0749673	+	0.158463i
$745$		0			0
$746$	−34.6918	+	13.7078i	−1.27016	+	0.501879i
$747$	26.6603	−	26.6603i	0.975451	−	0.975451i
$748$	6.47997	+	0.212577i	0.236931	+	0.00777258i
$749$	4.77024	−	4.77024i	0.174301	−	0.174301i
$750$		0			0
$751$	10.8586			0.396236			0.198118	−	0.980178i	$-0.436517\pi$
$751$	10.8586			0.396236			0.198118	+	0.980178i	$0.436517\pi$
$752$	17.2549	+	1.13332i	0.629222	+	0.0413280i
$753$			5.02690i			0.183190i
$754$	11.9543	+	5.18285i	0.435348	+	0.188748i
$755$		0			0
$756$	−6.08387	−	0.199583i	−0.221268	−	0.00725875i
$757$	18.8434	−	18.8434i	0.684874	−	0.684874i	−0.276220	−	0.961094i	$-0.589082\pi$
$757$	18.8434	−	18.8434i	0.684874	−	0.684874i	0.961094	+	0.276220i	$0.0890819\pi$
$758$	−2.83068	−	7.16389i	−0.102815	−	0.260204i
$759$			1.87494i			0.0680561i
$760$		0			0
$761$		−	22.2837i		−	0.807783i	−0.914807	−	0.403891i	$-0.867657\pi$
$761$		−	22.2837i		−	0.807783i	0.914807	−	0.403891i	$-0.132343\pi$
$762$	0.977894	−	0.386397i	0.0354254	−	0.0139977i
$763$	12.1580	−	12.1580i	0.440151	−	0.440151i
$764$	−30.3113	−	32.3675i	−1.09663	−	1.17102i
$765$		0			0
$766$	1.28968	−	2.97465i	0.0465980	−	0.107478i
$767$			25.0713i			0.905271i
$768$	−2.88575	−	3.76292i	−0.104130	−	0.135783i
$769$	−10.5399			−0.380077			−0.190039	−	0.981777i	$-0.560861\pi$
$769$	−10.5399			−0.380077			−0.190039	+	0.981777i	$0.560861\pi$
$770$		0			0
$771$	3.95571	−	3.95571i	0.142461	−	0.142461i
$772$	−11.6449	+	10.9052i	−0.419110	+	0.392486i
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	−0.776626	−	0.629962i	$-0.783070\pi$
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	0.629962	+	0.776626i	$0.283070\pi$
$774$	4.50679	+	11.4058i	0.161993	+	0.409973i
$775$		0			0
$776$	−5.17002	+	1.84926i	−0.185593	+	0.0663846i
$777$	3.89987			0.139907
$778$	3.60502	+	9.12358i	0.129246	+	0.327096i
$779$	−32.3125	−	32.3125i	−1.15772	−	1.15772i
$780$		0			0
$781$	−7.09809	+	7.09809i	−0.253990	+	0.253990i
$782$	−22.5800	+	52.0808i	−0.807459	+	1.86241i
$783$		−	6.04786i		−	0.216133i
$784$	1.04417	−	15.8976i	0.0372918	−	0.567770i
$785$		0			0
$786$	−4.65412	−	2.01782i	−0.166007	−	0.0719733i
$787$	8.16669	+	8.16669i	0.291111	+	0.291111i	0.837519	−	0.546408i	$-0.184005\pi$
$787$	8.16669	+	8.16669i	0.291111	+	0.291111i	−0.546408	+	0.837519i	$0.684005\pi$
$788$	16.2922	+	0.534470i	0.580387	+	0.0190397i
$789$	−4.84943	−	4.84943i	−0.172644	−	0.172644i
$790$		0			0
$791$			11.3458i			0.403409i
$792$	−5.32204	−	2.51781i	−0.189111	−	0.0894664i
$793$	−19.8643			−0.705403
$794$	−7.98290	−	20.2032i	−0.283303	−	0.716983i
$795$		0			0
$796$	7.86653	−	7.36679i	0.278822	−	0.261109i
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	0.312445	−	0.949936i	$-0.398852\pi$
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	−0.949936	+	0.312445i	$0.898852\pi$
$798$	3.04193	+	1.31885i	0.107683	+	0.0466868i
$799$	−19.6060			−0.693609
$800$		0			0
$801$	9.43033			0.333204
$802$	9.22250	+	3.99848i	0.325658	+	0.141191i
$803$	−3.35520	−	3.35520i	−0.118402	−	0.118402i
$804$	−6.46002	+	6.04964i	−0.227827	+	0.213354i
$805$		0			0
$806$	−7.91289	−	20.0260i	−0.278720	−	0.705385i
$807$	4.45835			0.156941
$808$	17.6867	−	37.3854i	0.622215	−	1.31521i
$809$			42.0296i			1.47768i	0.673879	+	0.738841i	$0.264627\pi$
$809$			42.0296i			1.47768i	−0.673879	+	0.738841i	$0.735373\pi$
$810$		0			0
$811$	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	$0.595762\pi$
$812$	−11.9839	−	0.393133i	−0.420551	−	0.0137963i
$813$	4.18646	+	4.18646i	0.146826	+	0.146826i
$814$	7.02587	+	3.04611i	0.246257	+	0.106766i
$815$		0			0
$816$	3.54448	+	4.04282i	0.124082	+	0.141527i
$817$		−	13.5612i		−	0.474447i
$818$	−16.4093	+	37.8482i	−0.573738	+	1.32333i
$819$	9.54757	−	9.54757i	0.333619	−	0.333619i
$820$		0			0
$821$	−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	$0.927146\pi$
$822$	−0.996763	−	2.52261i	−0.0347661	−	0.0879862i
$823$	43.7323			1.52441			0.762206	−	0.647334i	$-0.224116\pi$
$823$	43.7323			1.52441			0.762206	+	0.647334i	$0.224116\pi$
$824$	4.72869	+	13.2201i	0.164732	+	0.460544i
$825$		0			0
$826$	−8.47850	−	21.4574i	−0.295005	−	0.746599i
$827$	−19.9621	+	19.9621i	−0.694149	+	0.694149i	−0.963142	−	0.268993i	$-0.913309\pi$
$827$	−19.9621	+	19.9621i	−0.694149	+	0.694149i	0.268993	+	0.963142i	$0.413309\pi$
$828$	37.6253	−	35.2351i	1.30757	−	1.22451i
$829$	−31.3869	+	31.3869i	−1.09011	+	1.09011i	−0.0945964	+	0.995516i	$0.530156\pi$
$829$	−31.3869	+	31.3869i	−1.09011	+	1.09011i	−0.995516	+	0.0945964i	$0.969844\pi$
$830$		0			0
$831$	−6.77057			−0.234868
$832$	21.2513	+	2.09749i	0.736758	+	0.0727172i
$833$			18.0637i			0.625869i
$834$	3.87705	−	8.94244i	0.134251	−	0.309651i
$835$		0			0
$836$	4.45012	+	4.75199i	0.153911	+	0.164351i
$837$	−7.06737	+	7.06737i	−0.244284	+	0.244284i
$838$	5.70324	−	2.25353i	0.197015	−	0.0778469i
$839$			54.5335i			1.88271i	0.337423	+	0.941353i	$0.390445\pi$
$839$			54.5335i			1.88271i	−0.337423	+	0.941353i	$0.609555\pi$
$840$		0			0
$841$			17.0871i			0.589210i
$842$	0.391181	+	0.990001i	0.0134810	+	0.0341177i
$843$	−1.97735	+	1.97735i	−0.0681035	+	0.0681035i
$844$	30.4025	+	0.997361i	1.04650	+	0.0343306i
$845$		0			0
$846$	16.3348	+	7.08208i	0.561603	+	0.243487i
$847$			18.2192i			0.626018i
$848$	5.12615	+	5.84688i	0.176033	+	0.200783i
$849$	−3.65193			−0.125334
$850$		0			0
$851$	−47.4092	+	47.4092i	−1.62517	+	1.62517i
$852$	−8.32000	−	0.272939i	−0.285039	−	0.00935075i
$853$	−21.5932	+	21.5932i	−0.739336	+	0.739336i	−0.972449	−	0.233114i	$-0.925109\pi$
$853$	−21.5932	+	21.5932i	−0.739336	+	0.739336i	0.233114	+	0.972449i	$0.425109\pi$
$854$	17.0010	−	6.71765i	0.581764	−	0.229873i
$855$		0			0
$856$	9.93005	+	4.69781i	0.339402	+	0.160568i
$857$	41.3609			1.41286			0.706431	−	0.707782i	$-0.250304\pi$
$857$	41.3609			1.41286			0.706431	+	0.707782i	$0.250304\pi$
$858$	−0.743766	+	0.293885i	−0.0253917	+	0.0100331i
$859$	0.700596	+	0.700596i	0.0239040	+	0.0239040i	0.718958	−	0.695054i	$-0.244619\pi$
$859$	0.700596	+	0.700596i	0.0239040	+	0.0239040i	−0.695054	+	0.718958i	$0.744619\pi$
$860$		0			0
$861$	−3.65265	+	3.65265i	−0.124482	+	0.124482i
$862$	−21.6993	−	9.40787i	−0.739081	−	0.320433i
$863$			55.0780i			1.87488i	0.348150	+	0.937439i	$0.386810\pi$
$863$			55.0780i			1.87488i	−0.348150	+	0.937439i	$0.613190\pi$
$864$	−3.03054	−	9.43751i	−0.103101	−	0.321070i
$865$		0			0
$866$	15.9580	−	36.8072i	0.542276	−	1.25076i
$867$	−0.747840	−	0.747840i	−0.0253980	−	0.0253980i
$868$	13.5446	+	14.4634i	0.459734	+	0.490920i
$869$	−2.15969	−	2.15969i	−0.0732623	−	0.0732623i
$870$		0			0
$871$		−	39.8556i		−	1.35045i
$872$	25.3090	+	11.9734i	0.857070	+	0.405472i
$873$	−5.65335			−0.191337
$874$	−53.0124	+	20.9469i	−1.79317	+	0.708538i
$875$		0			0
$876$	0.129016	−	3.93278i	0.00435904	−	0.132876i
$877$	36.5100	+	36.5100i	1.23285	+	1.23285i	0.962863	+	0.269992i	$0.0870211\pi$
$877$	36.5100	+	36.5100i	1.23285	+	1.23285i	0.269992	+	0.962863i	$0.412979\pi$
$878$	−7.59537	+	17.5188i	−0.256331	+	0.591229i
$879$	4.65435			0.156987
$880$		0			0
$881$	54.3503			1.83111			0.915554	−	0.402196i	$-0.131753\pi$
$881$	54.3503			1.83111			0.915554	+	0.402196i	$0.131753\pi$
$882$	6.52497	−	15.0499i	0.219707	−	0.506755i
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.975274	+	0.220999i	$0.0709319\pi$
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.220999	+	0.975274i	$0.429068\pi$
$884$	−24.1991	−	0.793855i	−0.813902	−	0.0267002i
$885$		0			0
$886$	−17.7681	+	7.02075i	−0.596932	+	0.235867i
$887$	0.817003			0.0274323			0.0137161	−	0.999906i	$-0.495634\pi$
$887$	0.817003			0.0274323			0.0137161	+	0.999906i	$0.495634\pi$
$888$	2.13878	+	5.97944i	0.0717729	+	0.200657i
$889$		−	4.35737i		−	0.146141i
$890$		0			0
$891$	−4.15320	−	4.15320i	−0.139137	−	0.139137i
$892$	5.82051	−	5.45075i	0.194885	−	0.182505i
$893$	−13.9211	−	13.9211i	−0.465851	−	0.465851i
$894$	0.643232	−	1.48362i	0.0215129	−	0.0496196i
$895$		0			0
$896$	−18.8974	+	5.39155i	−0.631319	+	0.180119i
$897$		−	7.00186i		−	0.233785i
$898$	−12.1392	−	5.26302i	−0.405090	−	0.175629i
$899$	−13.9211	+	13.9211i	−0.464296	+	0.464296i
$900$		0			0
$901$	−6.23407	−	6.23407i	−0.207687	−	0.207687i
$902$	−9.43352	+	3.72748i	−0.314102	+	0.124112i
$903$	−1.53298			−0.0510144
$904$	−17.3958	+	6.22230i	−0.578575	+	0.206950i
$905$		0			0
$906$	4.49052	−	1.77434i	0.149187	−	0.0589487i
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	−0.760711	−	0.649091i	$-0.775149\pi$
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	0.649091	+	0.760711i	$0.275149\pi$
$908$	−0.354352	+	10.8017i	−0.0117596	+	0.358467i
$909$	30.1103	−	30.1103i	0.998695	−	0.998695i
$910$		0			0
$911$	34.6568			1.14823			0.574116	−	0.818774i	$-0.305346\pi$
$911$	34.6568			1.14823			0.574116	+	0.818774i	$0.305346\pi$
$912$	−0.353844	+	5.38731i	−0.0117170	+	0.178392i
$913$			9.25426i			0.306271i
$914$	−8.88510	−	3.85219i	−0.293893	−	0.127419i
$915$		0			0
$916$	−0.816725	+	24.8962i	−0.0269853	+	0.822593i
$917$	−14.8646	+	14.8646i	−0.490874	+	0.490874i
$918$	4.12997	+	10.4521i	0.136309	+	0.344972i
$919$		−	24.3452i		−	0.803074i	−0.915843	−	0.401537i	$-0.868476\pi$
$919$		−	24.3452i		−	0.803074i	0.915843	−	0.401537i	$-0.131524\pi$
$920$		0			0
$921$			1.25681i			0.0414135i
$922$	21.8377	−	8.62875i	0.719185	−	0.284173i
$923$	26.5074	−	26.5074i	0.872501	−	0.872501i
$924$	0.537172	−	0.503048i	0.0176717	−	0.0165491i
$925$		0			0
$926$	−14.9691	+	34.5263i	−0.491915	+	1.13460i
$927$			14.4560i			0.474797i
$928$	−5.96948	−	18.5898i	−0.195958	−	0.610238i
$929$	−3.16600			−0.103873			−0.0519366	−	0.998650i	$-0.516539\pi$
$929$	−3.16600			−0.103873			−0.0519366	+	0.998650i	$0.516539\pi$
$930$		0			0
$931$	−12.8260	+	12.8260i	−0.420354	+	0.420354i
$932$	22.6994	+	24.2392i	0.743542	+	0.793981i
$933$	1.89892	−	1.89892i	0.0621680	−	0.0621680i
$934$	1.08469	+	2.74513i	0.0354921	+	0.0898235i
$935$		0			0
$936$	19.8749	+	9.40260i	0.649630	+	0.307334i
$937$	−23.4847			−0.767211			−0.383606	−	0.923497i	$-0.625318\pi$
$937$	−23.4847			−0.767211			−0.383606	+	0.923497i	$0.625318\pi$
$938$	13.4782	+	34.1107i	0.440079	+	1.11375i
$939$	4.10129	+	4.10129i	0.133840	+	0.133840i
$940$		0			0
$941$	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	$0.0289931\pi$
$942$	−0.773412	+	1.78388i	−0.0251991	+	0.0581218i
$943$		−	88.8078i		−	2.89198i
$944$	28.2496	−	24.7674i	0.919446	−	0.806109i
$945$		0			0
$946$	−2.76177	−	1.19738i	−0.0897927	−	0.0389302i
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	0.994220	−	0.107363i	$-0.0342407\pi$
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	−0.107363	+	0.994220i	$0.534241\pi$
$948$	0.0830453	−	2.53147i	0.00269719	−	0.0822183i
$949$	12.5298	+	12.5298i	0.406734	+	0.406734i
$950$		0			0
$951$			4.65329i			0.150893i
$952$	20.9794	−	7.50412i	0.679946	−	0.243210i
$953$	−12.1516			−0.393630			−0.196815	−	0.980441i	$-0.563060\pi$
$953$	−12.1516			−0.393630			−0.196815	+	0.980441i	$0.563060\pi$
$954$	2.94208	+	7.44584i	0.0952535	+	0.241068i
$955$		0			0
$956$	−5.21179	−	5.56534i	−0.168561	−	0.179996i
$957$	0.517031	+	0.517031i	0.0167132	+	0.0167132i
$958$	−3.61488	−	1.56725i	−0.116791	−	0.0506357i
$959$	−11.2404			−0.362972
$960$		0			0
$961$	1.53571			0.0495392
$962$	−26.2377	−	11.3755i	−0.845938	−	0.366762i
$963$	7.99769	+	7.99769i	0.257722	+	0.257722i
$964$	13.0554	+	13.9411i	0.420488	+	0.449012i
$965$		0			0
$966$	2.36786	+	5.99259i	0.0761847	+	0.192809i
$967$	−48.2694			−1.55224			−0.776120	−	0.630585i	$-0.782815\pi$
$967$	−48.2694			−1.55224			−0.776120	+	0.630585i	$0.782815\pi$
$968$	−27.9344	+	9.99184i	−0.897845	+	0.321150i
$969$		−	6.12135i		−	0.196646i
$970$		0			0
$971$	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	$0.707106\pi$
$972$	0.504410	−	15.3759i	0.0161790	−	0.493183i
$973$	−28.5610	−	28.5610i	−0.915623	−	0.915623i
$974$	−21.9927	−	9.53509i	−0.704692	−	0.305524i
$975$		0			0
$976$	19.6236	+	22.3826i	0.628135	+	0.716449i
$977$			27.7522i			0.887872i	0.896059	+	0.443936i	$0.146418\pi$
$977$			27.7522i			0.887872i	−0.896059	+	0.443936i	$0.853582\pi$
$978$	−2.18661	+	5.04342i	−0.0699200	+	0.161271i
$979$	−1.63671	+	1.63671i	−0.0523096	+	0.0523096i
$980$		0			0
$981$	20.3839	+	20.3839i	0.650808	+	0.650808i
$982$	16.7859	+	42.4819i	0.535661	+	1.35565i
$983$	28.3604			0.904556			0.452278	−	0.891877i	$-0.350611\pi$
$983$	28.3604			0.904556			0.452278	+	0.891877i	$0.350611\pi$
$984$	−7.60361	−	3.59719i	−0.242394	−	0.114674i
$985$		0			0
$986$	8.13511	+	20.5884i	0.259075	+	0.655667i
$987$	−1.57366	+	1.57366i	−0.0500901	+	0.0500901i
$988$	−16.6187	−	17.7460i	−0.528711	−	0.564577i
$989$	18.6358	−	18.6358i	0.592585	−	0.592585i
$990$		0			0
$991$	−43.7506			−1.38979			−0.694893	−	0.719114i	$-0.744548\pi$
$991$	−43.7506			−1.38979			−0.694893	+	0.719114i	$0.744548\pi$
$992$	−14.7477	+	28.6993i	−0.468240	+	0.911203i
$993$		−	3.41483i		−	0.108366i
$994$	−13.7224	+	31.6507i	−0.435247	+	1.00390i
$995$		0			0
$996$	−5.60160	+	5.24575i	−0.177493	+	0.166218i
$997$	10.5572	−	10.5572i	0.334349	−	0.334349i	−0.519887	−	0.854235i	$-0.674026\pi$
$997$	10.5572	−	10.5572i	0.334349	−	0.334349i	0.854235	+	0.519887i	$0.174026\pi$
$998$	4.35079	−	1.71913i	0.137722	−	0.0544183i
$999$			13.2741i			0.419974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.h.149.2		16
4.3	odd	2		1600.2.q.g.49.4		16
5.2	odd	4		80.2.l.a.21.6	✓	16
5.3	odd	4		400.2.l.h.101.3		16
5.4	even	2		400.2.q.g.149.7		16
15.2	even	4		720.2.t.c.181.3		16
16.3	odd	4		1600.2.q.h.849.5		16
16.13	even	4		400.2.q.g.349.7		16
20.3	even	4		1600.2.l.i.1201.5		16
20.7	even	4		320.2.l.a.241.4		16
20.19	odd	2		1600.2.q.h.49.5		16
40.27	even	4		640.2.l.a.481.5		16
40.37	odd	4		640.2.l.b.481.4		16
60.47	odd	4		2880.2.t.c.2161.4		16
80.3	even	4		1600.2.l.i.401.5		16
80.13	odd	4		400.2.l.h.301.3		16
80.19	odd	4		1600.2.q.g.849.4		16
80.27	even	4		640.2.l.a.161.5		16
80.29	even	4	inner	400.2.q.h.349.2		16
80.37	odd	4		640.2.l.b.161.4		16
80.67	even	4		320.2.l.a.81.4		16
80.77	odd	4		80.2.l.a.61.6	yes	16
160.67	even	8		5120.2.a.u.1.3		8
160.77	odd	8		5120.2.a.v.1.3		8
160.147	even	8		5120.2.a.t.1.6		8
160.157	odd	8		5120.2.a.s.1.6		8
240.77	even	4		720.2.t.c.541.3		16
240.227	odd	4		2880.2.t.c.721.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.6	✓	16	5.2	odd	4
80.2.l.a.61.6	yes	16	80.77	odd	4
320.2.l.a.81.4		16	80.67	even	4
320.2.l.a.241.4		16	20.7	even	4
400.2.l.h.101.3		16	5.3	odd	4
400.2.l.h.301.3		16	80.13	odd	4
400.2.q.g.149.7		16	5.4	even	2
400.2.q.g.349.7		16	16.13	even	4
400.2.q.h.149.2		16	1.1	even	1	trivial
400.2.q.h.349.2		16	80.29	even	4	inner
640.2.l.a.161.5		16	80.27	even	4
640.2.l.a.481.5		16	40.27	even	4
640.2.l.b.161.4		16	80.37	odd	4
640.2.l.b.481.4		16	40.37	odd	4
720.2.t.c.181.3		16	15.2	even	4
720.2.t.c.541.3		16	240.77	even	4
1600.2.l.i.401.5		16	80.3	even	4
1600.2.l.i.1201.5		16	20.3	even	4
1600.2.q.g.49.4		16	4.3	odd	2
1600.2.q.g.849.4		16	80.19	odd	4
1600.2.q.h.49.5		16	20.19	odd	2
1600.2.q.h.849.5		16	16.3	odd	4
2880.2.t.c.721.1		16	240.227	odd	4
2880.2.t.c.2161.4		16	60.47	odd	4
5120.2.a.s.1.6		8	160.157	odd	8
5120.2.a.t.1.6		8	160.147	even	8
5120.2.a.u.1.3		8	160.67	even	8
5120.2.a.v.1.3		8	160.77	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29751 - 0.562546i) q^{2} +(0.209571 + 0.209571i) q^{3} +(1.36708 + 1.45982i) q^{4} +(-0.154028 - 0.389815i) q^{6} -1.73696 q^{7} +(-0.952595 - 2.66319i) q^{8} -2.91216i q^{9} +(0.505430 + 0.505430i) q^{11} +(-0.0194351 + 0.592438i) q^{12} +(-1.88750 - 1.88750i) q^{13} +(2.25374 + 0.977122i) q^{14} +(-0.262159 + 3.99140i) q^{16} -4.53524i q^{17} +(-1.63822 + 3.77857i) q^{18} +(3.22022 - 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +(-0.371475 - 0.940130i) q^{22} +8.85045 q^{23} +(0.358491 - 0.757764i) q^{24} +(1.38725 + 3.51086i) q^{26} +(1.23902 - 1.23902i) q^{27} +(-2.37458 - 2.53566i) q^{28} +(2.44059 - 2.44059i) q^{29} -5.70401 q^{31} +(2.58550 - 5.03142i) q^{32} +0.211847i q^{33} +(-2.55128 + 5.88454i) q^{34} +(4.25123 - 3.98117i) q^{36} +(-5.35670 + 5.35670i) q^{37} +(-5.98979 + 2.36676i) q^{38} -0.791130i q^{39} -10.0343i q^{41} +(0.267541 + 0.677095i) q^{42} +(2.10564 - 2.10564i) q^{43} +(-0.0468722 + 1.42880i) q^{44} +(-11.4836 - 4.97878i) q^{46} -4.32303i q^{47} +(-0.891424 + 0.781541i) q^{48} -3.98295 q^{49} +(0.950456 - 0.950456i) q^{51} +(0.175041 - 5.33578i) q^{52} +(1.37458 - 1.37458i) q^{53} +(-2.30465 + 0.910639i) q^{54} +(1.65462 + 4.62586i) q^{56} +1.34973 q^{57} +(-4.53964 + 1.79375i) q^{58} +(-6.64140 - 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +(7.40103 + 3.20877i) q^{62} +5.05832i q^{63} +(-6.18513 + 5.07388i) q^{64} +(0.119174 - 0.274875i) q^{66} +(10.5578 + 10.5578i) q^{67} +(6.62065 - 6.20006i) q^{68} +(1.85480 + 1.85480i) q^{69} +14.0437i q^{71} +(-7.75563 + 2.77411i) q^{72} -6.63830 q^{73} +(9.96378 - 3.93700i) q^{74} +(9.10325 + 0.298634i) q^{76} +(-0.877914 - 0.877914i) q^{77} +(-0.445047 + 1.02650i) q^{78} -4.27297 q^{79} -8.21715 q^{81} +(-5.64474 + 13.0196i) q^{82} +(9.15483 + 9.15483i) q^{83} +(0.0337580 - 1.02904i) q^{84} +(-3.91661 + 1.54758i) q^{86} +1.02295 q^{87} +(0.864585 - 1.82752i) q^{88} +3.23826i q^{89} +(3.27852 + 3.27852i) q^{91} +(12.0993 + 12.9201i) q^{92} +(-1.19540 - 1.19540i) q^{93} +(-2.43190 + 5.60919i) q^{94} +(1.59629 - 0.512594i) q^{96} -1.94129i q^{97} +(5.16794 + 2.24059i) q^{98} +(1.47189 - 1.47189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 4 q^{4} - 12 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} - 4 q^{14} + 16 q^{16} + 12 q^{18} + 8 q^{19} - 20 q^{22} + 24 q^{23} - 8 q^{24} - 16 q^{26} + 24 q^{27} + 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^4 - 12 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 - 4 * q^14 + 16 * q^16 + 12 * q^18 + 8 * q^19 - 20 * q^22 + 24 * q^23 - 8 * q^24 - 16 * q^26 + 24 * q^27 + 20 * q^28 + 16 * q^29 + 24 * q^32 - 16 * q^34 - 4 * q^36 - 16 * q^37 - 20 * q^38 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 - 16 * q^52 - 16 * q^53 - 32 * q^54 + 16 * q^56 - 28 * q^58 + 8 * q^59 + 16 * q^61 + 48 * q^62 + 16 * q^64 - 40 * q^67 - 8 * q^68 - 16 * q^69 - 96 * q^72 + 72 * q^74 - 16 * q^77 + 24 * q^78 - 16 * q^79 - 16 * q^81 + 44 * q^82 + 40 * q^83 + 64 * q^84 + 28 * q^86 - 16 * q^88 + 32 * q^91 + 20 * q^92 - 48 * q^93 + 36 * q^94 + 8 * q^96 - 32 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more