LMFDB - Embedded newform 400.2.l.h.101.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(101,400)] 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("400.101"); 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, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == 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			101.3
Root			$-0.966675 - 1.03225i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.h.301.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.562546 + 1.29751i) q^{2} +(-0.209571 + 0.209571i) q^{3} +(-1.36708 - 1.45982i) q^{4} +(-0.154028 - 0.389815i) q^{6} +1.73696i q^{7} +(2.66319 - 0.952595i) q^{8} +2.91216i q^{9} +(0.505430 + 0.505430i) q^{11} +(0.592438 + 0.0194351i) q^{12} +(1.88750 - 1.88750i) q^{13} +(-2.25374 - 0.977122i) q^{14} +(-0.262159 + 3.99140i) q^{16} -4.53524 q^{17} +(-3.77857 - 1.63822i) q^{18} +(-3.22022 + 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +(-0.940130 + 0.371475i) q^{22} +8.85045i q^{23} +(-0.358491 + 0.757764i) q^{24} +(1.38725 + 3.51086i) q^{26} +(-1.23902 - 1.23902i) q^{27} +(2.53566 - 2.37458i) q^{28} +(-2.44059 + 2.44059i) q^{29} -5.70401 q^{31} +(-5.03142 - 2.58550i) q^{32} -0.211847 q^{33} +(2.55128 - 5.88454i) q^{34} +(4.25123 - 3.98117i) q^{36} +(5.35670 + 5.35670i) q^{37} +(-2.36676 - 5.98979i) q^{38} +0.791130i q^{39} -10.0343i q^{41} +(0.677095 - 0.267541i) q^{42} +(2.10564 + 2.10564i) q^{43} +(0.0468722 - 1.42880i) q^{44} +(-11.4836 - 4.97878i) q^{46} -4.32303 q^{47} +(-0.781541 - 0.891424i) q^{48} +3.98295 q^{49} +(0.950456 - 0.950456i) q^{51} +(-5.33578 - 0.175041i) q^{52} +(1.37458 + 1.37458i) q^{53} +(2.30465 - 0.910639i) q^{54} +(1.65462 + 4.62586i) q^{56} -1.34973i q^{57} +(-1.79375 - 4.53964i) q^{58} +(6.64140 + 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +(3.20877 - 7.40103i) q^{62} -5.05832 q^{63} +(6.18513 - 5.07388i) q^{64} +(0.119174 - 0.274875i) q^{66} +(10.5578 - 10.5578i) q^{67} +(6.20006 + 6.62065i) q^{68} +(-1.85480 - 1.85480i) q^{69} +14.0437i q^{71} +(2.77411 + 7.75563i) q^{72} -6.63830i q^{73} +(-9.96378 + 3.93700i) q^{74} +(9.10325 + 0.298634i) q^{76} +(-0.877914 + 0.877914i) q^{77} +(-1.02650 - 0.445047i) q^{78} +4.27297 q^{79} -8.21715 q^{81} +(13.0196 + 5.64474i) q^{82} +(-9.15483 + 9.15483i) q^{83} +(-0.0337580 + 1.02904i) q^{84} +(-3.91661 + 1.54758i) q^{86} -1.02295i q^{87} +(1.82752 + 0.864585i) q^{88} -3.23826i q^{89} +(3.27852 + 3.27852i) q^{91} +(12.9201 - 12.0993i) q^{92} +(1.19540 - 1.19540i) q^{93} +(2.43190 - 5.60919i) q^{94} +(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} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 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}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 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 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * 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 $

$2$	−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	−0.765012	−	0.644016i	$-0.777267\pi$
$3$	−0.209571	+	0.209571i	−0.120996	+	0.120996i	0.644016	+	0.765012i	$0.277267\pi$
$4$	−1.36708	−	1.45982i	−0.683542	−	0.729911i
$5$		0			0
$5$		0			0
$6$	−0.154028	−	0.389815i	−0.0628817	−	0.159141i
$7$			1.73696i			0.656511i	0.944589	+	0.328255i	$0.106461\pi$
$7$			1.73696i			0.656511i	−0.944589	+	0.328255i	$0.893539\pi$
$8$	2.66319	−	0.952595i	0.941579	−	0.336793i
$9$			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	$0.715633\pi$
$12$	0.592438	+	0.0194351i	0.171022	+	0.00561042i
$13$	1.88750	−	1.88750i	0.523498	−	0.523498i	−0.395128	−	0.918626i	$-0.629300\pi$
$13$	1.88750	−	1.88750i	0.523498	−	0.523498i	0.918626	+	0.395128i	$0.129300\pi$
$14$	−2.25374	−	0.977122i	−0.602336	−	0.261147i
$15$		0			0
$16$	−0.262159	+	3.99140i	−0.0655399	+	0.997850i
$17$	−4.53524			−1.09996			−0.549979	−	0.835178i	$-0.685364\pi$
$17$	−4.53524			−1.09996			−0.549979	+	0.835178i	$0.685364\pi$
$18$	−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			0
$21$	−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	$0.374042\pi$
$23$			8.85045i			1.84545i	−0.385463	+	0.922723i	$0.625958\pi$
$24$	−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
$28$	2.53566	−	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			0
$31$	−5.70401			−1.02447			−0.512235	−	0.858845i	$-0.671182\pi$
$31$	−5.70401			−1.02447			−0.512235	+	0.858845i	$0.671182\pi$
$32$	−5.03142	−	2.58550i	−0.889438	−	0.457056i
$33$	−0.211847			−0.0368779
$34$	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	$-0.0360342\pi$
$37$	5.35670	+	5.35670i	0.880636	+	0.880636i	−0.112963	+	0.993599i	$0.536034\pi$
$38$	−2.36676	−	5.98979i	−0.383939	−	0.971673i
$39$			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	$-0.286591\pi$
$42$	0.677095	−	0.267541i	0.104478	−	0.0412825i
$43$	2.10564	+	2.10564i	0.321107	+	0.321107i	0.849192	−	0.528085i	$-0.177090\pi$
$43$	2.10564	+	2.10564i	0.321107	+	0.321107i	−0.528085	+	0.849192i	$0.677090\pi$
$44$	0.0468722	−	1.42880i	0.00706625	−	0.215400i
$45$		0			0
$46$	−11.4836	−	4.97878i	−1.69316	−	0.734082i
$47$	−4.32303			−0.630578			−0.315289	−	0.948996i	$-0.602101\pi$
$47$	−4.32303			−0.630578			−0.315289	+	0.948996i	$0.602101\pi$
$48$	−0.781541	−	0.891424i	−0.112806	−	0.128666i
$49$	3.98295			0.568993
$50$		0			0
$51$	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	0.795183	−	0.606369i	$-0.207375\pi$
$53$	1.37458	+	1.37458i	0.188814	+	0.188814i	−0.606369	+	0.795183i	$0.707375\pi$
$54$	2.30465	−	0.910639i	0.313623	−	0.123922i
$55$		0			0
$56$	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			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	$0.0919391\pi$
$62$	3.20877	−	7.40103i	0.407514	−	0.939932i
$63$	−5.05832			−0.637288
$64$	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	0.354954	−	0.934884i	$-0.384497\pi$
$67$	10.5578	−	10.5578i	1.28984	−	1.28984i	0.934884	−	0.354954i	$-0.115503\pi$
$68$	6.20006	+	6.62065i	0.751868	+	0.802871i
$69$	−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	$0.686427\pi$
$72$	2.77411	+	7.75563i	0.326932	+	0.914009i
$73$		−	6.63830i		−	0.776954i	−0.921458	−	0.388477i	$-0.873001\pi$
$73$		−	6.63830i		−	0.776954i	0.921458	−	0.388477i	$-0.126999\pi$
$74$	−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
$78$	−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	$0.422730\pi$
$80$		0			0
$81$	−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	$0.501555\pi$
$83$	−9.15483	+	9.15483i	−1.00487	+	1.00487i	−0.999988	+	0.00488547i	$0.998445\pi$
$84$	−0.0337580	+	1.02904i	−0.00368330	+	0.112278i
$85$		0			0
$86$	−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	$-0.0549025\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	1.59629	−	0.512594i	0.162920	−	0.0523164i
$97$	−1.94129			−0.197108			−0.0985541	−	0.995132i	$-0.531422\pi$
$97$	−1.94129			−0.197108			−0.0985541	+	0.995132i	$0.531422\pi$
$98$	−2.24059	+	5.16794i	−0.226334	+	0.522041i
$99$	−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	$0.490689\pi$
$102$	0.698555	+	1.76791i	0.0691673	+	0.175049i
$103$		−	4.96401i		−	0.489118i	−0.969634	−	0.244559i	$-0.921357\pi$
$103$		−	4.96401i		−	0.489118i	0.969634	−	0.244559i	$-0.0786433\pi$
$104$	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	$-0.189886\pi$
$107$	2.74631	+	2.74631i	0.265496	+	0.265496i	−0.561787	+	0.827282i	$0.689886\pi$
$108$	−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			0
$111$	−2.24522			−0.213107
$112$	−6.93292	−	0.455362i	−0.655099	−	0.0430276i
$113$	6.53194			0.614474			0.307237	−	0.951633i	$-0.400596\pi$
$113$	6.53194			0.614474			0.307237	+	0.951633i	$0.400596\pi$
$114$	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
$118$	−12.3534	+	4.88122i	−1.13722	+	0.449353i
$119$		−	7.87756i		−	0.722134i
$120$		0			0
$121$		−	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			0
$126$	2.84554	−	6.56324i	0.253500	−	0.584700i
$127$	2.50861			0.222603			0.111302	−	0.993787i	$-0.464498\pi$
$127$	2.50861			0.222603			0.111302	+	0.993787i	$0.464498\pi$
$128$	3.10401	+	10.8796i	0.274358	+	0.961628i
$129$	−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	$0.0726780\pi$
$132$	0.289613	+	0.309259i	0.0252076	+	0.0269176i
$133$	−5.59340	−	5.59340i	−0.485009	−	0.485009i
$134$	7.75963	+	19.6381i	0.670330	+	1.69647i
$135$		0			0
$136$	−12.0782	+	4.32025i	−1.03570	+	0.370458i
$137$		−	6.47131i		−	0.552881i	−0.961031	−	0.276440i	$-0.910845\pi$
$137$		−	6.47131i		−	0.552881i	0.961031	−	0.276440i	$-0.0891549\pi$
$138$	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	$-0.697035\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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			0
$151$			11.5196i			0.937453i	0.883343	+	0.468726i	$0.155287\pi$
$151$			11.5196i			0.937453i	−0.883343	+	0.468726i	$0.844713\pi$
$152$	−5.50848	+	11.6436i	−0.446796	+	0.944420i
$153$		−	13.2074i		−	1.06775i
$154$	−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	−0.825778	−	0.563995i	$-0.809264\pi$
$157$	−3.28013	+	3.28013i	−0.261783	+	0.261783i	0.563995	+	0.825778i	$0.309264\pi$
$158$	−2.40374	+	5.54423i	−0.191231	+	0.441076i
$159$	−0.576147			−0.0456914
$160$		0			0
$161$	−15.3729			−1.21156
$162$	4.62253	−	10.6619i	0.363180	−	0.837676i
$163$	9.27367	−	9.27367i	0.726370	−	0.726370i	−0.243525	−	0.969895i	$-0.578304\pi$
$163$	9.27367	−	9.27367i	0.726370	−	0.726370i	0.969895	+	0.243525i	$0.0783037\pi$
$164$	−14.6482	+	13.7177i	−1.14384	+	1.07117i
$165$		0			0
$166$	−6.72851	−	17.0285i	−0.522234	−	1.32167i
$167$			7.08065i			0.547917i	0.961742	+	0.273958i	$0.0883331\pi$
$167$			7.08065i			0.547917i	−0.961742	+	0.273958i	$0.911667\pi$
$168$	−1.31621	−	0.622686i	−0.101548	−	0.0480413i
$169$			5.87470i			0.451900i
$170$		0			0
$171$	−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	−0.480518	−	0.876985i	$-0.659551\pi$
$173$	5.21471	−	5.21471i	0.396467	−	0.396467i	0.876985	+	0.480518i	$0.159551\pi$
$174$	1.32730	+	0.575458i	0.100622	+	0.0436254i
$175$		0			0
$176$	−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	$0.141559\pi$
$180$		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	$0.508963\pi$
$182$	−6.09824	+	2.40961i	−0.452031	+	0.178612i
$183$			2.20556i			0.163040i
$184$	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
$188$	5.90994	+	6.31085i	0.431027	+	0.460266i
$189$	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	$0.796318\pi$
$192$	−0.232886	+	2.35956i	−0.0168071	+	0.170287i
$193$	−7.97695			−0.574193			−0.287097	−	0.957902i	$-0.592690\pi$
$193$	−7.97695			−0.574193			−0.287097	+	0.957902i	$0.592690\pi$
$194$	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	$-0.343772\pi$
$197$	−5.76327	−	5.76327i	−0.410616	−	0.410616i	−0.881953	+	0.471337i	$0.843772\pi$
$198$	−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			0
$201$			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
$205$		0			0
$206$	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			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	$0.0746147\pi$
$212$	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
$215$		0			0
$216$	−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
$220$		0			0
$221$	−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	$-0.457379\pi$
$223$	3.98714			0.266998			0.133499	+	0.991049i	$0.457379\pi$
$224$	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	−0.568839	−	0.822449i	$-0.692607\pi$
$227$	3.82103	−	3.82103i	0.253611	−	0.253611i	0.822449	+	0.568839i	$0.192607\pi$
$228$	−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	$0.885001\pi$
$230$		0			0
$231$		−	0.367971i		−	0.0242107i
$232$	−4.17485	+	8.82463i	−0.274092	+	0.579365i
$233$			16.6042i			1.08778i	0.839157	+	0.543889i	$0.183049\pi$
$233$			16.6042i			1.08778i	−0.839157	+	0.543889i	$0.816951\pi$
$234$	−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
$238$	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			0
$241$	9.54985			0.615160			0.307580	−	0.951522i	$-0.400481\pi$
$241$	9.54985			0.615160			0.307580	+	0.951522i	$0.400481\pi$
$242$	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
$245$		0			0
$246$	−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			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	$0.570203\pi$
$252$	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
$255$		0			0
$256$	−15.8625	−	2.09277i	−0.991409	−	0.130798i
$257$	−18.8752			−1.17740			−0.588702	−	0.808350i	$-0.700361\pi$
$257$	−18.8752			−1.17740			−0.588702	+	0.808350i	$0.700361\pi$
$258$	0.496482	−	1.14514i	0.0309096	−	0.0712931i
$259$	−9.30440	+	9.30440i	−0.578147	+	0.578147i
$260$		0			0
$261$	−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	$-0.747141\pi$
$263$		−	23.1398i		−	1.42686i	0.700727	−	0.713429i	$-0.252859\pi$
$264$	−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
$268$	−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	$0.401644\pi$
$270$		0			0
$271$	19.9763			1.21348			0.606738	−	0.794902i	$-0.292478\pi$
$271$	19.9763			1.21348			0.606738	+	0.794902i	$0.292478\pi$
$272$	1.18896	−	18.1020i	0.0720911	−	1.09759i
$273$	−1.37417			−0.0831683
$274$	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	$-0.00923738\pi$
$277$	16.1534	+	16.1534i	0.970563	+	0.970563i	−0.0290160	+	0.999579i	$0.509237\pi$
$278$	30.5850	−	12.0851i	1.83437	−	0.724817i
$279$		−	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	$0.909192\pi$
$282$	0.665868	+	1.68518i	0.0396518	+	0.100351i
$283$	−8.71287	−	8.71287i	−0.517926	−	0.517926i	0.399017	−	0.916943i	$-0.369351\pi$
$283$	−8.71287	−	8.71287i	−0.517926	−	0.517926i	−0.916943	+	0.399017i	$0.869351\pi$
$284$	20.5012	−	19.1989i	1.21653	−	1.13924i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	0.952686	−	0.303957i	$-0.0983079\pi$
$293$	11.1045	+	11.1045i	0.648729	+	0.648729i	−0.303957	+	0.952686i	$0.598308\pi$
$294$	−0.613487	−	1.55261i	−0.0357793	−	0.0905503i
$295$		0			0
$296$	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			0
$301$	−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
$305$		0			0
$306$	17.1367	+	7.42974i	0.979641	+	0.424730i
$307$	2.99854	−	2.99854i	0.171136	−	0.171136i	−0.616343	−	0.787478i	$-0.711386\pi$
$307$	2.99854	−	2.99854i	0.171136	−	0.171136i	0.787478	+	0.616343i	$0.211386\pi$
$308$	2.48178	+	0.0814153i	0.141413	+	0.00463907i
$309$	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	$-0.0827014\pi$
$312$	0.753627	+	2.10693i	0.0426657	+	0.119281i
$313$			19.5699i			1.10616i	0.833129	+	0.553078i	$0.186547\pi$
$313$			19.5699i			1.10616i	−0.833129	+	0.553078i	$0.813453\pi$
$314$	−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	−0.322890	−	0.946436i	$-0.604654\pi$
$317$	11.1019	−	11.1019i	0.623546	−	0.623546i	0.946436	+	0.322890i	$0.104654\pi$
$318$	0.324109	−	0.747558i	0.0181751	−	0.0419210i
$319$	−2.46709			−0.138131
$320$		0			0
$321$	−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
$325$		0			0
$326$	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			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	$0.852558\pi$
$332$	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
$335$		0			0
$336$	1.54837	−	1.35751i	0.0844706	−	0.0740582i
$337$	25.1380			1.36935			0.684677	−	0.728847i	$-0.259943\pi$
$337$	25.1380			1.36935			0.684677	+	0.728847i	$0.259943\pi$
$338$	−7.62251	−	3.30479i	−0.414610	−	0.179757i
$339$	−1.36891	+	1.36891i	−0.0743488	+	0.0743488i
$340$		0			0
$341$	−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
$345$		0			0
$346$	3.83265	+	9.69967i	0.206044	+	0.521458i
$347$	−7.36719	−	7.36719i	−0.395491	−	0.395491i	0.481148	−	0.876639i	$-0.340220\pi$
$347$	−7.36719	−	7.36719i	−0.395491	−	0.395491i	−0.876639	+	0.481148i	$0.840220\pi$
$348$	−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			0
$351$	−4.67729			−0.249655
$352$	−1.23624	−	3.84982i	−0.0658919	−	0.205196i
$353$	−0.502832			−0.0267630			−0.0133815	−	0.999910i	$-0.504260\pi$
$353$	−0.502832			−0.0267630			−0.0133815	+	0.999910i	$0.504260\pi$
$354$	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
$358$	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	$0.949799\pi$
$360$		0			0
$361$		−	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
$365$		0			0
$366$	−2.86175	−	1.24073i	−0.149586	−	0.0648540i
$367$	−1.95365			−0.101980			−0.0509898	−	0.998699i	$-0.516238\pi$
$367$	−1.95365			−0.101980			−0.0509898	+	0.998699i	$0.516238\pi$
$368$	−35.3257	−	2.32023i	−1.84148	−	0.120950i
$369$	29.2214			1.52121
$370$		0			0
$371$	−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	0.999431	−	0.0337233i	$-0.0107365\pi$
$373$	18.6509	+	18.6509i	0.965708	+	0.965708i	−0.0337233	+	0.999431i	$0.510736\pi$
$374$	4.26372	−	1.68473i	0.220472	−	0.0871153i
$375$		0			0
$376$	−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	$0.794675\pi$
$380$		0			0
$381$	−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	$-0.518655\pi$
$383$	−2.29258			−0.117145			−0.0585726	+	0.998283i	$0.518655\pi$
$384$	−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
$388$	2.65391	+	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			0
$391$		−	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
$395$		0			0
$396$	4.16090	+	0.136499i	0.209093	+	0.00685935i
$397$	10.8616	−	10.8616i	0.545126	−	0.545126i	−0.379901	−	0.925027i	$-0.624042\pi$
$397$	10.8616	−	10.8616i	0.545126	−	0.545126i	0.925027	+	0.379901i	$0.124042\pi$
$398$	−6.99190	−	3.03138i	−0.350472	−	0.151950i
$399$	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	$0.556793\pi$
$402$	−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
$405$		0			0
$406$	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	$0.743602\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−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			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	$0.755839\pi$
$422$	7.90436	+	20.0044i	0.384778	+	0.973798i
$423$		−	12.5893i		−	0.612115i
$424$	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
$428$	0.254685	−	7.76356i	0.0123107	−	0.375266i
$429$	−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	$0.368045\pi$
$432$	5.27024	−	4.62060i	0.253564	−	0.222309i
$433$	−28.3675			−1.36326			−0.681628	−	0.731699i	$-0.738728\pi$
$433$	−28.3675			−1.36326			−0.681628	+	0.731699i	$0.738728\pi$
$434$	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
$438$	−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			0
$441$			11.5990i			0.552333i
$442$	−6.29152	−	15.9226i	−0.299257	−	0.757361i
$443$	9.55246	+	9.55246i	0.453851	+	0.453851i	0.896630	−	0.442780i	$-0.146008\pi$
$443$	9.55246	+	9.55246i	0.453851	+	0.453851i	−0.442780	+	0.896630i	$0.646008\pi$
$444$	3.06941	+	3.27762i	0.145668	+	0.155549i
$445$		0			0
$446$	−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	$0.570854\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	−1.28574	−	3.59458i	−0.0602105	−	0.168332i
$457$		−	6.84779i		−	0.320326i	−0.987091	−	0.160163i	$-0.948798\pi$
$457$		−	6.84779i		−	0.320326i	0.987091	−	0.160163i	$-0.0512020\pi$
$458$	16.3813	−	6.47277i	0.765448	−	0.302453i
$459$	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	$0.376367\pi$
$462$	0.477448	+	0.207001i	0.0222129	+	0.00963054i
$463$	26.6096			1.23665			0.618326	−	0.785922i	$-0.287811\pi$
$463$	26.6096			1.23665			0.618326	+	0.785922i	$0.287811\pi$
$464$	−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	−0.740428	−	0.672135i	$-0.765377\pi$
$467$	−1.47583	+	1.47583i	−0.0682933	+	0.0682933i	0.672135	+	0.740428i	$0.265377\pi$
$468$	0.509748	−	15.5386i	0.0235631	−	0.718274i
$469$	18.3385	+	18.3385i	0.846792	+	0.846792i
$470$		0			0
$471$		−	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
$475$		0			0
$476$	−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	$0.520273\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	3.99759	+	10.1171i	0.181334	+	0.458922i
$487$		−	16.9499i		−	0.768073i	−0.923318	−	0.384036i	$-0.874534\pi$
$487$		−	16.9499i		−	0.768073i	0.923318	−	0.384036i	$-0.125466\pi$
$488$	9.00128	−	19.0265i	0.407469	−	0.861291i
$489$			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	$-0.509932\pi$
$492$	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
$495$		0			0
$496$	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	$0.226410\pi$
$500$		0			0
$501$	−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	$0.0112714\pi$
$503$			1.58801i			0.0708057i	−0.999373	+	0.0354029i	$0.988729\pi$
$504$	−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
$508$	−3.42948	−	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			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$			8.93031i			0.391244i	0.980679	+	0.195622i	$0.0626725\pi$
$521$			8.93031i			0.391244i	−0.980679	+	0.195622i	$0.937327\pi$
$522$	13.2201	−	5.22370i	0.578630	−	0.228635i
$523$	−15.0355	−	15.0355i	−0.657455	−	0.657455i	0.297323	−	0.954777i	$-0.403906\pi$
$523$	−15.0355	−	15.0355i	−0.657455	−	0.657455i	−0.954777	+	0.297323i	$0.903906\pi$
$524$	−24.1922	−	0.793629i	−1.05684	−	0.0346699i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		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	$0.195781\pi$
$542$	−11.2376	+	25.9196i	−0.482696	+	1.11334i
$543$	−5.47798			−0.235083
$544$	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	−0.617136	+	0.786856i	$0.711707\pi$
$547$	−32.8366	+	32.8366i	−1.40399	+	1.40399i	−0.786856	+	0.617136i	$0.788293\pi$
$548$	−9.44695	+	8.84682i	−0.403554	+	0.377918i
$549$	15.3240	+	15.3240i	0.654013	+	0.654013i
$550$		0			0
$551$		−	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
$555$		0			0
$556$	−1.52488	+	46.4829i	−0.0646694	+	1.97132i
$557$	−24.2077	+	24.2077i	−1.02571	+	1.02571i	−0.0260537	+	0.999661i	$0.508294\pi$
$557$	−24.2077	+	24.2077i	−1.02571	+	1.02571i	−0.999661	+	0.0260537i	$0.991706\pi$
$558$	21.5530	+	9.34444i	0.912411	+	0.395582i
$559$	7.94877			0.336197
$560$		0			0
$561$	0.960778			0.0405641
$562$	−12.2423	−	5.30773i	−0.516411	−	0.223893i
$563$	−22.3407	+	22.3407i	−0.941547	+	0.941547i	−0.998384	−	0.0568365i	$-0.981899\pi$
$563$	−22.3407	+	22.3407i	−0.941547	+	0.941547i	0.0568365	+	0.998384i	$0.481899\pi$
$564$	−2.56113	−	0.0840182i	−0.107843	−	0.00353781i
$565$		0			0
$566$	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			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	$0.498695\pi$
$572$	−2.60839	−	2.78534i	−0.109062	−	0.116461i
$573$	4.64666	−	4.64666i	0.194117	−	0.194117i
$574$	−9.80471	+	22.6146i	−0.409241	+	0.943915i
$575$		0			0
$576$	14.7759	+	18.0121i	0.615664	+	0.750503i
$577$	31.9232			1.32898			0.664490	−	0.747297i	$-0.268649\pi$
$577$	31.9232			1.32898			0.664490	+	0.747297i	$0.268649\pi$
$578$	−2.00740	+	4.63009i	−0.0834970	+	0.192586i
$579$	1.67174	−	1.67174i	0.0694751	−	0.0694751i
$580$		0			0
$581$	−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
$585$		0			0
$586$	−20.6549	+	8.16142i	−0.853248	+	0.337145i
$587$	26.2847	+	26.2847i	1.08488	+	1.08488i	0.996046	+	0.0888379i	$0.0283153\pi$
$587$	26.2847	+	26.2847i	1.08488	+	1.08488i	0.0888379	+	0.996046i	$0.471685\pi$
$588$	2.35965	+	0.0774089i	0.0973105	+	0.00319229i
$589$	18.3681	−	18.3681i	0.756846	−	0.756846i
$590$		0			0
$591$	2.41563			0.0993658
$592$	−22.7850	+	19.9764i	−0.936459	+	0.821026i
$593$	38.2085			1.56904			0.784518	−	0.620106i	$-0.212910\pi$
$593$	38.2085			1.56904			0.784518	+	0.620106i	$0.212910\pi$
$594$	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
$598$	−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			0
$601$			22.2022i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$601$			22.2022i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$602$	−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
$605$		0			0
$606$	2.43792	−	5.62307i	0.0990336	−	0.228421i
$607$	−12.9648			−0.526226			−0.263113	−	0.964765i	$-0.584749\pi$
$607$	−12.9648			−0.526226			−0.263113	+	0.964765i	$0.584749\pi$
$608$	24.5281	−	7.87639i	0.994747	−	0.319430i
$609$	1.77683			0.0720009
$610$		0			0
$611$	−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	0.541004	−	0.841020i	$-0.318044\pi$
$613$	−7.42804	−	7.42804i	−0.300016	−	0.300016i	−0.841020	+	0.541004i	$0.818044\pi$
$614$	2.20383	+	5.57746i	0.0889394	+	0.225088i
$615$		0			0
$616$	−1.50175	+	3.17435i	−0.0605074	+	0.127898i
$617$			23.2743i			0.936989i	0.883467	+	0.468494i	$0.155203\pi$
$617$			23.2743i			0.936989i	−0.883467	+	0.468494i	$0.844797\pi$
$618$	−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			0
$621$	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
$625$		0			0
$626$	−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
$630$		0			0
$631$			29.9258i			1.19133i	0.803234	+	0.595663i	$0.203111\pi$
$631$			29.9258i			1.19133i	−0.803234	+	0.595663i	$0.796889\pi$
$632$	11.3797	−	4.07041i	0.452661	−	0.161912i
$633$			4.50775i			0.179167i
$634$	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
$638$	1.38785	−	3.20109i	0.0549456	−	0.126732i
$639$	−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	$0.435284\pi$
$642$	0.647543	−	1.49356i	0.0255565	−	0.0589461i
$643$	13.7202	−	13.7202i	0.541074	−	0.541074i	−0.382770	−	0.923844i	$-0.625030\pi$
$643$	13.7202	−	13.7202i	0.541074	−	0.541074i	0.923844	+	0.382770i	$0.125030\pi$
$644$	21.0161	+	22.4417i	0.828150	+	0.884328i
$645$		0			0
$646$	10.7338	+	27.1652i	0.422316	+	1.06880i
$647$		−	18.6767i		−	0.734255i	−0.930171	−	0.367128i	$-0.880341\pi$
$647$		−	18.6767i		−	0.734255i	0.930171	−	0.367128i	$-0.119659\pi$
$648$	−21.8838	+	7.82762i	−0.859677	+	0.307498i
$649$			6.71353i			0.263529i
$650$		0			0
$651$	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	−0.911639	−	0.410992i	$-0.865183\pi$
$653$	−12.7935	+	12.7935i	−0.500647	+	0.500647i	0.410992	+	0.911639i	$0.365183\pi$
$654$	−3.80668	−	1.65041i	−0.148853	−	0.0645362i
$655$		0			0
$656$	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			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	$0.979888\pi$
$662$	15.1542	−	5.98792i	0.588987	−	0.232727i
$663$		−	3.58797i		−	0.139345i
$664$	−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
$668$	10.3365	−	9.67984i	0.399931	−	0.374524i
$669$	−0.835589	+	0.835589i	−0.0323057	+	0.0323057i
$670$		0			0
$671$	5.31923			0.205347
$672$	0.890358	+	2.77269i	0.0343463	+	0.106959i
$673$	21.5360			0.830150			0.415075	−	0.909787i	$-0.363755\pi$
$673$	21.5360			0.830150			0.415075	+	0.909787i	$0.363755\pi$
$674$	−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	$-0.366652\pi$
$677$	−13.1852	−	13.1852i	−0.506750	−	0.506750i	−0.913527	+	0.406778i	$0.866652\pi$
$678$	−1.00610	−	2.54625i	−0.0386392	−	0.0977881i
$679$		−	3.37195i		−	0.129404i
$680$		0			0
$681$			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	$-0.939499\pi$
$683$	−30.6011	−	30.6011i	−1.17092	−	1.17092i	−0.188926	−	0.981991i	$-0.560501\pi$
$684$	−0.869670	+	26.5101i	−0.0332527	+	1.01364i
$685$		0			0
$686$	−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
$690$		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	$0.487884\pi$
$692$	−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
$695$		0			0
$696$	−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
$700$		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	$0.0849345\pi$
$702$	2.63119	−	6.06885i	0.0993078	−	0.229054i
$703$	−34.4995			−1.30117
$704$	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
$708$	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	$0.712884\pi$
$710$		0			0
$711$			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
$715$		0			0
$716$	−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	$0.490401\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−4.08880	+	1.61561i	−0.151750	+	0.0599611i
$727$		−	39.3600i		−	1.45978i	−0.683563	−	0.729891i	$-0.739571\pi$
$727$		−	39.3600i		−	1.45978i	0.683563	−	0.729891i	$-0.260429\pi$
$728$	11.8544	+	5.60821i	0.439353	+	0.207854i
$729$		−	22.3717i		−	0.828581i
$730$		0			0
$731$	−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	$-0.400666\pi$
$733$	34.0787	−	34.0787i	1.25873	−	1.25873i	0.951701	−	0.307026i	$-0.0993339\pi$
$734$	1.09902	−	2.53488i	0.0405654	−	0.0935643i
$735$		0			0
$736$	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	$0.118559\pi$
$740$		0			0
$741$	−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	$-0.858135\pi$
$743$		−	23.5004i		−	0.862147i	0.902317	−	0.431074i	$-0.141865\pi$
$744$	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
$748$	−0.212577	+	6.47997i	−0.00777258	+	0.236931i
$749$	−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	$0.436517\pi$
$752$	1.13332	−	17.2549i	0.0413280	−	0.629222i
$753$	−5.02690			−0.183190
$754$	−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	$-0.410918\pi$
$757$	−18.8434	−	18.8434i	−0.684874	−	0.684874i	−0.961094	+	0.276220i	$0.910918\pi$
$758$	7.16389	−	2.83068i	0.260204	−	0.102815i
$759$		−	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	$-0.132343\pi$
$762$	−0.386397	−	0.977894i	−0.0139977	−	0.0354254i
$763$	12.1580	+	12.1580i	0.440151	+	0.440151i
$764$	30.3113	+	32.3675i	1.09663	+	1.17102i
$765$		0			0
$766$	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			0
$771$	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	0.629962	−	0.776626i	$-0.283070\pi$
$773$	−4.07768	−	4.07768i	−0.146664	−	0.146664i	−0.776626	+	0.629962i	$0.783070\pi$
$774$	−4.50679	−	11.4058i	−0.161993	−	0.409973i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−4.65412	−	2.01782i	−0.166007	−	0.0719733i
$787$	8.16669	−	8.16669i	0.291111	−	0.291111i	−0.546408	−	0.837519i	$-0.684005\pi$
$787$	8.16669	−	8.16669i	0.291111	−	0.291111i	0.837519	+	0.546408i	$0.184005\pi$
$788$	−0.534470	+	16.2922i	−0.0190397	+	0.580387i
$789$	4.84943	+	4.84943i	0.172644	+	0.172644i
$790$		0			0
$791$			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			0
$796$	7.86653	−	7.36679i	0.278822	−	0.261109i
$797$	−17.9971	+	17.9971i	−0.637491	+	0.637491i	−0.949936	−	0.312445i	$-0.898852\pi$
$797$	−17.9971	+	17.9971i	−0.637491	+	0.637491i	0.312445	+	0.949936i	$0.398852\pi$
$798$	−1.31885	+	3.04193i	−0.0466868	+	0.107683i
$799$	19.6060			0.693609
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	$-0.264627\pi$
$810$		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	$0.595762\pi$
$812$	−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
$815$		0			0
$816$	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
$820$		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	$0.927146\pi$
$822$	−2.52261	+	0.996763i	−0.0879862	+	0.0347661i
$823$			43.7323i			1.52441i	0.647334	+	0.762206i	$0.275884\pi$
$823$			43.7323i			1.52441i	−0.647334	+	0.762206i	$0.724116\pi$
$824$	−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	$-0.0866908\pi$
$827$	19.9621	+	19.9621i	0.694149	+	0.694149i	−0.268993	+	0.963142i	$0.586691\pi$
$828$	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	$-0.0301561\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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			0
$841$			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
$845$		0			0
$846$	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
$850$		0			0
$851$	−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	0.233114	−	0.972449i	$-0.425109\pi$
$853$	−21.5932	−	21.5932i	−0.739336	−	0.739336i	−0.972449	+	0.233114i	$0.925109\pi$
$854$	−17.0010	+	6.71765i	−0.581764	+	0.229873i
$855$		0			0
$856$	9.93005	+	4.69781i	0.339402	+	0.160568i
$857$		−	41.3609i		−	1.41286i	−0.707782	−	0.706431i	$-0.750304\pi$
$857$		−	41.3609i		−	1.41286i	0.707782	−	0.706431i	$-0.249696\pi$
$858$	−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	$0.755381\pi$
$860$		0			0
$861$	−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	$-0.886810\pi$
$863$	−55.0780			−1.87488			−0.937439	+	0.348150i	$0.886810\pi$
$864$	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
$868$	−14.4634	+	13.5446i	−0.490920	+	0.459734i
$869$	2.15969	+	2.15969i	0.0732623	+	0.0732623i
$870$		0			0
$871$		−	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
$875$		0			0
$876$	0.129016	−	3.93278i	0.00435904	−	0.132876i
$877$	36.5100	−	36.5100i	1.23285	−	1.23285i	0.269992	−	0.962863i	$-0.412979\pi$
$877$	36.5100	−	36.5100i	1.23285	−	1.23285i	0.962863	−	0.269992i	$-0.0870211\pi$
$878$	−17.5188	−	7.59537i	−0.591229	−	0.256331i
$879$	−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	$0.131753\pi$
$882$	−15.0499	−	6.52497i	−0.506755	−	0.219707i
$883$	−35.5476	+	35.5476i	−1.19627	+	1.19627i	−0.220999	+	0.975274i	$0.570932\pi$
$883$	−35.5476	+	35.5476i	−1.19627	+	1.19627i	−0.975274	+	0.220999i	$0.929068\pi$
$884$	24.1991	+	0.793855i	0.813902	+	0.0267002i
$885$		0			0
$886$	−17.7681	+	7.02075i	−0.596932	+	0.235867i
$887$		−	0.817003i		−	0.0274323i	−0.999906	−	0.0137161i	$-0.995634\pi$
$887$		−	0.817003i		−	0.0274323i	0.999906	−	0.0137161i	$-0.00436612\pi$
$888$	−5.97944	+	2.13878i	−0.200657	+	0.0717729i
$889$			4.35737i			0.146141i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$	−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
$905$		0			0
$906$	4.49052	−	1.77434i	0.149187	−	0.0589487i
$907$	3.36159	+	3.36159i	0.111620	+	0.111620i	0.760711	−	0.649091i	$-0.224851\pi$
$907$	3.36159	+	3.36159i	0.111620	+	0.111620i	−0.649091	+	0.760711i	$0.724851\pi$
$908$	−10.8017	−	0.354352i	−0.358467	−	0.0117596i
$909$	−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	$0.305346\pi$
$912$	5.38731	+	0.353844i	0.178392	+	0.0117170i
$913$	−9.25426			−0.306271
$914$	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
$918$	−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	$0.868476\pi$
$920$		0			0
$921$			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
$925$		0			0
$926$	−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			0
$931$	−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
$935$		0			0
$936$	19.8749	+	9.40260i	0.649630	+	0.307334i
$937$			23.4847i			0.767211i	0.923497	+	0.383606i	$0.125318\pi$
$937$			23.4847i			0.767211i	−0.923497	+	0.383606i	$0.874682\pi$
$938$	−34.1107	+	13.4782i	−1.11375	+	0.440079i
$939$	−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	$0.0289931\pi$
$942$	1.78388	+	0.773412i	0.0581218	+	0.0251991i
$943$	88.8078			2.89198
$944$	−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	−0.107363	−	0.994220i	$-0.534241\pi$
$947$	27.2916	−	27.2916i	0.886857	−	0.886857i	0.994220	+	0.107363i	$0.0342407\pi$
$948$	2.53147	+	0.0830453i	0.0822183	+	0.00269719i
$949$	−12.5298	−	12.5298i	−0.406734	−	0.406734i
$950$		0			0
$951$			4.65329i			0.150893i
$952$	−7.50412	−	20.9794i	−0.243210	−	0.679946i
$953$		−	12.1516i		−	0.393630i	−0.980441	−	0.196815i	$-0.936940\pi$
$953$		−	12.1516i		−	0.393630i	0.980441	−	0.196815i	$-0.0630598\pi$
$954$	−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
$958$	1.56725	−	3.61488i	0.0506357	−	0.116791i
$959$	11.2404			0.362972
$960$		0			0
$961$	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
$965$		0			0
$966$	2.36786	+	5.99259i	0.0761847	+	0.192809i
$967$			48.2694i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$967$			48.2694i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$968$	−9.99184	−	27.9344i	−0.321150	−	0.897845i
$969$			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	$0.707106\pi$
$972$	−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			0
$976$	19.6236	+	22.3826i	0.628135	+	0.716449i
$977$	27.7522			0.887872			0.443936	−	0.896059i	$-0.353582\pi$
$977$	27.7522			0.887872			0.443936	+	0.896059i	$0.353582\pi$
$978$	−5.04342	−	2.18661i	−0.161271	−	0.0699200i
$979$	1.63671	−	1.63671i	0.0523096	−	0.0523096i
$980$		0			0
$981$	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	$0.149389\pi$
$983$			28.3604i			0.904556i	−0.891877	+	0.452278i	$0.850611\pi$
$984$	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
$988$	17.7460	−	16.6187i	0.564577	−	0.528711i
$989$	−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	$0.744548\pi$
$992$	28.6993	+	14.7477i	0.911203	+	0.468240i
$993$	3.41483			0.108366
$994$	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	$-0.325974\pi$
$997$	−10.5572	−	10.5572i	−0.334349	−	0.334349i	−0.854235	+	0.519887i	$0.825974\pi$
$998$	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	400.2.l.h.101.3		16
4.3	odd	2		1600.2.l.i.1201.5		16
5.2	odd	4		400.2.q.h.149.2		16
5.3	odd	4		400.2.q.g.149.7		16
5.4	even	2		80.2.l.a.21.6	✓	16
15.14	odd	2		720.2.t.c.181.3		16
16.3	odd	4		1600.2.l.i.401.5		16
16.13	even	4	inner	400.2.l.h.301.3		16
20.3	even	4		1600.2.q.h.49.5		16
20.7	even	4		1600.2.q.g.49.4		16
20.19	odd	2		320.2.l.a.241.4		16
40.19	odd	2		640.2.l.a.481.5		16
40.29	even	2		640.2.l.b.481.4		16
60.59	even	2		2880.2.t.c.2161.4		16
80.3	even	4		1600.2.q.g.849.4		16
80.13	odd	4		400.2.q.h.349.2		16
80.19	odd	4		320.2.l.a.81.4		16
80.29	even	4		80.2.l.a.61.6	yes	16
80.59	odd	4		640.2.l.a.161.5		16
80.67	even	4		1600.2.q.h.849.5		16
80.69	even	4		640.2.l.b.161.4		16
80.77	odd	4		400.2.q.g.349.7		16
160.19	odd	8		5120.2.a.t.1.6		8
160.29	even	8		5120.2.a.s.1.6		8
160.99	odd	8		5120.2.a.u.1.3		8
160.109	even	8		5120.2.a.v.1.3		8
240.29	odd	4		720.2.t.c.541.3		16
240.179	even	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	5.4	even	2
80.2.l.a.61.6	yes	16	80.29	even	4
320.2.l.a.81.4		16	80.19	odd	4
320.2.l.a.241.4		16	20.19	odd	2
400.2.l.h.101.3		16	1.1	even	1	trivial
400.2.l.h.301.3		16	16.13	even	4	inner
400.2.q.g.149.7		16	5.3	odd	4
400.2.q.g.349.7		16	80.77	odd	4
400.2.q.h.149.2		16	5.2	odd	4
400.2.q.h.349.2		16	80.13	odd	4
640.2.l.a.161.5		16	80.59	odd	4
640.2.l.a.481.5		16	40.19	odd	2
640.2.l.b.161.4		16	80.69	even	4
640.2.l.b.481.4		16	40.29	even	2
720.2.t.c.181.3		16	15.14	odd	2
720.2.t.c.541.3		16	240.29	odd	4
1600.2.l.i.401.5		16	16.3	odd	4
1600.2.l.i.1201.5		16	4.3	odd	2
1600.2.q.g.49.4		16	20.7	even	4
1600.2.q.g.849.4		16	80.3	even	4
1600.2.q.h.49.5		16	20.3	even	4
1600.2.q.h.849.5		16	80.67	even	4
2880.2.t.c.721.1		16	240.179	even	4
2880.2.t.c.2161.4		16	60.59	even	2
5120.2.a.s.1.6		8	160.29	even	8
5120.2.a.t.1.6		8	160.19	odd	8
5120.2.a.u.1.3		8	160.99	odd	8
5120.2.a.v.1.3		8	160.109	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.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} +(-0.154028 - 0.389815i) q^{6} +1.73696i q^{7} +(2.66319 - 0.952595i) q^{8} +2.91216i q^{9} +(0.505430 + 0.505430i) q^{11} +(0.592438 + 0.0194351i) q^{12} +(1.88750 - 1.88750i) q^{13} +(-2.25374 - 0.977122i) q^{14} +(-0.262159 + 3.99140i) q^{16} -4.53524 q^{17} +(-3.77857 - 1.63822i) q^{18} +(-3.22022 + 3.22022i) q^{19} +(-0.364018 - 0.364018i) q^{21} +(-0.940130 + 0.371475i) q^{22} +8.85045i q^{23} +(-0.358491 + 0.757764i) q^{24} +(1.38725 + 3.51086i) q^{26} +(-1.23902 - 1.23902i) q^{27} +(2.53566 - 2.37458i) q^{28} +(-2.44059 + 2.44059i) q^{29} -5.70401 q^{31} +(-5.03142 - 2.58550i) q^{32} -0.211847 q^{33} +(2.55128 - 5.88454i) q^{34} +(4.25123 - 3.98117i) q^{36} +(5.35670 + 5.35670i) q^{37} +(-2.36676 - 5.98979i) q^{38} +0.791130i q^{39} -10.0343i q^{41} +(0.677095 - 0.267541i) q^{42} +(2.10564 + 2.10564i) q^{43} +(0.0468722 - 1.42880i) q^{44} +(-11.4836 - 4.97878i) q^{46} -4.32303 q^{47} +(-0.781541 - 0.891424i) q^{48} +3.98295 q^{49} +(0.950456 - 0.950456i) q^{51} +(-5.33578 - 0.175041i) q^{52} +(1.37458 + 1.37458i) q^{53} +(2.30465 - 0.910639i) q^{54} +(1.65462 + 4.62586i) q^{56} -1.34973i q^{57} +(-1.79375 - 4.53964i) q^{58} +(6.64140 + 6.64140i) q^{59} +(5.26208 - 5.26208i) q^{61} +(3.20877 - 7.40103i) q^{62} -5.05832 q^{63} +(6.18513 - 5.07388i) q^{64} +(0.119174 - 0.274875i) q^{66} +(10.5578 - 10.5578i) q^{67} +(6.20006 + 6.62065i) q^{68} +(-1.85480 - 1.85480i) q^{69} +14.0437i q^{71} +(2.77411 + 7.75563i) q^{72} -6.63830i q^{73} +(-9.96378 + 3.93700i) q^{74} +(9.10325 + 0.298634i) q^{76} +(-0.877914 + 0.877914i) q^{77} +(-1.02650 - 0.445047i) q^{78} +4.27297 q^{79} -8.21715 q^{81} +(13.0196 + 5.64474i) q^{82} +(-9.15483 + 9.15483i) q^{83} +(-0.0337580 + 1.02904i) q^{84} +(-3.91661 + 1.54758i) q^{86} -1.02295i q^{87} +(1.82752 + 0.864585i) q^{88} -3.23826i q^{89} +(3.27852 + 3.27852i) q^{91} +(12.9201 - 12.0993i) q^{92} +(1.19540 - 1.19540i) q^{93} +(2.43190 - 5.60919i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 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 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Introduction

L-functions

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