LMFDB - Embedded newform 3736.1.l.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3736,1,Mod(3,3736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3736, base_ring=CyclotomicField(466))

chi = DirichletCharacter(H, H._module([233, 233, 450]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3736.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3736 = 2^{3} \cdot 467 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3736.l (of order $466$, degree $232$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86450688720$
Analytic rank:	$0$
Dimension:	$232$
Coefficient field:	$\Q(\zeta_{466})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{232} - x^{231} + x^{230} - x^{229} + x^{228} - x^{227} + x^{226} - x^{225} + x^{224} - x^{223} + \cdots + 1 $ x^232 - x^231 + x^230 - x^229 + x^228 - x^227 + x^226 - x^225 + x^224 - x^223 + x^222 - x^221 + x^220 - x^219 + x^218 - x^217 + x^216 - x^215 + x^214 - x^213 + x^212 - x^211 + x^210 - x^209 + x^208 - x^207 + x^206 - x^205 + x^204 - x^203 + x^202 - x^201 + x^200 - x^199 + x^198 - x^197 + x^196 - x^195 + x^194 - x^193 + x^192 - x^191 + x^190 - x^189 + x^188 - x^187 + x^186 - x^185 + x^184 - x^183 + x^182 - x^181 + x^180 - x^179 + x^178 - x^177 + x^176 - x^175 + x^174 - x^173 + x^172 - x^171 + x^170 - x^169 + x^168 - x^167 + x^166 - x^165 + x^164 - x^163 + x^162 - x^161 + x^160 - x^159 + x^158 - x^157 + x^156 - x^155 + x^154 - x^153 + x^152 - x^151 + x^150 - x^149 + x^148 - x^147 + x^146 - x^145 + x^144 - x^143 + x^142 - x^141 + x^140 - x^139 + x^138 - x^137 + x^136 - x^135 + x^134 - x^133 + x^132 - x^131 + x^130 - x^129 + x^128 - x^127 + x^126 - x^125 + x^124 - x^123 + x^122 - x^121 + x^120 - x^119 + x^118 - x^117 + x^116 - x^115 + x^114 - x^113 + x^112 - x^111 + x^110 - x^109 + x^108 - x^107 + x^106 - x^105 + x^104 - x^103 + x^102 - x^101 + x^100 - x^99 + x^98 - x^97 + x^96 - x^95 + x^94 - x^93 + x^92 - x^91 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^82 - x^81 + x^80 - x^79 + x^78 - x^77 + x^76 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^68 - x^67 + x^66 - x^65 + x^64 - x^63 + x^62 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^53 + x^52 - x^51 + x^50 - x^49 + x^48 - x^47 + x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{233}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{233} - \cdots)$

Embedding invariants

Embedding label			91.1
Root			$-0.884490 - 0.466559i$ of defining polynomial
Character	$\chi$	$=$	3736.91
Dual form			3736.1.l.a.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362351 - 0.932042i) q^{2} +(1.82331 - 0.666725i) q^{3} +(-0.737404 + 0.675452i) q^{4} +(-1.28209 - 1.45781i) q^{6} +(0.896748 + 0.442541i) q^{8} +(2.11582 - 1.78621i) q^{9} +O(q^{10})$	\(q+(-0.362351 - 0.932042i) q^{2} +(1.82331 - 0.666725i) q^{3} +(-0.737404 + 0.675452i) q^{4} +(-1.28209 - 1.45781i) q^{6} +(0.896748 + 0.442541i) q^{8} +(2.11582 - 1.78621i) q^{9} +(-1.24604 + 0.594161i) q^{11} +(-0.894174 + 1.72320i) q^{12} +(0.0875288 - 0.996162i) q^{16} +(0.0299380 + 0.492814i) q^{17} +(-2.43149 - 1.32480i) q^{18} +(1.42395 - 0.878552i) q^{19} +(1.00529 + 0.946070i) q^{22} +(1.93010 + 0.209003i) q^{24} +(-0.530808 - 0.847492i) q^{25} +(1.70375 - 2.98186i) q^{27} +(-0.960181 + 0.279380i) q^{32} +(-1.87578 + 1.91411i) q^{33} +(0.448475 - 0.206475i) q^{34} +(-0.353711 + 2.74630i) q^{36} +(-1.33482 - 1.00884i) q^{38} +(0.999968 - 1.69659i) q^{41} +(0.540846 + 1.90662i) q^{43} +(0.517511 - 1.27978i) q^{44} +(-0.504574 - 1.87467i) q^{48} +(-0.979617 - 0.200872i) q^{49} +(-0.597559 + 0.801825i) q^{50} +(0.383158 + 0.878591i) q^{51} +(-3.39657 - 0.507491i) q^{54} +(2.01055 - 2.55126i) q^{57} +(0.0365455 - 0.773837i) q^{59} +(0.608316 + 0.793695i) q^{64} +(2.46372 + 1.05473i) q^{66} +(1.24684 - 0.636355i) q^{67} +(-0.354948 - 0.343181i) q^{68} +(2.68783 - 0.665448i) q^{72} +(-1.20886 - 0.351736i) q^{73} +(-1.53287 - 1.19134i) q^{75} +(-0.456608 + 1.60966i) q^{76} +(0.653910 - 3.84304i) q^{81} +(-1.94363 - 0.317251i) q^{82} +(-0.373057 + 1.88378i) q^{83} +(1.58107 - 1.19496i) q^{86} +(-1.38033 - 0.0186124i) q^{88} +(-0.284247 + 1.11581i) q^{89} +(-1.56444 + 1.14957i) q^{96} +(0.0115692 + 1.71607i) q^{97} +(0.167744 + 0.985831i) q^{98} +(-1.57511 + 3.48284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) $ 232 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	$ 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - 2 q^{76} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) $ 232 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - 2 * q^76 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{89}{233}\right)$

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 $

$2$	−0.362351	−	0.932042i	−0.362351	−	0.932042i
$2$	−0.362351	−	0.932042i	−0.362351	−	0.932042i
$3$	1.82331	−	0.666725i	1.82331	−	0.666725i	0.829121	−	0.559069i	$-0.188841\pi$
$3$	1.82331	−	0.666725i	1.82331	−	0.666725i	0.994188	−	0.107657i	$-0.0343348\pi$
$4$	−0.737404	+	0.675452i	−0.737404	+	0.675452i
$5$		0			0		0.484351	−	0.874874i	$-0.339056\pi$
$5$		0			0		−0.484351	+	0.874874i	$0.660944\pi$
$6$	−1.28209	−	1.45781i	−1.28209	−	1.45781i
$7$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$7$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$8$	0.896748	+	0.442541i	0.896748	+	0.442541i
$9$	2.11582	−	1.78621i	2.11582	−	1.78621i
$10$		0			0
$11$	−1.24604	+	0.594161i	−1.24604	+	0.594161i	−0.934463	−	0.356059i	$-0.884120\pi$
$11$	−1.24604	+	0.594161i	−1.24604	+	0.594161i	−0.311581	+	0.950220i	$0.600858\pi$
$12$	−0.894174	+	1.72320i	−0.894174	+	1.72320i
$13$		0			0		−0.127741	−	0.991808i	$-0.540773\pi$
$13$		0			0		0.127741	+	0.991808i	$0.459227\pi$
$14$		0			0
$15$		0			0
$16$	0.0875288	−	0.996162i	0.0875288	−	0.996162i
$17$	0.0299380	+	0.492814i	0.0299380	+	0.492814i	0.982237	+	0.187646i	$0.0600858\pi$
$17$	0.0299380	+	0.492814i	0.0299380	+	0.492814i	−0.952299	+	0.305167i	$0.901288\pi$
$18$	−2.43149	−	1.32480i	−2.43149	−	1.32480i
$19$	1.42395	−	0.878552i	1.42395	−	0.878552i	0.424315	−	0.905515i	$-0.360515\pi$
$19$	1.42395	−	0.878552i	1.42395	−	0.878552i	0.999636	+	0.0269632i	$0.00858369\pi$
$20$		0			0
$21$		0			0
$22$	1.00529	+	0.946070i	1.00529	+	0.946070i
$23$		0			0		−0.943724	−	0.330734i	$-0.892704\pi$
$23$		0			0		0.943724	+	0.330734i	$0.107296\pi$
$24$	1.93010	+	0.209003i	1.93010	+	0.209003i
$25$	−0.530808	−	0.847492i	−0.530808	−	0.847492i
$26$		0			0
$27$	1.70375	−	2.98186i	1.70375	−	2.98186i
$28$		0			0
$29$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$29$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$30$		0			0
$31$		0			0		0.864900	−	0.501945i	$-0.167382\pi$
$31$		0			0		−0.864900	+	0.501945i	$0.832618\pi$
$32$	−0.960181	+	0.279380i	−0.960181	+	0.279380i
$33$	−1.87578	+	1.91411i	−1.87578	+	1.91411i
$34$	0.448475	−	0.206475i	0.448475	−	0.206475i
$35$		0			0
$36$	−0.353711	+	2.74630i	−0.353711	+	2.74630i
$37$		0			0		−0.141101	−	0.989995i	$-0.545064\pi$
$37$		0			0		0.141101	+	0.989995i	$0.454936\pi$
$38$	−1.33482	−	1.00884i	−1.33482	−	1.00884i
$39$		0			0
$40$		0			0
$41$	0.999968	−	1.69659i	0.999968	−	1.69659i	0.349751	−	0.936843i	$-0.386266\pi$
$41$	0.999968	−	1.69659i	0.999968	−	1.69659i	0.650217	−	0.759749i	$-0.274678\pi$
$42$		0			0
$43$	0.540846	+	1.90662i	0.540846	+	1.90662i	0.399745	+	0.916626i	$0.369099\pi$
$43$	0.540846	+	1.90662i	0.540846	+	1.90662i	0.141101	+	0.989995i	$0.454936\pi$
$44$	0.517511	−	1.27978i	0.517511	−	1.27978i
$45$		0			0
$46$		0			0
$47$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$47$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$48$	−0.504574	−	1.87467i	−0.504574	−	1.87467i
$49$	−0.979617	−	0.200872i	−0.979617	−	0.200872i
$50$	−0.597559	+	0.801825i	−0.597559	+	0.801825i
$51$	0.383158	+	0.878591i	0.383158	+	0.878591i
$52$		0			0
$53$		0			0		−0.670466	−	0.741941i	$-0.733906\pi$
$53$		0			0		0.670466	+	0.741941i	$0.266094\pi$
$54$	−3.39657	−	0.507491i	−3.39657	−	0.507491i
$55$		0			0
$56$		0			0
$57$	2.01055	−	2.55126i	2.01055	−	2.55126i
$58$		0			0
$59$	0.0365455	−	0.773837i	0.0365455	−	0.773837i	−0.902634	−	0.430410i	$-0.858369\pi$
$59$	0.0365455	−	0.773837i	0.0365455	−	0.773837i	0.939179	−	0.343428i	$-0.111588\pi$
$60$		0			0
$61$		0			0		−0.650217	−	0.759749i	$-0.725322\pi$
$61$		0			0		0.650217	+	0.759749i	$0.274678\pi$
$62$		0			0
$63$		0			0
$64$	0.608316	+	0.793695i	0.608316	+	0.793695i
$65$		0			0
$66$	2.46372	+	1.05473i	2.46372	+	1.05473i
$67$	1.24684	−	0.636355i	1.24684	−	0.636355i	0.298741	−	0.954334i	$-0.403433\pi$
$67$	1.24684	−	0.636355i	1.24684	−	0.636355i	0.948098	+	0.317979i	$0.103004\pi$
$68$	−0.354948	−	0.343181i	−0.354948	−	0.343181i
$69$		0			0
$70$		0			0
$71$		0			0		−0.311581	−	0.950220i	$-0.600858\pi$
$71$		0			0		0.311581	+	0.950220i	$0.399142\pi$
$72$	2.68783	−	0.665448i	2.68783	−	0.665448i
$73$	−1.20886	−	0.351736i	−1.20886	−	0.351736i	−0.387350	−	0.921933i	$-0.626609\pi$
$73$	−1.20886	−	0.351736i	−1.20886	−	0.351736i	−0.821508	+	0.570197i	$0.806867\pi$
$74$		0			0
$75$	−1.53287	−	1.19134i	−1.53287	−	1.19134i
$76$	−0.456608	+	1.60966i	−0.456608	+	1.60966i
$77$		0			0
$78$		0			0
$79$		0			0		−0.680408	−	0.732833i	$-0.738197\pi$
$79$		0			0		0.680408	+	0.732833i	$0.261803\pi$
$80$		0			0
$81$	0.653910	−	3.84304i	0.653910	−	3.84304i
$82$	−1.94363	−	0.317251i	−1.94363	−	0.317251i
$83$	−0.373057	+	1.88378i	−0.373057	+	1.88378i	0.0875288	+	0.996162i	$0.472103\pi$
$83$	−0.373057	+	1.88378i	−0.373057	+	1.88378i	−0.460585	+	0.887615i	$0.652361\pi$
$84$		0			0
$85$		0			0
$86$	1.58107	−	1.19496i	1.58107	−	1.19496i
$87$		0			0
$88$	−1.38033	−	0.0186124i	−1.38033	−	0.0186124i
$89$	−0.284247	+	1.11581i	−0.284247	+	1.11581i	0.650217	+	0.759749i	$0.274678\pi$
$89$	−0.284247	+	1.11581i	−0.284247	+	1.11581i	−0.934463	+	0.356059i	$0.884120\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.56444	+	1.14957i	−1.56444	+	1.14957i
$97$	0.0115692	+	1.71607i	0.0115692	+	1.71607i	0.519333	+	0.854572i	$0.326180\pi$
$97$	0.0115692	+	1.71607i	0.0115692	+	1.71607i	−0.507764	+	0.861496i	$0.669528\pi$
$98$	0.167744	+	0.985831i	0.167744	+	0.985831i
$99$	−1.57511	+	3.48284i	−1.57511	+	3.48284i
$100$	0.963860	+	0.266408i	0.963860	+	0.266408i
$101$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$101$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$102$	0.680046	−	0.675477i	0.680046	−	0.675477i
$103$		0			0		0.718923	−	0.695089i	$-0.244635\pi$
$103$		0			0		−0.718923	+	0.695089i	$0.755365\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0733457	+	0.272505i	−0.0733457	+	0.272505i	−0.992646	−	0.121051i	$-0.961373\pi$
$107$	−0.0733457	+	0.272505i	−0.0733457	+	0.272505i	0.919301	+	0.393556i	$0.128755\pi$
$108$	0.757747	+	3.34964i	0.757747	+	3.34964i
$109$		0			0		−0.976820	−	0.214062i	$-0.931330\pi$
$109$		0			0		0.976820	+	0.214062i	$0.0686695\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.28357	+	1.02564i	−1.28357	+	1.02564i	−0.285846	+	0.958275i	$0.592275\pi$
$113$	−1.28357	+	1.02564i	−1.28357	+	1.02564i	−0.997728	+	0.0673651i	$0.978541\pi$
$114$	−3.10640	−	0.949468i	−3.10640	−	0.949468i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.734491	+	0.246339i	−0.734491	+	0.246339i
$119$		0			0
$120$		0			0
$121$	0.570104	−	0.703696i	0.570104	−	0.703696i
$122$		0			0
$123$	0.692090	−	3.76012i	0.692090	−	3.76012i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.956327	−	0.292300i	$-0.0944206\pi$
$127$		0			0		−0.956327	+	0.292300i	$0.905579\pi$
$128$	0.519333	−	0.854572i	0.519333	−	0.854572i
$129$	2.25732	+	3.11577i	2.25732	+	3.11577i
$130$		0			0
$131$	0.589677	−	0.0962505i	0.589677	−	0.0962505i	0.141101	−	0.989995i	$-0.454936\pi$
$131$	0.589677	−	0.0962505i	0.589677	−	0.0962505i	0.448576	+	0.893745i	$0.351931\pi$
$132$	0.0903203	−	2.67847i	0.0903203	−	2.67847i
$133$		0			0
$134$	−1.04490	−	0.931522i	−1.04490	−	0.931522i
$135$		0			0
$136$	−0.191243	+	0.455179i	−0.191243	+	0.455179i
$137$	−1.57858	+	1.22686i	−1.57858	+	1.22686i	−0.772743	+	0.634719i	$0.781116\pi$
$137$	−1.57858	+	1.22686i	−1.57858	+	1.22686i	−0.805835	+	0.592140i	$0.798283\pi$
$138$		0			0
$139$	0.730313	−	0.478247i	0.730313	−	0.478247i	−0.127741	−	0.991808i	$-0.540773\pi$
$139$	0.730313	−	0.478247i	0.730313	−	0.478247i	0.858053	+	0.513561i	$0.171674\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.59416	−	2.26404i	−1.59416	−	2.26404i
$145$		0			0
$146$	0.110198	+	1.25416i	0.110198	+	1.25416i
$147$	−1.92007	+	0.286883i	−1.92007	+	0.286883i
$148$		0			0
$149$		0			0		0.114357	−	0.993440i	$-0.463519\pi$
$149$		0			0		−0.114357	+	0.993440i	$0.536481\pi$
$150$	−0.554938	+	1.86038i	−0.554938	+	1.86038i
$151$		0			0		−0.996729	−	0.0808112i	$-0.974249\pi$
$151$		0			0		0.996729	+	0.0808112i	$0.0257511\pi$
$152$	1.66572	−	0.157684i	1.66572	−	0.157684i
$153$	0.943614	+	0.989229i	0.943614	+	0.989229i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.924523	−	0.381126i	$-0.124464\pi$
$157$		0			0		−0.924523	+	0.381126i	$0.875536\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−3.81881	+	0.783055i	−3.81881	+	0.783055i
$163$	−0.829438	−	1.65258i	−0.829438	−	1.65258i	−0.755348	−	0.655324i	$-0.772532\pi$
$163$	−0.829438	−	1.65258i	−0.829438	−	1.65258i	−0.0740898	−	0.997252i	$-0.523605\pi$
$164$	0.408586	+	1.92650i	0.408586	+	1.92650i
$165$		0			0
$166$	1.89094	−	0.334884i	1.89094	−	0.334884i
$167$		0			0		0.996729	−	0.0808112i	$-0.0257511\pi$
$167$		0			0		−0.996729	+	0.0808112i	$0.974249\pi$
$168$		0			0
$169$	−0.967365	+	0.253388i	−0.967365	+	0.253388i
$170$		0			0
$171$	1.44354	−	4.40234i	1.44354	−	4.40234i
$172$	−1.68665	−	1.04063i	−1.68665	−	1.04063i
$173$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$173$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$174$		0			0
$175$		0			0
$176$	0.482815	+	1.29327i	0.482815	+	1.29327i
$177$	−0.449303	−	1.43531i	−0.449303	−	1.43531i
$178$	1.14298	−	0.139384i	1.14298	−	0.139384i
$179$	−1.00549	+	1.51309i	−1.00549	+	1.51309i	−0.154437	+	0.988003i	$0.549356\pi$
$179$	−1.00549	+	1.51309i	−1.00549	+	1.51309i	−0.851051	+	0.525083i	$0.824034\pi$
$180$		0			0
$181$		0			0		0.586694	−	0.809809i	$-0.300429\pi$
$181$		0			0		−0.586694	+	0.809809i	$0.699571\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.330115	−	0.596280i	−0.330115	−	0.596280i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.728230	−	0.685333i	$-0.240343\pi$
$191$		0			0		−0.728230	+	0.685333i	$0.759657\pi$
$192$	1.63832	+	1.04157i	1.63832	+	1.04157i
$193$	1.31130	+	0.784839i	1.31130	+	0.784839i	0.986939	−	0.161094i	$-0.0515021\pi$
$193$	1.31130	+	0.784839i	1.31130	+	0.784839i	0.324364	+	0.945932i	$0.394850\pi$
$194$	1.59525	−	0.632601i	1.59525	−	0.632601i
$195$		0			0
$196$	0.858053	−	0.513561i	0.858053	−	0.513561i
$197$		0			0		0.608316	−	0.793695i	$-0.291845\pi$
$197$		0			0		−0.608316	+	0.793695i	$0.708155\pi$
$198$	3.81689	+	0.206056i	3.81689	+	0.206056i
$199$		0			0		0.349751	−	0.936843i	$-0.386266\pi$
$199$		0			0		−0.349751	+	0.936843i	$0.613734\pi$
$200$	−0.100952	−	0.994891i	−0.100952	−	0.994891i
$201$	1.84910	−	1.99157i	1.84910	−	1.99157i
$202$		0			0
$203$		0			0
$204$	−0.875988	−	0.389072i	−0.875988	−	0.389072i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.25230	+	1.94077i	−1.25230	+	1.94077i
$210$		0			0
$211$	1.21895	+	0.215876i	1.21895	+	0.215876i	0.746444	−	0.665448i	$-0.231760\pi$
$211$	1.21895	+	0.215876i	1.21895	+	0.215876i	0.472511	+	0.881325i	$0.343348\pi$
$212$		0			0
$213$		0			0
$214$	0.280563	−	0.0303811i	0.280563	−	0.0303811i
$215$		0			0
$216$	2.84743	−	1.91999i	2.84743	−	1.91999i
$217$		0			0
$218$		0			0
$219$	−2.43863	+	0.164653i	−2.43863	+	0.164653i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.992646	−	0.121051i	$-0.961373\pi$
$223$		0			0		0.992646	+	0.121051i	$0.0386266\pi$
$224$		0			0
$225$	−2.63690	−	0.845003i	−2.63690	−	0.845003i
$226$	1.42104	+	0.824704i	1.42104	+	0.824704i
$227$	−0.654418	−	0.162020i	−0.654418	−	0.162020i	−0.100952	−	0.994891i	$-0.532189\pi$
$227$	−0.654418	−	0.162020i	−0.654418	−	0.162020i	−0.553466	+	0.832871i	$0.686695\pi$
$228$	0.240663	+	3.23934i	0.240663	+	3.23934i
$229$		0			0		−0.324364	−	0.945932i	$-0.605150\pi$
$229$		0			0		0.324364	+	0.945932i	$0.394850\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.392923	+	1.01068i	−0.392923	+	1.01068i	0.586694	+	0.809809i	$0.300429\pi$
$233$	−0.392923	+	1.01068i	−0.392923	+	1.01068i	−0.979617	+	0.200872i	$0.935622\pi$
$234$		0			0
$235$		0			0
$236$	0.495741	+	0.595315i	0.495741	+	0.595315i
$237$		0			0
$238$		0			0
$239$		0			0		−0.0740898	−	0.997252i	$-0.523605\pi$
$239$		0			0		0.0740898	+	0.997252i	$0.476395\pi$
$240$		0			0
$241$	−0.775946	−	0.450321i	−0.775946	−	0.450321i	0.0606373	−	0.998160i	$-0.480687\pi$
$241$	−0.775946	−	0.450321i	−0.775946	−	0.450321i	−0.836584	+	0.547839i	$0.815451\pi$
$242$	−0.862452	−	0.276376i	−0.862452	−	0.276376i
$243$	−0.748297	−	4.06548i	−0.748297	−	4.06548i
$244$		0			0
$245$		0			0
$246$	−3.75536	+	0.717424i	−3.75536	+	0.717424i
$247$		0			0
$248$		0			0
$249$	0.575765	+	3.68344i	0.575765	+	3.68344i
$250$		0			0
$251$	−0.0335354	+	0.0226126i	−0.0335354	+	0.0226126i	−0.575722	−	0.817645i	$-0.695279\pi$
$251$	−0.0335354	+	0.0226126i	−0.0335354	+	0.0226126i	0.542187	+	0.840258i	$0.317597\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.984677	−	0.174386i	−0.984677	−	0.174386i
$257$	0.228381	+	1.98399i	0.228381	+	1.98399i	0.167744	+	0.985831i	$0.446352\pi$
$257$	0.228381	+	1.98399i	0.228381	+	1.98399i	0.0606373	+	0.998160i	$0.480687\pi$
$258$	2.08608	−	3.23292i	2.08608	−	3.23292i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.303380	−	0.514728i	−0.303380	−	0.514728i
$263$		0			0		−0.913911	−	0.405915i	$-0.866953\pi$
$263$		0			0		0.913911	+	0.405915i	$0.133047\pi$
$264$	−2.52917	+	0.886364i	−2.52917	+	0.886364i
$265$		0			0
$266$		0			0
$267$	0.225668	+	2.22398i	0.225668	+	2.22398i
$268$	−0.489596	+	1.31143i	−0.489596	+	1.31143i
$269$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$269$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$270$		0			0
$271$		0			0		0.858053	−	0.513561i	$-0.171674\pi$
$271$		0			0		−0.858053	+	0.513561i	$0.828326\pi$
$272$	0.493543	+	0.0133123i	0.493543	+	0.0133123i
$273$		0			0
$274$	1.71548	+	1.02675i	1.71548	+	1.02675i
$275$	1.16496	+	0.740627i	1.16496	+	0.740627i
$276$		0			0
$277$		0			0		0.913911	−	0.405915i	$-0.133047\pi$
$277$		0			0		−0.913911	+	0.405915i	$0.866953\pi$
$278$	−0.710376	−	0.507389i	−0.710376	−	0.507389i
$279$		0			0
$280$		0			0
$281$	−1.83431	−	0.615204i	−1.83431	−	0.615204i	−0.997728	−	0.0673651i	$-0.978541\pi$
$281$	−1.83431	−	0.615204i	−1.83431	−	0.615204i	−0.836584	−	0.547839i	$-0.815451\pi$
$282$		0			0
$283$	1.26354	+	1.28936i	1.26354	+	1.28936i	0.939179	+	0.343428i	$0.111588\pi$
$283$	1.26354	+	1.28936i	1.26354	+	1.28936i	0.324364	+	0.945932i	$0.394850\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.53254	+	2.30620i	−1.53254	+	2.30620i
$289$	0.750677	−	0.0915438i	0.750677	−	0.0915438i
$290$		0			0
$291$	1.16524	+	3.12121i	1.16524	+	3.12121i
$292$	1.12900	−	0.557154i	1.12900	−	0.557154i
$293$		0			0		0.399745	−	0.916626i	$-0.369099\pi$
$293$		0			0		−0.399745	+	0.916626i	$0.630901\pi$
$294$	0.963127	+	1.68564i	0.963127	+	1.68564i
$295$		0			0
$296$		0			0
$297$	−0.351249	+	4.72783i	−0.351249	+	4.72783i
$298$		0			0
$299$		0			0
$300$	1.93504	−	0.156886i	1.93504	−	0.156886i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.750543	−	1.49538i	−0.750543	−	1.49538i
$305$		0			0
$306$	0.580084	−	1.23794i	0.580084	−	1.23794i
$307$	0.286931	−	1.26838i	0.286931	−	1.26838i	−0.597559	−	0.801825i	$-0.703863\pi$
$307$	0.286931	−	1.26838i	0.286931	−	1.26838i	0.884490	−	0.466559i	$-0.154506\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.939179	−	0.343428i	$-0.888412\pi$
$311$		0			0		0.939179	+	0.343428i	$0.111588\pi$
$312$		0			0
$313$	0.111927	−	0.0971056i	0.111927	−	0.0971056i	−0.597559	−	0.801825i	$-0.703863\pi$
$313$	0.111927	−	0.0971056i	0.111927	−	0.0971056i	0.709486	+	0.704719i	$0.248927\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.285846	−	0.958275i	$-0.407725\pi$
$317$		0			0		−0.285846	+	0.958275i	$0.592275\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.0479540	+	0.545762i	0.0479540	+	0.545762i
$322$		0			0
$323$	0.475592	+	0.675441i	0.475592	+	0.675441i
$324$	2.11359	+	3.27555i	2.11359	+	3.27555i
$325$		0			0
$326$	−1.23972	+	1.37188i	−1.23972	+	1.37188i
$327$		0			0
$328$	1.64753	−	1.07889i	1.64753	−	1.07889i
$329$		0			0
$330$		0			0
$331$	−0.764581	+	1.81978i	−0.764581	+	1.81978i	−0.233773	+	0.972291i	$0.575107\pi$
$331$	−0.764581	+	1.81978i	−0.764581	+	1.81978i	−0.530808	+	0.847492i	$0.678112\pi$
$332$	−0.997308	−	1.64109i	−0.997308	−	1.64109i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.00820200	−	1.21660i	0.00820200	−	1.21660i	−0.789576	−	0.613653i	$-0.789700\pi$
$337$	0.00820200	−	1.21660i	0.00820200	−	1.21660i	0.797778	−	0.602951i	$-0.206009\pi$
$338$	0.586694	+	0.809809i	0.586694	+	0.809809i
$339$	−1.65653	+	2.72585i	−1.65653	+	2.72585i
$340$		0			0
$341$		0			0
$342$	−4.62623	+	0.249748i	−4.62623	+	0.249748i
$343$		0			0
$344$	−0.358754	+	1.94911i	−0.358754	+	1.94911i
$345$		0			0
$346$		0			0
$347$	0.147086	−	0.208893i	0.147086	−	0.208893i	−0.737404	−	0.675452i	$-0.763948\pi$
$347$	0.147086	−	0.208893i	0.147086	−	0.208893i	0.884490	+	0.466559i	$0.154506\pi$
$348$		0			0
$349$		0			0		0.948098	−	0.317979i	$-0.103004\pi$
$349$		0			0		−0.948098	+	0.317979i	$0.896996\pi$
$350$		0			0
$351$		0			0
$352$	1.03043	−	0.918621i	1.03043	−	0.918621i
$353$	−1.87367	−	0.572684i	−1.87367	−	0.572684i	−0.995549	−	0.0942425i	$-0.969957\pi$
$353$	−1.87367	−	0.572684i	−1.87367	−	0.572684i	−0.878119	−	0.478442i	$-0.841202\pi$
$354$	−1.17496	+	0.938855i	−1.17496	+	0.938855i
$355$		0			0
$356$	−0.544070	−	1.01480i	−0.544070	−	1.01480i
$357$		0			0
$358$	1.77460	+	0.388889i	1.77460	+	0.388889i
$359$		0			0		−0.220643	−	0.975355i	$-0.570815\pi$
$359$		0			0		0.220643	+	0.975355i	$0.429185\pi$
$360$		0			0
$361$	0.807208	−	1.60828i	0.807208	−	1.60828i
$362$		0			0
$363$	0.570303	−	1.66316i	0.570303	−	1.66316i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.963860	−	0.266408i	$-0.914163\pi$
$367$		0			0		0.963860	+	0.266408i	$0.0858369\pi$
$368$		0			0
$369$	−0.914723	−	5.37584i	−0.914723	−	5.37584i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$373$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$374$	−0.436140	+	0.523743i	−0.436140	+	0.523743i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.79333	−	0.0241814i	−1.79333	−	0.0241814i	−0.890700	−	0.454591i	$-0.849785\pi$
$379$	−1.79333	−	0.0241814i	−1.79333	−	0.0241814i	−0.902634	+	0.430410i	$0.858369\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.836584	−	0.547839i	$-0.815451\pi$
$383$		0			0		0.836584	+	0.547839i	$0.184549\pi$
$384$	0.377141	−	1.90440i	0.377141	−	1.90440i
$385$		0			0
$386$	0.256351	−	1.50658i	0.256351	−	1.50658i
$387$	4.54997	+	3.06800i	4.54997	+	3.06800i
$388$	−1.16765	−	1.25762i	−1.16765	−	1.25762i
$389$		0			0		0.660401	−	0.750913i	$-0.270386\pi$
$389$		0			0		−0.660401	+	0.750913i	$0.729614\pi$
$390$		0			0
$391$		0			0
$392$	−0.789576	−	0.613653i	−0.789576	−	0.613653i
$393$	1.01099	−	0.568647i	1.01099	−	0.568647i
$394$		0			0
$395$		0			0
$396$	−1.19100	−	3.63217i	−1.19100	−	3.63217i
$397$		0			0		0.233773	−	0.972291i	$-0.424893\pi$
$397$		0			0		−0.233773	+	0.972291i	$0.575107\pi$
$398$		0			0
$399$		0			0
$400$	−0.890700	+	0.454591i	−0.890700	+	0.454591i
$401$	−1.82508	−	0.781324i	−1.82508	−	0.781324i	−0.960181	−	0.279380i	$-0.909871\pi$
$401$	−1.82508	−	0.781324i	−1.82508	−	0.781324i	−0.864900	−	0.501945i	$-0.832618\pi$
$402$	−2.52625	−	1.00179i	−2.52625	−	1.00179i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0452163	+	0.957438i	−0.0452163	+	0.957438i
$409$	0.304587	−	0.319311i	0.304587	−	0.319311i	−0.553466	−	0.832871i	$-0.686695\pi$
$409$	0.304587	−	0.319311i	0.304587	−	0.319311i	0.858053	+	0.513561i	$0.171674\pi$
$410$		0			0
$411$	−2.06026	+	3.28942i	−2.06026	+	3.28942i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.01273	−	1.35891i	1.01273	−	1.35891i
$418$	2.26265	+	0.463961i	2.26265	+	0.463961i
$419$	−0.0594436	−	0.220854i	−0.0594436	−	0.220854i	0.929578	−	0.368626i	$-0.120172\pi$
$419$	−0.0594436	−	0.220854i	−0.0594436	−	0.220854i	−0.989021	+	0.147772i	$0.952790\pi$
$420$		0			0
$421$		0			0		−0.0337017	−	0.999432i	$-0.510730\pi$
$421$		0			0		0.0337017	+	0.999432i	$0.489270\pi$
$422$	−0.240484	−	1.21434i	−0.240484	−	1.21434i
$423$		0			0
$424$		0			0
$425$	0.401764	−	0.286962i	0.401764	−	0.286962i
$426$		0			0
$427$		0			0
$428$	−0.129979	−	0.250488i	−0.129979	−	0.250488i
$429$		0			0
$430$		0			0
$431$		0			0		0.127741	−	0.991808i	$-0.459227\pi$
$431$		0			0		−0.127741	+	0.991808i	$0.540773\pi$
$432$	−2.82128	−	1.95821i	−2.82128	−	1.95821i
$433$	0.304741	−	0.140301i	0.304741	−	0.140301i	−0.259904	−	0.965634i	$-0.583691\pi$
$433$	0.304741	−	0.140301i	0.304741	−	0.140301i	0.564646	+	0.825333i	$0.309013\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.03710	+	2.21325i	1.03710	+	2.21325i
$439$		0			0		−0.597559	−	0.801825i	$-0.703863\pi$
$439$		0			0		0.597559	+	0.801825i	$0.296137\pi$
$440$		0			0
$441$	−2.43149	+	1.32480i	−2.43149	+	1.32480i
$442$		0			0
$443$	1.82792	+	0.197938i	1.82792	+	0.197938i	0.956327	−	0.292300i	$-0.0944206\pi$
$443$	1.82792	+	0.197938i	1.82792	+	0.197938i	0.871589	+	0.490238i	$0.163090\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.547210	+	0.298146i	0.547210	+	0.298146i	0.728230	−	0.685333i	$-0.240343\pi$
$449$	0.547210	+	0.298146i	0.547210	+	0.298146i	−0.181020	+	0.983479i	$0.557940\pi$
$450$	0.167904	+	2.76388i	0.167904	+	2.76388i
$451$	−0.237956	+	2.70817i	−0.237956	+	2.70817i
$452$	0.253742	−	1.62330i	0.253742	−	1.62330i
$453$		0			0
$454$	0.0861198	+	0.668653i	0.0861198	+	0.668653i
$455$		0			0
$456$	2.93199	−	1.39808i	2.93199	−	1.39808i
$457$	−1.76523	−	0.239463i	−1.76523	−	0.239463i	−0.821508	−	0.570197i	$-0.806867\pi$
$457$	−1.76523	−	0.239463i	−1.76523	−	0.239463i	−0.943724	+	0.330734i	$0.892704\pi$
$458$		0			0
$459$	1.52051	+	0.750362i	1.52051	+	0.750362i
$460$		0			0
$461$		0			0		−0.660401	−	0.750913i	$-0.729614\pi$
$461$		0			0		0.660401	+	0.750913i	$0.270386\pi$
$462$		0			0
$463$		0			0		0.737404	−	0.675452i	$-0.236052\pi$
$463$		0			0		−0.737404	+	0.675452i	$0.763948\pi$
$464$		0			0
$465$		0			0
$466$	1.08437			1.08437
$467$	0.908355	−	0.418201i	0.908355	−	0.418201i
$467$	0.908355	−	0.418201i	0.908355	−	0.418201i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.375227	−	0.677764i	0.375227	−	0.677764i
$473$	−1.80676	−	2.05438i	−1.80676	−	2.05438i
$474$		0			0
$475$	−1.50041	−	0.740445i	−1.50041	−	0.740445i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$479$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$480$		0			0
$481$		0			0
$482$	−0.138553	+	0.886389i	−0.138553	+	0.886389i
$483$		0			0
$484$	0.0549163	+	0.903986i	0.0549163	+	0.903986i
$485$		0			0
$486$	−3.51806	+	2.17058i	−3.51806	+	2.17058i
$487$		0			0		−0.233773	−	0.972291i	$-0.575107\pi$
$487$		0			0		0.233773	+	0.972291i	$0.424893\pi$
$488$		0			0
$489$	−2.61414	−	2.46015i	−2.61414	−	2.46015i
$490$		0			0
$491$	0.174040	+	0.0188461i	0.174040	+	0.0188461i	0.194264	−	0.980949i	$-0.437768\pi$
$491$	0.174040	+	0.0188461i	0.174040	+	0.0188461i	−0.0202235	+	0.999795i	$0.506438\pi$
$492$	2.02943	+	3.24020i	2.02943	+	3.24020i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.22449	−	1.87133i	3.22449	−	1.87133i
$499$	−1.59221	+	0.463279i	−1.59221	+	0.463279i	−0.952299	−	0.305167i	$-0.901288\pi$
$499$	−1.59221	+	0.463279i	−1.59221	+	0.463279i	−0.639914	+	0.768447i	$0.721030\pi$
$500$		0			0
$501$		0			0
$502$	0.0332275	+	0.0230627i	0.0332275	+	0.0230627i
$503$		0			0		0.127741	−	0.991808i	$-0.459227\pi$
$503$		0			0		−0.127741	+	0.991808i	$0.540773\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.59486	+	1.10697i	−1.59486	+	1.10697i
$508$		0			0
$509$		0			0		0.813746	−	0.581221i	$-0.197425\pi$
$509$		0			0		−0.813746	+	0.581221i	$0.802575\pi$
$510$		0			0
$511$		0			0
$512$	0.194264	+	0.980949i	0.194264	+	0.980949i
$513$	−0.193654	−	5.74285i	−0.193654	−	5.74285i
$514$	1.76641	−	0.931761i	1.76641	−	0.931761i
$515$		0			0
$516$	−3.76911	−	0.772863i	−3.76911	−	0.772863i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.97786	+	0.295518i	1.97786	+	0.295518i	0.990924	+	0.134424i	$0.0429185\pi$
$521$	1.97786	+	0.295518i	1.97786	+	0.295518i	0.986939	+	0.161094i	$0.0515021\pi$
$522$		0			0
$523$	0.679343	−	1.08464i	0.679343	−	1.08464i	−0.311581	−	0.950220i	$-0.600858\pi$
$523$	0.679343	−	1.08464i	0.679343	−	1.08464i	0.990924	−	0.134424i	$-0.0429185\pi$
$524$	−0.369818	+	0.469274i	−0.369818	+	0.469274i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.74258	+	2.03612i	1.74258	+	2.03612i
$529$	0.781231	+	0.624242i	0.781231	+	0.624242i
$530$		0			0
$531$	−1.30491	−	1.70258i	−1.30491	−	1.70258i
$532$		0			0
$533$		0			0
$534$	1.99107	−	1.01619i	1.99107	−	1.01619i
$535$		0			0
$536$	1.39971	−	0.0188738i	1.39971	−	0.0188738i
$537$	−0.824503	+	3.42921i	−0.824503	+	3.42921i
$538$		0			0
$539$	1.34000	−	0.331754i	1.34000	−	0.331754i
$540$		0			0
$541$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$541$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$542$		0			0
$543$		0			0
$544$	−0.166428	−	0.464826i	−0.166428	−	0.464826i
$545$		0			0
$546$		0			0
$547$	1.61980	+	1.09222i	1.61980	+	1.09222i	0.929578	+	0.368626i	$0.120172\pi$
$547$	1.61980	+	1.09222i	1.61980	+	1.09222i	0.690227	+	0.723593i	$0.257511\pi$
$548$	0.335365	−	1.97094i	0.335365	−	1.97094i
$549$		0			0
$550$	0.268172	−	1.35416i	0.268172	−	1.35416i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.215502	+	0.845952i	−0.215502	+	0.845952i
$557$		0			0		0.843894	−	0.536510i	$-0.180258\pi$
$557$		0			0		−0.843894	+	0.536510i	$0.819742\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.999456	−	0.867106i	−0.999456	−	0.867106i
$562$	0.0912685	+	1.93258i	0.0912685	+	1.93258i
$563$	0.742312	−	0.545462i	0.742312	−	0.545462i	−0.154437	−	0.988003i	$-0.549356\pi$
$563$	0.742312	−	0.545462i	0.742312	−	0.545462i	0.896748	+	0.442541i	$0.145923\pi$
$564$		0			0
$565$		0			0
$566$	0.743892	−	1.64488i	0.743892	−	1.64488i
$567$		0			0
$568$		0			0
$569$	−1.09650	+	1.08913i	−1.09650	+	1.08913i	−0.100952	+	0.994891i	$0.532189\pi$
$569$	−1.09650	+	1.08913i	−1.09650	+	1.08913i	−0.995549	+	0.0942425i	$0.969957\pi$
$570$		0			0
$571$	0.609272	−	1.77680i	0.609272	−	1.77680i	−0.0202235	−	0.999795i	$-0.506438\pi$
$571$	0.609272	−	1.77680i	0.609272	−	1.77680i	0.629495	−	0.777005i	$-0.283262\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	2.70480	+	0.592734i	2.70480	+	0.592734i
$577$	−0.319484	+	0.102380i	−0.319484	+	0.102380i	−0.460585	−	0.887615i	$-0.652361\pi$
$577$	−0.319484	+	0.102380i	−0.319484	+	0.102380i	0.141101	+	0.989995i	$0.454936\pi$
$578$	−0.357331	−	0.666492i	−0.357331	−	0.666492i
$579$	2.91418	+	0.556725i	2.91418	+	0.556725i
$580$		0			0
$581$		0			0
$582$	2.48687	−	2.21703i	2.48687	−	2.21703i
$583$		0			0
$584$	−0.928384	−	0.850387i	−0.928384	−	0.850387i
$585$		0			0
$586$		0			0
$587$	1.14298	−	1.62327i	1.14298	−	1.62327i	0.472511	−	0.881325i	$-0.343348\pi$
$587$	1.14298	−	1.62327i	1.14298	−	1.62327i	0.670466	−	0.741941i	$-0.266094\pi$
$588$	1.22209	−	1.50847i	1.22209	−	1.50847i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.10923	−	1.62135i	1.10923	−	1.62135i	0.399745	−	0.916626i	$-0.369099\pi$
$593$	1.10923	−	1.62135i	1.10923	−	1.62135i	0.709486	−	0.704719i	$-0.248927\pi$
$594$	4.53381	−	1.38575i	4.53381	−	1.38575i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0337017	−	0.999432i	$-0.489270\pi$
$599$		0			0		−0.0337017	+	0.999432i	$0.510730\pi$
$600$	−0.847386	−	1.74669i	−0.847386	−	1.74669i
$601$	−1.07327	−	0.956813i	−1.07327	−	0.956813i	−0.0740898	−	0.997252i	$-0.523605\pi$
$601$	−1.07327	−	0.956813i	−1.07327	−	0.956813i	−0.999182	+	0.0404387i	$0.987124\pi$
$602$		0			0
$603$	1.50142	−	3.57353i	1.50142	−	3.57353i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.990924	−	0.134424i	$-0.0429185\pi$
$607$		0			0		−0.990924	+	0.134424i	$0.957082\pi$
$608$	−1.12180	+	1.24139i	−1.12180	+	1.24139i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.36400	−	0.0920953i	−1.36400	−	0.0920953i
$613$		0			0		−0.0875288	−	0.996162i	$-0.527897\pi$
$613$		0			0		0.0875288	+	0.996162i	$0.472103\pi$
$614$	−1.28616	+	0.192168i	−1.28616	+	0.192168i
$615$		0			0
$616$		0			0
$617$	0.118610	−	0.397631i	0.118610	−	0.397631i	−0.878119	−	0.478442i	$-0.841202\pi$
$617$	0.118610	−	0.397631i	0.118610	−	0.397631i	0.996729	+	0.0808112i	$0.0257511\pi$
$618$		0			0
$619$	0.517495	−	0.0489881i	0.517495	−	0.0489881i	0.167744	−	0.985831i	$-0.446352\pi$
$619$	0.517495	−	0.0489881i	0.517495	−	0.0489881i	0.349751	+	0.936843i	$0.386266\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.436485	+	0.899712i	−0.436485	+	0.899712i
$626$	−0.131063	−	0.0691345i	−0.131063	−	0.0691345i
$627$	−0.989379	+	4.37357i	−0.989379	+	4.37357i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.207472	−	0.978241i	$-0.566524\pi$
$631$		0			0		0.207472	+	0.978241i	$0.433476\pi$
$632$		0			0
$633$	2.36646	−	0.419099i	2.36646	−	0.419099i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.582212	−	1.33503i	0.582212	−	1.33503i	−0.337088	−	0.941473i	$-0.609442\pi$
$641$	0.582212	−	1.33503i	0.582212	−	1.33503i	0.919301	−	0.393556i	$-0.128755\pi$
$642$	0.491297	−	0.242452i	0.491297	−	0.242452i
$643$	0.569217	+	1.52470i	0.569217	+	1.52470i	0.829121	+	0.559069i	$0.188841\pi$
$643$	0.569217	+	1.52470i	0.569217	+	1.52470i	−0.259904	+	0.965634i	$0.583691\pi$
$644$		0			0
$645$		0			0
$646$	0.457208	−	0.688018i	0.457208	−	0.688018i
$647$		0			0		−0.805835	−	0.592140i	$-0.798283\pi$
$647$		0			0		0.805835	+	0.592140i	$0.201717\pi$
$648$	2.28709	−	3.15685i	2.28709	−	3.15685i
$649$	0.414246	+	0.985949i	0.414246	+	0.985949i
$650$		0			0
$651$		0			0
$652$	1.72787	+	0.658370i	1.72787	+	0.658370i
$653$		0			0		−0.948098	−	0.317979i	$-0.896996\pi$
$653$		0			0		0.948098	+	0.317979i	$0.103004\pi$
$654$		0			0
$655$		0			0
$656$	−1.60255	−	1.14463i	−1.60255	−	1.14463i
$657$	−3.18600	+	1.41507i	−3.18600	+	1.41507i
$658$		0			0
$659$	0.876525	+	0.557255i	0.876525	+	0.557255i	0.896748	−	0.442541i	$-0.145923\pi$
$659$	0.876525	+	0.557255i	0.876525	+	0.557255i	−0.0202235	+	0.999795i	$0.506438\pi$
$660$		0			0
$661$		0			0		0.929578	−	0.368626i	$-0.120172\pi$
$661$		0			0		−0.929578	+	0.368626i	$0.879828\pi$
$662$	1.97316	+	0.0532221i	1.97316	+	0.0532221i
$663$		0			0
$664$	−1.16819	+	1.52418i	−1.16819	+	1.52418i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.10513	+	0.508796i	1.10513	+	0.508796i	0.884490	−	0.466559i	$-0.154506\pi$
$673$	1.10513	+	0.508796i	1.10513	+	0.508796i	0.220643	+	0.975355i	$0.429185\pi$
$674$	−1.13690	+	0.433193i	−1.13690	+	0.433193i
$675$	−3.43146	+	0.138877i	−3.43146	+	0.138877i
$676$	0.542187	−	0.840258i	0.542187	−	0.840258i
$677$		0			0		−0.114357	−	0.993440i	$-0.536481\pi$
$677$		0			0		0.114357	+	0.993440i	$0.463519\pi$
$678$	3.14085	+	0.556244i	3.14085	+	0.556244i
$679$		0			0
$680$		0			0
$681$	−1.30123	+	0.140905i	−1.30123	+	0.140905i
$682$		0			0
$683$	−1.09511	+	0.738419i	−1.09511	+	0.738419i	−0.967365	−	0.253388i	$-0.918455\pi$
$683$	−1.09511	+	0.738419i	−1.09511	+	0.738419i	−0.127741	+	0.991808i	$0.540773\pi$
$684$	1.90909	+	4.22134i	1.90909	+	4.22134i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.94664	−	0.371886i	1.94664	−	0.371886i
$689$		0			0
$690$		0			0
$691$	0.149185	+	0.810519i	0.149185	+	0.810519i	0.970693	+	0.240323i	$0.0772532\pi$
$691$	0.149185	+	0.810519i	0.149185	+	0.810519i	−0.821508	+	0.570197i	$0.806867\pi$
$692$		0			0
$693$		0			0
$694$	−0.247994	−	0.0613979i	−0.247994	−	0.0613979i
$695$		0			0
$696$		0			0
$697$	0.866040	+	0.442005i	0.866040	+	0.442005i
$698$		0			0
$699$	−0.0425742	+	2.10476i	−0.0425742	+	2.10476i
$700$		0			0
$701$		0			0		0.362351	−	0.932042i	$-0.381974\pi$
$701$		0			0		−0.362351	+	0.932042i	$0.618026\pi$
$702$		0			0
$703$		0			0
$704$	−1.22957	−	0.627542i	−1.22957	−	0.627542i
$705$		0			0
$706$	0.145159	+	1.95385i	0.145159	+	1.95385i
$707$		0			0
$708$	1.30080	+	0.754921i	1.30080	+	0.754921i
$709$		0			0		−0.952299	−	0.305167i	$-0.901288\pi$
$709$		0			0		0.952299	+	0.305167i	$0.0987124\pi$
$710$		0			0
$711$		0			0
$712$	−0.748688	+	0.874808i	−0.748688	+	0.874808i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.280566	−	1.79491i	−0.280566	−	1.79491i
$717$		0			0
$718$		0			0
$719$		0			0		−0.973845	−	0.227213i	$-0.927039\pi$
$719$		0			0		0.973845	+	0.227213i	$0.0729614\pi$
$720$		0			0
$721$		0			0
$722$	−1.79148	−	0.169589i	−1.79148	−	0.169589i
$723$	−1.71503	−	0.303731i	−1.71503	−	0.303731i
$724$		0			0
$725$		0			0
$726$	−1.75678	+	0.0711001i	−1.75678	+	0.0711001i
$727$		0			0		0.934463	−	0.356059i	$-0.115880\pi$
$727$		0			0		−0.934463	+	0.356059i	$0.884120\pi$
$728$		0			0
$729$	−2.09554	−	3.55538i	−2.09554	−	3.55538i
$730$		0			0
$731$	−0.923417	+	0.323617i	−0.923417	+	0.323617i
$732$		0			0
$733$		0			0		0.680408	−	0.732833i	$-0.261803\pi$
$733$		0			0		−0.680408	+	0.732833i	$0.738197\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.17552	+	1.53375i	−1.17552	+	1.53375i
$738$	−4.67905	+	2.80050i	−4.67905	+	2.80050i
$739$	−1.10653	−	0.0298464i	−1.10653	−	0.0298464i	−0.530808	−	0.847492i	$-0.678112\pi$
$739$	−1.10653	−	0.0298464i	−1.10653	−	0.0298464i	−0.575722	+	0.817645i	$0.695279\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.728230	−	0.685333i	$-0.240343\pi$
$743$		0			0		−0.728230	+	0.685333i	$0.759657\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.57551	+	4.65209i	2.57551	+	4.65209i
$748$	0.646186	+	0.216722i	0.646186	+	0.216722i
$749$		0			0
$750$		0			0
$751$		0			0		−0.871589	−	0.490238i	$-0.836910\pi$
$751$		0			0		0.871589	+	0.490238i	$0.163090\pi$
$752$		0			0
$753$	−0.0460690	+	0.0635887i	−0.0460690	+	0.0635887i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.298741	−	0.954334i	$-0.596567\pi$
$757$		0			0		0.298741	+	0.954334i	$0.403433\pi$
$758$	0.627278	+	1.68022i	0.627278	+	1.68022i
$759$		0			0
$760$		0			0
$761$	0.703956	+	1.23204i	0.703956	+	1.23204i	0.963860	+	0.266408i	$0.0858369\pi$
$761$	0.703956	+	1.23204i	0.703956	+	1.23204i	−0.259904	+	0.965634i	$0.583691\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.91164	+	0.338550i	−1.91164	+	0.338550i
$769$	−0.564226	−	1.89152i	−0.564226	−	1.89152i	−0.436485	−	0.899712i	$-0.643777\pi$
$769$	−0.564226	−	1.89152i	−0.564226	−	1.89152i	−0.127741	−	0.991808i	$-0.540773\pi$
$770$		0			0
$771$	1.73919	+	3.46516i	1.73919	+	3.46516i
$772$	−1.49708	+	0.306979i	−1.49708	+	0.306979i
$773$		0			0		0.424315	−	0.905515i	$-0.360515\pi$
$773$		0			0		−0.424315	+	0.905515i	$0.639485\pi$
$774$	1.21082	−	5.35245i	1.21082	−	5.35245i
$775$		0			0
$776$	−0.749055	+	1.54400i	−0.749055	+	1.54400i
$777$		0			0
$778$		0			0
$779$	−0.0666375	−	3.29439i	−0.0666375	−	3.29439i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.285846	+	0.958275i	−0.285846	+	0.958275i
$785$		0			0
$786$	−0.896337	−	0.736237i	−0.896337	−	0.736237i
$787$	1.42206	−	0.212474i	1.42206	−	0.212474i	0.608316	−	0.793695i	$-0.291845\pi$
$787$	1.42206	−	0.212474i	1.42206	−	0.212474i	0.813746	+	0.581221i	$0.197425\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.95377	+	2.42618i	−2.95377	+	2.42618i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.789576	−	0.613653i	$-0.210300\pi$
$797$		0			0		−0.789576	+	0.613653i	$0.789700\pi$
$798$		0			0
$799$		0			0
$800$	0.746444	+	0.665448i	0.746444	+	0.665448i
$801$	1.39166	+	2.86857i	1.39166	+	2.86857i
$802$	−0.0669077	+	1.98416i	−0.0669077	+	1.98416i
$803$	1.71528	−	0.279977i	1.71528	−	0.279977i
$804$	−0.0183211	+	2.71757i	−0.0183211	+	2.71757i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.47266	+	0.0795021i	−1.47266	+	0.0795021i	−0.772743	−	0.634719i	$-0.781116\pi$
$809$	−1.47266	+	0.0795021i	−1.47266	+	0.0795021i	−0.699920	+	0.714221i	$0.746781\pi$
$810$		0			0
$811$	0.279764	−	1.51995i	0.279764	−	1.51995i	−0.484351	−	0.874874i	$-0.660944\pi$
$811$	0.279764	−	1.51995i	0.279764	−	1.51995i	0.764115	−	0.645080i	$-0.223176\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.908757	−	0.304785i	0.908757	−	0.304785i
$817$	2.44520	+	2.23977i	2.44520	+	2.23977i
$818$	−0.407978	−	0.168185i	−0.407978	−	0.168185i
$819$		0			0
$820$		0			0
$821$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$821$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$822$	3.81241	+	0.728323i	3.81241	+	0.728323i
$823$		0			0		−0.472511	−	0.881325i	$-0.656652\pi$
$823$		0			0		0.472511	+	0.881325i	$0.343348\pi$
$824$		0			0
$825$	2.61787	+	0.573685i	2.61787	+	0.573685i
$826$		0			0
$827$	−0.510575	+	1.89696i	−0.510575	+	1.89696i	−0.0740898	+	0.997252i	$0.523605\pi$
$827$	−0.510575	+	1.89696i	−0.510575	+	1.89696i	−0.436485	+	0.899712i	$0.643777\pi$
$828$		0			0
$829$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$829$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.0696649	−	0.488783i	0.0696649	−	0.488783i
$834$	−1.63352	−	0.451501i	−1.63352	−	0.451501i
$835$		0			0
$836$	−0.387442	−	2.27700i	−0.387442	−	2.27700i
$837$		0			0
$838$	−0.184305	+	0.135430i	−0.184305	+	0.135430i
$839$		0			0		−0.0471738	−	0.998887i	$-0.515021\pi$
$839$		0			0		0.0471738	+	0.998887i	$0.484979\pi$
$840$		0			0
$841$	−0.639914	+	0.768447i	−0.639914	+	0.768447i
$842$		0			0
$843$	−3.75469	+	0.101275i	−3.75469	+	0.101275i
$844$	−1.04468	+	0.664158i	−1.04468	+	0.664158i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.16348	+	1.50847i	3.16348	+	1.50847i
$850$	−0.413040	−	0.270480i	−0.413040	−	0.270480i
$851$		0			0
$852$		0			0
$853$		0			0		0.167744	−	0.985831i	$-0.446352\pi$
$853$		0			0		−0.167744	+	0.985831i	$0.553648\pi$
$854$		0			0
$855$		0			0
$856$	−0.186367	+	0.211910i	−0.186367	+	0.211910i
$857$	−0.395535	−	1.10471i	−0.395535	−	1.10471i	−0.960181	−	0.279380i	$-0.909871\pi$
$857$	−0.395535	−	1.10471i	−0.395535	−	1.10471i	0.564646	−	0.825333i	$-0.309013\pi$
$858$		0			0
$859$	0.410428	+	0.318982i	0.410428	+	0.318982i	0.797778	−	0.602951i	$-0.206009\pi$
$859$	0.410428	+	0.318982i	0.410428	+	0.318982i	−0.387350	+	0.921933i	$0.626609\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.311581	−	0.950220i	$-0.600858\pi$
$863$		0			0		0.311581	+	0.950220i	$0.399142\pi$
$864$	−0.802841	+	3.33911i	−0.802841	+	3.33911i
$865$		0			0
$866$	−0.241190	−	0.233194i	−0.241190	−	0.233194i
$867$	1.30768	−	0.667408i	1.30768	−	0.667408i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.08974	+	3.61022i	3.08974	+	3.61022i
$874$		0			0
$875$		0			0
$876$	1.68704	−	1.76860i	1.68704	−	1.76860i
$877$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$877$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0271183	−	0.0300092i	−0.0271183	−	0.0300092i	0.728230	−	0.685333i	$-0.240343\pi$
$881$	−0.0271183	−	0.0300092i	−0.0271183	−	0.0300092i	−0.755348	+	0.655324i	$0.772532\pi$
$882$	2.11582	+	1.78621i	2.11582	+	1.78621i
$883$	−0.289696	−	0.664281i	−0.289696	−	0.664281i	0.709486	−	0.704719i	$-0.248927\pi$
$883$	−0.289696	−	0.664281i	−0.289696	−	0.664281i	−0.999182	+	0.0404387i	$0.987124\pi$
$884$		0			0
$885$		0			0
$886$	−0.477860	−	1.77542i	−0.477860	−	1.77542i
$887$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$887$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.46858	+	5.17712i	1.46858	+	5.17712i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0796030	−	0.618056i	0.0796030	−	0.618056i
$899$		0			0
$900$	2.51522	−	1.15799i	2.51522	−	1.15799i
$901$		0			0
$902$	2.61035	−	0.759522i	2.61035	−	0.759522i
$903$		0			0
$904$	−1.60493	+	0.351708i	−1.60493	+	0.351708i
$905$		0			0
$906$		0			0
$907$	0.347025	−	0.607353i	0.347025	−	0.607353i	−0.639914	−	0.768447i	$-0.721030\pi$
$907$	0.347025	−	0.607353i	0.347025	−	0.607353i	0.986939	+	0.161094i	$0.0515021\pi$
$908$	0.592007	−	0.322554i	0.592007	−	0.322554i
$909$		0			0
$910$		0			0
$911$		0			0		−0.943724	−	0.330734i	$-0.892704\pi$
$911$		0			0		0.943724	+	0.330734i	$0.107296\pi$
$912$	−2.36548	−	2.22614i	−2.36548	−	2.22614i
$913$	−0.654421	−	2.56892i	−0.654421	−	2.56892i
$914$	0.416444	+	1.73204i	0.416444	+	1.73204i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.148412	−	1.68907i	0.148412	−	1.68907i
$919$		0			0		0.154437	−	0.988003i	$-0.450644\pi$
$919$		0			0		−0.154437	+	0.988003i	$0.549356\pi$
$920$		0			0
$921$	−0.322500	−	2.50396i	−0.322500	−	2.50396i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.0847894	+	0.153153i	−0.0847894	+	0.153153i	−0.913911	−	0.405915i	$-0.866953\pi$
$929$	−0.0847894	+	0.153153i	−0.0847894	+	0.153153i	0.829121	+	0.559069i	$0.188841\pi$
$930$		0			0
$931$	−1.57140	+	0.574612i	−1.57140	+	0.574612i
$932$	−0.392923	−	1.01068i	−0.392923	−	1.01068i
$933$		0			0
$934$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$935$		0			0
$936$		0			0
$937$	0.113899	−	0.0416490i	0.113899	−	0.0416490i	−0.285846	−	0.958275i	$-0.592275\pi$
$937$	0.113899	−	0.0416490i	0.113899	−	0.0416490i	0.399745	+	0.916626i	$0.369099\pi$
$938$		0			0
$939$	0.139335	−	0.251678i	0.139335	−	0.251678i
$940$		0			0
$941$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$941$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$942$		0			0
$943$		0			0
$944$	−0.767668	−	0.104138i	−0.767668	−	0.104138i
$945$		0			0
$946$	−1.26009	+	2.42838i	−1.26009	+	2.42838i
$947$	−0.199590	−	1.54966i	−0.199590	−	1.54966i	−0.718923	−	0.695089i	$-0.755365\pi$
$947$	−0.199590	−	1.54966i	−0.199590	−	1.54966i	0.519333	−	0.854572i	$-0.326180\pi$
$948$		0			0
$949$		0			0
$950$	−0.146450	+	1.66675i	−0.146450	+	1.66675i
$951$		0			0
$952$		0			0
$953$	1.70071	−	1.04931i	1.70071	−	1.04931i	0.829121	−	0.559069i	$-0.188841\pi$
$953$	1.70071	−	1.04931i	1.70071	−	1.04931i	0.871589	−	0.490238i	$-0.163090\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.496103	−	0.868264i	0.496103	−	0.868264i
$962$		0			0
$963$	0.331566	+	0.707582i	0.331566	+	0.707582i
$964$	0.876356	−	0.192046i	0.876356	−	0.192046i
$965$		0			0
$966$		0			0
$967$		0			0		0.699920	−	0.714221i	$-0.253219\pi$
$967$		0			0		−0.699920	+	0.714221i	$0.746781\pi$
$968$	0.822654	−	0.378744i	0.822654	−	0.378744i
$969$	1.31749	+	0.914448i	1.31749	+	0.914448i
$970$		0			0
$971$	−0.251358	−	1.76358i	−0.251358	−	1.76358i	−0.575722	−	0.817645i	$-0.695279\pi$
$971$	−0.251358	−	1.76358i	−0.251358	−	1.76358i	0.324364	−	0.945932i	$-0.394850\pi$
$972$	3.29784	+	2.49246i	3.29784	+	2.49246i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.527988	−	1.86129i	−0.527988	−	1.86129i	−0.507764	−	0.861496i	$-0.669528\pi$
$977$	−0.527988	−	1.86129i	−0.527988	−	1.86129i	−0.0202235	−	0.999795i	$-0.506438\pi$
$978$	−1.34573	+	3.32792i	−1.34573	+	3.32792i
$979$	−0.308785	−	1.55923i	−0.308785	−	1.55923i
$980$		0			0
$981$		0			0
$982$	−0.0454982	−	0.169042i	−0.0454982	−	0.169042i
$983$		0			0		−0.979617	−	0.200872i	$-0.935622\pi$
$983$		0			0		0.979617	+	0.200872i	$0.0643777\pi$
$984$	2.28463	−	3.06560i	2.28463	−	3.06560i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$991$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$992$		0			0
$993$	−0.180773	+	3.82779i	−0.180773	+	3.82779i
$994$		0			0
$995$		0			0
$996$	−2.91256	−	2.32728i	−2.91256	−	2.32728i
$997$		0			0		−0.564646	−	0.825333i	$-0.690987\pi$
$997$		0			0		0.564646	+	0.825333i	$0.309013\pi$
$998$	1.00873	+	1.31614i	1.00873	+	1.31614i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.91.1	✓	232
8.3	odd	2	CM	3736.1.l.a.91.1	✓	232
467.272	even	233	inner	3736.1.l.a.739.1	yes	232
3736.739	odd	466	inner	3736.1.l.a.739.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.91.1	✓	232	1.1	even	1	trivial
3736.1.l.a.91.1	✓	232	8.3	odd	2	CM
3736.1.l.a.739.1	yes	232	467.272	even	233	inner
3736.1.l.a.739.1	yes	232	3736.739	odd	466	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3736 = 2^{3} \cdot 467 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3736.l (of order \(466\), degree \(232\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362351 - 0.932042i) q^{2} +(1.82331 - 0.666725i) q^{3} +(-0.737404 + 0.675452i) q^{4} +(-1.28209 - 1.45781i) q^{6} +(0.896748 + 0.442541i) q^{8} +(2.11582 - 1.78621i) q^{9} +O(q^{10})\)	\(q+(-0.362351 - 0.932042i) q^{2} +(1.82331 - 0.666725i) q^{3} +(-0.737404 + 0.675452i) q^{4} +(-1.28209 - 1.45781i) q^{6} +(0.896748 + 0.442541i) q^{8} +(2.11582 - 1.78621i) q^{9} +(-1.24604 + 0.594161i) q^{11} +(-0.894174 + 1.72320i) q^{12} +(0.0875288 - 0.996162i) q^{16} +(0.0299380 + 0.492814i) q^{17} +(-2.43149 - 1.32480i) q^{18} +(1.42395 - 0.878552i) q^{19} +(1.00529 + 0.946070i) q^{22} +(1.93010 + 0.209003i) q^{24} +(-0.530808 - 0.847492i) q^{25} +(1.70375 - 2.98186i) q^{27} +(-0.960181 + 0.279380i) q^{32} +(-1.87578 + 1.91411i) q^{33} +(0.448475 - 0.206475i) q^{34} +(-0.353711 + 2.74630i) q^{36} +(-1.33482 - 1.00884i) q^{38} +(0.999968 - 1.69659i) q^{41} +(0.540846 + 1.90662i) q^{43} +(0.517511 - 1.27978i) q^{44} +(-0.504574 - 1.87467i) q^{48} +(-0.979617 - 0.200872i) q^{49} +(-0.597559 + 0.801825i) q^{50} +(0.383158 + 0.878591i) q^{51} +(-3.39657 - 0.507491i) q^{54} +(2.01055 - 2.55126i) q^{57} +(0.0365455 - 0.773837i) q^{59} +(0.608316 + 0.793695i) q^{64} +(2.46372 + 1.05473i) q^{66} +(1.24684 - 0.636355i) q^{67} +(-0.354948 - 0.343181i) q^{68} +(2.68783 - 0.665448i) q^{72} +(-1.20886 - 0.351736i) q^{73} +(-1.53287 - 1.19134i) q^{75} +(-0.456608 + 1.60966i) q^{76} +(0.653910 - 3.84304i) q^{81} +(-1.94363 - 0.317251i) q^{82} +(-0.373057 + 1.88378i) q^{83} +(1.58107 - 1.19496i) q^{86} +(-1.38033 - 0.0186124i) q^{88} +(-0.284247 + 1.11581i) q^{89} +(-1.56444 + 1.14957i) q^{96} +(0.0115692 + 1.71607i) q^{97} +(0.167744 + 0.985831i) q^{98} +(-1.57511 + 3.48284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 232 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - 2 q^{76} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) 232 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^8 - 3 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - 2 * q^19 - 2 * q^22 - 2 * q^24 - q^25 - 4 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 - 2 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 4 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - 2 * q^76 - 5 * q^81 - 2 * q^82 - 2 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Introduction

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