LMFDB - Embedded newform 3736.1.l.a.147.1

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			147.1
Root			$0.890700 - 0.454591i$ of defining polynomial
Character	$\chi$	$=$	3736.147
Dual form			3736.1.l.a.1347.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.311581 + 0.950220i) q^{2} +(-0.163525 - 0.438017i) q^{3} +(-0.805835 - 0.592140i) q^{4} +(0.467164 - 0.0189069i) q^{6} +(0.813746 - 0.581221i) q^{8} +(0.590229 - 0.512070i) q^{9} +O(q^{10})$	\(q+(-0.311581 + 0.950220i) q^{2} +(-0.163525 - 0.438017i) q^{3} +(-0.805835 - 0.592140i) q^{4} +(0.467164 - 0.0189069i) q^{6} +(0.813746 - 0.581221i) q^{8} +(0.590229 - 0.512070i) q^{9} +(0.332633 - 0.399445i) q^{11} +(-0.127593 + 0.449799i) q^{12} +(0.298741 + 0.954334i) q^{16} +(0.483160 - 0.995920i) q^{17} +(0.302675 + 0.720399i) q^{18} +(0.00952457 - 0.0938656i) q^{19} +(0.275919 + 0.440533i) q^{22} +(-0.387653 - 0.261390i) q^{24} +(-0.660401 - 0.750913i) q^{25} +(-0.731374 - 0.398488i) q^{27} +(-0.999909 - 0.0134828i) q^{32} +(-0.229357 - 0.0803796i) q^{33} +(0.795800 + 0.769417i) q^{34} +(-0.778845 + 0.0631459i) q^{36} +(0.0862253 + 0.0382971i) q^{38} +(-0.890822 + 1.38056i) q^{41} +(-0.988808 - 1.09422i) q^{43} +(-0.504574 + 0.124922i) q^{44} +(0.369163 - 0.286911i) q^{48} +(0.896748 - 0.442541i) q^{49} +(0.919301 - 0.393556i) q^{50} +(-0.515239 - 0.0487745i) q^{51} +(0.606533 - 0.570805i) q^{54} +(-0.0426723 + 0.0111774i) q^{57} +(-0.290163 + 0.168396i) q^{59} +(0.324364 - 0.945932i) q^{64} +(0.147842 - 0.192895i) q^{66} +(-0.980215 + 1.61296i) q^{67} +(-0.979071 + 0.516449i) q^{68} +(0.182670 - 0.759749i) q^{72} +(0.362007 - 0.00488132i) q^{73} +(-0.220921 + 0.412060i) q^{75} +(-0.0632568 + 0.0700003i) q^{76} +(0.0553100 - 0.388066i) q^{81} +(-1.03427 - 1.27663i) q^{82} +(0.571641 - 1.91638i) q^{83} +(1.34784 - 0.598647i) q^{86} +(0.0385125 - 0.518380i) q^{88} +(0.942056 - 1.41763i) q^{89} +(0.157604 + 0.440182i) q^{96} +(1.33996 - 1.44321i) q^{97} +(0.141101 + 0.989995i) q^{98} +(-0.00821434 - 0.406095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{140}{233}\right)$

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 $

$2$	−0.311581	+	0.950220i	−0.311581	+	0.950220i
$2$	−0.311581	+	0.950220i	−0.311581	+	0.950220i
$3$	−0.163525	−	0.438017i	−0.163525	−	0.438017i	0.829121	−	0.559069i	$-0.188841\pi$
$3$	−0.163525	−	0.438017i	−0.163525	−	0.438017i	−0.992646	+	0.121051i	$0.961373\pi$
$4$	−0.805835	−	0.592140i	−0.805835	−	0.592140i
$5$		0			0		0.412067	−	0.911153i	$-0.364807\pi$
$5$		0			0		−0.412067	+	0.911153i	$0.635193\pi$
$6$	0.467164	−	0.0189069i	0.467164	−	0.0189069i
$7$		0			0		0.973845	−	0.227213i	$-0.0729614\pi$
$7$		0			0		−0.973845	+	0.227213i	$0.927039\pi$
$8$	0.813746	−	0.581221i	0.813746	−	0.581221i
$9$	0.590229	−	0.512070i	0.590229	−	0.512070i
$10$		0			0
$11$	0.332633	−	0.399445i	0.332633	−	0.399445i	−0.575722	−	0.817645i	$-0.695279\pi$
$11$	0.332633	−	0.399445i	0.332633	−	0.399445i	0.908355	+	0.418201i	$0.137339\pi$
$12$	−0.127593	+	0.449799i	−0.127593	+	0.449799i
$13$		0			0		−0.996729	−	0.0808112i	$-0.974249\pi$
$13$		0			0		0.996729	+	0.0808112i	$0.0257511\pi$
$14$		0			0
$15$		0			0
$16$	0.298741	+	0.954334i	0.298741	+	0.954334i
$17$	0.483160	−	0.995920i	0.483160	−	0.995920i	−0.507764	−	0.861496i	$-0.669528\pi$
$17$	0.483160	−	0.995920i	0.483160	−	0.995920i	0.990924	−	0.134424i	$-0.0429185\pi$
$18$	0.302675	+	0.720399i	0.302675	+	0.720399i
$19$	0.00952457	−	0.0938656i	0.00952457	−	0.0938656i	−0.989021	−	0.147772i	$-0.952790\pi$
$19$	0.00952457	−	0.0938656i	0.00952457	−	0.0938656i	0.998546	+	0.0539068i	$0.0171674\pi$
$20$		0			0
$21$		0			0
$22$	0.275919	+	0.440533i	0.275919	+	0.440533i
$23$		0			0		−0.960181	−	0.279380i	$-0.909871\pi$
$23$		0			0		0.960181	+	0.279380i	$0.0901288\pi$
$24$	−0.387653	−	0.261390i	−0.387653	−	0.261390i
$25$	−0.660401	−	0.750913i	−0.660401	−	0.750913i
$26$		0			0
$27$	−0.731374	−	0.398488i	−0.731374	−	0.398488i
$28$		0			0
$29$		0			0		0.998546	−	0.0539068i	$-0.0171674\pi$
$29$		0			0		−0.998546	+	0.0539068i	$0.982833\pi$
$30$		0			0
$31$		0			0		0.246861	−	0.969051i	$-0.420601\pi$
$31$		0			0		−0.246861	+	0.969051i	$0.579399\pi$
$32$	−0.999909	−	0.0134828i	−0.999909	−	0.0134828i
$33$	−0.229357	−	0.0803796i	−0.229357	−	0.0803796i
$34$	0.795800	+	0.769417i	0.795800	+	0.769417i
$35$		0			0
$36$	−0.778845	+	0.0631459i	−0.778845	+	0.0631459i
$37$		0			0		0.00674156	−	0.999977i	$-0.497854\pi$
$37$		0			0		−0.00674156	+	0.999977i	$0.502146\pi$
$38$	0.0862253	+	0.0382971i	0.0862253	+	0.0382971i
$39$		0			0
$40$		0			0
$41$	−0.890822	+	1.38056i	−0.890822	+	1.38056i	0.0337017	+	0.999432i	$0.489270\pi$
$41$	−0.890822	+	1.38056i	−0.890822	+	1.38056i	−0.924523	+	0.381126i	$0.875536\pi$
$42$		0			0
$43$	−0.988808	−	1.09422i	−0.988808	−	1.09422i	−0.995549	−	0.0942425i	$-0.969957\pi$
$43$	−0.988808	−	1.09422i	−0.988808	−	1.09422i	0.00674156	−	0.999977i	$-0.497854\pi$
$44$	−0.504574	+	0.124922i	−0.504574	+	0.124922i
$45$		0			0
$46$		0			0
$47$		0			0		−0.890700	−	0.454591i	$-0.849785\pi$
$47$		0			0		0.890700	+	0.454591i	$0.150215\pi$
$48$	0.369163	−	0.286911i	0.369163	−	0.286911i
$49$	0.896748	−	0.442541i	0.896748	−	0.442541i
$50$	0.919301	−	0.393556i	0.919301	−	0.393556i
$51$	−0.515239	−	0.0487745i	−0.515239	−	0.0487745i
$52$		0			0
$53$		0			0		−0.114357	−	0.993440i	$-0.536481\pi$
$53$		0			0		0.114357	+	0.993440i	$0.463519\pi$
$54$	0.606533	−	0.570805i	0.606533	−	0.570805i
$55$		0			0
$56$		0			0
$57$	−0.0426723	+	0.0111774i	−0.0426723	+	0.0111774i
$58$		0			0
$59$	−0.290163	+	0.168396i	−0.290163	+	0.168396i	−0.639914	−	0.768447i	$-0.721030\pi$
$59$	−0.290163	+	0.168396i	−0.290163	+	0.168396i	0.349751	+	0.936843i	$0.386266\pi$
$60$		0			0
$61$		0			0		0.0337017	−	0.999432i	$-0.489270\pi$
$61$		0			0		−0.0337017	+	0.999432i	$0.510730\pi$
$62$		0			0
$63$		0			0
$64$	0.324364	−	0.945932i	0.324364	−	0.945932i
$65$		0			0
$66$	0.147842	−	0.192895i	0.147842	−	0.192895i
$67$	−0.980215	+	1.61296i	−0.980215	+	1.61296i	−0.207472	+	0.978241i	$0.566524\pi$
$67$	−0.980215	+	1.61296i	−0.980215	+	1.61296i	−0.772743	+	0.634719i	$0.781116\pi$
$68$	−0.979071	+	0.516449i	−0.979071	+	0.516449i
$69$		0			0
$70$		0			0
$71$		0			0		0.575722	−	0.817645i	$-0.304721\pi$
$71$		0			0		−0.575722	+	0.817645i	$0.695279\pi$
$72$	0.182670	−	0.759749i	0.182670	−	0.759749i
$73$	0.362007	−	0.00488132i	0.362007	−	0.00488132i	0.167744	−	0.985831i	$-0.446352\pi$
$73$	0.362007	−	0.00488132i	0.362007	−	0.00488132i	0.194264	+	0.980949i	$0.437768\pi$
$74$		0			0
$75$	−0.220921	+	0.412060i	−0.220921	+	0.412060i
$76$	−0.0632568	+	0.0700003i	−0.0632568	+	0.0700003i
$77$		0			0
$78$		0			0
$79$		0			0		0.982237	−	0.187646i	$-0.0600858\pi$
$79$		0			0		−0.982237	+	0.187646i	$0.939914\pi$
$80$		0			0
$81$	0.0553100	−	0.388066i	0.0553100	−	0.388066i
$82$	−1.03427	−	1.27663i	−1.03427	−	1.27663i
$83$	0.571641	−	1.91638i	0.571641	−	1.91638i	0.272900	−	0.962042i	$-0.412017\pi$
$83$	0.571641	−	1.91638i	0.571641	−	1.91638i	0.298741	−	0.954334i	$-0.403433\pi$
$84$		0			0
$85$		0			0
$86$	1.34784	−	0.598647i	1.34784	−	0.598647i
$87$		0			0
$88$	0.0385125	−	0.518380i	0.0385125	−	0.518380i
$89$	0.942056	−	1.41763i	0.942056	−	1.41763i	0.0337017	−	0.999432i	$-0.489270\pi$
$89$	0.942056	−	1.41763i	0.942056	−	1.41763i	0.908355	−	0.418201i	$-0.137339\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.157604	+	0.440182i	0.157604	+	0.440182i
$97$	1.33996	−	1.44321i	1.33996	−	1.44321i	0.542187	−	0.840258i	$-0.317597\pi$
$97$	1.33996	−	1.44321i	1.33996	−	1.44321i	0.797778	−	0.602951i	$-0.206009\pi$
$98$	0.141101	+	0.989995i	0.141101	+	0.989995i
$99$	−0.00821434	−	0.406095i	−0.00821434	−	0.406095i
$100$	0.0875288	+	0.996162i	0.0875288	+	0.996162i
$101$		0			0		−0.00674156	−	0.999977i	$-0.502146\pi$
$101$		0			0		0.00674156	+	0.999977i	$0.497854\pi$
$102$	0.206885	−	0.474393i	0.206885	−	0.474393i
$103$		0			0		−0.884490	−	0.466559i	$-0.845494\pi$
$103$		0			0		0.884490	+	0.466559i	$0.154506\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0106460	−	0.00827396i	−0.0106460	−	0.00827396i	0.608316	−	0.793695i	$-0.291845\pi$
$107$	−0.0106460	−	0.00827396i	−0.0106460	−	0.00827396i	−0.618962	+	0.785421i	$0.712446\pi$
$108$	0.353406	+	0.754192i	0.353406	+	0.754192i
$109$		0			0		−0.374884	−	0.927072i	$-0.622318\pi$
$109$		0			0		0.374884	+	0.927072i	$0.377682\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.327876	−	0.208449i	0.327876	−	0.208449i	−0.362351	−	0.932042i	$-0.618026\pi$
$113$	0.327876	−	0.208449i	0.327876	−	0.208449i	0.690227	+	0.723593i	$0.257511\pi$
$114$	0.00267482	−	0.0440307i	0.00267482	−	0.0440307i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.0696042	−	0.328187i	−0.0696042	−	0.328187i
$119$		0			0
$120$		0			0
$121$	0.132108	+	0.717743i	0.132108	+	0.717743i
$122$		0			0
$123$	0.750380	+	0.164440i	0.750380	+	0.164440i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.0606373	−	0.998160i	$-0.519313\pi$
$127$		0			0		0.0606373	+	0.998160i	$0.480687\pi$
$128$	0.797778	+	0.602951i	0.797778	+	0.602951i
$129$	−0.317592	+	0.612047i	−0.317592	+	0.612047i
$130$		0			0
$131$	−0.972876	+	1.20085i	−0.972876	+	1.20085i	0.00674156	+	0.999977i	$0.497854\pi$
$131$	−0.972876	+	1.20085i	−0.972876	+	1.20085i	−0.979617	+	0.200872i	$0.935622\pi$
$132$	0.137228	+	0.200584i	0.137228	+	0.200584i
$133$		0			0
$134$	−1.22725	−	1.43399i	−1.22725	−	1.43399i
$135$		0			0
$136$	−0.185681	−	1.09125i	−0.185681	−	1.09125i
$137$	−0.934647	−	1.74330i	−0.934647	−	1.74330i	−0.597559	−	0.801825i	$-0.703863\pi$
$137$	−0.934647	−	1.74330i	−0.934647	−	1.74330i	−0.337088	−	0.941473i	$-0.609442\pi$
$138$		0			0
$139$	0.0120520	+	0.255197i	0.0120520	+	0.255197i	0.996729	+	0.0808112i	$0.0257511\pi$
$139$	0.0120520	+	0.255197i	0.0120520	+	0.255197i	−0.984677	+	0.174386i	$0.944206\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.665012	+	0.410300i	0.665012	+	0.410300i
$145$		0			0
$146$	−0.108156	+	0.345507i	−0.108156	+	0.345507i
$147$	−0.340481	−	0.320425i	−0.340481	−	0.320425i
$148$		0			0
$149$		0			0		−0.154437	−	0.988003i	$-0.549356\pi$
$149$		0			0		0.154437	+	0.988003i	$0.450644\pi$
$150$	−0.322713	−	0.338313i	−0.322713	−	0.338313i
$151$		0			0		−0.902634	−	0.430410i	$-0.858369\pi$
$151$		0			0		0.902634	+	0.430410i	$0.141631\pi$
$152$	−0.0468061	−	0.0819186i	−0.0468061	−	0.0819186i
$153$	−0.224806	−	0.835233i	−0.224806	−	0.835233i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.836584	−	0.547839i	$-0.184549\pi$
$157$		0			0		−0.836584	+	0.547839i	$0.815451\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.351514	+	0.173470i	0.351514	+	0.173470i
$163$	1.63906	−	0.336093i	1.63906	−	0.336093i	0.709486	−	0.704719i	$-0.248927\pi$
$163$	1.63906	−	0.336093i	1.63906	−	0.336093i	0.929578	+	0.368626i	$0.120172\pi$
$164$	1.53534	−	0.585011i	1.53534	−	0.585011i
$165$		0			0
$166$	1.64287	+	1.14029i	1.64287	+	1.14029i
$167$		0			0		0.902634	−	0.430410i	$-0.141631\pi$
$167$		0			0		−0.902634	+	0.430410i	$0.858369\pi$
$168$		0			0
$169$	0.986939	+	0.161094i	0.986939	+	0.161094i
$170$		0			0
$171$	−0.0424441	−	0.0602795i	−0.0424441	−	0.0602795i
$172$	0.148885	+	1.46727i	0.148885	+	1.46727i
$173$		0			0		0.878119	−	0.478442i	$-0.158798\pi$
$173$		0			0		−0.878119	+	0.478442i	$0.841202\pi$
$174$		0			0
$175$		0			0
$176$	0.480575	+	0.198112i	0.480575	+	0.198112i
$177$	0.121209	+	0.0995593i	0.121209	+	0.0995593i
$178$	1.05354	+	1.33687i	1.05354	+	1.33687i
$179$	−1.09868	+	0.927526i	−1.09868	+	0.927526i	−0.997728	−	0.0673651i	$-0.978541\pi$
$179$	−1.09868	+	0.927526i	−1.09868	+	0.927526i	−0.100952	+	0.994891i	$0.532189\pi$
$180$		0			0
$181$		0			0		−0.460585	−	0.887615i	$-0.652361\pi$
$181$		0			0		0.460585	+	0.887615i	$0.347639\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.237101	−	0.524271i	−0.237101	−	0.524271i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.530808	−	0.847492i	$-0.321888\pi$
$191$		0			0		−0.530808	+	0.847492i	$0.678112\pi$
$192$	−0.467376	+	0.0126065i	−0.467376	+	0.0126065i
$193$	1.48755	−	0.263444i	1.48755	−	0.263444i	0.629495	−	0.777005i	$-0.283262\pi$
$193$	1.48755	−	0.263444i	1.48755	−	0.263444i	0.858053	+	0.513561i	$0.171674\pi$
$194$	0.953859	+	1.72294i	0.953859	+	1.72294i
$195$		0			0
$196$	−0.984677	−	0.174386i	−0.984677	−	0.174386i
$197$		0			0		−0.324364	−	0.945932i	$-0.605150\pi$
$197$		0			0		0.324364	+	0.945932i	$0.394850\pi$
$198$	0.388439	+	0.118726i	0.388439	+	0.118726i
$199$		0			0		0.924523	−	0.381126i	$-0.124464\pi$
$199$		0			0		−0.924523	+	0.381126i	$0.875536\pi$
$200$	−0.973845	−	0.227213i	−0.973845	−	0.227213i
$201$	0.866794	+	0.165592i	0.866794	+	0.165592i
$202$		0			0
$203$		0			0
$204$	0.386316	+	0.344398i	0.386316	+	0.344398i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0343260	−	0.0350273i	−0.0343260	−	0.0350273i
$210$		0			0
$211$	1.58940	−	1.10318i	1.58940	−	1.10318i	0.650217	−	0.759749i	$-0.274678\pi$
$211$	1.58940	−	1.10318i	1.58940	−	1.10318i	0.939179	−	0.343428i	$-0.111588\pi$
$212$		0			0
$213$		0			0
$214$	0.0111791	−	0.00753799i	0.0111791	−	0.00753799i
$215$		0			0
$216$	−0.826762	+	0.100822i	−0.826762	+	0.100822i
$217$		0			0
$218$		0			0
$219$	−0.0613353	−	0.157767i	−0.0613353	−	0.157767i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$223$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$224$		0			0
$225$	−0.774308	−	0.105039i	−0.774308	−	0.105039i
$226$	0.0959123	+	0.376503i	0.0959123	+	0.376503i
$227$	−0.209730	−	0.872293i	−0.209730	−	0.872293i	−0.973845	−	0.227213i	$-0.927039\pi$
$227$	−0.209730	−	0.872293i	−0.209730	−	0.872293i	0.764115	−	0.645080i	$-0.223176\pi$
$228$	0.0410054	+	0.0162608i	0.0410054	+	0.0162608i
$229$		0			0		−0.858053	−	0.513561i	$-0.828326\pi$
$229$		0			0		0.858053	+	0.513561i	$0.171674\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.436163	+	1.33016i	0.436163	+	1.33016i	0.896748	+	0.442541i	$0.145923\pi$
$233$	0.436163	+	1.33016i	0.436163	+	1.33016i	−0.460585	+	0.887615i	$0.652361\pi$
$234$		0			0
$235$		0			0
$236$	0.333537	+	0.0361175i	0.333537	+	0.0361175i
$237$		0			0
$238$		0			0
$239$		0			0		−0.929578	−	0.368626i	$-0.879828\pi$
$239$		0			0		0.929578	+	0.368626i	$0.120172\pi$
$240$		0			0
$241$	−0.483659	−	1.89860i	−0.483659	−	1.89860i	−0.436485	−	0.899712i	$-0.643777\pi$
$241$	−0.483659	−	1.89860i	−0.483659	−	1.89860i	−0.0471738	−	0.998887i	$-0.515021\pi$
$242$	−0.723175	−	0.0981026i	−0.723175	−	0.0981026i
$243$	−0.992605	+	0.217521i	−0.992605	+	0.217521i
$244$		0			0
$245$		0			0
$246$	−0.390057	+	0.661789i	−0.390057	+	0.661789i
$247$		0			0
$248$		0			0
$249$	−0.932884	+	0.0629869i	−0.932884	+	0.0629869i
$250$		0			0
$251$	−1.55097	+	0.189138i	−1.55097	+	0.189138i	−0.851051	−	0.525083i	$-0.824034\pi$
$251$	−1.55097	+	0.189138i	−1.55097	+	0.189138i	−0.699920	+	0.714221i	$0.746781\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.821508	+	0.570197i	−0.821508	+	0.570197i
$257$	−0.295384	+	1.88971i	−0.295384	+	1.88971i	0.141101	+	0.989995i	$0.454936\pi$
$257$	−0.295384	+	1.88971i	−0.295384	+	1.88971i	−0.436485	+	0.899712i	$0.643777\pi$
$258$	−0.482624	−	0.492485i	−0.482624	−	0.492485i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.837942	−	1.29861i	−0.837942	−	1.29861i
$263$		0			0		−0.746444	−	0.665448i	$-0.768240\pi$
$263$		0			0		0.746444	+	0.665448i	$0.231760\pi$
$264$	−0.233357	+	0.0678989i	−0.233357	+	0.0678989i
$265$		0			0
$266$		0			0
$267$	−0.774997	−	0.180819i	−0.774997	−	0.180819i
$268$	1.74499	−	0.719355i	1.74499	−	0.719355i
$269$		0			0		−0.956327	−	0.292300i	$-0.905579\pi$
$269$		0			0		0.956327	+	0.292300i	$0.0944206\pi$
$270$		0			0
$271$		0			0		−0.984677	−	0.174386i	$-0.944206\pi$
$271$		0			0		0.984677	+	0.174386i	$0.0557940\pi$
$272$	1.09478	+	0.163574i	1.09478	+	0.163574i
$273$		0			0
$274$	1.94773	−	0.344943i	1.94773	−	0.344943i
$275$	−0.519619	+	0.0140157i	−0.519619	+	0.0140157i
$276$		0			0
$277$		0			0		0.746444	−	0.665448i	$-0.231760\pi$
$277$		0			0		−0.746444	+	0.665448i	$0.768240\pi$
$278$	−0.246248	−	0.0680623i	−0.246248	−	0.0680623i
$279$		0			0
$280$		0			0
$281$	−0.409525	+	1.93093i	−0.409525	+	1.93093i	−0.0471738	+	0.998887i	$0.515021\pi$
$281$	−0.409525	+	1.93093i	−0.409525	+	1.93093i	−0.362351	+	0.932042i	$0.618026\pi$
$282$		0			0
$283$	1.20780	−	0.423282i	1.20780	−	0.423282i	0.349751	−	0.936843i	$-0.386266\pi$
$283$	1.20780	−	0.423282i	1.20780	−	0.423282i	0.858053	+	0.513561i	$0.171674\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.597080	+	0.504066i	−0.597080	+	0.504066i
$289$	−0.139452	−	0.176956i	−0.139452	−	0.176956i
$290$		0			0
$291$	−0.851268	−	0.350927i	−0.851268	−	0.350927i
$292$	−0.294609	−	0.210425i	−0.294609	−	0.210425i
$293$		0			0		0.995549	−	0.0942425i	$-0.0300429\pi$
$293$		0			0		−0.995549	+	0.0942425i	$0.969957\pi$
$294$	0.410561	−	0.223694i	0.410561	−	0.223694i
$295$		0			0
$296$		0			0
$297$	−0.402453	+	0.159594i	−0.402453	+	0.159594i
$298$		0			0
$299$		0			0
$300$	0.422023	−	0.201236i	0.422023	−	0.201236i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.0924245	−	0.0189518i	0.0924245	−	0.0189518i
$305$		0			0
$306$	0.863700	+	0.0466271i	0.863700	+	0.0466271i
$307$	0.0286002	−	0.0610348i	0.0286002	−	0.0610348i	−0.890700	−	0.454591i	$-0.849785\pi$
$307$	0.0286002	−	0.0610348i	0.0286002	−	0.0610348i	0.919301	+	0.393556i	$0.128755\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.349751	−	0.936843i	$-0.386266\pi$
$311$		0			0		−0.349751	+	0.936843i	$0.613734\pi$
$312$		0			0
$313$	1.31905	+	1.31018i	1.31905	+	1.31018i	0.919301	+	0.393556i	$0.128755\pi$
$313$	1.31905	+	1.31018i	1.31905	+	1.31018i	0.399745	+	0.916626i	$0.369099\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.690227	−	0.723593i	$-0.742489\pi$
$317$		0			0		0.690227	+	0.723593i	$0.257511\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.00188326	+	0.00601611i	−0.00188326	+	0.00601611i
$322$		0			0
$323$	−0.0888807	−	0.0548378i	−0.0888807	−	0.0548378i
$324$	−0.274360	+	0.279966i	−0.274360	+	0.279966i
$325$		0			0
$326$	−0.191338	+	1.66219i	−0.191338	+	1.66219i
$327$		0			0
$328$	0.0775073	+	1.64119i	0.0775073	+	1.64119i
$329$		0			0
$330$		0			0
$331$	0.211188	+	1.24115i	0.211188	+	1.24115i	0.871589	+	0.490238i	$0.163090\pi$
$331$	0.211188	+	1.24115i	0.211188	+	1.24115i	−0.660401	+	0.750913i	$0.729614\pi$
$332$	−1.59541	+	1.20579i	−1.59541	+	1.20579i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.441400	−	0.475409i	−0.441400	−	0.475409i	0.472511	−	0.881325i	$-0.343348\pi$
$337$	−0.441400	−	0.475409i	−0.441400	−	0.475409i	−0.913911	+	0.405915i	$0.866953\pi$
$338$	−0.460585	+	0.887615i	−0.460585	+	0.887615i
$339$	−0.144920	−	0.109529i	−0.144920	−	0.109529i
$340$		0			0
$341$		0			0
$342$	0.0705035	−	0.0215493i	0.0705035	−	0.0215493i
$343$		0			0
$344$	−1.44062	−	0.315701i	−1.44062	−	0.315701i
$345$		0			0
$346$		0			0
$347$	−1.69654	+	1.04673i	−1.69654	+	1.04673i	−0.805835	+	0.592140i	$0.798283\pi$
$347$	−1.69654	+	1.04673i	−1.69654	+	1.04673i	−0.890700	+	0.454591i	$0.849785\pi$
$348$		0			0
$349$		0			0		−0.207472	−	0.978241i	$-0.566524\pi$
$349$		0			0		0.207472	+	0.978241i	$0.433476\pi$
$350$		0			0
$351$		0			0
$352$	−0.337988	+	0.394924i	−0.337988	+	0.394924i
$353$	0.108753	−	1.79020i	0.108753	−	1.79020i	−0.387350	−	0.921933i	$-0.626609\pi$
$353$	0.108753	−	1.79020i	0.108753	−	1.79020i	0.496103	−	0.868264i	$-0.334764\pi$
$354$	−0.132370	+	0.0841546i	−0.132370	+	0.0841546i
$355$		0			0
$356$	−1.59858	+	0.584549i	−1.59858	+	0.584549i
$357$		0			0
$358$	−0.539026	−	1.33299i	−0.539026	−	1.33299i
$359$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$359$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$360$		0			0
$361$	0.970897	+	0.199084i	0.970897	+	0.199084i
$362$		0			0
$363$	0.292781	−	0.175234i	0.292781	−	0.175234i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0875288	−	0.996162i	$-0.527897\pi$
$367$		0			0		0.0875288	+	0.996162i	$0.472103\pi$
$368$		0			0
$369$	0.181154	+	1.27101i	0.181154	+	1.27101i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$373$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$374$	0.572049	−	0.0619450i	0.572049	−	0.0619450i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.120581	+	1.62302i	−0.120581	+	1.62302i	0.519333	+	0.854572i	$0.326180\pi$
$379$	−0.120581	+	1.62302i	−0.120581	+	1.62302i	−0.639914	+	0.768447i	$0.721030\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.0471738	−	0.998887i	$-0.484979\pi$
$383$		0			0		−0.0471738	+	0.998887i	$0.515021\pi$
$384$	0.133646	−	0.448038i	0.133646	−	0.448038i
$385$		0			0
$386$	−0.213161	+	1.49558i	−0.213161	+	1.49558i
$387$	−1.14394	−	0.139502i	−1.14394	−	0.139502i
$388$	−1.93437	+	0.369542i	−1.93437	+	0.369542i
$389$		0			0		−0.999182	−	0.0404387i	$-0.987124\pi$
$389$		0			0		0.999182	+	0.0404387i	$0.0128755\pi$
$390$		0			0
$391$		0			0
$392$	0.472511	−	0.881325i	0.472511	−	0.881325i
$393$	0.685082	+	0.229768i	0.685082	+	0.229768i
$394$		0			0
$395$		0			0
$396$	−0.233846	+	0.332110i	−0.233846	+	0.332110i
$397$		0			0		−0.871589	−	0.490238i	$-0.836910\pi$
$397$		0			0		0.871589	+	0.490238i	$0.163090\pi$
$398$		0			0
$399$		0			0
$400$	0.519333	−	0.854572i	0.519333	−	0.854572i
$401$	−0.753048	+	0.982534i	−0.753048	+	0.982534i	0.246861	+	0.969051i	$0.420601\pi$
$401$	−0.753048	+	0.982534i	−0.753048	+	0.982534i	−0.999909	+	0.0134828i	$0.995708\pi$
$402$	−0.427425	+	0.772049i	−0.427425	+	0.772049i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.447622	+	0.259778i	−0.447622	+	0.259778i
$409$	−0.220562	+	0.819466i	−0.220562	+	0.819466i	0.764115	+	0.645080i	$0.223176\pi$
$409$	−0.220562	+	0.819466i	−0.220562	+	0.819466i	−0.984677	+	0.174386i	$0.944206\pi$
$410$		0			0
$411$	−0.610756	+	0.694464i	−0.610756	+	0.694464i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.109810	−	0.0470101i	0.109810	−	0.0470101i
$418$	0.0439789	−	0.0217034i	0.0439789	−	0.0217034i
$419$	0.243879	−	0.189541i	0.243879	−	0.189541i	−0.484351	−	0.874874i	$-0.660944\pi$
$419$	0.243879	−	0.189541i	0.243879	−	0.189541i	0.728230	+	0.685333i	$0.240343\pi$
$420$		0			0
$421$		0			0		0.564646	−	0.825333i	$-0.309013\pi$
$421$		0			0		−0.564646	+	0.825333i	$0.690987\pi$
$422$	0.553035	+	1.85400i	0.553035	+	1.85400i
$423$		0			0
$424$		0			0
$425$	−1.06693	+	0.294896i	−1.06693	+	0.294896i
$426$		0			0
$427$		0			0
$428$	0.00367955	+	0.0129713i	0.00367955	+	0.0129713i
$429$		0			0
$430$		0			0
$431$		0			0		0.996729	−	0.0808112i	$-0.0257511\pi$
$431$		0			0		−0.996729	+	0.0808112i	$0.974249\pi$
$432$	0.161800	−	0.817020i	0.161800	−	0.817020i
$433$	−0.202882	−	0.196156i	−0.202882	−	0.196156i	0.586694	−	0.809809i	$-0.300429\pi$
$433$	−0.202882	−	0.196156i	−0.202882	−	0.196156i	−0.789576	+	0.613653i	$0.789700\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.169024	−	0.00912483i	0.169024	−	0.00912483i
$439$		0			0		−0.919301	−	0.393556i	$-0.871245\pi$
$439$		0			0		0.919301	+	0.393556i	$0.128755\pi$
$440$		0			0
$441$	0.302675	−	0.720399i	0.302675	−	0.720399i
$442$		0			0
$443$	1.00873	+	0.680180i	1.00873	+	0.680180i	0.948098	−	0.317979i	$-0.103004\pi$
$443$	1.00873	+	0.680180i	1.00873	+	0.680180i	0.0606373	+	0.998160i	$0.480687\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.446012	+	1.06155i	0.446012	+	1.06155i	0.976820	+	0.214062i	$0.0686695\pi$
$449$	0.446012	+	1.06155i	0.446012	+	1.06155i	−0.530808	+	0.847492i	$0.678112\pi$
$450$	0.341070	−	0.703035i	0.341070	−	0.703035i
$451$	0.255140	+	0.815053i	0.255140	+	0.815053i
$452$	−0.387645	−	0.0261732i	−0.387645	−	0.0261732i
$453$		0			0
$454$	0.894218	+	0.0724999i	0.894218	+	0.0724999i
$455$		0			0
$456$	−0.0282278	+	0.0338976i	−0.0282278	+	0.0338976i
$457$	−0.765917	−	0.701570i	−0.765917	−	0.701570i	0.194264	−	0.980949i	$-0.437768\pi$
$457$	−0.765917	−	0.701570i	−0.765917	−	0.701570i	−0.960181	+	0.279380i	$0.909871\pi$
$458$		0			0
$459$	−0.750233	+	0.535857i	−0.750233	+	0.535857i
$460$		0			0
$461$		0			0		0.999182	−	0.0404387i	$-0.0128755\pi$
$461$		0			0		−0.999182	+	0.0404387i	$0.987124\pi$
$462$		0			0
$463$		0			0		−0.805835	−	0.592140i	$-0.798283\pi$
$463$		0			0		0.805835	+	0.592140i	$0.201717\pi$
$464$		0			0
$465$		0			0
$466$	−1.39984			−1.39984
$467$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$467$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.138243	+	0.305680i	−0.138243	+	0.305680i
$473$	−0.765990	+	0.0310010i	−0.765990	+	0.0310010i
$474$		0			0
$475$	−0.0767749	+	0.0548368i	−0.0767749	+	0.0548368i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.272900	−	0.962042i	$-0.412017\pi$
$479$		0			0		−0.272900	+	0.962042i	$0.587983\pi$
$480$		0			0
$481$		0			0
$482$	1.95478	+	0.131984i	1.95478	+	0.131984i
$483$		0			0
$484$	0.318546	−	0.656609i	0.318546	−	0.656609i
$485$		0			0
$486$	0.102583	−	1.01097i	0.102583	−	1.01097i
$487$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$487$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$488$		0			0
$489$	−0.415242	−	0.662979i	−0.415242	−	0.662979i
$490$		0			0
$491$	0.495384	+	0.334033i	0.495384	+	0.334033i	0.781231	−	0.624242i	$-0.214592\pi$
$491$	0.495384	+	0.334033i	0.495384	+	0.334033i	−0.285846	+	0.958275i	$0.592275\pi$
$492$	−0.507311	−	0.576841i	−0.507311	−	0.576841i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.230817	−	0.906070i	0.230817	−	0.906070i
$499$	1.98511	+	0.0267673i	1.98511	+	0.0267673i	0.994188	−	0.107657i	$-0.0343348\pi$
$499$	1.98511	+	0.0267673i	1.98511	+	0.0267673i	0.990924	+	0.134424i	$0.0429185\pi$
$500$		0			0
$501$		0			0
$502$	0.303530	−	1.53270i	0.303530	−	1.53270i
$503$		0			0		0.996729	−	0.0808112i	$-0.0257511\pi$
$503$		0			0		−0.996729	+	0.0808112i	$0.974249\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0908273	−	0.458639i	−0.0908273	−	0.458639i
$508$		0			0
$509$		0			0		0.963860	−	0.266408i	$-0.0858369\pi$
$509$		0			0		−0.963860	+	0.266408i	$0.914163\pi$
$510$		0			0
$511$		0			0
$512$	−0.285846	−	0.958275i	−0.285846	−	0.958275i
$513$	−0.0443703	+	0.0648554i	−0.0443703	+	0.0648554i
$514$	−1.70360	−	0.869475i	−1.70360	−	0.869475i
$515$		0			0
$516$	0.618345	−	0.305150i	0.618345	−	0.305150i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.107909	+	0.101552i	−0.107909	+	0.101552i	−0.737404	−	0.675452i	$-0.763948\pi$
$521$	−0.107909	+	0.101552i	−0.107909	+	0.101552i	0.629495	+	0.777005i	$0.283262\pi$
$522$		0			0
$523$	−1.31313	+	1.49310i	−1.31313	+	1.49310i	−0.575722	+	0.817645i	$0.695279\pi$
$523$	−1.31313	+	1.49310i	−1.31313	+	1.49310i	−0.737404	+	0.675452i	$0.763948\pi$
$524$	1.49505	−	0.391608i	1.49505	−	0.391608i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.00819067	−	0.242896i	0.00819067	−	0.242896i
$529$	0.843894	+	0.536510i	0.843894	+	0.536510i
$530$		0			0
$531$	−0.0850319	+	0.247976i	−0.0850319	+	0.247976i
$532$		0			0
$533$		0			0
$534$	0.413292	−	0.680078i	0.413292	−	0.680078i
$535$		0			0
$536$	0.139841	+	1.88226i	0.139841	+	1.88226i
$537$	0.585934	+	0.329567i	0.585934	+	0.329567i
$538$		0			0
$539$	0.121517	−	0.505405i	0.121517	−	0.505405i
$540$		0			0
$541$		0			0		−0.948098	−	0.317979i	$-0.896996\pi$
$541$		0			0		0.948098	+	0.317979i	$0.103004\pi$
$542$		0			0
$543$		0			0
$544$	−0.496544	+	0.989315i	−0.496544	+	0.989315i
$545$		0			0
$546$		0			0
$547$	−0.744255	−	0.0907606i	−0.744255	−	0.0907606i	−0.259904	−	0.965634i	$-0.583691\pi$
$547$	−0.744255	−	0.0907606i	−0.744255	−	0.0907606i	−0.484351	+	0.874874i	$0.660944\pi$
$548$	−0.279105	+	1.95825i	−0.279105	+	1.95825i
$549$		0			0
$550$	0.148585	−	0.498120i	0.148585	−	0.498120i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.141400	−	0.212783i	0.141400	−	0.212783i
$557$		0			0		−0.999636	−	0.0269632i	$-0.991416\pi$
$557$		0			0		0.999636	+	0.0269632i	$0.00858369\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.190868	+	0.189586i	−0.190868	+	0.189586i
$562$	−1.70721	−	0.990778i	−1.70721	−	0.990778i
$563$	−0.183983	−	0.513856i	−0.183983	−	0.513856i	0.813746	−	0.581221i	$-0.197425\pi$
$563$	−0.183983	−	0.513856i	−0.183983	−	0.513856i	−0.997728	+	0.0673651i	$0.978541\pi$
$564$		0			0
$565$		0			0
$566$	0.0258826	+	1.27957i	0.0258826	+	1.27957i
$567$		0			0
$568$		0			0
$569$	−0.477742	+	1.09548i	−0.477742	+	1.09548i	0.496103	+	0.868264i	$0.334764\pi$
$569$	−0.477742	+	1.09548i	−0.477742	+	1.09548i	−0.973845	+	0.227213i	$0.927039\pi$
$570$		0			0
$571$	0.600211	−	0.359237i	0.600211	−	0.359237i	−0.181020	−	0.983479i	$-0.557940\pi$
$571$	0.600211	−	0.359237i	0.600211	−	0.359237i	0.781231	+	0.624242i	$0.214592\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.292935	−	0.724414i	−0.292935	−	0.724414i
$577$	0.279642	−	0.0379349i	0.279642	−	0.0379349i	0.00674156	−	0.999977i	$-0.497854\pi$
$577$	0.279642	−	0.0379349i	0.279642	−	0.0379349i	0.272900	+	0.962042i	$0.412017\pi$
$578$	0.211597	−	0.0773743i	0.211597	−	0.0773743i
$579$	−0.358644	−	0.608492i	−0.358644	−	0.608492i
$580$		0			0
$581$		0			0
$582$	0.598696	−	0.699550i	0.598696	−	0.699550i
$583$		0			0
$584$	0.291745	−	0.214378i	0.291745	−	0.214378i
$585$		0			0
$586$		0			0
$587$	1.05354	−	0.650012i	1.05354	−	0.650012i	0.114357	−	0.993440i	$-0.463519\pi$
$587$	1.05354	−	0.650012i	1.05354	−	0.650012i	0.939179	+	0.343428i	$0.111588\pi$
$588$	0.0846353	+	0.459822i	0.0846353	+	0.459822i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.595804	−	0.822384i	−0.595804	−	0.822384i	0.399745	−	0.916626i	$-0.369099\pi$
$593$	−0.595804	−	0.822384i	−0.595804	−	0.822384i	−0.995549	+	0.0942425i	$0.969957\pi$
$594$	−0.0262524	−	0.432145i	−0.0262524	−	0.432145i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.564646	−	0.825333i	$-0.690987\pi$
$599$		0			0		0.564646	+	0.825333i	$0.309013\pi$
$600$	0.0597247	+	0.463716i	0.0597247	+	0.463716i
$601$	1.15022	+	1.34398i	1.15022	+	1.34398i	0.929578	+	0.368626i	$0.120172\pi$
$601$	1.15022	+	1.34398i	1.15022	+	1.34398i	0.220643	+	0.975355i	$0.429185\pi$
$602$		0			0
$603$	0.247397	+	1.45396i	0.247397	+	1.45396i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.737404	−	0.675452i	$-0.236052\pi$
$607$		0			0		−0.737404	+	0.675452i	$0.763948\pi$
$608$	−0.0107893	+	0.0937286i	−0.0107893	+	0.0937286i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.313418	+	0.806177i	−0.313418	+	0.806177i
$613$		0			0		0.298741	−	0.954334i	$-0.403433\pi$
$613$		0			0		−0.298741	+	0.954334i	$0.596567\pi$
$614$	0.0490852	+	0.0461938i	0.0490852	+	0.0461938i
$615$		0			0
$616$		0			0
$617$	−1.28998	−	1.35234i	−1.28998	−	1.35234i	−0.902634	−	0.430410i	$-0.858369\pi$
$617$	−1.28998	−	1.35234i	−1.28998	−	1.35234i	−0.387350	−	0.921933i	$-0.626609\pi$
$618$		0			0
$619$	−0.783422	−	1.37112i	−0.783422	−	1.37112i	−0.924523	−	0.381126i	$-0.875536\pi$
$619$	−0.783422	−	1.37112i	−0.783422	−	1.37112i	0.141101	−	0.989995i	$-0.454936\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.127741	+	0.991808i	−0.127741	+	0.991808i
$626$	−1.65595	+	0.845156i	−1.65595	+	0.845156i
$627$	−0.00972942	+	0.0207632i	−0.00972942	+	0.0207632i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.934463	−	0.356059i	$-0.115880\pi$
$631$		0			0		−0.934463	+	0.356059i	$0.884120\pi$
$632$		0			0
$633$	−0.743116	−	0.515786i	−0.743116	−	0.515786i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.05689	−	0.100049i	1.05689	−	0.100049i	0.448576	−	0.893745i	$-0.351931\pi$
$641$	1.05689	−	0.100049i	1.05689	−	0.100049i	0.608316	+	0.793695i	$0.291845\pi$
$642$	−0.00512984	−	0.00366401i	−0.00512984	−	0.00366401i
$643$	−1.78222	−	0.734704i	−1.78222	−	0.734704i	−0.992646	−	0.121051i	$-0.961373\pi$
$643$	−1.78222	−	0.734704i	−1.78222	−	0.734704i	−0.789576	−	0.613653i	$-0.789700\pi$
$644$		0			0
$645$		0			0
$646$	0.0798015	−	0.0673699i	0.0798015	−	0.0673699i
$647$		0			0		0.337088	−	0.941473i	$-0.390558\pi$
$647$		0			0		−0.337088	+	0.941473i	$0.609442\pi$
$648$	−0.180544	−	0.347934i	−0.180544	−	0.347934i
$649$	−0.0292526	+	0.171918i	−0.0292526	+	0.171918i
$650$		0			0
$651$		0			0
$652$	−1.51983	−	0.699720i	−1.51983	−	0.699720i
$653$		0			0		0.207472	−	0.978241i	$-0.433476\pi$
$653$		0			0		−0.207472	+	0.978241i	$0.566524\pi$
$654$		0			0
$655$		0			0
$656$	−1.58364	−	0.437713i	−1.58364	−	0.437713i
$657$	0.211168	−	0.188254i	0.211168	−	0.188254i
$658$		0			0
$659$	1.59498	−	0.0430213i	1.59498	−	0.0430213i	0.781231	−	0.624242i	$-0.214592\pi$
$659$	1.59498	−	0.0430213i	1.59498	−	0.0430213i	0.813746	+	0.581221i	$0.197425\pi$
$660$		0			0
$661$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$661$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$662$	−1.24517	−	0.186044i	−1.24517	−	0.186044i
$663$		0			0
$664$	−0.648669	−	1.89169i	−0.648669	−	1.89169i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.466386	+	0.450924i	−0.466386	+	0.450924i	−0.890700	−	0.454591i	$-0.849785\pi$
$673$	−0.466386	+	0.450924i	−0.466386	+	0.450924i	0.424315	+	0.905515i	$0.360515\pi$
$674$	0.589275	−	0.271298i	0.589275	−	0.271298i
$675$	0.183770	+	0.812360i	0.183770	+	0.812360i
$676$	−0.699920	−	0.714221i	−0.699920	−	0.714221i
$677$		0			0		0.154437	−	0.988003i	$-0.450644\pi$
$677$		0			0		−0.154437	+	0.988003i	$0.549356\pi$
$678$	0.149231	−	0.103579i	0.149231	−	0.103579i
$679$		0			0
$680$		0			0
$681$	−0.347783	+	0.234507i	−0.347783	+	0.234507i
$682$		0			0
$683$	1.98367	−	0.241905i	1.98367	−	0.241905i	0.986939	−	0.161094i	$-0.0515021\pi$
$683$	1.98367	−	0.241905i	1.98367	−	0.241905i	0.996729	−	0.0808112i	$-0.0257511\pi$
$684$	−0.00149094	+	0.0737082i	−0.00149094	+	0.0737082i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.748855	−	1.27054i	0.748855	−	1.27054i
$689$		0			0
$690$		0			0
$691$	−0.0395094	+	0.00865816i	−0.0395094	+	0.00865816i	−0.233773	−	0.972291i	$-0.575107\pi$
$691$	−0.0395094	+	0.00865816i	−0.0395094	+	0.00865816i	0.194264	+	0.980949i	$0.437768\pi$
$692$		0			0
$693$		0			0
$694$	−0.466017	−	1.93822i	−0.466017	−	1.93822i
$695$		0			0
$696$		0			0
$697$	0.944516	+	1.55422i	0.944516	+	1.55422i
$698$		0			0
$699$	0.511308	−	0.408561i	0.511308	−	0.408561i
$700$		0			0
$701$		0			0		−0.311581	−	0.950220i	$-0.600858\pi$
$701$		0			0		0.311581	+	0.950220i	$0.399142\pi$
$702$		0			0
$703$		0			0
$704$	−0.269954	−	0.444214i	−0.269954	−	0.444214i
$705$		0			0
$706$	1.66719	+	0.661130i	1.66719	+	0.661130i
$707$		0			0
$708$	−0.0387216	−	0.152001i	−0.0387216	−	0.152001i
$709$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$709$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$710$		0			0
$711$		0			0
$712$	−0.0573637	−	1.70114i	−0.0573637	−	1.70114i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.43458	−	0.0968607i	1.43458	−	0.0968607i
$717$		0			0
$718$		0			0
$719$		0			0		0.952299	−	0.305167i	$-0.0987124\pi$
$719$		0			0		−0.952299	+	0.305167i	$0.901288\pi$
$720$		0			0
$721$		0			0
$722$	−0.491687	+	0.860535i	−0.491687	+	0.860535i
$723$	−0.752528	+	0.522319i	−0.752528	+	0.522319i
$724$		0			0
$725$		0			0
$726$	0.0752866	+	0.332806i	0.0752866	+	0.332806i
$727$		0			0		0.908355	−	0.418201i	$-0.137339\pi$
$727$		0			0		−0.908355	+	0.418201i	$0.862661\pi$
$728$		0			0
$729$	0.0450634	+	0.0698373i	0.0450634	+	0.0698373i
$730$		0			0
$731$	−1.56751	+	0.456091i	−1.56751	+	0.456091i
$732$		0			0
$733$		0			0		−0.982237	−	0.187646i	$-0.939914\pi$
$733$		0			0		0.982237	+	0.187646i	$0.0600858\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.318237	+	0.928065i	0.318237	+	0.928065i
$738$	−1.26418	−	0.223886i	−1.26418	−	0.223886i
$739$	−1.51145	−	0.225830i	−1.51145	−	0.225830i	−0.660401	−	0.750913i	$-0.729614\pi$
$739$	−1.51145	−	0.225830i	−1.51145	−	0.225830i	−0.851051	+	0.525083i	$0.824034\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.530808	−	0.847492i	$-0.321888\pi$
$743$		0			0		−0.530808	+	0.847492i	$0.678112\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.643921	−	1.42382i	−0.643921	−	1.42382i
$748$	−0.119378	+	0.562873i	−0.119378	+	0.562873i
$749$		0			0
$750$		0			0
$751$		0			0		0.948098	−	0.317979i	$-0.103004\pi$
$751$		0			0		−0.948098	+	0.317979i	$0.896996\pi$
$752$		0			0
$753$	0.336468	+	0.648423i	0.336468	+	0.648423i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.772743	−	0.634719i	$-0.781116\pi$
$757$		0			0		0.772743	+	0.634719i	$0.218884\pi$
$758$	−1.50465	−	0.620279i	−1.50465	−	0.620279i
$759$		0			0
$760$		0			0
$761$	−0.702047	+	0.382509i	−0.702047	+	0.382509i	−0.789576	−	0.613653i	$-0.789700\pi$
$761$	−0.702047	+	0.382509i	−0.702047	+	0.382509i	0.0875288	+	0.996162i	$0.472103\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.384093	+	0.266593i	0.384093	+	0.266593i
$769$	0.868989	−	0.910996i	0.868989	−	0.910996i	−0.127741	−	0.991808i	$-0.540773\pi$
$769$	0.868989	−	0.910996i	0.868989	−	0.910996i	0.996729	+	0.0808112i	$0.0257511\pi$
$770$		0			0
$771$	0.876027	−	0.179631i	0.876027	−	0.179631i
$772$	−1.35471	−	0.668544i	−1.35471	−	0.668544i
$773$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$773$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$774$	0.488987	−	1.04353i	0.488987	−	1.04353i
$775$		0			0
$776$	0.251567	−	1.95322i	0.251567	−	1.95322i
$777$		0			0
$778$		0			0
$779$	0.121102	+	0.0967667i	0.121102	+	0.0967667i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.690227	+	0.723593i	0.690227	+	0.723593i
$785$		0			0
$786$	−0.431788	+	0.579388i	−0.431788	+	0.579388i
$787$	1.28822	+	1.21234i	1.28822	+	1.21234i	0.963860	+	0.266408i	$0.0858369\pi$
$787$	1.28822	+	1.21234i	1.28822	+	1.21234i	0.324364	+	0.945932i	$0.394850\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.242716	−	0.325684i	−0.242716	−	0.325684i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.472511	−	0.881325i	$-0.656652\pi$
$797$		0			0		0.472511	+	0.881325i	$0.343348\pi$
$798$		0			0
$799$		0			0
$800$	0.650217	+	0.759749i	0.650217	+	0.759749i
$801$	−0.169898	−	1.31913i	−0.169898	−	1.31913i
$802$	−0.698988	−	1.02170i	−0.698988	−	1.02170i
$803$	0.118466	−	0.146226i	0.118466	−	0.146226i
$804$	−0.600439	−	0.646703i	−0.600439	−	0.646703i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.54128	+	0.471091i	−1.54128	+	0.471091i	−0.943724	−	0.330734i	$-0.892704\pi$
$809$	−1.54128	+	0.471091i	−1.54128	+	0.471091i	−0.597559	+	0.801825i	$0.703863\pi$
$810$		0			0
$811$	−1.16742	−	0.255830i	−1.16742	−	0.255830i	−0.412067	−	0.911153i	$-0.635193\pi$
$811$	−1.16742	−	0.255830i	−1.16742	−	0.255830i	−0.755348	+	0.655324i	$0.772532\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.107376	−	0.506281i	−0.107376	−	0.506281i
$817$	−0.112128	+	0.0823930i	−0.112128	+	0.0823930i
$818$	−0.709950	−	0.464912i	−0.709950	−	0.464912i
$819$		0			0
$820$		0			0
$821$		0			0		0.843894	−	0.536510i	$-0.180258\pi$
$821$		0			0		−0.843894	+	0.536510i	$0.819742\pi$
$822$	−0.469594	−	0.796734i	−0.469594	−	0.796734i
$823$		0			0		0.939179	−	0.343428i	$-0.111588\pi$
$823$		0			0		−0.939179	+	0.343428i	$0.888412\pi$
$824$		0			0
$825$	0.0911098	+	0.225310i	0.0911098	+	0.225310i
$826$		0			0
$827$	0.801837	+	0.623182i	0.801837	+	0.623182i	0.929578	−	0.368626i	$-0.120172\pi$
$827$	0.801837	+	0.623182i	0.801837	+	0.623182i	−0.127741	+	0.991808i	$0.540773\pi$
$828$		0			0
$829$		0			0		0.986939	−	0.161094i	$-0.0515021\pi$
$829$		0			0		−0.986939	+	0.161094i	$0.948498\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.00746246	−	1.10691i	−0.00746246	−	1.10691i
$834$	0.0104553	+	0.118991i	0.0104553	+	0.118991i
$835$		0			0
$836$	0.00691999	+	0.0485520i	0.00691999	+	0.0485520i
$837$		0			0
$838$	0.104117	+	0.290796i	0.104117	+	0.290796i
$839$		0			0		−0.864900	−	0.501945i	$-0.832618\pi$
$839$		0			0		0.864900	+	0.501945i	$0.167382\pi$
$840$		0			0
$841$	0.994188	−	0.107657i	0.994188	−	0.107657i
$842$		0			0
$843$	0.912747	−	0.136376i	0.912747	−	0.136376i
$844$	−1.93403	−	0.0521665i	−1.93403	−	0.0521665i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.382911	−	0.459822i	−0.382911	−	0.459822i
$850$	0.0522182	−	1.10570i	0.0522182	−	1.10570i
$851$		0			0
$852$		0			0
$853$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$853$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$854$		0			0
$855$		0			0
$856$	−0.0134721		0.000545240i	−0.0134721		0.000545240i
$857$	−0.413215	+	0.823292i	−0.413215	+	0.823292i	0.586694	+	0.809809i	$0.300429\pi$
$857$	−0.413215	+	0.823292i	−0.413215	+	0.823292i	−0.999909	+	0.0134828i	$0.995708\pi$
$858$		0			0
$859$	−0.746167	+	1.39175i	−0.746167	+	1.39175i	0.167744	+	0.985831i	$0.446352\pi$
$859$	−0.746167	+	1.39175i	−0.746167	+	1.39175i	−0.913911	+	0.405915i	$0.866953\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.575722	−	0.817645i	$-0.304721\pi$
$863$		0			0		−0.575722	+	0.817645i	$0.695279\pi$
$864$	0.725935	+	0.408313i	0.725935	+	0.408313i
$865$		0			0
$866$	0.249606	−	0.131664i	0.249606	−	0.131664i
$867$	−0.0547057	+	0.0900191i	−0.0547057	+	0.0900191i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.0518620	−	1.53798i	0.0518620	−	1.53798i
$874$		0			0
$875$		0			0
$876$	−0.0439941	+	0.163453i	−0.0439941	+	0.163453i
$877$		0			0		0.967365	−	0.253388i	$-0.0815451\pi$
$877$		0			0		−0.967365	+	0.253388i	$0.918455\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.178678	+	1.55221i	0.178678	+	1.55221i	0.709486	+	0.704719i	$0.248927\pi$
$881$	0.178678	+	1.55221i	0.178678	+	1.55221i	−0.530808	+	0.847492i	$0.678112\pi$
$882$	0.590229	+	0.512070i	0.590229	+	0.512070i
$883$	0.620388	+	0.0587283i	0.620388	+	0.0587283i	0.399745	−	0.916626i	$-0.369099\pi$
$883$	0.620388	+	0.0587283i	0.620388	+	0.0587283i	0.220643	+	0.975355i	$0.429185\pi$
$884$		0			0
$885$		0			0
$886$	−0.960623	+	0.746589i	−0.960623	+	0.746589i
$887$		0			0		−0.890700	−	0.454591i	$-0.849785\pi$
$887$		0			0		0.890700	+	0.454591i	$0.150215\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.136613	−	0.151177i	−0.136613	−	0.151177i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.14768	+	0.0930495i	−1.14768	+	0.0930495i
$899$		0			0
$900$	0.561767	+	0.543143i	0.561767	+	0.543143i
$901$		0			0
$902$	−0.853976	−	0.0115151i	−0.853976	−	0.0115151i
$903$		0			0
$904$	0.145653	−	0.360193i	0.145653	−	0.360193i
$905$		0			0
$906$		0			0
$907$	1.62368	+	0.884661i	1.62368	+	0.884661i	0.994188	+	0.107657i	$0.0343348\pi$
$907$	1.62368	+	0.884661i	1.62368	+	0.884661i	0.629495	+	0.777005i	$0.283262\pi$
$908$	−0.347512	+	0.827114i	−0.347512	+	0.827114i
$909$		0			0
$910$		0			0
$911$		0			0		−0.960181	−	0.279380i	$-0.909871\pi$
$911$		0			0		0.960181	+	0.279380i	$0.0901288\pi$
$912$	−0.0234149	−	0.0373844i	−0.0234149	−	0.0373844i
$913$	−0.575341	−	0.865788i	−0.575341	−	0.865788i
$914$	0.905290	−	0.509194i	0.905290	−	0.509194i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.275424	−	0.879849i	−0.275424	−	0.879849i
$919$		0			0		−0.997728	−	0.0673651i	$-0.978541\pi$
$919$		0			0		0.997728	+	0.0673651i	$0.0214592\pi$
$920$		0			0
$921$	−0.0314111	−	0.00254670i	−0.0314111	−	0.00254670i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.246202	+	0.544397i	−0.246202	+	0.544397i	−0.992646	−	0.121051i	$-0.961373\pi$
$929$	−0.246202	+	0.544397i	−0.246202	+	0.544397i	0.746444	+	0.665448i	$0.231760\pi$
$930$		0			0
$931$	−0.0329982	−	0.0883888i	−0.0329982	−	0.0883888i
$932$	0.436163	−	1.33016i	0.436163	−	1.33016i
$933$		0			0
$934$	0.884490	−	0.466559i	0.884490	−	0.466559i
$935$		0			0
$936$		0			0
$937$	−0.305322	−	0.817836i	−0.305322	−	0.817836i	−0.995549	−	0.0942425i	$-0.969957\pi$
$937$	−0.305322	−	0.817836i	−0.305322	−	0.817836i	0.690227	−	0.723593i	$-0.257511\pi$
$938$		0			0
$939$	0.358186	−	0.792012i	0.358186	−	0.792012i
$940$		0			0
$941$		0			0		0.973845	−	0.227213i	$-0.0729614\pi$
$941$		0			0		−0.973845	+	0.227213i	$0.927039\pi$
$942$		0			0
$943$		0			0
$944$	−0.247390	−	0.226606i	−0.247390	−	0.226606i
$945$		0			0
$946$	0.209210	−	0.737518i	0.209210	−	0.737518i
$947$	1.68227	+	0.136392i	1.68227	+	0.136392i	0.884490	−	0.466559i	$-0.154506\pi$
$947$	1.68227	+	0.136392i	1.68227	+	0.136392i	0.797778	+	0.602951i	$0.206009\pi$
$948$		0			0
$949$		0			0
$950$	−0.0281855	−	0.0900391i	−0.0281855	−	0.0900391i
$951$		0			0
$952$		0			0
$953$	−0.0445486	+	0.439031i	−0.0445486	+	0.439031i	0.948098	+	0.317979i	$0.103004\pi$
$953$	−0.0445486	+	0.439031i	−0.0445486	+	0.439031i	−0.992646	+	0.121051i	$0.961373\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.878119	−	0.478442i	−0.878119	−	0.478442i
$962$		0			0
$963$	−0.0105204		0.000567947i	−0.0105204		0.000567947i
$964$	−0.734487	+	1.81635i	−0.734487	+	1.81635i
$965$		0			0
$966$		0			0
$967$		0			0		−0.943724	−	0.330734i	$-0.892704\pi$
$967$		0			0		0.943724	+	0.330734i	$0.107296\pi$
$968$	0.524670	+	0.507276i	0.524670	+	0.507276i
$969$	−0.00948568	+	0.0478986i	−0.00948568	+	0.0478986i
$970$		0			0
$971$	0.00700224	−	1.03864i	0.00700224	−	1.03864i	−0.851051	−	0.525083i	$-0.824034\pi$
$971$	0.00700224	−	1.03864i	0.00700224	−	1.03864i	0.858053	−	0.513561i	$-0.171674\pi$
$972$	0.928679	+	0.412475i	0.928679	+	0.412475i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.32342	+	1.46450i	1.32342	+	1.46450i	0.781231	+	0.624242i	$0.214592\pi$
$977$	1.32342	+	1.46450i	1.32342	+	1.46450i	0.542187	+	0.840258i	$0.317597\pi$
$978$	0.759357	−	0.188000i	0.759357	−	0.188000i
$979$	−0.252907	−	0.847851i	−0.252907	−	0.847851i
$980$		0			0
$981$		0			0
$982$	−0.471757	+	0.366646i	−0.471757	+	0.366646i
$983$		0			0		0.896748	−	0.442541i	$-0.145923\pi$
$983$		0			0		−0.896748	+	0.442541i	$0.854077\pi$
$984$	0.706194	−	0.302324i	0.706194	−	0.302324i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.967365	−	0.253388i	$-0.0815451\pi$
$991$		0			0		−0.967365	+	0.253388i	$0.918455\pi$
$992$		0			0
$993$	0.509111	−	0.295463i	0.509111	−	0.295463i
$994$		0			0
$995$		0			0
$996$	0.789047	+	0.501641i	0.789047	+	0.501641i
$997$		0			0		0.586694	−	0.809809i	$-0.300429\pi$
$997$		0			0		−0.586694	+	0.809809i	$0.699571\pi$
$998$	−0.643957	+	1.87795i	−0.643957	+	1.87795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.147.1	✓	232
8.3	odd	2	CM	3736.1.l.a.147.1	✓	232
467.413	even	233	inner	3736.1.l.a.1347.1	yes	232
3736.1347	odd	466	inner	3736.1.l.a.1347.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.147.1	✓	232	1.1	even	1	trivial
3736.1.l.a.147.1	✓	232	8.3	odd	2	CM
3736.1.l.a.1347.1	yes	232	467.413	even	233	inner
3736.1.l.a.1347.1	yes	232	3736.1347	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)

\(f(q)\)	\(=\)	\(q+(-0.311581 + 0.950220i) q^{2} +(-0.163525 - 0.438017i) q^{3} +(-0.805835 - 0.592140i) q^{4} +(0.467164 - 0.0189069i) q^{6} +(0.813746 - 0.581221i) q^{8} +(0.590229 - 0.512070i) q^{9} +O(q^{10})\)	\(q+(-0.311581 + 0.950220i) q^{2} +(-0.163525 - 0.438017i) q^{3} +(-0.805835 - 0.592140i) q^{4} +(0.467164 - 0.0189069i) q^{6} +(0.813746 - 0.581221i) q^{8} +(0.590229 - 0.512070i) q^{9} +(0.332633 - 0.399445i) q^{11} +(-0.127593 + 0.449799i) q^{12} +(0.298741 + 0.954334i) q^{16} +(0.483160 - 0.995920i) q^{17} +(0.302675 + 0.720399i) q^{18} +(0.00952457 - 0.0938656i) q^{19} +(0.275919 + 0.440533i) q^{22} +(-0.387653 - 0.261390i) q^{24} +(-0.660401 - 0.750913i) q^{25} +(-0.731374 - 0.398488i) q^{27} +(-0.999909 - 0.0134828i) q^{32} +(-0.229357 - 0.0803796i) q^{33} +(0.795800 + 0.769417i) q^{34} +(-0.778845 + 0.0631459i) q^{36} +(0.0862253 + 0.0382971i) q^{38} +(-0.890822 + 1.38056i) q^{41} +(-0.988808 - 1.09422i) q^{43} +(-0.504574 + 0.124922i) q^{44} +(0.369163 - 0.286911i) q^{48} +(0.896748 - 0.442541i) q^{49} +(0.919301 - 0.393556i) q^{50} +(-0.515239 - 0.0487745i) q^{51} +(0.606533 - 0.570805i) q^{54} +(-0.0426723 + 0.0111774i) q^{57} +(-0.290163 + 0.168396i) q^{59} +(0.324364 - 0.945932i) q^{64} +(0.147842 - 0.192895i) q^{66} +(-0.980215 + 1.61296i) q^{67} +(-0.979071 + 0.516449i) q^{68} +(0.182670 - 0.759749i) q^{72} +(0.362007 - 0.00488132i) q^{73} +(-0.220921 + 0.412060i) q^{75} +(-0.0632568 + 0.0700003i) q^{76} +(0.0553100 - 0.388066i) q^{81} +(-1.03427 - 1.27663i) q^{82} +(0.571641 - 1.91638i) q^{83} +(1.34784 - 0.598647i) q^{86} +(0.0385125 - 0.518380i) q^{88} +(0.942056 - 1.41763i) q^{89} +(0.157604 + 0.440182i) q^{96} +(1.33996 - 1.44321i) q^{97} +(0.141101 + 0.989995i) q^{98} +(-0.00821434 - 0.406095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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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