LMFDB - Embedded newform 3736.1.l.a.291.1

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			291.1
Root			$0.989021 + 0.147772i$ of defining polynomial
Character	$\chi$	$=$	3736.291
Dual form			3736.1.l.a.2067.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.829121 - 0.559069i) q^{2} +(0.147843 + 0.00998213i) q^{3} +(0.374884 - 0.927072i) q^{4} +(0.128161 - 0.0743780i) q^{6} +(-0.207472 - 0.978241i) q^{8} +(-0.969166 - 0.131473i) q^{9} +O(q^{10})$	\(q+(0.829121 - 0.559069i) q^{2} +(0.147843 + 0.00998213i) q^{3} +(0.374884 - 0.927072i) q^{4} +(0.128161 - 0.0743780i) q^{6} +(-0.207472 - 0.978241i) q^{8} +(-0.969166 - 0.131473i) q^{9} +(-0.211416 - 0.503191i) q^{11} +(0.0646782 - 0.133319i) q^{12} +(-0.718923 - 0.695089i) q^{16} +(-0.778579 - 1.78530i) q^{17} +(-0.877058 + 0.432824i) q^{18} +(1.11387 - 0.291763i) q^{19} +(-0.456608 - 0.299011i) q^{22} +(-0.0209084 - 0.146697i) q^{24} +(-0.0471738 + 0.998887i) q^{25} +(-0.287131 - 0.0588769i) q^{27} +(-0.984677 - 0.174386i) q^{32} +(-0.0262334 - 0.0765037i) q^{33} +(-1.64364 - 1.04495i) q^{34} +(-0.485210 + 0.849199i) q^{36} +(0.760415 - 0.864634i) q^{38} +(0.0619640 - 0.0265270i) q^{41} +(-0.249559 - 1.93764i) q^{43} +(-0.545750 + 0.00735893i) q^{44} +(-0.0993493 - 0.109940i) q^{48} +(0.948098 + 0.317979i) q^{49} +(0.519333 + 0.854572i) q^{50} +(-0.0972864 - 0.271717i) q^{51} +(-0.270983 + 0.111710i) q^{54} +(0.167590 - 0.0320163i) q^{57} +(-1.38508 + 0.854568i) q^{59} +(-0.913911 + 0.405915i) q^{64} +(-0.0645215 - 0.0487645i) q^{66} +(0.472423 - 0.444595i) q^{67} +(-1.94698 + 0.0525159i) q^{68} +(0.0724630 + 0.975355i) q^{72} +(1.37839 - 0.244112i) q^{73} +(-0.0169453 + 0.147208i) q^{75} +(0.147086 - 1.14201i) q^{76} +(0.900834 + 0.248988i) q^{81} +(0.0365452 - 0.0566362i) q^{82} +(-1.15541 + 1.59480i) q^{83} +(-1.29019 - 1.46701i) q^{86} +(-0.448379 + 0.311213i) q^{88} +(1.20555 - 0.281272i) q^{89} +(-0.143837 - 0.0356109i) q^{96} +(0.388492 - 1.24105i) q^{97} +(0.963860 - 0.266408i) q^{98} +(0.138741 + 0.515471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{189}{233}\right)$

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 $

$2$	0.829121	−	0.559069i	0.829121	−	0.559069i
$2$	0.829121	−	0.559069i	0.829121	−	0.559069i
$3$	0.147843	+	0.00998213i	0.147843	+	0.00998213i	0.141101	−	0.989995i	$-0.454936\pi$
$3$	0.147843	+	0.00998213i	0.147843	+	0.00998213i	0.00674156	+	0.999977i	$0.497854\pi$
$4$	0.374884	−	0.927072i	0.374884	−	0.927072i
$5$		0			0		−0.690227	−	0.723593i	$-0.742489\pi$
$5$		0			0		0.690227	+	0.723593i	$0.257511\pi$
$6$	0.128161	−	0.0743780i	0.128161	−	0.0743780i
$7$		0			0		−0.986939	−	0.161094i	$-0.948498\pi$
$7$		0			0		0.986939	+	0.161094i	$0.0515021\pi$
$8$	−0.207472	−	0.978241i	−0.207472	−	0.978241i
$9$	−0.969166	−	0.131473i	−0.969166	−	0.131473i
$10$		0			0
$11$	−0.211416	−	0.503191i	−0.211416	−	0.503191i	0.781231	−	0.624242i	$-0.214592\pi$
$11$	−0.211416	−	0.503191i	−0.211416	−	0.503191i	−0.992646	+	0.121051i	$0.961373\pi$
$12$	0.0646782	−	0.133319i	0.0646782	−	0.133319i
$13$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$13$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$14$		0			0
$15$		0			0
$16$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$17$	−0.778579	−	1.78530i	−0.778579	−	1.78530i	−0.597559	−	0.801825i	$-0.703863\pi$
$17$	−0.778579	−	1.78530i	−0.778579	−	1.78530i	−0.181020	−	0.983479i	$-0.557940\pi$
$18$	−0.877058	+	0.432824i	−0.877058	+	0.432824i
$19$	1.11387	−	0.291763i	1.11387	−	0.291763i	0.349751	−	0.936843i	$-0.386266\pi$
$19$	1.11387	−	0.291763i	1.11387	−	0.291763i	0.764115	+	0.645080i	$0.223176\pi$
$20$		0			0
$21$		0			0
$22$	−0.456608	−	0.299011i	−0.456608	−	0.299011i
$23$		0			0		−0.858053	−	0.513561i	$-0.828326\pi$
$23$		0			0		0.858053	+	0.513561i	$0.171674\pi$
$24$	−0.0209084	−	0.146697i	−0.0209084	−	0.146697i
$25$	−0.0471738	+	0.998887i	−0.0471738	+	0.998887i
$26$		0			0
$27$	−0.287131	−	0.0588769i	−0.287131	−	0.0588769i
$28$		0			0
$29$		0			0		0.764115	−	0.645080i	$-0.223176\pi$
$29$		0			0		−0.764115	+	0.645080i	$0.776824\pi$
$30$		0			0
$31$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$31$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$32$	−0.984677	−	0.174386i	−0.984677	−	0.174386i
$33$	−0.0262334	−	0.0765037i	−0.0262334	−	0.0765037i
$34$	−1.64364	−	1.04495i	−1.64364	−	1.04495i
$35$		0			0
$36$	−0.485210	+	0.849199i	−0.485210	+	0.849199i
$37$		0			0		0.0875288	−	0.996162i	$-0.472103\pi$
$37$		0			0		−0.0875288	+	0.996162i	$0.527897\pi$
$38$	0.760415	−	0.864634i	0.760415	−	0.864634i
$39$		0			0
$40$		0			0
$41$	0.0619640	−	0.0265270i	0.0619640	−	0.0265270i	−0.362351	−	0.932042i	$-0.618026\pi$
$41$	0.0619640	−	0.0265270i	0.0619640	−	0.0265270i	0.424315	+	0.905515i	$0.360515\pi$
$42$		0			0
$43$	−0.249559	−	1.93764i	−0.249559	−	1.93764i	−0.337088	−	0.941473i	$-0.609442\pi$
$43$	−0.249559	−	1.93764i	−0.249559	−	1.93764i	0.0875288	−	0.996162i	$-0.472103\pi$
$44$	−0.545750	+	0.00735893i	−0.545750	+	0.00735893i
$45$		0			0
$46$		0			0
$47$		0			0		0.989021	−	0.147772i	$-0.0472103\pi$
$47$		0			0		−0.989021	+	0.147772i	$0.952790\pi$
$48$	−0.0993493	−	0.109940i	−0.0993493	−	0.109940i
$49$	0.948098	+	0.317979i	0.948098	+	0.317979i
$50$	0.519333	+	0.854572i	0.519333	+	0.854572i
$51$	−0.0972864	−	0.271717i	−0.0972864	−	0.271717i
$52$		0			0
$53$		0			0		−0.996729	−	0.0808112i	$-0.974249\pi$
$53$		0			0		0.996729	+	0.0808112i	$0.0257511\pi$
$54$	−0.270983	+	0.111710i	−0.270983	+	0.111710i
$55$		0			0
$56$		0			0
$57$	0.167590	−	0.0320163i	0.167590	−	0.0320163i
$58$		0			0
$59$	−1.38508	+	0.854568i	−1.38508	+	0.854568i	−0.997728	−	0.0673651i	$-0.978541\pi$
$59$	−1.38508	+	0.854568i	−1.38508	+	0.854568i	−0.387350	+	0.921933i	$0.626609\pi$
$60$		0			0
$61$		0			0		0.424315	−	0.905515i	$-0.360515\pi$
$61$		0			0		−0.424315	+	0.905515i	$0.639485\pi$
$62$		0			0
$63$		0			0
$64$	−0.913911	+	0.405915i	−0.913911	+	0.405915i
$65$		0			0
$66$	−0.0645215	−	0.0487645i	−0.0645215	−	0.0487645i
$67$	0.472423	−	0.444595i	0.472423	−	0.444595i	−0.412067	−	0.911153i	$-0.635193\pi$
$67$	0.472423	−	0.444595i	0.472423	−	0.444595i	0.884490	+	0.466559i	$0.154506\pi$
$68$	−1.94698	+	0.0525159i	−1.94698	+	0.0525159i
$69$		0			0
$70$		0			0
$71$		0			0		−0.992646	−	0.121051i	$-0.961373\pi$
$71$		0			0		0.992646	+	0.121051i	$0.0386266\pi$
$72$	0.0724630	+	0.975355i	0.0724630	+	0.975355i
$73$	1.37839	−	0.244112i	1.37839	−	0.244112i	0.564646	−	0.825333i	$-0.309013\pi$
$73$	1.37839	−	0.244112i	1.37839	−	0.244112i	0.813746	+	0.581221i	$0.197425\pi$
$74$		0			0
$75$	−0.0169453	+	0.147208i	−0.0169453	+	0.147208i
$76$	0.147086	−	1.14201i	0.147086	−	1.14201i
$77$		0			0
$78$		0			0
$79$		0			0		−0.772743	−	0.634719i	$-0.781116\pi$
$79$		0			0		0.772743	+	0.634719i	$0.218884\pi$
$80$		0			0
$81$	0.900834	+	0.248988i	0.900834	+	0.248988i
$82$	0.0365452	−	0.0566362i	0.0365452	−	0.0566362i
$83$	−1.15541	+	1.59480i	−1.15541	+	1.59480i	−0.436485	+	0.899712i	$0.643777\pi$
$83$	−1.15541	+	1.59480i	−1.15541	+	1.59480i	−0.718923	+	0.695089i	$0.755365\pi$
$84$		0			0
$85$		0			0
$86$	−1.29019	−	1.46701i	−1.29019	−	1.46701i
$87$		0			0
$88$	−0.448379	+	0.311213i	−0.448379	+	0.311213i
$89$	1.20555	−	0.281272i	1.20555	−	0.281272i	0.424315	−	0.905515i	$-0.360515\pi$
$89$	1.20555	−	0.281272i	1.20555	−	0.281272i	0.781231	+	0.624242i	$0.214592\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.143837	−	0.0356109i	−0.143837	−	0.0356109i
$97$	0.388492	−	1.24105i	0.388492	−	1.24105i	−0.530808	−	0.847492i	$-0.678112\pi$
$97$	0.388492	−	1.24105i	0.388492	−	1.24105i	0.919301	−	0.393556i	$-0.128755\pi$
$98$	0.963860	−	0.266408i	0.963860	−	0.266408i
$99$	0.138741	+	0.515471i	0.138741	+	0.515471i
$100$	0.908355	+	0.418201i	0.908355	+	0.418201i
$101$		0			0		−0.0875288	−	0.996162i	$-0.527897\pi$
$101$		0			0		0.0875288	+	0.996162i	$0.472103\pi$
$102$	−0.232570	−	0.170896i	−0.232570	−	0.170896i
$103$		0			0		−0.999636	−	0.0269632i	$-0.991416\pi$
$103$		0			0		0.999636	+	0.0269632i	$0.00858369\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.117370	−	0.129882i	0.117370	−	0.129882i	−0.680408	−	0.732833i	$-0.738197\pi$
$107$	0.117370	−	0.129882i	0.117370	−	0.129882i	0.797778	+	0.602951i	$0.206009\pi$
$108$	−0.162224	+	0.244119i	−0.162224	+	0.244119i
$109$		0			0		0.960181	−	0.279380i	$-0.0901288\pi$
$109$		0			0		−0.960181	+	0.279380i	$0.909871\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.533603	−	0.995272i	0.533603	−	0.995272i	−0.460585	−	0.887615i	$-0.652361\pi$
$113$	0.533603	−	0.995272i	0.533603	−	0.995272i	0.994188	−	0.107657i	$-0.0343348\pi$
$114$	0.121053	−	0.120240i	0.121053	−	0.120240i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.670636	+	1.48289i	−0.670636	+	1.48289i
$119$		0			0
$120$		0			0
$121$	0.491416	−	0.501456i	0.491416	−	0.501456i
$122$		0			0
$123$	0.00942574	−	0.00330330i	0.00942574	−	0.00330330i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.709486	−	0.704719i	$-0.751073\pi$
$127$		0			0		0.709486	+	0.704719i	$0.248927\pi$
$128$	−0.530808	+	0.847492i	−0.530808	+	0.847492i
$129$	−0.0175539	−	0.288957i	−0.0175539	−	0.288957i
$130$		0			0
$131$	0.959117	+	1.48640i	0.959117	+	1.48640i	0.871589	+	0.490238i	$0.163090\pi$
$131$	0.959117	+	1.48640i	0.959117	+	1.48640i	0.0875288	+	0.996162i	$0.472103\pi$
$132$	−0.0807589	−	0.00435979i	−0.0807589	−	0.00435979i
$133$		0			0
$134$	0.143137	−	0.632740i	0.143137	−	0.632740i
$135$		0			0
$136$	−1.58492	+	1.13204i	−1.58492	+	1.13204i
$137$	0.0799928	+	0.694914i	0.0799928	+	0.694914i	0.970693	+	0.240323i	$0.0772532\pi$
$137$	0.0799928	+	0.694914i	0.0799928	+	0.694914i	−0.890700	+	0.454591i	$0.849785\pi$
$138$		0			0
$139$	1.14632	+	1.62801i	1.14632	+	1.62801i	0.650217	+	0.759749i	$0.274678\pi$
$139$	1.14632	+	1.62801i	1.14632	+	1.62801i	0.496103	+	0.868264i	$0.334764\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.605371	+	0.768176i	0.605371	+	0.768176i
$145$		0			0
$146$	1.00638	−	0.973014i	1.00638	−	0.973014i
$147$	0.136996	+	0.0564751i	0.136996	+	0.0564751i
$148$		0			0
$149$		0			0		0.902634	−	0.430410i	$-0.141631\pi$
$149$		0			0		−0.902634	+	0.430410i	$0.858369\pi$
$150$	0.0682494	+	0.131527i	0.0682494	+	0.131527i
$151$		0			0		0.878119	−	0.478442i	$-0.158798\pi$
$151$		0			0		−0.878119	+	0.478442i	$0.841202\pi$
$152$	−0.516510	−	1.02910i	−0.516510	−	1.02910i
$153$	0.519854	+	1.83262i	0.519854	+	1.83262i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.311581	−	0.950220i	$-0.399142\pi$
$157$		0			0		−0.311581	+	0.950220i	$0.600858\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.886102	−	0.297187i	0.886102	−	0.297187i
$163$	−0.543140	−	0.305497i	−0.543140	−	0.305497i	0.194264	−	0.980949i	$-0.437768\pi$
$163$	−0.543140	−	0.305497i	−0.543140	−	0.305497i	−0.737404	+	0.675452i	$0.763948\pi$
$164$	−0.00136313	−	0.0673896i	−0.00136313	−	0.0673896i
$165$		0			0
$166$	−0.0663706	+	1.96824i	−0.0663706	+	1.96824i
$167$		0			0		−0.878119	−	0.478442i	$-0.841202\pi$
$167$		0			0		0.878119	+	0.478442i	$0.158798\pi$
$168$		0			0
$169$	−0.507764	+	0.861496i	−0.507764	+	0.861496i
$170$		0			0
$171$	−1.11788	+	0.136324i	−1.11788	+	0.136324i
$172$	−1.88988	−	0.495030i	−1.88988	−	0.495030i
$173$		0			0		0.979617	−	0.200872i	$-0.0643777\pi$
$173$		0			0		−0.979617	+	0.200872i	$0.935622\pi$
$174$		0			0
$175$		0			0
$176$	−0.197771	+	0.508709i	−0.197771	+	0.508709i
$177$	−0.213305	+	0.112516i	−0.213305	+	0.112516i
$178$	0.842293	−	0.907192i	0.842293	−	0.907192i
$179$	−1.60728	−	0.515058i	−1.60728	−	0.515058i	−0.639914	−	0.768447i	$-0.721030\pi$
$179$	−1.60728	−	0.515058i	−1.60728	−	0.515058i	−0.967365	+	0.253388i	$0.918455\pi$
$180$		0			0
$181$		0			0		0.0606373	−	0.998160i	$-0.480687\pi$
$181$		0			0		−0.0606373	+	0.998160i	$0.519313\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.733745	+	0.769215i	−0.733745	+	0.769215i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.836584	−	0.547839i	$-0.184549\pi$
$191$		0			0		−0.836584	+	0.547839i	$0.815451\pi$
$192$	−0.139167	+	0.0508890i	−0.139167	+	0.0508890i
$193$	1.28863	+	1.50571i	1.28863	+	1.50571i	0.746444	+	0.665448i	$0.231760\pi$
$193$	1.28863	+	1.50571i	1.28863	+	1.50571i	0.542187	+	0.840258i	$0.317597\pi$
$194$	−0.371724	−	1.24617i	−0.371724	−	1.24617i
$195$		0			0
$196$	0.650217	−	0.759749i	0.650217	−	0.759749i
$197$		0			0		−0.913911	−	0.405915i	$-0.866953\pi$
$197$		0			0		0.913911	+	0.405915i	$0.133047\pi$
$198$	0.403217	+	0.349822i	0.403217	+	0.349822i
$199$		0			0		−0.362351	−	0.932042i	$-0.618026\pi$
$199$		0			0		0.362351	+	0.932042i	$0.381974\pi$
$200$	0.986939	−	0.161094i	0.986939	−	0.161094i
$201$	0.0742824	−	0.0610144i	0.0742824	−	0.0610144i
$202$		0			0
$203$		0			0
$204$	−0.288372	−	0.0116709i	−0.288372	−	0.0116709i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.382301	−	0.498804i	−0.382301	−	0.498804i
$210$		0			0
$211$	0.0662061	+	1.96336i	0.0662061	+	1.96336i	0.220643	+	0.975355i	$0.429185\pi$
$211$	0.0662061	+	1.96336i	0.0662061	+	1.96336i	−0.154437	+	0.988003i	$0.549356\pi$
$212$		0			0
$213$		0			0
$214$	0.0247009	−	0.173306i	0.0247009	−	0.173306i
$215$		0			0
$216$	0.00197599	+	0.293099i	0.00197599	+	0.293099i
$217$		0			0
$218$		0			0
$219$	0.206222	−	0.0223310i	0.206222	−	0.0223310i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.680408	−	0.732833i	$-0.738197\pi$
$223$		0			0		0.680408	+	0.732833i	$0.261803\pi$
$224$		0			0
$225$	0.177045	−	0.961885i	0.177045	−	0.961885i
$226$	−0.114004	−	1.12352i	−0.114004	−	1.12352i
$227$	0.0346404	−	0.466261i	0.0346404	−	0.466261i	−0.952299	−	0.305167i	$-0.901288\pi$
$227$	0.0346404	−	0.466261i	0.0346404	−	0.466261i	0.986939	−	0.161094i	$-0.0515021\pi$
$228$	0.0331454	−	0.167370i	0.0331454	−	0.167370i
$229$		0			0		−0.746444	−	0.665448i	$-0.768240\pi$
$229$		0			0		0.746444	+	0.665448i	$0.231760\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.00873	+	0.680180i	1.00873	+	0.680180i	0.948098	−	0.317979i	$-0.103004\pi$
$233$	1.00873	+	0.680180i	1.00873	+	0.680180i	0.0606373	+	0.998160i	$0.480687\pi$
$234$		0			0
$235$		0			0
$236$	0.273001	+	1.60443i	0.273001	+	1.60443i
$237$		0			0
$238$		0			0
$239$		0			0		0.194264	−	0.980949i	$-0.437768\pi$
$239$		0			0		−0.194264	+	0.980949i	$0.562232\pi$
$240$		0			0
$241$	−0.175977	−	1.73427i	−0.175977	−	1.73427i	−0.575722	−	0.817645i	$-0.695279\pi$
$241$	−0.175977	−	1.73427i	−0.175977	−	1.73427i	0.399745	−	0.916626i	$-0.369099\pi$
$242$	0.127095	−	0.690503i	0.127095	−	0.690503i
$243$	0.407307	+	0.142743i	0.407307	+	0.142743i
$244$		0			0
$245$		0			0
$246$	0.00596831	−	0.00800847i	0.00596831	−	0.00800847i
$247$		0			0
$248$		0			0
$249$	−0.186739	+	0.224247i	−0.186739	+	0.224247i
$250$		0			0
$251$	−0.0106460	−	1.57912i	−0.0106460	−	1.57912i	−0.618962	−	0.785421i	$-0.712446\pi$
$251$	−0.0106460	−	1.57912i	−0.0106460	−	1.57912i	0.608316	−	0.793695i	$-0.291845\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0337017	+	0.999432i	0.0337017	+	0.999432i
$257$	1.36361	+	0.650218i	1.36361	+	0.650218i	0.963860	−	0.266408i	$-0.0858369\pi$
$257$	1.36361	+	0.650218i	1.36361	+	0.650218i	0.399745	+	0.916626i	$0.369099\pi$
$258$	−0.176101	−	0.229767i	−0.176101	−	0.229767i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.62622	+	0.696193i	1.62622	+	0.696193i
$263$		0			0		−0.999182	−	0.0404387i	$-0.987124\pi$
$263$		0			0		0.999182	+	0.0404387i	$0.0128755\pi$
$264$	−0.0693963	+	0.0415350i	−0.0693963	+	0.0415350i
$265$		0			0
$266$		0			0
$267$	0.181039	−	0.0295502i	0.181039	−	0.0295502i
$268$	−0.235067	−	0.604641i	−0.235067	−	0.604641i
$269$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$269$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$270$		0			0
$271$		0			0		0.650217	−	0.759749i	$-0.274678\pi$
$271$		0			0		−0.650217	+	0.759749i	$0.725322\pi$
$272$	−0.681207	+	1.82468i	−0.681207	+	1.82468i
$273$		0			0
$274$	0.454828	+	0.531446i	0.454828	+	0.531446i
$275$	0.512604	−	0.187443i	0.512604	−	0.187443i
$276$		0			0
$277$		0			0		0.999182	−	0.0404387i	$-0.0128755\pi$
$277$		0			0		−0.999182	+	0.0404387i	$0.987124\pi$
$278$	1.86061	+	0.708949i	1.86061	+	0.708949i
$279$		0			0
$280$		0			0
$281$	0.418466	+	0.925302i	0.418466	+	0.925302i	0.994188	+	0.107657i	$0.0343348\pi$
$281$	0.418466	+	0.925302i	0.418466	+	0.925302i	−0.575722	+	0.817645i	$0.695279\pi$
$282$		0			0
$283$	−0.251285	+	0.732814i	−0.251285	+	0.732814i	0.746444	+	0.665448i	$0.231760\pi$
$283$	−0.251285	+	0.732814i	−0.251285	+	0.732814i	−0.997728	+	0.0673651i	$0.978541\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.931389	+	0.298467i	0.931389	+	0.298467i
$289$	−1.90072	+	2.04717i	−1.90072	+	2.04717i
$290$		0			0
$291$	0.0698242	−	0.179602i	0.0698242	−	0.179602i
$292$	0.290428	−	1.36938i	0.290428	−	1.36938i
$293$		0			0		0.337088	−	0.941473i	$-0.390558\pi$
$293$		0			0		−0.337088	+	0.941473i	$0.609442\pi$
$294$	0.145159	−	0.0297652i	0.145159	−	0.0297652i
$295$		0			0
$296$		0			0
$297$	0.0310777	+	0.156929i	0.0310777	+	0.156929i
$298$		0			0
$299$		0			0
$300$	0.130119	+	0.0708953i	0.130119	+	0.0708953i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.00359	−	0.564482i	−1.00359	−	0.564482i
$305$		0			0
$306$	1.45558	+	1.22883i	1.45558	+	1.22883i
$307$	−0.469688	−	0.706799i	−0.469688	−	0.706799i	0.519333	−	0.854572i	$-0.326180\pi$
$307$	−0.469688	−	0.706799i	−0.469688	−	0.706799i	−0.989021	+	0.147772i	$0.952790\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.997728	−	0.0673651i	$-0.0214592\pi$
$311$		0			0		−0.997728	+	0.0673651i	$0.978541\pi$
$312$		0			0
$313$	−0.286502	−	0.262432i	−0.286502	−	0.262432i	0.519333	−	0.854572i	$-0.326180\pi$
$313$	−0.286502	−	0.262432i	−0.286502	−	0.262432i	−0.805835	+	0.592140i	$0.798283\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.460585	−	0.887615i	$-0.652361\pi$
$317$		0			0		0.460585	+	0.887615i	$0.347639\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.0186489	−	0.0180306i	0.0186489	−	0.0180306i
$322$		0			0
$323$	−1.38812	−	1.76143i	−1.38812	−	1.76143i
$324$	0.568538	−	0.741796i	0.568538	−	0.741796i
$325$		0			0
$326$	−0.621123	+	0.0503584i	−0.621123	+	0.0503584i
$327$		0			0
$328$	−0.0388056	−	0.0551121i	−0.0388056	−	0.0551121i
$329$		0			0
$330$		0			0
$331$	0.882404	−	0.630261i	0.882404	−	0.630261i	−0.0471738	−	0.998887i	$-0.515021\pi$
$331$	0.882404	−	0.630261i	0.882404	−	0.630261i	0.929578	+	0.368626i	$0.120172\pi$
$332$	1.04535	+	1.66901i	1.04535	+	1.66901i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.546044	−	1.74435i	−0.546044	−	1.74435i	−0.660401	−	0.750913i	$-0.729614\pi$
$337$	−0.546044	−	1.74435i	−0.546044	−	1.74435i	0.114357	−	0.993440i	$-0.463519\pi$
$338$	0.0606373	+	0.998160i	0.0606373	+	0.998160i
$339$	0.0888244	−	0.141818i	0.0888244	−	0.141818i
$340$		0			0
$341$		0			0
$342$	−0.850644	+	0.738001i	−0.850644	+	0.738001i
$343$		0			0
$344$	−1.84370	+	0.646134i	−1.84370	+	0.646134i
$345$		0			0
$346$		0			0
$347$	−0.614137	+	0.779299i	−0.614137	+	0.779299i	−0.989021	−	0.147772i	$-0.952790\pi$
$347$	−0.614137	+	0.779299i	−0.614137	+	0.779299i	0.374884	+	0.927072i	$0.377682\pi$
$348$		0			0
$349$		0			0		0.412067	−	0.911153i	$-0.364807\pi$
$349$		0			0		−0.412067	+	0.911153i	$0.635193\pi$
$350$		0			0
$351$		0			0
$352$	0.120427	+	0.532349i	0.120427	+	0.532349i
$353$	1.34532	−	1.33629i	1.34532	−	1.33629i	0.448576	−	0.893745i	$-0.351931\pi$
$353$	1.34532	−	1.33629i	1.34532	−	1.33629i	0.896748	−	0.442541i	$-0.145923\pi$
$354$	−0.113951	+	0.212541i	−0.113951	+	0.212541i
$355$		0			0
$356$	0.191181	−	1.22307i	0.191181	−	1.22307i
$357$		0			0
$358$	−1.62058	+	0.471533i	−1.62058	+	0.471533i
$359$		0			0		0.553466	−	0.832871i	$-0.313305\pi$
$359$		0			0		−0.553466	+	0.832871i	$0.686695\pi$
$360$		0			0
$361$	0.283984	−	0.159731i	0.283984	−	0.159731i
$362$		0			0
$363$	0.0776580	−	0.0692314i	0.0776580	−	0.0692314i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.908355	−	0.418201i	$-0.862661\pi$
$367$		0			0		0.908355	+	0.418201i	$0.137339\pi$
$368$		0			0
$369$	−0.0635409	+	0.0175625i	−0.0635409	+	0.0175625i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.737404	−	0.675452i	$-0.236052\pi$
$373$		0			0		−0.737404	+	0.675452i	$0.763948\pi$
$374$	−0.178320	+	1.04799i	−0.178320	+	1.04799i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.340880	−	0.236600i	0.340880	−	0.236600i	−0.387350	−	0.921933i	$-0.626609\pi$
$379$	0.340880	−	0.236600i	0.340880	−	0.236600i	0.728230	+	0.685333i	$0.240343\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.575722	−	0.817645i	$-0.304721\pi$
$383$		0			0		−0.575722	+	0.817645i	$0.695279\pi$
$384$	−0.0869361	+	0.119997i	−0.0869361	+	0.119997i
$385$		0			0
$386$	1.91022	+	0.527980i	1.91022	+	0.527980i
$387$	−0.0128814	+	1.91070i	−0.0128814	+	1.91070i
$388$	−1.00490	−	0.825410i	−1.00490	−	0.825410i
$389$		0			0		−0.864900	−	0.501945i	$-0.832618\pi$
$389$		0			0		0.864900	+	0.501945i	$0.167382\pi$
$390$		0			0
$391$		0			0
$392$	0.114357	−	0.993440i	0.114357	−	0.993440i
$393$	0.126961	+	0.229328i	0.126961	+	0.229328i
$394$		0			0
$395$		0			0
$396$	0.529890	+	0.0646192i	0.529890	+	0.0646192i
$397$		0			0		−0.929578	−	0.368626i	$-0.879828\pi$
$397$		0			0		0.929578	+	0.368626i	$0.120172\pi$
$398$		0			0
$399$		0			0
$400$	0.728230	−	0.685333i	0.728230	−	0.685333i
$401$	−1.08563	−	0.820505i	−1.08563	−	0.820505i	−0.100952	−	0.994891i	$-0.532189\pi$
$401$	−1.08563	−	0.820505i	−1.08563	−	0.820505i	−0.984677	+	0.174386i	$0.944206\pi$
$402$	0.0274779	−	0.0921173i	0.0274779	−	0.0921173i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.245620	+	0.151543i	−0.245620	+	0.151543i
$409$	−0.302082	+	1.06492i	−0.302082	+	1.06492i	0.650217	+	0.759749i	$0.274678\pi$
$409$	−0.302082	+	1.06492i	−0.302082	+	1.06492i	−0.952299	+	0.305167i	$0.901288\pi$
$410$		0			0
$411$	0.00488966	+	0.103537i	0.00488966	+	0.103537i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.153224	+	0.252133i	0.153224	+	0.252133i
$418$	−0.595840	−	0.199837i	−0.595840	−	0.199837i
$419$	−1.21037	−	1.33940i	−1.21037	−	1.33940i	−0.924523	−	0.381126i	$-0.875536\pi$
$419$	−1.21037	−	1.33940i	−1.21037	−	1.33940i	−0.285846	−	0.958275i	$-0.592275\pi$
$420$		0			0
$421$		0			0		0.998546	−	0.0539068i	$-0.0171674\pi$
$421$		0			0		−0.998546	+	0.0539068i	$0.982833\pi$
$422$	1.15254	+	1.59085i	1.15254	+	1.59085i
$423$		0			0
$424$		0			0
$425$	1.82005	−	0.693493i	1.82005	−	0.693493i
$426$		0			0
$427$		0			0
$428$	−0.0764101	−	0.157501i	−0.0764101	−	0.157501i
$429$		0			0
$430$		0			0
$431$		0			0		0.496103	−	0.868264i	$-0.334764\pi$
$431$		0			0		−0.496103	+	0.868264i	$0.665236\pi$
$432$	0.165501	+	0.241910i	0.165501	+	0.241910i
$433$	1.62679	+	1.03424i	1.62679	+	1.03424i	0.956327	+	0.292300i	$0.0944206\pi$
$433$	1.62679	+	1.03424i	1.62679	+	1.03424i	0.670466	+	0.741941i	$0.266094\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.158499	−	0.133808i	0.158499	−	0.133808i
$439$		0			0		0.519333	−	0.854572i	$-0.326180\pi$
$439$		0			0		−0.519333	+	0.854572i	$0.673820\pi$
$440$		0			0
$441$	−0.877058	−	0.432824i	−0.877058	−	0.432824i
$442$		0			0
$443$	0.225135	+	1.57959i	0.225135	+	1.57959i	0.709486	+	0.704719i	$0.248927\pi$
$443$	0.225135	+	1.57959i	0.225135	+	1.57959i	−0.484351	+	0.874874i	$0.660944\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.78031	+	0.878573i	−1.78031	+	0.878573i	−0.836584	+	0.547839i	$0.815451\pi$
$449$	−1.78031	+	0.878573i	−1.78031	+	0.878573i	−0.943724	+	0.330734i	$0.892704\pi$
$450$	−0.390968	−	0.896500i	−0.390968	−	0.896500i
$451$	−0.0264483	−	0.0255715i	−0.0264483	−	0.0255715i
$452$	−0.722649	−	0.867800i	−0.722649	−	0.867800i
$453$		0			0
$454$	−0.231951	−	0.405953i	−0.231951	−	0.405953i
$455$		0			0
$456$	−0.0660899	−	0.157301i	−0.0660899	−	0.157301i
$457$	1.42270	+	0.311773i	1.42270	+	0.311773i	0.858053	−	0.513561i	$-0.171674\pi$
$457$	1.42270	+	0.311773i	1.42270	+	0.311773i	0.564646	+	0.825333i	$0.309013\pi$
$458$		0			0
$459$	0.118441	+	0.558457i	0.118441	+	0.558457i
$460$		0			0
$461$		0			0		0.864900	−	0.501945i	$-0.167382\pi$
$461$		0			0		−0.864900	+	0.501945i	$0.832618\pi$
$462$		0			0
$463$		0			0		0.374884	−	0.927072i	$-0.377682\pi$
$463$		0			0		−0.374884	+	0.927072i	$0.622318\pi$
$464$		0			0
$465$		0			0
$466$	1.21663			1.21663
$467$	0.843894	+	0.536510i	0.843894	+	0.536510i
$467$	0.843894	+	0.536510i	0.843894	+	0.536510i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.12334	+	1.17764i	1.12334	+	1.17764i
$473$	−0.922240	+	0.535222i	−0.922240	+	0.535222i
$474$		0			0
$475$	0.238892	+	1.12639i	0.238892	+	1.12639i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$479$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$480$		0			0
$481$		0			0
$482$	−1.11548	−	1.33954i	−1.11548	−	1.33954i
$483$		0			0
$484$	−0.280662	−	0.643565i	−0.280662	−	0.643565i
$485$		0			0
$486$	0.417511	−	0.109361i	0.417511	−	0.109361i
$487$		0			0		0.929578	−	0.368626i	$-0.120172\pi$
$487$		0			0		−0.929578	+	0.368626i	$0.879828\pi$
$488$		0			0
$489$	−0.0772500	−	0.0505873i	−0.0772500	−	0.0505873i
$490$		0			0
$491$	−0.202882	−	1.42346i	−0.202882	−	1.42346i	−0.789576	−	0.613653i	$-0.789700\pi$
$491$	−0.202882	−	1.42346i	−0.202882	−	1.42346i	0.586694	−	0.809809i	$-0.300429\pi$
$492$	0.000471163	−	0.00997669i	0.000471163	−	0.00997669i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.0294596	+	0.290327i	−0.0294596	+	0.290327i
$499$	−0.0132765	−	0.00235127i	−0.0132765	−	0.00235127i	0.167744	−	0.985831i	$-0.446352\pi$
$499$	−0.0132765	−	0.00235127i	−0.0132765	−	0.00235127i	−0.181020	+	0.983479i	$0.557940\pi$
$500$		0			0
$501$		0			0
$502$	−0.891661	−	1.30333i	−0.891661	−	1.30333i
$503$		0			0		0.496103	−	0.868264i	$-0.334764\pi$
$503$		0			0		−0.496103	+	0.868264i	$0.665236\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0836690	+	0.122298i	−0.0836690	+	0.122298i
$508$		0			0
$509$		0			0		0.934463	−	0.356059i	$-0.115880\pi$
$509$		0			0		−0.934463	+	0.356059i	$0.884120\pi$
$510$		0			0
$511$		0			0
$512$	0.586694	+	0.809809i	0.586694	+	0.809809i
$513$	−0.337004	+	0.0181933i	−0.337004	+	0.0181933i
$514$	1.49411	−	0.223239i	1.49411	−	0.223239i
$515$		0			0
$516$	−0.274464	−	0.0920518i	−0.274464	−	0.0920518i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.51901	−	0.626196i	1.51901	−	0.626196i	0.542187	−	0.840258i	$-0.317597\pi$
$521$	1.51901	−	0.626196i	1.51901	−	0.626196i	0.976820	+	0.214062i	$0.0686695\pi$
$522$		0			0
$523$	−0.0158262	−	0.335114i	−0.0158262	−	0.335114i	−0.992646	−	0.121051i	$-0.961373\pi$
$523$	−0.0158262	−	0.335114i	−0.0158262	−	0.335114i	0.976820	−	0.214062i	$-0.0686695\pi$
$524$	1.73756	−	0.331942i	1.73756	−	0.331942i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.0343171	+	0.0732348i	−0.0343171	+	0.0732348i
$529$	0.472511	+	0.881325i	0.472511	+	0.881325i
$530$		0			0
$531$	1.45472	−	0.646118i	1.45472	−	0.646118i
$532$		0			0
$533$		0			0
$534$	0.133583	−	0.125714i	0.133583	−	0.125714i
$535$		0			0
$536$	−0.532935	−	0.369902i	−0.532935	−	0.369902i
$537$	−0.232484	−	0.0921918i	−0.232484	−	0.0921918i
$538$		0			0
$539$	−0.0404382	−	0.544300i	−0.0404382	−	0.544300i
$540$		0			0
$541$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$541$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$542$		0			0
$543$		0			0
$544$	0.455318	+	1.89372i	0.455318	+	1.89372i
$545$		0			0
$546$		0			0
$547$	−0.0129462	+	1.92032i	−0.0129462	+	1.92032i	0.272900	+	0.962042i	$0.412017\pi$
$547$	−0.0129462	+	1.92032i	−0.0129462	+	1.92032i	−0.285846	+	0.958275i	$0.592275\pi$
$548$	0.674223	+	0.186353i	0.674223	+	0.186353i
$549$		0			0
$550$	0.320218	−	0.441994i	0.320218	−	0.441994i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.93902	−	0.452404i	1.93902	−	0.452404i
$557$		0			0		−0.939179	−	0.343428i	$-0.888412\pi$
$557$		0			0		0.939179	+	0.343428i	$0.111588\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.116158	+	0.106399i	−0.116158	+	0.106399i
$562$	0.864267	+	0.533237i	0.864267	+	0.533237i
$563$	−0.847386	−	0.209794i	−0.847386	−	0.209794i	−0.207472	−	0.978241i	$-0.566524\pi$
$563$	−0.847386	−	0.209794i	−0.847386	−	0.209794i	−0.639914	+	0.768447i	$0.721030\pi$
$564$		0			0
$565$		0			0
$566$	0.201348	+	0.748077i	0.201348	+	0.748077i
$567$		0			0
$568$		0			0
$569$	1.43552	+	1.05484i	1.43552	+	1.05484i	0.986939	+	0.161094i	$0.0515021\pi$
$569$	1.43552	+	1.05484i	1.43552	+	1.05484i	0.448576	+	0.893745i	$0.351931\pi$
$570$		0			0
$571$	−1.48950	+	1.32787i	−1.48950	+	1.32787i	−0.699920	+	0.714221i	$0.746781\pi$
$571$	−1.48950	+	1.32787i	−1.48950	+	1.32787i	−0.789576	+	0.613653i	$0.789700\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.939098	−	0.273245i	0.939098	−	0.273245i
$577$	−0.348956	−	1.89587i	−0.348956	−	1.89587i	−0.436485	−	0.899712i	$-0.643777\pi$
$577$	−0.348956	−	1.89587i	−0.348956	−	1.89587i	0.0875288	−	0.996162i	$-0.472103\pi$
$578$	−0.431418	+	2.75998i	−0.431418	+	2.75998i
$579$	0.175485	+	0.235471i	0.175485	+	0.235471i
$580$		0			0
$581$		0			0
$582$	−0.0425173	−	0.187949i	−0.0425173	−	0.187949i
$583$		0			0
$584$	−0.524778	−	1.29775i	−0.524778	−	1.29775i
$585$		0			0
$586$		0			0
$587$	0.842293	−	1.06881i	0.842293	−	1.06881i	−0.154437	−	0.988003i	$-0.549356\pi$
$587$	0.842293	−	1.06881i	0.842293	−	1.06881i	0.996729	−	0.0808112i	$-0.0257511\pi$
$588$	0.103714	−	0.105833i	0.103714	−	0.105833i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.14292	+	0.349333i	−1.14292	+	0.349333i	−0.805835	−	0.592140i	$-0.798283\pi$
$593$	−1.14292	+	0.349333i	−1.14292	+	0.349333i	−0.337088	+	0.941473i	$0.609442\pi$
$594$	0.113502	+	0.112739i	0.113502	+	0.112739i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$599$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$600$	0.147520	−	0.0139648i	0.147520	−	0.0139648i
$601$	0.441125	−	1.95000i	0.441125	−	1.95000i	0.194264	−	0.980949i	$-0.437768\pi$
$601$	0.441125	−	1.95000i	0.441125	−	1.95000i	0.246861	−	0.969051i	$-0.420601\pi$
$602$		0			0
$603$	−0.516308	+	0.368775i	−0.516308	+	0.368775i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.976820	−	0.214062i	$-0.0686695\pi$
$607$		0			0		−0.976820	+	0.214062i	$0.931330\pi$
$608$	−1.14768	+	0.0930495i	−1.14768	+	0.0930495i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.89385	+	0.205078i	1.89385	+	0.205078i
$613$		0			0		0.718923	−	0.695089i	$-0.244635\pi$
$613$		0			0		−0.718923	+	0.695089i	$0.755365\pi$
$614$	−0.784578	−	0.323435i	−0.784578	−	0.323435i
$615$		0			0
$616$		0			0
$617$	0.0186293	+	0.0359013i	0.0186293	+	0.0359013i	0.896748	−	0.442541i	$-0.145923\pi$
$617$	0.0186293	+	0.0359013i	0.0186293	+	0.0359013i	−0.878119	+	0.478442i	$0.841202\pi$
$618$		0			0
$619$	0.601510	+	1.19845i	0.601510	+	1.19845i	0.963860	+	0.266408i	$0.0858369\pi$
$619$	0.601510	+	1.19845i	0.601510	+	1.19845i	−0.362351	+	0.932042i	$0.618026\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.995549	−	0.0942425i	−0.995549	−	0.0942425i
$626$	−0.384262	−	0.0574136i	−0.384262	−	0.0574136i
$627$	−0.0515414	−	0.0775609i	−0.0515414	−	0.0775609i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.0202235	−	0.999795i	$-0.506438\pi$
$631$		0			0		0.0202235	+	0.999795i	$0.493562\pi$
$632$		0			0
$633$	−0.00981039	+	0.290930i	−0.00981039	+	0.290930i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.564005	−	1.57524i	0.564005	−	1.57524i	−0.233773	−	0.972291i	$-0.575107\pi$
$641$	0.564005	−	1.57524i	0.564005	−	1.57524i	0.797778	−	0.602951i	$-0.206009\pi$
$642$	0.00538182	−	0.0253756i	0.00538182	−	0.0253756i
$643$	0.677207	−	1.74192i	0.677207	−	1.74192i	0.00674156	−	0.999977i	$-0.497854\pi$
$643$	0.677207	−	1.74192i	0.677207	−	1.74192i	0.670466	−	0.741941i	$-0.266094\pi$
$644$		0			0
$645$		0			0
$646$	−2.13568	−	0.684386i	−2.13568	−	0.684386i
$647$		0			0		0.970693	−	0.240323i	$-0.0772532\pi$
$647$		0			0		−0.970693	+	0.240323i	$0.922747\pi$
$648$	0.0566723	−	0.932891i	0.0566723	−	0.932891i
$649$	0.722838	+	0.516290i	0.722838	+	0.516290i
$650$		0			0
$651$		0			0
$652$	−0.486833	+	0.389004i	−0.486833	+	0.389004i
$653$		0			0		−0.412067	−	0.911153i	$-0.635193\pi$
$653$		0			0		0.412067	+	0.911153i	$0.364807\pi$
$654$		0			0
$655$		0			0
$656$	−0.0629860	−	0.0239996i	−0.0629860	−	0.0239996i
$657$	−1.36798	+	0.0553647i	−1.36798	+	0.0553647i
$658$		0			0
$659$	−0.997048	+	0.364588i	−0.997048	+	0.364588i	−0.789576	−	0.613653i	$-0.789700\pi$
$659$	−0.997048	+	0.364588i	−0.997048	+	0.364588i	−0.207472	+	0.978241i	$0.566524\pi$
$660$		0			0
$661$		0			0		−0.285846	−	0.958275i	$-0.592275\pi$
$661$		0			0		0.285846	+	0.958275i	$0.407725\pi$
$662$	0.379261	−	1.01589i	0.379261	−	1.01589i
$663$		0			0
$664$	1.79981	+	0.799391i	1.79981	+	0.799391i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.54249	+	0.980644i	−1.54249	+	0.980644i	−0.553466	+	0.832871i	$0.686695\pi$
$673$	−1.54249	+	0.980644i	−1.54249	+	0.980644i	−0.989021	+	0.147772i	$0.952790\pi$
$674$	−1.42795	−	1.14100i	−1.42795	−	1.14100i
$675$	0.0723564	−	0.284034i	0.0723564	−	0.284034i
$676$	0.608316	+	0.793695i	0.608316	+	0.793695i
$677$		0			0		−0.902634	−	0.430410i	$-0.858369\pi$
$677$		0			0		0.902634	+	0.430410i	$0.141631\pi$
$678$	−0.00563957	−	0.167243i	−0.00563957	−	0.167243i
$679$		0			0
$680$		0			0
$681$	0.00977563	−	0.0685877i	0.00977563	−	0.0685877i
$682$		0			0
$683$	−0.0116616	−	1.72976i	−0.0116616	−	1.72976i	−0.507764	−	0.861496i	$-0.669528\pi$
$683$	−0.0116616	−	1.72976i	−0.0116616	−	1.72976i	0.496103	−	0.868264i	$-0.334764\pi$
$684$	−0.292694	+	1.08746i	−0.292694	+	1.08746i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.16742	+	1.56648i	−1.16742	+	1.56648i
$689$		0			0
$690$		0			0
$691$	0.490556	+	0.171918i	0.490556	+	0.171918i	0.564646	−	0.825333i	$-0.309013\pi$
$691$	0.490556	+	0.171918i	0.490556	+	0.171918i	−0.0740898	+	0.997252i	$0.523605\pi$
$692$		0			0
$693$		0			0
$694$	−0.0735123	+	0.989478i	−0.0735123	+	0.989478i
$695$		0			0
$696$		0			0
$697$	−0.0956027	−	0.0899711i	−0.0956027	−	0.0899711i
$698$		0			0
$699$	0.142345	+	0.110629i	0.142345	+	0.110629i
$700$		0			0
$701$		0			0		−0.829121	−	0.559069i	$-0.811159\pi$
$701$		0			0		0.829121	+	0.559069i	$0.188841\pi$
$702$		0			0
$703$		0			0
$704$	0.397468	+	0.374055i	0.397468	+	0.374055i
$705$		0			0
$706$	0.368362	−	1.86007i	0.368362	−	1.86007i
$707$		0			0
$708$	0.0243457	+	0.239929i	0.0243457	+	0.239929i
$709$		0			0		0.181020	−	0.983479i	$-0.442060\pi$
$709$		0			0		−0.181020	+	0.983479i	$0.557940\pi$
$710$		0			0
$711$		0			0
$712$	−0.525269	−	1.12096i	−0.525269	−	1.12096i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.08004	+	1.29698i	−1.08004	+	1.29698i
$717$		0			0
$718$		0			0
$719$		0			0		0.629495	−	0.777005i	$-0.283262\pi$
$719$		0			0		−0.629495	+	0.777005i	$0.716738\pi$
$720$		0			0
$721$		0			0
$722$	0.146157	−	0.291203i	0.146157	−	0.291203i
$723$	−0.00870526	−	0.258157i	−0.00870526	−	0.258157i
$724$		0			0
$725$		0			0
$726$	0.0256828	−	0.100817i	0.0256828	−	0.100817i
$727$		0			0		−0.781231	−	0.624242i	$-0.785408\pi$
$727$		0			0		0.781231	+	0.624242i	$0.214592\pi$
$728$		0			0
$729$	−0.800395	−	0.342652i	−0.800395	−	0.342652i
$730$		0			0
$731$	−3.26497	+	1.95414i	−3.26497	+	1.95414i
$732$		0			0
$733$		0			0		0.772743	−	0.634719i	$-0.218884\pi$
$733$		0			0		−0.772743	+	0.634719i	$0.781116\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.323594	−	0.143725i	−0.323594	−	0.143725i
$738$	−0.0428645	+	0.0500852i	−0.0428645	+	0.0500852i
$739$	−0.666135	+	1.78431i	−0.666135	+	1.78431i	−0.0471738	+	0.998887i	$0.515021\pi$
$739$	−0.666135	+	1.78431i	−0.666135	+	1.78431i	−0.618962	+	0.785421i	$0.712446\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.836584	−	0.547839i	$-0.184549\pi$
$743$		0			0		−0.836584	+	0.547839i	$0.815451\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.32946	−	1.39372i	1.32946	−	1.39372i
$748$	0.438048	+	0.968601i	0.438048	+	0.968601i
$749$		0			0
$750$		0			0
$751$		0			0		0.484351	−	0.874874i	$-0.339056\pi$
$751$		0			0		−0.484351	+	0.874874i	$0.660944\pi$
$752$		0			0
$753$	0.0141890	−	0.233568i	0.0141890	−	0.233568i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$757$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$758$	0.150355	−	0.386745i	0.150355	−	0.386745i
$759$		0			0
$760$		0			0
$761$	1.57882	−	0.323740i	1.57882	−	0.323740i	0.670466	−	0.741941i	$-0.266094\pi$
$761$	1.57882	−	0.323740i	1.57882	−	0.323740i	0.908355	+	0.418201i	$0.137339\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.00499390	+	0.148095i	−0.00499390	+	0.148095i
$769$	−0.499447	+	0.962506i	−0.499447	+	0.962506i	0.496103	+	0.868264i	$0.334764\pi$
$769$	−0.499447	+	0.962506i	−0.499447	+	0.962506i	−0.995549	+	0.0942425i	$0.969957\pi$
$770$		0			0
$771$	0.195109	+	0.109742i	0.195109	+	0.109742i
$772$	1.87899	−	0.630187i	1.87899	−	0.630187i
$773$		0			0		−0.764115	−	0.645080i	$-0.776824\pi$
$773$		0			0		0.764115	+	0.645080i	$0.223176\pi$
$774$	1.05753	+	1.59140i	1.05753	+	1.59140i
$775$		0			0
$776$	−1.29465	−	0.122556i	−1.29465	−	0.122556i
$777$		0			0
$778$		0			0
$779$	0.0612800	−	0.0476263i	0.0612800	−	0.0476263i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.460585	−	0.887615i	−0.460585	−	0.887615i
$785$		0			0
$786$	0.233476	+	0.119161i	0.233476	+	0.119161i
$787$	−1.84837	−	0.761974i	−1.84837	−	0.761974i	−0.934463	−	0.356059i	$-0.884120\pi$
$787$	−1.84837	−	0.761974i	−1.84837	−	0.761974i	−0.913911	−	0.405915i	$-0.866953\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.475470	−	0.242668i	0.475470	−	0.242668i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.114357	−	0.993440i	$-0.536481\pi$
$797$		0			0		0.114357	+	0.993440i	$0.463519\pi$
$798$		0			0
$799$		0			0
$800$	0.220643	−	0.975355i	0.220643	−	0.975355i
$801$	−1.20535	+	0.114103i	−1.20535	+	0.114103i
$802$	−1.35884	−	0.0733572i	−1.35884	−	0.0733572i
$803$	−0.414249	−	0.641985i	−0.414249	−	0.641985i
$804$	−0.0287174	−	0.0917385i	−0.0287174	−	0.0917385i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.566336	+	0.491341i	−0.566336	+	0.491341i	−0.890700	−	0.454591i	$-0.849785\pi$
$809$	−0.566336	+	0.491341i	−0.566336	+	0.491341i	0.324364	+	0.945932i	$0.394850\pi$
$810$		0			0
$811$	1.68115	−	0.589169i	1.68115	−	0.589169i	0.690227	−	0.723593i	$-0.257511\pi$
$811$	1.68115	−	0.589169i	1.68115	−	0.589169i	0.990924	+	0.134424i	$0.0429185\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.118926	+	0.262966i	−0.118926	+	0.262966i
$817$	−0.843305	−	2.08545i	−0.843305	−	2.08545i
$818$	0.344899	+	1.05183i	0.344899	+	1.05183i
$819$		0			0
$820$		0			0
$821$		0			0		0.472511	−	0.881325i	$-0.343348\pi$
$821$		0			0		−0.472511	+	0.881325i	$0.656652\pi$
$822$	0.0619382	+	0.0831108i	0.0619382	+	0.0831108i
$823$		0			0		0.154437	−	0.988003i	$-0.450644\pi$
$823$		0			0		−0.154437	+	0.988003i	$0.549356\pi$
$824$		0			0
$825$	0.0776560	−	0.0225952i	0.0776560	−	0.0225952i
$826$		0			0
$827$	−0.801286	+	0.886707i	−0.801286	+	0.886707i	−0.995549	−	0.0942425i	$-0.969957\pi$
$827$	−0.801286	+	0.886707i	−0.801286	+	0.886707i	0.194264	+	0.980949i	$0.437768\pi$
$828$		0			0
$829$		0			0		−0.507764	−	0.861496i	$-0.669528\pi$
$829$		0			0		0.507764	+	0.861496i	$0.330472\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.170479	−	1.94021i	−0.170479	−	1.94021i
$834$	0.268001	+	0.123386i	0.268001	+	0.123386i
$835$		0			0
$836$	−0.605746	+	0.167426i	−0.605746	+	0.167426i
$837$		0			0
$838$	−1.75236	−	0.433846i	−1.75236	−	0.433846i
$839$		0			0		−0.851051	−	0.525083i	$-0.824034\pi$
$839$		0			0		0.851051	+	0.525083i	$0.175966\pi$
$840$		0			0
$841$	0.167744	−	0.985831i	0.167744	−	0.985831i
$842$		0			0
$843$	0.0526308	+	0.140977i	0.0526308	+	0.140977i
$844$	1.84499	+	0.674654i	1.84499	+	0.674654i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0444657	+	0.105833i	−0.0444657	+	0.105833i
$850$	1.12133	−	1.59252i	1.12133	−	1.59252i
$851$		0			0
$852$		0			0
$853$		0			0		−0.963860	−	0.266408i	$-0.914163\pi$
$853$		0			0		0.963860	+	0.266408i	$0.0858369\pi$
$854$		0			0
$855$		0			0
$856$	−0.151407	−	0.0878693i	−0.151407	−	0.0878693i
$857$	−0.0283507	−	0.117914i	−0.0283507	−	0.117914i	0.956327	−	0.292300i	$-0.0944206\pi$
$857$	−0.0283507	−	0.117914i	−0.0283507	−	0.117914i	−0.984677	+	0.174386i	$0.944206\pi$
$858$		0			0
$859$	0.153344	−	1.33213i	0.153344	−	1.33213i	−0.660401	−	0.750913i	$-0.729614\pi$
$859$	0.153344	−	1.33213i	0.153344	−	1.33213i	0.813746	−	0.581221i	$-0.197425\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.992646	−	0.121051i	$-0.961373\pi$
$863$		0			0		0.992646	+	0.121051i	$0.0386266\pi$
$864$	0.272465	+	0.108046i	0.272465	+	0.108046i
$865$		0			0
$866$	1.92702	−	0.0519775i	1.92702	−	0.0519775i
$867$	−0.301443	+	0.283686i	−0.301443	+	0.283686i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.539677	+	1.15171i	−0.539677	+	1.15171i
$874$		0			0
$875$		0			0
$876$	0.0566071	−	0.199554i	0.0566071	−	0.199554i
$877$		0			0		0.982237	−	0.187646i	$-0.0600858\pi$
$877$		0			0		−0.982237	+	0.187646i	$0.939914\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.57399	−	0.127613i	−1.57399	−	0.127613i	−0.737404	−	0.675452i	$-0.763948\pi$
$881$	−1.57399	−	0.127613i	−1.57399	−	0.127613i	−0.836584	+	0.547839i	$0.815451\pi$
$882$	−0.969166	+	0.131473i	−0.969166	+	0.131473i
$883$	−0.558974	−	1.56119i	−0.558974	−	1.56119i	−0.805835	−	0.592140i	$-0.798283\pi$
$883$	−0.558974	−	1.56119i	−0.558974	−	1.56119i	0.246861	−	0.969051i	$-0.420601\pi$
$884$		0			0
$885$		0			0
$886$	1.06977	+	1.18381i	1.06977	+	1.18381i
$887$		0			0		0.989021	−	0.147772i	$-0.0472103\pi$
$887$		0			0		−0.989021	+	0.147772i	$0.952790\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.0651619	−	0.505931i	−0.0651619	−	0.505931i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.984909	+	1.72376i	−0.984909	+	1.72376i
$899$		0			0
$900$	−0.825365	−	0.524729i	−0.825365	−	0.524729i
$901$		0			0
$902$	−0.0362251	−	0.00641544i	−0.0362251	−	0.00641544i
$903$		0			0
$904$	−1.08432	−	0.315501i	−1.08432	−	0.315501i
$905$		0			0
$906$		0			0
$907$	0.709930	+	0.145573i	0.709930	+	0.145573i	0.542187	−	0.840258i	$-0.317597\pi$
$907$	0.709930	+	0.145573i	0.709930	+	0.145573i	0.167744	+	0.985831i	$0.446352\pi$
$908$	−0.419271	−	0.206908i	−0.419271	−	0.206908i
$909$		0			0
$910$		0			0
$911$		0			0		−0.858053	−	0.513561i	$-0.828326\pi$
$911$		0			0		0.858053	+	0.513561i	$0.171674\pi$
$912$	−0.142738	−	0.0934726i	−0.142738	−	0.0934726i
$913$	1.04676	+	0.244225i	1.04676	+	0.244225i
$914$	1.35389	−	0.536889i	1.35389	−	0.536889i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.410418	+	0.396812i	0.410418	+	0.396812i
$919$		0			0		−0.639914	−	0.768447i	$-0.721030\pi$
$919$		0			0		0.639914	+	0.768447i	$0.278970\pi$
$920$		0			0
$921$	−0.0623847	−	0.109184i	−0.0623847	−	0.109184i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.992440	−	1.04042i	−0.992440	−	1.04042i	−0.999182	−	0.0404387i	$-0.987124\pi$
$929$	−0.992440	−	1.04042i	−0.992440	−	1.04042i	0.00674156	−	0.999977i	$-0.497854\pi$
$930$		0			0
$931$	1.14883	+	0.0775671i	1.14883	+	0.0775671i
$932$	1.00873	−	0.680180i	1.00873	−	0.680180i
$933$		0			0
$934$	0.999636	−	0.0269632i	0.999636	−	0.0269632i
$935$		0			0
$936$		0			0
$937$	−0.797674	−	0.0538577i	−0.797674	−	0.0538577i	−0.337088	−	0.941473i	$-0.609442\pi$
$937$	−0.797674	−	0.0538577i	−0.797674	−	0.0538577i	−0.460585	+	0.887615i	$0.652361\pi$
$938$		0			0
$939$	−0.0397376	−	0.0416586i	−0.0397376	−	0.0416586i
$940$		0			0
$941$		0			0		−0.986939	−	0.161094i	$-0.948498\pi$
$941$		0			0		0.986939	+	0.161094i	$0.0515021\pi$
$942$		0			0
$943$		0			0
$944$	1.58977	+	0.348384i	1.58977	+	0.348384i
$945$		0			0
$946$	−0.465423	+	0.959360i	−0.465423	+	0.959360i
$947$	0.468828	+	0.820529i	0.468828	+	0.820529i	0.999636	−	0.0269632i	$-0.00858369\pi$
$947$	0.468828	+	0.820529i	0.468828	+	0.820529i	−0.530808	+	0.847492i	$0.678112\pi$
$948$		0			0
$949$		0			0
$950$	0.827800	+	0.800357i	0.827800	+	0.800357i
$951$		0			0
$952$		0			0
$953$	−0.477609	+	0.125103i	−0.477609	+	0.125103i	−0.484351	−	0.874874i	$-0.660944\pi$
$953$	−0.477609	+	0.125103i	−0.477609	+	0.125103i	0.00674156	+	0.999977i	$0.497854\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.979617	−	0.200872i	−0.979617	−	0.200872i
$962$		0			0
$963$	−0.130827	+	0.110447i	−0.130827	+	0.110447i
$964$	−1.67377	−	0.487008i	−1.67377	−	0.487008i
$965$		0			0
$966$		0			0
$967$		0			0		−0.324364	−	0.945932i	$-0.605150\pi$
$967$		0			0		0.324364	+	0.945932i	$0.394850\pi$
$968$	−0.592500	−	0.376685i	−0.592500	−	0.376685i
$969$	−0.187641	−	0.274272i	−0.187641	−	0.274272i
$970$		0			0
$971$	0.127482	−	1.45087i	0.127482	−	1.45087i	−0.618962	−	0.785421i	$-0.712446\pi$
$971$	0.127482	−	1.45087i	0.127482	−	1.45087i	0.746444	−	0.665448i	$-0.231760\pi$
$972$	0.285026	−	0.324091i	0.285026	−	0.324091i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.129724	+	1.00721i	0.129724	+	1.00721i	0.919301	+	0.393556i	$0.128755\pi$
$977$	0.129724	+	1.00721i	0.129724	+	1.00721i	−0.789576	+	0.613653i	$0.789700\pi$
$978$	−0.0923314	+	0.00124500i	−0.0923314	+	0.00124500i
$979$	−0.396405	−	0.547154i	−0.396405	−	0.547154i
$980$		0			0
$981$		0			0
$982$	−0.964027	−	1.06680i	−0.964027	−	1.06680i
$983$		0			0		−0.948098	−	0.317979i	$-0.896996\pi$
$983$		0			0		0.948098	+	0.317979i	$0.103004\pi$
$984$	−0.00518700	−	0.00853530i	−0.00518700	−	0.00853530i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.982237	−	0.187646i	$-0.0600858\pi$
$991$		0			0		−0.982237	+	0.187646i	$0.939914\pi$
$992$		0			0
$993$	0.136749	−	0.0843714i	0.136749	−	0.0843714i
$994$		0			0
$995$		0			0
$996$	0.137887	+	0.257187i	0.137887	+	0.257187i
$997$		0			0		−0.956327	−	0.292300i	$-0.905579\pi$
$997$		0			0		0.956327	+	0.292300i	$0.0944206\pi$
$998$	−0.0123224	+	0.00547301i	−0.0123224	+	0.00547301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.291.1	✓	232
8.3	odd	2	CM	3736.1.l.a.291.1	✓	232
467.199	even	233	inner	3736.1.l.a.2067.1	yes	232
3736.2067	odd	466	inner	3736.1.l.a.2067.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.291.1	✓	232	1.1	even	1	trivial
3736.1.l.a.291.1	✓	232	8.3	odd	2	CM
3736.1.l.a.2067.1	yes	232	467.199	even	233	inner
3736.1.l.a.2067.1	yes	232	3736.2067	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)

\(f(q)\)	\(=\)	\(q+(0.829121 - 0.559069i) q^{2} +(0.147843 + 0.00998213i) q^{3} +(0.374884 - 0.927072i) q^{4} +(0.128161 - 0.0743780i) q^{6} +(-0.207472 - 0.978241i) q^{8} +(-0.969166 - 0.131473i) q^{9} +O(q^{10})\)	\(q+(0.829121 - 0.559069i) q^{2} +(0.147843 + 0.00998213i) q^{3} +(0.374884 - 0.927072i) q^{4} +(0.128161 - 0.0743780i) q^{6} +(-0.207472 - 0.978241i) q^{8} +(-0.969166 - 0.131473i) q^{9} +(-0.211416 - 0.503191i) q^{11} +(0.0646782 - 0.133319i) q^{12} +(-0.718923 - 0.695089i) q^{16} +(-0.778579 - 1.78530i) q^{17} +(-0.877058 + 0.432824i) q^{18} +(1.11387 - 0.291763i) q^{19} +(-0.456608 - 0.299011i) q^{22} +(-0.0209084 - 0.146697i) q^{24} +(-0.0471738 + 0.998887i) q^{25} +(-0.287131 - 0.0588769i) q^{27} +(-0.984677 - 0.174386i) q^{32} +(-0.0262334 - 0.0765037i) q^{33} +(-1.64364 - 1.04495i) q^{34} +(-0.485210 + 0.849199i) q^{36} +(0.760415 - 0.864634i) q^{38} +(0.0619640 - 0.0265270i) q^{41} +(-0.249559 - 1.93764i) q^{43} +(-0.545750 + 0.00735893i) q^{44} +(-0.0993493 - 0.109940i) q^{48} +(0.948098 + 0.317979i) q^{49} +(0.519333 + 0.854572i) q^{50} +(-0.0972864 - 0.271717i) q^{51} +(-0.270983 + 0.111710i) q^{54} +(0.167590 - 0.0320163i) q^{57} +(-1.38508 + 0.854568i) q^{59} +(-0.913911 + 0.405915i) q^{64} +(-0.0645215 - 0.0487645i) q^{66} +(0.472423 - 0.444595i) q^{67} +(-1.94698 + 0.0525159i) q^{68} +(0.0724630 + 0.975355i) q^{72} +(1.37839 - 0.244112i) q^{73} +(-0.0169453 + 0.147208i) q^{75} +(0.147086 - 1.14201i) q^{76} +(0.900834 + 0.248988i) q^{81} +(0.0365452 - 0.0566362i) q^{82} +(-1.15541 + 1.59480i) q^{83} +(-1.29019 - 1.46701i) q^{86} +(-0.448379 + 0.311213i) q^{88} +(1.20555 - 0.281272i) q^{89} +(-0.143837 - 0.0356109i) q^{96} +(0.388492 - 1.24105i) q^{97} +(0.963860 - 0.266408i) q^{98} +(0.138741 + 0.515471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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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