LMFDB - Embedded newform 3736.1.l.a.227.1

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			227.1
Root			$0.337088 - 0.941473i$ of defining polynomial
Character	$\chi$	$=$	3736.227
Dual form			3736.1.l.a.395.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194264 - 0.980949i) q^{2} +(1.15134 + 0.0155247i) q^{3} +(-0.924523 - 0.381126i) q^{4} +(0.238892 - 1.12639i) q^{6} +(-0.553466 + 0.832871i) q^{8} +(0.325705 + 0.00878524i) q^{9} +O(q^{10})$	\(q+(0.194264 - 0.980949i) q^{2} +(1.15134 + 0.0155247i) q^{3} +(-0.924523 - 0.381126i) q^{4} +(0.238892 - 1.12639i) q^{6} +(-0.553466 + 0.832871i) q^{8} +(0.325705 + 0.00878524i) q^{9} +(0.705078 + 0.823851i) q^{11} +(-1.05852 - 0.453158i) q^{12} +(0.709486 + 0.704719i) q^{16} +(0.811438 - 1.33524i) q^{17} +(0.0718906 - 0.317794i) q^{18} +(0.251770 - 0.935412i) q^{19} +(0.945127 - 0.531601i) q^{22} +(-0.650158 + 0.950325i) q^{24} +(0.948098 + 0.317979i) q^{25} +(-0.775641 - 0.0313916i) q^{27} +(0.829121 - 0.559069i) q^{32} +(0.798994 + 0.959479i) q^{33} +(-1.15216 - 1.05537i) q^{34} +(-0.297774 - 0.132257i) q^{36} +(-0.868682 - 0.428690i) q^{38} +(0.0134390 - 0.00108959i) q^{41} +(0.425518 + 0.555192i) q^{43} +(-0.337870 - 1.03039i) q^{44} +(0.805919 + 0.822386i) q^{48} +(0.246861 + 0.969051i) q^{49} +(0.496103 - 0.868264i) q^{50} +(0.954970 - 1.52471i) q^{51} +(-0.181473 + 0.754767i) q^{54} +(0.304394 - 1.07307i) q^{57} +(-0.349692 - 0.773232i) q^{59} +(-0.387350 - 0.921933i) q^{64} +(1.09642 - 0.597380i) q^{66} +(-0.574100 - 1.14384i) q^{67} +(-1.25909 + 0.925196i) q^{68} +(-0.187584 + 0.266408i) q^{72} +(-0.256093 - 0.172681i) q^{73} +(1.08665 + 0.380821i) q^{75} +(-0.589277 + 0.768854i) q^{76} +(-1.21789 - 0.0657481i) q^{81} +(0.00154189 - 0.0133947i) q^{82} +(1.62879 - 0.311163i) q^{83} +(0.627278 - 0.309558i) q^{86} +(-1.07640 + 0.131265i) q^{88} +(1.07845 - 0.861738i) q^{89} +(0.963280 - 0.630806i) q^{96} +(0.0171120 - 0.281684i) q^{97} +(0.998546 - 0.0539068i) q^{98} +(0.222410 + 0.274527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{131}{233}\right)$

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 $

$2$	0.194264	−	0.980949i	0.194264	−	0.980949i
$2$	0.194264	−	0.980949i	0.194264	−	0.980949i
$3$	1.15134	+	0.0155247i	1.15134	+	0.0155247i	0.586694	−	0.809809i	$-0.300429\pi$
$3$	1.15134	+	0.0155247i	1.15134	+	0.0155247i	0.564646	+	0.825333i	$0.309013\pi$
$4$	−0.924523	−	0.381126i	−0.924523	−	0.381126i
$5$		0			0		−0.986939	−	0.161094i	$-0.948498\pi$
$5$		0			0		0.986939	+	0.161094i	$0.0515021\pi$
$6$	0.238892	−	1.12639i	0.238892	−	1.12639i
$7$		0			0		−0.789576	−	0.613653i	$-0.789700\pi$
$7$		0			0		0.789576	+	0.613653i	$0.210300\pi$
$8$	−0.553466	+	0.832871i	−0.553466	+	0.832871i
$9$	0.325705	+	0.00878524i	0.325705	+	0.00878524i
$10$		0			0
$11$	0.705078	+	0.823851i	0.705078	+	0.823851i	0.990924	−	0.134424i	$-0.0429185\pi$
$11$	0.705078	+	0.823851i	0.705078	+	0.823851i	−0.285846	+	0.958275i	$0.592275\pi$
$12$	−1.05852	−	0.453158i	−1.05852	−	0.453158i
$13$		0			0		0.913911	−	0.405915i	$-0.133047\pi$
$13$		0			0		−0.913911	+	0.405915i	$0.866953\pi$
$14$		0			0
$15$		0			0
$16$	0.709486	+	0.704719i	0.709486	+	0.704719i
$17$	0.811438	−	1.33524i	0.811438	−	1.33524i	−0.127741	−	0.991808i	$-0.540773\pi$
$17$	0.811438	−	1.33524i	0.811438	−	1.33524i	0.939179	−	0.343428i	$-0.111588\pi$
$18$	0.0718906	−	0.317794i	0.0718906	−	0.317794i
$19$	0.251770	−	0.935412i	0.251770	−	0.935412i	−0.718923	−	0.695089i	$-0.755365\pi$
$19$	0.251770	−	0.935412i	0.251770	−	0.935412i	0.970693	−	0.240323i	$-0.0772532\pi$
$20$		0			0
$21$		0			0
$22$	0.945127	−	0.531601i	0.945127	−	0.531601i
$23$		0			0		−0.994188	−	0.107657i	$-0.965665\pi$
$23$		0			0		0.994188	+	0.107657i	$0.0343348\pi$
$24$	−0.650158	+	0.950325i	−0.650158	+	0.950325i
$25$	0.948098	+	0.317979i	0.948098	+	0.317979i
$26$		0			0
$27$	−0.775641	−	0.0313916i	−0.775641	−	0.0313916i
$28$		0			0
$29$		0			0		0.718923	−	0.695089i	$-0.244635\pi$
$29$		0			0		−0.718923	+	0.695089i	$0.755365\pi$
$30$		0			0
$31$		0			0		0.0202235	−	0.999795i	$-0.493562\pi$
$31$		0			0		−0.0202235	+	0.999795i	$0.506438\pi$
$32$	0.829121	−	0.559069i	0.829121	−	0.559069i
$33$	0.798994	+	0.959479i	0.798994	+	0.959479i
$34$	−1.15216	−	1.05537i	−1.15216	−	1.05537i
$35$		0			0
$36$	−0.297774	−	0.132257i	−0.297774	−	0.132257i
$37$		0			0		0.956327	−	0.292300i	$-0.0944206\pi$
$37$		0			0		−0.956327	+	0.292300i	$0.905579\pi$
$38$	−0.868682	−	0.428690i	−0.868682	−	0.428690i
$39$		0			0
$40$		0			0
$41$	0.0134390	−	0.00108959i	0.0134390	−	0.00108959i	−0.0740898	−	0.997252i	$-0.523605\pi$
$41$	0.0134390	−	0.00108959i	0.0134390	−	0.00108959i	0.0875288	+	0.996162i	$0.472103\pi$
$42$		0			0
$43$	0.425518	+	0.555192i	0.425518	+	0.555192i	0.956327	−	0.292300i	$-0.0944206\pi$
$43$	0.425518	+	0.555192i	0.425518	+	0.555192i	−0.530808	+	0.847492i	$0.678112\pi$
$44$	−0.337870	−	1.03039i	−0.337870	−	1.03039i
$45$		0			0
$46$		0			0
$47$		0			0		−0.337088	−	0.941473i	$-0.609442\pi$
$47$		0			0		0.337088	+	0.941473i	$0.390558\pi$
$48$	0.805919	+	0.822386i	0.805919	+	0.822386i
$49$	0.246861	+	0.969051i	0.246861	+	0.969051i
$50$	0.496103	−	0.868264i	0.496103	−	0.868264i
$51$	0.954970	−	1.52471i	0.954970	−	1.52471i
$52$		0			0
$53$		0			0		0.324364	−	0.945932i	$-0.394850\pi$
$53$		0			0		−0.324364	+	0.945932i	$0.605150\pi$
$54$	−0.181473	+	0.754767i	−0.181473	+	0.754767i
$55$		0			0
$56$		0			0
$57$	0.304394	−	1.07307i	0.304394	−	1.07307i
$58$		0			0
$59$	−0.349692	−	0.773232i	−0.349692	−	0.773232i	−0.999909	−	0.0134828i	$-0.995708\pi$
$59$	−0.349692	−	0.773232i	−0.349692	−	0.773232i	0.650217	−	0.759749i	$-0.274678\pi$
$60$		0			0
$61$		0			0		0.0875288	−	0.996162i	$-0.472103\pi$
$61$		0			0		−0.0875288	+	0.996162i	$0.527897\pi$
$62$		0			0
$63$		0			0
$64$	−0.387350	−	0.921933i	−0.387350	−	0.921933i
$65$		0			0
$66$	1.09642	−	0.597380i	1.09642	−	0.597380i
$67$	−0.574100	−	1.14384i	−0.574100	−	1.14384i	−0.973845	−	0.227213i	$-0.927039\pi$
$67$	−0.574100	−	1.14384i	−0.574100	−	1.14384i	0.399745	−	0.916626i	$-0.369099\pi$
$68$	−1.25909	+	0.925196i	−1.25909	+	0.925196i
$69$		0			0
$70$		0			0
$71$		0			0		−0.285846	−	0.958275i	$-0.592275\pi$
$71$		0			0		0.285846	+	0.958275i	$0.407725\pi$
$72$	−0.187584	+	0.266408i	−0.187584	+	0.266408i
$73$	−0.256093	−	0.172681i	−0.256093	−	0.172681i	0.424315	−	0.905515i	$-0.360515\pi$
$73$	−0.256093	−	0.172681i	−0.256093	−	0.172681i	−0.680408	+	0.732833i	$0.738197\pi$
$74$		0			0
$75$	1.08665	+	0.380821i	1.08665	+	0.380821i
$76$	−0.589277	+	0.768854i	−0.589277	+	0.768854i
$77$		0			0
$78$		0			0
$79$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$79$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$80$		0			0
$81$	−1.21789	−	0.0657481i	−1.21789	−	0.0657481i
$82$	0.00154189	−	0.0133947i	0.00154189	−	0.0133947i
$83$	1.62879	−	0.311163i	1.62879	−	0.311163i	0.709486	−	0.704719i	$-0.248927\pi$
$83$	1.62879	−	0.311163i	1.62879	−	0.311163i	0.919301	+	0.393556i	$0.128755\pi$
$84$		0			0
$85$		0			0
$86$	0.627278	−	0.309558i	0.627278	−	0.309558i
$87$		0			0
$88$	−1.07640	+	0.131265i	−1.07640	+	0.131265i
$89$	1.07845	−	0.861738i	1.07845	−	0.861738i	0.0875288	−	0.996162i	$-0.472103\pi$
$89$	1.07845	−	0.861738i	1.07845	−	0.861738i	0.990924	+	0.134424i	$0.0429185\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.963280	−	0.630806i	0.963280	−	0.630806i
$97$	0.0171120	−	0.281684i	0.0171120	−	0.281684i	−0.979617	−	0.200872i	$-0.935622\pi$
$97$	0.0171120	−	0.281684i	0.0171120	−	0.281684i	0.996729	−	0.0808112i	$-0.0257511\pi$
$98$	0.998546	−	0.0539068i	0.998546	−	0.0539068i
$99$	0.222410	+	0.274527i	0.222410	+	0.274527i
$100$	−0.755348	−	0.655324i	−0.755348	−	0.655324i
$101$		0			0		−0.956327	−	0.292300i	$-0.905579\pi$
$101$		0			0		0.956327	+	0.292300i	$0.0944206\pi$
$102$	−1.31015	−	1.23297i	−1.31015	−	1.23297i
$103$		0			0		−0.805835	−	0.592140i	$-0.798283\pi$
$103$		0			0		0.805835	+	0.592140i	$0.201717\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.33870	+	1.36606i	−1.33870	+	1.36606i	−0.460585	+	0.887615i	$0.652361\pi$
$107$	−1.33870	+	1.36606i	−1.33870	+	1.36606i	−0.878119	+	0.478442i	$0.841202\pi$
$108$	0.705134	+	0.324639i	0.705134	+	0.324639i
$109$		0			0		−0.362351	−	0.932042i	$-0.618026\pi$
$109$		0			0		0.362351	+	0.932042i	$0.381974\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.32927	+	0.291299i	−1.32927	+	0.291299i	−0.821508	−	0.570197i	$-0.806867\pi$
$113$	−1.32927	+	0.291299i	−1.32927	+	0.291299i	−0.507764	+	0.861496i	$0.669528\pi$
$114$	−0.993493	−	0.507054i	−0.993493	−	0.507054i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.826434	+	0.192820i	−0.826434	+	0.192820i
$119$		0			0
$120$		0			0
$121$	−0.0271601	+	0.173756i	−0.0271601	+	0.173756i
$122$		0			0
$123$	0.0154898	−	0.00104585i	0.0154898	−	0.00104585i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.890700	−	0.454591i	$-0.150215\pi$
$127$		0			0		−0.890700	+	0.454591i	$0.849785\pi$
$128$	−0.979617	+	0.200872i	−0.979617	+	0.200872i
$129$	0.481297	+	0.645820i	0.481297	+	0.645820i
$130$		0			0
$131$	0.0914270	+	0.794245i	0.0914270	+	0.794245i	0.956327	+	0.292300i	$0.0944206\pi$
$131$	0.0914270	+	0.794245i	0.0914270	+	0.794245i	−0.864900	+	0.501945i	$0.832618\pi$
$132$	−0.373006	−	1.19158i	−0.373006	−	1.19158i
$133$		0			0
$134$	−1.23358	+	0.340957i	−1.23358	+	0.340957i
$135$		0			0
$136$	0.662975	+	1.41483i	0.662975	+	1.41483i
$137$	−1.83213	+	0.642082i	−1.83213	+	0.642082i	−0.836584	+	0.547839i	$0.815451\pi$
$137$	−1.83213	+	0.642082i	−1.83213	+	0.642082i	−0.995549	+	0.0942425i	$0.969957\pi$
$138$		0			0
$139$	−0.772809	+	1.39591i	−0.772809	+	1.39591i	0.141101	+	0.989995i	$0.454936\pi$
$139$	−0.772809	+	1.39591i	−0.772809	+	1.39591i	−0.913911	+	0.405915i	$0.866953\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.224892	+	0.235764i	0.224892	+	0.235764i
$145$		0			0
$146$	−0.219141	+	0.217669i	−0.219141	+	0.217669i
$147$	0.269177	+	1.11954i	0.269177	+	1.11954i
$148$		0			0
$149$		0			0		−0.858053	−	0.513561i	$-0.828326\pi$
$149$		0			0		0.858053	+	0.513561i	$0.171674\pi$
$150$	0.584662	−	0.991965i	0.584662	−	0.991965i
$151$		0			0		0.746444	−	0.665448i	$-0.231760\pi$
$151$		0			0		−0.746444	+	0.665448i	$0.768240\pi$
$152$	0.639732	+	0.727411i	0.639732	+	0.727411i
$153$	0.276020	−	0.427764i	0.276020	−	0.427764i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.929578	−	0.368626i	$-0.879828\pi$
$157$		0			0		0.929578	+	0.368626i	$0.120172\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.301087	+	1.18192i	−0.301087	+	1.18192i
$163$	−1.60798	+	0.933194i	−1.60798	+	0.933194i	−0.618962	+	0.785421i	$0.712446\pi$
$163$	−1.60798	+	0.933194i	−1.60798	+	0.933194i	−0.989021	+	0.147772i	$0.952790\pi$
$164$	−0.0128400	−	0.00411461i	−0.0128400	−	0.00411461i
$165$		0			0
$166$	0.0111791	−	1.65820i	0.0111791	−	1.65820i
$167$		0			0		−0.746444	−	0.665448i	$-0.768240\pi$
$167$		0			0		0.746444	+	0.665448i	$0.231760\pi$
$168$		0			0
$169$	0.670466	−	0.741941i	0.670466	−	0.741941i
$170$		0			0
$171$	0.0902205	−	0.302457i	0.0902205	−	0.302457i
$172$	−0.181804	−	0.675464i	−0.181804	−	0.675464i
$173$		0			0		0.999182	−	0.0404387i	$-0.0128755\pi$
$173$		0			0		−0.999182	+	0.0404387i	$0.987124\pi$
$174$		0			0
$175$		0			0
$176$	−0.0803410	+	1.08139i	−0.0803410	+	1.08139i
$177$	−0.390610	−	0.895681i	−0.390610	−	0.895681i
$178$	−0.635817	−	1.22531i	−0.635817	−	1.22531i
$179$	−1.24458	+	0.791249i	−1.24458	+	0.791249i	−0.984677	−	0.174386i	$-0.944206\pi$
$179$	−1.24458	+	0.791249i	−1.24458	+	0.791249i	−0.259904	+	0.965634i	$0.583691\pi$
$180$		0			0
$181$		0			0		0.597559	−	0.801825i	$-0.296137\pi$
$181$		0			0		−0.597559	+	0.801825i	$0.703863\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.67216	−	0.272940i	1.67216	−	0.272940i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.871589	−	0.490238i	$-0.836910\pi$
$191$		0			0		0.871589	+	0.490238i	$0.163090\pi$
$192$	−0.431658	−	1.06747i	−0.431658	−	1.06747i
$193$	0.282100	+	1.97927i	0.282100	+	1.97927i	0.167744	+	0.985831i	$0.446352\pi$
$193$	0.282100	+	1.97927i	0.282100	+	1.97927i	0.114357	+	0.993440i	$0.463519\pi$
$194$	−0.272993	−	0.0715069i	−0.272993	−	0.0715069i
$195$		0			0
$196$	0.141101	−	0.989995i	0.141101	−	0.989995i
$197$		0			0		0.387350	−	0.921933i	$-0.373391\pi$
$197$		0			0		−0.387350	+	0.921933i	$0.626609\pi$
$198$	0.312503	−	0.164842i	0.312503	−	0.164842i
$199$		0			0		−0.0740898	−	0.997252i	$-0.523605\pi$
$199$		0			0		0.0740898	+	0.997252i	$0.476395\pi$
$200$	−0.789576	+	0.613653i	−0.789576	+	0.613653i
$201$	−0.643226	−	1.32586i	−0.643226	−	1.32586i
$202$		0			0
$203$		0			0
$204$	−1.46400	+	1.04567i	−1.46400	+	1.04567i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.948158	−	0.452117i	0.948158	−	0.452117i
$210$		0			0
$211$	0.00367955	+	0.545788i	0.00367955	+	0.545788i	0.963860	+	0.266408i	$0.0858369\pi$
$211$	0.00367955	+	0.545788i	0.00367955	+	0.545788i	−0.960181	+	0.279380i	$0.909871\pi$
$212$		0			0
$213$		0			0
$214$	1.07997	+	1.57858i	1.07997	+	1.57858i
$215$		0			0
$216$	0.455437	−	0.628636i	0.455437	−	0.628636i
$217$		0			0
$218$		0			0
$219$	−0.292169	−	0.202791i	−0.292169	−	0.202791i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$223$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$224$		0			0
$225$	0.306007	+	0.111897i	0.306007	+	0.111897i
$226$	0.0275204	+	1.36054i	0.0275204	+	1.36054i
$227$	0.0543180	+	0.0771429i	0.0543180	+	0.0771429i	0.843894	−	0.536510i	$-0.180258\pi$
$227$	0.0543180	+	0.0771429i	0.0543180	+	0.0771429i	−0.789576	+	0.613653i	$0.789700\pi$
$228$	−0.690394	+	0.876064i	−0.690394	+	0.876064i
$229$		0			0		−0.167744	−	0.985831i	$-0.553648\pi$
$229$		0			0		0.167744	+	0.985831i	$0.446352\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.350698	−	1.77088i	−0.350698	−	1.77088i	−0.597559	−	0.801825i	$-0.703863\pi$
$233$	−0.350698	−	1.77088i	−0.350698	−	1.77088i	0.246861	−	0.969051i	$-0.420601\pi$
$234$		0			0
$235$		0			0
$236$	0.0286002	+	0.848147i	0.0286002	+	0.848147i
$237$		0			0
$238$		0			0
$239$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$239$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$240$		0			0
$241$	0.0349825	+	1.72945i	0.0349825	+	1.72945i	0.519333	+	0.854572i	$0.326180\pi$
$241$	0.0349825	+	1.72945i	0.0349825	+	1.72945i	−0.484351	+	0.874874i	$0.660944\pi$
$242$	0.165169	+	0.0603970i	0.165169	+	0.0603970i
$243$	−0.626670	−	0.0423118i	−0.626670	−	0.0423118i
$244$		0			0
$245$		0			0
$246$	0.00198318	−	0.0153979i	0.00198318	−	0.0153979i
$247$		0			0
$248$		0			0
$249$	1.88012	−	0.332968i	1.88012	−	0.332968i
$250$		0			0
$251$	−0.212407	+	0.293183i	−0.212407	+	0.293183i	−0.902634	−	0.430410i	$-0.858369\pi$
$251$	−0.212407	+	0.293183i	−0.212407	+	0.293183i	0.690227	+	0.723593i	$0.257511\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.00674156	+	0.999977i	0.00674156	+	0.999977i
$257$	1.51788	−	0.908478i	1.51788	−	0.908478i	0.519333	−	0.854572i	$-0.326180\pi$
$257$	1.51788	−	0.908478i	1.51788	−	0.908478i	0.998546	−	0.0539068i	$-0.0171674\pi$
$258$	0.727016	−	0.346668i	0.727016	−	0.346668i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.796875	+	0.0646077i	0.796875	+	0.0646077i
$263$		0			0		0.813746	−	0.581221i	$-0.197425\pi$
$263$		0			0		−0.813746	+	0.581221i	$0.802575\pi$
$264$	−1.24134	+	0.134420i	−1.24134	+	0.134420i
$265$		0			0
$266$		0			0
$267$	1.25504	−	0.975410i	1.25504	−	0.975410i
$268$	0.0948222	+	1.27631i	0.0948222	+	1.27631i
$269$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$269$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$270$		0			0
$271$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$271$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$272$	1.51667	−	0.375495i	1.51667	−	0.375495i
$273$		0			0
$274$	0.273932	+	1.92196i	0.273932	+	1.92196i
$275$	0.406515	+	1.00529i	0.406515	+	1.00529i
$276$		0			0
$277$		0			0		−0.813746	−	0.581221i	$-0.802575\pi$
$277$		0			0		0.813746	+	0.581221i	$0.197425\pi$
$278$	1.21919	+	1.02926i	1.21919	+	1.02926i
$279$		0			0
$280$		0			0
$281$	−1.30586	−	0.304677i	−1.30586	−	0.304677i	−0.484351	−	0.874874i	$-0.660944\pi$
$281$	−1.30586	−	0.304677i	−1.30586	−	0.304677i	−0.821508	+	0.570197i	$0.806867\pi$
$282$		0			0
$283$	−0.832166	+	0.999313i	−0.832166	+	0.999313i	0.167744	+	0.985831i	$0.446352\pi$
$283$	−0.832166	+	0.999313i	−0.832166	+	0.999313i	−0.999909	+	0.0134828i	$0.995708\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.274961	−	0.174808i	0.274961	−	0.174808i
$289$	−0.663835	−	1.27931i	−0.663835	−	1.27931i
$290$		0			0
$291$	0.0240748	−	0.324048i	0.0240748	−	0.324048i
$292$	0.170951	+	0.257252i	0.170951	+	0.257252i
$293$		0			0		−0.530808	−	0.847492i	$-0.678112\pi$
$293$		0			0		0.530808	+	0.847492i	$0.321888\pi$
$294$	1.15050	−	0.0465629i	1.15050	−	0.0465629i
$295$		0			0
$296$		0			0
$297$	−0.521025	−	0.661147i	−0.521025	−	0.661147i
$298$		0			0
$299$		0			0
$300$	−0.859488	−	0.766227i	−0.859488	−	0.766227i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.837830	−	0.486235i	0.837830	−	0.486235i
$305$		0			0
$306$	−0.365994	−	0.353861i	−0.365994	−	0.353861i
$307$	0.159014	−	0.0732092i	0.159014	−	0.0732092i	−0.337088	−	0.941473i	$-0.609442\pi$
$307$	0.159014	−	0.0732092i	0.159014	−	0.0732092i	0.496103	+	0.868264i	$0.334764\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.999909	−	0.0134828i	$-0.00429185\pi$
$311$		0			0		−0.999909	+	0.0134828i	$0.995708\pi$
$312$		0			0
$313$	1.22433	+	0.182931i	1.22433	+	0.182931i	0.728230	−	0.685333i	$-0.240343\pi$
$313$	1.22433	+	0.182931i	1.22433	+	0.182931i	0.496103	+	0.868264i	$0.334764\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.507764	−	0.861496i	$-0.330472\pi$
$317$		0			0		−0.507764	+	0.861496i	$0.669528\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.56251	+	1.55201i	−1.56251	+	1.55201i
$322$		0			0
$323$	−1.04470	−	1.09520i	−1.04470	−	1.09520i
$324$	1.10091	+	0.524955i	1.10091	+	0.524955i
$325$		0			0
$326$	0.603043	+	1.75864i	0.603043	+	1.75864i
$327$		0			0
$328$	−0.00653057	+	0.0117960i	−0.00653057	+	0.0117960i
$329$		0			0
$330$		0			0
$331$	0.0970465	+	0.207103i	0.0970465	+	0.207103i	0.948098	−	0.317979i	$-0.103004\pi$
$331$	0.0970465	+	0.207103i	0.0970465	+	0.207103i	−0.851051	+	0.525083i	$0.824034\pi$
$332$	−1.62444	−	0.333095i	−1.62444	−	0.333095i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0469757	−	0.773274i	−0.0469757	−	0.773274i	−0.943724	−	0.330734i	$-0.892704\pi$
$337$	−0.0469757	−	0.773274i	−0.0469757	−	0.773274i	0.896748	−	0.442541i	$-0.145923\pi$
$338$	−0.597559	−	0.801825i	−0.597559	−	0.801825i
$339$	−1.53497	+	0.314748i	−1.53497	+	0.314748i
$340$		0			0
$341$		0			0
$342$	−0.279168	−	0.147258i	−0.279168	−	0.147258i
$343$		0			0
$344$	−0.697914	+	0.0471221i	−0.697914	+	0.0471221i
$345$		0			0
$346$		0			0
$347$	−1.26161	+	1.32260i	−1.26161	+	1.32260i	−0.337088	+	0.941473i	$0.609442\pi$
$347$	−1.26161	+	1.32260i	−1.26161	+	1.32260i	−0.924523	+	0.381126i	$0.875536\pi$
$348$		0			0
$349$		0			0		0.973845	−	0.227213i	$-0.0729614\pi$
$349$		0			0		−0.973845	+	0.227213i	$0.927039\pi$
$350$		0			0
$351$		0			0
$352$	1.04518	+	0.288886i	1.04518	+	0.288886i
$353$	−0.439758	−	0.224442i	−0.439758	−	0.224442i	0.220643	−	0.975355i	$-0.429185\pi$
$353$	−0.439758	−	0.224442i	−0.439758	−	0.224442i	−0.660401	+	0.750913i	$0.729614\pi$
$354$	−0.954499	+	0.209171i	−0.954499	+	0.209171i
$355$		0			0
$356$	−1.32549	+	0.385670i	−1.32549	+	0.385670i
$357$		0			0
$358$	0.534398	+	1.37458i	0.534398	+	1.37458i
$359$		0			0		−0.908355	−	0.418201i	$-0.862661\pi$
$359$		0			0		0.908355	+	0.418201i	$0.137339\pi$
$360$		0			0
$361$	0.0532922	+	0.0309282i	0.0532922	+	0.0309282i
$362$		0			0
$363$	−0.0339680	+	0.199630i	−0.0339680	+	0.199630i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$367$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$368$		0			0
$369$	0.00438673		0.000236819i	0.00438673		0.000236819i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.989021	−	0.147772i	$-0.0472103\pi$
$373$		0			0		−0.989021	+	0.147772i	$0.952790\pi$
$374$	0.0571005	−	1.69333i	0.0571005	−	1.69333i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.09879	−	0.133996i	1.09879	−	0.133996i	0.448576	−	0.893745i	$-0.351931\pi$
$379$	1.09879	−	0.133996i	1.09879	−	0.133996i	0.650217	+	0.759749i	$0.274678\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$383$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$384$	−1.13099	+	0.216064i	−1.13099	+	0.216064i
$385$		0			0
$386$	1.99637	+	0.107774i	1.99637	+	0.107774i
$387$	0.133716	+	0.184567i	0.133716	+	0.184567i
$388$	−0.123177	+	0.253901i	−0.123177	+	0.253901i
$389$		0			0		−0.207472	−	0.978241i	$-0.566524\pi$
$389$		0			0		0.207472	+	0.978241i	$0.433476\pi$
$390$		0			0
$391$		0			0
$392$	−0.943724	−	0.330734i	−0.943724	−	0.330734i
$393$	0.0929331	+	0.915865i	0.0929331	+	0.915865i
$394$		0			0
$395$		0			0
$396$	−0.100994	−	0.338573i	−0.100994	−	0.338573i
$397$		0			0		0.851051	−	0.525083i	$-0.175966\pi$
$397$		0			0		−0.851051	+	0.525083i	$0.824034\pi$
$398$		0			0
$399$		0			0
$400$	0.448576	+	0.893745i	0.448576	+	0.893745i
$401$	0.808898	−	0.440727i	0.808898	−	0.440727i	−0.0202235	−	0.999795i	$-0.506438\pi$
$401$	0.808898	−	0.440727i	0.808898	−	0.440727i	0.829121	+	0.559069i	$0.188841\pi$
$402$	−1.42556	+	0.373406i	−1.42556	+	0.373406i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.741345	+	1.63924i	0.741345	+	1.63924i
$409$	0.984996	+	1.52650i	0.984996	+	1.52650i	0.843894	+	0.536510i	$0.180258\pi$
$409$	0.984996	+	1.52650i	0.984996	+	1.52650i	0.141101	+	0.989995i	$0.454936\pi$
$410$		0			0
$411$	−2.11938	+	0.710810i	−2.11938	+	0.710810i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.911437	+	1.59517i	−0.911437	+	1.59517i
$418$	−0.259311	−	1.01792i	−0.259311	−	1.01792i
$419$	−1.20114	−	1.22568i	−1.20114	−	1.22568i	−0.967365	−	0.253388i	$-0.918455\pi$
$419$	−1.20114	−	1.22568i	−1.20114	−	1.22568i	−0.233773	−	0.972291i	$-0.575107\pi$
$420$		0			0
$421$		0			0		0.298741	−	0.954334i	$-0.403433\pi$
$421$		0			0		−0.298741	+	0.954334i	$0.596567\pi$
$422$	0.536105	+	0.102417i	0.536105	+	0.102417i
$423$		0			0
$424$		0			0
$425$	1.19390	−	1.00791i	1.19390	−	1.00791i
$426$		0			0
$427$		0			0
$428$	1.75830	−	0.752737i	1.75830	−	0.752737i
$429$		0			0
$430$		0			0
$431$		0			0		−0.913911	−	0.405915i	$-0.866953\pi$
$431$		0			0		0.913911	+	0.405915i	$0.133047\pi$
$432$	−0.528185	−	0.568881i	−0.528185	−	0.568881i
$433$	−1.47266	−	1.34894i	−1.47266	−	1.34894i	−0.772743	−	0.634719i	$-0.781116\pi$
$433$	−1.47266	−	1.34894i	−1.47266	−	1.34894i	−0.699920	−	0.714221i	$-0.746781\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.255685	+	0.247209i	−0.255685	+	0.247209i
$439$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$439$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$440$		0			0
$441$	0.0718906	+	0.317794i	0.0718906	+	0.317794i
$442$		0			0
$443$	−0.991652	+	1.44948i	−0.991652	+	1.44948i	−0.100952	+	0.994891i	$0.532189\pi$
$443$	−0.991652	+	1.44948i	−0.991652	+	1.44948i	−0.890700	+	0.454591i	$0.849785\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.126140	+	0.557603i	−0.126140	+	0.557603i	0.871589	+	0.490238i	$0.163090\pi$
$449$	−0.126140	+	0.557603i	−0.126140	+	0.557603i	−0.997728	+	0.0673651i	$0.978541\pi$
$450$	0.169211	−	0.278440i	0.169211	−	0.278440i
$451$	0.0103732	+	0.0103035i	0.0103732	+	0.0103035i
$452$	1.33996	+	0.237307i	1.33996	+	0.237307i
$453$		0			0
$454$	0.0862253	−	0.0382971i	0.0862253	−	0.0382971i
$455$		0			0
$456$	0.725256	+	0.847428i	0.725256	+	0.847428i
$457$	0.313780	−	0.840490i	0.313780	−	0.840490i	−0.680408	−	0.732833i	$-0.738197\pi$
$457$	0.313780	−	0.840490i	0.313780	−	0.840490i	0.994188	−	0.107657i	$-0.0343348\pi$
$458$		0			0
$459$	−0.671300	+	1.01019i	−0.671300	+	1.01019i
$460$		0			0
$461$		0			0		0.207472	−	0.978241i	$-0.433476\pi$
$461$		0			0		−0.207472	+	0.978241i	$0.566524\pi$
$462$		0			0
$463$		0			0		−0.924523	−	0.381126i	$-0.875536\pi$
$463$		0			0		0.924523	+	0.381126i	$0.124464\pi$
$464$		0			0
$465$		0			0
$466$	−1.80527			−1.80527
$467$	−0.737404	−	0.675452i	−0.737404	−	0.675452i
$467$	−0.737404	−	0.675452i	−0.737404	−	0.675452i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.837546	+	0.136709i	0.837546	+	0.136709i
$473$	−0.157372	+	0.742017i	−0.157372	+	0.742017i
$474$		0			0
$475$	0.536144	−	0.806804i	0.536144	−	0.806804i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.919301	−	0.393556i	$-0.871245\pi$
$479$		0			0		0.919301	+	0.393556i	$0.128755\pi$
$480$		0			0
$481$		0			0
$482$	1.70329	+	0.301652i	1.70329	+	0.301652i
$483$		0			0
$484$	0.0913328	−	0.150290i	0.0913328	−	0.150290i
$485$		0			0
$486$	−0.163245	+	0.606512i	−0.163245	+	0.606512i
$487$		0			0		−0.851051	−	0.525083i	$-0.824034\pi$
$487$		0			0		0.851051	+	0.525083i	$0.175966\pi$
$488$		0			0
$489$	−1.86582	+	1.04946i	−1.86582	+	1.04946i
$490$		0			0
$491$	0.801217	−	1.17113i	0.801217	−	1.17113i	−0.181020	−	0.983479i	$-0.557940\pi$
$491$	0.801217	−	1.17113i	0.801217	−	1.17113i	0.982237	−	0.187646i	$-0.0600858\pi$
$492$	−0.0147193	−	0.00493665i	−0.0147193	−	0.00493665i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0386142	−	1.90898i	0.0386142	−	1.90898i
$499$	0.972881	−	0.656004i	0.972881	−	0.656004i	0.0337017	−	0.999432i	$-0.489270\pi$
$499$	0.972881	−	0.656004i	0.972881	−	0.656004i	0.939179	+	0.343428i	$0.111588\pi$
$500$		0			0
$501$		0			0
$502$	0.246335	+	0.265315i	0.246335	+	0.265315i
$503$		0			0		−0.913911	−	0.405915i	$-0.866953\pi$
$503$		0			0		0.913911	+	0.405915i	$0.133047\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.783452	−	0.843817i	0.783452	−	0.843817i
$508$		0			0
$509$		0			0		0.764115	−	0.645080i	$-0.223176\pi$
$509$		0			0		−0.764115	+	0.645080i	$0.776824\pi$
$510$		0			0
$511$		0			0
$512$	0.982237	+	0.187646i	0.982237	+	0.187646i
$513$	−0.224647	+	0.717641i	−0.224647	+	0.717641i
$514$	−0.596302	−	1.66545i	−0.596302	−	1.66545i
$515$		0			0
$516$	−0.198831	−	0.780511i	−0.198831	−	0.780511i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.464108	−	1.93028i	0.464108	−	1.93028i	0.114357	−	0.993440i	$-0.463519\pi$
$521$	0.464108	−	1.93028i	0.464108	−	1.93028i	0.349751	−	0.936843i	$-0.386266\pi$
$522$		0			0
$523$	0.0639050	−	0.0214329i	0.0639050	−	0.0214329i	−0.285846	−	0.958275i	$-0.592275\pi$
$523$	0.0639050	−	0.0214329i	0.0639050	−	0.0214329i	0.349751	+	0.936843i	$0.386266\pi$
$524$	0.218181	−	0.769143i	0.218181	−	0.769143i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.109288	+	1.24380i	−0.109288	+	1.24380i
$529$	0.976820	+	0.214062i	0.976820	+	0.214062i
$530$		0			0
$531$	−0.107104	−	0.254918i	−0.107104	−	0.254918i
$532$		0			0
$533$		0			0
$534$	−0.713018	−	1.42062i	−0.713018	−	1.42062i
$535$		0			0
$536$	1.27042	+	0.154925i	1.27042	+	0.154925i
$537$	−1.44522	+	0.891674i	−1.44522	+	0.891674i
$538$		0			0
$539$	−0.624298	+	0.886633i	−0.624298	+	0.886633i
$540$		0			0
$541$		0			0		−0.100952	−	0.994891i	$-0.532189\pi$
$541$		0			0		0.100952	+	0.994891i	$0.467811\pi$
$542$		0			0
$543$		0			0
$544$	−0.0737072	−	1.56072i	−0.0737072	−	1.56072i
$545$		0			0
$546$		0			0
$547$	−0.425178	−	0.586870i	−0.425178	−	0.586870i	0.542187	−	0.840258i	$-0.317597\pi$
$547$	−0.425178	−	0.586870i	−0.425178	−	0.586870i	−0.967365	+	0.253388i	$0.918455\pi$
$548$	1.93856	+	0.104654i	1.93856	+	0.104654i
$549$		0			0
$550$	1.06511	−	0.203479i	1.06511	−	0.203479i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.24650	−	0.996014i	1.24650	−	0.996014i
$557$		0			0		0.374884	−	0.927072i	$-0.377682\pi$
$557$		0			0		−0.374884	+	0.927072i	$0.622318\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.92946	−	0.288286i	1.92946	−	0.288286i
$562$	−0.552554	+	1.22179i	−0.552554	+	1.22179i
$563$	−1.53814	+	1.00726i	−1.53814	+	1.00726i	−0.553466	+	0.832871i	$0.686695\pi$
$563$	−1.53814	+	1.00726i	−1.53814	+	1.00726i	−0.984677	+	0.174386i	$0.944206\pi$
$564$		0			0
$565$		0			0
$566$	0.818616	+	1.01044i	0.818616	+	1.01044i
$567$		0			0
$568$		0			0
$569$	−1.44998	−	1.36457i	−1.44998	−	1.36457i	−0.789576	−	0.613653i	$-0.789700\pi$
$569$	−1.44998	−	1.36457i	−1.44998	−	1.36457i	−0.660401	−	0.750913i	$-0.729614\pi$
$570$		0			0
$571$	−0.335457	+	1.97148i	−0.335457	+	1.97148i	−0.154437	+	0.988003i	$0.549356\pi$
$571$	−0.335457	+	1.97148i	−0.335457	+	1.97148i	−0.181020	+	0.983479i	$0.557940\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.118062	−	0.303681i	−0.118062	−	0.303681i
$577$	1.87563	−	0.685856i	1.87563	−	0.685856i	0.919301	−	0.393556i	$-0.128755\pi$
$577$	1.87563	−	0.685856i	1.87563	−	0.685856i	0.956327	−	0.292300i	$-0.0944206\pi$
$578$	−1.38389	+	0.402666i	−1.38389	+	0.402666i
$579$	0.294066	+	2.28319i	0.294066	+	2.28319i
$580$		0			0
$581$		0			0
$582$	−0.313198	−	0.0865669i	−0.313198	−	0.0865669i
$583$		0			0
$584$	0.285560	−	0.117720i	0.285560	−	0.117720i
$585$		0			0
$586$		0			0
$587$	−0.635817	+	0.666553i	−0.635817	+	0.666553i	−0.960181	−	0.279380i	$-0.909871\pi$
$587$	−0.635817	+	0.666553i	−0.635817	+	0.666553i	0.324364	+	0.945932i	$0.394850\pi$
$588$	0.177825	−	1.13763i	0.177825	−	1.13763i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.197421	−	0.162159i	0.197421	−	0.162159i	−0.530808	−	0.847492i	$-0.678112\pi$
$593$	0.197421	−	0.162159i	0.197421	−	0.162159i	0.728230	+	0.685333i	$0.240343\pi$
$594$	−0.749768	+	0.382663i	−0.749768	+	0.382663i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.298741	−	0.954334i	$-0.596567\pi$
$599$		0			0		0.298741	+	0.954334i	$0.403433\pi$
$600$	−0.918597	+	0.694264i	−0.918597	+	0.694264i
$601$	−1.55343	+	0.429362i	−1.55343	+	0.429362i	−0.934463	−	0.356059i	$-0.884120\pi$
$601$	−1.55343	+	0.429362i	−1.55343	+	0.429362i	−0.618962	+	0.785421i	$0.712446\pi$
$602$		0			0
$603$	−0.176938	−	0.377598i	−0.176938	−	0.377598i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$607$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$608$	−0.314212	−	0.916327i	−0.314212	−	0.916327i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.418219	+	0.290280i	−0.418219	+	0.290280i
$613$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$613$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$614$	−0.0409238	−	0.170207i	−0.0409238	−	0.170207i
$615$		0			0
$616$		0			0
$617$	0.967086	−	1.64080i	0.967086	−	1.64080i	0.220643	−	0.975355i	$-0.429185\pi$
$617$	0.967086	−	1.64080i	0.967086	−	1.64080i	0.746444	−	0.665448i	$-0.231760\pi$
$618$		0			0
$619$	0.924456	+	1.05116i	0.924456	+	1.05116i	0.998546	+	0.0539068i	$0.0171674\pi$
$619$	0.924456	+	1.05116i	0.924456	+	1.05116i	−0.0740898	+	0.997252i	$0.523605\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.797778	+	0.602951i	0.797778	+	0.602951i
$626$	0.417289	−	1.16547i	0.417289	−	1.16547i
$627$	1.09867	−	0.505820i	1.09867	−	0.505820i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.952299	−	0.305167i	$-0.901288\pi$
$631$		0			0		0.952299	+	0.305167i	$0.0987124\pi$
$632$		0			0
$633$	−0.00423679	+	0.628444i	−0.00423679	+	0.628444i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.925293	−	1.47733i	−0.925293	−	1.47733i	−0.878119	−	0.478442i	$-0.841202\pi$
$641$	−0.925293	−	1.47733i	−0.925293	−	1.47733i	−0.0471738	−	0.998887i	$-0.515021\pi$
$642$	1.21891	+	1.83424i	1.21891	+	1.83424i
$643$	−0.113226	+	1.52403i	−0.113226	+	1.52403i	0.586694	+	0.809809i	$0.300429\pi$
$643$	−0.113226	+	1.52403i	−0.113226	+	1.52403i	−0.699920	+	0.714221i	$0.746781\pi$
$644$		0			0
$645$		0			0
$646$	−1.27728	+	0.812039i	−1.27728	+	0.812039i
$647$		0			0		−0.836584	−	0.547839i	$-0.815451\pi$
$647$		0			0		0.836584	+	0.547839i	$0.184549\pi$
$648$	0.728820	−	0.977956i	0.728820	−	0.977956i
$649$	0.390468	−	0.833283i	0.390468	−	0.833283i
$650$		0			0
$651$		0			0
$652$	1.84228	−	0.249915i	1.84228	−	0.249915i
$653$		0			0		−0.973845	−	0.227213i	$-0.927039\pi$
$653$		0			0		0.973845	+	0.227213i	$0.0729614\pi$
$654$		0			0
$655$		0			0
$656$	0.0103027	+	0.00869770i	0.0103027	+	0.00869770i
$657$	−0.0818939	−	0.0584930i	−0.0818939	−	0.0584930i
$658$		0			0
$659$	−0.734487	−	1.81635i	−0.734487	−	1.81635i	−0.553466	−	0.832871i	$-0.686695\pi$
$659$	−0.734487	−	1.81635i	−0.734487	−	1.81635i	−0.181020	−	0.983479i	$-0.557940\pi$
$660$		0			0
$661$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$661$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$662$	0.222011	−	0.0549650i	0.222011	−	0.0549650i
$663$		0			0
$664$	−0.642320	+	1.52879i	−0.642320	+	1.52879i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.571267	−	0.523273i	0.571267	−	0.523273i	−0.337088	−	0.941473i	$-0.609442\pi$
$673$	0.571267	−	0.523273i	0.571267	−	0.523273i	0.908355	+	0.418201i	$0.137339\pi$
$674$	−0.767668	−	0.104138i	−0.767668	−	0.104138i
$675$	−0.725402	−	0.276400i	−0.725402	−	0.276400i
$676$	−0.902634	+	0.430410i	−0.902634	+	0.430410i
$677$		0			0		0.858053	−	0.513561i	$-0.171674\pi$
$677$		0			0		−0.858053	+	0.513561i	$0.828326\pi$
$678$	0.0105634	+	1.56687i	0.0105634	+	1.56687i
$679$		0			0
$680$		0			0
$681$	0.0613408	+	0.0896609i	0.0613408	+	0.0896609i
$682$		0			0
$683$	−0.243445	+	0.336025i	−0.243445	+	0.336025i	−0.913911	−	0.405915i	$-0.866953\pi$
$683$	−0.243445	+	0.336025i	−0.243445	+	0.336025i	0.670466	+	0.741941i	$0.266094\pi$
$684$	−0.198685	+	0.245243i	−0.198685	+	0.245243i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.0893550	+	0.693772i	−0.0893550	+	0.693772i
$689$		0			0
$690$		0			0
$691$	−1.25613	−	0.0848120i	−1.25613	−	0.0848120i	−0.575722	−	0.817645i	$-0.695279\pi$
$691$	−1.25613	−	0.0848120i	−1.25613	−	0.0848120i	−0.680408	+	0.732833i	$0.738197\pi$
$692$		0			0
$693$		0			0
$694$	1.05232	+	1.49451i	1.05232	+	1.49451i
$695$		0			0
$696$		0			0
$697$	0.00945009	−	0.0188284i	0.00945009	−	0.0188284i
$698$		0			0
$699$	−0.376280	−	2.04432i	−0.376280	−	2.04432i
$700$		0			0
$701$		0			0		−0.194264	−	0.980949i	$-0.562232\pi$
$701$		0			0		0.194264	+	0.980949i	$0.437768\pi$
$702$		0			0
$703$		0			0
$704$	0.486424	−	0.969153i	0.486424	−	0.969153i
$705$		0			0
$706$	−0.305595	+	0.387780i	−0.305595	+	0.387780i
$707$		0			0
$708$	0.0197613	+	0.976950i	0.0197613	+	0.976950i
$709$		0			0		−0.939179	−	0.343428i	$-0.888412\pi$
$709$		0			0		0.939179	+	0.343428i	$0.111588\pi$
$710$		0			0
$711$		0			0
$712$	0.120830	+	1.37516i	0.120830	+	1.37516i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.45221	−	0.257186i	1.45221	−	0.257186i
$717$		0			0
$718$		0			0
$719$		0			0		−0.472511	−	0.881325i	$-0.656652\pi$
$719$		0			0		0.472511	+	0.881325i	$0.343348\pi$
$720$		0			0
$721$		0			0
$722$	0.0406917	−	0.0462687i	0.0406917	−	0.0462687i
$723$	0.0134276	+	1.99172i	0.0134276	+	1.99172i
$724$		0			0
$725$		0			0
$726$	0.189228	+	0.0721017i	0.189228	+	0.0721017i
$727$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$727$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$728$		0			0
$729$	0.494820	+	0.0401182i	0.494820	+	0.0401182i
$730$		0			0
$731$	1.08659	−	0.117663i	1.08659	−	0.117663i
$732$		0			0
$733$		0			0		−0.436485	−	0.899712i	$-0.643777\pi$
$733$		0			0		0.436485	+	0.899712i	$0.356223\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.537569	−	1.27947i	0.537569	−	1.27947i
$738$	0.000619876	−	0.00434917i	0.000619876	−	0.00434917i
$739$	1.63832	−	0.405614i	1.63832	−	0.405614i	0.690227	−	0.723593i	$-0.257511\pi$
$739$	1.63832	−	0.405614i	1.63832	−	0.405614i	0.948098	+	0.317979i	$0.103004\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.871589	−	0.490238i	$-0.836910\pi$
$743$		0			0		0.871589	+	0.490238i	$0.163090\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.533238	−	0.0870381i	0.533238	−	0.0870381i
$748$	−1.64998	−	0.384965i	−1.64998	−	0.384965i
$749$		0			0
$750$		0			0
$751$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$751$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$752$		0			0
$753$	−0.249104	+	0.334256i	−0.249104	+	0.334256i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.399745	−	0.916626i	$-0.630901\pi$
$757$		0			0		0.399745	+	0.916626i	$0.369099\pi$
$758$	0.0820124	−	1.10389i	0.0820124	−	1.10389i
$759$		0			0
$760$		0			0
$761$	−1.45527	+	0.0588973i	−1.45527	+	0.0588973i	−0.755348	−	0.655324i	$-0.772532\pi$
$761$	−1.45527	+	0.0588973i	−1.45527	+	0.0588973i	−0.699920	+	0.714221i	$0.746781\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.00776253	+	1.15142i	−0.00776253	+	1.15142i
$769$	−0.116133	−	0.197036i	−0.116133	−	0.197036i	0.797778	−	0.602951i	$-0.206009\pi$
$769$	−0.116133	−	0.197036i	−0.116133	−	0.197036i	−0.913911	+	0.405915i	$0.866953\pi$
$770$		0			0
$771$	1.76170	−	1.02240i	1.76170	−	1.02240i
$772$	0.493543	−	1.93740i	0.493543	−	1.93740i
$773$		0			0		−0.718923	−	0.695089i	$-0.755365\pi$
$773$		0			0		0.718923	+	0.695089i	$0.244635\pi$
$774$	0.207027	−	0.0953139i	0.207027	−	0.0953139i
$775$		0			0
$776$	0.225135	+	0.170155i	0.225135	+	0.170155i
$777$		0			0
$778$		0			0
$779$	0.00236433	−	0.0128454i	0.00236433	−	0.0128454i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.507764	+	0.861496i	−0.507764	+	0.861496i
$785$		0			0
$786$	0.916471	+	0.0867567i	0.916471	+	0.0867567i
$787$	0.376765	+	1.56701i	0.376765	+	1.56701i	0.764115	+	0.645080i	$0.223176\pi$
$787$	0.376765	+	1.56701i	0.376765	+	1.56701i	−0.387350	+	0.921933i	$0.626609\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.351742	+	0.0332972i	−0.351742	+	0.0332972i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.943724	−	0.330734i	$-0.107296\pi$
$797$		0			0		−0.943724	+	0.330734i	$0.892704\pi$
$798$		0			0
$799$		0			0
$800$	0.963860	−	0.266408i	0.963860	−	0.266408i
$801$	0.358828	−	0.271198i	0.358828	−	0.271198i
$802$	−0.275191	−	0.879105i	−0.275191	−	0.879105i
$803$	−0.0383019	−	0.332737i	−0.0383019	−	0.332737i
$804$	0.0893582	+	1.47094i	0.0893582	+	1.47094i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.63546	−	0.862689i	−1.63546	−	0.862689i	−0.995549	−	0.0942425i	$-0.969957\pi$
$809$	−1.63546	−	0.862689i	−1.63546	−	0.862689i	−0.639914	−	0.768447i	$-0.721030\pi$
$810$		0			0
$811$	1.98658	−	0.134131i	1.98658	−	0.134131i	0.986939	−	0.161094i	$-0.0515021\pi$
$811$	1.98658	−	0.134131i	1.98658	−	0.134131i	0.999636	+	0.0269632i	$0.00858369\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.75203	−	0.408776i	1.75203	−	0.408776i
$817$	0.626466	−	0.258254i	0.626466	−	0.258254i
$818$	1.68877	−	0.669686i	1.68877	−	0.669686i
$819$		0			0
$820$		0			0
$821$		0			0		0.976820	−	0.214062i	$-0.0686695\pi$
$821$		0			0		−0.976820	+	0.214062i	$0.931330\pi$
$822$	0.285551	+	2.21708i	0.285551	+	2.21708i
$823$		0			0		0.960181	−	0.279380i	$-0.0901288\pi$
$823$		0			0		−0.960181	+	0.279380i	$0.909871\pi$
$824$		0			0
$825$	0.452429	+	1.16374i	0.452429	+	1.16374i
$826$		0			0
$827$	0.178817	−	0.182470i	0.178817	−	0.182470i	−0.618962	−	0.785421i	$-0.712446\pi$
$827$	0.178817	−	0.182470i	0.178817	−	0.182470i	0.797778	+	0.602951i	$0.206009\pi$
$828$		0			0
$829$		0			0		−0.670466	−	0.741941i	$-0.733906\pi$
$829$		0			0		0.670466	+	0.741941i	$0.266094\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.49422	+	0.456708i	1.49422	+	0.456708i
$834$	1.38772	+	1.20396i	1.38772	+	1.20396i
$835$		0			0
$836$	−1.04891	+	0.0566255i	−1.04891	+	0.0566255i
$837$		0			0
$838$	−1.43567	+	0.940150i	−1.43567	+	0.940150i
$839$		0			0		0.412067	−	0.911153i	$-0.364807\pi$
$839$		0			0		−0.412067	+	0.911153i	$0.635193\pi$
$840$		0			0
$841$	0.0337017	−	0.999432i	0.0337017	−	0.999432i
$842$		0			0
$843$	−1.49876	−	0.371060i	−1.49876	−	0.371060i
$844$	0.204612	−	0.505996i	0.204612	−	0.505996i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.973619	+	1.13763i	−0.973619	+	1.13763i
$850$	−0.756780	−	1.36696i	−0.756780	−	1.36696i
$851$		0			0
$852$		0			0
$853$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$853$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$854$		0			0
$855$		0			0
$856$	−0.396822	−	1.87104i	−0.396822	−	1.87104i
$857$	0.0563783	+	1.19379i	0.0563783	+	1.19379i	0.829121	+	0.559069i	$0.188841\pi$
$857$	0.0563783	+	1.19379i	0.0563783	+	1.19379i	−0.772743	+	0.634719i	$0.781116\pi$
$858$		0			0
$859$	1.32106	+	0.462974i	1.32106	+	0.462974i	0.896748	−	0.442541i	$-0.145923\pi$
$859$	1.32106	+	0.462974i	1.32106	+	0.462974i	0.424315	+	0.905515i	$0.360515\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.285846	−	0.958275i	$-0.592275\pi$
$863$		0			0		0.285846	+	0.958275i	$0.407725\pi$
$864$	−0.660651	+	0.407609i	−0.660651	+	0.407609i
$865$		0			0
$866$	−1.60933	+	1.18256i	−1.60933	+	1.18256i
$867$	−0.744439	−	1.48322i	−0.744439	−	1.48322i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.00804813	−	0.0915955i	0.00804813	−	0.0915955i
$874$		0			0
$875$		0			0
$876$	0.192829	+	0.298838i	0.192829	+	0.298838i
$877$		0			0		0.272900	−	0.962042i	$-0.412017\pi$
$877$		0			0		−0.272900	+	0.962042i	$0.587983\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.117433	+	0.342466i	−0.117433	+	0.342466i	−0.989021	−	0.147772i	$-0.952790\pi$
$881$	−0.117433	+	0.342466i	−0.117433	+	0.342466i	0.871589	+	0.490238i	$0.163090\pi$
$882$	0.325705	−	0.00878524i	0.325705	−	0.00878524i
$883$	−0.206234	+	0.329274i	−0.206234	+	0.329274i	−0.934463	−	0.356059i	$-0.884120\pi$
$883$	−0.206234	+	0.329274i	−0.206234	+	0.329274i	0.728230	+	0.685333i	$0.240343\pi$
$884$		0			0
$885$		0			0
$886$	1.22923	+	1.25434i	1.22923	+	1.25434i
$887$		0			0		−0.337088	−	0.941473i	$-0.609442\pi$
$887$		0			0		0.337088	+	0.941473i	$0.390558\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.804540	−	1.04972i	−0.804540	−	1.04972i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.522476	+	0.232059i	0.522476	+	0.232059i
$899$		0			0
$900$	−0.240264	−	0.220078i	−0.240264	−	0.220078i
$901$		0			0
$902$	0.0121224	−	0.00817400i	0.0121224	−	0.00817400i
$903$		0			0
$904$	0.493093	−	1.26834i	0.493093	−	1.26834i
$905$		0			0
$906$		0			0
$907$	0.148058	+	0.00599219i	0.148058	+	0.00599219i	0.114357	−	0.993440i	$-0.463519\pi$
$907$	0.148058	+	0.00599219i	0.148058	+	0.00599219i	0.0337017	+	0.999432i	$0.489270\pi$
$908$	−0.0208171	−	0.0920224i	−0.0208171	−	0.0920224i
$909$		0			0
$910$		0			0
$911$		0			0		−0.994188	−	0.107657i	$-0.965665\pi$
$911$		0			0		0.994188	+	0.107657i	$0.0343348\pi$
$912$	0.972175	−	0.546814i	0.972175	−	0.546814i
$913$	1.40477	+	1.12248i	1.40477	+	1.12248i
$914$	−0.763522	−	0.471079i	−0.763522	−	0.471079i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.860537	+	0.854755i	0.860537	+	0.854755i
$919$		0			0		−0.984677	−	0.174386i	$-0.944206\pi$
$919$		0			0		0.984677	+	0.174386i	$0.0557940\pi$
$920$		0			0
$921$	0.184216	−	0.0818200i	0.184216	−	0.0818200i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.40044	+	0.228588i	1.40044	+	0.228588i	0.813746	−	0.581221i	$-0.197425\pi$
$929$	1.40044	+	0.228588i	1.40044	+	0.228588i	0.586694	+	0.809809i	$0.300429\pi$
$930$		0			0
$931$	0.968614	+	0.0130608i	0.968614	+	0.0130608i
$932$	−0.350698	+	1.77088i	−0.350698	+	1.77088i
$933$		0			0
$934$	−0.805835	+	0.592140i	−0.805835	+	0.592140i
$935$		0			0
$936$		0			0
$937$	−1.03857	−	0.0140042i	−1.03857	−	0.0140042i	−0.507764	−	0.861496i	$-0.669528\pi$
$937$	−1.03857	−	0.0140042i	−1.03857	−	0.0140042i	−0.530808	+	0.847492i	$0.678112\pi$
$938$		0			0
$939$	1.40678	+	0.229623i	1.40678	+	0.229623i
$940$		0			0
$941$		0			0		−0.789576	−	0.613653i	$-0.789700\pi$
$941$		0			0		0.789576	+	0.613653i	$0.210300\pi$
$942$		0			0
$943$		0			0
$944$	0.296809	−	0.795032i	0.296809	−	0.795032i
$945$		0			0
$946$	0.697310	+	0.298521i	0.697310	+	0.298521i
$947$	−1.78545	+	0.793012i	−1.78545	+	0.793012i	−0.805835	+	0.592140i	$0.798283\pi$
$947$	−1.78545	+	0.793012i	−1.78545	+	0.793012i	−0.979617	+	0.200872i	$0.935622\pi$
$948$		0			0
$949$		0			0
$950$	−0.687281	−	0.682663i	−0.687281	−	0.682663i
$951$		0			0
$952$		0			0
$953$	0.485742	−	1.80470i	0.485742	−	1.80470i	−0.100952	−	0.994891i	$-0.532189\pi$
$953$	0.485742	−	1.80470i	0.485742	−	1.80470i	0.586694	−	0.809809i	$-0.300429\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.999182	−	0.0404387i	−0.999182	−	0.0404387i
$962$		0			0
$963$	−0.448024	+	0.433171i	−0.448024	+	0.433171i
$964$	0.626794	−	1.61225i	0.626794	−	1.61225i
$965$		0			0
$966$		0			0
$967$		0			0		−0.639914	−	0.768447i	$-0.721030\pi$
$967$		0			0		0.639914	+	0.768447i	$0.278970\pi$
$968$	−0.129684	−	0.118789i	−0.129684	−	0.118789i
$969$	−1.18580	−	1.27717i	−1.18580	−	1.27717i
$970$		0			0
$971$	0.857970	−	0.262238i	0.857970	−	0.262238i	0.167744	−	0.985831i	$-0.446352\pi$
$971$	0.857970	−	0.262238i	0.857970	−	0.262238i	0.690227	+	0.723593i	$0.257511\pi$
$972$	0.563245	+	0.277958i	0.563245	+	0.277958i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.815709	+	1.06429i	0.815709	+	1.06429i	0.996729	+	0.0808112i	$0.0257511\pi$
$977$	0.815709	+	1.06429i	0.815709	+	1.06429i	−0.181020	+	0.983479i	$0.557940\pi$
$978$	0.667005	+	2.03415i	0.667005	+	2.03415i
$979$	1.47034	+	0.280893i	1.47034	+	0.280893i
$980$		0			0
$981$		0			0
$982$	−0.993168	−	1.01346i	−0.993168	−	1.01346i
$983$		0			0		−0.246861	−	0.969051i	$-0.579399\pi$
$983$		0			0		0.246861	+	0.969051i	$0.420601\pi$
$984$	−0.00770203	+	0.0134799i	−0.00770203	+	0.0134799i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.272900	−	0.962042i	$-0.412017\pi$
$991$		0			0		−0.272900	+	0.962042i	$0.587983\pi$
$992$		0			0
$993$	0.108518	+	0.239953i	0.108518	+	0.239953i
$994$		0			0
$995$		0			0
$996$	−1.86511	−	0.408725i	−1.86511	−	0.408725i
$997$		0			0		−0.772743	−	0.634719i	$-0.781116\pi$
$997$		0			0		0.772743	+	0.634719i	$0.218884\pi$
$998$	−0.454512	−	1.08178i	−0.454512	−	1.08178i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.227.1	✓	232
8.3	odd	2	CM	3736.1.l.a.227.1	✓	232
467.395	even	233	inner	3736.1.l.a.395.1	yes	232
3736.395	odd	466	inner	3736.1.l.a.395.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.227.1	✓	232	1.1	even	1	trivial
3736.1.l.a.227.1	✓	232	8.3	odd	2	CM
3736.1.l.a.395.1	yes	232	467.395	even	233	inner
3736.1.l.a.395.1	yes	232	3736.395	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)

\(f(q)\)	\(=\)	\(q+(0.194264 - 0.980949i) q^{2} +(1.15134 + 0.0155247i) q^{3} +(-0.924523 - 0.381126i) q^{4} +(0.238892 - 1.12639i) q^{6} +(-0.553466 + 0.832871i) q^{8} +(0.325705 + 0.00878524i) q^{9} +O(q^{10})\)	\(q+(0.194264 - 0.980949i) q^{2} +(1.15134 + 0.0155247i) q^{3} +(-0.924523 - 0.381126i) q^{4} +(0.238892 - 1.12639i) q^{6} +(-0.553466 + 0.832871i) q^{8} +(0.325705 + 0.00878524i) q^{9} +(0.705078 + 0.823851i) q^{11} +(-1.05852 - 0.453158i) q^{12} +(0.709486 + 0.704719i) q^{16} +(0.811438 - 1.33524i) q^{17} +(0.0718906 - 0.317794i) q^{18} +(0.251770 - 0.935412i) q^{19} +(0.945127 - 0.531601i) q^{22} +(-0.650158 + 0.950325i) q^{24} +(0.948098 + 0.317979i) q^{25} +(-0.775641 - 0.0313916i) q^{27} +(0.829121 - 0.559069i) q^{32} +(0.798994 + 0.959479i) q^{33} +(-1.15216 - 1.05537i) q^{34} +(-0.297774 - 0.132257i) q^{36} +(-0.868682 - 0.428690i) q^{38} +(0.0134390 - 0.00108959i) q^{41} +(0.425518 + 0.555192i) q^{43} +(-0.337870 - 1.03039i) q^{44} +(0.805919 + 0.822386i) q^{48} +(0.246861 + 0.969051i) q^{49} +(0.496103 - 0.868264i) q^{50} +(0.954970 - 1.52471i) q^{51} +(-0.181473 + 0.754767i) q^{54} +(0.304394 - 1.07307i) q^{57} +(-0.349692 - 0.773232i) q^{59} +(-0.387350 - 0.921933i) q^{64} +(1.09642 - 0.597380i) q^{66} +(-0.574100 - 1.14384i) q^{67} +(-1.25909 + 0.925196i) q^{68} +(-0.187584 + 0.266408i) q^{72} +(-0.256093 - 0.172681i) q^{73} +(1.08665 + 0.380821i) q^{75} +(-0.589277 + 0.768854i) q^{76} +(-1.21789 - 0.0657481i) q^{81} +(0.00154189 - 0.0133947i) q^{82} +(1.62879 - 0.311163i) q^{83} +(0.627278 - 0.309558i) q^{86} +(-1.07640 + 0.131265i) q^{88} +(1.07845 - 0.861738i) q^{89} +(0.963280 - 0.630806i) q^{96} +(0.0171120 - 0.281684i) q^{97} +(0.998546 - 0.0539068i) q^{98} +(0.222410 + 0.274527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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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