LMFDB - Embedded newform 3736.1.l.a.139.1

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			139.1
Root			$0.530808 + 0.847492i$ of defining polynomial
Character	$\chi$	$=$	3736.139
Dual form			3736.1.l.a.2419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618962 + 0.785421i) q^{2} +(0.301829 - 0.920480i) q^{3} +(-0.233773 - 0.972291i) q^{4} +(0.536144 + 0.806804i) q^{6} +(0.908355 + 0.418201i) q^{8} +(0.0496528 + 0.0364857i) q^{9} +O(q^{10})$	\(q+(-0.618962 + 0.785421i) q^{2} +(0.301829 - 0.920480i) q^{3} +(-0.233773 - 0.972291i) q^{4} +(0.536144 + 0.806804i) q^{6} +(0.908355 + 0.418201i) q^{8} +(0.0496528 + 0.0364857i) q^{9} +(0.0322718 + 0.226425i) q^{11} +(-0.965534 - 0.0782819i) q^{12} +(-0.890700 + 0.454591i) q^{16} +(0.983200 + 1.72077i) q^{17} +(-0.0593898 + 0.0164152i) q^{18} +(-0.127098 + 0.156880i) q^{19} +(-0.197814 - 0.114802i) q^{22} +(0.659113 - 0.709897i) q^{24} +(0.246861 + 0.969051i) q^{25} +(0.836848 - 0.597722i) q^{27} +(0.194264 - 0.980949i) q^{32} +(0.218160 + 0.0386361i) q^{33} +(-1.96009 - 0.292862i) q^{34} +(0.0238672 - 0.0568064i) q^{36} +(-0.0445486 - 0.196928i) q^{38} +(0.380605 + 1.10995i) q^{41} +(-1.75236 + 0.835591i) q^{43} +(0.212607 - 0.0843097i) q^{44} +(0.149603 + 0.957080i) q^{48} +(-0.934463 + 0.356059i) q^{49} +(-0.913911 - 0.405915i) q^{50} +(1.88069 - 0.385639i) q^{51} +(-0.0485131 + 1.02725i) q^{54} +(0.106043 + 0.164342i) q^{57} +(-0.170479 - 0.0397754i) q^{59} +(0.650217 + 0.759749i) q^{64} +(-0.165378 + 0.147434i) q^{66} +(1.30056 + 1.47881i) q^{67} +(1.44324 - 1.35823i) q^{68} +(0.0298441 + 0.0539068i) q^{72} +(-0.373057 - 1.88378i) q^{73} +(0.966501 + 0.0652567i) q^{75} +(0.182245 + 0.0869014i) q^{76} +(-0.279199 - 0.891908i) q^{81} +(-1.10735 - 0.388079i) q^{82} +(0.106029 - 0.373780i) q^{83} +(0.428353 - 1.89354i) q^{86} +(-0.0653769 + 0.219171i) q^{88} +(1.95596 - 0.265337i) q^{89} +(-0.844310 - 0.474894i) q^{96} +(-0.674818 + 0.905494i) q^{97} +(0.298741 - 0.954334i) q^{98} +(-0.00665889 + 0.0124201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{166}{233}\right)$

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 $

$2$	−0.618962	+	0.785421i	−0.618962	+	0.785421i
$2$	−0.618962	+	0.785421i	−0.618962	+	0.785421i
$3$	0.301829	−	0.920480i	0.301829	−	0.920480i	−0.680408	−	0.732833i	$-0.738197\pi$
$3$	0.301829	−	0.920480i	0.301829	−	0.920480i	0.982237	−	0.187646i	$-0.0600858\pi$
$4$	−0.233773	−	0.972291i	−0.233773	−	0.972291i
$5$		0			0		−0.789576	−	0.613653i	$-0.789700\pi$
$5$		0			0		0.789576	+	0.613653i	$0.210300\pi$
$6$	0.536144	+	0.806804i	0.536144	+	0.806804i
$7$		0			0		−0.181020	−	0.983479i	$-0.557940\pi$
$7$		0			0		0.181020	+	0.983479i	$0.442060\pi$
$8$	0.908355	+	0.418201i	0.908355	+	0.418201i
$9$	0.0496528	+	0.0364857i	0.0496528	+	0.0364857i
$10$		0			0
$11$	0.0322718	+	0.226425i	0.0322718	+	0.226425i	0.999636	−	0.0269632i	$-0.00858369\pi$
$11$	0.0322718	+	0.226425i	0.0322718	+	0.226425i	−0.967365	+	0.253388i	$0.918455\pi$
$12$	−0.965534	−	0.0782819i	−0.965534	−	0.0782819i
$13$		0			0		−0.387350	−	0.921933i	$-0.626609\pi$
$13$		0			0		0.387350	+	0.921933i	$0.373391\pi$
$14$		0			0
$15$		0			0
$16$	−0.890700	+	0.454591i	−0.890700	+	0.454591i
$17$	0.983200	+	1.72077i	0.983200	+	1.72077i	0.608316	+	0.793695i	$0.291845\pi$
$17$	0.983200	+	1.72077i	0.983200	+	1.72077i	0.374884	+	0.927072i	$0.377682\pi$
$18$	−0.0593898	+	0.0164152i	−0.0593898	+	0.0164152i
$19$	−0.127098	+	0.156880i	−0.127098	+	0.156880i	−0.836584	−	0.547839i	$-0.815451\pi$
$19$	−0.127098	+	0.156880i	−0.127098	+	0.156880i	0.709486	+	0.704719i	$0.248927\pi$
$20$		0			0
$21$		0			0
$22$	−0.197814	−	0.114802i	−0.197814	−	0.114802i
$23$		0			0		0.821508	−	0.570197i	$-0.193133\pi$
$23$		0			0		−0.821508	+	0.570197i	$0.806867\pi$
$24$	0.659113	−	0.709897i	0.659113	−	0.709897i
$25$	0.246861	+	0.969051i	0.246861	+	0.969051i
$26$		0			0
$27$	0.836848	−	0.597722i	0.836848	−	0.597722i
$28$		0			0
$29$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$29$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$30$		0			0
$31$		0			0		0.952299	−	0.305167i	$-0.0987124\pi$
$31$		0			0		−0.952299	+	0.305167i	$0.901288\pi$
$32$	0.194264	−	0.980949i	0.194264	−	0.980949i
$33$	0.218160	+	0.0386361i	0.218160	+	0.0386361i
$34$	−1.96009	−	0.292862i	−1.96009	−	0.292862i
$35$		0			0
$36$	0.0238672	−	0.0568064i	0.0238672	−	0.0568064i
$37$		0			0		0.772743	−	0.634719i	$-0.218884\pi$
$37$		0			0		−0.772743	+	0.634719i	$0.781116\pi$
$38$	−0.0445486	−	0.196928i	−0.0445486	−	0.196928i
$39$		0			0
$40$		0			0
$41$	0.380605	+	1.10995i	0.380605	+	1.10995i	0.956327	+	0.292300i	$0.0944206\pi$
$41$	0.380605	+	1.10995i	0.380605	+	1.10995i	−0.575722	+	0.817645i	$0.695279\pi$
$42$		0			0
$43$	−1.75236	+	0.835591i	−1.75236	+	0.835591i	−0.772743	+	0.634719i	$0.781116\pi$
$43$	−1.75236	+	0.835591i	−1.75236	+	0.835591i	−0.979617	+	0.200872i	$0.935622\pi$
$44$	0.212607	−	0.0843097i	0.212607	−	0.0843097i
$45$		0			0
$46$		0			0
$47$		0			0		0.530808	−	0.847492i	$-0.321888\pi$
$47$		0			0		−0.530808	+	0.847492i	$0.678112\pi$
$48$	0.149603	+	0.957080i	0.149603	+	0.957080i
$49$	−0.934463	+	0.356059i	−0.934463	+	0.356059i
$50$	−0.913911	−	0.405915i	−0.913911	−	0.405915i
$51$	1.88069	−	0.385639i	1.88069	−	0.385639i
$52$		0			0
$53$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$53$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$54$	−0.0485131	+	1.02725i	−0.0485131	+	1.02725i
$55$		0			0
$56$		0			0
$57$	0.106043	+	0.164342i	0.106043	+	0.164342i
$58$		0			0
$59$	−0.170479	−	0.0397754i	−0.170479	−	0.0397754i	0.141101	−	0.989995i	$-0.454936\pi$
$59$	−0.170479	−	0.0397754i	−0.170479	−	0.0397754i	−0.311581	+	0.950220i	$0.600858\pi$
$60$		0			0
$61$		0			0		0.956327	−	0.292300i	$-0.0944206\pi$
$61$		0			0		−0.956327	+	0.292300i	$0.905579\pi$
$62$		0			0
$63$		0			0
$64$	0.650217	+	0.759749i	0.650217	+	0.759749i
$65$		0			0
$66$	−0.165378	+	0.147434i	−0.165378	+	0.147434i
$67$	1.30056	+	1.47881i	1.30056	+	1.47881i	0.781231	+	0.624242i	$0.214592\pi$
$67$	1.30056	+	1.47881i	1.30056	+	1.47881i	0.519333	+	0.854572i	$0.326180\pi$
$68$	1.44324	−	1.35823i	1.44324	−	1.35823i
$69$		0			0
$70$		0			0
$71$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$71$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$72$	0.0298441	+	0.0539068i	0.0298441	+	0.0539068i
$73$	−0.373057	−	1.88378i	−0.373057	−	1.88378i	−0.460585	−	0.887615i	$-0.652361\pi$
$73$	−0.373057	−	1.88378i	−0.373057	−	1.88378i	0.0875288	−	0.996162i	$-0.472103\pi$
$74$		0			0
$75$	0.966501	+	0.0652567i	0.966501	+	0.0652567i
$76$	0.182245	+	0.0869014i	0.182245	+	0.0869014i
$77$		0			0
$78$		0			0
$79$		0			0		−0.919301	−	0.393556i	$-0.871245\pi$
$79$		0			0		0.919301	+	0.393556i	$0.128755\pi$
$80$		0			0
$81$	−0.279199	−	0.891908i	−0.279199	−	0.891908i
$82$	−1.10735	−	0.388079i	−1.10735	−	0.388079i
$83$	0.106029	−	0.373780i	0.106029	−	0.373780i	−0.890700	−	0.454591i	$-0.849785\pi$
$83$	0.106029	−	0.373780i	0.106029	−	0.373780i	0.996729	+	0.0808112i	$0.0257511\pi$
$84$		0			0
$85$		0			0
$86$	0.428353	−	1.89354i	0.428353	−	1.89354i
$87$		0			0
$88$	−0.0653769	+	0.219171i	−0.0653769	+	0.219171i
$89$	1.95596	−	0.265337i	1.95596	−	0.265337i	0.956327	−	0.292300i	$-0.0944206\pi$
$89$	1.95596	−	0.265337i	1.95596	−	0.265337i	0.999636	+	0.0269632i	$0.00858369\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.844310	−	0.474894i	−0.844310	−	0.474894i
$97$	−0.674818	+	0.905494i	−0.674818	+	0.905494i	−0.999182	−	0.0404387i	$-0.987124\pi$
$97$	−0.674818	+	0.905494i	−0.674818	+	0.905494i	0.324364	+	0.945932i	$0.394850\pi$
$98$	0.298741	−	0.954334i	0.298741	−	0.954334i
$99$	−0.00665889	+	0.0124201i	−0.00665889	+	0.0124201i
$100$	0.884490	−	0.466559i	0.884490	−	0.466559i
$101$		0			0		−0.772743	−	0.634719i	$-0.781116\pi$
$101$		0			0		0.772743	+	0.634719i	$0.218884\pi$
$102$	−0.861185	+	1.71583i	−0.861185	+	1.71583i
$103$		0			0		−0.728230	−	0.685333i	$-0.759657\pi$
$103$		0			0		0.728230	+	0.685333i	$0.240343\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.238680	−	1.52694i	0.238680	−	1.52694i	−0.507764	−	0.861496i	$-0.669528\pi$
$107$	0.238680	−	1.52694i	0.238680	−	1.52694i	0.746444	−	0.665448i	$-0.231760\pi$
$108$	−0.776792	−	0.673928i	−0.776792	−	0.673928i
$109$		0			0		−0.0740898	−	0.997252i	$-0.523605\pi$
$109$		0			0		0.0740898	+	0.997252i	$0.476395\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.322181	−	0.862992i	−0.322181	−	0.862992i	−0.992646	−	0.121051i	$-0.961373\pi$
$113$	−0.322181	−	0.862992i	−0.322181	−	0.862992i	0.670466	−	0.741941i	$-0.266094\pi$
$114$	−0.194714	−	0.0184324i	−0.194714	−	0.0184324i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.136760	−	0.109278i	0.136760	−	0.109278i
$119$		0			0
$120$		0			0
$121$	0.909954	−	0.264765i	0.909954	−	0.264765i
$122$		0			0
$123$	1.13656	−	0.0153254i	1.13656	−	0.0153254i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.995549	−	0.0942425i	$-0.0300429\pi$
$127$		0			0		−0.995549	+	0.0942425i	$0.969957\pi$
$128$	−0.999182	+	0.0404387i	−0.999182	+	0.0404387i
$129$	0.240232	+	1.86522i	0.240232	+	1.86522i
$130$		0			0
$131$	−0.980215	+	0.343522i	−0.980215	+	0.343522i	−0.772743	−	0.634719i	$-0.781116\pi$
$131$	−0.980215	+	0.343522i	−0.980215	+	0.343522i	−0.207472	+	0.978241i	$0.566524\pi$
$132$	−0.0134345	−	0.221147i	−0.0134345	−	0.221147i
$133$		0			0
$134$	−1.96649	+	0.106162i	−1.96649	+	0.106162i
$135$		0			0
$136$	0.173469	+	1.97424i	0.173469	+	1.97424i
$137$	1.66937	−	0.112713i	1.66937	−	0.112713i	0.797778	−	0.602951i	$-0.206009\pi$
$137$	1.66937	−	0.112713i	1.66937	−	0.112713i	0.871589	+	0.490238i	$0.163090\pi$
$138$		0			0
$139$	0.177296	−	1.74727i	0.177296	−	1.74727i	−0.387350	−	0.921933i	$-0.626609\pi$
$139$	0.177296	−	1.74727i	0.177296	−	1.74727i	0.564646	−	0.825333i	$-0.309013\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0608119	−	0.00992605i	−0.0608119	−	0.00992605i
$145$		0			0
$146$	1.71047	+	0.872979i	1.71047	+	0.872979i
$147$	0.0456973	+	0.967623i	0.0456973	+	0.967623i
$148$		0			0
$149$		0			0		−0.994188	−	0.107657i	$-0.965665\pi$
$149$		0			0		0.994188	+	0.107657i	$0.0343348\pi$
$150$	−0.649481	+	0.718719i	−0.649481	+	0.718719i
$151$		0			0		0.167744	−	0.985831i	$-0.446352\pi$
$151$		0			0		−0.167744	+	0.985831i	$0.553648\pi$
$152$	−0.181057	+	0.0893507i	−0.181057	+	0.0893507i
$153$	−0.0139646	+	0.121314i	−0.0139646	+	0.121314i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.851051	−	0.525083i	$-0.175966\pi$
$157$		0			0		−0.851051	+	0.525083i	$0.824034\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.873337	+	0.332768i	0.873337	+	0.332768i
$163$	0.353139	−	1.66507i	0.353139	−	1.66507i	−0.337088	−	0.941473i	$-0.609442\pi$
$163$	0.353139	−	1.66507i	0.353139	−	1.66507i	0.690227	−	0.723593i	$-0.257511\pi$
$164$	0.990215	−	0.629534i	0.990215	−	0.629534i
$165$		0			0
$166$	0.227947	+	0.314633i	0.227947	+	0.314633i
$167$		0			0		−0.167744	−	0.985831i	$-0.553648\pi$
$167$		0			0		0.167744	+	0.985831i	$0.446352\pi$
$168$		0			0
$169$	−0.699920	+	0.714221i	−0.699920	+	0.714221i
$170$		0			0
$171$	−0.0120346	+	0.00315231i	−0.0120346	+	0.00315231i
$172$	1.22209	+	1.50847i	1.22209	+	1.50847i
$173$		0			0		−0.813746	−	0.581221i	$-0.802575\pi$
$173$		0			0		0.813746	+	0.581221i	$0.197425\pi$
$174$		0			0
$175$		0			0
$176$	−0.131675	−	0.187007i	−0.131675	−	0.187007i
$177$	−0.0880679	+	0.144917i	−0.0880679	+	0.144917i
$178$	−1.00226	+	1.70049i	−1.00226	+	1.70049i
$179$	1.45862	−	1.33607i	1.45862	−	1.33607i	0.629495	−	0.777005i	$-0.283262\pi$
$179$	1.45862	−	1.33607i	1.45862	−	1.33607i	0.829121	−	0.559069i	$-0.188841\pi$
$180$		0			0
$181$		0			0		0.127741	−	0.991808i	$-0.459227\pi$
$181$		0			0		−0.127741	+	0.991808i	$0.540773\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.357895	+	0.278154i	−0.357895	+	0.278154i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.864900	−	0.501945i	$-0.167382\pi$
$191$		0			0		−0.864900	+	0.501945i	$0.832618\pi$
$192$	0.895587	−	0.369197i	0.895587	−	0.369197i
$193$	−0.910022	+	1.33017i	−0.910022	+	1.33017i	0.0337017	+	0.999432i	$0.489270\pi$
$193$	−0.910022	+	1.33017i	−0.910022	+	1.33017i	−0.943724	+	0.330734i	$0.892704\pi$
$194$	−0.293508	−	1.09048i	−0.293508	−	1.09048i
$195$		0			0
$196$	0.564646	+	0.825333i	0.564646	+	0.825333i
$197$		0			0		0.650217	−	0.759749i	$-0.274678\pi$
$197$		0			0		−0.650217	+	0.759749i	$0.725322\pi$
$198$	−0.00563343	−	0.0129176i	−0.00563343	−	0.0129176i
$199$		0			0		0.575722	−	0.817645i	$-0.304721\pi$
$199$		0			0		−0.575722	+	0.817645i	$0.695279\pi$
$200$	−0.181020	+	0.983479i	−0.181020	+	0.983479i
$201$	1.75377	−	0.750794i	1.75377	−	0.750794i
$202$		0			0
$203$		0			0
$204$	−0.814608	−	1.73843i	−0.814608	−	1.73843i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0396233	−	0.0237153i	−0.0396233	−	0.0237153i
$210$		0			0
$211$	0.636195	−	0.878135i	0.636195	−	0.878135i	−0.362351	−	0.932042i	$-0.618026\pi$
$211$	0.636195	−	0.878135i	0.636195	−	0.878135i	0.998546	+	0.0539068i	$0.0171674\pi$
$212$		0			0
$213$		0			0
$214$	1.05156	+	1.13258i	1.05156	+	1.13258i
$215$		0			0
$216$	1.01012	−	0.192973i	1.01012	−	0.192973i
$217$		0			0
$218$		0			0
$219$	−1.84658	−	0.225187i	−1.84658	−	0.225187i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.507764	−	0.861496i	$-0.669528\pi$
$223$		0			0		0.507764	+	0.861496i	$0.330472\pi$
$224$		0			0
$225$	−0.0230991	+	0.0571230i	−0.0230991	+	0.0571230i
$226$	0.877230	+	0.281111i	0.877230	+	0.281111i
$227$	−0.918424	+	1.65893i	−0.918424	+	1.65893i	−0.181020	+	0.983479i	$0.557940\pi$
$227$	−0.918424	+	1.65893i	−0.918424	+	1.65893i	−0.737404	+	0.675452i	$0.763948\pi$
$228$	0.134998	−	0.141524i	0.134998	−	0.141524i
$229$		0			0		−0.0337017	−	0.999432i	$-0.510730\pi$
$229$		0			0		0.0337017	+	0.999432i	$0.489270\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.06220	−	1.34787i	−1.06220	−	1.34787i	−0.934463	−	0.356059i	$-0.884120\pi$
$233$	−1.06220	−	1.34787i	−1.06220	−	1.34787i	−0.127741	−	0.991808i	$-0.540773\pi$
$234$		0			0
$235$		0			0
$236$	0.00118016	+	0.175054i	0.00118016	+	0.175054i
$237$		0			0
$238$		0			0
$239$		0			0		0.690227	−	0.723593i	$-0.257511\pi$
$239$		0			0		−0.690227	+	0.723593i	$0.742489\pi$
$240$		0			0
$241$	0.395151	+	0.126627i	0.395151	+	0.126627i	0.496103	−	0.868264i	$-0.334764\pi$
$241$	0.395151	+	0.126627i	0.395151	+	0.126627i	−0.100952	+	0.994891i	$0.532189\pi$
$242$	−0.355274	+	0.878577i	−0.355274	+	0.878577i
$243$	0.123043	+	0.00165912i	0.123043	+	0.00165912i
$244$		0			0
$245$		0			0
$246$	−0.691450	+	0.902164i	−0.691450	+	0.902164i
$247$		0			0
$248$		0			0
$249$	−0.312054	−	0.210415i	−0.312054	−	0.210415i
$250$		0			0
$251$	1.84499	−	0.352467i	1.84499	−	0.352467i	0.858053	−	0.513561i	$-0.171674\pi$
$251$	1.84499	−	0.352467i	1.84499	−	0.352467i	0.986939	+	0.161094i	$0.0515021\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.586694	−	0.809809i	0.586694	−	0.809809i
$257$	0.794843	−	0.0860705i	0.794843	−	0.0860705i	0.298741	−	0.954334i	$-0.403433\pi$
$257$	0.794843	−	0.0860705i	0.794843	−	0.0860705i	0.496103	+	0.868264i	$0.334764\pi$
$258$	−1.61368	−	0.965815i	−1.61368	−	0.965815i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.336906	−	0.982509i	0.336906	−	0.982509i
$263$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$263$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$264$	0.182009	+	0.126330i	0.182009	+	0.126330i
$265$		0			0
$266$		0			0
$267$	0.346128	−	1.88051i	0.346128	−	1.88051i
$268$	1.13380	−	1.61023i	1.13380	−	1.61023i
$269$		0			0		−0.399745	−	0.916626i	$-0.630901\pi$
$269$		0			0		0.399745	+	0.916626i	$0.369099\pi$
$270$		0			0
$271$		0			0		−0.564646	−	0.825333i	$-0.690987\pi$
$271$		0			0		0.564646	+	0.825333i	$0.309013\pi$
$272$	−1.65798	−	1.08573i	−1.65798	−	1.08573i
$273$		0			0
$274$	−0.944747	+	1.38092i	−0.944747	+	1.38092i
$275$	−0.211451	+	0.0871686i	−0.211451	+	0.0871686i
$276$		0			0
$277$		0			0		0.424315	−	0.905515i	$-0.360515\pi$
$277$		0			0		−0.424315	+	0.905515i	$0.639485\pi$
$278$	1.26260	+	1.22074i	1.26260	+	1.22074i
$279$		0			0
$280$		0			0
$281$	−1.09360	−	0.873840i	−1.09360	−	0.873840i	−0.100952	−	0.994891i	$-0.532189\pi$
$281$	−1.09360	−	0.873840i	−1.09360	−	0.873840i	−0.992646	+	0.121051i	$0.961373\pi$
$282$		0			0
$283$	−0.277879	+	0.0492122i	−0.277879	+	0.0492122i	−0.311581	−	0.950220i	$-0.600858\pi$
$283$	−0.277879	+	0.0492122i	−0.277879	+	0.0492122i	0.0337017	+	0.999432i	$0.489270\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0454363	−	0.0416191i	0.0454363	−	0.0416191i
$289$	−1.48659	+	2.52222i	−1.48659	+	2.52222i
$290$		0			0
$291$	0.629809	+	0.894460i	0.629809	+	0.894460i
$292$	−1.74437	+	0.803096i	−1.74437	+	0.803096i
$293$		0			0		−0.979617	−	0.200872i	$-0.935622\pi$
$293$		0			0		0.979617	+	0.200872i	$0.0643777\pi$
$294$	−0.788277	−	0.563030i	−0.788277	−	0.563030i
$295$		0			0
$296$		0			0
$297$	0.162346	+	0.170194i	0.162346	+	0.170194i
$298$		0			0
$299$		0			0
$300$	−0.162494	−	0.954976i	−0.162494	−	0.954976i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.0418894	−	0.197511i	0.0418894	−	0.197511i
$305$		0			0
$306$	−0.0866388	−	0.0860566i	−0.0866388	−	0.0860566i
$307$	−1.44472	+	1.25341i	−1.44472	+	1.25341i	−0.530808	+	0.847492i	$0.678112\pi$
$307$	−1.44472	+	1.25341i	−1.44472	+	1.25341i	−0.913911	+	0.405915i	$0.866953\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.311581	−	0.950220i	$-0.600858\pi$
$311$		0			0		0.311581	+	0.950220i	$0.399142\pi$
$312$		0			0
$313$	−0.465335	+	1.29966i	−0.465335	+	1.29966i	0.448576	+	0.893745i	$0.351931\pi$
$313$	−0.465335	+	1.29966i	−0.465335	+	1.29966i	−0.913911	+	0.405915i	$0.866953\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.670466	−	0.741941i	$-0.266094\pi$
$317$		0			0		−0.670466	+	0.741941i	$0.733906\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.33348	−	0.680575i	−1.33348	−	0.680575i
$322$		0			0
$323$	−0.394917	−	0.0644605i	−0.394917	−	0.0644605i
$324$	−0.801925	+	0.479967i	−0.801925	+	0.479967i
$325$		0			0
$326$	1.08920	+	1.30797i	1.08920	+	1.30797i
$327$		0			0
$328$	−0.118456	+	1.16739i	−0.118456	+	1.16739i
$329$		0			0
$330$		0			0
$331$	−0.165206	−	1.88020i	−0.165206	−	1.88020i	−0.412067	−	0.911153i	$-0.635193\pi$
$331$	−0.165206	−	1.88020i	−0.165206	−	1.88020i	0.246861	−	0.969051i	$-0.420601\pi$
$332$	−0.388210	−	0.0157115i	−0.388210	−	0.0157115i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.777086	−	1.04272i	−0.777086	−	1.04272i	−0.997728	−	0.0673651i	$-0.978541\pi$
$337$	−0.777086	−	1.04272i	−0.777086	−	1.04272i	0.220643	−	0.975355i	$-0.429185\pi$
$338$	−0.127741	−	0.991808i	−0.127741	−	0.991808i
$339$	−0.891610	+	0.0360850i	−0.891610	+	0.0360850i
$340$		0			0
$341$		0			0
$342$	0.00497308	−	0.0114034i	0.00497308	−	0.0114034i
$343$		0			0
$344$	−1.94121	+	0.0261754i	−1.94121	+	0.0261754i
$345$		0			0
$346$		0			0
$347$	−0.764581	+	0.124799i	−0.764581	+	0.124799i	−0.530808	−	0.847492i	$-0.678112\pi$
$347$	−0.764581	+	0.124799i	−0.764581	+	0.124799i	−0.233773	+	0.972291i	$0.575107\pi$
$348$		0			0
$349$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$349$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$350$		0			0
$351$		0			0
$352$	0.228381	+	0.0123292i	0.228381	+	0.0123292i
$353$	1.86061	+	0.176132i	1.86061	+	0.176132i	0.963860	−	0.266408i	$-0.0858369\pi$
$353$	1.86061	+	0.176132i	1.86061	+	0.176132i	0.896748	+	0.442541i	$0.145923\pi$
$354$	−0.0593104	−	0.158869i	−0.0593104	−	0.158869i
$355$		0			0
$356$	−0.715236	−	1.83974i	−0.715236	−	1.83974i
$357$		0			0
$358$	0.146553	+	1.97261i	0.146553	+	1.97261i
$359$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$359$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$360$		0			0
$361$	0.199014	+	0.938363i	0.199014	+	0.938363i
$362$		0			0
$363$	0.0309391	−	0.917508i	0.0309391	−	0.917508i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$367$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$368$		0			0
$369$	−0.0215990	+	0.0689986i	−0.0215990	+	0.0689986i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.337088	−	0.941473i	$-0.609442\pi$
$373$		0			0		0.337088	+	0.941473i	$0.390558\pi$
$374$	0.00305578	−	0.453265i	0.00305578	−	0.453265i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.519300	+	1.74091i	−0.519300	+	1.74091i	0.141101	+	0.989995i	$0.454936\pi$
$379$	−0.519300	+	1.74091i	−0.519300	+	1.74091i	−0.660401	+	0.750913i	$0.729614\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.100952	−	0.994891i	$-0.532189\pi$
$383$		0			0		0.100952	+	0.994891i	$0.467811\pi$
$384$	−0.264359	+	0.931932i	−0.264359	+	0.931932i
$385$		0			0
$386$	−0.481471	−	1.53807i	−0.481471	−	1.53807i
$387$	−0.117497	−	0.0224466i	−0.117497	−	0.0224466i
$388$	1.03816	+	0.444440i	1.03816	+	0.444440i
$389$		0			0		0.553466	−	0.832871i	$-0.313305\pi$
$389$		0			0		−0.553466	+	0.832871i	$0.686695\pi$
$390$		0			0
$391$		0			0
$392$	−0.997728	−	0.0673651i	−0.997728	−	0.0673651i
$393$	0.0203480	+	1.00595i	0.0203480	+	1.00595i
$394$		0			0
$395$		0			0
$396$	0.0136326	+	0.00357089i	0.0136326	+	0.00357089i
$397$		0			0		−0.412067	−	0.911153i	$-0.635193\pi$
$397$		0			0		0.412067	+	0.911153i	$0.364807\pi$
$398$		0			0
$399$		0			0
$400$	−0.660401	−	0.750913i	−0.660401	−	0.750913i
$401$	−0.758035	+	0.675782i	−0.758035	+	0.675782i	−0.952299	−	0.305167i	$-0.901288\pi$
$401$	−0.758035	+	0.675782i	−0.758035	+	0.675782i	0.194264	+	0.980949i	$0.437768\pi$
$402$	−0.495824	+	1.84216i	−0.495824	+	1.84216i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.86961	+	0.436208i	1.86961	+	0.436208i
$409$	−0.172758	−	1.50079i	−0.172758	−	1.50079i	−0.737404	−	0.675452i	$-0.763948\pi$
$409$	−0.172758	−	1.50079i	−0.172758	−	1.50079i	0.564646	−	0.825333i	$-0.309013\pi$
$410$		0			0
$411$	0.400113	−	1.57064i	0.400113	−	1.57064i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.55481	−	0.690572i	−1.55481	−	0.690572i
$418$	0.0431518	−	0.0164421i	0.0431518	−	0.0164421i
$419$	−0.307078	−	1.96452i	−0.307078	−	1.96452i	−0.259904	−	0.965634i	$-0.583691\pi$
$419$	−0.307078	−	1.96452i	−0.307078	−	1.96452i	−0.0471738	−	0.998887i	$-0.515021\pi$
$420$		0			0
$421$		0			0		0.0606373	−	0.998160i	$-0.480687\pi$
$421$		0			0		−0.0606373	+	0.998160i	$0.519313\pi$
$422$	0.295926	+	1.04321i	0.295926	+	1.04321i
$423$		0			0
$424$		0			0
$425$	−1.42480	+	1.37756i	−1.42480	+	1.37756i
$426$		0			0
$427$		0			0
$428$	−1.54043	+	0.124893i	−1.54043	+	0.124893i
$429$		0			0
$430$		0			0
$431$		0			0		0.387350	−	0.921933i	$-0.373391\pi$
$431$		0			0		−0.387350	+	0.921933i	$0.626609\pi$
$432$	−0.473662	+	0.912815i	−0.473662	+	0.912815i
$433$	−0.590922	−	0.0882912i	−0.590922	−	0.0882912i	−0.154437	−	0.988003i	$-0.549356\pi$
$433$	−0.590922	−	0.0882912i	−0.590922	−	0.0882912i	−0.436485	+	0.899712i	$0.643777\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.31983	−	1.31096i	1.31983	−	1.31096i
$439$		0			0		0.913911	−	0.405915i	$-0.133047\pi$
$439$		0			0		−0.913911	+	0.405915i	$0.866953\pi$
$440$		0			0
$441$	−0.0593898	−	0.0164152i	−0.0593898	−	0.0164152i
$442$		0			0
$443$	−1.01577	+	1.09404i	−1.01577	+	1.09404i	−0.0202235	+	0.999795i	$0.506438\pi$
$443$	−1.01577	+	1.09404i	−1.01577	+	1.09404i	−0.995549	+	0.0942425i	$0.969957\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.86481	+	0.515428i	−1.86481	+	0.515428i	−0.864900	+	0.501945i	$0.832618\pi$
$449$	−1.86481	+	0.515428i	−1.86481	+	0.515428i	−0.999909	+	0.0134828i	$0.995708\pi$
$450$	−0.0305682	−	0.0534995i	−0.0305682	−	0.0534995i
$451$	−0.239037	+	0.121998i	−0.239037	+	0.121998i
$452$	−0.763762	+	0.514998i	−0.763762	+	0.514998i
$453$		0			0
$454$	−0.734491	−	1.74816i	−0.734491	−	1.74816i
$455$		0			0
$456$	0.0275973	+	0.193628i	0.0275973	+	0.193628i
$457$	−1.28209	+	0.317419i	−1.28209	+	0.317419i	−0.821508	−	0.570197i	$-0.806867\pi$
$457$	−1.28209	+	0.317419i	−1.28209	+	0.317419i	−0.460585	+	0.887615i	$0.652361\pi$
$458$		0			0
$459$	1.85133	+	0.852340i	1.85133	+	0.852340i
$460$		0			0
$461$		0			0		−0.553466	−	0.832871i	$-0.686695\pi$
$461$		0			0		0.553466	+	0.832871i	$0.313305\pi$
$462$		0			0
$463$		0			0		−0.233773	−	0.972291i	$-0.575107\pi$
$463$		0			0		0.233773	+	0.972291i	$0.424893\pi$
$464$		0			0
$465$		0			0
$466$	1.71611			1.71611
$467$	−0.989021	−	0.147772i	−0.989021	−	0.147772i
$467$	−0.989021	−	0.147772i	−0.989021	−	0.147772i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.138221	−	0.107425i	−0.138221	−	0.107425i
$473$	−0.245751	−	0.369813i	−0.245751	−	0.369813i
$474$		0			0
$475$	−0.183400	−	0.0844363i	−0.183400	−	0.0844363i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.996729	−	0.0808112i	$-0.974249\pi$
$479$		0			0		0.996729	+	0.0808112i	$0.0257511\pi$
$480$		0			0
$481$		0			0
$482$	−0.344039	+	0.231982i	−0.344039	+	0.231982i
$483$		0			0
$484$	−0.470152	−	0.822845i	−0.470152	−	0.822845i
$485$		0			0
$486$	−0.0774619	+	0.0956136i	−0.0774619	+	0.0956136i
$487$		0			0		0.412067	−	0.911153i	$-0.364807\pi$
$487$		0			0		−0.412067	+	0.911153i	$0.635193\pi$
$488$		0			0
$489$	−1.42607	−	0.827622i	−1.42607	−	0.827622i
$490$		0			0
$491$	1.21208	−	1.30547i	1.21208	−	1.30547i	0.272900	−	0.962042i	$-0.412017\pi$
$491$	1.21208	−	1.30547i	1.21208	−	1.30547i	0.939179	−	0.343428i	$-0.111588\pi$
$492$	−0.280598	−	1.10148i	−0.280598	−	1.10148i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.358414	−	0.114855i	0.358414	−	0.114855i
$499$	0.381626	−	1.92705i	0.381626	−	1.92705i	0.00674156	−	0.999977i	$-0.497854\pi$
$499$	0.381626	−	1.92705i	0.381626	−	1.92705i	0.374884	−	0.927072i	$-0.377682\pi$
$500$		0			0
$501$		0			0
$502$	−0.865145	+	1.66726i	−0.865145	+	1.66726i
$503$		0			0		0.387350	−	0.921933i	$-0.373391\pi$
$503$		0			0		−0.387350	+	0.921933i	$0.626609\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.446170	+	0.859835i	0.446170	+	0.859835i
$508$		0			0
$509$		0			0		0.718923	−	0.695089i	$-0.244635\pi$
$509$		0			0		−0.718923	+	0.695089i	$0.755365\pi$
$510$		0			0
$511$		0			0
$512$	0.272900	+	0.962042i	0.272900	+	0.962042i
$513$	−0.0125905	+	0.207254i	−0.0125905	+	0.207254i
$514$	−0.424376	+	0.677561i	−0.424376	+	0.677561i
$515$		0			0
$516$	1.75737	−	0.669613i	1.75737	−	0.669613i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.0269689	−	0.571056i	0.0269689	−	0.571056i	−0.943724	−	0.330734i	$-0.892704\pi$
$521$	0.0269689	−	0.571056i	0.0269689	−	0.571056i	0.970693	−	0.240323i	$-0.0772532\pi$
$522$		0			0
$523$	0.00332846	−	0.0130658i	0.00332846	−	0.0130658i	−0.967365	−	0.253388i	$-0.918455\pi$
$523$	0.00332846	−	0.0130658i	0.00332846	−	0.0130658i	0.970693	+	0.240323i	$0.0772532\pi$
$524$	0.563151	+	0.872748i	0.563151	+	0.872748i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.211879	+	0.0647606i	−0.211879	+	0.0647606i
$529$	0.349751	−	0.936843i	0.349751	−	0.936843i
$530$		0			0
$531$	−0.00701354	−	0.00819500i	−0.00701354	−	0.00819500i
$532$		0			0
$533$		0			0
$534$	1.26275	+	1.43582i	1.26275	+	1.43582i
$535$		0			0
$536$	0.562933	+	1.88718i	0.562933	+	1.88718i
$537$	−0.789576	−	1.74589i	−0.789576	−	1.74589i
$538$		0			0
$539$	−0.110778	−	0.200095i	−0.110778	−	0.200095i
$540$		0			0
$541$		0			0		−0.0202235	−	0.999795i	$-0.506438\pi$
$541$		0			0		0.0202235	+	0.999795i	$0.493562\pi$
$542$		0			0
$543$		0			0
$544$	1.87899	−	0.630187i	1.87899	−	0.630187i
$545$		0			0
$546$		0			0
$547$	−0.145547	−	0.0278053i	−0.145547	−	0.0278053i	0.114357	−	0.993440i	$-0.463519\pi$
$547$	−0.145547	−	0.0278053i	−0.145547	−	0.0278053i	−0.259904	+	0.965634i	$0.583691\pi$
$548$	−0.499843	−	1.59676i	−0.499843	−	1.59676i
$549$		0			0
$550$	0.0624159	−	0.220032i	0.0624159	−	0.220032i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.74030	+	0.236081i	−1.74030	+	0.236081i
$557$		0			0		−0.924523	−	0.381126i	$-0.875536\pi$
$557$		0			0		0.924523	+	0.381126i	$0.124464\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.148012	+	0.413390i	0.148012	+	0.413390i
$562$	1.36323	−	0.318062i	1.36323	−	0.318062i
$563$	1.73748	+	0.977269i	1.73748	+	0.977269i	0.908355	+	0.418201i	$0.137339\pi$
$563$	1.73748	+	0.977269i	1.73748	+	0.977269i	0.829121	+	0.559069i	$0.188841\pi$
$564$		0			0
$565$		0			0
$566$	0.133344	−	0.248712i	0.133344	−	0.248712i
$567$		0			0
$568$		0			0
$569$	0.715728	−	1.42602i	0.715728	−	1.42602i	−0.181020	−	0.983479i	$-0.557940\pi$
$569$	0.715728	−	1.42602i	0.715728	−	1.42602i	0.896748	−	0.442541i	$-0.145923\pi$
$570$		0			0
$571$	−0.0210016	+	0.622807i	−0.0210016	+	0.622807i	0.939179	+	0.343428i	$0.111588\pi$
$571$	−0.0210016	+	0.622807i	−0.0210016	+	0.622807i	−0.960181	+	0.279380i	$0.909871\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.00456517	+	0.0614473i	0.00456517	+	0.0614473i
$577$	0.223986	+	0.553908i	0.223986	+	0.553908i	0.996729	−	0.0808112i	$-0.0257511\pi$
$577$	0.223986	+	0.553908i	0.223986	+	0.553908i	−0.772743	+	0.634719i	$0.781116\pi$
$578$	−1.06086	−	2.72876i	−1.06086	−	2.72876i
$579$	0.949719	+	1.23914i	0.949719	+	1.23914i
$580$		0			0
$581$		0			0
$582$	−1.09236	−	0.0589711i	−1.09236	−	0.0589711i
$583$		0			0
$584$	0.448929	−	1.86715i	0.448929	−	1.86715i
$585$		0			0
$586$		0			0
$587$	−1.00226	+	0.163595i	−1.00226	+	0.163595i	−0.639914	−	0.768447i	$-0.721030\pi$
$587$	−1.00226	+	0.163595i	−1.00226	+	0.163595i	−0.362351	+	0.932042i	$0.618026\pi$
$588$	0.930129	−	0.270635i	0.930129	−	0.270635i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.531041	−	1.09462i	−0.531041	−	1.09462i	−0.979617	−	0.200872i	$-0.935622\pi$
$593$	−0.531041	−	1.09462i	−0.531041	−	1.09462i	0.448576	−	0.893745i	$-0.351931\pi$
$594$	−0.234160	+	0.0221665i	−0.234160	+	0.0221665i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.0606373	−	0.998160i	$-0.519313\pi$
$599$		0			0		0.0606373	+	0.998160i	$0.480687\pi$
$600$	0.850636	+	0.463468i	0.850636	+	0.463468i
$601$	1.45434	−	0.0785130i	1.45434	−	0.0785130i	0.690227	−	0.723593i	$-0.257511\pi$
$601$	1.45434	−	0.0785130i	1.45434	−	0.0785130i	0.764115	+	0.645080i	$0.223176\pi$
$602$		0			0
$603$	0.0106212	+	0.120879i	0.0106212	+	0.120879i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.970693	−	0.240323i	$-0.922747\pi$
$607$		0			0		0.970693	+	0.240323i	$0.0772532\pi$
$608$	0.129201	+	0.155152i	0.129201	+	0.155152i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.121217	−	0.0147822i	0.121217	−	0.0147822i
$613$		0			0		−0.890700	−	0.454591i	$-0.849785\pi$
$613$		0			0		0.890700	+	0.454591i	$0.150215\pi$
$614$	−0.0902271	−	1.91052i	−0.0902271	−	1.91052i
$615$		0			0
$616$		0			0
$617$	1.13160	−	1.25224i	1.13160	−	1.25224i	0.167744	−	0.985831i	$-0.446352\pi$
$617$	1.13160	−	1.25224i	1.13160	−	1.25224i	0.963860	−	0.266408i	$-0.0858369\pi$
$618$		0			0
$619$	−0.276982	+	0.136689i	−0.276982	+	0.136689i	−0.575722	−	0.817645i	$-0.695279\pi$
$619$	−0.276982	+	0.136689i	−0.276982	+	0.136689i	0.298741	+	0.954334i	$0.403433\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.878119	+	0.478442i	−0.878119	+	0.478442i
$626$	−0.732756	−	1.16992i	−0.732756	−	1.16992i
$627$	−0.0337889	+	0.0293145i	−0.0337889	+	0.0293145i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.843894	−	0.536510i	$-0.180258\pi$
$631$		0			0		−0.843894	+	0.536510i	$0.819742\pi$
$632$		0			0
$633$	−0.616284	−	0.850651i	−0.616284	−	0.850651i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.69454	+	0.347469i	1.69454	+	0.347469i	0.948098	−	0.317979i	$-0.103004\pi$
$641$	1.69454	+	0.347469i	1.69454	+	0.347469i	0.746444	+	0.665448i	$0.231760\pi$
$642$	1.35991	−	0.626094i	1.35991	−	0.626094i
$643$	0.827800	+	1.17565i	0.827800	+	1.17565i	0.982237	+	0.187646i	$0.0600858\pi$
$643$	0.827800	+	1.17565i	0.827800	+	1.17565i	−0.154437	+	0.988003i	$0.549356\pi$
$644$		0			0
$645$		0			0
$646$	0.295067	−	0.270277i	0.295067	−	0.270277i
$647$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$647$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$648$	0.119385	−	0.926930i	0.119385	−	0.926930i
$649$	0.00350448	−	0.0398844i	0.00350448	−	0.0398844i
$650$		0			0
$651$		0			0
$652$	−1.70148	+	0.0458941i	−1.70148	+	0.0458941i
$653$		0			0		−0.781231	−	0.624242i	$-0.785408\pi$
$653$		0			0		0.781231	+	0.624242i	$0.214592\pi$
$654$		0			0
$655$		0			0
$656$	−0.843576	−	0.815609i	−0.843576	−	0.815609i
$657$	0.0502076	−	0.107146i	0.0502076	−	0.107146i
$658$		0			0
$659$	1.84753	−	0.761628i	1.84753	−	0.761628i	0.908355	−	0.418201i	$-0.137339\pi$
$659$	1.84753	−	0.761628i	1.84753	−	0.761628i	0.939179	−	0.343428i	$-0.111588\pi$
$660$		0			0
$661$		0			0		−0.259904	−	0.965634i	$-0.583691\pi$
$661$		0			0		0.259904	+	0.965634i	$0.416309\pi$
$662$	1.57901	+	1.03402i	1.57901	+	1.03402i
$663$		0			0
$664$	0.252627	−	0.295183i	0.252627	−	0.295183i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.28616	+	0.192168i	−1.28616	+	0.192168i	−0.755348	−	0.655324i	$-0.772532\pi$
$673$	−1.28616	+	0.192168i	−1.28616	+	0.192168i	−0.530808	+	0.847492i	$0.678112\pi$
$674$	1.29996	+	0.0350638i	1.29996	+	0.0350638i
$675$	0.785808	+	0.663394i	0.785808	+	0.663394i
$676$	0.858053	+	0.513561i	0.858053	+	0.513561i
$677$		0			0		0.994188	−	0.107657i	$-0.0343348\pi$
$677$		0			0		−0.994188	+	0.107657i	$0.965665\pi$
$678$	0.523530	−	0.722625i	0.523530	−	0.722625i
$679$		0			0
$680$		0			0
$681$	1.24981	+	1.34610i	1.24981	+	1.34610i
$682$		0			0
$683$	−1.08727	+	0.207712i	−1.08727	+	0.207712i	−0.699920	−	0.714221i	$-0.746781\pi$
$683$	−1.08727	+	0.207712i	−1.08727	+	0.207712i	−0.387350	+	0.921933i	$0.626609\pi$
$684$	0.00587834	+	0.0109642i	0.00587834	+	0.0109642i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.18098	−	1.54087i	1.18098	−	1.54087i
$689$		0			0
$690$		0			0
$691$	−0.944936	−	0.0127416i	−0.944936	−	0.0127416i	−0.460585	−	0.887615i	$-0.652361\pi$
$691$	−0.944936	−	0.0127416i	−0.944936	−	0.0127416i	−0.484351	+	0.874874i	$0.660944\pi$
$692$		0			0
$693$		0			0
$694$	0.375227	−	0.677764i	0.375227	−	0.677764i
$695$		0			0
$696$		0			0
$697$	−1.53575	+	1.74623i	−1.53575	+	1.74623i
$698$		0			0
$699$	−1.56129	+	0.570913i	−1.56129	+	0.570913i
$700$		0			0
$701$		0			0		−0.618962	−	0.785421i	$-0.712446\pi$
$701$		0			0		0.618962	+	0.785421i	$0.287554\pi$
$702$		0			0
$703$		0			0
$704$	−0.151043	+	0.171744i	−0.151043	+	0.171744i
$705$		0			0
$706$	−1.28998	+	1.35234i	−1.28998	+	1.35234i
$707$		0			0
$708$	0.161490	+	0.0517499i	0.161490	+	0.0517499i
$709$		0			0		0.374884	−	0.927072i	$-0.377682\pi$
$709$		0			0		−0.374884	+	0.927072i	$0.622318\pi$
$710$		0			0
$711$		0			0
$712$	1.88767	+	0.576965i	1.88767	+	0.576965i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.64004	−	1.10586i	−1.64004	−	1.10586i
$717$		0			0
$718$		0			0
$719$		0			0		−0.976820	−	0.214062i	$-0.931330\pi$
$719$		0			0		0.976820	+	0.214062i	$0.0686695\pi$
$720$		0			0
$721$		0			0
$722$	−0.860192	−	0.424500i	−0.860192	−	0.424500i
$723$	0.235826	−	0.325508i	0.235826	−	0.325508i
$724$		0			0
$725$		0			0
$726$	0.701480	+	0.592202i	0.701480	+	0.592202i
$727$		0			0		−0.999636	−	0.0269632i	$-0.991416\pi$
$727$		0			0		0.999636	+	0.0269632i	$0.00858369\pi$
$728$		0			0
$729$	0.341811	−	0.996814i	0.341811	−	0.996814i
$730$		0			0
$731$	−3.16078	−	2.19385i	−3.16078	−	2.19385i
$732$		0			0
$733$		0			0		0.919301	−	0.393556i	$-0.128755\pi$
$733$		0			0		−0.919301	+	0.393556i	$0.871245\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.292869	+	0.342205i	−0.292869	+	0.342205i
$738$	−0.0408240	−	0.0596718i	−0.0408240	−	0.0596718i
$739$	1.23380	+	0.807957i	1.23380	+	0.807957i	0.986939	−	0.161094i	$-0.0515021\pi$
$739$	1.23380	+	0.807957i	1.23380	+	0.807957i	0.246861	+	0.969051i	$0.420601\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.864900	−	0.501945i	$-0.167382\pi$
$743$		0			0		−0.864900	+	0.501945i	$0.832618\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0189023	−	0.0146907i	0.0189023	−	0.0146907i
$748$	0.354113	+	0.282954i	0.354113	+	0.282954i
$749$		0			0
$750$		0			0
$751$		0			0		0.0202235	−	0.999795i	$-0.493562\pi$
$751$		0			0		−0.0202235	+	0.999795i	$0.506438\pi$
$752$		0			0
$753$	0.232433	−	1.80466i	0.232433	−	1.80466i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.519333	−	0.854572i	$-0.326180\pi$
$757$		0			0		−0.519333	+	0.854572i	$0.673820\pi$
$758$	−1.04592	−	1.48542i	−1.04592	−	1.48542i
$759$		0			0
$760$		0			0
$761$	0.730054	+	0.521444i	0.730054	+	0.521444i	0.884490	−	0.466559i	$-0.154506\pi$
$761$	0.730054	+	0.521444i	0.730054	+	0.521444i	−0.154437	+	0.988003i	$0.549356\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.568331	−	0.784463i	−0.568331	−	0.784463i
$769$	−1.26547	−	1.40037i	−1.26547	−	1.40037i	−0.878119	−	0.478442i	$-0.841202\pi$
$769$	−1.26547	−	1.40037i	−1.26547	−	1.40037i	−0.387350	−	0.921933i	$-0.626609\pi$
$770$		0			0
$771$	0.160680	−	0.757616i	0.160680	−	0.757616i
$772$	1.50605	+	0.573850i	1.50605	+	0.573850i
$773$		0			0		−0.709486	−	0.704719i	$-0.751073\pi$
$773$		0			0		0.709486	+	0.704719i	$0.248927\pi$
$774$	0.0903560	−	0.0783909i	0.0903560	−	0.0783909i
$775$		0			0
$776$	−0.991652	+	0.540300i	−0.991652	+	0.540300i
$777$		0			0
$778$		0			0
$779$	−0.222502	−	0.0813620i	−0.222502	−	0.0813620i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.670466	−	0.741941i	0.670466	−	0.741941i
$785$		0			0
$786$	−0.802691	−	0.606664i	−0.802691	−	0.606664i
$787$	−0.0687067	−	1.45484i	−0.0687067	−	1.45484i	−0.718923	−	0.695089i	$-0.755365\pi$
$787$	−0.0687067	−	1.45484i	−0.0687067	−	1.45484i	0.650217	−	0.759749i	$-0.274678\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0112427	+	0.00849712i	−0.0112427	+	0.00849712i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.997728	−	0.0673651i	$-0.0214592\pi$
$797$		0			0		−0.997728	+	0.0673651i	$0.978541\pi$
$798$		0			0
$799$		0			0
$800$	0.998546	−	0.0539068i	0.998546	−	0.0539068i
$801$	0.106800	+	0.0581899i	0.106800	+	0.0581899i
$802$	−0.0615789	−	1.01366i	−0.0615789	−	1.01366i
$803$	0.414495	−	0.145262i	0.414495	−	0.145262i
$804$	−1.13997	−	1.52966i	−1.13997	−	1.52966i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.186899	+	0.428565i	−0.186899	+	0.428565i	−0.984677	−	0.174386i	$-0.944206\pi$
$809$	−0.186899	+	0.428565i	−0.186899	+	0.428565i	0.797778	+	0.602951i	$0.206009\pi$
$810$		0			0
$811$	−1.59541	+	0.0215126i	−1.59541	+	0.0215126i	−0.805835	−	0.592140i	$-0.798283\pi$
$811$	−1.59541	+	0.0215126i	−1.59541	+	0.0215126i	−0.789576	+	0.613653i	$0.789700\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.49982	+	1.19843i	−1.49982	+	1.19843i
$817$	0.0916329	−	0.381112i	0.0916329	−	0.381112i
$818$	1.28568	+	0.793241i	1.28568	+	0.793241i
$819$		0			0
$820$		0			0
$821$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$821$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$822$	0.985958	+	1.28642i	0.985958	+	1.28642i
$823$		0			0		−0.362351	−	0.932042i	$-0.618026\pi$
$823$		0			0		0.362351	+	0.932042i	$0.381974\pi$
$824$		0			0
$825$	0.0164150	+	0.220946i	0.0164150	+	0.220946i
$826$		0			0
$827$	−0.187892	+	1.20203i	−0.187892	+	1.20203i	0.690227	+	0.723593i	$0.257511\pi$
$827$	−0.187892	+	1.20203i	−0.187892	+	1.20203i	−0.878119	+	0.478442i	$0.841202\pi$
$828$		0			0
$829$		0			0		−0.699920	−	0.714221i	$-0.746781\pi$
$829$		0			0		0.699920	+	0.714221i	$0.253219\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.53146	−	1.25792i	−1.53146	−	1.25792i
$834$	1.50476	−	0.793743i	1.50476	−	0.793743i
$835$		0			0
$836$	−0.0137953	+	0.0440694i	−0.0137953	+	0.0440694i
$837$		0			0
$838$	1.73305	+	0.974778i	1.73305	+	0.974778i
$839$		0			0		0.973845	−	0.227213i	$-0.0729614\pi$
$839$		0			0		−0.973845	+	0.227213i	$0.927039\pi$
$840$		0			0
$841$	0.00674156	−	0.999977i	0.00674156	−	0.999977i
$842$		0			0
$843$	−1.13443	+	0.742885i	−1.13443	+	0.742885i
$844$	−1.00253	−	0.413283i	−1.00253	−	0.413283i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0385730	+	0.270635i	−0.0385730	+	0.270635i
$850$	−0.200071	−	1.97172i	−0.200071	−	1.97172i
$851$		0			0
$852$		0			0
$853$		0			0		−0.298741	−	0.954334i	$-0.596567\pi$
$853$		0			0		0.298741	+	0.954334i	$0.403433\pi$
$854$		0			0
$855$		0			0
$856$	0.855375	−	1.28719i	0.855375	−	1.28719i
$857$	−0.242221	+	0.0812378i	−0.242221	+	0.0812378i	−0.436485	−	0.899712i	$-0.643777\pi$
$857$	−0.242221	+	0.0812378i	−0.242221	+	0.0812378i	0.194264	+	0.980949i	$0.437768\pi$
$858$		0			0
$859$	0.308171	+	0.0208073i	0.308171	+	0.0208073i	0.220643	−	0.975355i	$-0.429185\pi$
$859$	0.308171	+	0.0208073i	0.308171	+	0.0208073i	0.0875288	+	0.996162i	$0.472103\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$863$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$864$	−0.423766	−	0.937021i	−0.423766	−	0.937021i
$865$		0			0
$866$	0.435104	−	0.409474i	0.435104	−	0.409474i
$867$	1.87296	+	2.12966i	1.87296	+	2.12966i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0665442	+	0.0203392i	−0.0665442	+	0.0203392i
$874$		0			0
$875$		0			0
$876$	0.212733	+	1.84805i	0.212733	+	1.84805i
$877$		0			0		−0.542187	−	0.840258i	$-0.682403\pi$
$877$		0			0		0.542187	+	0.840258i	$0.317597\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.20199	+	1.44342i	−1.20199	+	1.44342i	−0.337088	+	0.941473i	$0.609442\pi$
$881$	−1.20199	+	1.44342i	−1.20199	+	1.44342i	−0.864900	+	0.501945i	$0.832618\pi$
$882$	0.0496528	−	0.0364857i	0.0496528	−	0.0364857i
$883$	1.21269	−	0.248665i	1.21269	−	0.248665i	0.448576	−	0.893745i	$-0.351931\pi$
$883$	1.21269	−	0.248665i	1.21269	−	0.248665i	0.764115	+	0.645080i	$0.223176\pi$
$884$		0			0
$885$		0			0
$886$	−0.230556	−	1.47498i	−0.230556	−	1.47498i
$887$		0			0		0.530808	−	0.847492i	$-0.321888\pi$
$887$		0			0		−0.530808	+	0.847492i	$0.678112\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.192940	−	0.0920012i	0.192940	−	0.0920012i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.749417	−	1.78369i	0.749417	−	1.78369i
$899$		0			0
$900$	0.0609402	+	0.00910524i	0.0609402	+	0.00910524i
$901$		0			0
$902$	0.0521345	−	0.263257i	0.0521345	−	0.263257i
$903$		0			0
$904$	0.0682494	−	0.918639i	0.0682494	−	0.918639i
$905$		0			0
$906$		0			0
$907$	−0.936983	+	0.669244i	−0.936983	+	0.669244i	−0.943724	−	0.330734i	$-0.892704\pi$
$907$	−0.936983	+	0.669244i	−0.936983	+	0.669244i	0.00674156	+	0.999977i	$0.497854\pi$
$908$	1.82767	+	0.505162i	1.82767	+	0.505162i
$909$		0			0
$910$		0			0
$911$		0			0		0.821508	−	0.570197i	$-0.193133\pi$
$911$		0			0		−0.821508	+	0.570197i	$0.806867\pi$
$912$	−0.169161	−	0.0981727i	−0.169161	−	0.0981727i
$913$	0.0880549	+	0.0119451i	0.0880549	+	0.0119451i
$914$	0.544259	−	1.20345i	0.544259	−	1.20345i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.81535	+	0.926508i	−1.81535	+	0.926508i
$919$		0			0		0.829121	−	0.559069i	$-0.188841\pi$
$919$		0			0		−0.829121	+	0.559069i	$0.811159\pi$
$920$		0			0
$921$	0.717678	+	1.70815i	0.717678	+	1.70815i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.40655	+	1.09316i	1.40655	+	1.09316i	0.982237	+	0.187646i	$0.0600858\pi$
$929$	1.40655	+	1.09316i	1.40655	+	1.09316i	0.424315	+	0.905515i	$0.360515\pi$
$930$		0			0
$931$	0.0629093	−	0.191853i	0.0629093	−	0.191853i
$932$	−1.06220	+	1.34787i	−1.06220	+	1.34787i
$933$		0			0
$934$	0.728230	−	0.685333i	0.728230	−	0.685333i
$935$		0			0
$936$		0			0
$937$	−0.309152	+	0.942813i	−0.309152	+	0.942813i	0.670466	+	0.741941i	$0.266094\pi$
$937$	−0.309152	+	0.942813i	−0.309152	+	0.942813i	−0.979617	+	0.200872i	$0.935622\pi$
$938$		0			0
$939$	1.05586	+	0.820606i	1.05586	+	0.820606i
$940$		0			0
$941$		0			0		−0.181020	−	0.983479i	$-0.557940\pi$
$941$		0			0		0.181020	+	0.983479i	$0.442060\pi$
$942$		0			0
$943$		0			0
$944$	0.169927	−	0.0420703i	0.169927	−	0.0420703i
$945$		0			0
$946$	0.442569	+	0.0358819i	0.442569	+	0.0358819i
$947$	−0.270952	−	0.644894i	−0.270952	−	0.644894i	0.728230	−	0.685333i	$-0.240343\pi$
$947$	−0.270952	−	0.644894i	−0.270952	−	0.644894i	−0.999182	+	0.0404387i	$0.987124\pi$
$948$		0			0
$949$		0			0
$950$	0.179836	−	0.0917837i	0.179836	−	0.0917837i
$951$		0			0
$952$		0			0
$953$	0.962013	−	1.18744i	0.962013	−	1.18744i	−0.0202235	−	0.999795i	$-0.506438\pi$
$953$	0.962013	−	1.18744i	0.962013	−	1.18744i	0.982237	−	0.187646i	$-0.0600858\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.813746	−	0.581221i	0.813746	−	0.581221i
$962$		0			0
$963$	0.0675627	−	0.0671088i	0.0675627	−	0.0671088i
$964$	0.0307431	−	0.413804i	0.0307431	−	0.413804i
$965$		0			0
$966$		0			0
$967$		0			0		−0.984677	−	0.174386i	$-0.944206\pi$
$967$		0			0		0.984677	+	0.174386i	$0.0557940\pi$
$968$	0.937286	+	0.140042i	0.937286	+	0.140042i
$969$	−0.178532	+	0.344057i	−0.178532	+	0.344057i
$970$		0			0
$971$	1.02064	−	0.838338i	1.02064	−	0.838338i	0.0337017	−	0.999432i	$-0.489270\pi$
$971$	1.02064	−	0.838338i	1.02064	−	0.838338i	0.986939	+	0.161094i	$0.0515021\pi$
$972$	−0.0271510	−	0.120021i	−0.0271510	−	0.120021i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.26354	−	0.602505i	1.26354	−	0.602505i	0.324364	−	0.945932i	$-0.394850\pi$
$977$	1.26354	−	0.602505i	1.26354	−	0.602505i	0.939179	+	0.343428i	$0.111588\pi$
$978$	1.53272	−	0.607801i	1.53272	−	0.607801i
$979$	0.123201	+	0.434316i	0.123201	+	0.434316i
$980$		0			0
$981$		0			0
$982$	0.275113	+	1.76003i	0.275113	+	1.76003i
$983$		0			0		0.934463	−	0.356059i	$-0.115880\pi$
$983$		0			0		−0.934463	+	0.356059i	$0.884120\pi$
$984$	1.03881	+	0.461389i	1.03881	+	0.461389i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.542187	−	0.840258i	$-0.682403\pi$
$991$		0			0		0.542187	+	0.840258i	$0.317597\pi$
$992$		0			0
$993$	−1.78055	−	0.415431i	−1.78055	−	0.415431i
$994$		0			0
$995$		0			0
$996$	−0.131635	+	0.352597i	−0.131635	+	0.352597i
$997$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$997$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$998$	1.27733	+	1.49251i	1.27733	+	1.49251i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.139.1	✓	232
8.3	odd	2	CM	3736.1.l.a.139.1	✓	232
467.84	even	233	inner	3736.1.l.a.2419.1	yes	232
3736.2419	odd	466	inner	3736.1.l.a.2419.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.139.1	✓	232	1.1	even	1	trivial
3736.1.l.a.139.1	✓	232	8.3	odd	2	CM
3736.1.l.a.2419.1	yes	232	467.84	even	233	inner
3736.1.l.a.2419.1	yes	232	3736.2419	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)

\(f(q)\)	\(=\)	\(q+(-0.618962 + 0.785421i) q^{2} +(0.301829 - 0.920480i) q^{3} +(-0.233773 - 0.972291i) q^{4} +(0.536144 + 0.806804i) q^{6} +(0.908355 + 0.418201i) q^{8} +(0.0496528 + 0.0364857i) q^{9} +O(q^{10})\)	\(q+(-0.618962 + 0.785421i) q^{2} +(0.301829 - 0.920480i) q^{3} +(-0.233773 - 0.972291i) q^{4} +(0.536144 + 0.806804i) q^{6} +(0.908355 + 0.418201i) q^{8} +(0.0496528 + 0.0364857i) q^{9} +(0.0322718 + 0.226425i) q^{11} +(-0.965534 - 0.0782819i) q^{12} +(-0.890700 + 0.454591i) q^{16} +(0.983200 + 1.72077i) q^{17} +(-0.0593898 + 0.0164152i) q^{18} +(-0.127098 + 0.156880i) q^{19} +(-0.197814 - 0.114802i) q^{22} +(0.659113 - 0.709897i) q^{24} +(0.246861 + 0.969051i) q^{25} +(0.836848 - 0.597722i) q^{27} +(0.194264 - 0.980949i) q^{32} +(0.218160 + 0.0386361i) q^{33} +(-1.96009 - 0.292862i) q^{34} +(0.0238672 - 0.0568064i) q^{36} +(-0.0445486 - 0.196928i) q^{38} +(0.380605 + 1.10995i) q^{41} +(-1.75236 + 0.835591i) q^{43} +(0.212607 - 0.0843097i) q^{44} +(0.149603 + 0.957080i) q^{48} +(-0.934463 + 0.356059i) q^{49} +(-0.913911 - 0.405915i) q^{50} +(1.88069 - 0.385639i) q^{51} +(-0.0485131 + 1.02725i) q^{54} +(0.106043 + 0.164342i) q^{57} +(-0.170479 - 0.0397754i) q^{59} +(0.650217 + 0.759749i) q^{64} +(-0.165378 + 0.147434i) q^{66} +(1.30056 + 1.47881i) q^{67} +(1.44324 - 1.35823i) q^{68} +(0.0298441 + 0.0539068i) q^{72} +(-0.373057 - 1.88378i) q^{73} +(0.966501 + 0.0652567i) q^{75} +(0.182245 + 0.0869014i) q^{76} +(-0.279199 - 0.891908i) q^{81} +(-1.10735 - 0.388079i) q^{82} +(0.106029 - 0.373780i) q^{83} +(0.428353 - 1.89354i) q^{86} +(-0.0653769 + 0.219171i) q^{88} +(1.95596 - 0.265337i) q^{89} +(-0.844310 - 0.474894i) q^{96} +(-0.674818 + 0.905494i) q^{97} +(0.298741 - 0.954334i) q^{98} +(-0.00665889 + 0.0124201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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

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