LMFDB - Embedded newform 3736.1.l.a.51.1

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			51.1
Root			$0.436485 + 0.899712i$ of defining polynomial
Character	$\chi$	$=$	3736.51
Dual form			3736.1.l.a.3443.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233773 + 0.972291i) q^{2} +(0.855488 - 0.628626i) q^{3} +(-0.890700 - 0.454591i) q^{4} +(0.411217 + 0.978739i) q^{6} +(0.650217 - 0.759749i) q^{8} +(0.0379490 - 0.121229i) q^{9} +O(q^{10})$	\(q+(-0.233773 + 0.972291i) q^{2} +(0.855488 - 0.628626i) q^{3} +(-0.890700 - 0.454591i) q^{4} +(0.411217 + 0.978739i) q^{6} +(0.650217 - 0.759749i) q^{8} +(0.0379490 - 0.121229i) q^{9} +(1.87013 + 0.544145i) q^{11} +(-1.04775 + 0.171020i) q^{12} +(0.586694 + 0.809809i) q^{16} +(-0.978828 - 1.66072i) q^{17} +(0.108998 + 0.0652375i) q^{18} +(0.406486 - 1.91660i) q^{19} +(-0.966254 + 1.69111i) q^{22} +(0.0786550 - 1.05870i) q^{24} +(-0.878119 - 0.478442i) q^{25} +(0.300607 + 0.876652i) q^{27} +(-0.924523 + 0.381126i) q^{32} +(1.94194 - 0.710105i) q^{33} +(1.84353 - 0.563473i) q^{34} +(-0.0889108 + 0.0907274i) q^{36} +(1.76847 + 0.843274i) q^{38} +(0.492033 + 0.382404i) q^{41} +(1.11356 + 1.37451i) q^{43} +(-1.41837 - 1.33482i) q^{44} +(1.01098 + 0.323971i) q^{48} +(0.746444 + 0.665448i) q^{49} +(0.670466 - 0.741941i) q^{50} +(-1.88135 - 0.805413i) q^{51} +(-0.922635 + 0.0873402i) q^{54} +(-0.857082 - 1.89516i) q^{57} +(-1.76602 + 0.871519i) q^{59} +(-0.154437 - 0.988003i) q^{64} +(0.236455 + 2.05414i) q^{66} +(-0.239943 - 1.86297i) q^{67} +(0.116892 + 1.92417i) q^{68} +(-0.0674285 - 0.107657i) q^{72} +(-1.56040 - 0.643260i) q^{73} +(-1.05198 + 0.142707i) q^{75} +(-1.23333 + 1.52233i) q^{76} +(0.912608 + 0.633428i) q^{81} +(-0.486833 + 0.389004i) q^{82} +(1.57363 - 0.970903i) q^{83} +(-1.59674 + 0.761386i) q^{86} +(1.62941 - 1.06702i) q^{88} +(1.82767 + 0.505162i) q^{89} +(-0.551333 + 0.907227i) q^{96} +(0.207153 - 0.694464i) q^{97} +(-0.821508 + 0.570197i) q^{98} +(0.136936 - 0.206065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{134}{233}\right)$

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 $

$2$	−0.233773	+	0.972291i	−0.233773	+	0.972291i
$2$	−0.233773	+	0.972291i	−0.233773	+	0.972291i
$3$	0.855488	−	0.628626i	0.855488	−	0.628626i	−0.0740898	−	0.997252i	$-0.523605\pi$
$3$	0.855488	−	0.628626i	0.855488	−	0.628626i	0.929578	+	0.368626i	$0.120172\pi$
$4$	−0.890700	−	0.454591i	−0.890700	−	0.454591i
$5$		0			0		0.246861	−	0.969051i	$-0.420601\pi$
$5$		0			0		−0.246861	+	0.969051i	$0.579399\pi$
$6$	0.411217	+	0.978739i	0.411217	+	0.978739i
$7$		0			0		−0.934463	−	0.356059i	$-0.884120\pi$
$7$		0			0		0.934463	+	0.356059i	$0.115880\pi$
$8$	0.650217	−	0.759749i	0.650217	−	0.759749i
$9$	0.0379490	−	0.121229i	0.0379490	−	0.121229i
$10$		0			0
$11$	1.87013	+	0.544145i	1.87013	+	0.544145i	0.998546	+	0.0539068i	$0.0171674\pi$
$11$	1.87013	+	0.544145i	1.87013	+	0.544145i	0.871589	+	0.490238i	$0.163090\pi$
$12$	−1.04775	+	0.171020i	−1.04775	+	0.171020i
$13$		0			0		−0.699920	−	0.714221i	$-0.746781\pi$
$13$		0			0		0.699920	+	0.714221i	$0.253219\pi$
$14$		0			0
$15$		0			0
$16$	0.586694	+	0.809809i	0.586694	+	0.809809i
$17$	−0.978828	−	1.66072i	−0.978828	−	1.66072i	−0.718923	−	0.695089i	$-0.755365\pi$
$17$	−0.978828	−	1.66072i	−0.978828	−	1.66072i	−0.259904	−	0.965634i	$-0.583691\pi$
$18$	0.108998	+	0.0652375i	0.108998	+	0.0652375i
$19$	0.406486	−	1.91660i	0.406486	−	1.91660i	0.00674156	−	0.999977i	$-0.497854\pi$
$19$	0.406486	−	1.91660i	0.406486	−	1.91660i	0.399745	−	0.916626i	$-0.369099\pi$
$20$		0			0
$21$		0			0
$22$	−0.966254	+	1.69111i	−0.966254	+	1.69111i
$23$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$23$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$24$	0.0786550	−	1.05870i	0.0786550	−	1.05870i
$25$	−0.878119	−	0.478442i	−0.878119	−	0.478442i
$26$		0			0
$27$	0.300607	+	0.876652i	0.300607	+	0.876652i
$28$		0			0
$29$		0			0		−0.00674156	−	0.999977i	$-0.502146\pi$
$29$		0			0		0.00674156	+	0.999977i	$0.497854\pi$
$30$		0			0
$31$		0			0		−0.813746	−	0.581221i	$-0.802575\pi$
$31$		0			0		0.813746	+	0.581221i	$0.197425\pi$
$32$	−0.924523	+	0.381126i	−0.924523	+	0.381126i
$33$	1.94194	−	0.710105i	1.94194	−	0.710105i
$34$	1.84353	−	0.563473i	1.84353	−	0.563473i
$35$		0			0
$36$	−0.0889108	+	0.0907274i	−0.0889108	+	0.0907274i
$37$		0			0		−0.194264	−	0.980949i	$-0.562232\pi$
$37$		0			0		0.194264	+	0.980949i	$0.437768\pi$
$38$	1.76847	+	0.843274i	1.76847	+	0.843274i
$39$		0			0
$40$		0			0
$41$	0.492033	+	0.382404i	0.492033	+	0.382404i	0.829121	−	0.559069i	$-0.188841\pi$
$41$	0.492033	+	0.382404i	0.492033	+	0.382404i	−0.337088	+	0.941473i	$0.609442\pi$
$42$		0			0
$43$	1.11356	+	1.37451i	1.11356	+	1.37451i	0.919301	+	0.393556i	$0.128755\pi$
$43$	1.11356	+	1.37451i	1.11356	+	1.37451i	0.194264	+	0.980949i	$0.437768\pi$
$44$	−1.41837	−	1.33482i	−1.41837	−	1.33482i
$45$		0			0
$46$		0			0
$47$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$47$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$48$	1.01098	+	0.323971i	1.01098	+	0.323971i
$49$	0.746444	+	0.665448i	0.746444	+	0.665448i
$50$	0.670466	−	0.741941i	0.670466	−	0.741941i
$51$	−1.88135	−	0.805413i	−1.88135	−	0.805413i
$52$		0			0
$53$		0			0		0.181020	−	0.983479i	$-0.442060\pi$
$53$		0			0		−0.181020	+	0.983479i	$0.557940\pi$
$54$	−0.922635	+	0.0873402i	−0.922635	+	0.0873402i
$55$		0			0
$56$		0			0
$57$	−0.857082	−	1.89516i	−0.857082	−	1.89516i
$58$		0			0
$59$	−1.76602	+	0.871519i	−1.76602	+	0.871519i	−0.805835	+	0.592140i	$0.798283\pi$
$59$	−1.76602	+	0.871519i	−1.76602	+	0.871519i	−0.960181	+	0.279380i	$0.909871\pi$
$60$		0			0
$61$		0			0		−0.829121	−	0.559069i	$-0.811159\pi$
$61$		0			0		0.829121	+	0.559069i	$0.188841\pi$
$62$		0			0
$63$		0			0
$64$	−0.154437	−	0.988003i	−0.154437	−	0.988003i
$65$		0			0
$66$	0.236455	+	2.05414i	0.236455	+	2.05414i
$67$	−0.239943	−	1.86297i	−0.239943	−	1.86297i	−0.460585	−	0.887615i	$-0.652361\pi$
$67$	−0.239943	−	1.86297i	−0.239943	−	1.86297i	0.220643	−	0.975355i	$-0.429185\pi$
$68$	0.116892	+	1.92417i	0.116892	+	1.92417i
$69$		0			0
$70$		0			0
$71$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$71$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$72$	−0.0674285	−	0.107657i	−0.0674285	−	0.107657i
$73$	−1.56040	−	0.643260i	−1.56040	−	0.643260i	−0.575722	−	0.817645i	$-0.695279\pi$
$73$	−1.56040	−	0.643260i	−1.56040	−	0.643260i	−0.984677	+	0.174386i	$0.944206\pi$
$74$		0			0
$75$	−1.05198	+	0.142707i	−1.05198	+	0.142707i
$76$	−1.23333	+	1.52233i	−1.23333	+	1.52233i
$77$		0			0
$78$		0			0
$79$		0			0		0.690227	−	0.723593i	$-0.257511\pi$
$79$		0			0		−0.690227	+	0.723593i	$0.742489\pi$
$80$		0			0
$81$	0.912608	+	0.633428i	0.912608	+	0.633428i
$82$	−0.486833	+	0.389004i	−0.486833	+	0.389004i
$83$	1.57363	−	0.970903i	1.57363	−	0.970903i	0.586694	−	0.809809i	$-0.300429\pi$
$83$	1.57363	−	0.970903i	1.57363	−	0.970903i	0.986939	−	0.161094i	$-0.0515021\pi$
$84$		0			0
$85$		0			0
$86$	−1.59674	+	0.761386i	−1.59674	+	0.761386i
$87$		0			0
$88$	1.62941	−	1.06702i	1.62941	−	1.06702i
$89$	1.82767	+	0.505162i	1.82767	+	0.505162i	0.998546	−	0.0539068i	$-0.0171674\pi$
$89$	1.82767	+	0.505162i	1.82767	+	0.505162i	0.829121	+	0.559069i	$0.188841\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.551333	+	0.907227i	−0.551333	+	0.907227i
$97$	0.207153	−	0.694464i	0.207153	−	0.694464i	−0.789576	−	0.613653i	$-0.789700\pi$
$97$	0.207153	−	0.694464i	0.207153	−	0.694464i	0.996729	−	0.0808112i	$-0.0257511\pi$
$98$	−0.821508	+	0.570197i	−0.821508	+	0.570197i
$99$	0.136936	−	0.206065i	0.136936	−	0.206065i
$100$	0.564646	+	0.825333i	0.564646	+	0.825333i
$101$		0			0		0.194264	−	0.980949i	$-0.437768\pi$
$101$		0			0		−0.194264	+	0.980949i	$0.562232\pi$
$102$	1.22290	−	1.64093i	1.22290	−	1.64093i
$103$		0			0		0.0606373	−	0.998160i	$-0.480687\pi$
$103$		0			0		−0.0606373	+	0.998160i	$0.519313\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.369994	+	0.118566i	−0.369994	+	0.118566i	−0.484351	−	0.874874i	$-0.660944\pi$
$107$	−0.369994	+	0.118566i	−0.369994	+	0.118566i	0.114357	+	0.993440i	$0.463519\pi$
$108$	0.130767	−	0.917488i	0.130767	−	0.917488i
$109$		0			0		−0.989021	−	0.147772i	$-0.952790\pi$
$109$		0			0		0.989021	+	0.147772i	$0.0472103\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.869741	+	0.754569i	0.869741	+	0.754569i	0.970693	−	0.240323i	$-0.0772532\pi$
$113$	0.869741	+	0.754569i	0.869741	+	0.754569i	−0.100952	+	0.994891i	$0.532189\pi$
$114$	2.04301	−	0.390296i	2.04301	−	0.390296i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.434524	−	1.92082i	−0.434524	−	1.92082i
$119$		0			0
$120$		0			0
$121$	2.35742	+	1.49874i	2.35742	+	1.49874i
$122$		0			0
$123$	0.661318	+	0.0178377i	0.661318	+	0.0178377i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.982237	−	0.187646i	$-0.939914\pi$
$127$		0			0		0.982237	+	0.187646i	$0.0600858\pi$
$128$	0.996729	+	0.0808112i	0.996729	+	0.0808112i
$129$	1.81669	+	0.475858i	1.81669	+	0.475858i
$130$		0			0
$131$	−0.719647	−	0.575034i	−0.719647	−	0.575034i	0.194264	−	0.980949i	$-0.437768\pi$
$131$	−0.719647	−	0.575034i	−0.719647	−	0.575034i	−0.913911	+	0.405915i	$0.866953\pi$
$132$	−2.05249	−	0.250298i	−2.05249	−	0.250298i
$133$		0			0
$134$	1.86744	+	0.202218i	1.86744	+	0.202218i
$135$		0			0
$136$	−1.89818	−	0.336167i	−1.89818	−	0.336167i
$137$	0.792234	+	0.107471i	0.792234	+	0.107471i	0.519333	−	0.854572i	$-0.326180\pi$
$137$	0.792234	+	0.107471i	0.792234	+	0.107471i	0.272900	+	0.962042i	$0.412017\pi$
$138$		0			0
$139$	−1.06227	+	0.217821i	−1.06227	+	0.217821i	−0.699920	−	0.714221i	$-0.746781\pi$
$139$	−1.06227	+	0.217821i	−1.06227	+	0.217821i	−0.362351	+	0.932042i	$0.618026\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.120437	−	0.0403929i	0.120437	−	0.0403929i
$145$		0			0
$146$	0.990215	−	1.36679i	0.990215	−	1.36679i
$147$	1.05689	+	0.100049i	1.05689	+	0.100049i
$148$		0			0
$149$		0			0		0.976820	−	0.214062i	$-0.0686695\pi$
$149$		0			0		−0.976820	+	0.214062i	$0.931330\pi$
$150$	0.107172	−	1.05619i	0.107172	−	1.05619i
$151$		0			0		0.943724	−	0.330734i	$-0.107296\pi$
$151$		0			0		−0.943724	+	0.330734i	$0.892704\pi$
$152$	−1.19183	−	1.55504i	−1.19183	−	1.55504i
$153$	−0.238473	+	0.0556395i	−0.238473	+	0.0556395i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.448576	−	0.893745i	$-0.648069\pi$
$157$		0			0		0.448576	+	0.893745i	$0.351931\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.829219	+	0.739242i	−0.829219	+	0.739242i
$163$	−0.819917	+	0.364168i	−0.819917	+	0.364168i	−0.772743	−	0.634719i	$-0.781116\pi$
$163$	−0.819917	+	0.364168i	−0.819917	+	0.364168i	−0.0471738	+	0.998887i	$0.515021\pi$
$164$	−0.264416	−	0.564282i	−0.264416	−	0.564282i
$165$		0			0
$166$	0.576127	+	1.75700i	0.576127	+	1.75700i
$167$		0			0		−0.943724	−	0.330734i	$-0.892704\pi$
$167$		0			0		0.943724	+	0.330734i	$0.107296\pi$
$168$		0			0
$169$	−0.0202235	+	0.999795i	−0.0202235	+	0.999795i
$170$		0			0
$171$	−0.216922	−	0.122011i	−0.216922	−	0.122011i
$172$	−0.367014	−	1.73049i	−0.367014	−	1.73049i
$173$		0			0		0.324364	−	0.945932i	$-0.394850\pi$
$173$		0			0		−0.324364	+	0.945932i	$0.605150\pi$
$174$		0			0
$175$		0			0
$176$	0.656543	+	1.83370i	0.656543	+	1.83370i
$177$	−0.962946	+	1.85574i	−0.962946	+	1.85574i
$178$	−0.918424	+	1.65893i	−0.918424	+	1.65893i
$179$	0.167412	+	1.90531i	0.167412	+	1.90531i	0.374884	+	0.927072i	$0.377682\pi$
$179$	0.167412	+	1.90531i	0.167412	+	1.90531i	−0.207472	+	0.978241i	$0.566524\pi$
$180$		0			0
$181$		0			0		0.967365	−	0.253388i	$-0.0815451\pi$
$181$		0			0		−0.967365	+	0.253388i	$0.918455\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.926865	−	3.63840i	−0.926865	−	3.63840i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$191$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$192$	−0.753202	−	0.748142i	−0.753202	−	0.748142i
$193$	−0.216498	+	0.556877i	−0.216498	+	0.556877i	−0.997728	−	0.0673651i	$-0.978541\pi$
$193$	−0.216498	+	0.556877i	−0.216498	+	0.556877i	0.781231	+	0.624242i	$0.214592\pi$
$194$	0.626794	+	0.363760i	0.626794	+	0.363760i
$195$		0			0
$196$	−0.362351	−	0.932042i	−0.362351	−	0.932042i
$197$		0			0		0.154437	−	0.988003i	$-0.450644\pi$
$197$		0			0		−0.154437	+	0.988003i	$0.549356\pi$
$198$	0.168343	+	0.181314i	0.168343	+	0.181314i
$199$		0			0		0.337088	−	0.941473i	$-0.390558\pi$
$199$		0			0		−0.337088	+	0.941473i	$0.609442\pi$
$200$	−0.934463	+	0.356059i	−0.934463	+	0.356059i
$201$	−1.37638	−	1.44291i	−1.37638	−	1.44291i
$202$		0			0
$203$		0			0
$204$	1.30958	+	1.57263i	1.30958	+	1.57263i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.80309	−	3.36312i	1.80309	−	3.36312i
$210$		0			0
$211$	0.256784	−	0.783109i	0.256784	−	0.783109i	−0.737404	−	0.675452i	$-0.763948\pi$
$211$	0.256784	−	0.783109i	0.256784	−	0.783109i	0.994188	−	0.107657i	$-0.0343348\pi$
$212$		0			0
$213$		0			0
$214$	−0.0287859	−	0.387460i	−0.0287859	−	0.387460i
$215$		0			0
$216$	0.861495	+	0.341628i	0.861495	+	0.341628i
$217$		0			0
$218$		0			0
$219$	−1.73927	+	0.430606i	−1.73927	+	0.430606i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$223$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$224$		0			0
$225$	−0.0913248	+	0.0882971i	−0.0913248	+	0.0882971i
$226$	−0.936983	+	0.669244i	−0.936983	+	0.669244i
$227$	−0.846935	+	1.35222i	−0.846935	+	1.35222i	0.0875288	+	0.996162i	$0.472103\pi$
$227$	−0.846935	+	1.35222i	−0.846935	+	1.35222i	−0.934463	+	0.356059i	$0.884120\pi$
$228$	−0.0981194	+	2.07764i	−0.0981194	+	2.07764i
$229$		0			0		−0.997728	−	0.0673651i	$-0.978541\pi$
$229$		0			0		0.997728	+	0.0673651i	$0.0214592\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.220921	−	0.918837i	−0.220921	−	0.918837i	−0.967365	−	0.253388i	$-0.918455\pi$
$233$	−0.220921	−	0.918837i	−0.220921	−	0.918837i	0.746444	−	0.665448i	$-0.231760\pi$
$234$		0			0
$235$		0			0
$236$	1.96918	+	0.0265525i	1.96918	+	0.0265525i
$237$		0			0
$238$		0			0
$239$		0			0		0.0471738	−	0.998887i	$-0.484979\pi$
$239$		0			0		−0.0471738	+	0.998887i	$0.515021\pi$
$240$		0			0
$241$	−1.48738	+	1.06237i	−1.48738	+	1.06237i	−0.507764	+	0.861496i	$0.669528\pi$
$241$	−1.48738	+	1.06237i	−1.48738	+	1.06237i	−0.979617	+	0.200872i	$0.935622\pi$
$242$	−2.00831	+	1.94173i	−2.00831	+	1.94173i
$243$	0.252491	−	0.00681045i	0.252491	−	0.00681045i
$244$		0			0
$245$		0			0
$246$	−0.171942	+	0.638823i	−0.171942	+	0.638823i
$247$		0			0
$248$		0			0
$249$	0.735890	−	1.81982i	0.735890	−	1.81982i
$250$		0			0
$251$	1.42061	+	0.563345i	1.42061	+	0.563345i	0.948098	−	0.317979i	$-0.103004\pi$
$251$	1.42061	+	0.563345i	1.42061	+	0.563345i	0.472511	+	0.881325i	$0.343348\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.311581	+	0.950220i	−0.311581	+	0.950220i
$257$	−1.32927	−	0.291299i	−1.32927	−	0.291299i	−0.507764	−	0.861496i	$-0.669528\pi$
$257$	−1.32927	−	0.291299i	−1.32927	−	0.291299i	−0.821508	+	0.570197i	$0.806867\pi$
$258$	−0.887366	+	1.65511i	−0.887366	+	1.65511i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.727335	−	0.565279i	0.727335	−	0.565279i
$263$		0			0		−0.639914	−	0.768447i	$-0.721030\pi$
$263$		0			0		0.639914	+	0.768447i	$0.278970\pi$
$264$	0.723181	−	1.93711i	0.723181	−	1.93711i
$265$		0			0
$266$		0			0
$267$	1.88111	−	0.716759i	1.88111	−	0.716759i
$268$	−0.633172	+	1.76842i	−0.633172	+	1.76842i
$269$		0			0		−0.680408	−	0.732833i	$-0.738197\pi$
$269$		0			0		0.680408	+	0.732833i	$0.261803\pi$
$270$		0			0
$271$		0			0		−0.362351	−	0.932042i	$-0.618026\pi$
$271$		0			0		0.362351	+	0.932042i	$0.381974\pi$
$272$	0.770596	−	1.76700i	0.770596	−	1.76700i
$273$		0			0
$274$	−0.289696	+	0.745158i	−0.289696	+	0.745158i
$275$	−1.38186	−	1.37257i	−1.38186	−	1.37257i
$276$		0			0
$277$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$277$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$278$	0.0365452	−	1.08376i	0.0365452	−	1.08376i
$279$		0			0
$280$		0			0
$281$	−0.00892432	+	0.0394501i	−0.00892432	+	0.0394501i	−0.979617	−	0.200872i	$-0.935622\pi$
$281$	−0.00892432	+	0.0394501i	−0.00892432	+	0.0394501i	0.970693	+	0.240323i	$0.0772532\pi$
$282$		0			0
$283$	−1.80356	−	0.659505i	−1.80356	−	0.659505i	−0.997728	−	0.0673651i	$-0.978541\pi$
$283$	−1.80356	−	0.659505i	−1.80356	−	0.659505i	−0.805835	−	0.592140i	$-0.798283\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0111188	+	0.126542i	0.0111188	+	0.126542i
$289$	−1.31555	+	2.37625i	−1.31555	+	2.37625i
$290$		0			0
$291$	−0.259341	−	0.724327i	−0.259341	−	0.724327i
$292$	1.09743	+	1.28230i	1.09743	+	1.28230i
$293$		0			0		0.919301	−	0.393556i	$-0.128755\pi$
$293$		0			0		−0.919301	+	0.393556i	$0.871245\pi$
$294$	−0.344350	+	1.00422i	−0.344350	+	1.00422i
$295$		0			0
$296$		0			0
$297$	0.0851506	+	1.80303i	0.0851506	+	1.80303i
$298$		0			0
$299$		0			0
$300$	1.00187	+	0.351112i	1.00187	+	0.351112i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.79057	−	0.795283i	1.79057	−	0.795283i
$305$		0			0
$306$	0.00165086	−	0.244873i	0.00165086	−	0.244873i
$307$	0.233980	+	1.64165i	0.233980	+	1.64165i	0.670466	+	0.741941i	$0.266094\pi$
$307$	0.233980	+	1.64165i	0.233980	+	1.64165i	−0.436485	+	0.899712i	$0.643777\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.805835	−	0.592140i	$-0.798283\pi$
$311$		0			0		0.805835	+	0.592140i	$0.201717\pi$
$312$		0			0
$313$	0.0729064	−	0.0598842i	0.0729064	−	0.0598842i	−0.597559	−	0.801825i	$-0.703863\pi$
$313$	0.0729064	−	0.0598842i	0.0729064	−	0.0598842i	0.670466	+	0.741941i	$0.266094\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$317$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.241992	+	0.334020i	−0.241992	+	0.334020i
$322$		0			0
$323$	−3.58083	+	1.20096i	−3.58083	+	1.20096i
$324$	−0.524909	−	0.979058i	−0.524909	−	0.979058i
$325$		0			0
$326$	−0.162403	−	0.882331i	−0.162403	−	0.882331i
$327$		0			0
$328$	0.610459	−	0.125176i	0.610459	−	0.125176i
$329$		0			0
$330$		0			0
$331$	−1.53852	−	0.272471i	−1.53852	−	0.272471i	−0.660401	−	0.750913i	$-0.729614\pi$
$331$	−1.53852	−	0.272471i	−1.53852	−	0.272471i	−0.878119	+	0.478442i	$0.841202\pi$
$332$	−1.84300	+	0.149424i	−1.84300	+	0.149424i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0882902	+	0.295986i	0.0882902	+	0.295986i	0.990924	−	0.134424i	$-0.0429185\pi$
$337$	0.0882902	+	0.295986i	0.0882902	+	0.295986i	−0.902634	+	0.430410i	$0.858369\pi$
$338$	−0.967365	−	0.253388i	−0.967365	−	0.253388i
$339$	1.21839	+	0.0987829i	1.21839	+	0.0987829i
$340$		0			0
$341$		0			0
$342$	0.169341	−	0.182389i	0.169341	−	0.182389i
$343$		0			0
$344$	1.76834	+	0.0476974i	1.76834	+	0.0476974i
$345$		0			0
$346$		0			0
$347$	−1.32719	−	0.445120i	−1.32719	−	0.445120i	−0.436485	−	0.899712i	$-0.643777\pi$
$347$	−1.32719	−	0.445120i	−1.32719	−	0.445120i	−0.890700	+	0.454591i	$0.849785\pi$
$348$		0			0
$349$		0			0		−0.220643	−	0.975355i	$-0.570815\pi$
$349$		0			0		0.220643	+	0.975355i	$0.429185\pi$
$350$		0			0
$351$		0			0
$352$	−1.93637	+	0.209682i	−1.93637	+	0.209682i
$353$	1.46637	−	0.280135i	1.46637	−	0.280135i	0.608316	−	0.793695i	$-0.291845\pi$
$353$	1.46637	−	0.280135i	1.46637	−	0.280135i	0.858053	+	0.513561i	$0.171674\pi$
$354$	−1.57921	−	1.37009i	−1.57921	−	1.37009i
$355$		0			0
$356$	−1.39826	−	1.28079i	−1.39826	−	1.28079i
$357$		0			0
$358$	−1.89166	−	0.282637i	−1.89166	−	0.282637i
$359$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$359$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$360$		0			0
$361$	−2.59423	−	1.15223i	−2.59423	−	1.15223i
$362$		0			0
$363$	2.95889	−	0.199779i	2.95889	−	0.199779i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.564646	−	0.825333i	$-0.690987\pi$
$367$		0			0		0.564646	+	0.825333i	$0.309013\pi$
$368$		0			0
$369$	0.0650306	−	0.0451368i	0.0650306	−	0.0451368i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.772743	−	0.634719i	$-0.781116\pi$
$373$		0			0		0.772743	+	0.634719i	$0.218884\pi$
$374$	3.75426	−	0.0506226i	3.75426	−	0.0506226i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.08792	+	0.712428i	−1.08792	+	0.712428i	−0.960181	−	0.279380i	$-0.909871\pi$
$379$	−1.08792	+	0.712428i	−1.08792	+	0.712428i	−0.127741	+	0.991808i	$0.540773\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.979617	−	0.200872i	$-0.935622\pi$
$383$		0			0		0.979617	+	0.200872i	$0.0643777\pi$
$384$	0.903490	−	0.557437i	0.903490	−	0.557437i
$385$		0			0
$386$	−0.490836	−	0.340682i	−0.490836	−	0.340682i
$387$	0.208889	−	0.0828352i	0.208889	−	0.0828352i
$388$	−0.500208	+	0.524389i	−0.500208	+	0.524389i
$389$		0			0		0.387350	−	0.921933i	$-0.373391\pi$
$389$		0			0		−0.387350	+	0.921933i	$0.626609\pi$
$390$		0			0
$391$		0			0
$392$	0.990924	−	0.134424i	0.990924	−	0.134424i
$393$	−0.977130	−	0.0395462i	−0.977130	−	0.0395462i
$394$		0			0
$395$		0			0
$396$	−0.215644	+	0.121292i	−0.215644	+	0.121292i
$397$		0			0		−0.660401	−	0.750913i	$-0.729614\pi$
$397$		0			0		0.660401	+	0.750913i	$0.270386\pi$
$398$		0			0
$399$		0			0
$400$	−0.127741	−	0.991808i	−0.127741	−	0.991808i
$401$	−0.110778	−	0.962347i	−0.110778	−	0.962347i	−0.924523	−	0.381126i	$-0.875536\pi$
$401$	−0.110778	−	0.962347i	−0.110778	−	0.962347i	0.813746	−	0.581221i	$-0.197425\pi$
$402$	1.72469	−	1.00093i	1.72469	−	1.00093i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.83520	+	0.905659i	−1.83520	+	0.905659i
$409$	−0.274822	−	0.0641202i	−0.274822	−	0.0641202i	0.0875288	−	0.996162i	$-0.472103\pi$
$409$	−0.274822	−	0.0641202i	−0.274822	−	0.0641202i	−0.362351	+	0.932042i	$0.618026\pi$
$410$		0			0
$411$	0.745305	−	0.406078i	0.745305	−	0.406078i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.771832	+	0.854114i	−0.771832	+	0.854114i
$418$	2.84842	+	2.53934i	2.84842	+	2.53934i
$419$	−1.86045	−	0.596187i	−1.86045	−	0.596187i	−0.995549	−	0.0942425i	$-0.969957\pi$
$419$	−1.86045	−	0.596187i	−1.86045	−	0.596187i	−0.864900	−	0.501945i	$-0.832618\pi$
$420$		0			0
$421$		0			0		0.992646	−	0.121051i	$-0.0386266\pi$
$421$		0			0		−0.992646	+	0.121051i	$0.961373\pi$
$422$	0.701381	+	0.432739i	0.701381	+	0.432739i
$423$		0			0
$424$		0			0
$425$	0.0649674	+	1.92663i	0.0649674	+	1.92663i
$426$		0			0
$427$		0			0
$428$	0.383453	+	0.0625893i	0.383453	+	0.0625893i
$429$		0			0
$430$		0			0
$431$		0			0		0.699920	−	0.714221i	$-0.253219\pi$
$431$		0			0		−0.699920	+	0.714221i	$0.746781\pi$
$432$	−0.533556	+	0.757761i	−0.533556	+	0.757761i
$433$	−1.57126	+	0.480254i	−1.57126	+	0.480254i	−0.952299	−	0.305167i	$-0.901288\pi$
$433$	−1.57126	+	0.480254i	−1.57126	+	0.480254i	−0.618962	+	0.785421i	$0.712446\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.0120794	−	1.79174i	−0.0120794	−	1.79174i
$439$		0			0		−0.670466	−	0.741941i	$-0.733906\pi$
$439$		0			0		0.670466	+	0.741941i	$0.266094\pi$
$440$		0			0
$441$	0.108998	−	0.0652375i	0.108998	−	0.0652375i
$442$		0			0
$443$	−0.0169453	+	0.228085i	−0.0169453	+	0.228085i	0.982237	+	0.187646i	$0.0600858\pi$
$443$	−0.0169453	+	0.228085i	−0.0169453	+	0.228085i	−0.999182	+	0.0404387i	$0.987124\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.49574	+	0.895227i	1.49574	+	0.895227i	0.999636	+	0.0269632i	$0.00858369\pi$
$449$	1.49574	+	0.895227i	1.49574	+	0.895227i	0.496103	+	0.868264i	$0.334764\pi$
$450$	−0.0645012	−	0.109436i	−0.0645012	−	0.109436i
$451$	0.712085	+	0.982885i	0.712085	+	0.982885i
$452$	−0.431658	−	1.06747i	−0.431658	−	1.06747i
$453$		0			0
$454$	−1.11676	−	1.13958i	−1.11676	−	1.13958i
$455$		0			0
$456$	−1.99713	−	0.581097i	−1.99713	−	0.581097i
$457$	−0.225971	−	0.119197i	−0.225971	−	0.119197i	0.349751	−	0.936843i	$-0.386266\pi$
$457$	−0.225971	−	0.119197i	−0.225971	−	0.119197i	−0.575722	+	0.817645i	$0.695279\pi$
$458$		0			0
$459$	1.16163	−	1.35732i	1.16163	−	1.35732i
$460$		0			0
$461$		0			0		−0.387350	−	0.921933i	$-0.626609\pi$
$461$		0			0		0.387350	+	0.921933i	$0.373391\pi$
$462$		0			0
$463$		0			0		−0.890700	−	0.454591i	$-0.849785\pi$
$463$		0			0		0.890700	+	0.454591i	$0.150215\pi$
$464$		0			0
$465$		0			0
$466$	0.945022			0.945022
$467$	0.956327	−	0.292300i	0.956327	−	0.292300i
$467$	0.956327	−	0.292300i	0.956327	−	0.292300i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.486157	+	1.90840i	−0.486157	+	1.90840i
$473$	1.33459	+	3.17645i	1.33459	+	3.17645i
$474$		0			0
$475$	−1.27393	+	1.48853i	−1.27393	+	1.48853i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.986939	−	0.161094i	$-0.0515021\pi$
$479$		0			0		−0.986939	+	0.161094i	$0.948498\pi$
$480$		0			0
$481$		0			0
$482$	−0.685222	−	1.69452i	−0.685222	−	1.69452i
$483$		0			0
$484$	−1.41844	−	2.40659i	−1.41844	−	2.40659i
$485$		0			0
$486$	−0.0524040	+	0.247087i	−0.0524040	+	0.247087i
$487$		0			0		0.660401	−	0.750913i	$-0.270386\pi$
$487$		0			0		−0.660401	+	0.750913i	$0.729614\pi$
$488$		0			0
$489$	−0.472504	+	0.826962i	−0.472504	+	0.826962i
$490$		0			0
$491$	−0.0869361	+	1.17016i	−0.0869361	+	1.17016i	0.764115	+	0.645080i	$0.223176\pi$
$491$	−0.0869361	+	1.17016i	−0.0869361	+	1.17016i	−0.851051	+	0.525083i	$0.824034\pi$
$492$	−0.580927	−	0.316517i	−0.580927	−	0.316517i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.59737	+	1.14092i	1.59737	+	1.14092i
$499$	−1.71883	+	0.708572i	−1.71883	+	0.708572i	−0.718923	+	0.695089i	$0.755365\pi$
$499$	−1.71883	+	0.708572i	−1.71883	+	0.708572i	−0.999909	+	0.0134828i	$0.995708\pi$
$500$		0			0
$501$		0			0
$502$	−0.879836	+	1.24955i	−0.879836	+	1.24955i
$503$		0			0		0.699920	−	0.714221i	$-0.253219\pi$
$503$		0			0		−0.699920	+	0.714221i	$0.746781\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.611196	+	0.868026i	0.611196	+	0.868026i
$508$		0			0
$509$		0			0		−0.0337017	−	0.999432i	$-0.510730\pi$
$509$		0			0		0.0337017	+	0.999432i	$0.489270\pi$
$510$		0			0
$511$		0			0
$512$	−0.851051	−	0.525083i	−0.851051	−	0.525083i
$513$	1.80239	−	0.219798i	1.80239	−	0.219798i
$514$	0.593976	−	1.22434i	0.593976	−	1.22434i
$515$		0			0
$516$	−1.40181	−	1.24970i	−1.40181	−	1.24970i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.66572	−	0.157684i	1.66572	−	0.157684i	0.781231	−	0.624242i	$-0.214592\pi$
$521$	1.66572	−	0.157684i	1.66572	−	0.157684i	0.884490	+	0.466559i	$0.154506\pi$
$522$		0			0
$523$	1.75608	−	0.956797i	1.75608	−	0.956797i	0.871589	−	0.490238i	$-0.163090\pi$
$523$	1.75608	−	0.956797i	1.75608	−	0.956797i	0.884490	−	0.466559i	$-0.154506\pi$
$524$	0.379584	+	0.839328i	0.379584	+	0.839328i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.71437	+	1.15599i	1.71437	+	1.15599i
$529$	−0.755348	+	0.655324i	−0.755348	+	0.655324i
$530$		0			0
$531$	0.0386349	+	0.247166i	0.0386349	+	0.247166i
$532$		0			0
$533$		0			0
$534$	0.257146	+	1.99654i	0.257146	+	1.99654i
$535$		0			0
$536$	−1.57140	−	1.02904i	−1.57140	−	1.02904i
$537$	1.34095	+	1.52473i	1.34095	+	1.52473i
$538$		0			0
$539$	1.03385	+	1.65065i	1.03385	+	1.65065i
$540$		0			0
$541$		0			0		−0.999182	−	0.0404387i	$-0.987124\pi$
$541$		0			0		0.999182	+	0.0404387i	$0.0128755\pi$
$542$		0			0
$543$		0			0
$544$	1.53789	+	1.16232i	1.53789	+	1.16232i
$545$		0			0
$546$		0			0
$547$	−1.83874	+	0.729158i	−1.83874	+	0.729158i	−0.864900	+	0.501945i	$0.832618\pi$
$547$	−1.83874	+	0.729158i	−1.83874	+	0.729158i	−0.973845	+	0.227213i	$0.927039\pi$
$548$	−0.656787	−	0.455867i	−0.656787	−	0.455867i
$549$		0			0
$550$	1.65758	−	1.02270i	1.65758	−	1.02270i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.04518	+	0.288886i	1.04518	+	0.288886i
$557$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$557$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.08011	−	2.52996i	−3.08011	−	2.52996i
$562$	−0.0362707	−	0.0178994i	−0.0362707	−	0.0178994i
$563$	1.02510	−	1.68682i	1.02510	−	1.68682i	0.374884	−	0.927072i	$-0.377682\pi$
$563$	1.02510	−	1.68682i	1.02510	−	1.68682i	0.650217	−	0.759749i	$-0.274678\pi$
$564$		0			0
$565$		0			0
$566$	1.06286	−	1.59941i	1.06286	−	1.59941i
$567$		0			0
$568$		0			0
$569$	−0.326148	+	0.437636i	−0.326148	+	0.437636i	−0.934463	−	0.356059i	$-0.884120\pi$
$569$	−0.326148	+	0.437636i	−0.326148	+	0.437636i	0.608316	+	0.793695i	$0.291845\pi$
$570$		0			0
$571$	1.60801	−	0.108570i	1.60801	−	0.108570i	0.764115	−	0.645080i	$-0.223176\pi$
$571$	1.60801	−	0.108570i	1.60801	−	0.108570i	0.843894	+	0.536510i	$0.180258\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.125635	−	0.0187715i	−0.125635	−	0.0187715i
$577$	1.18120	+	1.14204i	1.18120	+	1.14204i	0.986939	+	0.161094i	$0.0515021\pi$
$577$	1.18120	+	1.14204i	1.18120	+	1.14204i	0.194264	+	0.980949i	$0.437768\pi$
$578$	−2.00287	−	1.83460i	−2.00287	−	1.83460i
$579$	0.164856	+	0.612498i	0.164856	+	0.612498i
$580$		0			0
$581$		0			0
$582$	0.764884	−	0.0828263i	0.764884	−	0.0828263i
$583$		0			0
$584$	−1.50331	+	0.767254i	−1.50331	+	0.767254i
$585$		0			0
$586$		0			0
$587$	−0.918424	−	0.308027i	−0.918424	−	0.308027i	−0.181020	−	0.983479i	$-0.557940\pi$
$587$	−0.918424	−	0.308027i	−0.918424	−	0.308027i	−0.737404	+	0.675452i	$0.763948\pi$
$588$	−0.895892	−	0.569568i	−0.895892	−	0.569568i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.321741	+	0.408269i	0.321741	+	0.408269i	0.919301	−	0.393556i	$-0.128755\pi$
$593$	0.321741	+	0.408269i	0.321741	+	0.408269i	−0.597559	+	0.801825i	$0.703863\pi$
$594$	−1.77298	−	0.338709i	−1.77298	−	0.338709i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.992646	−	0.121051i	$-0.961373\pi$
$599$		0			0		0.992646	+	0.121051i	$0.0386266\pi$
$600$	−0.575594	+	0.892032i	−0.575594	+	0.892032i
$601$	0.120570	+	0.0130560i	0.120570	+	0.0130560i	0.167744	−	0.985831i	$-0.446352\pi$
$601$	0.120570	+	0.0130560i	0.120570	+	0.0130560i	−0.0471738	+	0.998887i	$0.515021\pi$
$602$		0			0
$603$	−0.234952	−	0.0416098i	−0.234952	−	0.0416098i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.884490	−	0.466559i	$-0.154506\pi$
$607$		0			0		−0.884490	+	0.466559i	$0.845494\pi$
$608$	0.354661	+	1.92687i	0.354661	+	1.92687i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.237701	+	0.0588497i	0.237701	+	0.0588497i
$613$		0			0		0.586694	−	0.809809i	$-0.300429\pi$
$613$		0			0		−0.586694	+	0.809809i	$0.699571\pi$
$614$	−1.65086	−	0.156277i	−1.65086	−	0.156277i
$615$		0			0
$616$		0			0
$617$	−0.0856708	+	0.844294i	−0.0856708	+	0.844294i	0.858053	+	0.513561i	$0.171674\pi$
$617$	−0.0856708	+	0.844294i	−0.0856708	+	0.844294i	−0.943724	+	0.330734i	$0.892704\pi$
$618$		0			0
$619$	−1.15860	−	1.51167i	−1.15860	−	1.51167i	−0.821508	−	0.570197i	$-0.806867\pi$
$619$	−1.15860	−	1.51167i	−1.15860	−	1.51167i	−0.337088	−	0.941473i	$-0.609442\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.542187	+	0.840258i	0.542187	+	0.840258i
$626$	0.0411813	+	0.0848856i	0.0411813	+	0.0848856i
$627$	−0.571618	−	4.01058i	−0.571618	−	4.01058i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$631$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$632$		0			0
$633$	−0.272606	−	0.831361i	−0.272606	−	0.831361i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.912135	−	0.390489i	0.912135	−	0.390489i	0.114357	−	0.993440i	$-0.463519\pi$
$641$	0.912135	−	0.390489i	0.912135	−	0.390489i	0.797778	+	0.602951i	$0.206009\pi$
$642$	−0.268193	−	0.313372i	−0.268193	−	0.313372i
$643$	−0.0227209	−	0.0634585i	−0.0227209	−	0.0634585i	0.929578	−	0.368626i	$-0.120172\pi$
$643$	−0.0227209	−	0.0634585i	−0.0227209	−	0.0634585i	−0.952299	+	0.305167i	$0.901288\pi$
$644$		0			0
$645$		0			0
$646$	−0.330584	−	3.76236i	−0.330584	−	3.76236i
$647$		0			0		−0.519333	−	0.854572i	$-0.673820\pi$
$647$		0			0		0.519333	+	0.854572i	$0.326180\pi$
$648$	1.07464	−	0.281487i	1.07464	−	0.281487i
$649$	−3.77692	+	0.668890i	−3.77692	+	0.668890i
$650$		0			0
$651$		0			0
$652$	0.895848	+	0.0483626i	0.895848	+	0.0483626i
$653$		0			0		0.220643	−	0.975355i	$-0.429185\pi$
$653$		0			0		−0.220643	+	0.975355i	$0.570815\pi$
$654$		0			0
$655$		0			0
$656$	−0.0210016	+	0.622807i	−0.0210016	+	0.622807i
$657$	−0.137197	+	0.164755i	−0.137197	+	0.164755i
$658$		0			0
$659$	1.41433	+	1.40483i	1.41433	+	1.40483i	0.764115	+	0.645080i	$0.223176\pi$
$659$	1.41433	+	1.40483i	1.41433	+	1.40483i	0.650217	+	0.759749i	$0.274678\pi$
$660$		0			0
$661$		0			0		−0.864900	−	0.501945i	$-0.832618\pi$
$661$		0			0		0.864900	+	0.501945i	$0.167382\pi$
$662$	0.624586	−	1.43219i	0.624586	−	1.43219i
$663$		0			0
$664$	0.285560	−	1.82686i	0.285560	−	1.82686i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.295384	−	0.0902836i	−0.295384	−	0.0902836i	0.141101	−	0.989995i	$-0.454936\pi$
$673$	−0.295384	−	0.0902836i	−0.295384	−	0.0902836i	−0.436485	+	0.899712i	$0.643777\pi$
$674$	−0.308424	+	0.0166504i	−0.308424	+	0.0166504i
$675$	0.155458	−	0.913628i	0.155458	−	0.913628i
$676$	0.472511	−	0.881325i	0.472511	−	0.881325i
$677$		0			0		−0.976820	−	0.214062i	$-0.931330\pi$
$677$		0			0		0.976820	+	0.214062i	$0.0686695\pi$
$678$	−0.380874	+	1.16154i	−0.380874	+	1.16154i
$679$		0			0
$680$		0			0
$681$	0.125498	+	1.68921i	0.125498	+	1.68921i
$682$		0			0
$683$	−0.720144	−	0.285574i	−0.720144	−	0.285574i	−0.0202235	−	0.999795i	$-0.506438\pi$
$683$	−0.720144	−	0.285574i	−0.720144	−	0.285574i	−0.699920	+	0.714221i	$0.746781\pi$
$684$	0.137747	+	0.207286i	0.137747	+	0.207286i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.459765	+	1.70819i	−0.459765	+	1.70819i
$689$		0			0
$690$		0			0
$691$	−1.10653	+	0.0298464i	−1.10653	+	0.0298464i	−0.575722	−	0.817645i	$-0.695279\pi$
$691$	−1.10653	+	0.0298464i	−1.10653	+	0.0298464i	−0.530808	+	0.847492i	$0.678112\pi$
$692$		0			0
$693$		0			0
$694$	0.743047	−	1.18635i	0.743047	−	1.18635i
$695$		0			0
$696$		0			0
$697$	0.153452	−	1.19144i	0.153452	−	1.19144i
$698$		0			0
$699$	−0.766599	−	0.647177i	−0.766599	−	0.647177i
$700$		0			0
$701$		0			0		−0.233773	−	0.972291i	$-0.575107\pi$
$701$		0			0		0.233773	+	0.972291i	$0.424893\pi$
$702$		0			0
$703$		0			0
$704$	0.248799	−	1.93173i	0.248799	−	1.93173i
$705$		0			0
$706$	−0.0704252	+	1.49123i	−0.0704252	+	1.49123i
$707$		0			0
$708$	1.70130	−	1.21516i	1.70130	−	1.21516i
$709$		0			0		0.718923	−	0.695089i	$-0.244635\pi$
$709$		0			0		−0.718923	+	0.695089i	$0.755365\pi$
$710$		0			0
$711$		0			0
$712$	1.57218	−	1.06010i	1.57218	−	1.06010i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.717024	−	1.77317i	0.717024	−	1.77317i
$717$		0			0
$718$		0			0
$719$		0			0		0.908355	−	0.418201i	$-0.137339\pi$
$719$		0			0		−0.908355	+	0.418201i	$0.862661\pi$
$720$		0			0
$721$		0			0
$722$	1.72677	−	2.25298i	1.72677	−	2.25298i
$723$	−0.604605	+	1.84385i	−0.604605	+	1.84385i
$724$		0			0
$725$		0			0
$726$	−0.497464	+	2.92360i	−0.497464	+	2.92360i
$727$		0			0		0.998546	−	0.0539068i	$-0.0171674\pi$
$727$		0			0		−0.998546	+	0.0539068i	$0.982833\pi$
$728$		0			0
$729$	−0.665413	+	0.517154i	−0.665413	+	0.517154i
$730$		0			0
$731$	1.19269	−	3.19473i	1.19269	−	3.19473i
$732$		0			0
$733$		0			0		−0.690227	−	0.723593i	$-0.742489\pi$
$733$		0			0		0.690227	+	0.723593i	$0.257511\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.565000	−	3.61457i	0.565000	−	3.61457i
$738$	0.0286837	+	0.0737805i	0.0286837	+	0.0737805i
$739$	0.0699784	−	0.160463i	0.0699784	−	0.160463i	−0.878119	−	0.478442i	$-0.841202\pi$
$739$	0.0699784	−	0.160463i	0.0699784	−	0.160463i	0.948098	+	0.317979i	$0.103004\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$743$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0579838	−	0.227615i	−0.0579838	−	0.227615i
$748$	−0.828425	+	3.66207i	−0.828425	+	3.66207i
$749$		0			0
$750$		0			0
$751$		0			0		0.999182	−	0.0404387i	$-0.0128755\pi$
$751$		0			0		−0.999182	+	0.0404387i	$0.987124\pi$
$752$		0			0
$753$	1.56945	−	0.411096i	1.56945	−	0.411096i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$757$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$758$	−0.438361	−	1.22432i	−0.438361	−	1.22432i
$759$		0			0
$760$		0			0
$761$	−0.387653	+	1.13050i	−0.387653	+	1.13050i	0.564646	+	0.825333i	$0.309013\pi$
$761$	−0.387653	+	1.13050i	−0.387653	+	1.13050i	−0.952299	+	0.305167i	$0.901288\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.330779	+	1.00877i	0.330779	+	1.00877i
$769$	−0.157734	−	1.55448i	−0.157734	−	1.55448i	−0.699920	−	0.714221i	$-0.746781\pi$
$769$	−0.157734	−	1.55448i	−0.157734	−	1.55448i	0.542187	−	0.840258i	$-0.317597\pi$
$770$		0			0
$771$	−1.32029	+	0.586412i	−1.32029	+	0.586412i
$772$	0.445986	−	0.397593i	0.445986	−	0.397593i
$773$		0			0		0.00674156	−	0.999977i	$-0.497854\pi$
$773$		0			0		−0.00674156	+	0.999977i	$0.502146\pi$
$774$	0.0317074	+	0.222465i	0.0317074	+	0.222465i
$775$		0			0
$776$	−0.392923	−	0.608936i	−0.392923	−	0.608936i
$777$		0			0
$778$		0			0
$779$	0.932922	−	0.787590i	0.932922	−	0.787590i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.100952	+	0.994891i	−0.100952	+	0.994891i
$785$		0			0
$786$	0.266877	−	0.940810i	0.266877	−	0.940810i
$787$	−0.120735	−	0.0114292i	−0.120735	−	0.0114292i	0.0337017	−	0.999432i	$-0.489270\pi$
$787$	−0.120735	−	0.0114292i	−0.120735	−	0.0114292i	−0.154437	+	0.988003i	$0.549356\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0675195	−	0.238024i	−0.0675195	−	0.238024i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$797$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$798$		0			0
$799$		0			0
$800$	0.994188	+	0.107657i	0.994188	+	0.107657i
$801$	0.130598	−	0.202396i	0.130598	−	0.202396i
$802$	0.961578	+	0.117263i	0.961578	+	0.117263i
$803$	−2.56813	−	2.05207i	−2.56813	−	2.05207i
$804$	0.570005	+	1.91089i	0.570005	+	1.91089i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.21208	−	1.30547i	1.21208	−	1.30547i	0.272900	−	0.962042i	$-0.412017\pi$
$809$	1.21208	−	1.30547i	1.21208	−	1.30547i	0.939179	−	0.343428i	$-0.111588\pi$
$810$		0			0
$811$	0.545602	+	0.0147165i	0.545602	+	0.0147165i	0.298741	−	0.954334i	$-0.403433\pi$
$811$	0.545602	+	0.0147165i	0.545602	+	0.0147165i	0.246861	+	0.969051i	$0.420601\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.451545	−	1.99606i	−0.451545	−	1.99606i
$817$	3.08703	−	1.57554i	3.08703	−	1.57554i
$818$	0.126589	−	0.252217i	0.126589	−	0.252217i
$819$		0			0
$820$		0			0
$821$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$821$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$822$	0.220594	+	0.819584i	0.220594	+	0.819584i
$823$		0			0		−0.737404	−	0.675452i	$-0.763948\pi$
$823$		0			0		0.737404	+	0.675452i	$0.236052\pi$
$824$		0			0
$825$	−2.04500	−	0.305549i	−2.04500	−	0.305549i
$826$		0			0
$827$	0.495013	−	0.158629i	0.495013	−	0.158629i	−0.0471738	−	0.998887i	$-0.515021\pi$
$827$	0.495013	−	0.158629i	0.495013	−	0.158629i	0.542187	+	0.840258i	$0.317597\pi$
$828$		0			0
$829$		0			0		−0.0202235	−	0.999795i	$-0.506438\pi$
$829$		0			0		0.0202235	+	0.999795i	$0.493562\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.374486	−	1.89100i	0.374486	−	1.89100i
$834$	−0.650014	−	0.950115i	−0.650014	−	0.950115i
$835$		0			0
$836$	−3.13486	+	2.17586i	−3.13486	+	2.17586i
$837$		0			0
$838$	1.01459	−	1.66953i	1.01459	−	1.66953i
$839$		0			0		−0.896748	−	0.442541i	$-0.854077\pi$
$839$		0			0		0.896748	+	0.442541i	$0.145923\pi$
$840$		0			0
$841$	−0.999909	+	0.0134828i	−0.999909	+	0.0134828i
$842$		0			0
$843$	0.0171647	+	0.0393591i	0.0171647	+	0.0393591i
$844$	−0.584712	+	0.580783i	−0.584712	+	0.580783i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.95751	+	0.569568i	−1.95751	+	0.569568i
$850$	−1.88843	−	0.387226i	−1.88843	−	0.387226i
$851$		0			0
$852$		0			0
$853$		0			0		−0.821508	−	0.570197i	$-0.806867\pi$
$853$		0			0		0.821508	+	0.570197i	$0.193133\pi$
$854$		0			0
$855$		0			0
$856$	−0.150496	+	0.358196i	−0.150496	+	0.358196i
$857$	−1.54348	−	1.16655i	−1.54348	−	1.16655i	−0.924523	−	0.381126i	$-0.875536\pi$
$857$	−1.54348	−	1.16655i	−1.54348	−	1.16655i	−0.618962	−	0.785421i	$-0.712446\pi$
$858$		0			0
$859$	−1.88731	+	0.256024i	−1.88731	+	0.256024i	−0.984677	−	0.174386i	$-0.944206\pi$
$859$	−1.88731	+	0.256024i	−1.88731	+	0.256024i	−0.902634	+	0.430410i	$0.858369\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$863$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$864$	−0.612033	−	0.695916i	−0.612033	−	0.695916i
$865$		0			0
$866$	−0.0996281	−	1.63999i	−0.0996281	−	1.63999i
$867$	0.368336	+	2.85984i	0.368336	+	2.85984i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0763279	−	0.0514672i	−0.0763279	−	0.0514672i
$874$		0			0
$875$		0			0
$876$	1.74492	+	0.407117i	1.74492	+	0.407117i
$877$		0			0		−0.412067	−	0.911153i	$-0.635193\pi$
$877$		0			0		0.412067	+	0.911153i	$0.364807\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.276640	+	1.50298i	−0.276640	+	1.50298i	0.496103	+	0.868264i	$0.334764\pi$
$881$	−0.276640	+	1.50298i	−0.276640	+	1.50298i	−0.772743	+	0.634719i	$0.781116\pi$
$882$	0.0379490	+	0.121229i	0.0379490	+	0.121229i
$883$	−0.429815	−	0.184006i	−0.429815	−	0.184006i	0.167744	−	0.985831i	$-0.446352\pi$
$883$	−0.429815	−	0.184006i	−0.429815	−	0.184006i	−0.597559	+	0.801825i	$0.703863\pi$
$884$		0			0
$885$		0			0
$886$	−0.217804	−	0.0697959i	−0.217804	−	0.0697959i
$887$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$887$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.36202	+	1.68119i	1.36202	+	1.68119i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.22008	+	1.24501i	−1.22008	+	1.24501i
$899$		0			0
$900$	0.121482	−	0.0371308i	0.121482	−	0.0371308i
$901$		0			0
$902$	−1.12212	+	0.462582i	−1.12212	+	0.462582i
$903$		0			0
$904$	1.13880	−	0.170152i	1.13880	−	0.170152i
$905$		0			0
$906$		0			0
$907$	−0.218678	−	0.637725i	−0.218678	−	0.637725i	−0.999909	−	0.0134828i	$-0.995708\pi$
$907$	−0.218678	−	0.637725i	−0.218678	−	0.637725i	0.781231	−	0.624242i	$-0.214592\pi$
$908$	1.36907	−	0.819415i	1.36907	−	0.819415i
$909$		0			0
$910$		0			0
$911$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$911$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$912$	1.03187	−	1.80595i	1.03187	−	1.80595i
$913$	3.47122	−	0.959434i	3.47122	−	0.959434i
$914$	0.168720	−	0.191844i	0.168720	−	0.191844i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.04815	+	1.44675i	1.04815	+	1.44675i
$919$		0			0		−0.374884	−	0.927072i	$-0.622318\pi$
$919$		0			0		0.374884	+	0.927072i	$0.377682\pi$
$920$		0			0
$921$	1.23215	+	1.25733i	1.23215	+	1.25733i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.289664	−	1.13707i	0.289664	−	1.13707i	−0.639914	−	0.768447i	$-0.721030\pi$
$929$	0.289664	−	1.13707i	0.289664	−	1.13707i	0.929578	−	0.368626i	$-0.120172\pi$
$930$		0			0
$931$	1.57882	−	1.16014i	1.57882	−	1.16014i
$932$	−0.220921	+	0.918837i	−0.220921	+	0.918837i
$933$		0			0
$934$	0.0606373	+	0.998160i	0.0606373	+	0.998160i
$935$		0			0
$936$		0			0
$937$	0.818349	−	0.601335i	0.818349	−	0.601335i	−0.100952	−	0.994891i	$-0.532189\pi$
$937$	0.818349	−	0.601335i	0.818349	−	0.601335i	0.919301	+	0.393556i	$0.128755\pi$
$938$		0			0
$939$	0.0247258	−	0.0970611i	0.0247258	−	0.0970611i
$940$		0			0
$941$		0			0		−0.934463	−	0.356059i	$-0.884120\pi$
$941$		0			0		0.934463	+	0.356059i	$0.115880\pi$
$942$		0			0
$943$		0			0
$944$	−1.74187	−	0.918820i	−1.74187	−	0.918820i
$945$		0			0
$946$	−3.40043	+	0.555036i	−3.40043	+	0.555036i
$947$	1.05737	+	1.07897i	1.05737	+	1.07897i	0.996729	+	0.0808112i	$0.0257511\pi$
$947$	1.05737	+	1.07897i	1.05737	+	1.07897i	0.0606373	+	0.998160i	$0.480687\pi$
$948$		0			0
$949$		0			0
$950$	−1.14947	−	1.58661i	−1.14947	−	1.58661i
$951$		0			0
$952$		0			0
$953$	−0.0696042	+	0.328187i	−0.0696042	+	0.328187i	−0.999182	−	0.0404387i	$-0.987124\pi$
$953$	−0.0696042	+	0.328187i	−0.0696042	+	0.328187i	0.929578	+	0.368626i	$0.120172\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.324364	+	0.945932i	0.324364	+	0.945932i
$962$		0			0
$963$	0.000332727		0.0493535i	0.000332727		0.0493535i
$964$	1.80775	−	0.270101i	1.80775	−	0.270101i
$965$		0			0
$966$		0			0
$967$		0			0		0.939179	−	0.343428i	$-0.111588\pi$
$967$		0			0		−0.939179	+	0.343428i	$0.888412\pi$
$968$	2.67150	−	0.816539i	2.67150	−	0.816539i
$969$	−2.30840	+	3.27841i	−2.30840	+	3.27841i
$970$		0			0
$971$	−0.0496308	−	0.250614i	−0.0496308	−	0.250614i	0.948098	−	0.317979i	$-0.103004\pi$
$971$	−0.0496308	−	0.250614i	−0.0496308	−	0.250614i	−0.997728	+	0.0673651i	$0.978541\pi$
$972$	−0.227990	−	0.108714i	−0.227990	−	0.108714i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.0254611	−	0.0314274i	−0.0254611	−	0.0314274i	0.764115	−	0.645080i	$-0.223176\pi$
$977$	−0.0254611	−	0.0314274i	−0.0254611	−	0.0314274i	−0.789576	+	0.613653i	$0.789700\pi$
$978$	−0.693589	−	0.652733i	−0.693589	−	0.652733i
$979$	3.14310	+	1.93924i	3.14310	+	1.93924i
$980$		0			0
$981$		0			0
$982$	−1.11742	−	0.358080i	−1.11742	−	0.358080i
$983$		0			0		−0.746444	−	0.665448i	$-0.768240\pi$
$983$		0			0		0.746444	+	0.665448i	$0.231760\pi$
$984$	0.443552	−	0.490837i	0.443552	−	0.490837i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.412067	−	0.911153i	$-0.635193\pi$
$991$		0			0		0.412067	+	0.911153i	$0.364807\pi$
$992$		0			0
$993$	−1.48747	+	0.734058i	−1.48747	+	0.734058i
$994$		0			0
$995$		0			0
$996$	−1.48273	+	1.28639i	−1.48273	+	1.28639i
$997$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$997$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$998$	−0.287122	−	1.83685i	−0.287122	−	1.83685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.51.1	✓	232
8.3	odd	2	CM	3736.1.l.a.51.1	✓	232
467.174	even	233	inner	3736.1.l.a.3443.1	yes	232
3736.3443	odd	466	inner	3736.1.l.a.3443.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.51.1	✓	232	1.1	even	1	trivial
3736.1.l.a.51.1	✓	232	8.3	odd	2	CM
3736.1.l.a.3443.1	yes	232	467.174	even	233	inner
3736.1.l.a.3443.1	yes	232	3736.3443	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)

\(f(q)\)	\(=\)	\(q+(-0.233773 + 0.972291i) q^{2} +(0.855488 - 0.628626i) q^{3} +(-0.890700 - 0.454591i) q^{4} +(0.411217 + 0.978739i) q^{6} +(0.650217 - 0.759749i) q^{8} +(0.0379490 - 0.121229i) q^{9} +O(q^{10})\)	\(q+(-0.233773 + 0.972291i) q^{2} +(0.855488 - 0.628626i) q^{3} +(-0.890700 - 0.454591i) q^{4} +(0.411217 + 0.978739i) q^{6} +(0.650217 - 0.759749i) q^{8} +(0.0379490 - 0.121229i) q^{9} +(1.87013 + 0.544145i) q^{11} +(-1.04775 + 0.171020i) q^{12} +(0.586694 + 0.809809i) q^{16} +(-0.978828 - 1.66072i) q^{17} +(0.108998 + 0.0652375i) q^{18} +(0.406486 - 1.91660i) q^{19} +(-0.966254 + 1.69111i) q^{22} +(0.0786550 - 1.05870i) q^{24} +(-0.878119 - 0.478442i) q^{25} +(0.300607 + 0.876652i) q^{27} +(-0.924523 + 0.381126i) q^{32} +(1.94194 - 0.710105i) q^{33} +(1.84353 - 0.563473i) q^{34} +(-0.0889108 + 0.0907274i) q^{36} +(1.76847 + 0.843274i) q^{38} +(0.492033 + 0.382404i) q^{41} +(1.11356 + 1.37451i) q^{43} +(-1.41837 - 1.33482i) q^{44} +(1.01098 + 0.323971i) q^{48} +(0.746444 + 0.665448i) q^{49} +(0.670466 - 0.741941i) q^{50} +(-1.88135 - 0.805413i) q^{51} +(-0.922635 + 0.0873402i) q^{54} +(-0.857082 - 1.89516i) q^{57} +(-1.76602 + 0.871519i) q^{59} +(-0.154437 - 0.988003i) q^{64} +(0.236455 + 2.05414i) q^{66} +(-0.239943 - 1.86297i) q^{67} +(0.116892 + 1.92417i) q^{68} +(-0.0674285 - 0.107657i) q^{72} +(-1.56040 - 0.643260i) q^{73} +(-1.05198 + 0.142707i) q^{75} +(-1.23333 + 1.52233i) q^{76} +(0.912608 + 0.633428i) q^{81} +(-0.486833 + 0.389004i) q^{82} +(1.57363 - 0.970903i) q^{83} +(-1.59674 + 0.761386i) q^{86} +(1.62941 - 1.06702i) q^{88} +(1.82767 + 0.505162i) q^{89} +(-0.551333 + 0.907227i) q^{96} +(0.207153 - 0.694464i) q^{97} +(-0.821508 + 0.570197i) q^{98} +(0.136936 - 0.206065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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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