LMFDB - Embedded newform 3736.1.l.a.83.1

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			83.1
Root			$-0.929578 + 0.368626i$ of defining polynomial
Character	$\chi$	$=$	3736.83
Dual form			3736.1.l.a.3691.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0606373 + 0.998160i) q^{2} +(1.10923 + 1.62135i) q^{3} +(-0.992646 + 0.121051i) q^{4} +(-1.55110 + 1.20550i) q^{6} +(-0.181020 - 0.983479i) q^{8} +(-1.03602 + 2.66485i) q^{9} +O(q^{10})$	\(q+(0.0606373 + 0.998160i) q^{2} +(1.10923 + 1.62135i) q^{3} +(-0.992646 + 0.121051i) q^{4} +(-1.55110 + 1.20550i) q^{6} +(-0.181020 - 0.983479i) q^{8} +(-1.03602 + 2.66485i) q^{9} +(-1.39667 + 1.17909i) q^{11} +(-1.29734 - 1.47515i) q^{12} +(0.970693 - 0.240323i) q^{16} +(0.0145707 - 0.308529i) q^{17} +(-2.72277 - 0.872521i) q^{18} +(0.544015 + 0.0441067i) q^{19} +(-1.26161 - 1.32260i) q^{22} +(1.39377 - 1.38440i) q^{24} +(-0.259904 - 0.965634i) q^{25} +(-3.55674 + 0.829841i) q^{27} +(0.298741 + 0.954334i) q^{32} +(-3.46094 - 0.956594i) q^{33} +(0.308845 - 0.00416448i) q^{34} +(0.705814 - 2.77067i) q^{36} +(-0.0110380 + 0.545688i) q^{38} +(1.58633 + 0.782846i) q^{41} +(-1.65689 - 0.0670571i) q^{43} +(1.24366 - 1.33949i) q^{44} +(1.46637 + 1.30726i) q^{48} +(0.629495 + 0.777005i) q^{49} +(0.948098 - 0.317979i) q^{50} +(0.516395 - 0.318606i) q^{51} +(-1.04399 - 3.49987i) q^{54} +(0.531926 + 0.930961i) q^{57} +(1.32876 + 1.47041i) q^{59} +(-0.934463 + 0.356059i) q^{64} +(0.744971 - 3.51258i) q^{66} +(-0.933693 - 1.68651i) q^{67} +(0.0228844 + 0.308024i) q^{68} +(2.80837 + 0.536510i) q^{72} +(0.100224 - 0.320167i) q^{73} +(1.27733 - 1.49251i) q^{75} +(-0.545354 + 0.0220714i) q^{76} +(-3.18235 - 2.91499i) q^{81} +(-0.685214 + 1.63088i) q^{82} +(0.310292 - 0.510590i) q^{83} +(-0.0335354 - 1.65790i) q^{86} +(1.41244 + 1.16015i) q^{88} +(0.0394557 - 0.252416i) q^{89} +(-1.21593 + 1.54294i) q^{96} +(0.484681 + 1.35369i) q^{97} +(-0.737404 + 0.675452i) q^{98} +(-1.69513 - 4.94347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{112}{233}\right)$

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 $

$2$	0.0606373	+	0.998160i	0.0606373	+	0.998160i
$2$	0.0606373	+	0.998160i	0.0606373	+	0.998160i
$3$	1.10923	+	1.62135i	1.10923	+	1.62135i	0.709486	+	0.704719i	$0.248927\pi$
$3$	1.10923	+	1.62135i	1.10923	+	1.62135i	0.399745	+	0.916626i	$0.369099\pi$
$4$	−0.992646	+	0.121051i	−0.992646	+	0.121051i
$5$		0			0		0.608316	−	0.793695i	$-0.291845\pi$
$5$		0			0		−0.608316	+	0.793695i	$0.708155\pi$
$6$	−1.55110	+	1.20550i	−1.55110	+	1.20550i
$7$		0			0		−0.902634	−	0.430410i	$-0.858369\pi$
$7$		0			0		0.902634	+	0.430410i	$0.141631\pi$
$8$	−0.181020	−	0.983479i	−0.181020	−	0.983479i
$9$	−1.03602	+	2.66485i	−1.03602	+	2.66485i
$10$		0			0
$11$	−1.39667	+	1.17909i	−1.39667	+	1.17909i	−0.436485	+	0.899712i	$0.643777\pi$
$11$	−1.39667	+	1.17909i	−1.39667	+	1.17909i	−0.960181	+	0.279380i	$0.909871\pi$
$12$	−1.29734	−	1.47515i	−1.29734	−	1.47515i
$13$		0			0		−0.246861	−	0.969051i	$-0.579399\pi$
$13$		0			0		0.246861	+	0.969051i	$0.420601\pi$
$14$		0			0
$15$		0			0
$16$	0.970693	−	0.240323i	0.970693	−	0.240323i
$17$	0.0145707	−	0.308529i	0.0145707	−	0.308529i	−0.979617	−	0.200872i	$-0.935622\pi$
$17$	0.0145707	−	0.308529i	0.0145707	−	0.308529i	0.994188	−	0.107657i	$-0.0343348\pi$
$18$	−2.72277	−	0.872521i	−2.72277	−	0.872521i
$19$	0.544015	+	0.0441067i	0.544015	+	0.0441067i	0.349751	−	0.936843i	$-0.386266\pi$
$19$	0.544015	+	0.0441067i	0.544015	+	0.0441067i	0.194264	+	0.980949i	$0.437768\pi$
$20$		0			0
$21$		0			0
$22$	−1.26161	−	1.32260i	−1.26161	−	1.32260i
$23$		0			0		−0.0875288	−	0.996162i	$-0.527897\pi$
$23$		0			0		0.0875288	+	0.996162i	$0.472103\pi$
$24$	1.39377	−	1.38440i	1.39377	−	1.38440i
$25$	−0.259904	−	0.965634i	−0.259904	−	0.965634i
$26$		0			0
$27$	−3.55674	+	0.829841i	−3.55674	+	0.829841i
$28$		0			0
$29$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$29$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$30$		0			0
$31$		0			0		−0.114357	−	0.993440i	$-0.536481\pi$
$31$		0			0		0.114357	+	0.993440i	$0.463519\pi$
$32$	0.298741	+	0.954334i	0.298741	+	0.954334i
$33$	−3.46094	−	0.956594i	−3.46094	−	0.956594i
$34$	0.308845	−	0.00416448i	0.308845	−	0.00416448i
$35$		0			0
$36$	0.705814	−	2.77067i	0.705814	−	2.77067i
$37$		0			0		−0.805835	−	0.592140i	$-0.798283\pi$
$37$		0			0		0.805835	+	0.592140i	$0.201717\pi$
$38$	−0.0110380	+	0.545688i	−0.0110380	+	0.545688i
$39$		0			0
$40$		0			0
$41$	1.58633	+	0.782846i	1.58633	+	0.782846i	0.999636	−	0.0269632i	$-0.00858369\pi$
$41$	1.58633	+	0.782846i	1.58633	+	0.782846i	0.586694	+	0.809809i	$0.300429\pi$
$42$		0			0
$43$	−1.65689	−	0.0670571i	−1.65689	−	0.0670571i	−0.805835	−	0.592140i	$-0.798283\pi$
$43$	−1.65689	−	0.0670571i	−1.65689	−	0.0670571i	−0.851051	+	0.525083i	$0.824034\pi$
$44$	1.24366	−	1.33949i	1.24366	−	1.33949i
$45$		0			0
$46$		0			0
$47$		0			0		−0.929578	−	0.368626i	$-0.879828\pi$
$47$		0			0		0.929578	+	0.368626i	$0.120172\pi$
$48$	1.46637	+	1.30726i	1.46637	+	1.30726i
$49$	0.629495	+	0.777005i	0.629495	+	0.777005i
$50$	0.948098	−	0.317979i	0.948098	−	0.317979i
$51$	0.516395	−	0.318606i	0.516395	−	0.318606i
$52$		0			0
$53$		0			0		0.220643	−	0.975355i	$-0.429185\pi$
$53$		0			0		−0.220643	+	0.975355i	$0.570815\pi$
$54$	−1.04399	−	3.49987i	−1.04399	−	3.49987i
$55$		0			0
$56$		0			0
$57$	0.531926	+	0.930961i	0.531926	+	0.930961i
$58$		0			0
$59$	1.32876	+	1.47041i	1.32876	+	1.47041i	0.764115	+	0.645080i	$0.223176\pi$
$59$	1.32876	+	1.47041i	1.32876	+	1.47041i	0.564646	+	0.825333i	$0.309013\pi$
$60$		0			0
$61$		0			0		−0.999636	−	0.0269632i	$-0.991416\pi$
$61$		0			0		0.999636	+	0.0269632i	$0.00858369\pi$
$62$		0			0
$63$		0			0
$64$	−0.934463	+	0.356059i	−0.934463	+	0.356059i
$65$		0			0
$66$	0.744971	−	3.51258i	0.744971	−	3.51258i
$67$	−0.933693	−	1.68651i	−0.933693	−	1.68651i	−0.699920	−	0.714221i	$-0.746781\pi$
$67$	−0.933693	−	1.68651i	−0.933693	−	1.68651i	−0.233773	−	0.972291i	$-0.575107\pi$
$68$	0.0228844	+	0.308024i	0.0228844	+	0.308024i
$69$		0			0
$70$		0			0
$71$		0			0		−0.436485	−	0.899712i	$-0.643777\pi$
$71$		0			0		0.436485	+	0.899712i	$0.356223\pi$
$72$	2.80837	+	0.536510i	2.80837	+	0.536510i
$73$	0.100224	−	0.320167i	0.100224	−	0.320167i	−0.890700	−	0.454591i	$-0.849785\pi$
$73$	0.100224	−	0.320167i	0.100224	−	0.320167i	0.990924	+	0.134424i	$0.0429185\pi$
$74$		0			0
$75$	1.27733	−	1.49251i	1.27733	−	1.49251i
$76$	−0.545354	+	0.0220714i	−0.545354	+	0.0220714i
$77$		0			0
$78$		0			0
$79$		0			0		−0.448576	−	0.893745i	$-0.648069\pi$
$79$		0			0		0.448576	+	0.893745i	$0.351931\pi$
$80$		0			0
$81$	−3.18235	−	2.91499i	−3.18235	−	2.91499i
$82$	−0.685214	+	1.63088i	−0.685214	+	1.63088i
$83$	0.310292	−	0.510590i	0.310292	−	0.510590i	−0.660401	−	0.750913i	$-0.729614\pi$
$83$	0.310292	−	0.510590i	0.310292	−	0.510590i	0.970693	+	0.240323i	$0.0772532\pi$
$84$		0			0
$85$		0			0
$86$	−0.0335354	−	1.65790i	−0.0335354	−	1.65790i
$87$		0			0
$88$	1.41244	+	1.16015i	1.41244	+	1.16015i
$89$	0.0394557	−	0.252416i	0.0394557	−	0.252416i	−0.960181	−	0.279380i	$-0.909871\pi$
$89$	0.0394557	−	0.252416i	0.0394557	−	0.252416i	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
$96$	−1.21593	+	1.54294i	−1.21593	+	1.54294i
$97$	0.484681	+	1.35369i	0.484681	+	1.35369i	0.896748	+	0.442541i	$0.145923\pi$
$97$	0.484681	+	1.35369i	0.484681	+	1.35369i	−0.412067	+	0.911153i	$0.635193\pi$
$98$	−0.737404	+	0.675452i	−0.737404	+	0.675452i
$99$	−1.69513	−	4.94347i	−1.69513	−	4.94347i
$100$	0.374884	+	0.927072i	0.374884	+	0.927072i
$101$		0			0		0.805835	−	0.592140i	$-0.201717\pi$
$101$		0			0		−0.805835	+	0.592140i	$0.798283\pi$
$102$	0.349333	+	0.496125i	0.349333	+	0.496125i
$103$		0			0		0.0740898	−	0.997252i	$-0.476395\pi$
$103$		0			0		−0.0740898	+	0.997252i	$0.523605\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.20302	+	1.07248i	−1.20302	+	1.07248i	−0.207472	+	0.978241i	$0.566524\pi$
$107$	−1.20302	+	1.07248i	−1.20302	+	1.07248i	−0.995549	+	0.0942425i	$0.969957\pi$
$108$	3.43013	−	1.25429i	3.43013	−	1.25429i
$109$		0			0		0.00674156	−	0.999977i	$-0.497854\pi$
$109$		0			0		−0.00674156	+	0.999977i	$0.502146\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.75410	+	0.310651i	1.75410	+	0.310651i	0.956327	−	0.292300i	$-0.0944206\pi$
$113$	1.75410	+	0.310651i	1.75410	+	0.310651i	0.797778	+	0.602951i	$0.206009\pi$
$114$	−0.896993	+	0.587398i	−0.896993	+	0.587398i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.38714	+	1.41548i	−1.38714	+	1.41548i
$119$		0			0
$120$		0			0
$121$	0.392676	−	2.30776i	0.392676	−	2.30776i
$122$		0			0
$123$	0.490344	+	3.44035i	0.490344	+	3.44035i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.836584	−	0.547839i	$-0.815451\pi$
$127$		0			0		0.836584	+	0.547839i	$0.184549\pi$
$128$	−0.412067	−	0.911153i	−0.412067	−	0.911153i
$129$	−1.72915	−	2.76077i	−1.72915	−	2.76077i
$130$		0			0
$131$	0.181104	+	0.431046i	0.181104	+	0.431046i	0.986939	−	0.161094i	$-0.0515021\pi$
$131$	0.181104	+	0.431046i	0.181104	+	0.431046i	−0.805835	+	0.592140i	$0.798283\pi$
$132$	3.55129	+	0.530607i	3.55129	+	0.530607i
$133$		0			0
$134$	1.62679	−	1.03424i	1.62679	−	1.03424i
$135$		0			0
$136$	−0.306070	+	0.0415200i	−0.306070	+	0.0415200i
$137$	0.252627	+	0.295183i	0.252627	+	0.295183i	0.871589	−	0.490238i	$-0.163090\pi$
$137$	0.252627	+	0.295183i	0.252627	+	0.295183i	−0.618962	+	0.785421i	$0.712446\pi$
$138$		0			0
$139$	−0.472062	+	1.66414i	−0.472062	+	1.66414i	0.246861	+	0.969051i	$0.420601\pi$
$139$	−0.472062	+	1.66414i	−0.472062	+	1.66414i	−0.718923	+	0.695089i	$0.755365\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.365231	+	2.83573i	−0.365231	+	2.83573i
$145$		0			0
$146$	0.325655	+	0.0806251i	0.325655	+	0.0806251i
$147$	−0.561537	+	1.88251i	−0.561537	+	1.88251i
$148$		0			0
$149$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$149$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$150$	1.56721	+	1.18448i	1.56721	+	1.18448i
$151$		0			0		−0.553466	−	0.832871i	$-0.686695\pi$
$151$		0			0		0.553466	+	0.832871i	$0.313305\pi$
$152$	−0.0550996	−	0.543012i	−0.0550996	−	0.543012i
$153$	0.807089	+	0.358470i	0.807089	+	0.358470i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$157$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	2.71666	−	3.35325i	2.71666	−	3.35325i
$163$	−0.909140	+	0.148395i	−0.909140	+	0.148395i	−0.597559	−	0.801825i	$-0.703863\pi$
$163$	−0.909140	+	0.148395i	−0.909140	+	0.148395i	−0.311581	+	0.950220i	$0.600858\pi$
$164$	−1.66943	−	0.585061i	−1.66943	−	0.585061i
$165$		0			0
$166$	0.528466	+	0.278760i	0.528466	+	0.278760i
$167$		0			0		0.553466	−	0.832871i	$-0.313305\pi$
$167$		0			0		−0.553466	+	0.832871i	$0.686695\pi$
$168$		0			0
$169$	−0.878119	+	0.478442i	−0.878119	+	0.478442i
$170$		0			0
$171$	−0.681147	+	1.40402i	−0.681147	+	1.40402i
$172$	1.65282	−	0.134005i	1.65282	−	0.134005i
$173$		0			0		−0.973845	−	0.227213i	$-0.927039\pi$
$173$		0			0		0.973845	+	0.227213i	$0.0729614\pi$
$174$		0			0
$175$		0			0
$176$	−1.07237	+	1.48019i	−1.07237	+	1.48019i
$177$	−0.910146	+	3.78541i	−0.910146	+	3.78541i
$178$	0.254344	+	0.0240772i	0.254344	+	0.0240772i
$179$	1.99528	+	0.134718i	1.99528	+	0.134718i	0.998546	+	0.0539068i	$0.0171674\pi$
$179$	1.99528	+	0.134718i	1.99528	+	0.134718i	0.996729	+	0.0808112i	$0.0257511\pi$
$180$		0			0
$181$		0			0		0.530808	−	0.847492i	$-0.321888\pi$
$181$		0			0		−0.530808	+	0.847492i	$0.678112\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.343434	+	0.448092i	0.343434	+	0.448092i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.690227	−	0.723593i	$-0.257511\pi$
$191$		0			0		−0.690227	+	0.723593i	$0.742489\pi$
$192$	−1.61383	−	1.12014i	−1.61383	−	1.12014i
$193$	0.521005	−	0.503732i	0.521005	−	0.503732i	−0.387350	−	0.921933i	$-0.626609\pi$
$193$	0.521005	−	0.503732i	0.521005	−	0.503732i	0.908355	+	0.418201i	$0.137339\pi$
$194$	−1.32181	+	0.565874i	−1.32181	+	0.565874i
$195$		0			0
$196$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$197$		0			0		−0.934463	−	0.356059i	$-0.884120\pi$
$197$		0			0		0.934463	+	0.356059i	$0.115880\pi$
$198$	4.83158	−	1.99177i	4.83158	−	1.99177i
$199$		0			0		−0.586694	−	0.809809i	$-0.699571\pi$
$199$		0			0		0.586694	+	0.809809i	$0.300429\pi$
$200$	−0.902634	+	0.430410i	−0.902634	+	0.430410i
$201$	1.69874	−	3.38457i	1.69874	−	3.38457i
$202$		0			0
$203$		0			0
$204$	−0.474030	+	0.378774i	−0.474030	+	0.378774i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.811813	+	0.579841i	−0.811813	+	0.579841i
$210$		0			0
$211$	0.877596	−	0.462922i	0.877596	−	0.462922i	0.0337017	−	0.999432i	$-0.489270\pi$
$211$	0.877596	−	0.462922i	0.877596	−	0.462922i	0.843894	+	0.536510i	$0.180258\pi$
$212$		0			0
$213$		0			0
$214$	−1.14346	−	1.13578i	−1.14346	−	1.13578i
$215$		0			0
$216$	1.45997	+	3.34776i	1.45997	+	3.34776i
$217$		0			0
$218$		0			0
$219$	0.630272	−	0.192642i	0.630272	−	0.192642i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.995549	−	0.0942425i	$-0.0300429\pi$
$223$		0			0		−0.995549	+	0.0942425i	$0.969957\pi$
$224$		0			0
$225$	2.84254	+	0.307808i	2.84254	+	0.307808i
$226$	−0.203715	+	1.76971i	−0.203715	+	1.76971i
$227$	−1.90036	+	0.363045i	−1.90036	+	0.363045i	−0.997728	−	0.0673651i	$-0.978541\pi$
$227$	−1.90036	+	0.363045i	−1.90036	+	0.363045i	−0.902634	+	0.430410i	$0.858369\pi$
$228$	−0.640709	−	0.859724i	−0.640709	−	0.859724i
$229$		0			0		−0.908355	−	0.418201i	$-0.862661\pi$
$229$		0			0		0.908355	+	0.418201i	$0.137339\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.0986867	−	1.62450i	0.0986867	−	1.62450i	−0.530808	−	0.847492i	$-0.678112\pi$
$233$	0.0986867	−	1.62450i	0.0986867	−	1.62450i	0.629495	−	0.777005i	$-0.283262\pi$
$234$		0			0
$235$		0			0
$236$	−1.49698	−	1.29875i	−1.49698	−	1.29875i
$237$		0			0
$238$		0			0
$239$		0			0		−0.597559	−	0.801825i	$-0.703863\pi$
$239$		0			0		0.597559	+	0.801825i	$0.296137\pi$
$240$		0			0
$241$	0.225726	−	1.96093i	0.225726	−	1.96093i	−0.0471738	−	0.998887i	$-0.515021\pi$
$241$	0.225726	−	1.96093i	0.225726	−	1.96093i	0.272900	−	0.962042i	$-0.412017\pi$
$242$	2.32733	+	0.252017i	2.32733	+	0.252017i
$243$	0.680906	−	4.77737i	0.680906	−	4.77737i
$244$		0			0
$245$		0			0
$246$	−3.40428	+	0.698055i	−3.40428	+	0.698055i
$247$		0			0
$248$		0			0
$249$	1.17203	−	0.0632723i	1.17203	−	0.0632723i
$250$		0			0
$251$	0.686005	+	1.57303i	0.686005	+	1.57303i	0.813746	+	0.581221i	$0.197425\pi$
$251$	0.686005	+	1.57303i	0.686005	+	1.57303i	−0.127741	+	0.991808i	$0.540773\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.884490	−	0.466559i	0.884490	−	0.466559i
$257$	−0.784578	+	1.67434i	−0.784578	+	1.67434i	−0.0471738	+	0.998887i	$0.515021\pi$
$257$	−0.784578	+	1.67434i	−0.784578	+	1.67434i	−0.737404	+	0.675452i	$0.763948\pi$
$258$	2.65084	−	1.89337i	2.65084	−	1.89337i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.419271	+	0.206908i	−0.419271	+	0.206908i
$263$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$263$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$264$	−0.314290	+	3.57693i	−0.314290	+	3.57693i
$265$		0			0
$266$		0			0
$267$	0.453020	−	0.216017i	0.453020	−	0.216017i
$268$	1.13098	+	1.56109i	1.13098	+	1.56109i
$269$		0			0		0.924523	−	0.381126i	$-0.124464\pi$
$269$		0			0		−0.924523	+	0.381126i	$0.875536\pi$
$270$		0			0
$271$		0			0		−0.718923	−	0.695089i	$-0.755365\pi$
$271$		0			0		0.718923	+	0.695089i	$0.244635\pi$
$272$	−0.0600028	−	0.302989i	−0.0600028	−	0.302989i
$273$		0			0
$274$	−0.279321	+	0.270061i	−0.279321	+	0.270061i
$275$	1.50157	+	1.04222i	1.50157	+	1.04222i
$276$		0			0
$277$		0			0		−0.781231	−	0.624242i	$-0.785408\pi$
$277$		0			0		0.781231	+	0.624242i	$0.214592\pi$
$278$	−1.68970	−	0.370285i	−1.68970	−	0.370285i
$279$		0			0
$280$		0			0
$281$	1.22923	+	1.25434i	1.22923	+	1.25434i	0.956327	+	0.292300i	$0.0944206\pi$
$281$	1.22923	+	1.25434i	1.22923	+	1.25434i	0.272900	+	0.962042i	$0.412017\pi$
$282$		0			0
$283$	1.47300	−	0.407133i	1.47300	−	0.407133i	0.564646	−	0.825333i	$-0.309013\pi$
$283$	1.47300	−	0.407133i	1.47300	−	0.407133i	0.908355	+	0.418201i	$0.137339\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.85266	−	0.192607i	−2.85266	−	0.192607i
$289$	0.900571	+	0.0852516i	0.900571	+	0.0852516i
$290$		0			0
$291$	−1.65718	+	2.28740i	−1.65718	+	2.28740i
$292$	−0.0607299	+	0.329945i	−0.0607299	+	0.329945i
$293$		0			0		−0.851051	−	0.525083i	$-0.824034\pi$
$293$		0			0		0.851051	+	0.525083i	$0.175966\pi$
$294$	−1.91309	−	0.446354i	−1.91309	−	0.446354i
$295$		0			0
$296$		0			0
$297$	3.98911	−	5.35273i	3.98911	−	5.35273i
$298$		0			0
$299$		0			0
$300$	−1.08727	+	1.63615i	−1.08727	+	1.63615i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.538671	−	0.0879250i	0.538671	−	0.0879250i
$305$		0			0
$306$	−0.308871	+	0.827341i	−0.308871	+	0.827341i
$307$	1.87768	+	0.686605i	1.87768	+	0.686605i	0.948098	+	0.317979i	$0.103004\pi$
$307$	1.87768	+	0.686605i	1.87768	+	0.686605i	0.929578	+	0.368626i	$0.120172\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.564646	−	0.825333i	$-0.309013\pi$
$311$		0			0		−0.564646	+	0.825333i	$0.690987\pi$
$312$		0			0
$313$	0.372376	+	1.13562i	0.372376	+	1.13562i	0.948098	+	0.317979i	$0.103004\pi$
$313$	0.372376	+	1.13562i	0.372376	+	1.13562i	−0.575722	+	0.817645i	$0.695279\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.797778	−	0.602951i	$-0.793991\pi$
$317$		0			0		0.797778	+	0.602951i	$0.206009\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−3.07330	−	0.760881i	−3.07330	−	0.760881i
$322$		0			0
$323$	0.0215349	−	0.167202i	0.0215349	−	0.167202i
$324$	3.51181	+	2.50833i	3.51181	+	2.50833i
$325$		0			0
$326$	−0.203250	−	0.898468i	−0.203250	−	0.898468i
$327$		0			0
$328$	0.482755	−	1.70183i	0.482755	−	1.70183i
$329$		0			0
$330$		0			0
$331$	−0.767668	+	0.104138i	−0.767668	+	0.104138i	−0.507764	−	0.861496i	$-0.669528\pi$
$331$	−0.767668	+	0.104138i	−0.767668	+	0.104138i	−0.259904	+	0.965634i	$0.583691\pi$
$332$	−0.246202	+	0.544397i	−0.246202	+	0.544397i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.629993	−	1.75954i	0.629993	−	1.75954i	−0.0202235	−	0.999795i	$-0.506438\pi$
$337$	0.629993	−	1.75954i	0.629993	−	1.75954i	0.650217	−	0.759749i	$-0.274678\pi$
$338$	−0.530808	−	0.847492i	−0.530808	−	0.847492i
$339$	1.44204	+	3.18859i	1.44204	+	3.18859i
$340$		0			0
$341$		0			0
$342$	−1.44274	−	0.594757i	−1.44274	−	0.594757i
$343$		0			0
$344$	0.233980	+	1.64165i	0.233980	+	1.64165i
$345$		0			0
$346$		0			0
$347$	−0.0630684	−	0.489677i	−0.0630684	−	0.489677i	−0.992646	−	0.121051i	$-0.961373\pi$
$347$	−0.0630684	−	0.489677i	−0.0630684	−	0.489677i	0.929578	−	0.368626i	$-0.120172\pi$
$348$		0			0
$349$		0			0		0.699920	−	0.714221i	$-0.253219\pi$
$349$		0			0		−0.699920	+	0.714221i	$0.746781\pi$
$350$		0			0
$351$		0			0
$352$	−1.54249	−	0.980644i	−1.54249	−	0.980644i
$353$	−1.05325	+	0.689724i	−1.05325	+	0.689724i	−0.952299	−	0.305167i	$-0.901288\pi$
$353$	−1.05325	+	0.689724i	−1.05325	+	0.689724i	−0.100952	+	0.994891i	$0.532189\pi$
$354$	−3.83363	−	0.678934i	−3.83363	−	0.678934i
$355$		0			0
$356$	−0.00861016	+	0.255336i	−0.00861016	+	0.255336i
$357$		0			0
$358$	−0.0134819	+	1.99977i	−0.0134819	+	1.99977i
$359$		0			0		0.939179	−	0.343428i	$-0.111588\pi$
$359$		0			0		−0.939179	+	0.343428i	$0.888412\pi$
$360$		0			0
$361$	−0.692932	−	0.113104i	−0.692932	−	0.113104i
$362$		0			0
$363$	4.17725	−	1.92318i	4.17725	−	1.92318i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.374884	−	0.927072i	$-0.622318\pi$
$367$		0			0		0.374884	+	0.927072i	$0.377682\pi$
$368$		0			0
$369$	−3.72963	+	3.41629i	−3.72963	+	3.41629i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.311581	−	0.950220i	$-0.399142\pi$
$373$		0			0		−0.311581	+	0.950220i	$0.600858\pi$
$374$	−0.426443	+	0.369973i	−0.426443	+	0.369973i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.279764	+	0.229794i	0.279764	+	0.229794i	0.764115	−	0.645080i	$-0.223176\pi$
$379$	0.279764	+	0.229794i	0.279764	+	0.229794i	−0.484351	+	0.874874i	$0.660944\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.272900	−	0.962042i	$-0.587983\pi$
$383$		0			0		0.272900	+	0.962042i	$0.412017\pi$
$384$	1.02022	−	1.67878i	1.02022	−	1.67878i
$385$		0			0
$386$	0.534398	+	0.489501i	0.534398	+	0.489501i
$387$	1.89526	−	4.34589i	1.89526	−	4.34589i
$388$	−0.644984	−	1.28507i	−0.644984	−	1.28507i
$389$		0			0		−0.789576	−	0.613653i	$-0.789700\pi$
$389$		0			0		0.789576	+	0.613653i	$0.210300\pi$
$390$		0			0
$391$		0			0
$392$	0.650217	−	0.759749i	0.650217	−	0.759749i
$393$	−0.497989	+	0.771762i	−0.497989	+	0.771762i
$394$		0			0
$395$		0			0
$396$	2.28108	+	4.70192i	2.28108	+	4.70192i
$397$		0			0		−0.507764	−	0.861496i	$-0.669528\pi$
$397$		0			0		0.507764	+	0.861496i	$0.330472\pi$
$398$		0			0
$399$		0			0
$400$	−0.484351	−	0.874874i	−0.484351	−	0.874874i
$401$	0.413097	−	1.94777i	0.413097	−	1.94777i	0.114357	−	0.993440i	$-0.463519\pi$
$401$	0.413097	−	1.94777i	0.413097	−	1.94777i	0.298741	−	0.954334i	$-0.403433\pi$
$402$	3.48135	+	1.49038i	3.48135	+	1.49038i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.406820	−	0.450190i	−0.406820	−	0.450190i
$409$	−1.71665	+	0.762454i	−1.71665	+	0.762454i	−0.718923	+	0.695089i	$0.755365\pi$
$409$	−1.71665	+	0.762454i	−1.71665	+	0.762454i	−0.997728	+	0.0673651i	$0.978541\pi$
$410$		0			0
$411$	−0.198372	+	0.737022i	−0.198372	+	0.737022i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.22177	+	1.08054i	−3.22177	+	1.08054i
$418$	−0.628000	−	0.775159i	−0.628000	−	0.775159i
$419$	0.633454	+	0.564719i	0.633454	+	0.564719i	0.919301	−	0.393556i	$-0.128755\pi$
$419$	0.633454	+	0.564719i	0.633454	+	0.564719i	−0.285846	+	0.958275i	$0.592275\pi$
$420$		0			0
$421$		0			0		0.989021	−	0.147772i	$-0.0472103\pi$
$421$		0			0		−0.989021	+	0.147772i	$0.952790\pi$
$422$	0.515285	+	0.847911i	0.515285	+	0.847911i
$423$		0			0
$424$		0			0
$425$	−0.301713	+	0.0661181i	−0.301713	+	0.0661181i
$426$		0			0
$427$		0			0
$428$	1.06435	−	1.21022i	1.06435	−	1.21022i
$429$		0			0
$430$		0			0
$431$		0			0		0.246861	−	0.969051i	$-0.420601\pi$
$431$		0			0		−0.246861	+	0.969051i	$0.579399\pi$
$432$	−3.25307	+	1.66029i	−3.25307	+	1.66029i
$433$	1.47467	−	0.0198846i	1.47467	−	0.0198846i	0.728230	−	0.685333i	$-0.240343\pi$
$433$	1.47467	−	0.0198846i	1.47467	−	0.0198846i	0.746444	+	0.665448i	$0.231760\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.230506	+	0.617431i	0.230506	+	0.617431i
$439$		0			0		−0.948098	−	0.317979i	$-0.896996\pi$
$439$		0			0		0.948098	+	0.317979i	$0.103004\pi$
$440$		0			0
$441$	−2.72277	+	0.872521i	−2.72277	+	0.872521i
$442$		0			0
$443$	−0.294397	+	0.292419i	−0.294397	+	0.292419i	−0.836584	−	0.547839i	$-0.815451\pi$
$443$	−0.294397	+	0.292419i	−0.294397	+	0.292419i	0.542187	+	0.840258i	$0.317597\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.831328	+	0.266402i	0.831328	+	0.266402i	0.690227	−	0.723593i	$-0.257511\pi$
$449$	0.831328	+	0.266402i	0.831328	+	0.266402i	0.141101	+	0.989995i	$0.454936\pi$
$450$	−0.134877	+	2.85597i	−0.134877	+	2.85597i
$451$	−3.13862	+	0.777054i	−3.13862	+	0.777054i
$452$	−1.77881	−	0.0960296i	−1.77881	−	0.0960296i
$453$		0			0
$454$	−0.477609	−	1.87485i	−0.477609	−	1.87485i
$455$		0			0
$456$	0.819292	−	0.691661i	0.819292	−	0.691661i
$457$	−0.803171	−	0.541571i	−0.803171	−	0.541571i	0.0875288	−	0.996162i	$-0.472103\pi$
$457$	−0.803171	−	0.541571i	−0.803171	−	0.541571i	−0.890700	+	0.454591i	$0.849785\pi$
$458$		0			0
$459$	0.204206	+	1.10945i	0.204206	+	1.10945i
$460$		0			0
$461$		0			0		0.789576	−	0.613653i	$-0.210300\pi$
$461$		0			0		−0.789576	+	0.613653i	$0.789700\pi$
$462$		0			0
$463$		0			0		0.992646	−	0.121051i	$-0.0386266\pi$
$463$		0			0		−0.992646	+	0.121051i	$0.961373\pi$
$464$		0			0
$465$		0			0
$466$	1.62749			1.62749
$467$	−0.999909	+	0.0134828i	−0.999909	+	0.0134828i
$467$	−0.999909	+	0.0134828i	−0.999909	+	0.0134828i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.20559	−	1.57298i	1.20559	−	1.57298i
$473$	2.39318	−	1.85996i	2.39318	−	1.85996i
$474$		0			0
$475$	−0.0988008	−	0.536783i	−0.0988008	−	0.536783i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.660401	−	0.750913i	$-0.729614\pi$
$479$		0			0		0.660401	+	0.750913i	$0.270386\pi$
$480$		0			0
$481$		0			0
$482$	1.97101	+	0.106405i	1.97101	+	0.106405i
$483$		0			0
$484$	−0.110431	+	2.33832i	−0.110431	+	2.33832i
$485$		0			0
$486$	4.80987	+	0.389966i	4.80987	+	0.389966i
$487$		0			0		0.507764	−	0.861496i	$-0.330472\pi$
$487$		0			0		−0.507764	+	0.861496i	$0.669528\pi$
$488$		0			0
$489$	−1.24905	−	1.30943i	−1.24905	−	1.30943i
$490$		0			0
$491$	1.37739	−	1.36813i	1.37739	−	1.36813i	0.519333	−	0.854572i	$-0.326180\pi$
$491$	1.37739	−	1.36813i	1.37739	−	1.36813i	0.858053	−	0.513561i	$-0.171674\pi$
$492$	−0.903197	−	3.35569i	−0.903197	−	3.35569i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.134225	+	1.16604i	0.134225	+	1.16604i
$499$	0.238840	+	0.762981i	0.238840	+	0.762981i	0.994188	+	0.107657i	$0.0343348\pi$
$499$	0.238840	+	0.762981i	0.238840	+	0.762981i	−0.755348	+	0.655324i	$0.772532\pi$
$500$		0			0
$501$		0			0
$502$	−1.52854	+	0.780127i	−1.52854	+	0.780127i
$503$		0			0		0.246861	−	0.969051i	$-0.420601\pi$
$503$		0			0		−0.246861	+	0.969051i	$0.579399\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.74976	−	0.893032i	−1.74976	−	0.893032i
$508$		0			0
$509$		0			0		0.976820	−	0.214062i	$-0.0686695\pi$
$509$		0			0		−0.976820	+	0.214062i	$0.931330\pi$
$510$		0			0
$511$		0			0
$512$	0.519333	+	0.854572i	0.519333	+	0.854572i
$513$	−1.97152	+	0.294570i	−1.97152	+	0.294570i
$514$	−1.71883	−	0.681606i	−1.71883	−	0.681606i
$515$		0			0
$516$	2.05063	+	2.53115i	2.05063	+	2.53115i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.441771	+	1.48100i	0.441771	+	1.48100i	0.829121	+	0.559069i	$0.188841\pi$
$521$	0.441771	+	1.48100i	0.441771	+	1.48100i	−0.387350	+	0.921933i	$0.626609\pi$
$522$		0			0
$523$	0.392636	−	1.45878i	0.392636	−	1.45878i	−0.436485	−	0.899712i	$-0.643777\pi$
$523$	0.392636	−	1.45878i	0.392636	−	1.45878i	0.829121	−	0.559069i	$-0.188841\pi$
$524$	−0.231951	−	0.405953i	−0.231951	−	0.405953i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−3.58940	−	0.0968169i	−3.58940	−	0.0968169i
$529$	−0.984677	+	0.174386i	−0.984677	+	0.174386i
$530$		0			0
$531$	−5.29505	+	2.01758i	−5.29505	+	2.01758i
$532$		0			0
$533$		0			0
$534$	0.243089	+	0.439087i	0.243089	+	0.439087i
$535$		0			0
$536$	−1.48963	+	1.22356i	−1.48963	+	1.22356i
$537$	1.99480	+	3.38446i	1.99480	+	3.38446i
$538$		0			0
$539$	−1.79535	−	0.342984i	−1.79535	−	0.342984i
$540$		0			0
$541$		0			0		0.542187	−	0.840258i	$-0.317597\pi$
$541$		0			0		−0.542187	+	0.840258i	$0.682403\pi$
$542$		0			0
$543$		0			0
$544$	0.298793	−	0.0782649i	0.298793	−	0.0782649i
$545$		0			0
$546$		0			0
$547$	0.00538981	−	0.0123590i	0.00538981	−	0.0123590i	−0.913911	−	0.405915i	$-0.866953\pi$
$547$	0.00538981	−	0.0123590i	0.00538981	−	0.0123590i	0.919301	+	0.393556i	$0.128755\pi$
$548$	−0.286502	−	0.262432i	−0.286502	−	0.262432i
$549$		0			0
$550$	−0.949249	+	1.56200i	−0.949249	+	1.56200i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.267144	−	1.70905i	0.267144	−	1.70905i
$557$		0			0		0.821508	−	0.570197i	$-0.193133\pi$
$557$		0			0		−0.821508	+	0.570197i	$0.806867\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.345565	+	1.05386i	−0.345565	+	1.05386i
$562$	−1.17750	+	1.30302i	−1.17750	+	1.30302i
$563$	0.817526	−	1.03739i	0.817526	−	1.03739i	−0.181020	−	0.983479i	$-0.557940\pi$
$563$	0.817526	−	1.03739i	0.817526	−	1.03739i	0.998546	−	0.0539068i	$-0.0171674\pi$
$564$		0			0
$565$		0			0
$566$	0.495703	+	1.44560i	0.495703	+	1.44560i
$567$		0			0
$568$		0			0
$569$	−1.00359	−	1.42530i	−1.00359	−	1.42530i	−0.902634	−	0.430410i	$-0.858369\pi$
$569$	−1.00359	−	1.42530i	−1.00359	−	1.42530i	−0.100952	−	0.994891i	$-0.532189\pi$
$570$		0			0
$571$	1.02580	−	0.472270i	1.02580	−	0.472270i	0.167744	−	0.985831i	$-0.446352\pi$
$571$	1.02580	−	0.472270i	1.02580	−	0.472270i	0.858053	+	0.513561i	$0.171674\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0192752	−	2.85909i	0.0192752	−	2.85909i
$577$	−1.46624	+	0.158773i	−1.46624	+	0.158773i	−0.805835	−	0.592140i	$-0.798283\pi$
$577$	−1.46624	+	0.158773i	−1.46624	+	0.158773i	−0.660401	+	0.750913i	$0.729614\pi$
$578$	−0.0304865	+	0.904084i	−0.0304865	+	0.904084i
$579$	1.39464	+	0.285973i	1.39464	+	0.285973i
$580$		0			0
$581$		0			0
$582$	−2.38367	−	1.51543i	−2.38367	−	1.51543i
$583$		0			0
$584$	−0.333020	−	0.0406112i	−0.333020	−	0.0406112i
$585$		0			0
$586$		0			0
$587$	0.254344	+	1.97479i	0.254344	+	1.97479i	0.220643	+	0.975355i	$0.429185\pi$
$587$	0.254344	+	1.97479i	0.254344	+	1.97479i	0.0337017	+	0.999432i	$0.489270\pi$
$588$	0.329528	−	1.93664i	0.329528	−	1.93664i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.42677	−	1.34273i	−1.42677	−	1.34273i	−0.851051	−	0.525083i	$-0.824034\pi$
$593$	−1.42677	−	1.34273i	−1.42677	−	1.34273i	−0.575722	−	0.817645i	$-0.695279\pi$
$594$	5.58477	+	3.65720i	5.58477	+	3.65720i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.989021	−	0.147772i	$-0.952790\pi$
$599$		0			0		0.989021	+	0.147772i	$0.0472103\pi$
$600$	−1.69907	−	0.986057i	−1.69907	−	0.986057i
$601$	−0.125048	+	0.0794998i	−0.125048	+	0.0794998i	−0.597559	−	0.801825i	$-0.703863\pi$
$601$	−0.125048	+	0.0794998i	−0.125048	+	0.0794998i	0.472511	+	0.881325i	$0.343348\pi$
$602$		0			0
$603$	5.46163	−	0.740899i	5.46163	−	0.740899i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.829121	−	0.559069i	$-0.188841\pi$
$607$		0			0		−0.829121	+	0.559069i	$0.811159\pi$
$608$	0.120427	+	0.532349i	0.120427	+	0.532349i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.844548	−	0.258135i	−0.844548	−	0.258135i
$613$		0			0		−0.970693	−	0.240323i	$-0.922747\pi$
$613$		0			0		0.970693	+	0.240323i	$0.0772532\pi$
$614$	−0.571485	+	1.91585i	−0.571485	+	1.91585i
$615$		0			0
$616$		0			0
$617$	−1.50577	−	1.13804i	−1.50577	−	1.13804i	−0.952299	−	0.305167i	$-0.901288\pi$
$617$	−1.50577	−	1.13804i	−1.50577	−	1.13804i	−0.553466	−	0.832871i	$-0.686695\pi$
$618$		0			0
$619$	−0.150710	−	1.48526i	−0.150710	−	1.48526i	−0.737404	−	0.675452i	$-0.763948\pi$
$619$	−0.150710	−	1.48526i	−0.150710	−	1.48526i	0.586694	−	0.809809i	$-0.300429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.864900	+	0.501945i	−0.864900	+	0.501945i
$626$	−1.11096	+	0.440552i	−1.11096	+	0.440552i
$627$	−1.84061	−	0.673052i	−1.84061	−	0.673052i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.943724	−	0.330734i	$-0.892704\pi$
$631$		0			0		0.943724	+	0.330734i	$0.107296\pi$
$632$		0			0
$633$	1.72401	+	0.909398i	1.72401	+	0.909398i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.17484	−	0.724853i	−1.17484	−	0.724853i	−0.207472	−	0.978241i	$-0.566524\pi$
$641$	−1.17484	−	0.724853i	−1.17484	−	0.724853i	−0.967365	+	0.253388i	$0.918455\pi$
$642$	0.573125	−	3.11378i	0.573125	−	3.11378i
$643$	1.14619	−	1.58207i	1.14619	−	1.58207i	0.399745	−	0.916626i	$-0.369099\pi$
$643$	1.14619	−	1.58207i	1.14619	−	1.58207i	0.746444	−	0.665448i	$-0.231760\pi$
$644$		0			0
$645$		0			0
$646$	0.168200	+	0.0113566i	0.168200	+	0.0113566i
$647$		0			0		−0.618962	−	0.785421i	$-0.712446\pi$
$647$		0			0		0.618962	+	0.785421i	$0.287554\pi$
$648$	−2.29076	+	3.65745i	−2.29076	+	3.65745i
$649$	−3.58959	−	0.486947i	−3.58959	−	0.486947i
$650$		0			0
$651$		0			0
$652$	0.884491	−	0.257356i	0.884491	−	0.257356i
$653$		0			0		−0.699920	−	0.714221i	$-0.746781\pi$
$653$		0			0		0.699920	+	0.714221i	$0.253219\pi$
$654$		0			0
$655$		0			0
$656$	1.72798	+	0.378672i	1.72798	+	0.378672i
$657$	0.749364	+	0.598780i	0.749364	+	0.598780i
$658$		0			0
$659$	0.677033	+	0.469919i	0.677033	+	0.469919i	0.858053	−	0.513561i	$-0.171674\pi$
$659$	0.677033	+	0.469919i	0.677033	+	0.469919i	−0.181020	+	0.983479i	$0.557940\pi$
$660$		0			0
$661$		0			0		0.919301	−	0.393556i	$-0.128755\pi$
$661$		0			0		−0.919301	+	0.393556i	$0.871245\pi$
$662$	−0.150496	−	0.759941i	−0.150496	−	0.759941i
$663$		0			0
$664$	−0.558324	−	0.212739i	−0.558324	−	0.212739i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.86876	+	0.0251984i	1.86876	+	0.0251984i	0.939179	−	0.343428i	$-0.111588\pi$
$673$	1.86876	+	0.0251984i	1.86876	+	0.0251984i	0.929578	+	0.368626i	$0.120172\pi$
$674$	1.79451	+	0.522140i	1.79451	+	0.522140i
$675$	1.72573	+	3.21883i	1.72573	+	3.21883i
$676$	0.813746	−	0.581221i	0.813746	−	0.581221i
$677$		0			0		0.424315	−	0.905515i	$-0.360515\pi$
$677$		0			0		−0.424315	+	0.905515i	$0.639485\pi$
$678$	−3.09529	+	1.63273i	−3.09529	+	1.63273i
$679$		0			0
$680$		0			0
$681$	−2.69656	−	2.67844i	−2.69656	−	2.67844i
$682$		0			0
$683$	−0.631258	−	1.44749i	−0.631258	−	1.44749i	−0.878119	−	0.478442i	$-0.841202\pi$
$683$	−0.631258	−	1.44749i	−0.631258	−	1.44749i	0.246861	−	0.969051i	$-0.420601\pi$
$684$	0.506179	−	1.47615i	0.506179	−	1.47615i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.62444	+	0.333095i	−1.62444	+	0.333095i
$689$		0			0
$690$		0			0
$691$	0.0915364	−	0.642237i	0.0915364	−	0.642237i	−0.890700	−	0.454591i	$-0.849785\pi$
$691$	0.0915364	−	0.642237i	0.0915364	−	0.642237i	0.982237	−	0.187646i	$-0.0600858\pi$
$692$		0			0
$693$		0			0
$694$	0.484952	−	0.0926451i	0.484952	−	0.0926451i
$695$		0			0
$696$		0			0
$697$	0.264645	−	0.478023i	0.264645	−	0.478023i
$698$		0			0
$699$	2.74334	−	1.64194i	2.74334	−	1.64194i
$700$		0			0
$701$		0			0		0.0606373	−	0.998160i	$-0.480687\pi$
$701$		0			0		−0.0606373	+	0.998160i	$0.519313\pi$
$702$		0			0
$703$		0			0
$704$	0.885307	−	1.59911i	0.885307	−	1.59911i
$705$		0			0
$706$	−0.752321	−	1.00949i	−0.752321	−	1.00949i
$707$		0			0
$708$	0.445224	−	3.86775i	0.445224	−	3.86775i
$709$		0			0		−0.994188	−	0.107657i	$-0.965665\pi$
$709$		0			0		0.994188	+	0.107657i	$0.0343348\pi$
$710$		0			0
$711$		0			0
$712$	−0.255389	+	0.00688859i	−0.255389	+	0.00688859i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.99691	+	0.107804i	−1.99691	+	0.107804i
$717$		0			0
$718$		0			0
$719$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$719$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$720$		0			0
$721$		0			0
$722$	0.0708786	−	0.698515i	0.0708786	−	0.698515i
$723$	3.42973	−	1.80914i	3.42973	−	1.80914i
$724$		0			0
$725$		0			0
$726$	2.17294	+	4.05294i	2.17294	+	4.05294i
$727$		0			0		−0.960181	−	0.279380i	$-0.909871\pi$
$727$		0			0		0.960181	+	0.279380i	$0.0901288\pi$
$728$		0			0
$729$	4.63103	−	2.28539i	4.63103	−	2.28539i
$730$		0			0
$731$	−0.0448311	+	0.510221i	−0.0448311	+	0.510221i
$732$		0			0
$733$		0			0		0.448576	−	0.893745i	$-0.351931\pi$
$733$		0			0		−0.448576	+	0.893745i	$0.648069\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.29261	+	1.25458i	3.29261	+	1.25458i
$738$	−3.63616	−	3.51562i	−3.63616	−	3.51562i
$739$	−0.387645	−	1.95744i	−0.387645	−	1.95744i	−0.259904	−	0.965634i	$-0.583691\pi$
$739$	−0.387645	−	1.95744i	−0.387645	−	1.95744i	−0.127741	−	0.991808i	$-0.540773\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.690227	−	0.723593i	$-0.257511\pi$
$743$		0			0		−0.690227	+	0.723593i	$0.742489\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.03918	+	1.35586i	1.03918	+	1.35586i
$748$	−0.395150	−	0.403224i	−0.395150	−	0.403224i
$749$		0			0
$750$		0			0
$751$		0			0		−0.542187	−	0.840258i	$-0.682403\pi$
$751$		0			0		0.542187	+	0.840258i	$0.317597\pi$
$752$		0			0
$753$	−1.78949	+	2.85710i	−1.78949	+	2.85710i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.233773	−	0.972291i	$-0.424893\pi$
$757$		0			0		−0.233773	+	0.972291i	$0.575107\pi$
$758$	−0.212407	+	0.293183i	−0.212407	+	0.293183i
$759$		0			0
$760$		0			0
$761$	1.12133	+	0.261623i	1.12133	+	0.261623i	0.746444	−	0.665448i	$-0.231760\pi$
$761$	1.12133	+	0.261623i	1.12133	+	0.261623i	0.374884	+	0.927072i	$0.377682\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.73756	+	0.916543i	1.73756	+	0.916543i
$769$	−0.618039	+	0.467106i	−0.618039	+	0.467106i	−0.864900	−	0.501945i	$-0.832618\pi$
$769$	−0.618039	+	0.467106i	−0.618039	+	0.467106i	0.246861	+	0.969051i	$0.420601\pi$
$770$		0			0
$771$	−3.58496	+	0.585157i	−3.58496	+	0.585157i
$772$	−0.456196	+	0.563096i	−0.456196	+	0.563096i
$773$		0			0		0.349751	−	0.936843i	$-0.386266\pi$
$773$		0			0		−0.349751	+	0.936843i	$0.613734\pi$
$774$	4.45281	+	1.62825i	4.45281	+	1.62825i
$775$		0			0
$776$	1.24359	−	0.721720i	1.24359	−	0.721720i
$777$		0			0
$778$		0			0
$779$	0.828459	+	0.495848i	0.828459	+	0.495848i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.797778	+	0.602951i	0.797778	+	0.602951i
$785$		0			0
$786$	−0.800539	−	0.450275i	−0.800539	−	0.450275i
$787$	0.0423566	−	0.141997i	0.0423566	−	0.141997i	−0.934463	−	0.356059i	$-0.884120\pi$
$787$	0.0423566	−	0.141997i	0.0423566	−	0.141997i	0.976820	+	0.214062i	$0.0686695\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−4.55494	+	2.56200i	−4.55494	+	2.56200i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.650217	−	0.759749i	$-0.725322\pi$
$797$		0			0		0.650217	+	0.759749i	$0.274678\pi$
$798$		0			0
$799$		0			0
$800$	0.843894	−	0.536510i	0.843894	−	0.536510i
$801$	0.631776	+	0.366651i	0.631776	+	0.366651i
$802$	1.96924	+	0.294229i	1.96924	+	0.294229i
$803$	0.237527	+	0.565339i	0.237527	+	0.565339i
$804$	−1.27654	+	3.56532i	−1.27654	+	3.56532i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.83545	+	0.756646i	1.83545	+	0.756646i	0.963860	+	0.266408i	$0.0858369\pi$
$809$	1.83545	+	0.756646i	1.83545	+	0.756646i	0.871589	+	0.490238i	$0.163090\pi$
$810$		0			0
$811$	0.245965	+	1.72574i	0.245965	+	1.72574i	0.608316	+	0.793695i	$0.291845\pi$
$811$	0.245965	+	1.72574i	0.245965	+	1.72574i	−0.362351	+	0.932042i	$0.618026\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.424693	−	0.433370i	0.424693	−	0.433370i
$817$	−0.898413	−	0.109560i	−0.898413	−	0.109560i
$818$	−0.865145	−	1.66726i	−0.865145	−	1.66726i
$819$		0			0
$820$		0			0
$821$		0			0		−0.984677	−	0.174386i	$-0.944206\pi$
$821$		0			0		0.984677	+	0.174386i	$0.0557940\pi$
$822$	−0.747695	−	0.153316i	−0.747695	−	0.153316i
$823$		0			0		0.0337017	−	0.999432i	$-0.489270\pi$
$823$		0			0		−0.0337017	+	0.999432i	$0.510730\pi$
$824$		0			0
$825$	−0.0242070	+	3.59062i	−0.0242070	+	3.59062i
$826$		0			0
$827$	−1.46246	+	1.30377i	−1.46246	+	1.30377i	−0.597559	+	0.801825i	$0.703863\pi$
$827$	−1.46246	+	1.30377i	−1.46246	+	1.30377i	−0.864900	+	0.501945i	$0.832618\pi$
$828$		0			0
$829$		0			0		−0.878119	−	0.478442i	$-0.841202\pi$
$829$		0			0		0.878119	+	0.478442i	$0.158798\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.248901	−	0.182896i	0.248901	−	0.182896i
$834$	−1.27391	−	3.15032i	−1.27391	−	3.15032i
$835$		0			0
$836$	0.735653	−	0.673848i	0.735653	−	0.673848i
$837$		0			0
$838$	−0.525269	+	0.666532i	−0.525269	+	0.666532i
$839$		0			0		0.670466	−	0.741941i	$-0.266094\pi$
$839$		0			0		−0.670466	+	0.741941i	$0.733906\pi$
$840$		0			0
$841$	−0.755348	+	0.655324i	−0.755348	+	0.655324i
$842$		0			0
$843$	−0.670226	+	3.38436i	−0.670226	+	3.38436i
$844$	−0.815105	+	0.565752i	−0.815105	+	0.565752i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.29400	+	1.93664i	2.29400	+	1.93664i
$850$	−0.0842915	−	0.297149i	−0.0842915	−	0.297149i
$851$		0			0
$852$		0			0
$853$		0			0		−0.737404	−	0.675452i	$-0.763948\pi$
$853$		0			0		0.737404	+	0.675452i	$0.236052\pi$
$854$		0			0
$855$		0			0
$856$	1.27254	+	0.989006i	1.27254	+	0.989006i
$857$	1.02697	−	0.269001i	1.02697	−	0.269001i	0.298741	−	0.954334i	$-0.403433\pi$
$857$	1.02697	−	0.269001i	1.02697	−	0.269001i	0.728230	+	0.685333i	$0.240343\pi$
$858$		0			0
$859$	0.970700	−	1.13422i	0.970700	−	1.13422i	−0.0202235	−	0.999795i	$-0.506438\pi$
$859$	0.970700	−	1.13422i	0.970700	−	1.13422i	0.990924	−	0.134424i	$-0.0429185\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.436485	−	0.899712i	$-0.643777\pi$
$863$		0			0		0.436485	+	0.899712i	$0.356223\pi$
$864$	−1.85449	−	3.14641i	−1.85449	−	3.14641i
$865$		0			0
$866$	0.109268	+	1.47075i	0.109268	+	1.47075i
$867$	0.860719	+	1.55470i	0.860719	+	1.55470i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−4.10953	−	0.110846i	−4.10953	−	0.110846i
$874$		0			0
$875$		0			0
$876$	−0.602318	+	0.267521i	−0.602318	+	0.267521i
$877$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$877$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.378646	−	1.67381i	0.378646	−	1.67381i	−0.311581	−	0.950220i	$-0.600858\pi$
$881$	0.378646	−	1.67381i	0.378646	−	1.67381i	0.690227	−	0.723593i	$-0.257511\pi$
$882$	−1.03602	−	2.66485i	−1.03602	−	2.66485i
$883$	−0.103211	+	0.0636792i	−0.103211	+	0.0636792i	−0.575722	−	0.817645i	$-0.695279\pi$
$883$	−0.103211	+	0.0636792i	−0.103211	+	0.0636792i	0.472511	+	0.881325i	$0.343348\pi$
$884$		0			0
$885$		0			0
$886$	−0.309732	−	0.276124i	−0.309732	−	0.276124i
$887$		0			0		−0.929578	−	0.368626i	$-0.879828\pi$
$887$		0			0		0.929578	+	0.368626i	$0.120172\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.88172	+	0.318987i	7.88172	+	0.318987i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.215502	+	0.845952i	−0.215502	+	0.845952i
$899$		0			0
$900$	−2.85890	+	0.0385495i	−2.85890	+	0.0385495i
$901$		0			0
$902$	−0.965942	−	3.08573i	−0.965942	−	3.08573i
$903$		0			0
$904$	−0.0120094	−	1.78136i	−0.0120094	−	1.78136i
$905$		0			0
$906$		0			0
$907$	−1.14270	+	0.266609i	−1.14270	+	0.266609i	−0.755348	−	0.655324i	$-0.772532\pi$
$907$	−1.14270	+	0.266609i	−1.14270	+	0.266609i	−0.387350	+	0.921933i	$0.626609\pi$
$908$	1.84244	−	0.590416i	1.84244	−	0.590416i
$909$		0			0
$910$		0			0
$911$		0			0		−0.0875288	−	0.996162i	$-0.527897\pi$
$911$		0			0		0.0875288	+	0.996162i	$0.472103\pi$
$912$	0.740068	+	0.775844i	0.740068	+	0.775844i
$913$	0.168658	+	1.07899i	0.168658	+	1.07899i
$914$	0.491872	−	0.834533i	0.491872	−	0.834533i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.09502	+	0.271104i	−1.09502	+	0.271104i
$919$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$919$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$920$		0			0
$921$	0.969551	+	3.80597i	0.969551	+	3.80597i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.18098	−	1.54087i	1.18098	−	1.54087i	0.399745	−	0.916626i	$-0.369099\pi$
$929$	1.18098	−	1.54087i	1.18098	−	1.54087i	0.781231	−	0.624242i	$-0.214592\pi$
$930$		0			0
$931$	0.308184	+	0.450467i	0.308184	+	0.450467i
$932$	0.0986867	+	1.62450i	0.0986867	+	1.62450i
$933$		0			0
$934$	−0.0740898	−	0.997252i	−0.0740898	−	0.997252i
$935$		0			0
$936$		0			0
$937$	−0.0532729	−	0.0778682i	−0.0532729	−	0.0778682i	0.797778	−	0.602951i	$-0.206009\pi$
$937$	−0.0532729	−	0.0778682i	−0.0532729	−	0.0778682i	−0.851051	+	0.525083i	$0.824034\pi$
$938$		0			0
$939$	−1.42819	+	1.86342i	−1.42819	+	1.86342i
$940$		0			0
$941$		0			0		−0.902634	−	0.430410i	$-0.858369\pi$
$941$		0			0		0.902634	+	0.430410i	$0.141631\pi$
$942$		0			0
$943$		0			0
$944$	1.64319	+	1.10799i	1.64319	+	1.10799i
$945$		0			0
$946$	2.00166	+	2.27600i	2.00166	+	2.27600i
$947$	−0.486157	−	1.90840i	−0.486157	−	1.90840i	−0.412067	−	0.911153i	$-0.635193\pi$
$947$	−0.486157	−	1.90840i	−0.486157	−	1.90840i	−0.0740898	−	0.997252i	$-0.523605\pi$
$948$		0			0
$949$		0			0
$950$	0.529804	−	0.131168i	0.529804	−	0.131168i
$951$		0			0
$952$		0			0
$953$	0.941932	+	0.0763684i	0.941932	+	0.0763684i	0.542187	−	0.840258i	$-0.317597\pi$
$953$	0.941932	+	0.0763684i	0.941932	+	0.0763684i	0.399745	+	0.916626i	$0.369099\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.973845	+	0.227213i	−0.973845	+	0.227213i
$962$		0			0
$963$	−1.61166	−	4.31699i	−1.61166	−	4.31699i
$964$	0.0133070	+	1.97383i	0.0133070	+	1.97383i
$965$		0			0
$966$		0			0
$967$		0			0		−0.963860	−	0.266408i	$-0.914163\pi$
$967$		0			0		0.963860	+	0.266408i	$0.0858369\pi$
$968$	−2.34072	+	0.0315624i	−2.34072	+	0.0315624i
$969$	0.294979	−	0.150550i	0.294979	−	0.150550i
$970$		0			0
$971$	0.780614	+	0.573607i	0.780614	+	0.573607i	0.908355	−	0.418201i	$-0.137339\pi$
$971$	0.780614	+	0.573607i	0.780614	+	0.573607i	−0.127741	+	0.991808i	$0.540773\pi$
$972$	−0.0975914	+	4.82466i	−0.0975914	+	4.82466i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.75480	+	0.0710199i	1.75480	+	0.0710199i	0.896748	−	0.442541i	$-0.145923\pi$
$977$	1.75480	+	0.0710199i	1.75480	+	0.0710199i	0.858053	+	0.513561i	$0.171674\pi$
$978$	1.23128	−	1.32615i	1.23128	−	1.32615i
$979$	0.242515	+	0.399063i	0.242515	+	0.399063i
$980$		0			0
$981$		0			0
$982$	1.44914	+	1.29189i	1.44914	+	1.29189i
$983$		0			0		−0.629495	−	0.777005i	$-0.716738\pi$
$983$		0			0		0.629495	+	0.777005i	$0.283262\pi$
$984$	3.29475	−	1.10501i	3.29475	−	1.10501i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$991$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$992$		0			0
$993$	−1.02037	−	1.12914i	−1.02037	−	1.12914i
$994$		0			0
$995$		0			0
$996$	−1.15575	+	0.204683i	−1.15575	+	0.204683i
$997$		0			0		0.728230	−	0.685333i	$-0.240343\pi$
$997$		0			0		−0.728230	+	0.685333i	$0.759657\pi$
$998$	−0.747094	+	0.284666i	−0.747094	+	0.284666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.83.1	✓	232
8.3	odd	2	CM	3736.1.l.a.83.1	✓	232
467.422	even	233	inner	3736.1.l.a.3691.1	yes	232
3736.3691	odd	466	inner	3736.1.l.a.3691.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.83.1	✓	232	1.1	even	1	trivial
3736.1.l.a.83.1	✓	232	8.3	odd	2	CM
3736.1.l.a.3691.1	yes	232	467.422	even	233	inner
3736.1.l.a.3691.1	yes	232	3736.3691	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)

\(f(q)\)	\(=\)	\(q+(0.0606373 + 0.998160i) q^{2} +(1.10923 + 1.62135i) q^{3} +(-0.992646 + 0.121051i) q^{4} +(-1.55110 + 1.20550i) q^{6} +(-0.181020 - 0.983479i) q^{8} +(-1.03602 + 2.66485i) q^{9} +O(q^{10})\)	\(q+(0.0606373 + 0.998160i) q^{2} +(1.10923 + 1.62135i) q^{3} +(-0.992646 + 0.121051i) q^{4} +(-1.55110 + 1.20550i) q^{6} +(-0.181020 - 0.983479i) q^{8} +(-1.03602 + 2.66485i) q^{9} +(-1.39667 + 1.17909i) q^{11} +(-1.29734 - 1.47515i) q^{12} +(0.970693 - 0.240323i) q^{16} +(0.0145707 - 0.308529i) q^{17} +(-2.72277 - 0.872521i) q^{18} +(0.544015 + 0.0441067i) q^{19} +(-1.26161 - 1.32260i) q^{22} +(1.39377 - 1.38440i) q^{24} +(-0.259904 - 0.965634i) q^{25} +(-3.55674 + 0.829841i) q^{27} +(0.298741 + 0.954334i) q^{32} +(-3.46094 - 0.956594i) q^{33} +(0.308845 - 0.00416448i) q^{34} +(0.705814 - 2.77067i) q^{36} +(-0.0110380 + 0.545688i) q^{38} +(1.58633 + 0.782846i) q^{41} +(-1.65689 - 0.0670571i) q^{43} +(1.24366 - 1.33949i) q^{44} +(1.46637 + 1.30726i) q^{48} +(0.629495 + 0.777005i) q^{49} +(0.948098 - 0.317979i) q^{50} +(0.516395 - 0.318606i) q^{51} +(-1.04399 - 3.49987i) q^{54} +(0.531926 + 0.930961i) q^{57} +(1.32876 + 1.47041i) q^{59} +(-0.934463 + 0.356059i) q^{64} +(0.744971 - 3.51258i) q^{66} +(-0.933693 - 1.68651i) q^{67} +(0.0228844 + 0.308024i) q^{68} +(2.80837 + 0.536510i) q^{72} +(0.100224 - 0.320167i) q^{73} +(1.27733 - 1.49251i) q^{75} +(-0.545354 + 0.0220714i) q^{76} +(-3.18235 - 2.91499i) q^{81} +(-0.685214 + 1.63088i) q^{82} +(0.310292 - 0.510590i) q^{83} +(-0.0335354 - 1.65790i) q^{86} +(1.41244 + 1.16015i) q^{88} +(0.0394557 - 0.252416i) q^{89} +(-1.21593 + 1.54294i) q^{96} +(0.484681 + 1.35369i) q^{97} +(-0.737404 + 0.675452i) q^{98} +(-1.69513 - 4.94347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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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