LMFDB - Embedded newform 3736.1.l.a.43.1

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			43.1
Root			$0.259904 - 0.965634i$ of defining polynomial
Character	$\chi$	$=$	3736.43
Dual form			3736.1.l.a.2259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.496103 - 0.868264i) q^{2} +(-0.531041 - 1.09462i) q^{3} +(-0.507764 - 0.861496i) q^{4} +(-1.21387 - 0.0819585i) q^{6} +(-0.999909 + 0.0134828i) q^{8} +(-0.297220 + 0.377153i) q^{9} +O(q^{10})$	\(q+(0.496103 - 0.868264i) q^{2} +(-0.531041 - 1.09462i) q^{3} +(-0.507764 - 0.861496i) q^{4} +(-1.21387 - 0.0819585i) q^{6} +(-0.999909 + 0.0134828i) q^{8} +(-0.297220 + 0.377153i) q^{9} +(-0.683855 + 0.502507i) q^{11} +(-0.673365 + 1.01330i) q^{12} +(-0.484351 + 0.874874i) q^{16} +(-1.61487 + 0.376774i) q^{17} +(0.180016 + 0.445172i) q^{18} +(-0.302822 - 1.77969i) q^{19} +(0.0970465 + 0.843062i) q^{22} +(0.545752 + 1.08736i) q^{24} +(-0.154437 + 0.988003i) q^{25} +(-0.617756 - 0.135376i) q^{27} +(0.519333 + 0.854572i) q^{32} +(0.913209 + 0.481708i) q^{33} +(-0.474003 + 1.58905i) q^{34} +(0.475833 + 0.0645493i) q^{36} +(-1.69547 - 0.619979i) q^{38} +(-0.964325 + 0.443969i) q^{41} +(1.50108 + 1.26724i) q^{43} +(0.780146 + 0.333983i) q^{44} +(1.21486 + 0.0655847i) q^{48} +(-0.960181 + 0.279380i) q^{49} +(0.781231 + 0.624242i) q^{50} +(1.26999 + 1.56758i) q^{51} +(-0.424013 + 0.469215i) q^{54} +(-1.78727 + 1.27656i) q^{57} +(-1.24232 - 1.49185i) q^{59} +(0.999636 - 0.0269632i) q^{64} +(0.871295 - 0.553930i) q^{66} +(-1.39674 - 1.08554i) q^{67} +(1.14456 + 1.19989i) q^{68} +(0.292108 - 0.381126i) q^{72} +(0.310292 - 0.510590i) q^{73} +(1.16350 - 0.355621i) q^{75} +(-1.37943 + 1.16454i) q^{76} +(0.292125 + 1.21498i) q^{81} +(-0.0929221 + 1.05754i) q^{82} +(-1.03782 - 0.0420023i) q^{83} +(1.84499 - 0.674654i) q^{86} +(0.677018 - 0.511682i) q^{88} +(-0.642320 - 0.433110i) q^{89} +(0.659641 - 1.02228i) q^{96} +(1.38087 + 0.463124i) q^{97} +(-0.233773 + 0.972291i) q^{98} +(0.0137336 - 0.407273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{155}{233}\right)$

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 $

$2$	0.496103	−	0.868264i	0.496103	−	0.868264i
$2$	0.496103	−	0.868264i	0.496103	−	0.868264i
$3$	−0.531041	−	1.09462i	−0.531041	−	1.09462i	−0.979617	−	0.200872i	$-0.935622\pi$
$3$	−0.531041	−	1.09462i	−0.531041	−	1.09462i	0.448576	−	0.893745i	$-0.351931\pi$
$4$	−0.507764	−	0.861496i	−0.507764	−	0.861496i
$5$		0			0		−0.650217	−	0.759749i	$-0.725322\pi$
$5$		0			0		0.650217	+	0.759749i	$0.274678\pi$
$6$	−1.21387	−	0.0819585i	−1.21387	−	0.0819585i
$7$		0			0		−0.141101	−	0.989995i	$-0.545064\pi$
$7$		0			0		0.141101	+	0.989995i	$0.454936\pi$
$8$	−0.999909	+	0.0134828i	−0.999909	+	0.0134828i
$9$	−0.297220	+	0.377153i	−0.297220	+	0.377153i
$10$		0			0
$11$	−0.683855	+	0.502507i	−0.683855	+	0.502507i	−0.878119	−	0.478442i	$-0.841202\pi$
$11$	−0.683855	+	0.502507i	−0.683855	+	0.502507i	0.194264	+	0.980949i	$0.437768\pi$
$12$	−0.673365	+	1.01330i	−0.673365	+	1.01330i
$13$		0			0		0.990924	−	0.134424i	$-0.0429185\pi$
$13$		0			0		−0.990924	+	0.134424i	$0.957082\pi$
$14$		0			0
$15$		0			0
$16$	−0.484351	+	0.874874i	−0.484351	+	0.874874i
$17$	−1.61487	+	0.376774i	−1.61487	+	0.376774i	−0.934463	−	0.356059i	$-0.884120\pi$
$17$	−1.61487	+	0.376774i	−1.61487	+	0.376774i	−0.680408	+	0.732833i	$0.738197\pi$
$18$	0.180016	+	0.445172i	0.180016	+	0.445172i
$19$	−0.302822	−	1.77969i	−0.302822	−	1.77969i	−0.575722	−	0.817645i	$-0.695279\pi$
$19$	−0.302822	−	1.77969i	−0.302822	−	1.77969i	0.272900	−	0.962042i	$-0.412017\pi$
$20$		0			0
$21$		0			0
$22$	0.0970465	+	0.843062i	0.0970465	+	0.843062i
$23$		0			0		0.890700	−	0.454591i	$-0.150215\pi$
$23$		0			0		−0.890700	+	0.454591i	$0.849785\pi$
$24$	0.545752	+	1.08736i	0.545752	+	1.08736i
$25$	−0.154437	+	0.988003i	−0.154437	+	0.988003i
$26$		0			0
$27$	−0.617756	−	0.135376i	−0.617756	−	0.135376i
$28$		0			0
$29$		0			0		0.575722	−	0.817645i	$-0.304721\pi$
$29$		0			0		−0.575722	+	0.817645i	$0.695279\pi$
$30$		0			0
$31$		0			0		−0.994188	−	0.107657i	$-0.965665\pi$
$31$		0			0		0.994188	+	0.107657i	$0.0343348\pi$
$32$	0.519333	+	0.854572i	0.519333	+	0.854572i
$33$	0.913209	+	0.481708i	0.913209	+	0.481708i
$34$	−0.474003	+	1.58905i	−0.474003	+	1.58905i
$35$		0			0
$36$	0.475833	+	0.0645493i	0.475833	+	0.0645493i
$37$		0			0		−0.871589	−	0.490238i	$-0.836910\pi$
$37$		0			0		0.871589	+	0.490238i	$0.163090\pi$
$38$	−1.69547	−	0.619979i	−1.69547	−	0.619979i
$39$		0			0
$40$		0			0
$41$	−0.964325	+	0.443969i	−0.964325	+	0.443969i	−0.836584	−	0.547839i	$-0.815451\pi$
$41$	−0.964325	+	0.443969i	−0.964325	+	0.443969i	−0.127741	+	0.991808i	$0.540773\pi$
$42$		0			0
$43$	1.50108	+	1.26724i	1.50108	+	1.26724i	0.871589	+	0.490238i	$0.163090\pi$
$43$	1.50108	+	1.26724i	1.50108	+	1.26724i	0.629495	+	0.777005i	$0.283262\pi$
$44$	0.780146	+	0.333983i	0.780146	+	0.333983i
$45$		0			0
$46$		0			0
$47$		0			0		−0.259904	−	0.965634i	$-0.583691\pi$
$47$		0			0		0.259904	+	0.965634i	$0.416309\pi$
$48$	1.21486	+	0.0655847i	1.21486	+	0.0655847i
$49$	−0.960181	+	0.279380i	−0.960181	+	0.279380i
$50$	0.781231	+	0.624242i	0.781231	+	0.624242i
$51$	1.26999	+	1.56758i	1.26999	+	1.56758i
$52$		0			0
$53$		0			0		−0.755348	−	0.655324i	$-0.772532\pi$
$53$		0			0		0.755348	+	0.655324i	$0.227468\pi$
$54$	−0.424013	+	0.469215i	−0.424013	+	0.469215i
$55$		0			0
$56$		0			0
$57$	−1.78727	+	1.27656i	−1.78727	+	1.27656i
$58$		0			0
$59$	−1.24232	−	1.49185i	−1.24232	−	1.49185i	−0.805835	−	0.592140i	$-0.798283\pi$
$59$	−1.24232	−	1.49185i	−1.24232	−	1.49185i	−0.436485	−	0.899712i	$-0.643777\pi$
$60$		0			0
$61$		0			0		0.836584	−	0.547839i	$-0.184549\pi$
$61$		0			0		−0.836584	+	0.547839i	$0.815451\pi$
$62$		0			0
$63$		0			0
$64$	0.999636	−	0.0269632i	0.999636	−	0.0269632i
$65$		0			0
$66$	0.871295	−	0.553930i	0.871295	−	0.553930i
$67$	−1.39674	−	1.08554i	−1.39674	−	1.08554i	−0.984677	−	0.174386i	$-0.944206\pi$
$67$	−1.39674	−	1.08554i	−1.39674	−	1.08554i	−0.412067	−	0.911153i	$-0.635193\pi$
$68$	1.14456	+	1.19989i	1.14456	+	1.19989i
$69$		0			0
$70$		0			0
$71$		0			0		0.878119	−	0.478442i	$-0.158798\pi$
$71$		0			0		−0.878119	+	0.478442i	$0.841202\pi$
$72$	0.292108	−	0.381126i	0.292108	−	0.381126i
$73$	0.310292	−	0.510590i	0.310292	−	0.510590i	−0.660401	−	0.750913i	$-0.729614\pi$
$73$	0.310292	−	0.510590i	0.310292	−	0.510590i	0.970693	+	0.240323i	$0.0772532\pi$
$74$		0			0
$75$	1.16350	−	0.355621i	1.16350	−	0.355621i
$76$	−1.37943	+	1.16454i	−1.37943	+	1.16454i
$77$		0			0
$78$		0			0
$79$		0			0		−0.207472	−	0.978241i	$-0.566524\pi$
$79$		0			0		0.207472	+	0.978241i	$0.433476\pi$
$80$		0			0
$81$	0.292125	+	1.21498i	0.292125	+	1.21498i
$82$	−0.0929221	+	1.05754i	−0.0929221	+	1.05754i
$83$	−1.03782	−	0.0420023i	−1.03782	−	0.0420023i	−0.484351	−	0.874874i	$-0.660944\pi$
$83$	−1.03782	−	0.0420023i	−1.03782	−	0.0420023i	−0.553466	+	0.832871i	$0.686695\pi$
$84$		0			0
$85$		0			0
$86$	1.84499	−	0.674654i	1.84499	−	0.674654i
$87$		0			0
$88$	0.677018	−	0.511682i	0.677018	−	0.511682i
$89$	−0.642320	−	0.433110i	−0.642320	−	0.433110i	0.194264	−	0.980949i	$-0.437768\pi$
$89$	−0.642320	−	0.433110i	−0.642320	−	0.433110i	−0.836584	+	0.547839i	$0.815451\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.659641	−	1.02228i	0.659641	−	1.02228i
$97$	1.38087	+	0.463124i	1.38087	+	0.463124i	0.908355	−	0.418201i	$-0.137339\pi$
$97$	1.38087	+	0.463124i	1.38087	+	0.463124i	0.472511	+	0.881325i	$0.343348\pi$
$98$	−0.233773	+	0.972291i	−0.233773	+	0.972291i
$99$	0.0137336	−	0.407273i	0.0137336	−	0.407273i
$100$	0.929578	−	0.368626i	0.929578	−	0.368626i
$101$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$101$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$102$	1.99112	−	0.325002i	1.99112	−	0.325002i
$103$		0			0		0.690227	−	0.723593i	$-0.257511\pi$
$103$		0			0		−0.690227	+	0.723593i	$0.742489\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.74064	−	0.0939691i	1.74064	−	0.0939691i	0.843894	−	0.536510i	$-0.180258\pi$
$107$	1.74064	−	0.0939691i	1.74064	−	0.0939691i	0.896748	+	0.442541i	$0.145923\pi$
$108$	0.197048	+	0.600933i	0.197048	+	0.600933i
$109$		0			0		0.597559	−	0.801825i	$-0.296137\pi$
$109$		0			0		−0.597559	+	0.801825i	$0.703863\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.774907	−	1.06960i	−0.774907	−	1.06960i	−0.995549	−	0.0942425i	$-0.969957\pi$
$113$	−0.774907	−	1.06960i	−0.774907	−	1.06960i	0.220643	−	0.975355i	$-0.429185\pi$
$114$	0.221725	+	2.18512i	0.221725	+	2.18512i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.91164	+	0.338550i	−1.91164	+	0.338550i
$119$		0			0
$120$		0			0
$121$	−0.0835960	+	0.267049i	−0.0835960	+	0.267049i
$122$		0			0
$123$	0.998072	+	0.819800i	0.998072	+	0.819800i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.100952	−	0.994891i	$-0.467811\pi$
$127$		0			0		−0.100952	+	0.994891i	$0.532189\pi$
$128$	0.472511	−	0.881325i	0.472511	−	0.881325i
$129$	0.590008	−	2.31607i	0.590008	−	2.31607i
$130$		0			0
$131$	−0.0721355	−	0.820972i	−0.0721355	−	0.820972i	−0.943724	−	0.330734i	$-0.892704\pi$
$131$	−0.0721355	−	0.820972i	−0.0721355	−	0.820972i	0.871589	−	0.490238i	$-0.163090\pi$
$132$	−0.0487055	−	1.03132i	−0.0487055	−	1.03132i
$133$		0			0
$134$	−1.63546	+	0.674204i	−1.63546	+	0.674204i
$135$		0			0
$136$	1.60964	−	0.398513i	1.60964	−	0.398513i
$137$	0.521963	+	0.159537i	0.521963	+	0.159537i	0.542187	−	0.840258i	$-0.317597\pi$
$137$	0.521963	+	0.159537i	0.521963	+	0.159537i	−0.0202235	+	0.999795i	$0.506438\pi$
$138$		0			0
$139$	1.71915	−	0.819757i	1.71915	−	0.819757i	0.728230	−	0.685333i	$-0.240343\pi$
$139$	1.71915	−	0.819757i	1.71915	−	0.819757i	0.990924	−	0.134424i	$-0.0429185\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.186002	−	0.442704i	−0.186002	−	0.442704i
$145$		0			0
$146$	−0.289391	−	0.522721i	−0.289391	−	0.522721i
$147$	0.815709	+	0.902668i	0.815709	+	0.902668i
$148$		0			0
$149$		0			0		−0.709486	−	0.704719i	$-0.751073\pi$
$149$		0			0		0.709486	+	0.704719i	$0.248927\pi$
$150$	0.268441	−	1.18665i	0.268441	−	1.18665i
$151$		0			0		0.737404	−	0.675452i	$-0.236052\pi$
$151$		0			0		−0.737404	+	0.675452i	$0.763948\pi$
$152$	0.326790	+	1.77544i	0.326790	+	1.77544i
$153$	0.337871	−	0.721038i	0.337871	−	0.721038i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.996729	−	0.0808112i	$-0.0257511\pi$
$157$		0			0		−0.996729	+	0.0808112i	$0.974249\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	1.19985	+	0.349115i	1.19985	+	0.349115i
$163$	−1.88128	−	0.659304i	−1.88128	−	0.659304i	−0.967365	−	0.253388i	$-0.918455\pi$
$163$	−1.88128	−	0.659304i	−1.88128	−	0.659304i	−0.913911	−	0.405915i	$-0.866953\pi$
$164$	0.872127	+	0.605330i	0.872127	+	0.605330i
$165$		0			0
$166$	−0.551333	+	0.880262i	−0.551333	+	0.880262i
$167$		0			0		−0.737404	−	0.675452i	$-0.763948\pi$
$167$		0			0		0.737404	+	0.675452i	$0.236052\pi$
$168$		0			0
$169$	0.963860	−	0.266408i	0.963860	−	0.266408i
$170$		0			0
$171$	0.761219	+	0.414749i	0.761219	+	0.414749i
$172$	0.329528	−	1.93664i	0.329528	−	1.93664i
$173$		0			0		0.976820	−	0.214062i	$-0.0686695\pi$
$173$		0			0		−0.976820	+	0.214062i	$0.931330\pi$
$174$		0			0
$175$		0			0
$176$	−0.108405	−	0.841677i	−0.108405	−	0.841677i
$177$	−0.973283	+	2.15210i	−0.973283	+	2.15210i
$178$	−0.694711	+	0.342836i	−0.694711	+	0.342836i
$179$	0.567488	+	0.0692042i	0.567488	+	0.0692042i	0.399745	−	0.916626i	$-0.369099\pi$
$179$	0.567488	+	0.0692042i	0.567488	+	0.0692042i	0.167744	+	0.985831i	$0.446352\pi$
$180$		0			0
$181$		0			0		−0.246861	−	0.969051i	$-0.579399\pi$
$181$		0			0		0.246861	+	0.969051i	$0.420601\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.915007	−	1.06914i	0.915007	−	1.06914i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.114357	−	0.993440i	$-0.463519\pi$
$191$		0			0		−0.114357	+	0.993440i	$0.536481\pi$
$192$	−0.560363	−	1.07990i	−0.560363	−	1.07990i
$193$	−0.901493	+	0.848390i	−0.901493	+	0.848390i	−0.989021	−	0.147772i	$-0.952790\pi$
$193$	−0.901493	+	0.848390i	−0.901493	+	0.848390i	0.0875288	+	0.996162i	$0.472103\pi$
$194$	1.08717	−	0.969199i	1.08717	−	0.969199i
$195$		0			0
$196$	0.728230	+	0.685333i	0.728230	+	0.685333i
$197$		0			0		−0.999636	−	0.0269632i	$-0.991416\pi$
$197$		0			0		0.999636	+	0.0269632i	$0.00858369\pi$
$198$	−0.346807	−	0.213974i	−0.346807	−	0.213974i
$199$		0			0		0.127741	−	0.991808i	$-0.459227\pi$
$199$		0			0		−0.127741	+	0.991808i	$0.540773\pi$
$200$	0.141101	−	0.989995i	0.141101	−	0.989995i
$201$	−0.446521	+	2.10537i	−0.446521	+	2.10537i
$202$		0			0
$203$		0			0
$204$	0.705613	−	1.89005i	0.705613	−	1.89005i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.10139	+	1.06488i	1.10139	+	1.06488i
$210$		0			0
$211$	−0.863886	−	1.37929i	−0.863886	−	1.37929i	−0.924523	−	0.381126i	$-0.875536\pi$
$211$	−0.863886	−	1.37929i	−0.863886	−	1.37929i	0.0606373	−	0.998160i	$-0.480687\pi$
$212$		0			0
$213$		0			0
$214$	0.781948	−	1.55796i	0.781948	−	1.55796i
$215$		0			0
$216$	0.619525	+	0.127035i	0.619525	+	0.127035i
$217$		0			0
$218$		0			0
$219$	−0.723679	−	0.0685062i	−0.723679	−	0.0685062i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.896748	−	0.442541i	$-0.854077\pi$
$223$		0			0		0.896748	+	0.442541i	$0.145923\pi$
$224$		0			0
$225$	−0.326726	−	0.351900i	−0.326726	−	0.351900i
$226$	−1.31313	+	0.142193i	−1.31313	+	0.142193i
$227$	−0.851545	−	1.11105i	−0.851545	−	1.11105i	−0.992646	−	0.121051i	$-0.961373\pi$
$227$	−0.851545	−	1.11105i	−0.851545	−	1.11105i	0.141101	−	0.989995i	$-0.454936\pi$
$228$	2.00726	+	0.891530i	2.00726	+	0.891530i
$229$		0			0		−0.989021	−	0.147772i	$-0.952790\pi$
$229$		0			0		0.989021	+	0.147772i	$0.0472103\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.713320	−	1.24843i	−0.713320	−	1.24843i	−0.960181	−	0.279380i	$-0.909871\pi$
$233$	−0.713320	−	1.24843i	−0.713320	−	1.24843i	0.246861	−	0.969051i	$-0.420601\pi$
$234$		0			0
$235$		0			0
$236$	−0.654418	+	1.82776i	−0.654418	+	1.82776i
$237$		0			0
$238$		0			0
$239$		0			0		−0.913911	−	0.405915i	$-0.866953\pi$
$239$		0			0		0.913911	+	0.405915i	$0.133047\pi$
$240$		0			0
$241$	−1.87648	+	0.203197i	−1.87648	+	0.203197i	−0.973845	−	0.227213i	$-0.927039\pi$
$241$	−1.87648	+	0.203197i	−1.87648	+	0.203197i	−0.902634	+	0.430410i	$0.858369\pi$
$242$	0.190397	+	0.205067i	0.190397	+	0.205067i
$243$	0.686116	−	0.563565i	0.686116	−	0.563565i
$244$		0			0
$245$		0			0
$246$	1.20695	−	0.459885i	1.20695	−	0.459885i
$247$		0			0
$248$		0			0
$249$	0.505148	+	1.15832i	0.505148	+	1.15832i
$250$		0			0
$251$	−1.10627	−	0.226843i	−1.10627	−	0.226843i	−0.387350	−	0.921933i	$-0.626609\pi$
$251$	−1.10627	−	0.226843i	−1.10627	−	0.226843i	−0.718923	+	0.695089i	$0.755365\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.530808	−	0.847492i	−0.530808	−	0.847492i
$257$	−1.20762	+	1.19950i	−1.20762	+	1.19950i	−0.233773	+	0.972291i	$0.575107\pi$
$257$	−1.20762	+	1.19950i	−1.20762	+	1.19950i	−0.973845	+	0.227213i	$0.927039\pi$
$258$	−1.71826	−	1.66129i	−1.71826	−	1.66129i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.748607	−	0.344653i	−0.748607	−	0.344653i
$263$		0			0		0.349751	−	0.936843i	$-0.386266\pi$
$263$		0			0		−0.349751	+	0.936843i	$0.613734\pi$
$264$	−0.919621	−	0.469351i	−0.919621	−	0.469351i
$265$		0			0
$266$		0			0
$267$	−0.132991	+	0.933094i	−0.132991	+	0.933094i
$268$	−0.225971	+	1.75449i	−0.225971	+	1.75449i
$269$		0			0		−0.851051	−	0.525083i	$-0.824034\pi$
$269$		0			0		0.851051	+	0.525083i	$0.175966\pi$
$270$		0			0
$271$		0			0		−0.728230	−	0.685333i	$-0.759657\pi$
$271$		0			0		0.728230	+	0.685333i	$0.240343\pi$
$272$	0.452535	−	1.59530i	0.452535	−	1.59530i
$273$		0			0
$274$	0.397468	−	0.374055i	0.397468	−	0.374055i
$275$	−0.390866	−	0.753257i	−0.390866	−	0.753257i
$276$		0			0
$277$		0			0		−0.349751	−	0.936843i	$-0.613734\pi$
$277$		0			0		0.349751	+	0.936843i	$0.386266\pi$
$278$	0.141111	−	1.89936i	0.141111	−	1.89936i
$279$		0			0
$280$		0			0
$281$	−1.89818	−	0.336167i	−1.89818	−	0.336167i	−0.902634	−	0.430410i	$-0.858369\pi$
$281$	−1.89818	−	0.336167i	−1.89818	−	0.336167i	−0.995549	+	0.0942425i	$0.969957\pi$
$282$		0			0
$283$	−1.42551	+	0.751939i	−1.42551	+	0.751939i	−0.989021	−	0.147772i	$-0.952790\pi$
$283$	−1.42551	+	0.751939i	−1.42551	+	0.751939i	−0.436485	+	0.899712i	$0.643777\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.476660	−	0.0581279i	−0.476660	−	0.0581279i
$289$	1.56910	−	0.774344i	1.56910	−	0.774344i
$290$		0			0
$291$	−0.226353	−	1.75746i	−0.226353	−	1.75746i
$292$	−0.597427	−	0.00805573i	−0.597427	−	0.00805573i
$293$		0			0		0.629495	−	0.777005i	$-0.283262\pi$
$293$		0			0		−0.629495	+	0.777005i	$0.716738\pi$
$294$	1.18843	−	0.260435i	1.18843	−	0.260435i
$295$		0			0
$296$		0			0
$297$	0.490483	−	0.217849i	0.490483	−	0.217849i
$298$		0			0
$299$		0			0
$300$	−0.897149	−	0.821776i	−0.897149	−	0.821776i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.70367	+	0.597062i	1.70367	+	0.597062i
$305$		0			0
$306$	−0.458433	−	0.651070i	−0.458433	−	0.651070i
$307$	0.521326	−	1.58988i	0.521326	−	1.58988i	−0.259904	−	0.965634i	$-0.583691\pi$
$307$	0.521326	−	1.58988i	0.521326	−	1.58988i	0.781231	−	0.624242i	$-0.214592\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$311$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$312$		0			0
$313$	1.76817	−	0.463149i	1.76817	−	0.463149i	0.781231	−	0.624242i	$-0.214592\pi$
$313$	1.76817	−	0.463149i	1.76817	−	0.463149i	0.986939	+	0.161094i	$0.0515021\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.220643	−	0.975355i	$-0.429185\pi$
$317$		0			0		−0.220643	+	0.975355i	$0.570815\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.02721	−	1.85544i	−1.02721	−	1.85544i
$322$		0			0
$323$	1.15956	+	2.75987i	1.15956	+	2.75987i
$324$	0.898372	−	0.868589i	0.898372	−	0.868589i
$325$		0			0
$326$	−1.50576	+	1.30636i	−1.50576	+	1.30636i
$327$		0			0
$328$	0.958251	−	0.456930i	0.958251	−	0.456930i
$329$		0			0
$330$		0			0
$331$	0.169927	−	0.0420703i	0.169927	−	0.0420703i	−0.154437	−	0.988003i	$-0.549356\pi$
$331$	0.169927	−	0.0420703i	0.169927	−	0.0420703i	0.324364	+	0.945932i	$0.394850\pi$
$332$	0.490782	+	0.915403i	0.490782	+	0.915403i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.89551	−	0.635728i	1.89551	−	0.635728i	0.939179	−	0.343428i	$-0.111588\pi$
$337$	1.89551	−	0.635728i	1.89551	−	0.635728i	0.956327	−	0.292300i	$-0.0944206\pi$
$338$	0.246861	−	0.969051i	0.246861	−	0.969051i
$339$	−0.759292	+	1.41623i	−0.759292	+	1.41623i
$340$		0			0
$341$		0			0
$342$	0.737754	−	0.455181i	0.737754	−	0.455181i
$343$		0			0
$344$	−1.51803	−	1.24689i	−1.51803	−	1.24689i
$345$		0			0
$346$		0			0
$347$	−0.767668	+	1.82713i	−0.767668	+	1.82713i	−0.259904	+	0.965634i	$0.583691\pi$
$347$	−0.767668	+	1.82713i	−0.767668	+	1.82713i	−0.507764	+	0.861496i	$0.669528\pi$
$348$		0			0
$349$		0			0		0.984677	−	0.174386i	$-0.0557940\pi$
$349$		0			0		−0.984677	+	0.174386i	$0.944206\pi$
$350$		0			0
$351$		0			0
$352$	−0.784578	−	0.323435i	−0.784578	−	0.323435i
$353$	0.193864	+	1.91055i	0.193864	+	1.91055i	0.374884	+	0.927072i	$0.377682\pi$
$353$	0.193864	+	1.91055i	0.193864	+	1.91055i	−0.181020	+	0.983479i	$0.557940\pi$
$354$	1.38574	+	1.91273i	1.38574	+	1.91273i
$355$		0			0
$356$	−0.0469757	+	0.773274i	−0.0469757	+	0.773274i
$357$		0			0
$358$	0.341620	−	0.458397i	0.341620	−	0.458397i
$359$		0			0		−0.311581	−	0.950220i	$-0.600858\pi$
$359$		0			0		0.311581	+	0.950220i	$0.399142\pi$
$360$		0			0
$361$	−2.13186	+	0.747124i	−2.13186	+	0.747124i
$362$		0			0
$363$	0.336710	−	0.0503087i	0.336710	−	0.0503087i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.929578	−	0.368626i	$-0.120172\pi$
$367$		0			0		−0.929578	+	0.368626i	$0.879828\pi$
$368$		0			0
$369$	0.119173	−	0.495654i	0.119173	−	0.495654i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$373$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$374$	−0.474362	−	1.32487i	−0.474362	−	1.32487i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.59541	+	1.20579i	−1.59541	+	1.20579i	−0.789576	+	0.613653i	$0.789700\pi$
$379$	−1.59541	+	1.20579i	−1.59541	+	1.20579i	−0.805835	+	0.592140i	$0.798283\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.902634	−	0.430410i	$-0.858369\pi$
$383$		0			0		0.902634	+	0.430410i	$0.141631\pi$
$384$	−1.21564	−	0.0491989i	−1.21564	−	0.0491989i
$385$		0			0
$386$	0.289393	+	1.20362i	0.289393	+	1.20362i
$387$	−0.924096	+	0.189488i	−0.924096	+	0.189488i
$388$	−0.302175	−	1.42477i	−0.302175	−	1.42477i
$389$		0			0		0.997728	−	0.0673651i	$-0.0214592\pi$
$389$		0			0		−0.997728	+	0.0673651i	$0.978541\pi$
$390$		0			0
$391$		0			0
$392$	0.956327	−	0.292300i	0.956327	−	0.292300i
$393$	−0.860343	+	0.514931i	−0.860343	+	0.514931i
$394$		0			0
$395$		0			0
$396$	−0.357838	+	0.194967i	−0.357838	+	0.194967i
$397$		0			0		−0.324364	−	0.945932i	$-0.605150\pi$
$397$		0			0		0.324364	+	0.945932i	$0.394850\pi$
$398$		0			0
$399$		0			0
$400$	−0.789576	−	0.613653i	−0.789576	−	0.613653i
$401$	1.51352	−	0.962228i	1.51352	−	0.962228i	0.519333	−	0.854572i	$-0.326180\pi$
$401$	1.51352	−	0.962228i	1.51352	−	0.962228i	0.994188	−	0.107657i	$-0.0343348\pi$
$402$	1.60649	+	1.43218i	1.60649	+	1.43218i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.29101	−	1.55032i	−1.29101	−	1.55032i
$409$	−0.264416	−	0.564282i	−0.264416	−	0.564282i	0.728230	−	0.685333i	$-0.240343\pi$
$409$	−0.264416	−	0.564282i	−0.264416	−	0.564282i	−0.992646	+	0.121051i	$0.961373\pi$
$410$		0			0
$411$	−0.102552	−	0.656071i	−0.102552	−	0.656071i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.81026	−	1.44649i	−1.81026	−	1.44649i
$418$	1.47100	−	0.428010i	1.47100	−	0.428010i
$419$	1.41691	+	0.0764922i	1.41691	+	0.0764922i	0.746444	−	0.665448i	$-0.231760\pi$
$419$	1.41691	+	0.0764922i	1.41691	+	0.0764922i	0.670466	+	0.741941i	$0.266094\pi$
$420$		0			0
$421$		0			0		0.0471738	−	0.998887i	$-0.484979\pi$
$421$		0			0		−0.0471738	+	0.998887i	$0.515021\pi$
$422$	−1.62616	+	0.0658136i	−1.62616	+	0.0658136i
$423$		0			0
$424$		0			0
$425$	−0.122859	−	1.65369i	−0.122859	−	1.65369i
$426$		0			0
$427$		0			0
$428$	−0.964790	−	1.45184i	−0.964790	−	1.45184i
$429$		0			0
$430$		0			0
$431$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$431$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$432$	0.417648	−	0.474889i	0.417648	−	0.474889i
$433$	0.133646	−	0.448038i	0.133646	−	0.448038i	−0.864900	−	0.501945i	$-0.832618\pi$
$433$	0.133646	−	0.448038i	0.133646	−	0.448038i	0.998546	+	0.0539068i	$0.0171674\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.418501	+	0.594358i	−0.418501	+	0.594358i
$439$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$439$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$440$		0			0
$441$	0.180016	−	0.445172i	0.180016	−	0.445172i
$442$		0			0
$443$	0.757101	+	1.50845i	0.757101	+	1.50845i	0.858053	+	0.513561i	$0.171674\pi$
$443$	0.757101	+	1.50845i	0.757101	+	1.50845i	−0.100952	+	0.994891i	$0.532189\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.658386	−	1.62816i	−0.658386	−	1.62816i	−0.772743	−	0.634719i	$-0.781116\pi$
$449$	−0.658386	−	1.62816i	−0.658386	−	1.62816i	0.114357	−	0.993440i	$-0.463519\pi$
$450$	−0.467632	+	0.109106i	−0.467632	+	0.109106i
$451$	0.436361	−	0.788191i	0.436361	−	0.788191i
$452$	−0.527984	+	1.21068i	−0.527984	+	1.21068i
$453$		0			0
$454$	−1.38714	+	0.188172i	−1.38714	+	0.188172i
$455$		0			0
$456$	1.76989	−	1.30054i	1.76989	−	1.30054i
$457$	−1.55110	+	0.296322i	−1.55110	+	0.296322i	−0.890700	−	0.454591i	$-0.849785\pi$
$457$	−1.55110	+	0.296322i	−1.55110	+	0.296322i	−0.660401	+	0.750913i	$0.729614\pi$
$458$		0			0
$459$	1.04860	−	0.0141394i	1.04860	−	0.0141394i
$460$		0			0
$461$		0			0		−0.997728	−	0.0673651i	$-0.978541\pi$
$461$		0			0		0.997728	+	0.0673651i	$0.0214592\pi$
$462$		0			0
$463$		0			0		−0.507764	−	0.861496i	$-0.669528\pi$
$463$		0			0		0.507764	+	0.861496i	$0.330472\pi$
$464$		0			0
$465$		0			0
$466$	−1.43785			−1.43785
$467$	−0.285846	+	0.958275i	−0.285846	+	0.958275i
$467$	−0.285846	+	0.958275i	−0.285846	+	0.958275i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.26232	+	1.47497i	1.26232	+	1.47497i
$473$	−1.66332	−	0.112305i	−1.66332	−	0.112305i
$474$		0			0
$475$	1.80510	−	0.0243401i	1.80510	−	0.0243401i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.553466	−	0.832871i	$-0.313305\pi$
$479$		0			0		−0.553466	+	0.832871i	$0.686695\pi$
$480$		0			0
$481$		0			0
$482$	−0.754498	+	1.73009i	−0.754498	+	1.73009i
$483$		0			0
$484$	0.272509	−	0.0635806i	0.272509	−	0.0635806i
$485$		0			0
$486$	−0.148939	−	0.875316i	−0.148939	−	0.875316i
$487$		0			0		0.324364	−	0.945932i	$-0.394850\pi$
$487$		0			0		−0.324364	+	0.945932i	$0.605150\pi$
$488$		0			0
$489$	0.277350	+	2.40939i	0.277350	+	2.40939i
$490$		0			0
$491$	−0.434536	−	0.865772i	−0.434536	−	0.865772i	−0.999182	−	0.0404387i	$-0.987124\pi$
$491$	−0.434536	−	0.865772i	−0.434536	−	0.865772i	0.564646	−	0.825333i	$-0.309013\pi$
$492$	0.199470	−	1.27610i	0.199470	−	1.27610i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.25633	+	0.136043i	1.25633	+	0.136043i
$499$	−1.01750	−	1.67431i	−1.01750	−	1.67431i	−0.680408	−	0.732833i	$-0.738197\pi$
$499$	−1.01750	−	1.67431i	−1.01750	−	1.67431i	−0.337088	−	0.941473i	$-0.609442\pi$
$500$		0			0
$501$		0			0
$502$	−0.745785	+	0.847999i	−0.745785	+	0.847999i
$503$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$503$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.803465	−	0.913584i	−0.803465	−	0.913584i
$508$		0			0
$509$		0			0		−0.0740898	−	0.997252i	$-0.523605\pi$
$509$		0			0		0.0740898	+	0.997252i	$0.476395\pi$
$510$		0			0
$511$		0			0
$512$	−0.999182	+	0.0404387i	−0.999182	+	0.0404387i
$513$	−0.0538573	+	1.14041i	−0.0538573	+	1.14041i
$514$	0.442384	+	1.64361i	0.442384	+	1.64361i
$515$		0			0
$516$	−2.29487	+	0.667728i	−2.29487	+	0.667728i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.06977	−	1.18381i	1.06977	−	1.18381i	0.0875288	−	0.996162i	$-0.472103\pi$
$521$	1.06977	−	1.18381i	1.06977	−	1.18381i	0.982237	−	0.187646i	$-0.0600858\pi$
$522$		0			0
$523$	0.104117	+	0.666088i	0.104117	+	0.666088i	0.982237	+	0.187646i	$0.0600858\pi$
$523$	0.104117	+	0.666088i	0.104117	+	0.666088i	−0.878119	+	0.478442i	$0.841202\pi$
$524$	−0.670636	+	0.479004i	−0.670636	+	0.479004i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.863747	+	0.565627i	−0.863747	+	0.565627i
$529$	0.586694	−	0.809809i	0.586694	−	0.809809i
$530$		0			0
$531$	0.931898	−	0.0251361i	0.931898	−	0.0251361i
$532$		0			0
$533$		0			0
$534$	0.744194	+	0.578382i	0.744194	+	0.578382i
$535$		0			0
$536$	1.41125	+	1.06661i	1.41125	+	1.06661i
$537$	−0.225608	−	0.657933i	−0.225608	−	0.657933i
$538$		0			0
$539$	0.516235	−	0.673553i	0.516235	−	0.673553i
$540$		0			0
$541$		0			0		0.858053	−	0.513561i	$-0.171674\pi$
$541$		0			0		−0.858053	+	0.513561i	$0.828326\pi$
$542$		0			0
$543$		0			0
$544$	−1.16064	−	1.18435i	−1.16064	−	1.18435i
$545$		0			0
$546$		0			0
$547$	1.17076	−	0.240066i	1.17076	−	0.240066i	0.424315	−	0.905515i	$-0.360515\pi$
$547$	1.17076	−	0.240066i	1.17076	−	0.240066i	0.746444	+	0.665448i	$0.231760\pi$
$548$	−0.127593	−	0.530677i	−0.127593	−	0.530677i
$549$		0			0
$550$	−0.847935	−	0.0343174i	−0.847935	−	0.0343174i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.57914	−	1.06480i	−1.57914	−	1.06480i
$557$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$557$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.65621	−	0.433822i	−1.65621	−	0.433822i
$562$	−1.23358	+	1.48135i	−1.23358	+	1.48135i
$563$	−0.600164	+	0.930109i	−0.600164	+	0.930109i	0.399745	+	0.916626i	$0.369099\pi$
$563$	−0.600164	+	0.930109i	−0.600164	+	0.930109i	−0.999909	+	0.0134828i	$0.995708\pi$
$564$		0			0
$565$		0			0
$566$	−0.0543160	+	1.61075i	−0.0543160	+	1.61075i
$567$		0			0
$568$		0			0
$569$	−0.0399187	+	0.00651575i	−0.0399187	+	0.00651575i	−0.181020	−	0.983479i	$-0.557940\pi$
$569$	−0.0399187	+	0.00651575i	−0.0399187	+	0.00651575i	0.141101	+	0.989995i	$0.454936\pi$
$570$		0			0
$571$	0.863386	−	0.129001i	0.863386	−	0.129001i	0.298741	−	0.954334i	$-0.403433\pi$
$571$	0.863386	−	0.129001i	0.863386	−	0.129001i	0.564646	+	0.825333i	$0.309013\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.286943	+	0.385030i	−0.286943	+	0.385030i
$577$	0.318122	−	0.342634i	0.318122	−	0.342634i	−0.553466	−	0.832871i	$-0.686695\pi$
$577$	0.318122	−	0.342634i	0.318122	−	0.342634i	0.871589	+	0.490238i	$0.163090\pi$
$578$	0.106101	−	1.74655i	0.106101	−	1.74655i
$579$	1.40739	+	0.536259i	1.40739	+	0.536259i
$580$		0			0
$581$		0			0
$582$	−1.63823	−	0.675345i	−1.63823	−	0.675345i
$583$		0			0
$584$	−0.303380	+	0.514728i	−0.303380	+	0.514728i
$585$		0			0
$586$		0			0
$587$	−0.694711	+	1.65348i	−0.694711	+	1.65348i	0.0606373	+	0.998160i	$0.480687\pi$
$587$	−0.694711	+	1.65348i	−0.694711	+	1.65348i	−0.755348	+	0.655324i	$0.772532\pi$
$588$	0.363457	−	1.16107i	0.363457	−	1.16107i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.61643	−	0.938098i	1.61643	−	0.938098i	0.629495	−	0.777005i	$-0.283262\pi$
$593$	1.61643	−	0.938098i	1.61643	−	0.938098i	0.986939	−	0.161094i	$-0.0515021\pi$
$594$	0.0541795	−	0.533944i	0.0541795	−	0.533944i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.0471738	−	0.998887i	$-0.515021\pi$
$599$		0			0		0.0471738	+	0.998887i	$0.484979\pi$
$600$	−1.15860	+	0.371276i	−1.15860	+	0.371276i
$601$	−1.27626	+	0.526126i	−1.27626	+	0.526126i	−0.913911	−	0.405915i	$-0.866953\pi$
$601$	−1.27626	+	0.526126i	−1.27626	+	0.526126i	−0.362351	+	0.932042i	$0.618026\pi$
$602$		0			0
$603$	0.824555	−	0.204142i	0.824555	−	0.204142i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.982237	−	0.187646i	$-0.939914\pi$
$607$		0			0		0.982237	+	0.187646i	$0.0600858\pi$
$608$	1.36361	−	1.18303i	1.36361	−	1.18303i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.792730	+	0.0750429i	−0.792730	+	0.0750429i
$613$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$613$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$614$	−1.12180	−	1.24139i	−1.12180	−	1.24139i
$615$		0			0
$616$		0			0
$617$	−0.362519	+	1.60252i	−0.362519	+	1.60252i	0.374884	+	0.927072i	$0.377682\pi$
$617$	−0.362519	+	1.60252i	−0.362519	+	1.60252i	−0.737404	+	0.675452i	$0.763948\pi$
$618$		0			0
$619$	−0.361514	−	1.96410i	−0.361514	−	1.96410i	−0.233773	−	0.972291i	$-0.575107\pi$
$619$	−0.361514	−	1.96410i	−0.361514	−	1.96410i	−0.127741	−	0.991808i	$-0.540773\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.952299	−	0.305167i	−0.952299	−	0.305167i
$626$	0.475058	−	1.76501i	0.475058	−	1.76501i
$627$	0.580750	−	1.77110i	0.580750	−	1.77110i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.821508	−	0.570197i	$-0.806867\pi$
$631$		0			0		0.821508	+	0.570197i	$0.193133\pi$
$632$		0			0
$633$	−1.05103	+	1.67808i	−1.05103	+	1.67808i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.143974	−	0.177711i	0.143974	−	0.177711i	−0.699920	−	0.714221i	$-0.746781\pi$
$641$	0.143974	−	0.177711i	0.143974	−	0.177711i	0.843894	+	0.536510i	$0.180258\pi$
$642$	−2.12061	−	0.0285944i	−2.12061	−	0.0285944i
$643$	0.0189286	+	0.146966i	0.0189286	+	0.146966i	0.998546	−	0.0539068i	$-0.0171674\pi$
$643$	0.0189286	+	0.146966i	0.0189286	+	0.146966i	−0.979617	+	0.200872i	$0.935622\pi$
$644$		0			0
$645$		0			0
$646$	2.97156	+	0.362376i	2.97156	+	0.362376i
$647$		0			0		−0.542187	−	0.840258i	$-0.682403\pi$
$647$		0			0		0.542187	+	0.840258i	$0.317597\pi$
$648$	−0.308480	−	1.21093i	−0.308480	−	1.21093i
$649$	1.59923	+	0.395936i	1.59923	+	0.395936i
$650$		0			0
$651$		0			0
$652$	0.387257	+	1.95548i	0.387257	+	1.95548i
$653$		0			0		−0.984677	−	0.174386i	$-0.944206\pi$
$653$		0			0		0.984677	+	0.174386i	$0.0557940\pi$
$654$		0			0
$655$		0			0
$656$	0.0786550	−	1.05870i	0.0786550	−	1.05870i
$657$	0.100346	+	0.268785i	0.100346	+	0.268785i
$658$		0			0
$659$	−0.435264	−	0.838816i	−0.435264	−	0.838816i	−0.999909	−	0.0134828i	$-0.995708\pi$
$659$	−0.435264	−	0.838816i	−0.435264	−	0.838816i	0.564646	−	0.825333i	$-0.309013\pi$
$660$		0			0
$661$		0			0		0.746444	−	0.665448i	$-0.231760\pi$
$661$		0			0		−0.746444	+	0.665448i	$0.768240\pi$
$662$	0.0477733	−	0.168413i	0.0477733	−	0.168413i
$663$		0			0
$664$	1.03829	+	0.0280058i	1.03829	+	0.0280058i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.571485	−	1.91585i	−0.571485	−	1.91585i	−0.311581	−	0.950220i	$-0.600858\pi$
$673$	−0.571485	−	1.91585i	−0.571485	−	1.91585i	−0.259904	−	0.965634i	$-0.583691\pi$
$674$	0.388386	−	1.96119i	0.388386	−	1.96119i
$675$	0.229156	−	0.589437i	0.229156	−	0.589437i
$676$	−0.718923	−	0.695089i	−0.718923	−	0.695089i
$677$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$677$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$678$	0.852971	+	1.36186i	0.852971	+	1.36186i
$679$		0			0
$680$		0			0
$681$	−0.763965	+	1.52213i	−0.763965	+	1.52213i
$682$		0			0
$683$	1.95478	+	0.400832i	1.95478	+	0.400832i	0.990924	+	0.134424i	$0.0429185\pi$
$683$	1.95478	+	0.400832i	1.95478	+	0.400832i	0.963860	+	0.266408i	$0.0858369\pi$
$684$	−0.0292151	−	0.866382i	−0.0292151	−	0.866382i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.83573	+	0.699469i	−1.83573	+	0.699469i
$689$		0			0
$690$		0			0
$691$	−0.0520855	+	0.0427822i	−0.0520855	+	0.0427822i	−0.660401	−	0.750913i	$-0.729614\pi$
$691$	−0.0520855	+	0.0427822i	−0.0520855	+	0.0427822i	0.608316	+	0.793695i	$0.291845\pi$
$692$		0			0
$693$		0			0
$694$	1.20559	+	1.57298i	1.20559	+	1.57298i
$695$		0			0
$696$		0			0
$697$	1.38998	−	1.08028i	1.38998	−	1.08028i
$698$		0			0
$699$	−0.987751	+	1.44378i	−0.987751	+	1.44378i
$700$		0			0
$701$		0			0		−0.496103	−	0.868264i	$-0.665236\pi$
$701$		0			0		0.496103	+	0.868264i	$0.334764\pi$
$702$		0			0
$703$		0			0
$704$	−0.670058	+	0.520764i	−0.670058	+	0.520764i
$705$		0			0
$706$	1.75504	+	0.779504i	1.75504	+	0.779504i
$707$		0			0
$708$	2.34822	−	0.254280i	2.34822	−	0.254280i
$709$		0			0		−0.680408	−	0.732833i	$-0.738197\pi$
$709$		0			0		0.680408	+	0.732833i	$0.261803\pi$
$710$		0			0
$711$		0			0
$712$	0.648101	+	0.424411i	0.648101	+	0.424411i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.228531	−	0.524029i	−0.228531	−	0.524029i
$717$		0			0
$718$		0			0
$719$		0			0		−0.00674156	−	0.999977i	$-0.502146\pi$
$719$		0			0		0.00674156	+	0.999977i	$0.497854\pi$
$720$		0			0
$721$		0			0
$722$	−0.408923	+	2.22167i	−0.408923	+	2.22167i
$723$	1.21891	+	1.94612i	1.21891	+	1.94612i
$724$		0			0
$725$		0			0
$726$	0.123361	−	0.317311i	0.123361	−	0.317311i
$727$		0			0		0.194264	−	0.980949i	$-0.437768\pi$
$727$		0			0		−0.194264	+	0.980949i	$0.562232\pi$
$728$		0			0
$729$	0.153843	+	0.0708285i	0.153843	+	0.0708285i
$730$		0			0
$731$	−2.90152	−	1.48086i	−2.90152	−	1.48086i
$732$		0			0
$733$		0			0		0.207472	−	0.978241i	$-0.433476\pi$
$733$		0			0		−0.207472	+	0.978241i	$0.566524\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.50066	+	0.0404774i	1.50066	+	0.0404774i
$738$	−0.371237	−	0.349369i	−0.371237	−	0.349369i
$739$	−0.541786	+	1.90994i	−0.541786	+	1.90994i	−0.154437	+	0.988003i	$0.549356\pi$
$739$	−0.541786	+	1.90994i	−0.541786	+	1.90994i	−0.387350	+	0.921933i	$0.626609\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.114357	−	0.993440i	$-0.463519\pi$
$743$		0			0		−0.114357	+	0.993440i	$0.536481\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.324302	−	0.378932i	0.324302	−	0.378932i
$748$	−1.38567	−	0.245402i	−1.38567	−	0.245402i
$749$		0			0
$750$		0			0
$751$		0			0		−0.858053	−	0.513561i	$-0.828326\pi$
$751$		0			0		0.858053	+	0.513561i	$0.171674\pi$
$752$		0			0
$753$	0.339170	+	1.33141i	0.339170	+	1.33141i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.412067	−	0.911153i	$-0.364807\pi$
$757$		0			0		−0.412067	+	0.911153i	$0.635193\pi$
$758$	0.255458	+	1.98343i	0.255458	+	1.98343i
$759$		0			0
$760$		0			0
$761$	1.92812	−	0.422533i	1.92812	−	0.422533i	0.929578	−	0.368626i	$-0.120172\pi$
$761$	1.92812	−	0.422533i	1.92812	−	0.422533i	0.998546	−	0.0539068i	$-0.0171674\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.645798	+	1.03109i	−0.645798	+	1.03109i
$769$	0.0386252	+	0.170743i	0.0386252	+	0.170743i	0.990924	−	0.134424i	$-0.0429185\pi$
$769$	0.0386252	+	0.170743i	0.0386252	+	0.170743i	−0.952299	+	0.305167i	$0.901288\pi$
$770$		0			0
$771$	1.95429	+	0.684893i	1.95429	+	0.684893i
$772$	1.18863	+	0.345850i	1.18863	+	0.345850i
$773$		0			0		−0.575722	−	0.817645i	$-0.695279\pi$
$773$		0			0		0.575722	+	0.817645i	$0.304721\pi$
$774$	−0.293921	+	0.896365i	−0.293921	+	0.896365i
$775$		0			0
$776$	−1.38698	−	0.444464i	−1.38698	−	0.444464i
$777$		0			0
$778$		0			0
$779$	1.08214	+	1.58175i	1.08214	+	1.58175i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.220643	−	0.975355i	0.220643	−	0.975355i
$785$		0			0
$786$	0.0202774	+	1.00246i	0.0202774	+	1.00246i
$787$	0.925547	+	1.02421i	0.925547	+	1.02421i	0.999636	+	0.0269632i	$0.00858369\pi$
$787$	0.925547	+	1.02421i	0.925547	+	1.02421i	−0.0740898	+	0.997252i	$0.523605\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.00824116	+	0.407421i	−0.00824116	+	0.407421i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.956327	−	0.292300i	$-0.905579\pi$
$797$		0			0		0.956327	+	0.292300i	$0.0944206\pi$
$798$		0			0
$799$		0			0
$800$	−0.924523	+	0.381126i	−0.924523	+	0.381126i
$801$	0.354259	−	0.113524i	0.354259	−	0.113524i
$802$	−0.0846061	−	1.79150i	−0.0846061	−	1.79150i
$803$	0.0443806	+	0.505094i	0.0443806	+	0.505094i
$804$	2.04049	−	0.684354i	2.04049	−	0.684354i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.864267	−	0.533237i	0.864267	−	0.533237i	−0.0202235	−	0.999795i	$-0.506438\pi$
$809$	0.864267	−	0.533237i	0.864267	−	0.533237i	0.884490	+	0.466559i	$0.154506\pi$
$810$		0			0
$811$	0.0312551	+	0.0256724i	0.0312551	+	0.0256724i	0.650217	−	0.759749i	$-0.274678\pi$
$811$	0.0312551	+	0.0256724i	0.0312551	+	0.0256724i	−0.618962	+	0.785421i	$0.712446\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.98656	+	0.351818i	−1.98656	+	0.351818i
$817$	1.80073	−	3.05521i	1.80073	−	3.05521i
$818$	−0.621123	−	0.0503584i	−0.621123	−	0.0503584i
$819$		0			0
$820$		0			0
$821$		0			0		−0.586694	−	0.809809i	$-0.699571\pi$
$821$		0			0		0.586694	+	0.809809i	$0.300429\pi$
$822$	−0.620519	−	0.236437i	−0.620519	−	0.236437i
$823$		0			0		0.0606373	−	0.998160i	$-0.480687\pi$
$823$		0			0		−0.0606373	+	0.998160i	$0.519313\pi$
$824$		0			0
$825$	−0.616961	+	0.827859i	−0.616961	+	0.827859i
$826$		0			0
$827$	−1.86621	+	0.100748i	−1.86621	+	0.100748i	−0.952299	−	0.305167i	$-0.901288\pi$
$827$	−1.86621	+	0.100748i	−1.86621	+	0.100748i	−0.913911	+	0.405915i	$0.866953\pi$
$828$		0			0
$829$		0			0		−0.963860	−	0.266408i	$-0.914163\pi$
$829$		0			0		0.963860	+	0.266408i	$0.0858369\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.44531	−	0.812934i	1.44531	−	0.812934i
$834$	−2.15401	+	0.854177i	−2.15401	+	0.854177i
$835$		0			0
$836$	0.358141	−	1.48955i	0.358141	−	1.48955i
$837$		0			0
$838$	0.769348	−	1.19230i	0.769348	−	1.19230i
$839$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$839$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$840$		0			0
$841$	−0.337088	−	0.941473i	−0.337088	−	0.941473i
$842$		0			0
$843$	0.640039	+	2.25630i	0.640039	+	2.25630i
$844$	−0.749599	+	1.44459i	−0.749599	+	1.44459i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.58009	+	1.16107i	1.58009	+	1.16107i
$850$	−1.49679	−	0.713724i	−1.49679	−	0.713724i
$851$		0			0
$852$		0			0
$853$		0			0		−0.233773	−	0.972291i	$-0.575107\pi$
$853$		0			0		0.233773	+	0.972291i	$0.424893\pi$
$854$		0			0
$855$		0			0
$856$	−1.73922	+	0.117429i	−1.73922	+	0.117429i
$857$	−0.345566	−	0.352627i	−0.345566	−	0.352627i	0.519333	−	0.854572i	$-0.326180\pi$
$857$	−0.345566	−	0.352627i	−0.345566	−	0.352627i	−0.864900	+	0.501945i	$0.832618\pi$
$858$		0			0
$859$	1.90987	−	0.583750i	1.90987	−	0.583750i	0.939179	−	0.343428i	$-0.111588\pi$
$859$	1.90987	−	0.583750i	1.90987	−	0.583750i	0.970693	−	0.240323i	$-0.0772532\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.878119	−	0.478442i	$-0.158798\pi$
$863$		0			0		−0.878119	+	0.478442i	$0.841202\pi$
$864$	−0.205133	−	0.598222i	−0.205133	−	0.598222i
$865$		0			0
$866$	−0.322713	−	0.338313i	−0.322713	−	0.338313i
$867$	−1.68087	−	1.30636i	−1.68087	−	1.30636i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.585090	+	0.383147i	−0.585090	+	0.383147i
$874$		0			0
$875$		0			0
$876$	0.308440	+	0.658232i	0.308440	+	0.658232i
$877$		0			0		0.813746	−	0.581221i	$-0.197425\pi$
$877$		0			0		−0.813746	+	0.581221i	$0.802575\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.853008	−	0.740051i	−0.853008	−	0.740051i	0.114357	−	0.993440i	$-0.463519\pi$
$881$	−0.853008	−	0.740051i	−0.853008	−	0.740051i	−0.967365	+	0.253388i	$0.918455\pi$
$882$	−0.297220	−	0.377153i	−0.297220	−	0.377153i
$883$	0.624588	+	0.770948i	0.624588	+	0.770948i	0.986939	−	0.161094i	$-0.0515021\pi$
$883$	0.624588	+	0.770948i	0.624588	+	0.770948i	−0.362351	+	0.932042i	$0.618026\pi$
$884$		0			0
$885$		0			0
$886$	1.68533	+	0.0909832i	1.68533	+	0.0909832i
$887$		0			0		−0.259904	−	0.965634i	$-0.583691\pi$
$887$		0			0		0.259904	+	0.965634i	$0.416309\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.810309	−	0.684078i	−0.810309	−	0.684078i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.74030	−	0.236081i	−1.74030	−	0.236081i
$899$		0			0
$900$	−0.137261	+	0.460156i	−0.137261	+	0.460156i
$901$		0			0
$902$	−0.467877	−	0.769900i	−0.467877	−	0.769900i
$903$		0			0
$904$	0.789257	+	1.05905i	0.789257	+	1.05905i
$905$		0			0
$906$		0			0
$907$	−0.249559	−	0.0546889i	−0.249559	−	0.0546889i	0.0875288	−	0.996162i	$-0.472103\pi$
$907$	−0.249559	−	0.0546889i	−0.249559	−	0.0546889i	−0.337088	+	0.941473i	$0.609442\pi$
$908$	−0.524778	+	1.29775i	−0.524778	+	1.29775i
$909$		0			0
$910$		0			0
$911$		0			0		0.890700	−	0.454591i	$-0.150215\pi$
$911$		0			0		−0.890700	+	0.454591i	$0.849785\pi$
$912$	−0.251167	−	2.18194i	−0.251167	−	2.18194i
$913$	0.730824	−	0.492787i	0.730824	−	0.492787i
$914$	−0.512220	+	1.49377i	−0.512220	+	1.49377i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.507938	−	0.917478i	0.507938	−	0.917478i
$919$		0			0		0.399745	−	0.916626i	$-0.369099\pi$
$919$		0			0		−0.399745	+	0.916626i	$0.630901\pi$
$920$		0			0
$921$	−2.01715	+	0.273638i	−2.01715	+	0.273638i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.629866	−	0.735970i	−0.629866	−	0.735970i	0.349751	−	0.936843i	$-0.386266\pi$
$929$	−0.629866	−	0.735970i	−0.629866	−	0.735970i	−0.979617	+	0.200872i	$0.935622\pi$
$930$		0			0
$931$	0.787972	+	1.62422i	0.787972	+	1.62422i
$932$	−0.713320	+	1.24843i	−0.713320	+	1.24843i
$933$		0			0
$934$	0.690227	+	0.723593i	0.690227	+	0.723593i
$935$		0			0
$936$		0			0
$937$	0.850138	+	1.75236i	0.850138	+	1.75236i	0.629495	+	0.777005i	$0.283262\pi$
$937$	0.850138	+	1.75236i	0.850138	+	1.75236i	0.220643	+	0.975355i	$0.429185\pi$
$938$		0			0
$939$	−1.44594	−	1.68952i	−1.44594	−	1.68952i
$940$		0			0
$941$		0			0		−0.141101	−	0.989995i	$-0.545064\pi$
$941$		0			0		0.141101	+	0.989995i	$0.454936\pi$
$942$		0			0
$943$		0			0
$944$	1.90690	−	0.364294i	1.90690	−	0.364294i
$945$		0			0
$946$	−0.922689	+	1.38849i	−0.922689	+	1.38849i
$947$	1.16274	−	0.157732i	1.16274	−	0.157732i	0.472511	−	0.881325i	$-0.343348\pi$
$947$	1.16274	−	0.157732i	1.16274	−	0.157732i	0.690227	+	0.723593i	$0.257511\pi$
$948$		0			0
$949$		0			0
$950$	0.874383	−	1.57938i	0.874383	−	1.57938i
$951$		0			0
$952$		0			0
$953$	−0.121564	−	0.714433i	−0.121564	−	0.714433i	−0.979617	−	0.200872i	$-0.935622\pi$
$953$	−0.121564	−	0.714433i	−0.121564	−	0.714433i	0.858053	−	0.513561i	$-0.171674\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.976820	+	0.214062i	0.976820	+	0.214062i
$962$		0			0
$963$	−0.481913	+	0.684418i	−0.481913	+	0.684418i
$964$	1.12786	+	1.51340i	1.12786	+	1.51340i
$965$		0			0
$966$		0			0
$967$		0			0		−0.884490	−	0.466559i	$-0.845494\pi$
$967$		0			0		0.884490	+	0.466559i	$0.154506\pi$
$968$	0.0799878	−	0.268152i	0.0799878	−	0.268152i
$969$	2.40523	−	2.73488i	2.40523	−	2.73488i
$970$		0			0
$971$	−1.37637	−	0.774160i	−1.37637	−	0.774160i	−0.387350	−	0.921933i	$-0.626609\pi$
$971$	−1.37637	−	0.774160i	−1.37637	−	0.774160i	−0.989021	+	0.147772i	$0.952790\pi$
$972$	−0.833894	−	0.304928i	−0.833894	−	0.304928i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.47300	+	1.24353i	1.47300	+	1.24353i	0.908355	+	0.418201i	$0.137339\pi$
$977$	1.47300	+	1.24353i	1.47300	+	1.24353i	0.564646	+	0.825333i	$0.309013\pi$
$978$	2.22958	+	0.954494i	2.22958	+	0.954494i
$979$	0.656895	−	0.0265857i	0.656895	−	0.0265857i
$980$		0			0
$981$		0			0
$982$	−0.967293	−	0.0522196i	−0.967293	−	0.0522196i
$983$		0			0		0.960181	−	0.279380i	$-0.0901288\pi$
$983$		0			0		−0.960181	+	0.279380i	$0.909871\pi$
$984$	−1.00903	−	0.806269i	−1.00903	−	0.806269i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.813746	−	0.581221i	$-0.197425\pi$
$991$		0			0		−0.813746	+	0.581221i	$0.802575\pi$
$992$		0			0
$993$	−0.136289	−	0.163664i	−0.136289	−	0.163664i
$994$		0			0
$995$		0			0
$996$	0.741390	−	1.02333i	0.741390	−	1.02333i
$997$		0			0		−0.864900	−	0.501945i	$-0.832618\pi$
$997$		0			0		0.864900	+	0.501945i	$0.167382\pi$
$998$	−1.95852	+	0.0528272i	−1.95852	+	0.0528272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.43.1	✓	232
8.3	odd	2	CM	3736.1.l.a.43.1	✓	232
467.391	even	233	inner	3736.1.l.a.2259.1	yes	232
3736.2259	odd	466	inner	3736.1.l.a.2259.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.43.1	✓	232	1.1	even	1	trivial
3736.1.l.a.43.1	✓	232	8.3	odd	2	CM
3736.1.l.a.2259.1	yes	232	467.391	even	233	inner
3736.1.l.a.2259.1	yes	232	3736.2259	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)

\(f(q)\)	\(=\)	\(q+(0.496103 - 0.868264i) q^{2} +(-0.531041 - 1.09462i) q^{3} +(-0.507764 - 0.861496i) q^{4} +(-1.21387 - 0.0819585i) q^{6} +(-0.999909 + 0.0134828i) q^{8} +(-0.297220 + 0.377153i) q^{9} +O(q^{10})\)	\(q+(0.496103 - 0.868264i) q^{2} +(-0.531041 - 1.09462i) q^{3} +(-0.507764 - 0.861496i) q^{4} +(-1.21387 - 0.0819585i) q^{6} +(-0.999909 + 0.0134828i) q^{8} +(-0.297220 + 0.377153i) q^{9} +(-0.683855 + 0.502507i) q^{11} +(-0.673365 + 1.01330i) q^{12} +(-0.484351 + 0.874874i) q^{16} +(-1.61487 + 0.376774i) q^{17} +(0.180016 + 0.445172i) q^{18} +(-0.302822 - 1.77969i) q^{19} +(0.0970465 + 0.843062i) q^{22} +(0.545752 + 1.08736i) q^{24} +(-0.154437 + 0.988003i) q^{25} +(-0.617756 - 0.135376i) q^{27} +(0.519333 + 0.854572i) q^{32} +(0.913209 + 0.481708i) q^{33} +(-0.474003 + 1.58905i) q^{34} +(0.475833 + 0.0645493i) q^{36} +(-1.69547 - 0.619979i) q^{38} +(-0.964325 + 0.443969i) q^{41} +(1.50108 + 1.26724i) q^{43} +(0.780146 + 0.333983i) q^{44} +(1.21486 + 0.0655847i) q^{48} +(-0.960181 + 0.279380i) q^{49} +(0.781231 + 0.624242i) q^{50} +(1.26999 + 1.56758i) q^{51} +(-0.424013 + 0.469215i) q^{54} +(-1.78727 + 1.27656i) q^{57} +(-1.24232 - 1.49185i) q^{59} +(0.999636 - 0.0269632i) q^{64} +(0.871295 - 0.553930i) q^{66} +(-1.39674 - 1.08554i) q^{67} +(1.14456 + 1.19989i) q^{68} +(0.292108 - 0.381126i) q^{72} +(0.310292 - 0.510590i) q^{73} +(1.16350 - 0.355621i) q^{75} +(-1.37943 + 1.16454i) q^{76} +(0.292125 + 1.21498i) q^{81} +(-0.0929221 + 1.05754i) q^{82} +(-1.03782 - 0.0420023i) q^{83} +(1.84499 - 0.674654i) q^{86} +(0.677018 - 0.511682i) q^{88} +(-0.642320 - 0.433110i) q^{89} +(0.659641 - 1.02228i) q^{96} +(1.38087 + 0.463124i) q^{97} +(-0.233773 + 0.972291i) q^{98} +(0.0137336 - 0.407273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more