LMFDB - Embedded newform 3736.1.l.a.75.1

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			75.1
Root			$-0.781231 - 0.624242i$ of defining polynomial
Character	$\chi$	$=$	3736.75
Dual form			3736.1.l.a.2939.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.902634 - 0.430410i) q^{2} +(-1.26547 + 1.40037i) q^{3} +(0.629495 + 0.777005i) q^{4} +(1.74499 - 0.719355i) q^{6} +(-0.233773 - 0.972291i) q^{8} +(-0.258685 - 2.54937i) q^{9} +O(q^{10})$	\(q+(-0.902634 - 0.430410i) q^{2} +(-1.26547 + 1.40037i) q^{3} +(0.629495 + 0.777005i) q^{4} +(1.74499 - 0.719355i) q^{6} +(-0.233773 - 0.972291i) q^{8} +(-0.258685 - 2.54937i) q^{9} +(-1.12426 + 0.106427i) q^{11} +(-1.88470 - 0.101746i) q^{12} +(-0.207472 + 0.978241i) q^{16} +(-0.879836 - 0.742774i) q^{17} +(-0.863775 + 2.41249i) q^{18} +(-1.65448 + 1.11560i) q^{19} +(1.06061 + 0.387830i) q^{22} +(1.65740 + 0.903034i) q^{24} +(0.349751 - 0.936843i) q^{25} +(2.37646 + 1.74626i) q^{27} +(0.608316 - 0.793695i) q^{32} +(1.27368 - 1.70907i) q^{33} +(0.474472 + 1.04914i) q^{34} +(1.81803 - 1.80582i) q^{36} +(1.97355 - 0.294873i) q^{38} +(-0.546044 + 1.74435i) q^{41} +(1.88767 - 0.576965i) q^{43} +(-0.790414 - 0.806564i) q^{44} +(-1.10735 - 1.52847i) q^{48} +(0.970693 - 0.240323i) q^{49} +(-0.718923 + 0.695089i) q^{50} +(2.15357 - 0.292143i) q^{51} +(-1.39347 - 2.59908i) q^{54} +(0.531433 - 3.72864i) q^{57} +(-0.325084 - 0.836183i) q^{59} +(-0.890700 + 0.454591i) q^{64} +(-1.88527 + 0.994460i) q^{66} +(-1.00855 - 0.641192i) q^{67} +(0.0232862 - 1.15121i) q^{68} +(-2.41826 + 0.847492i) q^{72} +(1.19502 + 1.55919i) q^{73} +(0.869331 + 1.67533i) q^{75} +(-1.90831 - 0.583272i) q^{76} +(-2.94252 + 0.603370i) q^{81} +(1.24366 - 1.33949i) q^{82} +(0.791074 - 0.924334i) q^{83} +(-1.95221 - 0.291685i) q^{86} +(0.366301 + 1.06823i) q^{88} +(-1.14475 - 1.62579i) q^{89} +(0.341666 + 1.85627i) q^{96} +(1.29838 - 0.927371i) q^{97} +(-0.979617 - 0.200872i) q^{98} +(0.562154 + 2.83864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3736\mathbb{Z}\right)^\times$.

$n$	$935$	$1869$	$2337$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{33}{233}\right)$

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 $

$2$	−0.902634	−	0.430410i	−0.902634	−	0.430410i
$2$	−0.902634	−	0.430410i	−0.902634	−	0.430410i
$3$	−1.26547	+	1.40037i	−1.26547	+	1.40037i	−0.387350	+	0.921933i	$0.626609\pi$
$3$	−1.26547	+	1.40037i	−1.26547	+	1.40037i	−0.878119	+	0.478442i	$0.841202\pi$
$4$	0.629495	+	0.777005i	0.629495	+	0.777005i
$5$		0			0		0.821508	−	0.570197i	$-0.193133\pi$
$5$		0			0		−0.821508	+	0.570197i	$0.806867\pi$
$6$	1.74499	−	0.719355i	1.74499	−	0.719355i
$7$		0			0		0.992646	−	0.121051i	$-0.0386266\pi$
$7$		0			0		−0.992646	+	0.121051i	$0.961373\pi$
$8$	−0.233773	−	0.972291i	−0.233773	−	0.972291i
$9$	−0.258685	−	2.54937i	−0.258685	−	2.54937i
$10$		0			0
$11$	−1.12426	+	0.106427i	−1.12426	+	0.106427i	−0.639914	−	0.768447i	$-0.721030\pi$
$11$	−1.12426	+	0.106427i	−1.12426	+	0.106427i	−0.484351	+	0.874874i	$0.660944\pi$
$12$	−1.88470	−	0.101746i	−1.88470	−	0.101746i
$13$		0			0		−0.709486	−	0.704719i	$-0.751073\pi$
$13$		0			0		0.709486	+	0.704719i	$0.248927\pi$
$14$		0			0
$15$		0			0
$16$	−0.207472	+	0.978241i	−0.207472	+	0.978241i
$17$	−0.879836	−	0.742774i	−0.879836	−	0.742774i	0.0875288	−	0.996162i	$-0.472103\pi$
$17$	−0.879836	−	0.742774i	−0.879836	−	0.742774i	−0.967365	+	0.253388i	$0.918455\pi$
$18$	−0.863775	+	2.41249i	−0.863775	+	2.41249i
$19$	−1.65448	+	1.11560i	−1.65448	+	1.11560i	−0.789576	+	0.613653i	$0.789700\pi$
$19$	−1.65448	+	1.11560i	−1.65448	+	1.11560i	−0.864900	+	0.501945i	$0.832618\pi$
$20$		0			0
$21$		0			0
$22$	1.06061	+	0.387830i	1.06061	+	0.387830i
$23$		0			0		0.919301	−	0.393556i	$-0.128755\pi$
$23$		0			0		−0.919301	+	0.393556i	$0.871245\pi$
$24$	1.65740	+	0.903034i	1.65740	+	0.903034i
$25$	0.349751	−	0.936843i	0.349751	−	0.936843i
$26$		0			0
$27$	2.37646	+	1.74626i	2.37646	+	1.74626i
$28$		0			0
$29$		0			0		−0.864900	−	0.501945i	$-0.832618\pi$
$29$		0			0		0.864900	+	0.501945i	$0.167382\pi$
$30$		0			0
$31$		0			0		0.311581	−	0.950220i	$-0.399142\pi$
$31$		0			0		−0.311581	+	0.950220i	$0.600858\pi$
$32$	0.608316	−	0.793695i	0.608316	−	0.793695i
$33$	1.27368	−	1.70907i	1.27368	−	1.70907i
$34$	0.474472	+	1.04914i	0.474472	+	1.04914i
$35$		0			0
$36$	1.81803	−	1.80582i	1.81803	−	1.80582i
$37$		0			0		0.896748	−	0.442541i	$-0.145923\pi$
$37$		0			0		−0.896748	+	0.442541i	$0.854077\pi$
$38$	1.97355	−	0.294873i	1.97355	−	0.294873i
$39$		0			0
$40$		0			0
$41$	−0.546044	+	1.74435i	−0.546044	+	1.74435i	0.114357	+	0.993440i	$0.463519\pi$
$41$	−0.546044	+	1.74435i	−0.546044	+	1.74435i	−0.660401	+	0.750913i	$0.729614\pi$
$42$		0			0
$43$	1.88767	−	0.576965i	1.88767	−	0.576965i	0.896748	−	0.442541i	$-0.145923\pi$
$43$	1.88767	−	0.576965i	1.88767	−	0.576965i	0.990924	−	0.134424i	$-0.0429185\pi$
$44$	−0.790414	−	0.806564i	−0.790414	−	0.806564i
$45$		0			0
$46$		0			0
$47$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$47$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$48$	−1.10735	−	1.52847i	−1.10735	−	1.52847i
$49$	0.970693	−	0.240323i	0.970693	−	0.240323i
$50$	−0.718923	+	0.695089i	−0.718923	+	0.695089i
$51$	2.15357	−	0.292143i	2.15357	−	0.292143i
$52$		0			0
$53$		0			0		−0.0606373	−	0.998160i	$-0.519313\pi$
$53$		0			0		0.0606373	+	0.998160i	$0.480687\pi$
$54$	−1.39347	−	2.59908i	−1.39347	−	2.59908i
$55$		0			0
$56$		0			0
$57$	0.531433	−	3.72864i	0.531433	−	3.72864i
$58$		0			0
$59$	−0.325084	−	0.836183i	−0.325084	−	0.836183i	−0.995549	−	0.0942425i	$-0.969957\pi$
$59$	−0.325084	−	0.836183i	−0.325084	−	0.836183i	0.670466	−	0.741941i	$-0.266094\pi$
$60$		0			0
$61$		0			0		−0.660401	−	0.750913i	$-0.729614\pi$
$61$		0			0		0.660401	+	0.750913i	$0.270386\pi$
$62$		0			0
$63$		0			0
$64$	−0.890700	+	0.454591i	−0.890700	+	0.454591i
$65$		0			0
$66$	−1.88527	+	0.994460i	−1.88527	+	0.994460i
$67$	−1.00855	−	0.641192i	−1.00855	−	0.641192i	−0.0740898	−	0.997252i	$-0.523605\pi$
$67$	−1.00855	−	0.641192i	−1.00855	−	0.641192i	−0.934463	+	0.356059i	$0.884120\pi$
$68$	0.0232862	−	1.15121i	0.0232862	−	1.15121i
$69$		0			0
$70$		0			0
$71$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$71$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$72$	−2.41826	+	0.847492i	−2.41826	+	0.847492i
$73$	1.19502	+	1.55919i	1.19502	+	1.55919i	0.746444	+	0.665448i	$0.231760\pi$
$73$	1.19502	+	1.55919i	1.19502	+	1.55919i	0.448576	+	0.893745i	$0.351931\pi$
$74$		0			0
$75$	0.869331	+	1.67533i	0.869331	+	1.67533i
$76$	−1.90831	−	0.583272i	−1.90831	−	0.583272i
$77$		0			0
$78$		0			0
$79$		0			0		−0.963860	−	0.266408i	$-0.914163\pi$
$79$		0			0		0.963860	+	0.266408i	$0.0858369\pi$
$80$		0			0
$81$	−2.94252	+	0.603370i	−2.94252	+	0.603370i
$82$	1.24366	−	1.33949i	1.24366	−	1.33949i
$83$	0.791074	−	0.924334i	0.791074	−	0.924334i	−0.207472	−	0.978241i	$-0.566524\pi$
$83$	0.791074	−	0.924334i	0.791074	−	0.924334i	0.998546	+	0.0539068i	$0.0171674\pi$
$84$		0			0
$85$		0			0
$86$	−1.95221	−	0.291685i	−1.95221	−	0.291685i
$87$		0			0
$88$	0.366301	+	1.06823i	0.366301	+	1.06823i
$89$	−1.14475	−	1.62579i	−1.14475	−	1.62579i	−0.660401	−	0.750913i	$-0.729614\pi$
$89$	−1.14475	−	1.62579i	−1.14475	−	1.62579i	−0.484351	−	0.874874i	$-0.660944\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.341666	+	1.85627i	0.341666	+	1.85627i
$97$	1.29838	−	0.927371i	1.29838	−	0.927371i	0.298741	−	0.954334i	$-0.403433\pi$
$97$	1.29838	−	0.927371i	1.29838	−	0.927371i	0.999636	+	0.0269632i	$0.00858369\pi$
$98$	−0.979617	−	0.200872i	−0.979617	−	0.200872i
$99$	0.562154	+	2.83864i	0.562154	+	2.83864i
$100$	0.948098	−	0.317979i	0.948098	−	0.317979i
$101$		0			0		−0.896748	−	0.442541i	$-0.854077\pi$
$101$		0			0		0.896748	+	0.442541i	$0.145923\pi$
$102$	−2.06962	−	0.663218i	−2.06962	−	0.663218i
$103$		0			0		−0.0202235	−	0.999795i	$-0.506438\pi$
$103$		0			0		0.0202235	+	0.999795i	$0.493562\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.05223	−	1.45239i	1.05223	−	1.45239i	0.167744	−	0.985831i	$-0.446352\pi$
$107$	1.05223	−	1.45239i	1.05223	−	1.45239i	0.884490	−	0.466559i	$-0.154506\pi$
$108$	0.139119	+	2.94578i	0.139119	+	2.94578i
$109$		0			0		−0.542187	−	0.840258i	$-0.682403\pi$
$109$		0			0		0.542187	+	0.840258i	$0.317597\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.03043	+	1.08024i	1.03043	+	1.08024i	0.996729	+	0.0808112i	$0.0257511\pi$
$113$	1.03043	+	1.08024i	1.03043	+	1.08024i	0.0337017	+	0.999432i	$0.489270\pi$
$114$	−2.08453	+	3.13686i	−2.08453	+	3.13686i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.0664698	+	0.894686i	−0.0664698	+	0.894686i
$119$		0			0
$120$		0			0
$121$	0.270408	−	0.0516587i	0.270408	−	0.0516587i
$122$		0			0
$123$	−1.75175	−	2.97209i	−1.75175	−	2.97209i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.553466	−	0.832871i	$-0.686695\pi$
$127$		0			0		0.553466	+	0.832871i	$0.313305\pi$
$128$	0.999636	−	0.0269632i	0.999636	−	0.0269632i
$129$	−1.58082	+	3.37358i	−1.58082	+	3.37358i
$130$		0			0
$131$	1.27163	+	1.36961i	1.27163	+	1.36961i	0.896748	+	0.442541i	$0.145923\pi$
$131$	1.27163	+	1.36961i	1.27163	+	1.36961i	0.374884	+	0.927072i	$0.377682\pi$
$132$	2.12974	−	0.0861941i	2.12974	−	0.0861941i
$133$		0			0
$134$	0.634379	+	1.01285i	0.634379	+	1.01285i
$135$		0			0
$136$	−0.516510	+	1.02910i	−0.516510	+	1.02910i
$137$	0.727335	−	1.40168i	0.727335	−	1.40168i	−0.181020	−	0.983479i	$-0.557940\pi$
$137$	0.727335	−	1.40168i	0.727335	−	1.40168i	0.908355	−	0.418201i	$-0.137339\pi$
$138$		0			0
$139$	1.50726	+	0.101768i	1.50726	+	0.101768i	0.797778	−	0.602951i	$-0.206009\pi$
$139$	1.50726	+	0.101768i	1.50726	+	0.101768i	0.709486	+	0.704719i	$0.248927\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.54757	+	0.275866i	2.54757	+	0.275866i
$145$		0			0
$146$	−0.407573	−	1.92173i	−0.407573	−	1.92173i
$147$	−0.891840	+	1.66345i	−0.891840	+	1.66345i
$148$		0			0
$149$		0			0		−0.436485	−	0.899712i	$-0.643777\pi$
$149$		0			0		0.436485	+	0.899712i	$0.356223\pi$
$150$	−0.0636102	−	1.88638i	−0.0636102	−	1.88638i
$151$		0			0		−0.399745	−	0.916626i	$-0.630901\pi$
$151$		0			0		0.399745	+	0.916626i	$0.369099\pi$
$152$	1.47146	+	1.34784i	1.47146	+	1.34784i
$153$	−1.66600	+	2.43517i	−1.66600	+	2.43517i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.154437	−	0.988003i	$-0.450644\pi$
$157$		0			0		−0.154437	+	0.988003i	$0.549356\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	2.91572	+	0.721868i	2.91572	+	0.721868i
$163$	−0.115792	−	0.286347i	−0.115792	−	0.286347i	0.858053	−	0.513561i	$-0.171674\pi$
$163$	−0.115792	−	0.286347i	−0.115792	−	0.286347i	−0.973845	+	0.227213i	$0.927039\pi$
$164$	−1.69910	+	0.673782i	−1.69910	+	0.673782i
$165$		0			0
$166$	−1.11189	+	0.493849i	−1.11189	+	0.493849i
$167$		0			0		0.399745	−	0.916626i	$-0.369099\pi$
$167$		0			0		−0.399745	+	0.916626i	$0.630901\pi$
$168$		0			0
$169$	0.00674156	+	0.999977i	0.00674156	+	0.999977i
$170$		0			0
$171$	3.27206	+	3.92928i	3.27206	+	3.92928i
$172$	1.63658	+	1.10353i	1.63658	+	1.10353i
$173$		0			0		0.805835	−	0.592140i	$-0.201717\pi$
$173$		0			0		−0.805835	+	0.592140i	$0.798283\pi$
$174$		0			0
$175$		0			0
$176$	0.129142	−	1.12188i	0.129142	−	1.12188i
$177$	1.58235	+	0.602925i	1.58235	+	0.602925i
$178$	0.333537	+	1.96020i	0.333537	+	1.96020i
$179$	0.701381	+	0.432739i	0.701381	+	0.432739i	0.829121	−	0.559069i	$-0.188841\pi$
$179$	0.701381	+	0.432739i	0.701381	+	0.432739i	−0.127741	+	0.991808i	$0.540773\pi$
$180$		0			0
$181$		0			0		−0.424315	−	0.905515i	$-0.639485\pi$
$181$		0			0		0.424315	+	0.905515i	$0.360515\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.06822	+	0.741436i	1.06822	+	0.741436i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.939179	−	0.343428i	$-0.111588\pi$
$191$		0			0		−0.939179	+	0.343428i	$0.888412\pi$
$192$	0.490556	−	1.82259i	0.490556	−	1.82259i
$193$	−0.161075	+	0.121738i	−0.161075	+	0.121738i	−0.680408	−	0.732833i	$-0.738197\pi$
$193$	−0.161075	+	0.121738i	−0.161075	+	0.121738i	0.519333	+	0.854572i	$0.326180\pi$
$194$	−1.57111	+	0.278242i	−1.57111	+	0.278242i
$195$		0			0
$196$	0.797778	+	0.602951i	0.797778	+	0.602951i
$197$		0			0		−0.890700	−	0.454591i	$-0.849785\pi$
$197$		0			0		0.890700	+	0.454591i	$0.150215\pi$
$198$	0.714358	−	2.80421i	0.714358	−	2.80421i
$199$		0			0		−0.114357	−	0.993440i	$-0.536481\pi$
$199$		0			0		0.114357	+	0.993440i	$0.463519\pi$
$200$	−0.992646	−	0.121051i	−0.992646	−	0.121051i
$201$	2.17420	−	0.600943i	2.17420	−	0.600943i
$202$		0			0
$203$		0			0
$204$	1.58266	+	1.48943i	1.58266	+	1.48943i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.74134	−	1.43031i	1.74134	−	1.43031i
$210$		0			0
$211$	−0.257908	−	0.114550i	−0.257908	−	0.114550i	0.272900	−	0.962042i	$-0.412017\pi$
$211$	−0.257908	−	0.114550i	−0.257908	−	0.114550i	−0.530808	+	0.847492i	$0.678112\pi$
$212$		0			0
$213$		0			0
$214$	−1.57490	+	0.858084i	−1.57490	+	0.858084i
$215$		0			0
$216$	1.14232	−	2.71884i	1.14232	−	2.71884i
$217$		0			0
$218$		0			0
$219$	−3.69572	−	0.299635i	−3.69572	−	0.299635i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.167744	−	0.985831i	$-0.446352\pi$
$223$		0			0		−0.167744	+	0.985831i	$0.553648\pi$
$224$		0			0
$225$	−2.47883	−	0.649298i	−2.47883	−	0.649298i
$226$	−0.465155	−	1.41857i	−0.465155	−	1.41857i
$227$	−1.84370	−	0.646134i	−1.84370	−	0.646134i	−0.992646	−	0.121051i	$-0.961373\pi$
$227$	−1.84370	−	0.646134i	−1.84370	−	0.646134i	−0.851051	−	0.525083i	$-0.824034\pi$
$228$	3.23170	−	1.93423i	3.23170	−	1.93423i
$229$		0			0		−0.519333	−	0.854572i	$-0.673820\pi$
$229$		0			0		0.519333	+	0.854572i	$0.326180\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.39501	−	0.665192i	1.39501	−	0.665192i	0.424315	−	0.905515i	$-0.360515\pi$
$233$	1.39501	−	0.665192i	1.39501	−	0.665192i	0.970693	+	0.240323i	$0.0772532\pi$
$234$		0			0
$235$		0			0
$236$	0.445080	−	0.778965i	0.445080	−	0.778965i
$237$		0			0
$238$		0			0
$239$		0			0		0.858053	−	0.513561i	$-0.171674\pi$
$239$		0			0		−0.858053	+	0.513561i	$0.828326\pi$
$240$		0			0
$241$	−0.233613	−	0.712445i	−0.233613	−	0.712445i	−0.997728	−	0.0673651i	$-0.978541\pi$
$241$	−0.233613	−	0.712445i	−0.233613	−	0.712445i	0.764115	−	0.645080i	$-0.223176\pi$
$242$	−0.266314	−	0.0697574i	−0.266314	−	0.0697574i
$243$	1.38130	−	2.34357i	1.38130	−	2.34357i
$244$		0			0
$245$		0			0
$246$	0.301967	+	3.43668i	0.301967	+	3.43668i
$247$		0			0
$248$		0			0
$249$	0.293335	+	2.27752i	0.293335	+	2.27752i
$250$		0			0
$251$	0.221445	−	0.527062i	0.221445	−	0.527062i	−0.772743	−	0.634719i	$-0.781116\pi$
$251$	0.221445	−	0.527062i	0.221445	−	0.527062i	0.994188	+	0.107657i	$0.0343348\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.913911	−	0.405915i	−0.913911	−	0.405915i
$257$	−0.215502	+	0.444208i	−0.215502	+	0.444208i	−0.979617	−	0.200872i	$-0.935622\pi$
$257$	−0.215502	+	0.444208i	−0.215502	+	0.444208i	0.764115	+	0.645080i	$0.223176\pi$
$258$	2.87893	−	2.36470i	2.87893	−	2.36470i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.558324	−	1.78358i	−0.558324	−	1.78358i
$263$		0			0		−0.728230	−	0.685333i	$-0.759657\pi$
$263$		0			0		0.728230	+	0.685333i	$0.240343\pi$
$264$	−1.95947	−	0.838857i	−1.95947	−	0.838857i
$265$		0			0
$266$		0			0
$267$	3.72536	+	0.454301i	3.72536	+	0.454301i
$268$	−0.136670	−	1.18728i	−0.136670	−	1.18728i
$269$		0			0		0.246861	−	0.969051i	$-0.420601\pi$
$269$		0			0		−0.246861	+	0.969051i	$0.579399\pi$
$270$		0			0
$271$		0			0		−0.797778	−	0.602951i	$-0.793991\pi$
$271$		0			0		0.797778	+	0.602951i	$0.206009\pi$
$272$	0.909153	−	0.706587i	0.909153	−	0.706587i
$273$		0			0
$274$	−1.25981	+	0.952152i	−1.25981	+	0.952152i
$275$	−0.293508	+	1.09048i	−0.293508	+	1.09048i
$276$		0			0
$277$		0			0		0.728230	−	0.685333i	$-0.240343\pi$
$277$		0			0		−0.728230	+	0.685333i	$0.759657\pi$
$278$	−1.31671	−	0.740601i	−1.31671	−	0.740601i
$279$		0			0
$280$		0			0
$281$	−0.000998962	−	0.0134461i	−0.000998962	−	0.0134461i	0.996729	−	0.0808112i	$-0.0257511\pi$
$281$	−0.000998962	−	0.0134461i	−0.000998962	−	0.0134461i	−0.997728	+	0.0673651i	$0.978541\pi$
$282$		0			0
$283$	1.18980	+	1.59651i	1.18980	+	1.59651i	0.670466	+	0.741941i	$0.266094\pi$
$283$	1.18980	+	1.59651i	1.18980	+	1.59651i	0.519333	+	0.854572i	$0.326180\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.18079	−	1.34550i	−2.18079	−	1.34550i
$289$	0.0546548	+	0.321207i	0.0546548	+	0.321207i
$290$		0			0
$291$	−0.344389	+	2.99177i	−0.344389	+	2.99177i
$292$	−0.459241	+	1.91004i	−0.459241	+	1.91004i
$293$		0			0		−0.990924	−	0.134424i	$-0.957082\pi$
$293$		0			0		0.990924	+	0.134424i	$0.0429185\pi$
$294$	1.52097	−	1.11763i	1.52097	−	1.11763i
$295$		0			0
$296$		0			0
$297$	−2.85762	−	1.71034i	−2.85762	−	1.71034i
$298$		0			0
$299$		0			0
$300$	−0.754498	+	1.73009i	−0.754498	+	1.73009i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.748066	−	1.84993i	−0.748066	−	1.84993i
$305$		0			0
$306$	2.55191	−	1.48100i	2.55191	−	1.48100i
$307$	0.0623073	−	1.31933i	0.0623073	−	1.31933i	−0.718923	−	0.695089i	$-0.755365\pi$
$307$	0.0623073	−	1.31933i	0.0623073	−	1.31933i	0.781231	−	0.624242i	$-0.214592\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.670466	−	0.741941i	$-0.733906\pi$
$311$		0			0		0.670466	+	0.741941i	$0.266094\pi$
$312$		0			0
$313$	−1.67122	−	0.389922i	−1.67122	−	0.389922i	−0.718923	−	0.695089i	$-0.755365\pi$
$313$	−1.67122	−	0.389922i	−1.67122	−	0.389922i	−0.952299	+	0.305167i	$0.901288\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0337017	−	0.999432i	$-0.510730\pi$
$317$		0			0		0.0337017	+	0.999432i	$0.489270\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.702320	+	3.31148i	0.702320	+	3.31148i
$322$		0			0
$323$	2.28430	+	0.247358i	2.28430	+	0.247358i
$324$	−2.32112	−	1.90653i	−2.32112	−	1.90653i
$325$		0			0
$326$	−0.0187292	+	0.308305i	−0.0187292	+	0.308305i
$327$		0			0
$328$	1.82367	+	0.123131i	1.82367	+	0.123131i
$329$		0			0
$330$		0			0
$331$	−0.610429	+	1.21622i	−0.610429	+	1.21622i	0.349751	+	0.936843i	$0.386266\pi$
$331$	−0.610429	+	1.21622i	−0.610429	+	1.21622i	−0.960181	+	0.279380i	$0.909871\pi$
$332$	1.21619	+	0.0328043i	1.21619	+	0.0328043i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.44961	−	1.03539i	−1.44961	−	1.03539i	−0.989021	−	0.147772i	$-0.952790\pi$
$337$	−1.44961	−	1.03539i	−1.44961	−	1.03539i	−0.460585	−	0.887615i	$-0.652361\pi$
$338$	0.424315	−	0.905515i	0.424315	−	0.905515i
$339$	−2.81672	+	0.0759755i	−2.81672	+	0.0759755i
$340$		0			0
$341$		0			0
$342$	−1.26227	−	4.95503i	−1.26227	−	4.95503i
$343$		0			0
$344$	−1.00226	−	1.70049i	−1.00226	−	1.70049i
$345$		0			0
$346$		0			0
$347$	1.41073	−	0.152762i	1.41073	−	0.152762i	0.629495	−	0.777005i	$-0.283262\pi$
$347$	1.41073	−	0.152762i	1.41073	−	0.152762i	0.781231	+	0.624242i	$0.214592\pi$
$348$		0			0
$349$		0			0		0.0740898	−	0.997252i	$-0.476395\pi$
$349$		0			0		−0.0740898	+	0.997252i	$0.523605\pi$
$350$		0			0
$351$		0			0
$352$	−0.599437	+	0.957065i	−0.599437	+	0.957065i
$353$	−1.07449	+	1.61693i	−1.07449	+	1.61693i	−0.337088	+	0.941473i	$0.609442\pi$
$353$	−1.07449	+	1.61693i	−1.07449	+	1.61693i	−0.737404	+	0.675452i	$0.763948\pi$
$354$	−1.16878	−	1.22528i	−1.16878	−	1.22528i
$355$		0			0
$356$	0.542628	−	1.91290i	0.542628	−	1.91290i
$357$		0			0
$358$	−0.446835	−	0.692486i	−0.446835	−	0.692486i
$359$		0			0		−0.0471738	−	0.998887i	$-0.515021\pi$
$359$		0			0		0.0471738	+	0.998887i	$0.484979\pi$
$360$		0			0
$361$	1.11785	−	2.76439i	1.11785	−	2.76439i
$362$		0			0
$363$	−0.269852	+	0.444045i	−0.269852	+	0.444045i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.948098	−	0.317979i	$-0.103004\pi$
$367$		0			0		−0.948098	+	0.317979i	$0.896996\pi$
$368$		0			0
$369$	4.58826	+	0.940831i	4.58826	+	0.940831i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.973845	−	0.227213i	$-0.0729614\pi$
$373$		0			0		−0.973845	+	0.227213i	$0.927039\pi$
$374$	−0.645090	−	1.12902i	−0.645090	−	1.12902i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.151655	−	0.442267i	−0.151655	−	0.442267i	0.843894	−	0.536510i	$-0.180258\pi$
$379$	−0.151655	−	0.442267i	−0.151655	−	0.442267i	−0.995549	+	0.0942425i	$0.969957\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.997728	−	0.0673651i	$-0.0214592\pi$
$383$		0			0		−0.997728	+	0.0673651i	$0.978541\pi$
$384$	−1.22725	+	1.43399i	−1.22725	+	1.43399i
$385$		0			0
$386$	0.197789	−	0.0405569i	0.197789	−	0.0405569i
$387$	−1.95921	−	4.66312i	−1.95921	−	4.66312i
$388$	1.53789	+	0.425069i	1.53789	+	0.425069i
$389$		0			0		−0.924523	−	0.381126i	$-0.875536\pi$
$389$		0			0		0.924523	+	0.381126i	$0.124464\pi$
$390$		0			0
$391$		0			0
$392$	−0.460585	−	0.887615i	−0.460585	−	0.887615i
$393$	−3.52718	+	0.0475607i	−3.52718	+	0.0475607i
$394$		0			0
$395$		0			0
$396$	−1.85176	+	2.22370i	−1.85176	+	2.22370i
$397$		0			0		0.960181	−	0.279380i	$-0.0901288\pi$
$397$		0			0		−0.960181	+	0.279380i	$0.909871\pi$
$398$		0			0
$399$		0			0
$400$	0.843894	+	0.536510i	0.843894	+	0.536510i
$401$	0.296735	−	0.156525i	0.296735	−	0.156525i	−0.311581	−	0.950220i	$-0.600858\pi$
$401$	0.296735	−	0.156525i	0.296735	−	0.156525i	0.608316	+	0.793695i	$0.291845\pi$
$402$	−2.22116	−	0.393366i	−2.22116	−	0.393366i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.787494	−	2.02560i	−0.787494	−	2.02560i
$409$	−0.0532729	−	0.0778682i	−0.0532729	−	0.0778682i	0.797778	−	0.602951i	$-0.206009\pi$
$409$	−0.0532729	−	0.0778682i	−0.0532729	−	0.0778682i	−0.851051	+	0.525083i	$0.824034\pi$
$410$		0			0
$411$	1.04246	+	2.79232i	1.04246	+	2.79232i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.04991	+	1.98195i	−2.04991	+	1.98195i
$418$	−2.18741	+	0.541555i	−2.18741	+	0.541555i
$419$	−0.512166	−	0.706939i	−0.512166	−	0.706939i	0.472511	−	0.881325i	$-0.343348\pi$
$419$	−0.512166	−	0.706939i	−0.512166	−	0.706939i	−0.984677	+	0.174386i	$0.944206\pi$
$420$		0			0
$421$		0			0		−0.999182	−	0.0404387i	$-0.987124\pi$
$421$		0			0		0.999182	+	0.0404387i	$0.0128755\pi$
$422$	0.183493	+	0.214403i	0.183493	+	0.214403i
$423$		0			0
$424$		0			0
$425$	−1.00359	+	0.564482i	−1.00359	+	0.564482i
$426$		0			0
$427$		0			0
$428$	1.79089	−	0.0966816i	1.79089	−	0.0966816i
$429$		0			0
$430$		0			0
$431$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$431$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$432$	−2.20131	+	1.96245i	−2.20131	+	1.96245i
$433$	0.807337	+	1.78516i	0.807337	+	1.78516i	0.586694	+	0.809809i	$0.300429\pi$
$433$	0.807337	+	1.78516i	0.807337	+	1.78516i	0.220643	+	0.975355i	$0.429185\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	3.20691	+	1.86113i	3.20691	+	1.86113i
$439$		0			0		−0.718923	−	0.695089i	$-0.755365\pi$
$439$		0			0		0.718923	+	0.695089i	$0.244635\pi$
$440$		0			0
$441$	−0.863775	−	2.41249i	−0.863775	−	2.41249i
$442$		0			0
$443$	−1.55338	−	0.846354i	−1.55338	−	0.846354i	−0.999909	−	0.0134828i	$-0.995708\pi$
$443$	−1.55338	−	0.846354i	−1.55338	−	0.846354i	−0.553466	−	0.832871i	$-0.686695\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.431415	−	1.20492i	0.431415	−	1.20492i	−0.507764	−	0.861496i	$-0.669528\pi$
$449$	0.431415	−	1.20492i	0.431415	−	1.20492i	0.939179	−	0.343428i	$-0.111588\pi$
$450$	1.95802	+	1.65299i	1.95802	+	1.65299i
$451$	0.428252	−	2.01923i	0.428252	−	2.01923i
$452$	−0.190703	+	1.48066i	−0.190703	+	1.48066i
$453$		0			0
$454$	1.38608	+	1.37677i	1.38608	+	1.37677i
$455$		0			0
$456$	−3.74956	+	0.354948i	−3.74956	+	0.354948i
$457$	1.66574	−	0.271892i	1.66574	−	0.271892i	0.746444	−	0.665448i	$-0.231760\pi$
$457$	1.66574	−	0.271892i	1.66574	−	0.271892i	0.919301	+	0.393556i	$0.128755\pi$
$458$		0			0
$459$	−0.793820	−	3.30159i	−0.793820	−	3.30159i
$460$		0			0
$461$		0			0		0.924523	−	0.381126i	$-0.124464\pi$
$461$		0			0		−0.924523	+	0.381126i	$0.875536\pi$
$462$		0			0
$463$		0			0		−0.629495	−	0.777005i	$-0.716738\pi$
$463$		0			0		0.629495	+	0.777005i	$0.283262\pi$
$464$		0			0
$465$		0			0
$466$	−1.54549			−1.54549
$467$	−0.412067	−	0.911153i	−0.412067	−	0.911153i
$467$	−0.412067	−	0.911153i	−0.412067	−	0.911153i
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.737018	+	0.511553i	−0.737018	+	0.511553i
$473$	−2.06084	+	0.849561i	−2.06084	+	0.849561i
$474$		0			0
$475$	0.466484	+	1.94017i	0.466484	+	1.94017i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.998546	−	0.0539068i	$-0.982833\pi$
$479$		0			0		0.998546	+	0.0539068i	$0.0171674\pi$
$480$		0			0
$481$		0			0
$482$	−0.0957760	+	0.743626i	−0.0957760	+	0.743626i
$483$		0			0
$484$	0.210360	+	0.177590i	0.210360	+	0.177590i
$485$		0			0
$486$	−2.25550	+	1.52086i	−2.25550	+	1.52086i
$487$		0			0		−0.960181	−	0.279380i	$-0.909871\pi$
$487$		0			0		0.960181	+	0.279380i	$0.0901288\pi$
$488$		0			0
$489$	0.547525	+	0.200212i	0.547525	+	0.200212i
$490$		0			0
$491$	0.364370	+	0.198527i	0.364370	+	0.198527i	0.650217	−	0.759749i	$-0.274678\pi$
$491$	0.364370	+	0.198527i	0.364370	+	0.198527i	−0.285846	+	0.958275i	$0.592275\pi$
$492$	1.20661	−	3.23203i	1.20661	−	3.23203i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.715491	−	2.18202i	0.715491	−	2.18202i
$499$	−0.471262	+	0.614875i	−0.471262	+	0.614875i	−0.967365	−	0.253388i	$-0.918455\pi$
$499$	−0.471262	+	0.614875i	−0.471262	+	0.614875i	0.496103	+	0.868264i	$0.334764\pi$
$500$		0			0
$501$		0			0
$502$	−0.426736	+	0.380432i	−0.426736	+	0.380432i
$503$		0			0		0.709486	−	0.704719i	$-0.248927\pi$
$503$		0			0		−0.709486	+	0.704719i	$0.751073\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.40887	−	1.25600i	−1.40887	−	1.25600i
$508$		0			0
$509$		0			0		0.871589	−	0.490238i	$-0.163090\pi$
$509$		0			0		−0.871589	+	0.490238i	$0.836910\pi$
$510$		0			0
$511$		0			0
$512$	0.650217	+	0.759749i	0.650217	+	0.759749i
$513$	−5.87992	−	0.237971i	−5.87992	−	0.237971i
$514$	0.385711	−	0.308202i	0.385711	−	0.308202i
$515$		0			0
$516$	−3.61641	+	0.895344i	−3.61641	+	0.895344i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.306531	+	0.571740i	0.306531	+	0.571740i	0.986939	−	0.161094i	$-0.0515021\pi$
$521$	0.306531	+	0.571740i	0.306531	+	0.571740i	−0.680408	+	0.732833i	$0.738197\pi$
$522$		0			0
$523$	0.347025	+	0.929540i	0.347025	+	0.929540i	0.986939	+	0.161094i	$0.0515021\pi$
$523$	0.347025	+	0.929540i	0.347025	+	0.929540i	−0.639914	+	0.768447i	$0.721030\pi$
$524$	−0.263708	+	1.85023i	−0.263708	+	1.85023i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.40763	+	1.60056i	1.40763	+	1.60056i
$529$	0.690227	−	0.723593i	0.690227	−	0.723593i
$530$		0			0
$531$	−2.04765	+	1.04507i	−2.04765	+	1.04507i
$532$		0			0
$533$		0			0
$534$	−3.16710	−	2.01350i	−3.16710	−	2.01350i
$535$		0			0
$536$	−0.387653	+	1.13050i	−0.387653	+	1.13050i
$537$	−1.49357	+	0.434578i	−1.49357	+	0.434578i
$538$		0			0
$539$	−1.06574	+	0.373494i	−1.06574	+	0.373494i
$540$		0			0
$541$		0			0		0.999909	−	0.0134828i	$-0.00429185\pi$
$541$		0			0		−0.999909	+	0.0134828i	$0.995708\pi$
$542$		0			0
$543$		0			0
$544$	−1.12475	+	0.246481i	−1.12475	+	0.246481i
$545$		0			0
$546$		0			0
$547$	−0.420032	−	0.999719i	−0.420032	−	0.999719i	−0.984677	−	0.174386i	$-0.944206\pi$
$547$	−0.420032	−	0.999719i	−0.420032	−	0.999719i	0.564646	−	0.825333i	$-0.309013\pi$
$548$	1.54697	−	0.317208i	1.54697	−	0.317208i
$549$		0			0
$550$	0.734284	−	0.857978i	0.734284	−	0.857978i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.869741	+	1.23521i	0.869741	+	1.23521i
$557$		0			0		−0.259904	−	0.965634i	$-0.583691\pi$
$557$		0			0		0.259904	+	0.965634i	$0.416309\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.39009	+	0.557644i	−2.39009	+	0.557644i
$562$	−0.00488562	+	0.0125668i	−0.00488562	+	0.0125668i
$563$	−0.361514	−	1.96410i	−0.361514	−	1.96410i	−0.233773	−	0.972291i	$-0.575107\pi$
$563$	−0.361514	−	1.96410i	−0.361514	−	1.96410i	−0.127741	−	0.991808i	$-0.540773\pi$
$564$		0			0
$565$		0			0
$566$	−0.386798	−	1.95317i	−0.386798	−	1.95317i
$567$		0			0
$568$		0			0
$569$	−1.73005	−	0.554401i	−1.73005	−	0.554401i	−0.737404	−	0.675452i	$-0.763948\pi$
$569$	−1.73005	−	0.554401i	−1.73005	−	0.554401i	−0.992646	+	0.121051i	$0.961373\pi$
$570$		0			0
$571$	0.696390	−	1.14592i	0.696390	−	1.14592i	−0.285846	−	0.958275i	$-0.592275\pi$
$571$	0.696390	−	1.14592i	0.696390	−	1.14592i	0.982237	−	0.187646i	$-0.0600858\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.38933	+	2.15313i	1.38933	+	2.15313i
$577$	1.89529	−	0.496447i	1.89529	−	0.496447i	0.896748	−	0.442541i	$-0.145923\pi$
$577$	1.89529	−	0.496447i	1.89529	−	0.496447i	0.998546	−	0.0539068i	$-0.0171674\pi$
$578$	0.0889173	−	0.313456i	0.0889173	−	0.313456i
$579$	0.0333558	−	0.379621i	0.0333558	−	0.379621i
$580$		0			0
$581$		0			0
$582$	1.59855	−	2.55225i	1.59855	−	2.55225i
$583$		0			0
$584$	1.23663	−	1.52640i	1.23663	−	1.52640i
$585$		0			0
$586$		0			0
$587$	0.333537	−	0.0361175i	0.333537	−	0.0361175i	0.0606373	−	0.998160i	$-0.480687\pi$
$587$	0.333537	−	0.0361175i	0.333537	−	0.0361175i	0.272900	+	0.962042i	$0.412017\pi$
$588$	−1.85392	+	0.354173i	−1.85392	+	0.354173i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0386252	−	0.170743i	0.0386252	−	0.170743i	−0.952299	−	0.305167i	$-0.901288\pi$
$593$	0.0386252	−	0.170743i	0.0386252	−	0.170743i	0.990924	+	0.134424i	$0.0429185\pi$
$594$	1.84324	+	2.77376i	1.84324	+	2.77376i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.999182	−	0.0404387i	$-0.0128755\pi$
$599$		0			0		−0.999182	+	0.0404387i	$0.987124\pi$
$600$	1.42568	−	1.23689i	1.42568	−	1.23689i
$601$	0.0214696	+	0.0342784i	0.0214696	+	0.0342784i	0.858053	−	0.513561i	$-0.171674\pi$
$601$	0.0214696	+	0.0342784i	0.0214696	+	0.0342784i	−0.836584	+	0.547839i	$0.815451\pi$
$602$		0			0
$603$	−1.37374	+	2.73704i	−1.37374	+	2.73704i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.986939	−	0.161094i	$-0.948498\pi$
$607$		0			0		0.986939	+	0.161094i	$0.0515021\pi$
$608$	−0.120999	+	1.99178i	−0.120999	+	1.99178i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.94088	+	0.238436i	−2.94088	+	0.238436i
$613$		0			0		−0.207472	−	0.978241i	$-0.566524\pi$
$613$		0			0		0.207472	+	0.978241i	$0.433476\pi$
$614$	−0.624094	+	1.16406i	−0.624094	+	1.16406i
$615$		0			0
$616$		0			0
$617$	0.0626567	+	1.85810i	0.0626567	+	1.85810i	0.399745	+	0.916626i	$0.369099\pi$
$617$	0.0626567	+	1.85810i	0.0626567	+	1.85810i	−0.337088	+	0.941473i	$0.609442\pi$
$618$		0			0
$619$	−0.865261	−	0.792567i	−0.865261	−	0.792567i	0.114357	−	0.993440i	$-0.463519\pi$
$619$	−0.865261	−	0.792567i	−0.865261	−	0.792567i	−0.979617	+	0.200872i	$0.935622\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.755348	−	0.655324i	−0.755348	−	0.655324i
$626$	1.34068	+	1.07127i	1.34068	+	1.07127i
$627$	−0.200643	+	4.24854i	−0.200643	+	4.24854i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.929578	−	0.368626i	$-0.120172\pi$
$631$		0			0		−0.929578	+	0.368626i	$0.879828\pi$
$632$		0			0
$633$	0.486789	−	0.216208i	0.486789	−	0.216208i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.86131	+	0.252497i	1.86131	+	0.252497i	0.976820	−	0.214062i	$-0.0686695\pi$
$641$	1.86131	+	0.252497i	1.86131	+	0.252497i	0.884490	+	0.466559i	$0.154506\pi$
$642$	0.791353	−	3.29133i	0.791353	−	3.29133i
$643$	0.199344	−	1.73174i	0.199344	−	1.73174i	−0.387350	−	0.921933i	$-0.626609\pi$
$643$	0.199344	−	1.73174i	0.199344	−	1.73174i	0.586694	−	0.809809i	$-0.300429\pi$
$644$		0			0
$645$		0			0
$646$	−1.95542	−	1.20646i	−1.95542	−	1.20646i
$647$		0			0		0.181020	−	0.983479i	$-0.442060\pi$
$647$		0			0		−0.181020	+	0.983479i	$0.557940\pi$
$648$	1.27453	+	2.71994i	1.27453	+	2.71994i
$649$	0.454473	+	0.905494i	0.454473	+	0.905494i
$650$		0			0
$651$		0			0
$652$	0.149603	−	0.270225i	0.149603	−	0.270225i
$653$		0			0		−0.0740898	−	0.997252i	$-0.523605\pi$
$653$		0			0		0.0740898	+	0.997252i	$0.476395\pi$
$654$		0			0
$655$		0			0
$656$	−1.59311	−	0.896067i	−1.59311	−	0.896067i
$657$	3.66583	−	3.44989i	3.66583	−	3.44989i
$658$		0			0
$659$	−0.519619	+	1.93057i	−0.519619	+	1.93057i	−0.233773	+	0.972291i	$0.575107\pi$
$659$	−0.519619	+	1.93057i	−0.519619	+	1.93057i	−0.285846	+	0.958275i	$0.592275\pi$
$660$		0			0
$661$		0			0		0.984677	−	0.174386i	$-0.0557940\pi$
$661$		0			0		−0.984677	+	0.174386i	$0.944206\pi$
$662$	1.07447	−	0.835068i	1.07447	−	0.835068i
$663$		0			0
$664$	−1.08365	−	0.553070i	−1.08365	−	0.553070i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.734057	−	1.62313i	0.734057	−	1.62313i	−0.0471738	−	0.998887i	$-0.515021\pi$
$673$	0.734057	−	1.62313i	0.734057	−	1.62313i	0.781231	−	0.624242i	$-0.214592\pi$
$674$	0.862823	+	1.55850i	0.862823	+	1.55850i
$675$	2.46714	−	1.61561i	2.46714	−	1.61561i
$676$	−0.772743	+	0.634719i	−0.772743	+	0.634719i
$677$		0			0		0.436485	−	0.899712i	$-0.356223\pi$
$677$		0			0		−0.436485	+	0.899712i	$0.643777\pi$
$678$	2.57517	+	1.14377i	2.57517	+	1.14377i
$679$		0			0
$680$		0			0
$681$	3.23797	−	1.76420i	3.23797	−	1.76420i
$682$		0			0
$683$	0.716228	−	1.70470i	0.716228	−	1.70470i	0.00674156	−	0.999977i	$-0.497854\pi$
$683$	0.716228	−	1.70470i	0.716228	−	1.70470i	0.709486	−	0.704719i	$-0.248927\pi$
$684$	−0.993325	+	5.01587i	−0.993325	+	5.01587i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.172771	+	1.96630i	0.172771	+	1.96630i
$689$		0			0
$690$		0			0
$691$	−0.197280	+	0.334715i	−0.197280	+	0.334715i	−0.943724	−	0.330734i	$-0.892704\pi$
$691$	−0.197280	+	0.334715i	−0.197280	+	0.334715i	0.746444	+	0.665448i	$0.231760\pi$
$692$		0			0
$693$		0			0
$694$	−1.33912	−	0.469302i	−1.33912	−	0.469302i
$695$		0			0
$696$		0			0
$697$	1.77609	−	1.12916i	1.77609	−	1.12916i
$698$		0			0
$699$	−0.833821	+	2.79531i	−0.833821	+	2.79531i
$700$		0			0
$701$		0			0		0.902634	−	0.430410i	$-0.141631\pi$
$701$		0			0		−0.902634	+	0.430410i	$0.858369\pi$
$702$		0			0
$703$		0			0
$704$	0.953002	−	0.605876i	0.953002	−	0.605876i
$705$		0			0
$706$	1.66581	−	0.997019i	1.66581	−	0.997019i
$707$		0			0
$708$	0.527608	+	1.60903i	0.527608	+	1.60903i
$709$		0			0		−0.967365	−	0.253388i	$-0.918455\pi$
$709$		0			0		0.967365	+	0.253388i	$0.0815451\pi$
$710$		0			0
$711$		0			0
$712$	−1.31313	+	1.49310i	−1.31313	+	1.49310i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.105276	+	0.817383i	0.105276	+	0.817383i
$717$		0			0
$718$		0			0
$719$		0			0		0.618962	−	0.785421i	$-0.287554\pi$
$719$		0			0		−0.618962	+	0.785421i	$0.712446\pi$
$720$		0			0
$721$		0			0
$722$	−2.19883	+	2.01410i	−2.19883	+	2.01410i
$723$	1.29332	+	0.574431i	1.29332	+	0.574431i
$724$		0			0
$725$		0			0
$726$	0.434699	−	0.284664i	0.434699	−	0.284664i
$727$		0			0		−0.484351	−	0.874874i	$-0.660944\pi$
$727$		0			0		0.484351	+	0.874874i	$0.339056\pi$
$728$		0			0
$729$	0.636549	+	2.03347i	0.636549	+	2.03347i
$730$		0			0
$731$	−2.08940	−	0.894479i	−2.08940	−	0.894479i
$732$		0			0
$733$		0			0		0.963860	−	0.266408i	$-0.0858369\pi$
$733$		0			0		−0.963860	+	0.266408i	$0.914163\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.20212	+	0.613533i	1.20212	+	0.613533i
$738$	−3.73657	−	2.82405i	−3.73657	−	2.82405i
$739$	1.34394	−	1.04450i	1.34394	−	1.04450i	0.349751	−	0.936843i	$-0.386266\pi$
$739$	1.34394	−	1.04450i	1.34394	−	1.04450i	0.994188	−	0.107657i	$-0.0343348\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.939179	−	0.343428i	$-0.111588\pi$
$743$		0			0		−0.939179	+	0.343428i	$0.888412\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.56111	−	1.77763i	−2.56111	−	1.77763i
$748$	0.0963401	+	1.29674i	0.0963401	+	1.29674i
$749$		0			0
$750$		0			0
$751$		0			0		−0.999909	−	0.0134828i	$-0.995708\pi$
$751$		0			0		0.999909	+	0.0134828i	$0.00429185\pi$
$752$		0			0
$753$	0.457853	+	0.977087i	0.457853	+	0.977087i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.934463	−	0.356059i	$-0.884120\pi$
$757$		0			0		0.934463	+	0.356059i	$0.115880\pi$
$758$	−0.0534671	+	0.464479i	−0.0534671	+	0.464479i
$759$		0			0
$760$		0			0
$761$	1.53479	−	1.12779i	1.53479	−	1.12779i	0.586694	−	0.809809i	$-0.300429\pi$
$761$	1.53479	−	1.12779i	1.53479	−	1.12779i	0.948098	−	0.317979i	$-0.103004\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.72496	−	0.766144i	1.72496	−	0.766144i
$769$	−0.0458618	+	1.36004i	−0.0458618	+	1.36004i	0.709486	+	0.704719i	$0.248927\pi$
$769$	−0.0458618	+	1.36004i	−0.0458618	+	1.36004i	−0.755348	+	0.655324i	$0.772532\pi$
$770$		0			0
$771$	−0.349345	−	0.863915i	−0.349345	−	0.863915i
$772$	−0.195987	−	0.0485221i	−0.195987	−	0.0485221i
$773$		0			0		0.864900	−	0.501945i	$-0.167382\pi$
$773$		0			0		−0.864900	+	0.501945i	$0.832618\pi$
$774$	−0.238604	+	5.05236i	−0.238604	+	5.05236i
$775$		0			0
$776$	−1.20520	−	1.04561i	−1.20520	−	1.04561i
$777$		0			0
$778$		0			0
$779$	−1.04258	−	3.49516i	−1.04258	−	3.49516i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.0337017	+	0.999432i	0.0337017	+	0.999432i
$785$		0			0
$786$	3.20422	+	1.47520i	3.20422	+	1.47520i
$787$	−0.0191116	+	0.0356469i	−0.0191116	+	0.0356469i	−0.890700	−	0.454591i	$-0.849785\pi$
$787$	−0.0191116	+	0.0356469i	−0.0191116	+	0.0356469i	0.871589	+	0.490238i	$0.163090\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	2.62856	−	1.21017i	2.62856	−	1.21017i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.460585	−	0.887615i	$-0.347639\pi$
$797$		0			0		−0.460585	+	0.887615i	$0.652361\pi$
$798$		0			0
$799$		0			0
$800$	−0.530808	−	0.847492i	−0.530808	−	0.847492i
$801$	−3.84860	+	3.33896i	−3.84860	+	3.33896i
$802$	−0.335213	+	0.0135667i	−0.335213	+	0.0135667i
$803$	−1.50946	−	1.62576i	−1.50946	−	1.62576i
$804$	1.83559	+	1.31107i	1.83559	+	1.31107i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.310796	+	1.22003i	0.310796	+	1.22003i	0.908355	+	0.418201i	$0.137339\pi$
$809$	0.310796	+	1.22003i	0.310796	+	1.22003i	−0.597559	+	0.801825i	$0.703863\pi$
$810$		0			0
$811$	−0.922460	−	1.56509i	−0.922460	−	1.56509i	−0.821508	−	0.570197i	$-0.806867\pi$
$811$	−0.922460	−	1.56509i	−0.922460	−	1.56509i	−0.100952	−	0.994891i	$-0.532189\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.161019	+	2.16732i	−0.161019	+	2.16732i
$817$	−2.47945	+	3.06046i	−2.47945	+	3.06046i
$818$	0.0145707	+	0.0932157i	0.0145707	+	0.0932157i
$819$		0			0
$820$		0			0
$821$		0			0		−0.690227	−	0.723593i	$-0.742489\pi$
$821$		0			0		0.690227	+	0.723593i	$0.257511\pi$
$822$	0.260886	−	2.96913i	0.260886	−	2.96913i
$823$		0			0		0.272900	−	0.962042i	$-0.412017\pi$
$823$		0			0		−0.272900	+	0.962042i	$0.587983\pi$
$824$		0			0
$825$	−1.15566	−	1.79099i	−1.15566	−	1.79099i
$826$		0			0
$827$	0.102705	−	0.141763i	0.102705	−	0.141763i	−0.755348	−	0.655324i	$-0.772532\pi$
$827$	0.102705	−	0.141763i	0.102705	−	0.141763i	0.858053	+	0.513561i	$0.171674\pi$
$828$		0			0
$829$		0			0		0.00674156	−	0.999977i	$-0.497854\pi$
$829$		0			0		−0.00674156	+	0.999977i	$0.502146\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.03256	−	0.509561i	−1.03256	−	0.509561i
$834$	2.70337	−	0.906674i	2.70337	−	0.906674i
$835$		0			0
$836$	2.20752	+	0.452656i	2.20752	+	0.452656i
$837$		0			0
$838$	0.158025	+	0.858548i	0.158025	+	0.858548i
$839$		0			0		0.362351	−	0.932042i	$-0.381974\pi$
$839$		0			0		−0.362351	+	0.932042i	$0.618026\pi$
$840$		0			0
$841$	0.496103	+	0.868264i	0.496103	+	0.868264i
$842$		0			0
$843$	0.0200937	+	0.0156167i	0.0200937	+	0.0156167i
$844$	−0.0733457	−	0.272505i	−0.0733457	−	0.272505i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.74137	−	0.354173i	−3.74137	−	0.354173i
$850$	1.14883	−	0.0775671i	1.14883	−	0.0775671i
$851$		0			0
$852$		0			0
$853$		0			0		0.979617	−	0.200872i	$-0.0643777\pi$
$853$		0			0		−0.979617	+	0.200872i	$0.935622\pi$
$854$		0			0
$855$		0			0
$856$	−1.65813	−	0.683548i	−1.65813	−	0.683548i
$857$	0.828958	−	0.181659i	0.828958	−	0.181659i	0.220643	−	0.975355i	$-0.429185\pi$
$857$	0.828958	−	0.181659i	0.828958	−	0.181659i	0.608316	+	0.793695i	$0.291845\pi$
$858$		0			0
$859$	−0.540445	−	1.04152i	−0.540445	−	1.04152i	−0.989021	−	0.147772i	$-0.952790\pi$
$859$	−0.540445	−	1.04152i	−0.540445	−	1.04152i	0.448576	−	0.893745i	$-0.351931\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.639914	−	0.768447i	$-0.278970\pi$
$863$		0			0		−0.639914	+	0.768447i	$0.721030\pi$
$864$	2.83164	−	0.823908i	2.83164	−	0.823908i
$865$		0			0
$866$	0.0396225	−	1.95883i	0.0396225	−	1.95883i
$867$	−0.518974	−	0.329940i	−0.518974	−	0.329940i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−2.70008	−	3.07015i	−2.70008	−	3.07015i
$874$		0			0
$875$		0			0
$876$	−2.09362	−	3.06021i	−2.09362	−	3.06021i
$877$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$877$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0346659	−	0.570641i	−0.0346659	−	0.570641i	−0.973845	−	0.227213i	$-0.927039\pi$
$881$	−0.0346659	−	0.570641i	−0.0346659	−	0.570641i	0.939179	−	0.343428i	$-0.111588\pi$
$882$	−0.258685	+	2.54937i	−0.258685	+	2.54937i
$883$	−1.78888	+	0.242672i	−1.78888	+	0.242672i	−0.952299	−	0.305167i	$-0.901288\pi$
$883$	−1.78888	+	0.242672i	−1.78888	+	0.242672i	−0.836584	+	0.547839i	$0.815451\pi$
$884$		0			0
$885$		0			0
$886$	1.03785	+	1.43254i	1.03785	+	1.43254i
$887$		0			0		0.781231	−	0.624242i	$-0.214592\pi$
$887$		0			0		−0.781231	+	0.624242i	$0.785408\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.24396	−	0.991512i	3.24396	−	0.991512i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.908020	+	0.901919i	−0.908020	+	0.901919i
$899$		0			0
$900$	−1.05591	−	2.33480i	−1.05591	−	2.33480i
$901$		0			0
$902$	−1.25565	+	1.63830i	−1.25565	+	1.63830i
$903$		0			0
$904$	0.809424	−	1.25441i	0.809424	−	1.25441i
$905$		0			0
$906$		0			0
$907$	−0.184305	−	0.135430i	−0.184305	−	0.135430i	0.496103	−	0.868264i	$-0.334764\pi$
$907$	−0.184305	−	0.135430i	−0.184305	−	0.135430i	−0.680408	+	0.732833i	$0.738197\pi$
$908$	−0.658549	−	1.83930i	−0.658549	−	1.83930i
$909$		0			0
$910$		0			0
$911$		0			0		0.919301	−	0.393556i	$-0.128755\pi$
$911$		0			0		−0.919301	+	0.393556i	$0.871245\pi$
$912$	3.53725	+	1.29346i	3.53725	+	1.29346i
$913$	−0.791002	+	1.12339i	−0.791002	+	1.12339i
$914$	−1.62058	−	0.471533i	−1.62058	−	0.471533i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.704509	+	3.32180i	−0.704509	+	3.32180i
$919$		0			0		0.127741	−	0.991808i	$-0.459227\pi$
$919$		0			0		−0.127741	+	0.991808i	$0.540773\pi$
$920$		0			0
$921$	1.76871	+	1.75683i	1.76871	+	1.75683i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.340880	−	0.236600i	0.340880	−	0.236600i	−0.387350	−	0.921933i	$-0.626609\pi$
$929$	0.340880	−	0.236600i	0.340880	−	0.236600i	0.728230	+	0.685333i	$0.240343\pi$
$930$		0			0
$931$	−1.33788	+	1.48051i	−1.33788	+	1.48051i
$932$	1.39501	+	0.665192i	1.39501	+	0.665192i
$933$		0			0
$934$	−0.0202235	+	0.999795i	−0.0202235	+	0.999795i
$935$		0			0
$936$		0			0
$937$	1.02463	−	1.13386i	1.02463	−	1.13386i	0.0337017	−	0.999432i	$-0.489270\pi$
$937$	1.02463	−	1.13386i	1.02463	−	1.13386i	0.990924	−	0.134424i	$-0.0429185\pi$
$938$		0			0
$939$	2.66092	−	1.84690i	2.66092	−	1.84690i
$940$		0			0
$941$		0			0		0.992646	−	0.121051i	$-0.0386266\pi$
$941$		0			0		−0.992646	+	0.121051i	$0.961373\pi$
$942$		0			0
$943$		0			0
$944$	0.885434	−	0.144526i	0.885434	−	0.144526i
$945$		0			0
$946$	2.22584	+	0.120163i	2.22584	+	0.120163i
$947$	0.979413	+	0.972832i	0.979413	+	0.972832i	0.999636	−	0.0269632i	$-0.00858369\pi$
$947$	0.979413	+	0.972832i	0.979413	+	0.972832i	−0.0202235	+	0.999795i	$0.506438\pi$
$948$		0			0
$949$		0			0
$950$	0.414002	−	1.95204i	0.414002	−	1.95204i
$951$		0			0
$952$		0			0
$953$	−1.38726	+	0.935416i	−1.38726	+	0.935416i	−0.387350	+	0.921933i	$0.626609\pi$
$953$	−1.38726	+	0.935416i	−1.38726	+	0.935416i	−0.999909	+	0.0134828i	$0.995708\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.805835	−	0.592140i	−0.805835	−	0.592140i
$962$		0			0
$963$	−3.97488	−	2.30682i	−3.97488	−	2.30682i
$964$	0.406515	−	0.629999i	0.406515	−	0.629999i
$965$		0			0
$966$		0			0
$967$		0			0		0.597559	−	0.801825i	$-0.296137\pi$
$967$		0			0		−0.597559	+	0.801825i	$0.703863\pi$
$968$	−0.113441	−	0.250839i	−0.113441	−	0.250839i
$969$	−3.23711	+	2.88586i	−3.23711	+	2.88586i
$970$		0			0
$971$	1.51352	−	0.746915i	1.51352	−	0.746915i	0.519333	−	0.854572i	$-0.326180\pi$
$971$	1.51352	−	0.746915i	1.51352	−	0.746915i	0.994188	+	0.107657i	$0.0343348\pi$
$972$	2.69049	−	0.401993i	2.69049	−	0.401993i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.0128943	−	0.00394112i	0.0128943	−	0.00394112i	−0.285846	−	0.958275i	$-0.592275\pi$
$977$	0.0128943	−	0.00394112i	0.0128943	−	0.00394112i	0.298741	+	0.954334i	$0.403433\pi$
$978$	−0.408041	−	0.416378i	−0.408041	−	0.416378i
$979$	1.46003	+	1.70598i	1.46003	+	1.70598i
$980$		0			0
$981$		0			0
$982$	−0.243445	−	0.336025i	−0.243445	−	0.336025i
$983$		0			0		0.970693	−	0.240323i	$-0.0772532\pi$
$983$		0			0		−0.970693	+	0.240323i	$0.922747\pi$
$984$	−2.48023	+	2.39800i	−2.48023	+	2.39800i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.141101	−	0.989995i	$-0.454936\pi$
$991$		0			0		−0.141101	+	0.989995i	$0.545064\pi$
$992$		0			0
$993$	−0.930687	−	2.39392i	−0.930687	−	2.39392i
$994$		0			0
$995$		0			0
$996$	−1.58499	+	1.66161i	−1.58499	+	1.66161i
$997$		0			0		−0.220643	−	0.975355i	$-0.570815\pi$
$997$		0			0		0.220643	+	0.975355i	$0.429185\pi$
$998$	0.690025	−	0.352172i	0.690025	−	0.352172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3736.1.l.a.75.1	✓	232
8.3	odd	2	CM	3736.1.l.a.75.1	✓	232
467.137	even	233	inner	3736.1.l.a.2939.1	yes	232
3736.2939	odd	466	inner	3736.1.l.a.2939.1	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3736.1.l.a.75.1	✓	232	1.1	even	1	trivial
3736.1.l.a.75.1	✓	232	8.3	odd	2	CM
3736.1.l.a.2939.1	yes	232	467.137	even	233	inner
3736.1.l.a.2939.1	yes	232	3736.2939	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)

\(f(q)\)	\(=\)	\(q+(-0.902634 - 0.430410i) q^{2} +(-1.26547 + 1.40037i) q^{3} +(0.629495 + 0.777005i) q^{4} +(1.74499 - 0.719355i) q^{6} +(-0.233773 - 0.972291i) q^{8} +(-0.258685 - 2.54937i) q^{9} +O(q^{10})\)	\(q+(-0.902634 - 0.430410i) q^{2} +(-1.26547 + 1.40037i) q^{3} +(0.629495 + 0.777005i) q^{4} +(1.74499 - 0.719355i) q^{6} +(-0.233773 - 0.972291i) q^{8} +(-0.258685 - 2.54937i) q^{9} +(-1.12426 + 0.106427i) q^{11} +(-1.88470 - 0.101746i) q^{12} +(-0.207472 + 0.978241i) q^{16} +(-0.879836 - 0.742774i) q^{17} +(-0.863775 + 2.41249i) q^{18} +(-1.65448 + 1.11560i) q^{19} +(1.06061 + 0.387830i) q^{22} +(1.65740 + 0.903034i) q^{24} +(0.349751 - 0.936843i) q^{25} +(2.37646 + 1.74626i) q^{27} +(0.608316 - 0.793695i) q^{32} +(1.27368 - 1.70907i) q^{33} +(0.474472 + 1.04914i) q^{34} +(1.81803 - 1.80582i) q^{36} +(1.97355 - 0.294873i) q^{38} +(-0.546044 + 1.74435i) q^{41} +(1.88767 - 0.576965i) q^{43} +(-0.790414 - 0.806564i) q^{44} +(-1.10735 - 1.52847i) q^{48} +(0.970693 - 0.240323i) q^{49} +(-0.718923 + 0.695089i) q^{50} +(2.15357 - 0.292143i) q^{51} +(-1.39347 - 2.59908i) q^{54} +(0.531433 - 3.72864i) q^{57} +(-0.325084 - 0.836183i) q^{59} +(-0.890700 + 0.454591i) q^{64} +(-1.88527 + 0.994460i) q^{66} +(-1.00855 - 0.641192i) q^{67} +(0.0232862 - 1.15121i) q^{68} +(-2.41826 + 0.847492i) q^{72} +(1.19502 + 1.55919i) q^{73} +(0.869331 + 1.67533i) q^{75} +(-1.90831 - 0.583272i) q^{76} +(-2.94252 + 0.603370i) q^{81} +(1.24366 - 1.33949i) q^{82} +(0.791074 - 0.924334i) q^{83} +(-1.95221 - 0.291685i) q^{86} +(0.366301 + 1.06823i) q^{88} +(-1.14475 - 1.62579i) q^{89} +(0.341666 + 1.85627i) q^{96} +(1.29838 - 0.927371i) q^{97} +(-0.979617 - 0.200872i) q^{98} +(0.562154 + 2.83864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) 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