LMFDB - Embedded newform 1386.2.k.r.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.r.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(1.32288 - 2.29129i) q^{10} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-2.64575 - 4.58258i) q^{19} -2.64575 q^{20} -1.00000 q^{22} +(-1.32288 - 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(2.00000 + 3.46410i) q^{26} +2.64575 q^{28} -2.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(3.50000 - 6.06218i) q^{35} +(-0.645751 - 1.11847i) q^{37} +(-2.64575 + 4.58258i) q^{38} +(1.32288 + 2.29129i) q^{40} -9.00000 q^{41} +9.29150 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.32288 + 2.29129i) q^{46} +(-1.96863 - 3.40976i) q^{47} +(-3.50000 + 6.06218i) q^{49} +2.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} +2.64575 q^{55} +(-1.32288 - 2.29129i) q^{56} +(1.00000 + 1.73205i) q^{58} +(3.29150 - 5.70105i) q^{59} +(-5.96863 - 10.3380i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.29150 - 9.16515i) q^{65} +(-3.79150 + 6.56708i) q^{67} +(-1.50000 - 2.59808i) q^{68} -7.00000 q^{70} +2.70850 q^{71} +(7.64575 - 13.2428i) q^{73} +(-0.645751 + 1.11847i) q^{74} +5.29150 q^{76} -2.64575 q^{77} +(-5.32288 - 9.21949i) q^{79} +(1.32288 - 2.29129i) q^{80} +(4.50000 + 7.79423i) q^{82} -15.5830 q^{83} -7.93725 q^{85} +(-4.64575 - 8.04668i) q^{86} +(0.500000 - 0.866025i) q^{88} +(1.35425 + 2.34563i) q^{89} +(5.29150 + 9.16515i) q^{91} +2.64575 q^{92} +(-1.96863 + 3.40976i) q^{94} +(7.00000 - 12.1244i) q^{95} -11.5830 q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{11} - 16 q^{13} - 2 q^{16} - 6 q^{17} - 4 q^{22} - 4 q^{25} + 8 q^{26} - 8 q^{29} + 8 q^{31} - 2 q^{32} + 12 q^{34} + 14 q^{35} + 8 q^{37} - 36 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{47} - 14 q^{49} + 8 q^{50} + 8 q^{52} + 8 q^{53} + 4 q^{58} - 8 q^{59} - 8 q^{61} - 16 q^{62} + 4 q^{64} + 6 q^{67} - 6 q^{68} - 28 q^{70} + 32 q^{71} + 20 q^{73} + 8 q^{74} - 16 q^{79} + 18 q^{82} - 20 q^{83} - 8 q^{86} + 2 q^{88} + 16 q^{89} + 8 q^{94} + 28 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^11 - 16 * q^13 - 2 * q^16 - 6 * q^17 - 4 * q^22 - 4 * q^25 + 8 * q^26 - 8 * q^29 + 8 * q^31 - 2 * q^32 + 12 * q^34 + 14 * q^35 + 8 * q^37 - 36 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^47 - 14 * q^49 + 8 * q^50 + 8 * q^52 + 8 * q^53 + 4 * q^58 - 8 * q^59 - 8 * q^61 - 16 * q^62 + 4 * q^64 + 6 * q^67 - 6 * q^68 - 28 * q^70 + 32 * q^71 + 20 * q^73 + 8 * q^74 - 16 * q^79 + 18 * q^82 - 20 * q^83 - 8 * q^86 + 2 * q^88 + 16 * q^89 + 8 * q^94 + 28 * q^95 - 4 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.32288	+	2.29129i	0.591608	+	1.02470i	0.994016	+	0.109235i	$0.0348400\pi$
$5$	1.32288	+	2.29129i	0.591608	+	1.02470i	−0.402408	+	0.915460i	$0.631827\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.32288	−	2.29129i	0.418330	−	0.724569i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.32288	+	2.29129i	−0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−2.64575	−	4.58258i	−0.606977	−	1.05131i	−0.991736	−	0.128298i	$-0.959049\pi$
$19$	−2.64575	−	4.58258i	−0.606977	−	1.05131i	0.384759	−	0.923017i	$-0.374285\pi$
$20$	−2.64575			−0.591608
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−1.32288	−	2.29129i	−0.275839	−	0.477767i	0.694508	−	0.719485i	$-0.255622\pi$
$23$	−1.32288	−	2.29129i	−0.275839	−	0.477767i	−0.970346	+	0.241719i	$0.922289\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$	2.64575			0.500000
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	3.50000	−	6.06218i	0.591608	−	1.02470i
$36$		0			0
$37$	−0.645751	−	1.11847i	−0.106161	−	0.183876i	0.808051	−	0.589112i	$-0.200523\pi$
$37$	−0.645751	−	1.11847i	−0.106161	−	0.183876i	−0.914212	+	0.405236i	$0.867189\pi$
$38$	−2.64575	+	4.58258i	−0.429198	+	0.743392i
$39$		0			0
$40$	1.32288	+	2.29129i	0.209165	+	0.362284i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	9.29150			1.41694			0.708470	−	0.705740i	$-0.249386\pi$
$43$	9.29150			1.41694			0.708470	+	0.705740i	$0.249386\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	−1.32288	+	2.29129i	−0.195047	+	0.337832i
$47$	−1.96863	−	3.40976i	−0.287154	−	0.497365i	0.685975	−	0.727625i	$-0.259376\pi$
$47$	−1.96863	−	3.40976i	−0.287154	−	0.497365i	−0.973129	+	0.230260i	$0.926042\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	2.00000			0.282843
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$	2.64575			0.356753
$56$	−1.32288	−	2.29129i	−0.176777	−	0.306186i
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	3.29150	−	5.70105i	0.428517	−	0.742213i	−0.568225	−	0.822874i	$-0.692369\pi$
$59$	3.29150	−	5.70105i	0.428517	−	0.742213i	0.996742	+	0.0806601i	$0.0257028\pi$
$60$		0			0
$61$	−5.96863	−	10.3380i	−0.764204	−	1.32364i	−0.940666	−	0.339333i	$-0.889799\pi$
$61$	−5.96863	−	10.3380i	−0.764204	−	1.32364i	0.176462	−	0.984307i	$-0.443535\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.29150	−	9.16515i	−0.656330	−	1.13680i
$66$		0			0
$67$	−3.79150	+	6.56708i	−0.463206	+	0.802296i	−0.999119	−	0.0419774i	$-0.986634\pi$
$67$	−3.79150	+	6.56708i	−0.463206	+	0.802296i	0.535913	+	0.844273i	$0.319968\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	−7.00000			−0.836660
$71$	2.70850			0.321440			0.160720	−	0.987000i	$-0.448618\pi$
$71$	2.70850			0.321440			0.160720	+	0.987000i	$0.448618\pi$
$72$		0			0
$73$	7.64575	−	13.2428i	0.894868	−	1.54996i	0.0608990	−	0.998144i	$-0.480603\pi$
$73$	7.64575	−	13.2428i	0.894868	−	1.54996i	0.833969	−	0.551812i	$-0.186063\pi$
$74$	−0.645751	+	1.11847i	−0.0750671	+	0.130020i
$75$		0			0
$76$	5.29150			0.606977
$77$	−2.64575			−0.301511
$78$		0			0
$79$	−5.32288	−	9.21949i	−0.598870	−	1.03727i	−0.992988	−	0.118214i	$-0.962283\pi$
$79$	−5.32288	−	9.21949i	−0.598870	−	1.03727i	0.394118	−	0.919060i	$-0.371050\pi$
$80$	1.32288	−	2.29129i	0.147902	−	0.256174i
$81$		0			0
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−15.5830			−1.71046			−0.855229	−	0.518251i	$-0.826583\pi$
$83$	−15.5830			−1.71046			−0.855229	+	0.518251i	$0.826583\pi$
$84$		0			0
$85$	−7.93725			−0.860916
$86$	−4.64575	−	8.04668i	−0.500964	−	0.867696i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	1.35425	+	2.34563i	0.143550	+	0.248636i	0.928831	−	0.370504i	$-0.120815\pi$
$89$	1.35425	+	2.34563i	0.143550	+	0.248636i	−0.785281	+	0.619140i	$0.787482\pi$
$90$		0			0
$91$	5.29150	+	9.16515i	0.554700	+	0.960769i
$92$	2.64575			0.275839
$93$		0			0
$94$	−1.96863	+	3.40976i	−0.203048	+	0.351690i
$95$	7.00000	−	12.1244i	0.718185	−	1.24393i
$96$		0			0
$97$	−11.5830			−1.17608			−0.588038	−	0.808833i	$-0.700099\pi$
$97$	−11.5830			−1.17608			−0.588038	+	0.808833i	$0.700099\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	3.64575	−	6.31463i	0.362766	−	0.628329i	−0.625649	−	0.780105i	$-0.715166\pi$
$101$	3.64575	−	6.31463i	0.362766	−	0.628329i	0.988415	+	0.151776i	$0.0484992\pi$
$102$		0			0
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−4.00000			−0.388514
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	0.997298	−	0.0734594i	$-0.0234039\pi$
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	−0.562267	+	0.826956i	$0.690071\pi$
$108$		0			0
$109$	1.96863	−	3.40976i	0.188560	−	0.326596i	−0.756210	−	0.654329i	$-0.772951\pi$
$109$	1.96863	−	3.40976i	0.188560	−	0.326596i	0.944770	+	0.327733i	$0.106285\pi$
$110$	−1.32288	−	2.29129i	−0.126131	−	0.218466i
$111$		0			0
$112$	−1.32288	+	2.29129i	−0.125000	+	0.216506i
$113$	−12.5830			−1.18371			−0.591855	−	0.806045i	$-0.701604\pi$
$113$	−12.5830			−1.18371			−0.591855	+	0.806045i	$0.701604\pi$
$114$		0			0
$115$	3.50000	−	6.06218i	0.326377	−	0.565301i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$		0			0
$118$	−6.58301			−0.606015
$119$	7.93725			0.727607
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−5.96863	+	10.3380i	−0.540374	+	0.935955i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	7.93725			0.709930
$126$		0			0
$127$	2.64575			0.234772			0.117386	−	0.993086i	$-0.462548\pi$
$127$	2.64575			0.234772			0.117386	+	0.993086i	$0.462548\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.29150	+	9.16515i	−0.464095	+	0.803837i
$131$	−9.29150	−	16.0934i	−0.811802	−	1.40608i	−0.911601	−	0.411075i	$-0.865153\pi$
$131$	−9.29150	−	16.0934i	−0.811802	−	1.40608i	0.0997990	−	0.995008i	$-0.468180\pi$
$132$		0			0
$133$	−7.00000	+	12.1244i	−0.606977	+	1.05131i
$134$	7.58301			0.655072
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−6.64575	+	11.5108i	−0.567785	+	0.983432i	0.429000	+	0.903305i	$0.358866\pi$
$137$	−6.64575	+	11.5108i	−0.567785	+	0.983432i	−0.996785	+	0.0801276i	$0.974467\pi$
$138$		0			0
$139$	−12.5830			−1.06728			−0.533638	−	0.845713i	$-0.679176\pi$
$139$	−12.5830			−1.06728			−0.533638	+	0.845713i	$0.679176\pi$
$140$	3.50000	+	6.06218i	0.295804	+	0.512348i
$141$		0			0
$142$	−1.35425	−	2.34563i	−0.113646	−	0.196841i
$143$	−2.00000	+	3.46410i	−0.167248	+	0.289683i
$144$		0			0
$145$	−2.64575	−	4.58258i	−0.219718	−	0.380562i
$146$	−15.2915			−1.26553
$147$		0			0
$148$	1.29150			0.106161
$149$	9.93725	+	17.2118i	0.814092	+	1.41005i	0.909978	+	0.414656i	$0.136098\pi$
$149$	9.93725	+	17.2118i	0.814092	+	1.41005i	−0.0958868	+	0.995392i	$0.530569\pi$
$150$		0			0
$151$	−11.3229	+	19.6118i	−0.921443	+	1.59599i	−0.124258	+	0.992250i	$0.539655\pi$
$151$	−11.3229	+	19.6118i	−0.921443	+	1.59599i	−0.797185	+	0.603735i	$0.793678\pi$
$152$	−2.64575	−	4.58258i	−0.214599	−	0.371696i
$153$		0			0
$154$	1.32288	+	2.29129i	0.106600	+	0.184637i
$155$	10.5830			0.850047
$156$		0			0
$157$	0.354249	−	0.613577i	0.0282721	−	0.0489688i	−0.851543	−	0.524285i	$-0.824333\pi$
$157$	0.354249	−	0.613577i	0.0282721	−	0.0489688i	0.879815	+	0.475316i	$0.157666\pi$
$158$	−5.32288	+	9.21949i	−0.423465	+	0.733463i
$159$		0			0
$160$	−2.64575			−0.209165
$161$	−3.50000	+	6.06218i	−0.275839	+	0.477767i
$162$		0			0
$163$	2.79150	+	4.83502i	0.218647	+	0.378708i	0.954395	−	0.298548i	$-0.0965022\pi$
$163$	2.79150	+	4.83502i	0.218647	+	0.378708i	−0.735747	+	0.677256i	$0.763169\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	7.79150	+	13.4953i	0.604738	+	1.04744i
$167$	−8.70850			−0.673884			−0.336942	−	0.941525i	$-0.609393\pi$
$167$	−8.70850			−0.673884			−0.336942	+	0.941525i	$0.609393\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	3.96863	+	6.87386i	0.304380	+	0.527201i
$171$		0			0
$172$	−4.64575	+	8.04668i	−0.354235	+	0.613553i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	5.29150			0.400000
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	1.35425	−	2.34563i	0.101505	−	0.175812i
$179$	2.35425	−	4.07768i	0.175965	−	0.304780i	−0.764530	−	0.644588i	$-0.777029\pi$
$179$	2.35425	−	4.07768i	0.175965	−	0.304780i	0.940495	+	0.339808i	$0.110362\pi$
$180$		0			0
$181$	−5.29150			−0.393314			−0.196657	−	0.980472i	$-0.563009\pi$
$181$	−5.29150			−0.393314			−0.196657	+	0.980472i	$0.563009\pi$
$182$	5.29150	−	9.16515i	0.392232	−	0.679366i
$183$		0			0
$184$	−1.32288	−	2.29129i	−0.0975237	−	0.168916i
$185$	1.70850	−	2.95920i	0.125611	−	0.217565i
$186$		0			0
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	3.93725			0.287154
$189$		0			0
$190$	−14.0000			−1.01567
$191$	3.35425	+	5.80973i	0.242705	+	0.420377i	0.961484	−	0.274861i	$-0.0886320\pi$
$191$	3.35425	+	5.80973i	0.242705	+	0.420377i	−0.718779	+	0.695239i	$0.755299\pi$
$192$		0			0
$193$	7.93725	−	13.7477i	0.571336	−	0.989583i	−0.425093	−	0.905150i	$-0.639759\pi$
$193$	7.93725	−	13.7477i	0.571336	−	0.989583i	0.996429	−	0.0844334i	$-0.0269080\pi$
$194$	5.79150	+	10.0312i	0.415806	+	0.720197i
$195$		0			0
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	−21.8745			−1.55849			−0.779247	−	0.626717i	$-0.784398\pi$
$197$	−21.8745			−1.55849			−0.779247	+	0.626717i	$0.784398\pi$
$198$		0			0
$199$	9.58301	−	16.5983i	0.679321	−	1.17662i	−0.295864	−	0.955230i	$-0.595608\pi$
$199$	9.58301	−	16.5983i	0.679321	−	1.17662i	0.975186	−	0.221389i	$-0.0710590\pi$
$200$	−1.00000	+	1.73205i	−0.0707107	+	0.122474i
$201$		0			0
$202$	−7.29150			−0.513028
$203$	2.64575	+	4.58258i	0.185695	+	0.321634i
$204$		0			0
$205$	−11.9059	−	20.6216i	−0.831543	−	1.44027i
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−5.29150			−0.366021
$210$		0			0
$211$	21.2915			1.46577			0.732884	−	0.680354i	$-0.238174\pi$
$211$	21.2915			1.46577			0.732884	+	0.680354i	$0.238174\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$	12.2915	+	21.2895i	0.838274	+	1.45193i
$216$		0			0
$217$	−10.5830			−0.718421
$218$	−3.93725			−0.266664
$219$		0			0
$220$	−1.32288	+	2.29129i	−0.0891883	+	0.154479i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	28.4575			1.90566			0.952828	−	0.303511i	$-0.0981588\pi$
$223$	28.4575			1.90566			0.952828	+	0.303511i	$0.0981588\pi$
$224$	2.64575			0.176777
$225$		0			0
$226$	6.29150	+	10.8972i	0.418505	+	0.724871i
$227$	1.20850	−	2.09318i	0.0802108	−	0.138929i	−0.823130	−	0.567854i	$-0.807774\pi$
$227$	1.20850	−	2.09318i	0.0802108	−	0.138929i	0.903340	+	0.428924i	$0.141107\pi$
$228$		0			0
$229$	−3.35425	−	5.80973i	−0.221655	−	0.383918i	0.733656	−	0.679521i	$-0.237813\pi$
$229$	−3.35425	−	5.80973i	−0.221655	−	0.383918i	−0.955311	+	0.295604i	$0.904479\pi$
$230$	−7.00000			−0.461566
$231$		0			0
$232$	−2.00000			−0.131306
$233$	10.0830	+	17.4643i	0.660560	+	1.14412i	0.980469	+	0.196675i	$0.0630143\pi$
$233$	10.0830	+	17.4643i	0.660560	+	1.14412i	−0.319909	+	0.947448i	$0.603652\pi$
$234$		0			0
$235$	5.20850	−	9.02138i	0.339765	−	0.588490i
$236$	3.29150	+	5.70105i	0.214259	+	0.371107i
$237$		0			0
$238$	−3.96863	−	6.87386i	−0.257248	−	0.445566i
$239$	−2.70850			−0.175198			−0.0875991	−	0.996156i	$-0.527919\pi$
$239$	−2.70850			−0.175198			−0.0875991	+	0.996156i	$0.527919\pi$
$240$		0			0
$241$	13.5830	−	23.5265i	0.874958	−	1.51547i	0.0181511	−	0.999835i	$-0.494222\pi$
$241$	13.5830	−	23.5265i	0.874958	−	1.51547i	0.856807	−	0.515637i	$-0.172445\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	11.9373			0.764204
$245$	−18.5203			−1.18322
$246$		0			0
$247$	10.5830	+	18.3303i	0.673380	+	1.16633i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$		0			0
$250$	−3.96863	−	6.87386i	−0.250998	−	0.434741i
$251$	−23.2915			−1.47015			−0.735073	−	0.677988i	$-0.762852\pi$
$251$	−23.2915			−1.47015			−0.735073	+	0.677988i	$0.762852\pi$
$252$		0			0
$253$	−2.64575			−0.166337
$254$	−1.32288	−	2.29129i	−0.0830046	−	0.143768i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.64575	+	8.04668i	0.289794	+	0.501938i	0.973760	−	0.227576i	$-0.0730799\pi$
$257$	4.64575	+	8.04668i	0.289794	+	0.501938i	−0.683966	+	0.729513i	$0.739747\pi$
$258$		0			0
$259$	−1.70850	+	2.95920i	−0.106161	+	0.183876i
$260$	10.5830			0.656330
$261$		0			0
$262$	−9.29150	+	16.0934i	−0.574031	+	0.994251i
$263$	10.9373	−	18.9439i	0.674420	−	1.16813i	−0.302218	−	0.953239i	$-0.597727\pi$
$263$	10.9373	−	18.9439i	0.674420	−	1.16813i	0.976638	−	0.214891i	$-0.0689396\pi$
$264$		0			0
$265$	10.5830			0.650109
$266$	14.0000			0.858395
$267$		0			0
$268$	−3.79150	−	6.56708i	−0.231603	−	0.401148i
$269$	−5.32288	+	9.21949i	−0.324541	+	0.562122i	−0.981419	−	0.191875i	$-0.938543\pi$
$269$	−5.32288	+	9.21949i	−0.324541	+	0.562122i	0.656878	+	0.753997i	$0.271877\pi$
$270$		0			0
$271$	−4.64575	−	8.04668i	−0.282209	−	0.488801i	0.689719	−	0.724077i	$-0.257734\pi$
$271$	−4.64575	−	8.04668i	−0.282209	−	0.488801i	−0.971929	+	0.235276i	$0.924401\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	13.2915			0.802969
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	8.58301	−	14.8662i	0.515703	−	0.893223i	−0.484131	−	0.874995i	$-0.660864\pi$
$277$	8.58301	−	14.8662i	0.515703	−	0.893223i	0.999834	−	0.0182280i	$-0.00580246\pi$
$278$	6.29150	+	10.8972i	0.377339	+	0.653571i
$279$		0			0
$280$	3.50000	−	6.06218i	0.209165	−	0.362284i
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	−15.2288	+	26.3770i	−0.905256	+	1.56795i	−0.0846819	+	0.996408i	$0.526987\pi$
$283$	−15.2288	+	26.3770i	−0.905256	+	1.56795i	−0.820574	+	0.571541i	$0.806346\pi$
$284$	−1.35425	+	2.34563i	−0.0803599	+	0.139187i
$285$		0			0
$286$	4.00000			0.236525
$287$	11.9059	+	20.6216i	0.702782	+	1.21725i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−2.64575	+	4.58258i	−0.155364	+	0.269098i
$291$		0			0
$292$	7.64575	+	13.2428i	0.447434	+	0.774978i
$293$	14.5830			0.851948			0.425974	−	0.904735i	$-0.359931\pi$
$293$	14.5830			0.851948			0.425974	+	0.904735i	$0.359931\pi$
$294$		0			0
$295$	17.4170			1.01406
$296$	−0.645751	−	1.11847i	−0.0375335	−	0.0650100i
$297$		0			0
$298$	9.93725	−	17.2118i	0.575650	−	0.997054i
$299$	5.29150	+	9.16515i	0.306015	+	0.530034i
$300$		0			0
$301$	−12.2915	−	21.2895i	−0.708470	−	1.22711i
$302$	22.6458			1.30312
$303$		0			0
$304$	−2.64575	+	4.58258i	−0.151744	+	0.262829i
$305$	15.7915	−	27.3517i	0.904219	−	1.56615i
$306$		0			0
$307$	−11.4170			−0.651602			−0.325801	−	0.945438i	$-0.605634\pi$
$307$	−11.4170			−0.651602			−0.325801	+	0.945438i	$0.605634\pi$
$308$	1.32288	−	2.29129i	0.0753778	−	0.130558i
$309$		0			0
$310$	−5.29150	−	9.16515i	−0.300537	−	0.520546i
$311$	11.2601	−	19.5031i	0.638503	−	1.10592i	−0.347258	−	0.937770i	$-0.612887\pi$
$311$	11.2601	−	19.5031i	0.638503	−	1.10592i	0.985761	−	0.168151i	$-0.0537795\pi$
$312$		0			0
$313$	10.2915	+	17.8254i	0.581710	+	1.00755i	0.995277	+	0.0970777i	$0.0309495\pi$
$313$	10.2915	+	17.8254i	0.581710	+	1.00755i	−0.413567	+	0.910474i	$0.635717\pi$
$314$	−0.708497			−0.0399828
$315$		0			0
$316$	10.6458			0.598870
$317$	4.61438	+	7.99234i	0.259169	+	0.448894i	0.966020	−	0.258469i	$-0.0832179\pi$
$317$	4.61438	+	7.99234i	0.259169	+	0.448894i	−0.706850	+	0.707363i	$0.749885\pi$
$318$		0			0
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	1.32288	+	2.29129i	0.0739510	+	0.128087i
$321$		0			0
$322$	7.00000			0.390095
$323$	15.8745			0.883281
$324$		0			0
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$	2.79150	−	4.83502i	0.154607	−	0.267787i
$327$		0			0
$328$	−9.00000			−0.496942
$329$	−5.20850	+	9.02138i	−0.287154	+	0.497365i
$330$		0			0
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	0.630232	−	0.776407i	$-0.282960\pi$
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	−0.987504	+	0.157593i	$0.949627\pi$
$332$	7.79150	−	13.4953i	0.427614	−	0.740650i
$333$		0			0
$334$	4.35425	+	7.54178i	0.238254	+	0.412668i
$335$	−20.0627			−1.09614
$336$		0			0
$337$	6.70850			0.365435			0.182718	−	0.983165i	$-0.441511\pi$
$337$	6.70850			0.365435			0.182718	+	0.983165i	$0.441511\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$	3.96863	−	6.87386i	0.215229	−	0.372788i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$		0			0
$343$	18.5203			1.00000
$344$	9.29150			0.500964
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	14.7915	−	25.6196i	0.794049	−	1.37533i	−0.129392	−	0.991594i	$-0.541302\pi$
$347$	14.7915	−	25.6196i	0.794049	−	1.37533i	0.923441	−	0.383740i	$-0.125364\pi$
$348$		0			0
$349$	−13.2288			−0.708119			−0.354060	−	0.935223i	$-0.615199\pi$
$349$	−13.2288			−0.708119			−0.354060	+	0.935223i	$0.615199\pi$
$350$	−2.64575	−	4.58258i	−0.141421	−	0.244949i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−11.6458	+	20.1710i	−0.619841	+	1.07360i	0.369674	+	0.929162i	$0.379469\pi$
$353$	−11.6458	+	20.1710i	−0.619841	+	1.07360i	−0.989514	+	0.144434i	$0.953864\pi$
$354$		0			0
$355$	3.58301	+	6.20595i	0.190166	+	0.329377i
$356$	−2.70850			−0.143550
$357$		0			0
$358$	−4.70850			−0.248852
$359$	10.2915	+	17.8254i	0.543165	+	0.940789i	0.998720	+	0.0505814i	$0.0161074\pi$
$359$	10.2915	+	17.8254i	0.543165	+	0.940789i	−0.455555	+	0.890208i	$0.650559\pi$
$360$		0			0
$361$	−4.50000	+	7.79423i	−0.236842	+	0.410223i
$362$	2.64575	+	4.58258i	0.139058	+	0.240855i
$363$		0			0
$364$	−10.5830			−0.554700
$365$	40.4575			2.11764
$366$		0			0
$367$	−5.35425	+	9.27383i	−0.279490	+	0.484090i	−0.971258	−	0.238029i	$-0.923499\pi$
$367$	−5.35425	+	9.27383i	−0.279490	+	0.484090i	0.691768	+	0.722119i	$0.256832\pi$
$368$	−1.32288	+	2.29129i	−0.0689597	+	0.119442i
$369$		0			0
$370$	−3.41699			−0.177641
$371$	−10.5830			−0.549442
$372$		0			0
$373$	7.90588	+	13.6934i	0.409351	+	0.709017i	0.994817	−	0.101680i	$-0.0324218\pi$
$373$	7.90588	+	13.6934i	0.409351	+	0.709017i	−0.585466	+	0.810697i	$0.699088\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$		0			0
$376$	−1.96863	−	3.40976i	−0.101524	−	0.175845i
$377$	8.00000			0.412021
$378$		0			0
$379$	−27.5830			−1.41684			−0.708422	−	0.705789i	$-0.750593\pi$
$379$	−27.5830			−1.41684			−0.708422	+	0.705789i	$0.750593\pi$
$380$	7.00000	+	12.1244i	0.359092	+	0.621966i
$381$		0			0
$382$	3.35425	−	5.80973i	0.171618	−	0.297252i
$383$	9.35425	+	16.2020i	0.477980	+	0.827885i	0.999681	−	0.0252428i	$-0.00803588\pi$
$383$	9.35425	+	16.2020i	0.477980	+	0.827885i	−0.521702	+	0.853128i	$0.674703\pi$
$384$		0			0
$385$	−3.50000	−	6.06218i	−0.178377	−	0.308957i
$386$	−15.8745			−0.807991
$387$		0			0
$388$	5.79150	−	10.0312i	0.294019	−	0.509256i
$389$	15.9686	−	27.6585i	0.809642	−	1.40234i	−0.103471	−	0.994632i	$-0.532995\pi$
$389$	15.9686	−	27.6585i	0.809642	−	1.40234i	0.913112	−	0.407708i	$-0.133672\pi$
$390$		0			0
$391$	7.93725			0.401404
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$		0			0
$394$	10.9373	+	18.9439i	0.551011	+	0.954379i
$395$	14.0830	−	24.3925i	0.708593	−	1.22732i
$396$		0			0
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	0.780870	−	0.624694i	$-0.214776\pi$
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	−0.931436	+	0.363906i	$0.881443\pi$
$398$	−19.1660			−0.960705
$399$		0			0
$400$	2.00000			0.100000
$401$	−17.9373	−	31.0682i	−0.895744	−	1.55147i	−0.832881	−	0.553451i	$-0.813310\pi$
$401$	−17.9373	−	31.0682i	−0.895744	−	1.55147i	−0.0628623	−	0.998022i	$-0.520023\pi$
$402$		0			0
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	3.64575	+	6.31463i	0.181383	+	0.314164i
$405$		0			0
$406$	2.64575	−	4.58258i	0.131306	−	0.227429i
$407$	−1.29150			−0.0640174
$408$		0			0
$409$	−17.9373	+	31.0682i	−0.886940	+	1.53623i	−0.0434664	+	0.999055i	$0.513840\pi$
$409$	−17.9373	+	31.0682i	−0.886940	+	1.53623i	−0.843474	+	0.537170i	$0.819493\pi$
$410$	−11.9059	+	20.6216i	−0.587990	+	1.01843i
$411$		0			0
$412$	−10.0000			−0.492665
$413$	−17.4170			−0.857034
$414$		0			0
$415$	−20.6144	−	35.7052i	−1.01192	−	1.75270i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	2.64575	+	4.58258i	0.129408	+	0.224141i
$419$	9.87451			0.482401			0.241201	−	0.970475i	$-0.422459\pi$
$419$	9.87451			0.482401			0.241201	+	0.970475i	$0.422459\pi$
$420$		0			0
$421$	6.12549			0.298538			0.149269	−	0.988797i	$-0.452308\pi$
$421$	6.12549			0.298538			0.149269	+	0.988797i	$0.452308\pi$
$422$	−10.6458	−	18.4390i	−0.518227	−	0.897596i
$423$		0			0
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	−15.7915	+	27.3517i	−0.764204	+	1.32364i
$428$	−9.00000			−0.435031
$429$		0			0
$430$	12.2915	−	21.2895i	0.592749	−	1.02667i
$431$	−8.64575	+	14.9749i	−0.416451	+	0.721315i	−0.995580	−	0.0939217i	$-0.970060\pi$
$431$	−8.64575	+	14.9749i	−0.416451	+	0.721315i	0.579128	+	0.815236i	$0.303393\pi$
$432$		0			0
$433$	1.58301			0.0760744			0.0380372	−	0.999276i	$-0.487889\pi$
$433$	1.58301			0.0760744			0.0380372	+	0.999276i	$0.487889\pi$
$434$	5.29150	+	9.16515i	0.254000	+	0.439941i
$435$		0			0
$436$	1.96863	+	3.40976i	0.0942801	+	0.163298i
$437$	−7.00000	+	12.1244i	−0.334855	+	0.579987i
$438$		0			0
$439$	4.67712	+	8.10102i	0.223227	+	0.386640i	0.955786	−	0.294063i	$-0.0950076\pi$
$439$	4.67712	+	8.10102i	0.223227	+	0.386640i	−0.732559	+	0.680703i	$0.761674\pi$
$440$	2.64575			0.126131
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−15.5830	−	26.9906i	−0.740371	−	1.28236i	−0.952326	−	0.305081i	$-0.901317\pi$
$443$	−15.5830	−	26.9906i	−0.740371	−	1.28236i	0.211956	−	0.977279i	$-0.432017\pi$
$444$		0			0
$445$	−3.58301	+	6.20595i	−0.169851	+	0.294190i
$446$	−14.2288	−	24.6449i	−0.673751	−	1.16697i
$447$		0			0
$448$	−1.32288	−	2.29129i	−0.0625000	−	0.108253i
$449$	−30.4575			−1.43738			−0.718689	−	0.695331i	$-0.755258\pi$
$449$	−30.4575			−1.43738			−0.718689	+	0.695331i	$0.755258\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$	6.29150	−	10.8972i	0.295927	−	0.512561i
$453$		0			0
$454$	−2.41699			−0.113435
$455$	−14.0000	+	24.2487i	−0.656330	+	1.13680i
$456$		0			0
$457$	20.2915	+	35.1459i	0.949196	+	1.64406i	0.747123	+	0.664686i	$0.231435\pi$
$457$	20.2915	+	35.1459i	0.949196	+	1.64406i	0.202074	+	0.979370i	$0.435232\pi$
$458$	−3.35425	+	5.80973i	−0.156734	+	0.271471i
$459$		0			0
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	24.5830			1.14494			0.572472	−	0.819924i	$-0.305984\pi$
$461$	24.5830			1.14494			0.572472	+	0.819924i	$0.305984\pi$
$462$		0			0
$463$	39.0405			1.81437			0.907183	−	0.420735i	$-0.138228\pi$
$463$	39.0405			1.81437			0.907183	+	0.420735i	$0.138228\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	10.0830	−	17.4643i	0.467086	−	0.809017i
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	0.943610	−	0.331061i	$-0.107406\pi$
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	−0.758512	+	0.651660i	$0.774073\pi$
$468$		0			0
$469$	20.0627			0.926412
$470$	−10.4170			−0.480500
$471$		0			0
$472$	3.29150	−	5.70105i	0.151504	−	0.262412i
$473$	4.64575	−	8.04668i	0.213612	−	0.369987i
$474$		0			0
$475$	10.5830			0.485582
$476$	−3.96863	+	6.87386i	−0.181902	+	0.315063i
$477$		0			0
$478$	1.35425	+	2.34563i	0.0619419	+	0.107287i
$479$	−16.9373	+	29.3362i	−0.773883	+	1.34040i	0.161537	+	0.986867i	$0.448355\pi$
$479$	−16.9373	+	29.3362i	−0.773883	+	1.34040i	−0.935420	+	0.353538i	$0.884979\pi$
$480$		0			0
$481$	2.58301	+	4.47390i	0.117775	+	0.203992i
$482$	−27.1660			−1.23738
$483$		0			0
$484$	1.00000			0.0454545
$485$	−15.3229	−	26.5400i	−0.695776	−	1.20512i
$486$		0			0
$487$	−10.9373	+	18.9439i	−0.495614	+	0.858429i	−0.999987	−	0.00505681i	$-0.998390\pi$
$487$	−10.9373	+	18.9439i	−0.495614	+	0.858429i	0.504373	+	0.863486i	$0.331724\pi$
$488$	−5.96863	−	10.3380i	−0.270187	−	0.467978i
$489$		0			0
$490$	9.26013	+	16.0390i	0.418330	+	0.724569i
$491$	1.00000			0.0451294			0.0225647	−	0.999745i	$-0.492817\pi$
$491$	1.00000			0.0451294			0.0225647	+	0.999745i	$0.492817\pi$
$492$		0			0
$493$	3.00000	−	5.19615i	0.135113	−	0.234023i
$494$	10.5830	−	18.3303i	0.476152	−	0.824719i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−3.58301	−	6.20595i	−0.160720	−	0.278375i
$498$		0			0
$499$	9.29150	+	16.0934i	0.415945	+	0.720437i	0.995527	−	0.0944762i	$-0.0301176\pi$
$499$	9.29150	+	16.0934i	0.415945	+	0.720437i	−0.579582	+	0.814914i	$0.696784\pi$
$500$	−3.96863	+	6.87386i	−0.177482	+	0.307409i
$501$		0			0
$502$	11.6458	+	20.1710i	0.519775	+	0.900277i
$503$	1.29150			0.0575853			0.0287926	−	0.999585i	$-0.490834\pi$
$503$	1.29150			0.0575853			0.0287926	+	0.999585i	$0.490834\pi$
$504$		0			0
$505$	19.2915			0.858461
$506$	1.32288	+	2.29129i	0.0588090	+	0.101860i
$507$		0			0
$508$	−1.32288	+	2.29129i	−0.0586931	+	0.101659i
$509$	12.5830	+	21.7944i	0.557732	+	0.966020i	0.997685	+	0.0679994i	$0.0216616\pi$
$509$	12.5830	+	21.7944i	0.557732	+	0.966020i	−0.439953	+	0.898021i	$0.645005\pi$
$510$		0			0
$511$	−40.4575			−1.78974
$512$	1.00000			0.0441942
$513$		0			0
$514$	4.64575	−	8.04668i	0.204915	−	0.354924i
$515$	−13.2288	+	22.9129i	−0.582929	+	1.00966i
$516$		0			0
$517$	−3.93725			−0.173160
$518$	3.41699			0.150134
$519$		0			0
$520$	−5.29150	−	9.16515i	−0.232048	−	0.401918i
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$		0			0
$523$	−1.35425	−	2.34563i	−0.0592172	−	0.102567i	0.834897	−	0.550406i	$-0.185527\pi$
$523$	−1.35425	−	2.34563i	−0.0592172	−	0.102567i	−0.894114	+	0.447839i	$0.852194\pi$
$524$	18.5830			0.811802
$525$		0			0
$526$	−21.8745			−0.953774
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	8.00000	−	13.8564i	0.347826	−	0.602452i
$530$	−5.29150	−	9.16515i	−0.229848	−	0.398109i
$531$		0			0
$532$	−7.00000	−	12.1244i	−0.303488	−	0.525657i
$533$	36.0000			1.55933
$534$		0			0
$535$	−11.9059	+	20.6216i	−0.514736	+	0.891549i
$536$	−3.79150	+	6.56708i	−0.163768	+	0.283654i
$537$		0			0
$538$	10.6458			0.458971
$539$	3.50000	+	6.06218i	0.150756	+	0.261116i
$540$		0			0
$541$	−1.90588	−	3.30108i	−0.0819402	−	0.141925i	0.822143	−	0.569281i	$-0.192778\pi$
$541$	−1.90588	−	3.30108i	−0.0819402	−	0.141925i	−0.904083	+	0.427356i	$0.859445\pi$
$542$	−4.64575	+	8.04668i	−0.199552	+	0.345634i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	10.4170			0.446215
$546$		0			0
$547$	14.7085			0.628890			0.314445	−	0.949276i	$-0.398182\pi$
$547$	14.7085			0.628890			0.314445	+	0.949276i	$0.398182\pi$
$548$	−6.64575	−	11.5108i	−0.283892	−	0.491716i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	5.29150	+	9.16515i	0.225426	+	0.390449i
$552$		0			0
$553$	−14.0830	+	24.3925i	−0.598870	+	1.03727i
$554$	−17.1660			−0.729314
$555$		0			0
$556$	6.29150	−	10.8972i	0.266819	−	0.462144i
$557$	−9.64575	+	16.7069i	−0.408704	+	0.707895i	−0.994745	−	0.102386i	$-0.967352\pi$
$557$	−9.64575	+	16.7069i	−0.408704	+	0.707895i	0.586041	+	0.810281i	$0.300686\pi$
$558$		0			0
$559$	−37.1660			−1.57195
$560$	−7.00000			−0.295804
$561$		0			0
$562$	−1.50000	−	2.59808i	−0.0632737	−	0.109593i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−16.6458	−	28.8313i	−0.700292	−	1.21294i
$566$	30.4575			1.28022
$567$		0			0
$568$	2.70850			0.113646
$569$	−7.58301	−	13.1342i	−0.317896	−	0.550612i	0.662153	−	0.749369i	$-0.269643\pi$
$569$	−7.58301	−	13.1342i	−0.317896	−	0.550612i	−0.980049	+	0.198757i	$0.936310\pi$
$570$		0			0
$571$	14.8745	−	25.7634i	0.622479	−	1.07816i	−0.366544	−	0.930401i	$-0.619459\pi$
$571$	14.8745	−	25.7634i	0.622479	−	1.07816i	0.989023	−	0.147764i	$-0.0472076\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		0			0
$574$	11.9059	−	20.6216i	0.496942	−	0.860729i
$575$	5.29150			0.220671
$576$		0			0
$577$	−11.3745	+	19.7012i	−0.473527	+	0.820173i	−0.999541	−	0.0303033i	$-0.990353\pi$
$577$	−11.3745	+	19.7012i	−0.473527	+	0.820173i	0.526014	+	0.850476i	$0.323686\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	5.29150			0.219718
$581$	20.6144	+	35.7052i	0.855229	+	1.48130i
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	7.64575	−	13.2428i	0.316383	−	0.547992i
$585$		0			0
$586$	−7.29150	−	12.6293i	−0.301209	−	0.521710i
$587$	−9.87451			−0.407565			−0.203782	−	0.979016i	$-0.565323\pi$
$587$	−9.87451			−0.407565			−0.203782	+	0.979016i	$0.565323\pi$
$588$		0			0
$589$	−21.1660			−0.872130
$590$	−8.70850	−	15.0836i	−0.358523	−	0.620980i
$591$		0			0
$592$	−0.645751	+	1.11847i	−0.0265402	+	0.0459690i
$593$	−12.8745	−	22.2993i	−0.528693	−	0.915723i	−0.999440	−	0.0334546i	$-0.989349\pi$
$593$	−12.8745	−	22.2993i	−0.528693	−	0.915723i	0.470748	−	0.882268i	$-0.343984\pi$
$594$		0			0
$595$	10.5000	+	18.1865i	0.430458	+	0.745575i
$596$	−19.8745			−0.814092
$597$		0			0
$598$	5.29150	−	9.16515i	0.216386	−	0.374791i
$599$	14.6771	−	25.4215i	0.599691	−	1.03870i	−0.393175	−	0.919463i	$-0.628623\pi$
$599$	14.6771	−	25.4215i	0.599691	−	1.03870i	0.992866	−	0.119232i	$-0.0380432\pi$
$600$		0			0
$601$	−38.5830			−1.57383			−0.786917	−	0.617059i	$-0.788324\pi$
$601$	−38.5830			−1.57383			−0.786917	+	0.617059i	$0.788324\pi$
$602$	−12.2915	+	21.2895i	−0.500964	+	0.867696i
$603$		0			0
$604$	−11.3229	−	19.6118i	−0.460721	−	0.797993i
$605$	1.32288	−	2.29129i	0.0537825	−	0.0931541i
$606$		0			0
$607$	6.55163	+	11.3478i	0.265923	+	0.460591i	0.967805	−	0.251702i	$-0.0809901\pi$
$607$	6.55163	+	11.3478i	0.265923	+	0.460591i	−0.701882	+	0.712293i	$0.747657\pi$
$608$	5.29150			0.214599
$609$		0			0
$610$	−31.5830			−1.27876
$611$	7.87451	+	13.6390i	0.318568	+	0.551777i
$612$		0			0
$613$	−3.90588	+	6.76518i	−0.157757	+	0.273243i	−0.934060	−	0.357117i	$-0.883760\pi$
$613$	−3.90588	+	6.76518i	−0.157757	+	0.273243i	0.776302	+	0.630361i	$0.217093\pi$
$614$	5.70850	+	9.88741i	0.230376	+	0.399023i
$615$		0			0
$616$	−2.64575			−0.106600
$617$	14.7085			0.592142			0.296071	−	0.955166i	$-0.404324\pi$
$617$	14.7085			0.592142			0.296071	+	0.955166i	$0.404324\pi$
$618$		0			0
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	−0.0787435	−	0.996895i	$-0.525091\pi$
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	0.902708	−	0.430254i	$-0.141576\pi$
$620$	−5.29150	+	9.16515i	−0.212512	+	0.368081i
$621$		0			0
$622$	−22.5203			−0.902980
$623$	3.58301	−	6.20595i	0.143550	−	0.248636i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$	10.2915	−	17.8254i	0.411331	−	0.712446i
$627$		0			0
$628$	0.354249	+	0.613577i	0.0141361	+	0.0244844i
$629$	3.87451			0.154487
$630$		0			0
$631$	41.8745			1.66700			0.833499	−	0.552521i	$-0.186334\pi$
$631$	41.8745			1.66700			0.833499	+	0.552521i	$0.186334\pi$
$632$	−5.32288	−	9.21949i	−0.211733	−	0.366732i
$633$		0			0
$634$	4.61438	−	7.99234i	0.183260	−	0.317416i
$635$	3.50000	+	6.06218i	0.138893	+	0.240570i
$636$		0			0
$637$	14.0000	−	24.2487i	0.554700	−	0.960769i
$638$	2.00000			0.0791808
$639$		0			0
$640$	1.32288	−	2.29129i	0.0522913	−	0.0905711i
$641$	−13.2915	+	23.0216i	−0.524983	+	0.909297i	0.474594	+	0.880205i	$0.342595\pi$
$641$	−13.2915	+	23.0216i	−0.524983	+	0.909297i	−0.999577	+	0.0290920i	$0.990738\pi$
$642$		0			0
$643$	−1.16601			−0.0459830			−0.0229915	−	0.999736i	$-0.507319\pi$
$643$	−1.16601			−0.0459830			−0.0229915	+	0.999736i	$0.507319\pi$
$644$	−3.50000	−	6.06218i	−0.137919	−	0.238883i
$645$		0			0
$646$	−7.93725	−	13.7477i	−0.312287	−	0.540897i
$647$	−13.1974	+	22.8585i	−0.518843	+	0.898662i	0.480918	+	0.876766i	$0.340304\pi$
$647$	−13.1974	+	22.8585i	−0.518843	+	0.898662i	−0.999760	+	0.0218961i	$0.993030\pi$
$648$		0			0
$649$	−3.29150	−	5.70105i	−0.129203	−	0.223786i
$650$	−8.00000			−0.313786
$651$		0			0
$652$	−5.58301			−0.218647
$653$	−22.5516	−	39.0606i	−0.882514	−	1.52856i	−0.848537	−	0.529136i	$-0.822516\pi$
$653$	−22.5516	−	39.0606i	−0.882514	−	1.52856i	−0.0339763	−	0.999423i	$-0.510817\pi$
$654$		0			0
$655$	24.5830	−	42.5790i	0.960537	−	1.66370i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	10.4170			0.406097
$659$	24.1660			0.941374			0.470687	−	0.882300i	$-0.344006\pi$
$659$	24.1660			0.941374			0.470687	+	0.882300i	$0.344006\pi$
$660$		0			0
$661$	−10.3542	+	17.9341i	−0.402734	+	0.697555i	−0.994055	−	0.108881i	$-0.965273\pi$
$661$	−10.3542	+	17.9341i	−0.402734	+	0.697555i	0.591321	+	0.806436i	$0.298607\pi$
$662$	−6.50000	+	11.2583i	−0.252630	+	0.437567i
$663$		0			0
$664$	−15.5830			−0.604738
$665$	−37.0405			−1.43637
$666$		0			0
$667$	2.64575	+	4.58258i	0.102444	+	0.177438i
$668$	4.35425	−	7.54178i	0.168471	−	0.291800i
$669$		0			0
$670$	10.0314	+	17.3748i	0.387546	+	0.671249i
$671$	−11.9373			−0.460833
$672$		0			0
$673$	−19.4170			−0.748470			−0.374235	−	0.927334i	$-0.622095\pi$
$673$	−19.4170			−0.748470			−0.374235	+	0.927334i	$0.622095\pi$
$674$	−3.35425	−	5.80973i	−0.129201	−	0.223782i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−4.06275	−	7.03688i	−0.156144	−	0.270449i	0.777331	−	0.629092i	$-0.216573\pi$
$677$	−4.06275	−	7.03688i	−0.156144	−	0.270449i	−0.933475	+	0.358642i	$0.883240\pi$
$678$		0			0
$679$	15.3229	+	26.5400i	0.588038	+	1.01851i
$680$	−7.93725			−0.304380
$681$		0			0
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	−8.58301	+	14.8662i	−0.328420	+	0.568839i	−0.982198	−	0.187846i	$-0.939849\pi$
$683$	−8.58301	+	14.8662i	−0.328420	+	0.568839i	0.653779	+	0.756686i	$0.273183\pi$
$684$		0			0
$685$	−35.1660			−1.34362
$686$	−9.26013	−	16.0390i	−0.353553	−	0.612372i
$687$		0			0
$688$	−4.64575	−	8.04668i	−0.177118	−	0.306777i
$689$	−8.00000	+	13.8564i	−0.304776	+	0.527887i
$690$		0			0
$691$	−7.08301	−	12.2681i	−0.269450	−	0.466701i	0.699270	−	0.714858i	$-0.253509\pi$
$691$	−7.08301	−	12.2681i	−0.269450	−	0.466701i	−0.968720	+	0.248156i	$0.920175\pi$
$692$	−4.00000			−0.152057
$693$		0			0
$694$	−29.5830			−1.12296
$695$	−16.6458	−	28.8313i	−0.631409	−	1.09363i
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	6.61438	+	11.4564i	0.250358	+	0.433633i
$699$		0			0
$700$	−2.64575	+	4.58258i	−0.100000	+	0.173205i
$701$	−42.4575			−1.60360			−0.801799	−	0.597594i	$-0.796124\pi$
$701$	−42.4575			−1.60360			−0.801799	+	0.597594i	$0.796124\pi$
$702$		0			0
$703$	−3.41699	+	5.91841i	−0.128874	+	0.223217i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	23.2915			0.876587
$707$	−19.2915			−0.725532
$708$		0			0
$709$	−7.87451	−	13.6390i	−0.295733	−	0.512225i	0.679422	−	0.733748i	$-0.262231\pi$
$709$	−7.87451	−	13.6390i	−0.295733	−	0.512225i	−0.975155	+	0.221523i	$0.928897\pi$
$710$	3.58301	−	6.20595i	0.134468	−	0.232905i
$711$		0			0
$712$	1.35425	+	2.34563i	0.0507526	+	0.0879061i
$713$	−10.5830			−0.396337
$714$		0			0
$715$	−10.5830			−0.395782
$716$	2.35425	+	4.07768i	0.0879824	+	0.152390i
$717$		0			0
$718$	10.2915	−	17.8254i	0.384075	−	0.665238i
$719$	−14.0314	−	24.3031i	−0.523282	−	0.906351i	−0.999633	−	0.0270956i	$-0.991374\pi$
$719$	−14.0314	−	24.3031i	−0.523282	−	0.906351i	0.476351	−	0.879255i	$-0.341959\pi$
$720$		0			0
$721$	13.2288	−	22.9129i	0.492665	−	0.853320i
$722$	9.00000			0.334945
$723$		0			0
$724$	2.64575	−	4.58258i	0.0983286	−	0.170310i
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	5.29150	+	9.16515i	0.196116	+	0.339683i
$729$		0			0
$730$	−20.2288	−	35.0372i	−0.748700	−	1.29679i
$731$	−13.9373	+	24.1400i	−0.515488	+	0.892851i
$732$		0			0
$733$	−5.96863	−	10.3380i	−0.220456	−	0.381841i	0.734490	−	0.678619i	$-0.237421\pi$
$733$	−5.96863	−	10.3380i	−0.220456	−	0.381841i	−0.954947	+	0.296778i	$0.904088\pi$
$734$	10.7085			0.395258
$735$		0			0
$736$	2.64575			0.0975237
$737$	3.79150	+	6.56708i	0.139662	+	0.241901i
$738$		0			0
$739$	12.2915	−	21.2895i	0.452150	−	0.783147i	−0.546369	−	0.837544i	$-0.683990\pi$
$739$	12.2915	−	21.2895i	0.452150	−	0.783147i	0.998519	+	0.0543973i	$0.0173238\pi$
$740$	1.70850	+	2.95920i	0.0628056	+	0.108783i
$741$		0			0
$742$	5.29150	+	9.16515i	0.194257	+	0.336463i
$743$	18.7085			0.686348			0.343174	−	0.939272i	$-0.388498\pi$
$743$	18.7085			0.686348			0.343174	+	0.939272i	$0.388498\pi$
$744$		0			0
$745$	−26.2915	+	45.5382i	−0.963246	+	1.66839i
$746$	7.90588	−	13.6934i	0.289455	−	0.501351i
$747$		0			0
$748$	−3.00000			−0.109691
$749$	11.9059	−	20.6216i	0.435031	−	0.753497i
$750$		0			0
$751$	14.6458	+	25.3672i	0.534431	+	0.925662i	0.999191	+	0.0402248i	$0.0128074\pi$
$751$	14.6458	+	25.3672i	0.534431	+	0.925662i	−0.464760	+	0.885437i	$0.653859\pi$
$752$	−1.96863	+	3.40976i	−0.0717884	+	0.124341i
$753$		0			0
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	−59.9150			−2.18053
$756$		0			0
$757$	−32.5830			−1.18425			−0.592125	−	0.805846i	$-0.701711\pi$
$757$	−32.5830			−1.18425			−0.592125	+	0.805846i	$0.701711\pi$
$758$	13.7915	+	23.8876i	0.500930	+	0.867636i
$759$		0			0
$760$	7.00000	−	12.1244i	0.253917	−	0.439797i
$761$	23.7915	+	41.2081i	0.862441	+	1.49379i	0.869566	+	0.493818i	$0.164399\pi$
$761$	23.7915	+	41.2081i	0.862441	+	1.49379i	−0.00712426	+	0.999975i	$0.502268\pi$
$762$		0			0
$763$	−10.4170			−0.377121
$764$	−6.70850			−0.242705
$765$		0			0
$766$	9.35425	−	16.2020i	0.337983	−	0.585403i
$767$	−13.1660	+	22.8042i	−0.475397	+	0.823412i
$768$		0			0
$769$	−30.7085			−1.10738			−0.553688	−	0.832724i	$-0.686780\pi$
$769$	−30.7085			−1.10738			−0.553688	+	0.832724i	$0.686780\pi$
$770$	−3.50000	+	6.06218i	−0.126131	+	0.218466i
$771$		0			0
$772$	7.93725	+	13.7477i	0.285668	+	0.494792i
$773$	−4.03137	+	6.98254i	−0.144998	+	0.251145i	−0.929372	−	0.369144i	$-0.879651\pi$
$773$	−4.03137	+	6.98254i	−0.144998	+	0.251145i	0.784374	+	0.620288i	$0.212984\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$	−11.5830			−0.415806
$777$		0			0
$778$	−31.9373			−1.14501
$779$	23.8118	+	41.2432i	0.853145	+	1.47769i
$780$		0			0
$781$	1.35425	−	2.34563i	0.0484588	−	0.0839332i
$782$	−3.96863	−	6.87386i	−0.141918	−	0.245809i
$783$		0			0
$784$	7.00000			0.250000
$785$	1.87451			0.0669041
$786$		0			0
$787$	−4.64575	+	8.04668i	−0.165603	+	0.286833i	−0.936869	−	0.349680i	$-0.886290\pi$
$787$	−4.64575	+	8.04668i	−0.165603	+	0.286833i	0.771266	+	0.636513i	$0.219624\pi$
$788$	10.9373	−	18.9439i	0.389624	−	0.674848i
$789$		0			0
$790$	−28.1660			−1.00210
$791$	16.6458	+	28.8313i	0.591855	+	1.02512i
$792$		0			0
$793$	23.8745	+	41.3519i	0.847809	+	1.46845i
$794$	−3.00000	+	5.19615i	−0.106466	+	0.184405i
$795$		0			0
$796$	9.58301	+	16.5983i	0.339661	+	0.588309i
$797$	−45.1033			−1.59764			−0.798820	−	0.601570i	$-0.794542\pi$
$797$	−45.1033			−1.59764			−0.798820	+	0.601570i	$0.794542\pi$
$798$		0			0
$799$	11.8118			0.417870
$800$	−1.00000	−	1.73205i	−0.0353553	−	0.0612372i
$801$		0			0
$802$	−17.9373	+	31.0682i	−0.633386	+	1.09706i
$803$	−7.64575	−	13.2428i	−0.269813	−	0.467329i
$804$		0			0
$805$	−18.5203			−0.652753
$806$	16.0000			0.563576
$807$		0			0
$808$	3.64575	−	6.31463i	0.128257	−	0.222148i
$809$	22.6660	−	39.2587i	0.796894	−	1.38026i	−0.124735	−	0.992190i	$-0.539808\pi$
$809$	22.6660	−	39.2587i	0.796894	−	1.38026i	0.921629	−	0.388072i	$-0.126859\pi$
$810$		0			0
$811$	16.5830			0.582308			0.291154	−	0.956676i	$-0.405961\pi$
$811$	16.5830			0.582308			0.291154	+	0.956676i	$0.405961\pi$
$812$	−5.29150			−0.185695
$813$		0			0
$814$	0.645751	+	1.11847i	0.0226336	+	0.0392025i
$815$	−7.38562	+	12.7923i	−0.258707	+	0.448094i
$816$		0			0
$817$	−24.5830	−	42.5790i	−0.860050	−	1.48965i
$818$	35.8745			1.25432
$819$		0			0
$820$	23.8118			0.831543
$821$	−15.1660	−	26.2683i	−0.529297	−	0.916770i	−0.999416	−	0.0341668i	$-0.989122\pi$
$821$	−15.1660	−	26.2683i	−0.529297	−	0.916770i	0.470119	−	0.882603i	$-0.344211\pi$
$822$		0			0
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	−0.740798	−	0.671728i	$-0.765553\pi$
$823$	6.06275	−	10.5010i	0.211334	−	0.366041i	0.952132	+	0.305686i	$0.0988859\pi$
$824$	5.00000	+	8.66025i	0.174183	+	0.301694i
$825$		0			0
$826$	8.70850	+	15.0836i	0.303007	+	0.524824i
$827$	−35.3320			−1.22861			−0.614307	−	0.789067i	$-0.710565\pi$
$827$	−35.3320			−1.22861			−0.614307	+	0.789067i	$0.710565\pi$
$828$		0			0
$829$	−9.93725	+	17.2118i	−0.345135	+	0.597792i	−0.985378	−	0.170381i	$-0.945500\pi$
$829$	−9.93725	+	17.2118i	−0.345135	+	0.597792i	0.640243	+	0.768172i	$0.278834\pi$
$830$	−20.6144	+	35.7052i	−0.715536	+	1.23934i
$831$		0			0
$832$	−4.00000			−0.138675
$833$	−10.5000	−	18.1865i	−0.363803	−	0.630126i
$834$		0			0
$835$	−11.5203	−	19.9537i	−0.398675	−	0.690525i
$836$	2.64575	−	4.58258i	0.0915052	−	0.158492i
$837$		0			0
$838$	−4.93725	−	8.55157i	−0.170555	−	0.295409i
$839$	37.1033			1.28095			0.640473	−	0.767980i	$-0.278738\pi$
$839$	37.1033			1.28095			0.640473	+	0.767980i	$0.278738\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−3.06275	−	5.30483i	−0.105549	−	0.182817i
$843$		0			0
$844$	−10.6458	+	18.4390i	−0.366442	+	0.634696i
$845$	3.96863	+	6.87386i	0.136525	+	0.236468i
$846$		0			0
$847$	−1.32288	+	2.29129i	−0.0454545	+	0.0787296i
$848$	−4.00000			−0.137361
$849$		0			0
$850$	−3.00000	+	5.19615i	−0.102899	+	0.178227i
$851$	−1.70850	+	2.95920i	−0.0585665	+	0.101440i
$852$		0			0
$853$	14.5203			0.497164			0.248582	−	0.968611i	$-0.420035\pi$
$853$	14.5203			0.497164			0.248582	+	0.968611i	$0.420035\pi$
$854$	31.5830			1.08075
$855$		0			0
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	4.91699	−	8.51648i	0.167961	−	0.290918i	−0.769742	−	0.638356i	$-0.779615\pi$
$857$	4.91699	−	8.51648i	0.167961	−	0.290918i	0.937703	+	0.347438i	$0.112948\pi$
$858$		0			0
$859$	−24.3745	−	42.2179i	−0.831647	−	1.44046i	−0.896731	−	0.442576i	$-0.854065\pi$
$859$	−24.3745	−	42.2179i	−0.831647	−	1.44046i	0.0650836	−	0.997880i	$-0.479269\pi$
$860$	−24.5830			−0.838274
$861$		0			0
$862$	17.2915			0.588951
$863$	−16.5516	−	28.6683i	−0.563424	−	0.975879i	−0.997194	−	0.0748557i	$-0.976150\pi$
$863$	−16.5516	−	28.6683i	−0.563424	−	0.975879i	0.433770	−	0.901024i	$-0.357183\pi$
$864$		0			0
$865$	−5.29150	+	9.16515i	−0.179916	+	0.311624i
$866$	−0.791503	−	1.37092i	−0.0268964	−	0.0465859i
$867$		0			0
$868$	5.29150	−	9.16515i	0.179605	−	0.311086i
$869$	−10.6458			−0.361132
$870$		0			0
$871$	15.1660	−	26.2683i	0.513881	−	0.890067i
$872$	1.96863	−	3.40976i	0.0666661	−	0.115469i
$873$		0			0
$874$	14.0000			0.473557
$875$	−10.5000	−	18.1865i	−0.354965	−	0.614817i
$876$		0			0
$877$	−5.38562	−	9.32817i	−0.181860	−	0.314990i	0.760654	−	0.649157i	$-0.224878\pi$
$877$	−5.38562	−	9.32817i	−0.181860	−	0.314990i	−0.942514	+	0.334167i	$0.891545\pi$
$878$	4.67712	−	8.10102i	0.157845	−	0.273396i
$879$		0			0
$880$	−1.32288	−	2.29129i	−0.0445941	−	0.0772393i
$881$	−23.1660			−0.780483			−0.390241	−	0.920713i	$-0.627608\pi$
$881$	−23.1660			−0.780483			−0.390241	+	0.920713i	$0.627608\pi$
$882$		0			0
$883$	−34.4170			−1.15822			−0.579112	−	0.815248i	$-0.696601\pi$
$883$	−34.4170			−1.15822			−0.579112	+	0.815248i	$0.696601\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	−15.5830	+	26.9906i	−0.523521	+	0.906765i
$887$	−15.5203	−	26.8819i	−0.521119	−	0.902605i	−0.999698	−	0.0245606i	$-0.992181\pi$
$887$	−15.5203	−	26.8819i	−0.521119	−	0.902605i	0.478579	−	0.878044i	$-0.341152\pi$
$888$		0			0
$889$	−3.50000	−	6.06218i	−0.117386	−	0.203319i
$890$	7.16601			0.240205
$891$		0			0
$892$	−14.2288	+	24.6449i	−0.476414	+	0.825173i
$893$	−10.4170	+	18.0428i	−0.348591	+	0.603778i
$894$		0			0
$895$	12.4575			0.416409
$896$	−1.32288	+	2.29129i	−0.0441942	+	0.0765466i
$897$		0			0
$898$	15.2288	+	26.3770i	0.508190	+	0.880211i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$	9.00000			0.299667
$903$		0			0
$904$	−12.5830			−0.418505
$905$	−7.00000	−	12.1244i	−0.232688	−	0.403027i
$906$		0			0
$907$	7.91699	−	13.7126i	0.262879	−	0.455321i	−0.704126	−	0.710075i	$-0.748661\pi$
$907$	7.91699	−	13.7126i	0.262879	−	0.455321i	0.967006	+	0.254754i	$0.0819945\pi$
$908$	1.20850	+	2.09318i	0.0401054	+	0.0694646i
$909$		0			0
$910$	28.0000			0.928191
$911$	18.3948			0.609446			0.304723	−	0.952441i	$-0.401436\pi$
$911$	18.3948			0.609446			0.304723	+	0.952441i	$0.401436\pi$
$912$		0			0
$913$	−7.79150	+	13.4953i	−0.257861	+	0.446629i
$914$	20.2915	−	35.1459i	0.671183	−	1.16252i
$915$		0			0
$916$	6.70850			0.221655
$917$	−24.5830	+	42.5790i	−0.811802	+	1.40608i
$918$		0			0
$919$	−4.67712	−	8.10102i	−0.154284	−	0.267228i	0.778514	−	0.627627i	$-0.215974\pi$
$919$	−4.67712	−	8.10102i	−0.154284	−	0.267228i	−0.932798	+	0.360399i	$0.882640\pi$
$920$	3.50000	−	6.06218i	0.115392	−	0.199864i
$921$		0			0
$922$	−12.2915	−	21.2895i	−0.404799	−	0.701133i
$923$	−10.8340			−0.356605
$924$		0			0
$925$	2.58301			0.0849287
$926$	−19.5203	−	33.8101i	−0.641476	−	1.11107i
$927$		0			0
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	−17.2288	−	29.8411i	−0.565257	−	0.979054i	−0.997026	−	0.0770697i	$-0.975444\pi$
$929$	−17.2288	−	29.8411i	−0.565257	−	0.979054i	0.431769	−	0.901984i	$-0.357890\pi$
$930$		0			0
$931$	37.0405			1.21395
$932$	−20.1660			−0.660560
$933$		0			0
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	−3.96863	+	6.87386i	−0.129788	+	0.224799i
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$	−10.0314	−	17.3748i	−0.327536	−	0.567309i
$939$		0			0
$940$	5.20850	+	9.02138i	0.169882	+	0.294245i
$941$	1.70850	−	2.95920i	0.0556954	−	0.0964673i	−0.836833	−	0.547458i	$-0.815596\pi$
$941$	1.70850	−	2.95920i	0.0556954	−	0.0964673i	0.892529	+	0.450990i	$0.148929\pi$
$942$		0			0
$943$	11.9059	+	20.6216i	0.387709	+	0.671531i
$944$	−6.58301			−0.214259
$945$		0			0
$946$	−9.29150			−0.302093
$947$	−7.70850	−	13.3515i	−0.250493	−	0.433866i	0.713169	−	0.700992i	$-0.247259\pi$
$947$	−7.70850	−	13.3515i	−0.250493	−	0.433866i	−0.963662	+	0.267126i	$0.913926\pi$
$948$		0			0
$949$	−30.5830	+	52.9713i	−0.992766	+	1.71952i
$950$	−5.29150	−	9.16515i	−0.171679	−	0.297357i
$951$		0			0
$952$	7.93725			0.257248
$953$	−26.7490			−0.866486			−0.433243	−	0.901277i	$-0.642631\pi$
$953$	−26.7490			−0.866486			−0.433243	+	0.901277i	$0.642631\pi$
$954$		0			0
$955$	−8.87451	+	15.3711i	−0.287172	+	0.497397i
$956$	1.35425	−	2.34563i	0.0437995	−	0.0758630i
$957$		0			0
$958$	33.8745			1.09444
$959$	35.1660			1.13557
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	2.58301	−	4.47390i	0.0832794	−	0.144244i
$963$		0			0
$964$	13.5830	+	23.5265i	0.437479	+	0.757736i
$965$	42.0000			1.35203
$966$		0			0
$967$	40.0627			1.28833			0.644166	−	0.764886i	$-0.277205\pi$
$967$	40.0627			1.28833			0.644166	+	0.764886i	$0.277205\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	−15.3229	+	26.5400i	−0.491988	+	0.852148i
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$		0			0
$973$	16.6458	+	28.8313i	0.533638	+	0.924289i
$974$	21.8745			0.700904
$975$		0			0
$976$	−5.96863	+	10.3380i	−0.191051	+	0.330910i
$977$	6.58301	−	11.4021i	0.210609	−	0.364785i	−0.741296	−	0.671178i	$-0.765789\pi$
$977$	6.58301	−	11.4021i	0.210609	−	0.364785i	0.951905	+	0.306392i	$0.0991220\pi$
$978$		0			0
$979$	2.70850			0.0865640
$980$	9.26013	−	16.0390i	0.295804	−	0.512348i
$981$		0			0
$982$	−0.500000	−	0.866025i	−0.0159556	−	0.0276360i
$983$	21.2601	−	36.8236i	0.678093	−	1.17449i	−0.297462	−	0.954734i	$-0.596140\pi$
$983$	21.2601	−	36.8236i	0.678093	−	1.17449i	0.975555	−	0.219757i	$-0.0705266\pi$
$984$		0			0
$985$	−28.9373	−	50.1208i	−0.922018	−	1.59698i
$986$	−6.00000			−0.191079
$987$		0			0
$988$	−21.1660			−0.673380
$989$	−12.2915	−	21.2895i	−0.390847	−	0.676967i
$990$		0			0
$991$	21.9373	−	37.9964i	0.696860	−	1.20700i	−0.272690	−	0.962102i	$-0.587913\pi$
$991$	21.9373	−	37.9964i	0.696860	−	1.20700i	0.969550	−	0.244895i	$-0.0787534\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$	−3.58301	+	6.20595i	−0.113646	+	0.196841i
$995$	50.7085			1.60757
$996$		0			0
$997$	−3.41699	+	5.91841i	−0.108217	+	0.187438i	−0.915048	−	0.403345i	$-0.867848\pi$
$997$	−3.41699	+	5.91841i	−0.108217	+	0.187438i	0.806831	+	0.590783i	$0.201181\pi$
$998$	9.29150	−	16.0934i	0.294117	−	0.509426i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.r.991.2		4
3.2	odd	2		462.2.i.e.67.1	✓	4
7.2	even	3	inner	1386.2.k.r.793.2		4
7.3	odd	6		9702.2.a.dm.1.2		2
7.4	even	3		9702.2.a.db.1.1		2
21.2	odd	6		462.2.i.e.331.1	yes	4
21.11	odd	6		3234.2.a.w.1.2		2
21.17	even	6		3234.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.e.67.1	✓	4	3.2	odd	2
462.2.i.e.331.1	yes	4	21.2	odd	6
1386.2.k.r.793.2		4	7.2	even	3	inner
1386.2.k.r.991.2		4	1.1	even	1	trivial
3234.2.a.w.1.2		2	21.11	odd	6
3234.2.a.ba.1.1		2	21.17	even	6
9702.2.a.db.1.1		2	7.4	even	3
9702.2.a.dm.1.2		2	7.3	odd	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.32288 + 2.29129i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(1.32288 - 2.29129i) q^{10} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-2.64575 - 4.58258i) q^{19} -2.64575 q^{20} -1.00000 q^{22} +(-1.32288 - 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(2.00000 + 3.46410i) q^{26} +2.64575 q^{28} -2.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(3.50000 - 6.06218i) q^{35} +(-0.645751 - 1.11847i) q^{37} +(-2.64575 + 4.58258i) q^{38} +(1.32288 + 2.29129i) q^{40} -9.00000 q^{41} +9.29150 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.32288 + 2.29129i) q^{46} +(-1.96863 - 3.40976i) q^{47} +(-3.50000 + 6.06218i) q^{49} +2.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} +2.64575 q^{55} +(-1.32288 - 2.29129i) q^{56} +(1.00000 + 1.73205i) q^{58} +(3.29150 - 5.70105i) q^{59} +(-5.96863 - 10.3380i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.29150 - 9.16515i) q^{65} +(-3.79150 + 6.56708i) q^{67} +(-1.50000 - 2.59808i) q^{68} -7.00000 q^{70} +2.70850 q^{71} +(7.64575 - 13.2428i) q^{73} +(-0.645751 + 1.11847i) q^{74} +5.29150 q^{76} -2.64575 q^{77} +(-5.32288 - 9.21949i) q^{79} +(1.32288 - 2.29129i) q^{80} +(4.50000 + 7.79423i) q^{82} -15.5830 q^{83} -7.93725 q^{85} +(-4.64575 - 8.04668i) q^{86} +(0.500000 - 0.866025i) q^{88} +(1.35425 + 2.34563i) q^{89} +(5.29150 + 9.16515i) q^{91} +2.64575 q^{92} +(-1.96863 + 3.40976i) q^{94} +(7.00000 - 12.1244i) q^{95} -11.5830 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{11} - 16 q^{13} - 2 q^{16} - 6 q^{17} - 4 q^{22} - 4 q^{25} + 8 q^{26} - 8 q^{29} + 8 q^{31} - 2 q^{32} + 12 q^{34} + 14 q^{35} + 8 q^{37} - 36 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{47} - 14 q^{49} + 8 q^{50} + 8 q^{52} + 8 q^{53} + 4 q^{58} - 8 q^{59} - 8 q^{61} - 16 q^{62} + 4 q^{64} + 6 q^{67} - 6 q^{68} - 28 q^{70} + 32 q^{71} + 20 q^{73} + 8 q^{74} - 16 q^{79} + 18 q^{82} - 20 q^{83} - 8 q^{86} + 2 q^{88} + 16 q^{89} + 8 q^{94} + 28 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^11 - 16 * q^13 - 2 * q^16 - 6 * q^17 - 4 * q^22 - 4 * q^25 + 8 * q^26 - 8 * q^29 + 8 * q^31 - 2 * q^32 + 12 * q^34 + 14 * q^35 + 8 * q^37 - 36 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^47 - 14 * q^49 + 8 * q^50 + 8 * q^52 + 8 * q^53 + 4 * q^58 - 8 * q^59 - 8 * q^61 - 16 * q^62 + 4 * q^64 + 6 * q^67 - 6 * q^68 - 28 * q^70 + 32 * q^71 + 20 * q^73 + 8 * q^74 - 16 * q^79 + 18 * q^82 - 20 * q^83 - 8 * q^86 + 2 * q^88 + 16 * q^89 + 8 * q^94 + 28 * q^95 - 4 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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