LMFDB - Embedded newform 891.2.e.j.595.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(298,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("891.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.e (of order $3$, degree $2$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			595.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	891.595
Dual form			891.2.e.j.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +4.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} -6.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} +2.00000 q^{26} +2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{34} +8.00000 q^{35} -6.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(6.00000 - 10.3923i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-3.00000 - 5.19615i) q^{43} +1.00000 q^{44} -4.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(5.50000 - 9.52628i) q^{50} +(-1.00000 - 1.73205i) q^{52} +4.00000 q^{55} +(3.00000 + 5.19615i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} -2.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +4.00000 q^{80} +10.0000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{88} +4.00000 q^{91} +(2.00000 + 3.46410i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-12.0000 + 20.7846i) q^{95} +(-1.00000 - 1.73205i) q^{97} +3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 + 4 * q^5 + 2 * q^7 + 6 * q^8	$ 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8} + 8 q^{10} + q^{11} + 2 q^{13} - 2 q^{14} + q^{16} + 4 q^{17} - 12 q^{19} - 4 q^{20} - q^{22} - 4 q^{23} - 11 q^{25} + 4 q^{26} + 4 q^{28} + 6 q^{29} - 4 q^{31} + 5 q^{32} + 2 q^{34} + 16 q^{35} - 12 q^{37} - 6 q^{38} + 12 q^{40} + 10 q^{41} - 6 q^{43} + 2 q^{44} - 8 q^{46} + 8 q^{47} + 3 q^{49} + 11 q^{50} - 2 q^{52} + 8 q^{55} + 6 q^{56} - 6 q^{58} - 4 q^{59} + 6 q^{61} - 8 q^{62} + 14 q^{64} - 8 q^{65} - 8 q^{67} + 2 q^{68} + 8 q^{70} - 4 q^{73} - 6 q^{74} - 6 q^{76} - 2 q^{77} + 10 q^{79} + 8 q^{80} + 20 q^{82} - 12 q^{83} + 8 q^{85} + 6 q^{86} + 3 q^{88} + 8 q^{91} + 4 q^{92} - 8 q^{94} - 24 q^{95} - 2 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 4 * q^5 + 2 * q^7 + 6 * q^8 + 8 * q^10 + q^11 + 2 * q^13 - 2 * q^14 + q^16 + 4 * q^17 - 12 * q^19 - 4 * q^20 - q^22 - 4 * q^23 - 11 * q^25 + 4 * q^26 + 4 * q^28 + 6 * q^29 - 4 * q^31 + 5 * q^32 + 2 * q^34 + 16 * q^35 - 12 * q^37 - 6 * q^38 + 12 * q^40 + 10 * q^41 - 6 * q^43 + 2 * q^44 - 8 * q^46 + 8 * q^47 + 3 * q^49 + 11 * q^50 - 2 * q^52 + 8 * q^55 + 6 * q^56 - 6 * q^58 - 4 * q^59 + 6 * q^61 - 8 * q^62 + 14 * q^64 - 8 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^70 - 4 * q^73 - 6 * q^74 - 6 * q^76 - 2 * q^77 + 10 * q^79 + 8 * q^80 + 20 * q^82 - 12 * q^83 + 8 * q^85 + 6 * q^86 + 3 * q^88 + 8 * q^91 + 4 * q^92 - 8 * q^94 - 24 * q^95 - 2 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.834512	−	0.550990i	$-0.185750\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	4.00000			1.26491
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	2.00000			0.392232
$27$		0			0
$28$	2.00000			0.377964
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	8.00000			1.35225
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$		0			0
$40$	6.00000	−	10.3923i	0.948683	−	1.64317i
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	1.00000			0.150756
$45$		0			0
$46$	−4.00000			−0.589768
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	5.50000	−	9.52628i	0.777817	−	1.34722i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	7.00000			0.875000
$65$	−4.00000	−	6.92820i	−0.496139	−	0.859338i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$	4.00000	+	6.92820i	0.478091	+	0.828079i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	4.00000			0.447214
$81$		0			0
$82$	10.0000			1.10432
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$	4.00000	−	6.92820i	0.433861	−	0.751469i
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	−12.0000	+	20.7846i	−1.23117	+	2.13246i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	3.00000			0.303046
$99$		0			0
$100$	−11.0000			−1.10000
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	0.969664	+	0.244443i	$0.0786053\pi$
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	−0.273138	+	0.961975i	$0.588061\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$		0			0
$112$	−1.00000	+	1.73205i	−0.0944911	+	0.163663i
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$	8.00000	+	13.8564i	0.746004	+	1.29212i
$116$	6.00000			0.557086
$117$		0			0
$118$	−4.00000			−0.368230
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.00000	+	5.19615i	−0.271607	+	0.470438i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	4.00000	−	6.92820i	0.350823	−	0.607644i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−6.00000	−	10.3923i	−0.520266	−	0.901127i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	6.00000			0.514496
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		0			0
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$	4.00000	−	6.92820i	0.338062	−	0.585540i
$141$		0			0
$142$		0			0
$143$	2.00000			0.167248
$144$		0			0
$145$	24.0000			1.99309
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	−18.0000			−1.45999
$153$		0			0
$154$	−2.00000			−0.161165
$155$	8.00000	+	13.8564i	0.642575	+	1.11297i
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$		0			0
$160$	−10.0000	−	17.3205i	−0.790569	−	1.36931i
$161$	−8.00000			−0.630488
$162$		0			0
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	8.00000			0.613572
$171$		0			0
$172$	−6.00000			−0.457496
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	11.0000	−	19.0526i	0.831522	−	1.44024i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$		0			0
$178$		0			0
$179$	−24.0000			−1.79384			−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000			−1.79384			−0.896922	+	0.442189i	$0.854202\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$	2.00000	+	3.46410i	0.148250	+	0.256776i
$183$		0			0
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$	−12.0000	+	20.7846i	−0.882258	+	1.52811i
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	8.00000			0.583460
$189$		0			0
$190$	−24.0000			−1.74114
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	−1.50000	−	2.59808i	−0.107143	−	0.185577i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	12.0000			0.850657			0.425329	−	0.905039i	$-0.360158\pi$
$199$	12.0000			0.850657			0.425329	+	0.905039i	$0.360158\pi$
$200$	−16.5000	−	28.5788i	−1.16673	−	2.02083i
$201$		0			0
$202$	−7.00000	+	12.1244i	−0.492518	+	0.853067i
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$	−20.0000	−	34.6410i	−1.39686	−	2.41943i
$206$	−8.00000			−0.557386
$207$		0			0
$208$	2.00000			0.138675
$209$	−3.00000	−	5.19615i	−0.207514	−	0.359425i
$210$		0			0
$211$	3.00000	−	5.19615i	0.206529	−	0.357718i	−0.744090	−	0.668079i	$-0.767117\pi$
$211$	3.00000	−	5.19615i	0.206529	−	0.357718i	0.950619	+	0.310361i	$0.100450\pi$
$212$		0			0
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−24.0000			−1.63679
$216$		0			0
$217$	−8.00000			−0.543075
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$		0			0
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$	10.0000			0.668153
$225$		0			0
$226$	−12.0000			−0.798228
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	−0.947960	−	0.318390i	$-0.896858\pi$
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	0.749714	+	0.661762i	$0.230191\pi$
$230$	−8.00000	+	13.8564i	−0.527504	+	0.913664i
$231$		0			0
$232$	9.00000	+	15.5885i	0.590879	+	1.02343i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	32.0000			2.08745
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	−2.00000	+	3.46410i	−0.129641	+	0.224544i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	−1.00000			−0.0642824
$243$		0			0
$244$	6.00000			0.384111
$245$	−6.00000	−	10.3923i	−0.383326	−	0.663940i
$246$		0			0
$247$	−6.00000	+	10.3923i	−0.381771	+	0.661247i
$248$	−6.00000	+	10.3923i	−0.381000	+	0.659912i
$249$		0			0
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	−5.00000	−	8.66025i	−0.313728	−	0.543393i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	−0.963391	−	0.268101i	$-0.913604\pi$
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	0.713878	+	0.700270i	$0.246937\pi$
$258$		0			0
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$	−8.00000			−0.496139
$261$		0			0
$262$	12.0000			0.741362
$263$	16.0000	+	27.7128i	0.986602	+	1.70885i	0.634588	+	0.772851i	$0.281170\pi$
$263$	16.0000	+	27.7128i	0.986602	+	1.70885i	0.352014	+	0.935995i	$0.385497\pi$
$264$		0			0
$265$		0			0
$266$	6.00000	−	10.3923i	0.367884	−	0.637193i
$267$		0			0
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	−16.0000			−0.975537			−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000			−0.975537			−0.487769	+	0.872973i	$0.662189\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$		0			0
$274$	2.00000	−	3.46410i	0.120824	−	0.209274i
$275$	5.50000	−	9.52628i	0.331662	−	0.574456i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−10.0000			−0.599760
$279$		0			0
$280$	24.0000			1.43427
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	−0.834772	−	0.550596i	$-0.814401\pi$
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	0.894216	+	0.447636i	$0.147734\pi$
$284$		0			0
$285$		0			0
$286$	1.00000	+	1.73205i	0.0591312	+	0.102418i
$287$	20.0000			1.18056
$288$		0			0
$289$	−13.0000			−0.764706
$290$	12.0000	+	20.7846i	0.704664	+	1.22051i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	−0.473763	−	0.880652i	$-0.657105\pi$
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	0.999549	−	0.0300351i	$-0.00956192\pi$
$294$		0			0
$295$	8.00000	+	13.8564i	0.465778	+	0.806751i
$296$	−18.0000			−1.04623
$297$		0			0
$298$	2.00000			0.115857
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$	6.00000	−	10.3923i	0.345834	−	0.599002i
$302$	7.00000	−	12.1244i	0.402805	−	0.697678i
$303$		0			0
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$	24.0000			1.37424
$306$		0			0
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$		0			0
$310$	−8.00000	+	13.8564i	−0.454369	+	0.786991i
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.720257	+	0.693708i	$0.244024\pi$
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.240640	+	0.970614i	$0.422643\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$	10.0000			0.562544
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	0.916710	−	0.399554i	$-0.130835\pi$
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	−0.804379	+	0.594117i	$0.797502\pi$
$318$		0			0
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	14.0000	−	24.2487i	0.782624	−	1.35554i
$321$		0			0
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	−12.0000			−0.667698
$324$		0			0
$325$	−22.0000			−1.22034
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$		0			0
$328$	15.0000	−	25.9808i	0.828236	−	1.43455i
$329$	−8.00000	+	13.8564i	−0.441054	+	0.763928i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$		0			0
$335$	16.0000	+	27.7128i	0.874173	+	1.51411i
$336$		0			0
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	−0.991250	−	0.131995i	$-0.957862\pi$
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	0.609936	+	0.792451i	$0.291195\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$	−4.00000	−	6.92820i	−0.216930	−	0.375735i
$341$	−4.00000			−0.216612
$342$		0			0
$343$	20.0000			1.07990
$344$	−9.00000	−	15.5885i	−0.485247	−	0.840473i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	0.462244	+	0.886753i	$0.347044\pi$
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	−0.999072	+	0.0430610i	$0.986289\pi$
$348$		0			0
$349$	−9.00000	−	15.5885i	−0.481759	−	0.834431i	0.518022	−	0.855367i	$-0.326669\pi$
$349$	−9.00000	−	15.5885i	−0.481759	−	0.834431i	−0.999781	+	0.0209364i	$0.993335\pi$
$350$	22.0000			1.17595
$351$		0			0
$352$	5.00000			0.266501
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−12.0000	−	20.7846i	−0.634220	−	1.09850i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$		0			0
$364$	2.00000	−	3.46410i	0.104828	−	0.181568i
$365$	−4.00000	+	6.92820i	−0.209370	+	0.362639i
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	−24.0000			−1.24770
$371$		0			0
$372$		0			0
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$		0			0
$376$	12.0000	+	20.7846i	0.618853	+	1.07188i
$377$	12.0000			0.618031
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	12.0000	+	20.7846i	0.615587	+	1.06623i
$381$		0			0
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	10.0000	−	17.3205i	0.510976	−	0.885037i	−0.488943	−	0.872316i	$-0.662617\pi$
$383$	10.0000	−	17.3205i	0.510976	−	0.885037i	0.999919	−	0.0127209i	$-0.00404928\pi$
$384$		0			0
$385$	4.00000	+	6.92820i	0.203859	+	0.353094i
$386$	14.0000			0.712581
$387$		0			0
$388$	−2.00000			−0.101535
$389$	−18.0000	−	31.1769i	−0.912636	−	1.58073i	−0.810326	−	0.585980i	$-0.800710\pi$
$389$	−18.0000	−	31.1769i	−0.912636	−	1.58073i	−0.102311	−	0.994753i	$-0.532624\pi$
$390$		0			0
$391$	−4.00000	+	6.92820i	−0.202289	+	0.350374i
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$		0			0
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	40.0000			2.01262
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	6.00000	+	10.3923i	0.300753	+	0.520919i
$399$		0			0
$400$	5.50000	−	9.52628i	0.275000	−	0.476314i
$401$	−14.0000	+	24.2487i	−0.699127	+	1.21092i	0.269643	+	0.962960i	$0.413094\pi$
$401$	−14.0000	+	24.2487i	−0.699127	+	1.21092i	−0.968770	+	0.247962i	$0.920239\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	14.0000			0.696526
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$	20.0000	−	34.6410i	0.987730	−	1.71080i
$411$		0			0
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$	−8.00000			−0.393654
$414$		0			0
$415$	−48.0000			−2.35623
$416$	−5.00000	−	8.66025i	−0.245145	−	0.424604i
$417$		0			0
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	16.0000	−	27.7128i	0.781651	−	1.35386i	−0.149328	−	0.988788i	$-0.547711\pi$
$419$	16.0000	−	27.7128i	0.781651	−	1.35386i	0.930979	−	0.365072i	$-0.118956\pi$
$420$		0			0
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	6.00000			0.292075
$423$		0			0
$424$		0			0
$425$	−11.0000	−	19.0526i	−0.533578	−	0.924185i
$426$		0			0
$427$	−6.00000	+	10.3923i	−0.290360	+	0.502919i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$		0			0
$430$	−12.0000	−	20.7846i	−0.578691	−	1.00232i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−4.00000	−	6.92820i	−0.192006	−	0.332564i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	12.0000			0.572078
$441$		0			0
$442$	4.00000			0.190261
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	0.909618	−	0.415445i	$-0.136374\pi$
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	−0.814595	+	0.580030i	$0.803041\pi$
$444$		0			0
$445$		0			0
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	7.00000	+	12.1244i	0.330719	+	0.572822i
$449$	−32.0000			−1.51017			−0.755087	−	0.655625i	$-0.772405\pi$
$449$	−32.0000			−1.51017			−0.755087	+	0.655625i	$0.772405\pi$
$450$		0			0
$451$	10.0000			0.470882
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		0			0
$454$	−6.00000	+	10.3923i	−0.281594	+	0.487735i
$455$	8.00000	−	13.8564i	0.375046	−	0.649598i
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−6.00000			−0.280362
$459$		0			0
$460$	16.0000			0.746004
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	−8.00000	+	13.8564i	−0.371792	+	0.643962i	−0.989841	−	0.142177i	$-0.954590\pi$
$463$	−8.00000	+	13.8564i	−0.371792	+	0.643962i	0.618050	+	0.786139i	$0.287923\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−16.0000			−0.738811
$470$	16.0000	+	27.7128i	0.738025	+	1.27830i
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	33.0000	+	57.1577i	1.51414	+	2.62257i
$476$	4.00000			0.183340
$477$		0			0
$478$		0			0
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	0.956431	+	0.291958i	$0.0943068\pi$
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	−0.225372	+	0.974273i	$0.572360\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−13.0000	+	22.5167i	−0.592134	+	1.02561i
$483$		0			0
$484$	0.500000	+	0.866025i	0.0227273	+	0.0393648i
$485$	−8.00000			−0.363261
$486$		0			0
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$	9.00000	+	15.5885i	0.407411	+	0.705656i
$489$		0			0
$490$	6.00000	−	10.3923i	0.271052	−	0.469476i
$491$	14.0000	−	24.2487i	0.631811	−	1.09433i	−0.355370	−	0.934726i	$-0.615645\pi$
$491$	14.0000	−	24.2487i	0.631811	−	1.09433i	0.987181	−	0.159603i	$-0.0510215\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$	−12.0000			−0.539906
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$		0			0
$502$	4.00000	+	6.92820i	0.178529	+	0.309221i
$503$	−40.0000			−1.78351			−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000			−1.78351			−0.891756	+	0.452517i	$0.850526\pi$
$504$		0			0
$505$	56.0000			2.49197
$506$	−2.00000	−	3.46410i	−0.0889108	−	0.153998i
$507$		0			0
$508$	−5.00000	+	8.66025i	−0.221839	+	0.384237i
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	11.0000			0.486136
$513$		0			0
$514$	−8.00000			−0.352865
$515$	16.0000	+	27.7128i	0.705044	+	1.22117i
$516$		0			0
$517$	−4.00000	+	6.92820i	−0.175920	+	0.304702i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$	−12.0000	−	20.7846i	−0.526235	−	0.911465i
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$		0			0
$523$	38.0000			1.66162			0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000			1.66162			0.830812	+	0.556553i	$0.187876\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	−16.0000	+	27.7128i	−0.697633	+	1.20834i
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$	−12.0000			−0.520266
$533$	−10.0000	−	17.3205i	−0.433148	−	0.750234i
$534$		0			0
$535$	24.0000	−	41.5692i	1.03761	−	1.79719i
$536$	−12.0000	+	20.7846i	−0.518321	+	0.897758i
$537$		0			0
$538$	−8.00000	−	13.8564i	−0.344904	−	0.597392i
$539$	3.00000			0.129219
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$		0			0
$544$	5.00000	−	8.66025i	0.214373	−	0.371305i
$545$	−4.00000	+	6.92820i	−0.171341	+	0.296772i
$546$		0			0
$547$	−19.0000	−	32.9090i	−0.812381	−	1.40709i	−0.911193	−	0.411980i	$-0.864837\pi$
$547$	−19.0000	−	32.9090i	−0.812381	−	1.40709i	0.0988117	−	0.995106i	$-0.468496\pi$
$548$	−4.00000			−0.170872
$549$		0			0
$550$	11.0000			0.469042
$551$	−18.0000	−	31.1769i	−0.766826	−	1.32818i
$552$		0			0
$553$	−10.0000	+	17.3205i	−0.425243	+	0.736543i
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$		0			0
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	38.0000			1.61011			0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000			1.61011			0.805056	+	0.593199i	$0.202135\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$	4.00000	+	6.92820i	0.169031	+	0.292770i
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	0.994228	−	0.107290i	$-0.0342173\pi$
$564$		0			0
$565$	24.0000	+	41.5692i	1.00969	+	1.74883i
$566$	2.00000			0.0840663
$567$		0			0
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	1.00000	−	1.73205i	0.0418121	−	0.0724207i
$573$		0			0
$574$	10.0000	+	17.3205i	0.417392	+	0.722944i
$575$	44.0000			1.83493
$576$		0			0
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$		0			0
$580$	12.0000	−	20.7846i	0.498273	−	0.863034i
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$		0			0
$584$	−6.00000			−0.248282
$585$		0			0
$586$	18.0000			0.743573
$587$	2.00000	+	3.46410i	0.0825488	+	0.142979i	0.904344	−	0.426804i	$-0.140361\pi$
$587$	2.00000	+	3.46410i	0.0825488	+	0.142979i	−0.821795	+	0.569783i	$0.807027\pi$
$588$		0			0
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$	−8.00000	+	13.8564i	−0.329355	+	0.570459i
$591$		0			0
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	−26.0000			−1.06769			−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000			−1.06769			−0.533846	+	0.845582i	$0.679254\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−1.00000	−	1.73205i	−0.0409616	−	0.0709476i
$597$		0			0
$598$	−4.00000	+	6.92820i	−0.163572	+	0.283315i
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	−0.424333	−	0.905506i	$-0.639492\pi$
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	0.996358	−	0.0852695i	$-0.0271751\pi$
$600$		0			0
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	12.0000			0.489083
$603$		0			0
$604$	−14.0000			−0.569652
$605$	2.00000	+	3.46410i	0.0813116	+	0.140836i
$606$		0			0
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	−0.746532	−	0.665350i	$-0.768282\pi$
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	0.949476	+	0.313841i	$0.101616\pi$
$608$	−15.0000	+	25.9808i	−0.608330	+	1.05366i
$609$		0			0
$610$	12.0000	+	20.7846i	0.485866	+	0.841544i
$611$	16.0000			0.647291
$612$		0			0
$613$	−46.0000			−1.85792			−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000			−1.85792			−0.928961	+	0.370177i	$0.879297\pi$
$614$	−11.0000	−	19.0526i	−0.443924	−	0.768899i
$615$		0			0
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	−0.719605	−	0.694383i	$-0.755677\pi$
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	0.961156	+	0.276005i	$0.0890106\pi$
$618$		0			0
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$	16.0000			0.642575
$621$		0			0
$622$	−12.0000			−0.481156
$623$		0			0
$624$		0			0
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	−17.0000	+	29.4449i	−0.679457	+	1.17685i
$627$		0			0
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	4.00000			0.159237			0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000			0.159237			0.0796187	+	0.996825i	$0.474630\pi$
$632$	15.0000	+	25.9808i	0.596668	+	1.03346i
$633$		0			0
$634$	−2.00000	+	3.46410i	−0.0794301	+	0.137577i
$635$	−20.0000	+	34.6410i	−0.793676	+	1.37469i
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$	−6.00000			−0.237542
$639$		0			0
$640$	−12.0000			−0.474342
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$		0			0
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$		0			0
$649$	−4.00000			−0.157014
$650$	−11.0000	−	19.0526i	−0.431455	−	0.747303i
$651$		0			0
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	8.00000	−	13.8564i	0.313064	−	0.542243i	−0.665960	−	0.745988i	$-0.731978\pi$
$653$	8.00000	−	13.8564i	0.313064	−	0.542243i	0.979024	+	0.203744i	$0.0653112\pi$
$654$		0			0
$655$	−24.0000	−	41.5692i	−0.937758	−	1.62424i
$656$	10.0000			0.390434
$657$		0			0
$658$	−16.0000			−0.623745
$659$	−22.0000	−	38.1051i	−0.856998	−	1.48436i	−0.874779	−	0.484523i	$-0.838993\pi$
$659$	−22.0000	−	38.1051i	−0.856998	−	1.48436i	0.0177803	−	0.999842i	$-0.494340\pi$
$660$		0			0
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.284087	−	0.958799i	$-0.408310\pi$
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.688301	−	0.725426i	$-0.258357\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	−18.0000	−	31.1769i	−0.698535	−	1.20990i
$665$	−48.0000			−1.86136
$666$		0			0
$667$	−24.0000			−0.929284
$668$		0			0
$669$		0			0
$670$	−16.0000	+	27.7128i	−0.618134	+	1.07064i
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$		0			0
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	0.498886	−	0.866668i	$-0.333743\pi$
$674$	−14.0000			−0.539260
$675$		0			0
$676$	9.00000			0.346154
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$	12.0000	−	20.7846i	0.460179	−	0.797053i
$681$		0			0
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	−32.0000			−1.22445			−0.612223	−	0.790685i	$-0.709725\pi$
$683$	−32.0000			−1.22445			−0.612223	+	0.790685i	$0.709725\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$		0			0
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$		0			0
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−20.0000			−0.759190
$695$	20.0000	+	34.6410i	0.758643	+	1.31401i
$696$		0			0
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$	9.00000	−	15.5885i	0.340655	−	0.590032i
$699$		0			0
$700$	−11.0000	−	19.0526i	−0.415761	−	0.720119i
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$	36.0000			1.35777
$704$	3.50000	+	6.06218i	0.131911	+	0.228477i
$705$		0			0
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	−14.0000	+	24.2487i	−0.526524	+	0.911967i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.00000	−	13.8564i	−0.299602	−	0.518927i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$		0			0
$718$	4.00000	+	6.92820i	0.149279	+	0.258558i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	−16.0000			−0.595871
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	33.0000	−	57.1577i	1.22559	−	2.12278i
$726$		0			0
$727$	−6.00000	−	10.3923i	−0.222528	−	0.385429i	0.733047	−	0.680178i	$-0.238097\pi$
$727$	−6.00000	−	10.3923i	−0.222528	−	0.385429i	−0.955575	+	0.294749i	$0.904764\pi$
$728$	12.0000			0.444750
$729$		0			0
$730$	−8.00000			−0.296093
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	−0.916096	−	0.400959i	$-0.868677\pi$
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	0.805289	+	0.592883i	$0.202010\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	10.0000	+	17.3205i	0.368605	+	0.638442i
$737$	−8.00000			−0.294684
$738$		0			0
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$	12.0000	+	20.7846i	0.441129	+	0.764057i
$741$		0			0
$742$		0			0
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	−0.681141	−	0.732152i	$-0.738516\pi$
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	0.974633	+	0.223810i	$0.0718494\pi$
$744$		0			0
$745$	−4.00000	−	6.92820i	−0.146549	−	0.253830i
$746$	−34.0000			−1.24483
$747$		0			0
$748$	2.00000			0.0731272
$749$	12.0000	+	20.7846i	0.438470	+	0.759453i
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$		0			0
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	−56.0000			−2.03805
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	2.00000	+	3.46410i	0.0726433	+	0.125822i
$759$		0			0
$760$	−36.0000	+	62.3538i	−1.30586	+	2.26181i
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	20.0000			0.722629
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	−4.00000	+	6.92820i	−0.144150	+	0.249675i
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$		0			0
$775$	44.0000			1.58053
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$		0			0
$778$	18.0000	−	31.1769i	0.645331	−	1.11775i
$779$	−30.0000	+	51.9615i	−1.07486	+	1.86171i
$780$		0			0
$781$		0			0
$782$	−8.00000			−0.286079
$783$		0			0
$784$	3.00000			0.107143
$785$	−20.0000	−	34.6410i	−0.713831	−	1.23639i
$786$		0			0
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$		0			0
$790$	20.0000	+	34.6410i	0.711568	+	1.23247i
$791$	−24.0000			−0.853342
$792$		0			0
$793$	12.0000			0.426132
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$		0			0
$796$	6.00000	−	10.3923i	0.212664	−	0.368345i
$797$	−14.0000	+	24.2487i	−0.495905	+	0.858933i	−0.999989	−	0.00472155i	$-0.998497\pi$
$797$	−14.0000	+	24.2487i	−0.495905	+	0.858933i	0.504083	+	0.863655i	$0.331830\pi$
$798$		0			0
$799$	8.00000	+	13.8564i	0.283020	+	0.490204i
$800$	−55.0000			−1.94454
$801$		0			0
$802$	−28.0000			−0.988714
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$		0			0
$805$	−16.0000	+	27.7128i	−0.563926	+	0.976748i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		0			0
$808$	21.0000	+	36.3731i	0.738777	+	1.27960i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	−40.0000	+	69.2820i	−1.40114	+	2.42684i
$816$		0			0
$817$	18.0000	+	31.1769i	0.629740	+	1.09074i
$818$	−6.00000			−0.209785
$819$		0			0
$820$	−40.0000			−1.39686
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$		0			0
$823$	24.0000	−	41.5692i	0.836587	−	1.44901i	−0.0561440	−	0.998423i	$-0.517881\pi$
$823$	24.0000	−	41.5692i	0.836587	−	1.44901i	0.892731	−	0.450589i	$-0.148786\pi$
$824$	−12.0000	+	20.7846i	−0.418040	+	0.724066i
$825$		0			0
$826$	−4.00000	−	6.92820i	−0.139178	−	0.241063i
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−24.0000	−	41.5692i	−0.833052	−	1.44289i
$831$		0			0
$832$	7.00000	−	12.1244i	0.242681	−	0.420336i
$833$	3.00000	−	5.19615i	0.103944	−	0.180036i
$834$		0			0
$835$		0			0
$836$	−6.00000			−0.207514
$837$		0			0
$838$	32.0000			1.10542
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	0.640159	−	0.768243i	$-0.278869\pi$
$839$	−10.0000	−	17.3205i	−0.345238	−	0.597970i	−0.985397	+	0.170272i	$0.945535\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	17.0000	−	29.4449i	0.585859	−	1.01474i
$843$		0			0
$844$	−3.00000	−	5.19615i	−0.103264	−	0.178859i
$845$	36.0000			1.23844
$846$		0			0
$847$	−2.00000			−0.0687208
$848$		0			0
$849$		0			0
$850$	11.0000	−	19.0526i	0.377297	−	0.653497i
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$		0			0
$853$	−25.0000	−	43.3013i	−0.855984	−	1.48261i	−0.875729	−	0.482802i	$-0.839619\pi$
$853$	−25.0000	−	43.3013i	−0.855984	−	1.48261i	0.0197457	−	0.999805i	$-0.493714\pi$
$854$	−12.0000			−0.410632
$855$		0			0
$856$	36.0000			1.23045
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$		0			0
$859$	18.0000	−	31.1769i	0.614152	−	1.06374i	−0.376381	−	0.926465i	$-0.622831\pi$
$859$	18.0000	−	31.1769i	0.614152	−	1.06374i	0.990533	−	0.137277i	$-0.0438352\pi$
$860$	−12.0000	+	20.7846i	−0.409197	+	0.708749i
$861$		0			0
$862$	12.0000	+	20.7846i	0.408722	+	0.707927i
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	24.0000			0.816024
$866$	−1.00000	−	1.73205i	−0.0339814	−	0.0588575i
$867$		0			0
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	−5.00000	+	8.66025i	−0.169613	+	0.293779i
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	−6.00000			−0.203186
$873$		0			0
$874$	24.0000			0.811812
$875$	−24.0000	−	41.5692i	−0.811348	−	1.40530i
$876$		0			0
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	0.256064	+	0.966660i	$0.417574\pi$
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	−0.965184	+	0.261571i	$0.915759\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$		0			0
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	−20.0000			−0.673817			−0.336909	−	0.941537i	$-0.609381\pi$
$881$	−20.0000			−0.673817			−0.336909	+	0.941537i	$0.609381\pi$
$882$		0			0
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$		0			0
$886$	−2.00000	+	3.46410i	−0.0671913	+	0.116379i
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$	−10.0000	−	17.3205i	−0.335389	−	0.580911i
$890$		0			0
$891$		0			0
$892$	8.00000			0.267860
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$		0			0
$895$	−48.0000	+	83.1384i	−1.60446	+	2.77901i
$896$	3.00000	−	5.19615i	0.100223	−	0.173591i
$897$		0			0
$898$	−16.0000	−	27.7128i	−0.533927	−	0.924789i
$899$	−24.0000			−0.800445
$900$		0			0
$901$		0			0
$902$	5.00000	+	8.66025i	0.166482	+	0.288355i
$903$		0			0
$904$	−18.0000	+	31.1769i	−0.598671	+	1.03693i
$905$	20.0000	−	34.6410i	0.664822	−	1.15151i
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	12.0000			0.398234
$909$		0			0
$910$	16.0000			0.530395
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	−0.922740	−	0.385422i	$-0.874056\pi$
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	0.127585	−	0.991828i	$-0.459277\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$		0			0
$916$	3.00000	+	5.19615i	0.0991228	+	0.171686i
$917$	24.0000			0.792550
$918$		0			0
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$	24.0000	+	41.5692i	0.791257	+	1.37050i
$921$		0			0
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$		0			0
$924$		0			0
$925$	33.0000	+	57.1577i	1.08503	+	1.87933i
$926$	−16.0000			−0.525793
$927$		0			0
$928$	30.0000			0.984798
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	0.947507	−	0.319736i	$-0.103594\pi$
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	−0.750653	+	0.660697i	$0.770261\pi$
$930$		0			0
$931$	−9.00000	+	15.5885i	−0.294963	+	0.510891i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	8.00000			0.261628
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$	−8.00000	−	13.8564i	−0.261209	−	0.452428i
$939$		0			0
$940$	16.0000	−	27.7128i	0.521862	−	0.903892i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$		0			0
$943$	20.0000	+	34.6410i	0.651290	+	1.12807i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	6.00000			0.195077
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	0.932002	+	0.362454i	$0.118061\pi$
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	−0.152106	+	0.988364i	$0.548606\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$	−33.0000	+	57.1577i	−1.07066	+	1.85444i
$951$		0			0
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	−64.0000			−2.07099
$956$		0			0
$957$		0			0
$958$	−16.0000	+	27.7128i	−0.516937	+	0.895360i
$959$	4.00000	−	6.92820i	0.129167	−	0.223723i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−12.0000			−0.386896
$963$		0			0
$964$	26.0000			0.837404
$965$	−28.0000	−	48.4974i	−0.901352	−	1.56119i
$966$		0			0
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	−0.113055	−	0.993589i	$-0.536064\pi$
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	0.917000	−	0.398886i	$-0.130603\pi$
$968$	−1.50000	+	2.59808i	−0.0482118	+	0.0835053i
$969$		0			0
$970$	−4.00000	−	6.92820i	−0.128432	−	0.222451i
$971$	4.00000			0.128366			0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000			0.128366			0.0641831	+	0.997938i	$0.479556\pi$
$972$		0			0
$973$	−20.0000			−0.641171
$974$	−2.00000	−	3.46410i	−0.0640841	−	0.110997i
$975$		0			0
$976$	−3.00000	+	5.19615i	−0.0960277	+	0.166325i
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	−0.420075	−	0.907489i	$-0.637996\pi$
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	0.995946	−	0.0899487i	$-0.0286703\pi$
$978$		0			0
$979$		0			0
$980$	−12.0000			−0.383326
$981$		0			0
$982$	28.0000			0.893516
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	6.00000	+	10.3923i	0.190885	+	0.330623i
$989$	24.0000			0.763156
$990$		0			0
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$		0			0
$994$		0			0
$995$	24.0000	−	41.5692i	0.760851	−	1.31783i
$996$		0			0
$997$	−25.0000	−	43.3013i	−0.791758	−	1.37136i	−0.924878	−	0.380265i	$-0.875833\pi$
$997$	−25.0000	−	43.3013i	−0.791758	−	1.37136i	0.133120	−	0.991100i	$-0.457501\pi$
$998$	16.0000			0.506471
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.e.j.595.1		2
3.2	odd	2		891.2.e.c.595.1		2
9.2	odd	6		891.2.e.c.298.1		2
9.4	even	3		99.2.a.a.1.1	✓	1
9.5	odd	6		99.2.a.c.1.1	yes	1
9.7	even	3	inner	891.2.e.j.298.1		2
36.23	even	6		1584.2.a.r.1.1		1
36.31	odd	6		1584.2.a.b.1.1		1
45.4	even	6		2475.2.a.j.1.1		1
45.13	odd	12		2475.2.c.b.199.2		2
45.14	odd	6		2475.2.a.c.1.1		1
45.22	odd	12		2475.2.c.b.199.1		2
45.23	even	12		2475.2.c.g.199.1		2
45.32	even	12		2475.2.c.g.199.2		2
63.13	odd	6		4851.2.a.g.1.1		1
63.41	even	6		4851.2.a.o.1.1		1
72.5	odd	6		6336.2.a.b.1.1		1
72.13	even	6		6336.2.a.cl.1.1		1
72.59	even	6		6336.2.a.f.1.1		1
72.67	odd	6		6336.2.a.cm.1.1		1
99.32	even	6		1089.2.a.d.1.1		1
99.76	odd	6		1089.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.a.a.1.1	✓	1	9.4	even	3
99.2.a.c.1.1	yes	1	9.5	odd	6
891.2.e.c.298.1		2	9.2	odd	6
891.2.e.c.595.1		2	3.2	odd	2
891.2.e.j.298.1		2	9.7	even	3	inner
891.2.e.j.595.1		2	1.1	even	1	trivial
1089.2.a.d.1.1		1	99.32	even	6
1089.2.a.h.1.1		1	99.76	odd	6
1584.2.a.b.1.1		1	36.31	odd	6
1584.2.a.r.1.1		1	36.23	even	6
2475.2.a.c.1.1		1	45.14	odd	6
2475.2.a.j.1.1		1	45.4	even	6
2475.2.c.b.199.1		2	45.22	odd	12
2475.2.c.b.199.2		2	45.13	odd	12
2475.2.c.g.199.1		2	45.23	even	12
2475.2.c.g.199.2		2	45.32	even	12
4851.2.a.g.1.1		1	63.13	odd	6
4851.2.a.o.1.1		1	63.41	even	6
6336.2.a.b.1.1		1	72.5	odd	6
6336.2.a.f.1.1		1	72.59	even	6
6336.2.a.cl.1.1		1	72.13	even	6
6336.2.a.cm.1.1		1	72.67	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +4.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} -6.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} +2.00000 q^{26} +2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{34} +8.00000 q^{35} -6.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(6.00000 - 10.3923i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-3.00000 - 5.19615i) q^{43} +1.00000 q^{44} -4.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(5.50000 - 9.52628i) q^{50} +(-1.00000 - 1.73205i) q^{52} +4.00000 q^{55} +(3.00000 + 5.19615i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} -2.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +4.00000 q^{80} +10.0000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{88} +4.00000 q^{91} +(2.00000 + 3.46410i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-12.0000 + 20.7846i) q^{95} +(-1.00000 - 1.73205i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 + 4 * q^5 + 2 * q^7 + 6 * q^8	\( 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8} + 8 q^{10} + q^{11} + 2 q^{13} - 2 q^{14} + q^{16} + 4 q^{17} - 12 q^{19} - 4 q^{20} - q^{22} - 4 q^{23} - 11 q^{25} + 4 q^{26} + 4 q^{28} + 6 q^{29} - 4 q^{31} + 5 q^{32} + 2 q^{34} + 16 q^{35} - 12 q^{37} - 6 q^{38} + 12 q^{40} + 10 q^{41} - 6 q^{43} + 2 q^{44} - 8 q^{46} + 8 q^{47} + 3 q^{49} + 11 q^{50} - 2 q^{52} + 8 q^{55} + 6 q^{56} - 6 q^{58} - 4 q^{59} + 6 q^{61} - 8 q^{62} + 14 q^{64} - 8 q^{65} - 8 q^{67} + 2 q^{68} + 8 q^{70} - 4 q^{73} - 6 q^{74} - 6 q^{76} - 2 q^{77} + 10 q^{79} + 8 q^{80} + 20 q^{82} - 12 q^{83} + 8 q^{85} + 6 q^{86} + 3 q^{88} + 8 q^{91} + 4 q^{92} - 8 q^{94} - 24 q^{95} - 2 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 4 * q^5 + 2 * q^7 + 6 * q^8 + 8 * q^10 + q^11 + 2 * q^13 - 2 * q^14 + q^16 + 4 * q^17 - 12 * q^19 - 4 * q^20 - q^22 - 4 * q^23 - 11 * q^25 + 4 * q^26 + 4 * q^28 + 6 * q^29 - 4 * q^31 + 5 * q^32 + 2 * q^34 + 16 * q^35 - 12 * q^37 - 6 * q^38 + 12 * q^40 + 10 * q^41 - 6 * q^43 + 2 * q^44 - 8 * q^46 + 8 * q^47 + 3 * q^49 + 11 * q^50 - 2 * q^52 + 8 * q^55 + 6 * q^56 - 6 * q^58 - 4 * q^59 + 6 * q^61 - 8 * q^62 + 14 * q^64 - 8 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^70 - 4 * q^73 - 6 * q^74 - 6 * q^76 - 2 * q^77 + 10 * q^79 + 8 * q^80 + 20 * q^82 - 12 * q^83 + 8 * q^85 + 6 * q^86 + 3 * q^88 + 8 * q^91 + 4 * q^92 - 8 * q^94 - 24 * q^95 - 2 * q^97 + 6 * q^98

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