LMFDB - Embedded newform 273.2.l.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (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:	$2.17991597518$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.a.256.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.00000 - 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +(1.00000 - 3.46410i) q^{13} +4.00000 q^{16} -6.00000 q^{17} +(0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} -6.00000 q^{23} +(2.50000 + 4.33013i) q^{25} +1.00000 q^{27} +(4.00000 + 3.46410i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(3.00000 + 5.19615i) q^{33} +(1.00000 + 1.73205i) q^{36} -1.00000 q^{37} +(2.50000 + 2.59808i) q^{39} +(2.00000 - 3.46410i) q^{43} +(-6.00000 + 10.3923i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(-2.00000 + 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.00000 + 6.92820i) q^{52} +(-3.00000 - 5.19615i) q^{53} -1.00000 q^{57} +(6.50000 + 11.2583i) q^{61} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +12.0000 q^{68} +(3.00000 - 5.19615i) q^{69} +(6.00000 - 10.3923i) q^{71} +(5.00000 + 8.66025i) q^{73} -5.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-15.0000 + 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{83} +(-5.00000 + 1.73205i) q^{84} +6.00000 q^{87} +6.00000 q^{89} +(-8.00000 + 5.19615i) q^{91} +12.0000 q^{92} +5.00000 q^{93} +(-2.50000 + 4.33013i) q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 4 q^{4} - 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 - 4 * q^4 - 4 * q^7 - q^9	$ 2 q - q^{3} - 4 q^{4} - 4 q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{16} - 12 q^{17} + q^{19} + 5 q^{21} - 12 q^{23} + 5 q^{25} + 2 q^{27} + 8 q^{28} - 6 q^{29} - 5 q^{31} + 6 q^{33} + 2 q^{36} - 2 q^{37} + 5 q^{39} + 4 q^{43} - 12 q^{44} - 6 q^{47} - 4 q^{48} + 2 q^{49} + 6 q^{51} - 4 q^{52} - 6 q^{53} - 2 q^{57} + 13 q^{61} - q^{63} - 16 q^{64} + 13 q^{67} + 24 q^{68} + 6 q^{69} + 12 q^{71} + 10 q^{73} - 10 q^{75} - 2 q^{76} - 30 q^{77} + q^{79} - q^{81} - 12 q^{83} - 10 q^{84} + 12 q^{87} + 12 q^{89} - 16 q^{91} + 24 q^{92} + 10 q^{93} - 5 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q - q^3 - 4 * q^4 - 4 * q^7 - q^9 + 6 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^16 - 12 * q^17 + q^19 + 5 * q^21 - 12 * q^23 + 5 * q^25 + 2 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^31 + 6 * q^33 + 2 * q^36 - 2 * q^37 + 5 * q^39 + 4 * q^43 - 12 * q^44 - 6 * q^47 - 4 * q^48 + 2 * q^49 + 6 * q^51 - 4 * q^52 - 6 * q^53 - 2 * q^57 + 13 * q^61 - q^63 - 16 * q^64 + 13 * q^67 + 24 * q^68 + 6 * q^69 + 12 * q^71 + 10 * q^73 - 10 * q^75 - 2 * q^76 - 30 * q^77 + q^79 - q^81 - 12 * q^83 - 10 * q^84 + 12 * q^87 + 12 * q^89 - 16 * q^91 + 24 * q^92 + 10 * q^93 - 5 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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			0			−	1.00000i	$-0.5\pi$
$2$		0			0				1.00000i	$0.5\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−2.00000			−1.00000
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$		0			0
$16$	4.00000			1.00000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$	1.00000			0.192450
$28$	4.00000	+	3.46410i	0.755929	+	0.654654i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	−6.00000	+	10.3923i	−0.904534	+	1.56670i
$45$		0			0
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	−2.00000	+	3.46410i	−0.288675	+	0.500000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−2.00000	+	6.92820i	−0.277350	+	0.960769i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	−0.500000	+	2.59808i	−0.0629941	+	0.327327i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	12.0000			1.45521
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$		0			0
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$		0			0
$75$	−5.00000			−0.577350
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−15.0000	+	5.19615i	−1.70941	+	0.592157i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−5.00000	+	1.73205i	−0.545545	+	0.188982i
$85$		0			0
$86$		0			0
$87$	6.00000			0.643268
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−8.00000	+	5.19615i	−0.838628	+	0.544705i
$92$	12.0000			1.25109
$93$	5.00000			0.518476
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−5.00000	−	8.66025i	−0.500000	−	0.866025i
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$	−2.00000			−0.192450
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$	−8.00000	−	6.92820i	−0.755929	−	0.654654i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$		0			0
$116$	6.00000	+	10.3923i	0.557086	+	0.964901i
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$		0			0
$119$	12.0000	+	10.3923i	1.10004	+	0.952661i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$		0			0
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$		0			0
$126$		0			0
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	−6.00000	−	10.3923i	−0.522233	−	0.904534i
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.0000			−1.02523			−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000			−1.02523			−0.512615	+	0.858619i	$0.671323\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		0			0
$143$	−15.0000	−	15.5885i	−1.25436	−	1.30357i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$		0			0
$146$		0			0
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	2.00000			0.164399
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	3.00000	+	5.19615i	0.242536	+	0.420084i
$154$		0			0
$155$		0			0
$156$	−5.00000	−	5.19615i	−0.400320	−	0.416025i
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	12.0000	+	10.3923i	0.945732	+	0.819028i
$162$		0			0
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	0.542583	−	0.840002i	$-0.317446\pi$
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	−0.998755	+	0.0498898i	$0.984113\pi$
$174$		0			0
$175$	2.50000	−	12.9904i	0.188982	−	0.981981i
$176$	12.0000	−	20.7846i	0.904534	−	1.56670i
$177$		0			0
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$	−13.0000			−0.960988
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−18.0000	+	31.1769i	−1.31629	+	2.27988i
$188$	6.00000	−	10.3923i	0.437595	−	0.757937i
$189$	−2.00000	−	1.73205i	−0.145479	−	0.125988i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	4.00000	−	6.92820i	0.288675	−	0.500000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$		0			0
$195$		0			0
$196$	−2.00000	−	13.8564i	−0.142857	−	0.989743i
$197$	12.0000	+	20.7846i	0.854965	+	1.48084i	0.876678	+	0.481078i	$0.159755\pi$
$197$	12.0000	+	20.7846i	0.854965	+	1.48084i	−0.0217133	+	0.999764i	$0.506912\pi$
$198$		0			0
$199$	−1.00000			−0.0708881			−0.0354441	−	0.999372i	$-0.511285\pi$
$199$	−1.00000			−0.0708881			−0.0354441	+	0.999372i	$0.511285\pi$
$200$		0			0
$201$	6.50000	+	11.2583i	0.458475	+	0.794101i
$202$		0			0
$203$	−3.00000	+	15.5885i	−0.210559	+	1.09410i
$204$	−6.00000	+	10.3923i	−0.420084	+	0.727607i
$205$		0			0
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	4.00000	−	13.8564i	0.277350	−	0.960769i
$209$	6.00000			0.415029
$210$		0			0
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	0.960985	−	0.276600i	$-0.0892077\pi$
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	−0.720035	+	0.693938i	$0.755874\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.50000	+	12.9904i	−0.169711	+	0.881845i
$218$		0			0
$219$	−10.0000			−0.675737
$220$		0			0
$221$	−6.00000	+	20.7846i	−0.403604	+	1.39812i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$	2.50000	−	4.33013i	0.166667	−	0.288675i
$226$		0			0
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	2.00000			0.132453
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	3.00000	−	15.5885i	0.197386	−	1.02565i
$232$		0			0
$233$	−6.00000	+	10.3923i	−0.393073	+	0.680823i	−0.992853	−	0.119342i	$-0.961921\pi$
$233$	−6.00000	+	10.3923i	−0.393073	+	0.680823i	0.599780	+	0.800165i	$0.295255\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−13.0000	−	22.5167i	−0.832240	−	1.44148i
$245$		0			0
$246$		0			0
$247$	3.50000	−	0.866025i	0.222700	−	0.0551039i
$248$		0			0
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$		0			0
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$	1.00000	−	5.19615i	0.0629941	−	0.327327i
$253$	−18.0000	+	31.1769i	−1.13165	+	1.96008i
$254$		0			0
$255$		0			0
$256$	16.0000			1.00000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	2.00000	+	1.73205i	0.124274	+	0.107624i
$260$		0			0
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	−13.0000	+	22.5167i	−0.794101	+	1.37542i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	−1.00000			−0.0607457			−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000			−0.0607457			−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−24.0000			−1.45521
$273$	−0.500000	−	9.52628i	−0.0302614	−	0.576557i
$274$		0			0
$275$	30.0000			1.80907
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	5.00000			0.300421			0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000			0.300421			0.150210	+	0.988654i	$0.452005\pi$
$278$		0			0
$279$	−2.50000	+	4.33013i	−0.149671	+	0.259238i
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$	−12.0000	+	20.7846i	−0.712069	+	1.23334i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	−2.50000	−	4.33013i	−0.146553	−	0.253837i
$292$	−10.0000	−	17.3205i	−0.585206	−	1.01361i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.00000	−	5.19615i	0.174078	−	0.301511i
$298$		0			0
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	10.0000			0.577350
$301$	−10.0000	+	3.46410i	−0.576390	+	0.199667i
$302$		0			0
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$		0			0
$306$		0			0
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	30.0000	−	10.3923i	1.70941	−	0.592157i
$309$	8.00000	+	13.8564i	0.455104	+	0.788263i
$310$		0			0
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	−0.880693	−	0.473688i	$-0.842923\pi$
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	0.0301210	−	0.999546i	$-0.490411\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$		0			0
$315$		0			0
$316$	−1.00000	+	1.73205i	−0.0562544	+	0.0974355i
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−36.0000			−2.01561
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$		0			0
$323$	−3.00000	−	5.19615i	−0.166924	−	0.289122i
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$	17.5000	−	4.33013i	0.970725	−	0.240192i
$326$		0			0
$327$	−10.0000			−0.553001
$328$		0			0
$329$	15.0000	−	5.19615i	0.826977	−	0.286473i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	12.0000			0.658586
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$		0			0
$335$		0			0
$336$	10.0000	−	3.46410i	0.545545	−	0.188982i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−30.0000			−1.62459
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.0000			0.966291			0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000			0.966291			0.483145	+	0.875540i	$0.339494\pi$
$348$	−12.0000			−0.643268
$349$	6.50000	+	11.2583i	0.347937	+	0.602645i	0.985883	−	0.167437i	$-0.0535490\pi$
$349$	6.50000	+	11.2583i	0.347937	+	0.602645i	−0.637946	+	0.770081i	$0.720216\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$		0			0
$356$	−12.0000			−0.635999
$357$	−15.0000	+	5.19615i	−0.793884	+	0.275010i
$358$		0			0
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	25.0000			1.31216
$364$	16.0000	−	10.3923i	0.838628	−	0.544705i
$365$		0			0
$366$		0			0
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	−24.0000			−1.25109
$369$		0			0
$370$		0			0
$371$	−3.00000	+	15.5885i	−0.155752	+	0.809312i
$372$	−10.0000			−0.518476
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.0000	+	5.19615i	−1.08156	+	0.267615i
$378$		0			0
$379$	−5.50000	−	9.52628i	−0.282516	−	0.489332i	0.689488	−	0.724297i	$-0.257836\pi$
$379$	−5.50000	−	9.52628i	−0.282516	−	0.489332i	−0.972004	+	0.234965i	$0.924502\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$		0			0
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.00000			−0.203331
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		0			0
$393$	9.00000	+	15.5885i	0.453990	+	0.786334i
$394$		0			0
$395$		0			0
$396$	12.0000			0.603023
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$		0			0
$399$	2.00000	+	1.73205i	0.100125	+	0.0867110i
$400$	10.0000	+	17.3205i	0.500000	+	0.866025i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$		0			0
$403$	−17.5000	+	4.33013i	−0.871737	+	0.215699i
$404$	12.0000	−	20.7846i	0.597022	−	1.03407i
$405$		0			0
$406$		0			0
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	2.00000			0.0988936			0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000			0.0988936			0.0494468	+	0.998777i	$0.484254\pi$
$410$		0			0
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	−16.0000	+	27.7128i	−0.788263	+	1.36531i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.50000	−	4.33013i	−0.122426	−	0.212047i
$418$		0			0
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$		0			0
$423$	6.00000			0.291730
$424$		0			0
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$		0			0
$427$	6.50000	−	33.7750i	0.314557	−	1.63449i
$428$	−12.0000			−0.580042
$429$	21.0000	−	5.19615i	1.01389	−	0.250873i
$430$		0			0
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.00201168	+	0.999998i	$0.500640\pi$
$431$	−18.0000	+	31.1769i	−0.867029	+	1.50174i	−0.865018	+	0.501741i	$0.832693\pi$
$432$	4.00000			0.192450
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	−0.967383	−	0.253317i	$-0.918479\pi$
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	0.703070	+	0.711120i	$0.251812\pi$
$434$		0			0
$435$		0			0
$436$	−10.0000	−	17.3205i	−0.478913	−	0.829502i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	5.00000			0.238637			0.119318	−	0.992856i	$-0.461929\pi$
$439$	5.00000			0.238637			0.119318	+	0.992856i	$0.461929\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		0			0
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$		0			0
$446$		0			0
$447$	6.00000			0.283790
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$		0			0
$451$		0			0
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	8.00000			0.375873
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$		0			0
$459$	−6.00000			−0.280056
$460$		0			0
$461$	18.0000	−	31.1769i	0.838344	−	1.45205i	−0.0529352	−	0.998598i	$-0.516858\pi$
$461$	18.0000	−	31.1769i	0.838344	−	1.45205i	0.891279	−	0.453456i	$-0.149809\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−12.0000	−	20.7846i	−0.557086	−	0.964901i
$465$		0			0
$466$		0			0
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	7.00000	−	1.73205i	0.323575	−	0.0800641i
$469$	−32.5000	+	11.2583i	−1.50071	+	0.519861i
$470$		0			0
$471$	11.0000			0.506853
$472$		0			0
$473$	−12.0000	−	20.7846i	−0.551761	−	0.955677i
$474$		0			0
$475$	−2.50000	+	4.33013i	−0.114708	+	0.198680i
$476$	−24.0000	−	20.7846i	−1.10004	−	0.952661i
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−1.00000	+	3.46410i	−0.0455961	+	0.157949i
$482$		0			0
$483$	−15.0000	+	5.19615i	−0.682524	+	0.236433i
$484$	25.0000	+	43.3013i	1.13636	+	1.96824i
$485$		0			0
$486$		0			0
$487$	17.0000			0.770344			0.385172	−	0.922845i	$-0.374142\pi$
$487$	17.0000			0.770344			0.385172	+	0.922845i	$0.374142\pi$
$488$		0			0
$489$	−19.0000			−0.859210
$490$		0			0
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$	−10.0000	−	17.3205i	−0.449013	−	0.777714i
$497$	−30.0000	+	10.3923i	−1.34568	+	0.466159i
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$		0			0
$501$	−18.0000			−0.804181
$502$		0			0
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	−24.0000			−1.06378			−0.531891	−	0.846813i	$-0.678518\pi$
$509$	−24.0000			−1.06378			−0.531891	+	0.846813i	$0.678518\pi$
$510$		0			0
$511$	5.00000	−	25.9808i	0.221187	−	1.14932i
$512$		0			0
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$		0			0
$515$		0			0
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	0.981347	+	0.192244i	$0.0615766\pi$
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$522$		0			0
$523$	−19.0000			−0.830812			−0.415406	−	0.909636i	$-0.636360\pi$
$523$	−19.0000			−0.830812			−0.415406	+	0.909636i	$0.636360\pi$
$524$	−18.0000	+	31.1769i	−0.786334	+	1.36197i
$525$	10.0000	+	8.66025i	0.436436	+	0.377964i
$526$		0			0
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$	12.0000	+	20.7846i	0.522233	+	0.904534i
$529$	13.0000			0.565217
$530$		0			0
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	9.00000	+	15.5885i	0.388379	+	0.672692i
$538$		0			0
$539$	39.0000	+	15.5885i	1.67985	+	0.671442i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$		0			0
$543$	−8.50000	+	14.7224i	−0.364770	+	0.631800i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−13.0000			−0.555840			−0.277920	−	0.960604i	$-0.589645\pi$
$547$	−13.0000			−0.555840			−0.277920	+	0.960604i	$0.589645\pi$
$548$	24.0000			1.02523
$549$	6.50000	−	11.2583i	0.277413	−	0.480494i
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$		0			0
$553$	−2.50000	+	0.866025i	−0.106311	+	0.0368271i
$554$		0			0
$555$		0			0
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	18.0000	−	31.1769i	0.762684	−	1.32101i	−0.178778	−	0.983890i	$-0.557214\pi$
$557$	18.0000	−	31.1769i	0.762684	−	1.32101i	0.941462	−	0.337119i	$-0.109452\pi$
$558$		0			0
$559$	−10.0000	−	10.3923i	−0.422955	−	0.439548i
$560$		0			0
$561$	−18.0000	−	31.1769i	−0.759961	−	1.31629i
$562$		0			0
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$		0			0
$566$		0			0
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$		0			0
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	0.727690	−	0.685907i	$-0.240594\pi$
$571$	−5.50000	−	9.52628i	−0.230168	−	0.398662i	−0.957857	+	0.287244i	$0.907261\pi$
$572$	30.0000	+	31.1769i	1.25436	+	1.30357i
$573$	−6.00000			−0.250654
$574$		0			0
$575$	−15.0000	−	25.9808i	−0.625543	−	1.08347i
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−17.5000	−	30.3109i	−0.728535	−	1.26186i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−17.5000	−	30.3109i	−0.728535	−	1.26186i	0.228968	−	0.973434i	$-0.426465\pi$
$578$		0			0
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$		0			0
$581$	12.0000	+	10.3923i	0.497844	+	0.431145i
$582$		0			0
$583$	−36.0000			−1.49097
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	13.0000	+	5.19615i	0.536111	+	0.214286i
$589$	2.50000	−	4.33013i	0.103011	−	0.178420i
$590$		0			0
$591$	−24.0000			−0.987228
$592$	−4.00000			−0.164399
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$	6.00000	+	10.3923i	0.245770	+	0.425685i
$597$	0.500000	−	0.866025i	0.0204636	−	0.0354441i
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−13.0000			−0.529401
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$		0			0
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$		0			0
$609$	−12.0000	−	10.3923i	−0.486265	−	0.421117i
$610$		0			0
$611$	15.0000	+	15.5885i	0.606835	+	0.630641i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−17.5000	+	30.3109i	−0.706818	+	1.22425i	0.259213	+	0.965820i	$0.416537\pi$
$613$	−17.5000	+	30.3109i	−0.706818	+	1.22425i	−0.966031	+	0.258425i	$0.916796\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	−0.961156	−	0.276005i	$-0.910989\pi$
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	0.719605	+	0.694383i	$0.244323\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$	−6.00000			−0.240772
$622$		0			0
$623$	−12.0000	−	10.3923i	−0.480770	−	0.416359i
$624$	10.0000	+	10.3923i	0.400320	+	0.416025i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$		0			0
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	11.0000	+	19.0526i	0.438948	+	0.760280i
$629$	6.00000			0.239236
$630$		0			0
$631$	−8.50000	+	14.7224i	−0.338380	+	0.586091i	−0.984128	−	0.177459i	$-0.943212\pi$
$631$	−8.50000	+	14.7224i	−0.338380	+	0.586091i	0.645748	+	0.763550i	$0.276545\pi$
$632$		0			0
$633$	−7.00000			−0.278225
$634$		0			0
$635$		0			0
$636$	−12.0000			−0.475831
$637$	25.0000	+	3.46410i	0.990536	+	0.137253i
$638$		0			0
$639$	−12.0000			−0.474713
$640$		0			0
$641$	24.0000			0.947943			0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000			0.947943			0.473972	+	0.880540i	$0.342820\pi$
$642$		0			0
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$644$	−24.0000	−	20.7846i	−0.945732	−	0.819028i
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−10.0000	−	8.66025i	−0.391931	−	0.339422i
$652$	−19.0000	−	32.9090i	−0.744097	−	1.28881i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.00000	−	8.66025i	0.195069	−	0.337869i
$658$		0			0
$659$	−9.00000	+	15.5885i	−0.350590	+	0.607240i	−0.986353	−	0.164644i	$-0.947352\pi$
$659$	−9.00000	+	15.5885i	−0.350590	+	0.607240i	0.635763	+	0.771885i	$0.280686\pi$
$660$		0			0
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	−0.711481	−	0.702706i	$-0.751975\pi$
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	0.964301	+	0.264807i	$0.0853084\pi$
$662$		0			0
$663$	−15.0000	−	15.5885i	−0.582552	−	0.605406i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	18.0000	+	31.1769i	0.696963	+	1.20717i
$668$	−18.0000	−	31.1769i	−0.696441	−	1.20627i
$669$	8.00000			0.309298
$670$		0			0
$671$	78.0000			3.01116
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$		0			0
$675$	2.50000	+	4.33013i	0.0962250	+	0.166667i
$676$	22.0000	+	13.8564i	0.846154	+	0.532939i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$		0			0
$679$	12.5000	−	4.33013i	0.479706	−	0.166175i
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$		0			0
$686$		0			0
$687$	3.50000	+	6.06218i	0.133533	+	0.231287i
$688$	8.00000	−	13.8564i	0.304997	−	0.528271i
$689$	−21.0000	+	5.19615i	−0.800036	+	0.197958i
$690$		0			0
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$	12.0000	+	20.7846i	0.456172	+	0.790112i
$693$	12.0000	+	10.3923i	0.455842	+	0.394771i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$	−5.00000	+	25.9808i	−0.188982	+	0.981981i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−0.500000	−	0.866025i	−0.0188579	−	0.0326628i
$704$	−24.0000	+	41.5692i	−0.904534	+	1.56670i
$705$		0			0
$706$		0			0
$707$	30.0000	−	10.3923i	1.12827	−	0.390843i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	−1.00000			−0.0375029
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$		0			0
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−40.0000	+	13.8564i	−1.48968	+	0.516040i
$722$		0			0
$723$	−13.0000	+	22.5167i	−0.483475	+	0.837404i
$724$	−34.0000			−1.26360
$725$	15.0000	−	25.9808i	0.557086	−	0.964901i
$726$		0			0
$727$	−1.00000			−0.0370879			−0.0185440	−	0.999828i	$-0.505903\pi$
$727$	−1.00000			−0.0370879			−0.0185440	+	0.999828i	$0.505903\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	26.0000			0.960988
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	−0.423802	−	0.905755i	$-0.639305\pi$
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	0.996308	−	0.0858539i	$-0.0273618\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−39.0000	−	67.5500i	−1.43658	−	2.48824i
$738$		0			0
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	0.340841	+	0.940121i	$0.389288\pi$
$739$	−17.5000	+	30.3109i	−0.643748	+	1.11500i	−0.984589	+	0.174883i	$0.944045\pi$
$740$		0			0
$741$	−1.00000	+	3.46410i	−0.0367359	+	0.127257i
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	36.0000	−	62.3538i	1.31629	−	2.27988i
$749$	−12.0000	−	10.3923i	−0.438470	−	0.379727i
$750$		0			0
$751$	−25.0000			−0.912263			−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000			−0.912263			−0.456131	+	0.889912i	$0.650765\pi$
$752$	−12.0000	+	20.7846i	−0.437595	+	0.757937i
$753$	−3.00000	−	5.19615i	−0.109326	−	0.189358i
$754$		0			0
$755$		0			0
$756$	4.00000	+	3.46410i	0.145479	+	0.125988i
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$		0			0
$759$	−18.0000	−	31.1769i	−0.653359	−	1.13165i
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$	5.00000	−	25.9808i	0.181012	−	0.940567i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−23.5000	−	40.7032i	−0.847432	−	1.46779i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−23.5000	−	40.7032i	−0.847432	−	1.46779i	0.0360609	−	0.999350i	$-0.488519\pi$
$770$		0			0
$771$	3.00000	−	5.19615i	0.108042	−	0.187135i
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	30.0000			1.07903			0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000			1.07903			0.539513	+	0.841978i	$0.318609\pi$
$774$		0			0
$775$	12.5000	−	21.6506i	0.449013	−	0.777714i
$776$		0			0
$777$	−2.50000	+	0.866025i	−0.0896870	+	0.0310685i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−36.0000	−	62.3538i	−1.28818	−	2.23120i
$782$		0			0
$783$	−3.00000	−	5.19615i	−0.107211	−	0.185695i
$784$	4.00000	+	27.7128i	0.142857	+	0.989743i
$785$		0			0
$786$		0			0
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	−24.0000	−	41.5692i	−0.854965	−	1.48084i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$		0			0
$791$	−15.0000	+	5.19615i	−0.533339	+	0.184754i
$792$		0			0
$793$	45.5000	−	11.2583i	1.61575	−	0.399795i
$794$		0			0
$795$		0			0
$796$	2.00000			0.0708881
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$	60.0000			2.11735
$804$	−13.0000	−	22.5167i	−0.458475	−	0.794101i
$805$		0			0
$806$		0			0
$807$	3.00000	−	5.19615i	0.105605	−	0.182913i
$808$		0			0
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$	−1.00000			−0.0351147			−0.0175574	−	0.999846i	$-0.505589\pi$
$811$	−1.00000			−0.0351147			−0.0175574	+	0.999846i	$0.505589\pi$
$812$	6.00000	−	31.1769i	0.210559	−	1.09410i
$813$	0.500000	−	0.866025i	0.0175358	−	0.0303728i
$814$		0			0
$815$		0			0
$816$	12.0000	−	20.7846i	0.420084	−	0.727607i
$817$	4.00000			0.139942
$818$		0			0
$819$	8.50000	+	4.33013i	0.297014	+	0.151307i
$820$		0			0
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$		0			0
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$		0			0
$825$	−15.0000	+	25.9808i	−0.522233	+	0.904534i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	−0.766039	−	0.642795i	$-0.777775\pi$
$829$	5.00000	−	8.66025i	0.173657	−	0.300783i	0.939696	+	0.342012i	$0.111108\pi$
$830$		0			0
$831$	−2.50000	+	4.33013i	−0.0867240	+	0.150210i
$832$	−8.00000	+	27.7128i	−0.277350	+	0.960769i
$833$	−6.00000	−	41.5692i	−0.207888	−	1.44029i
$834$		0			0
$835$		0			0
$836$	−12.0000			−0.415029
$837$	−2.50000	−	4.33013i	−0.0864126	−	0.149671i
$838$		0			0
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	−15.0000	+	25.9808i	−0.516627	+	0.894825i
$844$	−7.00000	−	12.1244i	−0.240950	−	0.417338i
$845$		0			0
$846$		0			0
$847$	−12.5000	+	64.9519i	−0.429505	+	2.23177i
$848$	−12.0000	−	20.7846i	−0.412082	−	0.713746i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$		0			0
$851$	6.00000			0.205677
$852$	−12.0000	−	20.7846i	−0.411113	−	0.712069i
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$		0			0
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−9.50000	+	16.4545i	−0.322637	+	0.558824i
$868$	5.00000	−	25.9808i	0.169711	−	0.881845i
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$		0			0
$871$	−32.5000	−	33.7750i	−1.10122	−	1.14442i
$872$		0			0
$873$	5.00000			0.169224
$874$		0			0
$875$		0			0
$876$	20.0000			0.675737
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$		0			0
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	12.0000	+	20.7846i	0.404290	+	0.700251i	0.994239	−	0.107190i	$-0.0341852\pi$
$881$	12.0000	+	20.7846i	0.404290	+	0.700251i	−0.589948	+	0.807441i	$0.700852\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	12.0000	−	41.5692i	0.403604	−	1.39812i
$885$		0			0
$886$		0			0
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		0			0
$889$	−4.00000	+	20.7846i	−0.134156	+	0.697093i
$890$		0			0
$891$	3.00000	+	5.19615i	0.100504	+	0.174078i
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$	−6.00000			−0.200782
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−15.0000	−	15.5885i	−0.500835	−	0.520483i
$898$		0			0
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$	−5.00000	+	8.66025i	−0.166667	+	0.288675i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$	2.00000	−	10.3923i	0.0665558	−	0.345834i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	−0.904542	−	0.426385i	$-0.859787\pi$
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	0.821531	+	0.570164i	$0.193120\pi$
$908$	24.0000			0.796468
$909$	12.0000			0.398015
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	−4.00000			−0.132453
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$		0			0
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−45.0000	+	15.5885i	−1.48603	+	0.514776i
$918$		0			0
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	0.691091	−	0.722767i	$-0.257130\pi$
$919$	−8.50000	−	14.7224i	−0.280389	−	0.485648i	−0.971481	+	0.237119i	$0.923797\pi$
$920$		0			0
$921$	−5.50000	+	9.52628i	−0.181231	+	0.313902i
$922$		0			0
$923$	−30.0000	−	31.1769i	−0.987462	−	1.02620i
$924$	−6.00000	+	31.1769i	−0.197386	+	1.02565i
$925$	−2.50000	−	4.33013i	−0.0821995	−	0.142374i
$926$		0			0
$927$	−16.0000			−0.525509
$928$		0			0
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	0.972166	+	0.234294i	$0.0752779\pi$
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	−0.283178	+	0.959067i	$0.591389\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$	30.0000			0.982156
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.00000			−0.0326686			−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000			−0.0326686			−0.0163343	+	0.999867i	$0.505200\pi$
$938$		0			0
$939$	−7.00000	−	12.1244i	−0.228436	−	0.395663i
$940$		0			0
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$	−1.00000	−	1.73205i	−0.0324785	−	0.0562544i
$949$	35.0000	−	8.66025i	1.13615	−	0.281124i
$950$		0			0
$951$	−3.00000	−	5.19615i	−0.0972817	−	0.168497i
$952$		0			0
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.281666	+	0.959512i	$0.590887\pi$
$953$	−30.0000	+	51.9615i	−0.971795	+	1.68320i	−0.690129	+	0.723686i	$0.742446\pi$
$954$		0			0
$955$		0			0
$956$	24.0000			0.776215
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$		0			0
$959$	24.0000	+	20.7846i	0.775000	+	0.671170i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$	−52.0000			−1.67481
$965$		0			0
$966$		0			0
$967$	−7.00000			−0.225105			−0.112552	−	0.993646i	$-0.535903\pi$
$967$	−7.00000			−0.225105			−0.112552	+	0.993646i	$0.535903\pi$
$968$		0			0
$969$	6.00000			0.192748
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$	1.00000	+	1.73205i	0.0320750	+	0.0555556i
$973$	12.5000	−	4.33013i	0.400732	−	0.138817i
$974$		0			0
$975$	−5.00000	+	17.3205i	−0.160128	+	0.554700i
$976$	26.0000	+	45.0333i	0.832240	+	1.44148i
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	18.0000	−	31.1769i	0.575282	−	0.996419i
$980$		0			0
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$		0			0
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.00000	+	15.5885i	−0.0954911	+	0.496186i
$988$	−7.00000	+	1.73205i	−0.222700	+	0.0551039i
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	0.441927	+	0.897051i	$0.354295\pi$
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	−0.997832	+	0.0658059i	$0.979038\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	−22.0000			−0.696747			−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000			−0.696747			−0.348373	+	0.937356i	$0.613266\pi$
$998$		0			0
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.a.16.1	yes	2
3.2	odd	2		819.2.s.b.289.1		2
7.4	even	3		273.2.j.a.172.1	yes	2
13.9	even	3		273.2.j.a.100.1	✓	2
21.11	odd	6		819.2.n.b.172.1		2
39.35	odd	6		819.2.n.b.100.1		2
91.74	even	3	inner	273.2.l.a.256.1	yes	2
273.74	odd	6		819.2.s.b.802.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.a.100.1	✓	2	13.9	even	3
273.2.j.a.172.1	yes	2	7.4	even	3
273.2.l.a.16.1	yes	2	1.1	even	1	trivial
273.2.l.a.256.1	yes	2	91.74	even	3	inner
819.2.n.b.100.1		2	39.35	odd	6
819.2.n.b.172.1		2	21.11	odd	6
819.2.s.b.289.1		2	3.2	odd	2
819.2.s.b.802.1		2	273.74	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.00000 - 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +(1.00000 - 3.46410i) q^{13} +4.00000 q^{16} -6.00000 q^{17} +(0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} -6.00000 q^{23} +(2.50000 + 4.33013i) q^{25} +1.00000 q^{27} +(4.00000 + 3.46410i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(3.00000 + 5.19615i) q^{33} +(1.00000 + 1.73205i) q^{36} -1.00000 q^{37} +(2.50000 + 2.59808i) q^{39} +(2.00000 - 3.46410i) q^{43} +(-6.00000 + 10.3923i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(-2.00000 + 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.00000 + 6.92820i) q^{52} +(-3.00000 - 5.19615i) q^{53} -1.00000 q^{57} +(6.50000 + 11.2583i) q^{61} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +12.0000 q^{68} +(3.00000 - 5.19615i) q^{69} +(6.00000 - 10.3923i) q^{71} +(5.00000 + 8.66025i) q^{73} -5.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-15.0000 + 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{83} +(-5.00000 + 1.73205i) q^{84} +6.00000 q^{87} +6.00000 q^{89} +(-8.00000 + 5.19615i) q^{91} +12.0000 q^{92} +5.00000 q^{93} +(-2.50000 + 4.33013i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 4 q^{4} - 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 - 4 * q^4 - 4 * q^7 - q^9	\( 2 q - q^{3} - 4 q^{4} - 4 q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{16} - 12 q^{17} + q^{19} + 5 q^{21} - 12 q^{23} + 5 q^{25} + 2 q^{27} + 8 q^{28} - 6 q^{29} - 5 q^{31} + 6 q^{33} + 2 q^{36} - 2 q^{37} + 5 q^{39} + 4 q^{43} - 12 q^{44} - 6 q^{47} - 4 q^{48} + 2 q^{49} + 6 q^{51} - 4 q^{52} - 6 q^{53} - 2 q^{57} + 13 q^{61} - q^{63} - 16 q^{64} + 13 q^{67} + 24 q^{68} + 6 q^{69} + 12 q^{71} + 10 q^{73} - 10 q^{75} - 2 q^{76} - 30 q^{77} + q^{79} - q^{81} - 12 q^{83} - 10 q^{84} + 12 q^{87} + 12 q^{89} - 16 q^{91} + 24 q^{92} + 10 q^{93} - 5 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q - q^3 - 4 * q^4 - 4 * q^7 - q^9 + 6 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^16 - 12 * q^17 + q^19 + 5 * q^21 - 12 * q^23 + 5 * q^25 + 2 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^31 + 6 * q^33 + 2 * q^36 - 2 * q^37 + 5 * q^39 + 4 * q^43 - 12 * q^44 - 6 * q^47 - 4 * q^48 + 2 * q^49 + 6 * q^51 - 4 * q^52 - 6 * q^53 - 2 * q^57 + 13 * q^61 - q^63 - 16 * q^64 + 13 * q^67 + 24 * q^68 + 6 * q^69 + 12 * q^71 + 10 * q^73 - 10 * q^75 - 2 * q^76 - 30 * q^77 + q^79 - q^81 - 12 * q^83 - 10 * q^84 + 12 * q^87 + 12 * q^89 - 16 * q^91 + 24 * q^92 + 10 * q^93 - 5 * q^97 - 12 * q^99

Introduction

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