LMFDB - Embedded newform 357.2.i.b.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(205,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("357.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.i (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:	$2.85065935216$
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			256.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	357.256
Dual form			357.2.i.b.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} -4.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{19} -8.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-5.50000 + 9.52628i) q^{25} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-2.00000 - 10.3923i) q^{35} -2.00000 q^{36} +(5.50000 + 9.52628i) q^{37} +(0.500000 - 0.866025i) q^{39} +10.0000 q^{41} -7.00000 q^{43} +(4.00000 + 6.92820i) q^{44} +(-2.00000 + 3.46410i) q^{45} +(-3.00000 - 5.19615i) q^{47} -4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(0.500000 + 0.866025i) q^{51} +(1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +16.0000 q^{55} -1.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-4.00000 + 6.92820i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(1.00000 + 1.73205i) q^{68} -2.00000 q^{69} -2.00000 q^{71} +(4.50000 - 7.79423i) q^{73} +(5.50000 + 9.52628i) q^{75} -2.00000 q^{76} +(-8.00000 + 6.92820i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-8.00000 + 13.8564i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000 q^{83} +(-1.00000 - 5.19615i) q^{84} +4.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(2.50000 + 0.866025i) q^{91} -4.00000 q^{92} +(-4.50000 - 7.79423i) q^{93} +(-2.00000 + 3.46410i) q^{95} +2.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 2 q^{4} - 4 q^{5} + 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 + 2 * q^4 - 4 * q^5 + 5 * q^7 - q^9	$ 2 q + q^{3} + 2 q^{4} - 4 q^{5} + 5 q^{7} - q^{9} - 4 q^{11} - 2 q^{12} + 2 q^{13} - 8 q^{15} - 4 q^{16} - q^{17} - q^{19} - 16 q^{20} + 4 q^{21} - 2 q^{23} - 11 q^{25} - 2 q^{27} + 8 q^{28} + 12 q^{29} + 9 q^{31} + 4 q^{33} - 4 q^{35} - 4 q^{36} + 11 q^{37} + q^{39} + 20 q^{41} - 14 q^{43} + 8 q^{44} - 4 q^{45} - 6 q^{47} - 8 q^{48} + 11 q^{49} + q^{51} + 2 q^{52} + 6 q^{53} + 32 q^{55} - 2 q^{57} - 8 q^{59} - 8 q^{60} - 6 q^{61} - q^{63} - 16 q^{64} - 4 q^{65} - 3 q^{67} + 2 q^{68} - 4 q^{69} - 4 q^{71} + 9 q^{73} + 11 q^{75} - 4 q^{76} - 16 q^{77} + 3 q^{79} - 16 q^{80} - q^{81} + 12 q^{83} - 2 q^{84} + 8 q^{85} + 6 q^{87} + 5 q^{91} - 8 q^{92} - 9 q^{93} - 4 q^{95} + 4 q^{97} + 8 q^{99}+O(q^{100}) $ 2 * q + q^3 + 2 * q^4 - 4 * q^5 + 5 * q^7 - q^9 - 4 * q^11 - 2 * q^12 + 2 * q^13 - 8 * q^15 - 4 * q^16 - q^17 - q^19 - 16 * q^20 + 4 * q^21 - 2 * q^23 - 11 * q^25 - 2 * q^27 + 8 * q^28 + 12 * q^29 + 9 * q^31 + 4 * q^33 - 4 * q^35 - 4 * q^36 + 11 * q^37 + q^39 + 20 * q^41 - 14 * q^43 + 8 * q^44 - 4 * q^45 - 6 * q^47 - 8 * q^48 + 11 * q^49 + q^51 + 2 * q^52 + 6 * q^53 + 32 * q^55 - 2 * q^57 - 8 * q^59 - 8 * q^60 - 6 * q^61 - q^63 - 16 * q^64 - 4 * q^65 - 3 * q^67 + 2 * q^68 - 4 * q^69 - 4 * q^71 + 9 * q^73 + 11 * q^75 - 4 * q^76 - 16 * q^77 + 3 * q^79 - 16 * q^80 - q^81 + 12 * q^83 - 2 * q^84 + 8 * q^85 + 6 * q^87 + 5 * q^91 - 8 * q^92 - 9 * q^93 - 4 * q^95 + 4 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	−4.00000			−1.03280
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−8.00000			−1.78885
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	−0.105869	−	0.994380i	$-0.533762\pi$
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	0.914093	−	0.405505i	$-0.132904\pi$
$32$		0			0
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$		0			0
$35$	−2.00000	−	10.3923i	−0.338062	−	1.75662i
$36$	−2.00000			−0.333333
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	4.00000	+	6.92820i	0.603023	+	1.04447i
$45$	−2.00000	+	3.46410i	−0.298142	+	0.516398i
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−4.00000			−0.577350
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	16.0000			2.15744
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$	−4.00000	+	6.92820i	−0.516398	+	0.894427i
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$		0			0
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	−8.00000			−1.00000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	−2.00000			−0.240772
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	−0.472831	−	0.881153i	$-0.656768\pi$
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	0.999517	−	0.0310925i	$-0.00989865\pi$
$74$		0			0
$75$	5.50000	+	9.52628i	0.635085	+	1.10000i
$76$	−2.00000			−0.229416
$77$	−8.00000	+	6.92820i	−0.911685	+	0.789542i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	−8.00000	+	13.8564i	−0.894427	+	1.54919i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	−	5.19615i	−0.109109	−	0.566947i
$85$	4.00000			0.433861
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	2.50000	+	0.866025i	0.262071	+	0.0907841i
$92$	−4.00000			−0.417029
$93$	−4.50000	−	7.79423i	−0.466628	−	0.808224i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$	11.0000	+	19.0526i	1.10000	+	1.90526i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$		0			0
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$		0			0
$105$	−10.0000	−	3.46410i	−0.975900	−	0.338062i
$106$		0			0
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	−2.00000	−	10.3923i	−0.188982	−	0.981981i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−4.00000	+	6.92820i	−0.373002	+	0.646058i
$116$	6.00000	−	10.3923i	0.557086	−	0.964901i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$		0			0
$119$	−2.00000	+	1.73205i	−0.183340	+	0.158777i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	−9.00000	−	15.5885i	−0.808224	−	1.39988i
$125$	24.0000			2.14663
$126$		0			0
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$		0			0
$129$	−3.50000	+	6.06218i	−0.308158	+	0.533745i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	8.00000			0.696311
$133$	−0.500000	−	2.59808i	−0.0433555	−	0.225282i
$134$		0			0
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$		0			0
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	−0.984757	−	0.173939i	$-0.944351\pi$
$137$	−4.00000	+	6.92820i	−0.341743	+	0.591916i	0.643013	+	0.765855i	$0.277684\pi$
$138$		0			0
$139$	−9.00000			−0.763370			−0.381685	−	0.924292i	$-0.624656\pi$
$139$	−9.00000			−0.763370			−0.381685	+	0.924292i	$0.624656\pi$
$140$	−20.0000	−	6.92820i	−1.69031	−	0.585540i
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−2.00000	+	3.46410i	−0.167248	+	0.289683i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	−12.0000	−	20.7846i	−0.996546	−	1.72607i
$146$		0			0
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$	22.0000			1.80839
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$		0			0
$153$	1.00000			0.0808452
$154$		0			0
$155$	−36.0000			−2.89159
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	−1.00000	−	5.19615i	−0.0788110	−	0.409514i
$162$		0			0
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$	10.0000	−	17.3205i	0.780869	−	1.35250i
$165$	8.00000	−	13.8564i	0.622799	−	1.07872i
$166$		0			0
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	−7.00000	+	12.1244i	−0.533745	+	0.924473i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−22.0000	+	19.0526i	−1.66304	+	1.44024i
$176$	16.0000			1.20605
$177$	4.00000	+	6.92820i	0.300658	+	0.520756i
$178$		0			0
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$	4.00000	+	6.92820i	0.298142	+	0.516398i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$		0			0
$185$	22.0000	−	38.1051i	1.61747	−	2.80154i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	−12.0000			−0.875190
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.863743	+	0.503932i	$0.168114\pi$
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.00454614	+	0.999990i	$0.498553\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$	13.0000	−	5.19615i	0.928571	−	0.371154i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$		0			0
$203$	15.0000	+	5.19615i	1.05279	+	0.364698i
$204$	2.00000			0.140028
$205$	−20.0000	−	34.6410i	−1.39686	−	2.41943i
$206$		0			0
$207$	−1.00000	+	1.73205i	−0.0695048	+	0.120386i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	4.00000			0.276686
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	−1.00000	+	1.73205i	−0.0685189	+	0.118678i
$214$		0			0
$215$	14.0000	+	24.2487i	0.954792	+	1.65375i
$216$		0			0
$217$	18.0000	−	15.5885i	1.22192	−	1.05821i
$218$		0			0
$219$	−4.50000	−	7.79423i	−0.304082	−	0.526685i
$220$	16.0000	−	27.7128i	1.07872	−	1.86840i
$221$	−0.500000	+	0.866025i	−0.0336336	+	0.0582552i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	11.0000			0.733333
$226$		0			0
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	−10.5000	−	18.1865i	−0.693860	−	1.20180i	−0.970564	−	0.240845i	$-0.922576\pi$
$229$	−10.5000	−	18.1865i	−0.693860	−	1.20180i	0.276704	−	0.960955i	$-0.410758\pi$
$230$		0			0
$231$	2.00000	+	10.3923i	0.131590	+	0.683763i
$232$		0			0
$233$	7.00000	+	12.1244i	0.458585	+	0.794293i	0.998886	−	0.0471787i	$-0.0150230\pi$
$233$	7.00000	+	12.1244i	0.458585	+	0.794293i	−0.540301	+	0.841472i	$0.681690\pi$
$234$		0			0
$235$	−12.0000	+	20.7846i	−0.782794	+	1.35584i
$236$	8.00000	+	13.8564i	0.520756	+	0.901975i
$237$	3.00000			0.194871
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	8.00000	+	13.8564i	0.516398	+	0.894427i
$241$	−3.00000	+	5.19615i	−0.193247	+	0.334714i	−0.946324	−	0.323218i	$-0.895235\pi$
$241$	−3.00000	+	5.19615i	−0.193247	+	0.334714i	0.753077	+	0.657932i	$0.228569\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−12.0000			−0.768221
$245$	4.00000	−	27.7128i	0.255551	−	1.77051i
$246$		0			0
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$		0			0
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$		0			0
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$	−5.00000	−	1.73205i	−0.314970	−	0.109109i
$253$	8.00000			0.502956
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$	5.50000	+	28.5788i	0.341753	+	1.77580i
$260$	−8.00000			−0.496139
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	−0.833546	−	0.552450i	$-0.813693\pi$
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	0.895209	+	0.445647i	$0.147026\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$		0			0
$267$		0			0
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	0.307029	+	0.951700i	$0.400665\pi$
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	−0.977711	+	0.209955i	$0.932668\pi$
$270$		0			0
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$	4.00000			0.242536
$273$	2.00000	−	1.73205i	0.121046	−	0.104828i
$274$		0			0
$275$	−22.0000	−	38.1051i	−1.32665	−	2.29783i
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	0.931305	+	0.364241i	$0.118672\pi$
$278$		0			0
$279$	−9.00000			−0.538816
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$	2.00000	+	3.46410i	0.118470	+	0.205196i
$286$		0			0
$287$	25.0000	+	8.66025i	1.47570	+	0.511199i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	−9.00000	−	15.5885i	−0.526685	−	0.912245i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$		0			0
$295$	32.0000			1.86311
$296$		0			0
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$	22.0000			1.27017
$301$	−17.5000	−	6.06218i	−1.00868	−	0.349418i
$302$		0			0
$303$	7.00000	+	12.1244i	0.402139	+	0.696526i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−12.0000	+	20.7846i	−0.687118	+	1.19012i
$306$		0			0
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$	4.00000	+	20.7846i	0.227921	+	1.18431i
$309$	19.0000			1.08087
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$	−8.00000	+	6.92820i	−0.450749	+	0.390360i
$316$	6.00000			0.337526
$317$	10.0000	+	17.3205i	0.561656	+	0.972817i	0.997352	+	0.0727229i	$0.0231689\pi$
$317$	10.0000	+	17.3205i	0.561656	+	0.972817i	−0.435696	+	0.900094i	$0.643498\pi$
$318$		0			0
$319$	−12.0000	+	20.7846i	−0.671871	+	1.16371i
$320$	16.0000	+	27.7128i	0.894427	+	1.54919i
$321$	12.0000			0.669775
$322$		0			0
$323$	1.00000			0.0556415
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	−5.50000	+	9.52628i	−0.305085	+	0.528423i
$326$		0			0
$327$	−0.500000	−	0.866025i	−0.0276501	−	0.0478913i
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	0.987504	−	0.157593i	$-0.0503735\pi$
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	−0.630232	+	0.776407i	$0.717040\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	5.50000	−	9.52628i	0.301398	−	0.522037i
$334$		0			0
$335$	12.0000			0.655630
$336$	−10.0000	−	3.46410i	−0.545545	−	0.188982i
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$		0			0
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$	4.00000	−	6.92820i	0.216930	−	0.375735i
$341$	18.0000	+	31.1769i	0.974755	+	1.68832i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$		0			0
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$	−6.00000	−	10.3923i	−0.321634	−	0.557086i
$349$	−30.0000			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	10.0000	−	17.3205i	0.532246	−	0.921878i	−0.467045	−	0.884234i	$-0.654681\pi$
$353$	10.0000	−	17.3205i	0.532246	−	0.921878i	0.999291	−	0.0376440i	$-0.0119853\pi$
$354$		0			0
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$		0			0
$357$	0.500000	+	2.59808i	0.0264628	+	0.137505i
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−5.00000			−0.262432
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$	−36.0000			−1.88433
$366$		0			0
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$	−5.00000	−	8.66025i	−0.260290	−	0.450835i
$370$		0			0
$371$	12.0000	−	10.3923i	0.623009	−	0.539542i
$372$	−18.0000			−0.933257
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$		0			0
$375$	12.0000	−	20.7846i	0.619677	−	1.07331i
$376$		0			0
$377$	6.00000			0.309016
$378$		0			0
$379$	−31.0000			−1.59236			−0.796182	−	0.605058i	$-0.793150\pi$
$379$	−31.0000			−1.59236			−0.796182	+	0.605058i	$0.793150\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$	0.500000	−	0.866025i	0.0256158	−	0.0443678i
$382$		0			0
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	40.0000	+	13.8564i	2.03859	+	0.706188i
$386$		0			0
$387$	3.50000	+	6.06218i	0.177915	+	0.308158i
$388$	2.00000	−	3.46410i	0.101535	−	0.175863i
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	0.999967	−	0.00812520i	$-0.00258636\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$	−18.0000			−0.907980
$394$		0			0
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$	4.00000	−	6.92820i	0.201008	−	0.348155i
$397$	−0.500000	−	0.866025i	−0.0250943	−	0.0434646i	0.853206	−	0.521575i	$-0.174655\pi$
$397$	−0.500000	−	0.866025i	−0.0250943	−	0.0434646i	−0.878300	+	0.478110i	$0.841322\pi$
$398$		0			0
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$	44.0000			2.20000
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$	4.50000	−	7.79423i	0.224161	−	0.388258i
$404$	14.0000	+	24.2487i	0.696526	+	1.20642i
$405$	4.00000			0.198762
$406$		0			0
$407$	−44.0000			−2.18100
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	4.00000	+	6.92820i	0.197305	+	0.341743i
$412$	38.0000			1.87213
$413$	−16.0000	+	13.8564i	−0.787309	+	0.681829i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$		0			0
$417$	−4.50000	+	7.79423i	−0.220366	+	0.381685i
$418$		0			0
$419$	−26.0000			−1.27018			−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000			−1.27018			−0.635092	+	0.772437i	$0.719038\pi$
$420$	−16.0000	+	13.8564i	−0.780720	+	0.676123i
$421$	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
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−5.50000	−	9.52628i	−0.266789	−	0.462092i
$426$		0			0
$427$	−3.00000	−	15.5885i	−0.145180	−	0.754378i
$428$	24.0000			1.16008
$429$	2.00000	+	3.46410i	0.0965609	+	0.167248i
$430$		0			0
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−41.0000			−1.97033			−0.985167	−	0.171598i	$-0.945107\pi$
$433$	−41.0000			−1.97033			−0.985167	+	0.171598i	$0.945107\pi$
$434$		0			0
$435$	−24.0000			−1.15071
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−1.00000	+	1.73205i	−0.0478365	+	0.0828552i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$	11.0000	−	19.0526i	0.522037	−	0.904194i
$445$		0			0
$446$		0			0
$447$	−10.0000			−0.472984
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−20.0000	+	34.6410i	−0.941763	+	1.63118i
$452$	12.0000	−	20.7846i	0.564433	−	0.977626i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$		0			0
$455$	−2.00000	−	10.3923i	−0.0937614	−	0.487199i
$456$		0			0
$457$	−18.5000	−	32.0429i	−0.865393	−	1.49891i	−0.866656	−	0.498906i	$-0.833735\pi$
$457$	−18.5000	−	32.0429i	−0.865393	−	1.49891i	0.00126243	−	0.999999i	$-0.499598\pi$
$458$		0			0
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$	8.00000	+	13.8564i	0.373002	+	0.646058i
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	15.0000			0.697109			0.348555	−	0.937288i	$-0.386673\pi$
$463$	15.0000			0.697109			0.348555	+	0.937288i	$0.386673\pi$
$464$	−12.0000	−	20.7846i	−0.557086	−	0.964901i
$465$	−18.0000	+	31.1769i	−0.834730	+	1.44579i
$466$		0			0
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$	−2.00000			−0.0924500
$469$	−6.00000	+	5.19615i	−0.277054	+	0.239936i
$470$		0			0
$471$	5.00000	+	8.66025i	0.230388	+	0.399043i
$472$		0			0
$473$	14.0000	−	24.2487i	0.643721	−	1.11496i
$474$		0			0
$475$	11.0000			0.504715
$476$	1.00000	+	5.19615i	0.0458349	+	0.238165i
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$		0			0
$481$	5.50000	+	9.52628i	0.250778	+	0.434361i
$482$		0			0
$483$	−5.00000	−	1.73205i	−0.227508	−	0.0788110i
$484$	−10.0000			−0.454545
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	7.50000	−	12.9904i	0.339857	−	0.588650i	−0.644548	−	0.764564i	$-0.722955\pi$
$487$	7.50000	−	12.9904i	0.339857	−	0.588650i	0.984406	+	0.175913i	$0.0562878\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$	−10.0000	−	17.3205i	−0.450835	−	0.780869i
$493$	−3.00000	+	5.19615i	−0.135113	+	0.234023i
$494$		0			0
$495$	−8.00000	−	13.8564i	−0.359573	−	0.622799i
$496$	−36.0000			−1.61645
$497$	−5.00000	−	1.73205i	−0.224281	−	0.0776931i
$498$		0			0
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$	24.0000	−	41.5692i	1.07331	−	1.85903i
$501$	7.00000	−	12.1244i	0.312737	−	0.541676i
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	56.0000			2.49197
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	1.00000	−	1.73205i	0.0443678	−	0.0768473i
$509$	4.00000	+	6.92820i	0.177297	+	0.307087i	0.940954	−	0.338535i	$-0.109931\pi$
$509$	4.00000	+	6.92820i	0.177297	+	0.307087i	−0.763657	+	0.645622i	$0.776598\pi$
$510$		0			0
$511$	18.0000	−	15.5885i	0.796273	−	0.689593i
$512$		0			0
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$		0			0
$515$	38.0000	−	65.8179i	1.67448	−	2.90028i
$516$	7.00000	+	12.1244i	0.308158	+	0.533745i
$517$	24.0000			1.05552
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$		0			0
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	0.972421	−	0.233233i	$-0.0749303\pi$
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	−0.688196	+	0.725525i	$0.741597\pi$
$524$	−36.0000			−1.57267
$525$	5.50000	+	28.5788i	0.240040	+	1.24728i
$526$		0			0
$527$	4.50000	+	7.79423i	0.196023	+	0.339522i
$528$	8.00000	−	13.8564i	0.348155	−	0.603023i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	8.00000			0.347170
$532$	−5.00000	−	1.73205i	−0.216777	−	0.0750939i
$533$	10.0000			0.433148
$534$		0			0
$535$	24.0000	−	41.5692i	1.03761	−	1.79719i
$536$		0			0
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$		0			0
$539$	−26.0000	+	10.3923i	−1.11990	+	0.447628i
$540$	8.00000			0.344265
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	0.586278	−	0.810110i	$-0.300593\pi$
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	−0.994715	+	0.102677i	$0.967259\pi$
$542$		0			0
$543$	3.50000	−	6.06218i	0.150199	−	0.260153i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$		0			0
$553$	1.50000	+	7.79423i	0.0637865	+	0.331444i
$554$		0			0
$555$	−22.0000	−	38.1051i	−0.933848	−	1.61747i
$556$	−9.00000	+	15.5885i	−0.381685	+	0.661098i
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	0.0360693	+	0.999349i	$0.488516\pi$
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	−0.883497	+	0.468438i	$0.844817\pi$
$558$		0			0
$559$	−7.00000			−0.296068
$560$	−32.0000	+	27.7128i	−1.35225	+	1.17108i
$561$	−4.00000			−0.168880
$562$		0			0
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$	−6.00000	+	10.3923i	−0.252646	+	0.437595i
$565$	−24.0000	−	41.5692i	−1.00969	−	1.74883i
$566$		0			0
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$		0			0
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−7.50000	+	12.9904i	−0.313865	+	0.543631i	−0.979196	−	0.202919i	$-0.934957\pi$
$571$	−7.50000	+	12.9904i	−0.313865	+	0.543631i	0.665330	+	0.746549i	$0.268291\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$	24.0000			1.00261
$574$		0			0
$575$	22.0000			0.917463
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	10.5000	−	18.1865i	0.437121	−	0.757115i	−0.560345	−	0.828259i	$-0.689332\pi$
$577$	10.5000	−	18.1865i	0.437121	−	0.757115i	0.997466	+	0.0711438i	$0.0226649\pi$
$578$		0			0
$579$	6.50000	+	11.2583i	0.270131	+	0.467880i
$580$	−48.0000			−1.99309
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$		0			0
$587$	−6.00000			−0.247647			−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000			−0.247647			−0.123823	+	0.992304i	$0.539516\pi$
$588$	2.00000	−	13.8564i	0.0824786	−	0.571429i
$589$	−9.00000			−0.370839
$590$		0			0
$591$	5.00000	−	8.66025i	0.205673	−	0.356235i
$592$	22.0000	−	38.1051i	0.904194	−	1.56611i
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	0.822035	−	0.569438i	$-0.192839\pi$
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	−0.904165	+	0.427184i	$0.859506\pi$
$594$		0			0
$595$	10.0000	+	3.46410i	0.409960	+	0.142014i
$596$	−20.0000			−0.819232
$597$	8.00000	+	13.8564i	0.327418	+	0.567105i
$598$		0			0
$599$	17.0000	−	29.4449i	0.694601	−	1.20308i	−0.275714	−	0.961240i	$-0.588914\pi$
$599$	17.0000	−	29.4449i	0.694601	−	1.20308i	0.970315	−	0.241845i	$-0.0777525\pi$
$600$		0			0
$601$	25.0000			1.01977			0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000			1.01977			0.509886	+	0.860242i	$0.329688\pi$
$602$		0			0
$603$	3.00000			0.122169
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	−10.0000	+	17.3205i	−0.406558	+	0.704179i
$606$		0			0
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	−0.999964	−	0.00851879i	$-0.997288\pi$
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	0.492604	−	0.870253i	$-0.336045\pi$
$608$		0			0
$609$	12.0000	−	10.3923i	0.486265	−	0.421117i
$610$		0			0
$611$	−3.00000	−	5.19615i	−0.121367	−	0.210214i
$612$	1.00000	−	1.73205i	0.0404226	−	0.0700140i
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$		0			0
$615$	−40.0000			−1.61296
$616$		0			0
$617$	8.00000			0.322068			0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000			0.322068			0.161034	+	0.986949i	$0.448517\pi$
$618$		0			0
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	−36.0000	+	62.3538i	−1.44579	+	2.50419i
$621$	1.00000	+	1.73205i	0.0401286	+	0.0695048i
$622$		0			0
$623$		0			0
$624$	−4.00000			−0.160128
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$		0			0
$627$	2.00000	−	3.46410i	0.0798723	−	0.138343i
$628$	10.0000	+	17.3205i	0.399043	+	0.691164i
$629$	−11.0000			−0.438599
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$	−6.00000	+	10.3923i	−0.238479	+	0.413057i
$634$		0			0
$635$	−2.00000	−	3.46410i	−0.0793676	−	0.137469i
$636$	−12.0000			−0.475831
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$		0			0
$643$	3.00000			0.118308			0.0591542	−	0.998249i	$-0.481160\pi$
$643$	3.00000			0.118308			0.0591542	+	0.998249i	$0.481160\pi$
$644$	−10.0000	−	3.46410i	−0.394055	−	0.136505i
$645$	28.0000			1.10250
$646$		0			0
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$		0			0
$649$	−16.0000	−	27.7128i	−0.628055	−	1.08782i
$650$		0			0
$651$	−4.50000	−	23.3827i	−0.176369	−	0.916440i
$652$	−32.0000			−1.25322
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$		0			0
$655$	−36.0000	+	62.3538i	−1.40664	+	2.43637i
$656$	−20.0000	−	34.6410i	−0.780869	−	1.35250i
$657$	−9.00000			−0.351123
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	−16.0000	−	27.7128i	−0.622799	−	1.07872i
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$		0			0
$663$	0.500000	+	0.866025i	0.0194184	+	0.0336336i
$664$		0			0
$665$	−8.00000	+	6.92820i	−0.310227	+	0.268664i
$666$		0			0
$667$	−6.00000	−	10.3923i	−0.232321	−	0.402392i
$668$	14.0000	−	24.2487i	0.541676	−	0.938211i
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	41.0000			1.58043			0.790217	−	0.612827i	$-0.209968\pi$
$673$	41.0000			1.58043			0.790217	+	0.612827i	$0.209968\pi$
$674$		0			0
$675$	5.50000	−	9.52628i	0.211695	−	0.366667i
$676$	−12.0000	+	20.7846i	−0.461538	+	0.799408i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$		0			0
$679$	5.00000	+	1.73205i	0.191882	+	0.0664700i
$680$		0			0
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	32.0000			1.22266
$686$		0			0
$687$	−21.0000			−0.801200
$688$	14.0000	+	24.2487i	0.533745	+	0.924473i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$	−12.0000			−0.456172
$693$	10.0000	+	3.46410i	0.379869	+	0.131590i
$694$		0			0
$695$	18.0000	+	31.1769i	0.682779	+	1.18261i
$696$		0			0
$697$	−5.00000	+	8.66025i	−0.189389	+	0.328031i
$698$		0			0
$699$	14.0000			0.529529
$700$	11.0000	+	57.1577i	0.415761	+	2.16036i
$701$	38.0000			1.43524			0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000			1.43524			0.717620	+	0.696435i	$0.245231\pi$
$702$		0			0
$703$	5.50000	−	9.52628i	0.207436	−	0.359290i
$704$	16.0000	−	27.7128i	0.603023	−	1.04447i
$705$	12.0000	+	20.7846i	0.451946	+	0.782794i
$706$		0			0
$707$	−28.0000	+	24.2487i	−1.05305	+	0.911967i
$708$	16.0000			0.601317
$709$	−21.0000	−	36.3731i	−0.788672	−	1.36602i	−0.926781	−	0.375602i	$-0.877436\pi$
$709$	−21.0000	−	36.3731i	−0.788672	−	1.36602i	0.138109	−	0.990417i	$-0.455897\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$		0			0
$713$	−18.0000			−0.674105
$714$		0			0
$715$	16.0000			0.598366
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−13.0000	+	22.5167i	−0.485494	+	0.840900i
$718$		0			0
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	0.826319	−	0.563202i	$-0.190431\pi$
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	−0.900907	+	0.434013i	$0.857097\pi$
$720$	16.0000			0.596285
$721$	9.50000	+	49.3634i	0.353798	+	1.83839i
$722$		0			0
$723$	3.00000	+	5.19615i	0.111571	+	0.193247i
$724$	7.00000	−	12.1244i	0.260153	−	0.450598i
$725$	−33.0000	+	57.1577i	−1.22559	+	2.12278i
$726$		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
$731$	3.50000	−	6.06218i	0.129452	−	0.224218i
$732$	−6.00000	+	10.3923i	−0.221766	+	0.384111i
$733$	11.5000	+	19.9186i	0.424762	+	0.735710i	0.996398	−	0.0847976i	$-0.0270244\pi$
$733$	11.5000	+	19.9186i	0.424762	+	0.735710i	−0.571636	+	0.820507i	$0.693691\pi$
$734$		0			0
$735$	−22.0000	−	17.3205i	−0.811482	−	0.638877i
$736$		0			0
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	−44.0000	−	76.2102i	−1.61747	−	2.80154i
$741$	−1.00000			−0.0367359
$742$		0			0
$743$	−4.00000			−0.146746			−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000			−0.146746			−0.0733729	+	0.997305i	$0.523376\pi$
$744$		0			0
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$		0			0
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−8.00000			−0.292509
$749$	6.00000	+	31.1769i	0.219235	+	1.13918i
$750$		0			0
$751$	−1.50000	−	2.59808i	−0.0547358	−	0.0948051i	0.837359	−	0.546653i	$-0.184098\pi$
$751$	−1.50000	−	2.59808i	−0.0547358	−	0.0948051i	−0.892095	+	0.451848i	$0.850765\pi$
$752$	−12.0000	+	20.7846i	−0.437595	+	0.757937i
$753$	−5.00000	+	8.66025i	−0.182210	+	0.315597i
$754$		0			0
$755$	32.0000			1.16460
$756$	−4.00000	+	3.46410i	−0.145479	+	0.125988i
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$		0			0
$759$	4.00000	−	6.92820i	0.145191	−	0.251478i
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$	2.00000	−	1.73205i	0.0724049	−	0.0627044i
$764$	48.0000			1.73658
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$		0			0
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	−13.0000			−0.468792			−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000			−0.468792			−0.234396	+	0.972141i	$0.575311\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$	13.0000	+	22.5167i	0.467880	+	0.810392i
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$		0			0
$775$	49.5000	+	85.7365i	1.77809	+	3.07975i
$776$		0			0
$777$	27.5000	+	9.52628i	0.986557	+	0.341753i
$778$		0			0
$779$	−5.00000	−	8.66025i	−0.179144	−	0.310286i
$780$	−4.00000	+	6.92820i	−0.143223	+	0.248069i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$		0			0
$783$	−6.00000			−0.214423
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	40.0000			1.42766
$786$		0			0
$787$	22.0000	−	38.1051i	0.784215	−	1.35830i	−0.145251	−	0.989395i	$-0.546399\pi$
$787$	22.0000	−	38.1051i	0.784215	−	1.35830i	0.929467	−	0.368906i	$-0.120268\pi$
$788$	10.0000	−	17.3205i	0.356235	−	0.617018i
$789$	−1.00000	−	1.73205i	−0.0356009	−	0.0616626i
$790$		0			0
$791$	30.0000	+	10.3923i	1.06668	+	0.369508i
$792$		0			0
$793$	−3.00000	−	5.19615i	−0.106533	−	0.184521i
$794$		0			0
$795$	−12.0000	+	20.7846i	−0.425596	+	0.737154i
$796$	16.0000	+	27.7128i	0.567105	+	0.982255i
$797$	−8.00000			−0.283375			−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000			−0.283375			−0.141687	+	0.989911i	$0.545253\pi$
$798$		0			0
$799$	6.00000			0.212265
$800$		0			0
$801$		0			0
$802$		0			0
$803$	18.0000	+	31.1769i	0.635206	+	1.10021i
$804$	6.00000			0.211604
$805$	−16.0000	+	13.8564i	−0.563926	+	0.488374i
$806$		0			0
$807$	11.0000	+	19.0526i	0.387218	+	0.670682i
$808$		0			0
$809$	22.0000	−	38.1051i	0.773479	−	1.33970i	−0.162167	−	0.986763i	$-0.551848\pi$
$809$	22.0000	−	38.1051i	0.773479	−	1.33970i	0.935645	−	0.352941i	$-0.114818\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	24.0000	−	20.7846i	0.842235	−	0.729397i
$813$	−24.0000			−0.841717
$814$		0			0
$815$	−32.0000	+	55.4256i	−1.12091	+	1.94147i
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	3.50000	+	6.06218i	0.122449	+	0.212089i
$818$		0			0
$819$	−0.500000	−	2.59808i	−0.0174714	−	0.0907841i
$820$	−80.0000			−2.79372
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	−0.999914	+	0.0131101i	$0.995827\pi$
$822$		0			0
$823$	−28.0000	+	48.4974i	−0.976019	+	1.69051i	−0.299487	+	0.954100i	$0.596815\pi$
$823$	−28.0000	+	48.4974i	−0.976019	+	1.69051i	−0.676532	+	0.736413i	$0.736518\pi$
$824$		0			0
$825$	−44.0000			−1.53188
$826$		0			0
$827$	14.0000			0.486828			0.243414	−	0.969923i	$-0.421733\pi$
$827$	14.0000			0.486828			0.243414	+	0.969923i	$0.421733\pi$
$828$	2.00000	+	3.46410i	0.0695048	+	0.120386i
$829$	−10.5000	+	18.1865i	−0.364680	+	0.631644i	−0.988725	−	0.149744i	$-0.952155\pi$
$829$	−10.5000	+	18.1865i	−0.364680	+	0.631644i	0.624045	+	0.781389i	$0.285488\pi$
$830$		0			0
$831$	−2.50000	−	4.33013i	−0.0867240	−	0.150210i
$832$	−8.00000			−0.277350
$833$	−6.50000	+	2.59808i	−0.225212	+	0.0900180i
$834$		0			0
$835$	−28.0000	−	48.4974i	−0.968980	−	1.67832i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$	−4.50000	+	7.79423i	−0.155543	+	0.269408i
$838$		0			0
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	13.0000	−	22.5167i	0.447744	−	0.775515i
$844$	−12.0000	+	20.7846i	−0.413057	+	0.715436i
$845$	24.0000	+	41.5692i	0.825625	+	1.43002i
$846$		0			0
$847$	−2.50000	−	12.9904i	−0.0859010	−	0.446355i
$848$	−24.0000			−0.824163
$849$	−12.5000	−	21.6506i	−0.428999	−	0.743048i
$850$		0			0
$851$	11.0000	−	19.0526i	0.377075	−	0.653113i
$852$	2.00000	+	3.46410i	0.0685189	+	0.118678i
$853$	37.0000			1.26686			0.633428	−	0.773802i	$-0.281647\pi$
$853$	37.0000			1.26686			0.633428	+	0.773802i	$0.281647\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	−0.584967	−	0.811057i	$-0.698893\pi$
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	0.994880	+	0.101068i	$0.0322260\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	56.0000			1.90958
$861$	20.0000	−	17.3205i	0.681598	−	0.590281i
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$	−9.00000	−	46.7654i	−0.305480	−	1.58732i
$869$	−12.0000			−0.407072
$870$		0			0
$871$	−1.50000	+	2.59808i	−0.0508256	+	0.0880325i
$872$		0			0
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$		0			0
$875$	60.0000	+	20.7846i	2.02837	+	0.702648i
$876$	−18.0000			−0.608164
$877$	21.0000	+	36.3731i	0.709120	+	1.22823i	0.965184	+	0.261571i	$0.0842407\pi$
$877$	21.0000	+	36.3731i	0.709120	+	1.22823i	−0.256064	+	0.966660i	$0.582426\pi$
$878$		0			0
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$	−32.0000	−	55.4256i	−1.07872	−	1.86840i
$881$	−32.0000			−1.07811			−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000			−1.07811			−0.539054	+	0.842271i	$0.681218\pi$
$882$		0			0
$883$	−17.0000			−0.572096			−0.286048	−	0.958215i	$-0.592342\pi$
$883$	−17.0000			−0.572096			−0.286048	+	0.958215i	$0.592342\pi$
$884$	1.00000	+	1.73205i	0.0336336	+	0.0582552i
$885$	16.0000	−	27.7128i	0.537834	−	0.931556i
$886$		0			0
$887$	−5.00000	−	8.66025i	−0.167884	−	0.290783i	0.769792	−	0.638295i	$-0.220360\pi$
$887$	−5.00000	−	8.66025i	−0.167884	−	0.290783i	−0.937676	+	0.347512i	$0.887027\pi$
$888$		0			0
$889$	2.50000	+	0.866025i	0.0838473	+	0.0290456i
$890$		0			0
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$		0			0
$895$	−24.0000			−0.802232
$896$		0			0
$897$	−2.00000			−0.0667781
$898$		0			0
$899$	27.0000	−	46.7654i	0.900500	−	1.55971i
$900$	11.0000	−	19.0526i	0.366667	−	0.635085i
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$		0			0
$903$	−14.0000	+	12.1244i	−0.465891	+	0.403473i
$904$		0			0
$905$	−14.0000	−	24.2487i	−0.465376	−	0.806054i
$906$		0			0
$907$	9.50000	−	16.4545i	0.315442	−	0.546362i	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	9.50000	−	16.4545i	0.315442	−	0.546362i	0.979531	+	0.201291i	$0.0645138\pi$
$908$	4.00000	+	6.92820i	0.132745	+	0.229920i
$909$	14.0000			0.464351
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$		0			0
$915$	12.0000	+	20.7846i	0.396708	+	0.687118i
$916$	−42.0000			−1.38772
$917$	−9.00000	−	46.7654i	−0.297206	−	1.54433i
$918$		0			0
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$		0			0
$921$	−6.50000	+	11.2583i	−0.214182	+	0.370975i
$922$		0			0
$923$	−2.00000			−0.0658308
$924$	20.0000	+	6.92820i	0.657952	+	0.227921i
$925$	−121.000			−3.97846
$926$		0			0
$927$	9.50000	−	16.4545i	0.312021	−	0.540436i
$928$		0			0
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	−0.997684	−	0.0680235i	$-0.978331\pi$
$929$	−17.0000	−	29.4449i	−0.557752	−	0.966055i	0.439932	−	0.898031i	$-0.355003\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	28.0000			0.917170
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$	−8.00000	+	13.8564i	−0.261628	+	0.453153i
$936$		0			0
$937$	43.0000			1.40475			0.702374	−	0.711808i	$-0.252123\pi$
$937$	43.0000			1.40475			0.702374	+	0.711808i	$0.252123\pi$
$938$		0			0
$939$	19.0000			0.620042
$940$	24.0000	+	41.5692i	0.782794	+	1.35584i
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	−0.478100	−	0.878306i	$-0.658674\pi$
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	0.999685	−	0.0251063i	$-0.00799243\pi$
$942$		0			0
$943$	−10.0000	−	17.3205i	−0.325645	−	0.564033i
$944$	32.0000			1.04151
$945$	2.00000	+	10.3923i	0.0650600	+	0.338062i
$946$		0			0
$947$	17.0000	+	29.4449i	0.552426	+	0.956830i	0.998099	+	0.0616337i	$0.0196311\pi$
$947$	17.0000	+	29.4449i	0.552426	+	0.956830i	−0.445673	+	0.895196i	$0.647036\pi$
$948$	3.00000	−	5.19615i	0.0974355	−	0.168763i
$949$	4.50000	−	7.79423i	0.146076	−	0.253011i
$950$		0			0
$951$	20.0000			0.648544
$952$		0			0
$953$	8.00000			0.259145			0.129573	−	0.991570i	$-0.458639\pi$
$953$	8.00000			0.259145			0.129573	+	0.991570i	$0.458639\pi$
$954$		0			0
$955$	48.0000	−	83.1384i	1.55324	−	2.69030i
$956$	−26.0000	+	45.0333i	−0.840900	+	1.45648i
$957$	12.0000	+	20.7846i	0.387905	+	0.671871i
$958$		0			0
$959$	−16.0000	+	13.8564i	−0.516667	+	0.447447i
$960$	32.0000			1.03280
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	6.00000	+	10.3923i	0.193247	+	0.334714i
$965$	52.0000			1.67394
$966$		0			0
$967$	−1.00000			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$968$		0			0
$969$	0.500000	−	0.866025i	0.0160623	−	0.0278207i
$970$		0			0
$971$	17.0000	+	29.4449i	0.545556	+	0.944931i	0.998572	+	0.0534281i	$0.0170148\pi$
$971$	17.0000	+	29.4449i	0.545556	+	0.944931i	−0.453016	+	0.891503i	$0.649652\pi$
$972$	2.00000			0.0641500
$973$	−22.5000	−	7.79423i	−0.721317	−	0.249871i
$974$		0			0
$975$	5.50000	+	9.52628i	0.176141	+	0.305085i
$976$	−12.0000	+	20.7846i	−0.384111	+	0.665299i
$977$	8.00000	−	13.8564i	0.255943	−	0.443306i	−0.709208	−	0.704999i	$-0.750947\pi$
$977$	8.00000	−	13.8564i	0.255943	−	0.443306i	0.965151	+	0.261693i	$0.0842808\pi$
$978$		0			0
$979$		0			0
$980$	−44.0000	−	34.6410i	−1.40553	−	1.10657i
$981$	−1.00000			−0.0319275
$982$		0			0
$983$	27.0000	−	46.7654i	0.861166	−	1.49158i	−0.00963785	−	0.999954i	$-0.503068\pi$
$983$	27.0000	−	46.7654i	0.861166	−	1.49158i	0.870804	−	0.491630i	$-0.163599\pi$
$984$		0			0
$985$	−20.0000	−	34.6410i	−0.637253	−	1.10375i
$986$		0			0
$987$	−15.0000	−	5.19615i	−0.477455	−	0.165395i
$988$	−2.00000			−0.0636285
$989$	7.00000	+	12.1244i	0.222587	+	0.385532i
$990$		0			0
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796392\pi$
$992$		0			0
$993$	13.0000			0.412543
$994$		0			0
$995$	64.0000			2.02894
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	13.5000	−	23.3827i	0.427549	−	0.740537i	−0.569105	−	0.822265i	$-0.692710\pi$
$997$	13.5000	−	23.3827i	0.427549	−	0.740537i	0.996655	+	0.0817275i	$0.0260437\pi$
$998$		0			0
$999$	−5.50000	−	9.52628i	−0.174012	−	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.i.b.256.1	yes	2
3.2	odd	2		1071.2.i.b.613.1		2
7.2	even	3	inner	357.2.i.b.205.1	✓	2
7.3	odd	6		2499.2.a.f.1.1		1
7.4	even	3		2499.2.a.e.1.1		1
21.2	odd	6		1071.2.i.b.919.1		2
21.11	odd	6		7497.2.a.g.1.1		1
21.17	even	6		7497.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.b.205.1	✓	2	7.2	even	3	inner
357.2.i.b.256.1	yes	2	1.1	even	1	trivial
1071.2.i.b.613.1		2	3.2	odd	2
1071.2.i.b.919.1		2	21.2	odd	6
2499.2.a.e.1.1		1	7.4	even	3
2499.2.a.f.1.1		1	7.3	odd	6
7497.2.a.g.1.1		1	21.11	odd	6
7497.2.a.k.1.1		1	21.17	even	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} -4.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{19} -8.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-5.50000 + 9.52628i) q^{25} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +6.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-2.00000 - 10.3923i) q^{35} -2.00000 q^{36} +(5.50000 + 9.52628i) q^{37} +(0.500000 - 0.866025i) q^{39} +10.0000 q^{41} -7.00000 q^{43} +(4.00000 + 6.92820i) q^{44} +(-2.00000 + 3.46410i) q^{45} +(-3.00000 - 5.19615i) q^{47} -4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(0.500000 + 0.866025i) q^{51} +(1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +16.0000 q^{55} -1.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-4.00000 + 6.92820i) q^{60} +(-3.00000 - 5.19615i) q^{61} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(1.00000 + 1.73205i) q^{68} -2.00000 q^{69} -2.00000 q^{71} +(4.50000 - 7.79423i) q^{73} +(5.50000 + 9.52628i) q^{75} -2.00000 q^{76} +(-8.00000 + 6.92820i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-8.00000 + 13.8564i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000 q^{83} +(-1.00000 - 5.19615i) q^{84} +4.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(2.50000 + 0.866025i) q^{91} -4.00000 q^{92} +(-4.50000 - 7.79423i) q^{93} +(-2.00000 + 3.46410i) q^{95} +2.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 2 q^{4} - 4 q^{5} + 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 + 2 * q^4 - 4 * q^5 + 5 * q^7 - q^9	\( 2 q + q^{3} + 2 q^{4} - 4 q^{5} + 5 q^{7} - q^{9} - 4 q^{11} - 2 q^{12} + 2 q^{13} - 8 q^{15} - 4 q^{16} - q^{17} - q^{19} - 16 q^{20} + 4 q^{21} - 2 q^{23} - 11 q^{25} - 2 q^{27} + 8 q^{28} + 12 q^{29} + 9 q^{31} + 4 q^{33} - 4 q^{35} - 4 q^{36} + 11 q^{37} + q^{39} + 20 q^{41} - 14 q^{43} + 8 q^{44} - 4 q^{45} - 6 q^{47} - 8 q^{48} + 11 q^{49} + q^{51} + 2 q^{52} + 6 q^{53} + 32 q^{55} - 2 q^{57} - 8 q^{59} - 8 q^{60} - 6 q^{61} - q^{63} - 16 q^{64} - 4 q^{65} - 3 q^{67} + 2 q^{68} - 4 q^{69} - 4 q^{71} + 9 q^{73} + 11 q^{75} - 4 q^{76} - 16 q^{77} + 3 q^{79} - 16 q^{80} - q^{81} + 12 q^{83} - 2 q^{84} + 8 q^{85} + 6 q^{87} + 5 q^{91} - 8 q^{92} - 9 q^{93} - 4 q^{95} + 4 q^{97} + 8 q^{99}+O(q^{100}) \) 2 * q + q^3 + 2 * q^4 - 4 * q^5 + 5 * q^7 - q^9 - 4 * q^11 - 2 * q^12 + 2 * q^13 - 8 * q^15 - 4 * q^16 - q^17 - q^19 - 16 * q^20 + 4 * q^21 - 2 * q^23 - 11 * q^25 - 2 * q^27 + 8 * q^28 + 12 * q^29 + 9 * q^31 + 4 * q^33 - 4 * q^35 - 4 * q^36 + 11 * q^37 + q^39 + 20 * q^41 - 14 * q^43 + 8 * q^44 - 4 * q^45 - 6 * q^47 - 8 * q^48 + 11 * q^49 + q^51 + 2 * q^52 + 6 * q^53 + 32 * q^55 - 2 * q^57 - 8 * q^59 - 8 * q^60 - 6 * q^61 - q^63 - 16 * q^64 - 4 * q^65 - 3 * q^67 + 2 * q^68 - 4 * q^69 - 4 * q^71 + 9 * q^73 + 11 * q^75 - 4 * q^76 - 16 * q^77 + 3 * q^79 - 16 * q^80 - q^81 + 12 * q^83 - 2 * q^84 + 8 * q^85 + 6 * q^87 + 5 * q^91 - 8 * q^92 - 9 * q^93 - 4 * q^95 + 4 * q^97 + 8 * q^99

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