LMFDB - Embedded newform 504.2.q.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (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:	$4.02446026187$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	504.121
Dual form			504.2.q.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q-1.73205i q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-3.00000 - 3.46410i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.19615i q^{27} +(-4.50000 - 7.79423i) q^{29} +4.00000 q^{31} +(-4.50000 - 2.59808i) q^{33} +(-2.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(1.50000 + 0.866025i) q^{39} +(-3.50000 + 6.06218i) q^{41} +(-1.50000 - 2.59808i) q^{43} +(1.50000 + 2.59808i) q^{45} +8.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(-4.50000 - 7.79423i) q^{53} -3.00000 q^{55} +(7.50000 + 4.33013i) q^{57} -4.00000 q^{59} +2.00000 q^{61} +(-6.00000 + 5.19615i) q^{63} +1.00000 q^{65} +12.0000 q^{67} +(-1.50000 + 0.866025i) q^{69} +8.00000 q^{71} +(6.50000 + 11.2583i) q^{73} +(-6.00000 - 3.46410i) q^{75} +(-1.50000 - 7.79423i) q^{77} +8.00000 q^{79} +9.00000 q^{81} +(6.50000 + 11.2583i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(-13.5000 + 7.79423i) q^{87} +(4.50000 - 7.79423i) q^{89} +(0.500000 + 2.59808i) q^{91} -6.92820i q^{93} +5.00000 q^{95} +(8.50000 + 14.7224i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - q^5 + 4 * q^7 - 6 * q^9	$ 2 q - q^{5} + 4 q^{7} - 6 q^{9} + 3 q^{11} - q^{13} - 3 q^{15} - 3 q^{17} - 5 q^{19} - 6 q^{21} - q^{23} + 4 q^{25} - 9 q^{29} + 8 q^{31} - 9 q^{33} - 5 q^{35} - 5 q^{37} + 3 q^{39} - 7 q^{41} - 3 q^{43} + 3 q^{45} + 16 q^{47} + 2 q^{49} - 9 q^{51} - 9 q^{53} - 6 q^{55} + 15 q^{57} - 8 q^{59} + 4 q^{61} - 12 q^{63} + 2 q^{65} + 24 q^{67} - 3 q^{69} + 16 q^{71} + 13 q^{73} - 12 q^{75} - 3 q^{77} + 16 q^{79} + 18 q^{81} + 13 q^{83} - 3 q^{85} - 27 q^{87} + 9 q^{89} + q^{91} + 10 q^{95} + 17 q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q - q^5 + 4 * q^7 - 6 * q^9 + 3 * q^11 - q^13 - 3 * q^15 - 3 * q^17 - 5 * q^19 - 6 * q^21 - q^23 + 4 * q^25 - 9 * q^29 + 8 * q^31 - 9 * q^33 - 5 * q^35 - 5 * q^37 + 3 * q^39 - 7 * q^41 - 3 * q^43 + 3 * q^45 + 16 * q^47 + 2 * q^49 - 9 * q^51 - 9 * q^53 - 6 * q^55 + 15 * q^57 - 8 * q^59 + 4 * q^61 - 12 * q^63 + 2 * q^65 + 24 * q^67 - 3 * q^69 + 16 * q^71 + 13 * q^73 - 12 * q^75 - 3 * q^77 + 16 * q^79 + 18 * q^81 + 13 * q^83 - 3 * q^85 - 27 * q^87 + 9 * q^89 + q^91 + 10 * q^95 + 17 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$		0			0
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$		0			0
$35$	−2.50000	−	0.866025i	−0.422577	−	0.146385i
$36$		0			0
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	−0.994999	−	0.0998840i	$-0.968153\pi$
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	0.584002	+	0.811752i	$0.301486\pi$
$38$		0			0
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$		0			0
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$		0			0
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	0.728689	−	0.684844i	$-0.240130\pi$
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	−0.957437	+	0.288641i	$0.906796\pi$
$44$		0			0
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$		0			0
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$		0			0
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	7.50000	+	4.33013i	0.993399	+	0.573539i
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$	−6.00000	+	5.19615i	−0.755929	+	0.654654i
$64$		0			0
$65$	1.00000			0.124035
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$	−1.50000	+	0.866025i	−0.180579	+	0.104257i
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$		0			0
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$		0			0
$77$	−1.50000	−	7.79423i	−0.170941	−	0.888235i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	6.50000	+	11.2583i	0.713468	+	1.23576i	0.963548	+	0.267537i	$0.0862098\pi$
$83$	6.50000	+	11.2583i	0.713468	+	1.23576i	−0.250080	+	0.968225i	$0.580457\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$		0			0
$87$	−13.5000	+	7.79423i	−1.44735	+	0.835629i
$88$		0			0
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$		0			0
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$		0			0
$93$		−	6.92820i		−	0.718421i
$94$		0			0
$95$	5.00000			0.512989
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$		0			0
$99$	−4.50000	+	7.79423i	−0.452267	+	0.783349i
$100$		0			0
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	−0.637678	−	0.770303i	$-0.720105\pi$
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	0.985941	+	0.167094i	$0.0534383\pi$
$102$		0			0
$103$	−4.50000	−	7.79423i	−0.443398	−	0.767988i	0.554541	−	0.832156i	$-0.312894\pi$
$103$	−4.50000	−	7.79423i	−0.443398	−	0.767988i	−0.997939	+	0.0641683i	$0.979561\pi$
$104$		0			0
$105$	−1.50000	+	4.33013i	−0.146385	+	0.422577i
$106$		0			0
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	−0.645766	−	0.763535i	$-0.723462\pi$
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	0.984124	+	0.177482i	$0.0567953\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$	7.50000	+	4.33013i	0.711868	+	0.410997i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$		0			0
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$		0			0
$119$	−7.50000	−	2.59808i	−0.687524	−	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	10.5000	+	6.06218i	0.946753	+	0.546608i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−4.50000	+	2.59808i	−0.396203	+	0.228748i
$130$		0			0
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$		0			0
$133$	2.50000	+	12.9904i	0.216777	+	1.12641i
$134$		0			0
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$		0			0
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	−0.999408	−	0.0344182i	$-0.989042\pi$
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	0.529511	+	0.848303i	$0.322376\pi$
$138$		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
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$		0			0
$147$	−12.0000	−	1.73205i	−0.989743	−	0.142857i
$148$		0			0
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	0.971274	−	0.237964i	$-0.0764802\pi$
$152$		0			0
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$	−13.5000	+	7.79423i	−1.07062	+	0.618123i
$160$		0			0
$161$	−2.50000	−	0.866025i	−0.197028	−	0.0682524i
$162$		0			0
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$		0			0
$165$			5.19615i			0.404520i
$166$		0			0
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	−0.846031	−	0.533133i	$-0.821014\pi$
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	0.884723	+	0.466118i	$0.154348\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	7.50000	−	12.9904i	0.573539	−	0.993399i
$172$		0			0
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$		0			0
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$		0			0
$177$			6.92820i			0.520756i
$178$		0			0
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	0.929114	+	0.369792i	$0.120571\pi$
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	−0.144308	+	0.989533i	$0.546095\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$		0			0
$185$	5.00000			0.367607
$186$		0			0
$187$	−9.00000			−0.658145
$188$		0			0
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$		0			0
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$	−18.0000			−1.29567			−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000			−1.29567			−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$		−	1.73205i		−	0.124035i
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	0.206184	−	0.978513i	$-0.433895\pi$
$200$		0			0
$201$		−	20.7846i		−	1.46603i
$202$		0			0
$203$	−22.5000	−	7.79423i	−1.57919	−	0.547048i
$204$		0			0
$205$	7.00000			0.488901
$206$		0			0
$207$	1.50000	+	2.59808i	0.104257	+	0.180579i
$208$		0			0
$209$	7.50000	+	12.9904i	0.518786	+	0.898563i
$210$		0			0
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.145014	−	0.989430i	$-0.453677\pi$
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.784364	−	0.620301i	$-0.212990\pi$
$212$		0			0
$213$		−	13.8564i		−	0.949425i
$214$		0			0
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$		0			0
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$		0			0
$219$	19.5000	−	11.2583i	1.31769	−	0.760767i
$220$		0			0
$221$	3.00000			0.201802
$222$		0			0
$223$	−6.50000	−	11.2583i	−0.435272	−	0.753914i	0.562046	−	0.827106i	$-0.310015\pi$
$223$	−6.50000	−	11.2583i	−0.435272	−	0.753914i	−0.997318	+	0.0731927i	$0.976681\pi$
$224$		0			0
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$		0			0
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	−0.502204	−	0.864749i	$-0.667477\pi$
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	0.999997	+	0.00254715i	$0.000810783\pi$
$228$		0			0
$229$	−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
$231$	−13.5000	+	2.59808i	−0.888235	+	0.170941i
$232$		0			0
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$		0			0
$237$		−	13.8564i		−	0.900070i
$238$		0			0
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	−0.682985	−	0.730433i	$-0.739318\pi$
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	0.974066	+	0.226266i	$0.0726518\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$		−	15.5885i		−	1.00000i
$244$		0			0
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	−2.50000	−	4.33013i	−0.159071	−	0.275519i
$248$		0			0
$249$	19.5000	−	11.2583i	1.23576	−	0.713468i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$	4.50000	+	2.59808i	0.281801	+	0.162698i
$256$		0			0
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	0.999379	+	0.0352486i	$0.0112223\pi$
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	−0.469163	+	0.883112i	$0.655444\pi$
$258$		0			0
$259$	2.50000	+	12.9904i	0.155342	+	0.807183i
$260$		0			0
$261$	13.5000	+	23.3827i	0.835629	+	1.44735i
$262$		0			0
$263$	−5.50000	+	9.52628i	−0.339145	+	0.587416i	−0.984272	−	0.176659i	$-0.943471\pi$
$263$	−5.50000	+	9.52628i	−0.339145	+	0.587416i	0.645128	+	0.764075i	$0.276804\pi$
$264$		0			0
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$		0			0
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$		0			0
$269$	3.50000	+	6.06218i	0.213399	+	0.369618i	0.952776	−	0.303674i	$-0.0982133\pi$
$269$	3.50000	+	6.06218i	0.213399	+	0.369618i	−0.739377	+	0.673291i	$0.764880\pi$
$270$		0			0
$271$	−15.5000	+	26.8468i	−0.941558	+	1.63083i	−0.179057	+	0.983839i	$0.557305\pi$
$271$	−15.5000	+	26.8468i	−0.941558	+	1.63083i	−0.762501	+	0.646988i	$0.776029\pi$
$272$		0			0
$273$	4.50000	−	0.866025i	0.272352	−	0.0524142i
$274$		0			0
$275$	−6.00000	−	10.3923i	−0.361814	−	0.626680i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	−24.0000			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$		0			0
$285$		−	8.66025i		−	0.512989i
$286$		0			0
$287$	3.50000	+	18.1865i	0.206598	+	1.07352i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	25.5000	−	14.7224i	1.49484	−	0.863044i
$292$		0			0
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	−0.880261	−	0.474490i	$-0.842633\pi$
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	0.851051	+	0.525084i	$0.175966\pi$
$294$		0			0
$295$	2.00000	+	3.46410i	0.116445	+	0.201688i
$296$		0			0
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$		0			0
$299$	1.00000			0.0578315
$300$		0			0
$301$	−7.50000	−	2.59808i	−0.432293	−	0.149751i
$302$		0			0
$303$	−10.5000	−	6.06218i	−0.603209	−	0.348263i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−13.5000	+	7.79423i	−0.767988	+	0.443398i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$	7.50000	+	2.59808i	0.422577	+	0.146385i
$316$		0			0
$317$	14.0000			0.786318			0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000			0.786318			0.393159	+	0.919470i	$0.371382\pi$
$318$		0			0
$319$	−27.0000			−1.51171
$320$		0			0
$321$	−10.5000	−	6.06218i	−0.586053	−	0.338358i
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$		0			0
$327$	−7.50000	+	4.33013i	−0.414751	+	0.239457i
$328$		0			0
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$		0			0
$333$	7.50000	−	12.9904i	0.410997	−	0.711868i
$334$		0			0
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	−0.994728	−	0.102552i	$-0.967299\pi$
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	0.586177	+	0.810183i	$0.300632\pi$
$338$		0			0
$339$	−1.50000	−	0.866025i	−0.0814688	−	0.0470360i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	1.50000	+	0.866025i	0.0807573	+	0.0466252i
$346$		0			0
$347$	−28.0000			−1.50312			−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000			−1.50312			−0.751559	+	0.659665i	$0.770698\pi$
$348$		0			0
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	0.543693	−	0.839284i	$-0.317025\pi$
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	−0.998688	+	0.0512103i	$0.983692\pi$
$350$		0			0
$351$	−4.50000	−	2.59808i	−0.240192	−	0.138675i
$352$		0			0
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	0.0769515	+	0.997035i	$0.475481\pi$
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	−0.901933	+	0.431875i	$0.857852\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$		0			0
$357$	−4.50000	+	12.9904i	−0.238165	+	0.687524i
$358$		0			0
$359$	−13.5000	+	23.3827i	−0.712503	+	1.23409i	0.251412	+	0.967880i	$0.419105\pi$
$359$	−13.5000	+	23.3827i	−0.712503	+	1.23409i	−0.963915	+	0.266211i	$0.914228\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$	3.00000	−	1.73205i	0.157459	−	0.0909091i
$364$		0			0
$365$	6.50000	−	11.2583i	0.340226	−	0.589288i
$366$		0			0
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$		0			0
$369$	10.5000	−	18.1865i	0.546608	−	0.946753i
$370$		0			0
$371$	−22.5000	−	7.79423i	−1.16814	−	0.404656i
$372$		0			0
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$			15.5885i			0.804984i
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	32.0000			1.64373			0.821865	−	0.569683i	$-0.192934\pi$
$379$	32.0000			1.64373			0.821865	+	0.569683i	$0.192934\pi$
$380$		0			0
$381$		−	13.8564i		−	0.709885i
$382$		0			0
$383$	17.5000	+	30.3109i	0.894208	+	1.54881i	0.834781	+	0.550581i	$0.185594\pi$
$383$	17.5000	+	30.3109i	0.894208	+	1.54881i	0.0594268	+	0.998233i	$0.481073\pi$
$384$		0			0
$385$	−6.00000	+	5.19615i	−0.305788	+	0.264820i
$386$		0			0
$387$	4.50000	+	7.79423i	0.228748	+	0.396203i
$388$		0			0
$389$	−18.5000	+	32.0429i	−0.937987	+	1.62464i	−0.168769	+	0.985656i	$0.553979\pi$
$389$	−18.5000	+	32.0429i	−0.937987	+	1.62464i	−0.769218	+	0.638986i	$0.779354\pi$
$390$		0			0
$391$	−1.50000	+	2.59808i	−0.0758583	+	0.131390i
$392$		0			0
$393$	−4.50000	+	2.59808i	−0.226995	+	0.131056i
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	0.360723	+	0.932673i	$0.382530\pi$
$397$	−12.5000	+	21.6506i	−0.627357	+	1.08661i	−0.988080	+	0.153941i	$0.950803\pi$
$398$		0			0
$399$	22.5000	−	4.33013i	1.12641	−	0.216777i
$400$		0			0
$401$	6.50000	+	11.2583i	0.324595	+	0.562214i	0.981430	−	0.191820i	$-0.0614388\pi$
$401$	6.50000	+	11.2583i	0.324595	+	0.562214i	−0.656836	+	0.754034i	$0.728105\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$		0			0
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$		0			0
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$	16.5000	+	9.52628i	0.813885	+	0.469897i
$412$		0			0
$413$	−8.00000	+	6.92820i	−0.393654	+	0.340915i
$414$		0			0
$415$	6.50000	−	11.2583i	0.319072	−	0.552650i
$416$		0			0
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	1.50000	+	2.59808i	0.0731055	+	0.126622i	0.900261	−	0.435351i	$-0.143376\pi$
$421$	1.50000	+	2.59808i	0.0731055	+	0.126622i	−0.827155	+	0.561973i	$0.810042\pi$
$422$		0			0
$423$	−24.0000			−1.16692
$424$		0			0
$425$	−12.0000			−0.582086
$426$		0			0
$427$	4.00000	−	3.46410i	0.193574	−	0.167640i
$428$		0			0
$429$	4.50000	−	2.59808i	0.217262	−	0.125436i
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	13.5000	+	7.79423i	0.647275	+	0.373705i
$436$		0			0
$437$	5.00000			0.239182
$438$		0			0
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$		0			0
$445$	−9.00000			−0.426641
$446$		0			0
$447$	22.5000	−	12.9904i	1.06421	−	0.614424i
$448$		0			0
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	10.5000	+	18.1865i	0.494426	+	0.856370i
$452$		0			0
$453$	−25.5000	−	14.7224i	−1.19809	−	0.691720i
$454$		0			0
$455$	2.00000	−	1.73205i	0.0937614	−	0.0811998i
$456$		0			0
$457$	−26.0000			−1.21623			−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000			−1.21623			−0.608114	+	0.793849i	$0.708074\pi$
$458$		0			0
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$		0			0
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	0.987801	+	0.155719i	$0.0497696\pi$
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	−0.359044	+	0.933321i	$0.616897\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$		0			0
$465$	−6.00000	+	3.46410i	−0.278243	+	0.160644i
$466$		0			0
$467$	−6.50000	+	11.2583i	−0.300784	+	0.520973i	−0.976314	−	0.216359i	$-0.930582\pi$
$467$	−6.50000	+	11.2583i	−0.300784	+	0.520973i	0.675530	+	0.737333i	$0.263915\pi$
$468$		0			0
$469$	24.0000	−	20.7846i	1.10822	−	0.959744i
$470$		0			0
$471$		−	24.2487i		−	1.11732i
$472$		0			0
$473$	−9.00000			−0.413820
$474$		0			0
$475$	10.0000	+	17.3205i	0.458831	+	0.794719i
$476$		0			0
$477$	13.5000	+	23.3827i	0.618123	+	1.07062i
$478$		0			0
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$		0			0
$481$	−2.50000	−	4.33013i	−0.113990	−	0.197437i
$482$		0			0
$483$	−1.50000	+	4.33013i	−0.0682524	+	0.197028i
$484$		0			0
$485$	8.50000	−	14.7224i	0.385965	−	0.668511i
$486$		0			0
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	−0.891303	−	0.453409i	$-0.850208\pi$
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	0.0529875	−	0.998595i	$-0.483126\pi$
$488$		0			0
$489$	25.5000	+	14.7224i	1.15315	+	0.665771i
$490$		0			0
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	−0.949520	−	0.313707i	$-0.898429\pi$
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	0.746438	+	0.665455i	$0.231763\pi$
$492$		0			0
$493$	−13.5000	+	23.3827i	−0.608009	+	1.05310i
$494$		0			0
$495$	9.00000			0.404520
$496$		0			0
$497$	16.0000	−	13.8564i	0.717698	−	0.621545i
$498$		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	$0.608475\pi$
$500$		0			0
$501$	−1.50000	−	0.866025i	−0.0670151	−	0.0386912i
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−7.00000			−0.311496
$506$		0			0
$507$	18.0000	−	10.3923i	0.799408	−	0.461538i
$508$		0			0
$509$	−16.5000	−	28.5788i	−0.731350	−	1.26673i	−0.956306	−	0.292366i	$-0.905557\pi$
$509$	−16.5000	−	28.5788i	−0.731350	−	1.26673i	0.224957	−	0.974369i	$-0.427776\pi$
$510$		0			0
$511$	32.5000	+	11.2583i	1.43772	+	0.498039i
$512$		0			0
$513$	−22.5000	−	12.9904i	−0.993399	−	0.573539i
$514$		0			0
$515$	−4.50000	+	7.79423i	−0.198294	+	0.343455i
$516$		0			0
$517$	12.0000	−	20.7846i	0.527759	−	0.914106i
$518$		0			0
$519$			3.46410i			0.152057i
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	−16.5000	+	28.5788i	−0.721495	+	1.24967i	0.238906	+	0.971043i	$0.423211\pi$
$523$	−16.5000	+	28.5788i	−0.721495	+	1.24967i	−0.960401	+	0.278623i	$0.910122\pi$
$524$		0			0
$525$	−18.0000	+	3.46410i	−0.785584	+	0.151186i
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	−3.50000	−	6.06218i	−0.151602	−	0.262582i
$534$		0			0
$535$	−7.00000			−0.302636
$536$		0			0
$537$	31.5000	−	18.1865i	1.35933	−	0.784807i
$538$		0			0
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$		0			0
$541$	5.50000	−	9.52628i	0.236463	−	0.409567i	−0.723234	−	0.690604i	$-0.757345\pi$
$541$	5.50000	−	9.52628i	0.236463	−	0.409567i	0.959697	+	0.281037i	$0.0906783\pi$
$542$		0			0
$543$			31.1769i			1.33793i
$544$		0			0
$545$	−2.50000	+	4.33013i	−0.107088	+	0.185482i
$546$		0			0
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	0.914510	−	0.404564i	$-0.132577\pi$
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	−0.807617	+	0.589707i	$0.799243\pi$
$548$		0			0
$549$	−6.00000			−0.256074
$550$		0			0
$551$	45.0000			1.91706
$552$		0			0
$553$	16.0000	−	13.8564i	0.680389	−	0.589234i
$554$		0			0
$555$		−	8.66025i		−	0.367607i
$556$		0			0
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	0.900967	+	0.433888i	$0.142859\pi$
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	−0.0747252	+	0.997204i	$0.523808\pi$
$558$		0			0
$559$	3.00000			0.126886
$560$		0			0
$561$			15.5885i			0.658145i
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−1.00000			−0.0420703
$566$		0			0
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$		0			0
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		0			0
$573$		−	6.92820i		−	0.289430i
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	0.833112	−	0.553104i	$-0.186557\pi$
$577$	−1.50000	−	2.59808i	−0.0624458	−	0.108159i	−0.895558	+	0.444945i	$0.853223\pi$
$578$		0			0
$579$			31.1769i			1.29567i
$580$		0			0
$581$	32.5000	+	11.2583i	1.34833	+	0.467074i
$582$		0			0
$583$	−27.0000			−1.11823
$584$		0			0
$585$	−3.00000			−0.124035
$586$		0			0
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	0.668708	−	0.743525i	$-0.266848\pi$
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	−0.978266	+	0.207355i	$0.933514\pi$
$588$		0			0
$589$	−10.0000	+	17.3205i	−0.412043	+	0.713679i
$590$		0			0
$591$			38.1051i			1.56744i
$592$		0			0
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	−0.565792	−	0.824548i	$-0.691430\pi$
$593$	10.5000	−	18.1865i	0.431183	−	0.746831i	0.996976	+	0.0777165i	$0.0247629\pi$
$594$		0			0
$595$	1.50000	+	7.79423i	0.0614940	+	0.319532i
$596$		0			0
$597$	−31.5000	+	18.1865i	−1.28921	+	0.744325i
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		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
$603$	−36.0000			−1.46603
$604$		0			0
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$		0			0
$609$	−13.5000	+	38.9711i	−0.547048	+	1.57919i
$610$		0			0
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$		0			0
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	0.811112	−	0.584891i	$-0.198863\pi$
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	−0.912086	+	0.409998i	$0.865529\pi$
$614$		0			0
$615$		−	12.1244i		−	0.488901i
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		0			0
$619$	−10.5000	+	18.1865i	−0.422031	+	0.730978i	−0.996138	−	0.0878015i	$-0.972016\pi$
$619$	−10.5000	+	18.1865i	−0.422031	+	0.730978i	0.574107	+	0.818780i	$0.305349\pi$
$620$		0			0
$621$	4.50000	−	2.59808i	0.180579	−	0.104257i
$622$		0			0
$623$	−4.50000	−	23.3827i	−0.180289	−	0.936808i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	22.5000	−	12.9904i	0.898563	−	0.518786i
$628$		0			0
$629$	15.0000			0.598089
$630$		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
$633$	−40.5000	−	23.3827i	−1.60973	−	0.929378i
$634$		0			0
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$		0			0
$639$	−24.0000			−0.949425
$640$		0			0
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	−0.812421	−	0.583071i	$-0.801851\pi$
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	0.911165	+	0.412042i	$0.135184\pi$
$642$		0			0
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	0.227497	+	0.973779i	$0.426946\pi$
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	−0.957066	+	0.289871i	$0.906387\pi$
$644$		0			0
$645$	4.50000	+	2.59808i	0.177187	+	0.102299i
$646$		0			0
$647$	−20.5000	−	35.5070i	−0.805938	−	1.39593i	−0.915656	−	0.401963i	$-0.868328\pi$
$647$	−20.5000	−	35.5070i	−0.805938	−	1.39593i	0.109718	−	0.993963i	$-0.465005\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$		0			0
$651$	−12.0000	−	13.8564i	−0.470317	−	0.543075i
$652$		0			0
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	−1.50000	+	2.59808i	−0.0586098	+	0.101515i
$656$		0			0
$657$	−19.5000	−	33.7750i	−0.760767	−	1.31769i
$658$		0			0
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$		0			0
$661$	38.0000			1.47803			0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000			1.47803			0.739014	+	0.673690i	$0.235292\pi$
$662$		0			0
$663$		−	5.19615i		−	0.201802i
$664$		0			0
$665$	10.0000	−	8.66025i	0.387783	−	0.335830i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$		0			0
$669$	−19.5000	+	11.2583i	−0.753914	+	0.435272i
$670$		0			0
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$		0			0
$675$	18.0000	+	10.3923i	0.692820	+	0.400000i
$676$		0			0
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$		0			0
$679$	42.5000	+	14.7224i	1.63100	+	0.564995i
$680$		0			0
$681$	−22.5000	−	12.9904i	−0.862202	−	0.497792i
$682$		0			0
$683$	−15.5000	−	26.8468i	−0.593091	−	1.02726i	−0.993813	−	0.111064i	$-0.964574\pi$
$683$	−15.5000	−	26.8468i	−0.593091	−	1.02726i	0.400722	−	0.916200i	$-0.368759\pi$
$684$		0			0
$685$	11.0000			0.420288
$686$		0			0
$687$	−31.5000	+	18.1865i	−1.20180	+	0.693860i
$688$		0			0
$689$	9.00000			0.342873
$690$		0			0
$691$	−12.0000			−0.456502			−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000			−0.456502			−0.228251	+	0.973602i	$0.573301\pi$
$692$		0			0
$693$	4.50000	+	23.3827i	0.170941	+	0.888235i
$694$		0			0
$695$	5.00000			0.189661
$696$		0			0
$697$	21.0000			0.795432
$698$		0			0
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$		0			0
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$		0			0
$703$	−12.5000	−	21.6506i	−0.471446	−	0.816569i
$704$		0			0
$705$	−12.0000	+	6.92820i	−0.451946	+	0.260931i
$706$		0			0
$707$	−3.50000	−	18.1865i	−0.131631	−	0.683975i
$708$		0			0
$709$	−18.0000			−0.676004			−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000			−0.676004			−0.338002	+	0.941145i	$0.609751\pi$
$710$		0			0
$711$	−24.0000			−0.900070
$712$		0			0
$713$	−2.00000	−	3.46410i	−0.0749006	−	0.129732i
$714$		0			0
$715$	1.50000	−	2.59808i	0.0560968	−	0.0971625i
$716$		0			0
$717$	−13.5000	−	7.79423i	−0.504167	−	0.291081i
$718$		0			0
$719$	−9.50000	+	16.4545i	−0.354290	+	0.613649i	−0.986996	−	0.160743i	$-0.948611\pi$
$719$	−9.50000	+	16.4545i	−0.354290	+	0.613649i	0.632706	+	0.774392i	$0.281944\pi$
$720$		0			0
$721$	−22.5000	−	7.79423i	−0.837944	−	0.290272i
$722$		0			0
$723$	−1.50000	−	0.866025i	−0.0557856	−	0.0322078i
$724$		0			0
$725$	−36.0000			−1.33701
$726$		0			0
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	0.664243	−	0.747517i	$-0.268754\pi$
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	−0.979490	+	0.201492i	$0.935421\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−4.50000	+	7.79423i	−0.166439	+	0.288280i
$732$		0			0
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	0.923396	+	0.383849i	$0.125402\pi$
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	−0.129275	+	0.991609i	$0.541265\pi$
$734$		0			0
$735$	4.50000	+	11.2583i	0.165985	+	0.415270i
$736$		0			0
$737$	18.0000	−	31.1769i	0.663039	−	1.14842i
$738$		0			0
$739$	8.50000	+	14.7224i	0.312678	+	0.541573i	0.978941	−	0.204143i	$-0.0654407\pi$
$739$	8.50000	+	14.7224i	0.312678	+	0.541573i	−0.666264	+	0.745716i	$0.732107\pi$
$740$		0			0
$741$	−7.50000	+	4.33013i	−0.275519	+	0.159071i
$742$		0			0
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	−0.856708	−	0.515802i	$-0.827494\pi$
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	0.875051	+	0.484030i	$0.160828\pi$
$744$		0			0
$745$	7.50000	−	12.9904i	0.274779	−	0.475931i
$746$		0			0
$747$	−19.5000	−	33.7750i	−0.713468	−	1.23576i
$748$		0			0
$749$	−3.50000	−	18.1865i	−0.127887	−	0.664521i
$750$		0			0
$751$	7.50000	+	12.9904i	0.273679	+	0.474026i	0.969801	−	0.243898i	$-0.0784261\pi$
$751$	7.50000	+	12.9904i	0.273679	+	0.474026i	−0.696122	+	0.717923i	$0.745093\pi$
$752$		0			0
$753$		−	6.92820i		−	0.252478i
$754$		0			0
$755$	−17.0000			−0.618693
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$			5.19615i			0.188608i
$760$		0			0
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	0.908879	+	0.417061i	$0.136940\pi$
$761$	22.5000	+	38.9711i	0.815624	+	1.41270i	−0.0932544	+	0.995642i	$0.529727\pi$
$762$		0			0
$763$	−12.5000	−	4.33013i	−0.452530	−	0.156761i
$764$		0			0
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$		0			0
$767$	2.00000	−	3.46410i	0.0722158	−	0.125081i
$768$		0			0
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	−0.213585	−	0.976924i	$-0.568514\pi$
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	0.952834	−	0.303492i	$-0.0981526\pi$
$770$		0			0
$771$	25.5000	−	14.7224i	0.918360	−	0.530215i
$772$		0			0
$773$	3.50000	+	6.06218i	0.125886	+	0.218041i	0.922079	−	0.387002i	$-0.126489\pi$
$773$	3.50000	+	6.06218i	0.125886	+	0.218041i	−0.796193	+	0.605043i	$0.793156\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$		0			0
$777$	22.5000	−	4.33013i	0.807183	−	0.155342i
$778$		0			0
$779$	−17.5000	−	30.3109i	−0.627003	−	1.08600i
$780$		0			0
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$		0			0
$783$	40.5000	−	23.3827i	1.44735	−	0.835629i
$784$		0			0
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$		0			0
$787$	20.0000			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$788$		0			0
$789$	16.5000	+	9.52628i	0.587416	+	0.339145i
$790$		0			0
$791$	−0.500000	−	2.59808i	−0.0177780	−	0.0923770i
$792$		0			0
$793$	−1.00000	+	1.73205i	−0.0355110	+	0.0615069i
$794$		0			0
$795$	13.5000	+	7.79423i	0.478796	+	0.276433i
$796$		0			0
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	−0.280875	−	0.959744i	$-0.590625\pi$
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	0.971601	−	0.236627i	$-0.0760420\pi$
$798$		0			0
$799$	−12.0000	−	20.7846i	−0.424529	−	0.735307i
$800$		0			0
$801$	−13.5000	+	23.3827i	−0.476999	+	0.826187i
$802$		0			0
$803$	39.0000			1.37628
$804$		0			0
$805$	0.500000	+	2.59808i	0.0176227	+	0.0915702i
$806$		0			0
$807$	10.5000	−	6.06218i	0.369618	−	0.213399i
$808$		0			0
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.704564	−	0.709640i	$-0.748858\pi$
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.262284	−	0.964991i	$-0.584476\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	46.5000	+	26.8468i	1.63083	+	0.941558i
$814$		0			0
$815$	17.0000			0.595484
$816$		0			0
$817$	15.0000			0.524784
$818$		0			0
$819$	−1.50000	−	7.79423i	−0.0524142	−	0.272352i
$820$		0			0
$821$	42.0000			1.46581			0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000			1.46581			0.732905	+	0.680331i	$0.238164\pi$
$822$		0			0
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$		0			0
$825$	−18.0000	+	10.3923i	−0.626680	+	0.361814i
$826$		0			0
$827$	−40.0000			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$827$	−40.0000			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$828$		0			0
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	0.819340	−	0.573307i	$-0.194340\pi$
$829$	−2.50000	−	4.33013i	−0.0868286	−	0.150392i	−0.906169	+	0.422916i	$0.861007\pi$
$830$		0			0
$831$	−28.5000	−	16.4545i	−0.988654	−	0.570800i
$832$		0			0
$833$	−19.5000	+	7.79423i	−0.675635	+	0.270054i
$834$		0			0
$835$	−1.00000			−0.0346064
$836$		0			0
$837$			20.7846i			0.718421i
$838$		0			0
$839$	−22.5000	−	38.9711i	−0.776786	−	1.34543i	−0.933785	−	0.357834i	$-0.883515\pi$
$839$	−22.5000	−	38.9711i	−0.776786	−	1.34543i	0.156999	−	0.987599i	$-0.449818\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	−40.5000	+	23.3827i	−1.39489	+	0.805342i
$844$		0			0
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$		0			0
$849$			41.5692i			1.42665i
$850$		0			0
$851$	5.00000			0.171398
$852$		0			0
$853$	−14.5000	−	25.1147i	−0.496471	−	0.859912i	0.503521	−	0.863983i	$-0.332038\pi$
$853$	−14.5000	−	25.1147i	−0.496471	−	0.859912i	−0.999992	+	0.00407068i	$0.998704\pi$
$854$		0			0
$855$	−15.0000			−0.512989
$856$		0			0
$857$	−3.50000	+	6.06218i	−0.119558	+	0.207080i	−0.919592	−	0.392874i	$-0.871481\pi$
$857$	−3.50000	+	6.06218i	−0.119558	+	0.207080i	0.800035	+	0.599954i	$0.204814\pi$
$858$		0			0
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	0.657201	−	0.753715i	$-0.271740\pi$
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	−0.981337	+	0.192295i	$0.938407\pi$
$860$		0			0
$861$	31.5000	−	6.06218i	1.07352	−	0.206598i
$862$		0			0
$863$	−5.50000	+	9.52628i	−0.187222	+	0.324278i	−0.944323	−	0.329020i	$-0.893282\pi$
$863$	−5.50000	+	9.52628i	−0.187222	+	0.324278i	0.757101	+	0.653298i	$0.226615\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$		0			0
$873$	−25.5000	−	44.1673i	−0.863044	−	1.49484i
$874$		0			0
$875$	−18.0000	+	15.5885i	−0.608511	+	0.526986i
$876$		0			0
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	0.992225	−	0.124459i	$-0.0397196\pi$
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	−0.603897	+	0.797062i	$0.706386\pi$
$878$		0			0
$879$	1.50000	+	0.866025i	0.0505937	+	0.0292103i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$		0			0
$885$	6.00000	−	3.46410i	0.201688	−	0.116445i
$886$		0			0
$887$	13.5000	+	23.3827i	0.453286	+	0.785114i	0.998588	−	0.0531258i	$-0.0169184\pi$
$887$	13.5000	+	23.3827i	0.453286	+	0.785114i	−0.545302	+	0.838240i	$0.683585\pi$
$888$		0			0
$889$	16.0000	−	13.8564i	0.536623	−	0.464729i
$890$		0			0
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$		0			0
$893$	−20.0000	+	34.6410i	−0.669274	+	1.15922i
$894$		0			0
$895$	10.5000	−	18.1865i	0.350976	−	0.607909i
$896$		0			0
$897$		−	1.73205i		−	0.0578315i
$898$		0			0
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$		0			0
$901$	−13.5000	+	23.3827i	−0.449750	+	0.778990i
$902$		0			0
$903$	−4.50000	+	12.9904i	−0.149751	+	0.432293i
$904$		0			0
$905$	9.00000	+	15.5885i	0.299170	+	0.518178i
$906$		0			0
$907$	3.50000	−	6.06218i	0.116216	−	0.201291i	−0.802049	−	0.597258i	$-0.796257\pi$
$907$	3.50000	−	6.06218i	0.116216	−	0.201291i	0.918265	+	0.395966i	$0.129590\pi$
$908$		0			0
$909$	−10.5000	+	18.1865i	−0.348263	+	0.603209i
$910$		0			0
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	0.998208	−	0.0598468i	$-0.0190612\pi$
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	−0.550933	+	0.834550i	$0.685728\pi$
$912$		0			0
$913$	39.0000			1.29071
$914$		0			0
$915$	−3.00000	+	1.73205i	−0.0991769	+	0.0572598i
$916$		0			0
$917$	−7.50000	−	2.59808i	−0.247672	−	0.0857960i
$918$		0			0
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	−0.738676	−	0.674060i	$-0.764549\pi$
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	0.953092	+	0.302682i	$0.0978821\pi$
$920$		0			0
$921$			6.92820i			0.228292i
$922$		0			0
$923$	−4.00000	+	6.92820i	−0.131662	+	0.228045i
$924$		0			0
$925$	10.0000	+	17.3205i	0.328798	+	0.569495i
$926$		0			0
$927$	13.5000	+	23.3827i	0.443398	+	0.767988i
$928$		0			0
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$		0			0
$931$	27.5000	+	21.6506i	0.901276	+	0.709571i
$932$		0			0
$933$		−	41.5692i		−	1.36092i
$934$		0			0
$935$	4.50000	+	7.79423i	0.147166	+	0.254899i
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		−	10.3923i		−	0.339140i
$940$		0			0
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$		0			0
$943$	7.00000			0.227951
$944$		0			0
$945$	4.50000	−	12.9904i	0.146385	−	0.422577i
$946$		0			0
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$		0			0
$949$	−13.0000			−0.421998
$950$		0			0
$951$		−	24.2487i		−	0.786318i
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$		0			0
$957$			46.7654i			1.51171i
$958$		0			0
$959$	5.50000	+	28.5788i	0.177604	+	0.922859i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−10.5000	+	18.1865i	−0.338358	+	0.586053i
$964$		0			0
$965$	9.00000	+	15.5885i	0.289720	+	0.501810i
$966$		0			0
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	−0.997224	−	0.0744567i	$-0.976278\pi$
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	0.563094	+	0.826393i	$0.309611\pi$
$968$		0			0
$969$		−	25.9808i		−	0.834622i
$970$		0			0
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	−0.281880	−	0.959450i	$-0.590958\pi$
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	0.971848	−	0.235610i	$-0.0757087\pi$
$972$		0			0
$973$	2.50000	+	12.9904i	0.0801463	+	0.416452i
$974$		0			0
$975$	6.00000	−	3.46410i	0.192154	−	0.110940i
$976$		0			0
$977$	22.0000			0.703842			0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000			0.703842			0.351921	+	0.936030i	$0.385529\pi$
$978$		0			0
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$		0			0
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$		0			0
$983$	20.5000	−	35.5070i	0.653848	−	1.13250i	−0.328333	−	0.944562i	$-0.606487\pi$
$983$	20.5000	−	35.5070i	0.653848	−	1.13250i	0.982181	−	0.187937i	$-0.0601800\pi$
$984$		0			0
$985$	11.0000	+	19.0526i	0.350489	+	0.607065i
$986$		0			0
$987$	−24.0000	−	27.7128i	−0.763928	−	0.882109i
$988$		0			0
$989$	−1.50000	+	2.59808i	−0.0476972	+	0.0826140i
$990$		0			0
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	0.960211	−	0.279276i	$-0.0900944\pi$
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	−0.721966	+	0.691929i	$0.756761\pi$
$992$		0			0
$993$		−	6.92820i		−	0.219860i
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		0			0
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	−0.950405	−	0.311014i	$-0.899332\pi$
$997$	−6.50000	+	11.2583i	−0.205857	+	0.356555i	0.744548	+	0.667568i	$0.232665\pi$
$998$		0			0
$999$	−22.5000	−	12.9904i	−0.711868	−	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.a.121.1	yes	2
3.2	odd	2		1512.2.q.b.793.1		2
4.3	odd	2		1008.2.q.b.625.1		2
7.4	even	3		504.2.t.a.193.1	yes	2
9.2	odd	6		1512.2.t.a.289.1		2
9.7	even	3		504.2.t.a.457.1	yes	2
12.11	even	2		3024.2.q.d.2305.1		2
21.11	odd	6		1512.2.t.a.361.1		2
28.11	odd	6		1008.2.t.e.193.1		2
36.7	odd	6		1008.2.t.e.961.1		2
36.11	even	6		3024.2.t.c.289.1		2
63.11	odd	6		1512.2.q.b.1369.1		2
63.25	even	3	inner	504.2.q.a.25.1	✓	2
84.11	even	6		3024.2.t.c.1873.1		2
252.11	even	6		3024.2.q.d.2881.1		2
252.151	odd	6		1008.2.q.b.529.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.a.25.1	✓	2	63.25	even	3	inner
504.2.q.a.121.1	yes	2	1.1	even	1	trivial
504.2.t.a.193.1	yes	2	7.4	even	3
504.2.t.a.457.1	yes	2	9.7	even	3
1008.2.q.b.529.1		2	252.151	odd	6
1008.2.q.b.625.1		2	4.3	odd	2
1008.2.t.e.193.1		2	28.11	odd	6
1008.2.t.e.961.1		2	36.7	odd	6
1512.2.q.b.793.1		2	3.2	odd	2
1512.2.q.b.1369.1		2	63.11	odd	6
1512.2.t.a.289.1		2	9.2	odd	6
1512.2.t.a.361.1		2	21.11	odd	6
3024.2.q.d.2305.1		2	12.11	even	2
3024.2.q.d.2881.1		2	252.11	even	6
3024.2.t.c.289.1		2	36.11	even	6
3024.2.t.c.1873.1		2	84.11	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-3.00000 - 3.46410i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.19615i q^{27} +(-4.50000 - 7.79423i) q^{29} +4.00000 q^{31} +(-4.50000 - 2.59808i) q^{33} +(-2.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(1.50000 + 0.866025i) q^{39} +(-3.50000 + 6.06218i) q^{41} +(-1.50000 - 2.59808i) q^{43} +(1.50000 + 2.59808i) q^{45} +8.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(-4.50000 - 7.79423i) q^{53} -3.00000 q^{55} +(7.50000 + 4.33013i) q^{57} -4.00000 q^{59} +2.00000 q^{61} +(-6.00000 + 5.19615i) q^{63} +1.00000 q^{65} +12.0000 q^{67} +(-1.50000 + 0.866025i) q^{69} +8.00000 q^{71} +(6.50000 + 11.2583i) q^{73} +(-6.00000 - 3.46410i) q^{75} +(-1.50000 - 7.79423i) q^{77} +8.00000 q^{79} +9.00000 q^{81} +(6.50000 + 11.2583i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(-13.5000 + 7.79423i) q^{87} +(4.50000 - 7.79423i) q^{89} +(0.500000 + 2.59808i) q^{91} -6.92820i q^{93} +5.00000 q^{95} +(8.50000 + 14.7224i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - q^5 + 4 * q^7 - 6 * q^9	\( 2 q - q^{5} + 4 q^{7} - 6 q^{9} + 3 q^{11} - q^{13} - 3 q^{15} - 3 q^{17} - 5 q^{19} - 6 q^{21} - q^{23} + 4 q^{25} - 9 q^{29} + 8 q^{31} - 9 q^{33} - 5 q^{35} - 5 q^{37} + 3 q^{39} - 7 q^{41} - 3 q^{43} + 3 q^{45} + 16 q^{47} + 2 q^{49} - 9 q^{51} - 9 q^{53} - 6 q^{55} + 15 q^{57} - 8 q^{59} + 4 q^{61} - 12 q^{63} + 2 q^{65} + 24 q^{67} - 3 q^{69} + 16 q^{71} + 13 q^{73} - 12 q^{75} - 3 q^{77} + 16 q^{79} + 18 q^{81} + 13 q^{83} - 3 q^{85} - 27 q^{87} + 9 q^{89} + q^{91} + 10 q^{95} + 17 q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q - q^5 + 4 * q^7 - 6 * q^9 + 3 * q^11 - q^13 - 3 * q^15 - 3 * q^17 - 5 * q^19 - 6 * q^21 - q^23 + 4 * q^25 - 9 * q^29 + 8 * q^31 - 9 * q^33 - 5 * q^35 - 5 * q^37 + 3 * q^39 - 7 * q^41 - 3 * q^43 + 3 * q^45 + 16 * q^47 + 2 * q^49 - 9 * q^51 - 9 * q^53 - 6 * q^55 + 15 * q^57 - 8 * q^59 + 4 * q^61 - 12 * q^63 + 2 * q^65 + 24 * q^67 - 3 * q^69 + 16 * q^71 + 13 * q^73 - 12 * q^75 - 3 * q^77 + 16 * q^79 + 18 * q^81 + 13 * q^83 - 3 * q^85 - 27 * q^87 + 9 * q^89 + q^91 + 10 * q^95 + 17 * q^97 - 9 * q^99

Introduction

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