LMFDB - Embedded newform 804.2.i.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.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:	$6.41997232251$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	804.37
Dual form			804.2.i.a.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{13} +2.00000 q^{15} +(-2.50000 - 4.33013i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{21} +(-4.50000 - 7.79423i) q^{23} -1.00000 q^{25} -1.00000 q^{27} +(-4.50000 + 7.79423i) q^{29} +(-4.50000 + 7.79423i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-3.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{41} -4.00000 q^{43} -2.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(2.50000 + 4.33013i) q^{51} -6.00000 q^{53} +(3.00000 - 5.19615i) q^{55} +(-2.50000 - 4.33013i) q^{57} -12.0000 q^{59} +(-7.50000 - 12.9904i) q^{61} +(1.50000 - 2.59808i) q^{63} +(-1.00000 - 1.73205i) q^{65} +(8.00000 - 1.73205i) q^{67} +(4.50000 + 7.79423i) q^{69} +(-3.50000 + 6.06218i) q^{71} +(-5.50000 - 9.52628i) q^{73} +1.00000 q^{75} +(4.50000 + 7.79423i) q^{77} +(-4.50000 + 7.79423i) q^{79} +1.00000 q^{81} +(1.50000 + 2.59808i) q^{83} +(5.00000 + 8.66025i) q^{85} +(4.50000 - 7.79423i) q^{87} +10.0000 q^{89} +3.00000 q^{91} +(4.50000 - 7.79423i) q^{93} +(-5.00000 - 8.66025i) q^{95} +(-1.50000 - 2.59808i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{5} + 3 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^5 + 3 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} - 4 q^{5} + 3 q^{7} + 2 q^{9} - 3 q^{11} + q^{13} + 4 q^{15} - 5 q^{17} + 5 q^{19} - 3 q^{21} - 9 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{29} - 9 q^{31} + 3 q^{33} - 6 q^{35} - 3 q^{37} - q^{39} + 3 q^{41} - 8 q^{43} - 4 q^{45} - 7 q^{47} - 2 q^{49} + 5 q^{51} - 12 q^{53} + 6 q^{55} - 5 q^{57} - 24 q^{59} - 15 q^{61} + 3 q^{63} - 2 q^{65} + 16 q^{67} + 9 q^{69} - 7 q^{71} - 11 q^{73} + 2 q^{75} + 9 q^{77} - 9 q^{79} + 2 q^{81} + 3 q^{83} + 10 q^{85} + 9 q^{87} + 20 q^{89} + 6 q^{91} + 9 q^{93} - 10 q^{95} - 3 q^{97} - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^5 + 3 * q^7 + 2 * q^9 - 3 * q^11 + q^13 + 4 * q^15 - 5 * q^17 + 5 * q^19 - 3 * q^21 - 9 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^29 - 9 * q^31 + 3 * q^33 - 6 * q^35 - 3 * q^37 - q^39 + 3 * q^41 - 8 * q^43 - 4 * q^45 - 7 * q^47 - 2 * q^49 + 5 * q^51 - 12 * q^53 + 6 * q^55 - 5 * q^57 - 24 * q^59 - 15 * q^61 + 3 * q^63 - 2 * q^65 + 16 * q^67 + 9 * q^69 - 7 * q^71 - 11 * q^73 + 2 * q^75 + 9 * q^77 - 9 * q^79 + 2 * q^81 + 3 * q^83 + 10 * q^85 + 9 * q^87 + 20 * q^89 + 6 * q^91 + 9 * q^93 - 10 * q^95 - 3 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$	−1.50000	+	2.59808i	−0.327327	+	0.566947i
$22$		0			0
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	0.105869	+	0.994380i	$0.466238\pi$
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	−0.914093	+	0.405505i	$0.867096\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	−3.00000	+	5.19615i	−0.507093	+	0.878310i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	0.489398	+	0.872060i	$0.337217\pi$
$47$	−3.50000	+	6.06218i	−0.510527	+	0.884260i	−0.999926	+	0.0121990i	$0.996117\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	2.50000	+	4.33013i	0.350070	+	0.606339i
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$		0			0
$57$	−2.50000	−	4.33013i	−0.331133	−	0.573539i
$58$		0			0
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	−7.50000	−	12.9904i	−0.960277	−	1.66325i	−0.721803	−	0.692099i	$-0.756686\pi$
$61$	−7.50000	−	12.9904i	−0.960277	−	1.66325i	−0.238474	−	0.971149i	$-0.576647\pi$
$62$		0			0
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$		0			0
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$		0			0
$67$	8.00000	−	1.73205i	0.977356	−	0.211604i
$67$	8.00000	−	1.73205i	0.977356	−	0.211604i
$68$		0			0
$69$	4.50000	+	7.79423i	0.541736	+	0.938315i
$70$		0			0
$71$	−3.50000	+	6.06218i	−0.415374	+	0.719448i	−0.995468	−	0.0951014i	$-0.969682\pi$
$71$	−3.50000	+	6.06218i	−0.415374	+	0.719448i	0.580094	+	0.814550i	$0.303016\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	4.50000	+	7.79423i	0.512823	+	0.888235i
$78$		0			0
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$		0			0
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$		0			0
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	3.00000			0.314485
$92$		0			0
$93$	4.50000	−	7.79423i	0.466628	−	0.808224i
$94$		0			0
$95$	−5.00000	−	8.66025i	−0.512989	−	0.888523i
$96$		0			0
$97$	−1.50000	−	2.59808i	−0.152302	−	0.263795i	0.779771	−	0.626064i	$-0.215335\pi$
$97$	−1.50000	−	2.59808i	−0.152302	−	0.263795i	−0.932073	+	0.362270i	$0.882002\pi$
$98$		0			0
$99$	−1.50000	+	2.59808i	−0.150756	+	0.261116i
$100$		0			0
$101$	−0.500000	+	0.866025i	−0.0497519	+	0.0861727i	−0.889829	−	0.456294i	$-0.849176\pi$
$101$	−0.500000	+	0.866025i	−0.0497519	+	0.0861727i	0.840077	+	0.542467i	$0.182510\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$		0			0
$105$	3.00000	−	5.19615i	0.292770	−	0.507093i
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$		0			0
$111$	1.50000	+	2.59808i	0.142374	+	0.246598i
$112$		0			0
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	−15.0000			−1.37505
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	0.191492	+	0.981494i	$0.438667\pi$
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	−0.945745	+	0.324910i	$0.894666\pi$
$128$		0			0
$129$	4.00000			0.352180
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	15.0000			1.30066
$134$		0			0
$135$	2.00000			0.172133
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	3.50000	−	6.06218i	0.294753	−	0.510527i
$142$		0			0
$143$	−3.00000			−0.250873
$144$		0			0
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$		0			0
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$		0			0
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.162758	−	0.986666i	$-0.552039\pi$
$152$		0			0
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$		0			0
$155$	9.00000	−	15.5885i	0.722897	−	1.25210i
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	−27.0000			−2.12790
$162$		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
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$		0			0
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$		0			0
$173$	−12.5000	−	21.6506i	−0.950357	−	1.64607i	−0.744652	−	0.667453i	$-0.767384\pi$
$173$	−12.5000	−	21.6506i	−0.950357	−	1.64607i	−0.205706	−	0.978614i	$-0.565949\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	16.0000			1.19590			0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000			1.19590			0.597948	+	0.801535i	$0.295983\pi$
$180$		0			0
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$		0			0
$183$	7.50000	+	12.9904i	0.554416	+	0.960277i
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	15.0000			1.09691
$188$		0			0
$189$	−1.50000	+	2.59808i	−0.109109	+	0.188982i
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$	1.00000	+	1.73205i	0.0716115	+	0.124035i
$196$		0			0
$197$	−6.50000	+	11.2583i	−0.463106	+	0.802123i	−0.999114	−	0.0420901i	$-0.986598\pi$
$197$	−6.50000	+	11.2583i	−0.463106	+	0.802123i	0.536008	+	0.844213i	$0.319932\pi$
$198$		0			0
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	−0.999317	−	0.0369532i	$-0.988235\pi$
$199$	−7.50000	−	12.9904i	−0.531661	−	0.920864i	0.467656	−	0.883911i	$-0.345099\pi$
$200$		0			0
$201$	−8.00000	+	1.73205i	−0.564276	+	0.122169i
$202$		0			0
$203$	13.5000	+	23.3827i	0.947514	+	1.64114i
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$		0			0
$209$	−15.0000			−1.03757
$210$		0			0
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	0.978317	−	0.207114i	$-0.0664070\pi$
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	−0.668524	+	0.743690i	$0.733074\pi$
$212$		0			0
$213$	3.50000	−	6.06218i	0.239816	−	0.415374i
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	13.5000	+	23.3827i	0.916440	+	1.58732i
$218$		0			0
$219$	5.50000	+	9.52628i	0.371656	+	0.643726i
$220$		0			0
$221$	2.50000	−	4.33013i	0.168168	−	0.291276i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	−0.958485	−	0.285141i	$-0.907959\pi$
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	0.726182	+	0.687502i	$0.241293\pi$
$228$		0			0
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	0.726900	−	0.686743i	$-0.240960\pi$
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	−4.50000	−	7.79423i	−0.296078	−	0.512823i
$232$		0			0
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	−0.627696	−	0.778459i	$-0.716002\pi$
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	0.988013	+	0.154371i	$0.0493352\pi$
$234$		0			0
$235$	7.00000	−	12.1244i	0.456630	−	0.790906i
$236$		0			0
$237$	4.50000	−	7.79423i	0.292306	−	0.506290i
$238$		0			0
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	−0.296037	−	0.955176i	$-0.595665\pi$
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	0.975226	−	0.221213i	$-0.0710015\pi$
$240$		0			0
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.00000	+	3.46410i	0.127775	+	0.221313i
$246$		0			0
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$		0			0
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$		0			0
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	0.584643	−	0.811290i	$-0.301234\pi$
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	−0.994920	+	0.100671i	$0.967901\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$		0			0
$255$	−5.00000	−	8.66025i	−0.313112	−	0.542326i
$256$		0			0
$257$	−8.50000	+	14.7224i	−0.530215	+	0.918360i	0.469163	+	0.883112i	$0.344556\pi$
$257$	−8.50000	+	14.7224i	−0.530215	+	0.918360i	−0.999379	+	0.0352486i	$0.988778\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$		0			0
$261$	−4.50000	+	7.79423i	−0.278543	+	0.482451i
$262$		0			0
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	−10.0000			−0.611990
$268$		0			0
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$	−3.00000			−0.181568
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	−30.0000			−1.80253			−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−30.0000			−1.80253			−0.901263	+	0.433273i	$0.857359\pi$
$278$		0			0
$279$	−4.50000	+	7.79423i	−0.269408	+	0.466628i
$280$		0			0
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$		0			0
$283$	−20.0000			−1.18888			−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000			−1.18888			−0.594438	+	0.804141i	$0.702626\pi$
$284$		0			0
$285$	5.00000	+	8.66025i	0.296174	+	0.512989i
$286$		0			0
$287$	−4.50000	−	7.79423i	−0.265627	−	0.460079i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	1.50000	+	2.59808i	0.0879316	+	0.152302i
$292$		0			0
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$		0			0
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$		0			0
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$		0			0
$303$	0.500000	−	0.866025i	0.0287242	−	0.0497519i
$304$		0			0
$305$	15.0000	+	25.9808i	0.858898	+	1.48765i
$306$		0			0
$307$	0.500000	+	0.866025i	0.0285365	+	0.0494267i	0.879941	−	0.475083i	$-0.157582\pi$
$307$	0.500000	+	0.866025i	0.0285365	+	0.0494267i	−0.851404	+	0.524510i	$0.824249\pi$
$308$		0			0
$309$	2.50000	−	4.33013i	0.142220	−	0.246332i
$310$		0			0
$311$	−32.0000			−1.81455			−0.907277	−	0.420534i	$-0.861843\pi$
$311$	−32.0000			−1.81455			−0.907277	+	0.420534i	$0.861843\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$	−3.00000	+	5.19615i	−0.169031	+	0.292770i
$316$		0			0
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$		0			0
$319$	−13.5000	−	23.3827i	−0.755855	−	1.30918i
$320$		0			0
$321$	−12.0000			−0.669775
$322$		0			0
$323$	12.5000	−	21.6506i	0.695519	−	1.20467i
$324$		0			0
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$		0			0
$327$	−18.0000			−0.995402
$328$		0			0
$329$	10.5000	+	18.1865i	0.578884	+	1.00266i
$330$		0			0
$331$	−16.5000	+	28.5788i	−0.906922	+	1.57084i	−0.0886058	+	0.996067i	$0.528241\pi$
$331$	−16.5000	+	28.5788i	−0.906922	+	1.57084i	−0.818316	+	0.574768i	$0.805092\pi$
$332$		0			0
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$		0			0
$335$	−16.0000	+	3.46410i	−0.874173	+	0.189264i
$336$		0			0
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	−0.999793	−	0.0203242i	$-0.993530\pi$
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	0.482295	−	0.876009i	$-0.339803\pi$
$338$		0			0
$339$	−1.50000	+	2.59808i	−0.0814688	+	0.141108i
$340$		0			0
$341$	−13.5000	−	23.3827i	−0.731066	−	1.26624i
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	−9.00000	−	15.5885i	−0.484544	−	0.839254i
$346$		0			0
$347$	14.5000	−	25.1147i	0.778401	−	1.34823i	−0.154462	−	0.987999i	$-0.549365\pi$
$347$	14.5000	−	25.1147i	0.778401	−	1.34823i	0.932863	−	0.360231i	$-0.117302\pi$
$348$		0			0
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$		0			0
$351$	−0.500000	−	0.866025i	−0.0266880	−	0.0462250i
$352$		0			0
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$	7.00000	−	12.1244i	0.371521	−	0.643494i
$356$		0			0
$357$	15.0000			0.793884
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$		0			0
$365$	11.0000	+	19.0526i	0.575766	+	0.997257i
$366$		0			0
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.104399	−	0.994535i	$-0.466708\pi$
$367$	17.5000	−	30.3109i	0.913493	−	1.58222i	0.809093	−	0.587680i	$-0.199959\pi$
$368$		0			0
$369$	1.50000	−	2.59808i	0.0780869	−	0.135250i
$370$		0			0
$371$	−9.00000	+	15.5885i	−0.467257	+	0.809312i
$372$		0			0
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	−0.902243	−	0.431228i	$-0.858080\pi$
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	0.824576	+	0.565751i	$0.191414\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	14.5000	+	25.1147i	0.744815	+	1.29006i	0.950281	+	0.311393i	$0.100796\pi$
$379$	14.5000	+	25.1147i	0.744815	+	1.29006i	−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	8.50000	−	14.7224i	0.435468	−	0.754253i
$382$		0			0
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	0.971897	+	0.235408i	$0.0756427\pi$
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	−0.282079	+	0.959391i	$0.591024\pi$
$384$		0			0
$385$	−9.00000	−	15.5885i	−0.458682	−	0.794461i
$386$		0			0
$387$	−4.00000			−0.203331
$388$		0			0
$389$	−2.50000	−	4.33013i	−0.126755	−	0.219546i	0.795663	−	0.605740i	$-0.207123\pi$
$389$	−2.50000	−	4.33013i	−0.126755	−	0.219546i	−0.922418	+	0.386194i	$0.873790\pi$
$390$		0			0
$391$	−22.5000	+	38.9711i	−1.13787	+	1.97086i
$392$		0			0
$393$	4.00000			0.201773
$394$		0			0
$395$	9.00000	−	15.5885i	0.452839	−	0.784340i
$396$		0			0
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$		0			0
$399$	−15.0000			−0.750939
$400$		0			0
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$		0			0
$403$	−9.00000			−0.448322
$404$		0			0
$405$	−2.00000			−0.0993808
$406$		0			0
$407$	9.00000			0.446113
$408$		0			0
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	−0.900725	−	0.434389i	$-0.856964\pi$
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	0.826555	+	0.562856i	$0.190297\pi$
$410$		0			0
$411$	6.00000			0.295958
$412$		0			0
$413$	−18.0000	+	31.1769i	−0.885722	+	1.53412i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$		0			0
$417$	−4.00000			−0.195881
$418$		0			0
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		0			0
$421$	12.5000	+	21.6506i	0.609213	+	1.05519i	0.991370	+	0.131090i	$0.0418478\pi$
$421$	12.5000	+	21.6506i	0.609213	+	1.05519i	−0.382158	+	0.924097i	$0.624819\pi$
$422$		0			0
$423$	−3.50000	+	6.06218i	−0.170176	+	0.294753i
$424$		0			0
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$		0			0
$427$	−45.0000			−2.17770
$428$		0			0
$429$	3.00000			0.144841
$430$		0			0
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$		0			0
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	−0.799681	−	0.600425i	$-0.794998\pi$
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	0.919824	+	0.392332i	$0.128332\pi$
$434$		0			0
$435$	−9.00000	+	15.5885i	−0.431517	+	0.747409i
$436$		0			0
$437$	22.5000	−	38.9711i	1.07632	−	1.86424i
$438$		0			0
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$		0			0
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$		0			0
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$		0			0
$445$	−20.0000			−0.948091
$446$		0			0
$447$	−6.00000			−0.283790
$448$		0			0
$449$	1.50000	−	2.59808i	0.0707894	−	0.122611i	−0.828458	−	0.560051i	$-0.810782\pi$
$449$	1.50000	−	2.59808i	0.0707894	−	0.122611i	0.899247	+	0.437440i	$0.144115\pi$
$450$		0			0
$451$	4.50000	+	7.79423i	0.211897	+	0.367016i
$452$		0			0
$453$	11.5000	+	19.9186i	0.540317	+	0.935857i
$454$		0			0
$455$	−6.00000			−0.281284
$456$		0			0
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$458$		0			0
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$		0			0
$465$	−9.00000	+	15.5885i	−0.417365	+	0.722897i
$466$		0			0
$467$	−0.500000	−	0.866025i	−0.0231372	−	0.0400749i	0.854225	−	0.519904i	$-0.174032\pi$
$467$	−0.500000	−	0.866025i	−0.0231372	−	0.0400749i	−0.877362	+	0.479829i	$0.840699\pi$
$468$		0			0
$469$	7.50000	−	23.3827i	0.346318	−	1.07971i
$470$		0			0
$471$	3.50000	+	6.06218i	0.161271	+	0.279330i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−8.50000	−	14.7224i	−0.388375	−	0.672685i	0.603856	−	0.797093i	$-0.293630\pi$
$479$	−8.50000	−	14.7224i	−0.388375	−	0.672685i	−0.992231	+	0.124408i	$0.960297\pi$
$480$		0			0
$481$	1.50000	−	2.59808i	0.0683941	−	0.118462i
$482$		0			0
$483$	27.0000			1.22854
$484$		0			0
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$		0			0
$489$	8.50000	−	14.7224i	0.384383	−	0.665771i
$490$		0			0
$491$	−40.0000			−1.80517			−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000			−1.80517			−0.902587	+	0.430507i	$0.858335\pi$
$492$		0			0
$493$	45.0000			2.02670
$494$		0			0
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$		0			0
$497$	10.5000	+	18.1865i	0.470989	+	0.815778i
$498$		0			0
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	0.647882	−	0.761741i	$-0.275655\pi$
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	−0.983628	+	0.180212i	$0.942322\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	20.5000	−	35.5070i	0.914050	−	1.58318i	0.105763	−	0.994391i	$-0.466271\pi$
$503$	20.5000	−	35.5070i	0.914050	−	1.58318i	0.808286	−	0.588789i	$-0.200395\pi$
$504$		0			0
$505$	1.00000	−	1.73205i	0.0444994	−	0.0770752i
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$	−33.0000			−1.45983
$512$		0			0
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$		0			0
$515$	5.00000	−	8.66025i	0.220326	−	0.381616i
$516$		0			0
$517$	−10.5000	−	18.1865i	−0.461789	−	0.799843i
$518$		0			0
$519$	12.5000	+	21.6506i	0.548689	+	0.950357i
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$		0			0
$525$	1.50000	−	2.59808i	0.0654654	−	0.113389i
$526$		0			0
$527$	45.0000			1.96023
$528$		0			0
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$	3.00000			0.129944
$534$		0			0
$535$	−24.0000			−1.03761
$536$		0			0
$537$	−16.0000			−0.690451
$538$		0			0
$539$	6.00000			0.258438
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	−8.50000	+	14.7224i	−0.364770	+	0.631800i
$544$		0			0
$545$	−36.0000			−1.54207
$546$		0			0
$547$	1.50000	−	2.59808i	0.0641354	−	0.111086i	−0.832175	−	0.554513i	$-0.812904\pi$
$547$	1.50000	−	2.59808i	0.0641354	−	0.111086i	0.896310	+	0.443428i	$0.146238\pi$
$548$		0			0
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$		0			0
$551$	−45.0000			−1.91706
$552$		0			0
$553$	13.5000	+	23.3827i	0.574078	+	0.994333i
$554$		0			0
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$		0			0
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$		0			0
$559$	−2.00000	−	3.46410i	−0.0845910	−	0.146516i
$560$		0			0
$561$	−15.0000			−0.633300
$562$		0			0
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$	1.50000	−	2.59808i	0.0629941	−	0.109109i
$568$		0			0
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$		0			0
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$		0			0
$573$	−1.50000	−	2.59808i	−0.0626634	−	0.108536i
$574$		0			0
$575$	4.50000	+	7.79423i	0.187663	+	0.325042i
$576$		0			0
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	−0.698417	−	0.715691i	$-0.746112\pi$
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	0.969015	+	0.247001i	$0.0794451\pi$
$578$		0			0
$579$	−14.0000			−0.581820
$580$		0			0
$581$	9.00000			0.373383
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$		0			0
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$		0			0
$587$	9.50000	+	16.4545i	0.392107	+	0.679149i	0.992727	−	0.120385i	$-0.0384130\pi$
$587$	9.50000	+	16.4545i	0.392107	+	0.679149i	−0.600620	+	0.799534i	$0.705080\pi$
$588$		0			0
$589$	−45.0000			−1.85419
$590$		0			0
$591$	6.50000	−	11.2583i	0.267374	−	0.463106i
$592$		0			0
$593$	7.50000	+	12.9904i	0.307988	+	0.533451i	0.977922	−	0.208970i	$-0.0670110\pi$
$593$	7.50000	+	12.9904i	0.307988	+	0.533451i	−0.669934	+	0.742421i	$0.733678\pi$
$594$		0			0
$595$	30.0000			1.22988
$596$		0			0
$597$	7.50000	+	12.9904i	0.306955	+	0.531661i
$598$		0			0
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	−0.895042	−	0.445983i	$-0.852854\pi$
$599$	−1.50000	+	2.59808i	−0.0612883	+	0.106155i	0.833753	+	0.552137i	$0.186188\pi$
$600$		0			0
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$		0			0
$603$	8.00000	−	1.73205i	0.325785	−	0.0705346i
$604$		0			0
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$		0			0
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	0.405887	+	0.913923i	$0.366962\pi$
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	−0.994424	+	0.105453i	$0.966371\pi$
$608$		0			0
$609$	−13.5000	−	23.3827i	−0.547048	−	0.947514i
$610$		0			0
$611$	−7.00000			−0.283190
$612$		0			0
$613$	8.50000	+	14.7224i	0.343312	+	0.594633i	0.985046	−	0.172294i	$-0.0551179\pi$
$613$	8.50000	+	14.7224i	0.343312	+	0.594633i	−0.641734	+	0.766927i	$0.721785\pi$
$614$		0			0
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	0.996138	−	0.0878015i	$-0.0279841\pi$
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	−0.574107	+	0.818780i	$0.694651\pi$
$620$		0			0
$621$	4.50000	+	7.79423i	0.180579	+	0.312772i
$622$		0			0
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	15.0000			0.599042
$628$		0			0
$629$	−7.50000	+	12.9904i	−0.299045	+	0.517960i
$630$		0			0
$631$	−19.5000	−	33.7750i	−0.776283	−	1.34456i	−0.934071	−	0.357088i	$-0.883770\pi$
$631$	−19.5000	−	33.7750i	−0.776283	−	1.34456i	0.157788	−	0.987473i	$-0.449564\pi$
$632$		0			0
$633$	−4.50000	−	7.79423i	−0.178859	−	0.309793i
$634$		0			0
$635$	17.0000	−	29.4449i	0.674624	−	1.16848i
$636$		0			0
$637$	1.00000	−	1.73205i	0.0396214	−	0.0686264i
$638$		0			0
$639$	−3.50000	+	6.06218i	−0.138458	+	0.239816i
$640$		0			0
$641$	−6.50000	+	11.2583i	−0.256735	+	0.444677i	−0.965365	−	0.260902i	$-0.915980\pi$
$641$	−6.50000	+	11.2583i	−0.256735	+	0.444677i	0.708631	+	0.705580i	$0.249313\pi$
$642$		0			0
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$		0			0
$647$	−6.50000	−	11.2583i	−0.255541	−	0.442611i	0.709501	−	0.704704i	$-0.248920\pi$
$647$	−6.50000	−	11.2583i	−0.255541	−	0.442611i	−0.965042	+	0.262094i	$0.915587\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$		0			0
$651$	−13.5000	−	23.3827i	−0.529107	−	0.916440i
$652$		0			0
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	0.764442	−	0.644692i	$-0.223014\pi$
$653$	−4.50000	−	7.79423i	−0.176099	−	0.305012i	−0.940541	+	0.339680i	$0.889681\pi$
$654$		0			0
$655$	8.00000			0.312586
$656$		0			0
$657$	−5.50000	−	9.52628i	−0.214575	−	0.371656i
$658$		0			0
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	−0.893762	−	0.448542i	$-0.851943\pi$
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	0.835330	+	0.549749i	$0.185277\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$		0			0
$663$	−2.50000	+	4.33013i	−0.0970920	+	0.168168i
$664$		0			0
$665$	−30.0000			−1.16335
$666$		0			0
$667$	81.0000			3.13633
$668$		0			0
$669$	−16.0000			−0.618596
$670$		0			0
$671$	45.0000			1.73721
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−2.50000	+	4.33013i	−0.0960828	+	0.166420i	−0.910060	−	0.414477i	$-0.863965\pi$
$677$	−2.50000	+	4.33013i	−0.0960828	+	0.166420i	0.813977	+	0.580897i	$0.197298\pi$
$678$		0			0
$679$	−9.00000			−0.345388
$680$		0			0
$681$	3.50000	−	6.06218i	0.134120	−	0.232303i
$682$		0			0
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	0.978011	+	0.208555i	$0.0668759\pi$
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	−0.308392	+	0.951259i	$0.599791\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	3.50000	+	6.06218i	0.133533	+	0.231287i
$688$		0			0
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$		0			0
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	−0.962768	−	0.270330i	$-0.912867\pi$
$691$	−6.50000	+	11.2583i	−0.247272	+	0.428287i	0.715496	+	0.698617i	$0.246201\pi$
$692$		0			0
$693$	4.50000	+	7.79423i	0.170941	+	0.296078i
$694$		0			0
$695$	−8.00000			−0.303457
$696$		0			0
$697$	−15.0000			−0.568166
$698$		0			0
$699$	−5.50000	+	9.52628i	−0.208029	+	0.360317i
$700$		0			0
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	−0.688917	−	0.724840i	$-0.741914\pi$
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	0.972188	+	0.234200i	$0.0752470\pi$
$702$		0			0
$703$	7.50000	−	12.9904i	0.282868	−	0.489942i
$704$		0			0
$705$	−7.00000	+	12.1244i	−0.263635	+	0.456630i
$706$		0			0
$707$	1.50000	+	2.59808i	0.0564133	+	0.0977107i
$708$		0			0
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	0.970254	+	0.242089i	$0.0778325\pi$
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	−0.275472	+	0.961309i	$0.588834\pi$
$710$		0			0
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$		0			0
$713$	81.0000			3.03347
$714$		0			0
$715$	6.00000			0.224387
$716$		0			0
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$		0			0
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$		0			0
$721$	7.50000	+	12.9904i	0.279315	+	0.483787i
$722$		0			0
$723$	14.0000			0.520666
$724$		0			0
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$		0			0
$727$	12.5000	+	21.6506i	0.463599	+	0.802978i	0.999137	−	0.0415337i	$-0.0132244\pi$
$727$	12.5000	+	21.6506i	0.463599	+	0.802978i	−0.535538	+	0.844511i	$0.679891\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.0000	+	17.3205i	0.369863	+	0.640622i
$732$		0			0
$733$	12.5000	−	21.6506i	0.461698	−	0.799684i	−0.537348	−	0.843361i	$-0.680574\pi$
$733$	12.5000	−	21.6506i	0.461698	−	0.799684i	0.999046	+	0.0436764i	$0.0139070\pi$
$734$		0			0
$735$	−2.00000	−	3.46410i	−0.0737711	−	0.127775i
$736$		0			0
$737$	−7.50000	+	23.3827i	−0.276266	+	0.861312i
$738$		0			0
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$		0			0
$741$	2.50000	−	4.33013i	0.0918398	−	0.159071i
$742$		0			0
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	0.970173	−	0.242415i	$-0.0779397\pi$
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	−0.695024	+	0.718986i	$0.744606\pi$
$744$		0			0
$745$	−12.0000			−0.439646
$746$		0			0
$747$	1.50000	+	2.59808i	0.0548821	+	0.0950586i
$748$		0			0
$749$	18.0000	−	31.1769i	0.657706	−	1.13918i
$750$		0			0
$751$	24.0000			0.875772			0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000			0.875772			0.437886	+	0.899030i	$0.355727\pi$
$752$		0			0
$753$	6.50000	+	11.2583i	0.236873	+	0.410276i
$754$		0			0
$755$	23.0000	+	39.8372i	0.837056	+	1.44982i
$756$		0			0
$757$	−3.50000	+	6.06218i	−0.127210	+	0.220334i	−0.922595	−	0.385771i	$-0.873935\pi$
$757$	−3.50000	+	6.06218i	−0.127210	+	0.220334i	0.795385	+	0.606105i	$0.207269\pi$
$758$		0			0
$759$	−27.0000			−0.980038
$760$		0			0
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$		0			0
$763$	27.0000	−	46.7654i	0.977466	−	1.69302i
$764$		0			0
$765$	5.00000	+	8.66025i	0.180775	+	0.313112i
$766$		0			0
$767$	−6.00000	−	10.3923i	−0.216647	−	0.375244i
$768$		0			0
$769$	4.50000	−	7.79423i	0.162274	−	0.281067i	−0.773410	−	0.633906i	$-0.781450\pi$
$769$	4.50000	−	7.79423i	0.162274	−	0.281067i	0.935684	+	0.352839i	$0.114784\pi$
$770$		0			0
$771$	8.50000	−	14.7224i	0.306120	−	0.530215i
$772$		0			0
$773$	−8.50000	+	14.7224i	−0.305724	+	0.529529i	−0.977422	−	0.211296i	$-0.932232\pi$
$773$	−8.50000	+	14.7224i	−0.305724	+	0.529529i	0.671698	+	0.740825i	$0.265565\pi$
$774$		0			0
$775$	4.50000	−	7.79423i	0.161645	−	0.279977i
$776$		0			0
$777$	9.00000			0.322873
$778$		0			0
$779$	15.0000			0.537431
$780$		0			0
$781$	−10.5000	−	18.1865i	−0.375720	−	0.650765i
$782$		0			0
$783$	4.50000	−	7.79423i	0.160817	−	0.278543i
$784$		0			0
$785$	7.00000	+	12.1244i	0.249841	+	0.432737i
$786$		0			0
$787$	−15.5000	−	26.8468i	−0.552515	−	0.956985i	−0.998092	−	0.0617409i	$-0.980335\pi$
$787$	−15.5000	−	26.8468i	−0.552515	−	0.956985i	0.445577	−	0.895244i	$-0.352999\pi$
$788$		0			0
$789$	−12.0000			−0.427211
$790$		0			0
$791$	−4.50000	−	7.79423i	−0.160002	−	0.277131i
$792$		0			0
$793$	7.50000	−	12.9904i	0.266333	−	0.461302i
$794$		0			0
$795$	−12.0000			−0.425596
$796$		0			0
$797$	−18.5000	+	32.0429i	−0.655304	+	1.13502i	0.326514	+	0.945192i	$0.394126\pi$
$797$	−18.5000	+	32.0429i	−0.655304	+	1.13502i	−0.981818	+	0.189827i	$0.939207\pi$
$798$		0			0
$799$	35.0000			1.23821
$800$		0			0
$801$	10.0000			0.353333
$802$		0			0
$803$	33.0000			1.16454
$804$		0			0
$805$	54.0000			1.90325
$806$		0			0
$807$	−6.00000			−0.211210
$808$		0			0
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	7.50000	−	12.9904i	0.263361	−	0.456154i	−0.703772	−	0.710426i	$-0.748502\pi$
$811$	7.50000	−	12.9904i	0.263361	−	0.456154i	0.967133	+	0.254272i	$0.0818358\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.0000	−	29.4449i	0.595484	−	1.03141i
$816$		0			0
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$		0			0
$819$	3.00000			0.104828
$820$		0			0
$821$	−6.50000	−	11.2583i	−0.226852	−	0.392918i	0.730022	−	0.683424i	$-0.239510\pi$
$821$	−6.50000	−	11.2583i	−0.226852	−	0.392918i	−0.956873	+	0.290505i	$0.906177\pi$
$822$		0			0
$823$	−15.5000	−	26.8468i	−0.540296	−	0.935820i	−0.998887	−	0.0471726i	$-0.984979\pi$
$823$	−15.5000	−	26.8468i	−0.540296	−	0.935820i	0.458591	−	0.888648i	$-0.348354\pi$
$824$		0			0
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$		0			0
$827$	−4.50000	−	7.79423i	−0.156480	−	0.271032i	0.777117	−	0.629356i	$-0.216681\pi$
$827$	−4.50000	−	7.79423i	−0.156480	−	0.271032i	−0.933597	+	0.358325i	$0.883348\pi$
$828$		0			0
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$		0			0
$831$	30.0000			1.04069
$832$		0			0
$833$	−5.00000	+	8.66025i	−0.173240	+	0.300060i
$834$		0			0
$835$	3.00000	−	5.19615i	0.103819	−	0.179820i
$836$		0			0
$837$	4.50000	−	7.79423i	0.155543	−	0.269408i
$838$		0			0
$839$	22.5000	−	38.9711i	0.776786	−	1.34543i	−0.156999	−	0.987599i	$-0.550182\pi$
$839$	22.5000	−	38.9711i	0.776786	−	1.34543i	0.933785	−	0.357834i	$-0.116485\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$	−7.50000	−	12.9904i	−0.258314	−	0.447412i
$844$		0			0
$845$	−12.0000	+	20.7846i	−0.412813	+	0.715012i
$846$		0			0
$847$	6.00000			0.206162
$848$		0			0
$849$	20.0000			0.686398
$850$		0			0
$851$	−13.5000	+	23.3827i	−0.462774	+	0.801548i
$852$		0			0
$853$	4.50000	+	7.79423i	0.154077	+	0.266869i	0.932723	−	0.360595i	$-0.117426\pi$
$853$	4.50000	+	7.79423i	0.154077	+	0.266869i	−0.778646	+	0.627464i	$0.784093\pi$
$854$		0			0
$855$	−5.00000	−	8.66025i	−0.170996	−	0.296174i
$856$		0			0
$857$	54.0000			1.84460			0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000			1.84460			0.922302	+	0.386469i	$0.126305\pi$
$858$		0			0
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	−0.996559	−	0.0828900i	$-0.973585\pi$
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	0.570064	+	0.821600i	$0.306918\pi$
$860$		0			0
$861$	4.50000	+	7.79423i	0.153360	+	0.265627i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	25.0000	+	43.3013i	0.850026	+	1.47229i
$866$		0			0
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$		0			0
$869$	−13.5000	−	23.3827i	−0.457956	−	0.793203i
$870$		0			0
$871$	5.50000	+	6.06218i	0.186360	+	0.205409i
$872$		0			0
$873$	−1.50000	−	2.59808i	−0.0507673	−	0.0879316i
$874$		0			0
$875$	18.0000	−	31.1769i	0.608511	−	1.05397i
$876$		0			0
$877$	−5.50000	−	9.52628i	−0.185722	−	0.321680i	0.758098	−	0.652141i	$-0.226129\pi$
$877$	−5.50000	−	9.52628i	−0.185722	−	0.321680i	−0.943820	+	0.330461i	$0.892796\pi$
$878$		0			0
$879$	26.0000			0.876958
$880$		0			0
$881$	21.5000	+	37.2391i	0.724353	+	1.25462i	0.959240	+	0.282594i	$0.0911949\pi$
$881$	21.5000	+	37.2391i	0.724353	+	1.25462i	−0.234886	+	0.972023i	$0.575472\pi$
$882$		0			0
$883$	−8.50000	+	14.7224i	−0.286048	+	0.495449i	−0.972863	−	0.231383i	$-0.925675\pi$
$883$	−8.50000	+	14.7224i	−0.286048	+	0.495449i	0.686815	+	0.726832i	$0.259008\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$		0			0
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	−0.997979	−	0.0635387i	$-0.979761\pi$
$887$	−16.5000	−	28.5788i	−0.554016	−	0.959583i	0.443964	−	0.896045i	$-0.353572\pi$
$888$		0			0
$889$	25.5000	+	44.1673i	0.855243	+	1.48132i
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	−35.0000			−1.17123
$894$		0			0
$895$	−32.0000			−1.06964
$896$		0			0
$897$	−4.50000	+	7.79423i	−0.150251	+	0.260242i
$898$		0			0
$899$	−40.5000	−	70.1481i	−1.35075	−	2.33957i
$900$		0			0
$901$	15.0000	+	25.9808i	0.499722	+	0.865545i
$902$		0			0
$903$	6.00000	−	10.3923i	0.199667	−	0.345834i
$904$		0			0
$905$	−17.0000	+	29.4449i	−0.565099	+	0.978780i
$906$		0			0
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	0.376228	+	0.926527i	$0.377221\pi$
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	−0.990510	+	0.137441i	$0.956112\pi$
$908$		0			0
$909$	−0.500000	+	0.866025i	−0.0165840	+	0.0287242i
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	−9.00000			−0.297857
$914$		0			0
$915$	−15.0000	−	25.9808i	−0.495885	−	0.858898i
$916$		0			0
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$		0			0
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	0.930652	−	0.365907i	$-0.119241\pi$
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	−0.782210	+	0.623015i	$0.785908\pi$
$920$		0			0
$921$	−0.500000	−	0.866025i	−0.0164756	−	0.0285365i
$922$		0			0
$923$	−7.00000			−0.230408
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$		0			0
$927$	−2.50000	+	4.33013i	−0.0821108	+	0.142220i
$928$		0			0
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	5.00000	−	8.66025i	0.163868	−	0.283828i
$932$		0			0
$933$	32.0000			1.04763
$934$		0			0
$935$	−30.0000			−0.981105
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$		0			0
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$	−27.0000			−0.879241
$944$		0			0
$945$	3.00000	−	5.19615i	0.0975900	−	0.169031i
$946$		0			0
$947$	−40.0000			−1.29983			−0.649913	−	0.760009i	$-0.725195\pi$
$947$	−40.0000			−1.29983			−0.649913	+	0.760009i	$0.725195\pi$
$948$		0			0
$949$	5.50000	−	9.52628i	0.178538	−	0.309236i
$950$		0			0
$951$	−7.50000	−	12.9904i	−0.243204	−	0.421242i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−3.00000	−	5.19615i	−0.0970777	−	0.168144i
$956$		0			0
$957$	13.5000	+	23.3827i	0.436393	+	0.755855i
$958$		0			0
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$	12.0000			0.386695
$964$		0			0
$965$	−28.0000			−0.901352
$966$		0			0
$967$	−18.5000	+	32.0429i	−0.594920	+	1.03043i	0.398638	+	0.917108i	$0.369483\pi$
$967$	−18.5000	+	32.0429i	−0.594920	+	1.03043i	−0.993558	+	0.113323i	$0.963850\pi$
$968$		0			0
$969$	−12.5000	+	21.6506i	−0.401558	+	0.695519i
$970$		0			0
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	−0.916705	−	0.399564i	$-0.869162\pi$
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	0.804385	+	0.594108i	$0.202495\pi$
$972$		0			0
$973$	6.00000	−	10.3923i	0.192351	−	0.333162i
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$		0			0
$979$	−15.0000	+	25.9808i	−0.479402	+	0.830349i
$980$		0			0
$981$	18.0000			0.574696
$982$		0			0
$983$	−48.0000			−1.53096			−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000			−1.53096			−0.765481	+	0.643458i	$0.777499\pi$
$984$		0			0
$985$	13.0000	−	22.5167i	0.414214	−	0.717440i
$986$		0			0
$987$	−10.5000	−	18.1865i	−0.334219	−	0.578884i
$988$		0			0
$989$	18.0000	+	31.1769i	0.572367	+	0.991368i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	16.5000	−	28.5788i	0.523612	−	0.906922i
$994$		0			0
$995$	15.0000	+	25.9808i	0.475532	+	0.823646i
$996$		0			0
$997$	−6.00000			−0.190022			−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000			−0.190022			−0.0950110	+	0.995476i	$0.530289\pi$
$998$		0			0
$999$	1.50000	+	2.59808i	0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.a.37.1	✓	2
3.2	odd	2		2412.2.l.d.37.1		2
67.29	even	3	inner	804.2.i.a.565.1	yes	2
201.29	odd	6		2412.2.l.d.1369.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.a.37.1	✓	2	1.1	even	1	trivial
804.2.i.a.565.1	yes	2	67.29	even	3	inner
2412.2.l.d.37.1		2	3.2	odd	2
2412.2.l.d.1369.1		2	201.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{13} +2.00000 q^{15} +(-2.50000 - 4.33013i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{21} +(-4.50000 - 7.79423i) q^{23} -1.00000 q^{25} -1.00000 q^{27} +(-4.50000 + 7.79423i) q^{29} +(-4.50000 + 7.79423i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-3.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{41} -4.00000 q^{43} -2.00000 q^{45} +(-3.50000 + 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(2.50000 + 4.33013i) q^{51} -6.00000 q^{53} +(3.00000 - 5.19615i) q^{55} +(-2.50000 - 4.33013i) q^{57} -12.0000 q^{59} +(-7.50000 - 12.9904i) q^{61} +(1.50000 - 2.59808i) q^{63} +(-1.00000 - 1.73205i) q^{65} +(8.00000 - 1.73205i) q^{67} +(4.50000 + 7.79423i) q^{69} +(-3.50000 + 6.06218i) q^{71} +(-5.50000 - 9.52628i) q^{73} +1.00000 q^{75} +(4.50000 + 7.79423i) q^{77} +(-4.50000 + 7.79423i) q^{79} +1.00000 q^{81} +(1.50000 + 2.59808i) q^{83} +(5.00000 + 8.66025i) q^{85} +(4.50000 - 7.79423i) q^{87} +10.0000 q^{89} +3.00000 q^{91} +(4.50000 - 7.79423i) q^{93} +(-5.00000 - 8.66025i) q^{95} +(-1.50000 - 2.59808i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{5} + 3 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^5 + 3 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} - 4 q^{5} + 3 q^{7} + 2 q^{9} - 3 q^{11} + q^{13} + 4 q^{15} - 5 q^{17} + 5 q^{19} - 3 q^{21} - 9 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{29} - 9 q^{31} + 3 q^{33} - 6 q^{35} - 3 q^{37} - q^{39} + 3 q^{41} - 8 q^{43} - 4 q^{45} - 7 q^{47} - 2 q^{49} + 5 q^{51} - 12 q^{53} + 6 q^{55} - 5 q^{57} - 24 q^{59} - 15 q^{61} + 3 q^{63} - 2 q^{65} + 16 q^{67} + 9 q^{69} - 7 q^{71} - 11 q^{73} + 2 q^{75} + 9 q^{77} - 9 q^{79} + 2 q^{81} + 3 q^{83} + 10 q^{85} + 9 q^{87} + 20 q^{89} + 6 q^{91} + 9 q^{93} - 10 q^{95} - 3 q^{97} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^5 + 3 * q^7 + 2 * q^9 - 3 * q^11 + q^13 + 4 * q^15 - 5 * q^17 + 5 * q^19 - 3 * q^21 - 9 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^29 - 9 * q^31 + 3 * q^33 - 6 * q^35 - 3 * q^37 - q^39 + 3 * q^41 - 8 * q^43 - 4 * q^45 - 7 * q^47 - 2 * q^49 + 5 * q^51 - 12 * q^53 + 6 * q^55 - 5 * q^57 - 24 * q^59 - 15 * q^61 + 3 * q^63 - 2 * q^65 + 16 * q^67 + 9 * q^69 - 7 * q^71 - 11 * q^73 + 2 * q^75 + 9 * q^77 - 9 * q^79 + 2 * q^81 + 3 * q^83 + 10 * q^85 + 9 * q^87 + 20 * q^89 + 6 * q^91 + 9 * q^93 - 10 * q^95 - 3 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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