LMFDB - Embedded newform 52.2.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(9,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("52.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.e (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:	$0.415222090511$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	52.9
Dual form			52.2.e.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{19} +3.00000 q^{21} +(0.500000 - 0.866025i) q^{23} -1.00000 q^{25} +9.00000 q^{27} +(0.500000 - 0.866025i) q^{29} -8.00000 q^{31} +(7.50000 + 12.9904i) q^{33} +(-1.00000 - 1.73205i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-7.50000 - 7.79423i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-6.00000 - 10.3923i) q^{45} +4.00000 q^{47} +(3.00000 - 5.19615i) q^{49} +9.00000 q^{51} -6.00000 q^{53} +(5.00000 - 8.66025i) q^{55} -9.00000 q^{57} +(-2.50000 - 4.33013i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-3.00000 + 5.19615i) q^{63} +(-2.00000 + 6.92820i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(5.50000 + 9.52628i) q^{71} +14.0000 q^{73} +(1.50000 - 2.59808i) q^{75} -5.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(1.50000 + 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{89} +(3.50000 - 0.866025i) q^{91} +(12.0000 - 20.7846i) q^{93} +(3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 4 q^{5} - q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 4 * q^5 - q^7 - 6 * q^9	$ 2 q - 3 q^{3} + 4 q^{5} - q^{7} - 6 q^{9} + 5 q^{11} - 2 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} + 6 q^{21} + q^{23} - 2 q^{25} + 18 q^{27} + q^{29} - 16 q^{31} + 15 q^{33} - 2 q^{35} - 3 q^{37} - 15 q^{39} - 3 q^{41} - q^{43} - 12 q^{45} + 8 q^{47} + 6 q^{49} + 18 q^{51} - 12 q^{53} + 10 q^{55} - 18 q^{57} - 5 q^{59} + 5 q^{61} - 6 q^{63} - 4 q^{65} - 7 q^{67} + 3 q^{69} + 11 q^{71} + 28 q^{73} + 3 q^{75} - 10 q^{77} - 8 q^{79} - 9 q^{81} + 24 q^{83} - 6 q^{85} + 3 q^{87} + 9 q^{89} + 7 q^{91} + 24 q^{93} + 6 q^{95} + q^{97} - 60 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 4 * q^5 - q^7 - 6 * q^9 + 5 * q^11 - 2 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 + 6 * q^21 + q^23 - 2 * q^25 + 18 * q^27 + q^29 - 16 * q^31 + 15 * q^33 - 2 * q^35 - 3 * q^37 - 15 * q^39 - 3 * q^41 - q^43 - 12 * q^45 + 8 * q^47 + 6 * q^49 + 18 * q^51 - 12 * q^53 + 10 * q^55 - 18 * q^57 - 5 * q^59 + 5 * q^61 - 6 * q^63 - 4 * q^65 - 7 * q^67 + 3 * q^69 + 11 * q^71 + 28 * q^73 + 3 * q^75 - 10 * q^77 - 8 * q^79 - 9 * q^81 + 24 * q^83 - 6 * q^85 + 3 * q^87 + 9 * q^89 + 7 * q^91 + 24 * q^93 + 6 * q^95 + q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$		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
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		0			0
$33$	7.50000	+	12.9904i	1.30558	+	2.26134i
$34$		0			0
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$		0			0
$39$	−7.50000	−	7.79423i	−1.20096	−	1.24808i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$	−6.00000	−	10.3923i	−0.894427	−	1.54919i
$46$		0			0
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	9.00000			1.26025
$52$		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
$55$	5.00000	−	8.66025i	0.674200	−	1.16775i
$56$		0			0
$57$	−9.00000			−1.19208
$58$		0			0
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	0.656136	−	0.754643i	$-0.272190\pi$
$59$	−2.50000	−	4.33013i	−0.325472	−	0.563735i	−0.981608	+	0.190909i	$0.938857\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	−3.00000	+	5.19615i	−0.377964	+	0.654654i
$64$		0			0
$65$	−2.00000	+	6.92820i	−0.248069	+	0.859338i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	5.50000	+	9.52628i	0.652730	+	1.13056i	0.982458	+	0.186485i	$0.0597097\pi$
$71$	5.50000	+	9.52628i	0.652730	+	1.13056i	−0.329728	+	0.944076i	$0.606957\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$		0			0
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$		0			0
$77$	−5.00000			−0.569803
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$		0			0
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$		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
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$		0			0
$93$	12.0000	−	20.7846i	1.24434	−	2.15526i
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$		0			0
$101$	−9.50000	+	16.4545i	−0.945285	+	1.63728i	−0.190106	+	0.981763i	$0.560883\pi$
$101$	−9.50000	+	16.4545i	−0.945285	+	1.63728i	−0.755179	+	0.655519i	$0.772450\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	6.00000			0.585540
$106$		0			0
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	0.467610	+	0.883935i	$0.345115\pi$
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	−0.999315	+	0.0370053i	$0.988218\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−4.50000	−	7.79423i	−0.427121	−	0.739795i
$112$		0			0
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	−0.999796	−	0.0202056i	$-0.993568\pi$
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	0.482399	−	0.875951i	$-0.339765\pi$
$114$		0			0
$115$	1.00000	−	1.73205i	0.0932505	−	0.161515i
$116$		0			0
$117$	21.0000	−	5.19615i	1.94145	−	0.480384i
$118$		0			0
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	−0.733527	−	0.679660i	$-0.762127\pi$
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	0.955366	+	0.295423i	$0.0954607\pi$
$128$		0			0
$129$	3.00000			0.264135
$130$		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
$133$	1.50000	−	2.59808i	0.130066	−	0.225282i
$134$		0			0
$135$	18.0000			1.54919
$136$		0			0
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$		0			0
$139$	5.50000	+	9.52628i	0.466504	+	0.808008i	0.999268	−	0.0382553i	$-0.0121800\pi$
$139$	5.50000	+	9.52628i	0.466504	+	0.808008i	−0.532764	+	0.846264i	$0.678847\pi$
$140$		0			0
$141$	−6.00000	+	10.3923i	−0.505291	+	0.875190i
$142$		0			0
$143$	12.5000	+	12.9904i	1.04530	+	1.08631i
$144$		0			0
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$		0			0
$147$	9.00000	+	15.5885i	0.742307	+	1.28571i
$148$		0			0
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	0.871742	+	0.489966i	$0.162991\pi$
$149$	10.5000	+	18.1865i	0.860194	+	1.48990i	−0.0115483	+	0.999933i	$0.503676\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−9.00000	+	15.5885i	−0.727607	+	1.26025i
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	3.50000	+	6.06218i	0.274141	+	0.474826i	0.969918	−	0.243432i	$-0.0782731\pi$
$163$	3.50000	+	6.06218i	0.274141	+	0.474826i	−0.695777	+	0.718258i	$0.744940\pi$
$164$		0			0
$165$	15.0000	+	25.9808i	1.16775	+	2.02260i
$166$		0			0
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	9.00000	−	15.5885i	0.688247	−	1.19208i
$172$		0			0
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	0.577597	−	0.816322i	$-0.303991\pi$
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	−0.995754	+	0.0920525i	$0.970657\pi$
$174$		0			0
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$		0			0
$177$	15.0000			1.12747
$178$		0			0
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$		0			0
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	−15.0000			−1.09691
$188$		0			0
$189$	−4.50000	−	7.79423i	−0.327327	−	0.566947i
$190$		0			0
$191$	−0.500000	−	0.866025i	−0.0361787	−	0.0626634i	0.847369	−	0.531004i	$-0.178185\pi$
$191$	−0.500000	−	0.866025i	−0.0361787	−	0.0626634i	−0.883548	+	0.468341i	$0.844852\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		0			0
$195$	−15.0000	−	15.5885i	−1.07417	−	1.11631i
$196$		0			0
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	−0.660003	−	0.751263i	$-0.729445\pi$
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	0.980614	+	0.195947i	$0.0627782\pi$
$198$		0			0
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	0.976923	+	0.213591i	$0.0685161\pi$
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	−0.303486	+	0.952836i	$0.598151\pi$
$200$		0			0
$201$	−10.5000	−	18.1865i	−0.740613	−	1.28278i
$202$		0			0
$203$	−1.00000			−0.0701862
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	−6.00000			−0.417029
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	−33.0000			−2.26112
$214$		0			0
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	4.00000	+	6.92820i	0.271538	+	0.470317i
$218$		0			0
$219$	−21.0000	+	36.3731i	−1.41905	+	2.45786i
$220$		0			0
$221$	10.5000	−	2.59808i	0.706306	−	0.174766i
$222$		0			0
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	−0.675098	−	0.737728i	$-0.735899\pi$
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	0.976440	+	0.215788i	$0.0692320\pi$
$224$		0			0
$225$	3.00000	+	5.19615i	0.200000	+	0.346410i
$226$		0			0
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$	7.50000	−	12.9904i	0.493464	−	0.854704i
$232$		0			0
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$		0			0
$237$	6.00000	−	10.3923i	0.389742	−	0.675053i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	10.5000	+	18.1865i	0.676364	+	1.17150i	0.976068	+	0.217465i	$0.0697789\pi$
$241$	10.5000	+	18.1865i	0.676364	+	1.17150i	−0.299704	+	0.954032i	$0.596888\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.00000	−	10.3923i	0.383326	−	0.663940i
$246$		0			0
$247$	−10.5000	+	2.59808i	−0.668099	+	0.165312i
$248$		0			0
$249$	−18.0000	+	31.1769i	−1.14070	+	1.97576i
$250$		0			0
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	0.688338	−	0.725390i	$-0.258341\pi$
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	−0.972375	+	0.233423i	$0.925007\pi$
$252$		0			0
$253$	−2.50000	−	4.33013i	−0.157174	−	0.272233i
$254$		0			0
$255$	18.0000			1.12720
$256$		0			0
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	−0.999083	−	0.0428069i	$-0.986370\pi$
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	13.5000	+	23.3827i	0.826187	+	1.43100i
$268$		0			0
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$		0			0
$271$	8.50000	−	14.7224i	0.516338	−	0.894324i	−0.483482	−	0.875354i	$-0.660628\pi$
$271$	8.50000	−	14.7224i	0.516338	−	0.894324i	0.999820	−	0.0189696i	$-0.00603859\pi$
$272$		0			0
$273$	−3.00000	+	10.3923i	−0.181568	+	0.628971i
$274$		0			0
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$		0			0
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$		0			0
$279$	24.0000	+	41.5692i	1.43684	+	2.48868i
$280$		0			0
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	0.432360	+	0.901701i	$0.357681\pi$
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	−0.997076	+	0.0764162i	$0.975652\pi$
$284$		0			0
$285$	−18.0000			−1.06623
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−3.00000			−0.175863
$292$		0			0
$293$	−9.50000	−	16.4545i	−0.554996	−	0.961281i	−0.997904	−	0.0647140i	$-0.979386\pi$
$293$	−9.50000	−	16.4545i	−0.554996	−	0.961281i	0.442908	−	0.896567i	$-0.353947\pi$
$294$		0			0
$295$	−5.00000	−	8.66025i	−0.291111	−	0.504219i
$296$		0			0
$297$	22.5000	−	38.9711i	1.30558	−	2.26134i
$298$		0			0
$299$	2.50000	+	2.59808i	0.144579	+	0.150251i
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$	−28.5000	−	49.3634i	−1.63728	−	2.83586i
$304$		0			0
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$		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
$309$	12.0000	−	20.7846i	0.682656	−	1.18240i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$		0			0
$317$	30.0000			1.68497			0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000			1.68497			0.842484	+	0.538721i	$0.181092\pi$
$318$		0			0
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$		0			0
$321$	−16.5000	−	28.5788i	−0.920940	−	1.59512i
$322$		0			0
$323$	4.50000	−	7.79423i	0.250387	−	0.433682i
$324$		0			0
$325$	1.00000	−	3.46410i	0.0554700	−	0.192154i
$326$		0			0
$327$	−15.0000	+	25.9808i	−0.829502	+	1.43674i
$328$		0			0
$329$	−2.00000	−	3.46410i	−0.110264	−	0.190982i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$		0			0
$333$	18.0000			0.986394
$334$		0			0
$335$	−7.00000	+	12.1244i	−0.382451	+	0.662424i
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		0			0
$339$	33.0000			1.79231
$340$		0			0
$341$	−20.0000	+	34.6410i	−1.08306	+	1.87592i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$		0			0
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$		0			0
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	0.491428	+	0.870918i	$0.336475\pi$
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	−0.999951	+	0.00987003i	$0.996858\pi$
$350$		0			0
$351$	−9.00000	+	31.1769i	−0.480384	+	1.66410i
$352$		0			0
$353$	−3.50000	+	6.06218i	−0.186286	+	0.322657i	−0.944009	−	0.329919i	$-0.892979\pi$
$353$	−3.50000	+	6.06218i	−0.186286	+	0.322657i	0.757723	+	0.652576i	$0.226312\pi$
$354$		0			0
$355$	11.0000	+	19.0526i	0.583819	+	1.01120i
$356$		0			0
$357$	−4.50000	−	7.79423i	−0.238165	−	0.412514i
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$		0			0
$363$	42.0000			2.20443
$364$		0			0
$365$	28.0000			1.46559
$366$		0			0
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	0.392481	+	0.919760i	$0.371617\pi$
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	−0.992776	+	0.119982i	$0.961716\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$	18.0000	−	31.1769i	0.929516	−	1.60997i
$376$		0			0
$377$	2.50000	+	2.59808i	0.128757	+	0.133808i
$378$		0			0
$379$	2.50000	−	4.33013i	0.128416	−	0.222424i	−0.794647	−	0.607072i	$-0.792344\pi$
$379$	2.50000	−	4.33013i	0.128416	−	0.222424i	0.923063	+	0.384648i	$0.125677\pi$
$380$		0			0
$381$	7.50000	+	12.9904i	0.384237	+	0.665517i
$382$		0			0
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$		0			0
$385$	−10.0000			−0.509647
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−3.00000			−0.151717
$392$		0			0
$393$	6.00000	−	10.3923i	0.302660	−	0.524222i
$394$		0			0
$395$	−8.00000			−0.402524
$396$		0			0
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	0.988080	+	0.153941i	$0.0491966\pi$
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	−0.360723	+	0.932673i	$0.617470\pi$
$398$		0			0
$399$	4.50000	+	7.79423i	0.225282	+	0.390199i
$400$		0			0
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		0			0
$403$	8.00000	−	27.7128i	0.398508	−	1.38047i
$404$		0			0
$405$	−9.00000	+	15.5885i	−0.447214	+	0.774597i
$406$		0			0
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$		0			0
$411$	45.0000			2.21969
$412$		0			0
$413$	−2.50000	+	4.33013i	−0.123017	+	0.213072i
$414$		0			0
$415$	24.0000			1.17811
$416$		0			0
$417$	−33.0000			−1.61602
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	−12.0000	−	20.7846i	−0.583460	−	1.01058i
$424$		0			0
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$		0			0
$427$	2.50000	−	4.33013i	0.120983	−	0.209550i
$428$		0			0
$429$	−52.5000	+	12.9904i	−2.53472	+	0.627182i
$430$		0			0
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$		0			0
$435$	3.00000	+	5.19615i	0.143839	+	0.249136i
$436$		0			0
$437$	3.00000			0.143509
$438$		0			0
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	0.978412	+	0.206666i	$0.0662612\pi$
$440$		0			0
$441$	−36.0000			−1.71429
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$		0			0
$447$	−63.0000			−2.97980
$448$		0			0
$449$	2.50000	+	4.33013i	0.117982	+	0.204351i	0.918968	−	0.394332i	$-0.129024\pi$
$449$	2.50000	+	4.33013i	0.117982	+	0.204351i	−0.800986	+	0.598684i	$0.795691\pi$
$450$		0			0
$451$	7.50000	+	12.9904i	0.353161	+	0.611693i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.00000	−	1.73205i	0.328165	−	0.0811998i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$	−13.5000	−	23.3827i	−0.630126	−	1.09141i
$460$		0			0
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	24.0000	−	41.5692i	1.11297	−	1.92773i
$466$		0			0
$467$	−16.0000			−0.740392			−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000			−0.740392			−0.370196	+	0.928954i	$0.620709\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	33.0000	−	57.1577i	1.52056	−	2.63369i
$472$		0			0
$473$	−5.00000			−0.229900
$474$		0			0
$475$	−1.50000	−	2.59808i	−0.0688247	−	0.119208i
$476$		0			0
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$		0			0
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	−0.898257	−	0.439470i	$-0.855166\pi$
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	0.829721	+	0.558179i	$0.188500\pi$
$480$		0			0
$481$	−7.50000	−	7.79423i	−0.341971	−	0.355386i
$482$		0			0
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	−0.981374	−	0.192109i	$-0.938467\pi$
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	0.324316	−	0.945949i	$-0.394866\pi$
$488$		0			0
$489$	−21.0000			−0.949653
$490$		0			0
$491$	−15.5000	+	26.8468i	−0.699505	+	1.21158i	0.269133	+	0.963103i	$0.413263\pi$
$491$	−15.5000	+	26.8468i	−0.699505	+	1.21158i	−0.968638	+	0.248476i	$0.920070\pi$
$492$		0			0
$493$	−3.00000			−0.135113
$494$		0			0
$495$	−60.0000			−2.69680
$496$		0			0
$497$	5.50000	−	9.52628i	0.246709	−	0.427312i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	13.5000	+	23.3827i	0.603136	+	1.04466i
$502$		0			0
$503$	11.5000	+	19.9186i	0.512760	+	0.888126i	0.999891	+	0.0147968i	$0.00471014\pi$
$503$	11.5000	+	19.9186i	0.512760	+	0.888126i	−0.487131	+	0.873329i	$0.661957\pi$
$504$		0			0
$505$	−19.0000	+	32.9090i	−0.845489	+	1.46443i
$506$		0			0
$507$	34.5000	−	18.1865i	1.53220	−	0.807692i
$508$		0			0
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	−0.805287	−	0.592886i	$-0.797989\pi$
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	0.916097	+	0.400956i	$0.131322\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$		0			0
$513$	13.5000	+	23.3827i	0.596040	+	1.03237i
$514$		0			0
$515$	−16.0000			−0.705044
$516$		0			0
$517$	10.0000	−	17.3205i	0.439799	−	0.761755i
$518$		0			0
$519$	33.0000			1.44854
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−7.50000	+	12.9904i	−0.327952	+	0.568030i	−0.982105	−	0.188332i	$-0.939692\pi$
$523$	−7.50000	+	12.9904i	−0.327952	+	0.568030i	0.654153	+	0.756362i	$0.273025\pi$
$524$		0			0
$525$	−3.00000			−0.130931
$526$		0			0
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	−15.0000	+	25.9808i	−0.650945	+	1.12747i
$532$		0			0
$533$	−7.50000	−	7.79423i	−0.324861	−	0.337606i
$534$		0			0
$535$	−11.0000	+	19.0526i	−0.475571	+	0.823714i
$536$		0			0
$537$	31.5000	+	54.5596i	1.35933	+	2.35442i
$538$		0			0
$539$	−15.0000	−	25.9808i	−0.646096	−	1.11907i
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$		0			0
$543$	−27.0000	+	46.7654i	−1.15868	+	2.00689i
$544$		0			0
$545$	20.0000			0.856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$		0			0
$551$	3.00000			0.127804
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$		0			0
$555$	−9.00000	−	15.5885i	−0.382029	−	0.661693i
$556$		0			0
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	−0.269642	−	0.962961i	$-0.586905\pi$
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	0.968769	−	0.247964i	$-0.0797613\pi$
$558$		0			0
$559$	3.50000	−	0.866025i	0.148034	−	0.0366290i
$560$		0			0
$561$	22.5000	−	38.9711i	0.949951	−	1.64536i
$562$		0			0
$563$	9.50000	+	16.4545i	0.400377	+	0.693474i	0.993771	−	0.111438i	$-0.0355457\pi$
$563$	9.50000	+	16.4545i	0.400377	+	0.693474i	−0.593394	+	0.804912i	$0.702212\pi$
$564$		0			0
$565$	−11.0000	−	19.0526i	−0.462773	−	0.801547i
$566$		0			0
$567$	9.00000			0.377964
$568$		0			0
$569$	−3.50000	+	6.06218i	−0.146728	+	0.254140i	−0.930016	−	0.367519i	$-0.880207\pi$
$569$	−3.50000	+	6.06218i	−0.146728	+	0.254140i	0.783289	+	0.621658i	$0.213541\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$	3.00000			0.125327
$574$		0			0
$575$	−0.500000	+	0.866025i	−0.0208514	+	0.0361158i
$576$		0			0
$577$	6.00000			0.249783			0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000			0.249783			0.124892	+	0.992170i	$0.460142\pi$
$578$		0			0
$579$	−16.5000	−	28.5788i	−0.685717	−	1.18770i
$580$		0			0
$581$	−6.00000	−	10.3923i	−0.248922	−	0.431145i
$582$		0			0
$583$	−15.0000	+	25.9808i	−0.621237	+	1.07601i
$584$		0			0
$585$	42.0000	−	10.3923i	1.73649	−	0.429669i
$586$		0			0
$587$	12.5000	−	21.6506i	0.515930	−	0.893617i	−0.483899	−	0.875124i	$-0.660780\pi$
$587$	12.5000	−	21.6506i	0.515930	−	0.893617i	0.999829	−	0.0184934i	$-0.00588696\pi$
$588$		0			0
$589$	−12.0000	−	20.7846i	−0.494451	−	0.856415i
$590$		0			0
$591$	13.5000	+	23.3827i	0.555316	+	0.961835i
$592$		0			0
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$		0			0
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$		0			0
$597$	−57.0000			−2.33285
$598$		0			0
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		0			0
$603$	42.0000			1.71037
$604$		0			0
$605$	−14.0000	−	24.2487i	−0.569181	−	0.985850i
$606$		0			0
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$		0			0
$609$	1.50000	−	2.59808i	0.0607831	−	0.105279i
$610$		0			0
$611$	−4.00000	+	13.8564i	−0.161823	+	0.560570i
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$		0			0
$615$	−9.00000	−	15.5885i	−0.362915	−	0.628587i
$616$		0			0
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	0.786933	−	0.617039i	$-0.211668\pi$
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	−0.927838	+	0.372985i	$0.878334\pi$
$618$		0			0
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$	4.50000	−	7.79423i	0.180579	−	0.312772i
$622$		0			0
$623$	−9.00000			−0.360577
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−22.5000	+	38.9711i	−0.898563	+	1.55636i
$628$		0			0
$629$	9.00000			0.358854
$630$		0			0
$631$	−18.5000	−	32.0429i	−0.736473	−	1.27561i	−0.954074	−	0.299571i	$-0.903156\pi$
$631$	−18.5000	−	32.0429i	−0.736473	−	1.27561i	0.217601	−	0.976038i	$-0.430177\pi$
$632$		0			0
$633$	19.5000	+	33.7750i	0.775055	+	1.34244i
$634$		0			0
$635$	5.00000	−	8.66025i	0.198419	−	0.343672i
$636$		0			0
$637$	15.0000	+	15.5885i	0.594322	+	0.617637i
$638$		0			0
$639$	33.0000	−	57.1577i	1.30546	−	2.26112i
$640$		0			0
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	0.911165	−	0.412042i	$-0.135184\pi$
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	−0.812421	+	0.583071i	$0.801851\pi$
$642$		0			0
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	0.991028	+	0.133652i	$0.0426705\pi$
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	−0.379768	+	0.925082i	$0.623996\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	14.5000	−	25.1147i	0.570054	−	0.987362i	−0.426506	−	0.904485i	$-0.640256\pi$
$647$	14.5000	−	25.1147i	0.570054	−	0.987362i	0.996560	−	0.0828774i	$-0.0264110\pi$
$648$		0			0
$649$	−25.0000			−0.981336
$650$		0			0
$651$	−24.0000			−0.940634
$652$		0			0
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		0			0
$655$	−8.00000			−0.312586
$656$		0			0
$657$	−42.0000	−	72.7461i	−1.63858	−	2.83810i
$658$		0			0
$659$	−16.5000	−	28.5788i	−0.642749	−	1.11327i	−0.984817	−	0.173598i	$-0.944461\pi$
$659$	−16.5000	−	28.5788i	−0.642749	−	1.11327i	0.342068	−	0.939675i	$-0.388873\pi$
$660$		0			0
$661$	18.5000	−	32.0429i	0.719567	−	1.24633i	−0.241605	−	0.970375i	$-0.577674\pi$
$661$	18.5000	−	32.0429i	0.719567	−	1.24633i	0.961172	−	0.275951i	$-0.0889928\pi$
$662$		0			0
$663$	−9.00000	+	31.1769i	−0.349531	+	1.21081i
$664$		0			0
$665$	3.00000	−	5.19615i	0.116335	−	0.201498i
$666$		0			0
$667$	−0.500000	−	0.866025i	−0.0193601	−	0.0335326i
$668$		0			0
$669$	13.5000	+	23.3827i	0.521940	+	0.904027i
$670$		0			0
$671$	25.0000			0.965114
$672$		0			0
$673$	−3.50000	+	6.06218i	−0.134915	+	0.233680i	−0.925565	−	0.378589i	$-0.876409\pi$
$673$	−3.50000	+	6.06218i	−0.134915	+	0.233680i	0.790650	+	0.612268i	$0.209743\pi$
$674$		0			0
$675$	−9.00000			−0.346410
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	0.500000	−	0.866025i	0.0191882	−	0.0332350i
$680$		0			0
$681$	63.0000			2.41417
$682$		0			0
$683$	5.50000	+	9.52628i	0.210452	+	0.364513i	0.951856	−	0.306546i	$-0.0991732\pi$
$683$	5.50000	+	9.52628i	0.210452	+	0.364513i	−0.741404	+	0.671059i	$0.765840\pi$
$684$		0			0
$685$	−15.0000	−	25.9808i	−0.573121	−	0.992674i
$686$		0			0
$687$	9.00000	−	15.5885i	0.343371	−	0.594737i
$688$		0			0
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	−0.814548	−	0.580097i	$-0.803015\pi$
$691$	2.50000	−	4.33013i	0.0951045	−	0.164726i	0.909652	+	0.415371i	$0.136348\pi$
$692$		0			0
$693$	15.0000	+	25.9808i	0.569803	+	0.986928i
$694$		0			0
$695$	11.0000	+	19.0526i	0.417254	+	0.722705i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	−33.0000	+	57.1577i	−1.24817	+	2.16190i
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−9.00000			−0.339441
$704$		0			0
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$		0			0
$707$	19.0000			0.714569
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$		0			0
$713$	−4.00000	+	6.92820i	−0.149801	+	0.259463i
$714$		0			0
$715$	25.0000	+	25.9808i	0.934947	+	0.971625i
$716$		0			0
$717$	−36.0000	+	62.3538i	−1.34444	+	2.32865i
$718$		0			0
$719$	−8.50000	−	14.7224i	−0.316997	−	0.549054i	0.662863	−	0.748740i	$-0.269341\pi$
$719$	−8.50000	−	14.7224i	−0.316997	−	0.549054i	−0.979860	+	0.199686i	$0.936008\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$		0			0
$723$	−63.0000			−2.34300
$724$		0			0
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$		0			0
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$		0			0
$735$	18.0000	+	31.1769i	0.663940	+	1.14998i
$736$		0			0
$737$	17.5000	+	30.3109i	0.644621	+	1.11652i
$738$		0			0
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	−0.970360	−	0.241665i	$-0.922307\pi$
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	0.694468	+	0.719524i	$0.255640\pi$
$740$		0			0
$741$	9.00000	−	31.1769i	0.330623	−	1.14531i
$742$		0			0
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	−0.467351	−	0.884072i	$-0.654791\pi$
$743$	14.5000	−	25.1147i	0.531953	−	0.921370i	0.999304	−	0.0372984i	$-0.0118752\pi$
$744$		0			0
$745$	21.0000	+	36.3731i	0.769380	+	1.33261i
$746$		0			0
$747$	−36.0000	−	62.3538i	−1.31717	−	2.28141i
$748$		0			0
$749$	11.0000			0.401931
$750$		0			0
$751$	4.50000	−	7.79423i	0.164207	−	0.284415i	−0.772166	−	0.635421i	$-0.780827\pi$
$751$	4.50000	−	7.79423i	0.164207	−	0.284415i	0.936374	+	0.351005i	$0.114160\pi$
$752$		0			0
$753$	27.0000			0.983935
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	−0.891997	−	0.452042i	$-0.850696\pi$
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	0.837478	+	0.546471i	$0.184029\pi$
$758$		0			0
$759$	15.0000			0.544466
$760$		0			0
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$		0			0
$763$	−5.00000	−	8.66025i	−0.181012	−	0.313522i
$764$		0			0
$765$	−18.0000	+	31.1769i	−0.650791	+	1.12720i
$766$		0			0
$767$	17.5000	−	4.33013i	0.631888	−	0.156352i
$768$		0			0
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	−0.612225	−	0.790684i	$-0.709725\pi$
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	0.990865	+	0.134860i	$0.0430586\pi$
$770$		0			0
$771$	−4.50000	−	7.79423i	−0.162064	−	0.280702i
$772$		0			0
$773$	0.500000	+	0.866025i	0.0179838	+	0.0311488i	0.874877	−	0.484345i	$-0.160942\pi$
$773$	0.500000	+	0.866025i	0.0179838	+	0.0311488i	−0.856893	+	0.515494i	$0.827609\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$		0			0
$777$	−4.50000	+	7.79423i	−0.161437	+	0.279616i
$778$		0			0
$779$	−9.00000			−0.322458
$780$		0			0
$781$	55.0000			1.96805
$782$		0			0
$783$	4.50000	−	7.79423i	0.160817	−	0.278543i
$784$		0			0
$785$	−44.0000			−1.57043
$786$		0			0
$787$	3.50000	+	6.06218i	0.124762	+	0.216093i	0.921640	−	0.388047i	$-0.126850\pi$
$787$	3.50000	+	6.06218i	0.124762	+	0.216093i	−0.796878	+	0.604140i	$0.793517\pi$
$788$		0			0
$789$	−22.5000	−	38.9711i	−0.801021	−	1.38741i
$790$		0			0
$791$	−5.50000	+	9.52628i	−0.195557	+	0.338716i
$792$		0			0
$793$	−17.5000	+	4.33013i	−0.621443	+	0.153767i
$794$		0			0
$795$	18.0000	−	31.1769i	0.638394	−	1.10573i
$796$		0			0
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$	−6.00000	−	10.3923i	−0.212265	−	0.367653i
$800$		0			0
$801$	−54.0000			−1.90800
$802$		0			0
$803$	35.0000	−	60.6218i	1.23512	−	2.13930i
$804$		0			0
$805$	−2.00000			−0.0704907
$806$		0			0
$807$	45.0000			1.58408
$808$		0			0
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	−0.134255	−	0.990947i	$-0.542864\pi$
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	0.925312	−	0.379206i	$-0.123803\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$		0			0
$813$	25.5000	+	44.1673i	0.894324	+	1.54901i
$814$		0			0
$815$	7.00000	+	12.1244i	0.245199	+	0.424698i
$816$		0			0
$817$	1.50000	−	2.59808i	0.0524784	−	0.0908952i
$818$		0			0
$819$	−15.0000	−	15.5885i	−0.524142	−	0.544705i
$820$		0			0
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	0.0854103	+	0.996346i	$0.472780\pi$
$821$	−23.5000	+	40.7032i	−0.820156	+	1.42055i	−0.905566	+	0.424205i	$0.860553\pi$
$822$		0			0
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	0.890984	−	0.454034i	$-0.150016\pi$
$823$	1.50000	+	2.59808i	0.0522867	+	0.0905632i	−0.838697	+	0.544598i	$0.816682\pi$
$824$		0			0
$825$	−7.50000	−	12.9904i	−0.261116	−	0.452267i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−15.5000	+	26.8468i	−0.538337	+	0.932427i	0.460657	+	0.887578i	$0.347614\pi$
$829$	−15.5000	+	26.8468i	−0.538337	+	0.932427i	−0.998994	+	0.0448490i	$0.985719\pi$
$830$		0			0
$831$	−27.0000			−0.936620
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$		0			0
$837$	−72.0000			−2.48868
$838$		0			0
$839$	21.5000	+	37.2391i	0.742262	+	1.28564i	0.951463	+	0.307763i	$0.0995805\pi$
$839$	21.5000	+	37.2391i	0.742262	+	1.28564i	−0.209200	+	0.977873i	$0.567086\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$		0			0
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$		0			0
$845$	−22.0000	−	13.8564i	−0.756823	−	0.476675i
$846$		0			0
$847$	−7.00000	+	12.1244i	−0.240523	+	0.416598i
$848$		0			0
$849$	−28.5000	−	49.3634i	−0.978117	−	1.69415i
$850$		0			0
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$	18.0000	−	31.1769i	0.615587	−	1.06623i
$856$		0			0
$857$	−2.00000			−0.0683187			−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000			−0.0683187			−0.0341593	+	0.999416i	$0.510875\pi$
$858$		0			0
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$		0			0
$861$	−4.50000	+	7.79423i	−0.153360	+	0.265627i
$862$		0			0
$863$	16.0000			0.544646			0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000			0.544646			0.272323	+	0.962206i	$0.412208\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$		0			0
$867$	12.0000	+	20.7846i	0.407541	+	0.705882i
$868$		0			0
$869$	−10.0000	+	17.3205i	−0.339227	+	0.587558i
$870$		0			0
$871$	−17.5000	−	18.1865i	−0.592965	−	0.616227i
$872$		0			0
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$		0			0
$875$	6.00000	+	10.3923i	0.202837	+	0.351324i
$876$		0			0
$877$	22.5000	+	38.9711i	0.759771	+	1.31596i	0.942967	+	0.332886i	$0.108022\pi$
$877$	22.5000	+	38.9711i	0.759771	+	1.31596i	−0.183196	+	0.983076i	$0.558644\pi$
$878$		0			0
$879$	57.0000			1.92256
$880$		0			0
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	0.0136556	+	0.999907i	$0.495653\pi$
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	−0.872772	+	0.488127i	$0.837680\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	30.0000			1.00844
$886$		0			0
$887$	26.5000	−	45.8993i	0.889783	−	1.54115i	0.0496513	−	0.998767i	$-0.484189\pi$
$887$	26.5000	−	45.8993i	0.889783	−	1.54115i	0.840132	−	0.542383i	$-0.182478\pi$
$888$		0			0
$889$	−5.00000			−0.167695
$890$		0			0
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	21.0000	−	36.3731i	0.701953	−	1.21582i
$896$		0			0
$897$	−10.5000	+	2.59808i	−0.350585	+	0.0867472i
$898$		0			0
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$	−1.50000	−	2.59808i	−0.0499169	−	0.0864586i
$904$		0			0
$905$	36.0000			1.19668
$906$		0			0
$907$	−1.50000	+	2.59808i	−0.0498067	+	0.0862677i	−0.889854	−	0.456246i	$-0.849194\pi$
$907$	−1.50000	+	2.59808i	−0.0498067	+	0.0862677i	0.840047	+	0.542513i	$0.182527\pi$
$908$		0			0
$909$	114.000			3.78114
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	30.0000	−	51.9615i	0.992855	−	1.71968i
$914$		0			0
$915$	−30.0000			−0.991769
$916$		0			0
$917$	2.00000	+	3.46410i	0.0660458	+	0.114395i
$918$		0			0
$919$	−16.5000	−	28.5788i	−0.544285	−	0.942729i	−0.998652	−	0.0519142i	$-0.983468\pi$
$919$	−16.5000	−	28.5788i	−0.544285	−	0.942729i	0.454367	−	0.890815i	$-0.349866\pi$
$920$		0			0
$921$	6.00000	−	10.3923i	0.197707	−	0.342438i
$922$		0			0
$923$	−38.5000	+	9.52628i	−1.26724	+	0.313561i
$924$		0			0
$925$	1.50000	−	2.59808i	0.0493197	−	0.0854242i
$926$		0			0
$927$	24.0000	+	41.5692i	0.788263	+	1.36531i
$928$		0			0
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$		0			0
$933$	36.0000	−	62.3538i	1.17859	−	2.04137i
$934$		0			0
$935$	−30.0000			−0.981105
$936$		0			0
$937$	−18.0000			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$938$		0			0
$939$	−21.0000	+	36.3731i	−0.685309	+	1.18699i
$940$		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
$943$	1.50000	+	2.59808i	0.0488467	+	0.0846050i
$944$		0			0
$945$	−9.00000	−	15.5885i	−0.292770	−	0.507093i
$946$		0			0
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	−0.997589	−	0.0694014i	$-0.977891\pi$
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	0.558898	+	0.829237i	$0.311224\pi$
$948$		0			0
$949$	−14.0000	+	48.4974i	−0.454459	+	1.57429i
$950$		0			0
$951$	−45.0000	+	77.9423i	−1.45922	+	2.52745i
$952$		0			0
$953$	0.500000	+	0.866025i	0.0161966	+	0.0280533i	0.874010	−	0.485908i	$-0.161511\pi$
$953$	0.500000	+	0.866025i	0.0161966	+	0.0280533i	−0.857814	+	0.513961i	$0.828178\pi$
$954$		0			0
$955$	−1.00000	−	1.73205i	−0.0323592	−	0.0560478i
$956$		0			0
$957$	15.0000			0.484881
$958$		0			0
$959$	−7.50000	+	12.9904i	−0.242188	+	0.419481i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	66.0000			2.12682
$964$		0			0
$965$	−11.0000	+	19.0526i	−0.354103	+	0.613324i
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$		0			0
$969$	13.5000	+	23.3827i	0.433682	+	0.751160i
$970$		0			0
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	5.50000	−	9.52628i	0.176322	−	0.305398i
$974$		0			0
$975$	7.50000	+	7.79423i	0.240192	+	0.249615i
$976$		0			0
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	0.364900	+	0.931047i	$0.381103\pi$
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	−0.988760	+	0.149511i	$0.952230\pi$
$978$		0			0
$979$	−22.5000	−	38.9711i	−0.719103	−	1.24552i
$980$		0			0
$981$	−30.0000	−	51.9615i	−0.957826	−	1.65900i
$982$		0			0
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$		0			0
$987$	12.0000			0.381964
$988$		0			0
$989$	−1.00000			−0.0317982
$990$		0			0
$991$	−13.5000	+	23.3827i	−0.428842	+	0.742775i	−0.996771	−	0.0803021i	$-0.974411\pi$
$991$	−13.5000	+	23.3827i	−0.428842	+	0.742775i	0.567929	+	0.823078i	$0.307745\pi$
$992$		0			0
$993$	51.0000			1.61844
$994$		0			0
$995$	19.0000	+	32.9090i	0.602340	+	1.04328i
$996$		0			0
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$		0			0
$999$	−13.5000	+	23.3827i	−0.427121	+	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.e.a.9.1	✓	2
3.2	odd	2		468.2.l.a.217.1		2
4.3	odd	2		208.2.i.d.113.1		2
5.2	odd	4		1300.2.bb.f.1049.2		4
5.3	odd	4		1300.2.bb.f.1049.1		4
5.4	even	2		1300.2.i.f.1101.1		2
7.2	even	3		2548.2.i.a.165.1		2
7.3	odd	6		2548.2.l.a.373.1		2
7.4	even	3		2548.2.l.h.373.1		2
7.5	odd	6		2548.2.i.h.165.1		2
7.6	odd	2		2548.2.k.d.1569.1		2
8.3	odd	2		832.2.i.a.321.1		2
8.5	even	2		832.2.i.j.321.1		2
12.11	even	2		1872.2.t.f.1153.1		2
13.2	odd	12		676.2.h.b.361.1		4
13.3	even	3	inner	52.2.e.a.29.1	yes	2
13.4	even	6		676.2.a.d.1.1		1
13.5	odd	4		676.2.h.b.485.1		4
13.6	odd	12		676.2.d.d.337.1		2
13.7	odd	12		676.2.d.d.337.2		2
13.8	odd	4		676.2.h.b.485.2		4
13.9	even	3		676.2.a.e.1.1		1
13.10	even	6		676.2.e.a.653.1		2
13.11	odd	12		676.2.h.b.361.2		4
13.12	even	2		676.2.e.a.529.1		2
39.17	odd	6		6084.2.a.k.1.1		1
39.20	even	12		6084.2.b.l.4393.1		2
39.29	odd	6		468.2.l.a.289.1		2
39.32	even	12		6084.2.b.l.4393.2		2
39.35	odd	6		6084.2.a.f.1.1		1
52.3	odd	6		208.2.i.d.81.1		2
52.7	even	12		2704.2.f.a.337.2		2
52.19	even	12		2704.2.f.a.337.1		2
52.35	odd	6		2704.2.a.b.1.1		1
52.43	odd	6		2704.2.a.a.1.1		1
65.3	odd	12		1300.2.bb.f.549.2		4
65.29	even	6		1300.2.i.f.601.1		2
65.42	odd	12		1300.2.bb.f.549.1		4
91.3	odd	6		2548.2.i.h.1745.1		2
91.16	even	3		2548.2.l.h.1537.1		2
91.55	odd	6		2548.2.k.d.393.1		2
91.68	odd	6		2548.2.l.a.1537.1		2
91.81	even	3		2548.2.i.a.1745.1		2
104.3	odd	6		832.2.i.a.705.1		2
104.29	even	6		832.2.i.j.705.1		2
156.107	even	6		1872.2.t.f.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.a.9.1	✓	2	1.1	even	1	trivial
52.2.e.a.29.1	yes	2	13.3	even	3	inner
208.2.i.d.81.1		2	52.3	odd	6
208.2.i.d.113.1		2	4.3	odd	2
468.2.l.a.217.1		2	3.2	odd	2
468.2.l.a.289.1		2	39.29	odd	6
676.2.a.d.1.1		1	13.4	even	6
676.2.a.e.1.1		1	13.9	even	3
676.2.d.d.337.1		2	13.6	odd	12
676.2.d.d.337.2		2	13.7	odd	12
676.2.e.a.529.1		2	13.12	even	2
676.2.e.a.653.1		2	13.10	even	6
676.2.h.b.361.1		4	13.2	odd	12
676.2.h.b.361.2		4	13.11	odd	12
676.2.h.b.485.1		4	13.5	odd	4
676.2.h.b.485.2		4	13.8	odd	4
832.2.i.a.321.1		2	8.3	odd	2
832.2.i.a.705.1		2	104.3	odd	6
832.2.i.j.321.1		2	8.5	even	2
832.2.i.j.705.1		2	104.29	even	6
1300.2.i.f.601.1		2	65.29	even	6
1300.2.i.f.1101.1		2	5.4	even	2
1300.2.bb.f.549.1		4	65.42	odd	12
1300.2.bb.f.549.2		4	65.3	odd	12
1300.2.bb.f.1049.1		4	5.3	odd	4
1300.2.bb.f.1049.2		4	5.2	odd	4
1872.2.t.f.289.1		2	156.107	even	6
1872.2.t.f.1153.1		2	12.11	even	2
2548.2.i.a.165.1		2	7.2	even	3
2548.2.i.a.1745.1		2	91.81	even	3
2548.2.i.h.165.1		2	7.5	odd	6
2548.2.i.h.1745.1		2	91.3	odd	6
2548.2.k.d.393.1		2	91.55	odd	6
2548.2.k.d.1569.1		2	7.6	odd	2
2548.2.l.a.373.1		2	7.3	odd	6
2548.2.l.a.1537.1		2	91.68	odd	6
2548.2.l.h.373.1		2	7.4	even	3
2548.2.l.h.1537.1		2	91.16	even	3
2704.2.a.a.1.1		1	52.43	odd	6
2704.2.a.b.1.1		1	52.35	odd	6
2704.2.f.a.337.1		2	52.19	even	12
2704.2.f.a.337.2		2	52.7	even	12
6084.2.a.f.1.1		1	39.35	odd	6
6084.2.a.k.1.1		1	39.17	odd	6
6084.2.b.l.4393.1		2	39.20	even	12
6084.2.b.l.4393.2		2	39.32	even	12

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{19} +3.00000 q^{21} +(0.500000 - 0.866025i) q^{23} -1.00000 q^{25} +9.00000 q^{27} +(0.500000 - 0.866025i) q^{29} -8.00000 q^{31} +(7.50000 + 12.9904i) q^{33} +(-1.00000 - 1.73205i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-7.50000 - 7.79423i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-6.00000 - 10.3923i) q^{45} +4.00000 q^{47} +(3.00000 - 5.19615i) q^{49} +9.00000 q^{51} -6.00000 q^{53} +(5.00000 - 8.66025i) q^{55} -9.00000 q^{57} +(-2.50000 - 4.33013i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-3.00000 + 5.19615i) q^{63} +(-2.00000 + 6.92820i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(5.50000 + 9.52628i) q^{71} +14.0000 q^{73} +(1.50000 - 2.59808i) q^{75} -5.00000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(1.50000 + 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{89} +(3.50000 - 0.866025i) q^{91} +(12.0000 - 20.7846i) q^{93} +(3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 4 q^{5} - q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 4 * q^5 - q^7 - 6 * q^9	\( 2 q - 3 q^{3} + 4 q^{5} - q^{7} - 6 q^{9} + 5 q^{11} - 2 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} + 6 q^{21} + q^{23} - 2 q^{25} + 18 q^{27} + q^{29} - 16 q^{31} + 15 q^{33} - 2 q^{35} - 3 q^{37} - 15 q^{39} - 3 q^{41} - q^{43} - 12 q^{45} + 8 q^{47} + 6 q^{49} + 18 q^{51} - 12 q^{53} + 10 q^{55} - 18 q^{57} - 5 q^{59} + 5 q^{61} - 6 q^{63} - 4 q^{65} - 7 q^{67} + 3 q^{69} + 11 q^{71} + 28 q^{73} + 3 q^{75} - 10 q^{77} - 8 q^{79} - 9 q^{81} + 24 q^{83} - 6 q^{85} + 3 q^{87} + 9 q^{89} + 7 q^{91} + 24 q^{93} + 6 q^{95} + q^{97} - 60 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 4 * q^5 - q^7 - 6 * q^9 + 5 * q^11 - 2 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 + 6 * q^21 + q^23 - 2 * q^25 + 18 * q^27 + q^29 - 16 * q^31 + 15 * q^33 - 2 * q^35 - 3 * q^37 - 15 * q^39 - 3 * q^41 - q^43 - 12 * q^45 + 8 * q^47 + 6 * q^49 + 18 * q^51 - 12 * q^53 + 10 * q^55 - 18 * q^57 - 5 * q^59 + 5 * q^61 - 6 * q^63 - 4 * q^65 - 7 * q^67 + 3 * q^69 + 11 * q^71 + 28 * q^73 + 3 * q^75 - 10 * q^77 - 8 * q^79 - 9 * q^81 + 24 * q^83 - 6 * q^85 + 3 * q^87 + 9 * q^89 + 7 * q^91 + 24 * q^93 + 6 * q^95 + q^97 - 60 * q^99

Introduction

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