LMFDB - Embedded newform 2548.2.i.h.1745.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(165,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2548.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.i (of order $3$, degree $2$, not 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1745.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2548.1745
Dual form			2548.2.i.h.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{19} -1.00000 q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-7.50000 - 12.9904i) q^{33} +3.00000 q^{37} +(10.5000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} -12.0000 q^{45} +(2.00000 - 3.46410i) q^{47} +(-4.50000 + 7.79423i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-5.00000 - 8.66025i) q^{55} -9.00000 q^{57} -5.00000 q^{59} +(-2.50000 - 4.33013i) q^{61} +(7.00000 + 1.73205i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(5.50000 - 9.52628i) q^{71} +(7.00000 + 12.1244i) q^{73} +3.00000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(-3.00000 + 5.19615i) q^{85} +3.00000 q^{87} +9.00000 q^{89} -24.0000 q^{93} -6.00000 q^{95} +(-0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^5 - 6 * q^9	$ 2 q + 3 q^{3} + 2 q^{5} - 6 q^{9} + 5 q^{11} + 2 q^{13} - 6 q^{15} - 6 q^{17} - 3 q^{19} - 2 q^{23} + q^{25} - 18 q^{27} + q^{29} - 8 q^{31} - 15 q^{33} + 6 q^{37} + 21 q^{39} + 3 q^{41} - q^{43} - 24 q^{45} + 4 q^{47} - 9 q^{51} + 6 q^{53} - 10 q^{55} - 18 q^{57} - 10 q^{59} - 5 q^{61} + 14 q^{65} - 7 q^{67} - 3 q^{69} + 11 q^{71} + 14 q^{73} + 6 q^{75} + 4 q^{79} - 9 q^{81} - 24 q^{83} - 6 q^{85} + 6 q^{87} + 18 q^{89} - 48 q^{93} - 12 q^{95} - q^{97} - 60 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^5 - 6 * q^9 + 5 * q^11 + 2 * q^13 - 6 * q^15 - 6 * q^17 - 3 * q^19 - 2 * q^23 + q^25 - 18 * q^27 + q^29 - 8 * q^31 - 15 * q^33 + 6 * q^37 + 21 * q^39 + 3 * q^41 - q^43 - 24 * q^45 + 4 * q^47 - 9 * q^51 + 6 * q^53 - 10 * q^55 - 18 * q^57 - 10 * q^59 - 5 * q^61 + 14 * q^65 - 7 * q^67 - 3 * q^69 + 11 * q^71 + 14 * q^73 + 6 * q^75 + 4 * q^79 - 9 * q^81 - 24 * q^83 - 6 * q^85 + 6 * q^87 + 18 * q^89 - 48 * q^93 - 12 * q^95 - q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		0			0
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		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
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$		0			0
$33$	−7.50000	−	12.9904i	−1.30558	−	2.26134i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$		0			0
$39$	10.5000	+	2.59808i	1.68135	+	0.416025i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	−12.0000			−1.78885
$46$		0			0
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.50000	+	7.79423i	−0.630126	+	1.09141i
$52$		0			0
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−5.00000	−	8.66025i	−0.674200	−	1.16775i
$56$		0			0
$57$	−9.00000			−1.19208
$58$		0			0
$59$	−5.00000			−0.650945			−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000			−0.650945			−0.325472	+	0.945552i	$0.605523\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.00000	+	1.73205i	0.868243	+	0.214834i
$66$		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	−0.329728	−	0.944076i	$-0.606957\pi$
$71$	5.50000	−	9.52628i	0.652730	−	1.13056i	0.982458	−	0.186485i	$-0.0597097\pi$
$72$		0			0
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$		0			0
$75$	3.00000			0.346410
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		0			0
$87$	3.00000			0.321634
$88$		0			0
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−24.0000			−2.48868
$94$		0			0
$95$	−6.00000			−0.615587
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$		0			0
$101$	9.50000	−	16.4545i	0.945285	−	1.63728i	0.190106	−	0.981763i	$-0.439117\pi$
$101$	9.50000	−	16.4545i	0.945285	−	1.63728i	0.755179	−	0.655519i	$-0.227550\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.0000			1.06341			0.531705	−	0.846930i	$-0.321551\pi$
$107$	11.0000			1.06341			0.531705	+	0.846930i	$0.321551\pi$
$108$		0			0
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$	4.50000	−	7.79423i	0.427121	−	0.739795i
$112$		0			0
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	0.482399	+	0.875951i	$0.339765\pi$
$113$	−5.50000	+	9.52628i	−0.517396	+	0.896157i	−0.999796	+	0.0202056i	$0.993568\pi$
$114$		0			0
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$		0			0
$117$	15.0000	−	15.5885i	1.38675	−	1.44115i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$	9.00000			0.811503
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	0.955366	−	0.295423i	$-0.0954607\pi$
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	−0.733527	+	0.679660i	$0.762127\pi$
$128$		0			0
$129$	1.50000	+	2.59808i	0.132068	+	0.228748i
$130$		0			0
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$		0			0
$137$	15.0000			1.28154			0.640768	−	0.767734i	$-0.278616\pi$
$137$	15.0000			1.28154			0.640768	+	0.767734i	$0.278616\pi$
$138$		0			0
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$		0			0
$143$	17.5000	+	4.33013i	1.46342	+	0.362103i
$144$		0			0
$145$	2.00000			0.166091
$146$		0			0
$147$		0			0
$148$		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		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$		0			0
$153$	9.00000	+	15.5885i	0.727607	+	1.26025i
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−11.0000	−	19.0526i	−0.877896	−	1.52056i	−0.0242497	−	0.999706i	$-0.507720\pi$
$158$		0			0
$159$	18.0000			1.42749
$160$		0			0
$161$		0			0
$162$		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
$165$	−30.0000			−2.33550
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		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	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.50000	+	12.9904i	−0.563735	+	0.976417i
$178$		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	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$		0			0
$189$		0			0
$190$		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	0.980614	−	0.195947i	$-0.0627782\pi$
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	−0.660003	+	0.751263i	$0.729445\pi$
$198$		0			0
$199$	19.0000			1.34687			0.673437	−	0.739244i	$-0.264817\pi$
$199$	19.0000			1.34687			0.673437	+	0.739244i	$0.264817\pi$
$200$		0			0
$201$	10.5000	+	18.1865i	0.740613	+	1.28278i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.00000			0.419058
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$		0			0
$209$	−15.0000			−1.03757
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$	−16.5000	−	28.5788i	−1.13056	−	1.95819i
$214$		0			0
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	42.0000			2.83810
$220$		0			0
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$		0			0
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$		0			0
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$		0			0
$227$	−21.0000			−1.39382			−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000			−1.39382			−0.696909	+	0.717159i	$0.745442\pi$
$228$		0			0
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	−0.947960	−	0.318390i	$-0.896858\pi$
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	0.749714	+	0.661762i	$0.230191\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	0.240112	+	0.970745i	$0.422816\pi$
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	−0.960746	+	0.277429i	$0.910518\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$		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
$241$	21.0000			1.35273			0.676364	−	0.736567i	$-0.263554\pi$
$241$	21.0000			1.35273			0.676364	+	0.736567i	$0.263554\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.50000	−	7.79423i	0.477214	−	0.495935i
$248$		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	$-0.741659\pi$
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	0.972375	+	0.233423i	$0.0749927\pi$
$252$		0			0
$253$	−2.50000	+	4.33013i	−0.157174	+	0.272233i
$254$		0			0
$255$	9.00000	+	15.5885i	0.563602	+	0.976187i
$256$		0			0
$257$	−3.00000			−0.187135			−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000			−0.187135			−0.0935674	+	0.995613i	$0.529827\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		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
$269$	−15.0000			−0.914566			−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000			−0.914566			−0.457283	+	0.889321i	$0.651177\pi$
$270$		0			0
$271$	17.0000			1.03268			0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000			1.03268			0.516338	+	0.856385i	$0.327295\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.00000			0.301511
$276$		0			0
$277$	−9.00000			−0.540758			−0.270379	−	0.962754i	$-0.587149\pi$
$277$	−9.00000			−0.540758			−0.270379	+	0.962754i	$0.587149\pi$
$278$		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	$-0.642319\pi$
$283$	9.50000	−	16.4545i	0.564716	−	0.978117i	0.997076	−	0.0764162i	$-0.0243478\pi$
$284$		0			0
$285$	−9.00000	+	15.5885i	−0.533114	+	0.923381i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	1.50000	+	2.59808i	0.0879316	+	0.152302i
$292$		0			0
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	−0.442908	−	0.896567i	$-0.646053\pi$
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	0.997904	−	0.0647140i	$-0.0206135\pi$
$294$		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
$299$	−1.00000	−	3.46410i	−0.0578315	−	0.200334i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−28.5000	−	49.3634i	−1.63728	−	2.83586i
$304$		0			0
$305$	−10.0000			−0.572598
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	12.0000	+	20.7846i	0.682656	+	1.18240i
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$		0			0
$319$	5.00000			0.279946
$320$		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
$325$	−2.50000	+	2.59808i	−0.138675	+	0.144115i
$326$		0			0
$327$	−30.0000			−1.65900
$328$		0			0
$329$		0			0
$330$		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
$333$	−9.00000	−	15.5885i	−0.493197	−	0.854242i
$334$		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
$339$	16.5000	+	28.5788i	0.896157	+	1.55219i
$340$		0			0
$341$	−40.0000			−2.16612
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$		0			0
$347$	33.0000			1.77153			0.885766	−	0.464131i	$-0.153633\pi$
$347$	33.0000			1.77153			0.885766	+	0.464131i	$0.153633\pi$
$348$		0			0
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	0.999951	+	0.00987003i	$0.00314178\pi$
$349$	9.50000	+	16.4545i	0.508523	+	0.880788i	−0.491428	+	0.870918i	$0.663525\pi$
$350$		0			0
$351$	−9.00000	−	31.1769i	−0.480384	−	1.66410i
$352$		0			0
$353$	3.50000	−	6.06218i	0.186286	−	0.322657i	−0.757723	−	0.652576i	$-0.773688\pi$
$353$	3.50000	−	6.06218i	0.186286	−	0.322657i	0.944009	+	0.329919i	$0.107021\pi$
$354$		0			0
$355$	−11.0000	−	19.0526i	−0.583819	−	1.01120i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		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	$-0.628383\pi$
$367$	11.5000	−	19.9186i	0.600295	−	1.03974i	0.992776	−	0.119982i	$-0.0382835\pi$
$368$		0			0
$369$	9.00000	−	15.5885i	0.468521	−	0.811503i
$370$		0			0
$371$		0			0
$372$		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	0.923063	−	0.384648i	$-0.125677\pi$
$379$	2.50000	+	4.33013i	0.128416	+	0.222424i	−0.794647	+	0.607072i	$0.792344\pi$
$380$		0			0
$381$	15.0000			0.768473
$382$		0			0
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	0.957790	−	0.287469i	$-0.0928139\pi$
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	−0.727851	+	0.685736i	$0.759481\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.00000			0.304997
$388$		0			0
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$	3.00000			0.151717
$392$		0			0
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	−0.988080	−	0.153941i	$-0.950803\pi$
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	0.360723	−	0.932673i	$-0.382530\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$		0			0
$403$	20.0000	−	20.7846i	0.996271	−	1.03536i
$404$		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
$409$	5.00000			0.247234			0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000			0.247234			0.123617	+	0.992330i	$0.460551\pi$
$410$		0			0
$411$	22.5000	−	38.9711i	1.10984	−	1.92230i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$		0			0
$417$	16.5000	+	28.5788i	0.808008	+	1.39951i
$418$		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
$421$	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
$423$	−24.0000			−1.16692
$424$		0			0
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	37.5000	−	38.9711i	1.81052	−	1.88154i
$430$		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	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		0			0
$435$	3.00000	−	5.19615i	0.143839	−	0.249136i
$436$		0			0
$437$	1.50000	+	2.59808i	0.0717547	+	0.124283i
$438$		0			0
$439$	13.0000			0.620456			0.310228	−	0.950662i	$-0.399595\pi$
$439$	13.0000			0.620456			0.310228	+	0.950662i	$0.399595\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$		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	−0.800986	−	0.598684i	$-0.795691\pi$
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	0.918968	+	0.394332i	$0.129024\pi$
$450$		0			0
$451$	15.0000			0.706322
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.0000			−0.795226			−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000			−0.795226			−0.397613	+	0.917553i	$0.630161\pi$
$458$		0			0
$459$	27.0000			1.26025
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		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
$467$	−8.00000	+	13.8564i	−0.370196	+	0.641198i	−0.989595	−	0.143878i	$-0.954043\pi$
$467$	−8.00000	+	13.8564i	−0.370196	+	0.641198i	0.619400	+	0.785076i	$0.287376\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−66.0000			−3.04112
$472$		0			0
$473$	2.50000	+	4.33013i	0.114950	+	0.199099i
$474$		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	−0.829721	−	0.558179i	$-0.811500\pi$
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	0.898257	+	0.439470i	$0.144834\pi$
$480$		0			0
$481$	3.00000	+	10.3923i	0.136788	+	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	29.0000			1.31412			0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000			1.31412			0.657058	+	0.753840i	$0.271801\pi$
$488$		0			0
$489$	21.0000			0.949653
$490$		0			0
$491$	−15.5000	−	26.8468i	−0.699505	−	1.21158i	−0.968638	−	0.248476i	$-0.920070\pi$
$491$	−15.5000	−	26.8468i	−0.699505	−	1.21158i	0.269133	−	0.963103i	$-0.413263\pi$
$492$		0			0
$493$	−1.50000	−	2.59808i	−0.0675566	−	0.117011i
$494$		0			0
$495$	−30.0000	+	51.9615i	−1.34840	+	2.33550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$		0			0
$501$	−27.0000			−1.20627
$502$		0			0
$503$	−11.5000	+	19.9186i	−0.512760	+	0.888126i	0.487131	+	0.873329i	$0.338043\pi$
$503$	−11.5000	+	19.9186i	−0.512760	+	0.888126i	−0.999891	+	0.0147968i	$0.995290\pi$
$504$		0			0
$505$	−19.0000	−	32.9090i	−0.845489	−	1.46443i
$506$		0			0
$507$	1.50000	+	38.9711i	0.0666173	+	1.73077i
$508$		0			0
$509$	5.00000			0.221621			0.110811	−	0.993842i	$-0.464655\pi$
$509$	5.00000			0.221621			0.110811	+	0.993842i	$0.464655\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	13.5000	+	23.3827i	0.596040	+	1.03237i
$514$		0			0
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	−10.0000	−	17.3205i	−0.439799	−	0.761755i
$518$		0			0
$519$	33.0000			1.44854
$520$		0			0
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	0.924229	−	0.381839i	$-0.124709\pi$
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	−0.792797	+	0.609486i	$0.791376\pi$
$522$		0			0
$523$	−15.0000			−0.655904			−0.327952	−	0.944694i	$-0.606358\pi$
$523$	−15.0000			−0.655904			−0.327952	+	0.944694i	$0.606358\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	−22.0000			−0.956522
$530$		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
$539$		0			0
$540$		0			0
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$		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
$551$	1.50000	−	2.59808i	0.0639021	−	0.110682i
$552$		0			0
$553$		0			0
$554$		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
$563$	19.0000			0.800755			0.400377	−	0.916350i	$-0.368879\pi$
$563$	19.0000			0.800755			0.400377	+	0.916350i	$0.368879\pi$
$564$		0			0
$565$	11.0000	+	19.0526i	0.462773	+	0.801547i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.00000			0.293455			0.146728	−	0.989177i	$-0.453126\pi$
$569$	7.00000			0.293455			0.146728	+	0.989177i	$0.453126\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$		0			0
$573$	−3.00000			−0.125327
$574$		0			0
$575$	−0.500000	−	0.866025i	−0.0208514	−	0.0361158i
$576$		0			0
$577$	3.00000	+	5.19615i	0.124892	+	0.216319i	0.921691	−	0.387926i	$-0.126808\pi$
$577$	3.00000	+	5.19615i	0.124892	+	0.216319i	−0.796799	+	0.604245i	$0.793475\pi$
$578$		0			0
$579$	16.5000	+	28.5788i	0.685717	+	1.18770i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	30.0000			1.24247
$584$		0			0
$585$	−12.0000	−	41.5692i	−0.496139	−	1.71868i
$586$		0			0
$587$	−12.5000	−	21.6506i	−0.515930	−	0.893617i	−0.999829	−	0.0184934i	$-0.994113\pi$
$587$	−12.5000	−	21.6506i	−0.515930	−	0.893617i	0.483899	−	0.875124i	$-0.339220\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$		0			0
$591$	27.0000			1.11063
$592$		0			0
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	0.271016	+	0.962575i	$0.412640\pi$
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	−0.969122	+	0.246581i	$0.920693\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	28.5000	−	49.3634i	1.16643	−	2.02031i
$598$		0			0
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	0.994732	−	0.102511i	$-0.0326876\pi$
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	−0.586143	+	0.810208i	$0.699354\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$		0			0
$603$	42.0000			1.71037
$604$		0			0
$605$	−28.0000			−1.13836
$606$		0			0
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	−0.998415	−	0.0562808i	$-0.982076\pi$
$607$	−13.5000	−	23.3827i	−0.547948	−	0.949074i	0.450467	−	0.892793i	$-0.351258\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.0000	+	3.46410i	0.566379	+	0.140143i
$612$		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	−0.927838	−	0.372985i	$-0.878334\pi$
$617$	−3.50000	+	6.06218i	−0.140905	+	0.244054i	0.786933	+	0.617039i	$0.211668\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$		0			0
$621$	9.00000			0.361158
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		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	0.217601	+	0.976038i	$0.430177\pi$
$631$	−18.5000	+	32.0429i	−0.736473	+	1.27561i	−0.954074	+	0.299571i	$0.903156\pi$
$632$		0			0
$633$	39.0000			1.55011
$634$		0			0
$635$	10.0000			0.396838
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−66.0000			−2.61092
$640$		0			0
$641$	−5.00000			−0.197488			−0.0987441	−	0.995113i	$-0.531483\pi$
$641$	−5.00000			−0.197488			−0.0987441	+	0.995113i	$0.531483\pi$
$642$		0			0
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	0.379768	+	0.925082i	$0.376004\pi$
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	−0.991028	+	0.133652i	$0.957330\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	−14.5000	+	25.1147i	−0.570054	+	0.987362i	0.426506	+	0.904485i	$0.359744\pi$
$647$	−14.5000	+	25.1147i	−0.570054	+	0.987362i	−0.996560	+	0.0828774i	$0.973589\pi$
$648$		0			0
$649$	−12.5000	+	21.6506i	−0.490668	+	0.849862i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$		0			0
$657$	42.0000	−	72.7461i	1.63858	−	2.83810i
$658$		0			0
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	0.342068	+	0.939675i	$0.388873\pi$
$659$	−16.5000	+	28.5788i	−0.642749	+	1.11327i	−0.984817	+	0.173598i	$0.944461\pi$
$660$		0			0
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	0.241605	+	0.970375i	$0.422326\pi$
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	−0.961172	+	0.275951i	$0.911007\pi$
$662$		0			0
$663$	−31.5000	−	7.79423i	−1.22336	−	0.302703i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.500000	−	0.866025i	−0.0193601	−	0.0335326i
$668$		0			0
$669$	−27.0000			−1.04388
$670$		0			0
$671$	−25.0000			−0.965114
$672$		0			0
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	0.790650	−	0.612268i	$-0.209743\pi$
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	−0.925565	+	0.378589i	$0.876409\pi$
$674$		0			0
$675$	−4.50000	−	7.79423i	−0.173205	−	0.300000i
$676$		0			0
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−31.5000	+	54.5596i	−1.20708	+	2.09073i
$682$		0			0
$683$	−11.0000			−0.420903			−0.210452	−	0.977604i	$-0.567493\pi$
$683$	−11.0000			−0.420903			−0.210452	+	0.977604i	$0.567493\pi$
$684$		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
$689$	−15.0000	+	15.5885i	−0.571454	+	0.593873i
$690$		0			0
$691$	5.00000			0.190209			0.0951045	−	0.995467i	$-0.469681\pi$
$691$	5.00000			0.190209			0.0951045	+	0.995467i	$0.469681\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.0000	+	19.0526i	0.417254	+	0.722705i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$		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
$703$	−4.50000	−	7.79423i	−0.169721	−	0.293965i
$704$		0			0
$705$	−24.0000			−0.903892
$706$		0			0
$707$		0			0
$708$		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
$711$	−24.0000			−0.900070
$712$		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	0.979860	−	0.199686i	$-0.0639923\pi$
$719$	8.50000	+	14.7224i	0.316997	+	0.549054i	−0.662863	+	0.748740i	$0.730659\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	31.5000	−	54.5596i	1.17150	−	2.02909i
$724$		0			0
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$		0			0
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$		0			0
$735$		0			0
$736$		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	0.999304	+	0.0372984i	$0.0118752\pi$
$743$	14.5000	+	25.1147i	0.531953	+	0.921370i	−0.467351	+	0.884072i	$0.654791\pi$
$744$		0			0
$745$	42.0000			1.53876
$746$		0			0
$747$	36.0000	+	62.3538i	1.31717	+	2.28141i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.00000			−0.328415			−0.164207	−	0.986426i	$-0.552507\pi$
$751$	−9.00000			−0.328415			−0.164207	+	0.986426i	$0.552507\pi$
$752$		0			0
$753$	−13.5000	−	23.3827i	−0.491967	−	0.852112i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$		0			0
$759$	7.50000	+	12.9904i	0.272233	+	0.471521i
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	36.0000			1.30158
$766$		0			0
$767$	−5.00000	−	17.3205i	−0.180540	−	0.625407i
$768$		0			0
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	0.612225	−	0.790684i	$-0.290275\pi$
$769$	−10.5000	−	18.1865i	−0.378640	−	0.655823i	−0.990865	+	0.134860i	$0.956941\pi$
$770$		0			0
$771$	−4.50000	+	7.79423i	−0.162064	+	0.280702i
$772$		0			0
$773$	1.00000			0.0359675			0.0179838	−	0.999838i	$-0.494275\pi$
$773$	1.00000			0.0359675			0.0179838	+	0.999838i	$0.494275\pi$
$774$		0			0
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$		0			0
$781$	−27.5000	−	47.6314i	−0.984027	−	1.70439i
$782$		0			0
$783$	−4.50000	−	7.79423i	−0.160817	−	0.278543i
$784$		0			0
$785$	−44.0000			−1.57043
$786$		0			0
$787$	7.00000			0.249523			0.124762	−	0.992187i	$-0.460183\pi$
$787$	7.00000			0.249523			0.124762	+	0.992187i	$0.460183\pi$
$788$		0			0
$789$	22.5000	+	38.9711i	0.801021	+	1.38741i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	12.5000	−	12.9904i	0.443888	−	0.461302i
$794$		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	$-0.674625\pi$
$797$	13.5000	−	23.3827i	0.478195	−	0.828257i	0.999687	+	0.0249984i	$0.00795805\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$		0			0
$801$	−27.0000	−	46.7654i	−0.953998	−	1.65237i
$802$		0			0
$803$	70.0000			2.47025
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−22.5000	+	38.9711i	−0.792038	+	1.37185i
$808$		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	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$	25.5000	−	44.1673i	0.894324	−	1.54901i
$814$		0			0
$815$	14.0000			0.490399
$816$		0			0
$817$	3.00000			0.104957
$818$		0			0
$819$		0			0
$820$		0			0
$821$	47.0000			1.64031			0.820156	−	0.572140i	$-0.193887\pi$
$821$	47.0000			1.64031			0.820156	+	0.572140i	$0.193887\pi$
$822$		0			0
$823$	−3.00000			−0.104573			−0.0522867	−	0.998632i	$-0.516651\pi$
$823$	−3.00000			−0.104573			−0.0522867	+	0.998632i	$0.516651\pi$
$824$		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	$-0.652386\pi$
$829$	15.5000	−	26.8468i	0.538337	−	0.932427i	0.998994	−	0.0448490i	$-0.0142807\pi$
$830$		0			0
$831$	−13.5000	+	23.3827i	−0.468310	+	0.811136i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.0000			−0.622916
$836$		0			0
$837$	36.0000	+	62.3538i	1.24434	+	2.15526i
$838$		0			0
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	0.209200	+	0.977873i	$0.432914\pi$
$839$	−21.5000	+	37.2391i	−0.742262	+	1.28564i	−0.951463	+	0.307763i	$0.900419\pi$
$840$		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
$845$	1.00000	+	25.9808i	0.0344010	+	0.893765i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−28.5000	−	49.3634i	−0.978117	−	1.69415i
$850$		0			0
$851$	−3.00000			−0.102839
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$	18.0000	+	31.1769i	0.615587	+	1.06623i
$856$		0			0
$857$	−1.00000	−	1.73205i	−0.0341593	−	0.0591657i	0.848440	−	0.529291i	$-0.177542\pi$
$857$	−1.00000	−	1.73205i	−0.0341593	−	0.0591657i	−0.882600	+	0.470125i	$0.844209\pi$
$858$		0			0
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	−0.999672	−	0.0255910i	$-0.991853\pi$
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	0.521999	+	0.852946i	$0.325187\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	−0.969456	−	0.245264i	$-0.921125\pi$
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	0.697133	+	0.716942i	$0.254459\pi$
$864$		0			0
$865$	22.0000			0.748022
$866$		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
$871$	−24.5000	−	6.06218i	−0.830151	−	0.205409i
$872$		0			0
$873$	6.00000			0.203069
$874$		0			0
$875$		0			0
$876$		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
$879$	−28.5000	−	49.3634i	−0.961281	−	1.66499i
$880$		0			0
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	0.872772	+	0.488127i	$0.162320\pi$
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	−0.0136556	+	0.999907i	$0.504347\pi$
$882$		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
$885$	15.0000	+	25.9808i	0.504219	+	0.873334i
$886$		0			0
$887$	53.0000			1.77957			0.889783	−	0.456384i	$-0.150856\pi$
$887$	53.0000			1.77957			0.889783	+	0.456384i	$0.150856\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$		0			0
$893$	−12.0000			−0.401565
$894$		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
$903$		0			0
$904$		0			0
$905$	−18.0000	+	31.1769i	−0.598340	+	1.03636i
$906$		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
$915$	−15.0000	+	25.9808i	−0.495885	+	0.858898i
$916$		0			0
$917$		0			0
$918$		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
$927$	48.0000			1.57653
$928$		0			0
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−72.0000			−2.35717
$934$		0			0
$935$	15.0000	+	25.9808i	0.490552	+	0.849662i
$936$		0			0
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$		0			0
$939$	−21.0000	−	36.3731i	−0.685309	−	1.18699i
$940$		0			0
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	−0.909345	−	0.416044i	$-0.863416\pi$
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	0.0943679	−	0.995537i	$-0.469917\pi$
$942$		0			0
$943$	−1.50000	−	2.59808i	−0.0488467	−	0.0846050i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0000			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$948$		0			0
$949$	−35.0000	+	36.3731i	−1.13615	+	1.18072i
$950$		0			0
$951$	45.0000	+	77.9423i	1.45922	+	2.52745i
$952$		0			0
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	−0.857814	−	0.513961i	$-0.828178\pi$
$953$	0.500000	−	0.866025i	0.0161966	−	0.0280533i	0.874010	+	0.485908i	$0.161511\pi$
$954$		0			0
$955$	−2.00000			−0.0647185
$956$		0			0
$957$	7.50000	−	12.9904i	0.242441	−	0.419919i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$	−33.0000	−	57.1577i	−1.06341	−	1.84188i
$964$		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
$969$	27.0000			0.867365
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.00000	+	10.3923i	0.0960769	+	0.332820i
$976$		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
$983$	−8.00000	−	13.8564i	−0.255160	−	0.441951i	0.709779	−	0.704425i	$-0.248795\pi$
$983$	−8.00000	−	13.8564i	−0.255160	−	0.441951i	−0.964939	+	0.262474i	$0.915462\pi$
$984$		0			0
$985$	18.0000			0.573528
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.500000	−	0.866025i	0.0158991	−	0.0275380i
$990$		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
$997$	−35.0000			−1.10846			−0.554231	−	0.832363i	$-0.686987\pi$
$997$	−35.0000			−1.10846			−0.554231	+	0.832363i	$0.686987\pi$
$998$		0			0
$999$	−27.0000			−0.854242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.i.h.1745.1		2
7.2	even	3		2548.2.k.d.393.1		2
7.3	odd	6		2548.2.l.h.1537.1		2
7.4	even	3		2548.2.l.a.1537.1		2
7.5	odd	6		52.2.e.a.29.1	yes	2
7.6	odd	2		2548.2.i.a.1745.1		2
13.9	even	3		2548.2.l.a.373.1		2
21.5	even	6		468.2.l.a.289.1		2
28.19	even	6		208.2.i.d.81.1		2
35.12	even	12		1300.2.bb.f.549.1		4
35.19	odd	6		1300.2.i.f.601.1		2
35.33	even	12		1300.2.bb.f.549.2		4
56.5	odd	6		832.2.i.j.705.1		2
56.19	even	6		832.2.i.a.705.1		2
84.47	odd	6		1872.2.t.f.289.1		2
91.5	even	12		676.2.h.b.361.1		4
91.9	even	3		2548.2.k.d.1569.1		2
91.12	odd	6		676.2.e.a.653.1		2
91.19	even	12		676.2.h.b.485.1		4
91.33	even	12		676.2.h.b.485.2		4
91.47	even	12		676.2.h.b.361.2		4
91.48	odd	6		2548.2.l.h.373.1		2
91.54	even	12		676.2.d.d.337.1		2
91.61	odd	6		52.2.e.a.9.1	✓	2
91.68	odd	6		676.2.a.e.1.1		1
91.74	even	3	inner	2548.2.i.h.165.1		2
91.75	odd	6		676.2.a.d.1.1		1
91.82	odd	6		676.2.e.a.529.1		2
91.87	odd	6		2548.2.i.a.165.1		2
91.89	even	12		676.2.d.d.337.2		2
273.68	even	6		6084.2.a.f.1.1		1
273.89	odd	12		6084.2.b.l.4393.1		2
273.152	even	6		468.2.l.a.217.1		2
273.236	odd	12		6084.2.b.l.4393.2		2
273.257	even	6		6084.2.a.k.1.1		1
364.75	even	6		2704.2.a.a.1.1		1
364.159	even	6		2704.2.a.b.1.1		1
364.243	even	6		208.2.i.d.113.1		2
364.271	odd	12		2704.2.f.a.337.2		2
364.327	odd	12		2704.2.f.a.337.1		2
455.152	even	12		1300.2.bb.f.1049.2		4
455.243	even	12		1300.2.bb.f.1049.1		4
455.334	odd	6		1300.2.i.f.1101.1		2
728.61	odd	6		832.2.i.j.321.1		2
728.243	even	6		832.2.i.a.321.1		2
1092.971	odd	6		1872.2.t.f.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.a.9.1	✓	2	91.61	odd	6
52.2.e.a.29.1	yes	2	7.5	odd	6
208.2.i.d.81.1		2	28.19	even	6
208.2.i.d.113.1		2	364.243	even	6
468.2.l.a.217.1		2	273.152	even	6
468.2.l.a.289.1		2	21.5	even	6
676.2.a.d.1.1		1	91.75	odd	6
676.2.a.e.1.1		1	91.68	odd	6
676.2.d.d.337.1		2	91.54	even	12
676.2.d.d.337.2		2	91.89	even	12
676.2.e.a.529.1		2	91.82	odd	6
676.2.e.a.653.1		2	91.12	odd	6
676.2.h.b.361.1		4	91.5	even	12
676.2.h.b.361.2		4	91.47	even	12
676.2.h.b.485.1		4	91.19	even	12
676.2.h.b.485.2		4	91.33	even	12
832.2.i.a.321.1		2	728.243	even	6
832.2.i.a.705.1		2	56.19	even	6
832.2.i.j.321.1		2	728.61	odd	6
832.2.i.j.705.1		2	56.5	odd	6
1300.2.i.f.601.1		2	35.19	odd	6
1300.2.i.f.1101.1		2	455.334	odd	6
1300.2.bb.f.549.1		4	35.12	even	12
1300.2.bb.f.549.2		4	35.33	even	12
1300.2.bb.f.1049.1		4	455.243	even	12
1300.2.bb.f.1049.2		4	455.152	even	12
1872.2.t.f.289.1		2	84.47	odd	6
1872.2.t.f.1153.1		2	1092.971	odd	6
2548.2.i.a.165.1		2	91.87	odd	6
2548.2.i.a.1745.1		2	7.6	odd	2
2548.2.i.h.165.1		2	91.74	even	3	inner
2548.2.i.h.1745.1		2	1.1	even	1	trivial
2548.2.k.d.393.1		2	7.2	even	3
2548.2.k.d.1569.1		2	91.9	even	3
2548.2.l.a.373.1		2	13.9	even	3
2548.2.l.a.1537.1		2	7.4	even	3
2548.2.l.h.373.1		2	91.48	odd	6
2548.2.l.h.1537.1		2	7.3	odd	6
2704.2.a.a.1.1		1	364.75	even	6
2704.2.a.b.1.1		1	364.159	even	6
2704.2.f.a.337.1		2	364.327	odd	12
2704.2.f.a.337.2		2	364.271	odd	12
6084.2.a.f.1.1		1	273.68	even	6
6084.2.a.k.1.1		1	273.257	even	6
6084.2.b.l.4393.1		2	273.89	odd	12
6084.2.b.l.4393.2		2	273.236	odd	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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{19} -1.00000 q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-7.50000 - 12.9904i) q^{33} +3.00000 q^{37} +(10.5000 + 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} -12.0000 q^{45} +(2.00000 - 3.46410i) q^{47} +(-4.50000 + 7.79423i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-5.00000 - 8.66025i) q^{55} -9.00000 q^{57} -5.00000 q^{59} +(-2.50000 - 4.33013i) q^{61} +(7.00000 + 1.73205i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(5.50000 - 9.52628i) q^{71} +(7.00000 + 12.1244i) q^{73} +3.00000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(-3.00000 + 5.19615i) q^{85} +3.00000 q^{87} +9.00000 q^{89} -24.0000 q^{93} -6.00000 q^{95} +(-0.500000 + 0.866025i) q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^5 - 6 * q^9	\( 2 q + 3 q^{3} + 2 q^{5} - 6 q^{9} + 5 q^{11} + 2 q^{13} - 6 q^{15} - 6 q^{17} - 3 q^{19} - 2 q^{23} + q^{25} - 18 q^{27} + q^{29} - 8 q^{31} - 15 q^{33} + 6 q^{37} + 21 q^{39} + 3 q^{41} - q^{43} - 24 q^{45} + 4 q^{47} - 9 q^{51} + 6 q^{53} - 10 q^{55} - 18 q^{57} - 10 q^{59} - 5 q^{61} + 14 q^{65} - 7 q^{67} - 3 q^{69} + 11 q^{71} + 14 q^{73} + 6 q^{75} + 4 q^{79} - 9 q^{81} - 24 q^{83} - 6 q^{85} + 6 q^{87} + 18 q^{89} - 48 q^{93} - 12 q^{95} - q^{97} - 60 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^5 - 6 * q^9 + 5 * q^11 + 2 * q^13 - 6 * q^15 - 6 * q^17 - 3 * q^19 - 2 * q^23 + q^25 - 18 * q^27 + q^29 - 8 * q^31 - 15 * q^33 + 6 * q^37 + 21 * q^39 + 3 * q^41 - q^43 - 24 * q^45 + 4 * q^47 - 9 * q^51 + 6 * q^53 - 10 * q^55 - 18 * q^57 - 10 * q^59 - 5 * q^61 + 14 * q^65 - 7 * q^67 - 3 * q^69 + 11 * q^71 + 14 * q^73 + 6 * q^75 + 4 * q^79 - 9 * q^81 - 24 * q^83 - 6 * q^85 + 6 * q^87 + 18 * q^89 - 48 * q^93 - 12 * q^95 - q^97 - 60 * q^99

Introduction

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