LMFDB - Embedded newform 1008.2.df.a.929.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			929.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.929
Dual form			1008.2.df.a.689.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{11} +(-1.50000 + 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(1.50000 + 2.59808i) q^{17} +(4.50000 + 2.59808i) q^{19} +(3.00000 + 3.46410i) q^{21} +5.19615i q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-4.50000 - 2.59808i) q^{29} +(3.00000 + 1.73205i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-7.50000 - 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} -3.00000 q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(5.50000 + 4.33013i) q^{49} +5.19615i q^{51} +(-7.50000 + 4.33013i) q^{53} +5.19615i q^{55} +(4.50000 + 7.79423i) q^{57} +(12.0000 - 6.92820i) q^{61} +(1.50000 + 7.79423i) q^{63} +(4.50000 - 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-4.50000 + 7.79423i) q^{69} -3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(6.00000 + 3.46410i) q^{75} +(1.50000 - 4.33013i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.50000 - 12.9904i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-4.50000 - 7.79423i) q^{87} +(1.50000 - 2.59808i) q^{89} +(-4.50000 + 0.866025i) q^{91} +(3.00000 + 5.19615i) q^{93} +(-13.5000 - 7.79423i) q^{95} +(-1.50000 - 0.866025i) q^{97} +(4.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 6 q^{5} + 5 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 6 * q^5 + 5 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 6 q^{5} + 5 q^{7} + 3 q^{9} - 3 q^{13} - 9 q^{15} + 3 q^{17} + 9 q^{19} + 6 q^{21} + 8 q^{25} - 9 q^{29} + 6 q^{31} + 3 q^{33} - 15 q^{35} - 7 q^{37} - 6 q^{39} + 3 q^{41} + q^{43} - 9 q^{45} + 11 q^{49} - 15 q^{53} + 9 q^{57} + 24 q^{61} + 3 q^{63} + 9 q^{65} - 4 q^{67} - 9 q^{69} - 9 q^{73} + 12 q^{75} + 3 q^{77} + 8 q^{79} - 9 q^{81} + 15 q^{83} - 9 q^{85} - 9 q^{87} + 3 q^{89} - 9 q^{91} + 6 q^{93} - 27 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 6 * q^5 + 5 * q^7 + 3 * q^9 - 3 * q^13 - 9 * q^15 + 3 * q^17 + 9 * q^19 + 6 * q^21 + 8 * q^25 - 9 * q^29 + 6 * q^31 + 3 * q^33 - 15 * q^35 - 7 * q^37 - 6 * q^39 + 3 * q^41 + q^43 - 9 * q^45 + 11 * q^49 - 15 * q^53 + 9 * q^57 + 24 * q^61 + 3 * q^63 + 9 * q^65 - 4 * q^67 - 9 * q^69 - 9 * q^73 + 12 * q^75 + 3 * q^77 + 8 * q^79 - 9 * q^81 + 15 * q^83 - 9 * q^85 - 9 * q^87 + 3 * q^89 - 9 * q^91 + 6 * q^93 - 27 * q^95 - 3 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		0			0
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$		−	1.73205i		−	0.522233i	−0.965307	−	0.261116i	$-0.915909\pi$
$11$		−	1.73205i		−	0.522233i	0.965307	−	0.261116i	$-0.0840907\pi$
$12$		0			0
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$		0			0
$23$			5.19615i			1.08347i	0.840548	+	0.541736i	$0.182233\pi$
$23$			5.19615i			1.08347i	−0.840548	+	0.541736i	$0.817767\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.50000	−	2.59808i	−0.835629	−	0.482451i	0.0201471	−	0.999797i	$-0.493587\pi$
$29$	−4.50000	−	2.59808i	−0.835629	−	0.482451i	−0.855776	+	0.517346i	$0.826920\pi$
$30$		0			0
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$		0			0
$39$	−3.00000			−0.480384
$40$		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	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$		0			0
$45$	−4.50000	−	7.79423i	−0.670820	−	1.16190i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$			5.19615i			0.727607i
$52$		0			0
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.917043	−	0.398788i	$-0.869431\pi$
$53$	−7.50000	+	4.33013i	−1.03020	+	0.594789i	−0.113161	+	0.993577i	$0.536098\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$		0			0
$57$	4.50000	+	7.79423i	0.596040	+	1.03237i
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$		0			0
$63$	1.50000	+	7.79423i	0.188982	+	0.981981i
$64$		0			0
$65$	4.50000	−	2.59808i	0.558156	−	0.322252i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$	−4.50000	+	7.79423i	−0.541736	+	0.938315i
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$		0			0
$73$	−4.50000	+	2.59808i	−0.526685	+	0.304082i	−0.739666	−	0.672975i	$-0.765016\pi$
$73$	−4.50000	+	2.59808i	−0.526685	+	0.304082i	0.212980	+	0.977056i	$0.431683\pi$
$74$		0			0
$75$	6.00000	+	3.46410i	0.692820	+	0.400000i
$76$		0			0
$77$	1.50000	−	4.33013i	0.170941	−	0.493464i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	−0.0800311	−	0.996792i	$-0.525502\pi$
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	0.903263	−	0.429087i	$-0.141165\pi$
$84$		0			0
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$		0			0
$87$	−4.50000	−	7.79423i	−0.482451	−	0.835629i
$88$		0			0
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	−4.50000	+	0.866025i	−0.471728	+	0.0907841i
$92$		0			0
$93$	3.00000	+	5.19615i	0.311086	+	0.538816i
$94$		0			0
$95$	−13.5000	−	7.79423i	−1.38507	−	0.799671i
$96$		0			0
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	0.421912	−	0.906637i	$-0.361359\pi$
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	−0.574214	+	0.818705i	$0.694692\pi$
$98$		0			0
$99$	4.50000	−	2.59808i	0.452267	−	0.261116i
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$		−	12.1244i		−	1.19465i	−0.802000	−	0.597324i	$-0.796231\pi$
$103$		−	12.1244i		−	1.19465i	0.802000	−	0.597324i	$-0.203769\pi$
$104$		0			0
$105$	−9.00000	−	10.3923i	−0.878310	−	1.01419i
$106$		0			0
$107$	7.50000	+	4.33013i	0.725052	+	0.418609i	0.816609	−	0.577191i	$-0.195851\pi$
$107$	7.50000	+	4.33013i	0.725052	+	0.418609i	−0.0915571	+	0.995800i	$0.529184\pi$
$108$		0			0
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−9.50000	−	16.4545i	−0.909935	−	1.57605i	−0.0957826	−	0.995402i	$-0.530535\pi$
$110$		0			0
$111$	−10.5000	+	6.06218i	−0.996616	+	0.575396i
$112$		0			0
$113$	1.50000	−	0.866025i	0.141108	−	0.0814688i	−0.427784	−	0.903881i	$-0.640706\pi$
$113$	1.50000	−	0.866025i	0.141108	−	0.0814688i	0.568892	+	0.822412i	$0.307372\pi$
$114$		0			0
$115$		−	15.5885i		−	1.45363i
$116$		0			0
$117$	−4.50000	−	2.59808i	−0.416025	−	0.240192i
$118$		0			0
$119$	1.50000	+	7.79423i	0.137505	+	0.714496i
$120$		0			0
$121$	8.00000			0.727273
$122$		0			0
$123$			5.19615i			0.468521i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$		0			0
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$		0			0
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$		0			0
$133$	9.00000	+	10.3923i	0.780399	+	0.901127i
$134$		0			0
$135$		−	15.5885i		−	1.34164i
$136$		0			0
$137$		−	12.1244i		−	1.03585i	−0.855425	−	0.517927i	$-0.826704\pi$
$137$		−	12.1244i		−	1.03585i	0.855425	−	0.517927i	$-0.173296\pi$
$138$		0			0
$139$	7.50000	−	4.33013i	0.636142	−	0.367277i	−0.146985	−	0.989139i	$-0.546957\pi$
$139$	7.50000	−	4.33013i	0.636142	−	0.367277i	0.783127	+	0.621862i	$0.213624\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	13.5000	+	7.79423i	1.12111	+	0.647275i
$146$		0			0
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$		0			0
$149$		−	1.73205i		−	0.141895i	−0.997480	−	0.0709476i	$-0.977398\pi$
$149$		−	1.73205i		−	0.141895i	0.997480	−	0.0709476i	$-0.0226023\pi$
$150$		0			0
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$		0			0
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$	−9.00000	−	5.19615i	−0.722897	−	0.417365i
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$	−15.0000			−1.18958
$160$		0			0
$161$	−4.50000	+	12.9904i	−0.354650	+	1.02379i
$162$		0			0
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$		0			0
$165$	−4.50000	+	7.79423i	−0.350325	+	0.606780i
$166$		0			0
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	0.985933	−	0.167139i	$-0.0534527\pi$
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	−0.637713	+	0.770274i	$0.720119\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$			15.5885i			1.19208i
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.5000	+	7.79423i	−1.00904	+	0.582568i	−0.910910	−	0.412606i	$-0.864619\pi$
$179$	−13.5000	+	7.79423i	−1.00904	+	0.582568i	−0.0981277	+	0.995174i	$0.531285\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	24.0000			1.77413
$184$		0			0
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$		0			0
$187$	4.50000	−	2.59808i	0.329073	−	0.189990i
$188$		0			0
$189$	−4.50000	+	12.9904i	−0.327327	+	0.944911i
$190$		0			0
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.153024	−	0.988222i	$-0.451099\pi$
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.932338	+	0.361588i	$0.117765\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$		0			0
$195$	9.00000			0.644503
$196$		0			0
$197$		−	13.8564i		−	0.987228i	−0.869681	−	0.493614i	$-0.835676\pi$
$197$		−	13.8564i		−	0.987228i	0.869681	−	0.493614i	$-0.164324\pi$
$198$		0			0
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	−0.210032	−	0.977695i	$-0.567357\pi$
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	0.741693	+	0.670740i	$0.234023\pi$
$200$		0			0
$201$	−6.00000	+	3.46410i	−0.423207	+	0.244339i
$202$		0			0
$203$	−9.00000	−	10.3923i	−0.631676	−	0.729397i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	−13.5000	+	7.79423i	−0.938315	+	0.541736i
$208$		0			0
$209$	4.50000	−	7.79423i	0.311272	−	0.539138i
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$		0			0
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$		0			0
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$		0			0
$217$	6.00000	+	6.92820i	0.407307	+	0.470317i
$218$		0			0
$219$	−9.00000			−0.608164
$220$		0			0
$221$	−4.50000	−	2.59808i	−0.302703	−	0.174766i
$222$		0			0
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	0.643046	−	0.765828i	$-0.277671\pi$
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	−0.341703	+	0.939808i	$0.611004\pi$
$224$		0			0
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$		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
$229$			8.66025i			0.572286i	0.958187	+	0.286143i	$0.0923732\pi$
$229$			8.66025i			0.572286i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	6.00000	−	5.19615i	0.394771	−	0.341882i
$232$		0			0
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	0.640107	−	0.768286i	$-0.278890\pi$
$233$	4.50000	+	2.59808i	0.294805	+	0.170206i	−0.345302	+	0.938492i	$0.612223\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			13.8564i			0.900070i
$238$		0			0
$239$	−1.50000	+	0.866025i	−0.0970269	+	0.0560185i	−0.547728	−	0.836656i	$-0.684507\pi$
$239$	−1.50000	+	0.866025i	−0.0970269	+	0.0560185i	0.450701	+	0.892675i	$0.351174\pi$
$240$		0			0
$241$		−	22.5167i		−	1.45043i	−0.688525	−	0.725213i	$-0.741741\pi$
$241$		−	22.5167i		−	1.45043i	0.688525	−	0.725213i	$-0.258259\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		0			0
$245$	−16.5000	−	12.9904i	−1.05415	−	0.829925i
$246$		0			0
$247$	−9.00000			−0.572656
$248$		0			0
$249$	22.5000	−	12.9904i	1.42588	−	0.823232i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		−	15.5885i		−	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
$259$	−14.0000	+	12.1244i	−0.869918	+	0.753371i
$260$		0			0
$261$		−	15.5885i		−	0.964901i
$262$		0			0
$263$		−	22.5167i		−	1.38844i	−0.719764	−	0.694218i	$-0.755750\pi$
$263$		−	22.5167i		−	1.38844i	0.719764	−	0.694218i	$-0.244250\pi$
$264$		0			0
$265$	22.5000	−	12.9904i	1.38216	−	0.797993i
$266$		0			0
$267$	4.50000	−	2.59808i	0.275396	−	0.159000i
$268$		0			0
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	0.783778	−	0.621041i	$-0.213290\pi$
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	−0.145948	+	0.989292i	$0.546623\pi$
$272$		0			0
$273$	−7.50000	−	2.59808i	−0.453921	−	0.157243i
$274$		0			0
$275$		−	6.92820i		−	0.417786i
$276$		0			0
$277$	−1.00000			−0.0600842			−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000			−0.0600842			−0.0300421	+	0.999549i	$0.509564\pi$
$278$		0			0
$279$			10.3923i			0.622171i
$280$		0			0
$281$	−16.5000	−	9.52628i	−0.984307	−	0.568290i	−0.0807396	−	0.996735i	$-0.525728\pi$
$281$	−16.5000	−	9.52628i	−0.984307	−	0.568290i	−0.903568	+	0.428445i	$0.859062\pi$
$282$		0			0
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	0.408177	−	0.912903i	$-0.366165\pi$
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	−0.586509	+	0.809943i	$0.699498\pi$
$284$		0			0
$285$	−13.5000	−	23.3827i	−0.799671	−	1.38507i
$286$		0			0
$287$	1.50000	+	7.79423i	0.0885422	+	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−1.50000	−	2.59808i	−0.0879316	−	0.152302i
$292$		0			0
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	9.00000			0.522233
$298$		0			0
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$	2.00000	−	1.73205i	0.115278	−	0.0998337i
$302$		0			0
$303$	−4.50000	−	2.59808i	−0.258518	−	0.149256i
$304$		0			0
$305$	−36.0000	+	20.7846i	−2.06135	+	1.19012i
$306$		0			0
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$		0			0
$309$	10.5000	−	18.1865i	0.597324	−	1.03460i
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.913356	−	0.407163i	$-0.866518\pi$
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.104065	+	0.994571i	$0.533185\pi$
$314$		0			0
$315$	−4.50000	−	23.3827i	−0.253546	−	1.31747i
$316$		0			0
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		0			0
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$		0			0
$321$	7.50000	+	12.9904i	0.418609	+	0.725052i
$322$		0			0
$323$			15.5885i			0.867365i
$324$		0			0
$325$	−6.00000	+	3.46410i	−0.332820	+	0.192154i
$326$		0			0
$327$		−	32.9090i		−	1.81987i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	−21.0000			−1.15079
$334$		0			0
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$		0			0
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	−0.999793	−	0.0203242i	$-0.993530\pi$
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	0.482295	−	0.876009i	$-0.339803\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	13.5000	−	23.3827i	0.726816	−	1.25888i
$346$		0			0
$347$	3.00000	+	1.73205i	0.161048	+	0.0929814i	0.578358	−	0.815783i	$-0.303694\pi$
$347$	3.00000	+	1.73205i	0.161048	+	0.0929814i	−0.417310	+	0.908764i	$0.637027\pi$
$348$		0			0
$349$	10.5000	+	6.06218i	0.562052	+	0.324501i	0.753969	−	0.656910i	$-0.228137\pi$
$349$	10.5000	+	6.06218i	0.562052	+	0.324501i	−0.191917	+	0.981411i	$0.561470\pi$
$350$		0			0
$351$	−4.50000	−	7.79423i	−0.240192	−	0.416025i
$352$		0			0
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$		0			0
$355$			10.3923i			0.551566i
$356$		0			0
$357$	−4.50000	+	12.9904i	−0.238165	+	0.687524i
$358$		0			0
$359$	19.5000	+	11.2583i	1.02917	+	0.594192i	0.916747	−	0.399468i	$-0.130805\pi$
$359$	19.5000	+	11.2583i	1.02917	+	0.594192i	0.112424	+	0.993660i	$0.464139\pi$
$360$		0			0
$361$	4.00000	+	6.92820i	0.210526	+	0.364642i
$362$		0			0
$363$	12.0000	+	6.92820i	0.629837	+	0.363636i
$364$		0			0
$365$	13.5000	−	7.79423i	0.706622	−	0.407969i
$366$		0			0
$367$		−	5.19615i		−	0.271237i	−0.990761	−	0.135618i	$-0.956698\pi$
$367$		−	5.19615i		−	0.271237i	0.990761	−	0.135618i	$-0.0433021\pi$
$368$		0			0
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$	−22.5000	+	4.33013i	−1.16814	+	0.224809i
$372$		0			0
$373$	−37.0000			−1.91579			−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000			−1.91579			−0.957894	+	0.287123i	$0.907301\pi$
$374$		0			0
$375$	4.50000	+	2.59808i	0.232379	+	0.134164i
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	−30.0000	−	17.3205i	−1.53695	−	0.887357i
$382$		0			0
$383$	9.00000			0.459879			0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000			0.459879			0.229939	+	0.973205i	$0.426147\pi$
$384$		0			0
$385$	−4.50000	+	12.9904i	−0.229341	+	0.662051i
$386$		0			0
$387$	3.00000			0.152499
$388$		0			0
$389$			36.3731i			1.84419i	0.386966	+	0.922094i	$0.373523\pi$
$389$			36.3731i			1.84419i	−0.386966	+	0.922094i	$0.626477\pi$
$390$		0			0
$391$	−13.5000	+	7.79423i	−0.682724	+	0.394171i
$392$		0			0
$393$	13.5000	+	7.79423i	0.680985	+	0.393167i
$394$		0			0
$395$	−12.0000	−	20.7846i	−0.603786	−	1.04579i
$396$		0			0
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	0.676257	−	0.736666i	$-0.263601\pi$
$397$	7.50000	+	4.33013i	0.376414	+	0.217323i	−0.299843	+	0.953989i	$0.596934\pi$
$398$		0			0
$399$	4.50000	+	23.3827i	0.225282	+	1.17060i
$400$		0			0
$401$			32.9090i			1.64340i	0.569924	+	0.821698i	$0.306973\pi$
$401$			32.9090i			1.64340i	−0.569924	+	0.821698i	$0.693027\pi$
$402$		0			0
$403$	−6.00000			−0.298881
$404$		0			0
$405$	13.5000	−	23.3827i	0.670820	−	1.16190i
$406$		0			0
$407$	10.5000	+	6.06218i	0.520466	+	0.300491i
$408$		0			0
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$		0			0
$411$	10.5000	−	18.1865i	0.517927	−	0.897076i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−22.5000	+	38.9711i	−1.10448	+	1.91302i
$416$		0			0
$417$	15.0000			0.734553
$418$		0			0
$419$	16.5000	+	28.5788i	0.806078	+	1.39617i	0.915561	+	0.402179i	$0.131747\pi$
$419$	16.5000	+	28.5788i	0.806078	+	1.39617i	−0.109483	+	0.993989i	$0.534920\pi$
$420$		0			0
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	−0.968359	−	0.249561i	$-0.919714\pi$
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	0.700306	+	0.713843i	$0.253047\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	36.0000	−	6.92820i	1.74216	−	0.335279i
$428$		0			0
$429$			5.19615i			0.250873i
$430$		0			0
$431$	−13.5000	+	7.79423i	−0.650272	+	0.375435i	−0.788560	−	0.614957i	$-0.789173\pi$
$431$	−13.5000	+	7.79423i	−0.650272	+	0.375435i	0.138288	+	0.990392i	$0.455840\pi$
$432$		0			0
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$		0			0
$435$	13.5000	+	23.3827i	0.647275	+	1.12111i
$436$		0			0
$437$	−13.5000	+	23.3827i	−0.645793	+	1.11855i
$438$		0			0
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−27.0000	+	15.5885i	−1.28864	+	0.743996i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$	−27.0000	+	15.5885i	−1.28281	+	0.740630i	−0.977361	−	0.211579i	$-0.932139\pi$
$443$	−27.0000	+	15.5885i	−1.28281	+	0.740630i	−0.305448	+	0.952209i	$0.598806\pi$
$444$		0			0
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$		0			0
$447$	1.50000	−	2.59808i	0.0709476	−	0.122885i
$448$		0			0
$449$			34.6410i			1.63481i	0.576063	+	0.817405i	$0.304588\pi$
$449$			34.6410i			1.63481i	−0.576063	+	0.817405i	$0.695412\pi$
$450$		0			0
$451$	4.50000	−	2.59808i	0.211897	−	0.122339i
$452$		0			0
$453$	25.5000	+	14.7224i	1.19809	+	0.691720i
$454$		0			0
$455$	13.5000	−	2.59808i	0.632890	−	0.121800i
$456$		0			0
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$		0			0
$459$	−13.5000	+	7.79423i	−0.630126	+	0.363803i
$460$		0			0
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	−0.636817	−	0.771015i	$-0.719749\pi$
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	0.986127	+	0.165992i	$0.0530827\pi$
$462$		0			0
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	0.854173	−	0.519989i	$-0.174064\pi$
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	−0.877410	+	0.479741i	$0.840731\pi$
$464$		0			0
$465$	−9.00000	−	15.5885i	−0.417365	−	0.722897i
$466$		0			0
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	0.829231	+	0.558906i	$0.188779\pi$
$468$		0			0
$469$	−8.00000	+	6.92820i	−0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.50000	−	0.866025i	−0.0689701	−	0.0398199i
$474$		0			0
$475$	18.0000	+	10.3923i	0.825897	+	0.476832i
$476$		0			0
$477$	−22.5000	−	12.9904i	−1.03020	−	0.594789i
$478$		0			0
$479$	27.0000			1.23366			0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000			1.23366			0.616831	+	0.787096i	$0.288416\pi$
$480$		0			0
$481$		−	12.1244i		−	0.552823i
$482$		0			0
$483$	−18.0000	+	15.5885i	−0.819028	+	0.709299i
$484$		0			0
$485$	4.50000	+	2.59808i	0.204334	+	0.117973i
$486$		0			0
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$		0			0
$489$	16.5000	−	9.52628i	0.746156	−	0.430793i
$490$		0			0
$491$	22.5000	−	12.9904i	1.01541	−	0.586248i	0.102639	−	0.994719i	$-0.467271\pi$
$491$	22.5000	−	12.9904i	1.01541	−	0.586248i	0.912771	+	0.408471i	$0.133938\pi$
$492$		0			0
$493$		−	15.5885i		−	0.702069i
$494$		0			0
$495$	−13.5000	+	7.79423i	−0.606780	+	0.350325i
$496$		0			0
$497$	3.00000	−	8.66025i	0.134568	−	0.388465i
$498$		0			0
$499$	−25.0000			−1.11915			−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000			−1.11915			−0.559577	+	0.828778i	$0.689036\pi$
$500$		0			0
$501$			15.5885i			0.696441i
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$	−15.0000	+	8.66025i	−0.666173	+	0.384615i
$508$		0			0
$509$	33.0000			1.46270			0.731350	−	0.682003i	$-0.238891\pi$
$509$	33.0000			1.46270			0.731350	+	0.682003i	$0.238891\pi$
$510$		0			0
$511$	−13.5000	+	2.59808i	−0.597205	+	0.114932i
$512$		0			0
$513$	−13.5000	+	23.3827i	−0.596040	+	1.03237i
$514$		0			0
$515$			36.3731i			1.60279i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	10.3923i		−	0.456172i
$520$		0			0
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.638588	−	0.769549i	$-0.720481\pi$
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.347155	−	0.937808i	$-0.612852\pi$
$522$		0			0
$523$	16.5000	+	9.52628i	0.721495	+	0.416555i	0.815303	−	0.579035i	$-0.196571\pi$
$523$	16.5000	+	9.52628i	0.721495	+	0.416555i	−0.0938079	+	0.995590i	$0.529904\pi$
$524$		0			0
$525$	12.0000	+	13.8564i	0.523723	+	0.604743i
$526$		0			0
$527$			10.3923i			0.452696i
$528$		0			0
$529$	−4.00000			−0.173913
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.50000	−	2.59808i	−0.194917	−	0.112535i
$534$		0			0
$535$	−22.5000	−	12.9904i	−0.972760	−	0.561623i
$536$		0			0
$537$	−27.0000			−1.16514
$538$		0			0
$539$	7.50000	−	9.52628i	0.323048	−	0.410326i
$540$		0			0
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	−0.691793	−	0.722096i	$-0.743179\pi$
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	0.971250	+	0.238062i	$0.0765123\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	28.5000	+	49.3634i	1.22081	+	2.11450i
$546$		0			0
$547$	−9.50000	+	16.4545i	−0.406191	+	0.703543i	−0.994459	−	0.105123i	$-0.966476\pi$
$547$	−9.50000	+	16.4545i	−0.406191	+	0.703543i	0.588269	+	0.808666i	$0.299810\pi$
$548$		0			0
$549$	36.0000	+	20.7846i	1.53644	+	0.887066i
$550$		0			0
$551$	−13.5000	−	23.3827i	−0.575119	−	0.996136i
$552$		0			0
$553$	4.00000	+	20.7846i	0.170097	+	0.883852i
$554$		0			0
$555$	31.5000	−	18.1865i	1.33710	−	0.771975i
$556$		0			0
$557$	10.5000	−	6.06218i	0.444899	−	0.256863i	−0.260774	−	0.965400i	$-0.583978\pi$
$557$	10.5000	−	6.06218i	0.444899	−	0.256863i	0.705674	+	0.708537i	$0.250645\pi$
$558$		0			0
$559$			1.73205i			0.0732579i
$560$		0			0
$561$	9.00000			0.379980
$562$		0			0
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	−4.50000	+	2.59808i	−0.189316	+	0.109302i
$566$		0			0
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$		0			0
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	−0.368933	−	0.929456i	$-0.620277\pi$
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	0.620466	+	0.784233i	$0.286943\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$	30.0000			1.25327
$574$		0			0
$575$			20.7846i			0.866778i
$576$		0			0
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.997587	−	0.0694283i	$-0.977883\pi$
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.438667	+	0.898650i	$0.644549\pi$
$578$		0			0
$579$	3.00000	−	1.73205i	0.124676	−	0.0719816i
$580$		0			0
$581$	30.0000	−	25.9808i	1.24461	−	1.07786i
$582$		0			0
$583$	7.50000	+	12.9904i	0.310618	+	0.538007i
$584$		0			0
$585$	13.5000	+	7.79423i	0.558156	+	0.322252i
$586$		0			0
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	−0.997162	−	0.0752860i	$-0.976013\pi$
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	0.563781	+	0.825925i	$0.309346\pi$
$588$		0			0
$589$	9.00000	+	15.5885i	0.370839	+	0.642311i
$590$		0			0
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$		0			0
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	−0.118342	−	0.992973i	$-0.537758\pi$
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	0.919111	−	0.394000i	$-0.128909\pi$
$594$		0			0
$595$	−4.50000	−	23.3827i	−0.184482	−	0.958597i
$596$		0			0
$597$	15.0000			0.613909
$598$		0			0
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	0.863354	−	0.504598i	$-0.168359\pi$
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	−0.00531761	+	0.999986i	$0.501693\pi$
$600$		0			0
$601$	−25.5000	−	14.7224i	−1.04017	−	0.600541i	−0.120286	−	0.992739i	$-0.538381\pi$
$601$	−25.5000	−	14.7224i	−1.04017	−	0.600541i	−0.919881	+	0.392199i	$0.871715\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−24.0000			−0.975739
$606$		0			0
$607$			15.5885i			0.632716i	0.948640	+	0.316358i	$0.102460\pi$
$607$			15.5885i			0.632716i	−0.948640	+	0.316358i	$0.897540\pi$
$608$		0			0
$609$	−4.50000	−	23.3827i	−0.182349	−	0.947514i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−23.5000	−	40.7032i	−0.949156	−	1.64399i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	−23.5000	−	40.7032i	−0.949156	−	1.64399i	−0.201948	−	0.979396i	$-0.564727\pi$
$614$		0			0
$615$		−	15.5885i		−	0.628587i
$616$		0			0
$617$	−4.50000	+	2.59808i	−0.181163	+	0.104595i	−0.587839	−	0.808978i	$-0.700021\pi$
$617$	−4.50000	+	2.59808i	−0.181163	+	0.104595i	0.406676	+	0.913573i	$0.366688\pi$
$618$		0			0
$619$		−	19.0526i		−	0.765787i	−0.923792	−	0.382893i	$-0.874928\pi$
$619$		−	19.0526i		−	0.765787i	0.923792	−	0.382893i	$-0.125072\pi$
$620$		0			0
$621$	−27.0000			−1.08347
$622$		0			0
$623$	6.00000	−	5.19615i	0.240385	−	0.208179i
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$	13.5000	−	7.79423i	0.539138	−	0.311272i
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		−	8.66025i		−	0.344214i
$634$		0			0
$635$	60.0000			2.38103
$636$		0			0
$637$	−12.0000	−	1.73205i	−0.475457	−	0.0686264i
$638$		0			0
$639$	9.00000	−	5.19615i	0.356034	−	0.205557i
$640$		0			0
$641$		−	12.1244i		−	0.478883i	−0.970911	−	0.239442i	$-0.923036\pi$
$641$		−	12.1244i		−	0.478883i	0.970911	−	0.239442i	$-0.0769644\pi$
$642$		0			0
$643$	−10.5000	+	6.06218i	−0.414080	+	0.239069i	−0.692541	−	0.721378i	$-0.743509\pi$
$643$	−10.5000	+	6.06218i	−0.414080	+	0.239069i	0.278462	+	0.960447i	$0.410176\pi$
$644$		0			0
$645$	−4.50000	+	2.59808i	−0.177187	+	0.102299i
$646$		0			0
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	0.894004	−	0.448059i	$-0.147885\pi$
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	−0.835033	+	0.550200i	$0.814551\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	3.00000	+	15.5885i	0.117579	+	0.610960i
$652$		0			0
$653$			39.8372i			1.55895i	0.626434	+	0.779474i	$0.284514\pi$
$653$			39.8372i			1.55895i	−0.626434	+	0.779474i	$0.715486\pi$
$654$		0			0
$655$	−27.0000			−1.05498
$656$		0			0
$657$	−13.5000	−	7.79423i	−0.526685	−	0.304082i
$658$		0			0
$659$	−10.5000	−	6.06218i	−0.409022	−	0.236149i	0.281347	−	0.959606i	$-0.409219\pi$
$659$	−10.5000	−	6.06218i	−0.409022	−	0.236149i	−0.690369	+	0.723457i	$0.742552\pi$
$660$		0			0
$661$	36.0000	+	20.7846i	1.40024	+	0.808428i	0.994417	−	0.105525i	$-0.0336523\pi$
$661$	36.0000	+	20.7846i	1.40024	+	0.808428i	0.405821	+	0.913953i	$0.366986\pi$
$662$		0			0
$663$	−4.50000	−	7.79423i	−0.174766	−	0.302703i
$664$		0			0
$665$	−27.0000	−	31.1769i	−1.04702	−	1.20899i
$666$		0			0
$667$	13.5000	−	23.3827i	0.522722	−	0.905381i
$668$		0			0
$669$	4.50000	+	7.79423i	0.173980	+	0.301342i
$670$		0			0
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$		0			0
$675$			20.7846i			0.800000i
$676$		0			0
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$		0			0
$679$	−3.00000	−	3.46410i	−0.115129	−	0.132940i
$680$		0			0
$681$	−31.5000	−	18.1865i	−1.20708	−	0.696909i
$682$		0			0
$683$	−7.50000	+	4.33013i	−0.286980	+	0.165688i	−0.636579	−	0.771212i	$-0.719651\pi$
$683$	−7.50000	+	4.33013i	−0.286980	+	0.165688i	0.349599	+	0.936899i	$0.386318\pi$
$684$		0			0
$685$			36.3731i			1.38974i
$686$		0			0
$687$	−7.50000	+	12.9904i	−0.286143	+	0.495614i
$688$		0			0
$689$	7.50000	−	12.9904i	0.285727	−	0.494894i
$690$		0			0
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$		0			0
$693$	13.5000	−	2.59808i	0.512823	−	0.0986928i
$694$		0			0
$695$	−22.5000	+	12.9904i	−0.853474	+	0.492753i
$696$		0			0
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$		0			0
$699$	4.50000	+	7.79423i	0.170206	+	0.294805i
$700$		0			0
$701$			34.6410i			1.30837i	0.756333	+	0.654187i	$0.226989\pi$
$701$			34.6410i			1.30837i	−0.756333	+	0.654187i	$0.773011\pi$
$702$		0			0
$703$	−31.5000	+	18.1865i	−1.18805	+	0.685918i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$		0			0
$711$	−12.0000	+	20.7846i	−0.450035	+	0.779484i
$712$		0			0
$713$	−9.00000	+	15.5885i	−0.337053	+	0.583792i
$714$		0			0
$715$	−4.50000	−	7.79423i	−0.168290	−	0.291488i
$716$		0			0
$717$	−3.00000			−0.112037
$718$		0			0
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$		0			0
$721$	10.5000	−	30.3109i	0.391040	−	1.12884i
$722$		0			0
$723$	19.5000	−	33.7750i	0.725213	−	1.25611i
$724$		0			0
$725$	−18.0000	−	10.3923i	−0.668503	−	0.385961i
$726$		0			0
$727$	10.5000	+	6.06218i	0.389423	+	0.224834i	0.681910	−	0.731436i	$-0.261149\pi$
$727$	10.5000	+	6.06218i	0.389423	+	0.224834i	−0.292487	+	0.956270i	$0.594483\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000			0.110959
$732$		0			0
$733$			43.3013i			1.59937i	0.600420	+	0.799684i	$0.295000\pi$
$733$			43.3013i			1.59937i	−0.600420	+	0.799684i	$0.705000\pi$
$734$		0			0
$735$	−13.5000	−	33.7750i	−0.497955	−	1.24581i
$736$		0			0
$737$	6.00000	+	3.46410i	0.221013	+	0.127602i
$738$		0			0
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	0.794443	−	0.607339i	$-0.207763\pi$
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	−0.923192	+	0.384338i	$0.874430\pi$
$740$		0			0
$741$	−13.5000	−	7.79423i	−0.495935	−	0.286328i
$742$		0			0
$743$	10.5000	−	6.06218i	0.385208	−	0.222400i	−0.294874	−	0.955536i	$-0.595278\pi$
$743$	10.5000	−	6.06218i	0.385208	−	0.222400i	0.680082	+	0.733136i	$0.261944\pi$
$744$		0			0
$745$			5.19615i			0.190372i
$746$		0			0
$747$	45.0000			1.64646
$748$		0			0
$749$	15.0000	+	17.3205i	0.548088	+	0.632878i
$750$		0			0
$751$	−37.0000			−1.35015			−0.675075	−	0.737749i	$-0.735889\pi$
$751$	−37.0000			−1.35015			−0.675075	+	0.737749i	$0.735889\pi$
$752$		0			0
$753$	−18.0000	−	10.3923i	−0.655956	−	0.378717i
$754$		0			0
$755$	−51.0000			−1.85608
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$		0			0
$759$	13.5000	+	7.79423i	0.490019	+	0.282913i
$760$		0			0
$761$	45.0000			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$762$		0			0
$763$	−9.50000	−	49.3634i	−0.343923	−	1.78708i
$764$		0			0
$765$	13.5000	−	23.3827i	0.488094	−	0.845403i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$		0			0
$771$	−4.50000	−	2.59808i	−0.162064	−	0.0935674i
$772$		0			0
$773$	25.5000	+	44.1673i	0.917171	+	1.58859i	0.803691	+	0.595047i	$0.202867\pi$
$773$	25.5000	+	44.1673i	0.917171	+	1.58859i	0.113480	+	0.993540i	$0.463800\pi$
$774$		0			0
$775$	12.0000	+	6.92820i	0.431053	+	0.248868i
$776$		0			0
$777$	−31.5000	+	6.06218i	−1.13006	+	0.217479i
$778$		0			0
$779$			15.5885i			0.558514i
$780$		0			0
$781$	−6.00000			−0.214697
$782$		0			0
$783$	13.5000	−	23.3827i	0.482451	−	0.835629i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	33.0000	+	19.0526i	1.17632	+	0.679150i	0.955161	−	0.296087i	$-0.0956817\pi$
$787$	33.0000	+	19.0526i	1.17632	+	0.679150i	0.221162	+	0.975237i	$0.429015\pi$
$788$		0			0
$789$	19.5000	−	33.7750i	0.694218	−	1.20242i
$790$		0			0
$791$	4.50000	−	0.866025i	0.160002	−	0.0307923i
$792$		0			0
$793$	−12.0000	+	20.7846i	−0.426132	+	0.738083i
$794$		0			0
$795$	45.0000			1.59599
$796$		0			0
$797$	−22.5000	−	38.9711i	−0.796991	−	1.38043i	−0.921567	−	0.388219i	$-0.873091\pi$
$797$	−22.5000	−	38.9711i	−0.796991	−	1.38043i	0.124576	−	0.992210i	$-0.460243\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	9.00000			0.317999
$802$		0			0
$803$	4.50000	+	7.79423i	0.158802	+	0.275052i
$804$		0			0
$805$	13.5000	−	38.9711i	0.475812	−	1.37355i
$806$		0			0
$807$			25.9808i			0.914566i
$808$		0			0
$809$	−1.50000	+	0.866025i	−0.0527372	+	0.0304478i	−0.526137	−	0.850400i	$-0.676360\pi$
$809$	−1.50000	+	0.866025i	−0.0527372	+	0.0304478i	0.473400	+	0.880848i	$0.343027\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$	10.5000	+	18.1865i	0.368251	+	0.637830i
$814$		0			0
$815$	−16.5000	+	28.5788i	−0.577970	+	1.00107i
$816$		0			0
$817$	4.50000	−	2.59808i	0.157435	−	0.0908952i
$818$		0			0
$819$	−9.00000	−	10.3923i	−0.314485	−	0.363137i
$820$		0			0
$821$	6.00000	−	3.46410i	0.209401	−	0.120898i	−0.391632	−	0.920122i	$-0.628089\pi$
$821$	6.00000	−	3.46410i	0.209401	−	0.120898i	0.601033	+	0.799224i	$0.294756\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$	6.00000	−	10.3923i	0.208893	−	0.361814i
$826$		0			0
$827$			24.2487i			0.843210i	0.906780	+	0.421605i	$0.138533\pi$
$827$			24.2487i			0.843210i	−0.906780	+	0.421605i	$0.861467\pi$
$828$		0			0
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.159391	−	0.987216i	$-0.449047\pi$
$829$	31.5000	−	18.1865i	1.09404	−	0.631644i	0.934649	+	0.355571i	$0.115714\pi$
$830$		0			0
$831$	−1.50000	−	0.866025i	−0.0520344	−	0.0300421i
$832$		0			0
$833$	−3.00000	+	20.7846i	−0.103944	+	0.720144i
$834$		0			0
$835$	−13.5000	−	23.3827i	−0.467187	−	0.809191i
$836$		0			0
$837$	−9.00000	+	15.5885i	−0.311086	+	0.538816i
$838$		0			0
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		0			0
$841$	−1.00000	−	1.73205i	−0.0344828	−	0.0597259i
$842$		0			0
$843$	−16.5000	−	28.5788i	−0.568290	−	0.984307i
$844$		0			0
$845$	15.0000	−	25.9808i	0.516016	−	0.893765i
$846$		0			0
$847$	20.0000	+	6.92820i	0.687208	+	0.238056i
$848$		0			0
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$		0			0
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$		0			0
$853$	22.5000	+	12.9904i	0.770385	+	0.444782i	0.833012	−	0.553255i	$-0.186614\pi$
$853$	22.5000	+	12.9904i	0.770385	+	0.444782i	−0.0626267	+	0.998037i	$0.519948\pi$
$854$		0			0
$855$		−	46.7654i		−	1.59934i
$856$		0			0
$857$	−27.0000			−0.922302			−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000			−0.922302			−0.461151	+	0.887322i	$0.652563\pi$
$858$		0			0
$859$			50.2295i			1.71381i	0.515476	+	0.856904i	$0.327615\pi$
$859$			50.2295i			1.71381i	−0.515476	+	0.856904i	$0.672385\pi$
$860$		0			0
$861$	−4.50000	+	12.9904i	−0.153360	+	0.442711i
$862$		0			0
$863$	37.5000	+	21.6506i	1.27651	+	0.736996i	0.976206	−	0.216846i	$-0.0695769\pi$
$863$	37.5000	+	21.6506i	1.27651	+	0.736996i	0.300309	+	0.953842i	$0.402910\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$		0			0
$869$	12.0000	−	6.92820i	0.407072	−	0.235023i
$870$		0			0
$871$		−	6.92820i		−	0.234753i
$872$		0			0
$873$		−	5.19615i		−	0.175863i
$874$		0			0
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$		0			0
$877$	23.0000			0.776655			0.388327	−	0.921521i	$-0.373053\pi$
$877$	23.0000			0.776655			0.388327	+	0.921521i	$0.373053\pi$
$878$		0			0
$879$		−	15.5885i		−	0.525786i
$880$		0			0
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.0000			−0.503651			−0.251825	−	0.967773i	$-0.581031\pi$
$887$	−15.0000			−0.503651			−0.251825	+	0.967773i	$0.581031\pi$
$888$		0			0
$889$	−50.0000	−	17.3205i	−1.67695	−	0.580911i
$890$		0			0
$891$	13.5000	+	7.79423i	0.452267	+	0.261116i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	40.5000	−	23.3827i	1.35377	−	0.781597i
$896$		0			0
$897$		−	15.5885i		−	0.520483i
$898$		0			0
$899$	−9.00000	−	15.5885i	−0.300167	−	0.519904i
$900$		0			0
$901$	−22.5000	−	12.9904i	−0.749584	−	0.432772i
$902$		0			0
$903$	4.50000	−	0.866025i	0.149751	−	0.0288195i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−19.0000			−0.630885			−0.315442	−	0.948945i	$-0.602153\pi$
$907$	−19.0000			−0.630885			−0.315442	+	0.948945i	$0.602153\pi$
$908$		0			0
$909$	−4.50000	−	7.79423i	−0.149256	−	0.258518i
$910$		0			0
$911$	−4.50000	−	2.59808i	−0.149092	−	0.0860781i	0.423598	−	0.905850i	$-0.360767\pi$
$911$	−4.50000	−	2.59808i	−0.149092	−	0.0860781i	−0.572690	+	0.819772i	$0.694100\pi$
$912$		0			0
$913$	−22.5000	−	12.9904i	−0.744641	−	0.429919i
$914$		0			0
$915$	−72.0000			−2.38025
$916$		0			0
$917$	22.5000	+	7.79423i	0.743015	+	0.257388i
$918$		0			0
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$		0			0
$921$	21.0000	−	36.3731i	0.691974	−	1.19853i
$922$		0			0
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$		0			0
$925$	−14.0000	+	24.2487i	−0.460317	+	0.797293i
$926$		0			0
$927$	31.5000	−	18.1865i	1.03460	−	0.597324i
$928$		0			0
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$	13.5000	+	33.7750i	0.442445	+	1.10693i
$932$		0			0
$933$	36.0000	−	20.7846i	1.17859	−	0.680458i
$934$		0			0
$935$	−13.5000	+	7.79423i	−0.441497	+	0.254899i
$936$		0			0
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$		0			0
$939$	−36.0000			−1.17482
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	−13.5000	+	7.79423i	−0.439620	+	0.253815i
$944$		0			0
$945$	13.5000	−	38.9711i	0.439155	−	1.26773i
$946$		0			0
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.463186	−	0.886261i	$-0.346706\pi$
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.999118	+	0.0419998i	$0.0133729\pi$
$948$		0			0
$949$	4.50000	−	7.79423i	0.146076	−	0.253011i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			20.7846i			0.673280i	0.941634	+	0.336640i	$0.109290\pi$
$953$			20.7846i			0.673280i	−0.941634	+	0.336640i	$0.890710\pi$
$954$		0			0
$955$	−45.0000	+	25.9808i	−1.45617	+	0.840718i
$956$		0			0
$957$	−13.5000	+	7.79423i	−0.436393	+	0.251952i
$958$		0			0
$959$	10.5000	−	30.3109i	0.339063	−	0.978790i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$			25.9808i			0.837218i
$964$		0			0
$965$	−3.00000	+	5.19615i	−0.0965734	+	0.167270i
$966$		0			0
$967$	−12.5000	−	21.6506i	−0.401973	−	0.696237i	0.591991	−	0.805945i	$-0.298342\pi$
$967$	−12.5000	−	21.6506i	−0.401973	−	0.696237i	−0.993964	+	0.109707i	$0.965009\pi$
$968$		0			0
$969$	−13.5000	+	23.3827i	−0.433682	+	0.751160i
$970$		0			0
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.107135	−	0.994244i	$-0.465832\pi$
$971$	28.5000	−	49.3634i	0.914609	−	1.58415i	0.807473	−	0.589904i	$-0.200834\pi$
$972$		0			0
$973$	22.5000	−	4.33013i	0.721317	−	0.138817i
$974$		0			0
$975$	−12.0000			−0.384308
$976$		0			0
$977$	−36.0000	−	20.7846i	−1.15174	−	0.664959i	−0.202431	−	0.979297i	$-0.564884\pi$
$977$	−36.0000	−	20.7846i	−1.15174	−	0.664959i	−0.949311	+	0.314338i	$0.898217\pi$
$978$		0			0
$979$	−4.50000	−	2.59808i	−0.143821	−	0.0830349i
$980$		0			0
$981$	28.5000	−	49.3634i	0.909935	−	1.57605i
$982$		0			0
$983$	39.0000			1.24391			0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000			1.24391			0.621953	+	0.783054i	$0.286339\pi$
$984$		0			0
$985$			41.5692i			1.32451i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.50000	+	2.59808i	0.143092	+	0.0826140i
$990$		0			0
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$		0			0
$993$		−	13.8564i		−	0.439720i
$994$		0			0
$995$	−22.5000	+	12.9904i	−0.713298	+	0.411823i
$996$		0			0
$997$		−	8.66025i		−	0.274273i	−0.990552	−	0.137136i	$-0.956210\pi$
$997$		−	8.66025i		−	0.274273i	0.990552	−	0.137136i	$-0.0437899\pi$
$998$		0			0
$999$	−31.5000	−	18.1865i	−0.996616	−	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.a.929.1		2
3.2	odd	2		3024.2.df.a.1601.1		2
4.3	odd	2		63.2.s.a.47.1	yes	2
7.3	odd	6		1008.2.ca.a.353.1		2
9.4	even	3		3024.2.ca.a.2609.1		2
9.5	odd	6		1008.2.ca.a.257.1		2
12.11	even	2		189.2.s.a.89.1		2
21.17	even	6		3024.2.ca.a.2033.1		2
28.3	even	6		63.2.i.a.38.1	yes	2
28.11	odd	6		441.2.i.a.227.1		2
28.19	even	6		441.2.o.a.146.1		2
28.23	odd	6		441.2.o.b.146.1		2
28.27	even	2		441.2.s.a.362.1		2
36.7	odd	6		567.2.p.b.404.1		2
36.11	even	6		567.2.p.a.404.1		2
36.23	even	6		63.2.i.a.5.1	✓	2
36.31	odd	6		189.2.i.a.152.1		2
63.31	odd	6		3024.2.df.a.17.1		2
63.59	even	6	inner	1008.2.df.a.689.1		2
84.11	even	6		1323.2.i.a.521.1		2
84.23	even	6		1323.2.o.a.440.1		2
84.47	odd	6		1323.2.o.b.440.1		2
84.59	odd	6		189.2.i.a.143.1		2
84.83	odd	2		1323.2.s.a.656.1		2
252.23	even	6		441.2.o.a.293.1		2
252.31	even	6		189.2.s.a.17.1		2
252.59	odd	6		63.2.s.a.59.1	yes	2
252.67	odd	6		1323.2.s.a.962.1		2
252.95	even	6		441.2.s.a.374.1		2
252.103	even	6		1323.2.o.a.881.1		2
252.115	even	6		567.2.p.a.80.1		2
252.131	odd	6		441.2.o.b.293.1		2
252.139	even	6		1323.2.i.a.1097.1		2
252.167	odd	6		441.2.i.a.68.1		2
252.227	odd	6		567.2.p.b.80.1		2
252.247	odd	6		1323.2.o.b.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.a.5.1	✓	2	36.23	even	6
63.2.i.a.38.1	yes	2	28.3	even	6
63.2.s.a.47.1	yes	2	4.3	odd	2
63.2.s.a.59.1	yes	2	252.59	odd	6
189.2.i.a.143.1		2	84.59	odd	6
189.2.i.a.152.1		2	36.31	odd	6
189.2.s.a.17.1		2	252.31	even	6
189.2.s.a.89.1		2	12.11	even	2
441.2.i.a.68.1		2	252.167	odd	6
441.2.i.a.227.1		2	28.11	odd	6
441.2.o.a.146.1		2	28.19	even	6
441.2.o.a.293.1		2	252.23	even	6
441.2.o.b.146.1		2	28.23	odd	6
441.2.o.b.293.1		2	252.131	odd	6
441.2.s.a.362.1		2	28.27	even	2
441.2.s.a.374.1		2	252.95	even	6
567.2.p.a.80.1		2	252.115	even	6
567.2.p.a.404.1		2	36.11	even	6
567.2.p.b.80.1		2	252.227	odd	6
567.2.p.b.404.1		2	36.7	odd	6
1008.2.ca.a.257.1		2	9.5	odd	6
1008.2.ca.a.353.1		2	7.3	odd	6
1008.2.df.a.689.1		2	63.59	even	6	inner
1008.2.df.a.929.1		2	1.1	even	1	trivial
1323.2.i.a.521.1		2	84.11	even	6
1323.2.i.a.1097.1		2	252.139	even	6
1323.2.o.a.440.1		2	84.23	even	6
1323.2.o.a.881.1		2	252.103	even	6
1323.2.o.b.440.1		2	84.47	odd	6
1323.2.o.b.881.1		2	252.247	odd	6
1323.2.s.a.656.1		2	84.83	odd	2
1323.2.s.a.962.1		2	252.67	odd	6
3024.2.ca.a.2033.1		2	21.17	even	6
3024.2.ca.a.2609.1		2	9.4	even	3
3024.2.df.a.17.1		2	63.31	odd	6
3024.2.df.a.1601.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} -3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{11} +(-1.50000 + 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(1.50000 + 2.59808i) q^{17} +(4.50000 + 2.59808i) q^{19} +(3.00000 + 3.46410i) q^{21} +5.19615i q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-4.50000 - 2.59808i) q^{29} +(3.00000 + 1.73205i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-7.50000 - 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} -3.00000 q^{39} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(5.50000 + 4.33013i) q^{49} +5.19615i q^{51} +(-7.50000 + 4.33013i) q^{53} +5.19615i q^{55} +(4.50000 + 7.79423i) q^{57} +(12.0000 - 6.92820i) q^{61} +(1.50000 + 7.79423i) q^{63} +(4.50000 - 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-4.50000 + 7.79423i) q^{69} -3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(6.00000 + 3.46410i) q^{75} +(1.50000 - 4.33013i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.50000 - 12.9904i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-4.50000 - 7.79423i) q^{87} +(1.50000 - 2.59808i) q^{89} +(-4.50000 + 0.866025i) q^{91} +(3.00000 + 5.19615i) q^{93} +(-13.5000 - 7.79423i) q^{95} +(-1.50000 - 0.866025i) q^{97} +(4.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 6 q^{5} + 5 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 6 * q^5 + 5 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 6 q^{5} + 5 q^{7} + 3 q^{9} - 3 q^{13} - 9 q^{15} + 3 q^{17} + 9 q^{19} + 6 q^{21} + 8 q^{25} - 9 q^{29} + 6 q^{31} + 3 q^{33} - 15 q^{35} - 7 q^{37} - 6 q^{39} + 3 q^{41} + q^{43} - 9 q^{45} + 11 q^{49} - 15 q^{53} + 9 q^{57} + 24 q^{61} + 3 q^{63} + 9 q^{65} - 4 q^{67} - 9 q^{69} - 9 q^{73} + 12 q^{75} + 3 q^{77} + 8 q^{79} - 9 q^{81} + 15 q^{83} - 9 q^{85} - 9 q^{87} + 3 q^{89} - 9 q^{91} + 6 q^{93} - 27 q^{95} - 3 q^{97} + 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 6 * q^5 + 5 * q^7 + 3 * q^9 - 3 * q^13 - 9 * q^15 + 3 * q^17 + 9 * q^19 + 6 * q^21 + 8 * q^25 - 9 * q^29 + 6 * q^31 + 3 * q^33 - 15 * q^35 - 7 * q^37 - 6 * q^39 + 3 * q^41 + q^43 - 9 * q^45 + 11 * q^49 - 15 * q^53 + 9 * q^57 + 24 * q^61 + 3 * q^63 + 9 * q^65 - 4 * q^67 - 9 * q^69 - 9 * q^73 + 12 * q^75 + 3 * q^77 + 8 * q^79 - 9 * q^81 + 15 * q^83 - 9 * q^85 - 9 * q^87 + 3 * q^89 - 9 * q^91 + 6 * q^93 - 27 * q^95 - 3 * q^97 + 9 * q^99

Introduction

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