LMFDB - Embedded newform 1008.2.r.d.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (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:	$8.04892052375$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.d.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +7.00000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{31} +(9.00000 + 5.19615i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(-3.00000 + 1.73205i) q^{39} +(1.00000 - 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-0.500000 - 0.866025i) q^{49} -10.3923i q^{51} +6.00000 q^{53} -18.0000 q^{55} -12.1244i q^{57} +(-2.50000 + 4.33013i) q^{61} +(-1.50000 + 2.59808i) q^{63} +(3.00000 - 5.19615i) q^{65} +(4.00000 + 6.92820i) q^{67} +(4.50000 - 2.59808i) q^{69} -3.00000 q^{71} +2.00000 q^{73} +(6.00000 + 3.46410i) q^{75} +(3.00000 + 5.19615i) q^{77} +(2.50000 - 4.33013i) q^{79} +9.00000 q^{81} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(9.00000 + 5.19615i) q^{87} -2.00000 q^{91} +(3.00000 - 1.73205i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(9.00000 - 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{5} + q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^5 + q^7 - 6 * q^9	$ 2 q + 3 q^{5} + q^{7} - 6 q^{9} - 6 q^{11} - 2 q^{13} + 9 q^{15} + 12 q^{17} + 14 q^{19} - 3 q^{21} + 3 q^{23} - 4 q^{25} - 6 q^{29} + 2 q^{31} + 18 q^{33} + 6 q^{35} + 4 q^{37} - 6 q^{39} + 2 q^{43} - 9 q^{45} - q^{49} + 12 q^{53} - 36 q^{55} - 5 q^{61} - 3 q^{63} + 6 q^{65} + 8 q^{67} + 9 q^{69} - 6 q^{71} + 4 q^{73} + 12 q^{75} + 6 q^{77} + 5 q^{79} + 18 q^{81} + 12 q^{83} + 18 q^{85} + 18 q^{87} - 4 q^{91} + 6 q^{93} + 21 q^{95} - 2 q^{97} + 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^5 + q^7 - 6 * q^9 - 6 * q^11 - 2 * q^13 + 9 * q^15 + 12 * q^17 + 14 * q^19 - 3 * q^21 + 3 * q^23 - 4 * q^25 - 6 * q^29 + 2 * q^31 + 18 * q^33 + 6 * q^35 + 4 * q^37 - 6 * q^39 + 2 * q^43 - 9 * q^45 - q^49 + 12 * q^53 - 36 * q^55 - 5 * q^61 - 3 * q^63 + 6 * q^65 + 8 * q^67 + 9 * q^69 - 6 * q^71 + 4 * q^73 + 12 * q^75 + 6 * q^77 + 5 * q^79 + 18 * q^81 + 12 * q^83 + 18 * q^85 + 18 * q^87 - 4 * q^91 + 6 * q^93 + 21 * q^95 - 2 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		0			0
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	4.50000	−	2.59808i	1.16190	−	0.670820i
$16$		0			0
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$		0			0
$33$	9.00000	+	5.19615i	1.56670	+	0.904534i
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$		0			0
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$		0			0
$45$	−4.50000	−	7.79423i	−0.670820	−	1.16190i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		−	10.3923i		−	1.45521i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−18.0000			−2.42712
$56$		0			0
$57$		−	12.1244i		−	1.60591i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$	−1.50000	+	2.59808i	−0.188982	+	0.327327i
$64$		0			0
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$		0			0
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	6.00000	+	3.46410i	0.692820	+	0.400000i
$76$		0			0
$77$	3.00000	+	5.19615i	0.341882	+	0.592157i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$		0			0
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$		0			0
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	9.00000	−	15.5885i	0.904534	−	1.56670i
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$		0			0
$105$		−	5.19615i		−	0.507093i
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		−	3.46410i		−	0.328798i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−17.0000			−1.50851			−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000			−1.50851			−0.754253	+	0.656584i	$0.772001\pi$
$128$		0			0
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$		0			0
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$		0			0
$135$	−13.5000	+	7.79423i	−1.16190	+	0.670820i
$136$		0			0
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.0000			1.00349
$144$		0			0
$145$	−18.0000			−1.49482
$146$		0			0
$147$	−1.50000	+	0.866025i	−0.123718	+	0.0714286i
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	11.5000	−	19.9186i	0.935857	−	1.62095i	0.162758	−	0.986666i	$-0.447961\pi$
$151$	11.5000	−	19.9186i	0.935857	−	1.62095i	0.773099	−	0.634285i	$-0.218706\pi$
$152$		0			0
$153$	−18.0000			−1.45521
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		0			0
$159$		−	10.3923i		−	0.824163i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−2.00000			−0.156652			−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000			−0.156652			−0.0783260	+	0.996928i	$0.524958\pi$
$164$		0			0
$165$			31.1769i			2.42712i
$166$		0			0
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−21.0000			−1.60591
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−18.0000			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$	−25.0000			−1.85824			−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$		0			0
$183$	7.50000	+	4.33013i	0.554416	+	0.320092i
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−18.0000	+	31.1769i	−1.31629	+	2.27988i
$188$		0			0
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$		0			0
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	−0.981635	−	0.190767i	$-0.938902\pi$
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	0.656027	+	0.754738i	$0.272236\pi$
$192$		0			0
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$		0			0
$195$	−9.00000	−	5.19615i	−0.644503	−	0.372104i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$		0			0
$201$	12.0000	−	6.92820i	0.846415	−	0.488678i
$202$		0			0
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$		0			0
$209$	−21.0000	+	36.3731i	−1.45260	+	2.51598i
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$		0			0
$213$			5.19615i			0.356034i
$214$		0			0
$215$	6.00000			0.409197
$216$		0			0
$217$	2.00000			0.135769
$218$		0			0
$219$		−	3.46410i		−	0.234082i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.167412	+	0.985887i	$0.553541\pi$
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$		0			0
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$		0			0
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.50000	−	4.33013i	−0.487177	−	0.281272i
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$		0			0
$243$		−	15.5885i		−	1.00000i
$244$		0			0
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$		0			0
$247$	−7.00000	−	12.1244i	−0.445399	−	0.771454i
$248$		0			0
$249$	−18.0000	−	10.3923i	−1.14070	−	0.658586i
$250$		0			0
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$		0			0
$255$	27.0000	−	15.5885i	1.69081	−	0.976187i
$256$		0			0
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$		0			0
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.00000			−0.548740			−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000			−0.548740			−0.274370	+	0.961624i	$0.588469\pi$
$270$		0			0
$271$	28.0000			1.70088			0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000			1.70088			0.850439	+	0.526073i	$0.176336\pi$
$272$		0			0
$273$			3.46410i			0.209657i
$274$		0			0
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$		0			0
$279$	−3.00000	−	5.19615i	−0.179605	−	0.311086i
$280$		0			0
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	−0.997076	−	0.0764162i	$-0.975652\pi$
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	0.432360	−	0.901701i	$-0.357681\pi$
$284$		0			0
$285$	31.5000	−	18.1865i	1.86590	−	1.07728i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	3.00000	+	1.73205i	0.175863	+	0.101535i
$292$		0			0
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	0.906509	−	0.422186i	$-0.138737\pi$
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	−0.818878	+	0.573967i	$0.805404\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−27.0000	−	15.5885i	−1.56670	−	0.904534i
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$		0			0
$303$	13.5000	+	7.79423i	0.775555	+	0.447767i
$304$		0			0
$305$	−15.0000			−0.858898
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$		0			0
$309$	−15.0000	+	8.66025i	−0.853320	+	0.492665i
$310$		0			0
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$		0			0
$315$	−9.00000			−0.507093
$316$		0			0
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$		−	20.7846i		−	1.16008i
$322$		0			0
$323$	42.0000			2.33694
$324$		0			0
$325$	8.00000			0.443760
$326$		0			0
$327$			17.3205i			0.957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.0000	−	22.5167i	0.714545	−	1.23763i	−0.248590	−	0.968609i	$-0.579967\pi$
$331$	13.0000	−	22.5167i	0.714545	−	1.23763i	0.963135	−	0.269019i	$-0.0866994\pi$
$332$		0			0
$333$	−6.00000			−0.328798
$334$		0			0
$335$	−12.0000	+	20.7846i	−0.655630	+	1.13558i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$		0			0
$339$	−22.5000	+	12.9904i	−1.22203	+	0.705541i
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	13.5000	+	7.79423i	0.726816	+	0.419627i
$346$		0			0
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$		0			0
$351$	9.00000	−	5.19615i	0.480384	−	0.277350i
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$		0			0
$357$	−9.00000	−	5.19615i	−0.476331	−	0.275010i
$358$		0			0
$359$	3.00000			0.158334			0.0791670	−	0.996861i	$-0.474774\pi$
$359$	3.00000			0.158334			0.0791670	+	0.996861i	$0.474774\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$		0			0
$363$	−37.5000	+	21.6506i	−1.96824	+	1.13636i
$364$		0			0
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		−	5.19615i		−	0.268328i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$		0			0
$381$			29.4449i			1.50851i
$382$		0			0
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	−9.00000	+	15.5885i	−0.458682	+	0.794461i
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$		0			0
$393$	−13.5000	+	7.79423i	−0.680985	+	0.393167i
$394$		0			0
$395$	15.0000			0.754732
$396$		0			0
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$		0			0
$399$	−10.5000	−	6.06218i	−0.525657	−	0.303488i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$		0			0
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		0			0
$411$	9.00000	+	5.19615i	0.443937	+	0.256307i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	36.0000			1.76717
$416$		0			0
$417$	7.50000	−	4.33013i	0.367277	−	0.212047i
$418$		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
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$	2.50000	+	4.33013i	0.120983	+	0.209550i
$428$		0			0
$429$		−	20.7846i		−	1.00349i
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$			31.1769i			1.49482i
$436$		0			0
$437$	10.5000	+	18.1865i	0.502283	+	0.869980i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		0			0
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9.00000	−	5.19615i	0.425685	−	0.245770i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−34.5000	−	19.9186i	−1.62095	−	0.935857i
$454$		0			0
$455$	−3.00000	−	5.19615i	−0.140642	−	0.243599i
$456$		0			0
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$		0			0
$459$			31.1769i			1.45521i
$460$		0			0
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		0			0
$463$	−6.50000	−	11.2583i	−0.302081	−	0.523219i	0.674526	−	0.738251i	$-0.264348\pi$
$463$	−6.50000	−	11.2583i	−0.302081	−	0.523219i	−0.976607	+	0.215032i	$0.931015\pi$
$464$		0			0
$465$	9.00000	+	5.19615i	0.417365	+	0.240966i
$466$		0			0
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$		0			0
$471$	19.5000	−	11.2583i	0.898513	−	0.518756i
$472$		0			0
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$		0			0
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$	−18.0000			−0.824163
$478$		0			0
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$		0			0
$483$		−	5.19615i		−	0.236433i
$484$		0			0
$485$	−6.00000			−0.272446
$486$		0			0
$487$	−29.0000			−1.31412			−0.657058	−	0.753840i	$-0.728199\pi$
$487$	−29.0000			−1.31412			−0.657058	+	0.753840i	$0.728199\pi$
$488$		0			0
$489$			3.46410i			0.156652i
$490$		0			0
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$		0			0
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$		0			0
$495$	54.0000			2.42712
$496$		0			0
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−27.0000			−1.20148
$506$		0			0
$507$	−13.5000	−	7.79423i	−0.599556	−	0.346154i
$508$		0			0
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	1.00000	−	1.73205i	0.0442374	−	0.0766214i
$512$		0			0
$513$			36.3731i			1.60591i
$514$		0			0
$515$	15.0000	−	25.9808i	0.660979	−	1.14485i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−9.00000	−	5.19615i	−0.395056	−	0.228086i
$520$		0			0
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$		0			0
$523$	13.0000			0.568450			0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000			0.568450			0.284225	+	0.958758i	$0.408264\pi$
$524$		0			0
$525$	6.00000	−	3.46410i	0.261861	−	0.151186i
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$		0			0
$537$			31.1769i			1.34538i
$538$		0			0
$539$	6.00000			0.258438
$540$		0			0
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$		0			0
$543$			43.3013i			1.85824i
$544$		0			0
$545$	−15.0000	−	25.9808i	−0.642529	−	1.11289i
$546$		0			0
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	−0.289605	−	0.957146i	$-0.593524\pi$
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	0.973715	−	0.227768i	$-0.0731428\pi$
$548$		0			0
$549$	7.50000	−	12.9904i	0.320092	−	0.554416i
$550$		0			0
$551$	−21.0000	+	36.3731i	−0.894630	+	1.54954i
$552$		0			0
$553$	−2.50000	−	4.33013i	−0.106311	−	0.184136i
$554$		0			0
$555$	9.00000	−	5.19615i	0.382029	−	0.220564i
$556$		0			0
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$	54.0000	+	31.1769i	2.27988	+	1.31629i
$562$		0			0
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$		0			0
$565$	22.5000	−	38.9711i	0.946582	−	1.63953i
$566$		0			0
$567$	4.50000	−	7.79423i	0.188982	−	0.327327i
$568$		0			0
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$	13.5000	+	7.79423i	0.563971	+	0.325609i
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−4.00000			−0.166522			−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000			−0.166522			−0.0832611	+	0.996528i	$0.526534\pi$
$578$		0			0
$579$	−25.5000	+	14.7224i	−1.05974	+	0.611843i
$580$		0			0
$581$	−6.00000	−	10.3923i	−0.248922	−	0.431145i
$582$		0			0
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$		0			0
$585$	−9.00000	+	15.5885i	−0.372104	+	0.644503i
$586$		0			0
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$		0			0
$591$		−	31.1769i		−	1.28245i
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$		0			0
$597$			24.2487i			0.992434i
$598$		0			0
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	−0.972739	−	0.231903i	$-0.925505\pi$
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	0.687203	+	0.726465i	$0.258838\pi$
$602$		0			0
$603$	−12.0000	−	20.7846i	−0.488678	−	0.846415i
$604$		0			0
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	0.551678	−	0.834058i	$-0.313988\pi$
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	−0.998154	+	0.0607380i	$0.980655\pi$
$608$		0			0
$609$	9.00000	−	5.19615i	0.364698	−	0.210559i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.0000	−	36.3731i	−0.845428	−	1.46432i	−0.885249	−	0.465118i	$-0.846012\pi$
$617$	−21.0000	−	36.3731i	−0.845428	−	1.46432i	0.0398207	−	0.999207i	$-0.487321\pi$
$618$		0			0
$619$	−3.50000	+	6.06218i	−0.140677	+	0.243659i	−0.927752	−	0.373198i	$-0.878261\pi$
$619$	−3.50000	+	6.06218i	−0.140677	+	0.243659i	0.787075	+	0.616858i	$0.211595\pi$
$620$		0			0
$621$	−13.5000	+	7.79423i	−0.541736	+	0.312772i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$	63.0000	+	36.3731i	2.51598	+	1.45260i
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$	12.0000	−	6.92820i	0.476957	−	0.275371i
$634$		0			0
$635$	−25.5000	−	44.1673i	−1.01194	−	1.75273i
$636$		0			0
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$		0			0
$639$	9.00000			0.356034
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$		0			0
$643$	−2.00000	−	3.46410i	−0.0788723	−	0.136611i	0.823891	−	0.566748i	$-0.191799\pi$
$643$	−2.00000	−	3.46410i	−0.0788723	−	0.136611i	−0.902764	+	0.430137i	$0.858465\pi$
$644$		0			0
$645$		−	10.3923i		−	0.409197i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		−	3.46410i		−	0.135769i
$652$		0			0
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$		0			0
$655$	13.5000	−	23.3827i	0.527489	−	0.913637i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		0			0
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	−0.0890776	−	0.996025i	$-0.528392\pi$
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	0.907122	−	0.420869i	$-0.138275\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−18.0000	+	10.3923i	−0.699062	+	0.403604i
$664$		0			0
$665$	21.0000			0.814345
$666$		0			0
$667$	−18.0000			−0.696963
$668$		0			0
$669$	42.0000	+	24.2487i	1.62381	+	0.937509i
$670$		0			0
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	0.963679	−	0.267063i	$-0.0860531\pi$
$674$		0			0
$675$	−18.0000	−	10.3923i	−0.692820	−	0.400000i
$676$		0			0
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$		0			0
$681$	22.5000	+	12.9904i	0.862202	+	0.497792i
$682$		0			0
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$	1.50000	−	0.866025i	0.0572286	−	0.0330409i
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	23.5000	−	40.7032i	0.893982	−	1.54842i	0.0589228	−	0.998263i	$-0.481233\pi$
$691$	23.5000	−	40.7032i	0.893982	−	1.54842i	0.835059	−	0.550160i	$-0.185433\pi$
$692$		0			0
$693$	−9.00000	−	15.5885i	−0.341882	−	0.592157i
$694$		0			0
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	15.5885i		−	0.589610i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.50000	+	7.79423i	0.169240	+	0.293132i
$708$		0			0
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.301388	−	0.953502i	$-0.402550\pi$
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.675063	−	0.737760i	$-0.264116\pi$
$710$		0			0
$711$	−7.50000	+	12.9904i	−0.281272	+	0.487177i
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$		0			0
$717$	−22.5000	+	12.9904i	−0.840278	+	0.485135i
$718$		0			0
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$		0			0
$723$	12.0000	+	6.92820i	0.446285	+	0.257663i
$724$		0			0
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	−0.999136	−	0.0415715i	$-0.986764\pi$
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	0.463566	−	0.886062i	$-0.346570\pi$
$734$		0			0
$735$	−4.50000	−	2.59808i	−0.165985	−	0.0958315i
$736$		0			0
$737$	−48.0000			−1.76810
$738$		0			0
$739$	−26.0000			−0.956425			−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000			−0.956425			−0.478213	+	0.878244i	$0.658715\pi$
$740$		0			0
$741$	−21.0000	+	12.1244i	−0.771454	+	0.445399i
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$		0			0
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$		0			0
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$		0			0
$753$			5.19615i			0.189358i
$754$		0			0
$755$	69.0000			2.51117
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$			31.1769i			1.13165i
$760$		0			0
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$		0			0
$765$	−27.0000	−	46.7654i	−0.976187	−	1.69081i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$	−27.0000	+	15.5885i	−0.972381	+	0.561405i
$772$		0			0
$773$	−51.0000			−1.83434			−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000			−1.83434			−0.917171	+	0.398493i	$0.869533\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$		0			0
$777$	−3.00000	−	1.73205i	−0.107624	−	0.0621370i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$		0			0
$785$	−19.5000	+	33.7750i	−0.695985	+	1.20548i
$786$		0			0
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$		0			0
$789$	31.5000	+	18.1865i	1.12143	+	0.647458i
$790$		0			0
$791$	−15.0000			−0.533339
$792$		0			0
$793$	10.0000			0.355110
$794$		0			0
$795$	27.0000	−	15.5885i	0.957591	−	0.552866i
$796$		0			0
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$	4.50000	+	7.79423i	0.158604	+	0.274710i
$806$		0			0
$807$			15.5885i			0.548740i
$808$		0			0
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$		−	48.4974i		−	1.70088i
$814$		0			0
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$		0			0
$817$	7.00000	−	12.1244i	0.244899	−	0.424178i
$818$		0			0
$819$	6.00000			0.209657
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		0			0
$825$	−36.0000	+	20.7846i	−1.25336	+	0.723627i
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$		0			0
$831$	−24.0000	−	13.8564i	−0.832551	−	0.480673i
$832$		0			0
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	−40.5000	−	23.3827i	−1.39489	−	0.805342i
$844$		0			0
$845$	27.0000			0.928828
$846$		0			0
$847$	−25.0000			−0.859010
$848$		0			0
$849$	−28.5000	+	16.4545i	−0.978117	+	0.564716i
$850$		0			0
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		0			0
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	0.393753	+	0.919216i	$0.371177\pi$
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	−0.992941	+	0.118609i	$0.962157\pi$
$854$		0			0
$855$	−31.5000	−	54.5596i	−1.07728	−	1.86590i
$856$		0			0
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.126459	+	0.991972i	$0.540361\pi$
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.795843	+	0.605503i	$0.792972\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.00000			−0.306364			−0.153182	−	0.988198i	$-0.548952\pi$
$863$	−9.00000			−0.306364			−0.153182	+	0.988198i	$0.548952\pi$
$864$		0			0
$865$	18.0000			0.612018
$866$		0			0
$867$		−	32.9090i		−	1.11765i
$868$		0			0
$869$	15.0000	+	25.9808i	0.508840	+	0.881337i
$870$		0			0
$871$	8.00000	−	13.8564i	0.271070	−	0.469506i
$872$		0			0
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	4.50000	−	2.59808i	0.151781	−	0.0876309i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	34.0000			1.14419			0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000			1.14419			0.572096	+	0.820187i	$0.306131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	−8.50000	+	14.7224i	−0.285081	+	0.493775i
$890$		0			0
$891$	−27.0000	+	46.7654i	−0.904534	+	1.56670i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−27.0000	−	46.7654i	−0.902510	−	1.56319i
$896$		0			0
$897$	−9.00000	−	5.19615i	−0.300501	−	0.173494i
$898$		0			0
$899$	−12.0000			−0.400222
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$	−3.00000	+	1.73205i	−0.0998337	+	0.0576390i
$904$		0			0
$905$	−37.5000	−	64.9519i	−1.24654	−	2.15907i
$906$		0			0
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	−0.468063	−	0.883695i	$-0.655048\pi$
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	0.999334	−	0.0364935i	$-0.0116188\pi$
$908$		0			0
$909$	13.5000	−	23.3827i	0.447767	−	0.775555i
$910$		0			0
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$		0			0
$913$	36.0000	+	62.3538i	1.19143	+	2.06361i
$914$		0			0
$915$			25.9808i			0.858898i
$916$		0			0
$917$	−9.00000			−0.297206
$918$		0			0
$919$	−11.0000			−0.362857			−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000			−0.362857			−0.181428	+	0.983404i	$0.558072\pi$
$920$		0			0
$921$		−	43.3013i		−	1.42683i
$922$		0			0
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$		0			0
$927$	15.0000	+	25.9808i	0.492665	+	0.853320i
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$	−3.50000	−	6.06218i	−0.114708	−	0.198680i
$932$		0			0
$933$	18.0000	−	10.3923i	0.589294	−	0.340229i
$934$		0			0
$935$	−108.000			−3.53198
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$	−15.0000	−	8.66025i	−0.489506	−	0.282617i
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$			15.5885i			0.507093i
$946$		0			0
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	27.0000	+	15.5885i	0.875535	+	0.505490i
$952$		0			0
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$		0			0
$955$	−27.0000			−0.873699
$956$		0			0
$957$	−54.0000	+	31.1769i	−1.74557	+	1.00781i
$958$		0			0
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	−36.0000			−1.16008
$964$		0			0
$965$	25.5000	−	44.1673i	0.820874	−	1.42180i
$966$		0			0
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	0.969715	−	0.244238i	$-0.0785377\pi$
$967$	8.50000	+	14.7224i	0.273342	+	0.473441i	−0.696374	+	0.717679i	$0.745204\pi$
$968$		0			0
$969$		−	72.7461i		−	2.33694i
$970$		0			0
$971$	15.0000			0.481373			0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$		0			0
$973$	5.00000			0.160293
$974$		0			0
$975$		−	13.8564i		−	0.443760i
$976$		0			0
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$		0			0
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$		0			0
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$		0			0
$993$	−39.0000	−	22.5167i	−1.23763	−	0.714545i
$994$		0			0
$995$	−21.0000	−	36.3731i	−0.665745	−	1.15310i
$996$		0			0
$997$	27.5000	−	47.6314i	0.870934	−	1.50850i	0.00990158	−	0.999951i	$-0.496848\pi$
$997$	27.5000	−	47.6314i	0.870934	−	1.50850i	0.861032	−	0.508551i	$-0.169818\pi$
$998$		0			0
$999$			10.3923i			0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.d.673.1		2
3.2	odd	2		3024.2.r.a.2017.1		2
4.3	odd	2		126.2.f.a.43.1	✓	2
9.2	odd	6		9072.2.a.w.1.1		1
9.4	even	3	inner	1008.2.r.d.337.1		2
9.5	odd	6		3024.2.r.a.1009.1		2
9.7	even	3		9072.2.a.c.1.1		1
12.11	even	2		378.2.f.a.127.1		2
28.3	even	6		882.2.h.f.79.1		2
28.11	odd	6		882.2.h.j.79.1		2
28.19	even	6		882.2.e.d.655.1		2
28.23	odd	6		882.2.e.b.655.1		2
28.27	even	2		882.2.f.h.295.1		2
36.7	odd	6		1134.2.a.a.1.1		1
36.11	even	6		1134.2.a.h.1.1		1
36.23	even	6		378.2.f.a.253.1		2
36.31	odd	6		126.2.f.a.85.1	yes	2
84.11	even	6		2646.2.h.e.667.1		2
84.23	even	6		2646.2.e.f.2125.1		2
84.47	odd	6		2646.2.e.j.2125.1		2
84.59	odd	6		2646.2.h.a.667.1		2
84.83	odd	2		2646.2.f.c.883.1		2
252.23	even	6		2646.2.h.e.361.1		2
252.31	even	6		882.2.e.d.373.1		2
252.59	odd	6		2646.2.e.j.1549.1		2
252.67	odd	6		882.2.e.b.373.1		2
252.83	odd	6		7938.2.a.u.1.1		1
252.95	even	6		2646.2.e.f.1549.1		2
252.103	even	6		882.2.h.f.67.1		2
252.131	odd	6		2646.2.h.a.361.1		2
252.139	even	6		882.2.f.h.589.1		2
252.167	odd	6		2646.2.f.c.1765.1		2
252.223	even	6		7938.2.a.l.1.1		1
252.247	odd	6		882.2.h.j.67.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	4.3	odd	2
126.2.f.a.85.1	yes	2	36.31	odd	6
378.2.f.a.127.1		2	12.11	even	2
378.2.f.a.253.1		2	36.23	even	6
882.2.e.b.373.1		2	252.67	odd	6
882.2.e.b.655.1		2	28.23	odd	6
882.2.e.d.373.1		2	252.31	even	6
882.2.e.d.655.1		2	28.19	even	6
882.2.f.h.295.1		2	28.27	even	2
882.2.f.h.589.1		2	252.139	even	6
882.2.h.f.67.1		2	252.103	even	6
882.2.h.f.79.1		2	28.3	even	6
882.2.h.j.67.1		2	252.247	odd	6
882.2.h.j.79.1		2	28.11	odd	6
1008.2.r.d.337.1		2	9.4	even	3	inner
1008.2.r.d.673.1		2	1.1	even	1	trivial
1134.2.a.a.1.1		1	36.7	odd	6
1134.2.a.h.1.1		1	36.11	even	6
2646.2.e.f.1549.1		2	252.95	even	6
2646.2.e.f.2125.1		2	84.23	even	6
2646.2.e.j.1549.1		2	252.59	odd	6
2646.2.e.j.2125.1		2	84.47	odd	6
2646.2.f.c.883.1		2	84.83	odd	2
2646.2.f.c.1765.1		2	252.167	odd	6
2646.2.h.a.361.1		2	252.131	odd	6
2646.2.h.a.667.1		2	84.59	odd	6
2646.2.h.e.361.1		2	252.23	even	6
2646.2.h.e.667.1		2	84.11	even	6
3024.2.r.a.1009.1		2	9.5	odd	6
3024.2.r.a.2017.1		2	3.2	odd	2
7938.2.a.l.1.1		1	252.223	even	6
7938.2.a.u.1.1		1	252.83	odd	6
9072.2.a.c.1.1		1	9.7	even	3
9072.2.a.w.1.1		1	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q-1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{7} -3.00000 q^{9} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(4.50000 - 2.59808i) q^{15} +6.00000 q^{17} +7.00000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{31} +(9.00000 + 5.19615i) q^{33} +3.00000 q^{35} +2.00000 q^{37} +(-3.00000 + 1.73205i) q^{39} +(1.00000 - 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-0.500000 - 0.866025i) q^{49} -10.3923i q^{51} +6.00000 q^{53} -18.0000 q^{55} -12.1244i q^{57} +(-2.50000 + 4.33013i) q^{61} +(-1.50000 + 2.59808i) q^{63} +(3.00000 - 5.19615i) q^{65} +(4.00000 + 6.92820i) q^{67} +(4.50000 - 2.59808i) q^{69} -3.00000 q^{71} +2.00000 q^{73} +(6.00000 + 3.46410i) q^{75} +(3.00000 + 5.19615i) q^{77} +(2.50000 - 4.33013i) q^{79} +9.00000 q^{81} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(9.00000 + 5.19615i) q^{87} -2.00000 q^{91} +(3.00000 - 1.73205i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{5} + q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^5 + q^7 - 6 * q^9	\( 2 q + 3 q^{5} + q^{7} - 6 q^{9} - 6 q^{11} - 2 q^{13} + 9 q^{15} + 12 q^{17} + 14 q^{19} - 3 q^{21} + 3 q^{23} - 4 q^{25} - 6 q^{29} + 2 q^{31} + 18 q^{33} + 6 q^{35} + 4 q^{37} - 6 q^{39} + 2 q^{43} - 9 q^{45} - q^{49} + 12 q^{53} - 36 q^{55} - 5 q^{61} - 3 q^{63} + 6 q^{65} + 8 q^{67} + 9 q^{69} - 6 q^{71} + 4 q^{73} + 12 q^{75} + 6 q^{77} + 5 q^{79} + 18 q^{81} + 12 q^{83} + 18 q^{85} + 18 q^{87} - 4 q^{91} + 6 q^{93} + 21 q^{95} - 2 q^{97} + 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^5 + q^7 - 6 * q^9 - 6 * q^11 - 2 * q^13 + 9 * q^15 + 12 * q^17 + 14 * q^19 - 3 * q^21 + 3 * q^23 - 4 * q^25 - 6 * q^29 + 2 * q^31 + 18 * q^33 + 6 * q^35 + 4 * q^37 - 6 * q^39 + 2 * q^43 - 9 * q^45 - q^49 + 12 * q^53 - 36 * q^55 - 5 * q^61 - 3 * q^63 + 6 * q^65 + 8 * q^67 + 9 * q^69 - 6 * q^71 + 4 * q^73 + 12 * q^75 + 6 * q^77 + 5 * q^79 + 18 * q^81 + 12 * q^83 + 18 * q^85 + 18 * q^87 - 4 * q^91 + 6 * q^93 + 21 * q^95 - 2 * q^97 + 18 * q^99

Introduction

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