LMFDB - Embedded newform 1008.2.t.f.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(193,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.193"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [2,0,3,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.f.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{3} +3.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.00000 q^{11} +(0.500000 + 0.866025i) q^{13} +(4.50000 + 2.59808i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-3.00000 - 3.46410i) q^{21} +9.00000 q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(4.00000 - 6.92820i) q^{31} +(4.50000 + 2.59808i) q^{33} +(-7.50000 - 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +1.73205i q^{39} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(4.50000 + 7.79423i) q^{45} +(5.50000 + 4.33013i) q^{49} -5.19615i q^{51} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(-1.00000 - 1.73205i) q^{61} +(-1.50000 - 7.79423i) q^{63} +(1.50000 + 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(13.5000 + 7.79423i) q^{69} -12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(6.00000 + 3.46410i) q^{75} +(-7.50000 - 2.59808i) q^{77} +(-8.00000 - 13.8564i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-4.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(-0.500000 - 2.59808i) q^{91} +(12.0000 - 6.92820i) q^{93} +(-10.5000 + 18.1865i) q^{95} +(0.500000 - 0.866025i) q^{97} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + q^{13} + 9 q^{15} - 3 q^{17} - 7 q^{19} - 6 q^{21} + 18 q^{23} + 8 q^{25} - 3 q^{29} + 8 q^{31} + 9 q^{33} - 15 q^{35} + q^{37} - 3 q^{41} - q^{43}+ \cdots + 9 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 6 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + q^13 + 9 * q^15 - 3 * q^17 - 7 * q^19 - 6 * q^21 + 18 * q^23 + 8 * q^25 - 3 * q^29 + 8 * q^31 + 9 * q^33 - 15 * q^35 + q^37 - 3 * q^41 - q^43 + 9 * q^45 + 11 * q^49 - 3 * q^53 + 18 * q^55 - 21 * q^57 - 2 * q^61 - 3 * q^63 + 3 * q^65 - 4 * q^67 + 27 * q^69 - 24 * q^71 - 11 * q^73 + 12 * q^75 - 15 * q^77 - 16 * q^79 - 9 * q^81 - 9 * q^83 - 9 * q^85 - 9 * q^87 - 3 * q^89 - q^91 + 24 * q^93 - 21 * q^95 + q^97 + 9 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	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	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		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
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	4.50000	+	2.59808i	1.16190	+	0.670820i
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$		0			0
$23$	9.00000			1.87663			0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000			1.87663			0.938315	+	0.345782i	$0.112386\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$		0			0
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$			1.73205i			0.277350i
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	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
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$	−10.5000	+	6.06218i	−1.39076	+	0.802955i
$58$		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
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$	−1.50000	−	7.79423i	−0.188982	−	0.981981i
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	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
$69$	13.5000	+	7.79423i	1.62521	+	0.938315i
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$		0			0
$75$	6.00000	+	3.46410i	0.692820	+	0.400000i
$76$		0			0
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$		0			0
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$		0			0
$87$	−4.50000	+	2.59808i	−0.482451	+	0.278543i
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	−0.500000	−	2.59808i	−0.0524142	−	0.272352i
$92$		0			0
$93$	12.0000	−	6.92820i	1.24434	−	0.718421i
$94$		0			0
$95$	−10.5000	+	18.1865i	−1.07728	+	1.86590i
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$		0			0
$99$	4.50000	+	7.79423i	0.452267	+	0.783349i
$100$		0			0
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$	−9.00000	−	10.3923i	−0.878310	−	1.01419i
$106$		0			0
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$		0			0
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	0.989002	+	0.147901i	$0.0472517\pi$
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	−0.366415	+	0.930451i	$0.619415\pi$
$110$		0			0
$111$	1.50000	−	0.866025i	0.142374	−	0.0821995i
$112$		0			0
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$		0			0
$115$	27.0000			2.51776
$116$		0			0
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$		0			0
$119$	1.50000	+	7.79423i	0.137505	+	0.714496i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$		−	5.19615i		−	0.468521i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$		0			0
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	14.0000	−	12.1244i	1.21395	−	1.05131i
$134$		0			0
$135$			15.5885i			1.34164i
$136$		0			0
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$		0			0
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$		0			0
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$		0			0
$151$	7.00000			0.569652			0.284826	−	0.958579i	$-0.408064\pi$
$151$	7.00000			0.569652			0.284826	+	0.958579i	$0.408064\pi$
$152$		0			0
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$		0			0
$155$	12.0000	−	20.7846i	0.963863	−	1.66946i
$156$		0			0
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$		0			0
$159$		−	5.19615i		−	0.412082i
$160$		0			0
$161$	−22.5000	−	7.79423i	−1.77325	−	0.614271i
$162$		0			0
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	0.206518	+	0.978443i	$0.433787\pi$
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	−0.950615	+	0.310372i	$0.899546\pi$
$164$		0			0
$165$	13.5000	+	7.79423i	1.05097	+	0.606780i
$166$		0			0
$167$	−7.50000	−	12.9904i	−0.580367	−	1.00523i	−0.995436	−	0.0954356i	$-0.969576\pi$
$167$	−7.50000	−	12.9904i	−0.580367	−	1.00523i	0.415068	−	0.909790i	$-0.363758\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−21.0000			−1.60591
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	−0.929114	−	0.369792i	$-0.879429\pi$
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	0.144308	−	0.989533i	$-0.453905\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$	4.50000	−	12.9904i	0.327327	−	0.944911i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$			5.19615i			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
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.844446	−	0.535641i	$-0.820070\pi$
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.0416556	−	0.999132i	$-0.513263\pi$
$200$		0			0
$201$	−6.00000	+	3.46410i	−0.423207	+	0.244339i
$202$		0			0
$203$	6.00000	−	5.19615i	0.421117	−	0.364698i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$	13.5000	+	23.3827i	0.938315	+	1.62521i
$208$		0			0
$209$	−10.5000	+	18.1865i	−0.726300	+	1.25799i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$	−18.0000	−	10.3923i	−1.23334	−	0.712069i
$214$		0			0
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$		0			0
$217$	−16.0000	+	13.8564i	−1.08615	+	0.940634i
$218$		0			0
$219$		−	19.0526i		−	1.28745i
$220$		0			0
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$		0			0
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$		0			0
$231$	−9.00000	−	10.3923i	−0.592157	−	0.683763i
$232$		0			0
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	27.7128i		−	1.80014i
$238$		0			0
$239$	−1.50000	−	2.59808i	−0.0970269	−	0.168056i	0.813426	−	0.581669i	$-0.197600\pi$
$239$	−1.50000	−	2.59808i	−0.0970269	−	0.168056i	−0.910453	+	0.413613i	$0.864267\pi$
$240$		0			0
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$		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
$247$	−7.00000			−0.445399
$248$		0			0
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$		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
$253$	27.0000			1.69748
$254$		0			0
$255$		−	15.5885i		−	0.976187i
$256$		0			0
$257$	−21.0000			−1.30994			−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000			−1.30994			−0.654972	+	0.755653i	$0.727320\pi$
$258$		0			0
$259$	−2.00000	+	1.73205i	−0.124274	+	0.107624i
$260$		0			0
$261$	−9.00000			−0.557086
$262$		0			0
$263$	−9.00000			−0.554964			−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000			−0.554964			−0.277482	+	0.960731i	$0.589500\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$	−4.50000	+	2.59808i	−0.275396	+	0.159000i
$268$		0			0
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$		0			0
$271$	2.50000	−	4.33013i	0.151864	−	0.263036i	−0.780049	−	0.625719i	$-0.784806\pi$
$271$	2.50000	−	4.33013i	0.151864	−	0.263036i	0.931913	+	0.362682i	$0.118139\pi$
$272$		0			0
$273$	1.50000	−	4.33013i	0.0907841	−	0.262071i
$274$		0			0
$275$	12.0000			0.723627
$276$		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
$279$	24.0000			1.43684
$280$		0			0
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	−0.361895	−	0.932219i	$-0.617870\pi$
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	0.988273	−	0.152699i	$-0.0487965\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$	−31.5000	+	18.1865i	−1.86590	+	1.07728i
$286$		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	−	0.866025i	0.0879316	−	0.0507673i
$292$		0			0
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			15.5885i			0.904534i
$298$		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
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	19.5000	+	11.2583i	1.10932	+	0.640464i
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$		0			0
$315$	−4.50000	−	23.3827i	−0.253546	−	1.31747i
$316$		0			0
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$		0			0
$321$	13.5000	−	7.79423i	0.753497	−	0.435031i
$322$		0			0
$323$	21.0000			1.16847
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$		0			0
$327$			22.5167i			1.24517i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		0			0
$333$	3.00000			0.164399
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$		0			0
$339$			15.5885i			0.846649i
$340$		0			0
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	40.5000	+	23.3827i	2.18045	+	1.25888i
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	0.374701	+	0.927146i	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$	−4.50000	+	2.59808i	−0.240192	+	0.138675i
$352$		0			0
$353$	3.00000			0.159674			0.0798369	−	0.996808i	$-0.474560\pi$
$353$	3.00000			0.159674			0.0798369	+	0.996808i	$0.474560\pi$
$354$		0			0
$355$	−36.0000			−1.91068
$356$		0			0
$357$	−4.50000	+	12.9904i	−0.238165	+	0.687524i
$358$		0			0
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	−0.722496	−	0.691375i	$-0.757005\pi$
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	0.959997	+	0.280012i	$0.0903384\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$		0			0
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	−17.0000			−0.887393			−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000			−0.887393			−0.443696	+	0.896177i	$0.646333\pi$
$368$		0			0
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	1.50000	+	7.79423i	0.0778761	+	0.404656i
$372$		0			0
$373$	−13.0000			−0.673114			−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000			−0.673114			−0.336557	+	0.941663i	$0.609263\pi$
$374$		0			0
$375$	−4.50000	−	2.59808i	−0.232379	−	0.134164i
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	6.00000	+	3.46410i	0.307389	+	0.177471i
$382$		0			0
$383$	−15.0000			−0.766464			−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000			−0.766464			−0.383232	+	0.923652i	$0.625189\pi$
$384$		0			0
$385$	−22.5000	−	7.79423i	−1.14671	−	0.397231i
$386$		0			0
$387$	−3.00000			−0.152499
$388$		0			0
$389$	27.0000			1.36895			0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000			1.36895			0.684477	+	0.729034i	$0.260031\pi$
$390$		0			0
$391$	−13.5000	−	23.3827i	−0.682724	−	1.18251i
$392$		0			0
$393$	−22.5000	−	12.9904i	−1.13497	−	0.655278i
$394$		0			0
$395$	−24.0000	−	41.5692i	−1.20757	−	2.09157i
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$		0			0
$399$	31.5000	−	6.06218i	1.57697	−	0.303488i
$400$		0			0
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$		0			0
$403$	8.00000			0.398508
$404$		0			0
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$		0			0
$407$	1.50000	−	2.59808i	0.0743522	−	0.128782i
$408$		0			0
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	−0.0487958	−	0.998809i	$-0.515538\pi$
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	0.889392	−	0.457146i	$-0.151128\pi$
$410$		0			0
$411$	−13.5000	−	7.79423i	−0.665906	−	0.384461i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−13.5000	+	23.3827i	−0.662689	+	1.14781i
$416$		0			0
$417$		−	12.1244i		−	0.593732i
$418$		0			0
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	1.00000	+	5.19615i	0.0483934	+	0.251459i
$428$		0			0
$429$			5.19615i			0.250873i
$430$		0			0
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	0.983057	+	0.183301i	$0.0586785\pi$
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	−0.332785	+	0.943003i	$0.607988\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	−13.5000	+	7.79423i	−0.647275	+	0.373705i
$436$		0			0
$437$	−31.5000	+	54.5596i	−1.50685	+	2.60994i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$		0			0
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$		0			0
$447$	−13.5000	−	7.79423i	−0.638528	−	0.368654i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$		0			0
$453$	10.5000	+	6.06218i	0.493333	+	0.284826i
$454$		0			0
$455$	−1.50000	−	7.79423i	−0.0703211	−	0.365399i
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$		0			0
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.739511	+	0.673145i	$0.235057\pi$
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.213205	+	0.977007i	$0.431610\pi$
$464$		0			0
$465$	36.0000	−	20.7846i	1.66946	−	0.963863i
$466$		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
$471$	33.0000	−	19.0526i	1.52056	−	0.877896i
$472$		0			0
$473$	−1.50000	+	2.59808i	−0.0689701	+	0.119460i
$474$		0			0
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$		0			0
$479$	3.00000			0.137073			0.0685367	−	0.997649i	$-0.478167\pi$
$479$	3.00000			0.137073			0.0685367	+	0.997649i	$0.478167\pi$
$480$		0			0
$481$	1.00000			0.0455961
$482$		0			0
$483$	−27.0000	−	31.1769i	−1.22854	−	1.41860i
$484$		0			0
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	0.430486	−	0.902597i	$-0.358342\pi$
$488$		0			0
$489$	−28.5000	+	16.4545i	−1.28881	+	0.744097i
$490$		0			0
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	0.999552	−	0.0299272i	$-0.00952753\pi$
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	−0.525694	+	0.850674i	$0.676194\pi$
$492$		0			0
$493$	9.00000			0.405340
$494$		0			0
$495$	13.5000	+	23.3827i	0.606780	+	1.05097i
$496$		0			0
$497$	30.0000	+	10.3923i	1.34568	+	0.466159i
$498$		0			0
$499$	25.0000			1.11915			0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000			1.11915			0.559577	+	0.828778i	$0.310964\pi$
$500$		0			0
$501$		−	25.9808i		−	1.16073i
$502$		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
$507$	18.0000	−	10.3923i	0.799408	−	0.461538i
$508$		0			0
$509$	−9.00000			−0.398918			−0.199459	−	0.979906i	$-0.563918\pi$
$509$	−9.00000			−0.398918			−0.199459	+	0.979906i	$0.563918\pi$
$510$		0			0
$511$	5.50000	+	28.5788i	0.243306	+	1.26425i
$512$		0			0
$513$	−31.5000	−	18.1865i	−1.39076	−	0.802955i
$514$		0			0
$515$	39.0000			1.71855
$516$		0			0
$517$		0			0
$518$		0			0
$519$			10.3923i			0.456172i
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	−0.932345	−	0.361569i	$-0.882241\pi$
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	0.779301	+	0.626650i	$0.215574\pi$
$524$		0			0
$525$	−12.0000	−	13.8564i	−0.523723	−	0.604743i
$526$		0			0
$527$	−24.0000			−1.04546
$528$		0			0
$529$	58.0000			2.52174
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.50000	−	2.59808i	0.0649722	−	0.112535i
$534$		0			0
$535$	13.5000	−	23.3827i	0.583656	−	1.01092i
$536$		0			0
$537$		−	36.3731i		−	1.56961i
$538$		0			0
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$		0			0
$543$	3.00000	+	1.73205i	0.128742	+	0.0743294i
$544$		0			0
$545$	19.5000	+	33.7750i	0.835288	+	1.44676i
$546$		0			0
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	−0.724157	−	0.689635i	$-0.757771\pi$
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	0.959320	+	0.282321i	$0.0911043\pi$
$548$		0			0
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$		0			0
$551$	−10.5000	−	18.1865i	−0.447315	−	0.774772i
$552$		0			0
$553$	8.00000	+	41.5692i	0.340195	+	1.76770i
$554$		0			0
$555$	4.50000	−	2.59808i	0.191014	−	0.110282i
$556$		0			0
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		−	15.5885i		−	0.658145i
$562$		0			0
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$		0			0
$565$	13.5000	+	23.3827i	0.567949	+	0.983717i
$566$		0			0
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		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
$573$		0			0
$574$		0			0
$575$	36.0000			1.50130
$576$		0			0
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$		0			0
$579$	−21.0000	+	12.1244i	−0.872730	+	0.503871i
$580$		0			0
$581$	18.0000	−	15.5885i	0.746766	−	0.646718i
$582$		0			0
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$		0			0
$585$	−4.50000	+	7.79423i	−0.186052	+	0.322252i
$586$		0			0
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$	27.0000	+	15.5885i	1.11063	+	0.641223i
$592$		0			0
$593$	−19.5000	+	33.7750i	−0.800769	+	1.38697i	0.118342	+	0.992973i	$0.462242\pi$
$593$	−19.5000	+	33.7750i	−0.800769	+	1.38697i	−0.919111	+	0.394000i	$0.871091\pi$
$594$		0			0
$595$	4.50000	+	23.3827i	0.184482	+	0.958597i
$596$		0			0
$597$		−	43.3013i		−	1.77220i
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	−0.490049	−	0.871695i	$-0.663021\pi$
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	0.999934	−	0.0114528i	$-0.00364562\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−6.00000			−0.243935
$606$		0			0
$607$	13.0000			0.527654			0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000			0.527654			0.263827	+	0.964570i	$0.415015\pi$
$608$		0			0
$609$	13.5000	−	2.59808i	0.547048	−	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$		0			0
$615$		−	15.5885i		−	0.628587i
$616$		0			0
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.819818	+	0.572624i	$0.194074\pi$
$617$	22.5000	+	38.9711i	0.905816	+	1.56892i	0.0859976	+	0.996295i	$0.472592\pi$
$618$		0			0
$619$	−17.0000			−0.683288			−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000			−0.683288			−0.341644	+	0.939829i	$0.610984\pi$
$620$		0			0
$621$			46.7654i			1.87663i
$622$		0			0
$623$	6.00000	−	5.19615i	0.240385	−	0.208179i
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$	−31.5000	+	18.1865i	−1.25799	+	0.726300i
$628$		0			0
$629$	−3.00000			−0.119618
$630$		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
$635$	12.0000			0.476205
$636$		0			0
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$		0			0
$639$	−18.0000	−	31.1769i	−0.712069	−	1.23334i
$640$		0			0
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$		0			0
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$	−4.50000	+	2.59808i	−0.177187	+	0.102299i
$646$		0			0
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	0.582397	−	0.812905i	$-0.302115\pi$
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	−0.995194	+	0.0979182i	$0.968782\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−36.0000	+	6.92820i	−1.41095	+	0.271538i
$652$		0			0
$653$	15.0000			0.586995			0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000			0.586995			0.293498	+	0.955960i	$0.405181\pi$
$654$		0			0
$655$	−45.0000			−1.75830
$656$		0			0
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$		0			0
$659$	1.50000	−	2.59808i	0.0584317	−	0.101207i	−0.835330	−	0.549749i	$-0.814723\pi$
$659$	1.50000	−	2.59808i	0.0584317	−	0.101207i	0.893762	+	0.448542i	$0.148057\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$		0			0
$663$	4.50000	−	2.59808i	0.174766	−	0.100901i
$664$		0			0
$665$	42.0000	−	36.3731i	1.62869	−	1.41049i
$666$		0			0
$667$	−13.5000	+	23.3827i	−0.522722	+	0.905381i
$668$		0			0
$669$	−1.50000	+	0.866025i	−0.0579934	+	0.0334825i
$670$		0			0
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$		0			0
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$		0			0
$675$			20.7846i			0.800000i
$676$		0			0
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$		0			0
$679$	−2.00000	+	1.73205i	−0.0767530	+	0.0664700i
$680$		0			0
$681$	4.50000	+	2.59808i	0.172440	+	0.0995585i
$682$		0			0
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	−27.0000			−1.03162
$686$		0			0
$687$	−19.5000	−	11.2583i	−0.743971	−	0.429532i
$688$		0			0
$689$	1.50000	−	2.59808i	0.0571454	−	0.0989788i
$690$		0			0
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	0.892458	+	0.451130i	$0.148979\pi$
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	−0.0555386	+	0.998457i	$0.517688\pi$
$692$		0			0
$693$	−4.50000	−	23.3827i	−0.170941	−	0.888235i
$694$		0			0
$695$	−10.5000	−	18.1865i	−0.398288	−	0.689855i
$696$		0			0
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$		0			0
$699$	−4.50000	+	2.59808i	−0.170206	+	0.0982683i
$700$		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
$703$	3.50000	+	6.06218i	0.132005	+	0.228639i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$		0			0
$711$	24.0000	−	41.5692i	0.900070	−	1.55897i
$712$		0			0
$713$	36.0000	−	62.3538i	1.34821	−	2.33517i
$714$		0			0
$715$	4.50000	+	7.79423i	0.168290	+	0.291488i
$716$		0			0
$717$		−	5.19615i		−	0.194054i
$718$		0			0
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	−32.5000	−	11.2583i	−1.21036	−	0.419282i
$722$		0			0
$723$	−19.5000	−	11.2583i	−0.725213	−	0.418702i
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	−0.961020	−	0.276479i	$-0.910832\pi$
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	0.719948	+	0.694028i	$0.244166\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000			0.110959
$732$		0			0
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$		0			0
$735$	13.5000	+	33.7750i	0.497955	+	1.24581i
$736$		0			0
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$		0			0
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	0.996235	−	0.0866983i	$-0.0276316\pi$
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	−0.573200	+	0.819415i	$0.694298\pi$
$740$		0			0
$741$	−10.5000	−	6.06218i	−0.385727	−	0.222700i
$742$		0			0
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$		0			0
$745$	−27.0000			−0.989203
$746$		0			0
$747$	−27.0000			−0.987878
$748$		0			0
$749$	−18.0000	+	15.5885i	−0.657706	+	0.569590i
$750$		0			0
$751$	13.0000			0.474377			0.237188	−	0.971464i	$-0.423774\pi$
$751$	13.0000			0.474377			0.237188	+	0.971464i	$0.423774\pi$
$752$		0			0
$753$	−18.0000	−	10.3923i	−0.655956	−	0.378717i
$754$		0			0
$755$	21.0000			0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	40.5000	+	23.3827i	1.47006	+	0.848738i
$760$		0			0
$761$	−45.0000			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$762$		0			0
$763$	−6.50000	−	33.7750i	−0.235316	−	1.22274i
$764$		0			0
$765$	13.5000	−	23.3827i	0.488094	−	0.845403i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$	−31.5000	−	18.1865i	−1.13444	−	0.654972i
$772$		0			0
$773$	−13.5000	−	23.3827i	−0.485561	−	0.841017i	0.514301	−	0.857610i	$-0.328051\pi$
$773$	−13.5000	−	23.3827i	−0.485561	−	0.841017i	−0.999862	+	0.0165929i	$0.994718\pi$
$774$		0			0
$775$	16.0000	−	27.7128i	0.574737	−	0.995474i
$776$		0			0
$777$	−4.50000	+	0.866025i	−0.161437	+	0.0310685i
$778$		0			0
$779$	21.0000			0.752403
$780$		0			0
$781$	−36.0000			−1.28818
$782$		0			0
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$		0			0
$785$	33.0000	−	57.1577i	1.17782	−	2.04004i
$786$		0			0
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$		0			0
$789$	−13.5000	−	7.79423i	−0.480613	−	0.277482i
$790$		0			0
$791$	−4.50000	−	23.3827i	−0.160002	−	0.831393i
$792$		0			0
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$		0			0
$795$		−	15.5885i		−	0.552866i
$796$		0			0
$797$	10.5000	+	18.1865i	0.371929	+	0.644200i	0.989862	−	0.142031i	$-0.0453631\pi$
$797$	10.5000	+	18.1865i	0.371929	+	0.644200i	−0.617933	+	0.786231i	$0.712030\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−9.00000			−0.317999
$802$		0			0
$803$	−16.5000	−	28.5788i	−0.582272	−	1.00853i
$804$		0			0
$805$	−67.5000	−	23.3827i	−2.37906	−	0.824131i
$806$		0			0
$807$		−	25.9808i		−	0.914566i
$808$		0			0
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	7.50000	−	4.33013i	0.263036	−	0.151864i
$814$		0			0
$815$	−28.5000	+	49.3634i	−0.998311	+	1.72913i
$816$		0			0
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$		0			0
$819$	6.00000	−	5.19615i	0.209657	−	0.181568i
$820$		0			0
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$		0			0
$825$	18.0000	+	10.3923i	0.626680	+	0.361814i
$826$		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
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		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
$835$	−22.5000	−	38.9711i	−0.778645	−	1.34865i
$836$		0			0
$837$	36.0000	+	20.7846i	1.24434	+	0.718421i
$838$		0			0
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	−0.707026	−	0.707187i	$-0.749964\pi$
$839$	7.50000	−	12.9904i	0.258929	−	0.448478i	0.965955	+	0.258709i	$0.0832972\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	31.5000	−	18.1865i	1.08492	−	0.626377i
$844$		0			0
$845$	18.0000	−	31.1769i	0.619219	−	1.07252i
$846$		0			0
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$		0			0
$849$	−6.00000	+	3.46410i	−0.205919	+	0.118888i
$850$		0			0
$851$	4.50000	−	7.79423i	0.154258	−	0.267183i
$852$		0			0
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	−0.857339	−	0.514753i	$-0.827884\pi$
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	0.874458	+	0.485101i	$0.161217\pi$
$854$		0			0
$855$	−63.0000			−2.15455
$856$		0			0
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$		0			0
$859$	25.0000			0.852989			0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000			0.852989			0.426494	+	0.904490i	$0.359748\pi$
$860$		0			0
$861$	−4.50000	+	12.9904i	−0.153360	+	0.442711i
$862$		0			0
$863$	−25.5000	+	44.1673i	−0.868030	+	1.50347i	−0.00402340	+	0.999992i	$0.501281\pi$
$863$	−25.5000	+	44.1673i	−0.868030	+	1.50347i	−0.864007	+	0.503480i	$0.832053\pi$
$864$		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
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$		0			0
$871$	−4.00000			−0.135535
$872$		0			0
$873$	3.00000			0.101535
$874$		0			0
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$		0			0
$877$	47.0000			1.58708			0.793539	−	0.608520i	$-0.208236\pi$
$877$	47.0000			1.58708			0.793539	+	0.608520i	$0.208236\pi$
$878$		0			0
$879$			15.5885i			0.525786i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.0000			1.10803			0.554016	−	0.832506i	$-0.313095\pi$
$887$	33.0000			1.10803			0.554016	+	0.832506i	$0.313095\pi$
$888$		0			0
$889$	−10.0000	−	3.46410i	−0.335389	−	0.116182i
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−31.5000	−	54.5596i	−1.05293	−	1.82373i
$896$		0			0
$897$			15.5885i			0.520483i
$898$		0			0
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$		0			0
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$		0			0
$903$	4.50000	−	0.866025i	0.149751	−	0.0288195i
$904$		0			0
$905$	6.00000			0.199447
$906$		0			0
$907$	43.0000			1.42779			0.713896	−	0.700252i	$-0.246929\pi$
$907$	43.0000			1.42779			0.713896	+	0.700252i	$0.246929\pi$
$908$		0			0
$909$	4.50000	+	7.79423i	0.149256	+	0.258518i
$910$		0			0
$911$	19.5000	−	33.7750i	0.646064	−	1.11902i	−0.337991	−	0.941149i	$-0.609747\pi$
$911$	19.5000	−	33.7750i	0.646064	−	1.11902i	0.984055	−	0.177866i	$-0.0569194\pi$
$912$		0			0
$913$	−13.5000	+	23.3827i	−0.446785	+	0.773854i
$914$		0			0
$915$		−	10.3923i		−	0.343559i
$916$		0			0
$917$	37.5000	+	12.9904i	1.23836	+	0.428980i
$918$		0			0
$919$	26.5000	−	45.8993i	0.874154	−	1.51408i	0.0164935	−	0.999864i	$-0.494750\pi$
$919$	26.5000	−	45.8993i	0.874154	−	1.51408i	0.857661	−	0.514216i	$-0.171917\pi$
$920$		0			0
$921$	42.0000	+	24.2487i	1.38395	+	0.799022i
$922$		0			0
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$	19.5000	+	33.7750i	0.640464	+	1.10932i
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	−45.5000	+	18.1865i	−1.49120	+	0.596040i
$932$		0			0
$933$	−36.0000	+	20.7846i	−1.17859	+	0.680458i
$934$		0			0
$935$	−13.5000	−	23.3827i	−0.441497	−	0.764696i
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$			17.3205i			0.565233i
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$		0			0
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$		0			0
$945$	13.5000	−	38.9711i	0.439155	−	1.26773i
$946$		0			0
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	5.50000	−	9.52628i	0.178538	−	0.309236i
$950$		0			0
$951$		−	31.1769i		−	1.01098i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−13.5000	+	7.79423i	−0.436393	+	0.251952i
$958$		0			0
$959$	22.5000	+	7.79423i	0.726563	+	0.251689i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	27.0000			0.870063
$964$		0			0
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$		0			0
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	0.980814	+	0.194946i	$0.0624533\pi$
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	−0.321578	+	0.946883i	$0.604213\pi$
$968$		0			0
$969$	31.5000	+	18.1865i	1.01193	+	0.584236i
$970$		0			0
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$		0			0
$973$	3.50000	+	18.1865i	0.112205	+	0.583033i
$974$		0			0
$975$			6.92820i			0.221880i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$	−19.5000	+	33.7750i	−0.622587	+	1.07835i
$982$		0			0
$983$	15.0000			0.478426			0.239213	−	0.970967i	$-0.423111\pi$
$983$	15.0000			0.478426			0.239213	+	0.970967i	$0.423111\pi$
$984$		0			0
$985$	54.0000			1.72058
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.50000	+	7.79423i	−0.143092	+	0.247842i
$990$		0			0
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	0.596288	−	0.802771i	$-0.296642\pi$
$991$	−12.5000	−	21.6506i	−0.397076	−	0.687755i	−0.993364	+	0.115015i	$0.963308\pi$
$992$		0			0
$993$			13.8564i			0.439720i
$994$		0			0
$995$	−37.5000	−	64.9519i	−1.18883	−	2.05911i
$996$		0			0
$997$	−13.0000			−0.411714			−0.205857	−	0.978582i	$-0.565998\pi$
$997$	−13.0000			−0.411714			−0.205857	+	0.978582i	$0.565998\pi$
$998$		0			0
$999$	4.50000	+	2.59808i	0.142374	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.f.961.1		2
3.2	odd	2		3024.2.t.a.289.1		2
4.3	odd	2		126.2.h.b.79.1	yes	2
7.4	even	3		1008.2.q.a.529.1		2
9.4	even	3		1008.2.q.a.625.1		2
9.5	odd	6		3024.2.q.f.2305.1		2
12.11	even	2		378.2.h.a.289.1		2
21.11	odd	6		3024.2.q.f.2881.1		2
28.3	even	6		882.2.e.c.655.1		2
28.11	odd	6		126.2.e.a.25.1	✓	2
28.19	even	6		882.2.f.g.295.1		2
28.23	odd	6		882.2.f.i.295.1		2
28.27	even	2		882.2.h.i.79.1		2
36.7	odd	6		1134.2.g.e.163.1		2
36.11	even	6		1134.2.g.c.163.1		2
36.23	even	6		378.2.e.b.37.1		2
36.31	odd	6		126.2.e.a.121.1	yes	2
63.4	even	3	inner	1008.2.t.f.193.1		2
63.32	odd	6		3024.2.t.a.1873.1		2
84.11	even	6		378.2.e.b.235.1		2
84.23	even	6		2646.2.f.d.883.1		2
84.47	odd	6		2646.2.f.a.883.1		2
84.59	odd	6		2646.2.e.g.2125.1		2
84.83	odd	2		2646.2.h.d.667.1		2
252.11	even	6		1134.2.g.c.487.1		2
252.23	even	6		2646.2.f.d.1765.1		2
252.31	even	6		882.2.h.i.67.1		2
252.47	odd	6		7938.2.a.be.1.1		1
252.59	odd	6		2646.2.h.d.361.1		2
252.67	odd	6		126.2.h.b.67.1	yes	2
252.79	odd	6		7938.2.a.m.1.1		1
252.95	even	6		378.2.h.a.361.1		2
252.103	even	6		882.2.f.g.589.1		2
252.131	odd	6		2646.2.f.a.1765.1		2
252.139	even	6		882.2.e.c.373.1		2
252.151	odd	6		1134.2.g.e.487.1		2
252.167	odd	6		2646.2.e.g.1549.1		2
252.187	even	6		7938.2.a.b.1.1		1
252.191	even	6		7938.2.a.t.1.1		1
252.247	odd	6		882.2.f.i.589.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	28.11	odd	6
126.2.e.a.121.1	yes	2	36.31	odd	6
126.2.h.b.67.1	yes	2	252.67	odd	6
126.2.h.b.79.1	yes	2	4.3	odd	2
378.2.e.b.37.1		2	36.23	even	6
378.2.e.b.235.1		2	84.11	even	6
378.2.h.a.289.1		2	12.11	even	2
378.2.h.a.361.1		2	252.95	even	6
882.2.e.c.373.1		2	252.139	even	6
882.2.e.c.655.1		2	28.3	even	6
882.2.f.g.295.1		2	28.19	even	6
882.2.f.g.589.1		2	252.103	even	6
882.2.f.i.295.1		2	28.23	odd	6
882.2.f.i.589.1		2	252.247	odd	6
882.2.h.i.67.1		2	252.31	even	6
882.2.h.i.79.1		2	28.27	even	2
1008.2.q.a.529.1		2	7.4	even	3
1008.2.q.a.625.1		2	9.4	even	3
1008.2.t.f.193.1		2	63.4	even	3	inner
1008.2.t.f.961.1		2	1.1	even	1	trivial
1134.2.g.c.163.1		2	36.11	even	6
1134.2.g.c.487.1		2	252.11	even	6
1134.2.g.e.163.1		2	36.7	odd	6
1134.2.g.e.487.1		2	252.151	odd	6
2646.2.e.g.1549.1		2	252.167	odd	6
2646.2.e.g.2125.1		2	84.59	odd	6
2646.2.f.a.883.1		2	84.47	odd	6
2646.2.f.a.1765.1		2	252.131	odd	6
2646.2.f.d.883.1		2	84.23	even	6
2646.2.f.d.1765.1		2	252.23	even	6
2646.2.h.d.361.1		2	252.59	odd	6
2646.2.h.d.667.1		2	84.83	odd	2
3024.2.q.f.2305.1		2	9.5	odd	6
3024.2.q.f.2881.1		2	21.11	odd	6
3024.2.t.a.289.1		2	3.2	odd	2
3024.2.t.a.1873.1		2	63.32	odd	6
7938.2.a.b.1.1		1	252.187	even	6
7938.2.a.m.1.1		1	252.79	odd	6
7938.2.a.t.1.1		1	252.191	even	6
7938.2.a.be.1.1		1	252.47	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +3.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.50000 + 2.59808i) q^{9} +3.00000 q^{11} +(0.500000 + 0.866025i) q^{13} +(4.50000 + 2.59808i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-3.00000 - 3.46410i) q^{21} +9.00000 q^{23} +4.00000 q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(4.00000 - 6.92820i) q^{31} +(4.50000 + 2.59808i) q^{33} +(-7.50000 - 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +1.73205i q^{39} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(4.50000 + 7.79423i) q^{45} +(5.50000 + 4.33013i) q^{49} -5.19615i q^{51} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(-1.00000 - 1.73205i) q^{61} +(-1.50000 - 7.79423i) q^{63} +(1.50000 + 2.59808i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(13.5000 + 7.79423i) q^{69} -12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(6.00000 + 3.46410i) q^{75} +(-7.50000 - 2.59808i) q^{77} +(-8.00000 - 13.8564i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-4.50000 + 2.59808i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(-0.500000 - 2.59808i) q^{91} +(12.0000 - 6.92820i) q^{93} +(-10.5000 + 18.1865i) q^{95} +(0.500000 - 0.866025i) q^{97} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + q^{13} + 9 q^{15} - 3 q^{17} - 7 q^{19} - 6 q^{21} + 18 q^{23} + 8 q^{25} - 3 q^{29} + 8 q^{31} + 9 q^{33} - 15 q^{35} + q^{37} - 3 q^{41} - q^{43}+ \cdots + 9 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 6 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + q^13 + 9 * q^15 - 3 * q^17 - 7 * q^19 - 6 * q^21 + 18 * q^23 + 8 * q^25 - 3 * q^29 + 8 * q^31 + 9 * q^33 - 15 * q^35 + q^37 - 3 * q^41 - q^43 + 9 * q^45 + 11 * q^49 - 3 * q^53 + 18 * q^55 - 21 * q^57 - 2 * q^61 - 3 * q^63 + 3 * q^65 - 4 * q^67 + 27 * q^69 - 24 * q^71 - 11 * q^73 + 12 * q^75 - 15 * q^77 - 16 * q^79 - 9 * q^81 - 9 * q^83 - 9 * q^85 - 9 * q^87 - 3 * q^89 - q^91 + 24 * q^93 - 21 * q^95 + q^97 + 9 * q^99

Introduction

L-functions

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Database

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