LMFDB - Embedded newform 1008.2.v.e.323.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 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("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.16
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11731 - 0.866958i) q^{2} +(0.496766 - 1.93732i) q^{4} +(-0.925496 - 0.925496i) q^{5} +1.00000 q^{7} +(-1.12454 - 2.59527i) q^{8} +(-1.83643 - 0.231700i) q^{10} +(1.72403 - 1.72403i) q^{11} +(0.328273 + 0.328273i) q^{13} +(1.11731 - 0.866958i) q^{14} +(-3.50645 - 1.92479i) q^{16} -2.34181i q^{17} +(-1.77976 + 1.77976i) q^{19} +(-2.25274 + 1.33323i) q^{20} +(0.431615 - 3.42094i) q^{22} -6.17143i q^{23} -3.28691i q^{25} +(0.651381 + 0.0821838i) q^{26} +(0.496766 - 1.93732i) q^{28} +(0.122671 - 0.122671i) q^{29} +1.74700i q^{31} +(-5.58651 + 0.889349i) q^{32} +(-2.03025 - 2.61653i) q^{34} +(-0.925496 - 0.925496i) q^{35} +(-1.68105 + 1.68105i) q^{37} +(-0.445568 + 3.53153i) q^{38} +(-1.36116 + 3.44266i) q^{40} -2.88812 q^{41} +(2.77330 + 2.77330i) q^{43} +(-2.48356 - 4.19644i) q^{44} +(-5.35037 - 6.89540i) q^{46} -5.92184 q^{47} +1.00000 q^{49} +(-2.84962 - 3.67251i) q^{50} +(0.799045 - 0.472895i) q^{52} +(0.973689 + 0.973689i) q^{53} -3.19117 q^{55} +(-1.12454 - 2.59527i) q^{56} +(0.0307109 - 0.243412i) q^{58} +(8.33124 - 8.33124i) q^{59} +(4.28808 + 4.28808i) q^{61} +(1.51457 + 1.95194i) q^{62} +(-5.47084 + 5.83695i) q^{64} -0.607630i q^{65} +(1.78259 - 1.78259i) q^{67} +(-4.53685 - 1.16333i) q^{68} +(-1.83643 - 0.231700i) q^{70} -8.57053i q^{71} +6.41750i q^{73} +(-0.420854 + 3.33565i) q^{74} +(2.56385 + 4.33210i) q^{76} +(1.72403 - 1.72403i) q^{77} +5.38299i q^{79} +(1.46381 + 5.02659i) q^{80} +(-3.22693 + 2.50388i) q^{82} +(3.46360 + 3.46360i) q^{83} +(-2.16734 + 2.16734i) q^{85} +(5.50297 + 0.694301i) q^{86} +(-6.41306 - 2.53559i) q^{88} +1.51391 q^{89} +(0.328273 + 0.328273i) q^{91} +(-11.9561 - 3.06576i) q^{92} +(-6.61653 + 5.13398i) q^{94} +3.29433 q^{95} +15.7177 q^{97} +(1.11731 - 0.866958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.11731	−	0.866958i	0.790058	−	0.613032i
$2$	1.11731	−	0.866958i	0.790058	−	0.613032i
$3$		0			0
$3$		0			0
$4$	0.496766	−	1.93732i	0.248383	−	0.968662i
$5$	−0.925496	−	0.925496i	−0.413894	−	0.413894i	0.469198	−	0.883093i	$-0.344543\pi$
$5$	−0.925496	−	0.925496i	−0.413894	−	0.413894i	−0.883093	+	0.469198i	$0.844543\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.12454	−	2.59527i	−0.397584	−	0.917566i
$9$		0			0
$10$	−1.83643	−	0.231700i	−0.580731	−	0.0732700i
$11$	1.72403	−	1.72403i	0.519815	−	0.519815i	−0.397701	−	0.917515i	$-0.630192\pi$
$11$	1.72403	−	1.72403i	0.519815	−	0.519815i	0.917515	+	0.397701i	$0.130192\pi$
$12$		0			0
$13$	0.328273	+	0.328273i	0.0910464	+	0.0910464i	0.751163	−	0.660117i	$-0.229493\pi$
$13$	0.328273	+	0.328273i	0.0910464	+	0.0910464i	−0.660117	+	0.751163i	$0.729493\pi$
$14$	1.11731	−	0.866958i	0.298614	−	0.231704i
$15$		0			0
$16$	−3.50645	−	1.92479i	−0.876612	−	0.481199i
$17$		−	2.34181i		−	0.567973i	−0.958828	−	0.283986i	$-0.908343\pi$
$17$		−	2.34181i		−	0.567973i	0.958828	−	0.283986i	$-0.0916570\pi$
$18$		0			0
$19$	−1.77976	+	1.77976i	−0.408306	+	0.408306i	−0.881147	−	0.472842i	$-0.843228\pi$
$19$	−1.77976	+	1.77976i	−0.408306	+	0.408306i	0.472842	+	0.881147i	$0.343228\pi$
$20$	−2.25274	+	1.33323i	−0.503728	+	0.298119i
$21$		0			0
$22$	0.431615	−	3.42094i	0.0920206	−	0.729347i
$23$		−	6.17143i		−	1.28683i	−0.765517	−	0.643416i	$-0.777517\pi$
$23$		−	6.17143i		−	1.28683i	0.765517	−	0.643416i	$-0.222483\pi$
$24$		0			0
$25$		−	3.28691i		−	0.657383i
$26$	0.651381	+	0.0821838i	0.127746	+	0.0161176i
$27$		0			0
$28$	0.496766	−	1.93732i	0.0938800	−	0.366120i
$29$	0.122671	−	0.122671i	0.0227794	−	0.0227794i	−0.695625	−	0.718405i	$-0.744873\pi$
$29$	0.122671	−	0.122671i	0.0227794	−	0.0227794i	0.718405	+	0.695625i	$0.244873\pi$
$30$		0			0
$31$			1.74700i			0.313770i	0.987617	+	0.156885i	$0.0501452\pi$
$31$			1.74700i			0.313770i	−0.987617	+	0.156885i	$0.949855\pi$
$32$	−5.58651	+	0.889349i	−0.987564	+	0.157216i
$33$		0			0
$34$	−2.03025	−	2.61653i	−0.348185	−	0.448731i
$35$	−0.925496	−	0.925496i	−0.156437	−	0.156437i
$36$		0			0
$37$	−1.68105	+	1.68105i	−0.276363	+	0.276363i	−0.831655	−	0.555292i	$-0.812606\pi$
$37$	−1.68105	+	1.68105i	−0.276363	+	0.276363i	0.555292	+	0.831655i	$0.312606\pi$
$38$	−0.445568	+	3.53153i	−0.0722807	+	0.572890i
$39$		0			0
$40$	−1.36116	+	3.44266i	−0.215218	+	0.544333i
$41$	−2.88812			−0.451048			−0.225524	−	0.974238i	$-0.572409\pi$
$41$	−2.88812			−0.451048			−0.225524	+	0.974238i	$0.572409\pi$
$42$		0			0
$43$	2.77330	+	2.77330i	0.422924	+	0.422924i	0.886209	−	0.463285i	$-0.153330\pi$
$43$	2.77330	+	2.77330i	0.422924	+	0.422924i	−0.463285	+	0.886209i	$0.653330\pi$
$44$	−2.48356	−	4.19644i	−0.374411	−	0.632638i
$45$		0			0
$46$	−5.35037	−	6.89540i	−0.788869	−	1.01667i
$47$	−5.92184			−0.863789			−0.431894	−	0.901924i	$-0.642155\pi$
$47$	−5.92184			−0.863789			−0.431894	+	0.901924i	$0.642155\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−2.84962	−	3.67251i	−0.402997	−	0.519371i
$51$		0			0
$52$	0.799045	−	0.472895i	0.110808	−	0.0655788i
$53$	0.973689	+	0.973689i	0.133746	+	0.133746i	0.770811	−	0.637064i	$-0.219851\pi$
$53$	0.973689	+	0.973689i	0.133746	+	0.133746i	−0.637064	+	0.770811i	$0.719851\pi$
$54$		0			0
$55$	−3.19117			−0.430297
$56$	−1.12454	−	2.59527i	−0.150273	−	0.346807i
$57$		0			0
$58$	0.0307109	−	0.243412i	0.00403254	−	0.0319615i
$59$	8.33124	−	8.33124i	1.08464	−	1.08464i	0.0885647	−	0.996070i	$-0.471772\pi$
$59$	8.33124	−	8.33124i	1.08464	−	1.08464i	0.996070	−	0.0885647i	$-0.0282280\pi$
$60$		0			0
$61$	4.28808	+	4.28808i	0.549033	+	0.549033i	0.926161	−	0.377128i	$-0.123088\pi$
$61$	4.28808	+	4.28808i	0.549033	+	0.549033i	−0.377128	+	0.926161i	$0.623088\pi$
$62$	1.51457	+	1.95194i	0.192351	+	0.247896i
$63$		0			0
$64$	−5.47084	+	5.83695i	−0.683854	+	0.729618i
$65$		−	0.607630i		−	0.0753672i
$66$		0			0
$67$	1.78259	−	1.78259i	0.217778	−	0.217778i	−0.589783	−	0.807561i	$-0.700787\pi$
$67$	1.78259	−	1.78259i	0.217778	−	0.217778i	0.807561	+	0.589783i	$0.200787\pi$
$68$	−4.53685	−	1.16333i	−0.550173	−	0.141075i
$69$		0			0
$70$	−1.83643	−	0.231700i	−0.219496	−	0.0276935i
$71$		−	8.57053i		−	1.01713i	−0.861022	−	0.508567i	$-0.830175\pi$
$71$		−	8.57053i		−	1.01713i	0.861022	−	0.508567i	$-0.169825\pi$
$72$		0			0
$73$			6.41750i			0.751112i	0.926800	+	0.375556i	$0.122548\pi$
$73$			6.41750i			0.751112i	−0.926800	+	0.375556i	$0.877452\pi$
$74$	−0.420854	+	3.33565i	−0.0489233	+	0.387762i
$75$		0			0
$76$	2.56385	+	4.33210i	0.294094	+	0.496927i
$77$	1.72403	−	1.72403i	0.196471	−	0.196471i
$78$		0			0
$79$			5.38299i			0.605633i	0.953049	+	0.302817i	$0.0979270\pi$
$79$			5.38299i			0.605633i	−0.953049	+	0.302817i	$0.902073\pi$
$80$	1.46381	+	5.02659i	0.163659	+	0.561990i
$81$		0			0
$82$	−3.22693	+	2.50388i	−0.356354	+	0.276507i
$83$	3.46360	+	3.46360i	0.380179	+	0.380179i	0.871167	−	0.490987i	$-0.163364\pi$
$83$	3.46360	+	3.46360i	0.380179	+	0.380179i	−0.490987	+	0.871167i	$0.663364\pi$
$84$		0			0
$85$	−2.16734	+	2.16734i	−0.235081	+	0.235081i
$86$	5.50297	+	0.694301i	0.593400	+	0.0748684i
$87$		0			0
$88$	−6.41306	−	2.53559i	−0.683634	−	0.270294i
$89$	1.51391			0.160474			0.0802368	−	0.996776i	$-0.474432\pi$
$89$	1.51391			0.160474			0.0802368	+	0.996776i	$0.474432\pi$
$90$		0			0
$91$	0.328273	+	0.328273i	0.0344123	+	0.0344123i
$92$	−11.9561	−	3.06576i	−1.24650	−	0.319627i
$93$		0			0
$94$	−6.61653	+	5.13398i	−0.682443	+	0.529530i
$95$	3.29433			0.337991
$96$		0			0
$97$	15.7177			1.59589			0.797943	−	0.602732i	$-0.205921\pi$
$97$	15.7177			1.59589			0.797943	+	0.602732i	$0.205921\pi$
$98$	1.11731	−	0.866958i	0.112865	−	0.0875760i
$99$		0			0
$100$	−6.36782	−	1.63283i	−0.636782	−	0.163283i
$101$	13.6438	+	13.6438i	1.35760	+	1.35760i	0.876861	+	0.480744i	$0.159633\pi$
$101$	13.6438	+	13.6438i	1.35760	+	1.35760i	0.480744	+	0.876861i	$0.340367\pi$
$102$		0			0
$103$	−11.9238			−1.17489			−0.587445	−	0.809264i	$-0.699866\pi$
$103$	−11.9238			−1.17489			−0.587445	+	0.809264i	$0.699866\pi$
$104$	0.482801	−	1.22111i	0.0473425	−	0.119740i
$105$		0			0
$106$	1.93206	+	0.243765i	0.187658	+	0.0236766i
$107$	13.6108	−	13.6108i	1.31580	−	1.31580i	0.398740	−	0.917064i	$-0.369447\pi$
$107$	13.6108	−	13.6108i	1.31580	−	1.31580i	0.917064	−	0.398740i	$-0.130553\pi$
$108$		0			0
$109$	4.97865	+	4.97865i	0.476868	+	0.476868i	0.904129	−	0.427260i	$-0.140521\pi$
$109$	4.97865	+	4.97865i	0.476868	+	0.476868i	−0.427260	+	0.904129i	$0.640521\pi$
$110$	−3.56552	+	2.76661i	−0.339959	+	0.263786i
$111$		0			0
$112$	−3.50645	−	1.92479i	−0.331328	−	0.181876i
$113$			0.0768901i			0.00723322i	0.999993	+	0.00361661i	$0.00115120\pi$
$113$			0.0768901i			0.00723322i	−0.999993	+	0.00361661i	$0.998849\pi$
$114$		0			0
$115$	−5.71163	+	5.71163i	−0.532612	+	0.532612i
$116$	−0.176714	−	0.298592i	−0.0164075	−	0.0277235i
$117$		0			0
$118$	2.08575	−	16.5314i	0.192008	−	1.52184i
$119$		−	2.34181i		−	0.214673i
$120$		0			0
$121$			5.05544i			0.459585i
$122$	8.50871	+	1.07353i	0.770343	+	0.0971930i
$123$		0			0
$124$	3.38450	+	0.867849i	0.303937	+	0.0779351i
$125$	−7.66951	+	7.66951i	−0.685981	+	0.685981i
$126$		0			0
$127$		−	15.0611i		−	1.33646i	−0.743956	−	0.668229i	$-0.767053\pi$
$127$		−	15.0611i		−	1.33646i	0.743956	−	0.668229i	$-0.232947\pi$
$128$	−1.05223	+	11.2647i	−0.0930051	+	0.995666i
$129$		0			0
$130$	−0.526790	−	0.678911i	−0.0462025	−	0.0595445i
$131$	−3.87027	−	3.87027i	−0.338147	−	0.338147i	0.517522	−	0.855670i	$-0.326854\pi$
$131$	−3.87027	−	3.87027i	−0.338147	−	0.338147i	−0.855670	+	0.517522i	$0.826854\pi$
$132$		0			0
$133$	−1.77976	+	1.77976i	−0.154325	+	0.154325i
$134$	0.446276	−	3.53714i	0.0385523	−	0.305562i
$135$		0			0
$136$	−6.07763	+	2.63345i	−0.521152	+	0.225817i
$137$	5.47491			0.467753			0.233877	−	0.972266i	$-0.424859\pi$
$137$	5.47491			0.467753			0.233877	+	0.972266i	$0.424859\pi$
$138$		0			0
$139$	11.1117	+	11.1117i	0.942478	+	0.942478i	0.998433	−	0.0559554i	$-0.0178205\pi$
$139$	11.1117	+	11.1117i	0.942478	+	0.942478i	−0.0559554	+	0.998433i	$0.517820\pi$
$140$	−2.25274	+	1.33323i	−0.190391	+	0.112678i
$141$		0			0
$142$	−7.43029	−	9.57595i	−0.623536	−	0.803596i
$143$	1.13190			0.0946545
$144$		0			0
$145$	−0.227063			−0.0188565
$146$	5.56371	+	7.17035i	0.460456	+	0.593422i
$147$		0			0
$148$	2.42165	+	4.09182i	0.199058	+	0.336346i
$149$	10.2234	+	10.2234i	0.837535	+	0.837535i	0.988534	−	0.150999i	$-0.0482490\pi$
$149$	10.2234	+	10.2234i	0.837535	+	0.837535i	−0.150999	+	0.988534i	$0.548249\pi$
$150$		0			0
$151$	5.98993			0.487454			0.243727	−	0.969844i	$-0.421630\pi$
$151$	5.98993			0.487454			0.243727	+	0.969844i	$0.421630\pi$
$152$	6.62037	+	2.61755i	0.536983	+	0.212312i
$153$		0			0
$154$	0.431615	−	3.42094i	0.0347805	−	0.275667i
$155$	1.61684	−	1.61684i	0.129868	−	0.129868i
$156$		0			0
$157$	9.57922	+	9.57922i	0.764505	+	0.764505i	0.977133	−	0.212628i	$-0.0682023\pi$
$157$	9.57922	+	9.57922i	0.764505	+	0.764505i	−0.212628	+	0.977133i	$0.568202\pi$
$158$	4.66683	+	6.01447i	0.371273	+	0.478486i
$159$		0			0
$160$	5.99338	+	4.34720i	0.473818	+	0.343676i
$161$		−	6.17143i		−	0.486377i
$162$		0			0
$163$	−7.81085	+	7.81085i	−0.611793	+	0.611793i	−0.943413	−	0.331620i	$-0.892405\pi$
$163$	−7.81085	+	7.81085i	−0.611793	+	0.611793i	0.331620	+	0.943413i	$0.392405\pi$
$164$	−1.43472	+	5.59522i	−0.112033	+	0.436913i
$165$		0			0
$166$	6.87271	+	0.867120i	0.533426	+	0.0673016i
$167$			5.28108i			0.408662i	0.978902	+	0.204331i	$0.0655019\pi$
$167$			5.28108i			0.408662i	−0.978902	+	0.204331i	$0.934498\pi$
$168$		0			0
$169$		−	12.7845i		−	0.983421i
$170$	−0.542598	+	4.30058i	−0.0416154	+	0.329839i
$171$		0			0
$172$	6.75045	−	3.99509i	0.514717	−	0.304623i
$173$	−11.8893	+	11.8893i	−0.903929	+	0.903929i	−0.995773	−	0.0918444i	$-0.970724\pi$
$173$	−11.8893	+	11.8893i	−0.903929	+	0.903929i	0.0918444	+	0.995773i	$0.470724\pi$
$174$		0			0
$175$		−	3.28691i		−	0.248467i
$176$	−9.36362	+	2.72681i	−0.705810	+	0.205541i
$177$		0			0
$178$	1.69150	−	1.31249i	0.126783	−	0.0983755i
$179$	−6.38837	−	6.38837i	−0.477489	−	0.477489i	0.426839	−	0.904328i	$-0.359627\pi$
$179$	−6.38837	−	6.38837i	−0.477489	−	0.477489i	−0.904328	+	0.426839i	$0.859627\pi$
$180$		0			0
$181$	5.56367	−	5.56367i	0.413545	−	0.413545i	−0.469427	−	0.882971i	$-0.655539\pi$
$181$	5.56367	−	5.56367i	0.413545	−	0.413545i	0.882971	+	0.469427i	$0.155539\pi$
$182$	0.651381	+	0.0821838i	0.0482836	+	0.00609187i
$183$		0			0
$184$	−16.0165	+	6.94000i	−1.18075	+	0.511623i
$185$	3.11161			0.228770
$186$		0			0
$187$	−4.03735	−	4.03735i	−0.295240	−	0.295240i
$188$	−2.94177	+	11.4725i	−0.214551	+	0.836719i
$189$		0			0
$190$	3.68079	−	2.85604i	0.267032	−	0.207199i
$191$	−2.43241			−0.176003			−0.0880014	−	0.996120i	$-0.528048\pi$
$191$	−2.43241			−0.176003			−0.0880014	+	0.996120i	$0.528048\pi$
$192$		0			0
$193$	24.8507			1.78879			0.894397	−	0.447273i	$-0.147605\pi$
$193$	24.8507			1.78879			0.894397	+	0.447273i	$0.147605\pi$
$194$	17.5615	−	13.6266i	1.26084	−	0.978330i
$195$		0			0
$196$	0.496766	−	1.93732i	0.0354833	−	0.138380i
$197$	−1.77151	−	1.77151i	−0.126215	−	0.126215i	0.641178	−	0.767393i	$-0.278446\pi$
$197$	−1.77151	−	1.77151i	−0.126215	−	0.126215i	−0.767393	+	0.641178i	$0.778446\pi$
$198$		0			0
$199$	−13.8970			−0.985130			−0.492565	−	0.870276i	$-0.663941\pi$
$199$	−13.8970			−0.985130			−0.492565	+	0.870276i	$0.663941\pi$
$200$	−8.53043	+	3.69626i	−0.603192	+	0.261365i
$201$		0			0
$202$	27.0729	+	3.41575i	1.90484	+	0.240331i
$203$	0.122671	−	0.122671i	0.00860980	−	0.00860980i
$204$		0			0
$205$	2.67294	+	2.67294i	0.186686	+	0.186686i
$206$	−13.3226	+	10.3375i	−0.928231	+	0.720245i
$207$		0			0
$208$	−0.519213	−	1.78293i	−0.0360009	−	0.123624i
$209$			6.13673i			0.424487i
$210$		0			0
$211$	−0.243974	+	0.243974i	−0.0167959	+	0.0167959i	−0.715455	−	0.698659i	$-0.753780\pi$
$211$	−0.243974	+	0.243974i	−0.0167959	+	0.0167959i	0.698659	+	0.715455i	$0.253780\pi$
$212$	2.37005	−	1.40265i	0.162775	−	0.0963347i
$213$		0			0
$214$	3.40749	−	27.0075i	0.232931	−	1.84619i
$215$		−	5.13335i		−	0.350091i
$216$		0			0
$217$			1.74700i			0.118594i
$218$	9.87898	+	1.24642i	0.669089	+	0.0844180i
$219$		0			0
$220$	−1.58526	+	6.18232i	−0.106878	+	0.416812i
$221$	0.768752	−	0.768752i	0.0517119	−	0.0517119i
$222$		0			0
$223$		−	7.07187i		−	0.473568i	−0.971562	−	0.236784i	$-0.923907\pi$
$223$		−	7.07187i		−	0.473568i	0.971562	−	0.236784i	$-0.0760933\pi$
$224$	−5.58651	+	0.889349i	−0.373264	+	0.0594221i
$225$		0			0
$226$	0.0666605	+	0.0859102i	0.00443419	+	0.00571466i
$227$	2.15348	+	2.15348i	0.142932	+	0.142932i	0.774952	−	0.632020i	$-0.217774\pi$
$227$	2.15348	+	2.15348i	0.142932	+	0.142932i	−0.632020	+	0.774952i	$0.717774\pi$
$228$		0			0
$229$	−14.4509	+	14.4509i	−0.954943	+	0.954943i	−0.999028	−	0.0440845i	$-0.985963\pi$
$229$	−14.4509	+	14.4509i	−0.954943	+	0.954943i	0.0440845	+	0.999028i	$0.485963\pi$
$230$	−1.42992	+	11.3334i	−0.0942862	+	0.747303i
$231$		0			0
$232$	−0.456311	−	0.180416i	−0.0299583	−	0.0118449i
$233$	−17.7969			−1.16591			−0.582955	−	0.812504i	$-0.698104\pi$
$233$	−17.7969			−1.16591			−0.582955	+	0.812504i	$0.698104\pi$
$234$		0			0
$235$	5.48063	+	5.48063i	0.357517	+	0.357517i
$236$	−12.0016	−	20.2790i	−0.781239	−	1.32005i
$237$		0			0
$238$	−2.03025	−	2.61653i	−0.131602	−	0.169604i
$239$	−9.62147			−0.622361			−0.311180	−	0.950351i	$-0.600724\pi$
$239$	−9.62147			−0.622361			−0.311180	+	0.950351i	$0.600724\pi$
$240$		0			0
$241$	27.3786			1.76361			0.881805	−	0.471614i	$-0.156329\pi$
$241$	27.3786			1.76361			0.881805	+	0.471614i	$0.156329\pi$
$242$	4.38286	+	5.64850i	0.281741	+	0.363099i
$243$		0			0
$244$	10.4376	−	6.17723i	0.668198	−	0.395457i
$245$	−0.925496	−	0.925496i	−0.0591278	−	0.0591278i
$246$		0			0
$247$	−1.16849			−0.0743495
$248$	4.53392	−	1.96456i	0.287904	−	0.124750i
$249$		0			0
$250$	−1.92008	+	15.2184i	−0.121436	+	0.962494i
$251$	−6.56293	+	6.56293i	−0.414249	+	0.414249i	−0.883216	−	0.468967i	$-0.844626\pi$
$251$	−6.56293	+	6.56293i	−0.414249	+	0.414249i	0.468967	+	0.883216i	$0.344626\pi$
$252$		0			0
$253$	−10.6397	−	10.6397i	−0.668914	−	0.668914i
$254$	−13.0574	−	16.8279i	−0.819292	−	1.05588i
$255$		0			0
$256$	8.59033	+	13.4984i	0.536896	+	0.843649i
$257$			13.6808i			0.853383i	0.904397	+	0.426691i	$0.140321\pi$
$257$			13.6808i			0.853383i	−0.904397	+	0.426691i	$0.859679\pi$
$258$		0			0
$259$	−1.68105	+	1.68105i	−0.104455	+	0.104455i
$260$	−1.17718	−	0.301850i	−0.0730053	−	0.0187199i
$261$		0			0
$262$	−7.67966	−	0.968932i	−0.474451	−	0.0598608i
$263$			26.5064i			1.63445i	0.576317	+	0.817226i	$0.304489\pi$
$263$			26.5064i			1.63445i	−0.576317	+	0.817226i	$0.695511\pi$
$264$		0			0
$265$		−	1.80229i		−	0.110714i
$266$	−0.445568	+	3.53153i	−0.0273195	+	0.216532i
$267$		0			0
$268$	−2.56792	−	4.33899i	−0.156861	−	0.265046i
$269$	−11.7053	+	11.7053i	−0.713684	+	0.713684i	−0.967304	−	0.253620i	$-0.918379\pi$
$269$	−11.7053	+	11.7053i	−0.713684	+	0.713684i	0.253620	+	0.967304i	$0.418379\pi$
$270$		0			0
$271$		−	26.7904i		−	1.62740i	−0.581286	−	0.813700i	$-0.697450\pi$
$271$		−	26.7904i		−	1.62740i	0.581286	−	0.813700i	$-0.302550\pi$
$272$	−4.50751	+	8.21143i	−0.273308	+	0.497891i
$273$		0			0
$274$	6.11718	−	4.74652i	0.369552	−	0.286748i
$275$	−5.66674	−	5.66674i	−0.341717	−	0.341717i
$276$		0			0
$277$	−0.376534	+	0.376534i	−0.0226237	+	0.0226237i	−0.718328	−	0.695704i	$-0.755092\pi$
$277$	−0.376534	+	0.376534i	−0.0226237	+	0.0226237i	0.695704	+	0.718328i	$0.255092\pi$
$278$	22.0485	+	2.78183i	1.32238	+	0.166843i
$279$		0			0
$280$	−1.36116	+	3.44266i	−0.0813446	+	0.205739i
$281$	−10.8174			−0.645314			−0.322657	−	0.946516i	$-0.604576\pi$
$281$	−10.8174			−0.645314			−0.322657	+	0.946516i	$0.604576\pi$
$282$		0			0
$283$	0.954650	+	0.954650i	0.0567481	+	0.0567481i	0.734911	−	0.678163i	$-0.237224\pi$
$283$	0.954650	+	0.954650i	0.0567481	+	0.0567481i	−0.678163	+	0.734911i	$0.737224\pi$
$284$	−16.6039	−	4.25755i	−0.985260	−	0.252639i
$285$		0			0
$286$	1.26469	−	0.981313i	0.0747826	−	0.0580263i
$287$	−2.88812			−0.170480
$288$		0			0
$289$	11.5159			0.677407
$290$	−0.253699	+	0.196854i	−0.0148977	+	0.0115597i
$291$		0			0
$292$	12.4328	+	3.18800i	0.727574	+	0.186564i
$293$	14.4106	+	14.4106i	0.841877	+	0.841877i	0.989103	−	0.147226i	$-0.0470346\pi$
$293$	14.4106	+	14.4106i	0.841877	+	0.841877i	−0.147226	+	0.989103i	$0.547035\pi$
$294$		0			0
$295$	−15.4211			−0.897849
$296$	6.25317	+	2.47237i	0.363458	+	0.143704i
$297$		0			0
$298$	20.2860	+	2.55946i	1.17514	+	0.148265i
$299$	2.02591	−	2.02591i	0.117161	−	0.117161i
$300$		0			0
$301$	2.77330	+	2.77330i	0.159850	+	0.159850i
$302$	6.69261	−	5.19302i	0.385117	−	0.298825i
$303$		0			0
$304$	9.66632	−	2.81497i	0.554402	−	0.161449i
$305$		−	7.93721i		−	0.454483i
$306$		0			0
$307$	15.9801	−	15.9801i	0.912034	−	0.912034i	−0.0843977	−	0.996432i	$-0.526897\pi$
$307$	15.9801	−	15.9801i	0.912034	−	0.912034i	0.996432	+	0.0843977i	$0.0268966\pi$
$308$	−2.48356	−	4.19644i	−0.141514	−	0.239115i
$309$		0			0
$310$	0.404779	−	3.20824i	0.0229899	−	0.182216i
$311$		−	7.61653i		−	0.431894i	−0.976405	−	0.215947i	$-0.930716\pi$
$311$		−	7.61653i		−	0.431894i	0.976405	−	0.215947i	$-0.0692838\pi$
$312$		0			0
$313$		−	30.7549i		−	1.73837i	−0.494490	−	0.869184i	$-0.664645\pi$
$313$		−	30.7549i		−	1.73837i	0.494490	−	0.869184i	$-0.335355\pi$
$314$	19.0078	+	2.39818i	1.07267	+	0.135337i
$315$		0			0
$316$	10.4286	+	2.67409i	0.586654	+	0.150429i
$317$	4.52751	−	4.52751i	0.254291	−	0.254291i	−0.568437	−	0.822727i	$-0.692452\pi$
$317$	4.52751	−	4.52751i	0.254291	−	0.254291i	0.822727	+	0.568437i	$0.192452\pi$
$318$		0			0
$319$		−	0.422976i		−	0.0236821i
$320$	10.4653	−	0.338835i	0.585028	−	0.0189415i
$321$		0			0
$322$	−5.35037	−	6.89540i	−0.298165	−	0.384266i
$323$	4.16787	+	4.16787i	0.231906	+	0.231906i
$324$		0			0
$325$	1.07900	−	1.07900i	0.0598524	−	0.0598524i
$326$	−1.95546	+	15.4988i	−0.108303	+	0.858400i
$327$		0			0
$328$	3.24780	+	7.49544i	0.179329	+	0.413867i
$329$	−5.92184			−0.326481
$330$		0			0
$331$	11.4312	+	11.4312i	0.628318	+	0.628318i	0.947645	−	0.319326i	$-0.103457\pi$
$331$	11.4312	+	11.4312i	0.628318	+	0.628318i	−0.319326	+	0.947645i	$0.603457\pi$
$332$	8.43071	−	4.98951i	0.462695	−	0.273835i
$333$		0			0
$334$	4.57847	+	5.90060i	0.250523	+	0.322867i
$335$	−3.29956			−0.180274
$336$		0			0
$337$	−10.7569			−0.585964			−0.292982	−	0.956118i	$-0.594648\pi$
$337$	−10.7569			−0.585964			−0.292982	+	0.956118i	$0.594648\pi$
$338$	−11.0836	−	14.2842i	−0.602869	−	0.776960i
$339$		0			0
$340$	3.12217	+	5.27549i	0.169324	+	0.286104i
$341$	3.01187	+	3.01187i	0.163102	+	0.163102i
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.07878	−	10.3161i	0.219913	−	0.556208i
$345$		0			0
$346$	−2.97652	+	23.5916i	−0.160019	+	1.26829i
$347$	16.3589	−	16.3589i	0.878193	−	0.878193i	−0.115154	−	0.993348i	$-0.536736\pi$
$347$	16.3589	−	16.3589i	0.878193	−	0.878193i	0.993348	+	0.115154i	$0.0367362\pi$
$348$		0			0
$349$	−25.8389	−	25.8389i	−1.38312	−	1.38312i	−0.839013	−	0.544112i	$-0.816867\pi$
$349$	−25.8389	−	25.8389i	−1.38312	−	1.38312i	−0.544112	−	0.839013i	$-0.683133\pi$
$350$	−2.84962	−	3.67251i	−0.152318	−	0.196304i
$351$		0			0
$352$	−8.09804	+	11.1646i	−0.431627	+	0.595074i
$353$			24.5770i			1.30810i	0.756451	+	0.654051i	$0.226932\pi$
$353$			24.5770i			1.30810i	−0.756451	+	0.654051i	$0.773068\pi$
$354$		0			0
$355$	−7.93199	+	7.93199i	−0.420986	+	0.420986i
$356$	0.752057	−	2.93292i	0.0398590	−	0.155445i
$357$		0			0
$358$	−12.6762	−	1.59934i	−0.669960	−	0.0845279i
$359$		−	17.5485i		−	0.926176i	−0.886312	−	0.463088i	$-0.846741\pi$
$359$		−	17.5485i		−	0.926176i	0.886312	−	0.463088i	$-0.153259\pi$
$360$		0			0
$361$			12.6649i			0.666573i
$362$	1.39288	−	11.0398i	0.0732081	−	0.580240i
$363$		0			0
$364$	0.799045	−	0.472895i	0.0418813	−	0.0247865i
$365$	5.93937	−	5.93937i	0.310881	−	0.310881i
$366$		0			0
$367$		−	15.7849i		−	0.823964i	−0.911192	−	0.411982i	$-0.864837\pi$
$367$		−	15.7849i		−	0.823964i	0.911192	−	0.411982i	$-0.135163\pi$
$368$	−11.8787	+	21.6398i	−0.619222	+	1.12805i
$369$		0			0
$370$	3.47663	−	2.69763i	0.180741	−	0.140243i
$371$	0.973689	+	0.973689i	0.0505514	+	0.0505514i
$372$		0			0
$373$	−11.5837	+	11.5837i	−0.599781	+	0.599781i	−0.940254	−	0.340473i	$-0.889413\pi$
$373$	−11.5837	+	11.5837i	−0.599781	+	0.599781i	0.340473	+	0.940254i	$0.389413\pi$
$374$	−8.01119	−	1.01076i	−0.414249	−	0.0522652i
$375$		0			0
$376$	6.65932	+	15.3688i	0.343428	+	0.792583i
$377$	0.0805389			0.00414796
$378$		0			0
$379$	−1.84371	−	1.84371i	−0.0947049	−	0.0947049i	0.658167	−	0.752872i	$-0.271332\pi$
$379$	−1.84371	−	1.84371i	−0.0947049	−	0.0947049i	−0.752872	+	0.658167i	$0.771332\pi$
$380$	1.63651	−	6.38218i	0.0839513	−	0.327399i
$381$		0			0
$382$	−2.71775	+	2.10880i	−0.139052	+	0.107895i
$383$	−4.04073			−0.206472			−0.103236	−	0.994657i	$-0.532920\pi$
$383$	−4.04073			−0.206472			−0.103236	+	0.994657i	$0.532920\pi$
$384$		0			0
$385$	−3.19117			−0.162637
$386$	27.7660	−	21.5445i	1.41325	−	1.09659i
$387$		0			0
$388$	7.80801	−	30.4502i	0.396391	−	1.54587i
$389$	−2.92444	−	2.92444i	−0.148275	−	0.148275i	0.629072	−	0.777347i	$-0.283435\pi$
$389$	−2.92444	−	2.92444i	−0.148275	−	0.148275i	−0.777347	+	0.629072i	$0.783435\pi$
$390$		0			0
$391$	−14.4523			−0.730885
$392$	−1.12454	−	2.59527i	−0.0567977	−	0.131081i
$393$		0			0
$394$	−3.51516	−	0.443502i	−0.177091	−	0.0223433i
$395$	4.98193	−	4.98193i	0.250668	−	0.250668i
$396$		0			0
$397$	−21.9555	−	21.9555i	−1.10191	−	1.10191i	−0.994180	−	0.107735i	$-0.965640\pi$
$397$	−21.9555	−	21.9555i	−1.10191	−	1.10191i	−0.107735	−	0.994180i	$-0.534360\pi$
$398$	−15.5272	+	12.0481i	−0.778310	+	0.603916i
$399$		0			0
$400$	−6.32664	+	11.5254i	−0.316332	+	0.576269i
$401$			3.18398i			0.159000i	0.996835	+	0.0795001i	$0.0253324\pi$
$401$			3.18398i			0.159000i	−0.996835	+	0.0795001i	$0.974668\pi$
$402$		0			0
$403$	−0.573491	+	0.573491i	−0.0285676	+	0.0285676i
$404$	33.2101	−	19.6546i	1.65227	−	0.977854i
$405$		0			0
$406$	0.0307109	−	0.243412i	0.00152416	−	0.0120803i
$407$			5.79636i			0.287315i
$408$		0			0
$409$			15.1001i			0.746650i	0.927701	+	0.373325i	$0.121782\pi$
$409$			15.1001i			0.746650i	−0.927701	+	0.373325i	$0.878218\pi$
$410$	5.30384	+	0.669177i	0.261938	+	0.0330483i
$411$		0			0
$412$	−5.92336	+	23.1003i	−0.291823	+	1.13807i
$413$	8.33124	−	8.33124i	0.409954	−	0.409954i
$414$		0			0
$415$		−	6.41109i		−	0.314708i
$416$	−2.12585	−	1.54195i	−0.104228	−	0.0756002i
$417$		0			0
$418$	5.32029	+	6.85664i	0.260224	+	0.335369i
$419$	2.19389	+	2.19389i	0.107178	+	0.107178i	0.758662	−	0.651484i	$-0.225853\pi$
$419$	2.19389	+	2.19389i	0.107178	+	0.107178i	−0.651484	+	0.758662i	$0.725853\pi$
$420$		0			0
$421$	−16.8539	+	16.8539i	−0.821410	+	0.821410i	−0.986310	−	0.164900i	$-0.947270\pi$
$421$	−16.8539	+	16.8539i	−0.821410	+	0.821410i	0.164900	+	0.986310i	$0.447270\pi$
$422$	−0.0610794	+	0.484110i	−0.00297330	+	0.0235661i
$423$		0			0
$424$	1.43204	−	3.62193i	0.0695458	−	0.175897i
$425$	−7.69733			−0.373376
$426$		0			0
$427$	4.28808	+	4.28808i	0.207515	+	0.207515i
$428$	−19.6071	−	33.1299i	−0.947746	−	1.60139i
$429$		0			0
$430$	−4.45040	−	5.73555i	−0.214617	−	0.276593i
$431$	−19.9661			−0.961735			−0.480868	−	0.876793i	$-0.659678\pi$
$431$	−19.9661			−0.961735			−0.480868	+	0.876793i	$0.659678\pi$
$432$		0			0
$433$	−3.83212			−0.184160			−0.0920800	−	0.995752i	$-0.529352\pi$
$433$	−3.83212			−0.184160			−0.0920800	+	0.995752i	$0.529352\pi$
$434$	1.51457	+	1.95194i	0.0727018	+	0.0936960i
$435$		0			0
$436$	12.1185	−	7.17203i	0.580370	−	0.343478i
$437$	10.9837	+	10.9837i	0.525421	+	0.525421i
$438$		0			0
$439$	−23.0120			−1.09830			−0.549151	−	0.835723i	$-0.685049\pi$
$439$	−23.0120			−1.09830			−0.549151	+	0.835723i	$0.685049\pi$
$440$	3.58858	+	8.28193i	0.171079	+	0.394826i
$441$		0			0
$442$	0.192459	−	1.52541i	0.00915434	−	0.0725564i
$443$	13.6982	−	13.6982i	0.650821	−	0.650821i	−0.302370	−	0.953191i	$-0.597778\pi$
$443$	13.6982	−	13.6982i	0.650821	−	0.650821i	0.953191	+	0.302370i	$0.0977778\pi$
$444$		0			0
$445$	−1.40111	−	1.40111i	−0.0664191	−	0.0664191i
$446$	−6.13102	−	7.90148i	−0.290312	−	0.374146i
$447$		0			0
$448$	−5.47084	+	5.83695i	−0.258473	+	0.275770i
$449$		−	27.3194i		−	1.28928i	−0.764486	−	0.644640i	$-0.777007\pi$
$449$		−	27.3194i		−	1.28928i	0.764486	−	0.644640i	$-0.222993\pi$
$450$		0			0
$451$	−4.97920	+	4.97920i	−0.234462	+	0.234462i
$452$	0.148961	+	0.0381964i	0.00700654	+	0.00179661i
$453$		0			0
$454$	4.27309	+	0.539129i	0.200546	+	0.0253026i
$455$		−	0.607630i		−	0.0284861i
$456$		0			0
$457$		−	30.4516i		−	1.42447i	−0.701942	−	0.712234i	$-0.747684\pi$
$457$		−	30.4516i		−	1.42447i	0.701942	−	0.712234i	$-0.252316\pi$
$458$	−3.61782	+	28.6745i	−0.169050	+	1.33987i
$459$		0			0
$460$	8.22793	+	13.9026i	0.383629	+	0.648213i
$461$	−17.8016	+	17.8016i	−0.829101	+	0.829101i	−0.987392	−	0.158291i	$-0.949402\pi$
$461$	−17.8016	+	17.8016i	−0.829101	+	0.829101i	0.158291	+	0.987392i	$0.449402\pi$
$462$		0			0
$463$		−	8.43314i		−	0.391921i	−0.980612	−	0.195961i	$-0.937218\pi$
$463$		−	8.43314i		−	0.391921i	0.980612	−	0.195961i	$-0.0627825\pi$
$464$	−0.666255	+	0.194022i	−0.0309301	+	0.00900726i
$465$		0			0
$466$	−19.8846	+	15.4291i	−0.921137	+	0.714741i
$467$	3.17711	+	3.17711i	0.147019	+	0.147019i	0.776785	−	0.629766i	$-0.216849\pi$
$467$	3.17711	+	3.17711i	0.147019	+	0.147019i	−0.629766	+	0.776785i	$0.716849\pi$
$468$		0			0
$469$	1.78259	−	1.78259i	0.0823124	−	0.0823124i
$470$	10.8751	+	1.37209i	0.501629	+	0.0632898i
$471$		0			0
$472$	−30.9906	−	12.2530i	−1.42646	−	0.563991i
$473$	9.56249			0.439684
$474$		0			0
$475$	5.84993	+	5.84993i	0.268413	+	0.268413i
$476$	−4.53685	−	1.16333i	−0.207946	−	0.0533213i
$477$		0			0
$478$	−10.7502	+	8.34141i	−0.491701	+	0.381527i
$479$	0.550076			0.0251336			0.0125668	−	0.999921i	$-0.496000\pi$
$479$	0.550076			0.0251336			0.0125668	+	0.999921i	$0.496000\pi$
$480$		0			0
$481$	−1.10368			−0.0503237
$482$	30.5904	−	23.7361i	1.39335	−	1.08115i
$483$		0			0
$484$	9.79402	+	2.51137i	0.445183	+	0.114153i
$485$	−14.5466	−	14.5466i	−0.660528	−	0.660528i
$486$		0			0
$487$	18.1678			0.823262			0.411631	−	0.911351i	$-0.364959\pi$
$487$	18.1678			0.823262			0.411631	+	0.911351i	$0.364959\pi$
$488$	6.30662	−	15.9508i	0.285487	−	0.722060i
$489$		0			0
$490$	−1.83643	−	0.231700i	−0.0829616	−	0.0104671i
$491$	−12.4565	+	12.4565i	−0.562156	+	0.562156i	−0.929919	−	0.367764i	$-0.880124\pi$
$491$	−12.4565	+	12.4565i	−0.562156	+	0.562156i	0.367764	+	0.929919i	$0.380124\pi$
$492$		0			0
$493$	−0.287272	−	0.287272i	−0.0129381	−	0.0129381i
$494$	−1.30557	+	1.01304i	−0.0587405	+	0.0455787i
$495$		0			0
$496$	3.36261	−	6.12575i	0.150986	−	0.275054i
$497$		−	8.57053i		−	0.384441i
$498$		0			0
$499$	−23.1835	+	23.1835i	−1.03784	+	1.03784i	−0.0385798	+	0.999256i	$0.512283\pi$
$499$	−23.1835	+	23.1835i	−1.03784	+	1.03784i	−0.999256	+	0.0385798i	$0.987717\pi$
$500$	11.0484	+	18.6683i	0.494098	+	0.834870i
$501$		0			0
$502$	−1.64305	+	13.0226i	−0.0733327	+	0.581228i
$503$			39.4375i			1.75843i	0.476426	+	0.879215i	$0.341932\pi$
$503$			39.4375i			1.75843i	−0.476426	+	0.879215i	$0.658068\pi$
$504$		0			0
$505$		−	25.2545i		−	1.12381i
$506$	−21.1121	−	2.66368i	−0.938547	−	0.118415i
$507$		0			0
$508$	−29.1783	−	7.48186i	−1.29458	−	0.331954i
$509$	1.26193	−	1.26193i	0.0559340	−	0.0559340i	−0.678587	−	0.734520i	$-0.737407\pi$
$509$	1.26193	−	1.26193i	0.0559340	−	0.0559340i	0.734520	+	0.678587i	$0.237407\pi$
$510$		0			0
$511$			6.41750i			0.283894i
$512$	21.3006	+	7.63443i	0.941362	+	0.337397i
$513$		0			0
$514$	11.8607	+	15.2857i	0.523151	+	0.674222i
$515$	11.0355	+	11.0355i	0.486280	+	0.486280i
$516$		0			0
$517$	−10.2094	+	10.2094i	−0.449010	+	0.449010i
$518$	−0.420854	+	3.33565i	−0.0184913	+	0.146560i
$519$		0			0
$520$	−1.57696	+	0.683302i	−0.0691544	+	0.0299648i
$521$	−27.2672			−1.19460			−0.597300	−	0.802018i	$-0.703760\pi$
$521$	−27.2672			−1.19460			−0.597300	+	0.802018i	$0.703760\pi$
$522$		0			0
$523$	−31.1608	−	31.1608i	−1.36257	−	1.36257i	−0.870633	−	0.491933i	$-0.836291\pi$
$523$	−31.1608	−	31.1608i	−1.36257	−	1.36257i	−0.491933	−	0.870633i	$-0.663709\pi$
$524$	−9.42059	+	5.57535i	−0.411541	+	0.243560i
$525$		0			0
$526$	22.9799	+	29.6158i	1.00197	+	1.29131i
$527$	4.09113			0.178213
$528$		0			0
$529$	−15.0865			−0.655936
$530$	−1.56251	−	2.01372i	−0.0678711	−	0.0874703i
$531$		0			0
$532$	2.56385	+	4.33210i	0.111157	+	0.187821i
$533$	−0.948090	−	0.948090i	−0.0410663	−	0.0410663i
$534$		0			0
$535$	−25.1935			−1.08921
$536$	−6.63089	−	2.62171i	−0.286411	−	0.113241i
$537$		0			0
$538$	−2.93045	+	23.2265i	−0.126341	+	1.00136i
$539$	1.72403	−	1.72403i	0.0742592	−	0.0742592i
$540$		0			0
$541$	12.9117	+	12.9117i	0.555119	+	0.555119i	0.927914	−	0.372795i	$-0.121600\pi$
$541$	12.9117	+	12.9117i	0.555119	+	0.555119i	−0.372795	+	0.927914i	$0.621600\pi$
$542$	−23.2261	−	29.9332i	−0.997648	−	1.28574i
$543$		0			0
$544$	2.08269	+	13.0825i	0.0892945	+	0.560909i
$545$		−	9.21544i		−	0.394746i
$546$		0			0
$547$	−17.6998	+	17.6998i	−0.756790	+	0.756790i	−0.975737	−	0.218947i	$-0.929738\pi$
$547$	−17.6998	+	17.6998i	−0.756790	+	0.756790i	0.218947	+	0.975737i	$0.429738\pi$
$548$	2.71975	−	10.6067i	0.116182	−	0.453095i
$549$		0			0
$550$	−11.2443	−	1.41868i	−0.479460	−	0.0604928i
$551$			0.436650i			0.0186019i
$552$		0			0
$553$			5.38299i			0.228908i
$554$	−0.0942661	+	0.747144i	−0.00400498	+	0.0317431i
$555$		0			0
$556$	27.0468	−	16.0070i	1.14704	−	0.678847i
$557$	−3.90087	+	3.90087i	−0.165285	+	0.165285i	−0.784903	−	0.619618i	$-0.787287\pi$
$557$	−3.90087	+	3.90087i	−0.165285	+	0.165285i	0.619618	+	0.784903i	$0.287287\pi$
$558$		0			0
$559$			1.82079i			0.0770114i
$560$	1.46381	+	5.02659i	0.0618573	+	0.212412i
$561$		0			0
$562$	−12.0864	+	9.37827i	−0.509836	+	0.395598i
$563$	−27.4905	−	27.4905i	−1.15859	−	1.15859i	−0.984780	−	0.173807i	$-0.944393\pi$
$563$	−27.4905	−	27.4905i	−1.15859	−	1.15859i	−0.173807	−	0.984780i	$-0.555607\pi$
$564$		0			0
$565$	0.0711615	−	0.0711615i	0.00299379	−	0.00299379i
$566$	1.89428	+	0.238999i	0.0796226	+	0.0100459i
$567$		0			0
$568$	−22.2428	+	9.63787i	−0.933288	+	0.404396i
$569$	19.2030			0.805031			0.402516	−	0.915413i	$-0.368136\pi$
$569$	19.2030			0.805031			0.402516	+	0.915413i	$0.368136\pi$
$570$		0			0
$571$	23.2363	+	23.2363i	0.972408	+	0.972408i	0.999629	−	0.0272217i	$-0.00866600\pi$
$571$	23.2363	+	23.2363i	0.972408	+	0.972408i	−0.0272217	+	0.999629i	$0.508666\pi$
$572$	0.562292	−	2.19286i	0.0235106	−	0.0916882i
$573$		0			0
$574$	−3.22693	+	2.50388i	−0.134689	+	0.104510i
$575$	−20.2850			−0.845941
$576$		0			0
$577$	25.0676			1.04358			0.521789	−	0.853074i	$-0.325265\pi$
$577$	25.0676			1.04358			0.521789	+	0.853074i	$0.325265\pi$
$578$	12.8669	−	9.98382i	0.535191	−	0.415272i
$579$		0			0
$580$	−0.112797	+	0.439894i	−0.00468364	+	0.0182656i
$581$	3.46360	+	3.46360i	0.143694	+	0.143694i
$582$		0			0
$583$	3.35734			0.139047
$584$	16.6551	−	7.21672i	0.689195	−	0.298630i
$585$		0			0
$586$	28.5945	+	3.60773i	1.18123	+	0.149034i
$587$	−6.53626	+	6.53626i	−0.269780	+	0.269780i	−0.829012	−	0.559231i	$-0.811096\pi$
$587$	−6.53626	+	6.53626i	−0.269780	+	0.269780i	0.559231	+	0.829012i	$0.311096\pi$
$588$		0			0
$589$	−3.10924	−	3.10924i	−0.128114	−	0.128114i
$590$	−17.2301	+	13.3694i	−0.709353	+	0.550410i
$591$		0			0
$592$	9.13018	−	2.65883i	0.375248	−	0.109277i
$593$		−	15.1162i		−	0.620749i	−0.950614	−	0.310375i	$-0.899545\pi$
$593$		−	15.1162i		−	0.620749i	0.950614	−	0.310375i	$-0.100455\pi$
$594$		0			0
$595$	−2.16734	+	2.16734i	−0.0888521	+	0.0888521i
$596$	24.8847	−	14.7274i	1.01932	−	0.603259i
$597$		0			0
$598$	0.507191	−	4.01995i	0.0207406	−	0.164388i
$599$			29.1264i			1.19007i	0.803700	+	0.595035i	$0.202862\pi$
$599$			29.1264i			1.19007i	−0.803700	+	0.595035i	$0.797138\pi$
$600$		0			0
$601$			14.2202i			0.580053i	0.957019	+	0.290026i	$0.0936641\pi$
$601$			14.2202i			0.580053i	−0.957019	+	0.290026i	$0.906336\pi$
$602$	5.50297	+	0.694301i	0.224284	+	0.0282976i
$603$		0			0
$604$	2.97560	−	11.6044i	0.121075	−	0.472178i
$605$	4.67879	−	4.67879i	0.190220	−	0.190220i
$606$		0			0
$607$		−	26.8584i		−	1.09015i	−0.838387	−	0.545075i	$-0.816501\pi$
$607$		−	26.8584i		−	1.09015i	0.838387	−	0.545075i	$-0.183499\pi$
$608$	8.35983	−	11.5255i	0.339036	−	0.467420i
$609$		0			0
$610$	−6.88123	−	8.86833i	−0.278613	−	0.359068i
$611$	−1.94398	−	1.94398i	−0.0786448	−	0.0786448i
$612$		0			0
$613$	−28.2483	+	28.2483i	−1.14094	+	1.14094i	−0.152659	+	0.988279i	$0.548784\pi$
$613$	−28.2483	+	28.2483i	−1.14094	+	1.14094i	−0.988279	+	0.152659i	$0.951216\pi$
$614$	4.00066	−	31.7089i	0.161454	−	1.27967i
$615$		0			0
$616$	−6.41306	−	2.53559i	−0.258389	−	0.102162i
$617$	−31.4617			−1.26660			−0.633300	−	0.773906i	$-0.718300\pi$
$617$	−31.4617			−1.26660			−0.633300	+	0.773906i	$0.718300\pi$
$618$		0			0
$619$	13.3846	+	13.3846i	0.537973	+	0.537973i	0.922933	−	0.384961i	$-0.125785\pi$
$619$	13.3846	+	13.3846i	0.537973	+	0.537973i	−0.384961	+	0.922933i	$0.625785\pi$
$620$	−2.32915	−	3.93553i	−0.0935408	−	0.158055i
$621$		0			0
$622$	−6.60322	−	8.51003i	−0.264765	−	0.341221i
$623$	1.51391			0.0606533
$624$		0			0
$625$	−2.23838			−0.0895353
$626$	−26.6632	−	34.3627i	−1.06567	−	1.37341i
$627$		0			0
$628$	23.3167	−	13.7994i	0.930437	−	0.550657i
$629$	3.93670	+	3.93670i	0.156966	+	0.156966i
$630$		0			0
$631$	15.5279			0.618154			0.309077	−	0.951037i	$-0.399980\pi$
$631$	15.5279			0.618154			0.309077	+	0.951037i	$0.399980\pi$
$632$	13.9703	−	6.05337i	0.555709	−	0.240790i
$633$		0			0
$634$	1.13347	−	8.98381i	0.0450160	−	0.356793i
$635$	−13.9390	+	13.9390i	−0.553152	+	0.553152i
$636$		0			0
$637$	0.328273	+	0.328273i	0.0130066	+	0.0130066i
$638$	−0.366703	−	0.472596i	−0.0145179	−	0.0187103i
$639$		0			0
$640$	11.3992	−	9.45157i	0.450595	−	0.373606i
$641$		−	33.1261i		−	1.30840i	−0.756320	−	0.654201i	$-0.773005\pi$
$641$		−	33.1261i		−	1.30840i	0.756320	−	0.654201i	$-0.226995\pi$
$642$		0			0
$643$	28.5683	−	28.5683i	1.12662	−	1.12662i	0.135902	−	0.990722i	$-0.456607\pi$
$643$	28.5683	−	28.5683i	1.12662	−	1.12662i	0.990722	−	0.135902i	$-0.0433933\pi$
$644$	−11.9561	−	3.06576i	−0.471135	−	0.120808i
$645$		0			0
$646$	8.27018	+	1.04344i	0.325386	+	0.0410534i
$647$		−	48.7052i		−	1.91480i	−0.288765	−	0.957400i	$-0.593245\pi$
$647$		−	48.7052i		−	1.91480i	0.288765	−	0.957400i	$-0.406755\pi$
$648$		0			0
$649$		−	28.7266i		−	1.12762i
$650$	0.270131	−	2.14103i	0.0105954	−	0.0839783i
$651$		0			0
$652$	11.2520	+	19.0123i	0.440661	+	0.744579i
$653$	−2.67453	+	2.67453i	−0.104662	+	0.104662i	−0.757499	−	0.652836i	$-0.773579\pi$
$653$	−2.67453	+	2.67453i	−0.104662	+	0.104662i	0.652836	+	0.757499i	$0.273579\pi$
$654$		0			0
$655$			7.16384i			0.279915i
$656$	10.1270	+	5.55904i	0.395394	+	0.217044i
$657$		0			0
$658$	−6.61653	+	5.13398i	−0.257939	+	0.200144i
$659$	20.0589	+	20.0589i	0.781384	+	0.781384i	0.980064	−	0.198680i	$-0.0636655\pi$
$659$	20.0589	+	20.0589i	0.781384	+	0.781384i	−0.198680	+	0.980064i	$0.563666\pi$
$660$		0			0
$661$	3.44403	−	3.44403i	0.133957	−	0.133957i	−0.636949	−	0.770906i	$-0.719804\pi$
$661$	3.44403	−	3.44403i	0.133957	−	0.133957i	0.770906	+	0.636949i	$0.219804\pi$
$662$	22.6827	+	2.86184i	0.881587	+	0.111229i
$663$		0			0
$664$	5.09402	−	12.8839i	0.197687	−	0.499993i
$665$	3.29433			0.127749
$666$		0			0
$667$	−0.757054	−	0.757054i	−0.0293132	−	0.0293132i
$668$	10.2312	+	2.62346i	0.395855	+	0.101505i
$669$		0			0
$670$	−3.68663	+	2.86058i	−0.142427	+	0.110514i
$671$	14.7856			0.570791
$672$		0			0
$673$	−32.1701			−1.24007			−0.620033	−	0.784576i	$-0.712881\pi$
$673$	−32.1701			−1.24007			−0.620033	+	0.784576i	$0.712881\pi$
$674$	−12.0188	+	9.32576i	−0.462946	+	0.359215i
$675$		0			0
$676$	−24.7677	−	6.35090i	−0.952602	−	0.244265i
$677$	−3.59090	−	3.59090i	−0.138009	−	0.138009i	0.634727	−	0.772736i	$-0.281113\pi$
$677$	−3.59090	−	3.59090i	−0.138009	−	0.138009i	−0.772736	+	0.634727i	$0.781113\pi$
$678$		0			0
$679$	15.7177			0.603188
$680$	8.06207	+	3.18757i	0.309166	+	0.122238i
$681$		0			0
$682$	5.97637	+	0.754030i	0.228847	+	0.0288733i
$683$	−4.35732	+	4.35732i	−0.166728	+	0.166728i	−0.785540	−	0.618811i	$-0.787615\pi$
$683$	−4.35732	+	4.35732i	−0.166728	+	0.166728i	0.618811	+	0.785540i	$0.287615\pi$
$684$		0			0
$685$	−5.06701	−	5.06701i	−0.193600	−	0.193600i
$686$	1.11731	−	0.866958i	0.0426591	−	0.0331006i
$687$		0			0
$688$	−4.38639	−	15.0624i	−0.167229	−	0.574250i
$689$			0.639271i			0.0243543i
$690$		0			0
$691$	−9.12084	+	9.12084i	−0.346973	+	0.346973i	−0.858981	−	0.512008i	$-0.828902\pi$
$691$	−9.12084	+	9.12084i	−0.346973	+	0.346973i	0.512008	+	0.858981i	$0.328902\pi$
$692$	17.1273	+	28.9397i	0.651081	+	1.10012i
$693$		0			0
$694$	4.09550	−	32.4605i	0.155463	−	1.23218i
$695$		−	20.5676i		−	0.780173i
$696$		0			0
$697$			6.76343i			0.256183i
$698$	−51.2713	−	6.46883i	−1.94065	−	0.244849i
$699$		0			0
$700$	−6.36782	−	1.63283i	−0.240681	−	0.0617151i
$701$	13.1832	−	13.1832i	0.497923	−	0.497923i	−0.412868	−	0.910791i	$-0.635473\pi$
$701$	13.1832	−	13.1832i	0.497923	−	0.497923i	0.910791	+	0.412868i	$0.135473\pi$
$702$		0			0
$703$		−	5.98374i		−	0.225681i
$704$	0.631189	+	19.4950i	0.0237888	+	0.734744i
$705$		0			0
$706$	21.3072	+	27.4601i	0.801908	+	1.03348i
$707$	13.6438	+	13.6438i	0.513126	+	0.513126i
$708$		0			0
$709$	5.95604	−	5.95604i	0.223684	−	0.223684i	−0.586364	−	0.810048i	$-0.699441\pi$
$709$	5.95604	−	5.95604i	0.223684	−	0.223684i	0.810048	+	0.586364i	$0.199441\pi$
$710$	−1.98579	+	15.7392i	−0.0745255	+	0.590682i
$711$		0			0
$712$	−1.70244	−	3.92899i	−0.0638017	−	0.147245i
$713$	10.7815			0.403769
$714$		0			0
$715$	−1.04757	−	1.04757i	−0.0391770	−	0.0391770i
$716$	−15.5499	+	9.20281i	−0.581126	+	0.343925i
$717$		0			0
$718$	−15.2139	−	19.6072i	−0.567776	−	0.731733i
$719$	−38.3917			−1.43177			−0.715884	−	0.698220i	$-0.753976\pi$
$719$	−38.3917			−1.43177			−0.715884	+	0.698220i	$0.753976\pi$
$720$		0			0
$721$	−11.9238			−0.444067
$722$	10.9799	+	14.1506i	0.408631	+	0.526631i
$723$		0			0
$724$	−8.01479	−	13.5425i	−0.297867	−	0.503302i
$725$	−0.403208	−	0.403208i	−0.0149748	−	0.0149748i
$726$		0			0
$727$	−5.05200			−0.187368			−0.0936842	−	0.995602i	$-0.529864\pi$
$727$	−5.05200			−0.187368			−0.0936842	+	0.995602i	$0.529864\pi$
$728$	0.482801	−	1.22111i	0.0178938	−	0.0452573i
$729$		0			0
$730$	1.48694	−	11.7853i	0.0550340	−	0.436194i
$731$	6.49454	−	6.49454i	0.240209	−	0.240209i
$732$		0			0
$733$	2.73691	+	2.73691i	0.101090	+	0.101090i	0.755843	−	0.654753i	$-0.227227\pi$
$733$	2.73691	+	2.73691i	0.101090	+	0.101090i	−0.654753	+	0.755843i	$0.727227\pi$
$734$	−13.6848	−	17.6366i	−0.505116	−	0.650979i
$735$		0			0
$736$	5.48855	+	34.4767i	0.202311	+	1.27083i
$737$		−	6.14648i		−	0.226408i
$738$		0			0
$739$	18.5031	−	18.5031i	0.680648	−	0.680648i	−0.279498	−	0.960146i	$-0.590168\pi$
$739$	18.5031	−	18.5031i	0.680648	−	0.680648i	0.960146	+	0.279498i	$0.0901682\pi$
$740$	1.54574	−	6.02819i	0.0568226	−	0.221601i
$741$		0			0
$742$	1.93206	+	0.243765i	0.0709282	+	0.00894891i
$743$			41.1110i			1.50822i	0.656751	+	0.754108i	$0.271930\pi$
$743$			41.1110i			1.50822i	−0.656751	+	0.754108i	$0.728070\pi$
$744$		0			0
$745$		−	18.9235i		−	0.693302i
$746$	−2.90001	+	22.9852i	−0.106177	+	0.841547i
$747$		0			0
$748$	−9.82728	+	5.81604i	−0.359321	+	0.212655i
$749$	13.6108	−	13.6108i	0.497327	−	0.497327i
$750$		0			0
$751$		−	27.5241i		−	1.00437i	−0.864760	−	0.502185i	$-0.832530\pi$
$751$		−	27.5241i		−	1.00437i	0.864760	−	0.502185i	$-0.167470\pi$
$752$	20.7646	+	11.3983i	0.757207	+	0.415654i
$753$		0			0
$754$	0.0899870	−	0.0698239i	0.00327713	−	0.00254284i
$755$	−5.54366	−	5.54366i	−0.201754	−	0.201754i
$756$		0			0
$757$	6.27349	−	6.27349i	0.228014	−	0.228014i	−0.583849	−	0.811863i	$-0.698454\pi$
$757$	6.27349	−	6.27349i	0.228014	−	0.228014i	0.811863	+	0.583849i	$0.198454\pi$
$758$	−3.65841	−	0.461576i	−0.132879	−	0.0167652i
$759$		0			0
$760$	−3.70459	−	8.54966i	−0.134380	−	0.310129i
$761$	−23.6884			−0.858704			−0.429352	−	0.903137i	$-0.641258\pi$
$761$	−23.6884			−0.858704			−0.429352	+	0.903137i	$0.641258\pi$
$762$		0			0
$763$	4.97865	+	4.97865i	0.180239	+	0.180239i
$764$	−1.20834	+	4.71236i	−0.0437161	+	0.170487i
$765$		0			0
$766$	−4.51475	+	3.50315i	−0.163125	+	0.126574i
$767$	5.46983			0.197504
$768$		0			0
$769$	−4.74756			−0.171201			−0.0856006	−	0.996330i	$-0.527281\pi$
$769$	−4.74756			−0.171201			−0.0856006	+	0.996330i	$0.527281\pi$
$770$	−3.56552	+	2.76661i	−0.128493	+	0.0997016i
$771$		0			0
$772$	12.3450	−	48.1439i	0.444307	−	1.73274i
$773$	−18.2666	−	18.2666i	−0.657005	−	0.657005i	0.297666	−	0.954670i	$-0.403792\pi$
$773$	−18.2666	−	18.2666i	−0.657005	−	0.657005i	−0.954670	+	0.297666i	$0.903792\pi$
$774$		0			0
$775$	5.74223			0.206267
$776$	−17.6751	−	40.7915i	−0.634498	−	1.46433i
$777$		0			0
$778$	−5.80287	−	0.732139i	−0.208043	−	0.0262485i
$779$	5.14017	−	5.14017i	0.184166	−	0.184166i
$780$		0			0
$781$	−14.7759	−	14.7759i	−0.528722	−	0.528722i
$782$	−16.1477	+	12.5296i	−0.577442	+	0.448056i
$783$		0			0
$784$	−3.50645	−	1.92479i	−0.125230	−	0.0687427i
$785$		−	17.7311i		−	0.632849i
$786$		0			0
$787$	28.1972	−	28.1972i	1.00512	−	1.00512i	0.00513510	−	0.999987i	$-0.498365\pi$
$787$	28.1972	−	28.1972i	1.00512	−	1.00512i	0.999987	−	0.00513510i	$-0.00163456\pi$
$788$	−4.31202	+	2.55196i	−0.153609	+	0.0909099i
$789$		0			0
$790$	1.24724	−	9.88550i	0.0443748	−	0.351710i
$791$			0.0768901i			0.00273390i
$792$		0			0
$793$			2.81532i			0.0999749i
$794$	−43.5656	−	5.49661i	−1.54609	−	0.195067i
$795$		0			0
$796$	−6.90355	+	26.9229i	−0.244690	+	0.954258i
$797$	24.8697	−	24.8697i	0.880930	−	0.880930i	−0.112699	−	0.993629i	$-0.535950\pi$
$797$	24.8697	−	24.8697i	0.880930	−	0.880930i	0.993629	+	0.112699i	$0.0359496\pi$
$798$		0			0
$799$			13.8678i			0.490608i
$800$	2.92321	+	18.3624i	0.103351	+	0.649208i
$801$		0			0
$802$	2.76038	+	3.55749i	0.0974723	+	0.125619i
$803$	11.0640	+	11.0640i	0.390439	+	0.390439i
$804$		0			0
$805$	−5.71163	+	5.71163i	−0.201309	+	0.201309i
$806$	−0.143575	+	1.13796i	−0.00505720	+	0.0400829i
$807$		0			0
$808$	20.0663	−	50.7521i	0.705930	−	1.78545i
$809$	44.9141			1.57910			0.789548	−	0.613688i	$-0.210315\pi$
$809$	44.9141			1.57910			0.789548	+	0.613688i	$0.210315\pi$
$810$		0			0
$811$	13.1446	+	13.1446i	0.461570	+	0.461570i	0.899170	−	0.437600i	$-0.144171\pi$
$811$	13.1446	+	13.1446i	0.461570	+	0.461570i	−0.437600	+	0.899170i	$0.644171\pi$
$812$	−0.176714	−	0.298592i	−0.00620146	−	0.0104785i
$813$		0			0
$814$	5.02520	+	6.47633i	0.176133	+	0.226995i
$815$	14.4578			0.506435
$816$		0			0
$817$	−9.87162			−0.345364
$818$	13.0911	+	16.8715i	0.457720	+	0.589896i
$819$		0			0
$820$	6.50618	−	3.85053i	0.227206	−	0.134466i
$821$	15.0363	+	15.0363i	0.524772	+	0.524772i	0.919009	−	0.394237i	$-0.128991\pi$
$821$	15.0363	+	15.0363i	0.524772	+	0.524772i	−0.394237	+	0.919009i	$0.628991\pi$
$822$		0			0
$823$	12.3186			0.429399			0.214699	−	0.976680i	$-0.431123\pi$
$823$	12.3186			0.429399			0.214699	+	0.976680i	$0.431123\pi$
$824$	13.4088	+	30.9455i	0.467117	+	1.07804i
$825$		0			0
$826$	2.08575	−	16.5314i	0.0725724	−	0.575202i
$827$	−29.2509	+	29.2509i	−1.01715	+	1.01715i	−0.0173016	+	0.999850i	$0.505508\pi$
$827$	−29.2509	+	29.2509i	−1.01715	+	1.01715i	−0.999850	+	0.0173016i	$0.994492\pi$
$828$		0			0
$829$	3.68627	+	3.68627i	0.128029	+	0.128029i	0.768218	−	0.640189i	$-0.221144\pi$
$829$	3.68627	+	3.68627i	0.128029	+	0.128029i	−0.640189	+	0.768218i	$0.721144\pi$
$830$	−5.55815	−	7.16318i	−0.192926	−	0.248638i
$831$		0			0
$832$	−3.71203	+	0.120185i	−0.128692	+	0.00416665i
$833$		−	2.34181i		−	0.0811389i
$834$		0			0
$835$	4.88761	−	4.88761i	0.169143	−	0.169143i
$836$	11.8888	+	3.04852i	0.411184	+	0.105435i
$837$		0			0
$838$	4.35327	+	0.549245i	0.150381	+	0.0189734i
$839$			26.5841i			0.917786i	0.888492	+	0.458893i	$0.151754\pi$
$839$			26.5841i			0.917786i	−0.888492	+	0.458893i	$0.848246\pi$
$840$		0			0
$841$			28.9699i			0.998962i
$842$	−4.21942	+	33.4427i	−0.145411	+	1.15251i
$843$		0			0
$844$	0.351458	+	0.593854i	0.0120977	+	0.0204413i
$845$	−11.8320	+	11.8320i	−0.407032	+	0.407032i
$846$		0			0
$847$			5.05544i			0.173707i
$848$	−1.54004	−	5.28834i	−0.0528851	−	0.181602i
$849$		0			0
$850$	−8.60031	+	6.67327i	−0.294988	+	0.228891i
$851$	10.3745	+	10.3745i	0.355632	+	0.355632i
$852$		0			0
$853$	8.95460	−	8.95460i	0.306600	−	0.306600i	−0.536989	−	0.843589i	$-0.680438\pi$
$853$	8.95460	−	8.95460i	0.306600	−	0.306600i	0.843589	+	0.536989i	$0.180438\pi$
$854$	8.50871	+	1.07353i	0.291162	+	0.0367355i
$855$		0			0
$856$	−50.6295	−	20.0178i	−1.73048	−	0.684195i
$857$	36.9763			1.26309			0.631543	−	0.775341i	$-0.282422\pi$
$857$	36.9763			1.26309			0.631543	+	0.775341i	$0.282422\pi$
$858$		0			0
$859$	1.95338	+	1.95338i	0.0666483	+	0.0666483i	0.739645	−	0.672997i	$-0.234993\pi$
$859$	1.95338	+	1.95338i	0.0666483	+	0.0666483i	−0.672997	+	0.739645i	$0.734993\pi$
$860$	−9.94496	−	2.55008i	−0.339120	−	0.0869569i
$861$		0			0
$862$	−22.3084	+	17.3098i	−0.759827	+	0.589575i
$863$	−11.1583			−0.379835			−0.189917	−	0.981800i	$-0.560822\pi$
$863$	−11.1583			−0.379835			−0.189917	+	0.981800i	$0.560822\pi$
$864$		0			0
$865$	22.0071			0.748262
$866$	−4.28167	+	3.32229i	−0.145497	+	0.112896i
$867$		0			0
$868$	3.38450	+	0.867849i	0.114877	+	0.0294567i
$869$	9.28043	+	9.28043i	0.314817	+	0.314817i
$870$		0			0
$871$	1.17035			0.0396558
$872$	7.32226	−	18.5196i	0.247963	−	0.627153i
$873$		0			0
$874$	21.7946	+	2.74979i	0.737213	+	0.0930131i
$875$	−7.66951	+	7.66951i	−0.259277	+	0.259277i
$876$		0			0
$877$	34.5959	+	34.5959i	1.16822	+	1.16822i	0.982626	+	0.185595i	$0.0594213\pi$
$877$	34.5959	+	34.5959i	1.16822	+	1.16822i	0.185595	+	0.982626i	$0.440579\pi$
$878$	−25.7115	+	19.9504i	−0.867722	+	0.673294i
$879$		0			0
$880$	11.1897	+	6.14234i	0.377203	+	0.207058i
$881$		−	51.6167i		−	1.73901i	−0.493924	−	0.869505i	$-0.664438\pi$
$881$		−	51.6167i		−	1.73901i	0.493924	−	0.869505i	$-0.335562\pi$
$882$		0			0
$883$	6.62392	−	6.62392i	0.222913	−	0.222913i	−0.586811	−	0.809724i	$-0.699617\pi$
$883$	6.62392	−	6.62392i	0.222913	−	0.222913i	0.809724	+	0.586811i	$0.199617\pi$
$884$	−1.10743	−	1.87121i	−0.0372470	−	0.0629357i
$885$		0			0
$886$	3.42938	−	27.1809i	0.115212	−	0.913160i
$887$			41.8546i			1.40534i	0.711515	+	0.702671i	$0.248009\pi$
$887$			41.8546i			1.40534i	−0.711515	+	0.702671i	$0.751991\pi$
$888$		0			0
$889$		−	15.0611i		−	0.505134i
$890$	−2.78019	−	0.350772i	−0.0931920	−	0.0117579i
$891$		0			0
$892$	−13.7005	−	3.51307i	−0.458727	−	0.117626i
$893$	10.5395	−	10.5395i	0.352690	−	0.352690i
$894$		0			0
$895$			11.8248i			0.395260i
$896$	−1.05223	+	11.2647i	−0.0351526	+	0.376326i
$897$		0			0
$898$	−23.6847	−	30.5242i	−0.790370	−	1.01861i
$899$	0.214305	+	0.214305i	0.00714748	+	0.00714748i
$900$		0			0
$901$	2.28020	−	2.28020i	0.0759643	−	0.0759643i
$902$	−1.24656	+	9.88008i	−0.0415058	+	0.328971i
$903$		0			0
$904$	0.199551	−	0.0864658i	0.00663695	−	0.00287581i
$905$	−10.2983			−0.342328
$906$		0			0
$907$	20.3030	+	20.3030i	0.674150	+	0.674150i	0.958670	−	0.284520i	$-0.0918343\pi$
$907$	20.3030	+	20.3030i	0.674150	+	0.674150i	−0.284520	+	0.958670i	$0.591834\pi$
$908$	5.24177	−	3.10221i	0.173954	−	0.102951i
$909$		0			0
$910$	−0.526790	−	0.678911i	−0.0174629	−	0.0225057i
$911$	−0.0607824			−0.00201381			−0.00100691	−	0.999999i	$-0.500321\pi$
$911$	−0.0607824			−0.00201381			−0.00100691	+	0.999999i	$0.500321\pi$
$912$		0			0
$913$	11.9427			0.395246
$914$	−26.4003	−	34.0239i	−0.873244	−	1.12541i
$915$		0			0
$916$	20.8174	+	35.1748i	0.687825	+	1.16221i
$917$	−3.87027	−	3.87027i	−0.127808	−	0.127808i
$918$		0			0
$919$	41.3187			1.36298			0.681489	−	0.731828i	$-0.261333\pi$
$919$	41.3187			1.36298			0.681489	+	0.731828i	$0.261333\pi$
$920$	21.2462	+	8.40028i	0.700465	+	0.276949i
$921$		0			0
$922$	−4.45666	+	35.3231i	−0.146772	+	1.16330i
$923$	2.81347	−	2.81347i	0.0926065	−	0.0926065i
$924$		0			0
$925$	5.52546	+	5.52546i	0.181676	+	0.181676i
$926$	−7.31118	−	9.42244i	−0.240260	−	0.309641i
$927$		0			0
$928$	−0.576204	+	0.794398i	−0.0189148	+	0.0260774i
$929$			41.2586i			1.35365i	0.736143	+	0.676826i	$0.236645\pi$
$929$			41.2586i			1.35365i	−0.736143	+	0.676826i	$0.763355\pi$
$930$		0			0
$931$	−1.77976	+	1.77976i	−0.0583294	+	0.0583294i
$932$	−8.84088	+	34.4783i	−0.289593	+	1.12937i
$933$		0			0
$934$	6.30423	+	0.795396i	0.206281	+	0.0260261i
$935$			7.47311i			0.244397i
$936$		0			0
$937$			53.0095i			1.73175i	0.500264	+	0.865873i	$0.333236\pi$
$937$			53.0095i			1.73175i	−0.500264	+	0.865873i	$0.666764\pi$
$938$	0.446276	−	3.53714i	0.0145714	−	0.115492i
$939$		0			0
$940$	13.3404	−	7.89517i	0.435115	−	0.257512i
$941$	−24.3743	+	24.3743i	−0.794580	+	0.794580i	−0.982235	−	0.187655i	$-0.939911\pi$
$941$	−24.3743	+	24.3743i	−0.794580	+	0.794580i	0.187655	+	0.982235i	$0.439911\pi$
$942$		0			0
$943$			17.8238i			0.580423i
$944$	−45.2490	+	13.1771i	−1.47273	+	0.428879i
$945$		0			0
$946$	10.6843	−	8.29028i	0.347376	−	0.269540i
$947$	22.4434	+	22.4434i	0.729314	+	0.729314i	0.970483	−	0.241169i	$-0.0775309\pi$
$947$	22.4434	+	22.4434i	0.729314	+	0.729314i	−0.241169	+	0.970483i	$0.577531\pi$
$948$		0			0
$949$	−2.10669	+	2.10669i	−0.0683861	+	0.0683861i
$950$	11.6078	+	1.46454i	0.376608	+	0.0475161i
$951$		0			0
$952$	−6.07763	+	2.63345i	−0.196977	+	0.0853507i
$953$	11.7067			0.379218			0.189609	−	0.981860i	$-0.439278\pi$
$953$	11.7067			0.379218			0.189609	+	0.981860i	$0.439278\pi$
$954$		0			0
$955$	2.25118	+	2.25118i	0.0728466	+	0.0728466i
$956$	−4.77962	+	18.6399i	−0.154584	+	0.602857i
$957$		0			0
$958$	0.614606	−	0.476893i	0.0198570	−	0.0154077i
$959$	5.47491			0.176794
$960$		0			0
$961$	27.9480			0.901549
$962$	−1.23316	+	0.956848i	−0.0397586	+	0.0308500i
$963$		0			0
$964$	13.6008	−	53.0412i	0.438051	−	1.70834i
$965$	−22.9992	−	22.9992i	−0.740372	−	0.740372i
$966$		0			0
$967$	53.7319			1.72790			0.863951	−	0.503576i	$-0.167983\pi$
$967$	53.7319			1.72790			0.863951	+	0.503576i	$0.167983\pi$
$968$	13.1202	−	5.68503i	0.421700	−	0.182724i
$969$		0			0
$970$	−28.8644	−	3.64178i	−0.926781	−	0.116931i
$971$	1.49392	−	1.49392i	0.0479423	−	0.0479423i	−0.682729	−	0.730671i	$-0.739207\pi$
$971$	1.49392	−	1.49392i	0.0479423	−	0.0479423i	0.730671	+	0.682729i	$0.239207\pi$
$972$		0			0
$973$	11.1117	+	11.1117i	0.356223	+	0.356223i
$974$	20.2991	−	15.7507i	0.650425	−	0.504686i
$975$		0			0
$976$	−6.78225	−	23.2896i	−0.217095	−	0.745482i
$977$		−	35.4073i		−	1.13278i	−0.824138	−	0.566390i	$-0.808340\pi$
$977$		−	35.4073i		−	1.13278i	0.824138	−	0.566390i	$-0.191660\pi$
$978$		0			0
$979$	2.61002	−	2.61002i	0.0834166	−	0.0834166i
$980$	−2.25274	+	1.33323i	−0.0719612	+	0.0425885i
$981$		0			0
$982$	−3.11852	+	24.7171i	−0.0995161	+	0.788755i
$983$		−	17.8771i		−	0.570191i	−0.958499	−	0.285096i	$-0.907975\pi$
$983$		−	17.8771i		−	0.570191i	0.958499	−	0.285096i	$-0.0920254\pi$
$984$		0			0
$985$			3.27905i			0.104479i
$986$	−0.570025	−	0.0719192i	−0.0181533	−	0.00229037i
$987$		0			0
$988$	−0.580469	+	2.26375i	−0.0184672	+	0.0720196i
$989$	17.1152	−	17.1152i	0.544232	−	0.544232i
$990$		0			0
$991$			54.7193i			1.73822i	0.494623	+	0.869108i	$0.335306\pi$
$991$			54.7193i			1.73822i	−0.494623	+	0.869108i	$0.664694\pi$
$992$	−1.55369	−	9.75960i	−0.0493297	−	0.309868i
$993$		0			0
$994$	−7.43029	−	9.57595i	−0.235675	−	0.303731i
$995$	12.8616	+	12.8616i	0.407740	+	0.407740i
$996$		0			0
$997$	38.1277	−	38.1277i	1.20751	−	1.20751i	0.235686	−	0.971829i	$-0.424266\pi$
$997$	38.1277	−	38.1277i	1.20751	−	1.20751i	0.971829	−	0.235686i	$-0.0757336\pi$
$998$	−5.80404	+	46.0023i	−0.183724	+	1.45618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.16	yes	40
3.2	odd	2	inner	1008.2.v.e.323.5	✓	40
4.3	odd	2		4032.2.v.e.1583.7		40
12.11	even	2		4032.2.v.e.1583.14		40
16.5	even	4		4032.2.v.e.3599.14		40
16.11	odd	4	inner	1008.2.v.e.827.5	yes	40
48.5	odd	4		4032.2.v.e.3599.7		40
48.11	even	4	inner	1008.2.v.e.827.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.5	✓	40	3.2	odd	2	inner
1008.2.v.e.323.16	yes	40	1.1	even	1	trivial
1008.2.v.e.827.5	yes	40	16.11	odd	4	inner
1008.2.v.e.827.16	yes	40	48.11	even	4	inner
4032.2.v.e.1583.7		40	4.3	odd	2
4032.2.v.e.1583.14		40	12.11	even	2
4032.2.v.e.3599.7		40	48.5	odd	4
4032.2.v.e.3599.14		40	16.5	even	4

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.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11731 - 0.866958i) q^{2} +(0.496766 - 1.93732i) q^{4} +(-0.925496 - 0.925496i) q^{5} +1.00000 q^{7} +(-1.12454 - 2.59527i) q^{8} +(-1.83643 - 0.231700i) q^{10} +(1.72403 - 1.72403i) q^{11} +(0.328273 + 0.328273i) q^{13} +(1.11731 - 0.866958i) q^{14} +(-3.50645 - 1.92479i) q^{16} -2.34181i q^{17} +(-1.77976 + 1.77976i) q^{19} +(-2.25274 + 1.33323i) q^{20} +(0.431615 - 3.42094i) q^{22} -6.17143i q^{23} -3.28691i q^{25} +(0.651381 + 0.0821838i) q^{26} +(0.496766 - 1.93732i) q^{28} +(0.122671 - 0.122671i) q^{29} +1.74700i q^{31} +(-5.58651 + 0.889349i) q^{32} +(-2.03025 - 2.61653i) q^{34} +(-0.925496 - 0.925496i) q^{35} +(-1.68105 + 1.68105i) q^{37} +(-0.445568 + 3.53153i) q^{38} +(-1.36116 + 3.44266i) q^{40} -2.88812 q^{41} +(2.77330 + 2.77330i) q^{43} +(-2.48356 - 4.19644i) q^{44} +(-5.35037 - 6.89540i) q^{46} -5.92184 q^{47} +1.00000 q^{49} +(-2.84962 - 3.67251i) q^{50} +(0.799045 - 0.472895i) q^{52} +(0.973689 + 0.973689i) q^{53} -3.19117 q^{55} +(-1.12454 - 2.59527i) q^{56} +(0.0307109 - 0.243412i) q^{58} +(8.33124 - 8.33124i) q^{59} +(4.28808 + 4.28808i) q^{61} +(1.51457 + 1.95194i) q^{62} +(-5.47084 + 5.83695i) q^{64} -0.607630i q^{65} +(1.78259 - 1.78259i) q^{67} +(-4.53685 - 1.16333i) q^{68} +(-1.83643 - 0.231700i) q^{70} -8.57053i q^{71} +6.41750i q^{73} +(-0.420854 + 3.33565i) q^{74} +(2.56385 + 4.33210i) q^{76} +(1.72403 - 1.72403i) q^{77} +5.38299i q^{79} +(1.46381 + 5.02659i) q^{80} +(-3.22693 + 2.50388i) q^{82} +(3.46360 + 3.46360i) q^{83} +(-2.16734 + 2.16734i) q^{85} +(5.50297 + 0.694301i) q^{86} +(-6.41306 - 2.53559i) q^{88} +1.51391 q^{89} +(0.328273 + 0.328273i) q^{91} +(-11.9561 - 3.06576i) q^{92} +(-6.61653 + 5.13398i) q^{94} +3.29433 q^{95} +15.7177 q^{97} +(1.11731 - 0.866958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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