LMFDB - Embedded newform 1008.2.v.e.323.5

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			323.5
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.883093	−	0.469198i	$-0.155457\pi$
$5$	0.925496	+	0.925496i	0.413894	+	0.413894i	−0.469198	+	0.883093i	$0.655457\pi$
$6$		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	−0.917515	−	0.397701i	$-0.869808\pi$
$11$	−1.72403	+	1.72403i	−0.519815	+	0.519815i	0.397701	+	0.917515i	$0.369808\pi$
$12$		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	$0.0916570\pi$
$17$			2.34181i			0.567973i	−0.958828	+	0.283986i	$0.908343\pi$
$18$		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	$0.222483\pi$
$23$			6.17143i			1.28683i	−0.765517	+	0.643416i	$0.777517\pi$
$24$		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	−0.718405	−	0.695625i	$-0.755127\pi$
$29$	−0.122671	+	0.122671i	−0.0227794	+	0.0227794i	0.695625	+	0.718405i	$0.255127\pi$
$30$		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	$-0.427591\pi$
$41$	2.88812			0.451048			0.225524	+	0.974238i	$0.427591\pi$
$42$		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	$-0.357845\pi$
$47$	5.92184			0.863789			0.431894	+	0.901924i	$0.357845\pi$
$48$		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	0.637064	−	0.770811i	$-0.280149\pi$
$53$	−0.973689	−	0.973689i	−0.133746	−	0.133746i	−0.770811	+	0.637064i	$0.780149\pi$
$54$		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	$0.528228\pi$
$59$	−8.33124	+	8.33124i	−1.08464	+	1.08464i	−0.996070	+	0.0885647i	$0.971772\pi$
$60$		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	$0.169825\pi$
$71$			8.57053i			1.01713i	−0.861022	+	0.508567i	$0.830175\pi$
$72$		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	0.490987	−	0.871167i	$-0.336636\pi$
$83$	−3.46360	−	3.46360i	−0.380179	−	0.380179i	−0.871167	+	0.490987i	$0.836636\pi$
$84$		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	$-0.525568\pi$
$89$	−1.51391			−0.160474			−0.0802368	+	0.996776i	$0.525568\pi$
$90$		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	$-0.840367\pi$
$101$	−13.6438	−	13.6438i	−1.35760	−	1.35760i	−0.480744	−	0.876861i	$-0.659633\pi$
$102$		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	$0.630553\pi$
$107$	−13.6108	+	13.6108i	−1.31580	+	1.31580i	−0.917064	+	0.398740i	$0.869447\pi$
$108$		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	$-0.998849\pi$
$113$		−	0.0768901i		−	0.00723322i	0.999993	−	0.00361661i	$-0.00115120\pi$
$114$		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	0.855670	−	0.517522i	$-0.173146\pi$
$131$	3.87027	+	3.87027i	0.338147	+	0.338147i	−0.517522	+	0.855670i	$0.673146\pi$
$132$		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	$-0.575141\pi$
$137$	−5.47491			−0.467753			−0.233877	+	0.972266i	$0.575141\pi$
$138$		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	0.150999	−	0.988534i	$-0.451751\pi$
$149$	−10.2234	−	10.2234i	−0.837535	−	0.837535i	−0.988534	+	0.150999i	$0.951751\pi$
$150$		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	$-0.934498\pi$
$167$		−	5.28108i		−	0.408662i	0.978902	−	0.204331i	$-0.0655019\pi$
$168$		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	−0.0918444	−	0.995773i	$-0.529276\pi$
$173$	11.8893	−	11.8893i	0.903929	−	0.903929i	0.995773	+	0.0918444i	$0.0292762\pi$
$174$		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	0.904328	−	0.426839i	$-0.140373\pi$
$179$	6.38837	+	6.38837i	0.477489	+	0.477489i	−0.426839	+	0.904328i	$0.640373\pi$
$180$		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	$-0.471952\pi$
$191$	2.43241			0.176003			0.0880014	+	0.996120i	$0.471952\pi$
$192$		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	0.767393	−	0.641178i	$-0.221554\pi$
$197$	1.77151	+	1.77151i	0.126215	+	0.126215i	−0.641178	+	0.767393i	$0.721554\pi$
$198$		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	0.632020	−	0.774952i	$-0.282226\pi$
$227$	−2.15348	−	2.15348i	−0.142932	−	0.142932i	−0.774952	+	0.632020i	$0.782226\pi$
$228$		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	$-0.301896\pi$
$233$	17.7969			1.16591			0.582955	+	0.812504i	$0.301896\pi$
$234$		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	$-0.399276\pi$
$239$	9.62147			0.622361			0.311180	+	0.950351i	$0.399276\pi$
$240$		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	−0.468967	−	0.883216i	$-0.655374\pi$
$251$	6.56293	−	6.56293i	0.414249	−	0.414249i	0.883216	+	0.468967i	$0.155374\pi$
$252$		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	$-0.859679\pi$
$257$		−	13.6808i		−	0.853383i	0.904397	−	0.426691i	$-0.140321\pi$
$258$		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	$-0.695511\pi$
$263$		−	26.5064i		−	1.63445i	0.576317	−	0.817226i	$-0.304489\pi$
$264$		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	−0.253620	−	0.967304i	$-0.581621\pi$
$269$	11.7053	−	11.7053i	0.713684	−	0.713684i	0.967304	+	0.253620i	$0.0816212\pi$
$270$		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	$-0.395424\pi$
$281$	10.8174			0.645314			0.322657	+	0.946516i	$0.395424\pi$
$282$		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	0.147226	−	0.989103i	$-0.452965\pi$
$293$	−14.4106	−	14.4106i	−0.841877	−	0.841877i	−0.989103	+	0.147226i	$0.952965\pi$
$294$		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	$0.0692838\pi$
$311$			7.61653i			0.431894i	−0.976405	+	0.215947i	$0.930716\pi$
$312$		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	−0.822727	−	0.568437i	$-0.807548\pi$
$317$	−4.52751	+	4.52751i	−0.254291	+	0.254291i	0.568437	+	0.822727i	$0.307548\pi$
$318$		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	−0.993348	−	0.115154i	$-0.963264\pi$
$347$	−16.3589	+	16.3589i	−0.878193	+	0.878193i	0.115154	+	0.993348i	$0.463264\pi$
$348$		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	$-0.773068\pi$
$353$		−	24.5770i		−	1.30810i	0.756451	−	0.654051i	$-0.226932\pi$
$354$		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	$0.153259\pi$
$359$			17.5485i			0.926176i	−0.886312	+	0.463088i	$0.846741\pi$
$360$		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	$-0.467080\pi$
$383$	4.04073			0.206472			0.103236	+	0.994657i	$0.467080\pi$
$384$		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	0.777347	−	0.629072i	$-0.216565\pi$
$389$	2.92444	+	2.92444i	0.148275	+	0.148275i	−0.629072	+	0.777347i	$0.716565\pi$
$390$		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	$-0.974668\pi$
$401$		−	3.18398i		−	0.159000i	0.996835	−	0.0795001i	$-0.0253324\pi$
$402$		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	0.651484	−	0.758662i	$-0.274147\pi$
$419$	−2.19389	−	2.19389i	−0.107178	−	0.107178i	−0.758662	+	0.651484i	$0.774147\pi$
$420$		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	$-0.340322\pi$
$431$	19.9661			0.961735			0.480868	+	0.876793i	$0.340322\pi$
$432$		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	−0.953191	−	0.302370i	$-0.902222\pi$
$443$	−13.6982	+	13.6982i	−0.650821	+	0.650821i	0.302370	+	0.953191i	$0.402222\pi$
$444$		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	$0.222993\pi$
$449$			27.3194i			1.28928i	−0.764486	+	0.644640i	$0.777007\pi$
$450$		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	−0.158291	−	0.987392i	$-0.550598\pi$
$461$	17.8016	−	17.8016i	0.829101	−	0.829101i	0.987392	+	0.158291i	$0.0505984\pi$
$462$		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	0.629766	−	0.776785i	$-0.283151\pi$
$467$	−3.17711	−	3.17711i	−0.147019	−	0.147019i	−0.776785	+	0.629766i	$0.783151\pi$
$468$		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	$-0.504000\pi$
$479$	−0.550076			−0.0251336			−0.0125668	+	0.999921i	$0.504000\pi$
$480$		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	−0.367764	−	0.929919i	$-0.619876\pi$
$491$	12.4565	−	12.4565i	0.562156	−	0.562156i	0.929919	+	0.367764i	$0.119876\pi$
$492$		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	$-0.658068\pi$
$503$		−	39.4375i		−	1.75843i	0.476426	−	0.879215i	$-0.341932\pi$
$504$		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	−0.734520	−	0.678587i	$-0.762593\pi$
$509$	−1.26193	+	1.26193i	−0.0559340	+	0.0559340i	0.678587	+	0.734520i	$0.262593\pi$
$510$		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	$-0.296240\pi$
$521$	27.2672			1.19460			0.597300	+	0.802018i	$0.296240\pi$
$522$		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	−0.619618	−	0.784903i	$-0.712713\pi$
$557$	3.90087	−	3.90087i	0.165285	−	0.165285i	0.784903	+	0.619618i	$0.212713\pi$
$558$		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	$0.0556068\pi$
$563$	27.4905	+	27.4905i	1.15859	+	1.15859i	0.173807	+	0.984780i	$0.444393\pi$
$564$		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	$-0.631864\pi$
$569$	−19.2030			−0.805031			−0.402516	+	0.915413i	$0.631864\pi$
$570$		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	−0.559231	−	0.829012i	$-0.688904\pi$
$587$	6.53626	−	6.53626i	0.269780	−	0.269780i	0.829012	+	0.559231i	$0.188904\pi$
$588$		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	$0.100455\pi$
$593$			15.1162i			0.620749i	−0.950614	+	0.310375i	$0.899545\pi$
$594$		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	$-0.797138\pi$
$599$		−	29.1264i		−	1.19007i	0.803700	−	0.595035i	$-0.202862\pi$
$600$		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	$-0.281700\pi$
$617$	31.4617			1.26660			0.633300	+	0.773906i	$0.281700\pi$
$618$		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	$0.226995\pi$
$641$			33.1261i			1.30840i	−0.756320	+	0.654201i	$0.773005\pi$
$642$		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	$0.406755\pi$
$647$			48.7052i			1.91480i	−0.288765	+	0.957400i	$0.593245\pi$
$648$		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	−0.652836	−	0.757499i	$-0.726421\pi$
$653$	2.67453	−	2.67453i	0.104662	−	0.104662i	0.757499	+	0.652836i	$0.226421\pi$
$654$		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	0.198680	−	0.980064i	$-0.436334\pi$
$659$	−20.0589	−	20.0589i	−0.781384	−	0.781384i	−0.980064	+	0.198680i	$0.936334\pi$
$660$		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	0.772736	−	0.634727i	$-0.218887\pi$
$677$	3.59090	+	3.59090i	0.138009	+	0.138009i	−0.634727	+	0.772736i	$0.718887\pi$
$678$		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	−0.618811	−	0.785540i	$-0.712385\pi$
$683$	4.35732	−	4.35732i	0.166728	−	0.166728i	0.785540	+	0.618811i	$0.212385\pi$
$684$		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	−0.910791	−	0.412868i	$-0.864527\pi$
$701$	−13.1832	+	13.1832i	−0.497923	+	0.497923i	0.412868	+	0.910791i	$0.364527\pi$
$702$		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	$-0.246024\pi$
$719$	38.3917			1.43177			0.715884	+	0.698220i	$0.246024\pi$
$720$		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	$-0.728070\pi$
$743$		−	41.1110i		−	1.50822i	0.656751	−	0.754108i	$-0.271930\pi$
$744$		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	$-0.358742\pi$
$761$	23.6884			0.858704			0.429352	+	0.903137i	$0.358742\pi$
$762$		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	0.954670	−	0.297666i	$-0.0962080\pi$
$773$	18.2666	+	18.2666i	0.657005	+	0.657005i	−0.297666	+	0.954670i	$0.596208\pi$
$774$		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	−0.993629	−	0.112699i	$-0.964050\pi$
$797$	−24.8697	+	24.8697i	−0.880930	+	0.880930i	0.112699	+	0.993629i	$0.464050\pi$
$798$		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	$-0.789685\pi$
$809$	−44.9141			−1.57910			−0.789548	+	0.613688i	$0.789685\pi$
$810$		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	0.394237	−	0.919009i	$-0.371009\pi$
$821$	−15.0363	−	15.0363i	−0.524772	−	0.524772i	−0.919009	+	0.394237i	$0.871009\pi$
$822$		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	$-0.494492\pi$
$827$	29.2509	−	29.2509i	1.01715	−	1.01715i	0.999850	−	0.0173016i	$-0.00550753\pi$
$828$		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	$-0.848246\pi$
$839$		−	26.5841i		−	0.917786i	0.888492	−	0.458893i	$-0.151754\pi$
$840$		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	$-0.717578\pi$
$857$	−36.9763			−1.26309			−0.631543	+	0.775341i	$0.717578\pi$
$858$		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	$-0.439178\pi$
$863$	11.1583			0.379835			0.189917	+	0.981800i	$0.439178\pi$
$864$		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	$0.335562\pi$
$881$			51.6167i			1.73901i	−0.493924	+	0.869505i	$0.664438\pi$
$882$		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	$-0.751991\pi$
$887$		−	41.8546i		−	1.40534i	0.711515	−	0.702671i	$-0.248009\pi$
$888$		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	$-0.499679\pi$
$911$	0.0607824			0.00201381			0.00100691	+	0.999999i	$0.499679\pi$
$912$		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	$-0.763355\pi$
$929$		−	41.2586i		−	1.35365i	0.736143	−	0.676826i	$-0.236645\pi$
$930$		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	−0.187655	−	0.982235i	$-0.560089\pi$
$941$	24.3743	−	24.3743i	0.794580	−	0.794580i	0.982235	+	0.187655i	$0.0600887\pi$
$942$		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	0.241169	−	0.970483i	$-0.422469\pi$
$947$	−22.4434	−	22.4434i	−0.729314	−	0.729314i	−0.970483	+	0.241169i	$0.922469\pi$
$948$		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	$-0.560722\pi$
$953$	−11.7067			−0.379218			−0.189609	+	0.981860i	$0.560722\pi$
$954$		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	−0.730671	−	0.682729i	$-0.760793\pi$
$971$	−1.49392	+	1.49392i	−0.0479423	+	0.0479423i	0.682729	+	0.730671i	$0.260793\pi$
$972$		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	$0.191660\pi$
$977$			35.4073i			1.13278i	−0.824138	+	0.566390i	$0.808340\pi$
$978$		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	$0.0920254\pi$
$983$			17.8771i			0.570191i	−0.958499	+	0.285096i	$0.907975\pi$
$984$		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.323.5	✓	40
3.2	odd	2	inner	1008.2.v.e.323.16	yes	40
4.3	odd	2		4032.2.v.e.1583.14		40
12.11	even	2		4032.2.v.e.1583.7		40
16.5	even	4		4032.2.v.e.3599.7		40
16.11	odd	4	inner	1008.2.v.e.827.16	yes	40
48.5	odd	4		4032.2.v.e.3599.14		40
48.11	even	4	inner	1008.2.v.e.827.5	yes	40

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

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

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