LMFDB - Embedded newform 432.2.k.d.109.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.10
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.451925 + 1.34006i) q^{2} +(-1.59153 + 1.21121i) q^{4} +(-2.86290 + 2.86290i) q^{5} -1.20181i q^{7} +(-2.34235 - 1.58537i) q^{8} +O(q^{10})$	\(q+(0.451925 + 1.34006i) q^{2} +(-1.59153 + 1.21121i) q^{4} +(-2.86290 + 2.86290i) q^{5} -1.20181i q^{7} +(-2.34235 - 1.58537i) q^{8} +(-5.13028 - 2.54265i) q^{10} +(0.703184 - 0.703184i) q^{11} +(-2.30746 - 2.30746i) q^{13} +(1.61049 - 0.543126i) q^{14} +(1.06592 - 3.85536i) q^{16} -5.47145 q^{17} +(3.25317 + 3.25317i) q^{19} +(1.08880 - 8.02397i) q^{20} +(1.26010 + 0.624523i) q^{22} +2.74108i q^{23} -11.3924i q^{25} +(2.04934 - 4.13494i) q^{26} +(1.45564 + 1.91271i) q^{28} +(4.25505 + 4.25505i) q^{29} -10.7309 q^{31} +(5.64814 - 0.313931i) q^{32} +(-2.47269 - 7.33208i) q^{34} +(3.44065 + 3.44065i) q^{35} +(-4.02946 + 4.02946i) q^{37} +(-2.88926 + 5.82963i) q^{38} +(11.2447 - 2.16717i) q^{40} -0.790699i q^{41} +(-4.88349 + 4.88349i) q^{43} +(-0.267431 + 1.97084i) q^{44} +(-3.67321 + 1.23876i) q^{46} -9.29335 q^{47} +5.55566 q^{49} +(15.2665 - 5.14851i) q^{50} +(6.46722 + 0.877561i) q^{52} +(-4.54517 + 4.54517i) q^{53} +4.02629i q^{55} +(-1.90531 + 2.81505i) q^{56} +(-3.77906 + 7.62498i) q^{58} +(-2.89721 + 2.89721i) q^{59} +(1.64598 + 1.64598i) q^{61} +(-4.84957 - 14.3801i) q^{62} +(2.97322 + 7.42698i) q^{64} +13.2121 q^{65} +(7.66887 + 7.66887i) q^{67} +(8.70797 - 6.62710i) q^{68} +(-3.05577 + 6.16560i) q^{70} +1.62879i q^{71} -1.69005i q^{73} +(-7.22073 - 3.57871i) q^{74} +(-9.11778 - 1.23723i) q^{76} +(-0.845091 - 0.845091i) q^{77} +8.99199 q^{79} +(7.98588 + 14.0891i) q^{80} +(1.05958 - 0.357336i) q^{82} +(3.57601 + 3.57601i) q^{83} +(15.6642 - 15.6642i) q^{85} +(-8.75114 - 4.33720i) q^{86} +(-2.76191 + 0.532299i) q^{88} -17.3745i q^{89} +(-2.77312 + 2.77312i) q^{91} +(-3.32003 - 4.36250i) q^{92} +(-4.19990 - 12.4537i) q^{94} -18.6270 q^{95} +4.51379 q^{97} +(2.51074 + 7.44493i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.451925	+	1.34006i	0.319559	+	0.947566i
$2$	0.451925	+	1.34006i	0.319559	+	0.947566i
$3$		0			0
$3$		0			0
$4$	−1.59153	+	1.21121i	−0.795764	+	0.605607i
$5$	−2.86290	+	2.86290i	−1.28033	+	1.28033i	−0.339848	+	0.940480i	$0.610376\pi$
$5$	−2.86290	+	2.86290i	−1.28033	+	1.28033i	−0.940480	+	0.339848i	$0.889624\pi$
$6$		0			0
$7$		−	1.20181i		−	0.454240i	−0.973867	−	0.227120i	$-0.927069\pi$
$7$		−	1.20181i		−	0.454240i	0.973867	−	0.227120i	$-0.0729310\pi$
$8$	−2.34235	−	1.58537i	−0.828146	−	0.560512i
$9$		0			0
$10$	−5.13028	−	2.54265i	−1.62234	−	0.804055i
$11$	0.703184	−	0.703184i	0.212018	−	0.212018i	−0.593106	−	0.805124i	$-0.702099\pi$
$11$	0.703184	−	0.703184i	0.212018	−	0.212018i	0.805124	+	0.593106i	$0.202099\pi$
$12$		0			0
$13$	−2.30746	−	2.30746i	−0.639975	−	0.639975i	0.310574	−	0.950549i	$-0.399479\pi$
$13$	−2.30746	−	2.30746i	−0.639975	−	0.639975i	−0.950549	+	0.310574i	$0.899479\pi$
$14$	1.61049	−	0.543126i	0.430423	−	0.145157i
$15$		0			0
$16$	1.06592	−	3.85536i	0.266481	−	0.963840i
$17$	−5.47145			−1.32702			−0.663511	−	0.748166i	$-0.730935\pi$
$17$	−5.47145			−1.32702			−0.663511	+	0.748166i	$0.730935\pi$
$18$		0			0
$19$	3.25317	+	3.25317i	0.746328	+	0.746328i	0.973787	−	0.227460i	$-0.0730421\pi$
$19$	3.25317	+	3.25317i	0.746328	+	0.746328i	−0.227460	+	0.973787i	$0.573042\pi$
$20$	1.08880	−	8.02397i	0.243464	−	1.79421i
$21$		0			0
$22$	1.26010	+	0.624523i	0.268653	+	0.133149i
$23$			2.74108i			0.571554i	0.958296	+	0.285777i	$0.0922517\pi$
$23$			2.74108i			0.571554i	−0.958296	+	0.285777i	$0.907748\pi$
$24$		0			0
$25$		−	11.3924i		−	2.27848i
$26$	2.04934	−	4.13494i	0.401909	−	0.810929i
$27$		0			0
$28$	1.45564	+	1.91271i	0.275091	+	0.361468i
$29$	4.25505	+	4.25505i	0.790142	+	0.790142i	0.981517	−	0.191375i	$-0.0612946\pi$
$29$	4.25505	+	4.25505i	0.790142	+	0.790142i	−0.191375	+	0.981517i	$0.561295\pi$
$30$		0			0
$31$	−10.7309			−1.92733			−0.963665	−	0.267112i	$-0.913931\pi$
$31$	−10.7309			−1.92733			−0.963665	+	0.267112i	$0.913931\pi$
$32$	5.64814	−	0.313931i	0.998459	−	0.0554957i
$33$		0			0
$34$	−2.47269	−	7.33208i	−0.424062	−	1.25744i
$35$	3.44065	+	3.44065i	0.581576	+	0.581576i
$36$		0			0
$37$	−4.02946	+	4.02946i	−0.662439	+	0.662439i	−0.955954	−	0.293515i	$-0.905175\pi$
$37$	−4.02946	+	4.02946i	−0.662439	+	0.662439i	0.293515	+	0.955954i	$0.405175\pi$
$38$	−2.88926	+	5.82963i	−0.468699	+	0.945691i
$39$		0			0
$40$	11.2447	−	2.16717i	1.77794	−	0.342660i
$41$		−	0.790699i		−	0.123486i	−0.998092	−	0.0617432i	$-0.980334\pi$
$41$		−	0.790699i		−	0.123486i	0.998092	−	0.0617432i	$-0.0196660\pi$
$42$		0			0
$43$	−4.88349	+	4.88349i	−0.744725	+	0.744725i	−0.973483	−	0.228758i	$-0.926533\pi$
$43$	−4.88349	+	4.88349i	−0.744725	+	0.744725i	0.228758	+	0.973483i	$0.426533\pi$
$44$	−0.267431	+	1.97084i	−0.0403167	+	0.297116i
$45$		0			0
$46$	−3.67321	+	1.23876i	−0.541586	+	0.182645i
$47$	−9.29335			−1.35558			−0.677788	−	0.735258i	$-0.737061\pi$
$47$	−9.29335			−1.35558			−0.677788	+	0.735258i	$0.737061\pi$
$48$		0			0
$49$	5.55566			0.793666
$50$	15.2665	−	5.14851i	2.15901	−	0.728109i
$51$		0			0
$52$	6.46722	+	0.877561i	0.896842	+	0.121696i
$53$	−4.54517	+	4.54517i	−0.624327	+	0.624327i	−0.946635	−	0.322308i	$-0.895541\pi$
$53$	−4.54517	+	4.54517i	−0.624327	+	0.624327i	0.322308	+	0.946635i	$0.395541\pi$
$54$		0			0
$55$			4.02629i			0.542905i
$56$	−1.90531	+	2.81505i	−0.254607	+	0.376177i
$57$		0			0
$58$	−3.77906	+	7.62498i	−0.496215	+	1.00121i
$59$	−2.89721	+	2.89721i	−0.377184	+	0.377184i	−0.870085	−	0.492901i	$-0.835936\pi$
$59$	−2.89721	+	2.89721i	−0.377184	+	0.377184i	0.492901	+	0.870085i	$0.335936\pi$
$60$		0			0
$61$	1.64598	+	1.64598i	0.210747	+	0.210747i	0.804585	−	0.593838i	$-0.202388\pi$
$61$	1.64598	+	1.64598i	0.210747	+	0.210747i	−0.593838	+	0.804585i	$0.702388\pi$
$62$	−4.84957	−	14.3801i	−0.615896	−	1.82627i
$63$		0			0
$64$	2.97322	+	7.42698i	0.371652	+	0.928372i
$65$	13.2121			1.63876
$66$		0			0
$67$	7.66887	+	7.66887i	0.936901	+	0.936901i	0.998124	−	0.0612228i	$-0.0195000\pi$
$67$	7.66887	+	7.66887i	0.936901	+	0.936901i	−0.0612228	+	0.998124i	$0.519500\pi$
$68$	8.70797	−	6.62710i	1.05600	−	0.803654i
$69$		0			0
$70$	−3.05577	+	6.16560i	−0.365234	+	0.736930i
$71$			1.62879i			0.193302i	0.995318	+	0.0966508i	$0.0308130\pi$
$71$			1.62879i			0.193302i	−0.995318	+	0.0966508i	$0.969187\pi$
$72$		0			0
$73$		−	1.69005i		−	0.197806i	−0.995097	−	0.0989030i	$-0.968467\pi$
$73$		−	1.69005i		−	0.197806i	0.995097	−	0.0989030i	$-0.0315333\pi$
$74$	−7.22073	−	3.57871i	−0.839393	−	0.416017i
$75$		0			0
$76$	−9.11778	−	1.23723i	−1.04588	−	0.141920i
$77$	−0.845091	−	0.845091i	−0.0963070	−	0.0963070i
$78$		0			0
$79$	8.99199			1.01168			0.505839	−	0.862628i	$-0.331183\pi$
$79$	8.99199			1.01168			0.505839	+	0.862628i	$0.331183\pi$
$80$	7.98588	+	14.0891i	0.892849	+	1.57521i
$81$		0			0
$82$	1.05958	−	0.357336i	0.117012	−	0.0394612i
$83$	3.57601	+	3.57601i	0.392518	+	0.392518i	0.875584	−	0.483066i	$-0.160477\pi$
$83$	3.57601	+	3.57601i	0.392518	+	0.392518i	−0.483066	+	0.875584i	$0.660477\pi$
$84$		0			0
$85$	15.6642	−	15.6642i	1.69902	−	1.69902i
$86$	−8.75114	−	4.33720i	−0.943660	−	0.467693i
$87$		0			0
$88$	−2.76191	+	0.532299i	−0.294420	+	0.0567432i
$89$		−	17.3745i		−	1.84170i	−0.389922	−	0.920848i	$-0.627498\pi$
$89$		−	17.3745i		−	1.84170i	0.389922	−	0.920848i	$-0.372502\pi$
$90$		0			0
$91$	−2.77312	+	2.77312i	−0.290702	+	0.290702i
$92$	−3.32003	−	4.36250i	−0.346137	−	0.454823i
$93$		0			0
$94$	−4.19990	−	12.4537i	−0.433186	−	1.28450i
$95$	−18.6270			−1.91109
$96$		0			0
$97$	4.51379			0.458305			0.229153	−	0.973390i	$-0.426404\pi$
$97$	4.51379			0.458305			0.229153	+	0.973390i	$0.426404\pi$
$98$	2.51074	+	7.44493i	0.253623	+	0.752051i
$99$		0			0
$100$	13.7986	+	18.1313i	1.37986	+	1.81313i
$101$	2.53458	−	2.53458i	0.252200	−	0.252200i	−0.569672	−	0.821872i	$-0.692930\pi$
$101$	2.53458	−	2.53458i	0.252200	−	0.252200i	0.821872	+	0.569672i	$0.192930\pi$
$102$		0			0
$103$			16.9964i			1.67470i	0.546666	+	0.837351i	$0.315897\pi$
$103$			16.9964i			1.67470i	−0.546666	+	0.837351i	$0.684103\pi$
$104$	1.74671	+	9.06306i	0.171279	+	0.888707i
$105$		0			0
$106$	−8.14488	−	4.03673i	−0.791100	−	0.392082i
$107$	5.06944	−	5.06944i	0.490081	−	0.490081i	−0.418250	−	0.908332i	$-0.637357\pi$
$107$	5.06944	−	5.06944i	0.490081	−	0.490081i	0.908332	+	0.418250i	$0.137357\pi$
$108$		0			0
$109$	−2.41205	−	2.41205i	−0.231033	−	0.231033i	0.582091	−	0.813124i	$-0.302235\pi$
$109$	−2.41205	−	2.41205i	−0.231033	−	0.231033i	−0.813124	+	0.582091i	$0.802235\pi$
$110$	−5.39547	+	1.81958i	−0.514438	+	0.173490i
$111$		0			0
$112$	−4.63340	−	1.28103i	−0.437815	−	0.121046i
$113$	−16.0036			−1.50549			−0.752745	−	0.658312i	$-0.771271\pi$
$113$	−16.0036			−1.50549			−0.752745	+	0.658312i	$0.771271\pi$
$114$		0			0
$115$	−7.84744	−	7.84744i	−0.731777	−	0.731777i
$116$	−11.9258	−	1.61826i	−1.10728	−	0.150251i
$117$		0			0
$118$	−5.19176	−	2.57312i	−0.477940	−	0.236874i
$119$			6.57563i			0.602787i
$120$		0			0
$121$			10.0111i			0.910097i
$122$	−1.46186	+	2.94958i	−0.132350	+	0.267043i
$123$		0			0
$124$	17.0786	−	12.9974i	1.53370	−	1.16720i
$125$	18.3008	+	18.3008i	1.63687	+	1.63687i
$126$		0			0
$127$	15.7173			1.39468			0.697342	−	0.716738i	$-0.254366\pi$
$127$	15.7173			1.39468			0.697342	+	0.716738i	$0.254366\pi$
$128$	−8.60893	+	7.34073i	−0.760929	+	0.648835i
$129$		0			0
$130$	5.97086	+	17.7050i	0.523679	+	1.55283i
$131$	3.48496	+	3.48496i	0.304482	+	0.304482i	0.842764	−	0.538283i	$-0.180927\pi$
$131$	3.48496	+	3.48496i	0.304482	+	0.304482i	−0.538283	+	0.842764i	$0.680927\pi$
$132$		0			0
$133$	3.90968	−	3.90968i	0.339012	−	0.339012i
$134$	−6.81100	+	13.7425i	−0.588381	+	1.18717i
$135$		0			0
$136$	12.8161	+	8.67427i	1.09897	+	0.743812i
$137$		−	2.91181i		−	0.248772i	−0.992234	−	0.124386i	$-0.960304\pi$
$137$		−	2.91181i		−	0.248772i	0.992234	−	0.124386i	$-0.0396962\pi$
$138$		0			0
$139$	−3.80255	+	3.80255i	−0.322528	+	0.322528i	−0.849736	−	0.527208i	$-0.823239\pi$
$139$	−3.80255	+	3.80255i	−0.322528	+	0.322528i	0.527208	+	0.849736i	$0.323239\pi$
$140$	−9.64326	−	1.30853i	−0.815004	−	0.110591i
$141$		0			0
$142$	−2.18268	+	0.736089i	−0.183166	+	0.0617713i
$143$	−3.24514			−0.271372
$144$		0			0
$145$	−24.3636			−2.02328
$146$	2.26478	−	0.763777i	0.187434	−	0.0632107i
$147$		0			0
$148$	1.53246	−	11.2935i	0.125968	−	0.928323i
$149$	−11.0659	+	11.0659i	−0.906553	+	0.906553i	−0.995992	−	0.0894389i	$-0.971493\pi$
$149$	−11.0659	+	11.0659i	−0.906553	+	0.906553i	0.0894389	+	0.995992i	$0.471493\pi$
$150$		0			0
$151$			12.9920i			1.05727i	0.848848	+	0.528637i	$0.177297\pi$
$151$			12.9920i			1.05727i	−0.848848	+	0.528637i	$0.822703\pi$
$152$	−2.46259	−	12.7775i	−0.199743	−	1.03639i
$153$		0			0
$154$	0.750556	−	1.51439i	0.0604815	−	0.122033i
$155$	30.7216	−	30.7216i	2.46762	−	2.46762i
$156$		0			0
$157$	−5.57674	−	5.57674i	−0.445072	−	0.445072i	0.448640	−	0.893712i	$-0.351908\pi$
$157$	−5.57674	−	5.57674i	−0.445072	−	0.445072i	−0.893712	+	0.448640i	$0.851908\pi$
$158$	4.06370	+	12.0498i	0.323291	+	0.958632i
$159$		0			0
$160$	−15.2713	+	17.0688i	−1.20730	+	1.34941i
$161$	3.29425			0.259623
$162$		0			0
$163$	−6.77442	−	6.77442i	−0.530614	−	0.530614i	0.390141	−	0.920755i	$-0.372426\pi$
$163$	−6.77442	−	6.77442i	−0.530614	−	0.530614i	−0.920755	+	0.390141i	$0.872426\pi$
$164$	0.957705	+	1.25842i	0.0747842	+	0.0982660i
$165$		0			0
$166$	−3.17599	+	6.40817i	−0.246504	+	0.497370i
$167$		−	14.1855i		−	1.09770i	−0.835920	−	0.548852i	$-0.815065\pi$
$167$		−	14.1855i		−	1.09770i	0.835920	−	0.548852i	$-0.184935\pi$
$168$		0			0
$169$		−	2.35123i		−	0.180864i
$170$	28.0701	+	13.9120i	2.15288	+	1.06700i
$171$		0			0
$172$	1.85726	−	13.6872i	0.141615	−	1.04364i
$173$	−14.4750	−	14.4750i	−1.10051	−	1.10051i	−0.994349	−	0.106162i	$-0.966144\pi$
$173$	−14.4750	−	14.4750i	−1.10051	−	1.10051i	−0.106162	−	0.994349i	$-0.533856\pi$
$174$		0			0
$175$	−13.6915			−1.03498
$176$	−1.96149	−	3.46057i	−0.147853	−	0.260850i
$177$		0			0
$178$	23.2829	−	7.85198i	1.74513	−	0.588531i
$179$	6.53727	+	6.53727i	0.488618	+	0.488618i	0.907870	−	0.419252i	$-0.137708\pi$
$179$	6.53727	+	6.53727i	0.488618	+	0.488618i	−0.419252	+	0.907870i	$0.637708\pi$
$180$		0			0
$181$	−0.365843	+	0.365843i	−0.0271929	+	0.0271929i	−0.720572	−	0.693380i	$-0.756121\pi$
$181$	−0.365843	+	0.365843i	−0.0271929	+	0.0271929i	0.693380	+	0.720572i	$0.256121\pi$
$182$	−4.96940	−	2.46291i	−0.368356	−	0.182563i
$183$		0			0
$184$	4.34562	−	6.42057i	0.320363	−	0.473331i
$185$		−	23.0719i		−	1.69628i
$186$		0			0
$187$	−3.84744	+	3.84744i	−0.281352	+	0.281352i
$188$	14.7906	−	11.2562i	1.07872	−	0.820946i
$189$		0			0
$190$	−8.41800	−	24.9613i	−0.610706	−	1.81088i
$191$	8.07939			0.584604			0.292302	−	0.956326i	$-0.405579\pi$
$191$	8.07939			0.584604			0.292302	+	0.956326i	$0.405579\pi$
$192$		0			0
$193$	8.16392			0.587652			0.293826	−	0.955859i	$-0.405071\pi$
$193$	8.16392			0.587652			0.293826	+	0.955859i	$0.405071\pi$
$194$	2.03989	+	6.04875i	0.146456	+	0.434275i
$195$		0			0
$196$	−8.84199	+	6.72909i	−0.631571	+	0.480649i
$197$	8.21908	−	8.21908i	0.585585	−	0.585585i	−0.350847	−	0.936433i	$-0.614106\pi$
$197$	8.21908	−	8.21908i	0.585585	−	0.585585i	0.936433	+	0.350847i	$0.114106\pi$
$198$		0			0
$199$		−	15.0015i		−	1.06343i	−0.846923	−	0.531715i	$-0.821548\pi$
$199$		−	15.0015i		−	1.06343i	0.846923	−	0.531715i	$-0.178452\pi$
$200$	−18.0611	+	26.6850i	−1.27712	+	1.88692i
$201$		0			0
$202$	4.54193	+	2.25105i	0.319569	+	0.158383i
$203$	5.11374	−	5.11374i	0.358914	−	0.358914i
$204$		0			0
$205$	2.26369	+	2.26369i	0.158103	+	0.158103i
$206$	−22.7762	+	7.68108i	−1.58689	+	0.535166i
$207$		0			0
$208$	−11.3557	+	6.43652i	−0.787375	+	0.446293i
$209$	4.57515			0.316469
$210$		0			0
$211$	−11.4347	−	11.4347i	−0.787198	−	0.787198i	0.193836	−	0.981034i	$-0.437907\pi$
$211$	−11.4347	−	11.4347i	−0.787198	−	0.787198i	−0.981034	+	0.193836i	$0.937907\pi$
$212$	1.72859	−	12.7389i	0.118720	−	0.874913i
$213$		0			0
$214$	9.08437	+	4.50235i	0.620994	+	0.307775i
$215$		−	27.9619i		−	1.90698i
$216$		0			0
$217$			12.8965i			0.875471i
$218$	2.14223	−	4.32236i	0.145090	−	0.292747i
$219$		0			0
$220$	−4.87670	−	6.40795i	−0.328787	−	0.432024i
$221$	12.6252	+	12.6252i	0.849261	+	0.849261i
$222$		0			0
$223$	−6.19380			−0.414768			−0.207384	−	0.978260i	$-0.566495\pi$
$223$	−6.19380			−0.414768			−0.207384	+	0.978260i	$0.566495\pi$
$224$	−0.377284	−	6.78797i	−0.0252084	−	0.453540i
$225$		0			0
$226$	−7.23242	−	21.4458i	−0.481093	−	1.42655i
$227$	9.42019	+	9.42019i	0.625240	+	0.625240i	0.946867	−	0.321627i	$-0.104230\pi$
$227$	9.42019	+	9.42019i	0.625240	+	0.625240i	−0.321627	+	0.946867i	$0.604230\pi$
$228$		0			0
$229$	3.52708	−	3.52708i	0.233076	−	0.233076i	−0.580899	−	0.813976i	$-0.697299\pi$
$229$	3.52708	−	3.52708i	0.233076	−	0.233076i	0.813976	+	0.580899i	$0.197299\pi$
$230$	6.96960	−	14.0625i	0.459561	−	0.927254i
$231$		0			0
$232$	−3.22100	−	16.7126i	−0.211469	−	1.09724i
$233$		−	5.08193i		−	0.332928i	−0.986048	−	0.166464i	$-0.946765\pi$
$233$		−	5.08193i		−	0.332928i	0.986048	−	0.166464i	$-0.0532350\pi$
$234$		0			0
$235$	26.6060	−	26.6060i	1.73558	−	1.73558i
$236$	1.10185	−	8.12012i	0.0717243	−	0.528575i
$237$		0			0
$238$	−8.81175	+	2.97169i	−0.571181	+	0.192626i
$239$	3.16393			0.204658			0.102329	−	0.994751i	$-0.467371\pi$
$239$	3.16393			0.204658			0.102329	+	0.994751i	$0.467371\pi$
$240$		0			0
$241$	−6.86502			−0.442215			−0.221107	−	0.975249i	$-0.570967\pi$
$241$	−6.86502			−0.442215			−0.221107	+	0.975249i	$0.570967\pi$
$242$	−13.4154	+	4.52425i	−0.862377	+	0.290830i
$243$		0			0
$244$	−4.61327	−	0.625992i	−0.295334	−	0.0400750i
$245$	−15.9053	+	15.9053i	−1.01615	+	1.01615i
$246$		0			0
$247$		−	15.0131i		−	0.955262i
$248$	25.1356	+	17.0125i	1.59611	+	1.08029i
$249$		0			0
$250$	−16.2536	+	32.7948i	−1.02797	+	2.07413i
$251$	−15.9818	+	15.9818i	−1.00876	+	1.00876i	−0.00880313	+	0.999961i	$0.502802\pi$
$251$	−15.9818	+	15.9818i	−1.00876	+	1.00876i	−0.999961	+	0.00880313i	$0.997198\pi$
$252$		0			0
$253$	1.92748	+	1.92748i	0.121180	+	0.121180i
$254$	7.10304	+	21.0621i	0.445684	+	1.32156i
$255$		0			0
$256$	−13.7276	−	8.21904i	−0.857976	−	0.513690i
$257$	11.1124			0.693171			0.346585	−	0.938018i	$-0.387341\pi$
$257$	11.1124			0.693171			0.346585	+	0.938018i	$0.387341\pi$
$258$		0			0
$259$	4.84263	+	4.84263i	0.300906	+	0.300906i
$260$	−21.0274	+	16.0026i	−1.30406	+	0.992442i
$261$		0			0
$262$	−3.09512	+	6.24499i	−0.191217	+	0.385817i
$263$			21.3694i			1.31770i	0.752276	+	0.658848i	$0.228956\pi$
$263$			21.3694i			1.31770i	−0.752276	+	0.658848i	$0.771044\pi$
$264$		0			0
$265$		−	26.0247i		−	1.59869i
$266$	7.00609	+	3.47233i	0.429571	+	0.212902i
$267$		0			0
$268$	−21.4939	−	2.91658i	−1.31295	−	0.178159i
$269$	7.85336	+	7.85336i	0.478828	+	0.478828i	0.904757	−	0.425929i	$-0.140053\pi$
$269$	7.85336	+	7.85336i	0.478828	+	0.478828i	−0.425929	+	0.904757i	$0.640053\pi$
$270$		0			0
$271$	12.6278			0.767086			0.383543	−	0.923523i	$-0.374704\pi$
$271$	12.6278			0.767086			0.383543	+	0.923523i	$0.374704\pi$
$272$	−5.83215	+	21.0944i	−0.353626	+	1.27904i
$273$		0			0
$274$	3.90200	−	1.31592i	0.235728	−	0.0794974i
$275$	−8.01095	−	8.01095i	−0.483078	−	0.483078i
$276$		0			0
$277$	−8.72278	+	8.72278i	−0.524101	+	0.524101i	−0.918807	−	0.394706i	$-0.870846\pi$
$277$	−8.72278	+	8.72278i	−0.524101	+	0.524101i	0.394706	+	0.918807i	$0.370846\pi$
$278$	−6.81411	−	3.37718i	−0.408683	−	0.202550i
$279$		0			0
$280$	−2.60452	−	13.5139i	−0.155650	−	0.807611i
$281$		−	12.8577i		−	0.767028i	−0.923535	−	0.383514i	$-0.874714\pi$
$281$		−	12.8577i		−	0.767028i	0.923535	−	0.383514i	$-0.125286\pi$
$282$		0			0
$283$	−11.0510	+	11.0510i	−0.656914	+	0.656914i	−0.954649	−	0.297735i	$-0.903769\pi$
$283$	−11.0510	+	11.0510i	−0.656914	+	0.656914i	0.297735	+	0.954649i	$0.403769\pi$
$284$	−1.97281	−	2.59226i	−0.117065	−	0.153822i
$285$		0			0
$286$	−1.46656	−	4.34869i	−0.0867194	−	0.257143i
$287$	−0.950267			−0.0560925
$288$		0			0
$289$	12.9368			0.760989
$290$	−11.0105	−	32.6487i	−0.646558	−	1.91719i
$291$		0			0
$292$	2.04702	+	2.68977i	0.119793	+	0.157407i
$293$	14.6007	−	14.6007i	0.852984	−	0.852984i	−0.137516	−	0.990500i	$-0.543912\pi$
$293$	14.6007	−	14.6007i	0.852984	−	0.852984i	0.990500	+	0.137516i	$0.0439117\pi$
$294$		0			0
$295$		−	16.5888i		−	0.965839i
$296$	15.8266	−	3.05024i	0.919901	−	0.177291i
$297$		0			0
$298$	−19.8299	−	9.82802i	−1.14872	−	0.569322i
$299$	6.32494	−	6.32494i	0.365781	−	0.365781i
$300$		0			0
$301$	5.86901	+	5.86901i	0.338284	+	0.338284i
$302$	−17.4101	+	5.87140i	−1.00184	+	0.337861i
$303$		0			0
$304$	16.0098	−	9.07451i	0.918222	−	0.520459i
$305$	−9.42458			−0.539650
$306$		0			0
$307$	12.0669	+	12.0669i	0.688692	+	0.688692i	0.961943	−	0.273251i	$-0.0880988\pi$
$307$	12.0669	+	12.0669i	0.688692	+	0.688692i	−0.273251	+	0.961943i	$0.588099\pi$
$308$	2.36857	+	0.321400i	0.134962	+	0.0183135i
$309$		0			0
$310$	55.0526	+	27.2849i	3.12678	+	1.54968i
$311$			21.7909i			1.23565i	0.786316	+	0.617825i	$0.211986\pi$
$311$			21.7909i			1.23565i	−0.786316	+	0.617825i	$0.788014\pi$
$312$		0			0
$313$			29.5914i			1.67261i	0.548267	+	0.836304i	$0.315288\pi$
$313$			29.5914i			1.67261i	−0.548267	+	0.836304i	$0.684712\pi$
$314$	4.95290	−	9.99344i	0.279509	−	0.563962i
$315$		0			0
$316$	−14.3110	+	10.8912i	−0.805057	+	0.612679i
$317$	−7.25614	−	7.25614i	−0.407546	−	0.407546i	0.473336	−	0.880882i	$-0.343050\pi$
$317$	−7.25614	−	7.25614i	−0.407546	−	0.407546i	−0.880882	+	0.473336i	$0.843050\pi$
$318$		0			0
$319$	5.98416			0.335049
$320$	−29.7747	−	12.7507i	−1.66446	−	0.712784i
$321$		0			0
$322$	1.48875	+	4.41449i	0.0829649	+	0.246010i
$323$	−17.7996	−	17.7996i	−0.990394	−	0.990394i
$324$		0			0
$325$	−26.2875	+	26.2875i	−1.45817	+	1.45817i
$326$	6.01661	−	12.1397i	0.333229	−	0.672354i
$327$		0			0
$328$	−1.25355	+	1.85209i	−0.0692156	+	0.102265i
$329$			11.1688i			0.615757i
$330$		0			0
$331$	−0.938113	+	0.938113i	−0.0515633	+	0.0515633i	−0.732418	−	0.680855i	$-0.761608\pi$
$331$	−0.938113	+	0.938113i	−0.0515633	+	0.0515633i	0.680855	+	0.732418i	$0.261608\pi$
$332$	−10.0226	−	1.36001i	−0.550064	−	0.0746402i
$333$		0			0
$334$	19.0094	−	6.41076i	1.04015	−	0.350781i
$335$	−43.9104			−2.39908
$336$		0			0
$337$	3.60268			0.196250			0.0981252	−	0.995174i	$-0.468715\pi$
$337$	3.60268			0.196250			0.0981252	+	0.995174i	$0.468715\pi$
$338$	3.15080	−	1.06258i	0.171381	−	0.0577968i
$339$		0			0
$340$	−5.95733	+	43.9028i	−0.323082	+	2.38096i
$341$	−7.54581	+	7.54581i	−0.408629	+	0.408629i
$342$		0			0
$343$		−	15.0895i		−	0.814755i
$344$	19.1810	−	3.69672i	1.03417	−	0.199314i
$345$		0			0
$346$	12.8557	−	25.9389i	0.691129	−	1.39449i
$347$	−8.59870	+	8.59870i	−0.461602	+	0.461602i	−0.899180	−	0.437578i	$-0.855836\pi$
$347$	−8.59870	+	8.59870i	−0.461602	+	0.461602i	0.437578	+	0.899180i	$0.355836\pi$
$348$		0			0
$349$	7.74273	+	7.74273i	0.414459	+	0.414459i	0.883289	−	0.468830i	$-0.155324\pi$
$349$	7.74273	+	7.74273i	0.414459	+	0.414459i	−0.468830	+	0.883289i	$0.655324\pi$
$350$	−6.18751	−	18.3474i	−0.330736	−	0.980710i
$351$		0			0
$352$	3.75093	−	4.19243i	0.199925	−	0.223457i
$353$	9.98938			0.531681			0.265840	−	0.964017i	$-0.414351\pi$
$353$	9.98938			0.531681			0.265840	+	0.964017i	$0.414351\pi$
$354$		0			0
$355$	−4.66306	−	4.66306i	−0.247489	−	0.247489i
$356$	21.0443	+	27.6520i	1.11534	+	1.46556i
$357$		0			0
$358$	−5.80599	+	11.7147i	−0.306856	+	0.619141i
$359$			1.11093i			0.0586324i	0.999570	+	0.0293162i	$0.00933298\pi$
$359$			1.11093i			0.0586324i	−0.999570	+	0.0293162i	$0.990667\pi$
$360$		0			0
$361$			2.16618i			0.114010i
$362$	−0.655586	−	0.324918i	−0.0344568	−	0.0170773i
$363$		0			0
$364$	1.05466	−	7.77235i	0.0552791	−	0.407382i
$365$	4.83846	+	4.83846i	0.253256	+	0.253256i
$366$		0			0
$367$	−22.2750			−1.16275			−0.581373	−	0.813637i	$-0.697484\pi$
$367$	−22.2750			−1.16275			−0.581373	+	0.813637i	$0.697484\pi$
$368$	10.5678	+	2.92178i	0.550887	+	0.152308i
$369$		0			0
$370$	30.9177	−	10.4268i	1.60734	−	0.542061i
$371$	5.46241	+	5.46241i	0.283594	+	0.283594i
$372$		0			0
$373$	−24.8024	+	24.8024i	−1.28422	+	1.28422i	−0.345975	+	0.938244i	$0.612452\pi$
$373$	−24.8024	+	24.8024i	−1.28422	+	1.28422i	−0.938244	+	0.345975i	$0.887548\pi$
$374$	−6.89455	−	3.41705i	−0.356509	−	0.176691i
$375$		0			0
$376$	21.7683	+	14.7334i	1.12261	+	0.759816i
$377$		−	19.6367i		−	1.01134i
$378$		0			0
$379$	12.8676	−	12.8676i	0.660963	−	0.660963i	−0.294644	−	0.955607i	$-0.595201\pi$
$379$	12.8676	−	12.8676i	0.660963	−	0.660963i	0.955607	+	0.294644i	$0.0952011\pi$
$380$	29.6454	−	22.5613i	1.52078	−	1.15737i
$381$		0			0
$382$	3.65128	+	10.8269i	0.186816	+	0.553951i
$383$	−4.20457			−0.214843			−0.107422	−	0.994214i	$-0.534259\pi$
$383$	−4.20457			−0.214843			−0.107422	+	0.994214i	$0.534259\pi$
$384$		0			0
$385$	4.83882			0.246609
$386$	3.68948	+	10.9402i	0.187790	+	0.556839i
$387$		0			0
$388$	−7.18382	+	5.46716i	−0.364703	+	0.277553i
$389$	10.3434	−	10.3434i	0.524432	−	0.524432i	−0.394475	−	0.918907i	$-0.629074\pi$
$389$	10.3434	−	10.3434i	0.524432	−	0.524432i	0.918907	+	0.394475i	$0.129074\pi$
$390$		0			0
$391$		−	14.9977i		−	0.758466i
$392$	−13.0133	−	8.80776i	−0.657271	−	0.444859i
$393$		0			0
$394$	14.7285	+	7.29967i	0.742010	+	0.367752i
$395$	−25.7432	+	25.7432i	−1.29528	+	1.29528i
$396$		0			0
$397$	−14.9557	−	14.9557i	−0.750606	−	0.750606i	0.223987	−	0.974592i	$-0.428093\pi$
$397$	−14.9557	−	14.9557i	−0.750606	−	0.750606i	−0.974592	+	0.223987i	$0.928093\pi$
$398$	20.1030	−	6.77957i	1.00767	−	0.339829i
$399$		0			0
$400$	−43.9218	−	12.1434i	−2.19609	−	0.607171i
$401$	−5.82579			−0.290926			−0.145463	−	0.989364i	$-0.546467\pi$
$401$	−5.82579			−0.290926			−0.145463	+	0.989364i	$0.546467\pi$
$402$		0			0
$403$	24.7612	+	24.7612i	1.23344	+	1.23344i
$404$	−0.963936	+	7.10377i	−0.0479576	+	0.353426i
$405$		0			0
$406$	9.16376	+	4.54170i	0.454790	+	0.225401i
$407$			5.66690i			0.280898i
$408$		0			0
$409$		−	3.80064i		−	0.187930i	−0.995576	−	0.0939648i	$-0.970046\pi$
$409$		−	3.80064i		−	0.187930i	0.995576	−	0.0939648i	$-0.0299541\pi$
$410$	−2.01047	+	4.05650i	−0.0992899	+	0.200336i
$411$		0			0
$412$	−20.5862	−	27.0502i	−1.01421	−	1.33267i
$413$	3.48188	+	3.48188i	0.171332	+	0.171332i
$414$		0			0
$415$	−20.4755			−1.00510
$416$	−13.7572	−	12.3085i	−0.674505	−	0.603473i
$417$		0			0
$418$	2.06762	+	6.13098i	0.101131	+	0.299876i
$419$	25.7118	+	25.7118i	1.25610	+	1.25610i	0.952938	+	0.303166i	$0.0980438\pi$
$419$	25.7118	+	25.7118i	1.25610	+	1.25610i	0.303166	+	0.952938i	$0.401956\pi$
$420$		0			0
$421$	−10.0115	+	10.0115i	−0.487930	+	0.487930i	−0.907652	−	0.419723i	$-0.862127\pi$
$421$	−10.0115	+	10.0115i	−0.487930	+	0.487930i	0.419723	+	0.907652i	$0.362127\pi$
$422$	10.1556	−	20.4908i	0.494366	−	0.997478i
$423$		0			0
$424$	17.8521	−	3.44062i	0.866977	−	0.167091i
$425$			62.3330i			3.02360i
$426$		0			0
$427$	1.97816	−	1.97816i	0.0957296	−	0.0957296i
$428$	−1.92798	+	14.2083i	−0.0931925	+	0.686786i
$429$		0			0
$430$	37.4706	−	12.6367i	1.80699	−	0.609394i
$431$	27.5690			1.32795			0.663977	−	0.747753i	$-0.268867\pi$
$431$	27.5690			1.32795			0.663977	+	0.747753i	$0.268867\pi$
$432$		0			0
$433$	−9.62973			−0.462775			−0.231388	−	0.972862i	$-0.574327\pi$
$433$	−9.62973			−0.462775			−0.231388	+	0.972862i	$0.574327\pi$
$434$	−17.2821	+	5.82825i	−0.829567	+	0.279765i
$435$		0			0
$436$	6.76036	+	0.917338i	0.323762	+	0.0439325i
$437$	−8.91719	+	8.91719i	−0.426567	+	0.426567i
$438$		0			0
$439$		−	1.30931i		−	0.0624900i	−0.999512	−	0.0312450i	$-0.990053\pi$
$439$		−	1.30931i		−	0.0624900i	0.999512	−	0.0312450i	$-0.00994721\pi$
$440$	6.38315	−	9.43099i	0.304305	−	0.449605i
$441$		0			0
$442$	−11.2129	+	22.6241i	−0.533342	+	1.07612i
$443$	−0.934873	+	0.934873i	−0.0444172	+	0.0444172i	−0.728967	−	0.684549i	$-0.759999\pi$
$443$	−0.934873	+	0.934873i	−0.0444172	+	0.0444172i	0.684549	+	0.728967i	$0.259999\pi$
$444$		0			0
$445$	49.7415	+	49.7415i	2.35798	+	2.35798i
$446$	−2.79913	−	8.30007i	−0.132543	−	0.393020i
$447$		0			0
$448$	8.92579	−	3.57323i	0.421704	−	0.168819i
$449$	−28.2118			−1.33140			−0.665699	−	0.746220i	$-0.731867\pi$
$449$	−28.2118			−1.33140			−0.665699	+	0.746220i	$0.731867\pi$
$450$		0			0
$451$	−0.556006	−	0.556006i	−0.0261813	−	0.0261813i
$452$	25.4702	−	19.3838i	1.19802	−	0.911735i
$453$		0			0
$454$	−8.36641	+	16.8808i	−0.392655	+	0.792257i
$455$		−	15.8784i		−	0.744389i
$456$		0			0
$457$			7.69298i			0.359862i	0.983679	+	0.179931i	$0.0575875\pi$
$457$			7.69298i			0.359862i	−0.983679	+	0.179931i	$0.942413\pi$
$458$	6.32049	+	3.13253i	0.295337	+	0.146374i
$459$		0			0
$460$	21.9943	+	2.98449i	1.02549	+	0.139153i
$461$	−14.7518	−	14.7518i	−0.687059	−	0.687059i	0.274522	−	0.961581i	$-0.411480\pi$
$461$	−14.7518	−	14.7518i	−0.687059	−	0.687059i	−0.961581	+	0.274522i	$0.911480\pi$
$462$		0			0
$463$	22.0144			1.02310			0.511548	−	0.859255i	$-0.329072\pi$
$463$	22.0144			1.02310			0.511548	+	0.859255i	$0.329072\pi$
$464$	20.9403	−	11.8692i	0.972129	−	0.551013i
$465$		0			0
$466$	6.81009	−	2.29665i	0.315471	−	0.106390i
$467$	16.2503	+	16.2503i	0.751975	+	0.751975i	0.974848	−	0.222872i	$-0.0715433\pi$
$467$	16.2503	+	16.2503i	0.751975	+	0.751975i	−0.222872	+	0.974848i	$0.571543\pi$
$468$		0			0
$469$	9.21650	−	9.21650i	0.425578	−	0.425578i
$470$	47.6775	+	23.6297i	2.19920	+	1.08996i
$471$		0			0
$472$	11.3794	−	2.19314i	0.523780	−	0.100947i
$473$			6.86798i			0.315790i
$474$		0			0
$475$	37.0614	−	37.0614i	1.70049	−	1.70049i
$476$	−7.96449	−	10.4653i	−0.365052	−	0.479676i
$477$		0			0
$478$	1.42986	+	4.23986i	0.0654002	+	0.193927i
$479$	−9.47673			−0.433003			−0.216501	−	0.976282i	$-0.569465\pi$
$479$	−9.47673			−0.433003			−0.216501	+	0.976282i	$0.569465\pi$
$480$		0			0
$481$	18.5957			0.847889
$482$	−3.10247	−	9.19954i	−0.141314	−	0.419028i
$483$		0			0
$484$	−12.1255	−	15.9329i	−0.551161	−	0.724222i
$485$	−12.9225	+	12.9225i	−0.586781	+	0.586781i
$486$		0			0
$487$		−	8.26985i		−	0.374743i	−0.982289	−	0.187371i	$-0.940003\pi$
$487$		−	8.26985i		−	0.374743i	0.982289	−	0.187371i	$-0.0599968\pi$
$488$	−1.24598	−	6.46496i	−0.0564030	−	0.292655i
$489$		0			0
$490$	−28.5021	−	14.1261i	−1.28759	−	0.638151i
$491$	29.1968	−	29.1968i	1.31763	−	1.31763i	0.401985	−	0.915646i	$-0.368320\pi$
$491$	29.1968	−	29.1968i	1.31763	−	1.31763i	0.915646	−	0.401985i	$-0.131680\pi$
$492$		0			0
$493$	−23.2813	−	23.2813i	−1.04854	−	1.04854i
$494$	20.1185	−	6.78480i	0.905174	−	0.305263i
$495$		0			0
$496$	−11.4383	+	41.3716i	−0.513597	+	1.85764i
$497$	1.95749			0.0878053
$498$		0			0
$499$	−7.86662	−	7.86662i	−0.352158	−	0.352158i	0.508754	−	0.860912i	$-0.330106\pi$
$499$	−7.86662	−	7.86662i	−0.352158	−	0.352158i	−0.860912	+	0.508754i	$0.830106\pi$
$500$	−51.2925	−	6.96006i	−2.29387	−	0.311263i
$501$		0			0
$502$	−28.6392	−	14.1940i	−1.27823	−	0.633511i
$503$		−	1.58988i		−	0.0708891i	−0.999372	−	0.0354446i	$-0.988715\pi$
$503$		−	1.58988i		−	0.0708891i	0.999372	−	0.0354446i	$-0.0112847\pi$
$504$		0			0
$505$			14.5125i			0.645797i
$506$	−1.71187	+	3.45402i	−0.0761018	+	0.153550i
$507$		0			0
$508$	−25.0145	+	19.0370i	−1.10984	+	0.844631i
$509$	−5.55265	−	5.55265i	−0.246117	−	0.246117i	0.573258	−	0.819375i	$-0.305679\pi$
$509$	−5.55265	−	5.55265i	−0.246117	−	0.246117i	−0.819375	+	0.573258i	$0.805679\pi$
$510$		0			0
$511$	−2.03112			−0.0898514
$512$	4.81016	−	22.1102i	0.212581	−	0.977143i
$513$		0			0
$514$	5.02196	+	14.8913i	0.221509	+	0.656825i
$515$	−48.6589	−	48.6589i	−2.14417	−	2.14417i
$516$		0			0
$517$	−6.53493	+	6.53493i	−0.287406	+	0.287406i
$518$	−4.30092	+	8.67793i	−0.188971	+	0.381286i
$519$		0			0
$520$	−30.9473	−	20.9460i	−1.35713	−	0.918542i
$521$			16.8515i			0.738278i	0.929374	+	0.369139i	$0.120347\pi$
$521$			16.8515i			0.738278i	−0.929374	+	0.369139i	$0.879653\pi$
$522$		0			0
$523$	−16.4956	+	16.4956i	−0.721302	+	0.721302i	−0.968870	−	0.247569i	$-0.920368\pi$
$523$	−16.4956	+	16.4956i	−0.721302	+	0.721302i	0.247569	+	0.968870i	$0.420368\pi$
$524$	−9.76743	−	1.32538i	−0.426692	−	0.0578994i
$525$		0			0
$526$	−28.6363	+	9.65737i	−1.24860	+	0.421082i
$527$	58.7138			2.55761
$528$		0			0
$529$	15.4865			0.673325
$530$	34.8747	−	11.7612i	1.51486	−	0.510875i
$531$		0			0
$532$	−1.48691	+	10.9578i	−0.0644656	+	0.475081i
$533$	−1.82451	+	1.82451i	−0.0790282	+	0.0790282i
$534$		0			0
$535$			29.0266i			1.25493i
$536$	−5.80521	−	30.1212i	−0.250747	−	1.30104i
$537$		0			0
$538$	−6.97486	+	14.0731i	−0.300707	+	0.606735i
$539$	3.90665	−	3.90665i	0.168271	−	0.168271i
$540$		0			0
$541$	13.9247	+	13.9247i	0.598668	+	0.598668i	0.939958	−	0.341290i	$-0.110864\pi$
$541$	13.9247	+	13.9247i	0.598668	+	0.598668i	−0.341290	+	0.939958i	$0.610864\pi$
$542$	5.70683	+	16.9221i	0.245129	+	0.726865i
$543$		0			0
$544$	−30.9035	+	1.71766i	−1.32498	+	0.0736440i
$545$	13.8109			0.591595
$546$		0			0
$547$	−13.9354	−	13.9354i	−0.595836	−	0.595836i	0.343366	−	0.939202i	$-0.388433\pi$
$547$	−13.9354	−	13.9354i	−0.595836	−	0.595836i	−0.939202	+	0.343366i	$0.888433\pi$
$548$	3.52682	+	4.63422i	0.150658	+	0.197964i
$549$		0			0
$550$	7.11482	−	14.3555i	0.303377	−	0.612121i
$551$			27.6847i			1.17941i
$552$		0			0
$553$		−	10.8066i		−	0.459545i
$554$	−15.6311	−	7.74702i	−0.664102	−	0.329139i
$555$		0			0
$556$	1.44616	−	10.6576i	0.0613310	−	0.451981i
$557$	−3.65967	−	3.65967i	−0.155065	−	0.155065i	0.625311	−	0.780376i	$-0.284972\pi$
$557$	−3.65967	−	3.65967i	−0.155065	−	0.155065i	−0.780376	+	0.625311i	$0.784972\pi$
$558$		0			0
$559$	22.5369			0.953210
$560$	16.9324	−	9.59749i	0.715526	−	0.405568i
$561$		0			0
$562$	17.2301	−	5.81073i	0.726810	−	0.245111i
$563$	−22.7038	−	22.7038i	−0.956851	−	0.956851i	0.0422558	−	0.999107i	$-0.486546\pi$
$563$	−22.7038	−	22.7038i	−0.956851	−	0.956851i	−0.999107	+	0.0422558i	$0.986546\pi$
$564$		0			0
$565$	45.8167	−	45.8167i	1.92752	−	1.92752i
$566$	−19.8032	−	9.81479i	−0.832392	−	0.412547i
$567$		0			0
$568$	2.58223	−	3.81519i	0.108348	−	0.160082i
$569$			35.4767i			1.48726i	0.668591	+	0.743630i	$0.266898\pi$
$569$			35.4767i			1.48726i	−0.668591	+	0.743630i	$0.733102\pi$
$570$		0			0
$571$	−19.0587	+	19.0587i	−0.797581	+	0.797581i	−0.982714	−	0.185132i	$-0.940729\pi$
$571$	−19.0587	+	19.0587i	−0.797581	+	0.797581i	0.185132	+	0.982714i	$0.440729\pi$
$572$	5.16473	−	3.93056i	0.215948	−	0.164345i
$573$		0			0
$574$	−0.429449	−	1.27342i	−0.0179249	−	0.0531513i
$575$	31.2275			1.30228
$576$		0			0
$577$	−26.7459			−1.11344			−0.556722	−	0.830699i	$-0.687941\pi$
$577$	−26.7459			−1.11344			−0.556722	+	0.830699i	$0.687941\pi$
$578$	5.84647	+	17.3361i	0.243181	+	0.721088i
$579$		0			0
$580$	38.7753	−	29.5095i	1.61006	−	1.22531i
$581$	4.29768	−	4.29768i	0.178298	−	0.178298i
$582$		0			0
$583$			6.39218i			0.264737i
$584$	−2.67936	+	3.95870i	−0.110873	+	0.163812i
$585$		0			0
$586$	26.1643	+	12.9674i	1.08084	+	0.535680i
$587$	−28.0637	+	28.0637i	−1.15831	+	1.15831i	−0.173475	+	0.984838i	$0.555499\pi$
$587$	−28.0637	+	28.0637i	−1.15831	+	1.15831i	−0.984838	+	0.173475i	$0.944501\pi$
$588$		0			0
$589$	−34.9095	−	34.9095i	−1.43842	−	1.43842i
$590$	22.2301	−	7.49691i	0.915197	−	0.308643i
$591$		0			0
$592$	11.2399	+	19.8301i	0.461958	+	0.815013i
$593$	−34.9362			−1.43466			−0.717329	−	0.696735i	$-0.754635\pi$
$593$	−34.9362			−1.43466			−0.717329	+	0.696735i	$0.754635\pi$
$594$		0			0
$595$	−18.8254	−	18.8254i	−0.771765	−	0.771765i
$596$	4.20852	−	31.0148i	0.172388	−	1.27042i
$597$		0			0
$598$	11.3342	+	5.61741i	0.463490	+	0.229713i
$599$			2.08750i			0.0852931i	0.999090	+	0.0426465i	$0.0135789\pi$
$599$			2.08750i			0.0852931i	−0.999090	+	0.0426465i	$0.986421\pi$
$600$		0			0
$601$			31.3973i			1.28072i	0.768074	+	0.640361i	$0.221215\pi$
$601$			31.3973i			1.28072i	−0.768074	+	0.640361i	$0.778785\pi$
$602$	−5.21248	+	10.5172i	−0.212445	+	0.428648i
$603$		0			0
$604$	−15.7361	−	20.6771i	−0.640292	−	0.841340i
$605$	−28.6607	−	28.6607i	−1.16522	−	1.16522i
$606$		0			0
$607$	39.9895			1.62312			0.811562	−	0.584266i	$-0.198618\pi$
$607$	39.9895			1.62312			0.811562	+	0.584266i	$0.198618\pi$
$608$	19.3956	+	17.3531i	0.786595	+	0.703759i
$609$		0			0
$610$	−4.25920	−	12.6295i	−0.172450	−	0.511354i
$611$	21.4441	+	21.4441i	0.867534	+	0.867534i
$612$		0			0
$613$	−3.66083	+	3.66083i	−0.147860	+	0.147860i	−0.777161	−	0.629302i	$-0.783341\pi$
$613$	−3.66083	+	3.66083i	−0.147860	+	0.147860i	0.629302	+	0.777161i	$0.283341\pi$
$614$	−10.7170	+	21.6236i	−0.432504	+	0.872659i
$615$		0			0
$616$	0.639720	+	3.31928i	0.0257751	+	0.133738i
$617$		−	7.19026i		−	0.289469i	−0.989471	−	0.144735i	$-0.953767\pi$
$617$		−	7.19026i		−	0.289469i	0.989471	−	0.144735i	$-0.0462328\pi$
$618$		0			0
$619$	−8.01743	+	8.01743i	−0.322248	+	0.322248i	−0.849629	−	0.527381i	$-0.823174\pi$
$619$	−8.01743	+	8.01743i	−0.322248	+	0.322248i	0.527381	+	0.849629i	$0.323174\pi$
$620$	−11.6839	+	86.1046i	−0.469235	+	3.45805i
$621$		0			0
$622$	−29.2012	+	9.84785i	−1.17086	+	0.394863i
$623$	−20.8808			−0.836572
$624$		0			0
$625$	−47.8248			−1.91299
$626$	−39.6543	+	13.3731i	−1.58491	+	0.534497i
$627$		0			0
$628$	15.6302	+	2.12091i	0.623711	+	0.0846337i
$629$	22.0470	−	22.0470i	0.879072	−	0.879072i
$630$		0			0
$631$		−	12.0416i		−	0.479370i	−0.970851	−	0.239685i	$-0.922956\pi$
$631$		−	12.0416i		−	0.479370i	0.970851	−	0.239685i	$-0.0770442\pi$
$632$	−21.0624	−	14.2556i	−0.837818	−	0.567058i
$633$		0			0
$634$	6.44444	−	13.0029i	0.255942	−	0.516411i
$635$	−44.9971	+	44.9971i	−1.78565	+	1.78565i
$636$		0			0
$637$	−12.8195	−	12.8195i	−0.507926	−	0.507926i
$638$	2.70439	+	8.01914i	0.107068	+	0.317481i
$639$		0			0
$640$	3.63073	−	45.6623i	0.143517	−	1.80496i
$641$	25.0039			0.987595			0.493798	−	0.869577i	$-0.335608\pi$
$641$	25.0039			0.987595			0.493798	+	0.869577i	$0.335608\pi$
$642$		0			0
$643$	−21.4045	−	21.4045i	−0.844110	−	0.844110i	0.145281	−	0.989390i	$-0.453592\pi$
$643$	−21.4045	−	21.4045i	−0.844110	−	0.844110i	−0.989390	+	0.145281i	$0.953592\pi$
$644$	−5.24289	+	3.99004i	−0.206599	+	0.157229i
$645$		0			0
$646$	15.8084	−	31.8965i	0.621974	−	1.25495i
$647$		−	27.5610i		−	1.08354i	−0.840528	−	0.541768i	$-0.817755\pi$
$647$		−	27.5610i		−	1.08354i	0.840528	−	0.541768i	$-0.182245\pi$
$648$		0			0
$649$			4.07454i			0.159940i
$650$	−47.1069	−	23.3469i	−1.84768	−	0.915742i
$651$		0			0
$652$	18.9870	+	2.57641i	0.743587	+	0.100900i
$653$	−9.98807	−	9.98807i	−0.390863	−	0.390863i	0.484132	−	0.874995i	$-0.339136\pi$
$653$	−9.98807	−	9.98807i	−0.390863	−	0.390863i	−0.874995	+	0.484132i	$0.839136\pi$
$654$		0			0
$655$	−19.9542			−0.779674
$656$	−3.04843	−	0.842824i	−0.119021	−	0.0329067i
$657$		0			0
$658$	−14.9669	+	5.04746i	−0.583470	+	0.196771i
$659$	0.498011	+	0.498011i	0.0193998	+	0.0193998i	0.716740	−	0.697340i	$-0.245633\pi$
$659$	0.498011	+	0.498011i	0.0193998	+	0.0193998i	−0.697340	+	0.716740i	$0.745633\pi$
$660$		0			0
$661$	23.7210	−	23.7210i	0.922641	−	0.922641i	−0.0745749	−	0.997215i	$-0.523760\pi$
$661$	23.7210	−	23.7210i	0.922641	−	0.922641i	0.997215	+	0.0745749i	$0.0237600\pi$
$662$	−1.68109	−	0.833172i	−0.0653372	−	0.0323822i
$663$		0			0
$664$	−2.70698	−	14.0456i	−0.105051	−	0.545074i
$665$			22.3860i			0.868093i
$666$		0			0
$667$	−11.6634	+	11.6634i	−0.451609	+	0.451609i
$668$	17.1816	+	22.5766i	0.664777	+	0.873513i
$669$		0			0
$670$	−19.8442	−	58.8426i	−0.766648	−	2.27329i
$671$	2.31486			0.0893641
$672$		0			0
$673$	−20.2512			−0.780628			−0.390314	−	0.920682i	$-0.627634\pi$
$673$	−20.2512			−0.780628			−0.390314	+	0.920682i	$0.627634\pi$
$674$	1.62814	+	4.82781i	0.0627136	+	0.185960i
$675$		0			0
$676$	2.84785	+	3.74205i	0.109533	+	0.143925i
$677$	−8.50446	+	8.50446i	−0.326853	+	0.326853i	−0.851388	−	0.524536i	$-0.824239\pi$
$677$	−8.50446	+	8.50446i	−0.326853	+	0.326853i	0.524536	+	0.851388i	$0.324239\pi$
$678$		0			0
$679$		−	5.42470i		−	0.208181i
$680$	−61.5247	+	11.8576i	−2.35936	+	0.454717i
$681$		0			0
$682$	−13.5220	−	6.70171i	−0.517784	−	0.256622i
$683$	−16.6360	+	16.6360i	−0.636558	+	0.636558i	−0.949705	−	0.313147i	$-0.898617\pi$
$683$	−16.6360	+	16.6360i	−0.636558	+	0.636558i	0.313147	+	0.949705i	$0.398617\pi$
$684$		0			0
$685$	8.33621	+	8.33621i	0.318510	+	0.318510i
$686$	20.2208	−	6.81931i	0.772035	−	0.260362i
$687$		0			0
$688$	13.6222	+	24.0330i	0.519341	+	0.916250i
$689$	20.9756			0.799107
$690$		0			0
$691$	−36.9863	−	36.9863i	−1.40703	−	1.40703i	−0.774708	−	0.632319i	$-0.782103\pi$
$691$	−36.9863	−	36.9863i	−1.40703	−	1.40703i	−0.632319	−	0.774708i	$-0.717897\pi$
$692$	40.5696	+	5.50504i	1.54222	+	0.209270i
$693$		0			0
$694$	−15.4087	−	7.63682i	−0.584908	−	0.289890i
$695$		−	21.7726i		−	0.825883i
$696$		0			0
$697$			4.32627i			0.163869i
$698$	−6.87660	+	13.8749i	−0.260283	+	0.525171i
$699$		0			0
$700$	21.7903	−	16.5833i	0.823598	−	0.626789i
$701$	7.43119	+	7.43119i	0.280672	+	0.280672i	0.833377	−	0.552705i	$-0.186404\pi$
$701$	7.43119	+	7.43119i	0.280672	+	0.280672i	−0.552705	+	0.833377i	$0.686404\pi$
$702$		0			0
$703$	−26.2170			−0.988793
$704$	7.31325	+	3.13181i	0.275628	+	0.118034i
$705$		0			0
$706$	4.51445	+	13.3864i	0.169903	+	0.503803i
$707$	−3.04607	−	3.04607i	−0.114559	−	0.114559i
$708$		0			0
$709$	−8.34792	+	8.34792i	−0.313513	+	0.313513i	−0.846269	−	0.532756i	$-0.821156\pi$
$709$	−8.34792	+	8.34792i	−0.313513	+	0.313513i	0.532756	+	0.846269i	$0.321156\pi$
$710$	4.14143	−	8.35613i	0.155425	−	0.313600i
$711$		0			0
$712$	−27.5450	+	40.6972i	−1.03229	+	1.52519i
$713$		−	29.4143i		−	1.10157i
$714$		0			0
$715$	9.29051	−	9.29051i	0.347445	−	0.347445i
$716$	−18.3223	−	2.48622i	−0.684736	−	0.0929143i
$717$		0			0
$718$	−1.48871	+	0.502055i	−0.0555581	+	0.0187365i
$719$	11.9929			0.447260			0.223630	−	0.974674i	$-0.428209\pi$
$719$	11.9929			0.447260			0.223630	+	0.974674i	$0.428209\pi$
$720$		0			0
$721$	20.4263			0.760717
$722$	−2.90282	+	0.978951i	−0.108032	+	0.0364328i
$723$		0			0
$724$	0.139135	−	1.02536i	0.00517092	−	0.0381073i
$725$	48.4752	−	48.4752i	1.80032	−	1.80032i
$726$		0			0
$727$			8.28631i			0.307322i	0.988124	+	0.153661i	$0.0491064\pi$
$727$			8.28631i			0.307322i	−0.988124	+	0.153661i	$0.950894\pi$
$728$	10.8920	−	2.09921i	0.403686	−	0.0778019i
$729$		0			0
$730$	−4.29721	+	8.67045i	−0.159047	+	0.320908i
$731$	26.7198	−	26.7198i	0.988267	−	0.988267i
$732$		0			0
$733$	−4.17925	−	4.17925i	−0.154364	−	0.154364i	0.625700	−	0.780064i	$-0.284814\pi$
$733$	−4.17925	−	4.17925i	−0.154364	−	0.154364i	−0.780064	+	0.625700i	$0.784814\pi$
$734$	−10.0666	−	29.8499i	−0.371566	−	1.10178i
$735$		0			0
$736$	0.860510	+	15.4820i	0.0317188	+	0.570674i
$737$	10.7852			0.397280
$738$		0			0
$739$	18.2256	+	18.2256i	0.670439	+	0.670439i	0.957817	−	0.287378i	$-0.0927835\pi$
$739$	18.2256	+	18.2256i	0.670439	+	0.670439i	−0.287378	+	0.957817i	$0.592784\pi$
$740$	27.9450	+	36.7196i	1.02728	+	1.34984i
$741$		0			0
$742$	−4.85137	+	9.78857i	−0.178099	+	0.359350i
$743$		−	25.9472i		−	0.951910i	−0.879470	−	0.475955i	$-0.842103\pi$
$743$		−	25.9472i		−	0.951910i	0.879470	−	0.475955i	$-0.157897\pi$
$744$		0			0
$745$		−	63.3611i		−	2.32137i
$746$	−44.4455	−	22.0279i	−1.62727	−	0.806499i
$747$		0			0
$748$	1.46324	−	10.7834i	0.0535012	−	0.394279i
$749$	−6.09249	−	6.09249i	−0.222615	−	0.222615i
$750$		0			0
$751$	−23.1219			−0.843729			−0.421864	−	0.906659i	$-0.638624\pi$
$751$	−23.1219			−0.843729			−0.421864	+	0.906659i	$0.638624\pi$
$752$	−9.90600	+	35.8292i	−0.361235	+	1.30656i
$753$		0			0
$754$	26.3144	−	8.87432i	0.958314	−	0.323184i
$755$	−37.1948	−	37.1948i	−1.35366	−	1.35366i
$756$		0			0
$757$	30.8635	−	30.8635i	1.12175	−	1.12175i	0.130275	−	0.991478i	$-0.458414\pi$
$757$	30.8635	−	30.8635i	1.12175	−	1.12175i	0.991478	−	0.130275i	$-0.0415859\pi$
$758$	23.0585	+	11.4282i	0.837523	+	0.415090i
$759$		0			0
$760$	43.6309	+	29.5306i	1.58266	+	1.07119i
$761$			26.6200i			0.964976i	0.875903	+	0.482488i	$0.160267\pi$
$761$			26.6200i			0.964976i	−0.875903	+	0.482488i	$0.839733\pi$
$762$		0			0
$763$	−2.89882	+	2.89882i	−0.104944	+	0.104944i
$764$	−12.8586	+	9.78587i	−0.465207	+	0.354040i
$765$		0			0
$766$	−1.90015	−	5.63438i	−0.0686551	−	0.203578i
$767$	13.3704			0.482777
$768$		0			0
$769$	−1.37452			−0.0495666			−0.0247833	−	0.999693i	$-0.507890\pi$
$769$	−1.37452			−0.0495666			−0.0247833	+	0.999693i	$0.507890\pi$
$770$	2.18678	+	6.48432i	0.0788062	+	0.233679i
$771$		0			0
$772$	−12.9931	+	9.88826i	−0.467632	+	0.355886i
$773$	18.8749	−	18.8749i	0.678882	−	0.678882i	−0.280865	−	0.959747i	$-0.590621\pi$
$773$	18.8749	−	18.8749i	0.678882	−	0.678882i	0.959747	+	0.280865i	$0.0906213\pi$
$774$		0			0
$775$			122.251i			4.39139i
$776$	−10.5729	−	7.15601i	−0.379544	−	0.256886i
$777$		0			0
$778$	18.5352	+	9.18636i	0.664521	+	0.329347i
$779$	2.57227	−	2.57227i	0.0921613	−	0.0921613i
$780$		0			0
$781$	1.14534	+	1.14534i	0.0409834	+	0.0409834i
$782$	20.0978	−	6.77783i	0.718697	−	0.242375i
$783$		0			0
$784$	5.92191	−	21.4191i	0.211497	−	0.764967i
$785$	31.9313			1.13968
$786$		0			0
$787$	31.9033	+	31.9033i	1.13723	+	1.13723i	0.988945	+	0.148285i	$0.0473752\pi$
$787$	31.9033	+	31.9033i	1.13723	+	1.13723i	0.148285	+	0.988945i	$0.452625\pi$
$788$	−3.12583	+	23.0360i	−0.111353	+	0.820622i
$789$		0			0
$790$	−46.1314	−	22.8635i	−1.64128	−	0.813446i
$791$			19.2332i			0.683854i
$792$		0			0
$793$		−	7.59610i		−	0.269745i
$794$	13.2827	−	26.8004i	0.471386	−	0.951112i
$795$		0			0
$796$	18.1701	+	23.8754i	0.644021	+	0.846240i
$797$	9.18820	+	9.18820i	0.325463	+	0.325463i	0.850858	−	0.525395i	$-0.176083\pi$
$797$	9.18820	+	9.18820i	0.325463	+	0.325463i	−0.525395	+	0.850858i	$0.676083\pi$
$798$		0			0
$799$	50.8482			1.79888
$800$	−3.57643	−	64.3458i	−0.126446	−	2.27497i
$801$		0			0
$802$	−2.63282	−	7.80692i	−0.0929681	−	0.275672i
$803$	−1.18842	−	1.18842i	−0.0419384	−	0.0419384i
$804$		0			0
$805$	−9.43110	+	9.43110i	−0.332403	+	0.332403i
$806$	−21.9913	+	44.3717i	−0.774612	+	1.56293i
$807$		0			0
$808$	−9.95511	+	1.91863i	−0.350220	+	0.0674973i
$809$		−	49.4434i		−	1.73834i	−0.494517	−	0.869168i	$-0.664655\pi$
$809$		−	49.4434i		−	1.73834i	0.494517	−	0.869168i	$-0.335345\pi$
$810$		0			0
$811$	−17.1895	+	17.1895i	−0.603607	+	0.603607i	−0.941268	−	0.337661i	$-0.890364\pi$
$811$	−17.1895	+	17.1895i	−0.603607	+	0.603607i	0.337661	+	0.941268i	$0.390364\pi$
$812$	−1.94483	+	14.3325i	−0.0682502	+	0.502972i
$813$		0			0
$814$	−7.59399	+	2.56101i	−0.266169	+	0.0897634i
$815$	38.7890			1.35872
$816$		0			0
$817$	−31.7736			−1.11162
$818$	5.09309	−	1.71760i	0.178076	−	0.0600546i
$819$		0			0
$820$	−6.34454	−	0.860915i	−0.221561	−	0.0300644i
$821$	26.9841	−	26.9841i	0.941750	−	0.941750i	−0.0566444	−	0.998394i	$-0.518040\pi$
$821$	26.9841	−	26.9841i	0.941750	−	0.941750i	0.998394	+	0.0566444i	$0.0180401\pi$
$822$		0			0
$823$		−	24.8761i		−	0.867126i	−0.901123	−	0.433563i	$-0.857256\pi$
$823$		−	24.8761i		−	0.867126i	0.901123	−	0.433563i	$-0.142744\pi$
$824$	26.9455	−	39.8115i	0.938691	−	1.38690i
$825$		0			0
$826$	−3.09239	+	6.23949i	−0.107598	+	0.217099i
$827$	−10.5355	+	10.5355i	−0.366354	+	0.366354i	−0.866146	−	0.499792i	$-0.833410\pi$
$827$	−10.5355	+	10.5355i	−0.366354	+	0.366354i	0.499792	+	0.866146i	$0.333410\pi$
$828$		0			0
$829$	−6.15536	−	6.15536i	−0.213785	−	0.213785i	0.592088	−	0.805873i	$-0.298304\pi$
$829$	−6.15536	−	6.15536i	−0.213785	−	0.213785i	−0.805873	+	0.592088i	$0.798304\pi$
$830$	−9.25340	−	27.4385i	−0.321190	−	0.952404i
$831$		0			0
$832$	10.2769	−	23.9981i	0.356287	−	0.831983i
$833$	−30.3975			−1.05321
$834$		0			0
$835$	40.6116	+	40.6116i	1.40542	+	1.40542i
$836$	−7.28147	+	5.54148i	−0.251835	+	0.191656i
$837$		0			0
$838$	−22.8356	+	46.0752i	−0.788843	+	1.59164i
$839$			57.7447i			1.99357i	0.0801365	+	0.996784i	$0.474464\pi$
$839$			57.7447i			1.99357i	−0.0801365	+	0.996784i	$0.525536\pi$
$840$		0			0
$841$			7.21084i			0.248650i
$842$	−17.9404	−	8.89156i	−0.618268	−	0.306423i
$843$		0			0
$844$	32.0485	+	4.34878i	1.10316	+	0.149691i
$845$	6.73135	+	6.73135i	0.231565	+	0.231565i
$846$		0			0
$847$	12.0314			0.413403
$848$	12.6785	+	22.3681i	0.435380	+	0.768122i
$849$		0			0
$850$	−83.5301	+	28.1698i	−2.86506	+	0.966217i
$851$	−11.0451	−	11.0451i	−0.378620	−	0.378620i
$852$		0			0
$853$	−3.07436	+	3.07436i	−0.105264	+	0.105264i	−0.757777	−	0.652513i	$-0.773715\pi$
$853$	−3.07436	+	3.07436i	−0.105264	+	0.105264i	0.652513	+	0.757777i	$0.273715\pi$
$854$	3.54483	+	1.75687i	0.121301	+	0.0601189i
$855$		0			0
$856$	−19.9113	+	3.83748i	−0.680555	+	0.131163i
$857$			29.7745i			1.01708i	0.861039	+	0.508539i	$0.169814\pi$
$857$			29.7745i			1.01708i	−0.861039	+	0.508539i	$0.830186\pi$
$858$		0			0
$859$	17.3519	−	17.3519i	0.592040	−	0.592040i	−0.346142	−	0.938182i	$-0.612509\pi$
$859$	17.3519	−	17.3519i	0.592040	−	0.592040i	0.938182	+	0.346142i	$0.112509\pi$
$860$	33.8678	+	44.5021i	1.15488	+	1.51751i
$861$		0			0
$862$	12.4591	+	36.9442i	0.424360	+	1.25832i
$863$	23.9565			0.815489			0.407745	−	0.913096i	$-0.366315\pi$
$863$	23.9565			0.815489			0.407745	+	0.913096i	$0.366315\pi$
$864$		0			0
$865$	82.8807			2.81803
$866$	−4.35191	−	12.9044i	−0.147884	−	0.438510i
$867$		0			0
$868$	−15.6204	−	20.5251i	−0.530191	−	0.696668i
$869$	6.32302	−	6.32302i	0.214494	−	0.214494i
$870$		0			0
$871$		−	35.3912i		−	1.19919i
$872$	1.82588	+	9.47386i	0.0618322	+	0.320825i
$873$		0			0
$874$	−15.9795	−	7.91968i	−0.540514	−	0.267887i
$875$	21.9940	−	21.9940i	0.743534	−	0.743534i
$876$		0			0
$877$	−17.7397	−	17.7397i	−0.599028	−	0.599028i	0.341026	−	0.940054i	$-0.389226\pi$
$877$	−17.7397	−	17.7397i	−0.599028	−	0.599028i	−0.940054	+	0.341026i	$0.889226\pi$
$878$	1.75456	−	0.591710i	0.0592134	−	0.0199692i
$879$		0			0
$880$	15.5228	+	4.29171i	0.523274	+	0.144674i
$881$	40.5347			1.36565			0.682824	−	0.730583i	$-0.260752\pi$
$881$	40.5347			1.36565			0.682824	+	0.730583i	$0.260752\pi$
$882$		0			0
$883$	10.9584	+	10.9584i	0.368781	+	0.368781i	0.867033	−	0.498252i	$-0.166024\pi$
$883$	10.9584	+	10.9584i	0.368781	+	0.368781i	−0.498252	+	0.867033i	$0.666024\pi$
$884$	−35.3851	−	4.80154i	−1.19013	−	0.161493i
$885$		0			0
$886$	−1.67528	−	0.830295i	−0.0562821	−	0.0278943i
$887$		−	9.45865i		−	0.317591i	−0.987312	−	0.158795i	$-0.949239\pi$
$887$		−	9.45865i		−	0.317591i	0.987312	−	0.158795i	$-0.0507610\pi$
$888$		0			0
$889$		−	18.8892i		−	0.633522i
$890$	−44.1773	+	89.1361i	−1.48083	+	2.98785i
$891$		0			0
$892$	9.85761	−	7.50202i	0.330057	−	0.251186i
$893$	−30.2328	−	30.2328i	−1.01170	−	1.01170i
$894$		0			0
$895$	−37.4311			−1.25118
$896$	8.82214	+	10.3463i	0.294727	+	0.345645i
$897$		0			0
$898$	−12.7496	−	37.8056i	−0.425460	−	1.26159i
$899$	−45.6606	−	45.6606i	−1.52287	−	1.52287i
$900$		0			0
$901$	24.8687	−	24.8687i	0.828496	−	0.828496i
$902$	0.493810	−	0.996356i	0.0164421	−	0.0331750i
$903$		0			0
$904$	37.4860	+	25.3716i	1.24677	+	0.843846i
$905$		−	2.09474i		−	0.0696317i
$906$		0			0
$907$	−21.0020	+	21.0020i	−0.697359	+	0.697359i	−0.963840	−	0.266481i	$-0.914139\pi$
$907$	−21.0020	+	21.0020i	−0.697359	+	0.697359i	0.266481	+	0.963840i	$0.414139\pi$
$908$	−26.4024	−	3.58263i	−0.876193	−	0.118894i
$909$		0			0
$910$	21.2780	−	7.17582i	0.705358	−	0.237876i
$911$	33.9604			1.12516			0.562580	−	0.826743i	$-0.309809\pi$
$911$	33.9604			1.12516			0.562580	+	0.826743i	$0.309809\pi$
$912$		0			0
$913$	5.02919			0.166442
$914$	−10.3091	+	3.47665i	−0.340993	+	0.114997i
$915$		0			0
$916$	−1.34140	+	9.88551i	−0.0443211	+	0.326626i
$917$	4.18824	−	4.18824i	0.138308	−	0.138308i
$918$		0			0
$919$		−	25.0230i		−	0.825433i	−0.910859	−	0.412717i	$-0.864580\pi$
$919$		−	25.0230i		−	0.825433i	0.910859	−	0.412717i	$-0.135420\pi$
$920$	5.94038	+	30.8225i	0.195849	+	1.01619i
$921$		0			0
$922$	13.1016	−	26.4350i	0.431478	−	0.870590i
$923$	3.75837	−	3.75837i	0.123708	−	0.123708i
$924$		0			0
$925$	45.9052	+	45.9052i	1.50935	+	1.50935i
$926$	9.94885	+	29.5006i	0.326940	+	0.969451i
$927$		0			0
$928$	25.3689	+	22.6973i	0.832774	+	0.745075i
$929$	−46.3294			−1.52002			−0.760010	−	0.649912i	$-0.774806\pi$
$929$	−46.3294			−1.52002			−0.760010	+	0.649912i	$0.774806\pi$
$930$		0			0
$931$	18.0735	+	18.0735i	0.592335	+	0.592335i
$932$	6.15530	+	8.08803i	0.201624	+	0.264932i
$933$		0			0
$934$	−14.4325	+	29.1204i	−0.472246	+	0.952847i
$935$		−	22.0297i		−	0.720447i
$936$		0			0
$937$		−	47.9416i		−	1.56618i	−0.621907	−	0.783091i	$-0.713642\pi$
$937$		−	47.9416i		−	1.56618i	0.621907	−	0.783091i	$-0.286358\pi$
$938$	16.5158	+	8.18551i	0.539261	+	0.267266i
$939$		0			0
$940$	−10.1186	+	74.5696i	−0.330033	+	2.43219i
$941$	−4.17064	−	4.17064i	−0.135959	−	0.135959i	0.635852	−	0.771811i	$-0.280649\pi$
$941$	−4.17064	−	4.17064i	−0.135959	−	0.135959i	−0.771811	+	0.635852i	$0.780649\pi$
$942$		0			0
$943$	2.16737			0.0705792
$944$	8.08158	+	14.2580i	0.263033	+	0.464058i
$945$		0			0
$946$	−9.20351	+	3.10381i	−0.299232	+	0.100914i
$947$	26.5689	+	26.5689i	0.863372	+	0.863372i	0.991728	−	0.128356i	$-0.0409700\pi$
$947$	26.5689	+	26.5689i	0.863372	+	0.863372i	−0.128356	+	0.991728i	$0.540970\pi$
$948$		0			0
$949$	−3.89974	+	3.89974i	−0.126591	+	0.126591i
$950$	66.4135	+	32.9156i	2.15474	+	1.06792i
$951$		0			0
$952$	10.4248	−	15.4024i	0.337869	−	0.499196i
$953$			18.8502i			0.610618i	0.952253	+	0.305309i	$0.0987597\pi$
$953$			18.8502i			0.610618i	−0.952253	+	0.305309i	$0.901240\pi$
$954$		0			0
$955$	−23.1305	+	23.1305i	−0.748485	+	0.748485i
$956$	−5.03548	+	3.83220i	−0.162859	+	0.123942i
$957$		0			0
$958$	−4.28277	−	12.6994i	−0.138370	−	0.410299i
$959$	−3.49943			−0.113002
$960$		0			0
$961$	84.1527			2.71460
$962$	8.40384	+	24.9193i	0.270951	+	0.803431i
$963$		0			0
$964$	10.9259	−	8.31500i	0.351899	−	0.267808i
$965$	−23.3725	+	23.3725i	−0.752388	+	0.752388i
$966$		0			0
$967$			45.5429i			1.46456i	0.681003	+	0.732280i	$0.261544\pi$
$967$			45.5429i			1.46456i	−0.681003	+	0.732280i	$0.738456\pi$
$968$	15.8712	−	23.4494i	0.510120	−	0.753693i
$969$		0			0
$970$	−23.1570	−	11.4770i	−0.743526	−	0.368503i
$971$	−17.7282	+	17.7282i	−0.568926	+	0.568926i	−0.931828	−	0.362901i	$-0.881786\pi$
$971$	−17.7282	+	17.7282i	−0.568926	+	0.568926i	0.362901	+	0.931828i	$0.381786\pi$
$972$		0			0
$973$	4.56993	+	4.56993i	0.146505	+	0.146505i
$974$	11.0821	−	3.73735i	0.355094	−	0.119752i
$975$		0			0
$976$	8.10036	−	4.59137i	0.259286	−	0.146966i
$977$	32.1971			1.03008			0.515038	−	0.857167i	$-0.327778\pi$
$977$	32.1971			1.03008			0.515038	+	0.857167i	$0.327778\pi$
$978$		0			0
$979$	−12.2175	−	12.2175i	−0.390472	−	0.390472i
$980$	6.04902	−	44.5785i	0.193229	−	1.42401i
$981$		0			0
$982$	52.3202	+	25.9307i	1.66960	+	0.827482i
$983$		−	56.6335i		−	1.80633i	−0.429295	−	0.903164i	$-0.641238\pi$
$983$		−	56.6335i		−	1.80633i	0.429295	−	0.903164i	$-0.358762\pi$
$984$		0			0
$985$			47.0608i			1.49948i
$986$	20.6770	−	41.7198i	0.658489	−	1.32863i
$987$		0			0
$988$	18.1841	+	23.8938i	0.578513	+	0.760163i
$989$	−13.3860	−	13.3860i	−0.425651	−	0.425651i
$990$		0			0
$991$	−50.9465			−1.61837			−0.809184	−	0.587555i	$-0.800090\pi$
$991$	−50.9465			−1.61837			−0.809184	+	0.587555i	$0.800090\pi$
$992$	−60.6097	+	3.36877i	−1.92436	+	0.106959i
$993$		0			0
$994$	0.884637	+	2.62315i	0.0280590	+	0.0832014i
$995$	42.9479	+	42.9479i	1.36154	+	1.36154i
$996$		0			0
$997$	−31.9397	+	31.9397i	−1.01154	+	1.01154i	−0.0116071	+	0.999933i	$0.503695\pi$
$997$	−31.9397	+	31.9397i	−1.01154	+	1.01154i	−0.999933	+	0.0116071i	$0.996305\pi$
$998$	6.98663	−	14.0969i	0.221158	−	0.446229i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.10	yes	32
3.2	odd	2	inner	432.2.k.d.109.7	✓	32
4.3	odd	2		1728.2.k.d.1297.1		32
12.11	even	2		1728.2.k.d.1297.16		32
16.5	even	4	inner	432.2.k.d.325.10	yes	32
16.11	odd	4		1728.2.k.d.433.1		32
48.5	odd	4	inner	432.2.k.d.325.7	yes	32
48.11	even	4		1728.2.k.d.433.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.7	✓	32	3.2	odd	2	inner
432.2.k.d.109.10	yes	32	1.1	even	1	trivial
432.2.k.d.325.7	yes	32	48.5	odd	4	inner
432.2.k.d.325.10	yes	32	16.5	even	4	inner
1728.2.k.d.433.1		32	16.11	odd	4
1728.2.k.d.433.16		32	48.11	even	4
1728.2.k.d.1297.1		32	4.3	odd	2
1728.2.k.d.1297.16		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.451925 + 1.34006i) q^{2} +(-1.59153 + 1.21121i) q^{4} +(-2.86290 + 2.86290i) q^{5} -1.20181i q^{7} +(-2.34235 - 1.58537i) q^{8} +O(q^{10})\)	\(q+(0.451925 + 1.34006i) q^{2} +(-1.59153 + 1.21121i) q^{4} +(-2.86290 + 2.86290i) q^{5} -1.20181i q^{7} +(-2.34235 - 1.58537i) q^{8} +(-5.13028 - 2.54265i) q^{10} +(0.703184 - 0.703184i) q^{11} +(-2.30746 - 2.30746i) q^{13} +(1.61049 - 0.543126i) q^{14} +(1.06592 - 3.85536i) q^{16} -5.47145 q^{17} +(3.25317 + 3.25317i) q^{19} +(1.08880 - 8.02397i) q^{20} +(1.26010 + 0.624523i) q^{22} +2.74108i q^{23} -11.3924i q^{25} +(2.04934 - 4.13494i) q^{26} +(1.45564 + 1.91271i) q^{28} +(4.25505 + 4.25505i) q^{29} -10.7309 q^{31} +(5.64814 - 0.313931i) q^{32} +(-2.47269 - 7.33208i) q^{34} +(3.44065 + 3.44065i) q^{35} +(-4.02946 + 4.02946i) q^{37} +(-2.88926 + 5.82963i) q^{38} +(11.2447 - 2.16717i) q^{40} -0.790699i q^{41} +(-4.88349 + 4.88349i) q^{43} +(-0.267431 + 1.97084i) q^{44} +(-3.67321 + 1.23876i) q^{46} -9.29335 q^{47} +5.55566 q^{49} +(15.2665 - 5.14851i) q^{50} +(6.46722 + 0.877561i) q^{52} +(-4.54517 + 4.54517i) q^{53} +4.02629i q^{55} +(-1.90531 + 2.81505i) q^{56} +(-3.77906 + 7.62498i) q^{58} +(-2.89721 + 2.89721i) q^{59} +(1.64598 + 1.64598i) q^{61} +(-4.84957 - 14.3801i) q^{62} +(2.97322 + 7.42698i) q^{64} +13.2121 q^{65} +(7.66887 + 7.66887i) q^{67} +(8.70797 - 6.62710i) q^{68} +(-3.05577 + 6.16560i) q^{70} +1.62879i q^{71} -1.69005i q^{73} +(-7.22073 - 3.57871i) q^{74} +(-9.11778 - 1.23723i) q^{76} +(-0.845091 - 0.845091i) q^{77} +8.99199 q^{79} +(7.98588 + 14.0891i) q^{80} +(1.05958 - 0.357336i) q^{82} +(3.57601 + 3.57601i) q^{83} +(15.6642 - 15.6642i) q^{85} +(-8.75114 - 4.33720i) q^{86} +(-2.76191 + 0.532299i) q^{88} -17.3745i q^{89} +(-2.77312 + 2.77312i) q^{91} +(-3.32003 - 4.36250i) q^{92} +(-4.19990 - 12.4537i) q^{94} -18.6270 q^{95} +4.51379 q^{97} +(2.51074 + 7.44493i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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