LMFDB - Embedded newform 216.2.q.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	216.121
Dual form			216.2.q.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05517 - 1.37354i) q^{3} +(-1.80911 - 1.51802i) q^{5} +(-3.12406 - 1.13706i) q^{7} +(-0.773215 - 2.89864i) q^{9} +O(q^{10})$	\(q+(1.05517 - 1.37354i) q^{3} +(-1.80911 - 1.51802i) q^{5} +(-3.12406 - 1.13706i) q^{7} +(-0.773215 - 2.89864i) q^{9} +(5.01156 - 4.20520i) q^{11} +(-0.627873 + 3.56084i) q^{13} +(-3.99399 + 0.883103i) q^{15} +(-0.719665 + 1.24650i) q^{17} +(2.42709 + 4.20384i) q^{19} +(-4.85823 + 3.09121i) q^{21} +(5.79603 - 2.10958i) q^{23} +(0.100243 + 0.568505i) q^{25} +(-4.79728 - 1.99653i) q^{27} +(-0.256977 - 1.45739i) q^{29} +(7.89572 - 2.87381i) q^{31} +(-0.487932 - 11.3208i) q^{33} +(3.92567 + 6.79947i) q^{35} +(-3.22636 + 5.58822i) q^{37} +(4.22844 + 4.61972i) q^{39} +(-0.539230 + 3.05812i) q^{41} +(-1.55533 + 1.30508i) q^{43} +(-3.00138 + 6.41772i) q^{45} +(-2.20272 - 0.801724i) q^{47} +(3.10451 + 2.60500i) q^{49} +(0.952739 + 2.30376i) q^{51} +6.20938 q^{53} -15.4501 q^{55} +(8.33513 + 1.10208i) q^{57} +(-4.52715 - 3.79873i) q^{59} +(2.85327 + 1.03850i) q^{61} +(-0.880377 + 9.93473i) q^{63} +(6.54133 - 5.48883i) q^{65} +(-1.08536 + 6.15538i) q^{67} +(3.21823 - 10.1870i) q^{69} +(-0.303323 + 0.525370i) q^{71} +(7.34739 + 12.7261i) q^{73} +(0.886636 + 0.462184i) q^{75} +(-20.4380 + 7.43883i) q^{77} +(-1.88041 - 10.6644i) q^{79} +(-7.80428 + 4.48255i) q^{81} +(0.963693 + 5.46537i) q^{83} +(3.19417 - 1.16258i) q^{85} +(-2.27293 - 1.18483i) q^{87} +(-3.09653 - 5.36334i) q^{89} +(6.01042 - 10.4103i) q^{91} +(4.38407 - 13.8774i) q^{93} +(1.99066 - 11.2896i) q^{95} +(7.43542 - 6.23906i) q^{97} +(-16.0644 - 11.2752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.05517	−	1.37354i	0.609205	−	0.793013i
$3$	1.05517	−	1.37354i	0.609205	−	0.793013i
$4$		0			0
$5$	−1.80911	−	1.51802i	−0.809059	−	0.678881i	0.141324	−	0.989963i	$-0.454864\pi$
$5$	−1.80911	−	1.51802i	−0.809059	−	0.678881i	−0.950383	+	0.311083i	$0.899308\pi$
$6$		0			0
$7$	−3.12406	−	1.13706i	−1.18078	−	0.429770i	−0.324305	−	0.945953i	$-0.605130\pi$
$7$	−3.12406	−	1.13706i	−1.18078	−	0.429770i	−0.856478	+	0.516183i	$0.827353\pi$
$8$		0			0
$9$	−0.773215	−	2.89864i	−0.257738	−	0.966215i
$10$		0			0
$11$	5.01156	−	4.20520i	1.51104	−	1.26792i	0.649347	−	0.760492i	$-0.275042\pi$
$11$	5.01156	−	4.20520i	1.51104	−	1.26792i	0.861696	−	0.507424i	$-0.169402\pi$
$12$		0			0
$13$	−0.627873	+	3.56084i	−0.174141	+	0.987600i	0.764991	+	0.644041i	$0.222744\pi$
$13$	−0.627873	+	3.56084i	−0.174141	+	0.987600i	−0.939131	+	0.343559i	$0.888368\pi$
$14$		0			0
$15$	−3.99399	+	0.883103i	−1.03124	+	0.228016i
$16$		0			0
$17$	−0.719665	+	1.24650i	−0.174544	+	0.302320i	−0.940004	−	0.341165i	$-0.889179\pi$
$17$	−0.719665	+	1.24650i	−0.174544	+	0.302320i	0.765459	+	0.643485i	$0.222512\pi$
$18$		0			0
$19$	2.42709	+	4.20384i	0.556812	+	0.964427i	0.997760	+	0.0668941i	$0.0213090\pi$
$19$	2.42709	+	4.20384i	0.556812	+	0.964427i	−0.440948	+	0.897533i	$0.645358\pi$
$20$		0			0
$21$	−4.85823	+	3.09121i	−1.06015	+	0.674558i
$22$		0			0
$23$	5.79603	−	2.10958i	1.20856	−	0.439878i	0.342353	−	0.939571i	$-0.388776\pi$
$23$	5.79603	−	2.10958i	1.20856	−	0.439878i	0.866202	+	0.499693i	$0.166554\pi$
$24$		0			0
$25$	0.100243	+	0.568505i	0.0200485	+	0.113701i
$26$		0			0
$27$	−4.79728	−	1.99653i	−0.923236	−	0.384233i
$28$		0			0
$29$	−0.256977	−	1.45739i	−0.0477194	−	0.270630i	0.951607	−	0.307316i	$-0.0994310\pi$
$29$	−0.256977	−	1.45739i	−0.0477194	−	0.270630i	−0.999327	+	0.0366861i	$0.988320\pi$
$30$		0			0
$31$	7.89572	−	2.87381i	1.41811	−	0.516151i	0.484613	−	0.874729i	$-0.338960\pi$
$31$	7.89572	−	2.87381i	1.41811	−	0.516151i	0.933500	+	0.358578i	$0.116738\pi$
$32$		0			0
$33$	−0.487932	−	11.3208i	−0.0849381	−	1.97070i
$34$		0			0
$35$	3.92567	+	6.79947i	0.663560	+	1.14932i
$36$		0			0
$37$	−3.22636	+	5.58822i	−0.530410	+	0.918697i	0.468961	+	0.883219i	$0.344629\pi$
$37$	−3.22636	+	5.58822i	−0.530410	+	0.918697i	−0.999370	+	0.0354779i	$0.988705\pi$
$38$		0			0
$39$	4.22844	+	4.61972i	0.677092	+	0.739747i
$40$		0			0
$41$	−0.539230	+	3.05812i	−0.0842135	+	0.477599i	0.913310	+	0.407265i	$0.133517\pi$
$41$	−0.539230	+	3.05812i	−0.0842135	+	0.477599i	−0.997524	+	0.0703336i	$0.977594\pi$
$42$		0			0
$43$	−1.55533	+	1.30508i	−0.237186	+	0.199023i	−0.753631	−	0.657298i	$-0.771699\pi$
$43$	−1.55533	+	1.30508i	−0.237186	+	0.199023i	0.516445	+	0.856320i	$0.327255\pi$
$44$		0			0
$45$	−3.00138	+	6.41772i	−0.447419	+	0.956698i
$46$		0			0
$47$	−2.20272	−	0.801724i	−0.321299	−	0.116943i	0.176335	−	0.984330i	$-0.443576\pi$
$47$	−2.20272	−	0.801724i	−0.321299	−	0.116943i	−0.497635	+	0.867387i	$0.665798\pi$
$48$		0			0
$49$	3.10451	+	2.60500i	0.443502	+	0.372142i
$50$		0			0
$51$	0.952739	+	2.30376i	0.133410	+	0.322591i
$52$		0			0
$53$	6.20938			0.852923			0.426462	−	0.904506i	$-0.359760\pi$
$53$	6.20938			0.852923			0.426462	+	0.904506i	$0.359760\pi$
$54$		0			0
$55$	−15.4501			−2.08329
$56$		0			0
$57$	8.33513	+	1.10208i	1.10402	+	0.145975i
$58$		0			0
$59$	−4.52715	−	3.79873i	−0.589384	−	0.494552i	0.298629	−	0.954369i	$-0.403471\pi$
$59$	−4.52715	−	3.79873i	−0.589384	−	0.494552i	−0.888014	+	0.459817i	$0.847915\pi$
$60$		0			0
$61$	2.85327	+	1.03850i	0.365323	+	0.132967i	0.518158	−	0.855285i	$-0.326618\pi$
$61$	2.85327	+	1.03850i	0.365323	+	0.132967i	−0.152835	+	0.988252i	$0.548840\pi$
$62$		0			0
$63$	−0.880377	+	9.93473i	−0.110917	+	1.25166i
$64$		0			0
$65$	6.54133	−	5.48883i	0.811353	−	0.680806i
$66$		0			0
$67$	−1.08536	+	6.15538i	−0.132598	+	0.751999i	0.843905	+	0.536493i	$0.180251\pi$
$67$	−1.08536	+	6.15538i	−0.132598	+	0.751999i	−0.976502	+	0.215506i	$0.930860\pi$
$68$		0			0
$69$	3.21823	−	10.1870i	0.387429	−	1.22638i
$70$		0			0
$71$	−0.303323	+	0.525370i	−0.0359978	+	0.0623500i	−0.883463	−	0.468501i	$-0.844794\pi$
$71$	−0.303323	+	0.525370i	−0.0359978	+	0.0623500i	0.847465	+	0.530851i	$0.178128\pi$
$72$		0			0
$73$	7.34739	+	12.7261i	0.859947	+	1.48947i	0.871978	+	0.489544i	$0.162837\pi$
$73$	7.34739	+	12.7261i	0.859947	+	1.48947i	−0.0120314	+	0.999928i	$0.503830\pi$
$74$		0			0
$75$	0.886636	+	0.462184i	0.102380	+	0.0533684i
$76$		0			0
$77$	−20.4380	+	7.43883i	−2.32913	+	0.847733i
$78$		0			0
$79$	−1.88041	−	10.6644i	−0.211563	−	1.19983i	−0.886772	−	0.462207i	$-0.847058\pi$
$79$	−1.88041	−	10.6644i	−0.211563	−	1.19983i	0.675209	−	0.737627i	$-0.264054\pi$
$80$		0			0
$81$	−7.80428	+	4.48255i	−0.867142	+	0.498061i
$82$		0			0
$83$	0.963693	+	5.46537i	0.105779	+	0.599903i	0.990906	+	0.134554i	$0.0429601\pi$
$83$	0.963693	+	5.46537i	0.105779	+	0.599903i	−0.885127	+	0.465349i	$0.845929\pi$
$84$		0			0
$85$	3.19417	−	1.16258i	0.346456	−	0.126100i
$86$		0			0
$87$	−2.27293	−	1.18483i	−0.243684	−	0.127027i
$88$		0			0
$89$	−3.09653	−	5.36334i	−0.328231	−	0.568513i	0.653930	−	0.756555i	$-0.273119\pi$
$89$	−3.09653	−	5.36334i	−0.328231	−	0.568513i	−0.982161	+	0.188042i	$0.939786\pi$
$90$		0			0
$91$	6.01042	−	10.4103i	0.630063	−	1.09130i
$92$		0			0
$93$	4.38407	−	13.8774i	0.454607	−	1.43902i
$94$		0			0
$95$	1.99066	−	11.2896i	0.204237	−	1.15829i
$96$		0			0
$97$	7.43542	−	6.23906i	0.754953	−	0.633481i	−0.181855	−	0.983325i	$-0.558210\pi$
$97$	7.43542	−	6.23906i	0.754953	−	0.633481i	0.936808	+	0.349845i	$0.113766\pi$
$98$		0			0
$99$	−16.0644	−	11.2752i	−1.61453	−	1.13320i
$100$		0			0
$101$	8.29442	+	3.01892i	0.825326	+	0.300394i	0.719939	−	0.694037i	$-0.244170\pi$
$101$	8.29442	+	3.01892i	0.825326	+	0.300394i	0.105387	+	0.994431i	$0.466392\pi$
$102$		0			0
$103$	−0.0219045	−	0.0183801i	−0.00215832	−	0.00181104i	0.641708	−	0.766949i	$-0.278226\pi$
$103$	−0.0219045	−	0.0183801i	−0.00215832	−	0.00181104i	−0.643866	+	0.765138i	$0.722671\pi$
$104$		0			0
$105$	13.4816	+	1.78256i	1.31567	+	0.173960i
$106$		0			0
$107$	1.29385			0.125081			0.0625407	−	0.998042i	$-0.480080\pi$
$107$	1.29385			0.125081			0.0625407	+	0.998042i	$0.480080\pi$
$108$		0			0
$109$	−11.3393			−1.08611			−0.543055	−	0.839697i	$-0.682733\pi$
$109$	−11.3393			−1.08611			−0.543055	+	0.839697i	$0.682733\pi$
$110$		0			0
$111$	4.27126	+	10.3281i	0.405410	+	0.980297i
$112$		0			0
$113$	−3.16696	−	2.65740i	−0.297923	−	0.249987i	0.481556	−	0.876415i	$-0.340072\pi$
$113$	−3.16696	−	2.65740i	−0.297923	−	0.249987i	−0.779479	+	0.626428i	$0.784516\pi$
$114$		0			0
$115$	−13.6880	−	4.98204i	−1.27642	−	0.464578i
$116$		0			0
$117$	10.8071	−	0.933317i	0.999116	−	0.0862852i
$118$		0			0
$119$	3.66562	−	3.07582i	0.336027	−	0.281960i
$120$		0			0
$121$	5.52193	−	31.3164i	0.501993	−	2.84695i
$122$		0			0
$123$	3.63147	+	3.96751i	0.327439	+	0.357738i
$124$		0			0
$125$	−5.22241	+	9.04548i	−0.467107	+	0.809052i
$126$		0			0
$127$	−1.34468	−	2.32905i	−0.119321	−	0.206670i	0.800178	−	0.599763i	$-0.204738\pi$
$127$	−1.34468	−	2.32905i	−0.119321	−	0.206670i	−0.919499	+	0.393093i	$0.871405\pi$
$128$		0			0
$129$	0.151429	+	3.51339i	0.0133326	+	0.309337i
$130$		0			0
$131$	−15.2427	+	5.54790i	−1.33176	+	0.484723i	−0.907209	−	0.420680i	$-0.861792\pi$
$131$	−15.2427	+	5.54790i	−1.33176	+	0.484723i	−0.424555	+	0.905402i	$0.639569\pi$
$132$		0			0
$133$	−2.80233	−	15.8928i	−0.242993	−	1.37808i
$134$		0			0
$135$	5.64801	+	10.8943i	0.486103	+	0.937634i
$136$		0			0
$137$	−0.369543	−	2.09578i	−0.0315722	−	0.179055i	0.964944	−	0.262457i	$-0.0845326\pi$
$137$	−0.369543	−	2.09578i	−0.0315722	−	0.179055i	−0.996516	+	0.0834017i	$0.973422\pi$
$138$		0			0
$139$	11.7355	−	4.27136i	0.995389	−	0.362292i	0.207584	−	0.978217i	$-0.433440\pi$
$139$	11.7355	−	4.27136i	0.995389	−	0.362292i	0.787805	+	0.615925i	$0.211218\pi$
$140$		0			0
$141$	−3.42545	+	2.17956i	−0.288475	+	0.183552i
$142$		0			0
$143$	11.8274	+	20.4857i	0.989060	+	1.71310i
$144$		0			0
$145$	−1.74745	+	3.02667i	−0.145118	+	0.251352i
$146$		0			0
$147$	6.85387	−	1.51544i	0.565297	−	0.124992i
$148$		0			0
$149$	0.0769101	−	0.436179i	0.00630072	−	0.0357332i	−0.981495	−	0.191486i	$-0.938669\pi$
$149$	0.0769101	−	0.436179i	0.00630072	−	0.0357332i	0.987796	+	0.155753i	$0.0497804\pi$
$150$		0			0
$151$	−11.2872	+	9.47105i	−0.918536	+	0.770743i	−0.973724	−	0.227733i	$-0.926869\pi$
$151$	−11.2872	+	9.47105i	−0.918536	+	0.770743i	0.0551874	+	0.998476i	$0.482424\pi$
$152$		0			0
$153$	4.16961	+	1.12224i	0.337093	+	0.0907280i
$154$		0			0
$155$	−18.6467	−	6.78685i	−1.49774	−	0.545133i
$156$		0			0
$157$	1.18154	+	0.991427i	0.0942969	+	0.0791245i	0.688717	−	0.725030i	$-0.258174\pi$
$157$	1.18154	+	0.991427i	0.0942969	+	0.0791245i	−0.594421	+	0.804154i	$0.702619\pi$
$158$		0			0
$159$	6.55197	−	8.52882i	0.519605	−	0.676379i
$160$		0			0
$161$	−20.5059			−1.61609
$162$		0			0
$163$	7.46055			0.584355			0.292178	−	0.956364i	$-0.405620\pi$
$163$	7.46055			0.584355			0.292178	+	0.956364i	$0.405620\pi$
$164$		0			0
$165$	−16.3025	+	21.2213i	−1.26915	+	1.65207i
$166$		0			0
$167$	4.55940	+	3.82579i	0.352817	+	0.296049i	0.801920	−	0.597431i	$-0.203812\pi$
$167$	4.55940	+	3.82579i	0.352817	+	0.296049i	−0.449103	+	0.893480i	$0.648256\pi$
$168$		0			0
$169$	−0.0693701	−	0.0252486i	−0.00533616	−	0.00194220i
$170$		0			0
$171$	10.3088	−	10.2857i	0.788332	−	0.786570i
$172$		0			0
$173$	−6.08118	+	5.10272i	−0.462344	+	0.387953i	−0.843993	−	0.536355i	$-0.819801\pi$
$173$	−6.08118	+	5.10272i	−0.462344	+	0.387953i	0.381649	+	0.924307i	$0.375356\pi$
$174$		0			0
$175$	0.333262	−	1.89002i	0.0251923	−	0.142872i
$176$		0			0
$177$	−9.99462	+	2.20989i	−0.751242	+	0.166105i
$178$		0			0
$179$	−8.30607	+	14.3865i	−0.620825	+	1.07530i	0.368507	+	0.929625i	$0.379869\pi$
$179$	−8.30607	+	14.3865i	−0.620825	+	1.07530i	−0.989332	+	0.145676i	$0.953464\pi$
$180$		0			0
$181$	9.51531	+	16.4810i	0.707267	+	1.22502i	0.965867	+	0.259038i	$0.0834055\pi$
$181$	9.51531	+	16.4810i	0.707267	+	1.22502i	−0.258600	+	0.965984i	$0.583261\pi$
$182$		0			0
$183$	4.43712	−	2.82327i	0.328001	−	0.208702i
$184$		0			0
$185$	14.3199	−	5.21201i	1.05282	−	0.383195i
$186$		0			0
$187$	1.63512	+	9.27324i	0.119572	+	0.678126i
$188$		0			0
$189$	12.7168	+	11.6921i	0.925010	+	0.850475i
$190$		0			0
$191$	−3.18969	−	18.0896i	−0.230798	−	1.30892i	−0.851285	−	0.524703i	$-0.824176\pi$
$191$	−3.18969	−	18.0896i	−0.230798	−	1.30892i	0.620488	−	0.784216i	$-0.286935\pi$
$192$		0			0
$193$	−20.9840	+	7.63754i	−1.51046	+	0.549762i	−0.958744	−	0.284270i	$-0.908249\pi$
$193$	−20.9840	+	7.63754i	−1.51046	+	0.549762i	−0.551715	+	0.834033i	$0.686026\pi$
$194$		0			0
$195$	−0.636872	−	14.7764i	−0.0456074	−	1.05816i
$196$		0			0
$197$	−1.28310	−	2.22240i	−0.0914173	−	0.158339i	0.816690	−	0.577076i	$-0.195806\pi$
$197$	−1.28310	−	2.22240i	−0.0914173	−	0.158339i	−0.908108	+	0.418737i	$0.862473\pi$
$198$		0			0
$199$	8.40047	−	14.5500i	0.595494	−	1.03143i	−0.397983	−	0.917393i	$-0.630290\pi$
$199$	8.40047	−	14.5500i	0.595494	−	1.03143i	0.993477	−	0.114032i	$-0.0363768\pi$
$200$		0			0
$201$	7.30941	+	7.98578i	0.515566	+	0.563274i
$202$		0			0
$203$	−0.854333	+	4.84517i	−0.0599625	+	0.340064i
$204$		0			0
$205$	5.61783	−	4.71392i	0.392366	−	0.329234i
$206$		0			0
$207$	−10.5965	−	15.1695i	−0.736508	−	1.05435i
$208$		0			0
$209$	29.8415	+	10.8614i	2.06418	+	0.751300i
$210$		0			0
$211$	20.3633	+	17.0869i	1.40187	+	1.17631i	0.960262	+	0.279100i	$0.0900360\pi$
$211$	20.3633	+	17.0869i	1.40187	+	1.17631i	0.441607	+	0.897208i	$0.354408\pi$
$212$		0			0
$213$	0.401558	+	0.970982i	0.0275143	+	0.0665306i
$214$		0			0
$215$	4.79491			0.327010
$216$		0			0
$217$	−27.9344			−1.89631
$218$		0			0
$219$	25.2325	+	3.33628i	1.70505	+	0.225445i
$220$		0			0
$221$	−3.98672	−	3.34526i	−0.268176	−	0.225026i
$222$		0			0
$223$	5.11510	+	1.86174i	0.342532	+	0.124672i	0.507558	−	0.861618i	$-0.330548\pi$
$223$	5.11510	+	1.86174i	0.342532	+	0.124672i	−0.165025	+	0.986289i	$0.552771\pi$
$224$		0			0
$225$	1.57038	−	0.730144i	0.104692	−	0.0486763i
$226$		0			0
$227$	−9.97792	+	8.37247i	−0.662258	+	0.555700i	−0.910763	−	0.412930i	$-0.864505\pi$
$227$	−9.97792	+	8.37247i	−0.662258	+	0.555700i	0.248505	+	0.968631i	$0.420061\pi$
$228$		0			0
$229$	−4.08352	+	23.1588i	−0.269847	+	1.53038i	0.485023	+	0.874501i	$0.338811\pi$
$229$	−4.08352	+	23.1588i	−0.269847	+	1.53038i	−0.754870	+	0.655875i	$0.772300\pi$
$230$		0			0
$231$	−11.3481	+	35.9216i	−0.746653	+	2.36347i
$232$		0			0
$233$	7.21311	−	12.4935i	0.472546	−	0.818475i	−0.526960	−	0.849890i	$-0.676668\pi$
$233$	7.21311	−	12.4935i	0.472546	−	0.818475i	0.999506	+	0.0314156i	$0.0100015\pi$
$234$		0			0
$235$	2.76792	+	4.79418i	0.180559	+	0.312738i
$236$		0			0
$237$	−16.6321	−	8.66993i	−1.08037	−	0.563173i
$238$		0			0
$239$	14.9025	−	5.42405i	0.963960	−	0.350853i	0.188376	−	0.982097i	$-0.439678\pi$
$239$	14.9025	−	5.42405i	0.963960	−	0.350853i	0.775584	+	0.631244i	$0.217455\pi$
$240$		0			0
$241$	1.17337	+	6.65453i	0.0755836	+	0.428656i	0.998994	+	0.0448422i	$0.0142785\pi$
$241$	1.17337	+	6.65453i	0.0755836	+	0.428656i	−0.923410	+	0.383814i	$0.874610\pi$
$242$		0			0
$243$	−2.07792	+	15.4493i	−0.133299	+	0.991076i
$244$		0			0
$245$	−1.66196	−	9.42545i	−0.106179	−	0.602170i
$246$		0			0
$247$	−16.4931	+	6.00300i	−1.04943	+	0.381962i
$248$		0			0
$249$	8.52377	+	4.44325i	0.540172	+	0.281580i
$250$		0			0
$251$	−11.1741	−	19.3541i	−0.705303	−	1.22162i	−0.966582	−	0.256358i	$-0.917477\pi$
$251$	−11.1741	−	19.3541i	−0.705303	−	1.22162i	0.261279	−	0.965263i	$-0.415856\pi$
$252$		0			0
$253$	20.1760	−	34.9458i	1.26845	−	2.19702i
$254$		0			0
$255$	1.77355	−	5.61403i	0.111064	−	0.351564i
$256$		0			0
$257$	−4.75635	+	26.9746i	−0.296693	+	1.68263i	0.363548	+	0.931575i	$0.381565\pi$
$257$	−4.75635	+	26.9746i	−0.296693	+	1.68263i	−0.660241	+	0.751054i	$0.729546\pi$
$258$		0			0
$259$	16.4335	−	13.7893i	1.02113	−	0.856828i
$260$		0			0
$261$	−4.02575	+	1.87176i	−0.249188	+	0.115859i
$262$		0			0
$263$	−7.19461	−	2.61862i	−0.443639	−	0.161471i	0.110535	−	0.993872i	$-0.464743\pi$
$263$	−7.19461	−	2.61862i	−0.443639	−	0.161471i	−0.554174	+	0.832401i	$0.686966\pi$
$264$		0			0
$265$	−11.2334	−	9.42598i	−0.690065	−	0.579033i
$266$		0			0
$267$	−10.6341	−	1.40606i	−0.650798	−	0.0860495i
$268$		0			0
$269$	20.5432			1.25254			0.626270	−	0.779606i	$-0.284581\pi$
$269$	20.5432			1.25254			0.626270	+	0.779606i	$0.284581\pi$
$270$		0			0
$271$	−3.59279			−0.218247			−0.109123	−	0.994028i	$-0.534804\pi$
$271$	−3.59279			−0.218247			−0.109123	+	0.994028i	$0.534804\pi$
$272$		0			0
$273$	−7.95697	−	19.2403i	−0.481578	−	1.16447i
$274$		0			0
$275$	2.89305	+	2.42756i	0.174457	+	0.146387i
$276$		0			0
$277$	−17.1955	−	6.25864i	−1.03318	−	0.376045i	−0.230886	−	0.972981i	$-0.574163\pi$
$277$	−17.1955	−	6.25864i	−1.03318	−	0.376045i	−0.802289	+	0.596936i	$0.796385\pi$
$278$		0			0
$279$	−14.4352	−	20.6648i	−0.864214	−	1.23717i
$280$		0			0
$281$	−17.6228	+	14.7873i	−1.05129	+	0.882137i	−0.993229	−	0.116176i	$-0.962936\pi$
$281$	−17.6228	+	14.7873i	−1.05129	+	0.882137i	−0.0580617	+	0.998313i	$0.518492\pi$
$282$		0			0
$283$	−0.765447	+	4.34107i	−0.0455011	+	0.258050i	−0.999070	−	0.0431266i	$-0.986268\pi$
$283$	−0.765447	+	4.34107i	−0.0455011	+	0.258050i	0.953569	+	0.301176i	$0.0973792\pi$
$284$		0			0
$285$	−13.4062	−	14.6467i	−0.794114	−	0.867597i
$286$		0			0
$287$	5.16187	−	8.94062i	0.304695	−	0.527748i
$288$		0			0
$289$	7.46416	+	12.9283i	0.439068	+	0.760489i
$290$		0			0
$291$	−0.723922	−	16.7961i	−0.0424371	−	0.984607i
$292$		0			0
$293$	7.30777	−	2.65981i	0.426924	−	0.155388i	−0.119617	−	0.992820i	$-0.538167\pi$
$293$	7.30777	−	2.65981i	0.426924	−	0.155388i	0.546541	+	0.837432i	$0.315944\pi$
$294$		0			0
$295$	2.42355	+	13.7446i	0.141104	+	0.800243i
$296$		0			0
$297$	−32.4377	+	10.1677i	−1.88223	+	0.589993i
$298$		0			0
$299$	3.87272	+	21.9633i	0.223965	+	1.27017i
$300$		0			0
$301$	6.34290	−	2.30863i	0.365599	−	0.133067i
$302$		0			0
$303$	12.8987	−	8.20721i	0.741009	−	0.471492i
$304$		0			0
$305$	−3.58540	−	6.21009i	−0.205299	−	0.355589i
$306$		0			0
$307$	−0.685470	+	1.18727i	−0.0391218	+	0.0677610i	−0.884923	−	0.465737i	$-0.845789\pi$
$307$	−0.685470	+	1.18727i	−0.0391218	+	0.0677610i	0.845801	+	0.533498i	$0.179123\pi$
$308$		0			0
$309$	−0.0483588	+	0.0106925i	−0.00275104	+	0.000608276i
$310$		0			0
$311$	−0.0407658	+	0.231194i	−0.00231162	+	0.0131098i	−0.985942	−	0.167089i	$-0.946563\pi$
$311$	−0.0407658	+	0.231194i	−0.00231162	+	0.0131098i	0.983630	+	0.180199i	$0.0576743\pi$
$312$		0			0
$313$	−5.93206	+	4.97759i	−0.335300	+	0.281350i	−0.794855	−	0.606799i	$-0.792453\pi$
$313$	−5.93206	+	4.97759i	−0.335300	+	0.281350i	0.459555	+	0.888149i	$0.348009\pi$
$314$		0			0
$315$	16.6739	−	16.6366i	0.939465	−	0.937365i
$316$		0			0
$317$	14.1755	+	5.15948i	0.796178	+	0.289785i	0.707902	−	0.706311i	$-0.249642\pi$
$317$	14.1755	+	5.15948i	0.796178	+	0.289785i	0.0882762	+	0.996096i	$0.471864\pi$
$318$		0			0
$319$	−7.41647	−	6.22316i	−0.415243	−	0.348430i
$320$		0			0
$321$	1.36524	−	1.77716i	0.0762003	−	0.0991912i
$322$		0			0
$323$	−6.98676			−0.388754
$324$		0			0
$325$	−2.08729			−0.115782
$326$		0			0
$327$	−11.9650	+	15.5750i	−0.661664	+	0.861300i
$328$		0			0
$329$	5.96981	+	5.00926i	0.329126	+	0.276170i
$330$		0			0
$331$	25.7564	+	9.37456i	1.41570	+	0.515273i	0.932797	−	0.360402i	$-0.117360\pi$
$331$	25.7564	+	9.37456i	1.41570	+	0.515273i	0.482902	+	0.875674i	$0.339583\pi$
$332$		0			0
$333$	18.6929	+	5.03117i	1.02437	+	0.275707i
$334$		0			0
$335$	11.3075	−	9.48816i	0.617797	−	0.518393i
$336$		0			0
$337$	0.922837	−	5.23367i	0.0502702	−	0.285096i	−0.949301	−	0.314368i	$-0.898208\pi$
$337$	0.922837	−	5.23367i	0.0502702	−	0.285096i	0.999572	+	0.0292713i	$0.00931868\pi$
$338$		0			0
$339$	−6.99173	+	1.54593i	−0.379739	+	0.0839632i
$340$		0			0
$341$	27.4850	−	47.6054i	1.48839	−	2.57797i
$342$		0			0
$343$	4.89930	+	8.48584i	0.264537	+	0.458192i
$344$		0			0
$345$	−21.2863	+	13.5441i	−1.14602	+	0.729192i
$346$		0			0
$347$	33.5217	−	12.2009i	1.79954	−	0.654978i	0.801134	−	0.598485i	$-0.204231\pi$
$347$	33.5217	−	12.2009i	1.79954	−	0.654978i	0.998403	−	0.0564923i	$-0.0179916\pi$
$348$		0			0
$349$	2.00325	+	11.3610i	0.107231	+	0.608140i	0.990306	+	0.138906i	$0.0443587\pi$
$349$	2.00325	+	11.3610i	0.107231	+	0.608140i	−0.883074	+	0.469234i	$0.844530\pi$
$350$		0			0
$351$	10.1214	−	15.8288i	0.540242	−	0.844877i
$352$		0			0
$353$	−5.29116	−	30.0077i	−0.281620	−	1.59715i	−0.717115	−	0.696955i	$-0.754538\pi$
$353$	−5.29116	−	30.0077i	−0.281620	−	1.59715i	0.435495	−	0.900191i	$-0.356573\pi$
$354$		0			0
$355$	1.34627	−	0.490001i	0.0714525	−	0.0260066i
$356$		0			0
$357$	−0.356890	−	8.28040i	−0.0188886	−	0.438245i
$358$		0			0
$359$	−9.94606	−	17.2271i	−0.524933	−	0.909211i	−0.999578	−	0.0290336i	$-0.990757\pi$
$359$	−9.94606	−	17.2271i	−0.524933	−	0.909211i	0.474645	−	0.880177i	$-0.342576\pi$
$360$		0			0
$361$	−2.28150	+	3.95168i	−0.120079	+	0.207983i
$362$		0			0
$363$	−37.1877	−	40.6288i	−1.95185	−	2.13246i
$364$		0			0
$365$	6.02621	−	34.1763i	0.315426	−	1.78887i
$366$		0			0
$367$	−25.5651	+	21.4517i	−1.33449	+	1.11977i	−0.351484	+	0.936194i	$0.614323\pi$
$367$	−25.5651	+	21.4517i	−1.33449	+	1.11977i	−0.983006	+	0.183576i	$0.941233\pi$
$368$		0			0
$369$	9.28135	−	0.801551i	0.483168	−	0.0417271i
$370$		0			0
$371$	−19.3985	−	7.06046i	−1.00712	−	0.366561i
$372$		0			0
$373$	−19.7894	−	16.6053i	−1.02466	−	0.859791i	−0.0344530	−	0.999406i	$-0.510969\pi$
$373$	−19.7894	−	16.6053i	−1.02466	−	0.859791i	−0.990206	+	0.139616i	$0.955413\pi$
$374$		0			0
$375$	6.91376	+	16.7177i	0.357025	+	0.863300i
$376$		0			0
$377$	5.35088			0.275584
$378$		0			0
$379$	−24.7076			−1.26914			−0.634572	−	0.772863i	$-0.718824\pi$
$379$	−24.7076			−1.26914			−0.634572	+	0.772863i	$0.718824\pi$
$380$		0			0
$381$	−4.61791	−	0.610588i	−0.236583	−	0.0312814i
$382$		0			0
$383$	−9.69578	−	8.13573i	−0.495431	−	0.415716i	0.360537	−	0.932745i	$-0.382594\pi$
$383$	−9.69578	−	8.13573i	−0.495431	−	0.415716i	−0.855968	+	0.517029i	$0.827038\pi$
$384$		0			0
$385$	48.2669	+	17.5677i	2.45991	+	0.895334i
$386$		0			0
$387$	4.98556	+	3.49925i	0.253430	+	0.177877i
$388$		0			0
$389$	−7.22304	+	6.06085i	−0.366223	+	0.307297i	−0.807265	−	0.590189i	$-0.799053\pi$
$389$	−7.22304	+	6.06085i	−0.366223	+	0.307297i	0.441043	+	0.897486i	$0.354609\pi$
$390$		0			0
$391$	−1.54161	+	8.74292i	−0.0779627	+	0.442149i
$392$		0			0
$393$	−8.46349	+	26.7905i	−0.426927	+	1.35140i
$394$		0			0
$395$	−12.7869	+	22.1475i	−0.643377	+	1.11436i
$396$		0			0
$397$	−4.78936	−	8.29542i	−0.240371	−	0.416335i	0.720449	−	0.693508i	$-0.243936\pi$
$397$	−4.78936	−	8.29542i	−0.240371	−	0.416335i	−0.960820	+	0.277173i	$0.910603\pi$
$398$		0			0
$399$	−24.7863	−	12.9206i	−1.24087	−	0.646837i
$400$		0			0
$401$	−1.20579	+	0.438871i	−0.0602142	+	0.0219162i	−0.371952	−	0.928252i	$-0.621311\pi$
$401$	−1.20579	+	0.438871i	−0.0602142	+	0.0219162i	0.311737	+	0.950168i	$0.399089\pi$
$402$		0			0
$403$	5.27567	+	29.9198i	0.262800	+	1.49041i
$404$		0			0
$405$	20.9234	+	3.73765i	1.03969	+	0.185725i
$406$		0			0
$407$	7.33048	+	41.5732i	0.363358	+	2.06071i
$408$		0			0
$409$	2.99971	−	1.09181i	0.148326	−	0.0539864i	−0.266790	−	0.963755i	$-0.585963\pi$
$409$	2.99971	−	1.09181i	0.148326	−	0.0539864i	0.415116	+	0.909768i	$0.363741\pi$
$410$		0			0
$411$	−3.26857	−	1.70383i	−0.161227	−	0.0840440i
$412$		0			0
$413$	9.82367	+	17.0151i	0.483391	+	0.837258i
$414$		0			0
$415$	6.55314	−	11.3504i	0.321681	−	0.557168i
$416$		0			0
$417$	6.51608	−	20.6261i	0.319094	−	1.01007i
$418$		0			0
$419$	1.96460	−	11.1418i	0.0959768	−	0.544312i	−0.898467	−	0.439041i	$-0.855318\pi$
$419$	1.96460	−	11.1418i	0.0959768	−	0.544312i	0.994444	−	0.105270i	$-0.0335708\pi$
$420$		0			0
$421$	−6.19259	+	5.19620i	−0.301808	+	0.253247i	−0.781096	−	0.624410i	$-0.785339\pi$
$421$	−6.19259	+	5.19620i	−0.301808	+	0.253247i	0.479288	+	0.877658i	$0.340895\pi$
$422$		0			0
$423$	−0.620738	+	7.00480i	−0.0301813	+	0.340585i
$424$		0			0
$425$	−0.780780	−	0.284181i	−0.0378734	−	0.0137848i
$426$		0			0
$427$	−7.73292	−	6.48869i	−0.374222	−	0.314010i
$428$		0			0
$429$	40.6179	+	5.37057i	1.96105	+	0.259293i
$430$		0			0
$431$	−2.71958			−0.130997			−0.0654987	−	0.997853i	$-0.520864\pi$
$431$	−2.71958			−0.130997			−0.0654987	+	0.997853i	$0.520864\pi$
$432$		0			0
$433$	6.02280			0.289437			0.144719	−	0.989473i	$-0.453772\pi$
$433$	6.02280			0.289437			0.144719	+	0.989473i	$0.453772\pi$
$434$		0			0
$435$	2.31339	+	5.59386i	0.110918	+	0.268205i
$436$		0			0
$437$	22.9358	+	19.2454i	1.09717	+	0.920634i
$438$		0			0
$439$	−3.90491	−	1.42127i	−0.186371	−	0.0678335i	0.247149	−	0.968978i	$-0.420506\pi$
$439$	−3.90491	−	1.42127i	−0.186371	−	0.0678335i	−0.433520	+	0.901144i	$0.642729\pi$
$440$		0			0
$441$	5.15050	−	11.0131i	0.245262	−	0.524434i
$442$		0			0
$443$	−3.22309	+	2.70450i	−0.153134	+	0.128494i	−0.716136	−	0.697961i	$-0.754091\pi$
$443$	−3.22309	+	2.70450i	−0.153134	+	0.128494i	0.563002	+	0.826456i	$0.309646\pi$
$444$		0			0
$445$	−2.53972	+	14.4035i	−0.120394	+	0.682790i
$446$		0			0
$447$	−0.517955	−	0.565884i	−0.0244984	−	0.0267654i
$448$		0			0
$449$	−14.4450	+	25.0195i	−0.681702	+	1.18074i	0.292759	+	0.956186i	$0.405426\pi$
$449$	−14.4450	+	25.0195i	−0.681702	+	1.18074i	−0.974461	+	0.224556i	$0.927907\pi$
$450$		0			0
$451$	10.1576	+	17.5936i	0.478305	+	0.828448i
$452$		0			0
$453$	1.09893	+	25.4970i	0.0516323	+	1.19795i
$454$		0			0
$455$	−26.6767	+	9.70951i	−1.25062	+	0.455189i
$456$		0			0
$457$	1.62466	+	9.21390i	0.0759983	+	0.431008i	0.998938	+	0.0460645i	$0.0146680\pi$
$457$	1.62466	+	9.21390i	0.0759983	+	0.431008i	−0.922940	+	0.384944i	$0.874221\pi$
$458$		0			0
$459$	5.94111	−	4.54295i	0.277307	−	0.212047i
$460$		0			0
$461$	4.77849	+	27.1001i	0.222556	+	1.26218i	0.867302	+	0.497782i	$0.165852\pi$
$461$	4.77849	+	27.1001i	0.222556	+	1.26218i	−0.644746	+	0.764397i	$0.723037\pi$
$462$		0			0
$463$	−2.11416	+	0.769493i	−0.0982536	+	0.0357614i	−0.390679	−	0.920527i	$-0.627760\pi$
$463$	−2.11416	+	0.769493i	−0.0982536	+	0.0357614i	0.292426	+	0.956288i	$0.405538\pi$
$464$		0			0
$465$	−28.9975	+	18.4507i	−1.34473	+	0.855630i
$466$		0			0
$467$	−5.56617	−	9.64089i	−0.257572	−	0.446127i	0.708019	−	0.706193i	$-0.249589\pi$
$467$	−5.56617	−	9.64089i	−0.257572	−	0.446127i	−0.965591	+	0.260066i	$0.916256\pi$
$468$		0			0
$469$	10.3898	−	17.9956i	0.479756	−	0.830962i
$470$		0			0
$471$	2.60849	−	0.576758i	0.120193	−	0.0265756i
$472$		0			0
$473$	−2.30653	+	13.0810i	−0.106054	+	0.601464i
$474$		0			0
$475$	−2.14660	+	1.80121i	−0.0984929	+	0.0826454i
$476$		0			0
$477$	−4.80118	−	17.9988i	−0.219831	−	0.824107i
$478$		0			0
$479$	4.10133	+	1.49276i	0.187395	+	0.0682061i	0.434013	−	0.900907i	$-0.357097\pi$
$479$	4.10133	+	1.49276i	0.187395	+	0.0682061i	−0.246618	+	0.969113i	$0.579319\pi$
$480$		0			0
$481$	−17.8730	−	14.9972i	−0.814939	−	0.683815i
$482$		0			0
$483$	−21.6373	+	28.1656i	−0.984529	+	1.28158i
$484$		0			0
$485$	−22.9225			−1.04086
$486$		0			0
$487$	19.0977			0.865400			0.432700	−	0.901538i	$-0.357561\pi$
$487$	19.0977			0.865400			0.432700	+	0.901538i	$0.357561\pi$
$488$		0			0
$489$	7.87218	−	10.2474i	0.355992	−	0.463401i
$490$		0			0
$491$	18.1286	+	15.2117i	0.818134	+	0.686496i	0.952534	−	0.304431i	$-0.0984664\pi$
$491$	18.1286	+	15.2117i	0.818134	+	0.686496i	−0.134400	+	0.990927i	$0.542911\pi$
$492$		0			0
$493$	2.00157	+	0.728511i	0.0901461	+	0.0328105i
$494$		0			0
$495$	11.9462	+	44.7843i	0.536943	+	2.01290i
$496$		0			0
$497$	1.54498	−	1.29639i	0.0693017	−	0.0581510i
$498$		0			0
$499$	0.368506	−	2.08990i	0.0164966	−	0.0935569i	−0.975448	−	0.220231i	$-0.929319\pi$
$499$	0.368506	−	2.08990i	0.0164966	−	0.0935569i	0.991944	+	0.126674i	$0.0404301\pi$
$500$		0			0
$501$	10.0658	−	2.22563i	0.449708	−	0.0994340i
$502$		0			0
$503$	18.3077	−	31.7099i	0.816300	−	1.41387i	−0.0920901	−	0.995751i	$-0.529355\pi$
$503$	18.3077	−	31.7099i	0.816300	−	1.41387i	0.908390	−	0.418123i	$-0.137312\pi$
$504$		0			0
$505$	−10.4227	−	18.0527i	−0.463805	−	0.803334i
$506$		0			0
$507$	−0.107877	+	0.0686407i	−0.00479101	+	0.00304844i
$508$		0			0
$509$	−7.39390	+	2.69116i	−0.327729	+	0.119284i	−0.500644	−	0.865653i	$-0.666904\pi$
$509$	−7.39390	+	2.69116i	−0.327729	+	0.119284i	0.172915	+	0.984937i	$0.444681\pi$
$510$		0			0
$511$	−8.48334	−	48.1114i	−0.375281	−	2.12832i
$512$		0			0
$513$	−3.25030	−	25.0127i	−0.143504	−	1.10434i
$514$		0			0
$515$	0.0117263	+	0.0665031i	0.000516722	+	0.00293048i
$516$		0			0
$517$	−14.4105	+	5.24498i	−0.633772	+	0.230674i
$518$		0			0
$519$	0.592072	+	13.7370i	0.0259891	+	0.602987i
$520$		0			0
$521$	−12.0107	−	20.8031i	−0.526196	−	0.911399i	−0.999534	−	0.0305180i	$-0.990284\pi$
$521$	−12.0107	−	20.8031i	−0.526196	−	0.911399i	0.473338	−	0.880881i	$-0.343049\pi$
$522$		0			0
$523$	14.4545	−	25.0359i	0.632051	−	1.09474i	−0.355081	−	0.934836i	$-0.615547\pi$
$523$	14.4545	−	25.0359i	0.632051	−	1.09474i	0.987132	−	0.159909i	$-0.0511200\pi$
$524$		0			0
$525$	−2.24437	−	2.45205i	−0.0979523	−	0.107016i
$526$		0			0
$527$	−2.10008	+	11.9102i	−0.0914811	+	0.518815i
$528$		0			0
$529$	11.5246	−	9.67027i	0.501069	−	0.420447i
$530$		0			0
$531$	−7.51070	+	16.0598i	−0.325937	+	0.696937i
$532$		0			0
$533$	−10.5509	−	3.84022i	−0.457011	−	0.166339i
$534$		0			0
$535$	−2.34072	−	1.96410i	−0.101198	−	0.0849154i
$536$		0			0
$537$	10.9961	+	26.5890i	0.474517	+	1.14740i
$538$		0			0
$539$	26.5130			1.14200
$540$		0			0
$541$	35.9506			1.54564			0.772818	−	0.634627i	$-0.218846\pi$
$541$	35.9506			1.54564			0.772818	+	0.634627i	$0.218846\pi$
$542$		0			0
$543$	32.6776	+	4.32068i	1.40233	+	0.185418i
$544$		0			0
$545$	20.5141	+	17.2134i	0.878727	+	0.737340i
$546$		0			0
$547$	−37.7721	−	13.7479i	−1.61502	−	0.587819i	−0.632594	−	0.774483i	$-0.718010\pi$
$547$	−37.7721	−	13.7479i	−1.61502	−	0.587819i	−0.982424	+	0.186665i	$0.940232\pi$
$548$		0			0
$549$	0.804066	−	9.07359i	0.0343167	−	0.387251i
$550$		0			0
$551$	5.50292	−	4.61750i	0.234432	−	0.196712i
$552$		0			0
$553$	−6.25154	+	35.4542i	−0.265842	+	1.50767i
$554$		0			0
$555$	7.95107	−	25.1685i	0.337504	−	1.06834i
$556$		0			0
$557$	−0.681677	+	1.18070i	−0.0288836	+	0.0500279i	−0.880106	−	0.474777i	$-0.842529\pi$
$557$	−0.681677	+	1.18070i	−0.0288836	+	0.0500279i	0.851222	+	0.524805i	$0.175862\pi$
$558$		0			0
$559$	−3.67063	−	6.35771i	−0.155251	−	0.268903i
$560$		0			0
$561$	14.4625	+	7.53898i	0.610607	+	0.318296i
$562$		0			0
$563$	−11.7964	+	4.29353i	−0.497158	+	0.180951i	−0.578415	−	0.815742i	$-0.696329\pi$
$563$	−11.7964	+	4.29353i	−0.497158	+	0.180951i	0.0812574	+	0.996693i	$0.474106\pi$
$564$		0			0
$565$	1.69539	+	9.61504i	0.0713256	+	0.404508i
$566$		0			0
$567$	29.4780	−	5.12978i	1.23796	−	0.215431i
$568$		0			0
$569$	−4.46885	−	25.3441i	−0.187344	−	1.06248i	−0.922907	−	0.385023i	$-0.874193\pi$
$569$	−4.46885	−	25.3441i	−0.187344	−	1.06248i	0.735563	−	0.677456i	$-0.236918\pi$
$570$		0			0
$571$	−15.3787	+	5.59740i	−0.643580	+	0.234244i	−0.643131	−	0.765756i	$-0.722365\pi$
$571$	−15.3787	+	5.59740i	−0.643580	+	0.234244i	−0.000448631		1.00000i	$0.500143\pi$
$572$		0			0
$573$	−28.2125	−	14.7065i	−1.17859	−	0.614375i
$574$		0			0
$575$	1.78032	+	3.08360i	0.0742443	+	0.128595i
$576$		0			0
$577$	−3.13334	+	5.42711i	−0.130443	+	0.225933i	−0.923847	−	0.382761i	$-0.874973\pi$
$577$	−3.13334	+	5.42711i	−0.130443	+	0.225933i	0.793405	+	0.608695i	$0.208307\pi$
$578$		0			0
$579$	−11.6513	+	36.8812i	−0.484211	+	1.53273i
$580$		0			0
$581$	3.20385	−	18.1699i	0.132918	−	0.753816i
$582$		0			0
$583$	31.1187	−	26.1117i	1.28880	−	1.08144i
$584$		0			0
$585$	−20.9680	−	14.7170i	−0.866921	−	0.608471i
$586$		0			0
$587$	−24.9140	−	9.06794i	−1.02831	−	0.374274i	−0.227873	−	0.973691i	$-0.573177\pi$
$587$	−24.9140	−	9.06794i	−1.02831	−	0.374274i	−0.800437	+	0.599417i	$0.795399\pi$
$588$		0			0
$589$	31.2446	+	26.2173i	1.28741	+	1.08027i
$590$		0			0
$591$	−4.40645	−	0.582628i	−0.181257	−	0.0239661i
$592$		0			0
$593$	−32.8477			−1.34889			−0.674446	−	0.738324i	$-0.735617\pi$
$593$	−32.8477			−1.34889			−0.674446	+	0.738324i	$0.735617\pi$
$594$		0			0
$595$	−11.3007			−0.463283
$596$		0			0
$597$	−11.1211	−	26.8912i	−0.455155	−	1.10058i
$598$		0			0
$599$	18.4451	+	15.4773i	0.753647	+	0.632385i	0.936465	−	0.350762i	$-0.114077\pi$
$599$	18.4451	+	15.4773i	0.753647	+	0.632385i	−0.182818	+	0.983147i	$0.558522\pi$
$600$		0			0
$601$	−11.4082	−	4.15223i	−0.465349	−	0.169373i	0.0986953	−	0.995118i	$-0.468533\pi$
$601$	−11.4082	−	4.15223i	−0.465349	−	0.169373i	−0.564044	+	0.825745i	$0.690755\pi$
$602$		0			0
$603$	18.6815	−	1.61336i	0.760768	−	0.0657011i
$604$		0			0
$605$	−57.5288	+	48.2724i	−2.33888	+	1.96255i
$606$		0			0
$607$	3.14954	−	17.8619i	0.127836	−	0.724993i	−0.851747	−	0.523953i	$-0.824457\pi$
$607$	3.14954	−	17.8619i	0.127836	−	0.724993i	0.979583	−	0.201040i	$-0.0644322\pi$
$608$		0			0
$609$	5.75355	+	6.28595i	0.233146	+	0.254720i
$610$		0			0
$611$	4.23784	−	7.34015i	0.171445	−	0.296951i
$612$		0			0
$613$	−12.8012	−	22.1723i	−0.517034	−	0.895529i	−0.999804	−	0.0197822i	$-0.993703\pi$
$613$	−12.8012	−	22.1723i	−0.517034	−	0.895529i	0.482770	−	0.875747i	$-0.339631\pi$
$614$		0			0
$615$	−0.546959	−	12.6903i	−0.0220555	−	0.511723i
$616$		0			0
$617$	14.6627	−	5.33678i	0.590298	−	0.214851i	−0.0295626	−	0.999563i	$-0.509411\pi$
$617$	14.6627	−	5.33678i	0.590298	−	0.214851i	0.619860	+	0.784712i	$0.287189\pi$
$618$		0			0
$619$	1.35448	+	7.68162i	0.0544410	+	0.308750i	0.999853	−	0.0171262i	$-0.00545172\pi$
$619$	1.35448	+	7.68162i	0.0544410	+	0.308750i	−0.945412	+	0.325877i	$0.894341\pi$
$620$		0			0
$621$	−32.0170	−	1.45173i	−1.28480	−	0.0582558i
$622$		0			0
$623$	3.57526	+	20.2763i	0.143240	+	0.812354i
$624$		0			0
$625$	25.8915	−	9.42372i	1.03566	−	0.376949i
$626$		0			0
$627$	46.4065	−	29.5277i	1.85330	−	1.17922i
$628$		0			0
$629$	−4.64380	−	8.04329i	−0.185160	−	0.320707i
$630$		0			0
$631$	13.8294	−	23.9533i	0.550540	−	0.953564i	−0.447695	−	0.894186i	$-0.647755\pi$
$631$	13.8294	−	23.9533i	0.550540	−	0.953564i	0.998236	−	0.0593777i	$-0.0189116\pi$
$632$		0			0
$633$	44.9563	−	9.94020i	1.78685	−	0.395087i
$634$		0			0
$635$	−1.10288	+	6.25477i	−0.0437666	+	0.248213i
$636$		0			0
$637$	−11.2252	+	9.41908i	−0.444759	+	0.373198i
$638$		0			0
$639$	1.75739	+	0.473000i	0.0695215	+	0.0187116i
$640$		0			0
$641$	−38.5129	−	14.0176i	−1.52117	−	0.553660i	−0.559729	−	0.828675i	$-0.689095\pi$
$641$	−38.5129	−	14.0176i	−1.52117	−	0.553660i	−0.961440	+	0.275015i	$0.911317\pi$
$642$		0			0
$643$	−21.5147	−	18.0530i	−0.848456	−	0.711939i	0.110993	−	0.993821i	$-0.464597\pi$
$643$	−21.5147	−	18.0530i	−0.848456	−	0.711939i	−0.959449	+	0.281882i	$0.909041\pi$
$644$		0			0
$645$	5.05946	−	6.58599i	0.199216	−	0.259323i
$646$		0			0
$647$	−36.3946			−1.43082			−0.715409	−	0.698706i	$-0.753760\pi$
$647$	−36.3946			−1.43082			−0.715409	+	0.698706i	$0.753760\pi$
$648$		0			0
$649$	−38.6625			−1.51764
$650$		0			0
$651$	−29.4756	+	38.3689i	−1.15524	+	1.50380i
$652$		0			0
$653$	−29.6865	−	24.9099i	−1.16172	−	0.974800i	−0.161794	−	0.986825i	$-0.551728\pi$
$653$	−29.6865	−	24.9099i	−1.16172	−	0.974800i	−0.999928	+	0.0120245i	$0.996172\pi$
$654$		0			0
$655$	35.9976	+	13.1021i	1.40654	+	0.511940i
$656$		0			0
$657$	31.2072	−	31.1374i	1.21751	−	1.21479i
$658$		0			0
$659$	34.5865	−	29.0215i	1.34730	−	1.13052i	0.367611	−	0.929980i	$-0.380176\pi$
$659$	34.5865	−	29.0215i	1.34730	−	1.13052i	0.979686	−	0.200537i	$-0.0642686\pi$
$660$		0			0
$661$	3.26344	−	18.5079i	0.126933	−	0.719873i	−0.853208	−	0.521571i	$-0.825346\pi$
$661$	3.26344	−	18.5079i	0.126933	−	0.719873i	0.980141	−	0.198302i	$-0.0635428\pi$
$662$		0			0
$663$	−8.80152	+	1.94609i	−0.341823	+	0.0755797i
$664$		0			0
$665$	−19.0559	+	33.0058i	−0.738957	+	1.27991i
$666$		0			0
$667$	−4.56392	−	7.90495i	−0.176716	−	0.306081i
$668$		0			0
$669$	7.95449	−	5.06132i	0.307538	−	0.195682i
$670$		0			0
$671$	18.6664	−	6.79403i	0.720610	−	0.262281i
$672$		0			0
$673$	−1.88525	−	10.6918i	−0.0726712	−	0.412139i	−0.999342	−	0.0362654i	$-0.988454\pi$
$673$	−1.88525	−	10.6918i	−0.0726712	−	0.412139i	0.926671	−	0.375873i	$-0.122657\pi$
$674$		0			0
$675$	0.654147	−	2.92741i	0.0251781	−	0.112676i
$676$		0			0
$677$	1.05481	+	5.98215i	0.0405398	+	0.229913i	0.998345	−	0.0575047i	$-0.0183144\pi$
$677$	1.05481	+	5.98215i	0.0405398	+	0.229913i	−0.957805	+	0.287417i	$0.907203\pi$
$678$		0			0
$679$	−30.3229	+	11.0366i	−1.16369	+	0.423547i
$680$		0			0
$681$	0.971463	+	22.5395i	0.0372265	+	0.863714i
$682$		0			0
$683$	0.213772	+	0.370264i	0.00817976	+	0.0141678i	0.870086	−	0.492899i	$-0.164063\pi$
$683$	0.213772	+	0.370264i	0.00817976	+	0.0141678i	−0.861907	+	0.507067i	$0.830730\pi$
$684$		0			0
$685$	−2.51290	+	4.35248i	−0.0960131	+	0.166300i
$686$		0			0
$687$	27.5007	+	30.0454i	1.04922	+	1.14630i
$688$		0			0
$689$	−3.89870	+	22.1106i	−0.148529	+	0.842347i
$690$		0			0
$691$	12.0105	−	10.0780i	0.456900	−	0.383385i	−0.385089	−	0.922879i	$-0.625829\pi$
$691$	12.0105	−	10.0780i	0.456900	−	0.383385i	0.841989	+	0.539495i	$0.181385\pi$
$692$		0			0
$693$	37.3655	+	53.4907i	1.41940	+	2.03194i
$694$		0			0
$695$	−27.7148	−	10.0873i	−1.05128	−	0.382635i
$696$		0			0
$697$	−3.42388	−	2.87297i	−0.129689	−	0.108822i
$698$		0			0
$699$	−9.54917	−	23.0903i	−0.361183	−	0.873354i
$700$		0			0
$701$	13.4963			0.509750			0.254875	−	0.966974i	$-0.417966\pi$
$701$	13.4963			0.509750			0.254875	+	0.966974i	$0.417966\pi$
$702$		0			0
$703$	−31.3226			−1.18135
$704$		0			0
$705$	9.50564	+	1.25685i	0.358003	+	0.0473357i
$706$		0			0
$707$	−22.4795	−	18.8626i	−0.845430	−	0.709400i
$708$		0			0
$709$	−46.3504	−	16.8702i	−1.74073	−	0.633572i	−0.741428	−	0.671033i	$-0.765851\pi$
$709$	−46.3504	−	16.8702i	−1.74073	−	0.633572i	−0.999298	+	0.0374605i	$0.988073\pi$
$710$		0			0
$711$	−29.4582	+	13.6965i	−1.10477	+	0.513659i
$712$		0			0
$713$	39.7013	−	33.3133i	1.48682	−	1.24759i
$714$		0			0
$715$	9.70067	−	55.0153i	0.362785	−	2.05745i
$716$		0			0
$717$	8.27455	−	26.1924i	0.309019	−	0.978174i
$718$		0			0
$719$	2.18513	−	3.78476i	0.0814916	−	0.141148i	−0.822399	−	0.568911i	$-0.807365\pi$
$719$	2.18513	−	3.78476i	0.0814916	−	0.141148i	0.903891	+	0.427763i	$0.140698\pi$
$720$		0			0
$721$	0.0475317	+	0.0823273i	0.00177017	+	0.00306603i
$722$		0			0
$723$	10.3784	+	5.41002i	0.385976	+	0.201201i
$724$		0			0
$725$	0.802772	−	0.292185i	0.0298142	−	0.0108515i
$726$		0			0
$727$	−0.593919	−	3.36828i	−0.0220272	−	0.124923i	0.971811	−	0.235760i	$-0.0757579\pi$
$727$	−0.593919	−	3.36828i	−0.0220272	−	0.124923i	−0.993839	+	0.110837i	$0.964647\pi$
$728$		0			0
$729$	19.0277	+	19.1559i	0.704730	+	0.709476i
$730$		0			0
$731$	−0.507458	−	2.87794i	−0.0187690	−	0.106444i
$732$		0			0
$733$	25.5095	−	9.28468i	0.942213	−	0.342938i	0.175174	−	0.984538i	$-0.443951\pi$
$733$	25.5095	−	9.28468i	0.942213	−	0.342938i	0.767039	+	0.641600i	$0.221729\pi$
$734$		0			0
$735$	−14.6999	−	7.66273i	−0.542213	−	0.282644i
$736$		0			0
$737$	20.4453	+	35.4122i	0.753111	+	1.30443i
$738$		0			0
$739$	−14.4365	+	25.0048i	−0.531055	+	0.919815i	0.468288	+	0.883576i	$0.344871\pi$
$739$	−14.4365	+	25.0048i	−0.531055	+	0.919815i	−0.999343	+	0.0362389i	$0.988462\pi$
$740$		0			0
$741$	−9.15775	+	28.9881i	−0.336418	+	1.06491i
$742$		0			0
$743$	−1.33348	+	7.56255i	−0.0489207	+	0.277443i	−0.999449	−	0.0331952i	$-0.989432\pi$
$743$	−1.33348	+	7.56255i	−0.0489207	+	0.277443i	0.950528	+	0.310638i	$0.100543\pi$
$744$		0			0
$745$	−0.801269	+	0.672344i	−0.0293562	+	0.0246328i
$746$		0			0
$747$	15.0970	−	7.01931i	0.552372	−	0.256823i
$748$		0			0
$749$	−4.04207	−	1.47119i	−0.147694	−	0.0537562i
$750$		0			0
$751$	17.2180	+	14.4476i	0.628293	+	0.527201i	0.900398	−	0.435067i	$-0.143275\pi$
$751$	17.2180	+	14.4476i	0.628293	+	0.527201i	−0.272105	+	0.962268i	$0.587720\pi$
$752$		0			0
$753$	−38.3743	−	5.07391i	−1.39844	−	0.184903i
$754$		0			0
$755$	34.7970			1.26639
$756$		0			0
$757$	49.3181			1.79250			0.896248	−	0.443554i	$-0.146283\pi$
$757$	49.3181			1.79250			0.896248	+	0.443554i	$0.146283\pi$
$758$		0			0
$759$	−26.7102	−	64.5863i	−0.969519	−	2.34433i
$760$		0			0
$761$	−16.0143	−	13.4376i	−0.580520	−	0.487114i	0.304598	−	0.952481i	$-0.401478\pi$
$761$	−16.0143	−	13.4376i	−0.580520	−	0.487114i	−0.885118	+	0.465367i	$0.845922\pi$
$762$		0			0
$763$	35.4247	+	12.8935i	1.28246	+	0.466778i
$764$		0			0
$765$	−5.83969	−	8.35982i	−0.211134	−	0.302250i
$766$		0			0
$767$	16.3691	−	13.7353i	0.591055	−	0.495954i
$768$		0			0
$769$	2.13017	−	12.0808i	0.0768158	−	0.435644i	−0.922009	−	0.387169i	$-0.873453\pi$
$769$	2.13017	−	12.0808i	0.0768158	−	0.435644i	0.998824	−	0.0484747i	$-0.0154360\pi$
$770$		0			0
$771$	32.0319	+	34.9959i	1.15360	+	1.26035i
$772$		0			0
$773$	−20.5863	+	35.6566i	−0.740439	+	1.28248i	0.211857	+	0.977301i	$0.432049\pi$
$773$	−20.5863	+	35.6566i	−0.740439	+	1.28248i	−0.952296	+	0.305177i	$0.901284\pi$
$774$		0			0
$775$	2.42526	+	4.20067i	0.0871179	+	0.150893i
$776$		0			0
$777$	−1.59999	−	37.1222i	−0.0573992	−	1.33175i
$778$		0			0
$779$	−14.1646	+	5.15550i	−0.507500	+	0.184715i
$780$		0			0
$781$	0.689167	+	3.90846i	0.0246603	+	0.139856i
$782$		0			0
$783$	−1.67694	+	7.50456i	−0.0599289	+	0.268191i
$784$		0			0
$785$	−0.632521	−	3.58720i	−0.0225756	−	0.128033i
$786$		0			0
$787$	−25.7666	+	9.37828i	−0.918481	+	0.334300i	−0.757634	−	0.652680i	$-0.773645\pi$
$787$	−25.7666	+	9.37828i	−0.918481	+	0.334300i	−0.160847	+	0.986979i	$0.551422\pi$
$788$		0			0
$789$	−11.1883	+	7.11897i	−0.398316	+	0.253442i
$790$		0			0
$791$	6.87214	+	11.9029i	0.244345	+	0.423218i
$792$		0			0
$793$	−5.48944	+	9.50798i	−0.194936	+	0.337638i
$794$		0			0
$795$	−24.8002	+	5.48352i	−0.879572	+	0.194480i
$796$		0			0
$797$	0.553907	−	3.14136i	0.0196204	−	0.111273i	−0.973425	−	0.229007i	$-0.926452\pi$
$797$	0.553907	−	3.14136i	0.0196204	−	0.111273i	0.993045	+	0.117734i	$0.0375632\pi$
$798$		0			0
$799$	2.58457	−	2.16871i	0.0914354	−	0.0767234i
$800$		0			0
$801$	−13.1521	+	13.1227i	−0.464708	+	0.463669i
$802$		0			0
$803$	90.3376	+	32.8802i	3.18794	+	1.16032i
$804$		0			0
$805$	37.0974	+	31.1284i	1.30751	+	1.09713i
$806$		0			0
$807$	21.6766	−	28.2168i	0.763054	−	0.993280i
$808$		0			0
$809$	28.6395			1.00691			0.503456	−	0.864021i	$-0.332062\pi$
$809$	28.6395			1.00691			0.503456	+	0.864021i	$0.332062\pi$
$810$		0			0
$811$	20.9087			0.734204			0.367102	−	0.930181i	$-0.380350\pi$
$811$	20.9087			0.734204			0.367102	+	0.930181i	$0.380350\pi$
$812$		0			0
$813$	−3.79102	+	4.93484i	−0.132957	+	0.173072i
$814$		0			0
$815$	−13.4970	−	11.3253i	−0.472778	−	0.396708i
$816$		0			0
$817$	−9.26126	−	3.37082i	−0.324011	−	0.117930i
$818$		0			0
$819$	−34.8232	−	9.37263i	−1.21682	−	0.327506i
$820$		0			0
$821$	−17.3832	+	14.5862i	−0.606678	+	0.509063i	−0.893584	−	0.448895i	$-0.851818\pi$
$821$	−17.3832	+	14.5862i	−0.606678	+	0.509063i	0.286906	+	0.957959i	$0.407373\pi$
$822$		0			0
$823$	−2.09366	+	11.8737i	−0.0729804	+	0.413892i	0.926328	+	0.376717i	$0.122947\pi$
$823$	−2.09366	+	11.8737i	−0.0729804	+	0.413892i	−0.999309	+	0.0371752i	$0.988164\pi$
$824$		0			0
$825$	6.38701	−	1.41222i	0.222367	−	0.0491671i
$826$		0			0
$827$	6.17501	−	10.6954i	0.214726	−	0.371917i	−0.738462	−	0.674295i	$-0.764447\pi$
$827$	6.17501	−	10.6954i	0.214726	−	0.371917i	0.953188	+	0.302379i	$0.0977808\pi$
$828$		0			0
$829$	20.8905	+	36.1835i	0.725559	+	1.25670i	0.958744	+	0.284272i	$0.0917519\pi$
$829$	20.8905	+	36.1835i	0.725559	+	1.25670i	−0.233185	+	0.972432i	$0.574915\pi$
$830$		0			0
$831$	−26.7407	+	17.0147i	−0.927624	+	0.590233i
$832$		0			0
$833$	−5.48133	+	1.99504i	−0.189917	+	0.0691241i
$834$		0			0
$835$	−2.44082	−	13.8426i	−0.0844679	−	0.479041i
$836$		0			0
$837$	−43.6156	−	1.97763i	−1.50758	−	0.0683570i
$838$		0			0
$839$	7.22155	+	40.9554i	0.249315	+	1.41394i	0.810253	+	0.586080i	$0.199330\pi$
$839$	7.22155	+	40.9554i	0.249315	+	1.41394i	−0.560938	+	0.827858i	$0.689559\pi$
$840$		0			0
$841$	25.1931	−	9.16955i	0.868729	−	0.316192i
$842$		0			0
$843$	1.71578	+	39.8088i	0.0590947	+	1.37109i
$844$		0			0
$845$	0.0871700	+	0.150983i	0.00299874	+	0.00519397i
$846$		0			0
$847$	−52.8596	+	91.5555i	−1.81628	+	3.14588i
$848$		0			0
$849$	5.15494	+	5.63195i	0.176917	+	0.193288i
$850$		0			0
$851$	−6.91126	+	39.1957i	−0.236915	+	1.34361i
$852$		0			0
$853$	−43.2582	+	36.2979i	−1.48113	+	1.24282i	−0.576166	+	0.817332i	$0.695452\pi$
$853$	−43.2582	+	36.2979i	−1.48113	+	1.24282i	−0.904966	+	0.425485i	$0.860104\pi$
$854$		0			0
$855$	−34.2637	+	2.95906i	−1.17179	+	0.101198i
$856$		0			0
$857$	35.9591	+	13.0880i	1.22834	+	0.447079i	0.873029	−	0.487669i	$-0.162153\pi$
$857$	35.9591	+	13.0880i	1.22834	+	0.447079i	0.355311	+	0.934748i	$0.384375\pi$
$858$		0			0
$859$	−10.7525	−	9.02244i	−0.366872	−	0.307842i	0.440651	−	0.897679i	$-0.354748\pi$
$859$	−10.7525	−	9.02244i	−0.366872	−	0.307842i	−0.807523	+	0.589837i	$0.799192\pi$
$860$		0			0
$861$	−6.83361	−	16.5239i	−0.232889	−	0.563134i
$862$		0			0
$863$	−29.2701			−0.996364			−0.498182	−	0.867072i	$-0.665999\pi$
$863$	−29.2701			−0.996364			−0.498182	+	0.867072i	$0.665999\pi$
$864$		0			0
$865$	18.7476			0.637437
$866$		0			0
$867$	25.6335	+	3.38931i	0.870560	+	0.115107i
$868$		0			0
$869$	−54.2696	−	45.5376i	−1.84097	−	1.54476i
$870$		0			0
$871$	−21.2369	−	7.72959i	−0.719584	−	0.261907i
$872$		0			0
$873$	−23.8340	−	16.7285i	−0.806659	−	0.566174i
$874$		0			0
$875$	26.6004	−	22.3204i	0.899258	−	0.754567i
$876$		0			0
$877$	1.49680	−	8.48877i	0.0505433	−	0.286646i	−0.949051	−	0.315122i	$-0.897955\pi$
$877$	1.49680	−	8.48877i	0.0505433	−	0.286646i	0.999594	+	0.0284766i	$0.00906562\pi$
$878$		0			0
$879$	4.05762	−	12.8441i	0.136860	−	0.433220i
$880$		0			0
$881$	10.5621	−	18.2940i	0.355845	−	0.616341i	−0.631418	−	0.775443i	$-0.717527\pi$
$881$	10.5621	−	18.2940i	0.355845	−	0.616341i	0.987262	+	0.159102i	$0.0508599\pi$
$882$		0			0
$883$	−16.4869	−	28.5561i	−0.554828	−	0.960990i	−0.997917	−	0.0645121i	$-0.979451\pi$
$883$	−16.4869	−	28.5561i	−0.554828	−	0.960990i	0.443089	−	0.896477i	$-0.353882\pi$
$884$		0			0
$885$	21.4360	+	11.1741i	0.720565	+	0.375615i
$886$		0			0
$887$	−14.8030	+	5.38784i	−0.497035	+	0.180906i	−0.578360	−	0.815782i	$-0.696307\pi$
$887$	−14.8030	+	5.38784i	−0.497035	+	0.180906i	0.0813247	+	0.996688i	$0.474085\pi$
$888$		0			0
$889$	1.55257	+	8.80508i	0.0520716	+	0.295313i
$890$		0			0
$891$	−20.2616	+	55.2832i	−0.678790	+	1.85206i
$892$		0			0
$893$	−1.97587	−	11.2057i	−0.0661200	−	0.374985i
$894$		0			0
$895$	36.8657	−	13.4180i	1.23228	−	0.448515i
$896$		0			0
$897$	34.2538	+	17.8558i	1.14370	+	0.596187i
$898$		0			0
$899$	−6.21727	−	10.7686i	−0.207358	−	0.359154i
$900$		0			0
$901$	−4.46867	+	7.73997i	−0.148873	+	0.257856i
$902$		0			0
$903$	3.52188	−	11.1482i	0.117201	−	0.370990i
$904$		0			0
$905$	7.80430	−	44.2604i	0.259424	−	1.47127i
$906$		0			0
$907$	−9.28697	+	7.79270i	−0.308369	+	0.258752i	−0.783817	−	0.620991i	$-0.786730\pi$
$907$	−9.28697	+	7.79270i	−0.308369	+	0.258752i	0.475449	+	0.879744i	$0.342286\pi$
$908$		0			0
$909$	2.33741	−	26.3768i	0.0775271	−	0.874865i
$910$		0			0
$911$	−14.8773	−	5.41491i	−0.492909	−	0.179404i	0.0835932	−	0.996500i	$-0.473360\pi$
$911$	−14.8773	−	5.41491i	−0.492909	−	0.179404i	−0.576502	+	0.817096i	$0.695583\pi$
$912$		0			0
$913$	27.8126	+	23.3376i	0.920463	+	0.772360i
$914$		0			0
$915$	−12.3130	−	1.62805i	−0.407056	−	0.0538216i
$916$		0			0
$917$	53.9275			1.78084
$918$		0			0
$919$	26.1407			0.862304			0.431152	−	0.902279i	$-0.358107\pi$
$919$	26.1407			0.862304			0.431152	+	0.902279i	$0.358107\pi$
$920$		0			0
$921$	0.907469	+	2.19429i	0.0299021	+	0.0723045i
$922$		0			0
$923$	−1.68031	−	1.40995i	−0.0553081	−	0.0464090i
$924$		0			0
$925$	−3.50034	−	1.27402i	−0.115091	−	0.0418896i
$926$		0			0
$927$	−0.0363404	+	0.0777052i	−0.00119358	+	0.00255217i
$928$		0			0
$929$	−21.9717	+	18.4364i	−0.720868	+	0.604880i	−0.927625	−	0.373512i	$-0.878153\pi$
$929$	−21.9717	+	18.4364i	−0.720868	+	0.604880i	0.206757	+	0.978392i	$0.433709\pi$
$930$		0			0
$931$	−3.41606	+	19.3734i	−0.111957	+	0.634939i
$932$		0			0
$933$	0.274539	+	0.299944i	0.00898801	+	0.00981972i
$934$		0			0
$935$	11.1189	−	19.2585i	0.363626	−	0.629819i
$936$		0			0
$937$	2.03156	+	3.51876i	0.0663681	+	0.114953i	0.897300	−	0.441421i	$-0.145525\pi$
$937$	2.03156	+	3.51876i	0.0663681	+	0.114953i	−0.830932	+	0.556374i	$0.812192\pi$
$938$		0			0
$939$	0.577553	+	13.4001i	0.0188477	+	0.437297i
$940$		0			0
$941$	26.6930	−	9.71544i	0.870165	−	0.316714i	0.131931	−	0.991259i	$-0.457882\pi$
$941$	26.6930	−	9.71544i	0.870165	−	0.316714i	0.738234	+	0.674545i	$0.235660\pi$
$942$		0			0
$943$	3.32597	+	18.8625i	0.108309	+	0.614248i
$944$		0			0
$945$	−5.25717	−	40.4567i	−0.171016	−	1.31606i
$946$		0			0
$947$	−4.07744	−	23.1243i	−0.132499	−	0.751440i	−0.976569	−	0.215206i	$-0.930958\pi$
$947$	−4.07744	−	23.1243i	−0.132499	−	0.751440i	0.844070	−	0.536234i	$-0.180153\pi$
$948$		0			0
$949$	−49.9287	+	18.1726i	−1.62075	+	0.589906i
$950$		0			0
$951$	22.0444	−	14.0265i	0.714839	−	0.454841i
$952$		0			0
$953$	1.83718	+	3.18209i	0.0595121	+	0.103078i	0.894246	−	0.447575i	$-0.147712\pi$
$953$	1.83718	+	3.18209i	0.0595121	+	0.103078i	−0.834734	+	0.550653i	$0.814379\pi$
$954$		0			0
$955$	−21.6900	+	37.5681i	−0.701871	+	1.21568i
$956$		0			0
$957$	−16.3734	+	3.62029i	−0.529277	+	0.117027i
$958$		0			0
$959$	−1.22857	+	6.96754i	−0.0396725	+	0.224994i
$960$		0			0
$961$	30.3362	−	25.4551i	0.978587	−	0.821132i
$962$		0			0
$963$	−1.00043	−	3.75042i	−0.0322383	−	0.120856i
$964$		0			0
$965$	49.5563	+	18.0370i	1.59527	+	0.580632i
$966$		0			0
$967$	−3.16791	−	2.65819i	−0.101873	−	0.0854816i	0.590429	−	0.807090i	$-0.298959\pi$
$967$	−3.16791	−	2.65819i	−0.101873	−	0.0854816i	−0.692302	+	0.721608i	$0.743403\pi$
$968$		0			0
$969$	−7.37225	+	9.59658i	−0.236831	+	0.308287i
$970$		0			0
$971$	−13.8659			−0.444978			−0.222489	−	0.974935i	$-0.571418\pi$
$971$	−13.8659			−0.444978			−0.222489	+	0.974935i	$0.571418\pi$
$972$		0			0
$973$	−41.5191			−1.33104
$974$		0			0
$975$	−2.20246	+	2.86698i	−0.0705352	+	0.0918168i
$976$		0			0
$977$	22.6955	+	19.0438i	0.726093	+	0.609264i	0.929063	−	0.369921i	$-0.120615\pi$
$977$	22.6955	+	19.0438i	0.726093	+	0.609264i	−0.202971	+	0.979185i	$0.565060\pi$
$978$		0			0
$979$	−38.0724	−	13.8572i	−1.21680	−	0.442878i
$980$		0			0
$981$	8.76774	+	32.8687i	0.279932	+	1.04942i
$982$		0			0
$983$	27.8033	−	23.3297i	0.886786	−	0.744102i	−0.0807766	−	0.996732i	$-0.525740\pi$
$983$	27.8033	−	23.3297i	0.886786	−	0.744102i	0.967563	+	0.252630i	$0.0812956\pi$
$984$		0			0
$985$	−1.05238	+	5.96835i	−0.0335316	+	0.190167i
$986$		0			0
$987$	13.1796	−	2.91411i	0.419511	−	0.0927573i
$988$		0			0
$989$	−6.26158	+	10.8454i	−0.199107	+	0.344863i
$990$		0			0
$991$	13.9778	+	24.2102i	0.444018	+	0.769062i	0.997983	−	0.0634780i	$-0.0202193\pi$
$991$	13.9778	+	24.2102i	0.444018	+	0.769062i	−0.553965	+	0.832540i	$0.686886\pi$
$992$		0			0
$993$	40.0538	−	25.4856i	1.27107	−	0.808761i
$994$		0			0
$995$	−37.2847	+	13.5705i	−1.18200	+	0.430214i
$996$		0			0
$997$	−8.26205	−	46.8564i	−0.261662	−	1.48396i	−0.778376	−	0.627799i	$-0.783956\pi$
$997$	−8.26205	−	46.8564i	−0.261662	−	1.48396i	0.516714	−	0.856158i	$-0.327155\pi$
$998$		0			0
$999$	26.6348	−	20.3667i	0.842688	−	0.644373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.121.3	yes	24
3.2	odd	2		648.2.q.a.577.3		24
4.3	odd	2		432.2.u.e.337.2		24
27.2	odd	18		648.2.q.a.73.3		24
27.5	odd	18		5832.2.a.i.1.9		12
27.22	even	9		5832.2.a.h.1.4		12
27.25	even	9	inner	216.2.q.a.25.3	✓	24
108.79	odd	18		432.2.u.e.241.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.25.3	✓	24	27.25	even	9	inner
216.2.q.a.121.3	yes	24	1.1	even	1	trivial
432.2.u.e.241.2		24	108.79	odd	18
432.2.u.e.337.2		24	4.3	odd	2
648.2.q.a.73.3		24	27.2	odd	18
648.2.q.a.577.3		24	3.2	odd	2
5832.2.a.h.1.4		12	27.22	even	9
5832.2.a.i.1.9		12	27.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05517 - 1.37354i) q^{3} +(-1.80911 - 1.51802i) q^{5} +(-3.12406 - 1.13706i) q^{7} +(-0.773215 - 2.89864i) q^{9} +O(q^{10})\)	\(q+(1.05517 - 1.37354i) q^{3} +(-1.80911 - 1.51802i) q^{5} +(-3.12406 - 1.13706i) q^{7} +(-0.773215 - 2.89864i) q^{9} +(5.01156 - 4.20520i) q^{11} +(-0.627873 + 3.56084i) q^{13} +(-3.99399 + 0.883103i) q^{15} +(-0.719665 + 1.24650i) q^{17} +(2.42709 + 4.20384i) q^{19} +(-4.85823 + 3.09121i) q^{21} +(5.79603 - 2.10958i) q^{23} +(0.100243 + 0.568505i) q^{25} +(-4.79728 - 1.99653i) q^{27} +(-0.256977 - 1.45739i) q^{29} +(7.89572 - 2.87381i) q^{31} +(-0.487932 - 11.3208i) q^{33} +(3.92567 + 6.79947i) q^{35} +(-3.22636 + 5.58822i) q^{37} +(4.22844 + 4.61972i) q^{39} +(-0.539230 + 3.05812i) q^{41} +(-1.55533 + 1.30508i) q^{43} +(-3.00138 + 6.41772i) q^{45} +(-2.20272 - 0.801724i) q^{47} +(3.10451 + 2.60500i) q^{49} +(0.952739 + 2.30376i) q^{51} +6.20938 q^{53} -15.4501 q^{55} +(8.33513 + 1.10208i) q^{57} +(-4.52715 - 3.79873i) q^{59} +(2.85327 + 1.03850i) q^{61} +(-0.880377 + 9.93473i) q^{63} +(6.54133 - 5.48883i) q^{65} +(-1.08536 + 6.15538i) q^{67} +(3.21823 - 10.1870i) q^{69} +(-0.303323 + 0.525370i) q^{71} +(7.34739 + 12.7261i) q^{73} +(0.886636 + 0.462184i) q^{75} +(-20.4380 + 7.43883i) q^{77} +(-1.88041 - 10.6644i) q^{79} +(-7.80428 + 4.48255i) q^{81} +(0.963693 + 5.46537i) q^{83} +(3.19417 - 1.16258i) q^{85} +(-2.27293 - 1.18483i) q^{87} +(-3.09653 - 5.36334i) q^{89} +(6.01042 - 10.4103i) q^{91} +(4.38407 - 13.8774i) q^{93} +(1.99066 - 11.2896i) q^{95} +(7.43542 - 6.23906i) q^{97} +(-16.0644 - 11.2752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

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Database

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