LMFDB - Embedded newform 432.2.u.e.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.4
Character	$\chi$	$=$	432.337
Dual form			432.2.u.e.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66239 - 0.486282i) q^{3} +(-2.11828 - 1.77745i) q^{5} +(-4.34143 - 1.58015i) q^{7} +(2.52706 - 1.61678i) q^{9} +O(q^{10})$	\(q+(1.66239 - 0.486282i) q^{3} +(-2.11828 - 1.77745i) q^{5} +(-4.34143 - 1.58015i) q^{7} +(2.52706 - 1.61678i) q^{9} +(-2.54255 + 2.13345i) q^{11} +(0.625780 - 3.54898i) q^{13} +(-4.38574 - 1.92472i) q^{15} +(1.18168 - 2.04672i) q^{17} +(-1.11760 - 1.93575i) q^{19} +(-7.98553 - 0.515662i) q^{21} +(-2.65318 + 0.965678i) q^{23} +(0.459548 + 2.60623i) q^{25} +(3.41474 - 3.91658i) q^{27} +(1.17009 + 6.63591i) q^{29} +(8.26703 - 3.00895i) q^{31} +(-3.18924 + 4.78301i) q^{33} +(6.38772 + 11.0639i) q^{35} +(3.78335 - 6.55296i) q^{37} +(-0.685516 - 6.20408i) q^{39} +(0.644709 - 3.65633i) q^{41} +(-4.43937 + 3.72507i) q^{43} +(-8.22676 - 1.06693i) q^{45} +(7.67045 + 2.79181i) q^{47} +(10.9888 + 9.22070i) q^{49} +(0.969117 - 3.97707i) q^{51} -9.41409 q^{53} +9.17792 q^{55} +(-2.79921 - 2.67449i) q^{57} +(-5.40831 - 4.53811i) q^{59} +(6.50974 + 2.36935i) q^{61} +(-13.5258 + 3.02599i) q^{63} +(-7.63370 + 6.40544i) q^{65} +(2.00705 - 11.3825i) q^{67} +(-3.94102 + 2.89552i) q^{69} +(-0.871998 + 1.51035i) q^{71} +(-3.68885 - 6.38927i) q^{73} +(2.03131 + 4.10909i) q^{75} +(14.4094 - 5.24461i) q^{77} +(-0.147982 - 0.839245i) q^{79} +(3.77205 - 8.17139i) q^{81} +(-1.93014 - 10.9464i) q^{83} +(-6.14106 + 2.23516i) q^{85} +(5.17207 + 10.4625i) q^{87} +(6.35169 + 11.0015i) q^{89} +(-8.32470 + 14.4188i) q^{91} +(12.2798 - 9.02215i) q^{93} +(-1.07329 + 6.08694i) q^{95} +(1.46774 - 1.23158i) q^{97} +(-2.97585 + 9.50209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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
$3$	1.66239	−	0.486282i	0.959779	−	0.280755i
$3$	1.66239	−	0.486282i	0.959779	−	0.280755i
$4$		0			0
$5$	−2.11828	−	1.77745i	−0.947324	−	0.794899i	0.0315211	−	0.999503i	$-0.489965\pi$
$5$	−2.11828	−	1.77745i	−0.947324	−	0.794899i	−0.978845	+	0.204604i	$0.934409\pi$
$6$		0			0
$7$	−4.34143	−	1.58015i	−1.64091	−	0.597241i	−0.653708	−	0.756747i	$-0.726788\pi$
$7$	−4.34143	−	1.58015i	−1.64091	−	0.597241i	−0.987197	+	0.159506i	$0.949010\pi$
$8$		0			0
$9$	2.52706	−	1.61678i	0.842353	−	0.538926i
$10$		0			0
$11$	−2.54255	+	2.13345i	−0.766606	+	0.643259i	−0.939837	−	0.341622i	$-0.889024\pi$
$11$	−2.54255	+	2.13345i	−0.766606	+	0.643259i	0.173231	+	0.984881i	$0.444579\pi$
$12$		0			0
$13$	0.625780	−	3.54898i	0.173560	−	0.984309i	−0.766232	−	0.642564i	$-0.777871\pi$
$13$	0.625780	−	3.54898i	0.173560	−	0.984309i	0.939793	−	0.341746i	$-0.111018\pi$
$14$		0			0
$15$	−4.38574	−	1.92472i	−1.13239	−	0.496962i
$16$		0			0
$17$	1.18168	−	2.04672i	0.286599	−	0.496403i	−0.686397	−	0.727227i	$-0.740809\pi$
$17$	1.18168	−	2.04672i	0.286599	−	0.496403i	0.972996	+	0.230824i	$0.0741421\pi$
$18$		0			0
$19$	−1.11760	−	1.93575i	−0.256396	−	0.444091i	0.708878	−	0.705331i	$-0.249202\pi$
$19$	−1.11760	−	1.93575i	−0.256396	−	0.444091i	−0.965274	+	0.261240i	$0.915868\pi$
$20$		0			0
$21$	−7.98553	−	0.515662i	−1.74259	−	0.112527i
$22$		0			0
$23$	−2.65318	+	0.965678i	−0.553226	+	0.201358i	−0.603479	−	0.797379i	$-0.706219\pi$
$23$	−2.65318	+	0.965678i	−0.553226	+	0.201358i	0.0502532	+	0.998737i	$0.483997\pi$
$24$		0			0
$25$	0.459548	+	2.60623i	0.0919097	+	0.521246i
$26$		0			0
$27$	3.41474	−	3.91658i	0.657167	−	0.753745i
$28$		0			0
$29$	1.17009	+	6.63591i	0.217280	+	1.23226i	0.876905	+	0.480663i	$0.159604\pi$
$29$	1.17009	+	6.63591i	0.217280	+	1.23226i	−0.659625	+	0.751595i	$0.729285\pi$
$30$		0			0
$31$	8.26703	−	3.00895i	1.48480	−	0.540424i	0.532727	−	0.846287i	$-0.321167\pi$
$31$	8.26703	−	3.00895i	1.48480	−	0.540424i	0.952075	+	0.305864i	$0.0989451\pi$
$32$		0			0
$33$	−3.18924	+	4.78301i	−0.555175	+	0.832616i
$34$		0			0
$35$	6.38772	+	11.0639i	1.07972	+	1.87013i
$36$		0			0
$37$	3.78335	−	6.55296i	0.621979	−	1.07730i	−0.367137	−	0.930167i	$-0.619662\pi$
$37$	3.78335	−	6.55296i	0.621979	−	1.07730i	0.989117	−	0.147133i	$-0.0470045\pi$
$38$		0			0
$39$	−0.685516	−	6.20408i	−0.109770	−	0.993448i
$40$		0			0
$41$	0.644709	−	3.65633i	0.100687	−	0.571022i	−0.892169	−	0.451702i	$-0.850817\pi$
$41$	0.644709	−	3.65633i	0.100687	−	0.571022i	0.992856	−	0.119321i	$-0.0380717\pi$
$42$		0			0
$43$	−4.43937	+	3.72507i	−0.676997	+	0.568068i	−0.915127	−	0.403165i	$-0.867910\pi$
$43$	−4.43937	+	3.72507i	−0.676997	+	0.568068i	0.238130	+	0.971233i	$0.423466\pi$
$44$		0			0
$45$	−8.22676	−	1.06693i	−1.22637	−	0.159048i
$46$		0			0
$47$	7.67045	+	2.79181i	1.11885	+	0.407228i	0.834232	−	0.551413i	$-0.185911\pi$
$47$	7.67045	+	2.79181i	1.11885	+	0.407228i	0.284618	+	0.958641i	$0.408133\pi$
$48$		0			0
$49$	10.9888	+	9.22070i	1.56983	+	1.31724i
$50$		0			0
$51$	0.969117	−	3.97707i	0.135704	−	0.556902i
$52$		0			0
$53$	−9.41409			−1.29312			−0.646562	−	0.762861i	$-0.723794\pi$
$53$	−9.41409			−1.29312			−0.646562	+	0.762861i	$0.723794\pi$
$54$		0			0
$55$	9.17792			1.23755
$56$		0			0
$57$	−2.79921	−	2.67449i	−0.370765	−	0.354245i
$58$		0			0
$59$	−5.40831	−	4.53811i	−0.704103	−	0.590812i	0.218835	−	0.975762i	$-0.429774\pi$
$59$	−5.40831	−	4.53811i	−0.704103	−	0.590812i	−0.922938	+	0.384950i	$0.874219\pi$
$60$		0			0
$61$	6.50974	+	2.36935i	0.833487	+	0.303364i	0.723289	−	0.690545i	$-0.242629\pi$
$61$	6.50974	+	2.36935i	0.833487	+	0.303364i	0.110198	+	0.993910i	$0.464852\pi$
$62$		0			0
$63$	−13.5258	+	3.02599i	−1.70409	+	0.381239i
$64$		0			0
$65$	−7.63370	+	6.40544i	−0.946844	+	0.794497i
$66$		0			0
$67$	2.00705	−	11.3825i	0.245200	−	1.39060i	−0.574827	−	0.818275i	$-0.694931\pi$
$67$	2.00705	−	11.3825i	0.245200	−	1.39060i	0.820027	−	0.572324i	$-0.193958\pi$
$68$		0			0
$69$	−3.94102	+	2.89552i	−0.474443	+	0.348580i
$70$		0			0
$71$	−0.871998	+	1.51035i	−0.103487	+	0.179245i	−0.913119	−	0.407693i	$-0.866333\pi$
$71$	−0.871998	+	1.51035i	−0.103487	+	0.179245i	0.809632	+	0.586938i	$0.199667\pi$
$72$		0			0
$73$	−3.68885	−	6.38927i	−0.431747	−	0.747808i	0.565277	−	0.824901i	$-0.308769\pi$
$73$	−3.68885	−	6.38927i	−0.431747	−	0.747808i	−0.997024	+	0.0770935i	$0.975436\pi$
$74$		0			0
$75$	2.03131	+	4.10909i	0.234555	+	0.474477i
$76$		0			0
$77$	14.4094	−	5.24461i	1.64211	−	0.597679i
$78$		0			0
$79$	−0.147982	−	0.839245i	−0.0166492	−	0.0944224i	0.975351	−	0.220660i	$-0.0708210\pi$
$79$	−0.147982	−	0.839245i	−0.0166492	−	0.0944224i	−0.992000	+	0.126237i	$0.959710\pi$
$80$		0			0
$81$	3.77205	−	8.17139i	0.419117	−	0.907932i
$82$		0			0
$83$	−1.93014	−	10.9464i	−0.211861	−	1.20152i	−0.886272	−	0.463166i	$-0.846713\pi$
$83$	−1.93014	−	10.9464i	−0.211861	−	1.20152i	0.674411	−	0.738356i	$-0.264398\pi$
$84$		0			0
$85$	−6.14106	+	2.23516i	−0.666092	+	0.242438i
$86$		0			0
$87$	5.17207	+	10.4625i	0.554504	+	1.12169i
$88$		0			0
$89$	6.35169	+	11.0015i	0.673278	+	1.16615i	0.976969	+	0.213381i	$0.0684476\pi$
$89$	6.35169	+	11.0015i	0.673278	+	1.16615i	−0.303691	+	0.952771i	$0.598219\pi$
$90$		0			0
$91$	−8.32470	+	14.4188i	−0.872665	+	1.51150i
$92$		0			0
$93$	12.2798	−	9.02215i	1.27336	−	0.935554i
$94$		0			0
$95$	−1.07329	+	6.08694i	−0.110117	+	0.624507i
$96$		0			0
$97$	1.46774	−	1.23158i	0.149027	−	0.125048i	−0.565226	−	0.824936i	$-0.691211\pi$
$97$	1.46774	−	1.23158i	0.149027	−	0.125048i	0.714253	+	0.699888i	$0.246767\pi$
$98$		0			0
$99$	−2.97585	+	9.50209i	−0.299084	+	0.954996i
$100$		0			0
$101$	−3.02762	−	1.10196i	−0.301260	−	0.109649i	0.186968	−	0.982366i	$-0.440134\pi$
$101$	−3.02762	−	1.10196i	−0.301260	−	0.109649i	−0.488227	+	0.872717i	$0.662356\pi$
$102$		0			0
$103$	12.7021	+	10.6584i	1.25158	+	1.05020i	0.996527	+	0.0832718i	$0.0265370\pi$
$103$	12.7021	+	10.6584i	1.25158	+	1.05020i	0.255052	+	0.966927i	$0.417907\pi$
$104$		0			0
$105$	15.9990	+	15.2862i	1.56135	+	1.49178i
$106$		0			0
$107$	3.34451			0.323326			0.161663	−	0.986846i	$-0.448314\pi$
$107$	3.34451			0.323326			0.161663	+	0.986846i	$0.448314\pi$
$108$		0			0
$109$	−11.3909			−1.09105			−0.545525	−	0.838095i	$-0.683670\pi$
$109$	−11.3909			−1.09105			−0.545525	+	0.838095i	$0.683670\pi$
$110$		0			0
$111$	3.10281	−	12.7333i	0.294505	−	1.20859i
$112$		0			0
$113$	9.75081	+	8.18190i	0.917279	+	0.769688i	0.973490	−	0.228731i	$-0.0734575\pi$
$113$	9.75081	+	8.18190i	0.917279	+	0.769688i	−0.0562110	+	0.998419i	$0.517902\pi$
$114$		0			0
$115$	7.33662	+	2.67031i	0.684143	+	0.249008i
$116$		0			0
$117$	−4.15653	−	9.98022i	−0.384271	−	0.922672i
$118$		0			0
$119$	−8.36429	+	7.01847i	−0.766753	+	0.643382i
$120$		0			0
$121$	0.00280367	−	0.0159004i	0.000254879	−	0.00144549i
$122$		0			0
$123$	−0.706251	−	6.39174i	−0.0636805	−	0.576324i
$124$		0			0
$125$	−3.25406	+	5.63620i	−0.291052	+	0.504117i
$126$		0			0
$127$	−4.27394	−	7.40269i	−0.379251	−	0.656882i	0.611702	−	0.791088i	$-0.290485\pi$
$127$	−4.27394	−	7.40269i	−0.379251	−	0.656882i	−0.990954	+	0.134206i	$0.957152\pi$
$128$		0			0
$129$	−5.56851	+	8.35129i	−0.490280	+	0.735290i
$130$		0			0
$131$	3.25409	−	1.18439i	0.284311	−	0.103481i	−0.195928	−	0.980618i	$-0.562772\pi$
$131$	3.25409	−	1.18439i	0.284311	−	0.103481i	0.480239	+	0.877138i	$0.340550\pi$
$132$		0			0
$133$	1.79323	+	10.1699i	0.155492	+	0.881841i
$134$		0			0
$135$	−14.1949	+	2.22688i	−1.22170	+	0.191660i
$136$		0			0
$137$	0.327558	+	1.85767i	0.0279852	+	0.158712i	0.995598	−	0.0937276i	$-0.0298783\pi$
$137$	0.327558	+	1.85767i	0.0279852	+	0.158712i	−0.967613	+	0.252439i	$0.918767\pi$
$138$		0			0
$139$	−3.10386	+	1.12971i	−0.263266	+	0.0958209i	−0.470281	−	0.882517i	$-0.655847\pi$
$139$	−3.10386	+	1.12971i	−0.263266	+	0.0958209i	0.207015	+	0.978338i	$0.433625\pi$
$140$		0			0
$141$	14.1089	+	0.911073i	1.18818	+	0.0767262i
$142$		0			0
$143$	5.98049	+	10.3585i	0.500114	+	0.866222i
$144$		0			0
$145$	9.31641	−	16.1365i	0.773686	−	1.34006i
$146$		0			0
$147$	22.7515	+	9.98471i	1.87651	+	0.823525i
$148$		0			0
$149$	0.792869	−	4.49658i	0.0649544	−	0.368374i	−0.934953	−	0.354771i	$-0.884559\pi$
$149$	0.792869	−	4.49658i	0.0649544	−	0.368374i	0.999907	−	0.0136032i	$-0.00433015\pi$
$150$		0			0
$151$	3.71749	−	3.11934i	0.302525	−	0.253848i	−0.478870	−	0.877886i	$-0.658953\pi$
$151$	3.71749	−	3.11934i	0.302525	−	0.253848i	0.781394	+	0.624038i	$0.214509\pi$
$152$		0			0
$153$	−0.322932	−	7.08270i	−0.0261075	−	0.572602i
$154$		0			0
$155$	−22.8601	−	8.32041i	−1.83617	−	0.668311i
$156$		0			0
$157$	−15.0493	−	12.6279i	−1.20107	−	1.00782i	−0.999599	−	0.0283209i	$-0.990984\pi$
$157$	−15.0493	−	12.6279i	−1.20107	−	1.00782i	−0.201469	−	0.979495i	$-0.564572\pi$
$158$		0			0
$159$	−15.6499	+	4.57791i	−1.24111	+	0.363052i
$160$		0			0
$161$	13.0445			1.02805
$162$		0			0
$163$	0.709003			0.0555334			0.0277667	−	0.999614i	$-0.491160\pi$
$163$	0.709003			0.0555334			0.0277667	+	0.999614i	$0.491160\pi$
$164$		0			0
$165$	15.2573	−	4.46306i	1.18778	−	0.347449i
$166$		0			0
$167$	4.31039	+	3.61685i	0.333548	+	0.279880i	0.794144	−	0.607730i	$-0.207920\pi$
$167$	4.31039	+	3.61685i	0.333548	+	0.279880i	−0.460595	+	0.887610i	$0.652364\pi$
$168$		0			0
$169$	0.0123641	+	0.00450016i	0.000951084	+	0.000346166i
$170$		0			0
$171$	−5.95393	−	3.08483i	−0.455308	−	0.235903i
$172$		0			0
$173$	−15.9699	+	13.4004i	−1.21417	+	1.01881i	−0.215064	+	0.976600i	$0.568996\pi$
$173$	−15.9699	+	13.4004i	−1.21417	+	1.01881i	−0.999109	+	0.0422116i	$0.986560\pi$
$174$		0			0
$175$	2.12314	−	12.0409i	0.160494	−	0.910207i
$176$		0			0
$177$	−11.1975	−	4.91413i	−0.841657	−	0.369369i
$178$		0			0
$179$	6.53207	−	11.3139i	0.488229	−	0.845638i	−0.511679	−	0.859177i	$-0.670976\pi$
$179$	6.53207	−	11.3139i	0.488229	−	0.845638i	0.999908	+	0.0135385i	$0.00430957\pi$
$180$		0			0
$181$	3.05258	+	5.28722i	0.226896	+	0.392996i	0.956887	−	0.290461i	$-0.0938088\pi$
$181$	3.05258	+	5.28722i	0.226896	+	0.392996i	−0.729990	+	0.683457i	$0.760475\pi$
$182$		0			0
$183$	11.9739	+	0.773207i	0.885135	+	0.0571571i
$184$		0			0
$185$	−19.6617	+	7.15629i	−1.44556	+	0.526141i
$186$		0			0
$187$	1.36211	+	7.72493i	0.0996076	+	0.564903i
$188$		0			0
$189$	−21.0136	+	11.6077i	−1.52852	+	0.844338i
$190$		0			0
$191$	−2.07106	−	11.7456i	−0.149857	−	0.849881i	−0.963338	−	0.268290i	$-0.913542\pi$
$191$	−2.07106	−	11.7456i	−0.149857	−	0.849881i	0.813481	−	0.581591i	$-0.197570\pi$
$192$		0			0
$193$	2.20202	−	0.801470i	0.158505	−	0.0576911i	−0.261549	−	0.965190i	$-0.584233\pi$
$193$	2.20202	−	0.801470i	0.158505	−	0.0576911i	0.420054	+	0.907499i	$0.362011\pi$
$194$		0			0
$195$	−9.57531	+	14.3604i	−0.685703	+	1.02837i
$196$		0			0
$197$	−2.00559	−	3.47378i	−0.142892	−	0.247497i	0.785692	−	0.618618i	$-0.212307\pi$
$197$	−2.00559	−	3.47378i	−0.142892	−	0.247497i	−0.928585	+	0.371121i	$0.878974\pi$
$198$		0			0
$199$	7.11561	−	12.3246i	0.504413	−	0.873668i	−0.495574	−	0.868565i	$-0.665042\pi$
$199$	7.11561	−	12.3246i	0.504413	−	0.873668i	0.999987	−	0.00510268i	$-0.00162424\pi$
$200$		0			0
$201$	−2.19864	−	19.8982i	−0.155080	−	1.40351i
$202$		0			0
$203$	5.40587	−	30.6582i	0.379418	−	2.15179i
$204$		0			0
$205$	−7.86461	+	6.59919i	−0.549288	+	0.460907i
$206$		0			0
$207$	−5.14345	+	6.72993i	−0.357495	+	0.467762i
$208$		0			0
$209$	6.97138	+	2.53738i	0.482220	+	0.175514i
$210$		0			0
$211$	11.4783	+	9.63148i	0.790202	+	0.663058i	0.945795	−	0.324763i	$-0.105285\pi$
$211$	11.4783	+	9.63148i	0.790202	+	0.663058i	−0.155593	+	0.987821i	$0.549729\pi$
$212$		0			0
$213$	−0.715144	+	2.93482i	−0.0490009	+	0.201090i
$214$		0			0
$215$	16.0249			1.09289
$216$		0			0
$217$	−40.6453			−2.75918
$218$		0			0
$219$	−9.23928	−	8.82762i	−0.624333	−	0.596515i
$220$		0			0
$221$	−6.52430	−	5.47454i	−0.438872	−	0.368257i
$222$		0			0
$223$	−16.3575	−	5.95364i	−1.09538	−	0.398685i	−0.269768	−	0.962925i	$-0.586947\pi$
$223$	−16.3575	−	5.95364i	−1.09538	−	0.398685i	−0.825610	+	0.564241i	$0.809169\pi$
$224$		0			0
$225$	5.37500	+	5.84310i	0.358333	+	0.389540i
$226$		0			0
$227$	2.34376	−	1.96665i	0.155561	−	0.130531i	−0.561685	−	0.827351i	$-0.689847\pi$
$227$	2.34376	−	1.96665i	0.155561	−	0.130531i	0.717246	+	0.696820i	$0.245402\pi$
$228$		0			0
$229$	−1.97712	+	11.2128i	−0.130652	+	0.740963i	0.847138	+	0.531374i	$0.178324\pi$
$229$	−1.97712	+	11.2128i	−0.130652	+	0.740963i	−0.977789	+	0.209590i	$0.932787\pi$
$230$		0			0
$231$	21.4037	−	15.7256i	1.40826	−	1.03467i
$232$		0			0
$233$	12.4791	−	21.6145i	0.817534	−	1.41601i	−0.0899604	−	0.995945i	$-0.528674\pi$
$233$	12.4791	−	21.6145i	0.817534	−	1.41601i	0.907494	−	0.420065i	$-0.137993\pi$
$234$		0			0
$235$	−11.2859	−	19.5477i	−0.736208	−	1.27515i
$236$		0			0
$237$	−0.654112	−	1.32319i	−0.0424892	−	0.0859503i
$238$		0			0
$239$	−5.80287	+	2.11207i	−0.375357	+	0.136619i	−0.522808	−	0.852451i	$-0.675115\pi$
$239$	−5.80287	+	2.11207i	−0.375357	+	0.136619i	0.147451	+	0.989069i	$0.452893\pi$
$240$		0			0
$241$	−0.690567	−	3.91640i	−0.0444833	−	0.252277i	0.954454	−	0.298357i	$-0.0964385\pi$
$241$	−0.690567	−	3.91640i	−0.0444833	−	0.252277i	−0.998938	+	0.0460792i	$0.985327\pi$
$242$		0			0
$243$	2.29701	−	15.4183i	0.147353	−	0.989084i
$244$		0			0
$245$	−6.88805	−	39.0641i	−0.440061	−	2.49571i
$246$		0			0
$247$	−7.56930	+	2.75500i	−0.481623	+	0.175296i
$248$		0			0
$249$	−8.53168	−	17.2585i	−0.540673	−	1.09372i
$250$		0			0
$251$	−8.38045	−	14.5154i	−0.528970	−	0.916202i	−0.999429	−	0.0337807i	$-0.989245\pi$
$251$	−8.38045	−	14.5154i	−0.528970	−	0.916202i	0.470460	−	0.882421i	$-0.344088\pi$
$252$		0			0
$253$	4.68560	−	8.11571i	0.294581	−	0.510230i
$254$		0			0
$255$	−9.12190	+	6.70200i	−0.571236	+	0.419695i
$256$		0			0
$257$	3.87433	−	21.9724i	0.241674	−	1.37060i	−0.586417	−	0.810009i	$-0.699462\pi$
$257$	3.87433	−	21.9724i	0.241674	−	1.37060i	0.828092	−	0.560593i	$-0.189427\pi$
$258$		0			0
$259$	−26.7798	+	22.4709i	−1.66402	+	1.39628i
$260$		0			0
$261$	13.6857	+	14.8776i	0.847123	+	0.920898i
$262$		0			0
$263$	11.9772	+	4.35936i	0.738549	+	0.268810i	0.683779	−	0.729689i	$-0.260335\pi$
$263$	11.9772	+	4.35936i	0.738549	+	0.268810i	0.0547697	+	0.998499i	$0.482558\pi$
$264$		0			0
$265$	19.9417	+	16.7331i	1.22501	+	1.02790i
$266$		0			0
$267$	15.9088	+	15.2000i	0.973601	+	0.930222i
$268$		0			0
$269$	9.74287			0.594033			0.297017	−	0.954872i	$-0.404008\pi$
$269$	9.74287			0.594033			0.297017	+	0.954872i	$0.404008\pi$
$270$		0			0
$271$	−1.82022			−0.110571			−0.0552853	−	0.998471i	$-0.517607\pi$
$271$	−1.82022			−0.110571			−0.0552853	+	0.998471i	$0.517607\pi$
$272$		0			0
$273$	−6.82726	+	28.0178i	−0.413205	+	1.69571i
$274$		0			0
$275$	−6.72868	−	5.64603i	−0.405755	−	0.340469i
$276$		0			0
$277$	−3.76497	−	1.37034i	−0.226215	−	0.0823356i	0.226426	−	0.974028i	$-0.427296\pi$
$277$	−3.76497	−	1.37034i	−0.226215	−	0.0823356i	−0.452641	+	0.891693i	$0.649518\pi$
$278$		0			0
$279$	16.0265	−	20.9698i	0.959479	−	1.25543i
$280$		0			0
$281$	−14.5917	+	12.2439i	−0.870470	+	0.730411i	−0.964197	−	0.265187i	$-0.914566\pi$
$281$	−14.5917	+	12.2439i	−0.870470	+	0.730411i	0.0937269	+	0.995598i	$0.470122\pi$
$282$		0			0
$283$	−4.74210	+	26.8938i	−0.281889	+	1.59867i	0.434302	+	0.900767i	$0.356995\pi$
$283$	−4.74210	+	26.8938i	−0.281889	+	1.59867i	−0.716191	+	0.697904i	$0.754116\pi$
$284$		0			0
$285$	1.17575	+	10.6408i	0.0696451	+	0.630305i
$286$		0			0
$287$	−8.57650	+	14.8549i	−0.506255	+	0.876859i
$288$		0			0
$289$	5.70728	+	9.88531i	0.335723	+	0.581489i
$290$		0			0
$291$	1.84106	−	2.76110i	0.107925	−	0.161859i
$292$		0			0
$293$	29.5763	−	10.7649i	1.72787	−	0.628893i	0.729393	−	0.684094i	$-0.239802\pi$
$293$	29.5763	−	10.7649i	1.72787	−	0.628893i	0.998475	+	0.0552016i	$0.0175802\pi$
$294$		0			0
$295$	3.39006	+	19.2260i	0.197377	+	1.11938i
$296$		0			0
$297$	−0.326315	+	17.2432i	−0.0189347	+	1.00055i
$298$		0			0
$299$	1.76686	+	10.0204i	0.102180	+	0.579493i
$300$		0			0
$301$	25.1594	−	9.15726i	1.45016	−	0.527816i
$302$		0			0
$303$	−5.56894	−	0.359612i	−0.319927	−	0.0206591i
$304$		0			0
$305$	−9.57806	−	16.5897i	−0.548438	−	0.949922i
$306$		0			0
$307$	−7.20856	+	12.4856i	−0.411414	+	0.712590i	−0.995045	−	0.0994290i	$-0.968298\pi$
$307$	−7.20856	+	12.4856i	−0.411414	+	0.712590i	0.583630	+	0.812019i	$0.301632\pi$
$308$		0			0
$309$	26.2988	+	11.5415i	1.49609	+	0.656572i
$310$		0			0
$311$	0.498129	−	2.82503i	0.0282463	−	0.160193i	−0.967422	−	0.253169i	$-0.918527\pi$
$311$	0.498129	−	2.82503i	0.0282463	−	0.160193i	0.995668	+	0.0929766i	$0.0296382\pi$
$312$		0			0
$313$	−23.9823	+	20.1235i	−1.35556	+	1.13745i	−0.378232	+	0.925711i	$0.623468\pi$
$313$	−23.9823	+	20.1235i	−1.35556	+	1.13745i	−0.977327	+	0.211738i	$0.932088\pi$
$314$		0			0
$315$	34.0300	+	17.6315i	1.91737	+	0.993422i
$316$		0			0
$317$	21.4752	+	7.81635i	1.20617	+	0.439010i	0.865374	−	0.501127i	$-0.167081\pi$
$317$	21.4752	+	7.81635i	1.20617	+	0.439010i	0.340796	+	0.940137i	$0.389303\pi$
$318$		0			0
$319$	−17.1324	−	14.3758i	−0.959230	−	0.804889i
$320$		0			0
$321$	5.55987	−	1.62638i	0.310322	−	0.0907755i
$322$		0			0
$323$	−5.28259			−0.293931
$324$		0			0
$325$	9.53702			0.529019
$326$		0			0
$327$	−18.9361	+	5.53919i	−1.04717	+	0.306318i
$328$		0			0
$329$	−28.8892	−	24.2409i	−1.59271	−	1.33645i
$330$		0			0
$331$	−0.915128	−	0.333080i	−0.0503000	−	0.0183077i	0.316748	−	0.948510i	$-0.397409\pi$
$331$	−0.915128	−	0.333080i	−0.0503000	−	0.0183077i	−0.367048	+	0.930202i	$0.619631\pi$
$332$		0			0
$333$	−1.03393	−	22.6766i	−0.0566589	−	1.24267i
$334$		0			0
$335$	−24.4834	+	20.5440i	−1.33767	+	1.12244i
$336$		0			0
$337$	0.485242	−	2.75194i	0.0264328	−	0.149908i	−0.968735	−	0.248098i	$-0.920194\pi$
$337$	0.485242	−	2.75194i	0.0264328	−	0.149908i	0.995168	+	0.0981905i	$0.0313054\pi$
$338$		0			0
$339$	20.1883	+	8.85983i	1.09648	+	0.481200i
$340$		0			0
$341$	−14.5999	+	25.2877i	−0.790626	+	1.36940i
$342$		0			0
$343$	−16.9668	−	29.3874i	−0.916122	−	1.58677i
$344$		0			0
$345$	13.4948	+	0.871422i	0.726537	+	0.0469158i
$346$		0			0
$347$	11.6858	−	4.25327i	0.627325	−	0.228327i	−0.00874184	−	0.999962i	$-0.502783\pi$
$347$	11.6858	−	4.25327i	0.627325	−	0.228327i	0.636066	+	0.771634i	$0.280560\pi$
$348$		0			0
$349$	0.0590634	+	0.334965i	0.00316159	+	0.0179303i	0.986348	−	0.164676i	$-0.0526578\pi$
$349$	0.0590634	+	0.334965i	0.00316159	+	0.0179303i	−0.983186	+	0.182606i	$0.941547\pi$
$350$		0			0
$351$	−11.7630	−	14.5697i	−0.627860	−	0.777676i
$352$		0			0
$353$	−3.05796	−	17.3425i	−0.162759	−	0.923050i	−0.951345	−	0.308127i	$-0.900298\pi$
$353$	−3.05796	−	17.3425i	−0.162759	−	0.923050i	0.788587	−	0.614924i	$-0.210813\pi$
$354$		0			0
$355$	4.53170	−	1.64940i	0.240518	−	0.0875412i
$356$		0			0
$357$	−10.4917	+	15.7348i	−0.555281	+	0.832775i
$358$		0			0
$359$	−7.74104	−	13.4079i	−0.408556	−	0.707641i	0.586172	−	0.810187i	$-0.300634\pi$
$359$	−7.74104	−	13.4079i	−0.408556	−	0.707641i	−0.994728	+	0.102546i	$0.967301\pi$
$360$		0			0
$361$	7.00192	−	12.1277i	0.368522	−	0.638299i
$362$		0			0
$363$	−0.00307130	−	0.0277960i	−0.000161201	−	0.00145891i
$364$		0			0
$365$	−3.54259	+	20.0910i	−0.185427	+	1.05161i
$366$		0			0
$367$	16.3877	−	13.7509i	0.855429	−	0.717790i	−0.105550	−	0.994414i	$-0.533660\pi$
$367$	16.3877	−	13.7509i	0.855429	−	0.717790i	0.960978	+	0.276624i	$0.0892157\pi$
$368$		0			0
$369$	−4.28225	−	10.2821i	−0.222925	−	0.535265i
$370$		0			0
$371$	40.8706	+	14.8757i	2.12190	+	0.772307i
$372$		0			0
$373$	5.72428	+	4.80324i	0.296392	+	0.248702i	0.778841	−	0.627222i	$-0.215808\pi$
$373$	5.72428	+	4.80324i	0.296392	+	0.248702i	−0.482449	+	0.875924i	$0.660253\pi$
$374$		0			0
$375$	−2.66873	+	10.9519i	−0.137812	+	0.565556i
$376$		0			0
$377$	24.2829			1.25063
$378$		0			0
$379$	−2.42680			−0.124656			−0.0623282	−	0.998056i	$-0.519853\pi$
$379$	−2.42680			−0.124656			−0.0623282	+	0.998056i	$0.519853\pi$
$380$		0			0
$381$	−10.7047	−	10.2278i	−0.548421	−	0.523986i
$382$		0			0
$383$	−2.53202	−	2.12462i	−0.129380	−	0.108563i	0.575801	−	0.817590i	$-0.304690\pi$
$383$	−2.53202	−	2.12462i	−0.129380	−	0.108563i	−0.705182	+	0.709027i	$0.749135\pi$
$384$		0			0
$385$	−39.8453	−	14.5025i	−2.03070	−	0.739115i
$386$		0			0
$387$	−5.19593	+	16.5909i	−0.264124	+	0.843365i
$388$		0			0
$389$	13.7988	−	11.5785i	0.699624	−	0.587055i	−0.222042	−	0.975037i	$-0.571272\pi$
$389$	13.7988	−	11.5785i	0.699624	−	0.587055i	0.921667	+	0.387982i	$0.126828\pi$
$390$		0			0
$391$	−1.15872	+	6.57144i	−0.0585991	+	0.332332i
$392$		0			0
$393$	4.83360	−	3.55132i	0.243823	−	0.179140i
$394$		0			0
$395$	−1.17825	+	2.04079i	−0.0592841	+	0.102683i
$396$		0			0
$397$	15.5962	+	27.0133i	0.782748	+	1.35576i	0.930335	+	0.366711i	$0.119516\pi$
$397$	15.5962	+	27.0133i	0.782748	+	1.35576i	−0.147587	+	0.989049i	$0.547151\pi$
$398$		0			0
$399$	7.92647	+	16.0343i	0.396820	+	0.802718i
$400$		0			0
$401$	−31.3540	+	11.4119i	−1.56575	+	0.569885i	−0.972044	−	0.234800i	$-0.924556\pi$
$401$	−31.3540	+	11.4119i	−1.56575	+	0.569885i	−0.593702	+	0.804685i	$0.702334\pi$
$402$		0			0
$403$	−5.50536	−	31.2224i	−0.274241	−	1.55530i
$404$		0			0
$405$	−22.5145	+	10.6047i	−1.11875	+	0.526950i
$406$		0			0
$407$	4.36106	+	24.7328i	0.216170	+	1.22596i
$408$		0			0
$409$	8.73494	−	3.17926i	0.431915	−	0.157204i	−0.116908	−	0.993143i	$-0.537298\pi$
$409$	8.73494	−	3.17926i	0.431915	−	0.157204i	0.548823	+	0.835938i	$0.315076\pi$
$410$		0			0
$411$	1.44788	+	2.92889i	0.0714188	+	0.144471i
$412$		0			0
$413$	16.3089	+	28.2478i	0.802508	+	1.38999i
$414$		0			0
$415$	−15.3681	+	26.6183i	−0.754388	+	1.30664i
$416$		0			0
$417$	−4.61045	+	3.38737i	−0.225775	+	0.165880i
$418$		0			0
$419$	−3.67038	+	20.8157i	−0.179310	+	1.01692i	0.753741	+	0.657171i	$0.228247\pi$
$419$	−3.67038	+	20.8157i	−0.179310	+	1.01692i	−0.933051	+	0.359744i	$0.882864\pi$
$420$		0			0
$421$	21.2843	−	17.8597i	1.03733	−	0.870427i	0.0456287	−	0.998958i	$-0.485471\pi$
$421$	21.2843	−	17.8597i	1.03733	−	0.870427i	0.991705	+	0.128532i	$0.0410264\pi$
$422$		0			0
$423$	23.8974	−	5.34633i	1.16193	−	0.259948i
$424$		0			0
$425$	5.87726	+	2.13915i	0.285089	+	0.103764i
$426$		0			0
$427$	−24.5176	−	20.5727i	−1.18649	−	0.995584i
$428$		0			0
$429$	14.9790	+	14.3116i	0.723195	+	0.690973i
$430$		0			0
$431$	15.7090			0.756675			0.378337	−	0.925668i	$-0.376496\pi$
$431$	15.7090			0.756675			0.378337	+	0.925668i	$0.376496\pi$
$432$		0			0
$433$	28.0524			1.34811			0.674055	−	0.738681i	$-0.264551\pi$
$433$	28.0524			1.34811			0.674055	+	0.738681i	$0.264551\pi$
$434$		0			0
$435$	7.64058	−	31.3555i	0.366338	−	1.50338i
$436$		0			0
$437$	4.83451	+	4.05664i	0.231266	+	0.194055i
$438$		0			0
$439$	30.0365	+	10.9324i	1.43356	+	0.521774i	0.937950	−	0.346770i	$-0.112721\pi$
$439$	30.0365	+	10.9324i	1.43356	+	0.521774i	0.495612	+	0.868544i	$0.334944\pi$
$440$		0			0
$441$	42.6772	+	5.53479i	2.03225	+	0.263562i
$442$		0			0
$443$	−15.1517	+	12.7138i	−0.719877	+	0.604049i	−0.927351	−	0.374192i	$-0.877920\pi$
$443$	−15.1517	+	12.7138i	−0.719877	+	0.604049i	0.207474	+	0.978241i	$0.433476\pi$
$444$		0			0
$445$	6.09985	−	34.5940i	0.289161	−	1.63991i
$446$		0			0
$447$	−0.868554	−	7.86062i	−0.0410812	−	0.371794i
$448$		0			0
$449$	−16.2934	+	28.2210i	−0.768934	+	1.33183i	0.169208	+	0.985580i	$0.445879\pi$
$449$	−16.2934	+	28.2210i	−0.768934	+	1.33183i	−0.938142	+	0.346252i	$0.887454\pi$
$450$		0			0
$451$	6.16139	+	10.6718i	0.290128	+	0.502517i
$452$		0			0
$453$	4.66302	−	6.99330i	0.219088	−	0.328574i
$454$		0			0
$455$	43.2627	−	15.7463i	2.02819	−	0.738200i
$456$		0			0
$457$	2.35282	+	13.3435i	0.110060	+	0.624184i	0.989078	+	0.147394i	$0.0470885\pi$
$457$	2.35282	+	13.3435i	0.110060	+	0.624184i	−0.879017	+	0.476790i	$0.841800\pi$
$458$		0			0
$459$	−3.98103	−	11.6171i	−0.185819	−	0.542242i
$460$		0			0
$461$	−2.81027	−	15.9378i	−0.130887	−	0.742298i	−0.977636	−	0.210305i	$-0.932554\pi$
$461$	−2.81027	−	15.9378i	−0.130887	−	0.742298i	0.846749	−	0.531993i	$-0.178557\pi$
$462$		0			0
$463$	20.5533	−	7.48077i	0.955191	−	0.347661i	0.183044	−	0.983105i	$-0.441405\pi$
$463$	20.5533	−	7.48077i	0.955191	−	0.347661i	0.772147	+	0.635444i	$0.219183\pi$
$464$		0			0
$465$	−42.0485	−	2.71526i	−1.94995	−	0.125917i
$466$		0			0
$467$	−9.27401	−	16.0631i	−0.429150	−	0.743309i	0.567648	−	0.823271i	$-0.307853\pi$
$467$	−9.27401	−	16.0631i	−0.429150	−	0.743309i	−0.996798	+	0.0799620i	$0.974520\pi$
$468$		0			0
$469$	−26.6996	+	46.2450i	−1.23287	+	2.13540i
$470$		0			0
$471$	−31.1585	−	13.6742i	−1.43571	−	0.630075i
$472$		0			0
$473$	3.34004	−	18.9423i	0.153575	−	0.870969i
$474$		0			0
$475$	4.53141	−	3.80230i	0.207915	−	0.174462i
$476$		0			0
$477$	−23.7900	+	15.2205i	−1.08927	+	0.696899i
$478$		0			0
$479$	−9.59880	−	3.49368i	−0.438580	−	0.159630i	0.113287	−	0.993562i	$-0.463862\pi$
$479$	−9.59880	−	3.49368i	−0.438580	−	0.159630i	−0.551867	+	0.833932i	$0.686084\pi$
$480$		0			0
$481$	−20.8888	−	17.5277i	−0.952445	−	0.799196i
$482$		0			0
$483$	21.6850	−	6.34331i	0.986702	−	0.288631i
$484$		0			0
$485$	−5.29817			−0.240577
$486$		0			0
$487$	26.5602			1.20356			0.601779	−	0.798663i	$-0.294459\pi$
$487$	26.5602			1.20356			0.601779	+	0.798663i	$0.294459\pi$
$488$		0			0
$489$	1.17864	−	0.344776i	0.0532998	−	0.0155913i
$490$		0			0
$491$	11.3296	+	9.50662i	0.511296	+	0.429028i	0.861585	−	0.507614i	$-0.169472\pi$
$491$	11.3296	+	9.50662i	0.511296	+	0.429028i	−0.350289	+	0.936642i	$0.613917\pi$
$492$		0			0
$493$	14.9645	+	5.44665i	0.673969	+	0.245305i
$494$		0			0
$495$	23.1931	−	14.8387i	1.04245	−	0.666948i
$496$		0			0
$497$	6.17229	−	5.17917i	0.276865	−	0.232317i
$498$		0			0
$499$	−5.41756	+	30.7245i	−0.242523	+	1.37542i	0.583651	+	0.812004i	$0.301623\pi$
$499$	−5.41756	+	30.7245i	−0.242523	+	1.37542i	−0.826175	+	0.563414i	$0.809488\pi$
$500$		0			0
$501$	8.92435	+	3.91653i	0.398711	+	0.174978i
$502$		0			0
$503$	−13.4588	+	23.3113i	−0.600098	+	1.03940i	0.392707	+	0.919663i	$0.371539\pi$
$503$	−13.4588	+	23.3113i	−0.600098	+	1.03940i	−0.992806	+	0.119737i	$0.961795\pi$
$504$		0			0
$505$	4.45467	+	7.71571i	0.198230	+	0.343344i
$506$		0			0
$507$	0.0227422	+	0.00146857i	0.00101002	+	6.52214e-5i
$508$		0			0
$509$	−1.66994	+	0.607808i	−0.0740187	+	0.0269406i	−0.378764	−	0.925493i	$-0.623651\pi$
$509$	−1.66994	+	0.607808i	−0.0740187	+	0.0269406i	0.304745	+	0.952434i	$0.401429\pi$
$510$		0			0
$511$	5.91886	+	33.5675i	0.261835	+	1.48494i
$512$		0			0
$513$	−11.3978	−	2.23289i	−0.503226	−	0.0985845i
$514$		0			0
$515$	−7.96201	−	45.1548i	−0.350848	−	1.98976i
$516$		0			0
$517$	−25.4587	+	9.26620i	−1.11967	+	0.407527i
$518$		0			0
$519$	−20.0319	+	30.0425i	−0.879301	+	1.31872i
$520$		0			0
$521$	−6.86853	−	11.8966i	−0.300916	−	0.521201i	0.675428	−	0.737426i	$-0.263959\pi$
$521$	−6.86853	−	11.8966i	−0.300916	−	0.521201i	−0.976344	+	0.216225i	$0.930626\pi$
$522$		0			0
$523$	16.2719	−	28.1837i	0.711519	−	1.23239i	−0.252768	−	0.967527i	$-0.581341\pi$
$523$	16.2719	−	28.1837i	0.711519	−	1.23239i	0.964287	−	0.264860i	$-0.0853256\pi$
$524$		0			0
$525$	−2.32581	−	21.0491i	−0.101506	−	0.918657i
$526$		0			0
$527$	3.61046	−	20.4759i	0.157274	−	0.891945i
$528$		0			0
$529$	−11.5122	+	9.65988i	−0.500530	+	0.419995i
$530$		0			0
$531$	−21.0043	−	2.72404i	−0.911507	−	0.118213i
$532$		0			0
$533$	−12.5728	−	4.57612i	−0.544587	−	0.198214i
$534$		0			0
$535$	−7.08461	−	5.94470i	−0.306295	−	0.257012i
$536$		0			0
$537$	5.35708	−	21.9845i	0.231175	−	0.948699i
$538$		0			0
$539$	−47.6114			−2.05077
$540$		0			0
$541$	−33.8894			−1.45702			−0.728511	−	0.685035i	$-0.759787\pi$
$541$	−33.8894			−1.45702			−0.728511	+	0.685035i	$0.759787\pi$
$542$		0			0
$543$	7.64565	+	7.30499i	0.328106	+	0.313487i
$544$		0			0
$545$	24.1291	+	20.2467i	1.03358	+	0.867275i
$546$		0			0
$547$	2.06227	+	0.750604i	0.0881762	+	0.0320935i	0.385732	−	0.922611i	$-0.373949\pi$
$547$	2.06227	+	0.750604i	0.0881762	+	0.0320935i	−0.297555	+	0.954705i	$0.596171\pi$
$548$		0			0
$549$	20.2812	−	4.53732i	0.865581	−	0.193648i
$550$		0			0
$551$	11.5378	−	9.68132i	0.491525	−	0.412438i
$552$		0			0
$553$	−0.683682	+	3.87735i	−0.0290731	+	0.164882i
$554$		0			0
$555$	−29.2054	+	21.4577i	−1.23970	+	0.910828i
$556$		0			0
$557$	8.46632	−	14.6641i	0.358730	−	0.621338i	−0.629019	−	0.777390i	$-0.716543\pi$
$557$	8.46632	−	14.6641i	0.358730	−	0.621338i	0.987749	+	0.156052i	$0.0498767\pi$
$558$		0			0
$559$	10.4421	+	18.0863i	0.441655	+	0.764968i
$560$		0			0
$561$	6.02086	+	12.1795i	0.254201	+	0.514217i
$562$		0			0
$563$	−22.9078	+	8.33777i	−0.965451	+	0.351395i	−0.776167	−	0.630527i	$-0.782839\pi$
$563$	−22.9078	+	8.33777i	−0.965451	+	0.351395i	−0.189284	+	0.981922i	$0.560617\pi$
$564$		0			0
$565$	−6.11204	−	34.6631i	−0.257135	−	1.45829i
$566$		0			0
$567$	−29.2881	+	29.5151i	−1.22999	+	1.23952i
$568$		0			0
$569$	4.14936	+	23.5322i	0.173950	+	0.986520i	0.939349	+	0.342964i	$0.111431\pi$
$569$	4.14936	+	23.5322i	0.173950	+	0.986520i	−0.765399	+	0.643557i	$0.777458\pi$
$570$		0			0
$571$	−13.4375	+	4.89084i	−0.562340	+	0.204675i	−0.607521	−	0.794304i	$-0.707836\pi$
$571$	−13.4375	+	4.89084i	−0.562340	+	0.204675i	0.0451806	+	0.998979i	$0.485614\pi$
$572$		0			0
$573$	−9.15458	−	18.5186i	−0.382438	−	0.773625i
$574$		0			0
$575$	−3.73604	−	6.47102i	−0.155804	−	0.269860i
$576$		0			0
$577$	5.44438	−	9.42994i	0.226652	−	0.392573i	−0.730162	−	0.683275i	$-0.760555\pi$
$577$	5.44438	−	9.42994i	0.226652	−	0.392573i	0.956814	+	0.290701i	$0.0938886\pi$
$578$		0			0
$579$	3.27087	−	2.40316i	0.135933	−	0.0998718i
$580$		0			0
$581$	−8.91736	+	50.5729i	−0.369955	+	2.09812i
$582$		0			0
$583$	23.9358	−	20.0845i	0.991318	−	0.831814i
$584$		0			0
$585$	−8.93464	+	28.5289i	−0.369402	+	1.17953i
$586$		0			0
$587$	26.9916	+	9.82413i	1.11406	+	0.405485i	0.832482	−	0.554053i	$-0.186919\pi$
$587$	26.9916	+	9.82413i	1.11406	+	0.405485i	0.281580	+	0.959538i	$0.409142\pi$
$588$		0			0
$589$	−15.0638	−	12.6401i	−0.620695	−	0.520825i
$590$		0			0
$591$	−5.02331	−	4.79949i	−0.206631	−	0.197425i
$592$		0			0
$593$	−7.61717			−0.312800			−0.156400	−	0.987694i	$-0.549989\pi$
$593$	−7.61717			−0.312800			−0.156400	+	0.987694i	$0.549989\pi$
$594$		0			0
$595$	30.1929			1.23779
$596$		0			0
$597$	5.83567	−	23.9485i	0.238838	−	0.980145i
$598$		0			0
$599$	2.75599	+	2.31255i	0.112607	+	0.0944882i	0.697352	−	0.716728i	$-0.254361\pi$
$599$	2.75599	+	2.31255i	0.112607	+	0.0944882i	−0.584746	+	0.811217i	$0.698806\pi$
$600$		0			0
$601$	14.0519	+	5.11446i	0.573188	+	0.208623i	0.612319	−	0.790611i	$-0.290237\pi$
$601$	14.0519	+	5.11446i	0.573188	+	0.208623i	−0.0391312	+	0.999234i	$0.512459\pi$
$602$		0			0
$603$	−13.3311	−	32.0093i	−0.542885	−	1.30352i
$604$		0			0
$605$	−0.0342011	+	0.0286981i	−0.00139047	+	0.00116674i
$606$		0			0
$607$	0.909063	−	5.15555i	0.0368977	−	0.209257i	−0.960785	−	0.277294i	$-0.910562\pi$
$607$	0.909063	−	5.15555i	0.0368977	−	0.209257i	0.997683	+	0.0680367i	$0.0216735\pi$
$608$		0			0
$609$	−5.92191	−	53.5946i	−0.239968	−	2.17176i
$610$		0			0
$611$	14.7081	−	25.4752i	0.595026	−	1.03062i
$612$		0			0
$613$	13.5114	+	23.4025i	0.545721	+	0.945217i	0.998561	+	0.0536249i	$0.0170775\pi$
$613$	13.5114	+	23.4025i	0.545721	+	0.945217i	−0.452840	+	0.891592i	$0.649589\pi$
$614$		0			0
$615$	−9.86495	+	14.7948i	−0.397793	+	0.596585i
$616$		0			0
$617$	−8.28311	+	3.01480i	−0.333465	+	0.121371i	−0.503326	−	0.864097i	$-0.667890\pi$
$617$	−8.28311	+	3.01480i	−0.333465	+	0.121371i	0.169861	+	0.985468i	$0.445668\pi$
$618$		0			0
$619$	−0.999388	−	5.66781i	−0.0401688	−	0.227809i	0.958114	−	0.286387i	$-0.0924543\pi$
$619$	−0.999388	−	5.66781i	−0.0401688	−	0.227809i	−0.998283	+	0.0585785i	$0.981343\pi$
$620$		0			0
$621$	−5.27776	+	13.6889i	−0.211789	+	0.549317i
$622$		0			0
$623$	−10.1915	−	57.7986i	−0.408312	−	2.31565i
$624$		0			0
$625$	29.3452	−	10.6808i	1.17381	−	0.427232i
$626$		0			0
$627$	12.8230	+	0.828039i	0.512102	+	0.0330687i
$628$		0			0
$629$	−8.94139	−	15.4869i	−0.356517	−	0.617505i
$630$		0			0
$631$	−4.13428	+	7.16078i	−0.164583	+	0.285066i	−0.936507	−	0.350649i	$-0.885961\pi$
$631$	−4.13428	+	7.16078i	−0.164583	+	0.285066i	0.771924	+	0.635715i	$0.219295\pi$
$632$		0			0
$633$	23.7651	+	10.4295i	0.944577	+	0.414536i
$634$		0			0
$635$	−4.10448	+	23.2777i	−0.162881	+	0.923747i
$636$		0			0
$637$	39.6006	−	33.2289i	1.56903	−	1.31658i
$638$		0			0
$639$	0.238303	+	5.22656i	0.00942711	+	0.206760i
$640$		0			0
$641$	36.9370	+	13.4440i	1.45892	+	0.531004i	0.945068	−	0.326873i	$-0.105995\pi$
$641$	36.9370	+	13.4440i	1.45892	+	0.531004i	0.513854	+	0.857878i	$0.328217\pi$
$642$		0			0
$643$	8.09074	+	6.78894i	0.319068	+	0.267730i	0.788228	−	0.615384i	$-0.210999\pi$
$643$	8.09074	+	6.78894i	0.319068	+	0.267730i	−0.469160	+	0.883113i	$0.655443\pi$
$644$		0			0
$645$	26.6397	−	7.79265i	1.04894	−	0.306835i
$646$		0			0
$647$	−0.453781			−0.0178400			−0.00891999	−	0.999960i	$-0.502839\pi$
$647$	−0.453781			−0.0178400			−0.00891999	+	0.999960i	$0.502839\pi$
$648$		0			0
$649$	23.4327			0.919815
$650$		0			0
$651$	−67.5682	+	19.7651i	−2.64821	+	0.774655i
$652$		0			0
$653$	16.4351	+	13.7907i	0.643154	+	0.539670i	0.904985	−	0.425444i	$-0.139882\pi$
$653$	16.4351	+	13.7907i	0.643154	+	0.539670i	−0.261831	+	0.965114i	$0.584326\pi$
$654$		0			0
$655$	−8.99826	−	3.27510i	−0.351591	−	0.127969i
$656$		0			0
$657$	−19.6520	−	10.1820i	−0.766697	−	0.397238i
$658$		0			0
$659$	−23.9140	+	20.0662i	−0.931556	+	0.781668i	−0.976096	−	0.217340i	$-0.930262\pi$
$659$	−23.9140	+	20.0662i	−0.931556	+	0.781668i	0.0445405	+	0.999008i	$0.485818\pi$
$660$		0			0
$661$	−3.68870	+	20.9197i	−0.143474	+	0.813680i	0.825106	+	0.564978i	$0.191115\pi$
$661$	−3.68870	+	20.9197i	−0.143474	+	0.813680i	−0.968580	+	0.248703i	$0.919996\pi$
$662$		0			0
$663$	−13.5081	−	5.92815i	−0.524611	−	0.230230i
$664$		0			0
$665$	14.2779	−	24.7300i	0.553673	−	0.958990i
$666$		0			0
$667$	−9.51261	−	16.4763i	−0.368330	−	0.637966i
$668$		0			0
$669$	−30.0876	−	1.94289i	−1.16325	−	0.0751165i
$670$		0			0
$671$	−21.6062	+	7.86402i	−0.834098	+	0.303587i
$672$		0			0
$673$	−4.62656	−	26.2385i	−0.178341	−	1.01142i	−0.934217	−	0.356705i	$-0.883900\pi$
$673$	−4.62656	−	26.2385i	−0.178341	−	1.01142i	0.755876	−	0.654715i	$-0.227211\pi$
$674$		0			0
$675$	11.7767	+	7.09973i	0.453286	+	0.273269i
$676$		0			0
$677$	−5.48151	−	31.0872i	−0.210672	−	1.19478i	−0.888262	−	0.459338i	$-0.848087\pi$
$677$	−5.48151	−	31.0872i	−0.210672	−	1.19478i	0.677590	−	0.735440i	$-0.263024\pi$
$678$		0			0
$679$	−8.31819	+	3.02757i	−0.319223	+	0.116188i
$680$		0			0
$681$	2.93989	−	4.40907i	0.112657	−	0.168956i
$682$		0			0
$683$	21.7798	+	37.7237i	0.833380	+	1.44346i	0.895343	+	0.445378i	$0.146931\pi$
$683$	21.7798	+	37.7237i	0.833380	+	1.44346i	−0.0619629	+	0.998078i	$0.519736\pi$
$684$		0			0
$685$	2.60806	−	4.51729i	0.0996488	−	0.172597i
$686$		0			0
$687$	2.16585	+	19.6015i	0.0826324	+	0.747843i
$688$		0			0
$689$	−5.89115	+	33.4104i	−0.224435	+	1.27283i
$690$		0			0
$691$	−2.11520	+	1.77487i	−0.0804661	+	0.0675191i	−0.682134	−	0.731228i	$-0.738948\pi$
$691$	−2.11520	+	1.77487i	−0.0804661	+	0.0675191i	0.601667	+	0.798747i	$0.294503\pi$
$692$		0			0
$693$	27.9342	−	36.5503i	1.06113	−	1.38843i
$694$		0			0
$695$	8.58284	+	3.12390i	0.325566	+	0.118496i
$696$		0			0
$697$	−6.72165	−	5.64013i	−0.254601	−	0.213635i
$698$		0			0
$699$	10.2344	−	42.0000i	0.387100	−	1.58858i
$700$		0			0
$701$	−24.8495			−0.938553			−0.469277	−	0.883051i	$-0.655485\pi$
$701$	−24.8495			−0.938553			−0.469277	+	0.883051i	$0.655485\pi$
$702$		0			0
$703$	−16.9132			−0.637892
$704$		0			0
$705$	−28.2671	−	27.0077i	−1.06460	−	1.01717i
$706$		0			0
$707$	11.4029	+	9.56819i	0.428851	+	0.359849i
$708$		0			0
$709$	11.0582	+	4.02484i	0.415298	+	0.151156i	0.541214	−	0.840885i	$-0.317965\pi$
$709$	11.0582	+	4.02484i	0.415298	+	0.151156i	−0.125916	+	0.992041i	$0.540187\pi$
$710$		0			0
$711$	−1.73083	−	1.88157i	−0.0649112	−	0.0705643i
$712$		0			0
$713$	−19.0282	+	15.9666i	−0.712613	+	0.597953i
$714$		0			0
$715$	5.74336	−	32.5722i	0.214790	−	1.21813i
$716$		0			0
$717$	−8.61955	+	6.33291i	−0.321903	+	0.236507i
$718$		0			0
$719$	−0.00129007	+	0.00223447i	−4.81115e−5	+	8.33316e-5i	−0.866049	−	0.499958i	$-0.833349\pi$
$719$	−0.00129007	+	0.00223447i	−4.81115e−5	+	8.33316e-5i	0.866001	+	0.500042i	$0.166682\pi$
$720$		0			0
$721$	−38.3036	−	66.3438i	−1.42650	−	2.47077i
$722$		0			0
$723$	−3.05246	−	6.17476i	−0.113522	−	0.229642i
$724$		0			0
$725$	−16.7570	+	6.09904i	−0.622339	+	0.226513i
$726$		0			0
$727$	−8.07131	−	45.7747i	−0.299348	−	1.69769i	−0.648983	−	0.760803i	$-0.724805\pi$
$727$	−8.07131	−	45.7747i	−0.299348	−	1.69769i	0.349634	−	0.936886i	$-0.386306\pi$
$728$		0			0
$729$	−3.67912	−	26.7482i	−0.136264	−	0.990673i
$730$		0			0
$731$	2.37829	+	13.4880i	0.0879644	+	0.498871i
$732$		0			0
$733$	−4.30442	+	1.56668i	−0.158987	+	0.0578667i	−0.420288	−	0.907391i	$-0.638071\pi$
$733$	−4.30442	+	1.56668i	−0.158987	+	0.0578667i	0.261300	+	0.965258i	$0.415849\pi$
$734$		0			0
$735$	−30.4468	−	61.5900i	−1.12305	−	2.27178i
$736$		0			0
$737$	19.1811	+	33.2226i	0.706544	+	1.22377i
$738$		0			0
$739$	9.79306	−	16.9621i	0.360244	−	0.623960i	−0.627757	−	0.778409i	$-0.716027\pi$
$739$	9.79306	−	16.9621i	0.360244	−	0.623960i	0.988001	+	0.154449i	$0.0493602\pi$
$740$		0			0
$741$	−11.2434	+	8.26069i	−0.413036	+	0.303464i
$742$		0			0
$743$	−5.38694	+	30.5509i	−0.197628	+	1.12080i	0.710999	+	0.703193i	$0.248243\pi$
$743$	−5.38694	+	30.5509i	−0.197628	+	1.12080i	−0.908627	+	0.417610i	$0.862868\pi$
$744$		0			0
$745$	−9.67196	+	8.11574i	−0.354353	+	0.297338i
$746$		0			0
$747$	−22.5755	−	24.5416i	−0.825994	−	0.897929i
$748$		0			0
$749$	−14.5200	−	5.28483i	−0.530548	−	0.193104i
$750$		0			0
$751$	10.2139	+	8.57051i	0.372712	+	0.312742i	0.809833	−	0.586660i	$-0.199558\pi$
$751$	10.2139	+	8.57051i	0.372712	+	0.312742i	−0.437122	+	0.899402i	$0.644002\pi$
$752$		0			0
$753$	−20.9901	−	20.0549i	−0.764923	−	0.730841i
$754$		0			0
$755$	−13.4191			−0.488373
$756$		0			0
$757$	2.37372			0.0862743			0.0431371	−	0.999069i	$-0.486265\pi$
$757$	2.37372			0.0862743			0.0431371	+	0.999069i	$0.486265\pi$
$758$		0			0
$759$	3.84276	−	15.7700i	0.139483	−	0.572414i
$760$		0			0
$761$	−10.4240	−	8.74680i	−0.377871	−	0.317071i	0.433995	−	0.900915i	$-0.357104\pi$
$761$	−10.4240	−	8.74680i	−0.377871	−	0.317071i	−0.811866	+	0.583844i	$0.801548\pi$
$762$		0			0
$763$	49.4527	+	17.9993i	1.79031	+	0.651619i
$764$		0			0
$765$	−11.9051	+	15.5771i	−0.430429	+	0.563193i
$766$		0			0
$767$	−19.4901	+	16.3541i	−0.703746	+	0.590513i
$768$		0			0
$769$	−8.98950	+	50.9820i	−0.324170	+	1.83846i	0.191276	+	0.981536i	$0.438737\pi$
$769$	−8.98950	+	50.9820i	−0.324170	+	1.83846i	−0.515446	+	0.856922i	$0.672374\pi$
$770$		0			0
$771$	−4.24416	−	38.4107i	−0.152850	−	1.38333i
$772$		0			0
$773$	−8.50609	+	14.7330i	−0.305943	+	0.529909i	−0.977471	−	0.211071i	$-0.932305\pi$
$773$	−8.50609	+	14.7330i	−0.305943	+	0.529909i	0.671528	+	0.740979i	$0.265638\pi$
$774$		0			0
$775$	11.6411	+	20.1630i	0.418161	+	0.724276i
$776$		0			0
$777$	−33.5912	+	50.3779i	−1.20508	+	1.80730i
$778$		0			0
$779$	−7.79826	+	2.83833i	−0.279402	+	0.101694i
$780$		0			0
$781$	−1.00515	−	5.70049i	−0.0359671	−	0.203979i
$782$		0			0
$783$	29.9856	+	18.0772i	1.07160	+	0.646025i
$784$		0			0
$785$	9.43329	+	53.4988i	0.336689	+	1.90946i
$786$		0			0
$787$	7.84670	−	2.85597i	0.279705	−	0.101804i	−0.198359	−	0.980129i	$-0.563561\pi$
$787$	7.84670	−	2.85597i	0.279705	−	0.101804i	0.478063	+	0.878325i	$0.341339\pi$
$788$		0			0
$789$	22.0307	+	1.42262i	0.784313	+	0.0506466i
$790$		0			0
$791$	−29.4038	−	50.9289i	−1.04548	−	1.81082i
$792$		0			0
$793$	12.4824	−	21.6202i	0.443265	−	0.767757i
$794$		0			0
$795$	41.2878	+	18.1195i	1.46433	+	0.642633i
$796$		0			0
$797$	1.59616	−	9.05229i	0.0565390	−	0.320648i	−0.943400	−	0.331656i	$-0.892393\pi$
$797$	1.59616	−	9.05229i	0.0565390	−	0.320648i	0.999939	+	0.0110074i	$0.00350383\pi$
$798$		0			0
$799$	14.7781	−	12.4003i	0.522810	−	0.438690i
$800$		0			0
$801$	33.8380	+	17.5320i	1.19561	+	0.619464i
$802$		0			0
$803$	23.0103	+	8.37505i	0.812014	+	0.295549i
$804$		0			0
$805$	−27.6319	−	23.1859i	−0.973897	−	0.817196i
$806$		0			0
$807$	16.1964	−	4.73779i	0.570141	−	0.166778i
$808$		0			0
$809$	−32.2162			−1.13266			−0.566330	−	0.824179i	$-0.691637\pi$
$809$	−32.2162			−1.13266			−0.566330	+	0.824179i	$0.691637\pi$
$810$		0			0
$811$	−12.1871			−0.427948			−0.213974	−	0.976839i	$-0.568641\pi$
$811$	−12.1871			−0.427948			−0.213974	+	0.976839i	$0.568641\pi$
$812$		0			0
$813$	−3.02591	+	0.885142i	−0.106123	+	0.0310433i
$814$		0			0
$815$	−1.50187	−	1.26022i	−0.0526081	−	0.0441435i
$816$		0			0
$817$	12.1723	+	4.43034i	0.425853	+	0.154998i
$818$		0			0
$819$	2.27500	+	49.8963i	0.0794950	+	1.74352i
$820$		0			0
$821$	9.44166	−	7.92250i	0.329516	−	0.276497i	−0.462986	−	0.886365i	$-0.653222\pi$
$821$	9.44166	−	7.92250i	0.329516	−	0.276497i	0.792503	+	0.609868i	$0.208778\pi$
$822$		0			0
$823$	−4.21456	+	23.9020i	−0.146910	+	0.833170i	0.818903	+	0.573932i	$0.194583\pi$
$823$	−4.21456	+	23.9020i	−0.146910	+	0.833170i	−0.965813	+	0.259238i	$0.916529\pi$
$824$		0			0
$825$	−13.9312	−	6.11385i	−0.485023	−	0.212857i
$826$		0			0
$827$	19.9384	−	34.5343i	0.693326	−	1.20088i	−0.277416	−	0.960750i	$-0.589478\pi$
$827$	19.9384	−	34.5343i	0.693326	−	1.20088i	0.970742	−	0.240126i	$-0.0771887\pi$
$828$		0			0
$829$	−6.07089	−	10.5151i	−0.210851	−	0.365204i	0.741130	−	0.671361i	$-0.234290\pi$
$829$	−6.07089	−	10.5151i	−0.210851	−	0.365204i	−0.951981	+	0.306157i	$0.900957\pi$
$830$		0			0
$831$	−6.92521	−	0.447192i	−0.240233	−	0.0155129i
$832$		0			0
$833$	31.8574	−	11.5952i	1.10379	−	0.401748i
$834$		0			0
$835$	−2.70186	−	15.3230i	−0.0935017	−	0.530274i
$836$		0			0
$837$	16.4450	−	42.6532i	0.568421	−	1.47431i
$838$		0			0
$839$	7.24221	+	41.0726i	0.250029	+	1.41798i	0.808518	+	0.588472i	$0.200270\pi$
$839$	7.24221	+	41.0726i	0.250029	+	1.41798i	−0.558489	+	0.829512i	$0.688619\pi$
$840$		0			0
$841$	−15.4151	+	5.61064i	−0.531556	+	0.193470i
$842$		0			0
$843$	−18.3031	+	27.4498i	−0.630393	+	0.945423i
$844$		0			0
$845$	−0.0181918	−	0.0315091i	−0.000625817	−	0.00108395i
$846$		0			0
$847$	−0.0372969	+	0.0646002i	−0.00128154	+	0.00221969i
$848$		0			0
$849$	5.19477	+	47.0139i	0.178284	+	1.61351i
$850$		0			0
$851$	−3.70986	+	21.0397i	−0.127172	+	0.721231i
$852$		0			0
$853$	−7.95429	+	6.67444i	−0.272350	+	0.228529i	−0.768725	−	0.639580i	$-0.779108\pi$
$853$	−7.95429	+	6.67444i	−0.272350	+	0.228529i	0.496375	+	0.868108i	$0.334664\pi$
$854$		0			0
$855$	7.12896	+	17.1173i	0.243805	+	0.585400i
$856$		0			0
$857$	41.5193	+	15.1118i	1.41827	+	0.516209i	0.933546	−	0.358457i	$-0.116697\pi$
$857$	41.5193	+	15.1118i	1.41827	+	0.516209i	0.484727	+	0.874666i	$0.338919\pi$
$858$		0			0
$859$	16.1496	+	13.5512i	0.551018	+	0.462359i	0.875286	−	0.483606i	$-0.160673\pi$
$859$	16.1496	+	13.5512i	0.551018	+	0.462359i	−0.324267	+	0.945965i	$0.605118\pi$
$860$		0			0
$861$	−7.03377	+	28.8653i	−0.239710	+	0.983725i
$862$		0			0
$863$	12.0754			0.411052			0.205526	−	0.978652i	$-0.434110\pi$
$863$	12.0754			0.411052			0.205526	+	0.978652i	$0.434110\pi$
$864$		0			0
$865$	57.6473			1.96007
$866$		0			0
$867$	14.2948	+	13.6578i	0.485476	+	0.463845i
$868$		0			0
$869$	2.16674	+	1.81811i	0.0735015	+	0.0616751i
$870$		0			0
$871$	−39.1404	−	14.2459i	−1.32622	−	0.482706i
$872$		0			0
$873$	1.71788	−	5.48530i	0.0581413	−	0.185649i
$874$		0			0
$875$	23.0333	−	19.3273i	0.778668	−	0.653380i
$876$		0			0
$877$	−1.39839	+	7.93068i	−0.0472204	+	0.267800i	−0.999273	−	0.0381356i	$-0.987858\pi$
$877$	−1.39839	+	7.93068i	−0.0472204	+	0.267800i	0.952052	+	0.305936i	$0.0989692\pi$
$878$		0			0
$879$	43.9325	−	32.2779i	1.48181	−	1.08871i
$880$		0			0
$881$	22.0711	−	38.2283i	0.743594	−	1.28794i	−0.207254	−	0.978287i	$-0.566453\pi$
$881$	22.0711	−	38.2283i	0.743594	−	1.28794i	0.950849	−	0.309656i	$-0.100214\pi$
$882$		0			0
$883$	20.1309	+	34.8678i	0.677460	+	1.17340i	0.975743	+	0.218918i	$0.0702527\pi$
$883$	20.1309	+	34.8678i	0.677460	+	1.17340i	−0.298283	+	0.954477i	$0.596414\pi$
$884$		0			0
$885$	14.9849	+	30.3125i	0.503710	+	1.01894i
$886$		0			0
$887$	−46.9731	+	17.0968i	−1.57720	+	0.574054i	−0.974593	−	0.223983i	$-0.928094\pi$
$887$	−46.9731	+	17.0968i	−1.57720	+	0.574054i	−0.602608	+	0.798037i	$0.705872\pi$
$888$		0			0
$889$	6.85766	+	38.8917i	0.229998	+	1.30439i
$890$		0			0
$891$	7.84262	+	28.8236i	0.262738	+	0.965628i
$892$		0			0
$893$	−3.16828	−	17.9682i	−0.106022	−	0.601283i
$894$		0			0
$895$	−33.9466	+	12.3555i	−1.13471	+	0.413000i
$896$		0			0
$897$	7.80994	+	15.7985i	0.260766	+	0.527498i
$898$		0			0
$899$	29.6403	+	51.3385i	0.988560	+	1.71224i
$900$		0			0
$901$	−11.1244	+	19.2680i	−0.370608	+	0.641911i
$902$		0			0
$903$	37.3716	−	27.4575i	1.24365	−	0.913727i
$904$		0			0
$905$	2.93154	−	16.6256i	0.0974478	−	0.552654i
$906$		0			0
$907$	26.4897	−	22.2275i	0.879578	−	0.738053i	−0.0865146	−	0.996251i	$-0.527573\pi$
$907$	26.4897	−	22.2275i	0.879578	−	0.738053i	0.966092	+	0.258197i	$0.0831285\pi$
$908$		0			0
$909$	−9.43261	+	2.11026i	−0.312860	+	0.0699931i
$910$		0			0
$911$	39.4580	+	14.3615i	1.30730	+	0.475819i	0.899368	−	0.437193i	$-0.144027\pi$
$911$	39.4580	+	14.3615i	1.30730	+	0.475819i	0.407933	+	0.913012i	$0.366250\pi$
$912$		0			0
$913$	28.2611	+	23.7138i	0.935304	+	0.784813i
$914$		0			0
$915$	−23.9897	−	22.9208i	−0.793075	−	0.757739i
$916$		0			0
$917$	−15.9989			−0.528330
$918$		0			0
$919$	−29.8567			−0.984880			−0.492440	−	0.870346i	$-0.663895\pi$
$919$	−29.8567			−0.984880			−0.492440	+	0.870346i	$0.663895\pi$
$920$		0			0
$921$	−5.91189	+	24.2613i	−0.194803	+	0.799436i
$922$		0			0
$923$	4.81450	+	4.03985i	0.158471	+	0.132973i
$924$		0			0
$925$	18.8171	+	6.84888i	0.618704	+	0.225190i
$926$		0			0
$927$	49.3313	+	6.39776i	1.62025	+	0.210130i
$928$		0			0
$929$	−37.0125	+	31.0572i	−1.21434	+	1.01895i	−0.215239	+	0.976561i	$0.569053\pi$
$929$	−37.0125	+	31.0572i	−1.21434	+	1.01895i	−0.999101	+	0.0423913i	$0.986502\pi$
$930$		0			0
$931$	5.56781	−	31.5766i	0.182478	−	1.03488i
$932$		0			0
$933$	−0.545679	−	4.93852i	−0.0178647	−	0.161680i
$934$		0			0
$935$	10.8453	−	18.7847i	0.354680	−	0.614324i
$936$		0			0
$937$	25.7774	+	44.6478i	0.842112	+	1.45858i	0.888106	+	0.459639i	$0.152021\pi$
$937$	25.7774	+	44.6478i	0.842112	+	1.45858i	−0.0459940	+	0.998942i	$0.514646\pi$
$938$		0			0
$939$	−30.0821	+	45.1152i	−0.981692	+	1.47228i
$940$		0			0
$941$	−16.4411	+	5.98409i	−0.535966	+	0.195076i	−0.595800	−	0.803133i	$-0.703165\pi$
$941$	−16.4411	+	5.98409i	−0.535966	+	0.195076i	0.0598343	+	0.998208i	$0.480943\pi$
$942$		0			0
$943$	1.82031	+	10.3235i	0.0592773	+	0.336179i
$944$		0			0
$945$	65.1449	+	12.7622i	2.11916	+	0.415154i
$946$		0			0
$947$	−2.87549	−	16.3077i	−0.0934410	−	0.529930i	−0.995214	−	0.0977201i	$-0.968845\pi$
$947$	−2.87549	−	16.3077i	−0.0934410	−	0.529930i	0.901773	−	0.432210i	$-0.142266\pi$
$948$		0			0
$949$	−24.9838	+	9.09336i	−0.811008	+	0.295183i
$950$		0			0
$951$	39.5011	+	2.55076i	1.28091	+	0.0827142i
$952$		0			0
$953$	−26.5362	−	45.9621i	−0.859593	−	1.48886i	−0.872318	−	0.488939i	$-0.837384\pi$
$953$	−26.5362	−	45.9621i	−0.859593	−	1.48886i	0.0127252	−	0.999919i	$-0.495949\pi$
$954$		0			0
$955$	−16.4901	+	28.5617i	−0.533606	+	0.924233i
$956$		0			0
$957$	−35.4713	−	15.5669i	−1.14663	−	0.503207i
$958$		0			0
$959$	1.51333	−	8.58255i	0.0488681	−	0.277145i
$960$		0			0
$961$	35.5426	−	29.8238i	1.14653	−	0.962057i
$962$		0			0
$963$	8.45178	−	5.40733i	0.272355	−	0.174249i
$964$		0			0
$965$	−6.08907	−	2.21624i	−0.196014	−	0.0713433i
$966$		0			0
$967$	−17.2540	−	14.4778i	−0.554851	−	0.465575i	0.321729	−	0.946832i	$-0.395736\pi$
$967$	−17.2540	−	14.4778i	−0.554851	−	0.465575i	−0.876580	+	0.481257i	$0.840180\pi$
$968$		0			0
$969$	−8.78170	+	2.56883i	−0.282109	+	0.0825226i
$970$		0			0
$971$	24.3804			0.782404			0.391202	−	0.920305i	$-0.372059\pi$
$971$	24.3804			0.782404			0.391202	+	0.920305i	$0.372059\pi$
$972$		0			0
$973$	15.2603			0.489222
$974$		0			0
$975$	15.8542	−	4.63769i	0.507741	−	0.148525i
$976$		0			0
$977$	−19.3521	−	16.2383i	−0.619127	−	0.519509i	0.278402	−	0.960465i	$-0.410195\pi$
$977$	−19.3521	−	16.2383i	−0.619127	−	0.519509i	−0.897529	+	0.440955i	$0.854640\pi$
$978$		0			0
$979$	−39.6205	−	14.4207i	−1.26628	−	0.460887i
$980$		0			0
$981$	−28.7855	+	18.4166i	−0.919049	+	0.587995i
$982$		0			0
$983$	44.1912	−	37.0808i	1.40948	−	1.18269i	0.452777	−	0.891624i	$-0.350433\pi$
$983$	44.1912	−	37.0808i	1.40948	−	1.18269i	0.956702	−	0.291070i	$-0.0940112\pi$
$984$		0			0
$985$	−1.92607	+	10.9233i	−0.0613697	+	0.348045i
$986$		0			0
$987$	−59.8130	−	26.2495i	−1.90387	−	0.835530i
$988$		0			0
$989$	8.18122	−	14.1703i	0.260148	−	0.450589i
$990$		0			0
$991$	23.2165	+	40.2122i	0.737496	+	1.27738i	0.953619	+	0.301015i	$0.0973255\pi$
$991$	23.2165	+	40.2122i	0.737496	+	1.27738i	−0.216123	+	0.976366i	$0.569341\pi$
$992$		0			0
$993$	−1.68327	−	0.108696i	−0.0534169	−	0.00344937i
$994$		0			0
$995$	−36.9792	+	13.4593i	−1.17232	+	0.426690i
$996$		0			0
$997$	2.70785	+	15.3570i	0.0857586	+	0.486361i	0.997190	+	0.0749097i	$0.0238669\pi$
$997$	2.70785	+	15.3570i	0.0857586	+	0.486361i	−0.911432	+	0.411451i	$0.865022\pi$
$998$		0			0
$999$	−12.7460	−	37.1944i	−0.403265	−	1.17678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.e.337.4		24
4.3	odd	2		216.2.q.a.121.1	yes	24
12.11	even	2		648.2.q.a.577.4		24
27.25	even	9	inner	432.2.u.e.241.4		24
108.59	even	18		5832.2.a.i.1.11		12
108.79	odd	18		216.2.q.a.25.1	✓	24
108.83	even	18		648.2.q.a.73.4		24
108.103	odd	18		5832.2.a.h.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.25.1	✓	24	108.79	odd	18
216.2.q.a.121.1	yes	24	4.3	odd	2
432.2.u.e.241.4		24	27.25	even	9	inner
432.2.u.e.337.4		24	1.1	even	1	trivial
648.2.q.a.73.4		24	108.83	even	18
648.2.q.a.577.4		24	12.11	even	2
5832.2.a.h.1.2		12	108.103	odd	18
5832.2.a.i.1.11		12	108.59	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.66239 - 0.486282i) q^{3} +(-2.11828 - 1.77745i) q^{5} +(-4.34143 - 1.58015i) q^{7} +(2.52706 - 1.61678i) q^{9} +O(q^{10})\)	\(q+(1.66239 - 0.486282i) q^{3} +(-2.11828 - 1.77745i) q^{5} +(-4.34143 - 1.58015i) q^{7} +(2.52706 - 1.61678i) q^{9} +(-2.54255 + 2.13345i) q^{11} +(0.625780 - 3.54898i) q^{13} +(-4.38574 - 1.92472i) q^{15} +(1.18168 - 2.04672i) q^{17} +(-1.11760 - 1.93575i) q^{19} +(-7.98553 - 0.515662i) q^{21} +(-2.65318 + 0.965678i) q^{23} +(0.459548 + 2.60623i) q^{25} +(3.41474 - 3.91658i) q^{27} +(1.17009 + 6.63591i) q^{29} +(8.26703 - 3.00895i) q^{31} +(-3.18924 + 4.78301i) q^{33} +(6.38772 + 11.0639i) q^{35} +(3.78335 - 6.55296i) q^{37} +(-0.685516 - 6.20408i) q^{39} +(0.644709 - 3.65633i) q^{41} +(-4.43937 + 3.72507i) q^{43} +(-8.22676 - 1.06693i) q^{45} +(7.67045 + 2.79181i) q^{47} +(10.9888 + 9.22070i) q^{49} +(0.969117 - 3.97707i) q^{51} -9.41409 q^{53} +9.17792 q^{55} +(-2.79921 - 2.67449i) q^{57} +(-5.40831 - 4.53811i) q^{59} +(6.50974 + 2.36935i) q^{61} +(-13.5258 + 3.02599i) q^{63} +(-7.63370 + 6.40544i) q^{65} +(2.00705 - 11.3825i) q^{67} +(-3.94102 + 2.89552i) q^{69} +(-0.871998 + 1.51035i) q^{71} +(-3.68885 - 6.38927i) q^{73} +(2.03131 + 4.10909i) q^{75} +(14.4094 - 5.24461i) q^{77} +(-0.147982 - 0.839245i) q^{79} +(3.77205 - 8.17139i) q^{81} +(-1.93014 - 10.9464i) q^{83} +(-6.14106 + 2.23516i) q^{85} +(5.17207 + 10.4625i) q^{87} +(6.35169 + 11.0015i) q^{89} +(-8.32470 + 14.4188i) q^{91} +(12.2798 - 9.02215i) q^{93} +(-1.07329 + 6.08694i) q^{95} +(1.46774 - 1.23158i) q^{97} +(-2.97585 + 9.50209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) \) 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

Varieties

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Database

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