LMFDB - Embedded newform 1080.2.m.c.539.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(539,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("1080.539");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.6
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34874 - 0.425328i) q^{2} +(1.63819 + 1.14731i) q^{4} +(2.17257 + 0.529077i) q^{5} +1.59486 q^{7} +(-1.72151 - 2.24419i) q^{8} +(-2.70520 - 1.63764i) q^{10} +3.61186i q^{11} +2.18660 q^{13} +(-2.15105 - 0.678339i) q^{14} +(1.36735 + 3.75904i) q^{16} -2.27828 q^{17} +5.81486 q^{19} +(2.95208 + 3.35935i) q^{20} +(1.53622 - 4.87145i) q^{22} -1.07910i q^{23} +(4.44016 + 2.29892i) q^{25} +(-2.94915 - 0.930020i) q^{26} +(2.61269 + 1.82980i) q^{28} -2.55585 q^{29} +5.93344i q^{31} +(-0.245375 - 5.65153i) q^{32} +(3.07281 + 0.969016i) q^{34} +(3.46495 + 0.843804i) q^{35} -2.49682 q^{37} +(-7.84272 - 2.47322i) q^{38} +(-2.55276 - 5.78649i) q^{40} -10.3047i q^{41} -0.983745i q^{43} +(-4.14393 + 5.91692i) q^{44} +(-0.458973 + 1.45543i) q^{46} +10.6532i q^{47} -4.45642 q^{49} +(-5.01082 - 4.98916i) q^{50} +(3.58206 + 2.50871i) q^{52} +8.26543i q^{53} +(-1.91095 + 7.84703i) q^{55} +(-2.74557 - 3.57918i) q^{56} +(3.44717 + 1.08707i) q^{58} -2.81213i q^{59} -8.34242i q^{61} +(2.52366 - 8.00266i) q^{62} +(-2.07281 + 7.72680i) q^{64} +(4.75054 + 1.15688i) q^{65} -6.00359i q^{67} +(-3.73226 - 2.61390i) q^{68} +(-4.31442 - 2.61181i) q^{70} +2.34652 q^{71} +5.96697i q^{73} +(3.36756 + 1.06197i) q^{74} +(9.52585 + 6.67146i) q^{76} +5.76041i q^{77} +11.2489i q^{79} +(0.981850 + 8.89022i) q^{80} +(-4.38289 + 13.8984i) q^{82} +6.40570 q^{83} +(-4.94973 - 1.20539i) q^{85} +(-0.418414 + 1.32681i) q^{86} +(8.10570 - 6.21785i) q^{88} +6.53221i q^{89} +3.48732 q^{91} +(1.23807 - 1.76778i) q^{92} +(4.53112 - 14.3684i) q^{94} +(12.6332 + 3.07651i) q^{95} -16.1661i q^{97} +(6.01054 + 1.89544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.34874	−	0.425328i	−0.953702	−	0.300752i
$2$	−1.34874	−	0.425328i	−0.953702	−	0.300752i
$3$		0			0
$3$		0			0
$4$	1.63819	+	1.14731i	0.819096	+	0.573656i
$5$	2.17257	+	0.529077i	0.971605	+	0.236610i
$5$	2.17257	+	0.529077i	0.971605	+	0.236610i
$6$		0			0
$7$	1.59486			0.602801			0.301400	−	0.953498i	$-0.402546\pi$
$7$	1.59486			0.602801			0.301400	+	0.953498i	$0.402546\pi$
$8$	−1.72151	−	2.24419i	−0.608646	−	0.793442i
$9$		0			0
$10$	−2.70520	−	1.63764i	−0.855461	−	0.517868i
$11$			3.61186i			1.08902i	0.838756	+	0.544508i	$0.183284\pi$
$11$			3.61186i			1.08902i	−0.838756	+	0.544508i	$0.816716\pi$
$12$		0			0
$13$	2.18660			0.606452			0.303226	−	0.952919i	$-0.401936\pi$
$13$	2.18660			0.606452			0.303226	+	0.952919i	$0.401936\pi$
$14$	−2.15105	−	0.678339i	−0.574893	−	0.181294i
$15$		0			0
$16$	1.36735	+	3.75904i	0.341837	+	0.939759i
$17$	−2.27828			−0.552564			−0.276282	−	0.961077i	$-0.589102\pi$
$17$	−2.27828			−0.552564			−0.276282	+	0.961077i	$0.589102\pi$
$18$		0			0
$19$	5.81486			1.33402			0.667010	−	0.745049i	$-0.267574\pi$
$19$	5.81486			1.33402			0.667010	+	0.745049i	$0.267574\pi$
$20$	2.95208	+	3.35935i	0.660105	+	0.751174i
$21$		0			0
$22$	1.53622	−	4.87145i	0.327524	−	1.03860i
$23$		−	1.07910i		−	0.225009i	−0.993651	−	0.112504i	$-0.964113\pi$
$23$		−	1.07910i		−	0.225009i	0.993651	−	0.112504i	$-0.0358873\pi$
$24$		0			0
$25$	4.44016	+	2.29892i	0.888031	+	0.459783i
$26$	−2.94915	−	0.930020i	−0.578375	−	0.182392i
$27$		0			0
$28$	2.61269	+	1.82980i	0.493752	+	0.345800i
$29$	−2.55585			−0.474609			−0.237305	−	0.971435i	$-0.576264\pi$
$29$	−2.55585			−0.474609			−0.237305	+	0.971435i	$0.576264\pi$
$30$		0			0
$31$			5.93344i			1.06568i	0.846217	+	0.532838i	$0.178875\pi$
$31$			5.93344i			1.06568i	−0.846217	+	0.532838i	$0.821125\pi$
$32$	−0.245375	−	5.65153i	−0.0433766	−	0.999059i
$33$		0			0
$34$	3.07281	+	0.969016i	0.526982	+	0.166185i
$35$	3.46495	+	0.843804i	0.585684	+	0.142629i
$36$		0			0
$37$	−2.49682			−0.410475			−0.205237	−	0.978712i	$-0.565797\pi$
$37$	−2.49682			−0.410475			−0.205237	+	0.978712i	$0.565797\pi$
$38$	−7.84272	−	2.47322i	−1.27226	−	0.401209i
$39$		0			0
$40$	−2.55276	−	5.78649i	−0.403626	−	0.914924i
$41$		−	10.3047i		−	1.60933i	−0.593731	−	0.804664i	$-0.702346\pi$
$41$		−	10.3047i		−	1.60933i	0.593731	−	0.804664i	$-0.297654\pi$
$42$		0			0
$43$		−	0.983745i		−	0.150020i	−0.997183	−	0.0750098i	$-0.976101\pi$
$43$		−	0.983745i		−	0.150020i	0.997183	−	0.0750098i	$-0.0238988\pi$
$44$	−4.14393	+	5.91692i	−0.624720	+	0.892009i
$45$		0			0
$46$	−0.458973	+	1.45543i	−0.0676719	+	0.214592i
$47$			10.6532i			1.55394i	0.629541	+	0.776968i	$0.283243\pi$
$47$			10.6532i			1.55394i	−0.629541	+	0.776968i	$0.716757\pi$
$48$		0			0
$49$	−4.45642			−0.636631
$50$	−5.01082	−	4.98916i	−0.708636	−	0.705574i
$51$		0			0
$52$	3.58206	+	2.50871i	0.496743	+	0.347895i
$53$			8.26543i			1.13534i	0.823255	+	0.567672i	$0.192156\pi$
$53$			8.26543i			1.13534i	−0.823255	+	0.567672i	$0.807844\pi$
$54$		0			0
$55$	−1.91095	+	7.84703i	−0.257672	+	1.05809i
$56$	−2.74557	−	3.57918i	−0.366892	−	0.478288i
$57$		0			0
$58$	3.44717	+	1.08707i	0.452636	+	0.142740i
$59$		−	2.81213i		−	0.366108i	−0.983103	−	0.183054i	$-0.941402\pi$
$59$		−	2.81213i		−	0.366108i	0.983103	−	0.183054i	$-0.0585983\pi$
$60$		0			0
$61$		−	8.34242i		−	1.06814i	−0.845441	−	0.534069i	$-0.820662\pi$
$61$		−	8.34242i		−	1.06814i	0.845441	−	0.534069i	$-0.179338\pi$
$62$	2.52366	−	8.00266i	0.320505	−	1.01634i
$63$		0			0
$64$	−2.07281	+	7.72680i	−0.259101	+	0.965850i
$65$	4.75054	+	1.15688i	0.589232	+	0.143493i
$66$		0			0
$67$		−	6.00359i		−	0.733455i	−0.930328	−	0.366728i	$-0.880478\pi$
$67$		−	6.00359i		−	0.733455i	0.930328	−	0.366728i	$-0.119522\pi$
$68$	−3.73226	−	2.61390i	−0.452603	−	0.316982i
$69$		0			0
$70$	−4.31442	−	2.61181i	−0.515672	−	0.312171i
$71$	2.34652			0.278480			0.139240	−	0.990259i	$-0.455534\pi$
$71$	2.34652			0.278480			0.139240	+	0.990259i	$0.455534\pi$
$72$		0			0
$73$			5.96697i			0.698381i	0.937052	+	0.349191i	$0.113543\pi$
$73$			5.96697i			0.698381i	−0.937052	+	0.349191i	$0.886457\pi$
$74$	3.36756	+	1.06197i	0.391471	+	0.123451i
$75$		0			0
$76$	9.52585	+	6.67146i	1.09269	+	0.765268i
$77$			5.76041i			0.656460i
$78$		0			0
$79$			11.2489i			1.26559i	0.774317	+	0.632797i	$0.218093\pi$
$79$			11.2489i			1.26559i	−0.774317	+	0.632797i	$0.781907\pi$
$80$	0.981850	+	8.89022i	0.109774	+	0.993957i
$81$		0			0
$82$	−4.38289	+	13.8984i	−0.484009	+	1.53482i
$83$	6.40570			0.703117			0.351559	−	0.936166i	$-0.385652\pi$
$83$	6.40570			0.703117			0.351559	+	0.936166i	$0.385652\pi$
$84$		0			0
$85$	−4.94973	−	1.20539i	−0.536874	−	0.130742i
$86$	−0.418414	+	1.32681i	−0.0451187	+	0.143074i
$87$		0			0
$88$	8.10570	−	6.21785i	0.864071	−	0.662825i
$89$			6.53221i			0.692413i	0.938158	+	0.346206i	$0.112530\pi$
$89$			6.53221i			0.692413i	−0.938158	+	0.346206i	$0.887470\pi$
$90$		0			0
$91$	3.48732			0.365570
$92$	1.23807	−	1.76778i	0.129078	−	0.184304i
$93$		0			0
$94$	4.53112	−	14.3684i	0.467349	−	1.48199i
$95$	12.6332	+	3.07651i	1.29614	+	0.315643i
$96$		0			0
$97$		−	16.1661i		−	1.64142i	−0.571348	−	0.820708i	$-0.693579\pi$
$97$		−	16.1661i		−	1.64142i	0.571348	−	0.820708i	$-0.306421\pi$
$98$	6.01054	+	1.89544i	0.607157	+	0.191468i
$99$		0			0
$100$	4.63625	+	8.86031i	0.463625	+	0.886031i
$101$	−9.33401			−0.928769			−0.464385	−	0.885634i	$-0.653724\pi$
$101$	−9.33401			−0.928769			−0.464385	+	0.885634i	$0.653724\pi$
$102$		0			0
$103$	19.4431			1.91579			0.957895	−	0.287120i	$-0.0926977\pi$
$103$	19.4431			1.91579			0.957895	+	0.287120i	$0.0926977\pi$
$104$	−3.76425	−	4.90714i	−0.369115	−	0.481185i
$105$		0			0
$106$	3.51552	−	11.1479i	0.341457	−	1.08278i
$107$	12.4680			1.20532			0.602662	−	0.797997i	$-0.294107\pi$
$107$	12.4680			1.20532			0.602662	+	0.797997i	$0.294107\pi$
$108$		0			0
$109$		−	7.46156i		−	0.714688i	−0.933973	−	0.357344i	$-0.883682\pi$
$109$		−	7.46156i		−	0.714688i	0.933973	−	0.357344i	$-0.116318\pi$
$110$	5.91493	−	9.77081i	0.563966	−	0.931610i
$111$		0			0
$112$	2.18073	+	5.99514i	0.206060	+	0.566488i
$113$	13.1420			1.23629			0.618146	−	0.786063i	$-0.287884\pi$
$113$	13.1420			1.23629			0.618146	+	0.786063i	$0.287884\pi$
$114$		0			0
$115$	0.570929	−	2.34443i	0.0532394	−	0.218620i
$116$	−4.18697	−	2.93236i	−0.388751	−	0.272262i
$117$		0			0
$118$	−1.19608	+	3.79283i	−0.110108	+	0.349158i
$119$	−3.63354			−0.333086
$120$		0			0
$121$	−2.04551			−0.185955
$122$	−3.54826	+	11.2517i	−0.321245	+	1.01869i
$123$		0			0
$124$	−6.80751	+	9.72011i	−0.611332	+	0.872892i
$125$	8.43026	+	7.34375i	0.754026	+	0.656845i
$126$		0			0
$127$	−17.9156			−1.58975			−0.794876	−	0.606772i	$-0.792464\pi$
$127$	−17.9156			−1.58975			−0.794876	+	0.606772i	$0.792464\pi$
$128$	6.08210	−	9.53982i	0.537587	−	0.843209i
$129$		0			0
$130$	−5.91519	−	3.58086i	−0.518796	−	0.314062i
$131$		−	13.8512i		−	1.21019i	−0.796155	−	0.605093i	$-0.793136\pi$
$131$		−	13.8512i		−	1.21019i	0.796155	−	0.605093i	$-0.206864\pi$
$132$		0			0
$133$	9.27389			0.804148
$134$	−2.55349	+	8.09728i	−0.220588	+	0.699498i
$135$		0			0
$136$	3.92208	+	5.11290i	0.336316	+	0.438428i
$137$	14.7529			1.26043			0.630214	−	0.776422i	$-0.282967\pi$
$137$	14.7529			1.26043			0.630214	+	0.776422i	$0.282967\pi$
$138$		0			0
$139$	8.56738			0.726676			0.363338	−	0.931657i	$-0.381637\pi$
$139$	8.56738			0.726676			0.363338	+	0.931657i	$0.381637\pi$
$140$	4.70816	+	5.35770i	0.397912	+	0.452808i
$141$		0			0
$142$	−3.16484	−	0.998038i	−0.265587	−	0.0837535i
$143$			7.89767i			0.660436i
$144$		0			0
$145$	−5.55277	−	1.35224i	−0.461132	−	0.112297i
$146$	2.53792	−	8.04789i	0.210040	−	0.666048i
$147$		0			0
$148$	−4.09027	−	2.86463i	−0.336218	−	0.235471i
$149$	17.2194			1.41067			0.705335	−	0.708874i	$-0.250797\pi$
$149$	17.2194			1.41067			0.705335	+	0.708874i	$0.250797\pi$
$150$		0			0
$151$			6.38199i			0.519359i	0.965695	+	0.259680i	$0.0836170\pi$
$151$			6.38199i			0.519359i	−0.965695	+	0.259680i	$0.916383\pi$
$152$	−10.0103	−	13.0497i	−0.811945	−	1.05847i
$153$		0			0
$154$	2.45006	−	7.76929i	0.197432	−	0.626067i
$155$	−3.13924	+	12.8908i	−0.252150	+	1.03542i
$156$		0			0
$157$	−24.3034			−1.93962			−0.969811	−	0.243857i	$-0.921587\pi$
$157$	−24.3034			−1.93962			−0.969811	+	0.243857i	$0.921587\pi$
$158$	4.78445	−	15.1718i	0.380630	−	1.20700i
$159$		0			0
$160$	2.45700	−	12.4082i	0.194243	−	0.980953i
$161$		−	1.72102i		−	0.135636i
$162$		0			0
$163$			19.9078i			1.55930i	0.626215	+	0.779650i	$0.284603\pi$
$163$			19.9078i			1.55930i	−0.626215	+	0.779650i	$0.715397\pi$
$164$	11.8227	−	16.8811i	0.923200	−	1.31819i
$165$		0			0
$166$	−8.63962	−	2.72452i	−0.670565	−	0.211464i
$167$			7.62227i			0.589829i	0.955524	+	0.294915i	$0.0952912\pi$
$167$			7.62227i			0.589829i	−0.955524	+	0.294915i	$0.904709\pi$
$168$		0			0
$169$	−8.21880			−0.632215
$170$	6.16321	+	3.73101i	0.472697	+	0.286155i
$171$		0			0
$172$	1.12866	−	1.61156i	0.0860597	−	0.122881i
$173$			13.7524i			1.04558i	0.852463	+	0.522788i	$0.175108\pi$
$173$			13.7524i			1.04558i	−0.852463	+	0.522788i	$0.824892\pi$
$174$		0			0
$175$	7.08143	+	3.66645i	0.535306	+	0.277158i
$176$	−13.5771	+	4.93867i	−1.02341	+	0.372266i
$177$		0			0
$178$	2.77833	−	8.81024i	0.208245	−	0.660356i
$179$		−	14.1889i		−	1.06053i	−0.847832	−	0.530265i	$-0.822092\pi$
$179$		−	14.1889i		−	1.06053i	0.847832	−	0.530265i	$-0.177908\pi$
$180$		0			0
$181$		−	19.4024i		−	1.44217i	−0.692846	−	0.721086i	$-0.743643\pi$
$181$		−	19.4024i		−	1.44217i	0.692846	−	0.721086i	$-0.256357\pi$
$182$	−4.70348	−	1.48325i	−0.348645	−	0.109946i
$183$		0			0
$184$	−2.42172	+	1.85769i	−0.178532	+	0.136951i
$185$	−5.42453	−	1.32101i	−0.398819	−	0.0971226i
$186$		0			0
$187$		−	8.22882i		−	0.601751i
$188$	−12.2226	+	17.4521i	−0.891424	+	1.27282i
$189$		0			0
$190$	−15.7304	−	9.52266i	−1.14120	−	0.690846i
$191$	−24.8392			−1.79730			−0.898651	−	0.438664i	$-0.855452\pi$
$191$	−24.8392			−1.79730			−0.898651	+	0.438664i	$0.855452\pi$
$192$		0			0
$193$			6.04021i			0.434784i	0.976084	+	0.217392i	$0.0697549\pi$
$193$			6.04021i			0.434784i	−0.976084	+	0.217392i	$0.930245\pi$
$194$	−6.87588	+	21.8038i	−0.493659	+	1.56542i
$195$		0			0
$196$	−7.30047	−	5.11290i	−0.521462	−	0.365207i
$197$		−	17.5571i		−	1.25089i	−0.780269	−	0.625444i	$-0.784918\pi$
$197$		−	17.5571i		−	1.25089i	0.780269	−	0.625444i	$-0.215082\pi$
$198$		0			0
$199$			11.9068i			0.844048i	0.906585	+	0.422024i	$0.138680\pi$
$199$			11.9068i			0.844048i	−0.906585	+	0.422024i	$0.861320\pi$
$200$	−2.48456	−	13.9222i	−0.175685	−	0.984446i
$201$		0			0
$202$	12.5891	+	3.97002i	0.885769	+	0.279329i
$203$	−4.07622			−0.286095
$204$		0			0
$205$	5.45199	−	22.3878i	0.380784	−	1.56363i
$206$	−26.2237	−	8.26971i	−1.82709	−	0.576178i
$207$		0			0
$208$	2.98984	+	8.21949i	0.207308	+	0.569919i
$209$			21.0024i			1.45277i
$210$		0			0
$211$	−6.86570			−0.472654			−0.236327	−	0.971674i	$-0.575944\pi$
$211$	−6.86570			−0.472654			−0.236327	+	0.971674i	$0.575944\pi$
$212$	−9.48303	+	13.5404i	−0.651297	+	0.929956i
$213$		0			0
$214$	−16.8160	−	5.30297i	−1.14952	−	0.362504i
$215$	0.520477	−	2.13726i	0.0354962	−	0.145760i
$216$		0			0
$217$			9.46301i			0.642391i
$218$	−3.17361	+	10.0637i	−0.214944	+	0.681599i
$219$		0			0
$220$	−12.1335	+	10.6625i	−0.818040	+	0.718864i
$221$	−4.98168			−0.335104
$222$		0			0
$223$	4.99364			0.334399			0.167200	−	0.985923i	$-0.446528\pi$
$223$	4.99364			0.334399			0.167200	+	0.985923i	$0.446528\pi$
$224$	−0.391339	−	9.01341i	−0.0261475	−	0.602234i
$225$		0			0
$226$	−17.7251	−	5.58964i	−1.17905	−	0.371817i
$227$	−12.3395			−0.819000			−0.409500	−	0.912310i	$-0.634297\pi$
$227$	−12.3395			−0.819000			−0.409500	+	0.912310i	$0.634297\pi$
$228$		0			0
$229$		−	25.0215i		−	1.65347i	−0.562593	−	0.826734i	$-0.690196\pi$
$229$		−	25.0215i		−	1.65347i	0.562593	−	0.826734i	$-0.309804\pi$
$230$	−1.76719	+	2.91920i	−0.116525	+	0.192486i
$231$		0			0
$232$	4.39992	+	5.73582i	0.288869	+	0.376575i
$233$	−6.88604			−0.451120			−0.225560	−	0.974229i	$-0.572421\pi$
$233$	−6.88604			−0.451120			−0.225560	+	0.974229i	$0.572421\pi$
$234$		0			0
$235$	−5.63638	+	23.1450i	−0.367677	+	1.50981i
$236$	3.22639	−	4.60681i	0.210020	−	0.299878i
$237$		0			0
$238$	4.90070	+	1.54545i	0.317665	+	0.100176i
$239$	8.26310			0.534495			0.267248	−	0.963628i	$-0.413886\pi$
$239$	8.26310			0.534495			0.267248	+	0.963628i	$0.413886\pi$
$240$		0			0
$241$	−18.2659			−1.17661			−0.588304	−	0.808640i	$-0.700204\pi$
$241$	−18.2659			−1.17661			−0.588304	+	0.808640i	$0.700204\pi$
$242$	2.75885	+	0.870011i	0.177346	+	0.0559264i
$243$		0			0
$244$	9.57136	−	13.6665i	0.612744	−	0.874908i
$245$	−9.68190	−	2.35779i	−0.618554	−	0.150634i
$246$		0			0
$247$	12.7147			0.809019
$248$	13.3158	−	10.2145i	0.845553	−	0.648620i
$249$		0			0
$250$	−8.24672	−	13.4904i	−0.521568	−	0.853209i
$251$		−	11.7200i		−	0.739758i	−0.929080	−	0.369879i	$-0.879399\pi$
$251$		−	11.7200i		−	0.739758i	0.929080	−	0.369879i	$-0.120601\pi$
$252$		0			0
$253$	3.89757			0.245038
$254$	24.1635	+	7.62000i	1.51615	+	0.478122i
$255$		0			0
$256$	−12.2607	+	10.2798i	−0.766294	+	0.642490i
$257$	−14.0351			−0.875484			−0.437742	−	0.899101i	$-0.644222\pi$
$257$	−14.0351			−0.875484			−0.437742	+	0.899101i	$0.644222\pi$
$258$		0			0
$259$	−3.98208			−0.247435
$260$	6.45500	+	7.34554i	0.400322	+	0.455551i
$261$		0			0
$262$	−5.89131	+	18.6817i	−0.363966	+	1.15416i
$263$			2.15821i			0.133081i	0.997784	+	0.0665404i	$0.0211961\pi$
$263$			2.15821i			0.133081i	−0.997784	+	0.0665404i	$0.978804\pi$
$264$		0			0
$265$	−4.37305	+	17.9573i	−0.268634	+	1.10311i
$266$	−12.5081	−	3.94444i	−0.766918	−	0.241849i
$267$		0			0
$268$	6.88799	−	9.83504i	0.420751	−	0.600771i
$269$	16.4601			1.00359			0.501794	−	0.864987i	$-0.332674\pi$
$269$	16.4601			1.00359			0.501794	+	0.864987i	$0.332674\pi$
$270$		0			0
$271$			17.3557i			1.05429i	0.849777	+	0.527143i	$0.176737\pi$
$271$			17.3557i			1.05429i	−0.849777	+	0.527143i	$0.823263\pi$
$272$	−3.11521	−	8.56414i	−0.188887	−	0.519277i
$273$		0			0
$274$	−19.8978	−	6.27483i	−1.20207	−	0.379076i
$275$	−8.30336	+	16.0372i	−0.500711	+	0.967080i
$276$		0			0
$277$	−4.12691			−0.247962			−0.123981	−	0.992285i	$-0.539566\pi$
$277$	−4.12691			−0.247962			−0.123981	+	0.992285i	$0.539566\pi$
$278$	−11.5552	−	3.64394i	−0.693032	−	0.218549i
$279$		0			0
$280$	−4.07129	−	9.22864i	−0.243306	−	0.551517i
$281$		−	4.04370i		−	0.241227i	−0.992700	−	0.120613i	$-0.961514\pi$
$281$		−	4.04370i		−	0.241227i	0.992700	−	0.120613i	$-0.0384862\pi$
$282$		0			0
$283$		−	16.6792i		−	0.991473i	−0.868473	−	0.495736i	$-0.834898\pi$
$283$		−	16.6792i		−	0.991473i	0.868473	−	0.495736i	$-0.165102\pi$
$284$	3.84404	+	2.69219i	0.228102	+	0.159752i
$285$		0			0
$286$	3.35910	−	10.6519i	0.198628	−	0.629860i
$287$		−	16.4346i		−	0.970104i
$288$		0			0
$289$	−11.8094			−0.694673
$290$	6.91409	+	4.18557i	0.406009	+	0.245785i
$291$		0			0
$292$	−6.84598	+	9.77505i	−0.400631	+	0.572042i
$293$		−	30.6478i		−	1.79046i	−0.445601	−	0.895232i	$-0.647010\pi$
$293$		−	30.6478i		−	1.79046i	0.445601	−	0.895232i	$-0.352990\pi$
$294$		0			0
$295$	1.48783	−	6.10956i	0.0866249	−	0.355712i
$296$	4.29830	+	5.60335i	0.249834	+	0.325688i
$297$		0			0
$298$	−23.2245	−	7.32390i	−1.34536	−	0.424262i
$299$		−	2.35957i		−	0.136457i
$300$		0			0
$301$		−	1.56894i		−	0.0904320i
$302$	2.71444	−	8.60764i	0.156198	−	0.495314i
$303$		0			0
$304$	7.95094	+	21.8583i	0.456018	+	1.25366i
$305$	4.41378	−	18.1245i	0.252732	−	1.03781i
$306$		0			0
$307$		−	32.3125i		−	1.84417i	−0.386988	−	0.922085i	$-0.626485\pi$
$307$		−	32.3125i		−	1.84417i	0.386988	−	0.922085i	$-0.373515\pi$
$308$	−6.60899	+	9.43666i	−0.376582	+	0.537704i
$309$		0			0
$310$	9.71685	−	16.0512i	0.551880	−	0.911645i
$311$	−5.05675			−0.286742			−0.143371	−	0.989669i	$-0.545794\pi$
$311$	−5.05675			−0.286742			−0.143371	+	0.989669i	$0.545794\pi$
$312$		0			0
$313$			10.5648i			0.597158i	0.954385	+	0.298579i	$0.0965127\pi$
$313$			10.5648i			0.597158i	−0.954385	+	0.298579i	$0.903487\pi$
$314$	32.7789	+	10.3369i	1.84982	+	0.583346i
$315$		0			0
$316$	−12.9059	+	18.4278i	−0.726016	+	1.03664i
$317$			4.83085i			0.271328i	0.990755	+	0.135664i	$0.0433167\pi$
$317$			4.83085i			0.271328i	−0.990755	+	0.135664i	$0.956683\pi$
$318$		0			0
$319$		−	9.23136i		−	0.516857i
$320$	−8.59140	+	15.6904i	−0.480274	+	0.877119i
$321$		0			0
$322$	−0.731999	+	2.32121i	−0.0407927	+	0.129356i
$323$	−13.2479			−0.737132
$324$		0			0
$325$	9.70882	+	5.02680i	0.538549	+	0.278837i
$326$	8.46735	−	26.8504i	0.468963	−	1.48711i
$327$		0			0
$328$	−23.1258	+	17.7397i	−1.27691	+	0.979510i
$329$			16.9904i			0.936713i
$330$		0			0
$331$	4.14240			0.227687			0.113843	−	0.993499i	$-0.463684\pi$
$331$	4.14240			0.227687			0.113843	+	0.993499i	$0.463684\pi$
$332$	10.4938	+	7.34934i	0.575921	+	0.403347i
$333$		0			0
$334$	3.24196	−	10.2805i	0.177392	−	0.562521i
$335$	3.17636	−	13.0432i	0.173543	−	0.712629i
$336$		0			0
$337$		−	23.5875i		−	1.28489i	−0.766332	−	0.642445i	$-0.777920\pi$
$337$		−	23.5875i		−	1.28489i	0.766332	−	0.642445i	$-0.222080\pi$
$338$	11.0850	+	3.49568i	0.602945	+	0.190140i
$339$		0			0
$340$	−6.72566	−	7.65354i	−0.364750	−	0.415072i
$341$	−21.4307			−1.16054
$342$		0			0
$343$	−18.2714			−0.986563
$344$	−2.20771	+	1.69353i	−0.119032	+	0.0913088i
$345$		0			0
$346$	5.84928	−	18.5484i	0.314459	−	0.997168i
$347$	10.0100			0.537365			0.268683	−	0.963229i	$-0.413412\pi$
$347$	10.0100			0.537365			0.268683	+	0.963229i	$0.413412\pi$
$348$		0			0
$349$		−	0.434946i		−	0.0232821i	−0.999932	−	0.0116411i	$-0.996294\pi$
$349$		−	0.434946i		−	0.0232821i	0.999932	−	0.0116411i	$-0.00370555\pi$
$350$	−7.99156	−	7.95702i	−0.427167	−	0.425320i
$351$		0			0
$352$	20.4125	−	0.886260i	1.08799	−	0.0472378i
$353$	−23.0388			−1.22623			−0.613115	−	0.789994i	$-0.710084\pi$
$353$	−23.0388			−1.22623			−0.613115	+	0.789994i	$0.710084\pi$
$354$		0			0
$355$	5.09798	+	1.24149i	0.270573	+	0.0658913i
$356$	−7.49448	+	10.7010i	−0.397207	+	0.567153i
$357$		0			0
$358$	−6.03495	+	19.1372i	−0.318957	+	1.01143i
$359$	12.9336			0.682611			0.341306	−	0.939952i	$-0.389131\pi$
$359$	12.9336			0.682611			0.341306	+	0.939952i	$0.389131\pi$
$360$		0			0
$361$	14.8126			0.779608
$362$	−8.25239	+	26.1688i	−0.433736	+	1.37540i
$363$		0			0
$364$	5.71289	+	4.00104i	0.299437	+	0.209711i
$365$	−3.15699	+	12.9637i	−0.165244	+	0.678551i
$366$		0			0
$367$	−21.3144			−1.11260			−0.556301	−	0.830981i	$-0.687780\pi$
$367$	−21.3144			−1.11260			−0.556301	+	0.830981i	$0.687780\pi$
$368$	4.05639	−	1.47551i	0.211454	−	0.0769165i
$369$		0			0
$370$	6.75441	+	4.08890i	0.351145	+	0.212572i
$371$			13.1822i			0.684386i
$372$		0			0
$373$	−28.2669			−1.46360			−0.731802	−	0.681517i	$-0.761321\pi$
$373$	−28.2669			−1.46360			−0.731802	+	0.681517i	$0.761321\pi$
$374$	−3.49995	+	11.0985i	−0.180978	+	0.573891i
$375$		0			0
$376$	23.9079	−	18.3397i	1.23296	−	0.945796i
$377$	−5.58861			−0.287828
$378$		0			0
$379$	−22.8586			−1.17417			−0.587084	−	0.809526i	$-0.699724\pi$
$379$	−22.8586			−1.17417			−0.587084	+	0.809526i	$0.699724\pi$
$380$	17.1659	+	19.5341i	0.880593	+	1.00208i
$381$		0			0
$382$	33.5016	+	10.5648i	1.71409	+	0.540543i
$383$		−	26.5168i		−	1.35494i	−0.735549	−	0.677472i	$-0.763076\pi$
$383$		−	26.5168i		−	1.35494i	0.735549	−	0.677472i	$-0.236924\pi$
$384$		0			0
$385$	−3.04770	+	12.5149i	−0.155325	+	0.637819i
$386$	2.56907	−	8.14666i	0.130762	−	0.414654i
$387$		0			0
$388$	18.5475	−	26.4831i	0.941608	−	1.34448i
$389$	−16.2240			−0.822589			−0.411295	−	0.911502i	$-0.634923\pi$
$389$	−16.2240			−0.822589			−0.411295	+	0.911502i	$0.634923\pi$
$390$		0			0
$391$			2.45850i			0.124332i
$392$	7.67177	+	10.0011i	0.387483	+	0.505130i
$393$		0			0
$394$	−7.46750	+	23.6799i	−0.376207	+	1.19298i
$395$	−5.95151	+	24.4390i	−0.299453	+	1.22966i
$396$		0			0
$397$	18.3726			0.922093			0.461046	−	0.887376i	$-0.347474\pi$
$397$	18.3726			0.922093			0.461046	+	0.887376i	$0.347474\pi$
$398$	5.06427	−	16.0591i	0.253849	−	0.804970i
$399$		0			0
$400$	−2.57047	+	19.8341i	−0.128523	+	0.991706i
$401$		−	13.0115i		−	0.649761i	−0.945755	−	0.324881i	$-0.894676\pi$
$401$		−	13.0115i		−	0.649761i	0.945755	−	0.324881i	$-0.105324\pi$
$402$		0			0
$403$			12.9740i			0.646282i
$404$	−15.2909	−	10.7090i	−0.760751	−	0.532794i
$405$		0			0
$406$	5.49776	+	1.73373i	0.272849	+	0.0860436i
$407$		−	9.01816i		−	0.447014i
$408$		0			0
$409$	27.8630			1.37774			0.688869	−	0.724885i	$-0.258107\pi$
$409$	27.8630			1.37774			0.688869	+	0.724885i	$0.258107\pi$
$410$	−16.8755	+	27.8764i	−0.833419	+	1.37672i
$411$		0			0
$412$	31.8516	+	22.3074i	1.56922	+	1.09900i
$413$		−	4.48496i		−	0.220690i
$414$		0			0
$415$	13.9169	+	3.38911i	0.683152	+	0.166365i
$416$	−0.536536	−	12.3576i	−0.0263058	−	0.605882i
$417$		0			0
$418$	8.93292	−	28.3268i	0.436923	−	1.38551i
$419$		−	21.9663i		−	1.07312i	−0.843861	−	0.536562i	$-0.819723\pi$
$419$		−	21.9663i		−	1.07312i	0.843861	−	0.536562i	$-0.180277\pi$
$420$		0			0
$421$			10.0594i			0.490263i	0.969490	+	0.245132i	$0.0788312\pi$
$421$			10.0594i			0.490263i	−0.969490	+	0.245132i	$0.921169\pi$
$422$	9.26004	+	2.92017i	0.450772	+	0.142152i
$423$		0			0
$424$	18.5492	−	14.2290i	0.900830	−	0.691022i
$425$	−10.1159	−	5.23758i	−0.490694	−	0.254060i
$426$		0			0
$427$		−	13.3050i		−	0.643874i
$428$	20.4249	+	14.3047i	0.987277	+	0.691442i
$429$		0			0
$430$	−1.61102	+	2.66123i	−0.0776904	+	0.128336i
$431$	9.80514			0.472297			0.236148	−	0.971717i	$-0.424115\pi$
$431$	9.80514			0.472297			0.236148	+	0.971717i	$0.424115\pi$
$432$		0			0
$433$		−	14.7117i		−	0.706997i	−0.935435	−	0.353499i	$-0.884992\pi$
$433$		−	14.7117i		−	0.706997i	0.935435	−	0.353499i	$-0.115008\pi$
$434$	4.02488	−	12.7631i	0.193200	−	0.612650i
$435$		0			0
$436$	8.56074	−	12.2235i	0.409985	−	0.585398i
$437$		−	6.27484i		−	0.300166i
$438$		0			0
$439$			20.5609i			0.981319i	0.871352	+	0.490659i	$0.163244\pi$
$439$			20.5609i			0.981319i	−0.871352	+	0.490659i	$0.836756\pi$
$440$	20.9000	−	9.22019i	0.996366	−	0.439555i
$441$		0			0
$442$	6.71898	+	2.11885i	0.319589	+	0.100783i
$443$	0.505156			0.0240007			0.0120003	−	0.999928i	$-0.496180\pi$
$443$	0.505156			0.0240007			0.0120003	+	0.999928i	$0.496180\pi$
$444$		0			0
$445$	−3.45604	+	14.1917i	−0.163832	+	0.672751i
$446$	−6.73512	−	2.12393i	−0.318917	−	0.100571i
$447$		0			0
$448$	−3.30584	+	12.3232i	−0.156186	+	0.582215i
$449$			11.5637i			0.545726i	0.962053	+	0.272863i	$0.0879706\pi$
$449$			11.5637i			0.545726i	−0.962053	+	0.272863i	$0.912029\pi$
$450$		0			0
$451$	37.2192			1.75258
$452$	21.5291	+	15.0779i	1.01264	+	0.709206i
$453$		0			0
$454$	16.6427	+	5.24832i	0.781082	+	0.246316i
$455$	7.57645	+	1.84506i	0.355190	+	0.0864976i
$456$		0			0
$457$		−	13.7815i		−	0.644670i	−0.946626	−	0.322335i	$-0.895532\pi$
$457$		−	13.7815i		−	0.644670i	0.946626	−	0.322335i	$-0.104468\pi$
$458$	−10.6423	+	33.7475i	−0.497284	+	1.57692i
$459$		0			0
$460$	3.62509	−	3.18560i	0.169021	−	0.148529i
$461$	−11.6050			−0.540501			−0.270250	−	0.962790i	$-0.587106\pi$
$461$	−11.6050			−0.540501			−0.270250	+	0.962790i	$0.587106\pi$
$462$		0			0
$463$	23.6187			1.09765			0.548827	−	0.835936i	$-0.315074\pi$
$463$	23.6187			1.09765			0.548827	+	0.835936i	$0.315074\pi$
$464$	−3.49474	−	9.60753i	−0.162239	−	0.446018i
$465$		0			0
$466$	9.28747	+	2.92882i	0.430234	+	0.135675i
$467$	−25.1522			−1.16390			−0.581952	−	0.813223i	$-0.697711\pi$
$467$	−25.1522			−1.16390			−0.581952	+	0.813223i	$0.697711\pi$
$468$		0			0
$469$		−	9.57489i		−	0.442128i
$470$	17.4462	−	28.8192i	0.804733	−	1.32933i
$471$		0			0
$472$	−6.31096	+	4.84111i	−0.290485	+	0.222830i
$473$	3.55314			0.163374
$474$		0			0
$475$	25.8189	+	13.3679i	1.18465	+	0.613360i
$476$	−5.95244	−	4.16881i	−0.272830	−	0.191077i
$477$		0			0
$478$	−11.1448	−	3.51453i	−0.509750	−	0.160751i
$479$	−18.6766			−0.853354			−0.426677	−	0.904404i	$-0.640316\pi$
$479$	−18.6766			−0.853354			−0.426677	+	0.904404i	$0.640316\pi$
$480$		0			0
$481$	−5.45954			−0.248933
$482$	24.6359	+	7.76898i	1.12213	+	0.353867i
$483$		0			0
$484$	−3.35093	−	2.34683i	−0.152315	−	0.106674i
$485$	8.55309	−	35.1220i	0.388376	−	1.59481i
$486$		0			0
$487$	−21.6007			−0.978823			−0.489411	−	0.872053i	$-0.662788\pi$
$487$	−21.6007			−0.978823			−0.489411	+	0.872053i	$0.662788\pi$
$488$	−18.7220	+	14.3616i	−0.847505	+	0.650117i
$489$		0			0
$490$	12.0555	+	7.29802i	0.544613	+	0.329691i
$491$			30.9795i			1.39809i	0.715079	+	0.699043i	$0.246391\pi$
$491$			30.9795i			1.39809i	−0.715079	+	0.699043i	$0.753609\pi$
$492$		0			0
$493$	5.82294			0.262252
$494$	−17.1489	−	5.40793i	−0.771564	−	0.243314i
$495$		0			0
$496$	−22.3040	+	8.11309i	−1.00148	+	0.364288i
$497$	3.74237			0.167868
$498$		0			0
$499$	−12.1240			−0.542745			−0.271372	−	0.962474i	$-0.587477\pi$
$499$	−12.1240			−0.542745			−0.271372	+	0.962474i	$0.587477\pi$
$500$	5.38482	+	21.7026i	0.240816	+	0.970571i
$501$		0			0
$502$	−4.98483	+	15.8072i	−0.222484	+	0.705509i
$503$			7.93957i			0.354008i	0.984210	+	0.177004i	$0.0566405\pi$
$503$			7.93957i			0.354008i	−0.984210	+	0.177004i	$0.943359\pi$
$504$		0			0
$505$	−20.2788	−	4.93841i	−0.902396	−	0.219756i
$506$	−5.25681	−	1.65775i	−0.233694	−	0.0736958i
$507$		0			0
$508$	−29.3492	−	20.5548i	−1.30216	−	0.911971i
$509$	14.5479			0.644826			0.322413	−	0.946599i	$-0.395506\pi$
$509$	14.5479			0.644826			0.322413	+	0.946599i	$0.395506\pi$
$510$		0			0
$511$			9.51650i			0.420985i
$512$	20.9088	−	8.64999i	0.924047	−	0.382279i
$513$		0			0
$514$	18.9296	+	5.96951i	0.834951	+	0.263304i
$515$	42.2417	+	10.2869i	1.86139	+	0.453296i
$516$		0			0
$517$	−38.4780			−1.69226
$518$	5.37079	+	1.69369i	0.235979	+	0.0744165i
$519$		0			0
$520$	−5.58185	−	12.6527i	−0.244780	−	0.554858i
$521$		−	40.9736i		−	1.79508i	−0.440929	−	0.897542i	$-0.645351\pi$
$521$		−	40.9736i		−	1.79508i	0.440929	−	0.897542i	$-0.354649\pi$
$522$		0			0
$523$		−	0.689354i		−	0.0301434i	−0.999886	−	0.0150717i	$-0.995202\pi$
$523$		−	0.689354i		−	0.0301434i	0.999886	−	0.0150717i	$-0.00479765\pi$
$524$	15.8917	−	22.6910i	0.694231	−	0.991259i
$525$		0			0
$526$	0.917946	−	2.91086i	0.0400244	−	0.126920i
$527$		−	13.5180i		−	0.588855i
$528$		0			0
$529$	21.8355			0.949371
$530$	13.5358	−	22.3597i	0.587958	−	0.971242i
$531$		0			0
$532$	15.1924	+	10.6400i	0.658675	+	0.461304i
$533$		−	22.5323i		−	0.975980i
$534$		0			0
$535$	27.0876	+	6.59651i	1.17110	+	0.285192i
$536$	−13.4732	+	10.3352i	−0.581954	+	0.446415i
$537$		0			0
$538$	−22.2003	−	7.00092i	−0.957124	−	0.301831i
$539$		−	16.0959i		−	0.693301i
$540$		0			0
$541$			2.61438i			0.112401i	0.998420	+	0.0562004i	$0.0178986\pi$
$541$			2.61438i			0.112401i	−0.998420	+	0.0562004i	$0.982101\pi$
$542$	7.38187	−	23.4083i	0.317079	−	1.00547i
$543$		0			0
$544$	0.559033	+	12.8758i	0.0239684	+	0.552044i
$545$	3.94774	−	16.2108i	0.169102	−	0.694394i
$546$		0			0
$547$			6.89720i			0.294903i	0.989069	+	0.147452i	$0.0471070\pi$
$547$			6.89720i			0.294903i	−0.989069	+	0.147452i	$0.952893\pi$
$548$	24.1681	+	16.9262i	1.03241	+	0.723052i
$549$		0			0
$550$	18.0201	−	18.0983i	0.768381	−	0.771716i
$551$	−14.8619			−0.633138
$552$		0			0
$553$			17.9404i			0.762902i
$554$	5.56613	+	1.75529i	0.236482	+	0.0745752i
$555$		0			0
$556$	14.0350	+	9.82946i	0.595217	+	0.416862i
$557$			29.1931i			1.23695i	0.785803	+	0.618477i	$0.212250\pi$
$557$			29.1931i			1.23695i	−0.785803	+	0.618477i	$0.787750\pi$
$558$		0			0
$559$		−	2.15105i		−	0.0909798i
$560$	1.56591	+	14.1787i	0.0661719	+	0.599158i
$561$		0			0
$562$	−1.71990	+	5.45389i	−0.0725495	+	0.230059i
$563$	31.4932			1.32728			0.663639	−	0.748053i	$-0.269011\pi$
$563$	31.4932			1.32728			0.663639	+	0.748053i	$0.269011\pi$
$564$		0			0
$565$	28.5519	+	6.95311i	1.20119	+	0.292519i
$566$	−7.09411	+	22.4958i	−0.298188	+	0.945570i
$567$		0			0
$568$	−4.03955	−	5.26603i	−0.169496	−	0.220958i
$569$			42.4551i			1.77981i	0.456145	+	0.889905i	$0.349230\pi$
$569$			42.4551i			1.77981i	−0.456145	+	0.889905i	$0.650770\pi$
$570$		0			0
$571$	−5.84033			−0.244410			−0.122205	−	0.992505i	$-0.538997\pi$
$571$	−5.84033			−0.244410			−0.122205	+	0.992505i	$0.538997\pi$
$572$	−9.06109	+	12.9379i	−0.378863	+	0.540961i
$573$		0			0
$574$	−6.99009	+	22.1660i	−0.291761	+	0.925190i
$575$	2.48077	−	4.79139i	0.103455	−	0.199815i
$576$		0			0
$577$		−	45.1309i		−	1.87882i	−0.342791	−	0.939412i	$-0.611372\pi$
$577$		−	45.1309i		−	1.87882i	0.342791	−	0.939412i	$-0.388628\pi$
$578$	15.9278	+	5.02288i	0.662511	+	0.208924i
$579$		0			0
$580$	−7.54507	−	8.58599i	−0.313292	−	0.356514i
$581$	10.2162			0.423840
$582$		0			0
$583$	−29.8535			−1.23641
$584$	13.3910	−	10.2722i	0.554125	−	0.425067i
$585$		0			0
$586$	−13.0354	+	41.3359i	−0.538486	+	1.70757i
$587$	−6.69464			−0.276317			−0.138159	−	0.990410i	$-0.544118\pi$
$587$	−6.69464			−0.276317			−0.138159	+	0.990410i	$0.544118\pi$
$588$		0			0
$589$			34.5021i			1.42163i
$590$	−4.60526	+	7.60738i	−0.189596	+	0.313191i
$591$		0			0
$592$	−3.41403	−	9.38564i	−0.140316	−	0.385748i
$593$	−1.59700			−0.0655810			−0.0327905	−	0.999462i	$-0.510439\pi$
$593$	−1.59700			−0.0655810			−0.0327905	+	0.999462i	$0.510439\pi$
$594$		0			0
$595$	−7.89414	−	1.92242i	−0.323628	−	0.0788116i
$596$	28.2087	+	19.7561i	1.15547	+	0.809239i
$597$		0			0
$598$	−1.00359	+	3.18244i	−0.0410398	+	0.130140i
$599$	−25.0749			−1.02453			−0.512266	−	0.858827i	$-0.671194\pi$
$599$	−25.0749			−1.02453			−0.512266	+	0.858827i	$0.671194\pi$
$600$		0			0
$601$	2.98059			0.121581			0.0607904	−	0.998151i	$-0.480638\pi$
$601$	2.98059			0.121581			0.0607904	+	0.998151i	$0.480638\pi$
$602$	−0.667312	+	2.11609i	−0.0271976	+	0.0862452i
$603$		0			0
$604$	−7.32214	+	10.4549i	−0.297934	+	0.425405i
$605$	−4.44401	−	1.08223i	−0.180675	−	0.0439989i
$606$		0			0
$607$	30.2075			1.22608			0.613042	−	0.790050i	$-0.289946\pi$
$607$	30.2075			1.22608			0.613042	+	0.790050i	$0.289946\pi$
$608$	−1.42682	−	32.8628i	−0.0578652	−	1.33276i
$609$		0			0
$610$	−13.6619	+	22.5679i	−0.553154	+	0.913750i
$611$			23.2943i			0.942388i
$612$		0			0
$613$	41.9630			1.69487			0.847434	−	0.530900i	$-0.178146\pi$
$613$	41.9630			1.69487			0.847434	+	0.530900i	$0.178146\pi$
$614$	−13.7434	+	43.5811i	−0.554638	+	1.75879i
$615$		0			0
$616$	12.9275	−	9.91660i	0.520863	−	0.399551i
$617$	−36.0698			−1.45211			−0.726057	−	0.687635i	$-0.758649\pi$
$617$	−36.0698			−1.45211			−0.726057	+	0.687635i	$0.758649\pi$
$618$		0			0
$619$	18.8294			0.756817			0.378408	−	0.925639i	$-0.376471\pi$
$619$	18.8294			0.756817			0.378408	+	0.925639i	$0.376471\pi$
$620$	−19.9325	+	17.5160i	−0.800508	+	0.703458i
$621$		0			0
$622$	6.82024	+	2.15078i	0.273467	+	0.0862383i
$623$			10.4180i			0.417387i
$624$		0			0
$625$	14.4300	+	20.4151i	0.577198	+	0.816604i
$626$	4.49351	−	14.2492i	0.179597	−	0.569511i
$627$		0			0
$628$	−39.8136	−	27.8836i	−1.58874	−	1.11268i
$629$	5.68846			0.226814
$630$		0			0
$631$		−	48.3505i		−	1.92480i	−0.271629	−	0.962402i	$-0.587562\pi$
$631$		−	48.3505i		−	1.92480i	0.271629	−	0.962402i	$-0.412438\pi$
$632$	25.2446	−	19.3650i	1.00418	−	0.770299i
$633$		0			0
$634$	2.05469	−	6.51555i	0.0816023	−	0.258766i
$635$	−38.9230	−	9.47873i	−1.54461	−	0.376152i
$636$		0			0
$637$	−9.74438			−0.386086
$638$	−3.92635	+	12.4507i	−0.155446	+	0.492928i
$639$		0			0
$640$	18.2611	−	17.5081i	0.721833	−	0.692067i
$641$		−	15.2377i		−	0.601853i	−0.953647	−	0.300927i	$-0.902704\pi$
$641$		−	15.2377i		−	0.601853i	0.953647	−	0.300927i	$-0.0972959\pi$
$642$		0			0
$643$			22.2897i			0.879019i	0.898238	+	0.439509i	$0.144848\pi$
$643$			22.2897i			0.879019i	−0.898238	+	0.439509i	$0.855152\pi$
$644$	1.97455	−	2.81937i	0.0778082	−	0.111099i
$645$		0			0
$646$	17.8679	+	5.63469i	0.703004	+	0.221694i
$647$		−	11.8135i		−	0.464437i	−0.972664	−	0.232218i	$-0.925402\pi$
$647$		−	11.8135i		−	0.464437i	0.972664	−	0.232218i	$-0.0745984\pi$
$648$		0			0
$649$	10.1570			0.398697
$650$	−10.9566	−	10.9093i	−0.429754	−	0.427897i
$651$		0			0
$652$	−22.8405	+	32.6128i	−0.894502	+	1.27722i
$653$			5.33196i			0.208656i	0.994543	+	0.104328i	$0.0332691\pi$
$653$			5.33196i			0.208656i	−0.994543	+	0.104328i	$0.966731\pi$
$654$		0			0
$655$	7.32836	−	30.0928i	0.286343	−	1.17582i
$656$	38.7358	−	14.0902i	1.51238	−	0.550128i
$657$		0			0
$658$	7.22651	−	22.9157i	0.281719	−	0.893346i
$659$		−	30.7464i		−	1.19771i	−0.800858	−	0.598854i	$-0.795623\pi$
$659$		−	30.7464i		−	1.19771i	0.800858	−	0.598854i	$-0.204377\pi$
$660$		0			0
$661$			40.7254i			1.58404i	0.610498	+	0.792018i	$0.290969\pi$
$661$			40.7254i			1.58404i	−0.610498	+	0.792018i	$0.709031\pi$
$662$	−5.58701	−	1.76188i	−0.217145	−	0.0684773i
$663$		0			0
$664$	−11.0275	−	14.3756i	−0.427949	−	0.557883i
$665$	20.1482	+	4.90660i	0.781314	+	0.190270i
$666$		0			0
$667$			2.75803i			0.106791i
$668$	−8.74512	+	12.4867i	−0.338359	+	0.483127i
$669$		0			0
$670$	−9.83174	+	16.2409i	−0.379833	+	0.627442i
$671$	30.1316			1.16322
$672$		0			0
$673$		−	3.14342i		−	0.121170i	−0.998163	−	0.0605850i	$-0.980703\pi$
$673$		−	3.14342i		−	0.121170i	0.998163	−	0.0605850i	$-0.0192966\pi$
$674$	−10.0324	+	31.8133i	−0.386434	+	1.22540i
$675$		0			0
$676$	−13.4640	−	9.42953i	−0.517845	−	0.362674i
$677$		−	35.1895i		−	1.35244i	−0.736699	−	0.676221i	$-0.763616\pi$
$677$		−	35.1895i		−	1.35244i	0.736699	−	0.676221i	$-0.236384\pi$
$678$		0			0
$679$		−	25.7826i		−	0.989447i
$680$	5.81590	+	13.1832i	0.223030	+	0.505554i
$681$		0			0
$682$	28.9045	+	9.11508i	1.10681	+	0.349035i
$683$	−29.6866			−1.13593			−0.567964	−	0.823054i	$-0.692269\pi$
$683$	−29.6866			−1.13593			−0.567964	+	0.823054i	$0.692269\pi$
$684$		0			0
$685$	32.0518	+	7.80543i	1.22464	+	0.298230i
$686$	24.6433	+	7.77133i	0.940887	+	0.296711i
$687$		0			0
$688$	3.69793	−	1.34512i	0.140982	−	0.0512823i
$689$			18.0731i			0.688532i
$690$		0			0
$691$	−33.5824			−1.27753			−0.638767	−	0.769400i	$-0.720555\pi$
$691$	−33.5824			−1.27753			−0.638767	+	0.769400i	$0.720555\pi$
$692$	−15.7783	+	22.5291i	−0.599801	+	0.856427i
$693$		0			0
$694$	−13.5009	−	4.25753i	−0.512486	−	0.161614i
$695$	18.6133	+	4.53280i	0.706041	+	0.171939i
$696$		0			0
$697$			23.4771i			0.889257i
$698$	−0.184994	+	0.586628i	−0.00700214	+	0.0222042i
$699$		0			0
$700$	7.39418	+	14.1310i	0.279474	+	0.534100i
$701$	−6.08892			−0.229975			−0.114988	−	0.993367i	$-0.536683\pi$
$701$	−6.08892			−0.229975			−0.114988	+	0.993367i	$0.536683\pi$
$702$		0			0
$703$	−14.5187			−0.547582
$704$	−27.9081	−	7.48668i	−1.05183	−	0.282165i
$705$		0			0
$706$	31.0733	+	9.79902i	1.16946	+	0.368791i
$707$	−14.8865			−0.559863
$708$		0			0
$709$			23.7395i			0.891556i	0.895144	+	0.445778i	$0.147073\pi$
$709$			23.7395i			0.891556i	−0.895144	+	0.445778i	$0.852927\pi$
$710$	−6.34780	−	3.84275i	−0.238229	−	0.144216i
$711$		0			0
$712$	14.6595	−	11.2453i	0.549389	−	0.421434i
$713$	6.40280			0.239787
$714$		0			0
$715$	−4.17847	+	17.1583i	−0.156266	+	0.641683i
$716$	16.2791	−	23.2442i	0.608380	−	0.868677i
$717$		0			0
$718$	−17.4441	−	5.50103i	−0.651008	−	0.205297i
$719$	−50.5874			−1.88659			−0.943295	−	0.331956i	$-0.892292\pi$
$719$	−50.5874			−1.88659			−0.943295	+	0.331956i	$0.892292\pi$
$720$		0			0
$721$	31.0091			1.15484
$722$	−19.9783	−	6.30019i	−0.743514	−	0.234469i
$723$		0			0
$724$	22.2606	−	31.7849i	0.827310	−	1.18128i
$725$	−11.3484	−	5.87568i	−0.421468	−	0.218217i
$726$		0			0
$727$	−26.3853			−0.978577			−0.489289	−	0.872122i	$-0.662744\pi$
$727$	−26.3853			−0.978577			−0.489289	+	0.872122i	$0.662744\pi$
$728$	−6.00345	−	7.82621i	−0.222503	−	0.290059i
$729$		0			0
$730$	9.77177	−	16.1419i	0.361669	−	0.597438i
$731$			2.24125i			0.0828955i
$732$		0			0
$733$	−37.4800			−1.38435			−0.692177	−	0.721727i	$-0.743348\pi$
$733$	−37.4800			−1.38435			−0.692177	+	0.721727i	$0.743348\pi$
$734$	28.7475	+	9.06560i	1.06109	+	0.334617i
$735$		0			0
$736$	−6.09859	+	0.264785i	−0.224797	+	0.00976012i
$737$	21.6841			0.798744
$738$		0			0
$739$	18.7497			0.689718			0.344859	−	0.938655i	$-0.387927\pi$
$739$	18.7497			0.689718			0.344859	+	0.938655i	$0.387927\pi$
$740$	−7.37081	−	8.38770i	−0.270956	−	0.308338i
$741$		0			0
$742$	5.60676	−	17.7794i	0.205831	−	0.652701i
$743$		−	27.8320i		−	1.02106i	−0.859861	−	0.510529i	$-0.829450\pi$
$743$		−	27.8320i		−	1.02106i	0.859861	−	0.510529i	$-0.170550\pi$
$744$		0			0
$745$	37.4105	+	9.11040i	1.37061	+	0.333779i
$746$	38.1247	+	12.0227i	1.39584	+	0.440182i
$747$		0			0
$748$	9.44103	−	13.4804i	0.345198	−	0.492892i
$749$	19.8847			0.726570
$750$		0			0
$751$		−	8.78033i		−	0.320399i	−0.987085	−	0.160199i	$-0.948786\pi$
$751$		−	8.78033i		−	0.320399i	0.987085	−	0.160199i	$-0.0512137\pi$
$752$	−40.0459	+	14.5667i	−1.46032	+	0.531193i
$753$		0			0
$754$	7.53757	+	2.37699i	0.274502	+	0.0865649i
$755$	−3.37657	+	13.8654i	−0.122886	+	0.504612i
$756$		0			0
$757$	15.1104			0.549197			0.274598	−	0.961559i	$-0.411455\pi$
$757$	15.1104			0.549197			0.274598	+	0.961559i	$0.411455\pi$
$758$	30.8303	+	9.72240i	1.11981	+	0.353133i
$759$		0			0
$760$	−14.8439	−	33.6476i	−0.538446	−	1.22053i
$761$			16.6305i			0.602854i	0.953489	+	0.301427i	$0.0974629\pi$
$761$			16.6305i			0.602854i	−0.953489	+	0.301427i	$0.902537\pi$
$762$		0			0
$763$		−	11.9001i		−	0.430814i
$764$	−40.6914	−	28.4983i	−1.47216	−	1.03103i
$765$		0			0
$766$	−11.2783	+	35.7642i	−0.407502	+	1.29221i
$767$		−	6.14899i		−	0.222027i
$768$		0			0
$769$	−10.4045			−0.375195			−0.187598	−	0.982246i	$-0.560070\pi$
$769$	−10.4045			−0.375195			−0.187598	+	0.982246i	$0.560070\pi$
$770$	9.43349	−	15.5831i	0.339959	−	0.561575i
$771$		0			0
$772$	−6.93000	+	9.89502i	−0.249416	+	0.356130i
$773$			3.04874i			0.109656i	0.998496	+	0.0548278i	$0.0174610\pi$
$773$			3.04874i			0.109656i	−0.998496	+	0.0548278i	$0.982539\pi$
$774$		0			0
$775$	−13.6405	+	26.3454i	−0.489981	+	0.946354i
$776$	−36.2798	+	27.8301i	−1.30237	+	0.999041i
$777$		0			0
$778$	21.8819	+	6.90052i	0.784505	+	0.247395i
$779$		−	59.9205i		−	2.14687i
$780$		0			0
$781$			8.47528i			0.303269i
$782$	1.04567	−	3.31588i	0.0373931	−	0.118576i
$783$		0			0
$784$	−6.09348	−	16.7518i	−0.217624	−	0.598280i
$785$	−52.8009	−	12.8584i	−1.88455	−	0.458935i
$786$		0			0
$787$		−	29.9306i		−	1.06691i	−0.845828	−	0.533455i	$-0.820893\pi$
$787$		−	29.9306i		−	1.06691i	0.845828	−	0.533455i	$-0.179107\pi$
$788$	20.1434	−	28.7618i	0.717580	−	1.02460i
$789$		0			0
$790$	18.4216	−	30.4304i	0.655411	−	1.08267i
$791$	20.9596			0.745238
$792$		0			0
$793$		−	18.2415i		−	0.647775i
$794$	−24.7798	−	7.81436i	−0.879402	−	0.277321i
$795$		0			0
$796$	−13.6608	+	19.5056i	−0.484193	+	0.691356i
$797$			34.7092i			1.22946i	0.788736	+	0.614731i	$0.210736\pi$
$797$			34.7092i			1.22946i	−0.788736	+	0.614731i	$0.789264\pi$
$798$		0			0
$799$		−	24.2711i		−	0.858649i
$800$	11.9029	−	25.6578i	0.420831	−	0.907139i
$801$		0			0
$802$	−5.53413	+	17.5491i	−0.195417	+	0.619679i
$803$	−21.5519			−0.760548
$804$		0			0
$805$	0.910553	−	3.73905i	0.0320928	−	0.131784i
$806$	5.51821	−	17.4986i	0.194371	−	0.616361i
$807$		0			0
$808$	16.0686	+	20.9473i	0.565291	+	0.736924i
$809$			37.9701i			1.33496i	0.744629	+	0.667478i	$0.232626\pi$
$809$			37.9701i			1.33496i	−0.744629	+	0.667478i	$0.767374\pi$
$810$		0			0
$811$	−5.59781			−0.196566			−0.0982828	−	0.995159i	$-0.531335\pi$
$811$	−5.59781			−0.196566			−0.0982828	+	0.995159i	$0.531335\pi$
$812$	−6.67764	−	4.67670i	−0.234339	−	0.164120i
$813$		0			0
$814$	−3.83567	+	12.1631i	−0.134440	+	0.426318i
$815$	−10.5328	+	43.2512i	−0.368947	+	1.51502i
$816$		0			0
$817$		−	5.72033i		−	0.200129i
$818$	−37.5800	−	11.8509i	−1.31395	−	0.414358i
$819$		0			0
$820$	34.6172	−	30.4204i	1.20888	−	1.06232i
$821$	14.5614			0.508195			0.254097	−	0.967179i	$-0.418222\pi$
$821$	14.5614			0.508195			0.254097	+	0.967179i	$0.418222\pi$
$822$		0			0
$823$	4.09828			0.142857			0.0714285	−	0.997446i	$-0.477244\pi$
$823$	4.09828			0.142857			0.0714285	+	0.997446i	$0.477244\pi$
$824$	−33.4716	−	43.6342i	−1.16604	−	1.52007i
$825$		0			0
$826$	−1.90758	+	6.04903i	−0.0663731	+	0.210473i
$827$	35.6559			1.23988			0.619938	−	0.784651i	$-0.287158\pi$
$827$	35.6559			1.23988			0.619938	+	0.784651i	$0.287158\pi$
$828$		0			0
$829$			25.9129i			0.899991i	0.893031	+	0.449995i	$0.148574\pi$
$829$			25.9129i			0.899991i	−0.893031	+	0.449995i	$0.851426\pi$
$830$	−17.3287	−	10.4903i	−0.601489	−	0.364122i
$831$		0			0
$832$	−4.53239	+	16.8954i	−0.157132	+	0.585742i
$833$	10.1530			0.351780
$834$		0			0
$835$	−4.03277	+	16.5599i	−0.139560	+	0.573081i
$836$	−24.0963	+	34.4060i	−0.833389	+	1.18996i
$837$		0			0
$838$	−9.34287	+	29.6268i	−0.322744	+	1.02344i
$839$	−9.17285			−0.316682			−0.158341	−	0.987385i	$-0.550614\pi$
$839$	−9.17285			−0.316682			−0.158341	+	0.987385i	$0.550614\pi$
$840$		0			0
$841$	−22.4676			−0.774746
$842$	4.27853	−	13.5674i	0.147448	−	0.467565i
$843$		0			0
$844$	−11.2473	−	7.87710i	−0.387150	−	0.271141i
$845$	−17.8560	−	4.34838i	−0.614263	−	0.149589i
$846$		0			0
$847$	−3.26230			−0.112094
$848$	−31.0700	+	11.3017i	−1.06695	+	0.388103i
$849$		0			0
$850$	11.4160	+	11.3667i	0.391567	+	0.389875i
$851$			2.69433i			0.0923605i
$852$		0			0
$853$	−16.1963			−0.554550			−0.277275	−	0.960791i	$-0.589431\pi$
$853$	−16.1963			−0.554550			−0.277275	+	0.960791i	$0.589431\pi$
$854$	−5.65899	+	17.9450i	−0.193647	+	0.614064i
$855$		0			0
$856$	−21.4637	−	27.9805i	−0.733615	−	0.956355i
$857$	38.3773			1.31094			0.655471	−	0.755220i	$-0.272470\pi$
$857$	38.3773			1.31094			0.655471	+	0.755220i	$0.272470\pi$
$858$		0			0
$859$	9.75306			0.332770			0.166385	−	0.986061i	$-0.446791\pi$
$859$	9.75306			0.332770			0.166385	+	0.986061i	$0.446791\pi$
$860$	3.30474	−	2.90409i	0.112691	−	0.0990287i
$861$		0			0
$862$	−13.2246	−	4.17040i	−0.450431	−	0.142044i
$863$			17.7874i			0.605489i	0.953072	+	0.302745i	$0.0979029\pi$
$863$			17.7874i			0.605489i	−0.953072	+	0.302745i	$0.902097\pi$
$864$		0			0
$865$	−7.27608	+	29.8781i	−0.247394	+	1.01589i
$866$	−6.25728	+	19.8422i	−0.212631	+	0.674265i
$867$		0			0
$868$	−10.8570	+	15.5022i	−0.368511	+	0.526180i
$869$	−40.6292			−1.37825
$870$		0			0
$871$		−	13.1274i		−	0.444806i
$872$	−16.7452	+	12.8451i	−0.567063	+	0.434992i
$873$		0			0
$874$	−2.66886	+	8.46312i	−0.0902757	+	0.286269i
$875$	13.4451	+	11.7123i	0.454527	+	0.395947i
$876$		0			0
$877$	5.30899			0.179272			0.0896360	−	0.995975i	$-0.471430\pi$
$877$	5.30899			0.179272			0.0896360	+	0.995975i	$0.471430\pi$
$878$	8.74512	−	27.7313i	0.295134	−	0.935886i
$879$		0			0
$880$	−32.1102	+	3.54630i	−1.08243	+	0.119546i
$881$			46.1938i			1.55631i	0.628073	+	0.778154i	$0.283844\pi$
$881$			46.1938i			1.55631i	−0.628073	+	0.778154i	$0.716156\pi$
$882$		0			0
$883$		−	35.4510i		−	1.19302i	−0.802605	−	0.596510i	$-0.796553\pi$
$883$		−	35.4510i		−	1.19302i	0.802605	−	0.596510i	$-0.203447\pi$
$884$	−8.16095	−	5.71554i	−0.274482	−	0.192234i
$885$		0			0
$886$	−0.681323	−	0.214857i	−0.0228895	−	0.00721825i
$887$			1.33801i			0.0449261i	0.999748	+	0.0224631i	$0.00715082\pi$
$887$			1.33801i			0.0449261i	−0.999748	+	0.0224631i	$0.992849\pi$
$888$		0			0
$889$	−28.5729			−0.958304
$890$	10.6974	−	17.6710i	0.358578	−	0.592332i
$891$		0			0
$892$	8.18055	+	5.72927i	0.273905	+	0.191830i
$893$			61.9471i			2.07298i
$894$		0			0
$895$	7.50704	−	30.8265i	0.250933	−	1.03042i
$896$	9.70010	−	15.2147i	0.324058	−	0.508287i
$897$		0			0
$898$	4.91838	−	15.5965i	0.164128	−	0.520460i
$899$		−	15.1650i		−	0.505780i
$900$		0			0
$901$		−	18.8310i		−	0.627351i
$902$	−50.1990	−	15.8304i	−1.67144	−	0.527093i
$903$		0			0
$904$	−22.6240	−	29.4931i	−0.752464	−	0.980926i
$905$	10.2654	−	42.1532i	0.341233	−	1.40122i
$906$		0			0
$907$		−	2.19143i		−	0.0727653i	−0.999338	−	0.0363827i	$-0.988416\pi$
$907$		−	2.19143i		−	0.0727653i	0.999338	−	0.0363827i	$-0.0115835\pi$
$908$	−20.2144	−	14.1572i	−0.670840	−	0.469824i
$909$		0			0
$910$	−9.43390	−	5.71098i	−0.312731	−	0.189317i
$911$	48.6279			1.61111			0.805557	−	0.592519i	$-0.201866\pi$
$911$	48.6279			1.61111			0.805557	+	0.592519i	$0.201866\pi$
$912$		0			0
$913$			23.1365i			0.765706i
$914$	−5.86164	+	18.5876i	−0.193886	+	0.614823i
$915$		0			0
$916$	28.7075	−	40.9900i	0.948522	−	1.35435i
$917$		−	22.0908i		−	0.729502i
$918$		0			0
$919$		−	14.9150i		−	0.492002i	−0.969270	−	0.246001i	$-0.920883\pi$
$919$		−	14.9150i		−	0.492002i	0.969270	−	0.246001i	$-0.0791166\pi$
$920$	−6.24423	+	2.75469i	−0.205866	+	0.0908195i
$921$		0			0
$922$	15.6522	+	4.93595i	0.515477	+	0.162557i
$923$	5.13088			0.168885
$924$		0			0
$925$	−11.0863	−	5.73998i	−0.364514	−	0.188730i
$926$	−31.8555	−	10.0457i	−1.04684	−	0.330122i
$927$		0			0
$928$	0.627142	+	14.4445i	0.0205869	+	0.474162i
$929$			11.8899i			0.390094i	0.980794	+	0.195047i	$0.0624860\pi$
$929$			11.8899i			0.390094i	−0.980794	+	0.195047i	$0.937514\pi$
$930$		0			0
$931$	−25.9134			−0.849278
$932$	−11.2807	−	7.90044i	−0.369510	−	0.258787i
$933$		0			0
$934$	33.9237	+	10.6979i	1.11002	+	0.350046i
$935$	4.35368	−	17.8777i	0.142381	−	0.584664i
$936$		0			0
$937$		−	36.1612i		−	1.18133i	−0.806916	−	0.590667i	$-0.798865\pi$
$937$		−	36.1612i		−	1.18133i	0.806916	−	0.590667i	$-0.201135\pi$
$938$	−4.07247	+	12.9140i	−0.132971	+	0.421658i
$939$		0			0
$940$	−35.7880	+	31.4492i	−1.16727	+	1.02576i
$941$	37.1768			1.21193			0.605965	−	0.795491i	$-0.292787\pi$
$941$	37.1768			1.21193			0.605965	+	0.795491i	$0.292787\pi$
$942$		0			0
$943$	−11.1199			−0.362113
$944$	10.5709	−	3.84516i	0.344053	−	0.125149i
$945$		0			0
$946$	−4.79226	−	1.51125i	−0.155810	−	0.0491350i
$947$	−31.9333			−1.03769			−0.518846	−	0.854868i	$-0.673638\pi$
$947$	−31.9333			−1.03769			−0.518846	+	0.854868i	$0.673638\pi$
$948$		0			0
$949$			13.0474i			0.423535i
$950$	−29.1372	−	29.0112i	−0.945335	−	0.941249i
$951$		0			0
$952$	6.25518	+	8.15437i	0.202732	+	0.264285i
$953$	−5.34819			−0.173245			−0.0866224	−	0.996241i	$-0.527607\pi$
$953$	−5.34819			−0.173245			−0.0866224	+	0.996241i	$0.527607\pi$
$954$		0			0
$955$	−53.9650	−	13.1419i	−1.74627	−	0.425260i
$956$	13.5365	+	9.48035i	0.437803	+	0.306617i
$957$		0			0
$958$	25.1898	+	7.94366i	0.813845	+	0.256648i
$959$	23.5289			0.759787
$960$		0			0
$961$	−4.20569			−0.135667
$962$	7.36349	+	2.32209i	0.237408	+	0.0748673i
$963$		0			0
$964$	−29.9230	−	20.9566i	−0.963755	−	0.674968i
$965$	−3.19573	+	13.1228i	−0.102874	+	0.422438i
$966$		0			0
$967$	−30.4607			−0.979550			−0.489775	−	0.871849i	$-0.662921\pi$
$967$	−30.4607			−0.979550			−0.489775	+	0.871849i	$0.662921\pi$
$968$	3.52136	+	4.59051i	0.113181	+	0.147545i
$969$		0			0
$970$	−26.4742	+	43.7325i	−0.850037	+	1.40417i
$971$			4.26310i			0.136809i	0.997658	+	0.0684046i	$0.0217909\pi$
$971$			4.26310i			0.136809i	−0.997658	+	0.0684046i	$0.978209\pi$
$972$		0			0
$973$	13.6638			0.438041
$974$	29.1338	+	9.18739i	0.933506	+	0.294383i
$975$		0			0
$976$	31.3595	−	11.4070i	1.00379	−	0.365129i
$977$	14.4535			0.462410			0.231205	−	0.972905i	$-0.425733\pi$
$977$	14.4535			0.462410			0.231205	+	0.972905i	$0.425733\pi$
$978$		0			0
$979$	−23.5934			−0.754048
$980$	−13.1557	−	14.9707i	−0.420243	−	0.478220i
$981$		0			0
$982$	13.1765	−	41.7833i	0.420478	−	1.33336i
$983$			17.2658i			0.550694i	0.961345	+	0.275347i	$0.0887928\pi$
$983$			17.2658i			0.550694i	−0.961345	+	0.275347i	$0.911207\pi$
$984$		0			0
$985$	9.28903	−	38.1440i	0.295973	−	1.21537i
$986$	−7.85363	−	2.47666i	−0.250110	−	0.0788729i
$987$		0			0
$988$	20.8292	+	14.5878i	0.662665	+	0.464099i
$989$	−1.06156			−0.0337558
$990$		0			0
$991$		−	48.1671i		−	1.53008i	−0.643984	−	0.765039i	$-0.722720\pi$
$991$		−	48.1671i		−	1.53008i	0.643984	−	0.765039i	$-0.277280\pi$
$992$	33.5330	−	1.45592i	1.06467	−	0.0462255i
$993$		0			0
$994$	−5.04748	−	1.59173i	−0.160096	−	0.0504867i
$995$	−6.29959	+	25.8683i	−0.199710	+	0.820081i
$996$		0			0
$997$	26.3097			0.833235			0.416617	−	0.909082i	$-0.363215\pi$
$997$	26.3097			0.833235			0.416617	+	0.909082i	$0.363215\pi$
$998$	16.3521	+	5.15667i	0.517617	+	0.163232i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.c.539.6	yes	48
3.2	odd	2	inner	1080.2.m.c.539.43	yes	48
4.3	odd	2		4320.2.m.c.2159.47		48
5.4	even	2	inner	1080.2.m.c.539.44	yes	48
8.3	odd	2	inner	1080.2.m.c.539.7	yes	48
8.5	even	2		4320.2.m.c.2159.2		48
12.11	even	2		4320.2.m.c.2159.1		48
15.14	odd	2	inner	1080.2.m.c.539.5	✓	48
20.19	odd	2		4320.2.m.c.2159.46		48
24.5	odd	2		4320.2.m.c.2159.48		48
24.11	even	2	inner	1080.2.m.c.539.42	yes	48
40.19	odd	2	inner	1080.2.m.c.539.41	yes	48
40.29	even	2		4320.2.m.c.2159.3		48
60.59	even	2		4320.2.m.c.2159.4		48
120.29	odd	2		4320.2.m.c.2159.45		48
120.59	even	2	inner	1080.2.m.c.539.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.c.539.5	✓	48	15.14	odd	2	inner
1080.2.m.c.539.6	yes	48	1.1	even	1	trivial
1080.2.m.c.539.7	yes	48	8.3	odd	2	inner
1080.2.m.c.539.8	yes	48	120.59	even	2	inner
1080.2.m.c.539.41	yes	48	40.19	odd	2	inner
1080.2.m.c.539.42	yes	48	24.11	even	2	inner
1080.2.m.c.539.43	yes	48	3.2	odd	2	inner
1080.2.m.c.539.44	yes	48	5.4	even	2	inner
4320.2.m.c.2159.1		48	12.11	even	2
4320.2.m.c.2159.2		48	8.5	even	2
4320.2.m.c.2159.3		48	40.29	even	2
4320.2.m.c.2159.4		48	60.59	even	2
4320.2.m.c.2159.45		48	120.29	odd	2
4320.2.m.c.2159.46		48	20.19	odd	2
4320.2.m.c.2159.47		48	4.3	odd	2
4320.2.m.c.2159.48		48	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34874 - 0.425328i) q^{2} +(1.63819 + 1.14731i) q^{4} +(2.17257 + 0.529077i) q^{5} +1.59486 q^{7} +(-1.72151 - 2.24419i) q^{8} +(-2.70520 - 1.63764i) q^{10} +3.61186i q^{11} +2.18660 q^{13} +(-2.15105 - 0.678339i) q^{14} +(1.36735 + 3.75904i) q^{16} -2.27828 q^{17} +5.81486 q^{19} +(2.95208 + 3.35935i) q^{20} +(1.53622 - 4.87145i) q^{22} -1.07910i q^{23} +(4.44016 + 2.29892i) q^{25} +(-2.94915 - 0.930020i) q^{26} +(2.61269 + 1.82980i) q^{28} -2.55585 q^{29} +5.93344i q^{31} +(-0.245375 - 5.65153i) q^{32} +(3.07281 + 0.969016i) q^{34} +(3.46495 + 0.843804i) q^{35} -2.49682 q^{37} +(-7.84272 - 2.47322i) q^{38} +(-2.55276 - 5.78649i) q^{40} -10.3047i q^{41} -0.983745i q^{43} +(-4.14393 + 5.91692i) q^{44} +(-0.458973 + 1.45543i) q^{46} +10.6532i q^{47} -4.45642 q^{49} +(-5.01082 - 4.98916i) q^{50} +(3.58206 + 2.50871i) q^{52} +8.26543i q^{53} +(-1.91095 + 7.84703i) q^{55} +(-2.74557 - 3.57918i) q^{56} +(3.44717 + 1.08707i) q^{58} -2.81213i q^{59} -8.34242i q^{61} +(2.52366 - 8.00266i) q^{62} +(-2.07281 + 7.72680i) q^{64} +(4.75054 + 1.15688i) q^{65} -6.00359i q^{67} +(-3.73226 - 2.61390i) q^{68} +(-4.31442 - 2.61181i) q^{70} +2.34652 q^{71} +5.96697i q^{73} +(3.36756 + 1.06197i) q^{74} +(9.52585 + 6.67146i) q^{76} +5.76041i q^{77} +11.2489i q^{79} +(0.981850 + 8.89022i) q^{80} +(-4.38289 + 13.8984i) q^{82} +6.40570 q^{83} +(-4.94973 - 1.20539i) q^{85} +(-0.418414 + 1.32681i) q^{86} +(8.10570 - 6.21785i) q^{88} +6.53221i q^{89} +3.48732 q^{91} +(1.23807 - 1.76778i) q^{92} +(4.53112 - 14.3684i) q^{94} +(12.6332 + 3.07651i) q^{95} -16.1661i q^{97} +(6.01054 + 1.89544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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