LMFDB - Embedded newform 1323.2.f.h.442.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			442.7
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.h.883.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +O(q^{10})$	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} -0.182134 q^{10} +(-0.799563 - 1.38488i) q^{11} +(-2.62690 + 4.54992i) q^{13} +(-1.98599 - 3.43983i) q^{16} +6.54721 q^{17} +1.90194 q^{19} +(2.65756 + 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} +(-1.53419 + 2.65729i) q^{23} +(-1.04789 - 1.81500i) q^{25} -0.359223 q^{26} +(3.19452 + 5.53306i) q^{29} +(-3.35961 + 5.81902i) q^{31} +(0.408966 - 0.708350i) q^{32} +(0.223829 + 0.387684i) q^{34} +4.22955 q^{37} +(0.0650215 + 0.112621i) q^{38} +(-0.363842 + 0.630193i) q^{40} +(3.69648 - 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} -3.19078 q^{44} -0.209797 q^{46} +(1.89959 + 3.29018i) q^{47} +(0.0716485 - 0.124099i) q^{50} +(5.24152 + 9.07858i) q^{52} -8.89862 q^{53} +4.25974 q^{55} +(-0.218422 + 0.378317i) q^{58} +(-5.44639 + 9.43343i) q^{59} +(-1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(-6.99751 - 12.1200i) q^{65} +(1.66267 - 2.87982i) q^{67} +(6.53190 - 11.3136i) q^{68} +12.3890 q^{71} +2.19863 q^{73} +(0.144596 + 0.250447i) q^{74} +(1.89749 - 3.28655i) q^{76} +(-0.406778 - 0.704560i) q^{79} +10.5805 q^{80} +0.505486 q^{82} +(3.41842 + 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} +(-0.385066 + 0.666954i) q^{86} +(-0.218422 - 0.378317i) q^{88} -0.470572 q^{89} +(3.06120 + 5.30216i) q^{92} +(-0.129882 + 0.224963i) q^{94} +(-2.53318 + 4.38760i) q^{95} +(2.57623 + 4.46216i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.0341870	+	0.0592136i	0.0241739	+	0.0418703i	0.877859	−	0.478919i	$-0.158971\pi$
$2$	0.0341870	+	0.0592136i	0.0241739	+	0.0418703i	−0.853685	+	0.520789i	$0.825638\pi$
$3$		0			0
$3$		0			0
$4$	0.997662	−	1.72800i	0.498831	−	0.864001i
$5$	−1.33190	+	2.30691i	−0.595642	+	1.03168i	0.397814	+	0.917466i	$0.369769\pi$
$5$	−1.33190	+	2.30691i	−0.595642	+	1.03168i	−0.993456	+	0.114216i	$0.963564\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.273176			0.0965824
$9$		0			0
$10$	−0.182134			−0.0575958
$11$	−0.799563	−	1.38488i	−0.241077	−	0.417558i	0.719944	−	0.694032i	$-0.244167\pi$
$11$	−0.799563	−	1.38488i	−0.241077	−	0.417558i	−0.961021	+	0.276474i	$0.910834\pi$
$12$		0			0
$13$	−2.62690	+	4.54992i	−0.728571	+	1.26192i	0.228916	+	0.973446i	$0.426482\pi$
$13$	−2.62690	+	4.54992i	−0.728571	+	1.26192i	−0.957487	+	0.288476i	$0.906852\pi$
$14$		0			0
$15$		0			0
$16$	−1.98599	−	3.43983i	−0.496496	−	0.859957i
$17$	6.54721			1.58793			0.793966	−	0.607963i	$-0.208013\pi$
$17$	6.54721			1.58793			0.793966	+	0.607963i	$0.208013\pi$
$18$		0			0
$19$	1.90194			0.436334			0.218167	−	0.975911i	$-0.429992\pi$
$19$	1.90194			0.436334			0.218167	+	0.975911i	$0.429992\pi$
$20$	2.65756	+	4.60304i	0.594249	+	1.02927i
$21$		0			0
$22$	0.0546693	−	0.0946900i	0.0116555	−	0.0201880i
$23$	−1.53419	+	2.65729i	−0.319900	+	0.554083i	−0.980467	−	0.196684i	$-0.936983\pi$
$23$	−1.53419	+	2.65729i	−0.319900	+	0.554083i	0.660567	+	0.750767i	$0.270316\pi$
$24$		0			0
$25$	−1.04789	−	1.81500i	−0.209578	−	0.363000i
$26$	−0.359223			−0.0704495
$27$		0			0
$28$		0			0
$29$	3.19452	+	5.53306i	0.593207	+	1.02746i	0.993797	+	0.111207i	$0.0354716\pi$
$29$	3.19452	+	5.53306i	0.593207	+	1.02746i	−0.400591	+	0.916257i	$0.631195\pi$
$30$		0			0
$31$	−3.35961	+	5.81902i	−0.603405	+	1.04513i	0.388897	+	0.921281i	$0.372856\pi$
$31$	−3.35961	+	5.81902i	−0.603405	+	1.04513i	−0.992301	+	0.123846i	$0.960477\pi$
$32$	0.408966	−	0.708350i	0.0722957	−	0.125220i
$33$		0			0
$34$	0.223829	+	0.387684i	0.0383864	+	0.0664872i
$35$		0			0
$36$		0			0
$37$	4.22955			0.695333			0.347667	−	0.937618i	$-0.386974\pi$
$37$	4.22955			0.695333			0.347667	+	0.937618i	$0.386974\pi$
$38$	0.0650215	+	0.112621i	0.0105479	+	0.0182695i
$39$		0			0
$40$	−0.363842	+	0.630193i	−0.0575285	+	0.0996423i
$41$	3.69648	−	6.40249i	0.577293	−	0.999901i	−0.418495	−	0.908219i	$-0.637442\pi$
$41$	3.69648	−	6.40249i	0.577293	−	0.999901i	0.995788	−	0.0916820i	$-0.0292243\pi$
$42$		0			0
$43$	5.63176	+	9.75450i	0.858836	+	1.48755i	0.873040	+	0.487648i	$0.162145\pi$
$43$	5.63176	+	9.75450i	0.858836	+	1.48755i	−0.0142043	+	0.999899i	$0.504522\pi$
$44$	−3.19078			−0.481028
$45$		0			0
$46$	−0.209797			−0.0309329
$47$	1.89959	+	3.29018i	0.277083	+	0.479922i	0.970659	−	0.240462i	$-0.0772989\pi$
$47$	1.89959	+	3.29018i	0.277083	+	0.479922i	−0.693575	+	0.720384i	$0.743966\pi$
$48$		0			0
$49$		0			0
$50$	0.0716485	−	0.124099i	0.0101326	−	0.0175502i
$51$		0			0
$52$	5.24152	+	9.07858i	0.726868	+	1.25897i
$53$	−8.89862			−1.22232			−0.611160	−	0.791507i	$-0.709297\pi$
$53$	−8.89862			−1.22232			−0.611160	+	0.791507i	$0.709297\pi$
$54$		0			0
$55$	4.25974			0.574383
$56$		0			0
$57$		0			0
$58$	−0.218422	+	0.378317i	−0.0286802	+	0.0496755i
$59$	−5.44639	+	9.43343i	−0.709060	+	1.22813i	0.256146	+	0.966638i	$0.417547\pi$
$59$	−5.44639	+	9.43343i	−0.709060	+	1.22813i	−0.965206	+	0.261490i	$0.915786\pi$
$60$		0			0
$61$	−1.35693	−	2.35027i	−0.173737	−	0.300922i	0.765986	−	0.642857i	$-0.222251\pi$
$61$	−1.35693	−	2.35027i	−0.173737	−	0.300922i	−0.939724	+	0.341935i	$0.888918\pi$
$62$	−0.459420			−0.0583465
$63$		0			0
$64$	−7.88802			−0.986002
$65$	−6.99751	−	12.1200i	−0.867935	−	1.50331i
$66$		0			0
$67$	1.66267	−	2.87982i	0.203127	−	0.351826i	−0.746407	−	0.665489i	$-0.768223\pi$
$67$	1.66267	−	2.87982i	0.203127	−	0.351826i	0.949534	+	0.313663i	$0.101556\pi$
$68$	6.53190	−	11.3136i	0.792110	−	1.37197i
$69$		0			0
$70$		0			0
$71$	12.3890			1.47031			0.735154	−	0.677900i	$-0.237110\pi$
$71$	12.3890			1.47031			0.735154	+	0.677900i	$0.237110\pi$
$72$		0			0
$73$	2.19863			0.257331			0.128665	−	0.991688i	$-0.458931\pi$
$73$	2.19863			0.257331			0.128665	+	0.991688i	$0.458931\pi$
$74$	0.144596	+	0.250447i	0.0168089	+	0.0291138i
$75$		0			0
$76$	1.89749	−	3.28655i	0.217657	−	0.376993i
$77$		0			0
$78$		0			0
$79$	−0.406778	−	0.704560i	−0.0457661	−	0.0792692i	0.842235	−	0.539111i	$-0.181240\pi$
$79$	−0.406778	−	0.704560i	−0.0457661	−	0.0792692i	−0.888001	+	0.459841i	$0.847906\pi$
$80$	10.5805			1.18294
$81$		0			0
$82$	0.505486			0.0558216
$83$	3.41842	+	5.92088i	0.375220	+	0.649901i	0.990360	−	0.138517i	$-0.0442337\pi$
$83$	3.41842	+	5.92088i	0.375220	+	0.649901i	−0.615140	+	0.788418i	$0.710900\pi$
$84$		0			0
$85$	−8.72020	+	15.1038i	−0.945838	+	1.63824i
$86$	−0.385066	+	0.666954i	−0.0415227	+	0.0719195i
$87$		0			0
$88$	−0.218422	−	0.378317i	−0.0232838	−	0.0403288i
$89$	−0.470572			−0.0498805			−0.0249403	−	0.999689i	$-0.507940\pi$
$89$	−0.470572			−0.0498805			−0.0249403	+	0.999689i	$0.507940\pi$
$90$		0			0
$91$		0			0
$92$	3.06120	+	5.30216i	0.319152	+	0.552788i
$93$		0			0
$94$	−0.129882	+	0.224963i	−0.0133963	+	0.0232031i
$95$	−2.53318	+	4.38760i	−0.259899	+	0.450158i
$96$		0			0
$97$	2.57623	+	4.46216i	0.261576	+	0.453064i	0.966661	−	0.256059i	$-0.0824243\pi$
$97$	2.57623	+	4.46216i	0.261576	+	0.453064i	−0.705085	+	0.709123i	$0.749091\pi$
$98$		0			0
$99$		0			0
$100$	−4.18177			−0.418177
$101$	−0.922440	−	1.59771i	−0.0917862	−	0.158978i	0.816477	−	0.577379i	$-0.195924\pi$
$101$	−0.922440	−	1.59771i	−0.0917862	−	0.158978i	−0.908263	+	0.418400i	$0.862591\pi$
$102$		0			0
$103$	−2.58901	+	4.48430i	−0.255103	+	0.441851i	−0.964923	−	0.262531i	$-0.915443\pi$
$103$	−2.58901	+	4.48430i	−0.255103	+	0.441851i	0.709821	+	0.704383i	$0.248776\pi$
$104$	−0.717607	+	1.24293i	−0.0703671	+	0.121879i
$105$		0			0
$106$	−0.304217	−	0.526920i	−0.0295482	−	0.0511790i
$107$	16.9489			1.63851			0.819256	−	0.573428i	$-0.194387\pi$
$107$	16.9489			1.63851			0.819256	+	0.573428i	$0.194387\pi$
$108$		0			0
$109$	−8.49992			−0.814145			−0.407073	−	0.913396i	$-0.633450\pi$
$109$	−8.49992			−0.814145			−0.407073	+	0.913396i	$0.633450\pi$
$110$	0.145628	+	0.252235i	0.0138851	+	0.0240496i
$111$		0			0
$112$		0			0
$113$	1.95196	−	3.38089i	0.183625	−	0.318048i	−0.759487	−	0.650522i	$-0.774550\pi$
$113$	1.95196	−	3.38089i	0.183625	−	0.318048i	0.943112	+	0.332474i	$0.107884\pi$
$114$		0			0
$115$	−4.08675	−	7.07847i	−0.381092	−	0.660070i
$116$	12.7482			1.18364
$117$		0			0
$118$	−0.744783			−0.0685628
$119$		0			0
$120$		0			0
$121$	4.22140	−	7.31167i	0.383763	−	0.664698i
$122$	0.0927788	−	0.160698i	0.00839980	−	0.0145489i
$123$		0			0
$124$	6.70352	+	11.6108i	0.601994	+	1.04268i
$125$	−7.73623			−0.691949
$126$		0			0
$127$	10.9533			0.971946			0.485973	−	0.873974i	$-0.338465\pi$
$127$	10.9533			0.971946			0.485973	+	0.873974i	$0.338465\pi$
$128$	−1.08760	−	1.88378i	−0.0961311	−	0.166504i
$129$		0			0
$130$	0.478448	−	0.828696i	0.0419626	−	0.0726814i
$131$	−2.22671	+	3.85678i	−0.194549	+	0.336968i	−0.946752	−	0.321962i	$-0.895658\pi$
$131$	−2.22671	+	3.85678i	−0.194549	+	0.336968i	0.752204	+	0.658931i	$0.228991\pi$
$132$		0			0
$133$		0			0
$134$	0.227366			0.0196414
$135$		0			0
$136$	1.78854			0.153366
$137$	−9.76800	−	16.9187i	−0.834537	−	1.44546i	−0.894407	−	0.447254i	$-0.852402\pi$
$137$	−9.76800	−	16.9187i	−0.834537	−	1.44546i	0.0598699	−	0.998206i	$-0.480931\pi$
$138$		0			0
$139$	−1.31540	+	2.27833i	−0.111570	+	0.193246i	−0.916404	−	0.400256i	$-0.868921\pi$
$139$	−1.31540	+	2.27833i	−0.111570	+	0.193246i	0.804833	+	0.593501i	$0.202255\pi$
$140$		0			0
$141$		0			0
$142$	0.423544	+	0.733599i	0.0355430	+	0.0615623i
$143$	8.40149			0.702568
$144$		0			0
$145$	−17.0190			−1.41335
$146$	0.0751647	+	0.130189i	0.00622067	+	0.0107745i
$147$		0			0
$148$	4.21966	−	7.30867i	0.346854	−	0.600769i
$149$	−4.40640	+	7.63212i	−0.360987	+	0.625247i	−0.988124	−	0.153662i	$-0.950893\pi$
$149$	−4.40640	+	7.63212i	−0.360987	+	0.625247i	0.627137	+	0.778909i	$0.284227\pi$
$150$		0			0
$151$	−2.33211	−	4.03933i	−0.189784	−	0.328716i	0.755394	−	0.655271i	$-0.227446\pi$
$151$	−2.33211	−	4.03933i	−0.189784	−	0.328716i	−0.945178	+	0.326555i	$0.894112\pi$
$152$	0.519564			0.0421422
$153$		0			0
$154$		0			0
$155$	−8.94931	−	15.5007i	−0.718826	−	1.24504i
$156$		0			0
$157$	2.03647	−	3.52727i	0.162528	−	0.281506i	−0.773247	−	0.634105i	$-0.781369\pi$
$157$	2.03647	−	3.52727i	0.162528	−	0.281506i	0.935775	+	0.352599i	$0.114702\pi$
$158$	0.0278130	−	0.0481736i	0.00221269	−	0.00383249i
$159$		0			0
$160$	1.08940	+	1.88690i	0.0861246	+	0.149172i
$161$		0			0
$162$		0			0
$163$	−12.1222			−0.949487			−0.474744	−	0.880124i	$-0.657459\pi$
$163$	−12.1222			−0.949487			−0.474744	+	0.880124i	$0.657459\pi$
$164$	−7.37568	−	12.7750i	−0.575944	−	0.997564i
$165$		0			0
$166$	−0.233731	+	0.404834i	−0.0181410	+	0.0314212i
$167$	−2.39951	+	4.15608i	−0.185680	+	0.321607i	−0.943805	−	0.330502i	$-0.892782\pi$
$167$	−2.39951	+	4.15608i	−0.185680	+	0.321607i	0.758126	+	0.652109i	$0.226115\pi$
$168$		0			0
$169$	−7.30121	−	12.6461i	−0.561631	−	0.972774i
$170$	−1.19247			−0.0914582
$171$		0			0
$172$	22.4744			1.71366
$173$	2.51585	+	4.35759i	0.191277	+	0.331301i	0.945674	−	0.325118i	$-0.105404\pi$
$173$	2.51585	+	4.35759i	0.191277	+	0.331301i	−0.754397	+	0.656419i	$0.772071\pi$
$174$		0			0
$175$		0			0
$176$	−3.17584	+	5.50072i	−0.239388	+	0.414632i
$177$		0			0
$178$	−0.0160874	−	0.0278642i	−0.00120580	−	0.00208851i
$179$	16.3979			1.22564			0.612819	−	0.790224i	$-0.290036\pi$
$179$	16.3979			1.22564			0.612819	+	0.790224i	$0.290036\pi$
$180$		0			0
$181$	−14.4345			−1.07291			−0.536454	−	0.843930i	$-0.680237\pi$
$181$	−14.4345			−1.07291			−0.536454	+	0.843930i	$0.680237\pi$
$182$		0			0
$183$		0			0
$184$	−0.419103	+	0.725908i	−0.0308967	+	0.0535147i
$185$	−5.63332	+	9.75719i	−0.414170	+	0.717363i
$186$		0			0
$187$	−5.23491	−	9.06713i	−0.382814	−	0.663054i
$188$	7.58059			0.552871
$189$		0			0
$190$	−0.346407			−0.0251310
$191$	1.42066	+	2.46065i	0.102795	+	0.178046i	0.912835	−	0.408328i	$-0.133888\pi$
$191$	1.42066	+	2.46065i	0.102795	+	0.178046i	−0.810040	+	0.586374i	$0.800555\pi$
$192$		0			0
$193$	−4.41443	+	7.64601i	−0.317758	+	0.550372i	−0.980020	−	0.198900i	$-0.936263\pi$
$193$	−4.41443	+	7.64601i	−0.317758	+	0.550372i	0.662262	+	0.749272i	$0.269596\pi$
$194$	−0.176147	+	0.305096i	−0.0126466	+	0.0219046i
$195$		0			0
$196$		0			0
$197$	−5.72354			−0.407785			−0.203893	−	0.978993i	$-0.565359\pi$
$197$	−5.72354			−0.407785			−0.203893	+	0.978993i	$0.565359\pi$
$198$		0			0
$199$	−11.4150			−0.809191			−0.404596	−	0.914496i	$-0.632588\pi$
$199$	−11.4150			−0.809191			−0.404596	+	0.914496i	$0.632588\pi$
$200$	−0.286259	−	0.495815i	−0.0202416	−	0.0350594i
$201$		0			0
$202$	0.0630709	−	0.109242i	0.00443765	−	0.00768624i
$203$		0			0
$204$		0			0
$205$	9.84665	+	17.0549i	0.687720	+	1.19117i
$206$	−0.354042			−0.0246673
$207$		0			0
$208$	20.8679			1.44693
$209$	−1.52072	−	2.63396i	−0.105190	−	0.182195i
$210$		0			0
$211$	10.6919	−	18.5189i	0.736059	−	1.27489i	−0.218199	−	0.975904i	$-0.570018\pi$
$211$	10.6919	−	18.5189i	0.736059	−	1.27489i	0.954257	−	0.298986i	$-0.0966486\pi$
$212$	−8.87782	+	15.3768i	−0.609731	+	1.05609i
$213$		0			0
$214$	0.579432	+	1.00361i	0.0396091	+	0.0686050i
$215$	−30.0037			−2.04623
$216$		0			0
$217$		0			0
$218$	−0.290587	−	0.503311i	−0.0196810	−	0.0340885i
$219$		0			0
$220$	4.24978	−	7.36084i	0.286520	−	0.496268i
$221$	−17.1989	+	29.7893i	−1.15692	+	2.00385i
$222$		0			0
$223$	−3.58387	−	6.20744i	−0.239994	−	0.415681i	0.720719	−	0.693228i	$-0.243812\pi$
$223$	−3.58387	−	6.20744i	−0.239994	−	0.415681i	−0.960712	+	0.277547i	$0.910479\pi$
$224$		0			0
$225$		0			0
$226$	0.266926			0.0177557
$227$	−6.89434	−	11.9413i	−0.457593	−	0.792575i	0.541240	−	0.840868i	$-0.317955\pi$
$227$	−6.89434	−	11.9413i	−0.457593	−	0.792575i	−0.998833	+	0.0482933i	$0.984622\pi$
$228$		0			0
$229$	13.1972	−	22.8581i	0.872092	−	1.51051i	0.0122645	−	0.999925i	$-0.496096\pi$
$229$	13.1972	−	22.8581i	0.872092	−	1.51051i	0.859828	−	0.510584i	$-0.170571\pi$
$230$	0.279428	−	0.483983i	0.0184249	−	0.0319129i
$231$		0			0
$232$	0.872666	+	1.51150i	0.0572933	+	0.0992349i
$233$	12.6446			0.828375			0.414187	−	0.910192i	$-0.364066\pi$
$233$	12.6446			0.828375			0.414187	+	0.910192i	$0.364066\pi$
$234$		0			0
$235$	−10.1202			−0.660170
$236$	10.8673	+	18.8228i	0.707403	+	1.22526i
$237$		0			0
$238$		0			0
$239$	−7.71640	+	13.3652i	−0.499133	+	0.864523i	−0.999999	−	0.00100121i	$-0.999681\pi$
$239$	−7.71640	+	13.3652i	−0.499133	+	0.864523i	0.500867	+	0.865524i	$0.333015\pi$
$240$		0			0
$241$	−0.589942	−	1.02181i	−0.0380015	−	0.0658205i	0.846399	−	0.532549i	$-0.178766\pi$
$241$	−0.589942	−	1.02181i	−0.0380015	−	0.0658205i	−0.884401	+	0.466729i	$0.845432\pi$
$242$	0.577267			0.0371082
$243$		0			0
$244$	−5.41504			−0.346662
$245$		0			0
$246$		0			0
$247$	−4.99620	+	8.65367i	−0.317900	+	0.550620i
$248$	−0.917767	+	1.58962i	−0.0582783	+	0.100941i
$249$		0			0
$250$	−0.264478	−	0.458090i	−0.0167271	−	0.0289721i
$251$	−5.54970			−0.350294			−0.175147	−	0.984542i	$-0.556040\pi$
$251$	−5.54970			−0.350294			−0.175147	+	0.984542i	$0.556040\pi$
$252$		0			0
$253$	4.90672			0.308483
$254$	0.374459	+	0.648583i	0.0234957	+	0.0406957i
$255$		0			0
$256$	−7.81365	+	13.5336i	−0.488353	+	0.845853i
$257$	4.91538	−	8.51369i	0.306613	−	0.531069i	−0.671006	−	0.741452i	$-0.734138\pi$
$257$	4.91538	−	8.51369i	0.306613	−	0.531069i	0.977619	+	0.210382i	$0.0674709\pi$
$258$		0			0
$259$		0			0
$260$	−27.9246			−1.73181
$261$		0			0
$262$	−0.304498			−0.0188120
$263$	5.96612	+	10.3336i	0.367887	+	0.637199i	0.989235	−	0.146336i	$-0.0467480\pi$
$263$	5.96612	+	10.3336i	0.367887	+	0.637199i	−0.621348	+	0.783535i	$0.713415\pi$
$264$		0			0
$265$	11.8520	−	20.5283i	0.728065	−	1.26105i
$266$		0			0
$267$		0			0
$268$	−3.31756	−	5.74618i	−0.202652	−	0.351004i
$269$	−29.9648			−1.82699			−0.913494	−	0.406853i	$-0.866626\pi$
$269$	−29.9648			−1.82699			−0.913494	+	0.406853i	$0.866626\pi$
$270$		0			0
$271$	−7.09650			−0.431082			−0.215541	−	0.976495i	$-0.569151\pi$
$271$	−7.09650			−0.431082			−0.215541	+	0.976495i	$0.569151\pi$
$272$	−13.0027	−	22.5213i	−0.788402	−	1.36555i
$273$		0			0
$274$	0.667877	−	1.15680i	0.0403479	−	0.0698847i
$275$	−1.67571	+	2.90242i	−0.101049	+	0.175022i
$276$		0			0
$277$	4.91175	+	8.50741i	0.295119	+	0.511161i	0.975013	−	0.222150i	$-0.0713075\pi$
$277$	4.91175	+	8.50741i	0.295119	+	0.511161i	−0.679894	+	0.733311i	$0.737974\pi$
$278$	−0.179878			−0.0107883
$279$		0			0
$280$		0			0
$281$	−11.9389	−	20.6787i	−0.712213	−	1.23359i	−0.964025	−	0.265813i	$-0.914360\pi$
$281$	−11.9389	−	20.6787i	−0.712213	−	1.23359i	0.251812	−	0.967776i	$-0.418974\pi$
$282$		0			0
$283$	1.50798	−	2.61189i	0.0896399	−	0.155261i	−0.817719	−	0.575618i	$-0.804762\pi$
$283$	1.50798	−	2.61189i	0.0896399	−	0.155261i	0.907359	+	0.420357i	$0.138095\pi$
$284$	12.3601	−	21.4083i	0.733435	−	1.27035i
$285$		0			0
$286$	0.287222	+	0.497483i	0.0169838	+	0.0294168i
$287$		0			0
$288$		0			0
$289$	25.8659			1.52153
$290$	−0.581830	−	1.00776i	−0.0341662	−	0.0591776i
$291$		0			0
$292$	2.19350	−	3.79925i	0.128365	−	0.222334i
$293$	8.52913	−	14.7729i	0.498277	−	0.863041i	−0.501721	−	0.865030i	$-0.667300\pi$
$293$	8.52913	−	14.7729i	0.498277	−	0.863041i	0.999998	+	0.00198814i	$0.000632845\pi$
$294$		0			0
$295$	−14.5081	−	25.1287i	−0.844692	−	1.46305i
$296$	1.15541			0.0671570
$297$		0			0
$298$	−0.602567			−0.0349058
$299$	−8.06031	−	13.9609i	−0.466140	−	0.807378i
$300$		0			0
$301$		0			0
$302$	0.159456	−	0.276185i	0.00917564	−	0.0158927i
$303$		0			0
$304$	−3.77722	−	6.54234i	−0.216638	−	0.375229i
$305$	7.22917			0.413941
$306$		0			0
$307$	23.2178			1.32511			0.662554	−	0.749014i	$-0.269473\pi$
$307$	23.2178			1.32511			0.662554	+	0.749014i	$0.269473\pi$
$308$		0			0
$309$		0			0
$310$	0.611900	−	1.05984i	0.0347536	−	0.0601950i
$311$	0.895467	−	1.55100i	0.0507773	−	0.0879489i	−0.839520	−	0.543329i	$-0.817163\pi$
$311$	0.895467	−	1.55100i	0.0507773	−	0.0879489i	0.890297	+	0.455381i	$0.150497\pi$
$312$		0			0
$313$	−2.30458	−	3.99166i	−0.130263	−	0.225622i	0.793515	−	0.608551i	$-0.208249\pi$
$313$	−2.30458	−	3.99166i	−0.130263	−	0.225622i	−0.923778	+	0.382929i	$0.874915\pi$
$314$	0.278483			0.0157157
$315$		0			0
$316$	−1.62331			−0.0913183
$317$	−12.9421	−	22.4163i	−0.726898	−	1.25902i	−0.958188	−	0.286140i	$-0.907628\pi$
$317$	−12.9421	−	22.4163i	−0.726898	−	1.25902i	0.231290	−	0.972885i	$-0.425705\pi$
$318$		0			0
$319$	5.10843	−	8.84807i	0.286017	−	0.495397i
$320$	10.5060	−	18.1970i	0.587304	−	1.01724i
$321$		0			0
$322$		0			0
$323$	12.4524			0.692869
$324$		0			0
$325$	11.0108			0.610771
$326$	−0.414423	−	0.717802i	−0.0229528	−	0.0397554i
$327$		0			0
$328$	1.00979	−	1.74901i	0.0557563	−	0.0965728i
$329$		0			0
$330$		0			0
$331$	−0.0806617	−	0.139710i	−0.00443357	−	0.00767917i	0.863800	−	0.503835i	$-0.168078\pi$
$331$	−0.0806617	−	0.139710i	−0.00443357	−	0.00767917i	−0.868234	+	0.496156i	$0.834745\pi$
$332$	13.6417			0.748687
$333$		0			0
$334$	−0.328128			−0.0179544
$335$	4.42899	+	7.67124i	0.241982	+	0.419125i
$336$		0			0
$337$	4.52675	−	7.84057i	0.246588	−	0.427103i	−0.715989	−	0.698112i	$-0.754024\pi$
$337$	4.52675	−	7.84057i	0.246588	−	0.427103i	0.962577	+	0.271009i	$0.0873572\pi$
$338$	0.499213	−	0.864662i	0.0271536	−	0.0470314i
$339$		0			0
$340$	17.3996	+	30.1370i	0.943627	+	1.63441i
$341$	10.7449			0.581869
$342$		0			0
$343$		0			0
$344$	1.53846	+	2.66470i	0.0829484	+	0.143671i
$345$		0			0
$346$	−0.172019	+	0.297945i	−0.00924779	+	0.0160176i
$347$	−2.90984	+	5.03999i	−0.156208	+	0.270561i	−0.933498	−	0.358582i	$-0.883260\pi$
$347$	−2.90984	+	5.03999i	−0.156208	+	0.270561i	0.777290	+	0.629142i	$0.216594\pi$
$348$		0			0
$349$	−13.6310	−	23.6095i	−0.729648	−	1.26379i	−0.957032	−	0.289983i	$-0.906350\pi$
$349$	−13.6310	−	23.6095i	−0.729648	−	1.26379i	0.227384	−	0.973805i	$-0.426983\pi$
$350$		0			0
$351$		0			0
$352$	−1.30798			−0.0697154
$353$	−12.0948	−	20.9488i	−0.643741	−	1.11499i	−0.984591	−	0.174874i	$-0.944048\pi$
$353$	−12.0948	−	20.9488i	−0.643741	−	1.11499i	0.340850	−	0.940118i	$-0.389285\pi$
$354$		0			0
$355$	−16.5009	+	28.5804i	−0.875777	+	1.51689i
$356$	−0.469472	+	0.813149i	−0.0248820	+	0.0430968i
$357$		0			0
$358$	0.560595	+	0.970979i	0.0296284	+	0.0513179i
$359$	21.0376			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$359$	21.0376			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$360$		0			0
$361$	−15.3826			−0.809612
$362$	−0.493472	−	0.854719i	−0.0259363	−	0.0449230i
$363$		0			0
$364$		0			0
$365$	−2.92835	+	5.07205i	−0.153277	+	0.265483i
$366$		0			0
$367$	−17.5190	−	30.3438i	−0.914485	−	1.58393i	−0.807654	−	0.589657i	$-0.799263\pi$
$367$	−17.5190	−	30.3438i	−0.914485	−	1.58393i	−0.106831	−	0.994277i	$-0.534070\pi$
$368$	12.1875			0.635317
$369$		0			0
$370$	−0.770345			−0.0400483
$371$		0			0
$372$		0			0
$373$	−0.564310	+	0.977414i	−0.0292189	+	0.0506086i	−0.880265	−	0.474482i	$-0.842635\pi$
$373$	−0.564310	+	0.977414i	−0.0292189	+	0.0506086i	0.851046	+	0.525091i	$0.175969\pi$
$374$	0.357931	−	0.619955i	0.0185082	−	0.0320571i
$375$		0			0
$376$	0.518922	+	0.898800i	0.0267614	+	0.0463521i
$377$	−33.5667			−1.72877
$378$		0			0
$379$	−21.9619			−1.12811			−0.564054	−	0.825738i	$-0.690759\pi$
$379$	−21.9619			−1.12811			−0.564054	+	0.825738i	$0.690759\pi$
$380$	5.05452	+	8.75468i	0.259291	+	0.449106i
$381$		0			0
$382$	−0.0971359	+	0.168244i	−0.00496991	+	0.00860813i
$383$	−11.5200	+	19.9533i	−0.588647	+	1.01957i	0.405763	+	0.913978i	$0.367006\pi$
$383$	−11.5200	+	19.9533i	−0.588647	+	1.01957i	−0.994410	+	0.105588i	$0.966328\pi$
$384$		0			0
$385$		0			0
$386$	−0.603664			−0.0307257
$387$		0			0
$388$	10.2808			0.521930
$389$	7.88753	+	13.6616i	0.399914	+	0.692671i	0.993715	−	0.111941i	$-0.0357067\pi$
$389$	7.88753	+	13.6616i	0.399914	+	0.692671i	−0.593801	+	0.804612i	$0.702373\pi$
$390$		0			0
$391$	−10.0446	+	17.3978i	−0.507979	+	0.879846i
$392$		0			0
$393$		0			0
$394$	−0.195671	−	0.338912i	−0.00985774	−	0.0170741i
$395$	2.16714			0.109041
$396$		0			0
$397$	16.5055			0.828389			0.414195	−	0.910188i	$-0.364063\pi$
$397$	16.5055			0.828389			0.414195	+	0.910188i	$0.364063\pi$
$398$	−0.390246	−	0.675926i	−0.0195613	−	0.0338811i
$399$		0			0
$400$	−4.16220	+	7.20914i	−0.208110	+	0.360457i
$401$	10.8300	−	18.7581i	0.540823	−	0.936733i	−0.458034	−	0.888935i	$-0.651446\pi$
$401$	10.8300	−	18.7581i	0.540823	−	0.936733i	0.998857	−	0.0477986i	$-0.0152206\pi$
$402$		0			0
$403$	−17.6507	−	30.5720i	−0.879246	−	1.52290i
$404$	−3.68113			−0.183143
$405$		0			0
$406$		0			0
$407$	−3.38179	−	5.85743i	−0.167629	−	0.290342i
$408$		0			0
$409$	15.2860	−	26.4762i	0.755846	−	1.30916i	−0.189107	−	0.981956i	$-0.560559\pi$
$409$	15.2860	−	26.4762i	0.755846	−	1.30916i	0.944953	−	0.327207i	$-0.106107\pi$
$410$	−0.673255	+	1.16611i	−0.0332497	+	0.0575901i
$411$		0			0
$412$	5.16592	+	8.94763i	0.254507	+	0.440818i
$413$		0			0
$414$		0			0
$415$	−18.2119			−0.893988
$416$	2.14863	+	3.72153i	0.105345	+	0.182463i
$417$		0			0
$418$	0.103978	−	0.180094i	0.00508571	−	0.00880871i
$419$	−10.8081	+	18.7202i	−0.528011	+	0.914542i	0.471456	+	0.881890i	$0.343729\pi$
$419$	−10.8081	+	18.7202i	−0.528011	+	0.914542i	−0.999467	+	0.0326524i	$0.989605\pi$
$420$		0			0
$421$	13.6217	+	23.5935i	0.663881	+	1.14988i	0.979587	+	0.201019i	$0.0644252\pi$
$421$	13.6217	+	23.5935i	0.663881	+	1.14988i	−0.315706	+	0.948857i	$0.602241\pi$
$422$	1.46209			0.0711735
$423$		0			0
$424$	−2.43089			−0.118055
$425$	−6.86077	−	11.8832i	−0.332796	−	0.576420i
$426$		0			0
$427$		0			0
$428$	16.9093	−	29.2877i	0.817341	−	1.41568i
$429$		0			0
$430$	−1.02574	−	1.77663i	−0.0494654	−	0.0856765i
$431$	−8.19687			−0.394829			−0.197415	−	0.980320i	$-0.563255\pi$
$431$	−8.19687			−0.394829			−0.197415	+	0.980320i	$0.563255\pi$
$432$		0			0
$433$	3.41468			0.164099			0.0820494	−	0.996628i	$-0.473853\pi$
$433$	3.41468			0.164099			0.0820494	+	0.996628i	$0.473853\pi$
$434$		0			0
$435$		0			0
$436$	−8.48005	+	14.6879i	−0.406121	+	0.703422i
$437$	−2.91793	+	5.05400i	−0.139583	+	0.241765i
$438$		0			0
$439$	−3.29416	−	5.70564i	−0.157221	−	0.272316i	0.776644	−	0.629939i	$-0.216920\pi$
$439$	−3.29416	−	5.70564i	−0.157221	−	0.272316i	−0.933866	+	0.357624i	$0.883587\pi$
$440$	1.16366			0.0554753
$441$		0			0
$442$	−2.35191			−0.111869
$443$	14.3456	+	24.8473i	0.681581	+	1.18053i	0.974498	+	0.224395i	$0.0720407\pi$
$443$	14.3456	+	24.8473i	0.681581	+	1.18053i	−0.292917	+	0.956138i	$0.594626\pi$
$444$		0			0
$445$	0.626752	−	1.08557i	0.0297109	−	0.0514608i
$446$	0.245043	−	0.424428i	0.0116031	−	0.0200972i
$447$		0			0
$448$		0			0
$449$	−0.457724			−0.0216013			−0.0108007	−	0.999942i	$-0.503438\pi$
$449$	−0.457724			−0.0216013			−0.0108007	+	0.999942i	$0.503438\pi$
$450$		0			0
$451$	−11.8223			−0.556689
$452$	−3.89479	−	6.74598i	−0.183196	−	0.317304i
$453$		0			0
$454$	0.471393	−	0.816477i	0.0221236	−	0.0383192i
$455$		0			0
$456$		0			0
$457$	−10.1105	−	17.5119i	−0.472950	−	0.819173i	0.526571	−	0.850131i	$-0.323477\pi$
$457$	−10.1105	−	17.5119i	−0.472950	−	0.819173i	−0.999521	+	0.0309581i	$0.990144\pi$
$458$	1.80468			0.0843273
$459$		0			0
$460$	−16.3088			−0.760402
$461$	12.1036	+	20.9640i	0.563719	+	0.976390i	0.997168	+	0.0752117i	$0.0239633\pi$
$461$	12.1036	+	20.9640i	0.563719	+	0.976390i	−0.433449	+	0.901178i	$0.642703\pi$
$462$		0			0
$463$	2.40242	−	4.16111i	0.111650	−	0.193383i	−0.804786	−	0.593565i	$-0.797720\pi$
$463$	2.40242	−	4.16111i	0.111650	−	0.193383i	0.916436	+	0.400182i	$0.131053\pi$
$464$	12.6885	−	21.9772i	0.589050	−	1.02026i
$465$		0			0
$466$	0.432281	+	0.748732i	0.0200250	+	0.0346843i
$467$	27.2456			1.26078			0.630389	−	0.776279i	$-0.282895\pi$
$467$	27.2456			1.26078			0.630389	+	0.776279i	$0.282895\pi$
$468$		0			0
$469$		0			0
$470$	−0.345979	−	0.599254i	−0.0159588	−	0.0276415i
$471$		0			0
$472$	−1.48783	+	2.57699i	−0.0684827	+	0.118616i
$473$	9.00590	−	15.5987i	0.414092	−	0.717228i
$474$		0			0
$475$	−1.99302	−	3.45202i	−0.0914462	−	0.158389i
$476$		0			0
$477$		0			0
$478$	−1.05520			−0.0482638
$479$	10.2628	+	17.7756i	0.468917	+	0.812188i	0.999369	−	0.0355269i	$-0.0113109\pi$
$479$	10.2628	+	17.7756i	0.468917	+	0.812188i	−0.530452	+	0.847715i	$0.677978\pi$
$480$		0			0
$481$	−11.1106	+	19.2441i	−0.506600	+	0.877457i
$482$	0.0403366	−	0.0698651i	0.00183728	−	0.00318227i
$483$		0			0
$484$	−8.42306	−	14.5892i	−0.382866	−	0.663144i
$485$	−13.7251			−0.623224
$486$		0			0
$487$	25.8449			1.17114			0.585571	−	0.810621i	$-0.300870\pi$
$487$	25.8449			1.17114			0.585571	+	0.810621i	$0.300870\pi$
$488$	−0.370682	−	0.642039i	−0.0167800	−	0.0290638i
$489$		0			0
$490$		0			0
$491$	7.80775	−	13.5234i	0.352359	−	0.610303i	−0.634303	−	0.773084i	$-0.718713\pi$
$491$	7.80775	−	13.5234i	0.352359	−	0.610303i	0.986662	+	0.162781i	$0.0520463\pi$
$492$		0			0
$493$	20.9152	+	36.2261i	0.941971	+	1.63154i
$494$	−0.683220			−0.0307395
$495$		0			0
$496$	26.6886			1.19835
$497$		0			0
$498$		0			0
$499$	−10.6345	+	18.4195i	−0.476066	+	0.824571i	−0.999624	−	0.0274192i	$-0.991271\pi$
$499$	−10.6345	+	18.4195i	−0.476066	+	0.824571i	0.523558	+	0.851990i	$0.324604\pi$
$500$	−7.71814	+	13.3682i	−0.345166	+	0.597845i
$501$		0			0
$502$	−0.189728	−	0.328618i	−0.00846795	−	0.0146669i
$503$	16.3298			0.728110			0.364055	−	0.931377i	$-0.381392\pi$
$503$	16.3298			0.728110			0.364055	+	0.931377i	$0.381392\pi$
$504$		0			0
$505$	4.91437			0.218687
$506$	0.167746	+	0.290544i	0.00745722	+	0.0129163i
$507$		0			0
$508$	10.9277	−	18.9273i	0.484837	−	0.839762i
$509$	−6.73089	+	11.6582i	−0.298342	+	0.516743i	−0.975757	−	0.218858i	$-0.929767\pi$
$509$	−6.73089	+	11.6582i	−0.298342	+	0.516743i	0.677415	+	0.735601i	$0.263100\pi$
$510$		0			0
$511$		0			0
$512$	−5.41890			−0.239484
$513$		0			0
$514$	0.672168			0.0296481
$515$	−6.89659	−	11.9452i	−0.303900	−	0.526370i
$516$		0			0
$517$	3.03768	−	5.26142i	0.133597	−	0.231397i
$518$		0			0
$519$		0			0
$520$	−1.91155	−	3.31091i	−0.0838272	−	0.145193i
$521$	1.42619			0.0624826			0.0312413	−	0.999512i	$-0.490054\pi$
$521$	1.42619			0.0624826			0.0312413	+	0.999512i	$0.490054\pi$
$522$		0			0
$523$	−7.71060			−0.337161			−0.168581	−	0.985688i	$-0.553918\pi$
$523$	−7.71060			−0.337161			−0.168581	+	0.985688i	$0.553918\pi$
$524$	4.44301	+	7.69553i	0.194094	+	0.336181i
$525$		0			0
$526$	−0.407928	+	0.706551i	−0.0177865	+	0.0308071i
$527$	−21.9961	+	38.0984i	−0.958165	+	1.65959i
$528$		0			0
$529$	6.79254	+	11.7650i	0.295328	+	0.511523i
$530$	1.62074			0.0704005
$531$		0			0
$532$		0			0
$533$	19.4206	+	33.6374i	0.841198	+	1.45700i
$534$		0			0
$535$	−22.5742	+	39.0996i	−0.975966	+	1.69042i
$536$	0.454201	−	0.786699i	0.0196185	−	0.0339802i
$537$		0			0
$538$	−1.02441	−	1.77432i	−0.0441653	−	0.0764966i
$539$		0			0
$540$		0			0
$541$	28.0456			1.20577			0.602886	−	0.797827i	$-0.294017\pi$
$541$	28.0456			1.20577			0.602886	+	0.797827i	$0.294017\pi$
$542$	−0.242608	−	0.420209i	−0.0104209	−	0.0180495i
$543$		0			0
$544$	2.67759	−	4.63771i	0.114801	−	0.198840i
$545$	11.3210	−	19.6086i	0.484939	−	0.839939i
$546$		0			0
$547$	17.7305	+	30.7101i	0.758101	+	1.31307i	0.943818	+	0.330466i	$0.107206\pi$
$547$	17.7305	+	30.7101i	0.758101	+	1.31307i	−0.185717	+	0.982603i	$0.559461\pi$
$548$	−38.9807			−1.66517
$549$		0			0
$550$	−0.229150			−0.00977099
$551$	6.07577	+	10.5235i	0.258836	+	0.448318i
$552$		0			0
$553$		0			0
$554$	−0.335836	+	0.581685i	−0.0142683	+	0.0247134i
$555$		0			0
$556$	2.62464	+	4.54601i	0.111310	+	0.192794i
$557$	−35.0419			−1.48477			−0.742386	−	0.669972i	$-0.766306\pi$
$557$	−35.0419			−1.48477			−0.742386	+	0.669972i	$0.766306\pi$
$558$		0			0
$559$	−59.1763			−2.50289
$560$		0			0
$561$		0			0
$562$	0.816308	−	1.41389i	0.0344339	−	0.0596412i
$563$	8.01311	−	13.8791i	0.337712	−	0.584935i	−0.646290	−	0.763092i	$-0.723680\pi$
$563$	8.01311	−	13.8791i	0.337712	−	0.584935i	0.984002	+	0.178157i	$0.0570135\pi$
$564$		0			0
$565$	5.19961	+	9.00599i	0.218749	+	0.378885i
$566$	0.206213			0.00866776
$567$		0			0
$568$	3.38439			0.142006
$569$	0.185651	+	0.321557i	0.00778290	+	0.0134804i	0.869891	−	0.493245i	$-0.164189\pi$
$569$	0.185651	+	0.321557i	0.00778290	+	0.0134804i	−0.862108	+	0.506725i	$0.830856\pi$
$570$		0			0
$571$	−14.6152	+	25.3142i	−0.611626	+	1.05937i	0.379340	+	0.925257i	$0.376151\pi$
$571$	−14.6152	+	25.3142i	−0.611626	+	1.05937i	−0.990966	+	0.134110i	$0.957182\pi$
$572$	8.38185	−	14.5178i	0.350463	−	0.607019i
$573$		0			0
$574$		0			0
$575$	6.43065			0.268177
$576$		0			0
$577$	−15.0570			−0.626833			−0.313417	−	0.949616i	$-0.601474\pi$
$577$	−15.0570			−0.626833			−0.313417	+	0.949616i	$0.601474\pi$
$578$	0.884279	+	1.53162i	0.0367811	+	0.0637068i
$579$		0			0
$580$	−16.9793	+	29.4089i	−0.705025	+	1.22114i
$581$		0			0
$582$		0			0
$583$	7.11501	+	12.3236i	0.294674	+	0.510390i
$584$	0.600615			0.0248536
$585$		0			0
$586$	1.16634			0.0481811
$587$	0.835901	+	1.44782i	0.0345013	+	0.0597580i	0.882760	−	0.469823i	$-0.155682\pi$
$587$	0.835901	+	1.44782i	0.0345013	+	0.0597580i	−0.848259	+	0.529581i	$0.822349\pi$
$588$		0			0
$589$	−6.38977	+	11.0674i	−0.263286	+	0.456025i
$590$	0.991973	−	1.71815i	0.0408389	−	0.0707350i
$591$		0			0
$592$	−8.39982	−	14.5489i	−0.345231	−	0.597957i
$593$	10.8174			0.444218			0.222109	−	0.975022i	$-0.428706\pi$
$593$	10.8174			0.444218			0.222109	+	0.975022i	$0.428706\pi$
$594$		0			0
$595$		0			0
$596$	8.79221	+	15.2286i	0.360143	+	0.623786i
$597$		0			0
$598$	0.551116	−	0.954560i	0.0225368	−	0.0390349i
$599$	8.32007	−	14.4108i	0.339949	−	0.588809i	−0.644474	−	0.764626i	$-0.722924\pi$
$599$	8.32007	−	14.4108i	0.339949	−	0.588809i	0.984423	+	0.175817i	$0.0562568\pi$
$600$		0			0
$601$	12.9011	+	22.3453i	0.526246	+	0.911485i	0.999532	+	0.0305765i	$0.00973432\pi$
$601$	12.9011	+	22.3453i	0.526246	+	0.911485i	−0.473286	+	0.880909i	$0.656932\pi$
$602$		0			0
$603$		0			0
$604$	−9.30663			−0.378681
$605$	11.2449	+	19.4768i	0.457171	+	0.791843i
$606$		0			0
$607$	18.9025	−	32.7400i	0.767227	−	1.32888i	−0.171834	−	0.985126i	$-0.554969\pi$
$607$	18.9025	−	32.7400i	0.767227	−	1.32888i	0.939061	−	0.343750i	$-0.111697\pi$
$608$	0.777828	−	1.34724i	0.0315451	−	0.0546377i
$609$		0			0
$610$	0.247143	+	0.428065i	0.0100065	+	0.0173318i
$611$	−19.9601			−0.807499
$612$		0			0
$613$	−12.9544			−0.523222			−0.261611	−	0.965173i	$-0.584254\pi$
$613$	−12.9544			−0.523222			−0.261611	+	0.965173i	$0.584254\pi$
$614$	0.793745	+	1.37481i	0.0320330	+	0.0554827i
$615$		0			0
$616$		0			0
$617$	−16.2202	+	28.0941i	−0.652999	+	1.13103i	0.329393	+	0.944193i	$0.393156\pi$
$617$	−16.2202	+	28.0941i	−0.652999	+	1.13103i	−0.982391	+	0.186834i	$0.940177\pi$
$618$		0			0
$619$	16.5987	+	28.7498i	0.667157	+	1.15555i	0.978696	+	0.205317i	$0.0658224\pi$
$619$	16.5987	+	28.7498i	0.667157	+	1.15555i	−0.311538	+	0.950234i	$0.600844\pi$
$620$	−35.7136			−1.43429
$621$		0			0
$622$	0.122453			0.00490993
$623$		0			0
$624$		0			0
$625$	15.5433	−	26.9218i	0.621732	−	1.07687i
$626$	0.157574	−	0.272925i	0.00629791	−	0.0109083i
$627$		0			0
$628$	−4.06342	−	7.03804i	−0.162148	−	0.280848i
$629$	27.6917			1.10414
$630$		0			0
$631$	32.2773			1.28494			0.642470	−	0.766311i	$-0.277910\pi$
$631$	32.2773			1.28494			0.642470	+	0.766311i	$0.277910\pi$
$632$	−0.111122	−	0.192469i	−0.00442020	−	0.00765601i
$633$		0			0
$634$	0.884900	−	1.53269i	0.0351439	−	0.0608709i
$635$	−14.5886	+	25.2682i	−0.578931	+	1.00274i
$636$		0			0
$637$		0			0
$638$	0.698568			0.0276566
$639$		0			0
$640$	5.79428			0.229039
$641$	21.5407	+	37.3096i	0.850806	+	1.47364i	0.880482	+	0.474079i	$0.157219\pi$
$641$	21.5407	+	37.3096i	0.850806	+	1.47364i	−0.0296762	+	0.999560i	$0.509448\pi$
$642$		0			0
$643$	3.20088	−	5.54409i	0.126230	−	0.218638i	−0.795983	−	0.605319i	$-0.793045\pi$
$643$	3.20088	−	5.54409i	0.126230	−	0.218638i	0.922213	+	0.386682i	$0.126379\pi$
$644$		0			0
$645$		0			0
$646$	0.425709	+	0.737350i	0.0167493	+	0.0290107i
$647$	3.88807			0.152856			0.0764278	−	0.997075i	$-0.475649\pi$
$647$	3.88807			0.152856			0.0764278	+	0.997075i	$0.475649\pi$
$648$		0			0
$649$	17.4189			0.683753
$650$	0.376427	+	0.651991i	0.0147647	+	0.0255732i
$651$		0			0
$652$	−12.0939	+	20.9473i	−0.473634	+	0.820358i
$653$	7.55174	−	13.0800i	0.295522	−	0.511860i	−0.679584	−	0.733598i	$-0.737840\pi$
$653$	7.55174	−	13.0800i	0.295522	−	0.511860i	0.975106	+	0.221738i	$0.0711730\pi$
$654$		0			0
$655$	−5.93150	−	10.2737i	−0.231763	−	0.401425i
$656$	−29.3646			−1.14650
$657$		0			0
$658$		0			0
$659$	7.13002	+	12.3496i	0.277746	+	0.481070i	0.970824	−	0.239792i	$-0.0770793\pi$
$659$	7.13002	+	12.3496i	0.277746	+	0.481070i	−0.693078	+	0.720862i	$0.743746\pi$
$660$		0			0
$661$	−9.70965	+	16.8176i	−0.377662	+	0.654129i	−0.990722	−	0.135907i	$-0.956605\pi$
$661$	−9.70965	+	16.8176i	−0.377662	+	0.654129i	0.613060	+	0.790036i	$0.289938\pi$
$662$	0.00551516	−	0.00955254i	0.000214353	−	0.000371270i
$663$		0			0
$664$	0.933832	+	1.61744i	0.0362397	+	0.0627690i
$665$		0			0
$666$		0			0
$667$	−19.6039			−0.759067
$668$	4.78781	+	8.29273i	0.185246	+	0.320855i
$669$		0			0
$670$	−0.302828	+	0.524513i	−0.0116993	+	0.0202637i
$671$	−2.16991	+	3.75839i	−0.0837683	+	0.145091i
$672$		0			0
$673$	−2.96563	−	5.13663i	−0.114317	−	0.198002i	0.803190	−	0.595723i	$-0.203135\pi$
$673$	−2.96563	−	5.13663i	−0.114317	−	0.198002i	−0.917506	+	0.397721i	$0.869801\pi$
$674$	0.619024			0.0238439
$675$		0			0
$676$	−29.1366			−1.12064
$677$	−18.4913	−	32.0278i	−0.710678	−	1.23093i	−0.964603	−	0.263706i	$-0.915055\pi$
$677$	−18.4913	−	32.0278i	−0.710678	−	1.23093i	0.253925	−	0.967224i	$-0.418278\pi$
$678$		0			0
$679$		0			0
$680$	−2.38215	+	4.12601i	−0.0913513	+	0.158225i
$681$		0			0
$682$	0.367336	+	0.636244i	0.0140660	+	0.0243630i
$683$	−13.1360			−0.502635			−0.251317	−	0.967905i	$-0.580864\pi$
$683$	−13.1360			−0.502635			−0.251317	+	0.967905i	$0.580864\pi$
$684$		0			0
$685$	52.0398			1.98834
$686$		0			0
$687$		0			0
$688$	22.3692	−	38.7446i	0.852818	−	1.47712i
$689$	23.3758	−	40.4881i	0.890547	−	1.54247i
$690$		0			0
$691$	7.38292	+	12.7876i	0.280860	+	0.486463i	0.971597	−	0.236643i	$-0.0760472\pi$
$691$	7.38292	+	12.7876i	0.280860	+	0.486463i	−0.690737	+	0.723106i	$0.742714\pi$
$692$	10.0399			0.381659
$693$		0			0
$694$	−0.397915			−0.0151046
$695$	−3.50394	−	6.06900i	−0.132912	−	0.230210i
$696$		0			0
$697$	24.2016	−	41.9184i	0.916702	−	1.58777i
$698$	0.932003	−	1.61428i	0.0352768	−	0.0611012i
$699$		0			0
$700$		0			0
$701$	30.4627			1.15056			0.575281	−	0.817956i	$-0.304893\pi$
$701$	30.4627			1.15056			0.575281	+	0.817956i	$0.304893\pi$
$702$		0			0
$703$	8.04433			0.303398
$704$	6.30697	+	10.9240i	0.237703	+	0.411713i
$705$		0			0
$706$	0.826969	−	1.43235i	0.0311234	−	0.0539073i
$707$		0			0
$708$		0			0
$709$	−7.05152	−	12.2136i	−0.264825	−	0.458691i	0.702693	−	0.711494i	$-0.251981\pi$
$709$	−7.05152	−	12.2136i	−0.264825	−	0.458691i	−0.967518	+	0.252803i	$0.918648\pi$
$710$	−2.25646			−0.0846836
$711$		0			0
$712$	−0.128549			−0.00481758
$713$	−10.3086	−	17.8549i	−0.386058	−	0.668673i
$714$		0			0
$715$	−11.1899	+	19.3815i	−0.418479	+	0.724827i
$716$	16.3596	−	28.3356i	0.611386	−	1.05895i
$717$		0			0
$718$	0.719212	+	1.24571i	0.0268408	+	0.0464896i
$719$	14.9958			0.559249			0.279624	−	0.960109i	$-0.409790\pi$
$719$	14.9958			0.559249			0.279624	+	0.960109i	$0.409790\pi$
$720$		0			0
$721$		0			0
$722$	−0.525886	−	0.910861i	−0.0195715	−	0.0338987i
$723$		0			0
$724$	−14.4008	+	24.9429i	−0.535200	+	0.926994i
$725$	6.69501	−	11.5961i	0.248646	−	0.430668i
$726$		0			0
$727$	13.0527	+	22.6080i	0.484099	+	0.838485i	0.999833	−	0.0182642i	$-0.00581399\pi$
$727$	13.0527	+	22.6080i	0.484099	+	0.838485i	−0.515734	+	0.856749i	$0.672481\pi$
$728$		0			0
$729$		0			0
$730$	−0.400446			−0.0148212
$731$	36.8723	+	63.8648i	1.36377	+	2.36212i
$732$		0			0
$733$	14.1911	−	24.5796i	0.524159	−	0.907869i	−0.475446	−	0.879745i	$-0.657713\pi$
$733$	14.1911	−	24.5796i	0.524159	−	0.907869i	0.999604	−	0.0281244i	$-0.00895345\pi$
$734$	1.19784	−	2.07473i	0.0442132	−	0.0765796i
$735$		0			0
$736$	1.25486	+	2.17348i	0.0462548	+	0.0801156i
$737$	−5.31763			−0.195877
$738$		0			0
$739$	46.5865			1.71371			0.856857	−	0.515555i	$-0.172414\pi$
$739$	46.5865			1.71371			0.856857	+	0.515555i	$0.172414\pi$
$740$	11.2403	+	19.4688i	0.413202	+	0.715686i
$741$		0			0
$742$		0			0
$743$	0.169513	−	0.293606i	0.00621884	−	0.0107713i	−0.862899	−	0.505376i	$-0.831354\pi$
$743$	0.169513	−	0.293606i	0.00621884	−	0.0107713i	0.869118	+	0.494605i	$0.164687\pi$
$744$		0			0
$745$	−11.7377	−	20.3304i	−0.430038	−	0.744847i
$746$	−0.0771683			−0.00282533
$747$		0			0
$748$	−20.8907			−0.763839
$749$		0			0
$750$		0			0
$751$	18.1831	−	31.4940i	0.663510	−	1.14923i	−0.316177	−	0.948700i	$-0.602399\pi$
$751$	18.1831	−	31.4940i	0.663510	−	1.14923i	0.979687	−	0.200533i	$-0.0642673\pi$
$752$	7.54511	−	13.0685i	0.275142	−	0.476560i
$753$		0			0
$754$	−1.14754	−	1.98760i	−0.0417911	−	0.0723843i
$755$	12.4245			0.452174
$756$		0			0
$757$	−27.4703			−0.998424			−0.499212	−	0.866480i	$-0.666377\pi$
$757$	−27.4703			−0.998424			−0.499212	+	0.866480i	$0.666377\pi$
$758$	−0.750812	−	1.30044i	−0.0272707	−	0.0472343i
$759$		0			0
$760$	−0.692005	+	1.19859i	−0.0251017	+	0.0434773i
$761$	−16.5178	+	28.6097i	−0.598771	+	1.03710i	0.394232	+	0.919011i	$0.371011\pi$
$761$	−16.5178	+	28.6097i	−0.598771	+	1.03710i	−0.993003	+	0.118091i	$0.962323\pi$
$762$		0			0
$763$		0			0
$764$	5.66934			0.205110
$765$		0			0
$766$	−1.57534			−0.0569194
$767$	−28.6143	−	49.5614i	−1.03320	−	1.78956i
$768$		0			0
$769$	1.28876	−	2.23219i	0.0464738	−	0.0804949i	−0.841853	−	0.539707i	$-0.818535\pi$
$769$	1.28876	−	2.23219i	0.0464738	−	0.0804949i	0.888327	+	0.459212i	$0.151868\pi$
$770$		0			0
$771$		0			0
$772$	8.80822	+	15.2563i	0.317015	+	0.549086i
$773$	6.72973			0.242051			0.121026	−	0.992649i	$-0.461382\pi$
$773$	6.72973			0.242051			0.121026	+	0.992649i	$0.461382\pi$
$774$		0			0
$775$	14.0820			0.505842
$776$	0.703765	+	1.21896i	0.0252637	+	0.0437580i
$777$		0			0
$778$	−0.539302	+	0.934099i	−0.0193349	+	0.0334891i
$779$	7.03047	−	12.1771i	0.251893	−	0.436291i
$780$		0			0
$781$	−9.90581	−	17.1574i	−0.354458	−	0.613939i
$782$	−1.37358			−0.0491193
$783$		0			0
$784$		0			0
$785$	5.42473	+	9.39590i	0.193617	+	0.335354i
$786$		0			0
$787$	14.3341	−	24.8274i	0.510956	−	0.885003i	−0.488963	−	0.872305i	$-0.662625\pi$
$787$	14.3341	−	24.8274i	0.510956	−	0.885003i	0.999919	−	0.0126980i	$-0.00404201\pi$
$788$	−5.71016	+	9.89029i	−0.203416	+	0.352327i
$789$		0			0
$790$	0.0740881	+	0.128324i	0.00263594	+	0.00456558i
$791$		0			0
$792$		0			0
$793$	14.2581			0.506320
$794$	0.564275	+	0.977352i	0.0200254	+	0.0346849i
$795$		0			0
$796$	−11.3884	+	19.7252i	−0.403650	+	0.699142i
$797$	11.4913	−	19.9035i	0.407042	−	0.705017i	−0.587515	−	0.809213i	$-0.699894\pi$
$797$	11.4913	−	19.9035i	0.407042	−	0.705017i	0.994557	+	0.104196i	$0.0332270\pi$
$798$		0			0
$799$	12.4370	+	21.5415i	0.439989	+	0.762084i
$800$	−1.71421			−0.0606064
$801$		0			0
$802$	1.48098			0.0522951
$803$	−1.75795	−	3.04485i	−0.0620366	−	0.107451i
$804$		0			0
$805$		0			0
$806$	1.20685	−	2.09033i	0.0425095	−	0.0736287i
$807$		0			0
$808$	−0.251989	−	0.436457i	−0.00886493	−	0.0153545i
$809$	16.4779			0.579332			0.289666	−	0.957128i	$-0.406456\pi$
$809$	16.4779			0.579332			0.289666	+	0.957128i	$0.406456\pi$
$810$		0			0
$811$	−40.4318			−1.41975			−0.709876	−	0.704326i	$-0.751249\pi$
$811$	−40.4318			−1.41975			−0.709876	+	0.704326i	$0.751249\pi$
$812$		0			0
$813$		0			0
$814$	0.231227	−	0.400496i	0.00810449	−	0.0140374i
$815$	16.1456	−	27.9649i	0.565554	−	0.979569i
$816$		0			0
$817$	10.7113	+	18.5524i	0.374739	+	0.649068i
$818$	2.09033			0.0730868
$819$		0			0
$820$	39.2945			1.37222
$821$	−14.0543	−	24.3428i	−0.490499	−	0.849569i	0.509441	−	0.860506i	$-0.329852\pi$
$821$	−14.0543	−	24.3428i	−0.490499	−	0.849569i	−0.999940	+	0.0109361i	$0.996519\pi$
$822$		0			0
$823$	−12.9529	+	22.4351i	−0.451510	+	0.782038i	−0.998480	−	0.0551142i	$-0.982448\pi$
$823$	−12.9529	+	22.4351i	−0.451510	+	0.782038i	0.546970	+	0.837152i	$0.315781\pi$
$824$	−0.707256	+	1.22500i	−0.0246384	+	0.0426750i
$825$		0			0
$826$		0			0
$827$	17.7998			0.618961			0.309480	−	0.950906i	$-0.399845\pi$
$827$	17.7998			0.618961			0.309480	+	0.950906i	$0.399845\pi$
$828$		0			0
$829$	15.7069			0.545523			0.272761	−	0.962082i	$-0.412063\pi$
$829$	15.7069			0.545523			0.272761	+	0.962082i	$0.412063\pi$
$830$	−0.622611	−	1.07839i	−0.0216111	−	0.0374316i
$831$		0			0
$832$	20.7210	−	35.8899i	0.718373	−	1.24426i
$833$		0			0
$834$		0			0
$835$	−6.39180	−	11.0709i	−0.221197	−	0.383125i
$836$	−6.06866			−0.209889
$837$		0			0
$838$	−1.47799			−0.0510563
$839$	−3.69822	−	6.40550i	−0.127677	−	0.221142i	0.795099	−	0.606479i	$-0.207419\pi$
$839$	−3.69822	−	6.40550i	−0.127677	−	0.221142i	−0.922776	+	0.385337i	$0.874085\pi$
$840$		0			0
$841$	−5.90986	+	10.2362i	−0.203788	+	0.352971i
$842$	−0.931370	+	1.61318i	−0.0320971	+	0.0555938i
$843$		0			0
$844$	−21.3338	−	36.9511i	−0.734338	−	1.27191i
$845$	38.8978			1.33812
$846$		0			0
$847$		0			0
$848$	17.6725	+	30.6097i	0.606878	+	1.05114i
$849$		0			0
$850$	0.469098	−	0.812501i	0.0160899	−	0.0278686i
$851$	−6.48892	+	11.2391i	−0.222437	+	0.385273i
$852$		0			0
$853$	26.5631	+	46.0086i	0.909503	+	1.57530i	0.814756	+	0.579804i	$0.196871\pi$
$853$	26.5631	+	46.0086i	0.909503	+	1.57530i	0.0947464	+	0.995501i	$0.469796\pi$
$854$		0			0
$855$		0			0
$856$	4.63004			0.158251
$857$	−1.90765	−	3.30414i	−0.0651640	−	0.112867i	0.831603	−	0.555371i	$-0.187424\pi$
$857$	−1.90765	−	3.30414i	−0.0651640	−	0.112867i	−0.896767	+	0.442504i	$0.854090\pi$
$858$		0			0
$859$	−19.4884	+	33.7549i	−0.664936	+	1.15170i	0.314367	+	0.949301i	$0.398208\pi$
$859$	−19.4884	+	33.7549i	−0.664936	+	1.15170i	−0.979303	+	0.202401i	$0.935126\pi$
$860$	−29.9336	+	51.8464i	−1.02073	+	1.76795i
$861$		0			0
$862$	−0.280226	−	0.485366i	−0.00954454	−	0.0165316i
$863$	−26.6736			−0.907978			−0.453989	−	0.891007i	$-0.650000\pi$
$863$	−26.6736			−0.907978			−0.453989	+	0.891007i	$0.650000\pi$
$864$		0			0
$865$	−13.4034			−0.455730
$866$	0.116737	+	0.202195i	0.00396690	+	0.00687087i
$867$		0			0
$868$		0			0
$869$	−0.650490	+	1.12668i	−0.0220664	+	0.0382200i
$870$		0			0
$871$	8.73531	+	15.1300i	0.295985	+	0.512661i
$872$	−2.32198			−0.0786321
$873$		0			0
$874$	−0.399020			−0.0134971
$875$		0			0
$876$		0			0
$877$	−12.0068	+	20.7963i	−0.405440	+	0.702242i	−0.994373	−	0.105940i	$-0.966215\pi$
$877$	−12.0068	+	20.7963i	−0.405440	+	0.702242i	0.588933	+	0.808182i	$0.299548\pi$
$878$	0.225235	−	0.390118i	0.00760130	−	0.0131658i
$879$		0			0
$880$	−8.45978	−	14.6528i	−0.285179	−	0.493945i
$881$	4.67326			0.157446			0.0787231	−	0.996897i	$-0.474916\pi$
$881$	4.67326			0.157446			0.0787231	+	0.996897i	$0.474916\pi$
$882$		0			0
$883$	−35.6948			−1.20122			−0.600612	−	0.799541i	$-0.705076\pi$
$883$	−35.6948			−1.20122			−0.600612	+	0.799541i	$0.705076\pi$
$884$	34.3173	+	59.4393i	1.15422	+	1.99916i
$885$		0			0
$886$	−0.980867	+	1.69891i	−0.0329529	+	0.0570761i
$887$	14.5516	−	25.2041i	0.488596	−	0.846272i	−0.511318	−	0.859391i	$-0.670843\pi$
$887$	14.5516	−	25.2041i	0.488596	−	0.846272i	0.999914	+	0.0131191i	$0.00417605\pi$
$888$		0			0
$889$		0			0
$890$	0.0857071			0.00287291
$891$		0			0
$892$	−14.3020			−0.478865
$893$	3.61290	+	6.25772i	0.120901	+	0.209407i
$894$		0			0
$895$	−21.8403	+	37.8285i	−0.730041	+	1.26447i
$896$		0			0
$897$		0			0
$898$	−0.0156482	−	0.0271035i	−0.000522187	−	0.000904455i
$899$	−42.9294			−1.43177
$900$		0			0
$901$	−58.2611			−1.94096
$902$	−0.404168	−	0.700040i	−0.0134573	−	0.0233088i
$903$		0			0
$904$	0.533229	−	0.923579i	0.0177349	−	0.0307178i
$905$	19.2252	−	33.2991i	0.639069	−	1.10690i
$906$		0			0
$907$	20.6071	+	35.6925i	0.684247	+	1.18515i	0.973673	+	0.227950i	$0.0732024\pi$
$907$	20.6071	+	35.6925i	0.684247	+	1.18515i	−0.289426	+	0.957201i	$0.593464\pi$
$908$	−27.5129			−0.913047
$909$		0			0
$910$		0			0
$911$	−28.8619	−	49.9903i	−0.956239	−	1.65625i	−0.731508	−	0.681833i	$-0.761183\pi$
$911$	−28.8619	−	49.9903i	−0.956239	−	1.65625i	−0.224731	−	0.974421i	$-0.572150\pi$
$912$		0			0
$913$	5.46649	−	9.46824i	0.180914	−	0.313353i
$914$	0.691296	−	1.19736i	0.0228660	−	0.0396051i
$915$		0			0
$916$	−26.3326	−	45.6094i	−0.870054	−	1.50698i
$917$		0			0
$918$		0			0
$919$	−51.5598			−1.70080			−0.850400	−	0.526137i	$-0.823640\pi$
$919$	−51.5598			−1.70080			−0.850400	+	0.526137i	$0.823640\pi$
$920$	−1.11640	−	1.93367i	−0.0368068	−	0.0637512i
$921$		0			0
$922$	−0.827569	+	1.43339i	−0.0272545	+	0.0472062i
$923$	−32.5447	+	56.3691i	−1.07122	+	1.85541i
$924$		0			0
$925$	−4.43211	−	7.67664i	−0.145727	−	0.252406i
$926$	0.328525			0.0107960
$927$		0			0
$928$	5.22579			0.171545
$929$	−25.1412	−	43.5458i	−0.824856	−	1.42869i	−0.902029	−	0.431675i	$-0.857923\pi$
$929$	−25.1412	−	43.5458i	−0.824856	−	1.42869i	0.0771732	−	0.997018i	$-0.475411\pi$
$930$		0			0
$931$		0			0
$932$	12.6150	−	21.8499i	0.413219	−	0.715717i
$933$		0			0
$934$	0.931446	+	1.61331i	0.0304779	+	0.0527892i
$935$	27.8894			0.912081
$936$		0			0
$937$	18.1400			0.592607			0.296303	−	0.955094i	$-0.404246\pi$
$937$	18.1400			0.592607			0.296303	+	0.955094i	$0.404246\pi$
$938$		0			0
$939$		0			0
$940$	−10.0966	+	17.4877i	−0.329313	+	0.570387i
$941$	−8.51660	+	14.7512i	−0.277633	+	0.480875i	−0.970796	−	0.239906i	$-0.922883\pi$
$941$	−8.51660	+	14.7512i	−0.277633	+	0.480875i	0.693163	+	0.720781i	$0.256217\pi$
$942$		0			0
$943$	11.3422	+	19.6452i	0.369352	+	0.639737i
$944$	43.2658			1.40818
$945$		0			0
$946$	1.23154			0.0400408
$947$	15.7530	+	27.2849i	0.511903	+	0.886641i	0.999905	+	0.0137988i	$0.00439243\pi$
$947$	15.7530	+	27.2849i	0.511903	+	0.886641i	−0.488002	+	0.872842i	$0.662274\pi$
$948$		0			0
$949$	−5.77559	+	10.0036i	−0.187484	+	0.324731i
$950$	0.136271	−	0.236028i	0.00442121	−	0.00765777i
$951$		0			0
$952$		0			0
$953$	−16.0677			−0.520485			−0.260242	−	0.965543i	$-0.583803\pi$
$953$	−16.0677			−0.520485			−0.260242	+	0.965543i	$0.583803\pi$
$954$		0			0
$955$	−7.56866			−0.244916
$956$	15.3967	+	26.6679i	0.497966	+	0.862502i
$957$		0			0
$958$	−0.701705	+	1.21539i	−0.0226711	+	0.0392674i
$959$		0			0
$960$		0			0
$961$	−7.07402	−	12.2526i	−0.228194	−	0.395244i
$962$	−1.51935			−0.0489859
$963$		0			0
$964$	−2.35425			−0.0758253
$965$	−11.7591	−	20.3674i	−0.378539	−	0.655649i
$966$		0			0
$967$	13.3049	−	23.0448i	0.427857	−	0.741069i	−0.568826	−	0.822458i	$-0.692602\pi$
$967$	13.3049	−	23.0448i	0.427857	−	0.741069i	0.996682	+	0.0813886i	$0.0259355\pi$
$968$	1.15319	−	1.99738i	0.0370648	−	0.0641981i
$969$		0			0
$970$	−0.469219	−	0.812711i	−0.0150657	−	0.0260946i
$971$	56.5678			1.81535			0.907674	−	0.419676i	$-0.137856\pi$
$971$	56.5678			1.81535			0.907674	+	0.419676i	$0.137856\pi$
$972$		0			0
$973$		0			0
$974$	0.883558	+	1.53037i	0.0283110	+	0.0490361i
$975$		0			0
$976$	−5.38969	+	9.33522i	−0.172520	+	0.298813i
$977$	26.8780	−	46.5541i	0.859904	−	1.48940i	−0.0121160	−	0.999927i	$-0.503857\pi$
$977$	26.8780	−	46.5541i	0.859904	−	1.48940i	0.872020	−	0.489471i	$-0.162810\pi$
$978$		0			0
$979$	0.376252	+	0.651687i	0.0120251	+	0.0208280i
$980$		0			0
$981$		0			0
$982$	1.06769			0.0340715
$983$	13.7051	+	23.7379i	0.437125	+	0.757122i	0.997466	−	0.0711394i	$-0.0226635\pi$
$983$	13.7051	+	23.7379i	0.437125	+	0.757122i	−0.560342	+	0.828262i	$0.689330\pi$
$984$		0			0
$985$	7.62316	−	13.2037i	0.242894	−	0.420705i
$986$	−1.43005	+	2.47692i	−0.0455421	+	0.0788813i
$987$		0			0
$988$	9.96904	+	17.2669i	0.317157	+	0.549333i
$989$	−34.5607			−1.09897
$990$		0			0
$991$	−17.3374			−0.550740			−0.275370	−	0.961338i	$-0.588800\pi$
$991$	−17.3374			−0.550740			−0.275370	+	0.961338i	$0.588800\pi$
$992$	2.74794	+	4.75957i	0.0872471	+	0.151116i
$993$		0			0
$994$		0			0
$995$	15.2037	−	26.3335i	0.481988	−	0.834828i
$996$		0			0
$997$	17.8319	+	30.8858i	0.564742	+	0.978162i	0.997074	+	0.0764472i	$0.0243576\pi$
$997$	17.8319	+	30.8858i	0.564742	+	0.978162i	−0.432332	+	0.901715i	$0.642309\pi$
$998$	−1.45425			−0.0460334
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.h.442.7		24
3.2	odd	2		441.2.f.h.148.6	yes	24
7.2	even	3		1323.2.g.h.361.8		24
7.3	odd	6		1323.2.h.h.226.5		24
7.4	even	3		1323.2.h.h.226.6		24
7.5	odd	6		1323.2.g.h.361.7		24
7.6	odd	2	inner	1323.2.f.h.442.8		24
9.2	odd	6		441.2.f.h.295.6	yes	24
9.4	even	3		3969.2.a.bi.1.6		12
9.5	odd	6		3969.2.a.bh.1.7		12
9.7	even	3	inner	1323.2.f.h.883.7		24
21.2	odd	6		441.2.g.h.67.5		24
21.5	even	6		441.2.g.h.67.6		24
21.11	odd	6		441.2.h.h.373.7		24
21.17	even	6		441.2.h.h.373.8		24
21.20	even	2		441.2.f.h.148.5	✓	24
63.2	odd	6		441.2.h.h.214.7		24
63.11	odd	6		441.2.g.h.79.5		24
63.13	odd	6		3969.2.a.bi.1.5		12
63.16	even	3		1323.2.h.h.802.6		24
63.20	even	6		441.2.f.h.295.5	yes	24
63.25	even	3		1323.2.g.h.667.8		24
63.34	odd	6	inner	1323.2.f.h.883.8		24
63.38	even	6		441.2.g.h.79.6		24
63.41	even	6		3969.2.a.bh.1.8		12
63.47	even	6		441.2.h.h.214.8		24
63.52	odd	6		1323.2.g.h.667.7		24
63.61	odd	6		1323.2.h.h.802.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.5	✓	24	21.20	even	2
441.2.f.h.148.6	yes	24	3.2	odd	2
441.2.f.h.295.5	yes	24	63.20	even	6
441.2.f.h.295.6	yes	24	9.2	odd	6
441.2.g.h.67.5		24	21.2	odd	6
441.2.g.h.67.6		24	21.5	even	6
441.2.g.h.79.5		24	63.11	odd	6
441.2.g.h.79.6		24	63.38	even	6
441.2.h.h.214.7		24	63.2	odd	6
441.2.h.h.214.8		24	63.47	even	6
441.2.h.h.373.7		24	21.11	odd	6
441.2.h.h.373.8		24	21.17	even	6
1323.2.f.h.442.7		24	1.1	even	1	trivial
1323.2.f.h.442.8		24	7.6	odd	2	inner
1323.2.f.h.883.7		24	9.7	even	3	inner
1323.2.f.h.883.8		24	63.34	odd	6	inner
1323.2.g.h.361.7		24	7.5	odd	6
1323.2.g.h.361.8		24	7.2	even	3
1323.2.g.h.667.7		24	63.52	odd	6
1323.2.g.h.667.8		24	63.25	even	3
1323.2.h.h.226.5		24	7.3	odd	6
1323.2.h.h.226.6		24	7.4	even	3
1323.2.h.h.802.5		24	63.61	odd	6
1323.2.h.h.802.6		24	63.16	even	3
3969.2.a.bh.1.7		12	9.5	odd	6
3969.2.a.bh.1.8		12	63.41	even	6
3969.2.a.bi.1.5		12	63.13	odd	6
3969.2.a.bi.1.6		12	9.4	even	3

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +O(q^{10})\)	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} -0.182134 q^{10} +(-0.799563 - 1.38488i) q^{11} +(-2.62690 + 4.54992i) q^{13} +(-1.98599 - 3.43983i) q^{16} +6.54721 q^{17} +1.90194 q^{19} +(2.65756 + 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} +(-1.53419 + 2.65729i) q^{23} +(-1.04789 - 1.81500i) q^{25} -0.359223 q^{26} +(3.19452 + 5.53306i) q^{29} +(-3.35961 + 5.81902i) q^{31} +(0.408966 - 0.708350i) q^{32} +(0.223829 + 0.387684i) q^{34} +4.22955 q^{37} +(0.0650215 + 0.112621i) q^{38} +(-0.363842 + 0.630193i) q^{40} +(3.69648 - 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} -3.19078 q^{44} -0.209797 q^{46} +(1.89959 + 3.29018i) q^{47} +(0.0716485 - 0.124099i) q^{50} +(5.24152 + 9.07858i) q^{52} -8.89862 q^{53} +4.25974 q^{55} +(-0.218422 + 0.378317i) q^{58} +(-5.44639 + 9.43343i) q^{59} +(-1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(-6.99751 - 12.1200i) q^{65} +(1.66267 - 2.87982i) q^{67} +(6.53190 - 11.3136i) q^{68} +12.3890 q^{71} +2.19863 q^{73} +(0.144596 + 0.250447i) q^{74} +(1.89749 - 3.28655i) q^{76} +(-0.406778 - 0.704560i) q^{79} +10.5805 q^{80} +0.505486 q^{82} +(3.41842 + 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} +(-0.385066 + 0.666954i) q^{86} +(-0.218422 - 0.378317i) q^{88} -0.470572 q^{89} +(3.06120 + 5.30216i) q^{92} +(-0.129882 + 0.224963i) q^{94} +(-2.53318 + 4.38760i) q^{95} +(2.57623 + 4.46216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

Modular forms

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Database

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