LMFDB - Embedded newform 1323.2.g.h.667.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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			667.8
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.h.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +O(q^{10})$	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +(0.0910670 + 0.157733i) q^{10} +1.59913 q^{11} +(-2.62690 - 4.54992i) q^{13} +(-1.98599 - 3.43983i) q^{16} +(-3.27360 - 5.67005i) q^{17} +(-0.950968 + 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +3.06837 q^{23} +2.09578 q^{25} +(0.179612 - 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +(-3.35961 + 5.81902i) q^{31} +(0.408966 - 0.708350i) q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 + 3.66290i) q^{37} -0.130043 q^{38} +0.727684 q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 - 2.76329i) q^{44} +(0.104898 + 0.181689i) q^{46} +(1.89959 + 3.29018i) q^{47} +(0.0716485 + 0.124099i) q^{50} -10.4830 q^{52} +(4.44931 + 7.70643i) q^{53} +4.25974 q^{55} +0.436843 q^{58} +(-5.44639 + 9.43343i) q^{59} +(-1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(-6.99751 - 12.1200i) q^{65} +(1.66267 - 2.87982i) q^{67} -13.0638 q^{68} +12.3890 q^{71} +(-1.09932 - 1.90407i) q^{73} -0.289191 q^{74} +(1.89749 + 3.28655i) q^{76} +(-0.406778 - 0.704560i) q^{79} +(-5.29025 - 9.16298i) q^{80} +(-0.252743 + 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +0.770132 q^{86} +0.436843 q^{88} +(0.235286 - 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +(-0.129882 + 0.224963i) q^{94} +(-2.53318 + 4.38760i) q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.0341870	+	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
$5$	2.66379			1.19128			0.595642	−	0.803250i	$-0.296898\pi$
$5$	2.66379			1.19128			0.595642	+	0.803250i	$0.296898\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.273176			0.0965824
$9$		0			0
$10$	0.0910670	+	0.157733i	0.0287979	+	0.0498794i
$11$	1.59913			0.482155			0.241077	−	0.970506i	$-0.422499\pi$
$11$	1.59913			0.482155			0.241077	+	0.970506i	$0.422499\pi$
$12$		0			0
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	−0.957487	−	0.288476i	$-0.906852\pi$
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	0.228916	−	0.973446i	$-0.426482\pi$
$14$		0			0
$15$		0			0
$16$	−1.98599	−	3.43983i	−0.496496	−	0.859957i
$17$	−3.27360	−	5.67005i	−0.793966	−	1.37519i	−0.923494	−	0.383613i	$-0.874680\pi$
$17$	−3.27360	−	5.67005i	−0.793966	−	1.37519i	0.129528	−	0.991576i	$-0.458654\pi$
$18$		0			0
$19$	−0.950968	+	1.64713i	−0.218167	+	0.377877i	−0.954248	−	0.299017i	$-0.903341\pi$
$19$	−0.950968	+	1.64713i	−0.218167	+	0.377877i	0.736081	+	0.676894i	$0.236674\pi$
$20$	2.65756	−	4.60304i	0.594249	−	1.02927i
$21$		0			0
$22$	0.0546693	+	0.0946900i	0.0116555	+	0.0201880i
$23$	3.06837			0.639800			0.319900	−	0.947451i	$-0.396351\pi$
$23$	3.06837			0.639800			0.319900	+	0.947451i	$0.396351\pi$
$24$		0			0
$25$	2.09578			0.419157
$26$	0.179612	−	0.311096i	0.0352247	−	0.0610110i
$27$		0			0
$28$		0			0
$29$	3.19452	−	5.53306i	0.593207	−	1.02746i	−0.400591	−	0.916257i	$-0.631195\pi$
$29$	3.19452	−	5.53306i	0.593207	−	1.02746i	0.993797	−	0.111207i	$-0.0354716\pi$
$30$		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
$37$	−2.11477	+	3.66290i	−0.347667	+	0.602176i	−0.985835	−	0.167721i	$-0.946359\pi$
$37$	−2.11477	+	3.66290i	−0.347667	+	0.602176i	0.638168	+	0.769897i	$0.279693\pi$
$38$	−0.130043			−0.0210958
$39$		0			0
$40$	0.727684			0.115057
$41$	3.69648	+	6.40249i	0.577293	+	0.999901i	0.995788	+	0.0916820i	$0.0292243\pi$
$41$	3.69648	+	6.40249i	0.577293	+	0.999901i	−0.418495	+	0.908219i	$0.637442\pi$
$42$		0			0
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	−0.0142043	−	0.999899i	$-0.504522\pi$
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	0.873040	−	0.487648i	$-0.162145\pi$
$44$	1.59539	−	2.76329i	0.240514	−	0.416582i
$45$		0			0
$46$	0.104898	+	0.181689i	0.0154664	+	0.0267887i
$47$	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
$52$	−10.4830			−1.45374
$53$	4.44931	+	7.70643i	0.611160	+	1.05856i	0.991045	+	0.133527i	$0.0426301\pi$
$53$	4.44931	+	7.70643i	0.611160	+	1.05856i	−0.379885	+	0.925034i	$0.624037\pi$
$54$		0			0
$55$	4.25974			0.574383
$56$		0			0
$57$		0			0
$58$	0.436843			0.0573604
$59$	−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	$0.101556\pi$
$68$	−13.0638			−1.58422
$69$		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
$73$	−1.09932	−	1.90407i	−0.128665	−	0.222855i	0.794494	−	0.607271i	$-0.207736\pi$
$73$	−1.09932	−	1.90407i	−0.128665	−	0.222855i	−0.923160	+	0.384417i	$0.874403\pi$
$74$	−0.289191			−0.0336178
$75$		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	$0.847906\pi$
$80$	−5.29025	−	9.16298i	−0.591468	−	1.02445i
$81$		0			0
$82$	−0.252743	+	0.437764i	−0.0279108	+	0.0483429i
$83$	3.41842	−	5.92088i	0.375220	−	0.649901i	−0.615140	−	0.788418i	$-0.710900\pi$
$83$	3.41842	−	5.92088i	0.375220	−	0.649901i	0.990360	+	0.138517i	$0.0442337\pi$
$84$		0			0
$85$	−8.72020	−	15.1038i	−0.945838	−	1.63824i
$86$	0.770132			0.0830455
$87$		0			0
$88$	0.436843			0.0465677
$89$	0.235286	−	0.407527i	0.0249403	−	0.0431978i	−0.853286	−	0.521443i	$-0.825394\pi$
$89$	0.235286	−	0.407527i	0.0249403	−	0.0431978i	0.878226	+	0.478246i	$0.158727\pi$
$90$		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	−0.705085	−	0.709123i	$-0.749091\pi$
$97$	2.57623	−	4.46216i	0.261576	−	0.453064i	0.966661	+	0.256059i	$0.0824243\pi$
$98$		0			0
$99$		0			0
$100$	2.09088	−	3.62152i	0.209088	−	0.362152i
$101$	1.84488			0.183572			0.0917862	−	0.995779i	$-0.470742\pi$
$101$	1.84488			0.183572			0.0917862	+	0.995779i	$0.470742\pi$
$102$		0			0
$103$	5.17802			0.510206			0.255103	−	0.966914i	$-0.417891\pi$
$103$	5.17802			0.510206			0.255103	+	0.966914i	$0.417891\pi$
$104$	−0.717607	−	1.24293i	−0.0703671	−	0.121879i
$105$		0			0
$106$	−0.304217	+	0.526920i	−0.0295482	+	0.0511790i
$107$	−8.47445	+	14.6782i	−0.819256	+	1.41899i	0.0869755	+	0.996210i	$0.472280\pi$
$107$	−8.47445	+	14.6782i	−0.819256	+	1.41899i	−0.906231	+	0.422782i	$0.861054\pi$
$108$		0			0
$109$	4.24996	+	7.36115i	0.407073	+	0.705070i	0.994560	−	0.104163i	$-0.0332163\pi$
$109$	4.24996	+	7.36115i	0.407073	+	0.705070i	−0.587488	+	0.809233i	$0.699883\pi$
$110$	0.145628	+	0.252235i	0.0138851	+	0.0240496i
$111$		0			0
$112$		0			0
$113$	1.95196	+	3.38089i	0.183625	+	0.318048i	0.943112	−	0.332474i	$-0.107884\pi$
$113$	1.95196	+	3.38089i	0.183625	+	0.318048i	−0.759487	+	0.650522i	$0.774550\pi$
$114$		0			0
$115$	8.17351			0.762183
$116$	−6.37410	−	11.0403i	−0.591820	−	1.02506i
$117$		0			0
$118$	−0.744783			−0.0685628
$119$		0			0
$120$		0			0
$121$	−8.44279			−0.767527
$122$	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
$131$	4.45342			0.389097			0.194549	−	0.980893i	$-0.437676\pi$
$131$	4.45342			0.389097			0.194549	+	0.980893i	$0.437676\pi$
$132$		0			0
$133$		0			0
$134$	0.227366			0.0196414
$135$		0			0
$136$	−0.894271	−	1.54892i	−0.0766831	−	0.132819i
$137$	19.5360			1.66907			0.834537	−	0.550952i	$-0.185735\pi$
$137$	19.5360			1.66907			0.834537	+	0.550952i	$0.185735\pi$
$138$		0			0
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	0.804833	−	0.593501i	$-0.202255\pi$
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	−0.916404	+	0.400256i	$0.868921\pi$
$140$		0			0
$141$		0			0
$142$	0.423544	+	0.733599i	0.0355430	+	0.0615623i
$143$	−4.20075	−	7.27590i	−0.351284	−	0.608442i
$144$		0			0
$145$	8.50952	−	14.7389i	0.706677	−	1.22400i
$146$	0.0751647	−	0.130189i	0.00622067	−	0.0107745i
$147$		0			0
$148$	4.21966	+	7.30867i	0.346854	+	0.600769i
$149$	8.81281			0.721973			0.360987	−	0.932571i	$-0.382440\pi$
$149$	8.81281			0.721973			0.360987	+	0.932571i	$0.382440\pi$
$150$		0			0
$151$	4.66422			0.379569			0.189784	−	0.981826i	$-0.439221\pi$
$151$	4.66422			0.379569			0.189784	+	0.981826i	$0.439221\pi$
$152$	−0.259782	+	0.449956i	−0.0210711	+	0.0364962i
$153$		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
$163$	6.06112	−	10.4982i	0.474744	−	0.822280i	−0.524838	−	0.851202i	$-0.675874\pi$
$163$	6.06112	−	10.4982i	0.474744	−	0.822280i	0.999582	+	0.0289220i	$0.00920745\pi$
$164$	14.7514			1.15189
$165$		0			0
$166$	0.467462			0.0362821
$167$	−2.39951	−	4.15608i	−0.185680	−	0.321607i	0.758126	−	0.652109i	$-0.226115\pi$
$167$	−2.39951	−	4.15608i	−0.185680	−	0.321607i	−0.943805	+	0.330502i	$0.892782\pi$
$168$		0			0
$169$	−7.30121	+	12.6461i	−0.561631	+	0.972774i
$170$	0.596235	−	1.03271i	0.0457291	−	0.0792051i
$171$		0			0
$172$	−11.2372	−	19.4634i	−0.856828	−	1.48407i
$173$	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
$178$	0.0321749			0.00241161
$179$	−8.19896	−	14.2010i	−0.612819	−	1.06143i	−0.990763	−	0.135605i	$-0.956702\pi$
$179$	−8.19896	−	14.2010i	−0.612819	−	1.06143i	0.377944	−	0.925828i	$-0.376631\pi$
$180$		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
$184$	0.838207			0.0617934
$185$	−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	$0.269596\pi$
$194$	0.352294			0.0252932
$195$		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
$199$	5.70752	+	9.88572i	0.404596	+	0.700780i	0.994274	−	0.106858i	$-0.0340789\pi$
$199$	5.70752	+	9.88572i	0.404596	+	0.700780i	−0.589679	+	0.807638i	$0.700746\pi$
$200$	0.572518			0.0404832
$201$		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
$206$	0.177021	+	0.306609i	0.0123336	+	0.0213625i
$207$		0			0
$208$	−10.4340	+	18.0722i	−0.723466	+	1.25308i
$209$	−1.52072	+	2.63396i	−0.105190	+	0.182195i
$210$		0			0
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	0.954257	+	0.298986i	$0.0966486\pi$
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	−0.218199	+	0.975904i	$0.570018\pi$
$212$	17.7556			1.21946
$213$		0			0
$214$	−1.15886			−0.0792183
$215$	15.0018	−	25.9840i	1.02312	−	1.77209i
$216$		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	−0.960712	−	0.277547i	$-0.910479\pi$
$223$	−3.58387	+	6.20744i	−0.239994	+	0.415681i	0.720719	+	0.693228i	$0.243812\pi$
$224$		0			0
$225$		0			0
$226$	−0.133463	+	0.231165i	−0.00887784	+	0.0153769i
$227$	13.7887			0.915187			0.457593	−	0.889162i	$-0.348712\pi$
$227$	13.7887			0.915187			0.457593	+	0.889162i	$0.348712\pi$
$228$		0			0
$229$	−26.3943			−1.74418			−0.872092	−	0.489341i	$-0.837237\pi$
$229$	−26.3943			−1.74418			−0.872092	+	0.489341i	$0.837237\pi$
$230$	0.279428	+	0.483983i	0.0184249	+	0.0319129i
$231$		0			0
$232$	0.872666	−	1.51150i	0.0572933	−	0.0992349i
$233$	−6.32230	+	10.9505i	−0.414187	+	0.717394i	−0.995343	−	0.0963989i	$-0.969268\pi$
$233$	−6.32230	+	10.9505i	−0.414187	+	0.717394i	0.581155	+	0.813793i	$0.302601\pi$
$234$		0			0
$235$	5.06010	+	8.76436i	0.330085	+	0.571724i
$236$	10.8673	+	18.8228i	0.707403	+	1.22526i
$237$		0			0
$238$		0			0
$239$	−7.71640	−	13.3652i	−0.499133	−	0.864523i	0.500867	−	0.865524i	$-0.333015\pi$
$239$	−7.71640	−	13.3652i	−0.499133	−	0.864523i	−0.999999	+	0.00100121i	$0.999681\pi$
$240$		0			0
$241$	1.17988			0.0760029			0.0380015	−	0.999278i	$-0.487901\pi$
$241$	1.17988			0.0760029			0.0380015	+	0.999278i	$0.487901\pi$
$242$	−0.288634	−	0.499928i	−0.0185541	−	0.0321366i
$243$		0			0
$244$	−5.41504			−0.346662
$245$		0			0
$246$		0			0
$247$	9.99240			0.635801
$248$	−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
$257$	−9.83076			−0.613226			−0.306613	−	0.951834i	$-0.599196\pi$
$257$	−9.83076			−0.613226			−0.306613	+	0.951834i	$0.599196\pi$
$258$		0			0
$259$		0			0
$260$	−27.9246			−1.73181
$261$		0			0
$262$	0.152249	+	0.263703i	0.00940598	+	0.0162916i
$263$	−11.9322			−0.735774			−0.367887	−	0.929870i	$-0.619919\pi$
$263$	−11.9322			−0.735774			−0.367887	+	0.929870i	$0.619919\pi$
$264$		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
$269$	14.9824	+	25.9503i	0.913494	+	1.58222i	0.809092	+	0.587682i	$0.199959\pi$
$269$	14.9824	+	25.9503i	0.913494	+	1.58222i	0.104401	+	0.994535i	$0.466707\pi$
$270$		0			0
$271$	3.54825	−	6.14575i	0.215541	−	0.373328i	−0.737899	−	0.674911i	$-0.764182\pi$
$271$	3.54825	−	6.14575i	0.215541	−	0.373328i	0.953440	+	0.301584i	$0.0975152\pi$
$272$	−13.0027	+	22.5213i	−0.788402	+	1.36555i
$273$		0			0
$274$	0.667877	+	1.15680i	0.0403479	+	0.0698847i
$275$	3.35142			0.202098
$276$		0			0
$277$	−9.82351			−0.590237			−0.295119	−	0.955461i	$-0.595359\pi$
$277$	−9.82351			−0.590237			−0.295119	+	0.955461i	$0.595359\pi$
$278$	0.0899388	−	0.155779i	0.00539417	−	0.00934298i
$279$		0			0
$280$		0			0
$281$	−11.9389	+	20.6787i	−0.712213	+	1.23359i	0.251812	+	0.967776i	$0.418974\pi$
$281$	−11.9389	+	20.6787i	−0.712213	+	1.23359i	−0.964025	+	0.265813i	$0.914360\pi$
$282$		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
$289$	−12.9330	+	22.4006i	−0.760763	+	1.31768i
$290$	1.16366			0.0683324
$291$		0			0
$292$	−4.38699			−0.256729
$293$	8.52913	+	14.7729i	0.498277	+	0.863041i	0.999998	−	0.00198814i	$-0.000632845\pi$
$293$	8.52913	+	14.7729i	0.498277	+	0.863041i	−0.501721	+	0.865030i	$0.667300\pi$
$294$		0			0
$295$	−14.5081	+	25.1287i	−0.844692	+	1.46305i
$296$	−0.577706	+	1.00062i	−0.0335785	+	0.0581596i
$297$		0			0
$298$	0.301283	+	0.521838i	0.0174529	+	0.0302293i
$299$	−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
$304$	7.55444			0.433277
$305$	−3.61458	−	6.26064i	−0.206970	−	0.358483i
$306$		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
$310$	−1.22380			−0.0695072
$311$	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
$320$	−21.0120			−1.17461
$321$		0			0
$322$		0			0
$323$	12.4524			0.692869
$324$		0			0
$325$	−5.50541	−	9.53566i	−0.305385	−	0.528943i
$326$	0.828846			0.0459055
$327$		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	$0.834745\pi$
$332$	−6.82086	−	11.8141i	−0.374343	−	0.648382i
$333$		0			0
$334$	0.164064	−	0.284168i	0.00897719	−	0.0155490i
$335$	4.42899	−	7.67124i	0.241982	−	0.419125i
$336$		0			0
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	0.962577	−	0.271009i	$-0.0873572\pi$
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	−0.715989	+	0.698112i	$0.754024\pi$
$338$	−0.998425			−0.0543072
$339$		0			0
$340$	−34.7993			−1.88725
$341$	−5.37245	+	9.30535i	−0.290934	+	0.503913i
$342$		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	0.227384	+	0.973805i	$0.426983\pi$
$349$	−13.6310	+	23.6095i	−0.729648	+	1.26379i	−0.957032	+	0.289983i	$0.906350\pi$
$350$		0			0
$351$		0			0
$352$	0.653988	−	1.13274i	0.0348577	−	0.0603753i
$353$	24.1896			1.28748			0.643741	−	0.765244i	$-0.277382\pi$
$353$	24.1896			1.28748			0.643741	+	0.765244i	$0.277382\pi$
$354$		0			0
$355$	33.0018			1.75155
$356$	−0.469472	−	0.813149i	−0.0248820	−	0.0430968i
$357$		0			0
$358$	0.560595	−	0.970979i	0.0296284	−	0.0513179i
$359$	−10.5188	+	18.2191i	−0.555161	+	0.961567i	0.442730	+	0.896655i	$0.354010\pi$
$359$	−10.5188	+	18.2191i	−0.555161	+	0.961567i	−0.997891	+	0.0649124i	$0.979323\pi$
$360$		0			0
$361$	7.69132	+	13.3218i	0.404806	+	0.701145i
$362$	−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
$367$	35.0380			1.82897			0.914485	−	0.404620i	$-0.132596\pi$
$367$	35.0380			1.82897			0.914485	+	0.404620i	$0.132596\pi$
$368$	−6.09375	−	10.5547i	−0.317659	−	0.550201i
$369$		0			0
$370$	−0.770345			−0.0400483
$371$		0			0
$372$		0			0
$373$	1.12862			0.0584377			0.0292189	−	0.999573i	$-0.490698\pi$
$373$	1.12862			0.0584377			0.0292189	+	0.999573i	$0.490698\pi$
$374$	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
$383$	23.0401			1.17729			0.588647	−	0.808390i	$-0.299661\pi$
$383$	23.0401			1.17729			0.588647	+	0.808390i	$0.299661\pi$
$384$		0			0
$385$		0			0
$386$	−0.603664			−0.0307257
$387$		0			0
$388$	−5.14042	−	8.90346i	−0.260965	−	0.452005i
$389$	−15.7751			−0.799828			−0.399914	−	0.916553i	$-0.630960\pi$
$389$	−15.7751			−0.799828			−0.399914	+	0.916553i	$0.630960\pi$
$390$		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
$395$	−1.08357	−	1.87680i	−0.0545204	−	0.0944321i
$396$		0			0
$397$	−8.25277	+	14.2942i	−0.414195	+	0.717406i	−0.995344	−	0.0963911i	$-0.969270\pi$
$397$	−8.25277	+	14.2942i	−0.414195	+	0.717406i	0.581149	+	0.813797i	$0.302603\pi$
$398$	−0.390246	+	0.675926i	−0.0195613	+	0.0338811i
$399$		0			0
$400$	−4.16220	−	7.20914i	−0.208110	−	0.360457i
$401$	−21.6600			−1.08165			−0.540823	−	0.841136i	$-0.681887\pi$
$401$	−21.6600			−1.08165			−0.540823	+	0.841136i	$0.681887\pi$
$402$		0			0
$403$	35.3015			1.75849
$404$	1.84057	−	3.18796i	0.0915716	−	0.158607i
$405$		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
$415$	9.10596	−	15.7720i	0.446994	−	0.774216i
$416$	−4.29725			−0.210690
$417$		0			0
$418$	−0.207955			−0.0101714
$419$	−10.8081	−	18.7202i	−0.528011	−	0.914542i	−0.999467	−	0.0326524i	$-0.989605\pi$
$419$	−10.8081	−	18.7202i	−0.528011	−	0.914542i	0.471456	−	0.881890i	$-0.343729\pi$
$420$		0			0
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	−0.315706	−	0.948857i	$-0.602241\pi$
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	0.979587	−	0.201019i	$-0.0644252\pi$
$422$	−0.731046	+	1.26621i	−0.0355867	+	0.0616380i
$423$		0			0
$424$	1.21545	+	2.10521i	0.0590273	+	0.102238i
$425$	−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
$430$	2.05147			0.0989307
$431$	4.09843	+	7.09869i	0.197415	+	0.341932i	0.947689	−	0.319194i	$-0.103412\pi$
$431$	4.09843	+	7.09869i	0.197415	+	0.341932i	−0.750275	+	0.661126i	$0.770079\pi$
$432$		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
$436$	16.9601			0.812242
$437$	−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
$446$	−0.490087			−0.0232063
$447$		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
$451$	5.91114	+	10.2384i	0.278345	+	0.482107i
$452$	7.78958			0.366391
$453$		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	$0.990144\pi$
$458$	−0.902342	−	1.56290i	−0.0421637	−	0.0730296i
$459$		0			0
$460$	8.15440	−	14.1238i	0.380201	−	0.658527i
$461$	12.1036	−	20.9640i	0.563719	−	0.976390i	−0.433449	−	0.901178i	$-0.642703\pi$
$461$	12.1036	−	20.9640i	0.563719	−	0.976390i	0.997168	−	0.0752117i	$-0.0239633\pi$
$462$		0			0
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	0.916436	−	0.400182i	$-0.131053\pi$
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	−0.804786	+	0.593565i	$0.797720\pi$
$464$	−25.3770			−1.17810
$465$		0			0
$466$	−0.864561			−0.0400500
$467$	−13.6228	+	23.5954i	−0.630389	+	1.09187i	0.357083	+	0.934073i	$0.383771\pi$
$467$	−13.6228	+	23.5954i	−0.630389	+	1.09187i	−0.987472	+	0.157793i	$0.949562\pi$
$468$		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
$478$	0.527601	−	0.913832i	0.0241319	−	0.0417977i
$479$	−20.5255			−0.937834			−0.468917	−	0.883242i	$-0.655356\pi$
$479$	−20.5255			−0.937834			−0.468917	+	0.883242i	$0.655356\pi$
$480$		0			0
$481$	22.2212			1.01320
$482$	0.0403366	+	0.0698651i	0.00183728	+	0.00318227i
$483$		0			0
$484$	−8.42306	+	14.5892i	−0.382866	+	0.663144i
$485$	6.86254	−	11.8863i	0.311612	−	0.539727i
$486$		0			0
$487$	−12.9224	−	22.3823i	−0.585571	−	1.01424i	−0.994804	−	0.101809i	$-0.967537\pi$
$487$	−12.9224	−	22.3823i	−0.585571	−	1.01424i	0.409233	−	0.912430i	$-0.365796\pi$
$488$	−0.370682	−	0.642039i	−0.0167800	−	0.0290638i
$489$		0			0
$490$		0			0
$491$	7.80775	+	13.5234i	0.352359	+	0.610303i	0.986662	−	0.162781i	$-0.0520463\pi$
$491$	7.80775	+	13.5234i	0.352359	+	0.610303i	−0.634303	+	0.773084i	$0.718713\pi$
$492$		0			0
$493$	−41.8303			−1.88394
$494$	0.341610	+	0.591686i	0.0153698	+	0.0266212i
$495$		0			0
$496$	26.6886			1.19835
$497$		0			0
$498$		0			0
$499$	21.2690			0.952133			0.476066	−	0.879409i	$-0.342062\pi$
$499$	21.2690			0.952133			0.476066	+	0.879409i	$0.342062\pi$
$500$	−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
$509$	13.4618			0.596683			0.298342	−	0.954459i	$-0.403567\pi$
$509$	13.4618			0.596683			0.298342	+	0.954459i	$0.403567\pi$
$510$		0			0
$511$		0			0
$512$	−5.41890			−0.239484
$513$		0			0
$514$	−0.336084	−	0.582115i	−0.0148240	−	0.0256760i
$515$	13.7932			0.607800
$516$		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
$521$	−0.713095	−	1.23512i	−0.0312413	−	0.0541115i	0.849982	−	0.526812i	$-0.176613\pi$
$521$	−0.713095	−	1.23512i	−0.0312413	−	0.0541115i	−0.881223	+	0.472700i	$0.843279\pi$
$522$		0			0
$523$	3.85530	−	6.67758i	0.168581	−	0.291990i	−0.769340	−	0.638839i	$-0.779415\pi$
$523$	3.85530	−	6.67758i	0.168581	−	0.291990i	0.937921	+	0.346849i	$0.112748\pi$
$524$	4.44301	−	7.69553i	0.194094	−	0.336181i
$525$		0			0
$526$	−0.407928	−	0.706551i	−0.0177865	−	0.0308071i
$527$	43.9922			1.91633
$528$		0			0
$529$	−13.5851			−0.590656
$530$	−0.810371	+	1.40360i	−0.0352003	+	0.0609686i
$531$		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
$541$	−14.0228	+	24.2882i	−0.602886	+	1.04423i	0.389495	+	0.921028i	$0.372649\pi$
$541$	−14.0228	+	24.2882i	−0.602886	+	1.04423i	−0.992382	+	0.123201i	$0.960684\pi$
$542$	0.485216			0.0208418
$543$		0			0
$544$	−5.35517			−0.229601
$545$	11.3210	+	19.6086i	0.484939	+	0.839939i
$546$		0			0
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	−0.185717	−	0.982603i	$-0.559461\pi$
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	0.943818	−	0.330466i	$-0.107206\pi$
$548$	19.4903	−	33.7583i	0.832586	−	1.44208i
$549$		0			0
$550$	0.114575	+	0.198450i	0.00488550	+	0.00846193i
$551$	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
$556$	−5.24928			−0.222619
$557$	17.5209	+	30.3472i	0.742386	+	1.28585i	0.951406	+	0.307940i	$0.0996395\pi$
$557$	17.5209	+	30.3472i	0.742386	+	1.28585i	−0.209019	+	0.977911i	$0.567027\pi$
$558$		0			0
$559$	−59.1763			−2.50289
$560$		0			0
$561$		0			0
$562$	−1.63262			−0.0688677
$563$	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	$0.957182\pi$
$572$	−16.7637			−0.700926
$573$		0			0
$574$		0			0
$575$	6.43065			0.268177
$576$		0			0
$577$	7.52852	+	13.0398i	0.313417	+	0.542853i	0.979100	−	0.203381i	$-0.0651930\pi$
$577$	7.52852	+	13.0398i	0.313417	+	0.542853i	−0.665683	+	0.746235i	$0.731860\pi$
$578$	−1.76856			−0.0735623
$579$		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
$584$	−0.300307	−	0.520148i	−0.0124268	−	0.0215239i
$585$		0			0
$586$	−0.583171	+	1.01008i	−0.0240906	+	0.0417261i
$587$	0.835901	−	1.44782i	0.0345013	−	0.0597580i	−0.848259	−	0.529581i	$-0.822349\pi$
$587$	0.835901	−	1.44782i	0.0345013	−	0.0597580i	0.882760	+	0.469823i	$0.155682\pi$
$588$		0			0
$589$	−6.38977	−	11.0674i	−0.263286	−	0.456025i
$590$	−1.98395			−0.0816778
$591$		0			0
$592$	16.7996			0.690461
$593$	−5.40871	+	9.36816i	−0.222109	+	0.384704i	−0.955448	−	0.295159i	$-0.904627\pi$
$593$	−5.40871	+	9.36816i	−0.222109	+	0.384704i	0.733339	+	0.679863i	$0.237961\pi$
$594$		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	−0.473286	−	0.880909i	$-0.656932\pi$
$601$	12.9011	−	22.3453i	0.526246	−	0.911485i	0.999532	−	0.0305765i	$-0.00973432\pi$
$602$		0			0
$603$		0			0
$604$	4.65332	−	8.05978i	0.189341	−	0.327948i
$605$	−22.4898			−0.914342
$606$		0			0
$607$	−37.8049			−1.53445			−0.767227	−	0.641376i	$-0.778364\pi$
$607$	−37.8049			−1.53445			−0.767227	+	0.641376i	$0.778364\pi$
$608$	0.777828	+	1.34724i	0.0315451	+	0.0546377i
$609$		0			0
$610$	0.247143	−	0.428065i	0.0100065	−	0.0173318i
$611$	9.98005	−	17.2860i	0.403750	−	0.699315i
$612$		0			0
$613$	6.47719	+	11.2188i	0.261611	+	0.453124i	0.966670	−	0.256025i	$-0.0824129\pi$
$613$	6.47719	+	11.2188i	0.261611	+	0.453124i	−0.705059	+	0.709149i	$0.749080\pi$
$614$	0.793745	+	1.37481i	0.0320330	+	0.0554827i
$615$		0			0
$616$		0			0
$617$	−16.2202	−	28.0941i	−0.652999	−	1.13103i	−0.982391	−	0.186834i	$-0.940177\pi$
$617$	−16.2202	−	28.0941i	−0.652999	−	1.13103i	0.329393	−	0.944193i	$-0.393156\pi$
$618$		0			0
$619$	−33.1974			−1.33431			−0.667157	−	0.744917i	$-0.732489\pi$
$619$	−33.1974			−1.33431			−0.667157	+	0.744917i	$0.732489\pi$
$620$	17.8568	+	30.9289i	0.717146	+	1.24213i
$621$		0			0
$622$	0.122453			0.00490993
$623$		0			0
$624$		0			0
$625$	−31.0866			−1.24346
$626$	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
$635$	29.1772			1.15786
$636$		0			0
$637$		0			0
$638$	0.698568			0.0276566
$639$		0			0
$640$	−2.89714	−	5.01799i	−0.114519	−	0.198353i
$641$	−43.0814			−1.70161			−0.850806	−	0.525480i	$-0.823886\pi$
$641$	−43.0814			−1.70161			−0.850806	+	0.525480i	$0.823886\pi$
$642$		0			0
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	0.922213	−	0.386682i	$-0.126379\pi$
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	−0.795983	+	0.605319i	$0.793045\pi$
$644$		0			0
$645$		0			0
$646$	0.425709	+	0.737350i	0.0167493	+	0.0290107i
$647$	−1.94403	−	3.36716i	−0.0764278	−	0.132377i	0.825278	−	0.564726i	$-0.191018\pi$
$647$	−1.94403	−	3.36716i	−0.0764278	−	0.132377i	−0.901706	+	0.432349i	$0.857685\pi$
$648$		0			0
$649$	−8.70947	+	15.0852i	−0.341877	+	0.592148i
$650$	0.376427	−	0.651991i	0.0147647	−	0.0255732i
$651$		0			0
$652$	−12.0939	−	20.9473i	−0.473634	−	0.820358i
$653$	−15.1035			−0.591044			−0.295522	−	0.955336i	$-0.595494\pi$
$653$	−15.1035			−0.591044			−0.295522	+	0.955336i	$0.595494\pi$
$654$		0			0
$655$	11.8630			0.463525
$656$	14.6823	−	25.4305i	0.573248	−	0.992895i
$657$		0			0
$658$		0			0
$659$	7.13002	−	12.3496i	0.277746	−	0.481070i	−0.693078	−	0.720862i	$-0.743746\pi$
$659$	7.13002	−	12.3496i	0.277746	−	0.481070i	0.970824	+	0.239792i	$0.0770793\pi$
$660$		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
$667$	9.80197	−	16.9775i	0.379534	−	0.657372i
$668$	−9.57561			−0.370492
$669$		0			0
$670$	0.605656			0.0233985
$671$	−2.16991	−	3.75839i	−0.0837683	−	0.145091i
$672$		0			0
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	−0.917506	−	0.397721i	$-0.869801\pi$
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	0.803190	+	0.595723i	$0.203135\pi$
$674$	−0.309512	+	0.536091i	−0.0119220	+	0.0206494i
$675$		0			0
$676$	14.5683	+	25.2330i	0.560318	+	0.970500i
$677$	−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
$682$	−0.734671			−0.0281320
$683$	6.56800	+	11.3761i	0.251317	+	0.435294i	0.963889	−	0.266305i	$-0.0858029\pi$
$683$	6.56800	+	11.3761i	0.251317	+	0.435294i	−0.712571	+	0.701600i	$0.752470\pi$
$684$		0			0
$685$	52.0398			1.98834
$686$		0			0
$687$		0			0
$688$	−44.7384			−1.70564
$689$	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
$698$	−1.86401			−0.0705536
$699$		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
$703$	−4.02217	−	6.96660i	−0.151699	−	0.262750i
$704$	−12.6139			−0.475406
$705$		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	$0.918648\pi$
$710$	1.12823	+	1.95415i	0.0423418	+	0.0733381i
$711$		0			0
$712$	0.0642745	−	0.111327i	0.00240879	−	0.00417215i
$713$	−10.3086	+	17.8549i	−0.386058	+	0.668673i
$714$		0			0
$715$	−11.1899	−	19.3815i	−0.418479	−	0.724827i
$716$	−32.7192			−1.22277
$717$		0			0
$718$	−1.43842			−0.0536815
$719$	−7.49790	+	12.9867i	−0.279624	+	0.484324i	−0.971291	−	0.237893i	$-0.923543\pi$
$719$	−7.49790	+	12.9867i	−0.279624	+	0.484324i	0.691667	+	0.722217i	$0.256877\pi$
$720$		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	−0.515734	−	0.856749i	$-0.672481\pi$
$727$	13.0527	−	22.6080i	0.484099	−	0.838485i	0.999833	+	0.0182642i	$0.00581399\pi$
$728$		0			0
$729$		0			0
$730$	0.200223	−	0.346796i	0.00741059	−	0.0128355i
$731$	−73.7447			−2.72754
$732$		0			0
$733$	−28.3821			−1.04832			−0.524159	−	0.851621i	$-0.675620\pi$
$733$	−28.3821			−1.04832			−0.524159	+	0.851621i	$0.675620\pi$
$734$	1.19784	+	2.07473i	0.0442132	+	0.0765796i
$735$		0			0
$736$	1.25486	−	2.17348i	0.0462548	−	0.0801156i
$737$	2.65881	−	4.60520i	0.0979386	−	0.169635i
$738$		0			0
$739$	−23.2933	−	40.3451i	−0.856857	−	1.48412i	−0.874912	−	0.484282i	$-0.839081\pi$
$739$	−23.2933	−	40.3451i	−0.856857	−	1.48412i	0.0180552	−	0.999837i	$-0.494253\pi$
$740$	11.2403	+	19.4688i	0.413202	+	0.715686i
$741$		0			0
$742$		0			0
$743$	0.169513	+	0.293606i	0.00621884	+	0.0107713i	0.869118	−	0.494605i	$-0.164687\pi$
$743$	0.169513	+	0.293606i	0.00621884	+	0.0107713i	−0.862899	+	0.505376i	$0.831354\pi$
$744$		0			0
$745$	23.4755			0.860075
$746$	0.0385841	+	0.0668297i	0.00141267	+	0.00244681i
$747$		0			0
$748$	−20.8907			−0.763839
$749$		0			0
$750$		0			0
$751$	−36.3662			−1.32702			−0.663510	−	0.748168i	$-0.730934\pi$
$751$	−36.3662			−1.32702			−0.663510	+	0.748168i	$0.730934\pi$
$752$	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
$761$	33.0357			1.19754			0.598771	−	0.800920i	$-0.295656\pi$
$761$	33.0357			1.19754			0.598771	+	0.800920i	$0.295656\pi$
$762$		0			0
$763$		0			0
$764$	5.66934			0.205110
$765$		0			0
$766$	0.787671	+	1.36429i	0.0284597	+	0.0492937i
$767$	57.2285			2.06640
$768$		0			0
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	0.888327	−	0.459212i	$-0.151868\pi$
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	−0.841853	+	0.539707i	$0.818535\pi$
$770$		0			0
$771$		0			0
$772$	8.80822	+	15.2563i	0.317015	+	0.549086i
$773$	−3.36486	−	5.82811i	−0.121026	−	0.209623i	0.799147	−	0.601136i	$-0.205285\pi$
$773$	−3.36486	−	5.82811i	−0.121026	−	0.209623i	−0.920172	+	0.391513i	$0.871952\pi$
$774$		0			0
$775$	−7.04102	+	12.1954i	−0.252921	+	0.438072i
$776$	0.703765	−	1.21896i	0.0252637	−	0.0437580i
$777$		0			0
$778$	−0.539302	−	0.934099i	−0.0193349	−	0.0334891i
$779$	−14.0609			−0.503785
$780$		0			0
$781$	19.8116			0.708916
$782$	0.686792	−	1.18956i	0.0245596	−	0.0425385i
$783$		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
$793$	−7.12905	+	12.3479i	−0.253160	+	0.438486i
$794$	−1.12855			−0.0400507
$795$		0			0
$796$	22.7767			0.807300
$797$	11.4913	+	19.9035i	0.407042	+	0.705017i	0.994557	−	0.104196i	$-0.0332270\pi$
$797$	11.4913	+	19.9035i	0.407042	+	0.705017i	−0.587515	+	0.809213i	$0.699894\pi$
$798$		0			0
$799$	12.4370	−	21.5415i	0.439989	−	0.762084i
$800$	0.857104	−	1.48455i	0.0303032	−	0.0524867i
$801$		0			0
$802$	−0.740489	−	1.28256i	−0.0261476	−	0.0452889i
$803$	−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
$808$	0.503977			0.0177299
$809$	−8.23894	−	14.2703i	−0.289666	−	0.501716i	0.684064	−	0.729422i	$-0.260211\pi$
$809$	−8.23894	−	14.2703i	−0.289666	−	0.501716i	−0.973730	+	0.227706i	$0.926878\pi$
$810$		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
$814$	−0.462453			−0.0162090
$815$	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	$0.315781\pi$
$824$	1.41451			0.0492769
$825$		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
$829$	−7.85344	−	13.6026i	−0.272761	−	0.472436i	0.696807	−	0.717259i	$-0.254604\pi$
$829$	−7.85344	−	13.6026i	−0.272761	−	0.472436i	−0.969568	+	0.244823i	$0.921270\pi$
$830$	1.24522			0.0432223
$831$		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
$836$	3.03433	+	5.25561i	0.104944	+	0.181769i
$837$		0			0
$838$	0.738994	−	1.27998i	0.0255281	−	0.0442160i
$839$	−3.69822	+	6.40550i	−0.127677	+	0.221142i	−0.922776	−	0.385337i	$-0.874085\pi$
$839$	−3.69822	+	6.40550i	−0.127677	+	0.221142i	0.795099	+	0.606479i	$0.207419\pi$
$840$		0			0
$841$	−5.90986	−	10.2362i	−0.203788	−	0.352971i
$842$	1.86274			0.0641942
$843$		0			0
$844$	42.6675			1.46868
$845$	−19.4489	+	33.6865i	−0.669062	+	1.15885i
$846$		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	0.0947464	−	0.995501i	$-0.469796\pi$
$853$	26.5631	−	46.0086i	0.909503	−	1.57530i	0.814756	−	0.579804i	$-0.196871\pi$
$854$		0			0
$855$		0			0
$856$	−2.31502	+	4.00973i	−0.0791257	+	0.137050i
$857$	3.81530			0.130328			0.0651640	−	0.997875i	$-0.479243\pi$
$857$	3.81530			0.130328			0.0651640	+	0.997875i	$0.479243\pi$
$858$		0			0
$859$	38.9768			1.32987			0.664936	−	0.746901i	$-0.268459\pi$
$859$	38.9768			1.32987			0.664936	+	0.746901i	$0.268459\pi$
$860$	−29.9336	−	51.8464i	−1.02073	−	1.76795i
$861$		0			0
$862$	−0.280226	+	0.485366i	−0.00954454	+	0.0165316i
$863$	13.3368	−	23.1000i	0.453989	−	0.786332i	−0.544640	−	0.838670i	$-0.683334\pi$
$863$	13.3368	−	23.1000i	0.453989	−	0.786332i	0.998629	+	0.0523375i	$0.0166672\pi$
$864$		0			0
$865$	6.70171	+	11.6077i	0.227865	+	0.394674i
$866$	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
$871$	−17.4706			−0.591970
$872$	1.16099	+	2.01089i	0.0393160	+	0.0680974i
$873$		0			0
$874$	−0.399020			−0.0134971
$875$		0			0
$876$		0			0
$877$	24.0135			0.810879			0.405440	−	0.914122i	$-0.367118\pi$
$877$	24.0135			0.810879			0.405440	+	0.914122i	$0.367118\pi$
$878$	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
$887$	−29.1032			−0.977191			−0.488596	−	0.872510i	$-0.662491\pi$
$887$	−29.1032			−0.977191			−0.488596	+	0.872510i	$0.662491\pi$
$888$		0			0
$889$		0			0
$890$	0.0857071			0.00287291
$891$		0			0
$892$	7.15098	+	12.3859i	0.239433	+	0.414710i
$893$	−7.22579			−0.241802
$894$		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
$899$	21.4647	+	37.1779i	0.715887	+	1.23995i
$900$		0			0
$901$	29.1306	−	50.4556i	0.970480	−	1.68092i
$902$	−0.404168	+	0.700040i	−0.0134573	+	0.0233088i
$903$		0			0
$904$	0.533229	+	0.923579i	0.0177349	+	0.0307178i
$905$	−38.4505			−1.27814
$906$		0			0
$907$	−41.2142			−1.36849			−0.684247	−	0.729250i	$-0.739869\pi$
$907$	−41.2142			−1.36849			−0.684247	+	0.729250i	$0.739869\pi$
$908$	13.7564	−	23.8269i	0.456524	−	0.790722i
$909$		0			0
$910$		0			0
$911$	−28.8619	+	49.9903i	−0.956239	+	1.65625i	−0.224731	+	0.974421i	$0.572150\pi$
$911$	−28.8619	+	49.9903i	−0.956239	+	1.65625i	−0.731508	+	0.681833i	$0.761183\pi$
$912$		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
$919$	25.7799	−	44.6521i	0.850400	−	1.47294i	−0.0304476	−	0.999536i	$-0.509693\pi$
$919$	25.7799	−	44.6521i	0.850400	−	1.47294i	0.880848	−	0.473400i	$-0.156973\pi$
$920$	2.23281			0.0736135
$921$		0			0
$922$	1.65514			0.0545090
$923$	−32.5447	−	56.3691i	−1.07122	−	1.85541i
$924$		0			0
$925$	−4.43211	+	7.67664i	−0.145727	+	0.252406i
$926$	−0.164263	+	0.284511i	−0.00539801	+	0.00934962i
$927$		0			0
$928$	−2.61290	−	4.52567i	−0.0857725	−	0.148562i
$929$	−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
$934$	−1.86289			−0.0609557
$935$	−13.9447	−	24.1529i	−0.456040	−	0.789885i
$936$		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
$940$	20.1931			0.658627
$941$	−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
$950$	−0.272542			−0.00884243
$951$		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
$955$	3.78433	+	6.55465i	0.122458	+	0.212104i
$956$	−30.7935			−0.995932
$957$		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
$962$	0.759676	+	1.31580i	0.0244929	+	0.0424230i
$963$		0			0
$964$	1.17713	−	2.03884i	0.0379126	−	0.0656666i
$965$	−11.7591	+	20.3674i	−0.378539	+	0.655649i
$966$		0			0
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	0.996682	−	0.0813886i	$-0.0259355\pi$
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	−0.568826	+	0.822458i	$0.692602\pi$
$968$	−2.30637			−0.0741296
$969$		0			0
$970$	0.938438			0.0301314
$971$	−28.2839	+	48.9892i	−0.907674	+	1.57214i	−0.0903867	+	0.995907i	$0.528810\pi$
$971$	−28.2839	+	48.9892i	−0.907674	+	1.57214i	−0.817287	+	0.576231i	$0.804523\pi$
$972$		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
$982$	−0.533847	+	0.924650i	−0.0170357	+	0.0295068i
$983$	−27.4102			−0.874249			−0.437125	−	0.899401i	$-0.644003\pi$
$983$	−27.4102			−0.874249			−0.437125	+	0.899401i	$0.644003\pi$
$984$		0			0
$985$	−15.2463			−0.485788
$986$	−1.43005	−	2.47692i	−0.0455421	−	0.0788813i
$987$		0			0
$988$	9.96904	−	17.2669i	0.317157	−	0.549333i
$989$	17.2804	−	29.9305i	0.549483	−	0.951733i
$990$		0			0
$991$	8.66869	+	15.0146i	0.275370	+	0.476955i	0.970228	−	0.242192i	$-0.0778663\pi$
$991$	8.66869	+	15.0146i	0.275370	+	0.476955i	−0.694858	+	0.719147i	$0.744533\pi$
$992$	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
$997$	−35.6638			−1.12948			−0.564742	−	0.825268i	$-0.691024\pi$
$997$	−35.6638			−1.12948			−0.564742	+	0.825268i	$0.691024\pi$
$998$	0.727124	+	1.25942i	0.0230167	+	0.0398661i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.5	✓	24	63.5	even	6
441.2.f.h.148.6	yes	24	63.23	odd	6
441.2.f.h.295.5	yes	24	21.5	even	6
441.2.f.h.295.6	yes	24	21.2	odd	6
441.2.g.h.67.5		24	63.32	odd	6
441.2.g.h.67.6		24	63.59	even	6
441.2.g.h.79.5		24	3.2	odd	2
441.2.g.h.79.6		24	21.20	even	2
441.2.h.h.214.7		24	21.11	odd	6
441.2.h.h.214.8		24	21.17	even	6
441.2.h.h.373.7		24	9.5	odd	6
441.2.h.h.373.8		24	63.41	even	6
1323.2.f.h.442.7		24	63.58	even	3
1323.2.f.h.442.8		24	63.40	odd	6
1323.2.f.h.883.7		24	7.2	even	3
1323.2.f.h.883.8		24	7.5	odd	6
1323.2.g.h.361.7		24	63.31	odd	6	inner
1323.2.g.h.361.8		24	63.4	even	3	inner
1323.2.g.h.667.7		24	7.6	odd	2	inner
1323.2.g.h.667.8		24	1.1	even	1	trivial
1323.2.h.h.226.5		24	63.13	odd	6
1323.2.h.h.226.6		24	9.4	even	3
1323.2.h.h.802.5		24	7.3	odd	6
1323.2.h.h.802.6		24	7.4	even	3
3969.2.a.bh.1.7		12	63.2	odd	6
3969.2.a.bh.1.8		12	63.47	even	6
3969.2.a.bi.1.5		12	63.61	odd	6
3969.2.a.bi.1.6		12	63.16	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +O(q^{10})\)	\(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +(0.0910670 + 0.157733i) q^{10} +1.59913 q^{11} +(-2.62690 - 4.54992i) q^{13} +(-1.98599 - 3.43983i) q^{16} +(-3.27360 - 5.67005i) q^{17} +(-0.950968 + 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +3.06837 q^{23} +2.09578 q^{25} +(0.179612 - 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +(-3.35961 + 5.81902i) q^{31} +(0.408966 - 0.708350i) q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 + 3.66290i) q^{37} -0.130043 q^{38} +0.727684 q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 - 2.76329i) q^{44} +(0.104898 + 0.181689i) q^{46} +(1.89959 + 3.29018i) q^{47} +(0.0716485 + 0.124099i) q^{50} -10.4830 q^{52} +(4.44931 + 7.70643i) q^{53} +4.25974 q^{55} +0.436843 q^{58} +(-5.44639 + 9.43343i) q^{59} +(-1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(-6.99751 - 12.1200i) q^{65} +(1.66267 - 2.87982i) q^{67} -13.0638 q^{68} +12.3890 q^{71} +(-1.09932 - 1.90407i) q^{73} -0.289191 q^{74} +(1.89749 + 3.28655i) q^{76} +(-0.406778 - 0.704560i) q^{79} +(-5.29025 - 9.16298i) q^{80} +(-0.252743 + 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +0.770132 q^{86} +0.436843 q^{88} +(0.235286 - 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +(-0.129882 + 0.224963i) q^{94} +(-2.53318 + 4.38760i) q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

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Database

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