LMFDB - Embedded newform 441.2.g.h.79.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.5
Character	$\chi$	$=$	441.79
Dual form			441.2.g.h.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0341870 - 0.0592136i) q^{2} +(-1.15559 - 1.29020i) q^{3} +(0.997662 - 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 + 2.98188i) q^{9} +O(q^{10})$	\(q+(-0.0341870 - 0.0592136i) q^{2} +(-1.15559 - 1.29020i) q^{3} +(0.997662 - 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 + 2.98188i) q^{9} +(0.0910670 + 0.157733i) q^{10} -1.59913 q^{11} +(-3.38235 + 0.709679i) q^{12} +(-2.62690 - 4.54992i) q^{13} +(3.07825 + 3.43682i) q^{15} +(-1.98599 - 3.43983i) q^{16} +(3.27360 + 5.67005i) q^{17} +(0.187823 - 0.0824469i) q^{18} +(-0.950968 + 1.64713i) q^{19} +(-2.65756 + 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} -3.06837 q^{23} +(0.315680 + 0.352452i) q^{24} +2.09578 q^{25} +(-0.179612 + 0.311096i) q^{26} +(4.22767 - 3.02106i) q^{27} +(-3.19452 + 5.53306i) q^{29} +(0.0982704 - 0.299769i) q^{30} +(-3.35961 + 5.81902i) q^{31} +(-0.408966 + 0.708350i) q^{32} +(1.84793 + 2.06319i) q^{33} +(0.223829 - 0.387684i) q^{34} +(4.82424 + 3.54381i) q^{36} +(-2.11477 + 3.66290i) q^{37} +0.130043 q^{38} +(-2.83469 + 8.64707i) q^{39} +0.727684 q^{40} +(-3.69648 - 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(-1.59539 + 2.76329i) q^{44} +(0.876986 - 7.94311i) q^{45} +(0.104898 + 0.181689i) q^{46} +(-1.89959 - 3.29018i) q^{47} +(-2.14308 + 6.53735i) q^{48} +(-0.0716485 - 0.124099i) q^{50} +(3.53255 - 10.7758i) q^{51} -10.4830 q^{52} +(-4.44931 - 7.70643i) q^{53} +(-0.323419 - 0.147054i) q^{54} +4.25974 q^{55} +(3.22405 - 0.676463i) q^{57} +0.436843 q^{58} +(5.44639 - 9.43343i) q^{59} +(9.00989 - 1.89044i) q^{60} +(-1.35693 - 2.35027i) q^{61} +0.459420 q^{62} -7.88802 q^{64} +(6.99751 + 12.1200i) q^{65} +(0.0589937 - 0.179957i) q^{66} +(1.66267 - 2.87982i) q^{67} +13.0638 q^{68} +(3.54578 + 3.95881i) q^{69} -12.3890 q^{71} +(0.0899364 - 0.814579i) q^{72} +(-1.09932 - 1.90407i) q^{73} +0.289191 q^{74} +(-2.42187 - 2.70398i) q^{75} +(1.89749 + 3.28655i) q^{76} +(0.608933 - 0.127765i) q^{78} +(-0.406778 - 0.704560i) q^{79} +(5.29025 + 9.16298i) q^{80} +(-8.78322 - 1.96342i) q^{81} +(-0.252743 + 0.437764i) q^{82} +(-3.41842 + 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} -0.770132 q^{86} +(10.8303 - 2.27239i) q^{87} +0.436843 q^{88} +(-0.235286 + 0.407527i) q^{89} +(-0.500321 + 0.219621i) q^{90} +(-3.06120 + 5.30216i) q^{92} +(11.3900 - 2.38983i) q^{93} +(-0.129882 + 0.224963i) q^{94} +(2.53318 - 4.38760i) q^{95} +(1.38651 - 0.290914i) q^{96} +(2.57623 - 4.46216i) q^{97} +(0.526472 - 4.76840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	0.853685	−	0.520789i	$-0.174362\pi$
$2$	−0.0341870	−	0.0592136i	−0.0241739	−	0.0418703i	−0.877859	+	0.478919i	$0.841029\pi$
$3$	−1.15559	−	1.29020i	−0.667180	−	0.744897i
$3$	−1.15559	−	1.29020i	−0.667180	−	0.744897i
$4$	0.997662	−	1.72800i	0.498831	−	0.864001i
$5$	−2.66379			−1.19128			−0.595642	−	0.803250i	$-0.703102\pi$
$5$	−2.66379			−1.19128			−0.595642	+	0.803250i	$0.703102\pi$
$6$	−0.0368912	+	0.112535i	−0.0150608	+	0.0459421i
$7$		0			0
$7$		0			0
$8$	−0.273176			−0.0965824
$9$	−0.329225	+	2.98188i	−0.109742	+	0.993960i
$10$	0.0910670	+	0.157733i	0.0287979	+	0.0498794i
$11$	−1.59913			−0.482155			−0.241077	−	0.970506i	$-0.577501\pi$
$11$	−1.59913			−0.482155			−0.241077	+	0.970506i	$0.577501\pi$
$12$	−3.38235	+	0.709679i	−0.976402	+	0.204867i
$13$	−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
$15$	3.07825	+	3.43682i	0.794801	+	0.887383i
$16$	−1.98599	−	3.43983i	−0.496496	−	0.859957i
$17$	3.27360	+	5.67005i	0.793966	+	1.37519i	0.923494	+	0.383613i	$0.125320\pi$
$17$	3.27360	+	5.67005i	0.793966	+	1.37519i	−0.129528	+	0.991576i	$0.541346\pi$
$18$	0.187823	−	0.0824469i	0.0442703	−	0.0194329i
$19$	−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	$-0.603649\pi$
$23$	−3.06837			−0.639800			−0.319900	+	0.947451i	$0.603649\pi$
$24$	0.315680	+	0.352452i	0.0644378	+	0.0719439i
$25$	2.09578			0.419157
$26$	−0.179612	+	0.311096i	−0.0352247	+	0.0610110i
$27$	4.22767	−	3.02106i	0.813615	−	0.581404i
$28$		0			0
$29$	−3.19452	+	5.53306i	−0.593207	+	1.02746i	0.400591	+	0.916257i	$0.368805\pi$
$29$	−3.19452	+	5.53306i	−0.593207	+	1.02746i	−0.993797	+	0.111207i	$0.964528\pi$
$30$	0.0982704	−	0.299769i	0.0179416	−	0.0547300i
$31$	−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
$33$	1.84793	+	2.06319i	0.321684	+	0.359155i
$34$	0.223829	−	0.387684i	0.0383864	−	0.0664872i
$35$		0			0
$36$	4.82424	+	3.54381i	0.804040	+	0.590635i
$37$	−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
$39$	−2.83469	+	8.64707i	−0.453913	+	1.38464i
$40$	0.727684			0.115057
$41$	−3.69648	−	6.40249i	−0.577293	−	0.999901i	−0.995788	−	0.0916820i	$-0.970776\pi$
$41$	−3.69648	−	6.40249i	−0.577293	−	0.999901i	0.418495	−	0.908219i	$-0.362558\pi$
$42$		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
$45$	0.876986	−	7.94311i	0.130733	−	1.18409i
$46$	0.104898	+	0.181689i	0.0154664	+	0.0267887i
$47$	−1.89959	−	3.29018i	−0.277083	−	0.479922i	0.693575	−	0.720384i	$-0.256034\pi$
$47$	−1.89959	−	3.29018i	−0.277083	−	0.479922i	−0.970659	+	0.240462i	$0.922701\pi$
$48$	−2.14308	+	6.53735i	−0.309327	+	0.943585i
$49$		0			0
$50$	−0.0716485	−	0.124099i	−0.0101326	−	0.0175502i
$51$	3.53255	−	10.7758i	0.494655	−	1.50892i
$52$	−10.4830			−1.45374
$53$	−4.44931	−	7.70643i	−0.611160	−	1.05856i	−0.991045	−	0.133527i	$-0.957370\pi$
$53$	−4.44931	−	7.70643i	−0.611160	−	1.05856i	0.379885	−	0.925034i	$-0.375963\pi$
$54$	−0.323419	−	0.147054i	−0.0440118	−	0.0200116i
$55$	4.25974			0.574383
$56$		0			0
$57$	3.22405	−	0.676463i	0.427036	−	0.0895997i
$58$	0.436843			0.0573604
$59$	5.44639	−	9.43343i	0.709060	−	1.22813i	−0.256146	−	0.966638i	$-0.582453\pi$
$59$	5.44639	−	9.43343i	0.709060	−	1.22813i	0.965206	−	0.261490i	$-0.0842138\pi$
$60$	9.00989	−	1.89044i	1.16317	−	0.244054i
$61$	−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
$66$	0.0589937	−	0.179957i	0.00726162	−	0.0221512i
$67$	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
$69$	3.54578	+	3.95881i	0.426862	+	0.476585i
$70$		0			0
$71$	−12.3890			−1.47031			−0.735154	−	0.677900i	$-0.762890\pi$
$71$	−12.3890			−1.47031			−0.735154	+	0.677900i	$0.762890\pi$
$72$	0.0899364	−	0.814579i	0.0105991	−	0.0959990i
$73$	−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
$75$	−2.42187	−	2.70398i	−0.279653	−	0.312228i
$76$	1.89749	+	3.28655i	0.217657	+	0.376993i
$77$		0			0
$78$	0.608933	−	0.127765i	0.0689481	−	0.0144666i
$79$	−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
$81$	−8.78322	−	1.96342i	−0.975914	−	0.218158i
$82$	−0.252743	+	0.437764i	−0.0279108	+	0.0483429i
$83$	−3.41842	+	5.92088i	−0.375220	+	0.649901i	−0.990360	−	0.138517i	$-0.955766\pi$
$83$	−3.41842	+	5.92088i	−0.375220	+	0.649901i	0.615140	+	0.788418i	$0.289100\pi$
$84$		0			0
$85$	−8.72020	−	15.1038i	−0.945838	−	1.63824i
$86$	−0.770132			−0.0830455
$87$	10.8303	−	2.27239i	1.16113	−	0.243626i
$88$	0.436843			0.0465677
$89$	−0.235286	+	0.407527i	−0.0249403	+	0.0431978i	−0.878226	−	0.478246i	$-0.841273\pi$
$89$	−0.235286	+	0.407527i	−0.0249403	+	0.0431978i	0.853286	+	0.521443i	$0.174606\pi$
$90$	−0.500321	+	0.219621i	−0.0527385	+	0.0231501i
$91$		0			0
$92$	−3.06120	+	5.30216i	−0.319152	+	0.552788i
$93$	11.3900	−	2.38983i	1.18109	−	0.247814i
$94$	−0.129882	+	0.224963i	−0.0133963	+	0.0232031i
$95$	2.53318	−	4.38760i	0.259899	−	0.450158i
$96$	1.38651	−	0.290914i	0.141510	−	0.0296913i
$97$	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
$99$	0.526472	−	4.76840i	0.0529125	−	0.479243i
$100$	2.09088	−	3.62152i	0.209088	−	0.362152i
$101$	−1.84488			−0.183572			−0.0917862	−	0.995779i	$-0.529258\pi$
$101$	−1.84488			−0.183572			−0.0917862	+	0.995779i	$0.529258\pi$
$102$	−0.758844	+	0.159219i	−0.0751368	+	0.0157650i
$103$	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	$-0.527720\pi$
$107$	8.47445	−	14.6782i	0.819256	−	1.41899i	0.906231	−	0.422782i	$-0.138946\pi$
$108$	−1.00262	−	10.3194i	−0.0964773	−	0.992987i
$109$	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
$111$	7.16967	−	1.50433i	0.680515	−	0.142784i
$112$		0			0
$113$	−1.95196	−	3.38089i	−0.183625	−	0.318048i	0.759487	−	0.650522i	$-0.225450\pi$
$113$	−1.95196	−	3.38089i	−0.183625	−	0.318048i	−0.943112	+	0.332474i	$0.892116\pi$
$114$	−0.150276	−	0.167781i	−0.0140747	−	0.0157142i
$115$	8.17351			0.762183
$116$	6.37410	+	11.0403i	0.591820	+	1.02506i
$117$	14.4322	−	6.33515i	1.33425	−	0.585685i
$118$	−0.744783			−0.0685628
$119$		0			0
$120$	−0.840905	−	0.938858i	−0.0767637	−	0.0857056i
$121$	−8.44279			−0.767527
$122$	−0.0927788	+	0.160698i	−0.00839980	+	0.0145489i
$123$	−3.98887	+	12.1678i	−0.359664	+	1.09714i
$124$	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
$129$	−19.0933	+	4.00611i	−1.68107	+	0.352718i
$130$	0.478448	−	0.828696i	0.0419626	−	0.0726814i
$131$	−4.45342			−0.389097			−0.194549	−	0.980893i	$-0.562324\pi$
$131$	−4.45342			−0.389097			−0.194549	+	0.980893i	$0.562324\pi$
$132$	5.40881	−	1.13487i	0.470777	−	0.0987774i
$133$		0			0
$134$	−0.227366			−0.0196414
$135$	−11.2616	+	8.04749i	−0.969246	+	0.692617i
$136$	−0.894271	−	1.54892i	−0.0766831	−	0.132819i
$137$	−19.5360			−1.66907			−0.834537	−	0.550952i	$-0.814265\pi$
$137$	−19.5360			−1.66907			−0.834537	+	0.550952i	$0.814265\pi$
$138$	0.113196	−	0.345298i	0.00963588	−	0.0293937i
$139$	−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
$141$	−2.04984	+	6.25295i	−0.172628	+	0.526593i
$142$	0.423544	+	0.733599i	0.0355430	+	0.0615623i
$143$	4.20075	+	7.27590i	0.351284	+	0.608442i
$144$	10.9110	−	4.78950i	0.909249	−	0.399125i
$145$	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	$-0.617560\pi$
$149$	−8.81281			−0.721973			−0.360987	+	0.932571i	$0.617560\pi$
$150$	−0.0773159	+	0.235848i	−0.00631282	+	0.0192569i
$151$	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
$153$	−17.9852	+	7.89478i	−1.45401	+	0.638255i
$154$		0			0
$155$	8.94931	−	15.5007i	0.718826	−	1.24504i
$156$	12.1141	+	13.5252i	0.969904	+	1.08288i
$157$	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
$159$	−4.80125	+	14.6460i	−0.380764	+	1.16150i
$160$	1.08940	−	1.88690i	0.0861246	−	0.149172i
$161$		0			0
$162$	0.184011	+	0.587210i	0.0144573	+	0.0461355i
$163$	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
$165$	−4.92251	−	5.49591i	−0.383217	−	0.427856i
$166$	0.467462			0.0362821
$167$	2.39951	+	4.15608i	0.185680	+	0.321607i	0.943805	−	0.330502i	$-0.107218\pi$
$167$	2.39951	+	4.15608i	0.185680	+	0.321607i	−0.758126	+	0.652109i	$0.773885\pi$
$168$		0			0
$169$	−7.30121	+	12.6461i	−0.561631	+	0.972774i
$170$	−0.596235	+	1.03271i	−0.0457291	+	0.0792051i
$171$	−4.59845	−	3.37795i	−0.351652	−	0.258318i
$172$	−11.2372	−	19.4634i	−0.856828	−	1.48407i
$173$	−2.51585	−	4.35759i	−0.191277	−	0.331301i	0.754397	−	0.656419i	$-0.227929\pi$
$173$	−2.51585	−	4.35759i	−0.191277	−	0.331301i	−0.945674	+	0.325118i	$0.894596\pi$
$174$	−0.504812	−	0.563615i	−0.0382697	−	0.0427275i
$175$		0			0
$176$	3.17584	+	5.50072i	0.239388	+	0.414632i
$177$	−18.4648	+	3.87425i	−1.38790	+	0.291206i
$178$	0.0321749			0.00241161
$179$	8.19896	+	14.2010i	0.612819	+	1.06143i	0.990763	+	0.135605i	$0.0432977\pi$
$179$	8.19896	+	14.2010i	0.612819	+	1.06143i	−0.377944	+	0.925828i	$0.623369\pi$
$180$	−12.8508	−	9.43997i	−0.957840	−	0.703614i
$181$	−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
$183$	−1.46426	+	4.46666i	−0.108242	+	0.330185i
$184$	0.838207			0.0617934
$185$	5.63332	−	9.75719i	0.414170	−	0.717363i
$186$	−0.530902	−	0.592744i	−0.0389276	−	0.0434621i
$187$	−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	0.810040	−	0.586374i	$-0.199445\pi$
$191$	−1.42066	−	2.46065i	−0.102795	−	0.178046i	−0.912835	+	0.408328i	$0.866112\pi$
$192$	9.11531	+	10.1771i	0.657841	+	0.734470i
$193$	−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
$195$	7.55102	−	23.0340i	0.540739	−	1.64950i
$196$		0			0
$197$	5.72354			0.407785			0.203893	−	0.978993i	$-0.434641\pi$
$197$	5.72354			0.407785			0.203893	+	0.978993i	$0.434641\pi$
$198$	−0.300353	+	0.131843i	−0.0213452	+	0.00936968i
$199$	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
$201$	−5.63690	+	1.18272i	−0.397596	+	0.0834229i
$202$	0.0630709	+	0.109242i	0.00443765	+	0.00768624i
$203$		0			0
$204$	−15.0964	−	16.8549i	−1.05696	−	1.18008i
$205$	9.84665	+	17.0549i	0.687720	+	1.19117i
$206$	−0.177021	−	0.306609i	−0.0123336	−	0.0213625i
$207$	1.01019	−	9.14952i	0.0702127	−	0.635936i
$208$	−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
$213$	14.3166	+	15.9843i	0.980960	+	1.09523i
$214$	−1.15886			−0.0792183
$215$	−15.0018	+	25.9840i	−1.02312	+	1.77209i
$216$	−1.15490	+	0.825283i	−0.0785809	+	0.0561534i
$217$		0			0
$218$	0.290587	−	0.503311i	0.0196810	−	0.0340885i
$219$	−1.18627	+	3.61867i	−0.0801609	+	0.244527i
$220$	4.24978	−	7.36084i	0.286520	−	0.496268i
$221$	17.1989	−	29.7893i	1.15692	−	2.00385i
$222$	−0.334186	−	0.373114i	−0.0224291	−	0.0250418i
$223$	−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
$225$	−0.689984	+	6.24938i	−0.0459989	+	0.416625i
$226$	−0.133463	+	0.231165i	−0.00887784	+	0.0153769i
$227$	−13.7887			−0.915187			−0.457593	−	0.889162i	$-0.651288\pi$
$227$	−13.7887			−0.915187			−0.457593	+	0.889162i	$0.651288\pi$
$228$	2.04758	−	6.24604i	0.135604	−	0.413654i
$229$	−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	−0.581155	−	0.813793i	$-0.697399\pi$
$233$	6.32230	−	10.9505i	0.414187	−	0.717394i	0.995343	+	0.0963989i	$0.0307324\pi$
$234$	−0.868520	−	0.638001i	−0.0567769	−	0.0417074i
$235$	5.06010	+	8.76436i	0.330085	+	0.571724i
$236$	−10.8673	−	18.8228i	−0.707403	−	1.22526i
$237$	−0.438954	+	1.33901i	−0.0285131	+	0.0869779i
$238$		0			0
$239$	7.71640	+	13.3652i	0.499133	+	0.864523i	0.999999	−	0.00100121i	$-0.000318696\pi$
$239$	7.71640	+	13.3652i	0.499133	+	0.864523i	−0.500867	+	0.865524i	$0.666985\pi$
$240$	5.70871	−	17.4141i	0.368496	−	1.12408i
$241$	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
$243$	7.61660	+	13.6010i	0.488605	+	0.872505i
$244$	−5.41504			−0.346662
$245$		0			0
$246$	0.856869	−	0.179787i	0.0546320	−	0.0114628i
$247$	9.99240			0.635801
$248$	0.917767	−	1.58962i	0.0582783	−	0.100941i
$249$	11.5894	−	2.43166i	0.734449	−	0.154101i
$250$	−0.264478	−	0.458090i	−0.0167271	−	0.0289721i
$251$	5.54970			0.350294			0.175147	−	0.984542i	$-0.443960\pi$
$251$	5.54970			0.350294			0.175147	+	0.984542i	$0.443960\pi$
$252$		0			0
$253$	4.90672			0.308483
$254$	−0.374459	−	0.648583i	−0.0234957	−	0.0406957i
$255$	−9.40996	+	28.7046i	−0.589275	+	1.79755i
$256$	−7.81365	+	13.5336i	−0.488353	+	0.845853i
$257$	9.83076			0.613226			0.306613	−	0.951834i	$-0.400804\pi$
$257$	9.83076			0.613226			0.306613	+	0.951834i	$0.400804\pi$
$258$	0.889957	+	0.993623i	0.0554063	+	0.0618603i
$259$		0			0
$260$	27.9246			1.73181
$261$	−15.4472	−	11.3473i	−0.956159	−	0.702379i
$262$	0.152249	+	0.263703i	0.00940598	+	0.0162916i
$263$	11.9322			0.735774			0.367887	−	0.929870i	$-0.380081\pi$
$263$	11.9322			0.735774			0.367887	+	0.929870i	$0.380081\pi$
$264$	−0.504812	−	0.563615i	−0.0310690	−	0.0346881i
$265$	11.8520	+	20.5283i	0.728065	+	1.26105i
$266$		0			0
$267$	0.797685	−	0.167369i	0.0488175	−	0.0102428i
$268$	−3.31756	−	5.74618i	−0.202652	−	0.351004i
$269$	−14.9824	−	25.9503i	−0.913494	−	1.58222i	−0.809092	−	0.587682i	$-0.800041\pi$
$269$	−14.9824	−	25.9503i	−0.913494	−	1.58222i	−0.104401	−	0.994535i	$-0.533293\pi$
$270$	0.861522	+	0.391722i	0.0524305	+	0.0238394i
$271$	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
$276$	10.3783	−	2.17756i	0.624702	−	0.131074i
$277$	−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
$279$	−16.2456	−	11.9337i	−0.972596	−	0.714454i
$280$		0			0
$281$	11.9389	−	20.6787i	0.712213	−	1.23359i	−0.251812	−	0.967776i	$-0.581026\pi$
$281$	11.9389	−	20.6787i	0.712213	−	1.23359i	0.964025	−	0.265813i	$-0.0856403\pi$
$282$	0.440337	−	0.0923907i	0.0262217	−	0.00550179i
$283$	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
$285$	−8.58819	+	1.80196i	−0.508721	+	0.106739i
$286$	0.287222	−	0.497483i	0.0169838	−	0.0294168i
$287$		0			0
$288$	−1.97757	−	1.45269i	−0.116530	−	0.0856008i
$289$	−12.9330	+	22.4006i	−0.760763	+	1.31768i
$290$	−1.16366			−0.0683324
$291$	−8.73414	+	1.83258i	−0.512004	+	0.107428i
$292$	−4.38699			−0.256729
$293$	−8.52913	−	14.7729i	−0.498277	−	0.863041i	0.501721	−	0.865030i	$-0.332700\pi$
$293$	−8.52913	−	14.7729i	−0.498277	−	0.863041i	−0.999998	+	0.00198814i	$0.999367\pi$
$294$		0			0
$295$	−14.5081	+	25.1287i	−0.844692	+	1.46305i
$296$	0.577706	−	1.00062i	0.0335785	−	0.0581596i
$297$	−6.76057	+	4.83107i	−0.392288	+	0.280327i
$298$	0.301283	+	0.521838i	0.0174529	+	0.0302293i
$299$	8.06031	+	13.9609i	0.466140	+	0.807378i
$300$	−7.08868	+	1.48733i	−0.409265	+	0.0858712i
$301$		0			0
$302$	−0.159456	−	0.276185i	−0.00917564	−	0.0158927i
$303$	2.13192	+	2.38026i	0.122476	+	0.136742i
$304$	7.55444			0.433277
$305$	3.61458	+	6.26064i	0.206970	+	0.358483i
$306$	1.08234	+	0.795068i	0.0618731	+	0.0454510i
$307$	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
$309$	−5.98367	−	6.68068i	−0.340399	−	0.380050i
$310$	−1.22380			−0.0695072
$311$	−0.895467	+	1.55100i	−0.0507773	+	0.0879489i	−0.890297	−	0.455381i	$-0.849503\pi$
$311$	−0.895467	+	1.55100i	−0.0507773	+	0.0879489i	0.839520	+	0.543329i	$0.182837\pi$
$312$	0.774369	−	2.36217i	0.0438400	−	0.133732i
$313$	−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	$0.0923721\pi$
$317$	12.9421	+	22.4163i	0.726898	+	1.25902i	−0.231290	+	0.972885i	$0.574295\pi$
$318$	1.03138	−	0.216402i	0.0578370	−	0.0121352i
$319$	5.10843	−	8.84807i	0.286017	−	0.495397i
$320$	21.0120			1.17461
$321$	−28.7307	+	6.02823i	−1.60359	+	0.336463i
$322$		0			0
$323$	−12.4524			−0.692869
$324$	−12.1555	+	13.2186i	−0.675305	+	0.734367i
$325$	−5.50541	−	9.53566i	−0.305385	−	0.528943i
$326$	−0.828846			−0.0459055
$327$	4.58613	−	13.9898i	0.253614	−	0.773636i
$328$	1.00979	+	1.74901i	0.0557563	+	0.0965728i
$329$		0			0
$330$	−0.157147	+	0.479368i	−0.00865065	+	0.0263884i
$331$	−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
$333$	−10.2261	−	7.51192i	−0.560386	−	0.411651i
$334$	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
$339$	−2.10636	+	6.42534i	−0.114402	+	0.348976i
$340$	−34.7993			−1.88725
$341$	5.37245	−	9.30535i	0.290934	−	0.503913i
$342$	−0.0428134	+	0.387773i	−0.00231508	+	0.0209683i
$343$		0			0
$344$	−1.53846	+	2.66470i	−0.0829484	+	0.143671i
$345$	−9.44522	−	10.5454i	−0.508514	−	0.567748i
$346$	−0.172019	+	0.297945i	−0.00924779	+	0.0160176i
$347$	2.90984	−	5.03999i	0.156208	−	0.270561i	−0.777290	−	0.629142i	$-0.783406\pi$
$347$	2.90984	−	5.03999i	0.156208	−	0.270561i	0.933498	+	0.358582i	$0.116740\pi$
$348$	6.87829	−	20.9819i	0.368715	−	1.12475i
$349$	−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
$351$	−24.8513	−	11.2995i	−1.32646	−	0.603124i
$352$	0.653988	−	1.13274i	0.0348577	−	0.0603753i
$353$	−24.1896			−1.28748			−0.643741	−	0.765244i	$-0.722618\pi$
$353$	−24.1896			−1.28748			−0.643741	+	0.765244i	$0.722618\pi$
$354$	0.860664	+	0.960918i	0.0457438	+	0.0510722i
$355$	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	$-0.645990\pi$
$359$	10.5188	−	18.2191i	0.555161	−	0.961567i	0.997891	−	0.0649124i	$-0.0206768\pi$
$360$	−0.239572	+	2.16987i	−0.0126265	+	0.114362i
$361$	7.69132	+	13.3218i	0.404806	+	0.701145i
$362$	0.493472	+	0.854719i	0.0259363	+	0.0449230i
$363$	9.75641	+	10.8929i	0.512079	+	0.571728i
$364$		0			0
$365$	2.92835	+	5.07205i	0.153277	+	0.265483i
$366$	0.314546	−	0.0659974i	0.0164416	−	0.00344974i
$367$	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
$369$	20.3084	−	8.91460i	1.05721	−	0.464076i
$370$	−0.770345			−0.0400483
$371$		0			0
$372$	7.23377	−	22.0662i	0.375054	−	1.14408i
$373$	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
$375$	−8.93990	−	9.98127i	−0.461655	−	0.515431i
$376$	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
$381$	−12.6575	−	14.1319i	−0.648463	−	0.723999i
$382$	−0.0971359	+	0.168244i	−0.00496991	+	0.00860813i
$383$	−23.0401			−1.17729			−0.588647	−	0.808390i	$-0.700339\pi$
$383$	−23.0401			−1.17729			−0.588647	+	0.808390i	$0.700339\pi$
$384$	1.17363	−	3.58009i	0.0598915	−	0.182696i
$385$		0			0
$386$	0.603664			0.0307257
$387$	27.2326	+	20.0047i	1.38431	+	1.01689i
$388$	−5.14042	−	8.90346i	−0.260965	−	0.452005i
$389$	15.7751			0.799828			0.399914	−	0.916553i	$-0.369040\pi$
$389$	15.7751			0.799828			0.399914	+	0.916553i	$0.369040\pi$
$390$	−1.62207	+	0.340340i	−0.0821368	+	0.0172338i
$391$	−10.0446	−	17.3978i	−0.507979	−	0.879846i
$392$		0			0
$393$	5.14633	+	5.74580i	0.259598	+	0.289837i
$394$	−0.195671	−	0.338912i	−0.00985774	−	0.0170741i
$395$	1.08357	+	1.87680i	0.0545204	+	0.0944321i
$396$	−7.71457	−	5.66700i	−0.387672	−	0.284778i
$397$	−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	$-0.318113\pi$
$401$	21.6600			1.08165			0.540823	+	0.841136i	$0.318113\pi$
$402$	0.262742	+	0.293347i	0.0131044	+	0.0146308i
$403$	35.3015			1.75849
$404$	−1.84057	+	3.18796i	−0.0915716	+	0.158607i
$405$	23.3967	+	5.23014i	1.16259	+	0.259888i
$406$		0			0
$407$	3.38179	−	5.85743i	0.167629	−	0.290342i
$408$	−0.965008	+	2.94371i	−0.0477750	+	0.145735i
$409$	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
$411$	22.5756	+	25.2053i	1.11357	+	1.24329i
$412$	5.16592	−	8.94763i	0.254507	−	0.440818i
$413$		0			0
$414$	−0.576311	+	0.252978i	−0.0283242	+	0.0124332i
$415$	9.10596	−	15.7720i	0.446994	−	0.774216i
$416$	4.29725			0.210690
$417$	−1.41944	+	4.32994i	−0.0695104	+	0.212038i
$418$	−0.207955			−0.0101714
$419$	10.8081	+	18.7202i	0.528011	+	0.914542i	0.999467	+	0.0326524i	$0.0103954\pi$
$419$	10.8081	+	18.7202i	0.528011	+	0.914542i	−0.471456	+	0.881890i	$0.656271\pi$
$420$		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
$423$	10.4363	−	4.58113i	0.507431	−	0.222742i
$424$	1.21545	+	2.10521i	0.0590273	+	0.102238i
$425$	6.86077	+	11.8832i	0.332796	+	0.576420i
$426$	0.457046	−	1.39419i	0.0221439	−	0.0675490i
$427$		0			0
$428$	−16.9093	−	29.2877i	−0.817341	−	1.41568i
$429$	4.53302	−	13.8278i	0.218856	−	0.667610i
$430$	2.05147			0.0989307
$431$	−4.09843	−	7.09869i	−0.197415	−	0.341932i	0.750275	−	0.661126i	$-0.229921\pi$
$431$	−4.09843	−	7.09869i	−0.197415	−	0.341932i	−0.947689	+	0.319194i	$0.896588\pi$
$432$	−18.7880	−	8.54266i	−0.903940	−	0.411009i
$433$	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
$435$	−28.8497	+	6.05318i	−1.38324	+	0.290228i
$436$	16.9601			0.812242
$437$	2.91793	−	5.05400i	0.139583	−	0.241765i
$438$	0.254829	−	0.0534678i	0.0121762	−	0.00255479i
$439$	−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	$-0.927959\pi$
$443$	−14.3456	−	24.8473i	−0.681581	−	1.18053i	0.292917	−	0.956138i	$-0.405374\pi$
$444$	4.55344	−	13.8900i	0.216097	−	0.659191i
$445$	0.626752	−	1.08557i	0.0297109	−	0.0514608i
$446$	0.490087			0.0232063
$447$	10.1840	+	11.3703i	0.481686	+	0.537796i
$448$		0			0
$449$	0.457724			0.0216013			0.0108007	−	0.999942i	$-0.496562\pi$
$449$	0.457724			0.0216013			0.0108007	+	0.999942i	$0.496562\pi$
$450$	0.393636	−	0.172791i	0.0185562	−	0.00814544i
$451$	5.91114	+	10.2384i	0.278345	+	0.482107i
$452$	−7.78958			−0.366391
$453$	−5.38992	−	6.01777i	−0.253241	−	0.282739i
$454$	0.471393	+	0.816477i	0.0221236	+	0.0383192i
$455$		0			0
$456$	−0.880733	+	0.184794i	−0.0412441	+	0.00865376i
$457$	−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
$459$	30.9693	+	14.0813i	1.44552	+	0.657259i
$460$	8.15440	−	14.1238i	0.380201	−	0.658527i
$461$	−12.1036	+	20.9640i	−0.563719	+	0.976390i	0.433449	+	0.901178i	$0.357297\pi$
$461$	−12.1036	+	20.9640i	−0.563719	+	0.976390i	−0.997168	+	0.0752117i	$0.976037\pi$
$462$		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
$465$	−30.3407	+	6.36602i	−1.40701	+	0.295217i
$466$	−0.864561			−0.0400500
$467$	13.6228	−	23.5954i	0.630389	−	1.09187i	−0.357083	−	0.934073i	$-0.616229\pi$
$467$	13.6228	−	23.5954i	0.630389	−	1.09187i	0.987472	−	0.157793i	$-0.0504379\pi$
$468$	3.45128	−	31.2592i	0.159535	−	1.44496i
$469$		0			0
$470$	0.345979	−	0.599254i	0.0159588	−	0.0276415i
$471$	−6.90420	+	1.44862i	−0.318129	+	0.0667491i
$472$	−1.48783	+	2.57699i	−0.0684827	+	0.118616i
$473$	−9.00590	+	15.5987i	−0.414092	+	0.717228i
$474$	0.0942940	−	0.0197846i	0.00433107	−	0.000908735i
$475$	−1.99302	+	3.45202i	−0.0914462	+	0.158389i
$476$		0			0
$477$	24.4445	−	10.7302i	1.11924	−	0.491301i
$478$	0.527601	−	0.913832i	0.0241319	−	0.0417977i
$479$	20.5255			0.937834			0.468917	−	0.883242i	$-0.344644\pi$
$479$	20.5255			0.937834			0.468917	+	0.883242i	$0.344644\pi$
$480$	−3.69337	+	0.774935i	−0.168579	+	0.0353708i
$481$	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
$486$	0.544976	−	0.915984i	0.0247206	−	0.0415499i
$487$	−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
$489$	−20.5489	+	4.31153i	−0.929253	+	0.194974i
$490$		0			0
$491$	−7.80775	−	13.5234i	−0.352359	−	0.610303i	0.634303	−	0.773084i	$-0.281287\pi$
$491$	−7.80775	−	13.5234i	−0.352359	−	0.610303i	−0.986662	+	0.162781i	$0.947954\pi$
$492$	17.0465	+	19.0322i	0.768516	+	0.858037i
$493$	−41.8303			−1.88394
$494$	−0.341610	−	0.591686i	−0.0153698	−	0.0266212i
$495$	−1.40241	+	12.7020i	−0.0630337	+	0.570914i
$496$	26.6886			1.19835
$497$		0			0
$498$	−0.540194	−	0.603119i	−0.0242067	−	0.0270264i
$499$	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
$501$	2.58931	−	7.89857i	0.115682	−	0.352882i
$502$	−0.189728	−	0.328618i	−0.00846795	−	0.0146669i
$503$	−16.3298			−0.728110			−0.364055	−	0.931377i	$-0.618608\pi$
$503$	−16.3298			−0.728110			−0.364055	+	0.931377i	$0.618608\pi$
$504$		0			0
$505$	4.91437			0.218687
$506$	−0.167746	−	0.290544i	−0.00745722	−	0.0129163i
$507$	24.7531	−	5.19365i	1.09933	−	0.230658i
$508$	10.9277	−	18.9273i	0.484837	−	0.839762i
$509$	−13.4618			−0.596683			−0.298342	−	0.954459i	$-0.596433\pi$
$509$	−13.4618			−0.596683			−0.298342	+	0.954459i	$0.596433\pi$
$510$	2.02140	−	0.424126i	0.0895092	−	0.0187806i
$511$		0			0
$512$	5.41890			0.239484
$513$	0.955696	+	9.83644i	0.0421950	+	0.434289i
$514$	−0.336084	−	0.582115i	−0.0148240	−	0.0256760i
$515$	−13.7932			−0.607800
$516$	−12.1261	+	36.9899i	−0.533820	+	1.62839i
$517$	3.03768	+	5.26142i	0.133597	+	0.231397i
$518$		0			0
$519$	−2.71486	+	8.28153i	−0.119169	+	0.363519i
$520$	−1.91155	−	3.31091i	−0.0838272	−	0.145193i
$521$	0.713095	+	1.23512i	0.0312413	+	0.0541115i	0.881223	−	0.472700i	$-0.156721\pi$
$521$	0.713095	+	1.23512i	0.0312413	+	0.0541115i	−0.849982	+	0.526812i	$0.823387\pi$
$522$	−0.143820	+	1.30261i	−0.00629482	+	0.0570139i
$523$	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
$528$	3.42705	−	10.4540i	0.149143	−	0.454954i
$529$	−13.5851			−0.590656
$530$	0.810371	−	1.40360i	0.0352003	−	0.0609686i
$531$	26.3363	+	19.3462i	1.14290	+	0.839554i
$532$		0			0
$533$	−19.4206	+	33.6374i	−0.841198	+	1.45700i
$534$	−0.0371809	−	0.0415120i	−0.00160898	−	0.00179640i
$535$	−22.5742	+	39.0996i	−0.975966	+	1.69042i
$536$	−0.454201	+	0.786699i	−0.0196185	+	0.0339802i
$537$	8.84749	−	26.9888i	0.381797	−	1.16465i
$538$	−1.02441	+	1.77432i	−0.0441653	+	0.0764966i
$539$		0			0
$540$	2.67078	+	27.4888i	0.114932	+	1.18293i
$541$	−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
$543$	16.6804	+	18.6234i	0.715823	+	0.799205i
$544$	−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
$549$	7.45497	−	3.27244i	0.318171	−	0.139664i
$550$	0.114575	+	0.198450i	0.00488550	+	0.00846193i
$551$	−6.07577	−	10.5235i	−0.258836	−	0.448318i
$552$	−0.968623	−	1.08145i	−0.0412273	−	0.0460297i
$553$		0			0
$554$	0.335836	+	0.581685i	0.0142683	+	0.0247134i
$555$	−19.0985	+	4.00721i	−0.810687	+	0.170097i
$556$	−5.24928			−0.222619
$557$	−17.5209	−	30.3472i	−0.742386	−	1.28585i	−0.951406	−	0.307940i	$-0.900361\pi$
$557$	−17.5209	−	30.3472i	−0.742386	−	1.28585i	0.209019	−	0.977911i	$-0.432973\pi$
$558$	−0.151253	+	1.36994i	−0.00640303	+	0.0579940i
$559$	−59.1763			−2.50289
$560$		0			0
$561$	−5.64899	+	17.2319i	−0.238500	+	0.727533i
$562$	−1.63262			−0.0688677
$563$	−8.01311	+	13.8791i	−0.337712	+	0.584935i	−0.984002	−	0.178157i	$-0.942986\pi$
$563$	−8.01311	+	13.8791i	−0.337712	+	0.584935i	0.646290	+	0.763092i	$0.276320\pi$
$564$	8.76005	+	9.78047i	0.368865	+	0.411832i
$565$	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	0.862108	−	0.506725i	$-0.169144\pi$
$569$	−0.185651	−	0.321557i	−0.00778290	−	0.0134804i	−0.869891	+	0.493245i	$0.835811\pi$
$570$	0.400305	+	0.446934i	0.0167669	+	0.0187200i
$571$	−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
$573$	−1.53303	+	4.67643i	−0.0640432	+	0.195361i
$574$		0			0
$575$	−6.43065			−0.268177
$576$	2.59693	−	23.5211i	0.108205	−	0.980047i
$577$	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
$579$	14.9661	−	3.14017i	0.621972	−	0.130501i
$580$	−16.9793	−	29.4089i	−0.705025	−	1.22114i
$581$		0			0
$582$	0.407107	+	0.454529i	0.0168751	+	0.0188408i
$583$	7.11501	+	12.3236i	0.294674	+	0.510390i
$584$	0.300307	+	0.520148i	0.0124268	+	0.0215239i
$585$	−38.4443	+	16.8755i	−1.58948	+	0.697717i
$586$	−0.583171	+	1.01008i	−0.0240906	+	0.0417261i
$587$	−0.835901	+	1.44782i	−0.0345013	+	0.0597580i	−0.882760	−	0.469823i	$-0.844318\pi$
$587$	−0.835901	+	1.44782i	−0.0345013	+	0.0597580i	0.848259	+	0.529581i	$0.177651\pi$
$588$		0			0
$589$	−6.38977	−	11.0674i	−0.263286	−	0.456025i
$590$	1.98395			0.0816778
$591$	−6.61407	−	7.38451i	−0.272066	−	0.303758i
$592$	16.7996			0.690461
$593$	5.40871	−	9.36816i	0.222109	−	0.384704i	−0.733339	−	0.679863i	$-0.762039\pi$
$593$	5.40871	−	9.36816i	0.222109	−	0.384704i	0.955448	+	0.295159i	$0.0953726\pi$
$594$	0.517188	+	0.235158i	0.0212205	+	0.00964867i
$595$		0			0
$596$	−8.79221	+	15.2286i	−0.360143	+	0.623786i
$597$	6.15899	−	18.7877i	0.252071	−	0.768929i
$598$	0.551116	−	0.954560i	0.0225368	−	0.0390349i
$599$	−8.32007	+	14.4108i	−0.339949	+	0.588809i	−0.984423	−	0.175817i	$-0.943743\pi$
$599$	−8.32007	+	14.4108i	−0.339949	+	0.588809i	0.644474	+	0.764626i	$0.277076\pi$
$600$	0.661596	+	0.738662i	0.0270096	+	0.0301558i
$601$	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
$603$	8.03989	+	5.90598i	0.327410	+	0.240510i
$604$	4.65332	−	8.05978i	0.189341	−	0.327948i
$605$	22.4898			0.914342
$606$	0.0680598	−	0.207613i	0.00276474	−	0.00843369i
$607$	−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
$612$	−4.30093	+	38.9547i	−0.173855	+	1.57465i
$613$	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
$615$	10.6255	−	32.4126i	0.428462	−	1.30700i
$616$		0			0
$617$	16.2202	+	28.0941i	0.652999	+	1.13103i	0.982391	+	0.186834i	$0.0598227\pi$
$617$	16.2202	+	28.0941i	0.652999	+	1.13103i	−0.329393	+	0.944193i	$0.606844\pi$
$618$	−0.191023	+	0.582707i	−0.00768409	+	0.0234399i
$619$	−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
$621$	−12.9721	+	9.26976i	−0.520551	+	0.371983i
$622$	0.122453			0.00490993
$623$		0			0
$624$	35.3741	−	7.42212i	1.41610	−	0.297122i
$625$	−31.0866			−1.24346
$626$	−0.157574	+	0.272925i	−0.00629791	+	0.0109083i
$627$	−5.15566	+	1.08175i	−0.205897	+	0.0432009i
$628$	−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
$633$	11.5376	−	35.1948i	0.458578	−	1.39887i
$634$	0.884900	−	1.53269i	0.0351439	−	0.0608709i
$635$	−29.1772			−1.15786
$636$	20.5182	+	22.9083i	0.813601	+	0.908374i
$637$		0			0
$638$	−0.698568			−0.0276566
$639$	4.07878	−	36.9426i	0.161354	−	1.46143i
$640$	−2.89714	−	5.01799i	−0.114519	−	0.198353i
$641$	43.0814			1.70161			0.850806	−	0.525480i	$-0.176114\pi$
$641$	43.0814			1.70161			0.850806	+	0.525480i	$0.176114\pi$
$642$	1.33917	+	1.49516i	0.0528528	+	0.0590094i
$643$	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
$645$	50.8604	−	10.6714i	2.00263	−	0.420187i
$646$	0.425709	+	0.737350i	0.0167493	+	0.0290107i
$647$	1.94403	+	3.36716i	0.0764278	+	0.132377i	0.901706	−	0.432349i	$-0.142315\pi$
$647$	1.94403	+	3.36716i	0.0764278	+	0.132377i	−0.825278	+	0.564726i	$0.808982\pi$
$648$	2.39937	+	0.536359i	0.0942561	+	0.0210702i
$649$	−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	$-0.404506\pi$
$653$	15.1035			0.591044			0.295522	+	0.955336i	$0.404506\pi$
$654$	−0.985170	+	0.206706i	−0.0385232	+	0.00808286i
$655$	11.8630			0.463525
$656$	−14.6823	+	25.4305i	−0.573248	+	0.992895i
$657$	6.03964	−	2.65116i	0.235629	−	0.103432i
$658$		0			0
$659$	−7.13002	+	12.3496i	−0.277746	+	0.481070i	−0.970824	−	0.239792i	$-0.922921\pi$
$659$	−7.13002	+	12.3496i	−0.277746	+	0.481070i	0.693078	+	0.720862i	$0.256254\pi$
$660$	−14.4079	+	3.02305i	−0.560829	+	0.117672i
$661$	−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
$663$	−58.3089	+	12.2343i	−2.26453	+	0.475139i
$664$	0.933832	−	1.61744i	0.0362397	−	0.0627690i
$665$		0			0
$666$	−0.0952089	+	0.862333i	−0.00368927	+	0.0334147i
$667$	9.80197	−	16.9775i	0.379534	−	0.657372i
$668$	9.57561			0.370492
$669$	12.1503	−	2.54936i	0.469758	−	0.0985638i
$670$	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
$675$	8.86027	−	6.33150i	0.341032	−	0.243699i
$676$	14.5683	+	25.2330i	0.560318	+	0.970500i
$677$	18.4913	+	32.0278i	0.710678	+	1.23093i	0.964603	+	0.263706i	$0.0849449\pi$
$677$	18.4913	+	32.0278i	0.710678	+	1.23093i	−0.253925	+	0.967224i	$0.581722\pi$
$678$	0.452477	−	0.0949379i	0.0173773	−	0.00364607i
$679$		0			0
$680$	2.38215	+	4.12601i	0.0913513	+	0.158225i
$681$	15.9341	+	17.7901i	0.610594	+	0.681719i
$682$	−0.734671			−0.0281320
$683$	−6.56800	−	11.3761i	−0.251317	−	0.435294i	0.712571	−	0.701600i	$-0.247530\pi$
$683$	−6.56800	−	11.3761i	−0.251317	−	0.435294i	−0.963889	+	0.266305i	$0.914197\pi$
$684$	−10.4248	+	4.57608i	−0.398602	+	0.174971i
$685$	52.0398			1.98834
$686$		0			0
$687$	30.5010	+	34.0539i	1.16369	+	1.29924i
$688$	−44.7384			−1.70564
$689$	−23.3758	+	40.4881i	−0.890547	+	1.54247i
$690$	−0.301530	+	0.919803i	−0.0114791	+	0.0350163i
$691$	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
$696$	−2.95858	+	0.620763i	−0.112145	+	0.0235300i
$697$	24.2016	−	41.9184i	0.916702	−	1.58777i
$698$	1.86401			0.0705536
$699$	−21.4344	+	4.49731i	−0.810722	+	0.170104i
$700$		0			0
$701$	−30.4627			−1.15056			−0.575281	−	0.817956i	$-0.695107\pi$
$701$	−30.4627			−1.15056			−0.575281	+	0.817956i	$0.695107\pi$
$702$	0.180504	+	1.85783i	0.00681270	+	0.0701193i
$703$	−4.02217	−	6.96660i	−0.151699	−	0.262750i
$704$	12.6139			0.475406
$705$	5.46036	−	16.6565i	0.205649	−	0.627322i
$706$	0.826969	+	1.43235i	0.0311234	+	0.0539073i
$707$		0			0
$708$	−11.7269	+	35.7724i	−0.440725	+	1.34441i
$709$	−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
$711$	2.23484	−	0.981005i	0.0838129	−	0.0367906i
$712$	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
$717$	8.32677	−	25.4004i	0.310969	−	0.948595i
$718$	−1.43842			−0.0536815
$719$	7.49790	−	12.9867i	0.279624	−	0.484324i	−0.691667	−	0.722217i	$-0.743123\pi$
$719$	7.49790	−	12.9867i	0.279624	−	0.484324i	0.971291	+	0.237893i	$0.0764567\pi$
$720$	−29.0646	+	12.7582i	−1.08317	+	0.475471i
$721$		0			0
$722$	0.525886	−	0.910861i	0.0195715	−	0.0338987i
$723$	−1.36346	−	1.52228i	−0.0507076	−	0.0566143i
$724$	−14.4008	+	24.9429i	−0.535200	+	0.926994i
$725$	−6.69501	+	11.5961i	−0.248646	+	0.430668i
$726$	0.311465	−	0.950107i	0.0115595	−	0.0352618i
$727$	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
$729$	8.74633	−	25.5441i	0.323938	−	0.946078i
$730$	0.200223	−	0.346796i	0.00741059	−	0.0128355i
$731$	73.7447			2.72754
$732$	6.25756	+	6.98648i	0.231286	+	0.258228i
$733$	−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
$738$	−1.22215	−	0.897772i	−0.0449880	−	0.0330474i
$739$	−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
$741$	−11.5471	−	12.8922i	−0.424194	−	0.473606i
$742$		0			0
$743$	−0.169513	−	0.293606i	−0.00621884	−	0.0107713i	0.862899	−	0.505376i	$-0.168646\pi$
$743$	−0.169513	−	0.293606i	−0.00621884	−	0.0107713i	−0.869118	+	0.494605i	$0.835313\pi$
$744$	−3.11149	+	0.652846i	−0.114073	+	0.0239345i
$745$	23.4755			0.860075
$746$	−0.0385841	−	0.0668297i	−0.00141267	−	0.00244681i
$747$	−16.5299	−	12.1426i	−0.604798	−	0.444275i
$748$	−20.8907			−0.763839
$749$		0			0
$750$	−0.285398	+	0.870593i	−0.0104213	+	0.0317896i
$751$	−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
$753$	−6.41318	−	7.16022i	−0.233709	−	0.260933i
$754$	−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
$759$	−5.67015	−	6.33064i	−0.205814	−	0.229788i
$760$	−0.692005	+	1.19859i	−0.0251017	+	0.0434773i
$761$	−33.0357			−1.19754			−0.598771	−	0.800920i	$-0.704344\pi$
$761$	−33.0357			−1.19754			−0.598771	+	0.800920i	$0.704344\pi$
$762$	−0.404079	+	1.23262i	−0.0146382	+	0.0446532i
$763$		0			0
$764$	−5.66934			−0.205110
$765$	47.9087	−	21.0300i	1.73214	−	0.760342i
$766$	0.787671	+	1.36429i	0.0284597	+	0.0492937i
$767$	−57.2285			−2.06640
$768$	26.4905	−	5.55818i	0.955893	−	0.200563i
$769$	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
$771$	−11.3603	−	12.6836i	−0.409132	−	0.456790i
$772$	8.80822	+	15.2563i	0.317015	+	0.549086i
$773$	3.36486	+	5.82811i	0.121026	+	0.209623i	0.920172	−	0.391513i	$-0.128048\pi$
$773$	3.36486	+	5.82811i	0.121026	+	0.209623i	−0.799147	+	0.601136i	$0.794715\pi$
$774$	0.253547	−	2.29644i	0.00911355	−	0.0825439i
$775$	−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
$780$	−32.2694	−	36.0283i	−1.15543	−	1.29002i
$781$	19.8116			0.708916
$782$	−0.686792	+	1.18956i	−0.0245596	+	0.0425385i
$783$	3.21039	+	33.0428i	0.114730	+	1.18085i
$784$		0			0
$785$	−5.42473	+	9.39590i	−0.193617	+	0.335354i
$786$	0.164292	−	0.501164i	0.00586010	−	0.0178759i
$787$	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
$789$	−13.7888	−	15.3950i	−0.490894	−	0.548076i
$790$	0.0740881	−	0.128324i	0.00263594	−	0.00456558i
$791$		0			0
$792$	−0.143820	+	1.30261i	−0.00511041	+	0.0462864i
$793$	−7.12905	+	12.3479i	−0.253160	+	0.438486i
$794$	1.12855			0.0400507
$795$	12.7895	−	39.0138i	0.453598	−	1.38368i
$796$	22.7767			0.807300
$797$	−11.4913	−	19.9035i	−0.407042	−	0.705017i	0.587515	−	0.809213i	$-0.300106\pi$
$797$	−11.4913	−	19.9035i	−0.407042	−	0.705017i	−0.994557	+	0.104196i	$0.966773\pi$
$798$		0			0
$799$	12.4370	−	21.5415i	0.439989	−	0.762084i
$800$	−0.857104	+	1.48455i	−0.0303032	+	0.0524867i
$801$	−1.13774	−	0.835762i	−0.0401999	−	0.0295302i
$802$	−0.740489	−	1.28256i	−0.0261476	−	0.0452889i
$803$	1.75795	+	3.04485i	0.0620366	+	0.107451i
$804$	−3.57998	+	10.9205i	−0.126256	+	0.385138i
$805$		0			0
$806$	−1.20685	−	2.09033i	−0.0425095	−	0.0736287i
$807$	−16.1675	+	49.3182i	−0.569123	+	1.73608i
$808$	0.503977			0.0177299
$809$	8.23894	+	14.2703i	0.289666	+	0.501716i	0.973730	−	0.227706i	$-0.0731225\pi$
$809$	8.23894	+	14.2703i	0.289666	+	0.501716i	−0.684064	+	0.729422i	$0.739789\pi$
$810$	−0.490166	−	1.56420i	−0.0172227	−	0.0549605i
$811$	−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
$813$	−12.0296	+	2.52402i	−0.421895	+	0.0885212i
$814$	−0.462453			−0.0162090
$815$	−16.1456	+	27.9649i	−0.565554	+	0.979569i
$816$	−44.0827	+	9.24933i	−1.54320	+	0.323791i
$817$	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	0.999940	−	0.0109361i	$-0.00348114\pi$
$821$	14.0543	+	24.3428i	0.490499	+	0.849569i	−0.509441	+	0.860506i	$0.670148\pi$
$822$	0.720706	−	2.19848i	0.0251375	−	0.0766807i
$823$	−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
$825$	3.87287	+	4.32400i	0.134836	+	0.150542i
$826$		0			0
$827$	−17.7998			−0.618961			−0.309480	−	0.950906i	$-0.600155\pi$
$827$	−17.7998			−0.618961			−0.309480	+	0.950906i	$0.600155\pi$
$828$	−14.8026	−	10.8737i	−0.514425	−	0.377889i
$829$	−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
$831$	11.3519	+	12.6743i	0.393795	+	0.439666i
$832$	20.7210	+	35.8899i	0.718373	+	1.24426i
$833$		0			0
$834$	0.304918	−	0.0639772i	0.0105584	−	0.00221535i
$835$	−6.39180	−	11.0709i	−0.221197	−	0.383125i
$836$	−3.03433	−	5.25561i	−0.104944	−	0.181769i
$837$	3.37632	+	34.7505i	0.116703	+	1.20115i
$838$	0.738994	−	1.27998i	0.0255281	−	0.0442160i
$839$	3.69822	−	6.40550i	0.127677	−	0.221142i	−0.795099	−	0.606479i	$-0.792581\pi$
$839$	3.69822	−	6.40550i	0.127677	−	0.221142i	0.922776	+	0.385337i	$0.125915\pi$
$840$		0			0
$841$	−5.90986	−	10.2362i	−0.203788	−	0.352971i
$842$	−1.86274			−0.0641942
$843$	−40.4761	+	8.49261i	−1.39407	+	0.292501i
$844$	42.6675			1.46868
$845$	19.4489	−	33.6865i	0.669062	−	1.15885i
$846$	−0.628052	−	0.461357i	−0.0215929	−	0.0158618i
$847$		0			0
$848$	−17.6725	+	30.6097i	−0.606878	+	1.05114i
$849$	−5.11246	+	1.07269i	−0.175459	+	0.0368145i
$850$	0.469098	−	0.812501i	0.0160899	−	0.0278686i
$851$	6.48892	−	11.2391i	0.222437	−	0.385273i
$852$	41.9041	−	8.79223i	1.43561	−	0.301217i
$853$	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
$855$	12.2493	+	8.99815i	0.418917	+	0.307730i
$856$	−2.31502	+	4.00973i	−0.0791257	+	0.137050i
$857$	−3.81530			−0.130328			−0.0651640	−	0.997875i	$-0.520757\pi$
$857$	−3.81530			−0.130328			−0.0651640	+	0.997875i	$0.520757\pi$
$858$	−0.973762	+	0.204313i	−0.0332437	+	0.00697512i
$859$	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	−0.998629	−	0.0523375i	$-0.983333\pi$
$863$	−13.3368	+	23.1000i	−0.453989	+	0.786332i	0.544640	+	0.838670i	$0.316666\pi$
$864$	0.410999	+	4.23018i	0.0139825	+	0.143914i
$865$	6.70171	+	11.6077i	0.227865	+	0.394674i
$866$	−0.116737	−	0.202195i	−0.00396690	−	0.00687087i
$867$	43.8464	−	9.19976i	1.48910	−	0.312440i
$868$		0			0
$869$	0.650490	+	1.12668i	0.0220664	+	0.0382200i
$870$	1.34471	+	1.50135i	0.0455900	+	0.0509006i
$871$	−17.4706			−0.591970
$872$	−1.16099	−	2.01089i	−0.0393160	−	0.0680974i
$873$	12.4575	+	9.15106i	0.421621	+	0.309717i
$874$	−0.399020			−0.0134971
$875$		0			0
$876$	5.06956	+	5.66009i	0.171285	+	0.191237i
$877$	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
$879$	−9.20379	+	28.0757i	−0.310436	+	0.946969i
$880$	−8.45978	−	14.6528i	−0.285179	−	0.493945i
$881$	−4.67326			−0.157446			−0.0787231	−	0.996897i	$-0.525084\pi$
$881$	−4.67326			−0.157446			−0.0787231	+	0.996897i	$0.525084\pi$
$882$		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
$885$	49.1864	−	10.3202i	1.65338	−	0.346909i
$886$	−0.980867	+	1.69891i	−0.0329529	+	0.0570761i
$887$	29.1032			0.977191			0.488596	−	0.872510i	$-0.337509\pi$
$887$	29.1032			0.977191			0.488596	+	0.872510i	$0.337509\pi$
$888$	−1.95858	+	0.410946i	−0.0657258	+	0.0137905i
$889$		0			0
$890$	−0.0857071			−0.00287291
$891$	14.0455	+	3.13975i	0.470541	+	0.105186i
$892$	7.15098	+	12.3859i	0.239433	+	0.414710i
$893$	7.22579			0.241802
$894$	0.325115	−	0.991746i	0.0108735	−	0.0331690i
$895$	−21.8403	−	37.8285i	−0.730041	−	1.26447i
$896$		0			0
$897$	8.69788	−	26.5324i	0.290414	−	0.885892i
$898$	−0.0156482	−	0.0271035i	−0.000522187	−	0.000904455i
$899$	−21.4647	−	37.1779i	−0.715887	−	1.23995i
$900$	10.1106	+	7.42706i	0.337019	+	0.247569i
$901$	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
$906$	−0.172068	+	0.524886i	−0.00571659	+	0.0174382i
$907$	−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
$909$	0.607380	−	5.50121i	0.0201455	−	0.182464i
$910$		0			0
$911$	28.8619	−	49.9903i	0.956239	−	1.65625i	0.224731	−	0.974421i	$-0.427850\pi$
$911$	28.8619	−	49.9903i	0.956239	−	1.65625i	0.731508	−	0.681833i	$-0.238817\pi$
$912$	−8.72983	−	9.74673i	−0.289074	−	0.322746i
$913$	5.46649	−	9.46824i	0.180914	−	0.313353i
$914$	−0.691296	+	1.19736i	−0.0228660	+	0.0396051i
$915$	3.90050	−	11.8983i	0.128946	−	0.393344i
$916$	−26.3326	+	45.6094i	−0.870054	+	1.50698i
$917$		0			0
$918$	−0.224942	−	2.31520i	−0.00742419	−	0.0764130i
$919$	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
$921$	−26.8302	−	29.9555i	−0.884085	−	0.987068i
$922$	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
$927$	−1.70473	+	15.4402i	−0.0559908	+	0.507124i
$928$	−2.61290	−	4.52567i	−0.0857725	−	0.148562i
$929$	25.1412	+	43.5458i	0.824856	+	1.42869i	0.902029	+	0.431675i	$0.142077\pi$
$929$	25.1412	+	43.5458i	0.824856	+	1.42869i	−0.0771732	+	0.997018i	$0.524589\pi$
$930$	1.41421	+	1.57895i	0.0463738	+	0.0517757i
$931$		0			0
$932$	−12.6150	−	21.8499i	−0.413219	−	0.715717i
$933$	3.03588	−	0.636983i	0.0993904	−	0.0208539i
$934$	−1.86289			−0.0609557
$935$	13.9447	+	24.1529i	0.456040	+	0.789885i
$936$	−3.94253	+	1.73061i	−0.128866	+	0.0565669i
$937$	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
$939$	−2.48688	+	7.58609i	−0.0811561	+	0.247563i
$940$	20.1931			0.658627
$941$	8.51660	−	14.7512i	0.277633	−	0.480875i	−0.693163	−	0.720781i	$-0.743783\pi$
$941$	8.51660	−	14.7512i	0.277633	−	0.480875i	0.970796	+	0.239906i	$0.0771166\pi$
$942$	0.321812	+	0.359298i	0.0104852	+	0.0117066i
$943$	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	$-0.995608\pi$
$947$	−15.7530	−	27.2849i	−0.511903	−	0.886641i	0.488002	−	0.872842i	$-0.337726\pi$
$948$	1.87588	+	2.09439i	0.0609257	+	0.0680227i
$949$	−5.77559	+	10.0036i	−0.187484	+	0.324731i
$950$	0.272542			0.00884243
$951$	13.9658	−	42.6019i	0.452871	−	1.38146i
$952$		0			0
$953$	16.0677			0.520485			0.260242	−	0.965543i	$-0.416197\pi$
$953$	16.0677			0.520485			0.260242	+	0.965543i	$0.416197\pi$
$954$	−1.47106	−	1.08061i	−0.0476272	−	0.0349862i
$955$	3.78433	+	6.55465i	0.122458	+	0.212104i
$956$	30.7935			0.995932
$957$	−17.3190	+	3.63384i	−0.559844	+	0.117465i
$958$	−0.701705	−	1.21539i	−0.0226711	−	0.0392674i
$959$		0			0
$960$	−24.2813	−	27.1097i	−0.783675	−	0.874962i
$961$	−7.07402	−	12.2526i	−0.228194	−	0.395244i
$962$	−0.759676	−	1.31580i	−0.0244929	−	0.0424230i
$963$	40.9786	+	30.1022i	1.32052	+	0.970030i
$964$	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
$969$	14.3898	+	16.0660i	0.462268	+	0.516116i
$970$	0.938438			0.0301314
$971$	28.2839	−	48.9892i	0.907674	−	1.57214i	0.0903867	−	0.995907i	$-0.471190\pi$
$971$	28.2839	−	48.9892i	0.907674	−	1.57214i	0.817287	−	0.576231i	$-0.195477\pi$
$972$	31.1014	+	0.407712i	0.997577	+	0.0130774i
$973$		0			0
$974$	−0.883558	+	1.53037i	−0.0283110	+	0.0490361i
$975$	−5.94089	+	18.1224i	−0.190261	+	0.580381i
$976$	−5.38969	+	9.33522i	−0.172520	+	0.298813i
$977$	−26.8780	+	46.5541i	−0.859904	+	1.48940i	0.0121160	+	0.999927i	$0.496143\pi$
$977$	−26.8780	+	46.5541i	−0.859904	+	1.48940i	−0.872020	+	0.489471i	$0.837190\pi$
$978$	0.957806	+	1.06938i	0.0306273	+	0.0341949i
$979$	0.376252	−	0.651687i	0.0120251	−	0.0208280i
$980$		0			0
$981$	−23.3493	+	10.2494i	−0.745485	+	0.327238i
$982$	−0.533847	+	0.924650i	−0.0170357	+	0.0295068i
$983$	27.4102			0.874249			0.437125	−	0.899401i	$-0.355997\pi$
$983$	27.4102			0.874249			0.437125	+	0.899401i	$0.355997\pi$
$984$	1.08966	−	3.32397i	0.0347372	−	0.105964i
$985$	−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
$990$	0.800077	−	0.351202i	0.0254281	−	0.0111619i
$991$	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
$993$	−0.0870420	+	0.265517i	−0.00276220	+	0.00842594i
$994$		0			0
$995$	−15.2037	−	26.3335i	−0.481988	−	0.834828i
$996$	7.36039	−	22.4525i	0.233223	−	0.711435i
$997$	−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
$999$	2.12529	+	21.8744i	0.0672411	+	0.692075i

Twists

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

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

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0341870 - 0.0592136i) q^{2} +(-1.15559 - 1.29020i) q^{3} +(0.997662 - 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 + 2.98188i) q^{9} +O(q^{10})\)	\(q+(-0.0341870 - 0.0592136i) q^{2} +(-1.15559 - 1.29020i) q^{3} +(0.997662 - 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 + 2.98188i) q^{9} +(0.0910670 + 0.157733i) q^{10} -1.59913 q^{11} +(-3.38235 + 0.709679i) q^{12} +(-2.62690 - 4.54992i) q^{13} +(3.07825 + 3.43682i) q^{15} +(-1.98599 - 3.43983i) q^{16} +(3.27360 + 5.67005i) q^{17} +(0.187823 - 0.0824469i) q^{18} +(-0.950968 + 1.64713i) q^{19} +(-2.65756 + 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} -3.06837 q^{23} +(0.315680 + 0.352452i) q^{24} +2.09578 q^{25} +(-0.179612 + 0.311096i) q^{26} +(4.22767 - 3.02106i) q^{27} +(-3.19452 + 5.53306i) q^{29} +(0.0982704 - 0.299769i) q^{30} +(-3.35961 + 5.81902i) q^{31} +(-0.408966 + 0.708350i) q^{32} +(1.84793 + 2.06319i) q^{33} +(0.223829 - 0.387684i) q^{34} +(4.82424 + 3.54381i) q^{36} +(-2.11477 + 3.66290i) q^{37} +0.130043 q^{38} +(-2.83469 + 8.64707i) q^{39} +0.727684 q^{40} +(-3.69648 - 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(-1.59539 + 2.76329i) q^{44} +(0.876986 - 7.94311i) q^{45} +(0.104898 + 0.181689i) q^{46} +(-1.89959 - 3.29018i) q^{47} +(-2.14308 + 6.53735i) q^{48} +(-0.0716485 - 0.124099i) q^{50} +(3.53255 - 10.7758i) q^{51} -10.4830 q^{52} +(-4.44931 - 7.70643i) q^{53} +(-0.323419 - 0.147054i) q^{54} +4.25974 q^{55} +(3.22405 - 0.676463i) q^{57} +0.436843 q^{58} +(5.44639 - 9.43343i) q^{59} +(9.00989 - 1.89044i) q^{60} +(-1.35693 - 2.35027i) q^{61} +0.459420 q^{62} -7.88802 q^{64} +(6.99751 + 12.1200i) q^{65} +(0.0589937 - 0.179957i) q^{66} +(1.66267 - 2.87982i) q^{67} +13.0638 q^{68} +(3.54578 + 3.95881i) q^{69} -12.3890 q^{71} +(0.0899364 - 0.814579i) q^{72} +(-1.09932 - 1.90407i) q^{73} +0.289191 q^{74} +(-2.42187 - 2.70398i) q^{75} +(1.89749 + 3.28655i) q^{76} +(0.608933 - 0.127765i) q^{78} +(-0.406778 - 0.704560i) q^{79} +(5.29025 + 9.16298i) q^{80} +(-8.78322 - 1.96342i) q^{81} +(-0.252743 + 0.437764i) q^{82} +(-3.41842 + 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} -0.770132 q^{86} +(10.8303 - 2.27239i) q^{87} +0.436843 q^{88} +(-0.235286 + 0.407527i) q^{89} +(-0.500321 + 0.219621i) q^{90} +(-3.06120 + 5.30216i) q^{92} +(11.3900 - 2.38983i) q^{93} +(-0.129882 + 0.224963i) q^{94} +(2.53318 - 4.38760i) q^{95} +(1.38651 - 0.290914i) q^{96} +(2.57623 - 4.46216i) q^{97} +(0.526472 - 4.76840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Introduction

L-functions

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