LMFDB - Embedded newform 343.2.k.a.100.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(2,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

chi = DirichletCharacter(H, H._module([194]))

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

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

chi := DirichletCharacter("343.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.k (of order $147$, degree $84$, 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$2688$
Relative dimension:	$32$ over $\Q(\zeta_{147})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{147}]$

Embedding invariants

Embedding label			100.18
Character	$\chi$	$=$	343.100
Dual form			343.2.k.a.319.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0410343 + 0.0562257i) q^{2} +(0.0464488 - 0.868538i) q^{3} +(0.608421 - 1.90012i) q^{4} +(2.18704 - 0.0467471i) q^{5} +(0.0507401 - 0.0330282i) q^{6} +(0.491678 + 2.59966i) q^{7} +(0.263924 - 0.0876287i) q^{8} +(2.23069 + 0.239276i) q^{9} +(0.0923718 + 0.121049i) q^{10} +(-0.0538109 + 0.455689i) q^{11} +(-1.62207 - 0.616695i) q^{12} +(0.380637 + 0.729611i) q^{13} +(-0.125992 + 0.134320i) q^{14} +(0.0609836 - 1.90169i) q^{15} +(-3.23240 - 2.30652i) q^{16} +(-5.21134 + 1.24819i) q^{17} +(0.0780812 + 0.135241i) q^{18} +(1.89029 - 3.27408i) q^{19} +(1.24181 - 4.18408i) q^{20} +(2.28074 - 0.306290i) q^{21} +(-0.0278295 + 0.0156733i) q^{22} +(6.02513 - 4.70044i) q^{23} +(-0.0638499 - 0.233298i) q^{24} +(-0.214492 + 0.00917355i) q^{25} +(-0.0254037 + 0.0513406i) q^{26} +(0.727883 - 4.50221i) q^{27} +(5.23883 + 0.647440i) q^{28} +(-8.89005 + 3.59918i) q^{29} +(0.109427 - 0.0746058i) q^{30} +(-5.54910 + 5.14881i) q^{31} +(-0.00889661 - 0.832541i) q^{32} +(0.393283 + 0.0679030i) q^{33} +(-0.284024 - 0.241793i) q^{34} +(1.19684 + 5.66257i) q^{35} +(1.81185 - 4.09300i) q^{36} +(-1.82345 - 1.92358i) q^{37} +(0.261654 - 0.0280665i) q^{38} +(0.651374 - 0.296708i) q^{39} +(0.573115 - 0.203985i) q^{40} +(-0.0588253 + 0.159847i) q^{41} +(0.110810 + 0.115668i) q^{42} +(11.4522 + 3.80238i) q^{43} +(0.833125 + 0.379498i) q^{44} +(4.88978 + 0.419027i) q^{45} +(0.511522 + 0.145888i) q^{46} +(3.83521 + 2.05325i) q^{47} +(-2.15344 + 2.70033i) q^{48} +(-6.51651 + 2.55640i) q^{49} +(-0.00931729 - 0.0116835i) q^{50} +(0.842038 + 4.58423i) q^{51} +(1.61794 - 0.279348i) q^{52} +(-4.99262 - 2.95407i) q^{53} +(0.283008 - 0.143819i) q^{54} +(-0.0963842 + 0.999123i) q^{55} +(0.357571 + 0.643028i) q^{56} +(-2.75586 - 1.79387i) q^{57} +(-0.567163 - 0.352160i) q^{58} +(-6.06431 + 7.27967i) q^{59} +(-3.57635 - 1.27291i) q^{60} +(-1.16482 + 0.0998189i) q^{61} +(-0.517199 - 0.100724i) q^{62} +(0.474744 + 5.91669i) q^{63} +(-6.31831 + 4.71547i) q^{64} +(0.866575 + 1.57789i) q^{65} +(0.0123202 + 0.0248990i) q^{66} +(9.50150 - 2.93082i) q^{67} +(-0.798978 + 10.6616i) q^{68} +(-3.80265 - 5.45138i) q^{69} +(-0.269271 + 0.299653i) q^{70} +(-13.0583 - 5.28670i) q^{71} +(0.609699 - 0.132322i) q^{72} +(-3.13506 + 1.67842i) q^{73} +(0.0333304 - 0.181457i) q^{74} +(-0.00199531 + 0.186720i) q^{75} +(-5.07106 - 5.58380i) q^{76} +(-1.21110 + 0.0841620i) q^{77} +(0.0434113 + 0.0244488i) q^{78} +(10.5440 - 1.58926i) q^{79} +(-7.17721 - 4.89334i) q^{80} +(2.70081 + 0.586151i) q^{81} +(-0.0114014 + 0.00325172i) q^{82} +(-2.42532 + 0.472331i) q^{83} +(0.805664 - 4.52005i) q^{84} +(-11.3391 + 2.97345i) q^{85} +(0.256139 + 0.799934i) q^{86} +(2.71309 + 7.88852i) q^{87} +(0.0257295 + 0.124983i) q^{88} +(-8.79623 + 8.89073i) q^{89} +(0.177088 + 0.292126i) q^{90} +(-1.70959 + 1.34826i) q^{91} +(-5.26560 - 14.3083i) q^{92} +(4.21419 + 5.05876i) q^{93} +(0.0419291 + 0.299891i) q^{94} +(3.98108 - 7.24890i) q^{95} +(-0.723506 - 0.0309435i) q^{96} +(0.0543670 + 0.238197i) q^{97} +(-0.411135 - 0.261495i) q^{98} +(-0.229071 + 1.00362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 84 q^{8} - 98 q^{9} - 84 q^{10} - 91 q^{11} - 119 q^{12} - 84 q^{13} - 119 q^{14} - 98 q^{15} - 84 q^{16} - 91 q^{17} - 42 q^{18}+ \cdots - 182 q^{99}+O(q^{100}) $ 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 84 * q^8 - 98 * q^9 - 84 * q^10 - 91 * q^11 - 119 * q^12 - 84 * q^13 - 119 * q^14 - 98 * q^15 - 84 * q^16 - 91 * q^17 - 42 * q^18 + 126 * q^19 + 84 * q^20 - 84 * q^21 - 98 * q^22 - 105 * q^23 - 126 * q^24 - 84 * q^25 - 98 * q^26 - 105 * q^27 - 126 * q^28 - 126 * q^29 - 91 * q^30 - 133 * q^31 - 126 * q^32 - 84 * q^33 - 168 * q^34 - 98 * q^35 - 42 * q^36 - 105 * q^37 + 28 * q^38 - 77 * q^39 - 56 * q^40 - 56 * q^41 - 126 * q^42 - 84 * q^43 - 28 * q^44 - 105 * q^45 - 119 * q^47 - 14 * q^48 - 28 * q^49 - 196 * q^50 - 28 * q^51 - 28 * q^52 - 91 * q^53 + 126 * q^54 + 301 * q^55 - 70 * q^56 + 21 * q^57 + 308 * q^58 + 28 * q^59 - 112 * q^60 - 105 * q^61 - 70 * q^62 - 133 * q^63 - 140 * q^64 - 84 * q^65 - 252 * q^66 - 91 * q^67 - 175 * q^68 - 168 * q^69 - 168 * q^70 - 161 * q^71 - 21 * q^72 + 42 * q^73 - 210 * q^75 - 21 * q^76 + 42 * q^77 + 280 * q^78 - 91 * q^79 - 168 * q^80 - 126 * q^81 - 84 * q^82 - 98 * q^83 - 14 * q^84 - 140 * q^85 - 28 * q^86 + 14 * q^87 + 28 * q^88 - 84 * q^89 + 329 * q^90 + 406 * q^91 + 336 * q^92 + 14 * q^93 - 112 * q^94 + 238 * q^95 + 560 * q^96 + 196 * q^97 + 63 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{76}{147}\right)$

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 $

$2$	0.0410343	+	0.0562257i	0.0290156	+	0.0397576i	0.822022	−	0.569456i	$-0.192846\pi$
$2$	0.0410343	+	0.0562257i	0.0290156	+	0.0397576i	−0.793007	+	0.609213i	$0.791485\pi$
$3$	0.0464488	−	0.868538i	0.0268172	−	0.501450i	−0.953176	−	0.302417i	$-0.902206\pi$
$3$	0.0464488	−	0.868538i	0.0268172	−	0.501450i	0.979993	−	0.199033i	$-0.0637801\pi$
$4$	0.608421	−	1.90012i	0.304210	−	0.950061i
$5$	2.18704	−	0.0467471i	0.978072	−	0.0209059i	0.470397	−	0.882455i	$-0.344111\pi$
$5$	2.18704	−	0.0467471i	0.978072	−	0.0209059i	0.507675	+	0.861549i	$0.330505\pi$
$6$	0.0507401	−	0.0330282i	0.0207146	−	0.0134837i
$7$	0.491678	+	2.59966i	0.185837	+	0.982581i
$7$	0.491678	+	2.59966i	0.185837	+	0.982581i
$8$	0.263924	−	0.0876287i	0.0933112	−	0.0309814i
$9$	2.23069	+	0.239276i	0.743563	+	0.0797586i
$10$	0.0923718	+	0.121049i	0.0292105	+	0.0382792i
$11$	−0.0538109	+	0.455689i	−0.0162246	+	0.137395i	−0.998833	−	0.0482935i	$-0.984622\pi$
$11$	−0.0538109	+	0.455689i	−0.0162246	+	0.137395i	0.982609	+	0.185689i	$0.0594516\pi$
$12$	−1.62207	−	0.616695i	−0.468251	−	0.178024i
$13$	0.380637	+	0.729611i	0.105570	+	0.202358i	0.933592	−	0.358338i	$-0.116656\pi$
$13$	0.380637	+	0.729611i	0.105570	+	0.202358i	−0.828022	+	0.560695i	$0.810534\pi$
$14$	−0.125992	+	0.134320i	−0.0336729	+	0.0358986i
$15$	0.0609836	−	1.90169i	0.0157459	−	0.491015i
$16$	−3.23240	−	2.30652i	−0.808101	−	0.576630i
$17$	−5.21134	+	1.24819i	−1.26394	+	0.302730i	−0.809008	−	0.587798i	$-0.799995\pi$
$17$	−5.21134	+	1.24819i	−1.26394	+	0.302730i	−0.454929	+	0.890528i	$0.650335\pi$
$18$	0.0780812	+	0.135241i	0.0184039	+	0.0318765i
$19$	1.89029	−	3.27408i	0.433663	−	0.751126i	−0.563523	−	0.826100i	$-0.690554\pi$
$19$	1.89029	−	3.27408i	0.433663	−	0.751126i	0.997185	+	0.0749749i	$0.0238877\pi$
$20$	1.24181	−	4.18408i	0.277678	−	0.935589i
$21$	2.28074	−	0.306290i	0.497699	−	0.0668379i
$22$	−0.0278295	+	0.0156733i	−0.00593327	+	0.00334156i
$23$	6.02513	−	4.70044i	1.25633	−	0.980110i	0.256419	−	0.966566i	$-0.417457\pi$
$23$	6.02513	−	4.70044i	1.25633	−	0.980110i	0.999908	−	0.0135439i	$-0.00431128\pi$
$24$	−0.0638499	−	0.233298i	−0.0130333	−	0.0476218i
$25$	−0.214492	+	0.00917355i	−0.0428983	+	0.00183471i
$26$	−0.0254037	+	0.0513406i	−0.00498208	+	0.0100687i
$27$	0.727883	−	4.50221i	0.140081	−	0.866451i
$28$	5.23883	+	0.647440i	0.990045	+	0.122355i
$29$	−8.89005	+	3.59918i	−1.65084	+	0.668351i	−0.996160	−	0.0875546i	$-0.972095\pi$
$29$	−8.89005	+	3.59918i	−1.65084	+	0.668351i	−0.654680	+	0.755906i	$0.727197\pi$
$30$	0.109427	−	0.0746058i	0.0199785	−	0.0136211i
$31$	−5.54910	+	5.14881i	−0.996648	+	0.924754i	−0.997165	−	0.0752456i	$-0.976026\pi$
$31$	−5.54910	+	5.14881i	−0.996648	+	0.924754i	0.000517002		1.00000i	$0.499835\pi$
$32$	−0.00889661	−	0.832541i	−0.00157271	−	0.147174i
$33$	0.393283	+	0.0679030i	0.0684619	+	0.0118204i
$34$	−0.284024	−	0.241793i	−0.0487097	−	0.0414672i
$35$	1.19684	+	5.66257i	0.202304	+	0.957150i
$36$	1.81185	−	4.09300i	0.301975	−	0.682167i
$37$	−1.82345	−	1.92358i	−0.299774	−	0.316234i	0.558421	−	0.829557i	$-0.311407\pi$
$37$	−1.82345	−	1.92358i	−0.299774	−	0.316234i	−0.858195	+	0.513324i	$0.828414\pi$
$38$	0.261654	−	0.0280665i	0.0424459	−	0.00455298i
$39$	0.651374	−	0.296708i	0.104303	−	0.0475114i
$40$	0.573115	−	0.203985i	0.0906174	−	0.0322528i
$41$	−0.0588253	+	0.159847i	−0.00918696	+	0.0249640i	−0.942979	−	0.332853i	$-0.891989\pi$
$41$	−0.0588253	+	0.159847i	−0.00918696	+	0.0249640i	0.933792	+	0.357816i	$0.116479\pi$
$42$	0.110810	+	0.115668i	0.0170984	+	0.0178480i
$43$	11.4522	+	3.80238i	1.74644	+	0.579857i	0.996647	−	0.0818174i	$-0.0260724\pi$
$43$	11.4522	+	3.80238i	1.74644	+	0.579857i	0.749791	+	0.661675i	$0.230154\pi$
$44$	0.833125	+	0.379498i	0.125598	+	0.0572114i
$45$	4.88978	+	0.419027i	0.728926	+	0.0624648i
$46$	0.511522	+	0.145888i	0.0754199	+	0.0215101i
$47$	3.83521	+	2.05325i	0.559422	+	0.299498i	0.727311	−	0.686308i	$-0.240770\pi$
$47$	3.83521	+	2.05325i	0.559422	+	0.299498i	−0.167889	+	0.985806i	$0.553695\pi$
$48$	−2.15344	+	2.70033i	−0.310822	+	0.389759i
$49$	−6.51651	+	2.55640i	−0.930929	+	0.365199i
$50$	−0.00931729	−	0.0116835i	−0.00131766	−	0.00165230i
$51$	0.842038	+	4.58423i	0.117909	+	0.641920i
$52$	1.61794	−	0.279348i	0.224368	−	0.0387385i
$53$	−4.99262	−	2.95407i	−0.685789	−	0.405772i	0.124168	−	0.992261i	$-0.460374\pi$
$53$	−4.99262	−	2.95407i	−0.685789	−	0.405772i	−0.809957	+	0.586489i	$0.800510\pi$
$54$	0.283008	−	0.143819i	0.0385125	−	0.0195713i
$55$	−0.0963842	+	0.999123i	−0.0129964	+	0.134722i
$56$	0.357571	+	0.643028i	0.0477824	+	0.0859282i
$57$	−2.75586	−	1.79387i	−0.365023	−	0.237603i
$58$	−0.567163	−	0.352160i	−0.0744721	−	0.0462408i
$59$	−6.06431	+	7.27967i	−0.789506	+	0.947732i	−0.999551	−	0.0299596i	$-0.990462\pi$
$59$	−6.06431	+	7.27967i	−0.789506	+	0.947732i	0.210045	+	0.977692i	$0.432639\pi$
$60$	−3.57635	−	1.27291i	−0.461705	−	0.164332i
$61$	−1.16482	+	0.0998189i	−0.149141	+	0.0127805i	−0.159712	−	0.987164i	$-0.551057\pi$
$61$	−1.16482	+	0.0998189i	−0.149141	+	0.0127805i	0.0105717	+	0.999944i	$0.496635\pi$
$62$	−0.517199	−	0.100724i	−0.0656843	−	0.0127920i
$63$	0.474744	+	5.91669i	0.0598121	+	0.745433i
$64$	−6.31831	+	4.71547i	−0.789788	+	0.589434i
$65$	0.866575	+	1.57789i	0.107485	+	0.195713i
$66$	0.0123202	+	0.0248990i	0.00151651	+	0.00306485i
$67$	9.50150	−	2.93082i	1.16079	−	0.358057i	0.346240	−	0.938146i	$-0.387458\pi$
$67$	9.50150	−	2.93082i	1.16079	−	0.358057i	0.814553	+	0.580089i	$0.196982\pi$
$68$	−0.798978	+	10.6616i	−0.0968903	+	1.29291i
$69$	−3.80265	−	5.45138i	−0.457785	−	0.656269i
$70$	−0.269271	+	0.299653i	−0.0321840	+	0.0358154i
$71$	−13.0583	−	5.28670i	−1.54973	−	0.627416i	−0.568922	−	0.822391i	$-0.692639\pi$
$71$	−13.0583	−	5.28670i	−1.54973	−	0.627416i	−0.980808	+	0.194975i	$0.937537\pi$
$72$	0.609699	−	0.132322i	0.0718538	−	0.0155943i
$73$	−3.13506	+	1.67842i	−0.366931	+	0.196444i	−0.645118	−	0.764083i	$-0.723192\pi$
$73$	−3.13506	+	1.67842i	−0.366931	+	0.196444i	0.278187	+	0.960527i	$0.410267\pi$
$74$	0.0333304	−	0.181457i	0.00387458	−	0.0210940i
$75$	−0.00199531	+	0.186720i	−0.000230398	+	0.0215606i
$76$	−5.07106	−	5.58380i	−0.581691	−	0.640506i
$77$	−1.21110	+	0.0841620i	−0.138017	+	0.00959115i
$78$	0.0434113	+	0.0244488i	0.00491536	+	0.00276828i
$79$	10.5440	−	1.58926i	1.18630	−	0.178806i	0.473898	−	0.880580i	$-0.342846\pi$
$79$	10.5440	−	1.58926i	1.18630	−	0.178806i	0.712400	+	0.701774i	$0.247608\pi$
$80$	−7.17721	−	4.89334i	−0.802436	−	0.547092i
$81$	2.70081	+	0.586151i	0.300090	+	0.0651278i
$82$	−0.0114014	+	0.00325172i	−0.00125907	+	0.000359092i
$83$	−2.42532	+	0.472331i	−0.266213	+	0.0518450i	−0.322499	−	0.946570i	$-0.604523\pi$
$83$	−2.42532	+	0.472331i	−0.266213	+	0.0518450i	0.0562862	+	0.998415i	$0.482074\pi$
$84$	0.805664	−	4.52005i	0.0879051	−	0.493178i
$85$	−11.3391	+	2.97345i	−1.22989	+	0.322516i
$86$	0.256139	+	0.799934i	0.0276202	+	0.0862591i
$87$	2.71309	+	7.88852i	0.290874	+	0.845738i
$88$	0.0257295	+	0.124983i	0.00274277	+	0.0133232i
$89$	−8.79623	+	8.89073i	−0.932399	+	0.942416i	−0.998464	−	0.0553995i	$-0.982357\pi$
$89$	−8.79623	+	8.89073i	−0.932399	+	0.942416i	0.0660654	+	0.997815i	$0.478955\pi$
$90$	0.177088	+	0.292126i	0.0186668	+	0.0307928i
$91$	−1.70959	+	1.34826i	−0.179214	+	0.141336i
$92$	−5.26560	−	14.3083i	−0.548977	−	1.49175i
$93$	4.21419	+	5.05876i	0.436991	+	0.524569i
$94$	0.0419291	+	0.299891i	0.00432466	+	0.0309314i
$95$	3.98108	−	7.24890i	0.408450	−	0.743721i
$96$	−0.723506	−	0.0309435i	−0.0738425	−	0.00315816i
$97$	0.0543670	+	0.238197i	0.00552013	+	0.0241853i	0.977613	−	0.210411i	$-0.0674803\pi$
$97$	0.0543670	+	0.238197i	0.00552013	+	0.0241853i	−0.972093	+	0.234596i	$0.924623\pi$
$98$	−0.411135	−	0.261495i	−0.0415309	−	0.0264150i
$99$	−0.229071	+	1.00362i	−0.0230225	+	0.100868i
$100$	−0.113070	+	0.413142i	−0.0113070	+	0.0413142i
$101$	5.45577	+	13.0725i	0.542869	+	1.30076i	0.926158	+	0.377135i	$0.123091\pi$
$101$	5.45577	+	13.0725i	0.542869	+	1.30076i	−0.383289	+	0.923628i	$0.625209\pi$
$102$	−0.223199	+	0.235454i	−0.0221000	+	0.0233135i
$103$	−2.76421	+	3.62239i	−0.272366	+	0.356924i	−0.910870	−	0.412694i	$-0.864588\pi$
$103$	−2.76421	+	3.62239i	−0.272366	+	0.356924i	0.638504	+	0.769619i	$0.279554\pi$
$104$	0.164394	+	0.159207i	0.0161202	+	0.0156115i
$105$	4.97375	−	0.776485i	0.485388	−	0.0757771i
$106$	−0.0387739	−	0.401932i	−0.00376605	−	0.0390391i
$107$	−1.47247	−	2.31587i	−0.142349	−	0.223884i	0.765237	−	0.643748i	$-0.222622\pi$
$107$	−1.47247	−	2.31587i	−0.142349	−	0.223884i	−0.907587	+	0.419865i	$0.862077\pi$
$108$	−8.11190	−	4.12231i	−0.780568	−	0.396669i
$109$	5.02903	−	7.90952i	0.481693	−	0.757595i	−0.513228	−	0.858252i	$-0.671550\pi$
$109$	5.02903	−	7.90952i	0.481693	−	0.757595i	0.994921	+	0.100657i	$0.0320946\pi$
$110$	−0.0601315	+	0.0355790i	−0.00573331	+	0.00339233i
$111$	−1.75539	+	1.49439i	−0.166615	+	0.141841i
$112$	4.40687	−	9.53723i	0.416410	−	0.901183i
$113$	8.84508	+	2.31945i	0.832075	+	0.218196i	0.645032	−	0.764156i	$-0.276844\pi$
$113$	8.84508	+	2.31945i	0.832075	+	0.218196i	0.187044	+	0.982352i	$0.440109\pi$
$114$	−0.0122232	−	0.228560i	−0.00114481	−	0.0214066i
$115$	12.9575	−	10.5617i	1.20829	−	0.984883i
$116$	1.43000	+	19.0820i	0.132772	+	1.77172i
$117$	0.674505	+	1.71861i	0.0623580	+	0.158886i
$118$	−0.658149	−	0.0422546i	−0.0605875	−	0.00388985i
$119$	−5.80718	−	12.9340i	−0.532343	−	1.18566i
$120$	−0.150548	−	0.507246i	−0.0137431	−	0.0463050i
$121$	10.4927	+	2.51314i	0.953880	+	0.228467i
$122$	−0.0534101	−	0.0613971i	−0.00483552	−	0.00555863i
$123$	0.136101	+	0.0585167i	0.0122718	+	0.00527627i
$124$	6.40719	+	13.6766i	0.575383	+	1.22820i
$125$	−11.3839	+	0.730869i	−1.01820	+	0.0653709i
$126$	−0.313189	+	0.269480i	−0.0279011	+	0.0240072i
$127$	−0.672325	−	4.15857i	−0.0596592	−	0.369013i	−0.999616	−	0.0277190i	$-0.991176\pi$
$127$	−0.672325	−	4.15857i	−0.0596592	−	0.369013i	0.939957	−	0.341294i	$-0.110865\pi$
$128$	−2.11560	−	0.652575i	−0.186994	−	0.0576800i
$129$	3.83445	−	9.77002i	0.337604	−	0.860202i
$130$	−0.0531588	+	0.113471i	−0.00466234	+	0.00995210i
$131$	−4.29158	+	3.81462i	−0.374957	+	0.333285i	−0.830591	−	0.556882i	$-0.811997\pi$
$131$	−4.29158	+	3.81462i	−0.374957	+	0.333285i	0.455635	+	0.890167i	$0.349412\pi$
$132$	0.368306	−	0.705973i	0.0320569	−	0.0614471i
$133$	9.44092	+	3.30433i	0.818632	+	0.286522i
$134$	0.554675	+	0.413965i	0.0479166	+	0.0357611i
$135$	1.38144	−	9.88053i	0.118895	−	0.850380i
$136$	−1.26602	+	0.786090i	−0.108560	+	0.0674067i
$137$	−8.10168	−	0.173170i	−0.692173	−	0.0147950i	−0.326038	−	0.945357i	$-0.605714\pi$
$137$	−8.10168	−	0.173170i	−0.692173	−	0.0147950i	−0.366135	+	0.930562i	$0.619319\pi$
$138$	0.150469	−	0.437500i	0.0128088	−	0.0372425i
$139$	22.9962	+	2.96503i	1.95051	+	0.251490i	0.998508	−	0.0546007i	$-0.0173886\pi$
$139$	22.9962	+	2.96503i	1.95051	+	0.251490i	0.952002	+	0.306091i	$0.0990212\pi$
$140$	11.4878	+	1.17108i	0.970894	+	0.0989740i
$141$	1.96147	−	3.23565i	0.165186	−	0.272491i
$142$	−0.238587	−	0.951146i	−0.0200218	−	0.0798184i
$143$	−0.352958	+	0.134191i	−0.0295158	+	0.0112216i
$144$	−6.65859	−	5.91856i	−0.554883	−	0.493214i
$145$	−19.2746	+	8.28712i	−1.60067	+	0.688208i
$146$	−0.223015	−	0.107398i	−0.0184569	−	0.00888835i
$147$	1.91764	+	5.77857i	0.158164	+	0.476609i
$148$	−4.76446	+	2.29444i	−0.391636	+	0.188602i
$149$	3.07849	−	3.53886i	0.252200	−	0.289914i	−0.614320	−	0.789057i	$-0.710569\pi$
$149$	3.07849	−	3.53886i	0.252200	−	0.289914i	0.866520	+	0.499143i	$0.166352\pi$
$150$	−0.0105803	+	0.00754973i	−0.000863882	+	0.000616433i
$151$	−10.8109	−	16.2265i	−0.879777	−	1.32049i	−0.946494	−	0.322722i	$-0.895402\pi$
$151$	−10.8109	−	16.2265i	−0.879777	−	1.32049i	0.0667171	−	0.997772i	$-0.478747\pi$
$152$	0.211989	−	1.02975i	0.0171946	−	0.0835239i
$153$	−11.9235	+	1.53737i	−0.963962	+	0.124289i
$154$	−0.0544285	−	0.0646412i	−0.00438597	−	0.00520894i
$155$	−11.8954	+	11.5200i	−0.955461	+	0.925312i
$156$	−0.167473	−	1.41821i	−0.0134085	−	0.113548i
$157$	−2.76438	+	11.0204i	−0.220622	+	0.879525i	0.754219	+	0.656623i	$0.228016\pi$
$157$	−2.76438	+	11.0204i	−0.220622	+	0.879525i	−0.974841	+	0.222902i	$0.928447\pi$
$158$	0.522024	+	0.527633i	0.0415300	+	0.0419762i
$159$	−2.79762	+	4.19907i	−0.221866	+	0.333008i
$160$	−0.0583761	−	1.82038i	−0.00461503	−	0.143914i
$161$	15.1820	+	13.3522i	1.19651	+	1.05230i
$162$	0.0778688	+	0.175907i	0.00611795	+	0.0138206i
$163$	3.68314	−	8.82514i	0.288486	−	0.691238i	−0.711448	−	0.702739i	$-0.751960\pi$
$163$	3.68314	−	8.82514i	0.288486	−	0.691238i	0.999934	+	0.0115008i	$0.00366091\pi$
$164$	0.267939	+	0.209030i	0.0209225	+	0.0163225i
$165$	0.863299	+	0.130121i	0.0672078	+	0.0101299i
$166$	−0.126078	−	0.116984i	−0.00978557	−	0.00907968i
$167$	4.88642	−	5.38049i	0.378122	−	0.416355i	−0.521343	−	0.853347i	$-0.674569\pi$
$167$	4.88642	−	5.38049i	0.378122	−	0.416355i	0.899465	+	0.436993i	$0.143956\pi$
$168$	0.575103	−	0.280696i	0.0443701	−	0.0216562i
$169$	7.05007	−	10.1068i	0.542313	−	0.777447i
$170$	−0.632474	−	0.515533i	−0.0485085	−	0.0395396i
$171$	5.00006	−	6.85115i	0.382364	−	0.523921i
$172$	14.1927	−	19.4471i	1.08218	−	1.48283i
$173$	14.3050	+	11.6601i	1.08759	+	0.886500i	0.994029	−	0.109114i	$-0.0348013\pi$
$173$	14.3050	+	11.6601i	1.08759	+	0.886500i	0.0935596	+	0.995614i	$0.470175\pi$
$174$	−0.332208	+	0.476245i	−0.0251846	+	0.0361040i
$175$	−0.129309	−	0.553096i	−0.00977484	−	0.0418101i
$176$	1.22499	−	1.34885i	0.0923374	−	0.101674i
$177$	6.04099	+	5.60522i	0.454068	+	0.421314i
$178$	−0.860835	−	0.129750i	−0.0645223	−	0.00972517i
$179$	3.73955	+	2.91737i	0.279507	+	0.218054i	0.745114	−	0.666937i	$-0.232395\pi$
$179$	3.73955	+	2.91737i	0.279507	+	0.218054i	−0.465607	+	0.884992i	$0.654164\pi$
$180$	3.77125	−	9.03624i	0.281092	−	0.673522i
$181$	−6.96103	−	15.7251i	−0.517409	−	1.16884i	−0.961987	−	0.273096i	$-0.911952\pi$
$181$	−6.96103	−	15.7251i	−0.517409	−	1.16884i	0.444577	−	0.895740i	$-0.353354\pi$
$182$	−0.145959	−	0.0407980i	−0.0108192	−	0.00302415i
$183$	0.0325917	+	1.01633i	0.00240925	+	0.0751293i
$184$	1.17828	−	1.76853i	0.0868641	−	0.130378i
$185$	−4.07788	−	4.12169i	−0.299812	−	0.303032i
$186$	−0.111506	+	0.444528i	−0.00817604	+	0.0325944i
$187$	−0.288359	−	2.44192i	−0.0210869	−	0.178571i
$188$	6.23486	−	6.03812i	0.454724	−	0.440375i
$189$	12.0621	−	0.321389i	0.877390	−	0.0233776i
$190$	0.570935	−	0.0736139i	0.0414200	−	0.00534052i
$191$	−3.92252	+	19.0539i	−0.283824	+	1.37869i	0.553893	+	0.832588i	$0.313142\pi$
$191$	−3.92252	+	19.0539i	−0.283824	+	1.37869i	−0.837717	+	0.546105i	$0.816110\pi$
$192$	3.80209	+	5.70671i	0.274392	+	0.411847i
$193$	8.16666	−	5.82742i	0.587849	−	0.419467i	−0.247736	−	0.968828i	$-0.579687\pi$
$193$	8.16666	−	5.82742i	0.587849	−	0.419467i	0.835585	+	0.549361i	$0.185129\pi$
$194$	−0.0111619	+	0.0128311i	−0.000801379	+	0.000921218i
$195$	1.41071	−	0.679362i	0.101023	−	0.0486501i
$196$	0.892689	+	13.9375i	0.0637635	+	0.995538i
$197$	−4.56901	−	2.20032i	−0.325529	−	0.156766i	0.263980	−	0.964528i	$-0.414965\pi$
$197$	−4.56901	−	2.20032i	−0.325529	−	0.156766i	−0.589509	+	0.807762i	$0.700679\pi$
$198$	−0.0658292	+	0.0283033i	−0.00467828	+	0.00201143i
$199$	−16.8476	−	14.9752i	−1.19430	−	1.06156i	−0.996691	−	0.0812812i	$-0.974099\pi$
$199$	−16.8476	−	14.9752i	−1.19430	−	1.06156i	−0.197604	−	0.980282i	$-0.563316\pi$
$200$	−0.0558056	+	0.0212167i	−0.00394605	+	0.00150025i
$201$	−2.10420	−	8.38854i	−0.148419	−	0.591682i
$202$	−0.511138	+	0.843175i	−0.0359635	+	0.0593256i
$203$	−13.7277	−	21.3415i	−0.963496	−	1.49788i
$204$	9.22291	+	1.18916i	0.645733	+	0.0832580i
$205$	−0.121181	+	0.352342i	−0.00846362	+	0.0246086i
$206$	−0.317099	−	0.00677787i	−0.0220933	−	0.000472236i
$207$	14.5649	−	9.04355i	1.01233	−	0.628570i
$208$	0.452488	−	3.23634i	0.0313744	−	0.224400i
$209$	1.39024	+	1.03757i	0.0961652	+	0.0717699i
$210$	0.247753	+	0.247790i	0.0170966	+	0.0170992i
$211$	−4.66710	+	8.94596i	−0.321297	+	0.615866i	−0.992054	−	0.125811i	$-0.959847\pi$
$211$	−4.66710	+	8.94596i	−0.321297	+	0.615866i	0.670758	+	0.741677i	$0.265969\pi$
$212$	−8.65071	+	7.68928i	−0.594133	+	0.528102i
$213$	−5.19824	+	11.0960i	−0.356178	+	0.760287i
$214$	0.0697896	−	0.177821i	0.00477072	−	0.0121556i
$215$	25.2240	+	7.78059i	1.72027	+	0.530632i
$216$	−0.202418	−	1.25202i	−0.0137728	−	0.0851895i
$217$	−16.1136	−	11.8942i	−1.09386	−	0.807434i
$218$	0.651081	−	0.0418008i	0.0440968	−	0.00283111i
$219$	1.31215	+	2.80088i	0.0886668	+	0.189266i
$220$	1.83982	+	0.791029i	0.124040	+	0.0533312i
$221$	−2.89432	−	3.32714i	−0.194693	−	0.223808i
$222$	−0.156054	−	0.0373772i	−0.0104737	−	0.00250859i
$223$	2.75942	+	9.29740i	0.184784	+	0.622600i	0.999110	+	0.0421911i	$0.0134338\pi$
$223$	2.75942	+	9.29740i	0.184784	+	0.622600i	−0.814325	+	0.580409i	$0.802893\pi$
$224$	2.15995	−	0.432470i	0.144318	−	0.0288956i
$225$	−0.480659	−	0.0308593i	−0.0320439	−	0.00205729i
$226$	0.232538	+	0.592498i	0.0154682	+	0.0394124i
$227$	−1.06512	−	14.2131i	−0.0706947	−	0.943355i	−0.913946	−	0.405836i	$-0.866980\pi$
$227$	−1.06512	−	14.2131i	−0.0706947	−	0.943355i	0.843251	−	0.537520i	$-0.180639\pi$
$228$	−5.08529	+	4.14505i	−0.336781	+	0.274512i
$229$	−1.10211	−	20.6081i	−0.0728294	−	1.36182i	−0.766830	−	0.641850i	$-0.778167\pi$
$229$	−1.10211	−	20.6081i	−0.0728294	−	1.36182i	0.694001	−	0.719974i	$-0.255846\pi$
$230$	1.12554	+	0.295151i	0.0742158	+	0.0194617i
$231$	0.0168439	+	1.05579i	0.00110825	+	0.0694660i
$232$	−2.03090	+	1.72893i	−0.133335	+	0.113510i
$233$	−7.08704	+	4.19331i	−0.464288	+	0.274713i	−0.722494	−	0.691377i	$-0.757004\pi$
$233$	−7.08704	+	4.19331i	−0.464288	+	0.274713i	0.258207	+	0.966090i	$0.416868\pi$
$234$	−0.0689523	+	0.108446i	−0.00450756	+	0.00708937i
$235$	8.48372	+	4.31126i	0.553417	+	0.281235i
$236$	10.1426	+	15.9520i	0.660228	+	1.03839i
$237$	−0.890573	−	9.23172i	−0.0578489	−	0.599665i
$238$	0.488933	−	0.857251i	0.0316928	−	0.0555673i
$239$	6.79543	+	6.58100i	0.439560	+	0.425690i	0.882102	−	0.471058i	$-0.156128\pi$
$239$	6.79543	+	6.58100i	0.439560	+	0.425690i	−0.442543	+	0.896747i	$0.645924\pi$
$240$	−4.58342	+	6.00638i	−0.295858	+	0.387710i
$241$	−8.77121	+	9.25282i	−0.565003	+	0.596027i	−0.944234	−	0.329275i	$-0.893196\pi$
$241$	−8.77121	+	9.25282i	−0.565003	+	0.596027i	0.379231	+	0.925302i	$0.376189\pi$
$242$	0.289256	+	0.693084i	0.0185941	+	0.0445531i
$243$	4.24627	−	15.5152i	0.272398	−	0.995302i
$244$	−0.519035	+	2.27404i	−0.0332278	+	0.145581i
$245$	−14.1323	+	5.89556i	−0.902881	+	0.376653i
$246$	0.00229466	+	0.0100536i	0.000146302	+	0.000640992i
$247$	3.10832	+	0.132939i	0.197778	+	0.00845871i
$248$	−1.01336	+	1.84516i	−0.0643482	+	0.117167i
$249$	0.297584	+	2.12842i	0.0188586	+	0.134883i
$250$	−0.508223	−	0.610076i	−0.0321428	−	0.0385846i
$251$	−4.60725	−	12.5194i	−0.290807	−	0.790217i	−0.996645	−	0.0818436i	$-0.973919\pi$
$251$	−4.60725	−	12.5194i	−0.290807	−	0.790217i	0.705838	−	0.708373i	$-0.250571\pi$
$252$	11.5313	+	2.69776i	0.726402	+	0.169943i
$253$	1.81772	+	2.99852i	0.114279	+	0.188515i
$254$	0.206230	−	0.208446i	0.0129400	−	0.0130790i
$255$	2.05587	+	9.98650i	0.128743	+	0.625379i
$256$	5.07810	+	14.7649i	0.317381	+	0.922809i
$257$	−7.30492	−	22.8136i	−0.455668	−	1.42307i	−0.860861	−	0.508840i	$-0.830075\pi$
$257$	−7.30492	−	22.8136i	−0.455668	−	1.42307i	0.405193	−	0.914231i	$-0.367204\pi$
$258$	0.706670	−	0.185311i	0.0439954	−	0.0115369i
$259$	4.10410	−	5.68614i	0.255016	−	0.353320i
$260$	3.52543	−	0.686577i	0.218638	−	0.0425797i
$261$	−20.6921	+	5.90148i	−1.28081	+	0.365292i
$262$	−0.390581	−	0.0847671i	−0.0241302	−	0.00523693i
$263$	−8.14754	−	5.55490i	−0.502399	−	0.342530i	0.285455	−	0.958392i	$-0.407855\pi$
$263$	−8.14754	−	5.55490i	−0.502399	−	0.342530i	−0.787854	+	0.615862i	$0.788808\pi$
$264$	0.109747	−	0.0165417i	0.00675447	−	0.00101807i
$265$	−11.0571	−	6.22726i	−0.679234	−	0.382538i
$266$	0.201613	+	0.666413i	0.0123617	+	0.0408604i
$267$	7.31336	+	8.05282i	0.447570	+	0.492825i
$268$	0.211982	−	19.8372i	0.0129489	−	1.21175i
$269$	0.303412	−	1.65184i	0.0184994	−	0.100714i	−0.973006	−	0.230780i	$-0.925872\pi$
$269$	0.303412	−	1.65184i	0.0184994	−	0.100714i	0.991505	+	0.130065i	$0.0415186\pi$
$270$	0.612226	−	0.327768i	0.0372589	−	0.0199473i
$271$	−18.1650	+	3.94231i	−1.10344	+	0.239478i	−0.726779	−	0.686871i	$-0.758984\pi$
$271$	−18.1650	+	3.94231i	−1.10344	+	0.239478i	−0.376665	+	0.926349i	$0.622929\pi$
$272$	19.7241	+	7.98542i	1.19595	+	0.484187i
$273$	1.09161	+	1.54747i	0.0660671	+	0.0936571i
$274$	−0.322710	−	0.462629i	−0.0194956	−	0.0279484i
$275$	0.00736170	−	0.0982351i	0.000443927	−	0.00592380i
$276$	−12.6719	+	3.90877i	−0.762759	+	0.235280i
$277$	2.45766	+	4.96690i	0.147666	+	0.298432i	0.957606	−	0.288081i	$-0.0930173\pi$
$277$	2.45766	+	4.96690i	0.147666	+	0.298432i	−0.809940	+	0.586513i	$0.800500\pi$
$278$	0.776920	+	1.41464i	0.0465966	+	0.0848447i
$279$	−13.6103	+	10.1576i	−0.814828	+	0.608122i
$280$	0.812080	+	1.38961i	0.0485311	+	0.0830451i
$281$	−8.12443	−	1.58223i	−0.484663	−	0.0943881i	−0.0570902	−	0.998369i	$-0.518182\pi$
$281$	−8.12443	−	1.58223i	−0.484663	−	0.0943881i	−0.427573	+	0.903981i	$0.640631\pi$
$282$	0.262414	−	0.0224874i	0.0156265	−	0.00133911i
$283$	26.1477	+	9.30658i	1.55432	+	0.553219i	0.966698	−	0.255918i	$-0.0823777\pi$
$283$	26.1477	+	9.30658i	1.55432	+	0.553219i	0.587621	+	0.809137i	$0.300065\pi$
$284$	−17.9903	+	21.5958i	−1.06753	+	1.28147i
$285$	−6.11102	−	3.79442i	−0.361986	−	0.224762i
$286$	−0.0220284	−	0.0143389i	−0.00130256	−	0.000847875i
$287$	−0.444472	−	0.0743325i	−0.0262364	−	0.00438771i
$288$	0.179361	−	1.85927i	0.0105690	−	0.109558i
$289$	10.4448	−	5.30784i	0.614399	−	0.312226i
$290$	−1.25687	−	0.743672i	−0.0738059	−	0.0436700i
$291$	0.209409	−	0.0361558i	0.0122758	−	0.00211949i
$292$	1.28176	+	6.97818i	0.0750096	+	0.408367i
$293$	−5.80632	−	7.28089i	−0.339209	−	0.425354i	0.582744	−	0.812655i	$-0.301979\pi$
$293$	−5.80632	−	7.28089i	−0.339209	−	0.425354i	−0.921953	+	0.387301i	$0.873407\pi$
$294$	−0.246215	+	0.344940i	−0.0143596	+	0.0201173i
$295$	−12.9226	+	16.2044i	−0.752381	+	0.943456i
$296$	−0.649813	−	0.347890i	−0.0377696	−	0.0202207i
$297$	2.01244	+	0.573956i	0.116774	+	0.0333043i
$298$	0.325298	+	0.0278762i	0.0188440	+	0.00161483i
$299$	5.72288	+	2.60684i	0.330963	+	0.150757i
$300$	0.353577	+	0.117396i	0.0204138	+	0.00677784i
$301$	−4.25413	+	31.6413i	−0.245204	+	1.82378i
$302$	0.468730	−	1.27369i	0.0269724	−	0.0732927i
$303$	11.6074	−	4.13134i	0.666826	−	0.237339i
$304$	−13.6619	+	6.22315i	−0.783565	+	0.356922i
$305$	−2.54285	+	0.272760i	−0.145603	+	0.0156182i
$306$	−0.575714	−	0.607325i	−0.0329114	−	0.0347185i
$307$	−7.43461	+	16.7949i	−0.424315	+	0.958536i	0.566593	+	0.823998i	$0.308261\pi$
$307$	−7.43461	+	16.7949i	−0.424315	+	0.958536i	−0.990908	+	0.134538i	$0.957045\pi$
$308$	−0.576937	+	2.35244i	−0.0328741	+	0.134042i
$309$	3.01778	+	2.56908i	0.171676	+	0.146150i
$310$	−1.13584	−	0.196111i	−0.0645115	−	0.0111383i
$311$	−0.242543	−	22.6970i	−0.0137533	−	1.28703i	−0.772235	−	0.635337i	$-0.780861\pi$
$311$	−0.242543	−	22.6970i	−0.0137533	−	1.28703i	0.758482	−	0.651694i	$-0.225941\pi$
$312$	0.145913	−	0.135388i	0.00826070	−	0.00766481i
$313$	12.9564	−	8.83350i	0.732337	−	0.499299i	−0.138811	−	0.990319i	$-0.544328\pi$
$313$	12.9564	−	8.83350i	0.732337	−	0.499299i	0.871148	+	0.491020i	$0.163376\pi$
$314$	−0.733065	+	0.296785i	−0.0413693	+	0.0167486i
$315$	1.31487	+	12.9178i	0.0740845	+	0.727837i
$316$	3.39543	−	21.0019i	0.191008	−	1.18145i
$317$	−0.244141	+	0.493406i	−0.0137123	+	0.0277125i	−0.903030	−	0.429577i	$-0.858663\pi$
$317$	−0.244141	+	0.493406i	−0.0137123	+	0.0277125i	0.889318	+	0.457289i	$0.151180\pi$
$318$	−0.350894	+	0.0150073i	−0.0196771	+	0.000841568i
$319$	−1.16173	−	4.24477i	−0.0650441	−	0.237661i
$320$	−13.5979	+	10.6083i	−0.760147	+	0.593021i
$321$	−2.07981	+	1.17133i	−0.116084	+	0.0653772i
$322$	−0.127756	+	1.40152i	−0.00711957	+	0.0781035i
$323$	−5.76429	+	19.4218i	−0.320734	+	1.08066i
$324$	2.75698	−	4.77524i	0.153166	−	0.265291i
$325$	−0.0883366	−	0.153004i	−0.00490003	−	0.00848711i
$326$	0.647335	−	0.155046i	0.0358526	−	0.00858718i
$327$	−6.63613	−	4.73529i	−0.366979	−	0.261862i
$328$	−0.00151818	+	0.0473423i	−8.38272e−5	+	0.00261404i
$329$	−3.45209	+	10.9798i	−0.190320	+	0.605335i
$330$	0.0281087	+	0.0538791i	0.00154733	+	0.00296594i
$331$	−3.38665	−	1.28757i	−0.186147	−	0.0707713i	0.260534	−	0.965465i	$-0.416101\pi$
$331$	−3.38665	−	1.28757i	−0.186147	−	0.0707713i	−0.446681	+	0.894693i	$0.647394\pi$
$332$	−0.578128	+	4.89578i	−0.0317289	+	0.268691i
$333$	−3.60729	−	4.72721i	−0.197678	−	0.259049i
$334$	0.503032	+	0.0539580i	0.0275247	+	0.00295245i
$335$	20.6431	−	6.85399i	1.12785	−	0.374473i
$336$	−8.07875	−	4.27053i	−0.440732	−	0.232976i
$337$	23.0385	−	14.9964i	1.25499	−	0.816906i	0.265865	−	0.964010i	$-0.414342\pi$
$337$	23.0385	−	14.9964i	1.25499	−	0.816906i	0.989121	+	0.147105i	$0.0469954\pi$
$338$	0.857557	−	0.0183300i	0.0466449	−	0.000997018i
$339$	2.42538	−	7.57455i	0.131728	−	0.411393i
$340$	−1.24899	+	23.3547i	−0.0677362	+	1.26659i
$341$	−2.04765	−	2.80573i	−0.110887	−	0.151939i
$342$	0.590385			0.0319243
$343$	−9.84979	−	15.6838i	−0.531839	−	0.846846i
$344$	3.35570			0.180927
$345$	−8.57137	−	11.7446i	−0.461467	−	0.632309i
$346$	−0.0686018	+	1.28277i	−0.00368806	+	0.0689622i
$347$	−1.15062	+	3.59343i	−0.0617684	+	0.192905i	−0.978356	−	0.206928i	$-0.933653\pi$
$347$	−1.15062	+	3.59343i	−0.0617684	+	0.192905i	0.916588	+	0.399834i	$0.130932\pi$
$348$	16.6399	−	0.355671i	0.891990	−	0.0190660i
$349$	−6.28353	+	4.09013i	−0.336350	+	0.218939i	−0.702614	−	0.711572i	$-0.747984\pi$
$349$	−6.28353	+	4.09013i	−0.336350	+	0.218939i	0.366264	+	0.930511i	$0.380637\pi$
$350$	0.0257921	−	0.0299664i	0.00137865	−	0.00160177i
$351$	3.56192	−	1.18264i	0.190121	−	0.0631246i
$352$	0.379858	+	0.0407457i	0.0202465	+	0.00217175i
$353$	−15.1484	−	19.8513i	−0.806265	−	1.05658i	−0.997186	−	0.0749722i	$-0.976113\pi$
$353$	−15.1484	−	19.8513i	−0.806265	−	1.05658i	0.190920	−	0.981606i	$-0.438853\pi$
$354$	−0.0672699	+	0.569665i	−0.00357536	+	0.0302773i
$355$	−28.8060	−	10.9518i	−1.52886	−	0.581260i
$356$	11.5417	+	22.1232i	0.611708	+	1.17253i
$357$	−11.5034	+	4.44298i	−0.608826	+	0.235147i
$358$	−0.0105815	+	0.329971i	−0.000559251	+	0.0174395i
$359$	−18.3249	−	13.0759i	−0.967151	−	0.690122i	−0.0163313	−	0.999867i	$-0.505199\pi$
$359$	−18.3249	−	13.0759i	−0.967151	−	0.690122i	−0.950820	+	0.309745i	$0.899756\pi$
$360$	1.32725	−	0.317894i	0.0699522	−	0.0167545i
$361$	2.35360	+	4.07655i	0.123874	+	0.214555i
$362$	0.598514	−	1.03666i	0.0314572	−	0.0544854i
$363$	2.67013	−	8.99656i	0.140146	−	0.472197i
$364$	1.52171	+	4.06874i	0.0797595	+	0.213260i
$365$	−6.77803	+	3.81731i	−0.354778	+	0.199807i
$366$	−0.0558065	+	0.0435369i	−0.00291705	+	0.00227571i
$367$	7.02030	+	25.6511i	0.366457	+	1.33898i	0.877563	+	0.479461i	$0.159168\pi$
$367$	7.02030	+	25.6511i	0.366457	+	1.33898i	−0.511106	+	0.859518i	$0.670764\pi$
$368$	−30.3173	+	1.29664i	−1.58040	+	0.0675918i
$369$	−0.169468	+	0.342494i	−0.00882218	+	0.0178295i
$370$	0.0644122	−	0.398412i	0.00334863	−	0.0207125i
$371$	5.22482	−	14.4316i	0.271259	−	0.749251i
$372$	12.1763	−	4.92962i	0.631310	−	0.255589i
$373$	−26.8239	+	18.2882i	−1.38889	+	0.946929i	−0.389222	+	0.921144i	$0.627256\pi$
$373$	−26.8239	+	18.2882i	−1.38889	+	0.946929i	−0.999668	+	0.0257853i	$0.991791\pi$
$374$	0.125466	−	0.116415i	0.00648769	−	0.00601970i
$375$	0.106020	+	9.92127i	0.00547483	+	0.512332i
$376$	1.19213	+	0.205829i	0.0614792	+	0.0106148i
$377$	−6.00988	−	5.11629i	−0.309525	−	0.263502i
$378$	0.513031	+	0.665014i	0.0263874	+	0.0342046i
$379$	4.06734	−	9.18819i	0.208925	−	0.471966i	−0.778975	−	0.627055i	$-0.784260\pi$
$379$	4.06734	−	9.18819i	0.208925	−	0.471966i	0.987901	+	0.155089i	$0.0495664\pi$
$380$	−11.3516	−	11.9749i	−0.582326	−	0.614301i
$381$	−3.64310	+	0.390779i	−0.186642	+	0.0200202i
$382$	−1.23228	+	0.561316i	−0.0630488	+	0.0287194i
$383$	7.69796	−	2.73988i	0.393347	−	0.140001i	−0.131256	−	0.991349i	$-0.541901\pi$
$383$	7.69796	−	2.73988i	0.393347	−	0.140001i	0.524603	+	0.851347i	$0.324214\pi$
$384$	−0.665053	+	1.80716i	−0.0339383	+	0.0922214i
$385$	−2.64478	+	0.240680i	−0.134790	+	0.0122662i
$386$	0.662764	+	0.220053i	0.0337338	+	0.0112004i
$387$	24.6364	+	11.2222i	1.25234	+	0.570454i
$388$	0.485682	+	0.0416202i	0.0246568	+	0.00211295i
$389$	15.4458	+	4.40521i	0.783134	+	0.223353i	0.642069	−	0.766647i	$-0.278076\pi$
$389$	15.4458	+	4.40521i	0.783134	+	0.223353i	0.141065	+	0.990000i	$0.454947\pi$
$390$	0.0960850	+	0.0514410i	0.00486545	+	0.00260482i
$391$	−25.5320	+	32.0161i	−1.29121	+	1.61912i
$392$	−1.49585	+	1.24573i	−0.0755517	+	0.0629187i
$393$	3.11380	+	3.90458i	0.157070	+	0.196960i
$394$	−0.0637715	−	0.347185i	−0.00321276	−	0.0174909i
$395$	22.9859	−	3.96867i	1.15655	−	0.199686i
$396$	1.76764	+	1.04589i	0.0888272	+	0.0525579i
$397$	19.8353	−	10.0799i	0.995507	−	0.505897i	0.121907	−	0.992542i	$-0.461099\pi$
$397$	19.8353	−	10.0799i	0.995507	−	0.505897i	0.873600	+	0.486645i	$0.161779\pi$
$398$	0.150662	−	1.56176i	0.00755198	−	0.0782842i
$399$	3.30845	−	8.04631i	0.165630	−	0.402820i
$400$	0.714482	+	0.465076i	0.0357241	+	0.0232538i
$401$	4.16338	+	2.58510i	0.207909	+	0.129094i	0.627491	−	0.778624i	$-0.284082\pi$
$401$	4.16338	+	2.58510i	0.207909	+	0.129094i	−0.419582	+	0.907717i	$0.637823\pi$
$402$	0.385308	−	0.462528i	0.0192174	−	0.0230688i
$403$	−5.86882	−	2.08885i	−0.292347	−	0.104053i
$404$	28.1588	−	2.41305i	1.40095	−	0.120054i
$405$	5.93416	+	1.15568i	0.294871	+	0.0574261i
$406$	0.636635	−	1.64758i	0.0315957	−	0.0817681i
$407$	0.974673	−	0.727418i	0.0483128	−	0.0360568i
$408$	0.623944	+	1.13610i	0.0308898	+	0.0562453i
$409$	5.57940	+	11.2759i	0.275883	+	0.557558i	0.989765	−	0.142709i	$-0.0455814\pi$
$409$	5.57940	+	11.2759i	0.275883	+	0.557558i	−0.713881	+	0.700267i	$0.753064\pi$
$410$	−0.0247832	+	0.00764461i	−0.00122396	+	0.000377540i
$411$	−0.526719	+	7.02857i	−0.0259811	+	0.346694i
$412$	5.20118	+	7.45628i	0.256244	+	0.367344i
$413$	−21.9064	−	12.1859i	−1.07794	−	0.599630i
$414$	1.10614	+	0.447826i	0.0543638	+	0.0220095i
$415$	−5.28218	+	1.14638i	−0.259292	+	0.0562736i
$416$	0.604044	−	0.323387i	0.0296157	−	0.0158554i
$417$	3.64338	−	19.8353i	0.178417	−	0.971340i
$418$	−0.00129027	+	0.120743i	−6.31093e−5	+	0.00590574i
$419$	12.8034	+	14.0980i	0.625487	+	0.688731i	0.968048	−	0.250764i	$-0.0806820\pi$
$419$	12.8034	+	14.0980i	0.625487	+	0.688731i	−0.342561	+	0.939496i	$0.611294\pi$
$420$	1.55072	−	9.92317i	0.0756672	−	0.484201i
$421$	22.5606	+	12.7059i	1.09954	+	0.619248i	0.930474	−	0.366357i	$-0.119395\pi$
$421$	22.5606	+	12.7059i	1.09954	+	0.619248i	0.169063	+	0.985605i	$0.445926\pi$
$422$	−0.694504	+	0.104680i	−0.0338079	+	0.00509573i
$423$	8.06386	+	5.49784i	0.392078	+	0.267314i
$424$	−1.57653	−	0.342152i	−0.0765632	−	0.0166164i
$425$	1.10634	−	0.315533i	0.0536653	−	0.0153056i
$426$	−0.837188	+	0.163042i	−0.0405619	+	0.00789943i
$427$	−0.832214	−	2.97907i	−0.0402737	−	0.144167i
$428$	−5.29632	+	1.38886i	−0.256007	+	0.0671330i
$429$	0.100156	+	0.312790i	0.00483556	+	0.0151017i
$430$	0.597581	+	1.73751i	0.0288179	+	0.0837902i
$431$	0.970989	+	4.71664i	0.0467709	+	0.227193i	0.996236	−	0.0866791i	$-0.0276255\pi$
$431$	0.970989	+	4.71664i	0.0467709	+	0.227193i	−0.949465	+	0.313872i	$0.898374\pi$
$432$	−12.7373	+	12.8741i	−0.612821	+	0.619405i
$433$	−3.72068	−	6.13766i	−0.178805	−	0.294957i	0.752927	−	0.658104i	$-0.228641\pi$
$433$	−3.72068	−	6.13766i	−0.178805	−	0.294957i	−0.931732	+	0.363147i	$0.881702\pi$
$434$	0.00755442	−	1.39407i	0.000362624	−	0.0669174i
$435$	6.30240	+	17.1256i	0.302177	+	0.821112i
$436$	−11.9693	−	14.3681i	−0.573226	−	0.688107i
$437$	−4.00037	−	28.6120i	−0.191364	−	1.36870i
$438$	−0.103638	+	0.188708i	−0.00495203	+	0.00901684i
$439$	6.81690	+	0.291551i	0.325353	+	0.0139150i	0.204836	−	0.978796i	$-0.434334\pi$
$439$	6.81690	+	0.291551i	0.325353	+	0.0139150i	0.120517	+	0.992711i	$0.461545\pi$
$440$	0.0621138	+	0.272139i	0.00296116	+	0.0129737i
$441$	−15.1480	+	4.14328i	−0.721332	+	0.197299i
$442$	0.0683047	−	0.299262i	0.00324892	−	0.0142345i
$443$	−3.87884	+	14.1727i	−0.184289	+	0.673366i	0.811714	+	0.584055i	$0.198535\pi$
$443$	−3.87884	+	14.1727i	−0.184289	+	0.673366i	−0.996004	+	0.0893112i	$0.971533\pi$
$444$	1.77150	+	4.24468i	0.0840719	+	0.201444i
$445$	−18.8221	+	19.8556i	−0.892251	+	0.941243i
$446$	−0.409522	+	0.536662i	−0.0193914	+	0.0254117i
$447$	−2.93064	−	2.83816i	−0.138614	−	0.134241i
$448$	−15.3652	−	14.1070i	−0.725938	−	0.666492i
$449$	−3.51838	−	36.4717i	−0.166043	−	1.72120i	−0.583165	−	0.812354i	$-0.698186\pi$
$449$	−3.51838	−	36.4717i	−0.166043	−	1.72120i	0.417122	−	0.908850i	$-0.363039\pi$
$450$	−0.0179884	−	0.0282917i	−0.000847981	−	0.00133368i
$451$	−0.0696752	−	0.0354075i	−0.00328088	−	0.00166728i
$452$	9.78878	−	15.3955i	0.460425	−	0.724145i
$453$	−14.5955	+	8.63595i	−0.685755	+	0.405752i
$454$	0.755434	−	0.643111i	0.0354543	−	0.0301827i
$455$	−3.67591	+	3.02862i	−0.172329	+	0.141984i
$456$	−0.884531	−	0.231951i	−0.0414220	−	0.0108621i
$457$	0.295700	+	5.52924i	0.0138323	+	0.258647i	0.997080	+	0.0763701i	$0.0243331\pi$
$457$	0.295700	+	5.52924i	0.0138323	+	0.258647i	−0.983247	+	0.182277i	$0.941653\pi$
$458$	1.11348	−	0.907606i	0.0520296	−	0.0424097i
$459$	1.82636	+	24.3711i	0.0852473	+	1.13755i
$460$	−12.1849	−	31.0467i	−0.568125	−	1.44756i
$461$	22.7995	+	1.46378i	1.06188	+	0.0681748i	0.585189	−	0.810897i	$-0.301020\pi$
$461$	22.7995	+	1.46378i	1.06188	+	0.0681748i	0.476689	+	0.879072i	$0.341837\pi$
$462$	−0.0586714	+	0.0442707i	−0.00272964	+	0.00205966i
$463$	−5.05800	−	17.0421i	−0.235065	−	0.792012i	−0.990587	−	0.136888i	$-0.956290\pi$
$463$	−5.05800	−	17.0421i	−0.235065	−	0.792012i	0.755521	−	0.655124i	$-0.227384\pi$
$464$	37.0378	+	8.87106i	1.71944	+	0.411829i
$465$	9.45307	+	10.8667i	0.438375	+	0.503931i
$466$	−0.526583	−	0.226405i	−0.0243935	−	0.0104880i
$467$	−10.6384	−	22.7084i	−0.492284	−	1.05082i	−0.983688	−	0.179885i	$-0.942427\pi$
$467$	−10.6384	−	22.7084i	−0.492284	−	1.05082i	0.491403	−	0.870932i	$-0.336484\pi$
$468$	3.67596	−	0.236004i	0.169921	−	0.0109093i
$469$	12.2908	+	23.2597i	0.567538	+	1.07403i
$470$	0.105719	+	0.653912i	0.00487648	+	0.0301627i
$471$	9.44325	+	2.91286i	0.435122	+	0.134217i
$472$	−0.962608	+	2.45269i	−0.0443076	+	0.112894i
$473$	−2.34895	+	5.01401i	−0.108005	+	0.230545i
$474$	0.482516	−	0.428890i	0.0221627	−	0.0196996i
$475$	−0.375417	+	0.719603i	−0.0172253	+	0.0330177i
$476$	−28.1095	+	3.16501i	−1.28840	+	0.145068i
$477$	−10.4301	−	7.78422i	−0.477564	−	0.356415i
$478$	−0.0911764	+	0.652124i	−0.00417031	+	0.0298275i
$479$	25.0822	−	15.5739i	1.14603	−	0.711589i	0.183573	−	0.983006i	$-0.441234\pi$
$479$	25.0822	−	15.5739i	1.14603	−	0.711589i	0.962462	+	0.271417i	$0.0874922\pi$
$480$	−1.58378	−	0.0338527i	−0.0722894	−	0.00154516i
$481$	0.709387	−	2.06259i	0.0323452	−	0.0940462i
$482$	−0.880167	−	0.113485i	−0.0400905	−	0.00516910i
$483$	12.3021	−	12.5659i	0.559764	−	0.571770i
$484$	11.1592	−	18.4083i	0.507238	−	0.836743i
$485$	0.130038	+	0.518405i	0.00590471	+	0.0235396i
$486$	1.04660	−	0.397906i	0.0474746	−	0.0180494i
$487$	20.2952	+	18.0396i	0.919665	+	0.817454i	0.983575	−	0.180502i	$-0.0577721\pi$
$487$	20.2952	+	18.0396i	0.919665	+	0.817454i	−0.0639102	+	0.997956i	$0.520357\pi$
$488$	−0.298678	+	0.128417i	−0.0135205	+	0.00581315i
$489$	−7.49389	−	3.60886i	−0.338885	−	0.163199i
$490$	−0.911392	−	0.552681i	−0.0411725	−	0.0249676i
$491$	5.29601	−	2.55043i	0.239006	−	0.115099i	−0.310547	−	0.950558i	$-0.600512\pi$
$491$	5.29601	−	2.55043i	0.239006	−	0.115099i	0.549553	+	0.835459i	$0.314798\pi$
$492$	0.193996	−	0.223006i	0.00874600	−	0.0100539i
$493$	41.8366	−	29.8530i	1.88423	−	1.34451i
$494$	0.120073	+	0.180223i	0.00540234	+	0.00810860i
$495$	−0.454069	+	2.20567i	−0.0204089	+	0.0991375i
$496$	29.8128	−	3.84393i	1.33863	−	0.172598i
$497$	7.32319	−	36.5464i	0.328490	−	1.63933i
$498$	−0.107461	+	0.104070i	−0.00481543	+	0.00466349i
$499$	−0.223818	−	1.89536i	−0.0100195	−	0.0848481i	0.987184	−	0.159589i	$-0.0510169\pi$
$499$	−0.223818	−	1.89536i	−0.0100195	−	0.0848481i	−0.997203	+	0.0747410i	$0.976187\pi$
$500$	−5.53745	+	22.0754i	−0.247642	+	0.987244i
$501$	−4.44619	−	4.49396i	−0.198641	−	0.200775i
$502$	0.514857	−	0.772770i	0.0229792	−	0.0344904i
$503$	−0.0993071	−	3.09676i	−0.00442788	−	0.138078i	−0.999313	−	0.0370638i	$-0.988200\pi$
$503$	−0.0993071	−	3.09676i	−0.00442788	−	0.138078i	0.994885	−	0.101014i	$-0.0322087\pi$
$504$	0.643768	+	1.51995i	0.0286757	+	0.0677041i
$505$	12.5431	+	28.3350i	0.558159	+	1.26089i
$506$	−0.0940052	+	0.225245i	−0.00417904	+	0.0100133i
$507$	−8.45067	−	6.59270i	−0.375308	−	0.292792i
$508$	−8.31084	−	1.25266i	−0.368734	−	0.0555777i
$509$	−24.2667	−	22.5162i	−1.07560	−	0.998013i	−1.00000		0.000875430i	$-0.999721\pi$
$509$	−24.2667	−	22.5162i	−1.07560	−	0.998013i	−0.0756030	−	0.997138i	$-0.524088\pi$
$510$	−0.477137	+	0.525381i	−0.0211280	+	0.0232643i
$511$	−5.90476	−	7.32486i	−0.261211	−	0.324033i
$512$	−3.15507	+	4.52304i	−0.139436	+	0.199892i
$513$	−13.3647	−	10.8936i	−0.590066	−	0.480966i
$514$	0.982957	−	1.34686i	0.0433564	−	0.0594075i
$515$	−5.87609	+	8.05151i	−0.258932	+	0.354792i
$516$	−16.2313	−	13.2302i	−0.714542	−	0.582427i
$517$	−1.14202	+	1.63717i	−0.0502260	+	0.0720028i
$518$	0.488116	−	0.00257082i	0.0214466	−	0.000112955i
$519$	10.7917	−	11.8828i	0.473702	−	0.521598i
$520$	0.366978	+	0.340506i	0.0160931	+	0.0149322i
$521$	−6.35061	−	0.957200i	−0.278225	−	0.0419357i	0.00844739	−	0.999964i	$-0.497311\pi$
$521$	−6.35061	−	0.957200i	−0.278225	−	0.0419357i	−0.286673	+	0.958029i	$0.592549\pi$
$522$	−1.18090	−	0.921267i	−0.0516866	−	0.0403228i
$523$	2.86164	−	6.85675i	0.125131	−	0.299825i	−0.848031	−	0.529947i	$-0.822212\pi$
$523$	2.86164	−	6.85675i	0.125131	−	0.299825i	0.973162	+	0.230122i	$0.0739126\pi$
$524$	4.63716	+	10.4754i	0.202575	+	0.457621i
$525$	−0.486391	+	0.0866191i	−0.0212278	+	0.00378037i
$526$	−0.0220000	−	0.686042i	−0.000959248	−	0.0299129i
$527$	22.4916	−	33.7586i	0.979749	−	1.47055i
$528$	−1.11463	−	1.12661i	−0.0485081	−	0.0490292i
$529$	8.61208	−	34.3327i	0.374438	−	1.49273i
$530$	−0.103589	−	0.877226i	−0.00449962	−	0.0381043i
$531$	−15.2694	+	14.7876i	−0.662637	+	0.641729i
$532$	12.0227	−	15.9285i	0.521249	−	0.690588i
$533$	−0.139017	+	0.0179243i	−0.00602151	+	0.000776388i
$534$	−0.152677	+	0.741641i	−0.00660700	+	0.0320939i
$535$	−3.32861	−	4.99606i	−0.143909	−	0.215998i
$536$	2.25085	−	1.60612i	0.0972218	−	0.0693738i
$537$	2.70754	−	3.11243i	0.116839	−	0.134311i
$538$	0.105326	−	0.0507224i	0.00454093	−	0.00218680i
$539$	−0.814262	−	3.10706i	−0.0350727	−	0.133831i
$540$	−17.9337	−	8.63642i	−0.771744	−	0.371653i
$541$	−1.45068	+	0.623719i	−0.0623695	+	0.0268158i	−0.425946	−	0.904748i	$-0.640059\pi$
$541$	−1.45068	+	0.623719i	−0.0623695	+	0.0268158i	0.363577	+	0.931564i	$0.381555\pi$
$542$	−0.967046	−	0.859570i	−0.0415382	−	0.0369217i
$543$	−13.9812	+	5.31551i	−0.599989	+	0.228110i
$544$	1.08553	+	4.32755i	0.0465418	+	0.185542i
$545$	10.6289	−	17.5335i	0.455293	−	0.751053i
$546$	−0.0422142	+	0.124876i	−0.00180660	+	0.00534419i
$547$	−5.45838	−	0.703781i	−0.233384	−	0.0300915i	0.0102971	−	0.999947i	$-0.496722\pi$
$547$	−5.45838	−	0.703781i	−0.233384	−	0.0300915i	−0.243681	+	0.969855i	$0.578355\pi$
$548$	−5.25828	+	15.2888i	−0.224622	+	0.653106i
$549$	−2.62225	−	0.0560495i	−0.111915	−	0.00239214i
$550$	0.00582542	−	0.00361709i	0.000248397	−	0.000154233i
$551$	−5.02077	+	35.9102i	−0.213892	+	1.52983i
$552$	−1.48131	−	1.10553i	−0.0630486	−	0.0470544i
$553$	9.31582	+	26.6296i	0.396149	+	1.13240i
$554$	−0.178419	+	0.341997i	−0.00758031	+	0.0145300i
$555$	−3.76925	+	3.35034i	−0.159996	+	0.142214i
$556$	19.6253	−	41.8916i	0.832297	−	1.77660i
$557$	−10.2195	+	26.0390i	−0.433016	+	1.10331i	0.533295	+	0.845929i	$0.320954\pi$
$557$	−10.2195	+	26.0390i	−0.433016	+	1.10331i	−0.966311	+	0.257377i	$0.917142\pi$
$558$	−1.12961	−	0.348438i	−0.0478202	−	0.0147506i
$559$	1.58486	+	9.80295i	0.0670326	+	0.414620i
$560$	9.19215	−	21.0643i	0.388439	−	0.890128i
$561$	−2.13429	+	0.137026i	−0.0901099	+	0.00578524i
$562$	−0.244418	−	0.521728i	−0.0103101	−	0.0220078i
$563$	25.8589	+	11.1180i	1.08982	+	0.468570i	0.862916	−	0.505347i	$-0.168635\pi$
$563$	25.8589	+	11.1180i	1.08982	+	0.468570i	0.226906	+	0.973917i	$0.427139\pi$
$564$	−4.95473	−	5.69567i	−0.208632	−	0.239831i
$565$	19.4529	+	4.65925i	0.818392	+	0.196016i
$566$	0.549682	+	1.85206i	0.0231049	+	0.0778479i
$567$	−0.195867	+	7.30938i	−0.00822566	+	0.306965i
$568$	−3.90965	−	0.251008i	−0.164045	−	0.0105321i
$569$	4.11014	+	10.4725i	0.172306	+	0.439029i	0.990774	−	0.135523i	$-0.0432716\pi$
$569$	4.11014	+	10.4725i	0.172306	+	0.439029i	−0.818468	+	0.574552i	$0.805176\pi$
$570$	−0.0374172	−	0.499298i	−0.00156723	−	0.0209133i
$571$	16.5436	−	13.4848i	0.692327	−	0.564320i	−0.219140	−	0.975693i	$-0.570325\pi$
$571$	16.5436	−	13.4848i	0.692327	−	0.564320i	0.911467	+	0.411374i	$0.134951\pi$
$572$	0.0402329	+	0.752308i	0.00168222	+	0.0314556i
$573$	16.3668	+	4.29189i	0.683734	+	0.179296i
$574$	−0.0140592	−	0.0280410i	−0.000586819	−	0.00117041i
$575$	−1.24922	+	1.06348i	−0.0520961	+	0.0443501i
$576$	−15.2225	+	9.00694i	−0.634270	+	0.375289i
$577$	9.27094	−	14.5811i	0.385954	−	0.607019i	−0.594422	−	0.804153i	$-0.702619\pi$
$577$	9.27094	−	14.5811i	0.385954	−	0.607019i	0.980377	+	0.197134i	$0.0631634\pi$
$578$	0.727031	+	0.369463i	0.0302405	+	0.0153676i
$579$	−4.68200	−	7.36373i	−0.194577	−	0.306026i
$580$	4.01949	+	41.6662i	0.166900	+	1.73009i
$581$	−2.42038	−	6.07278i	−0.100414	−	0.251941i
$582$	0.0106258	+	0.0102905i	0.000440454	+	0.000426556i
$583$	1.61479	−	2.11612i	0.0668779	−	0.0876408i
$584$	−0.680339	+	0.717696i	−0.0281526	+	0.0296985i
$585$	1.55551	+	3.72713i	0.0643123	+	0.154098i
$586$	0.171116	−	0.625231i	0.00706872	−	0.0258280i
$587$	3.68187	−	16.1313i	0.151967	−	0.665812i	−0.840345	−	0.542052i	$-0.817648\pi$
$587$	3.68187	−	16.1313i	0.151967	−	0.665812i	0.992312	−	0.123760i	$-0.0394952\pi$
$588$	12.1467	−	0.127953i	0.500923	−	0.00527668i
$589$	6.36821	+	27.9010i	0.262398	+	1.14964i
$590$	−1.44137	−	0.0616457i	−0.0593403	−	0.00253791i
$591$	−2.12329	+	3.86616i	−0.0873404	+	0.159033i
$592$	1.45737	+	10.4236i	0.0598975	+	0.428407i
$593$	19.8030	+	23.7717i	0.813211	+	0.976188i	0.999981	−	0.00621583i	$-0.00197857\pi$
$593$	19.8030	+	23.7717i	0.813211	+	0.976188i	−0.186769	+	0.982404i	$0.559802\pi$
$594$	0.0503079	+	0.136703i	0.00206416	+	0.00560898i
$595$	−13.3051	−	28.0157i	−0.545457	−	1.14853i
$596$	−4.85124	−	8.00263i	−0.198715	−	0.327801i
$597$	−13.7891	+	13.9372i	−0.564349	+	0.570412i
$598$	0.0882629	+	0.428743i	0.00360934	+	0.0175326i
$599$	−4.46935	−	12.9950i	−0.182613	−	0.530960i	0.816298	−	0.577631i	$-0.196023\pi$
$599$	−4.46935	−	12.9950i	−0.182613	−	0.530960i	−0.998910	+	0.0466716i	$0.985139\pi$
$600$	0.0158354	+	0.0494547i	0.000646479	+	0.00201898i
$601$	−6.64844	+	1.74343i	−0.271196	+	0.0711159i	−0.386748	−	0.922186i	$-0.626402\pi$
$601$	−6.64844	+	1.74343i	−0.271196	+	0.0711159i	0.115552	+	0.993301i	$0.463136\pi$
$602$	−1.95362	+	1.05919i	−0.0796237	+	0.0431692i
$603$	21.8962	−	4.26428i	0.891681	−	0.173655i
$604$	−37.4099	+	10.6695i	−1.52219	+	0.434134i
$605$	23.0654	+	5.00583i	0.937740	+	0.203516i
$606$	0.708588	+	0.483107i	0.0287844	+	0.0196249i
$607$	23.1377	−	3.48744i	0.939130	−	0.141551i	0.338399	−	0.941003i	$-0.390115\pi$
$607$	23.1377	−	3.48744i	0.939130	−	0.141551i	0.600730	+	0.799452i	$0.294877\pi$
$608$	−2.74262	−	1.54462i	−0.111228	−	0.0626425i
$609$	−19.1735	+	10.9317i	−0.776950	+	0.442976i
$610$	−0.119680	−	0.131781i	−0.00484570	−	0.00533565i
$611$	−0.0382536	+	3.57975i	−0.00154757	+	0.144821i
$612$	−4.33334	+	23.5916i	−0.175165	+	0.953633i
$613$	−24.5493	+	13.1430i	−0.991536	+	0.530839i	−0.886054	−	0.463582i	$-0.846564\pi$
$613$	−24.5493	+	13.1430i	−0.991536	+	0.530839i	−0.105482	+	0.994421i	$0.533639\pi$
$614$	−1.24938	+	0.271150i	−0.0504209	+	0.0109427i
$615$	0.300393	+	0.121616i	0.0121130	+	0.00490402i
$616$	−0.312262	+	0.128339i	−0.0125814	+	0.00517093i
$617$	17.1672	+	24.6105i	0.691126	+	0.990781i	0.999222	+	0.0394260i	$0.0125529\pi$
$617$	17.1672	+	24.6105i	0.691126	+	0.990781i	−0.308096	+	0.951355i	$0.599692\pi$
$618$	−0.0206157	+	0.275097i	−0.000829285	+	0.0110660i
$619$	−4.92537	+	1.51927i	−0.197967	+	0.0610648i	−0.392153	−	0.919900i	$-0.628270\pi$
$619$	−4.92537	+	1.51927i	−0.197967	+	0.0610648i	0.194186	+	0.980965i	$0.437793\pi$
$620$	14.6521	+	29.6117i	0.588442	+	1.18924i
$621$	−16.7768	−	30.5478i	−0.673229	−	1.22584i
$622$	1.26621	−	0.944993i	0.0507702	−	0.0378908i
$623$	−27.4378	−	18.4959i	−1.09927	−	0.741021i
$624$	−2.78987	−	0.543327i	−0.111684	−	0.0217505i
$625$	−23.7933	+	2.03895i	−0.951731	+	0.0815580i
$626$	1.02832	+	0.366005i	0.0411001	+	0.0146285i
$627$	0.965740	−	1.15929i	0.0385679	−	0.0462974i
$628$	19.2582	+	11.9577i	0.768488	+	0.477165i
$629$	11.9036	+	7.74840i	0.474629	+	0.308949i
$630$	−0.672359	+	0.604002i	−0.0267874	+	0.0240640i
$631$	−1.25587	+	13.0184i	−0.0499953	+	0.518254i	0.936061	+	0.351839i	$0.114444\pi$
$631$	−1.25587	+	13.0184i	−0.0499953	+	0.518254i	−0.986056	+	0.166415i	$0.946781\pi$
$632$	2.64356	−	1.34341i	0.105155	−	0.0534378i
$633$	7.55312	+	4.46908i	0.300210	+	0.177630i
$634$	−0.0377603	+	0.00651956i	−0.00149965	+	0.000258925i
$635$	−1.66480	−	9.06351i	−0.0660655	−	0.359674i
$636$	6.27661	+	7.87062i	0.248884	+	0.312090i
$637$	−4.34560	−	3.78145i	−0.172179	−	0.149827i
$638$	0.190995	−	0.239500i	0.00756155	−	0.00948189i
$639$	−27.8639	−	14.9175i	−1.10228	−	0.590128i
$640$	−4.65739	−	1.32831i	−0.184099	−	0.0525059i
$641$	−15.8742	−	1.36033i	−0.626993	−	0.0537298i	−0.232452	−	0.972608i	$-0.574675\pi$
$641$	−15.8742	−	1.36033i	−0.626993	−	0.0537298i	−0.394541	+	0.918878i	$0.629096\pi$
$642$	−0.151202	−	0.0688744i	−0.00596749	−	0.00271826i
$643$	17.9221	+	5.95055i	0.706779	+	0.234667i	0.645838	−	0.763475i	$-0.276508\pi$
$643$	17.9221	+	5.95055i	0.706779	+	0.234667i	0.0609409	+	0.998141i	$0.480590\pi$
$644$	34.6079	−	20.7239i	1.36374	−	0.816636i
$645$	7.92936	−	21.5466i	0.312218	−	0.848398i
$646$	−1.32854	+	0.472858i	−0.0522706	+	0.0186043i
$647$	28.3390	−	12.9087i	1.11412	−	0.507494i	0.229266	−	0.973364i	$-0.426367\pi$
$647$	28.3390	−	12.9087i	1.11412	−	0.507494i	0.884853	+	0.465870i	$0.154259\pi$
$648$	0.764171	−	0.0819691i	0.0300195	−	0.00322005i
$649$	−2.99094	−	3.15517i	−0.117405	−	0.123851i
$650$	0.00497791	−	0.0112452i	0.000195250	−	0.000441072i
$651$	−11.0791	+	13.4428i	−0.434222	+	0.526863i
$652$	−14.5279	−	12.3678i	−0.568958	−	0.484361i
$653$	19.8917	+	3.43443i	0.778421	+	0.134400i	0.545517	−	0.838100i	$-0.316333\pi$
$653$	19.8917	+	3.43443i	0.778421	+	0.134400i	0.232905	+	0.972500i	$0.425177\pi$
$654$	−0.00606361	−	0.567430i	−0.000237106	−	0.0221883i
$655$	−9.20751	+	8.54332i	−0.359767	+	0.333815i
$656$	0.558838	−	0.381009i	0.0218190	−	0.0148759i
$657$	−7.39495	+	2.99388i	−0.288504	+	0.116802i
$658$	−0.759000	+	0.256451i	−0.0295889	+	0.00999752i
$659$	−3.22253	+	19.9325i	−0.125532	+	0.776459i	0.844871	+	0.534969i	$0.179677\pi$
$659$	−3.22253	+	19.9325i	−0.125532	+	0.776459i	−0.970403	+	0.241490i	$0.922364\pi$
$660$	0.772496	−	1.56121i	0.0300694	−	0.0607699i
$661$	−22.9362	+	0.980953i	−0.892114	+	0.0381547i	−0.484292	−	0.874907i	$-0.660923\pi$
$661$	−22.9362	+	0.980953i	−0.892114	+	0.0381547i	−0.407822	+	0.913061i	$0.633712\pi$
$662$	−0.0665739	−	0.243251i	−0.00258747	−	0.00945422i
$663$	−3.02419	+	2.35929i	−0.117450	+	0.0916271i
$664$	−0.598710	+	0.337187i	−0.0232344	+	0.0130854i
$665$	20.8021	+	6.78535i	0.806671	+	0.263125i
$666$	0.117768	−	0.396800i	0.00456342	−	0.0153757i
$667$	−36.6460	+	63.4727i	−1.41894	+	2.45767i
$668$	−7.25059	−	12.5584i	−0.280534	−	0.485899i
$669$	8.20331	−	1.96481i	0.317158	−	0.0759638i
$670$	1.23245	+	0.879426i	0.0476135	+	0.0339752i
$671$	0.0171939	−	0.536169i	0.000663763	−	0.0206986i
$672$	−0.275289	−	1.89609i	−0.0106195	−	0.0731431i
$673$	0.184702	+	0.354039i	0.00711975	+	0.0136472i	0.890133	−	0.455701i	$-0.150611\pi$
$673$	0.184702	+	0.354039i	0.00711975	+	0.0136472i	−0.883013	+	0.469348i	$0.844489\pi$
$674$	1.78855	+	0.679990i	0.0688924	+	0.0261922i
$675$	−0.114823	+	0.972364i	−0.00441956	+	0.0374263i
$676$	−14.9148	−	19.5452i	−0.573645	−	0.751738i
$677$	34.2916	+	3.67830i	1.31793	+	0.141369i	0.738834	−	0.673888i	$-0.235377\pi$
$677$	34.2916	+	3.67830i	1.31793	+	0.141369i	0.579100	+	0.815257i	$0.303404\pi$
$678$	0.525408	−	0.174448i	0.0201782	−	0.00669962i
$679$	−0.592502	+	0.258452i	−0.0227381	+	0.00991849i
$680$	−2.73209	+	1.77839i	−0.104771	+	0.0681982i
$681$	−12.3941	+	0.264919i	−0.474942	+	0.0101517i
$682$	0.0737300	−	0.230262i	0.00282327	−	0.00881718i
$683$	1.92030	−	35.9073i	0.0734782	−	1.37396i	−0.687974	−	0.725735i	$-0.741500\pi$
$683$	1.92030	−	35.9073i	0.0734782	−	1.37396i	0.761453	−	0.648220i	$-0.224486\pi$
$684$	−9.97589	−	13.6691i	−0.381438	−	0.522652i
$685$	−17.7268			−0.677305
$686$	0.477654	−	1.19738i	0.0182369	−	0.0457164i
$687$	−17.9501			−0.684840
$688$	−28.2477	−	38.7055i	−1.07694	−	1.47563i
$689$	0.254941	−	4.76710i	0.00971249	−	0.181612i
$690$	0.308630	−	0.963863i	0.0117493	−	0.0366936i
$691$	−16.9936	+	0.363233i	−0.646468	+	0.0138180i	−0.343456	−	0.939169i	$-0.611598\pi$
$691$	−16.9936	+	0.363233i	−0.646468	+	0.0138180i	−0.303012	+	0.952987i	$0.597992\pi$
$692$	30.8591	−	20.0870i	1.17309	−	0.763594i
$693$	−2.72171	−	0.102047i	−0.103389	−	0.00387643i
$694$	−0.249258	+	0.0827593i	−0.00946170	+	0.00314150i
$695$	50.4321	+	5.40962i	1.91300	+	0.205199i
$696$	1.40731	+	1.84422i	0.0533440	+	0.0699051i
$697$	0.107039	−	0.906444i	0.00405440	−	0.0343340i
$698$	−0.487810	−	0.185461i	−0.0184639	−	0.00701980i
$699$	3.31286	+	6.35014i	0.125304	+	0.240184i
$700$	−1.12962	−	0.0908119i	−0.0426958	−	0.00343237i
$701$	−0.681323	+	21.2462i	−0.0257332	+	0.802456i	0.902551	+	0.430584i	$0.141692\pi$
$701$	−0.681323	+	21.2462i	−0.0257332	+	0.802456i	−0.928284	+	0.371873i	$0.878716\pi$
$702$	0.212656	+	0.151743i	0.00802616	+	0.00572716i
$703$	−9.74480	+	2.33401i	−0.367532	+	0.0880290i
$704$	−1.80880	−	3.13293i	−0.0681715	−	0.118077i
$705$	4.13855	−	7.16818i	0.155867	−	0.269969i
$706$	0.494552	−	1.66631i	0.0186127	−	0.0627124i
$707$	−31.3016	+	20.6106i	−1.17722	+	0.775143i
$708$	14.3261	−	8.06829i	0.538406	−	0.303225i
$709$	−8.38049	+	6.53795i	−0.314736	+	0.245538i	−0.760092	−	0.649816i	$-0.774846\pi$
$709$	−8.38049	+	6.53795i	−0.314736	+	0.245538i	0.445356	+	0.895354i	$0.353077\pi$
$710$	−0.566262	−	2.06904i	−0.0212514	−	0.0776496i
$711$	23.9008	−	1.02221i	0.896349	−	0.0383358i
$712$	−1.54245	+	3.11728i	−0.0578058	+	0.116825i
$713$	−9.23238	+	57.1055i	−0.345755	+	2.13862i
$714$	−0.721845	−	0.464475i	−0.0270144	−	0.0173825i
$715$	−0.765658	+	0.309981i	−0.0286340	+	0.0115926i
$716$	7.81858	−	5.33061i	0.292194	−	0.199214i
$717$	6.03149	−	5.59640i	0.225250	−	0.209001i
$718$	−0.0167440	−	1.56689i	−0.000624879	−	0.0584759i
$719$	−11.3899	−	1.96654i	−0.424772	−	0.0733397i	−0.0462453	−	0.998930i	$-0.514726\pi$
$719$	−11.3899	−	1.96654i	−0.424772	−	0.0733397i	−0.378527	+	0.925590i	$0.623569\pi$
$720$	−14.8393	−	12.6328i	−0.553026	−	0.470798i
$721$	−10.7761	−	5.40497i	−0.401323	−	0.201292i
$722$	−0.132629	+	0.299611i	−0.00493594	+	0.0111504i
$723$	7.62901	+	8.04791i	0.283726	+	0.299305i
$724$	−34.1148	+	3.65934i	−1.26787	+	0.135998i
$725$	1.87382	−	0.853547i	0.0695920	−	0.0317000i
$726$	0.615405	−	0.219037i	0.0228398	−	0.00812922i
$727$	18.1725	−	49.3805i	0.673981	−	1.83142i	0.131575	−	0.991306i	$-0.457997\pi$
$727$	18.1725	−	49.3805i	0.673981	−	1.83142i	0.542406	−	0.840117i	$-0.317514\pi$
$728$	−0.333055	+	0.505648i	−0.0123438	+	0.0187406i
$729$	−5.40967	−	1.79613i	−0.200358	−	0.0665235i
$730$	−0.492763	−	0.224459i	−0.0182380	−	0.00830760i
$731$	−64.4273	−	5.52105i	−2.38293	−	0.204203i
$732$	1.95098	+	0.556428i	0.0721104	+	0.0205662i
$733$	−33.2693	−	17.8114i	−1.22883	−	0.657878i	−0.275933	−	0.961177i	$-0.588987\pi$
$733$	−33.2693	−	17.8114i	−1.22883	−	0.657878i	−0.952896	+	0.303299i	$0.901912\pi$
$734$	−1.15418	+	1.44730i	−0.0426016	+	0.0534207i
$735$	4.46408	+	12.5483i	0.164660	+	0.462851i
$736$	−3.96691	−	4.97435i	−0.146222	−	0.183357i
$737$	0.824260	+	4.48744i	0.0303620	+	0.165297i
$738$	−0.0262110	+	0.00452550i	−0.000964840	+	0.000166586i
$739$	14.7678	+	8.73789i	0.543241	+	0.321429i	0.754820	−	0.655932i	$-0.227724\pi$
$739$	14.7678	+	8.73789i	0.543241	+	0.321429i	−0.211579	+	0.977361i	$0.567860\pi$
$740$	−10.3128	+	5.24075i	−0.379105	+	0.192654i
$741$	0.259840	−	2.69352i	0.00954547	−	0.0989488i
$742$	1.02582	−	0.298420i	0.0376591	−	0.0109553i
$743$	27.3944	+	17.8318i	1.00500	+	0.654185i	0.939101	−	0.343641i	$-0.111660\pi$
$743$	27.3944	+	17.8318i	1.00500	+	0.654185i	0.0659028	+	0.997826i	$0.479007\pi$
$744$	1.55552	+	0.965843i	0.0570280	+	0.0354095i
$745$	6.56735	−	7.88352i	0.240609	−	0.288830i
$746$	−2.12897	−	0.757750i	−0.0779471	−	0.0277432i
$747$	−5.52315	+	0.473303i	−0.202081	+	0.0173172i
$748$	−4.81539	−	0.937797i	−0.176068	−	0.0342892i
$749$	5.29650	−	4.96660i	0.193530	−	0.181476i
$750$	−0.553480	+	0.413073i	−0.0202102	+	0.0150833i
$751$	24.9605	+	45.4491i	0.910823	+	1.65846i	0.739404	+	0.673262i	$0.235107\pi$
$751$	24.9605	+	45.4491i	0.910823	+	1.65846i	0.171419	+	0.985198i	$0.445165\pi$
$752$	−7.66106	−	15.4829i	−0.279370	−	0.564604i
$753$	−11.0876	+	3.42006i	−0.404053	+	0.124634i
$754$	0.0410559	−	0.547853i	0.00149517	−	0.0199516i
$755$	−24.4023	−	34.9826i	−0.888091	−	1.27315i
$756$	6.72817	−	23.1151i	0.244701	−	0.840686i
$757$	15.2907	+	6.19052i	0.555750	+	0.224998i	0.635883	−	0.771786i	$-0.280636\pi$
$757$	15.2907	+	6.19052i	0.555750	+	0.224998i	−0.0801321	+	0.996784i	$0.525534\pi$
$758$	0.683513	−	0.148342i	0.0248263	−	0.00538801i
$759$	2.68876	−	1.43948i	0.0975958	−	0.0522499i
$760$	0.415490	−	2.26201i	0.0150714	−	0.0820519i
$761$	−0.267257	+	25.0098i	−0.00968806	+	0.906604i	0.886449	+	0.462826i	$0.153165\pi$
$761$	−0.267257	+	25.0098i	−0.00968806	+	0.906604i	−0.896137	+	0.443778i	$0.853638\pi$
$762$	−0.171464	−	0.188801i	−0.00621147	−	0.00683952i
$763$	23.0348	+	9.18484i	0.833915	+	0.332514i
$764$	33.8182	+	19.0461i	1.22350	+	0.689062i
$765$	−26.0054	+	3.91968i	−0.940226	+	0.141716i
$766$	0.469932	+	0.320394i	0.0169793	+	0.0115763i
$767$	−7.61963	−	1.65367i	−0.275129	−	0.0597107i
$768$	13.0598	−	3.72470i	0.471254	−	0.134404i
$769$	−53.9740	+	10.5114i	−1.94635	+	0.379052i	−0.948245	+	0.317540i	$0.897143\pi$
$769$	−53.9740	+	10.5114i	−1.94635	+	0.379052i	−0.998106	+	0.0615120i	$0.980408\pi$
$770$	−0.122059	−	0.138828i	−0.00439869	−	0.00500302i
$771$	−20.1537	+	5.28493i	−0.725819	+	0.190332i
$772$	−6.10404	−	19.0632i	−0.219689	−	0.686099i
$773$	7.65587	+	22.2600i	0.275363	+	0.800637i	0.994402	+	0.105667i	$0.0336979\pi$
$773$	7.65587	+	22.2600i	0.275363	+	0.800637i	−0.719039	+	0.694970i	$0.755418\pi$
$774$	0.379962	+	1.84569i	0.0136575	+	0.0663420i
$775$	1.14300	−	1.15528i	0.0410579	−	0.0414990i
$776$	0.0352217	+	0.0581019i	0.00126439	+	0.00208574i
$777$	−4.74800	−	3.82868i	−0.170334	−	0.137353i
$778$	0.386121	+	1.04922i	0.0138431	+	0.0376162i
$779$	0.412156	+	0.494757i	0.0147670	+	0.0177265i
$780$	−0.432566	−	3.09386i	−0.0154884	−	0.110778i
$781$	3.11177	−	5.66602i	0.111348	−	0.202746i
$782$	−2.84782	−	0.121798i	−0.101838	−	0.00435548i
$783$	9.73336	+	42.6447i	0.347842	+	1.52400i
$784$	26.9604	+	6.76715i	0.962870	+	0.241684i
$785$	−5.53063	+	24.2313i	−0.197397	+	0.864851i
$786$	−0.0917654	+	0.335297i	−0.00327317	+	0.0119597i
$787$	−3.49750	−	8.38033i	−0.124673	−	0.298727i	0.848350	−	0.529435i	$-0.177596\pi$
$787$	−3.49750	−	8.38033i	−0.124673	−	0.298727i	−0.973023	+	0.230709i	$0.925896\pi$
$788$	−6.96076	+	7.34297i	−0.247967	+	0.261582i
$789$	−5.20308	+	6.81843i	−0.185235	+	0.242742i
$790$	1.16635	+	1.12955i	0.0414969	+	0.0401875i
$791$	−1.68087	+	24.1347i	−0.0597648	+	0.858130i
$792$	0.0274891	+	0.284954i	0.000976783	+	0.0101254i
$793$	−0.516205	−	0.811874i	−0.0183310	−	0.0288305i
$794$	1.38068	+	0.701634i	0.0489985	+	0.0249000i
$795$	−5.92220	+	9.31429i	−0.210039	+	0.330344i
$796$	−38.7051	+	22.9013i	−1.37187	+	0.811716i
$797$	−15.8191	+	13.4670i	−0.560341	+	0.477025i	−0.882924	−	0.469516i	$-0.844428\pi$
$797$	−15.8191	+	13.4670i	−0.560341	+	0.477025i	0.322583	+	0.946541i	$0.395449\pi$
$798$	0.588170	−	0.144154i	0.0208210	−	0.00510301i
$799$	−22.5494	−	5.91316i	−0.797742	−	0.209192i
$800$	0.00954560	+	0.178491i	0.000337488	+	0.00631062i
$801$	−21.7490	+	17.7277i	−0.768463	+	0.626379i
$802$	0.0254920	+	0.340167i	0.000900153	+	0.0120117i
$803$	−0.596136	−	1.51893i	−0.0210372	−	0.0536018i
$804$	−17.2195	−	1.10553i	−0.607285	−	0.0389890i
$805$	33.8277	+	28.4921i	1.19227	+	1.00421i
$806$	−0.123376	−	0.415693i	−0.00434572	−	0.0146422i
$807$	−1.42059	−	0.340251i	−0.0500072	−	0.0119774i
$808$	2.58543	+	2.97206i	0.0909553	+	0.104557i
$809$	−0.454448	−	0.195390i	−0.0159775	−	0.00686955i	0.386986	−	0.922086i	$-0.373516\pi$
$809$	−0.454448	−	0.195390i	−0.0159775	−	0.00686955i	−0.402963	+	0.915216i	$0.632020\pi$
$810$	0.178525	+	0.381075i	0.00627273	+	0.0133896i
$811$	45.5888	−	2.92690i	1.60084	−	0.102777i	0.762155	−	0.647395i	$-0.224141\pi$
$811$	45.5888	−	2.92690i	1.60084	−	0.102777i	0.838685	+	0.544617i	$0.183325\pi$
$812$	−48.9037	+	13.0997i	−1.71618	+	0.459710i
$813$	2.58030	+	15.9601i	0.0904952	+	0.559745i
$814$	0.0808946	+	0.0249527i	0.00283535	+	0.000874591i
$815$	7.64262	−	19.4731i	0.267709	−	0.682112i
$816$	7.85180	−	16.7602i	0.274868	−	0.586726i
$817$	34.0972	−	30.3077i	1.19291	−	1.06033i
$818$	−0.405050	+	0.776404i	−0.0141622	+	0.0271463i
$819$	−4.13617	+	2.59849i	−0.144530	+	0.0907986i
$820$	0.595764	+	0.444630i	0.0208050	+	0.0155272i
$821$	2.89502	−	20.7061i	0.101037	−	0.722649i	−0.871583	−	0.490247i	$-0.836906\pi$
$821$	2.89502	−	20.7061i	0.101037	−	0.722649i	0.972620	−	0.232401i	$-0.0746582\pi$
$822$	−0.416800	+	0.258797i	−0.0145376	+	0.00902658i
$823$	−45.9854	−	0.982921i	−1.60295	−	0.0342625i	−0.788701	−	0.614777i	$-0.789246\pi$
$823$	−45.9854	−	0.982921i	−1.60295	−	0.0342625i	−0.814250	+	0.580515i	$0.802851\pi$
$824$	−0.412116	+	1.19826i	−0.0143567	+	0.0417433i
$825$	−0.0849789	−	0.0109568i	−0.00295859	−	0.000381467i
$826$	−0.213750	−	1.73174i	−0.00743731	−	0.0602550i
$827$	−2.27962	+	3.76047i	−0.0792701	+	0.130764i	−0.892275	−	0.451493i	$-0.850892\pi$
$827$	−2.27962	+	3.76047i	−0.0792701	+	0.130764i	0.813005	+	0.582257i	$0.197830\pi$
$828$	−8.32228	−	33.1774i	−0.289219	−	1.15299i
$829$	−43.1057	+	16.3884i	−1.49712	+	0.569192i	−0.961389	−	0.275193i	$-0.911258\pi$
$829$	−43.1057	+	16.3884i	−1.49712	+	0.569192i	−0.535735	+	0.844386i	$0.679966\pi$
$830$	−0.281206	−	0.249953i	−0.00976082	−	0.00867601i
$831$	4.42809	−	1.90386i	0.153609	−	0.0660442i
$832$	−5.84544	−	2.81502i	−0.202654	−	0.0975932i
$833$	30.7689	−	21.4561i	1.06608	−	0.743409i
$834$	1.26476	−	0.609076i	0.0437950	−	0.0210906i
$835$	10.4353	−	11.9958i	0.361127	−	0.415130i
$836$	2.81736	−	2.01036i	0.0974403	−	0.0695297i
$837$	19.1420	+	28.7310i	0.661643	+	0.993087i
$838$	−0.267291	+	1.29838i	−0.00923340	+	0.0448518i
$839$	−25.9003	+	3.33947i	−0.894177	+	0.115291i	−0.561235	−	0.827656i	$-0.689674\pi$
$839$	−25.9003	+	3.33947i	−0.894177	+	0.115291i	−0.332941	+	0.942948i	$0.608041\pi$
$840$	1.24465	−	0.640776i	0.0429445	−	0.0221089i
$841$	45.2467	−	43.8190i	1.56023	−	1.51100i
$842$	0.211360	+	1.78986i	0.00728393	+	0.0616828i
$843$	−1.75160	+	6.98288i	−0.0603283	+	0.240503i
$844$	14.1589	+	14.3110i	0.487368	+	0.492604i
$845$	14.9463	−	22.4335i	0.514168	−	0.771736i
$846$	0.0217741	+	0.678996i	0.000748608	+	0.0233444i
$847$	−1.37430	+	28.5131i	−0.0472216	+	0.979722i
$848$	9.32455	+	21.0643i	0.320206	+	0.723352i
$849$	9.29764	−	22.2780i	0.319094	−	0.764578i
$850$	0.0631389	+	0.0492571i	0.00216564	+	0.00168950i
$851$	−20.0282	−	3.01876i	−0.686558	−	0.103482i
$852$	17.9211	+	16.6284i	0.613967	+	0.569678i
$853$	−10.6750	+	11.7543i	−0.365504	+	0.402461i	−0.895155	−	0.445755i	$-0.852935\pi$
$853$	−10.6750	+	11.7543i	−0.365504	+	0.402461i	0.529651	+	0.848216i	$0.322323\pi$
$854$	0.133351	−	0.169036i	0.00456319	−	0.00578429i
$855$	10.6150	−	15.2175i	0.363027	−	0.520426i
$856$	−0.591558	−	0.482182i	−0.0202190	−	0.0164806i
$857$	1.65151	−	2.26292i	0.0564144	−	0.0772998i	−0.778627	−	0.627488i	$-0.784083\pi$
$857$	1.65151	−	2.26292i	0.0564144	−	0.0772998i	0.835041	+	0.550188i	$0.185444\pi$
$858$	−0.0134770	+	0.0184664i	−0.000460099	+	0.000630434i
$859$	−17.5824	−	14.3315i	−0.599904	−	0.488985i	0.282633	−	0.959228i	$-0.408792\pi$
$859$	−17.5824	−	14.3315i	−0.599904	−	0.488985i	−0.882537	+	0.470243i	$0.844166\pi$
$860$	30.1309	−	43.1949i	1.02746	−	1.47293i
$861$	−0.0852058	+	0.382588i	−0.00290381	+	0.0130386i
$862$	−0.225353	+	0.248138i	−0.00767555	+	0.00845163i
$863$	−12.0620	−	11.1919i	−0.410594	−	0.380975i	0.447657	−	0.894205i	$-0.352258\pi$
$863$	−12.0620	−	11.1919i	−0.410594	−	0.380975i	−0.858251	+	0.513230i	$0.828449\pi$
$864$	−3.75475	−	0.565938i	−0.127739	−	0.0192536i
$865$	31.8306	+	24.8323i	1.08227	+	0.844324i
$866$	0.192419	−	0.461052i	0.00653865	−	0.0156672i
$867$	−4.12491	−	9.31824i	−0.140089	−	0.316464i
$868$	−32.4043	+	23.3810i	−1.09987	+	0.793604i
$869$	0.156823	+	4.89032i	0.00531986	+	0.165893i
$870$	−0.704288	+	1.05709i	−0.0238776	+	0.0358389i
$871$	5.75499	+	5.81681i	0.195000	+	0.197095i
$872$	0.634178	−	2.52820i	0.0214760	−	0.0856156i
$873$	0.0642810	+	0.544353i	0.00217558	+	0.0184236i
$874$	1.44458	−	1.39899i	0.0488635	−	0.0473217i
$875$	−7.49722	−	29.2349i	−0.253452	−	0.988320i
$876$	6.12035	−	0.789132i	0.206787	−	0.0266623i
$877$	−10.0379	+	48.7597i	−0.338956	+	1.64650i	0.361185	+	0.932494i	$0.382372\pi$
$877$	−10.0379	+	48.7597i	−0.338956	+	1.64650i	−0.700141	+	0.714005i	$0.746880\pi$
$878$	0.263334	+	0.395249i	0.00888708	+	0.0133390i
$879$	−6.59343	+	4.70482i	−0.222391	+	0.158690i
$880$	2.61605	−	3.00726i	0.0881870	−	0.101375i
$881$	24.1355	−	11.6230i	0.813145	−	0.391590i	0.0193780	−	0.999812i	$-0.493831\pi$
$881$	24.1355	−	11.6230i	0.813145	−	0.391590i	0.793767	+	0.608222i	$0.208117\pi$
$882$	−0.854545	−	0.681690i	−0.0287740	−	0.0229537i
$883$	−17.2985	−	8.33054i	−0.582143	−	0.280345i	0.119546	−	0.992829i	$-0.461856\pi$
$883$	−17.2985	−	8.33054i	−0.582143	−	0.280345i	−0.701689	+	0.712484i	$0.747570\pi$
$884$	−8.08295	+	3.47527i	−0.271859	+	0.116886i
$885$	13.4739	+	11.9764i	0.452920	+	0.402583i
$886$	−0.956036	+	0.363476i	−0.0321187	+	0.0122112i
$887$	13.1258	+	52.3271i	0.440722	+	1.75697i	0.631536	+	0.775346i	$0.282425\pi$
$887$	13.1258	+	52.3271i	0.440722	+	1.75697i	−0.190814	+	0.981626i	$0.561113\pi$
$888$	−0.332339	+	0.548228i	−0.0111526	+	0.0183973i
$889$	10.4803	−	3.79249i	0.351498	−	0.127196i
$890$	−1.88874	−	0.243526i	−0.0633108	−	0.00816302i
$891$	−0.412435	+	1.19919i	−0.0138171	+	0.0401742i
$892$	19.3451	+	0.413494i	0.647722	+	0.0138448i
$893$	13.9722	−	8.67552i	0.467561	−	0.290315i
$894$	0.0393213	−	0.281239i	0.00131510	−	0.00940604i
$895$	8.31491	+	6.20558i	0.277937	+	0.207430i
$896$	0.656283	−	5.82069i	0.0219249	−	0.194456i
$897$	2.52996	−	4.84945i	0.0844728	−	0.161919i
$898$	1.90627	−	1.69441i	0.0636131	−	0.0565432i
$899$	30.8003	−	65.7454i	1.02725	−	2.19273i
$900$	−0.351079	+	0.894536i	−0.0117026	+	0.0298179i
$901$	29.7055	+	9.16293i	0.989634	+	0.305262i
$902$	−0.000868254	−	0.00537046i	−2.89097e−5	−	0.000178817i
$903$	27.2841	+	5.16458i	0.907957	+	0.171866i
$904$	2.53768	−	0.162924i	0.0844020	−	0.00541879i
$905$	−15.9591	−	34.0659i	−0.530499	−	1.13239i
$906$	−1.08448	−	0.466271i	−0.0360293	−	0.0154908i
$907$	7.44959	+	8.56361i	0.247360	+	0.284350i	0.864639	−	0.502394i	$-0.167547\pi$
$907$	7.44959	+	8.56361i	0.247360	+	0.284350i	−0.617279	+	0.786744i	$0.711765\pi$
$908$	−27.6546	−	6.62367i	−0.917752	−	0.219814i
$909$	9.04219	+	30.4661i	0.299910	+	1.01050i
$910$	−0.321124	−	0.0824036i	−0.0106452	−	0.00273165i
$911$	−3.89741	−	0.250222i	−0.129127	−	0.00829022i	−0.000627438	−	1.00000i	$-0.500200\pi$
$911$	−3.89741	−	0.250222i	−0.129127	−	0.00829022i	−0.128499	+	0.991710i	$0.541016\pi$
$912$	4.77046	+	12.1549i	0.157966	+	0.402490i
$913$	−0.0847273	−	1.13061i	−0.00280406	−	0.0374176i
$914$	−0.298751	+	0.243514i	−0.00988182	+	0.00805473i
$915$	0.118790	+	2.22123i	0.00392707	+	0.0734315i
$916$	−39.8285	−	10.4443i	−1.31597	−	0.345088i
$917$	−12.0268	−	9.28110i	−0.397160	−	0.306489i
$918$	−1.29534	+	1.10274i	−0.0427526	+	0.0363958i
$919$	6.81520	−	4.03246i	0.224813	−	0.133019i	−0.392457	−	0.919770i	$-0.628375\pi$
$919$	6.81520	−	4.03246i	0.224813	−	0.133019i	0.617270	+	0.786752i	$0.288239\pi$
$920$	2.49427	−	3.92293i	0.0822337	−	0.129335i
$921$	14.2417	+	7.23734i	0.469279	+	0.238478i
$922$	0.853258	+	1.34198i	0.0281006	+	0.0441958i
$923$	−1.11323	−	11.5398i	−0.0366423	−	0.379836i
$924$	2.01638	+	0.610360i	0.0663341	+	0.0200794i
$925$	0.408761	+	0.395863i	0.0134400	+	0.0130159i
$926$	0.750651	−	0.983698i	0.0246679	−	0.0323263i
$927$	−7.03284	+	7.41901i	−0.230989	+	0.243672i
$928$	3.07556	+	7.36930i	0.100960	+	0.241909i
$929$	10.4191	−	38.0699i	0.341840	−	1.24903i	−0.564129	−	0.825687i	$-0.690788\pi$
$929$	10.4191	−	38.0699i	0.341840	−	1.24903i	0.905969	−	0.423345i	$-0.139144\pi$
$930$	−0.223088	+	0.977412i	−0.00731534	+	0.0320506i
$931$	−3.94825	+	26.1679i	−0.129399	+	0.857618i
$932$	3.65590	+	16.0175i	0.119753	+	0.524672i
$933$	−19.7245	−	0.843593i	−0.645751	−	0.0276180i
$934$	0.840256	−	1.52997i	0.0274940	−	0.0500621i
$935$	−0.744803	−	5.32708i	−0.0243577	−	0.174214i
$936$	0.328618	+	0.394476i	0.0107412	+	0.0128939i
$937$	−19.5250	−	53.0558i	−0.637854	−	1.73326i	−0.679037	−	0.734104i	$-0.737602\pi$
$937$	−19.5250	−	53.0558i	−0.637854	−	1.73326i	0.0411823	−	0.999152i	$-0.486888\pi$
$938$	−0.803447	+	1.64551i	−0.0262335	+	0.0537276i
$939$	−7.07042	−	11.6634i	−0.230734	−	0.380621i
$940$	13.3536	−	13.4970i	0.435546	−	0.440225i
$941$	9.86435	+	47.9167i	0.321569	+	1.56204i	0.751843	+	0.659342i	$0.229165\pi$
$941$	9.86435	+	47.9167i	0.321569	+	1.56204i	−0.430275	+	0.902698i	$0.641583\pi$
$942$	0.223719	+	0.650480i	0.00728916	+	0.0211938i
$943$	0.396923	+	1.23961i	0.0129256	+	0.0403671i
$944$	36.3930	−	9.54337i	1.18449	−	0.310610i
$945$	26.3653	−	1.26676i	0.857662	−	0.0412076i
$946$	−0.378304	+	0.0736747i	−0.0122997	+	0.00239537i
$947$	6.96392	−	1.98614i	0.226297	−	0.0645409i	−0.159214	−	0.987244i	$-0.550896\pi$
$947$	6.96392	−	1.98614i	0.226297	−	0.0645409i	0.385511	+	0.922703i	$0.374025\pi$
$948$	−18.0833	−	3.92457i	−0.587317	−	0.127464i
$949$	−2.41791	−	1.64850i	−0.0784887	−	0.0535127i
$950$	−0.0558652	+	0.00842032i	−0.00181251	+	0.000273191i
$951$	0.417202	+	0.234964i	0.0135287	+	0.00761922i
$952$	−2.66605	−	2.90473i	−0.0864070	−	0.0941427i
$953$	−27.8534	−	30.6697i	−0.902261	−	0.993489i	0.0977378	−	0.995212i	$-0.468839\pi$
$953$	−27.8534	−	30.6697i	−0.902261	−	0.993489i	−0.999999	+	0.00172287i	$0.999452\pi$
$954$	0.00968013	−	0.905862i	0.000313406	−	0.0293284i
$955$	−7.68798	+	41.8549i	−0.248777	+	1.35439i
$956$	16.6392	−	8.90813i	0.538150	−	0.288109i
$957$	−3.74070	+	0.811837i	−0.120920	+	0.0262430i
$958$	1.90488	+	0.771201i	0.0615439	+	0.0249164i
$959$	−3.53323	−	21.1468i	−0.114094	−	0.682866i
$960$	8.58208	+	12.3031i	0.276985	+	0.397079i
$961$	1.96561	−	26.2293i	0.0634068	−	0.846105i
$962$	0.145080	−	0.0447513i	0.00467757	−	0.00144284i
$963$	−2.73050	−	5.51831i	−0.0879891	−	0.177825i
$964$	12.2449	+	22.2960i	0.394382	+	0.718105i
$965$	17.5884	−	13.1265i	0.566190	−	0.422558i
$966$	1.21134	+	0.176060i	0.0389741	+	0.00566463i
$967$	−35.0872	−	6.83322i	−1.12833	−	0.219742i	−0.407735	−	0.913101i	$-0.633681\pi$
$967$	−35.0872	−	6.83322i	−1.12833	−	0.219742i	−0.720592	+	0.693359i	$0.756130\pi$
$968$	2.98949	−	0.256183i	0.0960859	−	0.00823402i
$969$	16.6008	+	5.90862i	0.533295	+	0.189812i
$970$	−0.0238117	+	0.0285838i	−0.000764547	+	0.000917771i
$971$	29.6326	+	18.3993i	0.950956	+	0.590462i	0.912623	−	0.408803i	$-0.134054\pi$
$971$	29.6326	+	18.3993i	0.950956	+	0.590462i	0.0383335	+	0.999265i	$0.487795\pi$
$972$	−26.8973	−	17.5082i	−0.862732	−	0.561576i
$973$	3.59864	+	61.2402i	0.115367	+	1.96327i
$974$	−0.181492	+	1.88136i	−0.00581539	+	0.0602826i
$975$	−0.136992	+	0.0696168i	−0.00438727	+	0.00222952i
$976$	3.99542	+	2.36404i	0.127890	+	0.0756709i
$977$	25.1854	−	4.34842i	0.805752	−	0.139118i	0.247606	−	0.968861i	$-0.420356\pi$
$977$	25.1854	−	4.34842i	0.805752	−	0.139118i	0.558146	+	0.829742i	$0.311513\pi$
$978$	−0.104595	−	0.569436i	−0.00334458	−	0.0182086i
$979$	−3.57807	−	4.48676i	−0.114356	−	0.143398i
$980$	2.60388	+	30.4401i	0.0831780	+	0.972375i
$981$	13.1108	−	16.4404i	0.418594	−	0.524900i
$982$	0.360718	+	0.193117i	0.0115110	+	0.00616262i
$983$	−14.3269	−	4.08609i	−0.456957	−	0.130326i	0.0379356	−	0.999280i	$-0.487922\pi$
$983$	−14.3269	−	4.08609i	−0.456957	−	0.130326i	−0.494892	+	0.868954i	$0.664793\pi$
$984$	0.0410480	+	0.00351759i	0.00130856	+	0.000112137i
$985$	−10.0955	−	4.59859i	−0.321668	−	0.146523i
$986$	3.39524	+	1.12730i	0.108127	+	0.0359005i
$987$	9.37601	+	3.50826i	0.298442	+	0.111669i
$988$	2.14377	−	5.82531i	0.0682023	−	0.185328i
$989$	86.8736	−	30.9204i	2.76242	−	0.983211i
$990$	−0.142648	+	0.0649777i	−0.00453365	+	0.00206513i
$991$	38.6671	−	4.14765i	1.22830	−	0.131754i	0.530275	−	0.847826i	$-0.322089\pi$
$991$	38.6671	−	4.14765i	1.22830	−	0.131754i	0.698027	+	0.716072i	$0.254062\pi$
$992$	4.33597	+	4.57405i	0.137667	+	0.145226i
$993$	−1.27561	+	2.88162i	−0.0404802	+	0.0914455i
$994$	2.35535	−	1.08790i	0.0747072	−	0.0345062i
$995$	−37.5464	−	31.9637i	−1.19030	−	1.01332i
$996$	4.22532	+	0.729529i	0.133884	+	0.0231160i
$997$	0.489496	+	45.8068i	0.0155025	+	1.45072i	0.696041	+	0.718002i	$0.254943\pi$
$997$	0.489496	+	45.8068i	0.0155025	+	1.45072i	−0.680538	+	0.732713i	$0.738254\pi$
$998$	0.0973840	−	0.0903591i	0.00308264	−	0.00286027i
$999$	−9.98760	+	6.80943i	−0.315994	+	0.215441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.k.a.100.18	✓	2688
343.319	even	147	inner	343.2.k.a.319.18	yes	2688

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.2.k.a.100.18	✓	2688	1.1	even	1	trivial
343.2.k.a.319.18	yes	2688	343.319	even	147	inner

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.k (of order \(147\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0410343 + 0.0562257i) q^{2} +(0.0464488 - 0.868538i) q^{3} +(0.608421 - 1.90012i) q^{4} +(2.18704 - 0.0467471i) q^{5} +(0.0507401 - 0.0330282i) q^{6} +(0.491678 + 2.59966i) q^{7} +(0.263924 - 0.0876287i) q^{8} +(2.23069 + 0.239276i) q^{9} +(0.0923718 + 0.121049i) q^{10} +(-0.0538109 + 0.455689i) q^{11} +(-1.62207 - 0.616695i) q^{12} +(0.380637 + 0.729611i) q^{13} +(-0.125992 + 0.134320i) q^{14} +(0.0609836 - 1.90169i) q^{15} +(-3.23240 - 2.30652i) q^{16} +(-5.21134 + 1.24819i) q^{17} +(0.0780812 + 0.135241i) q^{18} +(1.89029 - 3.27408i) q^{19} +(1.24181 - 4.18408i) q^{20} +(2.28074 - 0.306290i) q^{21} +(-0.0278295 + 0.0156733i) q^{22} +(6.02513 - 4.70044i) q^{23} +(-0.0638499 - 0.233298i) q^{24} +(-0.214492 + 0.00917355i) q^{25} +(-0.0254037 + 0.0513406i) q^{26} +(0.727883 - 4.50221i) q^{27} +(5.23883 + 0.647440i) q^{28} +(-8.89005 + 3.59918i) q^{29} +(0.109427 - 0.0746058i) q^{30} +(-5.54910 + 5.14881i) q^{31} +(-0.00889661 - 0.832541i) q^{32} +(0.393283 + 0.0679030i) q^{33} +(-0.284024 - 0.241793i) q^{34} +(1.19684 + 5.66257i) q^{35} +(1.81185 - 4.09300i) q^{36} +(-1.82345 - 1.92358i) q^{37} +(0.261654 - 0.0280665i) q^{38} +(0.651374 - 0.296708i) q^{39} +(0.573115 - 0.203985i) q^{40} +(-0.0588253 + 0.159847i) q^{41} +(0.110810 + 0.115668i) q^{42} +(11.4522 + 3.80238i) q^{43} +(0.833125 + 0.379498i) q^{44} +(4.88978 + 0.419027i) q^{45} +(0.511522 + 0.145888i) q^{46} +(3.83521 + 2.05325i) q^{47} +(-2.15344 + 2.70033i) q^{48} +(-6.51651 + 2.55640i) q^{49} +(-0.00931729 - 0.0116835i) q^{50} +(0.842038 + 4.58423i) q^{51} +(1.61794 - 0.279348i) q^{52} +(-4.99262 - 2.95407i) q^{53} +(0.283008 - 0.143819i) q^{54} +(-0.0963842 + 0.999123i) q^{55} +(0.357571 + 0.643028i) q^{56} +(-2.75586 - 1.79387i) q^{57} +(-0.567163 - 0.352160i) q^{58} +(-6.06431 + 7.27967i) q^{59} +(-3.57635 - 1.27291i) q^{60} +(-1.16482 + 0.0998189i) q^{61} +(-0.517199 - 0.100724i) q^{62} +(0.474744 + 5.91669i) q^{63} +(-6.31831 + 4.71547i) q^{64} +(0.866575 + 1.57789i) q^{65} +(0.0123202 + 0.0248990i) q^{66} +(9.50150 - 2.93082i) q^{67} +(-0.798978 + 10.6616i) q^{68} +(-3.80265 - 5.45138i) q^{69} +(-0.269271 + 0.299653i) q^{70} +(-13.0583 - 5.28670i) q^{71} +(0.609699 - 0.132322i) q^{72} +(-3.13506 + 1.67842i) q^{73} +(0.0333304 - 0.181457i) q^{74} +(-0.00199531 + 0.186720i) q^{75} +(-5.07106 - 5.58380i) q^{76} +(-1.21110 + 0.0841620i) q^{77} +(0.0434113 + 0.0244488i) q^{78} +(10.5440 - 1.58926i) q^{79} +(-7.17721 - 4.89334i) q^{80} +(2.70081 + 0.586151i) q^{81} +(-0.0114014 + 0.00325172i) q^{82} +(-2.42532 + 0.472331i) q^{83} +(0.805664 - 4.52005i) q^{84} +(-11.3391 + 2.97345i) q^{85} +(0.256139 + 0.799934i) q^{86} +(2.71309 + 7.88852i) q^{87} +(0.0257295 + 0.124983i) q^{88} +(-8.79623 + 8.89073i) q^{89} +(0.177088 + 0.292126i) q^{90} +(-1.70959 + 1.34826i) q^{91} +(-5.26560 - 14.3083i) q^{92} +(4.21419 + 5.05876i) q^{93} +(0.0419291 + 0.299891i) q^{94} +(3.98108 - 7.24890i) q^{95} +(-0.723506 - 0.0309435i) q^{96} +(0.0543670 + 0.238197i) q^{97} +(-0.411135 - 0.261495i) q^{98} +(-0.229071 + 1.00362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 84 q^{8} - 98 q^{9} - 84 q^{10} - 91 q^{11} - 119 q^{12} - 84 q^{13} - 119 q^{14} - 98 q^{15} - 84 q^{16} - 91 q^{17} - 42 q^{18}+ \cdots - 182 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 84 * q^8 - 98 * q^9 - 84 * q^10 - 91 * q^11 - 119 * q^12 - 84 * q^13 - 119 * q^14 - 98 * q^15 - 84 * q^16 - 91 * q^17 - 42 * q^18 + 126 * q^19 + 84 * q^20 - 84 * q^21 - 98 * q^22 - 105 * q^23 - 126 * q^24 - 84 * q^25 - 98 * q^26 - 105 * q^27 - 126 * q^28 - 126 * q^29 - 91 * q^30 - 133 * q^31 - 126 * q^32 - 84 * q^33 - 168 * q^34 - 98 * q^35 - 42 * q^36 - 105 * q^37 + 28 * q^38 - 77 * q^39 - 56 * q^40 - 56 * q^41 - 126 * q^42 - 84 * q^43 - 28 * q^44 - 105 * q^45 - 119 * q^47 - 14 * q^48 - 28 * q^49 - 196 * q^50 - 28 * q^51 - 28 * q^52 - 91 * q^53 + 126 * q^54 + 301 * q^55 - 70 * q^56 + 21 * q^57 + 308 * q^58 + 28 * q^59 - 112 * q^60 - 105 * q^61 - 70 * q^62 - 133 * q^63 - 140 * q^64 - 84 * q^65 - 252 * q^66 - 91 * q^67 - 175 * q^68 - 168 * q^69 - 168 * q^70 - 161 * q^71 - 21 * q^72 + 42 * q^73 - 210 * q^75 - 21 * q^76 + 42 * q^77 + 280 * q^78 - 91 * q^79 - 168 * q^80 - 126 * q^81 - 84 * q^82 - 98 * q^83 - 14 * q^84 - 140 * q^85 - 28 * q^86 + 14 * q^87 + 28 * q^88 - 84 * q^89 + 329 * q^90 + 406 * q^91 + 336 * q^92 + 14 * q^93 - 112 * q^94 + 238 * q^95 + 560 * q^96 + 196 * q^97 + 63 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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