LMFDB - Embedded newform 189.2.w.a.184.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			184.15
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.162199 + 0.919879i) q^{2} +(0.568714 + 1.63602i) q^{3} +(1.05952 - 0.385633i) q^{4} +(-0.120368 + 0.682641i) q^{5} +(-1.41270 + 0.788509i) q^{6} +(1.39323 - 2.24920i) q^{7} +(1.46066 + 2.52993i) q^{8} +(-2.35313 + 1.86086i) q^{9} +O(q^{10})$	\(q+(0.162199 + 0.919879i) q^{2} +(0.568714 + 1.63602i) q^{3} +(1.05952 - 0.385633i) q^{4} +(-0.120368 + 0.682641i) q^{5} +(-1.41270 + 0.788509i) q^{6} +(1.39323 - 2.24920i) q^{7} +(1.46066 + 2.52993i) q^{8} +(-2.35313 + 1.86086i) q^{9} -0.647471 q^{10} +(-0.190344 - 1.07949i) q^{11} +(1.23346 + 1.51408i) q^{12} +(-2.28797 - 1.91983i) q^{13} +(2.29497 + 0.916784i) q^{14} +(-1.18527 + 0.191303i) q^{15} +(-0.362862 + 0.304477i) q^{16} -2.82277 q^{17} +(-2.09344 - 1.86276i) q^{18} -4.31412 q^{19} +(0.135717 + 0.769688i) q^{20} +(4.47209 + 1.00020i) q^{21} +(0.962130 - 0.350187i) q^{22} +(-1.16694 - 0.979182i) q^{23} +(-3.30833 + 3.82847i) q^{24} +(4.24695 + 1.54576i) q^{25} +(1.39491 - 2.41605i) q^{26} +(-4.38266 - 2.79147i) q^{27} +(0.608786 - 2.92034i) q^{28} +(1.70800 - 1.43318i) q^{29} +(-0.368226 - 1.05928i) q^{30} +(2.21437 - 0.805964i) q^{31} +(4.13678 + 3.47117i) q^{32} +(1.65782 - 0.925330i) q^{33} +(-0.457851 - 2.59660i) q^{34} +(1.36770 + 1.22181i) q^{35} +(-1.77557 + 2.87905i) q^{36} +(-3.73989 - 6.47768i) q^{37} +(-0.699748 - 3.96847i) q^{38} +(1.83969 - 4.83500i) q^{39} +(-1.90285 + 0.692582i) q^{40} +(5.03687 + 4.22644i) q^{41} +(-0.194695 + 4.27601i) q^{42} +(8.56785 + 3.11844i) q^{43} +(-0.617961 - 1.07034i) q^{44} +(-0.987055 - 1.83033i) q^{45} +(0.711451 - 1.23227i) q^{46} +(-5.76741 - 2.09917i) q^{47} +(-0.704496 - 0.420489i) q^{48} +(-3.11782 - 6.26731i) q^{49} +(-0.733062 + 4.15740i) q^{50} +(-1.60535 - 4.61811i) q^{51} +(-3.16449 - 1.15178i) q^{52} +(-6.34664 - 10.9927i) q^{53} +(1.85695 - 4.48429i) q^{54} +0.759819 q^{55} +(7.72536 + 0.239468i) q^{56} +(-2.45350 - 7.05799i) q^{57} +(1.59539 + 1.33869i) q^{58} +(8.79403 + 7.37907i) q^{59} +(-1.18204 + 0.659768i) q^{60} +(-0.654284 - 0.238140i) q^{61} +(1.10056 + 1.90622i) q^{62} +(0.906986 + 7.88526i) q^{63} +(-2.99575 + 5.18880i) q^{64} +(1.58596 - 1.33078i) q^{65} +(1.12009 + 1.37491i) q^{66} +(0.581514 - 3.29793i) q^{67} +(-2.99077 + 1.08855i) q^{68} +(0.938305 - 2.46602i) q^{69} +(-0.902077 + 1.45629i) q^{70} +(-2.60327 + 4.50899i) q^{71} +(-8.14496 - 3.23519i) q^{72} +(-5.66293 + 9.80848i) q^{73} +(5.35207 - 4.49092i) q^{74} +(-0.113603 + 7.82720i) q^{75} +(-4.57088 + 1.66367i) q^{76} +(-2.69319 - 1.07586i) q^{77} +(4.74601 + 0.908057i) q^{78} +(1.92269 + 10.9041i) q^{79} +(-0.164172 - 0.284354i) q^{80} +(2.07444 - 8.75767i) q^{81} +(-3.07083 + 5.31884i) q^{82} +(-2.86339 + 2.40267i) q^{83} +(5.12397 - 0.664852i) q^{84} +(0.339771 - 1.92694i) q^{85} +(-1.47889 + 8.38719i) q^{86} +(3.31608 + 1.97925i) q^{87} +(2.45302 - 2.05833i) q^{88} -12.2609 q^{89} +(1.52358 - 1.20485i) q^{90} +(-7.50576 + 2.47133i) q^{91} +(-1.61400 - 0.587448i) q^{92} +(2.57792 + 3.16439i) q^{93} +(0.995508 - 5.64580i) q^{94} +(0.519282 - 2.94500i) q^{95} +(-3.32626 + 8.74195i) q^{96} +(5.23327 + 1.90476i) q^{97} +(5.25946 - 3.88457i) q^{98} +(2.45669 + 2.18599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.162199	+	0.919879i	0.114692	+	0.650453i	0.986902	+	0.161320i	$0.0515753\pi$
$2$	0.162199	+	0.919879i	0.114692	+	0.650453i	−0.872210	+	0.489132i	$0.837314\pi$
$3$	0.568714	+	1.63602i	0.328347	+	0.944557i
$3$	0.568714	+	1.63602i	0.328347	+	0.944557i
$4$	1.05952	−	0.385633i	0.529758	−	0.192816i
$5$	−0.120368	+	0.682641i	−0.0538303	+	0.305287i	−0.999821	−	0.0189063i	$-0.993982\pi$
$5$	−0.120368	+	0.682641i	−0.0538303	+	0.305287i	0.945991	+	0.324193i	$0.105093\pi$
$6$	−1.41270	+	0.788509i	−0.576731	+	0.321908i
$7$	1.39323	−	2.24920i	0.526592	−	0.850118i
$7$	1.39323	−	2.24920i	0.526592	−	0.850118i
$8$	1.46066	+	2.52993i	0.516420	+	0.894467i
$9$	−2.35313	+	1.86086i	−0.784376	+	0.620285i
$10$	−0.647471			−0.204748
$11$	−0.190344	−	1.07949i	−0.0573909	−	0.325480i	0.942573	−	0.334001i	$-0.108399\pi$
$11$	−0.190344	−	1.07949i	−0.0573909	−	0.325480i	−0.999964	+	0.00852096i	$0.997288\pi$
$12$	1.23346	+	1.51408i	0.356071	+	0.437077i
$13$	−2.28797	−	1.91983i	−0.634569	−	0.532466i	0.267776	−	0.963481i	$-0.413711\pi$
$13$	−2.28797	−	1.91983i	−0.634569	−	0.532466i	−0.902345	+	0.431015i	$0.858156\pi$
$14$	2.29497	+	0.916784i	0.613358	+	0.245021i
$15$	−1.18527	+	0.191303i	−0.306036	+	0.0493942i
$16$	−0.362862	+	0.304477i	−0.0907154	+	0.0761193i
$17$	−2.82277			−0.684622			−0.342311	−	0.939587i	$-0.611210\pi$
$17$	−2.82277			−0.684622			−0.342311	+	0.939587i	$0.611210\pi$
$18$	−2.09344	−	1.86276i	−0.493428	−	0.439058i
$19$	−4.31412			−0.989727			−0.494863	−	0.868971i	$-0.664782\pi$
$19$	−4.31412			−0.989727			−0.494863	+	0.868971i	$0.664782\pi$
$20$	0.135717	+	0.769688i	0.0303472	+	0.172107i
$21$	4.47209	+	1.00020i	0.975890	+	0.218262i
$22$	0.962130	−	0.350187i	0.205127	−	0.0746600i
$23$	−1.16694	−	0.979182i	−0.243325	−	0.204174i	0.512967	−	0.858408i	$-0.328546\pi$
$23$	−1.16694	−	0.979182i	−0.243325	−	0.204174i	−0.756291	+	0.654235i	$0.772991\pi$
$24$	−3.30833	+	3.82847i	−0.675310	+	0.781484i
$25$	4.24695	+	1.54576i	0.849390	+	0.309153i
$26$	1.39491	−	2.41605i	0.273564	−	0.473827i
$27$	−4.38266	−	2.79147i	−0.843442	−	0.537220i
$28$	0.608786	−	2.92034i	0.115050	−	0.551893i
$29$	1.70800	−	1.43318i	0.317168	−	0.266135i	−0.470279	−	0.882518i	$-0.655847\pi$
$29$	1.70800	−	1.43318i	0.317168	−	0.266135i	0.787447	+	0.616382i	$0.211402\pi$
$30$	−0.368226	−	1.05928i	−0.0672285	−	0.193396i
$31$	2.21437	−	0.805964i	0.397712	−	0.144755i	−0.135418	−	0.990789i	$-0.543238\pi$
$31$	2.21437	−	0.805964i	0.397712	−	0.144755i	0.533130	+	0.846033i	$0.321016\pi$
$32$	4.13678	+	3.47117i	0.731286	+	0.613622i
$33$	1.65782	−	0.925330i	0.288590	−	0.161079i
$34$	−0.457851	−	2.59660i	−0.0785209	−	0.445314i
$35$	1.36770	+	1.22181i	0.231183	+	0.206523i
$36$	−1.77557	+	2.87905i	−0.295929	+	0.479842i
$37$	−3.73989	−	6.47768i	−0.614834	−	1.06492i	−0.990414	−	0.138134i	$-0.955890\pi$
$37$	−3.73989	−	6.47768i	−0.614834	−	1.06492i	0.375580	−	0.926790i	$-0.377444\pi$
$38$	−0.699748	−	3.96847i	−0.113514	−	0.643770i
$39$	1.83969	−	4.83500i	0.294586	−	0.774220i
$40$	−1.90285	+	0.692582i	−0.300868	+	0.109507i
$41$	5.03687	+	4.22644i	0.786627	+	0.660059i	0.944908	−	0.327336i	$-0.106151\pi$
$41$	5.03687	+	4.22644i	0.786627	+	0.660059i	−0.158281	+	0.987394i	$0.550595\pi$
$42$	−0.194695	+	4.27601i	−0.0300421	+	0.659803i
$43$	8.56785	+	3.11844i	1.30659	+	0.475558i	0.899136	−	0.437670i	$-0.144196\pi$
$43$	8.56785	+	3.11844i	1.30659	+	0.475558i	0.407449	+	0.913228i	$0.366418\pi$
$44$	−0.617961	−	1.07034i	−0.0931611	−	0.161360i
$45$	−0.987055	−	1.83033i	−0.147141	−	0.272850i
$46$	0.711451	−	1.23227i	0.104898	−	0.181688i
$47$	−5.76741	−	2.09917i	−0.841264	−	0.306195i	−0.114790	−	0.993390i	$-0.536620\pi$
$47$	−5.76741	−	2.09917i	−0.841264	−	0.306195i	−0.726473	+	0.687195i	$0.758842\pi$
$48$	−0.704496	−	0.420489i	−0.101685	−	0.0606924i
$49$	−3.11782	−	6.26731i	−0.445402	−	0.895331i
$50$	−0.733062	+	4.15740i	−0.103671	+	0.587946i
$51$	−1.60535	−	4.61811i	−0.224794	−	0.646664i
$52$	−3.16449	−	1.15178i	−0.438836	−	0.159723i
$53$	−6.34664	−	10.9927i	−0.871778	−	1.50996i	−0.860156	−	0.510031i	$-0.829634\pi$
$53$	−6.34664	−	10.9927i	−0.871778	−	1.50996i	−0.0116216	−	0.999932i	$-0.503699\pi$
$54$	1.85695	−	4.48429i	0.252699	−	0.610234i
$55$	0.759819			0.102454
$56$	7.72536	+	0.239468i	1.03235	+	0.0320002i
$57$	−2.45350	−	7.05799i	−0.324974	−	0.934854i
$58$	1.59539	+	1.33869i	0.209485	+	0.175779i
$59$	8.79403	+	7.37907i	1.14489	+	0.960673i	0.999588	−	0.0287150i	$-0.00914152\pi$
$59$	8.79403	+	7.37907i	1.14489	+	0.960673i	0.145298	+	0.989388i	$0.453586\pi$
$60$	−1.18204	+	0.659768i	−0.152601	+	0.0851756i
$61$	−0.654284	−	0.238140i	−0.0837724	−	0.0304907i	0.299794	−	0.954004i	$-0.403082\pi$
$61$	−0.654284	−	0.238140i	−0.0837724	−	0.0304907i	−0.383566	+	0.923513i	$0.625304\pi$
$62$	1.10056	+	1.90622i	0.139771	+	0.242091i
$63$	0.906986	+	7.88526i	0.114269	+	0.993450i
$64$	−2.99575	+	5.18880i	−0.374469	+	0.648600i
$65$	1.58596	−	1.33078i	0.196714	−	0.165062i
$66$	1.12009	+	1.37491i	0.137873	+	0.169240i
$67$	0.581514	−	3.29793i	0.0710433	−	0.402906i	−0.928461	−	0.371429i	$-0.878868\pi$
$67$	0.581514	−	3.29793i	0.0710433	−	0.402906i	0.999504	−	0.0314771i	$-0.0100211\pi$
$68$	−2.99077	+	1.08855i	−0.362684	+	0.132006i
$69$	0.938305	−	2.46602i	0.112959	−	0.296874i
$70$	−0.902077	+	1.45629i	−0.107819	+	0.174060i
$71$	−2.60327	+	4.50899i	−0.308951	+	0.535119i	−0.978133	−	0.207980i	$-0.933311\pi$
$71$	−2.60327	+	4.50899i	−0.308951	+	0.535119i	0.669182	+	0.743098i	$0.266645\pi$
$72$	−8.14496	−	3.23519i	−0.959892	−	0.381271i
$73$	−5.66293	+	9.80848i	−0.662795	+	1.14800i	0.317083	+	0.948398i	$0.397297\pi$
$73$	−5.66293	+	9.80848i	−0.662795	+	1.14800i	−0.979878	+	0.199597i	$0.936037\pi$
$74$	5.35207	−	4.49092i	0.622166	−	0.522059i
$75$	−0.113603	+	7.82720i	−0.0131177	+	0.903807i
$76$	−4.57088	+	1.66367i	−0.524316	+	0.190835i
$77$	−2.69319	−	1.07586i	−0.306918	−	0.122606i
$78$	4.74601	+	0.908057i	0.537380	+	0.102817i
$79$	1.92269	+	10.9041i	0.216320	+	1.22681i	0.878602	+	0.477555i	$0.158477\pi$
$79$	1.92269	+	10.9041i	0.216320	+	1.22681i	−0.662282	+	0.749255i	$0.730412\pi$
$80$	−0.164172	−	0.284354i	−0.0183550	−	0.0317917i
$81$	2.07444	−	8.75767i	0.230493	−	0.973074i
$82$	−3.07083	+	5.31884i	−0.339117	+	0.587367i
$83$	−2.86339	+	2.40267i	−0.314298	+	0.263727i	−0.786266	−	0.617889i	$-0.787988\pi$
$83$	−2.86339	+	2.40267i	−0.314298	+	0.263727i	0.471968	+	0.881616i	$0.343544\pi$
$84$	5.12397	−	0.664852i	0.559071	−	0.0725413i
$85$	0.339771	−	1.92694i	0.0368534	−	0.209006i
$86$	−1.47889	+	8.38719i	−0.159473	+	0.904414i
$87$	3.31608	+	1.97925i	0.355521	+	0.212198i
$88$	2.45302	−	2.05833i	0.261493	−	0.219419i
$89$	−12.2609			−1.29966			−0.649828	−	0.760081i	$-0.725159\pi$
$89$	−12.2609			−1.29966			−0.649828	+	0.760081i	$0.725159\pi$
$90$	1.52358	−	1.20485i	0.160600	−	0.127002i
$91$	−7.50576	+	2.47133i	−0.786818	+	0.259066i
$92$	−1.61400	−	0.587448i	−0.168271	−	0.0612457i
$93$	2.57792	+	3.16439i	0.267317	+	0.328132i
$94$	0.995508	−	5.64580i	0.102679	−	0.582320i
$95$	0.519282	−	2.94500i	0.0532772	−	0.302150i
$96$	−3.32626	+	8.74195i	−0.339485	+	0.892222i
$97$	5.23327	+	1.90476i	0.531358	+	0.193399i	0.593745	−	0.804653i	$-0.297649\pi$
$97$	5.23327	+	1.90476i	0.531358	+	0.193399i	−0.0623864	+	0.998052i	$0.519871\pi$
$98$	5.25946	−	3.88457i	0.531286	−	0.392401i
$99$	2.45669	+	2.18599i	0.246906	+	0.219700i
$100$	5.09582			0.509582
$101$	9.94470	−	8.34460i	0.989535	−	0.830318i	0.00403463	−	0.999992i	$-0.498716\pi$
$101$	9.94470	−	8.34460i	0.989535	−	0.830318i	0.985500	+	0.169673i	$0.0542713\pi$
$102$	3.98771	−	2.22578i	0.394842	−	0.220385i
$103$	−1.94705	+	11.0423i	−0.191849	+	1.08803i	0.724987	+	0.688762i	$0.241846\pi$
$103$	−1.94705	+	11.0423i	−0.191849	+	1.08803i	−0.916836	+	0.399265i	$0.869265\pi$
$104$	1.51511	−	8.59263i	0.148569	−	0.842577i
$105$	−1.22108	+	2.93244i	−0.119165	+	0.286177i
$106$	9.08253	−	7.62115i	0.882173	−	0.740231i
$107$	−3.22108	+	5.57907i	−0.311393	+	0.539349i	−0.978664	−	0.205466i	$-0.934129\pi$
$107$	−3.22108	+	5.57907i	−0.311393	+	0.539349i	0.667271	+	0.744815i	$0.267462\pi$
$108$	−5.71998	−	1.26752i	−0.550405	−	0.121967i
$109$	1.71199	+	2.96526i	0.163979	+	0.284021i	0.936292	−	0.351222i	$-0.114234\pi$
$109$	1.71199	+	2.96526i	0.163979	+	0.284021i	−0.772313	+	0.635242i	$0.780900\pi$
$110$	0.123242	+	0.698941i	0.0117507	+	0.0666414i
$111$	8.47069	−	9.80248i	0.804002	−	0.930410i
$112$	0.179280	+	1.24036i	0.0169404	+	0.117203i
$113$	−17.8536	+	6.49819i	−1.67953	+	0.611299i	−0.993245	−	0.116035i	$-0.962982\pi$
$113$	−17.8536	+	6.49819i	−1.67953	+	0.611299i	−0.686284	+	0.727333i	$0.740759\pi$
$114$	6.09454	−	3.40172i	0.570806	−	0.318601i
$115$	0.808893	−	0.678742i	0.0754297	−	0.0632930i
$116$	1.25697	−	2.17714i	0.116707	−	0.202142i
$117$	8.95642	+	0.260038i	0.828022	+	0.0240406i
$118$	−5.36146	+	9.28632i	−0.493563	+	0.854875i
$119$	−3.93277	+	6.34897i	−0.360516	+	0.582009i
$120$	−2.21526	−	2.71923i	−0.202224	−	0.248230i
$121$	9.20754	−	3.35127i	0.837049	−	0.304661i
$122$	0.112935	−	0.640488i	0.0102247	−	0.0579870i
$123$	−4.05000	+	10.6441i	−0.365176	+	0.959743i
$124$	2.03535	−	1.70787i	0.182780	−	0.153371i
$125$	−3.29933	+	5.71461i	−0.295101	+	0.511130i
$126$	−7.10637	+	2.11330i	−0.633086	+	0.188268i
$127$	7.25292	+	12.5624i	0.643592	+	1.11473i	0.984625	+	0.174683i	$0.0558901\pi$
$127$	7.25292	+	12.5624i	0.643592	+	1.11473i	−0.341032	+	0.940052i	$0.610777\pi$
$128$	4.89004	+	1.77983i	0.432223	+	0.157316i
$129$	−0.229183	+	15.7907i	−0.0201784	+	1.39029i
$130$	1.48139	+	1.24304i	0.129927	+	0.109022i
$131$	−16.8263	−	14.1190i	−1.47012	−	1.23358i	−0.916022	−	0.401128i	$-0.868618\pi$
$131$	−16.8263	−	14.1190i	−1.47012	−	1.23358i	−0.554100	−	0.832450i	$-0.686937\pi$
$132$	1.39965	−	1.61971i	0.121824	−	0.140978i
$133$	−6.01056	+	9.70332i	−0.521182	+	0.841385i
$134$	3.12802			0.270220
$135$	2.43311	−	2.65578i	0.209409	−	0.228573i
$136$	−4.12310	−	7.14141i	−0.353553	−	0.612371i
$137$	−15.2418	−	5.54757i	−1.30220	−	0.473961i	−0.404486	−	0.914544i	$-0.632550\pi$
$137$	−15.2418	−	5.54757i	−1.30220	−	0.473961i	−0.897712	+	0.440583i	$0.854772\pi$
$138$	2.42063	+	0.463140i	0.206058	+	0.0394251i
$139$	0.468944	−	2.65951i	0.0397753	−	0.225577i	−0.958440	−	0.285294i	$-0.907909\pi$
$139$	0.468944	−	2.65951i	0.0397753	−	0.225577i	0.998215	+	0.0597171i	$0.0190198\pi$
$140$	1.92027	+	0.767099i	0.162292	+	0.0648317i
$141$	0.154274	−	10.6294i	0.0129922	−	0.895160i
$142$	−4.56997	−	1.66333i	−0.383504	−	0.139584i
$143$	−1.63695	+	2.83528i	−0.136889	+	0.237098i
$144$	0.287273	−	1.39171i	0.0239394	−	0.115976i
$145$	0.772761	+	1.33846i	0.0641743	+	0.111153i
$146$	−9.94113	−	3.61828i	−0.822734	−	0.299451i
$147$	8.48031	−	8.66512i	0.699444	−	0.714687i
$148$	−6.46048	−	5.42099i	−0.531048	−	0.445602i
$149$	17.7689	−	6.46736i	1.45569	−	0.529827i	0.511513	−	0.859276i	$-0.329085\pi$
$149$	17.7689	−	6.46736i	1.45569	−	0.529827i	0.944173	+	0.329449i	$0.106863\pi$
$150$	−7.21850	+	1.16507i	−0.589388	+	0.0951273i
$151$	2.67448	+	15.1677i	0.217646	+	1.23433i	0.876256	+	0.481846i	$0.160034\pi$
$151$	2.67448	+	15.1677i	0.217646	+	1.23433i	−0.658610	+	0.752485i	$0.728855\pi$
$152$	−6.30145	−	10.9144i	−0.511115	−	0.885278i
$153$	6.64234	−	5.25276i	0.537001	−	0.424661i
$154$	0.552829	−	2.65191i	0.0445482	−	0.213697i
$155$	0.283645	+	1.60863i	0.0227829	+	0.129208i
$156$	0.0846476	−	5.83221i	0.00677723	−	0.466951i
$157$	−7.10355	−	5.96058i	−0.566925	−	0.475706i	0.313699	−	0.949522i	$-0.398432\pi$
$157$	−7.10355	−	5.96058i	−0.566925	−	0.475706i	−0.880624	+	0.473816i	$0.842876\pi$
$158$	−9.71861	+	3.53729i	−0.773171	+	0.281411i
$159$	14.3749	−	16.6349i	1.14000	−	1.31924i
$160$	−2.86750	+	2.40612i	−0.226696	+	0.190220i
$161$	−3.82820	+	1.26046i	−0.301704	+	0.0993385i
$162$	8.39246	+	0.487740i	0.659374	+	0.0383205i
$163$	−0.449912	+	0.779271i	−0.0352399	+	0.0610372i	−0.883107	−	0.469171i	$-0.844553\pi$
$163$	−0.449912	+	0.779271i	−0.0352399	+	0.0610372i	0.847868	+	0.530208i	$0.177886\pi$
$164$	6.96650	+	2.53560i	0.543992	+	0.197997i
$165$	0.432119	+	1.24308i	0.0336404	+	0.0967736i
$166$	−2.67460	−	2.24426i	−0.207589	−	0.174188i
$167$	10.2745	−	3.73960i	0.795061	−	0.289379i	0.0876229	−	0.996154i	$-0.472073\pi$
$167$	10.2745	−	3.73960i	0.795061	−	0.289379i	0.707438	+	0.706775i	$0.249851\pi$
$168$	4.00175	+	12.7750i	0.308741	+	0.985616i
$169$	−0.708386	−	4.01746i	−0.0544912	−	0.309035i
$170$	1.82766			0.140175
$171$	10.1517	−	8.02795i	0.776318	−	0.613913i
$172$	10.2804			0.783870
$173$	12.3566	−	10.3684i	0.939457	−	0.788298i	−0.0380337	−	0.999276i	$-0.512109\pi$
$173$	12.3566	−	10.3684i	0.939457	−	0.788298i	0.977491	+	0.210978i	$0.0676650\pi$
$174$	−1.28281	+	3.37142i	−0.0972493	+	0.255587i
$175$	9.39372	−	7.39865i	0.710099	−	0.559285i
$176$	0.397750	+	0.333752i	0.0299815	+	0.0251575i
$177$	−7.07102	+	18.5838i	−0.531491	+	1.39684i
$178$	−1.98872	−	11.2786i	−0.149061	−	0.845365i
$179$	−2.62154			−0.195943			−0.0979714	−	0.995189i	$-0.531235\pi$
$179$	−2.62154			−0.195943			−0.0979714	+	0.995189i	$0.531235\pi$
$180$	−1.75164	−	1.55863i	−0.130559	−	0.116173i
$181$	−5.97259	−	10.3448i	−0.443939	−	0.768925i	0.554039	−	0.832491i	$-0.313086\pi$
$181$	−5.97259	−	10.3448i	−0.443939	−	0.768925i	−0.997978	+	0.0635660i	$0.979753\pi$
$182$	−3.49076	−	6.50354i	−0.258752	−	0.482075i
$183$	0.0175016	−	1.20585i	0.00129375	−	0.0891394i
$184$	0.772760	−	4.38254i	0.0569686	−	0.323085i
$185$	4.87209	−	1.77330i	0.358204	−	0.130375i
$186$	−2.49272	+	2.88463i	−0.182775	+	0.211512i
$187$	0.537297	+	3.04716i	0.0392910	+	0.222830i
$188$	−6.92018			−0.504706
$189$	−12.3846	+	5.96831i	−0.900850	+	0.434130i
$190$	2.79327			0.202645
$191$	−0.135979	−	0.771173i	−0.00983906	−	0.0558001i	0.979493	−	0.201479i	$-0.0645746\pi$
$191$	−0.135979	−	0.771173i	−0.00983906	−	0.0558001i	−0.989332	+	0.145678i	$0.953464\pi$
$192$	−10.1927	−	1.95017i	−0.735595	−	0.140742i
$193$	−20.1889	+	7.34816i	−1.45323	+	0.528932i	−0.943491	−	0.331397i	$-0.892480\pi$
$193$	−20.1889	+	7.34816i	−1.45323	+	0.528932i	−0.509739	+	0.860329i	$0.670258\pi$
$194$	−0.903310	+	5.12293i	−0.0648539	+	0.367805i
$195$	3.07913	+	1.83783i	0.220501	+	0.131610i
$196$	−5.72026	−	5.43799i	−0.408590	−	0.388428i
$197$	−6.70472	−	11.6129i	−0.477692	−	0.827386i	0.521981	−	0.852957i	$-0.325193\pi$
$197$	−6.70472	−	11.6129i	−0.477692	−	0.827386i	−0.999673	+	0.0255707i	$0.991860\pi$
$198$	−1.61237	+	2.61442i	−0.114586	+	0.185799i
$199$	20.4327			1.44843			0.724216	−	0.689573i	$-0.242202\pi$
$199$	20.4327			1.44843			0.724216	+	0.689573i	$0.242202\pi$
$200$	2.29266	+	13.0023i	0.162116	+	0.919404i
$201$	5.72620	−	0.924209i	0.403895	−	0.0651887i
$202$	9.28904	+	7.79443i	0.653575	+	0.548414i
$203$	−0.843877	−	5.83839i	−0.0592286	−	0.409775i
$204$	−3.48179	−	4.27389i	−0.243774	−	0.299232i
$205$	−3.49142	+	2.92965i	−0.243851	+	0.204616i
$206$	−10.4734			−0.729714
$207$	4.56808	+	0.132629i	0.317504	+	0.00921833i
$208$	1.41476			0.0980961
$209$	0.821166	+	4.65707i	0.0568013	+	0.322136i
$210$	−2.89555	−	0.647603i	−0.199812	−	0.0446888i
$211$	17.9061	−	6.51729i	1.23271	−	0.448669i	0.358184	−	0.933651i	$-0.383396\pi$
$211$	17.9061	−	6.51729i	1.23271	−	0.448669i	0.874524	+	0.484982i	$0.161174\pi$
$212$	−10.9635	−	9.19948i	−0.752977	−	0.631823i
$213$	−8.85732	−	1.69467i	−0.606894	−	0.116117i
$214$	−5.65452	−	2.05808i	−0.386535	−	0.140687i
$215$	−3.16007	+	5.47341i	−0.215515	+	0.373283i
$216$	0.660686	−	15.1652i	0.0449540	−	1.03186i
$217$	1.27235	−	6.10346i	0.0863728	−	0.414330i
$218$	−2.45000	+	2.05579i	−0.165935	+	0.139236i
$219$	−19.2675	−	3.68645i	−1.30197	−	0.249107i
$220$	0.805041	−	0.293011i	0.0542758	−	0.0197548i
$221$	6.45841	+	5.41925i	0.434439	+	0.364538i
$222$	10.3910	+	6.20205i	0.697401	+	0.416254i
$223$	1.21682	+	6.90091i	0.0814840	+	0.462119i	0.998060	+	0.0622585i	$0.0198303\pi$
$223$	1.21682	+	6.90091i	0.0814840	+	0.462119i	−0.916576	+	0.399860i	$0.869059\pi$
$224$	13.5708	−	4.46831i	0.906740	−	0.298551i
$225$	−12.8701	+	4.26558i	−0.858005	+	0.284372i
$226$	−8.87340	−	15.3692i	−0.590250	−	1.02234i
$227$	−0.855160	−	4.84985i	−0.0567589	−	0.321896i	0.943187	−	0.332261i	$-0.107812\pi$
$227$	−0.855160	−	4.84985i	−0.0567589	−	0.321896i	−0.999946	+	0.0103654i	$0.996701\pi$
$228$	−5.32132	−	6.53191i	−0.352413	−	0.432586i
$229$	−5.95890	+	2.16886i	−0.393775	+	0.143322i	−0.531316	−	0.847174i	$-0.678302\pi$
$229$	−5.95890	+	2.16886i	−0.393775	+	0.143322i	0.137541	+	0.990496i	$0.456080\pi$
$230$	0.755562	+	0.633992i	0.0498203	+	0.0418042i
$231$	0.228478	−	5.01798i	0.0150328	−	0.330159i
$232$	6.12066	+	2.22774i	0.401841	+	0.146258i
$233$	11.8213	+	20.4751i	0.774440	+	1.34137i	0.935109	+	0.354361i	$0.115302\pi$
$233$	11.8213	+	20.4751i	0.774440	+	1.34137i	−0.160669	+	0.987008i	$0.551365\pi$
$234$	1.21352	+	8.28100i	0.0793305	+	0.541346i
$235$	2.12719	−	3.68440i	0.138763	−	0.240344i
$236$	12.1630	+	4.42698i	0.791746	+	0.288172i
$237$	−16.7459	+	9.34689i	−1.08776	+	0.607146i
$238$	−6.47818	−	2.58787i	−0.419918	−	0.167747i
$239$	−1.24719	+	7.07319i	−0.0806743	+	0.457527i	0.917532	+	0.397662i	$0.130178\pi$
$239$	−1.24719	+	7.07319i	−0.0806743	+	0.457527i	−0.998206	+	0.0598652i	$0.980933\pi$
$240$	0.371842	−	0.430304i	0.0240023	−	0.0277760i
$241$	−12.2688	−	4.46546i	−0.790300	−	0.287646i	−0.0848393	−	0.996395i	$-0.527038\pi$
$241$	−12.2688	−	4.46546i	−0.790300	−	0.287646i	−0.705461	+	0.708749i	$0.749260\pi$
$242$	4.57622	+	7.92625i	0.294171	+	0.509519i
$243$	15.5075	−	1.58679i	0.994806	−	0.101792i
$244$	−0.785059			−0.0502583
$245$	4.65361	−	1.37397i	0.297308	−	0.0877794i
$246$	−10.4482	−	1.99905i	−0.666150	−	0.127455i
$247$	9.87057	+	8.28239i	0.628050	+	0.526996i
$248$	5.27347	+	4.42497i	0.334866	+	0.280986i
$249$	−5.55926	−	3.31813i	−0.352304	−	0.210278i
$250$	−5.79190	−	2.10808i	−0.366312	−	0.133327i
$251$	6.20322	+	10.7443i	0.391543	+	0.678173i	0.992653	−	0.120993i	$-0.0386079\pi$
$251$	6.20322	+	10.7443i	0.391543	+	0.678173i	−0.601110	+	0.799166i	$0.705275\pi$
$252$	4.00178	+	8.00481i	0.252089	+	0.504255i
$253$	−0.834900	+	1.44609i	−0.0524897	+	0.0909149i
$254$	−10.3795	+	8.70942i	−0.651267	+	0.546478i
$255$	3.34574	−	0.540003i	0.209519	−	0.0338163i
$256$	−2.92489	+	16.5879i	−0.182806	+	1.03674i
$257$	28.9743	−	10.5458i	1.80736	−	0.657827i	0.809907	−	0.586558i	$-0.199517\pi$
$257$	28.9743	−	10.5458i	1.80736	−	0.657827i	0.997457	−	0.0712687i	$-0.0227048\pi$
$258$	−14.5627	+	2.35042i	−0.906634	+	0.146331i
$259$	−19.7801	−	0.613137i	−1.22908	−	0.0380985i
$260$	1.16716	−	2.02158i	0.0723841	−	0.125373i
$261$	−1.35220	+	6.55080i	−0.0836991	+	0.405484i
$262$	10.2585	−	17.7683i	0.633773	−	1.09773i
$263$	−10.0322	+	8.41798i	−0.618609	+	0.519075i	−0.897366	−	0.441287i	$-0.854522\pi$
$263$	−10.0322	+	8.41798i	−0.618609	+	0.519075i	0.278757	+	0.960362i	$0.410078\pi$
$264$	4.76254	+	2.84259i	0.293114	+	0.174950i
$265$	8.26800	−	3.00931i	0.507899	−	0.184860i
$266$	−9.90079	−	3.95512i	−0.607056	−	0.242504i
$267$	−6.97296	−	20.0591i	−0.426738	−	1.22760i
$268$	−0.655666	−	3.71847i	−0.0400512	−	0.227141i
$269$	15.9926	+	27.7001i	0.975088	+	1.68890i	0.679643	+	0.733543i	$0.262135\pi$
$269$	15.9926	+	27.7001i	0.975088	+	1.68890i	0.295445	+	0.955360i	$0.404532\pi$
$270$	2.83764	+	1.80740i	0.172693	+	0.109995i
$271$	−6.82324	+	11.8182i	−0.414482	+	0.717904i	−0.995374	−	0.0960766i	$-0.969371\pi$
$271$	−6.82324	+	11.8182i	−0.414482	+	0.717904i	0.580892	+	0.813981i	$0.302704\pi$
$272$	1.02427	−	0.859468i	0.0621058	−	0.0521129i
$273$	−8.31178	−	10.8741i	−0.503052	−	0.658131i
$274$	2.63088	−	14.9205i	0.158937	−	0.901378i
$275$	0.860262	−	4.87879i	0.0518757	−	0.294202i
$276$	0.0431732	−	2.97463i	0.00259872	−	0.179052i
$277$	−0.727829	+	0.610721i	−0.0437310	+	0.0366947i	−0.664391	−	0.747385i	$-0.731309\pi$
$277$	−0.727829	+	0.610721i	−0.0437310	+	0.0366947i	0.620660	+	0.784080i	$0.286865\pi$
$278$	2.52249			0.151289
$279$	−3.71091	+	6.01716i	−0.222167	+	0.360238i
$280$	−1.09336	+	5.24483i	−0.0653406	+	0.313438i
$281$	23.0562	+	8.39175i	1.37541	+	0.500610i	0.920785	−	0.390071i	$-0.127549\pi$
$281$	23.0562	+	8.39175i	1.37541	+	0.500610i	0.454630	+	0.890681i	$0.349772\pi$
$282$	9.80281	−	1.58218i	0.583749	−	0.0942172i
$283$	−4.35947	+	24.7238i	−0.259143	+	1.46968i	0.526065	+	0.850444i	$0.323667\pi$
$283$	−4.35947	+	24.7238i	−0.259143	+	1.46968i	−0.785209	+	0.619231i	$0.787444\pi$
$284$	−1.01939	+	5.78126i	−0.0604898	+	0.343055i
$285$	5.11340	−	0.825303i	0.302892	−	0.0488867i
$286$	−2.87362	−	1.04591i	−0.169921	−	0.0618462i
$287$	16.5236	−	5.44054i	0.975359	−	0.321145i
$288$	−16.1937	−	0.470164i	−0.954224	−	0.0277047i
$289$	−9.03198			−0.531293
$290$	−1.10588	+	0.927944i	−0.0649395	+	0.0544907i
$291$	−0.139986	+	9.64500i	−0.00820611	+	0.565400i
$292$	−2.21750	+	12.5761i	−0.129769	+	0.735958i
$293$	−0.478180	+	2.71189i	−0.0279356	+	0.158430i	−0.995584	−	0.0938703i	$-0.970076\pi$
$293$	−0.478180	+	2.71189i	−0.0279356	+	0.158430i	0.967649	+	0.252301i	$0.0811872\pi$
$294$	9.34636	+	6.39538i	0.545091	+	0.372986i
$295$	−6.09578	+	5.11497i	−0.354910	+	0.297805i
$296$	10.9254	−	18.9233i	0.635026	−	1.09990i
$297$	−2.17917	+	5.26239i	−0.126448	+	0.305355i
$298$	8.83129	+	15.2962i	0.511583	+	0.886088i
$299$	0.790064	+	4.48068i	0.0456906	+	0.259124i
$300$	2.89806	+	8.33686i	0.167320	+	0.481329i
$301$	18.9510	−	14.9261i	1.09232	−	0.860327i
$302$	−13.5187	+	4.92039i	−0.777911	+	0.283137i
$303$	19.3076	+	11.5241i	1.10919	+	0.662040i
$304$	1.56543	−	1.31355i	0.0897835	−	0.0753373i
$305$	0.241319	−	0.417977i	0.0138179	−	0.0239333i
$306$	5.90929	+	5.25815i	0.337812	+	0.300588i
$307$	13.8889	−	24.0564i	0.792684	−	1.37297i	−0.131616	−	0.991301i	$-0.542017\pi$
$307$	13.8889	−	24.0564i	0.792684	−	1.37297i	0.924300	−	0.381668i	$-0.124650\pi$
$308$	−3.26837	−	0.101312i	−0.186233	−	0.00577277i
$309$	−19.1727	+	3.09448i	−1.09070	+	0.176039i
$310$	−1.43374	+	0.521838i	−0.0814309	+	0.0296384i
$311$	3.34598	−	18.9760i	0.189733	−	1.07603i	−0.729988	−	0.683460i	$-0.760475\pi$
$311$	3.34598	−	18.9760i	0.189733	−	1.07603i	0.919722	−	0.392571i	$-0.128414\pi$
$312$	14.9194	−	2.40799i	0.844644	−	0.136326i
$313$	8.74687	−	7.33950i	0.494402	−	0.414853i	−0.361198	−	0.932489i	$-0.617632\pi$
$313$	8.74687	−	7.33950i	0.494402	−	0.414853i	0.855601	+	0.517636i	$0.173188\pi$
$314$	4.33082	−	7.50120i	0.244402	−	0.423317i
$315$	−5.49198	−	0.329988i	−0.309438	−	0.0185927i
$316$	6.24211	+	10.8117i	0.351146	+	0.608203i
$317$	−12.7895	−	4.65501i	−0.718331	−	0.261451i	−0.0431142	−	0.999070i	$-0.513728\pi$
$317$	−12.7895	−	4.65501i	−0.718331	−	0.261451i	−0.675217	+	0.737619i	$0.735950\pi$
$318$	17.6337	+	10.5250i	0.988850	+	0.590210i
$319$	−1.87222	−	1.57098i	−0.104824	−	0.0879579i
$320$	−3.18149	−	2.66959i	−0.177851	−	0.149235i
$321$	−10.9593	−	2.09686i	−0.611691	−	0.117035i
$322$	−1.78041	−	3.31703i	−0.0992182	−	0.184851i
$323$	12.1778			0.677589
$324$	−1.17934	−	10.0789i	−0.0655190	−	0.559937i
$325$	−6.74929	−	11.6901i	−0.374383	−	0.648450i
$326$	−0.789810	−	0.287467i	−0.0437435	−	0.0159213i
$327$	−3.87760	+	4.48724i	−0.214432	+	0.248145i
$328$	−3.33546	+	18.9163i	−0.184170	+	1.04448i
$329$	−12.7568	+	10.0475i	−0.703304	+	0.553934i
$330$	−1.07339	+	0.599124i	−0.0590883	+	0.0329807i
$331$	−1.31438	−	0.478396i	−0.0722450	−	0.0262950i	0.305645	−	0.952146i	$-0.401128\pi$
$331$	−1.31438	−	0.478396i	−0.0722450	−	0.0262950i	−0.377890	+	0.925851i	$0.623350\pi$
$332$	−2.10726	+	3.64988i	−0.115651	+	0.200313i
$333$	20.8545	+	8.28342i	1.14282	+	0.453929i
$334$	5.10649	+	8.84469i	0.279414	+	0.483960i
$335$	2.18131	+	0.793932i	0.119178	+	0.0433771i
$336$	−1.92729	+	0.998714i	−0.105142	+	0.0544843i
$337$	−18.4861	−	15.5117i	−1.00700	−	0.844976i	−0.0190638	−	0.999818i	$-0.506069\pi$
$337$	−18.4861	−	15.5117i	−1.00700	−	0.844976i	−0.987939	+	0.154842i	$0.950513\pi$
$338$	3.58067	−	1.30326i	0.194763	−	0.0708879i
$339$	−20.7848	−	25.5133i	−1.12888	−	1.38569i
$340$	−0.383097	−	2.17265i	−0.0207763	−	0.117829i
$341$	−1.29153	−	2.23699i	−0.0699400	−	0.121140i
$342$	9.03134	+	8.03619i	0.488359	+	0.434547i
$343$	−18.4403	−	1.71922i	−0.995682	−	0.0928292i
$344$	4.62525	+	26.2311i	0.249377	+	1.41428i
$345$	1.57046	+	0.937356i	0.0845510	+	0.0504656i
$346$	11.5419	+	9.68484i	0.620499	+	0.520660i
$347$	5.53986	−	2.01635i	0.297395	−	0.108243i	−0.189013	−	0.981975i	$-0.560529\pi$
$347$	5.53986	−	2.01635i	0.297395	−	0.108243i	0.486409	+	0.873731i	$0.338307\pi$
$348$	4.27671	+	0.818264i	0.229256	+	0.0438636i
$349$	15.9532	−	13.3863i	0.853953	−	0.716552i	−0.106703	−	0.994291i	$-0.534029\pi$
$349$	15.9532	−	13.3863i	0.853953	−	0.716552i	0.960657	+	0.277739i	$0.0895850\pi$
$350$	8.32951	+	7.44103i	0.445231	+	0.397740i
$351$	4.66821	+	14.8008i	0.249171	+	0.790007i
$352$	2.95969	−	5.12634i	0.157752	−	0.273235i
$353$	−5.24320	−	1.90837i	−0.279067	−	0.101572i	0.198695	−	0.980061i	$-0.436330\pi$
$353$	−5.24320	−	1.90837i	−0.279067	−	0.101572i	−0.477762	+	0.878489i	$0.658552\pi$
$354$	−18.2418	−	3.49020i	−0.969539	−	0.185502i
$355$	−2.76467	−	2.31984i	−0.146734	−	0.123124i
$356$	−12.9907	+	4.72822i	−0.688504	+	0.250595i
$357$	−12.6237	−	2.82334i	−0.668116	−	0.149427i
$358$	−0.425212	−	2.41149i	−0.0224731	−	0.127451i
$359$	−1.53091			−0.0807981			−0.0403990	−	0.999184i	$-0.512863\pi$
$359$	−1.53091			−0.0807981			−0.0403990	+	0.999184i	$0.512863\pi$
$360$	3.18887	−	5.17067i	0.168068	−	0.272518i
$361$	−0.388375			−0.0204408
$362$	8.54724	−	7.17198i	0.449233	−	0.376951i
$363$	10.7192	+	13.1578i	0.562612	+	0.690606i
$364$	−6.99946	+	5.51289i	−0.366871	+	0.288954i
$365$	−6.01404	−	5.04638i	−0.314789	−	0.264139i
$366$	1.11208	−	0.179490i	0.0581293	−	0.00938208i
$367$	−4.82247	−	27.3496i	−0.251731	−	1.42764i	−0.804326	−	0.594188i	$-0.797474\pi$
$367$	−4.82247	−	27.3496i	−0.251731	−	1.42764i	0.552595	−	0.833450i	$-0.313637\pi$
$368$	0.721578			0.0376148
$369$	−19.7172	−	0.572464i	−1.02644	−	0.0298013i
$370$	2.42147	+	4.19411i	0.125886	+	0.218041i
$371$	−33.5671	−	1.04050i	−1.74272	−	0.0540201i
$372$	3.95164	+	2.35860i	0.204883	+	0.122288i
$373$	2.23812	−	12.6930i	0.115885	−	0.657219i	−0.870423	−	0.492305i	$-0.836154\pi$
$373$	2.23812	−	12.6930i	0.115885	−	0.657219i	0.986308	−	0.164914i	$-0.0527345\pi$
$374$	−2.71587	+	0.988496i	−0.140434	+	0.0511139i
$375$	−11.2256	−	2.14780i	−0.579687	−	0.110912i
$376$	−3.11346	−	17.6573i	−0.160565	−	0.910608i
$377$	−6.65932			−0.342973
$378$	−7.49890	−	10.4243i	−0.385702	−	0.536169i
$379$	−10.5063			−0.539672			−0.269836	−	0.962906i	$-0.586969\pi$
$379$	−10.5063			−0.539672			−0.269836	+	0.962906i	$0.586969\pi$
$380$	−0.585498	−	3.32053i	−0.0300354	−	0.170339i
$381$	−16.4276	+	19.0103i	−0.841609	+	0.973930i
$382$	0.687330	−	0.250168i	0.0351669	−	0.0127997i
$383$	−0.383358	+	2.17413i	−0.0195887	+	0.111093i	−0.993034	−	0.117825i	$-0.962408\pi$
$383$	−0.383358	+	2.17413i	−0.0195887	+	0.111093i	0.973446	+	0.228918i	$0.0735188\pi$
$384$	−0.130805	+	9.01243i	−0.00667510	+	0.459913i
$385$	1.05860	−	1.70899i	0.0539514	−	0.0870980i
$386$	−10.0341	−	17.3795i	−0.510720	−	0.884593i
$387$	−25.9642	+	8.60543i	−1.31984	+	0.437439i
$388$	6.27928			0.318782
$389$	0.921736	+	5.22742i	0.0467339	+	0.265041i	0.999218	−	0.0395483i	$-0.0125919\pi$
$389$	0.921736	+	5.22742i	0.0467339	+	0.265041i	−0.952484	+	0.304589i	$0.901481\pi$
$390$	−1.19115	+	3.13052i	−0.0603160	+	0.158520i
$391$	3.29401	+	2.76400i	0.166585	+	0.139782i
$392$	11.3018	−	17.0423i	0.570828	−	0.860764i
$393$	13.5295	−	35.5578i	0.682475	−	1.79366i
$394$	9.59498	−	8.05114i	0.483388	−	0.405611i
$395$	−7.67504			−0.386173
$396$	3.44589	+	1.36871i	0.173162	+	0.0687803i
$397$	6.12431			0.307370			0.153685	−	0.988120i	$-0.450886\pi$
$397$	6.12431			0.307370			0.153685	+	0.988120i	$0.450886\pi$
$398$	3.31417	+	18.7956i	0.166124	+	0.942137i
$399$	−19.2931	−	4.31500i	−0.965865	−	0.216020i
$400$	−2.01171	+	0.732201i	−0.100585	+	0.0366101i
$401$	−3.44123	−	2.88754i	−0.171847	−	0.144197i	0.552808	−	0.833309i	$-0.313556\pi$
$401$	−3.44123	−	2.88754i	−0.171847	−	0.144197i	−0.724655	+	0.689112i	$0.758001\pi$
$402$	1.77895	+	5.11750i	0.0887258	+	0.255238i
$403$	−6.61373	−	2.40720i	−0.329453	−	0.119911i
$404$	7.31863	−	12.6762i	0.364116	−	0.630667i
$405$	5.72865	+	2.47024i	0.284659	+	0.122747i
$406$	5.23373	−	1.72325i	0.259746	−	0.0855234i
$407$	−6.28075	+	5.27017i	−0.311325	+	0.261233i
$408$	9.33864	−	10.8069i	0.462332	−	0.535021i
$409$	−16.5279	+	6.01568i	−0.817254	+	0.297456i	−0.716617	−	0.697467i	$-0.754310\pi$
$409$	−16.5279	+	6.01568i	−0.817254	+	0.297456i	−0.100637	+	0.994923i	$0.532088\pi$
$410$	−3.26123	−	2.73650i	−0.161061	−	0.135146i
$411$	0.407707	−	28.0909i	0.0201107	−	1.38562i
$412$	2.19533	+	12.4503i	0.108156	+	0.613383i
$413$	28.8491	−	9.49880i	1.41957	−	0.467406i
$414$	0.618939	+	4.22360i	0.0304192	+	0.207578i
$415$	−1.29550	−	2.24387i	−0.0635936	−	0.110147i
$416$	−2.80075	−	15.8839i	−0.137318	−	0.778770i
$417$	4.61772	−	0.745300i	0.226130	−	0.0364975i
$418$	−4.15074	+	1.51075i	−0.203019	+	0.0738931i
$419$	−1.57587	−	1.32231i	−0.0769864	−	0.0645993i	0.603482	−	0.797376i	$-0.293779\pi$
$419$	−1.57587	−	1.32231i	−0.0769864	−	0.0645993i	−0.680469	+	0.732777i	$0.738224\pi$
$420$	−0.162907	+	3.57786i	−0.00794903	+	0.174582i
$421$	−4.02943	−	1.46659i	−0.196382	−	0.0714773i	0.241957	−	0.970287i	$-0.422211\pi$
$421$	−4.02943	−	1.46659i	−0.196382	−	0.0714773i	−0.438339	+	0.898810i	$0.644433\pi$
$422$	8.89948	+	15.4144i	0.433220	+	0.750359i
$423$	17.4777	−	5.79271i	0.849796	−	0.281651i
$424$	18.5405	−	32.1131i	0.900408	−	1.55955i
$425$	−11.9882	−	4.36333i	−0.581511	−	0.211653i
$426$	0.122243	−	8.42254i	0.00592270	−	0.408073i
$427$	−1.44719	+	1.13983i	−0.0700345	+	0.0551603i
$428$	−1.26131	+	7.15327i	−0.0609679	+	0.345766i
$429$	−5.56953	−	1.06562i	−0.268899	−	0.0514486i
$430$	−5.54744	−	2.01910i	−0.267521	−	0.0973697i
$431$	−4.87769	−	8.44840i	−0.234950	−	0.406945i	0.724308	−	0.689476i	$-0.242159\pi$
$431$	−4.87769	−	8.44840i	−0.234950	−	0.406945i	−0.959258	+	0.282531i	$0.908826\pi$
$432$	2.44024	−	0.321499i	0.117406	−	0.0154681i
$433$	18.7527			0.901200			0.450600	−	0.892726i	$-0.351210\pi$
$433$	18.7527			0.901200			0.450600	+	0.892726i	$0.351210\pi$
$434$	5.82081	+	0.180431i	0.279408	+	0.00866098i
$435$	−1.75027	+	2.02545i	−0.0839190	+	0.0971131i
$436$	2.95739	+	2.48154i	0.141633	+	0.118844i
$437$	5.03433	+	4.22431i	0.240825	+	0.202076i
$438$	0.265917	−	18.3217i	0.0127060	−	0.875443i
$439$	32.5183	+	11.8357i	1.55202	+	0.564887i	0.968889	−	0.247495i	$-0.0796072\pi$
$439$	32.5183	+	11.8357i	1.55202	+	0.564887i	0.583126	+	0.812382i	$0.301829\pi$
$440$	1.10983	+	1.92229i	0.0529093	+	0.0916416i
$441$	18.9992	+	8.94600i	0.904723	+	0.426000i
$442$	−3.93750	+	6.81995i	−0.187288	+	0.324392i
$443$	−12.6830	+	10.6423i	−0.602587	+	0.505631i	−0.892276	−	0.451490i	$-0.850893\pi$
$443$	−12.6830	+	10.6423i	−0.602587	+	0.505631i	0.289689	+	0.957121i	$0.406448\pi$
$444$	5.19468	−	13.6525i	0.246529	−	0.647918i
$445$	1.47583	−	8.36982i	0.0699608	−	0.396768i
$446$	−6.15063	+	2.23865i	−0.291241	+	0.106003i
$447$	20.6862	+	25.3922i	0.978422	+	1.20101i
$448$	7.49687	+	13.9672i	0.354194	+	0.659890i
$449$	14.4571	−	25.0404i	0.682272	−	1.18173i	−0.292013	−	0.956414i	$-0.594325\pi$
$449$	14.4571	−	25.0404i	0.682272	−	1.18173i	0.974286	−	0.225316i	$-0.0723415\pi$
$450$	−6.01134	−	11.1470i	−0.283377	−	0.525476i
$451$	3.60368	−	6.24175i	0.169690	−	0.293912i
$452$	−16.4103	+	13.7699i	−0.771877	+	0.647681i
$453$	−23.2937	+	13.0016i	−1.09443	+	0.610868i
$454$	4.32257	−	1.57329i	0.202868	−	0.0738380i
$455$	−0.783579	−	5.42122i	−0.0367348	−	0.254150i
$456$	14.2725	−	16.5165i	0.668372	−	0.773456i
$457$	0.0281528	+	0.159662i	0.00131693	+	0.00746870i	0.985459	−	0.169913i	$-0.0543485\pi$
$457$	0.0281528	+	0.159662i	0.00131693	+	0.00746870i	−0.984142	+	0.177381i	$0.943237\pi$
$458$	−2.96162	−	5.12968i	−0.138387	−	0.239694i
$459$	12.3712	+	7.87969i	0.577439	+	0.367792i
$460$	0.595291	−	1.03107i	0.0277556	−	0.0480741i
$461$	8.06275	−	6.76545i	0.375520	−	0.315098i	−0.435421	−	0.900227i	$-0.643400\pi$
$461$	8.06275	−	6.76545i	0.375520	−	0.315098i	0.810940	+	0.585129i	$0.198956\pi$
$462$	4.65299	−	0.603741i	0.216477	−	0.0280886i
$463$	−0.766878	+	4.34918i	−0.0356398	+	0.202123i	−0.997428	−	0.0716697i	$-0.977167\pi$
$463$	−0.766878	+	4.34918i	−0.0356398	+	0.202123i	0.961789	+	0.273793i	$0.0882784\pi$
$464$	−0.183397	+	1.04009i	−0.00851397	+	0.0482851i
$465$	−2.47044	+	1.37890i	−0.114564	+	0.0639450i
$466$	−16.9172	+	14.1952i	−0.783675	+	0.657581i
$467$	−20.9637			−0.970083			−0.485042	−	0.874491i	$-0.661196\pi$
$467$	−20.9637			−0.970083			−0.485042	+	0.874491i	$0.661196\pi$
$468$	9.58976	−	3.17837i	0.443287	−	0.146920i
$469$	−6.60753	−	5.90272i	−0.305107	−	0.272562i
$470$	3.73423	+	1.35915i	0.172247	+	0.0626929i
$471$	5.71175	−	15.0114i	0.263184	−	0.691690i
$472$	−5.82348	+	33.0266i	−0.268048	+	1.52017i
$473$	1.73550	−	9.84252i	0.0797985	−	0.452560i
$474$	−11.3142	−	13.8881i	−0.519678	−	0.637904i
$475$	−18.3219	−	6.66861i	−0.840665	−	0.305977i
$476$	−1.71846	+	8.24345i	−0.0787656	+	0.377838i
$477$	35.3903	+	14.0571i	1.62041	+	0.643629i
$478$	−6.70877			−0.306852
$479$	7.57287	−	6.35439i	0.346013	−	0.290340i	−0.453174	−	0.891422i	$-0.649708\pi$
$479$	7.57287	−	6.35439i	0.346013	−	0.290340i	0.799187	+	0.601083i	$0.205264\pi$
$480$	−5.56724	−	3.32290i	−0.254109	−	0.151669i
$481$	−3.87932	+	22.0007i	−0.176882	+	1.00315i
$482$	2.11770	−	12.0101i	0.0964585	−	0.547043i
$483$	−4.23930	−	5.54617i	−0.192895	−	0.252360i
$484$	8.46319	−	7.10146i	0.384690	−	0.322794i
$485$	−1.93018	+	3.34318i	−0.0876451	+	0.151806i
$486$	3.97496	+	14.0076i	0.180308	+	0.635399i
$487$	−16.3816	−	28.3737i	−0.742320	−	1.28574i	−0.951437	−	0.307845i	$-0.900392\pi$
$487$	−16.3816	−	28.3737i	−0.742320	−	1.28574i	0.209117	−	0.977891i	$-0.432941\pi$
$488$	−0.353207	−	2.00313i	−0.0159889	−	0.0906776i
$489$	−1.53077	−	0.292884i	−0.0692240	−	0.0132447i
$490$	2.01869	+	4.05790i	0.0911953	+	0.183317i
$491$	−21.4366	+	7.80228i	−0.967420	+	0.352112i	−0.776937	−	0.629579i	$-0.783228\pi$
$491$	−21.4366	+	7.80228i	−0.967420	+	0.352112i	−0.190483	+	0.981691i	$0.561005\pi$
$492$	−0.186348	+	12.8394i	−0.00840123	+	0.578844i
$493$	−4.82129	+	4.04554i	−0.217140	+	0.182202i
$494$	−6.01780	+	10.4231i	−0.270754	+	0.468959i
$495$	−1.78795	+	1.41391i	−0.0803624	+	0.0635506i
$496$	−0.558112	+	0.966678i	−0.0250600	+	0.0434051i
$497$	6.51468	+	12.1373i	0.292223	+	0.544434i
$498$	2.15057	−	5.65205i	0.0963693	−	0.253274i
$499$	10.9955	−	4.00202i	0.492225	−	0.179155i	−0.0839689	−	0.996468i	$-0.526760\pi$
$499$	10.9955	−	4.00202i	0.492225	−	0.179155i	0.576194	+	0.817313i	$0.304537\pi$
$500$	−1.29196	+	7.32705i	−0.0577781	+	0.327676i
$501$	11.9613	+	14.6825i	0.534391	+	0.655964i
$502$	−8.87728	+	7.44892i	−0.396212	+	0.332462i
$503$	9.67648	−	16.7602i	0.431453	−	0.747299i	−0.565546	−	0.824717i	$-0.691334\pi$
$503$	9.67648	−	16.7602i	0.431453	−	0.747299i	0.996999	+	0.0774184i	$0.0246677\pi$
$504$	−18.6244	+	13.8123i	−0.829596	+	0.615248i
$505$	4.49934	+	7.79309i	0.200218	+	0.346788i
$506$	−1.46565	−	0.533452i	−0.0651560	−	0.0237148i
$507$	6.16977	−	3.44372i	0.274009	−	0.152941i
$508$	12.5291	+	10.5131i	0.555888	+	0.466445i
$509$	11.9415	+	10.0201i	0.529299	+	0.444135i	0.867859	−	0.496810i	$-0.165495\pi$
$509$	11.9415	+	10.0201i	0.529299	+	0.444135i	−0.338560	+	0.940945i	$0.609940\pi$
$510$	1.03942	+	2.99009i	0.0460261	+	0.132403i
$511$	14.1715	+	26.4025i	0.626909	+	1.16798i
$512$	−5.32552			−0.235357
$513$	18.9073	+	12.0428i	0.834778	+	0.531701i
$514$	14.4004	+	24.9423i	0.635176	+	1.10016i
$515$	−7.30355	−	2.65827i	−0.321833	−	0.117138i
$516$	5.84658	+	16.8189i	0.257381	+	0.740410i
$517$	−1.16825	+	6.62545i	−0.0513794	+	0.291387i
$518$	−2.64432	−	18.2948i	−0.116185	−	0.803826i
$519$	23.9904	+	14.3190i	1.05306	+	0.628536i
$520$	5.68332	+	2.06856i	0.249230	+	0.0907122i
$521$	11.0207	−	19.0885i	0.482827	−	0.836280i	−0.516979	−	0.855998i	$-0.672943\pi$
$521$	11.0207	−	19.0885i	0.482827	−	0.836280i	0.999806	+	0.0197179i	$0.00627680\pi$
$522$	−6.24527	−	0.181324i	−0.273348	−	0.00793632i
$523$	4.28506	+	7.42194i	0.187373	+	0.324539i	0.944373	−	0.328875i	$-0.106669\pi$
$523$	4.28506	+	7.42194i	0.187373	+	0.324539i	−0.757001	+	0.653414i	$0.773336\pi$
$524$	−23.2725	−	8.47049i	−1.01666	−	0.370035i
$525$	17.4467	+	11.1606i	0.761435	+	0.487089i
$526$	−9.37073	−	7.86298i	−0.408583	−	0.342842i
$527$	−6.25065	+	2.27505i	−0.272283	+	0.0991027i
$528$	−0.319819	+	0.840536i	−0.0139183	+	0.0365796i
$529$	−3.59095	−	20.3653i	−0.156128	−	0.885447i
$530$	4.10926	+	7.11745i	0.178495	+	0.309162i
$531$	−34.4249	−	0.999483i	−1.49391	−	0.0433739i
$532$	−2.62638	+	12.5987i	−0.113868	+	0.546223i
$533$	−3.41015	−	19.3399i	−0.147710	−	0.837705i
$534$	17.3210	−	9.66786i	0.749552	−	0.418369i
$535$	−3.42079	−	2.87038i	−0.147894	−	0.124097i
$536$	9.19294	−	3.34596i	0.397075	−	0.144523i
$537$	−1.49090	−	4.28889i	−0.0643372	−	0.185079i
$538$	−22.8867	+	19.2042i	−0.986716	+	0.827953i
$539$	−6.17207	+	4.55861i	−0.265850	+	0.196353i
$540$	1.55377	−	3.75213i	0.0668634	−	0.161466i
$541$	−1.32655	+	2.29765i	−0.0570327	+	0.0987836i	−0.893132	−	0.449794i	$-0.851497\pi$
$541$	−1.32655	+	2.29765i	−0.0570327	+	0.0987836i	0.836099	+	0.548578i	$0.184831\pi$
$542$	−11.9780	−	4.35965i	−0.514501	−	0.187263i
$543$	13.5277	−	15.6545i	0.580527	−	0.671800i
$544$	−11.6772	−	9.79830i	−0.500654	−	0.420099i
$545$	−2.23028	+	0.811756i	−0.0955347	+	0.0347718i
$546$	8.65469	−	9.40961i	0.370387	−	0.402694i
$547$	5.33357	+	30.2482i	0.228047	+	1.29332i	0.856774	+	0.515693i	$0.172465\pi$
$547$	5.33357	+	30.2482i	0.228047	+	1.29332i	−0.628727	+	0.777626i	$0.716424\pi$
$548$	−18.2883			−0.781238
$549$	1.98276	−	0.657153i	0.0846220	−	0.0280466i
$550$	4.62743			0.197314
$551$	−7.36851	+	6.18292i	−0.313909	+	0.263401i
$552$	7.60940	−	1.22816i	0.323878	−	0.0522739i
$553$	27.2043	+	10.8674i	1.15685	+	0.462131i
$554$	−0.679843	−	0.570456i	−0.0288838	−	0.0242364i
$555$	5.67198	+	6.96235i	0.240762	+	0.295535i
$556$	−0.528741	−	2.99864i	−0.0224236	−	0.127171i
$557$	7.31483			0.309939			0.154970	−	0.987919i	$-0.450472\pi$
$557$	7.31483			0.309939			0.154970	+	0.987919i	$0.450472\pi$
$558$	−6.13696	−	2.43761i	−0.259798	−	0.103192i
$559$	−13.6161	−	23.5838i	−0.575899	−	0.997487i
$560$	−0.868298	−	0.0269152i	−0.0366923	−	0.00113737i
$561$	−4.67965	+	2.61199i	−0.197575	+	0.110278i
$562$	−3.97970	+	22.5700i	−0.167874	+	0.952058i
$563$	3.60603	−	1.31249i	0.151976	−	0.0553147i	−0.264912	−	0.964273i	$-0.585343\pi$
$563$	3.60603	−	1.31249i	0.151976	−	0.0553147i	0.416888	+	0.908958i	$0.363121\pi$
$564$	−3.93560	−	11.3216i	−0.165719	−	0.476724i
$565$	−2.28693	−	12.9698i	−0.0962118	−	0.545644i
$566$	−23.4500			−0.985676
$567$	−16.8076	−	16.8673i	−0.705852	−	0.708359i
$568$	−15.2099			−0.638195
$569$	2.65353	+	15.0489i	0.111242	+	0.630883i	0.988543	+	0.150942i	$0.0482308\pi$
$569$	2.65353	+	15.0489i	0.111242	+	0.630883i	−0.877301	+	0.479941i	$0.840658\pi$
$570$	1.58857	+	4.56984i	0.0665378	+	0.191410i
$571$	−10.1966	+	3.71126i	−0.426715	+	0.155311i	−0.546445	−	0.837495i	$-0.684019\pi$
$571$	−10.1966	+	3.71126i	−0.426715	+	0.155311i	0.119730	+	0.992806i	$0.461797\pi$
$572$	−0.640999	+	3.63529i	−0.0268015	+	0.151999i
$573$	1.18432	−	0.661040i	0.0494758	−	0.0276154i
$574$	7.68476	+	14.3173i	0.320756	+	0.597592i
$575$	−3.44237	−	5.96236i	−0.143557	−	0.248648i
$576$	−2.60620	−	17.7846i	−0.108592	−	0.741024i
$577$	4.87012			0.202746			0.101373	−	0.994849i	$-0.467676\pi$
$577$	4.87012			0.202746			0.101373	+	0.994849i	$0.467676\pi$
$578$	−1.46498	−	8.30833i	−0.0609352	−	0.345581i
$579$	−23.5035	−	28.8505i	−0.976771	−	1.19899i
$580$	1.33491	+	1.12012i	0.0554290	+	0.0465105i
$581$	1.41472	+	9.78781i	0.0586926	+	0.406067i
$582$	−8.89494	+	1.43564i	−0.368707	+	0.0595094i
$583$	−10.6585	+	8.94355i	−0.441430	+	0.370404i
$584$	−33.0864			−1.36912
$585$	−1.25558	+	6.08272i	−0.0519119	+	0.251490i
$586$	−2.57217			−0.106255
$587$	−5.04555	−	28.6148i	−0.208252	−	1.18106i	−0.892239	−	0.451563i	$-0.850867\pi$
$587$	−5.04555	−	28.6148i	−0.208252	−	1.18106i	0.683987	−	0.729494i	$-0.260244\pi$
$588$	5.64348	−	12.4511i	0.232733	−	0.513476i
$589$	−9.55305	+	3.47703i	−0.393627	+	0.143268i
$590$	−5.69388	−	4.77773i	−0.234413	−	0.196696i
$591$	15.1859	−	17.5735i	0.624665	−	0.722877i
$592$	3.32937	+	1.21179i	0.136836	+	0.0498043i
$593$	−9.39992	+	16.2811i	−0.386008	+	0.668586i	−0.991909	−	0.126955i	$-0.959480\pi$
$593$	−9.39992	+	16.2811i	−0.386008	+	0.668586i	0.605900	+	0.795541i	$0.292813\pi$
$594$	−5.19422	−	1.15101i	−0.213121	−	0.0472267i
$595$	−3.86069	−	3.44888i	−0.158273	−	0.141390i
$596$	16.3324	−	13.7045i	0.669003	−	0.561360i
$597$	11.6203	+	33.4283i	0.475589	+	1.36813i
$598$	−3.99353	+	1.45353i	−0.163308	+	0.0594391i
$599$	27.0687	+	22.7133i	1.10600	+	0.928042i	0.997814	−	0.0660892i	$-0.0210522\pi$
$599$	27.0687	+	22.7133i	1.10600	+	0.928042i	0.108183	+	0.994131i	$0.465497\pi$
$600$	−19.9682	+	11.1455i	−0.815200	+	0.455011i
$601$	−1.98534	−	11.2594i	−0.0809839	−	0.459282i	−0.998151	−	0.0607801i	$-0.980641\pi$
$601$	−1.98534	−	11.2594i	−0.0809839	−	0.459282i	0.917167	−	0.398502i	$-0.130470\pi$
$602$	16.8041	+	15.0116i	0.684882	+	0.611828i
$603$	4.76860	+	8.84257i	0.194192	+	0.360097i
$604$	8.68282	+	15.0391i	0.353299	+	0.611932i
$605$	1.17942	+	6.68884i	0.0479503	+	0.271940i
$606$	−7.46905	+	19.6299i	−0.303409	+	0.797409i
$607$	24.0548	−	8.75524i	0.976355	−	0.355364i	0.195933	−	0.980617i	$-0.437226\pi$
$607$	24.0548	−	8.75524i	0.976355	−	0.355364i	0.780422	+	0.625253i	$0.215004\pi$
$608$	−17.8465	−	14.9750i	−0.723773	−	0.607318i
$609$	9.07180	−	4.70097i	0.367608	−	0.190493i
$610$	0.423630	+	0.154189i	0.0171523	+	0.00624291i
$611$	9.16561	+	15.8753i	0.370801	+	0.642246i
$612$	5.01203	−	8.12689i	0.202599	−	0.328510i
$613$	−17.4146	+	30.1629i	−0.703368	+	1.21827i	0.263910	+	0.964547i	$0.414988\pi$
$613$	−17.4146	+	30.1629i	−0.703368	+	1.21827i	−0.967277	+	0.253721i	$0.918345\pi$
$614$	24.3817	+	8.87422i	0.983966	+	0.358134i
$615$	−6.77859	−	4.04590i	−0.273339	−	0.163147i
$616$	−1.21197	−	8.38506i	−0.0488317	−	0.337844i
$617$	−2.32600	+	13.1914i	−0.0936412	+	0.531066i	0.901514	+	0.432750i	$0.142457\pi$
$617$	−2.32600	+	13.1914i	−0.0936412	+	0.531066i	−0.995155	+	0.0983159i	$0.968654\pi$
$618$	−5.95634	−	17.1346i	−0.239599	−	0.689256i
$619$	−19.0302	−	6.92644i	−0.764890	−	0.278397i	−0.0700325	−	0.997545i	$-0.522310\pi$
$619$	−19.0302	−	6.92644i	−0.764890	−	0.278397i	−0.694857	+	0.719148i	$0.744533\pi$
$620$	0.920868	+	1.59499i	0.0369829	+	0.0640563i
$621$	2.38095	+	7.54891i	0.0955442	+	0.302927i
$622$	17.9983			0.721668
$623$	−17.0823	+	27.5773i	−0.684388	+	1.10486i
$624$	0.804595	+	2.31458i	0.0322096	+	0.0926574i
$625$	13.8068	+	11.5853i	0.552274	+	0.463413i
$626$	8.17018	+	6.85560i	0.326546	+	0.274005i
$627$	−7.15205	+	3.99198i	−0.285625	+	0.159424i
$628$	−9.82492	−	3.57598i	−0.392057	−	0.142697i
$629$	10.5568	+	18.2850i	0.420929	+	0.729070i
$630$	−0.587247	−	5.10548i	−0.0233965	−	0.203407i
$631$	−20.8763	+	36.1588i	−0.831072	+	1.43946i	0.0661170	+	0.997812i	$0.478939\pi$
$631$	−20.8763	+	36.1588i	−0.831072	+	1.43946i	−0.897189	+	0.441647i	$0.854394\pi$
$632$	−24.7783	+	20.7915i	−0.985628	+	0.827040i
$633$	20.8459	+	25.5883i	0.828549	+	1.01704i
$634$	2.20759	−	12.5199i	0.0876745	−	0.497227i
$635$	−9.44865	+	3.43903i	−0.374958	+	0.136474i
$636$	8.81544	−	23.1684i	0.349555	−	0.918687i
$637$	−4.89874	+	20.3251i	−0.194095	+	0.805310i
$638$	1.14144	−	1.97703i	0.0451899	−	0.0782712i
$639$	−2.26476	−	15.4545i	−0.0895924	−	0.611372i
$640$	−1.80359	+	3.12391i	−0.0712932	+	0.123483i
$641$	33.2316	−	27.8846i	1.31257	−	1.10138i	0.324744	−	0.945802i	$-0.394722\pi$
$641$	33.2316	−	27.8846i	1.31257	−	1.10138i	0.987824	−	0.155574i	$-0.0497227\pi$
$642$	0.151254	−	10.4214i	0.00596952	−	0.411299i
$643$	0.708601	−	0.257910i	0.0279445	−	0.0101710i	−0.328010	−	0.944674i	$-0.606378\pi$
$643$	0.708601	−	0.257910i	0.0279445	−	0.0101710i	0.355955	+	0.934503i	$0.384156\pi$
$644$	−3.56997	+	2.81176i	−0.140676	+	0.110799i
$645$	−10.7518	−	2.05714i	−0.423351	−	0.0810000i
$646$	1.97523	+	11.2021i	0.0777142	+	0.440739i
$647$	4.79079	+	8.29790i	0.188346	+	0.326224i	0.944699	−	0.327939i	$-0.106354\pi$
$647$	4.79079	+	8.29790i	0.188346	+	0.326224i	−0.756353	+	0.654163i	$0.773021\pi$
$648$	25.1864	−	7.54377i	0.989413	−	0.296347i
$649$	6.29177	−	10.8977i	0.246974	−	0.427771i
$650$	9.65875	−	8.10465i	0.378847	−	0.317891i
$651$	10.7090	−	1.38953i	0.419718	−	0.0544598i
$652$	−0.176177	+	0.999152i	−0.00689964	+	0.0391298i
$653$	8.11119	−	46.0009i	0.317416	−	1.80015i	−0.240928	−	0.970543i	$-0.577452\pi$
$653$	8.11119	−	46.0009i	0.317416	−	1.80015i	0.558343	−	0.829610i	$-0.311437\pi$
$654$	−4.75666	−	2.83909i	−0.186000	−	0.111017i
$655$	11.6635	−	9.78687i	0.455732	−	0.382405i
$656$	−3.11454			−0.121602
$657$	−4.92656	−	33.6185i	−0.192203	−	1.31158i
$658$	−11.3116	−	10.1050i	−0.440971	−	0.393934i
$659$	34.4366	+	12.5339i	1.34146	+	0.488251i	0.910272	−	0.414011i	$-0.135873\pi$
$659$	34.4366	+	12.5339i	1.34146	+	0.488251i	0.431187	+	0.902262i	$0.358095\pi$
$660$	0.937210	+	1.15042i	0.0364808	+	0.0447802i
$661$	−2.04259	+	11.5841i	−0.0794477	+	0.450570i	0.918970	+	0.394329i	$0.129023\pi$
$661$	−2.04259	+	11.5841i	−0.0794477	+	0.450570i	−0.998417	+	0.0562415i	$0.982088\pi$
$662$	0.226874	−	1.28667i	0.00881772	−	0.0500078i
$663$	−5.19302	+	13.6481i	−0.201680	+	0.530048i
$664$	−10.2610	−	3.73470i	−0.398205	−	0.144935i
$665$	−5.90041	−	5.27103i	−0.228808	−	0.204402i
$666$	−4.23716	+	20.5271i	−0.164187	+	0.795411i
$667$	−3.39648			−0.131512
$668$	9.44385	−	7.92433i	0.365394	−	0.306602i
$669$	−10.5980	+	5.91538i	−0.409743	+	0.228702i
$670$	−0.376514	+	2.13532i	−0.0145460	+	0.0824944i
$671$	−0.132532	+	0.751624i	−0.00511632	+	0.0290161i
$672$	15.0282	+	19.6610i	0.579724	+	0.758439i
$673$	33.7092	−	28.2854i	1.29940	−	1.09032i	0.309146	−	0.951015i	$-0.399957\pi$
$673$	33.7092	−	28.2854i	1.29940	−	1.09032i	0.990249	−	0.139308i	$-0.0444877\pi$
$674$	11.2704	−	19.5210i	0.434121	−	0.751920i
$675$	−14.2980	−	18.6298i	−0.550329	−	0.717062i
$676$	−2.29981	−	3.98339i	−0.0884542	−	0.153207i
$677$	−1.29282	−	7.33197i	−0.0496873	−	0.281790i	0.949833	−	0.312757i	$-0.101253\pi$
$677$	−1.29282	−	7.33197i	−0.0496873	−	0.281790i	−0.999520	+	0.0309666i	$0.990141\pi$
$678$	20.0979	−	23.2577i	0.771854	−	0.893208i
$679$	11.5753	−	9.11692i	0.444221	−	0.349875i
$680$	5.37131	−	1.95500i	0.205981	−	0.0749708i
$681$	7.44812	−	4.15724i	0.285413	−	0.159306i
$682$	1.84827	−	1.55088i	0.0707740	−	0.0593864i
$683$	−7.00552	+	12.1339i	−0.268059	+	0.464291i	−0.968360	−	0.249556i	$-0.919715\pi$
$683$	−7.00552	+	12.1339i	−0.268059	+	0.464291i	0.700302	+	0.713847i	$0.253049\pi$
$684$	7.66004	−	12.4206i	0.292889	−	0.474912i
$685$	5.62164	−	9.73696i	0.214792	−	0.372030i
$686$	−1.40953	−	17.2417i	−0.0538161	−	0.658291i
$687$	−6.93721	−	8.51542i	−0.264671	−	0.324884i
$688$	−4.05844	+	1.47715i	−0.154727	+	0.0563159i
$689$	−6.58325	+	37.3355i	−0.250802	+	1.42237i
$690$	−0.607525	+	1.59668i	−0.0231281	+	0.0607844i
$691$	11.3150	−	9.49442i	0.430443	−	0.361185i	−0.401676	−	0.915782i	$-0.631572\pi$
$691$	11.3150	−	9.49442i	0.430443	−	0.361185i	0.832119	+	0.554597i	$0.187128\pi$
$692$	9.09365	−	15.7507i	0.345689	−	0.598750i
$693$	8.33946	−	2.48000i	0.316790	−	0.0942073i
$694$	2.75336	+	4.76895i	0.104516	+	0.181027i
$695$	1.75905	+	0.640241i	0.0667245	+	0.0242857i
$696$	−0.163723	+	11.2805i	−0.00620589	+	0.427585i
$697$	−14.2179	−	11.9303i	−0.538542	−	0.451890i
$698$	14.9014	+	12.5037i	0.564025	+	0.473273i
$699$	−26.7748	+	30.9844i	−1.01272	+	1.17194i
$700$	7.09965	−	11.4615i	0.268341	−	0.433205i
$701$	23.2751			0.879089			0.439544	−	0.898221i	$-0.355140\pi$
$701$	23.2751			0.879089			0.439544	+	0.898221i	$0.355140\pi$
$702$	−12.8577	+	6.69487i	−0.485284	+	0.252682i
$703$	16.1343	+	27.9455i	0.608518	+	1.05398i
$704$	6.17150	+	2.24624i	0.232597	+	0.0846584i
$705$	7.23752	+	1.38476i	0.272581	+	0.0521530i
$706$	0.905023	−	5.13264i	0.0340610	−	0.193169i
$707$	−4.91341	−	33.9936i	−0.184788	−	1.27846i
$708$	−0.325351	+	22.4167i	−0.0122275	+	0.842470i
$709$	−12.0766	−	4.39553i	−0.453547	−	0.165078i	0.105138	−	0.994458i	$-0.466472\pi$
$709$	−12.0766	−	4.39553i	−0.453547	−	0.165078i	−0.558685	+	0.829380i	$0.688694\pi$
$710$	1.68554	−	2.91944i	0.0632572	−	0.109565i
$711$	−24.8153	−	22.0810i	−0.930648	−	0.828101i
$712$	−17.9090	−	31.0193i	−0.671169	−	1.16250i
$713$	−3.37323	−	1.22775i	−0.126328	−	0.0459798i
$714$	0.549579	−	12.0702i	0.0205675	−	0.451716i
$715$	−1.73844	−	1.45873i	−0.0650140	−	0.0545533i
$716$	−2.77756	+	1.01095i	−0.103802	+	0.0377810i
$717$	−12.2812	+	1.98219i	−0.458649	+	0.0740261i
$718$	−0.248312	−	1.40825i	−0.00926692	−	0.0525553i
$719$	5.63512	+	9.76032i	0.210155	+	0.363998i	0.951763	−	0.306835i	$-0.0992699\pi$
$719$	5.63512	+	9.76032i	0.210155	+	0.363998i	−0.741608	+	0.670833i	$0.765937\pi$
$720$	0.915459	+	0.363621i	0.0341171	+	0.0135514i
$721$	22.1236	+	19.7637i	0.823926	+	0.736040i
$722$	−0.0629942	−	0.357258i	−0.00234440	−	0.0132958i
$723$	0.328179	−	22.6115i	0.0122051	−	0.840931i
$724$	−10.3174	−	8.65729i	−0.383442	−	0.321746i
$725$	9.46915	−	3.44649i	0.351676	−	0.127999i
$726$	−10.3649	+	11.9946i	−0.384679	+	0.445160i
$727$	6.71577	−	5.63520i	0.249074	−	0.208998i	−0.509699	−	0.860353i	$-0.670243\pi$
$727$	6.71577	−	5.63520i	0.249074	−	0.208998i	0.758773	+	0.651355i	$0.225799\pi$
$728$	−17.2157	−	15.3793i	−0.638055	−	0.569995i
$729$	11.4153	+	24.4681i	0.422790	+	0.906228i
$730$	3.66658	−	6.35070i	0.135706	−	0.235050i
$731$	−24.1851	−	8.80264i	−0.894517	−	0.325577i
$732$	−0.446474	−	1.28437i	−0.0165021	−	0.0474718i
$733$	−28.9205	−	24.2672i	−1.06820	−	0.896329i	−0.0733153	−	0.997309i	$-0.523358\pi$
$733$	−28.9205	−	24.2672i	−1.06820	−	0.896329i	−0.994889	+	0.100979i	$0.967802\pi$
$734$	24.3761	−	8.87218i	0.899739	−	0.327478i
$735$	4.89441	+	6.83202i	0.180533	+	0.252003i
$736$	−1.42848	−	8.10131i	−0.0526545	−	0.298618i
$737$	−3.67079			−0.135215
$738$	−2.67152	−	18.2303i	−0.0983400	−	0.671066i
$739$	−8.13702			−0.299325			−0.149663	−	0.988737i	$-0.547819\pi$
$739$	−8.13702			−0.299325			−0.149663	+	0.988737i	$0.547819\pi$
$740$	4.47823	−	3.75768i	0.164623	−	0.138135i
$741$	−7.93664	+	20.8588i	−0.291560	+	0.766266i
$742$	−4.48743	−	31.0465i	−0.164739	−	1.13975i
$743$	−15.6473	−	13.1296i	−0.574042	−	0.481678i	0.308942	−	0.951081i	$-0.400025\pi$
$743$	−15.6473	−	13.1296i	−0.574042	−	0.481678i	−0.882984	+	0.469402i	$0.844469\pi$
$744$	−4.24024	+	11.1440i	−0.155455	+	0.408561i
$745$	2.27607	+	12.9083i	0.0833889	+	0.472922i
$746$	12.0390			0.440781
$747$	2.26690	−	10.9821i	0.0829417	−	0.401815i
$748$	1.74436	+	3.02132i	0.0637801	+	0.110470i
$749$	8.06075	+	15.0178i	0.294533	+	0.548738i
$750$	0.154929	−	10.6746i	0.00565719	−	0.389780i
$751$	6.92360	−	39.2657i	0.252646	−	1.43282i	−0.549399	−	0.835560i	$-0.685143\pi$
$751$	6.92360	−	39.2657i	0.252646	−	1.43282i	0.802045	−	0.597264i	$-0.203746\pi$
$752$	2.73192	−	0.994338i	0.0996229	−	0.0362598i
$753$	−14.0500	+	16.2590i	−0.512011	+	0.592511i
$754$	−1.08014	−	6.12577i	−0.0393363	−	0.223087i
$755$	−10.6760			−0.388541
$756$	−10.8202	+	11.0994i	−0.393526	+	0.403683i
$757$	−12.7537			−0.463541			−0.231770	−	0.972771i	$-0.574452\pi$
$757$	−12.7537			−0.463541			−0.231770	+	0.972771i	$0.574452\pi$
$758$	−1.70411	−	9.66451i	−0.0618962	−	0.351031i
$759$	−2.84065	−	0.543503i	−0.103109	−	0.0197279i
$760$	8.20914	−	2.98788i	0.297777	−	0.108382i
$761$	−5.38155	+	30.5203i	−0.195081	+	1.10636i	0.717223	+	0.696844i	$0.245413\pi$
$761$	−5.38155	+	30.5203i	−0.195081	+	1.10636i	−0.912303	+	0.409515i	$0.865698\pi$
$762$	−20.1518	−	12.0279i	−0.730021	−	0.435724i
$763$	9.05468	+	0.280673i	0.327801	+	0.0101611i
$764$	−0.441461	−	0.764633i	−0.0159715	−	0.0276634i
$765$	2.78623	+	5.16660i	0.100736	+	0.186799i
$766$	−2.06212			−0.0745074
$767$	−5.95389	−	33.7662i	−0.214982	−	1.21923i
$768$	−28.8016	+	4.64858i	−1.03929	+	0.167741i
$769$	−17.6461	−	14.8068i	−0.636335	−	0.533948i	0.266555	−	0.963820i	$-0.414114\pi$
$769$	−17.6461	−	14.8068i	−0.636335	−	0.533948i	−0.902890	+	0.429871i	$0.858559\pi$
$770$	1.74376	+	0.696590i	0.0628409	+	0.0251034i
$771$	33.7312	+	41.4050i	1.21480	+	1.49116i
$772$	−18.5568	+	15.5710i	−0.667874	+	0.560413i
$773$	−51.4707			−1.85127			−0.925636	−	0.378415i	$-0.876469\pi$
$773$	−51.4707			−1.85127			−0.925636	+	0.378415i	$0.876469\pi$
$774$	−12.1273	−	22.4882i	−0.435908	−	0.808320i
$775$	10.6501			0.382565
$776$	2.82512	+	16.0220i	0.101416	+	0.575157i
$777$	−10.2461	−	32.7094i	−0.367578	−	1.17344i
$778$	−4.65909	+	1.69577i	−0.167037	+	0.0607963i
$779$	−21.7297	−	18.2334i	−0.778546	−	0.653278i
$780$	3.97112	+	0.759796i	0.142189	+	0.0272051i
$781$	5.36295	+	1.95195i	0.191901	+	0.0698464i
$782$	−2.00826	+	3.47841i	−0.0718153	+	0.124388i
$783$	−11.4863	+	1.51330i	−0.410486	+	0.0540811i
$784$	3.03959	+	1.32487i	0.108557	+	0.0473166i
$785$	4.92398	−	4.13171i	0.175744	−	0.147467i
$786$	34.9034	+	6.67808i	1.24496	+	0.238199i
$787$	34.3972	−	12.5195i	1.22613	−	0.446273i	0.353857	−	0.935299i	$-0.384870\pi$
$787$	34.3972	−	12.5195i	1.22613	−	0.446273i	0.872269	+	0.489026i	$0.162648\pi$
$788$	−11.5821	−	9.71853i	−0.412595	−	0.346208i
$789$	−19.4774	−	11.6254i	−0.693414	−	0.413875i
$790$	−1.24489	−	7.06010i	−0.0442911	−	0.251187i
$791$	−10.2585	+	49.2099i	−0.364750	+	1.74970i
$792$	−1.94202	+	9.40823i	−0.0690068	+	0.334307i
$793$	1.03979	+	1.80097i	0.0369241	+	0.0639544i
$794$	0.993359	+	5.63362i	0.0352530	+	0.199930i
$795$	9.62542	+	11.8152i	0.341378	+	0.419042i
$796$	21.6487	−	7.87950i	0.767319	−	0.279281i
$797$	40.2253	+	33.7531i	1.42485	+	1.19559i	0.948678	+	0.316245i	$0.102422\pi$
$797$	40.2253	+	33.7531i	1.42485	+	1.19559i	0.476177	+	0.879350i	$0.342022\pi$
$798$	0.839938	−	18.4472i	0.0297335	−	0.653025i
$799$	16.2801	+	5.92546i	0.575947	+	0.209628i
$800$	12.2031	+	21.1364i	0.431444	+	0.747283i
$801$	28.8516	−	22.8158i	1.01942	−	0.806157i
$802$	2.09802	−	3.63387i	0.0740836	−	0.128317i
$803$	11.6661	+	4.24611i	0.411688	+	0.149842i
$804$	5.71060	−	3.18743i	0.201397	−	0.112412i
$805$	−0.399652	−	2.76501i	−0.0140859	−	0.0974537i
$806$	1.14159	−	6.47427i	0.0402108	−	0.228046i
$807$	−36.2227	+	41.9177i	−1.27510	+	1.47557i
$808$	35.6371	+	12.9708i	1.25371	+	0.456312i
$809$	−12.0492	−	20.8698i	−0.423626	−	0.733741i	0.572665	−	0.819789i	$-0.305909\pi$
$809$	−12.0492	−	20.8698i	−0.423626	−	0.733741i	−0.996291	+	0.0860480i	$0.972576\pi$
$810$	−1.34314	+	5.67033i	−0.0471930	+	0.199235i
$811$	−44.5592			−1.56469			−0.782343	−	0.622848i	$-0.785976\pi$
$811$	−44.5592			−1.56469			−0.782343	+	0.622848i	$0.785976\pi$
$812$	−3.14558	−	5.86045i	−0.110388	−	0.205661i
$813$	−23.2153	−	4.44179i	−0.814196	−	0.155780i
$814$	−5.86666	−	4.92271i	−0.205626	−	0.172541i
$815$	−0.477808	−	0.400928i	−0.0167369	−	0.0140439i
$816$	1.98863	+	1.18694i	0.0696159	+	0.0415513i
$817$	−36.9627	−	13.4533i	−1.29316	−	0.470673i
$818$	−8.21451	−	14.2280i	−0.287214	−	0.497469i
$819$	13.0632	−	19.7825i	0.456467	−	0.691257i
$820$	−2.56945	+	4.45042i	−0.0897291	+	0.155415i
$821$	24.5416	−	20.5929i	0.856509	−	0.718696i	−0.104704	−	0.994503i	$-0.533390\pi$
$821$	24.5416	−	20.5929i	0.856509	−	0.718696i	0.961213	+	0.275807i	$0.0889451\pi$
$822$	25.9064	−	4.18130i	0.903589	−	0.145839i
$823$	6.07521	−	34.4543i	0.211769	−	1.20100i	−0.674658	−	0.738131i	$-0.735709\pi$
$823$	6.07521	−	34.4543i	0.211769	−	1.20100i	0.886427	−	0.462869i	$-0.153180\pi$
$824$	−30.7802	+	11.2031i	−1.07228	+	0.390277i
$825$	8.47104	−	1.36723i	0.294924	−	0.0476007i
$826$	13.4171	+	24.9970i	0.466839	+	0.869757i
$827$	5.08741	−	8.81166i	0.176907	−	0.306411i	−0.763913	−	0.645320i	$-0.776724\pi$
$827$	5.08741	−	8.81166i	0.176907	−	0.306411i	0.940819	+	0.338908i	$0.110058\pi$
$828$	4.89111	−	1.62108i	0.169978	−	0.0563364i
$829$	8.01494	−	13.8823i	0.278370	−	0.482151i	−0.692610	−	0.721313i	$-0.743539\pi$
$829$	8.01494	−	13.8823i	0.278370	−	0.482151i	0.970980	+	0.239161i	$0.0768724\pi$
$830$	1.85396	−	1.55566i	0.0643519	−	0.0539977i
$831$	−1.41308	−	0.843418i	−0.0490192	−	0.0292579i
$832$	16.8158	−	6.12046i	0.582984	−	0.212189i
$833$	8.80087	+	17.6912i	0.304932	+	0.612963i
$834$	1.43458	+	4.12685i	0.0496753	+	0.142901i
$835$	1.31609	+	7.46390i	0.0455450	+	0.258299i
$836$	2.66596	+	4.61757i	0.0922040	+	0.159702i
$837$	−11.9546	−	2.64909i	−0.413213	−	0.0915660i
$838$	0.960763	−	1.66409i	0.0331890	−	0.0574850i
$839$	−6.42307	+	5.38959i	−0.221749	+	0.186069i	−0.746894	−	0.664944i	$-0.768456\pi$
$839$	−6.42307	+	5.38959i	−0.221749	+	0.186069i	0.525145	+	0.851013i	$0.324011\pi$
$840$	−9.20246	+	1.19405i	−0.317515	+	0.0411986i
$841$	−4.17254	+	23.6637i	−0.143881	+	0.815989i
$842$	0.695515	−	3.94446i	0.0239690	−	0.135935i
$843$	−0.616733	+	42.4929i	−0.0212414	+	1.46353i
$844$	16.4586	−	13.8104i	0.566527	−	0.475372i
$845$	2.82775			0.0972775
$846$	8.16347	+	15.1378i	0.280666	+	0.520448i
$847$	5.29055	−	25.3787i	0.181785	−	0.872023i
$848$	5.64998	+	2.05642i	0.194021	+	0.0706179i
$849$	−42.9279	+	6.92857i	−1.47328	+	0.237788i
$850$	2.06926	−	11.7354i	0.0709752	−	0.402520i
$851$	−1.97859	+	11.2211i	−0.0678250	+	0.384655i
$852$	−10.0380	+	1.62013i	−0.343896	+	0.0555049i
$853$	−13.6318	−	4.96157i	−0.466744	−	0.169881i	0.0979328	−	0.995193i	$-0.468777\pi$
$853$	−13.6318	−	4.96157i	−0.466744	−	0.169881i	−0.564677	+	0.825312i	$0.690999\pi$
$854$	−1.28324	−	1.14636i	−0.0439116	−	0.0392277i
$855$	4.25827	+	7.89627i	0.145630	+	0.270047i
$856$	−18.8196			−0.643239
$857$	−1.93667	+	1.62506i	−0.0661553	+	0.0555109i	−0.675266	−	0.737575i	$-0.735971\pi$
$857$	−1.93667	+	1.62506i	−0.0661553	+	0.0555109i	0.609110	+	0.793085i	$0.291527\pi$
$858$	0.0768671	−	5.29614i	0.00262420	−	0.180807i
$859$	0.734874	−	4.16768i	0.0250736	−	0.142199i	−0.969701	−	0.244295i	$-0.921444\pi$
$859$	0.734874	−	4.16768i	0.0250736	−	0.142199i	0.994775	+	0.102095i	$0.0325547\pi$
$860$	−1.23743	+	7.01780i	−0.0421959	+	0.239305i
$861$	18.2980	+	23.9389i	0.623596	+	0.815836i
$862$	6.98035	−	5.85721i	0.237752	−	0.199497i
$863$	20.6266	−	35.7263i	0.702137	−	1.21614i	−0.265578	−	0.964090i	$-0.585563\pi$
$863$	20.6266	−	35.7263i	0.702137	−	1.21614i	0.967715	−	0.252048i	$-0.0811040\pi$
$864$	−8.44039	−	26.7606i	−0.287148	−	0.910416i
$865$	5.59058	+	9.68318i	0.190086	+	0.329238i
$866$	3.04169	+	17.2503i	0.103361	+	0.586187i
$867$	−5.13661	−	14.7765i	−0.174448	−	0.501837i
$868$	−1.00561	−	6.95737i	−0.0341328	−	0.236149i
$869$	11.4050	−	4.15107i	0.386887	−	0.140815i
$870$	−2.14706	−	1.28151i	−0.0727923	−	0.0434472i
$871$	−7.66197	+	6.42916i	−0.259616	+	0.217844i
$872$	−5.00128	+	8.66247i	−0.169365	+	0.293348i
$873$	−15.8590	+	5.25623i	−0.536747	+	0.177896i
$874$	−3.06928	+	5.31616i	−0.103820	+	0.179822i
$875$	8.25658	+	15.3826i	0.279123	+	0.520028i
$876$	−21.8358	+	3.52430i	−0.737764	+	0.119075i
$877$	−23.2190	+	8.45104i	−0.784051	+	0.285371i	−0.702861	−	0.711327i	$-0.748094\pi$
$877$	−23.2190	+	8.45104i	−0.784051	+	0.285371i	−0.0811903	+	0.996699i	$0.525872\pi$
$878$	−5.61296	+	31.8327i	−0.189428	+	1.07430i
$879$	−4.70866	+	0.759978i	−0.158819	+	0.0256334i
$880$	−0.275709	+	0.231347i	−0.00929415	+	0.00779872i
$881$	−17.7327	+	30.7140i	−0.597430	+	1.03478i	0.395769	+	0.918350i	$0.370478\pi$
$881$	−17.7327	+	30.7140i	−0.597430	+	1.03478i	−0.993199	+	0.116430i	$0.962855\pi$
$882$	−5.14758	+	18.9280i	−0.173328	+	0.637338i
$883$	−18.5207	−	32.0788i	−0.623271	−	1.07954i	−0.988873	−	0.148765i	$-0.952470\pi$
$883$	−18.5207	−	32.0788i	−0.623271	−	1.07954i	0.365602	−	0.930771i	$-0.380863\pi$
$884$	8.93263	+	3.25121i	0.300437	+	0.109350i
$885$	−11.8349	−	7.06387i	−0.397827	−	0.237449i
$886$	−11.8468	−	9.94064i	−0.398001	−	0.333962i
$887$	26.5384	+	22.2684i	0.891072	+	0.747698i	0.968425	−	0.249305i	$-0.0802023\pi$
$887$	26.5384	+	22.2684i	0.891072	+	0.747698i	−0.0773527	+	0.997004i	$0.524647\pi$
$888$	37.1724	+	7.11221i	1.24742	+	0.238670i
$889$	38.3604	+	1.18908i	1.28657	+	0.0398805i
$890$	7.93860			0.266102
$891$	−9.84870	−	0.572372i	−0.329944	−	0.0191752i
$892$	3.95045	+	6.84238i	0.132271	+	0.229100i
$893$	24.8813	+	9.05606i	0.832621	+	0.303049i
$894$	−20.0025	+	23.1474i	−0.668984	+	0.774164i
$895$	0.315549	−	1.78957i	0.0105476	−	0.0598187i
$896$	10.8162	−	8.51898i	0.361342	−	0.284599i
$897$	−6.88116	+	3.84078i	−0.229755	+	0.128240i
$898$	25.3791	+	9.23723i	0.846911	+	0.308250i
$899$	2.62705	−	4.55018i	0.0876169	−	0.151757i
$900$	−11.9911	+	9.48257i	−0.399704	+	0.316086i
$901$	17.9151	+	31.0298i	0.596838	+	1.03375i
$902$	6.32617	+	2.30254i	0.210638	+	0.0766661i
$903$	35.1971	+	22.5156i	1.17129	+	0.749271i
$904$	−42.5181	−	35.6769i	−1.41413	−	1.18660i
$905$	7.78072	−	2.83195i	0.258640	−	0.0941372i
$906$	−15.7381	−	19.3185i	−0.522864	−	0.641815i
$907$	4.34811	+	24.6593i	0.144376	+	0.818800i	0.967866	+	0.251468i	$0.0809133\pi$
$907$	4.34811	+	24.6593i	0.144376	+	0.818800i	−0.823489	+	0.567332i	$0.807976\pi$
$908$	−2.77632	−	4.80872i	−0.0921353	−	0.159583i
$909$	−7.87309	+	38.1416i	−0.261134	+	1.26508i
$910$	4.85976	−	1.60012i	0.161100	−	0.0530433i
$911$	−0.303692	−	1.72232i	−0.0100618	−	0.0570632i	0.979363	−	0.202107i	$-0.0647788\pi$
$911$	−0.303692	−	1.72232i	−0.0100618	−	0.0570632i	−0.989425	+	0.145044i	$0.953668\pi$
$912$	3.03928	+	1.81404i	0.100641	+	0.0600689i
$913$	3.13869	+	2.63368i	0.103876	+	0.0871620i
$914$	−0.142304	+	0.0517943i	−0.00470699	+	0.00171320i
$915$	0.821060	+	0.157094i	0.0271434	+	0.00519336i
$916$	−5.47717	+	4.59589i	−0.180971	+	0.151853i
$917$	−55.1993	+	18.1748i	−1.82284	+	0.600185i
$918$	−5.24175	+	12.6581i	−0.173004	+	0.417780i
$919$	−2.41044	+	4.17500i	−0.0795130	+	0.137721i	−0.903040	−	0.429557i	$-0.858670\pi$
$919$	−2.41044	+	4.17500i	−0.0795130	+	0.137721i	0.823527	+	0.567277i	$0.192003\pi$
$920$	2.89869	+	1.05504i	0.0955669	+	0.0347835i
$921$	47.2555	+	9.04142i	1.55712	+	0.297925i
$922$	7.53117	+	6.31940i	0.248026	+	0.208118i
$923$	14.6127	−	5.31859i	0.480983	−	0.175064i
$924$	−1.69302	−	5.40474i	−0.0556963	−	0.177803i
$925$	−5.87017	−	33.2914i	−0.193010	−	1.09461i
$926$	−4.12510			−0.135559
$927$	−15.9664	−	29.6071i	−0.524406	−	0.972424i
$928$	12.0404			0.395246
$929$	−1.79987	+	1.51027i	−0.0590519	+	0.0495504i	−0.671836	−	0.740700i	$-0.734494\pi$
$929$	−1.79987	+	1.51027i	−0.0590519	+	0.0495504i	0.612784	+	0.790250i	$0.290050\pi$
$930$	−1.66913	−	2.04885i	−0.0547328	−	0.0671845i
$931$	13.4506	+	27.0379i	0.440826	+	0.886133i
$932$	20.4208	+	17.1350i	0.668904	+	0.561277i
$933$	32.9481	−	5.31782i	1.07867	−	0.174098i
$934$	−3.40030	−	19.2840i	−0.111261	−	0.630993i
$935$	−2.14479			−0.0701422
$936$	12.4244	+	23.0390i	0.406104	+	0.753053i
$937$	28.6990	+	49.7082i	0.937557	+	1.62390i	0.770009	+	0.638033i	$0.220251\pi$
$937$	28.6990	+	49.7082i	0.937557	+	1.62390i	0.167548	+	0.985864i	$0.446415\pi$
$938$	4.35805	−	7.03554i	0.142295	−	0.229719i
$939$	16.9820	+	10.1360i	0.554188	+	0.330776i
$940$	0.832969	−	4.72400i	0.0271684	−	0.154080i
$941$	11.9720	−	4.35744i	0.390275	−	0.142049i	−0.139427	−	0.990232i	$-0.544526\pi$
$941$	11.9720	−	4.35744i	0.390275	−	0.142049i	0.529702	+	0.848184i	$0.322304\pi$
$942$	14.7351	+	2.81928i	0.480096	+	0.0918571i
$943$	−1.73929	−	9.86403i	−0.0566392	−	0.321217i
$944$	−5.43778			−0.176985
$945$	−2.58350	−	9.17266i	−0.0840412	−	0.298387i
$946$	9.33542			0.303521
$947$	3.26247	+	18.5024i	0.106016	+	0.601246i	0.990810	+	0.135263i	$0.0431881\pi$
$947$	3.26247	+	18.5024i	0.106016	+	0.601246i	−0.884794	+	0.465983i	$0.845701\pi$
$948$	−14.1381	+	16.3610i	−0.459185	+	0.531379i
$949$	31.7873	−	11.5696i	1.03186	−	0.375566i
$950$	3.16252	−	17.9355i	0.102606	−	0.581906i
$951$	0.342109	−	23.5713i	0.0110937	−	0.764352i
$952$	−21.8069	−	0.675962i	−0.706766	−	0.0219081i
$953$	−27.2775	−	47.2461i	−0.883606	−	1.53045i	−0.847303	−	0.531110i	$-0.821775\pi$
$953$	−27.2775	−	47.2461i	−0.883606	−	1.53045i	−0.0363035	−	0.999341i	$-0.511558\pi$
$954$	−7.19051	+	34.8348i	−0.232802	+	1.12782i
$955$	0.542802			0.0175647
$956$	1.40623	+	7.97513i	0.0454807	+	0.257934i
$957$	1.50540	−	3.95643i	0.0486626	−	0.127893i
$958$	7.07359	+	5.93544i	0.228537	+	0.191765i
$959$	−33.7130	+	26.5529i	−1.08865	+	0.857438i
$960$	2.55815	−	6.72322i	0.0825638	−	0.216991i
$961$	−19.4935	+	16.3570i	−0.628824	+	0.527646i
$962$	−20.8672			−0.672785
$963$	−2.80223	−	19.1222i	−0.0903006	−	0.616205i
$964$	−14.7210			−0.474131
$965$	−2.58606	−	14.6663i	−0.0832482	−	0.472124i
$966$	4.41419	−	4.79922i	0.142024	−	0.154413i
$967$	3.92952	−	1.43023i	0.126365	−	0.0459931i	−0.278064	−	0.960563i	$-0.589693\pi$
$967$	3.92952	−	1.43023i	0.126365	−	0.0459931i	0.404429	+	0.914570i	$0.367470\pi$
$968$	21.9276	+	18.3994i	0.704778	+	0.591379i
$969$	6.92566	+	19.9231i	0.222484	+	0.640021i
$970$	−3.38839	−	1.23327i	−0.108795	−	0.0395980i
$971$	13.8265	−	23.9482i	0.443713	−	0.768534i	−0.554248	−	0.832351i	$-0.686994\pi$
$971$	13.8265	−	23.9482i	0.443713	−	0.768534i	0.997962	+	0.0638176i	$0.0203276\pi$
$972$	15.8185	−	7.66142i	0.507380	−	0.245740i
$973$	−5.32844	−	4.76007i	−0.170822	−	0.152601i
$974$	23.4433	−	19.6713i	0.751172	−	0.630308i
$975$	15.2868	−	17.6903i	0.489571	−	0.566543i
$976$	0.309923	−	0.112803i	0.00992038	−	0.00361072i
$977$	−19.1807	−	16.0945i	−0.613646	−	0.514910i	0.282153	−	0.959369i	$-0.408951\pi$
$977$	−19.1807	−	16.0945i	−0.613646	−	0.514910i	−0.895799	+	0.444460i	$0.853396\pi$
$978$	0.0211268	−	1.45563i	0.000675560	−	0.0465460i
$979$	2.33379	+	13.2356i	0.0745884	+	0.423012i
$980$	4.40074	−	3.25032i	0.140576	−	0.103828i
$981$	−9.54647	−	3.79187i	−0.304795	−	0.121065i
$982$	−10.6542	−	18.4535i	−0.339988	−	0.588876i
$983$	−8.96300	−	50.8317i	−0.285875	−	1.62128i	−0.702142	−	0.712037i	$-0.747773\pi$
$983$	−8.96300	−	50.8317i	−0.285875	−	1.62128i	0.416267	−	0.909243i	$-0.363338\pi$
$984$	−32.8444	+	5.30109i	−1.04704	+	0.168993i
$985$	8.73449	−	3.17910i	0.278304	−	0.101294i
$986$	−4.50342	−	3.77881i	−0.143418	−	0.120342i
$987$	−23.6928	−	15.1562i	−0.754150	−	0.482429i
$988$	13.6520	+	4.96892i	0.434328	+	0.158082i
$989$	−6.94468	−	12.0285i	−0.220828	−	0.382485i
$990$	−1.59063	−	1.41536i	−0.0505536	−	0.0449832i
$991$	−15.1711	+	26.2772i	−0.481927	+	0.834722i	−0.999785	−	0.0207445i	$-0.993396\pi$
$991$	−15.1711	+	26.2772i	−0.481927	+	0.834722i	0.517858	+	0.855467i	$0.326730\pi$
$992$	11.9580	+	4.35235i	0.379666	+	0.138187i
$993$	0.0351587	−	2.42243i	0.00111573	−	0.0768734i
$994$	−10.1082	+	7.96138i	−0.320613	+	0.252520i
$995$	−2.45944	+	13.9482i	−0.0779695	+	0.442187i
$996$	−7.16971	−	1.37178i	−0.227181	−	0.0434666i
$997$	−4.69870	−	1.71019i	−0.148809	−	0.0541622i	0.266542	−	0.963823i	$-0.414119\pi$
$997$	−4.69870	−	1.71019i	−0.148809	−	0.0541622i	−0.415351	+	0.909661i	$0.636341\pi$
$998$	5.46483	+	9.46537i	0.172986	+	0.299621i
$999$	−1.69163	+	38.8292i	−0.0535208	+	1.22850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.15	yes	132
3.2	odd	2		567.2.w.a.37.8		132
7.4	even	3		189.2.u.a.130.8	yes	132
21.11	odd	6		567.2.u.a.361.15		132
27.11	odd	18		567.2.u.a.289.15		132
27.16	even	9		189.2.u.a.16.8	✓	132
189.11	odd	18		567.2.w.a.46.8		132
189.151	even	9	inner	189.2.w.a.151.15	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.8	✓	132	27.16	even	9
189.2.u.a.130.8	yes	132	7.4	even	3
189.2.w.a.151.15	yes	132	189.151	even	9	inner
189.2.w.a.184.15	yes	132	1.1	even	1	trivial
567.2.u.a.289.15		132	27.11	odd	18
567.2.u.a.361.15		132	21.11	odd	6
567.2.w.a.37.8		132	3.2	odd	2
567.2.w.a.46.8		132	189.11	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.162199 + 0.919879i) q^{2} +(0.568714 + 1.63602i) q^{3} +(1.05952 - 0.385633i) q^{4} +(-0.120368 + 0.682641i) q^{5} +(-1.41270 + 0.788509i) q^{6} +(1.39323 - 2.24920i) q^{7} +(1.46066 + 2.52993i) q^{8} +(-2.35313 + 1.86086i) q^{9} +O(q^{10})\)	\(q+(0.162199 + 0.919879i) q^{2} +(0.568714 + 1.63602i) q^{3} +(1.05952 - 0.385633i) q^{4} +(-0.120368 + 0.682641i) q^{5} +(-1.41270 + 0.788509i) q^{6} +(1.39323 - 2.24920i) q^{7} +(1.46066 + 2.52993i) q^{8} +(-2.35313 + 1.86086i) q^{9} -0.647471 q^{10} +(-0.190344 - 1.07949i) q^{11} +(1.23346 + 1.51408i) q^{12} +(-2.28797 - 1.91983i) q^{13} +(2.29497 + 0.916784i) q^{14} +(-1.18527 + 0.191303i) q^{15} +(-0.362862 + 0.304477i) q^{16} -2.82277 q^{17} +(-2.09344 - 1.86276i) q^{18} -4.31412 q^{19} +(0.135717 + 0.769688i) q^{20} +(4.47209 + 1.00020i) q^{21} +(0.962130 - 0.350187i) q^{22} +(-1.16694 - 0.979182i) q^{23} +(-3.30833 + 3.82847i) q^{24} +(4.24695 + 1.54576i) q^{25} +(1.39491 - 2.41605i) q^{26} +(-4.38266 - 2.79147i) q^{27} +(0.608786 - 2.92034i) q^{28} +(1.70800 - 1.43318i) q^{29} +(-0.368226 - 1.05928i) q^{30} +(2.21437 - 0.805964i) q^{31} +(4.13678 + 3.47117i) q^{32} +(1.65782 - 0.925330i) q^{33} +(-0.457851 - 2.59660i) q^{34} +(1.36770 + 1.22181i) q^{35} +(-1.77557 + 2.87905i) q^{36} +(-3.73989 - 6.47768i) q^{37} +(-0.699748 - 3.96847i) q^{38} +(1.83969 - 4.83500i) q^{39} +(-1.90285 + 0.692582i) q^{40} +(5.03687 + 4.22644i) q^{41} +(-0.194695 + 4.27601i) q^{42} +(8.56785 + 3.11844i) q^{43} +(-0.617961 - 1.07034i) q^{44} +(-0.987055 - 1.83033i) q^{45} +(0.711451 - 1.23227i) q^{46} +(-5.76741 - 2.09917i) q^{47} +(-0.704496 - 0.420489i) q^{48} +(-3.11782 - 6.26731i) q^{49} +(-0.733062 + 4.15740i) q^{50} +(-1.60535 - 4.61811i) q^{51} +(-3.16449 - 1.15178i) q^{52} +(-6.34664 - 10.9927i) q^{53} +(1.85695 - 4.48429i) q^{54} +0.759819 q^{55} +(7.72536 + 0.239468i) q^{56} +(-2.45350 - 7.05799i) q^{57} +(1.59539 + 1.33869i) q^{58} +(8.79403 + 7.37907i) q^{59} +(-1.18204 + 0.659768i) q^{60} +(-0.654284 - 0.238140i) q^{61} +(1.10056 + 1.90622i) q^{62} +(0.906986 + 7.88526i) q^{63} +(-2.99575 + 5.18880i) q^{64} +(1.58596 - 1.33078i) q^{65} +(1.12009 + 1.37491i) q^{66} +(0.581514 - 3.29793i) q^{67} +(-2.99077 + 1.08855i) q^{68} +(0.938305 - 2.46602i) q^{69} +(-0.902077 + 1.45629i) q^{70} +(-2.60327 + 4.50899i) q^{71} +(-8.14496 - 3.23519i) q^{72} +(-5.66293 + 9.80848i) q^{73} +(5.35207 - 4.49092i) q^{74} +(-0.113603 + 7.82720i) q^{75} +(-4.57088 + 1.66367i) q^{76} +(-2.69319 - 1.07586i) q^{77} +(4.74601 + 0.908057i) q^{78} +(1.92269 + 10.9041i) q^{79} +(-0.164172 - 0.284354i) q^{80} +(2.07444 - 8.75767i) q^{81} +(-3.07083 + 5.31884i) q^{82} +(-2.86339 + 2.40267i) q^{83} +(5.12397 - 0.664852i) q^{84} +(0.339771 - 1.92694i) q^{85} +(-1.47889 + 8.38719i) q^{86} +(3.31608 + 1.97925i) q^{87} +(2.45302 - 2.05833i) q^{88} -12.2609 q^{89} +(1.52358 - 1.20485i) q^{90} +(-7.50576 + 2.47133i) q^{91} +(-1.61400 - 0.587448i) q^{92} +(2.57792 + 3.16439i) q^{93} +(0.995508 - 5.64580i) q^{94} +(0.519282 - 2.94500i) q^{95} +(-3.32626 + 8.74195i) q^{96} +(5.23327 + 1.90476i) q^{97} +(5.25946 - 3.88457i) q^{98} +(2.45669 + 2.18599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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