LMFDB - Embedded newform 722.2.i.b.505.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			505.17
Character	$\chi$	$=$	722.505
Dual form			722.2.i.b.539.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.851919 - 0.523673i) q^{2} +(1.09053 - 2.91268i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.922218 + 1.25472i) q^{5} +(-0.596247 - 3.05245i) q^{6} +(-0.123579 + 0.189152i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(-5.03213 - 4.38249i) q^{9} +O(q^{10})$	\(q+(0.851919 - 0.523673i) q^{2} +(1.09053 - 2.91268i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.922218 + 1.25472i) q^{5} +(-0.596247 - 3.05245i) q^{6} +(-0.123579 + 0.189152i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(-5.03213 - 4.38249i) q^{9} +(1.44272 + 0.585982i) q^{10} +(2.00307 + 0.687654i) q^{11} +(-2.10644 - 2.28820i) q^{12} +(-2.24772 - 2.72926i) q^{13} +(-0.00622570 + 0.225857i) q^{14} +(4.66032 - 1.31781i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(1.80595 + 3.56866i) q^{17} +(-6.58196 - 1.09833i) q^{18} +(-2.85614 - 3.29279i) q^{19} +(1.53594 - 0.256304i) q^{20} +(0.416172 + 0.566222i) q^{21} +(2.06656 - 0.463127i) q^{22} +(-1.90585 - 5.09029i) q^{23} +(-2.99279 - 0.846280i) q^{24} +(0.768730 - 2.45777i) q^{25} +(-3.34411 - 1.14804i) q^{26} +(-10.0466 + 5.43696i) q^{27} +(0.112971 + 0.195672i) q^{28} +(8.28479 + 0.457085i) q^{29} +(3.28011 - 3.56315i) q^{30} +(-7.60895 + 4.11776i) q^{31} +(-0.926494 - 0.376309i) q^{32} +(4.18733 - 5.08439i) q^{33} +(3.40734 + 2.09448i) q^{34} +(-0.351300 + 0.0193817i) q^{35} +(-6.18247 + 2.51110i) q^{36} +(9.38488 + 3.22183i) q^{37} +(-4.15754 - 1.30951i) q^{38} +(-10.4007 + 3.57055i) q^{39} +(1.17428 - 1.02268i) q^{40} +(6.44802 + 6.27273i) q^{41} +(0.651060 + 0.264438i) q^{42} +(0.435395 - 0.176842i) q^{43} +(1.51801 - 1.47675i) q^{44} +(0.858085 - 10.3555i) q^{45} +(-4.28927 - 3.33847i) q^{46} +(2.27259 + 11.6344i) q^{47} +(-2.99279 + 0.846280i) q^{48} +(2.79136 + 6.36366i) q^{49} +(-0.632170 - 2.49638i) q^{50} +(12.3638 - 1.36843i) q^{51} +(-3.45011 + 0.773188i) q^{52} +(-0.213691 - 1.09398i) q^{53} +(-5.71173 + 9.89300i) q^{54} +(0.984450 + 3.14746i) q^{55} +(0.198711 + 0.107537i) q^{56} +(-12.7056 + 4.72812i) q^{57} +(7.29734 - 3.94912i) q^{58} +(-0.621116 - 0.604231i) q^{59} +(0.928465 - 4.75322i) q^{60} +(-1.30457 + 0.615643i) q^{61} +(-4.32586 + 7.49260i) q^{62} +(1.45082 - 0.410253i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(1.35157 - 5.33723i) q^{65} +(0.904708 - 6.52428i) q^{66} +(-9.25540 + 6.41755i) q^{67} +3.99960 q^{68} -16.9048 q^{69} +(-0.289129 + 0.200478i) q^{70} +(2.74702 + 1.29635i) q^{71} +(-3.95197 + 5.37685i) q^{72} +(0.105582 + 0.208636i) q^{73} +(9.68235 - 2.16987i) q^{74} +(-6.32037 - 4.91934i) q^{75} +(-4.22765 + 1.06159i) q^{76} +(-0.377608 + 0.293904i) q^{77} +(-6.99072 + 8.48837i) q^{78} +(12.9767 - 5.27068i) q^{79} +(0.464842 - 1.48618i) q^{80} +(2.13030 + 15.3626i) q^{81} +(8.77806 + 1.96721i) q^{82} +(-5.41320 - 12.3409i) q^{83} +(0.693129 - 0.115663i) q^{84} +(-2.81220 + 5.55706i) q^{85} +(0.278314 - 0.378660i) q^{86} +(10.3662 - 23.6325i) q^{87} +(0.519893 - 2.05301i) q^{88} +(-2.62813 + 5.19332i) q^{89} +(-4.69190 - 9.27144i) q^{90} +(0.794014 - 0.0878814i) q^{91} +(-5.40238 - 0.597936i) q^{92} +(3.69591 + 26.6530i) q^{93} +(8.02867 + 8.72146i) q^{94} +(1.49756 - 6.62033i) q^{95} +(-2.10644 + 2.28820i) q^{96} +(-0.937566 - 0.650094i) q^{97} +(5.71049 + 3.95957i) q^{98} +(-7.06607 - 12.2388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{47}{57}\right)$

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 $

$2$	0.851919	−	0.523673i	0.602398	−	0.370293i
$2$	0.851919	−	0.523673i	0.602398	−	0.370293i
$3$	1.09053	−	2.91268i	0.629619	−	1.68164i	−0.0975949	−	0.995226i	$-0.531115\pi$
$3$	1.09053	−	2.91268i	0.629619	−	1.68164i	0.727214	−	0.686411i	$-0.240815\pi$
$4$	0.451533	−	0.892254i	0.225767	−	0.446127i
$5$	0.922218	+	1.25472i	0.412429	+	0.561129i	0.961556	−	0.274609i	$-0.0885486\pi$
$5$	0.922218	+	1.25472i	0.412429	+	0.561129i	−0.549127	+	0.835739i	$0.685040\pi$
$6$	−0.596247	−	3.05245i	−0.243417	−	1.24616i
$7$	−0.123579	+	0.189152i	−0.0467084	+	0.0714926i	−0.859757	−	0.510703i	$-0.829385\pi$
$7$	−0.123579	+	0.189152i	−0.0467084	+	0.0714926i	0.813049	+	0.582196i	$0.197806\pi$
$8$	−0.0825793	−	0.996584i	−0.0291962	−	0.352346i
$9$	−5.03213	−	4.38249i	−1.67738	−	1.46083i
$10$	1.44272	+	0.585982i	0.456228	+	0.185304i
$11$	2.00307	+	0.687654i	0.603948	+	0.207336i	0.609679	−	0.792648i	$-0.291298\pi$
$11$	2.00307	+	0.687654i	0.603948	+	0.207336i	−0.00573174	+	0.999984i	$0.501824\pi$
$12$	−2.10644	−	2.28820i	−0.608077	−	0.660548i
$13$	−2.24772	−	2.72926i	−0.623405	−	0.756959i	0.361059	−	0.932543i	$-0.382415\pi$
$13$	−2.24772	−	2.72926i	−0.623405	−	0.756959i	−0.984465	+	0.175584i	$0.943819\pi$
$14$	−0.00622570	+	0.225857i	−0.00166389	+	0.0603628i
$15$	4.66032	−	1.31781i	1.20329	−	0.340258i
$16$	−0.592235	−	0.805765i	−0.148059	−	0.201441i
$17$	1.80595	+	3.56866i	0.438008	+	0.865528i	0.999282	+	0.0378975i	$0.0120660\pi$
$17$	1.80595	+	3.56866i	0.438008	+	0.865528i	−0.561273	+	0.827631i	$0.689688\pi$
$18$	−6.58196	−	1.09833i	−1.55138	−	0.258880i
$19$	−2.85614	−	3.29279i	−0.655243	−	0.755419i
$19$	−2.85614	−	3.29279i	−0.655243	−	0.755419i
$20$	1.53594	−	0.256304i	0.343448	−	0.0573113i
$21$	0.416172	+	0.566222i	0.0908161	+	0.123560i
$22$	2.06656	−	0.463127i	0.440592	−	0.0987389i
$23$	−1.90585	−	5.09029i	−0.397396	−	1.06140i	−0.970327	−	0.241795i	$-0.922264\pi$
$23$	−1.90585	−	5.09029i	−0.397396	−	1.06140i	0.572931	−	0.819603i	$-0.305806\pi$
$24$	−2.99279	−	0.846280i	−0.610900	−	0.172746i
$25$	0.768730	−	2.45777i	0.153746	−	0.491554i
$26$	−3.34411	−	1.14804i	−0.655835	−	0.225148i
$27$	−10.0466	+	5.43696i	−1.93347	+	1.04634i
$28$	0.112971	+	0.195672i	0.0213496	+	0.0369785i
$29$	8.28479	+	0.457085i	1.53845	+	0.0848785i	0.804346	−	0.594161i	$-0.202516\pi$
$29$	8.28479	+	0.457085i	1.53845	+	0.0848785i	0.734101	+	0.679040i	$0.237604\pi$
$30$	3.28011	−	3.56315i	0.598864	−	0.650539i
$31$	−7.60895	+	4.11776i	−1.36661	+	0.739571i	−0.982945	−	0.183901i	$-0.941127\pi$
$31$	−7.60895	+	4.11776i	−1.36661	+	0.739571i	−0.383664	+	0.923473i	$0.625338\pi$
$32$	−0.926494	−	0.376309i	−0.163783	−	0.0665227i
$33$	4.18733	−	5.08439i	0.728920	−	0.885079i
$34$	3.40734	+	2.09448i	0.584354	+	0.359201i
$35$	−0.351300	+	0.0193817i	−0.0593805	+	0.00327611i
$36$	−6.18247	+	2.51110i	−1.03041	+	0.418517i
$37$	9.38488	+	3.22183i	1.54287	+	0.529666i	0.959297	−	0.282398i	$-0.0911299\pi$
$37$	9.38488	+	3.22183i	1.54287	+	0.529666i	0.583568	+	0.812064i	$0.301656\pi$
$38$	−4.15754	−	1.30951i	−0.674443	−	0.212431i
$39$	−10.4007	+	3.57055i	−1.66544	+	0.571746i
$40$	1.17428	−	1.02268i	0.185670	−	0.161700i
$41$	6.44802	+	6.27273i	1.00701	+	0.979636i	0.999793	−	0.0203375i	$-0.00647407\pi$
$41$	6.44802	+	6.27273i	1.00701	+	0.979636i	0.00721887	+	0.999974i	$0.497702\pi$
$42$	0.651060	+	0.264438i	0.100461	+	0.0408036i
$43$	0.435395	−	0.176842i	0.0663972	−	0.0269682i	−0.342869	−	0.939383i	$-0.611399\pi$
$43$	0.435395	−	0.176842i	0.0663972	−	0.0269682i	0.409266	+	0.912415i	$0.365785\pi$
$44$	1.51801	−	1.47675i	0.228849	−	0.222628i
$45$	0.858085	−	10.3555i	0.127916	−	1.54371i
$46$	−4.28927	−	3.33847i	−0.632419	−	0.492231i
$47$	2.27259	+	11.6344i	0.331491	+	1.69705i	0.658953	+	0.752184i	$0.270999\pi$
$47$	2.27259	+	11.6344i	0.331491	+	1.69705i	−0.327463	+	0.944864i	$0.606194\pi$
$48$	−2.99279	+	0.846280i	−0.431972	+	0.122150i
$49$	2.79136	+	6.36366i	0.398766	+	0.909095i
$50$	−0.632170	−	2.49638i	−0.0894024	−	0.353042i
$51$	12.3638	−	1.36843i	1.73128	−	0.191618i
$52$	−3.45011	+	0.773188i	−0.478444	+	0.107222i
$53$	−0.213691	−	1.09398i	−0.0293527	−	0.150269i	0.963895	−	0.266283i	$-0.0857955\pi$
$53$	−0.213691	−	1.09398i	−0.0293527	−	0.150269i	−0.993248	+	0.116013i	$0.962988\pi$
$54$	−5.71173	+	9.89300i	−0.777268	+	1.34627i
$55$	0.984450	+	3.14746i	0.132743	+	0.424404i
$56$	0.198711	+	0.107537i	0.0265538	+	0.0143702i
$57$	−12.7056	+	4.72812i	−1.68289	+	0.626255i
$58$	7.29734	−	3.94912i	0.958187	−	0.518545i
$59$	−0.621116	−	0.604231i	−0.0808624	−	0.0786642i	0.655755	−	0.754973i	$-0.272350\pi$
$59$	−0.621116	−	0.604231i	−0.0808624	−	0.0786642i	−0.736618	+	0.676309i	$0.763578\pi$
$60$	0.928465	−	4.75322i	0.119864	−	0.613639i
$61$	−1.30457	+	0.615643i	−0.167033	+	0.0788250i	−0.508469	−	0.861080i	$-0.669789\pi$
$61$	−1.30457	+	0.615643i	−0.167033	+	0.0788250i	0.341436	+	0.939905i	$0.389087\pi$
$62$	−4.32586	+	7.49260i	−0.549384	+	0.951561i
$63$	1.45082	−	0.410253i	0.182786	−	0.0516870i
$64$	−0.986361	+	0.164595i	−0.123295	+	0.0205743i
$65$	1.35157	−	5.33723i	0.167642	−	0.662002i
$66$	0.904708	−	6.52428i	0.111362	−	0.803083i
$67$	−9.25540	+	6.41755i	−1.13073	+	0.784029i	−0.978892	−	0.204377i	$-0.934483\pi$
$67$	−9.25540	+	6.41755i	−1.13073	+	0.784029i	−0.151835	+	0.988406i	$0.548518\pi$
$68$	3.99960			0.485023
$69$	−16.9048			−2.03509
$70$	−0.289129	+	0.200478i	−0.0345576	+	0.0239617i
$71$	2.74702	+	1.29635i	0.326011	+	0.153849i	0.582792	−	0.812621i	$-0.301960\pi$
$71$	2.74702	+	1.29635i	0.326011	+	0.153849i	−0.256781	+	0.966470i	$0.582662\pi$
$72$	−3.95197	+	5.37685i	−0.465744	+	0.633668i
$73$	0.105582	+	0.208636i	0.0123574	+	0.0244190i	0.898349	−	0.439282i	$-0.144767\pi$
$73$	0.105582	+	0.208636i	0.0123574	+	0.0244190i	−0.885992	+	0.463701i	$0.846521\pi$
$74$	9.68235	−	2.16987i	1.12555	−	0.252242i
$75$	−6.32037	−	4.91934i	−0.729813	−	0.568037i
$76$	−4.22765	+	1.06159i	−0.484945	+	0.121773i
$77$	−0.377608	+	0.293904i	−0.0430324	+	0.0334935i
$78$	−6.99072	+	8.48837i	−0.791544	+	0.961118i
$79$	12.9767	−	5.27068i	1.45999	−	0.592998i	0.498269	−	0.867022i	$-0.333969\pi$
$79$	12.9767	−	5.27068i	1.45999	−	0.592998i	0.961723	+	0.274025i	$0.0883550\pi$
$80$	0.464842	−	1.48618i	0.0519709	−	0.166160i
$81$	2.13030	+	15.3626i	0.236700	+	1.70696i
$82$	8.77806	+	1.96721i	0.969374	+	0.217242i
$83$	−5.41320	−	12.3409i	−0.594176	−	1.35458i	−0.913461	−	0.406926i	$-0.866601\pi$
$83$	−5.41320	−	12.3409i	−0.594176	−	1.35458i	0.319285	−	0.947659i	$-0.396557\pi$
$84$	0.693129	−	0.115663i	0.0756266	−	0.0126198i
$85$	−2.81220	+	5.55706i	−0.305026	+	0.602748i
$86$	0.278314	−	0.378660i	0.0300114	−	0.0408320i
$87$	10.3662	−	23.6325i	1.11137	−	2.53367i
$88$	0.519893	−	2.05301i	0.0554208	−	0.218852i
$89$	−2.62813	+	5.19332i	−0.278581	+	0.550491i	−0.988029	−	0.154266i	$-0.950699\pi$
$89$	−2.62813	+	5.19332i	−0.278581	+	0.550491i	0.709448	+	0.704758i	$0.248944\pi$
$90$	−4.69190	−	9.27144i	−0.494569	−	0.977296i
$91$	0.794014	−	0.0878814i	0.0832352	−	0.00921247i
$92$	−5.40238	−	0.597936i	−0.563237	−	0.0623391i
$93$	3.69591	+	26.6530i	0.383248	+	2.76379i
$94$	8.02867	+	8.72146i	0.828094	+	0.899550i
$95$	1.49756	−	6.62033i	0.153647	−	0.679232i
$96$	−2.10644	+	2.28820i	−0.214988	+	0.233539i
$97$	−0.937566	−	0.650094i	−0.0951954	−	0.0660070i	0.521254	−	0.853402i	$-0.325465\pi$
$97$	−0.937566	−	0.650094i	−0.0951954	−	0.0660070i	−0.616449	+	0.787395i	$0.711429\pi$
$98$	5.71049	+	3.95957i	0.576847	+	0.399977i
$99$	−7.06607	−	12.2388i	−0.710166	−	1.23004i
$100$	−1.84585	−	1.79567i	−0.184585	−	0.179567i
$101$	−2.25223	−	1.96147i	−0.224106	−	0.195174i	0.537408	−	0.843322i	$-0.319403\pi$
$101$	−2.25223	−	1.96147i	−0.224106	−	0.195174i	−0.761514	+	0.648148i	$0.775544\pi$
$102$	9.81638	−	7.64039i	0.971966	−	0.756512i
$103$	7.93396	+	12.1438i	0.781757	+	1.19657i	0.976459	+	0.215705i	$0.0692050\pi$
$103$	7.93396	+	12.1438i	0.781757	+	1.19657i	−0.194702	+	0.980862i	$0.562374\pi$
$104$	−2.53432	+	2.46542i	−0.248510	+	0.241755i
$105$	−0.326651	+	1.04436i	−0.0318778	+	0.101919i
$106$	−0.754933	−	0.820076i	−0.0733256	−	0.0796528i
$107$	−8.94332	−	4.83988i	−0.864583	−	0.467889i	−0.0178091	−	0.999841i	$-0.505669\pi$
$107$	−8.94332	−	4.83988i	−0.864583	−	0.467889i	−0.846774	+	0.531952i	$0.821459\pi$
$108$	0.314766	+	11.4191i	0.0302884	+	1.09881i
$109$	1.18367	−	6.05972i	0.113375	−	0.580416i	−0.880877	−	0.473346i	$-0.843046\pi$
$109$	1.18367	−	6.05972i	0.113375	−	0.580416i	0.994252	−	0.107070i	$-0.0341468\pi$
$110$	2.48691	+	2.16585i	0.237118	+	0.206506i
$111$	19.6187	−	23.8217i	1.86212	−	2.26105i
$112$	0.225600	−	0.0124467i	0.0213172	−	0.00117610i
$113$	0.133930	+	0.204995i	0.0125991	+	0.0192844i	0.843410	−	0.537270i	$-0.180544\pi$
$113$	0.133930	+	0.204995i	0.0125991	+	0.0192844i	−0.830811	+	0.556554i	$0.812123\pi$
$114$	−8.34813	+	10.6815i	−0.781874	+	1.00042i
$115$	4.62930	−	7.08566i	0.431684	−	0.660742i
$116$	4.14870	−	7.18575i	0.385197	−	0.667180i
$117$	−0.650104	+	23.5846i	−0.0601022	+	2.18039i
$118$	−0.845560	−	0.189495i	−0.0778401	−	0.0174444i
$119$	−0.898196	−	0.0994123i	−0.0823375	−	0.00911311i
$120$	−1.69816	−	4.53558i	−0.155020	−	0.414040i
$121$	−5.14113	−	4.00150i	−0.467376	−	0.363773i
$122$	−0.788996	+	1.20765i	−0.0714323	+	0.109335i
$123$	25.3022	−	11.9404i	2.28143	−	1.07663i
$124$	0.238392	+	8.64843i	0.0214083	+	0.776652i
$125$	11.1568	−	3.83014i	0.997895	−	0.342578i
$126$	1.02114	−	1.10926i	0.0909707	−	0.0988205i
$127$	6.88485	+	11.9249i	0.610932	+	1.05817i	0.991084	+	0.133241i	$0.0425384\pi$
$127$	6.88485	+	11.9249i	0.610932	+	1.05817i	−0.380152	+	0.924924i	$0.624128\pi$
$128$	−0.754107	+	0.656752i	−0.0666542	+	0.0580492i
$129$	−0.0402727	−	1.46102i	−0.00354582	−	0.128636i
$130$	−1.64354	−	5.25468i	−0.144148	−	0.460866i
$131$	−0.157705	+	5.72124i	−0.0137787	+	0.499867i	0.960982	+	0.276613i	$0.0892119\pi$
$131$	−0.157705	+	5.72124i	−0.0137787	+	0.499867i	−0.974760	+	0.223254i	$0.928332\pi$
$132$	−2.64585	−	6.03193i	−0.230292	−	0.525012i
$133$	0.975795	−	0.133323i	0.0846122	−	0.0115606i
$134$	−4.52416	+	10.3140i	−0.390828	+	0.890997i
$135$	−16.0871	−	7.59167i	−1.38455	−	0.653387i
$136$	3.40734	−	2.09448i	0.292177	−	0.179601i
$137$	−2.20004	+	1.52547i	−0.187962	+	0.130330i	−0.660051	−	0.751221i	$-0.729465\pi$
$137$	−2.20004	+	1.52547i	−0.187962	+	0.130330i	0.472089	+	0.881551i	$0.343500\pi$
$138$	−14.4015	+	8.85257i	−1.22594	+	0.753581i
$139$	−1.86424	+	13.4439i	−0.158123	+	1.14030i	0.730916	+	0.682468i	$0.239093\pi$
$139$	−1.86424	+	13.4439i	−0.158123	+	1.14030i	−0.889039	+	0.457832i	$0.848626\pi$
$140$	−0.141330	+	0.322200i	−0.0119446	+	0.0272309i
$141$	36.3655	+	6.06834i	3.06253	+	0.511046i
$142$	3.01910	−	0.334154i	0.253358	−	0.0280416i
$143$	−2.62555	−	7.01254i	−0.219560	−	0.586418i
$144$	−0.551050	+	6.65018i	−0.0459208	+	0.554182i
$145$	7.06687	+	10.8167i	0.586872	+	0.898274i
$146$	0.199204	+	0.122450i	0.0164863	+	0.0101341i
$147$	21.5794	−	1.19057i	1.77984	−	0.0981964i
$148$	7.11228	−	6.91894i	0.584626	−	0.568733i
$149$	0.00765005	+	0.00216323i	0.000626717	+	0.000177219i	0.272417	−	0.962179i	$-0.412177\pi$
$149$	0.00765005	+	0.00216323i	0.000626717	+	0.000177219i	−0.271790	+	0.962357i	$0.587616\pi$
$150$	−7.96057	−	0.881076i	−0.649978	−	0.0719395i
$151$	−3.14958	−	12.4374i	−0.256310	−	1.01214i	−0.954973	−	0.296693i	$-0.904116\pi$
$151$	−3.14958	−	12.4374i	−0.256310	−	1.01214i	0.698663	−	0.715450i	$-0.253779\pi$
$152$	−3.04569	+	3.11830i	−0.247038	+	0.252927i
$153$	6.55182	−	25.8726i	0.529683	−	2.09167i
$154$	−0.167782	+	0.448125i	−0.0135202	+	0.0361110i
$155$	−12.1838	−	5.74966i	−0.978623	−	0.461824i
$156$	−1.51041	+	10.8923i	−0.120929	+	0.872078i
$157$	3.73147	−	9.96632i	0.297804	−	0.795399i	−0.698971	−	0.715150i	$-0.746358\pi$
$157$	3.73147	−	9.96632i	0.297804	−	0.795399i	0.996775	−	0.0802490i	$-0.0255715\pi$
$158$	8.29499	−	11.2857i	0.659914	−	0.897845i
$159$	−3.41944	−	0.570604i	−0.271179	−	0.0452518i
$160$	−0.382266	−	1.50953i	−0.0302208	−	0.119339i
$161$	1.19836	+	0.268558i	0.0944438	+	0.0211654i
$162$	9.85984	+	11.9721i	0.774662	+	0.940620i
$163$	−18.8547	−	10.2037i	−1.47681	−	0.799212i	−0.479871	−	0.877339i	$-0.659317\pi$
$163$	−18.8547	−	10.2037i	−1.47681	−	0.799212i	−0.996943	+	0.0781269i	$0.975106\pi$
$164$	8.50837	−	2.92093i	0.664392	−	0.228086i
$165$	10.2411	+	0.565019i	0.797271	+	0.0439867i
$166$	−11.0742	−	7.67866i	−0.859523	−	0.595980i
$167$	6.18462	+	0.341215i	0.478580	+	0.0264040i	0.292773	−	0.956182i	$-0.405422\pi$
$167$	6.18462	+	0.341215i	0.478580	+	0.0264040i	0.185808	+	0.982586i	$0.440510\pi$
$168$	0.529921	−	0.461508i	0.0408843	−	0.0356061i
$169$	0.0956489	−	0.489669i	0.00735760	−	0.0376668i
$170$	0.514313	+	6.20684i	0.0394460	+	0.476043i
$171$	−0.0581702	+	29.0867i	−0.00444839	+	2.22432i
$172$	0.0388072	−	0.468334i	0.00295902	−	0.0357101i
$173$	−5.23987	−	1.48169i	−0.398380	−	0.112651i	0.0670201	−	0.997752i	$-0.478651\pi$
$173$	−5.23987	−	1.48169i	−0.398380	−	0.112651i	−0.465400	+	0.885101i	$0.654089\pi$
$174$	−3.54455	−	25.5615i	−0.268712	−	1.93781i
$175$	0.369892	+	0.449135i	0.0279612	+	0.0339514i
$176$	−0.632200	−	2.02126i	−0.0476539	−	0.152358i
$177$	−2.43728	+	1.15018i	−0.183197	+	0.0864528i
$178$	0.480649	+	5.80057i	0.0360262	+	0.434771i
$179$	2.20551	−	1.71662i	0.164848	−	0.128306i	−0.528429	−	0.848977i	$-0.677219\pi$
$179$	2.20551	−	1.71662i	0.164848	−	0.128306i	0.693277	+	0.720671i	$0.256166\pi$
$180$	−8.85232	−	5.44150i	−0.659813	−	0.405586i
$181$	5.92123	+	3.63976i	0.440121	+	0.270542i	0.725961	−	0.687736i	$-0.241395\pi$
$181$	5.92123	+	3.63976i	0.440121	+	0.270542i	−0.285840	+	0.958277i	$0.592272\pi$
$182$	0.630414	−	0.490671i	0.0467294	−	0.0363710i
$183$	0.370493	+	4.47118i	0.0273876	+	0.330519i
$184$	−4.91552	+	2.31969i	−0.362377	+	0.171010i
$185$	4.61240	+	14.7467i	0.339110	+	1.08420i
$186$	17.1061	+	20.7708i	1.25428	+	1.52299i
$187$	1.16344	+	8.39015i	0.0850794	+	0.613548i
$188$	11.4070	+	3.22558i	0.831939	+	0.235250i
$189$	0.213141	−	2.57223i	0.0155037	−	0.187102i
$190$	−2.19109	−	6.42422i	−0.158958	−	0.466062i
$191$	−1.12262	−	13.5480i	−0.0812299	−	0.980299i	−0.908333	−	0.418248i	$-0.862644\pi$
$191$	−1.12262	−	13.5480i	−0.0812299	−	0.980299i	0.827103	−	0.562051i	$-0.189987\pi$
$192$	−0.596247	+	3.05245i	−0.0430304	+	0.220292i
$193$	−19.4889	+	16.9729i	−1.40284	+	1.22174i	−0.460252	+	0.887788i	$0.652241\pi$
$193$	−19.4889	+	16.9729i	−1.40284	+	1.22174i	−0.942591	+	0.333949i	$0.891619\pi$
$194$	−1.13917	−	0.0628496i	−0.0817874	−	0.00451234i
$195$	−14.0717	−	9.75712i	−1.00770	−	0.698722i
$196$	6.93840	+	0.382802i	0.495600	+	0.0273430i
$197$	−19.9682	+	6.85510i	−1.42268	+	0.488406i	−0.925336	−	0.379149i	$-0.876217\pi$
$197$	−19.9682	+	6.85510i	−1.42268	+	0.488406i	−0.497342	+	0.867555i	$0.665690\pi$
$198$	−12.4288	−	6.72615i	−0.883279	−	0.478007i
$199$	−8.02812	−	9.74800i	−0.569098	−	0.691017i	0.405726	−	0.913995i	$-0.367019\pi$
$199$	−8.02812	−	9.74800i	−0.569098	−	0.691017i	−0.974824	+	0.222977i	$0.928422\pi$
$200$	−2.51285	−	0.563144i	−0.177686	−	0.0398203i
$201$	8.59897	+	33.9566i	0.606525	+	2.39511i
$202$	−2.94589	−	0.491582i	−0.207272	−	0.0345876i
$203$	−1.11028	+	1.51060i	−0.0779266	+	0.106023i
$204$	4.36170	−	11.6496i	0.305380	−	0.815633i
$205$	−1.92406	+	13.8753i	−0.134382	+	0.969094i
$206$	13.1185	+	6.19077i	0.914009	+	0.431331i
$207$	−12.7177	+	33.9673i	−0.883938	+	2.36089i
$208$	−0.867960	+	3.42750i	−0.0601822	+	0.237654i
$209$	−3.45673	−	8.55972i	−0.239107	−	0.592088i
$210$	0.268623	+	1.06077i	0.0185368	+	0.0732000i
$211$	8.36912	+	0.926294i	0.576154	+	0.0637687i	0.393363	−	0.919383i	$-0.371311\pi$
$211$	8.36912	+	0.926294i	0.576154	+	0.0637687i	0.182791	+	0.983152i	$0.441487\pi$
$212$	−1.07259	−	0.303301i	−0.0736660	−	0.0208308i
$213$	6.77157	−	6.58749i	0.463980	−	0.451367i
$214$	−10.1535	+	0.560184i	−0.694079	+	0.0382934i
$215$	0.623418	+	0.383214i	0.0425167	+	0.0261349i
$216$	6.24804	+	9.56333i	0.425125	+	0.650702i
$217$	0.161425	−	1.94811i	0.0109583	−	0.132247i
$218$	−2.16492	−	5.78224i	−0.146627	−	0.391623i
$219$	0.722830	−	0.0800028i	0.0488443	−	0.00540609i
$220$	3.25285	+	0.542805i	0.219307	+	0.0365959i
$221$	5.68051	−	12.9503i	0.382113	−	0.871129i
$222$	4.23879	−	30.5679i	0.284489	−	2.05158i
$223$	−4.69035	+	2.88315i	−0.314089	+	0.193070i	−0.671743	−	0.740784i	$-0.734454\pi$
$223$	−4.69035	+	2.88315i	−0.314089	+	0.193070i	0.357654	+	0.933854i	$0.383577\pi$
$224$	0.185675	−	0.128744i	0.0124059	−	0.00860206i
$225$	−14.6395	+	8.99886i	−0.975966	+	0.599924i
$226$	0.221448	+	0.104504i	0.0147305	+	0.00695150i
$227$	2.29880	−	5.24074i	0.152577	−	0.347840i	−0.822818	−	0.568305i	$-0.807599\pi$
$227$	2.29880	−	5.24074i	0.152577	−	0.347840i	0.975395	+	0.220465i	$0.0707573\pi$
$228$	−1.51830	+	13.4715i	−0.100552	+	0.892172i
$229$	−2.21517	−	5.05008i	−0.146383	−	0.333719i	0.827252	−	0.561831i	$-0.189903\pi$
$229$	−2.21517	−	5.05008i	−0.146383	−	0.333719i	−0.973635	+	0.228112i	$0.926745\pi$
$230$	0.233216	−	8.46065i	0.0153778	−	0.557879i
$231$	0.444255	+	1.42036i	0.0292298	+	0.0934530i
$232$	−0.228629	−	8.29424i	−0.0150102	−	0.544544i
$233$	−11.2160	+	9.76806i	−0.734788	+	0.639927i	−0.940932	−	0.338594i	$-0.890049\pi$
$233$	−11.2160	+	9.76806i	−0.734788	+	0.639927i	0.206145	+	0.978521i	$0.433908\pi$
$234$	11.7968	+	20.4326i	0.771179	+	1.33572i
$235$	−12.5021	+	13.5809i	−0.815547	+	0.885920i
$236$	−0.819583	+	0.281363i	−0.0533503	+	0.0183152i
$237$	−1.20030	−	43.5448i	−0.0779682	−	2.82854i
$238$	−0.817250	+	0.385670i	−0.0529745	+	0.0249993i
$239$	−0.123631	+	0.189232i	−0.00799704	+	0.0122404i	−0.841143	−	0.540813i	$-0.818117\pi$
$239$	−0.123631	+	0.189232i	−0.00799704	+	0.0122404i	0.833146	+	0.553054i	$0.186538\pi$
$240$	−3.82185	−	2.97467i	−0.246699	−	0.192014i
$241$	2.78643	+	7.44222i	0.179490	+	0.479396i	0.995062	−	0.0992602i	$-0.0316476\pi$
$241$	2.78643	+	7.44222i	0.179490	+	0.479396i	−0.815572	+	0.578656i	$0.803577\pi$
$242$	−6.47531	−	0.716687i	−0.416249	−	0.0460704i
$243$	13.6287	+	3.05427i	0.874283	+	0.195931i
$244$	−0.0397483	+	1.44199i	−0.00254462	+	0.0923142i
$245$	−5.41039	+	9.37107i	−0.345657	+	0.598696i
$246$	15.3026	−	23.4224i	0.975658	−	1.49336i
$247$	−2.56708	+	15.1964i	−0.163339	+	0.966924i
$248$	4.73204	+	7.24292i	0.300485	+	0.459926i
$249$	−41.8482	+	2.30883i	−2.65202	+	0.146316i
$250$	7.49896	−	9.10548i	0.474276	−	0.575881i
$251$	−0.424280	−	0.369505i	−0.0267803	−	0.0233230i	0.643258	−	0.765649i	$-0.277582\pi$
$251$	−0.424280	−	0.369505i	−0.0267803	−	0.0233230i	−0.670039	+	0.742326i	$0.733722\pi$
$252$	0.289044	−	1.47974i	0.0182080	−	0.0932150i
$253$	−0.317181	−	11.5068i	−0.0199410	−	0.723423i
$254$	12.1101	+	6.55366i	0.759855	+	0.411213i
$255$	13.1191	+	14.2512i	0.821553	+	0.892444i
$256$	−0.298515	+	0.954405i	−0.0186572	+	0.0596503i
$257$	−13.2194	+	12.8600i	−0.824604	+	0.802187i	−0.982694	−	0.185238i	$-0.940694\pi$
$257$	−13.2194	+	12.8600i	−0.824604	+	0.802187i	0.158090	+	0.987425i	$0.449466\pi$
$258$	−0.799406	−	1.22358i	−0.0497688	−	0.0761769i
$259$	−1.76919	+	1.37701i	−0.109932	+	0.0855635i
$260$	−4.15189	−	3.61588i	−0.257489	−	0.224248i
$261$	−39.6870	−	38.6081i	−2.45656	−	2.38978i
$262$	2.86171	+	4.95662i	0.176797	+	0.306221i
$263$	−12.9726	−	8.99501i	−0.799926	−	0.554656i	0.0978024	−	0.995206i	$-0.468819\pi$
$263$	−12.9726	−	8.99501i	−0.799926	−	0.554656i	−0.897728	+	0.440550i	$0.854784\pi$
$264$	−5.41281	−	3.75316i	−0.333135	−	0.230991i
$265$	1.17557	−	1.27701i	0.0722146	−	0.0784460i
$266$	0.761481	−	0.624578i	0.0466894	−	0.0382953i
$267$	12.2604	+	13.3184i	0.750327	+	0.815072i
$268$	1.54697	+	11.1559i	0.0944960	+	0.681456i
$269$	25.3422	+	2.80487i	1.54514	+	0.171016i	0.841781	−	0.539819i	$-0.181507\pi$
$269$	25.3422	+	2.80487i	1.54514	+	0.171016i	0.703359	+	0.710835i	$0.251683\pi$
$270$	−17.6804	+	1.95687i	−1.07600	+	0.119091i
$271$	8.52309	+	16.8421i	0.517741	+	1.02308i	0.989926	+	0.141584i	$0.0452197\pi$
$271$	8.52309	+	16.8421i	0.517741	+	1.02308i	−0.472185	+	0.881499i	$0.656535\pi$
$272$	1.80595	−	3.56866i	0.109502	−	0.216382i
$273$	0.609927	−	2.40855i	0.0369144	−	0.145772i
$274$	−1.07541	+	2.45168i	−0.0649677	+	0.148111i
$275$	3.22991	−	4.39446i	0.194771	−	0.264996i
$276$	−7.63307	+	15.0834i	−0.459457	+	0.907911i
$277$	11.2192	−	1.87215i	0.674094	−	0.112486i	0.182360	−	0.983232i	$-0.441626\pi$
$277$	11.2192	−	1.87215i	0.674094	−	0.112486i	0.491734	+	0.870746i	$0.336363\pi$
$278$	5.45204	+	12.4294i	0.326992	+	0.745466i
$279$	56.3353	+	12.6250i	3.37271	+	0.755841i
$280$	0.0483256	+	0.348499i	0.00288801	+	0.0208268i
$281$	−9.34792	+	29.8870i	−0.557650	+	1.78291i	0.0620560	+	0.998073i	$0.480234\pi$
$281$	−9.34792	+	29.8870i	−0.557650	+	1.78291i	−0.619706	+	0.784834i	$0.712748\pi$
$282$	34.1583	−	13.8739i	2.03410	−	0.826180i
$283$	6.68338	−	8.11518i	0.397286	−	0.482398i	−0.534623	−	0.845091i	$-0.679546\pi$
$283$	6.68338	−	8.11518i	0.397286	−	0.482398i	0.931909	+	0.362693i	$0.118143\pi$
$284$	2.39705	−	1.86570i	0.142239	−	0.110709i
$285$	−17.6498	−	11.5816i	−1.04548	−	0.686035i
$286$	−5.90903	−	4.59919i	−0.349409	−	0.271956i
$287$	−1.98334	+	0.444476i	−0.117073	+	0.0262366i
$288$	3.01307	+	5.95399i	0.177547	+	0.350842i
$289$	0.594113	−	0.808319i	0.0349478	−	0.0475482i
$290$	11.6848	+	5.51419i	0.686155	+	0.323804i
$291$	−2.91596	+	2.02188i	−0.170937	+	0.118525i
$292$	0.233830			0.0136839
$293$	−24.3276			−1.42123			−0.710616	−	0.703580i	$-0.751584\pi$
$293$	−24.3276			−1.42123			−0.710616	+	0.703580i	$0.751584\pi$
$294$	17.7604	−	12.3148i	1.03581	−	0.718214i
$295$	0.185338	−	1.33656i	0.0107908	−	0.0778176i
$296$	2.43583	−	9.61888i	0.141580	−	0.559086i
$297$	−23.8628	+	3.98200i	−1.38466	+	0.231059i
$298$	0.00765005	−	0.00216323i	0.000443156	−	0.000125313i
$299$	−9.60888	+	16.6431i	−0.555696	+	0.962494i
$300$	−7.24316	+	3.41813i	−0.418184	+	0.197346i
$301$	−0.0203557	+	0.104210i	−0.00117328	+	0.00600655i
$302$	−9.19633	−	8.94633i	−0.529190	−	0.514804i
$303$	−8.16928	+	4.42099i	−0.469313	+	0.253979i
$304$	−0.961713	+	4.25148i	−0.0551580	+	0.243839i
$305$	−1.97556	−	1.06912i	−0.113120	−	0.0612177i
$306$	−7.96713	−	25.4723i	−0.455451	−	1.45616i
$307$	−5.81415	+	10.0704i	−0.331831	+	0.574748i	−0.982871	−	0.184295i	$-0.941000\pi$
$307$	−5.81415	+	10.0704i	−0.331831	+	0.574748i	0.651040	+	0.759044i	$0.274333\pi$
$308$	0.0917345	+	0.469630i	0.00522706	+	0.0267596i
$309$	44.0234	−	9.86587i	2.50440	−	0.561250i
$310$	−13.3905	+	1.48206i	−0.760531	+	0.0841755i
$311$	−3.61073	−	14.2585i	−0.204746	−	0.808523i	−0.983457	−	0.181141i	$-0.942021\pi$
$311$	−3.61073	−	14.2585i	−0.204746	−	0.808523i	0.778711	−	0.627382i	$-0.215874\pi$
$312$	4.41724	+	10.0703i	0.250077	+	0.570117i
$313$	20.6095	−	5.82780i	1.16492	−	0.329407i	0.365864	−	0.930668i	$-0.380774\pi$
$313$	20.6095	−	5.82780i	1.16492	−	0.329407i	0.799052	+	0.601262i	$0.205335\pi$
$314$	−2.04018	−	10.4446i	−0.115134	−	0.589422i
$315$	1.85273	+	1.44203i	0.104389	+	0.0812494i
$316$	1.15663	−	13.9584i	0.0650653	−	0.785221i
$317$	20.7554	−	20.1911i	1.16574	−	1.13405i	0.177028	−	0.984206i	$-0.443352\pi$
$317$	20.7554	−	20.1911i	1.16574	−	1.13405i	0.988710	−	0.149841i	$-0.0478763\pi$
$318$	−3.21190	+	1.30456i	−0.180114	+	0.0731561i
$319$	16.2807	+	6.61264i	0.911543	+	0.370237i
$320$	−1.11616	−	1.08582i	−0.0623953	−	0.0606991i
$321$	−23.8500	+	20.7710i	−1.33118	+	1.15932i
$322$	1.16154	−	0.398758i	0.0647302	−	0.0222219i
$323$	6.59282	−	16.1392i	0.366834	−	0.898010i
$324$	14.6693	+	5.03597i	0.814960	+	0.279776i
$325$	−8.43577	+	3.42631i	−0.467932	+	0.190058i
$326$	−21.4061	+	1.18101i	−1.18557	+	0.0654099i
$327$	−16.3592	−	10.0560i	−0.904666	−	0.556096i
$328$	5.71884	−	6.94400i	0.315770	−	0.383418i
$329$	−2.48150	−	1.00790i	−0.136810	−	0.0555673i
$330$	9.02050	−	4.88165i	0.496562	−	0.268726i
$331$	−6.92318	+	7.52058i	−0.380533	+	0.413369i	−0.896362	−	0.443323i	$-0.853800\pi$
$331$	−6.92318	+	7.52058i	−0.380533	+	0.413369i	0.515829	+	0.856691i	$0.327484\pi$
$332$	−13.4554	−	0.742356i	−0.738462	−	0.0407421i
$333$	−33.1063	−	57.3418i	−1.81421	−	3.14231i
$334$	5.44748	−	2.94803i	0.298073	−	0.161309i
$335$	−16.5878	−	5.69458i	−0.906286	−	0.311128i
$336$	0.209770	−	0.670673i	0.0114439	−	0.0365882i
$337$	−5.85511	−	1.65567i	−0.318948	−	0.0901900i	0.108867	−	0.994056i	$-0.465278\pi$
$337$	−5.85511	−	1.65567i	−0.318948	−	0.0901900i	−0.427815	+	0.903866i	$0.640716\pi$
$338$	−0.174941	−	0.467247i	−0.00951554	−	0.0254149i
$339$	0.743142	−	0.166542i	0.0403619	−	0.00904532i
$340$	3.68851	+	5.01840i	0.200037	+	0.272161i
$341$	−18.0728	+	3.01582i	−0.978699	+	0.163316i
$342$	15.1824	+	24.8100i	0.820969	+	1.34157i
$343$	−3.10868	−	0.518747i	−0.167853	−	0.0280097i
$344$	−0.212193	−	0.419305i	−0.0114407	−	0.0226074i
$345$	−15.5899	−	21.2108i	−0.839331	−	1.14195i
$346$	−5.23987	+	1.48169i	−0.281697	+	0.0796563i
$347$	0.810032	−	29.3865i	0.0434848	−	1.57755i	−0.592323	−	0.805701i	$-0.701789\pi$
$347$	0.810032	−	29.3865i	0.0434848	−	1.57755i	0.635808	−	0.771847i	$-0.280667\pi$
$348$	−16.4055	−	19.9201i	−0.879428	−	1.06783i
$349$	11.9772	+	13.0107i	0.641126	+	0.696449i	0.968660	−	0.248391i	$-0.0799018\pi$
$349$	11.9772	+	13.0107i	0.641126	+	0.696449i	−0.327534	+	0.944839i	$0.606218\pi$
$350$	0.550318	+	0.188924i	0.0294157	+	0.0100984i
$351$	37.4209	+	15.1990i	1.99738	+	0.811265i
$352$	−1.59706	−	1.39088i	−0.0851236	−	0.0741342i
$353$	−1.64813	−	19.8899i	−0.0877210	−	1.05863i	−0.888256	−	0.459349i	$-0.848083\pi$
$353$	−1.64813	−	19.8899i	−0.0877210	−	1.05863i	0.800535	−	0.599286i	$-0.204549\pi$
$354$	−1.47405	+	2.25620i	−0.0783448	+	0.119916i
$355$	0.906792	+	4.64227i	0.0481275	+	0.246386i
$356$	3.44708	+	4.68992i	0.182695	+	0.248565i
$357$	−1.26907	+	2.50775i	−0.0671662	+	0.132724i
$358$	0.979972	−	2.61739i	0.0517932	−	0.138333i
$359$	−14.0852	+	8.65815i	−0.743389	+	0.456960i	−0.842896	−	0.538077i	$-0.819151\pi$
$359$	−14.0852	+	8.65815i	−0.743389	+	0.456960i	0.0995063	+	0.995037i	$0.468274\pi$
$360$	−10.3910			−0.547656
$361$	−2.68497	+	18.8093i	−0.141314	+	0.989965i
$362$	6.95045			0.365308
$363$	−17.2617	+	10.6107i	−0.906003	+	0.556918i
$364$	0.280111	−	0.748143i	0.0146818	−	0.0392134i
$365$	−0.164410	+	0.324884i	−0.00860563	+	0.0170052i
$366$	2.65707	+	3.61507i	0.138887	+	0.188963i
$367$	−4.60702	−	23.5854i	−0.240484	−	1.23115i	−0.884649	−	0.466258i	$-0.845602\pi$
$367$	−4.60702	−	23.5854i	−0.240484	−	1.23115i	0.644164	−	0.764887i	$-0.277205\pi$
$368$	−2.97287	+	4.55031i	−0.154971	+	0.237201i
$369$	−4.95713	−	59.8236i	−0.258058	−	3.11429i
$370$	11.6518	+	10.1476i	0.605749	+	0.527548i
$371$	0.233335	+	0.0947725i	0.0121142	+	0.00492034i
$372$	25.4501	+	8.73702i	1.31953	+	0.452994i
$373$	12.9428	+	14.0597i	0.670155	+	0.727982i	0.974452	−	0.224595i	$-0.0721058\pi$
$373$	12.9428	+	14.0597i	0.670155	+	0.727982i	−0.304297	+	0.952577i	$0.598422\pi$
$374$	5.38485	+	6.53847i	0.278444	+	0.338096i
$375$	1.01089	−	36.6731i	0.0522020	−	1.89379i
$376$	11.4070	−	3.22558i	0.588269	−	0.166347i
$377$	−17.3744	−	23.6387i	−0.894826	−	1.21746i
$378$	−1.16543	−	2.30295i	−0.0599432	−	0.118451i
$379$	4.48949	+	0.749164i	0.230610	+	0.0384820i	0.278771	−	0.960358i	$-0.410073\pi$
$379$	4.48949	+	0.749164i	0.230610	+	0.0384820i	−0.0481612	+	0.998840i	$0.515336\pi$
$380$	−5.23082	−	4.32551i	−0.268335	−	0.221894i
$381$	42.2416	−	7.04888i	2.16410	−	0.361125i
$382$	−8.05110	−	10.9539i	−0.411930	−	0.560451i
$383$	18.9124	−	4.23836i	0.966376	−	0.216570i	0.293199	−	0.956051i	$-0.405280\pi$
$383$	18.9124	−	4.23836i	0.966376	−	0.216570i	0.673177	+	0.739481i	$0.264929\pi$
$384$	1.09053	+	2.91268i	0.0556510	+	0.148637i
$385$	−0.717005	−	0.202750i	−0.0365420	−	0.0103331i
$386$	−7.71473	+	24.6654i	−0.392670	+	1.25543i
$387$	−2.96598	−	1.01822i	−0.150769	−	0.0517591i
$388$	−1.00339	+	0.543008i	−0.0509395	+	0.0275671i
$389$	−9.89084	−	17.1314i	−0.501486	−	0.868599i	−0.999999	−	0.00171634i	$-0.999454\pi$
$389$	−9.89084	−	17.1314i	−0.501486	−	0.868599i	0.498513	−	0.866882i	$-0.333880\pi$
$390$	−17.0975	−	0.943297i	−0.865767	−	0.0477657i
$391$	14.7236	−	15.9941i	0.744607	−	0.808859i
$392$	6.11142	−	3.30733i	0.308673	−	0.167046i
$393$	16.4922	+	6.69854i	0.831919	+	0.337896i
$394$	−13.4215	+	16.2968i	−0.676165	+	0.821022i
$395$	18.5806	+	11.4214i	0.934891	+	0.574675i
$396$	−14.1107	+	0.778508i	−0.709088	+	0.0391215i
$397$	−4.72385	+	1.91866i	−0.237083	+	0.0962948i	−0.491758	−	0.870732i	$-0.663646\pi$
$397$	−4.72385	+	1.91866i	−0.237083	+	0.0962948i	0.254675	+	0.967027i	$0.418032\pi$
$398$	−11.9441	−	4.10040i	−0.598702	−	0.205535i
$399$	0.675808	−	2.98757i	0.0338327	−	0.149566i
$400$	−2.43565	+	0.836161i	−0.121783	+	0.0418080i
$401$	7.25263	−	6.31632i	0.362179	−	0.315422i	−0.456445	−	0.889752i	$-0.650878\pi$
$401$	7.25263	−	6.31632i	0.362179	−	0.315422i	0.818624	+	0.574330i	$0.194737\pi$
$402$	25.1078	+	24.4252i	1.25226	+	1.21822i
$403$	28.3412	+	11.5112i	1.41178	+	0.573414i
$404$	−2.76709	+	1.12390i	−0.137668	+	0.0559159i
$405$	−17.3112	+	16.8406i	−0.860203	+	0.836818i
$406$	−0.154814	+	1.86833i	−0.00768331	+	0.0927237i
$407$	16.5830	+	12.9071i	0.821991	+	0.639781i
$408$	−2.38475	−	12.2086i	−0.118063	−	0.604416i
$409$	−37.7032	+	10.6614i	−1.86430	+	0.527174i	−0.864608	+	0.502447i	$0.832433\pi$
$409$	−37.7032	+	10.6614i	−1.86430	+	0.527174i	−0.999694	+	0.0247274i	$0.992128\pi$
$410$	5.62698	+	12.8282i	0.277897	+	0.633541i
$411$	2.04400	+	8.07158i	0.100823	+	0.398142i
$412$	14.4178	−	1.59577i	0.710316	−	0.0786177i
$413$	0.191048	−	0.0428149i	0.00940086	−	0.00210678i
$414$	6.95336	+	35.5973i	0.341739	+	1.74951i
$415$	10.4922	−	18.1730i	0.515042	−	0.892079i
$416$	1.05545	+	3.37448i	0.0517479	+	0.165447i
$417$	37.1249	+	20.0910i	1.81801	+	0.983860i
$418$	−7.42735	−	5.48200i	−0.363284	−	0.268133i
$419$	−7.23427	+	3.91499i	−0.353417	+	0.191260i	−0.642950	−	0.765908i	$-0.722290\pi$
$419$	−7.23427	+	3.91499i	−0.353417	+	0.191260i	0.289533	+	0.957168i	$0.406500\pi$
$420$	0.784341	+	0.763019i	0.0382719	+	0.0372315i
$421$	−7.31742	+	37.4611i	−0.356629	+	1.82574i	0.182121	+	0.983276i	$0.441704\pi$
$421$	−7.31742	+	37.4611i	−0.356629	+	1.82574i	−0.538750	+	0.842466i	$0.681103\pi$
$422$	7.61489	−	3.59355i	0.370687	−	0.174931i
$423$	39.5515	−	68.5053i	1.92306	−	3.33084i
$424$	−1.07259	+	0.303301i	−0.0520898	+	0.0147296i
$425$	10.1592	−	1.69528i	0.492795	−	0.0822330i
$426$	2.31914	−	9.15809i	0.112363	−	0.443711i
$427$	0.0447679	−	0.322843i	0.00216647	−	0.0156234i
$428$	−8.35661	+	5.79435i	−0.403932	+	0.280080i
$429$	−23.2885			−1.12438
$430$	0.731780			0.0352896
$431$	−23.1939	+	16.0823i	−1.11721	+	0.774657i	−0.976527	−	0.215397i	$-0.930895\pi$
$431$	−23.1939	+	16.0823i	−1.11721	+	0.774657i	−0.140685	+	0.990054i	$0.544931\pi$
$432$	10.3309	+	4.87526i	0.497045	+	0.234561i
$433$	−3.44021	+	4.68057i	−0.165326	+	0.224934i	−0.880540	−	0.473971i	$-0.842820\pi$
$433$	−3.44021	+	4.68057i	−0.165326	+	0.224934i	0.715215	+	0.698905i	$0.246329\pi$
$434$	−0.882653	−	1.74417i	−0.0423687	−	0.0837228i
$435$	39.2121	−	8.78764i	1.88008	−	0.421335i
$436$	−4.87234	−	3.79230i	−0.233343	−	0.181618i
$437$	−11.3179	+	20.8141i	−0.541409	+	0.995674i
$438$	0.573897	−	0.446682i	0.0274219	−	0.0213433i
$439$	−9.22670	+	11.2034i	−0.440366	+	0.534707i	−0.944322	−	0.329022i	$-0.893281\pi$
$439$	−9.22670	+	11.2034i	−0.440366	+	0.534707i	0.503956	+	0.863729i	$0.331877\pi$
$440$	3.05542	−	1.24100i	0.145661	−	0.0591625i
$441$	13.8422	−	44.2559i	0.659151	−	2.10742i
$442$	−1.94236	−	14.0073i	−0.0923888	−	0.666260i
$443$	−26.9475	−	6.03908i	−1.28032	−	0.286925i	−0.475113	−	0.879925i	$-0.657593\pi$
$443$	−26.9475	−	6.03908i	−1.28032	−	0.286925i	−0.805203	+	0.592999i	$0.797944\pi$
$444$	−12.3965	−	28.2611i	−0.588311	−	1.34121i
$445$	−8.93989	+	1.49180i	−0.423792	+	0.0707183i
$446$	−2.48597	+	4.91242i	−0.117714	+	0.232610i
$447$	0.0146434	−	0.0199231i	0.000692610	−	0.000942330i
$448$	0.0907601	−	0.206912i	0.00428801	−	0.00977568i
$449$	8.02843	−	31.7036i	0.378885	−	1.49618i	−0.427077	−	0.904215i	$-0.640457\pi$
$449$	8.02843	−	31.7036i	0.378885	−	1.49618i	0.805962	−	0.591968i	$-0.201649\pi$
$450$	−7.75921	+	15.3326i	−0.365772	+	0.722786i
$451$	8.60236	+	16.9987i	0.405069	+	0.800439i
$452$	0.243382	−	0.0269375i	0.0114477	−	0.00126703i
$453$	−39.6610	−	4.38968i	−1.86344	−	0.206245i
$454$	−0.786040	−	5.66851i	−0.0368907	−	0.266036i
$455$	0.842521	+	0.915221i	0.0394980	+	0.0429062i
$456$	5.76119	+	12.2717i	0.269792	+	0.574676i
$457$	−21.6678	+	23.5375i	−1.01358	+	1.10104i	−0.0187121	+	0.999825i	$0.505957\pi$
$457$	−21.6678	+	23.5375i	−1.01358	+	1.10104i	−0.994865	+	0.101213i	$0.967728\pi$
$458$	−4.53174	−	3.14224i	−0.211754	−	0.146827i
$459$	−37.5464	−	26.0341i	−1.75252	−	1.21517i
$460$	−4.23193	−	7.32992i	−0.197315	−	0.341759i
$461$	5.30811	+	5.16381i	0.247223	+	0.240502i	0.810461	−	0.585792i	$-0.199217\pi$
$461$	5.30811	+	5.16381i	0.247223	+	0.240502i	−0.563238	+	0.826295i	$0.690445\pi$
$462$	1.12228	+	0.977390i	0.0522130	+	0.0454723i
$463$	−24.4483	+	19.0289i	−1.13621	+	0.884349i	−0.994414	−	0.105547i	$-0.966341\pi$
$463$	−24.4483	+	19.0289i	−1.13621	+	0.884349i	−0.141797	+	0.989896i	$0.545288\pi$
$464$	−4.53824	−	6.94630i	−0.210683	−	0.322474i
$465$	−30.0337	+	29.2172i	−1.39278	+	1.35492i
$466$	−4.43990	+	14.1951i	−0.205674	+	0.657577i
$467$	−9.16707	−	9.95809i	−0.424201	−	0.460806i	0.486615	−	0.873616i	$-0.338231\pi$
$467$	−9.16707	−	9.95809i	−0.424201	−	0.460806i	−0.910817	+	0.412811i	$0.864547\pi$
$468$	20.7499	+	11.2293i	0.959164	+	0.519074i
$469$	−0.0701179	−	2.54375i	−0.00323775	−	0.117459i
$470$	−3.53883	+	18.1168i	−0.163234	+	0.835668i
$471$	−24.9594	−	21.7372i	−1.15007	−	1.00160i
$472$	−0.550876	+	0.668892i	−0.0253561	+	0.0307882i
$473$	0.993733	−	0.0548258i	0.0456919	−	0.00252089i
$474$	−23.8258	−	36.4681i	−1.09436	−	1.67504i
$475$	−10.2885	+	4.48845i	−0.472070	+	0.205944i
$476$	−0.494267	+	0.756531i	−0.0226547	+	0.0346756i
$477$	−3.71902	+	6.44153i	−0.170282	+	0.294937i
$478$	−0.00622833	+	0.225952i	−0.000284877	+	0.0103348i
$479$	−27.1807	−	6.09134i	−1.24192	−	0.278320i	−0.452270	−	0.891881i	$-0.649386\pi$
$479$	−27.1807	−	6.09134i	−1.24192	−	0.278320i	−0.789648	+	0.613561i	$0.789737\pi$
$480$	−4.81366	−	0.532776i	−0.219713	−	0.0243178i
$481$	−12.3014	−	32.8555i	−0.560895	−	1.49808i
$482$	6.27110	+	4.88100i	0.285641	+	0.222323i
$483$	2.08907	−	3.19756i	0.0950561	−	0.145494i
$484$	−5.89175	+	2.78038i	−0.267807	+	0.126381i
$485$	−0.0489527	−	1.77591i	−0.00222283	−	0.0806401i
$486$	13.2100	−	4.53500i	0.599218	−	0.205712i
$487$	−0.795633	+	0.864288i	−0.0360536	+	0.0391646i	−0.753490	−	0.657459i	$-0.771631\pi$
$487$	−0.795633	+	0.864288i	−0.0360536	+	0.0391646i	0.717436	+	0.696624i	$0.245315\pi$
$488$	0.721271	+	1.24928i	0.0326504	+	0.0565522i
$489$	−50.2817	+	43.7903i	−2.27382	+	1.98027i
$490$	0.298160	+	10.8167i	0.0134695	+	0.488647i
$491$	−5.71163	−	18.2611i	−0.257762	−	0.824112i	−0.989752	−	0.142796i	$-0.954391\pi$
$491$	−5.71163	−	18.2611i	−0.257762	−	0.824112i	0.731990	−	0.681315i	$-0.238592\pi$
$492$	0.770920	−	27.9675i	0.0347557	−	1.26087i
$493$	13.3308	+	30.3911i	0.600388	+	1.36875i
$494$	5.77100	+	14.2904i	0.259650	+	0.642956i
$495$	8.83983	−	20.1528i	0.397321	−	0.905801i
$496$	7.82424	+	3.69235i	0.351319	+	0.165791i
$497$	−0.584681	+	0.359402i	−0.0262265	+	0.0161214i
$498$	−34.4422	+	23.8817i	−1.54339	+	1.07017i
$499$	−3.14130	+	1.93095i	−0.140624	+	0.0864411i	−0.592198	−	0.805792i	$-0.701740\pi$
$499$	−3.14130	+	1.93095i	−0.140624	+	0.0864411i	0.451574	+	0.892233i	$0.350863\pi$
$500$	1.62021	−	11.6841i	0.0724582	−	0.522531i
$501$	7.73838	−	17.6417i	0.345725	−	0.788174i
$502$	−0.554952	−	0.0926051i	−0.0247687	−	0.00413317i
$503$	22.2917	−	2.46724i	0.993937	−	0.110009i	0.401699	−	0.915772i	$-0.368420\pi$
$503$	22.2917	−	2.46724i	0.993937	−	0.110009i	0.592238	+	0.805763i	$0.298245\pi$
$504$	−0.528659	−	1.41199i	−0.0235484	−	0.0628949i
$505$	0.384053	−	4.63484i	0.0170902	−	0.206247i
$506$	−6.29599	−	9.63673i	−0.279891	−	0.428405i
$507$	−1.32194	−	0.812594i	−0.0587095	−	0.0360886i
$508$	13.7488	−	0.758542i	0.610004	−	0.0336549i
$509$	9.30085	−	9.04801i	0.412253	−	0.401046i	−0.461716	−	0.887028i	$-0.652766\pi$
$509$	9.30085	−	9.04801i	0.412253	−	0.401046i	0.873969	+	0.485982i	$0.161538\pi$
$510$	18.6394	+	5.27073i	0.825367	+	0.233392i
$511$	−0.0525115	−	0.00581197i	−0.00232297	−	0.000257106i
$512$	0.245485	+	0.969400i	0.0108490	+	0.0428418i
$513$	46.5973	+	17.5528i	2.05732	+	0.774973i
$514$	−4.52741	+	17.8784i	−0.199696	+	0.788580i
$515$	−7.92031	+	21.1542i	−0.349010	+	0.932165i
$516$	−1.32179	−	0.623766i	−0.0581884	−	0.0274598i
$517$	−3.44828	+	24.8672i	−0.151655	+	1.09366i
$518$	−0.786101	+	2.09958i	−0.0345393	+	0.0922503i
$519$	−10.0299	+	13.6462i	−0.440265	+	0.599003i
$520$	−5.43062	−	0.906210i	−0.238148	−	0.0397399i
$521$	7.05223	+	27.8486i	0.308964	+	1.22007i	0.907870	+	0.419252i	$0.137708\pi$
$521$	7.05223	+	27.8486i	0.308964	+	1.22007i	−0.598906	+	0.800819i	$0.704398\pi$
$522$	−54.0281	−	12.1080i	−2.36475	−	0.529952i
$523$	−7.52800	−	9.14075i	−0.329177	−	0.399697i	0.581009	−	0.813897i	$-0.302658\pi$
$523$	−7.52800	−	9.14075i	−0.329177	−	0.399697i	−0.910186	+	0.414200i	$0.864061\pi$
$524$	5.03359	+	2.72404i	0.219893	+	0.119000i
$525$	1.71157	−	0.587581i	0.0746988	−	0.0256441i
$526$	−15.7621	−	0.869618i	−0.687259	−	0.0379171i
$527$	−28.4363	−	19.7173i	−1.23871	−	0.858899i
$528$	−6.57671	−	0.362847i	−0.286214	−	0.0157909i
$529$	−4.93432	+	4.29730i	−0.214536	+	0.186839i
$530$	0.332755	−	1.70352i	0.0144540	−	0.0739962i
$531$	0.477503	+	5.76260i	0.0207219	+	0.250076i
$532$	0.321646	−	0.930857i	0.0139451	−	0.0403578i
$533$	2.62654	−	31.6976i	0.113768	−	1.37298i
$534$	17.4194	+	4.92573i	0.753810	+	0.213157i
$535$	−2.17498	−	15.6848i	−0.0940326	−	0.678114i
$536$	7.15994	+	8.69383i	0.309262	+	0.375516i
$537$	−2.59478	−	8.29599i	−0.111973	−	0.357998i
$538$	23.0583	−	10.8815i	0.994115	−	0.469134i
$539$	1.21529	+	14.6663i	0.0523461	+	0.631724i
$540$	−14.0375	+	10.9259i	−0.604080	+	0.470174i
$541$	17.8793	+	10.9904i	0.768693	+	0.472514i	0.851696	−	0.524036i	$-0.175574\pi$
$541$	17.8793	+	10.9904i	0.768693	+	0.472514i	−0.0830037	+	0.996549i	$0.526451\pi$
$542$	16.0807	+	9.88479i	0.690726	+	0.424588i
$543$	17.0588	−	13.2774i	0.732062	−	0.569786i
$544$	−0.330285	−	3.98594i	−0.0141608	−	0.170896i
$545$	8.69487	−	4.10321i	0.372447	−	0.175762i
$546$	−0.741682	−	2.37129i	−0.0317411	−	0.101482i
$547$	−23.1579	−	28.1191i	−0.990160	−	1.20228i	−0.979315	−	0.202343i	$-0.935144\pi$
$547$	−23.1579	−	28.1191i	−0.990160	−	1.20228i	−0.0108449	−	0.999941i	$-0.503452\pi$
$548$	0.367719	+	2.65179i	0.0157082	+	0.113279i
$549$	9.26283	+	2.61928i	0.395328	+	0.111788i
$550$	0.450369	−	5.43514i	0.0192038	−	0.231755i
$551$	−22.1574	−	28.5856i	−0.943937	−	1.21779i
$552$	1.39598	+	16.8470i	0.0594171	+	0.717057i
$553$	−0.606688	+	3.10591i	−0.0257990	+	0.132077i
$554$	8.57742	−	7.47008i	0.364420	−	0.317373i
$555$	47.9823	+	2.64726i	2.03673	+	0.112370i
$556$	11.1536	+	7.73377i	0.473020	+	0.327985i
$557$	2.31648	+	0.127804i	0.0981525	+	0.00541522i	0.104097	−	0.994567i	$-0.466805\pi$
$557$	2.31648	+	0.127804i	0.0981525	+	0.00541522i	−0.00594494	+	0.999982i	$0.501892\pi$
$558$	54.6045	−	18.7458i	2.31159	−	0.793571i
$559$	−1.46129	−	0.790813i	−0.0618062	−	0.0334478i
$560$	0.223669	+	0.271586i	0.00945175	+	0.0114766i
$561$	25.7066	+	5.76098i	1.08533	+	0.243229i
$562$	7.68732	+	30.3565i	0.324270	+	1.28051i
$563$	24.4956	+	4.08759i	1.03237	+	0.172271i	0.656440	−	0.754378i	$-0.272062\pi$
$563$	24.4956	+	4.08759i	1.03237	+	0.172271i	0.375926	+	0.926650i	$0.377325\pi$
$564$	21.8348	−	29.7073i	0.919409	−	1.25090i
$565$	−0.133700	+	0.357096i	−0.00562479	+	0.0150231i
$566$	1.44400	−	10.4134i	0.0606959	−	0.437707i
$567$	−3.16913	−	1.49555i	−0.133091	−	0.0628071i
$568$	1.06508	−	2.84469i	0.0446896	−	0.119361i
$569$	1.81146	−	7.15328i	0.0759403	−	0.299881i	−0.919764	−	0.392472i	$-0.871620\pi$
$569$	1.81146	−	7.15328i	0.0759403	−	0.299881i	0.995704	+	0.0925906i	$0.0295148\pi$
$570$	−21.1012	−	0.623884i	−0.883831	−	0.0261316i
$571$	6.28623	+	24.8238i	0.263071	+	1.03884i	0.950033	+	0.312149i	$0.101049\pi$
$571$	6.28623	+	24.8238i	0.263071	+	1.03884i	−0.686962	+	0.726693i	$0.741056\pi$
$572$	−7.44249	−	0.823735i	−0.311186	−	0.0344421i
$573$	−40.6853	−	11.5047i	−1.69965	−	0.480616i
$574$	−1.45688	+	1.41728i	−0.0608091	+	0.0591560i
$575$	−13.9758	+	0.771068i	−0.582832	+	0.0321557i
$576$	5.68483	+	3.49445i	0.236868	+	0.145602i
$577$	−22.9981	−	35.2013i	−0.957425	−	1.46545i	−0.883636	−	0.468175i	$-0.844912\pi$
$577$	−22.9981	−	35.2013i	−0.957425	−	1.46545i	−0.0737896	−	0.997274i	$-0.523509\pi$
$578$	0.0828411	−	0.999744i	0.00344574	−	0.0415838i
$579$	28.1834	+	75.2745i	1.17126	+	3.12830i
$580$	12.8421	−	1.42137i	0.533240	−	0.0590190i
$581$	3.00325	+	0.501154i	0.124596	+	0.0207914i
$582$	−1.42536	+	3.24949i	−0.0590830	+	0.134696i
$583$	0.324241	−	2.33826i	0.0134287	−	0.0968406i
$584$	0.199204	−	0.122450i	0.00824313	−	0.00506703i
$585$	−30.1916	+	20.9344i	−1.24827	+	0.865532i
$586$	−20.7251	+	12.7397i	−0.856148	+	0.526272i
$587$	29.0488	+	13.7085i	1.19897	+	0.565809i	0.919022	−	0.394206i	$-0.128980\pi$
$587$	29.0488	+	13.7085i	1.19897	+	0.565809i	0.279950	+	0.960015i	$0.409682\pi$
$588$	8.68152	−	19.7919i	0.358020	−	0.816204i
$589$	35.2911	+	13.2938i	1.45415	+	0.547763i
$590$	−0.542028	−	1.23570i	−0.0223149	−	0.0508729i
$591$	−1.80927	+	65.6368i	−0.0744232	+	2.69994i
$592$	−2.96202	−	9.47009i	−0.121738	−	0.389218i
$593$	0.684353	+	24.8271i	0.0281030	+	1.01953i	0.873925	+	0.486060i	$0.161566\pi$
$593$	0.684353	+	24.8271i	0.0281030	+	1.01953i	−0.845822	+	0.533465i	$0.820890\pi$
$594$	−18.2439	+	15.8887i	−0.748558	+	0.651920i
$595$	−0.703598	−	1.21867i	−0.0288447	−	0.0499605i
$596$	0.00538441	−	0.00584902i	0.000220554	−	0.000239585i
$597$	−37.1477	+	12.7528i	−1.52036	+	0.521939i
$598$	0.529533	+	19.2105i	0.0216542	+	0.785575i
$599$	37.6528	−	17.7688i	1.53845	−	0.726012i	0.544805	−	0.838563i	$-0.316604\pi$
$599$	37.6528	−	17.7688i	1.53845	−	0.726012i	0.993646	+	0.112551i	$0.0359020\pi$
$600$	−4.38061	+	6.70502i	−0.178838	+	0.273731i
$601$	−3.93109	−	3.05969i	−0.160352	−	0.124807i	0.530858	−	0.847461i	$-0.321870\pi$
$601$	−3.93109	−	3.05969i	−0.160352	−	0.124807i	−0.691211	+	0.722653i	$0.742922\pi$
$602$	0.0372304	+	0.0994380i	0.00151740	+	0.00405279i
$603$	74.6993	+	8.26771i	3.04199	+	0.336687i
$604$	−12.5195	−	2.80568i	−0.509411	−	0.114162i
$605$	0.279534	−	10.1410i	0.0113647	−	0.412289i
$606$	−4.64441	+	8.04436i	−0.188666	+	0.326780i
$607$	17.7925	−	27.2335i	0.722176	−	1.10537i	−0.267708	−	0.963500i	$-0.586266\pi$
$607$	17.7925	−	27.2335i	0.722176	−	1.10537i	0.989885	−	0.141873i	$-0.0453125\pi$
$608$	1.40708	+	4.12554i	0.0570648	+	0.167313i
$609$	3.18908	+	4.88125i	0.129228	+	0.197798i
$610$	−2.24289	+	0.123744i	−0.0908120	+	0.00501024i
$611$	26.6450	−	32.3533i	1.07794	−	1.30887i
$612$	−20.1265	−	17.5282i	−0.813567	−	0.708536i
$613$	2.47726	−	12.6822i	0.100056	−	0.512229i	−0.897417	−	0.441183i	$-0.854559\pi$
$613$	2.47726	−	12.6822i	0.100056	−	0.512229i	0.997473	−	0.0710467i	$-0.0226339\pi$
$614$	0.320410	+	11.6239i	0.0129307	+	0.469102i
$615$	38.3161	+	20.7356i	1.54505	+	0.836142i
$616$	0.324083	+	0.352048i	0.0130577	+	0.0141844i
$617$	7.30441	−	23.3535i	0.294065	−	0.940177i	−0.683573	−	0.729882i	$-0.739575\pi$
$617$	7.30441	−	23.3535i	0.294065	−	0.940177i	0.977638	−	0.210295i	$-0.0674425\pi$
$618$	32.3379	−	31.4588i	1.30082	−	1.26546i
$619$	20.3697	+	31.1781i	0.818727	+	1.25315i	0.964565	+	0.263846i	$0.0849912\pi$
$619$	20.3697	+	31.1781i	0.818727	+	1.25315i	−0.145838	+	0.989309i	$0.546588\pi$
$620$	−10.6315	+	8.27485i	−0.426973	+	0.332326i
$621$	46.8230	+	40.7782i	1.87894	+	1.63637i
$622$	−10.5428	−	10.2562i	−0.422728	−	0.411237i
$623$	−0.657544	−	1.13890i	−0.0263440	−	0.0456291i
$624$	9.03666	+	6.26588i	0.361756	+	0.250836i
$625$	4.51363	+	3.12968i	0.180545	+	0.125187i
$626$	14.5057	−	15.7574i	0.579766	−	0.629794i
$627$	−28.7014	+	0.733709i	−1.14622	+	0.0293015i
$628$	−7.20761	−	7.82955i	−0.287615	−	0.312433i
$629$	5.45103	+	39.3100i	0.217347	+	1.56739i
$630$	2.33353	+	0.258275i	0.0929700	+	0.0102899i
$631$	−7.90064	+	0.874443i	−0.314520	+	0.0348110i	−0.265882	−	0.964005i	$-0.585663\pi$
$631$	−7.90064	+	0.874443i	−0.314520	+	0.0348110i	−0.0486372	+	0.998817i	$0.515488\pi$
$632$	−6.32428	−	12.4971i	−0.251566	−	0.497109i
$633$	11.8248	−	23.3664i	0.469993	−	0.928732i
$634$	7.10835	−	28.0702i	0.282309	−	1.11481i
$635$	−8.61313	+	19.6360i	−0.341802	+	0.779229i
$636$	−2.05312	+	2.79336i	−0.0814113	+	0.110764i
$637$	11.0939	−	21.9221i	0.439555	−	0.868584i
$638$	17.3327	−	2.89231i	0.686208	−	0.114508i
$639$	−8.14213	−	18.5622i	−0.322098	−	0.734309i
$640$	−1.51949	−	0.340526i	−0.0600632	−	0.0134605i
$641$	−2.86778	−	20.6809i	−0.113270	−	0.816847i	−0.959034	−	0.283290i	$-0.908574\pi$
$641$	−2.86778	−	20.6809i	−0.113270	−	0.816847i	0.845764	−	0.533557i	$-0.179145\pi$
$642$	−9.44108	+	30.1848i	−0.372610	+	1.19130i
$643$	38.5129	−	15.6426i	1.51880	−	0.616884i	0.543826	−	0.839198i	$-0.316975\pi$
$643$	38.5129	−	15.6426i	1.51880	−	0.616884i	0.974975	+	0.222314i	$0.0713610\pi$
$644$	0.780721	−	0.947977i	0.0307647	−	0.0373555i
$645$	1.79604	−	1.39791i	0.0707188	−	0.0550427i
$646$	−2.83512	−	17.2018i	−0.111546	−	0.676796i
$647$	16.0900	+	12.5234i	0.632563	+	0.492344i	0.879004	−	0.476814i	$-0.158208\pi$
$647$	16.0900	+	12.5234i	0.632563	+	0.492344i	−0.246441	+	0.969158i	$0.579261\pi$
$648$	15.1342	−	3.39166i	0.594529	−	0.133237i
$649$	−0.828636	−	1.63743i	−0.0325268	−	0.0642747i
$650$	−5.39233	+	7.33652i	−0.211504	+	0.287762i
$651$	−5.49819	−	2.59466i	−0.215491	−	0.101693i
$652$	−17.6178	+	12.2159i	−0.689966	+	0.478412i
$653$	25.6015			1.00187			0.500933	−	0.865486i	$-0.332990\pi$
$653$	25.6015			1.00187			0.500933	+	0.865486i	$0.332990\pi$
$654$	−19.2027			−0.750887
$655$	−7.32401	+	5.07835i	−0.286173	+	0.198428i
$656$	1.23560	−	8.91053i	0.0482422	−	0.347898i
$657$	0.383041	−	1.51259i	0.0149438	−	0.0590119i
$658$	−2.64185	+	0.440847i	−0.102990	+	0.0171860i
$659$	−29.9461	+	8.46794i	−1.16653	+	0.329864i	−0.799687	−	0.600417i	$-0.795001\pi$
$659$	−29.9461	+	8.46794i	−1.16653	+	0.329864i	−0.366847	+	0.930281i	$0.619563\pi$
$660$	5.12835	−	8.88257i	0.199621	−	0.345753i
$661$	26.4086	−	12.4625i	1.02718	−	0.484736i	0.162311	−	0.986740i	$-0.448105\pi$
$661$	26.4086	−	12.4625i	1.02718	−	0.484736i	0.864866	+	0.502004i	$0.167404\pi$
$662$	−1.95967	+	10.0324i	−0.0761647	+	0.389921i
$663$	−31.5252	−	30.6682i	−1.22434	−	1.19105i
$664$	−11.8517	+	6.41381i	−0.459934	+	0.248904i
$665$	1.06718	+	1.10140i	0.0413834	+	0.0427105i
$666$	−58.2323	−	31.5137i	−2.25645	−	1.22113i
$667$	−13.4628	−	43.0431i	−0.521283	−	1.66664i
$668$	3.09701	−	5.36418i	0.119827	−	0.207547i
$669$	3.28271	+	16.8057i	0.126917	+	0.649744i
$670$	−17.1135	+	3.83523i	−0.661153	+	0.148168i
$671$	−3.03650	+	0.336080i	−0.117223	+	0.0129742i
$672$	−0.172506	−	0.681210i	−0.00665456	−	0.0262783i
$673$	−9.75050	−	22.2289i	−0.375854	−	0.856861i	−0.997302	−	0.0734055i	$-0.976613\pi$
$673$	−9.75050	−	22.2289i	−0.375854	−	0.856861i	0.621448	−	0.783455i	$-0.286545\pi$
$674$	−5.85511	+	1.65567i	−0.225531	+	0.0637740i
$675$	5.63965	+	28.8718i	0.217070	+	1.11128i
$676$	−0.393720	−	0.306445i	−0.0151431	−	0.0117863i
$677$	0.407087	−	4.91281i	0.0156456	−	0.188815i	−0.984280	−	0.176615i	$-0.943485\pi$
$677$	0.407087	−	4.91281i	0.0156456	−	0.188815i	0.999926	−	0.0121993i	$-0.00388326\pi$
$678$	0.545883	−	0.531044i	0.0209645	−	0.0203946i
$679$	0.238830	−	0.0970042i	0.00916544	−	0.00372268i
$680$	5.77031	+	2.34370i	0.221281	+	0.0898767i
$681$	−12.7577	−	12.4109i	−0.488876	−	0.475586i
$682$	−13.8173	+	12.0335i	−0.529092	+	0.460786i
$683$	6.56972	−	2.25539i	0.251383	−	0.0863000i	−0.196128	−	0.980578i	$-0.562837\pi$
$683$	6.56972	−	2.25539i	0.251383	−	0.0863000i	0.447511	+	0.894278i	$0.352310\pi$
$684$	25.9265	+	13.1855i	0.991325	+	0.504162i
$685$	−3.94296	−	1.35362i	−0.150653	−	0.0517191i
$686$	−2.92000	+	1.18600i	−0.111486	+	0.0452817i
$687$	−17.1250	+	0.944812i	−0.653359	+	0.0360468i
$688$	−0.400350	−	0.246094i	−0.0152632	−	0.00938225i
$689$	−2.50543	+	3.04217i	−0.0954491	+	0.115897i
$690$	−24.3888	−	9.90589i	−0.928468	−	0.377111i
$691$	31.4894	−	17.0412i	1.19791	−	0.648279i	0.250447	−	0.968130i	$-0.419422\pi$
$691$	31.4894	−	17.0412i	1.19791	−	0.648279i	0.947468	+	0.319851i	$0.103633\pi$
$692$	−3.68802	+	4.00626i	−0.140198	+	0.152295i
$693$	3.18820	+	0.175898i	0.121110	+	0.00668181i
$694$	−14.6988	−	25.4591i	−0.557959	−	0.966414i
$695$	−18.5877	+	10.0591i	−0.705070	+	0.381565i
$696$	−24.4078	−	8.37921i	−0.925175	−	0.317613i
$697$	−10.7404	+	34.3391i	−0.406823	+	1.30069i
$698$	17.0170	+	4.81195i	0.644103	+	0.182135i
$699$	16.2198	+	43.3212i	0.613489	+	1.63856i
$700$	0.567761	−	0.127238i	0.0214593	−	0.00480915i
$701$	25.7174	+	34.9898i	0.971334	+	1.32155i	0.946791	+	0.321849i	$0.104304\pi$
$701$	25.7174	+	34.9898i	0.971334	+	1.32155i	0.0245432	+	0.999699i	$0.492187\pi$
$702$	39.8389	−	6.64794i	1.50362	−	0.250910i
$703$	−16.1957	−	40.1045i	−0.610831	−	1.51257i
$704$	−2.08893	−	0.348581i	−0.0787296	−	0.0131377i
$705$	25.9229	+	51.2250i	0.976313	+	1.92925i
$706$	−11.8199	−	16.0815i	−0.444848	−	0.605237i
$707$	0.649344	−	0.183617i	0.0244211	−	0.00690563i
$708$	−0.0742601	+	2.69402i	−0.00279086	+	0.101247i
$709$	15.7898	+	19.1725i	0.592999	+	0.720039i	0.979318	−	0.202326i	$-0.0648502\pi$
$709$	15.7898	+	19.1725i	0.592999	+	0.720039i	−0.386319	+	0.922365i	$0.626254\pi$
$710$	3.20354	+	3.47998i	0.120227	+	0.130601i
$711$	−88.3991	−	30.3475i	−3.31523	−	1.13812i
$712$	5.39262	+	2.19029i	0.202097	+	0.0820846i
$713$	35.4621	+	30.8839i	1.32806	+	1.15661i
$714$	0.232095	+	2.80097i	0.00868595	+	0.104824i
$715$	6.37746	−	9.76143i	0.238504	−	0.365057i
$716$	−0.535799	−	2.74299i	−0.0200237	−	0.102510i
$717$	0.416348	+	0.566461i	0.0155488	+	0.0211549i
$718$	−7.46543	+	14.7521i	−0.278607	+	0.550543i
$719$	−3.56788	+	9.52938i	−0.133059	+	0.355386i	−0.986029	−	0.166575i	$-0.946729\pi$
$719$	−3.56788	+	9.52938i	−0.133059	+	0.355386i	0.852969	+	0.521961i	$0.174799\pi$
$720$	−8.85232	+	5.44150i	−0.329907	+	0.202793i
$721$	−3.27750			−0.122060
$722$	7.56256	+	17.4301i	0.281449	+	0.648680i
$723$	24.7155			0.919180
$724$	5.92123	−	3.63976i	0.220061	−	0.135271i
$725$	7.49218	−	20.0107i	0.278253	−	0.743179i
$726$	−9.14901	+	18.0789i	−0.339552	+	0.670972i
$727$	−2.37033	−	3.22495i	−0.0879107	−	0.119607i	0.759587	−	0.650405i	$-0.225401\pi$
$727$	−2.37033	−	3.22495i	−0.0879107	−	0.119607i	−0.847498	+	0.530798i	$0.821892\pi$
$728$	−0.153150	−	0.784044i	−0.00567613	−	0.0290586i
$729$	−1.69024	+	2.58710i	−0.0626014	+	0.0958185i
$730$	0.0300684	+	0.362872i	0.00111288	+	0.0134305i
$731$	1.41740	+	1.23441i	0.0524243	+	0.0456563i
$732$	4.15672	+	1.68831i	0.153637	+	0.0624019i
$733$	−45.1511	−	15.5004i	−1.66769	−	0.572520i	−0.680599	−	0.732656i	$-0.738280\pi$
$733$	−45.1511	−	15.5004i	−1.66769	−	0.572520i	−0.987095	+	0.160136i	$0.948807\pi$
$734$	−16.2758	−	17.6803i	−0.600751	−	0.652590i
$735$	21.3947	+	25.9782i	0.789157	+	0.958220i
$736$	−0.149768	+	5.43331i	−0.00552053	+	0.200274i
$737$	−22.9523	+	6.49028i	−0.845457	+	0.239073i
$738$	−35.5511	−	48.3690i	−1.30865	−	1.78049i
$739$	−0.966049	−	1.90897i	−0.0355367	−	0.0702224i	0.873795	−	0.486295i	$-0.161652\pi$
$739$	−0.966049	−	1.90897i	−0.0355367	−	0.0702224i	−0.909331	+	0.416072i	$0.863406\pi$
$740$	15.2404	+	2.54318i	0.560249	+	0.0934890i
$741$	41.4628	+	24.0492i	1.52317	+	0.883471i
$742$	0.248412	−	0.0414527i	0.00911951	−	0.00152178i
$743$	16.1545	+	21.9790i	0.592651	+	0.806331i	0.993975	−	0.109605i	$-0.0349586\pi$
$743$	16.1545	+	21.9790i	0.592651	+	0.806331i	−0.401324	+	0.915936i	$0.631450\pi$
$744$	26.2568	−	5.88428i	0.962620	−	0.215728i
$745$	0.00434077	+	0.0115937i	0.000159033	+	0.000424759i
$746$	18.3889	+	5.19989i	0.673267	+	0.190382i
$747$	−26.8437	+	85.8241i	−0.982159	+	3.14014i
$748$	8.01148	+	2.75034i	0.292929	+	0.100563i
$749$	2.02068	−	1.09354i	0.0738339	−	0.0399569i
$750$	−18.3435	−	31.7719i	−0.669810	−	1.16015i
$751$	−0.295128	−	0.0162827i	−0.0107694	−	0.000594163i	0.0497023	−	0.998764i	$-0.484173\pi$
$751$	−0.295128	−	0.0162827i	−0.0107694	−	0.000594163i	−0.0604716	+	0.998170i	$0.519260\pi$
$752$	8.02867	−	8.72146i	0.292775	−	0.318039i
$753$	−1.53894	+	0.832834i	−0.0560822	+	0.0303502i
$754$	−27.1805	−	11.0398i	−0.989856	−	0.402045i
$755$	12.7009	−	15.4219i	0.462234	−	0.561260i
$756$	−2.19884	−	1.35162i	−0.0799711	−	0.0491581i
$757$	−15.6437	+	0.863090i	−0.568582	+	0.0313695i	−0.337099	−	0.941469i	$-0.609446\pi$
$757$	−15.6437	+	0.863090i	−0.568582	+	0.0313695i	−0.231483	+	0.972839i	$0.574358\pi$
$758$	4.21700	−	1.71280i	0.153168	−	0.0622117i
$759$	−33.8614	−	11.6246i	−1.22909	−	0.421947i
$760$	−6.72139	−	0.945745i	−0.243810	−	0.0343058i
$761$	−1.65541	+	0.568304i	−0.0600087	+	0.0206010i	−0.354540	−	0.935041i	$-0.615363\pi$
$761$	−1.65541	+	0.568304i	−0.0600087	+	0.0206010i	0.294532	+	0.955642i	$0.404836\pi$
$762$	32.2952	−	28.1259i	1.16993	−	1.01889i
$763$	0.999929	+	0.972746i	0.0361998	+	0.0352158i
$764$	−12.5952	−	5.11571i	−0.455677	−	0.185080i
$765$	38.5051	−	15.6394i	1.39216	−	0.565445i
$766$	13.8923	−	13.5146i	0.501949	−	0.488303i
$767$	−0.253006	+	3.05333i	−0.00913551	+	0.110249i
$768$	2.45434	+	1.91029i	0.0885633	+	0.0689316i
$769$	9.36715	+	47.9546i	0.337788	+	1.72929i	0.633263	+	0.773936i	$0.281715\pi$
$769$	9.36715	+	47.9546i	0.337788	+	1.72929i	−0.295475	+	0.955350i	$0.595478\pi$
$770$	−0.717005	+	0.202750i	−0.0258391	+	0.00730659i
$771$	23.0410	+	52.5282i	0.829801	+	1.89176i
$772$	6.34426	+	25.0529i	0.228335	+	0.901674i
$773$	−47.6112	+	5.26961i	−1.71246	+	0.189535i	−0.912094	−	0.409982i	$-0.865535\pi$
$773$	−47.6112	+	5.26961i	−1.71246	+	0.189535i	−0.800363	+	0.599516i	$0.795360\pi$
$774$	−3.05999	+	0.685759i	−0.109989	+	0.0246491i
$775$	4.27126	+	21.8665i	0.153428	+	0.785467i
$776$	−0.570450	+	0.988048i	−0.0204780	+	0.0354689i
$777$	2.08145	+	6.65476i	0.0746715	+	0.238738i
$778$	−17.3975	−	9.41504i	−0.623730	−	0.337546i
$779$	2.23838	−	39.1478i	0.0801983	−	1.40262i
$780$	−15.0597	+	8.14990i	−0.539223	+	0.291813i
$781$	4.61103	+	4.48568i	0.164996	+	0.160510i
$782$	4.16766	−	21.3361i	0.149035	−	0.762977i
$783$	−85.7194	+	40.4520i	−3.06336	+	1.44563i
$784$	3.47447	−	6.01797i	0.124088	−	0.214927i
$785$	15.9462	−	4.50916i	0.569145	−	0.160939i
$786$	17.5578	−	2.92988i	0.626267	−	0.104506i
$787$	−8.11342	+	32.0392i	−0.289212	+	1.14207i	0.638755	+	0.769411i	$0.279450\pi$
$787$	−8.11342	+	32.0392i	−0.289212	+	1.14207i	−0.927967	+	0.372663i	$0.878445\pi$
$788$	−2.89983	+	20.9120i	−0.103302	+	0.744961i
$789$	−40.3467	+	27.9758i	−1.43638	+	0.995963i
$790$	21.8103			0.775974
$791$	−0.0553262			−0.00196717
$792$	−11.6135	+	8.05260i	−0.412667	+	0.286137i
$793$	4.61256	+	2.17672i	0.163797	+	0.0772976i
$794$	−3.01959	+	4.10829i	−0.107161	+	0.145798i
$795$	−2.43752	−	4.81667i	−0.0864500	−	0.170830i
$796$	−12.3227	+	2.76157i	−0.436765	+	0.0978813i
$797$	−7.36793	−	5.73469i	−0.260986	−	0.203133i	0.475264	−	0.879843i	$-0.342353\pi$
$797$	−7.36793	−	5.73469i	−0.260986	−	0.203133i	−0.736250	+	0.676710i	$0.763405\pi$
$798$	−0.988777	−	2.89907i	−0.0350023	−	0.102626i
$799$	−37.4150	+	29.1212i	−1.32365	+	1.03024i
$800$	−1.63711	+	1.98783i	−0.0578804	+	0.0702803i
$801$	35.9848	−	14.6157i	1.27146	−	0.516422i
$802$	2.87097	−	9.17900i	0.101377	−	0.324122i
$803$	0.0680187	+	0.490515i	0.00240033	+	0.0173099i
$804$	34.1806	+	7.66006i	1.20546	+	0.270149i
$805$	0.768181	+	1.75128i	0.0270748	+	0.0617244i
$806$	30.1725	−	5.03491i	1.06278	−	0.177347i
$807$	35.8062	−	70.7549i	1.26044	−	2.49069i
$808$	−1.76878	+	2.40652i	−0.0622256	+	0.0846610i
$809$	17.3143	−	39.4725i	0.608737	−	1.38778i	−0.293258	−	0.956033i	$-0.594739\pi$
$809$	17.3143	−	39.4725i	0.608737	−	1.38778i	0.901995	−	0.431747i	$-0.142103\pi$
$810$	−5.92880	+	23.4123i	−0.208317	+	0.822624i
$811$	−7.86630	+	15.5442i	−0.276223	+	0.545832i	−0.987602	−	0.156976i	$-0.949825\pi$
$811$	−7.86630	+	15.5442i	−0.276223	+	0.545832i	0.711379	+	0.702808i	$0.248071\pi$
$812$	0.846505	+	1.67274i	0.0297065	+	0.0587016i
$813$	58.3503	−	6.45821i	2.04644	−	0.226499i
$814$	20.8865	+	2.31172i	0.732072	+	0.0810257i
$815$	−4.58539	−	33.0674i	−0.160619	−	1.15830i
$816$	−8.42493	−	9.15191i	−0.294931	−	0.320381i
$817$	−1.82585	−	0.928581i	−0.0638785	−	0.0324869i
$818$	−26.5370	+	28.8268i	−0.927843	+	1.00791i
$819$	−4.38072	−	3.03752i	−0.153075	−	0.106140i
$820$	11.5115	+	7.98192i	0.402000	+	0.278741i
$821$	−4.12094	−	7.13768i	−0.143822	−	0.249107i	0.785111	−	0.619355i	$-0.212606\pi$
$821$	−4.12094	−	7.13768i	−0.143822	−	0.249107i	−0.928933	+	0.370248i	$0.879273\pi$
$822$	5.96819	+	5.80595i	0.208165	+	0.202506i
$823$	−1.00907	−	0.878801i	−0.0351740	−	0.0306331i	0.638986	−	0.769218i	$-0.279354\pi$
$823$	−1.00907	−	0.878801i	−0.0351740	−	0.0306331i	−0.674160	+	0.738585i	$0.735494\pi$
$824$	11.4472	−	8.90970i	0.398781	−	0.310384i
$825$	−9.27732	−	14.2000i	−0.322995	−	0.494381i
$826$	0.140337	−	0.136522i	0.00488294	−	0.00475019i
$827$	13.3609	−	42.7173i	0.464605	−	1.48543i	−0.367086	−	0.930187i	$-0.619644\pi$
$827$	13.3609	−	42.7173i	0.464605	−	1.48543i	0.831691	−	0.555239i	$-0.187373\pi$
$828$	24.5651	+	26.6848i	0.853695	+	0.927360i
$829$	6.87186	+	3.71886i	0.238669	+	0.129161i	0.590880	−	0.806759i	$-0.298781\pi$
$829$	6.87186	+	3.71886i	0.238669	+	0.129161i	−0.352211	+	0.935921i	$0.614570\pi$
$830$	−0.578211	−	20.9764i	−0.0200700	−	0.728103i
$831$	6.78188	−	34.7194i	0.235261	−	1.20440i
$832$	2.66628	+	2.32207i	0.0924368	+	0.0805033i
$833$	−17.6687	+	21.4539i	−0.612184	+	0.743334i
$834$	42.1485	−	2.32540i	1.45948	−	0.0805220i
$835$	5.27544	+	8.07466i	0.182564	+	0.279435i
$836$	−9.19828	−	0.780716i	−0.318129	−	0.0270016i
$837$	54.0562	−	82.7392i	1.86846	−	2.85989i
$838$	−4.11284	+	7.12365i	−0.142076	+	0.246082i
$839$	−0.368593	+	13.3719i	−0.0127253	+	0.461649i	0.966243	+	0.257634i	$0.0829429\pi$
$839$	−0.368593	+	13.3719i	−0.0127253	+	0.461649i	−0.978968	+	0.204015i	$0.934601\pi$
$840$	1.06777	+	0.239292i	0.0368415	+	0.00825637i
$841$	39.6048	+	4.38346i	1.36568	+	0.151154i
$842$	13.3835	+	35.7458i	0.461226	+	1.23188i
$843$	76.8570	+	59.8202i	2.64710	+	2.06032i
$844$	4.60543	−	7.04913i	0.158525	−	0.242641i
$845$	0.702608	−	0.331569i	0.0241704	−	0.0114063i
$846$	−2.17963	−	79.0731i	−0.0749373	−	2.71859i
$847$	1.39223	−	0.477952i	0.0478375	−	0.0164226i
$848$	−0.754933	+	0.820076i	−0.0259245	+	0.0281615i
$849$	−16.3485	−	28.3164i	−0.561079	−	0.971818i
$850$	7.76708	−	6.76436i	0.266409	−	0.232016i
$851$	−1.48608	−	53.9121i	−0.0509420	−	1.84808i
$852$	−2.82012	−	9.01643i	−0.0966158	−	0.308898i
$853$	−0.899874	+	32.6457i	−0.0308111	+	1.11777i	0.813382	+	0.581730i	$0.197624\pi$
$853$	−0.899874	+	32.6457i	−0.0308111	+	1.11777i	−0.844193	+	0.536039i	$0.819920\pi$
$854$	−0.130925	−	0.298480i	−0.00448017	−	0.0102138i
$855$	−36.5495	+	26.7513i	−1.24997	+	0.914877i
$856$	−4.08482	+	9.31245i	−0.139616	+	0.318293i
$857$	36.1112	+	17.0413i	1.23354	+	0.582120i	0.928893	−	0.370347i	$-0.120761\pi$
$857$	36.1112	+	17.0413i	1.23354	+	0.582120i	0.304642	+	0.952467i	$0.401463\pi$
$858$	−19.8400	+	12.1956i	−0.677325	+	0.416350i
$859$	−39.5430	+	27.4185i	−1.34919	+	0.935508i	−0.999999	−	0.00154321i	$-0.999509\pi$
$859$	−39.5430	+	27.4185i	−1.34919	+	0.935508i	−0.349192	+	0.937051i	$0.613544\pi$
$860$	0.623418	−	0.383214i	0.0212584	−	0.0130675i
$861$	−0.868275	+	6.26154i	−0.0295907	+	0.213393i
$862$	−11.3375	+	25.8469i	−0.386156	+	0.880347i
$863$	22.4857	+	3.75220i	0.765422	+	0.127726i	0.534411	−	0.845225i	$-0.320533\pi$
$863$	22.4857	+	3.75220i	0.765422	+	0.127726i	0.231011	+	0.972951i	$0.425797\pi$
$864$	11.3541	−	1.25667i	0.386275	−	0.0427529i
$865$	−2.97319	−	7.94102i	−0.101091	−	0.270003i
$866$	−0.479691	+	5.78902i	−0.0163006	+	0.196719i
$867$	−1.70648	−	2.61196i	−0.0579550	−	0.0887068i
$868$	−1.66532	−	1.02367i	−0.0565248	−	0.0347456i
$869$	29.6176	−	1.63405i	1.00471	−	0.0554313i
$870$	28.8037	−	28.0207i	0.976537	−	0.949990i
$871$	38.3187	+	10.8355i	1.29838	+	0.367147i
$872$	−6.13677	−	0.679217i	−0.207817	−	0.0230012i
$873$	1.86893	+	7.38023i	0.0632536	+	0.249783i
$874$	1.25784	+	23.6588i	0.0425471	+	0.800272i
$875$	−0.654269	+	2.58365i	−0.0221183	+	0.0873433i
$876$	0.254999	−	0.681072i	0.00861562	−	0.0230113i
$877$	−7.87857	−	3.71799i	−0.266040	−	0.125547i	0.289114	−	0.957295i	$-0.406639\pi$
$877$	−7.87857	−	3.71799i	−0.266040	−	0.125547i	−0.555155	+	0.831747i	$0.687341\pi$
$878$	−1.99351	+	14.3761i	−0.0672776	+	0.485171i
$879$	−26.5300	+	70.8585i	−0.894835	+	2.39000i
$880$	1.95309	−	2.65727i	0.0658386	−	0.0895767i
$881$	−1.16110	−	0.193754i	−0.0391185	−	0.00652772i	0.145003	−	0.989431i	$-0.453681\pi$
$881$	−1.16110	−	0.193754i	−0.0391185	−	0.00652772i	−0.184121	+	0.982903i	$0.558944\pi$
$882$	−11.3832	−	44.9512i	−0.383292	−	1.51359i
$883$	32.7421	+	7.33767i	1.10186	+	0.246932i	0.731422	−	0.681925i	$-0.238857\pi$
$883$	32.7421	+	7.33767i	1.10186	+	0.246932i	0.370437	+	0.928858i	$0.379208\pi$
$884$	−8.98999	−	10.9159i	−0.302366	−	0.367143i
$885$	−3.69086	−	1.99739i	−0.124067	−	0.0671417i
$886$	−26.1196	+	8.96688i	−0.877506	+	0.301248i
$887$	−20.5948	−	1.13625i	−0.691505	−	0.0381514i	−0.294073	−	0.955783i	$-0.595011\pi$
$887$	−20.5948	−	1.13625i	−0.691505	−	0.0381514i	−0.397432	+	0.917632i	$0.630099\pi$
$888$	−25.3604	−	17.5845i	−0.851039	−	0.590097i
$889$	−3.10644	−	0.171387i	−0.104187	−	0.00574814i
$890$	−6.83485	+	5.95248i	−0.229105	+	0.199527i
$891$	−6.29704	+	32.2373i	−0.210959	+	1.07999i
$892$	0.454651	+	5.48682i	0.0152228	+	0.183712i
$893$	31.8188	−	40.7125i	1.06477	−	1.36239i
$894$	0.00204183	−	0.0246412i	6.82891e−5	−	0.000824126i
$895$	4.18785	+	1.18421i	0.139984	+	0.0395838i
$896$	−0.0310340	−	0.223801i	−0.00103677	−	0.00747667i
$897$	37.9972	+	46.1374i	1.26869	+	1.54048i
$898$	−9.76272	−	31.2131i	−0.325786	−	1.04160i
$899$	−64.9208	+	30.6368i	−2.16523	+	1.02180i
$900$	1.41905	+	17.1254i	0.0473018	+	0.570848i
$901$	3.51812	−	2.73826i	0.117206	−	0.0912247i
$902$	16.2303	+	9.97672i	0.540409	+	0.332188i
$903$	0.281331	+	0.172934i	0.00936212	+	0.00575487i
$904$	0.193235	−	0.150401i	0.00642692	−	0.00500227i
$905$	0.893767	+	10.7862i	0.0297098	+	0.358544i
$906$	−36.0867	+	17.0297i	−1.19890	+	0.565775i
$907$	17.1011	+	54.6753i	0.567833	+	1.81546i	0.578727	+	0.815522i	$0.303550\pi$
$907$	17.1011	+	54.6753i	0.567833	+	1.81546i	−0.0108938	+	0.999941i	$0.503468\pi$
$908$	−3.63809	−	4.41749i	−0.120734	−	0.146599i
$909$	2.73741	+	19.7408i	0.0907942	+	0.654760i
$910$	1.19704	+	0.338490i	0.0396814	+	0.0112208i
$911$	1.39975	−	16.8925i	0.0463757	−	0.559672i	−0.933302	−	0.359093i	$-0.883086\pi$
$911$	1.39975	−	16.8925i	0.0463757	−	0.559672i	0.979678	−	0.200579i	$-0.0642823\pi$
$912$	11.3344	+	7.43754i	0.375321	+	0.246282i
$913$	−2.35677	−	28.4420i	−0.0779977	−	0.941292i
$914$	−6.13326	+	31.3989i	−0.202870	+	1.03858i
$915$	−5.26842	+	4.58827i	−0.174169	+	0.151684i
$916$	−5.50618	−	0.303784i	−0.181929	−	0.0100373i
$917$	−1.06269	−	0.736854i	−0.0350932	−	0.0243331i
$918$	−45.6199	−	2.51692i	−1.50568	−	0.0830708i
$919$	−48.8961	+	16.7861i	−1.61293	+	0.553721i	−0.976108	−	0.217287i	$-0.930279\pi$
$919$	−48.8961	+	16.7861i	−1.61293	+	0.553721i	−0.636826	+	0.771008i	$0.719753\pi$
$920$	−7.44375	−	4.02835i	−0.245413	−	0.132811i
$921$	22.9914	+	27.9169i	0.757591	+	0.919892i
$922$	7.22622	+	1.61943i	0.237983	+	0.0533332i
$923$	−2.63646	−	10.4112i	−0.0867802	−	0.342687i
$924$	1.46792	+	0.244953i	0.0482910	+	0.00805835i
$925$	15.1330	−	20.5891i	0.497569	−	0.676967i
$926$	−10.8631	+	29.0140i	−0.356983	+	0.953460i
$927$	13.2955	−	95.8799i	0.436680	−	3.14911i
$928$	−7.50380	−	3.54113i	−0.246324	−	0.116243i
$929$	−3.58033	+	9.56263i	−0.117467	+	0.313740i	−0.982013	−	0.188814i	$-0.939536\pi$
$929$	−3.58033	+	9.56263i	−0.117467	+	0.313740i	0.864546	+	0.502553i	$0.167606\pi$
$930$	−10.2860	+	40.6186i	−0.337292	+	1.33194i
$931$	12.9817	−	27.3669i	0.425459	−	0.896913i
$932$	3.65118	+	14.4182i	0.119598	+	0.472283i
$933$	−45.4679	−	5.03239i	−1.48855	−	0.164753i
$934$	−13.0244	−	3.68295i	−0.426171	−	0.120510i
$935$	−9.45436	+	9.19735i	−0.309191	+	0.300785i
$936$	23.5577	−	1.29971i	0.770008	−	0.0424825i
$937$	−30.7939	−	18.9290i	−1.00599	−	0.618382i	−0.0803454	−	0.996767i	$-0.525602\pi$
$937$	−30.7939	−	18.9290i	−1.00599	−	0.618382i	−0.925648	+	0.378385i	$0.876480\pi$
$938$	−1.39183	−	2.13035i	−0.0454448	−	0.0695584i
$939$	5.50075	−	66.3842i	0.179510	−	2.16637i
$940$	6.47250	+	17.2873i	0.211110	+	0.563849i
$941$	−15.3335	+	1.69711i	−0.499859	+	0.0553244i	−0.356403	−	0.934332i	$-0.615997\pi$
$941$	−15.3335	+	1.69711i	−0.499859	+	0.0553244i	−0.143456	+	0.989657i	$0.545822\pi$
$942$	−32.6466	−	5.44775i	−1.06368	−	0.177497i
$943$	19.6411	−	44.7771i	0.639601	−	1.45814i
$944$	−0.119021	+	0.858321i	−0.00387382	+	0.0279360i
$945$	3.42400	−	2.10472i	0.111383	−	0.0684667i
$946$	0.817870	−	0.567098i	0.0265912	−	0.0184380i
$947$	−20.6716	+	12.7068i	−0.671737	+	0.412915i	−0.817126	−	0.576459i	$-0.804434\pi$
$947$	−20.6716	+	12.7068i	−0.671737	+	0.412915i	0.145389	+	0.989375i	$0.453557\pi$
$948$	−39.3950	−	18.5910i	−1.27949	−	0.603806i
$949$	0.332101	−	0.757115i	0.0107805	−	0.0245770i
$950$	−6.41451	+	9.21162i	−0.208114	+	0.298864i
$951$	−36.1759	−	82.4729i	−1.17309	−	2.67437i
$952$	−0.0249003	+	0.903338i	−0.000807024	+	0.0292773i
$953$	−9.62735	−	30.7803i	−0.311860	−	0.997073i	−0.969779	−	0.243984i	$-0.921545\pi$
$953$	−9.62735	−	30.7803i	−0.311860	−	0.997073i	0.657919	−	0.753089i	$-0.271437\pi$
$954$	0.204950	+	7.43522i	0.00663551	+	0.240724i
$955$	15.9637	−	13.9028i	0.516573	−	0.449884i
$956$	0.113019	+	0.195755i	0.00365530	+	0.00633116i
$957$	37.0151	−	40.2091i	1.19653	−	1.29978i
$958$	−26.3456	+	9.04447i	−0.851189	+	0.292213i
$959$	−0.0166672	−	0.604657i	−0.000538213	−	0.0195254i
$960$	−4.37985	+	2.06690i	−0.141359	+	0.0667090i
$961$	23.9848	−	36.7115i	0.773704	−	1.18424i
$962$	−27.6853	−	21.5484i	−0.892611	−	0.694747i
$963$	23.7932	+	63.5489i	0.766726	+	2.04784i
$964$	7.89852	+	0.874208i	0.254394	+	0.0281563i
$965$	−39.2693	−	8.80047i	−1.26413	−	0.283297i
$966$	0.105244	−	3.81806i	0.00338617	−	0.122844i
$967$	23.0175	−	39.8674i	0.740192	−	1.28205i	−0.212216	−	0.977223i	$-0.568068\pi$
$967$	23.0175	−	39.8674i	0.740192	−	1.28205i	0.952408	−	0.304827i	$-0.0985986\pi$
$968$	−3.56329	+	5.45401i	−0.114528	+	0.175299i
$969$	−39.8187	−	36.8031i	−1.27916	−	1.18229i
$970$	−0.971702	−	1.48730i	−0.0311995	−	0.0477543i
$971$	−16.5190	+	0.911381i	−0.530121	+	0.0292476i	−0.318172	−	0.948033i	$-0.603069\pi$
$971$	−16.5190	+	0.911381i	−0.530121	+	0.0292476i	−0.211949	+	0.977281i	$0.567981\pi$
$972$	8.87900	−	10.7812i	0.284794	−	0.345806i
$973$	−2.31256	−	2.01401i	−0.0741373	−	0.0645663i
$974$	−0.225211	+	1.15295i	−0.00721623	+	0.0369431i
$975$	0.780283	+	28.3072i	0.0249890	+	0.906556i
$976$	1.26868	+	0.686574i	0.0406094	+	0.0219767i
$977$	−6.50099	−	7.06196i	−0.207985	−	0.225932i	0.623007	−	0.782216i	$-0.285911\pi$
$977$	−6.50099	−	7.06196i	−0.207985	−	0.225932i	−0.830992	+	0.556284i	$0.812227\pi$
$978$	−19.9041	+	63.6370i	−0.636463	+	2.03489i
$979$	−8.83553	+	8.59534i	−0.282385	+	0.274708i
$980$	5.91841	+	9.05880i	0.189057	+	0.289373i
$981$	−32.5130	+	25.3059i	−1.03806	+	0.807955i
$982$	−14.4287	−	12.5660i	−0.460438	−	0.400996i
$983$	6.07208	+	5.90701i	0.193669	+	0.188404i	0.787739	−	0.616009i	$-0.211252\pi$
$983$	6.07208	+	5.90701i	0.193669	+	0.188404i	−0.594070	+	0.804414i	$0.702480\pi$
$984$	−13.9891	−	24.2298i	−0.445956	−	0.772418i
$985$	−27.0163	−	18.7327i	−0.860812	−	0.596873i
$986$	27.2717	+	18.9098i	0.868509	+	0.602211i
$987$	−5.64185	+	6.12868i	−0.179582	+	0.195078i
$988$	12.3999	+	9.15217i	0.394494	+	0.291169i
$989$	−1.72997	−	1.87925i	−0.0550100	−	0.0597568i
$990$	−3.02264	−	21.7977i	−0.0960660	−	0.692777i
$991$	29.5998	+	3.27610i	0.940268	+	0.104069i	0.567058	−	0.823678i	$-0.308082\pi$
$991$	29.5998	+	3.27610i	0.940268	+	0.104069i	0.373210	+	0.927747i	$0.378257\pi$
$992$	8.59920	−	0.951759i	0.273025	−	0.0302184i
$993$	14.3551	+	28.3665i	0.455546	+	0.900183i
$994$	−0.309892	+	0.612363i	−0.00982917	+	0.0194230i
$995$	4.82737	−	19.0628i	0.153038	−	0.604333i
$996$	−16.8358	+	38.3818i	−0.533463	+	1.21617i
$997$	0.852015	−	1.15921i	0.0269836	−	0.0367125i	−0.792064	−	0.610438i	$-0.790994\pi$
$997$	0.852015	−	1.15921i	0.0269836	−	0.0367125i	0.819048	+	0.573725i	$0.194502\pi$
$998$	−1.66495	+	3.29002i	−0.0527029	+	0.104144i
$999$	−111.803	+	18.6567i	−3.53730	+	0.590272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.505.17	✓	612
361.178	even	57	inner	722.2.i.b.539.17	yes	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.505.17	✓	612	1.1	even	1	trivial
722.2.i.b.539.17	yes	612	361.178	even	57	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.851919 - 0.523673i) q^{2} +(1.09053 - 2.91268i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.922218 + 1.25472i) q^{5} +(-0.596247 - 3.05245i) q^{6} +(-0.123579 + 0.189152i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(-5.03213 - 4.38249i) q^{9} +O(q^{10})\)	\(q+(0.851919 - 0.523673i) q^{2} +(1.09053 - 2.91268i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.922218 + 1.25472i) q^{5} +(-0.596247 - 3.05245i) q^{6} +(-0.123579 + 0.189152i) q^{7} +(-0.0825793 - 0.996584i) q^{8} +(-5.03213 - 4.38249i) q^{9} +(1.44272 + 0.585982i) q^{10} +(2.00307 + 0.687654i) q^{11} +(-2.10644 - 2.28820i) q^{12} +(-2.24772 - 2.72926i) q^{13} +(-0.00622570 + 0.225857i) q^{14} +(4.66032 - 1.31781i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(1.80595 + 3.56866i) q^{17} +(-6.58196 - 1.09833i) q^{18} +(-2.85614 - 3.29279i) q^{19} +(1.53594 - 0.256304i) q^{20} +(0.416172 + 0.566222i) q^{21} +(2.06656 - 0.463127i) q^{22} +(-1.90585 - 5.09029i) q^{23} +(-2.99279 - 0.846280i) q^{24} +(0.768730 - 2.45777i) q^{25} +(-3.34411 - 1.14804i) q^{26} +(-10.0466 + 5.43696i) q^{27} +(0.112971 + 0.195672i) q^{28} +(8.28479 + 0.457085i) q^{29} +(3.28011 - 3.56315i) q^{30} +(-7.60895 + 4.11776i) q^{31} +(-0.926494 - 0.376309i) q^{32} +(4.18733 - 5.08439i) q^{33} +(3.40734 + 2.09448i) q^{34} +(-0.351300 + 0.0193817i) q^{35} +(-6.18247 + 2.51110i) q^{36} +(9.38488 + 3.22183i) q^{37} +(-4.15754 - 1.30951i) q^{38} +(-10.4007 + 3.57055i) q^{39} +(1.17428 - 1.02268i) q^{40} +(6.44802 + 6.27273i) q^{41} +(0.651060 + 0.264438i) q^{42} +(0.435395 - 0.176842i) q^{43} +(1.51801 - 1.47675i) q^{44} +(0.858085 - 10.3555i) q^{45} +(-4.28927 - 3.33847i) q^{46} +(2.27259 + 11.6344i) q^{47} +(-2.99279 + 0.846280i) q^{48} +(2.79136 + 6.36366i) q^{49} +(-0.632170 - 2.49638i) q^{50} +(12.3638 - 1.36843i) q^{51} +(-3.45011 + 0.773188i) q^{52} +(-0.213691 - 1.09398i) q^{53} +(-5.71173 + 9.89300i) q^{54} +(0.984450 + 3.14746i) q^{55} +(0.198711 + 0.107537i) q^{56} +(-12.7056 + 4.72812i) q^{57} +(7.29734 - 3.94912i) q^{58} +(-0.621116 - 0.604231i) q^{59} +(0.928465 - 4.75322i) q^{60} +(-1.30457 + 0.615643i) q^{61} +(-4.32586 + 7.49260i) q^{62} +(1.45082 - 0.410253i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(1.35157 - 5.33723i) q^{65} +(0.904708 - 6.52428i) q^{66} +(-9.25540 + 6.41755i) q^{67} +3.99960 q^{68} -16.9048 q^{69} +(-0.289129 + 0.200478i) q^{70} +(2.74702 + 1.29635i) q^{71} +(-3.95197 + 5.37685i) q^{72} +(0.105582 + 0.208636i) q^{73} +(9.68235 - 2.16987i) q^{74} +(-6.32037 - 4.91934i) q^{75} +(-4.22765 + 1.06159i) q^{76} +(-0.377608 + 0.293904i) q^{77} +(-6.99072 + 8.48837i) q^{78} +(12.9767 - 5.27068i) q^{79} +(0.464842 - 1.48618i) q^{80} +(2.13030 + 15.3626i) q^{81} +(8.77806 + 1.96721i) q^{82} +(-5.41320 - 12.3409i) q^{83} +(0.693129 - 0.115663i) q^{84} +(-2.81220 + 5.55706i) q^{85} +(0.278314 - 0.378660i) q^{86} +(10.3662 - 23.6325i) q^{87} +(0.519893 - 2.05301i) q^{88} +(-2.62813 + 5.19332i) q^{89} +(-4.69190 - 9.27144i) q^{90} +(0.794014 - 0.0878814i) q^{91} +(-5.40238 - 0.597936i) q^{92} +(3.69591 + 26.6530i) q^{93} +(8.02867 + 8.72146i) q^{94} +(1.49756 - 6.62033i) q^{95} +(-2.10644 + 2.28820i) q^{96} +(-0.937566 - 0.650094i) q^{97} +(5.71049 + 3.95957i) q^{98} +(-7.06607 - 12.2388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9}+O(q^{10}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21} + 33 q^{22} + 39 q^{23} + 20 q^{25} - 8 q^{26} + 158 q^{27} - 37 q^{28} - 42 q^{29} - 29 q^{30} + 12 q^{31} + 17 q^{32} + 60 q^{33} - q^{34} - 14 q^{35} + 23 q^{36} - 6 q^{37} + 76 q^{38} - 108 q^{39} + q^{40} + 8 q^{41} + 11 q^{42} + 7 q^{43} - 5 q^{44} - 101 q^{45} - 21 q^{46} + 105 q^{47} - 62 q^{49} - 78 q^{50} - 3 q^{51} + 4 q^{52} + 146 q^{53} - 79 q^{54} + 4 q^{55} - 21 q^{56} - 28 q^{57} + 8 q^{58} - 4 q^{59} - 14 q^{60} - 93 q^{61} - 6 q^{62} - 95 q^{63} - 34 q^{64} - 76 q^{65} - 16 q^{66} - 6 q^{67} + 78 q^{68} + 38 q^{69} + 81 q^{70} - 151 q^{71} + 23 q^{72} + 7 q^{73} - 35 q^{74} - 12 q^{75} - 7 q^{76} + 78 q^{77} - 3 q^{78} - 10 q^{79} + q^{80} + 58 q^{81} - 30 q^{82} + 67 q^{83} - 22 q^{84} - 6 q^{85} - 12 q^{86} - 109 q^{87} + 10 q^{88} - 25 q^{89} - 73 q^{90} + 37 q^{91} + q^{92} + 56 q^{93} - 39 q^{94} - 29 q^{95} - 153 q^{97} + 164 q^{98} - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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