LMFDB - Embedded newform 84.2.n.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(11,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("84.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.n (of order $6$, degree $2$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29776 + 0.561968i) q^{2} +(0.373317 + 1.69134i) q^{3} +(1.36838 - 1.45860i) q^{4} +(0.432549 + 0.249732i) q^{5} +(-1.43496 - 1.98517i) q^{6} +(-0.261928 + 2.63275i) q^{7} +(-0.956154 + 2.66191i) q^{8} +(-2.72127 + 1.26281i) q^{9} +(-0.701688 - 0.0810151i) q^{10} +(-0.695249 - 1.20421i) q^{11} +(2.97784 + 1.76988i) q^{12} +2.75054 q^{13} +(-1.13960 - 3.56389i) q^{14} +(-0.260904 + 0.824817i) q^{15} +(-0.255045 - 3.99186i) q^{16} +(5.04311 - 2.91164i) q^{17} +(2.82191 - 3.16810i) q^{18} +(-2.14907 - 1.24076i) q^{19} +(0.956154 - 0.289187i) q^{20} +(-4.55067 + 0.539842i) q^{21} +(1.57899 + 1.17207i) q^{22} +(2.53203 - 4.38560i) q^{23} +(-4.85915 - 0.623445i) q^{24} +(-2.37527 - 4.11408i) q^{25} +(-3.56955 + 1.54571i) q^{26} +(-3.15174 - 4.13116i) q^{27} +(3.48172 + 3.98467i) q^{28} +6.32275i q^{29} +(-0.124928 - 1.21704i) q^{30} +(5.98869 - 3.45757i) q^{31} +(2.57429 + 5.03717i) q^{32} +(1.77718 - 1.62545i) q^{33} +(-4.90852 + 6.61269i) q^{34} +(-0.770780 + 1.07338i) q^{35} +(-1.88180 + 5.69726i) q^{36} +(-3.67154 + 6.35929i) q^{37} +(3.48625 + 0.402514i) q^{38} +(1.02682 + 4.65209i) q^{39} +(-1.07835 + 0.912624i) q^{40} -5.74438i q^{41} +(5.60232 - 3.25792i) q^{42} -3.52627i q^{43} +(-2.70783 - 0.633726i) q^{44} +(-1.49245 - 0.133360i) q^{45} +(-0.821409 + 7.11439i) q^{46} +(-2.53203 + 4.38560i) q^{47} +(6.65638 - 1.92160i) q^{48} +(-6.86279 - 1.37918i) q^{49} +(5.39452 + 4.00429i) q^{50} +(6.80726 + 7.44266i) q^{51} +(3.76379 - 4.01194i) q^{52} +(-4.54223 + 2.62246i) q^{53} +(6.41180 + 3.59010i) q^{54} -0.694505i q^{55} +(-6.75771 - 3.21455i) q^{56} +(1.29627 - 4.09801i) q^{57} +(-3.55318 - 8.20544i) q^{58} +(-1.57587 - 2.72949i) q^{59} +(0.846063 + 1.50922i) q^{60} +(2.45426 - 4.25091i) q^{61} +(-5.82886 + 7.85256i) q^{62} +(-2.61190 - 7.49520i) q^{63} +(-6.17154 - 5.09039i) q^{64} +(1.18974 + 0.686897i) q^{65} +(-1.39290 + 3.10817i) q^{66} +(-9.30445 + 5.37193i) q^{67} +(2.65399 - 11.3402i) q^{68} +(8.36279 + 2.64530i) q^{69} +(0.397085 - 1.82615i) q^{70} -4.54224 q^{71} +(-0.759544 - 8.45122i) q^{72} +(4.98752 + 8.63864i) q^{73} +(1.19108 - 10.3162i) q^{74} +(6.07159 - 5.55325i) q^{75} +(-4.75054 + 1.43679i) q^{76} +(3.35249 - 1.51500i) q^{77} +(-3.94690 - 5.46028i) q^{78} +(1.84576 + 1.06565i) q^{79} +(0.886577 - 1.79037i) q^{80} +(5.81061 - 6.87291i) q^{81} +(3.22815 + 7.45485i) q^{82} +12.0165 q^{83} +(-5.43965 + 7.37633i) q^{84} +2.90852 q^{85} +(1.98165 + 4.57626i) q^{86} +(-10.6939 + 2.36039i) q^{87} +(3.87026 - 0.699285i) q^{88} +(-2.12318 - 1.22582i) q^{89} +(2.01179 - 0.665637i) q^{90} +(-0.720443 + 7.24148i) q^{91} +(-2.93206 - 9.69440i) q^{92} +(8.08361 + 8.83814i) q^{93} +(0.821409 - 7.11439i) q^{94} +(-0.619718 - 1.07338i) q^{95} +(-7.55854 + 6.23445i) q^{96} +0.526031 q^{97} +(9.68134 - 2.06681i) q^{98} +(3.41265 + 2.39900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.29776	+	0.561968i	−0.917658	+	0.397371i
$2$	−1.29776	+	0.561968i	−0.917658	+	0.397371i
$3$	0.373317	+	1.69134i	0.215535	+	0.976496i
$3$	0.373317	+	1.69134i	0.215535	+	0.976496i
$4$	1.36838	−	1.45860i	0.684192	−	0.729302i
$5$	0.432549	+	0.249732i	0.193442	+	0.111684i	0.593593	−	0.804766i	$-0.297709\pi$
$5$	0.432549	+	0.249732i	0.193442	+	0.111684i	−0.400151	+	0.916449i	$0.631042\pi$
$6$	−1.43496	−	1.98517i	−0.585818	−	0.810442i
$7$	−0.261928	+	2.63275i	−0.0989995	+	0.995087i
$7$	−0.261928	+	2.63275i	−0.0989995	+	0.995087i
$8$	−0.956154	+	2.66191i	−0.338051	+	0.941128i
$9$	−2.72127	+	1.26281i	−0.907090	+	0.420938i
$10$	−0.701688	−	0.0810151i	−0.221893	−	0.0256192i
$11$	−0.695249	−	1.20421i	−0.209626	−	0.363082i	0.741971	−	0.670432i	$-0.233891\pi$
$11$	−0.695249	−	1.20421i	−0.209626	−	0.363082i	−0.951597	+	0.307350i	$0.900558\pi$
$12$	2.97784	+	1.76988i	0.859627	+	0.510922i
$13$	2.75054			0.762861			0.381431	−	0.924397i	$-0.375432\pi$
$13$	2.75054			0.762861			0.381431	+	0.924397i	$0.375432\pi$
$14$	−1.13960	−	3.56389i	−0.304571	−	0.952490i
$15$	−0.260904	+	0.824817i	−0.0673652	+	0.212967i
$16$	−0.255045	−	3.99186i	−0.0637614	−	0.997965i
$17$	5.04311	−	2.91164i	1.22313	−	0.706177i	0.257550	−	0.966265i	$-0.417085\pi$
$17$	5.04311	−	2.91164i	1.22313	−	0.706177i	0.965585	+	0.260088i	$0.0837515\pi$
$18$	2.82191	−	3.16810i	0.665130	−	0.746728i
$19$	−2.14907	−	1.24076i	−0.493030	−	0.284651i	0.232801	−	0.972524i	$-0.425211\pi$
$19$	−2.14907	−	1.24076i	−0.493030	−	0.284651i	−0.725831	+	0.687874i	$0.758544\pi$
$20$	0.956154	−	0.289187i	0.213802	−	0.0646643i
$21$	−4.55067	+	0.539842i	−0.993037	+	0.117803i
$22$	1.57899	+	1.17207i	0.336643	+	0.249886i
$23$	2.53203	−	4.38560i	0.527964	−	0.914460i	−0.471505	−	0.881863i	$-0.656289\pi$
$23$	2.53203	−	4.38560i	0.527964	−	0.914460i	0.999469	−	0.0325966i	$-0.0103777\pi$
$24$	−4.85915	−	0.623445i	−0.991869	−	0.127260i
$25$	−2.37527	−	4.11408i	−0.475054	−	0.822817i
$26$	−3.56955	+	1.54571i	−0.700046	+	0.303139i
$27$	−3.15174	−	4.13116i	−0.606553	−	0.795043i
$28$	3.48172	+	3.98467i	0.657984	+	0.753032i
$29$			6.32275i			1.17411i	0.809549	+	0.587053i	$0.199712\pi$
$29$			6.32275i			1.17411i	−0.809549	+	0.587053i	$0.800288\pi$
$30$	−0.124928	−	1.21704i	−0.0228086	−	0.222200i
$31$	5.98869	−	3.45757i	1.07560	−	0.620998i	0.145894	−	0.989300i	$-0.453394\pi$
$31$	5.98869	−	3.45757i	1.07560	−	0.620998i	0.929706	+	0.368302i	$0.120061\pi$
$32$	2.57429	+	5.03717i	0.455074	+	0.890454i
$33$	1.77718	−	1.62545i	0.309367	−	0.282955i
$34$	−4.90852	+	6.61269i	−0.841805	+	1.13407i
$35$	−0.770780	+	1.07338i	−0.130286	+	0.181435i
$36$	−1.88180	+	5.69726i	−0.313633	+	0.949544i
$37$	−3.67154	+	6.35929i	−0.603598	+	1.04546i	0.388674	+	0.921375i	$0.372933\pi$
$37$	−3.67154	+	6.35929i	−0.603598	+	1.04546i	−0.992271	+	0.124086i	$0.960400\pi$
$38$	3.48625	+	0.402514i	0.565545	+	0.0652964i
$39$	1.02682	+	4.65209i	0.164423	+	0.744931i
$40$	−1.07835	+	0.912624i	−0.170502	+	0.144299i
$41$		−	5.74438i		−	0.897121i	−0.893753	−	0.448560i	$-0.851937\pi$
$41$		−	5.74438i		−	0.897121i	0.893753	−	0.448560i	$-0.148063\pi$
$42$	5.60232	−	3.25792i	0.864457	−	0.502707i
$43$		−	3.52627i		−	0.537751i	−0.963175	−	0.268875i	$-0.913348\pi$
$43$		−	3.52627i		−	0.537751i	0.963175	−	0.268875i	$-0.0866520\pi$
$44$	−2.70783	−	0.633726i	−0.408220	−	0.0955378i
$45$	−1.49245	−	0.133360i	−0.222481	−	0.0198802i
$46$	−0.821409	+	7.11439i	−0.121110	+	1.04896i
$47$	−2.53203	+	4.38560i	−0.369334	+	0.639705i	−0.989462	−	0.144796i	$-0.953747\pi$
$47$	−2.53203	+	4.38560i	−0.369334	+	0.639705i	0.620128	+	0.784501i	$0.287081\pi$
$48$	6.65638	−	1.92160i	0.960766	−	0.277359i
$49$	−6.86279	−	1.37918i	−0.980398	−	0.197026i
$50$	5.39452	+	4.00429i	0.762900	+	0.566292i
$51$	6.80726	+	7.44266i	0.953207	+	1.04218i
$52$	3.76379	−	4.01194i	0.521944	−	0.556356i
$53$	−4.54223	+	2.62246i	−0.623923	+	0.360222i	−0.778395	−	0.627775i	$-0.783966\pi$
$53$	−4.54223	+	2.62246i	−0.623923	+	0.360222i	0.154472	+	0.987997i	$0.450632\pi$
$54$	6.41180	+	3.59010i	0.872536	+	0.488551i
$55$		−	0.694505i		−	0.0936470i
$56$	−6.75771	−	3.21455i	−0.903037	−	0.429562i
$57$	1.29627	−	4.09801i	0.171696	−	0.542794i
$58$	−3.55318	−	8.20544i	−0.466556	−	1.07743i
$59$	−1.57587	−	2.72949i	−0.205161	−	0.355349i	0.745023	−	0.667039i	$-0.232438\pi$
$59$	−1.57587	−	2.72949i	−0.205161	−	0.355349i	−0.950184	+	0.311689i	$0.899105\pi$
$60$	0.846063	+	1.50922i	0.109226	+	0.194840i
$61$	2.45426	−	4.25091i	0.314236	−	0.544273i	−0.665039	−	0.746809i	$-0.731585\pi$
$61$	2.45426	−	4.25091i	0.314236	−	0.544273i	0.979275	+	0.202536i	$0.0649183\pi$
$62$	−5.82886	+	7.85256i	−0.740267	+	0.997276i
$63$	−2.61190	−	7.49520i	−0.329068	−	0.944306i
$64$	−6.17154	−	5.09039i	−0.771443	−	0.636299i
$65$	1.18974	+	0.686897i	0.147569	+	0.0851991i
$66$	−1.39290	+	3.10817i	−0.171455	+	0.382590i
$67$	−9.30445	+	5.37193i	−1.13672	+	0.656286i	−0.945616	−	0.325284i	$-0.894540\pi$
$67$	−9.30445	+	5.37193i	−1.13672	+	0.656286i	−0.191104	+	0.981570i	$0.561207\pi$
$68$	2.65399	−	11.3402i	0.321844	−	1.37520i
$69$	8.36279	+	2.64530i	1.00676	+	0.318457i
$70$	0.397085	−	1.82615i	0.0474607	−	0.218267i
$71$	−4.54224			−0.539065			−0.269532	−	0.962991i	$-0.586869\pi$
$71$	−4.54224			−0.539065			−0.269532	+	0.962991i	$0.586869\pi$
$72$	−0.759544	−	8.45122i	−0.0895132	−	0.995986i
$73$	4.98752	+	8.63864i	0.583745	+	1.01108i	0.995031	+	0.0995695i	$0.0317466\pi$
$73$	4.98752	+	8.63864i	0.583745	+	1.01108i	−0.411286	+	0.911507i	$0.634920\pi$
$74$	1.19108	−	10.3162i	0.138460	−	1.19923i
$75$	6.07159	−	5.55325i	0.701087	−	0.641234i
$76$	−4.75054	+	1.43679i	−0.544924	+	0.164811i
$77$	3.35249	−	1.51500i	0.382051	−	0.172651i
$78$	−3.94690	−	5.46028i	−0.446898	−	0.618255i
$79$	1.84576	+	1.06565i	0.207664	+	0.119895i	0.600225	−	0.799831i	$-0.295078\pi$
$79$	1.84576	+	1.06565i	0.207664	+	0.119895i	−0.392561	+	0.919726i	$0.628411\pi$
$80$	0.886577	−	1.79037i	0.0991223	−	0.200169i
$81$	5.81061	−	6.87291i	0.645623	−	0.763656i
$82$	3.22815	+	7.45485i	0.356490	+	0.823250i
$83$	12.0165			1.31899			0.659493	−	0.751710i	$-0.270771\pi$
$83$	12.0165			1.31899			0.659493	+	0.751710i	$0.270771\pi$
$84$	−5.43965	+	7.37633i	−0.593514	+	0.804823i
$85$	2.90852			0.315474
$86$	1.98165	+	4.57626i	0.213687	+	0.493471i
$87$	−10.6939	+	2.36039i	−1.14651	+	0.253060i
$88$	3.87026	−	0.699285i	0.412571	−	0.0745440i
$89$	−2.12318	−	1.22582i	−0.225056	−	0.129936i	0.383233	−	0.923652i	$-0.374811\pi$
$89$	−2.12318	−	1.22582i	−0.225056	−	0.129936i	−0.608289	+	0.793715i	$0.708144\pi$
$90$	2.01179	−	0.665637i	0.212061	−	0.0701643i
$91$	−0.720443	+	7.24148i	−0.0755229	+	0.759114i
$92$	−2.93206	−	9.69440i	−0.305688	−	1.01071i
$93$	8.08361	+	8.83814i	0.838231	+	0.916473i
$94$	0.821409	−	7.11439i	0.0847219	−	0.733793i
$95$	−0.619718	−	1.07338i	−0.0635817	−	0.110127i
$96$	−7.55854	+	6.23445i	−0.771441	+	0.636301i
$97$	0.526031			0.0534104			0.0267052	−	0.999643i	$-0.491498\pi$
$97$	0.526031			0.0534104			0.0267052	+	0.999643i	$0.491498\pi$
$98$	9.68134	−	2.06681i	0.977963	−	0.208779i
$99$	3.41265	+	2.39900i	0.342984	+	0.241109i
$100$	−9.25110	−	2.16508i	−0.925110	−	0.216508i
$101$	−13.9396	+	8.04803i	−1.38704	+	0.800809i	−0.992981	−	0.118275i	$-0.962264\pi$
$101$	−13.9396	+	8.04803i	−1.38704	+	0.800809i	−0.394061	+	0.919084i	$0.628930\pi$
$102$	−13.0168	−	5.83336i	−1.28885	−	0.577589i
$103$	1.62521	+	0.938316i	0.160137	+	0.0924550i	0.577927	−	0.816089i	$-0.303862\pi$
$103$	1.62521	+	0.938316i	0.160137	+	0.0924550i	−0.417790	+	0.908544i	$0.637195\pi$
$104$	−2.62993	+	7.32168i	−0.257886	+	0.717950i
$105$	−2.10320	−	0.902940i	−0.205252	−	0.0881179i
$106$	4.42101	−	5.95591i	0.429406	−	0.578490i
$107$	−3.63924	+	6.30335i	−0.351819	+	0.609368i	−0.986568	−	0.163350i	$-0.947770\pi$
$107$	−3.63924	+	6.30335i	−0.351819	+	0.609368i	0.634749	+	0.772718i	$0.281103\pi$
$108$	−10.3385	−	1.05588i	−0.994825	−	0.101602i
$109$	0.921005	+	1.59523i	0.0882163	+	0.152795i	0.906757	−	0.421653i	$-0.138550\pi$
$109$	0.921005	+	1.59523i	0.0882163	+	0.152795i	−0.818541	+	0.574448i	$0.805217\pi$
$110$	0.390289	+	0.901303i	0.0372126	+	0.0859359i
$111$	−12.1264	−	3.83579i	−1.15099	−	0.364077i
$112$	10.5764	+	0.374109i	0.999375	+	0.0353500i
$113$		−	10.2728i		−	0.966382i	−0.875515	−	0.483191i	$-0.839478\pi$
$113$		−	10.2728i		−	0.966382i	0.875515	−	0.483191i	$-0.160522\pi$
$114$	0.620689	+	6.04671i	0.0581329	+	0.566326i
$115$	2.19045	−	1.26466i	0.204260	−	0.117930i
$116$	9.22238	+	8.65196i	0.856277	+	0.803314i
$117$	−7.48495	+	3.47341i	−0.691983	+	0.321117i
$118$	3.57899	+	2.65665i	0.329473	+	0.244564i
$119$	6.34471	+	14.0399i	0.581618	+	1.28704i
$120$	−1.94612	−	1.48316i	−0.177656	−	0.135393i
$121$	4.53326	−	7.85183i	0.412114	−	0.713803i
$122$	−0.796182	+	6.89589i	−0.0720830	+	0.624325i
$123$	9.71570	−	2.14447i	0.876035	−	0.193361i
$124$	3.15161	−	13.4664i	0.283023	−	1.20932i
$125$		−	4.87005i		−	0.435590i
$126$	7.60169	+	8.25920i	0.677212	+	0.735788i
$127$		−	1.51224i		−	0.134190i	−0.997747	−	0.0670949i	$-0.978627\pi$
$127$		−	1.51224i		−	0.134190i	0.997747	−	0.0670949i	$-0.0213730\pi$
$128$	10.8698	+	3.13792i	0.960767	+	0.277356i
$129$	5.96412	−	1.31642i	0.525111	−	0.115904i
$130$	−1.93002	−	0.222835i	−0.169274	−	0.0195439i
$131$	−3.32518	+	5.75939i	−0.290523	+	0.503200i	−0.973933	−	0.226834i	$-0.927162\pi$
$131$	−3.32518	+	5.75939i	−0.290523	+	0.503200i	0.683411	+	0.730034i	$0.260496\pi$
$132$	0.0609683	−	4.81644i	0.00530661	−	0.419217i
$133$	3.82953	−	5.33298i	0.332062	−	0.462428i
$134$	9.05614	−	12.2003i	0.782331	−	1.05395i
$135$	−0.331598	−	2.57402i	−0.0285394	−	0.221537i
$136$	2.92854	+	16.2083i	0.251121	+	1.38985i
$137$	−10.5583	+	6.09586i	−0.902060	+	0.520805i	−0.877868	−	0.478903i	$-0.841035\pi$
$137$	−10.5583	+	6.09586i	−0.902060	+	0.520805i	−0.0241922	+	0.999707i	$0.507701\pi$
$138$	−12.3395	+	1.26664i	−1.05041	+	0.107823i
$139$		−	0.0477837i		−	0.00405296i	−0.999998	−	0.00202648i	$-0.999355\pi$
$139$		−	0.0477837i		−	0.00405296i	0.999998	−	0.00202648i	$-0.000645050\pi$
$140$	0.510916	+	2.59306i	0.0431802	+	0.219154i
$141$	−8.36279	−	2.64530i	−0.704274	−	0.222774i
$142$	5.89476	−	2.55259i	0.494677	−	0.214209i
$143$	−1.91231	−	3.31221i	−0.159915	−	0.276981i
$144$	5.73502	+	10.5409i	0.477918	+	0.878404i
$145$	−1.57899	+	2.73490i	−0.131128	+	0.227121i
$146$	−11.3273	−	8.40809i	−0.937451	−	0.695859i
$147$	−0.229323	−	12.1222i	−0.0189143	−	0.999821i
$148$	4.25161	+	14.0573i	0.349480	+	1.15550i
$149$	−1.98650	−	1.14691i	−0.162740	−	0.0939583i	0.416418	−	0.909173i	$-0.363285\pi$
$149$	−1.98650	−	1.14691i	−0.162740	−	0.0939583i	−0.579158	+	0.815215i	$0.696619\pi$
$150$	−4.75875	+	10.6188i	−0.388550	+	0.867025i
$151$	11.3759	−	6.56789i	0.925759	−	0.534487i	0.0402913	−	0.999188i	$-0.487171\pi$
$151$	11.3759	−	6.56789i	0.925759	−	0.534487i	0.885468	+	0.464701i	$0.153838\pi$
$152$	5.35764	−	4.53427i	0.434562	−	0.367777i
$153$	−10.0468	+	14.2919i	−0.812236	+	1.15543i
$154$	−3.49935	+	3.85011i	−0.281986	+	0.310250i
$155$	3.45387			0.277421
$156$	8.19064	+	4.86813i	0.655776	+	0.389762i
$157$	−4.20480	−	7.28292i	−0.335579	−	0.581241i	0.648017	−	0.761626i	$-0.275599\pi$
$157$	−4.20480	−	7.28292i	−0.335579	−	0.581241i	−0.983596	+	0.180386i	$0.942265\pi$
$158$	−2.99422	−	0.345705i	−0.238207	−	0.0275028i
$159$	−6.13116	−	6.70345i	−0.486232	−	0.531618i
$160$	−0.144439	+	2.82170i	−0.0114189	+	0.223075i
$161$	10.8830	+	7.81491i	0.857700	+	0.615901i
$162$	−3.67845	+	12.1848i	−0.289006	+	0.957327i
$163$	−10.7040	−	6.17993i	−0.838399	−	0.484050i	0.0183210	−	0.999832i	$-0.494168\pi$
$163$	−10.7040	−	6.17993i	−0.838399	−	0.484050i	−0.856720	+	0.515782i	$0.827501\pi$
$164$	−8.37876	−	7.86052i	−0.654272	−	0.613803i
$165$	1.17464	−	0.259270i	0.0914459	−	0.0201842i
$166$	−15.5946	+	6.75291i	−1.21038	+	0.524127i
$167$	−2.36549			−0.183047			−0.0915237	−	0.995803i	$-0.529174\pi$
$167$	−2.36549			−0.183047			−0.0915237	+	0.995803i	$0.529174\pi$
$168$	2.91413	−	12.6296i	0.224830	−	0.974398i
$169$	−5.43456			−0.418043
$170$	−3.77458	+	1.63450i	−0.289497	+	0.125360i
$171$	7.41504	+	0.662584i	0.567043	+	0.0506691i
$172$	−5.14342	−	4.82529i	−0.392182	−	0.367925i
$173$	8.28769	+	4.78490i	0.630102	+	0.363789i	0.780791	−	0.624792i	$-0.214816\pi$
$173$	8.28769	+	4.78490i	0.630102	+	0.363789i	−0.150690	+	0.988581i	$0.548149\pi$
$174$	12.5517	−	9.07287i	0.951545	−	0.687813i
$175$	11.4535	−	5.17590i	0.865805	−	0.391261i
$176$	−4.62971	+	3.08247i	−0.348977	+	0.232350i
$177$	4.02820	−	3.68430i	0.302778	−	0.276929i
$178$	3.44425	+	0.397665i	0.258158	+	0.0298062i
$179$	−10.3771	−	17.9736i	−0.775619	−	1.34341i	−0.934446	−	0.356105i	$-0.884105\pi$
$179$	−10.3771	−	17.9736i	−0.775619	−	1.34341i	0.158827	−	0.987306i	$-0.449229\pi$
$180$	−2.23676	+	1.99440i	−0.166718	+	0.148654i
$181$	−6.43456			−0.478277			−0.239138	−	0.970985i	$-0.576865\pi$
$181$	−6.43456			−0.478277			−0.239138	+	0.970985i	$0.576865\pi$
$182$	−3.13451	−	9.80260i	−0.232346	−	0.726617i
$183$	8.10595	+	2.56406i	0.599209	+	0.189541i
$184$	9.25306	+	10.9333i	0.682145	+	0.806016i
$185$	−3.17624	+	1.83380i	−0.233522	+	0.134824i
$186$	−15.4574	−	6.92710i	−1.13339	−	0.507920i
$187$	−7.01244	−	4.04864i	−0.512801	−	0.296066i
$188$	2.93206	+	9.69440i	0.213842	+	0.707037i
$189$	11.7019	−	7.21570i	0.851186	−	0.524865i
$190$	1.40745	+	1.04474i	0.102107	+	0.0757932i
$191$	8.76689	−	15.1847i	0.634350	−	1.09873i	−0.352303	−	0.935886i	$-0.614601\pi$
$191$	8.76689	−	15.1847i	0.634350	−	1.09873i	0.986652	−	0.162840i	$-0.0520655\pi$
$192$	6.30565	−	12.3385i	0.455071	−	0.890455i
$193$	1.09255	+	1.89234i	0.0786432	+	0.136214i	0.902665	−	0.430344i	$-0.141608\pi$
$193$	1.09255	+	1.89234i	0.0786432	+	0.136214i	−0.824022	+	0.566558i	$0.808275\pi$
$194$	−0.682665	+	0.295612i	−0.0490125	+	0.0212237i
$195$	−0.717627	+	2.26869i	−0.0513903	+	0.162464i
$196$	−11.4026	+	8.12283i	−0.814473	+	0.580202i
$197$		−	6.27706i		−	0.447222i	−0.974678	−	0.223611i	$-0.928215\pi$
$197$		−	6.27706i		−	0.447222i	0.974678	−	0.223611i	$-0.0717845\pi$
$198$	−5.77697	−	1.19554i	−0.410552	−	0.0849634i
$199$	−0.749564	+	0.432761i	−0.0531352	+	0.0306776i	−0.526332	−	0.850279i	$-0.676433\pi$
$199$	−0.749564	+	0.432761i	−0.0531352	+	0.0306776i	0.473197	+	0.880957i	$0.343100\pi$
$200$	13.2224	−	2.38905i	0.934968	−	0.168932i
$201$	−12.5593	−	13.7316i	−0.885863	−	0.968550i
$202$	13.5676	−	18.2781i	0.954612	−	1.28604i
$203$	−16.6462	−	1.65611i	−1.16834	−	0.116236i
$204$	20.1708	+	0.255330i	1.41224	+	0.0178767i
$205$	1.43456	−	2.48472i	0.100194	−	0.173541i
$206$	−2.63644	−	0.304397i	−0.183690	−	0.0212084i
$207$	−1.35213	+	15.1319i	−0.0939798	+	1.05174i
$208$	−0.701512	−	10.9798i	−0.0486411	−	0.761309i
$209$			3.45056i			0.238680i
$210$	3.23688	−	0.0101278i	0.223366	−	0.000698884i
$211$			3.90417i			0.268774i	0.990929	+	0.134387i	$0.0429065\pi$
$211$			3.90417i			0.268774i	−0.990929	+	0.134387i	$0.957094\pi$
$212$	−2.39039	+	10.2138i	−0.164173	+	0.701489i
$213$	−1.69570	−	7.68248i	−0.116187	−	0.526395i
$214$	1.18060	−	10.2254i	0.0807041	−	0.698994i
$215$	0.880622	−	1.52528i	0.0600580	−	0.104023i
$216$	14.0103	−	4.43963i	0.953283	−	0.302079i
$217$	7.53433	+	16.6724i	0.511463	+	1.13179i
$218$	−2.09171	−	1.55265i	−0.141669	−	0.105159i
$219$	−12.7490	+	11.6605i	−0.861495	+	0.787947i
$220$	−1.01301	−	0.950350i	−0.0682969	−	0.0640726i
$221$	13.8713	−	8.00858i	0.933082	−	0.538715i
$222$	17.8928	−	1.83668i	1.20088	−	0.123270i
$223$			23.5017i			1.57379i	0.617085	+	0.786896i	$0.288313\pi$
$223$			23.5017i			1.57379i	−0.617085	+	0.786896i	$0.711687\pi$
$224$	−13.9359	+	5.45808i	−0.931132	+	0.364684i
$225$	11.6591	+	8.19601i	0.777271	+	0.546401i
$226$	5.77297	+	13.3316i	0.384012	+	0.886808i
$227$	9.58391	+	16.5998i	0.636107	+	1.10177i	0.986280	+	0.165084i	$0.0527895\pi$
$227$	9.58391	+	16.5998i	0.636107	+	1.10177i	−0.350173	+	0.936685i	$0.613877\pi$
$228$	−4.20356	−	7.49840i	−0.278388	−	0.496593i
$229$	−5.73805	+	9.93860i	−0.379181	+	0.656761i	−0.990943	−	0.134281i	$-0.957128\pi$
$229$	−5.73805	+	9.93860i	−0.379181	+	0.656761i	0.611762	+	0.791042i	$0.290461\pi$
$230$	−2.13199	+	2.87219i	−0.140579	+	0.189386i
$231$	3.81393	+	5.10462i	0.250938	+	0.335859i
$232$	−16.8306	−	6.04552i	−1.10498	−	0.396908i
$233$	−17.5088	−	10.1087i	−1.14704	−	0.662245i	−0.198877	−	0.980025i	$-0.563729\pi$
$233$	−17.5088	−	10.1087i	−1.14704	−	0.662245i	−0.948164	+	0.317780i	$0.897063\pi$
$234$	7.76175	−	8.71397i	0.507402	−	0.569650i
$235$	−2.19045	+	1.26466i	−0.142889	+	0.0824971i
$236$	−6.13764	−	1.43642i	−0.399526	−	0.0935031i
$237$	−1.11332	+	3.51963i	−0.0723181	+	0.228625i
$238$	−16.1239	−	14.6550i	−1.04516	−	0.949942i
$239$	−6.90774			−0.446824			−0.223412	−	0.974724i	$-0.571720\pi$
$239$	−6.90774			−0.446824			−0.223412	+	0.974724i	$0.571720\pi$
$240$	3.35910	+	0.831129i	0.216829	+	0.0536491i
$241$	−4.03326	−	6.98581i	−0.259805	−	0.449995i	0.706385	−	0.707828i	$-0.250325\pi$
$241$	−4.03326	−	6.98581i	−0.259805	−	0.449995i	−0.966190	+	0.257833i	$0.916992\pi$
$242$	−1.47063	+	12.7374i	−0.0945354	+	0.818789i
$243$	13.7936	+	7.26194i	0.884862	+	0.465854i
$244$	−2.84201	−	9.39667i	−0.181941	−	0.601560i
$245$	−2.62406	−	2.31042i	−0.167645	−	0.147608i
$246$	−11.4036	+	8.24293i	−0.727065	+	0.525550i
$247$	−5.91109	−	3.41277i	−0.376113	−	0.217149i
$248$	3.47764	+	19.2473i	0.220830	+	1.22221i
$249$	4.48598	+	20.3241i	0.284287	+	1.28799i
$250$	2.73681	+	6.32017i	0.173091	+	0.399723i
$251$	20.4073			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$251$	20.4073			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$252$	−14.5066	−	6.44659i	−0.913830	−	0.406097i
$253$	−7.04155			−0.442699
$254$	0.849832	+	1.96254i	0.0533232	+	0.123140i
$255$	1.08580	+	4.91931i	0.0679956	+	0.308059i
$256$	−15.8699	+	2.03621i	−0.991869	+	0.127263i
$257$	23.5645	+	13.6050i	1.46991	+	0.848655i	0.999430	−	0.0337537i	$-0.0107462\pi$
$257$	23.5645	+	13.6050i	1.46991	+	0.848655i	0.470484	+	0.882409i	$0.344080\pi$
$258$	−7.00024	+	5.06004i	−0.435816	+	0.315024i
$259$	−15.7808	−	11.3319i	−0.980570	−	0.704133i
$260$	2.62993	−	0.795420i	0.163102	−	0.0493299i
$261$	−7.98445	−	17.2059i	−0.494225	−	1.06502i
$262$	1.07872	−	9.34297i	0.0666433	−	0.577211i
$263$	1.80247	+	3.12196i	0.111145	+	0.192508i	0.916232	−	0.400648i	$-0.131215\pi$
$263$	1.80247	+	3.12196i	0.111145	+	0.192508i	−0.805087	+	0.593156i	$0.797882\pi$
$264$	2.62756	+	6.28487i	0.161715	+	0.386807i
$265$	−2.61965			−0.160924
$266$	−1.97287	+	9.07302i	−0.120964	+	0.556302i
$267$	1.28066	−	4.04864i	0.0783749	−	0.247772i
$268$	−4.89656	+	20.9224i	−0.299105	+	1.27804i
$269$	22.6598	−	13.0827i	1.38160	−	0.797664i	0.389247	−	0.921134i	$-0.372735\pi$
$269$	22.6598	−	13.0827i	1.38160	−	0.797664i	0.992348	+	0.123469i	$0.0394020\pi$
$270$	1.87685	+	3.15413i	0.114222	+	0.191954i
$271$	19.9722	+	11.5309i	1.21322	+	0.700455i	0.963460	−	0.267851i	$-0.0863137\pi$
$271$	19.9722	+	11.5309i	1.21322	+	0.700455i	0.249764	+	0.968307i	$0.419647\pi$
$272$	−12.9091	−	19.3888i	−0.782729	−	1.17562i
$273$	−12.5168	+	1.48485i	−0.757549	+	0.0898675i
$274$	10.2766	−	13.8444i	0.620830	−	0.836373i
$275$	−3.30281	+	5.72063i	−0.199167	+	0.344967i
$276$	15.3020	−	8.57820i	0.921069	−	0.516347i
$277$	10.1455	+	17.5725i	0.609585	+	1.05583i	0.991309	+	0.131555i	$0.0419971\pi$
$277$	10.1455	+	17.5725i	0.609585	+	1.05583i	−0.381724	+	0.924276i	$0.624670\pi$
$278$	0.0268529	+	0.0620120i	0.00161053	+	0.00371923i
$279$	−11.9306	+	16.9716i	−0.714264	+	1.01606i
$280$	−2.12027	−	3.07807i	−0.126710	−	0.183950i
$281$			27.6637i			1.65028i	0.564929	+	0.825140i	$0.308904\pi$
$281$			27.6637i			1.65028i	−0.564929	+	0.825140i	$0.691096\pi$
$282$	12.3395	−	1.26664i	0.734807	−	0.0754272i
$283$	−15.0435	+	8.68535i	−0.894242	+	0.516291i	−0.875328	−	0.483530i	$-0.839354\pi$
$283$	−15.0435	+	8.68535i	−0.894242	+	0.516291i	−0.0189142	+	0.999821i	$0.506021\pi$
$284$	−6.21553	+	6.62533i	−0.368824	+	0.393141i
$285$	1.58411	−	1.44887i	0.0938343	−	0.0858235i
$286$	4.34308	+	3.22382i	0.256812	+	0.190628i
$287$	15.1235	+	1.50461i	0.892714	+	0.0888146i
$288$	−13.3663	−	10.4566i	−0.787618	−	0.616164i
$289$	8.45533	−	14.6451i	0.497373	−	0.861474i
$290$	0.512239	−	4.43660i	0.0300797	−	0.260526i
$291$	0.196376	+	0.889698i	0.0115118	+	0.0521550i
$292$	19.4252	+	4.54617i	1.13677	+	0.266044i
$293$		−	19.9672i		−	1.16650i	−0.812294	−	0.583248i	$-0.801782\pi$
$293$		−	19.9672i		−	1.16650i	0.812294	−	0.583248i	$-0.198218\pi$
$294$	7.10988	+	15.6029i	0.414657	+	0.909978i
$295$		−	1.57418i		−	0.0916525i
$296$	−13.4173	−	15.8538i	−0.779866	−	0.921482i
$297$	−2.78353	+	6.66754i	−0.161517	+	0.386890i
$298$	3.22253	+	0.372066i	0.186676	+	0.0215532i
$299$	6.96442	−	12.0627i	0.402763	−	0.697606i
$300$	0.208294	−	16.4550i	0.0120258	−	0.950031i
$301$	9.28379	+	0.923629i	0.535109	+	0.0532371i
$302$	−11.0723	+	14.9165i	−0.637141	+	0.858346i
$303$	−18.8159	−	20.5722i	−1.08094	−	1.18184i
$304$	−4.40485	+	8.89523i	−0.252635	+	0.510176i
$305$	2.12318	−	1.22582i	0.121573	−	0.0701901i
$306$	5.00682	−	24.1935i	0.286221	−	1.38305i
$307$		−	14.1529i		−	0.807746i	−0.914815	−	0.403873i	$-0.867664\pi$
$307$		−	14.1529i		−	0.807746i	0.914815	−	0.403873i	$-0.132336\pi$
$308$	2.37770	−	6.96305i	0.135482	−	0.396757i
$309$	−0.980294	+	3.09908i	−0.0557670	+	0.176300i
$310$	−4.48231	+	1.94096i	−0.254578	+	0.110239i
$311$	−12.2774	−	21.2652i	−0.696190	−	1.20584i	−0.969778	−	0.243990i	$-0.921544\pi$
$311$	−12.2774	−	21.2652i	−0.696190	−	1.20584i	0.273588	−	0.961847i	$-0.411790\pi$
$312$	−13.3653	−	1.71481i	−0.756659	−	0.0970819i
$313$	−0.0260312	+	0.0450873i	−0.00147137	+	0.00254848i	−0.866760	−	0.498725i	$-0.833802\pi$
$313$	−0.0260312	+	0.0450873i	−0.00147137	+	0.00254848i	0.865289	+	0.501274i	$0.167135\pi$
$314$	9.54960	+	7.08856i	0.538915	+	0.400031i
$315$	0.742018	−	3.89432i	0.0418080	−	0.219420i
$316$	4.08007	−	1.23401i	0.229522	−	0.0694185i
$317$	5.86864	+	3.38826i	0.329616	+	0.190304i	0.655671	−	0.755047i	$-0.272386\pi$
$317$	5.86864	+	3.38826i	0.329616	+	0.190304i	−0.326055	+	0.945351i	$0.605719\pi$
$318$	11.7239	+	5.25398i	0.657445	+	0.294629i
$319$	7.61390	−	4.39589i	0.426297	−	0.246122i
$320$	−1.39826	−	3.74308i	−0.0781650	−	0.209244i
$321$	−12.0197	−	3.80205i	−0.670875	−	0.212210i
$322$	−18.5153	−	4.02603i	−1.03182	−	0.224362i
$323$	−14.4507			−0.804056
$324$	−2.07369	−	17.8802i	−0.115205	−	0.993342i
$325$	−6.53326	−	11.3159i	−0.362400	−	0.627695i
$326$	17.3641	+	2.00482i	0.961711	+	0.111037i
$327$	−2.35425	+	2.15326i	−0.130190	+	0.119076i
$328$	15.2910	+	5.49251i	0.844305	+	0.303273i
$329$	−10.8830	−	7.81491i	−0.599999	−	0.430850i
$330$	−1.37871	+	0.996584i	−0.0758955	+	0.0548601i
$331$	15.4949	+	8.94598i	0.851676	+	0.491715i	0.861216	−	0.508239i	$-0.169703\pi$
$331$	15.4949	+	8.94598i	0.851676	+	0.491715i	−0.00953987	+	0.999954i	$0.503037\pi$
$332$	16.4433	−	17.5274i	0.902441	−	0.961939i
$333$	1.96065	−	21.9418i	0.107443	−	1.20240i
$334$	3.06985	−	1.32933i	0.167975	−	0.0727378i
$335$	−5.36618			−0.293185
$336$	3.31560	+	18.0279i	0.180881	+	0.983505i
$337$	7.09362			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$337$	7.09362			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$338$	7.05277	−	3.05404i	0.383620	−	0.166118i
$339$	17.3748	−	3.83500i	0.943668	−	0.208289i
$340$	3.97998	−	4.24238i	0.215845	−	0.230076i
$341$	−8.32726	−	4.80775i	−0.450946	−	0.260354i
$342$	−9.99533	+	3.30714i	−0.540486	+	0.178829i
$343$	5.42861	−	17.7068i	0.293118	−	0.956076i
$344$	9.38661	+	3.37165i	0.506092	+	0.181787i
$345$	2.95670	+	3.23268i	0.159183	+	0.174042i
$346$	−13.4444	−	1.55226i	−0.722777	−	0.0834501i
$347$	−4.59539	−	7.95946i	−0.246694	−	0.427286i	0.715913	−	0.698190i	$-0.246011\pi$
$347$	−4.59539	−	7.95946i	−0.246694	−	0.427286i	−0.962606	+	0.270904i	$0.912677\pi$
$348$	−11.1905	+	18.8281i	−0.599876	+	1.00929i
$349$	−22.1330			−1.18475			−0.592377	−	0.805661i	$-0.701810\pi$
$349$	−22.1330			−1.18475			−0.592377	+	0.805661i	$0.701810\pi$
$350$	−11.9553	+	13.1536i	−0.639037	+	0.703090i
$351$	−8.66898	−	11.3629i	−0.462716	−	0.606507i
$352$	4.27602	−	6.60206i	0.227913	−	0.351891i
$353$	−9.28947	+	5.36328i	−0.494429	+	0.285458i	−0.726410	−	0.687262i	$-0.758813\pi$
$353$	−9.28947	+	5.36328i	−0.494429	+	0.285458i	0.231981	+	0.972720i	$0.425479\pi$
$354$	−3.15719	+	7.04507i	−0.167803	+	0.374441i
$355$	−1.96474	−	1.13434i	−0.104278	−	0.0602047i
$356$	−4.69330	+	1.41948i	−0.248745	+	0.0752325i
$357$	−21.3777	+	15.9724i	−1.13143	+	0.845349i
$358$	23.5676	+	17.4939i	1.24559	+	0.924584i
$359$	1.80247	−	3.12196i	0.0951305	−	0.164771i	−0.814533	−	0.580118i	$-0.803007\pi$
$359$	1.80247	−	3.12196i	0.0951305	−	0.164771i	0.909663	+	0.415347i	$0.136340\pi$
$360$	1.78200	−	3.84525i	0.0939197	−	0.202662i
$361$	−6.42101	−	11.1215i	−0.337948	−	0.585342i
$362$	8.35054	−	3.61601i	0.438895	−	0.190053i
$363$	14.9725	+	4.73606i	0.785851	+	0.248579i
$364$	9.57661	+	10.9600i	0.501951	+	0.574459i
$365$			4.98218i			0.260779i
$366$	−11.9605	+	1.22774i	−0.625187	+	0.0641749i
$367$	−13.0134	+	7.51328i	−0.679293	+	0.392190i	−0.799589	−	0.600548i	$-0.794949\pi$
$367$	−13.0134	+	7.51328i	−0.679293	+	0.392190i	0.120295	+	0.992738i	$0.461616\pi$
$368$	−18.1525	−	8.98897i	−0.946263	−	0.468582i
$369$	7.25407	+	15.6320i	0.377632	+	0.813769i
$370$	3.09148	−	4.16479i	0.160718	−	0.216517i
$371$	−5.71454	−	12.6455i	−0.296684	−	0.656520i
$372$	23.9528	+	0.303204i	1.24190	+	0.0157204i
$373$	−1.32846	+	2.30096i	−0.0687850	+	0.119139i	−0.898367	−	0.439246i	$-0.855246\pi$
$373$	−1.32846	+	2.30096i	−0.0687850	+	0.119139i	0.829582	+	0.558385i	$0.188579\pi$
$374$	11.3757	+	1.31341i	0.588223	+	0.0679148i
$375$	8.23691	−	1.81807i	0.425352	−	0.0938848i
$376$	−9.25306	−	10.9333i	−0.477190	−	0.563843i
$377$			17.3909i			0.895679i
$378$	−11.1313	+	15.9403i	−0.572531	+	0.819883i
$379$			17.7150i			0.909957i	0.890502	+	0.454979i	$0.150353\pi$
$379$			17.7150i			0.909957i	−0.890502	+	0.454979i	$0.849647\pi$
$380$	−2.41365	−	0.564879i	−0.123818	−	0.0289777i
$381$	2.55772	−	0.564546i	0.131036	−	0.0289226i
$382$	−2.84405	+	24.6329i	−0.145514	+	1.26033i
$383$	−16.4609	+	28.5111i	−0.841111	+	1.45685i	0.0478445	+	0.998855i	$0.484765\pi$
$383$	−16.4609	+	28.5111i	−0.841111	+	1.45685i	−0.888956	+	0.457993i	$0.848569\pi$
$384$	−1.24940	+	19.5560i	−0.0637583	+	0.997965i
$385$	1.82846	+	0.181910i	0.0931869	+	0.00927101i
$386$	−2.48130	−	1.84184i	−0.126295	−	0.0937473i
$387$	4.45301	+	9.59592i	0.226359	+	0.487788i
$388$	0.719813	−	0.767271i	0.0365430	−	0.0389523i
$389$	−5.90821	+	3.41111i	−0.299558	+	0.172950i	−0.642244	−	0.766500i	$-0.721997\pi$
$389$	−5.90821	+	3.41111i	−0.299558	+	0.172950i	0.342686	+	0.939450i	$0.388663\pi$
$390$	−0.343619	−	3.34751i	−0.0173998	−	0.169508i
$391$		−	29.4894i		−	1.49134i
$392$	10.2331	−	16.9494i	0.516852	−	0.856075i
$393$	−10.9824	−	3.47394i	−0.553991	−	0.175237i
$394$	3.52751	+	8.14615i	0.177713	+	0.410397i
$395$	0.532254	+	0.921890i	0.0267806	+	0.0463853i
$396$	8.16901	−	1.69494i	0.410508	−	0.0851740i
$397$	10.4221	−	18.0516i	0.523069	−	0.905982i	−0.476571	−	0.879136i	$-0.658120\pi$
$397$	10.4221	−	18.0516i	0.523069	−	0.905982i	0.999640	−	0.0268459i	$-0.00854633\pi$
$398$	0.729560	−	0.982853i	0.0365695	−	0.0492660i
$399$	10.4495	+	4.48615i	0.523130	+	0.224588i
$400$	−15.8170	+	10.5310i	−0.790852	+	0.526551i
$401$	3.31292	+	1.91271i	0.165439	+	0.0955164i	0.580434	−	0.814308i	$-0.302883\pi$
$401$	3.31292	+	1.91271i	0.165439	+	0.0955164i	−0.414994	+	0.909824i	$0.636216\pi$
$402$	24.0157	+	10.7624i	1.19779	+	0.536782i
$403$	16.4721	−	9.51017i	0.820534	−	0.473735i
$404$	−7.33586	+	31.3452i	−0.364972	+	1.55948i
$405$	4.22976	−	1.52177i	0.210178	−	0.0756175i
$406$	22.5336	−	7.20542i	1.11832	−	0.357599i
$407$	10.2105			0.506118
$408$	−26.3205	+	11.0040i	−1.30306	+	0.544779i
$409$	1.93456	+	3.35075i	0.0956576	+	0.165684i	0.909883	−	0.414865i	$-0.136171\pi$
$409$	1.93456	+	3.35075i	0.0956576	+	0.165684i	−0.814225	+	0.580549i	$0.802838\pi$
$410$	−0.465381	+	4.03076i	−0.0229836	+	0.199065i
$411$	−14.2518	−	15.5821i	−0.702989	−	0.768607i
$412$	3.59255	−	1.08656i	0.176992	−	0.0535310i
$413$	7.59884	−	3.43395i	0.373914	−	0.168974i
$414$	−6.74886	−	20.3974i	−0.331689	−	1.00248i
$415$	5.19774	+	3.00092i	0.255147	+	0.147309i
$416$	7.08066	+	13.8549i	0.347158	+	0.679293i
$417$	0.0808186	−	0.0178385i	0.00395770	−	0.000873554i
$418$	−1.93910	−	4.47802i	−0.0948447	−	0.219027i
$419$	13.5133			0.660170			0.330085	−	0.943951i	$-0.392923\pi$
$419$	13.5133			0.660170			0.330085	+	0.943951i	$0.392923\pi$
$420$	−4.19502	+	1.83217i	−0.204696	+	0.0894006i
$421$	11.3825			0.554749			0.277374	−	0.960762i	$-0.410536\pi$
$421$	11.3825			0.554749			0.277374	+	0.960762i	$0.410536\pi$
$422$	−2.19401	−	5.06669i	−0.106803	−	0.246642i
$423$	1.35213	−	15.1319i	0.0657430	−	0.735736i
$424$	−2.63768	−	14.5985i	−0.128097	−	0.708965i
$425$	−23.9575	−	13.8319i	−1.16211	−	0.670944i
$426$	6.51792	+	9.01712i	0.315794	+	0.436881i
$427$	10.5488	+	7.57490i	0.510490	+	0.366575i
$428$	4.21420	+	13.9336i	0.203701	+	0.673507i
$429$	4.88819	−	4.47087i	0.236004	−	0.215856i
$430$	−0.285681	+	2.47434i	−0.0137768	+	0.119323i
$431$	12.9623	+	22.4513i	0.624370	+	1.08144i	0.988662	+	0.150155i	$0.0479774\pi$
$431$	12.9623	+	22.4513i	0.624370	+	1.08144i	−0.364293	+	0.931284i	$0.618689\pi$
$432$	−15.6872	+	13.6350i	−0.754750	+	0.656012i
$433$	23.3825			1.12369			0.561845	−	0.827242i	$-0.310092\pi$
$433$	23.3825			1.12369			0.561845	+	0.827242i	$0.310092\pi$
$434$	−19.1471	−	17.4028i	−0.919091	−	0.835360i
$435$	−5.21511	−	1.64963i	−0.250046	−	0.0790939i
$436$	3.58709	+	0.839505i	0.171791	+	0.0402050i
$437$	−10.8830	+	6.28330i	−0.520604	+	0.300571i
$438$	9.99229	−	22.2971i	0.477450	−	1.06540i
$439$	−15.3054	−	8.83658i	−0.730487	−	0.421747i	0.0881133	−	0.996110i	$-0.471916\pi$
$439$	−15.3054	−	8.83658i	−0.730487	−	0.421747i	−0.818600	+	0.574364i	$0.805250\pi$
$440$	1.84871	+	0.664053i	0.0881338	+	0.0316575i
$441$	20.4171	−	4.91328i	0.972245	−	0.233966i
$442$	−13.5011	+	18.1884i	−0.642180	+	0.865136i
$443$	−17.5681	+	30.4288i	−0.834685	+	1.44572i	0.0596013	+	0.998222i	$0.481017\pi$
$443$	−17.5681	+	30.4288i	−0.834685	+	1.44572i	−0.894286	+	0.447495i	$0.852316\pi$
$444$	−22.1885	+	12.4387i	−1.05302	+	0.590316i
$445$	−0.612252	−	1.06045i	−0.0290235	−	0.0502702i
$446$	−13.2072	−	30.4997i	−0.625380	−	1.44420i
$447$	1.19822	−	3.78801i	0.0566737	−	0.179167i
$448$	15.0182	−	14.9148i	0.709546	−	0.704660i
$449$		−	5.52733i		−	0.260851i	−0.991458	−	0.130425i	$-0.958366\pi$
$449$		−	5.52733i		−	0.260851i	0.991458	−	0.130425i	$-0.0416343\pi$
$450$	−19.7366	−	4.08448i	−0.930392	−	0.192544i
$451$	−6.91742	+	3.99377i	−0.325728	+	0.188059i
$452$	−14.9839	−	14.0571i	−0.704784	−	0.661191i
$453$	15.3554	+	16.7887i	0.721458	+	0.788800i
$454$	−21.7662	−	16.1568i	−1.02154	−	0.758277i
$455$	−2.12006	+	2.95238i	−0.0993899	+	0.138410i
$456$	9.66909	+	7.36889i	0.452797	+	0.345080i
$457$	−11.9761	+	20.7432i	−0.560219	+	0.970327i	0.437258	+	0.899336i	$0.355950\pi$
$457$	−11.9761	+	20.7432i	−0.560219	+	0.970327i	−0.997477	+	0.0709914i	$0.977384\pi$
$458$	1.86147	−	16.1226i	0.0869808	−	0.753358i
$459$	−27.9231	−	11.6572i	−1.30334	−	0.544110i
$460$	1.15275	−	4.92553i	0.0537471	−	0.229654i
$461$			2.99679i			0.139574i	0.997562	+	0.0697871i	$0.0222320\pi$
$461$			2.99679i			0.139574i	−0.997562	+	0.0697871i	$0.977768\pi$
$462$	−7.81821	−	4.48129i	−0.363736	−	0.208488i
$463$			22.4152i			1.04172i	0.853642	+	0.520861i	$0.174389\pi$
$463$			22.4152i			1.04172i	−0.853642	+	0.520861i	$0.825611\pi$
$464$	25.2395	−	1.61259i	1.17172	−	0.0748626i
$465$	1.28939	+	5.84167i	0.0597939	+	0.270901i
$466$	28.4031	+	3.27935i	1.31575	+	0.151913i
$467$	6.03065	−	10.4454i	0.279065	−	0.483355i	−0.692088	−	0.721814i	$-0.743309\pi$
$467$	6.03065	−	10.4454i	0.279065	−	0.483355i	0.971153	+	0.238459i	$0.0766421\pi$
$468$	−5.17596	+	15.6705i	−0.239259	+	0.724370i
$469$	−11.7059	−	25.9034i	−0.540527	−	1.19611i
$470$	2.13199	−	2.87219i	0.0983414	−	0.132484i
$471$	10.7482	−	9.83059i	0.495250	−	0.452969i
$472$	8.77243	−	1.58502i	0.403784	−	0.0729564i
$473$	−4.24635	+	2.45163i	−0.195248	+	0.112726i
$474$	−0.533088	−	5.19330i	−0.0244855	−	0.238536i
$475$			11.7886i			0.540898i
$476$	29.1607	+	9.95761i	1.33658	+	0.456406i
$477$	9.04895	−	12.8724i	0.414323	−	0.589386i
$478$	8.96461	−	3.88192i	0.410032	−	0.177555i
$479$	6.70352	+	11.6108i	0.306292	+	0.530513i	0.977548	−	0.210713i	$-0.0675784\pi$
$479$	6.70352	+	11.6108i	0.306292	+	0.530513i	−0.671256	+	0.741225i	$0.734245\pi$
$480$	−4.82638	+	0.809095i	−0.220293	+	0.0369300i
$481$	−10.0987	+	17.4915i	−0.460461	+	0.797542i
$482$	9.16001	+	6.79937i	0.417227	+	0.309703i
$483$	−9.15487	+	21.3243i	−0.416561	+	0.970288i
$484$	−5.24946	−	17.3566i	−0.238612	−	0.788934i
$485$	0.227534	+	0.131367i	0.0103318	+	0.00596507i
$486$	−21.9819	−	1.67272i	−0.997117	−	0.0758762i
$487$	−10.5727	+	6.10416i	−0.479095	+	0.276606i	−0.720039	−	0.693933i	$-0.755876\pi$
$487$	−10.5727	+	6.10416i	−0.479095	+	0.276606i	0.240944	+	0.970539i	$0.422543\pi$
$488$	8.96888	+	10.5975i	0.406002	+	0.479728i
$489$	6.45640	−	20.4111i	0.291969	−	0.923023i
$490$	4.70380	+	1.52375i	0.212496	+	0.0688359i
$491$	39.8981			1.80058			0.900288	−	0.435294i	$-0.143356\pi$
$491$	39.8981			1.80058			0.900288	+	0.435294i	$0.143356\pi$
$492$	10.1669	−	17.1058i	0.458358	−	0.771190i
$493$	18.4096	+	31.8864i	0.829126	+	1.43609i
$494$	9.58906	+	1.10713i	0.431432	+	0.0498121i
$495$	0.877029	+	1.88993i	0.0394195	+	0.0849462i
$496$	−15.3295	−	23.0242i	−0.688316	−	1.03382i
$497$	1.18974	−	11.9586i	0.0533672	−	0.536417i
$498$	−17.2432	−	23.8549i	−0.772687	−	1.06896i
$499$	7.33971	+	4.23758i	0.328571	+	0.189700i	0.655206	−	0.755450i	$-0.272582\pi$
$499$	7.33971	+	4.23758i	0.328571	+	0.189700i	−0.326636	+	0.945150i	$0.605915\pi$
$500$	−7.10346	−	6.66410i	−0.317677	−	0.298028i
$501$	−0.883079	−	4.00086i	−0.0394531	−	0.178745i
$502$	−26.4838	+	11.4682i	−1.18203	+	0.511852i
$503$	−42.5519			−1.89730			−0.948648	−	0.316334i	$-0.897548\pi$
$503$	−42.5519			−1.89730			−0.948648	+	0.316334i	$0.897548\pi$
$504$	22.4489	+	0.213918i	0.999955	+	0.00952869i
$505$	−8.03941			−0.357749
$506$	9.13828	−	3.95712i	0.406246	−	0.175916i
$507$	−2.02881	−	9.19169i	−0.0901027	−	0.408217i
$508$	−2.20576	−	2.06933i	−0.0978649	−	0.0918117i
$509$	−14.9018	−	8.60356i	−0.660511	−	0.381346i	0.131961	−	0.991255i	$-0.457873\pi$
$509$	−14.9018	−	8.60356i	−0.660511	−	0.381346i	−0.792472	+	0.609909i	$0.791206\pi$
$510$	−4.17361	−	5.77392i	−0.184810	−	0.255673i
$511$	−24.0498	+	10.8682i	−1.06390	+	0.480781i
$512$	19.4511	−	11.5609i	0.859626	−	0.510924i
$513$	1.64751	+	12.7887i	0.0727392	+	0.564636i
$514$	−38.2267	−	4.41356i	−1.68611	−	0.194674i
$515$	0.468656	+	0.811735i	0.0206514	+	0.0357693i
$516$	6.24108	−	10.5006i	0.274748	−	0.462265i
$517$	7.04155			0.309687
$518$	26.8479	+	5.83790i	1.17963	+	0.256503i
$519$	−4.99896	+	15.8036i	−0.219430	+	0.693701i
$520$	−2.96603	+	2.51021i	−0.130069	+	0.110080i
$521$	9.47744	−	5.47180i	0.415214	−	0.239724i	−0.277814	−	0.960635i	$-0.589610\pi$
$521$	9.47744	−	5.47180i	0.415214	−	0.239724i	0.693028	+	0.720911i	$0.256276\pi$
$522$	20.0311	+	17.8422i	0.876737	+	0.780932i
$523$	4.79287	+	2.76716i	0.209578	+	0.121000i	0.601115	−	0.799162i	$-0.294723\pi$
$523$	4.79287	+	2.76716i	0.209578	+	0.121000i	−0.391537	+	0.920162i	$0.628057\pi$
$524$	3.85053	+	12.7312i	0.168211	+	0.556164i
$525$	13.0300	+	17.4396i	0.568676	+	0.761125i
$526$	−4.09362	−	3.03864i	−0.178490	−	0.132491i
$527$	20.1344	−	34.8739i	0.877069	−	1.51913i
$528$	−6.94185	−	6.67967i	−0.302105	−	0.290696i
$529$	−1.32230	−	2.29030i	−0.0574915	−	0.0995782i
$530$	3.39968	−	1.47216i	0.147673	−	0.0639464i
$531$	7.73521	+	5.43764i	0.335679	+	0.235974i
$532$	−2.53842	−	12.8833i	−0.110055	−	0.558563i
$533$		−	15.8001i		−	0.684379i
$534$	0.613212	+	5.97386i	0.0265363	+	0.258514i
$535$	−3.14830	+	1.81767i	−0.136113	+	0.0785848i
$536$	−5.40311	−	29.9040i	−0.233379	−	1.29166i
$537$	26.5256	−	24.2610i	1.14466	−	1.04694i
$538$	−22.0551	+	29.7123i	−0.950863	+	1.28099i
$539$	3.11052	+	9.22309i	0.133980	+	0.397267i
$540$	−4.20823	−	3.03858i	−0.181093	−	0.130760i
$541$	−6.26409	+	10.8497i	−0.269314	+	0.466466i	−0.968685	−	0.248293i	$-0.920130\pi$
$541$	−6.26409	+	10.8497i	−0.269314	+	0.466466i	0.699371	+	0.714759i	$0.253464\pi$
$542$	−32.3992	−	3.74073i	−1.39167	−	0.160678i
$543$	−2.40213	−	10.8830i	−0.103085	−	0.467035i
$544$	27.6488	+	17.9076i	1.18543	+	0.767782i
$545$			0.920019i			0.0394093i
$546$	15.4094	−	8.96101i	0.659461	−	0.383496i
$547$		−	37.4911i		−	1.60300i	−0.597992	−	0.801502i	$-0.704034\pi$
$547$		−	37.4911i		−	1.60300i	0.597992	−	0.801502i	$-0.295966\pi$
$548$	−5.55644	+	23.7419i	−0.237359	+	1.01420i
$549$	−1.31061	+	14.6671i	−0.0559354	+	0.625978i
$550$	1.07146	−	9.28010i	0.0456871	−	0.395705i
$551$	7.84505	−	13.5880i	0.334210	−	0.578869i
$552$	−15.0377	+	19.7317i	−0.640045	+	0.839836i
$553$	−3.28905	+	4.58030i	−0.139864	+	0.194774i
$554$	−23.0417	−	17.1036i	−0.978947	−	0.726661i
$555$	−4.28733	−	4.68752i	−0.181987	−	0.198974i
$556$	−0.0696975	−	0.0653865i	−0.00295583	−	0.00277301i
$557$	−26.0411	+	15.0348i	−1.10340	+	0.637046i	−0.937111	−	0.349031i	$-0.886511\pi$
$557$	−26.0411	+	15.0348i	−1.10340	+	0.637046i	−0.166286	+	0.986078i	$0.553177\pi$
$558$	5.94559	−	28.7297i	0.251697	−	1.21622i
$559$		−	9.69912i		−	0.410229i
$560$	4.48138	+	2.80309i	0.189373	+	0.118452i
$561$	4.22976	−	13.3719i	0.178581	−	0.564560i
$562$	−15.5461	−	35.9010i	−0.655773	−	1.51439i
$563$	3.41956	+	5.92285i	0.144117	+	0.249618i	0.929043	−	0.369971i	$-0.120632\pi$
$563$	3.41956	+	5.92285i	0.144117	+	0.249618i	−0.784926	+	0.619589i	$0.787299\pi$
$564$	−15.3020	+	8.57820i	−0.644329	+	0.361207i
$565$	2.56544	−	4.44348i	0.107929	−	0.186939i
$566$	14.6420	−	19.7255i	0.615449	−	0.829124i
$567$	16.5727	+	17.0981i	0.695988	+	0.718053i
$568$	4.34308	−	12.0910i	0.182232	−	0.507329i
$569$	29.0006	+	16.7435i	1.21577	+	0.701924i	0.964010	−	0.265866i	$-0.0856578\pi$
$569$	29.0006	+	16.7435i	1.21577	+	0.701924i	0.251759	+	0.967790i	$0.418991\pi$
$570$	−1.24158	+	2.77050i	−0.0520040	+	0.116044i
$571$	−24.2464	+	13.9986i	−1.01468	+	0.585825i	−0.912558	−	0.408947i	$-0.865896\pi$
$571$	−24.2464	+	13.9986i	−1.01468	+	0.585825i	−0.102121	+	0.994772i	$0.532563\pi$
$572$	−7.44798	−	1.74309i	−0.311416	−	0.0728821i
$573$	28.9553	+	9.15909i	1.20963	+	0.382627i
$574$	−20.4723	+	6.54630i	−0.854498	+	0.273237i
$575$	−24.0570			−1.00324
$576$	23.2226	+	6.05882i	0.967610	+	0.252451i
$577$	−18.8181	−	32.5939i	−0.783409	−	1.35690i	−0.929945	−	0.367698i	$-0.880146\pi$
$577$	−18.8181	−	32.5939i	−0.783409	−	1.35690i	0.146537	−	0.989205i	$-0.453187\pi$
$578$	−2.74298	+	23.7575i	−0.114093	+	0.988180i
$579$	−2.79273	+	2.55431i	−0.116062	+	0.106154i
$580$	1.82846	+	6.04552i	0.0759227	+	0.251027i
$581$	−3.14747	+	31.6366i	−0.130579	+	1.31251i
$582$	−0.754832	−	1.04426i	−0.0312888	−	0.0432860i
$583$	6.31596	+	3.64652i	0.261580	+	0.151023i
$584$	−27.7641	+	5.01647i	−1.14889	+	0.207583i
$585$	−4.10503	−	0.366812i	−0.169722	−	0.0151658i
$586$	11.2209	+	25.9127i	0.463531	+	1.07044i
$587$	−19.7791			−0.816373			−0.408186	−	0.912899i	$-0.633839\pi$
$587$	−19.7791			−0.816373			−0.408186	+	0.912899i	$0.633839\pi$
$588$	−17.9953	−	16.2533i	−0.742112	−	0.670276i
$589$	−17.1601			−0.707071
$590$	0.884640	+	2.04292i	0.0364201	+	0.0841057i
$591$	10.6167	−	2.34333i	0.436711	−	0.0963919i
$592$	26.3218	+	13.0344i	1.08182	+	0.535709i
$593$	−19.5061	−	11.2619i	−0.801020	−	0.462469i	0.0428074	−	0.999083i	$-0.486370\pi$
$593$	−19.5061	−	11.2619i	−0.801020	−	0.462469i	−0.843828	+	0.536614i	$0.819703\pi$
$594$	−0.134576	−	10.2171i	−0.00552171	−	0.419215i
$595$	−0.761825	+	7.65743i	−0.0312318	+	0.313924i
$596$	−4.39118	+	1.32811i	−0.179870	+	0.0544013i
$597$	−1.01177	−	1.10621i	−0.0414091	−	0.0452742i
$598$	−2.25932	+	19.5684i	−0.0923903	+	0.800210i
$599$	13.3658	+	23.1503i	0.546113	+	0.945895i	0.998536	+	0.0540915i	$0.0172263\pi$
$599$	13.3658	+	23.1503i	0.546113	+	0.945895i	−0.452423	+	0.891803i	$0.649440\pi$
$600$	8.97687	+	21.4718i	0.366479	+	0.876582i
$601$	31.1478			1.27055			0.635273	−	0.772288i	$-0.280888\pi$
$601$	31.1478			1.27055			0.635273	+	0.772288i	$0.280888\pi$
$602$	−12.5672	+	4.01854i	−0.512202	+	0.163783i
$603$	18.5362	−	26.3682i	0.754851	−	1.07380i
$604$	5.98669	−	25.5804i	0.243595	−	1.04085i
$605$	3.92171	−	2.26420i	0.159440	−	0.0920529i
$606$	35.9794	+	16.1239i	1.46156	+	0.654989i
$607$	10.8934	+	6.28933i	0.442151	+	0.255276i	0.704510	−	0.709694i	$-0.251167\pi$
$607$	10.8934	+	6.28933i	0.442151	+	0.255276i	−0.262358	+	0.964970i	$0.584500\pi$
$608$	0.717627	−	14.0193i	0.0291036	−	0.568558i
$609$	−3.41329	−	28.7727i	−0.138313	−	1.16593i
$610$	−2.06651	+	2.78398i	−0.0836707	+	0.112720i
$611$	−6.96442	+	12.0627i	−0.281750	+	0.488006i
$612$	7.09827	+	34.2111i	0.286931	+	1.38290i
$613$	−2.27131	−	3.93403i	−0.0917374	−	0.158894i	0.816505	−	0.577339i	$-0.195909\pi$
$613$	−2.27131	−	3.93403i	−0.0917374	−	0.158894i	−0.908242	+	0.418445i	$0.862575\pi$
$614$	7.95344	+	18.3671i	0.320975	+	0.741234i
$615$	4.73806	+	1.49873i	0.191057	+	0.0604348i
$616$	0.827315	+	10.3726i	0.0333335	+	0.417924i
$617$		−	35.4652i		−	1.42777i	−0.700261	−	0.713887i	$-0.746933\pi$
$617$		−	35.4652i		−	1.42777i	0.700261	−	0.713887i	$-0.253067\pi$
$618$	−0.469390	−	4.57276i	−0.0188816	−	0.183944i
$619$	35.9030	−	20.7286i	1.44306	−	0.833153i	0.445011	−	0.895525i	$-0.353200\pi$
$619$	35.9030	−	20.7286i	1.44306	−	0.833153i	0.998053	+	0.0623719i	$0.0198665\pi$
$620$	4.72622	−	5.03782i	0.189810	−	0.202324i
$621$	−26.0979	+	3.36206i	−1.04727	+	0.134915i
$622$	27.8836	+	20.6976i	1.11803	+	0.829900i
$623$	3.78339	−	5.26873i	0.151578	−	0.211087i
$624$	18.3086	−	5.28542i	0.732931	−	0.211586i
$625$	−10.6601	+	18.4639i	−0.426405	+	0.738556i
$626$	0.00844472	−	0.0731414i	0.000337519	−	0.00292332i
$627$	−5.83608	+	1.28815i	−0.233071	+	0.0514439i
$628$	−16.3767	−	3.83271i	−0.653500	−	0.152942i
$629$			42.7609i			1.70499i
$630$	1.22551	+	5.47089i	0.0488256	+	0.217966i
$631$		−	22.2919i		−	0.887428i	−0.896168	−	0.443714i	$-0.853661\pi$
$631$		−	22.2919i		−	0.887428i	0.896168	−	0.443714i	$-0.146339\pi$
$632$	−4.60149	+	3.89432i	−0.183037	+	0.154908i
$633$	−6.60328	+	1.45749i	−0.262457	+	0.0579301i
$634$	−9.52021	−	1.09918i	−0.378096	−	0.0436540i
$635$	0.377656	−	0.654119i	0.0149868	−	0.0259579i
$636$	−18.1675	−	0.229970i	−0.720386	−	0.00911891i
$637$	−18.8763	−	3.79350i	−0.747908	−	0.150304i
$638$	−7.41070	+	9.98359i	−0.293393	+	0.395254i
$639$	12.3607	−	5.73600i	0.488980	−	0.226913i
$640$	3.91810	+	4.07186i	0.154876	+	0.160954i
$641$	29.5411	−	17.0555i	1.16680	−	0.673653i	0.213877	−	0.976861i	$-0.431391\pi$
$641$	29.5411	−	17.0555i	1.16680	−	0.673653i	0.952925	+	0.303207i	$0.0980575\pi$
$642$	17.7354	−	1.82052i	0.699959	−	0.0718502i
$643$		−	24.2299i		−	0.955533i	−0.878487	−	0.477766i	$-0.841447\pi$
$643$		−	24.2299i		−	0.955533i	0.878487	−	0.477766i	$-0.158553\pi$
$644$	26.2910	−	5.18015i	1.03601	−	0.204127i
$645$	2.90852	+	0.920019i	0.114523	+	0.0362257i
$646$	18.7536	−	8.12080i	0.737849	−	0.319509i
$647$	−0.714092	−	1.23684i	−0.0280738	−	0.0486253i	0.851647	−	0.524116i	$-0.175604\pi$
$647$	−0.714092	−	1.23684i	−0.0280738	−	0.0486253i	−0.879721	+	0.475490i	$0.842271\pi$
$648$	12.7392	+	22.0389i	0.500444	+	0.865769i
$649$	−2.19125	+	3.79535i	−0.0860140	+	0.148981i
$650$	14.8378	+	11.0139i	0.581987	+	0.432002i
$651$	−25.3860	+	18.9672i	−0.994955	+	0.743383i
$652$	−23.6612	+	7.15630i	−0.926644	+	0.280262i
$653$	−4.35426	−	2.51393i	−0.170395	−	0.0983778i	0.412377	−	0.911013i	$-0.364699\pi$
$653$	−4.35426	−	2.51393i	−0.170395	−	0.0983778i	−0.582772	+	0.812636i	$0.698032\pi$
$654$	1.84520	−	4.11743i	0.0721529	−	0.161004i
$655$	−2.87661	+	1.66081i	−0.112398	+	0.0648933i
$656$	−22.9307	+	1.46508i	−0.895295	+	0.0572017i
$657$	−24.4814	−	17.2097i	−0.955109	−	0.671416i
$658$	18.5153	+	4.02603i	0.721801	+	0.156951i
$659$	−19.7930			−0.771025			−0.385512	−	0.922703i	$-0.625975\pi$
$659$	−19.7930			−0.771025			−0.385512	+	0.922703i	$0.625975\pi$
$660$	1.22919	−	2.06812i	0.0478463	−	0.0805015i
$661$	11.3306	+	19.6252i	0.440709	+	0.763331i	0.997742	−	0.0671595i	$-0.0213936\pi$
$661$	11.3306	+	19.6252i	0.440709	+	0.763331i	−0.557033	+	0.830490i	$0.688060\pi$
$662$	−25.1361	−	2.90215i	−0.976941	−	0.112795i
$663$	18.7236	+	20.4713i	0.727165	+	0.795039i
$664$	−11.4897	+	31.9870i	−0.445885	+	1.24134i
$665$	2.98828	−	1.35042i	0.115880	−	0.0523669i
$666$	9.78613	+	29.5771i	0.379205	+	1.14609i
$667$	27.7290	+	16.0094i	1.07367	+	0.619885i
$668$	−3.23691	+	3.45032i	−0.125240	+	0.133497i
$669$	−39.7495	+	8.77360i	−1.53680	+	0.339207i
$670$	6.96403	−	3.01562i	0.269044	−	0.116503i
$671$	−6.82530			−0.263488
$672$	−14.4340	−	21.5328i	−0.556803	−	0.830644i
$673$	−11.2766			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$673$	−11.2766			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$674$	−9.20584	+	3.98638i	−0.354596	+	0.153550i
$675$	−9.50972	+	22.7792i	−0.366029	+	0.876770i
$676$	−7.43656	+	7.92686i	−0.286022	+	0.304879i
$677$	8.73729	+	5.04448i	0.335801	+	0.193875i	0.658414	−	0.752656i	$-0.271228\pi$
$677$	8.73729	+	5.04448i	0.335801	+	0.193875i	−0.322612	+	0.946531i	$0.604561\pi$
$678$	−20.3932	+	14.7410i	−0.783197	+	0.566124i
$679$	−0.137782	+	1.38491i	−0.00528760	+	0.0531480i
$680$	−2.78100	+	7.74223i	−0.106646	+	0.296901i
$681$	−24.4981	+	22.4067i	−0.938770	+	0.858625i
$682$	13.5086	+	1.55967i	0.517272	+	0.0597229i
$683$	−3.11743	−	5.39955i	−0.119285	−	0.206608i	0.800199	−	0.599734i	$-0.204727\pi$
$683$	−3.11743	−	5.39955i	−0.119285	−	0.206608i	−0.919485	+	0.393126i	$0.871394\pi$
$684$	11.1131	−	9.90894i	0.424919	−	0.378878i
$685$	−6.08933			−0.232662
$686$	2.90558	+	26.0299i	0.110935	+	0.993828i
$687$	−18.9517	−	5.99476i	−0.723052	−	0.228714i
$688$	−14.0764	+	0.899358i	−0.536656	+	0.0342877i
$689$	−12.4936	+	7.21316i	−0.475967	+	0.274799i
$690$	−5.65376	−	2.53369i	−0.215235	−	0.0964559i
$691$	−14.7810	−	8.53381i	−0.562295	−	0.324641i	0.191771	−	0.981440i	$-0.438577\pi$
$691$	−14.7810	−	8.53381i	−0.562295	−	0.324641i	−0.754066	+	0.656798i	$0.771910\pi$
$692$	18.3200	−	5.54087i	0.696423	−	0.210632i
$693$	−7.20985	+	8.35630i	−0.273879	+	0.317429i
$694$	10.4367	+	7.74704i	0.396172	+	0.294074i
$695$	0.0119331	−	0.0206688i	0.000452650	−	0.000784012i
$696$	3.94189	−	30.7232i	0.149417	−	1.16456i
$697$	−16.7256	−	28.9695i	−0.633526	−	1.09730i
$698$	28.7235	−	12.4380i	1.08720	−	0.470787i
$699$	10.5610	−	33.3872i	0.399452	−	1.26282i
$700$	8.12324	−	23.7888i	0.307030	−	0.899131i
$701$			21.4324i			0.809489i	0.914430	+	0.404744i	$0.132640\pi$
$701$			21.4324i			0.809489i	−0.914430	+	0.404744i	$0.867360\pi$
$702$	17.6359	+	9.87470i	0.665623	+	0.372696i
$703$	15.7808	−	9.11104i	0.595183	−	0.343629i
$704$	−1.83913	+	10.9709i	−0.0693147	+	0.413481i
$705$	−2.95670	−	3.23268i	−0.111356	−	0.121750i
$706$	9.04155	−	12.1807i	0.340283	−	0.458425i
$707$	−17.5373	−	38.8075i	−0.659559	−	1.45951i
$708$	0.138192	−	10.9171i	0.00519359	−	0.410289i
$709$	4.27131	−	7.39813i	0.160412	−	0.277843i	−0.774604	−	0.632446i	$-0.782051\pi$
$709$	4.27131	−	7.39813i	0.160412	−	0.277843i	0.935017	+	0.354604i	$0.115384\pi$
$710$	3.18724	+	0.367990i	0.119615	+	0.0138104i
$711$	−6.36852	−	0.569070i	−0.238838	−	0.0213418i
$712$	5.29310	−	4.47964i	0.198367	−	0.167882i
$713$		−	35.0186i		−	1.31146i
$714$	18.7673	−	32.7420i	0.702347	−	1.22534i
$715$		−	1.91026i		−	0.0714396i
$716$	−40.4162	−	9.45880i	−1.51042	−	0.353492i
$717$	−2.57878	−	11.6833i	−0.0963061	−	0.436322i
$718$	−0.584734	+	5.06450i	−0.0218221	+	0.189005i
$719$	13.7366	−	23.7924i	0.512287	−	0.887308i	−0.487611	−	0.873061i	$-0.662132\pi$
$719$	13.7366	−	23.7924i	0.512287	−	0.887308i	0.999899	−	0.0142470i	$-0.00453511\pi$
$720$	−0.151713	+	5.99165i	−0.00565402	+	0.223296i
$721$	−2.89604	+	4.03301i	−0.107854	+	0.150197i
$722$	14.5829	+	10.8247i	0.542719	+	0.402854i
$723$	10.3097	−	9.42953i	0.383422	−	0.350688i
$724$	−8.80495	+	9.38546i	−0.327233	+	0.348808i
$725$	26.0123	−	15.0182i	0.966074	−	0.557763i
$726$	−22.0922	+	2.26775i	−0.819920	+	0.0841641i
$727$			45.7930i			1.69837i	0.528096	+	0.849185i	$0.322906\pi$
$727$			45.7930i			1.69837i	−0.528096	+	0.849185i	$0.677094\pi$
$728$	−18.5873	−	8.84172i	−0.688892	−	0.327696i
$729$	−7.13303	+	26.0407i	−0.264186	+	0.964472i
$730$	−2.79982	−	6.46569i	−0.103626	−	0.239306i
$731$	−10.2672	−	17.7834i	−0.379747	−	0.657741i
$732$	14.8320	−	8.31475i	0.548207	−	0.307322i
$733$	21.6466	−	37.4930i	0.799535	−	1.38483i	−0.120385	−	0.992727i	$-0.538413\pi$
$733$	21.6466	−	37.4930i	0.799535	−	1.38483i	0.919919	−	0.392107i	$-0.128254\pi$
$734$	12.6661	−	17.0636i	0.467514	−	0.629828i
$735$	2.92811	−	5.30071i	0.108005	−	0.195520i
$736$	28.6091	+	1.46446i	1.05455	+	0.0539807i
$737$	12.9378	+	7.46966i	0.476571	+	0.275148i
$738$	−18.1987	−	16.2101i	−0.669905	−	0.596702i
$739$	−4.48246	+	2.58795i	−0.164890	+	0.0951993i	−0.580174	−	0.814492i	$-0.697016\pi$
$739$	−4.48246	+	2.58795i	−0.164890	+	0.0951993i	0.415284	+	0.909692i	$0.363682\pi$
$740$	−1.67153	+	7.14223i	−0.0614466	+	0.262553i
$741$	3.56544	−	11.2717i	0.130980	−	0.414077i
$742$	14.5225	+	13.1994i	0.533137	+	0.484567i
$743$	49.5492			1.81778			0.908891	−	0.417034i	$-0.136930\pi$
$743$	49.5492			1.81778			0.908891	+	0.417034i	$0.136930\pi$
$744$	−31.2555	+	13.0672i	−1.14588	+	0.479068i
$745$	−0.572839	−	0.992187i	−0.0209872	−	0.0363509i
$746$	0.430963	−	3.73265i	0.0157787	−	0.136662i
$747$	−32.7002	+	15.1746i	−1.19644	+	0.555211i
$748$	−15.5011	+	4.68828i	−0.566775	+	0.171420i
$749$	−15.6420	−	11.2323i	−0.571544	−	0.410418i
$750$	−9.66787	+	6.98830i	−0.353021	+	0.255177i
$751$	−26.4899	−	15.2939i	−0.966630	−	0.558084i	−0.0684228	−	0.997656i	$-0.521797\pi$
$751$	−26.4899	−	15.2939i	−0.966630	−	0.558084i	−0.898207	+	0.439572i	$0.855130\pi$
$752$	18.1525	+	8.98897i	0.661953	+	0.327794i
$753$	7.61838	+	34.5156i	0.277629	+	1.25782i
$754$	−9.77315	−	22.5694i	−0.355917	−	0.821927i
$755$	6.56086			0.238774
$756$	5.48782	−	26.9422i	0.199590	−	0.979879i
$757$	46.4533			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$757$	46.4533			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$758$	−9.95524	−	22.9899i	−0.361591	−	0.835030i
$759$	−2.62873	−	11.9097i	−0.0954169	−	0.432294i
$760$	3.44980	−	0.623315i	0.125137	−	0.0226100i
$761$	34.1633	+	19.7242i	1.23842	+	0.715002i	0.968771	−	0.247956i	$-0.0797589\pi$
$761$	34.1633	+	19.7242i	1.23842	+	0.715002i	0.269649	+	0.962959i	$0.413092\pi$
$762$	−3.00206	+	2.17000i	−0.108753	+	0.0786109i
$763$	−4.44108	+	2.00694i	−0.160778	+	0.0726563i
$764$	−10.1520	−	33.5659i	−0.367285	−	1.21437i
$765$	−7.91488	+	3.67292i	−0.286163	+	0.132795i
$766$	5.34004	−	46.2511i	0.192943	−	1.67112i
$767$	−4.33449	−	7.50756i	−0.156509	−	0.271082i
$768$	−9.36843	−	26.0813i	−0.338054	−	0.941127i
$769$	39.7256			1.43254			0.716270	−	0.697823i	$-0.245848\pi$
$769$	39.7256			1.43254			0.716270	+	0.697823i	$0.245848\pi$
$770$	−2.47514	+	0.791458i	−0.0891978	+	0.0285222i
$771$	−14.2136	+	44.9346i	−0.511891	+	1.61828i
$772$	4.25520	+	0.995865i	0.153148	+	0.0358420i
$773$	18.9935	−	10.9659i	0.683149	−	0.394416i	−0.117891	−	0.993026i	$-0.537613\pi$
$773$	18.9935	−	10.9659i	0.683149	−	0.394416i	0.801040	+	0.598610i	$0.204280\pi$
$774$	−11.1716	−	9.95079i	−0.401553	−	0.357674i
$775$	−28.4495	−	16.4253i	−1.02194	−	0.590015i
$776$	−0.502967	+	1.40025i	−0.0180554	+	0.0502660i
$777$	13.2749	−	30.9211i	0.476236	−	1.10929i
$778$	5.75054	−	7.74704i	0.206167	−	0.277745i
$779$	−7.12742	+	12.3451i	−0.255366	+	0.442307i
$780$	2.32713	+	4.15117i	0.0833245	+	0.148636i
$781$	3.15799	+	5.46980i	0.113002	+	0.195725i
$782$	16.5721	+	38.2703i	0.592617	+	1.36854i
$783$	26.1203	−	19.9277i	0.933464	−	0.712157i
$784$	−3.75519	+	27.7470i	−0.134114	+	0.990966i
$785$		−	4.20029i		−	0.149915i
$786$	16.2049	−	1.66341i	0.578008	−	0.0593320i
$787$	4.36864	−	2.52223i	0.155725	−	0.0899080i	−0.420112	−	0.907472i	$-0.638009\pi$
$787$	4.36864	−	2.52223i	0.155725	−	0.0899080i	0.575838	+	0.817564i	$0.304676\pi$
$788$	−9.15574	−	8.58944i	−0.326160	−	0.305986i
$789$	−4.60741	+	4.21406i	−0.164028	+	0.150025i
$790$	−1.20881	−	0.897287i	−0.0430076	−	0.0319240i
$791$	27.0457	+	2.69073i	0.961634	+	0.0956714i
$792$	−9.64894	+	6.79035i	−0.342860	+	0.241285i
$793$	6.75054	−	11.6923i	0.239719	−	0.415205i
$794$	−3.38101	+	29.2835i	−0.119987	+	1.03923i
$795$	−0.977959	−	4.43072i	−0.0346846	−	0.157141i
$796$	−0.394466	+	1.68550i	−0.0139815	+	0.0597410i
$797$			28.3335i			1.00362i	0.864977	+	0.501812i	$0.167333\pi$
$797$			28.3335i			1.00362i	−0.864977	+	0.501812i	$0.832667\pi$
$798$	−16.0821	+	0.0503187i	−0.569299	+	0.00178126i
$799$			29.4894i			1.04326i
$800$	14.6087	−	22.5554i	0.516496	−	0.797455i
$801$	7.32571	+	0.654602i	0.258841	+	0.0231292i
$802$	−5.37427	−	0.620500i	−0.189772	−	0.0219106i
$803$	6.93514	−	12.0120i	0.244736	−	0.423895i
$804$	−37.2148	−	0.471079i	−1.31247	−	0.0166137i
$805$	2.75579	+	6.09816i	0.0971288	+	0.214932i
$806$	−16.0325	+	21.5987i	−0.564721	+	0.760783i
$807$	30.5866	+	33.4415i	1.07670	+	1.17720i
$808$	−8.09475	−	44.8011i	−0.284772	−	1.57610i
$809$	17.5088	−	10.1087i	0.615577	−	0.355404i	−0.159568	−	0.987187i	$-0.551010\pi$
$809$	17.5088	−	10.1087i	0.615577	−	0.355404i	0.775145	+	0.631783i	$0.217677\pi$
$810$	−4.63404	+	4.35189i	−0.162824	+	0.152910i
$811$			1.33368i			0.0468317i	0.999726	+	0.0234158i	$0.00745418\pi$
$811$			1.33368i			0.0468317i	−0.999726	+	0.0234158i	$0.992546\pi$
$812$	−25.1941	+	22.0141i	−0.884139	+	0.772543i
$813$	−12.0468	+	38.0845i	−0.422500	+	1.33568i
$814$	−13.2509	+	5.73799i	−0.464443	+	0.201117i
$815$	−3.08666	−	5.34625i	−0.108121	−	0.187271i
$816$	27.9739	−	29.0719i	0.979282	−	1.01772i
$817$	−4.37527	+	7.57819i	−0.153071	+	0.265127i
$818$	−4.39361	−	3.26133i	−0.153619	−	0.114030i
$819$	−7.18412	−	20.6158i	−0.251033	−	0.720375i
$820$	−1.66120	−	5.49251i	−0.0580117	−	0.191807i
$821$	−4.59977	−	2.65568i	−0.160533	−	0.0926838i	0.417581	−	0.908640i	$-0.362878\pi$
$821$	−4.59977	−	2.65568i	−0.160533	−	0.0926838i	−0.578114	+	0.815956i	$0.696211\pi$
$822$	27.2521	+	12.2128i	0.950526	+	0.425971i
$823$	−13.2508	+	7.65035i	−0.461894	+	0.266675i	−0.712840	−	0.701326i	$-0.752592\pi$
$823$	−13.2508	+	7.65035i	−0.461894	+	0.266675i	0.250946	+	0.968001i	$0.419258\pi$
$824$	−4.05167	+	3.42899i	−0.141146	+	0.119455i
$825$	−10.9085	−	3.45056i	−0.379786	−	0.120133i
$826$	−7.93173	+	8.72676i	−0.275980	+	0.303643i
$827$	−0.288306			−0.0100254			−0.00501270	−	0.999987i	$-0.501596\pi$
$827$	−0.288306			−0.0100254			−0.00501270	+	0.999987i	$0.501596\pi$
$828$	20.2211	+	22.6784i	0.702733	+	0.788130i
$829$	20.5551	+	35.6025i	0.713908	+	1.23653i	0.963379	+	0.268143i	$0.0864100\pi$
$829$	20.5551	+	35.6025i	0.713908	+	1.23653i	−0.249471	+	0.968382i	$0.580257\pi$
$830$	−8.43186	−	0.973522i	−0.292674	−	0.0337914i
$831$	−25.9337	+	23.7196i	−0.899629	+	0.822825i
$832$	−16.9750	−	14.0013i	−0.588504	−	0.485408i
$833$	−38.6255	+	13.0266i	−1.33829	+	0.451345i
$834$	−0.0948589	+	0.0685676i	−0.00328469	+	0.00237430i
$835$	−1.02319	−	0.590740i	−0.0354090	−	0.0204434i
$836$	5.03300	+	4.72170i	0.174070	+	0.163303i
$837$	−33.1586	−	13.8429i	−1.14613	−	0.478480i
$838$	−17.5371	+	7.59406i	−0.605810	+	0.262333i
$839$	−25.7705			−0.889695			−0.444848	−	0.895606i	$-0.646742\pi$
$839$	−25.7705			−0.889695			−0.444848	+	0.895606i	$0.646742\pi$
$840$	4.41453	−	4.73519i	0.152316	−	0.163379i
$841$	−10.9772			−0.378523
$842$	−14.7718	+	6.39659i	−0.509070	+	0.220441i
$843$	−46.7888	+	10.3273i	−1.61149	+	0.355693i
$844$	5.69463	+	5.34240i	0.196017	+	0.183893i
$845$	−2.35071	−	1.35718i	−0.0808669	−	0.0466885i
$846$	6.74886	+	20.3974i	0.232031	+	0.701279i
$847$	19.4846	+	13.9916i	0.669497	+	0.480756i
$848$	11.6270	+	17.4631i	0.399271	+	0.599685i
$849$	−20.3059	−	22.2013i	−0.696896	−	0.761945i
$850$	38.8642	+	4.48717i	1.33303	+	0.153909i
$851$	18.5929	+	32.2038i	0.637355	+	1.10393i
$852$	−13.5261	−	8.03924i	−0.463395	−	0.275420i
$853$	−51.4656			−1.76215			−0.881074	−	0.472978i	$-0.843179\pi$
$853$	−51.4656			−1.76215			−0.881074	+	0.472978i	$0.843179\pi$
$854$	−17.9466	−	3.90238i	−0.614122	−	0.133537i
$855$	3.04190	+	2.13838i	0.104031	+	0.0731309i
$856$	−13.2993	−	15.7143i	−0.454560	−	0.537104i
$857$	30.8099	−	17.7881i	1.05245	−	0.607631i	0.129114	−	0.991630i	$-0.458787\pi$
$857$	30.8099	−	17.7881i	1.05245	−	0.607631i	0.923334	+	0.383999i	$0.125453\pi$
$858$	−3.83123	+	8.54914i	−0.130796	+	0.291863i
$859$	44.4334	+	25.6536i	1.51605	+	0.875290i	0.999823	+	0.0188372i	$0.00599642\pi$
$859$	44.4334	+	25.6536i	1.51605	+	0.875290i	0.516225	+	0.856453i	$0.327337\pi$
$860$	−1.01975	−	3.37165i	−0.0347732	−	0.114972i
$861$	3.10106	+	26.1407i	0.105684	+	0.890874i
$862$	−29.4388	−	21.8521i	−1.00269	−	0.744286i
$863$	−5.89152	+	10.2044i	−0.200550	+	0.347362i	−0.948706	−	0.316161i	$-0.897606\pi$
$863$	−5.89152	+	10.2044i	−0.200550	+	0.347362i	0.748156	+	0.663523i	$0.230939\pi$
$864$	12.6959	−	26.5107i	0.431923	−	0.901911i
$865$	2.38989	+	4.13941i	0.0812587	+	0.140744i
$866$	−30.3450	+	13.1402i	−1.03116	+	0.446522i
$867$	27.9263	+	8.83360i	0.948428	+	0.300005i
$868$	34.6282	+	11.8246i	1.17536	+	0.401354i
$869$		−	2.96357i		−	0.100532i
$870$	7.69503	−	0.789888i	0.260886	−	0.0267797i
$871$	−25.5922	+	14.7757i	−0.867160	+	0.500655i
$872$	−5.12698	+	0.926351i	−0.173621	+	0.0313702i
$873$	−1.43147	+	0.664279i	−0.0484480	+	0.0224824i
$874$	10.5925	−	14.2701i	0.358298	−	0.482694i
$875$	12.8216	+	1.27560i	0.433450	+	0.0431232i
$876$	−0.437369	+	34.5518i	−0.0147773	+	1.16740i
$877$	−0.664314	+	1.15063i	−0.0224323	+	0.0388539i	−0.877024	−	0.480447i	$-0.840474\pi$
$877$	−0.664314	+	1.15063i	−0.0224323	+	0.0388539i	0.854591	+	0.519301i	$0.173808\pi$
$878$	24.8287	+	2.86666i	0.837927	+	0.0967450i
$879$	33.7713	−	7.45409i	1.13908	−	0.251420i
$880$	−2.77237	+	0.177130i	−0.0934564	+	0.00597106i
$881$		−	23.8258i		−	0.802713i	−0.915922	−	0.401356i	$-0.868539\pi$
$881$		−	23.8258i		−	0.802713i	0.915922	−	0.401356i	$-0.131461\pi$
$882$	−23.7355	+	17.8501i	−0.799217	+	0.601043i
$883$			30.2235i			1.01710i	0.861032	+	0.508551i	$0.169819\pi$
$883$			30.2235i			1.01710i	−0.861032	+	0.508551i	$0.830181\pi$
$884$	7.29989	−	31.1915i	0.245522	−	1.04908i
$885$	2.66248	−	0.587670i	0.0894983	−	0.0197543i
$886$	5.69923	−	49.3621i	0.191469	−	1.65835i
$887$	−10.9556	+	18.9756i	−0.367852	+	0.637138i	−0.989229	−	0.146373i	$-0.953240\pi$
$887$	−10.9556	+	18.9756i	−0.367852	+	0.637138i	0.621377	+	0.783511i	$0.286573\pi$
$888$	21.8052	−	28.6117i	0.731736	−	0.960147i
$889$	3.98136	+	0.396099i	0.133531	+	0.0132847i
$890$	1.39050	+	1.03215i	0.0466096	+	0.0345978i
$891$	−12.3162	−	2.21879i	−0.412609	−	0.0743323i
$892$	34.2797	+	32.1594i	1.14777	+	1.07678i
$893$	10.8830	−	6.28330i	0.364185	−	0.210262i
$894$	0.573737	+	5.58930i	0.0191886	+	0.186934i
$895$		−	10.3660i		−	0.346496i
$896$	−11.1085	+	27.7957i	−0.371109	+	0.928589i
$897$	23.0021	+	7.27599i	0.768019	+	0.242938i
$898$	3.10618	+	7.17317i	0.103655	+	0.239372i
$899$	21.8614	+	37.8650i	0.729117	+	1.26287i
$900$	27.9088	−	5.79064i	0.930294	−	0.193021i
$901$	−15.2713	+	26.4507i	−0.508761	+	0.881200i
$902$	6.73281	−	9.07034i	0.224178	−	0.302009i
$903$	1.90363	+	16.0469i	0.0633487	+	0.534006i
$904$	27.3452	+	9.82235i	0.909489	+	0.326687i
$905$	−2.78326	−	1.60692i	−0.0925187	−	0.0534157i
$906$	−29.3623	−	13.1585i	−0.975498	−	0.437162i
$907$	42.4039	−	24.4819i	1.40800	−	0.812907i	0.412802	−	0.910821i	$-0.364550\pi$
$907$	42.4039	−	24.4819i	1.40800	−	0.812907i	0.995195	+	0.0979134i	$0.0312168\pi$
$908$	37.3270	+	8.73583i	1.23874	+	0.289909i
$909$	27.7702	−	39.5040i	0.921081	−	1.31026i
$910$	1.09220	−	5.02289i	0.0362059	−	0.166507i
$911$	−51.8251			−1.71704			−0.858522	−	0.512777i	$-0.828617\pi$
$911$	−51.8251			−1.71704			−0.858522	+	0.512777i	$0.828617\pi$
$912$	−16.6893	−	4.12936i	−0.552637	−	0.136737i
$913$	−8.35449	−	14.4704i	−0.276493	−	0.478900i
$914$	3.88515	−	33.6500i	0.128509	−	1.11304i
$915$	2.86589	+	3.13340i	0.0947435	+	0.103587i
$916$	6.64461	+	21.9694i	0.219544	+	0.725889i
$917$	−14.2921	−	10.2629i	−0.471966	−	0.338912i
$918$	42.7885	−	0.563592i	1.41223	−	0.0186013i
$919$	−43.7375	−	25.2518i	−1.44277	−	0.832981i	−0.444732	−	0.895664i	$-0.646701\pi$
$919$	−43.7375	−	25.2518i	−1.44277	−	0.832981i	−0.998034	+	0.0626826i	$0.980034\pi$
$920$	1.27200	+	7.03999i	0.0419365	+	0.232102i
$921$	23.9373	−	5.28350i	0.788761	−	0.174097i
$922$	−1.68410	−	3.88912i	−0.0554628	−	0.128081i
$923$	−12.4936			−0.411232
$924$	12.6645	+	1.42208i	0.416633	+	0.0467829i
$925$	34.8836			1.14696
$926$	−12.5966	−	29.0896i	−0.413950	−	0.955944i
$927$	−5.60755	−	0.501073i	−0.184176	−	0.0164574i
$928$	−31.8488	+	16.2766i	−1.04549	+	0.534304i
$929$	1.07011	+	0.617830i	0.0351093	+	0.0202703i	0.517452	−	0.855712i	$-0.326881\pi$
$929$	1.07011	+	0.617830i	0.0351093	+	0.0202703i	−0.482343	+	0.875983i	$0.660214\pi$
$930$	−4.95615	−	6.85652i	−0.162519	−	0.224834i
$931$	13.0374	+	11.4791i	0.427282	+	0.376211i
$932$	−38.7034	+	11.7058i	−1.26777	+	0.383436i
$933$	31.3833	−	28.7040i	1.02744	−	0.939727i
$934$	−1.95639	+	16.9447i	−0.0640151	+	0.554447i
$935$	−2.02215	−	3.50247i	−0.0661314	−	0.114543i
$936$	−2.08915	−	23.2454i	−0.0682861	−	0.759799i
$937$	−29.4139			−0.960909			−0.480455	−	0.877020i	$-0.659528\pi$
$937$	−29.4139			−0.960909			−0.480455	+	0.877020i	$0.659528\pi$
$938$	29.7483	+	27.0382i	0.971317	+	0.882828i
$939$	−0.0859759	−	0.0271957i	−0.00280572	−	0.000887499i
$940$	−1.15275	+	4.92553i	−0.0375984	+	0.160653i
$941$	−38.8530	+	22.4318i	−1.26657	+	0.731256i	−0.974338	−	0.225090i	$-0.927732\pi$
$941$	−38.8530	+	22.4318i	−1.26657	+	0.731256i	−0.292235	+	0.956346i	$0.594399\pi$
$942$	−8.42414	+	18.7979i	−0.274473	+	0.612469i
$943$	−25.1925	−	14.5449i	−0.820381	−	0.473647i
$944$	−10.4938	+	6.98680i	−0.341545	+	0.227401i
$945$	6.86362	−	0.198808i	0.223274	−	0.00646722i
$946$	4.13303	−	5.56796i	0.134376	−	0.181030i
$947$	8.77882	−	15.2054i	0.285273	−	0.494108i	−0.687402	−	0.726277i	$-0.741249\pi$
$947$	8.77882	−	15.2054i	0.285273	−	0.494108i	0.972675	+	0.232169i	$0.0745823\pi$
$948$	3.61029	+	6.44010i	0.117257	+	0.209165i
$949$	13.7183	+	23.7609i	0.445316	+	0.771311i
$950$	−6.62481	−	15.2988i	−0.214937	−	0.496359i
$951$	−3.53984	+	11.1908i	−0.114787	+	0.362886i
$952$	−43.4395	+	3.46472i	−1.40788	+	0.112292i
$953$			37.1546i			1.20356i	0.798663	+	0.601778i	$0.205541\pi$
$953$			37.1546i			1.20356i	−0.798663	+	0.601778i	$0.794459\pi$
$954$	−4.50954	+	21.7905i	−0.146002	+	0.705495i
$955$	7.58422	−	4.37875i	0.245420	−	0.141693i
$956$	−9.45244	+	10.0756i	−0.305714	+	0.325870i
$957$	10.2773	+	11.2366i	0.332219	+	0.363229i
$958$	−15.2245	−	11.3010i	−0.491881	−	0.365118i
$959$	−13.2834	−	29.3942i	−0.428943	−	0.949188i
$960$	5.80882	−	3.76229i	0.187479	−	0.121427i
$961$	8.40960	−	14.5658i	0.271277	−	0.469866i
$962$	3.27610	−	28.3749i	0.105626	−	0.914845i
$963$	1.94340	−	21.7488i	0.0626252	−	0.700845i
$964$	−15.7086	−	3.67635i	−0.505939	−	0.118407i
$965$			1.09138i			0.0351326i
$966$	−0.102685	−	32.8186i	−0.00330384	−	1.05592i
$967$		−	53.9045i		−	1.73345i	−0.498786	−	0.866725i	$-0.666221\pi$
$967$		−	53.9045i		−	1.73345i	0.498786	−	0.866725i	$-0.333779\pi$
$968$	16.5664	+	19.5747i	0.532464	+	0.629154i
$969$	−5.39468	−	24.4410i	−0.173302	−	0.785158i
$970$	−0.369110	−	0.0426165i	−0.0118514	−	0.00136833i
$971$	19.1783	−	33.2177i	0.615460	−	1.06601i	−0.374844	−	0.927088i	$-0.622304\pi$
$971$	19.1783	−	33.2177i	0.615460	−	1.06601i	0.990304	−	0.138920i	$-0.0443631\pi$
$972$	29.4673	−	10.1823i	0.945164	−	0.326597i
$973$	0.125803	+	0.0125159i	0.00403305	+	0.000401242i
$974$	10.2906	−	13.8633i	0.329731	−	0.444208i
$975$	16.7001	−	15.2744i	0.534832	−	0.489172i
$976$	−17.5950	−	8.71290i	−0.563202	−	0.278893i
$977$	−15.5907	+	9.00127i	−0.498789	+	0.287976i	−0.728214	−	0.685350i	$-0.759649\pi$
$977$	−15.5907	+	9.00127i	−0.498789	+	0.287976i	0.229424	+	0.973327i	$0.426316\pi$
$978$	3.09149	+	30.1171i	0.0988551	+	0.963039i
$979$			3.40899i			0.108952i
$980$	−6.96072	+	0.665919i	−0.222352	+	0.0212720i
$981$	−4.52078	−	3.17799i	−0.144337	−	0.101465i
$982$	−51.7783	+	22.4214i	−1.65231	+	0.715497i
$983$	−6.87845	−	11.9138i	−0.219388	−	0.379992i	0.735233	−	0.677815i	$-0.237073\pi$
$983$	−6.87845	−	11.9138i	−0.219388	−	0.379992i	−0.954621	+	0.297823i	$0.903740\pi$
$984$	−3.58130	+	27.9128i	−0.114168	+	0.889827i
$985$	1.56758	−	2.71514i	0.0499474	−	0.0865114i
$986$	−41.8104	−	31.0354i	−1.33151	−	0.988368i
$987$	9.15487	−	21.3243i	0.291403	−	0.678759i
$988$	−13.0665	+	3.95195i	−0.415701	+	0.125728i
$989$	−15.4648	−	8.92860i	−0.491751	−	0.283913i
$990$	−2.20026	−	1.95983i	−0.0699288	−	0.0622874i
$991$	1.60779	−	0.928258i	0.0510731	−	0.0294871i	−0.474246	−	0.880392i	$-0.657279\pi$
$991$	1.60779	−	0.928258i	0.0510731	−	0.0294871i	0.525319	+	0.850905i	$0.323946\pi$
$992$	32.8330	+	21.2653i	1.04245	+	0.675172i
$993$	−9.34619	+	29.5468i	−0.296593	+	0.937640i
$994$	5.17634	+	16.1880i	0.164184	+	0.513454i
$995$	−0.432298			−0.0137048
$996$	35.7833	+	21.2679i	1.13384	+	0.673899i
$997$	−30.1748	−	52.2642i	−0.955644	−	1.65522i	−0.732888	−	0.680350i	$-0.761828\pi$
$997$	−30.1748	−	52.2642i	−0.955644	−	1.65522i	−0.222756	−	0.974874i	$-0.571505\pi$
$998$	−11.9066	−	1.37471i	−0.376897	−	0.0435156i
$999$	37.8430	−	4.87513i	1.19730	−	0.154242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.23.2	yes	24
3.2	odd	2	inner	84.2.n.a.23.11	yes	24
4.3	odd	2	inner	84.2.n.a.23.6	yes	24
7.2	even	3		588.2.e.e.491.10		12
7.3	odd	6		588.2.n.e.263.7		24
7.4	even	3	inner	84.2.n.a.11.7	yes	24
7.5	odd	6		588.2.e.d.491.10		12
7.6	odd	2		588.2.n.e.275.2		24
12.11	even	2	inner	84.2.n.a.23.7	yes	24
21.2	odd	6		588.2.e.e.491.3		12
21.5	even	6		588.2.e.d.491.3		12
21.11	odd	6	inner	84.2.n.a.11.6	yes	24
21.17	even	6		588.2.n.e.263.6		24
21.20	even	2		588.2.n.e.275.11		24
28.3	even	6		588.2.n.e.263.11		24
28.11	odd	6	inner	84.2.n.a.11.11	yes	24
28.19	even	6		588.2.e.d.491.4		12
28.23	odd	6		588.2.e.e.491.4		12
28.27	even	2		588.2.n.e.275.6		24
84.11	even	6	inner	84.2.n.a.11.2	✓	24
84.23	even	6		588.2.e.e.491.9		12
84.47	odd	6		588.2.e.d.491.9		12
84.59	odd	6		588.2.n.e.263.2		24
84.83	odd	2		588.2.n.e.275.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.2	✓	24	84.11	even	6	inner
84.2.n.a.11.6	yes	24	21.11	odd	6	inner
84.2.n.a.11.7	yes	24	7.4	even	3	inner
84.2.n.a.11.11	yes	24	28.11	odd	6	inner
84.2.n.a.23.2	yes	24	1.1	even	1	trivial
84.2.n.a.23.6	yes	24	4.3	odd	2	inner
84.2.n.a.23.7	yes	24	12.11	even	2	inner
84.2.n.a.23.11	yes	24	3.2	odd	2	inner
588.2.e.d.491.3		12	21.5	even	6
588.2.e.d.491.4		12	28.19	even	6
588.2.e.d.491.9		12	84.47	odd	6
588.2.e.d.491.10		12	7.5	odd	6
588.2.e.e.491.3		12	21.2	odd	6
588.2.e.e.491.4		12	28.23	odd	6
588.2.e.e.491.9		12	84.23	even	6
588.2.e.e.491.10		12	7.2	even	3
588.2.n.e.263.2		24	84.59	odd	6
588.2.n.e.263.6		24	21.17	even	6
588.2.n.e.263.7		24	7.3	odd	6
588.2.n.e.263.11		24	28.3	even	6
588.2.n.e.275.2		24	7.6	odd	2
588.2.n.e.275.6		24	28.27	even	2
588.2.n.e.275.7		24	84.83	odd	2
588.2.n.e.275.11		24	21.20	even	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29776 + 0.561968i) q^{2} +(0.373317 + 1.69134i) q^{3} +(1.36838 - 1.45860i) q^{4} +(0.432549 + 0.249732i) q^{5} +(-1.43496 - 1.98517i) q^{6} +(-0.261928 + 2.63275i) q^{7} +(-0.956154 + 2.66191i) q^{8} +(-2.72127 + 1.26281i) q^{9} +(-0.701688 - 0.0810151i) q^{10} +(-0.695249 - 1.20421i) q^{11} +(2.97784 + 1.76988i) q^{12} +2.75054 q^{13} +(-1.13960 - 3.56389i) q^{14} +(-0.260904 + 0.824817i) q^{15} +(-0.255045 - 3.99186i) q^{16} +(5.04311 - 2.91164i) q^{17} +(2.82191 - 3.16810i) q^{18} +(-2.14907 - 1.24076i) q^{19} +(0.956154 - 0.289187i) q^{20} +(-4.55067 + 0.539842i) q^{21} +(1.57899 + 1.17207i) q^{22} +(2.53203 - 4.38560i) q^{23} +(-4.85915 - 0.623445i) q^{24} +(-2.37527 - 4.11408i) q^{25} +(-3.56955 + 1.54571i) q^{26} +(-3.15174 - 4.13116i) q^{27} +(3.48172 + 3.98467i) q^{28} +6.32275i q^{29} +(-0.124928 - 1.21704i) q^{30} +(5.98869 - 3.45757i) q^{31} +(2.57429 + 5.03717i) q^{32} +(1.77718 - 1.62545i) q^{33} +(-4.90852 + 6.61269i) q^{34} +(-0.770780 + 1.07338i) q^{35} +(-1.88180 + 5.69726i) q^{36} +(-3.67154 + 6.35929i) q^{37} +(3.48625 + 0.402514i) q^{38} +(1.02682 + 4.65209i) q^{39} +(-1.07835 + 0.912624i) q^{40} -5.74438i q^{41} +(5.60232 - 3.25792i) q^{42} -3.52627i q^{43} +(-2.70783 - 0.633726i) q^{44} +(-1.49245 - 0.133360i) q^{45} +(-0.821409 + 7.11439i) q^{46} +(-2.53203 + 4.38560i) q^{47} +(6.65638 - 1.92160i) q^{48} +(-6.86279 - 1.37918i) q^{49} +(5.39452 + 4.00429i) q^{50} +(6.80726 + 7.44266i) q^{51} +(3.76379 - 4.01194i) q^{52} +(-4.54223 + 2.62246i) q^{53} +(6.41180 + 3.59010i) q^{54} -0.694505i q^{55} +(-6.75771 - 3.21455i) q^{56} +(1.29627 - 4.09801i) q^{57} +(-3.55318 - 8.20544i) q^{58} +(-1.57587 - 2.72949i) q^{59} +(0.846063 + 1.50922i) q^{60} +(2.45426 - 4.25091i) q^{61} +(-5.82886 + 7.85256i) q^{62} +(-2.61190 - 7.49520i) q^{63} +(-6.17154 - 5.09039i) q^{64} +(1.18974 + 0.686897i) q^{65} +(-1.39290 + 3.10817i) q^{66} +(-9.30445 + 5.37193i) q^{67} +(2.65399 - 11.3402i) q^{68} +(8.36279 + 2.64530i) q^{69} +(0.397085 - 1.82615i) q^{70} -4.54224 q^{71} +(-0.759544 - 8.45122i) q^{72} +(4.98752 + 8.63864i) q^{73} +(1.19108 - 10.3162i) q^{74} +(6.07159 - 5.55325i) q^{75} +(-4.75054 + 1.43679i) q^{76} +(3.35249 - 1.51500i) q^{77} +(-3.94690 - 5.46028i) q^{78} +(1.84576 + 1.06565i) q^{79} +(0.886577 - 1.79037i) q^{80} +(5.81061 - 6.87291i) q^{81} +(3.22815 + 7.45485i) q^{82} +12.0165 q^{83} +(-5.43965 + 7.37633i) q^{84} +2.90852 q^{85} +(1.98165 + 4.57626i) q^{86} +(-10.6939 + 2.36039i) q^{87} +(3.87026 - 0.699285i) q^{88} +(-2.12318 - 1.22582i) q^{89} +(2.01179 - 0.665637i) q^{90} +(-0.720443 + 7.24148i) q^{91} +(-2.93206 - 9.69440i) q^{92} +(8.08361 + 8.83814i) q^{93} +(0.821409 - 7.11439i) q^{94} +(-0.619718 - 1.07338i) q^{95} +(-7.55854 + 6.23445i) q^{96} +0.526031 q^{97} +(9.68134 - 2.06681i) q^{98} +(3.41265 + 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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