LMFDB - Embedded newform 84.2.n.a.11.7

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			11.7
Character	$\chi$	$=$	84.11
Dual form			84.2.n.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.162204 - 1.40488i) q^{2} +(1.27809 - 1.16897i) q^{3} +(-1.94738 - 0.455755i) q^{4} +(-0.432549 + 0.249732i) q^{5} +(-1.43496 - 1.98517i) q^{6} +(0.261928 + 2.63275i) q^{7} +(-0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +O(q^{10})$	\(q+(0.162204 - 1.40488i) q^{2} +(1.27809 - 1.16897i) q^{3} +(-1.94738 - 0.455755i) 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} +(0.267006 - 2.98809i) q^{9} +(0.280683 + 0.648187i) q^{10} +(-0.695249 + 1.20421i) q^{11} +(-3.02168 + 1.69394i) q^{12} +2.75054 q^{13} +(3.74119 + 0.0590654i) q^{14} +(-0.260904 + 0.824817i) q^{15} +(3.58458 + 1.77505i) q^{16} +(-5.04311 - 2.91164i) q^{17} +(-4.15461 - 0.859793i) q^{18} +(2.14907 - 1.24076i) q^{19} +(0.956154 - 0.289187i) q^{20} +(3.41238 + 3.05870i) q^{21} +(1.57899 + 1.17207i) q^{22} +(2.53203 + 4.38560i) q^{23} +(1.88965 + 4.51987i) q^{24} +(-2.37527 + 4.11408i) q^{25} +(0.446148 - 3.86417i) q^{26} +(-3.15174 - 4.13116i) q^{27} +(0.689816 - 5.24635i) q^{28} +6.32275i q^{29} +(1.11645 + 0.500328i) q^{30} +(-5.98869 - 3.45757i) q^{31} +(3.07517 - 4.74798i) q^{32} +(0.519097 + 2.35181i) 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} +(-1.39454 - 3.22044i) q^{38} +(3.51542 - 3.21530i) q^{39} +(-0.251182 - 1.39019i) q^{40} -5.74438i q^{41} +(4.85061 - 4.29786i) q^{42} -3.52627i q^{43} +(1.90274 - 2.02819i) q^{44} +(0.630730 + 1.35918i) q^{45} +(6.57194 - 2.84583i) 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} +(-9.84916 + 2.17393i) q^{51} +(-5.35634 - 1.25357i) q^{52} +(4.54223 + 2.62246i) q^{53} +(-6.31502 + 3.75773i) q^{54} -0.694505i q^{55} +(-7.25860 - 1.82009i) q^{56} +(1.29627 - 4.09801i) q^{57} +(8.88271 + 1.02558i) q^{58} +(-1.57587 + 2.72949i) q^{59} +(0.883994 - 1.48732i) q^{60} +(2.45426 + 4.25091i) q^{61} +(-5.82886 + 7.85256i) q^{62} +(7.93685 - 0.0797041i) q^{63} +(-6.17154 - 5.09039i) q^{64} +(-1.18974 + 0.686897i) q^{65} +(3.38821 - 0.347796i) q^{66} +(9.30445 + 5.37193i) q^{67} +(8.49386 + 7.96850i) q^{68} +(8.36279 + 2.64530i) q^{69} +(-1.63300 + 0.908747i) q^{70} -4.54224 q^{71} +(7.69874 + 3.56782i) q^{72} +(4.98752 - 8.63864i) q^{73} +(-9.52959 + 4.12657i) q^{74} +(1.77346 + 8.03477i) 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} +(-1.99379 + 0.127386i) q^{80} +(-8.85742 - 1.59568i) q^{81} +(-8.07016 - 0.931761i) q^{82} +12.0165 q^{83} +(-5.25119 - 7.51166i) q^{84} +2.90852 q^{85} +(-4.95398 - 0.571975i) q^{86} +(7.39112 + 8.08102i) q^{87} +(-2.54073 - 3.00210i) 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} +(-11.6959 + 2.58154i) q^{93} +(-6.57194 + 2.84583i) q^{94} +(-0.619718 + 1.07338i) q^{95} +(-1.61992 - 9.66312i) q^{96} +0.526031 q^{97} +(0.824419 + 9.86511i) q^{98} +(3.41265 + 2.39900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.162204	−	1.40488i	0.114696	−	0.993401i
$2$	0.162204	−	1.40488i	0.114696	−	0.993401i
$3$	1.27809	−	1.16897i	0.737903	−	0.674907i
$3$	1.27809	−	1.16897i	0.737903	−	0.674907i
$4$	−1.94738	−	0.455755i	−0.973690	−	0.227877i
$5$	−0.432549	+	0.249732i	−0.193442	+	0.111684i	−0.593593	−	0.804766i	$-0.702291\pi$
$5$	−0.432549	+	0.249732i	−0.193442	+	0.111684i	0.400151	+	0.916449i	$0.368958\pi$
$6$	−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
$9$	0.267006	−	2.98809i	0.0890021	−	0.996031i
$10$	0.280683	+	0.648187i	0.0887597	+	0.204975i
$11$	−0.695249	+	1.20421i	−0.209626	+	0.363082i	−0.951597	−	0.307350i	$-0.900558\pi$
$11$	−0.695249	+	1.20421i	−0.209626	+	0.363082i	0.741971	+	0.670432i	$0.233891\pi$
$12$	−3.02168	+	1.69394i	−0.872285	+	0.488998i
$13$	2.75054			0.762861			0.381431	−	0.924397i	$-0.375432\pi$
$13$	2.75054			0.762861			0.381431	+	0.924397i	$0.375432\pi$
$14$	3.74119	+	0.0590654i	0.999875	+	0.0157859i
$15$	−0.260904	+	0.824817i	−0.0673652	+	0.212967i
$16$	3.58458	+	1.77505i	0.896144	+	0.443764i
$17$	−5.04311	−	2.91164i	−1.22313	−	0.706177i	−0.257550	−	0.966265i	$-0.582915\pi$
$17$	−5.04311	−	2.91164i	−1.22313	−	0.706177i	−0.965585	+	0.260088i	$0.916248\pi$
$18$	−4.15461	−	0.859793i	−0.979250	−	0.202655i
$19$	2.14907	−	1.24076i	0.493030	−	0.284651i	−0.232801	−	0.972524i	$-0.574789\pi$
$19$	2.14907	−	1.24076i	0.493030	−	0.284651i	0.725831	+	0.687874i	$0.241456\pi$
$20$	0.956154	−	0.289187i	0.213802	−	0.0646643i
$21$	3.41238	+	3.05870i	0.744643	+	0.667463i
$22$	1.57899	+	1.17207i	0.336643	+	0.249886i
$23$	2.53203	+	4.38560i	0.527964	+	0.914460i	0.999469	+	0.0325966i	$0.0103777\pi$
$23$	2.53203	+	4.38560i	0.527964	+	0.914460i	−0.471505	+	0.881863i	$0.656289\pi$
$24$	1.88965	+	4.51987i	0.385724	+	0.922614i
$25$	−2.37527	+	4.11408i	−0.475054	+	0.822817i
$26$	0.446148	−	3.86417i	0.0874968	−	0.757827i
$27$	−3.15174	−	4.13116i	−0.606553	−	0.795043i
$28$	0.689816	−	5.24635i	0.130363	−	0.991466i
$29$			6.32275i			1.17411i	0.809549	+	0.587053i	$0.199712\pi$
$29$			6.32275i			1.17411i	−0.809549	+	0.587053i	$0.800288\pi$
$30$	1.11645	+	0.500328i	0.203835	+	0.0913470i
$31$	−5.98869	−	3.45757i	−1.07560	−	0.620998i	−0.145894	−	0.989300i	$-0.546606\pi$
$31$	−5.98869	−	3.45757i	−1.07560	−	0.620998i	−0.929706	+	0.368302i	$0.879939\pi$
$32$	3.07517	−	4.74798i	0.543619	−	0.839332i
$33$	0.519097	+	2.35181i	0.0903631	+	0.409397i
$34$	−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	−0.992271	−	0.124086i	$-0.960400\pi$
$37$	−3.67154	−	6.35929i	−0.603598	−	1.04546i	0.388674	−	0.921375i	$-0.372933\pi$
$38$	−1.39454	−	3.22044i	−0.226224	−	0.522425i
$39$	3.51542	−	3.21530i	0.562918	−	0.514860i
$40$	−0.251182	−	1.39019i	−0.0397153	−	0.219808i
$41$		−	5.74438i		−	0.897121i	−0.893753	−	0.448560i	$-0.851937\pi$
$41$		−	5.74438i		−	0.897121i	0.893753	−	0.448560i	$-0.148063\pi$
$42$	4.85061	−	4.29786i	0.748465	−	0.663174i
$43$		−	3.52627i		−	0.537751i	−0.963175	−	0.268875i	$-0.913348\pi$
$43$		−	3.52627i		−	0.537751i	0.963175	−	0.268875i	$-0.0866520\pi$
$44$	1.90274	−	2.02819i	0.286848	−	0.305760i
$45$	0.630730	+	1.35918i	0.0940237	+	0.202614i
$46$	6.57194	−	2.84583i	0.968980	−	0.419595i
$47$	−2.53203	−	4.38560i	−0.369334	−	0.639705i	0.620128	−	0.784501i	$-0.287081\pi$
$47$	−2.53203	−	4.38560i	−0.369334	−	0.639705i	−0.989462	+	0.144796i	$0.953747\pi$
$48$	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
$51$	−9.84916	+	2.17393i	−1.37916	+	0.304411i
$52$	−5.35634	−	1.25357i	−0.742790	−	0.173839i
$53$	4.54223	+	2.62246i	0.623923	+	0.360222i	0.778395	−	0.627775i	$-0.216034\pi$
$53$	4.54223	+	2.62246i	0.623923	+	0.360222i	−0.154472	+	0.987997i	$0.549368\pi$
$54$	−6.31502	+	3.75773i	−0.859365	+	0.511363i
$55$		−	0.694505i		−	0.0936470i
$56$	−7.25860	−	1.82009i	−0.969971	−	0.243219i
$57$	1.29627	−	4.09801i	0.171696	−	0.542794i
$58$	8.88271	+	1.02558i	1.16636	+	0.134665i
$59$	−1.57587	+	2.72949i	−0.205161	+	0.355349i	−0.950184	−	0.311689i	$-0.899105\pi$
$59$	−1.57587	+	2.72949i	−0.205161	+	0.355349i	0.745023	+	0.667039i	$0.232438\pi$
$60$	0.883994	−	1.48732i	0.114123	−	0.192013i
$61$	2.45426	+	4.25091i	0.314236	+	0.544273i	0.979275	−	0.202536i	$-0.0649183\pi$
$61$	2.45426	+	4.25091i	0.314236	+	0.544273i	−0.665039	+	0.746809i	$0.731585\pi$
$62$	−5.82886	+	7.85256i	−0.740267	+	0.997276i
$63$	7.93685	−	0.0797041i	0.999950	−	0.0100418i
$64$	−6.17154	−	5.09039i	−0.771443	−	0.636299i
$65$	−1.18974	+	0.686897i	−0.147569	+	0.0851991i
$66$	3.38821	−	0.347796i	0.417060	−	0.0428108i
$67$	9.30445	+	5.37193i	1.13672	+	0.656286i	0.945616	−	0.325284i	$-0.105460\pi$
$67$	9.30445	+	5.37193i	1.13672	+	0.656286i	0.191104	+	0.981570i	$0.438793\pi$
$68$	8.49386	+	7.96850i	1.03003	+	0.966322i
$69$	8.36279	+	2.64530i	1.00676	+	0.318457i
$70$	−1.63300	+	0.908747i	−0.195181	+	0.108616i
$71$	−4.54224			−0.539065			−0.269532	−	0.962991i	$-0.586869\pi$
$71$	−4.54224			−0.539065			−0.269532	+	0.962991i	$0.586869\pi$
$72$	7.69874	+	3.56782i	0.907305	+	0.420472i
$73$	4.98752	−	8.63864i	0.583745	−	1.01108i	−0.411286	−	0.911507i	$-0.634920\pi$
$73$	4.98752	−	8.63864i	0.583745	−	1.01108i	0.995031	−	0.0995695i	$-0.0317466\pi$
$74$	−9.52959	+	4.12657i	−1.10779	+	0.479704i
$75$	1.77346	+	8.03477i	0.204781	+	0.927776i
$76$	−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	$-0.704922\pi$
$79$	−1.84576	+	1.06565i	−0.207664	+	0.119895i	0.392561	+	0.919726i	$0.371589\pi$
$80$	−1.99379	+	0.127386i	−0.222913	+	0.0142422i
$81$	−8.85742	−	1.59568i	−0.984157	−	0.177298i
$82$	−8.07016	−	0.931761i	−0.891200	−	0.102896i
$83$	12.0165			1.31899			0.659493	−	0.751710i	$-0.270771\pi$
$83$	12.0165			1.31899			0.659493	+	0.751710i	$0.270771\pi$
$84$	−5.25119	−	7.51166i	−0.572952	−	0.819589i
$85$	2.90852			0.315474
$86$	−4.95398	−	0.571975i	−0.534202	−	0.0616776i
$87$	7.39112	+	8.08102i	0.792411	+	0.866376i
$88$	−2.54073	−	3.00210i	−0.270842	−	0.320025i
$89$	2.12318	−	1.22582i	0.225056	−	0.129936i	−0.383233	−	0.923652i	$-0.625189\pi$
$89$	2.12318	−	1.22582i	0.225056	−	0.129936i	0.608289	+	0.793715i	$0.291856\pi$
$90$	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
$93$	−11.6959	+	2.58154i	−1.21280	+	0.267693i
$94$	−6.57194	+	2.84583i	−0.677844	+	0.293525i
$95$	−0.619718	+	1.07338i	−0.0635817	+	0.110127i
$96$	−1.61992	−	9.66312i	−0.165333	−	0.986238i
$97$	0.526031			0.0534104			0.0267052	−	0.999643i	$-0.491498\pi$
$97$	0.526031			0.0534104			0.0267052	+	0.999643i	$0.491498\pi$
$98$	0.824419	+	9.86511i	0.0832789	+	0.996526i
$99$	3.41265	+	2.39900i	0.342984	+	0.241109i
$100$	6.50056	−	6.92914i	0.650056	−	0.692914i
$101$	13.9396	+	8.04803i	1.38704	+	0.800809i	0.992981	−	0.118275i	$-0.0377364\pi$
$101$	13.9396	+	8.04803i	1.38704	+	0.800809i	0.394061	+	0.919084i	$0.371070\pi$
$102$	1.45654	+	14.1895i	0.144219	+	1.40497i
$103$	−1.62521	+	0.938316i	−0.160137	+	0.0924550i	−0.577927	−	0.816089i	$-0.696138\pi$
$103$	−1.62521	+	0.938316i	−0.160137	+	0.0924550i	0.417790	+	0.908544i	$0.362805\pi$
$104$	−2.62993	+	7.32168i	−0.257886	+	0.717950i
$105$	−2.23988	−	0.470855i	−0.218590	−	0.0459507i
$106$	4.42101	−	5.95591i	0.429406	−	0.578490i
$107$	−3.63924	−	6.30335i	−0.351819	−	0.609368i	0.634749	−	0.772718i	$-0.281103\pi$
$107$	−3.63924	−	6.30335i	−0.351819	−	0.609368i	−0.986568	+	0.163350i	$0.947770\pi$
$108$	4.25484	+	9.48137i	0.409423	+	0.912345i
$109$	0.921005	−	1.59523i	0.0882163	−	0.152795i	−0.818541	−	0.574448i	$-0.805217\pi$
$109$	0.921005	−	1.59523i	0.0882163	−	0.152795i	0.906757	+	0.421653i	$0.138550\pi$
$110$	−0.975696	−	0.112651i	−0.0930290	−	0.0107409i
$111$	−12.1264	−	3.83579i	−1.15099	−	0.364077i
$112$	−3.73438	+	9.90224i	−0.352866	+	0.935674i
$113$		−	10.2728i		−	0.966382i	−0.875515	−	0.483191i	$-0.839478\pi$
$113$		−	10.2728i		−	0.966382i	0.875515	−	0.483191i	$-0.160522\pi$
$114$	−5.54695	−	2.48582i	−0.519519	−	0.232819i
$115$	−2.19045	−	1.26466i	−0.204260	−	0.117930i
$116$	2.88162	−	12.3128i	0.267552	−	1.14321i
$117$	0.734410	−	8.21886i	0.0678963	−	0.759834i
$118$	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
$122$	6.37011	−	2.75843i	0.576723	−	0.249737i
$123$	−6.71502	−	7.34181i	−0.605473	−	0.661988i
$124$	10.0864	+	9.46258i	0.905790	+	0.849764i
$125$		−	4.87005i		−	0.435590i
$126$	1.17541	−	11.1633i	0.104714	−	0.994502i
$127$		−	1.51224i		−	0.134190i	−0.997747	−	0.0670949i	$-0.978627\pi$
$127$		−	1.51224i		−	0.134190i	0.997747	−	0.0670949i	$-0.0213730\pi$
$128$	−8.15244	+	7.84460i	−0.720581	+	0.693371i
$129$	−4.12211	−	4.50687i	−0.362931	−	0.396808i
$130$	0.772028	+	1.78286i	0.0677113	+	0.156367i
$131$	−3.32518	−	5.75939i	−0.290523	−	0.503200i	0.683411	−	0.730034i	$-0.260496\pi$
$131$	−3.32518	−	5.75939i	−0.290523	−	0.503200i	−0.973933	+	0.226834i	$0.927162\pi$
$132$	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
$135$	2.39497	+	0.999839i	0.206126	+	0.0860524i
$136$	12.5725	−	10.6403i	1.07809	−	0.912402i
$137$	10.5583	+	6.09586i	0.902060	+	0.520805i	0.877868	−	0.478903i	$-0.158965\pi$
$137$	10.5583	+	6.09586i	0.902060	+	0.520805i	0.0241922	+	0.999707i	$0.492299\pi$
$138$	5.07281	−	11.3196i	0.431826	−	0.963592i
$139$		−	0.0477837i		−	0.00405296i	−0.999998	−	0.00202648i	$-0.999355\pi$
$139$		−	0.0477837i		−	0.00405296i	0.999998	−	0.00202648i	$-0.000645050\pi$
$140$	1.01180	+	2.44157i	0.0855129	+	0.206350i
$141$	−8.36279	−	2.64530i	−0.704274	−	0.222774i
$142$	−0.736770	+	6.38131i	−0.0618283	+	0.535507i
$143$	−1.91231	+	3.31221i	−0.159915	+	0.276981i
$144$	6.26113	−	10.2371i	0.521761	−	0.853092i
$145$	−1.57899	−	2.73490i	−0.131128	−	0.227121i
$146$	−11.3273	−	8.40809i	−0.937451	−	0.695859i
$147$	−7.15900	+	9.78513i	−0.590464	+	0.807064i
$148$	4.25161	+	14.0573i	0.349480	+	1.15550i
$149$	1.98650	−	1.14691i	0.162740	−	0.0939583i	−0.416418	−	0.909173i	$-0.636715\pi$
$149$	1.98650	−	1.14691i	0.162740	−	0.0939583i	0.579158	+	0.815215i	$0.303381\pi$
$150$	11.5756	−	1.18822i	0.945141	−	0.0970179i
$151$	−11.3759	−	6.56789i	−0.925759	−	0.534487i	−0.0402913	−	0.999188i	$-0.512829\pi$
$151$	−11.3759	−	6.56789i	−0.925759	−	0.534487i	−0.885468	+	0.464701i	$0.846162\pi$
$152$	1.24797	+	6.90699i	0.101223	+	0.560231i
$153$	−10.0468	+	14.2919i	−0.812236	+	1.15543i
$154$	−2.67219	+	4.46410i	−0.215331	+	0.359728i
$155$	3.45387			0.277421
$156$	−8.31125	+	4.65924i	−0.665432	+	0.373038i
$157$	−4.20480	+	7.28292i	−0.335579	+	0.581241i	−0.983596	−	0.180386i	$-0.942265\pi$
$157$	−4.20480	+	7.28292i	−0.335579	+	0.581241i	0.648017	+	0.761626i	$0.275599\pi$
$158$	1.19772	+	2.76592i	0.0952855	+	0.220045i
$159$	8.87093	−	1.95802i	0.703511	−	0.155281i
$160$	−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	$-0.505832\pi$
$163$	10.7040	−	6.17993i	0.838399	−	0.484050i	0.856720	+	0.515782i	$0.172499\pi$
$164$	−2.61803	+	11.1865i	−0.204433	+	0.873517i
$165$	−0.811857	−	0.887636i	−0.0632030	−	0.0691024i
$166$	1.94913	−	16.8818i	0.151282	−	1.31028i
$167$	−2.36549			−0.183047			−0.0915237	−	0.995803i	$-0.529174\pi$
$167$	−2.36549			−0.183047			−0.0915237	+	0.995803i	$0.529174\pi$
$168$	−11.4047	+	6.15888i	−0.879895	+	0.475168i
$169$	−5.43456			−0.418043
$170$	0.471774	−	4.08613i	0.0361834	−	0.313392i
$171$	−3.13371	−	6.75291i	−0.239641	−	0.516408i
$172$	−1.60711	+	6.86698i	−0.122541	+	0.523602i
$173$	−8.28769	+	4.78490i	−0.630102	+	0.363789i	−0.780791	−	0.624792i	$-0.785184\pi$
$173$	−8.28769	+	4.78490i	−0.630102	+	0.363789i	0.150690	+	0.988581i	$0.451851\pi$
$174$	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
$177$	1.17660	+	5.33067i	0.0884386	+	0.400678i
$178$	−1.37774	−	3.18164i	−0.103266	−	0.238474i
$179$	−10.3771	+	17.9736i	−0.775619	+	1.34341i	0.158827	+	0.987306i	$0.449229\pi$
$179$	−10.3771	+	17.9736i	−0.775619	+	1.34341i	−0.934446	+	0.356105i	$0.884105\pi$
$180$	−0.608820	−	2.93429i	−0.0453788	−	0.218709i
$181$	−6.43456			−0.478277			−0.239138	−	0.970985i	$-0.576865\pi$
$181$	−6.43456			−0.478277			−0.239138	+	0.970985i	$0.576865\pi$
$182$	10.2903	+	0.162461i	0.762766	+	0.0120424i
$183$	8.10595	+	2.56406i	0.599209	+	0.189541i
$184$	−14.0951	+	2.54672i	−1.03910	+	0.187747i
$185$	3.17624	+	1.83380i	0.233522	+	0.134824i
$186$	1.72964	+	16.8500i	0.126823	+	1.23550i
$187$	7.01244	−	4.04864i	0.512801	−	0.296066i
$188$	2.93206	+	9.69440i	0.213842	+	0.707037i
$189$	10.0508	−	9.37983i	0.731089	−	0.682282i
$190$	1.40745	+	1.04474i	0.102107	+	0.0757932i
$191$	8.76689	+	15.1847i	0.634350	+	1.09873i	0.986652	+	0.162840i	$0.0520655\pi$
$191$	8.76689	+	15.1847i	0.634350	+	1.09873i	−0.352303	+	0.935886i	$0.614601\pi$
$192$	−13.8383	+	0.708404i	−0.998692	+	0.0511247i
$193$	1.09255	−	1.89234i	0.0786432	−	0.136214i	−0.824022	−	0.566558i	$-0.808275\pi$
$193$	1.09255	−	1.89234i	0.0786432	−	0.136214i	0.902665	+	0.430344i	$0.141608\pi$
$194$	0.0853244	−	0.739011i	0.00612593	−	0.0530579i
$195$	−0.717627	+	2.26869i	−0.0513903	+	0.162464i
$196$	13.9930	+	0.441950i	0.999502	+	0.0315679i
$197$		−	6.27706i		−	0.447222i	−0.974678	−	0.223611i	$-0.928215\pi$
$197$		−	6.27706i		−	0.447222i	0.974678	−	0.223611i	$-0.0717845\pi$
$198$	3.92386	−	4.40524i	0.278856	−	0.313066i
$199$	0.749564	+	0.432761i	0.0531352	+	0.0306776i	0.526332	−	0.850279i	$-0.323567\pi$
$199$	0.749564	+	0.432761i	0.0531352	+	0.0306776i	−0.473197	+	0.880957i	$0.656900\pi$
$200$	−8.68021	−	10.2564i	−0.613783	−	0.725240i
$201$	18.1715	−	4.01087i	1.28172	−	0.282905i
$202$	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
$206$	1.05461	+	2.43543i	0.0734779	+	0.169684i
$207$	13.7806	−	6.39495i	0.957821	−	0.444480i
$208$	9.85950	+	4.88235i	0.683633	+	0.338530i
$209$			3.45056i			0.238680i
$210$	−1.02481	+	3.07039i	−0.0707187	+	0.211877i
$211$			3.90417i			0.268774i	0.990929	+	0.134387i	$0.0429065\pi$
$211$			3.90417i			0.268774i	−0.990929	+	0.134387i	$0.957094\pi$
$212$	−7.65024	−	7.17706i	−0.525421	−	0.492922i
$213$	−5.80537	+	5.30976i	−0.397778	+	0.363818i
$214$	−9.44576	+	4.09027i	−0.645699	+	0.279605i
$215$	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
$219$	−3.72385	−	16.8712i	−0.251635	−	1.14005i
$220$	−0.316524	+	1.35246i	−0.0213400	+	0.0911831i
$221$	−13.8713	−	8.00858i	−0.933082	−	0.538715i
$222$	−7.35578	+	16.4139i	−0.493688	+	1.10163i
$223$			23.5017i			1.57379i	0.617085	+	0.786896i	$0.288313\pi$
$223$			23.5017i			1.57379i	−0.617085	+	0.786896i	$0.711687\pi$
$224$	13.3057	+	6.85254i	0.889027	+	0.457855i
$225$	11.6591	+	8.19601i	0.777271	+	0.546401i
$226$	−14.4320	−	1.66629i	−0.960004	−	0.110840i
$227$	9.58391	−	16.5998i	0.636107	−	1.10177i	−0.350173	−	0.936685i	$-0.613877\pi$
$227$	9.58391	−	16.5998i	0.636107	−	1.10177i	0.986280	−	0.165084i	$-0.0527895\pi$
$228$	−4.39202	+	7.38959i	−0.290869	+	0.489388i
$229$	−5.73805	−	9.93860i	−0.379181	−	0.656761i	0.611762	−	0.791042i	$-0.290461\pi$
$229$	−5.73805	−	9.93860i	−0.379181	−	0.656761i	−0.990943	+	0.134281i	$0.957128\pi$
$230$	−2.13199	+	2.87219i	−0.140579	+	0.189386i
$231$	−6.05576	+	1.98266i	−0.398440	+	0.130449i
$232$	−16.8306	−	6.04552i	−1.10498	−	0.396908i
$233$	17.5088	−	10.1087i	1.14704	−	0.662245i	0.198877	−	0.980025i	$-0.436271\pi$
$233$	17.5088	−	10.1087i	1.14704	−	0.662245i	0.948164	+	0.317780i	$0.102937\pi$
$234$	−11.4274	−	2.36489i	−0.747032	−	0.154598i
$235$	2.19045	+	1.26466i	0.142889	+	0.0824971i
$236$	4.31280	−	4.59714i	0.280739	−	0.299248i
$237$	−1.11332	+	3.51963i	−0.0723181	+	0.228625i
$238$	−18.6953	−	11.1909i	−1.21183	−	0.725398i
$239$	−6.90774			−0.446824			−0.223412	−	0.974724i	$-0.571720\pi$
$239$	−6.90774			−0.446824			−0.223412	+	0.974724i	$0.571720\pi$
$240$	−2.39933	+	2.49350i	−0.154876	+	0.160955i
$241$	−4.03326	+	6.98581i	−0.259805	+	0.449995i	−0.966190	−	0.257833i	$-0.916992\pi$
$241$	−4.03326	+	6.98581i	−0.259805	+	0.449995i	0.706385	+	0.707828i	$0.250325\pi$
$242$	11.7662	−	5.09509i	0.756360	−	0.327525i
$243$	−13.1858	+	8.31466i	−0.845872	+	0.533386i
$244$	−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
$248$	14.9299	−	12.6354i	0.948047	−	0.802348i
$249$	15.3582	−	14.0470i	0.973285	−	0.890193i
$250$	−6.84183	−	0.789941i	−0.432716	−	0.0499603i
$251$	20.4073			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$251$	20.4073			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$252$	−15.4924	−	3.46204i	−0.975929	−	0.218088i
$253$	−7.04155			−0.442699
$254$	−2.12452	−	0.245292i	−0.133304	−	0.0153910i
$255$	3.71734	−	3.39999i	0.232789	−	0.212915i
$256$	9.69836	+	12.7256i	0.606148	+	0.795352i
$257$	−23.5645	+	13.6050i	−1.46991	+	0.848655i	−0.999430	−	0.0337537i	$-0.989254\pi$
$257$	−23.5645	+	13.6050i	−1.46991	+	0.848655i	−0.470484	+	0.882409i	$0.655920\pi$
$258$	−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
$261$	18.8930	+	1.68821i	1.16945	+	0.104498i
$262$	−8.63061	+	3.73729i	−0.533201	+	0.230891i
$263$	1.80247	−	3.12196i	0.111145	−	0.192508i	−0.805087	−	0.593156i	$-0.797882\pi$
$263$	1.80247	−	3.12196i	0.111145	−	0.192508i	0.916232	+	0.400648i	$0.131215\pi$
$264$	−6.75664	−	0.866899i	−0.415842	−	0.0533540i
$265$	−2.61965			−0.160924
$266$	8.11336	−	4.51500i	0.497462	−	0.276833i
$267$	1.28066	−	4.04864i	0.0783749	−	0.247772i
$268$	−15.6710	−	14.7017i	−0.957260	−	0.898051i
$269$	−22.6598	−	13.0827i	−1.38160	−	0.797664i	−0.389247	−	0.921134i	$-0.627265\pi$
$269$	−22.6598	−	13.0827i	−1.38160	−	0.797664i	−0.992348	+	0.123469i	$0.960598\pi$
$270$	1.79313	−	3.20247i	0.109126	−	0.194896i
$271$	−19.9722	+	11.5309i	−1.21322	+	0.700455i	−0.963460	−	0.267851i	$-0.913686\pi$
$271$	−19.9722	+	11.5309i	−1.21322	+	0.700455i	−0.249764	+	0.968307i	$0.580353\pi$
$272$	−12.9091	−	19.3888i	−0.782729	−	1.17562i
$273$	9.38588	+	8.41306i	0.568059	+	0.509181i
$274$	10.2766	−	13.8444i	0.620830	−	0.836373i
$275$	−3.30281	−	5.72063i	−0.199167	−	0.344967i
$276$	−15.0799	−	8.96278i	−0.907704	−	0.539496i
$277$	10.1455	−	17.5725i	0.609585	−	1.05583i	−0.381724	−	0.924276i	$-0.624670\pi$
$277$	10.1455	−	17.5725i	0.609585	−	1.05583i	0.991309	−	0.131555i	$-0.0419971\pi$
$278$	−0.0671305	−	0.00775071i	−0.00402622	−	0.000464857i
$279$	−11.9306	+	16.9716i	−0.714264	+	1.01606i
$280$	3.59423	−	1.02543i	0.214797	−	0.0612811i
$281$			27.6637i			1.65028i	0.564929	+	0.825140i	$0.308904\pi$
$281$			27.6637i			1.65028i	−0.564929	+	0.825140i	$0.691096\pi$
$282$	−5.07281	+	11.3196i	−0.302081	+	0.674075i
$283$	15.0435	+	8.68535i	0.894242	+	0.516291i	0.875328	−	0.483530i	$-0.160646\pi$
$283$	15.0435	+	8.68535i	0.894242	+	0.516291i	0.0189142	+	0.999821i	$0.493979\pi$
$284$	8.84547	+	2.07015i	0.524882	+	0.122841i
$285$	0.462703	+	2.09631i	0.0274081	+	0.124175i
$286$	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
$290$	−4.09833	+	1.77469i	−0.240662	+	0.104213i
$291$	0.672313	−	0.614916i	0.0394117	−	0.0360470i
$292$	−13.6497	+	14.5496i	−0.798788	+	0.851452i
$293$		−	19.9672i		−	1.16650i	−0.812294	−	0.583248i	$-0.801782\pi$
$293$		−	19.9672i		−	1.16650i	0.812294	−	0.583248i	$-0.198218\pi$
$294$	12.5857	+	11.6447i	0.734014	+	0.679134i
$295$		−	1.57418i		−	0.0916525i
$296$	20.4384	−	3.69285i	1.18796	−	0.214643i
$297$	7.16602	−	0.923163i	0.415815	−	0.0535673i
$298$	−1.28905	−	2.97683i	−0.0746726	−	0.172443i
$299$	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
$303$	27.2239	−	6.00894i	1.56397	−	0.345204i
$304$	9.90592	−	0.632903i	0.568144	−	0.0362995i
$305$	−2.12318	−	1.22582i	−0.121573	−	0.0701901i
$306$	18.4487	+	16.4328i	1.05464	+	0.939399i
$307$		−	14.1529i		−	0.807746i	−0.914815	−	0.403873i	$-0.867664\pi$
$307$		−	14.1529i		−	0.807746i	0.914815	−	0.403873i	$-0.132336\pi$
$308$	5.83809	+	4.47820i	0.332656	+	0.255169i
$309$	−0.980294	+	3.09908i	−0.0557670	+	0.176300i
$310$	0.560231	−	4.85227i	0.0318190	−	0.275591i
$311$	−12.2774	+	21.2652i	−0.696190	+	1.20584i	0.273588	+	0.961847i	$0.411790\pi$
$311$	−12.2774	+	21.2652i	−0.696190	+	1.20584i	−0.969778	+	0.243990i	$0.921544\pi$
$312$	5.19756	+	12.4321i	0.294254	+	0.703827i
$313$	−0.0260312	−	0.0450873i	−0.00147137	−	0.00254848i	0.865289	−	0.501274i	$-0.167135\pi$
$313$	−0.0260312	−	0.0450873i	−0.00147137	−	0.00254848i	−0.866760	+	0.498725i	$0.833802\pi$
$314$	9.54960	+	7.08856i	0.538915	+	0.400031i
$315$	−3.41317	+	2.01656i	−0.192311	+	0.113621i
$316$	4.08007	−	1.23401i	0.229522	−	0.0694185i
$317$	−5.86864	+	3.38826i	−0.329616	+	0.190304i	−0.655671	−	0.755047i	$-0.727614\pi$
$317$	−5.86864	+	3.38826i	−0.329616	+	0.190304i	0.326055	+	0.945351i	$0.394281\pi$
$318$	−1.31188	−	12.7802i	−0.0735664	−	0.716678i
$319$	−7.61390	−	4.39589i	−0.426297	−	0.246122i
$320$	3.94073	+	0.660611i	0.220293	+	0.0369293i
$321$	−12.0197	−	3.80205i	−0.670875	−	0.212210i
$322$	9.21375	+	16.5569i	0.513462	+	0.922681i
$323$	−14.4507			−0.804056
$324$	16.5215	+	7.14420i	0.917862	+	0.396900i
$325$	−6.53326	+	11.3159i	−0.362400	+	0.627695i
$326$	−6.94584	−	16.0402i	−0.384695	−	0.888384i
$327$	−0.687654	−	3.11547i	−0.0380273	−	0.172286i
$328$	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	$-0.830297\pi$
$331$	−15.4949	+	8.94598i	−0.851676	+	0.491715i	0.00953987	+	0.999954i	$0.496963\pi$
$332$	−23.4008	−	5.47659i	−1.28428	−	0.300567i
$333$	−19.9825	+	9.27294i	−1.09503	+	0.508154i
$334$	−0.383693	+	3.32324i	−0.0209947	+	0.181839i
$335$	−5.36618			−0.293185
$336$	6.80259	+	17.0213i	0.371112	+	0.928588i
$337$	7.09362			0.386414			0.193207	−	0.981158i	$-0.438111\pi$
$337$	7.09362			0.386414			0.193207	+	0.981158i	$0.438111\pi$
$338$	−0.881507	+	7.63490i	−0.0479476	+	0.415284i
$339$	−12.0086	−	13.1295i	−0.652217	−	0.713096i
$340$	−5.66400	−	1.32557i	−0.307174	−	0.0718893i
$341$	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
$345$	−4.27793	+	0.944236i	−0.230316	+	0.0508359i
$346$	5.37792	+	12.4194i	0.289119	+	0.667669i
$347$	−4.59539	+	7.95946i	−0.246694	+	0.427286i	−0.962606	−	0.270904i	$-0.912677\pi$
$347$	−4.59539	+	7.95946i	−0.246694	+	0.427286i	0.715913	+	0.698190i	$0.246011\pi$
$348$	−10.7104	−	19.1053i	−0.574136	−	1.02415i
$349$	−22.1330			−1.18475			−0.592377	−	0.805661i	$-0.701810\pi$
$349$	−22.1330			−1.18475			−0.592377	+	0.805661i	$0.701810\pi$
$350$	−9.12933	+	15.2513i	−0.487983	+	0.815215i
$351$	−8.66898	−	11.3629i	−0.462716	−	0.606507i
$352$	3.57954	+	7.00417i	0.190790	+	0.373324i
$353$	9.28947	+	5.36328i	0.494429	+	0.285458i	0.726410	−	0.687262i	$-0.241187\pi$
$353$	9.28947	+	5.36328i	0.494429	+	0.285458i	−0.231981	+	0.972720i	$0.574521\pi$
$354$	7.67981	−	0.788325i	0.408177	−	0.0418990i
$355$	1.96474	−	1.13434i	0.104278	−	0.0602047i
$356$	−4.69330	+	1.41948i	−0.248745	+	0.0752325i
$357$	−8.30320	−	25.3610i	−0.439452	−	1.34225i
$358$	23.5676	+	17.4939i	1.24559	+	0.924584i
$359$	1.80247	+	3.12196i	0.0951305	+	0.164771i	0.909663	−	0.415347i	$-0.136340\pi$
$359$	1.80247	+	3.12196i	0.0951305	+	0.164771i	−0.814533	+	0.580118i	$0.803007\pi$
$360$	−4.22108	+	0.379366i	−0.222471	+	0.0199943i
$361$	−6.42101	+	11.1215i	−0.337948	+	0.585342i
$362$	−1.04371	+	9.03978i	−0.0548562	+	0.475120i
$363$	14.9725	+	4.73606i	0.785851	+	0.248579i
$364$	1.89736	−	14.4303i	0.0994489	−	0.756351i
$365$			4.98218i			0.260779i
$366$	4.91701	−	10.9720i	0.257016	−	0.573515i
$367$	13.0134	+	7.51328i	0.679293	+	0.392190i	0.799589	−	0.600548i	$-0.205051\pi$
$367$	13.0134	+	7.51328i	0.679293	+	0.392190i	−0.120295	+	0.992738i	$0.538384\pi$
$368$	1.29156	+	20.2150i	0.0673274	+	1.05378i
$369$	−17.1647	−	1.53378i	−0.893561	−	0.0798456i
$370$	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	0.829582	−	0.558385i	$-0.188579\pi$
$373$	−1.32846	−	2.30096i	−0.0687850	−	0.119139i	−0.898367	+	0.439246i	$0.855246\pi$
$374$	−4.55040	−	10.5083i	−0.235296	−	0.543374i
$375$	−5.69295	−	6.22434i	−0.293983	−	0.321423i
$376$	14.0951	−	2.54672i	0.726898	−	0.131337i
$377$			17.3909i			0.895679i
$378$	−11.5473	−	15.6416i	−0.593927	−	0.804519i
$379$			17.7150i			0.909957i	0.890502	+	0.454979i	$0.150353\pi$
$379$			17.7150i			0.909957i	−0.890502	+	0.454979i	$0.849647\pi$
$380$	1.69603	−	1.80785i	0.0870043	−	0.0927405i
$381$	−1.76777	−	1.93278i	−0.0905656	−	0.0990191i
$382$	22.7547	−	9.85342i	1.16423	−	0.504145i
$383$	−16.4609	−	28.5111i	−0.841111	−	1.45685i	−0.888956	−	0.457993i	$-0.848569\pi$
$383$	−16.4609	−	28.5111i	−0.841111	−	1.45685i	0.0478445	−	0.998855i	$-0.484765\pi$
$384$	−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
$387$	−10.5368	−	0.941536i	−0.535617	−	0.0478609i
$388$	−1.02438	−	0.239741i	−0.0520051	−	0.0121710i
$389$	5.90821	+	3.41111i	0.299558	+	0.172950i	0.642244	−	0.766500i	$-0.278003\pi$
$389$	5.90821	+	3.41111i	0.299558	+	0.172950i	−0.342686	+	0.939450i	$0.611337\pi$
$390$	3.07083	+	1.37617i	0.155498	+	0.0696851i
$391$		−	29.4894i		−	1.49134i
$392$	2.89061	−	19.5868i	0.145998	−	0.989285i
$393$	−10.9824	−	3.47394i	−0.553991	−	0.175237i
$394$	−8.81852	−	1.01816i	−0.444271	−	0.0512944i
$395$	0.532254	−	0.921890i	0.0267806	−	0.0463853i
$396$	−5.55237	−	6.22710i	−0.279017	−	0.312923i
$397$	10.4221	+	18.0516i	0.523069	+	0.905982i	0.999640	+	0.0268459i	$0.00854633\pi$
$397$	10.4221	+	18.0516i	0.523069	+	0.905982i	−0.476571	+	0.879136i	$0.658120\pi$
$398$	0.729560	−	0.982853i	0.0365695	−	0.0492660i
$399$	11.1286	+	2.33938i	0.557125	+	0.117116i
$400$	−15.8170	+	10.5310i	−0.790852	+	0.526551i
$401$	−3.31292	+	1.91271i	−0.165439	+	0.0955164i	−0.580434	−	0.814308i	$-0.697117\pi$
$401$	−3.31292	+	1.91271i	−0.165439	+	0.0955164i	0.414994	+	0.909824i	$0.363784\pi$
$402$	−2.68729	−	26.1794i	−0.134030	−	1.30571i
$403$	−16.4721	−	9.51017i	−0.820534	−	0.473735i
$404$	−23.4778	−	22.0256i	−1.16806	−	1.09582i
$405$	4.22976	−	1.52177i	0.210178	−	0.0756175i
$406$	−0.373456	+	23.6546i	−0.0185343	+	1.17396i
$407$	10.2105			0.506118
$408$	3.63050	−	28.2962i	0.179736	−	1.40087i
$409$	1.93456	−	3.35075i	0.0956576	−	0.165684i	−0.814225	−	0.580549i	$-0.802838\pi$
$409$	1.93456	−	3.35075i	0.0956576	−	0.165684i	0.909883	+	0.414865i	$0.136171\pi$
$410$	3.72343	−	1.61235i	0.183887	−	0.0796282i
$411$	20.6204	−	4.55138i	1.01713	−	0.224503i
$412$	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
$416$	8.45837	−	13.0595i	0.414706	−	0.640294i
$417$	−0.0558579	−	0.0610717i	−0.00273537	−	0.00299069i
$418$	4.84763	+	0.559695i	0.237105	+	0.0273756i
$419$	13.5133			0.660170			0.330085	−	0.943951i	$-0.392923\pi$
$419$	13.5133			0.660170			0.330085	+	0.943951i	$0.392923\pi$
$420$	4.14730	+	1.93777i	0.202368	+	0.0945534i
$421$	11.3825			0.554749			0.277374	−	0.960762i	$-0.410536\pi$
$421$	11.3825			0.554749			0.277374	+	0.960762i	$0.410536\pi$
$422$	5.48489	+	0.633271i	0.267000	+	0.0308272i
$423$	−13.7806	+	6.39495i	−0.670038	+	0.310933i
$424$	−11.3238	+	9.58353i	−0.549933	+	0.465418i
$425$	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
$429$	1.42779	+	6.46873i	0.0689345	+	0.312313i
$430$	2.28568	−	0.989763i	0.110225	−	0.0477306i
$431$	12.9623	−	22.4513i	0.624370	−	1.08144i	−0.364293	−	0.931284i	$-0.618689\pi$
$431$	12.9623	−	22.4513i	0.624370	−	1.08144i	0.988662	−	0.150155i	$-0.0479774\pi$
$432$	−3.96462	−	20.4030i	−0.190748	−	0.981639i
$433$	23.3825			1.12369			0.561845	−	0.827242i	$-0.310092\pi$
$433$	23.3825			1.12369			0.561845	+	0.827242i	$0.310092\pi$
$434$	−22.2006	−	13.2892i	−1.06566	−	0.637900i
$435$	−5.21511	−	1.64963i	−0.250046	−	0.0790939i
$436$	−2.52058	+	2.68676i	−0.120714	+	0.128673i
$437$	10.8830	+	6.28330i	0.520604	+	0.300571i
$438$	−24.3060	+	2.49499i	−1.16139	+	0.119215i
$439$	15.3054	−	8.83658i	0.730487	−	0.421747i	−0.0881133	−	0.996110i	$-0.528084\pi$
$439$	15.3054	−	8.83658i	0.730487	−	0.421747i	0.818600	+	0.574364i	$0.194750\pi$
$440$	1.84871	+	0.664053i	0.0881338	+	0.0316575i
$441$	2.28873	+	20.8749i	0.108987	+	0.994043i
$442$	−13.5011	+	18.1884i	−0.642180	+	0.865136i
$443$	−17.5681	−	30.4288i	−0.834685	−	1.44572i	−0.894286	−	0.447495i	$-0.852316\pi$
$443$	−17.5681	−	30.4288i	−0.834685	−	1.44572i	0.0596013	−	0.998222i	$-0.481017\pi$
$444$	21.8665	+	12.9964i	1.03774	+	0.616782i
$445$	−0.612252	+	1.06045i	−0.0290235	+	0.0502702i
$446$	33.0171	+	3.81208i	1.56341	+	0.180507i
$447$	1.19822	−	3.78801i	0.0566737	−	0.179167i
$448$	11.7852	−	17.5815i	0.556801	−	0.830646i
$449$		−	5.52733i		−	0.260851i	−0.991458	−	0.130425i	$-0.958366\pi$
$449$		−	5.52733i		−	0.260851i	0.991458	−	0.130425i	$-0.0416343\pi$
$450$	13.4056	−	15.0502i	0.631944	−	0.709471i
$451$	6.91742	+	3.99377i	0.325728	+	0.188059i
$452$	−4.68187	+	20.0050i	−0.220216	+	0.940956i
$453$	−22.2171	+	4.90381i	−1.04385	+	0.230401i
$454$	−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	−0.997477	−	0.0709914i	$-0.977384\pi$
$457$	−11.9761	−	20.7432i	−0.560219	−	0.970327i	0.437258	−	0.899336i	$-0.355950\pi$
$458$	−14.8933	+	6.44920i	−0.695918	+	0.301351i
$459$	3.86613	+	30.0107i	0.180455	+	1.40078i
$460$	3.68926	+	3.46107i	0.172013	+	0.161373i
$461$			2.99679i			0.139574i	0.997562	+	0.0697871i	$0.0222320\pi$
$461$			2.99679i			0.139574i	−0.997562	+	0.0697871i	$0.977768\pi$
$462$	1.80313	+	8.82922i	0.0838892	+	0.410772i
$463$			22.4152i			1.04172i	0.853642	+	0.520861i	$0.174389\pi$
$463$			22.4152i			1.04172i	−0.853642	+	0.520861i	$0.825611\pi$
$464$	−11.2232	+	22.6644i	−0.521025	+	1.05217i
$465$	4.41434	−	4.03748i	0.204710	−	0.187234i
$466$	−11.3616	−	26.2375i	−0.526314	−	1.21543i
$467$	6.03065	+	10.4454i	0.279065	+	0.483355i	0.971153	−	0.238459i	$-0.0766421\pi$
$467$	6.03065	+	10.4454i	0.279065	+	0.483355i	−0.692088	+	0.721814i	$0.743309\pi$
$468$	−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
$471$	3.13945	+	14.2235i	0.144658	+	0.655384i
$472$	−5.75888	−	6.80464i	−0.265074	−	0.313209i
$473$	4.24635	+	2.45163i	0.195248	+	0.112726i
$474$	4.76408	+	2.13498i	0.218821	+	0.0980630i
$475$			11.7886i			0.540898i
$476$	−18.7543	+	24.4494i	−0.859602	+	1.12064i
$477$	9.04895	−	12.8724i	0.414323	−	0.589386i
$478$	−1.12046	+	9.70455i	−0.0512488	+	0.443876i
$479$	6.70352	−	11.6108i	0.306292	−	0.530513i	−0.671256	−	0.741225i	$-0.734245\pi$
$479$	6.70352	−	11.6108i	0.306292	−	0.530513i	0.977548	+	0.210713i	$0.0675784\pi$
$480$	3.11389	+	3.77522i	0.142129	+	0.172315i
$481$	−10.0987	−	17.4915i	−0.460461	−	0.797542i
$482$	9.16001	+	6.79937i	0.417227	+	0.309703i
$483$	−4.77398	+	22.7100i	−0.217223	+	1.03334i
$484$	−5.24946	−	17.3566i	−0.238612	−	0.788934i
$485$	−0.227534	+	0.131367i	−0.0103318	+	0.00596507i
$486$	9.54231	+	19.8732i	0.432848	+	0.901467i
$487$	10.5727	+	6.10416i	0.479095	+	0.276606i	0.720039	−	0.693933i	$-0.244124\pi$
$487$	10.5727	+	6.10416i	0.479095	+	0.276606i	−0.240944	+	0.970539i	$0.577457\pi$
$488$	−13.6622	+	2.46851i	−0.618458	+	0.111744i
$489$	6.45640	−	20.4111i	0.291969	−	0.923023i
$490$	−2.82024	−	4.06126i	−0.127405	−	0.183469i
$491$	39.8981			1.80058			0.900288	−	0.435294i	$-0.143356\pi$
$491$	39.8981			1.80058			0.900288	+	0.435294i	$0.143356\pi$
$492$	9.73063	+	17.3577i	0.438691	+	0.782545i
$493$	18.4096	−	31.8864i	0.829126	−	1.43609i
$494$	−3.83573	−	8.85794i	−0.172578	−	0.398537i
$495$	−2.07525	−	0.185437i	−0.0932753	−	0.00833478i
$496$	−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	$-0.727418\pi$
$499$	−7.33971	+	4.23758i	−0.328571	+	0.189700i	0.326636	+	0.945150i	$0.394085\pi$
$500$	−2.21955	+	9.48383i	−0.0992611	+	0.424130i
$501$	−3.02330	+	2.76520i	−0.135071	+	0.123540i
$502$	3.31014	−	28.6698i	0.147739	−	1.27959i
$503$	−42.5519			−1.89730			−0.948648	−	0.316334i	$-0.897548\pi$
$503$	−42.5519			−1.89730			−0.948648	+	0.316334i	$0.897548\pi$
$504$	−7.37669	+	21.2034i	−0.328584	+	0.944475i
$505$	−8.03941			−0.357749
$506$	−1.14217	+	9.89254i	−0.0507756	+	0.439777i
$507$	−6.94583	+	6.35285i	−0.308475	+	0.282140i
$508$	−0.689212	+	2.94491i	−0.0305788	+	0.130659i
$509$	14.9018	−	8.60356i	0.660511	−	0.381346i	−0.131961	−	0.991255i	$-0.542127\pi$
$509$	14.9018	−	8.60356i	0.660511	−	0.381346i	0.792472	+	0.609909i	$0.208794\pi$
$510$	−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
$513$	−11.8991	−	4.96758i	−0.525359	−	0.219324i
$514$	15.2911	+	35.3121i	0.674462	+	1.55755i
$515$	0.468656	−	0.811735i	0.0206514	−	0.0357693i
$516$	5.97328	+	10.6553i	0.262959	+	0.469072i
$517$	7.04155			0.309687
$518$	−13.3603	−	24.0082i	−0.587019	−	1.05486i
$519$	−4.99896	+	15.8036i	−0.219430	+	0.693701i
$520$	−0.690884	−	3.82376i	−0.0302973	−	0.167683i
$521$	−9.47744	−	5.47180i	−0.415214	−	0.239724i	0.277814	−	0.960635i	$-0.410390\pi$
$521$	−9.47744	−	5.47180i	−0.415214	−	0.239724i	−0.693028	+	0.720911i	$0.743724\pi$
$522$	5.43626	−	26.2685i	0.237938	−	1.14974i
$523$	−4.79287	+	2.76716i	−0.209578	+	0.121000i	−0.601115	−	0.799162i	$-0.705277\pi$
$523$	−4.79287	+	2.76716i	−0.209578	+	0.121000i	0.391537	+	0.920162i	$0.371943\pi$
$524$	3.85053	+	12.7312i	0.168211	+	0.556164i
$525$	−20.6891	+	6.77361i	−0.902945	+	0.295624i
$526$	−4.09362	−	3.03864i	−0.178490	−	0.132491i
$527$	20.1344	+	34.8739i	0.877069	+	1.51913i
$528$	−2.31384	+	9.35165i	−0.100697	+	0.406979i
$529$	−1.32230	+	2.29030i	−0.0574915	+	0.0995782i
$530$	−0.424917	+	3.68029i	−0.0184572	+	0.159862i
$531$	7.73521	+	5.43764i	0.335679	+	0.235974i
$532$	−5.02702	−	12.1307i	−0.217949	−	0.525931i
$533$		−	15.8001i		−	0.684379i
$534$	−5.48012	−	2.45587i	−0.237148	−	0.106276i
$535$	3.14830	+	1.81767i	0.136113	+	0.0785848i
$536$	−23.1961	+	19.6312i	−1.00192	+	0.847940i
$537$	7.74788	+	35.1023i	0.334346	+	1.51478i
$538$	−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	0.699371	−	0.714759i	$-0.253464\pi$
$541$	−6.26409	−	10.8497i	−0.269314	−	0.466466i	−0.968685	+	0.248293i	$0.920130\pi$
$542$	12.9600	+	29.9289i	0.556681	+	1.28556i
$543$	−8.22391	+	7.52182i	−0.352922	+	0.322792i
$544$	−29.3329	+	14.9908i	−1.25764	+	0.642725i
$545$			0.920019i			0.0394093i
$546$	13.3418	−	11.8214i	0.570975	−	0.505910i
$547$		−	37.4911i		−	1.60300i	−0.597992	−	0.801502i	$-0.704034\pi$
$547$		−	37.4911i		−	1.60300i	0.597992	−	0.801502i	$-0.295966\pi$
$548$	−17.7829	−	16.6830i	−0.759647	−	0.712661i
$549$	13.3574	−	6.19855i	0.570081	−	0.264548i
$550$	−8.57253	+	3.71214i	−0.365534	+	0.158286i
$551$	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
$555$	6.20318	−	1.36918i	0.263310	−	0.0581185i
$556$	−0.0217777	+	0.0930531i	−0.000923578	+	0.00394633i
$557$	26.0411	+	15.0348i	1.10340	+	0.637046i	0.937111	−	0.349031i	$-0.113489\pi$
$557$	26.0411	+	15.0348i	1.10340	+	0.637046i	0.166286	+	0.986078i	$0.446823\pi$
$558$	21.9079	+	19.5139i	0.927433	+	0.826088i
$559$		−	9.69912i		−	0.410229i
$560$	−0.857607	−	5.21580i	−0.0362405	−	0.220408i
$561$	4.22976	−	13.3719i	0.178581	−	0.564560i
$562$	38.8642	+	4.48717i	1.63939	+	0.189280i
$563$	3.41956	−	5.92285i	0.144117	−	0.249618i	−0.784926	−	0.619589i	$-0.787299\pi$
$563$	3.41956	−	5.92285i	0.144117	−	0.249618i	0.929043	+	0.369971i	$0.120632\pi$
$564$	15.0799	+	8.96278i	0.634979	+	0.377401i
$565$	2.56544	+	4.44348i	0.107929	+	0.186939i
$566$	14.6420	−	19.7255i	0.615449	−	0.829124i
$567$	1.88103	−	23.7373i	0.0789957	−	0.996875i
$568$	4.34308	−	12.0910i	0.182232	−	0.507329i
$569$	−29.0006	+	16.7435i	−1.21577	+	0.701924i	−0.964010	−	0.265866i	$-0.914342\pi$
$569$	−29.0006	+	16.7435i	−1.21577	+	0.701924i	−0.251759	+	0.967790i	$0.581009\pi$
$570$	3.02012	−	0.310012i	0.126499	−	0.0129850i
$571$	24.2464	+	13.9986i	1.01468	+	0.585825i	0.912558	−	0.408947i	$-0.134104\pi$
$571$	24.2464	+	13.9986i	1.01468	+	0.585825i	0.102121	+	0.994772i	$0.467437\pi$
$572$	5.23354	−	5.57859i	0.218826	−	0.233253i
$573$	28.9553	+	9.15909i	1.20963	+	0.382627i
$574$	0.339294	−	21.4908i	0.0141619	−	0.897009i
$575$	−24.0570			−1.00324
$576$	−16.8584	+	17.0820i	−0.702434	+	0.711749i
$577$	−18.8181	+	32.5939i	−0.783409	+	1.35690i	0.146537	+	0.989205i	$0.453187\pi$
$577$	−18.8181	+	32.5939i	−0.783409	+	1.35690i	−0.929945	+	0.367698i	$0.880146\pi$
$578$	21.9461	−	9.50325i	0.912836	−	0.395283i
$579$	−0.815732	−	3.69573i	−0.0339007	−	0.153589i
$580$	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
$584$	18.2264	+	21.5362i	0.754216	+	0.891174i
$585$	1.73485	+	3.73846i	0.0717270	+	0.154566i
$586$	−28.0515	−	3.23876i	−1.15880	−	0.133792i
$587$	−19.7791			−0.816373			−0.408186	−	0.912899i	$-0.633839\pi$
$587$	−19.7791			−0.816373			−0.408186	+	0.912899i	$0.633839\pi$
$588$	18.4009	−	15.7926i	0.758841	−	0.651276i
$589$	−17.1601			−0.707071
$590$	−2.21154	−	0.255339i	−0.0910477	−	0.0105121i
$591$	−7.33771	−	8.02262i	−0.301833	−	0.330007i
$592$	−1.87282	−	29.3126i	−0.0769724	−	1.20474i
$593$	19.5061	−	11.2619i	0.801020	−	0.462469i	−0.0428074	−	0.999083i	$-0.513630\pi$
$593$	19.5061	−	11.2619i	0.801020	−	0.462469i	0.843828	+	0.536614i	$0.180297\pi$
$594$	−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
$597$	1.46389	−	0.323114i	0.0599132	−	0.0132242i
$598$	18.0764	−	7.82756i	0.739198	−	0.320093i
$599$	13.3658	−	23.1503i	0.546113	−	0.945895i	−0.452423	−	0.891803i	$-0.649440\pi$
$599$	13.3658	−	23.1503i	0.546113	−	0.945895i	0.998536	−	0.0540915i	$-0.0172263\pi$
$600$	−23.0836	−	2.96170i	−0.942382	−	0.120911i
$601$	31.1478			1.27055			0.635273	−	0.772288i	$-0.280888\pi$
$601$	31.1478			1.27055			0.635273	+	0.772288i	$0.280888\pi$
$602$	0.208280	−	13.1924i	0.00848887	−	0.537684i
$603$	18.5362	−	26.3682i	0.754851	−	1.07380i
$604$	19.1599	+	17.9748i	0.779605	+	0.731384i
$605$	−3.92171	−	2.26420i	−0.159440	−	0.0920529i
$606$	−4.02601	−	39.2211i	−0.163545	−	1.59325i
$607$	−10.8934	+	6.28933i	−0.442151	+	0.255276i	−0.704510	−	0.709694i	$-0.748833\pi$
$607$	−10.8934	+	6.28933i	−0.442151	+	0.255276i	0.262358	+	0.964970i	$0.415500\pi$
$608$	0.717627	−	14.0193i	0.0291036	−	0.568558i
$609$	−19.3394	+	21.5757i	−0.783672	+	0.874290i
$610$	−2.06651	+	2.78398i	−0.0836707	+	0.112720i
$611$	−6.96442	−	12.0627i	−0.281750	−	0.488006i
$612$	26.0785	−	23.2528i	1.05416	−	0.939940i
$613$	−2.27131	+	3.93403i	−0.0917374	+	0.158894i	−0.908242	−	0.418445i	$-0.862575\pi$
$613$	−2.27131	+	3.93403i	−0.0917374	+	0.158894i	0.816505	+	0.577339i	$0.195909\pi$
$614$	−19.8831	−	2.29565i	−0.802415	−	0.0926449i
$615$	4.73806	+	1.49873i	0.191057	+	0.0604348i
$616$	7.23830	−	7.47544i	0.291639	−	0.301194i
$617$		−	35.4652i		−	1.42777i	−0.700261	−	0.713887i	$-0.746933\pi$
$617$		−	35.4652i		−	1.42777i	0.700261	−	0.713887i	$-0.253067\pi$
$618$	4.19482	+	1.87988i	0.168741	+	0.0756198i
$619$	−35.9030	−	20.7286i	−1.44306	−	0.833153i	−0.445011	−	0.895525i	$-0.646800\pi$
$619$	−35.9030	−	20.7286i	−1.44306	−	0.833153i	−0.998053	+	0.0623719i	$0.980134\pi$
$620$	−6.72599	−	1.57412i	−0.270122	−	0.0632180i
$621$	10.1373	−	24.2825i	0.406797	−	0.974423i
$622$	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
$626$	−0.0675646	+	0.0292573i	−0.00270043	+	0.00116936i
$627$	4.03361	+	4.41012i	0.161087	+	0.176123i
$628$	11.5076	−	12.2663i	0.459202	−	0.489477i
$629$			42.7609i			1.70499i
$630$	2.27940	+	5.12220i	0.0908135	+	0.204073i
$631$		−	22.2919i		−	0.887428i	−0.896168	−	0.443714i	$-0.853661\pi$
$631$		−	22.2919i		−	0.887428i	0.896168	−	0.443714i	$-0.146339\pi$
$632$	−1.07183	−	5.93217i	−0.0426353	−	0.235969i
$633$	4.56386	+	4.98986i	0.181397	+	0.198329i
$634$	3.80819	+	8.79434i	0.151242	+	0.349268i
$635$	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
$639$	−1.21281	+	13.5726i	−0.0479779	+	0.536926i
$640$	1.56728	−	5.42910i	0.0619522	−	0.214604i
$641$	−29.5411	−	17.0555i	−1.16680	−	0.673653i	−0.213877	−	0.976861i	$-0.568609\pi$
$641$	−29.5411	−	17.0555i	−1.16680	−	0.673653i	−0.952925	+	0.303207i	$0.901943\pi$
$642$	−7.29107	+	16.2695i	−0.287756	+	0.642108i
$643$		−	24.2299i		−	0.955533i	−0.878487	−	0.477766i	$-0.841447\pi$
$643$		−	24.2299i		−	0.955533i	0.878487	−	0.477766i	$-0.158553\pi$
$644$	24.7550	−	10.2586i	0.975483	−	0.404247i
$645$	2.90852	+	0.920019i	0.114523	+	0.0362257i
$646$	−2.34395	+	20.3015i	−0.0922217	+	0.798750i
$647$	−0.714092	+	1.23684i	−0.0280738	+	0.0486253i	−0.879721	−	0.475490i	$-0.842271\pi$
$647$	−0.714092	+	1.23684i	−0.0280738	+	0.0486253i	0.851647	+	0.524116i	$0.175604\pi$
$648$	12.7166	−	22.0519i	0.499556	−	0.866282i
$649$	−2.19125	−	3.79535i	−0.0860140	−	0.148981i
$650$	14.8378	+	11.0139i	0.581987	+	0.432002i
$651$	−9.86004	−	30.1162i	−0.386445	−	1.18035i
$652$	−23.6612	+	7.15630i	−0.926644	+	0.280262i
$653$	4.35426	−	2.51393i	0.170395	−	0.0983778i	−0.412377	−	0.911013i	$-0.635301\pi$
$653$	4.35426	−	2.51393i	0.170395	−	0.0983778i	0.582772	+	0.812636i	$0.301968\pi$
$654$	−4.48840	+	0.460730i	−0.175510	+	0.0180160i
$655$	2.87661	+	1.66081i	0.112398	+	0.0648933i
$656$	10.1966	−	20.5912i	0.398110	−	0.803949i
$657$	−24.4814	−	17.2097i	−0.955109	−	0.671416i
$658$	−9.21375	−	16.5569i	−0.359190	−	0.645456i
$659$	−19.7930			−0.771025			−0.385512	−	0.922703i	$-0.625975\pi$
$659$	−19.7930			−0.771025			−0.385512	+	0.922703i	$0.625975\pi$
$660$	1.17645	+	2.09857i	0.0457932	+	0.0816868i
$661$	11.3306	−	19.6252i	0.440709	−	0.763331i	−0.557033	−	0.830490i	$-0.688060\pi$
$661$	11.3306	−	19.6252i	0.440709	−	0.763331i	0.997742	+	0.0671595i	$0.0213936\pi$
$662$	10.0547	+	23.2195i	0.390787	+	0.902453i
$663$	−27.0905	+	5.97948i	−1.05211	+	0.232224i
$664$	−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
$668$	4.60652	+	1.07808i	0.178231	+	0.0417124i
$669$	27.4729	+	30.0372i	1.06216	+	1.16131i
$670$	−0.870415	+	7.53884i	−0.0336271	+	0.291251i
$671$	−6.82530			−0.263488
$672$	25.0163	−	6.79591i	0.965025	−	0.262158i
$673$	−11.2766			−0.434680			−0.217340	−	0.976096i	$-0.569738\pi$
$673$	−11.2766			−0.434680			−0.217340	+	0.976096i	$0.569738\pi$
$674$	1.15061	−	9.96568i	0.0443200	−	0.383864i
$675$	24.4822	−	3.15392i	0.942320	−	0.121394i
$676$	10.5831	+	2.47682i	0.407044	+	0.0952625i
$677$	−8.73729	+	5.04448i	−0.335801	+	0.193875i	−0.658414	−	0.752656i	$-0.728772\pi$
$677$	−8.73729	+	5.04448i	−0.335801	+	0.193875i	0.322612	+	0.946531i	$0.395439\pi$
$678$	−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
$681$	−7.15568	−	32.4193i	−0.274206	−	1.24231i
$682$	−5.40360	−	12.4786i	−0.206914	−	0.477832i
$683$	−3.11743	+	5.39955i	−0.119285	+	0.206608i	−0.919485	−	0.393126i	$-0.871394\pi$
$683$	−3.11743	+	5.39955i	−0.119285	+	0.206608i	0.800199	+	0.599734i	$0.204727\pi$
$684$	3.02485	+	14.5787i	0.115658	+	0.557430i
$685$	−6.08933			−0.232662
$686$	−25.7565	+	4.75444i	−0.983386	+	0.181525i
$687$	−18.9517	−	5.99476i	−0.723052	−	0.228714i
$688$	6.25932	−	12.6402i	0.238634	−	0.481902i
$689$	12.4936	+	7.21316i	0.475967	+	0.274799i
$690$	0.632641	+	6.16314i	0.0240842	+	0.234627i
$691$	14.7810	−	8.53381i	0.562295	−	0.324641i	−0.191771	−	0.981440i	$-0.561423\pi$
$691$	14.7810	−	8.53381i	0.562295	−	0.324641i	0.754066	+	0.656798i	$0.228090\pi$
$692$	18.3200	−	5.54087i	0.696423	−	0.210632i
$693$	−5.42211	+	9.61303i	−0.205969	+	0.365169i
$694$	10.4367	+	7.74704i	0.396172	+	0.294074i
$695$	0.0119331	+	0.0206688i	0.000452650	+	0.000784012i
$696$	−28.5780	+	11.9478i	−1.08325	+	0.452881i
$697$	−16.7256	+	28.9695i	−0.633526	+	1.09730i
$698$	−3.59007	+	31.0943i	−0.135886	+	1.17694i
$699$	10.5610	−	33.3872i	0.399452	−	1.26282i
$700$	19.9454	+	15.2994i	0.753866	+	0.578264i
$701$			21.4324i			0.809489i	0.914430	+	0.404744i	$0.132640\pi$
$701$			21.4324i			0.809489i	−0.914430	+	0.404744i	$0.867360\pi$
$702$	−17.3697	+	10.3358i	−0.655576	+	0.390099i
$703$	−15.7808	−	9.11104i	−0.595183	−	0.343629i
$704$	10.4206	−	3.89272i	0.392743	−	0.146712i
$705$	4.27793	−	0.944236i	0.161116	−	0.0355620i
$706$	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	0.935017	−	0.354604i	$-0.115384\pi$
$709$	4.27131	+	7.39813i	0.160412	+	0.277843i	−0.774604	+	0.632446i	$0.782051\pi$
$710$	−1.27493	−	2.94422i	−0.0478472	−	0.110495i
$711$	2.69143	+	5.79983i	0.100937	+	0.217511i
$712$	1.23293	+	6.82378i	0.0462061	+	0.255732i
$713$		−	35.0186i		−	1.31146i
$714$	−36.9760	+	7.55135i	−1.38379	+	0.282602i
$715$		−	1.91026i		−	0.0714396i
$716$	28.3997	−	30.2721i	1.06135	−	1.13132i
$717$	−8.82868	+	8.07495i	−0.329713	+	0.301565i
$718$	4.67835	−	2.02585i	0.174594	−	0.0756042i
$719$	13.7366	+	23.7924i	0.512287	+	0.887308i	0.999899	+	0.0142470i	$0.00453511\pi$
$719$	13.7366	+	23.7924i	0.512287	+	0.887308i	−0.487611	+	0.873061i	$0.662132\pi$
$720$	−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
$723$	3.01137	+	13.6432i	0.111994	+	0.507397i
$724$	12.5305	+	2.93258i	0.465693	+	0.108988i
$725$	−26.0123	−	15.0182i	−0.966074	−	0.557763i
$726$	9.08220	−	20.2663i	0.337072	−	0.752154i
$727$			45.7930i			1.69837i	0.528096	+	0.849185i	$0.322906\pi$
$727$			45.7930i			1.69837i	−0.528096	+	0.849185i	$0.677094\pi$
$728$	−19.9650	−	5.00622i	−0.739953	−	0.185543i
$729$	−7.13303	+	26.0407i	−0.264186	+	0.964472i
$730$	6.99937	+	0.808129i	0.259058	+	0.0299102i
$731$	−10.2672	+	17.7834i	−0.379747	+	0.657741i
$732$	−14.6168	−	8.68752i	−0.540252	−	0.321100i
$733$	21.6466	+	37.4930i	0.799535	+	1.38483i	0.919919	+	0.392107i	$0.128254\pi$
$733$	21.6466	+	37.4930i	0.799535	+	1.38483i	−0.120385	+	0.992727i	$0.538413\pi$
$734$	12.6661	−	17.0636i	0.467514	−	0.629828i
$735$	0.652957	−	6.02038i	0.0240847	−	0.222065i
$736$	28.6091	+	1.46446i	1.05455	+	0.0539807i
$737$	−12.9378	+	7.46966i	−0.476571	+	0.275148i
$738$	−4.93897	+	23.8656i	−0.181806	+	0.878506i
$739$	4.48246	+	2.58795i	0.164890	+	0.0951993i	0.580174	−	0.814492i	$-0.302984\pi$
$739$	4.48246	+	2.58795i	0.164890	+	0.0951993i	−0.415284	+	0.909692i	$0.636318\pi$
$740$	−5.34958	−	5.01870i	−0.196655	−	0.184491i
$741$	3.56544	−	11.2717i	0.130980	−	0.414077i
$742$	16.8384	+	10.0794i	0.618159	+	0.370026i
$743$	49.5492			1.81778			0.908891	−	0.417034i	$-0.136930\pi$
$743$	49.5492			1.81778			0.908891	+	0.417034i	$0.136930\pi$
$744$	4.31121	−	33.6017i	0.158057	−	1.23190i
$745$	−0.572839	+	0.992187i	−0.0209872	+	0.0363509i
$746$	−3.44806	+	1.49310i	−0.126242	+	0.0546664i
$747$	3.20849	−	35.9066i	0.117393	−	1.31375i
$748$	−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	$-0.478203\pi$
$751$	26.4899	−	15.2939i	0.966630	−	0.558084i	0.898207	+	0.439572i	$0.144870\pi$
$752$	−1.29156	−	20.2150i	−0.0470985	−	0.737165i
$753$	26.0822	−	23.8555i	0.950489	−	0.869344i
$754$	24.4322	+	2.82088i	0.889769	+	0.102730i
$755$	6.56086			0.238774
$756$	−23.8476	+	13.6854i	−0.867330	+	0.497733i
$757$	46.4533			1.68837			0.844187	−	0.536049i	$-0.180084\pi$
$757$	46.4533			1.68837			0.844187	+	0.536049i	$0.180084\pi$
$758$	24.8874	+	2.87344i	0.903952	+	0.104368i
$759$	−8.99971	+	8.23138i	−0.326669	+	0.298780i
$760$	−2.26470	−	2.67595i	−0.0821495	−	0.0970670i
$761$	−34.1633	+	19.7242i	−1.23842	+	0.715002i	−0.968771	−	0.247956i	$-0.920241\pi$
$761$	−34.1633	+	19.7242i	−1.23842	+	0.715002i	−0.269649	+	0.962959i	$0.586908\pi$
$762$	−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
$765$	0.776595	−	8.69095i	0.0280778	−	0.314222i
$766$	−42.7247	+	18.5010i	−1.54371	+	0.668467i
$767$	−4.33449	+	7.50756i	−0.156509	+	0.271082i
$768$	27.2713	+	4.92733i	0.984067	+	0.177800i
$769$	39.7256			1.43254			0.716270	−	0.697823i	$-0.245848\pi$
$769$	39.7256			1.43254			0.716270	+	0.697823i	$0.245848\pi$
$770$	0.0410212	−	2.59827i	0.00147830	−	0.0936353i
$771$	−14.2136	+	44.9346i	−0.511891	+	1.61828i
$772$	−2.99005	+	3.18718i	−0.107614	+	0.114709i
$773$	−18.9935	−	10.9659i	−0.683149	−	0.394416i	0.117891	−	0.993026i	$-0.462387\pi$
$773$	−18.9935	−	10.9659i	−0.683149	−	0.394416i	−0.801040	+	0.598610i	$0.795720\pi$
$774$	−3.03186	+	14.6503i	−0.108978	+	0.526592i
$775$	28.4495	−	16.4253i	1.02194	−	0.590015i
$776$	−0.502967	+	1.40025i	−0.0180554	+	0.0502660i
$777$	6.92246	−	32.9305i	0.248342	−	1.18137i
$778$	5.75054	−	7.74704i	0.206167	−	0.277745i
$779$	−7.12742	−	12.3451i	−0.255366	−	0.442307i
$780$	2.43146	−	4.09094i	0.0870601	−	0.146479i
$781$	3.15799	−	5.46980i	0.113002	−	0.195725i
$782$	−41.4291	−	4.78330i	−1.48150	−	0.171051i
$783$	26.1203	−	19.9277i	0.933464	−	0.712157i
$784$	−27.0483	−	7.23803i	−0.966011	−	0.258501i
$785$		−	4.20029i		−	0.149915i
$786$	−6.66187	+	14.8655i	−0.237621	+	0.530236i
$787$	−4.36864	−	2.52223i	−0.155725	−	0.0899080i	0.420112	−	0.907472i	$-0.361991\pi$
$787$	−4.36864	−	2.52223i	−0.155725	−	0.0899080i	−0.575838	+	0.817564i	$0.695324\pi$
$788$	−2.86080	+	12.2238i	−0.101912	+	0.435456i
$789$	−1.34578	−	6.09717i	−0.0479111	−	0.217065i
$790$	−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
$794$	27.0508	−	11.7137i	0.959997	−	0.415705i
$795$	−3.34813	+	3.06230i	−0.118746	+	0.108608i
$796$	−1.26245	−	1.18437i	−0.0447465	−	0.0419788i
$797$			28.3335i			1.00362i	0.864977	+	0.501812i	$0.167333\pi$
$797$			28.3335i			1.00362i	−0.864977	+	0.501812i	$0.832667\pi$
$798$	5.09165	−	15.2549i	0.180243	−	0.540016i
$799$			29.4894i			1.04326i
$800$	12.2292	+	23.9292i	0.432369	+	0.846026i
$801$	−3.09595	−	6.67155i	−0.109390	−	0.235728i
$802$	2.14977	+	4.96450i	0.0759109	+	0.175303i
$803$	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
$807$	−44.2545	+	9.76797i	−1.55783	+	0.343849i
$808$	−34.7515	+	29.4108i	−1.22256	+	1.03467i
$809$	−17.5088	−	10.1087i	−0.615577	−	0.355404i	0.159568	−	0.987187i	$-0.448990\pi$
$809$	−17.5088	−	10.1087i	−0.615577	−	0.355404i	−0.775145	+	0.631783i	$0.782323\pi$
$810$	−1.45182	−	6.18914i	−0.0510119	−	0.217464i
$811$			1.33368i			0.0468317i	0.999726	+	0.0234158i	$0.00745418\pi$
$811$			1.33368i			0.0468317i	−0.999726	+	0.0234158i	$0.992546\pi$
$812$	33.1713	+	4.36154i	1.16409	+	0.153060i
$813$	−12.0468	+	38.0845i	−0.422500	+	1.33568i
$814$	1.65619	−	14.3446i	0.0580495	−	0.502778i
$815$	−3.08666	+	5.34625i	−0.108121	+	0.187271i
$816$	−39.1639	−	9.69018i	−1.37101	−	0.339224i
$817$	−4.37527	−	7.57819i	−0.153071	−	0.265127i
$818$	−4.39361	−	3.26133i	−0.153619	−	0.114030i
$819$	21.8306	−	0.219229i	0.762823	−	0.00766048i
$820$	−1.66120	−	5.49251i	−0.0580117	−	0.191807i
$821$	4.59977	−	2.65568i	0.160533	−	0.0926838i	−0.417581	−	0.908640i	$-0.637122\pi$
$821$	4.59977	−	2.65568i	0.160533	−	0.0926838i	0.578114	+	0.815956i	$0.303789\pi$
$822$	−3.04944	−	29.7074i	−0.106361	−	1.03616i
$823$	13.2508	+	7.65035i	0.461894	+	0.266675i	0.712840	−	0.701326i	$-0.247408\pi$
$823$	13.2508	+	7.65035i	0.461894	+	0.266675i	−0.250946	+	0.968001i	$0.580742\pi$
$824$	−0.943763	−	5.22334i	−0.0328775	−	0.181964i
$825$	−10.9085	−	3.45056i	−0.379786	−	0.120133i
$826$	−6.05686	+	10.1185i	−0.210745	+	0.352066i
$827$	−0.288306			−0.0100254			−0.00501270	−	0.999987i	$-0.501596\pi$
$827$	−0.288306			−0.0100254			−0.00501270	+	0.999987i	$0.501596\pi$
$828$	−29.7507	+	6.17280i	−1.03391	+	0.214520i
$829$	20.5551	−	35.6025i	0.713908	−	1.23653i	−0.249471	−	0.968382i	$-0.580257\pi$
$829$	20.5551	−	35.6025i	0.713908	−	1.23653i	0.963379	−	0.268143i	$-0.0864100\pi$
$830$	3.37284	+	7.78897i	0.117073	+	0.270359i
$831$	−7.57498	−	34.3190i	−0.262773	−	1.19051i
$832$	−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
$836$	1.57261	−	6.71956i	0.0543898	−	0.232401i
$837$	4.59102	+	35.6376i	0.158689	+	1.23182i
$838$	2.19192	−	18.9846i	0.0757186	−	0.655814i
$839$	−25.7705			−0.889695			−0.444848	−	0.895606i	$-0.646742\pi$
$839$	−25.7705			−0.889695			−0.444848	+	0.895606i	$0.646742\pi$
$840$	3.39504	−	5.51215i	0.117140	−	0.190187i
$841$	−10.9772			−0.378523
$842$	1.84629	−	15.9910i	0.0636272	−	0.551088i
$843$	32.3381	+	35.3566i	1.11378	+	1.21775i
$844$	1.77934	−	7.60289i	0.0612475	−	0.261702i
$845$	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
$849$	29.3798	−	6.48478i	1.00831	−	0.222557i
$850$	−15.5461	−	35.9010i	−0.533227	−	1.23139i
$851$	18.5929	−	32.2038i	0.637355	−	1.10393i
$852$	13.7252	−	7.69428i	0.470218	−	0.263602i
$853$	−51.4656			−1.76215			−0.881074	−	0.472978i	$-0.843179\pi$
$853$	−51.4656			−1.76215			−0.881074	+	0.472978i	$0.843179\pi$
$854$	8.93078	+	16.0484i	0.305605	+	0.549166i
$855$	3.04190	+	2.13838i	0.104031	+	0.0731309i
$856$	20.2586	−	3.66036i	0.692426	−	0.125109i
$857$	−30.8099	−	17.7881i	−1.05245	−	0.607631i	−0.129114	−	0.991630i	$-0.541213\pi$
$857$	−30.8099	−	17.7881i	−1.05245	−	0.607631i	−0.923334	+	0.383999i	$0.874547\pi$
$858$	9.31938	−	0.956627i	0.318159	−	0.0326587i
$859$	−44.4334	+	25.6536i	−1.51605	+	0.875290i	−0.516225	+	0.856453i	$0.672663\pi$
$859$	−44.4334	+	25.6536i	−1.51605	+	0.875290i	−0.999823	+	0.0188372i	$0.994004\pi$
$860$	−1.01975	−	3.37165i	−0.0347732	−	0.114972i
$861$	17.5703	−	19.6020i	0.598795	−	0.668035i
$862$	−29.4388	−	21.8521i	−1.00269	−	0.744286i
$863$	−5.89152	−	10.2044i	−0.200550	−	0.347362i	0.748156	−	0.663523i	$-0.230939\pi$
$863$	−5.89152	−	10.2044i	−0.200550	−	0.347362i	−0.948706	+	0.316161i	$0.897606\pi$
$864$	−29.3068	+	2.26037i	−0.997039	+	0.0768995i
$865$	2.38989	−	4.13941i	0.0812587	−	0.140744i
$866$	3.79273	−	32.8496i	0.128882	−	1.11628i
$867$	27.9263	+	8.83360i	0.948428	+	0.300005i
$868$	−22.2707	+	29.0336i	−0.755917	+	0.985466i
$869$		−	2.96357i		−	0.100532i
$870$	−3.16345	+	7.05903i	−0.107251	+	0.239324i
$871$	25.5922	+	14.7757i	0.867160	+	0.500655i
$872$	3.36573	+	3.97692i	0.113978	+	0.134675i
$873$	0.140454	−	1.57183i	0.00475364	−	0.0531984i
$874$	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	0.854591	−	0.519301i	$-0.173808\pi$
$877$	−0.664314	−	1.15063i	−0.0224323	−	0.0388539i	−0.877024	+	0.480447i	$0.840474\pi$
$878$	−9.93174	−	22.9356i	−0.335180	−	0.774039i
$879$	−23.3411	−	25.5198i	−0.787275	−	0.860760i
$880$	1.23278	−	2.48950i	0.0415571	−	0.0839212i
$881$		−	23.8258i		−	0.802713i	−0.915922	−	0.401356i	$-0.868539\pi$
$881$		−	23.8258i		−	0.802713i	0.915922	−	0.401356i	$-0.131461\pi$
$882$	29.6980	+	0.170605i	0.999983	+	0.00574457i
$883$			30.2235i			1.01710i	0.861032	+	0.508551i	$0.169819\pi$
$883$			30.2235i			1.01710i	−0.861032	+	0.508551i	$0.830181\pi$
$884$	23.3627	+	21.9176i	0.785772	+	0.737170i
$885$	−1.84018	−	2.01194i	−0.0618569	−	0.0676307i
$886$	−45.5985	+	19.7454i	−1.53191	+	0.663359i
$887$	−10.9556	−	18.9756i	−0.367852	−	0.637138i	0.621377	−	0.783511i	$-0.286573\pi$
$887$	−10.9556	−	18.9756i	−0.367852	−	0.637138i	−0.989229	+	0.146373i	$0.953240\pi$
$888$	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
$891$	8.07964	−	9.55676i	0.270678	−	0.320164i
$892$	10.7110	−	45.7668i	0.358632	−	1.53239i
$893$	−10.8830	−	6.28330i	−0.364185	−	0.210262i
$894$	−5.12735	−	2.29778i	−0.171484	−	0.0768493i
$895$		−	10.3660i		−	0.346496i
$896$	−22.7882	−	19.4087i	−0.761302	−	0.648398i
$897$	23.0021	+	7.27599i	0.768019	+	0.242938i
$898$	−7.76524	−	0.896555i	−0.259129	−	0.0299184i
$899$	21.8614	−	37.8650i	0.729117	−	1.26287i
$900$	−18.9692	−	21.2744i	−0.632308	−	0.709147i
$901$	−15.2713	−	26.4507i	−0.508761	−	0.881200i
$902$	6.73281	−	9.07034i	0.224178	−	0.302009i
$903$	10.7858	−	12.0330i	0.358928	−	0.400432i
$904$	27.3452	+	9.82235i	0.909489	+	0.326687i
$905$	2.78326	−	1.60692i	0.0925187	−	0.0534157i
$906$	3.28557	+	32.0078i	0.109156	+	1.06339i
$907$	−42.4039	−	24.4819i	−1.40800	−	0.812907i	−0.412802	−	0.910821i	$-0.635450\pi$
$907$	−42.4039	−	24.4819i	−1.40800	−	0.812907i	−0.995195	+	0.0979134i	$0.968783\pi$
$908$	−26.2290	+	27.9583i	−0.870439	+	0.927827i
$909$	27.7702	−	39.5040i	0.921081	−	1.31026i
$910$	−4.49162	+	2.49954i	−0.148896	+	0.0828590i
$911$	−51.8251			−1.71704			−0.858522	−	0.512777i	$-0.828617\pi$
$911$	−51.8251			−1.71704			−0.858522	+	0.512777i	$0.828617\pi$
$912$	11.9208	−	12.3887i	0.394736	−	0.410229i
$913$	−8.35449	+	14.4704i	−0.276493	+	0.478900i
$914$	−31.0843	+	13.4604i	−1.02818	+	0.445229i
$915$	−4.14655	+	0.915237i	−0.137081	+	0.0302568i
$916$	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	$-0.353299\pi$
$919$	43.7375	−	25.2518i	1.44277	−	0.832981i	0.998034	+	0.0626826i	$0.0199656\pi$
$920$	5.46081	−	4.62158i	0.180038	−	0.152369i
$921$	−16.5443	−	18.0886i	−0.545153	−	0.596038i
$922$	4.21013	+	0.486091i	0.138653	+	0.0160086i
$923$	−12.4936			−0.411232
$924$	12.6965	−	1.10105i	0.417683	−	0.0362218i
$925$	34.8836			1.14696
$926$	31.4907	+	3.63583i	1.03485	+	0.119481i
$927$	2.36984	+	5.10682i	0.0778356	+	0.167730i
$928$	30.0203	+	19.4435i	0.985464	+	0.638266i
$929$	−1.07011	+	0.617830i	−0.0351093	+	0.0202703i	−0.517452	−	0.855712i	$-0.673119\pi$
$929$	−1.07011	+	0.617830i	−0.0351093	+	0.0202703i	0.482343	+	0.875983i	$0.339786\pi$
$930$	−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
$933$	9.16676	+	41.5307i	0.300106	+	1.35965i
$934$	15.6527	−	6.77806i	0.512173	−	0.221785i
$935$	−2.02215	+	3.50247i	−0.0661314	+	0.114543i
$936$	21.1757	+	9.81343i	0.692148	+	0.320762i
$937$	−29.4139			−0.960909			−0.480455	−	0.877020i	$-0.659528\pi$
$937$	−29.4139			−0.960909			−0.480455	+	0.877020i	$0.659528\pi$
$938$	34.4924	+	20.6470i	1.12622	+	0.674148i
$939$	−0.0859759	−	0.0271957i	−0.00280572	−	0.000887499i
$940$	−3.68926	−	3.46107i	−0.120331	−	0.112888i
$941$	38.8530	+	22.4318i	1.26657	+	0.731256i	0.974338	−	0.225090i	$-0.0722677\pi$
$941$	38.8530	+	22.4318i	1.26657	+	0.731256i	0.292235	+	0.956346i	$0.405601\pi$
$942$	20.4915	−	2.10344i	0.667651	−	0.0685337i
$943$	25.1925	−	14.5449i	0.820381	−	0.473647i
$944$	−10.4938	+	6.98680i	−0.341545	+	0.227401i
$945$	−2.00502	+	6.56725i	−0.0652233	+	0.213633i
$946$	4.13303	−	5.56796i	0.134376	−	0.181030i
$947$	8.77882	+	15.2054i	0.285273	+	0.494108i	0.972675	−	0.232169i	$-0.0745823\pi$
$947$	8.77882	+	15.2054i	0.285273	+	0.494108i	−0.687402	+	0.726277i	$0.741249\pi$
$948$	3.77215	−	6.34665i	0.122514	−	0.206130i
$949$	13.7183	−	23.7609i	0.445316	−	0.771311i
$950$	16.5616	+	1.91216i	0.537328	+	0.0620386i
$951$	−3.53984	+	11.1908i	−0.114787	+	0.362886i
$952$	31.3065	+	30.3134i	1.01465	+	0.982462i
$953$			37.1546i			1.20356i	0.798663	+	0.601778i	$0.205541\pi$
$953$			37.1546i			1.20356i	−0.798663	+	0.601778i	$0.794459\pi$
$954$	−16.6164	−	14.8006i	−0.537976	−	0.479189i
$955$	−7.58422	−	4.37875i	−0.245420	−	0.141693i
$956$	13.4520	+	3.14823i	0.435068	+	0.101821i
$957$	−14.8699	+	3.28212i	−0.480675	+	0.106096i
$958$	−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
$962$	−26.2115	+	11.3503i	−0.845092	+	0.365948i
$963$	−19.8067	+	9.19136i	−0.638262	+	0.296187i
$964$	11.0381	−	11.7658i	0.355513	−	0.378952i
$965$			1.09138i			0.0351326i
$966$	31.1305	+	10.3905i	1.00161	+	0.334310i
$967$		−	53.9045i		−	1.73345i	−0.498786	−	0.866725i	$-0.666221\pi$
$967$		−	53.9045i		−	1.73345i	0.498786	−	0.866725i	$-0.333779\pi$
$968$	−25.2354	+	4.55957i	−0.811095	+	0.146550i
$969$	−18.4692	+	16.8924i	−0.593316	+	0.542663i
$970$	0.147648	+	0.340967i	0.00474069	+	0.0109478i
$971$	19.1783	+	33.2177i	0.615460	+	1.06601i	0.990304	+	0.138920i	$0.0443631\pi$
$971$	19.1783	+	33.2177i	0.615460	+	1.06601i	−0.374844	+	0.927088i	$0.622304\pi$
$972$	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
$975$	4.87795	+	22.0999i	0.156220	+	0.707764i
$976$	1.25190	+	19.5941i	0.0400722	+	0.627193i
$977$	15.5907	+	9.00127i	0.498789	+	0.287976i	0.728214	−	0.685350i	$-0.240351\pi$
$977$	15.5907	+	9.00127i	0.498789	+	0.287976i	−0.229424	+	0.973327i	$0.573684\pi$
$978$	−27.6279	−	12.3812i	−0.883444	−	0.395908i
$979$			3.40899i			0.108952i
$980$	−6.16304	+	3.30334i	−0.196871	+	0.105521i
$981$	−4.52078	−	3.17799i	−0.144337	−	0.101465i
$982$	6.47163	−	56.0521i	0.206518	−	1.78869i
$983$	−6.87845	+	11.9138i	−0.219388	+	0.379992i	−0.954621	−	0.297823i	$-0.903740\pi$
$983$	−6.87845	+	11.9138i	−0.219388	+	0.379992i	0.735233	+	0.677815i	$0.237073\pi$
$984$	25.9638	−	10.8549i	0.827696	−	0.346041i
$985$	1.56758	+	2.71514i	0.0499474	+	0.0865114i
$986$	−41.8104	−	31.0354i	−1.33151	−	0.988368i
$987$	4.77398	−	22.7100i	0.151957	−	0.722869i
$988$	−13.0665	+	3.95195i	−0.415701	+	0.125728i
$989$	15.4648	−	8.92860i	0.491751	−	0.283913i
$990$	−0.597130	+	2.88539i	−0.0189780	+	0.0917038i
$991$	−1.60779	−	0.928258i	−0.0510731	−	0.0294871i	0.474246	−	0.880392i	$-0.342721\pi$
$991$	−1.60779	−	0.928258i	−0.0510731	−	0.0294871i	−0.525319	+	0.850905i	$0.676054\pi$
$992$	−34.8327	+	17.8015i	−1.10594	+	0.565200i
$993$	−9.34619	+	29.5468i	−0.296593	+	0.937640i
$994$	−16.9934	−	0.268289i	−0.538998	−	0.00850962i
$995$	−0.432298			−0.0137048
$996$	−36.3102	+	20.3553i	−1.15053	+	0.644982i
$997$	−30.1748	+	52.2642i	−0.955644	+	1.65522i	−0.222756	+	0.974874i	$0.571505\pi$
$997$	−30.1748	+	52.2642i	−0.955644	+	1.65522i	−0.732888	+	0.680350i	$0.761828\pi$
$998$	4.76277	+	10.9988i	0.150763	+	0.348160i
$999$	−14.6995	+	35.2106i	−0.465073	+	1.11401i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.162204 - 1.40488i) q^{2} +(1.27809 - 1.16897i) q^{3} +(-1.94738 - 0.455755i) q^{4} +(-0.432549 + 0.249732i) q^{5} +(-1.43496 - 1.98517i) q^{6} +(0.261928 + 2.63275i) q^{7} +(-0.956154 + 2.66191i) q^{8} +(0.267006 - 2.98809i) q^{9} +O(q^{10})\)	\(q+(0.162204 - 1.40488i) q^{2} +(1.27809 - 1.16897i) q^{3} +(-1.94738 - 0.455755i) 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} +(0.267006 - 2.98809i) q^{9} +(0.280683 + 0.648187i) q^{10} +(-0.695249 + 1.20421i) q^{11} +(-3.02168 + 1.69394i) q^{12} +2.75054 q^{13} +(3.74119 + 0.0590654i) q^{14} +(-0.260904 + 0.824817i) q^{15} +(3.58458 + 1.77505i) q^{16} +(-5.04311 - 2.91164i) q^{17} +(-4.15461 - 0.859793i) q^{18} +(2.14907 - 1.24076i) q^{19} +(0.956154 - 0.289187i) q^{20} +(3.41238 + 3.05870i) q^{21} +(1.57899 + 1.17207i) q^{22} +(2.53203 + 4.38560i) q^{23} +(1.88965 + 4.51987i) q^{24} +(-2.37527 + 4.11408i) q^{25} +(0.446148 - 3.86417i) q^{26} +(-3.15174 - 4.13116i) q^{27} +(0.689816 - 5.24635i) q^{28} +6.32275i q^{29} +(1.11645 + 0.500328i) q^{30} +(-5.98869 - 3.45757i) q^{31} +(3.07517 - 4.74798i) q^{32} +(0.519097 + 2.35181i) 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} +(-1.39454 - 3.22044i) q^{38} +(3.51542 - 3.21530i) q^{39} +(-0.251182 - 1.39019i) q^{40} -5.74438i q^{41} +(4.85061 - 4.29786i) q^{42} -3.52627i q^{43} +(1.90274 - 2.02819i) q^{44} +(0.630730 + 1.35918i) q^{45} +(6.57194 - 2.84583i) 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} +(-9.84916 + 2.17393i) q^{51} +(-5.35634 - 1.25357i) q^{52} +(4.54223 + 2.62246i) q^{53} +(-6.31502 + 3.75773i) q^{54} -0.694505i q^{55} +(-7.25860 - 1.82009i) q^{56} +(1.29627 - 4.09801i) q^{57} +(8.88271 + 1.02558i) q^{58} +(-1.57587 + 2.72949i) q^{59} +(0.883994 - 1.48732i) q^{60} +(2.45426 + 4.25091i) q^{61} +(-5.82886 + 7.85256i) q^{62} +(7.93685 - 0.0797041i) q^{63} +(-6.17154 - 5.09039i) q^{64} +(-1.18974 + 0.686897i) q^{65} +(3.38821 - 0.347796i) q^{66} +(9.30445 + 5.37193i) q^{67} +(8.49386 + 7.96850i) q^{68} +(8.36279 + 2.64530i) q^{69} +(-1.63300 + 0.908747i) q^{70} -4.54224 q^{71} +(7.69874 + 3.56782i) q^{72} +(4.98752 - 8.63864i) q^{73} +(-9.52959 + 4.12657i) q^{74} +(1.77346 + 8.03477i) 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} +(-1.99379 + 0.127386i) q^{80} +(-8.85742 - 1.59568i) q^{81} +(-8.07016 - 0.931761i) q^{82} +12.0165 q^{83} +(-5.25119 - 7.51166i) q^{84} +2.90852 q^{85} +(-4.95398 - 0.571975i) q^{86} +(7.39112 + 8.08102i) q^{87} +(-2.54073 - 3.00210i) 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} +(-11.6959 + 2.58154i) q^{93} +(-6.57194 + 2.84583i) q^{94} +(-0.619718 + 1.07338i) q^{95} +(-1.61992 - 9.66312i) q^{96} +0.526031 q^{97} +(0.824419 + 9.86511i) q^{98} +(3.41265 + 2.39900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 - 2 * q^9	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37} + 34 q^{40} + 38 q^{42} - 18 q^{45} + 24 q^{46} + 8 q^{48} + 16 q^{52} + 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} + 4 q^{61} - 68 q^{64} + 30 q^{66} + 36 q^{69} - 90 q^{70} + 20 q^{72} - 24 q^{76} - 104 q^{78} + 26 q^{81} - 68 q^{82} - 76 q^{84} - 40 q^{85} - 34 q^{88} - 40 q^{90} - 6 q^{93} - 24 q^{94} - 62 q^{96} + 72 q^{97}+O(q^{100}) \) 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

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