LMFDB - Embedded newform 84.2.n.a.23.7

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			23.7
Character	$\chi$	$=$	84.23
Dual form			84.2.n.a.11.7

$q$-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} +(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} - 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 $

$2$	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	0.400151	−	0.916449i	$-0.368958\pi$
$5$	−0.432549	−	0.249732i	−0.193442	−	0.111684i	−0.593593	+	0.804766i	$0.702291\pi$
$6$	−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	0.741971	−	0.670432i	$-0.233891\pi$
$11$	−0.695249	−	1.20421i	−0.209626	−	0.363082i	−0.951597	+	0.307350i	$0.900558\pi$
$12$	−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	−0.965585	−	0.260088i	$-0.916248\pi$
$17$	−5.04311	+	2.91164i	−1.22313	+	0.706177i	−0.257550	+	0.966265i	$0.582915\pi$
$18$	−4.15461	+	0.859793i	−0.979250	+	0.202655i
$19$	2.14907	+	1.24076i	0.493030	+	0.284651i	0.725831	−	0.687874i	$-0.241456\pi$
$19$	2.14907	+	1.24076i	0.493030	+	0.284651i	−0.232801	+	0.972524i	$0.574789\pi$
$20$	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	−0.471505	−	0.881863i	$-0.656289\pi$
$23$	2.53203	−	4.38560i	0.527964	−	0.914460i	0.999469	−	0.0325966i	$-0.0103777\pi$
$24$	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	$-0.800288\pi$
$29$		−	6.32275i		−	1.17411i	0.809549	−	0.587053i	$-0.199712\pi$
$30$	1.11645	−	0.500328i	0.203835	−	0.0913470i
$31$	−5.98869	+	3.45757i	−1.07560	+	0.620998i	−0.929706	−	0.368302i	$-0.879939\pi$
$31$	−5.98869	+	3.45757i	−1.07560	+	0.620998i	−0.145894	+	0.989300i	$0.546606\pi$
$32$	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	0.388674	+	0.921375i	$0.372933\pi$
$37$	−3.67154	+	6.35929i	−0.603598	+	1.04546i	−0.992271	+	0.124086i	$0.960400\pi$
$38$	−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	$0.148063\pi$
$41$			5.74438i			0.897121i	−0.893753	+	0.448560i	$0.851937\pi$
$42$	4.85061	+	4.29786i	0.748465	+	0.663174i
$43$			3.52627i			0.537751i	0.963175	+	0.268875i	$0.0866520\pi$
$43$			3.52627i			0.537751i	−0.963175	+	0.268875i	$0.913348\pi$
$44$	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	−0.989462	−	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
$51$	−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	−0.154472	−	0.987997i	$-0.549368\pi$
$53$	4.54223	−	2.62246i	0.623923	−	0.360222i	0.778395	+	0.627775i	$0.216034\pi$
$54$	−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	0.745023	−	0.667039i	$-0.232438\pi$
$59$	−1.57587	−	2.72949i	−0.205161	−	0.355349i	−0.950184	+	0.311689i	$0.899105\pi$
$60$	0.883994	+	1.48732i	0.114123	+	0.192013i
$61$	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
$63$	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	0.191104	−	0.981570i	$-0.438793\pi$
$67$	9.30445	−	5.37193i	1.13672	−	0.656286i	0.945616	+	0.325284i	$0.105460\pi$
$68$	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	0.995031	+	0.0995695i	$0.0317466\pi$
$73$	4.98752	+	8.63864i	0.583745	+	1.01108i	−0.411286	+	0.911507i	$0.634920\pi$
$74$	−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	0.392561	−	0.919726i	$-0.371589\pi$
$79$	−1.84576	−	1.06565i	−0.207664	−	0.119895i	−0.600225	+	0.799831i	$0.704922\pi$
$80$	−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	0.608289	−	0.793715i	$-0.291856\pi$
$89$	2.12318	+	1.22582i	0.225056	+	0.129936i	−0.383233	+	0.923652i	$0.625189\pi$
$90$	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	0.394061	−	0.919084i	$-0.371070\pi$
$101$	13.9396	−	8.04803i	1.38704	−	0.800809i	0.992981	+	0.118275i	$0.0377364\pi$
$102$	1.45654	−	14.1895i	0.144219	−	1.40497i
$103$	−1.62521	−	0.938316i	−0.160137	−	0.0924550i	0.417790	−	0.908544i	$-0.362805\pi$
$103$	−1.62521	−	0.938316i	−0.160137	−	0.0924550i	−0.577927	+	0.816089i	$0.696138\pi$
$104$	−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	−0.986568	−	0.163350i	$-0.947770\pi$
$107$	−3.63924	+	6.30335i	−0.351819	+	0.609368i	0.634749	+	0.772718i	$0.281103\pi$
$108$	4.25484	−	9.48137i	0.409423	−	0.912345i
$109$	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	$0.805217\pi$
$110$	−0.975696	+	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	$0.160522\pi$
$113$			10.2728i			0.966382i	−0.875515	+	0.483191i	$0.839478\pi$
$114$	−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	$0.0213730\pi$
$127$			1.51224i			0.134190i	−0.997747	+	0.0670949i	$0.978627\pi$
$128$	−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	−0.973933	−	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
$135$	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	0.0241922	−	0.999707i	$-0.492299\pi$
$137$	10.5583	−	6.09586i	0.902060	−	0.520805i	0.877868	+	0.478903i	$0.158965\pi$
$138$	5.07281	+	11.3196i	0.431826	+	0.963592i
$139$			0.0477837i			0.00405296i	0.999998	+	0.00202648i	$0.000645050\pi$
$139$			0.0477837i			0.00405296i	−0.999998	+	0.00202648i	$0.999355\pi$
$140$	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	0.579158	−	0.815215i	$-0.303381\pi$
$149$	1.98650	+	1.14691i	0.162740	+	0.0939583i	−0.416418	+	0.909173i	$0.636715\pi$
$150$	11.5756	+	1.18822i	0.945141	+	0.0970179i
$151$	−11.3759	+	6.56789i	−0.925759	+	0.534487i	−0.885468	−	0.464701i	$-0.846162\pi$
$151$	−11.3759	+	6.56789i	−0.925759	+	0.534487i	−0.0402913	+	0.999188i	$0.512829\pi$
$152$	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	0.648017	−	0.761626i	$-0.275599\pi$
$157$	−4.20480	−	7.28292i	−0.335579	−	0.581241i	−0.983596	+	0.180386i	$0.942265\pi$
$158$	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	0.856720	−	0.515782i	$-0.172499\pi$
$163$	10.7040	+	6.17993i	0.838399	+	0.484050i	−0.0183210	+	0.999832i	$0.505832\pi$
$164$	−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	0.150690	−	0.988581i	$-0.451851\pi$
$173$	−8.28769	−	4.78490i	−0.630102	−	0.363789i	−0.780791	+	0.624792i	$0.785184\pi$
$174$	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	−0.934446	−	0.356105i	$-0.884105\pi$
$179$	−10.3771	−	17.9736i	−0.775619	−	1.34341i	0.158827	−	0.987306i	$-0.449229\pi$
$180$	−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	−0.352303	−	0.935886i	$-0.614601\pi$
$191$	8.76689	−	15.1847i	0.634350	−	1.09873i	0.986652	−	0.162840i	$-0.0520655\pi$
$192$	−13.8383	−	0.708404i	−0.998692	−	0.0511247i
$193$	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	$0.808275\pi$
$194$	0.0853244	+	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	$0.0717845\pi$
$197$			6.27706i			0.447222i	−0.974678	+	0.223611i	$0.928215\pi$
$198$	3.92386	+	4.40524i	0.278856	+	0.313066i
$199$	0.749564	−	0.432761i	0.0531352	−	0.0306776i	−0.473197	−	0.880957i	$-0.656900\pi$
$199$	0.749564	−	0.432761i	0.0531352	−	0.0306776i	0.526332	+	0.850279i	$0.323567\pi$
$200$	−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	$-0.957094\pi$
$211$		−	3.90417i		−	0.268774i	0.990929	−	0.134387i	$-0.0429065\pi$
$212$	−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	$-0.711687\pi$
$223$		−	23.5017i		−	1.57379i	0.617085	−	0.786896i	$-0.288313\pi$
$224$	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	0.986280	+	0.165084i	$0.0527895\pi$
$227$	9.58391	+	16.5998i	0.636107	+	1.10177i	−0.350173	+	0.936685i	$0.613877\pi$
$228$	−4.39202	−	7.38959i	−0.290869	−	0.489388i
$229$	−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
$231$	−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	0.948164	−	0.317780i	$-0.102937\pi$
$233$	17.5088	+	10.1087i	1.14704	+	0.662245i	0.198877	+	0.980025i	$0.436271\pi$
$234$	−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	0.706385	−	0.707828i	$-0.250325\pi$
$241$	−4.03326	−	6.98581i	−0.259805	−	0.449995i	−0.966190	+	0.257833i	$0.916992\pi$
$242$	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	−0.470484	−	0.882409i	$-0.655920\pi$
$257$	−23.5645	−	13.6050i	−1.46991	−	0.848655i	−0.999430	+	0.0337537i	$0.989254\pi$
$258$	−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	0.916232	−	0.400648i	$-0.131215\pi$
$263$	1.80247	+	3.12196i	0.111145	+	0.192508i	−0.805087	+	0.593156i	$0.797882\pi$
$264$	−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	−0.992348	−	0.123469i	$-0.960598\pi$
$269$	−22.6598	+	13.0827i	−1.38160	+	0.797664i	−0.389247	+	0.921134i	$0.627265\pi$
$270$	1.79313	+	3.20247i	0.109126	+	0.194896i
$271$	−19.9722	−	11.5309i	−1.21322	−	0.700455i	−0.249764	−	0.968307i	$-0.580353\pi$
$271$	−19.9722	−	11.5309i	−1.21322	−	0.700455i	−0.963460	+	0.267851i	$0.913686\pi$
$272$	−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	0.991309	+	0.131555i	$0.0419971\pi$
$277$	10.1455	+	17.5725i	0.609585	+	1.05583i	−0.381724	+	0.924276i	$0.624670\pi$
$278$	−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	$-0.691096\pi$
$281$		−	27.6637i		−	1.65028i	0.564929	−	0.825140i	$-0.308904\pi$
$282$	−5.07281	−	11.3196i	−0.302081	−	0.674075i
$283$	15.0435	−	8.68535i	0.894242	−	0.516291i	0.0189142	−	0.999821i	$-0.493979\pi$
$283$	15.0435	−	8.68535i	0.894242	−	0.516291i	0.875328	+	0.483530i	$0.160646\pi$
$284$	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	$0.198218\pi$
$293$			19.9672i			1.16650i	−0.812294	+	0.583248i	$0.801782\pi$
$294$	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	$0.132336\pi$
$307$			14.1529i			0.807746i	−0.914815	+	0.403873i	$0.867664\pi$
$308$	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	−0.969778	−	0.243990i	$-0.921544\pi$
$311$	−12.2774	−	21.2652i	−0.696190	−	1.20584i	0.273588	−	0.961847i	$-0.411790\pi$
$312$	5.19756	−	12.4321i	0.294254	−	0.703827i
$313$	−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
$315$	−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	0.326055	−	0.945351i	$-0.394281\pi$
$317$	−5.86864	−	3.38826i	−0.329616	−	0.190304i	−0.655671	+	0.755047i	$0.727614\pi$
$318$	−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	0.00953987	−	0.999954i	$-0.496963\pi$
$331$	−15.4949	−	8.94598i	−0.851676	−	0.491715i	−0.861216	+	0.508239i	$0.830297\pi$
$332$	−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	0.715913	−	0.698190i	$-0.246011\pi$
$347$	−4.59539	−	7.95946i	−0.246694	−	0.427286i	−0.962606	+	0.270904i	$0.912677\pi$
$348$	−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	−0.231981	−	0.972720i	$-0.574521\pi$
$353$	9.28947	−	5.36328i	0.494429	−	0.285458i	0.726410	+	0.687262i	$0.241187\pi$
$354$	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	−0.814533	−	0.580118i	$-0.803007\pi$
$359$	1.80247	−	3.12196i	0.0951305	−	0.164771i	0.909663	+	0.415347i	$0.136340\pi$
$360$	−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	−0.120295	−	0.992738i	$-0.538384\pi$
$367$	13.0134	−	7.51328i	0.679293	−	0.392190i	0.799589	+	0.600548i	$0.205051\pi$
$368$	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	−0.898367	−	0.439246i	$-0.855246\pi$
$373$	−1.32846	+	2.30096i	−0.0687850	+	0.119139i	0.829582	+	0.558385i	$0.188579\pi$
$374$	−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	$-0.849647\pi$
$379$		−	17.7150i		−	0.909957i	0.890502	−	0.454979i	$-0.150353\pi$
$380$	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	0.0478445	+	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
$387$	−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	−0.342686	−	0.939450i	$-0.611337\pi$
$389$	5.90821	−	3.41111i	0.299558	−	0.172950i	0.642244	+	0.766500i	$0.278003\pi$
$390$	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	−0.476571	−	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
$399$	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	0.414994	−	0.909824i	$-0.363784\pi$
$401$	−3.31292	−	1.91271i	−0.165439	−	0.0955164i	−0.580434	+	0.814308i	$0.697117\pi$
$402$	−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	0.909883	−	0.414865i	$-0.136171\pi$
$409$	1.93456	+	3.35075i	0.0956576	+	0.165684i	−0.814225	+	0.580549i	$0.802838\pi$
$410$	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	0.988662	+	0.150155i	$0.0479774\pi$
$431$	12.9623	+	22.4513i	0.624370	+	1.08144i	−0.364293	+	0.931284i	$0.618689\pi$
$432$	−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	0.818600	−	0.574364i	$-0.194750\pi$
$439$	15.3054	+	8.83658i	0.730487	+	0.421747i	−0.0881133	+	0.996110i	$0.528084\pi$
$440$	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	0.0596013	+	0.998222i	$0.481017\pi$
$443$	−17.5681	+	30.4288i	−0.834685	+	1.44572i	−0.894286	+	0.447495i	$0.852316\pi$
$444$	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	$0.0416343\pi$
$449$			5.52733i			0.260851i	−0.991458	+	0.130425i	$0.958366\pi$
$450$	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	0.437258	+	0.899336i	$0.355950\pi$
$457$	−11.9761	+	20.7432i	−0.560219	+	0.970327i	−0.997477	+	0.0709914i	$0.977384\pi$
$458$	−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	$-0.977768\pi$
$461$		−	2.99679i		−	0.139574i	0.997562	−	0.0697871i	$-0.0222320\pi$
$462$	1.80313	−	8.82922i	0.0838892	−	0.410772i
$463$		−	22.4152i		−	1.04172i	−0.853642	−	0.520861i	$-0.825611\pi$
$463$		−	22.4152i		−	1.04172i	0.853642	−	0.520861i	$-0.174389\pi$
$464$	−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	−0.692088	−	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
$471$	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	0.977548	−	0.210713i	$-0.0675784\pi$
$479$	6.70352	+	11.6108i	0.306292	+	0.530513i	−0.671256	+	0.741225i	$0.734245\pi$
$480$	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	−0.240944	−	0.970539i	$-0.577457\pi$
$487$	10.5727	−	6.10416i	0.479095	−	0.276606i	0.720039	+	0.693933i	$0.244124\pi$
$488$	−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	0.326636	−	0.945150i	$-0.394085\pi$
$499$	−7.33971	−	4.23758i	−0.328571	−	0.189700i	−0.655206	+	0.755450i	$0.727418\pi$
$500$	−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	0.792472	−	0.609909i	$-0.208794\pi$
$509$	14.9018	+	8.60356i	0.660511	+	0.381346i	−0.131961	+	0.991255i	$0.542127\pi$
$510$	−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	−0.693028	−	0.720911i	$-0.743724\pi$
$521$	−9.47744	+	5.47180i	−0.415214	+	0.239724i	0.277814	+	0.960635i	$0.410390\pi$
$522$	5.43626	+	26.2685i	0.237938	+	1.14974i
$523$	−4.79287	−	2.76716i	−0.209578	−	0.121000i	0.391537	−	0.920162i	$-0.371943\pi$
$523$	−4.79287	−	2.76716i	−0.209578	−	0.121000i	−0.601115	+	0.799162i	$0.705277\pi$
$524$	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	−0.968685	−	0.248293i	$-0.920130\pi$
$541$	−6.26409	+	10.8497i	−0.269314	+	0.466466i	0.699371	+	0.714759i	$0.253464\pi$
$542$	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	$0.295966\pi$
$547$			37.4911i			1.60300i	−0.597992	+	0.801502i	$0.704034\pi$
$548$	−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	0.166286	−	0.986078i	$-0.446823\pi$
$557$	26.0411	−	15.0348i	1.10340	−	0.637046i	0.937111	+	0.349031i	$0.113489\pi$
$558$	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	0.929043	−	0.369971i	$-0.120632\pi$
$563$	3.41956	+	5.92285i	0.144117	+	0.249618i	−0.784926	+	0.619589i	$0.787299\pi$
$564$	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	−0.251759	−	0.967790i	$-0.581009\pi$
$569$	−29.0006	−	16.7435i	−1.21577	−	0.701924i	−0.964010	+	0.265866i	$0.914342\pi$
$570$	3.02012	+	0.310012i	0.126499	+	0.0129850i
$571$	24.2464	−	13.9986i	1.01468	−	0.585825i	0.102121	−	0.994772i	$-0.467437\pi$
$571$	24.2464	−	13.9986i	1.01468	−	0.585825i	0.912558	+	0.408947i	$0.134104\pi$
$572$	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	−0.929945	−	0.367698i	$-0.880146\pi$
$577$	−18.8181	−	32.5939i	−0.783409	−	1.35690i	0.146537	−	0.989205i	$-0.453187\pi$
$578$	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	0.843828	−	0.536614i	$-0.180297\pi$
$593$	19.5061	+	11.2619i	0.801020	+	0.462469i	−0.0428074	+	0.999083i	$0.513630\pi$
$594$	−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	0.998536	+	0.0540915i	$0.0172263\pi$
$599$	13.3658	+	23.1503i	0.546113	+	0.945895i	−0.452423	+	0.891803i	$0.649440\pi$
$600$	−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	0.262358	−	0.964970i	$-0.415500\pi$
$607$	−10.8934	−	6.28933i	−0.442151	−	0.255276i	−0.704510	+	0.709694i	$0.748833\pi$
$608$	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	0.816505	−	0.577339i	$-0.195909\pi$
$613$	−2.27131	−	3.93403i	−0.0917374	−	0.158894i	−0.908242	+	0.418445i	$0.862575\pi$
$614$	−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	$0.253067\pi$
$617$			35.4652i			1.42777i	−0.700261	+	0.713887i	$0.746933\pi$
$618$	4.19482	−	1.87988i	0.168741	−	0.0756198i
$619$	−35.9030	+	20.7286i	−1.44306	+	0.833153i	−0.998053	−	0.0623719i	$-0.980134\pi$
$619$	−35.9030	+	20.7286i	−1.44306	+	0.833153i	−0.445011	+	0.895525i	$0.646800\pi$
$620$	−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	$0.146339\pi$
$631$			22.2919i			0.887428i	−0.896168	+	0.443714i	$0.853661\pi$
$632$	−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	−0.952925	−	0.303207i	$-0.901943\pi$
$641$	−29.5411	+	17.0555i	−1.16680	+	0.673653i	−0.213877	+	0.976861i	$0.568609\pi$
$642$	−7.29107	−	16.2695i	−0.287756	−	0.642108i
$643$			24.2299i			0.955533i	0.878487	+	0.477766i	$0.158553\pi$
$643$			24.2299i			0.955533i	−0.878487	+	0.477766i	$0.841447\pi$
$644$	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	0.851647	−	0.524116i	$-0.175604\pi$
$647$	−0.714092	−	1.23684i	−0.0280738	−	0.0486253i	−0.879721	+	0.475490i	$0.842271\pi$
$648$	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	0.582772	−	0.812636i	$-0.301968\pi$
$653$	4.35426	+	2.51393i	0.170395	+	0.0983778i	−0.412377	+	0.911013i	$0.635301\pi$
$654$	−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	0.997742	−	0.0671595i	$-0.0213936\pi$
$661$	11.3306	+	19.6252i	0.440709	+	0.763331i	−0.557033	+	0.830490i	$0.688060\pi$
$662$	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	0.322612	−	0.946531i	$-0.395439\pi$
$677$	−8.73729	−	5.04448i	−0.335801	−	0.193875i	−0.658414	+	0.752656i	$0.728772\pi$
$678$	−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	0.800199	−	0.599734i	$-0.204727\pi$
$683$	−3.11743	−	5.39955i	−0.119285	−	0.206608i	−0.919485	+	0.393126i	$0.871394\pi$
$684$	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	0.754066	−	0.656798i	$-0.228090\pi$
$691$	14.7810	+	8.53381i	0.562295	+	0.324641i	−0.191771	+	0.981440i	$0.561423\pi$
$692$	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	$-0.867360\pi$
$701$		−	21.4324i		−	0.809489i	0.914430	−	0.404744i	$-0.132640\pi$
$702$	−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	−0.774604	−	0.632446i	$-0.782051\pi$
$709$	4.27131	−	7.39813i	0.160412	−	0.277843i	0.935017	+	0.354604i	$0.115384\pi$
$710$	−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	−0.487611	−	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
$723$	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	$-0.677094\pi$
$727$		−	45.7930i		−	1.69837i	0.528096	−	0.849185i	$-0.322906\pi$
$728$	−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	−0.120385	−	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
$735$	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	−0.415284	−	0.909692i	$-0.636318\pi$
$739$	4.48246	−	2.58795i	0.164890	−	0.0951993i	0.580174	+	0.814492i	$0.302984\pi$
$740$	−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	0.898207	−	0.439572i	$-0.144870\pi$
$751$	26.4899	+	15.2939i	0.966630	+	0.558084i	0.0684228	+	0.997656i	$0.478203\pi$
$752$	−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	−0.269649	−	0.962959i	$-0.586908\pi$
$761$	−34.1633	−	19.7242i	−1.23842	−	0.715002i	−0.968771	+	0.247956i	$0.920241\pi$
$762$	−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	−0.801040	−	0.598610i	$-0.795720\pi$
$773$	−18.9935	+	10.9659i	−0.683149	+	0.394416i	0.117891	+	0.993026i	$0.462387\pi$
$774$	−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	−0.575838	−	0.817564i	$-0.695324\pi$
$787$	−4.36864	+	2.52223i	−0.155725	+	0.0899080i	0.420112	+	0.907472i	$0.361991\pi$
$788$	−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	$-0.832667\pi$
$797$		−	28.3335i		−	1.00362i	0.864977	−	0.501812i	$-0.167333\pi$
$798$	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	−0.775145	−	0.631783i	$-0.782323\pi$
$809$	−17.5088	+	10.1087i	−0.615577	+	0.355404i	0.159568	+	0.987187i	$0.448990\pi$
$810$	−1.45182	+	6.18914i	−0.0510119	+	0.217464i
$811$		−	1.33368i		−	0.0468317i	−0.999726	−	0.0234158i	$-0.992546\pi$
$811$		−	1.33368i		−	0.0468317i	0.999726	−	0.0234158i	$-0.00745418\pi$
$812$	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	0.578114	−	0.815956i	$-0.303789\pi$
$821$	4.59977	+	2.65568i	0.160533	+	0.0926838i	−0.417581	+	0.908640i	$0.637122\pi$
$822$	−3.04944	+	29.7074i	−0.106361	+	1.03616i
$823$	13.2508	−	7.65035i	0.461894	−	0.266675i	−0.250946	−	0.968001i	$-0.580742\pi$
$823$	13.2508	−	7.65035i	0.461894	−	0.266675i	0.712840	+	0.701326i	$0.247408\pi$
$824$	−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	0.963379	+	0.268143i	$0.0864100\pi$
$829$	20.5551	+	35.6025i	0.713908	+	1.23653i	−0.249471	+	0.968382i	$0.580257\pi$
$830$	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	−0.923334	−	0.383999i	$-0.874547\pi$
$857$	−30.8099	+	17.7881i	−1.05245	+	0.607631i	−0.129114	+	0.991630i	$0.541213\pi$
$858$	9.31938	+	0.956627i	0.318159	+	0.0326587i
$859$	−44.4334	−	25.6536i	−1.51605	−	0.875290i	−0.999823	−	0.0188372i	$-0.994004\pi$
$859$	−44.4334	−	25.6536i	−1.51605	−	0.875290i	−0.516225	−	0.856453i	$-0.672663\pi$
$860$	−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	−0.948706	−	0.316161i	$-0.897606\pi$
$863$	−5.89152	+	10.2044i	−0.200550	+	0.347362i	0.748156	+	0.663523i	$0.230939\pi$
$864$	−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	−0.877024	−	0.480447i	$-0.840474\pi$
$877$	−0.664314	+	1.15063i	−0.0224323	+	0.0388539i	0.854591	+	0.519301i	$0.173808\pi$
$878$	−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	$0.131461\pi$
$881$			23.8258i			0.802713i	−0.915922	+	0.401356i	$0.868539\pi$
$882$	29.6980	−	0.170605i	0.999983	−	0.00574457i
$883$		−	30.2235i		−	1.01710i	−0.861032	−	0.508551i	$-0.830181\pi$
$883$		−	30.2235i		−	1.01710i	0.861032	−	0.508551i	$-0.169819\pi$
$884$	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	−0.989229	−	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
$891$	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	−0.995195	−	0.0979134i	$-0.968783\pi$
$907$	−42.4039	+	24.4819i	−1.40800	+	0.812907i	−0.412802	+	0.910821i	$0.635450\pi$
$908$	−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	0.998034	−	0.0626826i	$-0.0199656\pi$
$919$	43.7375	+	25.2518i	1.44277	+	0.832981i	0.444732	+	0.895664i	$0.353299\pi$
$920$	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	0.482343	−	0.875983i	$-0.339786\pi$
$929$	−1.07011	−	0.617830i	−0.0351093	−	0.0202703i	−0.517452	+	0.855712i	$0.673119\pi$
$930$	−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	0.292235	−	0.956346i	$-0.405601\pi$
$941$	38.8530	−	22.4318i	1.26657	−	0.731256i	0.974338	+	0.225090i	$0.0722677\pi$
$942$	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	−0.687402	−	0.726277i	$-0.741249\pi$
$947$	8.77882	−	15.2054i	0.285273	−	0.494108i	0.972675	+	0.232169i	$0.0745823\pi$
$948$	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	$-0.794459\pi$
$953$		−	37.1546i		−	1.20356i	0.798663	−	0.601778i	$-0.205541\pi$
$954$	−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	$0.333779\pi$
$967$			53.9045i			1.73345i	−0.498786	+	0.866725i	$0.666221\pi$
$968$	−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	−0.374844	−	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
$975$	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	−0.229424	−	0.973327i	$-0.573684\pi$
$977$	15.5907	−	9.00127i	0.498789	−	0.287976i	0.728214	+	0.685350i	$0.240351\pi$
$978$	−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	0.735233	−	0.677815i	$-0.237073\pi$
$983$	−6.87845	−	11.9138i	−0.219388	−	0.379992i	−0.954621	+	0.297823i	$0.903740\pi$
$984$	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	−0.525319	−	0.850905i	$-0.676054\pi$
$991$	−1.60779	+	0.928258i	−0.0510731	+	0.0294871i	0.474246	+	0.880392i	$0.342721\pi$
$992$	−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	−0.732888	−	0.680350i	$-0.761828\pi$
$997$	−30.1748	−	52.2642i	−0.955644	−	1.65522i	−0.222756	−	0.974874i	$-0.571505\pi$
$998$	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.23.7	yes	24
3.2	odd	2	inner	84.2.n.a.23.6	yes	24
4.3	odd	2	inner	84.2.n.a.23.11	yes	24
7.2	even	3		588.2.e.e.491.9		12
7.3	odd	6		588.2.n.e.263.2		24
7.4	even	3	inner	84.2.n.a.11.2	✓	24
7.5	odd	6		588.2.e.d.491.9		12
7.6	odd	2		588.2.n.e.275.7		24
12.11	even	2	inner	84.2.n.a.23.2	yes	24
21.2	odd	6		588.2.e.e.491.4		12
21.5	even	6		588.2.e.d.491.4		12
21.11	odd	6	inner	84.2.n.a.11.11	yes	24
21.17	even	6		588.2.n.e.263.11		24
21.20	even	2		588.2.n.e.275.6		24
28.3	even	6		588.2.n.e.263.6		24
28.11	odd	6	inner	84.2.n.a.11.6	yes	24
28.19	even	6		588.2.e.d.491.3		12
28.23	odd	6		588.2.e.e.491.3		12
28.27	even	2		588.2.n.e.275.11		24
84.11	even	6	inner	84.2.n.a.11.7	yes	24
84.23	even	6		588.2.e.e.491.10		12
84.47	odd	6		588.2.e.d.491.10		12
84.59	odd	6		588.2.n.e.263.7		24
84.83	odd	2		588.2.n.e.275.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.2	✓	24	7.4	even	3	inner
84.2.n.a.11.6	yes	24	28.11	odd	6	inner
84.2.n.a.11.7	yes	24	84.11	even	6	inner
84.2.n.a.11.11	yes	24	21.11	odd	6	inner
84.2.n.a.23.2	yes	24	12.11	even	2	inner
84.2.n.a.23.6	yes	24	3.2	odd	2	inner
84.2.n.a.23.7	yes	24	1.1	even	1	trivial
84.2.n.a.23.11	yes	24	4.3	odd	2	inner
588.2.e.d.491.3		12	28.19	even	6
588.2.e.d.491.4		12	21.5	even	6
588.2.e.d.491.9		12	7.5	odd	6
588.2.e.d.491.10		12	84.47	odd	6
588.2.e.e.491.3		12	28.23	odd	6
588.2.e.e.491.4		12	21.2	odd	6
588.2.e.e.491.9		12	7.2	even	3
588.2.e.e.491.10		12	84.23	even	6
588.2.n.e.263.2		24	7.3	odd	6
588.2.n.e.263.6		24	28.3	even	6
588.2.n.e.263.7		24	84.59	odd	6
588.2.n.e.263.11		24	21.17	even	6
588.2.n.e.275.2		24	84.83	odd	2
588.2.n.e.275.6		24	21.20	even	2
588.2.n.e.275.7		24	7.6	odd	2
588.2.n.e.275.11		24	28.27	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+(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 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

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Database

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