LMFDB - Embedded newform 560.2.bd.b.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.2
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32495 + 0.494478i) q^{2} +(-1.01907 - 1.01907i) q^{3} +(1.51098 - 1.31032i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.85412 + 0.846307i) q^{6} +1.00000i q^{7} +(-1.35405 + 2.48325i) q^{8} -0.922998i q^{9} +O(q^{10})$	\(q+(-1.32495 + 0.494478i) q^{2} +(-1.01907 - 1.01907i) q^{3} +(1.51098 - 1.31032i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.85412 + 0.846307i) q^{6} +1.00000i q^{7} +(-1.35405 + 2.48325i) q^{8} -0.922998i q^{9} +(0.587232 - 1.28653i) q^{10} +(-0.470736 + 0.470736i) q^{11} +(-2.87510 - 0.204491i) q^{12} +(0.292225 + 0.292225i) q^{13} +(-0.494478 - 1.32495i) q^{14} +1.44118 q^{15} +(0.566136 - 3.95973i) q^{16} -0.132722 q^{17} +(0.456402 + 1.22293i) q^{18} +(-4.85793 - 4.85793i) q^{19} +(-0.141891 + 1.99496i) q^{20} +(1.01907 - 1.01907i) q^{21} +(0.390933 - 0.856470i) q^{22} +5.82127i q^{23} +(3.91048 - 1.15073i) q^{24} -1.00000i q^{25} +(-0.531682 - 0.242684i) q^{26} +(-3.99780 + 3.99780i) q^{27} +(1.31032 + 1.51098i) q^{28} +(0.717720 + 0.717720i) q^{29} +(-1.90949 + 0.712633i) q^{30} -0.807390 q^{31} +(1.20790 + 5.52639i) q^{32} +0.959425 q^{33} +(0.175850 - 0.0656283i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-1.20942 - 1.39463i) q^{36} +(-3.01315 + 3.01315i) q^{37} +(8.83865 + 4.03437i) q^{38} -0.595595i q^{39} +(-0.798466 - 2.71338i) q^{40} +8.65729i q^{41} +(-0.846307 + 1.85412i) q^{42} +(-6.17882 + 6.17882i) q^{43} +(-0.0944601 + 1.32809i) q^{44} +(0.652658 + 0.652658i) q^{45} +(-2.87849 - 7.71289i) q^{46} -10.3679 q^{47} +(-4.61217 + 3.45831i) q^{48} -1.00000 q^{49} +(0.494478 + 1.32495i) q^{50} +(0.135253 + 0.135253i) q^{51} +(0.824454 + 0.0586393i) q^{52} +(1.81854 - 1.81854i) q^{53} +(3.32006 - 7.27372i) q^{54} -0.665721i q^{55} +(-2.48325 - 1.35405i) q^{56} +9.90112i q^{57} +(-1.30584 - 0.596046i) q^{58} +(-7.11797 + 7.11797i) q^{59} +(2.17760 - 1.88840i) q^{60} +(-0.0812868 - 0.0812868i) q^{61} +(1.06975 - 0.399237i) q^{62} +0.922998 q^{63} +(-4.33309 - 6.72491i) q^{64} -0.413268 q^{65} +(-1.27119 + 0.474415i) q^{66} +(-8.01128 - 8.01128i) q^{67} +(-0.200541 + 0.173908i) q^{68} +(5.93228 - 5.93228i) q^{69} +(1.28653 + 0.587232i) q^{70} +10.3168i q^{71} +(2.29204 + 1.24979i) q^{72} +2.48023i q^{73} +(2.50234 - 5.48222i) q^{74} +(-1.01907 + 1.01907i) q^{75} +(-13.7057 - 0.974815i) q^{76} +(-0.470736 - 0.470736i) q^{77} +(0.294509 + 0.789133i) q^{78} +4.42224 q^{79} +(2.39964 + 3.20027i) q^{80} +5.37908 q^{81} +(-4.28084 - 11.4705i) q^{82} +(-6.74931 - 6.74931i) q^{83} +(0.204491 - 2.87510i) q^{84} +(0.0938488 - 0.0938488i) q^{85} +(5.13134 - 11.2419i) q^{86} -1.46281i q^{87} +(-0.531556 - 1.80636i) q^{88} -12.2935i q^{89} +(-1.18746 - 0.542014i) q^{90} +(-0.292225 + 0.292225i) q^{91} +(7.62771 + 8.79584i) q^{92} +(0.822786 + 0.822786i) q^{93} +(13.7369 - 5.12669i) q^{94} +6.87014 q^{95} +(4.40084 - 6.86270i) q^{96} +8.24412 q^{97} +(1.32495 - 0.494478i) q^{98} +(0.434488 + 0.434488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.32495	+	0.494478i	−0.936881	+	0.349649i
$2$	−1.32495	+	0.494478i	−0.936881	+	0.349649i
$3$	−1.01907	−	1.01907i	−0.588360	−	0.588360i	0.348827	−	0.937187i	$-0.386580\pi$
$3$	−1.01907	−	1.01907i	−0.588360	−	0.588360i	−0.937187	+	0.348827i	$0.886580\pi$
$4$	1.51098	−	1.31032i	0.755491	−	0.655159i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.85412	+	0.846307i	0.756942	+	0.345503i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.35405	+	2.48325i	−0.478730	+	0.877962i
$9$		−	0.922998i		−	0.307666i
$10$	0.587232	−	1.28653i	0.185699	−	0.406836i
$11$	−0.470736	+	0.470736i	−0.141932	+	0.141932i	−0.774503	−	0.632571i	$-0.782000\pi$
$11$	−0.470736	+	0.470736i	−0.141932	+	0.141932i	0.632571	+	0.774503i	$0.282000\pi$
$12$	−2.87510	−	0.204491i	−0.829970	−	0.0590315i
$13$	0.292225	+	0.292225i	0.0810486	+	0.0810486i	0.746469	−	0.665420i	$-0.231748\pi$
$13$	0.292225	+	0.292225i	0.0810486	+	0.0810486i	−0.665420	+	0.746469i	$0.731748\pi$
$14$	−0.494478	−	1.32495i	−0.132155	−	0.354108i
$15$	1.44118			0.372111
$16$	0.566136	−	3.95973i	0.141534	−	0.989933i
$17$	−0.132722			−0.0321899			−0.0160949	−	0.999870i	$-0.505123\pi$
$17$	−0.132722			−0.0321899			−0.0160949	+	0.999870i	$0.505123\pi$
$18$	0.456402	+	1.22293i	0.107575	+	0.288246i
$19$	−4.85793	−	4.85793i	−1.11448	−	1.11448i	−0.992536	−	0.121948i	$-0.961086\pi$
$19$	−4.85793	−	4.85793i	−1.11448	−	1.11448i	−0.121948	−	0.992536i	$-0.538914\pi$
$20$	−0.141891	+	1.99496i	−0.0317279	+	0.446087i
$21$	1.01907	−	1.01907i	0.222379	−	0.222379i
$22$	0.390933	−	0.856470i	0.0833471	−	0.182600i
$23$			5.82127i			1.21382i	0.794771	+	0.606910i	$0.207591\pi$
$23$			5.82127i			1.21382i	−0.794771	+	0.606910i	$0.792409\pi$
$24$	3.91048	−	1.15073i	0.798223	−	0.234892i
$25$		−	1.00000i		−	0.200000i
$26$	−0.531682	−	0.242684i	−0.104271	−	0.0475943i
$27$	−3.99780	+	3.99780i	−0.769378	+	0.769378i
$28$	1.31032	+	1.51098i	0.247627	+	0.285549i
$29$	0.717720	+	0.717720i	0.133277	+	0.133277i	0.770598	−	0.637321i	$-0.219958\pi$
$29$	0.717720	+	0.717720i	0.133277	+	0.133277i	−0.637321	+	0.770598i	$0.719958\pi$
$30$	−1.90949	+	0.712633i	−0.348624	+	0.130108i
$31$	−0.807390			−0.145012			−0.0725058	−	0.997368i	$-0.523100\pi$
$31$	−0.807390			−0.145012			−0.0725058	+	0.997368i	$0.523100\pi$
$32$	1.20790	+	5.52639i	0.213529	+	0.976937i
$33$	0.959425			0.167014
$34$	0.175850	−	0.0656283i	0.0301581	−	0.0112552i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	−1.20942	−	1.39463i	−0.201570	−	0.232439i
$37$	−3.01315	+	3.01315i	−0.495359	+	0.495359i	−0.909990	−	0.414630i	$-0.863911\pi$
$37$	−3.01315	+	3.01315i	−0.495359	+	0.495359i	0.414630	+	0.909990i	$0.363911\pi$
$38$	8.83865	+	4.03437i	1.43382	+	0.654461i
$39$		−	0.595595i		−	0.0953715i
$40$	−0.798466	−	2.71338i	−0.126249	−	0.429024i
$41$			8.65729i			1.35204i	0.736883	+	0.676021i	$0.236297\pi$
$41$			8.65729i			1.35204i	−0.736883	+	0.676021i	$0.763703\pi$
$42$	−0.846307	+	1.85412i	−0.130588	+	0.286097i
$43$	−6.17882	+	6.17882i	−0.942262	+	0.942262i	−0.998422	−	0.0561600i	$-0.982114\pi$
$43$	−6.17882	+	6.17882i	−0.942262	+	0.942262i	0.0561600	+	0.998422i	$0.482114\pi$
$44$	−0.0944601	+	1.32809i	−0.0142404	+	0.200217i
$45$	0.652658	+	0.652658i	0.0972925	+	0.0972925i
$46$	−2.87849	−	7.71289i	−0.424411	−	1.13720i
$47$	−10.3679			−1.51231			−0.756154	−	0.654393i	$-0.772924\pi$
$47$	−10.3679			−1.51231			−0.756154	+	0.654393i	$0.772924\pi$
$48$	−4.61217	+	3.45831i	−0.665710	+	0.499164i
$49$	−1.00000			−0.142857
$50$	0.494478	+	1.32495i	0.0699298	+	0.187376i
$51$	0.135253	+	0.135253i	0.0189392	+	0.0189392i
$52$	0.824454	+	0.0586393i	0.114331	+	0.00813180i
$53$	1.81854	−	1.81854i	0.249796	−	0.249796i	−0.571091	−	0.820887i	$-0.693480\pi$
$53$	1.81854	−	1.81854i	0.249796	−	0.249796i	0.820887	+	0.571091i	$0.193480\pi$
$54$	3.32006	−	7.27372i	0.451803	−	0.989827i
$55$		−	0.665721i		−	0.0897658i
$56$	−2.48325	−	1.35405i	−0.331839	−	0.180943i
$57$			9.90112i			1.31144i
$58$	−1.30584	−	0.596046i	−0.171465	−	0.0782646i
$59$	−7.11797	+	7.11797i	−0.926681	+	0.926681i	−0.997490	−	0.0708086i	$-0.977442\pi$
$59$	−7.11797	+	7.11797i	−0.926681	+	0.926681i	0.0708086	+	0.997490i	$0.477442\pi$
$60$	2.17760	−	1.88840i	0.281127	−	0.243792i
$61$	−0.0812868	−	0.0812868i	−0.0104077	−	0.0104077i	0.701884	−	0.712291i	$-0.252343\pi$
$61$	−0.0812868	−	0.0812868i	−0.0104077	−	0.0104077i	−0.712291	+	0.701884i	$0.752343\pi$
$62$	1.06975	−	0.399237i	0.135859	−	0.0507032i
$63$	0.922998			0.116287
$64$	−4.33309	−	6.72491i	−0.541636	−	0.840613i
$65$	−0.413268			−0.0512596
$66$	−1.27119	+	0.474415i	−0.156473	+	0.0583964i
$67$	−8.01128	−	8.01128i	−0.978734	−	0.978734i	0.0210450	−	0.999779i	$-0.493301\pi$
$67$	−8.01128	−	8.01128i	−0.978734	−	0.978734i	−0.999779	+	0.0210450i	$0.993301\pi$
$68$	−0.200541	+	0.173908i	−0.0243192	+	0.0210895i
$69$	5.93228	−	5.93228i	0.714162	−	0.714162i
$70$	1.28653	+	0.587232i	0.153770	+	0.0701876i
$71$			10.3168i			1.22438i	0.790710	+	0.612191i	$0.209712\pi$
$71$			10.3168i			1.22438i	−0.790710	+	0.612191i	$0.790288\pi$
$72$	2.29204	+	1.24979i	0.270119	+	0.147289i
$73$			2.48023i			0.290289i	0.989410	+	0.145145i	$0.0463648\pi$
$73$			2.48023i			0.290289i	−0.989410	+	0.145145i	$0.953635\pi$
$74$	2.50234	−	5.48222i	0.290891	−	0.637295i
$75$	−1.01907	+	1.01907i	−0.117672	+	0.117672i
$76$	−13.7057	−	0.974815i	−1.57215	−	0.111819i
$77$	−0.470736	−	0.470736i	−0.0536453	−	0.0536453i
$78$	0.294509	+	0.789133i	0.0333465	+	0.0893517i
$79$	4.42224			0.497540			0.248770	−	0.968563i	$-0.419974\pi$
$79$	4.42224			0.497540			0.248770	+	0.968563i	$0.419974\pi$
$80$	2.39964	+	3.20027i	0.268287	+	0.357801i
$81$	5.37908			0.597676
$82$	−4.28084	−	11.4705i	−0.472740	−	1.26670i
$83$	−6.74931	−	6.74931i	−0.740833	−	0.740833i	0.231905	−	0.972738i	$-0.425504\pi$
$83$	−6.74931	−	6.74931i	−0.740833	−	0.740833i	−0.972738	+	0.231905i	$0.925504\pi$
$84$	0.204491	−	2.87510i	0.0223118	−	0.313699i
$85$	0.0938488	−	0.0938488i	0.0101793	−	0.0101793i
$86$	5.13134	−	11.2419i	0.553326	−	1.21225i
$87$		−	1.46281i		−	0.156830i
$88$	−0.531556	−	1.80636i	−0.0566640	−	0.192558i
$89$		−	12.2935i		−	1.30311i	−0.758600	−	0.651557i	$-0.774116\pi$
$89$		−	12.2935i		−	1.30311i	0.758600	−	0.651557i	$-0.225884\pi$
$90$	−1.18746	−	0.542014i	−0.125170	−	0.0571332i
$91$	−0.292225	+	0.292225i	−0.0306335	+	0.0306335i
$92$	7.62771	+	8.79584i	0.795244	+	0.917030i
$93$	0.822786	+	0.822786i	0.0853190	+	0.0853190i
$94$	13.7369	−	5.12669i	1.41685	−	0.528777i
$95$	6.87014			0.704862
$96$	4.40084	−	6.86270i	0.449158	−	0.700422i
$97$	8.24412			0.837064			0.418532	−	0.908202i	$-0.362545\pi$
$97$	8.24412			0.837064			0.418532	+	0.908202i	$0.362545\pi$
$98$	1.32495	−	0.494478i	0.133840	−	0.0499499i
$99$	0.434488	+	0.434488i	0.0436677	+	0.0436677i
$100$	−1.31032	−	1.51098i	−0.131032	−	0.151098i
$101$	−9.16265	+	9.16265i	−0.911717	+	0.911717i	−0.996407	−	0.0846900i	$-0.973010\pi$
$101$	−9.16265	+	9.16265i	−0.911717	+	0.911717i	0.0846900	+	0.996407i	$0.473010\pi$
$102$	−0.246083	−	0.112324i	−0.0243659	−	0.0111217i
$103$		−	7.73879i		−	0.762526i	−0.924467	−	0.381263i	$-0.875489\pi$
$103$		−	7.73879i		−	0.762526i	0.924467	−	0.381263i	$-0.124511\pi$
$104$	−1.12136	+	0.329981i	−0.109958	+	0.0323573i
$105$			1.44118i			0.140645i
$106$	−1.51024	+	3.30870i	−0.146688	+	0.321369i
$107$	−2.96053	+	2.96053i	−0.286205	+	0.286205i	−0.835578	−	0.549372i	$-0.814867\pi$
$107$	−2.96053	+	2.96053i	−0.286205	+	0.286205i	0.549372	+	0.835578i	$0.314867\pi$
$108$	−0.802219	+	11.2790i	−0.0771935	+	1.08532i
$109$	1.61623	+	1.61623i	0.154807	+	0.154807i	0.780261	−	0.625454i	$-0.215086\pi$
$109$	1.61623	+	1.61623i	0.154807	+	0.154807i	−0.625454	+	0.780261i	$0.715086\pi$
$110$	0.329185	+	0.882047i	0.0313865	+	0.0840999i
$111$	6.14122			0.582899
$112$	3.95973	+	0.566136i	0.374160	+	0.0534948i
$113$	8.42803			0.792843			0.396421	−	0.918069i	$-0.370252\pi$
$113$	8.42803			0.792843			0.396421	+	0.918069i	$0.370252\pi$
$114$	−4.89589	−	13.1185i	−0.458542	−	1.22866i
$115$	−4.11626	−	4.11626i	−0.383843	−	0.383843i
$116$	2.02490	+	0.144021i	0.188008	+	0.0133720i
$117$	0.269723	−	0.269723i	0.0249359	−	0.0249359i
$118$	5.91127	−	12.9506i	0.544177	−	1.19220i
$119$		−	0.132722i		−	0.0121666i
$120$	−1.95143	+	3.57882i	−0.178141	+	0.326700i
$121$			10.5568i			0.959710i
$122$	0.147895	+	0.0675063i	0.0133898	+	0.00611173i
$123$	8.82237	−	8.82237i	0.795486	−	0.795486i
$124$	−1.21995	+	1.05794i	−0.109555	+	0.0950056i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−1.22293	+	0.456402i	−0.108947	+	0.0406596i
$127$	15.0949			1.33945			0.669726	−	0.742608i	$-0.266412\pi$
$127$	15.0949			1.33945			0.669726	+	0.742608i	$0.266412\pi$
$128$	9.06644	+	6.76754i	0.801368	+	0.598172i
$129$	12.5933			1.10878
$130$	0.547560	−	0.204352i	0.0480242	−	0.0179229i
$131$	−0.0762292	−	0.0762292i	−0.00666018	−	0.00666018i	0.703769	−	0.710429i	$-0.251499\pi$
$131$	−0.0762292	−	0.0762292i	−0.00666018	−	0.00666018i	−0.710429	+	0.703769i	$0.751499\pi$
$132$	1.44967	−	1.25715i	0.126178	−	0.109421i
$133$	4.85793	−	4.85793i	0.421236	−	0.421236i
$134$	14.5759	+	6.65314i	1.25917	+	0.574743i
$135$		−	5.65375i		−	0.486597i
$136$	0.179713	−	0.329583i	0.0154102	−	0.0282615i
$137$			17.7998i			1.52074i	0.649492	+	0.760368i	$0.274982\pi$
$137$			17.7998i			1.52074i	−0.649492	+	0.760368i	$0.725018\pi$
$138$	−4.92658	+	10.7933i	−0.419379	+	0.918791i
$139$	4.64119	−	4.64119i	0.393661	−	0.393661i	−0.482329	−	0.875990i	$-0.660209\pi$
$139$	4.64119	−	4.64119i	0.393661	−	0.393661i	0.875990	+	0.482329i	$0.160209\pi$
$140$	−1.99496	−	0.141891i	−0.168605	−	0.0119920i
$141$	10.5656	+	10.5656i	0.889782	+	0.889782i
$142$	−5.10144	−	13.6693i	−0.428104	−	1.14710i
$143$	−0.275122			−0.0230068
$144$	−3.65482	−	0.522542i	−0.304569	−	0.0435452i
$145$	−1.01501			−0.0842919
$146$	−1.22642	−	3.28618i	−0.101499	−	0.271967i
$147$	1.01907	+	1.01907i	0.0840514	+	0.0840514i
$148$	−0.604634	+	8.50101i	−0.0497006	+	0.698779i
$149$	9.34465	−	9.34465i	0.765543	−	0.765543i	−0.211775	−	0.977318i	$-0.567924\pi$
$149$	9.34465	−	9.34465i	0.765543	−	0.765543i	0.977318	+	0.211775i	$0.0679244\pi$
$150$	0.846307	−	1.85412i	0.0691007	−	0.151388i
$151$		−	13.7542i		−	1.11930i	−0.828728	−	0.559651i	$-0.810935\pi$
$151$		−	13.7542i		−	1.11930i	0.828728	−	0.559651i	$-0.189065\pi$
$152$	18.6413	−	5.48557i	1.51201	−	0.444939i
$153$			0.122502i			0.00990373i
$154$	0.856470	+	0.390933i	0.0690163	+	0.0315023i
$155$	0.570911	−	0.570911i	0.0458567	−	0.0458567i
$156$	−0.780418	−	0.899933i	−0.0624834	−	0.0720523i
$157$	−5.25137	−	5.25137i	−0.419105	−	0.419105i	0.465790	−	0.884895i	$-0.345770\pi$
$157$	−5.25137	−	5.25137i	−0.419105	−	0.419105i	−0.884895	+	0.465790i	$0.845770\pi$
$158$	−5.85924	+	2.18670i	−0.466136	+	0.173964i
$159$	−3.70643			−0.293939
$160$	−4.76186	−	3.05363i	−0.376458	−	0.241411i
$161$	−5.82127			−0.458780
$162$	−7.12701	+	2.65984i	−0.559951	+	0.208977i
$163$	−2.18867	−	2.18867i	−0.171429	−	0.171429i	0.616178	−	0.787607i	$-0.288680\pi$
$163$	−2.18867	−	2.18867i	−0.171429	−	0.171429i	−0.787607	+	0.616178i	$0.788680\pi$
$164$	11.3438	+	13.0810i	0.885802	+	1.02146i
$165$	−0.678416	+	0.678416i	−0.0528146	+	0.0528146i
$166$	12.2799	+	5.60511i	0.953104	+	0.435041i
$167$		−	4.94745i		−	0.382846i	−0.981508	−	0.191423i	$-0.938690\pi$
$167$		−	4.94745i		−	0.382846i	0.981508	−	0.191423i	$-0.0613101\pi$
$168$	1.15073	+	3.91048i	0.0887810	+	0.301700i
$169$		−	12.8292i		−	0.986862i
$170$	−0.0779387	+	0.170751i	−0.00597763	+	0.0130960i
$171$	−4.48385	+	4.48385i	−0.342889	+	0.342889i
$172$	−1.23987	+	17.4323i	−0.0945394	+	1.32920i
$173$	−16.4367	−	16.4367i	−1.24966	−	1.24966i	−0.955870	−	0.293790i	$-0.905083\pi$
$173$	−16.4367	−	16.4367i	−1.24966	−	1.24966i	−0.293790	−	0.955870i	$-0.594917\pi$
$174$	0.723329	+	1.93815i	0.0548354	+	0.146931i
$175$	1.00000			0.0755929
$176$	1.59749	+	2.13049i	0.120415	+	0.160592i
$177$	14.5074			1.09044
$178$	6.07889	+	16.2883i	0.455632	+	1.22086i
$179$	−9.17881	−	9.17881i	−0.686056	−	0.686056i	0.275302	−	0.961358i	$-0.411222\pi$
$179$	−9.17881	−	9.17881i	−0.686056	−	0.686056i	−0.961358	+	0.275302i	$0.911222\pi$
$180$	1.84134	+	0.130965i	0.137246	+	0.00976159i
$181$	1.03314	−	1.03314i	0.0767927	−	0.0767927i	−0.667667	−	0.744460i	$-0.732707\pi$
$181$	1.03314	−	1.03314i	0.0767927	−	0.0767927i	0.744460	+	0.667667i	$0.232707\pi$
$182$	0.242684	−	0.531682i	0.0179890	−	0.0394109i
$183$			0.165674i			0.0122469i
$184$	−14.4557	−	7.88230i	−1.06569	−	0.581091i
$185$		−	4.26124i		−	0.313293i
$186$	−1.49700	−	0.683300i	−0.109765	−	0.0501020i
$187$	0.0624772	−	0.0624772i	0.00456878	−	0.00456878i
$188$	−15.6657	+	13.5852i	−1.14254	+	0.990803i
$189$	−3.99780	−	3.99780i	−0.290797	−	0.290797i
$190$	−9.10259	+	3.39714i	−0.660372	+	0.246454i
$191$	11.3540			0.821546			0.410773	−	0.911738i	$-0.365259\pi$
$191$	11.3540			0.821546			0.410773	+	0.911738i	$0.365259\pi$
$192$	−2.43743	+	11.2689i	−0.175906	+	0.813260i
$193$	−17.0414			−1.22667			−0.613333	−	0.789825i	$-0.710172\pi$
$193$	−17.0414			−1.22667			−0.613333	+	0.789825i	$0.710172\pi$
$194$	−10.9230	+	4.07654i	−0.784229	+	0.292679i
$195$	0.421149	+	0.421149i	0.0301591	+	0.0301591i
$196$	−1.51098	+	1.31032i	−0.107927	+	0.0935941i
$197$	11.1920	−	11.1920i	0.797399	−	0.797399i	−0.185286	−	0.982685i	$-0.559321\pi$
$197$	11.1920	−	11.1920i	0.797399	−	0.797399i	0.982685	+	0.185286i	$0.0593210\pi$
$198$	−0.790520	−	0.360830i	−0.0561798	−	0.0256431i
$199$			9.26370i			0.656686i	0.944559	+	0.328343i	$0.106490\pi$
$199$			9.26370i			0.656686i	−0.944559	+	0.328343i	$0.893510\pi$
$200$	2.48325	+	1.35405i	0.175592	+	0.0957459i
$201$			16.3281i			1.15169i
$202$	7.60931	−	16.6708i	0.535389	−	1.17295i
$203$	−0.717720	+	0.717720i	−0.0503741	+	0.0503741i
$204$	0.381590	+	0.0271405i	0.0267166	+	0.00190022i
$205$	−6.12163	−	6.12163i	−0.427553	−	0.427553i
$206$	3.82666	+	10.2535i	0.266616	+	0.714396i
$207$	5.37302			0.373451
$208$	1.32257	−	0.991694i	0.0917038	−	0.0687616i
$209$	4.57360			0.316363
$210$	−0.712633	−	1.90949i	−0.0491763	−	0.131767i
$211$	18.7823	+	18.7823i	1.29303	+	1.29303i	0.932906	+	0.360120i	$0.117264\pi$
$211$	18.7823	+	18.7823i	1.29303	+	1.29303i	0.360120	+	0.932906i	$0.382736\pi$
$212$	0.364917	−	5.13064i	0.0250626	−	0.352374i
$213$	10.5136	−	10.5136i	0.720377	−	0.720377i
$214$	2.45864	−	5.38647i	0.168069	−	0.368212i
$215$		−	8.73818i		−	0.595939i
$216$	−4.51432	−	15.3408i	−0.307161	−	1.04381i
$217$		−	0.807390i		−	0.0548092i
$218$	−2.94062	−	1.34223i	−0.199164	−	0.0909075i
$219$	2.52753	−	2.52753i	0.170795	−	0.170795i
$220$	−0.872306	−	1.00589i	−0.0588109	−	0.0678173i
$221$	−0.0387848	−	0.0387848i	−0.00260895	−	0.00260895i
$222$	−8.13681	+	3.03670i	−0.546107	+	0.203810i
$223$	−26.8322			−1.79681			−0.898407	−	0.439163i	$-0.855275\pi$
$223$	−26.8322			−1.79681			−0.898407	+	0.439163i	$0.855275\pi$
$224$	−5.52639	+	1.20790i	−0.369247	+	0.0807063i
$225$	−0.922998			−0.0615332
$226$	−11.1667	+	4.16748i	−0.742799	+	0.277217i
$227$	−12.9286	−	12.9286i	−0.858099	−	0.858099i	0.133015	−	0.991114i	$-0.457534\pi$
$227$	−12.9286	−	12.9286i	−0.858099	−	0.858099i	−0.991114	+	0.133015i	$0.957534\pi$
$228$	12.9736	+	14.9604i	0.859198	+	0.990778i
$229$	−1.04263	+	1.04263i	−0.0688987	+	0.0688987i	−0.740716	−	0.671818i	$-0.765514\pi$
$229$	−1.04263	+	1.04263i	−0.0688987	+	0.0688987i	0.671818	+	0.740716i	$0.265514\pi$
$230$	7.48924	+	3.41844i	0.493826	+	0.225405i
$231$			0.959425i			0.0631255i
$232$	−2.75411	+	0.810450i	−0.180816	+	0.0532086i
$233$			8.57846i			0.561994i	0.959709	+	0.280997i	$0.0906650\pi$
$233$			8.57846i			0.561994i	−0.959709	+	0.280997i	$0.909335\pi$
$234$	−0.223997	+	0.490741i	−0.0146431	+	0.0320808i
$235$	7.33119	−	7.33119i	0.478234	−	0.478234i
$236$	−1.42833	+	20.0819i	−0.0929762	+	1.30722i
$237$	−4.50656	−	4.50656i	−0.292733	−	0.292733i
$238$	0.0656283	+	0.175850i	0.00425405	+	0.0113987i
$239$	7.28275			0.471082			0.235541	−	0.971864i	$-0.424314\pi$
$239$	7.28275			0.471082			0.235541	+	0.971864i	$0.424314\pi$
$240$	0.815904	−	5.70669i	0.0526664	−	0.368365i
$241$	−27.1055			−1.74602			−0.873008	−	0.487706i	$-0.837834\pi$
$241$	−27.1055			−1.74602			−0.873008	+	0.487706i	$0.837834\pi$
$242$	−5.22012	−	13.9872i	−0.335562	−	0.899134i
$243$	6.51176	+	6.51176i	0.417729	+	0.417729i
$244$	−0.229334	−	0.0163114i	−0.0146816	−	0.00104423i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	−7.32673	+	16.0517i	−0.467135	+	1.02342i
$247$		−	2.83921i		−	0.180655i
$248$	1.09325	−	2.00495i	0.0694213	−	0.127315i
$249$			13.7560i			0.871752i
$250$	−1.28653	−	0.587232i	−0.0813673	−	0.0371398i
$251$	−4.48203	+	4.48203i	−0.282903	+	0.282903i	−0.834266	−	0.551362i	$-0.814108\pi$
$251$	−4.48203	+	4.48203i	−0.282903	+	0.282903i	0.551362	+	0.834266i	$0.314108\pi$
$252$	1.39463	−	1.20942i	0.0878536	−	0.0761863i
$253$	−2.74028	−	2.74028i	−0.172280	−	0.172280i
$254$	−19.9999	+	7.46408i	−1.25491	+	0.468338i
$255$	−0.191277			−0.0119782
$256$	−15.3590	−	4.48349i	−0.959936	−	0.280218i
$257$	1.38891			0.0866377			0.0433189	−	0.999061i	$-0.486207\pi$
$257$	1.38891			0.0866377			0.0433189	+	0.999061i	$0.486207\pi$
$258$	−16.6855	+	6.22711i	−1.03879	+	0.387683i
$259$	−3.01315	−	3.01315i	−0.187228	−	0.187228i
$260$	−0.624441	+	0.541513i	−0.0387262	+	0.0335832i
$261$	0.662454	−	0.662454i	0.0410049	−	0.0410049i
$262$	0.138694	+	0.0633062i	0.00856852	+	0.00391107i
$263$		−	6.89854i		−	0.425382i	−0.977119	−	0.212691i	$-0.931777\pi$
$263$		−	6.89854i		−	0.425382i	0.977119	−	0.212691i	$-0.0682228\pi$
$264$	−1.29911	+	2.38249i	−0.0799547	+	0.146632i
$265$			2.57180i			0.157985i
$266$	−4.03437	+	8.83865i	−0.247363	+	0.541932i
$267$	−12.5280	+	12.5280i	−0.766699	+	0.766699i
$268$	−22.6022	−	1.60758i	−1.38065	−	0.0981987i
$269$	7.24216	+	7.24216i	0.441562	+	0.441562i	0.892537	−	0.450975i	$-0.148923\pi$
$269$	7.24216	+	7.24216i	0.441562	+	0.441562i	−0.450975	+	0.892537i	$0.648923\pi$
$270$	2.79566	+	7.49093i	0.170138	+	0.455884i
$271$	12.4349			0.755368			0.377684	−	0.925935i	$-0.376721\pi$
$271$	12.4349			0.755368			0.377684	+	0.925935i	$0.376721\pi$
$272$	−0.0751388	+	0.525545i	−0.00455596	+	0.0318658i
$273$	0.595595			0.0360470
$274$	−8.80160	−	23.5838i	−0.531724	−	1.42475i
$275$	0.470736	+	0.470736i	0.0283864	+	0.0283864i
$276$	1.19040	−	16.7367i	0.0716536	−	1.00743i
$277$	−1.59897	+	1.59897i	−0.0960729	+	0.0960729i	−0.753510	−	0.657437i	$-0.771641\pi$
$277$	−1.59897	+	1.59897i	−0.0960729	+	0.0960729i	0.657437	+	0.753510i	$0.271641\pi$
$278$	−3.85438	+	8.44432i	−0.231170	+	0.506456i
$279$			0.745220i			0.0446151i
$280$	2.71338	−	0.798466i	0.162156	−	0.0477174i
$281$		−	16.2874i		−	0.971623i	−0.874064	−	0.485812i	$-0.838524\pi$
$281$		−	16.2874i		−	0.971623i	0.874064	−	0.485812i	$-0.161476\pi$
$282$	−19.2233	−	8.77440i	−1.14473	−	0.522508i
$283$	−1.16739	+	1.16739i	−0.0693940	+	0.0693940i	−0.740952	−	0.671558i	$-0.765625\pi$
$283$	−1.16739	+	1.16739i	−0.0693940	+	0.0693940i	0.671558	+	0.740952i	$0.265625\pi$
$284$	13.5183	+	15.5885i	0.802164	+	0.925009i
$285$	−7.00115	−	7.00115i	−0.414712	−	0.414712i
$286$	0.364522	−	0.136042i	0.0215546	−	0.00804431i
$287$	−8.65729			−0.511024
$288$	5.10084	−	1.11489i	0.300570	−	0.0656955i
$289$	−16.9824			−0.998964
$290$	1.34484	−	0.501900i	0.0789715	−	0.0294726i
$291$	−8.40133	−	8.40133i	−0.492495	−	0.492495i
$292$	3.24989	+	3.74759i	0.190186	+	0.219311i
$293$	13.4988	−	13.4988i	0.788610	−	0.788610i	−0.192656	−	0.981266i	$-0.561710\pi$
$293$	13.4988	−	13.4988i	0.788610	−	0.788610i	0.981266	+	0.192656i	$0.0617101\pi$
$294$	−1.85412	−	0.846307i	−0.108135	−	0.0493576i
$295$		−	10.0663i		−	0.586085i
$296$	−3.40246	−	11.5624i	−0.197764	−	0.672050i
$297$		−	3.76382i		−	0.218399i
$298$	−7.76046	+	17.0019i	−0.449551	+	0.984894i
$299$	−1.70112	+	1.70112i	−0.0983783	+	0.0983783i
$300$	−0.204491	+	2.87510i	−0.0118063	+	0.165994i
$301$	−6.17882	−	6.17882i	−0.356141	−	0.356141i
$302$	6.80116	+	18.2237i	0.391363	+	1.04865i
$303$	18.6747			1.07284
$304$	−21.9863	+	16.4858i	−1.26100	+	0.945528i
$305$	0.114957			0.00658241
$306$	−0.0605748	−	0.162309i	−0.00346283	−	0.00927861i
$307$	18.2462	+	18.2462i	1.04136	+	1.04136i	0.999107	+	0.0422580i	$0.0134552\pi$
$307$	18.2462	+	18.2462i	1.04136	+	1.04136i	0.0422580	+	0.999107i	$0.486545\pi$
$308$	−1.32809	−	0.0944601i	−0.0756748	−	0.00538237i
$309$	−7.88636	+	7.88636i	−0.448639	+	0.448639i
$310$	−0.474125	+	1.03873i	−0.0269285	+	0.0589960i
$311$			8.27624i			0.469302i	0.972080	+	0.234651i	$0.0753948\pi$
$311$			8.27624i			0.469302i	−0.972080	+	0.234651i	$0.924605\pi$
$312$	1.47901	+	0.806466i	0.0837326	+	0.0456571i
$313$		−	3.64672i		−	0.206125i	−0.994675	−	0.103062i	$-0.967136\pi$
$313$		−	3.64672i		−	0.206125i	0.994675	−	0.103062i	$-0.0328641\pi$
$314$	9.55450	+	4.36112i	0.539191	+	0.246112i
$315$	−0.652658	+	0.652658i	−0.0367731	+	0.0367731i
$316$	6.68192	−	5.79453i	0.375887	−	0.325968i
$317$	−1.10850	−	1.10850i	−0.0622595	−	0.0622595i	0.675291	−	0.737551i	$-0.264018\pi$
$317$	−1.10850	−	1.10850i	−0.0622595	−	0.0622595i	−0.737551	+	0.675291i	$0.764018\pi$
$318$	4.91084	−	1.83275i	0.275386	−	0.102776i
$319$	−0.675713			−0.0378327
$320$	7.81918	+	1.69127i	0.437106	+	0.0945449i
$321$	6.03397			0.336783
$322$	7.71289	−	2.87849i	0.429823	−	0.160412i
$323$	0.644755	+	0.644755i	0.0358751	+	0.0358751i
$324$	8.12770	−	7.04831i	0.451539	−	0.391573i
$325$	0.292225	−	0.292225i	0.0162097	−	0.0162097i
$326$	3.98212	+	1.81762i	0.220549	+	0.100669i
$327$		−	3.29410i		−	0.182164i
$328$	−21.4982	−	11.7224i	−1.18704	−	0.647262i
$329$		−	10.3679i		−	0.571599i
$330$	0.563405	−	1.23433i	0.0310144	−	0.0679475i
$331$	2.42473	−	2.42473i	0.133275	−	0.133275i	−0.637322	−	0.770597i	$-0.719958\pi$
$331$	2.42473	−	2.42473i	0.133275	−	0.133275i	0.770597	+	0.637322i	$0.219958\pi$
$332$	−19.0418	−	1.35435i	−1.04506	−	0.0743296i
$333$	2.78113	+	2.78113i	0.152405	+	0.152405i
$334$	2.44641	+	6.55513i	0.133862	+	0.358681i
$335$	11.3297			0.619005
$336$	−3.45831	−	4.61217i	−0.188666	−	0.251615i
$337$	29.0855			1.58439			0.792194	−	0.610269i	$-0.208939\pi$
$337$	29.0855			1.58439			0.792194	+	0.610269i	$0.208939\pi$
$338$	6.34377	+	16.9981i	0.345055	+	0.924572i
$339$	−8.58875	−	8.58875i	−0.466477	−	0.466477i
$340$	0.0188322	−	0.264776i	0.00102132	−	0.0143595i
$341$	0.380068	−	0.380068i	0.0205818	−	0.0205818i
$342$	3.72371	−	8.15805i	0.201355	−	0.441137i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.97713	−	23.7100i	−0.376182	−	1.27836i
$345$			8.38951i			0.451676i
$346$	29.9054	+	13.6502i	1.60772	+	0.733840i
$347$	−18.5684	+	18.5684i	−0.996803	+	0.996803i	−0.999995	−	0.00319163i	$-0.998984\pi$
$347$	−18.5684	+	18.5684i	−0.996803	+	0.996803i	0.00319163	+	0.999995i	$0.498984\pi$
$348$	−1.91675	−	2.21028i	−0.102748	−	0.118484i
$349$	19.2865	+	19.2865i	1.03238	+	1.03238i	0.999458	+	0.0329271i	$0.0104829\pi$
$349$	19.2865	+	19.2865i	1.03238	+	1.03238i	0.0329271	+	0.999458i	$0.489517\pi$
$350$	−1.32495	+	0.494478i	−0.0708215	+	0.0264310i
$351$	−2.33652			−0.124714
$352$	−3.17007	−	2.03287i	−0.168965	−	0.108352i
$353$	−7.46872			−0.397520			−0.198760	−	0.980048i	$-0.563691\pi$
$353$	−7.46872			−0.397520			−0.198760	+	0.980048i	$0.563691\pi$
$354$	−19.2216	+	7.17360i	−1.02162	+	0.381273i
$355$	−7.29509	−	7.29509i	−0.387183	−	0.387183i
$356$	−16.1085	−	18.5753i	−0.853746	−	0.984491i
$357$	−0.135253	+	0.135253i	−0.00715836	+	0.00715836i
$358$	16.7002	+	7.62273i	0.882632	+	0.402874i
$359$			32.8821i			1.73545i	0.497046	+	0.867724i	$0.334418\pi$
$359$			32.8821i			1.73545i	−0.497046	+	0.867724i	$0.665582\pi$
$360$	−2.50445	+	0.736982i	−0.131996	+	0.0388424i
$361$			28.1989i			1.48415i
$362$	−0.857993	+	1.87972i	−0.0450951	+	0.0987961i
$363$	10.7581	−	10.7581i	0.564655	−	0.564655i
$364$	−0.0586393	+	0.824454i	−0.00307353	+	0.0432131i
$365$	−1.75379	−	1.75379i	−0.0917976	−	0.0917976i
$366$	−0.0819220	−	0.219509i	−0.00428213	−	0.0114739i
$367$	32.1346			1.67741			0.838707	−	0.544583i	$-0.183312\pi$
$367$	32.1346			1.67741			0.838707	+	0.544583i	$0.183312\pi$
$368$	23.0507	+	3.29563i	1.20160	+	0.171797i
$369$	7.99066			0.415977
$370$	2.10709	+	5.64593i	0.109543	+	0.293518i
$371$	1.81854	+	1.81854i	0.0944138	+	0.0944138i
$372$	2.32133	+	0.165104i	0.120355	+	0.00856026i
$373$	17.5031	−	17.5031i	0.906276	−	0.906276i	−0.0896938	−	0.995969i	$-0.528589\pi$
$373$	17.5031	−	17.5031i	0.906276	−	0.906276i	0.995969	+	0.0896938i	$0.0285888\pi$
$374$	−0.0518855	+	0.113673i	−0.00268293	+	0.00587787i
$375$		−	1.44118i		−	0.0744223i
$376$	14.0386	−	25.7460i	0.723987	−	1.32775i
$377$			0.419471i			0.0216039i
$378$	7.27372	+	3.32006i	0.374120	+	0.170766i
$379$	−23.8382	+	23.8382i	−1.22449	+	1.22449i	−0.258465	+	0.966021i	$0.583217\pi$
$379$	−23.8382	+	23.8382i	−1.22449	+	1.22449i	−0.966021	+	0.258465i	$0.916783\pi$
$380$	10.3807	−	9.00207i	0.532517	−	0.461796i
$381$	−15.3827	−	15.3827i	−0.788079	−	0.788079i
$382$	−15.0435	+	5.61430i	−0.769690	+	0.287253i
$383$	−30.3263			−1.54960			−0.774801	−	0.632205i	$-0.782150\pi$
$383$	−30.3263			−1.54960			−0.774801	+	0.632205i	$0.782150\pi$
$384$	−2.34274	−	16.1359i	−0.119552	−	0.823433i
$385$	0.665721			0.0339283
$386$	22.5790	−	8.42659i	1.14924	−	0.428902i
$387$	5.70304	+	5.70304i	0.289902	+	0.289902i
$388$	12.4567	−	10.8024i	0.632394	−	0.548410i
$389$	−7.77160	+	7.77160i	−0.394036	+	0.394036i	−0.876123	−	0.482087i	$-0.839879\pi$
$389$	−7.77160	+	7.77160i	−0.394036	+	0.394036i	0.482087	+	0.876123i	$0.339879\pi$
$390$	−0.766250	−	0.349752i	−0.0388006	−	0.0177104i
$391$		−	0.772612i		−	0.0390727i
$392$	1.35405	−	2.48325i	0.0683899	−	0.125423i
$393$			0.155366i			0.00783716i
$394$	−9.29466	+	20.3631i	−0.468258	+	1.02588i
$395$	−3.12699	+	3.12699i	−0.157336	+	0.157336i
$396$	1.22582	+	0.0871865i	0.0615999	+	0.00438129i
$397$	−0.284095	−	0.284095i	−0.0142583	−	0.0142583i	0.699942	−	0.714200i	$-0.253209\pi$
$397$	−0.284095	−	0.284095i	−0.0142583	−	0.0142583i	−0.714200	+	0.699942i	$0.753209\pi$
$398$	−4.58070	−	12.2739i	−0.229610	−	0.615237i
$399$	−9.90112			−0.495676
$400$	−3.95973	−	0.566136i	−0.197987	−	0.0283068i
$401$	−18.6782			−0.932745			−0.466372	−	0.884588i	$-0.654439\pi$
$401$	−18.6782			−0.932745			−0.466372	+	0.884588i	$0.654439\pi$
$402$	−8.07389	−	21.6339i	−0.402689	−	1.07900i
$403$	−0.235940	−	0.235940i	−0.0117530	−	0.0117530i
$404$	−1.83862	+	25.8506i	−0.0914748	+	1.28611i
$405$	−3.80359	+	3.80359i	−0.189002	+	0.189002i
$406$	0.596046	−	1.30584i	0.0295812	−	0.0648077i
$407$		−	2.83680i		−	0.140615i
$408$	−0.519007	+	0.152728i	−0.0256947	+	0.00756116i
$409$		−	12.8944i		−	0.637589i	−0.947824	−	0.318794i	$-0.896722\pi$
$409$		−	12.8944i		−	0.637589i	0.947824	−	0.318794i	$-0.103278\pi$
$410$	11.1379	+	5.08383i	0.550060	+	0.251073i
$411$	18.1392	−	18.1392i	0.894740	−	0.894740i
$412$	−10.1403	−	11.6932i	−0.499575	−	0.576081i
$413$	−7.11797	−	7.11797i	−0.350253	−	0.350253i
$414$	−7.11898	+	2.65684i	−0.349879	+	0.130577i
$415$	9.54497			0.468544
$416$	−1.26197	+	1.96793i	−0.0618732	+	0.0964856i
$417$	−9.45939			−0.463228
$418$	−6.05979	+	2.26155i	−0.296394	+	0.110616i
$419$	12.4495	+	12.4495i	0.608200	+	0.608200i	0.942475	−	0.334275i	$-0.108492\pi$
$419$	12.4495	+	12.4495i	0.608200	+	0.608200i	−0.334275	+	0.942475i	$0.608492\pi$
$420$	1.88840	+	2.17760i	0.0921447	+	0.106256i
$421$	−15.0748	+	15.0748i	−0.734700	+	0.734700i	−0.971547	−	0.236847i	$-0.923886\pi$
$421$	−15.0748	+	15.0748i	−0.734700	+	0.734700i	0.236847	+	0.971547i	$0.423886\pi$
$422$	−34.1730	−	15.5982i	−1.66352	−	0.759306i
$423$			9.56952i			0.465286i
$424$	2.05350	+	6.97829i	0.0997266	+	0.338896i
$425$			0.132722i			0.00643798i
$426$	−8.73120	+	19.1286i	−0.423028	+	0.926786i
$427$	0.0812868	−	0.0812868i	0.00393374	−	0.00393374i
$428$	−0.594074	+	8.35255i	−0.0287157	+	0.403736i
$429$	0.280368	+	0.280368i	0.0135363	+	0.0135363i
$430$	4.32084	+	11.5776i	0.208369	+	0.558324i
$431$	24.6487			1.18729			0.593643	−	0.804729i	$-0.297689\pi$
$431$	24.6487			1.18729			0.593643	+	0.804729i	$0.297689\pi$
$432$	13.5669	+	18.0935i	0.652740	+	0.870526i
$433$	−3.48916			−0.167678			−0.0838391	−	0.996479i	$-0.526718\pi$
$433$	−3.48916			−0.167678			−0.0838391	+	0.996479i	$0.526718\pi$
$434$	0.399237	+	1.06975i	0.0191640	+	0.0513497i
$435$	1.03436	+	1.03436i	0.0495940	+	0.0495940i
$436$	4.55987	+	0.324321i	0.218378	+	0.0155321i
$437$	28.2793	−	28.2793i	1.35278	−	1.35278i
$438$	−2.09904	+	4.59866i	−0.100296	+	0.219732i
$439$		−	22.1066i		−	1.05509i	−0.849527	−	0.527546i	$-0.823112\pi$
$439$		−	22.1066i		−	1.05509i	0.849527	−	0.527546i	$-0.176888\pi$
$440$	1.65315	+	0.901421i	0.0788110	+	0.0429736i
$441$			0.922998i			0.0439523i
$442$	0.0705661	+	0.0322096i	0.00335649	+	0.00153206i
$443$	10.1569	−	10.1569i	0.482567	−	0.482567i	−0.423384	−	0.905951i	$-0.639158\pi$
$443$	10.1569	−	10.1569i	0.482567	−	0.482567i	0.905951	+	0.423384i	$0.139158\pi$
$444$	9.27928	−	8.04695i	0.440375	−	0.381891i
$445$	8.69285	+	8.69285i	0.412081	+	0.412081i
$446$	35.5513	−	13.2679i	1.68340	−	0.628254i
$447$	−19.0457			−0.900830
$448$	6.72491	−	4.33309i	0.317722	−	0.204719i
$449$	−35.3464			−1.66810			−0.834049	−	0.551690i	$-0.813983\pi$
$449$	−35.3464			−1.66810			−0.834049	+	0.551690i	$0.813983\pi$
$450$	1.22293	−	0.456402i	0.0576493	−	0.0215150i
$451$	−4.07530	−	4.07530i	−0.191898	−	0.191898i
$452$	12.7346	−	11.0434i	0.598986	−	0.519438i
$453$	−14.0165	+	14.0165i	−0.658553	+	0.658553i
$454$	23.5226	+	10.7368i	1.10397	+	0.503903i
$455$		−	0.413268i		−	0.0193743i
$456$	−24.5870	−	13.4066i	−1.15139	−	0.627823i
$457$			35.0003i			1.63724i	0.574334	+	0.818621i	$0.305261\pi$
$457$			35.0003i			1.63724i	−0.574334	+	0.818621i	$0.694739\pi$
$458$	0.865872	−	1.89698i	0.0404595	−	0.0886403i
$459$	0.530598	−	0.530598i	0.0247662	−	0.0247662i
$460$	−11.6132	−	0.825989i	−0.541469	−	0.0385119i
$461$	−17.3224	−	17.3224i	−0.806782	−	0.806782i	0.177363	−	0.984145i	$-0.443243\pi$
$461$	−17.3224	−	17.3224i	−0.806782	−	0.806782i	−0.984145	+	0.177363i	$0.943243\pi$
$462$	−0.474415	−	1.27119i	−0.0220718	−	0.0591411i
$463$	5.08083			0.236126			0.118063	−	0.993006i	$-0.462331\pi$
$463$	5.08083			0.236126			0.118063	+	0.993006i	$0.462331\pi$
$464$	3.24831	−	2.43565i	0.150799	−	0.113072i
$465$	−1.16360			−0.0539605
$466$	−4.24186	−	11.3660i	−0.196500	−	0.526521i
$467$	9.71963	+	9.71963i	0.449771	+	0.449771i	0.895278	−	0.445508i	$-0.146977\pi$
$467$	9.71963	+	9.71963i	0.449771	+	0.449771i	−0.445508	+	0.895278i	$0.646977\pi$
$468$	0.0541239	−	0.760969i	0.00250188	−	0.0351758i
$469$	8.01128	−	8.01128i	0.369927	−	0.369927i
$470$	−6.08834	+	13.3386i	−0.280834	+	0.615262i
$471$			10.7030i			0.493169i
$472$	−8.03762	−	27.3138i	−0.369962	−	1.25722i
$473$		−	5.81719i		−	0.267475i
$474$	8.19936	+	3.74257i	0.376609	+	0.171902i
$475$	−4.85793	+	4.85793i	−0.222897	+	0.222897i
$476$	−0.173908	−	0.200541i	−0.00797108	−	0.00919178i
$477$	−1.67851	−	1.67851i	−0.0768536	−	0.0768536i
$478$	−9.64928	+	3.60116i	−0.441348	+	0.164713i
$479$	8.70318			0.397658			0.198829	−	0.980034i	$-0.436286\pi$
$479$	8.70318			0.397658			0.198829	+	0.980034i	$0.436286\pi$
$480$	1.74080	+	7.96453i	0.0794565	+	0.363529i
$481$	−1.76104			−0.0802964
$482$	35.9134	−	13.4031i	1.63581	−	0.610493i
$483$	5.93228	+	5.93228i	0.269928	+	0.269928i
$484$	13.8328	+	15.9512i	0.628763	+	0.725053i
$485$	−5.82948	+	5.82948i	−0.264703	+	0.264703i
$486$	−11.8477	−	5.40783i	−0.537421	−	0.245304i
$487$		−	11.0606i		−	0.501203i	−0.968090	−	0.250602i	$-0.919372\pi$
$487$		−	11.0606i		−	0.501203i	0.968090	−	0.250602i	$-0.0806284\pi$
$488$	0.311922	−	0.0917891i	0.0141200	−	0.00415510i
$489$			4.46080i			0.201724i
$490$	−0.587232	+	1.28653i	−0.0265284	+	0.0581195i
$491$	23.7013	−	23.7013i	1.06963	−	1.06963i	0.0722380	−	0.997387i	$-0.476986\pi$
$491$	23.7013	−	23.7013i	1.06963	−	1.06963i	0.997387	−	0.0722380i	$-0.0230141\pi$
$492$	1.77034	−	24.8906i	0.0798131	−	1.12215i
$493$	−0.0952574	−	0.0952574i	−0.00429018	−	0.00429018i
$494$	1.40393	+	3.76181i	0.0631658	+	0.169252i
$495$	−0.614459			−0.0276179
$496$	−0.457092	+	3.19705i	−0.0205241	+	0.143552i
$497$	−10.3168			−0.462773
$498$	−6.80205	−	18.2260i	−0.304807	−	0.816728i
$499$	10.8823	+	10.8823i	0.487160	+	0.487160i	0.907409	−	0.420249i	$-0.138057\pi$
$499$	10.8823	+	10.8823i	0.487160	+	0.487160i	−0.420249	+	0.907409i	$0.638057\pi$
$500$	1.99496	+	0.141891i	0.0892173	+	0.00634558i
$501$	−5.04180	+	5.04180i	−0.225251	+	0.225251i
$502$	3.72220	−	8.15474i	0.166130	−	0.363964i
$503$		−	5.99893i		−	0.267479i	−0.991017	−	0.133740i	$-0.957301\pi$
$503$		−	5.99893i		−	0.267479i	0.991017	−	0.133740i	$-0.0426986\pi$
$504$	−1.24979	+	2.29204i	−0.0556699	+	0.102095i
$505$		−	12.9579i		−	0.576621i
$506$	4.98575	+	2.27573i	0.221643	+	0.101168i
$507$	−13.0738	+	13.0738i	−0.580630	+	0.580630i
$508$	22.8081	−	19.7791i	1.01194	−	0.877554i
$509$	12.4584	+	12.4584i	0.552209	+	0.552209i	0.927078	−	0.374869i	$-0.122312\pi$
$509$	12.4584	+	12.4584i	0.552209	+	0.552209i	−0.374869	+	0.927078i	$0.622312\pi$
$510$	0.253432	−	0.0945822i	0.0112222	−	0.00418817i
$511$	−2.48023			−0.109719
$512$	22.5669	−	1.65428i	0.997324	−	0.0731096i
$513$	38.8421			1.71492
$514$	−1.84023	+	0.686785i	−0.0811692	+	0.0302928i
$515$	5.47215	+	5.47215i	0.241132	+	0.241132i
$516$	19.0282	−	16.5012i	0.837672	−	0.726425i
$517$	4.88053	−	4.88053i	0.214645	−	0.214645i
$518$	5.48222	+	2.50234i	0.240875	+	0.109946i
$519$			33.5003i			1.47050i
$520$	0.559587	−	1.02625i	0.0245395	−	0.0450040i
$521$		−	14.0377i		−	0.615002i	−0.951548	−	0.307501i	$-0.900507\pi$
$521$		−	14.0377i		−	0.615002i	0.951548	−	0.307501i	$-0.0994927\pi$
$522$	−0.550149	+	1.20529i	−0.0240794	+	0.0527540i
$523$	22.1978	−	22.1978i	0.970644	−	0.970644i	−0.0289373	−	0.999581i	$-0.509212\pi$
$523$	22.1978	−	22.1978i	0.970644	−	0.970644i	0.999581	+	0.0289373i	$0.00921232\pi$
$524$	−0.215065	−	0.0152965i	−0.00939518	−	0.000668232i
$525$	−1.01907	−	1.01907i	−0.0444758	−	0.0444758i
$526$	3.41118	+	9.14022i	0.148734	+	0.398532i
$527$	0.107159			0.00466791
$528$	0.543164	−	3.79907i	0.0236382	−	0.165333i
$529$	−10.8872			−0.473357
$530$	−1.27170	−	3.40751i	−0.0552391	−	0.148013i
$531$	6.56987	+	6.56987i	0.285108	+	0.285108i
$532$	0.974815	−	13.7057i	0.0422636	−	0.594216i
$533$	−2.52988	+	2.52988i	−0.109581	+	0.109581i
$534$	10.4041	−	22.7937i	0.450230	−	0.986382i
$535$		−	4.18682i		−	0.181012i
$536$	30.7417	−	9.04634i	1.32784	−	0.390743i
$537$			18.7077i			0.807296i
$538$	−13.1766	−	6.01440i	−0.568083	−	0.259299i
$539$	0.470736	−	0.470736i	0.0202760	−	0.0202760i
$540$	−7.40821	−	8.54272i	−0.318798	−	0.367620i
$541$	5.87778	+	5.87778i	0.252705	+	0.252705i	0.822079	−	0.569374i	$-0.192814\pi$
$541$	5.87778	+	5.87778i	0.252705	+	0.252705i	−0.569374	+	0.822079i	$0.692814\pi$
$542$	−16.4756	+	6.14880i	−0.707690	+	0.264114i
$543$	−2.10568			−0.0903634
$544$	−0.160315	−	0.733475i	−0.00687347	−	0.0314475i
$545$	−2.28570			−0.0979085
$546$	−0.789133	+	0.294509i	−0.0337718	+	0.0126038i
$547$	−11.6287	−	11.6287i	−0.497209	−	0.497209i	0.413359	−	0.910568i	$-0.364355\pi$
$547$	−11.6287	−	11.6287i	−0.497209	−	0.497209i	−0.910568	+	0.413359i	$0.864355\pi$
$548$	23.3233	+	26.8951i	0.996324	+	1.14890i
$549$	−0.0750275	+	0.0750275i	−0.00320210	+	0.00320210i
$550$	−0.856470	−	0.390933i	−0.0365200	−	0.0166694i
$551$		−	6.97326i		−	0.297071i
$552$	6.69873	+	22.7639i	0.285117	+	0.968898i
$553$			4.42224i			0.188053i
$554$	1.32790	−	2.90921i	0.0564171	−	0.123601i
$555$	−4.34250	+	4.34250i	−0.184329	+	0.184329i
$556$	0.931324	−	13.0942i	0.0394969	−	0.555318i
$557$	−21.9190	−	21.9190i	−0.928739	−	0.928739i	0.0688851	−	0.997625i	$-0.478056\pi$
$557$	−21.9190	−	21.9190i	−0.928739	−	0.928739i	−0.997625	+	0.0688851i	$0.978056\pi$
$558$	−0.368495	−	0.987378i	−0.0155996	−	0.0417991i
$559$	−3.61121			−0.152738
$560$	−3.20027	+	2.39964i	−0.135236	+	0.101403i
$561$	−0.127337			−0.00537617
$562$	8.05375	+	21.5799i	0.339727	+	0.910295i
$563$	−11.2631	−	11.2631i	−0.474682	−	0.474682i	0.428744	−	0.903426i	$-0.358956\pi$
$563$	−11.2631	−	11.2631i	−0.474682	−	0.474682i	−0.903426	+	0.428744i	$0.858956\pi$
$564$	29.8086	+	2.12014i	1.25517	+	0.0892739i
$565$	−5.95952	+	5.95952i	−0.250719	+	0.250719i
$566$	0.969483	−	2.12398i	0.0407504	−	0.0892775i
$567$			5.37908i			0.225900i
$568$	−25.6193	−	13.9695i	−1.07496	−	0.586148i
$569$		−	19.1107i		−	0.801162i	−0.916261	−	0.400581i	$-0.868808\pi$
$569$		−	19.1107i		−	0.801162i	0.916261	−	0.400581i	$-0.131192\pi$
$570$	12.7381	+	5.81425i	0.533540	+	0.243532i
$571$	18.3607	−	18.3607i	0.768373	−	0.768373i	−0.209447	−	0.977820i	$-0.567166\pi$
$571$	18.3607	−	18.3607i	0.768373	−	0.768373i	0.977820	+	0.209447i	$0.0671664\pi$
$572$	−0.415704	+	0.360497i	−0.0173815	+	0.0150731i
$573$	−11.5705	−	11.5705i	−0.483364	−	0.483364i
$574$	11.4705	−	4.28084i	0.478768	−	0.178679i
$575$	5.82127			0.242764
$576$	−6.20707	+	3.99943i	−0.258628	+	0.166643i
$577$	28.0312			1.16696			0.583478	−	0.812129i	$-0.301692\pi$
$577$	28.0312			1.16696			0.583478	+	0.812129i	$0.301692\pi$
$578$	22.5008	−	8.39742i	0.935910	−	0.349287i
$579$	17.3663	+	17.3663i	0.721721	+	0.721721i
$580$	−1.53366	+	1.32998i	−0.0636818	+	0.0552246i
$581$	6.74931	−	6.74931i	0.280009	−	0.280009i
$582$	15.2856	+	6.97706i	0.633609	+	0.289209i
$583$			1.71210i			0.0709081i
$584$	−6.15905	−	3.35836i	−0.254863	−	0.138970i
$585$			0.381446i			0.0157708i
$586$	−11.2104	+	24.5602i	−0.463097	+	1.01457i
$587$	−25.4832	+	25.4832i	−1.05180	+	1.05180i	−0.0532194	+	0.998583i	$0.516948\pi$
$587$	−25.4832	+	25.4832i	−1.05180	+	1.05180i	−0.998583	+	0.0532194i	$0.983052\pi$
$588$	2.87510	+	0.204491i	0.118567	+	0.00843308i
$589$	3.92224	+	3.92224i	0.161613	+	0.161613i
$590$	4.97758	+	13.3374i	0.204924	+	0.549092i
$591$	−22.8109			−0.938315
$592$	10.2254	+	13.6371i	0.420263	+	0.560483i
$593$	−27.1759			−1.11598			−0.557990	−	0.829848i	$-0.688427\pi$
$593$	−27.1759			−1.11598			−0.557990	+	0.829848i	$0.688427\pi$
$594$	1.86113	+	4.98687i	0.0763630	+	0.204614i
$595$	0.0938488	+	0.0938488i	0.00384743	+	0.00384743i
$596$	1.87514	−	26.3641i	0.0768088	−	1.07991i
$597$	9.44035	−	9.44035i	0.386368	−	0.386368i
$598$	1.41273	−	3.09507i	0.0577709	−	0.126567i
$599$			3.46480i			0.141568i	0.997492	+	0.0707840i	$0.0225501\pi$
$599$			3.46480i			0.141568i	−0.997492	+	0.0707840i	$0.977450\pi$
$600$	−1.15073	−	3.91048i	−0.0469785	−	0.159645i
$601$			4.91505i			0.200489i	0.994963	+	0.100245i	$0.0319625\pi$
$601$			4.91505i			0.200489i	−0.994963	+	0.100245i	$0.968037\pi$
$602$	11.2419	+	5.13134i	0.458187	+	0.209138i
$603$	−7.39439	+	7.39439i	−0.301123	+	0.301123i
$604$	−18.0224	−	20.7824i	−0.733321	−	0.845623i
$605$	−7.46480	−	7.46480i	−0.303487	−	0.303487i
$606$	−24.7431	+	9.23425i	−1.00512	+	0.375116i
$607$	2.15943			0.0876488			0.0438244	−	0.999039i	$-0.486046\pi$
$607$	2.15943			0.0876488			0.0438244	+	0.999039i	$0.486046\pi$
$608$	20.9789	−	32.7147i	0.850806	−	1.32676i
$609$	1.46281			0.0592761
$610$	−0.152312	+	0.0568437i	−0.00616693	+	0.00230153i
$611$	−3.02975	−	3.02975i	−0.122571	−	0.122571i
$612$	0.160517	+	0.185099i	0.00648852	+	0.00748218i
$613$	−24.8094	+	24.8094i	−1.00204	+	1.00204i	−0.00204495	+	0.999998i	$0.500651\pi$
$613$	−24.8094	+	24.8094i	−1.00204	+	1.00204i	−0.999998	+	0.00204495i	$0.999349\pi$
$614$	−33.1976	−	15.1529i	−1.33975	−	0.611523i
$615$			12.4767i			0.503110i
$616$	1.80636	−	0.531556i	0.0727802	−	0.0214170i
$617$		−	45.7600i		−	1.84223i	−0.389291	−	0.921115i	$-0.627280\pi$
$617$		−	45.7600i		−	1.84223i	0.389291	−	0.921115i	$-0.372720\pi$
$618$	6.54939	−	14.3487i	0.263455	−	0.577188i
$619$	8.18650	−	8.18650i	0.329043	−	0.329043i	−0.523179	−	0.852223i	$-0.675254\pi$
$619$	8.18650	−	8.18650i	0.329043	−	0.329043i	0.852223	+	0.523179i	$0.175254\pi$
$620$	0.114562	−	1.61071i	0.00460091	−	0.0646877i
$621$	−23.2723	−	23.2723i	−0.933885	−	0.933885i
$622$	−4.09242	−	10.9656i	−0.164091	−	0.439680i
$623$	12.2935			0.492531
$624$	−2.35840	−	0.337187i	−0.0944114	−	0.0134983i
$625$	−1.00000			−0.0400000
$626$	1.80322	+	4.83172i	0.0720713	+	0.193114i
$627$	−4.66081	−	4.66081i	−0.186135	−	0.186135i
$628$	−14.8157	−	1.05377i	−0.591211	−	0.0420498i
$629$	0.399913	−	0.399913i	0.0159456	−	0.0159456i
$630$	0.542014	−	1.18746i	0.0215943	−	0.0473097i
$631$		−	17.0667i		−	0.679414i	−0.940531	−	0.339707i	$-0.889672\pi$
$631$		−	17.0667i		−	0.679414i	0.940531	−	0.339707i	$-0.110328\pi$
$632$	−5.98794	+	10.9815i	−0.238187	+	0.436822i
$633$		−	38.2809i		−	1.52153i
$634$	2.01683	+	0.920576i	0.0800987	+	0.0365607i
$635$	−10.6737	+	10.6737i	−0.423572	+	0.423572i
$636$	−5.60035	+	4.85660i	−0.222069	+	0.192577i
$637$	−0.292225	−	0.292225i	−0.0115784	−	0.0115784i
$638$	0.895286	−	0.334125i	0.0354447	−	0.0132282i
$639$	9.52240			0.376700
$640$	−11.1963	+	1.62557i	−0.442573	+	0.0642562i
$641$	−45.9122			−1.81342			−0.906712	−	0.421751i	$-0.861416\pi$
$641$	−45.9122			−1.81342			−0.906712	+	0.421751i	$0.861416\pi$
$642$	−7.99470	+	2.98367i	−0.315526	+	0.117756i
$643$	−5.29140	−	5.29140i	−0.208673	−	0.208673i	0.595030	−	0.803703i	$-0.297140\pi$
$643$	−5.29140	−	5.29140i	−0.208673	−	0.208673i	−0.803703	+	0.595030i	$0.797140\pi$
$644$	−8.79584	+	7.62771i	−0.346605	+	0.300574i
$645$	−8.90480	+	8.90480i	−0.350626	+	0.350626i
$646$	−1.17309	−	0.535450i	−0.0461544	−	0.0210670i
$647$		−	0.584699i		−	0.0229869i	−0.999934	−	0.0114935i	$-0.996341\pi$
$647$		−	0.584699i		−	0.0229869i	0.999934	−	0.0114935i	$-0.00365856\pi$
$648$	−7.28356	+	13.3576i	−0.286125	+	0.524737i
$649$		−	6.70137i		−	0.263052i
$650$	−0.242684	+	0.531682i	−0.00951886	+	0.0208543i
$651$	−0.822786	+	0.822786i	−0.0322475	+	0.0322475i
$652$	−6.17488	−	0.439188i	−0.241827	−	0.0171999i
$653$	32.8462	+	32.8462i	1.28537	+	1.28537i	0.937568	+	0.347802i	$0.113072\pi$
$653$	32.8462	+	32.8462i	1.28537	+	1.28537i	0.347802	+	0.937568i	$0.386928\pi$
$654$	1.62886	+	4.36452i	0.0636935	+	0.170666i
$655$	0.107804			0.00421227
$656$	34.2806	+	4.90120i	1.33843	+	0.191360i
$657$	2.28925			0.0893121
$658$	5.12669	+	13.7369i	0.199859	+	0.535520i
$659$	−16.6389	−	16.6389i	−0.648159	−	0.648159i	0.304389	−	0.952548i	$-0.401548\pi$
$659$	−16.6389	−	16.6389i	−0.648159	−	0.648159i	−0.952548	+	0.304389i	$0.901548\pi$
$660$	−0.136134	+	1.91401i	−0.00529901	+	0.0745029i
$661$	−25.8541	+	25.8541i	−1.00561	+	1.00561i	−0.00562234	+	0.999984i	$0.501790\pi$
$661$	−25.8541	+	25.8541i	−1.00561	+	1.00561i	−0.999984	+	0.00562234i	$0.998210\pi$
$662$	−2.01367	+	4.41163i	−0.0782635	+	0.171463i
$663$			0.0790487i			0.00307000i
$664$	25.8992	−	7.62133i	1.00508	−	0.295765i
$665$			6.87014i			0.266413i
$666$	−5.06007	−	2.30965i	−0.196074	−	0.0894972i
$667$	−4.17804	+	4.17804i	−0.161774	+	0.161774i
$668$	−6.48274	−	7.47552i	−0.250825	−	0.289236i
$669$	27.3438	+	27.3438i	1.05717	+	1.05717i
$670$	−15.0112	+	5.60227i	−0.579934	+	0.216435i
$671$	0.0765292			0.00295438
$672$	6.86270	+	4.40084i	0.264735	+	0.169766i
$673$	−28.6871			−1.10580			−0.552902	−	0.833246i	$-0.686480\pi$
$673$	−28.6871			−1.10580			−0.552902	+	0.833246i	$0.686480\pi$
$674$	−38.5368	+	14.3821i	−1.48438	+	0.553980i
$675$	3.99780	+	3.99780i	0.153876	+	0.153876i
$676$	−16.8103	−	19.3847i	−0.646551	−	0.745566i
$677$	−23.6401	+	23.6401i	−0.908563	+	0.908563i	−0.996156	−	0.0875934i	$-0.972082\pi$
$677$	−23.6401	+	23.6401i	−0.908563	+	0.908563i	0.0875934	+	0.996156i	$0.472082\pi$
$678$	15.6266	+	7.13271i	0.600136	+	0.273930i
$679$			8.24412i			0.316380i
$680$	0.105974	+	0.360127i	0.00406392	+	0.0138102i
$681$			26.3502i			1.00974i
$682$	−0.315635	+	0.691506i	−0.0120863	+	0.0264791i
$683$	15.8902	−	15.8902i	0.608022	−	0.608022i	−0.334407	−	0.942429i	$-0.608536\pi$
$683$	15.8902	−	15.8902i	0.608022	−	0.608022i	0.942429	+	0.334407i	$0.108536\pi$
$684$	−0.899752	+	12.6503i	−0.0344029	+	0.483696i
$685$	−12.5863	−	12.5863i	−0.480899	−	0.480899i
$686$	0.494478	+	1.32495i	0.0188793	+	0.0505868i
$687$	2.12502			0.0810745
$688$	20.9684	+	27.9645i	0.799414	+	1.06614i
$689$	1.06284			0.0404912
$690$	−4.14843	−	11.1157i	−0.157928	−	0.423166i
$691$	31.6424	+	31.6424i	1.20373	+	1.20373i	0.973023	+	0.230709i	$0.0741046\pi$
$691$	31.6424	+	31.6424i	1.20373	+	1.20373i	0.230709	+	0.973023i	$0.425895\pi$
$692$	−46.3729	−	3.29827i	−1.76283	−	0.125381i
$693$	−0.434488	+	0.434488i	−0.0165048	+	0.0165048i
$694$	15.4205	−	33.7838i	0.585355	−	1.28242i
$695$			6.56364i			0.248973i
$696$	3.63253	+	1.98072i	0.137691	+	0.0750791i
$697$		−	1.14901i		−	0.0435220i
$698$	−35.0905	−	16.0169i	−1.32819	−	0.606249i
$699$	8.74204	−	8.74204i	0.330654	−	0.330654i
$700$	1.51098	−	1.31032i	0.0571098	−	0.0495253i
$701$	23.7735	+	23.7735i	0.897912	+	0.897912i	0.995251	−	0.0973391i	$-0.0310331\pi$
$701$	23.7735	+	23.7735i	0.897912	+	0.897912i	−0.0973391	+	0.995251i	$0.531033\pi$
$702$	3.09577	−	1.15536i	0.116842	−	0.0436061i
$703$	29.2754			1.10414
$704$	5.20540	+	1.12591i	0.196186	+	0.0424345i
$705$	−14.9420			−0.562747
$706$	9.89568	−	3.69312i	0.372429	−	0.138992i
$707$	−9.16265	−	9.16265i	−0.344597	−	0.344597i
$708$	21.9204	−	19.0093i	0.823821	−	0.714414i
$709$	−32.0976	+	32.0976i	−1.20545	+	1.20545i	−0.232968	+	0.972485i	$0.574844\pi$
$709$	−32.0976	+	32.0976i	−1.20545	+	1.20545i	−0.972485	+	0.232968i	$0.925156\pi$
$710$	13.2729	+	6.05837i	0.498123	+	0.227366i
$711$		−	4.08171i		−	0.153076i
$712$	30.5280	+	16.6461i	1.14408	+	0.623839i
$713$		−	4.70004i		−	0.176018i
$714$	0.112324	−	0.246083i	0.00420361	−	0.00920944i
$715$	0.194540	−	0.194540i	0.00727540	−	0.00727540i
$716$	−25.8962	−	1.84186i	−0.967785	−	0.0688337i
$717$	−7.42162	−	7.42162i	−0.277166	−	0.277166i
$718$	−16.2595	−	43.5671i	−0.606798	−	1.62591i
$719$	−26.7682			−0.998285			−0.499142	−	0.866520i	$-0.666352\pi$
$719$	−26.7682			−0.998285			−0.499142	+	0.866520i	$0.666352\pi$
$720$	2.95384	−	2.21486i	0.110083	−	0.0825429i
$721$	7.73879			0.288208
$722$	−13.9437	−	37.3621i	−0.518932	−	1.39047i
$723$	27.6223	+	27.6223i	1.02729	+	1.02729i
$724$	0.207315	−	2.91480i	0.00770479	−	0.108328i
$725$	0.717720	−	0.717720i	0.0266554	−	0.0266554i
$726$	−8.93431	+	19.5736i	−0.331583	+	0.726445i
$727$			47.7280i			1.77013i	0.465465	+	0.885066i	$0.345887\pi$
$727$			47.7280i			1.77013i	−0.465465	+	0.885066i	$0.654113\pi$
$728$	−0.329981	−	1.12136i	−0.0122299	−	0.0415602i
$729$		−	29.4091i		−	1.08923i
$730$	3.19089	+	1.45647i	0.118100	+	0.0539064i
$731$	0.820068	−	0.820068i	0.0303313	−	0.0303313i
$732$	0.217085	+	0.250330i	0.00802369	+	0.00925246i
$733$	2.09739	+	2.09739i	0.0774687	+	0.0774687i	0.744779	−	0.667311i	$-0.232555\pi$
$733$	2.09739	+	2.09739i	0.0774687	+	0.0774687i	−0.667311	+	0.744779i	$0.732555\pi$
$734$	−42.5767	+	15.8899i	−1.57154	+	0.586506i
$735$	−1.44118			−0.0531588
$736$	−32.1706	+	7.03152i	−1.18582	+	0.259185i
$737$	7.54240			0.277828
$738$	−10.5872	+	3.95121i	−0.389721	+	0.145446i
$739$	−25.4037	−	25.4037i	−0.934492	−	0.934492i	0.0634908	−	0.997982i	$-0.479777\pi$
$739$	−25.4037	−	25.4037i	−0.934492	−	0.934492i	−0.997982	+	0.0634908i	$0.979777\pi$
$740$	−5.58358	−	6.43866i	−0.205257	−	0.236690i
$741$	−2.89335	+	2.89335i	−0.106290	+	0.106290i
$742$	−3.30870	−	1.51024i	−0.121466	−	0.0554428i
$743$			15.3933i			0.564727i	0.959307	+	0.282364i	$0.0911185\pi$
$743$			15.3933i			0.564727i	−0.959307	+	0.282364i	$0.908882\pi$
$744$	−3.15728	+	0.929091i	−0.115752	+	0.0340621i
$745$			13.2153i			0.484172i
$746$	−14.5358	+	31.8456i	−0.532194	+	1.16595i
$747$	−6.22960	+	6.22960i	−0.227929	+	0.227929i
$748$	0.0125370	−	0.176267i	0.000458397	−	0.00644495i
$749$	−2.96053	−	2.96053i	−0.108175	−	0.108175i
$750$	0.712633	+	1.90949i	0.0260217	+	0.0697248i
$751$	−27.8461			−1.01612			−0.508059	−	0.861322i	$-0.669637\pi$
$751$	−27.8461			−1.01612			−0.508059	+	0.861322i	$0.669637\pi$
$752$	−5.86962	+	41.0540i	−0.214043	+	1.49709i
$753$	9.13500			0.332898
$754$	−0.207419	−	0.555778i	−0.00755377	−	0.0202402i
$755$	9.72570	+	9.72570i	0.353955	+	0.353955i
$756$	−11.2790	−	0.802219i	−0.410213	−	0.0291764i
$757$	−18.1685	+	18.1685i	−0.660347	+	0.660347i	−0.955462	−	0.295115i	$-0.904642\pi$
$757$	−18.1685	+	18.1685i	−0.660347	+	0.660347i	0.295115	+	0.955462i	$0.404642\pi$
$758$	19.7969	−	43.3719i	0.719057	−	1.57534i
$759$			5.58507i			0.202725i
$760$	−9.30253	+	17.0603i	−0.337438	+	0.618842i
$761$			17.9680i			0.651341i	0.945483	+	0.325670i	$0.105590\pi$
$761$			17.9680i			0.651341i	−0.945483	+	0.325670i	$0.894410\pi$
$762$	27.9877	+	12.7749i	1.01389	+	0.462785i
$763$	−1.61623	+	1.61623i	−0.0585115	+	0.0585115i
$764$	17.1557	−	14.8773i	0.620670	−	0.538243i
$765$	−0.0866222	−	0.0866222i	−0.00313183	−	0.00313183i
$766$	40.1808	−	14.9957i	1.45179	−	0.541817i
$767$	−4.16010			−0.150212
$768$	11.0829	+	20.2208i	0.399919	+	0.729657i
$769$	7.56360			0.272751			0.136375	−	0.990657i	$-0.456455\pi$
$769$	7.56360			0.272751			0.136375	+	0.990657i	$0.456455\pi$
$770$	−0.882047	+	0.329185i	−0.0317868	+	0.0118630i
$771$	−1.41539	−	1.41539i	−0.0509741	−	0.0509741i
$772$	−25.7492	+	22.3296i	−0.926735	+	0.803661i
$773$	−3.07711	+	3.07711i	−0.110676	+	0.110676i	−0.760276	−	0.649600i	$-0.774936\pi$
$773$	−3.07711	+	3.07711i	−0.110676	+	0.110676i	0.649600	+	0.760276i	$0.274936\pi$
$774$	−10.3763	−	4.73621i	−0.372967	−	0.170240i
$775$			0.807390i			0.0290023i
$776$	−11.1630	+	20.4722i	−0.400727	+	0.734911i
$777$			6.14122i			0.220315i
$778$	6.45409	−	14.1399i	0.231390	−	0.506939i
$779$	42.0565	−	42.0565i	1.50683	−	1.50683i
$780$	1.18819	+	0.0845098i	0.0425439	+	0.00302594i
$781$	−4.85650	−	4.85650i	−0.173779	−	0.173779i
$782$	0.382040	+	1.02367i	0.0136617	+	0.0366065i
$783$	−5.73861			−0.205081
$784$	−0.566136	+	3.95973i	−0.0202191	+	0.141419i
$785$	7.42656			0.265065
$786$	−0.0768249	−	0.205852i	−0.00274025	−	0.00734248i
$787$	27.6537	+	27.6537i	0.985749	+	0.985749i	0.999900	−	0.0141507i	$-0.00450446\pi$
$787$	27.6537	+	27.6537i	0.985749	+	0.985749i	−0.0141507	+	0.999900i	$0.504504\pi$
$788$	2.24585	−	31.5761i	0.0800050	−	1.12485i
$789$	−7.03009	+	7.03009i	−0.250278	+	0.250278i
$790$	2.59688	−	5.68934i	0.0923927	−	0.202418i
$791$			8.42803i			0.299666i
$792$	−1.66726	+	0.490624i	−0.0592436	+	0.0174336i
$793$		−	0.0475080i		−	0.00168706i
$794$	0.516890	+	0.235932i	0.0183437	+	0.00837293i
$795$	2.62084	−	2.62084i	0.0929518	−	0.0929518i
$796$	12.1384	+	13.9973i	0.430234	+	0.496121i
$797$	−30.5139	−	30.5139i	−1.08086	−	1.08086i	−0.996429	−	0.0844294i	$-0.973093\pi$
$797$	−30.5139	−	30.5139i	−1.08086	−	1.08086i	−0.0844294	−	0.996429i	$-0.526907\pi$
$798$	13.1185	−	4.89589i	0.464389	−	0.173313i
$799$	1.37605			0.0486810
$800$	5.52639	−	1.20790i	0.195387	−	0.0427058i
$801$	−11.3469			−0.400924
$802$	24.7477	−	9.23596i	0.873871	−	0.326133i
$803$	−1.16754	−	1.16754i	−0.0412014	−	0.0412014i
$804$	21.3950	+	24.6715i	0.754543	+	0.870095i
$805$	4.11626	−	4.11626i	0.145079	−	0.145079i
$806$	0.429275	+	0.195941i	0.0151206	+	0.00690173i
$807$		−	14.7605i		−	0.519595i
$808$	−10.3465	−	35.1599i	−0.363987	−	1.23692i
$809$			11.3535i			0.399166i	0.979881	+	0.199583i	$0.0639588\pi$
$809$			11.3535i			0.399166i	−0.979881	+	0.199583i	$0.936041\pi$
$810$	3.15877	−	6.92035i	0.110988	−	0.243156i
$811$	21.0413	−	21.0413i	0.738860	−	0.738860i	−0.233497	−	0.972357i	$-0.575017\pi$
$811$	21.0413	−	21.0413i	0.738860	−	0.738860i	0.972357	+	0.233497i	$0.0750170\pi$
$812$	−0.144021	+	2.02490i	−0.00505415	+	0.0710602i
$813$	−12.6720	−	12.6720i	−0.444428	−	0.444428i
$814$	1.40274	+	3.75862i	0.0491659	+	0.131739i
$815$	3.09524			0.108422
$816$	0.612138	−	0.458995i	0.0214291	−	0.0160680i
$817$	60.0325			2.10027
$818$	6.37602	+	17.0845i	0.222932	+	0.597345i
$819$	0.269723	+	0.269723i	0.00942488	+	0.00942488i
$820$	−17.2709	−	1.22840i	−0.603128	−	0.0428974i
$821$	5.22180	−	5.22180i	0.182242	−	0.182242i	−0.610090	−	0.792332i	$-0.708867\pi$
$821$	5.22180	−	5.22180i	0.182242	−	0.182242i	0.792332	+	0.610090i	$0.208867\pi$
$822$	−15.0641	+	33.0029i	−0.525420	+	1.15111i
$823$		−	27.8678i		−	0.971411i	−0.874122	−	0.485706i	$-0.838563\pi$
$823$		−	27.8678i		−	0.971411i	0.874122	−	0.485706i	$-0.161437\pi$
$824$	19.2174	+	10.4787i	0.669469	+	0.365044i
$825$		−	0.959425i		−	0.0334029i
$826$	12.9506	+	5.91127i	0.450610	+	0.205679i
$827$	−26.6562	+	26.6562i	−0.926928	+	0.926928i	−0.997506	−	0.0705779i	$-0.977516\pi$
$827$	−26.6562	+	26.6562i	−0.926928	+	0.926928i	0.0705779	+	0.997506i	$0.477516\pi$
$828$	8.11854	−	7.04036i	0.282139	−	0.244670i
$829$	23.7075	+	23.7075i	0.823397	+	0.823397i	0.986594	−	0.163197i	$-0.0521805\pi$
$829$	23.7075	+	23.7075i	0.823397	+	0.823397i	−0.163197	+	0.986594i	$0.552181\pi$
$830$	−12.6466	+	4.71978i	−0.438970	+	0.163826i
$831$	3.25892			0.113051
$832$	0.698949	−	3.23142i	0.0242317	−	0.112029i
$833$	0.132722			0.00459855
$834$	12.5332	−	4.67746i	0.433990	−	0.161967i
$835$	3.49838	+	3.49838i	0.121066	+	0.121066i
$836$	6.91063	−	5.99287i	0.239009	−	0.207268i
$837$	3.22779	−	3.22779i	0.111569	−	0.111569i
$838$	−22.6511	−	10.3390i	−0.782468	−	0.357154i
$839$			25.6178i			0.884426i	0.896910	+	0.442213i	$0.145807\pi$
$839$			25.6178i			0.884426i	−0.896910	+	0.442213i	$0.854193\pi$
$840$	−3.57882	−	1.95143i	−0.123481	−	0.0673309i
$841$		−	27.9698i		−	0.964474i
$842$	12.5192	−	27.4275i	0.431439	−	0.945213i
$843$	−16.5980	+	16.5980i	−0.571664	+	0.571664i
$844$	52.9905	+	3.76894i	1.82401	+	0.129732i
$845$	9.07162	+	9.07162i	0.312073	+	0.312073i
$846$	−4.73192	−	12.6791i	−0.162687	−	0.435917i
$847$	−10.5568			−0.362736
$848$	−6.17139	−	8.23047i	−0.211926	−	0.282636i
$849$	2.37930			0.0816573
$850$	−0.0656283	−	0.175850i	−0.00225103	−	0.00603162i
$851$	−17.5404	−	17.5404i	−0.601277	−	0.601277i
$852$	2.10970	−	29.6619i	0.0722771	−	1.01620i
$853$	−1.11778	+	1.11778i	−0.0382721	+	0.0382721i	−0.725984	−	0.687712i	$-0.758615\pi$
$853$	−1.11778	+	1.11778i	−0.0382721	+	0.0382721i	0.687712	+	0.725984i	$0.258615\pi$
$854$	−0.0675063	+	0.147895i	−0.00231002	+	0.00506088i
$855$		−	6.34113i		−	0.216862i
$856$	−3.34303	−	11.3605i	−0.114263	−	0.388292i
$857$		−	42.7733i		−	1.46111i	−0.682856	−	0.730553i	$-0.739262\pi$
$857$		−	42.7733i		−	1.46111i	0.682856	−	0.730553i	$-0.260738\pi$
$858$	−0.510109	−	0.232837i	−0.0174148	−	0.00794894i
$859$	21.2595	−	21.2595i	0.725366	−	0.725366i	−0.244327	−	0.969693i	$-0.578567\pi$
$859$	21.2595	−	21.2595i	0.725366	−	0.725366i	0.969693	+	0.244327i	$0.0785670\pi$
$860$	−11.4498	−	13.2032i	−0.390434	−	0.450226i
$861$	8.82237	+	8.82237i	0.300666	+	0.300666i
$862$	−32.6583	+	12.1882i	−1.11234	+	0.415133i
$863$	−42.6615			−1.45221			−0.726107	−	0.687582i	$-0.758672\pi$
$863$	−42.6615			−1.45221			−0.726107	+	0.687582i	$0.758672\pi$
$864$	−26.9224	−	17.2645i	−0.915918	−	0.587349i
$865$	23.2450			0.790354
$866$	4.62296	−	1.72531i	0.157095	−	0.0586285i
$867$	17.3062	+	17.3062i	0.587750	+	0.587750i
$868$	−1.05794	−	1.21995i	−0.0359088	−	0.0414079i
$869$	−2.08171	+	2.08171i	−0.0706170	+	0.0706170i
$870$	−1.88195	−	0.859010i	−0.0638041	−	0.0291232i
$871$		−	4.68219i		−	0.158650i
$872$	−6.20197	+	1.82505i	−0.210025	+	0.0618040i
$873$		−	7.60931i		−	0.257536i
$874$	−23.4851	+	51.4522i	−0.794397	+	1.74040i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	0.507186	−	7.13092i	0.0171362	−	0.240931i
$877$	20.5053	+	20.5053i	0.692413	+	0.692413i	0.962762	−	0.270349i	$-0.0871391\pi$
$877$	20.5053	+	20.5053i	0.692413	+	0.692413i	−0.270349	+	0.962762i	$0.587139\pi$
$878$	10.9312	+	29.2902i	0.368912	+	0.988495i
$879$	−27.5125			−0.927973
$880$	−2.63608	−	0.376888i	−0.0888622	−	0.0127049i
$881$	29.9986			1.01068			0.505339	−	0.862921i	$-0.331367\pi$
$881$	29.9986			1.01068			0.505339	+	0.862921i	$0.331367\pi$
$882$	−0.456402	−	1.22293i	−0.0153679	−	0.0411780i
$883$	−23.9376	−	23.9376i	−0.805563	−	0.805563i	0.178396	−	0.983959i	$-0.442909\pi$
$883$	−23.9376	−	23.9376i	−0.805563	−	0.805563i	−0.983959	+	0.178396i	$0.942909\pi$
$884$	−0.109423	−	0.00778274i	−0.00368031	−	0.000261762i
$885$	−10.2583	+	10.2583i	−0.344829	+	0.344829i
$886$	−8.43498	+	18.4797i	−0.283379	+	0.620837i
$887$		−	6.74584i		−	0.226503i	−0.993566	−	0.113252i	$-0.963873\pi$
$887$		−	6.74584i		−	0.226503i	0.993566	−	0.113252i	$-0.0361266\pi$
$888$	−8.31553	+	15.2502i	−0.279051	+	0.511763i
$889$			15.0949i			0.506265i
$890$	−15.8160	−	7.21916i	−0.530154	−	0.241987i
$891$	−2.53213	+	2.53213i	−0.0848295	+	0.0848295i
$892$	−40.5429	+	35.1587i	−1.35748	+	1.17720i
$893$	50.3663	+	50.3663i	1.68544	+	1.68544i
$894$	25.2346	−	9.41767i	0.843970	−	0.314974i
$895$	12.9808			0.433900
$896$	−6.76754	+	9.06644i	−0.226088	+	0.302889i
$897$	3.46712			0.115764
$898$	46.8322	−	17.4780i	1.56281	−	0.583249i
$899$	−0.579480	−	0.579480i	−0.0193267	−	0.0193267i
$900$	−1.39463	+	1.20942i	−0.0464878	+	0.0403140i
$901$	−0.241361	+	0.241361i	−0.00804089	+	0.00804089i
$902$	7.41471	+	3.38442i	0.246883	+	0.112689i
$903$			12.5933i			0.419079i
$904$	−11.4120	+	20.9289i	−0.379557	+	0.696086i
$905$			1.46108i			0.0485680i
$906$	11.6403	−	25.5020i	0.386723	−	0.847247i
$907$	−5.66629	+	5.66629i	−0.188146	+	0.188146i	−0.794894	−	0.606748i	$-0.792474\pi$
$907$	−5.66629	+	5.66629i	−0.188146	+	0.188146i	0.606748	+	0.794894i	$0.292474\pi$
$908$	−36.4754	−	2.59431i	−1.21048	−	0.0860951i
$909$	8.45710	+	8.45710i	0.280504	+	0.280504i
$910$	0.204352	+	0.547560i	0.00677421	+	0.0181514i
$911$	35.7991			1.18608			0.593039	−	0.805173i	$-0.297928\pi$
$911$	35.7991			1.18608			0.593039	+	0.805173i	$0.297928\pi$
$912$	39.2058	+	5.60538i	1.29823	+	0.185613i
$913$	6.35429			0.210296
$914$	−17.3069	−	46.3736i	−0.572460	−	1.53390i
$915$	−0.117149	−	0.117149i	−0.00387282	−	0.00387282i
$916$	−0.209219	+	2.94156i	−0.00691277	+	0.0971920i
$917$	0.0762292	−	0.0762292i	0.00251731	−	0.00251731i
$918$	−0.440646	+	0.965384i	−0.0145435	+	0.0318624i
$919$		−	13.9376i		−	0.459758i	−0.973219	−	0.229879i	$-0.926167\pi$
$919$		−	13.9376i		−	0.459758i	0.973219	−	0.229879i	$-0.0738330\pi$
$920$	15.7953	−	4.64809i	0.520757	−	0.153243i
$921$		−	37.1882i		−	1.22539i
$922$	31.5168	+	14.3857i	1.03795	+	0.473768i
$923$	−3.01483	+	3.01483i	−0.0992344	+	0.0992344i
$924$	1.25715	+	1.44967i	0.0413572	+	0.0476908i
$925$	3.01315	+	3.01315i	0.0990719	+	0.0990719i
$926$	−6.73184	+	2.51236i	−0.221222	+	0.0825613i
$927$	−7.14288			−0.234603
$928$	−3.09946	+	4.83333i	−0.101745	+	0.158662i
$929$	−33.7136			−1.10611			−0.553053	−	0.833146i	$-0.686537\pi$
$929$	−33.7136			−1.10611			−0.553053	+	0.833146i	$0.686537\pi$
$930$	1.54171	−	0.575373i	0.0505545	−	0.0188672i
$931$	4.85793	+	4.85793i	0.159212	+	0.159212i
$932$	11.2405	+	12.9619i	0.368195	+	0.424581i
$933$	8.43405	−	8.43405i	0.276118	−	0.276118i
$934$	−17.6842	−	8.07187i	−0.578643	−	0.264120i
$935$			0.0883560i			0.00288955i
$936$	0.304571	+	1.03501i	0.00995523	+	0.0338303i
$937$		−	13.9887i		−	0.456990i	−0.973545	−	0.228495i	$-0.926620\pi$
$937$		−	13.9887i		−	0.456990i	0.973545	−	0.228495i	$-0.0733805\pi$
$938$	−6.65314	+	14.5759i	−0.217233	+	0.475921i
$939$	−3.71626	+	3.71626i	−0.121276	+	0.121276i
$940$	1.47111	−	20.6835i	0.0479824	−	0.674621i
$941$	18.6062	+	18.6062i	0.606545	+	0.606545i	0.942042	−	0.335496i	$-0.108904\pi$
$941$	18.6062	+	18.6062i	0.606545	+	0.606545i	−0.335496	+	0.942042i	$0.608904\pi$
$942$	−5.29241	−	14.1810i	−0.172436	−	0.462041i
$943$	−50.3964			−1.64113
$944$	24.1555	+	32.2150i	0.786196	+	1.04851i
$945$	5.65375			0.183916
$946$	2.87647	+	7.70748i	0.0935222	+	0.250592i
$947$	−30.1439	−	30.1439i	−0.979546	−	0.979546i	0.0202490	−	0.999795i	$-0.493554\pi$
$947$	−30.1439	−	30.1439i	−0.979546	−	0.979546i	−0.999795	+	0.0202490i	$0.993554\pi$
$948$	−12.7144	−	0.904308i	−0.412943	−	0.0293706i
$949$	−0.724786	+	0.724786i	−0.0235275	+	0.0235275i
$950$	4.03437	−	8.83865i	0.130892	−	0.286764i
$951$			2.25927i			0.0732619i
$952$	0.329583	+	0.179713i	0.0106818	+	0.00582453i
$953$		−	34.9829i		−	1.13321i	−0.823990	−	0.566604i	$-0.808257\pi$
$953$		−	34.9829i		−	1.13321i	0.823990	−	0.566604i	$-0.191743\pi$
$954$	3.05392	+	1.39395i	0.0988744	+	0.0451309i
$955$	−8.02848	+	8.02848i	−0.259796	+	0.259796i
$956$	11.0041	−	9.54272i	0.355898	−	0.308634i
$957$	0.688598	+	0.688598i	0.0222592	+	0.0222592i
$958$	−11.5313	+	4.30353i	−0.372558	+	0.139041i
$959$	−17.7998			−0.574784
$960$	−6.24476	−	9.69180i	−0.201549	−	0.312802i
$961$	−30.3481			−0.978972
$962$	2.33329	−	0.870795i	0.0752281	−	0.0280755i
$963$	2.73256	+	2.73256i	0.0880556	+	0.0880556i
$964$	−40.9559	+	35.5168i	−1.31910	+	1.14392i
$965$	12.0501	−	12.0501i	0.387906	−	0.387906i
$966$	−10.7933	−	4.92658i	−0.347270	−	0.158510i
$967$		−	48.2481i		−	1.55155i	−0.631007	−	0.775777i	$-0.717358\pi$
$967$		−	48.2481i		−	1.55155i	0.631007	−	0.775777i	$-0.282642\pi$
$968$	−26.2152	−	14.2945i	−0.842590	−	0.459442i
$969$		−	1.31410i		−	0.0422150i
$970$	4.84121	−	10.6063i	0.155442	−	0.340548i
$971$	20.4102	−	20.4102i	0.654994	−	0.654994i	−0.299197	−	0.954191i	$-0.596719\pi$
$971$	20.4102	−	20.4102i	0.654994	−	0.654994i	0.954191	+	0.299197i	$0.0967188\pi$
$972$	18.3716	+	1.30668i	0.589270	+	0.0419118i
$973$	4.64119	+	4.64119i	0.148790	+	0.148790i
$974$	5.46922	+	14.6547i	0.175245	+	0.469568i
$975$	−0.595595			−0.0190743
$976$	−0.367893	+	0.275855i	−0.0117760	+	0.00882989i
$977$	−16.7479			−0.535813			−0.267906	−	0.963445i	$-0.586332\pi$
$977$	−16.7479			−0.535813			−0.267906	+	0.963445i	$0.586332\pi$
$978$	−2.20577	−	5.91034i	−0.0705327	−	0.188992i
$979$	5.78702	+	5.78702i	0.184954	+	0.184954i
$980$	0.141891	−	1.99496i	0.00453256	−	0.0637267i
$981$	1.49178	−	1.49178i	0.0476288	−	0.0476288i
$982$	−19.6833	+	43.1228i	−0.628118	+	1.37610i
$983$			17.8737i			0.570084i	0.958515	+	0.285042i	$0.0920076\pi$
$983$			17.8737i			0.570084i	−0.958515	+	0.285042i	$0.907992\pi$
$984$	9.96223	+	33.8541i	0.317584	+	1.07923i
$985$			15.8279i			0.504319i
$986$	0.173314	+	0.0791085i	0.00551944	+	0.00251933i
$987$	−10.5656	+	10.5656i	−0.336306	+	0.336306i
$988$	−3.72027	−	4.29000i	−0.118358	−	0.136483i
$989$	−35.9686	−	35.9686i	−1.14374	−	1.14374i
$990$	0.814127	−	0.303837i	0.0258747	−	0.00965656i
$991$	53.8224			1.70972			0.854862	−	0.518855i	$-0.173642\pi$
$991$	53.8224			1.70972			0.854862	+	0.518855i	$0.173642\pi$
$992$	−0.975248	−	4.46195i	−0.0309642	−	0.141667i
$993$	−4.94194			−0.156828
$994$	13.6693	−	5.10144i	0.433563	−	0.161808i
$995$	−6.55042	−	6.55042i	−0.207662	−	0.207662i
$996$	18.0248	+	20.7851i	0.571136	+	0.658601i
$997$	−5.05018	+	5.05018i	−0.159941	+	0.159941i	−0.782540	−	0.622600i	$-0.786077\pi$
$997$	−5.05018	+	5.05018i	−0.159941	+	0.159941i	0.622600	+	0.782540i	$0.286077\pi$
$998$	−19.7996	−	9.03747i	−0.626746	−	0.286076i
$999$		−	24.0920i		−	0.762237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.2	✓	52
4.3	odd	2		2240.2.bd.b.1681.18		52
16.5	even	4	inner	560.2.bd.b.421.2	yes	52
16.11	odd	4		2240.2.bd.b.561.18		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.2	✓	52	1.1	even	1	trivial
560.2.bd.b.421.2	yes	52	16.5	even	4	inner
2240.2.bd.b.561.18		52	16.11	odd	4
2240.2.bd.b.1681.18		52	4.3	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32495 + 0.494478i) q^{2} +(-1.01907 - 1.01907i) q^{3} +(1.51098 - 1.31032i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.85412 + 0.846307i) q^{6} +1.00000i q^{7} +(-1.35405 + 2.48325i) q^{8} -0.922998i q^{9} +O(q^{10})\)	\(q+(-1.32495 + 0.494478i) q^{2} +(-1.01907 - 1.01907i) q^{3} +(1.51098 - 1.31032i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.85412 + 0.846307i) q^{6} +1.00000i q^{7} +(-1.35405 + 2.48325i) q^{8} -0.922998i q^{9} +(0.587232 - 1.28653i) q^{10} +(-0.470736 + 0.470736i) q^{11} +(-2.87510 - 0.204491i) q^{12} +(0.292225 + 0.292225i) q^{13} +(-0.494478 - 1.32495i) q^{14} +1.44118 q^{15} +(0.566136 - 3.95973i) q^{16} -0.132722 q^{17} +(0.456402 + 1.22293i) q^{18} +(-4.85793 - 4.85793i) q^{19} +(-0.141891 + 1.99496i) q^{20} +(1.01907 - 1.01907i) q^{21} +(0.390933 - 0.856470i) q^{22} +5.82127i q^{23} +(3.91048 - 1.15073i) q^{24} -1.00000i q^{25} +(-0.531682 - 0.242684i) q^{26} +(-3.99780 + 3.99780i) q^{27} +(1.31032 + 1.51098i) q^{28} +(0.717720 + 0.717720i) q^{29} +(-1.90949 + 0.712633i) q^{30} -0.807390 q^{31} +(1.20790 + 5.52639i) q^{32} +0.959425 q^{33} +(0.175850 - 0.0656283i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-1.20942 - 1.39463i) q^{36} +(-3.01315 + 3.01315i) q^{37} +(8.83865 + 4.03437i) q^{38} -0.595595i q^{39} +(-0.798466 - 2.71338i) q^{40} +8.65729i q^{41} +(-0.846307 + 1.85412i) q^{42} +(-6.17882 + 6.17882i) q^{43} +(-0.0944601 + 1.32809i) q^{44} +(0.652658 + 0.652658i) q^{45} +(-2.87849 - 7.71289i) q^{46} -10.3679 q^{47} +(-4.61217 + 3.45831i) q^{48} -1.00000 q^{49} +(0.494478 + 1.32495i) q^{50} +(0.135253 + 0.135253i) q^{51} +(0.824454 + 0.0586393i) q^{52} +(1.81854 - 1.81854i) q^{53} +(3.32006 - 7.27372i) q^{54} -0.665721i q^{55} +(-2.48325 - 1.35405i) q^{56} +9.90112i q^{57} +(-1.30584 - 0.596046i) q^{58} +(-7.11797 + 7.11797i) q^{59} +(2.17760 - 1.88840i) q^{60} +(-0.0812868 - 0.0812868i) q^{61} +(1.06975 - 0.399237i) q^{62} +0.922998 q^{63} +(-4.33309 - 6.72491i) q^{64} -0.413268 q^{65} +(-1.27119 + 0.474415i) q^{66} +(-8.01128 - 8.01128i) q^{67} +(-0.200541 + 0.173908i) q^{68} +(5.93228 - 5.93228i) q^{69} +(1.28653 + 0.587232i) q^{70} +10.3168i q^{71} +(2.29204 + 1.24979i) q^{72} +2.48023i q^{73} +(2.50234 - 5.48222i) q^{74} +(-1.01907 + 1.01907i) q^{75} +(-13.7057 - 0.974815i) q^{76} +(-0.470736 - 0.470736i) q^{77} +(0.294509 + 0.789133i) q^{78} +4.42224 q^{79} +(2.39964 + 3.20027i) q^{80} +5.37908 q^{81} +(-4.28084 - 11.4705i) q^{82} +(-6.74931 - 6.74931i) q^{83} +(0.204491 - 2.87510i) q^{84} +(0.0938488 - 0.0938488i) q^{85} +(5.13134 - 11.2419i) q^{86} -1.46281i q^{87} +(-0.531556 - 1.80636i) q^{88} -12.2935i q^{89} +(-1.18746 - 0.542014i) q^{90} +(-0.292225 + 0.292225i) q^{91} +(7.62771 + 8.79584i) q^{92} +(0.822786 + 0.822786i) q^{93} +(13.7369 - 5.12669i) q^{94} +6.87014 q^{95} +(4.40084 - 6.86270i) q^{96} +8.24412 q^{97} +(1.32495 - 0.494478i) q^{98} +(0.434488 + 0.434488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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