LMFDB - Embedded newform 280.2.bj.e.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (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:	$2.23581125660$
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			131.2
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.e.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37955 - 0.311173i) q^{2} +(2.75363 - 1.58981i) q^{3} +(1.80634 + 0.858559i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-4.29350 + 1.33638i) q^{6} +(1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 - 6.15745i) q^{9} +O(q^{10})$	\(q+(-1.37955 - 0.311173i) q^{2} +(2.75363 - 1.58981i) q^{3} +(1.80634 + 0.858559i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-4.29350 + 1.33638i) q^{6} +(1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 - 6.15745i) q^{9} +(-0.959261 + 1.03914i) q^{10} +(1.21003 + 2.09584i) q^{11} +(6.33896 - 0.507586i) q^{12} +1.53832 q^{13} +(-0.681512 - 3.67907i) q^{14} -3.17962i q^{15} +(2.52575 + 3.10171i) q^{16} +(-6.58087 + 3.79947i) q^{17} +(-6.82035 + 7.38832i) q^{18} +(-1.52991 - 0.883293i) q^{19} +(1.64671 - 1.13506i) q^{20} +(6.73663 + 5.03864i) q^{21} +(-1.01714 - 3.26785i) q^{22} +(-5.66247 - 3.26923i) q^{23} +(-8.90289 - 1.27227i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.12220 - 0.478684i) q^{26} -13.0683i q^{27} +(-0.204642 + 5.28754i) q^{28} +2.34486i q^{29} +(-0.989412 + 4.38647i) q^{30} +(1.04132 + 1.80363i) q^{31} +(-2.51925 - 5.06492i) q^{32} +(6.66397 + 3.84745i) q^{33} +(10.2610 - 3.19379i) q^{34} +(2.62717 + 0.313017i) q^{35} +(11.7081 - 8.07028i) q^{36} +(-2.47037 - 1.42627i) q^{37} +(1.83574 + 1.69462i) q^{38} +(4.23598 - 2.44564i) q^{39} +(-2.62492 + 1.05347i) q^{40} -6.90356i q^{41} +(-7.72566 - 9.04733i) q^{42} -1.39343 q^{43} +(0.386332 + 4.82469i) q^{44} +(-3.55500 - 6.15745i) q^{45} +(6.79439 + 6.27208i) q^{46} +(5.65799 - 9.79993i) q^{47} +(11.8861 + 4.52550i) q^{48} +(-4.82637 + 5.07012i) q^{49} +(0.420294 + 1.35032i) q^{50} +(-12.0809 + 20.9247i) q^{51} +(2.77874 + 1.32074i) q^{52} +(-6.82251 + 3.93898i) q^{53} +(-4.06649 + 18.0284i) q^{54} +2.42006 q^{55} +(1.92765 - 7.23078i) q^{56} -5.61708 q^{57} +(0.729658 - 3.23487i) q^{58} +(4.90087 - 2.82952i) q^{59} +(2.72990 - 5.74349i) q^{60} +(-4.93580 + 8.54905i) q^{61} +(-0.875325 - 2.81223i) q^{62} +(18.6792 + 2.22555i) q^{63} +(1.89937 + 7.77125i) q^{64} +(0.769162 - 1.33223i) q^{65} +(-7.99610 - 7.38141i) q^{66} +(3.13260 + 5.42583i) q^{67} +(-15.1494 + 1.21307i) q^{68} -20.7898 q^{69} +(-3.52692 - 1.24933i) q^{70} +3.98199i q^{71} +(-18.6632 + 7.49016i) q^{72} +(-2.73292 + 1.57785i) q^{73} +(2.96419 + 2.73633i) q^{74} +(-2.75363 - 1.58981i) q^{75} +(-2.00518 - 2.90905i) q^{76} +(-3.83499 + 5.12736i) q^{77} +(-6.60478 + 2.05578i) q^{78} +(1.75753 + 1.01471i) q^{79} +(3.94903 - 0.636512i) q^{80} +(-10.1111 - 17.5129i) q^{81} +(-2.14820 + 9.52384i) q^{82} +0.288923i q^{83} +(7.84269 + 14.8853i) q^{84} +7.59894i q^{85} +(1.92231 + 0.433596i) q^{86} +(3.72789 + 6.45690i) q^{87} +(0.968343 - 6.77613i) q^{88} +(12.0399 + 6.95124i) q^{89} +(2.98829 + 9.60076i) q^{90} +(1.60371 + 3.74075i) q^{91} +(-7.42153 - 10.7669i) q^{92} +(5.73485 + 3.31102i) q^{93} +(-10.8550 + 11.7589i) q^{94} +(-1.52991 + 0.883293i) q^{95} +(-14.9894 - 9.94181i) q^{96} -0.249149i q^{97} +(8.23592 - 5.49268i) q^{98} +17.2067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.37955	−	0.311173i	−0.975493	−	0.220032i
$2$	−1.37955	−	0.311173i	−0.975493	−	0.220032i
$3$	2.75363	−	1.58981i	1.58981	−	0.917878i	0.596475	−	0.802632i	$-0.296568\pi$
$3$	2.75363	−	1.58981i	1.58981	−	0.917878i	0.993337	−	0.115247i	$-0.0367658\pi$
$4$	1.80634	+	0.858559i	0.903172	+	0.429280i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−4.29350	+	1.33638i	−1.75281	+	0.545574i
$7$	1.04250	+	2.43170i	0.394030	+	0.919098i
$7$	1.04250	+	2.43170i	0.394030	+	0.919098i
$8$	−2.22479	−	1.74651i	−0.786582	−	0.617486i
$9$	3.55500	−	6.15745i	1.18500	−	2.05248i
$10$	−0.959261	+	1.03914i	−0.303345	+	0.328606i
$11$	1.21003	+	2.09584i	0.364838	+	0.631919i	0.988750	−	0.149576i	$-0.0477909\pi$
$11$	1.21003	+	2.09584i	0.364838	+	0.631919i	−0.623912	+	0.781495i	$0.714458\pi$
$12$	6.33896	−	0.507586i	1.82990	−	0.146528i
$13$	1.53832			0.426654			0.213327	−	0.976981i	$-0.431570\pi$
$13$	1.53832			0.426654			0.213327	+	0.976981i	$0.431570\pi$
$14$	−0.681512	−	3.67907i	−0.182142	−	0.983272i
$15$		−	3.17962i		−	0.820975i
$16$	2.52575	+	3.10171i	0.631438	+	0.775427i
$17$	−6.58087	+	3.79947i	−1.59610	+	0.921506i	−0.603866	+	0.797086i	$0.706374\pi$
$17$	−6.58087	+	3.79947i	−1.59610	+	0.921506i	−0.992230	+	0.124421i	$0.960293\pi$
$18$	−6.82035	+	7.38832i	−1.60757	+	1.74144i
$19$	−1.52991	−	0.883293i	−0.350985	−	0.202641i	0.314134	−	0.949379i	$-0.398286\pi$
$19$	−1.52991	−	0.883293i	−0.350985	−	0.202641i	−0.665119	+	0.746737i	$0.731619\pi$
$20$	1.64671	−	1.13506i	0.368215	−	0.253807i
$21$	6.73663	+	5.03864i	1.47005	+	1.09952i
$22$	−1.01714	−	3.26785i	−0.216855	−	0.696708i
$23$	−5.66247	−	3.26923i	−1.18071	−	0.681681i	−0.224528	−	0.974468i	$-0.572084\pi$
$23$	−5.66247	−	3.26923i	−1.18071	−	0.681681i	−0.956178	+	0.292787i	$0.905417\pi$
$24$	−8.90289	−	1.27227i	−1.81729	−	0.259700i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.12220	−	0.478684i	−0.416198	−	0.0938777i
$27$		−	13.0683i		−	2.51499i
$28$	−0.204642	+	5.28754i	−0.0386736	+	0.999252i
$29$			2.34486i			0.435430i	0.976012	+	0.217715i	$0.0698604\pi$
$29$			2.34486i			0.435430i	−0.976012	+	0.217715i	$0.930140\pi$
$30$	−0.989412	+	4.38647i	−0.180641	+	0.800855i
$31$	1.04132	+	1.80363i	0.187027	+	0.323941i	0.944258	−	0.329207i	$-0.106781\pi$
$31$	1.04132	+	1.80363i	0.187027	+	0.323941i	−0.757230	+	0.653148i	$0.773448\pi$
$32$	−2.51925	−	5.06492i	−0.445344	−	0.895360i
$33$	6.66397	+	3.84745i	1.16005	+	0.669754i
$34$	10.2610	−	3.19379i	1.75974	−	0.547730i
$35$	2.62717	+	0.313017i	0.444073	+	0.0529095i
$36$	11.7081	−	8.07028i	1.95135	−	1.34505i
$37$	−2.47037	−	1.42627i	−0.406126	−	0.234477i	0.282998	−	0.959121i	$-0.408671\pi$
$37$	−2.47037	−	1.42627i	−0.406126	−	0.234477i	−0.689124	+	0.724644i	$0.742004\pi$
$38$	1.83574	+	1.69462i	0.297796	+	0.274903i
$39$	4.23598	−	2.44564i	0.678300	−	0.391617i
$40$	−2.62492	+	1.05347i	−0.415036	+	0.166568i
$41$		−	6.90356i		−	1.07815i	−0.842256	−	0.539077i	$-0.818773\pi$
$41$		−	6.90356i		−	1.07815i	0.842256	−	0.539077i	$-0.181227\pi$
$42$	−7.72566	−	9.04733i	−1.19210	−	1.39603i
$43$	−1.39343			−0.212496			−0.106248	−	0.994340i	$-0.533884\pi$
$43$	−1.39343			−0.212496			−0.106248	+	0.994340i	$0.533884\pi$
$44$	0.386332	+	4.82469i	0.0582418	+	0.727349i
$45$	−3.55500	−	6.15745i	−0.529949	−	0.917898i
$46$	6.79439	+	6.27208i	1.00178	+	0.924768i
$47$	5.65799	−	9.79993i	0.825303	−	1.42947i	−0.0763851	−	0.997078i	$-0.524338\pi$
$47$	5.65799	−	9.79993i	0.825303	−	1.42947i	0.901688	−	0.432388i	$-0.142329\pi$
$48$	11.8861	+	4.52550i	1.71561	+	0.653199i
$49$	−4.82637	+	5.07012i	−0.689481	+	0.724304i
$50$	0.420294	+	1.35032i	0.0594385	+	0.190964i
$51$	−12.0809	+	20.9247i	−1.69166	+	2.93004i
$52$	2.77874	+	1.32074i	0.385342	+	0.183154i
$53$	−6.82251	+	3.93898i	−0.937144	+	0.541060i	−0.889064	−	0.457783i	$-0.848644\pi$
$53$	−6.82251	+	3.93898i	−0.937144	+	0.541060i	−0.0480800	+	0.998843i	$0.515310\pi$
$54$	−4.06649	+	18.0284i	−0.553379	+	2.45335i
$55$	2.42006			0.326321
$56$	1.92765	−	7.23078i	0.257594	−	0.966253i
$57$	−5.61708			−0.744000
$58$	0.729658	−	3.23487i	0.0958087	−	0.424759i
$59$	4.90087	−	2.82952i	0.638038	−	0.368372i	−0.145820	−	0.989311i	$-0.546582\pi$
$59$	4.90087	−	2.82952i	0.638038	−	0.368372i	0.783859	+	0.620939i	$0.213249\pi$
$60$	2.72990	−	5.74349i	0.352428	−	0.741482i
$61$	−4.93580	+	8.54905i	−0.631964	+	1.09459i	0.355186	+	0.934796i	$0.384418\pi$
$61$	−4.93580	+	8.54905i	−0.631964	+	1.09459i	−0.987150	+	0.159798i	$0.948916\pi$
$62$	−0.875325	−	2.81223i	−0.111166	−	0.357154i
$63$	18.6792	+	2.22555i	2.35336	+	0.280393i
$64$	1.89937	+	7.77125i	0.237422	+	0.971407i
$65$	0.769162	−	1.33223i	0.0954027	−	0.165242i
$66$	−7.99610	−	7.38141i	−0.984251	−	0.908589i
$67$	3.13260	+	5.42583i	0.382708	+	0.662870i	0.991448	−	0.130499i	$-0.0416581\pi$
$67$	3.13260	+	5.42583i	0.382708	+	0.662870i	−0.608740	+	0.793370i	$0.708325\pi$
$68$	−15.1494	+	1.21307i	−1.83713	+	0.147107i
$69$	−20.7898			−2.50280
$70$	−3.52692	−	1.24933i	−0.421548	−	0.149323i
$71$			3.98199i			0.472575i	0.971683	+	0.236287i	$0.0759307\pi$
$71$			3.98199i			0.472575i	−0.971683	+	0.236287i	$0.924069\pi$
$72$	−18.6632	+	7.49016i	−2.19948	+	0.882723i
$73$	−2.73292	+	1.57785i	−0.319865	+	0.184674i	−0.651332	−	0.758793i	$-0.725790\pi$
$73$	−2.73292	+	1.57785i	−0.319865	+	0.184674i	0.331468	+	0.943467i	$0.392456\pi$
$74$	2.96419	+	2.73633i	0.344580	+	0.318091i
$75$	−2.75363	−	1.58981i	−0.317962	−	0.183576i
$76$	−2.00518	−	2.90905i	−0.230010	−	0.333691i
$77$	−3.83499	+	5.12736i	−0.437038	+	0.584317i
$78$	−6.60478	+	2.05578i	−0.747845	+	0.232771i
$79$	1.75753	+	1.01471i	0.197738	+	0.114164i	0.595600	−	0.803281i	$-0.296914\pi$
$79$	1.75753	+	1.01471i	0.197738	+	0.114164i	−0.397862	+	0.917445i	$0.630248\pi$
$80$	3.94903	−	0.636512i	0.441515	−	0.0711642i
$81$	−10.1111	−	17.5129i	−1.12345	−	1.94588i
$82$	−2.14820	+	9.52384i	−0.237229	+	1.05173i
$83$			0.288923i			0.0317134i	0.999874	+	0.0158567i	$0.00504756\pi$
$83$			0.288923i			0.0317134i	−0.999874	+	0.0158567i	$0.994952\pi$
$84$	7.84269	+	14.8853i	0.855708	+	1.62412i
$85$			7.59894i			0.824220i
$86$	1.92231	+	0.433596i	0.207288	+	0.0467559i
$87$	3.72789	+	6.45690i	0.399672	+	0.692252i
$88$	0.968343	−	6.77613i	0.103226	−	0.722338i
$89$	12.0399	+	6.95124i	1.27623	+	0.736830i	0.976152	−	0.217086i	$-0.0696553\pi$
$89$	12.0399	+	6.95124i	1.27623	+	0.736830i	0.300074	+	0.953916i	$0.402989\pi$
$90$	2.98829	+	9.60076i	0.314994	+	1.01201i
$91$	1.60371	+	3.74075i	0.168114	+	0.392137i
$92$	−7.42153	−	10.7669i	−0.773748	−	1.12253i
$93$	5.73485	+	3.31102i	0.594677	+	0.343337i
$94$	−10.8550	+	11.7589i	−1.11961	+	1.21284i
$95$	−1.52991	+	0.883293i	−0.156965	+	0.0906240i
$96$	−14.9894	−	9.94181i	−1.52984	−	1.01468i
$97$		−	0.249149i		−	0.0252972i	−0.999920	−	0.0126486i	$-0.995974\pi$
$97$		−	0.249149i		−	0.0252972i	0.999920	−	0.0126486i	$-0.00402629\pi$
$98$	8.23592	−	5.49268i	0.831954	−	0.554845i
$99$	17.2067			1.72934
$100$	−0.159637	−	1.99362i	−0.0159637	−	0.199362i
$101$	4.87755	+	8.44817i	0.485335	+	0.840624i	0.999858	−	0.0168520i	$-0.00536443\pi$
$101$	4.87755	+	8.44817i	0.485335	+	0.840624i	−0.514523	+	0.857476i	$0.672031\pi$
$102$	23.1774	−	25.1075i	2.29491	−	2.48602i
$103$	2.99947	−	5.19523i	0.295546	−	0.511902i	−0.679565	−	0.733615i	$-0.737832\pi$
$103$	2.99947	−	5.19523i	0.295546	−	0.511902i	0.975112	+	0.221713i	$0.0711649\pi$
$104$	−3.42244	−	2.68670i	−0.335598	−	0.263453i
$105$	7.73190	−	3.31477i	0.754557	−	0.323489i
$106$	10.6377	−	3.31106i	1.03323	−	0.321598i
$107$	−0.0626308	+	0.108480i	−0.00605475	+	0.0104871i	−0.869037	−	0.494747i	$-0.835261\pi$
$107$	−0.0626308	+	0.108480i	−0.00605475	+	0.0104871i	0.862982	+	0.505234i	$0.168594\pi$
$108$	11.2199	−	23.6058i	1.07963	−	2.27147i
$109$	0.399788	−	0.230818i	0.0382928	−	0.0221083i	−0.480731	−	0.876868i	$-0.659629\pi$
$109$	0.399788	−	0.230818i	0.0382928	−	0.0221083i	0.519024	+	0.854760i	$0.326295\pi$
$110$	−3.33861	−	0.753058i	−0.318324	−	0.0718012i
$111$	−9.06999			−0.860885
$112$	−4.90932	+	9.37542i	−0.463888	+	0.885894i
$113$	−9.65049			−0.907842			−0.453921	−	0.891042i	$-0.649975\pi$
$113$	−9.65049			−0.907842			−0.453921	+	0.891042i	$0.649975\pi$
$114$	7.74907	+	1.74788i	0.725767	+	0.163704i
$115$	−5.66247	+	3.26923i	−0.528028	+	0.304857i
$116$	−2.01321	+	4.23563i	−0.186921	+	0.393268i
$117$	5.46874	−	9.47214i	0.505586	−	0.875700i
$118$	−7.64148	+	2.37846i	−0.703455	+	0.218955i
$119$	−16.0998	−	12.0418i	−1.47586	−	1.10387i
$120$	−5.55326	+	7.07399i	−0.506941	+	0.645764i
$121$	2.57165	−	4.45422i	0.233786	−	0.404929i
$122$	9.46944	−	10.2580i	0.857322	−	0.928716i
$123$	−10.9754	−	19.0099i	−0.989615	−	1.71406i
$124$	0.332468	+	4.15201i	0.0298565	+	0.372861i
$125$	−1.00000			−0.0894427
$126$	−25.0764	−	8.88272i	−2.23399	−	0.791336i
$127$		−	9.40385i		−	0.834457i	−0.908802	−	0.417229i	$-0.863001\pi$
$127$		−	9.40385i		−	0.834457i	0.908802	−	0.417229i	$-0.136999\pi$
$128$	−0.202090	−	11.3119i	−0.0178624	−	0.999840i
$129$	−3.83699	+	2.21529i	−0.337828	+	0.195045i
$130$	−1.47565	+	1.59854i	−0.129423	+	0.140201i
$131$	16.2949	+	9.40788i	1.42369	+	0.821970i	0.996612	−	0.0822423i	$-0.0262081\pi$
$131$	16.2949	+	9.40788i	1.42369	+	0.821970i	0.427082	+	0.904213i	$0.359541\pi$
$132$	8.73416	+	12.6712i	0.760211	+	1.10289i
$133$	0.552971	−	4.64112i	0.0479486	−	0.402436i
$134$	−2.63323	−	8.46001i	−0.227476	−	0.730833i
$135$	−11.3175	−	6.53414i	−0.974052	−	0.562369i
$136$	21.2769	+	3.04057i	1.82448	+	0.260727i
$137$	7.55473	+	13.0852i	0.645444	+	1.11794i	0.984199	+	0.177067i	$0.0566609\pi$
$137$	7.55473	+	13.0852i	0.645444	+	1.11794i	−0.338755	+	0.940875i	$0.610006\pi$
$138$	28.6807	+	6.46922i	2.44146	+	0.550697i
$139$		−	11.1193i		−	0.943129i	−0.881831	−	0.471565i	$-0.843689\pi$
$139$		−	11.1193i		−	0.943129i	0.881831	−	0.471565i	$-0.156311\pi$
$140$	4.47683	+	2.82100i	0.378361	+	0.238418i
$141$		−	35.9806i		−	3.03011i
$142$	1.23909	−	5.49337i	0.103982	−	0.460993i
$143$	1.86142	+	3.22407i	0.155660	+	0.269611i
$144$	28.0776	−	4.52560i	2.33980	−	0.377134i
$145$	2.03071	+	1.17243i	0.168641	+	0.0973652i
$146$	4.26120	−	1.32633i	0.352660	−	0.109767i
$147$	−5.22951	+	21.6343i	−0.431323	+	1.78437i
$148$	−3.23780	−	4.69729i	−0.266145	−	0.386115i
$149$	−9.67998	−	5.58874i	−0.793014	−	0.457847i	0.0480082	−	0.998847i	$-0.484713\pi$
$149$	−9.67998	−	5.58874i	−0.793014	−	0.457847i	−0.841023	+	0.541000i	$0.818046\pi$
$150$	3.30408	+	3.05009i	0.269777	+	0.249039i
$151$	13.1832	−	7.61131i	1.07283	−	0.619399i	0.143878	−	0.989595i	$-0.454043\pi$
$151$	13.1832	−	7.61131i	1.07283	−	0.619399i	0.928954	+	0.370196i	$0.120710\pi$
$152$	1.86104	+	4.63715i	0.150950	+	0.376122i
$153$			54.0285i			4.36794i
$154$	6.88607	−	5.88013i	0.554896	−	0.473834i
$155$	2.08265			0.167282
$156$	9.75137	−	0.780832i	0.780734	−	0.0625166i
$157$	0.357836	+	0.619791i	0.0285584	+	0.0494647i	0.879951	−	0.475064i	$-0.157575\pi$
$157$	0.357836	+	0.619791i	0.0285584	+	0.0494647i	−0.851393	+	0.524528i	$0.824242\pi$
$158$	−2.10886	−	1.94675i	−0.167772	−	0.154875i
$159$	−12.5245	+	21.6930i	−0.993255	+	1.72037i
$160$	−5.64597	−	0.350728i	−0.446353	−	0.0277275i
$161$	2.04664	−	17.1776i	0.161298	−	1.35379i
$162$	8.49926	+	27.3063i	0.667765	+	2.14539i
$163$	0.890005	−	1.54153i	0.0697105	−	0.120742i	−0.829063	−	0.559155i	$-0.811126\pi$
$163$	0.890005	−	1.54153i	0.0697105	−	0.120742i	0.898774	+	0.438413i	$0.144459\pi$
$164$	5.92712	−	12.4702i	0.462830	−	0.973759i
$165$	6.66397	−	3.84745i	0.518790	−	0.299523i
$166$	0.0899050	−	0.398585i	0.00697798	−	0.0309362i
$167$	5.69155			0.440426			0.220213	−	0.975452i	$-0.429325\pi$
$167$	5.69155			0.440426			0.220213	+	0.975452i	$0.429325\pi$
$168$	−6.18752	−	22.9755i	−0.477378	−	1.77260i
$169$	−10.6336			−0.817966
$170$	2.36458	−	10.4831i	0.181355	−	0.804021i
$171$	−10.8777	+	6.28022i	−0.831835	+	0.480260i
$172$	−2.51701	−	1.19634i	−0.191920	−	0.0912200i
$173$	−9.46941	+	16.4015i	−0.719946	+	1.24698i	0.241075	+	0.970506i	$0.422500\pi$
$173$	−9.46941	+	16.4015i	−0.719946	+	1.24698i	−0.961021	+	0.276476i	$0.910833\pi$
$174$	−3.13362	−	10.0677i	−0.237559	−	0.763228i
$175$	1.58467	−	2.11869i	0.119789	−	0.160158i
$176$	−3.44443	+	9.04673i	−0.259634	+	0.681923i
$177$	8.99680	−	15.5829i	0.676241	−	1.17128i
$178$	−14.4467	−	13.3361i	−1.08282	−	0.999583i
$179$	−1.49172	−	2.58374i	−0.111497	−	0.193118i	0.804877	−	0.593441i	$-0.202231\pi$
$179$	−1.49172	−	2.58374i	−0.111497	−	0.193118i	−0.916374	+	0.400323i	$0.868898\pi$
$180$	−1.13502	−	14.1746i	−0.0845995	−	1.05652i
$181$	14.9790			1.11338			0.556691	−	0.830720i	$-0.312071\pi$
$181$	14.9790			1.11338			0.556691	+	0.830720i	$0.312071\pi$
$182$	−1.04839	−	5.65960i	−0.0777116	−	0.419517i
$183$			31.3880i			2.32026i
$184$	6.88804	+	17.1629i	0.507793	+	1.26527i
$185$	−2.47037	+	1.42627i	−0.181625	+	0.104861i
$186$	−6.88125	−	6.35226i	−0.504557	−	0.465770i
$187$	−15.9261	−	9.19496i	−1.16463	−	0.672402i
$188$	18.6341	−	12.8443i	1.35903	−	0.936767i
$189$	31.7782	−	13.6237i	2.31152	−	0.990981i
$190$	2.38545	−	0.742486i	0.173059	−	0.0538656i
$191$	−22.4510	−	12.9621i	−1.62450	−	0.937904i	−0.985696	−	0.168532i	$-0.946097\pi$
$191$	−22.4510	−	12.9621i	−1.62450	−	0.937904i	−0.638801	−	0.769372i	$-0.720569\pi$
$192$	17.5850	+	18.3795i	1.26909	+	1.32643i
$193$	−3.55040	−	6.14947i	−0.255563	−	0.442648i	0.709485	−	0.704720i	$-0.248928\pi$
$193$	−3.55040	−	6.14947i	−0.255563	−	0.442648i	−0.965048	+	0.262072i	$0.915594\pi$
$194$	−0.0775284	+	0.343715i	−0.00556621	+	0.0246773i
$195$		−	4.89129i		−	0.350272i
$196$	−13.0711	+	5.01466i	−0.933649	+	0.358190i
$197$			0.614082i			0.0437515i	0.999761	+	0.0218758i	$0.00696383\pi$
$197$			0.614082i			0.0437515i	−0.999761	+	0.0218758i	$0.993036\pi$
$198$	−23.7375	−	5.35425i	−1.68695	−	0.380510i
$199$	−4.47143	−	7.74474i	−0.316971	−	0.549010i	0.662884	−	0.748723i	$-0.269332\pi$
$199$	−4.47143	−	7.74474i	−0.316971	−	0.549010i	−0.979854	+	0.199713i	$0.935999\pi$
$200$	−0.400131	+	2.79998i	−0.0282936	+	0.197989i
$201$	17.2521	+	9.96050i	1.21687	+	0.702559i
$202$	−4.10001	−	13.1725i	−0.288476	−	0.926812i
$203$	−5.70202	+	2.44453i	−0.400203	+	0.171572i
$204$	−39.7873	+	27.4250i	−2.78567	+	1.92014i
$205$	−5.97866	−	3.45178i	−0.417568	−	0.241083i
$206$	−5.75455	+	6.23376i	−0.400938	+	0.434326i
$207$	−40.2602	+	23.2442i	−2.79828	+	1.61559i
$208$	3.88542	+	4.77143i	0.269406	+	0.330839i
$209$		−	4.27525i		−	0.295725i
$210$	−11.6981	+	2.16695i	−0.807242	+	0.149534i
$211$	10.6756			0.734942			0.367471	−	0.930035i	$-0.380224\pi$
$211$	10.6756			0.734942			0.367471	+	0.930035i	$0.380224\pi$
$212$	−15.7056	+	1.25762i	−1.07867	+	0.0863734i
$213$	6.33061	+	10.9649i	0.433766	+	0.751305i
$214$	0.120159	−	0.130165i	0.00821387	−	0.00889788i
$215$	−0.696713	+	1.20674i	−0.0475154	+	0.0822992i
$216$	−22.8239	+	29.0742i	−1.55297	+	1.97825i
$217$	−3.30030	+	4.41248i	−0.224039	+	0.299539i
$218$	−0.623354	+	0.194023i	−0.0422189	+	0.0131409i
$219$	−5.01698	+	8.68967i	−0.339016	+	0.587194i
$220$	4.37147	+	2.07777i	0.294724	+	0.140083i
$221$	−10.1235	+	5.84481i	−0.680981	+	0.393164i
$222$	12.5125	+	2.82233i	0.839787	+	0.189423i
$223$	1.40260			0.0939252			0.0469626	−	0.998897i	$-0.485046\pi$
$223$	1.40260			0.0939252			0.0469626	+	0.998897i	$0.485046\pi$
$224$	9.69006	−	11.4063i	0.647444	−	0.762113i
$225$	−7.11001			−0.474000
$226$	13.3134	+	3.00297i	0.885593	+	0.199755i
$227$	3.48428	−	2.01165i	0.231260	−	0.133518i	−0.379893	−	0.925030i	$-0.624039\pi$
$227$	3.48428	−	2.01165i	0.231260	−	0.133518i	0.611153	+	0.791512i	$0.290706\pi$
$228$	−10.1464	−	4.82260i	−0.671960	−	0.319384i
$229$	10.8680	−	18.8239i	0.718178	−	1.24392i	−0.243542	−	0.969890i	$-0.578310\pi$
$229$	10.8680	−	18.8239i	0.718178	−	1.24392i	0.961721	−	0.274031i	$-0.0883571\pi$
$230$	8.82898	−	2.74807i	0.582165	−	0.181203i
$231$	−2.40863	+	20.2158i	−0.158476	+	1.33010i
$232$	4.09534	−	5.21683i	0.268872	−	0.342502i
$233$	5.69230	−	9.85935i	0.372915	−	0.645907i	−0.617098	−	0.786886i	$-0.711692\pi$
$233$	5.69230	−	9.85935i	0.372915	−	0.645907i	0.990013	+	0.140979i	$0.0450251\pi$
$234$	−10.4919	+	11.3656i	−0.685877	+	0.742994i
$235$	−5.65799	−	9.79993i	−0.369087	−	0.639277i
$236$	11.2820	−	0.903392i	0.734393	−	0.0588058i
$237$	6.45281			0.419155
$238$	18.4634	+	21.6221i	1.19681	+	1.40155i
$239$		−	25.7524i		−	1.66578i	−0.553435	−	0.832892i	$-0.686683\pi$
$239$		−	25.7524i		−	1.66578i	0.553435	−	0.832892i	$-0.313317\pi$
$240$	9.86226	−	8.03094i	0.636606	−	0.518395i
$241$	−1.67062	+	0.964530i	−0.107614	+	0.0621309i	−0.552841	−	0.833287i	$-0.686456\pi$
$241$	−1.67062	+	0.964530i	−0.107614	+	0.0621309i	0.445227	+	0.895418i	$0.353123\pi$
$242$	−4.93376	+	5.34462i	−0.317154	+	0.343565i
$243$	−21.7321	−	12.5470i	−1.39412	−	0.804893i
$244$	−16.2556	+	11.2048i	−1.04066	+	0.717317i
$245$	1.97767	+	6.71482i	0.126349	+	0.428994i
$246$	9.22576	+	29.6404i	0.588213	+	1.88980i
$247$	−2.35349	−	1.35879i	−0.149749	−	0.0864577i
$248$	0.833333	−	5.83138i	0.0529167	−	0.370293i
$249$	0.459334	+	0.795589i	0.0291091	+	0.0504184i
$250$	1.37955	+	0.311173i	0.0872507	+	0.0196803i
$251$		−	12.9948i		−	0.820222i	−0.912036	−	0.410111i	$-0.865490\pi$
$251$		−	12.9948i		−	0.820222i	0.912036	−	0.410111i	$-0.134510\pi$
$252$	31.8303	+	20.0573i	2.00512	+	1.26349i
$253$		−	15.8235i		−	0.994813i
$254$	−2.92622	+	12.9731i	−0.183607	+	0.814007i
$255$	12.0809	+	20.9247i	0.756534	+	1.31036i
$256$	−3.24116	+	15.6683i	−0.202573	+	0.979267i
$257$	−14.4110	−	8.32019i	−0.898933	−	0.518999i	−0.0220792	−	0.999756i	$-0.507029\pi$
$257$	−14.4110	−	8.32019i	−0.898933	−	0.518999i	−0.876854	+	0.480757i	$0.840362\pi$
$258$	5.98267	−	1.86214i	0.372465	−	0.115932i
$259$	0.892891	−	7.49409i	0.0554815	−	0.465660i
$260$	2.53317	−	1.74609i	0.157100	−	0.108288i
$261$	14.4384	+	8.33600i	0.893713	+	0.515985i
$262$	−19.5523	−	18.0492i	−1.20794	−	1.11508i
$263$	−5.95477	+	3.43799i	−0.367187	+	0.211995i	−0.672229	−	0.740343i	$-0.734663\pi$
$263$	−5.95477	+	3.43799i	−0.367187	+	0.211995i	0.305042	+	0.952339i	$0.401330\pi$
$264$	−8.10631	−	20.1985i	−0.498909	−	1.24313i
$265$			7.87796i			0.483939i
$266$	−2.20704	+	6.23061i	−0.135323	+	0.382023i
$267$	44.2046			2.70528
$268$	1.00016	+	12.4904i	0.0610945	+	0.762975i
$269$	11.0639	+	19.1633i	0.674580	+	1.16841i	0.976591	+	0.215102i	$0.0690085\pi$
$269$	11.0639	+	19.1633i	0.674580	+	1.16841i	−0.302012	+	0.953304i	$0.597658\pi$
$270$	13.5798	+	12.5359i	0.826441	+	0.762910i
$271$	−5.29547	+	9.17203i	−0.321677	+	0.557161i	−0.980834	−	0.194844i	$-0.937580\pi$
$271$	−5.29547	+	9.17203i	−0.321677	+	0.557161i	0.659157	+	0.752005i	$0.270913\pi$
$272$	−28.4065	−	10.8154i	−1.72240	−	0.655781i
$273$	10.3631	+	7.75105i	0.627204	+	0.469115i
$274$	−6.35041	−	20.4025i	−0.383642	−	1.23256i
$275$	1.21003	−	2.09584i	0.0729677	−	0.126384i
$276$	−37.5535	−	17.8493i	−2.26046	−	1.07440i
$277$	16.5032	−	9.52815i	0.991583	−	0.572491i	0.0858360	−	0.996309i	$-0.472644\pi$
$277$	16.5032	−	9.52815i	0.991583	−	0.572491i	0.905747	+	0.423818i	$0.139311\pi$
$278$	−3.46003	+	15.3397i	−0.207519	+	0.920016i
$279$	14.8076			0.886511
$280$	−5.29821	−	5.28479i	−0.316629	−	0.315826i
$281$	−17.6280			−1.05160			−0.525799	−	0.850609i	$-0.676234\pi$
$281$	−17.6280			−1.05160			−0.525799	+	0.850609i	$0.676234\pi$
$282$	−11.1962	+	49.6372i	−0.666722	+	2.95585i
$283$	0.485654	−	0.280393i	0.0288691	−	0.0166676i	−0.485496	−	0.874239i	$-0.661361\pi$
$283$	0.485654	−	0.280393i	0.0288691	−	0.0166676i	0.514365	+	0.857571i	$0.328028\pi$
$284$	−3.41877	+	7.19284i	−0.202867	+	0.426816i
$285$	−2.80854	+	4.86453i	−0.166364	+	0.288150i
$286$	−1.56469	−	5.02701i	−0.0925219	−	0.297253i
$287$	16.7874	−	7.19699i	0.990930	−	0.424825i
$288$	−40.1429	−	2.49368i	−2.36544	−	0.146941i
$289$	20.3719	−	35.2852i	1.19835	−	2.07560i
$290$	−2.43665	−	2.24934i	−0.143085	−	0.132086i
$291$	−0.396100	−	0.686065i	−0.0232198	−	0.0402179i
$292$	−6.29128	+	0.503769i	−0.368169	+	0.0294808i
$293$	23.8016			1.39051			0.695253	−	0.718765i	$-0.255292\pi$
$293$	23.8016			1.39051			0.695253	+	0.718765i	$0.255292\pi$
$294$	13.9464	−	28.2184i	0.813371	−	1.64573i
$295$		−	5.65903i		−	0.329482i
$296$	3.00505	+	7.48768i	0.174665	+	0.435212i
$297$	27.3890	−	15.8130i	1.58927	−	0.917565i
$298$	11.6150	+	10.7221i	0.672839	+	0.621115i
$299$	−8.71070	−	5.02913i	−0.503753	−	0.290842i
$300$	−3.60906	−	5.23591i	−0.208369	−	0.302295i
$301$	−1.45265	−	3.38840i	−0.0837295	−	0.195304i
$302$	−20.5553	+	6.39797i	−1.18283	+	0.368162i
$303$	26.8620	+	15.5088i	1.54318	+	0.890956i
$304$	−1.12445	−	6.97630i	−0.0644918	−	0.400119i
$305$	4.93580	+	8.54905i	0.282623	+	0.489517i
$306$	16.8122	−	74.5353i	0.961089	−	4.26090i
$307$			9.32160i			0.532012i	0.963971	+	0.266006i	$0.0857041\pi$
$307$			9.32160i			0.532012i	−0.963971	+	0.266006i	$0.914296\pi$
$308$	−11.3295	+	5.96920i	−0.645555	+	0.340127i
$309$		−	19.0744i		−	1.08510i
$310$	−2.87313	−	0.648063i	−0.163183	−	0.0368075i
$311$	2.73260	+	4.73300i	0.154951	+	0.268384i	0.933041	−	0.359769i	$-0.117145\pi$
$311$	2.73260	+	4.73300i	0.154951	+	0.268384i	−0.778090	+	0.628153i	$0.783811\pi$
$312$	−13.6955	−	1.95716i	−0.775356	−	0.110802i
$313$	−19.9919	−	11.5423i	−1.13001	−	0.652412i	−0.186073	−	0.982536i	$-0.559576\pi$
$313$	−19.9919	−	11.5423i	−1.13001	−	0.652412i	−0.943937	+	0.330124i	$0.892909\pi$
$314$	−0.300793	−	0.966384i	−0.0169747	−	0.0545362i
$315$	11.2670	−	15.0639i	0.634822	−	0.848754i
$316$	2.30352	+	3.34187i	0.129583	+	0.187995i
$317$	26.2154	+	15.1355i	1.47241	+	0.850094i	0.999518	−	0.0310291i	$-0.00987845\pi$
$317$	26.2154	+	15.1355i	1.47241	+	0.850094i	0.472887	+	0.881123i	$0.343212\pi$
$318$	24.0285	−	26.0294i	1.34745	−	1.45966i
$319$	−4.91445	+	2.83736i	−0.275157	+	0.158862i
$320$	7.67979	+	2.24072i	0.429313	+	0.125260i
$321$			0.398285i			0.0222301i
$322$	−8.16866	+	23.0606i	−0.455222	+	1.28512i
$323$	13.4242			0.746941
$324$	−3.22821	−	40.3153i	−0.179345	−	2.23974i
$325$	−0.769162	−	1.33223i	−0.0426654	−	0.0738987i
$326$	−1.70749	+	1.84968i	−0.0945693	+	0.102445i
$327$	0.733914	−	1.27118i	0.0405855	−	0.0702962i
$328$	−12.0572	+	15.3590i	−0.665746	+	0.848057i
$329$	29.7290	+	3.54209i	1.63901	+	0.195282i
$330$	−10.3905	+	3.23412i	−0.571980	+	0.178032i
$331$	0.262181	−	0.454110i	0.0144108	−	0.0249602i	−0.858730	−	0.512428i	$-0.828746\pi$
$331$	0.262181	−	0.454110i	0.0144108	−	0.0249602i	0.873141	+	0.487468i	$0.162079\pi$
$332$	−0.248058	+	0.521895i	−0.0136139	+	0.0286427i
$333$	−17.5643	+	10.1408i	−0.962519	+	0.555711i
$334$	−7.85181	−	1.77106i	−0.429632	−	0.0969079i
$335$	6.26521			0.342305
$336$	1.38667	+	33.6214i	0.0756491	+	1.83420i
$337$	−3.41643			−0.186105			−0.0930524	−	0.995661i	$-0.529662\pi$
$337$	−3.41643			−0.186105			−0.0930524	+	0.995661i	$0.529662\pi$
$338$	14.6696	+	3.30887i	0.797920	+	0.179979i
$339$	−26.5739	+	15.3425i	−1.44330	+	0.833288i
$340$	−6.52414	+	13.7263i	−0.353821	+	0.744412i
$341$	−2.52007	+	4.36489i	−0.136470	+	0.236372i
$342$	16.9606	−	5.27908i	0.917122	−	0.285460i
$343$	−17.3606	−	6.45067i	−0.937382	−	0.348304i
$344$	3.10008	+	2.43364i	0.167145	+	0.131213i
$345$	−10.3949	+	18.0045i	−0.559643	+	0.969330i
$346$	18.1673	−	19.6801i	0.976678	−	1.05801i
$347$	4.64349	+	8.04275i	0.249275	+	0.431758i	0.963325	−	0.268337i	$-0.0864742\pi$
$347$	4.64349	+	8.04275i	0.249275	+	0.431758i	−0.714050	+	0.700095i	$0.753141\pi$
$348$	1.19022	+	14.8640i	0.0638026	+	0.796794i
$349$	−18.6699			−0.999374			−0.499687	−	0.866206i	$-0.666552\pi$
$349$	−18.6699			−0.999374			−0.499687	+	0.866206i	$0.666552\pi$
$350$	−2.84541	+	2.42974i	−0.152094	+	0.129875i
$351$		−	20.1032i		−	1.07303i
$352$	7.56687	−	11.4086i	0.403316	−	0.608083i
$353$	−11.7057	+	6.75828i	−0.623030	+	0.359707i	−0.778048	−	0.628205i	$-0.783790\pi$
$353$	−11.7057	+	6.75828i	−0.623030	+	0.359707i	0.155018	+	0.987912i	$0.450457\pi$
$354$	−17.2606	+	18.6979i	−0.917388	+	0.993783i
$355$	3.44850	+	1.99099i	0.183027	+	0.105671i
$356$	15.7801	+	22.8933i	0.836345	+	1.21334i
$357$	−63.4770	−	7.56303i	−3.35956	−	0.400278i
$358$	1.25392	+	4.02860i	0.0662720	+	0.212918i
$359$	22.8266	+	13.1789i	1.20474	+	0.695558i	0.961606	−	0.274435i	$-0.0884907\pi$
$359$	22.8266	+	13.1789i	1.20474	+	0.695558i	0.243135	+	0.969992i	$0.421824\pi$
$360$	−2.84494	+	19.9079i	−0.149941	+	1.04924i
$361$	−7.93959	−	13.7518i	−0.417873	−	0.723777i
$362$	−20.6644	−	4.66106i	−1.08610	−	0.244980i
$363$		−	16.3537i		−	0.858348i
$364$	−0.314805	+	8.13395i	−0.0165003	+	0.426335i
$365$			3.15571i			0.165177i
$366$	9.76707	−	43.3014i	0.510533	−	2.26340i
$367$	17.7819	+	30.7992i	0.928208	+	1.60770i	0.786319	+	0.617821i	$0.211984\pi$
$367$	17.7819	+	30.7992i	0.928208	+	1.60770i	0.141889	+	0.989883i	$0.454682\pi$
$368$	−4.16180	−	25.8206i	−0.216949	−	1.34599i
$369$	−42.5083	−	24.5422i	−2.21289	−	1.27761i
$370$	3.85182	−	1.19890i	0.200247	−	0.0623280i
$371$	−16.6909	−	12.4839i	−0.866550	−	0.648133i
$372$	7.51641	+	10.9046i	0.389708	+	0.565375i
$373$	−20.6623	−	11.9294i	−1.06985	−	0.617680i	−0.141712	−	0.989908i	$-0.545261\pi$
$373$	−20.6623	−	11.9294i	−1.06985	−	0.617680i	−0.928141	+	0.372228i	$0.878594\pi$
$374$	19.1098	+	17.6407i	0.988142	+	0.912180i
$375$	−2.75363	+	1.58981i	−0.142197	+	0.0820975i
$376$	−29.7035	+	11.9210i	−1.53184	+	0.614779i
$377$			3.60716i			0.185778i
$378$	−48.0791	+	8.90619i	−2.47292	+	0.458085i
$379$	−25.9215			−1.33150			−0.665748	−	0.746177i	$-0.731887\pi$
$379$	−25.9215			−1.33150			−0.665748	+	0.746177i	$0.731887\pi$
$380$	−3.52190	+	0.282013i	−0.180670	+	0.0144670i
$381$	−14.9504	−	25.8948i	−0.765930	−	1.32663i
$382$	26.9389	+	24.8681i	1.37832	+	1.27236i
$383$	16.8541	−	29.1922i	0.861205	−	1.49165i	−0.00956071	−	0.999954i	$-0.503043\pi$
$383$	16.8541	−	29.1922i	0.861205	−	1.49165i	0.870766	−	0.491697i	$-0.163623\pi$
$384$	−18.5403	−	30.8276i	−0.946130	−	1.57316i
$385$	2.52293	+	5.88488i	0.128580	+	0.299921i
$386$	2.98442	+	9.58832i	0.151903	+	0.488032i
$387$	−4.95364	+	8.57995i	−0.251807	+	0.436143i
$388$	0.213909	−	0.450049i	0.0108596	−	0.0228478i
$389$	−29.0131	+	16.7507i	−1.47102	+	0.849294i	−0.999470	−	0.0325451i	$-0.989639\pi$
$389$	−29.0131	+	16.7507i	−1.47102	+	0.849294i	−0.471550	+	0.881839i	$0.656305\pi$
$390$	−1.52204	+	6.74780i	−0.0770713	+	0.341688i
$391$	49.6853			2.51269
$392$	19.5927	−	2.85064i	0.989581	−	0.143979i
$393$	59.8271			3.01788
$394$	0.191085	−	0.847159i	0.00962675	−	0.0426793i
$395$	1.75753	−	1.01471i	0.0884311	−	0.0510557i
$396$	31.0812	+	14.7730i	1.56189	+	0.742369i
$397$	2.24042	−	3.88052i	0.112443	−	0.194757i	−0.804312	−	0.594208i	$-0.797466\pi$
$397$	2.24042	−	3.88052i	0.112443	−	0.194757i	0.916755	+	0.399450i	$0.130799\pi$
$398$	3.75863	+	12.0757i	0.188403	+	0.605299i
$399$	−5.85583	−	13.6591i	−0.293158	−	0.683809i
$400$	1.42328	−	3.73822i	0.0711640	−	0.186911i
$401$	−15.5291	+	26.8973i	−0.775488	+	1.34318i	0.159032	+	0.987273i	$0.449163\pi$
$401$	−15.5291	+	26.8973i	−0.775488	+	1.34318i	−0.934520	+	0.355911i	$0.884171\pi$
$402$	−20.7008	−	19.1094i	−1.03246	−	0.953092i
$403$	1.60189	+	2.77456i	0.0797960	+	0.138211i
$404$	1.55728	+	19.4480i	0.0774775	+	0.967572i
$405$	−20.2222			−1.00485
$406$	8.62691	−	1.59805i	0.428147	−	0.0793101i
$407$		−	6.90332i		−	0.342185i
$408$	63.4227	−	25.4536i	3.13989	−	1.26014i
$409$	−22.6647	+	13.0855i	−1.12070	+	0.647034i	−0.941579	−	0.336794i	$-0.890658\pi$
$409$	−22.6647	+	13.0855i	−1.12070	+	0.647034i	−0.179117	+	0.983828i	$0.557324\pi$
$410$	7.17379	+	6.62231i	0.354288	+	0.327053i
$411$	41.6059	+	24.0212i	2.05227	+	1.18488i
$412$	9.87849	−	6.80915i	0.486678	−	0.335463i
$413$	11.9897	+	8.96767i	0.589976	+	0.441270i
$414$	62.7741	−	19.5388i	3.08518	−	0.960280i
$415$	0.250215	+	0.144462i	0.0122826	+	0.00709134i
$416$	−3.87541	−	7.79148i	−0.190008	−	0.382009i
$417$	−17.6776	−	30.6186i	−0.865678	−	1.49940i
$418$	−1.33034	+	5.89794i	−0.0650691	+	0.288478i
$419$			3.71538i			0.181508i	0.995873	+	0.0907540i	$0.0289277\pi$
$419$			3.71538i			0.181508i	−0.995873	+	0.0907540i	$0.971072\pi$
$420$	16.8124	+	0.650683i	0.820361	+	0.0317501i
$421$			9.89335i			0.482172i	0.970504	+	0.241086i	$0.0775037\pi$
$421$			9.89335i			0.482172i	−0.970504	+	0.241086i	$0.922496\pi$
$422$	−14.7276	−	3.32197i	−0.716930	−	0.161711i
$423$	−40.2283	−	69.6775i	−1.95597	−	3.38784i
$424$	22.0581	+	3.15222i	1.07124	+	0.153085i
$425$	6.58087	+	3.79947i	0.319219	+	0.184301i
$426$	−5.32144	−	17.0966i	−0.257824	−	0.828335i
$427$	−25.9344	−	3.08997i	−1.25505	−	0.149534i
$428$	−0.206269	+	0.142179i	−0.00997039	+	0.00687250i
$429$	10.2513	+	5.91862i	0.494940	+	0.285753i
$430$	1.33666	−	1.44797i	0.0644594	−	0.0698273i
$431$	−21.9155	+	12.6529i	−1.05563	+	0.609471i	−0.924222	−	0.381857i	$-0.875285\pi$
$431$	−21.9155	+	12.6529i	−1.05563	+	0.609471i	−0.131413	+	0.991328i	$0.541951\pi$
$432$	40.5340	−	33.0072i	1.95019	−	1.58806i
$433$		−	3.51643i		−	0.168989i	−0.996424	−	0.0844944i	$-0.973073\pi$
$433$		−	3.51643i		−	0.168989i	0.996424	−	0.0844944i	$-0.0269275\pi$
$434$	5.92599	−	5.06030i	0.284457	−	0.242902i
$435$	7.45579			0.357478
$436$	0.920326	−	0.0736943i	0.0440756	−	0.00352931i
$437$	5.77537	+	10.0032i	0.276273	+	0.478520i
$438$	9.62519	−	10.4267i	0.459909	−	0.498208i
$439$	−4.56047	+	7.89896i	−0.217659	+	0.376997i	−0.954092	−	0.299514i	$-0.903175\pi$
$439$	−4.56047	+	7.89896i	−0.217659	+	0.376997i	0.736433	+	0.676511i	$0.236509\pi$
$440$	−5.38413	−	4.22668i	−0.256678	−	0.201499i
$441$	14.0613	+	47.7424i	0.669584	+	2.27345i
$442$	15.7847	−	4.91308i	0.750801	−	0.233691i
$443$	−1.72708	+	2.99140i	−0.0820563	+	0.142126i	−0.904133	−	0.427251i	$-0.859482\pi$
$443$	−1.72708	+	2.99140i	−0.0820563	+	0.142126i	0.822077	+	0.569377i	$0.192815\pi$
$444$	−16.3835	−	7.78712i	−0.777527	−	0.369561i
$445$	12.0399	−	6.95124i	0.570746	−	0.329520i
$446$	−1.93497	−	0.436451i	−0.0916233	−	0.0206666i
$447$	−35.5402			−1.68099
$448$	−16.9173	+	12.7203i	−0.799266	+	0.600977i
$449$	10.3646			0.489133			0.244567	−	0.969632i	$-0.421354\pi$
$449$	10.3646			0.489133			0.244567	+	0.969632i	$0.421354\pi$
$450$	9.80864	+	2.21244i	0.462384	+	0.104295i
$451$	14.4687	−	8.35353i	0.681306	−	0.393352i
$452$	−17.4321	−	8.28552i	−0.819937	−	0.389718i
$453$	24.2011	−	41.9175i	1.13707	−	1.96946i
$454$	−5.43272	+	1.69097i	−0.254970	+	0.0793610i
$455$	4.04144	+	0.481521i	0.189465	+	0.0225740i
$456$	12.4968	+	9.81031i	0.585217	+	0.459410i
$457$	13.4566	−	23.3076i	0.629475	−	1.09028i	−0.358183	−	0.933652i	$-0.616603\pi$
$457$	13.4566	−	23.3076i	0.629475	−	1.09028i	0.987657	−	0.156630i	$-0.0500632\pi$
$458$	−20.8505	+	22.5868i	−0.974281	+	1.05541i
$459$	49.6525	+	86.0006i	2.31758	+	4.01417i
$460$	−13.0352	+	1.04378i	−0.607768	+	0.0486665i
$461$	−9.19023			−0.428032			−0.214016	−	0.976830i	$-0.568654\pi$
$461$	−9.19023			−0.428032			−0.214016	+	0.976830i	$0.568654\pi$
$462$	9.61344	−	27.1393i	0.447258	−	1.26263i
$463$			10.8548i			0.504464i	0.967667	+	0.252232i	$0.0811645\pi$
$463$			10.8548i			0.504464i	−0.967667	+	0.252232i	$0.918835\pi$
$464$	−7.27308	+	5.92254i	−0.337644	+	0.274947i
$465$	5.73485	−	3.31102i	0.265947	−	0.153545i
$466$	−10.9208	+	11.8302i	−0.505896	+	0.548024i
$467$	25.9792	+	14.9991i	1.20218	+	0.694077i	0.961039	−	0.276414i	$-0.0891463\pi$
$467$	25.9792	+	14.9991i	1.20218	+	0.694077i	0.241137	+	0.970491i	$0.422480\pi$
$468$	18.0108	−	12.4147i	0.832551	−	0.573870i
$469$	−9.92825	+	13.2740i	−0.458444	+	0.612937i
$470$	4.75604	+	15.2801i	0.219380	+	0.704821i
$471$	1.97070	+	1.13778i	0.0908051	+	0.0524263i
$472$	−15.8452	−	2.26436i	−0.729334	−	0.104225i
$473$	−1.68609	−	2.92039i	−0.0775265	−	0.134280i
$474$	−8.90201	−	2.00794i	−0.408883	−	0.0922277i
$475$			1.76659i			0.0810565i
$476$	−18.7431	−	35.5742i	−0.859090	−	1.63054i
$477$			56.0123i			2.56463i
$478$	−8.01344	+	35.5269i	−0.366526	+	1.62496i
$479$	−4.67977	−	8.10560i	−0.213824	−	0.370355i	0.739084	−	0.673613i	$-0.235259\pi$
$479$	−4.67977	−	8.10560i	−0.213824	−	0.370355i	−0.952908	+	0.303259i	$0.901925\pi$
$480$	−16.1045	+	8.01026i	−0.735068	+	0.365616i
$481$	−3.80022	−	2.19406i	−0.173275	−	0.100041i
$482$	2.60484	−	0.810773i	0.118647	−	0.0369297i
$483$	−21.6735	−	50.5547i	−0.986177	−	2.30032i
$484$	8.46949	−	5.83794i	0.384977	−	0.265361i
$485$	−0.215769	−	0.124575i	−0.00979758	−	0.00565664i
$486$	26.0764	+	24.0718i	1.18285	+	1.09192i
$487$	−14.9682	+	8.64189i	−0.678273	+	0.391601i	−0.799204	−	0.601060i	$-0.794745\pi$
$487$	−14.9682	+	8.64189i	−0.678273	+	0.391601i	0.120931	+	0.992661i	$0.461412\pi$
$488$	25.9122	−	10.3994i	1.17299	−	0.470759i
$489$		−	5.65976i		−	0.255943i
$490$	−0.638839	−	9.87886i	−0.0288598	−	0.446281i
$491$	−28.4313			−1.28309			−0.641543	−	0.767087i	$-0.721705\pi$
$491$	−28.4313			−1.28309			−0.641543	+	0.767087i	$0.721705\pi$
$492$	−3.50415	−	43.7614i	−0.157979	−	1.97291i
$493$	−8.90924	−	15.4313i	−0.401252	−	0.694989i
$494$	2.82395	+	2.60687i	0.127056	+	0.117289i
$495$	8.60334	−	14.9014i	0.386691	−	0.669769i
$496$	−2.96419	+	7.78539i	−0.133096	+	0.349575i
$497$	−9.68301	+	4.15124i	−0.434343	+	0.186209i
$498$	−0.386110	−	1.24049i	−0.0173020	−	0.0555877i
$499$	12.1835	−	21.1025i	0.545409	−	0.944676i	−0.453172	−	0.891423i	$-0.649708\pi$
$499$	12.1835	−	21.1025i	0.545409	−	0.944676i	0.998581	−	0.0532527i	$-0.0169589\pi$
$500$	−1.80634	−	0.858559i	−0.0807821	−	0.0383959i
$501$	15.6725	−	9.04850i	0.700194	−	0.404257i
$502$	−4.04361	+	17.9270i	−0.180475	+	0.800121i
$503$	−22.0798			−0.984489			−0.492245	−	0.870457i	$-0.663823\pi$
$503$	−22.0798			−0.984489			−0.492245	+	0.870457i	$0.663823\pi$
$504$	−37.6703	−	37.5749i	−1.67797	−	1.67372i
$505$	9.75511			0.434097
$506$	−4.92383	+	21.8293i	−0.218891	+	0.970433i
$507$	−29.2809	+	16.9054i	−1.30041	+	0.750794i
$508$	8.07377	−	16.9866i	0.358215	−	0.753658i
$509$	7.47946	−	12.9548i	0.331521	−	0.574212i	−0.651289	−	0.758830i	$-0.725771\pi$
$509$	7.47946	−	12.9548i	0.331521	−	0.574212i	0.982810	+	0.184618i	$0.0591048\pi$
$510$	−10.1550	−	32.6260i	−0.449673	−	1.44470i
$511$	−6.68596	−	5.00074i	−0.295770	−	0.221220i
$512$	9.34690	−	20.6067i	0.413078	−	0.910695i
$513$	−11.5431	+	19.9933i	−0.509641	+	0.882724i
$514$	17.2917	+	15.9625i	0.762706	+	0.704074i
$515$	−2.99947	−	5.19523i	−0.132172	−	0.228929i
$516$	−8.83287	+	0.707284i	−0.388845	+	0.0311365i
$517$	27.3854			1.20441
$518$	−3.56375	+	10.0607i	−0.156582	+	0.442040i
$519$			60.2183i			2.64329i
$520$	−4.03798	+	1.62057i	−0.177077	+	0.0710668i
$521$	13.6812	−	7.89884i	0.599384	−	0.346055i	−0.169415	−	0.985545i	$-0.554188\pi$
$521$	13.6812	−	7.89884i	0.599384	−	0.346055i	0.768799	+	0.639490i	$0.220855\pi$
$522$	−17.3246	−	15.9928i	−0.758277	−	0.699986i
$523$	17.4282	+	10.0622i	0.762083	+	0.439989i	0.830043	−	0.557699i	$-0.188316\pi$
$523$	17.4282	+	10.0622i	0.762083	+	0.439989i	−0.0679602	+	0.997688i	$0.521649\pi$
$524$	21.3570	+	30.9840i	0.932985	+	1.35354i
$525$	0.995275	−	8.35341i	0.0434374	−	0.364573i
$526$	9.28474	−	2.88993i	0.404834	−	0.126007i
$527$	−13.7056	−	7.91296i	−0.597027	−	0.344694i
$528$	4.89789	+	30.3874i	0.213153	+	1.32244i
$529$	9.87568	+	17.1052i	0.429377	+	0.743703i
$530$	2.45140	−	10.8681i	0.106482	−	0.472079i
$531$		−	40.2358i		−	1.74608i
$532$	4.98353	−	7.90870i	0.216064	−	0.342886i
$533$		−	10.6199i		−	0.459999i
$534$	−60.9827	−	13.7553i	−2.63898	−	0.595249i
$535$	0.0626308	+	0.108480i	0.00270776	+	0.00468999i
$536$	2.50690	−	17.5425i	0.108282	−	0.757719i
$537$	−8.21532	−	4.74312i	−0.354517	−	0.204681i
$538$	−9.30021	−	29.8796i	−0.400961	−	1.28820i
$539$	−16.4662	−	3.98027i	−0.709250	−	0.171442i
$540$	−14.8333	−	21.5196i	−0.638322	−	0.926056i
$541$	14.0280	+	8.09904i	0.603109	+	0.348205i	0.770264	−	0.637726i	$-0.220125\pi$
$541$	14.0280	+	8.09904i	0.603109	+	0.348205i	−0.167155	+	0.985931i	$0.553458\pi$
$542$	10.1595	−	11.0055i	0.436387	−	0.472727i
$543$	41.2467	−	23.8138i	1.77007	−	1.02195i
$544$	35.8228	+	23.7598i	1.53589	+	1.01869i
$545$		−	0.461636i		−	0.0197743i
$546$	−11.8846	−	13.9177i	−0.508612	−	0.595624i
$547$	−29.9614			−1.28106			−0.640529	−	0.767934i	$-0.721285\pi$
$547$	−29.9614			−1.28106			−0.640529	+	0.767934i	$0.721285\pi$
$548$	2.41203	+	30.1225i	0.103037	+	1.28677i
$549$	35.0936	+	60.7838i	1.49776	+	2.59419i
$550$	−2.32147	+	2.51479i	−0.0989879	+	0.107231i
$551$	2.07120	−	3.58743i	0.0882362	−	0.152830i
$552$	46.2530	+	36.3097i	1.96866	+	1.54544i
$553$	−0.635244	+	5.33165i	−0.0270133	+	0.226725i
$554$	−25.7320	+	8.00924i	−1.09325	+	0.340280i
$555$	−4.53499	+	7.85484i	−0.192500	+	0.333419i
$556$	9.54661	−	20.0853i	0.404866	−	0.851808i
$557$	36.5898	−	21.1251i	1.55036	−	0.895100i	0.552246	−	0.833681i	$-0.313771\pi$
$557$	36.5898	−	21.1251i	1.55036	−	0.895100i	0.998112	−	0.0614182i	$-0.0195623\pi$
$558$	−20.4280	−	4.60773i	−0.864784	−	0.195061i
$559$	−2.14354			−0.0906621
$560$	5.66469	+	8.93931i	0.239377	+	0.377755i
$561$	−58.4730			−2.46873
$562$	24.3188	+	5.48535i	1.02583	+	0.231386i
$563$	19.4740	−	11.2433i	0.820731	−	0.473849i	−0.0299372	−	0.999552i	$-0.509531\pi$
$563$	19.4740	−	11.2433i	0.820731	−	0.473849i	0.850669	+	0.525702i	$0.176197\pi$
$564$	30.8914	−	64.9932i	1.30076	−	2.73671i
$565$	−4.82525	+	8.35757i	−0.203000	+	0.351606i
$566$	−0.757237	+	0.235695i	−0.0318291	+	0.00990698i
$567$	32.0454	−	42.8445i	1.34578	−	1.79930i
$568$	6.95460	−	8.85908i	0.291808	−	0.371719i
$569$	−15.7198	+	27.2275i	−0.659008	+	1.14144i	0.321864	+	0.946786i	$0.395690\pi$
$569$	−15.7198	+	27.2275i	−0.659008	+	1.14144i	−0.980873	+	0.194650i	$0.937643\pi$
$570$	5.38824	−	5.83695i	0.225689	−	0.244483i
$571$	−4.27788	−	7.40950i	−0.179024	−	0.310078i	0.762523	−	0.646961i	$-0.223961\pi$
$571$	−4.27788	−	7.40950i	−0.179024	−	0.310078i	−0.941546	+	0.336883i	$0.890627\pi$
$572$	0.594304	+	7.42192i	0.0248491	+	0.310326i
$573$	−82.4291			−3.44353
$574$	−25.3987	+	4.70486i	−1.06012	+	0.196377i
$575$			6.53845i			0.272672i
$576$	54.6034	+	15.9315i	2.27514	+	0.663814i
$577$	35.0221	−	20.2200i	1.45799	−	0.841771i	0.459078	−	0.888396i	$-0.348180\pi$
$577$	35.0221	−	20.2200i	1.45799	−	0.841771i	0.998912	+	0.0466251i	$0.0148466\pi$
$578$	−39.0840	+	42.3387i	−1.62568	+	1.76106i
$579$	−19.5530	−	11.2889i	−0.812595	−	0.469152i
$580$	2.66156	+	3.86130i	0.110515	+	0.160332i
$581$	−0.702576	+	0.301204i	−0.0291478	+	0.0124960i
$582$	0.332957	+	1.06972i	0.0138015	+	0.0443413i
$583$	−16.5109	−	9.53258i	−0.683812	−	0.394799i
$584$	8.83593	+	1.26270i	0.365633	+	0.0522508i
$585$	−5.46874	−	9.47214i	−0.226105	−	0.391625i
$586$	−32.8357	−	7.40642i	−1.35643	−	0.305956i
$587$			46.5032i			1.91939i	0.281038	+	0.959697i	$0.409321\pi$
$587$			46.5032i			1.91939i	−0.281038	+	0.959697i	$0.590679\pi$
$588$	−28.0206	+	34.5891i	−1.15555	+	1.42643i
$589$		−	3.67918i		−	0.151598i
$590$	−1.76094	+	7.80695i	−0.0724966	+	0.321407i
$591$	0.976274	+	1.69096i	0.0401586	+	0.0695567i
$592$	−1.81567	−	11.2648i	−0.0746237	−	0.462978i
$593$	5.42655	+	3.13302i	0.222842	+	0.128658i	0.607265	−	0.794499i	$-0.292267\pi$
$593$	5.42655	+	3.13302i	0.222842	+	0.128658i	−0.384424	+	0.923157i	$0.625600\pi$
$594$	−42.7052	+	13.2922i	−1.75221	+	0.545387i
$595$	−18.4784	+	7.92193i	−0.757539	+	0.324767i
$596$	−12.6871	−	18.4060i	−0.519684	−	0.753940i
$597$	−24.6253	−	14.2175i	−1.00785	−	0.581882i
$598$	10.4520	+	9.64849i	0.427413	+	0.394556i
$599$	35.7470	−	20.6385i	1.46058	−	0.843268i	0.461544	−	0.887117i	$-0.347295\pi$
$599$	35.7470	−	20.6385i	1.46058	−	0.843268i	0.999038	+	0.0438493i	$0.0139621\pi$
$600$	3.34963	+	8.34626i	0.136748	+	0.340735i
$601$		−	18.4478i		−	0.752502i	−0.926518	−	0.376251i	$-0.877213\pi$
$601$		−	18.4478i		−	0.752502i	0.926518	−	0.376251i	$-0.122787\pi$
$602$	0.949637	+	5.12651i	0.0387043	+	0.208941i
$603$	44.5457			1.81404
$604$	30.3481	−	2.43010i	1.23485	−	0.0988792i
$605$	−2.57165	−	4.45422i	−0.104552	−	0.181090i
$606$	−32.2317	−	29.7539i	−1.30932	−	1.20867i
$607$	−3.76477	+	6.52077i	−0.152807	+	0.264670i	−0.932258	−	0.361793i	$-0.882165\pi$
$607$	−3.76477	+	6.52077i	−0.152807	+	0.264670i	0.779451	+	0.626463i	$0.215498\pi$
$608$	−0.619591	+	9.97409i	−0.0251277	+	0.404503i
$609$	−11.8149	+	15.7965i	−0.478765	+	0.640106i
$610$	−4.14897	−	13.3298i	−0.167987	−	0.539707i
$611$	8.70382	−	15.0755i	0.352119	−	0.609888i
$612$	−46.3867	+	97.5940i	−1.87507	+	3.94500i
$613$	−15.3991	+	8.89067i	−0.621963	+	0.359091i	−0.777633	−	0.628719i	$-0.783580\pi$
$613$	−15.3991	+	8.89067i	−0.621963	+	0.359091i	0.155670	+	0.987809i	$0.450246\pi$
$614$	2.90063	−	12.8597i	0.117060	−	0.518974i
$615$	−21.9507			−0.885138
$616$	17.4871	−	4.70943i	0.704573	−	0.189748i
$617$	−25.4606			−1.02500			−0.512502	−	0.858686i	$-0.671281\pi$
$617$	−25.4606			−1.02500			−0.512502	+	0.858686i	$0.671281\pi$
$618$	−5.93542	+	26.3141i	−0.238758	+	1.05851i
$619$	1.54568	−	0.892398i	0.0621261	−	0.0358685i	−0.468615	−	0.883402i	$-0.655247\pi$
$619$	1.54568	−	0.892398i	0.0621261	−	0.0358685i	0.530741	+	0.847534i	$0.321914\pi$
$620$	3.76198	+	1.78808i	0.151085	+	0.0718109i
$621$	−42.7231	+	73.9987i	−1.71442	+	2.96946i
$622$	−2.29699	−	7.37974i	−0.0921009	−	0.295901i
$623$	−4.35170	+	36.5242i	−0.174347	+	1.46331i
$624$	18.2847	+	6.96168i	0.731974	+	0.278690i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	23.9883	+	22.1442i	0.958765	+	0.885061i
$627$	−6.79685	−	11.7725i	−0.271440	−	0.470148i
$628$	0.114248	+	1.42678i	0.00455899	+	0.0569346i
$629$	21.6762			0.864288
$630$	−20.2309	+	17.2755i	−0.806018	+	0.688271i
$631$			25.2033i			1.00333i	0.865063	+	0.501663i	$0.167278\pi$
$631$			25.2033i			1.00333i	−0.865063	+	0.501663i	$0.832722\pi$
$632$	−2.13793	−	5.32708i	−0.0850424	−	0.211900i
$633$	29.3968	−	16.9723i	1.16842	−	0.674587i
$634$	−31.4559	−	29.0378i	−1.24927	−	1.15324i
$635$	−8.14398	−	4.70193i	−0.323184	−	0.186590i
$636$	−41.2482	+	28.4320i	−1.63560	+	1.12740i
$637$	−7.42451	+	7.79949i	−0.294170	+	0.309027i
$638$	7.66267	−	2.38505i	0.303368	−	0.0944251i
$639$	24.5189	+	14.1560i	0.969952	+	0.560002i
$640$	−9.89744	−	5.48094i	−0.391231	−	0.216653i
$641$	1.24626	+	2.15858i	0.0492242	+	0.0852587i	0.889588	−	0.456765i	$-0.150992\pi$
$641$	1.24626	+	2.15858i	0.0492242	+	0.0852587i	−0.840363	+	0.542023i	$0.817658\pi$
$642$	0.123935	−	0.549456i	0.00489134	−	0.0216853i
$643$			39.1121i			1.54243i	0.636575	+	0.771215i	$0.280350\pi$
$643$			39.1121i			1.54243i	−0.636575	+	0.771215i	$0.719650\pi$
$644$	18.4450	−	29.2715i	0.726833	−	1.15346i
$645$			4.43057i			0.174454i
$646$	−18.5194	−	4.17724i	−0.728635	−	0.164351i
$647$	7.69474	+	13.3277i	0.302512	+	0.523965i	0.976704	−	0.214590i	$-0.0688416\pi$
$647$	7.69474	+	13.3277i	0.302512	+	0.523965i	−0.674193	+	0.738556i	$0.735508\pi$
$648$	−8.09153	+	56.6217i	−0.317865	+	2.22431i
$649$	11.8604	+	6.84761i	0.465562	+	0.268792i
$650$	0.646548	+	2.07722i	0.0253597	+	0.0814754i
$651$	−2.07281	+	17.3972i	−0.0812398	+	0.681851i
$652$	2.93115	−	2.02042i	0.114793	−	0.0791256i
$653$	1.33623	+	0.771475i	0.0522909	+	0.0301902i	0.525918	−	0.850536i	$-0.323722\pi$
$653$	1.33623	+	0.771475i	0.0522909	+	0.0301902i	−0.473627	+	0.880726i	$0.657055\pi$
$654$	−1.40803	+	1.52528i	−0.0550583	+	0.0596433i
$655$	16.2949	−	9.40788i	0.636696	−	0.367596i
$656$	21.4128	−	17.4367i	0.836030	−	0.680788i
$657$			22.4371i			0.875355i
$658$	−39.9106	−	14.1374i	−1.55588	−	0.551132i
$659$	23.4292			0.912670			0.456335	−	0.889808i	$-0.349162\pi$
$659$	23.4292			0.912670			0.456335	+	0.889808i	$0.349162\pi$
$660$	15.3407	−	1.22839i	0.597135	−	0.0478151i
$661$	−10.1419	−	17.5663i	−0.394474	−	0.683249i	0.598560	−	0.801078i	$-0.295740\pi$
$661$	−10.1419	−	17.5663i	−0.394474	−	0.683249i	−0.993034	+	0.117829i	$0.962407\pi$
$662$	−0.502999	+	0.544887i	−0.0195496	+	0.0211776i
$663$	−18.5843	+	32.1889i	−0.721754	+	1.25011i
$664$	0.504609	−	0.642793i	0.0195826	−	0.0249452i
$665$	−3.74284	−	2.79945i	−0.145141	−	0.108558i
$666$	27.3865	−	8.52421i	1.06120	−	0.330306i
$667$	7.66589	−	13.2777i	0.296825	−	0.514115i
$668$	10.2809	+	4.88654i	0.397780	+	0.189066i
$669$	3.86225	−	2.22987i	0.149323	−	0.0862119i
$670$	−8.64320	−	1.94956i	−0.333916	−	0.0753181i
$671$	−23.8899			−0.922259
$672$	8.54907	−	46.8140i	0.329787	−	1.80589i
$673$	−14.3296			−0.552364			−0.276182	−	0.961105i	$-0.589069\pi$
$673$	−14.3296			−0.552364			−0.276182	+	0.961105i	$0.589069\pi$
$674$	4.71315	+	1.06310i	0.181544	+	0.0409491i
$675$	−11.3175	+	6.53414i	−0.435609	+	0.251499i
$676$	−19.2079	−	9.12955i	−0.738764	−	0.351136i
$677$	9.11144	−	15.7815i	0.350181	−	0.606531i	−0.636100	−	0.771607i	$-0.719453\pi$
$677$	9.11144	−	15.7815i	0.350181	−	0.606531i	0.986281	+	0.165075i	$0.0527868\pi$
$678$	41.4344	−	12.8967i	1.59128	−	0.495295i
$679$	0.605857	−	0.259739i	0.0232506	−	0.00996787i
$680$	13.2717	−	16.9060i	0.508945	−	0.648317i
$681$	6.39628	−	11.0787i	0.245106	−	0.424536i
$682$	4.83481	−	5.23743i	0.185135	−	0.200552i
$683$	11.4579	+	19.8456i	0.438422	+	0.759370i	0.997568	−	0.0696995i	$-0.0222041\pi$
$683$	11.4579	+	19.8456i	0.438422	+	0.759370i	−0.559146	+	0.829069i	$0.688871\pi$
$684$	−25.0407	+	2.00511i	−0.957456	+	0.0766675i
$685$	15.1095			0.577302
$686$	21.9426	+	14.3012i	0.837771	+	0.546022i
$687$		−	69.1124i		−	2.63680i
$688$	−3.51945	−	4.32200i	−0.134178	−	0.164775i
$689$	−10.4952	+	6.05942i	−0.399836	+	0.230846i
$690$	19.9429	−	21.6036i	0.759212	−	0.822435i
$691$	14.4278	+	8.32990i	0.548860	+	0.316884i	0.748662	−	0.662952i	$-0.230697\pi$
$691$	14.4278	+	8.32990i	0.548860	+	0.316884i	−0.199802	+	0.979836i	$0.564030\pi$
$692$	−31.1867	+	21.4967i	−1.18554	+	0.817181i
$693$	17.9380	+	41.8415i	0.681410	+	1.58943i
$694$	−3.90326	−	12.5403i	−0.148166	−	0.476025i
$695$	−9.62962	−	5.55967i	−0.365272	−	0.210890i
$696$	2.98329	−	20.8761i	0.113081	−	0.791305i
$697$	26.2299	+	45.4314i	0.993526	+	1.72084i
$698$	25.7561	+	5.80955i	0.974882	+	0.219895i
$699$		−	36.1987i		−	1.36916i
$700$	4.68147	−	2.46655i	0.176943	−	0.0932267i
$701$		−	3.87396i		−	0.146317i	−0.997320	−	0.0731587i	$-0.976692\pi$
$701$		−	3.87396i		−	0.146317i	0.997320	−	0.0731587i	$-0.0233080\pi$
$702$	−6.25558	+	27.7335i	−0.236101	+	1.04673i
$703$	2.51962	+	4.36412i	0.0950294	+	0.164596i
$704$	−13.9890	+	13.3842i	−0.527229	+	0.504438i
$705$	−31.1601	−	17.9903i	−1.17356	−	0.677553i
$706$	18.2516	−	5.68093i	0.686909	−	0.213804i
$707$	−15.4586	+	20.6680i	−0.581380	+	0.777301i
$708$	29.6302	−	20.4238i	1.11357	−	0.767573i
$709$	−24.1848	−	13.9631i	−0.908281	−	0.524396i	−0.0284031	−	0.999597i	$-0.509042\pi$
$709$	−24.1848	−	13.9631i	−0.908281	−	0.524396i	−0.879878	+	0.475200i	$0.842376\pi$
$710$	−4.13786	−	3.81976i	−0.155291	−	0.143353i
$711$	12.4961	−	7.21462i	0.468640	−	0.270569i
$712$	−14.6458	−	36.4929i	−0.548874	−	1.36763i
$713$		−	13.6173i		−	0.509972i
$714$	85.2166	+	30.1859i	3.18915	+	1.12968i
$715$	3.72284			0.139226
$716$	−0.476269	−	5.94786i	−0.0177990	−	0.222282i
$717$	−40.9415	−	70.9127i	−1.52899	−	2.64828i
$718$	−27.3896	−	25.2841i	−1.02217	−	0.943593i
$719$	8.27114	−	14.3260i	0.308461	−	0.534271i	−0.669565	−	0.742754i	$-0.733519\pi$
$719$	8.27114	−	14.3260i	0.308461	−	0.534271i	0.978026	+	0.208483i	$0.0668526\pi$
$720$	10.1195	−	26.5788i	0.377133	−	0.990532i
$721$	15.7602	+	1.87777i	0.586942	+	0.0699317i
$722$	6.67392	+	21.4419i	0.248378	+	0.797985i
$723$	−3.06684	+	5.31193i	−0.114057	+	0.197553i
$724$	27.0572	+	12.8604i	1.00557	+	0.477952i
$725$	2.03071	−	1.17243i	0.0754188	−	0.0435430i
$726$	−5.08883	+	22.5609i	−0.188864	+	0.837312i
$727$	6.76375			0.250854			0.125427	−	0.992103i	$-0.459970\pi$
$727$	6.76375			0.250854			0.125427	+	0.992103i	$0.459970\pi$
$728$	2.96535	−	11.1233i	0.109903	−	0.412256i
$729$	−19.1232			−0.708268
$730$	0.981970	−	4.35347i	0.0363444	−	0.161129i
$731$	9.16996	−	5.29428i	0.339163	−	0.195816i
$732$	−26.9484	+	56.6974i	−0.996043	+	2.09560i
$733$	17.1394	−	29.6863i	0.633059	−	1.09649i	−0.353864	−	0.935297i	$-0.615133\pi$
$733$	17.1394	−	29.6863i	0.633059	−	1.09649i	0.986923	−	0.161193i	$-0.0515341\pi$
$734$	−14.9473	−	48.0224i	−0.551713	−	1.77254i
$735$	16.1211	+	15.3460i	0.594635	+	0.566047i
$736$	−2.29322	+	36.9159i	−0.0845291	+	1.36074i
$737$	−7.58110	+	13.1309i	−0.279253	+	0.483681i
$738$	51.0057	+	47.0847i	1.87754	+	1.73321i
$739$	−19.2212	−	33.2921i	−0.707063	−	1.22467i	−0.965942	−	0.258759i	$-0.916687\pi$
$739$	−19.2212	−	33.2921i	−0.707063	−	1.22467i	0.258879	−	0.965910i	$-0.416647\pi$
$740$	−5.68687	+	0.455371i	−0.209053	+	0.0167398i
$741$	−8.64088			−0.317431
$742$	19.1414	+	22.4160i	0.702703	+	0.822918i
$743$		−	30.1845i		−	1.10736i	−0.832729	−	0.553681i	$-0.813223\pi$
$743$		−	30.1845i		−	1.10736i	0.832729	−	0.553681i	$-0.186777\pi$
$744$	−6.97610	−	17.3823i	−0.255756	−	0.637267i
$745$	−9.67998	+	5.58874i	−0.354647	+	0.204755i
$746$	24.7927	+	22.8868i	0.907725	+	0.837945i
$747$	1.77903	+	1.02712i	0.0650913	+	0.0375805i
$748$	−20.8736	−	30.2828i	−0.763216	−	1.10725i
$749$	−0.329083	−	0.0392089i	−0.0120244	−	0.00143266i
$750$	4.29350	−	1.33638i	0.156776	−	0.0487976i
$751$	−26.8007	−	15.4734i	−0.977972	−	0.564632i	−0.0763147	−	0.997084i	$-0.524315\pi$
$751$	−26.8007	−	15.4734i	−0.977972	−	0.564632i	−0.901657	+	0.432451i	$0.857649\pi$
$752$	44.6872	−	7.20275i	1.62957	−	0.262657i
$753$	−20.6592	−	35.7828i	−0.752864	−	1.30400i
$754$	1.12245	−	4.97627i	0.0408772	−	0.181225i
$755$		−	15.2226i		−	0.554008i
$756$	69.0991	+	2.67431i	2.51311	+	0.0972638i
$757$			32.7932i			1.19189i	0.803025	+	0.595945i	$0.203223\pi$
$757$			32.7932i			1.19189i	−0.803025	+	0.595945i	$0.796777\pi$
$758$	35.7601	+	8.06605i	1.29886	+	0.292972i
$759$	−25.1563	−	43.5721i	−0.913117	−	1.58157i
$760$	4.94641	+	0.706866i	0.179425	+	0.0256407i
$761$	−11.1966	−	6.46436i	−0.405876	−	0.234333i	0.283140	−	0.959079i	$-0.408624\pi$
$761$	−11.1966	−	6.46436i	−0.405876	−	0.234333i	−0.689016	+	0.724746i	$0.741957\pi$
$762$	12.5671	+	40.3754i	0.455258	+	1.46265i
$763$	0.978062	+	0.731538i	0.0354082	+	0.0264835i
$764$	−29.4255	−	42.6895i	−1.06458	−	1.54445i
$765$	46.7900	+	27.0142i	1.69170	+	0.976702i
$766$	−32.3350	+	35.0277i	−1.16831	+	1.26560i
$767$	7.53912	−	4.35271i	0.272222	−	0.157167i
$768$	15.9846	+	48.2975i	0.576796	+	1.74279i
$769$			1.25520i			0.0452635i	0.999744	+	0.0226318i	$0.00720453\pi$
$769$			1.25520i			0.0452635i	−0.999744	+	0.0226318i	$0.992795\pi$
$770$	−1.64930	−	8.90358i	−0.0594368	−	0.320863i
$771$	−52.9102			−1.90551
$772$	−1.13355	−	14.1563i	−0.0407974	−	0.509496i
$773$	11.0046	+	19.0605i	0.395808	+	0.685559i	0.993204	−	0.116387i	$-0.0371313\pi$
$773$	11.0046	+	19.0605i	0.395808	+	0.685559i	−0.597396	+	0.801946i	$0.703798\pi$
$774$	9.50366	−	10.2951i	0.341602	−	0.370049i
$775$	1.04132	−	1.80363i	0.0374055	−	0.0647882i
$776$	−0.435142	+	0.554304i	−0.0156207	+	0.0198984i
$777$	−9.45550	−	22.0555i	−0.339214	−	0.791238i
$778$	45.2375	−	14.0804i	1.62184	−	0.504808i
$779$	−6.09787	+	10.5618i	−0.218479	+	0.378416i
$780$	4.19946	−	8.83535i	0.150365	−	0.316356i
$781$	−8.34560	+	4.81833i	−0.298629	+	0.172413i
$782$	−68.5436	−	15.4607i	−2.45111	−	0.552874i
$783$	30.6433			1.09510
$784$	−27.9162	−	2.16410i	−0.997009	−	0.0772894i
$785$	0.715672			0.0255434
$786$	−82.5347	−	18.6165i	−2.94392	−	0.664030i
$787$	29.8525	−	17.2354i	1.06413	−	0.614375i	0.137557	−	0.990494i	$-0.456075\pi$
$787$	29.8525	−	17.2354i	1.06413	−	0.614375i	0.926571	+	0.376119i	$0.122742\pi$
$788$	−0.527226	+	1.10924i	−0.0187816	+	0.0395151i
$789$	−10.9315	+	18.9339i	−0.389172	+	0.674066i
$790$	−2.74037	+	0.852955i	−0.0974978	+	0.0303468i
$791$	−10.0607	−	23.4671i	−0.357717	−	0.834395i
$792$	−38.2812	−	30.0517i	−1.36026	−	1.06784i
$793$	−7.59285	+	13.1512i	−0.269630	+	0.467013i
$794$	−4.29829	+	4.65623i	−0.152541	+	0.165243i
$795$	12.5245	+	21.6930i	0.444197	+	0.769372i
$796$	−1.42761	−	17.8286i	−0.0506004	−	0.631919i
$797$	−21.2444			−0.752515			−0.376258	−	0.926515i	$-0.622789\pi$
$797$	−21.2444			−0.752515			−0.376258	+	0.926515i	$0.622789\pi$
$798$	3.82811	+	20.6656i	0.135514	+	0.731555i
$799$			85.9894i			3.04209i
$800$	−3.12672	+	4.71419i	−0.110546	+	0.166672i
$801$	85.6037	−	49.4233i	3.02466	−	1.74629i
$802$	29.7930	−	32.2740i	1.05203	−	1.13963i
$803$	−6.61385	−	3.81851i	−0.233398	−	0.134752i
$804$	22.6115	+	32.8040i	0.797447	+	1.15691i
$805$	−13.8529	−	10.3613i	−0.488252	−	0.365186i
$806$	−1.34653	−	4.32612i	−0.0474296	−	0.152381i
$807$	60.9321	+	35.1791i	2.14491	+	1.23836i
$808$	3.90332	−	27.3141i	0.137318	−	0.960907i
$809$	−1.39597	−	2.41789i	−0.0490796	−	0.0850084i	0.840442	−	0.541902i	$-0.182295\pi$
$809$	−1.39597	−	2.41789i	−0.0490796	−	0.0850084i	−0.889522	+	0.456893i	$0.848962\pi$
$810$	27.8976	+	6.29259i	0.980222	+	0.221099i
$811$			46.1196i			1.61948i	0.586790	+	0.809739i	$0.300391\pi$
$811$			46.1196i			1.61948i	−0.586790	+	0.809739i	$0.699609\pi$
$812$	−12.3986	−	0.479857i	−0.435105	−	0.0168397i
$813$			33.6752i			1.18104i
$814$	−2.14812	+	9.52350i	−0.0752917	+	0.333799i
$815$	−0.890005	−	1.54153i	−0.0311755	−	0.0539975i
$816$	−95.4156	+	15.3792i	−3.34021	+	0.538381i
$817$	2.13181	+	1.23080i	0.0745828	+	0.0430604i
$818$	35.3390	−	10.9995i	1.23560	−	0.384588i
$819$	28.7346	+	3.42362i	1.00407	+	0.119631i
$820$	−7.83595	−	11.3681i	−0.273643	−	0.396992i
$821$	−47.1623	−	27.2292i	−1.64598	−	0.950305i	−0.978649	−	0.205540i	$-0.934105\pi$
$821$	−47.1623	−	27.2292i	−1.64598	−	0.950305i	−0.667327	−	0.744765i	$-0.732562\pi$
$822$	−49.9229	−	46.0852i	−1.74126	−	1.60740i
$823$	−11.9130	+	6.87795i	−0.415259	+	0.239750i	−0.693047	−	0.720892i	$-0.743732\pi$
$823$	−11.9130	+	6.87795i	−0.415259	+	0.239750i	0.277788	+	0.960643i	$0.410399\pi$
$824$	−15.7467	+	6.31968i	−0.548564	+	0.220157i
$825$		−	7.69489i		−	0.267902i
$826$	−13.7500	−	16.1023i	−0.478423	−	0.560270i
$827$	19.8375			0.689816			0.344908	−	0.938636i	$-0.387910\pi$
$827$	19.8375			0.689816			0.344908	+	0.938636i	$0.387910\pi$
$828$	−92.6802	+	7.42129i	−3.22086	+	0.257908i
$829$	−1.25335	−	2.17087i	−0.0435308	−	0.0753975i	0.843439	−	0.537225i	$-0.180527\pi$
$829$	−1.25335	−	2.17087i	−0.0435308	−	0.0753975i	−0.886970	+	0.461827i	$0.847194\pi$
$830$	−0.300233	−	0.277153i	−0.0104212	−	0.00962011i
$831$	30.2959	−	52.4741i	1.05095	−	1.82031i
$832$	2.92185	+	11.9547i	0.101297	+	0.414455i
$833$	12.4979	−	51.7035i	0.433028	−	1.79142i
$834$	14.8596	+	47.7408i	0.514546	+	1.65313i
$835$	2.84578	−	4.92903i	0.0984822	−	0.170576i
$836$	3.67056	−	7.72257i	0.126949	−	0.267091i
$837$	23.5703	−	13.6083i	0.814708	−	0.470372i
$838$	1.15612	−	5.12556i	0.0399376	−	0.177060i
$839$	−27.1009			−0.935628			−0.467814	−	0.883827i	$-0.654958\pi$
$839$	−27.1009			−0.935628			−0.467814	+	0.883827i	$0.654958\pi$
$840$	−22.9912	−	6.12921i	−0.793270	−	0.211478i
$841$	23.5016			0.810400
$842$	3.07854	−	13.6484i	0.106094	−	0.470356i
$843$	−48.5411	+	28.0252i	−1.67184	+	0.965240i
$844$	19.2839	+	9.16568i	0.663778	+	0.315496i
$845$	−5.31678	+	9.20893i	−0.182903	+	0.316797i
$846$	33.8155	+	108.642i	1.16260	+	3.73519i
$847$	13.5123	+	1.60994i	0.464288	+	0.0553180i
$848$	−29.4495	−	11.2125i	−1.01130	−	0.385040i
$849$	0.891543	−	1.54420i	0.0305977	−	0.0529967i
$850$	−7.89638	−	7.28936i	−0.270844	−	0.250023i
$851$	9.32558	+	16.1524i	0.319677	+	0.553697i
$852$	2.02120	+	25.2417i	0.0692453	+	0.864765i
$853$	−8.16785			−0.279662			−0.139831	−	0.990175i	$-0.544656\pi$
$853$	−8.16785			−0.279662			−0.139831	+	0.990175i	$0.544656\pi$
$854$	34.8164	+	12.3329i	1.19139	+	0.422021i
$855$			12.5604i			0.429558i
$856$	0.328802	−	0.131959i	0.0112382	−	0.00451026i
$857$	−13.4380	+	7.75845i	−0.459035	+	0.265024i	−0.711638	−	0.702546i	$-0.752046\pi$
$857$	−13.4380	+	7.75845i	−0.459035	+	0.265024i	0.252604	+	0.967570i	$0.418713\pi$
$858$	−12.3006	−	11.3550i	−0.419935	−	0.387653i
$859$	46.6347	+	26.9246i	1.59116	+	0.918654i	0.993109	+	0.117192i	$0.0373894\pi$
$859$	46.6347	+	26.9246i	1.59116	+	0.918654i	0.598046	+	0.801462i	$0.295944\pi$
$860$	−2.29456	+	1.58162i	−0.0782440	+	0.0539328i
$861$	34.7845	−	46.5067i	1.18545	−	1.58494i
$862$	34.1710	−	10.6359i	1.16387	−	0.362261i
$863$	33.2448	+	19.1939i	1.13167	+	0.653368i	0.944353	−	0.328932i	$-0.106689\pi$
$863$	33.2448	+	19.1939i	1.13167	+	0.653368i	0.187313	+	0.982300i	$0.440022\pi$
$864$	−66.1897	+	32.9222i	−2.25182	+	1.12004i
$865$	9.46941	+	16.4015i	0.321969	+	0.557667i
$866$	−1.09422	+	4.85110i	−0.0371830	+	0.164847i
$867$		−	129.550i		−	4.39975i
$868$	−9.74985	+	5.13695i	−0.330932	+	0.174359i
$869$			4.91134i			0.166606i
$870$	−10.2857	−	2.32004i	−0.348717	−	0.0786566i
$871$	4.81896	+	8.34668i	0.163284	+	0.282816i
$872$	−1.29257	−	0.184715i	−0.0437720	−	0.00625524i
$873$	−1.53412	−	0.885726i	−0.0519222	−	0.0299773i
$874$	−4.85471	−	15.5971i	−0.164213	−	0.527581i
$875$	−1.04250	−	2.43170i	−0.0352431	−	0.0822066i
$876$	−16.5230	+	11.3891i	−0.558260	+	0.384804i
$877$	−15.9417	−	9.20394i	−0.538313	−	0.310795i	0.206082	−	0.978535i	$-0.433929\pi$
$877$	−15.9417	−	9.20394i	−0.538313	−	0.310795i	−0.744395	+	0.667740i	$0.767262\pi$
$878$	8.74936	−	9.47796i	0.295277	−	0.319866i
$879$	65.5410	−	37.8401i	2.21064	−	1.27632i
$880$	6.11248	+	7.50633i	0.206052	+	0.253038i
$881$		−	21.5756i		−	0.726902i	−0.931613	−	0.363451i	$-0.881598\pi$
$881$		−	21.5756i		−	0.726902i	0.931613	−	0.363451i	$-0.118402\pi$
$882$	−4.54215	−	70.2388i	−0.152942	−	2.36506i
$883$	23.5384			0.792131			0.396065	−	0.918222i	$-0.370375\pi$
$883$	23.5384			0.792131			0.396065	+	0.918222i	$0.370375\pi$
$884$	−23.3046	+	1.86610i	−0.783820	+	0.0627637i
$885$	−8.99680	−	15.5829i	−0.302424	−	0.523814i
$886$	3.31345	−	3.58938i	0.111318	−	0.120587i
$887$	−16.6515	+	28.8413i	−0.559104	+	0.968397i	0.438467	+	0.898747i	$0.355521\pi$
$887$	−16.6515	+	28.8413i	−0.559104	+	0.968397i	−0.997572	+	0.0696497i	$0.977812\pi$
$888$	20.1788	+	15.8409i	0.677157	+	0.531585i
$889$	22.8674	−	9.80356i	0.766948	−	0.328801i
$890$	−18.7727	+	5.84313i	−0.629263	+	0.195862i
$891$	24.4695	−	42.3824i	0.819759	−	1.41986i
$892$	2.53358	+	1.20422i	0.0848306	+	0.0403202i
$893$	−17.3124	+	9.99533i	−0.579338	+	0.334481i
$894$	49.0296	+	11.0591i	1.63979	+	0.369872i
$895$	−2.98345			−0.0997256
$896$	27.2965	−	12.2841i	0.911913	−	0.410384i
$897$	−31.9815			−1.06783
$898$	−14.2985	−	3.22516i	−0.477146	−	0.107625i
$899$	−4.22926	+	2.44176i	−0.141054	+	0.0814374i
$900$	−12.8431	−	6.10436i	−0.428104	−	0.203479i
$901$	29.9320	−	51.8438i	0.997181	−	1.72717i
$902$	−22.5598	+	7.02187i	−0.751159	+	0.233803i
$903$	−9.38700	−	7.02097i	−0.312380	−	0.233643i
$904$	21.4703	+	16.8547i	0.714092	+	0.560580i
$905$	7.48951	−	12.9722i	0.248960	−	0.431211i
$906$	−46.4303	+	50.2968i	−1.54254	+	1.67100i
$907$	−25.9103	−	44.8780i	−0.860338	−	1.49015i	−0.871603	−	0.490213i	$-0.836919\pi$
$907$	−25.9103	−	44.8780i	−0.860338	−	1.49015i	0.0112647	−	0.999937i	$-0.496414\pi$
$908$	8.02092	−	0.642268i	0.266184	−	0.0213144i
$909$	69.3589			2.30049
$910$	−5.42555	−	1.92187i	−0.179855	−	0.0637093i
$911$		−	3.37980i		−	0.111978i	−0.998431	−	0.0559889i	$-0.982169\pi$
$911$		−	3.37980i		−	0.111978i	0.998431	−	0.0559889i	$-0.0178312\pi$
$912$	−14.1873	−	17.4225i	−0.469790	−	0.576918i
$913$	−0.605536	+	0.349606i	−0.0200403	+	0.0115703i
$914$	−25.8168	+	27.9667i	−0.853945	+	0.925057i
$915$	27.1828	+	15.6940i	0.898635	+	0.518827i
$916$	35.7928	−	24.6717i	1.18263	−	0.815175i
$917$	−5.88965	+	49.4322i	−0.194493	+	1.63240i
$918$	−41.7373	−	134.093i	−1.37754	−	4.42573i
$919$	−16.6978	−	9.64048i	−0.550810	−	0.318010i	0.198639	−	0.980073i	$-0.436348\pi$
$919$	−16.6978	−	9.64048i	−0.550810	−	0.318010i	−0.749448	+	0.662063i	$0.769681\pi$
$920$	18.3075	+	2.61624i	0.603582	+	0.0862549i
$921$	14.8196	+	25.6683i	0.488322	+	0.845799i
$922$	12.6784	+	2.85975i	0.417542	+	0.0941808i
$923$			6.12558i			0.201626i
$924$	−21.7073	+	34.4487i	−0.714117	+	1.13328i
$925$			2.85253i			0.0937908i
$926$	3.37771	−	14.9747i	0.110998	−	0.492101i
$927$	−21.3262	−	36.9381i	−0.700446	−	1.21321i
$928$	11.8765	−	5.90729i	0.389867	−	0.193916i
$929$	29.0690	+	16.7830i	0.953724	+	0.550633i	0.894236	−	0.447596i	$-0.147720\pi$
$929$	29.0690	+	16.7830i	0.953724	+	0.550633i	0.0594882	+	0.998229i	$0.481053\pi$
$930$	−8.94184	+	2.78320i	−0.293215	+	0.0912648i
$931$	11.8623	−	3.49373i	0.388771	−	0.114502i
$932$	18.7471	−	12.9222i	0.614081	−	0.423280i
$933$	15.0492	+	8.68863i	0.492687	+	0.284453i
$934$	−31.1725	−	28.7761i	−1.01999	−	0.941584i
$935$	−15.9261	+	9.19496i	−0.520840	+	0.300707i
$936$	−28.7100	+	11.5223i	−0.938417	+	0.376618i
$937$			21.4342i			0.700224i	0.936708	+	0.350112i	$0.113856\pi$
$937$			21.4342i			0.700224i	−0.936708	+	0.350112i	$0.886144\pi$
$938$	17.8271	−	15.2228i	0.582075	−	0.497043i
$939$	−73.4006			−2.39534
$940$	−1.80645	−	22.5598i	−0.0589200	−	0.735818i
$941$	7.43223	+	12.8730i	0.242284	+	0.419648i	0.961364	−	0.275279i	$-0.0887702\pi$
$941$	7.43223	+	12.8730i	0.242284	+	0.419648i	−0.719081	+	0.694927i	$0.755437\pi$
$942$	−2.36464	−	2.18286i	−0.0770442	−	0.0711216i
$943$	−22.5693	+	39.0912i	−0.734957	+	1.27298i
$944$	21.1547	+	8.05439i	0.688527	+	0.262148i
$945$	4.09059	−	34.3326i	0.133067	−	1.11684i
$946$	1.41731	+	4.55351i	0.0460806	+	0.148047i
$947$	21.9761	−	38.0637i	0.714127	−	1.23690i	−0.249168	−	0.968460i	$-0.580157\pi$
$947$	21.9761	−	38.0637i	0.714127	−	1.23690i	0.963295	−	0.268444i	$-0.0865095\pi$
$948$	11.6560	+	5.54012i	0.378569	+	0.179935i
$949$	−4.20412	+	2.42725i	−0.136472	+	0.0787919i
$950$	0.549713	−	2.43710i	0.0178351	−	0.0790700i
$951$	96.2503			3.12113
$952$	14.7875	+	54.9089i	0.479265	+	1.77961i
$953$	−24.5807			−0.796246			−0.398123	−	0.917332i	$-0.630338\pi$
$953$	−24.5807			−0.796246			−0.398123	+	0.917332i	$0.630338\pi$
$954$	17.4295	−	77.2721i	0.564301	−	2.50178i
$955$	−22.4510	+	12.9621i	−0.726497	+	0.419443i
$956$	22.1100	−	46.5177i	0.715088	−	1.50449i
$957$	−9.02174	+	15.6261i	−0.291631	+	0.505120i
$958$	3.93376	+	12.6383i	0.127094	+	0.408326i
$959$	−23.9434	+	32.0122i	−0.773173	+	1.03373i
$960$	24.7097	−	6.03930i	0.797501	−	0.194917i
$961$	13.3313	−	23.0905i	0.430042	−	0.744854i
$962$	4.55989	+	4.20935i	0.147017	+	0.135715i
$963$	0.445305	+	0.771291i	0.0143498	+	0.0248545i
$964$	−3.84581	+	0.307950i	−0.123865	+	0.00991840i
$965$	−7.10080			−0.228583
$966$	14.1685	+	76.4872i	0.455865	+	2.46093i
$967$			9.58755i			0.308315i	0.988046	+	0.154157i	$0.0492663\pi$
$967$			9.58755i			0.308315i	−0.988046	+	0.154157i	$0.950734\pi$
$968$	−13.5007	+	5.41829i	−0.433930	+	0.174150i
$969$	36.9653	−	21.3419i	1.18750	−	0.685601i
$970$	0.258901	+	0.238999i	0.00831283	+	0.00767379i
$971$	−19.5510	−	11.2878i	−0.627421	−	0.362242i	0.152332	−	0.988329i	$-0.451322\pi$
$971$	−19.5510	−	11.2878i	−0.627421	−	0.362242i	−0.779753	+	0.626088i	$0.784655\pi$
$972$	−28.4833	−	41.3226i	−0.913602	−	1.32542i
$973$	27.0389	−	11.5920i	0.866828	−	0.371621i
$974$	23.3386	−	7.26427i	0.747816	−	0.232762i
$975$	−4.23598	−	2.44564i	−0.135660	−	0.0783233i
$976$	−38.9832	+	6.28339i	−1.24782	+	0.201126i
$977$	9.57609	+	16.5863i	0.306366	+	0.530642i	0.977565	−	0.210636i	$-0.0675535\pi$
$977$	9.57609	+	16.5863i	0.306366	+	0.530642i	−0.671198	+	0.741278i	$0.734220\pi$
$978$	−1.76116	+	7.80795i	−0.0563158	+	0.249671i
$979$			33.6449i			1.07529i
$980$	−2.19272	+	13.8272i	−0.0700438	+	0.441694i
$981$		−	3.28223i		−	0.104794i
$982$	39.2225	+	8.84703i	1.25164	+	0.282320i
$983$	14.3326	+	24.8248i	0.457139	+	0.791787i	0.998808	−	0.0488042i	$-0.0155410\pi$
$983$	14.3326	+	24.8248i	0.457139	+	0.791787i	−0.541670	+	0.840591i	$0.682208\pi$
$984$	−8.78317	+	61.4616i	−0.279997	+	1.95932i
$985$	0.531810	+	0.307041i	0.0169449	+	0.00978314i
$986$	7.48900	+	24.0606i	0.238498	+	0.766245i
$987$	87.4941	−	37.5099i	2.78497	−	1.19395i
$988$	−3.08461	−	4.47506i	−0.0981347	−	0.142370i
$989$	7.89023	+	4.55543i	0.250895	+	0.144854i
$990$	−16.5057	+	17.8802i	−0.524585	+	0.568270i
$991$	−17.8817	+	10.3240i	−0.568030	+	0.327952i	−0.756362	−	0.654153i	$-0.773025\pi$
$991$	−17.8817	+	10.3240i	−0.568030	+	0.327952i	0.188332	+	0.982105i	$0.439692\pi$
$992$	6.51187	−	9.81800i	0.206752	−	0.311722i
$993$		−	1.66727i		−	0.0529093i
$994$	14.6500	−	2.71377i	0.464670	−	0.0860757i
$995$	−8.94285			−0.283507
$996$	0.146654	+	1.83147i	0.00464689	+	0.0580324i
$997$	−9.92952	−	17.1984i	−0.314471	−	0.544680i	0.664854	−	0.746973i	$-0.268494\pi$
$997$	−9.92952	−	17.1984i	−0.314471	−	0.544680i	−0.979325	+	0.202294i	$0.935160\pi$
$998$	−23.3743	+	25.3208i	−0.739901	+	0.801517i
$999$	−18.6389	+	32.2834i	−0.589707	+	1.02140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.e.131.2	✓	24
4.3	odd	2		1120.2.bz.f.271.1		24
7.3	odd	6		280.2.bj.f.171.9	yes	24
8.3	odd	2		280.2.bj.f.131.9	yes	24
8.5	even	2		1120.2.bz.e.271.1		24
28.3	even	6		1120.2.bz.e.591.1		24
56.3	even	6	inner	280.2.bj.e.171.2	yes	24
56.45	odd	6		1120.2.bz.f.591.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.2	✓	24	1.1	even	1	trivial
280.2.bj.e.171.2	yes	24	56.3	even	6	inner
280.2.bj.f.131.9	yes	24	8.3	odd	2
280.2.bj.f.171.9	yes	24	7.3	odd	6
1120.2.bz.e.271.1		24	8.5	even	2
1120.2.bz.e.591.1		24	28.3	even	6
1120.2.bz.f.271.1		24	4.3	odd	2
1120.2.bz.f.591.1		24	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37955 - 0.311173i) q^{2} +(2.75363 - 1.58981i) q^{3} +(1.80634 + 0.858559i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-4.29350 + 1.33638i) q^{6} +(1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 - 6.15745i) q^{9} +O(q^{10})\)	\(q+(-1.37955 - 0.311173i) q^{2} +(2.75363 - 1.58981i) q^{3} +(1.80634 + 0.858559i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-4.29350 + 1.33638i) q^{6} +(1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 - 6.15745i) q^{9} +(-0.959261 + 1.03914i) q^{10} +(1.21003 + 2.09584i) q^{11} +(6.33896 - 0.507586i) q^{12} +1.53832 q^{13} +(-0.681512 - 3.67907i) q^{14} -3.17962i q^{15} +(2.52575 + 3.10171i) q^{16} +(-6.58087 + 3.79947i) q^{17} +(-6.82035 + 7.38832i) q^{18} +(-1.52991 - 0.883293i) q^{19} +(1.64671 - 1.13506i) q^{20} +(6.73663 + 5.03864i) q^{21} +(-1.01714 - 3.26785i) q^{22} +(-5.66247 - 3.26923i) q^{23} +(-8.90289 - 1.27227i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.12220 - 0.478684i) q^{26} -13.0683i q^{27} +(-0.204642 + 5.28754i) q^{28} +2.34486i q^{29} +(-0.989412 + 4.38647i) q^{30} +(1.04132 + 1.80363i) q^{31} +(-2.51925 - 5.06492i) q^{32} +(6.66397 + 3.84745i) q^{33} +(10.2610 - 3.19379i) q^{34} +(2.62717 + 0.313017i) q^{35} +(11.7081 - 8.07028i) q^{36} +(-2.47037 - 1.42627i) q^{37} +(1.83574 + 1.69462i) q^{38} +(4.23598 - 2.44564i) q^{39} +(-2.62492 + 1.05347i) q^{40} -6.90356i q^{41} +(-7.72566 - 9.04733i) q^{42} -1.39343 q^{43} +(0.386332 + 4.82469i) q^{44} +(-3.55500 - 6.15745i) q^{45} +(6.79439 + 6.27208i) q^{46} +(5.65799 - 9.79993i) q^{47} +(11.8861 + 4.52550i) q^{48} +(-4.82637 + 5.07012i) q^{49} +(0.420294 + 1.35032i) q^{50} +(-12.0809 + 20.9247i) q^{51} +(2.77874 + 1.32074i) q^{52} +(-6.82251 + 3.93898i) q^{53} +(-4.06649 + 18.0284i) q^{54} +2.42006 q^{55} +(1.92765 - 7.23078i) q^{56} -5.61708 q^{57} +(0.729658 - 3.23487i) q^{58} +(4.90087 - 2.82952i) q^{59} +(2.72990 - 5.74349i) q^{60} +(-4.93580 + 8.54905i) q^{61} +(-0.875325 - 2.81223i) q^{62} +(18.6792 + 2.22555i) q^{63} +(1.89937 + 7.77125i) q^{64} +(0.769162 - 1.33223i) q^{65} +(-7.99610 - 7.38141i) q^{66} +(3.13260 + 5.42583i) q^{67} +(-15.1494 + 1.21307i) q^{68} -20.7898 q^{69} +(-3.52692 - 1.24933i) q^{70} +3.98199i q^{71} +(-18.6632 + 7.49016i) q^{72} +(-2.73292 + 1.57785i) q^{73} +(2.96419 + 2.73633i) q^{74} +(-2.75363 - 1.58981i) q^{75} +(-2.00518 - 2.90905i) q^{76} +(-3.83499 + 5.12736i) q^{77} +(-6.60478 + 2.05578i) q^{78} +(1.75753 + 1.01471i) q^{79} +(3.94903 - 0.636512i) q^{80} +(-10.1111 - 17.5129i) q^{81} +(-2.14820 + 9.52384i) q^{82} +0.288923i q^{83} +(7.84269 + 14.8853i) q^{84} +7.59894i q^{85} +(1.92231 + 0.433596i) q^{86} +(3.72789 + 6.45690i) q^{87} +(0.968343 - 6.77613i) q^{88} +(12.0399 + 6.95124i) q^{89} +(2.98829 + 9.60076i) q^{90} +(1.60371 + 3.74075i) q^{91} +(-7.42153 - 10.7669i) q^{92} +(5.73485 + 3.31102i) q^{93} +(-10.8550 + 11.7589i) q^{94} +(-1.52991 + 0.883293i) q^{95} +(-14.9894 - 9.94181i) q^{96} -0.249149i q^{97} +(8.23592 - 5.49268i) q^{98} +17.2067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

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