LMFDB - Embedded newform 280.2.bj.e.131.4

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			131.4
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.e.171.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967093 + 1.03186i) q^{2} +(2.26702 - 1.30886i) q^{3} +(-0.129462 - 1.99581i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.841856 + 3.60504i) q^{6} +(-1.72615 - 2.00510i) q^{7} +(2.18459 + 1.79654i) q^{8} +(1.92625 - 3.33637i) q^{9} +O(q^{10})$	\(q+(-0.967093 + 1.03186i) q^{2} +(2.26702 - 1.30886i) q^{3} +(-0.129462 - 1.99581i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.841856 + 3.60504i) q^{6} +(-1.72615 - 2.00510i) q^{7} +(2.18459 + 1.79654i) q^{8} +(1.92625 - 3.33637i) q^{9} +(0.410069 + 1.35346i) q^{10} +(0.530792 + 0.919359i) q^{11} +(-2.90573 - 4.35508i) q^{12} -0.831440 q^{13} +(3.73832 + 0.157972i) q^{14} -2.61773i q^{15} +(-3.96648 + 0.516763i) q^{16} +(4.14632 - 2.39388i) q^{17} +(1.57979 + 5.21420i) q^{18} +(-2.03733 - 1.17625i) q^{19} +(-1.79315 - 0.885785i) q^{20} +(-6.53761 - 2.28630i) q^{21} +(-1.46197 - 0.341404i) q^{22} +(-1.32189 - 0.763194i) q^{23} +(7.30394 + 1.21347i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.804080 - 0.857928i) q^{26} -2.23163i q^{27} +(-3.77831 + 3.70464i) q^{28} -3.07820i q^{29} +(2.70112 + 2.53159i) q^{30} +(4.78548 + 8.28870i) q^{31} +(3.30273 - 4.59260i) q^{32} +(2.40663 + 1.38947i) q^{33} +(-1.53973 + 6.59352i) q^{34} +(-2.59954 + 0.492342i) q^{35} +(-6.90812 - 3.41249i) q^{36} +(10.0658 + 5.81151i) q^{37} +(3.18402 - 0.964691i) q^{38} +(-1.88489 + 1.08824i) q^{39} +(2.64815 - 0.993639i) q^{40} +8.76255i q^{41} +(8.68161 - 4.53483i) q^{42} -4.99479 q^{43} +(1.76615 - 1.17838i) q^{44} +(-1.92625 - 3.33637i) q^{45} +(2.06590 - 0.625924i) q^{46} +(1.75877 - 3.04628i) q^{47} +(-8.31571 + 6.36310i) q^{48} +(-1.04082 + 6.92219i) q^{49} +(1.37716 + 0.321598i) q^{50} +(6.26653 - 10.8539i) q^{51} +(0.107640 + 1.65939i) q^{52} +(6.61057 - 3.81661i) q^{53} +(2.30272 + 2.15819i) q^{54} +1.06158 q^{55} +(-0.168690 - 7.48141i) q^{56} -6.15823 q^{57} +(3.17626 + 2.97690i) q^{58} +(-3.31455 + 1.91365i) q^{59} +(-5.22448 + 0.338897i) q^{60} +(-6.51711 + 11.2880i) q^{61} +(-13.1808 - 3.07800i) q^{62} +(-10.0147 + 1.89675i) q^{63} +(1.54487 + 7.84942i) q^{64} +(-0.415720 + 0.720048i) q^{65} +(-3.76118 + 1.13956i) q^{66} +(-7.36855 - 12.7627i) q^{67} +(-5.31451 - 7.96533i) q^{68} -3.99567 q^{69} +(2.00597 - 3.15849i) q^{70} +9.99651i q^{71} +(10.2020 - 3.82800i) q^{72} +(-7.06104 + 4.07669i) q^{73} +(-15.7313 + 4.76624i) q^{74} +(-2.26702 - 1.30886i) q^{75} +(-2.08382 + 4.21840i) q^{76} +(0.927176 - 2.65124i) q^{77} +(0.699953 - 2.99737i) q^{78} +(-8.17894 - 4.72211i) q^{79} +(-1.53571 + 3.69345i) q^{80} +(2.85786 + 4.94996i) q^{81} +(-9.04171 - 8.47421i) q^{82} -13.7576i q^{83} +(-3.71663 + 13.3438i) q^{84} -4.78776i q^{85} +(4.83043 - 5.15392i) q^{86} +(-4.02894 - 6.97833i) q^{87} +(-0.492104 + 2.96202i) q^{88} +(10.1864 + 5.88110i) q^{89} +(5.30552 + 1.23896i) q^{90} +(1.43519 + 1.66712i) q^{91} +(-1.35205 + 2.73704i) q^{92} +(21.6976 + 12.5271i) q^{93} +(1.44243 + 4.76083i) q^{94} +(-2.03733 + 1.17625i) q^{95} +(1.47625 - 14.7343i) q^{96} +6.01605i q^{97} +(-6.13615 - 7.76837i) q^{98} +4.08976 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 $

$2$	−0.967093	+	1.03186i	−0.683838	+	0.729634i
$2$	−0.967093	+	1.03186i	−0.683838	+	0.729634i
$3$	2.26702	−	1.30886i	1.30886	−	0.755673i	0.326958	−	0.945039i	$-0.393976\pi$
$3$	2.26702	−	1.30886i	1.30886	−	0.755673i	0.981907	+	0.189366i	$0.0606431\pi$
$4$	−0.129462	−	1.99581i	−0.0647312	−	0.997903i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.841856	+	3.60504i	−0.343686	+	1.47175i
$7$	−1.72615	−	2.00510i	−0.652423	−	0.757855i
$7$	−1.72615	−	2.00510i	−0.652423	−	0.757855i
$8$	2.18459	+	1.79654i	0.772369	+	0.635174i
$9$	1.92625	−	3.33637i	0.642084	−	1.11212i
$10$	0.410069	+	1.35346i	0.129675	+	0.428000i
$11$	0.530792	+	0.919359i	0.160040	+	0.277197i	0.934883	−	0.354957i	$-0.115504\pi$
$11$	0.530792	+	0.919359i	0.160040	+	0.277197i	−0.774843	+	0.632154i	$0.782171\pi$
$12$	−2.90573	−	4.35508i	−0.838813	−	1.25720i
$13$	−0.831440			−0.230600			−0.115300	−	0.993331i	$-0.536783\pi$
$13$	−0.831440			−0.230600			−0.115300	+	0.993331i	$0.536783\pi$
$14$	3.73832	+	0.157972i	0.999108	+	0.0422198i
$15$		−	2.61773i		−	0.675895i
$16$	−3.96648	+	0.516763i	−0.991620	+	0.129191i
$17$	4.14632	−	2.39388i	1.00563	−	0.580601i	0.0957209	−	0.995408i	$-0.469484\pi$
$17$	4.14632	−	2.39388i	1.00563	−	0.580601i	0.909909	+	0.414807i	$0.136151\pi$
$18$	1.57979	+	5.21420i	0.372361	+	1.22900i
$19$	−2.03733	−	1.17625i	−0.467396	−	0.269851i	0.247753	−	0.968823i	$-0.420308\pi$
$19$	−2.03733	−	1.17625i	−0.467396	−	0.269851i	−0.715149	+	0.698972i	$0.753641\pi$
$20$	−1.79315	−	0.885785i	−0.400960	−	0.198068i
$21$	−6.53761	−	2.28630i	−1.42662	−	0.498910i
$22$	−1.46197	−	0.341404i	−0.311694	−	0.0727875i
$23$	−1.32189	−	0.763194i	−0.275633	−	0.159137i	0.355812	−	0.934558i	$-0.384204\pi$
$23$	−1.32189	−	0.763194i	−0.275633	−	0.159137i	−0.631445	+	0.775421i	$0.717538\pi$
$24$	7.30394	+	1.21347i	1.49091	+	0.247698i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.804080	−	0.857928i	0.157693	−	0.168254i
$27$		−	2.23163i		−	0.429477i
$28$	−3.77831	+	3.70464i	−0.714033	+	0.700112i
$29$		−	3.07820i		−	0.571607i	−0.958288	−	0.285803i	$-0.907740\pi$
$29$		−	3.07820i		−	0.571607i	0.958288	−	0.285803i	$-0.0922604\pi$
$30$	2.70112	+	2.53159i	0.493156	+	0.462202i
$31$	4.78548	+	8.28870i	0.859498	+	1.48869i	0.872409	+	0.488777i	$0.162557\pi$
$31$	4.78548	+	8.28870i	0.859498	+	1.48869i	−0.0129107	+	0.999917i	$0.504110\pi$
$32$	3.30273	−	4.59260i	0.583845	−	0.811865i
$33$	2.40663	+	1.38947i	0.418941	+	0.241876i
$34$	−1.53973	+	6.59352i	−0.264062	+	1.13078i
$35$	−2.59954	+	0.492342i	−0.439402	+	0.0832209i
$36$	−6.90812	−	3.41249i	−1.15135	−	0.568749i
$37$	10.0658	+	5.81151i	1.65481	+	0.955407i	0.975053	+	0.221972i	$0.0712494\pi$
$37$	10.0658	+	5.81151i	1.65481	+	0.955407i	0.679760	+	0.733435i	$0.262084\pi$
$38$	3.18402	−	0.964691i	0.516516	−	0.156493i
$39$	−1.88489	+	1.08824i	−0.301824	+	0.174258i
$40$	2.64815	−	0.993639i	0.418709	−	0.157108i
$41$			8.76255i			1.36848i	0.729256	+	0.684241i	$0.239866\pi$
$41$			8.76255i			1.36848i	−0.729256	+	0.684241i	$0.760134\pi$
$42$	8.68161	−	4.53483i	1.33960	−	0.699739i
$43$	−4.99479			−0.761699			−0.380849	−	0.924637i	$-0.624368\pi$
$43$	−4.99479			−0.761699			−0.380849	+	0.924637i	$0.624368\pi$
$44$	1.76615	−	1.17838i	0.266256	−	0.177648i
$45$	−1.92625	−	3.33637i	−0.287149	−	0.497356i
$46$	2.06590	−	0.625924i	0.304600	−	0.0922875i
$47$	1.75877	−	3.04628i	0.256543	−	0.444345i	−0.708771	−	0.705439i	$-0.750750\pi$
$47$	1.75877	−	3.04628i	0.256543	−	0.444345i	0.965313	+	0.261094i	$0.0840832\pi$
$48$	−8.31571	+	6.36310i	−1.20027	+	0.918434i
$49$	−1.04082	+	6.92219i	−0.148688	+	0.988884i
$50$	1.37716	+	0.321598i	0.194760	+	0.0454808i
$51$	6.26653	−	10.8539i	0.877489	−	1.51986i
$52$	0.107640	+	1.65939i	0.0149270	+	0.230116i
$53$	6.61057	−	3.81661i	0.908031	−	0.524252i	0.0282341	−	0.999601i	$-0.491012\pi$
$53$	6.61057	−	3.81661i	0.908031	−	0.524252i	0.879797	+	0.475349i	$0.157678\pi$
$54$	2.30272	+	2.15819i	0.313361	+	0.293693i
$55$	1.06158			0.143144
$56$	−0.168690	−	7.48141i	−0.0225422	−	0.999746i
$57$	−6.15823			−0.815678
$58$	3.17626	+	2.97690i	0.417064	+	0.390886i
$59$	−3.31455	+	1.91365i	−0.431517	+	0.249137i	−0.699993	−	0.714150i	$-0.746813\pi$
$59$	−3.31455	+	1.91365i	−0.431517	+	0.249137i	0.268476	+	0.963287i	$0.413480\pi$
$60$	−5.22448	+	0.338897i	−0.674477	+	0.0437515i
$61$	−6.51711	+	11.2880i	−0.834430	+	1.44528i	0.0600638	+	0.998195i	$0.480870\pi$
$61$	−6.51711	+	11.2880i	−0.834430	+	1.44528i	−0.894494	+	0.447080i	$0.852464\pi$
$62$	−13.1808	−	3.07800i	−1.67396	−	0.390907i
$63$	−10.0147	+	1.89675i	−1.26174	+	0.238968i
$64$	1.54487	+	7.84942i	0.193109	+	0.981177i
$65$	−0.415720	+	0.720048i	−0.0515637	+	0.0893110i
$66$	−3.76118	+	1.13956i	−0.462969	+	0.140270i
$67$	−7.36855	−	12.7627i	−0.900212	−	1.55921i	−0.827219	−	0.561880i	$-0.810078\pi$
$67$	−7.36855	−	12.7627i	−0.900212	−	1.55921i	−0.0729933	−	0.997332i	$-0.523255\pi$
$68$	−5.31451	−	7.96533i	−0.644479	−	0.965938i
$69$	−3.99567			−0.481022
$70$	2.00597	−	3.15849i	0.239759	−	0.377512i
$71$			9.99651i			1.18637i	0.805067	+	0.593184i	$0.202129\pi$
$71$			9.99651i			1.18637i	−0.805067	+	0.593184i	$0.797871\pi$
$72$	10.2020	−	3.82800i	1.20232	−	0.451134i
$73$	−7.06104	+	4.07669i	−0.826432	+	0.477141i	−0.852630	−	0.522516i	$-0.824994\pi$
$73$	−7.06104	+	4.07669i	−0.826432	+	0.477141i	0.0261973	+	0.999657i	$0.491660\pi$
$74$	−15.7313	+	4.76624i	−1.82872	+	0.554064i
$75$	−2.26702	−	1.30886i	−0.261773	−	0.151135i
$76$	−2.08382	+	4.21840i	−0.239030	+	0.483884i
$77$	0.927176	−	2.65124i	0.105662	−	0.302137i
$78$	0.699953	−	2.99737i	0.0792541	−	0.339386i
$79$	−8.17894	−	4.72211i	−0.920202	−	0.531279i	−0.0365026	−	0.999334i	$-0.511622\pi$
$79$	−8.17894	−	4.72211i	−0.920202	−	0.531279i	−0.883700	+	0.468055i	$0.844955\pi$
$80$	−1.53571	+	3.69345i	−0.171698	+	0.412941i
$81$	2.85786	+	4.94996i	0.317540	+	0.549995i
$82$	−9.04171	−	8.47421i	−0.998490	−	0.935819i
$83$		−	13.7576i		−	1.51010i	−0.655669	−	0.755049i	$-0.727613\pi$
$83$		−	13.7576i		−	1.51010i	0.655669	−	0.755049i	$-0.272387\pi$
$84$	−3.71663	+	13.3438i	−0.405517	+	1.45593i
$85$		−	4.78776i		−	0.519305i
$86$	4.83043	−	5.15392i	0.520879	−	0.555761i
$87$	−4.02894	−	6.97833i	−0.431948	−	0.748156i
$88$	−0.492104	+	2.96202i	−0.0524585	+	0.315752i
$89$	10.1864	+	5.88110i	1.07975	+	0.623396i	0.930830	−	0.365453i	$-0.119086\pi$
$89$	10.1864	+	5.88110i	1.07975	+	0.623396i	0.148923	+	0.988849i	$0.452419\pi$
$90$	5.30552	+	1.23896i	0.559251	+	0.130598i
$91$	1.43519	+	1.66712i	0.150449	+	0.174761i
$92$	−1.35205	+	2.73704i	−0.140961	+	0.285356i
$93$	21.6976	+	12.5271i	2.24993	+	1.29900i
$94$	1.44243	+	4.76083i	0.148776	+	0.491043i
$95$	−2.03733	+	1.17625i	−0.209026	+	0.120681i
$96$	1.47625	−	14.7343i	0.150670	−	1.50382i
$97$			6.01605i			0.610837i	0.952218	+	0.305418i	$0.0987963\pi$
$97$			6.01605i			0.610837i	−0.952218	+	0.305418i	$0.901204\pi$
$98$	−6.13615	−	7.76837i	−0.619845	−	0.784724i
$99$	4.08976			0.411036
$100$	−1.66369	+	1.11002i	−0.166369	+	0.111002i
$101$	−6.35344	−	11.0045i	−0.632191	−	1.09499i	−0.987103	−	0.160087i	$-0.948822\pi$
$101$	−6.35344	−	11.0045i	−0.632191	−	1.09499i	0.354912	−	0.934900i	$-0.384511\pi$
$102$	5.13941	+	16.9629i	0.508878	+	1.67958i
$103$	0.337209	−	0.584063i	0.0332262	−	0.0575495i	−0.848934	−	0.528499i	$-0.822755\pi$
$103$	0.337209	−	0.584063i	0.0332262	−	0.0575495i	0.882160	+	0.470949i	$0.156088\pi$
$104$	−1.81636	−	1.49372i	−0.178108	−	0.146471i
$105$	−5.24880	+	4.51859i	−0.512230	+	0.440969i
$106$	−2.45483	+	10.5122i	−0.238434	+	1.02103i
$107$	−3.79703	+	6.57665i	−0.367073	+	0.635789i	−0.989107	−	0.147201i	$-0.952973\pi$
$107$	−3.79703	+	6.57665i	−0.367073	+	0.635789i	0.622033	+	0.782991i	$0.286307\pi$
$108$	−4.45389	+	0.288912i	−0.428576	+	0.0278006i
$109$	−2.84932	+	1.64505i	−0.272915	+	0.157568i	−0.630212	−	0.776423i	$-0.717032\pi$
$109$	−2.84932	+	1.64505i	−0.272915	+	0.157568i	0.357297	+	0.933991i	$0.383699\pi$
$110$	−1.02665	+	1.09540i	−0.0978874	+	0.104443i
$111$	30.4259			2.88790
$112$	7.88290	+	7.06116i	0.744864	+	0.667217i
$113$	15.0551			1.41626			0.708132	−	0.706080i	$-0.249538\pi$
$113$	15.0551			1.41626			0.708132	+	0.706080i	$0.249538\pi$
$114$	5.95558	−	6.35442i	0.557791	−	0.595146i
$115$	−1.32189	+	0.763194i	−0.123267	+	0.0711682i
$116$	−6.14348	+	0.398511i	−0.570408	+	0.0370008i
$117$	−1.60156	+	2.77399i	−0.148065	+	0.256455i
$118$	1.23086	−	5.27082i	0.113309	−	0.485219i
$119$	−11.9571	−	4.18157i	−1.09611	−	0.383324i
$120$	4.70286	−	5.71867i	0.429311	−	0.522040i
$121$	4.93652	−	8.55030i	0.448774	−	0.777300i
$122$	−5.34492	−	17.6412i	−0.483907	−	1.59716i
$123$	11.4690	+	19.8649i	1.03412	+	1.79116i
$124$	15.9231	−	10.6240i	1.42994	−	0.954060i
$125$	−1.00000			−0.0894427
$126$	7.72800	−	12.1681i	0.688465	−	1.08402i
$127$			9.06617i			0.804493i	0.915531	+	0.402246i	$0.131770\pi$
$127$			9.06617i			0.804493i	−0.915531	+	0.402246i	$0.868230\pi$
$128$	−9.59352	−	5.99703i	−0.847955	−	0.530068i
$129$	−11.3233	+	6.53751i	−0.996961	+	0.575596i
$130$	−0.340948	−	1.12532i	−0.0299031	−	0.0986969i
$131$	−10.0620	−	5.80928i	−0.879119	−	0.507559i	−0.00875088	−	0.999962i	$-0.502786\pi$
$131$	−10.0620	−	5.80928i	−0.879119	−	0.507559i	−0.870368	+	0.492402i	$0.836119\pi$
$132$	2.46154	−	4.98306i	0.214250	−	0.433719i
$133$	1.15824	+	6.11544i	0.100432	+	0.530276i
$134$	20.2954	+	4.73942i	1.75325	+	0.409424i
$135$	−1.93265	−	1.11581i	−0.166336	−	0.0960340i
$136$	13.3587	+	2.21940i	1.14550	+	0.190312i
$137$	−0.257971	−	0.446818i	−0.0220399	−	0.0381743i	0.854795	−	0.518966i	$-0.173683\pi$
$137$	−0.257971	−	0.446818i	−0.0220399	−	0.0381743i	−0.876835	+	0.480791i	$0.840349\pi$
$138$	3.86418	−	4.12296i	0.328941	−	0.350970i
$139$			9.35115i			0.793154i	0.918001	+	0.396577i	$0.129802\pi$
$139$			9.35115i			0.793154i	−0.918001	+	0.396577i	$0.870198\pi$
$140$	1.31916	+	5.12443i	0.111489	+	0.433094i
$141$		−	9.20796i		−	0.775450i
$142$	−10.3150	−	9.66755i	−0.865614	−	0.811283i
$143$	−0.441322	−	0.764392i	−0.0369052	−	0.0639217i
$144$	−5.91633	+	14.2290i	−0.493027	+	1.18575i
$145$	−2.66580	−	1.53910i	−0.221382	−	0.127815i
$146$	2.62211	−	11.2285i	0.217008	−	0.929280i
$147$	6.70066	+	17.0550i	0.552661	+	1.40667i
$148$	10.2955	−	20.8418i	0.846285	−	1.71319i
$149$	3.15569	+	1.82194i	0.258524	+	0.149259i	0.623661	−	0.781695i	$-0.285644\pi$
$149$	3.15569	+	1.82194i	0.258524	+	0.149259i	−0.365137	+	0.930954i	$0.618978\pi$
$150$	3.54298	−	1.07345i	0.289283	−	0.0876468i
$151$	14.1378	−	8.16245i	1.15052	−	0.664251i	0.201503	−	0.979488i	$-0.435417\pi$
$151$	14.1378	−	8.16245i	1.15052	−	0.664251i	0.949013	+	0.315237i	$0.102084\pi$
$152$	−2.33755	−	6.22979i	−0.189600	−	0.505303i
$153$		−	18.4449i		−	1.49118i
$154$	1.83904	+	3.52071i	0.148194	+	0.283707i
$155$	9.57096			0.768758
$156$	2.41594	+	3.62099i	0.193430	+	0.289911i
$157$	−7.61469	−	13.1890i	−0.607719	−	1.05260i	−0.991615	−	0.129224i	$-0.958751\pi$
$157$	−7.61469	−	13.1890i	−0.607719	−	1.05260i	0.383897	−	0.923376i	$-0.374582\pi$
$158$	12.7823	−	3.87278i	1.01691	−	0.308102i
$159$	9.99086	−	17.3047i	0.792327	−	1.37235i
$160$	−2.32595	−	5.15655i	−0.183882	−	0.407661i
$161$	0.751504	+	3.96790i	0.0592268	+	0.312715i
$162$	−7.87147	−	1.83816i	−0.618441	−	0.144420i
$163$	−2.76559	+	4.79015i	−0.216618	+	0.375193i	−0.953772	−	0.300532i	$-0.902836\pi$
$163$	−2.76559	+	4.79015i	−0.216618	+	0.375193i	0.737154	+	0.675725i	$0.236169\pi$
$164$	17.4884	−	1.13442i	1.36561	−	0.0885834i
$165$	2.40663	−	1.38947i	0.187356	−	0.108170i
$166$	14.1959	+	13.3049i	1.10182	+	1.03266i
$167$	11.1473			0.862608			0.431304	−	0.902207i	$-0.358054\pi$
$167$	11.1473			0.862608			0.431304	+	0.902207i	$0.358054\pi$
$168$	−10.1746	−	16.7397i	−0.784986	−	1.29150i
$169$	−12.3087			−0.946824
$170$	4.94029	+	4.63021i	0.378903	+	0.355121i
$171$	−7.84883	+	4.53153i	−0.600215	+	0.346534i
$172$	0.646638	+	9.96864i	0.0493057	+	0.760101i
$173$	−0.910856	+	1.57765i	−0.0692511	+	0.119946i	−0.898572	−	0.438826i	$-0.855394\pi$
$173$	−0.910856	+	1.57765i	−0.0692511	+	0.119946i	0.829321	+	0.558773i	$0.188728\pi$
$174$	11.0970	+	2.59140i	0.841262	+	0.196453i
$175$	−0.873389	+	2.49744i	−0.0660220	+	0.188789i
$176$	−2.58047	−	3.37233i	−0.194510	−	0.254199i
$177$	−5.00943	+	8.67659i	−0.376532	+	0.652172i
$178$	−15.9196	+	4.82332i	−1.19323	+	0.361523i
$179$	−1.28415	−	2.22422i	−0.0959822	−	0.166246i	0.814036	−	0.580815i	$-0.197266\pi$
$179$	−1.28415	−	2.22422i	−0.0959822	−	0.166246i	−0.910018	+	0.414569i	$0.863933\pi$
$180$	−6.40936	+	4.27636i	−0.477726	+	0.318741i
$181$	−11.7984			−0.876969			−0.438484	−	0.898739i	$-0.644485\pi$
$181$	−11.7984			−0.876969			−0.438484	+	0.898739i	$0.644485\pi$
$182$	−3.10819	−	0.131344i	−0.230394	−	0.00973589i
$183$			34.1200i			2.52223i
$184$	−1.51668	−	4.04210i	−0.111811	−	0.297987i
$185$	10.0658	−	5.81151i	0.740055	−	0.427271i
$186$	−33.9097	+	10.2739i	−2.48638	+	0.753322i
$187$	4.40167	+	2.54131i	0.321882	+	0.185839i
$188$	−6.30747	−	3.11578i	−0.460020	−	0.227242i
$189$	−4.47463	+	3.85212i	−0.325481	+	0.280201i
$190$	0.756562	−	3.23979i	0.0548868	−	0.235039i
$191$	−1.34645	−	0.777371i	−0.0974254	−	0.0562486i	0.450496	−	0.892779i	$-0.351247\pi$
$191$	−1.34645	−	0.777371i	−0.0974254	−	0.0562486i	−0.547921	+	0.836530i	$0.684581\pi$
$192$	13.7761	+	15.7728i	0.994203	+	1.13830i
$193$	−1.46380	−	2.53537i	−0.105367	−	0.182500i	0.808521	−	0.588467i	$-0.200268\pi$
$193$	−1.46380	−	2.53537i	−0.105367	−	0.182500i	−0.913888	+	0.405967i	$0.866935\pi$
$194$	−6.20771	−	5.81808i	−0.445687	−	0.417713i
$195$			2.17648i			0.155861i
$196$	13.9501	+	1.18110i	0.996435	+	0.0843644i
$197$			8.32978i			0.593473i	0.954959	+	0.296736i	$0.0958982\pi$
$197$			8.32978i			0.593473i	−0.954959	+	0.296736i	$0.904102\pi$
$198$	−3.95518	+	4.22005i	−0.281082	+	0.299906i
$199$	−8.17280	−	14.1557i	−0.579355	−	1.00347i	−0.995553	−	0.0941979i	$-0.969971\pi$
$199$	−8.17280	−	14.1557i	−0.579355	−	1.00347i	0.416199	−	0.909274i	$-0.363362\pi$
$200$	0.463556	−	2.79018i	0.0327784	−	0.197296i
$201$	−33.4093	−	19.2889i	−2.35651	−	1.36053i
$202$	17.4994	+	4.08651i	1.23126	+	0.287526i
$203$	−6.17208	+	5.31343i	−0.433195	+	0.372929i
$204$	−22.4736	−	11.1016i	−1.57347	−	0.777267i
$205$	7.58860	+	4.38128i	0.530010	+	0.306002i
$206$	0.276558	+	0.912796i	0.0192687	+	0.0635975i
$207$	−5.09259	+	2.94021i	−0.353960	+	0.204359i
$208$	3.29789	−	0.429658i	0.228667	−	0.0297914i
$209$		−	2.49739i		−	0.172748i
$210$	0.413528	−	9.78591i	0.0285362	−	0.675292i
$211$	11.9709			0.824112			0.412056	−	0.911159i	$-0.364811\pi$
$211$	11.9709			0.824112			0.412056	+	0.911159i	$0.364811\pi$
$212$	−8.47304	−	12.6993i	−0.581931	−	0.872192i
$213$	13.0841	+	22.6623i	0.896506	+	1.55279i
$214$	−3.11409	−	10.2782i	−0.212875	−	0.702606i
$215$	−2.49740	+	4.32562i	−0.170321	+	0.295005i
$216$	4.00921	−	4.87519i	0.272792	−	0.331715i
$217$	8.35917	−	23.9029i	0.567458	−	1.62263i
$218$	1.05809	−	4.53101i	0.0716631	−	0.306879i
$219$	−10.6717	+	18.4839i	−0.721125	+	1.24903i
$220$	−0.137435	−	2.11872i	−0.00926589	−	0.142844i
$221$	−3.44742	+	1.99037i	−0.231898	+	0.133887i
$222$	−29.4247	+	31.3952i	−1.97486	+	2.10711i
$223$	−26.5000			−1.77457			−0.887285	−	0.461222i	$-0.847411\pi$
$223$	−26.5000			−1.77457			−0.887285	+	0.461222i	$0.847411\pi$
$224$	−14.9096	+	1.30523i	−0.996190	+	0.0872097i
$225$	−3.85251			−0.256834
$226$	−14.5597	+	15.5347i	−0.968495	+	1.03335i
$227$	−8.49854	+	4.90663i	−0.564068	+	0.325665i	−0.754777	−	0.655982i	$-0.772255\pi$
$227$	−8.49854	+	4.90663i	−0.564068	+	0.325665i	0.190709	+	0.981647i	$0.438921\pi$
$228$	0.797259	+	12.2906i	0.0527998	+	0.813967i
$229$	10.1949	−	17.6581i	0.673698	−	1.16688i	−0.303149	−	0.952943i	$-0.598038\pi$
$229$	10.1949	−	17.6581i	0.673698	−	1.16688i	0.976848	−	0.213937i	$-0.0686287\pi$
$230$	0.490883	−	2.10208i	0.0323679	−	0.138607i
$231$	−1.36819	−	7.22397i	−0.0900202	−	0.475302i
$232$	5.53011	−	6.72460i	0.363070	−	0.441491i
$233$	9.40026	−	16.2817i	0.615831	−	1.06665i	−0.374407	−	0.927265i	$-0.622154\pi$
$233$	9.40026	−	16.2817i	0.615831	−	1.06665i	0.990238	−	0.139387i	$-0.0445131\pi$
$234$	−1.31350	−	4.33529i	−0.0858664	−	0.283407i
$235$	−1.75877	−	3.04628i	−0.114729	−	0.198717i
$236$	4.24839	+	6.36744i	0.276547	+	0.414485i
$237$	−24.7224			−1.60589
$238$	15.8784	−	8.29408i	1.02925	−	0.537626i
$239$			17.6775i			1.14346i	0.820442	+	0.571730i	$0.193727\pi$
$239$			17.6775i			1.14346i	−0.820442	+	0.571730i	$0.806273\pi$
$240$	1.35275	+	10.3832i	0.0873194	+	0.670231i
$241$	2.91495	−	1.68295i	0.187768	−	0.108408i	−0.403169	−	0.915126i	$-0.632091\pi$
$241$	2.91495	−	1.68295i	0.187768	−	0.108408i	0.590937	+	0.806717i	$0.298758\pi$
$242$	4.04863	+	13.3627i	0.260255	+	0.858988i
$243$	18.7556	+	10.8285i	1.20317	+	0.694651i
$244$	23.3723	+	11.5455i	1.49626	+	0.739126i
$245$	5.47438	+	4.36247i	0.349746	+	0.278708i
$246$	−31.5893	−	7.37681i	−2.01406	−	0.470328i
$247$	1.69392	+	0.977985i	0.107782	+	0.0622277i
$248$	−4.43668	+	26.7047i	−0.281730	+	1.69575i
$249$	−18.0069	−	31.1888i	−1.14114	−	1.97651i
$250$	0.967093	−	1.03186i	0.0611643	−	0.0652604i
$251$			11.8507i			0.748011i	0.927426	+	0.374006i	$0.122016\pi$
$251$			11.8507i			0.748011i	−0.927426	+	0.374006i	$0.877984\pi$
$252$	5.08207	+	19.7419i	0.320141	+	1.24362i
$253$		−	1.62039i		−	0.101873i
$254$	−9.35501	−	8.76783i	−0.586985	−	0.550143i
$255$	−6.26653	−	10.8539i	−0.392425	−	0.679700i
$256$	15.4659	−	4.09946i	0.966619	−	0.256216i
$257$	8.52403	+	4.92135i	0.531714	+	0.306985i	0.741714	−	0.670716i	$-0.234013\pi$
$257$	8.52403	+	4.92135i	0.531714	+	0.306985i	−0.210000	+	0.977701i	$0.567346\pi$
$258$	4.20490	−	18.0064i	0.261786	−	1.12103i
$259$	−5.72250	−	30.2145i	−0.355579	−	1.87744i
$260$	1.49090	+	0.736477i	0.0924615	+	0.0456744i
$261$	−10.2700	−	5.92938i	−0.635697	−	0.367020i
$262$	15.7252	−	4.76441i	0.971507	−	0.294346i
$263$	7.04488	−	4.06736i	0.434406	−	0.250804i	−0.266816	−	0.963747i	$-0.585972\pi$
$263$	7.04488	−	4.06736i	0.434406	−	0.250804i	0.701222	+	0.712943i	$0.252638\pi$
$264$	2.76127	+	7.35904i	0.169944	+	0.452918i
$265$		−	7.63323i		−	0.468905i
$266$	−7.43039	−	4.71906i	−0.455586	−	0.289344i
$267$	30.7903			1.88433
$268$	−24.5179	+	16.3585i	−1.49767	+	0.999254i
$269$	−12.5033	−	21.6564i	−0.762342	−	1.32041i	−0.941640	−	0.336620i	$-0.890716\pi$
$269$	−12.5033	−	21.6564i	−0.762342	−	1.32041i	0.179299	−	0.983795i	$-0.442617\pi$
$270$	3.02041	−	0.915121i	0.183816	−	0.0556925i
$271$	−4.77233	+	8.26592i	−0.289898	+	0.502119i	−0.973785	−	0.227469i	$-0.926955\pi$
$271$	−4.77233	+	8.26592i	−0.289898	+	0.502119i	0.683887	+	0.729588i	$0.260288\pi$
$272$	−15.2092	+	11.6379i	−0.922194	+	0.705654i
$273$	5.43563	+	1.90092i	0.328980	+	0.115049i
$274$	0.710535	+	0.165926i	0.0429250	+	0.0100239i
$275$	0.530792	−	0.919359i	0.0320080	−	0.0554395i
$276$	0.517289	+	7.97458i	0.0311371	+	0.480013i
$277$	1.14340	−	0.660142i	0.0687002	−	0.0396641i	−0.465256	−	0.885176i	$-0.654038\pi$
$277$	1.14340	−	0.660142i	0.0687002	−	0.0396641i	0.533957	+	0.845512i	$0.320705\pi$
$278$	−9.64906	−	9.04343i	−0.578712	−	0.542389i
$279$	36.8722			2.20748
$280$	−6.56344	−	3.59462i	−0.392241	−	0.214819i
$281$	27.6475			1.64931			0.824656	−	0.565634i	$-0.191369\pi$
$281$	27.6475			1.64931			0.824656	+	0.565634i	$0.191369\pi$
$282$	9.50131	+	8.90496i	0.565795	+	0.530282i
$283$	0.646465	−	0.373237i	0.0384284	−	0.0221866i	−0.480663	−	0.876906i	$-0.659604\pi$
$283$	0.646465	−	0.373237i	0.0384284	−	0.0221866i	0.519091	+	0.854719i	$0.326271\pi$
$284$	19.9511	−	1.29417i	1.18388	−	0.0767950i
$285$	−3.07912	+	5.33318i	−0.182391	+	0.315911i
$286$	1.21554	+	0.283857i	0.0718766	+	0.0167848i
$287$	17.5698	−	15.1255i	1.03711	−	0.892829i
$288$	−8.96072	−	19.8656i	−0.528015	−	1.17059i
$289$	2.96131	−	5.12914i	0.174195	−	0.301714i
$290$	4.16620	−	1.26227i	0.244648	−	0.0741232i
$291$	7.87419	+	13.6385i	0.461593	+	0.799503i
$292$	9.05043	+	13.5647i	0.529636	+	0.793813i
$293$	−9.44068			−0.551530			−0.275765	−	0.961225i	$-0.588931\pi$
$293$	−9.44068			−0.551530			−0.275765	+	0.961225i	$0.588931\pi$
$294$	−24.0785	−	9.57967i	−1.40429	−	0.558697i
$295$			3.82731i			0.222835i
$296$	11.5491	+	30.7795i	0.671278	+	1.78902i
$297$	2.05167	−	1.18453i	0.119050	−	0.0687335i
$298$	−4.93183	+	1.49424i	−0.285693	+	0.0865591i
$299$	1.09907	+	0.634550i	0.0635610	+	0.0366970i
$300$	−2.31875	+	4.69398i	−0.133873	+	0.271007i
$301$	8.62176	+	10.0150i	0.496950	+	0.577257i
$302$	−5.25006	+	22.4820i	−0.302107	+	1.29370i
$303$	−28.8068	−	16.6316i	−1.65491	−	0.955460i
$304$	8.68888	+	3.61277i	0.498342	+	0.207207i
$305$	6.51711	+	11.2880i	0.373168	+	0.646347i
$306$	19.0325	+	17.8379i	1.08801	+	1.01972i
$307$		−	10.3689i		−	0.591782i	−0.955222	−	0.295891i	$-0.904384\pi$
$307$		−	10.3689i		−	0.591782i	0.955222	−	0.295891i	$-0.0956165\pi$
$308$	−5.41140	−	1.50723i	−0.308343	−	0.0858823i
$309$		−	1.76544i		−	0.100433i
$310$	−9.25601	+	9.87588i	−0.525706	+	0.560912i
$311$	−10.3775	−	17.9743i	−0.588454	−	1.01923i	−0.994435	−	0.105350i	$-0.966404\pi$
$311$	−10.3775	−	17.9743i	−0.588454	−	1.01923i	0.405981	−	0.913881i	$-0.366930\pi$
$312$	−6.07279	−	1.00892i	−0.343804	−	0.0571190i
$313$	0.926714	+	0.535039i	0.0523810	+	0.0302422i	0.525962	−	0.850508i	$-0.323705\pi$
$313$	0.926714	+	0.535039i	0.0523810	+	0.0302422i	−0.473581	+	0.880750i	$0.657039\pi$
$314$	20.9733	+	4.89774i	1.18359	+	0.276396i
$315$	−3.36473	+	9.62139i	−0.189581	+	0.542104i
$316$	−8.36555	+	16.9349i	−0.470599	+	0.952663i
$317$	9.56540	+	5.52258i	0.537246	+	0.310179i	0.743962	−	0.668222i	$-0.232944\pi$
$317$	9.56540	+	5.52258i	0.537246	+	0.310179i	−0.206716	+	0.978401i	$0.566278\pi$
$318$	8.19388	+	27.0444i	0.459490	+	1.51657i
$319$	2.82997	−	1.63388i	0.158448	−	0.0914799i
$320$	7.57023	+	2.58681i	0.423189	+	0.144607i
$321$			19.8792i			1.10955i
$322$	−4.82109	−	3.06189i	−0.268669	−	0.170632i
$323$	−11.2632			−0.626704
$324$	9.50917	−	6.34457i	0.528287	−	0.352476i
$325$	0.415720	+	0.720048i	0.0230600	+	0.0399411i
$326$	−2.26817	−	7.48622i	−0.125622	−	0.414623i
$327$	−4.30631	+	7.45874i	−0.238139	+	0.412469i
$328$	−15.7423	+	19.1426i	−0.869223	+	1.05697i
$329$	−9.14398	+	1.73183i	−0.504124	+	0.0954789i
$330$	−0.893702	+	3.82705i	−0.0491967	+	0.210672i
$331$	12.8859	−	22.3190i	0.708271	−	1.22676i	−0.257227	−	0.966351i	$-0.582809\pi$
$331$	12.8859	−	22.3190i	0.708271	−	1.22676i	0.965498	−	0.260410i	$-0.0838578\pi$
$332$	−27.4576	+	1.78110i	−1.50693	+	0.0977504i
$333$	38.7787	−	22.3889i	2.12506	−	1.22690i
$334$	−10.7805	+	11.5025i	−0.589884	+	0.629388i
$335$	−14.7371			−0.805174
$336$	27.1128	+	5.69014i	1.47912	+	0.310423i
$337$	−16.8577			−0.918299			−0.459149	−	0.888359i	$-0.651846\pi$
$337$	−16.8577			−0.918299			−0.459149	+	0.888359i	$0.651846\pi$
$338$	11.9037	−	12.7008i	0.647474	−	0.690835i
$339$	34.1302	−	19.7051i	1.85370	−	1.07023i
$340$	−9.55543	+	0.619835i	−0.518216	+	0.0336152i
$341$	−5.08019	+	8.79916i	−0.275108	+	0.476501i
$342$	2.91466	−	12.4813i	0.157607	−	0.674911i
$343$	15.6763	−	9.86180i	0.846438	−	0.532487i
$344$	−10.9116	−	8.97336i	−0.588313	−	0.483811i
$345$	−1.99783	+	3.46035i	−0.107560	+	0.186299i
$346$	−0.747028	−	2.46561i	−0.0401604	−	0.132552i
$347$	−17.5896	−	30.4662i	−0.944262	−	1.63551i	−0.757223	−	0.653157i	$-0.773444\pi$
$347$	−17.5896	−	30.4662i	−0.944262	−	1.63551i	−0.187039	−	0.982352i	$-0.559889\pi$
$348$	−13.4058	+	8.94442i	−0.718626	+	0.479471i
$349$	−14.2781			−0.764290			−0.382145	−	0.924102i	$-0.624815\pi$
$349$	−14.2781			−0.764290			−0.382145	+	0.924102i	$0.624815\pi$
$350$	−1.73235	−	3.31647i	−0.0925981	−	0.177273i
$351$			1.85546i			0.0990374i
$352$	5.97531	+	0.598675i	0.318485	+	0.0319095i
$353$	−21.0137	+	12.1322i	−1.11844	+	0.645734i	−0.941003	−	0.338398i	$-0.890115\pi$
$353$	−21.0137	+	12.1322i	−1.11844	+	0.645734i	−0.177441	+	0.984132i	$0.556782\pi$
$354$	−4.10842	−	13.5601i	−0.218360	−	0.720710i
$355$	8.65723	+	4.99825i	0.459478	+	0.265280i
$356$	10.4188	−	21.0914i	0.552195	−	1.11784i
$357$	−32.5801	+	6.17054i	−1.72432	+	0.326580i
$358$	3.53698	+	0.825963i	0.186935	+	0.0436535i
$359$	7.32290	+	4.22788i	0.386488	+	0.223139i	0.680637	−	0.732620i	$-0.261703\pi$
$359$	7.32290	+	4.22788i	0.386488	+	0.223139i	−0.294149	+	0.955759i	$0.595036\pi$
$360$	1.78585	−	10.7492i	0.0941227	−	0.566532i
$361$	−6.73285	−	11.6616i	−0.354361	−	0.613771i
$362$	11.4102	−	12.1743i	0.599704	−	0.639866i
$363$		−	25.8449i		−	1.35651i
$364$	3.14144	−	3.08019i	0.164656	−	0.161446i
$365$			8.15339i			0.426768i
$366$	−35.2070	−	32.9972i	−1.84030	−	1.72479i
$367$	11.3411	+	19.6433i	0.592000	+	1.02537i	0.993963	+	0.109718i	$0.0349947\pi$
$367$	11.3411	+	19.6433i	0.592000	+	1.02537i	−0.401963	+	0.915656i	$0.631672\pi$
$368$	5.63764	+	2.34409i	0.293882	+	0.122194i
$369$	29.2351	+	16.8789i	1.52192	+	0.878680i
$370$	−3.73794	+	16.0068i	−0.194326	+	0.832153i
$371$	−19.0635	−	6.66677i	−0.989728	−	0.346122i
$372$	22.1926	−	44.9259i	1.15063	−	2.32930i
$373$	−17.9804	−	10.3810i	−0.930992	−	0.537508i	−0.0438667	−	0.999037i	$-0.513968\pi$
$373$	−17.9804	−	10.3810i	−0.930992	−	0.537508i	−0.887125	+	0.461529i	$0.847301\pi$
$374$	−6.87909	+	2.08422i	−0.355709	+	0.107772i
$375$	−2.26702	+	1.30886i	−0.117068	+	0.0675895i
$376$	9.31496	−	3.49517i	0.480382	−	0.180249i
$377$			2.55934i			0.131812i
$378$	0.352535	−	8.34254i	0.0181324	−	0.429094i
$379$	−12.4789			−0.640997			−0.320498	−	0.947249i	$-0.603850\pi$
$379$	−12.4789			−0.640997			−0.320498	+	0.947249i	$0.603850\pi$
$380$	2.61133	+	3.91384i	0.133959	+	0.200776i
$381$	11.8664	+	20.5532i	0.607934	+	1.05297i
$382$	2.10427	−	0.637551i	0.107664	−	0.0326200i
$383$	−2.86705	+	4.96588i	−0.146499	+	0.253744i	−0.929931	−	0.367733i	$-0.880134\pi$
$383$	−2.86705	+	4.96588i	−0.146499	+	0.253744i	0.783432	+	0.621478i	$0.213467\pi$
$384$	−29.5980	−	1.03877i	−1.51042	−	0.0530097i
$385$	−1.83245	−	2.12858i	−0.0933905	−	0.108482i
$386$	4.03178	+	0.941509i	0.205212	+	0.0479216i
$387$	−9.62123	+	16.6645i	−0.489075	+	0.847102i
$388$	12.0069	−	0.778852i	0.609556	−	0.0395402i
$389$	10.6658	−	6.15789i	0.540776	−	0.312217i	−0.204617	−	0.978842i	$-0.565595\pi$
$389$	10.6658	−	6.15789i	0.540776	−	0.312217i	0.745393	+	0.666625i	$0.232262\pi$
$390$	−2.24582	−	2.10486i	−0.113722	−	0.106584i
$391$	−7.30797			−0.369580
$392$	−14.7098	+	13.2523i	−0.742955	+	0.669341i
$393$	−30.4143			−1.53420
$394$	−8.59516	−	8.05568i	−0.433018	−	0.405839i
$395$	−8.17894	+	4.72211i	−0.411527	+	0.237595i
$396$	−0.529470	−	8.16237i	−0.0266069	−	0.410174i
$397$	−4.71322	+	8.16353i	−0.236550	+	0.409716i	−0.959722	−	0.280952i	$-0.909350\pi$
$397$	−4.71322	+	8.16353i	−0.236550	+	0.409716i	0.723172	+	0.690668i	$0.242683\pi$
$398$	22.5105	+	5.25671i	1.12835	+	0.263495i
$399$	10.6300	+	12.3478i	0.532167	+	0.618165i
$400$	2.43077	+	3.17669i	0.121538	+	0.158834i
$401$	−4.36749	+	7.56471i	−0.218102	+	0.377764i	−0.954228	−	0.299081i	$-0.903320\pi$
$401$	−4.36749	+	7.56471i	−0.218102	+	0.377764i	0.736126	+	0.676845i	$0.236653\pi$
$402$	52.2133	−	15.8195i	2.60416	−	0.789007i
$403$	−3.97884	−	6.89155i	−0.198200	−	0.343293i
$404$	−21.1403	+	14.1049i	−1.05177	+	0.701745i
$405$	5.71572			0.284016
$406$	0.486269	−	11.5073i	0.0241331	−	0.571097i
$407$			12.3388i			0.611613i
$408$	33.1894	−	12.4533i	1.64312	−	0.616532i
$409$	−1.47110	+	0.849342i	−0.0727414	+	0.0419973i	−0.535930	−	0.844263i	$-0.680039\pi$
$409$	−1.47110	+	0.849342i	−0.0727414	+	0.0419973i	0.463188	+	0.886260i	$0.346705\pi$
$410$	−11.8597	+	3.59325i	−0.585710	+	0.177458i
$411$	−1.16965	−	0.675297i	−0.0576945	−	0.0333100i
$412$	−1.20933	−	0.597390i	−0.0595796	−	0.0294313i
$413$	9.55846	+	3.34273i	0.470341	+	0.164485i
$414$	1.89113	−	8.09829i	0.0929440	−	0.398009i
$415$	−11.9145	−	6.87882i	−0.584858	−	0.337668i
$416$	−2.74602	+	3.81847i	−0.134635	+	0.187216i
$417$	12.2394	+	21.1992i	0.599366	+	1.03813i
$418$	2.57695	+	2.41521i	0.126043	+	0.118132i
$419$			31.2350i			1.52593i	0.646441	+	0.762964i	$0.276257\pi$
$419$			31.2350i			1.52593i	−0.646441	+	0.762964i	$0.723743\pi$
$420$	9.69775	+	9.89059i	0.473202	+	0.482611i
$421$		−	5.19927i		−	0.253397i	−0.991941	−	0.126698i	$-0.959562\pi$
$421$		−	5.19927i		−	0.253397i	0.991941	−	0.126698i	$-0.0404380\pi$
$422$	−11.5770	+	12.3523i	−0.563559	+	0.601300i
$423$	−6.77567	−	11.7358i	−0.329444	−	0.570614i
$424$	21.2981	+	3.53843i	1.03433	+	0.171841i
$425$	−4.14632	−	2.39388i	−0.201126	−	0.116120i
$426$	−36.0378	−	8.41562i	−1.74604	−	0.407738i
$427$	33.8829	−	6.41729i	1.63971	−	0.310554i
$428$	13.6173	+	6.72671i	0.658217	+	0.325148i
$429$	−2.00097	−	1.15526i	−0.0966078	−	0.0557766i
$430$	−2.04821	−	6.76023i	−0.0987734	−	0.326007i
$431$	6.96178	−	4.01939i	0.335337	−	0.193607i	−0.322871	−	0.946443i	$-0.604648\pi$
$431$	6.96178	−	4.01939i	0.335337	−	0.193607i	0.658208	+	0.752836i	$0.271315\pi$
$432$	1.15322	+	8.85170i	0.0554845	+	0.425878i
$433$			1.55972i			0.0749554i	0.999297	+	0.0374777i	$0.0119323\pi$
$433$			1.55972i			0.0749554i	−0.999297	+	0.0374777i	$0.988068\pi$
$434$	16.5803	+	31.7418i	0.795879	+	1.52365i
$435$	−8.05788			−0.386346
$436$	3.65209	+	5.47371i	0.174903	+	0.262143i
$437$	1.79542	+	3.10976i	0.0858866	+	0.148760i
$438$	−8.75225	−	28.8873i	−0.418198	−	1.38029i
$439$	−14.5960	+	25.2810i	−0.696628	+	1.20659i	0.273001	+	0.962014i	$0.411984\pi$
$439$	−14.5960	+	25.2810i	−0.696628	+	1.20659i	−0.969629	+	0.244581i	$0.921350\pi$
$440$	2.31913	+	1.90718i	0.110560	+	0.0909214i
$441$	21.0901	+	16.8064i	1.00429	+	0.800306i
$442$	1.28020	−	5.48211i	0.0608927	−	0.260758i
$443$	0.172721	−	0.299162i	0.00820624	−	0.0142136i	−0.861893	−	0.507090i	$-0.830721\pi$
$443$	0.172721	−	0.299162i	0.00820624	−	0.0142136i	0.870099	+	0.492876i	$0.164055\pi$
$444$	−3.93901	−	60.7242i	−0.186937	−	2.88184i
$445$	10.1864	−	5.88110i	0.482880	−	0.278791i
$446$	25.6279	−	27.3442i	1.21352	−	1.29479i
$447$	9.53869			0.451164
$448$	13.0722	−	16.6469i	0.617601	−	0.786491i
$449$	31.8546			1.50331			0.751656	−	0.659555i	$-0.229255\pi$
$449$	31.8546			1.50331			0.751656	+	0.659555i	$0.229255\pi$
$450$	3.72573	−	3.97524i	0.175633	−	0.187395i
$451$	−8.05594	+	4.65110i	−0.379339	+	0.219012i
$452$	−1.94907	−	30.0470i	−0.0916764	−	1.41329i
$453$	21.3671	−	37.0089i	1.00391	−	1.73883i
$454$	3.15593	−	13.5145i	0.148115	−	0.634265i
$455$	2.16136	−	0.409353i	0.101326	−	0.0191907i
$456$	−13.4532	−	11.0635i	−0.630004	−	0.518097i
$457$	−8.96314	+	15.5246i	−0.419278	+	0.726211i	−0.995867	−	0.0908235i	$-0.971050\pi$
$457$	−8.96314	+	15.5246i	−0.419278	+	0.726211i	0.576589	+	0.817034i	$0.304383\pi$
$458$	8.36123	+	27.5967i	0.390695	+	1.28951i
$459$	−5.34225	−	9.25304i	−0.249355	−	0.431895i
$460$	1.69432	+	2.53943i	0.0789982	+	0.118402i
$461$	−7.34814			−0.342237			−0.171119	−	0.985250i	$-0.554738\pi$
$461$	−7.34814			−0.342237			−0.171119	+	0.985250i	$0.554738\pi$
$462$	8.77727	+	5.57447i	0.408356	+	0.259348i
$463$		−	38.4082i		−	1.78498i	−0.451069	−	0.892489i	$-0.648957\pi$
$463$		−	38.4082i		−	1.78498i	0.451069	−	0.892489i	$-0.351043\pi$
$464$	1.59070	+	12.2096i	0.0738464	+	0.566816i
$465$	21.6976	−	12.5271i	1.00620	−	0.580930i
$466$	7.70951	+	25.4457i	0.357136	+	1.17875i
$467$	1.63140	+	0.941892i	0.0754924	+	0.0435855i	0.537271	−	0.843410i	$-0.319455\pi$
$467$	1.63140	+	0.941892i	0.0754924	+	0.0435855i	−0.461779	+	0.886995i	$0.652789\pi$
$468$	5.74369	+	2.83728i	0.265502	+	0.131153i
$469$	−12.8712	+	36.8050i	−0.594338	+	1.69950i
$470$	4.84422	+	1.13123i	0.223447	+	0.0521799i
$471$	−34.5253	−	19.9332i	−1.59084	−	0.918474i
$472$	−10.6789	−	1.77417i	−0.491536	−	0.0816630i
$473$	−2.65120	−	4.59201i	−0.121902	−	0.211141i
$474$	23.9089	−	25.5100i	1.09817	−	1.17171i
$475$			2.35251i			0.107941i
$476$	−6.79761	+	24.4054i	−0.311568	+	1.11862i
$477$		−	29.4070i		−	1.34646i
$478$	−18.2406	−	17.0957i	−0.834307	−	0.781941i
$479$	−2.87010	−	4.97116i	−0.131138	−	0.227138i	0.792977	−	0.609251i	$-0.208530\pi$
$479$	−2.87010	−	4.97116i	−0.131138	−	0.227138i	−0.924116	+	0.382113i	$0.875197\pi$
$480$	−12.0222	−	8.64565i	−0.548735	−	0.394618i
$481$	−8.36914	−	4.83192i	−0.381600	−	0.220317i
$482$	−1.08246	+	4.63538i	−0.0493049	+	0.211136i
$483$	6.89712	+	8.01170i	0.313830	+	0.364545i
$484$	−17.7038	−	8.74539i	−0.804720	−	0.397518i
$485$	5.21005	+	3.00802i	0.236576	+	0.136587i
$486$	−29.3119	+	8.88090i	−1.32962	+	0.402846i
$487$	−8.46493	+	4.88723i	−0.383583	+	0.221461i	−0.679376	−	0.733790i	$-0.737749\pi$
$487$	−8.46493	+	4.88723i	−0.383583	+	0.221461i	0.295793	+	0.955252i	$0.404416\pi$
$488$	−34.5165	+	12.9513i	−1.56249	+	0.586278i
$489$			14.4791i			0.654769i
$490$	−9.79569	+	1.42988i	−0.442524	+	0.0645952i
$491$	−6.81442			−0.307530			−0.153765	−	0.988107i	$-0.549140\pi$
$491$	−6.81442			−0.307530			−0.153765	+	0.988107i	$0.549140\pi$
$492$	38.1616	−	25.4616i	1.72046	−	1.14790i
$493$	−7.36883	−	12.7632i	−0.331875	−	0.574825i
$494$	−2.64732	+	0.802082i	−0.119109	+	0.0360874i
$495$	2.04488	−	3.54184i	0.0919105	−	0.159194i
$496$	−23.2648	−	30.4040i	−1.04462	−	1.36518i
$497$	20.0440	−	17.2555i	0.899094	−	0.774013i
$498$	49.5968	+	11.5820i	2.22249	+	0.519000i
$499$	−10.3761	+	17.9719i	−0.464497	+	0.804532i	−0.999179	−	0.0405216i	$-0.987098\pi$
$499$	−10.3761	+	17.9719i	−0.464497	+	0.804532i	0.534682	+	0.845053i	$0.320431\pi$
$500$	0.129462	+	1.99581i	0.00578973	+	0.0892551i
$501$	25.2713	−	14.5904i	1.12904	−	0.651850i
$502$	−12.2283	−	11.4608i	−0.545774	−	0.511518i
$503$	15.9862			0.712789			0.356395	−	0.934336i	$-0.384006\pi$
$503$	15.9862			0.712789			0.356395	+	0.934336i	$0.384006\pi$
$504$	−25.2857	−	13.8483i	−1.12631	−	0.616851i
$505$	−12.7069			−0.565449
$506$	1.67201	+	1.56707i	0.0743300	+	0.0696647i
$507$	−27.9041	+	16.1104i	−1.23926	+	0.715489i
$508$	18.0943	−	1.17373i	0.802806	−	0.0520758i
$509$	−4.40064	+	7.62213i	−0.195055	+	0.337845i	−0.946919	−	0.321474i	$-0.895822\pi$
$509$	−4.40064	+	7.62213i	−0.195055	+	0.337845i	0.751864	+	0.659319i	$0.229155\pi$
$510$	17.2600	+	4.03060i	0.764287	+	0.178478i
$511$	20.3626	+	7.12108i	0.900787	+	0.315018i
$512$	−10.7269	+	19.9232i	−0.474067	+	0.880489i
$513$	−2.62496	+	4.54657i	−0.115895	+	0.200736i
$514$	−13.3217	+	4.03618i	−0.587593	+	0.178028i
$515$	−0.337209	−	0.584063i	−0.0148592	−	0.0257369i
$516$	14.5135	+	21.7527i	0.638923	+	0.957611i
$517$	3.73417			0.164228
$518$	36.7113	+	23.3154i	1.61300	+	1.02442i
$519$			4.76875i			0.209325i
$520$	−2.20178	+	0.826152i	−0.0965542	+	0.0362291i
$521$	−18.9597	+	10.9464i	−0.830641	+	0.479571i	−0.854072	−	0.520155i	$-0.825874\pi$
$521$	−18.9597	+	10.9464i	−0.830641	+	0.479571i	0.0234312	+	0.999725i	$0.492541\pi$
$522$	16.0503	−	4.86291i	0.702503	−	0.212844i
$523$	−2.23839	−	1.29233i	−0.0978779	−	0.0565099i	0.450262	−	0.892896i	$-0.351331\pi$
$523$	−2.23839	−	1.29233i	−0.0978779	−	0.0565099i	−0.548140	+	0.836387i	$0.684664\pi$
$524$	−10.2916	+	20.8338i	−0.449588	+	0.910130i
$525$	1.28882	+	6.80489i	0.0562486	+	0.296990i
$526$	−2.61611	+	11.2028i	−0.114068	+	0.488467i
$527$	39.6843	+	22.9117i	1.72867	+	0.998050i
$528$	−10.2639	−	4.26765i	−0.446679	−	0.185725i
$529$	−10.3351	−	17.9009i	−0.449351	−	0.778299i
$530$	7.87641	+	7.38204i	0.342129	+	0.320655i
$531$			14.7447i			0.639867i
$532$	12.0553	−	3.10334i	0.522662	−	0.134547i
$533$		−	7.28554i		−	0.315572i
$534$	−29.7771	+	31.7712i	−1.28858	+	1.37487i
$535$	3.79703	+	6.57665i	0.164160	+	0.284334i
$536$	6.83148	−	41.1192i	0.295075	−	1.77608i
$537$	−5.82241	−	3.36157i	−0.251255	−	0.145062i
$538$	34.4382	+	8.04210i	1.48474	+	0.346719i
$539$	−6.91644	+	2.71736i	−0.297912	+	0.117045i
$540$	−1.97674	+	4.00164i	−0.0850654	+	0.172203i
$541$	19.9482	+	11.5171i	0.857639	+	0.495158i	0.863221	−	0.504826i	$-0.168444\pi$
$541$	19.9482	+	11.5171i	0.857639	+	0.495158i	−0.00558207	+	0.999984i	$0.501777\pi$
$542$	−3.91397	−	12.9183i	−0.168119	−	0.554887i
$543$	−26.7472	+	15.4425i	−1.14783	+	0.662702i
$544$	2.70003	−	26.9487i	0.115763	−	1.15542i
$545$			3.29011i			0.140933i
$546$	−7.21824	+	3.77044i	−0.308912	+	0.161360i
$547$	7.90194			0.337863			0.168931	−	0.985628i	$-0.445968\pi$
$547$	7.90194			0.337863			0.168931	+	0.985628i	$0.445968\pi$
$548$	−0.858365	+	0.572705i	−0.0366675	+	0.0244648i
$549$	25.1072	+	43.4869i	1.07155	+	1.85598i
$550$	0.435323	+	1.43681i	0.0185622	+	0.0612657i
$551$	−3.62074	+	6.27131i	−0.154249	+	0.267167i
$552$	−8.72890	−	7.17839i	−0.371527	−	0.305533i
$553$	4.64978	+	24.5506i	0.197729	+	1.04400i
$554$	−0.424601	+	1.81824i	−0.0180396	+	0.0772498i
$555$	15.2130	−	26.3496i	0.645754	−	1.11848i
$556$	18.6631	−	1.21062i	0.791491	−	0.0513418i
$557$	3.75347	−	2.16707i	0.159040	−	0.0918216i	−0.418368	−	0.908278i	$-0.637398\pi$
$557$	3.75347	−	2.16707i	0.159040	−	0.0918216i	0.577408	+	0.816456i	$0.304064\pi$
$558$	−35.6588	+	38.0469i	−1.50956	+	1.61065i
$559$	4.15287			0.175648
$560$	10.0566	−	3.29621i	0.424968	−	0.139290i
$561$	13.3049			0.561733
$562$	−26.7377	+	28.5283i	−1.12786	+	1.20339i
$563$	−15.5194	+	8.96012i	−0.654064	+	0.377624i	−0.790011	−	0.613092i	$-0.789925\pi$
$563$	−15.5194	+	8.96012i	−0.654064	+	0.377624i	0.135948	+	0.990716i	$0.456592\pi$
$564$	−18.3773	+	1.19209i	−0.773824	+	0.0501958i
$565$	7.52754	−	13.0381i	0.316686	−	0.548517i
$566$	−0.240065	+	1.02802i	−0.0100907	+	0.0432107i
$567$	4.99204	−	14.2746i	0.209646	−	0.599479i
$568$	−17.9592	+	21.8383i	−0.753549	+	0.916314i
$569$	2.80014	−	4.84999i	0.117388	−	0.203322i	−0.801344	−	0.598204i	$-0.795881\pi$
$569$	2.80014	−	4.84999i	0.117388	−	0.203322i	0.918732	+	0.394882i	$0.129215\pi$
$570$	−2.52530	−	8.33489i	−0.105773	−	0.349110i
$571$	11.5275	+	19.9663i	0.482412	+	0.835562i	0.999796	−	0.0201912i	$-0.00642748\pi$
$571$	11.5275	+	19.9663i	0.482412	+	0.835562i	−0.517384	+	0.855753i	$0.673094\pi$
$572$	−1.46844	+	0.979753i	−0.0613987	+	0.0409655i
$573$	−4.06989			−0.170022
$574$	−1.38424	+	32.7572i	−0.0577770	+	1.36726i
$575$			1.52639i			0.0636548i
$576$	29.1644	+	9.96571i	1.21518	+	0.415238i
$577$	−1.95920	+	1.13114i	−0.0815624	+	0.0470900i	−0.540227	−	0.841520i	$-0.681661\pi$
$577$	−1.95920	+	1.13114i	−0.0815624	+	0.0470900i	0.458664	+	0.888610i	$0.348328\pi$
$578$	2.42868	+	8.01601i	0.101020	+	0.333422i
$579$	−6.63692	−	3.83183i	−0.275821	−	0.159245i
$580$	−2.72662	+	5.51967i	−0.113217	+	0.229192i
$581$	−27.5854	+	23.7478i	−1.14443	+	0.985223i
$582$	−21.6881	−	5.06465i	−0.898999	−	0.209936i
$583$	7.01768	+	4.05166i	0.290643	+	0.167803i
$584$	−22.7494	−	3.77955i	−0.941378	−	0.156399i
$585$	1.60156	+	2.77399i	0.0662165	+	0.114690i
$586$	9.13002	−	9.74144i	0.377157	−	0.402415i
$587$		−	23.9357i		−	0.987932i	−0.869481	−	0.493966i	$-0.835547\pi$
$587$		−	23.9357i		−	0.987932i	0.869481	−	0.493966i	$-0.164453\pi$
$588$	33.1710	−	15.5812i	1.36795	−	0.642558i
$589$		−	22.5158i		−	0.927746i
$590$	−3.94924	−	3.70136i	−0.162588	−	0.152383i
$591$	10.9026	+	18.8838i	0.448471	+	0.776775i
$592$	−42.9291	−	17.8496i	−1.76438	−	0.733613i
$593$	22.7060	+	13.1093i	0.932422	+	0.538334i	0.887577	−	0.460660i	$-0.152387\pi$
$593$	22.7060	+	13.1093i	0.932422	+	0.538334i	0.0448454	+	0.998994i	$0.485720\pi$
$594$	−0.761886	+	3.26258i	−0.0312605	+	0.133865i
$595$	−9.59991	+	8.26439i	−0.393558	+	0.338807i
$596$	3.22769	−	6.53402i	0.132211	−	0.267644i
$597$	−37.0558	−	21.3942i	−1.51659	−	0.875606i
$598$	−1.71767	+	0.520418i	−0.0702408	+	0.0212815i
$599$	−21.8531	+	12.6169i	−0.892894	+	0.515513i	−0.874888	−	0.484325i	$-0.839065\pi$
$599$	−21.8531	+	12.6169i	−0.892894	+	0.515513i	−0.0180062	+	0.999838i	$0.505732\pi$
$600$	−2.60108	−	6.93213i	−0.106189	−	0.283003i
$601$		−	36.0223i		−	1.46938i	−0.678404	−	0.734689i	$-0.737328\pi$
$601$		−	36.0223i		−	1.46938i	0.678404	−	0.734689i	$-0.262672\pi$
$602$	−18.6721	−	0.789038i	−0.761020	−	0.0321588i
$603$	−56.7748			−2.31205
$604$	−18.1210	−	27.1595i	−0.737332	−	1.10511i
$605$	−4.93652	−	8.55030i	−0.200698	−	0.347619i
$606$	45.0203	−	13.6402i	1.82882	−	0.554095i
$607$	−14.7983	+	25.6315i	−0.600646	+	1.04035i	0.392078	+	0.919932i	$0.371756\pi$
$607$	−14.7983	+	25.6315i	−0.600646	+	1.04035i	−0.992723	+	0.120417i	$0.961577\pi$
$608$	−12.1308	+	5.47181i	−0.491970	+	0.221911i
$609$	−7.03766	+	20.1241i	−0.285181	+	0.815468i
$610$	−17.9502	−	4.19178i	−0.726783	−	0.169720i
$611$	−1.46231	+	2.53280i	−0.0591588	+	0.102466i
$612$	−36.8124	+	2.38792i	−1.48805	+	0.0965258i
$613$	−36.2849	+	20.9491i	−1.46553	+	0.846126i	−0.999258	−	0.0385129i	$-0.987738\pi$
$613$	−36.2849	+	20.9491i	−1.46553	+	0.846126i	−0.466276	+	0.884639i	$0.654405\pi$
$614$	10.6992	+	10.0276i	0.431784	+	0.404683i
$615$	22.9380			0.924949
$616$	6.78857	−	4.12616i	0.273519	−	0.166248i
$617$	−27.0195			−1.08776			−0.543882	−	0.839162i	$-0.683046\pi$
$617$	−27.0195			−1.08776			−0.543882	+	0.839162i	$0.683046\pi$
$618$	1.82169	+	1.70735i	0.0732790	+	0.0686796i
$619$	40.2079	−	23.2141i	1.61609	−	0.933052i	0.628176	−	0.778072i	$-0.283802\pi$
$619$	40.2079	−	23.2141i	1.61609	−	0.933052i	0.987918	−	0.154980i	$-0.0495313\pi$
$620$	−1.23908	−	19.1018i	−0.0497626	−	0.767146i
$621$	−1.70316	+	2.94997i	−0.0683456	+	0.118378i
$622$	28.5830	+	6.67476i	1.14607	+	0.267634i
$623$	−5.79103	−	30.5763i	−0.232013	−	1.22501i
$624$	6.91402	−	5.29053i	0.276782	−	0.211791i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.44830	+	0.438805i	−0.0578858	+	0.0175382i
$627$	−3.26874	−	5.66163i	−0.130541	−	0.226104i
$628$	−25.3369	+	16.9049i	−1.01105	+	0.674580i
$629$	55.6482			2.21884
$630$	−6.67390	−	12.7767i	−0.265894	−	0.509036i
$631$		−	23.9781i		−	0.954555i	−0.878753	−	0.477277i	$-0.841624\pi$
$631$		−	23.9781i		−	0.954555i	0.878753	−	0.477277i	$-0.158376\pi$
$632$	−9.38415	−	25.0097i	−0.373281	−	0.994832i
$633$	27.1383	−	15.6683i	1.07865	−	0.622759i
$634$	−14.9491	+	4.52928i	−0.593707	+	0.179881i
$635$	7.85154	+	4.53309i	0.311579	+	0.179890i
$636$	−35.8302	−	17.6995i	−1.42076	−	0.701831i
$637$	0.865375	−	5.75539i	0.0342874	−	0.228037i
$638$	−1.05091	+	4.50024i	−0.0416058	+	0.178166i
$639$	33.3520	+	19.2558i	1.31939	+	0.761748i
$640$	−9.99034	+	5.30972i	−0.394903	+	0.209885i
$641$	10.8998	+	18.8790i	0.430516	+	0.745676i	0.996918	−	0.0784533i	$-0.0249982\pi$
$641$	10.8998	+	18.8790i	0.430516	+	0.745676i	−0.566401	+	0.824129i	$0.691665\pi$
$642$	−20.5125	−	19.2250i	−0.809565	−	0.758752i
$643$			7.09006i			0.279605i	0.990179	+	0.139802i	$0.0446467\pi$
$643$			7.09006i			0.279605i	−0.990179	+	0.139802i	$0.955353\pi$
$644$	7.82187	−	2.01355i	0.308225	−	0.0793450i
$645$			13.0750i			0.514828i
$646$	10.8926	−	11.6221i	0.428564	−	0.457264i
$647$	−6.27831	−	10.8744i	−0.246826	−	0.427515i	0.715817	−	0.698287i	$-0.246054\pi$
$647$	−6.27831	−	10.8744i	−0.246826	−	0.427515i	−0.962643	+	0.270772i	$0.912721\pi$
$648$	−2.64956	+	15.9479i	−0.104084	+	0.626493i
$649$	−3.51867	−	2.03151i	−0.138120	−	0.0797436i
$650$	−1.14503	−	0.267389i	−0.0449117	−	0.0104879i
$651$	−12.3352	−	65.1293i	−0.483455	−	2.55262i
$652$	9.91824	+	4.89944i	0.388428	+	0.191877i
$653$	−3.51459	−	2.02915i	−0.137537	−	0.0794068i	0.429653	−	0.902994i	$-0.358636\pi$
$653$	−3.51459	−	2.02915i	−0.137537	−	0.0794068i	−0.567189	+	0.823587i	$0.691969\pi$
$654$	−3.53176	−	11.6568i	−0.138103	−	0.455817i
$655$	−10.0620	+	5.80928i	−0.393154	+	0.226987i
$656$	−4.52817	−	34.7565i	−0.176795	−	1.35701i
$657$			31.4110i			1.22546i
$658$	7.05607	−	11.1101i	0.275074	−	0.433118i
$659$	−15.1907			−0.591746			−0.295873	−	0.955227i	$-0.595610\pi$
$659$	−15.1907			−0.591746			−0.295873	+	0.955227i	$0.595610\pi$
$660$	−3.08468	−	4.62329i	−0.120071	−	0.179961i
$661$	9.77442	+	16.9298i	0.380181	+	0.658492i	0.991088	−	0.133210i	$-0.0425285\pi$
$661$	9.77442	+	16.9298i	0.380181	+	0.658492i	−0.610907	+	0.791702i	$0.709195\pi$
$662$	10.5682	+	34.8809i	0.410744	+	1.35568i
$663$	−5.21024	+	9.02440i	−0.202349	+	0.350479i
$664$	24.7162	−	30.0548i	0.959174	−	1.16635i
$665$	5.87524	+	2.05465i	0.227832	+	0.0796761i
$666$	−14.4004	+	61.6662i	−0.558006	+	2.38952i
$667$	−2.34926	+	4.06904i	−0.0909637	+	0.157554i
$668$	−1.44316	−	22.2479i	−0.0558376	−	0.860799i
$669$	−60.0760	+	34.6849i	−2.32267	+	1.34099i
$670$	14.2521	−	15.2066i	0.550609	−	0.587482i
$671$	−13.8369			−0.534168
$672$	−32.0920	+	22.4736i	−1.23798	+	0.866940i
$673$	−49.5831			−1.91129			−0.955644	−	0.294524i	$-0.904839\pi$
$673$	−49.5831			−1.91129			−0.955644	+	0.294524i	$0.904839\pi$
$674$	16.3030	−	17.3948i	0.627968	−	0.670022i
$675$	−1.93265	+	1.11581i	−0.0743876	+	0.0429477i
$676$	1.59351	+	24.5658i	0.0612890	+	0.944838i
$677$	13.1028	−	22.6948i	0.503582	−	0.872230i	−0.496409	−	0.868089i	$-0.665348\pi$
$677$	13.1028	−	22.6948i	0.503582	−	0.872230i	0.999991	−	0.00414150i	$-0.00131829\pi$
$678$	−12.6742	+	54.2741i	−0.486751	+	2.08439i
$679$	12.0627	−	10.3846i	0.462926	−	0.398524i
$680$	8.60141	−	10.4593i	0.329849	−	0.401095i
$681$	−12.8442	+	22.2469i	−0.492192	+	0.852502i
$682$	−4.16646	−	13.7516i	−0.159542	−	0.526578i
$683$	12.5578	+	21.7507i	0.480510	+	0.832268i	0.999750	−	0.0223606i	$-0.00711819\pi$
$683$	12.5578	+	21.7507i	0.480510	+	0.832268i	−0.519240	+	0.854629i	$0.673785\pi$
$684$	10.0602	+	15.0781i	0.384660	+	0.576525i
$685$	−0.515941			−0.0197131
$686$	−4.98441	+	25.7129i	−0.190306	+	0.981725i
$687$		−	53.3750i		−	2.03638i
$688$	19.8117	−	2.58113i	0.755316	−	0.0984046i
$689$	−5.49629	+	3.17329i	−0.209392	+	0.120893i
$690$	−1.63850	−	5.40796i	−0.0623766	−	0.205878i
$691$	2.76681	+	1.59742i	0.105254	+	0.0607686i	0.551703	−	0.834041i	$-0.313978\pi$
$691$	2.76681	+	1.59742i	0.105254	+	0.0607686i	−0.446449	+	0.894809i	$0.647312\pi$
$692$	3.26660	+	1.61365i	0.124178	+	0.0613416i
$693$	−7.05954	−	8.20036i	−0.268170	−	0.311506i
$694$	48.4476	+	11.3136i	1.83905	+	0.429458i
$695$	8.09834	+	4.67558i	0.307187	+	0.177355i
$696$	3.73528	−	22.4830i	0.141586	−	0.852214i
$697$	20.9765	+	36.3324i	0.794541	+	1.37619i
$698$	13.8083	−	14.7330i	0.522651	−	0.557652i
$699$		−	49.2147i		−	1.86147i
$700$	5.09747	+	1.41979i	0.192666	+	0.0536630i
$701$		−	44.9260i		−	1.69683i	−0.529331	−	0.848416i	$-0.677557\pi$
$701$		−	44.9260i		−	1.69683i	0.529331	−	0.848416i	$-0.322443\pi$
$702$	−1.91458	−	1.79441i	−0.0722610	−	0.0677255i
$703$	−13.6716	−	23.6800i	−0.515635	−	0.893107i
$704$	−6.39643	+	5.58670i	−0.241075	+	0.210557i
$705$	−7.97433	−	4.60398i	−0.300331	−	0.173396i
$706$	7.80341	−	33.4161i	0.293685	−	1.25763i
$707$	−11.0980	+	31.7346i	−0.417385	+	1.19350i
$708$	17.9653	+	8.87455i	0.675178	+	0.333526i
$709$	10.4928	+	6.05803i	0.394066	+	0.227514i	0.683920	−	0.729557i	$-0.260274\pi$
$709$	10.4928	+	6.05803i	0.394066	+	0.227514i	−0.289855	+	0.957071i	$0.593607\pi$
$710$	−13.5298	+	4.09926i	−0.507766	+	0.153842i
$711$	−31.5094	+	18.1920i	−1.18169	+	0.682252i
$712$	11.6874	+	31.1481i	0.438004	+	1.16732i
$713$		−	14.6090i		−	0.547111i
$714$	25.1409	−	39.5856i	0.940875	−	1.48145i
$715$	−0.882644			−0.0330090
$716$	−4.27286	+	2.85088i	−0.159684	+	0.106542i
$717$	23.1374	+	40.0751i	0.864082	+	1.49663i
$718$	−11.4445	+	3.46744i	−0.427105	+	0.129404i
$719$	−15.1586	+	26.2555i	−0.565321	+	0.979165i	0.431699	+	0.902018i	$0.357914\pi$
$719$	−15.1586	+	26.2555i	−0.565321	+	0.979165i	−0.997020	+	0.0771470i	$0.975419\pi$
$720$	9.36455	+	12.2382i	0.348996	+	0.456091i
$721$	−1.75318	+	0.332044i	−0.0652917	+	0.0123660i
$722$	18.5445	+	4.33054i	0.690153	+	0.161166i
$723$	4.40550	−	7.63055i	0.163842	−	0.283783i
$724$	1.52745	+	23.5473i	0.0567672	+	0.875129i
$725$	−2.66580	+	1.53910i	−0.0990052	+	0.0571607i
$726$	26.6683	+	24.9945i	0.989754	+	0.927631i
$727$	−9.03069			−0.334930			−0.167465	−	0.985878i	$-0.553558\pi$
$727$	−9.03069			−0.334930			−0.167465	+	0.985878i	$0.553558\pi$
$728$	0.140256	+	6.22035i	0.00519823	+	0.230541i
$729$	39.5452			1.46464
$730$	−8.41314	−	7.88508i	−0.311384	−	0.291840i
$731$	−20.7100	+	11.9569i	−0.765987	+	0.442243i
$732$	68.0970	−	4.41726i	2.51694	−	0.163267i
$733$	−4.94704	+	8.56852i	−0.182723	+	0.316486i	−0.942807	−	0.333339i	$-0.891825\pi$
$733$	−4.94704	+	8.56852i	−0.182723	+	0.316486i	0.760084	+	0.649825i	$0.225158\pi$
$734$	−31.2370	−	7.29454i	−1.15298	−	0.269246i
$735$	18.1204	+	2.72457i	0.668382	+	0.100497i
$736$	−7.87089	+	3.55030i	−0.290125	+	0.130866i
$737$	7.82234	−	13.5487i	0.288140	−	0.499073i
$738$	−45.6897	+	13.8430i	−1.68186	+	0.509569i
$739$	16.4166	+	28.4344i	0.603894	+	1.04598i	0.992225	+	0.124455i	$0.0397183\pi$
$739$	16.4166	+	28.4344i	0.603894	+	1.04598i	−0.388331	+	0.921520i	$0.626948\pi$
$740$	−12.9018	−	19.3371i	−0.474279	−	0.710845i
$741$	5.12020			0.188095
$742$	25.3153	−	13.2234i	0.929356	−	0.485448i
$743$			51.2689i			1.88088i	0.339966	+	0.940438i	$0.389584\pi$
$743$			51.2689i			1.88088i	−0.339966	+	0.940438i	$0.610416\pi$
$744$	24.8948	+	66.3472i	0.912689	+	2.43241i
$745$	3.15569	−	1.82194i	0.115616	−	0.0667507i
$746$	28.1005	−	8.51386i	1.02883	−	0.311715i
$747$	−45.9006	−	26.5007i	−1.67941	−	0.969610i
$748$	4.50210	−	9.11388i	0.164613	−	0.333236i
$749$	19.7411	−	3.73888i	0.721323	−	0.136616i
$750$	0.841856	−	3.60504i	0.0307403	−	0.131637i
$751$	38.3610	+	22.1477i	1.39981	+	0.808182i	0.994373	−	0.105940i	$-0.0337851\pi$
$751$	38.3610	+	22.1477i	1.39981	+	0.808182i	0.405440	+	0.914122i	$0.367118\pi$
$752$	−5.40192	+	12.9919i	−0.196988	+	0.473765i
$753$	15.5110	+	26.8658i	0.565252	+	0.979045i
$754$	−2.64087	−	2.47512i	−0.0961749	−	0.0901384i
$755$		−	16.3249i		−	0.594124i
$756$	8.26738	+	8.43178i	0.300682	+	0.306661i
$757$		−	30.6126i		−	1.11263i	−0.830970	−	0.556317i	$-0.812214\pi$
$757$		−	30.6126i		−	1.11263i	0.830970	−	0.556317i	$-0.187786\pi$
$758$	12.0682	−	12.8764i	0.438338	−	0.467693i
$759$	−2.12087	−	3.67346i	−0.0769828	−	0.133338i
$760$	−6.56393	−	1.09052i	−0.238099	−	0.0395573i
$761$	−15.9088	−	9.18496i	−0.576694	−	0.332955i	0.183124	−	0.983090i	$-0.441379\pi$
$761$	−15.9088	−	9.18496i	−0.576694	−	0.332955i	−0.759819	+	0.650135i	$0.774712\pi$
$762$	−32.6839	−	7.63242i	−1.18401	−	0.276493i
$763$	8.21684	+	2.87354i	0.297470	+	0.104029i
$764$	−1.37717	+	2.78788i	−0.0498241	+	0.100862i
$765$	−15.9737	−	9.22243i	−0.577531	−	0.333438i
$766$	−2.35138	−	7.76085i	−0.0849587	−	0.280411i
$767$	2.75585	−	1.59109i	0.0995079	−	0.0574509i
$768$	29.6959	−	29.5363i	1.07156	−	1.06580i
$769$			31.3711i			1.13127i	0.824656	+	0.565635i	$0.191369\pi$
$769$			31.3711i			1.13127i	−0.824656	+	0.565635i	$0.808631\pi$
$770$	3.96855	+	0.167701i	0.143016	+	0.00604352i
$771$	25.7655			0.927922
$772$	−4.87061	+	3.24969i	−0.175297	+	0.116959i
$773$	3.23165	+	5.59739i	0.116235	+	0.201324i	0.918273	−	0.395949i	$-0.129584\pi$
$773$	3.23165	+	5.59739i	0.116235	+	0.201324i	−0.802038	+	0.597273i	$0.796251\pi$
$774$	−7.89074	−	26.0438i	−0.283627	−	0.936126i
$775$	4.78548	−	8.28870i	0.171900	−	0.297739i
$776$	−10.8081	+	13.1426i	−0.387988	+	0.471792i
$777$	−52.5197	−	61.0069i	−1.88413	−	2.18861i
$778$	−3.96073	+	16.9608i	−0.141999	+	0.608075i
$779$	10.3070	−	17.8522i	0.369286	−	0.639623i
$780$	4.34384	−	0.281773i	0.155534	−	0.0100891i
$781$	−9.19038	+	5.30607i	−0.328858	+	0.189866i
$782$	7.06749	−	7.54079i	0.252733	−	0.269658i
$783$	−6.86939			−0.245492
$784$	0.551236	−	27.9946i	0.0196870	−	0.999806i
$785$	−15.2294			−0.543560
$786$	29.4134	−	31.3832i	1.04914	−	1.11940i
$787$	−7.74289	+	4.47036i	−0.276004	+	0.159351i	−0.631613	−	0.775284i	$-0.717607\pi$
$787$	−7.74289	+	4.47036i	−0.276004	+	0.159351i	0.355609	+	0.934635i	$0.384273\pi$
$788$	16.6246	−	1.07839i	0.592228	−	0.0384162i
$789$	10.6472	−	18.4416i	0.379052	−	0.656538i
$790$	3.03724	−	13.0062i	0.108060	−	0.462741i
$791$	−25.9873	−	30.1869i	−0.924003	−	1.07332i
$792$	8.93445	+	7.34743i	0.317472	+	0.261080i
$793$	5.41858	−	9.38526i	0.192420	−	0.333280i
$794$	−3.86549	−	12.7583i	−0.137181	−	0.452774i
$795$	−9.99086	−	17.3047i	−0.354339	−	0.613734i
$796$	−27.1940	+	18.1440i	−0.963865	+	0.643095i
$797$	33.8447			1.19884			0.599420	−	0.800434i	$-0.295398\pi$
$797$	33.8447			1.19884			0.599420	+	0.800434i	$0.295398\pi$
$798$	−23.0214	−	0.972829i	−0.814950	−	0.0344378i
$799$		−	16.8411i		−	0.595796i
$800$	−5.62867	−	0.563945i	−0.199004	−	0.0199385i
$801$	39.2430	−	22.6570i	1.38658	−	0.800545i
$802$	−3.58194	−	11.8224i	−0.126483	−	0.417464i
$803$	−7.49589	−	4.32776i	−0.264524	−	0.152723i
$804$	−34.1716	+	69.1757i	−1.20514	+	2.43964i
$805$	3.81206	+	1.33313i	0.134357	+	0.0469867i
$806$	10.9590	+	2.55917i	0.386015	+	0.0901431i
$807$	−56.6906	−	32.7303i	−1.99560	−	1.15216i
$808$	5.89036	−	35.4545i	0.207222	−	1.24729i
$809$	−5.94518	−	10.2974i	−0.209021	−	0.362036i	0.742385	−	0.669973i	$-0.233695\pi$
$809$	−5.94518	−	10.2974i	−0.209021	−	0.362036i	−0.951407	+	0.307938i	$0.900361\pi$
$810$	−5.52763	+	5.89781i	−0.194221	+	0.207228i
$811$			8.26996i			0.290398i	0.989403	+	0.145199i	$0.0463822\pi$
$811$			8.26996i			0.290398i	−0.989403	+	0.145199i	$0.953618\pi$
$812$	11.4036	+	11.6304i	0.400189	+	0.408146i
$813$			24.9853i			0.876274i
$814$	−12.7319	−	11.9328i	−0.446254	−	0.418244i
$815$	2.76559	+	4.79015i	0.0968745	+	0.167792i
$816$	−19.2471	+	46.2902i	−0.673784	+	1.62048i
$817$	10.1761	+	5.87515i	0.356015	+	0.205545i
$818$	0.546293	−	2.33936i	0.0191007	−	0.0817939i
$819$	8.32665	−	1.57703i	0.290957	−	0.0551060i
$820$	7.76174	−	15.7126i	0.271052	−	0.548707i
$821$	−27.5875	−	15.9277i	−0.962811	−	0.555879i	−0.0657739	−	0.997835i	$-0.520952\pi$
$821$	−27.5875	−	15.9277i	−0.962811	−	0.555879i	−0.897037	+	0.441955i	$0.854285\pi$
$822$	1.82797	−	0.553837i	0.0637578	−	0.0193173i
$823$	26.7631	−	15.4517i	0.932903	−	0.538612i	0.0451746	−	0.998979i	$-0.485616\pi$
$823$	26.7631	−	15.4517i	0.932903	−	0.538612i	0.887729	+	0.460367i	$0.152282\pi$
$824$	1.78596	−	0.670129i	0.0622168	−	0.0233450i
$825$		−	2.77894i		−	0.0967503i
$826$	−12.6931	+	6.63025i	−0.441651	+	0.230696i
$827$	42.4762			1.47704			0.738521	−	0.674230i	$-0.235524\pi$
$827$	42.4762			1.47704			0.738521	+	0.674230i	$0.235524\pi$
$828$	6.52738	+	9.78317i	0.226842	+	0.339989i
$829$	14.1168	+	24.4510i	0.490297	+	0.849220i	0.999938	−	0.0111677i	$-0.00355488\pi$
$829$	14.1168	+	24.4510i	0.490297	+	0.849220i	−0.509640	+	0.860388i	$0.670222\pi$
$830$	18.6204	−	5.64158i	0.646322	−	0.195822i
$831$	1.72807	−	2.99311i	0.0599462	−	0.103830i
$832$	−1.28447	−	6.52632i	−0.0445309	−	0.226259i
$833$	12.2553	+	31.1932i	0.424622	+	1.08078i
$834$	−33.7112	−	7.87233i	−1.16733	−	0.272596i
$835$	5.57367	−	9.65389i	0.192885	−	0.334087i
$836$	−4.98430	+	0.323318i	−0.172386	+	0.0111822i
$837$	18.4973	−	10.6794i	0.639360	−	0.369134i
$838$	−32.2300	−	30.2071i	−1.11337	−	1.04349i
$839$	−13.1554			−0.454174			−0.227087	−	0.973874i	$-0.572920\pi$
$839$	−13.1554			−0.454174			−0.227087	+	0.973874i	$0.572920\pi$
$840$	−19.5843	+	0.441586i	−0.675723	+	0.0152361i
$841$	19.5247			0.673266
$842$	5.36490	+	5.02817i	0.184887	+	0.173282i
$843$	62.6775	−	36.1869i	2.15873	−	1.24634i
$844$	−1.54978	−	23.8916i	−0.0533458	−	0.822384i
$845$	−6.15435	+	10.6597i	−0.211716	+	0.366703i
$846$	18.6624	+	4.35808i	0.641626	+	0.149834i
$847$	−25.6653	+	4.86091i	−0.881872	+	0.167023i
$848$	−24.2484	+	18.5546i	−0.832693	+	0.637168i
$849$	0.977033	−	1.69227i	0.0335317	−	0.0580786i
$850$	6.48002	−	1.96331i	0.222263	−	0.0673410i
$851$	−8.87062	−	15.3644i	−0.304081	−	0.526684i
$852$	43.5356	−	29.0472i	1.49151	−	0.995140i
$853$	−37.8973			−1.29758			−0.648789	−	0.760968i	$-0.724724\pi$
$853$	−37.8973			−1.29758			−0.648789	+	0.760968i	$0.724724\pi$
$854$	−26.1462	+	41.1685i	−0.894705	+	1.40876i
$855$			9.06305i			0.309950i
$856$	−20.1102	+	7.54576i	−0.687353	+	0.257909i
$857$	29.0059	−	16.7466i	0.990822	−	0.572051i	0.0853020	−	0.996355i	$-0.472814\pi$
$857$	29.0059	−	16.7466i	0.990822	−	0.572051i	0.905520	+	0.424304i	$0.139481\pi$
$858$	3.12719	−	0.947474i	0.106761	−	0.0323462i
$859$	14.2225	+	8.21139i	0.485267	+	0.280169i	0.722609	−	0.691257i	$-0.242943\pi$
$859$	14.2225	+	8.21139i	0.485267	+	0.280169i	−0.237342	+	0.971426i	$0.576276\pi$
$860$	8.95641	+	4.42431i	0.305411	+	0.150868i
$861$	20.0338	−	57.2862i	0.682750	−	1.95231i
$862$	−2.58525	+	11.0707i	−0.0880541	+	0.377069i
$863$	−0.525428	−	0.303356i	−0.0178858	−	0.0103264i	0.491030	−	0.871142i	$-0.336620\pi$
$863$	−0.525428	−	0.303356i	−0.0178858	−	0.0103264i	−0.508916	+	0.860816i	$0.669954\pi$
$864$	−10.2490	−	7.37046i	−0.348677	−	0.250748i
$865$	0.910856	+	1.57765i	0.0309700	+	0.0536417i
$866$	−1.60941	−	1.50840i	−0.0546900	−	0.0512574i
$867$		−	15.5038i		−	0.526537i
$868$	−48.7877	−	13.5888i	−1.65596	−	0.461232i
$869$		−	10.0258i		−	0.340103i
$870$	7.79272	−	8.31459i	0.264198	−	0.281891i
$871$	6.12651	+	10.6114i	0.207589	+	0.359554i
$872$	−9.18000	−	1.52515i	−0.310874	−	0.0516481i
$873$	20.0717	+	11.5884i	0.679325	+	0.392209i
$874$	−4.94517	−	1.15481i	−0.167273	−	0.0390619i
$875$	1.72615	+	2.00510i	0.0583545	+	0.0677846i
$876$	38.2718	+	18.9056i	1.29309	+	0.638762i
$877$	30.2747	+	17.4791i	1.02230	+	0.590227i	0.914770	−	0.403974i	$-0.132371\pi$
$877$	30.2747	+	17.4791i	1.02230	+	0.590227i	0.107533	+	0.994201i	$0.465705\pi$
$878$	−11.9707	−	39.5100i	−0.403992	−	1.33340i
$879$	−21.4022	+	12.3566i	−0.721879	+	0.416777i
$880$	−4.21075	+	0.548588i	−0.141944	+	0.0184929i
$881$		−	5.42608i		−	0.182809i	−0.995814	−	0.0914046i	$-0.970864\pi$
$881$		−	5.42608i		−	0.182809i	0.995814	−	0.0914046i	$-0.0291357\pi$
$882$	−37.7379	+	5.50861i	−1.27070	+	0.185484i
$883$	2.94901			0.0992421			0.0496210	−	0.998768i	$-0.484199\pi$
$883$	2.94901			0.0992421			0.0496210	+	0.998768i	$0.484199\pi$
$884$	4.41870	+	6.62269i	0.148617	+	0.222745i
$885$	5.00943	+	8.67659i	0.168390	+	0.291660i
$886$	0.141655	+	0.467542i	0.00475900	+	0.0157074i
$887$	17.0925	−	29.6050i	0.573909	−	0.994039i	−0.422251	−	0.906479i	$-0.638760\pi$
$887$	17.0925	−	29.6050i	0.573909	−	0.994039i	0.996159	−	0.0875599i	$-0.0279069\pi$
$888$	66.4682	+	54.6615i	2.23053	+	1.83432i
$889$	18.1785	−	15.6496i	0.609689	−	0.524870i
$890$	−3.78270	+	16.1985i	−0.126796	+	0.542974i
$891$	−3.03386	+	5.25480i	−0.101638	+	0.176042i
$892$	3.43075	+	52.8888i	0.114870	+	1.77085i
$893$	−7.16640	+	4.13752i	−0.239814	+	0.138457i
$894$	−9.22480	+	9.84257i	−0.308523	+	0.329185i
$895$	−2.56831			−0.0858491
$896$	4.53523	+	29.5877i	0.151511	+	0.988456i
$897$	3.32216			0.110924
$898$	−30.8064	+	32.8694i	−1.02802	+	1.09687i
$899$	25.5142	−	14.7307i	0.850947	−	0.491295i
$900$	0.498755	+	7.68885i	0.0166252	+	0.256295i
$901$	18.2730	−	31.6498i	0.608763	−	1.05441i
$902$	2.99157	−	12.8106i	0.0996083	−	0.426547i
$903$	32.6540	+	11.4196i	1.08666	+	0.380020i
$904$	32.8892	+	27.0471i	1.09388	+	0.899573i
$905$	−5.89920	+	10.2177i	−0.196096	+	0.339648i
$906$	17.5240	+	57.8388i	0.582194	+	1.92157i
$907$	−0.892664	−	1.54614i	−0.0296404	−	0.0513387i	0.850825	−	0.525450i	$-0.176103\pi$
$907$	−0.892664	−	1.54614i	−0.0296404	−	0.0513387i	−0.880465	+	0.474111i	$0.842770\pi$
$908$	10.8929	+	16.3262i	0.361494	+	0.541804i
$909$	−48.9533			−1.62368
$910$	−1.66784	+	2.62610i	−0.0552884	+	0.0870543i
$911$		−	21.9749i		−	0.728062i	−0.931387	−	0.364031i	$-0.881400\pi$
$911$		−	21.9749i		−	0.728062i	0.931387	−	0.364031i	$-0.118600\pi$
$912$	24.4265	−	3.18235i	0.808842	−	0.105378i
$913$	12.6482	−	7.30245i	0.418595	−	0.241676i
$914$	−7.35101	−	24.2624i	−0.243150	−	0.802530i
$915$	29.5488	+	17.0600i	0.976854	+	0.563987i
$916$	−36.5620	−	18.0610i	−1.20804	−	0.596752i
$917$	5.72030	+	30.2029i	0.188901	+	0.997388i
$918$	14.7143	+	3.43611i	0.485643	+	0.113409i
$919$	−22.0415	−	12.7257i	−0.727083	−	0.419782i	0.0902709	−	0.995917i	$-0.471227\pi$
$919$	−22.0415	−	12.7257i	−0.727083	−	0.419782i	−0.817354	+	0.576136i	$0.804560\pi$
$920$	−4.25890	−	0.707567i	−0.140412	−	0.0233278i
$921$	−13.5714	−	23.5064i	−0.447194	−	0.774562i
$922$	7.10634	−	7.58224i	0.234035	−	0.249708i
$923$		−	8.31150i		−	0.273576i
$924$	−14.2405	+	3.66587i	−0.468478	+	0.120598i
$925$		−	11.6230i		−	0.382163i
$926$	39.6318	+	37.1443i	1.30238	+	1.22064i
$927$	−1.29910	−	2.25011i	−0.0426680	−	0.0739032i
$928$	−14.1369	−	10.1664i	−0.464067	−	0.333730i
$929$	−14.0070	−	8.08693i	−0.459554	−	0.265324i	0.252303	−	0.967648i	$-0.418812\pi$
$929$	−14.0070	−	8.08693i	−0.459554	−	0.265324i	−0.711857	+	0.702325i	$0.752145\pi$
$930$	−8.05738	+	34.5037i	−0.264212	+	1.13142i
$931$	10.2627	−	12.8785i	0.336348	−	0.422077i
$932$	−33.7121	−	16.6532i	−1.10428	−	0.545494i
$933$	−47.0520	−	27.1655i	−1.54041	−	0.889358i
$934$	−2.54962	+	0.772481i	−0.0834261	+	0.0252763i
$935$	4.40167	−	2.54131i	0.143950	−	0.0831096i
$936$	−8.48235	+	3.18275i	−0.277254	+	0.104032i
$937$			6.52678i			0.213221i	0.994301	+	0.106610i	$0.0339997\pi$
$937$			6.52678i			0.213221i	−0.994301	+	0.106610i	$0.966000\pi$
$938$	−25.5299	−	48.8751i	−0.833580	−	1.59583i
$939$	2.80117			0.0914128
$940$	−5.85208	+	3.90454i	−0.190874	+	0.127352i
$941$	−24.0737	−	41.6969i	−0.784780	−	1.35928i	−0.929131	−	0.369752i	$-0.879443\pi$
$941$	−24.0737	−	41.6969i	−0.784780	−	1.35928i	0.144351	−	0.989527i	$-0.453891\pi$
$942$	53.9574	−	16.3480i	1.75803	−	0.532646i
$943$	6.68753	−	11.5831i	0.217776	−	0.377199i
$944$	12.1582	−	9.30331i	0.395715	−	0.302797i
$945$	1.09872	+	5.80120i	0.0357415	+	0.188713i
$946$	7.30226	+	1.70524i	0.237417	+	0.0554422i
$947$	5.11860	−	8.86568i	0.166332	−	0.288096i	−0.770795	−	0.637083i	$-0.780141\pi$
$947$	5.11860	−	8.86568i	0.166332	−	0.288096i	0.937128	+	0.348987i	$0.113474\pi$
$948$	3.20062	+	49.3411i	0.103951	+	1.60253i
$949$	5.87083	−	3.38953i	0.190575	−	0.110029i
$950$	−2.42746	−	2.27509i	−0.0787570	−	0.0738138i
$951$	28.9133			0.937577
$952$	−18.6090	−	30.6165i	−0.603122	−	0.992287i
$953$	−11.8097			−0.382553			−0.191276	−	0.981536i	$-0.561263\pi$
$953$	−11.8097			−0.382553			−0.191276	+	0.981536i	$0.561263\pi$
$954$	30.3439	+	28.4393i	0.982420	+	0.920758i
$955$	−1.34645	+	0.777371i	−0.0435700	+	0.0251551i
$956$	35.2808	−	2.28857i	1.14106	−	0.0740175i
$957$	4.27706	−	7.40809i	0.138258	−	0.239470i
$958$	7.90519	+	1.84604i	0.255405	+	0.0596428i
$959$	−0.450617	+	1.28853i	−0.0145512	+	0.0416088i
$960$	20.5477	−	4.04405i	0.663173	−	0.130521i
$961$	−30.3017	+	52.4840i	−0.977473	+	1.69303i
$962$	13.0796	−	3.96284i	0.421703	−	0.127767i
$963$	14.6281	+	25.3366i	0.471384	+	0.816460i
$964$	−3.73621	−	5.59979i	−0.120335	−	0.180357i
$965$	−2.92760			−0.0942427
$966$	−14.9371	−	0.631205i	−0.480593	−	0.0203087i
$967$		−	15.7493i		−	0.506464i	−0.967406	−	0.253232i	$-0.918506\pi$
$967$		−	15.7493i		−	0.506464i	0.967406	−	0.253232i	$-0.0814935\pi$
$968$	26.1453	−	9.81024i	0.840340	−	0.315313i
$969$	−25.5340	+	14.7421i	−0.820270	+	0.473583i
$970$	−8.14245	+	2.46699i	−0.261438	+	0.0792104i
$971$	32.4559	+	18.7384i	1.04156	+	0.601344i	0.920274	−	0.391274i	$-0.127965\pi$
$971$	32.4559	+	18.7384i	1.04156	+	0.601344i	0.121284	+	0.992618i	$0.461299\pi$
$972$	19.1835	−	38.8344i	0.615312	−	1.24561i
$973$	18.7500	−	16.1415i	0.601096	−	0.517472i
$974$	3.14345	−	13.4610i	0.100723	−	0.431319i
$975$	1.88489	+	1.08824i	0.0603648	+	0.0348516i
$976$	20.0168	−	48.1413i	0.640721	−	1.54096i
$977$	−16.6883	−	28.9049i	−0.533905	−	0.924751i	−0.999215	−	0.0396031i	$-0.987391\pi$
$977$	−16.6883	−	28.9049i	−0.533905	−	0.924751i	0.465310	−	0.885148i	$-0.345943\pi$
$978$	−14.9404	−	14.0027i	−0.477742	−	0.447756i
$979$			12.4866i			0.399073i
$980$	7.99791	−	11.4906i	0.255484	−	0.367053i
$981$			12.6752i			0.404687i
$982$	6.59018	−	7.03151i	0.210301	−	0.224385i
$983$	28.8827	+	50.0263i	0.921215	+	1.59559i	0.797538	+	0.603269i	$0.206135\pi$
$983$	28.8827	+	50.0263i	0.921215	+	1.59559i	0.123677	+	0.992323i	$0.460531\pi$
$984$	−10.6331	+	64.0012i	−0.338969	+	2.04028i
$985$	7.21380	+	4.16489i	0.229851	+	0.132704i
$986$	20.2961	+	4.73960i	0.646361	+	0.150940i
$987$	−18.4628	+	15.8943i	−0.587679	+	0.505922i
$988$	1.73257	−	3.50735i	0.0551204	−	0.111584i
$989$	6.60257	+	3.81200i	0.209950	+	0.121214i
$990$	1.67708	+	5.53531i	0.0533012	+	0.175924i
$991$	25.6882	−	14.8311i	0.816014	−	0.471126i	−0.0330261	−	0.999454i	$-0.510514\pi$
$991$	25.6882	−	14.8311i	0.816014	−	0.471126i	0.849040	+	0.528329i	$0.177181\pi$
$992$	53.8718	+	5.39749i	1.71043	+	0.171371i
$993$		−	67.4634i		−	2.14089i
$994$	−1.57917	+	37.3702i	−0.0500882	+	1.18531i
$995$	−16.3456			−0.518190
$996$	−59.9157	+	39.9760i	−1.89850	+	1.26669i
$997$	10.3363	+	17.9031i	0.327355	+	0.566996i	0.981986	−	0.188953i	$-0.0605093\pi$
$997$	10.3363	+	17.9031i	0.327355	+	0.566996i	−0.654631	+	0.755949i	$0.727176\pi$
$998$	−8.50981	−	28.0871i	−0.269373	−	0.889082i
$999$	12.9691	−	22.4632i	0.410325	−	0.710704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.e.131.4	✓	24
4.3	odd	2		1120.2.bz.f.271.2		24
7.3	odd	6		280.2.bj.f.171.5	yes	24
8.3	odd	2		280.2.bj.f.131.5	yes	24
8.5	even	2		1120.2.bz.e.271.2		24
28.3	even	6		1120.2.bz.e.591.2		24
56.3	even	6	inner	280.2.bj.e.171.4	yes	24
56.45	odd	6		1120.2.bz.f.591.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.4	✓	24	1.1	even	1	trivial
280.2.bj.e.171.4	yes	24	56.3	even	6	inner
280.2.bj.f.131.5	yes	24	8.3	odd	2
280.2.bj.f.171.5	yes	24	7.3	odd	6
1120.2.bz.e.271.2		24	8.5	even	2
1120.2.bz.e.591.2		24	28.3	even	6
1120.2.bz.f.271.2		24	4.3	odd	2
1120.2.bz.f.591.2		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)

\(f(q)\)	\(=\)	\(q+(-0.967093 + 1.03186i) q^{2} +(2.26702 - 1.30886i) q^{3} +(-0.129462 - 1.99581i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.841856 + 3.60504i) q^{6} +(-1.72615 - 2.00510i) q^{7} +(2.18459 + 1.79654i) q^{8} +(1.92625 - 3.33637i) q^{9} +O(q^{10})\)	\(q+(-0.967093 + 1.03186i) q^{2} +(2.26702 - 1.30886i) q^{3} +(-0.129462 - 1.99581i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.841856 + 3.60504i) q^{6} +(-1.72615 - 2.00510i) q^{7} +(2.18459 + 1.79654i) q^{8} +(1.92625 - 3.33637i) q^{9} +(0.410069 + 1.35346i) q^{10} +(0.530792 + 0.919359i) q^{11} +(-2.90573 - 4.35508i) q^{12} -0.831440 q^{13} +(3.73832 + 0.157972i) q^{14} -2.61773i q^{15} +(-3.96648 + 0.516763i) q^{16} +(4.14632 - 2.39388i) q^{17} +(1.57979 + 5.21420i) q^{18} +(-2.03733 - 1.17625i) q^{19} +(-1.79315 - 0.885785i) q^{20} +(-6.53761 - 2.28630i) q^{21} +(-1.46197 - 0.341404i) q^{22} +(-1.32189 - 0.763194i) q^{23} +(7.30394 + 1.21347i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.804080 - 0.857928i) q^{26} -2.23163i q^{27} +(-3.77831 + 3.70464i) q^{28} -3.07820i q^{29} +(2.70112 + 2.53159i) q^{30} +(4.78548 + 8.28870i) q^{31} +(3.30273 - 4.59260i) q^{32} +(2.40663 + 1.38947i) q^{33} +(-1.53973 + 6.59352i) q^{34} +(-2.59954 + 0.492342i) q^{35} +(-6.90812 - 3.41249i) q^{36} +(10.0658 + 5.81151i) q^{37} +(3.18402 - 0.964691i) q^{38} +(-1.88489 + 1.08824i) q^{39} +(2.64815 - 0.993639i) q^{40} +8.76255i q^{41} +(8.68161 - 4.53483i) q^{42} -4.99479 q^{43} +(1.76615 - 1.17838i) q^{44} +(-1.92625 - 3.33637i) q^{45} +(2.06590 - 0.625924i) q^{46} +(1.75877 - 3.04628i) q^{47} +(-8.31571 + 6.36310i) q^{48} +(-1.04082 + 6.92219i) q^{49} +(1.37716 + 0.321598i) q^{50} +(6.26653 - 10.8539i) q^{51} +(0.107640 + 1.65939i) q^{52} +(6.61057 - 3.81661i) q^{53} +(2.30272 + 2.15819i) q^{54} +1.06158 q^{55} +(-0.168690 - 7.48141i) q^{56} -6.15823 q^{57} +(3.17626 + 2.97690i) q^{58} +(-3.31455 + 1.91365i) q^{59} +(-5.22448 + 0.338897i) q^{60} +(-6.51711 + 11.2880i) q^{61} +(-13.1808 - 3.07800i) q^{62} +(-10.0147 + 1.89675i) q^{63} +(1.54487 + 7.84942i) q^{64} +(-0.415720 + 0.720048i) q^{65} +(-3.76118 + 1.13956i) q^{66} +(-7.36855 - 12.7627i) q^{67} +(-5.31451 - 7.96533i) q^{68} -3.99567 q^{69} +(2.00597 - 3.15849i) q^{70} +9.99651i q^{71} +(10.2020 - 3.82800i) q^{72} +(-7.06104 + 4.07669i) q^{73} +(-15.7313 + 4.76624i) q^{74} +(-2.26702 - 1.30886i) q^{75} +(-2.08382 + 4.21840i) q^{76} +(0.927176 - 2.65124i) q^{77} +(0.699953 - 2.99737i) q^{78} +(-8.17894 - 4.72211i) q^{79} +(-1.53571 + 3.69345i) q^{80} +(2.85786 + 4.94996i) q^{81} +(-9.04171 - 8.47421i) q^{82} -13.7576i q^{83} +(-3.71663 + 13.3438i) q^{84} -4.78776i q^{85} +(4.83043 - 5.15392i) q^{86} +(-4.02894 - 6.97833i) q^{87} +(-0.492104 + 2.96202i) q^{88} +(10.1864 + 5.88110i) q^{89} +(5.30552 + 1.23896i) q^{90} +(1.43519 + 1.66712i) q^{91} +(-1.35205 + 2.73704i) q^{92} +(21.6976 + 12.5271i) q^{93} +(1.44243 + 4.76083i) q^{94} +(-2.03733 + 1.17625i) q^{95} +(1.47625 - 14.7343i) q^{96} +6.01605i q^{97} +(-6.13615 - 7.76837i) q^{98} +4.08976 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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