LMFDB - Embedded newform 220.2.l.c.23.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.8

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.102586 + 1.41049i) q^{2} +(-2.05029 + 2.05029i) q^{3} +(-1.97895 + 0.289393i) q^{4} +(-2.23513 + 0.0646962i) q^{5} +(-3.10225 - 2.68158i) q^{6} +(3.00953 + 3.00953i) q^{7} +(-0.611199 - 2.76160i) q^{8} -5.40741i q^{9} +(-0.320547 - 3.14599i) q^{10} -1.00000i q^{11} +(3.46409 - 4.65078i) q^{12} +(-0.709511 - 0.709511i) q^{13} +(-3.93617 + 4.55365i) q^{14} +(4.45003 - 4.71532i) q^{15} +(3.83250 - 1.14539i) q^{16} +(-1.02729 + 1.02729i) q^{17} +(7.62709 - 0.554726i) q^{18} -5.70480 q^{19} +(4.40450 - 0.774863i) q^{20} -12.3409 q^{21} +(1.41049 - 0.102586i) q^{22} +(-3.28163 + 3.28163i) q^{23} +(6.91523 + 4.40895i) q^{24} +(4.99163 - 0.289209i) q^{25} +(0.927971 - 1.07354i) q^{26} +(4.93591 + 4.93591i) q^{27} +(-6.82666 - 5.08478i) q^{28} +0.344387i q^{29} +(7.10742 + 5.79299i) q^{30} +5.97347i q^{31} +(2.00872 + 5.28820i) q^{32} +(2.05029 + 2.05029i) q^{33} +(-1.55436 - 1.34359i) q^{34} +(-6.92141 - 6.53200i) q^{35} +(1.56487 + 10.7010i) q^{36} +(1.57859 - 1.57859i) q^{37} +(-0.585234 - 8.04655i) q^{38} +2.90941 q^{39} +(1.54478 + 6.13300i) q^{40} -6.42941 q^{41} +(-1.26600 - 17.4066i) q^{42} +(-3.02329 + 3.02329i) q^{43} +(0.289393 + 1.97895i) q^{44} +(0.349839 + 12.0863i) q^{45} +(-4.96535 - 4.29205i) q^{46} +(-6.62597 - 6.62597i) q^{47} +(-5.50937 + 10.2061i) q^{48} +11.1146i q^{49} +(0.919998 + 7.01096i) q^{50} -4.21249i q^{51} +(1.60942 + 1.19876i) q^{52} +(1.92847 + 1.92847i) q^{53} +(-6.45568 + 7.46839i) q^{54} +(0.0646962 + 2.23513i) q^{55} +(6.47170 - 10.1506i) q^{56} +(11.6965 - 11.6965i) q^{57} +(-0.485753 + 0.0353294i) q^{58} +1.69997 q^{59} +(-7.44182 + 10.6192i) q^{60} +2.56189 q^{61} +(-8.42550 + 0.612796i) q^{62} +(16.2738 - 16.2738i) q^{63} +(-7.25287 + 3.37578i) q^{64} +(1.63175 + 1.53995i) q^{65} +(-2.68158 + 3.10225i) q^{66} +(7.39211 + 7.39211i) q^{67} +(1.73566 - 2.33025i) q^{68} -13.4566i q^{69} +(8.50326 - 10.4327i) q^{70} -4.24031i q^{71} +(-14.9331 + 3.30501i) q^{72} +(11.1536 + 11.1536i) q^{73} +(2.38853 + 2.06464i) q^{74} +(-9.64134 + 10.8273i) q^{75} +(11.2895 - 1.65093i) q^{76} +(3.00953 - 3.00953i) q^{77} +(0.298466 + 4.10369i) q^{78} -0.182925 q^{79} +(-8.49205 + 2.80805i) q^{80} -4.01788 q^{81} +(-0.659570 - 9.06861i) q^{82} +(-10.3602 + 10.3602i) q^{83} +(24.4220 - 3.57136i) q^{84} +(2.22966 - 2.36259i) q^{85} +(-4.57447 - 3.95417i) q^{86} +(-0.706094 - 0.706094i) q^{87} +(-2.76160 + 0.611199i) q^{88} -6.52843i q^{89} +(-17.0117 + 1.73333i) q^{90} -4.27059i q^{91} +(5.54451 - 7.44388i) q^{92} +(-12.2474 - 12.2474i) q^{93} +(8.66612 - 10.0256i) q^{94} +(12.7510 - 0.369079i) q^{95} +(-14.9608 - 6.72389i) q^{96} +(-12.5123 + 12.5123i) q^{97} +(-15.6770 + 1.14020i) q^{98} -5.40741 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.102586	+	1.41049i	0.0725395	+	0.997366i
$2$	0.102586	+	1.41049i	0.0725395	+	0.997366i
$3$	−2.05029	+	2.05029i	−1.18374	+	1.18374i	−0.204970	+	0.978768i	$0.565710\pi$
$3$	−2.05029	+	2.05029i	−1.18374	+	1.18374i	−0.978768	+	0.204970i	$0.934290\pi$
$4$	−1.97895	+	0.289393i	−0.989476	+	0.144697i
$5$	−2.23513	+	0.0646962i	−0.999581	+	0.0289330i
$5$	−2.23513	+	0.0646962i	−0.999581	+	0.0289330i
$6$	−3.10225	−	2.68158i	−1.26649	−	1.09475i
$7$	3.00953	+	3.00953i	1.13750	+	1.13750i	0.988897	+	0.148599i	$0.0474765\pi$
$7$	3.00953	+	3.00953i	1.13750	+	1.13750i	0.148599	+	0.988897i	$0.452523\pi$
$8$	−0.611199	−	2.76160i	−0.216092	−	0.976373i
$9$		−	5.40741i		−	1.80247i
$10$	−0.320547	−	3.14599i	−0.101366	−	0.994849i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	3.46409	−	4.65078i	0.999997	−	1.34256i
$13$	−0.709511	−	0.709511i	−0.196783	−	0.196783i	0.601836	−	0.798619i	$-0.294436\pi$
$13$	−0.709511	−	0.709511i	−0.196783	−	0.196783i	−0.798619	+	0.601836i	$0.794436\pi$
$14$	−3.93617	+	4.55365i	−1.05199	+	1.21701i
$15$	4.45003	−	4.71532i	1.14899	−	1.21749i
$16$	3.83250	−	1.14539i	0.958126	−	0.286348i
$17$	−1.02729	+	1.02729i	−0.249154	+	0.249154i	−0.820623	−	0.571469i	$-0.806374\pi$
$17$	−1.02729	+	1.02729i	−0.249154	+	0.249154i	0.571469	+	0.820623i	$0.306374\pi$
$18$	7.62709	−	0.554726i	1.79772	−	0.130750i
$19$	−5.70480			−1.30877			−0.654386	−	0.756161i	$-0.727073\pi$
$19$	−5.70480			−1.30877			−0.654386	+	0.756161i	$0.727073\pi$
$20$	4.40450	−	0.774863i	0.984875	−	0.173265i
$21$	−12.3409			−2.69300
$22$	1.41049	−	0.102586i	0.300717	−	0.0218715i
$23$	−3.28163	+	3.28163i	−0.684268	+	0.684268i	−0.960959	−	0.276691i	$-0.910762\pi$
$23$	−3.28163	+	3.28163i	−0.684268	+	0.684268i	0.276691	+	0.960959i	$0.410762\pi$
$24$	6.91523	+	4.40895i	1.41157	+	0.899974i
$25$	4.99163	−	0.289209i	0.998326	−	0.0578418i
$26$	0.927971	−	1.07354i	0.181990	−	0.210539i
$27$	4.93591	+	4.93591i	0.949916	+	0.949916i
$28$	−6.82666	−	5.08478i	−1.29012	−	0.960934i
$29$			0.344387i			0.0639510i	0.999489	+	0.0319755i	$0.0101799\pi$
$29$			0.344387i			0.0639510i	−0.999489	+	0.0319755i	$0.989820\pi$
$30$	7.10742	+	5.79299i	1.29763	+	1.05765i
$31$			5.97347i			1.07287i	0.843943	+	0.536433i	$0.180229\pi$
$31$			5.97347i			1.07287i	−0.843943	+	0.536433i	$0.819771\pi$
$32$	2.00872	+	5.28820i	0.355095	+	0.934830i
$33$	2.05029	+	2.05029i	0.356910	+	0.356910i
$34$	−1.55436	−	1.34359i	−0.266571	−	0.230424i
$35$	−6.92141	−	6.53200i	−1.16993	−	1.10411i
$36$	1.56487	+	10.7010i	0.260812	+	1.78350i
$37$	1.57859	−	1.57859i	0.259519	−	0.259519i	−0.565339	−	0.824858i	$-0.691255\pi$
$37$	1.57859	−	1.57859i	0.259519	−	0.259519i	0.824858	+	0.565339i	$0.191255\pi$
$38$	−0.585234	−	8.04655i	−0.0949376	−	1.30532i
$39$	2.90941			0.465879
$40$	1.54478	+	6.13300i	0.244251	+	0.969712i
$41$	−6.42941			−1.00411			−0.502053	−	0.864837i	$-0.667422\pi$
$41$	−6.42941			−1.00411			−0.502053	+	0.864837i	$0.667422\pi$
$42$	−1.26600	−	17.4066i	−0.195349	−	2.68590i
$43$	−3.02329	+	3.02329i	−0.461048	+	0.461048i	−0.898999	−	0.437951i	$-0.855704\pi$
$43$	−3.02329	+	3.02329i	−0.461048	+	0.461048i	0.437951	+	0.898999i	$0.355704\pi$
$44$	0.289393	+	1.97895i	0.0436277	+	0.298338i
$45$	0.349839	+	12.0863i	0.0521509	+	1.80172i
$46$	−4.96535	−	4.29205i	−0.732101	−	0.632829i
$47$	−6.62597	−	6.62597i	−0.966498	−	0.966498i	0.0329591	−	0.999457i	$-0.489507\pi$
$47$	−6.62597	−	6.62597i	−0.966498	−	0.966498i	−0.999457	+	0.0329591i	$0.989507\pi$
$48$	−5.50937	+	10.2061i	−0.795209	+	1.47313i
$49$			11.1146i			1.58780i
$50$	0.919998	+	7.01096i	0.130107	+	0.991500i
$51$		−	4.21249i		−	0.589866i
$52$	1.60942	+	1.19876i	0.223186	+	0.166238i
$53$	1.92847	+	1.92847i	0.264896	+	0.264896i	0.827039	−	0.562144i	$-0.190023\pi$
$53$	1.92847	+	1.92847i	0.264896	+	0.264896i	−0.562144	+	0.827039i	$0.690023\pi$
$54$	−6.45568	+	7.46839i	−0.878507	+	1.01632i
$55$	0.0646962	+	2.23513i	0.00872363	+	0.301385i
$56$	6.47170	−	10.1506i	0.864818	−	1.35642i
$57$	11.6965	−	11.6965i	1.54924	−	1.54924i
$58$	−0.485753	+	0.0353294i	−0.0637825	+	0.00463897i
$59$	1.69997			0.221318			0.110659	−	0.993858i	$-0.464704\pi$
$59$	1.69997			0.221318			0.110659	+	0.993858i	$0.464704\pi$
$60$	−7.44182	+	10.6192i	−0.960734	+	1.37093i
$61$	2.56189			0.328016			0.164008	−	0.986459i	$-0.447558\pi$
$61$	2.56189			0.328016			0.164008	+	0.986459i	$0.447558\pi$
$62$	−8.42550	+	0.612796i	−1.07004	+	0.0778251i
$63$	16.2738	−	16.2738i	2.05031	−	2.05031i
$64$	−7.25287	+	3.37578i	−0.906609	+	0.421972i
$65$	1.63175	+	1.53995i	0.202394	+	0.191007i
$66$	−2.68158	+	3.10225i	−0.330080	+	0.381860i
$67$	7.39211	+	7.39211i	0.903090	+	0.903090i	0.995702	−	0.0926126i	$-0.0295218\pi$
$67$	7.39211	+	7.39211i	0.903090	+	0.903090i	−0.0926126	+	0.995702i	$0.529522\pi$
$68$	1.73566	−	2.33025i	0.210480	−	0.282584i
$69$		−	13.4566i		−	1.61999i
$70$	8.50326	−	10.4327i	1.01633	−	1.24694i
$71$		−	4.24031i		−	0.503232i	−0.967827	−	0.251616i	$-0.919038\pi$
$71$		−	4.24031i		−	0.503232i	0.967827	−	0.251616i	$-0.0809619\pi$
$72$	−14.9331	+	3.30501i	−1.75988	+	0.389499i
$73$	11.1536	+	11.1536i	1.30543	+	1.30543i	0.924674	+	0.380760i	$0.124338\pi$
$73$	11.1536	+	11.1536i	1.30543	+	1.30543i	0.380760	+	0.924674i	$0.375662\pi$
$74$	2.38853	+	2.06464i	0.277661	+	0.240010i
$75$	−9.64134	+	10.8273i	−1.11329	+	1.25023i
$76$	11.2895	−	1.65093i	1.29500	−	0.189375i
$77$	3.00953	−	3.00953i	0.342968	−	0.342968i
$78$	0.298466	+	4.10369i	0.0337946	+	0.464652i
$79$	−0.182925			−0.0205806			−0.0102903	−	0.999947i	$-0.503276\pi$
$79$	−0.182925			−0.0205806			−0.0102903	+	0.999947i	$0.503276\pi$
$80$	−8.49205	+	2.80805i	−0.949440	+	0.313949i
$81$	−4.01788			−0.446431
$82$	−0.659570	−	9.06861i	−0.0728373	−	1.00146i
$83$	−10.3602	+	10.3602i	−1.13719	+	1.13719i	−0.148233	+	0.988953i	$0.547358\pi$
$83$	−10.3602	+	10.3602i	−1.13719	+	1.13719i	−0.988953	+	0.148233i	$0.952642\pi$
$84$	24.4220	−	3.57136i	2.66466	−	0.389668i
$85$	2.22966	−	2.36259i	0.241841	−	0.256259i
$86$	−4.57447	−	3.95417i	−0.493278	−	0.426389i
$87$	−0.706094	−	0.706094i	−0.0757012	−	0.0757012i
$88$	−2.76160	+	0.611199i	−0.294388	+	0.0651541i
$89$		−	6.52843i		−	0.692012i	−0.938232	−	0.346006i	$-0.887538\pi$
$89$		−	6.52843i		−	0.692012i	0.938232	−	0.346006i	$-0.112462\pi$
$90$	−17.0117	+	1.73333i	−1.79319	+	0.182709i
$91$		−	4.27059i		−	0.447680i
$92$	5.54451	−	7.44388i	0.578055	−	0.776078i
$93$	−12.2474	−	12.2474i	−1.26999	−	1.26999i
$94$	8.66612	−	10.0256i	0.893842	−	1.03406i
$95$	12.7510	−	0.369079i	1.30822	−	0.0378667i
$96$	−14.9608	−	6.72389i	−1.52693	−	0.686254i
$97$	−12.5123	+	12.5123i	−1.27043	+	1.27043i	−0.324565	+	0.945863i	$0.605218\pi$
$97$	−12.5123	+	12.5123i	−1.27043	+	1.27043i	−0.945863	+	0.324565i	$0.894782\pi$
$98$	−15.6770	+	1.14020i	−1.58362	+	0.115178i
$99$	−5.40741			−0.543465
$100$	−9.79450	+	2.01688i	−0.979450	+	0.201688i
$101$	9.05577			0.901083			0.450541	−	0.892756i	$-0.351231\pi$
$101$	9.05577			0.901083			0.450541	+	0.892756i	$0.351231\pi$
$102$	5.94166	−	0.432144i	0.588312	−	0.0427886i
$103$	6.99102	−	6.99102i	0.688846	−	0.688846i	−0.273131	−	0.961977i	$-0.588059\pi$
$103$	6.99102	−	6.99102i	0.688846	−	0.688846i	0.961977	+	0.273131i	$0.0880592\pi$
$104$	−1.52573	+	2.39304i	−0.149610	+	0.234657i
$105$	27.5835	−	0.798406i	2.69187	−	0.0779165i
$106$	−2.52225	+	2.91792i	−0.244982	+	0.283413i
$107$	7.14008	+	7.14008i	0.690258	+	0.690258i	0.962289	−	0.272031i	$-0.0876953\pi$
$107$	7.14008	+	7.14008i	0.690258	+	0.690258i	−0.272031	+	0.962289i	$0.587695\pi$
$108$	−11.1963	−	8.33950i	−1.07737	−	0.802469i
$109$			3.15539i			0.302231i	0.988516	+	0.151116i	$0.0482866\pi$
$109$			3.15539i			0.302231i	−0.988516	+	0.151116i	$0.951713\pi$
$110$	−3.14599	+	0.320547i	−0.299958	+	0.0305630i
$111$			6.47316i			0.614405i
$112$	14.9811	+	8.08695i	1.41558	+	0.764145i
$113$	0.917236	+	0.917236i	0.0862863	+	0.0862863i	0.748933	−	0.662646i	$-0.230567\pi$
$113$	0.917236	+	0.917236i	0.0862863	+	0.0862863i	−0.662646	+	0.748933i	$0.730567\pi$
$114$	17.6977	+	15.2979i	1.65754	+	1.43278i
$115$	7.12257	−	7.54719i	0.664183	−	0.703779i
$116$	−0.0996633	−	0.681525i	−0.00925350	−	0.0632780i
$117$	−3.83662	+	3.83662i	−0.354696	+	0.354696i
$118$	0.174394	+	2.39779i	0.0160543	+	0.220735i
$119$	−6.18332			−0.566824
$120$	−15.7417	−	9.40721i	−1.43701	−	0.858756i
$121$	−1.00000			−0.0909091
$122$	0.262814	+	3.61351i	0.0237941	+	0.327152i
$123$	13.1822	−	13.1822i	1.18860	−	1.18860i
$124$	−1.72868	−	11.8212i	−0.155240	−	1.06158i
$125$	−11.1382	+	0.969359i	−0.996234	+	0.0867021i
$126$	24.6235	+	21.2845i	2.19363	+	1.89618i
$127$	−7.13455	−	7.13455i	−0.633089	−	0.633089i	0.315752	−	0.948842i	$-0.397743\pi$
$127$	−7.13455	−	7.13455i	−0.633089	−	0.633089i	−0.948842	+	0.315752i	$0.897743\pi$
$128$	−5.50554	−	9.88378i	−0.486625	−	0.873611i
$129$		−	12.3973i		−	1.09152i
$130$	−2.00468	+	2.45955i	−0.175822	+	0.215716i
$131$			6.06882i			0.530235i	0.964216	+	0.265118i	$0.0854108\pi$
$131$			6.06882i			0.530235i	−0.964216	+	0.265118i	$0.914589\pi$
$132$	−4.65078	−	3.46409i	−0.404798	−	0.301511i
$133$	−17.1688	−	17.1688i	−1.48872	−	1.48872i
$134$	−9.66815	+	11.1848i	−0.835201	+	0.966220i
$135$	−11.3517	−	10.7131i	−0.977002	−	0.922034i
$136$	3.46484	+	2.20908i	0.297108	+	0.189427i
$137$	−9.93269	+	9.93269i	−0.848607	+	0.848607i	−0.989959	−	0.141352i	$-0.954855\pi$
$137$	−9.93269	+	9.93269i	−0.848607	+	0.848607i	0.141352	+	0.989959i	$0.454855\pi$
$138$	18.9804	−	1.38047i	1.61572	−	0.117513i
$139$	3.35375			0.284461			0.142231	−	0.989834i	$-0.454573\pi$
$139$	3.35375			0.284461			0.142231	+	0.989834i	$0.454573\pi$
$140$	15.5875	+	10.9235i	1.31738	+	0.923205i
$141$	27.1704			2.28816
$142$	5.98090	−	0.434997i	0.501906	−	0.0365042i
$143$	−0.709511	+	0.709511i	−0.0593323	+	0.0593323i
$144$	−6.19361	−	20.7239i	−0.516134	−	1.72699i
$145$	−0.0222805	−	0.769750i	−0.00185030	−	0.0639242i
$146$	−14.5879	+	16.8763i	−1.20730	+	1.39669i
$147$	−22.7882	−	22.7882i	−1.87954	−	1.87954i
$148$	−2.66712	+	3.58079i	−0.219236	+	0.294339i
$149$			1.25924i			0.103161i	0.998669	+	0.0515805i	$0.0164259\pi$
$149$			1.25924i			0.103161i	−0.998669	+	0.0515805i	$0.983574\pi$
$150$	−16.2608	−	12.4883i	−1.32769	−	1.01966i
$151$		−	11.8156i		−	0.961542i	−0.876846	−	0.480771i	$-0.840357\pi$
$151$		−	11.8156i		−	0.961542i	0.876846	−	0.480771i	$-0.159643\pi$
$152$	3.48677	+	15.7544i	0.282814	+	1.27785i
$153$	5.55498	+	5.55498i	0.449093	+	0.449093i
$154$	4.55365	+	3.93617i	0.366943	+	0.317186i
$155$	−0.386460	−	13.3515i	−0.0310412	−	1.07242i
$156$	−5.75759	+	0.841965i	−0.460976	+	0.0674111i
$157$	−14.1962	+	14.1962i	−1.13298	+	1.13298i	−0.143297	+	0.989680i	$0.545770\pi$
$157$	−14.1962	+	14.1962i	−1.13298	+	1.13298i	−0.989680	+	0.143297i	$0.954230\pi$
$158$	−0.0187656	−	0.258013i	−0.00149291	−	0.0205264i
$159$	−7.90786			−0.627134
$160$	−4.83189	−	11.6899i	−0.381994	−	0.924165i
$161$	−19.7524			−1.55670
$162$	−0.412179	−	5.66717i	−0.0323839	−	0.445255i
$163$	0.600905	−	0.600905i	0.0470665	−	0.0470665i	−0.683182	−	0.730248i	$-0.739404\pi$
$163$	0.600905	−	0.600905i	0.0470665	−	0.0470665i	0.730248	+	0.683182i	$0.239404\pi$
$164$	12.7235	−	1.86063i	0.993538	−	0.145291i
$165$	−4.71532	−	4.45003i	−0.367087	−	0.346435i
$166$	−15.6758	−	13.5502i	−1.21668	−	1.05170i
$167$	4.99031	+	4.99031i	0.386162	+	0.386162i	0.873316	−	0.487154i	$-0.161965\pi$
$167$	4.99031	+	4.99031i	0.386162	+	0.386162i	−0.487154	+	0.873316i	$0.661965\pi$
$168$	7.54273	+	34.0805i	0.581934	+	2.62937i
$169$		−	11.9932i		−	0.922553i
$170$	3.56113	+	2.90255i	0.273127	+	0.222615i
$171$			30.8482i			2.35902i
$172$	5.10803	−	6.85788i	0.389484	−	0.522908i
$173$	8.80565	+	8.80565i	0.669481	+	0.669481i	0.957596	−	0.288115i	$-0.0930285\pi$
$173$	8.80565	+	8.80565i	0.669481	+	0.669481i	−0.288115	+	0.957596i	$0.593029\pi$
$174$	0.923502	−	1.06837i	0.0700105	−	0.0809931i
$175$	15.8929	+	14.1521i	1.20139	+	1.06980i
$176$	−1.14539	−	3.83250i	−0.0863371	−	0.288886i
$177$	−3.48545	+	3.48545i	−0.261982	+	0.261982i
$178$	9.20827	−	0.669727i	0.690189	−	0.0501982i
$179$	−2.48595			−0.185809			−0.0929043	−	0.995675i	$-0.529615\pi$
$179$	−2.48595			−0.185809			−0.0929043	+	0.995675i	$0.529615\pi$
$180$	−4.19001	−	23.8169i	−0.312305	−	1.77521i
$181$	18.3428			1.36341			0.681704	−	0.731628i	$-0.261239\pi$
$181$	18.3428			1.36341			0.681704	+	0.731628i	$0.261239\pi$
$182$	6.02362	−	0.438104i	0.446501	−	0.0324745i
$183$	−5.25262	+	5.25262i	−0.388285	+	0.388285i
$184$	11.0683	+	7.05683i	0.815965	+	0.520236i
$185$	−3.42623	+	3.63049i	−0.251902	+	0.266919i
$186$	16.0183	−	18.5312i	1.17452	−	1.35877i
$187$	1.02729	+	1.02729i	0.0751228	+	0.0751228i
$188$	15.0300	+	11.1950i	1.09618	+	0.816477i
$189$			29.7096i			2.16105i
$190$	1.82866	+	17.9472i	0.132665	+	1.30203i
$191$			23.5527i			1.70421i	0.523369	+	0.852106i	$0.324675\pi$
$191$			23.5527i			1.70421i	−0.523369	+	0.852106i	$0.675325\pi$
$192$	7.94919	−	21.7919i	0.573683	−	1.57269i
$193$	−0.787715	−	0.787715i	−0.0567009	−	0.0567009i	0.678188	−	0.734889i	$-0.262766\pi$
$193$	−0.787715	−	0.787715i	−0.0567009	−	0.0567009i	−0.734889	+	0.678188i	$0.762766\pi$
$194$	−18.9320	−	16.3648i	−1.35924	−	1.17493i
$195$	−6.50292	+	0.188228i	−0.465684	+	0.0134793i
$196$	−3.21649	−	21.9952i	−0.229749	−	1.57109i
$197$	16.9591	−	16.9591i	1.20828	−	1.20828i	0.236700	−	0.971583i	$-0.423934\pi$
$197$	16.9591	−	16.9591i	1.20828	−	1.20828i	0.971583	−	0.236700i	$-0.0760657\pi$
$198$	−0.554726	−	7.62709i	−0.0394227	−	0.542034i
$199$	3.86644			0.274084			0.137042	−	0.990565i	$-0.456240\pi$
$199$	3.86644			0.274084			0.137042	+	0.990565i	$0.456240\pi$
$200$	−3.84956	−	13.6081i	−0.272205	−	0.962239i
$201$	−30.3120			−2.13804
$202$	0.928998	+	12.7731i	0.0653641	+	0.898709i
$203$	−1.03644	+	1.03644i	−0.0727441	+	0.0727441i
$204$	1.21907	+	8.33631i	0.0853517	+	0.583659i
$205$	14.3706	−	0.415958i	1.00369	−	0.0290518i
$206$	10.5779	+	9.14357i	0.737000	+	0.637063i
$207$	17.7451	+	17.7451i	1.23337	+	1.23337i
$208$	−3.53187	−	1.90654i	−0.244891	−	0.132194i
$209$			5.70480i			0.394609i
$210$	3.95583	+	38.8242i	0.272978	+	2.67913i
$211$			7.23621i			0.498161i	0.968483	+	0.249081i	$0.0801284\pi$
$211$			7.23621i			0.498161i	−0.968483	+	0.249081i	$0.919872\pi$
$212$	−4.37443	−	3.25826i	−0.300437	−	0.223778i
$213$	8.69387	+	8.69387i	0.595694	+	0.595694i
$214$	−9.33852	+	10.8035i	−0.638368	+	0.738510i
$215$	6.56187	−	6.95306i	0.447516	−	0.474195i
$216$	10.6142	−	16.6478i	0.722203	−	1.13274i
$217$	−17.9774	+	17.9774i	−1.22038	+	1.22038i
$218$	−4.45064	+	0.323699i	−0.301435	+	0.0219237i
$219$	−45.7365			−3.09058
$220$	−0.774863	−	4.40450i	−0.0522413	−	0.296951i
$221$	1.45775			0.0980586
$222$	−9.13031	+	0.664057i	−0.612786	+	0.0445686i
$223$	4.49599	−	4.49599i	0.301074	−	0.301074i	−0.540360	−	0.841434i	$-0.681712\pi$
$223$	4.49599	−	4.49599i	0.301074	−	0.301074i	0.841434	+	0.540360i	$0.181712\pi$
$224$	−9.86969	+	21.9603i	−0.659446	+	1.46729i
$225$	−1.56387	−	26.9918i	−0.104258	−	1.79945i
$226$	−1.19965	+	1.38785i	−0.0797998	+	0.0923182i
$227$	3.42222	+	3.42222i	0.227141	+	0.227141i	0.811497	−	0.584356i	$-0.198653\pi$
$227$	3.42222	+	3.42222i	0.227141	+	0.227141i	−0.584356	+	0.811497i	$0.698653\pi$
$228$	−19.7620	+	26.5318i	−1.30877	+	1.75711i
$229$		−	5.20745i		−	0.344118i	−0.985087	−	0.172059i	$-0.944958\pi$
$229$		−	5.20745i		−	0.344118i	0.985087	−	0.172059i	$-0.0550420\pi$
$230$	11.3759	+	9.27206i	0.750105	+	0.611382i
$231$			12.3409i			0.811969i
$232$	0.951058	−	0.210489i	0.0624400	−	0.0138193i
$233$	−6.57758	−	6.57758i	−0.430911	−	0.430911i	0.458027	−	0.888938i	$-0.348556\pi$
$233$	−6.57758	−	6.57758i	−0.430911	−	0.430911i	−0.888938	+	0.458027i	$0.848556\pi$
$234$	−5.80509	−	5.01792i	−0.379491	−	0.328032i
$235$	15.2386	+	14.3813i	0.994057	+	0.938129i
$236$	−3.36417	+	0.491962i	−0.218989	+	0.0320240i
$237$	0.375050	−	0.375050i	0.0243621	−	0.0243621i
$238$	−0.634324	−	8.72150i	−0.0411171	−	0.565331i
$239$	−0.684835			−0.0442983			−0.0221491	−	0.999755i	$-0.507051\pi$
$239$	−0.684835			−0.0442983			−0.0221491	+	0.999755i	$0.507051\pi$
$240$	11.6539	−	23.1685i	0.752254	−	1.49552i
$241$	16.2456			1.04647			0.523236	−	0.852188i	$-0.324725\pi$
$241$	16.2456			1.04647			0.523236	+	0.852188i	$0.324725\pi$
$242$	−0.102586	−	1.41049i	−0.00659450	−	0.0906696i
$243$	−6.56988	+	6.56988i	−0.421458	+	0.421458i
$244$	−5.06985	+	0.741393i	−0.324564	+	0.0474628i
$245$	−0.719071	−	24.8426i	−0.0459398	−	1.58713i
$246$	19.9456	+	17.2410i	1.27169	+	1.09925i
$247$	4.04762	+	4.04762i	0.257544	+	0.257544i
$248$	16.4963	−	3.65098i	1.04752	−	0.231837i
$249$		−	42.4831i		−	2.69226i
$250$	−2.50990	−	15.6109i	−0.158740	−	0.987320i
$251$		−	2.97231i		−	0.187610i	−0.995591	−	0.0938052i	$-0.970097\pi$
$251$		−	2.97231i		−	0.187610i	0.995591	−	0.0938052i	$-0.0299031\pi$
$252$	−27.4955	+	36.9146i	−1.73206	+	2.32540i
$253$	3.28163	+	3.28163i	0.206314	+	0.206314i
$254$	9.33129	−	10.7951i	0.585497	−	0.677345i
$255$	0.272532	+	9.41547i	0.0170666	+	0.589619i
$256$	13.3762	−	8.77943i	0.836010	−	0.548715i
$257$	0.484275	−	0.484275i	0.0302082	−	0.0302082i	−0.691841	−	0.722050i	$-0.743200\pi$
$257$	0.484275	−	0.484275i	0.0302082	−	0.0302082i	0.722050	+	0.691841i	$0.243200\pi$
$258$	17.4862	−	1.27179i	1.08864	−	0.0791783i
$259$	9.50165			0.590404
$260$	−3.67481	−	2.57526i	−0.227902	−	0.159711i
$261$	1.86224			0.115270
$262$	−8.56000	+	0.622578i	−0.528839	+	0.0384630i
$263$	16.7193	−	16.7193i	1.03096	−	1.03096i	0.0314517	−	0.999505i	$-0.489987\pi$
$263$	16.7193	−	16.7193i	1.03096	−	1.03096i	0.999505	−	0.0314517i	$-0.0100130\pi$
$264$	4.40895	−	6.91523i	0.271352	−	0.425603i
$265$	−4.43515	−	4.18562i	−0.272449	−	0.257120i
$266$	22.4551	−	25.9777i	1.37681	−	1.59279i
$267$	13.3852	+	13.3852i	0.819161	+	0.819161i
$268$	−16.7679	−	12.4894i	−1.02426	−	0.762911i
$269$			16.6300i			1.01395i	0.861960	+	0.506976i	$0.169237\pi$
$269$			16.6300i			1.01395i	−0.861960	+	0.506976i	$0.830763\pi$
$270$	13.9461	−	17.1105i	0.848734	−	1.04131i
$271$		−	22.0740i		−	1.34090i	−0.741956	−	0.670449i	$-0.766102\pi$
$271$		−	22.0740i		−	1.34090i	0.741956	−	0.670449i	$-0.233898\pi$
$272$	−2.76044	+	5.11374i	−0.167376	+	0.310066i
$273$	8.75598	+	8.75598i	0.529936	+	0.529936i
$274$	−15.0289	−	12.9910i	−0.907929	−	0.784814i
$275$	−0.289209	−	4.99163i	−0.0174400	−	0.301007i
$276$	3.89426	+	26.6300i	0.234407	+	1.60294i
$277$	−11.6408	+	11.6408i	−0.699428	+	0.699428i	−0.964287	−	0.264859i	$-0.914674\pi$
$277$	−11.6408	+	11.6408i	−0.699428	+	0.699428i	0.264859	+	0.964287i	$0.414674\pi$
$278$	0.344049	+	4.73042i	0.0206347	+	0.283712i
$279$	32.3010			1.93381
$280$	−13.8084	+	23.1065i	−0.825210	+	1.38088i
$281$	2.90866			0.173516			0.0867581	−	0.996229i	$-0.472349\pi$
$281$	2.90866			0.173516			0.0867581	+	0.996229i	$0.472349\pi$
$282$	2.78731	+	38.3235i	0.165982	+	2.28213i
$283$	−11.1007	+	11.1007i	−0.659868	+	0.659868i	−0.955349	−	0.295480i	$-0.904520\pi$
$283$	−11.1007	+	11.1007i	−0.659868	+	0.659868i	0.295480	+	0.955349i	$0.404520\pi$
$284$	1.22712	+	8.39136i	0.0728160	+	0.497936i
$285$	−25.3866	+	26.9000i	−1.50377	+	1.59342i
$286$	−1.07354	−	0.927971i	−0.0634799	−	0.0548720i
$287$	−19.3495	−	19.3495i	−1.14217	−	1.14217i
$288$	28.5955	−	10.8620i	1.68500	−	0.640049i
$289$			14.8894i			0.875844i
$290$	1.08344	−	0.110392i	0.0636216	−	0.00648245i
$291$		−	51.3077i		−	3.00771i
$292$	−25.3003	−	18.8447i	−1.48059	−	1.10280i
$293$	11.6325	+	11.6325i	0.679575	+	0.679575i	0.959904	−	0.280329i	$-0.0904435\pi$
$293$	11.6325	+	11.6325i	0.679575	+	0.679575i	−0.280329	+	0.959904i	$0.590443\pi$
$294$	29.8047	−	34.4802i	1.73825	−	2.01093i
$295$	−3.79967	+	0.109982i	−0.221225	+	0.00640339i
$296$	−5.32427	−	3.39461i	−0.309467	−	0.197307i
$297$	4.93591	−	4.93591i	0.286410	−	0.286410i
$298$	−1.77614	+	0.129181i	−0.102889	+	0.00748324i
$299$	4.65671			0.269304
$300$	15.9464	−	24.2168i	0.920667	−	1.39816i
$301$	−18.1974			−1.04888
$302$	16.6658	−	1.21212i	0.959009	−	0.0697497i
$303$	−18.5670	+	18.5670i	−1.06665	+	1.06665i
$304$	−21.8637	+	6.53423i	−1.25397	+	0.374764i
$305$	−5.72615	+	0.165744i	−0.327879	+	0.00949049i
$306$	−7.26536	+	8.40509i	−0.415333	+	0.480487i
$307$	−9.89105	−	9.89105i	−0.564512	−	0.564512i	0.366074	−	0.930586i	$-0.380702\pi$
$307$	−9.89105	−	9.89105i	−0.564512	−	0.564512i	−0.930586	+	0.366074i	$0.880702\pi$
$308$	−5.08478	+	6.82666i	−0.289732	+	0.388985i
$309$			28.6673i			1.63083i
$310$	18.7925	−	1.91478i	1.06734	−	0.108752i
$311$		−	16.6409i		−	0.943617i	−0.881701	−	0.471809i	$-0.843601\pi$
$311$		−	16.6409i		−	0.943617i	0.881701	−	0.471809i	$-0.156399\pi$
$312$	−1.77823	−	8.03463i	−0.100673	−	0.454872i
$313$	−21.9753	−	21.9753i	−1.24212	−	1.24212i	−0.959121	−	0.282996i	$-0.908672\pi$
$313$	−21.9753	−	21.9753i	−1.24212	−	1.24212i	−0.282996	−	0.959121i	$-0.591328\pi$
$314$	−21.4798	−	18.5672i	−1.21218	−	1.04781i
$315$	−35.3212	+	37.4269i	−1.99013	+	2.10877i
$316$	0.361999	−	0.0529372i	0.0203641	−	0.00297795i
$317$	11.6086	−	11.6086i	0.652005	−	0.652005i	−0.301470	−	0.953476i	$-0.597477\pi$
$317$	11.6086	−	11.6086i	0.652005	−	0.652005i	0.953476	+	0.301470i	$0.0974774\pi$
$318$	−0.811238	−	11.1539i	−0.0454920	−	0.625482i
$319$	0.344387			0.0192820
$320$	15.9927	−	8.01454i	0.894020	−	0.448026i
$321$	−29.2785			−1.63417
$322$	−2.02632	−	27.8605i	−0.112923	−	1.55260i
$323$	5.86048	−	5.86048i	0.326086	−	0.326086i
$324$	7.95119	−	1.16275i	0.441733	−	0.0645971i
$325$	−3.74681	−	3.33642i	−0.207836	−	0.185071i
$326$	0.909213	+	0.785924i	0.0503567	+	0.0435283i
$327$	−6.46947	−	6.46947i	−0.357763	−	0.357763i
$328$	3.92965	+	17.7555i	0.216979	+	0.980382i
$329$		−	39.8822i		−	2.19878i
$330$	5.79299	−	7.10742i	0.318894	−	0.391251i
$331$		−	2.78049i		−	0.152830i	−0.997076	−	0.0764148i	$-0.975653\pi$
$331$		−	2.78049i		−	0.152830i	0.997076	−	0.0764148i	$-0.0243473\pi$
$332$	17.5043	−	23.5006i	0.960671	−	1.28976i
$333$	−8.53610	−	8.53610i	−0.467775	−	0.467775i
$334$	−6.52683	+	7.55071i	−0.357132	+	0.413156i
$335$	−17.0006	−	16.0441i	−0.928841	−	0.876582i
$336$	−47.2964	+	14.1351i	−2.58023	+	0.771134i
$337$	8.07923	−	8.07923i	0.440103	−	0.440103i	−0.451943	−	0.892047i	$-0.649269\pi$
$337$	8.07923	−	8.07923i	0.440103	−	0.440103i	0.892047	+	0.451943i	$0.149269\pi$
$338$	16.9162	−	1.23034i	0.920123	−	0.0669215i
$339$	−3.76121			−0.204281
$340$	−3.72868	+	5.32070i	−0.202216	+	0.288555i
$341$	5.97347			0.323481
$342$	−43.5110	+	3.16460i	−2.35281	+	0.171122i
$343$	−12.3830	+	12.3830i	−0.668619	+	0.668619i
$344$	10.1970	+	6.50129i	0.549784	+	0.350526i
$345$	0.870592	+	30.0773i	0.0468711	+	1.61931i
$346$	−11.5169	+	13.3236i	−0.619153	+	0.716281i
$347$	9.64663	+	9.64663i	0.517858	+	0.517858i	0.916923	−	0.399064i	$-0.130665\pi$
$347$	9.64663	+	9.64663i	0.517858	+	0.517858i	−0.399064	+	0.916923i	$0.630665\pi$
$348$	1.60167	+	1.19299i	0.0858583	+	0.0639508i
$349$		−	8.92010i		−	0.477482i	−0.971083	−	0.238741i	$-0.923265\pi$
$349$		−	8.92010i		−	0.477482i	0.971083	−	0.238741i	$-0.0767347\pi$
$350$	−18.3310	+	23.8685i	−0.979831	+	1.27582i
$351$		−	7.00416i		−	0.373854i
$352$	5.28820	−	2.00872i	0.281862	−	0.107065i
$353$	19.4271	+	19.4271i	1.03400	+	1.03400i	0.999401	+	0.0345986i	$0.0110153\pi$
$353$	19.4271	+	19.4271i	1.03400	+	1.03400i	0.0345986	+	0.999401i	$0.488985\pi$
$354$	−5.27374	−	4.55862i	−0.280296	−	0.242288i
$355$	0.274332	+	9.47764i	0.0145600	+	0.503021i
$356$	1.88928	+	12.9194i	0.100132	+	0.684729i
$357$	12.6776	−	12.6776i	0.670971	−	0.670971i
$358$	−0.255024	−	3.50640i	−0.0134784	−	0.185319i
$359$	−10.2926			−0.543225			−0.271612	−	0.962407i	$-0.587557\pi$
$359$	−10.2926			−0.543225			−0.271612	+	0.962407i	$0.587557\pi$
$360$	33.1637	−	8.35324i	1.74788	−	0.440255i
$361$	13.5448			0.712882
$362$	1.88172	+	25.8723i	0.0989009	+	1.35982i
$363$	2.05029	−	2.05029i	0.107613	−	0.107613i
$364$	1.23588	+	8.45130i	0.0647778	+	0.442969i
$365$	−25.6514	−	24.2082i	−1.34266	−	1.26712i
$366$	−7.94760	−	6.86991i	−0.415428	−	0.359096i
$367$	−16.6035	−	16.6035i	−0.866694	−	0.866694i	0.125411	−	0.992105i	$-0.459975\pi$
$367$	−16.6035	−	16.6035i	−0.866694	−	0.866694i	−0.992105	+	0.125411i	$0.959975\pi$
$368$	−8.81811	+	16.3356i	−0.459676	+	0.851553i
$369$			34.7665i			1.80987i
$370$	−5.47225	−	4.46022i	−0.284489	−	0.231876i
$371$			11.6076i			0.602636i
$372$	27.7813	+	20.6926i	1.44039	+	1.07286i
$373$	−4.03877	−	4.03877i	−0.209119	−	0.209119i	0.594774	−	0.803893i	$-0.297242\pi$
$373$	−4.03877	−	4.03877i	−0.209119	−	0.209119i	−0.803893	+	0.594774i	$0.797242\pi$
$374$	−1.34359	+	1.55436i	−0.0694755	+	0.0803743i
$375$	20.8492	−	24.8241i	1.07665	−	1.28191i
$376$	−14.2485	+	22.3481i	−0.734810	+	1.15251i
$377$	0.244346	−	0.244346i	0.0125845	−	0.0125845i
$378$	−41.9050	+	3.04779i	−2.15536	+	0.156762i
$379$	37.7938			1.94134			0.970669	−	0.240420i	$-0.0772851\pi$
$379$	37.7938			1.94134			0.970669	+	0.240420i	$0.0772851\pi$
$380$	−25.1268	+	4.42044i	−1.28898	+	0.226764i
$381$	29.2559			1.49882
$382$	−33.2208	+	2.41618i	−1.69972	+	0.123623i
$383$	−18.1611	+	18.1611i	−0.927987	+	0.927987i	−0.997576	−	0.0695892i	$-0.977831\pi$
$383$	−18.1611	+	18.1611i	−0.927987	+	0.927987i	0.0695892	+	0.997576i	$0.477831\pi$
$384$	31.5526	+	8.97668i	1.61016	+	0.458089i
$385$	−6.53200	+	6.92141i	−0.332902	+	0.352748i
$386$	1.03025	−	1.19187i	0.0524385	−	0.0606646i
$387$	16.3482	+	16.3482i	0.831026	+	0.831026i
$388$	21.1402	−	28.3822i	1.07323	−	1.44089i
$389$		−	21.8372i		−	1.10719i	−0.832787	−	0.553594i	$-0.813256\pi$
$389$		−	21.8372i		−	1.10719i	0.832787	−	0.553594i	$-0.186744\pi$
$390$	−0.932604	−	9.15298i	−0.0472242	−	0.463479i
$391$		−	6.74237i		−	0.340976i
$392$	30.6941	−	6.79323i	1.55028	−	0.343110i
$393$	−12.4429	−	12.4429i	−0.627660	−	0.627660i
$394$	25.6603	+	22.1808i	1.29275	+	1.11745i
$395$	0.408861	−	0.0118345i	0.0205720	−	0.000595460i
$396$	10.7010	−	1.56487i	0.537746	−	0.0786377i
$397$	20.4719	−	20.4719i	1.02746	−	1.02746i	0.0278432	−	0.999612i	$-0.491136\pi$
$397$	20.4719	−	20.4719i	1.02746	−	1.02746i	0.999612	−	0.0278432i	$-0.00886393\pi$
$398$	0.396643	+	5.45356i	0.0198819	+	0.273362i
$399$	70.4022			3.52452
$400$	18.7992	−	6.82576i	0.939959	−	0.341288i
$401$	13.4235			0.670339			0.335170	−	0.942158i	$-0.391206\pi$
$401$	13.4235			0.670339			0.335170	+	0.942158i	$0.391206\pi$
$402$	−3.10959	−	42.7547i	−0.155092	−	2.13241i
$403$	4.23824	−	4.23824i	0.211122	−	0.211122i
$404$	−17.9209	+	2.62068i	−0.891600	+	0.130384i
$405$	8.98049	−	0.259941i	0.446244	−	0.0129166i
$406$	−1.56822	−	1.35557i	−0.0778293	−	0.0672756i
$407$	−1.57859	−	1.57859i	−0.0782479	−	0.0782479i
$408$	−11.6332	+	2.57467i	−0.575930	+	0.127465i
$409$			8.82027i			0.436134i	0.975934	+	0.218067i	$0.0699752\pi$
$409$			8.82027i			0.436134i	−0.975934	+	0.218067i	$0.930025\pi$
$410$	2.06093	+	20.2269i	0.101782	+	0.998934i
$411$		−	40.7299i		−	2.00906i
$412$	−11.8117	+	15.8581i	−0.581923	+	0.781270i
$413$	5.11613	+	5.11613i	0.251748	+	0.251748i
$414$	−23.2089	+	26.8497i	−1.14066	+	1.31959i
$415$	22.4863	−	23.8268i	1.10381	−	1.16961i
$416$	2.32682	−	5.17725i	0.114082	−	0.253835i
$417$	−6.87617	+	6.87617i	−0.336728	+	0.336728i
$418$	−8.04655	+	0.585234i	−0.393570	+	0.0286248i
$419$	−9.54658			−0.466381			−0.233190	−	0.972431i	$-0.574917\pi$
$419$	−9.54658			−0.466381			−0.233190	+	0.972431i	$0.574917\pi$
$420$	−54.3553	+	9.56248i	−2.65227	+	0.466601i
$421$	−14.5350			−0.708390			−0.354195	−	0.935172i	$-0.615245\pi$
$421$	−14.5350			−0.708390			−0.354195	+	0.935172i	$0.615245\pi$
$422$	−10.2066	+	0.742336i	−0.496849	+	0.0361363i
$423$	−35.8294	+	35.8294i	−1.74208	+	1.74208i
$424$	4.14698	−	6.50434i	0.201395	−	0.315879i
$425$	−4.83074	+	5.42495i	−0.234325	+	0.263149i
$426$	−11.3707	+	13.1545i	−0.550914	+	0.637336i
$427$	7.71008	+	7.71008i	0.373117	+	0.373117i
$428$	−16.1962	−	12.0636i	−0.782871	−	0.583115i
$429$		−	2.90941i		−	0.140468i
$430$	10.4804	+	8.54214i	0.505408	+	0.411939i
$431$			25.6238i			1.23425i	0.786864	+	0.617127i	$0.211703\pi$
$431$			25.6238i			1.23425i	−0.786864	+	0.617127i	$0.788297\pi$
$432$	24.5704	+	13.2633i	1.18214	+	0.638132i
$433$	12.6473	+	12.6473i	0.607790	+	0.607790i	0.942368	−	0.334578i	$-0.108594\pi$
$433$	12.6473	+	12.6473i	0.607790	+	0.607790i	−0.334578	+	0.942368i	$0.608594\pi$
$434$	−27.2011	−	23.5126i	−1.30569	−	1.12864i
$435$	1.62390	+	1.53253i	0.0778598	+	0.0734793i
$436$	−0.913148	−	6.24436i	−0.0437319	−	0.299051i
$437$	18.7211	−	18.7211i	0.895550	−	0.895550i
$438$	−4.69193	−	64.5107i	−0.224189	−	3.08244i
$439$	25.5128			1.21766			0.608830	−	0.793300i	$-0.291639\pi$
$439$	25.5128			1.21766			0.608830	+	0.793300i	$0.291639\pi$
$440$	6.13300	−	1.54478i	0.292379	−	0.0736443i
$441$	60.1012			2.86196
$442$	0.149545	+	2.05613i	0.00711312	+	0.0978002i
$443$	2.20795	−	2.20795i	0.104903	−	0.104903i	−0.652707	−	0.757610i	$-0.726367\pi$
$443$	2.20795	−	2.20795i	0.104903	−	0.104903i	0.757610	+	0.652707i	$0.226367\pi$
$444$	−1.87329	−	12.8101i	−0.0889024	−	0.607939i
$445$	0.422364	+	14.5919i	0.0200220	+	0.691722i
$446$	6.80277	+	5.88032i	0.322121	+	0.278441i
$447$	−2.58181	−	2.58181i	−0.122116	−	0.122116i
$448$	−31.9873	−	11.6682i	−1.51126	−	0.551273i
$449$		−	3.06554i		−	0.144672i	−0.997380	−	0.0723359i	$-0.976955\pi$
$449$		−	3.06554i		−	0.144672i	0.997380	−	0.0723359i	$-0.0230454\pi$
$450$	37.9112	−	4.97481i	1.78715	−	0.234515i
$451$			6.42941i			0.302749i
$452$	−2.08061	−	1.54972i	−0.0978636	−	0.0728929i
$453$	24.2255	+	24.2255i	1.13821	+	1.13821i
$454$	−4.47593	+	5.17807i	−0.210066	+	0.243019i
$455$	0.276291	+	9.54534i	0.0129527	+	0.447493i
$456$	−39.4500	−	25.1522i	−1.84742	−	1.17786i
$457$	−3.67461	+	3.67461i	−0.171891	+	0.171891i	−0.787810	−	0.615919i	$-0.788785\pi$
$457$	−3.67461	+	3.67461i	−0.171891	+	0.171891i	0.615919	+	0.787810i	$0.288785\pi$
$458$	7.34505	−	0.534213i	0.343212	−	0.0249622i
$459$	−10.1412			−0.473351
$460$	−11.9111	+	16.9968i	−0.555359	+	0.792478i
$461$	8.55849			0.398609			0.199304	−	0.979938i	$-0.436132\pi$
$461$	8.55849			0.398609			0.199304	+	0.979938i	$0.436132\pi$
$462$	−17.4066	+	1.26600i	−0.809830	+	0.0588998i
$463$	−10.4394	+	10.4394i	−0.485160	+	0.485160i	−0.906775	−	0.421615i	$-0.861463\pi$
$463$	−10.4394	+	10.4394i	−0.485160	+	0.485160i	0.421615	+	0.906775i	$0.361463\pi$
$464$	0.394458	+	1.31986i	0.0183122	+	0.0612731i
$465$	28.1668	+	26.5821i	1.30621	+	1.23272i
$466$	8.60282	−	9.95236i	0.398518	−	0.461034i
$467$	−13.9260	−	13.9260i	−0.644420	−	0.644420i	0.307219	−	0.951639i	$-0.400602\pi$
$467$	−13.9260	−	13.9260i	−0.644420	−	0.644420i	−0.951639	+	0.307219i	$0.900602\pi$
$468$	6.48219	−	8.70278i	0.299639	−	0.402286i
$469$			44.4936i			2.05452i
$470$	−18.7213	+	22.9692i	−0.863550	+	1.05949i
$471$		−	58.2126i		−	2.68229i
$472$	−1.03902	−	4.69465i	−0.0478249	−	0.216089i
$473$	3.02329	+	3.02329i	0.139011	+	0.139011i
$474$	0.567478	+	0.490528i	0.0260651	+	0.0225307i
$475$	−28.4763	+	1.64988i	−1.30658	+	0.0757017i
$476$	12.2365	−	1.78941i	0.560859	−	0.0820176i
$477$	10.4280	−	10.4280i	0.477467	−	0.477467i
$478$	−0.0702547	−	0.965951i	−0.00321337	−	0.0441816i
$479$	15.2334			0.696034			0.348017	−	0.937488i	$-0.386855\pi$
$479$	15.2334			0.696034			0.348017	+	0.937488i	$0.386855\pi$
$480$	33.8744	+	14.0609i	1.54615	+	0.641788i
$481$	−2.24006			−0.102138
$482$	1.66658	+	22.9142i	0.0759105	+	1.04371i
$483$	40.4982	−	40.4982i	1.84273	−	1.84273i
$484$	1.97895	−	0.289393i	0.0899524	−	0.0131542i
$485$	27.1571	−	28.7761i	1.23314	−	1.30665i
$486$	−9.94072	−	8.59276i	−0.450920	−	0.389775i
$487$	−19.8451	−	19.8451i	−0.899265	−	0.899265i	0.0961059	−	0.995371i	$-0.469361\pi$
$487$	−19.8451	−	19.8451i	−0.899265	−	0.899265i	−0.995371	+	0.0961059i	$0.969361\pi$
$488$	−1.56582	−	7.07491i	−0.0708815	−	0.320266i
$489$			2.46406i			0.111429i
$490$	34.9664	−	3.56275i	1.57962	−	0.160949i
$491$			32.4227i			1.46322i	0.681725	+	0.731608i	$0.261230\pi$
$491$			32.4227i			1.46322i	−0.681725	+	0.731608i	$0.738770\pi$
$492$	−22.2721	+	29.9018i	−1.00410	+	1.34808i
$493$	−0.353785	−	0.353785i	−0.0159337	−	0.0159337i
$494$	−5.29389	+	6.12435i	−0.238183	+	0.275547i
$495$	12.0863	−	0.349839i	0.543238	−	0.0157241i
$496$	6.84196	+	22.8933i	0.307213	+	1.02794i
$497$	12.7613	−	12.7613i	0.572424	−	0.572424i
$498$	59.9219	−	4.35819i	2.68517	−	0.195295i
$499$	−35.1679			−1.57433			−0.787166	−	0.616741i	$-0.788453\pi$
$499$	−35.1679			−1.57433			−0.787166	+	0.616741i	$0.788453\pi$
$500$	21.7615	−	5.14165i	0.973204	−	0.229942i
$501$	−20.4632			−0.914228
$502$	4.19241	−	0.304918i	0.187116	−	0.0136092i
$503$	26.4539	−	26.4539i	1.17952	−	1.17952i	0.199657	−	0.979866i	$-0.436017\pi$
$503$	26.4539	−	26.4539i	1.17952	−	1.17952i	0.979866	−	0.199657i	$-0.0639827\pi$
$504$	−54.8882	−	34.9952i	−2.44492	−	1.55881i
$505$	−20.2408	+	0.585874i	−0.900706	+	0.0260710i
$506$	−4.29205	+	4.96535i	−0.190805	+	0.220737i
$507$	24.5896	+	24.5896i	1.09206	+	1.09206i
$508$	16.1836	+	12.0542i	0.718032	+	0.534821i
$509$			29.1842i			1.29356i	0.762675	+	0.646782i	$0.223886\pi$
$509$			29.1842i			1.29356i	−0.762675	+	0.646782i	$0.776114\pi$
$510$	−13.2524	+	1.35030i	−0.586828	+	0.0597923i
$511$			67.1345i			2.96985i
$512$	13.7555	+	17.9663i	0.607913	+	0.794004i
$513$	−28.1584	−	28.1584i	−1.24322	−	1.24322i
$514$	0.732744	+	0.633384i	0.0323199	+	0.0279374i
$515$	−15.1736	+	16.0781i	−0.668627	+	0.708488i
$516$	3.58769	+	24.5336i	0.157939	+	1.08003i
$517$	−6.62597	+	6.62597i	−0.291410	+	0.291410i
$518$	0.974739	+	13.4020i	0.0428276	+	0.588849i
$519$	−36.1083			−1.58498
$520$	3.25539	−	5.44747i	0.142758	−	0.238887i
$521$	−16.8395			−0.737750			−0.368875	−	0.929479i	$-0.620257\pi$
$521$	−16.8395			−0.737750			−0.368875	+	0.929479i	$0.620257\pi$
$522$	0.191040	+	2.62667i	0.00836161	+	0.114966i
$523$	−5.35783	+	5.35783i	−0.234281	+	0.234281i	−0.814477	−	0.580196i	$-0.802976\pi$
$523$	−5.35783	+	5.35783i	−0.234281	+	0.234281i	0.580196	+	0.814477i	$0.302976\pi$
$524$	−1.75628	−	12.0099i	−0.0767233	−	0.524655i
$525$	−61.6010	+	3.56909i	−2.68849	+	0.155768i
$526$	25.2976	+	21.8672i	1.10303	+	0.953456i
$527$	−6.13648	−	6.13648i	−0.267309	−	0.267309i
$528$	10.2061	+	5.50937i	0.444166	+	0.239765i
$529$			1.46177i			0.0635554i
$530$	5.44878	−	6.68511i	0.236680	−	0.290382i
$531$		−	9.19247i		−	0.398919i
$532$	38.9448	+	29.0077i	1.68847	+	1.25764i
$533$	4.56174	+	4.56174i	0.197591	+	0.197591i
$534$	−17.5065	+	20.2528i	−0.757581	+	0.876424i
$535$	−16.4210	−	15.4971i	−0.709940	−	0.669997i
$536$	15.8960	−	24.9321i	0.686602	−	1.07690i
$537$	5.09693	−	5.09693i	0.219949	−	0.219949i
$538$	−23.4565	+	1.70602i	−1.01128	+	0.0735515i
$539$	11.1146			0.478739
$540$	25.5648	+	17.9155i	1.10014	+	0.770962i
$541$	17.8325			0.766678			0.383339	−	0.923608i	$-0.374774\pi$
$541$	17.8325			0.766678			0.383339	+	0.923608i	$0.374774\pi$
$542$	31.1350	−	2.26449i	1.33736	−	0.0972680i
$543$	−37.6081	+	37.6081i	−1.61392	+	1.61392i
$544$	−7.49604	−	3.36897i	−0.321390	−	0.144443i
$545$	−0.204141	−	7.05271i	−0.00874446	−	0.302105i
$546$	−11.4520	+	13.2484i	−0.490098	+	0.566981i
$547$	−12.1248	−	12.1248i	−0.518419	−	0.518419i	0.398673	−	0.917093i	$-0.369471\pi$
$547$	−12.1248	−	12.1248i	−0.518419	−	0.518419i	−0.917093	+	0.398673i	$0.869471\pi$
$548$	16.7819	−	22.5308i	0.716886	−	0.962467i
$549$		−	13.8532i		−	0.591239i
$550$	7.01096	−	0.919998i	0.298948	−	0.0392289i
$551$		−	1.96466i		−	0.0836972i
$552$	−37.1618	+	8.22468i	−1.58171	+	0.350066i
$553$	−0.550518	−	0.550518i	−0.0234104	−	0.0234104i
$554$	−17.6134	−	15.2250i	−0.748321	−	0.646849i
$555$	−0.418788	−	14.4684i	−0.0177766	−	0.614148i
$556$	−6.63691	+	0.970553i	−0.281468	+	0.0411606i
$557$	−13.6724	+	13.6724i	−0.579317	+	0.579317i	−0.934715	−	0.355398i	$-0.884345\pi$
$557$	−13.6724	+	13.6724i	−0.579317	+	0.579317i	0.355398	+	0.934715i	$0.384345\pi$
$558$	3.31364	+	45.5602i	0.140278	+	1.92872i
$559$	4.29012			0.181453
$560$	−34.0080	−	17.1062i	−1.43710	−	0.722868i
$561$	−4.21249			−0.177851
$562$	0.298389	+	4.10263i	0.0125868	+	0.173059i
$563$	20.3216	−	20.3216i	0.856455	−	0.856455i	−0.134464	−	0.990919i	$-0.542931\pi$
$563$	20.3216	−	20.3216i	0.856455	−	0.856455i	0.990919	+	0.134464i	$0.0429311\pi$
$564$	−53.7689	+	7.86293i	−2.26408	+	0.331089i
$565$	−2.10949	−	1.99080i	−0.0887467	−	0.0837537i
$566$	−16.7962	−	14.5186i	−0.705996	−	0.610263i
$567$	−12.0919	−	12.0919i	−0.507814	−	0.507814i
$568$	−11.7100	+	2.59167i	−0.491342	+	0.108744i
$569$			42.4250i			1.77855i	0.457376	+	0.889273i	$0.348789\pi$
$569$			42.4250i			1.77855i	−0.457376	+	0.889273i	$0.651211\pi$
$570$	−40.5464	−	33.0479i	−1.69830	−	1.38422i
$571$		−	21.7300i		−	0.909370i	−0.890652	−	0.454685i	$-0.849752\pi$
$571$		−	21.7300i		−	0.909370i	0.890652	−	0.454685i	$-0.150248\pi$
$572$	1.19876	−	1.60942i	0.0501227	−	0.0672931i
$573$	−48.2899	−	48.2899i	−2.01734	−	2.01734i
$574$	25.3073	−	29.2773i	1.05631	−	1.22201i
$575$	−15.4316	+	17.3298i	−0.643543	+	0.722701i
$576$	18.2542	+	39.2193i	0.760592	+	1.63414i
$577$	−13.2020	+	13.2020i	−0.549605	+	0.549605i	−0.926327	−	0.376721i	$-0.877051\pi$
$577$	−13.2020	+	13.2020i	−0.549605	+	0.549605i	0.376721	+	0.926327i	$0.377051\pi$
$578$	−21.0013	+	1.52744i	−0.873537	+	0.0635333i
$579$	3.23009			0.134238
$580$	0.266853	+	1.51685i	0.0110805	+	0.0629838i
$581$	−62.3590			−2.58709
$582$	72.3688	−	5.26346i	2.99979	−	0.218178i
$583$	1.92847	−	1.92847i	0.0798690	−	0.0798690i
$584$	23.9848	−	37.6190i	0.992497	−	1.55668i
$585$	8.32714	−	8.82356i	0.344285	−	0.364809i
$586$	−15.2141	+	17.6008i	−0.628489	+	0.727081i
$587$	−9.51052	−	9.51052i	−0.392541	−	0.392541i	0.483051	−	0.875592i	$-0.339529\pi$
$587$	−9.51052	−	9.51052i	−0.392541	−	0.392541i	−0.875592	+	0.483051i	$0.839529\pi$
$588$	51.6915	+	38.5020i	2.13172	+	1.58779i
$589$		−	34.0774i		−	1.40414i
$590$	−0.544922	−	5.34810i	−0.0224341	−	0.220178i
$591$			69.5421i			2.86058i
$592$	4.24185	−	7.85806i	0.174339	−	0.322964i
$593$	24.0839	+	24.0839i	0.989005	+	0.989005i	0.999940	−	0.0109350i	$-0.00348078\pi$
$593$	24.0839	+	24.0839i	0.989005	+	0.989005i	−0.0109350	+	0.999940i	$0.503481\pi$
$594$	7.46839	+	6.45568i	0.306432	+	0.264880i
$595$	13.8205	−	0.400037i	0.566587	−	0.0163999i
$596$	−0.364416	−	2.49198i	−0.0149271	−	0.102075i
$597$	−7.92733	+	7.92733i	−0.324444	+	0.324444i
$598$	0.477714	+	6.56823i	0.0195352	+	0.268595i
$599$	5.24145			0.214160			0.107080	−	0.994250i	$-0.465850\pi$
$599$	5.24145			0.214160			0.107080	+	0.994250i	$0.465850\pi$
$600$	35.7934	+	20.0079i	1.46126	+	0.816820i
$601$	13.4589			0.549002			0.274501	−	0.961587i	$-0.411487\pi$
$601$	13.4589			0.549002			0.274501	+	0.961587i	$0.411487\pi$
$602$	−1.86681	−	25.6672i	−0.0760853	−	1.04612i
$603$	39.9722	−	39.9722i	1.62779	−	1.62779i
$604$	3.41936	+	23.3826i	0.139132	+	0.951423i
$605$	2.23513	−	0.0646962i	0.0908710	−	0.00263027i
$606$	−28.0932	−	24.2838i	−1.14121	−	0.986462i
$607$	28.8057	+	28.8057i	1.16919	+	1.16919i	0.982400	+	0.186787i	$0.0598073\pi$
$607$	28.8057	+	28.8057i	1.16919	+	1.16919i	0.186787	+	0.982400i	$0.440193\pi$
$608$	−11.4594	−	30.1681i	−0.464739	−	1.22348i
$609$		−	4.25003i		−	0.172220i
$610$	−0.821205	−	8.05967i	−0.0332496	−	0.326326i
$611$			9.40240i			0.380380i
$612$	−12.6006	−	9.38546i	−0.509349	−	0.379385i
$613$	6.95305	+	6.95305i	0.280831	+	0.280831i	0.833440	−	0.552609i	$-0.186368\pi$
$613$	6.95305	+	6.95305i	0.280831	+	0.280831i	−0.552609	+	0.833440i	$0.686368\pi$
$614$	12.9365	−	14.9659i	0.522076	−	0.603974i
$615$	−28.6111	+	30.3168i	−1.15371	+	1.22249i
$616$	−10.1506	−	6.47170i	−0.408978	−	0.260752i
$617$	−20.0159	+	20.0159i	−0.805810	+	0.805810i	−0.983997	−	0.178186i	$-0.942977\pi$
$617$	−20.0159	+	20.0159i	−0.805810	+	0.805810i	0.178186	+	0.983997i	$0.442977\pi$
$618$	−40.4349	+	2.94087i	−1.62653	+	0.118299i
$619$	−17.1665			−0.689978			−0.344989	−	0.938607i	$-0.612117\pi$
$619$	−17.1665			−0.689978			−0.344989	+	0.938607i	$0.612117\pi$
$620$	4.62862	+	26.3101i	0.185890	+	1.05664i
$621$	−32.3957			−1.29999
$622$	23.4717	−	1.70712i	0.941131	−	0.0684495i
$623$	19.6475	−	19.6475i	0.787161	−	0.787161i
$624$	11.1503	−	3.33242i	0.446371	−	0.133403i
$625$	24.8327	−	2.88725i	0.993309	−	0.115490i
$626$	28.7415	−	33.2502i	1.14874	−	1.32895i
$627$	−11.6965	−	11.6965i	−0.467114	−	0.467114i
$628$	23.9852	−	32.2018i	0.957115	−	1.28499i
$629$			3.24334i			0.129320i
$630$	−56.4137	−	45.9807i	−2.24758	−	1.83191i
$631$			29.6327i			1.17966i	0.807528	+	0.589830i	$0.200805\pi$
$631$			29.6327i			1.17966i	−0.807528	+	0.589830i	$0.799195\pi$
$632$	0.111803	+	0.505165i	0.00444730	+	0.0200944i
$633$	−14.8364	−	14.8364i	−0.589692	−	0.589692i
$634$	17.5647	+	15.1829i	0.697584	+	0.602991i
$635$	16.4082	+	15.4851i	0.651141	+	0.614507i
$636$	15.6493	−	2.28848i	0.620534	−	0.0907442i
$637$	7.88592	−	7.88592i	0.312452	−	0.312452i
$638$	0.0353294	+	0.485753i	0.00139870	+	0.0192312i
$639$	−22.9291			−0.907061
$640$	12.9450	+	21.7354i	0.511698	+	0.859166i
$641$	13.9877			0.552482			0.276241	−	0.961088i	$-0.410911\pi$
$641$	13.9877			0.552482			0.276241	+	0.961088i	$0.410911\pi$
$642$	−3.00358	−	41.2970i	−0.118542	−	1.62986i
$643$	23.4698	−	23.4698i	0.925560	−	0.925560i	−0.0718555	−	0.997415i	$-0.522892\pi$
$643$	23.4698	−	23.4698i	0.925560	−	0.925560i	0.997415	+	0.0718555i	$0.0228920\pi$
$644$	39.0890	−	5.71621i	1.54032	−	0.225250i
$645$	0.802057	+	27.7096i	0.0315810	+	1.09106i
$646$	8.86734	+	7.66493i	0.348881	+	0.301573i
$647$	−24.5523	−	24.5523i	−0.965252	−	0.965252i	0.0341646	−	0.999416i	$-0.489123\pi$
$647$	−24.5523	−	24.5523i	−0.965252	−	0.965252i	−0.999416	+	0.0341646i	$0.989123\pi$
$648$	2.45573	+	11.0958i	0.0964700	+	0.435883i
$649$		−	1.69997i		−	0.0667298i
$650$	4.32161	−	5.62710i	0.169507	−	0.220713i
$651$		−	73.7177i		−	2.88923i
$652$	−1.01526	+	1.36306i	−0.0397608	+	0.0533815i
$653$	−28.7840	−	28.7840i	−1.12640	−	1.12640i	−0.990757	−	0.135646i	$-0.956689\pi$
$653$	−28.7840	−	28.7840i	−1.12640	−	1.12640i	−0.135646	−	0.990757i	$-0.543311\pi$
$654$	8.46143	−	9.78879i	0.330868	−	0.382772i
$655$	−0.392630	−	13.5646i	−0.0153413	−	0.530013i
$656$	−24.6407	+	7.36420i	−0.962059	+	0.287524i
$657$	60.3123	−	60.3123i	2.35301	−	2.35301i
$658$	56.2533	−	4.09137i	2.19298	−	0.159498i
$659$	35.6989			1.39063			0.695316	−	0.718704i	$-0.255264\pi$
$659$	35.6989			1.39063			0.695316	+	0.718704i	$0.255264\pi$
$660$	10.6192	+	7.44182i	0.413352	+	0.289672i
$661$	−13.7561			−0.535050			−0.267525	−	0.963551i	$-0.586206\pi$
$661$	−13.7561			−0.535050			−0.267525	+	0.963551i	$0.586206\pi$
$662$	3.92185	−	0.285240i	0.152427	−	0.0110862i
$663$	−2.98881	+	2.98881i	−0.116076	+	0.116076i
$664$	34.9430	+	22.2787i	1.35605	+	0.864581i
$665$	39.4853	+	37.2638i	1.53117	+	1.44503i
$666$	11.1644	−	12.9158i	0.432611	−	0.500475i
$667$	−1.13015	−	1.13015i	−0.0437596	−	0.0437596i
$668$	−11.3197	−	8.43142i	−0.437974	−	0.326221i
$669$			18.4362i			0.712785i
$670$	20.8860	−	25.6250i	0.806896	−	0.989980i
$671$		−	2.56189i		−	0.0989005i
$672$	−24.7894	−	65.2609i	−0.956271	−	2.51749i
$673$	−29.4881	−	29.4881i	−1.13668	−	1.13668i	−0.989041	−	0.147640i	$-0.952832\pi$
$673$	−29.4881	−	29.4881i	−1.13668	−	1.13668i	−0.147640	−	0.989041i	$-0.547168\pi$
$674$	12.2245	+	10.5668i	0.470869	+	0.407019i
$675$	26.0657	+	23.2107i	1.00327	+	0.893380i
$676$	3.47075	+	23.7339i	0.133490	+	0.912844i
$677$	10.2511	−	10.2511i	0.393981	−	0.393981i	−0.482122	−	0.876104i	$-0.660134\pi$
$677$	10.2511	−	10.2511i	0.393981	−	0.393981i	0.876104	+	0.482122i	$0.160134\pi$
$678$	−0.385848	−	5.30514i	−0.0148184	−	0.203743i
$679$	−75.3122			−2.89022
$680$	−7.88729	−	4.71343i	−0.302464	−	0.180752i
$681$	−14.0331			−0.537750
$682$	0.612796	+	8.42550i	0.0234652	+	0.322629i
$683$	−16.6264	+	16.6264i	−0.636192	+	0.636192i	−0.949614	−	0.313422i	$-0.898524\pi$
$683$	−16.6264	+	16.6264i	−0.636192	+	0.636192i	0.313422	+	0.949614i	$0.398524\pi$
$684$	−8.92727	−	61.0472i	−0.341343	−	2.33420i
$685$	21.5583	−	22.8435i	0.823699	−	0.872805i
$686$	−18.7364	−	16.1957i	−0.715359	−	0.618356i
$687$	10.6768	+	10.6768i	0.407346	+	0.407346i
$688$	−8.12393	+	15.0496i	−0.309722	+	0.573762i
$689$		−	2.73654i		−	0.104254i
$690$	−42.3344	+	4.31348i	−1.61164	+	0.164211i
$691$			11.9445i			0.454392i	0.973849	+	0.227196i	$0.0729558\pi$
$691$			11.9445i			0.454392i	−0.973849	+	0.227196i	$0.927044\pi$
$692$	−19.9742	−	14.8777i	−0.759307	−	0.565564i
$693$	−16.2738	−	16.2738i	−0.618190	−	0.618190i
$694$	−12.6168	+	14.5961i	−0.478929	+	0.554059i
$695$	−7.49607	+	0.216975i	−0.284342	+	0.00823032i
$696$	−1.51839	+	2.38151i	−0.0575543	+	0.0902711i
$697$	6.60486	−	6.60486i	0.250177	−	0.250177i
$698$	12.5817	−	0.915080i	0.476224	−	0.0346363i
$699$	26.9719			1.02017
$700$	−35.5467	−	23.4070i	−1.34354	−	0.884702i
$701$	19.3802			0.731980			0.365990	−	0.930619i	$-0.380730\pi$
$701$	19.3802			0.731980			0.365990	+	0.930619i	$0.380730\pi$
$702$	9.87928	−	0.718531i	0.372869	−	0.0271192i
$703$	−9.00555	+	9.00555i	−0.339651	+	0.339651i
$704$	3.37578	+	7.25287i	0.127229	+	0.273353i
$705$	−60.7294	+	1.75782i	−2.28720	+	0.0662033i
$706$	−25.4087	+	29.3946i	−0.956270	+	1.10628i
$707$	27.2537	+	27.2537i	1.02498	+	1.02498i
$708$	5.88887	−	7.90620i	0.221317	−	0.297133i
$709$		−	25.2399i		−	0.947903i	−0.880551	−	0.473952i	$-0.842827\pi$
$709$		−	25.2399i		−	0.947903i	0.880551	−	0.473952i	$-0.157173\pi$
$710$	−13.3400	+	1.35922i	−0.500640	+	0.0510105i
$711$			0.989150i			0.0370960i
$712$	−18.0289	+	3.99017i	−0.675662	+	0.149538i
$713$	−19.6027	−	19.6027i	−0.734128	−	0.734128i
$714$	19.1822	+	16.5811i	0.717876	+	0.620532i
$715$	1.53995	−	1.63175i	0.0575908	−	0.0610241i
$716$	4.91957	−	0.719417i	0.183853	−	0.0268859i
$717$	1.40411	−	1.40411i	0.0524376	−	0.0524376i
$718$	−1.05588	−	14.5176i	−0.0394052	−	0.541794i
$719$	7.56372			0.282079			0.141040	−	0.990004i	$-0.454956\pi$
$719$	7.56372			0.282079			0.141040	+	0.990004i	$0.454956\pi$
$720$	15.1843	+	45.9200i	0.565885	+	1.71134i
$721$	42.0794			1.56712
$722$	1.38951	+	19.1047i	0.0517121	+	0.711004i
$723$	−33.3083	+	33.3083i	−1.23875	+	1.23875i
$724$	−36.2995	+	5.30828i	−1.34906	+	0.197281i
$725$	0.0995997	+	1.71905i	0.00369904	+	0.0638439i
$726$	3.10225	+	2.68158i	0.115135	+	0.0995229i
$727$	5.03908	+	5.03908i	0.186889	+	0.186889i	0.794350	−	0.607461i	$-0.207812\pi$
$727$	5.03908	+	5.03908i	0.186889	+	0.186889i	−0.607461	+	0.794350i	$0.707812\pi$
$728$	−11.7937	+	2.61018i	−0.437103	+	0.0967399i
$729$		−	38.9940i		−	1.44422i
$730$	31.5139	−	38.6645i	1.16638	−	1.43104i
$731$		−	6.21159i		−	0.229744i
$732$	8.87461	−	11.9148i	0.328015	−	0.440382i
$733$	−28.3393	−	28.3393i	−1.04674	−	1.04674i	−0.998853	−	0.0478835i	$-0.984752\pi$
$733$	−28.3393	−	28.3393i	−1.04674	−	1.04674i	−0.0478835	−	0.998853i	$-0.515248\pi$
$734$	21.7157	−	25.1223i	0.801541	−	0.927280i
$735$	52.4089	+	49.4603i	1.93313	+	1.82437i
$736$	−23.9458	−	10.7620i	−0.882654	−	0.396694i
$737$	7.39211	−	7.39211i	0.272292	−	0.272292i
$738$	−49.0377	+	3.56657i	−1.80510	+	0.131287i
$739$	−7.46962			−0.274775			−0.137387	−	0.990517i	$-0.543870\pi$
$739$	−7.46962			−0.274775			−0.137387	+	0.990517i	$0.543870\pi$
$740$	5.72971	−	8.17609i	0.210628	−	0.300559i
$741$	−16.5976			−0.609729
$742$	−16.3724	+	1.19078i	−0.601048	+	0.0437149i
$743$	−12.8563	+	12.8563i	−0.471652	+	0.471652i	−0.902449	−	0.430797i	$-0.858232\pi$
$743$	−12.8563	+	12.8563i	−0.471652	+	0.471652i	0.430797	+	0.902449i	$0.358232\pi$
$744$	−26.3367	+	41.3079i	−0.965552	+	1.51442i
$745$	−0.0814680	−	2.81457i	−0.00298476	−	0.103118i
$746$	5.28231	−	6.11095i	0.193399	−	0.223738i
$747$	56.0222	+	56.0222i	2.04974	+	2.04974i
$748$	−2.33025	−	1.73566i	−0.0852022	−	0.0634622i
$749$			42.9766i			1.57033i
$750$	37.1530	+	26.8609i	1.35664	+	0.980822i
$751$		−	33.0689i		−	1.20670i	−0.797476	−	0.603351i	$-0.793832\pi$
$751$		−	33.0689i		−	1.20670i	0.797476	−	0.603351i	$-0.206168\pi$
$752$	−32.9834	−	17.8047i	−1.20278	−	0.649272i
$753$	6.09411	+	6.09411i	0.222082	+	0.222082i
$754$	0.369714	+	0.319581i	0.0134642	+	0.0116384i
$755$	0.764426	+	26.4095i	0.0278203	+	0.961139i
$756$	−8.59775	−	58.7938i	−0.312697	−	2.13831i
$757$	−5.26299	+	5.26299i	−0.191287	+	0.191287i	−0.796252	−	0.604965i	$-0.793187\pi$
$757$	−5.26299	+	5.26299i	−0.191287	+	0.191287i	0.604965	+	0.796252i	$0.293187\pi$
$758$	3.87713	+	53.3077i	0.140824	+	1.93622i
$759$	−13.4566			−0.488445
$760$	−8.81264	−	34.9875i	−0.319668	−	1.26913i
$761$	18.7528			0.679789			0.339895	−	0.940464i	$-0.389609\pi$
$761$	18.7528			0.679789			0.339895	+	0.940464i	$0.389609\pi$
$762$	3.00125	+	41.2650i	0.108724	+	1.49487i
$763$	−9.49625	+	9.49625i	−0.343787	+	0.343787i
$764$	−6.81599	−	46.6096i	−0.246594	−	1.68628i
$765$	−12.7755	−	12.0567i	−0.461899	−	0.435912i
$766$	−27.4790	−	23.7529i	−0.992857	−	0.858226i
$767$	−1.20615	−	1.20615i	−0.0435516	−	0.0435516i
$768$	−9.42464	+	45.4255i	−0.340082	+	1.63915i
$769$			43.7854i			1.57894i	0.613787	+	0.789472i	$0.289645\pi$
$769$			43.7854i			1.57894i	−0.613787	+	0.789472i	$0.710355\pi$
$770$	−10.4327	−	8.50326i	−0.375967	−	0.306436i
$771$			1.98581i			0.0715173i
$772$	1.78681	+	1.33089i	0.0643087	+	0.0478998i
$773$	−3.18433	−	3.18433i	−0.114532	−	0.114532i	0.647518	−	0.762050i	$-0.275807\pi$
$773$	−3.18433	−	3.18433i	−0.114532	−	0.114532i	−0.762050	+	0.647518i	$0.775807\pi$
$774$	−21.3818	+	24.7360i	−0.768554	+	0.889119i
$775$	1.72758	+	29.8173i	0.0620565	+	1.07107i
$776$	42.2014	+	26.9064i	1.51494	+	0.965883i
$777$	−19.4812	+	19.4812i	−0.698884	+	0.698884i
$778$	30.8010	−	2.24019i	1.10427	−	0.0803148i
$779$	36.6785			1.31414
$780$	12.8145	−	2.25440i	0.458833	−	0.0807203i
$781$	−4.24031			−0.151730
$782$	9.51003	−	0.691675i	0.340078	−	0.0247342i
$783$	−1.69986	+	1.69986i	−0.0607481	+	0.0607481i
$784$	12.7306	+	42.5967i	0.454663	+	1.52131i
$785$	30.8118	−	32.6487i	1.09972	−	1.16528i
$786$	16.2741	−	18.8270i	0.580476	−	0.671536i
$787$	−24.1876	−	24.1876i	−0.862195	−	0.862195i	0.129398	−	0.991593i	$-0.458696\pi$
$787$	−24.1876	−	24.1876i	−0.862195	−	0.862195i	−0.991593	+	0.129398i	$0.958696\pi$
$788$	−28.6533	+	38.4690i	−1.02073	+	1.37040i
$789$			68.5590i			2.44077i
$790$	0.0586360	+	0.575479i	0.00208617	+	0.0204746i
$791$			5.52091i			0.196301i
$792$	3.30501	+	14.9331i	0.117438	+	0.530625i
$793$	−1.81769	−	1.81769i	−0.0645479	−	0.0645479i
$794$	30.9755	+	26.7752i	1.09928	+	0.950218i
$795$	17.6751	−	0.511608i	0.626871	−	0.0181449i
$796$	−7.65149	+	1.11892i	−0.271200	+	0.0396591i
$797$	−24.2353	+	24.2353i	−0.858459	+	0.858459i	−0.991157	−	0.132697i	$-0.957636\pi$
$797$	−24.2353	+	24.2353i	−0.858459	+	0.858459i	0.132697	+	0.991157i	$0.457636\pi$
$798$	7.22230	+	99.3014i	0.255667	+	3.51523i
$799$	13.6136			0.481614
$800$	11.5562	+	25.8158i	0.408573	+	0.912726i
$801$	−35.3019			−1.24733
$802$	1.37707	+	18.9337i	0.0486260	+	0.668573i
$803$	11.1536	−	11.1536i	0.393603	−	0.393603i
$804$	59.9860	−	8.77209i	2.11554	−	0.309368i
$805$	44.1492	−	1.27790i	1.55605	−	0.0450402i
$806$	6.41277	+	5.54320i	0.225880	+	0.195251i
$807$	−34.0965	−	34.0965i	−1.20025	−	1.20025i
$808$	−5.53488	−	25.0084i	−0.194716	−	0.879793i
$809$			27.7783i			0.976634i	0.872666	+	0.488317i	$0.162389\pi$
$809$			27.7783i			0.976634i	−0.872666	+	0.488317i	$0.837611\pi$
$810$	1.28792	+	12.6402i	0.0452529	+	0.444132i
$811$		−	6.85883i		−	0.240846i	−0.992723	−	0.120423i	$-0.961575\pi$
$811$		−	6.85883i		−	0.240846i	0.992723	−	0.120423i	$-0.0384251\pi$
$812$	1.75113	−	2.35101i	0.0614527	−	0.0825044i
$813$	45.2581	+	45.2581i	1.58727	+	1.58727i
$814$	2.06464	−	2.38853i	0.0723657	−	0.0837178i
$815$	−1.30422	+	1.38198i	−0.0456850	+	0.0484086i
$816$	−4.82495	−	16.1444i	−0.168907	−	0.565166i
$817$	17.2473	−	17.2473i	0.603406	−	0.603406i
$818$	−12.4409	+	0.904838i	−0.434985	+	0.0316369i
$819$	−23.0929			−0.806930
$820$	−28.3183	+	4.98192i	−0.988919	+	0.173976i
$821$	−19.5203			−0.681262			−0.340631	−	0.940197i	$-0.610641\pi$
$821$	−19.5203			−0.681262			−0.340631	+	0.940197i	$0.610641\pi$
$822$	57.4490	−	4.17833i	2.00376	−	0.145736i
$823$	−35.2865	+	35.2865i	−1.23001	+	1.23001i	−0.266053	+	0.963958i	$0.585720\pi$
$823$	−35.2865	+	35.2865i	−1.23001	+	1.23001i	−0.963958	+	0.266053i	$0.914280\pi$
$824$	−23.5793	−	15.0335i	−0.821424	−	0.523717i
$825$	10.8273	+	9.64134i	0.376957	+	0.335669i
$826$	−6.69140	+	7.74109i	−0.232823	+	0.269347i
$827$	−19.2150	−	19.2150i	−0.668171	−	0.668171i	0.289122	−	0.957292i	$-0.406637\pi$
$827$	−19.2150	−	19.2150i	−0.668171	−	0.668171i	−0.957292	+	0.289122i	$0.906637\pi$
$828$	−40.2521	−	29.9815i	−1.39886	−	1.04193i
$829$		−	21.8101i		−	0.757497i	−0.925500	−	0.378748i	$-0.876355\pi$
$829$		−	21.8101i		−	0.757497i	0.925500	−	0.378748i	$-0.123645\pi$
$830$	35.9142	+	29.2723i	1.24660	+	1.01606i
$831$		−	47.7341i		−	1.65588i
$832$	7.54114	+	2.75084i	0.261442	+	0.0953683i
$833$	−11.4179	−	11.4179i	−0.395607	−	0.395607i
$834$	−10.4042	−	8.99336i	−0.360267	−	0.311415i
$835$	−11.4769	−	10.8311i	−0.397173	−	0.374827i
$836$	−1.65093	−	11.2895i	−0.0570987	−	0.390457i
$837$	−29.4845	+	29.4845i	−1.01913	+	1.01913i
$838$	−0.979348	−	13.4653i	−0.0338310	−	0.465152i
$839$	9.74722			0.336512			0.168256	−	0.985743i	$-0.446187\pi$
$839$	9.74722			0.336512			0.168256	+	0.985743i	$0.446187\pi$
$840$	−19.0639	−	75.6865i	−0.657766	−	2.61143i
$841$	28.8814			0.995910
$842$	−1.49109	−	20.5014i	−0.0513863	−	0.706524i
$843$	−5.96361	+	5.96361i	−0.205398	+	0.205398i
$844$	−2.09411	−	14.3201i	−0.0720823	−	0.492918i
$845$	0.775913	+	26.8064i	0.0266922	+	0.922167i
$846$	−54.2125	−	46.8613i	−1.86386	−	1.61112i
$847$	−3.00953	−	3.00953i	−0.103409	−	0.103409i
$848$	9.59971	+	5.18201i	0.329656	+	0.177951i
$849$		−	45.5194i		−	1.56222i
$850$	−8.14739	−	6.25718i	−0.279453	−	0.214620i
$851$			10.3607i			0.355161i
$852$	−19.7207	−	14.6888i	−0.675620	−	0.503230i
$853$	2.88173	+	2.88173i	0.0986684	+	0.0986684i	0.754718	−	0.656049i	$-0.227774\pi$
$853$	2.88173	+	2.88173i	0.0986684	+	0.0986684i	−0.656049	+	0.754718i	$0.727774\pi$
$854$	−10.0840	+	11.6659i	−0.345068	+	0.399200i
$855$	−1.99576	−	68.9498i	−0.0682536	−	2.35803i
$856$	15.3540	−	24.0821i	0.524790	−	0.823108i
$857$	−35.4851	+	35.4851i	−1.21215	+	1.21215i	−0.241829	+	0.970319i	$0.577747\pi$
$857$	−35.4851	+	35.4851i	−1.21215	+	1.21215i	−0.970319	+	0.241829i	$0.922253\pi$
$858$	4.10369	−	0.298466i	0.140098	−	0.0101895i
$859$	−7.49975			−0.255888			−0.127944	−	0.991781i	$-0.540838\pi$
$859$	−7.49975			−0.255888			−0.127944	+	0.991781i	$0.540838\pi$
$860$	−10.9734	+	15.6587i	−0.374191	+	0.533958i
$861$	79.3445			2.70405
$862$	−36.1420	+	2.62865i	−1.23100	+	0.0895321i
$863$	13.4941	−	13.4941i	0.459344	−	0.459344i	−0.439096	−	0.898440i	$-0.644701\pi$
$863$	13.4941	−	13.4941i	0.459344	−	0.459344i	0.898440	+	0.439096i	$0.144701\pi$
$864$	−16.1872	+	36.0169i	−0.550699	+	1.22532i
$865$	−20.2515	−	19.1121i	−0.688571	−	0.649831i
$866$	−16.5414	+	19.1363i	−0.562100	+	0.650277i
$867$	−30.5276	−	30.5276i	−1.03677	−	1.03677i
$868$	30.3738	−	40.7788i	1.03095	−	1.38412i
$869$			0.182925i			0.00620530i
$870$	−1.99503	+	2.44770i	−0.0676378	+	0.0829848i
$871$		−	10.4896i		−	0.355425i
$872$	8.71392	−	1.92857i	0.295090	−	0.0653096i
$873$	67.6590	+	67.6590i	2.28991	+	2.28991i
$874$	28.3264	+	24.4853i	0.958153	+	0.828228i
$875$	−36.4382	−	30.6036i	−1.23184	−	1.03459i
$876$	90.5103	−	13.2358i	3.05806	−	0.447197i
$877$	16.5863	−	16.5863i	0.560081	−	0.560081i	−0.369250	−	0.929330i	$-0.620385\pi$
$877$	16.5863	−	16.5863i	0.560081	−	0.560081i	0.929330	+	0.369250i	$0.120385\pi$
$878$	2.61727	+	35.9855i	0.0883285	+	1.21445i
$879$	−47.6999			−1.60888
$880$	2.80805	+	8.49205i	0.0946593	+	0.286267i
$881$	−48.8838			−1.64694			−0.823469	−	0.567362i	$-0.807964\pi$
$881$	−48.8838			−1.64694			−0.823469	+	0.567362i	$0.807964\pi$
$882$	6.16556	+	84.7720i	0.207605	+	2.85442i
$883$	−6.52604	+	6.52604i	−0.219619	+	0.219619i	−0.808338	−	0.588719i	$-0.799632\pi$
$883$	−6.52604	+	6.52604i	−0.219619	+	0.219619i	0.588719	+	0.808338i	$0.299632\pi$
$884$	−2.88481	+	0.421862i	−0.0970266	+	0.0141888i
$885$	7.56494	−	8.01593i	0.254293	−	0.269453i
$886$	3.34079	+	2.88778i	0.112236	+	0.0970167i
$887$	0.365873	+	0.365873i	0.0122848	+	0.0122848i	0.713223	−	0.700938i	$-0.247235\pi$
$887$	0.365873	+	0.365873i	0.0122848	+	0.0122848i	−0.700938	+	0.713223i	$0.747235\pi$
$888$	17.8763	−	3.95639i	0.599888	−	0.132768i
$889$		−	42.9434i		−	1.44027i
$890$	−20.5384	+	2.09267i	−0.688447	+	0.0701464i
$891$			4.01788i			0.134604i
$892$	−7.59624	+	10.1985i	−0.254341	+	0.341470i
$893$	37.7999	+	37.7999i	1.26492	+	1.26492i
$894$	3.37676	−	3.90647i	0.112936	−	0.130652i
$895$	5.55642	−	0.160831i	0.185731	−	0.00537600i
$896$	13.1765	−	46.3147i	0.440195	−	1.54726i
$897$	−9.54762	+	9.54762i	−0.318786	+	0.318786i
$898$	4.32391	−	0.314483i	0.144291	−	0.0104944i
$899$	−2.05718			−0.0686109
$900$	10.9061	+	52.9629i	0.363536	+	1.76543i
$901$	−3.96219			−0.132000
$902$	−9.06861	+	0.659570i	−0.301952	+	0.0219613i
$903$	37.3101	−	37.3101i	1.24160	−	1.24160i
$904$	1.97243	−	3.09365i	0.0656019	−	0.102893i
$905$	−40.9985	+	1.18671i	−1.36284	+	0.0394475i
$906$	−31.6846	+	36.6550i	−1.05265	+	1.21778i
$907$	12.9148	+	12.9148i	0.428830	+	0.428830i	0.888230	−	0.459400i	$-0.151936\pi$
$907$	12.9148	+	12.9148i	0.428830	+	0.428830i	−0.459400	+	0.888230i	$0.651936\pi$
$908$	−7.76278	−	5.78204i	−0.257617	−	0.191884i
$909$		−	48.9683i		−	1.62418i
$910$	−13.4352	+	1.36893i	−0.445374	+	0.0453795i
$911$			1.42800i			0.0473117i	0.999720	+	0.0236559i	$0.00753059\pi$
$911$			1.42800i			0.0473117i	−0.999720	+	0.0236559i	$0.992469\pi$
$912$	31.4299	−	58.2241i	1.04075	−	1.92799i
$913$	10.3602	+	10.3602i	0.342874	+	0.342874i
$914$	−5.55995	−	4.80602i	−0.183907	−	0.158969i
$915$	11.4005	−	12.0801i	0.376888	−	0.399357i
$916$	1.50700	+	10.3053i	0.0497928	+	0.340497i
$917$	−18.2643	+	18.2643i	−0.603141	+	0.603141i
$918$	−1.04035	−	14.3040i	−0.0343366	−	0.472104i
$919$	8.37592			0.276296			0.138148	−	0.990412i	$-0.455885\pi$
$919$	8.37592			0.276296			0.138148	+	0.990412i	$0.455885\pi$
$920$	−25.1956	−	15.0569i	−0.830675	−	0.496410i
$921$	40.5591			1.33647
$922$	0.877984	+	12.0717i	0.0289149	+	0.397559i
$923$	−3.00854	+	3.00854i	−0.0990274	+	0.0990274i
$924$	−3.57136	−	24.4220i	−0.117489	−	0.803424i
$925$	7.42320	−	8.33629i	0.244073	−	0.274095i
$926$	−15.7956	−	13.6537i	−0.519075	−	0.448688i
$927$	−37.8033	−	37.8033i	−1.24162	−	1.24162i
$928$	−1.82119	+	0.691778i	−0.0597833	+	0.0227087i
$929$		−	8.25659i		−	0.270890i	−0.990785	−	0.135445i	$-0.956754\pi$
$929$		−	8.25659i		−	0.270890i	0.990785	−	0.135445i	$-0.0432464\pi$
$930$	−34.6042	+	42.4559i	−1.13472	+	1.39219i
$931$		−	63.4065i		−	2.07807i
$932$	14.9202	+	11.1132i	0.488728	+	0.364025i
$933$	34.1187	+	34.1187i	1.11700	+	1.11700i
$934$	18.2139	−	21.0711i	0.595977	−	0.689469i
$935$	−2.36259	−	2.22966i	−0.0772649	−	0.0729178i
$936$	12.9401	+	8.25027i	0.422962	+	0.269668i
$937$	−33.6219	+	33.6219i	−1.09838	+	1.09838i	−0.103780	+	0.994600i	$0.533094\pi$
$937$	−33.6219	+	33.6219i	−1.09838	+	1.09838i	−0.994600	+	0.103780i	$0.966906\pi$
$938$	−62.7577	+	4.56443i	−2.04911	+	0.149034i
$939$	90.1116			2.94068
$940$	−34.3183	−	24.0499i	−1.11934	−	0.784420i
$941$	−15.7061			−0.512004			−0.256002	−	0.966676i	$-0.582405\pi$
$941$	−15.7061			−0.512004			−0.256002	+	0.966676i	$0.582405\pi$
$942$	82.1082	−	5.97181i	2.67523	−	0.194572i
$943$	21.0990	−	21.0990i	0.687077	−	0.687077i
$944$	6.51516	−	1.94714i	0.212050	−	0.0633739i
$945$	−1.92209	−	66.4048i	−0.0625257	−	2.16015i
$946$	−3.95417	+	4.57447i	−0.128561	+	0.148729i
$947$	16.0464	+	16.0464i	0.521437	+	0.521437i	0.918005	−	0.396568i	$-0.129799\pi$
$947$	16.0464	+	16.0464i	0.521437	+	0.521437i	−0.396568	+	0.918005i	$0.629799\pi$
$948$	−0.633668	+	0.850742i	−0.0205806	+	0.0276308i
$949$		−	15.8272i		−	0.513774i
$950$	−5.24841	−	39.9962i	−0.170281	−	1.29765i
$951$			47.6022i			1.54361i
$952$	3.77924	+	17.0759i	0.122486	+	0.553432i
$953$	41.4062	+	41.4062i	1.34128	+	1.34128i	0.894789	+	0.446490i	$0.147326\pi$
$953$	41.4062	+	41.4062i	1.34128	+	1.34128i	0.446490	+	0.894789i	$0.352674\pi$
$954$	15.7784	+	13.6388i	0.510844	+	0.441574i
$955$	−1.52377	−	52.6433i	−0.0493080	−	1.70350i
$956$	1.35526	−	0.198187i	0.0438321	−	0.00640982i
$957$	−0.706094	+	0.706094i	−0.0228248	+	0.0228248i
$958$	1.56274	+	21.4866i	0.0504899	+	0.694200i
$959$	−59.7856			−1.93058
$960$	−16.3576	+	49.2219i	−0.527940	+	1.58863i
$961$	−4.68230			−0.151042
$962$	−0.229799	−	3.15957i	−0.00740902	−	0.101869i
$963$	38.6094	−	38.6094i	1.24417	−	1.24417i
$964$	−32.1493	+	4.70137i	−1.03546	+	0.151421i
$965$	1.81161	+	1.70968i	0.0583177	+	0.0550367i
$966$	61.2767	+	52.9676i	1.97155	+	1.70421i
$967$	2.79981	+	2.79981i	0.0900358	+	0.0900358i	0.750690	−	0.660654i	$-0.229721\pi$
$967$	2.79981	+	2.79981i	0.0900358	+	0.0900358i	−0.660654	+	0.750690i	$0.729721\pi$
$968$	0.611199	+	2.76160i	0.0196447	+	0.0887612i
$969$			24.0314i			0.772000i
$970$	43.3742	+	35.3527i	1.39266	+	1.13511i
$971$			39.7551i			1.27580i	0.770119	+	0.637901i	$0.220197\pi$
$971$			39.7551i			1.27580i	−0.770119	+	0.637901i	$0.779803\pi$
$972$	11.1002	−	14.9028i	0.356039	−	0.478006i
$973$	10.0932	+	10.0932i	0.323574	+	0.323574i
$974$	25.9554	−	30.0270i	0.831664	−	0.962128i
$975$	14.5227	−	0.841428i	0.465099	−	0.0269473i
$976$	9.81844	−	2.93436i	0.314280	−	0.0939267i
$977$	20.1333	−	20.1333i	0.644121	−	0.644121i	−0.307445	−	0.951566i	$-0.599474\pi$
$977$	20.1333	−	20.1333i	0.644121	−	0.644121i	0.951566	+	0.307445i	$0.0994740\pi$
$978$	−3.47553	+	0.252779i	−0.111135	+	0.00808298i
$979$	−6.52843			−0.208649
$980$	8.61229	+	48.9542i	0.275109	+	1.56378i
$981$	17.0625			0.544763
$982$	−45.7318	+	3.32613i	−1.45936	+	0.106141i
$983$	4.38592	−	4.38592i	0.139889	−	0.139889i	−0.633694	−	0.773583i	$-0.718462\pi$
$983$	4.38592	−	4.38592i	0.139889	−	0.139889i	0.773583	+	0.633694i	$0.218462\pi$
$984$	−44.4609	−	28.3470i	−1.41736	−	0.903669i
$985$	−36.8085	+	39.0029i	−1.17282	+	1.24274i
$986$	0.462716	−	0.535302i	0.0147359	−	0.0170475i
$987$	81.7702	+	81.7702i	2.60277	+	2.60277i
$988$	−9.18140	−	6.83869i	−0.292099	−	0.217568i
$989$		−	19.8427i		−	0.630961i
$990$	1.73333	+	17.0117i	0.0550889	+	0.540666i
$991$			41.8022i			1.32789i	0.747781	+	0.663945i	$0.231119\pi$
$991$			41.8022i			1.32789i	−0.747781	+	0.663945i	$0.768881\pi$
$992$	−31.5889	+	11.9990i	−1.00295	+	0.380970i
$993$	5.70082	+	5.70082i	0.180910	+	0.180910i
$994$	19.3089	+	16.6906i	0.612440	+	0.529393i
$995$	−8.64200	+	0.250144i	−0.273970	+	0.00793009i
$996$	12.2943	+	84.0721i	0.389561	+	2.66393i
$997$	−9.16317	+	9.16317i	−0.290200	+	0.290200i	−0.837159	−	0.546959i	$-0.815785\pi$
$997$	−9.16317	+	9.16317i	−0.290200	+	0.290200i	0.546959	+	0.837159i	$0.315785\pi$
$998$	−3.60775	−	49.6039i	−0.114201	−	1.57019i
$999$	15.5836			0.493042

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.8	✓	28
4.3	odd	2		220.2.l.d.23.1	yes	28
5.2	odd	4		220.2.l.d.67.1	yes	28
20.7	even	4	inner	220.2.l.c.67.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.8	✓	28	1.1	even	1	trivial
220.2.l.c.67.8	yes	28	20.7	even	4	inner
220.2.l.d.23.1	yes	28	4.3	odd	2
220.2.l.d.67.1	yes	28	5.2	odd	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.c.23.8

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$