LMFDB - Embedded newform 220.2.l.d.23.1

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			23.1
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41049 - 0.102586i) 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} +(-2.76160 - 0.611199i) q^{8} -5.40741i q^{9} +(3.15926 + 0.138041i) q^{10} +1.00000i q^{11} +(4.65078 - 3.46409i) 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} +(-0.554726 + 7.62709i) q^{18} +5.70480 q^{19} +(-4.44194 - 0.518802i) q^{20} -12.3409 q^{21} +(0.102586 - 1.41049i) 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} +(-5.08478 - 6.82666i) q^{28} +0.344387i q^{29} +(6.76044 - 6.19440i) q^{30} -5.97347i q^{31} +(-5.28820 - 2.00872i) 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} +(-8.04655 - 0.585234i) q^{38} -2.90941 q^{39} +(6.21208 + 1.18745i) q^{40} -6.42941 q^{41} +(17.4066 + 1.26600i) 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} +(10.2061 - 5.50937i) q^{48} +11.1146i q^{49} +(-7.07030 - 0.104147i) q^{50} +4.21249i q^{51} +(-1.19876 - 1.60942i) 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} +(0.0353294 - 0.485753i) q^{58} -1.69997 q^{59} +(-10.1710 + 8.04359i) q^{60} +2.56189 q^{61} +(-0.612796 + 8.42550i) 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} +(-2.33025 + 1.73566i) q^{68} -13.4566i q^{69} +(-9.09247 - 9.92335i) q^{70} +4.24031i q^{71} +(-3.30501 + 14.9331i) 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} +(4.10369 + 0.298466i) q^{78} +0.182925 q^{79} +(-8.64025 - 2.31215i) q^{80} -4.01788 q^{81} +(9.06861 + 0.659570i) 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} +(0.611199 - 2.76160i) q^{88} -6.52843i q^{89} +(0.746443 - 17.0834i) q^{90} +4.27059i q^{91} +(7.44388 - 5.54451i) 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} +(1.14020 - 15.6770i) q^{98} +5.40741 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * 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

)

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

$2$	−1.41049	−	0.102586i	−0.997366	−	0.0725395i
$2$	−1.41049	−	0.102586i	−0.997366	−	0.0725395i
$3$	2.05029	−	2.05029i	1.18374	−	1.18374i	0.204970	−	0.978768i	$-0.434290\pi$
$3$	2.05029	−	2.05029i	1.18374	−	1.18374i	0.978768	−	0.204970i	$-0.0657096\pi$
$4$	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	$-0.952523\pi$
$7$	−3.00953	−	3.00953i	−1.13750	−	1.13750i	−0.148599	−	0.988897i	$-0.547477\pi$
$8$	−2.76160	−	0.611199i	−0.976373	−	0.216092i
$9$		−	5.40741i		−	1.80247i
$10$	3.15926	+	0.138041i	0.999047	+	0.0436523i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	4.65078	−	3.46409i	1.34256	−	0.999997i
$13$	−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	$0.306374\pi$
$18$	−0.554726	+	7.62709i	−0.130750	+	1.79772i
$19$	5.70480			1.30877			0.654386	−	0.756161i	$-0.272927\pi$
$19$	5.70480			1.30877			0.654386	+	0.756161i	$0.272927\pi$
$20$	−4.44194	−	0.518802i	−0.993248	−	0.116008i
$21$	−12.3409			−2.69300
$22$	0.102586	−	1.41049i	0.0218715	−	0.300717i
$23$	3.28163	−	3.28163i	0.684268	−	0.684268i	−0.276691	−	0.960959i	$-0.589238\pi$
$23$	3.28163	−	3.28163i	0.684268	−	0.684268i	0.960959	+	0.276691i	$0.0892379\pi$
$24$	−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
$28$	−5.08478	−	6.82666i	−0.960934	−	1.29012i
$29$			0.344387i			0.0639510i	0.999489	+	0.0319755i	$0.0101799\pi$
$29$			0.344387i			0.0639510i	−0.999489	+	0.0319755i	$0.989820\pi$
$30$	6.76044	−	6.19440i	1.23428	−	1.13094i
$31$		−	5.97347i		−	1.07287i	−0.843943	−	0.536433i	$-0.819771\pi$
$31$		−	5.97347i		−	1.07287i	0.843943	−	0.536433i	$-0.180229\pi$
$32$	−5.28820	−	2.00872i	−0.934830	−	0.355095i
$33$	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	$0.191255\pi$
$38$	−8.04655	−	0.585234i	−1.30532	−	0.0949376i
$39$	−2.90941			−0.465879
$40$	6.21208	+	1.18745i	0.982217	+	0.187752i
$41$	−6.42941			−1.00411			−0.502053	−	0.864837i	$-0.667422\pi$
$41$	−6.42941			−1.00411			−0.502053	+	0.864837i	$0.667422\pi$
$42$	17.4066	+	1.26600i	2.68590	+	0.195349i
$43$	3.02329	−	3.02329i	0.461048	−	0.461048i	−0.437951	−	0.898999i	$-0.644296\pi$
$43$	3.02329	−	3.02329i	0.461048	−	0.461048i	0.898999	+	0.437951i	$0.144296\pi$
$44$	−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	0.999457	−	0.0329591i	$-0.0104931\pi$
$47$	6.62597	+	6.62597i	0.966498	+	0.966498i	−0.0329591	+	0.999457i	$0.510493\pi$
$48$	10.2061	−	5.50937i	1.47313	−	0.795209i
$49$			11.1146i			1.58780i
$50$	−7.07030	−	0.104147i	−0.999892	−	0.0147286i
$51$			4.21249i			0.589866i
$52$	−1.19876	−	1.60942i	−0.166238	−	0.223186i
$53$	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
$58$	0.0353294	−	0.485753i	0.00463897	−	0.0637825i
$59$	−1.69997			−0.221318			−0.110659	−	0.993858i	$-0.535296\pi$
$59$	−1.69997			−0.221318			−0.110659	+	0.993858i	$0.535296\pi$
$60$	−10.1710	+	8.04359i	−1.31307	+	1.03842i
$61$	2.56189			0.328016			0.164008	−	0.986459i	$-0.447558\pi$
$61$	2.56189			0.328016			0.164008	+	0.986459i	$0.447558\pi$
$62$	−0.612796	+	8.42550i	−0.0778251	+	1.07004i
$63$	−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	0.0926126	−	0.995702i	$-0.470478\pi$
$67$	−7.39211	−	7.39211i	−0.903090	−	0.903090i	−0.995702	+	0.0926126i	$0.970478\pi$
$68$	−2.33025	+	1.73566i	−0.282584	+	0.210480i
$69$		−	13.4566i		−	1.61999i
$70$	−9.09247	−	9.92335i	−1.08676	−	1.18607i
$71$			4.24031i			0.503232i	0.967827	+	0.251616i	$0.0809619\pi$
$71$			4.24031i			0.503232i	−0.967827	+	0.251616i	$0.919038\pi$
$72$	−3.30501	+	14.9331i	−0.389499	+	1.75988i
$73$	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
$78$	4.10369	+	0.298466i	0.464652	+	0.0337946i
$79$	0.182925			0.0205806			0.0102903	−	0.999947i	$-0.496724\pi$
$79$	0.182925			0.0205806			0.0102903	+	0.999947i	$0.496724\pi$
$80$	−8.64025	−	2.31215i	−0.966010	−	0.258507i
$81$	−4.01788			−0.446431
$82$	9.06861	+	0.659570i	1.00146	+	0.0728373i
$83$	10.3602	−	10.3602i	1.13719	−	1.13719i	0.148233	−	0.988953i	$-0.452642\pi$
$83$	10.3602	−	10.3602i	1.13719	−	1.13719i	0.988953	−	0.148233i	$-0.0473584\pi$
$84$	−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
$88$	0.611199	−	2.76160i	0.0651541	−	0.294388i
$89$		−	6.52843i		−	0.692012i	−0.938232	−	0.346006i	$-0.887538\pi$
$89$		−	6.52843i		−	0.692012i	0.938232	−	0.346006i	$-0.112462\pi$
$90$	0.746443	−	17.0834i	0.0786820	−	1.80075i
$91$			4.27059i			0.447680i
$92$	7.44388	−	5.54451i	0.776078	−	0.578055i
$93$	−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	$0.894782\pi$
$98$	1.14020	−	15.6770i	0.115178	−	1.58362i
$99$	5.40741			0.543465
$100$	9.96189	+	0.872214i	0.996189	+	0.0872214i
$101$	9.05577			0.901083			0.450541	−	0.892756i	$-0.351231\pi$
$101$	9.05577			0.901083			0.450541	+	0.892756i	$0.351231\pi$
$102$	0.432144	−	5.94166i	0.0427886	−	0.588312i
$103$	−6.99102	+	6.99102i	−0.688846	+	0.688846i	−0.961977	−	0.273131i	$-0.911941\pi$
$103$	−6.99102	+	6.99102i	−0.688846	+	0.688846i	0.273131	+	0.961977i	$0.411941\pi$
$104$	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	0.272031	−	0.962289i	$-0.412305\pi$
$107$	−7.14008	−	7.14008i	−0.690258	−	0.690258i	−0.962289	+	0.272031i	$0.912305\pi$
$108$	−8.33950	−	11.1963i	−0.802469	−	1.07737i
$109$			3.15539i			0.302231i	0.988516	+	0.151116i	$0.0482866\pi$
$109$			3.15539i			0.302231i	−0.988516	+	0.151116i	$0.951713\pi$
$110$	−0.138041	+	3.15926i	−0.0131617	+	0.301224i
$111$		−	6.47316i		−	0.614405i
$112$	−8.08695	−	14.9811i	−0.764145	−	1.41558i
$113$	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
$118$	2.39779	+	0.174394i	0.220735	+	0.0160543i
$119$	6.18332			0.566824
$120$	15.1712	−	10.3020i	1.38494	−	0.940438i
$121$	−1.00000			−0.0909091
$122$	−3.61351	−	0.262814i	−0.327152	−	0.0237941i
$123$	−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	0.948842	−	0.315752i	$-0.102257\pi$
$127$	7.13455	+	7.13455i	0.633089	+	0.633089i	−0.315752	+	0.948842i	$0.602257\pi$
$128$	−9.88378	−	5.50554i	−0.873611	−	0.486625i
$129$		−	12.3973i		−	1.09152i
$130$	−2.14359	−	2.33947i	−0.188005	−	0.205185i
$131$		−	6.06882i		−	0.530235i	−0.964216	−	0.265118i	$-0.914589\pi$
$131$		−	6.06882i		−	0.530235i	0.964216	−	0.265118i	$-0.0854108\pi$
$132$	3.46409	+	4.65078i	0.301511	+	0.404798i
$133$	−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	$0.454855\pi$
$138$	−1.38047	+	18.9804i	−0.117513	+	1.61572i
$139$	−3.35375			−0.284461			−0.142231	−	0.989834i	$-0.545427\pi$
$139$	−3.35375			−0.284461			−0.142231	+	0.989834i	$0.545427\pi$
$140$	11.8068	+	14.9295i	0.997859	+	1.26178i
$141$	27.1704			2.28816
$142$	0.434997	−	5.98090i	0.0365042	−	0.501906i
$143$	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
$148$	3.58079	−	2.66712i	0.294339	−	0.219236i
$149$			1.25924i			0.103161i	0.998669	+	0.0515805i	$0.0164259\pi$
$149$			1.25924i			0.103161i	−0.998669	+	0.0515805i	$0.983574\pi$
$150$	−14.7097	+	14.2827i	−1.20104	+	1.16617i
$151$			11.8156i			0.961542i	0.876846	+	0.480771i	$0.159643\pi$
$151$			11.8156i			0.961542i	−0.876846	+	0.480771i	$0.840357\pi$
$152$	−15.7544	−	3.48677i	−1.27785	−	0.282814i
$153$	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	$0.954230\pi$
$158$	−0.258013	−	0.0187656i	−0.0205264	−	0.00149291i
$159$	7.90786			0.627134
$160$	11.9498	+	4.14763i	0.944713	+	0.327899i
$161$	−19.7524			−1.55670
$162$	5.66717	+	0.412179i	0.445255	+	0.0323839i
$163$	−0.600905	+	0.600905i	−0.0470665	+	0.0470665i	−0.730248	−	0.683182i	$-0.760596\pi$
$163$	−0.600905	+	0.600905i	−0.0470665	+	0.0470665i	0.683182	+	0.730248i	$0.260596\pi$
$164$	−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	0.487154	−	0.873316i	$-0.338035\pi$
$167$	−4.99031	−	4.99031i	−0.386162	−	0.386162i	−0.873316	+	0.487154i	$0.838035\pi$
$168$	34.0805	+	7.54273i	2.62937	+	0.581934i
$169$		−	11.9932i		−	0.922553i
$170$	−3.38728	+	3.10367i	−0.259793	+	0.238040i
$171$		−	30.8482i		−	2.35902i
$172$	6.85788	−	5.10803i	0.522908	−	0.389484i
$173$	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
$178$	−0.669727	+	9.20827i	−0.0501982	+	0.690189i
$179$	2.48595			0.185809			0.0929043	−	0.995675i	$-0.470385\pi$
$179$	2.48595			0.185809			0.0929043	+	0.995675i	$0.470385\pi$
$180$	−2.80538	+	24.0194i	−0.209100	+	1.79030i
$181$	18.3428			1.36341			0.681704	−	0.731628i	$-0.261239\pi$
$181$	18.3428			1.36341			0.681704	+	0.731628i	$0.261239\pi$
$182$	0.438104	−	6.02362i	0.0324745	−	0.446501i
$183$	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
$188$	11.1950	+	15.0300i	0.816477	+	1.09618i
$189$			29.7096i			2.16105i
$190$	18.0230	+	0.787495i	1.30752	+	0.0571309i
$191$		−	23.5527i		−	1.70421i	−0.523369	−	0.852106i	$-0.675325\pi$
$191$		−	23.5527i		−	1.70421i	0.523369	−	0.852106i	$-0.324675\pi$
$192$	21.7919	−	7.94919i	1.57269	−	0.573683i
$193$	−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	$-0.0760657\pi$
$198$	−7.62709	−	0.554726i	−0.542034	−	0.0394227i
$199$	−3.86644			−0.274084			−0.137042	−	0.990565i	$-0.543760\pi$
$199$	−3.86644			−0.274084			−0.137042	+	0.990565i	$0.543760\pi$
$200$	−13.9616	−	2.25220i	−0.987238	−	0.159255i
$201$	−30.3120			−2.13804
$202$	−12.7731	−	0.928998i	−0.898709	−	0.0653641i
$203$	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
$208$	−1.90654	−	3.53187i	−0.132194	−	0.244891i
$209$			5.70480i			0.394609i
$210$	−38.9880	−	1.70354i	−2.69043	−	0.117556i
$211$		−	7.23621i		−	0.498161i	−0.968483	−	0.249081i	$-0.919872\pi$
$211$		−	7.23621i		−	0.498161i	0.968483	−	0.249081i	$-0.0801284\pi$
$212$	3.25826	+	4.37443i	0.223778	+	0.300437i
$213$	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
$218$	0.323699	−	4.45064i	0.0219237	−	0.301435i
$219$	45.7365			3.09058
$220$	0.518802	−	4.44194i	0.0349776	−	0.299476i
$221$	1.45775			0.0980586
$222$	−0.664057	+	9.13031i	−0.0445686	+	0.612786i
$223$	−4.49599	+	4.49599i	−0.301074	+	0.301074i	−0.841434	−	0.540360i	$-0.818288\pi$
$223$	−4.49599	+	4.49599i	−0.301074	+	0.301074i	0.540360	+	0.841434i	$0.318288\pi$
$224$	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	0.584356	−	0.811497i	$-0.301347\pi$
$227$	−3.42222	−	3.42222i	−0.227141	−	0.227141i	−0.811497	+	0.584356i	$0.801347\pi$
$228$	26.5318	−	19.7620i	1.75711	−	1.30877i
$229$		−	5.20745i		−	0.344118i	−0.985087	−	0.172059i	$-0.944958\pi$
$229$		−	5.20745i		−	0.344118i	0.985087	−	0.172059i	$-0.0550420\pi$
$230$	10.8205	−	9.91454i	0.713485	−	0.653746i
$231$		−	12.3409i		−	0.811969i
$232$	0.210489	−	0.951058i	0.0138193	−	0.0624400i
$233$	−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
$238$	−8.72150	−	0.634324i	−0.565331	−	0.0411171i
$239$	0.684835			0.0442983			0.0221491	−	0.999755i	$-0.492949\pi$
$239$	0.684835			0.0442983			0.0221491	+	0.999755i	$0.492949\pi$
$240$	−22.4557	+	12.9745i	−1.44951	+	0.837498i
$241$	16.2456			1.04647			0.523236	−	0.852188i	$-0.324725\pi$
$241$	16.2456			1.04647			0.523236	+	0.852188i	$0.324725\pi$
$242$	1.41049	+	0.102586i	0.0906696	+	0.00659450i
$243$	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
$248$	−3.65098	+	16.4963i	−0.231837	+	1.04752i
$249$		−	42.4831i		−	2.69226i
$250$	15.8098	−	0.224639i	0.999899	−	0.0142074i
$251$			2.97231i			0.187610i	0.995591	+	0.0938052i	$0.0299031\pi$
$251$			2.97231i			0.187610i	−0.995591	+	0.0938052i	$0.970097\pi$
$252$	−36.9146	+	27.4955i	−2.32540	+	1.73206i
$253$	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	$0.243200\pi$
$258$	−1.27179	+	17.4862i	−0.0791783	+	1.08864i
$259$	−9.50165			−0.590404
$260$	2.78351	+	3.51970i	0.172626	+	0.218283i
$261$	1.86224			0.115270
$262$	−0.622578	+	8.56000i	−0.0384630	+	0.528839i
$263$	−16.7193	+	16.7193i	−1.03096	+	1.03096i	−0.0314517	+	0.999505i	$0.510013\pi$
$263$	−16.7193	+	16.7193i	−1.03096	+	1.03096i	−0.999505	+	0.0314517i	$0.989987\pi$
$264$	−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
$268$	−12.4894	−	16.7679i	−0.762911	−	1.02426i
$269$			16.6300i			1.01395i	0.861960	+	0.506976i	$0.169237\pi$
$269$			16.6300i			1.01395i	−0.861960	+	0.506976i	$0.830763\pi$
$270$	−14.9125	−	16.2752i	−0.907544	−	0.990476i
$271$			22.0740i			1.34090i	0.741956	+	0.670449i	$0.233898\pi$
$271$			22.0740i			1.34090i	−0.741956	+	0.670449i	$0.766102\pi$
$272$	−5.11374	+	2.76044i	−0.310066	+	0.167376i
$273$	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	$0.414674\pi$
$278$	4.73042	+	0.344049i	0.283712	+	0.0206347i
$279$	−32.3010			−1.93381
$280$	−15.1218	−	22.2691i	−0.903701	−	1.33084i
$281$	2.90866			0.173516			0.0867581	−	0.996229i	$-0.472349\pi$
$281$	2.90866			0.173516			0.0867581	+	0.996229i	$0.472349\pi$
$282$	−38.3235	−	2.78731i	−2.28213	−	0.165982i
$283$	11.1007	−	11.1007i	0.659868	−	0.659868i	−0.295480	−	0.955349i	$-0.595480\pi$
$283$	11.1007	−	11.1007i	0.659868	−	0.659868i	0.955349	+	0.295480i	$0.0954797\pi$
$284$	−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
$288$	−10.8620	+	28.5955i	−0.640049	+	1.68500i
$289$			14.8894i			0.875844i
$290$	−0.0475394	+	1.08801i	−0.00279161	+	0.0638901i
$291$			51.3077i			3.00771i
$292$	18.8447	+	25.3003i	1.10280	+	1.48059i
$293$	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
$298$	0.129181	−	1.77614i	0.00748324	−	0.102889i
$299$	−4.65671			−0.269304
$300$	22.2131	−	18.6365i	1.28247	−	1.07598i
$301$	−18.1974			−1.04888
$302$	1.21212	−	16.6658i	0.0697497	−	0.959009i
$303$	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	0.930586	−	0.366074i	$-0.119298\pi$
$307$	9.89105	+	9.89105i	0.564512	+	0.564512i	−0.366074	+	0.930586i	$0.619298\pi$
$308$	6.82666	−	5.08478i	0.388985	−	0.289732i
$309$			28.6673i			1.63083i
$310$	0.824582	−	18.8718i	0.0468331	−	1.07184i
$311$			16.6409i			0.943617i	0.881701	+	0.471809i	$0.156399\pi$
$311$			16.6409i			0.943617i	−0.881701	+	0.471809i	$0.843601\pi$
$312$	8.03463	+	1.77823i	0.454872	+	0.100673i
$313$	−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	$0.0974774\pi$
$318$	−11.1539	−	0.811238i	−0.625482	−	0.0454920i
$319$	−0.344387			−0.0192820
$320$	−16.4295	−	7.07607i	−0.918438	−	0.395564i
$321$	−29.2785			−1.63417
$322$	27.8605	+	2.02632i	1.55260	+	0.112923i
$323$	−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
$328$	17.7555	+	3.92965i	0.980382	+	0.216979i
$329$		−	39.8822i		−	2.19878i
$330$	6.19440	+	6.76044i	0.340990	+	0.372150i
$331$			2.78049i			0.152830i	0.997076	+	0.0764148i	$0.0243473\pi$
$331$			2.78049i			0.152830i	−0.997076	+	0.0764148i	$0.975653\pi$
$332$	23.5006	−	17.5043i	1.28976	−	0.960671i
$333$	−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	$0.149269\pi$
$338$	−1.23034	+	16.9162i	−0.0669215	+	0.920123i
$339$	3.76121			0.204281
$340$	5.09612	−	4.03020i	0.276376	−	0.218568i
$341$	5.97347			0.323481
$342$	−3.16460	+	43.5110i	−0.171122	+	2.35281i
$343$	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	0.399064	−	0.916923i	$-0.369335\pi$
$347$	−9.64663	−	9.64663i	−0.517858	−	0.517858i	−0.916923	+	0.399064i	$0.869335\pi$
$348$	1.19299	+	1.60167i	0.0639508	+	0.0858583i
$349$		−	8.92010i		−	0.477482i	−0.971083	−	0.238741i	$-0.923265\pi$
$349$		−	8.92010i		−	0.477482i	0.971083	−	0.238741i	$-0.0767347\pi$
$350$	20.9649	+	21.5917i	1.12062	+	1.15413i
$351$			7.00416i			0.373854i
$352$	2.00872	−	5.28820i	0.107065	−	0.281862i
$353$	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
$358$	−3.50640	−	0.255024i	−0.185319	−	0.0134784i
$359$	10.2926			0.543225			0.271612	−	0.962407i	$-0.412443\pi$
$359$	10.2926			0.543225			0.271612	+	0.962407i	$0.412443\pi$
$360$	6.42101	−	33.5913i	0.338417	−	1.77042i
$361$	13.5448			0.712882
$362$	−25.8723	−	1.88172i	−1.35982	−	0.0989009i
$363$	−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	0.992105	−	0.125411i	$-0.0400250\pi$
$367$	16.6035	+	16.6035i	0.866694	+	0.866694i	−0.125411	+	0.992105i	$0.540025\pi$
$368$	16.3356	−	8.81811i	0.851553	−	0.459676i
$369$			34.7665i			1.80987i
$370$	5.20510	−	4.76928i	0.270600	−	0.247943i
$371$		−	11.6076i		−	0.602636i
$372$	−20.6926	−	27.7813i	−1.07286	−	1.44039i
$373$	−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
$378$	3.04779	−	41.9050i	0.156762	−	2.15536i
$379$	−37.7938			−1.94134			−0.970669	−	0.240420i	$-0.922715\pi$
$379$	−37.7938			−1.94134			−0.970669	+	0.240420i	$0.922715\pi$
$380$	−25.3404	−	2.95966i	−1.29993	−	0.151827i
$381$	29.2559			1.49882
$382$	−2.41618	+	33.2208i	−0.123623	+	1.69972i
$383$	18.1611	−	18.1611i	0.927987	−	0.927987i	−0.0695892	−	0.997576i	$-0.522169\pi$
$383$	18.1611	−	18.1611i	0.927987	−	0.927987i	0.997576	+	0.0695892i	$0.0221688\pi$
$384$	−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
$388$	−28.3822	+	21.1402i	−1.44089	+	1.07323i
$389$		−	21.8372i		−	1.10719i	−0.832787	−	0.553594i	$-0.813256\pi$
$389$		−	21.8372i		−	1.10719i	0.832787	−	0.553594i	$-0.186744\pi$
$390$	−9.19160	−	0.401617i	−0.465435	−	0.0203367i
$391$			6.74237i			0.340976i
$392$	6.79323	−	30.6941i	0.343110	−	1.55028i
$393$	−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	$-0.00886393\pi$
$398$	5.45356	+	0.396643i	0.273362	+	0.0198819i
$399$	−70.4022			−3.52452
$400$	19.4617	+	4.60898i	0.973084	+	0.230449i
$401$	13.4235			0.670339			0.335170	−	0.942158i	$-0.391206\pi$
$401$	13.4235			0.670339			0.335170	+	0.942158i	$0.391206\pi$
$402$	42.7547	+	3.10959i	2.13241	+	0.155092i
$403$	−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
$408$	2.57467	−	11.6332i	0.127465	−	0.575930i
$409$			8.82027i			0.436134i	0.975934	+	0.218067i	$0.0699752\pi$
$409$			8.82027i			0.436134i	−0.975934	+	0.218067i	$0.930025\pi$
$410$	−20.3122	−	0.887521i	−1.00315	−	0.0438315i
$411$			40.7299i			2.00906i
$412$	−15.8581	+	11.8117i	−0.781270	+	0.581923i
$413$	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
$418$	0.585234	−	8.04655i	0.0286248	−	0.393570i
$419$	9.54658			0.466381			0.233190	−	0.972431i	$-0.425083\pi$
$419$	9.54658			0.466381			0.233190	+	0.972431i	$0.425083\pi$
$420$	54.8174	+	6.40246i	2.67481	+	0.312408i
$421$	−14.5350			−0.708390			−0.354195	−	0.935172i	$-0.615245\pi$
$421$	−14.5350			−0.708390			−0.354195	+	0.935172i	$0.615245\pi$
$422$	−0.742336	+	10.2066i	−0.0361363	+	0.496849i
$423$	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
$428$	−12.0636	−	16.1962i	−0.583115	−	0.782871i
$429$		−	2.90941i		−	0.140468i
$430$	9.96872	−	9.13404i	0.480734	−	0.440483i
$431$		−	25.6238i		−	1.23425i	−0.786864	−	0.617127i	$-0.788297\pi$
$431$		−	25.6238i		−	1.23425i	0.786864	−	0.617127i	$-0.211703\pi$
$432$	−13.2633	−	24.5704i	−0.638132	−	1.18214i
$433$	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
$438$	−64.5107	−	4.69193i	−3.08244	−	0.224189i
$439$	−25.5128			−1.21766			−0.608830	−	0.793300i	$-0.708361\pi$
$439$	−25.5128			−1.21766			−0.608830	+	0.793300i	$0.708361\pi$
$440$	−1.18745	+	6.21208i	−0.0566093	+	0.296149i
$441$	60.1012			2.86196
$442$	−2.05613	−	0.149545i	−0.0978002	−	0.00711312i
$443$	−2.20795	+	2.20795i	−0.104903	+	0.104903i	−0.757610	−	0.652707i	$-0.773633\pi$
$443$	−2.20795	+	2.20795i	−0.104903	+	0.104903i	0.652707	+	0.757610i	$0.273633\pi$
$444$	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
$448$	−11.6682	−	31.9873i	−0.551273	−	1.51126i
$449$		−	3.06554i		−	0.144672i	−0.997380	−	0.0723359i	$-0.976955\pi$
$449$		−	3.06554i		−	0.144672i	0.997380	−	0.0723359i	$-0.0230454\pi$
$450$	−0.563166	+	38.2320i	−0.0265479	+	1.80228i
$451$		−	6.42941i		−	0.302749i
$452$	1.54972	+	2.08061i	0.0728929	+	0.0978636i
$453$	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	$0.288785\pi$
$458$	−0.534213	+	7.34505i	−0.0249622	+	0.343212i
$459$	10.1412			0.473351
$460$	−16.2793	+	12.8743i	−0.759028	+	0.600267i
$461$	8.55849			0.398609			0.199304	−	0.979938i	$-0.436132\pi$
$461$	8.55849			0.398609			0.199304	+	0.979938i	$0.436132\pi$
$462$	−1.26600	+	17.4066i	−0.0588998	+	0.809830i
$463$	10.4394	−	10.4394i	0.485160	−	0.485160i	−0.421615	−	0.906775i	$-0.638537\pi$
$463$	10.4394	−	10.4394i	0.485160	−	0.485160i	0.906775	+	0.421615i	$0.138537\pi$
$464$	−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	0.951639	−	0.307219i	$-0.0993982\pi$
$467$	13.9260	+	13.9260i	0.644420	+	0.644420i	−0.307219	+	0.951639i	$0.599398\pi$
$468$	−8.70278	+	6.48219i	−0.402286	+	0.299639i
$469$			44.4936i			2.05452i
$470$	20.0185	+	21.8479i	0.923386	+	1.00777i
$471$			58.2126i			2.68229i
$472$	4.69465	+	1.03902i	0.216089	+	0.0478249i
$473$	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
$478$	−0.965951	−	0.0702547i	−0.0441816	−	0.00321337i
$479$	−15.2334			−0.696034			−0.348017	−	0.937488i	$-0.613145\pi$
$479$	−15.2334			−0.696034			−0.348017	+	0.937488i	$0.613145\pi$
$480$	33.0044	−	15.9967i	1.50644	−	0.730145i
$481$	−2.24006			−0.102138
$482$	−22.9142	−	1.66658i	−1.04371	−	0.0759105i
$483$	−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	0.995371	−	0.0961059i	$-0.0306388\pi$
$487$	19.8451	+	19.8451i	0.899265	+	0.899265i	−0.0961059	+	0.995371i	$0.530639\pi$
$488$	−7.07491	−	1.56582i	−0.320266	−	0.0708815i
$489$			2.46406i			0.111429i
$490$	−1.53427	+	35.1139i	−0.0693111	+	1.58629i
$491$		−	32.4227i		−	1.46322i	−0.681725	−	0.731608i	$-0.738770\pi$
$491$		−	32.4227i		−	1.46322i	0.681725	−	0.731608i	$-0.261230\pi$
$492$	−29.9018	+	22.2721i	−1.34808	+	1.00410i
$493$	−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
$498$	−4.35819	+	59.9219i	−0.195295	+	2.68517i
$499$	35.1679			1.57433			0.787166	−	0.616741i	$-0.211547\pi$
$499$	35.1679			1.57433			0.787166	+	0.616741i	$0.211547\pi$
$500$	−22.3226	−	1.30502i	−0.998295	−	0.0583621i
$501$	−20.4632			−0.914228
$502$	0.304918	−	4.19241i	0.0136092	−	0.187116i
$503$	−26.4539	+	26.4539i	−1.17952	+	1.17952i	−0.199657	+	0.979866i	$0.563983\pi$
$503$	−26.4539	+	26.4539i	−1.17952	+	1.17952i	−0.979866	+	0.199657i	$0.936017\pi$
$504$	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
$508$	12.0542	+	16.1836i	0.534821	+	0.718032i
$509$			29.1842i			1.29356i	0.762675	+	0.646782i	$0.223886\pi$
$509$			29.1842i			1.29356i	−0.762675	+	0.646782i	$0.776114\pi$
$510$	−0.581495	+	13.3084i	−0.0257490	+	0.589304i
$511$		−	67.1345i		−	2.96985i
$512$	−17.9663	−	13.7555i	−0.794004	−	0.607913i
$513$	−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
$518$	13.4020	+	0.974739i	0.588849	+	0.0428276i
$519$	36.1083			1.58498
$520$	−3.56503	−	5.25005i	−0.156337	−	0.230230i
$521$	−16.8395			−0.737750			−0.368875	−	0.929479i	$-0.620257\pi$
$521$	−16.8395			−0.737750			−0.368875	+	0.929479i	$0.620257\pi$
$522$	−2.62667	−	0.191040i	−0.114966	−	0.00836161i
$523$	5.35783	−	5.35783i	0.234281	−	0.234281i	−0.580196	−	0.814477i	$-0.697024\pi$
$523$	5.35783	−	5.35783i	0.234281	−	0.234281i	0.814477	+	0.580196i	$0.197024\pi$
$524$	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
$528$	5.50937	+	10.2061i	0.239765	+	0.444166i
$529$			1.46177i			0.0635554i
$530$	5.82633	+	6.35875i	0.253080	+	0.276206i
$531$			9.19247i			0.398919i
$532$	−29.0077	−	38.9448i	−1.25764	−	1.68847i
$533$	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
$538$	1.70602	−	23.4565i	0.0735515	−	1.01128i
$539$	−11.1146			−0.478739
$540$	19.3642	+	24.4858i	0.833305	+	1.05370i
$541$	17.8325			0.766678			0.383339	−	0.923608i	$-0.374774\pi$
$541$	17.8325			0.766678			0.383339	+	0.923608i	$0.374774\pi$
$542$	2.26449	−	31.1350i	0.0972680	−	1.33736i
$543$	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	0.917093	−	0.398673i	$-0.130529\pi$
$547$	12.1248	+	12.1248i	0.518419	+	0.518419i	−0.398673	+	0.917093i	$0.630529\pi$
$548$	−22.5308	+	16.7819i	−0.962467	+	0.716886i
$549$		−	13.8532i		−	0.591239i
$550$	0.104147	−	7.07030i	0.00444084	−	0.301479i
$551$			1.96466i			0.0836972i
$552$	−8.22468	+	37.1618i	−0.350066	+	1.58171i
$553$	−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	$0.384345\pi$
$558$	45.5602	+	3.31364i	1.92872	+	0.140278i
$559$	−4.29012			−0.181453
$560$	19.0446	+	32.9616i	0.804782	+	1.39288i
$561$	−4.21249			−0.177851
$562$	−4.10263	−	0.298389i	−0.173059	−	0.0125868i
$563$	−20.3216	+	20.3216i	−0.856455	+	0.856455i	−0.990919	−	0.134464i	$-0.957069\pi$
$563$	−20.3216	+	20.3216i	−0.856455	+	0.856455i	0.134464	+	0.990919i	$0.457069\pi$
$564$	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
$568$	2.59167	−	11.7100i	0.108744	−	0.491342i
$569$			42.4250i			1.77855i	0.457376	+	0.889273i	$0.348789\pi$
$569$			42.4250i			1.77855i	−0.457376	+	0.889273i	$0.651211\pi$
$570$	38.5670	−	35.3378i	1.61539	−	1.48014i
$571$			21.7300i			0.909370i	0.890652	+	0.454685i	$0.150248\pi$
$571$			21.7300i			0.909370i	−0.890652	+	0.454685i	$0.849752\pi$
$572$	1.60942	−	1.19876i	0.0672931	−	0.0501227i
$573$	−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	$0.377051\pi$
$578$	1.52744	−	21.0013i	0.0635333	−	0.873537i
$579$	−3.23009			−0.134238
$580$	0.178668	−	1.52975i	0.00741880	−	0.0635192i
$581$	−62.3590			−2.58709
$582$	5.26346	−	72.3688i	0.218178	−	2.99979i
$583$	−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	0.875592	−	0.483051i	$-0.160471\pi$
$587$	9.51052	+	9.51052i	0.392541	+	0.392541i	−0.483051	+	0.875592i	$0.660471\pi$
$588$	38.5020	+	51.6915i	1.58779	+	2.13172i
$589$		−	34.0774i		−	1.40414i
$590$	−5.37067	−	0.234666i	−0.221107	−	0.00966104i
$591$		−	69.5421i		−	2.86058i
$592$	7.85806	−	4.24185i	0.322964	−	0.174339i
$593$	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
$598$	6.56823	+	0.477714i	0.268595	+	0.0195352i
$599$	−5.24145			−0.214160			−0.107080	−	0.994250i	$-0.534150\pi$
$599$	−5.24145			−0.214160			−0.107080	+	0.994250i	$0.534150\pi$
$600$	−33.2432	+	24.0078i	−1.35715	+	0.980115i
$601$	13.4589			0.549002			0.274501	−	0.961587i	$-0.411487\pi$
$601$	13.4589			0.549002			0.274501	+	0.961587i	$0.411487\pi$
$602$	25.6672	+	1.86681i	1.04612	+	0.0760853i
$603$	−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	$-0.940193\pi$
$607$	−28.8057	−	28.8057i	−1.16919	−	1.16919i	−0.186787	−	0.982400i	$-0.559807\pi$
$608$	−30.1681	−	11.4594i	−1.22348	−	0.464739i
$609$		−	4.25003i		−	0.172220i
$610$	8.09367	+	0.353645i	0.327703	+	0.0143187i
$611$		−	9.40240i		−	0.380380i
$612$	9.38546	+	12.6006i	0.379385	+	0.509349i
$613$	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	$0.442977\pi$
$618$	2.94087	−	40.4349i	0.118299	−	1.62653i
$619$	17.1665			0.689978			0.344989	−	0.938607i	$-0.387883\pi$
$619$	17.1665			0.689978			0.344989	+	0.938607i	$0.387883\pi$
$620$	−3.09905	+	26.5338i	−0.124461	+	1.06562i
$621$	−32.3957			−1.29999
$622$	1.70712	−	23.4717i	0.0684495	−	0.941131i
$623$	−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
$628$	−32.2018	+	23.9852i	−1.28499	+	0.957115i
$629$			3.24334i			0.129320i
$630$	−53.6596	+	49.1668i	−2.13785	+	1.95885i
$631$		−	29.6327i		−	1.17966i	−0.807528	−	0.589830i	$-0.799195\pi$
$631$		−	29.6327i		−	1.17966i	0.807528	−	0.589830i	$-0.200805\pi$
$632$	−0.505165	−	0.111803i	−0.0200944	−	0.00444730i
$633$	−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
$638$	0.485753	+	0.0353294i	0.0192312	+	0.00139870i
$639$	22.9291			0.907061
$640$	22.4477	+	11.6662i	0.887325	+	0.461145i
$641$	13.9877			0.552482			0.276241	−	0.961088i	$-0.410911\pi$
$641$	13.9877			0.552482			0.276241	+	0.961088i	$0.410911\pi$
$642$	41.2970	+	3.00358i	1.62986	+	0.118542i
$643$	−23.4698	+	23.4698i	−0.925560	+	0.925560i	−0.997415	−	0.0718555i	$-0.977108\pi$
$643$	−23.4698	+	23.4698i	−0.925560	+	0.925560i	0.0718555	+	0.997415i	$0.477108\pi$
$644$	−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	0.999416	−	0.0341646i	$-0.0108770\pi$
$647$	24.5523	+	24.5523i	0.965252	+	0.965252i	−0.0341646	+	0.999416i	$0.510877\pi$
$648$	11.0958	+	2.45573i	0.435883	+	0.0964700i
$649$		−	1.69997i		−	0.0667298i
$650$	4.94256	+	5.09035i	0.193863	+	0.199660i
$651$			73.7177i			2.88923i
$652$	−1.36306	+	1.01526i	−0.0533815	+	0.0397608i
$653$	−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
$658$	−4.09137	+	56.2533i	−0.159498	+	2.19298i
$659$	−35.6989			−1.39063			−0.695316	−	0.718704i	$-0.744736\pi$
$659$	−35.6989			−1.39063			−0.695316	+	0.718704i	$0.744736\pi$
$660$	−8.04359	−	10.1710i	−0.313096	−	0.395905i
$661$	−13.7561			−0.535050			−0.267525	−	0.963551i	$-0.586206\pi$
$661$	−13.7561			−0.535050			−0.267525	+	0.963551i	$0.586206\pi$
$662$	0.285240	−	3.92185i	0.0110862	−	0.152427i
$663$	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
$668$	−8.43142	−	11.3197i	−0.326221	−	0.437974i
$669$			18.4362i			0.712785i
$670$	−22.3332	−	24.3740i	−0.862807	−	0.941651i
$671$			2.56189i			0.0989005i
$672$	65.2609	+	24.7894i	2.51749	+	0.956271i
$673$	−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	$0.160134\pi$
$678$	−5.30514	−	0.385848i	−0.203743	−	0.0148184i
$679$	75.3122			2.89022
$680$	−7.60145	+	5.16175i	−0.291502	+	0.197944i
$681$	−14.0331			−0.537750
$682$	−8.42550	−	0.612796i	−0.322629	−	0.0234652i
$683$	16.6264	−	16.6264i	0.636192	−	0.636192i	−0.313422	−	0.949614i	$-0.601476\pi$
$683$	16.6264	−	16.6264i	0.636192	−	0.636192i	0.949614	+	0.313422i	$0.101476\pi$
$684$	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
$688$	15.0496	−	8.12393i	0.573762	−	0.309722i
$689$		−	2.73654i		−	0.104254i
$690$	1.85756	−	42.5130i	0.0707162	−	1.61844i
$691$		−	11.9445i		−	0.454392i	−0.973849	−	0.227196i	$-0.927044\pi$
$691$		−	11.9445i		−	0.454392i	0.973849	−	0.227196i	$-0.0729558\pi$
$692$	14.8777	+	19.9742i	0.565564	+	0.759307i
$693$	−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
$698$	−0.915080	+	12.5817i	−0.0346363	+	0.476224i
$699$	−26.9719			−1.02017
$700$	−27.3557	−	32.6056i	−1.03395	−	1.23238i
$701$	19.3802			0.731980			0.365990	−	0.930619i	$-0.380730\pi$
$701$	19.3802			0.731980			0.365990	+	0.930619i	$0.380730\pi$
$702$	0.718531	−	9.87928i	0.0271192	−	0.372869i
$703$	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
$708$	−7.90620	+	5.88887i	−0.297133	+	0.221317i
$709$		−	25.2399i		−	0.947903i	−0.880551	−	0.473952i	$-0.842827\pi$
$709$		−	25.2399i		−	0.947903i	0.880551	−	0.473952i	$-0.157173\pi$
$710$	−0.585335	+	13.3962i	−0.0219672	+	0.502752i
$711$		−	0.989150i		−	0.0370960i
$712$	−3.99017	+	18.0289i	−0.149538	+	0.675662i
$713$	−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
$718$	−14.5176	−	1.05588i	−0.541794	−	0.0394052i
$719$	−7.56372			−0.282079			−0.141040	−	0.990004i	$-0.545044\pi$
$719$	−7.56372			−0.282079			−0.141040	+	0.990004i	$0.545044\pi$
$720$	−12.5028	+	46.7214i	−0.465951	+	1.74120i
$721$	42.0794			1.56712
$722$	−19.1047	−	1.38951i	−0.711004	−	0.0517121i
$723$	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	0.607461	−	0.794350i	$-0.292188\pi$
$727$	−5.03908	−	5.03908i	−0.186889	−	0.186889i	−0.794350	+	0.607461i	$0.792188\pi$
$728$	2.61018	−	11.7937i	0.0967399	−	0.437103i
$729$		−	38.9940i		−	1.44422i
$730$	33.6976	+	36.7769i	1.24720	+	1.36117i
$731$			6.21159i			0.229744i
$732$	11.9148	−	8.87461i	0.440382	−	0.328015i
$733$	−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
$738$	3.56657	−	49.0377i	0.131287	−	1.80510i
$739$	7.46962			0.274775			0.137387	−	0.990517i	$-0.456130\pi$
$739$	7.46962			0.274775			0.137387	+	0.990517i	$0.456130\pi$
$740$	−7.83099	+	6.19304i	−0.287873	+	0.227661i
$741$	−16.5976			−0.609729
$742$	−1.19078	+	16.3724i	−0.0437149	+	0.601048i
$743$	12.8563	−	12.8563i	0.471652	−	0.471652i	−0.430797	−	0.902449i	$-0.641768\pi$
$743$	12.8563	−	12.8563i	0.471652	−	0.471652i	0.902449	+	0.430797i	$0.141768\pi$
$744$	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
$748$	−1.73566	−	2.33025i	−0.0634622	−	0.0852022i
$749$			42.9766i			1.57033i
$750$	31.9542	−	32.8753i	1.16680	−	1.20044i
$751$			33.0689i			1.20670i	0.797476	+	0.603351i	$0.206168\pi$
$751$			33.0689i			1.20670i	−0.797476	+	0.603351i	$0.793832\pi$
$752$	17.8047	+	32.9834i	0.649272	+	1.20278i
$753$	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	$0.293187\pi$
$758$	53.3077	+	3.87713i	1.93622	+	0.140824i
$759$	13.4566			0.488445
$760$	35.4387	+	6.77414i	1.28550	+	0.245724i
$761$	18.7528			0.679789			0.339895	−	0.940464i	$-0.389609\pi$
$761$	18.7528			0.679789			0.339895	+	0.940464i	$0.389609\pi$
$762$	−41.2650	−	3.00125i	−1.49487	−	0.108724i
$763$	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
$768$	45.4255	−	9.42464i	1.63915	−	0.340082i
$769$			43.7854i			1.57894i	0.613787	+	0.789472i	$0.289645\pi$
$769$			43.7854i			1.57894i	−0.613787	+	0.789472i	$0.710355\pi$
$770$	9.92335	−	9.09247i	0.357613	−	0.327670i
$771$		−	1.98581i		−	0.0715173i
$772$	−1.33089	−	1.78681i	−0.0478998	−	0.0643087i
$773$	−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
$778$	−2.24019	+	30.8010i	−0.0803148	+	1.10427i
$779$	−36.6785			−1.31414
$780$	12.9234	+	1.50941i	0.462733	+	0.0540455i
$781$	−4.24031			−0.151730
$782$	0.691675	−	9.51003i	0.0247342	−	0.340078i
$783$	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	0.991593	−	0.129398i	$-0.0413044\pi$
$787$	24.1876	+	24.1876i	0.862195	+	0.862195i	−0.129398	+	0.991593i	$0.541304\pi$
$788$	38.4690	−	28.6533i	1.37040	−	1.02073i
$789$			68.5590i			2.44077i
$790$	0.577907	+	0.0252511i	0.0205610	+	0.000898392i
$791$		−	5.52091i		−	0.196301i
$792$	−14.9331	−	3.30501i	−0.530625	−	0.117438i
$793$	−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	$0.457636\pi$
$798$	99.3014	+	7.22230i	3.51523	+	0.255667i
$799$	−13.6136			−0.481614
$800$	−26.9777	−	8.49741i	−0.953804	−	0.300429i
$801$	−35.3019			−1.24733
$802$	−18.9337	−	1.37707i	−0.668573	−	0.0486260i
$803$	−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
$808$	−25.0084	−	5.53488i	−0.879793	−	0.194716i
$809$			27.7783i			0.976634i	0.872666	+	0.488317i	$0.162389\pi$
$809$			27.7783i			0.976634i	−0.872666	+	0.488317i	$0.837611\pi$
$810$	−12.6935	−	0.554631i	−0.446006	−	0.0194877i
$811$			6.85883i			0.240846i	0.992723	+	0.120423i	$0.0384251\pi$
$811$			6.85883i			0.240846i	−0.992723	+	0.120423i	$0.961575\pi$
$812$	2.35101	−	1.75113i	0.0825044	−	0.0614527i
$813$	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
$818$	0.904838	−	12.4409i	0.0316369	−	0.434985i
$819$	23.0929			0.806930
$820$	28.5591	+	3.33559i	0.997326	+	0.116484i
$821$	−19.5203			−0.681262			−0.340631	−	0.940197i	$-0.610641\pi$
$821$	−19.5203			−0.681262			−0.340631	+	0.940197i	$0.610641\pi$
$822$	4.17833	−	57.4490i	0.145736	−	2.00376i
$823$	35.2865	−	35.2865i	1.23001	−	1.23001i	0.266053	−	0.963958i	$-0.414280\pi$
$823$	35.2865	−	35.2865i	1.23001	−	1.23001i	0.963958	−	0.266053i	$-0.0857196\pi$
$824$	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	0.957292	−	0.289122i	$-0.0933632\pi$
$827$	19.2150	+	19.2150i	0.668171	+	0.668171i	−0.289122	+	0.957292i	$0.593363\pi$
$828$	−29.9815	−	40.2521i	−1.04193	−	1.39886i
$829$		−	21.8101i		−	0.757497i	−0.925500	−	0.378748i	$-0.876355\pi$
$829$		−	21.8101i		−	0.757497i	0.925500	−	0.378748i	$-0.123645\pi$
$830$	34.1609	−	31.3006i	1.18574	−	1.08646i
$831$			47.7341i			1.65588i
$832$	−2.75084	−	7.54114i	−0.0953683	−	0.261442i
$833$	−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
$838$	−13.4653	−	0.979348i	−0.465152	−	0.0338310i
$839$	−9.74722			−0.336512			−0.168256	−	0.985743i	$-0.553813\pi$
$839$	−9.74722			−0.336512			−0.168256	+	0.985743i	$0.553813\pi$
$840$	−76.6624	−	14.6541i	−2.64511	−	0.505615i
$841$	28.8814			0.995910
$842$	20.5014	+	1.49109i	0.706524	+	0.0513863i
$843$	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
$848$	5.18201	+	9.59971i	0.177951	+	0.329656i
$849$		−	45.5194i		−	1.56222i
$850$	7.37023	−	7.15625i	0.252797	−	0.245457i
$851$		−	10.3607i		−	0.355161i
$852$	14.6888	+	19.7207i	0.503230	+	0.675620i
$853$	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	$0.922253\pi$
$858$	−0.298466	+	4.10369i	−0.0101895	+	0.140098i
$859$	7.49975			0.255888			0.127944	−	0.991781i	$-0.459162\pi$
$859$	7.49975			0.255888			0.127944	+	0.991781i	$0.459162\pi$
$860$	−14.9978	+	11.8608i	−0.511420	+	0.404450i
$861$	79.3445			2.70405
$862$	−2.62865	+	36.1420i	−0.0895321	+	1.23100i
$863$	−13.4941	+	13.4941i	−0.459344	+	0.459344i	−0.898440	−	0.439096i	$-0.855299\pi$
$863$	−13.4941	+	13.4941i	−0.459344	+	0.459344i	0.439096	+	0.898440i	$0.355299\pi$
$864$	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
$868$	−40.7788	+	30.3738i	−1.38412	+	1.03095i
$869$			0.182925i			0.00620530i
$870$	2.13327	+	2.32821i	0.0723245	+	0.0789336i
$871$			10.4896i			0.355425i
$872$	1.92857	−	8.71392i	0.0653096	−	0.295090i
$873$	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	$0.120385\pi$
$878$	35.9855	+	2.61727i	1.21445	+	0.0883285i
$879$	47.6999			1.60888
$880$	2.31215	−	8.64025i	0.0779427	−	0.291263i
$881$	−48.8838			−1.64694			−0.823469	−	0.567362i	$-0.807964\pi$
$881$	−48.8838			−1.64694			−0.823469	+	0.567362i	$0.807964\pi$
$882$	−84.7720	−	6.16556i	−2.85442	−	0.207605i
$883$	6.52604	−	6.52604i	0.219619	−	0.219619i	−0.588719	−	0.808338i	$-0.700368\pi$
$883$	6.52604	−	6.52604i	0.219619	−	0.219619i	0.808338	+	0.588719i	$0.200368\pi$
$884$	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	0.700938	−	0.713223i	$-0.252765\pi$
$887$	−0.365873	−	0.365873i	−0.0122848	−	0.0122848i	−0.713223	+	0.700938i	$0.752765\pi$
$888$	−3.95639	+	17.8763i	−0.132768	+	0.599888i
$889$		−	42.9434i		−	1.44027i
$890$	0.901189	−	20.6250i	0.0302079	−	0.691352i
$891$		−	4.01788i		−	0.134604i
$892$	−10.1985	+	7.59624i	−0.341470	+	0.254341i
$893$	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
$898$	−0.314483	+	4.32391i	−0.0104944	+	0.144291i
$899$	2.05718			0.0686109
$900$	4.71642	−	53.8681i	0.157214	−	1.79560i
$901$	−3.96219			−0.132000
$902$	−0.659570	+	9.06861i	−0.0219613	+	0.301952i
$903$	−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	0.459400	−	0.888230i	$-0.348064\pi$
$907$	−12.9148	−	12.9148i	−0.428830	−	0.428830i	−0.888230	+	0.459400i	$0.848064\pi$
$908$	−5.78204	−	7.76278i	−0.191884	−	0.257617i
$909$		−	48.9683i		−	1.62418i
$910$	−0.589516	+	13.4919i	−0.0195423	+	0.447253i
$911$		−	1.42800i		−	0.0473117i	−0.999720	−	0.0236559i	$-0.992469\pi$
$911$		−	1.42800i		−	0.0473117i	0.999720	−	0.0236559i	$-0.00753059\pi$
$912$	58.2241	−	31.4299i	1.92799	−	1.04075i
$913$	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
$918$	−14.3040	−	1.04035i	−0.472104	−	0.0343366i
$919$	−8.37592			−0.276296			−0.138148	−	0.990412i	$-0.544115\pi$
$919$	−8.37592			−0.276296			−0.138148	+	0.990412i	$0.544115\pi$
$920$	24.2825	−	16.4890i	0.800571	−	0.543627i
$921$	40.5591			1.33647
$922$	−12.0717	−	0.877984i	−0.397559	−	0.0289149i
$923$	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
$928$	0.691778	−	1.82119i	0.0227087	−	0.0597833i
$929$		−	8.25659i		−	0.270890i	−0.990785	−	0.135445i	$-0.956754\pi$
$929$		−	8.25659i		−	0.270890i	0.990785	−	0.135445i	$-0.0432464\pi$
$930$	−37.0020	−	40.3833i	−1.21334	−	1.32422i
$931$			63.4065i			2.07807i
$932$	−11.1132	−	14.9202i	−0.364025	−	0.488728i
$933$	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	$0.966906\pi$
$938$	4.56443	−	62.7577i	0.149034	−	2.04911i
$939$	−90.1116			−2.94068
$940$	−25.9946	−	32.8698i	−0.847851	−	1.07209i
$941$	−15.7061			−0.512004			−0.256002	−	0.966676i	$-0.582405\pi$
$941$	−15.7061			−0.512004			−0.256002	+	0.966676i	$0.582405\pi$
$942$	5.97181	−	82.1082i	0.194572	−	2.67523i
$943$	−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	0.396568	−	0.918005i	$-0.370201\pi$
$947$	−16.0464	−	16.0464i	−0.521437	−	0.521437i	−0.918005	+	0.396568i	$0.870201\pi$
$948$	0.850742	−	0.633668i	0.0276308	−	0.0205806i
$949$		−	15.8272i		−	0.513774i
$950$	−40.3347	−	0.594138i	−1.30863	−	0.0192764i
$951$		−	47.6022i		−	1.54361i
$952$	−17.0759	−	3.77924i	−0.553432	−	0.122486i
$953$	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
$958$	21.4866	+	1.56274i	0.694200	+	0.0504899i
$959$	59.7856			1.93058
$960$	−48.1934	+	19.1773i	−1.55543	+	0.618946i
$961$	−4.68230			−0.151042
$962$	3.15957	+	0.229799i	0.101869	+	0.00740902i
$963$	−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	0.660654	−	0.750690i	$-0.270279\pi$
$967$	−2.79981	−	2.79981i	−0.0900358	−	0.0900358i	−0.750690	+	0.660654i	$0.770279\pi$
$968$	2.76160	+	0.611199i	0.0887612	+	0.0196447i
$969$			24.0314i			0.772000i
$970$	−41.2568	+	37.8024i	−1.32467	+	1.21376i
$971$		−	39.7551i		−	1.27580i	−0.770119	−	0.637901i	$-0.779803\pi$
$971$		−	39.7551i		−	1.27580i	0.770119	−	0.637901i	$-0.220197\pi$
$972$	14.9028	−	11.1002i	0.478006	−	0.356039i
$973$	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	$0.0994740\pi$
$978$	0.252779	−	3.47553i	0.00808298	−	0.111135i
$979$	6.52843			0.208649
$980$	5.76627	−	49.3704i	0.184197	−	1.57708i
$981$	17.0625			0.544763
$982$	−3.32613	+	45.7318i	−0.106141	+	1.45936i
$983$	−4.38592	+	4.38592i	−0.139889	+	0.139889i	−0.773583	−	0.633694i	$-0.781538\pi$
$983$	−4.38592	+	4.38592i	−0.139889	+	0.139889i	0.633694	+	0.773583i	$0.281538\pi$
$984$	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
$988$	−6.83869	−	9.18140i	−0.217568	−	0.292099i
$989$		−	19.8427i		−	0.630961i
$990$	17.0834	+	0.746443i	0.542947	+	0.0237235i
$991$		−	41.8022i		−	1.32789i	−0.747781	−	0.663945i	$-0.768881\pi$
$991$		−	41.8022i		−	1.32789i	0.747781	−	0.663945i	$-0.231119\pi$
$992$	−11.9990	+	31.5889i	−0.380970	+	1.00295i
$993$	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	$0.315785\pi$
$998$	−49.6039	−	3.60775i	−1.57019	−	0.114201i
$999$	−15.5836			−0.493042

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instead) (See

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Twists

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

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

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

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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.d.23.1

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