LMFDB - Embedded newform 220.2.l.d.67.1

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)

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);

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")

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			67.1
Character	$\chi$	$=$	220.67
Dual form			220.2.l.d.23.1

$q$-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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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	0.978768	+	0.204970i	$0.0657096\pi$
$3$	2.05029	+	2.05029i	1.18374	+	1.18374i	0.204970	+	0.978768i	$0.434290\pi$
$4$	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	−0.148599	+	0.988897i	$0.547477\pi$
$7$	−3.00953	+	3.00953i	−1.13750	+	1.13750i	−0.988897	+	0.148599i	$0.952523\pi$
$8$	−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	−0.798619	−	0.601836i	$-0.794436\pi$
$13$	−0.709511	+	0.709511i	−0.196783	+	0.196783i	0.601836	+	0.798619i	$0.294436\pi$
$14$	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	0.571469	−	0.820623i	$-0.306374\pi$
$17$	−1.02729	−	1.02729i	−0.249154	−	0.249154i	−0.820623	+	0.571469i	$0.806374\pi$
$18$	−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	0.960959	−	0.276691i	$-0.0892379\pi$
$23$	3.28163	+	3.28163i	0.684268	+	0.684268i	−0.276691	+	0.960959i	$0.589238\pi$
$24$	−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	$-0.989820\pi$
$29$		−	0.344387i		−	0.0639510i	0.999489	−	0.0319755i	$-0.0101799\pi$
$30$	6.76044	+	6.19440i	1.23428	+	1.13094i
$31$			5.97347i			1.07287i	0.843943	+	0.536433i	$0.180229\pi$
$31$			5.97347i			1.07287i	−0.843943	+	0.536433i	$0.819771\pi$
$32$	−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	0.824858	−	0.565339i	$-0.191255\pi$
$37$	1.57859	+	1.57859i	0.259519	+	0.259519i	−0.565339	+	0.824858i	$0.691255\pi$
$38$	−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	0.898999	−	0.437951i	$-0.144296\pi$
$43$	3.02329	+	3.02329i	0.461048	+	0.461048i	−0.437951	+	0.898999i	$0.644296\pi$
$44$	−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	$-0.510493\pi$
$47$	6.62597	−	6.62597i	0.966498	−	0.966498i	0.999457	+	0.0329591i	$0.0104931\pi$
$48$	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	−0.562144	−	0.827039i	$-0.690023\pi$
$53$	1.92847	−	1.92847i	0.264896	−	0.264896i	0.827039	+	0.562144i	$0.190023\pi$
$54$	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	−0.995702	−	0.0926126i	$-0.970478\pi$
$67$	−7.39211	+	7.39211i	−0.903090	+	0.903090i	0.0926126	+	0.995702i	$0.470478\pi$
$68$	−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	$-0.919038\pi$
$71$		−	4.24031i		−	0.503232i	0.967827	−	0.251616i	$-0.0809619\pi$
$72$	−3.30501	−	14.9331i	−0.389499	−	1.75988i
$73$	11.1536	−	11.1536i	1.30543	−	1.30543i	0.380760	−	0.924674i	$-0.375662\pi$
$73$	11.1536	−	11.1536i	1.30543	−	1.30543i	0.924674	−	0.380760i	$-0.124338\pi$
$74$	−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	0.988953	+	0.148233i	$0.0473584\pi$
$83$	10.3602	+	10.3602i	1.13719	+	1.13719i	0.148233	+	0.988953i	$0.452642\pi$
$84$	−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	$0.112462\pi$
$89$			6.52843i			0.692012i	−0.938232	+	0.346006i	$0.887538\pi$
$90$	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	−0.945863	−	0.324565i	$-0.894782\pi$
$97$	−12.5123	−	12.5123i	−1.27043	−	1.27043i	−0.324565	−	0.945863i	$-0.605218\pi$
$98$	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	0.273131	−	0.961977i	$-0.411941\pi$
$103$	−6.99102	−	6.99102i	−0.688846	−	0.688846i	−0.961977	+	0.273131i	$0.911941\pi$
$104$	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	$-0.912305\pi$
$107$	−7.14008	+	7.14008i	−0.690258	+	0.690258i	0.272031	+	0.962289i	$0.412305\pi$
$108$	−8.33950	+	11.1963i	−0.802469	+	1.07737i
$109$		−	3.15539i		−	0.302231i	−0.988516	−	0.151116i	$-0.951713\pi$
$109$		−	3.15539i		−	0.302231i	0.988516	−	0.151116i	$-0.0482866\pi$
$110$	−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	−0.662646	−	0.748933i	$-0.730567\pi$
$113$	0.917236	−	0.917236i	0.0862863	−	0.0862863i	0.748933	+	0.662646i	$0.230567\pi$
$114$	−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	−0.315752	−	0.948842i	$-0.602257\pi$
$127$	7.13455	−	7.13455i	0.633089	−	0.633089i	0.948842	+	0.315752i	$0.102257\pi$
$128$	−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	$0.0854108\pi$
$131$			6.06882i			0.530235i	−0.964216	+	0.265118i	$0.914589\pi$
$132$	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	0.141352	−	0.989959i	$-0.454855\pi$
$137$	−9.93269	−	9.93269i	−0.848607	−	0.848607i	−0.989959	+	0.141352i	$0.954855\pi$
$138$	−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	$-0.983574\pi$
$149$		−	1.25924i		−	0.103161i	0.998669	−	0.0515805i	$-0.0164259\pi$
$150$	−14.7097	−	14.2827i	−1.20104	−	1.16617i
$151$		−	11.8156i		−	0.961542i	−0.876846	−	0.480771i	$-0.840357\pi$
$151$		−	11.8156i		−	0.961542i	0.876846	−	0.480771i	$-0.159643\pi$
$152$	−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	−0.989680	−	0.143297i	$-0.954230\pi$
$157$	−14.1962	−	14.1962i	−1.13298	−	1.13298i	−0.143297	−	0.989680i	$-0.545770\pi$
$158$	−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	0.683182	−	0.730248i	$-0.260596\pi$
$163$	−0.600905	−	0.600905i	−0.0470665	−	0.0470665i	−0.730248	+	0.683182i	$0.760596\pi$
$164$	−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	$-0.838035\pi$
$167$	−4.99031	+	4.99031i	−0.386162	+	0.386162i	0.487154	+	0.873316i	$0.338035\pi$
$168$	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	−0.288115	−	0.957596i	$-0.593029\pi$
$173$	8.80565	−	8.80565i	0.669481	−	0.669481i	0.957596	+	0.288115i	$0.0930285\pi$
$174$	−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	$0.324675\pi$
$191$			23.5527i			1.70421i	−0.523369	+	0.852106i	$0.675325\pi$
$192$	21.7919	+	7.94919i	1.57269	+	0.573683i
$193$	−0.787715	+	0.787715i	−0.0567009	+	0.0567009i	−0.734889	−	0.678188i	$-0.762766\pi$
$193$	−0.787715	+	0.787715i	−0.0567009	+	0.0567009i	0.678188	+	0.734889i	$0.262766\pi$
$194$	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	0.971583	+	0.236700i	$0.0760657\pi$
$197$	16.9591	+	16.9591i	1.20828	+	1.20828i	0.236700	+	0.971583i	$0.423934\pi$
$198$	−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	$0.0801284\pi$
$211$			7.23621i			0.498161i	−0.968483	+	0.249081i	$0.919872\pi$
$212$	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	0.540360	−	0.841434i	$-0.318288\pi$
$223$	−4.49599	−	4.49599i	−0.301074	−	0.301074i	−0.841434	+	0.540360i	$0.818288\pi$
$224$	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	$-0.801347\pi$
$227$	−3.42222	+	3.42222i	−0.227141	+	0.227141i	0.584356	+	0.811497i	$0.301347\pi$
$228$	26.5318	+	19.7620i	1.75711	+	1.30877i
$229$			5.20745i			0.344118i	0.985087	+	0.172059i	$0.0550420\pi$
$229$			5.20745i			0.344118i	−0.985087	+	0.172059i	$0.944958\pi$
$230$	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	−0.888938	−	0.458027i	$-0.848556\pi$
$233$	−6.57758	+	6.57758i	−0.430911	+	0.430911i	0.458027	+	0.888938i	$0.348556\pi$
$234$	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	$-0.970097\pi$
$251$		−	2.97231i		−	0.187610i	0.995591	−	0.0938052i	$-0.0299031\pi$
$252$	−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	0.722050	−	0.691841i	$-0.243200\pi$
$257$	0.484275	+	0.484275i	0.0302082	+	0.0302082i	−0.691841	+	0.722050i	$0.743200\pi$
$258$	−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	−0.999505	−	0.0314517i	$-0.989987\pi$
$263$	−16.7193	−	16.7193i	−1.03096	−	1.03096i	−0.0314517	−	0.999505i	$-0.510013\pi$
$264$	−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	$-0.830763\pi$
$269$		−	16.6300i		−	1.01395i	0.861960	−	0.506976i	$-0.169237\pi$
$270$	−14.9125	+	16.2752i	−0.907544	+	0.990476i
$271$		−	22.0740i		−	1.34090i	−0.741956	−	0.670449i	$-0.766102\pi$
$271$		−	22.0740i		−	1.34090i	0.741956	−	0.670449i	$-0.233898\pi$
$272$	−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	0.264859	−	0.964287i	$-0.414674\pi$
$277$	−11.6408	−	11.6408i	−0.699428	−	0.699428i	−0.964287	+	0.264859i	$0.914674\pi$
$278$	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	0.955349	−	0.295480i	$-0.0954797\pi$
$283$	11.1007	+	11.1007i	0.659868	+	0.659868i	−0.295480	+	0.955349i	$0.595480\pi$
$284$	−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	−0.280329	−	0.959904i	$-0.590443\pi$
$293$	11.6325	−	11.6325i	0.679575	−	0.679575i	0.959904	+	0.280329i	$0.0904435\pi$
$294$	−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	−0.366074	−	0.930586i	$-0.619298\pi$
$307$	9.89105	−	9.89105i	0.564512	−	0.564512i	0.930586	+	0.366074i	$0.119298\pi$
$308$	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	$-0.843601\pi$
$311$		−	16.6409i		−	0.943617i	0.881701	−	0.471809i	$-0.156399\pi$
$312$	8.03463	−	1.77823i	0.454872	−	0.100673i
$313$	−21.9753	+	21.9753i	−1.24212	+	1.24212i	−0.282996	+	0.959121i	$0.591328\pi$
$313$	−21.9753	+	21.9753i	−1.24212	+	1.24212i	−0.959121	+	0.282996i	$0.908672\pi$
$314$	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	0.953476	−	0.301470i	$-0.0974774\pi$
$317$	11.6086	+	11.6086i	0.652005	+	0.652005i	−0.301470	+	0.953476i	$0.597477\pi$
$318$	−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	$-0.975653\pi$
$331$		−	2.78049i		−	0.152830i	0.997076	−	0.0764148i	$-0.0243473\pi$
$332$	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	0.892047	−	0.451943i	$-0.149269\pi$
$337$	8.07923	+	8.07923i	0.440103	+	0.440103i	−0.451943	+	0.892047i	$0.649269\pi$
$338$	−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	−0.916923	−	0.399064i	$-0.869335\pi$
$347$	−9.64663	+	9.64663i	−0.517858	+	0.517858i	0.399064	+	0.916923i	$0.369335\pi$
$348$	1.19299	−	1.60167i	0.0639508	−	0.0858583i
$349$			8.92010i			0.477482i	0.971083	+	0.238741i	$0.0767347\pi$
$349$			8.92010i			0.477482i	−0.971083	+	0.238741i	$0.923265\pi$
$350$	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	0.0345986	−	0.999401i	$-0.488985\pi$
$353$	19.4271	−	19.4271i	1.03400	−	1.03400i	0.999401	−	0.0345986i	$-0.0110153\pi$
$354$	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	−0.125411	−	0.992105i	$-0.540025\pi$
$367$	16.6035	−	16.6035i	0.866694	−	0.866694i	0.992105	+	0.125411i	$0.0400250\pi$
$368$	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	−0.803893	−	0.594774i	$-0.797242\pi$
$373$	−4.03877	+	4.03877i	−0.209119	+	0.209119i	0.594774	+	0.803893i	$0.297242\pi$
$374$	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	0.997576	−	0.0695892i	$-0.0221688\pi$
$383$	18.1611	+	18.1611i	0.927987	+	0.927987i	−0.0695892	+	0.997576i	$0.522169\pi$
$384$	−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	$0.186744\pi$
$389$			21.8372i			1.10719i	−0.832787	+	0.553594i	$0.813256\pi$
$390$	−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	0.999612	+	0.0278432i	$0.00886393\pi$
$397$	20.4719	+	20.4719i	1.02746	+	1.02746i	0.0278432	+	0.999612i	$0.491136\pi$
$398$	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	$-0.930025\pi$
$409$		−	8.82027i		−	0.436134i	0.975934	−	0.218067i	$-0.0699752\pi$
$410$	−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	$0.211703\pi$
$431$			25.6238i			1.23425i	−0.786864	+	0.617127i	$0.788297\pi$
$432$	−13.2633	+	24.5704i	−0.638132	+	1.18214i
$433$	12.6473	−	12.6473i	0.607790	−	0.607790i	−0.334578	−	0.942368i	$-0.608594\pi$
$433$	12.6473	−	12.6473i	0.607790	−	0.607790i	0.942368	+	0.334578i	$0.108594\pi$
$434$	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	0.652707	−	0.757610i	$-0.273633\pi$
$443$	−2.20795	−	2.20795i	−0.104903	−	0.104903i	−0.757610	+	0.652707i	$0.773633\pi$
$444$	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	$0.0230454\pi$
$449$			3.06554i			0.144672i	−0.997380	+	0.0723359i	$0.976955\pi$
$450$	−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	0.615919	−	0.787810i	$-0.288785\pi$
$457$	−3.67461	−	3.67461i	−0.171891	−	0.171891i	−0.787810	+	0.615919i	$0.788785\pi$
$458$	−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	0.906775	−	0.421615i	$-0.138537\pi$
$463$	10.4394	+	10.4394i	0.485160	+	0.485160i	−0.421615	+	0.906775i	$0.638537\pi$
$464$	−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	$-0.599398\pi$
$467$	13.9260	−	13.9260i	0.644420	−	0.644420i	0.951639	+	0.307219i	$0.0993982\pi$
$468$	−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	−0.0961059	−	0.995371i	$-0.530639\pi$
$487$	19.8451	−	19.8451i	0.899265	−	0.899265i	0.995371	+	0.0961059i	$0.0306388\pi$
$488$	−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	$0.261230\pi$
$491$			32.4227i			1.46322i	−0.681725	+	0.731608i	$0.738770\pi$
$492$	−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	−0.979866	−	0.199657i	$-0.936017\pi$
$503$	−26.4539	−	26.4539i	−1.17952	−	1.17952i	−0.199657	−	0.979866i	$-0.563983\pi$
$504$	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	$-0.776114\pi$
$509$		−	29.1842i		−	1.29356i	0.762675	−	0.646782i	$-0.223886\pi$
$510$	−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	0.814477	−	0.580196i	$-0.197024\pi$
$523$	5.35783	+	5.35783i	0.234281	+	0.234281i	−0.580196	+	0.814477i	$0.697024\pi$
$524$	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	−0.398673	−	0.917093i	$-0.630529\pi$
$547$	12.1248	−	12.1248i	0.518419	−	0.518419i	0.917093	+	0.398673i	$0.130529\pi$
$548$	−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	0.355398	−	0.934715i	$-0.384345\pi$
$557$	−13.6724	−	13.6724i	−0.579317	−	0.579317i	−0.934715	+	0.355398i	$0.884345\pi$
$558$	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	0.134464	−	0.990919i	$-0.457069\pi$
$563$	−20.3216	−	20.3216i	−0.856455	−	0.856455i	−0.990919	+	0.134464i	$0.957069\pi$
$564$	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	$-0.651211\pi$
$569$		−	42.4250i		−	1.77855i	0.457376	−	0.889273i	$-0.348789\pi$
$570$	38.5670	+	35.3378i	1.61539	+	1.48014i
$571$		−	21.7300i		−	0.909370i	−0.890652	−	0.454685i	$-0.849752\pi$
$571$		−	21.7300i		−	0.909370i	0.890652	−	0.454685i	$-0.150248\pi$
$572$	1.60942	+	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	0.376721	−	0.926327i	$-0.377051\pi$
$577$	−13.2020	−	13.2020i	−0.549605	−	0.549605i	−0.926327	+	0.376721i	$0.877051\pi$
$578$	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	−0.483051	−	0.875592i	$-0.660471\pi$
$587$	9.51052	−	9.51052i	0.392541	−	0.392541i	0.875592	+	0.483051i	$0.160471\pi$
$588$	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	−0.0109350	−	0.999940i	$-0.503481\pi$
$593$	24.0839	−	24.0839i	0.989005	−	0.989005i	0.999940	+	0.0109350i	$0.00348078\pi$
$594$	−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	−0.186787	+	0.982400i	$0.559807\pi$
$607$	−28.8057	+	28.8057i	−1.16919	+	1.16919i	−0.982400	+	0.186787i	$0.940193\pi$
$608$	−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	−0.552609	−	0.833440i	$-0.686368\pi$
$613$	6.95305	−	6.95305i	0.280831	−	0.280831i	0.833440	+	0.552609i	$0.186368\pi$
$614$	−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	0.178186	−	0.983997i	$-0.442977\pi$
$617$	−20.0159	−	20.0159i	−0.805810	−	0.805810i	−0.983997	+	0.178186i	$0.942977\pi$
$618$	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	$0.200805\pi$
$631$			29.6327i			1.17966i	−0.807528	+	0.589830i	$0.799195\pi$
$632$	−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	0.0718555	−	0.997415i	$-0.477108\pi$
$643$	−23.4698	−	23.4698i	−0.925560	−	0.925560i	−0.997415	+	0.0718555i	$0.977108\pi$
$644$	−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	$-0.510877\pi$
$647$	24.5523	−	24.5523i	0.965252	−	0.965252i	0.999416	+	0.0341646i	$0.0108770\pi$
$648$	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	−0.135646	+	0.990757i	$0.543311\pi$
$653$	−28.7840	+	28.7840i	−1.12640	+	1.12640i	−0.990757	+	0.135646i	$0.956689\pi$
$654$	−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	−0.147640	+	0.989041i	$0.547168\pi$
$673$	−29.4881	+	29.4881i	−1.13668	+	1.13668i	−0.989041	+	0.147640i	$0.952832\pi$
$674$	−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	0.876104	−	0.482122i	$-0.160134\pi$
$677$	10.2511	+	10.2511i	0.393981	+	0.393981i	−0.482122	+	0.876104i	$0.660134\pi$
$678$	−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	0.949614	−	0.313422i	$-0.101476\pi$
$683$	16.6264	+	16.6264i	0.636192	+	0.636192i	−0.313422	+	0.949614i	$0.601476\pi$
$684$	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	$0.0729558\pi$
$691$			11.9445i			0.454392i	−0.973849	+	0.227196i	$0.927044\pi$
$692$	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	$0.157173\pi$
$709$			25.2399i			0.947903i	−0.880551	+	0.473952i	$0.842827\pi$
$710$	−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	−0.794350	−	0.607461i	$-0.792188\pi$
$727$	−5.03908	+	5.03908i	−0.186889	+	0.186889i	0.607461	+	0.794350i	$0.292188\pi$
$728$	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	−0.0478835	+	0.998853i	$0.515248\pi$
$733$	−28.3393	+	28.3393i	−1.04674	+	1.04674i	−0.998853	+	0.0478835i	$0.984752\pi$
$734$	−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	0.902449	−	0.430797i	$-0.141768\pi$
$743$	12.8563	+	12.8563i	0.471652	+	0.471652i	−0.430797	+	0.902449i	$0.641768\pi$
$744$	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	$-0.793832\pi$
$751$		−	33.0689i		−	1.20670i	0.797476	−	0.603351i	$-0.206168\pi$
$752$	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	0.604965	−	0.796252i	$-0.293187\pi$
$757$	−5.26299	−	5.26299i	−0.191287	−	0.191287i	−0.796252	+	0.604965i	$0.793187\pi$
$758$	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	$-0.710355\pi$
$769$		−	43.7854i		−	1.57894i	0.613787	−	0.789472i	$-0.289645\pi$
$770$	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	−0.762050	−	0.647518i	$-0.775807\pi$
$773$	−3.18433	+	3.18433i	−0.114532	+	0.114532i	0.647518	+	0.762050i	$0.275807\pi$
$774$	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	−0.129398	−	0.991593i	$-0.541304\pi$
$787$	24.1876	−	24.1876i	0.862195	−	0.862195i	0.991593	+	0.129398i	$0.0413044\pi$
$788$	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	0.132697	−	0.991157i	$-0.457636\pi$
$797$	−24.2353	−	24.2353i	−0.858459	−	0.858459i	−0.991157	+	0.132697i	$0.957636\pi$
$798$	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	$-0.837611\pi$
$809$		−	27.7783i		−	0.976634i	0.872666	−	0.488317i	$-0.162389\pi$
$810$	−12.6935	+	0.554631i	−0.446006	+	0.0194877i
$811$		−	6.85883i		−	0.240846i	−0.992723	−	0.120423i	$-0.961575\pi$
$811$		−	6.85883i		−	0.240846i	0.992723	−	0.120423i	$-0.0384251\pi$
$812$	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	0.963958	+	0.266053i	$0.0857196\pi$
$823$	35.2865	+	35.2865i	1.23001	+	1.23001i	0.266053	+	0.963958i	$0.414280\pi$
$824$	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	$-0.593363\pi$
$827$	19.2150	−	19.2150i	0.668171	−	0.668171i	0.957292	+	0.289122i	$0.0933632\pi$
$828$	−29.9815	+	40.2521i	−1.04193	+	1.39886i
$829$			21.8101i			0.757497i	0.925500	+	0.378748i	$0.123645\pi$
$829$			21.8101i			0.757497i	−0.925500	+	0.378748i	$0.876355\pi$
$830$	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	−0.656049	−	0.754718i	$-0.727774\pi$
$853$	2.88173	−	2.88173i	0.0986684	−	0.0986684i	0.754718	+	0.656049i	$0.227774\pi$
$854$	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	−0.970319	−	0.241829i	$-0.922253\pi$
$857$	−35.4851	−	35.4851i	−1.21215	−	1.21215i	−0.241829	−	0.970319i	$-0.577747\pi$
$858$	−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	0.439096	−	0.898440i	$-0.355299\pi$
$863$	−13.4941	−	13.4941i	−0.459344	−	0.459344i	−0.898440	+	0.439096i	$0.855299\pi$
$864$	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	0.929330	−	0.369250i	$-0.120385\pi$
$877$	16.5863	+	16.5863i	0.560081	+	0.560081i	−0.369250	+	0.929330i	$0.620385\pi$
$878$	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	0.808338	−	0.588719i	$-0.200368\pi$
$883$	6.52604	+	6.52604i	0.219619	+	0.219619i	−0.588719	+	0.808338i	$0.700368\pi$
$884$	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	$-0.752765\pi$
$887$	−0.365873	+	0.365873i	−0.0122848	+	0.0122848i	0.700938	+	0.713223i	$0.252765\pi$
$888$	−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	−0.888230	−	0.459400i	$-0.848064\pi$
$907$	−12.9148	+	12.9148i	−0.428830	+	0.428830i	0.459400	+	0.888230i	$0.348064\pi$
$908$	−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	$0.00753059\pi$
$911$			1.42800i			0.0473117i	−0.999720	+	0.0236559i	$0.992469\pi$
$912$	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	$0.0432464\pi$
$929$			8.25659i			0.270890i	−0.990785	+	0.135445i	$0.956754\pi$
$930$	−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	−0.994600	−	0.103780i	$-0.966906\pi$
$937$	−33.6219	−	33.6219i	−1.09838	−	1.09838i	−0.103780	−	0.994600i	$-0.533094\pi$
$938$	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	−0.918005	−	0.396568i	$-0.870201\pi$
$947$	−16.0464	+	16.0464i	−0.521437	+	0.521437i	0.396568	+	0.918005i	$0.370201\pi$
$948$	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	0.446490	−	0.894789i	$-0.352674\pi$
$953$	41.4062	−	41.4062i	1.34128	−	1.34128i	0.894789	−	0.446490i	$-0.147326\pi$
$954$	−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	−0.750690	−	0.660654i	$-0.770279\pi$
$967$	−2.79981	+	2.79981i	−0.0900358	+	0.0900358i	0.660654	+	0.750690i	$0.270279\pi$
$968$	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	$0.220197\pi$
$971$			39.7551i			1.27580i	−0.770119	+	0.637901i	$0.779803\pi$
$972$	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	0.951566	−	0.307445i	$-0.0994740\pi$
$977$	20.1333	+	20.1333i	0.644121	+	0.644121i	−0.307445	+	0.951566i	$0.599474\pi$
$978$	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	0.633694	−	0.773583i	$-0.281538\pi$
$983$	−4.38592	−	4.38592i	−0.139889	−	0.139889i	−0.773583	+	0.633694i	$0.781538\pi$
$984$	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	$0.231119\pi$
$991$			41.8022i			1.32789i	−0.747781	+	0.663945i	$0.768881\pi$
$992$	−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	0.546959	−	0.837159i	$-0.315785\pi$
$997$	−9.16317	−	9.16317i	−0.290200	−	0.290200i	−0.837159	+	0.546959i	$0.815785\pi$
$998$	−49.6039	+	3.60775i	−1.57019	+	0.114201i
$999$	−15.5836			−0.493042

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.8	✓	28	5.3	odd	4
220.2.l.c.67.8	yes	28	4.3	odd	2
220.2.l.d.23.1	yes	28	20.3	even	4	inner
220.2.l.d.67.1	yes	28	1.1	even	1	trivial

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

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

\(f(q)\)	\(=\)	\(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

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