LMFDB - Embedded newform 990.2.t.a.461.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			461.24
Character	$\chi$	$=$	990.461
Dual form			990.2.t.a.131.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.71148 + 0.266168i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.08625 + 1.34910i) q^{6} +(-0.915692 - 0.528675i) q^{7} +1.00000 q^{8} +(2.85831 + 0.911080i) q^{9} -1.00000i q^{10} +(-3.30978 - 0.212926i) q^{11} +(-0.625231 - 1.61527i) q^{12} +(-4.33706 + 2.50400i) q^{13} +(0.915692 - 0.528675i) q^{14} +(-1.61527 + 0.625231i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.08152 q^{17} +(-2.21817 + 2.01983i) q^{18} +1.38667i q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.42647 - 1.14854i) q^{21} +(1.83929 - 2.75989i) q^{22} +(-4.52401 + 2.61194i) q^{23} +(1.71148 + 0.266168i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.00801i q^{26} +(4.64943 + 2.32008i) q^{27} +1.05735i q^{28} +(-3.32715 + 5.76280i) q^{29} +(0.266168 - 1.71148i) q^{30} +(3.35865 + 5.81736i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.60794 - 1.24538i) q^{33} +(2.04076 - 3.53470i) q^{34} +1.05735 q^{35} +(-0.640136 - 2.93091i) q^{36} +5.98254 q^{37} +(-1.20089 - 0.693335i) q^{38} +(-8.08927 + 3.13116i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.10662 + 1.91672i) q^{41} +(1.70790 - 0.661088i) q^{42} +(-2.85341 - 1.64742i) q^{43} +(1.47049 + 2.97282i) q^{44} +(-2.93091 + 0.640136i) q^{45} -5.22388i q^{46} +(1.01676 + 0.587024i) q^{47} +(-1.08625 + 1.34910i) q^{48} +(-2.94100 - 5.09397i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.98543 - 1.08637i) q^{51} +(4.33706 + 2.50400i) q^{52} +0.0346036i q^{53} +(-4.33397 + 2.86648i) q^{54} +(2.97282 - 1.47049i) q^{55} +(-0.915692 - 0.528675i) q^{56} +(-0.369087 + 2.37325i) q^{57} +(-3.32715 - 5.76280i) q^{58} +(-9.41442 + 5.43542i) q^{59} +(1.34910 + 1.08625i) q^{60} +(3.91068 + 2.25783i) q^{61} -6.71730 q^{62} +(-2.13567 - 2.34539i) q^{63} +1.00000 q^{64} +(2.50400 - 4.33706i) q^{65} +(3.88250 - 4.23393i) q^{66} +(-4.21923 - 7.30793i) q^{67} +(2.04076 + 3.53470i) q^{68} +(-8.43796 + 3.26613i) q^{69} +(-0.528675 + 0.915692i) q^{70} +5.03435i q^{71} +(2.85831 + 0.911080i) q^{72} -12.8897i q^{73} +(-2.99127 + 5.18103i) q^{74} +(1.08625 - 1.34910i) q^{75} +(1.20089 - 0.693335i) q^{76} +(2.91817 + 1.94478i) q^{77} +(1.33297 - 8.57109i) q^{78} +(8.56074 + 4.94255i) q^{79} -1.00000i q^{80} +(7.33987 + 5.20830i) q^{81} -2.21324 q^{82} +(-1.65561 + 2.86759i) q^{83} +(-0.281433 + 1.80963i) q^{84} +(3.53470 - 2.04076i) q^{85} +(2.85341 - 1.64742i) q^{86} +(-7.22822 + 8.97732i) q^{87} +(-3.30978 - 0.212926i) q^{88} -3.71184i q^{89} +(0.911080 - 2.85831i) q^{90} +5.29522 q^{91} +(4.52401 + 2.61194i) q^{92} +(4.19986 + 10.8502i) q^{93} +(-1.01676 + 0.587024i) q^{94} +(-0.693335 - 1.20089i) q^{95} +(-0.625231 - 1.61527i) q^{96} +(-2.76338 + 4.78632i) q^{97} +5.88201 q^{98} +(-9.26639 - 3.62409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.71148	+	0.266168i	0.988122	+	0.153672i
$3$	1.71148	+	0.266168i	0.988122	+	0.153672i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.08625	+	1.34910i	−0.443458	+	0.550767i
$7$	−0.915692	−	0.528675i	−0.346099	−	0.199820i	0.316867	−	0.948470i	$-0.397369\pi$
$7$	−0.915692	−	0.528675i	−0.346099	−	0.199820i	−0.662966	+	0.748650i	$0.730703\pi$
$8$	1.00000			0.353553
$9$	2.85831	+	0.911080i	0.952770	+	0.303693i
$10$		−	1.00000i		−	0.316228i
$11$	−3.30978	−	0.212926i	−0.997937	−	0.0641997i
$11$	−3.30978	−	0.212926i	−0.997937	−	0.0641997i
$12$	−0.625231	−	1.61527i	−0.180489	−	0.466287i
$13$	−4.33706	+	2.50400i	−1.20288	+	0.694486i	−0.961196	−	0.275868i	$-0.911035\pi$
$13$	−4.33706	+	2.50400i	−1.20288	+	0.694486i	−0.241689	+	0.970354i	$0.577701\pi$
$14$	0.915692	−	0.528675i	0.244729	−	0.141294i
$15$	−1.61527	+	0.625231i	−0.417060	+	0.161434i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.08152			−0.989914			−0.494957	−	0.868917i	$-0.664816\pi$
$17$	−4.08152			−0.989914			−0.494957	+	0.868917i	$0.664816\pi$
$18$	−2.21817	+	2.01983i	−0.522828	+	0.476078i
$19$			1.38667i			0.318124i	0.987269	+	0.159062i	$0.0508469\pi$
$19$			1.38667i			0.318124i	−0.987269	+	0.159062i	$0.949153\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.42647	−	1.14854i	−0.311281	−	0.250633i
$22$	1.83929	−	2.75989i	0.392138	−	0.588411i
$23$	−4.52401	+	2.61194i	−0.943322	+	0.544627i	−0.891000	−	0.454003i	$-0.849995\pi$
$23$	−4.52401	+	2.61194i	−0.943322	+	0.544627i	−0.0523215	+	0.998630i	$0.516662\pi$
$24$	1.71148	+	0.266168i	0.349354	+	0.0543313i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	5.00801i		−	0.982151i
$27$	4.64943	+	2.32008i	0.894784	+	0.446500i
$28$			1.05735i			0.199820i
$29$	−3.32715	+	5.76280i	−0.617837	+	1.07013i	0.372043	+	0.928216i	$0.378658\pi$
$29$	−3.32715	+	5.76280i	−0.617837	+	1.07013i	−0.989880	+	0.141909i	$0.954676\pi$
$30$	0.266168	−	1.71148i	0.0485954	−	0.312472i
$31$	3.35865	+	5.81736i	0.603232	+	1.04483i	0.992328	+	0.123631i	$0.0394539\pi$
$31$	3.35865	+	5.81736i	0.603232	+	1.04483i	−0.389097	+	0.921197i	$0.627213\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−5.60794	−	1.24538i	−0.976218	−	0.216792i
$34$	2.04076	−	3.53470i	0.349987	−	0.606196i
$35$	1.05735			0.178725
$36$	−0.640136	−	2.93091i	−0.106689	−	0.488485i
$37$	5.98254			0.983524			0.491762	−	0.870730i	$-0.336353\pi$
$37$	5.98254			0.983524			0.491762	+	0.870730i	$0.336353\pi$
$38$	−1.20089	−	0.693335i	−0.194810	−	0.112474i
$39$	−8.08927	+	3.13116i	−1.29532	+	0.501387i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	1.10662	+	1.91672i	0.172825	+	0.299342i	0.939406	−	0.342805i	$-0.111377\pi$
$41$	1.10662	+	1.91672i	0.172825	+	0.299342i	−0.766581	+	0.642147i	$0.778044\pi$
$42$	1.70790	−	0.661088i	0.263535	−	0.102008i
$43$	−2.85341	−	1.64742i	−0.435141	−	0.251228i	0.266394	−	0.963864i	$-0.414168\pi$
$43$	−2.85341	−	1.64742i	−0.435141	−	0.251228i	−0.701534	+	0.712636i	$0.747501\pi$
$44$	1.47049	+	2.97282i	0.221685	+	0.448169i
$45$	−2.93091	+	0.640136i	−0.436914	+	0.0954259i
$46$		−	5.22388i		−	0.770219i
$47$	1.01676	+	0.587024i	0.148309	+	0.0856263i	0.572318	−	0.820032i	$-0.306044\pi$
$47$	1.01676	+	0.587024i	0.148309	+	0.0856263i	−0.424009	+	0.905658i	$0.639378\pi$
$48$	−1.08625	+	1.34910i	−0.156786	+	0.194726i
$49$	−2.94100	−	5.09397i	−0.420144	−	0.727710i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−6.98543	−	1.08637i	−0.978156	−	0.152122i
$52$	4.33706	+	2.50400i	0.601442	+	0.347243i
$53$			0.0346036i			0.00475317i	0.999997	+	0.00237658i	$0.000756491\pi$
$53$			0.0346036i			0.00475317i	−0.999997	+	0.00237658i	$0.999244\pi$
$54$	−4.33397	+	2.86648i	−0.589778	+	0.390079i
$55$	2.97282	−	1.47049i	0.400855	−	0.198281i
$56$	−0.915692	−	0.528675i	−0.122365	−	0.0706472i
$57$	−0.369087	+	2.37325i	−0.0488867	+	0.314345i
$58$	−3.32715	−	5.76280i	−0.436877	−	0.756693i
$59$	−9.41442	+	5.43542i	−1.22565	+	0.707631i	−0.966117	−	0.258103i	$-0.916903\pi$
$59$	−9.41442	+	5.43542i	−1.22565	+	0.707631i	−0.259535	+	0.965734i	$0.583569\pi$
$60$	1.34910	+	1.08625i	0.174168	+	0.140234i
$61$	3.91068	+	2.25783i	0.500712	+	0.289086i	0.729007	−	0.684506i	$-0.239982\pi$
$61$	3.91068	+	2.25783i	0.500712	+	0.289086i	−0.228296	+	0.973592i	$0.573315\pi$
$62$	−6.71730			−0.853098
$63$	−2.13567	−	2.34539i	−0.269069	−	0.295491i
$64$	1.00000			0.125000
$65$	2.50400	−	4.33706i	0.310584	−	0.537946i
$66$	3.88250	−	4.23393i	0.477903	−	0.521161i
$67$	−4.21923	−	7.30793i	−0.515461	−	0.892805i	−0.999839	−	0.0179463i	$-0.994287\pi$
$67$	−4.21923	−	7.30793i	−0.515461	−	0.892805i	0.484377	−	0.874859i	$-0.339046\pi$
$68$	2.04076	+	3.53470i	0.247479	+	0.428645i
$69$	−8.43796	+	3.26613i	−1.01581	+	0.393196i
$70$	−0.528675	+	0.915692i	−0.0631888	+	0.109446i
$71$			5.03435i			0.597467i	0.954337	+	0.298734i	$0.0965642\pi$
$71$			5.03435i			0.597467i	−0.954337	+	0.298734i	$0.903436\pi$
$72$	2.85831	+	0.911080i	0.336855	+	0.107372i
$73$		−	12.8897i		−	1.50862i	−0.656519	−	0.754310i	$-0.727972\pi$
$73$		−	12.8897i		−	1.50862i	0.656519	−	0.754310i	$-0.272028\pi$
$74$	−2.99127	+	5.18103i	−0.347728	+	0.602283i
$75$	1.08625	−	1.34910i	0.125429	−	0.155781i
$76$	1.20089	−	0.693335i	0.137752	−	0.0795309i
$77$	2.91817	+	1.94478i	0.332557	+	0.221628i
$78$	1.33297	−	8.57109i	0.150929	−	0.970485i
$79$	8.56074	+	4.94255i	0.963159	+	0.556080i	0.897144	−	0.441739i	$-0.145638\pi$
$79$	8.56074	+	4.94255i	0.963159	+	0.556080i	0.0660149	+	0.997819i	$0.478971\pi$
$80$		−	1.00000i		−	0.111803i
$81$	7.33987	+	5.20830i	0.815541	+	0.578700i
$82$	−2.21324			−0.244412
$83$	−1.65561	+	2.86759i	−0.181726	+	0.314759i	−0.942468	−	0.334295i	$-0.891502\pi$
$83$	−1.65561	+	2.86759i	−0.181726	+	0.314759i	0.760742	+	0.649054i	$0.224835\pi$
$84$	−0.281433	+	1.80963i	−0.0307068	+	0.197447i
$85$	3.53470	−	2.04076i	0.383392	−	0.221352i
$86$	2.85341	−	1.64742i	0.307691	−	0.177645i
$87$	−7.22822	+	8.97732i	−0.774947	+	0.962470i
$88$	−3.30978	−	0.212926i	−0.352824	−	0.0226980i
$89$		−	3.71184i		−	0.393454i	−0.980458	−	0.196727i	$-0.936969\pi$
$89$		−	3.71184i		−	0.393454i	0.980458	−	0.196727i	$-0.0630313\pi$
$90$	0.911080	−	2.85831i	0.0960363	−	0.301292i
$91$	5.29522			0.555090
$92$	4.52401	+	2.61194i	0.471661	+	0.272313i
$93$	4.19986	+	10.8502i	0.435506	+	1.12512i
$94$	−1.01676	+	0.587024i	−0.104870	+	0.0605469i
$95$	−0.693335	−	1.20089i	−0.0711346	−	0.123209i
$96$	−0.625231	−	1.61527i	−0.0638123	−	0.164857i
$97$	−2.76338	+	4.78632i	−0.280579	+	0.485977i	−0.971527	−	0.236927i	$-0.923860\pi$
$97$	−2.76338	+	4.78632i	−0.280579	+	0.485977i	0.690949	+	0.722904i	$0.257193\pi$
$98$	5.88201			0.594173
$99$	−9.26639	−	3.62409i	−0.931307	−	0.364234i
$100$	−1.00000			−0.100000
$101$	8.10726	−	14.0422i	0.806703	−	1.39725i	−0.108433	−	0.994104i	$-0.534583\pi$
$101$	8.10726	−	14.0422i	0.806703	−	1.39725i	0.915135	−	0.403146i	$-0.132083\pi$
$102$	4.43354	−	5.50638i	0.438986	−	0.545212i
$103$	0.0495545	+	0.0858309i	0.00488275	+	0.00845717i	0.868456	−	0.495765i	$-0.165112\pi$
$103$	0.0495545	+	0.0858309i	0.00488275	+	0.00845717i	−0.863574	+	0.504223i	$0.831779\pi$
$104$	−4.33706	+	2.50400i	−0.425284	+	0.245538i
$105$	1.80963	+	0.281433i	0.176602	+	0.0274650i
$106$	−0.0299676	−	0.0173018i	−0.00291071	−	0.00168050i
$107$	14.5678			1.40833			0.704163	−	0.710039i	$-0.251323\pi$
$107$	14.5678			1.40833			0.704163	+	0.710039i	$0.251323\pi$
$108$	−0.315465	−	5.18657i	−0.0303557	−	0.499078i
$109$			0.522284i			0.0500257i	0.999687	+	0.0250129i	$0.00796267\pi$
$109$			0.522284i			0.0500257i	−0.999687	+	0.0250129i	$0.992037\pi$
$110$	−0.212926	+	3.30978i	−0.0203017	+	0.315575i
$111$	10.2390	+	1.59236i	0.971842	+	0.151140i
$112$	0.915692	−	0.528675i	0.0865248	−	0.0499551i
$113$	−11.8462	+	6.83942i	−1.11440	+	0.643399i	−0.939965	−	0.341270i	$-0.889143\pi$
$113$	−11.8462	+	6.83942i	−1.11440	+	0.643399i	−0.174434	+	0.984669i	$0.555810\pi$
$114$	−1.87075	−	1.50626i	−0.175212	−	0.141075i
$115$	2.61194	−	4.52401i	0.243565	−	0.421866i
$116$	6.65431			0.617837
$117$	−14.6780	+	3.20581i	−1.35698	+	0.296377i
$118$		−	10.8708i		−	1.00074i
$119$	3.73742	+	2.15780i	0.342608	+	0.197805i
$120$	−1.61527	+	0.625231i	−0.147453	+	0.0570755i
$121$	10.9093	+	1.40948i	0.991757	+	0.128135i
$122$	−3.91068	+	2.25783i	−0.354057	+	0.204415i
$123$	1.38379	+	3.57498i	0.124772	+	0.322345i
$124$	3.35865	−	5.81736i	0.301616	−	0.522414i
$125$			1.00000i			0.0894427i
$126$	3.09900	−	0.676848i	0.276081	−	0.0602985i
$127$		−	16.8759i		−	1.49749i	−0.662856	−	0.748747i	$-0.730656\pi$
$127$		−	16.8759i		−	1.49749i	0.662856	−	0.748747i	$-0.269344\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.44505	−	3.57900i	−0.391365	−	0.315113i
$130$	2.50400	+	4.33706i	0.219616	+	0.380386i
$131$	−5.09537	−	8.82545i	−0.445185	−	0.771083i	0.552880	−	0.833261i	$-0.313529\pi$
$131$	−5.09537	−	8.82545i	−0.445185	−	0.771083i	−0.998065	+	0.0621779i	$0.980195\pi$
$132$	1.72544	+	5.47931i	0.150181	+	0.476913i
$133$	0.733098	−	1.26976i	0.0635676	−	0.110102i
$134$	8.43847			0.728973
$135$	−5.18657	+	0.315465i	−0.446389	+	0.0271509i
$136$	−4.08152			−0.349987
$137$	−14.0381	−	8.10490i	−1.19936	−	0.692448i	−0.238944	−	0.971033i	$-0.576801\pi$
$137$	−14.0381	−	8.10490i	−1.19936	−	0.692448i	−0.960412	+	0.278585i	$0.910135\pi$
$138$	1.39043	−	8.94055i	0.118361	−	0.761070i
$139$	−10.3611	+	5.98197i	−0.878815	+	0.507384i	−0.870267	−	0.492580i	$-0.836054\pi$
$139$	−10.3611	+	5.98197i	−0.878815	+	0.507384i	−0.00854719	+	0.999963i	$0.502721\pi$
$140$	−0.528675	−	0.915692i	−0.0446812	−	0.0773901i
$141$	1.58391	+	1.27531i	0.133389	+	0.107400i
$142$	−4.35988	−	2.51718i	−0.365873	−	0.211237i
$143$	14.8879	−	7.36424i	1.24499	−	0.615828i
$144$	−2.21817	+	2.01983i	−0.184848	+	0.168319i
$145$		−	6.65431i		−	0.552610i
$146$	11.1628	+	6.44483i	0.923837	+	0.533378i
$147$	−3.67761	−	9.50101i	−0.303324	−	0.783630i
$148$	−2.99127	−	5.18103i	−0.245881	−	0.425878i
$149$	9.11819	+	15.7932i	0.746991	+	1.29383i	0.949259	+	0.314497i	$0.101836\pi$
$149$	9.11819	+	15.7932i	0.746991	+	1.29383i	−0.202267	+	0.979330i	$0.564831\pi$
$150$	0.625231	+	1.61527i	0.0510499	+	0.131886i
$151$	−4.70634	−	2.71721i	−0.382997	−	0.221123i	0.296125	−	0.955149i	$-0.404306\pi$
$151$	−4.70634	−	2.71721i	−0.382997	−	0.221123i	−0.679121	+	0.734026i	$0.737639\pi$
$152$			1.38667i			0.112474i
$153$	−11.6662	−	3.71859i	−0.943160	−	0.300630i
$154$	−3.14331	+	1.55483i	−0.253295	+	0.125291i
$155$	−5.81736	−	3.35865i	−0.467261	−	0.269773i
$156$	6.75630	+	5.43993i	0.540937	+	0.435543i
$157$	3.89848	+	6.75237i	0.311133	+	0.538898i	0.978608	−	0.205734i	$-0.0659583\pi$
$157$	3.89848	+	6.75237i	0.311133	+	0.538898i	−0.667475	+	0.744632i	$0.732625\pi$
$158$	−8.56074	+	4.94255i	−0.681056	+	0.393208i
$159$	−0.00921035	+	0.0592232i	−0.000730429	+	0.00469671i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	5.52347			0.435310
$162$	−8.18045	+	3.75236i	−0.642717	+	0.294813i
$163$	−7.29928			−0.571723			−0.285862	−	0.958271i	$-0.592280\pi$
$163$	−7.29928			−0.571723			−0.285862	+	0.958271i	$0.592280\pi$
$164$	1.10662	−	1.91672i	0.0864126	−	0.149671i
$165$	5.47931	−	1.72544i	0.426564	−	0.134326i
$166$	−1.65561	−	2.86759i	−0.128500	−	0.222568i
$167$	−0.940284	−	1.62862i	−0.0727614	−	0.126026i	0.827349	−	0.561688i	$-0.189848\pi$
$167$	−0.940284	−	1.62862i	−0.0727614	−	0.126026i	−0.900111	+	0.435661i	$0.856514\pi$
$168$	−1.42647	−	1.14854i	−0.110055	−	0.0886121i
$169$	6.04008	−	10.4617i	0.464621	−	0.804748i
$170$			4.08152i			0.313038i
$171$	−1.26337	+	3.96353i	−0.0966121	+	0.303099i
$172$			3.29483i			0.251228i
$173$	−9.37390	+	16.2361i	−0.712684	+	1.23441i	0.251162	+	0.967945i	$0.419187\pi$
$173$	−9.37390	+	16.2361i	−0.712684	+	1.23441i	−0.963846	+	0.266460i	$0.914146\pi$
$174$	−4.16048	−	10.7485i	−0.315405	−	0.814840i
$175$	−0.915692	+	0.528675i	−0.0692198	+	0.0399641i
$176$	1.83929	−	2.75989i	0.138642	−	0.208035i
$177$	−17.5593	+	6.79678i	−1.31984	+	0.510877i
$178$	3.21455	+	1.85592i	0.240940	+	0.139107i
$179$			8.56019i			0.639819i	0.947448	+	0.319909i	$0.103653\pi$
$179$			8.56019i			0.639819i	−0.947448	+	0.319909i	$0.896347\pi$
$180$	2.01983	+	2.21817i	0.150549	+	0.165333i
$181$	13.5719			1.00879			0.504395	−	0.863473i	$-0.331716\pi$
$181$	13.5719			1.00879			0.504395	+	0.863473i	$0.331716\pi$
$182$	−2.64761	+	4.58580i	−0.196254	+	0.339922i
$183$	6.09208	+	4.90513i	0.450340	+	0.362598i
$184$	−4.52401	+	2.61194i	−0.333515	+	0.192555i
$185$	−5.18103	+	2.99127i	−0.380917	+	0.219923i
$186$	−11.4965	−	1.78793i	−0.842965	−	0.131097i
$187$	13.5089	+	0.869063i	0.987872	+	0.0635522i
$188$		−	1.17405i		−	0.0856263i
$189$	−3.03088	−	4.58252i	−0.220464	−	0.333329i
$190$	1.38667			0.100600
$191$	−0.648106	−	0.374184i	−0.0468953	−	0.0270750i	0.476369	−	0.879245i	$-0.341953\pi$
$191$	−0.648106	−	0.374184i	−0.0468953	−	0.0270750i	−0.523264	+	0.852170i	$0.675286\pi$
$192$	1.71148	+	0.266168i	0.123515	+	0.0192090i
$193$	−10.8573	+	6.26848i	−0.781527	+	0.451215i	−0.836971	−	0.547247i	$-0.815676\pi$
$193$	−10.8573	+	6.26848i	−0.781527	+	0.451215i	0.0554439	+	0.998462i	$0.482343\pi$
$194$	−2.76338	−	4.78632i	−0.198399	−	0.343638i
$195$	5.43993	−	6.75630i	0.389562	−	0.483829i
$196$	−2.94100	+	5.09397i	−0.210072	+	0.363855i
$197$	−2.06029			−0.146790			−0.0733948	−	0.997303i	$-0.523383\pi$
$197$	−2.06029			−0.146790			−0.0733948	+	0.997303i	$0.523383\pi$
$198$	7.77175	−	6.21289i	0.552314	−	0.441531i
$199$	19.7096			1.39717			0.698587	−	0.715525i	$-0.253812\pi$
$199$	19.7096			1.39717			0.698587	+	0.715525i	$0.253812\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−5.27599	−	13.6304i	−0.372140	−	0.961413i
$202$	8.10726	+	14.0422i	0.570425	+	0.988005i
$203$	6.09330	−	3.51797i	0.427666	−	0.246913i
$204$	2.55189	+	6.59274i	0.178668	+	0.461584i
$205$	−1.91672	−	1.10662i	−0.133870	−	0.0772898i
$206$	−0.0991090			−0.00690525
$207$	−15.3107	+	3.34399i	−1.06417	+	0.232424i
$208$		−	5.00801i		−	0.347243i
$209$	0.295258	−	4.58957i	0.0204235	−	0.317467i
$210$	−1.14854	+	1.42647i	−0.0792570	+	0.0984358i
$211$	15.7652	−	9.10203i	1.08532	−	0.626609i	0.152993	−	0.988227i	$-0.451109\pi$
$211$	15.7652	−	9.10203i	1.08532	−	0.626609i	0.932326	+	0.361618i	$0.117776\pi$
$212$	0.0299676	−	0.0173018i	0.00205818	−	0.00118829i
$213$	−1.33998	+	8.61618i	−0.0918140	+	0.590371i
$214$	−7.28392	+	12.6161i	−0.497918	+	0.862420i
$215$	3.29483			0.224706
$216$	4.64943	+	2.32008i	0.316354	+	0.157862i
$217$		−	7.10254i		−	0.482152i
$218$	−0.452311	−	0.261142i	−0.0306344	−	0.0176868i
$219$	3.43081	−	22.0603i	0.231833	−	1.49070i
$220$	−2.75989	−	1.83929i	−0.186072	−	0.124005i
$221$	17.7018	−	10.2201i	1.19075	−	0.687481i
$222$	−6.49852	+	8.07104i	−0.436152	+	0.541693i
$223$	−2.85879	+	4.95157i	−0.191439	+	0.331582i	−0.945727	−	0.324961i	$-0.894649\pi$
$223$	−2.85879	+	4.95157i	−0.191439	+	0.331582i	0.754288	+	0.656543i	$0.227982\pi$
$224$			1.05735i			0.0706472i
$225$	2.21817	−	2.01983i	0.147878	−	0.134655i
$226$		−	13.6788i		−	0.909903i
$227$	−6.12933	+	10.6163i	−0.406818	+	0.704630i	−0.994531	−	0.104440i	$-0.966695\pi$
$227$	−6.12933	+	10.6163i	−0.406818	+	0.704630i	0.587713	+	0.809069i	$0.300028\pi$
$228$	2.23984	−	0.866988i	0.148337	−	0.0574177i
$229$	9.63480	+	16.6880i	0.636685	+	1.10277i	0.986155	+	0.165824i	$0.0530283\pi$
$229$	9.63480	+	16.6880i	0.636685	+	1.10277i	−0.349470	+	0.936948i	$0.613638\pi$
$230$	2.61194	+	4.52401i	0.172226	+	0.298304i
$231$	4.47675	+	4.10516i	0.294549	+	0.270100i
$232$	−3.32715	+	5.76280i	−0.218438	+	0.378346i
$233$	23.5355			1.54186			0.770930	−	0.636919i	$-0.219792\pi$
$233$	23.5355			1.54186			0.770930	+	0.636919i	$0.219792\pi$
$234$	4.56270	−	14.3144i	0.298273	−	0.935764i
$235$	−1.17405			−0.0765865
$236$	9.41442	+	5.43542i	0.612826	+	0.353815i
$237$	13.3360	+	10.7376i	0.866264	+	0.697485i
$238$	−3.73742	+	2.15780i	−0.242261	+	0.139869i
$239$	−0.402515	−	0.697176i	−0.0260365	−	0.0450966i	0.852714	−	0.522379i	$-0.174955\pi$
$239$	−0.402515	−	0.697176i	−0.0260365	−	0.0450966i	−0.878750	+	0.477282i	$0.841622\pi$
$240$	0.266168	−	1.71148i	0.0171811	−	0.110475i
$241$	22.0083	+	12.7065i	1.41768	+	0.818499i	0.996095	−	0.0882896i	$-0.0281401\pi$
$241$	22.0083	+	12.7065i	1.41768	+	0.818499i	0.421586	+	0.906788i	$0.361473\pi$
$242$	−6.67531	+	8.74301i	−0.429105	+	0.562022i
$243$	11.1757	+	10.8675i	0.716924	+	0.697152i
$244$		−	4.51567i		−	0.289086i
$245$	5.09397	+	2.94100i	0.325442	+	0.187894i
$246$	−3.78791	−	0.589094i	−0.241509	−	0.0375592i
$247$	−3.47223	−	6.01407i	−0.220932	−	0.382666i
$248$	3.35865	+	5.81736i	0.213275	+	0.369402i
$249$	−3.59679	+	4.46715i	−0.227937	+	0.283094i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$			30.2373i			1.90856i	0.298910	+	0.954281i	$0.403377\pi$
$251$			30.2373i			1.90856i	−0.298910	+	0.954281i	$0.596623\pi$
$252$	−0.963331	+	3.02224i	−0.0606841	+	0.190383i
$253$	15.5296	−	7.68167i	0.976340	−	0.482942i
$254$	14.6149	+	8.43794i	0.917023	+	0.529444i
$255$	6.59274	−	2.55189i	0.412854	−	0.159806i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	18.6493	−	10.7672i	1.16331	−	0.671637i	0.211214	−	0.977440i	$-0.432258\pi$
$257$	18.6493	−	10.7672i	1.16331	−	0.671637i	0.952095	+	0.305803i	$0.0989249\pi$
$258$	5.32203	−	2.06003i	0.331335	−	0.128252i
$259$	−5.47817	−	3.16282i	−0.340397	−	0.196528i
$260$	−5.00801			−0.310584
$261$	−14.7604	+	13.4406i	−0.913646	+	0.831950i
$262$	10.1907			0.629586
$263$	−4.55377	+	7.88736i	−0.280798	+	0.486356i	−0.971581	−	0.236706i	$-0.923932\pi$
$263$	−4.55377	+	7.88736i	−0.280798	+	0.486356i	0.690784	+	0.723061i	$0.257266\pi$
$264$	−5.60794	−	1.24538i	−0.345145	−	0.0766476i
$265$	−0.0173018	−	0.0299676i	−0.00106284	−	0.00184089i
$266$	0.733098	+	1.26976i	0.0449491	+	0.0778541i
$267$	0.987971	−	6.35273i	0.0604629	−	0.388781i
$268$	−4.21923	+	7.30793i	−0.257731	+	0.446403i
$269$		−	6.51179i		−	0.397031i	−0.980098	−	0.198515i	$-0.936388\pi$
$269$		−	6.51179i		−	0.397031i	0.980098	−	0.198515i	$-0.0636120\pi$
$270$	2.32008	−	4.64943i	0.141196	−	0.282955i
$271$		−	21.1590i		−	1.28532i	−0.766153	−	0.642658i	$-0.777832\pi$
$271$		−	21.1590i		−	1.28532i	0.766153	−	0.642658i	$-0.222168\pi$
$272$	2.04076	−	3.53470i	0.123739	−	0.214323i
$273$	9.06265	+	1.40942i	0.548497	+	0.0853018i
$274$	14.0381	−	8.10490i	0.848073	−	0.489635i
$275$	−1.83929	+	2.75989i	−0.110913	+	0.166428i
$276$	7.04753	+	5.67442i	0.424211	+	0.341560i
$277$	9.87865	+	5.70344i	0.593550	+	0.342686i	0.766500	−	0.642244i	$-0.221996\pi$
$277$	9.87865	+	5.70344i	0.593550	+	0.342686i	−0.172950	+	0.984931i	$0.555330\pi$
$278$		−	11.9639i		−	0.717549i
$279$	4.29999	+	19.6878i	0.257434	+	1.17868i
$280$	1.05735			0.0631888
$281$	12.1595	−	21.0609i	0.725376	−	1.25639i	−0.233443	−	0.972370i	$-0.574999\pi$
$281$	12.1595	−	21.0609i	0.725376	−	1.25639i	0.958819	−	0.284018i	$-0.0916674\pi$
$282$	−1.89640	+	0.734051i	−0.112929	+	0.0437121i
$283$	−15.0537	+	8.69126i	−0.894850	+	0.516642i	−0.875526	−	0.483171i	$-0.839485\pi$
$283$	−15.0537	+	8.69126i	−0.894850	+	0.516642i	−0.0193242	+	0.999813i	$0.506151\pi$
$284$	4.35988	−	2.51718i	0.258711	−	0.149367i
$285$	−0.866988	−	2.23984i	−0.0513559	−	0.132677i
$286$	−1.06634	+	16.5754i	−0.0630538	+	0.980125i
$287$		−	2.34017i		−	0.138136i
$288$	−0.640136	−	2.93091i	−0.0377204	−	0.172705i
$289$	−0.341192			−0.0200701
$290$	5.76280	+	3.32715i	0.338403	+	0.195377i
$291$	−6.00343	+	7.45615i	−0.351927	+	0.437087i
$292$	−11.1628	+	6.44483i	−0.653251	+	0.377155i
$293$	4.16935	+	7.22153i	0.243576	+	0.421886i	0.961730	−	0.273998i	$-0.0883461\pi$
$293$	4.16935	+	7.22153i	0.243576	+	0.421886i	−0.718154	+	0.695884i	$0.755013\pi$
$294$	10.0669	+	1.56560i	0.587115	+	0.0913077i
$295$	5.43542	−	9.41442i	0.316462	−	0.548129i
$296$	5.98254			0.347728
$297$	−14.8946	−	8.66896i	−0.864273	−	0.503024i
$298$	−18.2364			−1.05641
$299$	13.0806	−	22.6563i	0.756471	−	1.31025i
$300$	−1.71148	−	0.266168i	−0.0988122	−	0.0153672i
$301$	1.74190	+	3.01705i	0.100401	+	0.173900i
$302$	4.70634	−	2.71721i	0.270820	−	0.156358i
$303$	17.6130	−	21.8750i	1.01184	−	1.25669i
$304$	−1.20089	−	0.693335i	−0.0688758	−	0.0397655i
$305$	−4.51567			−0.258566
$306$	9.05352	−	8.24397i	0.517555	−	0.471276i
$307$			13.4611i			0.768267i	0.923277	+	0.384134i	$0.125500\pi$
$307$			13.4611i			0.768267i	−0.923277	+	0.384134i	$0.874500\pi$
$308$	0.225138	−	3.49960i	0.0128284	−	0.199408i
$309$	0.0619660	+	0.160088i	0.00352512	+	0.00910706i
$310$	5.81736	−	3.35865i	0.330404	−	0.190759i
$311$	−23.1813	+	13.3837i	−1.31449	+	0.758922i	−0.982836	−	0.184479i	$-0.940940\pi$
$311$	−23.1813	+	13.3837i	−1.31449	+	0.758922i	−0.331655	+	0.943401i	$0.607607\pi$
$312$	−8.08927	+	3.13116i	−0.457965	+	0.177267i
$313$	−10.3246	+	17.8827i	−0.583579	+	1.01079i	0.411472	+	0.911422i	$0.365015\pi$
$313$	−10.3246	+	17.8827i	−0.583579	+	1.01079i	−0.995051	+	0.0993655i	$0.968319\pi$
$314$	−7.79696			−0.440008
$315$	3.02224	+	0.963331i	0.170284	+	0.0542776i
$316$		−	9.88509i		−	0.556080i
$317$	−5.43650	−	3.13877i	−0.305344	−	0.176291i	0.339497	−	0.940607i	$-0.389743\pi$
$317$	−5.43650	−	3.13877i	−0.305344	−	0.176291i	−0.644841	+	0.764317i	$0.723077\pi$
$318$	−0.0466836	−	0.0375880i	−0.00261789	−	0.00210783i
$319$	12.2392	−	18.3652i	0.685264	−	1.02825i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	24.9325	+	3.87749i	1.39160	+	0.216420i
$322$	−2.76174	+	4.78347i	−0.153905	+	0.266572i
$323$		−	5.65972i		−	0.314915i
$324$	0.840585	−	8.96066i	0.0466992	−	0.497814i
$325$			5.00801i			0.277794i
$326$	3.64964	−	6.32136i	0.202135	−	0.350108i
$327$	−0.139015	+	0.893877i	−0.00768756	+	0.0494315i
$328$	1.10662	+	1.91672i	0.0611029	+	0.105833i
$329$	−0.620690	−	1.07507i	−0.0342198	−	0.0592704i
$330$	−1.24538	+	5.60794i	−0.0685557	+	0.308707i
$331$	−14.6814	+	25.4289i	−0.806962	+	1.39770i	0.107996	+	0.994151i	$0.465557\pi$
$331$	−14.6814	+	25.4289i	−0.806962	+	1.39770i	−0.914958	+	0.403548i	$0.867777\pi$
$332$	3.31121			0.181726
$333$	17.1000	+	5.45058i	0.937072	+	0.298690i
$334$	1.88057			0.102900
$335$	7.30793	+	4.21923i	0.399275	+	0.230521i
$336$	1.70790	−	0.661088i	0.0931738	−	0.0360653i
$337$	−17.1659	+	9.91076i	−0.935089	+	0.539874i	−0.888417	−	0.459037i	$-0.848195\pi$
$337$	−17.1659	+	9.91076i	−0.935089	+	0.539874i	−0.0466712	+	0.998910i	$0.514861\pi$
$338$	6.04008	+	10.4617i	0.328537	+	0.569042i
$339$	−22.0950	+	8.55243i	−1.20003	+	0.464504i
$340$	−3.53470	−	2.04076i	−0.191696	−	0.110676i
$341$	−9.87774	−	19.9693i	−0.534910	−	1.08140i
$342$	−2.80083	−	3.07587i	−0.151452	−	0.166324i
$343$			13.6208i			0.735454i
$344$	−2.85341	−	1.64742i	−0.153845	−	0.0888227i
$345$	5.67442	−	7.04753i	0.305501	−	0.379426i
$346$	−9.37390	−	16.2361i	−0.503944	−	0.872857i
$347$	3.66105	+	6.34113i	0.196536	+	0.340410i	0.947403	−	0.320043i	$-0.103698\pi$
$347$	3.66105	+	6.34113i	0.196536	+	0.340410i	−0.750867	+	0.660453i	$0.770364\pi$
$348$	11.3887	+	1.77116i	0.610498	+	0.0949443i
$349$	−6.53255	−	3.77157i	−0.349679	−	0.201888i	0.314865	−	0.949137i	$-0.398041\pi$
$349$	−6.53255	−	3.77157i	−0.349679	−	0.201888i	−0.664544	+	0.747249i	$0.731374\pi$
$350$		−	1.05735i		−	0.0565178i
$351$	−25.9744	+	1.57985i	−1.38641	+	0.0843264i
$352$	1.47049	+	2.97282i	0.0783775	+	0.158452i
$353$	−9.12857	−	5.27038i	−0.485865	−	0.280514i	0.236992	−	0.971511i	$-0.423838\pi$
$353$	−9.12857	−	5.27038i	−0.485865	−	0.280514i	−0.722857	+	0.690997i	$0.757172\pi$
$354$	2.89346	−	18.6052i	0.153786	−	0.988854i
$355$	−2.51718	−	4.35988i	−0.133598	−	0.231398i
$356$	−3.21455	+	1.85592i	−0.170371	+	0.0983635i
$357$	5.82217	+	4.68780i	0.308142	+	0.248105i
$358$	−7.41335	−	4.28010i	−0.391808	−	0.226210i
$359$	−31.7635			−1.67641			−0.838206	−	0.545354i	$-0.816395\pi$
$359$	−31.7635			−1.67641			−0.838206	+	0.545354i	$0.816395\pi$
$360$	−2.93091	+	0.640136i	−0.154472	+	0.0337381i
$361$	17.0771			0.898797
$362$	−6.78594	+	11.7536i	−0.356661	+	0.617755i
$363$	18.2959	+	5.31600i	0.960286	+	0.279018i
$364$	−2.64761	−	4.58580i	−0.138772	−	0.240361i
$365$	6.44483	+	11.1628i	0.337338	+	0.584286i
$366$	−7.29401	+	2.82333i	−0.381264	+	0.147578i
$367$	−0.0479495	+	0.0830510i	−0.00250294	+	0.00433523i	−0.867274	−	0.497831i	$-0.834130\pi$
$367$	−0.0479495	+	0.0830510i	−0.00250294	+	0.00433523i	0.864771	+	0.502166i	$0.167463\pi$
$368$		−	5.22388i		−	0.272313i
$369$	1.41678	+	6.48681i	0.0737544	+	0.337690i
$370$		−	5.98254i		−	0.311018i
$371$	0.0182941	−	0.0316862i	0.000949780	−	0.00164507i
$372$	7.29665	−	9.06231i	0.378314	−	0.469859i
$373$	−12.8307	+	7.40784i	−0.664351	+	0.383563i	−0.793933	−	0.608006i	$-0.791970\pi$
$373$	−12.8307	+	7.40784i	−0.664351	+	0.383563i	0.129582	+	0.991569i	$0.458636\pi$
$374$	−7.50710	+	11.2646i	−0.388183	+	0.582476i
$375$	−0.266168	+	1.71148i	−0.0137448	+	0.0883803i
$376$	1.01676	+	0.587024i	0.0524352	+	0.0302735i
$377$		−	33.3248i		−	1.71632i
$378$	5.48402	−	0.333558i	0.282068	−	0.0171564i
$379$	−5.85541			−0.300772			−0.150386	−	0.988627i	$-0.548052\pi$
$379$	−5.85541			−0.300772			−0.150386	+	0.988627i	$0.548052\pi$
$380$	−0.693335	+	1.20089i	−0.0355673	+	0.0616044i
$381$	4.49182	−	28.8827i	0.230123	−	1.47971i
$382$	0.648106	−	0.374184i	0.0331600	−	0.0191449i
$383$	−4.27679	+	2.46921i	−0.218534	+	0.126171i	−0.605271	−	0.796019i	$-0.706935\pi$
$383$	−4.27679	+	2.46921i	−0.218534	+	0.126171i	0.386737	+	0.922190i	$0.373602\pi$
$384$	−1.08625	+	1.34910i	−0.0554323	+	0.0688459i
$385$	−3.49960	−	0.225138i	−0.178356	−	0.0114741i
$386$		−	12.5370i		−	0.638114i
$387$	−6.65499	−	7.30851i	−0.338292	−	0.371512i
$388$	5.52676			0.280579
$389$	30.4964	+	17.6071i	1.54623	+	0.892715i	0.998425	+	0.0561072i	$0.0178689\pi$
$389$	30.4964	+	17.6071i	1.54623	+	0.892715i	0.547803	+	0.836608i	$0.315464\pi$
$390$	3.13116	+	8.08927i	0.158552	+	0.409616i
$391$	18.4648	−	10.6607i	0.933807	−	0.539134i
$392$	−2.94100	−	5.09397i	−0.148543	−	0.257284i
$393$	−6.37157	−	16.4608i	−0.321403	−	0.830336i
$394$	1.03014	−	1.78426i	0.0518979	−	0.0898899i
$395$	−9.88509			−0.497373
$396$	1.49464	+	9.83697i	0.0751087	+	0.494326i
$397$	−12.4144			−0.623060			−0.311530	−	0.950236i	$-0.600841\pi$
$397$	−12.4144			−0.623060			−0.311530	+	0.950236i	$0.600841\pi$
$398$	−9.85479	+	17.0690i	−0.493976	+	0.855591i
$399$	1.59265	−	1.97804i	0.0797322	−	0.0990260i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	20.4887	−	11.8291i	1.02316	−	0.590719i	0.108139	−	0.994136i	$-0.465511\pi$
$401$	20.4887	−	11.8291i	1.02316	−	0.590719i	0.915016	+	0.403417i	$0.132178\pi$
$402$	14.4422	+	2.24605i	0.720314	+	0.112023i
$403$	−29.1334	−	16.8202i	−1.45124	−	0.837872i
$404$	−16.2145			−0.806703
$405$	−8.96066	−	0.840585i	−0.445259	−	0.0417690i
$406$			7.03594i			0.349188i
$407$	−19.8009	−	1.27384i	−0.981495	−	0.0631420i
$408$	−6.98543	−	1.08637i	−0.345830	−	0.0537833i
$409$	−16.4693	+	9.50856i	−0.814355	+	0.470168i	−0.848466	−	0.529250i	$-0.822473\pi$
$409$	−16.4693	+	9.50856i	−0.814355	+	0.470168i	0.0341109	+	0.999418i	$0.489140\pi$
$410$	1.91672	−	1.10662i	0.0946602	−	0.0546521i
$411$	−21.8686	−	17.6078i	−1.07870	−	0.868531i
$412$	0.0495545	−	0.0858309i	0.00244138	−	0.00422859i
$413$	11.4943			0.565597
$414$	4.75937	−	14.9315i	0.233910	−	0.733841i
$415$		−	3.31121i		−	0.162541i
$416$	4.33706	+	2.50400i	0.212642	+	0.122769i
$417$	−19.3249	+	7.48022i	−0.946347	+	0.366308i
$418$	3.82706	+	2.55049i	0.187188	+	0.124748i
$419$	3.86278	−	2.23018i	0.188709	−	0.108951i	−0.402669	−	0.915346i	$-0.631917\pi$
$419$	3.86278	−	2.23018i	0.188709	−	0.108951i	0.591378	+	0.806394i	$0.298584\pi$
$420$	−0.661088	−	1.70790i	−0.0322578	−	0.0833371i
$421$	12.3649	−	21.4167i	0.602629	−	1.04378i	−0.389792	−	0.920903i	$-0.627453\pi$
$421$	12.3649	−	21.4167i	0.602629	−	1.04378i	0.992421	−	0.122881i	$-0.0392135\pi$
$422$			18.2041i			0.886159i
$423$	2.37138	+	2.60424i	0.115300	+	0.126623i
$424$			0.0346036i			0.00168050i
$425$	−2.04076	+	3.53470i	−0.0989914	+	0.171458i
$426$	−6.79184	−	5.46855i	−0.329066	−	0.264952i
$427$	−2.38732	−	4.13496i	−0.115531	−	0.200105i
$428$	−7.28392	−	12.6161i	−0.352081	−	0.609823i
$429$	27.4404	−	8.64104i	1.32484	−	0.417193i
$430$	−1.64742	+	2.85341i	−0.0794454	+	0.137604i
$431$	−6.85682			−0.330282			−0.165141	−	0.986270i	$-0.552808\pi$
$431$	−6.85682			−0.330282			−0.165141	+	0.986270i	$0.552808\pi$
$432$	−4.33397	+	2.86648i	−0.208518	+	0.137914i
$433$	23.1663			1.11330			0.556651	−	0.830747i	$-0.312086\pi$
$433$	23.1663			1.11330			0.556651	+	0.830747i	$0.312086\pi$
$434$	6.15098	+	3.55127i	0.295257	+	0.170467i
$435$	1.77116	−	11.3887i	0.0849207	−	0.546046i
$436$	0.452311	−	0.261142i	0.0216618	−	0.0125064i
$437$	−3.62190	−	6.27331i	−0.173259	−	0.300093i
$438$	17.3894	+	14.0013i	0.830899	+	0.669010i
$439$	28.5870	+	16.5047i	1.36438	+	0.787728i	0.990204	−	0.139628i	$-0.0445907\pi$
$439$	28.5870	+	16.5047i	1.36438	+	0.787728i	0.374181	+	0.927356i	$0.377924\pi$
$440$	2.97282	−	1.47049i	0.141724	−	0.0701029i
$441$	−3.76529	−	17.2396i	−0.179299	−	0.820935i
$442$			20.4403i			0.972245i
$443$	−20.7202	−	11.9628i	−0.984447	−	0.568371i	−0.0808370	−	0.996727i	$-0.525759\pi$
$443$	−20.7202	−	11.9628i	−0.984447	−	0.568371i	−0.903610	+	0.428357i	$0.859093\pi$
$444$	−3.74047	−	9.66340i	−0.177515	−	0.458605i
$445$	1.85592	+	3.21455i	0.0879790	+	0.152384i
$446$	−2.85879	−	4.95157i	−0.135368	−	0.234464i
$447$	11.4019	+	29.4566i	0.539294	+	1.39325i
$448$	−0.915692	−	0.528675i	−0.0432624	−	0.0249776i
$449$			4.03838i			0.190583i	0.995449	+	0.0952915i	$0.0303783\pi$
$449$			4.03838i			0.190583i	−0.995449	+	0.0952915i	$0.969622\pi$
$450$	0.640136	+	2.93091i	0.0301763	+	0.138164i
$451$	−3.25455	−	6.57957i	−0.153251	−	0.309820i
$452$	11.8462	+	6.83942i	0.557200	+	0.321699i
$453$	−7.33157	−	5.90312i	−0.344467	−	0.277353i
$454$	−6.12933	−	10.6163i	−0.287664	−	0.498249i
$455$	−4.58580	+	2.64761i	−0.214985	+	0.124122i
$456$	−0.369087	+	2.37325i	−0.0172841	+	0.111138i
$457$	34.4097	+	19.8664i	1.60962	+	0.929313i	0.989455	+	0.144839i	$0.0462665\pi$
$457$	34.4097	+	19.8664i	1.60962	+	0.929313i	0.620162	+	0.784474i	$0.287067\pi$
$458$	−19.2696			−0.900409
$459$	−18.9768	−	9.46946i	−0.885759	−	0.441997i
$460$	−5.22388			−0.243565
$461$	12.3436	−	21.3798i	0.574900	−	0.995756i	−0.421153	−	0.906990i	$-0.638374\pi$
$461$	12.3436	−	21.3798i	0.574900	−	0.995756i	0.996052	−	0.0887662i	$-0.0282924\pi$
$462$	−5.79355	+	1.82440i	−0.269540	+	0.0848788i
$463$	−7.42646	−	12.8630i	−0.345137	−	0.597794i	0.640242	−	0.768173i	$-0.278834\pi$
$463$	−7.42646	−	12.8630i	−0.345137	−	0.597794i	−0.985379	+	0.170379i	$0.945501\pi$
$464$	−3.32715	−	5.76280i	−0.154459	−	0.267531i
$465$	−9.06231	−	7.29665i	−0.420254	−	0.338374i
$466$	−11.7677	+	20.3823i	−0.545130	+	0.944193i
$467$		−	17.9420i		−	0.830256i	−0.909763	−	0.415128i	$-0.863737\pi$
$467$		−	17.9420i		−	0.830256i	0.909763	−	0.415128i	$-0.136263\pi$
$468$	10.1153	+	11.1086i	0.467581	+	0.513497i
$469$			8.92242i			0.411999i
$470$	0.587024	−	1.01676i	0.0270774	−	0.0468995i
$471$	4.87490	+	12.5942i	0.224624	+	0.580309i
$472$	−9.41442	+	5.43542i	−0.433334	+	0.250185i
$473$	9.09338	+	6.06015i	0.418114	+	0.278646i
$474$	−15.9671	+	6.18046i	−0.733391	+	0.283878i
$475$	1.20089	+	0.693335i	0.0551006	+	0.0318124i
$476$		−	4.31560i		−	0.197805i
$477$	−0.0315266	+	0.0989077i	−0.00144351	+	0.00452867i
$478$	0.805030			0.0368212
$479$	−16.3488	+	28.3170i	−0.746997	+	1.29384i	0.202258	+	0.979332i	$0.435172\pi$
$479$	−16.3488	+	28.3170i	−0.746997	+	1.29384i	−0.949256	+	0.314505i	$0.898161\pi$
$480$	1.34910	+	1.08625i	0.0615777	+	0.0495802i
$481$	−25.9467	+	14.9803i	−1.18307	+	0.683044i
$482$	−22.0083	+	12.7065i	−1.00245	+	0.578766i
$483$	9.45329	+	1.47017i	0.430140	+	0.0668950i
$484$	−4.23402	−	10.1525i	−0.192455	−	0.461477i
$485$		−	5.52676i		−	0.250957i
$486$	−14.9994	+	4.24471i	−0.680387	+	0.192544i
$487$	−41.1610			−1.86518			−0.932591	−	0.360936i	$-0.882457\pi$
$487$	−41.1610			−1.86518			−0.932591	+	0.360936i	$0.882457\pi$
$488$	3.91068	+	2.25783i	0.177028	+	0.102207i
$489$	−12.4925	−	1.94283i	−0.564932	−	0.0878579i
$490$	−5.09397	+	2.94100i	−0.230122	+	0.132861i
$491$	−19.6521	−	34.0384i	−0.886885	−	1.53613i	−0.843538	−	0.537069i	$-0.819531\pi$
$491$	−19.6521	−	34.0384i	−0.886885	−	1.53613i	−0.0433467	−	0.999060i	$-0.513802\pi$
$492$	2.40413	−	2.98588i	0.108386	−	0.134614i
$493$	13.5798	−	23.5210i	0.611606	−	1.05933i
$494$	6.94445			0.312446
$495$	9.83697	−	1.49464i	0.442139	−	0.0671793i
$496$	−6.71730			−0.301616
$497$	2.66154	−	4.60992i	0.119386	−	0.206783i
$498$	−2.07027	−	5.34849i	−0.0927710	−	0.239671i
$499$	−19.9968	−	34.6354i	−0.895178	−	1.55049i	−0.833584	−	0.552393i	$-0.813715\pi$
$499$	−19.9968	−	34.6354i	−0.895178	−	1.55049i	−0.0615941	−	0.998101i	$-0.519618\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	−1.17579	−	3.03762i	−0.0525304	−	0.135711i
$502$	−26.1863	−	15.1187i	−1.16875	−	0.674779i
$503$	−26.7500			−1.19272			−0.596362	−	0.802715i	$-0.703388\pi$
$503$	−26.7500			−1.19272			−0.596362	+	0.802715i	$0.703388\pi$
$504$	−2.13567	−	2.34539i	−0.0951302	−	0.104472i
$505$			16.2145i			0.721537i
$506$	−1.11230	+	17.2899i	−0.0494478	+	0.768630i
$507$	13.1220	−	16.2973i	0.582770	−	0.723789i
$508$	−14.6149	+	8.43794i	−0.648434	+	0.374373i
$509$	−5.00397	+	2.88905i	−0.221797	+	0.128055i	−0.606782	−	0.794868i	$-0.707540\pi$
$509$	−5.00397	+	2.88905i	−0.221797	+	0.128055i	0.384985	+	0.922923i	$0.374207\pi$
$510$	−1.08637	+	6.98543i	−0.0481052	+	0.309320i
$511$	−6.81444	+	11.8030i	−0.301453	+	0.522132i
$512$	1.00000			0.0441942
$513$	−3.21719	+	6.44722i	−0.142042	+	0.284652i
$514$			21.5343i			0.949838i
$515$	−0.0858309	−	0.0495545i	−0.00378216	−	0.00218363i
$516$	−0.876978	+	5.63903i	−0.0386068	+	0.248244i
$517$	−3.24025	−	2.15942i	−0.142506	−	0.0949711i
$518$	5.47817	−	3.16282i	0.240697	−	0.138966i
$519$	−20.3647	+	25.2926i	−0.893913	+	1.11022i
$520$	2.50400	−	4.33706i	0.109808	−	0.190193i
$521$		−	29.7698i		−	1.30424i	−0.758117	−	0.652119i	$-0.773880\pi$
$521$		−	29.7698i		−	1.30424i	0.758117	−	0.652119i	$-0.226120\pi$
$522$	−4.25966	−	19.5032i	−0.186440	−	0.853631i
$523$		−	0.902037i		−	0.0394433i	−0.999806	−	0.0197217i	$-0.993722\pi$
$523$		−	0.902037i		−	0.0394433i	0.999806	−	0.0197217i	$-0.00627801\pi$
$524$	−5.09537	+	8.82545i	−0.222592	+	0.385541i
$525$	−1.70790	+	0.661088i	−0.0745390	+	0.0288522i
$526$	−4.55377	−	7.88736i	−0.198554	−	0.343905i
$527$	−13.7084	−	23.7437i	−0.597147	−	1.03429i
$528$	3.88250	−	4.23393i	0.168964	−	0.184258i
$529$	2.14445	−	3.71430i	0.0932370	−	0.161491i
$530$	0.0346036			0.00150308
$531$	−31.8614	+	6.95881i	−1.38267	+	0.301987i
$532$	−1.46620			−0.0635676
$533$	−9.59897	−	5.54197i	−0.415777	−	0.240049i
$534$	5.00764	+	4.03197i	0.216702	+	0.174480i
$535$	−12.6161	+	7.28392i	−0.545442	+	0.314911i
$536$	−4.21923	−	7.30793i	−0.182243	−	0.315654i
$537$	−2.27845	+	14.6506i	−0.0983223	+	0.632219i
$538$	5.63937	+	3.25589i	0.243131	+	0.140372i
$539$	8.64945	+	17.4862i	0.372558	+	0.753182i
$540$	2.86648	+	4.33397i	0.123354	+	0.186504i
$541$			40.9054i			1.75866i	0.476212	+	0.879330i	$0.342009\pi$
$541$			40.9054i			1.75866i	−0.476212	+	0.879330i	$0.657991\pi$
$542$	18.3242	+	10.5795i	0.787092	+	0.454428i
$543$	23.2280	+	3.61240i	0.996807	+	0.155023i
$544$	2.04076	+	3.53470i	0.0874969	+	0.151549i
$545$	−0.261142	−	0.452311i	−0.0111861	−	0.0193749i
$546$	−5.75192	+	7.14378i	−0.246159	+	0.305725i
$547$	−0.575875	−	0.332482i	−0.0246227	−	0.0142159i	0.487638	−	0.873046i	$-0.337859\pi$
$547$	−0.575875	−	0.332482i	−0.0246227	−	0.0142159i	−0.512261	+	0.858830i	$0.671192\pi$
$548$			16.2098i			0.692448i
$549$	9.12087	+	10.0165i	0.389269	+	0.427495i
$550$	−1.47049	−	2.97282i	−0.0627020	−	0.126761i
$551$	−7.99110	−	4.61366i	−0.340432	−	0.196549i
$552$	−8.43796	+	3.26613i	−0.359143	+	0.139016i
$553$	−5.22600	−	9.05170i	−0.222232	−	0.384918i
$554$	−9.87865	+	5.70344i	−0.419703	+	0.242316i
$555$	−9.66340	+	3.74047i	−0.410189	+	0.158774i
$556$	10.3611	+	5.98197i	0.439407	+	0.253692i
$557$	−23.0650			−0.977294			−0.488647	−	0.872482i	$-0.662509\pi$
$557$	−23.0650			−0.977294			−0.488647	+	0.872482i	$0.662509\pi$
$558$	−19.2001	−	6.12000i	−0.812806	−	0.259080i
$559$	16.5005			0.697899
$560$	−0.528675	+	0.915692i	−0.0223406	+	0.0386951i
$561$	22.8889	+	5.08303i	0.966372	+	0.214606i
$562$	12.1595	+	21.0609i	0.512918	+	0.888401i
$563$	6.36854	+	11.0306i	0.268402	+	0.464886i	0.968449	−	0.249210i	$-0.0801711\pi$
$563$	6.36854	+	11.0306i	0.268402	+	0.464886i	−0.700047	+	0.714097i	$0.746838\pi$
$564$	0.312494	−	2.00936i	0.0131584	−	0.0846092i
$565$	6.83942	−	11.8462i	0.287737	−	0.498375i
$566$		−	17.3825i		−	0.730642i
$567$	−3.96756	−	8.64960i	−0.166622	−	0.363249i
$568$			5.03435i			0.211237i
$569$	1.05386	−	1.82534i	0.0441801	−	0.0765222i	−0.843090	−	0.537773i	$-0.819266\pi$
$569$	1.05386	−	1.82534i	0.0441801	−	0.0765222i	0.887270	+	0.461251i	$0.152599\pi$
$570$	2.37325	+	0.369087i	0.0994046	+	0.0154593i
$571$	−15.0594	+	8.69454i	−0.630216	+	0.363855i	−0.780836	−	0.624737i	$-0.785206\pi$
$571$	−15.0594	+	8.69454i	−0.630216	+	0.363855i	0.150620	+	0.988592i	$0.451873\pi$
$572$	−13.8216	−	9.21119i	−0.577909	−	0.385139i
$573$	−1.00962	−	0.812913i	−0.0421776	−	0.0339599i
$574$	2.02665	+	1.17009i	0.0845907	+	0.0488385i
$575$			5.22388i			0.217851i
$576$	2.85831	+	0.911080i	0.119096	+	0.0379617i
$577$	−32.1255			−1.33740			−0.668701	−	0.743532i	$-0.733149\pi$
$577$	−32.1255			−1.33740			−0.668701	+	0.743532i	$0.733149\pi$
$578$	0.170596	−	0.295481i	0.00709585	−	0.0122904i
$579$	−20.2505	+	7.83849i	−0.841584	+	0.325757i
$580$	−5.76280	+	3.32715i	−0.239287	+	0.138153i
$581$	3.03205	−	1.75056i	0.125791	−	0.0726253i
$582$	−3.45550	−	8.92720i	−0.143235	−	0.370044i
$583$	0.00736801	−	0.114530i	0.000305152	−	0.00474336i
$584$		−	12.8897i		−	0.533378i
$585$	11.1086	−	10.1153i	0.459285	−	0.418217i
$586$	−8.33870			−0.344469
$587$	−15.7386	−	9.08669i	−0.649602	−	0.375048i	0.138702	−	0.990334i	$-0.455707\pi$
$587$	−15.7386	−	9.08669i	−0.649602	−	0.375048i	−0.788304	+	0.615286i	$0.789040\pi$
$588$	−6.38931	+	7.93541i	−0.263491	+	0.327251i
$589$	−8.06675	+	4.65734i	−0.332385	+	0.191902i
$590$	5.43542	+	9.41442i	0.223773	+	0.387585i
$591$	−3.52614	−	0.548383i	−0.145046	−	0.0225574i
$592$	−2.99127	+	5.18103i	−0.122941	+	0.212939i
$593$	35.1732			1.44439			0.722195	−	0.691689i	$-0.243133\pi$
$593$	35.1732			1.44439			0.722195	+	0.691689i	$0.243133\pi$
$594$	14.9548	−	8.56463i	0.613604	−	0.351411i
$595$	−4.31560			−0.176922
$596$	9.11819	−	15.7932i	0.373496	−	0.646914i
$597$	33.7325	+	5.24605i	1.38058	+	0.214707i
$598$	13.0806	+	22.6563i	0.534906	+	0.926484i
$599$	26.0983	−	15.0679i	1.06635	−	0.615656i	0.139167	−	0.990269i	$-0.455558\pi$
$599$	26.0983	−	15.0679i	1.06635	−	0.615656i	0.927181	+	0.374613i	$0.122224\pi$
$600$	1.08625	−	1.34910i	0.0443458	−	0.0550767i
$601$	27.2900	+	15.7559i	1.11318	+	0.642697i	0.939652	−	0.342131i	$-0.111149\pi$
$601$	27.2900	+	15.7559i	1.11318	+	0.642697i	0.173532	+	0.984828i	$0.444482\pi$
$602$	−3.48379			−0.141989
$603$	−5.40177	−	24.7324i	−0.219977	−	1.00718i
$604$			5.43442i			0.221123i
$605$	−10.1525	+	4.23402i	−0.412758	+	0.172137i
$606$	10.1378	+	26.1908i	0.411821	+	1.06393i
$607$	−21.1523	+	12.2123i	−0.858547	+	0.495682i	−0.863525	−	0.504305i	$-0.831749\pi$
$607$	−21.1523	+	12.2123i	−0.858547	+	0.495682i	0.00497869	+	0.999988i	$0.498415\pi$
$608$	1.20089	−	0.693335i	0.0487026	−	0.0281184i
$609$	11.3649	−	4.39908i	0.460530	−	0.178260i
$610$	2.25783	−	3.91068i	0.0914170	−	0.158339i
$611$	−5.87965			−0.237865
$612$	2.61273	+	11.9626i	0.105613	+	0.483558i
$613$			3.19506i			0.129047i	0.997916	+	0.0645236i	$0.0205528\pi$
$613$			3.19506i			0.129047i	−0.997916	+	0.0645236i	$0.979447\pi$
$614$	−11.6577	−	6.73057i	−0.470466	−	0.271624i
$615$	−2.98588	−	2.40413i	−0.120402	−	0.0969437i
$616$	2.91817	+	1.94478i	0.117577	+	0.0783572i
$617$	20.6567	−	11.9261i	0.831607	−	0.480128i	−0.0227957	−	0.999740i	$-0.507257\pi$
$617$	20.6567	−	11.9261i	0.831607	−	0.480128i	0.854403	+	0.519612i	$0.173923\pi$
$618$	−0.169623	−	0.0263796i	−0.00682323	−	0.00106114i
$619$	−17.3766	+	30.0971i	−0.698424	+	1.20971i	0.270589	+	0.962695i	$0.412782\pi$
$619$	−17.3766	+	30.0971i	−0.698424	+	1.20971i	−0.969013	+	0.247011i	$0.920552\pi$
$620$			6.71730i			0.269773i
$621$	−27.0940	+	1.64795i	−1.08724	+	0.0661301i
$622$		−	26.7675i		−	1.07328i
$623$	−1.96236	+	3.39890i	−0.0786202	+	0.136174i
$624$	1.33297	−	8.57109i	0.0533615	−	0.343118i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.3246	−	17.8827i	−0.412652	−	0.714735i
$627$	1.72692	−	7.77636i	0.0689667	−	0.310558i
$628$	3.89848	−	6.75237i	0.155566	−	0.269449i
$629$	−24.4179			−0.973604
$630$	−2.34539	+	2.13567i	−0.0934424	+	0.0850870i
$631$	−26.2444			−1.04477			−0.522387	−	0.852708i	$-0.674958\pi$
$631$	−26.2444			−1.04477			−0.522387	+	0.852708i	$0.674958\pi$
$632$	8.56074	+	4.94255i	0.340528	+	0.196604i
$633$	29.4044	−	11.3817i	1.16872	−	0.452383i
$634$	5.43650	−	3.13877i	0.215911	−	0.124656i
$635$	8.43794	+	14.6149i	0.334850	+	0.579977i
$636$	0.0558940	−	0.0216352i	0.00221634	−	0.000857892i
$637$	25.5106	+	14.7286i	1.01077	+	0.583568i
$638$	9.78511	+	19.7821i	0.387396	+	0.783179i
$639$	−4.58670	+	14.3897i	−0.181447	+	0.569249i
$640$		−	1.00000i		−	0.0395285i
$641$	−7.89607	−	4.55880i	−0.311876	−	0.180062i	0.335890	−	0.941901i	$-0.390963\pi$
$641$	−7.89607	−	4.55880i	−0.311876	−	0.180062i	−0.647766	+	0.761840i	$0.724296\pi$
$642$	−15.8243	+	19.6535i	−0.624534	+	0.775660i
$643$	−11.9790	−	20.7482i	−0.472405	−	0.818230i	0.527096	−	0.849806i	$-0.323281\pi$
$643$	−11.9790	−	20.7482i	−0.472405	−	0.818230i	−0.999501	+	0.0315756i	$0.989947\pi$
$644$	−2.76174	−	4.78347i	−0.108828	−	0.188495i
$645$	5.63903	+	0.876978i	0.222037	+	0.0345310i
$646$	4.90146	+	2.82986i	0.192845	+	0.111339i
$647$			12.2356i			0.481033i	0.970645	+	0.240516i	$0.0773168\pi$
$647$			12.2356i			0.481033i	−0.970645	+	0.240516i	$0.922683\pi$
$648$	7.33987	+	5.20830i	0.288337	+	0.204601i
$649$	32.3170	−	15.9855i	1.26855	−	0.627485i
$650$	−4.33706	−	2.50400i	−0.170114	−	0.0982151i
$651$	1.89047	−	12.1558i	0.0740933	−	0.476425i
$652$	3.64964	+	6.32136i	0.142931	+	0.247563i
$653$	29.2278	−	16.8747i	1.14377	−	0.660357i	0.196410	−	0.980522i	$-0.437072\pi$
$653$	29.2278	−	16.8747i	1.14377	−	0.660357i	0.947362	+	0.320165i	$0.103738\pi$
$654$	−0.704613	−	0.567329i	−0.0275525	−	0.0221843i
$655$	8.82545	+	5.09537i	0.344839	+	0.199093i
$656$	−2.21324			−0.0864126
$657$	11.7435	−	36.8426i	0.458158	−	1.43737i
$658$	1.24138			0.0483941
$659$	21.2069	−	36.7314i	0.826102	−	1.43085i	−0.0749725	−	0.997186i	$-0.523887\pi$
$659$	21.2069	−	36.7314i	0.826102	−	1.43085i	0.901074	−	0.433665i	$-0.142780\pi$
$660$	−4.23393	−	3.88250i	−0.164806	−	0.151126i
$661$	16.3119	+	28.2531i	0.634460	+	1.09892i	0.986629	+	0.162980i	$0.0521107\pi$
$661$	16.3119	+	28.2531i	0.634460	+	1.09892i	−0.352170	+	0.935936i	$0.614556\pi$
$662$	−14.6814	−	25.4289i	−0.570608	−	0.988323i
$663$	33.0165	−	12.7799i	1.28226	−	0.496330i
$664$	−1.65561	+	2.86759i	−0.0642499	+	0.111284i
$665$			1.46620i			0.0568566i
$666$	−13.2703	+	12.0837i	−0.514214	+	0.468234i
$667$		−	34.7613i		−	1.34596i
$668$	−0.940284	+	1.62862i	−0.0363807	+	0.0630132i
$669$	−6.21070	+	7.71358i	−0.240120	+	0.298224i
$670$	−7.30793	+	4.21923i	−0.282330	+	0.163003i
$671$	−12.4628	−	8.30563i	−0.481119	−	0.320635i
$672$	−0.281433	+	1.80963i	−0.0108565	+	0.0698080i
$673$	−30.8226	−	17.7954i	−1.18812	−	0.685963i	−0.230243	−	0.973133i	$-0.573952\pi$
$673$	−30.8226	−	17.7954i	−1.18812	−	0.685963i	−0.957880	+	0.287170i	$0.907286\pi$
$674$		−	19.8215i		−	0.763497i
$675$	4.33397	−	2.86648i	0.166814	−	0.110331i
$676$	−12.0802			−0.464621
$677$	16.1560	−	27.9830i	0.620926	−	1.07548i	−0.368388	−	0.929672i	$-0.620090\pi$
$677$	16.1560	−	27.9830i	0.620926	−	1.07548i	0.989314	−	0.145803i	$-0.0465766\pi$
$678$	3.64087	−	23.4110i	0.139827	−	0.899095i
$679$	5.06081	−	2.92186i	0.194216	−	0.112131i
$680$	3.53470	−	2.04076i	0.135550	−	0.0782596i
$681$	−13.3159	+	16.5382i	−0.510268	+	0.633744i
$682$	22.2328	+	1.43029i	0.851338	+	0.0547687i
$683$			2.61049i			0.0998875i	0.998752	+	0.0499438i	$0.0159042\pi$
$683$			2.61049i			0.0998875i	−0.998752	+	0.0499438i	$0.984096\pi$
$684$	4.06420	−	0.887657i	0.155399	−	0.0339404i
$685$	16.2098			0.619345
$686$	−11.7960	−	6.81040i	−0.450372	−	0.260022i
$687$	12.0479	+	31.1255i	0.459658	+	1.18751i
$688$	2.85341	−	1.64742i	0.108785	−	0.0628071i
$689$	−0.0866475	−	0.150078i	−0.00330101	−	0.00571751i
$690$	3.26613	+	8.43796i	0.124339	+	0.321228i
$691$	−2.16019	+	3.74157i	−0.0821777	+	0.142336i	−0.904185	−	0.427141i	$-0.859521\pi$
$691$	−2.16019	+	3.74157i	−0.0821777	+	0.142336i	0.822007	+	0.569477i	$0.192854\pi$
$692$	18.7478			0.712684
$693$	6.56920	+	8.21746i	0.249543	+	0.312155i
$694$	−7.32211			−0.277943
$695$	5.98197	−	10.3611i	0.226909	−	0.393018i
$696$	−7.22822	+	8.97732i	−0.273985	+	0.340284i
$697$	−4.51670	−	7.82315i	−0.171082	−	0.296323i
$698$	6.53255	−	3.77157i	0.247261	−	0.142756i
$699$	40.2805	+	6.26439i	1.52355	+	0.236941i
$700$	0.915692	+	0.528675i	0.0346099	+	0.0199820i
$701$	−44.1237			−1.66653			−0.833265	−	0.552874i	$-0.813531\pi$
$701$	−44.1237			−1.66653			−0.833265	+	0.552874i	$0.813531\pi$
$702$	11.6190	−	23.2844i	0.438531	−	0.878813i
$703$			8.29581i			0.312882i
$704$	−3.30978	−	0.212926i	−0.124742	−	0.00802496i
$705$	−2.00936	−	0.312494i	−0.0756768	−	0.0117692i
$706$	9.12857	−	5.27038i	0.343558	−	0.198354i
$707$	−14.8475	+	8.57222i	−0.558398	+	0.322391i
$708$	14.6658	+	11.8084i	0.551176	+	0.443787i
$709$	−15.5092	+	26.8627i	−0.582459	+	1.00885i	0.412728	+	0.910854i	$0.364576\pi$
$709$	−15.5092	+	26.8627i	−0.582459	+	1.00885i	−0.995187	+	0.0979942i	$0.968757\pi$
$710$	5.03435			0.188936
$711$	19.9662	+	21.9268i	0.748791	+	0.822321i
$712$		−	3.71184i		−	0.139107i
$713$	−30.3892	−	17.5452i	−1.13808	−	0.657072i
$714$	−6.97084	+	2.69824i	−0.260877	+	0.100979i
$715$	−9.21119	+	13.8216i	−0.344479	+	0.516897i
$716$	7.41335	−	4.28010i	0.277050	−	0.159955i
$717$	−0.503329	−	1.30034i	−0.0187972	−	0.0485620i
$718$	15.8817	−	27.5080i	0.592701	−	1.02659i
$719$			13.8269i			0.515656i	0.966191	+	0.257828i	$0.0830068\pi$
$719$			13.8269i			0.515656i	−0.966191	+	0.257828i	$0.916993\pi$
$720$	0.911080	−	2.85831i	0.0339539	−	0.106523i
$721$		−	0.104793i		−	0.00390269i
$722$	−8.53857	+	14.7892i	−0.317773	+	0.550399i
$723$	34.2847	+	27.6048i	1.27506	+	1.02663i
$724$	−6.78594	−	11.7536i	−0.252197	−	0.436819i
$725$	3.32715	+	5.76280i	0.123567	+	0.214025i
$726$	−13.7517	+	13.1867i	−0.510375	+	0.489405i
$727$	25.9981	−	45.0300i	0.964216	−	1.67007i	0.252509	−	0.967595i	$-0.418744\pi$
$727$	25.9981	−	45.0300i	0.964216	−	1.67007i	0.711707	−	0.702476i	$-0.247922\pi$
$728$	5.29522			0.196254
$729$	16.2344	+	21.5741i	0.601275	+	0.799042i
$730$	−12.8897			−0.477067
$731$	11.6462	+	6.72396i	0.430752	+	0.248695i
$732$	1.20192	−	7.72846i	0.0444244	−	0.285652i
$733$	−12.1638	+	7.02279i	−0.449281	+	0.259393i	−0.707527	−	0.706687i	$-0.750189\pi$
$733$	−12.1638	+	7.02279i	−0.449281	+	0.259393i	0.258245	+	0.966079i	$0.416856\pi$
$734$	−0.0479495	−	0.0830510i	−0.00176985	−	0.00306547i
$735$	7.93541	+	6.38931i	0.292702	+	0.235673i
$736$	4.52401	+	2.61194i	0.166757	+	0.0962773i
$737$	12.4087	+	25.0860i	0.457080	+	0.924056i
$738$	−6.32613	−	2.01644i	−0.232868	−	0.0742262i
$739$			1.73685i			0.0638911i	0.999490	+	0.0319455i	$0.0101703\pi$
$739$			1.73685i			0.0638911i	−0.999490	+	0.0319455i	$0.989830\pi$
$740$	5.18103	+	2.99127i	0.190459	+	0.109961i
$741$	−4.34188	−	11.2171i	−0.159503	−	0.412072i
$742$	0.0182941	+	0.0316862i	0.000671596	+	0.00116324i
$743$	−1.07106	−	1.85513i	−0.0392933	−	0.0680580i	0.845710	−	0.533643i	$-0.179177\pi$
$743$	−1.07106	−	1.85513i	−0.0392933	−	0.0680580i	−0.885003	+	0.465585i	$0.845844\pi$
$744$	4.19986	+	10.8502i	0.153974	+	0.397789i
$745$	−15.7932	−	9.11819i	−0.578617	−	0.334065i
$746$		−	14.8157i		−	0.542440i
$747$	−7.34484	+	6.68808i	−0.268734	+	0.244704i
$748$	−6.00184	−	12.1336i	−0.219449	−	0.443649i
$749$	−13.3397	−	7.70165i	−0.487420	−	0.281412i
$750$	−1.34910	−	1.08625i	−0.0492621	−	0.0396641i
$751$	18.8637	+	32.6729i	0.688348	+	1.19225i	0.972372	+	0.233436i	$0.0749969\pi$
$751$	18.8637	+	32.6729i	0.688348	+	1.19225i	−0.284025	+	0.958817i	$0.591670\pi$
$752$	−1.01676	+	0.587024i	−0.0370773	+	0.0214066i
$753$	−8.04820	+	51.7505i	−0.293293	+	1.88589i
$754$	28.8602	+	16.6624i	1.05102	+	0.606809i
$755$	5.43442			0.197779
$756$	−2.45314	+	4.91608i	−0.0892199	+	0.178796i
$757$	23.4098			0.850845			0.425422	−	0.904995i	$-0.360126\pi$
$757$	23.4098			0.850845			0.425422	+	0.904995i	$0.360126\pi$
$758$	2.92771	−	5.07094i	0.106339	−	0.184185i
$759$	28.6232	−	9.01351i	1.03896	−	0.327170i
$760$	−0.693335	−	1.20089i	−0.0251499	−	0.0435609i
$761$	−13.4756	−	23.3404i	−0.488490	−	0.846089i	0.511423	−	0.859329i	$-0.329119\pi$
$761$	−13.4756	−	23.3404i	−0.488490	−	0.846089i	−0.999912	+	0.0132405i	$0.995785\pi$
$762$	22.7672	+	18.3314i	0.824770	+	0.664076i
$763$	0.276119	−	0.478252i	0.00999617	−	0.0173139i
$764$			0.748369i			0.0270750i
$765$	11.9626	−	2.61273i	0.432507	−	0.0944634i
$766$		−	4.93842i		−	0.178432i
$767$	27.2206	−	47.1475i	0.982879	−	1.70240i
$768$	−0.625231	−	1.61527i	−0.0225611	−	0.0582859i
$769$	−11.9803	+	6.91685i	−0.432022	+	0.249428i	−0.700208	−	0.713939i	$-0.746909\pi$
$769$	−11.9803	+	6.91685i	−0.432022	+	0.249428i	0.268186	+	0.963367i	$0.413576\pi$
$770$	1.94478	−	2.91817i	0.0700848	−	0.105164i
$771$	34.7837	−	13.4639i	1.25270	−	0.484891i
$772$	10.8573	+	6.26848i	0.390764	+	0.225608i
$773$			40.2226i			1.44671i	0.690478	+	0.723353i	$0.257400\pi$
$773$			40.2226i			1.44671i	−0.690478	+	0.723353i	$0.742600\pi$
$774$	9.65685	−	2.10914i	0.347108	−	0.0758115i
$775$	6.71730			0.241293
$776$	−2.76338	+	4.78632i	−0.0991996	+	0.171819i
$777$	−8.53392	−	6.87121i	−0.306153	−	0.246503i
$778$	−30.4964	+	17.6071i	−1.09335	+	0.631245i
$779$	−2.65786	+	1.53452i	−0.0952278	+	0.0549798i
$780$	−8.57109	−	1.33297i	−0.306894	−	0.0477280i
$781$	1.07195	−	16.6626i	0.0383572	−	0.596235i
$782$			21.3214i			0.762450i
$783$	−28.8395	+	19.0745i	−1.03064	+	0.681666i
$784$	5.88201			0.210072
$785$	−6.75237	−	3.89848i	−0.241002	−	0.139143i
$786$	17.4412	+	2.71245i	0.622108	+	0.0967498i
$787$	40.0385	−	23.1162i	1.42722	−	0.824004i	0.430317	−	0.902678i	$-0.358402\pi$
$787$	40.0385	−	23.1162i	1.42722	−	0.824004i	0.996900	+	0.0786737i	$0.0250685\pi$
$788$	1.03014	+	1.78426i	0.0366974	+	0.0635617i
$789$	−9.89304	+	12.2870i	−0.352201	+	0.437428i
$790$	4.94255	−	8.56074i	0.175848	−	0.304578i
$791$	14.4633			0.514257
$792$	−9.26639	−	3.62409i	−0.329267	−	0.128776i
$793$	−22.6145			−0.803064
$794$	6.20719	−	10.7512i	0.220285	−	0.381544i
$795$	−0.0216352	−	0.0558940i	−0.000767322	−	0.00198236i
$796$	−9.85479	−	17.0690i	−0.349294	−	0.604994i
$797$	14.4588	−	8.34779i	0.512157	−	0.295694i	−0.221563	−	0.975146i	$-0.571116\pi$
$797$	14.4588	−	8.34779i	0.512157	−	0.295694i	0.733720	+	0.679452i	$0.237783\pi$
$798$	0.916710	+	2.36830i	0.0324512	+	0.0838368i
$799$	−4.14991	−	2.39595i	−0.146813	−	0.0847627i
$800$	−1.00000			−0.0353553
$801$	3.38178	−	10.6096i	0.119489	−	0.374871i
$802$			23.6583i			0.835403i
$803$	−2.74455	+	42.6620i	−0.0968529	+	1.50551i
$804$	−9.16626	+	11.3843i	−0.323269	+	0.401494i
$805$	−4.78347	+	2.76174i	−0.168595	+	0.0973384i
$806$	29.1334	−	16.8202i	1.02618	−	0.592465i
$807$	1.73323	−	11.1448i	0.0610125	−	0.392315i
$808$	8.10726	−	14.0422i	0.285213	−	0.494003i
$809$	−7.89639			−0.277622			−0.138811	−	0.990319i	$-0.544328\pi$
$809$	−7.89639			−0.277622			−0.138811	+	0.990319i	$0.544328\pi$
$810$	5.20830	−	7.33987i	0.183001	−	0.257897i
$811$			43.3459i			1.52208i	0.648706	+	0.761040i	$0.275311\pi$
$811$			43.3459i			1.52208i	−0.648706	+	0.761040i	$0.724689\pi$
$812$	−6.09330	−	3.51797i	−0.213833	−	0.123456i
$813$	5.63184	−	36.2131i	0.197517	−	1.27005i
$814$	11.0036	−	16.5112i	0.385677	−	0.578716i
$815$	6.32136	−	3.64964i	0.221428	−	0.127841i
$816$	4.43354	−	5.50638i	0.155205	−	0.192762i
$817$	2.28442	−	3.95673i	0.0799217	−	0.138429i
$818$		−	19.0171i		−	0.664918i
$819$	15.1354	+	4.82437i	0.528873	+	0.168577i
$820$			2.21324i			0.0772898i
$821$	−18.1604	+	31.4547i	−0.633802	+	1.09778i	0.352965	+	0.935636i	$0.385173\pi$
$821$	−18.1604	+	31.4547i	−0.633802	+	1.09778i	−0.986768	+	0.162141i	$0.948160\pi$
$822$	26.1832	−	10.1349i	0.913242	−	0.353494i
$823$	−14.8019	−	25.6377i	−0.515963	−	0.893674i	−0.999828	−	0.0185314i	$-0.994101\pi$
$823$	−14.8019	−	25.6377i	−0.515963	−	0.893674i	0.483865	−	0.875142i	$-0.339232\pi$
$824$	0.0495545	+	0.0858309i	0.00172631	+	0.00299006i
$825$	−3.88250	+	4.23393i	−0.135171	+	0.147407i
$826$	−5.74714	+	9.95434i	−0.199969	+	0.346356i
$827$	−12.8344			−0.446295			−0.223148	−	0.974785i	$-0.571633\pi$
$827$	−12.8344			−0.446295			−0.223148	+	0.974785i	$0.571633\pi$
$828$	10.5513	+	11.5875i	0.366684	+	0.402692i
$829$	−4.28623			−0.148867			−0.0744334	−	0.997226i	$-0.523715\pi$
$829$	−4.28623			−0.148867			−0.0744334	+	0.997226i	$0.523715\pi$
$830$	2.86759	+	1.65561i	0.0995356	+	0.0574669i
$831$	15.3890	+	12.3907i	0.533839	+	0.429828i
$832$	−4.33706	+	2.50400i	−0.150361	+	0.0868107i
$833$	12.0038	+	20.7911i	0.415906	+	0.720370i
$834$	3.18441	−	20.4760i	0.110267	−	0.709026i
$835$	1.62862	+	0.940284i	0.0563607	+	0.0325399i
$836$	−4.12232	+	2.03909i	−0.142573	+	0.0705233i
$837$	2.11908	+	34.8397i	0.0732460	+	1.20424i
$838$			4.46035i			0.154080i
$839$	21.6342	+	12.4905i	0.746896	+	0.431220i	0.824571	−	0.565758i	$-0.191416\pi$
$839$	21.6342	+	12.4905i	0.746896	+	0.431220i	−0.0776755	+	0.996979i	$0.524750\pi$
$840$	1.80963	+	0.281433i	0.0624382	+	0.00971035i
$841$	−7.63991	−	13.2327i	−0.263445	−	0.456300i
$842$	12.3649	+	21.4167i	0.426123	+	0.738067i
$843$	26.4165	−	32.8088i	0.909832	−	1.12999i
$844$	−15.7652	−	9.10203i	−0.542660	−	0.313305i
$845$			12.0802i			0.415570i
$846$	−3.44103	+	0.751551i	−0.118305	+	0.0258389i
$847$	−9.24443	−	7.05814i	−0.317642	−	0.242521i
$848$	−0.0299676	−	0.0173018i	−0.00102909	−	0.000594146i
$849$	−28.0774	+	10.8681i	−0.963614	+	0.372992i
$850$	−2.04076	−	3.53470i	−0.0699975	−	0.121239i
$851$	−27.0651	+	15.6260i	−0.927779	+	0.535654i
$852$	8.13182	−	3.14763i	0.278591	−	0.107836i
$853$	−32.8015	−	18.9379i	−1.12310	−	0.648423i	−0.180911	−	0.983500i	$-0.557905\pi$
$853$	−32.8015	−	18.9379i	−1.12310	−	0.648423i	−0.942191	+	0.335076i	$0.891238\pi$
$854$	4.77464			0.163385
$855$	−0.887657	−	4.06420i	−0.0303572	−	0.138993i
$856$	14.5678			0.497918
$857$	9.26853	−	16.0536i	0.316607	−	0.548379i	−0.663171	−	0.748468i	$-0.730790\pi$
$857$	9.26853	−	16.0536i	0.316607	−	0.548379i	0.979778	+	0.200089i	$0.0641231\pi$
$858$	−6.23685	+	28.0846i	−0.212923	+	0.958794i
$859$	−14.1421	−	24.4949i	−0.482524	−	0.835755i	0.517275	−	0.855819i	$-0.326946\pi$
$859$	−14.1421	−	24.4949i	−0.482524	−	0.835755i	−0.999799	+	0.0200639i	$0.993613\pi$
$860$	−1.64742	−	2.85341i	−0.0561764	−	0.0973004i
$861$	0.622878	−	4.00515i	0.0212276	−	0.136495i
$862$	3.42841	−	5.93818i	0.116772	−	0.202255i
$863$			38.0301i			1.29456i	0.762252	+	0.647280i	$0.224094\pi$
$863$			38.0301i			1.29456i	−0.762252	+	0.647280i	$0.775906\pi$
$864$	−0.315465	−	5.18657i	−0.0107324	−	0.176451i
$865$		−	18.7478i		−	0.637444i
$866$	−11.5832	+	20.0626i	−0.393612	+	0.681755i
$867$	−0.583942	−	0.0908142i	−0.0198317	−	0.00308421i
$868$	−6.15098	+	3.55127i	−0.208778	+	0.120538i
$869$	−27.2818	−	18.1816i	−0.925472	−	0.616767i
$870$	8.97732	+	7.22822i	0.304360	+	0.245060i
$871$	36.5982	+	21.1300i	1.24008	+	0.715961i
$872$			0.522284i			0.0176868i
$873$	−12.2593	+	11.1631i	−0.414915	+	0.377814i
$874$	7.24379			0.245025
$875$	0.528675	−	0.915692i	0.0178725	−	0.0309561i
$876$	−20.8202	+	8.05901i	−0.703450	+	0.272289i
$877$	34.2501	−	19.7743i	1.15654	−	0.667731i	0.206071	−	0.978537i	$-0.433932\pi$
$877$	34.2501	−	19.7743i	1.15654	−	0.667731i	0.950474	+	0.310805i	$0.100599\pi$
$878$	−28.5870	+	16.5047i	−0.964766	+	0.557008i
$879$	5.21361	+	13.4692i	0.175851	+	0.454306i
$880$	−0.212926	+	3.30978i	−0.00717775	+	0.111573i
$881$		−	1.43415i		−	0.0483176i	−0.999708	−	0.0241588i	$-0.992309\pi$
$881$		−	1.43415i		−	0.0483176i	0.999708	−	0.0241588i	$-0.00769073\pi$
$882$	16.8126	+	5.35898i	0.566110	+	0.180446i
$883$	29.5724			0.995192			0.497596	−	0.867409i	$-0.334216\pi$
$883$	29.5724			0.995192			0.497596	+	0.867409i	$0.334216\pi$
$884$	−17.7018	−	10.2201i	−0.595376	−	0.343741i
$885$	11.8084	−	14.6658i	0.396935	−	0.492986i
$886$	20.7202	−	11.9628i	0.696109	−	0.401899i
$887$	−0.459977	−	0.796704i	−0.0154445	−	0.0267507i	0.858200	−	0.513316i	$-0.171583\pi$
$887$	−0.459977	−	0.796704i	−0.0154445	−	0.0267507i	−0.873644	+	0.486565i	$0.838250\pi$
$888$	10.2390	+	1.59236i	0.343598	+	0.0534361i
$889$	−8.92187	+	15.4531i	−0.299230	+	0.518281i
$890$	−3.71184			−0.124421
$891$	−23.1844	−	18.8012i	−0.776706	−	0.629863i
$892$	5.71758			0.191439
$893$	−0.814009	+	1.40990i	−0.0272398	+	0.0471806i
$894$	−31.2112	−	4.85394i	−1.04386	−	0.162340i
$895$	−4.28010	−	7.41335i	−0.143068	−	0.247801i
$896$	0.915692	−	0.528675i	0.0305911	−	0.0176618i
$897$	28.4175	−	35.2941i	0.948834	−	1.17844i
$898$	−3.49734	−	2.01919i	−0.116708	−	0.0673813i
$899$	−44.6990			−1.49080
$900$	−2.85831	−	0.911080i	−0.0952770	−	0.0303693i
$901$		−	0.141235i		−	0.00470523i
$902$	7.32535	+	0.471257i	0.243907	+	0.0156912i
$903$	2.17817	+	5.62725i	0.0724851	+	0.187263i
$904$	−11.8462	+	6.83942i	−0.394000	+	0.227476i
$905$	−11.7536	+	6.78594i	−0.390703	+	0.225572i
$906$	8.77803	−	3.39776i	0.291631	−	0.112883i
$907$	−18.0827	+	31.3201i	−0.600425	+	1.03997i	0.392331	+	0.919824i	$0.371669\pi$
$907$	−18.0827	+	31.3201i	−0.600425	+	1.03997i	−0.992757	+	0.120143i	$0.961665\pi$
$908$	12.2587			0.406818
$909$	35.9666	−	32.7506i	1.19294	−	1.08627i
$910$		−	5.29522i		−	0.175535i
$911$	7.17296	+	4.14131i	0.237651	+	0.137208i	0.614097	−	0.789231i	$-0.289521\pi$
$911$	7.17296	+	4.14131i	0.237651	+	0.137208i	−0.376446	+	0.926439i	$0.622854\pi$
$912$	−1.87075	−	1.50626i	−0.0619469	−	0.0498774i
$913$	6.09028	−	9.13859i	0.201559	−	0.302443i
$914$	−34.4097	+	19.8664i	−1.13817	+	0.657123i
$915$	−7.72846	−	1.20192i	−0.255495	−	0.0397344i
$916$	9.63480	−	16.6880i	0.318343	−	0.551386i
$917$			10.7752i			0.355828i
$918$	17.6892	−	11.6996i	0.583830	−	0.386145i
$919$		−	7.65289i		−	0.252446i	−0.992002	−	0.126223i	$-0.959715\pi$
$919$		−	7.65289i		−	0.252446i	0.992002	−	0.126223i	$-0.0402854\pi$
$920$	2.61194	−	4.52401i	0.0861131	−	0.149152i
$921$	−3.58292	+	23.0384i	−0.118061	+	0.759142i
$922$	12.3436	+	21.3798i	0.406516	+	0.704106i
$923$	−12.6060	−	21.8343i	−0.414933	−	0.718684i
$924$	1.31680	−	5.92956i	0.0433195	−	0.195068i
$925$	2.99127	−	5.18103i	0.0983524	−	0.170351i
$926$	14.8529			0.488097
$927$	0.0634433	+	0.290479i	0.00208375	+	0.00954060i
$928$	6.65431			0.218438
$929$	−22.3193	−	12.8861i	−0.732274	−	0.422778i	0.0869797	−	0.996210i	$-0.472278\pi$
$929$	−22.3193	−	12.8861i	−0.732274	−	0.422778i	−0.819253	+	0.573432i	$0.805612\pi$
$930$	10.8502	−	4.19986i	0.355793	−	0.137719i
$931$	7.06365	−	4.07820i	0.231502	−	0.133658i
$932$	−11.7677	−	20.3823i	−0.385465	−	0.667645i
$933$	−43.2366	+	16.7358i	−1.41550	+	0.547907i
$934$	15.5382	+	8.97099i	0.508426	+	0.293540i
$935$	−12.1336	+	6.00184i	−0.396812	+	0.196281i
$936$	−14.6780	+	3.20581i	−0.479766	+	0.104785i
$937$			25.7244i			0.840380i	0.907436	+	0.420190i	$0.138037\pi$
$937$			25.7244i			0.840380i	−0.907436	+	0.420190i	$0.861963\pi$
$938$	−7.72704	−	4.46121i	−0.252297	−	0.145664i
$939$	−22.4300	+	27.8577i	−0.731976	+	0.909102i
$940$	0.587024	+	1.01676i	0.0191466	+	0.0331629i
$941$	20.6037	+	35.6867i	0.671663	+	1.16335i	0.977432	+	0.211249i	$0.0677530\pi$
$941$	20.6037	+	35.6867i	0.671663	+	1.16335i	−0.305769	+	0.952106i	$0.598914\pi$
$942$	−13.3443	−	2.07530i	−0.434782	−	0.0676169i
$943$	−10.0127	−	5.78085i	−0.326059	−	0.188250i
$944$		−	10.8708i		−	0.353815i
$945$	4.91608	+	2.45314i	0.159920	+	0.0798007i
$946$	−9.79494	+	4.84502i	−0.318461	+	0.157525i
$947$	39.6156	+	22.8721i	1.28733	+	0.743242i	0.978178	−	0.207769i	$-0.0666203\pi$
$947$	39.6156	+	22.8721i	1.28733	+	0.743242i	0.309156	+	0.951011i	$0.399954\pi$
$948$	2.63109	−	16.9181i	0.0854539	−	0.549475i
$949$	32.2757	+	55.9032i	1.04772	+	1.81470i
$950$	−1.20089	+	0.693335i	−0.0389620	+	0.0224947i
$951$	−8.46901	−	6.81895i	−0.274626	−	0.221120i
$952$	3.73742	+	2.15780i	0.121130	+	0.0699347i
$953$	−48.5152			−1.57156			−0.785781	−	0.618505i	$-0.787739\pi$
$953$	−48.5152			−1.57156			−0.785781	+	0.618505i	$0.787739\pi$
$954$	−0.0698933	−	0.0767567i	−0.00226288	−	0.00248509i
$955$	0.748369			0.0242166
$956$	−0.402515	+	0.697176i	−0.0130183	+	0.0225483i
$957$	25.8353	−	28.1739i	0.835138	−	0.910733i
$958$	−16.3488	−	28.3170i	−0.528207	−	0.914881i
$959$	8.56972	+	14.8432i	0.276731	+	0.479312i
$960$	−1.61527	+	0.625231i	−0.0521325	+	0.0201792i
$961$	−7.06108	+	12.2302i	−0.227777	+	0.394521i
$962$		−	29.9606i		−	0.965969i
$963$	41.6394	+	13.2725i	1.34181	+	0.427699i
$964$		−	25.4130i		−	0.818499i
$965$	6.26848	−	10.8573i	0.201790	−	0.349510i
$966$	−5.99985	+	7.45171i	−0.193042	+	0.239755i
$967$	6.60473	−	3.81324i	0.212394	−	0.122626i	−0.390030	−	0.920802i	$-0.627535\pi$
$967$	6.60473	−	3.81324i	0.212394	−	0.122626i	0.602423	+	0.798177i	$0.294202\pi$
$968$	10.9093	+	1.40948i	0.350639	+	0.0453024i
$969$	1.50643	−	9.68648i	0.0483936	−	0.311175i
$970$	4.78632	+	2.76338i	0.153679	+	0.0887268i
$971$			49.9776i			1.60386i	0.597419	+	0.801929i	$0.296193\pi$
$971$			49.9776i			1.60386i	−0.597419	+	0.801929i	$0.703807\pi$
$972$	3.82368	−	15.1122i	0.122645	−	0.484725i
$973$	12.6501			0.405543
$974$	20.5805	−	35.6464i	0.659441	−	1.14219i
$975$	−1.33297	+	8.57109i	−0.0426892	+	0.274495i
$976$	−3.91068	+	2.25783i	−0.125178	+	0.0722715i
$977$	52.6085	−	30.3735i	1.68310	−	0.971736i	0.723512	−	0.690312i	$-0.242527\pi$
$977$	52.6085	−	30.3735i	1.68310	−	0.971736i	0.959584	−	0.281424i	$-0.0908066\pi$
$978$	7.92881	−	9.84745i	0.253536	−	0.314887i
$979$	−0.790348	+	12.2854i	−0.0252596	+	0.392642i
$980$		−	5.88201i		−	0.187894i
$981$	−0.475843	+	1.49285i	−0.0151925	+	0.0476630i
$982$	39.3041			1.25424
$983$	−7.03999	−	4.06454i	−0.224541	−	0.129639i	0.383510	−	0.923537i	$-0.374715\pi$
$983$	−7.03999	−	4.06454i	−0.224541	−	0.129639i	−0.608051	+	0.793898i	$0.708048\pi$
$984$	1.38379	+	3.57498i	0.0441135	+	0.113966i
$985$	1.78426	−	1.03014i	0.0568513	−	0.0328231i
$986$	13.5798	+	23.5210i	0.432470	+	0.749061i
$987$	−0.776149	−	2.00516i	−0.0247051	−	0.0638250i
$988$	−3.47223	+	6.01407i	−0.110466	+	0.191333i
$989$	17.2118			0.547303
$990$	−3.62409	+	9.26639i	−0.115181	+	0.294505i
$991$	−24.1067			−0.765775			−0.382887	−	0.923795i	$-0.625070\pi$
$991$	−24.1067			−0.765775			−0.382887	+	0.923795i	$0.625070\pi$
$992$	3.35865	−	5.81736i	0.106637	−	0.184701i
$993$	−31.8952	+	39.6133i	−1.01216	+	1.25709i
$994$	2.66154	+	4.60992i	0.0844188	+	0.146218i
$995$	−17.0690	+	9.85479i	−0.541123	+	0.312418i
$996$	5.66706	+	0.881337i	0.179568	+	0.0279262i
$997$	−32.0996	−	18.5327i	−1.01661	−	0.586937i	−0.103487	−	0.994631i	$-0.533000\pi$
$997$	−32.0996	−	18.5327i	−1.01661	−	0.586937i	−0.913119	+	0.407693i	$0.866333\pi$
$998$	39.9935			1.26597
$999$	27.8154	+	13.8800i	0.880041	+	0.439144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.461.24	yes	48
3.2	odd	2		2970.2.t.b.791.20		48
9.4	even	3		2970.2.t.a.2771.20		48
9.5	odd	6		990.2.t.b.131.24	yes	48
11.10	odd	2		990.2.t.b.461.24	yes	48
33.32	even	2		2970.2.t.a.791.20		48
99.32	even	6	inner	990.2.t.a.131.24	✓	48
99.76	odd	6		2970.2.t.b.2771.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.24	✓	48	99.32	even	6	inner
990.2.t.a.461.24	yes	48	1.1	even	1	trivial
990.2.t.b.131.24	yes	48	9.5	odd	6
990.2.t.b.461.24	yes	48	11.10	odd	2
2970.2.t.a.791.20		48	33.32	even	2
2970.2.t.a.2771.20		48	9.4	even	3
2970.2.t.b.791.20		48	3.2	odd	2
2970.2.t.b.2771.20		48	99.76	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.71148 + 0.266168i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.08625 + 1.34910i) q^{6} +(-0.915692 - 0.528675i) q^{7} +1.00000 q^{8} +(2.85831 + 0.911080i) q^{9} -1.00000i q^{10} +(-3.30978 - 0.212926i) q^{11} +(-0.625231 - 1.61527i) q^{12} +(-4.33706 + 2.50400i) q^{13} +(0.915692 - 0.528675i) q^{14} +(-1.61527 + 0.625231i) q^{15} +(-0.500000 + 0.866025i) q^{16} -4.08152 q^{17} +(-2.21817 + 2.01983i) q^{18} +1.38667i q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.42647 - 1.14854i) q^{21} +(1.83929 - 2.75989i) q^{22} +(-4.52401 + 2.61194i) q^{23} +(1.71148 + 0.266168i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.00801i q^{26} +(4.64943 + 2.32008i) q^{27} +1.05735i q^{28} +(-3.32715 + 5.76280i) q^{29} +(0.266168 - 1.71148i) q^{30} +(3.35865 + 5.81736i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.60794 - 1.24538i) q^{33} +(2.04076 - 3.53470i) q^{34} +1.05735 q^{35} +(-0.640136 - 2.93091i) q^{36} +5.98254 q^{37} +(-1.20089 - 0.693335i) q^{38} +(-8.08927 + 3.13116i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(1.10662 + 1.91672i) q^{41} +(1.70790 - 0.661088i) q^{42} +(-2.85341 - 1.64742i) q^{43} +(1.47049 + 2.97282i) q^{44} +(-2.93091 + 0.640136i) q^{45} -5.22388i q^{46} +(1.01676 + 0.587024i) q^{47} +(-1.08625 + 1.34910i) q^{48} +(-2.94100 - 5.09397i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.98543 - 1.08637i) q^{51} +(4.33706 + 2.50400i) q^{52} +0.0346036i q^{53} +(-4.33397 + 2.86648i) q^{54} +(2.97282 - 1.47049i) q^{55} +(-0.915692 - 0.528675i) q^{56} +(-0.369087 + 2.37325i) q^{57} +(-3.32715 - 5.76280i) q^{58} +(-9.41442 + 5.43542i) q^{59} +(1.34910 + 1.08625i) q^{60} +(3.91068 + 2.25783i) q^{61} -6.71730 q^{62} +(-2.13567 - 2.34539i) q^{63} +1.00000 q^{64} +(2.50400 - 4.33706i) q^{65} +(3.88250 - 4.23393i) q^{66} +(-4.21923 - 7.30793i) q^{67} +(2.04076 + 3.53470i) q^{68} +(-8.43796 + 3.26613i) q^{69} +(-0.528675 + 0.915692i) q^{70} +5.03435i q^{71} +(2.85831 + 0.911080i) q^{72} -12.8897i q^{73} +(-2.99127 + 5.18103i) q^{74} +(1.08625 - 1.34910i) q^{75} +(1.20089 - 0.693335i) q^{76} +(2.91817 + 1.94478i) q^{77} +(1.33297 - 8.57109i) q^{78} +(8.56074 + 4.94255i) q^{79} -1.00000i q^{80} +(7.33987 + 5.20830i) q^{81} -2.21324 q^{82} +(-1.65561 + 2.86759i) q^{83} +(-0.281433 + 1.80963i) q^{84} +(3.53470 - 2.04076i) q^{85} +(2.85341 - 1.64742i) q^{86} +(-7.22822 + 8.97732i) q^{87} +(-3.30978 - 0.212926i) q^{88} -3.71184i q^{89} +(0.911080 - 2.85831i) q^{90} +5.29522 q^{91} +(4.52401 + 2.61194i) q^{92} +(4.19986 + 10.8502i) q^{93} +(-1.01676 + 0.587024i) q^{94} +(-0.693335 - 1.20089i) q^{95} +(-0.625231 - 1.61527i) q^{96} +(-2.76338 + 4.78632i) q^{97} +5.88201 q^{98} +(-9.26639 - 3.62409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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