LMFDB - Embedded newform 990.2.t.b.131.24

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			131.24
Character	$\chi$	$=$	990.131
Dual form			990.2.t.b.461.24

$q$-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} +(-1.83929 + 2.75989i) 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} +(-3.30978 - 0.212926i) 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} +(-2.41331 + 5.21305i) 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} +(-5.72129 + 0.516539i) 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} +(-0.225138 + 3.49960i) 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} +(1.83929 - 2.75989i) 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} +(-2.74278 + 9.56437i) 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} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 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 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * 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 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	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	$-0.602631\pi$
$7$	0.915692	−	0.528675i	0.346099	−	0.199820i	0.662966	+	0.748650i	$0.269297\pi$
$8$	−1.00000			−0.353553
$9$	2.85831	−	0.911080i	0.952770	−	0.303693i
$10$		−	1.00000i		−	0.316228i
$11$	−1.83929	+	2.75989i	−0.554567	+	0.832139i
$11$	−1.83929	+	2.75989i	−0.554567	+	0.832139i
$12$	−0.625231	+	1.61527i	−0.180489	+	0.466287i
$13$	4.33706	+	2.50400i	1.20288	+	0.694486i	0.961196	−	0.275868i	$-0.0889652\pi$
$13$	4.33706	+	2.50400i	1.20288	+	0.694486i	0.241689	+	0.970354i	$0.422299\pi$
$14$	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	$-0.335184\pi$
$17$	4.08152			0.989914			0.494957	+	0.868917i	$0.335184\pi$
$18$	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
$22$	−3.30978	−	0.212926i	−0.705648	−	0.0453961i
$23$	−4.52401	−	2.61194i	−0.943322	−	0.544627i	−0.0523215	−	0.998630i	$-0.516662\pi$
$23$	−4.52401	−	2.61194i	−0.943322	−	0.544627i	−0.891000	+	0.454003i	$0.849995\pi$
$24$	−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	0.989880	+	0.141909i	$0.0453242\pi$
$29$	3.32715	+	5.76280i	0.617837	+	1.07013i	−0.372043	+	0.928216i	$0.621342\pi$
$30$	−0.266168	−	1.71148i	−0.0485954	−	0.312472i
$31$	3.35865	−	5.81736i	0.603232	−	1.04483i	−0.389097	−	0.921197i	$-0.627213\pi$
$31$	3.35865	−	5.81736i	0.603232	−	1.04483i	0.992328	−	0.123631i	$-0.0394539\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.41331	+	5.21305i	−0.420103	+	0.907476i
$34$	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	$-0.888623\pi$
$41$	−1.10662	+	1.91672i	−0.172825	+	0.299342i	0.766581	+	0.642147i	$0.221956\pi$
$42$	1.70790	+	0.661088i	0.263535	+	0.102008i
$43$	2.85341	−	1.64742i	0.435141	−	0.251228i	−0.266394	−	0.963864i	$-0.585832\pi$
$43$	2.85341	−	1.64742i	0.435141	−	0.251228i	0.701534	+	0.712636i	$0.252499\pi$
$44$	−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	−0.424009	−	0.905658i	$-0.639378\pi$
$47$	1.01676	−	0.587024i	0.148309	−	0.0856263i	0.572318	+	0.820032i	$0.306044\pi$
$48$	−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	$-0.999244\pi$
$53$		−	0.0346036i		−	0.00475317i	0.999997	−	0.00237658i	$-0.000756491\pi$
$54$	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	−0.259535	−	0.965734i	$-0.583569\pi$
$59$	−9.41442	−	5.43542i	−1.22565	−	0.707631i	−0.966117	+	0.258103i	$0.916903\pi$
$60$	1.34910	−	1.08625i	0.174168	−	0.140234i
$61$	−3.91068	+	2.25783i	−0.500712	+	0.289086i	−0.729007	−	0.684506i	$-0.760018\pi$
$61$	−3.91068	+	2.25783i	−0.500712	+	0.289086i	0.228296	+	0.973592i	$0.426685\pi$
$62$	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
$66$	−5.72129	+	0.516539i	−0.704242	+	0.0635815i
$67$	−4.21923	+	7.30793i	−0.515461	+	0.892805i	0.484377	+	0.874859i	$0.339046\pi$
$67$	−4.21923	+	7.30793i	−0.515461	+	0.892805i	−0.999839	+	0.0179463i	$0.994287\pi$
$68$	−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	$-0.903436\pi$
$71$		−	5.03435i		−	0.597467i	0.954337	−	0.298734i	$-0.0965642\pi$
$72$	−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
$77$	−0.225138	+	3.49960i	−0.0256568	+	0.398817i
$78$	1.33297	+	8.57109i	0.150929	+	0.970485i
$79$	−8.56074	+	4.94255i	−0.963159	+	0.556080i	−0.897144	−	0.441739i	$-0.854362\pi$
$79$	−8.56074	+	4.94255i	−0.963159	+	0.556080i	−0.0660149	+	0.997819i	$0.521029\pi$
$80$			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	$-0.108498\pi$
$83$	1.65561	+	2.86759i	0.181726	+	0.314759i	−0.760742	+	0.649054i	$0.775165\pi$
$84$	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
$88$	1.83929	−	2.75989i	0.196069	−	0.294206i
$89$			3.71184i			0.393454i	0.980458	+	0.196727i	$0.0630313\pi$
$89$			3.71184i			0.393454i	−0.980458	+	0.196727i	$0.936969\pi$
$90$	−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	0.690949	−	0.722904i	$-0.257193\pi$
$97$	−2.76338	−	4.78632i	−0.280579	−	0.485977i	−0.971527	+	0.236927i	$0.923860\pi$
$98$	−5.88201			−0.594173
$99$	−2.74278	+	9.56437i	−0.275660	+	0.961255i
$100$	−1.00000			−0.100000
$101$	−8.10726	−	14.0422i	−0.806703	−	1.39725i	−0.915135	−	0.403146i	$-0.867917\pi$
$101$	−8.10726	−	14.0422i	−0.806703	−	1.39725i	0.108433	−	0.994104i	$-0.465417\pi$
$102$	4.43354	+	5.50638i	0.438986	+	0.545212i
$103$	0.0495545	−	0.0858309i	0.00488275	−	0.00845717i	−0.863574	−	0.504223i	$-0.831779\pi$
$103$	0.0495545	−	0.0858309i	0.00488275	−	0.00845717i	0.868456	+	0.495765i	$0.165112\pi$
$104$	−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	$-0.748677\pi$
$107$	−14.5678			−1.40833			−0.704163	+	0.710039i	$0.748677\pi$
$108$	−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	$0.992037\pi$
$110$	2.75989	+	1.83929i	0.263145	+	0.175370i
$111$	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	−0.174434	−	0.984669i	$-0.555810\pi$
$113$	−11.8462	−	6.83942i	−1.11440	−	0.643399i	−0.939965	+	0.341270i	$0.889143\pi$
$114$	−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
$121$	−4.23402	−	10.1525i	−0.384911	−	0.922954i
$122$	−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	$-0.686471\pi$
$131$	5.09537	−	8.82545i	0.445185	−	0.771083i	0.998065	+	0.0621779i	$0.0198046\pi$
$132$	−3.30798	−	4.69652i	−0.287923	−	0.408779i
$133$	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	−0.960412	−	0.278585i	$-0.910135\pi$
$137$	−14.0381	+	8.10490i	−1.19936	+	0.692448i	−0.238944	+	0.971033i	$0.576801\pi$
$138$	−1.39043	−	8.94055i	−0.118361	−	0.761070i
$139$	10.3611	+	5.98197i	0.878815	+	0.507384i	0.870267	−	0.492580i	$-0.163946\pi$
$139$	10.3611	+	5.98197i	0.878815	+	0.507384i	0.00854719	+	0.999963i	$0.497279\pi$
$140$	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	0.202267	+	0.979330i	$0.435169\pi$
$149$	−9.11819	+	15.7932i	−0.746991	+	1.29383i	−0.949259	+	0.314497i	$0.898164\pi$
$150$	−0.625231	+	1.61527i	−0.0510499	+	0.131886i
$151$	4.70634	−	2.71721i	0.382997	−	0.221123i	−0.296125	−	0.955149i	$-0.595694\pi$
$151$	4.70634	−	2.71721i	0.382997	−	0.221123i	0.679121	+	0.734026i	$0.262361\pi$
$152$		−	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	−0.667475	−	0.744632i	$-0.732625\pi$
$157$	3.89848	−	6.75237i	0.311133	−	0.538898i	0.978608	+	0.205734i	$0.0659583\pi$
$158$	−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
$165$	4.69652	−	3.30798i	0.365623	−	0.257526i
$166$	−1.65561	+	2.86759i	−0.128500	+	0.222568i
$167$	0.940284	−	1.62862i	0.0727614	−	0.126026i	−0.827349	−	0.561688i	$-0.810152\pi$
$167$	0.940284	−	1.62862i	0.0727614	−	0.126026i	0.900111	+	0.435661i	$0.143486\pi$
$168$	−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	0.963846	+	0.266460i	$0.0858541\pi$
$173$	9.37390	+	16.2361i	0.712684	+	1.23441i	−0.251162	+	0.967945i	$0.580813\pi$
$174$	−4.16048	+	10.7485i	−0.315405	+	0.814840i
$175$	0.915692	+	0.528675i	0.0692198	+	0.0399641i
$176$	3.30978	+	0.212926i	0.249484	+	0.0160499i
$177$	−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	$-0.896347\pi$
$179$		−	8.56019i		−	0.639819i	0.947448	−	0.319909i	$-0.103653\pi$
$180$	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
$187$	−7.50710	+	11.2646i	−0.548974	+	0.823746i
$188$			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	−0.523264	−	0.852170i	$-0.675286\pi$
$191$	−0.648106	+	0.374184i	−0.0468953	+	0.0270750i	0.476369	+	0.879245i	$0.341953\pi$
$192$	1.71148	−	0.266168i	0.123515	−	0.0192090i
$193$	10.8573	+	6.26848i	0.781527	+	0.451215i	0.836971	−	0.547247i	$-0.184324\pi$
$193$	10.8573	+	6.26848i	0.781527	+	0.451215i	−0.0554439	+	0.998462i	$0.517657\pi$
$194$	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	$-0.476617\pi$
$197$	2.06029			0.146790			0.0733948	+	0.997303i	$0.476617\pi$
$198$	−9.65438	+	2.40687i	−0.686107	+	0.171049i
$199$	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
$209$	−3.82706	−	2.55049i	−0.264723	−	0.176421i
$210$	−1.14854	−	1.42647i	−0.0792570	−	0.0984358i
$211$	−15.7652	−	9.10203i	−1.08532	−	0.626609i	−0.152993	−	0.988227i	$-0.548891\pi$
$211$	−15.7652	−	9.10203i	−1.08532	−	0.626609i	−0.932326	+	0.361618i	$0.882224\pi$
$212$	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
$220$	−0.212926	+	3.30978i	−0.0143555	+	0.223146i
$221$	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	0.754288	−	0.656543i	$-0.227982\pi$
$223$	−2.85879	−	4.95157i	−0.191439	−	0.331582i	−0.945727	+	0.324961i	$0.894649\pi$
$224$		−	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	$-0.0333049\pi$
$227$	6.12933	+	10.6163i	0.406818	+	0.704630i	−0.587713	+	0.809069i	$0.699972\pi$
$228$	−2.23984	−	0.866988i	−0.148337	−	0.0574177i
$229$	9.63480	−	16.6880i	0.636685	−	1.10277i	−0.349470	−	0.936948i	$-0.613638\pi$
$229$	9.63480	−	16.6880i	0.636685	−	1.10277i	0.986155	−	0.165824i	$-0.0530283\pi$
$230$	−2.61194	+	4.52401i	−0.172226	+	0.298304i
$231$	0.546162	+	6.04941i	0.0359349	+	0.398022i
$232$	−3.32715	−	5.76280i	−0.218438	−	0.378346i
$233$	−23.5355			−1.54186			−0.770930	−	0.636919i	$-0.780208\pi$
$233$	−23.5355			−1.54186			−0.770930	+	0.636919i	$0.780208\pi$
$234$	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	$-0.825045\pi$
$239$	0.402515	−	0.697176i	0.0260365	−	0.0450966i	0.878750	+	0.477282i	$0.158378\pi$
$240$	0.266168	+	1.71148i	0.0171811	+	0.110475i
$241$	−22.0083	+	12.7065i	−1.41768	+	0.818499i	−0.996095	−	0.0882896i	$-0.971860\pi$
$241$	−22.0083	+	12.7065i	−1.41768	+	0.818499i	−0.421586	+	0.906788i	$0.638527\pi$
$242$	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	$-0.596623\pi$
$251$		−	30.2373i		−	1.90856i	0.298910	−	0.954281i	$-0.403377\pi$
$252$	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	0.952095	−	0.305803i	$-0.0989249\pi$
$257$	18.6493	+	10.7672i	1.16331	+	0.671637i	0.211214	+	0.977440i	$0.432258\pi$
$258$	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	$-0.0760677\pi$
$263$	4.55377	+	7.88736i	0.280798	+	0.486356i	−0.690784	+	0.723061i	$0.742734\pi$
$264$	2.41331	−	5.21305i	0.148529	−	0.320841i
$265$	−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	$0.0636120\pi$
$269$			6.51179i			0.397031i	−0.980098	+	0.198515i	$0.936388\pi$
$270$	−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
$275$	−3.30978	−	0.212926i	−0.199587	−	0.0128399i
$276$	7.04753	−	5.67442i	0.424211	−	0.341560i
$277$	−9.87865	+	5.70344i	−0.593550	+	0.342686i	−0.766500	−	0.642244i	$-0.778004\pi$
$277$	−9.87865	+	5.70344i	−0.593550	+	0.342686i	0.172950	+	0.984931i	$0.444670\pi$
$278$			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	−0.958819	−	0.284018i	$-0.908333\pi$
$281$	−12.1595	−	21.0609i	−0.725376	−	1.25639i	0.233443	−	0.972370i	$-0.425001\pi$
$282$	1.89640	+	0.734051i	0.112929	+	0.0437121i
$283$	15.0537	+	8.69126i	0.894850	+	0.516642i	0.875526	−	0.483171i	$-0.160515\pi$
$283$	15.0537	+	8.69126i	0.894850	+	0.516642i	0.0193242	+	0.999813i	$0.493849\pi$
$284$	4.35988	+	2.51718i	0.258711	+	0.149367i
$285$	0.866988	−	2.23984i	0.0513559	−	0.132677i
$286$	−13.8216	−	9.21119i	−0.817286	−	0.544669i
$287$			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	$-0.911654\pi$
$293$	−4.16935	+	7.22153i	−0.243576	+	0.421886i	0.718154	+	0.695884i	$0.244987\pi$
$294$	−10.0669	+	1.56560i	−0.587115	+	0.0913077i
$295$	5.43542	+	9.41442i	0.316462	+	0.548129i
$296$	−5.98254			−0.347728
$297$	−2.14848	+	17.0992i	−0.124667	+	0.992199i
$298$	−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	$0.874500\pi$
$308$	−2.91817	−	1.94478i	−0.166278	−	0.110814i
$309$	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	−0.331655	−	0.943401i	$-0.607607\pi$
$311$	−23.1813	−	13.3837i	−1.31449	−	0.758922i	−0.982836	+	0.184479i	$0.940940\pi$
$312$	−8.08927	−	3.13116i	−0.457965	−	0.177267i
$313$	−10.3246	−	17.8827i	−0.583579	−	1.01079i	−0.995051	−	0.0993655i	$-0.968319\pi$
$313$	−10.3246	−	17.8827i	−0.583579	−	1.01079i	0.411472	−	0.911422i	$-0.365015\pi$
$314$	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	−0.644841	−	0.764317i	$-0.723077\pi$
$317$	−5.43650	+	3.13877i	−0.305344	+	0.176291i	0.339497	+	0.940607i	$0.389743\pi$
$318$	0.0466836	−	0.0375880i	0.00261789	−	0.00210783i
$319$	−22.0243	−	1.41688i	−1.23312	−	0.0793299i
$320$	−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
$330$	5.21305	+	2.41331i	0.286969	+	0.132848i
$331$	−14.6814	−	25.4289i	−0.806962	−	1.39770i	−0.914958	−	0.403548i	$-0.867777\pi$
$331$	−14.6814	−	25.4289i	−0.806962	−	1.39770i	0.107996	−	0.994151i	$-0.465557\pi$
$332$	−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	$-0.151805\pi$
$337$	17.1659	+	9.91076i	0.935089	+	0.539874i	0.0466712	+	0.998910i	$0.485139\pi$
$338$	−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	$-0.896302\pi$
$347$	−3.66105	+	6.34113i	−0.196536	+	0.340410i	0.750867	+	0.660453i	$0.229636\pi$
$348$	−11.3887	+	1.77116i	−0.610498	+	0.0949443i
$349$	6.53255	−	3.77157i	0.349679	−	0.201888i	−0.314865	−	0.949137i	$-0.601959\pi$
$349$	6.53255	−	3.77157i	0.349679	−	0.201888i	0.664544	+	0.747249i	$0.268626\pi$
$350$			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	−0.722857	−	0.690997i	$-0.757172\pi$
$353$	−9.12857	+	5.27038i	−0.485865	+	0.280514i	0.236992	+	0.971511i	$0.423838\pi$
$354$	−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	$-0.183605\pi$
$359$	31.7635			1.67641			0.838206	+	0.545354i	$0.183605\pi$
$360$	2.93091	+	0.640136i	0.154472	+	0.0337381i
$361$	17.0771			0.898797
$362$	6.78594	+	11.7536i	0.356661	+	0.617755i
$363$	−9.94869	−	16.2488i	−0.522171	−	0.852841i
$364$	−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	0.864771	−	0.502166i	$-0.167463\pi$
$367$	−0.0479495	−	0.0830510i	−0.00250294	−	0.00433523i	−0.867274	+	0.497831i	$0.834130\pi$
$368$			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	$-0.208030\pi$
$373$	12.8307	+	7.40784i	0.664351	+	0.383563i	−0.129582	+	0.991569i	$0.541364\pi$
$374$	−13.5089	−	0.869063i	−0.698531	−	0.0449382i
$375$	−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	0.386737	−	0.922190i	$-0.373602\pi$
$383$	−4.27679	−	2.46921i	−0.218534	−	0.126171i	−0.605271	+	0.796019i	$0.706935\pi$
$384$	1.08625	+	1.34910i	0.0554323	+	0.0688459i
$385$	1.94478	−	2.91817i	0.0991149	−	0.148724i
$386$			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	0.547803	−	0.836608i	$-0.315464\pi$
$389$	30.4964	−	17.6071i	1.54623	−	0.892715i	0.998425	−	0.0561072i	$-0.0178689\pi$
$390$	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
$396$	−6.91160	−	7.15750i	−0.347321	−	0.359678i
$397$	−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	0.915016	−	0.403417i	$-0.132178\pi$
$401$	20.4887	+	11.8291i	1.02316	+	0.590719i	0.108139	+	0.994136i	$0.465511\pi$
$402$	−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
$407$	−11.0036	+	16.5112i	−0.545430	+	0.818429i
$408$	−6.98543	+	1.08637i	−0.345830	+	0.0537833i
$409$	16.4693	+	9.50856i	0.814355	+	0.470168i	0.848466	−	0.529250i	$-0.177527\pi$
$409$	16.4693	+	9.50856i	0.814355	+	0.470168i	−0.0341109	+	0.999418i	$0.510860\pi$
$410$	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
$418$	0.295258	−	4.58957i	0.0144416	−	0.224483i
$419$	3.86278	+	2.23018i	0.188709	+	0.108951i	0.591378	−	0.806394i	$-0.298584\pi$
$419$	3.86278	+	2.23018i	0.188709	+	0.108951i	−0.402669	+	0.915346i	$0.631917\pi$
$420$	0.661088	−	1.70790i	0.0322578	−	0.0833371i
$421$	12.3649	+	21.4167i	0.602629	+	1.04378i	0.992421	+	0.122881i	$0.0392135\pi$
$421$	12.3649	+	21.4167i	0.602629	+	1.04378i	−0.389792	+	0.920903i	$0.627453\pi$
$422$		−	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
$429$	−23.5202	+	16.5664i	−1.13557	+	0.799833i
$430$	−1.64742	−	2.85341i	−0.0794454	−	0.137604i
$431$	6.85682			0.330282			0.165141	−	0.986270i	$-0.447192\pi$
$431$	6.85682			0.330282			0.165141	+	0.986270i	$0.447192\pi$
$432$	−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	$-0.955409\pi$
$439$	−28.5870	+	16.5047i	−1.36438	+	0.787728i	−0.374181	+	0.927356i	$0.622076\pi$
$440$	−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	−0.903610	−	0.428357i	$-0.859093\pi$
$443$	−20.7202	+	11.9628i	−0.984447	+	0.568371i	−0.0808370	+	0.996727i	$0.525759\pi$
$444$	−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	$-0.969622\pi$
$449$		−	4.03838i		−	0.190583i	0.995449	−	0.0952915i	$-0.0303783\pi$
$450$	−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	−0.620162	+	0.784474i	$0.712933\pi$
$457$	−34.4097	+	19.8664i	−1.60962	+	0.929313i	−0.989455	+	0.144839i	$0.953734\pi$
$458$	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	−0.996052	−	0.0887662i	$-0.971708\pi$
$461$	−12.3436	−	21.3798i	−0.574900	−	0.995756i	0.421153	−	0.906990i	$-0.361626\pi$
$462$	−4.96586	+	3.49770i	−0.231033	+	0.162728i
$463$	−7.42646	+	12.8630i	−0.345137	+	0.597794i	−0.985379	−	0.170379i	$-0.945501\pi$
$463$	−7.42646	+	12.8630i	−0.345137	+	0.597794i	0.640242	+	0.768173i	$0.278834\pi$
$464$	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	$0.136263\pi$
$467$			17.9420i			0.830256i	−0.909763	+	0.415128i	$0.863737\pi$
$468$	−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
$473$	−0.701556	+	10.9052i	−0.0322576	+	0.501420i
$474$	−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	0.949256	+	0.314505i	$0.101839\pi$
$479$	16.3488	+	28.3170i	0.746997	+	1.29384i	−0.202258	+	0.979332i	$0.564828\pi$
$480$	−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
$484$	10.9093	+	1.40948i	0.495878	+	0.0640673i
$485$			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	0.0433467	−	0.999060i	$-0.486198\pi$
$491$	19.6521	−	34.0384i	0.886885	−	1.53613i	0.843538	−	0.537069i	$-0.180469\pi$
$492$	−2.40413	−	2.98588i	−0.108386	−	0.134614i
$493$	13.5798	+	23.5210i	0.611606	+	1.05933i
$494$	−6.94445			−0.312446
$495$	7.15750	−	6.91160i	0.321706	−	0.310653i
$496$	−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	−0.0615941	+	0.998101i	$0.519618\pi$
$499$	−19.9968	+	34.6354i	−0.895178	+	1.55049i	−0.833584	+	0.552393i	$0.813715\pi$
$500$	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	$-0.296612\pi$
$503$	26.7500			1.19272			0.596362	+	0.802715i	$0.296612\pi$
$504$	−2.13567	+	2.34539i	−0.0951302	+	0.104472i
$505$			16.2145i			0.721537i
$506$	14.4173	+	9.60823i	0.640929	+	0.427138i
$507$	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	0.384985	−	0.922923i	$-0.374207\pi$
$509$	−5.00397	−	2.88905i	−0.221797	−	0.128055i	−0.606782	+	0.794868i	$0.707540\pi$
$510$	−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
$517$	−0.249986	+	3.88585i	−0.0109944	+	0.170899i
$518$	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	$0.226120\pi$
$521$			29.7698i			1.30424i	−0.758117	+	0.652119i	$0.773880\pi$
$522$	−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
$528$	5.72129	−	0.516539i	0.248987	−	0.0224795i
$529$	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	$-0.662141\pi$
$547$	0.575875	−	0.332482i	0.0246227	−	0.0142159i	0.512261	+	0.858830i	$0.328808\pi$
$548$		−	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	$-0.337491\pi$
$557$	23.0650			0.977294			0.488647	+	0.872482i	$0.337491\pi$
$558$	19.2001	−	6.12000i	0.812806	−	0.259080i
$559$	16.5005			0.697899
$560$	0.528675	+	0.915692i	0.0223406	+	0.0386951i
$561$	−9.84998	+	21.2772i	−0.415866	+	0.898323i
$562$	12.1595	−	21.0609i	0.512918	−	0.888401i
$563$	−6.36854	+	11.0306i	−0.268402	+	0.464886i	−0.968449	−	0.249210i	$-0.919829\pi$
$563$	−6.36854	+	11.0306i	−0.268402	+	0.464886i	0.700047	+	0.714097i	$0.253162\pi$
$564$	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	$-0.180734\pi$
$569$	−1.05386	−	1.82534i	−0.0441801	−	0.0765222i	−0.887270	+	0.461251i	$0.847401\pi$
$570$	2.37325	−	0.369087i	0.0994046	−	0.0154593i
$571$	15.0594	+	8.69454i	0.630216	+	0.363855i	0.780836	−	0.624737i	$-0.214794\pi$
$571$	15.0594	+	8.69454i	0.630216	+	0.363855i	−0.150620	+	0.988592i	$0.548127\pi$
$572$	1.06634	−	16.5754i	0.0445858	−	0.693053i
$573$	−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
$583$	0.0955022	+	0.0636460i	0.00395530	+	0.00263595i
$584$			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	−0.788304	−	0.615286i	$-0.789040\pi$
$587$	−15.7386	+	9.08669i	−0.649602	+	0.375048i	0.138702	+	0.990334i	$0.455707\pi$
$588$	−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	$-0.756867\pi$
$593$	−35.1732			−1.44439			−0.722195	+	0.691689i	$0.756867\pi$
$594$	−15.8826	+	6.68898i	−0.651672	+	0.274452i
$595$	−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	0.927181	−	0.374613i	$-0.122224\pi$
$599$	26.0983	+	15.0679i	1.06635	+	0.615656i	0.139167	+	0.990269i	$0.455558\pi$
$600$	−1.08625	−	1.34910i	−0.0443458	−	0.0550767i
$601$	−27.2900	+	15.7559i	−1.11318	+	0.642697i	−0.939652	−	0.342131i	$-0.888851\pi$
$601$	−27.2900	+	15.7559i	−1.11318	+	0.642697i	−0.173532	+	0.984828i	$0.555518\pi$
$602$	3.48379			0.141989
$603$	−5.40177	+	24.7324i	−0.219977	+	1.00718i
$604$			5.43442i			0.221123i
$605$	−1.40948	+	10.9093i	−0.0573035	+	0.443527i
$606$	10.1378	−	26.1908i	0.411821	−	1.06393i
$607$	21.1523	+	12.2123i	0.858547	+	0.495682i	0.863525	−	0.504305i	$-0.168251\pi$
$607$	21.1523	+	12.2123i	0.858547	+	0.495682i	−0.00497869	+	0.999988i	$0.501585\pi$
$608$	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
$616$	0.225138	−	3.49960i	0.00907106	−	0.141003i
$617$	20.6567	+	11.9261i	0.831607	+	0.480128i	0.854403	−	0.519612i	$-0.173923\pi$
$617$	20.6567	+	11.9261i	0.831607	+	0.480128i	−0.0227957	+	0.999740i	$0.507257\pi$
$618$	0.169623	−	0.0263796i	0.00682323	−	0.00106114i
$619$	−17.3766	−	30.0971i	−0.698424	−	1.20971i	−0.969013	−	0.247011i	$-0.920552\pi$
$619$	−17.3766	−	30.0971i	−0.698424	−	1.20971i	0.270589	−	0.962695i	$-0.412782\pi$
$620$		−	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
$627$	−7.22878	−	3.34646i	−0.288690	−	0.133645i
$628$	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	−0.647766	−	0.761840i	$-0.724296\pi$
$641$	−7.89607	+	4.55880i	−0.311876	+	0.180062i	0.335890	+	0.941901i	$0.390963\pi$
$642$	−15.8243	−	19.6535i	−0.624534	−	0.775660i
$643$	−11.9790	+	20.7482i	−0.472405	+	0.818230i	−0.999501	−	0.0315756i	$-0.989947\pi$
$643$	−11.9790	+	20.7482i	−0.472405	+	0.818230i	0.527096	+	0.849806i	$0.323281\pi$
$644$	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	$-0.922683\pi$
$647$		−	12.2356i		−	0.481033i	0.970645	−	0.240516i	$-0.0773168\pi$
$648$	−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	0.947362	−	0.320165i	$-0.103738\pi$
$653$	29.2278	+	16.8747i	1.14377	+	0.660357i	0.196410	+	0.980522i	$0.437072\pi$
$654$	−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	−0.901074	−	0.433665i	$-0.857220\pi$
$659$	−21.2069	−	36.7314i	−0.826102	−	1.43085i	0.0749725	−	0.997186i	$-0.476113\pi$
$660$	0.516539	+	5.72129i	0.0201062	+	0.222701i
$661$	16.3119	−	28.2531i	0.634460	−	1.09892i	−0.352170	−	0.935936i	$-0.614556\pi$
$661$	16.3119	−	28.2531i	0.634460	−	1.09892i	0.986629	−	0.162980i	$-0.0521107\pi$
$662$	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
$671$	0.961504	−	14.9459i	0.0371185	−	0.576979i
$672$	−0.281433	−	1.80963i	−0.0108565	−	0.0698080i
$673$	30.8226	−	17.7954i	1.18812	−	0.685963i	0.230243	−	0.973133i	$-0.426048\pi$
$673$	30.8226	−	17.7954i	1.18812	−	0.685963i	0.957880	+	0.287170i	$0.0927144\pi$
$674$			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	−0.989314	−	0.145803i	$-0.953423\pi$
$677$	−16.1560	−	27.9830i	−0.620926	−	1.07548i	0.368388	−	0.929672i	$-0.379910\pi$
$678$	−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
$682$	−12.3551	+	18.5390i	−0.473100	+	0.709896i
$683$		−	2.61049i		−	0.0998875i	−0.998752	−	0.0499438i	$-0.984096\pi$
$683$		−	2.61049i		−	0.0998875i	0.998752	−	0.0499438i	$-0.0159042\pi$
$684$	−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	0.822007	−	0.569477i	$-0.192854\pi$
$691$	−2.16019	−	3.74157i	−0.0821777	−	0.142336i	−0.904185	+	0.427141i	$0.859521\pi$
$692$	−18.7478			−0.712684
$693$	2.54490	+	10.2081i	0.0966729	+	0.387772i
$694$	−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	$-0.186469\pi$
$701$	44.1237			1.66653			0.833265	+	0.552874i	$0.186469\pi$
$702$	11.6190	+	23.2844i	0.438531	+	0.878813i
$703$			8.29581i			0.312882i
$704$	−1.83929	+	2.75989i	−0.0693209	+	0.104017i
$705$	−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	−0.995187	−	0.0979942i	$-0.968757\pi$
$709$	−15.5092	−	26.8627i	−0.582459	−	1.00885i	0.412728	−	0.910854i	$-0.364576\pi$
$710$	−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
$715$	16.5754	+	1.06634i	0.619886	+	0.0398787i
$716$	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	$-0.916993\pi$
$719$		−	13.8269i		−	0.515656i	0.966191	−	0.257828i	$-0.0830068\pi$
$720$	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
$726$	9.09753	−	16.7402i	0.337641	−	0.621288i
$727$	25.9981	+	45.0300i	0.964216	+	1.67007i	0.711707	+	0.702476i	$0.247922\pi$
$727$	25.9981	+	45.0300i	0.964216	+	1.67007i	0.252509	+	0.967595i	$0.418744\pi$
$728$	−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	$-0.249811\pi$
$733$	12.1638	+	7.02279i	0.449281	+	0.259393i	−0.258245	+	0.966079i	$0.583144\pi$
$734$	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	$-0.820823\pi$
$743$	1.07106	−	1.85513i	0.0392933	−	0.0680580i	0.885003	+	0.465585i	$0.154156\pi$
$744$	−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	−0.284025	−	0.958817i	$-0.591670\pi$
$751$	18.8637	−	32.6729i	0.688348	−	1.19225i	0.972372	−	0.233436i	$-0.0749969\pi$
$752$	−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
$759$	24.5340	−	17.2805i	0.890529	−	0.627242i
$760$	−0.693335	+	1.20089i	−0.0251499	+	0.0435609i
$761$	13.4756	−	23.3404i	0.488490	−	0.846089i	−0.511423	−	0.859329i	$-0.670881\pi$
$761$	13.4756	−	23.3404i	0.488490	−	0.846089i	0.999912	+	0.0132405i	$0.00421469\pi$
$762$	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	$-0.253091\pi$
$769$	11.9803	+	6.91685i	0.432022	+	0.249428i	−0.268186	+	0.963367i	$0.586424\pi$
$770$	3.49960	+	0.225138i	0.126117	+	0.00811340i
$771$	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	$-0.742600\pi$
$773$		−	40.2226i		−	1.44671i	0.690478	−	0.723353i	$-0.257400\pi$
$774$	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
$781$	13.8943	+	9.25963i	0.497176	+	0.331336i
$782$		−	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	$-0.641598\pi$
$787$	−40.0385	−	23.1162i	−1.42722	−	0.824004i	−0.996900	+	0.0786737i	$0.974931\pi$
$788$	−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
$792$	2.74278	−	9.56437i	0.0974604	−	0.339855i
$793$	−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	0.733720	−	0.679452i	$-0.237783\pi$
$797$	14.4588	+	8.34779i	0.512157	+	0.295694i	−0.221563	+	0.975146i	$0.571116\pi$
$798$	−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
$803$	35.5741	+	23.7078i	1.25538	+	0.836631i
$804$	−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	$-0.455672\pi$
$809$	7.89639			0.277622			0.138811	+	0.990319i	$0.455672\pi$
$810$	−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
$814$	−19.8009	−	1.27384i	−0.694022	−	0.0446481i
$815$	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	0.986768	+	0.162141i	$0.0518400\pi$
$821$	18.1604	+	31.4547i	0.633802	+	1.09778i	−0.352965	+	0.935636i	$0.614827\pi$
$822$	−26.1832	−	10.1349i	−0.913242	−	0.353494i
$823$	−14.8019	+	25.6377i	−0.515963	+	0.893674i	0.483865	+	0.875142i	$0.339232\pi$
$823$	−14.8019	+	25.6377i	−0.515963	+	0.893674i	−0.999828	+	0.0185314i	$0.994101\pi$
$824$	−0.0495545	+	0.0858309i	−0.00172631	+	0.00299006i
$825$	−5.72129	+	0.516539i	−0.199190	+	0.0179836i
$826$	−5.74714	−	9.95434i	−0.199969	−	0.346356i
$827$	12.8344			0.446295			0.223148	−	0.974785i	$-0.428367\pi$
$827$	12.8344			0.446295			0.223148	+	0.974785i	$0.428367\pi$
$828$	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	−0.0776755	−	0.996979i	$-0.524750\pi$
$839$	21.6342	−	12.4905i	0.746896	−	0.431220i	0.824571	+	0.565758i	$0.191416\pi$
$840$	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	$-0.442095\pi$
$853$	32.8015	−	18.9379i	1.12310	−	0.648423i	0.942191	+	0.335076i	$0.108762\pi$
$854$	−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	$-0.269210\pi$
$857$	−9.26853	−	16.0536i	−0.316607	−	0.548379i	−0.979778	+	0.200089i	$0.935877\pi$
$858$	−26.1070	−	12.0859i	−0.891279	−	0.412605i
$859$	−14.1421	+	24.4949i	−0.482524	+	0.835755i	−0.999799	−	0.0200639i	$-0.993613\pi$
$859$	−14.1421	+	24.4949i	−0.482524	+	0.835755i	0.517275	+	0.855819i	$0.326946\pi$
$860$	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	$-0.775906\pi$
$863$		−	38.0301i		−	1.29456i	0.762252	−	0.647280i	$-0.224094\pi$
$864$	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
$869$	2.10480	−	32.7175i	0.0714003	−	1.10987i
$870$	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	$-0.566068\pi$
$877$	−34.2501	−	19.7743i	−1.15654	−	0.667731i	−0.950474	+	0.310805i	$0.899401\pi$
$878$	−28.5870	−	16.5047i	−0.964766	−	0.557008i
$879$	−5.21361	+	13.4692i	−0.175851	+	0.454306i
$880$	−2.75989	−	1.83929i	−0.0930360	−	0.0620025i
$881$			1.43415i			0.0483176i	0.999708	+	0.0241588i	$0.00769073\pi$
$881$			1.43415i			0.0483176i	−0.999708	+	0.0241588i	$0.992309\pi$
$882$	−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	$-0.828417\pi$
$887$	0.459977	−	0.796704i	0.0154445	−	0.0267507i	0.873644	+	0.486565i	$0.161750\pi$
$888$	−10.2390	+	1.59236i	−0.343598	+	0.0534361i
$889$	−8.92187	−	15.4531i	−0.299230	−	0.518281i
$890$	3.71184			0.124421
$891$	0.874192	+	29.8368i	0.0292865	+	0.999571i
$892$	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
$902$	4.07080	−	6.10831i	0.135543	−	0.203384i
$903$	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	−0.992757	−	0.120143i	$-0.961665\pi$
$907$	−18.0827	−	31.3201i	−0.600425	−	1.03997i	0.392331	−	0.919824i	$-0.371669\pi$
$908$	−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	−0.376446	−	0.926439i	$-0.622854\pi$
$911$	7.17296	−	4.14131i	0.237651	−	0.137208i	0.614097	+	0.789231i	$0.289521\pi$
$912$	1.87075	−	1.50626i	0.0619469	−	0.0498774i
$913$	−10.9594	−	0.705044i	−0.362703	−	0.0233335i
$914$	−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
$924$	−5.51203	−	2.55172i	−0.181332	−	0.0839453i
$925$	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	−0.819253	−	0.573432i	$-0.805612\pi$
$929$	−22.3193	+	12.8861i	−0.732274	+	0.422778i	0.0869797	+	0.996210i	$0.472278\pi$
$930$	−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	0.305769	+	0.952106i	$0.401086\pi$
$941$	−20.6037	+	35.6867i	−0.671663	+	1.16335i	−0.977432	+	0.211249i	$0.932247\pi$
$942$	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	0.309156	−	0.951011i	$-0.399954\pi$
$947$	39.6156	−	22.8721i	1.28733	−	0.743242i	0.978178	+	0.207769i	$0.0666203\pi$
$948$	−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	$-0.212261\pi$
$953$	48.5152			1.57156			0.785781	+	0.618505i	$0.212261\pi$
$954$	0.0698933	−	0.0767567i	0.00226288	−	0.00248509i
$955$	0.748369			0.0242166
$956$	0.402515	+	0.697176i	0.0130183	+	0.0225483i
$957$	−38.0712	+	3.43721i	−1.23067	+	0.111109i
$958$	−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	$-0.372465\pi$
$967$	−6.60473	−	3.81324i	−0.212394	−	0.122626i	−0.602423	+	0.798177i	$0.705798\pi$
$968$	4.23402	+	10.1525i	0.136086	+	0.326313i
$969$	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	$-0.703807\pi$
$971$		−	49.9776i		−	1.60386i	0.597419	−	0.801929i	$-0.296193\pi$
$972$	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	0.959584	+	0.281424i	$0.0908066\pi$
$977$	52.6085	+	30.3735i	1.68310	+	0.971736i	0.723512	+	0.690312i	$0.242527\pi$
$978$	−7.92881	−	9.84745i	−0.253536	−	0.314887i
$979$	−10.2443	−	6.82715i	−0.327408	−	0.218197i
$980$			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	−0.608051	−	0.793898i	$-0.708048\pi$
$983$	−7.03999	+	4.06454i	−0.224541	+	0.129639i	0.383510	+	0.923537i	$0.374715\pi$
$984$	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
$990$	9.56437	+	2.74278i	0.303976	+	0.0871713i
$991$	−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	$-0.467000\pi$
$997$	32.0996	−	18.5327i	1.01661	−	0.586937i	0.913119	+	0.407693i	$0.133667\pi$
$998$	−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.b.131.24	yes	48
3.2	odd	2		2970.2.t.a.2771.20		48
9.2	odd	6		990.2.t.a.461.24	yes	48
9.7	even	3		2970.2.t.b.791.20		48
11.10	odd	2		990.2.t.a.131.24	✓	48
33.32	even	2		2970.2.t.b.2771.20		48
99.43	odd	6		2970.2.t.a.791.20		48
99.65	even	6	inner	990.2.t.b.461.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.24	✓	48	11.10	odd	2
990.2.t.a.461.24	yes	48	9.2	odd	6
990.2.t.b.131.24	yes	48	1.1	even	1	trivial
990.2.t.b.461.24	yes	48	99.65	even	6	inner
2970.2.t.a.791.20		48	99.43	odd	6
2970.2.t.a.2771.20		48	3.2	odd	2
2970.2.t.b.791.20		48	9.7	even	3
2970.2.t.b.2771.20		48	33.32	even	2

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} +(-1.83929 + 2.75989i) 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} +(-3.30978 - 0.212926i) 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} +(-2.41331 + 5.21305i) 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} +(-5.72129 + 0.516539i) 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} +(-0.225138 + 3.49960i) 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} +(1.83929 - 2.75989i) 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} +(-2.74278 + 9.56437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * 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 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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