LMFDB - Embedded newform 231.2.n.a.89.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(89,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.14
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.304723 + 0.175932i) q^{2} +(1.71292 + 0.256725i) q^{3} +(-0.938096 - 1.62483i) q^{4} +(0.734005 - 1.27133i) q^{5} +(0.476800 + 0.379587i) q^{6} +(-1.51718 - 2.16753i) q^{7} -1.36389i q^{8} +(2.86818 + 0.879497i) q^{9} +O(q^{10})$	\(q+(0.304723 + 0.175932i) q^{2} +(1.71292 + 0.256725i) q^{3} +(-0.938096 - 1.62483i) q^{4} +(0.734005 - 1.27133i) q^{5} +(0.476800 + 0.379587i) q^{6} +(-1.51718 - 2.16753i) q^{7} -1.36389i q^{8} +(2.86818 + 0.879497i) q^{9} +(0.447337 - 0.258270i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.18975 - 3.02403i) q^{12} +0.272166i q^{13} +(-0.0809820 - 0.927416i) q^{14} +(1.58367 - 1.98926i) q^{15} +(-1.63624 + 2.83405i) q^{16} +(3.22650 + 5.58847i) q^{17} +(0.719271 + 0.772609i) q^{18} +(0.930556 + 0.537257i) q^{19} -2.75427 q^{20} +(-2.04235 - 4.10229i) q^{21} -0.351864 q^{22} +(-2.22978 - 1.28736i) q^{23} +(0.350145 - 2.33624i) q^{24} +(1.42247 + 2.46380i) q^{25} +(-0.0478826 + 0.0829352i) q^{26} +(4.68718 + 2.24284i) q^{27} +(-2.09860 + 4.49850i) q^{28} +7.84993i q^{29} +(0.832556 - 0.327553i) q^{30} +(3.23246 - 1.86626i) q^{31} +(-3.35953 + 1.93963i) q^{32} +(-1.61179 + 0.634130i) q^{33} +2.27058i q^{34} +(-3.86927 + 0.337865i) q^{35} +(-1.26160 - 5.48536i) q^{36} +(5.70464 - 9.88072i) q^{37} +(0.189041 + 0.327429i) q^{38} +(-0.0698716 + 0.466198i) q^{39} +(-1.73396 - 1.00110i) q^{40} -7.96103 q^{41} +(0.0993748 - 1.60938i) q^{42} -0.650193 q^{43} +(1.62483 + 0.938096i) q^{44} +(3.22340 - 3.00087i) q^{45} +(-0.452977 - 0.784580i) q^{46} +(2.60049 - 4.50418i) q^{47} +(-3.53032 + 4.43443i) q^{48} +(-2.39634 + 6.57705i) q^{49} +1.00103i q^{50} +(4.09204 + 10.4009i) q^{51} +(0.442223 - 0.255317i) q^{52} +(-6.72637 + 3.88347i) q^{53} +(1.03371 + 1.50807i) q^{54} +1.46801i q^{55} +(-2.95627 + 2.06927i) q^{56} +(1.45604 + 1.15917i) q^{57} +(-1.38105 + 2.39206i) q^{58} +(-5.97454 - 10.3482i) q^{59} +(-4.71784 - 0.707088i) q^{60} +(-4.82646 - 2.78656i) q^{61} +1.31334 q^{62} +(-2.44521 - 7.55122i) q^{63} +5.17999 q^{64} +(0.346013 + 0.199771i) q^{65} +(-0.602715 - 0.0903322i) q^{66} +(4.30125 + 7.44998i) q^{67} +(6.05354 - 10.4850i) q^{68} +(-3.48894 - 2.77759i) q^{69} +(-1.23850 - 0.577773i) q^{70} +7.89503i q^{71} +(1.19954 - 3.91190i) q^{72} +(-12.5458 + 7.24334i) q^{73} +(3.47667 - 2.00726i) q^{74} +(1.80406 + 4.58547i) q^{75} -2.01599i q^{76} +(2.39768 + 1.11854i) q^{77} +(-0.103311 + 0.129769i) q^{78} +(2.76046 - 4.78125i) q^{79} +(2.40202 + 4.16041i) q^{80} +(7.45297 + 5.04512i) q^{81} +(-2.42591 - 1.40060i) q^{82} -6.97936 q^{83} +(-4.74961 + 7.16681i) q^{84} +9.47309 q^{85} +(-0.198129 - 0.114390i) q^{86} +(-2.01527 + 13.4463i) q^{87} +(0.681946 + 1.18117i) q^{88} +(3.13404 - 5.42832i) q^{89} +(1.51019 - 0.347335i) q^{90} +(0.589926 - 0.412924i) q^{91} +4.83068i q^{92} +(6.01606 - 2.36691i) q^{93} +(1.58486 - 0.915018i) q^{94} +(1.36607 - 0.788698i) q^{95} +(-6.25256 + 2.45995i) q^{96} -9.46459i q^{97} +(-1.88733 + 1.58259i) q^{98} +(-2.92367 + 0.672426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.304723	+	0.175932i	0.215472	+	0.124403i	0.603852	−	0.797097i	$-0.293632\pi$
$2$	0.304723	+	0.175932i	0.215472	+	0.124403i	−0.388380	+	0.921499i	$0.626965\pi$
$3$	1.71292	+	0.256725i	0.988954	+	0.148220i
$3$	1.71292	+	0.256725i	0.988954	+	0.148220i
$4$	−0.938096	−	1.62483i	−0.469048	−	0.812415i
$5$	0.734005	−	1.27133i	0.328257	−	0.568558i	−0.653909	−	0.756573i	$-0.726872\pi$
$5$	0.734005	−	1.27133i	0.328257	−	0.568558i	0.982166	+	0.188015i	$0.0602054\pi$
$6$	0.476800	+	0.379587i	0.194653	+	0.154966i
$7$	−1.51718	−	2.16753i	−0.573439	−	0.819248i
$7$	−1.51718	−	2.16753i	−0.573439	−	0.819248i
$8$		−	1.36389i		−	0.482209i
$9$	2.86818	+	0.879497i	0.956062	+	0.293166i
$10$	0.447337	−	0.258270i	0.141460	−	0.0816722i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.18975	−	3.02403i	−0.343451	−	0.872963i
$13$			0.272166i			0.0754851i	0.999287	+	0.0377426i	$0.0120167\pi$
$13$			0.272166i			0.0754851i	−0.999287	+	0.0377426i	$0.987983\pi$
$14$	−0.0809820	−	0.927416i	−0.0216434	−	0.247862i
$15$	1.58367	−	1.98926i	0.408903	−	0.513624i
$16$	−1.63624	+	2.83405i	−0.409060	+	0.708512i
$17$	3.22650	+	5.58847i	0.782542	+	1.35540i	0.930456	+	0.366403i	$0.119411\pi$
$17$	3.22650	+	5.58847i	0.782542	+	1.35540i	−0.147914	+	0.989000i	$0.547256\pi$
$18$	0.719271	+	0.772609i	0.169534	+	0.182106i
$19$	0.930556	+	0.537257i	0.213484	+	0.123255i	0.602930	−	0.797794i	$-0.294000\pi$
$19$	0.930556	+	0.537257i	0.213484	+	0.123255i	−0.389445	+	0.921050i	$0.627333\pi$
$20$	−2.75427			−0.615873
$21$	−2.04235	−	4.10229i	−0.445676	−	0.895194i
$22$	−0.351864			−0.0750177
$23$	−2.22978	−	1.28736i	−0.464941	−	0.268434i	0.249178	−	0.968458i	$-0.419839\pi$
$23$	−2.22978	−	1.28736i	−0.464941	−	0.268434i	−0.714120	+	0.700024i	$0.753173\pi$
$24$	0.350145	−	2.33624i	0.0714730	−	0.476883i
$25$	1.42247	+	2.46380i	0.284495	+	0.492759i
$26$	−0.0478826	+	0.0829352i	−0.00939056	+	0.0162649i
$27$	4.68718	+	2.24284i	0.902048	+	0.431635i
$28$	−2.09860	+	4.49850i	−0.396599	+	0.850137i
$29$			7.84993i			1.45769i	0.684676	+	0.728847i	$0.259944\pi$
$29$			7.84993i			1.45769i	−0.684676	+	0.728847i	$0.740056\pi$
$30$	0.832556	−	0.327553i	0.152003	−	0.0598028i
$31$	3.23246	−	1.86626i	0.580568	−	0.335191i	−0.180791	−	0.983521i	$-0.557866\pi$
$31$	3.23246	−	1.86626i	0.580568	−	0.335191i	0.761359	+	0.648331i	$0.224533\pi$
$32$	−3.35953	+	1.93963i	−0.593887	+	0.342881i
$33$	−1.61179	+	0.634130i	−0.280577	+	0.110388i
$34$			2.27058i			0.389402i
$35$	−3.86927	+	0.337865i	−0.654026	+	0.0571096i
$36$	−1.26160	−	5.48536i	−0.210267	−	0.914227i
$37$	5.70464	−	9.88072i	0.937837	−	1.62438i	0.168341	−	0.985729i	$-0.446159\pi$
$37$	5.70464	−	9.88072i	0.937837	−	1.62438i	0.769496	−	0.638652i	$-0.220508\pi$
$38$	0.189041	+	0.327429i	0.0306666	+	0.0531160i
$39$	−0.0698716	+	0.466198i	−0.0111884	+	0.0746514i
$40$	−1.73396	−	1.00110i	−0.274164	−	0.158289i
$41$	−7.96103			−1.24330			−0.621652	−	0.783293i	$-0.713538\pi$
$41$	−7.96103			−1.24330			−0.621652	+	0.783293i	$0.713538\pi$
$42$	0.0993748	−	1.60938i	0.0153339	−	0.248333i
$43$	−0.650193			−0.0991535			−0.0495768	−	0.998770i	$-0.515787\pi$
$43$	−0.650193			−0.0991535			−0.0495768	+	0.998770i	$0.515787\pi$
$44$	1.62483	+	0.938096i	0.244952	+	0.141423i
$45$	3.22340	−	3.00087i	0.480516	−	0.447343i
$46$	−0.452977	−	0.784580i	−0.0667879	−	0.115680i
$47$	2.60049	−	4.50418i	0.379320	−	0.657002i	−0.611643	−	0.791134i	$-0.709491\pi$
$47$	2.60049	−	4.50418i	0.379320	−	0.657002i	0.990963	+	0.134132i	$0.0428246\pi$
$48$	−3.53032	+	4.43443i	−0.509557	+	0.640056i
$49$	−2.39634	+	6.57705i	−0.342335	+	0.939578i
$50$			1.00103i			0.141568i
$51$	4.09204	+	10.4009i	0.573001	+	1.45642i
$52$	0.442223	−	0.255317i	0.0613252	−	0.0354061i
$53$	−6.72637	+	3.88347i	−0.923937	+	0.533435i	−0.884889	−	0.465802i	$-0.845766\pi$
$53$	−6.72637	+	3.88347i	−0.923937	+	0.533435i	−0.0390483	+	0.999237i	$0.512433\pi$
$54$	1.03371	+	1.50807i	0.140670	+	0.205223i
$55$			1.46801i			0.197946i
$56$	−2.95627	+	2.06927i	−0.395049	+	0.276518i
$57$	1.45604	+	1.15917i	0.192857	+	0.153536i
$58$	−1.38105	+	2.39206i	−0.181341	+	0.314092i
$59$	−5.97454	−	10.3482i	−0.777819	−	1.34722i	−0.933197	−	0.359366i	$-0.882993\pi$
$59$	−5.97454	−	10.3482i	−0.777819	−	1.34722i	0.155378	−	0.987855i	$-0.450340\pi$
$60$	−4.71784	−	0.707088i	−0.609071	−	0.0912847i
$61$	−4.82646	−	2.78656i	−0.617965	−	0.356782i	0.158111	−	0.987421i	$-0.449459\pi$
$61$	−4.82646	−	2.78656i	−0.617965	−	0.356782i	−0.776076	+	0.630639i	$0.782793\pi$
$62$	1.31334			0.166795
$63$	−2.44521	−	7.55122i	−0.308068	−	0.951364i
$64$	5.17999			0.647498
$65$	0.346013	+	0.199771i	0.0429177	+	0.0247785i
$66$	−0.602715	−	0.0903322i	−0.0741891	−	0.0111191i
$67$	4.30125	+	7.44998i	0.525481	+	0.910159i	0.999560	+	0.0296770i	$0.00944785\pi$
$67$	4.30125	+	7.44998i	0.525481	+	0.910159i	−0.474079	+	0.880482i	$0.657219\pi$
$68$	6.05354	−	10.4850i	0.734100	−	1.27150i
$69$	−3.48894	−	2.77759i	−0.420018	−	0.334383i
$70$	−1.23850	−	0.577773i	−0.148029	−	0.0690571i
$71$			7.89503i			0.936968i	0.883472	+	0.468484i	$0.155200\pi$
$71$			7.89503i			0.936968i	−0.883472	+	0.468484i	$0.844800\pi$
$72$	1.19954	−	3.91190i	0.141367	−	0.461021i
$73$	−12.5458	+	7.24334i	−1.46838	+	0.847769i	−0.999372	−	0.0354260i	$-0.988721\pi$
$73$	−12.5458	+	7.24334i	−1.46838	+	0.847769i	−0.469006	+	0.883195i	$0.655388\pi$
$74$	3.47667	−	2.00726i	0.404155	−	0.233339i
$75$	1.80406	+	4.58547i	0.208315	+	0.529484i
$76$		−	2.01599i		−	0.231250i
$77$	2.39768	+	1.11854i	0.273241	+	0.127470i
$78$	−0.103311	+	0.129769i	−0.0116976	+	0.0146934i
$79$	2.76046	−	4.78125i	0.310576	−	0.537933i	−0.667911	−	0.744241i	$-0.732811\pi$
$79$	2.76046	−	4.78125i	0.310576	−	0.537933i	0.978487	+	0.206308i	$0.0661448\pi$
$80$	2.40202	+	4.16041i	0.268554	+	0.465148i
$81$	7.45297	+	5.04512i	0.828108	+	0.560569i
$82$	−2.42591	−	1.40060i	−0.267897	−	0.154671i
$83$	−6.97936			−0.766084			−0.383042	−	0.923731i	$-0.625124\pi$
$83$	−6.97936			−0.766084			−0.383042	+	0.923731i	$0.625124\pi$
$84$	−4.74961	+	7.16681i	−0.518225	+	0.781963i
$85$	9.47309			1.02750
$86$	−0.198129	−	0.114390i	−0.0213648	−	0.0123350i
$87$	−2.01527	+	13.4463i	−0.216060	+	1.44159i
$88$	0.681946	+	1.18117i	0.0726957	+	0.125913i
$89$	3.13404	−	5.42832i	0.332207	−	0.575400i	−0.650737	−	0.759303i	$-0.725540\pi$
$89$	3.13404	−	5.42832i	0.332207	−	0.575400i	0.982944	+	0.183903i	$0.0588732\pi$
$90$	1.51019	−	0.347335i	0.159188	−	0.0366123i
$91$	0.589926	−	0.412924i	0.0618410	−	0.0432861i
$92$			4.83068i			0.503634i
$93$	6.01606	−	2.36691i	0.623837	−	0.245437i
$94$	1.58486	−	0.915018i	0.163466	−	0.0943769i
$95$	1.36607	−	0.788698i	0.140155	−	0.0809187i
$96$	−6.25256	+	2.45995i	−0.638149	+	0.251068i
$97$		−	9.46459i		−	0.960983i	−0.876999	−	0.480492i	$-0.840458\pi$
$97$		−	9.46459i		−	0.960983i	0.876999	−	0.480492i	$-0.159542\pi$
$98$	−1.88733	+	1.58259i	−0.190650	+	0.159865i
$99$	−2.92367	+	0.672426i	−0.293840	+	0.0675813i
$100$	2.66883	−	4.62255i	0.266883	−	0.462255i
$101$	−1.09793	−	1.90168i	−0.109248	−	0.189224i	0.806218	−	0.591619i	$-0.201511\pi$
$101$	−1.09793	−	1.90168i	−0.109248	−	0.189224i	−0.915466	+	0.402395i	$0.868178\pi$
$102$	−0.582914	+	3.88933i	−0.0577171	+	0.385101i
$103$	−4.49945	−	2.59776i	−0.443344	−	0.255965i	0.261671	−	0.965157i	$-0.415726\pi$
$103$	−4.49945	−	2.59776i	−0.443344	−	0.255965i	−0.705015	+	0.709192i	$0.749060\pi$
$104$	0.371205			0.0363996
$105$	−6.71448	−	0.414601i	−0.655266	−	0.0404609i
$106$	−2.73291			−0.265443
$107$	11.3158	+	6.53319i	1.09394	+	0.631587i	0.934623	−	0.355640i	$-0.115737\pi$
$107$	11.3158	+	6.53319i	1.09394	+	0.631587i	0.159318	+	0.987227i	$0.449070\pi$
$108$	−0.752790	−	9.71987i	−0.0724373	−	0.935295i
$109$	−0.951169	−	1.64747i	−0.0911054	−	0.157799i	0.816871	−	0.576820i	$-0.195707\pi$
$109$	−0.951169	−	1.64747i	−0.0911054	−	0.157799i	−0.907977	+	0.419021i	$0.862373\pi$
$110$	−0.258270	+	0.447337i	−0.0246251	+	0.0426519i
$111$	12.3082	−	15.4604i	1.16824	−	1.46743i
$112$	8.62534	−	0.753166i	0.815018	−	0.0711675i
$113$			3.06975i			0.288778i	0.989521	+	0.144389i	$0.0461216\pi$
$113$			3.06975i			0.288778i	−0.989521	+	0.144389i	$0.953878\pi$
$114$	0.239753	+	0.609391i	0.0224550	+	0.0570747i
$115$	−3.27334	+	1.88986i	−0.305241	+	0.176231i
$116$	12.7548	−	7.36398i	1.18425	−	0.683729i
$117$	−0.239369	+	0.780621i	−0.0221296	+	0.0721684i
$118$		−	4.20445i		−	0.387051i
$119$	7.21798	−	15.4722i	0.661671	−	1.41834i
$120$	−2.71313	−	2.15996i	−0.247674	−	0.197177i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−0.980490	−	1.69826i	−0.0887693	−	0.153753i
$123$	−13.6366	−	2.04379i	−1.22957	−	0.184283i
$124$	−6.06472	−	3.50147i	−0.544628	−	0.314441i
$125$	11.5165			1.03006
$126$	0.583388	−	2.73122i	0.0519723	−	0.243317i
$127$	0.787463			0.0698761			0.0349380	−	0.999389i	$-0.488877\pi$
$127$	0.787463			0.0698761			0.0349380	+	0.999389i	$0.488877\pi$
$128$	8.29753	+	4.79058i	0.733405	+	0.423431i
$129$	−1.11373	−	0.166921i	−0.0980583	−	0.0146965i
$130$	0.0702922	+	0.121750i	0.00616504	+	0.0106782i
$131$	10.6895	−	18.5147i	0.933942	−	1.61763i	0.157432	−	0.987530i	$-0.449679\pi$
$131$	10.6895	−	18.5147i	0.933942	−	1.61763i	0.776510	−	0.630105i	$-0.216988\pi$
$132$	2.54237	+	2.02402i	0.221285	+	0.176168i
$133$	−0.247301	−	2.83212i	−0.0214437	−	0.245576i
$134$			3.02691i			0.261485i
$135$	6.29182	−	4.31272i	0.541513	−	0.371180i
$136$	7.62208	−	4.40061i	0.653588	−	0.377349i
$137$	−2.02944	+	1.17170i	−0.173387	+	0.100105i	−0.584182	−	0.811623i	$-0.698584\pi$
$137$	−2.02944	+	1.17170i	−0.173387	+	0.100105i	0.410795	+	0.911728i	$0.365251\pi$
$138$	−0.574493	−	1.46021i	−0.0489041	−	0.124302i
$139$		−	2.57202i		−	0.218156i	−0.994033	−	0.109078i	$-0.965210\pi$
$139$		−	2.57202i		−	0.218156i	0.994033	−	0.109078i	$-0.0347898\pi$
$140$	4.17872	+	5.96995i	0.353166	+	0.504553i
$141$	5.61076	−	7.04768i	0.472511	−	0.593522i
$142$	−1.38899	+	2.40580i	−0.116561	+	0.201890i
$143$	−0.136083	−	0.235702i	−0.0113798	−	0.0197104i
$144$	−7.18557	+	6.68951i	−0.598798	+	0.557459i
$145$	9.97988	+	5.76189i	0.828784	+	0.478499i
$146$	−5.09734			−0.421859
$147$	−5.79323	+	10.6508i	−0.477818	+	0.878459i
$148$	−21.4060			−1.75956
$149$	−7.40429	−	4.27487i	−0.606583	−	0.350211i	0.165044	−	0.986286i	$-0.447223\pi$
$149$	−7.40429	−	4.27487i	−0.606583	−	0.350211i	−0.771627	+	0.636075i	$0.780557\pi$
$150$	−0.256990	+	1.71469i	−0.0209832	+	0.140004i
$151$	2.96879	+	5.14210i	0.241597	+	0.418458i	0.961169	−	0.275959i	$-0.0889955\pi$
$151$	2.96879	+	5.14210i	0.241597	+	0.418458i	−0.719572	+	0.694417i	$0.755662\pi$
$152$	0.732761	−	1.26918i	0.0594347	−	0.102944i
$153$	4.33917	+	18.8665i	0.350801	+	1.52526i
$154$	0.533841	+	0.762675i	0.0430181	+	0.0614581i
$155$		−	5.47939i		−	0.440115i
$156$	0.823038	−	0.323809i	0.0658958	−	0.0259254i
$157$	−4.78460	+	2.76239i	−0.381852	+	0.220463i	−0.678624	−	0.734486i	$-0.737423\pi$
$157$	−4.78460	+	2.76239i	−0.381852	+	0.220463i	0.296772	+	0.954948i	$0.404090\pi$
$158$	1.68235	−	0.971306i	0.133841	−	0.0772730i
$159$	−12.5187	+	4.92525i	−0.992798	+	0.390597i
$160$			5.69478i			0.450212i
$161$	0.592577	+	6.78627i	0.0467016	+	0.534833i
$162$	1.38350	+	2.84858i	0.108698	+	0.223806i
$163$	0.428680	−	0.742496i	0.0335768	−	0.0581567i	−0.848749	−	0.528796i	$-0.822643\pi$
$163$	0.428680	−	0.742496i	0.0335768	−	0.0581567i	0.882325	+	0.470640i	$0.155977\pi$
$164$	7.46821	+	12.9353i	0.583169	+	1.01008i
$165$	−0.376874	+	2.51458i	−0.0293396	+	0.195760i
$166$	−2.12677	−	1.22789i	−0.165070	−	0.0953030i
$167$	0.994062			0.0769228			0.0384614	−	0.999260i	$-0.487754\pi$
$167$	0.994062			0.0769228			0.0384614	+	0.999260i	$0.487754\pi$
$168$	−5.59509	+	2.78554i	−0.431671	+	0.214909i
$169$	12.9259			0.994302
$170$	2.88667	+	1.66662i	0.221397	+	0.127824i
$171$	2.19649	+	2.35937i	0.167970	+	0.180426i
$172$	0.609944	+	1.05645i	0.0465078	+	0.0805538i
$173$	−3.73501	+	6.46923i	−0.283968	+	0.491846i	−0.972358	−	0.233494i	$-0.924984\pi$
$173$	−3.73501	+	6.46923i	−0.283968	+	0.491846i	0.688391	+	0.725340i	$0.258317\pi$
$174$	−2.97973	+	3.74285i	−0.225893	+	0.283745i
$175$	3.18220	−	6.82126i	0.240551	−	0.515639i
$176$		−	3.27248i		−	0.246672i
$177$	−7.57726	−	19.2594i	−0.569542	−	1.44763i
$178$	1.91003	−	1.10276i	0.143163	−	0.0826551i
$179$	−8.72974	+	5.04012i	−0.652491	+	0.376716i	−0.789410	−	0.613866i	$-0.789613\pi$
$179$	−8.72974	+	5.04012i	−0.652491	+	0.376716i	0.136919	+	0.990582i	$0.456280\pi$
$180$	−7.89975	−	2.42237i	−0.588813	−	0.180553i
$181$			19.3563i			1.43875i	0.694624	+	0.719373i	$0.255571\pi$
$181$			19.3563i			1.43875i	−0.694624	+	0.719373i	$0.744429\pi$
$182$	0.252411	−	0.0220405i	0.0187099	−	0.00163375i
$183$	−7.55196	−	6.01222i	−0.558257	−	0.444436i
$184$	−1.75583	+	3.04118i	−0.129441	+	0.224199i
$185$	−8.37447	−	14.5050i	−0.615703	−	1.06643i
$186$	2.24965	+	0.337167i	0.164952	+	0.0247223i
$187$	−5.58847	−	3.22650i	−0.408669	−	0.235945i
$188$	−9.75802			−0.711677
$189$	−2.24987	−	13.5624i	−0.163654	−	0.986518i
$190$	0.555029			0.0402661
$191$	−19.9198	−	11.5007i	−1.44134	−	0.832160i	−0.443404	−	0.896322i	$-0.646229\pi$
$191$	−19.9198	−	11.5007i	−1.44134	−	0.832160i	−0.997939	+	0.0641620i	$0.979563\pi$
$192$	8.87290	+	1.32983i	0.640346	+	0.0959722i
$193$	3.87378	+	6.70958i	0.278841	+	0.482966i	0.971097	−	0.238685i	$-0.0767165\pi$
$193$	3.87378	+	6.70958i	0.278841	+	0.482966i	−0.692256	+	0.721652i	$0.743383\pi$
$194$	1.66512	−	2.88408i	0.119549	−	0.207065i
$195$	0.541407	+	0.431022i	0.0387710	+	0.0308661i
$196$	12.9346	−	2.27625i	0.923898	−	0.162589i
$197$			23.3188i			1.66139i	0.556725	+	0.830697i	$0.312058\pi$
$197$			23.3188i			1.66139i	−0.556725	+	0.830697i	$0.687942\pi$
$198$	−1.00921	−	0.309463i	−0.0717215	−	0.0219926i
$199$	−7.11152	+	4.10584i	−0.504122	+	0.291055i	−0.730414	−	0.683004i	$-0.760673\pi$
$199$	−7.11152	+	4.10584i	−0.504122	+	0.291055i	0.226292	+	0.974060i	$0.427340\pi$
$200$	3.36035	−	1.94010i	0.237613	−	0.137186i
$201$	5.45509	+	13.8654i	0.384773	+	0.977993i
$202$		−	0.772647i		−	0.0543632i
$203$	17.0149	−	11.9097i	1.19421	−	0.835900i
$204$	13.0610	−	16.4059i	0.914453	−	1.14865i
$205$	−5.84344	+	10.1211i	−0.408124	+	0.706891i
$206$	−0.914059	−	1.58320i	−0.0636855	−	0.110306i
$207$	−5.26319	−	5.65348i	−0.365817	−	0.392944i
$208$	−0.771331	−	0.445328i	−0.0534821	−	0.0308779i
$209$	−1.07451			−0.0743256
$210$	−1.97312	−	1.30763i	−0.136158	−	0.0902351i
$211$	−20.8395			−1.43465			−0.717326	−	0.696738i	$-0.754634\pi$
$211$	−20.8395			−1.43465			−0.717326	+	0.696738i	$0.754634\pi$
$212$	12.6200	+	7.28613i	0.866742	+	0.500414i
$213$	−2.02685	+	13.5236i	−0.138877	+	0.926619i
$214$	2.29880	+	3.98163i	0.157142	+	0.272179i
$215$	−0.477245	+	0.826613i	−0.0325479	+	0.0563745i
$216$	3.05899	−	6.39281i	0.208138	−	0.434976i
$217$	−8.94940	−	4.17500i	−0.607525	−	0.283417i
$218$		−	0.669364i		−	0.0453351i
$219$	−23.3495	+	9.18643i	−1.57782	+	0.620762i
$220$	2.38527	−	1.37713i	0.160815	−	0.0928464i
$221$	−1.52099	+	0.878143i	−0.102313	+	0.0590703i
$222$	6.47057	−	2.54572i	0.434276	−	0.170858i
$223$		−	4.62893i		−	0.309976i	−0.987916	−	0.154988i	$-0.950466\pi$
$223$		−	4.62893i		−	0.309976i	0.987916	−	0.154988i	$-0.0495339\pi$
$224$	9.30120	+	4.33912i	0.621463	+	0.289919i
$225$	1.91301	+	8.31768i	0.127534	+	0.554512i
$226$	−0.540067	+	0.935424i	−0.0359248	+	0.0622235i
$227$	−1.30163	−	2.25449i	−0.0863922	−	0.149636i	0.819591	−	0.572948i	$-0.194200\pi$
$227$	−1.30163	−	2.25449i	−0.0863922	−	0.149636i	−0.905984	+	0.423313i	$0.860867\pi$
$228$	0.517555	−	3.45323i	0.0342759	−	0.228696i
$229$	−0.497823	−	0.287418i	−0.0328971	−	0.0189931i	0.483461	−	0.875366i	$-0.339379\pi$
$229$	−0.497823	−	0.287418i	−0.0328971	−	0.0189931i	−0.516358	+	0.856373i	$0.672713\pi$
$230$	−1.32995			−0.0876944
$231$	3.81987	+	2.53152i	0.251329	+	0.166562i
$232$	10.7065			0.702913
$233$	−15.8259	−	9.13706i	−1.03679	−	0.598589i	−0.117865	−	0.993030i	$-0.537605\pi$
$233$	−15.8259	−	9.13706i	−1.03679	−	0.598589i	−0.918921	+	0.394441i	$0.870938\pi$
$234$	−0.210278	+	0.195761i	−0.0137463	+	0.0127973i
$235$	−3.81754	−	6.61218i	−0.249029	−	0.431331i
$236$	−11.2094	+	19.4152i	−0.729668	+	1.26382i
$237$	5.95591	−	7.48122i	0.386878	−	0.485958i
$238$	4.92155	−	3.44488i	0.319017	−	0.223298i
$239$		−	21.9357i		−	1.41890i	−0.704754	−	0.709452i	$-0.748943\pi$
$239$		−	21.9357i		−	1.41890i	0.704754	−	0.709452i	$-0.251057\pi$
$240$	3.04638	+	7.74311i	0.196643	+	0.499816i
$241$	14.3570	−	8.28903i	0.924817	−	0.533943i	0.0396480	−	0.999214i	$-0.487376\pi$
$241$	14.3570	−	8.28903i	0.924817	−	0.533943i	0.885168	+	0.465271i	$0.154043\pi$
$242$	0.304723	−	0.175932i	0.0195884	−	0.0113093i
$243$	11.4711	+	10.5552i	0.735873	+	0.677119i
$244$			10.4562i			0.669392i
$245$	6.60270	+	7.87414i	0.421831	+	0.503060i
$246$	−3.79582	−	3.02191i	−0.242013	−	0.192670i
$247$	−0.146223	+	0.253265i	−0.00930393	+	0.0161149i
$248$	−2.54538	−	4.40873i	−0.161632	−	0.279955i
$249$	−11.9551	−	1.79177i	−0.757623	−	0.113549i
$250$	3.50933	+	2.02611i	0.221950	+	0.128143i
$251$	−13.7011			−0.864805			−0.432402	−	0.901681i	$-0.642334\pi$
$251$	−13.7011			−0.864805			−0.432402	+	0.901681i	$0.642334\pi$
$252$	−9.97560	+	11.0568i	−0.628404	+	0.696514i
$253$	2.57473			0.161872
$254$	0.239958	+	0.138540i	0.0150563	+	0.00869278i
$255$	16.2266	+	2.43197i	1.01615	+	0.152296i
$256$	−3.49435	−	6.05240i	−0.218397	−	0.378275i
$257$	−4.27079	+	7.39722i	−0.266404	+	0.461426i	−0.967931	−	0.251218i	$-0.919169\pi$
$257$	−4.27079	+	7.39722i	−0.266404	+	0.461426i	0.701526	+	0.712644i	$0.252502\pi$
$258$	−0.310012	−	0.246805i	−0.0193005	−	0.0153654i
$259$	−30.0717	+	2.62586i	−1.86856	+	0.163163i
$260$		−	0.749617i		−	0.0464893i
$261$	−6.90399	+	22.5150i	−0.427346	+	1.39365i
$262$	6.51465	−	3.76124i	0.402476	−	0.232370i
$263$	8.53234	−	4.92615i	0.526127	−	0.303759i	−0.213311	−	0.976984i	$-0.568425\pi$
$263$	8.53234	−	4.92615i	0.526127	−	0.303759i	0.739438	+	0.673225i	$0.235091\pi$
$264$	0.864885	+	2.19831i	0.0532300	+	0.135297i
$265$			11.4019i			0.700416i
$266$	0.422902	−	0.906521i	0.0259298	−	0.0555823i
$267$	6.76194	−	8.49368i	0.413824	−	0.519805i
$268$	8.06996	−	13.9776i	0.492951	−	0.853817i
$269$	−5.73460	−	9.93262i	−0.349645	−	0.605602i	0.636542	−	0.771242i	$-0.280364\pi$
$269$	−5.73460	−	9.93262i	−0.349645	−	0.605602i	−0.986186	+	0.165640i	$0.947031\pi$
$270$	2.67601	−	0.207253i	0.162857	−	0.0126130i
$271$	2.81476	+	1.62510i	0.170985	+	0.0987181i	0.583050	−	0.812436i	$-0.301859\pi$
$271$	2.81476	+	1.62510i	0.170985	+	0.0987181i	−0.412065	+	0.911154i	$0.635192\pi$
$272$	−21.1173			−1.28043
$273$	1.11650	−	0.555856i	0.0675738	−	0.0336419i
$274$	−0.824556			−0.0498132
$275$	−2.46380	−	1.42247i	−0.148572	−	0.0857783i
$276$	−1.24016	+	8.27457i	−0.0746486	+	0.498071i
$277$	−1.47961	−	2.56276i	−0.0889012	−	0.153981i	0.818146	−	0.575011i	$-0.195002\pi$
$277$	−1.47961	−	2.56276i	−0.0889012	−	0.153981i	−0.907047	+	0.421029i	$0.861669\pi$
$278$	0.452501	−	0.783755i	0.0271392	−	0.0470065i
$279$	10.9127	−	2.50985i	0.653325	−	0.150261i
$280$	0.460811	+	5.27727i	0.0275387	+	0.315377i
$281$			7.68274i			0.458314i	0.973390	+	0.229157i	$0.0735968\pi$
$281$			7.68274i			0.458314i	−0.973390	+	0.229157i	$0.926403\pi$
$282$	2.94964	−	1.16048i	0.175649	−	0.0691056i
$283$	12.7952	−	7.38730i	0.760594	−	0.439129i	−0.0689150	−	0.997623i	$-0.521954\pi$
$283$	12.7952	−	7.38730i	0.760594	−	0.439129i	0.829509	+	0.558493i	$0.188620\pi$
$284$	12.8281	−	7.40630i	0.761207	−	0.439483i
$285$	2.54244	−	1.00027i	0.150601	−	0.0592511i
$286$		−	0.0957653i		−	0.00566272i
$287$	12.0783	+	17.2557i	0.712960	+	1.01857i
$288$	−11.3417	+	2.60851i	−0.668313	+	0.153708i
$289$	−12.3207	+	21.3400i	−0.724745	+	1.25530i
$290$	2.02740	+	3.51156i	0.119053	+	0.206206i
$291$	2.42979	−	16.2121i	0.142437	−	0.950369i
$292$	23.5384	+	13.5899i	1.37748	+	0.795288i
$293$	0.648302			0.0378742			0.0189371	−	0.999821i	$-0.493972\pi$
$293$	0.648302			0.0378742			0.0189371	+	0.999821i	$0.493972\pi$
$294$	−3.63914	+	2.22632i	−0.212239	+	0.129841i
$295$	−17.5414			−1.02130
$296$	−13.4762	−	7.78051i	−0.783291	−	0.452233i
$297$	−5.18064	+	0.401233i	−0.300611	+	0.0232819i
$298$	−1.50417	−	2.60531i	−0.0871344	−	0.150921i
$299$	0.350376	−	0.606869i	0.0202628	−	0.0350962i
$300$	5.75822	−	7.23290i	0.332451	−	0.417592i
$301$	0.986459	+	1.40931i	0.0568585	+	0.0812313i
$302$			2.08922i			0.120221i
$303$	−1.39246	−	3.53928i	−0.0799950	−	0.203327i
$304$	−3.04522	+	1.75816i	−0.174656	+	0.100837i
$305$	−7.08529	+	4.09069i	−0.405703	+	0.234232i
$306$	−1.99697	+	6.51245i	−0.114159	+	0.372292i
$307$		−	28.3731i		−	1.61934i	−0.586887	−	0.809669i	$-0.699647\pi$
$307$		−	28.3731i		−	1.61934i	0.586887	−	0.809669i	$-0.300353\pi$
$308$	−0.431808	−	4.94512i	−0.0246046	−	0.281774i
$309$	−7.04029	−	5.60487i	−0.400508	−	0.318850i
$310$	0.964000	−	1.66970i	0.0547515	−	0.0948324i
$311$	−12.2392	−	21.1990i	−0.694024	−	1.20208i	−0.970509	−	0.241067i	$-0.922503\pi$
$311$	−12.2392	−	21.1990i	−0.694024	−	1.20208i	0.276485	−	0.961018i	$-0.410831\pi$
$312$	0.635844	+	0.0952973i	0.0359976	+	0.00539515i
$313$	13.7890	+	7.96106i	0.779398	+	0.449986i	0.836217	−	0.548399i	$-0.184762\pi$
$313$	13.7890	+	7.96106i	0.779398	+	0.449986i	−0.0568188	+	0.998385i	$0.518096\pi$
$314$	−1.94397			−0.109705
$315$	−11.3949	−	2.43395i	−0.642031	−	0.137138i
$316$	−10.3583			−0.582700
$317$	27.7927	+	16.0461i	1.56099	+	0.901240i	0.997157	+	0.0753533i	$0.0240085\pi$
$317$	27.7927	+	16.0461i	1.56099	+	0.901240i	0.563836	+	0.825887i	$0.309325\pi$
$318$	−4.68125	−	0.701604i	−0.262511	−	0.0393440i
$319$	−3.92496	−	6.79824i	−0.219756	−	0.380628i
$320$	3.80214	−	6.58549i	0.212546	−	0.368140i
$321$	17.7059	+	14.0959i	0.988244	+	0.786755i
$322$	−1.01335	+	2.17219i	−0.0564718	+	0.121051i
$323$			6.93385i			0.385809i
$324$	1.20586	−	16.8426i	0.0669922	−	0.935701i
$325$	−0.670560	+	0.387148i	−0.0371960	+	0.0214751i
$326$	0.261258	−	0.150837i	0.0144697	−	0.00835410i
$327$	−1.20633	−	3.06618i	−0.0667101	−	0.169560i
$328$			10.8580i			0.599533i
$329$	−13.7083	+	1.19701i	−0.755764	+	0.0659934i
$330$	−0.557238	+	0.699948i	−0.0306750	+	0.0385309i
$331$	−13.7773	+	23.8629i	−0.757267	+	1.31163i	0.186972	+	0.982365i	$0.440133\pi$
$331$	−13.7773	+	23.8629i	−0.757267	+	1.31163i	−0.944239	+	0.329260i	$0.893201\pi$
$332$	6.54731	+	11.3403i	0.359330	+	0.622378i
$333$	25.0520	−	23.3225i	1.37284	−	1.27807i
$334$	0.302914	+	0.174887i	0.0165747	+	0.00956941i
$335$	12.6285			0.689971
$336$	14.9679	+	0.924226i	0.816564	+	0.0504206i
$337$	30.9233			1.68450			0.842250	−	0.539088i	$-0.181231\pi$
$337$	30.9233			1.68450			0.842250	+	0.539088i	$0.181231\pi$
$338$	3.93883	+	2.27408i	0.214244	+	0.123694i
$339$	−0.788080	+	5.25823i	−0.0428026	+	0.285588i
$340$	−8.88666	−	15.3922i	−0.481947	−	0.834757i
$341$	−1.86626	+	3.23246i	−0.101064	+	0.175048i
$342$	0.254233	+	1.10539i	0.0137473	+	0.0597726i
$343$	17.8916	−	4.78442i	0.966056	−	0.258334i
$344$			0.886794i			0.0478127i
$345$	−6.09214	+	2.39684i	−0.327990	+	0.129041i
$346$	−2.27629	+	1.31422i	−0.122374	+	0.0706527i
$347$	3.54952	−	2.04931i	0.190548	−	0.110013i	−0.401691	−	0.915775i	$-0.631577\pi$
$347$	3.54952	−	2.04931i	0.190548	−	0.110013i	0.592239	+	0.805762i	$0.298244\pi$
$348$	23.7384	−	9.33944i	1.27251	−	0.500647i
$349$		−	32.4529i		−	1.73717i	−0.495544	−	0.868583i	$-0.665031\pi$
$349$		−	32.4529i		−	1.73717i	0.495544	−	0.868583i	$-0.334969\pi$
$350$	2.16977	−	1.51875i	0.115979	−	0.0811805i
$351$	−0.610424	+	1.27569i	−0.0325820	+	0.0680912i
$352$	1.93963	−	3.35953i	0.103382	−	0.179064i
$353$	2.21737	+	3.84060i	0.118019	+	0.204414i	0.918982	−	0.394299i	$-0.129012\pi$
$353$	2.21737	+	3.84060i	0.118019	+	0.204414i	−0.800964	+	0.598713i	$0.795679\pi$
$354$	1.07939	−	7.20189i	0.0573687	−	0.382776i
$355$	10.0372	+	5.79500i	0.532721	+	0.307566i
$356$	−11.7601			−0.623285
$357$	16.3359	−	24.6497i	0.864588	−	1.30460i
$358$	−3.54687			−0.187458
$359$	−11.4780	−	6.62682i	−0.605785	−	0.349750i	0.165529	−	0.986205i	$-0.447067\pi$
$359$	−11.4780	−	6.62682i	−0.605785	−	0.349750i	−0.771314	+	0.636455i	$0.780400\pi$
$360$	−4.09286	−	4.39637i	−0.215713	−	0.231709i
$361$	−8.92271	−	15.4546i	−0.469616	−	0.813399i
$362$	−3.40540	+	5.89833i	−0.178984	+	0.310009i
$363$	1.07879	−	1.35507i	0.0566218	−	0.0711227i
$364$	−1.22434	−	0.571167i	−0.0641727	−	0.0299373i
$365$			21.2666i			1.11314i
$366$	−1.24351	−	3.16069i	−0.0649996	−	0.165212i
$367$	16.1166	−	9.30493i	0.841280	−	0.485713i	−0.0164189	−	0.999865i	$-0.505227\pi$
$367$	16.1166	−	9.30493i	0.841280	−	0.485713i	0.857699	+	0.514152i	$0.171893\pi$
$368$	7.29691	−	4.21287i	0.380378	−	0.219611i
$369$	−22.8337	−	7.00170i	−1.18868	−	0.364494i
$370$		−	5.89335i		−	0.306381i
$371$	18.6226	+	8.68766i	0.966838	+	0.451041i
$372$	−9.48946	−	7.55469i	−0.492006	−	0.391693i
$373$	17.0061	−	29.4555i	0.880545	−	1.52515i	0.0298087	−	0.999556i	$-0.490510\pi$
$373$	17.0061	−	29.4555i	0.880545	−	1.52515i	0.850736	−	0.525593i	$-0.176156\pi$
$374$	−1.13529	−	1.96638i	−0.0587045	−	0.101679i
$375$	19.7268	+	2.95656i	1.01869	+	0.152676i
$376$	−6.14321	−	3.54679i	−0.316812	−	0.182912i
$377$	−2.13648			−0.110034
$378$	1.70047	−	4.52860i	0.0874627	−	0.232926i
$379$	−16.2355			−0.833962			−0.416981	−	0.908915i	$-0.636912\pi$
$379$	−16.2355			−0.833962			−0.416981	+	0.908915i	$0.636912\pi$
$380$	−2.56300	−	1.47975i	−0.131479	−	0.0759095i
$381$	1.34886	+	0.202161i	0.0691043	+	0.0103570i
$382$	−4.04668	−	7.00905i	−0.207046	−	0.358614i
$383$	−14.8309	+	25.6879i	−0.757823	+	1.31259i	0.186136	+	0.982524i	$0.440404\pi$
$383$	−14.8309	+	25.6879i	−0.757823	+	1.31259i	−0.943959	+	0.330064i	$0.892930\pi$
$384$	12.9831	+	10.3361i	0.662543	+	0.527460i
$385$	3.18195	−	2.22723i	0.162167	−	0.113510i
$386$			2.72609i			0.138754i
$387$	−1.86487	−	0.571843i	−0.0947969	−	0.0290684i
$388$	−15.3783	+	8.87869i	−0.780717	+	0.450747i
$389$	16.4858	−	9.51809i	0.835864	−	0.482586i	−0.0199921	−	0.999800i	$-0.506364\pi$
$389$	16.4858	−	9.51809i	0.835864	−	0.482586i	0.855856	+	0.517214i	$0.173031\pi$
$390$	0.0891488	+	0.226593i	0.00451422	+	0.0114740i
$391$		−	16.6147i		−	0.840244i
$392$	8.97039	+	3.26835i	0.453073	+	0.165077i
$393$	23.0633	−	28.9699i	1.16339	−	1.46134i
$394$	−4.10252	+	7.10577i	−0.206682	+	0.357984i
$395$	−4.05238	−	7.01893i	−0.203897	−	0.353161i
$396$	3.83526	+	4.11967i	0.192729	+	0.207021i
$397$	−19.6279	−	11.3321i	−0.985094	−	0.568744i	−0.0812896	−	0.996691i	$-0.525904\pi$
$397$	−19.6279	−	11.3321i	−0.985094	−	0.568744i	−0.903804	+	0.427946i	$0.859237\pi$
$398$	−2.88939			−0.144832
$399$	0.303468	−	4.91468i	0.0151924	−	0.246042i
$400$	−9.31002			−0.465501
$401$	−18.5299	−	10.6982i	−0.925338	−	0.534244i	−0.0400042	−	0.999200i	$-0.512737\pi$
$401$	−18.5299	−	10.6982i	−0.925338	−	0.534244i	−0.885334	+	0.464955i	$0.846070\pi$
$402$	−0.777082	+	5.18485i	−0.0387573	+	0.258597i
$403$	0.507933	+	0.879765i	0.0253019	+	0.0438242i
$404$	−2.05993	+	3.56791i	−0.102486	+	0.177510i
$405$	11.8846	−	5.77207i	0.590548	−	0.286817i
$406$	7.28015	−	0.635703i	0.361308	−	0.0315494i
$407$			11.4093i			0.565537i
$408$	14.1857	−	5.58111i	0.702299	−	0.276306i
$409$	−23.3112	+	13.4587i	−1.15266	+	0.665490i	−0.949535	−	0.313662i	$-0.898444\pi$
$409$	−23.3112	+	13.4587i	−1.15266	+	0.665490i	−0.203128	+	0.979152i	$0.565111\pi$
$410$	−3.56126	+	2.05610i	−0.175878	+	0.101543i
$411$	−3.77707	+	1.48601i	−0.186309	+	0.0732997i
$412$			9.74779i			0.480239i
$413$	−13.3656	+	28.6500i	−0.657677	+	1.40978i
$414$	−0.609187	−	2.64871i	−0.0299399	−	0.130177i
$415$	−5.12289	+	8.87310i	−0.251473	+	0.435563i
$416$	−0.527900	−	0.914349i	−0.0258824	−	0.0448296i
$417$	0.660301	−	4.40567i	0.0323351	−	0.215746i
$418$	−0.327429	−	0.189041i	−0.0160151	−	0.00924632i
$419$	18.6168			0.909490			0.454745	−	0.890622i	$-0.349730\pi$
$419$	18.6168			0.909490			0.454745	+	0.890622i	$0.349730\pi$
$420$	5.62517	+	11.2988i	0.274480	+	0.551326i
$421$	32.6455			1.59104			0.795522	−	0.605925i	$-0.207197\pi$
$421$	32.6455			1.59104			0.795522	+	0.605925i	$0.207197\pi$
$422$	−6.35029	−	3.66634i	−0.309127	−	0.178475i
$423$	11.4201	−	10.6317i	0.555264	−	0.516930i
$424$	5.29664	+	9.17404i	0.257227	+	0.445531i
$425$	−9.17923	+	15.8989i	−0.445258	+	0.771210i
$426$	−2.99686	+	3.76435i	−0.145198	+	0.182384i
$427$	1.28266	+	14.6892i	0.0620723	+	0.710859i
$428$		−	24.5150i		−	1.18498i
$429$	−0.172588	−	0.438675i	−0.00833264	−	0.0211794i
$430$	−0.290855	+	0.167925i	−0.0140263	+	0.00809809i
$431$	−12.0910	+	6.98077i	−0.582405	+	0.336252i	−0.762089	−	0.647473i	$-0.775826\pi$
$431$	−12.0910	+	6.98077i	−0.582405	+	0.336252i	0.179684	+	0.983724i	$0.442493\pi$
$432$	−14.0257	+	9.61388i	−0.674810	+	0.462548i
$433$			25.3034i			1.21601i	0.793935	+	0.608003i	$0.208029\pi$
$433$			25.3034i			1.21601i	−0.793935	+	0.608003i	$0.791971\pi$
$434$	−1.99257	−	2.84670i	−0.0956466	−	0.136646i
$435$	15.6155	+	12.4317i	0.748707	+	0.596056i
$436$	−1.78457	+	3.09097i	−0.0854656	+	0.148031i
$437$	−1.38329	−	2.39593i	−0.0661717	−	0.114613i
$438$	−8.73134	−	1.30861i	−0.417199	−	0.0625280i
$439$	22.4666	+	12.9711i	1.07227	+	0.619077i	0.928802	−	0.370577i	$-0.120840\pi$
$439$	22.4666	+	12.9711i	1.07227	+	0.619077i	0.143472	+	0.989654i	$0.454173\pi$
$440$	2.00221			0.0954516
$441$	−12.6576	+	16.7566i	−0.602745	+	0.797934i
$442$	−0.617974			−0.0293940
$443$	3.27368	+	1.89006i	0.155537	+	0.0897995i	0.575749	−	0.817627i	$-0.304711\pi$
$443$	3.27368	+	1.89006i	0.155537	+	0.0897995i	−0.420211	+	0.907426i	$0.638044\pi$
$444$	−36.6667	−	5.49544i	−1.74013	−	0.260802i
$445$	−4.60080	−	7.96882i	−0.218099	−	0.377758i
$446$	0.814377	−	1.41054i	0.0385619	−	0.0667911i
$447$	−11.5855	−	9.22337i	−0.547975	−	0.436251i
$448$	−7.85896	−	11.2278i	−0.371301	−	0.530462i
$449$			25.8678i			1.22078i	0.792103	+	0.610388i	$0.208986\pi$
$449$			25.8678i			1.22078i	−0.792103	+	0.610388i	$0.791014\pi$
$450$	−0.880407	+	2.87115i	−0.0415028	+	0.135347i
$451$	6.89446	−	3.98052i	0.324647	−	0.187435i
$452$	4.98782	−	2.87972i	0.234607	−	0.135451i
$453$	3.76520	+	9.57016i	0.176904	+	0.449645i
$454$		−	0.915994i		−	0.0429897i
$455$	−0.0919551	−	1.05308i	−0.00431092	−	0.0493692i
$456$	1.58099	−	1.98588i	0.0740366	−	0.0929975i
$457$	−12.8931	+	22.3315i	−0.603113	+	1.04462i	0.389234	+	0.921139i	$0.372740\pi$
$457$	−12.8931	+	22.3315i	−0.603113	+	1.04462i	−0.992347	+	0.123483i	$0.960594\pi$
$458$	−0.101132	−	0.175166i	−0.00472560	−	0.00818498i
$459$	2.58916	+	33.4307i	0.120852	+	1.56041i
$460$	6.14141	+	3.54575i	0.286345	+	0.165321i
$461$	−8.34255			−0.388552			−0.194276	−	0.980947i	$-0.562236\pi$
$461$	−8.34255			−0.388552			−0.194276	+	0.980947i	$0.562236\pi$
$462$	0.718628	+	1.44345i	0.0334336	+	0.0671554i
$463$	−6.47547			−0.300941			−0.150470	−	0.988615i	$-0.548079\pi$
$463$	−6.47547			−0.300941			−0.150470	+	0.988615i	$0.548079\pi$
$464$	−22.2471	−	12.8444i	−1.03279	−	0.596284i
$465$	1.40669	−	9.38575i	0.0652339	−	0.435254i
$466$	−3.21500	−	5.56855i	−0.148932	−	0.257958i
$467$	9.75639	−	16.8986i	0.451472	−	0.781972i	−0.547006	−	0.837129i	$-0.684232\pi$
$467$	9.75639	−	16.8986i	0.451472	−	0.781972i	0.998478	+	0.0551566i	$0.0175658\pi$
$468$	1.49293	−	0.343364i	0.0690106	−	0.0158720i
$469$	9.62226	−	20.6260i	0.444315	−	0.952420i
$470$		−	2.68651i		−	0.123920i
$471$	−8.90480	+	3.50342i	−0.410311	+	0.161429i
$472$	−14.1138	+	8.14863i	−0.649642	+	0.375071i
$473$	0.563084	−	0.325097i	0.0258906	−	0.0149480i
$474$	3.13109	−	1.23187i	0.143816	−	0.0565816i
$475$			3.05693i			0.140262i
$476$	−31.9109	+	2.78646i	−1.46263	+	0.127717i
$477$	−22.7080	+	5.22269i	−1.03973	+	0.239131i
$478$	3.85920	−	6.68432i	0.176516	−	0.305734i
$479$	12.2251	+	21.1745i	0.558580	+	0.967489i	0.997615	+	0.0690192i	$0.0219870\pi$
$479$	12.2251	+	21.1745i	0.558580	+	0.967489i	−0.439035	+	0.898470i	$0.644680\pi$
$480$	−1.46199	+	9.75471i	−0.0667305	+	0.445239i
$481$	2.68919	+	1.55261i	0.122617	+	0.0707927i
$482$	5.83322			0.265696
$483$	−0.727164	+	11.7765i	−0.0330871	+	0.535847i
$484$	−1.87619			−0.0852814
$485$	−12.0327	−	6.94706i	−0.546375	−	0.315450i
$486$	1.63851	+	5.23457i	0.0743245	+	0.237445i
$487$	12.1876	+	21.1095i	0.552273	+	0.956565i	0.998110	+	0.0614505i	$0.0195726\pi$
$487$	12.1876	+	21.1095i	0.552273	+	0.956565i	−0.445837	+	0.895114i	$0.647094\pi$
$488$	−3.80057	+	6.58277i	−0.172044	+	0.297988i
$489$	0.924911	−	1.16178i	0.0418259	−	0.0525376i
$490$	0.626682	+	3.56106i	0.0283106	+	0.160872i
$491$		−	39.5253i		−	1.78375i	−0.452278	−	0.891877i	$-0.649389\pi$
$491$		−	39.5253i		−	1.78375i	0.452278	−	0.891877i	$-0.350611\pi$
$492$	9.47163	+	24.0744i	0.427014	+	1.08536i
$493$	−43.8691	+	25.3278i	−1.97576	+	1.14071i
$494$	−0.0891150	+	0.0514505i	−0.00400947	+	0.00231487i
$495$	−1.29111	+	4.21053i	−0.0580311	+	0.189249i
$496$			12.2146i			0.548452i
$497$	17.1127	−	11.9782i	0.767609	−	0.537294i
$498$	−3.32776	−	2.64928i	−0.149121	−	0.118717i
$499$	−2.18091	+	3.77744i	−0.0976307	+	0.169101i	−0.910704	−	0.413061i	$-0.864460\pi$
$499$	−2.18091	+	3.77744i	−0.0976307	+	0.169101i	0.813073	+	0.582162i	$0.197793\pi$
$500$	−10.8035	−	18.7123i	−0.483149	−	0.836839i
$501$	1.70275	+	0.255200i	0.0760732	+	0.0114015i
$502$	−4.17504	−	2.41046i	−0.186341	−	0.107584i
$503$	2.79047			0.124421			0.0622104	−	0.998063i	$-0.480185\pi$
$503$	2.79047			0.124421			0.0622104	+	0.998063i	$0.480185\pi$
$504$	−10.2991	+	3.33501i	−0.458756	+	0.148553i
$505$	−3.22356			−0.143446
$506$	0.784580	+	0.452977i	0.0348788	+	0.0201373i
$507$	22.1411	+	3.31840i	0.983319	+	0.147375i
$508$	−0.738716	−	1.27949i	−0.0327752	−	0.0567684i
$509$	14.6881	−	25.4406i	0.651039	−	1.12763i	−0.331832	−	0.943339i	$-0.607667\pi$
$509$	14.6881	−	25.4406i	0.651039	−	1.12763i	0.982871	−	0.184294i	$-0.0590000\pi$
$510$	4.51677	+	3.59586i	0.200006	+	0.159228i
$511$	34.7344	+	16.2040i	1.53656	+	0.716822i
$512$		−	21.6214i		−	0.955540i
$513$	3.15670	+	4.60531i	0.139372	+	0.203329i
$514$	−2.60282	+	1.50274i	−0.114805	+	0.0662829i
$515$	−6.60524	+	3.81354i	−0.291062	+	0.168045i
$516$	0.773567	+	1.96621i	0.0340544	+	0.0865574i
$517$			5.20097i			0.228739i
$518$	−9.62551	−	4.49041i	−0.422921	−	0.197297i
$519$	−8.05858	+	10.1224i	−0.353732	+	0.444324i
$520$	0.272466	−	0.471925i	0.0119484	−	0.0206953i
$521$	2.52839	+	4.37930i	0.110771	+	0.191861i	0.916081	−	0.400993i	$-0.131335\pi$
$521$	2.52839	+	4.37930i	0.110771	+	0.191861i	−0.805311	+	0.592853i	$0.798001\pi$
$522$	−6.06492	+	5.64622i	−0.265454	+	0.247129i
$523$	2.84483	+	1.64246i	0.124396	+	0.0718198i	0.560907	−	0.827879i	$-0.310453\pi$
$523$	2.84483	+	1.64246i	0.124396	+	0.0718198i	−0.436511	+	0.899699i	$0.643786\pi$
$524$	−40.1109			−1.75225
$525$	7.20203	−	10.8673i	0.314322	−	0.474289i
$526$	3.46667			0.151154
$527$	20.8591	+	12.0430i	0.908637	+	0.524602i
$528$	0.840126	−	5.60549i	0.0365618	−	0.243948i
$529$	−8.18539	−	14.1775i	−0.355886	−	0.616413i
$530$	−2.00597	+	3.47444i	−0.0871337	+	0.150920i
$531$	−8.03487	−	34.9352i	−0.348684	−	1.51606i
$532$	−4.36972	+	3.05862i	−0.189451	+	0.132608i
$533$		−	2.16672i		−	0.0938510i
$534$	3.55483	−	1.39858i	0.153833	−	0.0605225i
$535$	16.6117	−	9.59079i	0.718188	−	0.414646i
$536$	10.1610	−	5.86644i	0.438887	−	0.253392i
$537$	−16.2473	+	6.39217i	−0.701121	+	0.275843i
$538$		−	4.03560i		−	0.173987i
$539$	−1.21323	−	6.89406i	−0.0522575	−	0.296948i
$540$	−12.9098	−	6.17739i	−0.555547	−	0.265832i
$541$	−0.298183	+	0.516468i	−0.0128199	+	0.0222047i	−0.872364	−	0.488857i	$-0.837414\pi$
$541$	−0.298183	+	0.516468i	−0.0128199	+	0.0222047i	0.859544	+	0.511061i	$0.170747\pi$
$542$	0.571816	+	0.990414i	0.0245616	+	0.0425419i
$543$	−4.96925	+	33.1559i	−0.213251	+	1.42285i
$544$	−21.6791	−	12.5164i	−0.929483	−	0.536638i
$545$	−2.79265			−0.119624
$546$	0.438017	+	0.0270464i	0.0187454	+	0.00115748i
$547$	20.9835			0.897190			0.448595	−	0.893735i	$-0.351925\pi$
$547$	20.9835			0.897190			0.448595	+	0.893735i	$0.351925\pi$
$548$	3.80761	+	2.19833i	0.162653	+	0.0939079i
$549$	−11.3924	−	12.2372i	−0.486216	−	0.522272i
$550$	−0.500517	−	0.866921i	−0.0213421	−	0.0369656i
$551$	−4.21743	+	7.30480i	−0.179668	+	0.311195i
$552$	−3.78834	+	4.75853i	−0.161242	+	0.202537i
$553$	−14.5516	+	1.27065i	−0.618797	+	0.0540334i
$554$		−	1.04124i		−	0.0442382i
$555$	−10.6210	−	26.9958i	−0.450836	−	1.14591i
$556$	−4.17910	+	2.41280i	−0.177233	+	0.102326i
$557$	11.7436	−	6.78020i	0.497594	−	0.287286i	−0.230125	−	0.973161i	$-0.573914\pi$
$557$	11.7436	−	6.78020i	0.497594	−	0.287286i	0.727720	+	0.685875i	$0.240580\pi$
$558$	3.76691	+	1.15508i	0.159466	+	0.0488985i
$559$		−	0.176960i		−	0.00748462i
$560$	5.37352	−	11.5185i	0.227073	−	0.486746i
$561$	−8.74428	−	6.96144i	−0.369184	−	0.293912i
$562$	−1.35164	+	2.34111i	−0.0570155	+	0.0987537i
$563$	2.41041	+	4.17496i	0.101587	+	0.175954i	0.912339	−	0.409437i	$-0.134275\pi$
$563$	2.41041	+	4.17496i	0.101587	+	0.175954i	−0.810752	+	0.585390i	$0.800941\pi$
$564$	−16.7147	−	2.50512i	−0.703816	−	0.105485i
$565$	3.90268	+	2.25321i	0.164187	+	0.0947934i
$566$	5.19865			0.218516
$567$	−0.372051	−	23.8089i	−0.0156247	−	0.999878i
$568$	10.7680			0.451814
$569$	3.00271	+	1.73362i	0.125880	+	0.0726770i	0.561618	−	0.827397i	$-0.310179\pi$
$569$	3.00271	+	1.73362i	0.125880	+	0.0726770i	−0.435738	+	0.900074i	$0.643512\pi$
$570$	0.950721	+	0.142490i	0.0398213	+	0.00596824i
$571$	16.5906	+	28.7358i	0.694296	+	1.20256i	0.970417	+	0.241433i	$0.0776174\pi$
$571$	16.5906	+	28.7358i	0.694296	+	1.20256i	−0.276122	+	0.961123i	$0.589049\pi$
$572$	−0.255317	+	0.442223i	−0.0106754	+	0.0184903i
$573$	−31.1684	−	24.8136i	−1.30208	−	1.03660i
$574$	0.644701	+	7.38319i	0.0269093	+	0.308168i
$575$		−	7.32496i		−	0.305472i
$576$	14.8572	+	4.55578i	0.619048	+	0.189824i
$577$	30.5232	−	17.6226i	1.27070	−	0.733639i	0.295580	−	0.955318i	$-0.404487\pi$
$577$	30.5232	−	17.6226i	1.27070	−	0.733639i	0.975120	+	0.221679i	$0.0711538\pi$
$578$	−7.50879	+	4.33520i	−0.312324	+	0.180321i
$579$	4.91296	+	12.4875i	0.204176	+	0.518962i
$580$		−	21.6208i		−	0.897755i
$581$	10.5889	+	15.1280i	0.439303	+	0.627613i
$582$	3.59264	−	4.51272i	0.148920	−	0.187058i
$583$	3.88347	−	6.72637i	0.160837	−	0.278578i
$584$	9.87914	+	17.1112i	0.408802	+	0.708065i
$585$	0.816732	+	0.877298i	0.0337677	+	0.0362718i
$586$	0.197553	+	0.114057i	0.00816083	+	0.00471166i
$587$	25.6375			1.05817			0.529086	−	0.848568i	$-0.322535\pi$
$587$	25.6375			1.05817			0.529086	+	0.848568i	$0.322535\pi$
$588$	22.7403	−	0.578413i	0.937792	−	0.0238533i
$589$	4.01065			0.165256
$590$	−5.34526	−	3.08609i	−0.220061	−	0.127052i
$591$	−5.98650	+	39.9432i	−0.246252	+	1.64304i
$592$	18.6683	+	32.3344i	0.767262	+	1.32894i
$593$	7.01190	−	12.1450i	0.287944	−	0.498734i	−0.685375	−	0.728191i	$-0.740362\pi$
$593$	7.01190	−	12.1450i	0.287944	−	0.498734i	0.973319	+	0.229456i	$0.0736948\pi$
$594$	−1.64925	−	0.789175i	−0.0676696	−	0.0323803i
$595$	−14.3724	−	20.5332i	−0.589209	−	0.841778i
$596$			16.0410i			0.657063i
$597$	−13.2355	+	5.20727i	−0.541694	+	0.213119i
$598$	0.213536	−	0.123285i	0.00873212	−	0.00504149i
$599$	−37.0026	+	21.3635i	−1.51188	+	0.872887i	−0.511981	+	0.858997i	$0.671088\pi$
$599$	−37.0026	+	21.3635i	−1.51188	+	0.872887i	−0.999904	+	0.0138903i	$0.995578\pi$
$600$	6.25408	−	2.46055i	0.255322	−	0.100452i
$601$		−	24.5416i		−	1.00107i	−0.865715	−	0.500536i	$-0.833136\pi$
$601$		−	24.5416i		−	1.00107i	0.865715	−	0.500536i	$-0.166864\pi$
$602$	0.0526540	+	0.603000i	0.00214602	+	0.0245764i
$603$	5.78454	+	25.1508i	0.235565	+	1.02422i
$604$	5.57002	−	9.64756i	0.226641	−	0.392554i
$605$	−0.734005	−	1.27133i	−0.0298416	−	0.0516871i
$606$	0.198357	−	1.32348i	0.00805772	−	0.0537628i
$607$	−35.5131	−	20.5035i	−1.44143	−	0.832211i	−0.443487	−	0.896281i	$-0.646259\pi$
$607$	−35.5131	−	20.5035i	−1.44143	−	0.832211i	−0.997945	+	0.0640699i	$0.979592\pi$
$608$	−4.16831			−0.169047
$609$	32.2027	−	16.0323i	1.30492	−	0.649660i
$610$	−2.87874			−0.116557
$611$	1.22588	+	0.707763i	0.0495939	+	0.0286330i
$612$	26.5842	−	24.7490i	1.07460	−	1.00042i
$613$	7.25232	+	12.5614i	0.292918	+	0.507349i	0.974499	−	0.224394i	$-0.0720403\pi$
$613$	7.25232	+	12.5614i	0.292918	+	0.507349i	−0.681580	+	0.731743i	$0.738707\pi$
$614$	4.99174	−	8.64594i	0.201450	−	0.348922i
$615$	−12.6077	+	15.8365i	−0.508391	+	0.638591i
$616$	1.52557	−	3.27018i	0.0614671	−	0.131759i
$617$			18.6982i			0.752761i	0.926465	+	0.376381i	$0.122831\pi$
$617$			18.6982i			0.752761i	−0.926465	+	0.376381i	$0.877169\pi$
$618$	−1.15926	−	2.94655i	−0.0466324	−	0.118528i
$619$	−3.38445	+	1.95401i	−0.136033	+	0.0785384i	−0.566472	−	0.824081i	$-0.691692\pi$
$619$	−3.38445	+	1.95401i	−0.136033	+	0.0785384i	0.430439	+	0.902620i	$0.358359\pi$
$620$	−8.90307	+	5.14019i	−0.357556	+	0.206435i
$621$	−7.56403	−	11.0352i	−0.303534	−	0.442825i
$622$		−	8.61311i		−	0.345354i
$623$	−16.5209	+	1.44261i	−0.661896	+	0.0577968i
$624$	−1.20690	−	0.960830i	−0.0483147	−	0.0384640i
$625$	1.34078	−	2.32230i	0.0536312	−	0.0928919i
$626$	2.80121	+	4.85184i	0.111959	+	0.193919i
$627$	−1.84055	−	0.275854i	−0.0735047	−	0.0110165i
$628$	8.97682	+	5.18277i	0.358214	+	0.206815i
$629$	73.6242			2.93559
$630$	−3.04409	−	2.74641i	−0.121279	−	0.109420i
$631$	−11.0778			−0.441001			−0.220500	−	0.975387i	$-0.570769\pi$
$631$	−11.0778			−0.441001			−0.220500	+	0.975387i	$0.570769\pi$
$632$	−6.52112	−	3.76497i	−0.259396	−	0.149762i
$633$	−35.6964	−	5.35002i	−1.41881	−	0.212644i
$634$	5.64605	+	9.77925i	0.224233	+	0.388384i
$635$	0.578002	−	1.00113i	0.0229373	−	0.0397286i
$636$	19.7464	+	15.7204i	0.782997	+	0.623355i
$637$	−1.79005	−	0.652202i	−0.0709242	−	0.0258412i
$638$		−	2.76211i		−	0.109353i
$639$	−6.94366	+	22.6444i	−0.274687	+	0.895799i
$640$	12.1809	−	7.03262i	0.481491	−	0.277989i
$641$	35.9402	−	20.7501i	1.41955	−	0.819580i	0.423294	−	0.905992i	$-0.360874\pi$
$641$	35.9402	−	20.7501i	1.41955	−	0.819580i	0.996259	+	0.0864129i	$0.0275404\pi$
$642$	2.91547	+	7.41037i	0.115064	+	0.292464i
$643$			31.7613i			1.25254i	0.779605	+	0.626272i	$0.215420\pi$
$643$			31.7613i			1.25254i	−0.779605	+	0.626272i	$0.784580\pi$
$644$	10.4706	−	7.32901i	0.412601	−	0.288803i
$645$	−1.02969	+	1.29340i	−0.0405442	+	0.0509276i
$646$	−1.21989	+	2.11290i	−0.0479958	+	0.0831311i
$647$	5.21187	+	9.02722i	0.204900	+	0.354897i	0.950101	−	0.311943i	$-0.100980\pi$
$647$	5.21187	+	9.02722i	0.204900	+	0.354897i	−0.745201	+	0.666840i	$0.767647\pi$
$648$	6.88100	−	10.1651i	0.270311	−	0.399321i
$649$	10.3482	+	5.97454i	0.406203	+	0.234521i
$650$	−0.272447			−0.0106863
$651$	−14.2578	−	9.44896i	−0.558806	−	0.370334i
$652$	−1.60857			−0.0629965
$653$	31.1222	+	17.9684i	1.21790	+	0.703158i	0.964469	−	0.264195i	$-0.0851061\pi$
$653$	31.1222	+	17.9684i	1.21790	+	0.703158i	0.253435	+	0.967352i	$0.418439\pi$
$654$	0.171842	−	1.14657i	0.00671956	−	0.0448343i
$655$	−15.6922	−	27.1797i	−0.613146	−	1.06200i
$656$	13.0262	−	22.5620i	0.508586	−	0.880897i
$657$	−42.3543	+	9.74122i	−1.65240	+	0.380041i
$658$	−4.38784	−	2.04698i	−0.171056	−	0.0797994i
$659$			5.67538i			0.221081i	0.993872	+	0.110541i	$0.0352583\pi$
$659$			5.67538i			0.221081i	−0.993872	+	0.110541i	$0.964742\pi$
$660$	4.43931	−	1.74656i	0.172800	−	0.0679849i
$661$	−2.18609	+	1.26214i	−0.0850291	+	0.0490916i	−0.541912	−	0.840435i	$-0.682299\pi$
$661$	−2.18609	+	1.26214i	−0.0850291	+	0.0490916i	0.456883	+	0.889527i	$0.348966\pi$
$662$	−8.39651	+	4.84773i	−0.326340	+	0.188412i
$663$	−2.83077	+	1.11371i	−0.109938	+	0.0432531i
$664$			9.51910i			0.369413i
$665$	−3.78209	−	1.76439i	−0.146663	−	0.0684200i
$666$	11.7371	−	2.69946i	0.454804	−	0.104602i
$667$	10.1057	−	17.5036i	0.391295	−	0.677742i
$668$	−0.932526	−	1.61518i	−0.0360805	−	0.0624933i
$669$	1.18836	−	7.92898i	0.0459446	−	0.306552i
$670$	3.84821	+	2.22177i	0.148669	+	0.0858343i
$671$	5.57311			0.215148
$672$	14.8182	+	9.82040i	0.571626	+	0.378830i
$673$	−37.0969			−1.42998			−0.714991	−	0.699134i	$-0.753569\pi$
$673$	−37.0969			−1.42998			−0.714991	+	0.699134i	$0.753569\pi$
$674$	9.42305	+	5.44040i	0.362962	+	0.209556i
$675$	1.14149	+	14.7386i	0.0439358	+	0.567290i
$676$	−12.1258	−	21.0024i	−0.466375	−	0.807786i
$677$	21.1778	−	36.6810i	0.813929	−	1.40977i	−0.0961652	−	0.995365i	$-0.530658\pi$
$677$	21.1778	−	36.6810i	0.813929	−	1.40977i	0.910094	−	0.414401i	$-0.136009\pi$
$678$	−1.16524	+	1.46366i	−0.0447507	+	0.0562114i
$679$	−20.5147	+	14.3595i	−0.787284	+	0.551066i
$680$		−	12.9203i		−	0.495470i
$681$	−1.65080	−	4.19592i	−0.0632590	−	0.160788i
$682$	−1.13739	+	0.656671i	−0.0435528	+	0.0251452i
$683$	−6.46937	+	3.73509i	−0.247544	+	0.142919i	−0.618639	−	0.785675i	$-0.712316\pi$
$683$	−6.46937	+	3.73509i	−0.247544	+	0.142919i	0.371095	+	0.928595i	$0.378982\pi$
$684$	1.77306	−	5.78224i	0.0677946	−	0.221089i
$685$			3.44012i			0.131440i
$686$	6.29372	+	1.68978i	0.240295	+	0.0645162i
$687$	−0.778944	−	0.620128i	−0.0297186	−	0.0236594i
$688$	1.06387	−	1.84268i	0.0405597	−	0.0702515i
$689$	−1.05695	−	1.83068i	−0.0402664	−	0.0697435i
$690$	−2.27810	−	0.341431i	−0.0867257	−	0.0129981i
$691$	−20.6766	−	11.9376i	−0.786574	−	0.454128i	0.0521813	−	0.998638i	$-0.483383\pi$
$691$	−20.6766	−	11.9376i	−0.786574	−	0.454128i	−0.838755	+	0.544509i	$0.816716\pi$
$692$	14.0152			0.532777
$693$	5.89323	+	5.31694i	0.223865	+	0.201974i
$694$	1.44216			0.0547437
$695$	−3.26990	−	1.88788i	−0.124034	−	0.0716113i
$696$	18.3393	+	2.74861i	0.695149	+	0.104186i
$697$	−25.6863	−	44.4900i	−0.972938	−	1.68518i
$698$	5.70951	−	9.88916i	0.216108	−	0.374310i
$699$	−24.7627	−	19.7139i	−0.936612	−	0.745650i
$700$	−14.0686	+	1.22847i	−0.531743	+	0.0464318i
$701$		−	16.0718i		−	0.607025i	−0.952827	−	0.303512i	$-0.901841\pi$
$701$		−	16.0718i		−	0.607025i	0.952827	−	0.303512i	$-0.0981594\pi$
$702$	−0.410445	+	0.281339i	−0.0154912	+	0.0106185i
$703$	10.6170	−	6.12971i	0.400426	−	0.231186i
$704$	−4.48600	+	2.58999i	−0.169072	+	0.0976140i
$705$	−4.84163	−	12.3062i	−0.182346	−	0.463478i
$706$			1.56043i			0.0587274i
$707$	−2.45617	+	5.26498i	−0.0923739	+	0.198010i
$708$	−24.1851	+	30.3790i	−0.908933	+	1.14171i
$709$	22.4194	−	38.8316i	0.841979	−	1.45835i	−0.0462400	−	0.998930i	$-0.514724\pi$
$709$	22.4194	−	38.8316i	0.841979	−	1.45835i	0.888219	−	0.459420i	$-0.151943\pi$
$710$	2.03905	+	3.53174i	0.0765242	+	0.132544i
$711$	12.1226	−	11.2857i	0.454633	−	0.423247i
$712$	−7.40364	−	4.27449i	−0.277463	−	0.160193i
$713$	−9.61024			−0.359906
$714$	9.31460	−	4.63732i	0.348590	−	0.173547i
$715$	−0.399542			−0.0149420
$716$	16.3787	+	9.45622i	0.612099	+	0.353396i
$717$	5.63144	−	37.5741i	0.210310	−	1.40323i
$718$	−2.33174	−	4.03869i	−0.0870198	−	0.150723i
$719$	8.55503	−	14.8178i	0.319049	−	0.552609i	−0.661241	−	0.750174i	$-0.729970\pi$
$719$	8.55503	−	14.8178i	0.319049	−	0.552609i	0.980290	+	0.197565i	$0.0633033\pi$
$720$	3.23036	+	14.0454i	0.120388	+	0.523441i
$721$	1.19576	+	13.6939i	0.0445323	+	0.509989i
$722$		−	6.27916i		−	0.233686i
$723$	26.7204	−	10.5126i	0.993742	−	0.390969i
$724$	31.4508	−	18.1581i	1.16886	−	0.674841i
$725$	−19.3406	+	11.1663i	−0.718292	+	0.414706i
$726$	0.567132	−	0.223127i	0.0210483	−	0.00828104i
$727$			48.6343i			1.80375i	0.432001	+	0.901873i	$0.357808\pi$
$727$			48.6343i			1.80375i	−0.432001	+	0.901873i	$0.642192\pi$
$728$	−0.563183	−	0.804596i	−0.0208730	−	0.0298203i
$729$	16.9393	+	21.0252i	0.627383	+	0.778711i
$730$	−3.74148	+	6.48043i	−0.138478	+	0.239851i
$731$	−2.09785	−	3.63359i	−0.0775918	−	0.134393i
$732$	−2.68437	+	17.9107i	−0.0992172	+	0.661998i
$733$	−2.03822	−	1.17676i	−0.0752832	−	0.0434648i	0.461886	−	0.886939i	$-0.347173\pi$
$733$	−2.03822	−	1.17676i	−0.0752832	−	0.0434648i	−0.537169	+	0.843475i	$0.680506\pi$
$734$	6.54814			0.241696
$735$	9.28840	+	15.1828i	0.342608	+	0.560027i
$736$	9.98802			0.368163
$737$	−7.44998	−	4.30125i	−0.274423	−	0.158438i
$738$	−5.72614	−	6.15077i	−0.210782	−	0.226413i
$739$	16.9541	+	29.3654i	0.623666	+	1.08022i	0.988797	+	0.149266i	$0.0476910\pi$
$739$	16.9541	+	29.3654i	0.623666	+	1.08022i	−0.365131	+	0.930956i	$0.618976\pi$
$740$	−15.7121	+	27.2142i	−0.577588	+	1.00041i
$741$	−0.315487	+	0.396284i	−0.0115897	+	0.0145579i
$742$	4.14631	+	5.92365i	0.152216	+	0.217464i
$743$		−	20.8218i		−	0.763876i	−0.924188	−	0.381938i	$-0.875257\pi$
$743$		−	20.8218i		−	0.763876i	0.924188	−	0.381938i	$-0.124743\pi$
$744$	−3.22821	−	8.20527i	−0.118352	−	0.300820i
$745$	−10.8696	+	6.27555i	−0.398231	+	0.229919i
$746$	10.3643	−	5.98385i	0.379465	−	0.219084i
$747$	−20.0181	−	6.13833i	−0.732424	−	0.224590i
$748$			12.1071i			0.442679i
$749$	−3.00725	−	34.4393i	−0.109882	−	1.25839i
$750$	5.49105	+	4.37150i	0.200505	+	0.159625i
$751$	−0.262883	+	0.455327i	−0.00959275	+	0.0166151i	−0.870782	−	0.491669i	$-0.836387\pi$
$751$	−0.262883	+	0.455327i	−0.00959275	+	0.0166151i	0.861189	+	0.508285i	$0.169720\pi$
$752$	8.51004	+	14.7398i	0.310329	+	0.537506i
$753$	−23.4689	−	3.51741i	−0.855253	−	0.128181i
$754$	−0.651035	−	0.375875i	−0.0237093	−	0.0136886i
$755$	8.71643			0.317224
$756$	−19.9260	+	16.3785i	−0.724700	+	0.595679i
$757$	−13.7127			−0.498395			−0.249198	−	0.968453i	$-0.580167\pi$
$757$	−13.7127			−0.498395			−0.249198	+	0.968453i	$0.580167\pi$
$758$	−4.94734	−	2.85635i	−0.179695	−	0.103747i
$759$	4.41030	+	0.660996i	0.160084	+	0.0239926i
$760$	−1.07570	−	1.86317i	−0.0390197	−	0.0675842i
$761$	−7.51905	+	13.0234i	−0.272565	+	0.472097i	−0.969518	−	0.245020i	$-0.921205\pi$
$761$	−7.51905	+	13.0234i	−0.272565	+	0.472097i	0.696953	+	0.717117i	$0.254539\pi$
$762$	0.375463	+	0.298911i	0.0136016	+	0.0108284i
$763$	−2.12785	+	4.56119i	−0.0770333	+	0.165126i
$764$			43.1550i			1.56129i
$765$	27.1706	+	8.33155i	0.982354	+	0.301228i
$766$	−9.03863	+	5.21846i	−0.326579	+	0.188551i
$767$	2.81642	−	1.62606i	0.101695	−	0.0587137i
$768$	−4.43175	−	11.2644i	−0.159917	−	0.406467i
$769$		−	18.0955i		−	0.652539i	−0.945277	−	0.326270i	$-0.894208\pi$
$769$		−	18.0955i		−	0.652539i	0.945277	−	0.326270i	$-0.105792\pi$
$770$	1.36146	−	0.118882i	0.0490635	−	0.00428423i
$771$	−9.21457	+	11.5744i	−0.331854	+	0.416843i
$772$	7.26795	−	12.5885i	0.261579	−	0.453069i
$773$	22.4346	+	38.8579i	0.806917	+	1.39762i	0.914989	+	0.403478i	$0.132199\pi$
$773$	22.4346	+	38.8579i	0.806917	+	1.39762i	−0.108073	+	0.994143i	$0.534468\pi$
$774$	−0.467665	−	0.502345i	−0.0168099	−	0.0180564i
$775$	9.19618	+	5.30942i	0.330337	+	0.190720i
$776$	−12.9087			−0.463395
$777$	−52.1845	−	3.22225i	−1.87211	−	0.115598i
$778$	6.69815			0.240140
$779$	−7.40819	−	4.27712i	−0.265426	−	0.153244i
$780$	0.192445	−	1.28403i	0.00689064	−	0.0459758i
$781$	−3.94752	−	6.83730i	−0.141253	−	0.244658i
$782$	2.92307	−	5.06290i	0.104529	−	0.181049i
$783$	−17.6061	+	36.7940i	−0.629192	+	1.31491i
$784$	−14.7187	−	17.5530i	−0.525667	−	0.626892i
$785$			8.11043i			0.289474i
$786$	12.1247	−	4.77022i	0.432473	−	0.170148i
$787$	21.9515	−	12.6737i	0.782486	−	0.451768i	−0.0548247	−	0.998496i	$-0.517460\pi$
$787$	21.9515	−	12.6737i	0.782486	−	0.451768i	0.837311	+	0.546728i	$0.184127\pi$
$788$	37.8890	−	21.8752i	1.34974	−	0.779273i
$789$	15.8799	−	6.24763i	0.565338	−	0.222422i
$790$		−	2.85177i		−	0.101462i
$791$	6.65376	−	4.65736i	0.236581	−	0.165597i
$792$	0.917117	+	3.98757i	0.0325883	+	0.141692i
$793$	0.758405	−	1.31360i	0.0269317	−	0.0466471i
$794$	−3.98738	−	6.90634i	−0.141507	−	0.245097i
$795$	−2.92716	+	19.5306i	−0.103816	+	0.692679i
$796$	13.3426	+	7.70334i	0.472915	+	0.273038i
$797$	38.3992			1.36017			0.680086	−	0.733133i	$-0.261943\pi$
$797$	38.3992			1.36017			0.680086	+	0.733133i	$0.261943\pi$
$798$	0.957123	−	1.44423i	0.0338818	−	0.0511251i
$799$	33.5619			1.18734
$800$	−9.55769	−	5.51813i	−0.337915	−	0.195095i
$801$	13.7632	−	12.8130i	0.486298	−	0.452726i
$802$	−3.76433	−	6.52000i	−0.132923	−	0.230229i
$803$	7.24334	−	12.5458i	0.255612	−	0.442733i
$804$	17.4116	−	21.8707i	0.614059	−	0.771321i
$805$	9.06257	+	4.22779i	0.319414	+	0.149010i
$806$			0.357447i			0.0125905i
$807$	−7.27296	−	18.4860i	−0.256020	−	0.650738i
$808$	−2.59368	+	1.49746i	−0.0912454	+	0.0526806i
$809$	−3.31977	+	1.91667i	−0.116717	+	0.0673866i	−0.557222	−	0.830364i	$-0.688133\pi$
$809$	−3.31977	+	1.91667i	−0.116717	+	0.0673866i	0.440505	+	0.897750i	$0.354799\pi$
$810$	4.63699	+	0.331989i	0.162927	+	0.0116649i
$811$		−	24.8542i		−	0.872750i	−0.899765	−	0.436375i	$-0.856262\pi$
$811$		−	24.8542i		−	0.872750i	0.899765	−	0.436375i	$-0.143738\pi$
$812$	−35.3129	−	16.4739i	−1.23924	−	0.578120i
$813$	4.40426	+	3.50629i	0.154464	+	0.122971i
$814$	−2.00726	+	3.47667i	−0.0703543	+	0.121857i
$815$	−0.629307	−	1.08999i	−0.0220437	−	0.0381807i
$816$	−36.1723	−	5.42134i	−1.26628	−	0.189785i
$817$	−0.605041	−	0.349321i	−0.0211677	−	0.0122212i
$818$	−9.47127			−0.331155
$819$	2.05518	−	0.665503i	0.0718139	−	0.0232546i
$820$	21.9268			0.765718
$821$	16.0917	+	9.29058i	0.561606	+	0.324243i	0.753790	−	0.657116i	$-0.228224\pi$
$821$	16.0917	+	9.29058i	0.561606	+	0.324243i	−0.192184	+	0.981359i	$0.561557\pi$
$822$	−1.41240	−	0.211684i	−0.0492630	−	0.00738332i
$823$	1.88720	+	3.26873i	0.0657836	+	0.113941i	0.897041	−	0.441947i	$-0.145712\pi$
$823$	1.88720	+	3.26873i	0.0657836	+	0.113941i	−0.831258	+	0.555887i	$0.812379\pi$
$824$	−3.54307	+	6.13677i	−0.123429	+	0.213785i
$825$	−3.85510	−	3.06910i	−0.134217	−	0.106852i
$826$	−9.11326	+	6.37890i	−0.317091	+	0.221950i
$827$		−	2.66414i		−	0.0926413i	−0.998927	−	0.0463206i	$-0.985250\pi$
$827$		−	2.66414i		−	0.0926413i	0.998927	−	0.0463206i	$-0.0147496\pi$
$828$	−4.24857	+	13.8553i	−0.147648	+	0.481505i
$829$	18.7354	−	10.8169i	0.650707	−	0.375686i	−0.138020	−	0.990429i	$-0.544074\pi$
$829$	18.7354	−	10.8169i	0.650707	−	0.375686i	0.788727	+	0.614743i	$0.210740\pi$
$830$	−3.12213	+	1.80256i	−0.108371	+	0.0625678i
$831$	−1.87653	−	4.76966i	−0.0650961	−	0.165458i
$832$			1.40981i			0.0488765i
$833$	−44.4874	+	7.82899i	−1.54140	+	0.271258i
$834$	0.976307	−	1.22634i	0.0338068	−	0.0424647i
$835$	0.729647	−	1.26379i	0.0252505	−	0.0437351i
$836$	1.00800	+	1.74590i	0.0348623	+	0.0603833i
$837$	19.3369	−	1.49761i	0.668380	−	0.0517651i
$838$	5.67297	+	3.27529i	0.195970	+	0.113143i
$839$	−38.6192			−1.33328			−0.666641	−	0.745379i	$-0.732269\pi$
$839$	−38.6192			−1.33328			−0.666641	+	0.745379i	$0.732269\pi$
$840$	−0.565471	+	9.15783i	−0.0195106	+	0.315975i
$841$	−32.6213			−1.12487
$842$	9.94784	+	5.74339i	0.342825	+	0.197930i
$843$	−1.97235	+	13.1599i	−0.0679312	+	0.453251i
$844$	19.5495	+	33.8607i	0.672921	+	1.16553i
$845$	9.48770	−	16.4332i	0.326387	−	0.565318i
$846$	5.35042	−	1.23056i	0.183951	−	0.0423076i
$847$	−2.63572	+	0.230151i	−0.0905645	+	0.00790810i
$848$		−	25.4171i		−	0.872828i
$849$	23.8136	−	9.36901i	0.817280	−	0.321543i
$850$	−5.59425	+	3.22984i	−0.191881	+	0.110783i
$851$	−25.4402	+	14.6879i	−0.872078	+	0.503494i
$852$	23.8749	−	9.39311i	0.817939	−	0.321803i
$853$		−	13.4419i		−	0.460244i	−0.973162	−	0.230122i	$-0.926088\pi$
$853$		−	13.4419i		−	0.460244i	0.973162	−	0.230122i	$-0.0739124\pi$
$854$	−2.19344	+	4.70180i	−0.0750580	+	0.160892i
$855$	4.61179	−	1.06068i	0.157720	−	0.0362746i
$856$	8.91057	−	15.4336i	0.304557	−	0.527508i
$857$	−20.4075	−	35.3468i	−0.697106	−	1.20742i	−0.969466	−	0.245227i	$-0.921138\pi$
$857$	−20.4075	−	35.3468i	−0.697106	−	1.20742i	0.272360	−	0.962195i	$-0.412196\pi$
$858$	0.0245853	−	0.164038i	0.000839328	−	0.00560017i
$859$	12.9076	+	7.45222i	0.440402	+	0.254266i	0.703768	−	0.710430i	$-0.251499\pi$
$859$	12.9076	+	7.45222i	0.440402	+	0.254266i	−0.263366	+	0.964696i	$0.584833\pi$
$860$	1.79081			0.0610660
$861$	16.2592	+	32.6585i	0.554112	+	1.11300i
$862$	−4.91256			−0.167323
$863$	−6.04993	−	3.49293i	−0.205942	−	0.118901i	0.393482	−	0.919332i	$-0.371270\pi$
$863$	−6.04993	−	3.49293i	−0.205942	−	0.118901i	−0.599424	+	0.800432i	$0.704604\pi$
$864$	−20.0970	+	1.55649i	−0.683714	+	0.0529527i
$865$	5.48303	+	9.49689i	0.186429	+	0.322904i
$866$	−4.45169	+	7.71055i	−0.151274	+	0.262015i
$867$	−26.5828	+	33.3907i	−0.902800	+	1.13401i
$868$	1.61174	+	18.4578i	0.0547059	+	0.626498i
$869$			5.52092i			0.187284i
$870$	2.57127	+	6.53551i	0.0871742	+	0.221574i
$871$	−2.02763	+	1.17065i	−0.0687035	+	0.0396660i
$872$	−2.24698	+	1.29729i	−0.0760922	+	0.0439318i
$873$	8.32408	−	27.1462i	0.281727	−	0.918759i
$874$		−	0.973460i		−	0.0329278i
$875$	−17.4725	−	24.9622i	−0.590679	−	0.843878i
$876$	36.8305	+	29.3213i	1.24439	+	0.990674i
$877$	−17.2309	+	29.8448i	−0.581847	+	1.00779i	0.413413	+	0.910543i	$0.364336\pi$
$877$	−17.2309	+	29.8448i	−0.581847	+	1.00779i	−0.995260	+	0.0972452i	$0.968997\pi$
$878$	4.56407	+	7.90520i	0.154030	+	0.266788i
$879$	1.11049	+	0.166435i	0.0374559	+	0.00561372i
$880$	−4.16041	−	2.40202i	−0.140248	−	0.0809719i
$881$	−41.1161			−1.38524			−0.692618	−	0.721305i	$-0.743543\pi$
$881$	−41.1161			−1.38524			−0.692618	+	0.721305i	$0.743543\pi$
$882$	−6.80510	+	2.87924i	−0.229140	+	0.0969492i
$883$	14.7920			0.497791			0.248895	−	0.968530i	$-0.419932\pi$
$883$	14.7920			0.497791			0.248895	+	0.968530i	$0.419932\pi$
$884$	2.85367	+	1.64757i	0.0959792	+	0.0554136i
$885$	−30.0469	−	4.50330i	−1.01002	−	0.151377i
$886$	0.665045	+	1.15189i	0.0223426	+	0.0386985i
$887$	−18.0677	+	31.2941i	−0.606653	+	1.05075i	0.385135	+	0.922860i	$0.374155\pi$
$887$	−18.0677	+	31.2941i	−0.606653	+	1.05075i	−0.991788	+	0.127894i	$0.959178\pi$
$888$	−21.0863	−	16.7871i	−0.707609	−	0.563337i
$889$	−1.19472	−	1.70685i	−0.0400697	−	0.0572458i
$890$		−	3.23771i		−	0.108528i
$891$	−8.97702	−	0.642717i	−0.300742	−	0.0215318i
$892$	−7.52122	+	4.34238i	−0.251829	+	0.145394i
$893$	4.83980	−	2.79426i	0.161958	−	0.0935063i
$894$	−1.90768	−	4.84884i	−0.0638024	−	0.162169i
$895$			14.7979i			0.494639i
$896$	−2.20512	−	25.2533i	−0.0736678	−	0.843653i
$897$	0.755964	−	0.949568i	0.0252409	−	0.0317051i
$898$	−4.55097	+	7.88252i	−0.151868	+	0.263043i
$899$	14.6500	+	25.3746i	0.488606	+	0.846290i
$900$	11.7202	−	10.9111i	0.390674	−	0.363703i
$901$	−43.4053	−	25.0601i	−1.44604	−	0.834872i
$902$	2.80120			0.0932698
$903$	1.32792	+	2.66728i	0.0441904	+	0.0887617i
$904$	4.18681			0.139251
$905$	24.6084	+	14.2077i	0.818010	+	0.472278i
$906$	−0.536355	+	3.57867i	−0.0178192	+	0.118893i
$907$	14.5435	+	25.1901i	0.482909	+	0.836423i	0.999807	−	0.0196238i	$-0.00624684\pi$
$907$	14.5435	+	25.1901i	0.482909	+	0.836423i	−0.516898	+	0.856047i	$0.672914\pi$
$908$	−2.44211	+	4.22985i	−0.0810442	+	0.140373i
$909$	−1.47656	−	6.41999i	−0.0489743	−	0.212938i
$910$	0.157250	−	0.337076i	0.00521278	−	0.0111740i
$911$		−	27.1032i		−	0.897969i	−0.893540	−	0.448984i	$-0.851786\pi$
$911$		−	27.1032i		−	0.897969i	0.893540	−	0.448984i	$-0.148214\pi$
$912$	−5.66759	+	2.22980i	−0.187673	+	0.0738362i
$913$	6.04430	−	3.48968i	0.200037	−	0.115492i
$914$	−7.85764	+	4.53661i	−0.259908	+	0.150058i
$915$	−13.1867	+	5.18806i	−0.435939	+	0.171512i
$916$			1.07850i			0.0356348i
$917$	−56.3489	+	4.92039i	−1.86080	+	0.162485i
$918$	−5.09256	+	10.6426i	−0.168079	+	0.351259i
$919$	−19.6999	+	34.1212i	−0.649839	+	1.12555i	0.333322	+	0.942813i	$0.391830\pi$
$919$	−19.6999	+	34.1212i	−0.649839	+	1.12555i	−0.983161	+	0.182741i	$0.941503\pi$
$920$	2.57757	+	4.46449i	0.0849800	+	0.147190i
$921$	7.28407	−	48.6008i	0.240018	−	1.60145i
$922$	−2.54217	−	1.46772i	−0.0837219	−	0.0483369i
$923$	−2.14876			−0.0707272
$924$	0.529881	−	8.58145i	0.0174318	−	0.282309i
$925$	32.4588			1.06724
$926$	−1.97323	−	1.13924i	−0.0648443	−	0.0374379i
$927$	−10.6205	−	11.4081i	−0.348824	−	0.374692i
$928$	−15.2259	−	26.3721i	−0.499816	−	0.865706i
$929$	−26.1579	+	45.3069i	−0.858214	+	1.48647i	0.0154163	+	0.999881i	$0.495093\pi$
$929$	−26.1579	+	45.3069i	−0.858214	+	1.48647i	−0.873631	+	0.486590i	$0.838241\pi$
$930$	2.07991	−	2.61257i	0.0682028	−	0.0856697i
$931$	−5.76349	+	4.83286i	−0.188891	+	0.158391i
$932$			34.2858i			1.12307i
$933$	−15.5225	−	39.4543i	−0.508185	−	1.29168i
$934$	5.94600	−	3.43292i	0.194559	−	0.112329i
$935$	−8.20393	+	4.73654i	−0.268297	+	0.154902i
$936$	1.06468	+	0.326473i	0.0348003	+	0.0106711i
$937$			55.1711i			1.80236i	0.433443	+	0.901181i	$0.357298\pi$
$937$			55.1711i			1.80236i	−0.433443	+	0.901181i	$0.642702\pi$
$938$	6.56090	−	4.59236i	0.214221	−	0.149946i
$939$	21.5756	+	17.1766i	0.704092	+	0.560538i
$940$	−7.16244	+	12.4057i	−0.233613	+	0.404630i
$941$	−18.9439	−	32.8118i	−0.617553	−	1.06963i	−0.989931	−	0.141552i	$-0.954791\pi$
$941$	−18.9439	−	32.8118i	−0.617553	−	1.06963i	0.372378	−	0.928081i	$-0.378542\pi$
$942$	−3.32986	−	0.499065i	−0.108493	−	0.0162604i
$943$	17.7514	+	10.2487i	0.578064	+	0.333745i
$944$	39.1031			1.27270
$945$	−18.8937	−	7.09452i	−0.614613	−	0.230785i
$946$	0.228780			0.00743827
$947$	19.9736	+	11.5317i	0.649053	+	0.374731i	0.788093	−	0.615556i	$-0.211068\pi$
$947$	19.9736	+	11.5317i	0.649053	+	0.374731i	−0.139040	+	0.990287i	$0.544402\pi$
$948$	−17.7429	−	2.65923i	−0.576263	−	0.0863677i
$949$	−1.97139	−	3.41454i	−0.0639939	−	0.110841i
$950$	−0.537812	+	0.931518i	−0.0174489	+	0.0302224i
$951$	43.4872	+	34.6208i	1.41017	+	1.12266i
$952$	−21.1025	−	9.84455i	−0.683935	−	0.319064i
$953$		−	17.7216i		−	0.574058i	−0.957922	−	0.287029i	$-0.907332\pi$
$953$		−	17.7216i		−	0.574058i	0.957922	−	0.287029i	$-0.0926676\pi$
$954$	−7.83848	−	2.40358i	−0.253780	−	0.0778189i
$955$	−29.2424	+	16.8831i	−0.946262	+	0.546325i
$956$	−35.6418	+	20.5778i	−1.15274	+	0.665534i
$957$	−4.97787	−	12.6525i	−0.160912	−	0.408996i
$958$			8.60316i			0.277956i
$959$	5.61870	+	2.62119i	0.181437	+	0.0846426i
$960$	8.20341	−	10.3043i	0.264764	−	0.332570i
$961$	−8.53412	+	14.7815i	−0.275294	+	0.476824i
$962$	0.546306	+	0.946230i	0.0176136	+	0.0305077i
$963$	26.7099	+	28.6906i	0.860716	+	0.924543i
$964$	−26.9365	−	15.5518i	−0.867566	−	0.500890i
$965$	11.3735			0.366126
$966$	−2.29344	+	3.46063i	−0.0737902	+	0.111344i
$967$	−40.9164			−1.31578			−0.657892	−	0.753112i	$-0.728552\pi$
$967$	−40.9164			−1.31578			−0.657892	+	0.753112i	$0.728552\pi$
$968$	−1.18117	−	0.681946i	−0.0379641	−	0.0219186i
$969$	−1.78009	+	11.8771i	−0.0571847	+	0.381548i
$970$	−2.44442	−	4.23386i	−0.0784856	−	0.135941i
$971$	19.3208	−	33.4647i	0.620036	−	1.07393i	−0.369443	−	0.929253i	$-0.620451\pi$
$971$	19.3208	−	33.4647i	0.620036	−	1.07393i	0.989479	−	0.144680i	$-0.0462152\pi$
$972$	6.38945	−	28.5405i	0.204942	−	0.915436i
$973$	−5.57493	+	3.90222i	−0.178724	+	0.125099i
$974$			8.57676i			0.274817i
$975$	−1.24801	+	0.491004i	−0.0399682	+	0.0157247i
$976$	15.7945	−	9.11895i	0.505569	−	0.291890i
$977$	−32.3036	+	18.6505i	−1.03348	+	0.596683i	−0.917981	−	0.396624i	$-0.870182\pi$
$977$	−32.3036	+	18.6505i	−1.03348	+	0.596683i	−0.115504	+	0.993307i	$0.536848\pi$
$978$	0.486237	−	0.191301i	0.0155481	−	0.00611712i
$979$			6.26808i			0.200329i
$980$	6.60017	−	18.1150i	0.210835	−	0.578661i
$981$	−1.27918	−	5.56180i	−0.0408411	−	0.177575i
$982$	6.95378	−	12.0443i	0.221904	−	0.384349i
$983$	−17.1356	−	29.6797i	−0.546541	−	0.946637i	−0.998508	−	0.0546022i	$-0.982611\pi$
$983$	−17.1356	−	29.6797i	−0.546541	−	0.946637i	0.451967	−	0.892035i	$-0.350722\pi$
$984$	−2.78751	+	18.5989i	−0.0888627	+	0.592910i
$985$	29.6460	+	17.1161i	0.944599	+	0.545364i
$986$	−17.8239			−0.567629
$987$	−23.7886	−	1.46888i	−0.757198	−	0.0467549i
$988$	0.548684			0.0174560
$989$	1.44979	+	0.837035i	0.0461006	+	0.0266162i
$990$	−1.13420	+	1.05590i	−0.0360472	+	0.0335586i
$991$	−10.9316	−	18.9341i	−0.347253	−	0.601460i	0.638507	−	0.769616i	$-0.279552\pi$
$991$	−10.9316	−	18.9341i	−0.347253	−	0.601460i	−0.985760	+	0.168156i	$0.946219\pi$
$992$	−7.23971	+	12.5395i	−0.229861	+	0.398131i
$993$	−29.7256	+	37.3383i	−0.943312	+	1.18490i
$994$	7.32198	−	0.639356i	0.232239	−	0.0202791i
$995$			12.0548i			0.382164i
$996$	8.30369	+	21.1058i	0.263112	+	0.668764i
$997$	−22.2108	+	12.8234i	−0.703424	+	0.406122i	−0.808621	−	0.588329i	$-0.799786\pi$
$997$	−22.2108	+	12.8234i	−0.703424	+	0.406122i	0.105197	+	0.994451i	$0.466453\pi$
$998$	−1.32915	+	0.767383i	−0.0420734	+	0.0242911i
$999$	48.8996	−	33.5181i	1.54711	−	1.06047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.14	yes	52
3.2	odd	2	inner	231.2.n.a.89.13	✓	52
7.3	odd	6	inner	231.2.n.a.122.13	yes	52
21.17	even	6	inner	231.2.n.a.122.14	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.13	✓	52	3.2	odd	2	inner
231.2.n.a.89.14	yes	52	1.1	even	1	trivial
231.2.n.a.122.13	yes	52	7.3	odd	6	inner
231.2.n.a.122.14	yes	52	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.304723 + 0.175932i) q^{2} +(1.71292 + 0.256725i) q^{3} +(-0.938096 - 1.62483i) q^{4} +(0.734005 - 1.27133i) q^{5} +(0.476800 + 0.379587i) q^{6} +(-1.51718 - 2.16753i) q^{7} -1.36389i q^{8} +(2.86818 + 0.879497i) q^{9} +O(q^{10})\)	\(q+(0.304723 + 0.175932i) q^{2} +(1.71292 + 0.256725i) q^{3} +(-0.938096 - 1.62483i) q^{4} +(0.734005 - 1.27133i) q^{5} +(0.476800 + 0.379587i) q^{6} +(-1.51718 - 2.16753i) q^{7} -1.36389i q^{8} +(2.86818 + 0.879497i) q^{9} +(0.447337 - 0.258270i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.18975 - 3.02403i) q^{12} +0.272166i q^{13} +(-0.0809820 - 0.927416i) q^{14} +(1.58367 - 1.98926i) q^{15} +(-1.63624 + 2.83405i) q^{16} +(3.22650 + 5.58847i) q^{17} +(0.719271 + 0.772609i) q^{18} +(0.930556 + 0.537257i) q^{19} -2.75427 q^{20} +(-2.04235 - 4.10229i) q^{21} -0.351864 q^{22} +(-2.22978 - 1.28736i) q^{23} +(0.350145 - 2.33624i) q^{24} +(1.42247 + 2.46380i) q^{25} +(-0.0478826 + 0.0829352i) q^{26} +(4.68718 + 2.24284i) q^{27} +(-2.09860 + 4.49850i) q^{28} +7.84993i q^{29} +(0.832556 - 0.327553i) q^{30} +(3.23246 - 1.86626i) q^{31} +(-3.35953 + 1.93963i) q^{32} +(-1.61179 + 0.634130i) q^{33} +2.27058i q^{34} +(-3.86927 + 0.337865i) q^{35} +(-1.26160 - 5.48536i) q^{36} +(5.70464 - 9.88072i) q^{37} +(0.189041 + 0.327429i) q^{38} +(-0.0698716 + 0.466198i) q^{39} +(-1.73396 - 1.00110i) q^{40} -7.96103 q^{41} +(0.0993748 - 1.60938i) q^{42} -0.650193 q^{43} +(1.62483 + 0.938096i) q^{44} +(3.22340 - 3.00087i) q^{45} +(-0.452977 - 0.784580i) q^{46} +(2.60049 - 4.50418i) q^{47} +(-3.53032 + 4.43443i) q^{48} +(-2.39634 + 6.57705i) q^{49} +1.00103i q^{50} +(4.09204 + 10.4009i) q^{51} +(0.442223 - 0.255317i) q^{52} +(-6.72637 + 3.88347i) q^{53} +(1.03371 + 1.50807i) q^{54} +1.46801i q^{55} +(-2.95627 + 2.06927i) q^{56} +(1.45604 + 1.15917i) q^{57} +(-1.38105 + 2.39206i) q^{58} +(-5.97454 - 10.3482i) q^{59} +(-4.71784 - 0.707088i) q^{60} +(-4.82646 - 2.78656i) q^{61} +1.31334 q^{62} +(-2.44521 - 7.55122i) q^{63} +5.17999 q^{64} +(0.346013 + 0.199771i) q^{65} +(-0.602715 - 0.0903322i) q^{66} +(4.30125 + 7.44998i) q^{67} +(6.05354 - 10.4850i) q^{68} +(-3.48894 - 2.77759i) q^{69} +(-1.23850 - 0.577773i) q^{70} +7.89503i q^{71} +(1.19954 - 3.91190i) q^{72} +(-12.5458 + 7.24334i) q^{73} +(3.47667 - 2.00726i) q^{74} +(1.80406 + 4.58547i) q^{75} -2.01599i q^{76} +(2.39768 + 1.11854i) q^{77} +(-0.103311 + 0.129769i) q^{78} +(2.76046 - 4.78125i) q^{79} +(2.40202 + 4.16041i) q^{80} +(7.45297 + 5.04512i) q^{81} +(-2.42591 - 1.40060i) q^{82} -6.97936 q^{83} +(-4.74961 + 7.16681i) q^{84} +9.47309 q^{85} +(-0.198129 - 0.114390i) q^{86} +(-2.01527 + 13.4463i) q^{87} +(0.681946 + 1.18117i) q^{88} +(3.13404 - 5.42832i) q^{89} +(1.51019 - 0.347335i) q^{90} +(0.589926 - 0.412924i) q^{91} +4.83068i q^{92} +(6.01606 - 2.36691i) q^{93} +(1.58486 - 0.915018i) q^{94} +(1.36607 - 0.788698i) q^{95} +(-6.25256 + 2.45995i) q^{96} -9.46459i q^{97} +(-1.88733 + 1.58259i) q^{98} +(-2.92367 + 0.672426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

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