LMFDB - Embedded newform 231.2.n.a.89.19

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			89.19
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14233 + 0.659525i) q^{2} +(-1.64912 - 0.529528i) q^{3} +(-0.130055 - 0.225261i) q^{4} +(0.422862 - 0.732419i) q^{5} +(-1.53460 - 1.69253i) q^{6} +(-0.990003 - 2.45355i) q^{7} -2.98120i q^{8} +(2.43920 + 1.74651i) q^{9} +O(q^{10})$	\(q+(1.14233 + 0.659525i) q^{2} +(-1.64912 - 0.529528i) q^{3} +(-0.130055 - 0.225261i) q^{4} +(0.422862 - 0.732419i) q^{5} +(-1.53460 - 1.69253i) q^{6} +(-0.990003 - 2.45355i) q^{7} -2.98120i q^{8} +(2.43920 + 1.74651i) q^{9} +(0.966096 - 0.557776i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.0951936 + 0.440350i) q^{12} -3.39294i q^{13} +(0.487264 - 3.45569i) q^{14} +(-1.08519 + 0.983930i) q^{15} +(1.70606 - 2.95499i) q^{16} +(2.38249 + 4.12660i) q^{17} +(1.63450 + 3.60381i) q^{18} +(-5.64791 - 3.26082i) q^{19} -0.219981 q^{20} +(0.333413 + 4.57043i) q^{21} +1.31905 q^{22} +(5.32135 + 3.07228i) q^{23} +(-1.57863 + 4.91635i) q^{24} +(2.14238 + 3.71070i) q^{25} +(2.23773 - 3.87586i) q^{26} +(-3.09771 - 4.17183i) q^{27} +(-0.423934 + 0.542104i) q^{28} -2.17818i q^{29} +(-1.88857 + 0.408265i) q^{30} +(-3.76047 + 2.17111i) q^{31} +(-1.26581 + 0.730815i) q^{32} +(-1.69294 + 0.365976i) q^{33} +6.28525i q^{34} +(-2.21566 - 0.312415i) q^{35} +(0.0761920 - 0.776599i) q^{36} +(-0.892063 + 1.54510i) q^{37} +(-4.30118 - 7.44987i) q^{38} +(-1.79666 + 5.59537i) q^{39} +(-2.18348 - 1.26063i) q^{40} +2.64903 q^{41} +(-2.63344 + 5.44083i) q^{42} +10.5181 q^{43} +(-0.225261 - 0.130055i) q^{44} +(2.31062 - 1.04798i) q^{45} +(4.05249 + 7.01912i) q^{46} +(0.000610157 - 0.00105682i) q^{47} +(-4.37825 + 3.96972i) q^{48} +(-5.03979 + 4.85804i) q^{49} +5.65180i q^{50} +(-1.74387 - 8.06685i) q^{51} +(-0.764298 + 0.441268i) q^{52} +(0.207291 - 0.119679i) q^{53} +(-0.787180 - 6.80863i) q^{54} -0.845724i q^{55} +(-7.31450 + 2.95139i) q^{56} +(7.58739 + 8.36822i) q^{57} +(1.43656 - 2.48820i) q^{58} +(3.95668 + 6.85317i) q^{59} +(0.362775 + 0.116486i) q^{60} +(6.25792 + 3.61301i) q^{61} -5.72759 q^{62} +(1.87033 - 7.71374i) q^{63} -8.75221 q^{64} +(-2.48505 - 1.43475i) q^{65} +(-2.17527 - 0.698474i) q^{66} +(-2.33660 - 4.04712i) q^{67} +(0.619708 - 1.07337i) q^{68} +(-7.14869 - 7.88437i) q^{69} +(-2.32497 - 1.81816i) q^{70} -15.7429i q^{71} +(5.20669 - 7.27173i) q^{72} +(13.8849 - 8.01645i) q^{73} +(-2.03806 + 1.17668i) q^{74} +(-1.56811 - 7.25385i) q^{75} +1.69634i q^{76} +(-2.08414 - 1.62983i) q^{77} +(-5.74266 + 5.20682i) q^{78} +(-4.61451 + 7.99256i) q^{79} +(-1.44286 - 2.49910i) q^{80} +(2.89939 + 8.52018i) q^{81} +(3.02607 + 1.74710i) q^{82} +7.22472 q^{83} +(0.986178 - 0.669510i) q^{84} +4.02986 q^{85} +(12.0152 + 6.93695i) q^{86} +(-1.15341 + 3.59208i) q^{87} +(-1.49060 - 2.58179i) q^{88} +(0.713428 - 1.23569i) q^{89} +(3.33066 + 0.326771i) q^{90} +(-8.32474 + 3.35902i) q^{91} -1.59826i q^{92} +(7.35113 - 1.58914i) q^{93} +(0.00139400 - 0.000804826i) q^{94} +(-4.77657 + 2.75776i) q^{95} +(2.47446 - 0.534921i) q^{96} +6.92343i q^{97} +(-8.96110 + 2.22562i) q^{98} +(2.98567 + 0.292923i) 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 $

$2$	1.14233	+	0.659525i	0.807749	+	0.466354i	0.846174	−	0.532907i	$-0.178901\pi$
$2$	1.14233	+	0.659525i	0.807749	+	0.466354i	−0.0384243	+	0.999262i	$0.512234\pi$
$3$	−1.64912	−	0.529528i	−0.952120	−	0.305723i
$3$	−1.64912	−	0.529528i	−0.952120	−	0.305723i
$4$	−0.130055	−	0.225261i	−0.0650273	−	0.112631i
$5$	0.422862	−	0.732419i	0.189110	−	0.327548i	−0.755844	−	0.654752i	$-0.772773\pi$
$5$	0.422862	−	0.732419i	0.189110	−	0.327548i	0.944954	+	0.327204i	$0.106106\pi$
$6$	−1.53460	−	1.69253i	−0.626499	−	0.690973i
$7$	−0.990003	−	2.45355i	−0.374186	−	0.927354i
$7$	−0.990003	−	2.45355i	−0.374186	−	0.927354i
$8$		−	2.98120i		−	1.05401i
$9$	2.43920	+	1.74651i	0.813067	+	0.582171i
$10$	0.966096	−	0.557776i	0.305507	−	0.176384i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	0.0951936	+	0.440350i	0.0274800	+	0.127118i
$13$		−	3.39294i		−	0.941033i	−0.882391	−	0.470516i	$-0.844068\pi$
$13$		−	3.39294i		−	0.941033i	0.882391	−	0.470516i	$-0.155932\pi$
$14$	0.487264	−	3.45569i	0.130227	−	0.923573i
$15$	−1.08519	+	0.983930i	−0.280194	+	0.254050i
$16$	1.70606	−	2.95499i	0.426516	−	0.738747i
$17$	2.38249	+	4.12660i	0.577839	+	1.00085i	0.995727	+	0.0923477i	$0.0294371\pi$
$17$	2.38249	+	4.12660i	0.577839	+	1.00085i	−0.417888	+	0.908499i	$0.637230\pi$
$18$	1.63450	+	3.60381i	0.385256	+	0.849425i
$19$	−5.64791	−	3.26082i	−1.29572	−	0.748084i	−0.316057	−	0.948740i	$-0.602359\pi$
$19$	−5.64791	−	3.26082i	−1.29572	−	0.748084i	−0.979662	+	0.200656i	$0.935693\pi$
$20$	−0.219981			−0.0491892
$21$	0.333413	+	4.57043i	0.0727568	+	0.997350i
$22$	1.31905			0.281222
$23$	5.32135	+	3.07228i	1.10958	+	0.640615i	0.938720	−	0.344680i	$-0.112013\pi$
$23$	5.32135	+	3.07228i	1.10958	+	0.640615i	0.170858	+	0.985296i	$0.445346\pi$
$24$	−1.57863	+	4.91635i	−0.322236	+	1.00355i
$25$	2.14238	+	3.71070i	0.428475	+	0.742141i
$26$	2.23773	−	3.87586i	0.438855	−	0.760119i
$27$	−3.09771	−	4.17183i	−0.596154	−	0.802870i
$28$	−0.423934	+	0.542104i	−0.0801160	+	0.102448i
$29$		−	2.17818i		−	0.404478i	−0.979336	−	0.202239i	$-0.935178\pi$
$29$		−	2.17818i		−	0.404478i	0.979336	−	0.202239i	$-0.0648218\pi$
$30$	−1.88857	+	0.408265i	−0.344804	+	0.0745387i
$31$	−3.76047	+	2.17111i	−0.675400	+	0.389942i	−0.798120	−	0.602499i	$-0.794172\pi$
$31$	−3.76047	+	2.17111i	−0.675400	+	0.389942i	0.122720	+	0.992441i	$0.460838\pi$
$32$	−1.26581	+	0.730815i	−0.223765	+	0.129191i
$33$	−1.69294	+	0.365976i	−0.294704	+	0.0637082i
$34$			6.28525i			1.07791i
$35$	−2.21566	−	0.312415i	−0.374515	−	0.0528078i
$36$	0.0761920	−	0.776599i	0.0126987	−	0.129433i
$37$	−0.892063	+	1.54510i	−0.146654	+	0.254013i	−0.929989	−	0.367588i	$-0.880184\pi$
$37$	−0.892063	+	1.54510i	−0.146654	+	0.254013i	0.783335	+	0.621600i	$0.213517\pi$
$38$	−4.30118	−	7.44987i	−0.697744	−	1.20853i
$39$	−1.79666	+	5.59537i	−0.287696	+	0.895977i
$40$	−2.18348	−	1.26063i	−0.345239	−	0.199324i
$41$	2.64903			0.413710			0.206855	−	0.978372i	$-0.433677\pi$
$41$	2.64903			0.413710			0.206855	+	0.978372i	$0.433677\pi$
$42$	−2.63344	+	5.44083i	−0.406349	+	0.839539i
$43$	10.5181			1.60400			0.801998	−	0.597326i	$-0.203770\pi$
$43$	10.5181			1.60400			0.801998	+	0.597326i	$0.203770\pi$
$44$	−0.225261	−	0.130055i	−0.0339594	−	0.0196065i
$45$	2.31062	−	1.04798i	0.344447	−	0.156224i
$46$	4.05249	+	7.01912i	0.597508	+	1.03491i
$47$	0.000610157	−	0.00105682i	8.90005e−5	−	0.000154153i	−0.865981	−	0.500077i	$-0.833305\pi$
$47$	0.000610157	−	0.00105682i	8.90005e−5	−	0.000154153i	0.866070	+	0.499923i	$0.166638\pi$
$48$	−4.37825	+	3.96972i	−0.631946	+	0.572980i
$49$	−5.03979	+	4.85804i	−0.719970	+	0.694006i
$50$			5.65180i			0.799285i
$51$	−1.74387	−	8.06685i	−0.244190	−	1.12959i
$52$	−0.764298	+	0.441268i	−0.105989	+	0.0611928i
$53$	0.207291	−	0.119679i	0.0284736	−	0.0164392i	−0.485696	−	0.874128i	$-0.661434\pi$
$53$	0.207291	−	0.119679i	0.0284736	−	0.0164392i	0.514169	+	0.857689i	$0.328100\pi$
$54$	−0.787180	−	6.80863i	−0.107122	−	0.926537i
$55$		−	0.845724i		−	0.114037i
$56$	−7.31450	+	2.95139i	−0.977442	+	0.394397i
$57$	7.58739	+	8.36822i	1.00497	+	1.10840i
$58$	1.43656	−	2.48820i	0.188630	−	0.326717i
$59$	3.95668	+	6.85317i	0.515116	+	0.892207i	0.999846	+	0.0175430i	$0.00558439\pi$
$59$	3.95668	+	6.85317i	0.515116	+	0.892207i	−0.484730	+	0.874664i	$0.661082\pi$
$60$	0.362775	+	0.116486i	0.0468340	+	0.0150383i
$61$	6.25792	+	3.61301i	0.801245	+	0.462599i	0.843906	−	0.536491i	$-0.180250\pi$
$61$	6.25792	+	3.61301i	0.801245	+	0.462599i	−0.0426614	+	0.999090i	$0.513584\pi$
$62$	−5.72759			−0.727405
$63$	1.87033	−	7.71374i	0.235640	−	0.971840i
$64$	−8.75221			−1.09403
$65$	−2.48505	−	1.43475i	−0.308233	−	0.177958i
$66$	−2.17527	−	0.698474i	−0.267757	−	0.0859761i
$67$	−2.33660	−	4.04712i	−0.285462	−	0.494434i	0.687259	−	0.726412i	$-0.258814\pi$
$67$	−2.33660	−	4.04712i	−0.285462	−	0.494434i	−0.972721	+	0.231978i	$0.925480\pi$
$68$	0.619708	−	1.07337i	0.0751506	−	0.130165i
$69$	−7.14869	−	7.88437i	−0.860601	−	0.949167i
$70$	−2.32497	−	1.81816i	−0.277887	−	0.217312i
$71$		−	15.7429i		−	1.86834i	−0.356823	−	0.934172i	$-0.616140\pi$
$71$		−	15.7429i		−	1.86834i	0.356823	−	0.934172i	$-0.383860\pi$
$72$	5.20669	−	7.27173i	0.613615	−	0.856982i
$73$	13.8849	−	8.01645i	1.62510	−	0.938254i	0.639579	−	0.768725i	$-0.279109\pi$
$73$	13.8849	−	8.01645i	1.62510	−	0.938254i	0.985525	−	0.169529i	$-0.0542248\pi$
$74$	−2.03806	+	1.17668i	−0.236920	+	0.136786i
$75$	−1.56811	−	7.25385i	−0.181070	−	0.837602i
$76$			1.69634i			0.194583i
$77$	−2.08414	−	1.62983i	−0.237510	−	0.185737i
$78$	−5.74266	+	5.20682i	−0.650228	+	0.589557i
$79$	−4.61451	+	7.99256i	−0.519173	+	0.899234i	0.480579	+	0.876951i	$0.340427\pi$
$79$	−4.61451	+	7.99256i	−0.519173	+	0.899234i	−0.999752	+	0.0222821i	$0.992907\pi$
$80$	−1.44286	−	2.49910i	−0.161316	−	0.279408i
$81$	2.89939	+	8.52018i	0.322155	+	0.946687i
$82$	3.02607	+	1.74710i	0.334174	+	0.192935i
$83$	7.22472			0.793016			0.396508	−	0.918031i	$-0.370222\pi$
$83$	7.22472			0.793016			0.396508	+	0.918031i	$0.370222\pi$
$84$	0.986178	−	0.669510i	0.107601	−	0.0730496i
$85$	4.02986			0.437100
$86$	12.0152	+	6.93695i	1.29563	+	0.748031i
$87$	−1.15341	+	3.59208i	−0.123658	+	0.385112i
$88$	−1.49060	−	2.58179i	−0.158898	−	0.275220i
$89$	0.713428	−	1.23569i	0.0756232	−	0.130983i	−0.825734	−	0.564060i	$-0.809239\pi$
$89$	0.713428	−	1.23569i	0.0756232	−	0.130983i	0.901357	+	0.433077i	$0.142572\pi$
$90$	3.33066	+	0.326771i	0.351083	+	0.0344447i
$91$	−8.32474	+	3.35902i	−0.872670	+	0.352121i
$92$		−	1.59826i		−	0.166630i
$93$	7.35113	−	1.58914i	0.762276	−	0.164787i
$94$	0.00139400		0.000804826i	0.000143780		8.30115e-5i
$95$	−4.77657	+	2.75776i	−0.490066	+	0.282940i
$96$	2.47446	−	0.534921i	0.252548	−	0.0545951i
$97$			6.92343i			0.702968i	0.936194	+	0.351484i	$0.114323\pi$
$97$			6.92343i			0.702968i	−0.936194	+	0.351484i	$0.885677\pi$
$98$	−8.96110	+	2.22562i	−0.905208	+	0.224822i
$99$	2.98567	+	0.292923i	0.300071	+	0.0294399i
$100$	0.557251	−	0.965188i	0.0557251	−	0.0965188i
$101$	2.90472	+	5.03112i	0.289030	+	0.500615i	0.973579	−	0.228352i	$-0.0733338\pi$
$101$	2.90472	+	5.03112i	0.289030	+	0.500615i	−0.684548	+	0.728968i	$0.740000\pi$
$102$	3.32821	−	10.3651i	0.329542	−	1.02630i
$103$	−9.82857	−	5.67453i	−0.968438	−	0.559128i	−0.0696781	−	0.997570i	$-0.522197\pi$
$103$	−9.82857	−	5.67453i	−0.968438	−	0.559128i	−0.898760	+	0.438442i	$0.855531\pi$
$104$	−10.1150			−0.991860
$105$	3.48846	+	1.68846i	0.340439	+	0.164777i
$106$	0.315726			0.0306660
$107$	12.2228	+	7.05686i	1.18163	+	0.682212i	0.956390	−	0.292092i	$-0.0943514\pi$
$107$	12.2228	+	7.05686i	1.18163	+	0.682212i	0.225236	+	0.974304i	$0.427685\pi$
$108$	−0.536881	+	1.24036i	−0.0516614	+	0.119354i
$109$	−4.98213	−	8.62929i	−0.477201	−	0.826536i	0.522458	−	0.852665i	$-0.325015\pi$
$109$	−4.98213	−	8.62929i	−0.477201	−	0.826536i	−0.999659	+	0.0261288i	$0.991682\pi$
$110$	0.557776	−	0.966096i	0.0531819	−	0.0921137i
$111$	2.28929	−	2.07568i	0.217290	−	0.197015i
$112$	−8.93921	−	1.26046i	−0.844676	−	0.119102i
$113$			13.9153i			1.30904i	0.756043	+	0.654522i	$0.227130\pi$
$113$			13.9153i			1.30904i	−0.756043	+	0.654522i	$0.772870\pi$
$114$	3.14826	+	14.5633i	0.294861	+	1.36398i
$115$	4.50040	−	2.59831i	0.419664	−	0.242293i
$116$	−0.490659	+	0.283282i	−0.0455566	+	0.0263021i
$117$	5.92581	−	8.27607i	0.547842	−	0.765123i
$118$			10.4381i			0.960906i
$119$	7.76612	−	9.93090i	0.711919	−	0.910364i
$120$	2.93329	+	3.23515i	0.267771	+	0.295328i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	4.76574	+	8.25451i	0.431470	+	0.747328i
$123$	−4.36858	−	1.40274i	−0.393901	−	0.126481i
$124$	0.978132	+	0.564725i	0.0878388	+	0.0507138i
$125$	7.85234			0.702335
$126$	7.22394	−	7.57811i	0.643560	−	0.675112i
$127$	−5.14049			−0.456145			−0.228072	−	0.973644i	$-0.573242\pi$
$127$	−5.14049			−0.456145			−0.228072	+	0.973644i	$0.573242\pi$
$128$	−7.46630	−	4.31067i	−0.659934	−	0.381013i
$129$	−17.3456	−	5.56963i	−1.52720	−	0.490379i
$130$	−1.89250	−	3.27791i	−0.165983	−	0.287492i
$131$	0.714009	−	1.23670i	0.0623833	−	0.108051i	−0.833147	−	0.553052i	$-0.813463\pi$
$131$	0.714009	−	1.23670i	0.0623833	−	0.108051i	0.895530	+	0.445001i	$0.146797\pi$
$132$	0.302615	+	0.333758i	0.0263393	+	0.0290499i
$133$	−2.40913	+	17.0856i	−0.208898	+	1.48151i
$134$		−	6.16419i		−	0.532505i
$135$	−4.36543	+	0.504710i	−0.375717	+	0.0434385i
$136$	12.3022	−	7.10267i	1.05490	−	0.609049i
$137$	−5.56238	+	3.21144i	−0.475226	+	0.274372i	−0.718425	−	0.695605i	$-0.755137\pi$
$137$	−5.56238	+	3.21144i	−0.475226	+	0.274372i	0.243199	+	0.969976i	$0.421803\pi$
$138$	−2.96623	−	13.7213i	−0.252502	−	1.16803i
$139$		−	0.388689i		−	0.0329682i	−0.999864	−	0.0164841i	$-0.994753\pi$
$139$		−	0.388689i		−	0.0329682i	0.999864	−	0.0164841i	$-0.00524729\pi$
$140$	0.217782	+	0.539733i	0.0184059	+	0.0456157i
$141$	−0.00156584	+	0.00141973i	−0.000131867	+	0.000119563i
$142$	10.3829	−	17.9836i	0.871310	−	1.50915i
$143$	−1.69647	−	2.93837i	−0.141866	−	0.245719i
$144$	9.32235	−	4.22815i	0.776862	−	0.352346i
$145$	−1.59534	−	0.921070i	−0.132486	−	0.0764907i
$146$	21.1482			1.75024
$147$	10.8837	−	5.34279i	0.897671	−	0.440666i
$148$	0.464068			0.0381461
$149$	−16.0113	−	9.24413i	−1.31170	−	0.757308i	−0.329319	−	0.944219i	$-0.606819\pi$
$149$	−16.0113	−	9.24413i	−1.31170	−	0.757308i	−0.982377	+	0.186910i	$0.940153\pi$
$150$	2.99278	−	9.32050i	0.244360	−	0.761015i
$151$	−6.24768	−	10.8213i	−0.508429	−	0.880625i	−0.999952	−	0.00976056i	$-0.996893\pi$
$151$	−6.24768	−	10.8213i	−0.508429	−	0.880625i	0.491523	−	0.870864i	$-0.336440\pi$
$152$	−9.72115	+	16.8375i	−0.788489	+	1.36570i
$153$	−1.39577	+	14.2266i	−0.112842	+	1.15016i
$154$	−1.30586	−	3.23635i	−0.105229	−	0.260792i
$155$			3.67232i			0.294967i
$156$	1.49408	−	0.322987i	0.119622	−	0.0258596i
$157$	5.11799	−	2.95487i	0.408460	−	0.235825i	−0.281668	−	0.959512i	$-0.590888\pi$
$157$	5.11799	−	2.95487i	0.408460	−	0.235825i	0.690128	+	0.723687i	$0.257554\pi$
$158$	−10.5426	+	6.08676i	−0.838723	+	0.484237i
$159$	−0.405221	+	0.0875995i	−0.0321361	+	0.00694710i
$160$			1.23614i			0.0977251i
$161$	2.26984	−	16.0978i	0.178888	−	1.26868i
$162$	−2.30720	+	11.6451i	−0.181271	+	0.914924i
$163$	−1.40127	+	2.42707i	−0.109756	+	0.190103i	−0.915671	−	0.401928i	$-0.868340\pi$
$163$	−1.40127	+	2.42707i	−0.109756	+	0.190103i	0.805916	+	0.592031i	$0.201674\pi$
$164$	−0.344519	−	0.596724i	−0.0269024	−	0.0465964i
$165$	−0.447835	+	1.39470i	−0.0348639	+	0.108577i
$166$	8.25301	+	4.76488i	0.640558	+	0.369826i
$167$	8.42956			0.652299			0.326149	−	0.945318i	$-0.394249\pi$
$167$	8.42956			0.652299			0.326149	+	0.945318i	$0.394249\pi$
$168$	13.6253	−	0.993970i	1.05122	−	0.0766865i
$169$	1.48794			0.114457
$170$	4.60343	+	2.65779i	0.353067	+	0.203843i
$171$	−8.08132	−	17.8179i	−0.617994	−	1.36257i
$172$	−1.36793	−	2.36932i	−0.104304	−	0.180659i
$173$	−12.9830	+	22.4872i	−0.987076	+	1.70967i	−0.354757	+	0.934959i	$0.615436\pi$
$173$	−12.9830	+	22.4872i	−0.987076	+	1.70967i	−0.632319	+	0.774708i	$0.717897\pi$
$174$	−3.68664	+	3.34264i	−0.279483	+	0.253405i
$175$	6.98343	−	8.93003i	0.527897	−	0.675047i
$176$		−	3.41213i		−	0.257199i
$177$	−2.89610	−	13.3969i	−0.217684	−	1.00697i
$178$	1.62994	−	0.941046i	0.122169	−	0.0705344i
$179$	−20.8630	+	12.0453i	−1.55937	+	0.900305i	−0.562057	+	0.827098i	$0.689990\pi$
$179$	−20.8630	+	12.0453i	−1.55937	+	0.900305i	−0.997317	+	0.0732066i	$0.976677\pi$
$180$	−0.536577	−	0.384199i	−0.0399941	−	0.0286365i
$181$		−	14.6301i		−	1.08745i	−0.839263	−	0.543725i	$-0.817013\pi$
$181$		−	14.6301i		−	1.08745i	0.839263	−	0.543725i	$-0.182987\pi$
$182$	−11.7250	−	1.65326i	−0.869112	−	0.122548i
$183$	−8.40688	−	9.27204i	−0.621454	−	0.685409i
$184$	9.15908	−	15.8640i	0.675216	−	1.16951i
$185$	0.754440	+	1.30673i	0.0554675	+	0.0960726i
$186$	9.44549	+	3.03292i	0.692577	+	0.222385i
$187$	4.12660	+	2.38249i	0.301767	+	0.174225i
$188$	−0.000317415	0		−2.31498e−5	0
$189$	−7.16905	+	11.7305i	−0.521471	+	0.853269i
$190$	−7.27523			−0.527801
$191$	−6.56491	−	3.79026i	−0.475021	−	0.274253i	0.243318	−	0.969946i	$-0.421764\pi$
$191$	−6.56491	−	3.79026i	−0.475021	−	0.274253i	−0.718339	+	0.695693i	$0.755097\pi$
$192$	14.4335	+	4.63454i	1.04164	+	0.334469i
$193$	−0.315137	−	0.545833i	−0.0226841	−	0.0392899i	0.854461	−	0.519516i	$-0.173888\pi$
$193$	−0.315137	−	0.545833i	−0.0226841	−	0.0392899i	−0.877145	+	0.480226i	$0.840555\pi$
$194$	−4.56617	+	7.90884i	−0.327832	+	0.567822i
$195$	3.33842	+	3.68198i	0.239069	+	0.263672i
$196$	1.74977	+	0.503458i	0.124984	+	0.0359613i
$197$		−	5.87161i		−	0.418335i	−0.977880	−	0.209167i	$-0.932925\pi$
$197$		−	5.87161i		−	0.418335i	0.977880	−	0.209167i	$-0.0670754\pi$
$198$	3.21743	+	2.30373i	0.228652	+	0.163719i
$199$	−16.0809	+	9.28429i	−1.13994	+	0.658146i	−0.946416	−	0.322950i	$-0.895326\pi$
$199$	−16.0809	+	9.28429i	−1.13994	+	0.658146i	−0.193525	+	0.981095i	$0.561992\pi$
$200$	11.0623	−	6.38684i	0.782225	−	0.451618i
$201$	1.71028	+	7.91148i	0.120634	+	0.558033i
$202$			7.66294i			0.539162i
$203$	−5.34427	+	2.15641i	−0.375094	+	0.151350i
$204$	−1.59035	+	1.44196i	−0.111347	+	0.100957i
$205$	1.12018	−	1.94020i	0.0782365	−	0.135510i
$206$	−7.48498	−	12.9644i	−0.521503	−	0.903270i
$207$	7.61406	+	16.7877i	0.529214	+	1.16683i
$208$	−10.0261	−	5.78857i	−0.695185	−	0.401365i
$209$	−6.52164			−0.451112
$210$	2.87139	+	4.22951i	0.198144	+	0.291864i
$211$	2.42371			0.166855			0.0834276	−	0.996514i	$-0.473413\pi$
$211$	2.42371			0.166855			0.0834276	+	0.996514i	$0.473413\pi$
$212$	−0.0539182	−	0.0311297i	−0.00370312	−	0.00213800i
$213$	−8.33633	+	25.9620i	−0.571196	+	1.77889i
$214$	9.30834	+	16.1225i	0.636305	+	1.10211i
$215$	4.44771	−	7.70366i	0.303331	−	0.525385i
$216$	−12.4371	+	9.23488i	−0.846234	+	0.628354i
$217$	9.04979	+	7.07708i	0.614340	+	0.480423i
$218$		−	13.1433i		−	0.890179i
$219$	−27.1428	+	5.86765i	−1.83414	+	0.396499i
$220$	−0.190509	+	0.109990i	−0.0128441	+	0.00741555i
$221$	14.0013	−	8.08365i	0.941829	−	0.543765i
$222$	3.98409	−	0.861270i	0.267395	−	0.0578046i
$223$			18.0076i			1.20588i	0.797787	+	0.602939i	$0.206004\pi$
$223$			18.0076i			1.20588i	−0.797787	+	0.602939i	$0.793996\pi$
$224$	3.04624	+	2.38221i	0.203536	+	0.159168i
$225$	−1.25510	+	12.7928i	−0.0836735	+	0.852855i
$226$	−9.17750	+	15.8959i	−0.610478	+	1.05738i
$227$	4.74999	+	8.22722i	0.315268	+	0.546060i	0.979494	−	0.201471i	$-0.0645723\pi$
$227$	4.74999	+	8.22722i	0.315268	+	0.546060i	−0.664227	+	0.747531i	$0.731239\pi$
$228$	0.898259	−	2.79747i	0.0594887	−	0.185267i
$229$	4.69239	+	2.70915i	0.310082	+	0.179026i	0.646963	−	0.762521i	$-0.276039\pi$
$229$	4.69239	+	2.70915i	0.310082	+	0.179026i	−0.336881	+	0.941547i	$0.609372\pi$
$230$	6.85458			0.451978
$231$	2.57396	+	3.79140i	0.169354	+	0.249456i
$232$	−6.49358			−0.426324
$233$	−12.3675	−	7.14037i	−0.810221	−	0.467781i	0.0368119	−	0.999322i	$-0.488280\pi$
$233$	−12.3675	−	7.14037i	−0.810221	−	0.467781i	−0.847032	+	0.531541i	$0.821613\pi$
$234$	12.2275	−	5.54578i	0.799337	−	0.362539i
$235$	−0.000516024	0	0.000893780i	−3.36617e−5	0	5.83038e-5i
$236$	1.02917	−	1.78257i	0.0669932	−	0.116036i
$237$	11.8422	−	10.7372i	0.769232	−	0.697456i
$238$	15.4211	−	6.22241i	0.999604	−	0.403339i
$239$			26.6308i			1.72261i	0.508093	+	0.861303i	$0.330351\pi$
$239$			26.6308i			1.72261i	−0.508093	+	0.861303i	$0.669649\pi$
$240$	1.05610	+	4.88536i	0.0681711	+	0.315349i
$241$	−10.1612	+	5.86659i	−0.654543	+	0.377900i	−0.790194	−	0.612856i	$-0.790020\pi$
$241$	−10.1612	+	5.86659i	−0.654543	+	0.377900i	0.135652	+	0.990757i	$0.456687\pi$
$242$	1.14233	−	0.659525i	0.0734318	−	0.0423958i
$243$	−0.269777	−	15.5861i	−0.0173062	−	0.999850i
$244$		−	1.87956i		−	0.120326i
$245$	1.42698	+	5.74552i	0.0911667	+	0.367068i
$246$	−4.06522	−	4.48358i	−0.259189	−	0.285862i
$247$	−11.0638	+	19.1630i	−0.703971	+	1.21931i
$248$	6.47249	+	11.2107i	0.411004	+	0.711879i
$249$	−11.9144	−	3.82569i	−0.755046	−	0.242443i
$250$	8.96996	+	5.17881i	0.567310	+	0.327537i
$251$	−10.0062			−0.631587			−0.315793	−	0.948828i	$-0.602271\pi$
$251$	−10.0062			−0.631587			−0.315793	+	0.948828i	$0.602271\pi$
$252$	−1.98085	+	0.581895i	−0.124782	+	0.0366559i
$253$	6.14457			0.386306
$254$	−5.87213	−	3.39028i	−0.368450	−	0.212725i
$255$	−6.64573	−	2.13392i	−0.416172	−	0.133632i
$256$	3.06623	+	5.31086i	0.191639	+	0.331929i
$257$	−3.67041	+	6.35734i	−0.228954	+	0.396560i	−0.957498	−	0.288439i	$-0.906864\pi$
$257$	−3.67041	+	6.35734i	−0.228954	+	0.396560i	0.728544	+	0.684999i	$0.240197\pi$
$258$	−16.1411	−	17.8022i	−1.00490	−	1.10832i
$259$	4.67412	+	0.659066i	0.290436	+	0.0409524i
$260$			0.746382i			0.0462886i
$261$	3.80422	−	5.31302i	0.235475	−	0.328867i
$262$	1.63127	−	0.941813i	0.100780	−	0.0581854i
$263$	8.79901	−	5.08011i	0.542570	−	0.313253i	−0.203550	−	0.979065i	$-0.565248\pi$
$263$	8.79901	−	5.08011i	0.542570	−	0.313253i	0.746120	+	0.665811i	$0.231914\pi$
$264$	1.09105	+	5.04700i	0.0671492	+	0.310621i
$265$		−	0.202432i		−	0.0124353i
$266$	−14.0204	+	17.9286i	−0.859647	+	1.09927i
$267$	−1.83086	+	1.66003i	−0.112047	+	0.101592i
$268$	−0.607772	+	1.05269i	−0.0371256	+	0.0643034i
$269$	−3.89436	−	6.74522i	−0.237443	−	0.411264i	0.722537	−	0.691333i	$-0.242976\pi$
$269$	−3.89436	−	6.74522i	−0.237443	−	0.411264i	−0.959980	+	0.280069i	$0.909643\pi$
$270$	−5.31963	−	2.30257i	−0.323743	−	0.140130i
$271$	0.568839	+	0.328419i	0.0345545	+	0.0199501i	0.517178	−	0.855878i	$-0.326983\pi$
$271$	0.568839	+	0.328419i	0.0345545	+	0.0199501i	−0.482623	+	0.875828i	$0.660316\pi$
$272$	16.2587			0.985829
$273$	15.5072	−	1.13125i	0.938539	−	0.0684665i
$274$	−8.47209			−0.511818
$275$	3.71070	+	2.14238i	0.223764	+	0.129190i
$276$	−0.846322	+	2.63572i	−0.0509426	+	0.158652i
$277$	−2.66630	−	4.61817i	−0.160203	−	0.277479i	0.774739	−	0.632282i	$-0.217881\pi$
$277$	−2.66630	−	4.61817i	−0.160203	−	0.277479i	−0.934941	+	0.354802i	$0.884548\pi$
$278$	0.256350	−	0.444012i	0.0153749	−	0.0266300i
$279$	−12.9644	−	1.27194i	−0.776158	−	0.0761488i
$280$	−0.931371	+	6.60531i	−0.0556601	+	0.394743i
$281$			0.189814i			0.0113233i	0.999984	+	0.00566167i	$0.00180217\pi$
$281$			0.189814i			0.0113233i	−0.999984	+	0.00566167i	$0.998198\pi$
$282$	−0.00272505		0.000589094i	−0.000162275		3.50800e-5i
$283$	−2.71318	+	1.56646i	−0.161282	+	0.0931161i	−0.578469	−	0.815705i	$-0.696349\pi$
$283$	−2.71318	+	1.56646i	−0.161282	+	0.0931161i	0.417187	+	0.908821i	$0.363016\pi$
$284$	−3.54627	+	2.04744i	−0.210433	+	0.121493i
$285$	9.33746	−	2.01854i	0.553103	−	0.119568i
$286$		−	4.47546i		−	0.264639i
$287$	−2.62255	−	6.49953i	−0.154804	−	0.383655i
$288$	−4.36394	−	0.428145i	−0.257147	−	0.0252287i
$289$	−2.85253	+	4.94072i	−0.167796	+	0.290631i
$290$	−1.21494	−	2.10433i	−0.0713435	−	0.123571i
$291$	3.66615	−	11.4176i	0.214914	−	0.669310i
$292$	−3.61159	−	2.08515i	−0.211352	−	0.122024i
$293$	28.1783			1.64620			0.823098	−	0.567900i	$-0.192244\pi$
$293$	28.1783			1.64620			0.823098	+	0.567900i	$0.192244\pi$
$294$	15.9565	+	1.07483i	0.930600	+	0.0626855i
$295$	6.69252			0.389654
$296$	4.60624	+	2.65942i	0.267732	+	0.154575i
$297$	−4.76861	−	2.06406i	−0.276703	−	0.119769i
$298$	−12.1935	−	21.1197i	−0.706348	−	1.22343i
$299$	10.4241	−	18.0550i	0.602840	−	1.04415i
$300$	−1.43007	+	1.29663i	−0.0825651	+	0.0748610i
$301$	−10.4130	−	25.8067i	−0.600193	−	1.48747i
$302$		−	16.4820i		−	0.948432i
$303$	−2.12611	−	9.83506i	−0.122142	−	0.565009i
$304$	−19.2714	+	11.1263i	−1.10529	+	0.638139i
$305$	5.29248	−	3.05561i	0.303046	−	0.174964i
$306$	−10.9773	+	15.3310i	−0.627528	+	0.876413i
$307$		−	31.3773i		−	1.79080i	−0.445264	−	0.895399i	$-0.646890\pi$
$307$		−	31.3773i		−	1.79080i	0.445264	−	0.895399i	$-0.353110\pi$
$308$	−0.0960857	+	0.681443i	−0.00547499	+	0.0388288i
$309$	13.2037	+	14.5625i	0.751131	+	0.828431i
$310$	−2.42198	+	4.19500i	−0.137559	+	0.238260i
$311$	10.0088	+	17.3358i	0.567549	+	0.983024i	0.996808	+	0.0798422i	$0.0254416\pi$
$311$	10.0088	+	17.3358i	0.567549	+	0.983024i	−0.429258	+	0.903182i	$0.641225\pi$
$312$	16.6809	+	5.35619i	0.944370	+	0.303234i
$313$	13.1634	+	7.59987i	0.744037	+	0.429570i	0.823535	−	0.567265i	$-0.191999\pi$
$313$	13.1634	+	7.59987i	0.744037	+	0.429570i	−0.0794985	+	0.996835i	$0.525332\pi$
$314$	7.79525			0.439911
$315$	−4.85880	−	4.63172i	−0.273762	−	0.260968i
$316$	2.40055			0.135042
$317$	6.33337	+	3.65657i	0.355717	+	0.205374i	0.667201	−	0.744878i	$-0.267492\pi$
$317$	6.33337	+	3.65657i	0.355717	+	0.205374i	−0.311483	+	0.950252i	$0.600826\pi$
$318$	−0.520671	−	0.167186i	−0.0291978	−	0.00937531i
$319$	−1.08909	−	1.88636i	−0.0609773	−	0.105616i
$320$	−3.70098	+	6.41028i	−0.206891	+	0.358346i
$321$	−16.4201	−	18.1099i	−0.916482	−	1.01080i
$322$	13.2098	−	16.8919i	0.736152	−	0.941351i
$323$		−	31.0755i		−	1.72909i
$324$	1.54219	−	1.76121i	0.0856770	−	0.0978450i
$325$	12.5902	−	7.26896i	0.698379	−	0.403209i
$326$	−3.20142	+	1.84834i	−0.177310	+	0.102370i
$327$	3.64667	+	16.8689i	0.201662	+	0.932854i
$328$		−	7.89729i		−	0.436055i
$329$	−0.00319702		0.000450790i	−0.000176257		2.48529e-5i
$330$	−1.43142	+	1.29785i	−0.0787968	+	0.0714444i
$331$	−4.41713	+	7.65069i	−0.242787	+	0.420520i	−0.961507	−	0.274780i	$-0.911395\pi$
$331$	−4.41713	+	7.65069i	−0.242787	+	0.420520i	0.718720	+	0.695300i	$0.244728\pi$
$332$	−0.939607	−	1.62745i	−0.0515677	−	0.0893178i
$333$	−4.87445	+	2.21081i	−0.267118	+	0.121151i
$334$	9.62934	+	5.55950i	0.526894	+	0.304202i
$335$	−3.95225			−0.215934
$336$	14.0744	+	6.81221i	0.767821	+	0.371636i
$337$	0.619139			0.0337267			0.0168633	−	0.999858i	$-0.494632\pi$
$337$	0.619139			0.0337267			0.0168633	+	0.999858i	$0.494632\pi$
$338$	1.69972	+	0.981335i	0.0924527	+	0.0533776i
$339$	7.36855	−	22.9480i	0.400205	−	1.24637i
$340$	−0.524102	−	0.907771i	−0.0284234	−	0.0492308i
$341$	−2.17111	+	3.76047i	−0.117572	+	0.203641i
$342$	2.51983	−	25.6838i	0.136257	−	1.38882i
$343$	16.9088	+	7.55588i	0.912991	+	0.407979i
$344$		−	31.3565i		−	1.69063i
$345$	−8.79757	+	1.90183i	−0.473645	+	0.102391i
$346$	−29.6617	+	17.1252i	−1.59462	+	0.920655i
$347$	6.74652	−	3.89510i	0.362172	−	0.209100i	−0.307861	−	0.951431i	$-0.599613\pi$
$347$	6.74652	−	3.89510i	0.362172	−	0.209100i	0.670033	+	0.742331i	$0.266280\pi$
$348$	0.959162	−	0.207349i	0.0514165	−	0.0111151i
$349$		−	17.3647i		−	0.929510i	−0.885439	−	0.464755i	$-0.846142\pi$
$349$		−	17.3647i		−	0.929510i	0.885439	−	0.464755i	$-0.153858\pi$
$350$	13.8669	−	5.59530i	0.741220	−	0.299081i
$351$	−14.1548	+	10.5103i	−0.755527	+	0.561001i
$352$	−0.730815	+	1.26581i	−0.0389526	+	0.0674678i
$353$	−9.11873	−	15.7941i	−0.485341	−	0.840636i	0.514517	−	0.857480i	$-0.327971\pi$
$353$	−9.11873	−	15.7941i	−0.485341	−	0.840636i	−0.999858	+	0.0168445i	$0.994638\pi$
$354$	5.52727	−	17.2137i	0.293771	−	0.914898i
$355$	−11.5304	−	6.65710i	−0.611972	−	0.353322i
$356$	−0.371138			−0.0196703
$357$	−18.0660	+	12.2649i	−0.956152	+	0.649126i
$358$	−31.7766			−1.67944
$359$	−9.97584	−	5.75955i	−0.526504	−	0.303977i	0.213087	−	0.977033i	$-0.431648\pi$
$359$	−9.97584	−	5.75955i	−0.526504	−	0.303977i	−0.739592	+	0.673056i	$0.764981\pi$
$360$	−3.12424	−	6.88842i	−0.164662	−	0.363052i
$361$	11.7659	+	20.3792i	0.619259	+	1.07259i
$362$	9.64894	−	16.7125i	0.507137	−	0.878387i
$363$	−1.28315	+	1.16342i	−0.0673477	+	0.0610635i
$364$	1.83933	+	1.43838i	0.0964070	+	0.0753918i
$365$		−	13.5594i		−	0.709732i
$366$	−3.48829	−	16.1363i	−0.182336	−	0.843457i
$367$	16.1031	−	9.29714i	0.840576	−	0.485307i	−0.0168837	−	0.999857i	$-0.505375\pi$
$367$	16.1031	−	9.29714i	0.840576	−	0.485307i	0.857460	+	0.514550i	$0.172041\pi$
$368$	18.1571	−	10.4830i	0.946505	−	0.546465i
$369$	6.46153	+	4.62657i	0.336374	+	0.240850i
$370$			1.99029i			0.103470i
$371$	−0.498858	−	0.390115i	−0.0258994	−	0.0202538i
$372$	−1.31402	−	1.44925i	−0.0681288	−	0.0751400i
$373$	−4.13362	+	7.15964i	−0.214031	+	0.370712i	−0.952972	−	0.303057i	$-0.901993\pi$
$373$	−4.13362	+	7.15964i	−0.214031	+	0.370712i	0.738941	+	0.673770i	$0.235326\pi$
$374$	3.14262	+	5.44318i	0.162501	+	0.281460i
$375$	−12.9495	−	4.15803i	−0.668707	−	0.214720i
$376$	−0.00315059	−	0.00181900i	−0.000162479	−	9.38075e-5i
$377$	−7.39044			−0.380627
$378$	−15.9260	+	8.67195i	−0.819144	+	0.446037i
$379$	26.9023			1.38188			0.690940	−	0.722912i	$-0.257197\pi$
$379$	26.9023			1.38188			0.690940	+	0.722912i	$0.257197\pi$
$380$	1.24243	+	0.717318i	0.0637353	+	0.0367976i
$381$	8.47729	+	2.72203i	0.434305	+	0.139454i
$382$	−4.99953	−	8.65945i	−0.255798	−	0.443056i
$383$	−12.0826	+	20.9277i	−0.617394	+	1.06936i	0.372565	+	0.928006i	$0.378478\pi$
$383$	−12.0826	+	20.9277i	−0.617394	+	1.06936i	−0.989959	+	0.141352i	$0.954855\pi$
$384$	10.0302	+	11.0624i	0.511852	+	0.564527i
$385$	−2.07502	+	0.837270i	−0.105753	+	0.0426712i
$386$		−	0.831362i		−	0.0423152i
$387$	25.6558	+	18.3700i	1.30416	+	0.933800i
$388$	1.55958	−	0.900424i	0.0791756	−	0.0457121i
$389$	1.12580	−	0.649984i	0.0570806	−	0.0329555i	−0.471188	−	0.882033i	$-0.656175\pi$
$389$	1.12580	−	0.649984i	0.0570806	−	0.0329555i	0.528269	+	0.849077i	$0.322841\pi$
$390$	1.38522	+	6.40780i	0.0701433	+	0.324472i
$391$			29.2788i			1.48069i
$392$	14.4828	+	15.0246i	0.731490	+	0.758856i
$393$	−1.83235	+	1.66138i	−0.0924301	+	0.0838055i
$394$	3.87247	−	6.70732i	0.195092	−	0.337910i
$395$	3.90260	+	6.75951i	0.196361	+	0.340108i
$396$	−0.322315	−	0.710650i	−0.0161969	−	0.0357115i
$397$	1.74812	+	1.00928i	0.0877356	+	0.0506542i	0.543226	−	0.839587i	$-0.317203\pi$
$397$	1.74812	+	1.00928i	0.0877356	+	0.0506542i	−0.455490	+	0.890241i	$0.650536\pi$
$398$	−24.4929			−1.22772
$399$	13.0203	−	26.9006i	0.651829	−	1.34671i
$400$	14.6201			0.731005
$401$	29.0584	+	16.7769i	1.45111	+	0.837797i	0.998544	−	0.0539351i	$-0.0171764\pi$
$401$	29.0584	+	16.7769i	1.45111	+	0.837797i	0.452563	+	0.891732i	$0.350510\pi$
$402$	−3.26411	+	10.1655i	−0.162799	+	0.507009i
$403$	7.36644	+	12.7590i	0.366948	+	0.635573i
$404$	0.755544	−	1.30864i	0.0375897	−	0.0651073i
$405$	7.46639	+	1.47929i	0.371008	+	0.0735066i
$406$	−7.52712	−	1.06135i	−0.373565	−	0.0526739i
$407$			1.78413i			0.0884359i
$408$	−24.0489	+	5.19881i	−1.19060	+	0.257379i
$409$	−31.9113	+	18.4240i	−1.57791	+	0.911007i	−0.582760	+	0.812644i	$0.698027\pi$
$409$	−31.9113	+	18.4240i	−1.57791	+	0.911007i	−0.995151	+	0.0983629i	$0.968639\pi$
$410$	2.55922	−	1.47757i	0.126391	−	0.0729719i
$411$	10.8736	−	2.35062i	0.536354	−	0.115947i
$412$			2.95199i			0.145434i
$413$	12.8974	−	16.4926i	0.634642	−	0.811546i
$414$	−2.37414	+	24.1988i	−0.116683	+	1.18930i
$415$	3.05506	−	5.29152i	0.149967	−	0.259750i
$416$	2.47961	+	4.29481i	0.121573	+	0.210571i
$417$	−0.205822	+	0.640996i	−0.0100791	+	0.0313897i
$418$	−7.44987	−	4.30118i	−0.364385	−	0.210378i
$419$	9.51994			0.465079			0.232540	−	0.972587i	$-0.425296\pi$
$419$	9.51994			0.465079			0.232540	+	0.972587i	$0.425296\pi$
$420$	−0.0733445	−	1.00541i	−0.00357884	−	0.0490588i
$421$	−39.5719			−1.92861			−0.964307	−	0.264786i	$-0.914699\pi$
$421$	−39.5719			−1.92861			−0.964307	+	0.264786i	$0.914699\pi$
$422$	2.76868	+	1.59850i	0.134777	+	0.0778136i
$423$	0.00333405	−	0.00151216i	0.000162107	−	7.35235e-5i
$424$	−0.356788	−	0.617974i	−0.0173271	−	0.0300115i
$425$	−10.2084	+	17.6814i	−0.495179	+	0.857675i
$426$	−26.6454	+	24.1592i	−1.29098	+	1.17052i
$427$	2.66933	−	18.9310i	0.129178	−	0.916135i
$428$		−	3.67111i		−	0.177450i
$429$	1.24173	+	5.74406i	0.0599515	+	0.277326i
$430$	10.1615	−	5.86675i	0.490031	−	0.282920i
$431$	24.8817	−	14.3655i	1.19851	−	0.691961i	0.238288	−	0.971194i	$-0.423414\pi$
$431$	24.8817	−	14.3655i	1.19851	−	0.691961i	0.960223	+	0.279234i	$0.0900804\pi$
$432$	−17.6126	+	2.03628i	−0.847387	+	0.0979707i
$433$		−	24.7832i		−	1.19100i	−0.803354	−	0.595502i	$-0.796953\pi$
$433$		−	24.7832i		−	1.19100i	0.803354	−	0.595502i	$-0.203047\pi$
$434$	5.67034	+	14.0529i	0.272185	+	0.674562i
$435$	2.14318	+	2.36373i	0.102757	+	0.113332i
$436$	−1.29590	+	2.24456i	−0.0620622	+	0.107495i
$437$	−20.0363	−	34.7040i	−0.958468	−	1.66012i
$438$	−34.8759	−	11.1986i	−1.66644	−	0.535088i
$439$	9.40202	+	5.42826i	0.448734	+	0.259077i	0.707295	−	0.706918i	$-0.249915\pi$
$439$	9.40202	+	5.42826i	0.448734	+	0.259077i	−0.258561	+	0.965995i	$0.583248\pi$
$440$	−2.52127			−0.120197
$441$	−20.7777	+	3.04769i	−0.989413	+	0.145128i
$442$	21.3255			1.01435
$443$	−24.0971	−	13.9124i	−1.14489	−	0.661000i	−0.197250	−	0.980353i	$-0.563201\pi$
$443$	−24.0971	−	13.9124i	−1.14489	−	0.661000i	−0.947636	+	0.319353i	$0.896534\pi$
$444$	−0.765304	−	0.245737i	−0.0363197	−	0.0116622i
$445$	−0.603363	−	1.04506i	−0.0286022	−	0.0495404i
$446$	−11.8765	+	20.5706i	−0.562366	+	0.974047i
$447$	21.5095	+	23.7231i	1.01737	+	1.12206i
$448$	8.66472	+	21.4740i	0.409369	+	1.01455i
$449$		−	11.2893i		−	0.532774i	−0.963866	−	0.266387i	$-0.914170\pi$
$449$		−	11.2893i		−	0.532774i	0.963866	−	0.266387i	$-0.0858299\pi$
$450$	−9.87093	+	13.7859i	−0.465320	+	0.649872i
$451$	2.29413	−	1.32452i	0.108026	−	0.0623691i
$452$	3.13458	−	1.80975i	0.147438	−	0.0851235i
$453$	4.57300	+	21.1540i	0.214858	+	0.993900i
$454$			12.5309i			0.588106i
$455$	−1.06001	+	7.51760i	−0.0496939	+	0.352431i
$456$	24.9473	−	22.6195i	1.16826	−	1.05925i
$457$	5.24915	−	9.09179i	0.245545	−	0.425296i	−0.716740	−	0.697341i	$-0.754367\pi$
$457$	5.24915	−	9.09179i	0.245545	−	0.425296i	0.962285	+	0.272045i	$0.0876998\pi$
$458$	3.57351	+	6.18950i	0.166979	+	0.289216i
$459$	9.83520	−	22.7223i	0.459068	−	1.06059i
$460$	−1.17059	−	0.675843i	−0.0545792	−	0.0315113i
$461$	6.24064			0.290656			0.145328	−	0.989384i	$-0.453576\pi$
$461$	6.24064			0.290656			0.145328	+	0.989384i	$0.453576\pi$
$462$	0.439789	+	6.02862i	0.0204608	+	0.280477i
$463$	29.2294			1.35841			0.679204	−	0.733950i	$-0.262325\pi$
$463$	29.2294			1.35841			0.679204	+	0.733950i	$0.262325\pi$
$464$	−6.43649	−	3.71611i	−0.298807	−	0.172516i
$465$	1.94459	−	6.05609i	0.0901784	−	0.280845i
$466$	−9.41850	−	16.3133i	−0.436303	−	0.755700i
$467$	−15.9460	+	27.6192i	−0.737892	+	1.27807i	0.215552	+	0.976492i	$0.430845\pi$
$467$	−15.9460	+	27.6192i	−0.737892	+	1.27807i	−0.953443	+	0.301573i	$0.902488\pi$
$468$	−2.63495	−	0.258515i	−0.121801	−	0.0119499i
$469$	−7.61655	+	9.73963i	−0.351699	+	0.449734i
$470$		−	0.00136132i		−	6.27931e-5i
$471$	−10.0049	+	2.16282i	−0.461000	+	0.0996577i
$472$	20.4306	−	11.7956i	0.940396	−	0.542938i
$473$	9.10895	−	5.25906i	0.418830	−	0.241812i
$474$	20.6091	−	4.45522i	0.946608	−	0.204635i
$475$		−	27.9436i		−	1.28214i
$476$	−3.24706	−	0.457847i	−0.148829	−	0.0209854i
$477$	0.714645	+	0.0701138i	0.0327214	+	0.00321029i
$478$	−17.5637	+	30.4212i	−0.803344	+	1.39143i
$479$	10.2223	+	17.7056i	0.467069	+	0.808987i	0.999292	−	0.0376167i	$-0.0119766\pi$
$479$	10.2223	+	17.7056i	0.467069	+	0.808987i	−0.532223	+	0.846604i	$0.678643\pi$
$480$	0.654569	−	2.03854i	0.0298768	−	0.0930461i
$481$	5.24243	+	3.02672i	0.239034	+	0.138007i
$482$	−15.4766			−0.704942
$483$	−12.2674	+	25.3452i	−0.558188	+	1.15325i
$484$	−0.260109			−0.0118231
$485$	5.07085	+	2.92766i	0.230255	+	0.132938i
$486$	9.97126	−	17.9824i	0.452305	−	0.815699i
$487$	11.2235	+	19.4397i	0.508587	+	0.880898i	0.999951	+	0.00994368i	$0.00316522\pi$
$487$	11.2235	+	19.4397i	0.508587	+	0.880898i	−0.491364	+	0.870954i	$0.663501\pi$
$488$	10.7711	−	18.6561i	0.487585	−	0.844521i
$489$	3.59606	−	3.26052i	0.162619	−	0.147446i
$490$	−2.15922	+	7.50441i	−0.0975437	+	0.339015i
$491$			2.30968i			0.104235i	0.998641	+	0.0521173i	$0.0165970\pi$
$491$			2.30968i			0.104235i	−0.998641	+	0.0521173i	$0.983403\pi$
$492$	0.252171	+	1.16650i	0.0113688	+	0.0525900i
$493$	8.98847	−	5.18949i	0.404820	−	0.233723i
$494$	−25.2770	+	14.5937i	−1.13727	+	0.656600i
$495$	1.47707	−	2.06289i	0.0663892	−	0.0927201i
$496$			14.8162i			0.665266i
$497$	−38.6261	+	15.5856i	−1.73262	+	0.699108i
$498$	−11.0871	−	12.2281i	−0.496824	−	0.547953i
$499$	−4.46825	+	7.73924i	−0.200026	+	0.346456i	−0.948537	−	0.316667i	$-0.897436\pi$
$499$	−4.46825	+	7.73924i	−0.200026	+	0.346456i	0.748510	+	0.663123i	$0.230769\pi$
$500$	−1.02123	−	1.76883i	−0.0456709	−	0.0791043i
$501$	−13.9014	−	4.46369i	−0.621067	−	0.199423i
$502$	−11.4304	−	6.59935i	−0.510164	−	0.294543i
$503$	20.2569			0.903208			0.451604	−	0.892218i	$-0.350852\pi$
$503$	20.2569			0.903208			0.451604	+	0.892218i	$0.350852\pi$
$504$	−22.9962	−	5.57582i	−1.02433	−	0.248367i
$505$	4.91319			0.218634
$506$	7.01912	+	4.05249i	0.312038	+	0.180155i
$507$	−2.45380	−	0.787907i	−0.108977	−	0.0349922i
$508$	0.668544	+	1.15795i	0.0296618	+	0.0513758i
$509$	15.0590	−	26.0830i	0.667479	−	1.15611i	−0.311128	−	0.950368i	$-0.600707\pi$
$509$	15.0590	−	26.0830i	0.667479	−	1.15611i	0.978607	−	0.205740i	$-0.0659600\pi$
$510$	−6.18424	−	6.82067i	−0.273843	−	0.302024i
$511$	−33.4148	−	26.1309i	−1.47819	−	1.15596i
$512$			25.3317i			1.11951i
$513$	3.89197	+	33.6632i	0.171835	+	1.48627i
$514$	−8.38564	+	4.84145i	−0.369875	+	0.213547i
$515$	−8.31226	+	4.79909i	−0.366282	+	0.211473i
$516$	1.00126	+	4.63165i	0.0440779	+	0.203897i
$517$		−	0.00122031i		−	5.36693e-5i
$518$	4.90472	+	3.83557i	0.215501	+	0.168525i
$519$	33.3181	−	30.2092i	1.46250	−	1.32604i
$520$	−4.27726	+	7.40843i	−0.187570	+	0.324881i
$521$	3.30873	+	5.73088i	0.144958	+	0.251075i	0.929357	−	0.369182i	$-0.120362\pi$
$521$	3.30873	+	5.73088i	0.144958	+	0.251075i	−0.784399	+	0.620256i	$0.787029\pi$
$522$	7.84974	−	3.56024i	0.343574	−	0.155828i
$523$	−0.999850	−	0.577263i	−0.0437204	−	0.0252420i	0.477980	−	0.878370i	$-0.341369\pi$
$523$	−0.999850	−	0.577263i	−0.0437204	−	0.0252420i	−0.521701	+	0.853128i	$0.674702\pi$
$524$	−0.371441			−0.0162265
$525$	−16.2452	+	11.0288i	−0.708999	+	0.481335i
$526$	13.4018			0.584348
$527$	−17.9186	−	10.3453i	−0.780544	−	0.450648i
$528$	−1.80682	+	5.62701i	−0.0786316	+	0.244884i
$529$	7.37785	+	12.7788i	0.320776	+	0.555601i
$530$	0.133509	−	0.231244i	0.00579924	−	0.0100446i
$531$	−2.31801	+	23.6266i	−0.100593	+	1.02531i
$532$	4.16205	−	1.67938i	0.180448	−	0.0728104i
$533$		−	8.98802i		−	0.389314i
$534$	−3.18628	+	0.688800i	−0.137884	+	0.0298073i
$535$	10.3371	−	5.96816i	0.446914	−	0.258026i
$536$	−12.0652	+	6.96587i	−0.521139	+	0.300880i
$537$	40.7839	−	8.81655i	1.75996	−	0.380462i
$538$		−	10.2737i		−	0.442931i
$539$	−1.93556	+	6.72708i	−0.0833706	+	0.289756i
$540$	0.681436	+	0.917723i	0.0293243	+	0.0394925i
$541$	12.3100	−	21.3215i	0.529247	−	0.916683i	−0.470171	−	0.882575i	$-0.655808\pi$
$541$	12.3100	−	21.3215i	0.529247	−	0.916683i	0.999418	−	0.0341077i	$-0.0108589\pi$
$542$	0.433201	+	0.750327i	0.0186076	+	0.0322293i
$543$	−7.74707	+	24.1269i	−0.332459	+	1.03538i
$544$	−6.03155	−	3.48232i	−0.258601	−	0.149303i
$545$	−8.42701			−0.360973
$546$	18.4604	+	8.93512i	0.790034	+	0.382388i
$547$	−31.2278			−1.33520			−0.667602	−	0.744519i	$-0.732679\pi$
$547$	−31.2278			−1.33520			−0.667602	+	0.744519i	$0.732679\pi$
$548$	1.44682	+	0.835325i	0.0618053	+	0.0356833i
$549$	8.95416	+	19.7424i	0.382154	+	0.842585i
$550$	2.82590	+	4.89460i	0.120497	+	0.208706i
$551$	−7.10266	+	12.3022i	−0.302583	+	0.524090i
$552$	−23.5049	+	21.3116i	−1.00043	+	0.907084i
$553$	24.1785	+	3.40925i	1.02817	+	0.144976i
$554$		−	7.03397i		−	0.298845i
$555$	−0.552213	−	2.55445i	−0.0234402	−	0.108430i
$556$	−0.0875566	+	0.0505508i	−0.00371323	+	0.00214383i
$557$	16.8856	−	9.74890i	0.715466	−	0.413074i	−0.0976158	−	0.995224i	$-0.531122\pi$
$557$	16.8856	−	9.74890i	0.715466	−	0.413074i	0.813082	+	0.582150i	$0.197788\pi$
$558$	−13.9707	−	10.0033i	−0.591429	−	0.423474i
$559$		−	35.6873i		−	1.50941i
$560$	−4.70324	+	6.01424i	−0.198748	+	0.254148i
$561$	−5.54366	−	6.11416i	−0.234053	−	0.258140i
$562$	−0.125187	+	0.216830i	−0.00528068	+	0.00914641i
$563$	17.3559	+	30.0613i	0.731464	+	1.26693i	0.956258	+	0.292526i	$0.0944958\pi$
$563$	17.3559	+	30.0613i	0.731464	+	1.26693i	−0.224794	+	0.974406i	$0.572171\pi$
$564$	0.000523455	0	0.000168080i	2.20414e−5	0	7.07744e-6i
$565$	10.1918	+	5.88426i	0.428774	+	0.247553i
$566$	−4.13247			−0.173700
$567$	18.0343	−	15.5488i	0.757368	−	0.652989i
$568$	−46.9328			−1.96926
$569$	−31.7117	−	18.3087i	−1.32942	−	0.767542i	−0.344212	−	0.938892i	$-0.611854\pi$
$569$	−31.7117	−	18.3087i	−1.32942	−	0.767542i	−0.985210	+	0.171350i	$0.945187\pi$
$570$	11.9977	+	3.85244i	0.502530	+	0.161361i
$571$	2.49554	+	4.32241i	0.104435	+	0.180887i	0.913507	−	0.406822i	$-0.133363\pi$
$571$	2.49554	+	4.32241i	0.104435	+	0.180887i	−0.809072	+	0.587709i	$0.800030\pi$
$572$	−0.441268	+	0.764298i	−0.0184503	+	0.0319569i
$573$	8.81929	+	9.72690i	0.368431	+	0.406347i
$574$	1.29078	−	9.15425i	0.0538761	−	0.382091i
$575$			26.3279i			1.09795i
$576$	−21.3484	−	15.2858i	−0.889516	−	0.636910i
$577$	−20.6852	+	11.9426i	−0.861134	+	0.497176i	−0.864392	−	0.502818i	$-0.832296\pi$
$577$	−20.6852	+	11.9426i	−0.861134	+	0.497176i	0.00325756	+	0.999995i	$0.498963\pi$
$578$	−6.51705	+	3.76262i	−0.271074	+	0.156504i
$579$	0.230665	+	1.06702i	0.00958611	+	0.0443438i
$580$			0.479157i			0.0198959i
$581$	−7.15249	−	17.7262i	−0.296735	−	0.735406i
$582$	11.7181	−	10.6247i	0.485732	−	0.440409i
$583$	0.119679	−	0.207291i	0.00495662	−	0.00858511i
$584$	−23.8986	−	41.3936i	−0.988931	−	1.71288i
$585$	−3.55574	−	7.83981i	−0.147012	−	0.324136i
$586$	32.1889	+	18.5843i	1.32971	+	0.767710i
$587$	−29.9093			−1.23449			−0.617244	−	0.786772i	$-0.711751\pi$
$587$	−29.9093			−1.23449			−0.617244	+	0.786772i	$0.711751\pi$
$588$	−2.61900	−	1.75682i	−0.108006	−	0.0724499i
$589$	28.3184			1.16684
$590$	7.64507	+	4.41388i	0.314742	+	0.181717i
$591$	−3.10918	+	9.68299i	−0.127895	+	0.398305i
$592$	3.04383	+	5.27207i	0.125101	+	0.216681i
$593$	−4.70014	+	8.14089i	−0.193012	+	0.334306i	−0.946247	−	0.323445i	$-0.895159\pi$
$593$	−4.70014	+	8.14089i	−0.193012	+	0.334306i	0.753235	+	0.657751i	$0.228492\pi$
$594$	−4.08603	−	5.50285i	−0.167652	−	0.225785i
$595$	−3.98958	−	9.88745i	−0.163557	−	0.405346i
$596$			4.80896i			0.196983i
$597$	31.4356	−	6.79565i	1.28657	−	0.278127i
$598$	23.8155	−	13.7499i	0.973888	−	0.562274i
$599$	−14.8428	+	8.56952i	−0.606462	+	0.350141i	−0.771580	−	0.636133i	$-0.780533\pi$
$599$	−14.8428	+	8.56952i	−0.606462	+	0.350141i	0.165117	+	0.986274i	$0.447200\pi$
$600$	−21.6251	+	4.67486i	−0.882842	+	0.190850i
$601$			2.09584i			0.0854912i	0.999086	+	0.0427456i	$0.0136105\pi$
$601$			2.09584i			0.0854912i	−0.999086	+	0.0427456i	$0.986390\pi$
$602$	5.12510	−	36.3474i	0.208883	−	1.48141i
$603$	1.36889	−	13.9526i	0.0557456	−	0.568195i
$604$	−1.62508	+	2.81472i	−0.0661235	+	0.114529i
$605$	−0.422862	−	0.732419i	−0.0171918	−	0.0297771i
$606$	4.05774	−	12.6371i	0.164834	−	0.513348i
$607$	−1.82016	−	1.05087i	−0.0738781	−	0.0426535i	0.462606	−	0.886564i	$-0.346914\pi$
$607$	−1.82016	−	1.05087i	−0.0738781	−	0.0426535i	−0.536484	+	0.843910i	$0.680248\pi$
$608$	9.53223			0.386583
$609$	9.95522	−	0.726234i	0.403406	−	0.0294285i
$610$	8.06101			0.326381
$611$	−0.00358574	−	0.00207023i	−0.000145063	−	8.37524e-5i
$612$	3.38624	−	1.53583i	0.136880	−	0.0620821i
$613$	−22.8530	−	39.5826i	−0.923024	−	1.59872i	−0.794709	−	0.606991i	$-0.792376\pi$
$613$	−22.8530	−	39.5826i	−0.923024	−	1.59872i	−0.128315	−	0.991733i	$-0.540957\pi$
$614$	20.6941	−	35.8433i	0.835147	−	1.44652i
$615$	−2.87470	+	2.60646i	−0.115919	+	0.105103i
$616$	−4.85885	+	6.21323i	−0.195769	+	0.250338i
$617$			23.0184i			0.926687i	0.886179	+	0.463343i	$0.153350\pi$
$617$			23.0184i			0.926687i	−0.886179	+	0.463343i	$0.846650\pi$
$618$	5.47864	+	25.3433i	0.220383	+	1.01946i
$619$	12.2404	−	7.06701i	0.491984	−	0.284047i	−0.233413	−	0.972378i	$-0.574989\pi$
$619$	12.2404	−	7.06701i	0.491984	−	0.284047i	0.725397	+	0.688331i	$0.241656\pi$
$620$	0.827230	−	0.477601i	0.0332223	−	0.0191809i
$621$	−3.66694	−	31.7168i	−0.147149	−	1.27275i
$622$			26.4043i			1.05872i
$623$	−3.73813	−	0.527088i	−0.149765	−	0.0211173i
$624$	13.4690	+	14.8552i	0.539193	+	0.594682i
$625$	−7.39142	+	12.8023i	−0.295657	+	0.512092i
$626$	10.0246	+	17.3631i	0.400663	+	0.693969i
$627$	10.7550	+	3.45339i	0.429512	+	0.137915i
$628$	−1.33124	−	0.768590i	−0.0531221	−	0.0306701i
$629$	−8.50133			−0.338970
$630$	−2.49562	−	8.49545i	−0.0994279	−	0.338467i
$631$	−42.2819			−1.68322			−0.841608	−	0.540089i	$-0.818391\pi$
$631$	−42.2819			−1.68322			−0.841608	+	0.540089i	$0.818391\pi$
$632$	23.8274	+	13.7568i	0.947803	+	0.547214i
$633$	−3.99699	−	1.28342i	−0.158866	−	0.0510115i
$634$	4.82320	+	8.35402i	0.191554	+	0.331781i
$635$	−2.17372	+	3.76499i	−0.0862614	+	0.149409i
$636$	0.0724336	+	0.0798879i	0.00287218	+	0.00316776i
$637$	16.4830	+	17.0997i	0.653082	+	0.677515i
$638$		−	2.87313i		−	0.113748i
$639$	27.4952	−	38.4002i	1.08769	−	1.51909i
$640$	−6.31443	+	3.64564i	−0.249600	+	0.144106i
$641$	−8.63549	+	4.98570i	−0.341081	+	0.196923i	−0.660750	−	0.750606i	$-0.729762\pi$
$641$	−8.63549	+	4.98570i	−0.341081	+	0.196923i	0.319669	+	0.947529i	$0.396428\pi$
$642$	−6.81325	−	31.5170i	−0.268898	−	1.24388i
$643$			29.3008i			1.15551i	0.816210	+	0.577755i	$0.196071\pi$
$643$			29.3008i			1.15551i	−0.816210	+	0.577755i	$0.803929\pi$
$644$	−3.92140	+	1.58228i	−0.154525	+	0.0623506i
$645$	−11.4141	+	10.3491i	−0.449430	+	0.407495i
$646$	20.4951	−	35.4985i	0.806368	−	1.39667i
$647$	−16.8477	−	29.1811i	−0.662351	−	1.14723i	−0.979996	−	0.199016i	$-0.936225\pi$
$647$	−16.8477	−	29.1811i	−0.662351	−	1.14723i	0.317645	−	0.948210i	$-0.397108\pi$
$648$	25.4003	−	8.64366i	0.997819	−	0.339555i
$649$	6.85317	+	3.95668i	0.269010	+	0.155313i
$650$	19.1762			0.752153
$651$	−11.1767	−	16.4631i	−0.438049	−	0.645239i
$652$	0.728965			0.0285485
$653$	15.0798	+	8.70632i	0.590118	+	0.340705i	0.765144	−	0.643859i	$-0.222668\pi$
$653$	15.0798	+	8.70632i	0.590118	+	0.340705i	−0.175026	+	0.984564i	$0.556001\pi$
$654$	−6.95977	+	21.6750i	−0.272148	+	0.847558i
$655$	−0.603855	−	1.04591i	−0.0235946	−	0.0408670i
$656$	4.51942	−	7.82786i	0.176454	−	0.305627i
$657$	47.8689	+	4.69641i	1.86754	+	0.183224i
$658$	−0.00335474	−	0.00262346i	−0.000130782	−	0.000102273i
$659$			41.4179i			1.61341i	0.590953	+	0.806706i	$0.298752\pi$
$659$			41.4179i			1.61341i	−0.590953	+	0.806706i	$0.701248\pi$
$660$	0.372415	−	0.0805076i	0.0144962	−	0.00313375i
$661$	−19.4844	+	11.2493i	−0.757855	+	0.437548i	−0.828525	−	0.559952i	$-0.810820\pi$
$661$	−19.4844	+	11.2493i	−0.757855	+	0.437548i	0.0706699	+	0.997500i	$0.477486\pi$
$662$	−10.0916	+	5.82641i	−0.392222	+	0.226450i
$663$	−27.3704	+	5.91684i	−1.06298	+	0.229791i
$664$		−	21.5383i		−	0.835848i
$665$	11.4951	+	8.98936i	0.445761	+	0.348592i
$666$	−7.02632	−	0.689351i	−0.272264	−	0.0267118i
$667$	6.69199	−	11.5909i	0.259115	−	0.448800i
$668$	−1.09630	−	1.89885i	−0.0424172	−	0.0734688i
$669$	9.53552	−	29.6967i	0.368665	−	1.14814i
$670$	−4.51477	−	2.60660i	−0.174421	−	0.100702i
$671$	7.22603			0.278958
$672$	−3.76218	−	5.54163i	−0.145129	−	0.213773i
$673$	5.02675			0.193767			0.0968835	−	0.995296i	$-0.469113\pi$
$673$	5.02675			0.193767			0.0968835	+	0.995296i	$0.469113\pi$
$674$	0.707261	+	0.408338i	0.0272427	+	0.0157286i
$675$	8.84398	−	20.4323i	0.340405	−	0.786440i
$676$	−0.193514	−	0.335176i	−0.00744284	−	0.0128914i
$677$	15.1151	−	26.1801i	0.580920	−	1.00618i	−0.414451	−	0.910072i	$-0.636026\pi$
$677$	15.1151	−	26.1801i	0.580920	−	1.00618i	0.995371	−	0.0961107i	$-0.0306403\pi$
$678$	23.5521	−	21.3545i	0.904514	−	0.820115i
$679$	16.9870	−	6.85422i	0.651900	−	0.263041i
$680$		−	12.0138i		−	0.460708i
$681$	−3.47676	−	16.0829i	−0.133230	−	0.616299i
$682$	−4.96024	+	2.86380i	−0.189937	+	0.109660i
$683$	−33.3794	+	19.2716i	−1.27723	+	0.737408i	−0.976338	−	0.216250i	$-0.930617\pi$
$683$	−33.3794	+	19.2716i	−1.27723	+	0.737408i	−0.300891	+	0.953659i	$0.597284\pi$
$684$	−2.96268	+	4.13771i	−0.113281	+	0.158209i
$685$			5.43198i			0.207545i
$686$	14.3322	+	19.7831i	0.547205	+	0.755322i
$687$	−6.30375	−	6.95248i	−0.240503	−	0.265254i
$688$	17.9446	−	31.0809i	0.684130	−	1.18495i
$689$	−0.406065	−	0.703326i	−0.0154699	−	0.0267946i
$690$	−11.3040	−	3.62969i	−0.430337	−	0.138180i
$691$	−37.5866	−	21.7006i	−1.42986	−	0.825531i	−0.432752	−	0.901513i	$-0.642457\pi$
$691$	−37.5866	−	21.7006i	−1.42986	−	0.825531i	−0.997109	+	0.0759821i	$0.975791\pi$
$692$	6.75397			0.256748
$693$	−2.23712	−	7.61546i	−0.0849811	−	0.289288i
$694$	10.2757			0.390059
$695$	−0.284683	−	0.164362i	−0.0107987	−	0.00623461i
$696$	10.7087	+	3.43853i	0.405912	+	0.130337i
$697$	6.31130	+	10.9315i	0.239058	+	0.414060i
$698$	11.4524	−	19.8362i	0.433481	−	0.750811i
$699$	16.6144	+	18.3243i	0.628416	+	0.693087i
$700$	−2.91981	−	0.411703i	−0.110359	−	0.0155609i
$701$			33.9854i			1.28361i	0.766867	+	0.641806i	$0.221815\pi$
$701$			33.9854i			1.28361i	−0.766867	+	0.641806i	$0.778185\pi$
$702$	−23.1013	+	2.67086i	−0.871902	+	0.100805i
$703$	10.0766	−	5.81772i	0.380046	−	0.219419i
$704$	−7.57964	+	4.37611i	−0.285668	+	0.164931i
$705$	0.000377705		0.00174720i	1.42252e−5		6.58034e-5i
$706$		−	24.0561i		−	0.905364i
$707$	9.46841	−	12.1077i	0.356096	−	0.455357i
$708$	−2.64114	+	2.39470i	−0.0992603	+	0.0899985i
$709$	−12.0985	+	20.9552i	−0.454369	+	0.786990i	−0.998652	−	0.0519119i	$-0.983469\pi$
$709$	−12.0985	+	20.9552i	−0.454369	+	0.786990i	0.544283	+	0.838902i	$0.316802\pi$
$710$	−8.78104	−	15.2092i	−0.329546	−	0.570791i
$711$	−25.2148	+	11.4362i	−0.945629	+	0.428890i
$712$	−3.68384	−	2.12687i	−0.138058	−	0.0797077i
$713$	−26.6810			−0.999212
$714$	−28.7263	+	2.09558i	−1.07505	+	0.0784253i
$715$	−2.86949			−0.107313
$716$	5.42666	+	3.13308i	0.202804	+	0.117089i
$717$	14.1018	−	43.9175i	0.526640	−	1.64013i
$718$	−7.59713	−	13.1586i	−0.283522	−	0.491075i
$719$	−14.5925	+	25.2750i	−0.544209	+	0.942598i	0.454447	+	0.890774i	$0.349837\pi$
$719$	−14.5925	+	25.2750i	−0.544209	+	0.942598i	−0.998656	+	0.0518241i	$0.983496\pi$
$720$	0.845294	−	8.61579i	0.0315022	−	0.321091i
$721$	−4.19240	+	29.7327i	−0.156133	+	1.10730i
$722$			31.0396i			1.15518i
$723$	19.8636	−	4.29406i	0.738736	−	0.159698i
$724$	−3.29560	+	1.90272i	−0.122480	+	0.0707139i
$725$	8.08258	−	4.66648i	0.300179	−	0.173309i
$726$	−2.23308	+	0.482740i	−0.0828773	+	0.0179162i
$727$		−	6.01471i		−	0.223073i	−0.993760	−	0.111537i	$-0.964423\pi$
$727$		−	6.01471i		−	0.223073i	0.993760	−	0.111537i	$-0.0355773\pi$
$728$	10.0139	+	24.8177i	0.371140	+	0.919805i
$729$	−7.80839	+	25.8463i	−0.289200	+	0.957269i
$730$	8.94277	−	15.4893i	0.330987	−	0.573286i
$731$	25.0593	+	43.4040i	0.926852	+	1.60535i
$732$	−0.995277	+	3.09961i	−0.0367865	+	0.114565i
$733$	−13.3867	−	7.72883i	−0.494450	−	0.285471i	0.231969	−	0.972723i	$-0.425483\pi$
$733$	−13.3867	−	7.72883i	−0.494450	−	0.285471i	−0.726419	+	0.687252i	$0.758817\pi$
$734$	24.5268			0.905300
$735$	0.689142	−	10.2307i	0.0254194	−	0.377364i
$736$	−8.98108			−0.331047
$737$	−4.04712	−	2.33660i	−0.149077	−	0.0860699i
$738$	4.32986	+	9.54661i	0.159384	+	0.351415i
$739$	24.2840	+	42.0612i	0.893302	+	1.54724i	0.835892	+	0.548894i	$0.184951\pi$
$739$	24.2840	+	42.0612i	0.893302	+	1.54724i	0.0574100	+	0.998351i	$0.481716\pi$
$740$	0.196237	−	0.339892i	0.00721380	−	0.0124947i
$741$	28.3929	−	25.7436i	1.04304	−	0.945714i
$742$	−0.312570	−	0.774649i	−0.0114748	−	0.0284383i
$743$		−	19.4569i		−	0.713806i	−0.934142	−	0.356903i	$-0.883833\pi$
$743$		−	19.4569i		−	0.713806i	0.934142	−	0.356903i	$-0.116167\pi$
$744$	−4.73755	−	21.9151i	−0.173687	−	0.803448i
$745$	−13.5411	+	7.81798i	−0.496109	+	0.286429i
$746$	−9.44392	+	5.45245i	−0.345767	+	0.199628i
$747$	17.6225	+	12.6181i	0.644775	+	0.461670i
$748$		−	1.23942i		−	0.0453175i
$749$	5.21368	−	36.9756i	0.190504	−	1.35106i
$750$	−12.0502	−	13.2903i	−0.440012	−	0.485294i
$751$	4.96755	−	8.60405i	0.181268	−	0.313966i	−0.761044	−	0.648700i	$-0.775313\pi$
$751$	4.96755	−	8.60405i	0.181268	−	0.313966i	0.942313	+	0.334734i	$0.108646\pi$
$752$	−0.00208193	−	0.00360601i	−7.59202e−5	−	0.000131498i
$753$	16.5015	+	5.29857i	0.601347	+	0.193091i
$754$	−8.44232	−	4.87418i	−0.307451	−	0.177507i
$755$	−10.5676			−0.384596
$756$	3.57479	+	0.0893020i	0.130014	+	0.00324788i
$757$	−28.0336			−1.01890			−0.509449	−	0.860501i	$-0.670151\pi$
$757$	−28.0336			−1.01890			−0.509449	+	0.860501i	$0.670151\pi$
$758$	30.7314	+	17.7428i	1.11621	+	0.644446i
$759$	−10.1331	−	3.25372i	−0.367810	−	0.118103i
$760$	8.22141	+	14.2399i	0.298222	+	0.516535i
$761$	12.0808	−	20.9246i	0.437928	−	0.758514i	−0.559601	−	0.828762i	$-0.689046\pi$
$761$	12.0808	−	20.9246i	0.437928	−	0.758514i	0.997530	+	0.0702477i	$0.0223790\pi$
$762$	7.88861	+	8.70044i	0.285774	+	0.315184i
$763$	−16.2401	+	20.7669i	−0.587930	+	0.751813i
$764$			1.97176i			0.0713358i
$765$	9.82964	+	7.03820i	0.355391	+	0.254467i
$766$	−27.6047	+	15.9376i	−0.997399	+	0.575849i
$767$	23.2524	−	13.4248i	0.839596	−	0.484741i
$768$	−2.24433	−	10.3819i	−0.0809853	−	0.374625i
$769$		−	4.43453i		−	0.159913i	−0.996798	−	0.0799567i	$-0.974522\pi$
$769$		−	4.43453i		−	0.159913i	0.996798	−	0.0799567i	$-0.0254782\pi$
$770$	−2.92256	−	0.412091i	−0.105322	−	0.0148507i
$771$	9.41934	−	8.54044i	0.339229	−	0.307576i
$772$	−0.0819700	+	0.141976i	−0.00295016	+	0.00510984i
$773$	−5.39872	−	9.35087i	−0.194179	−	0.336327i	0.752452	−	0.658647i	$-0.228871\pi$
$773$	−5.39872	−	9.35087i	−0.194179	−	0.336327i	−0.946631	+	0.322319i	$0.895537\pi$
$774$	17.1919	+	37.9052i	0.617950	+	1.36248i
$775$	−16.1127	−	9.30265i	−0.578784	−	0.334161i
$776$	20.6401			0.740936
$777$	−7.35919	−	3.56196i	−0.264010	−	0.127785i
$778$	1.71472			0.0614757
$779$	−14.9615	−	8.63803i	−0.536052	−	0.309490i
$780$	0.395230	−	1.23087i	0.0141515	−	0.0440723i
$781$	−7.87147	−	13.6338i	−0.281663	−	0.487855i
$782$	−19.3101	+	33.4460i	−0.690526	+	1.19603i
$783$	−9.08700	+	6.74737i	−0.324743	+	0.241131i
$784$	5.75725	+	23.1806i	0.205616	+	0.827879i
$785$		−	4.99802i		−	0.178387i
$786$	−3.18888	+	0.689362i	−0.113743	+	0.0245887i
$787$	2.15468	−	1.24401i	0.0768061	−	0.0443440i	−0.461105	−	0.887346i	$-0.652547\pi$
$787$	2.15468	−	1.24401i	0.0768061	−	0.0443440i	0.537911	+	0.843001i	$0.319214\pi$
$788$	−1.32265	+	0.763630i	−0.0471173	+	0.0272032i
$789$	−17.2007	+	3.71840i	−0.612361	+	0.132378i
$790$			10.2954i			0.366296i
$791$	34.1419	−	13.7762i	1.21395	−	0.489826i
$792$	0.873262	−	8.90085i	0.0310300	−	0.316278i
$793$	12.2587	−	21.2328i	0.435321	−	0.753998i
$794$	1.33129	+	2.30586i	0.0472456	+	0.0818318i
$795$	−0.107193	+	0.333834i	−0.00380175	+	0.0118399i
$796$	4.18278	+	2.41493i	0.148255	+	0.0855948i
$797$	−51.9216			−1.83916			−0.919579	−	0.392905i	$-0.871470\pi$
$797$	−51.9216			−1.83916			−0.919579	+	0.392905i	$0.871470\pi$
$798$	32.6150	−	22.1422i	1.15456	−	0.783824i
$799$	0.00581477			0.000205712
$800$	−5.42367	−	3.13136i	−0.191756	−	0.110710i
$801$	3.89834	−	1.76809i	0.137741	−	0.0624725i
$802$	22.1295	+	38.3295i	0.781421	+	1.35346i
$803$	8.01645	−	13.8849i	0.282894	−	0.489987i
$804$	1.55972	−	1.41418i	0.0550071	−	0.0498744i
$805$	−10.8305	−	8.46960i	−0.381724	−	0.298514i
$806$			19.4334i			0.684512i
$807$	2.85048	+	13.1859i	0.100342	+	0.464164i
$808$	14.9988	−	8.65954i	0.527655	−	0.304641i
$809$	3.35027	−	1.93428i	0.117789	−	0.0680057i	−0.439948	−	0.898023i	$-0.645003\pi$
$809$	3.35027	−	1.93428i	0.117789	−	0.0680057i	0.557737	+	0.830018i	$0.311670\pi$
$810$	7.55345	+	6.61411i	0.265401	+	0.232396i
$811$			49.5607i			1.74031i	0.492775	+	0.870156i	$0.335982\pi$
$811$			49.5607i			1.74031i	−0.492775	+	0.870156i	$0.664018\pi$
$812$	1.18080	+	0.923405i	0.0414380	+	0.0324052i
$813$	−0.764177	−	0.842819i	−0.0268009	−	0.0295590i
$814$	−1.17668	+	2.03806i	−0.0412425	+	0.0714340i
$815$	1.18509	+	2.05263i	0.0415118	+	0.0719005i
$816$	−26.8126	−	8.60944i	−0.938628	−	0.301391i
$817$	−59.4053	−	34.2977i	−2.07833	−	1.19992i
$818$	−48.6043			−1.69941
$819$	−26.1723	−	6.34593i	−0.914534	−	0.221745i
$820$	−0.582736			−0.0203500
$821$	−6.64413	−	3.83599i	−0.231882	−	0.133877i	0.379558	−	0.925168i	$-0.376076\pi$
$821$	−6.64413	−	3.83599i	−0.231882	−	0.133877i	−0.611440	+	0.791291i	$0.709409\pi$
$822$	13.9715	+	4.48621i	0.487312	+	0.156475i
$823$	21.0617	+	36.4800i	0.734166	+	1.27161i	0.955088	+	0.296321i	$0.0957599\pi$
$823$	21.0617	+	36.4800i	0.734166	+	1.27161i	−0.220922	+	0.975291i	$0.570907\pi$
$824$	−16.9169	+	29.3009i	−0.589327	+	1.02074i
$825$	−4.98495	−	5.49796i	−0.173554	−	0.191414i
$826$	25.6104	−	10.3338i	0.891099	−	0.359558i
$827$		−	8.11227i		−	0.282091i	−0.990003	−	0.141046i	$-0.954954\pi$
$827$		−	8.11227i		−	0.282091i	0.990003	−	0.141046i	$-0.0450464\pi$
$828$	2.79138	−	3.89847i	0.0970070	−	0.135481i
$829$	6.25843	−	3.61331i	0.217364	−	0.125495i	−0.387365	−	0.921926i	$-0.626615\pi$
$829$	6.25843	−	3.61331i	0.217364	−	0.125495i	0.604729	+	0.796431i	$0.293281\pi$
$830$	6.97977	−	4.02977i	0.242271	−	0.139876i
$831$	1.95161	+	9.02781i	0.0677005	+	0.313171i
$832$			29.6957i			1.02951i
$833$	−32.0544	−	9.22292i	−1.11062	−	0.319555i
$834$	−0.657869	+	0.596484i	−0.0227801	+	0.0206546i
$835$	3.56454	−	6.17397i	0.123356	−	0.213659i
$836$	0.848169	+	1.46907i	0.0293346	+	0.0508089i
$837$	20.7063	+	8.96258i	0.715715	+	0.309792i
$838$	10.8749	+	6.27863i	0.375668	+	0.216892i
$839$	24.7103			0.853093			0.426546	−	0.904466i	$-0.359730\pi$
$839$	24.7103			0.853093			0.426546	+	0.904466i	$0.359730\pi$
$840$	5.03364	−	10.3998i	0.173677	−	0.358826i
$841$	24.2555			0.836398
$842$	−45.2041	−	26.0986i	−1.55784	−	0.899418i
$843$	0.100512	−	0.313026i	0.00346180	−	0.0107812i
$844$	−0.315215	−	0.545968i	−0.0108501	−	0.0187930i
$845$	0.629195	−	1.08980i	0.0216450	−	0.0374902i
$846$	0.00480588		0.000471505i	0.000165230		1.62107e-5i
$847$	−2.61984	−	0.369406i	−0.0900186	−	0.0126929i
$848$		−	0.816722i		−	0.0280464i
$849$	5.30385	−	1.14657i	0.182028	−	0.0393502i
$850$	−23.3227	+	13.4654i	−0.799961	+	0.461858i
$851$	−9.49397	+	5.48134i	−0.325449	+	0.187898i
$852$	6.93241	−	1.49863i	0.237500	−	0.0513422i
$853$			25.3066i			0.866483i	0.901278	+	0.433241i	$0.142630\pi$
$853$			25.3066i			0.866483i	−0.901278	+	0.433241i	$0.857370\pi$
$854$	15.5347	−	19.8650i	0.531587	−	0.679765i
$855$	−16.4675	−	1.61562i	−0.563176	−	0.0552531i
$856$	21.0379	−	36.4387i	0.719059	−	1.24545i
$857$	−22.2467	−	38.5324i	−0.759933	−	1.31624i	−0.942884	−	0.333120i	$-0.891899\pi$
$857$	−22.2467	−	38.5324i	−0.759933	−	1.31624i	0.182952	−	0.983122i	$-0.441435\pi$
$858$	−2.36988	+	7.38057i	−0.0809064	+	0.251969i
$859$	−22.4893	−	12.9842i	−0.767326	−	0.443016i	0.0645938	−	0.997912i	$-0.479425\pi$
$859$	−22.4893	−	12.9842i	−0.767326	−	0.443016i	−0.831920	+	0.554896i	$0.812758\pi$
$860$	−2.31378			−0.0788993
$861$	0.883224	+	12.1072i	0.0301002	+	0.412613i
$862$	37.8976			1.29080
$863$	36.2164	+	20.9096i	1.23282	+	0.711770i	0.967617	−	0.252422i	$-0.0812273\pi$
$863$	36.2164	+	20.9096i	1.23282	+	0.711770i	0.265204	+	0.964192i	$0.414561\pi$
$864$	6.96994	+	3.01689i	0.237122	+	0.102637i
$865$	10.9800	+	19.0179i	0.373331	+	0.646629i
$866$	16.3451	−	28.3106i	0.555429	−	0.962032i
$867$	7.32041	−	6.63735i	0.248614	−	0.225416i
$868$	0.417225	−	2.95897i	0.0141615	−	0.100434i
$869$			9.22902i			0.313073i
$870$	0.889275	+	4.11364i	0.0301492	+	0.139465i
$871$	−13.7316	+	7.92796i	−0.465279	+	0.268629i
$872$	−25.7256	+	14.8527i	−0.871179	+	0.502975i
$873$	−12.0918	+	16.8876i	−0.409247	+	0.571560i
$874$		−	52.8578i		−	1.78794i
$875$	−7.77384	−	19.2661i	−0.262804	−	0.651313i
$876$	4.85180	+	5.35110i	0.163927	+	0.180797i
$877$	−3.71617	+	6.43659i	−0.125486	+	0.217348i	−0.921923	−	0.387374i	$-0.873382\pi$
$877$	−3.71617	+	6.43659i	−0.125486	+	0.217348i	0.796437	+	0.604722i	$0.206716\pi$
$878$	7.16014	+	12.4017i	0.241643	+	0.418538i
$879$	−46.4695	−	14.9212i	−1.56738	−	0.503280i
$880$	−2.49910	−	1.44286i	−0.0842448	−	0.0486388i
$881$	−40.3349			−1.35892			−0.679459	−	0.733713i	$-0.737786\pi$
$881$	−40.3349			−1.35892			−0.679459	+	0.733713i	$0.737786\pi$
$882$	−25.7450	−	10.2219i	−0.866879	−	0.344190i
$883$	22.6495			0.762217			0.381109	−	0.924530i	$-0.375542\pi$
$883$	22.6495			0.762217			0.381109	+	0.924530i	$0.375542\pi$
$884$	−3.64187	−	2.10263i	−0.122489	−	0.0707192i
$885$	−11.0368	−	3.54388i	−0.370997	−	0.119126i
$886$	−18.3512	−	31.7852i	−0.616520	−	1.06784i
$887$	16.2497	−	28.1452i	0.545610	−	0.945024i	−0.452958	−	0.891532i	$-0.649631\pi$
$887$	16.2497	−	28.1452i	0.545610	−	0.945024i	0.998568	−	0.0534925i	$-0.0170353\pi$
$888$	−6.18802	−	6.82483i	−0.207656	−	0.229026i
$889$	5.08910	+	12.6124i	0.170683	+	0.423007i
$890$		−	1.59173i		−	0.0533550i
$891$	6.77104	+	5.92900i	0.226838	+	0.198629i
$892$	4.05641	−	2.34197i	0.135819	−	0.0784149i
$893$	−0.00689222	+	0.00397922i	−0.000230639	+	0.000133160i
$894$	8.92502	+	41.2857i	0.298497	+	1.38080i
$895$			20.3739i			0.681026i
$896$	−3.18477	+	22.5865i	−0.106396	+	0.754562i
$897$	−26.7512	+	24.2551i	−0.893197	+	0.809854i
$898$	7.44556	−	12.8961i	0.248461	−	0.430348i
$899$	4.72906	+	8.19097i	0.157723	+	0.273184i
$900$	3.04496	−	1.38104i	0.101499	−	0.0460347i
$901$	0.987737	+	0.570270i	0.0329063	+	0.0189985i
$902$	3.49421			0.116344
$903$	3.50688	+	48.0723i	0.116702	+	1.59975i
$904$	41.4843			1.37975
$905$	−10.7154	−	6.18653i	−0.356192	−	0.205647i
$906$	−8.72768	+	27.1808i	−0.289958	+	0.903022i
$907$	15.4063	+	26.6845i	0.511558	+	0.886045i	0.999910	+	0.0133983i	$0.00426494\pi$
$907$	15.4063	+	26.6845i	0.511558	+	0.886045i	−0.488352	+	0.872647i	$0.662402\pi$
$908$	1.23552	−	2.13998i	0.0410020	−	0.0710176i
$909$	−1.70172	+	17.3450i	−0.0564425	+	0.575299i
$910$	−6.16892	+	7.88848i	−0.204498	+	0.261501i
$911$			19.6247i			0.650197i	0.945680	+	0.325098i	$0.105397\pi$
$911$			19.6247i			0.650197i	−0.945680	+	0.325098i	$0.894603\pi$
$912$	37.6725	−	8.14394i	1.24746	−	0.269673i
$913$	6.25679	−	3.61236i	0.207069	−	0.119552i
$914$	11.9925	−	6.92388i	0.396677	−	0.229022i
$915$	−10.3460	+	2.23656i	−0.342027	+	0.0739384i
$916$		−	1.40935i		−	0.0465663i
$917$	−3.74117	−	0.527518i	−0.123544	−	0.0174202i
$918$	26.2210	−	19.4699i	0.865422	−	0.642601i
$919$	−0.672054	+	1.16403i	−0.0221690	+	0.0383979i	−0.876897	−	0.480678i	$-0.840391\pi$
$919$	−0.672054	+	1.16403i	−0.0221690	+	0.0383979i	0.854728	+	0.519076i	$0.173724\pi$
$920$	−7.74605	−	13.4166i	−0.255380	−	0.442331i
$921$	−16.6152	+	51.7450i	−0.547488	+	1.70506i
$922$	7.12887	+	4.11585i	0.234777	+	0.135548i
$923$	−53.4149			−1.75817
$924$	0.519300	−	1.07290i	0.0170837	−	0.0352959i
$925$	−7.64454			−0.251351
$926$	33.3897	+	19.2775i	1.09725	+	0.633499i
$927$	−14.0632	−	31.0070i	−0.461897	−	1.01840i
$928$	1.59185	+	2.75716i	0.0522549	+	0.0905081i
$929$	−4.41709	+	7.65062i	−0.144920	+	0.251009i	−0.929343	−	0.369217i	$-0.879626\pi$
$929$	−4.41709	+	7.65062i	−0.144920	+	0.251009i	0.784423	+	0.620226i	$0.212959\pi$
$930$	6.21551	−	5.63555i	0.203815	−	0.184797i
$931$	44.3055	−	11.0039i	1.45205	−	0.360639i
$932$			3.71455i			0.121674i
$933$	−7.32598	−	33.8888i	−0.239842	−	1.10947i
$934$	−36.4311	+	21.0335i	−1.19206	+	0.688238i
$935$	3.48996	−	2.01493i	0.114134	−	0.0658953i
$936$	−24.6726	−	17.6660i	−0.806448	−	0.577431i
$937$		−	2.64773i		−	0.0864975i	−0.999064	−	0.0432488i	$-0.986229\pi$
$937$		−	2.64773i		−	0.0864975i	0.999064	−	0.0432488i	$-0.0137708\pi$
$938$	−15.1241	+	6.10257i	−0.493821	+	0.199256i
$939$	−17.6836	−	19.5035i	−0.577083	−	0.636471i
$940$	−0.000134223	0	0.000232480i	−4.37786e−6	0	7.58267e-6i
$941$	−19.4874	−	33.7532i	−0.635271	−	1.10032i	−0.986458	−	0.164016i	$-0.947555\pi$
$941$	−19.4874	−	33.7532i	−0.635271	−	1.10032i	0.351187	−	0.936305i	$-0.385778\pi$
$942$	−12.8553	−	4.12780i	−0.418849	−	0.134491i
$943$	14.0964	+	8.13859i	0.459043	+	0.265029i
$944$	27.0014			0.878820
$945$	5.56012	+	10.2111i	0.180871	+	0.332168i
$946$	13.8739			0.451080
$947$	12.4981	+	7.21581i	0.406135	+	0.234482i	0.689128	−	0.724640i	$-0.257994\pi$
$947$	12.4981	+	7.21581i	0.406135	+	0.234482i	−0.282993	+	0.959122i	$0.591327\pi$
$948$	−3.95880	−	1.27116i	−0.128576	−	0.0412853i
$949$	−27.1994	−	47.1107i	−0.882928	−	1.52928i
$950$	18.4295	−	31.9208i	0.597932	−	1.03565i
$951$	−8.50823	−	9.38382i	−0.275898	−	0.304291i
$952$	−29.6059	−	23.1523i	−0.959534	−	0.750371i
$953$		−	26.4460i		−	0.856669i	−0.903620	−	0.428335i	$-0.859100\pi$
$953$		−	26.4460i		−	0.856669i	0.903620	−	0.428335i	$-0.140900\pi$
$954$	0.770119	+	0.551419i	0.0249335	+	0.0178529i
$955$	−5.55211	+	3.20551i	−0.179662	+	0.103728i
$956$	5.99889	−	3.46346i	0.194018	−	0.112016i
$957$	0.797161	+	3.68754i	0.0257686	+	0.119201i
$958$			26.9674i			0.871279i
$959$	13.3862	+	10.4682i	0.432263	+	0.338036i
$960$	9.49779	−	8.61156i	0.306540	−	0.277937i
$961$	−6.07259	+	10.5180i	−0.195890	+	0.339292i
$962$	3.99239	+	6.91503i	0.128720	+	0.222949i
$963$	17.4891	+	38.5604i	0.563577	+	1.24259i
$964$	2.64303	+	1.52595i	0.0851263	+	0.0491477i
$965$	−0.533038			−0.0171591
$966$	−30.7293	+	20.8619i	−0.988698	+	0.671221i
$967$	−18.7011			−0.601386			−0.300693	−	0.953721i	$-0.597218\pi$
$967$	−18.7011			−0.601386			−0.300693	+	0.953721i	$0.597218\pi$
$968$	−2.58179	−	1.49060i	−0.0829819	−	0.0479096i
$969$	−16.4554	+	51.2473i	−0.528622	+	1.64630i
$970$	3.86172	+	6.68870i	0.123992	+	0.214761i
$971$	23.9027	−	41.4007i	0.767074	−	1.32861i	−0.172069	−	0.985085i	$-0.555045\pi$
$971$	23.9027	−	41.4007i	0.767074	−	1.32861i	0.939143	−	0.343526i	$-0.111621\pi$
$972$	−3.47586	+	2.08782i	−0.111488	+	0.0669668i
$973$	−0.953668	+	0.384804i	−0.0305732	+	0.0123362i
$974$			29.6088i			0.948727i
$975$	−24.6119	+	5.32052i	−0.788211	+	0.170393i
$976$	21.3528	−	12.3281i	0.683487	−	0.394611i
$977$	43.2978	−	24.9980i	1.38522	−	0.799756i	0.392446	−	0.919775i	$-0.371629\pi$
$977$	43.2978	−	24.9980i	1.38522	−	0.799756i	0.992772	+	0.120019i	$0.0382955\pi$
$978$	6.25828	−	1.35290i	0.200118	−	0.0432609i
$979$		−	1.42686i		−	0.0456025i
$980$	1.10866	−	1.06867i	0.0354147	−	0.0341376i
$981$	2.91876	−	29.7499i	0.0931889	−	0.949842i
$982$	−1.52329	+	2.63842i	−0.0486102	+	0.0841954i
$983$	12.6653	+	21.9370i	0.403962	+	0.699683i	0.994200	−	0.107547i	$-0.0342995\pi$
$983$	12.6653	+	21.9370i	0.403962	+	0.699683i	−0.590238	+	0.807229i	$0.700966\pi$
$984$	−4.18184	+	13.0236i	−0.133312	+	0.415177i
$985$	−4.30048	−	2.48288i	−0.137025	−	0.0791112i
$986$	13.6904			0.435991
$987$	0.00503357	+	0.00243632i	0.000160220	+	7.75489e-5i
$988$	5.75558			0.183109
$989$	55.9706	+	32.3146i	1.77976	+	1.02755i
$990$	3.04783	−	1.38234i	0.0968663	−	0.0439337i
$991$	−19.7673	−	34.2380i	−0.627929	−	1.08761i	−0.987967	−	0.154668i	$-0.950569\pi$
$991$	−19.7673	−	34.2380i	−0.627929	−	1.08761i	0.360037	−	0.932938i	$-0.382764\pi$
$992$	3.17335	−	5.49641i	0.100754	−	0.174511i
$993$	11.3356	−	10.2779i	0.359725	−	0.326160i
$994$	−54.4028	−	7.67097i	−1.72555	−	0.243308i
$995$			15.7039i			0.497847i
$996$	0.687747	+	3.18141i	0.0217921	+	0.100807i
$997$	22.2640	−	12.8541i	0.705107	−	0.407094i	−0.104139	−	0.994563i	$-0.533209\pi$
$997$	22.2640	−	12.8541i	0.705107	−	0.407094i	0.809247	+	0.587469i	$0.199875\pi$
$998$	−10.2084	+	5.89384i	−0.323142	+	0.186566i
$999$	9.20925	−	1.06473i	0.291368	−	0.0336865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.19	yes	52
3.2	odd	2	inner	231.2.n.a.89.8	✓	52
7.3	odd	6	inner	231.2.n.a.122.8	yes	52
21.17	even	6	inner	231.2.n.a.122.19	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.8	✓	52	3.2	odd	2	inner
231.2.n.a.89.19	yes	52	1.1	even	1	trivial
231.2.n.a.122.8	yes	52	7.3	odd	6	inner
231.2.n.a.122.19	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)

\(f(q)\)	\(=\)	\(q+(1.14233 + 0.659525i) q^{2} +(-1.64912 - 0.529528i) q^{3} +(-0.130055 - 0.225261i) q^{4} +(0.422862 - 0.732419i) q^{5} +(-1.53460 - 1.69253i) q^{6} +(-0.990003 - 2.45355i) q^{7} -2.98120i q^{8} +(2.43920 + 1.74651i) q^{9} +O(q^{10})\)	\(q+(1.14233 + 0.659525i) q^{2} +(-1.64912 - 0.529528i) q^{3} +(-0.130055 - 0.225261i) q^{4} +(0.422862 - 0.732419i) q^{5} +(-1.53460 - 1.69253i) q^{6} +(-0.990003 - 2.45355i) q^{7} -2.98120i q^{8} +(2.43920 + 1.74651i) q^{9} +(0.966096 - 0.557776i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.0951936 + 0.440350i) q^{12} -3.39294i q^{13} +(0.487264 - 3.45569i) q^{14} +(-1.08519 + 0.983930i) q^{15} +(1.70606 - 2.95499i) q^{16} +(2.38249 + 4.12660i) q^{17} +(1.63450 + 3.60381i) q^{18} +(-5.64791 - 3.26082i) q^{19} -0.219981 q^{20} +(0.333413 + 4.57043i) q^{21} +1.31905 q^{22} +(5.32135 + 3.07228i) q^{23} +(-1.57863 + 4.91635i) q^{24} +(2.14238 + 3.71070i) q^{25} +(2.23773 - 3.87586i) q^{26} +(-3.09771 - 4.17183i) q^{27} +(-0.423934 + 0.542104i) q^{28} -2.17818i q^{29} +(-1.88857 + 0.408265i) q^{30} +(-3.76047 + 2.17111i) q^{31} +(-1.26581 + 0.730815i) q^{32} +(-1.69294 + 0.365976i) q^{33} +6.28525i q^{34} +(-2.21566 - 0.312415i) q^{35} +(0.0761920 - 0.776599i) q^{36} +(-0.892063 + 1.54510i) q^{37} +(-4.30118 - 7.44987i) q^{38} +(-1.79666 + 5.59537i) q^{39} +(-2.18348 - 1.26063i) q^{40} +2.64903 q^{41} +(-2.63344 + 5.44083i) q^{42} +10.5181 q^{43} +(-0.225261 - 0.130055i) q^{44} +(2.31062 - 1.04798i) q^{45} +(4.05249 + 7.01912i) q^{46} +(0.000610157 - 0.00105682i) q^{47} +(-4.37825 + 3.96972i) q^{48} +(-5.03979 + 4.85804i) q^{49} +5.65180i q^{50} +(-1.74387 - 8.06685i) q^{51} +(-0.764298 + 0.441268i) q^{52} +(0.207291 - 0.119679i) q^{53} +(-0.787180 - 6.80863i) q^{54} -0.845724i q^{55} +(-7.31450 + 2.95139i) q^{56} +(7.58739 + 8.36822i) q^{57} +(1.43656 - 2.48820i) q^{58} +(3.95668 + 6.85317i) q^{59} +(0.362775 + 0.116486i) q^{60} +(6.25792 + 3.61301i) q^{61} -5.72759 q^{62} +(1.87033 - 7.71374i) q^{63} -8.75221 q^{64} +(-2.48505 - 1.43475i) q^{65} +(-2.17527 - 0.698474i) q^{66} +(-2.33660 - 4.04712i) q^{67} +(0.619708 - 1.07337i) q^{68} +(-7.14869 - 7.88437i) q^{69} +(-2.32497 - 1.81816i) q^{70} -15.7429i q^{71} +(5.20669 - 7.27173i) q^{72} +(13.8849 - 8.01645i) q^{73} +(-2.03806 + 1.17668i) q^{74} +(-1.56811 - 7.25385i) q^{75} +1.69634i q^{76} +(-2.08414 - 1.62983i) q^{77} +(-5.74266 + 5.20682i) q^{78} +(-4.61451 + 7.99256i) q^{79} +(-1.44286 - 2.49910i) q^{80} +(2.89939 + 8.52018i) q^{81} +(3.02607 + 1.74710i) q^{82} +7.22472 q^{83} +(0.986178 - 0.669510i) q^{84} +4.02986 q^{85} +(12.0152 + 6.93695i) q^{86} +(-1.15341 + 3.59208i) q^{87} +(-1.49060 - 2.58179i) q^{88} +(0.713428 - 1.23569i) q^{89} +(3.33066 + 0.326771i) q^{90} +(-8.32474 + 3.35902i) q^{91} -1.59826i q^{92} +(7.35113 - 1.58914i) q^{93} +(0.00139400 - 0.000804826i) q^{94} +(-4.77657 + 2.75776i) q^{95} +(2.47446 - 0.534921i) q^{96} +6.92343i q^{97} +(-8.96110 + 2.22562i) q^{98} +(2.98567 + 0.292923i) 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

Introduction

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