LMFDB - Embedded newform 280.2.bf.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(109,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 4]))

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

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

chi := DirichletCharacter("280.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bf (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	280.109
Dual form			280.2.bf.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39743 + 0.217250i) q^{2} +(0.284947 - 0.493542i) q^{3} +(1.90560 - 0.607183i) q^{4} +(0.172645 + 2.22939i) q^{5} +(-0.290970 + 0.751594i) q^{6} +(-2.45778 + 0.979438i) q^{7} +(-2.53103 + 1.26249i) q^{8} +(1.33761 + 2.31681i) q^{9} +O(q^{10})$	\(q+(-1.39743 + 0.217250i) q^{2} +(0.284947 - 0.493542i) q^{3} +(1.90560 - 0.607183i) q^{4} +(0.172645 + 2.22939i) q^{5} +(-0.290970 + 0.751594i) q^{6} +(-2.45778 + 0.979438i) q^{7} +(-2.53103 + 1.26249i) q^{8} +(1.33761 + 2.31681i) q^{9} +(-0.725596 - 3.07791i) q^{10} +(-1.13768 - 0.656841i) q^{11} +(0.243325 - 1.11351i) q^{12} -5.78900 q^{13} +(3.22179 - 1.90265i) q^{14} +(1.14949 + 0.550050i) q^{15} +(3.26266 - 2.31410i) q^{16} +(5.97698 + 3.45081i) q^{17} +(-2.37254 - 2.94698i) q^{18} +(-3.72412 + 2.15012i) q^{19} +(1.68264 + 4.14351i) q^{20} +(-0.216944 + 1.49211i) q^{21} +(1.73253 + 0.670726i) q^{22} +(2.45396 - 1.41679i) q^{23} +(-0.0981190 + 1.60891i) q^{24} +(-4.94039 + 0.769789i) q^{25} +(8.08970 - 1.25766i) q^{26} +3.23427 q^{27} +(-4.08887 + 3.35875i) q^{28} +2.89432i q^{29} +(-1.72583 - 0.518927i) q^{30} +(-3.49184 + 6.04805i) q^{31} +(-4.05659 + 3.94260i) q^{32} +(-0.648358 + 0.374330i) q^{33} +(-9.10209 - 3.52376i) q^{34} +(-2.60788 - 5.31027i) q^{35} +(3.95568 + 3.60275i) q^{36} +(1.65034 + 2.85848i) q^{37} +(4.73707 - 3.81370i) q^{38} +(-1.64956 + 2.85711i) q^{39} +(-3.25155 - 5.42470i) q^{40} -0.235857 q^{41} +(-0.0209980 - 2.13224i) q^{42} +4.69228 q^{43} +(-2.56680 - 0.560899i) q^{44} +(-4.93415 + 3.38205i) q^{45} +(-3.12143 + 2.51299i) q^{46} +(5.38956 - 3.11166i) q^{47} +(-0.212423 - 2.26966i) q^{48} +(5.08140 - 4.81449i) q^{49} +(6.73659 - 2.14902i) q^{50} +(3.40624 - 1.96660i) q^{51} +(-11.0315 + 3.51498i) q^{52} +(-2.28241 + 3.95326i) q^{53} +(-4.51966 + 0.702646i) q^{54} +(1.26794 - 2.64974i) q^{55} +(4.98420 - 5.58191i) q^{56} +2.45068i q^{57} +(-0.628792 - 4.04460i) q^{58} +(-3.12758 - 1.80571i) q^{59} +(2.52446 + 0.350225i) q^{60} +(6.27862 - 3.62496i) q^{61} +(3.56565 - 9.21031i) q^{62} +(-5.55673 - 4.38411i) q^{63} +(4.81225 - 6.39079i) q^{64} +(-0.999444 - 12.9060i) q^{65} +(0.824710 - 0.663954i) q^{66} +(7.96587 - 13.7973i) q^{67} +(13.4850 + 2.94676i) q^{68} -1.61484i q^{69} +(4.79798 + 6.85415i) q^{70} +9.13804 q^{71} +(-6.31048 - 4.17521i) q^{72} +(-1.47515 - 0.851681i) q^{73} +(-2.92724 - 3.63598i) q^{74} +(-1.02782 + 2.65764i) q^{75} +(-5.79118 + 6.35850i) q^{76} +(3.43951 + 0.500085i) q^{77} +(1.68443 - 4.35098i) q^{78} +(-5.80943 - 10.0622i) q^{79} +(5.72232 + 6.87423i) q^{80} +(-3.09124 + 5.35418i) q^{81} +(0.329593 - 0.0512399i) q^{82} -8.84830 q^{83} +(0.492574 + 2.97509i) q^{84} +(-6.66132 + 13.9208i) q^{85} +(-6.55712 + 1.01940i) q^{86} +(1.42847 + 0.824728i) q^{87} +(3.70877 + 0.226178i) q^{88} +(3.83779 + 6.64725i) q^{89} +(6.16036 - 5.79811i) q^{90} +(14.2281 - 5.66996i) q^{91} +(3.81602 - 4.18985i) q^{92} +(1.98998 + 3.44674i) q^{93} +(-6.85551 + 5.51921i) q^{94} +(-5.43642 - 7.93131i) q^{95} +(0.789928 + 3.12553i) q^{96} +5.71252i q^{97} +(-6.05494 + 7.83184i) q^{98} -3.51439i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) $ 88 * q - 2 * q^4 - 40 * q^9	$ 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) $ 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.39743	+	0.217250i	−0.988130	+	0.153619i
$2$	−1.39743	+	0.217250i	−0.988130	+	0.153619i
$3$	0.284947	−	0.493542i	0.164514	−	0.284947i	−0.771969	−	0.635661i	$-0.780728\pi$
$3$	0.284947	−	0.493542i	0.164514	−	0.284947i	0.936483	+	0.350714i	$0.114061\pi$
$4$	1.90560	−	0.607183i	0.952802	−	0.303591i
$5$	0.172645	+	2.22939i	0.0772094	+	0.997015i
$5$	0.172645	+	2.22939i	0.0772094	+	0.997015i
$6$	−0.290970	+	0.751594i	−0.118788	+	0.306837i
$7$	−2.45778	+	0.979438i	−0.928955	+	0.370193i
$7$	−2.45778	+	0.979438i	−0.928955	+	0.370193i
$8$	−2.53103	+	1.26249i	−0.894855	+	0.446357i
$9$	1.33761	+	2.31681i	0.445870	+	0.772270i
$10$	−0.725596	−	3.07791i	−0.229454	−	0.973320i
$11$	−1.13768	−	0.656841i	−0.343024	−	0.198045i	0.318584	−	0.947895i	$-0.396793\pi$
$11$	−1.13768	−	0.656841i	−0.343024	−	0.198045i	−0.661609	+	0.749849i	$0.730126\pi$
$12$	0.243325	−	1.11351i	0.0702420	−	0.321443i
$13$	−5.78900			−1.60558			−0.802790	−	0.596262i	$-0.796652\pi$
$13$	−5.78900			−1.60558			−0.802790	+	0.596262i	$0.796652\pi$
$14$	3.22179	−	1.90265i	0.861060	−	0.508504i
$15$	1.14949	+	0.550050i	0.296798	+	0.142022i
$16$	3.26266	−	2.31410i	0.815665	−	0.578525i
$17$	5.97698	+	3.45081i	1.44963	+	0.836945i	0.998459	−	0.0554914i	$-0.0176726\pi$
$17$	5.97698	+	3.45081i	1.44963	+	0.836945i	0.451173	+	0.892437i	$0.351006\pi$
$18$	−2.37254	−	2.94698i	−0.559213	−	0.694609i
$19$	−3.72412	+	2.15012i	−0.854371	+	0.493271i	−0.862123	−	0.506698i	$-0.830866\pi$
$19$	−3.72412	+	2.15012i	−0.854371	+	0.493271i	0.00775206	+	0.999970i	$0.497532\pi$
$20$	1.68264	+	4.14351i	0.376250	+	0.926518i
$21$	−0.216944	+	1.49211i	−0.0473410	+	0.325605i
$22$	1.73253	+	0.670726i	0.369376	+	0.142999i
$23$	2.45396	−	1.41679i	0.511686	−	0.295422i	−0.221840	−	0.975083i	$-0.571206\pi$
$23$	2.45396	−	1.41679i	0.511686	−	0.295422i	0.733526	+	0.679661i	$0.237873\pi$
$24$	−0.0981190	+	1.60891i	−0.0200285	+	0.328418i
$25$	−4.94039	+	0.769789i	−0.988077	+	0.153958i
$26$	8.08970	−	1.25766i	1.58652	−	0.246648i
$27$	3.23427			0.622436
$28$	−4.08887	+	3.35875i	−0.772723	+	0.634743i
$29$			2.89432i			0.537462i	0.963215	+	0.268731i	$0.0866043\pi$
$29$			2.89432i			0.537462i	−0.963215	+	0.268731i	$0.913396\pi$
$30$	−1.72583	−	0.518927i	−0.315093	−	0.0947427i
$31$	−3.49184	+	6.04805i	−0.627153	+	1.08626i	0.360967	+	0.932579i	$0.382447\pi$
$31$	−3.49184	+	6.04805i	−0.627153	+	1.08626i	−0.988120	+	0.153683i	$0.950887\pi$
$32$	−4.05659	+	3.94260i	−0.717110	+	0.696960i
$33$	−0.648358	+	0.374330i	−0.112865	+	0.0651624i
$34$	−9.10209	−	3.52376i	−1.56100	−	0.604320i
$35$	−2.60788	−	5.31027i	−0.440812	−	0.897600i
$36$	3.95568	+	3.60275i	0.659281	+	0.600458i
$37$	1.65034	+	2.85848i	0.271315	+	0.469931i	0.969199	−	0.246280i	$-0.0792083\pi$
$37$	1.65034	+	2.85848i	0.271315	+	0.469931i	−0.697884	+	0.716211i	$0.745875\pi$
$38$	4.73707	−	3.81370i	0.768454	−	0.618664i
$39$	−1.64956	+	2.85711i	−0.264140	+	0.457505i
$40$	−3.25155	−	5.42470i	−0.514115	−	0.857721i
$41$	−0.235857			−0.0368346			−0.0184173	−	0.999830i	$-0.505863\pi$
$41$	−0.235857			−0.0368346			−0.0184173	+	0.999830i	$0.505863\pi$
$42$	−0.0209980	−	2.13224i	−0.00324007	−	0.329012i
$43$	4.69228			0.715566			0.357783	−	0.933805i	$-0.383533\pi$
$43$	4.69228			0.715566			0.357783	+	0.933805i	$0.383533\pi$
$44$	−2.56680	−	0.560899i	−0.386959	−	0.0845587i
$45$	−4.93415	+	3.38205i	−0.735539	+	0.504166i
$46$	−3.12143	+	2.51299i	−0.460230	+	0.370520i
$47$	5.38956	−	3.11166i	0.786148	−	0.453883i	−0.0524567	−	0.998623i	$-0.516705\pi$
$47$	5.38956	−	3.11166i	0.786148	−	0.453883i	0.838605	+	0.544740i	$0.183372\pi$
$48$	−0.212423	−	2.26966i	−0.0306606	−	0.327596i
$49$	5.08140	−	4.81449i	0.725915	−	0.687785i
$50$	6.73659	−	2.14902i	0.952698	−	0.303918i
$51$	3.40624	−	1.96660i	0.476970	−	0.275379i
$52$	−11.0315	+	3.51498i	−1.52980	+	0.487440i
$53$	−2.28241	+	3.95326i	−0.313514	+	0.543022i	−0.979120	−	0.203281i	$-0.934839\pi$
$53$	−2.28241	+	3.95326i	−0.313514	+	0.543022i	0.665607	+	0.746303i	$0.268173\pi$
$54$	−4.51966	+	0.702646i	−0.615048	+	0.0956181i
$55$	1.26794	−	2.64974i	0.170969	−	0.357291i
$56$	4.98420	−	5.58191i	0.666042	−	0.745914i
$57$			2.45068i			0.324600i
$58$	−0.628792	−	4.04460i	−0.0825645	−	0.531083i
$59$	−3.12758	−	1.80571i	−0.407176	−	0.235083i	0.282399	−	0.959297i	$-0.408870\pi$
$59$	−3.12758	−	1.80571i	−0.407176	−	0.235083i	−0.689576	+	0.724213i	$0.742203\pi$
$60$	2.52446	+	0.350225i	0.325907	+	0.0452139i
$61$	6.27862	−	3.62496i	0.803895	−	0.464129i	−0.0409364	−	0.999162i	$-0.513034\pi$
$61$	6.27862	−	3.62496i	0.803895	−	0.464129i	0.844831	+	0.535033i	$0.179701\pi$
$62$	3.56565	−	9.21031i	0.452839	−	1.16971i
$63$	−5.55673	−	4.38411i	−0.700082	−	0.552346i
$64$	4.81225	−	6.39079i	0.601532	−	0.798849i
$65$	−0.999444	−	12.9060i	−0.123966	−	1.60079i
$66$	0.824710	−	0.663954i	0.101515	−	0.0817271i
$67$	7.96587	−	13.7973i	0.973186	−	1.68561i	0.287391	−	0.957813i	$-0.407212\pi$
$67$	7.96587	−	13.7973i	0.973186	−	1.68561i	0.685795	−	0.727795i	$-0.259455\pi$
$68$	13.4850	+	2.94676i	1.63530	+	0.357348i
$69$		−	1.61484i		−	0.194404i
$70$	4.79798	+	6.85415i	0.573468	+	0.819228i
$71$	9.13804			1.08449			0.542243	−	0.840222i	$-0.317575\pi$
$71$	9.13804			1.08449			0.542243	+	0.840222i	$0.317575\pi$
$72$	−6.31048	−	4.17521i	−0.743697	−	0.492053i
$73$	−1.47515	−	0.851681i	−0.172654	−	0.0996817i	0.411183	−	0.911553i	$-0.365116\pi$
$73$	−1.47515	−	0.851681i	−0.172654	−	0.0996817i	−0.583837	+	0.811871i	$0.698449\pi$
$74$	−2.92724	−	3.63598i	−0.340285	−	0.422674i
$75$	−1.02782	+	2.65764i	−0.118683	+	0.306878i
$76$	−5.79118	+	6.35850i	−0.664294	+	0.729370i
$77$	3.43951	+	0.500085i	0.391969	+	0.0569899i
$78$	1.68443	−	4.35098i	0.190724	−	0.492651i
$79$	−5.80943	−	10.0622i	−0.653612	−	1.13209i	−0.982240	−	0.187629i	$-0.939920\pi$
$79$	−5.80943	−	10.0622i	−0.653612	−	1.13209i	0.328628	−	0.944459i	$-0.393414\pi$
$80$	5.72232	+	6.87423i	0.639775	+	0.768562i
$81$	−3.09124	+	5.35418i	−0.343471	+	0.594909i
$82$	0.329593	−	0.0512399i	0.0363974	−	0.00565850i
$83$	−8.84830			−0.971228			−0.485614	−	0.874173i	$-0.661404\pi$
$83$	−8.84830			−0.971228			−0.485614	+	0.874173i	$0.661404\pi$
$84$	0.492574	+	2.97509i	0.0537442	+	0.324609i
$85$	−6.66132	+	13.9208i	−0.722522	+	1.50992i
$86$	−6.55712	+	1.01940i	−0.707073	+	0.109925i
$87$	1.42847	+	0.824728i	0.153148	+	0.0884201i
$88$	3.70877	+	0.226178i	0.395356	+	0.0241106i
$89$	3.83779	+	6.64725i	0.406805	+	0.704607i	0.994530	−	0.104454i	$-0.0333094\pi$
$89$	3.83779	+	6.64725i	0.406805	+	0.704607i	−0.587724	+	0.809061i	$0.699976\pi$
$90$	6.16036	−	5.79811i	0.649359	−	0.611174i
$91$	14.2281	−	5.66996i	1.49151	−	0.594374i
$92$	3.81602	−	4.18985i	0.397848	−	0.436822i
$93$	1.98998	+	3.44674i	0.206351	+	0.357411i
$94$	−6.85551	+	5.51921i	−0.707091	+	0.569263i
$95$	−5.43642	−	7.93131i	−0.557765	−	0.813736i
$96$	0.789928	+	3.12553i	0.0806217	+	0.318998i
$97$			5.71252i			0.580019i	0.957024	+	0.290009i	$0.0936584\pi$
$97$			5.71252i			0.580019i	−0.957024	+	0.290009i	$0.906342\pi$
$98$	−6.05494	+	7.83184i	−0.611641	+	0.791135i
$99$		−	3.51439i		−	0.353210i
$100$	−8.94702	+	4.46663i	−0.894702	+	0.446663i
$101$	10.1318	+	5.84960i	1.00815	+	0.582057i	0.910650	−	0.413178i	$-0.135581\pi$
$101$	10.1318	+	5.84960i	1.00815	+	0.582057i	0.0975025	+	0.995235i	$0.468915\pi$
$102$	−4.33273	+	3.48818i	−0.429005	+	0.345382i
$103$	−5.48808	+	3.16854i	−0.540757	+	0.312206i	−0.745386	−	0.666634i	$-0.767735\pi$
$103$	−5.48808	+	3.16854i	−0.540757	+	0.312206i	0.204629	+	0.978840i	$0.434401\pi$
$104$	14.6521	−	7.30853i	1.43676	−	0.716661i
$105$	−3.36395	−	0.226047i	−0.328288	−	0.0220599i
$106$	2.33066	−	6.02024i	0.226374	−	0.584738i
$107$	2.18605	+	3.78635i	0.211333	+	0.366040i	0.952132	−	0.305687i	$-0.0988861\pi$
$107$	2.18605	+	3.78635i	0.211333	+	0.366040i	−0.740799	+	0.671727i	$0.765553\pi$
$108$	6.16324	−	1.96379i	0.593058	−	0.188966i
$109$	−7.13617	−	4.12007i	−0.683521	−	0.394631i	0.117659	−	0.993054i	$-0.462461\pi$
$109$	−7.13617	−	4.12007i	−0.683521	−	0.394631i	−0.801180	+	0.598423i	$0.795794\pi$
$110$	−1.19620	+	3.97828i	−0.114053	+	0.379314i
$111$	1.88104			0.178540
$112$	−5.75239	+	8.88313i	−0.543550	+	0.839377i
$113$		−	10.8426i		−	1.01999i	−0.860178	−	0.509994i	$-0.829648\pi$
$113$		−	10.8426i		−	1.01999i	0.860178	−	0.509994i	$-0.170352\pi$
$114$	−0.532411	−	3.42465i	−0.0498648	−	0.320747i
$115$	3.58226	+	5.22624i	0.334047	+	0.487349i
$116$	1.75738	+	5.51543i	0.163169	+	0.512095i
$117$	−7.74343	−	13.4120i	−0.715880	−	1.23994i
$118$	4.76286	+	1.84388i	0.438457	+	0.169743i
$119$	−18.0700	−	2.62727i	−1.65647	−	0.240841i
$120$	−3.60384	+	0.0590258i	−0.328984	+	0.00538829i
$121$	−4.63712	−	8.03173i	−0.421556	−	0.730157i
$122$	−7.98639	+	6.42965i	−0.723054	+	0.582113i
$123$	−0.0672066	+	0.116405i	−0.00605981	+	0.0104959i
$124$	−2.98180	+	13.6454i	−0.267773	+	1.22539i
$125$	−2.56910	−	10.8812i	−0.229787	−	0.973241i
$126$	8.71757	+	4.91927i	0.776623	+	0.438244i
$127$			8.58500i			0.761796i	0.924617	+	0.380898i	$0.124385\pi$
$127$			8.58500i			0.761796i	−0.924617	+	0.380898i	$0.875615\pi$
$128$	−5.33637	+	9.97613i	−0.471673	+	0.881773i
$129$	1.33705	−	2.31584i	0.117721	−	0.203898i
$130$	4.20047	+	17.8180i	0.368406	+	1.56274i
$131$	−7.22534	+	4.17155i	−0.631281	+	0.364470i	−0.781248	−	0.624221i	$-0.785417\pi$
$131$	−7.22534	+	4.17155i	−0.631281	+	0.364470i	0.149967	+	0.988691i	$0.452083\pi$
$132$	−1.00823	+	1.10700i	−0.0877549	+	0.0963516i
$133$	7.04717	−	8.93207i	0.611067	−	0.774509i
$134$	−8.13426	+	21.0113i	−0.702693	+	1.81510i
$135$	0.558382	+	7.21046i	0.0480579	+	0.620578i
$136$	−19.4846	−	1.18826i	−1.67079	−	0.101892i
$137$	3.30547	+	1.90841i	0.282405	+	0.163047i	0.634512	−	0.772913i	$-0.281201\pi$
$137$	3.30547	+	1.90841i	0.282405	+	0.163047i	−0.352107	+	0.935960i	$0.614535\pi$
$138$	0.350825	+	2.25663i	0.0298642	+	0.192097i
$139$			11.6838i			0.991011i	0.868605	+	0.495505i	$0.165017\pi$
$139$			11.6838i			0.991011i	−0.868605	+	0.495505i	$0.834983\pi$
$140$	−8.19389	−	8.53582i	−0.692510	−	0.721408i
$141$		−	3.54663i		−	0.298680i
$142$	−12.7697	+	1.98524i	−1.07161	+	0.166598i
$143$	6.58604	+	3.80245i	0.550753	+	0.317977i
$144$	9.72550	+	4.46359i	0.810458	+	0.371966i
$145$	−6.45258	+	0.499692i	−0.535858	+	0.0414971i
$146$	2.24645	+	0.869684i	0.185917	+	0.0719756i
$147$	−0.928226	−	3.87976i	−0.0765588	−	0.319997i
$148$	4.88052	+	4.44507i	0.401176	+	0.365382i
$149$	17.5413	−	10.1275i	1.43704	−	0.829674i	0.439394	−	0.898294i	$-0.355193\pi$
$149$	17.5413	−	10.1275i	1.43704	−	0.829674i	0.997643	+	0.0686208i	$0.0218599\pi$
$150$	0.858936	−	3.93715i	0.0701318	−	0.321467i
$151$	4.82838	−	8.36300i	0.392928	−	0.680571i	−0.599906	−	0.800070i	$-0.704796\pi$
$151$	4.82838	−	8.36300i	0.392928	−	0.680571i	0.992834	+	0.119499i	$0.0381289\pi$
$152$	6.71137	−	10.1437i	0.544364	−	0.822761i
$153$			18.4634i			1.49268i
$154$	−4.91511	+	0.0484033i	−0.396071	+	0.00390045i
$155$	−14.0863	−	6.74052i	−1.13144	−	0.541412i
$156$	−1.40861	+	6.44611i	−0.112779	+	0.516102i
$157$	0.206359	−	0.357425i	0.0164693	−	0.0285256i	−0.857673	−	0.514195i	$-0.828091\pi$
$157$	0.206359	−	0.357425i	0.0164693	−	0.0285256i	0.874143	+	0.485669i	$0.161424\pi$
$158$	10.3043	+	12.7991i	0.819764	+	1.01824i
$159$	1.30073	+	2.25294i	0.103155	+	0.178669i
$160$	−9.48996	−	8.36306i	−0.750247	−	0.661158i
$161$	−4.64364	+	5.88568i	−0.365970	+	0.463856i
$162$	3.15658	−	8.15365i	0.248004	−	0.640611i
$163$	7.22173	+	12.5084i	0.565650	+	0.979734i	0.996989	+	0.0775442i	$0.0247079\pi$
$163$	7.22173	+	12.5084i	0.565650	+	0.979734i	−0.431339	+	0.902190i	$0.641959\pi$
$164$	−0.449450	+	0.143208i	−0.0350961	+	0.0111827i
$165$	−0.946464	−	1.38082i	−0.0736821	−	0.107497i
$166$	12.3649	−	1.92230i	0.959699	−	0.149199i
$167$			18.6416i			1.44253i	0.692660	+	0.721264i	$0.256439\pi$
$167$			18.6416i			1.44253i	−0.692660	+	0.721264i	$0.743561\pi$
$168$	−1.33468	−	4.05046i	−0.102972	−	0.312500i
$169$	20.5125			1.57788
$170$	6.28441	−	20.9005i	0.481992	−	1.60300i
$171$	−9.96284	−	5.75205i	−0.761877	−	0.439870i
$172$	8.94164	−	2.84907i	0.681793	−	0.217240i
$173$	−0.111079	−	0.192395i	−0.00844520	−	0.0146275i	0.861772	−	0.507296i	$-0.169355\pi$
$173$	−0.111079	−	0.192395i	−0.00844520	−	0.0146275i	−0.870217	+	0.492668i	$0.836022\pi$
$174$	−2.17536	−	0.842161i	−0.164913	−	0.0638441i
$175$	11.3884	−	6.73078i	0.860885	−	0.508799i
$176$	−5.23187	+	0.489664i	−0.394367	+	0.0369098i
$177$	−1.78239	+	1.02906i	−0.133973	+	0.0773491i
$178$	−6.80715	−	8.45529i	−0.510218	−	0.633751i
$179$	17.5417	+	10.1277i	1.31113	+	0.756981i	0.982283	−	0.187402i	$-0.0600069\pi$
$179$	17.5417	+	10.1277i	1.31113	+	0.756981i	0.328846	+	0.944383i	$0.393340\pi$
$180$	−7.34901	+	9.44077i	−0.547763	+	0.703674i
$181$			16.3642i			1.21634i	0.793806	+	0.608171i	$0.208096\pi$
$181$			16.3642i			1.21634i	−0.793806	+	0.608171i	$0.791904\pi$
$182$	−18.6509	+	11.0144i	−1.38250	+	0.816443i
$183$		−	4.13169i		−	0.305423i
$184$	−4.42237	+	6.68405i	−0.326021	+	0.492754i
$185$	−6.08775	+	4.17277i	−0.447580	+	0.306788i
$186$	−3.52965	−	4.38425i	−0.258807	−	0.321469i
$187$	−4.53327	−	7.85186i	−0.331506	−	0.574185i
$188$	8.38102	−	9.20205i	0.611249	−	0.671128i
$189$	−7.94914	+	3.16777i	−0.578215	+	0.230421i
$190$	9.32008	+	9.90237i	0.676149	+	0.718393i
$191$	−0.777294	−	1.34631i	−0.0562430	−	0.0974158i	0.836533	−	0.547916i	$-0.184579\pi$
$191$	−0.777294	−	1.34631i	−0.0562430	−	0.0974158i	−0.892776	+	0.450501i	$0.851246\pi$
$192$	−1.78289	−	4.19609i	−0.128669	−	0.302826i
$193$	−11.3185	−	6.53475i	−0.814725	−	0.470382i	0.0338690	−	0.999426i	$-0.489217\pi$
$193$	−11.3185	−	6.53475i	−0.814725	−	0.470382i	−0.848594	+	0.529045i	$0.822550\pi$
$194$	−1.24105	−	7.98283i	−0.0891020	−	0.573134i
$195$	−6.65442	−	3.18424i	−0.476533	−	0.228028i
$196$	6.75987	−	12.2599i	0.482848	−	0.875704i
$197$	25.7367			1.83367			0.916833	−	0.399270i	$-0.130737\pi$
$197$	25.7367			1.83367			0.916833	+	0.399270i	$0.130737\pi$
$198$	0.763503	+	4.91111i	0.0542598	+	0.349017i
$199$	3.72841	−	6.45779i	0.264300	−	0.457781i	−0.703080	−	0.711111i	$-0.748193\pi$
$199$	3.72841	−	6.45779i	0.264300	−	0.457781i	0.967380	+	0.253330i	$0.0815258\pi$
$200$	11.5324	−	8.18554i	0.815466	−	0.578805i
$201$	−4.53970	−	7.86299i	−0.320206	−	0.554612i
$202$	−15.4293	−	5.97325i	−1.08560	−	0.420277i
$203$	−2.83481	−	7.11362i	−0.198965	−	0.499278i
$204$	5.29687	−	5.81577i	0.370855	−	0.407185i
$205$	−0.0407196	−	0.525817i	−0.00284398	−	0.0367247i
$206$	6.98082	−	5.62010i	0.486377	−	0.391571i
$207$	6.56489	+	3.79024i	0.456291	+	0.263440i
$208$	−18.8875	+	13.3963i	−1.30961	+	0.928868i
$209$	5.64915			0.390760
$210$	4.74998	−	0.414935i	0.327780	−	0.0286332i
$211$		−	1.26257i		−	0.0869190i	−0.999055	−	0.0434595i	$-0.986162\pi$
$211$		−	1.26257i		−	0.0869190i	0.999055	−	0.0434595i	$-0.0138379\pi$
$212$	−1.94903	+	8.91919i	−0.133860	+	0.612572i
$213$	2.60386	−	4.51001i	0.178413	−	0.309021i
$214$	−3.87743	−	4.81623i	−0.265056	−	0.329230i
$215$	0.810101	+	10.4609i	0.0552485	+	0.713430i
$216$	−8.18605	+	4.08323i	−0.556990	+	0.277828i
$217$	2.65851	−	18.2848i	0.180471	−	1.24126i
$218$	10.8674	+	4.20716i	0.736031	+	0.284945i
$219$	−0.840681	+	0.485367i	−0.0568080	+	0.0327981i
$220$	0.807318	−	5.81923i	0.0544294	−	0.392333i
$221$	−34.6008	−	19.9768i	−2.32750	−	1.34378i
$222$	−2.62861	+	0.408656i	−0.176421	+	0.0274272i
$223$		−	7.75525i		−	0.519330i	−0.965699	−	0.259665i	$-0.916388\pi$
$223$		−	7.75525i		−	0.519330i	0.965699	−	0.259665i	$-0.0836121\pi$
$224$	6.10868	−	13.6632i	0.408154	−	0.912913i
$225$	−8.39177	−	10.4163i	−0.559451	−	0.694417i
$226$	2.35556	+	15.1518i	0.156690	+	1.00788i
$227$	−10.6407	+	18.4302i	−0.706248	+	1.22326i	0.259992	+	0.965611i	$0.416280\pi$
$227$	−10.6407	+	18.4302i	−0.706248	+	1.22326i	−0.966239	+	0.257646i	$0.917053\pi$
$228$	1.48801	+	4.67003i	0.0985459	+	0.309280i
$229$	12.7173	−	7.34233i	0.840382	−	0.485195i	−0.0170118	−	0.999855i	$-0.505415\pi$
$229$	12.7173	−	7.34233i	0.840382	−	0.485195i	0.857394	+	0.514660i	$0.172082\pi$
$230$	−6.14134	−	6.52504i	−0.404948	−	0.430248i
$231$	1.22689	−	1.55505i	0.0807235	−	0.102315i
$232$	−3.65404	−	7.32563i	−0.239900	−	0.480951i
$233$	4.30490	−	2.48543i	0.282023	−	0.162826i	−0.352316	−	0.935881i	$-0.614606\pi$
$233$	4.30490	−	2.48543i	0.282023	−	0.162826i	0.634339	+	0.773055i	$0.281272\pi$
$234$	13.7346	+	17.0600i	0.897861	+	1.11525i
$235$	7.86760	+	11.4782i	0.513226	+	0.748757i
$236$	−7.05633	−	1.54196i	−0.459328	−	0.100373i
$237$	−6.62151			−0.430113
$238$	25.8223	−	0.254294i	1.67381	−	0.0164834i
$239$	−20.4836			−1.32497			−0.662487	−	0.749073i	$-0.730499\pi$
$239$	−20.4836			−1.32497			−0.662487	+	0.749073i	$0.730499\pi$
$240$	5.02328	−	0.865419i	0.324251	−	0.0558626i
$241$	1.87263	−	3.24350i	0.120627	−	0.208932i	−0.799388	−	0.600815i	$-0.794843\pi$
$241$	1.87263	−	3.24350i	0.120627	−	0.208932i	0.920015	+	0.391883i	$0.128176\pi$
$242$	8.22493	+	10.2163i	0.528718	+	0.656731i
$243$	6.61308	+	11.4542i	0.424229	+	0.734787i
$244$	9.76355	−	10.7200i	0.625047	−	0.686279i
$245$	11.6107	+	10.4972i	0.741779	+	0.670644i
$246$	0.0686272	−	0.177268i	0.00437551	−	0.0113022i
$247$	21.5589	−	12.4470i	1.37176	−	0.791986i
$248$	1.20239	−	19.7162i	0.0763516	−	1.25198i
$249$	−2.52130	+	4.36701i	−0.159781	+	0.276748i
$250$	5.95406	+	14.6475i	0.376568	+	0.926389i
$251$			16.1680i			1.02052i	0.860021	+	0.510258i	$0.170450\pi$
$251$			16.1680i			1.02052i	−0.860021	+	0.510258i	$0.829550\pi$
$252$	−13.2509	−	4.98043i	−0.834727	−	0.313738i
$253$	−3.72244			−0.234028
$254$	−1.86509	−	11.9969i	−0.117026	−	0.752753i
$255$	4.97239	+	7.25433i	0.311383	+	0.454284i
$256$	5.28987	−	15.1002i	0.330617	−	0.943765i
$257$	−3.69675	+	2.13432i	−0.230597	+	0.133135i	−0.610848	−	0.791748i	$-0.709171\pi$
$257$	−3.69675	+	2.13432i	−0.230597	+	0.133135i	0.380250	+	0.924884i	$0.375838\pi$
$258$	−1.36531	+	3.52669i	−0.0850007	+	0.219562i
$259$	−6.85589	−	5.40911i	−0.426004	−	0.336106i
$260$	−9.74082	−	23.9868i	−0.604100	−	1.48760i
$261$	−6.70559	+	3.87148i	−0.415066	+	0.239638i
$262$	9.19062	−	7.39915i	0.567798	−	0.457121i
$263$	−1.06182	−	0.613041i	−0.0654745	−	0.0378017i	0.466905	−	0.884307i	$-0.345369\pi$
$263$	−1.06182	−	0.613041i	−0.0654745	−	0.0378017i	−0.532380	+	0.846506i	$0.678702\pi$
$264$	1.16843	−	1.76598i	0.0719118	−	0.108689i
$265$	−9.20741	−	4.40589i	−0.565607	−	0.270651i
$266$	−7.90741	+	14.0129i	−0.484834	+	0.859187i
$267$	4.37427			0.267701
$268$	6.80232	−	31.1289i	0.415518	−	1.90150i
$269$	−13.6639	−	7.88884i	−0.833101	−	0.480991i	0.0218126	−	0.999762i	$-0.493056\pi$
$269$	−13.6639	−	7.88884i	−0.833101	−	0.480991i	−0.854913	+	0.518771i	$0.826390\pi$
$270$	−2.34677	−	9.95479i	−0.142820	−	0.605829i
$271$	9.09231	+	15.7483i	0.552319	+	0.956644i	0.998107	+	0.0615053i	$0.0195901\pi$
$271$	9.09231	+	15.7483i	0.552319	+	0.956644i	−0.445788	+	0.895138i	$0.647077\pi$
$272$	27.4864	−	2.57252i	1.66661	−	0.155982i
$273$	1.25589	−	8.63781i	0.0760097	−	0.522784i
$274$	−5.03375	−	1.94875i	−0.304100	−	0.117728i
$275$	6.12622	+	2.36927i	0.369425	+	0.142873i
$276$	−0.980505	−	3.07725i	−0.0590195	−	0.185229i
$277$	8.20064	−	14.2039i	0.492729	−	0.853431i	−0.507236	−	0.861807i	$-0.669333\pi$
$277$	8.20064	−	14.2039i	0.492729	−	0.853431i	0.999965	+	0.00837612i	$0.00266623\pi$
$278$	−2.53832	−	16.3273i	−0.152238	−	0.979247i
$279$	−18.6829			−1.11852
$280$	13.3048	+	10.1481i	0.795112	+	0.606463i
$281$	−8.43894			−0.503425			−0.251712	−	0.967802i	$-0.580994\pi$
$281$	−8.43894			−0.503425			−0.251712	+	0.967802i	$0.580994\pi$
$282$	0.770507	+	4.95616i	0.0458830	+	0.295135i
$283$	−6.67093	+	11.5544i	−0.396546	+	0.686837i	−0.993297	−	0.115589i	$-0.963125\pi$
$283$	−6.67093	+	11.5544i	−0.396546	+	0.686837i	0.596751	+	0.802426i	$0.296458\pi$
$284$	17.4135	−	5.54846i	1.03330	−	0.329241i
$285$	−5.46353	+	0.423099i	−0.323631	+	0.0250622i
$286$	−10.0296	−	3.88283i	−0.593063	−	0.229597i
$287$	0.579685	−	0.231007i	0.0342177	−	0.0136359i
$288$	−14.5604	−	4.12468i	−0.857979	−	0.243049i
$289$	15.3162	+	26.5285i	0.900955	+	1.56050i
$290$	8.90846	−	2.10011i	0.523123	−	0.123323i
$291$	2.81937	+	1.62776i	0.165274	+	0.0954212i
$292$	−3.32819	−	0.727279i	−0.194767	−	0.0425608i
$293$	5.87552			0.343252			0.171626	−	0.985162i	$-0.445098\pi$
$293$	5.87552			0.343252			0.171626	+	0.985162i	$0.445098\pi$
$294$	2.14001	+	5.22003i	0.124808	+	0.304438i
$295$	3.48568	−	7.28436i	0.202944	−	0.424112i
$296$	−7.78586	−	5.15136i	−0.452544	−	0.299417i
$297$	−3.67957	−	2.12440i	−0.213511	−	0.123270i
$298$	−22.3125	+	17.9632i	−1.29253	+	1.04058i
$299$	−14.2060	+	8.20182i	−0.821552	+	0.474323i
$300$	−0.344953	+	5.68849i	−0.0199159	+	0.328425i
$301$	−11.5326	+	4.59580i	−0.664729	+	0.264897i
$302$	−4.93044	+	12.7356i	−0.283715	+	0.732854i
$303$	5.77405	−	3.33365i	0.331711	−	0.191513i
$304$	−7.17493	+	15.6331i	−0.411510	+	0.896619i
$305$	9.16544	+	13.3717i	0.524812	+	0.765660i
$306$	−4.01117	−	25.8012i	−0.229304	−	1.47496i
$307$	2.60524			0.148689			0.0743445	−	0.997233i	$-0.476314\pi$
$307$	2.60524			0.148689			0.0743445	+	0.997233i	$0.476314\pi$
$308$	6.85800	−	1.13545i	0.390771	−	0.0646983i
$309$			3.61147i			0.205449i
$310$	21.1490	+	6.35913i	1.20118	+	0.361174i
$311$	3.56830	−	6.18047i	0.202339	−	0.350462i	−0.746942	−	0.664889i	$-0.768479\pi$
$311$	3.56830	−	6.18047i	0.202339	−	0.350462i	0.949282	+	0.314427i	$0.101812\pi$
$312$	0.568010	−	9.31399i	0.0321573	−	0.527301i
$313$	8.27677	−	4.77859i	0.467830	−	0.270102i	−0.247501	−	0.968888i	$-0.579609\pi$
$313$	8.27677	−	4.77859i	0.467830	−	0.270102i	0.715331	+	0.698786i	$0.246276\pi$
$314$	−0.210721	+	0.544307i	−0.0118917	+	0.0307170i
$315$	8.81456	−	13.1450i	0.496644	−	0.740639i
$316$	−17.1801	−	15.6472i	−0.966455	−	0.880226i
$317$	6.19362	+	10.7277i	0.347868	+	0.602526i	0.985871	−	0.167509i	$-0.0535723\pi$
$317$	6.19362	+	10.7277i	0.347868	+	0.602526i	−0.638002	+	0.770035i	$0.720239\pi$
$318$	−2.30713	−	2.86573i	−0.129377	−	0.160702i
$319$	1.90111	−	3.29282i	0.106442	−	0.184363i
$320$	15.0784	+	9.62506i	0.842908	+	0.538057i
$321$	2.49163			0.139069
$322$	5.21048	−	9.23363i	0.290369	−	0.514570i
$323$	−29.6787			−1.65136
$324$	−2.63971	+	12.0799i	−0.146651	+	0.671105i
$325$	28.5999	−	4.45631i	1.58644	−	0.247191i
$326$	−12.8093	−	15.9107i	−0.709441	−	0.881210i
$327$	−4.06686	+	2.34800i	−0.224898	+	0.129845i
$328$	0.596961	−	0.297766i	0.0329617	−	0.0164414i
$329$	−10.1987	+	12.9265i	−0.562272	+	0.712663i
$330$	1.62260	+	1.72397i	0.0893211	+	0.0949016i
$331$	−17.7881	+	10.2699i	−0.977720	+	0.564487i	−0.901581	−	0.432610i	$-0.857593\pi$
$331$	−17.7881	+	10.2699i	−0.977720	+	0.564487i	−0.0761392	+	0.997097i	$0.524259\pi$
$332$	−16.8614	+	5.37254i	−0.925388	+	0.294856i
$333$	−4.41503	+	7.64706i	−0.241942	+	0.419056i
$334$	−4.04989	−	26.0502i	−0.221600	−	1.42541i
$335$	32.1349	+	15.3770i	1.75572	+	0.840136i
$336$	2.74508	+	5.37027i	0.149756	+	0.292972i
$337$			27.7246i			1.51026i	0.655577	+	0.755128i	$0.272426\pi$
$337$			27.7246i			1.51026i	−0.655577	+	0.755128i	$0.727574\pi$
$338$	−28.6647	+	4.45635i	−1.55915	+	0.242393i
$339$	−5.35129	−	3.08957i	−0.290642	−	0.167802i
$340$	−4.24136	+	30.5722i	−0.230020	+	1.65801i
$341$	7.94522	−	4.58717i	0.430258	−	0.248409i
$342$	15.1720	+	5.87364i	0.820407	+	0.317610i
$343$	−7.77349	+	16.8099i	−0.419729	+	0.907649i
$344$	−11.8763	+	5.92395i	−0.640328	+	0.319398i
$345$	3.60012	−	0.278795i	0.193824	−	0.0150098i
$346$	0.197023	+	0.244726i	0.0105920	+	0.0131565i
$347$	−2.86736	+	4.96642i	−0.153928	+	0.266611i	−0.932668	−	0.360735i	$-0.882526\pi$
$347$	−2.86736	+	4.96642i	−0.153928	+	0.266611i	0.778740	+	0.627347i	$0.215859\pi$
$348$	3.22286	+	0.704262i	0.172763	+	0.0377524i
$349$		−	20.0270i		−	1.07202i	−0.844211	−	0.536012i	$-0.819930\pi$
$349$		−	20.0270i		−	1.07202i	0.844211	−	0.536012i	$-0.180070\pi$
$350$	−14.4523	+	11.8799i	−0.772506	+	0.635008i
$351$	−18.7232			−0.999370
$352$	7.20477	−	1.82089i	0.384016	−	0.0970540i
$353$	0.618505	+	0.357094i	0.0329197	+	0.0190062i	0.516370	−	0.856366i	$-0.327283\pi$
$353$	0.618505	+	0.357094i	0.0329197	+	0.0190062i	−0.483450	+	0.875372i	$0.660616\pi$
$354$	2.26719	−	1.82526i	0.120500	−	0.0970117i
$355$	1.57764	+	20.3723i	0.0837325	+	1.08125i
$356$	11.3494	+	10.3368i	0.601518	+	0.547849i
$357$	−6.44565	+	8.16967i	−0.341140	+	0.432385i
$358$	−26.7135	−	10.3418i	−1.41185	−	0.546581i
$359$	10.3432	+	17.9149i	0.545893	+	0.945514i	0.998550	+	0.0538296i	$0.0171428\pi$
$359$	10.3432	+	17.9149i	0.545893	+	0.945514i	−0.452657	+	0.891685i	$0.649524\pi$
$360$	8.21870	−	14.7894i	0.433163	−	0.779468i
$361$	−0.253963	+	0.439877i	−0.0133665	+	0.0231514i
$362$	−3.55513	−	22.8678i	−0.186853	−	1.20190i
$363$	−5.28533			−0.277408
$364$	23.6704	−	19.4438i	1.24067	−	1.01913i
$365$	1.64405	−	3.43574i	0.0860537	−	0.179835i
$366$	0.897610	+	5.77373i	0.0469188	+	0.301798i
$367$	−19.9690	−	11.5291i	−1.04237	−	0.601813i	−0.121867	−	0.992546i	$-0.538888\pi$
$367$	−19.9690	−	11.5291i	−1.04237	−	0.601813i	−0.920504	+	0.390733i	$0.872222\pi$
$368$	4.72783	−	10.3012i	0.246455	−	0.536989i
$369$	−0.315484	−	0.546435i	−0.0164235	−	0.0284463i
$370$	7.60065	−	7.15370i	0.395139	−	0.371903i
$371$	1.73771	−	11.9517i	0.0902174	−	0.620503i
$372$	5.88491	+	5.35985i	0.305119	+	0.277895i
$373$	−1.27301	−	2.20492i	−0.0659140	−	0.114166i	0.831185	−	0.555996i	$-0.187663\pi$
$373$	−1.27301	−	2.20492i	−0.0659140	−	0.114166i	−0.897099	+	0.441829i	$0.854330\pi$
$374$	8.04074	+	9.98755i	0.415777	+	0.516444i
$375$	−6.10237	−	1.83259i	−0.315125	−	0.0946347i
$376$	−9.71272	+	14.6800i	−0.500895	+	0.757062i
$377$		−	16.7552i		−	0.862938i
$378$	10.4201	−	6.15368i	0.535954	−	0.316511i
$379$		−	11.7578i		−	0.603955i	−0.953315	−	0.301978i	$-0.902353\pi$
$379$		−	11.7578i		−	0.603955i	0.953315	−	0.301978i	$-0.0976468\pi$
$380$	−15.1754	−	11.8131i	−0.778483	−	0.605997i
$381$	4.23706	+	2.44627i	0.217071	+	0.125326i
$382$	1.37870	+	1.71251i	0.0705404	+	0.0876195i
$383$	−4.21382	+	2.43285i	−0.215316	+	0.124313i	−0.603780	−	0.797151i	$-0.706339\pi$
$383$	−4.21382	+	2.43285i	−0.215316	+	0.124313i	0.388463	+	0.921464i	$0.373006\pi$
$384$	3.40306	+	5.47639i	0.173662	+	0.279466i
$385$	−0.521069	+	7.75437i	−0.0265561	+	0.395199i
$386$	17.2365	+	6.67289i	0.877314	+	0.339641i
$387$	6.27645	+	10.8711i	0.319050	+	0.552610i
$388$	3.46854	+	10.8858i	0.176089	+	0.552643i
$389$	0.441858	+	0.255107i	0.0224031	+	0.0129344i	0.511160	−	0.859486i	$-0.329216\pi$
$389$	0.441858	+	0.255107i	0.0224031	+	0.0129344i	−0.488757	+	0.872420i	$0.662549\pi$
$390$	9.99084	+	3.00407i	0.505906	+	0.152117i
$391$	19.5564			0.989008
$392$	−6.78296	+	18.6008i	−0.342591	+	0.939485i
$393$			4.75468i			0.239842i
$394$	−35.9652	+	5.59131i	−1.81190	+	0.281686i
$395$	21.4297	−	14.6887i	1.07824	−	0.739068i
$396$	−2.13388	−	6.69704i	−0.107231	−	0.336539i
$397$	−8.37688	−	14.5092i	−0.420423	−	0.728195i	0.575557	−	0.817761i	$-0.304785\pi$
$397$	−8.37688	−	14.5092i	−0.420423	−	0.728195i	−0.995981	+	0.0895667i	$0.971452\pi$
$398$	−3.80722	+	9.83429i	−0.190839	+	0.492948i
$399$	−2.40029	−	6.02324i	−0.120165	−	0.301539i
$400$	−14.3374	+	13.9441i	−0.716871	+	0.697206i
$401$	−5.31395	−	9.20403i	−0.265366	−	0.459627i	0.702294	−	0.711887i	$-0.252159\pi$
$401$	−5.31395	−	9.20403i	−0.265366	−	0.459627i	−0.967659	+	0.252260i	$0.918826\pi$
$402$	8.05213	+	10.0017i	0.401604	+	0.498840i
$403$	20.2143	−	35.0121i	1.00694	−	1.74408i
$404$	22.8590	+	4.99517i	1.13728	+	0.248519i
$405$	−12.4703	−	5.96721i	−0.619652	−	0.296513i
$406$	5.50687	+	9.32490i	0.273302	+	0.462787i
$407$		−	4.33605i		−	0.214930i
$408$	−6.13852	+	9.27786i	−0.303902	+	0.459322i
$409$	17.2537	−	29.8843i	0.853140	−	1.47768i	−0.0252198	−	0.999682i	$-0.508029\pi$
$409$	17.2537	−	29.8843i	0.853140	−	1.47768i	0.878360	−	0.478000i	$-0.158638\pi$
$410$	0.171137	+	0.725945i	0.00845183	+	0.0358519i
$411$	1.88376	−	1.08759i	0.0929192	−	0.0536469i
$412$	−8.53422	+	9.37026i	−0.420451	+	0.461640i
$413$	9.45550	+	1.37477i	0.465275	+	0.0676482i
$414$	−9.99738	−	3.87036i	−0.491344	−	0.190218i
$415$	−1.52762	−	19.7263i	−0.0749879	−	0.968328i
$416$	23.4836	−	22.8237i	1.15138	−	1.11902i
$417$	5.76647	+	3.32927i	0.282385	+	0.163035i
$418$	−7.89428	+	1.22728i	−0.386122	+	0.0600282i
$419$			26.1080i			1.27546i	0.770260	+	0.637730i	$0.220126\pi$
$419$			26.1080i			1.27546i	−0.770260	+	0.637730i	$0.779874\pi$
$420$	−6.54761	+	1.61178i	−0.319491	+	0.0786466i
$421$			24.7651i			1.20698i	0.797371	+	0.603489i	$0.206223\pi$
$421$			24.7651i			1.20698i	−0.797371	+	0.603489i	$0.793777\pi$
$422$	0.274294	+	1.76435i	0.0133524	+	0.0858873i
$423$	14.4183	+	8.32439i	0.701040	+	0.404746i
$424$	0.785930	−	12.8873i	0.0381681	−	0.625865i
$425$	−32.1850	−	12.4473i	−1.56120	−	0.603785i
$426$	−2.65890	+	6.86810i	−0.128824	+	0.332760i
$427$	−11.8811	+	15.0589i	−0.574965	+	0.728751i
$428$	6.46475	+	5.88795i	0.312486	+	0.284605i
$429$	3.75334	−	2.16699i	0.181213	−	0.104623i
$430$	−3.40470	−	14.4424i	−0.164189	−	0.696475i
$431$	−4.08664	+	7.07827i	−0.196847	+	0.340948i	−0.947504	−	0.319743i	$-0.896403\pi$
$431$	−4.08664	+	7.07827i	−0.196847	+	0.340948i	0.750658	+	0.660691i	$0.229737\pi$
$432$	10.5523	−	7.48443i	0.507699	−	0.360095i
$433$			5.56784i			0.267573i	0.991010	+	0.133787i	$0.0427137\pi$
$433$			5.56784i			0.267573i	−0.991010	+	0.133787i	$0.957286\pi$
$434$	0.257317	+	26.1293i	0.0123516	+	1.25425i
$435$	−1.59202	+	3.32701i	−0.0763317	+	0.159518i
$436$	−16.1004	−	3.51826i	−0.771067	−	0.168494i
$437$	−6.09256	+	10.5526i	−0.291447	+	0.504800i
$438$	1.06934	−	0.860904i	0.0510952	−	0.0411356i
$439$	−8.31423	−	14.4007i	−0.396817	−	0.687306i	0.596515	−	0.802602i	$-0.296552\pi$
$439$	−8.31423	−	14.4007i	−0.396817	−	0.687306i	−0.993331	+	0.115296i	$0.963218\pi$
$440$	0.136063	+	8.30735i	0.00648653	+	0.396037i
$441$	17.9512	+	5.33273i	0.854819	+	0.253939i
$442$	52.6920	+	20.3990i	2.50630	+	0.970283i
$443$	−17.8267	−	30.8767i	−0.846971	−	1.46700i	−0.883898	−	0.467679i	$-0.845090\pi$
$443$	−17.8267	−	30.8767i	−0.846971	−	1.46700i	0.0369268	−	0.999318i	$-0.488243\pi$
$444$	3.58452	−	1.14213i	0.170114	−	0.0542033i
$445$	−14.1568	+	9.70357i	−0.671095	+	0.459993i
$446$	1.68483	+	10.8374i	0.0797790	+	0.513166i
$447$		−	11.5431i		−	0.545972i
$448$	−5.56810	+	20.4205i	−0.263068	+	0.964777i
$449$	18.1039			0.854378			0.427189	−	0.904162i	$-0.359504\pi$
$449$	18.1039			0.854378			0.427189	+	0.904162i	$0.359504\pi$
$450$	13.9898	+	12.7328i	0.659486	+	0.600232i
$451$	0.268330	+	0.154920i	0.0126352	+	0.00729492i
$452$	−6.58345	−	20.6617i	−0.309660	−	0.971847i
$453$	−2.75166	−	4.76602i	−0.129284	−	0.223927i
$454$	10.8656	−	28.0666i	0.509949	−	1.31723i
$455$	15.0970	+	30.7411i	0.707758	+	1.44117i
$456$	−3.09395	−	6.20275i	−0.144888	−	0.290470i
$457$	8.19412	−	4.73088i	0.383305	−	0.221301i	−0.295950	−	0.955203i	$-0.595636\pi$
$457$	8.19412	−	4.73088i	0.383305	−	0.221301i	0.679255	+	0.733902i	$0.262303\pi$
$458$	−16.1764	+	13.0232i	−0.755872	+	0.608535i
$459$	19.3312	+	11.1609i	0.902303	+	0.520945i
$460$	9.99965	+	7.78406i	0.466236	+	0.362934i
$461$		−	15.3616i		−	0.715462i	−0.933825	−	0.357731i	$-0.883550\pi$
$461$		−	15.3616i		−	0.715462i	0.933825	−	0.357731i	$-0.116450\pi$
$462$	−1.37666	+	2.43961i	−0.0640478	+	0.113501i
$463$			24.4642i			1.13695i	0.822702	+	0.568473i	$0.192466\pi$
$463$			24.4642i			1.13695i	−0.822702	+	0.568473i	$0.807534\pi$
$464$	6.69775	+	9.44318i	0.310935	+	0.438389i
$465$	−7.34058	+	5.03151i	−0.340411	+	0.233331i
$466$	−5.47582	+	4.40845i	−0.253662	+	0.204218i
$467$	−6.97250	−	12.0767i	−0.322649	−	0.558844i	0.658385	−	0.752681i	$-0.271240\pi$
$467$	−6.97250	−	12.0767i	−0.322649	−	0.558844i	−0.981034	+	0.193837i	$0.937907\pi$
$468$	−22.8994	−	20.8563i	−1.05853	−	0.964083i
$469$	−6.06480	+	41.7128i	−0.280046	+	1.92612i
$470$	−13.4881	−	14.3308i	−0.622157	−	0.661028i
$471$	−0.117603	−	0.203694i	−0.00541885	−	0.00938572i
$472$	10.1957	+	0.621781i	0.469295	+	0.0286198i
$473$	−5.33833	−	3.08209i	−0.245457	−	0.141714i
$474$	9.25307	−	1.43852i	0.425008	−	0.0660736i
$475$	16.7434	−	13.4892i	0.768242	−	0.618928i
$476$	−36.0295	+	5.96525i	−1.65141	+	0.273417i
$477$	−12.2119			−0.559146
$478$	28.6243	−	4.45007i	1.30925	−	0.203541i
$479$	7.44203	−	12.8900i	0.340035	−	0.588958i	−0.644404	−	0.764685i	$-0.722894\pi$
$479$	7.44203	−	12.8900i	0.340035	−	0.588958i	0.984439	+	0.175728i	$0.0562278\pi$
$480$	−6.83165	+	2.30067i	−0.311821	+	0.105011i
$481$	−9.55383	−	16.5477i	−0.435617	−	0.754511i
$482$	−1.91222	+	4.93938i	−0.0870992	+	0.224983i
$483$	1.58164	+	3.96894i	0.0719671	+	0.180593i
$484$	−13.7132	−	12.4897i	−0.623329	−	0.567714i
$485$	−12.7355	+	0.986241i	−0.578287	+	0.0447829i
$486$	−11.7297	−	14.5697i	−0.532071	−	0.660895i
$487$	−33.2378	−	19.1899i	−1.50615	−	0.869576i	−0.999974	−	0.00714591i	$-0.997725\pi$
$487$	−33.2378	−	19.1899i	−1.50615	−	0.869576i	−0.506176	−	0.862430i	$-0.668941\pi$
$488$	−11.3149	+	17.1016i	−0.512203	+	0.774152i
$489$	8.23124			0.372229
$490$	−18.5056	−	12.1467i	−0.835998	−	0.548732i
$491$		−	35.3833i		−	1.59683i	−0.602111	−	0.798413i	$-0.705673\pi$
$491$		−	35.3833i		−	1.59683i	0.602111	−	0.798413i	$-0.294327\pi$
$492$	−0.0573899	+	0.262629i	−0.00258734	+	0.0118402i
$493$	−9.98777	+	17.2993i	−0.449826	+	0.779122i
$494$	−27.4229	+	22.0775i	−1.23381	+	0.993314i
$495$	7.83496	−	0.606744i	0.352155	−	0.0272711i
$496$	2.60311	+	27.8132i	0.116883	+	1.24885i
$497$	−22.4593	+	8.95014i	−1.00744	+	0.401469i
$498$	2.57459	−	6.65033i	0.115370	−	0.298009i
$499$	27.6050	−	15.9377i	1.23577	−	0.713471i	0.267542	−	0.963546i	$-0.413789\pi$
$499$	27.6050	−	15.9377i	1.23577	−	0.713471i	0.968226	+	0.250075i	$0.0804553\pi$
$500$	−11.5025	−	19.1753i	−0.514409	−	0.857545i
$501$	9.20040	+	5.31186i	0.411044	+	0.237316i
$502$	−3.51251	−	22.5936i	−0.156771	−	1.00840i
$503$		−	37.5112i		−	1.67254i	−0.548317	−	0.836270i	$-0.684731\pi$
$503$		−	37.5112i		−	1.67254i	0.548317	−	0.836270i	$-0.315269\pi$
$504$	19.5991	+	4.08103i	0.873015	+	0.181784i
$505$	−11.2919	+	23.5977i	−0.502481	+	1.05008i
$506$	5.20183	−	0.808700i	0.231250	−	0.0359511i
$507$	5.84497	−	10.1238i	0.259584	−	0.449613i
$508$	5.21266	+	16.3596i	0.231275	+	0.725841i
$509$	16.1154	−	9.30424i	0.714303	−	0.412403i	−0.0983491	−	0.995152i	$-0.531356\pi$
$509$	16.1154	−	9.30424i	0.714303	−	0.412403i	0.812652	+	0.582749i	$0.198023\pi$
$510$	−8.52456	−	9.05715i	−0.377474	−	0.401057i
$511$	4.45978	+	0.648425i	0.197289	+	0.0286847i
$512$	−4.11168	+	22.2507i	−0.181712	+	0.983352i
$513$	−12.0448	+	6.95407i	−0.531791	+	0.307030i
$514$	4.70226	−	3.78568i	0.207408	−	0.166979i
$515$	−8.01142	−	11.6881i	−0.353025	−	0.515037i
$516$	1.14175	−	5.22491i	0.0502628	−	0.230014i
$517$	−8.17548			−0.359557
$518$	10.7557	+	6.06940i	0.472580	+	0.266674i
$519$	−0.126607			−0.00555742
$520$	18.8232	+	31.4036i	0.825453	+	1.37714i
$521$	−5.62331	+	9.73985i	−0.246361	+	0.426711i	−0.962514	−	0.271234i	$-0.912568\pi$
$521$	−5.62331	+	9.73985i	−0.246361	+	0.426711i	0.716152	+	0.697944i	$0.245902\pi$
$522$	8.52950	−	6.86690i	0.373326	−	0.300556i
$523$	10.3364	+	17.9032i	0.451981	+	0.782854i	0.998509	−	0.0545867i	$-0.0173841\pi$
$523$	10.3364	+	17.9032i	0.451981	+	0.782854i	−0.546528	+	0.837441i	$0.684051\pi$
$524$	−11.2358	+	12.3364i	−0.490836	+	0.538920i
$525$	−0.0768233	−	7.53859i	−0.00335284	−	0.329011i
$526$	1.61700	+	0.626000i	0.0705044	+	0.0272949i
$527$	−41.7414	+	24.0994i	−1.81828	+	1.04979i
$528$	−1.24913	+	2.72168i	−0.0543616	+	0.118446i
$529$	−7.48539	+	12.9651i	−0.325452	+	0.563699i
$530$	13.8239	+	4.15659i	0.600470	+	0.180551i
$531$		−	9.66135i		−	0.419267i
$532$	8.00571	−	21.2999i	0.347092	−	0.923469i
$533$	1.36537			0.0591409
$534$	−6.11272	+	0.950311i	−0.264523	+	0.0411240i
$535$	−8.06385	+	5.52726i	−0.348631	+	0.238964i
$536$	−2.74298	+	44.9782i	−0.118479	+	1.94276i
$537$	9.99691	−	5.77172i	0.431399	−	0.249068i
$538$	20.8081	+	8.05559i	0.897101	+	0.347301i
$539$	−8.94338	+	2.13969i	−0.385219	+	0.0921629i
$540$	5.44213	+	13.4013i	0.234192	+	0.576698i
$541$	10.0313	−	5.79157i	0.431279	−	0.248999i	−0.268612	−	0.963248i	$-0.586565\pi$
$541$	10.0313	−	5.79157i	0.431279	−	0.248999i	0.699891	+	0.714249i	$0.253232\pi$
$542$	−16.1272	−	20.0319i	−0.692721	−	0.860442i
$543$	8.07643	+	4.66293i	0.346593	+	0.200105i
$544$	−37.8513	+	9.56633i	−1.62286	+	0.410153i
$545$	7.95323	−	16.6206i	0.340679	−	0.711950i
$546$	0.121557	+	12.3435i	0.00520218	+	0.528255i
$547$	3.89427			0.166507			0.0832535	−	0.996528i	$-0.473469\pi$
$547$	3.89427			0.166507			0.0832535	+	0.996528i	$0.473469\pi$
$548$	7.45767	+	1.62966i	0.318576	+	0.0696155i
$549$	16.7967	+	9.69758i	0.716866	+	0.413883i
$550$	−9.07567	−	1.97997i	−0.386988	−	0.0844260i
$551$	−6.22314	−	10.7788i	−0.265115	−	0.459192i
$552$	2.03872	+	4.08722i	0.0867736	+	0.173964i
$553$	24.1336	+	19.0408i	1.02627	+	0.809697i
$554$	−8.37399	+	21.6305i	−0.355777	+	0.918993i
$555$	0.324753	+	4.19358i	0.0137850	+	0.178007i
$556$	7.09423	+	22.2648i	0.300862	+	0.944237i
$557$	−10.5570	+	18.2852i	−0.447314	+	0.774771i	−0.998210	−	0.0598032i	$-0.980953\pi$
$557$	−10.5570	+	18.2852i	−0.447314	+	0.774771i	0.550896	+	0.834574i	$0.314286\pi$
$558$	26.1080	−	4.05886i	1.10524	−	0.171825i
$559$	−27.1636			−1.14890
$560$	−20.7971	−	11.2907i	−0.878838	−	0.477119i
$561$	−5.16697			−0.218150
$562$	11.7928	−	1.83336i	0.497449	−	0.0773357i
$563$	13.3308	−	23.0896i	0.561825	−	0.973110i	−0.435512	−	0.900183i	$-0.643433\pi$
$563$	13.3308	−	23.0896i	0.561825	−	0.973110i	0.997337	−	0.0729268i	$-0.0232339\pi$
$564$	−2.15345	−	6.75848i	−0.0906768	−	0.284583i
$565$	24.1725	−	1.87193i	1.01694	−	0.0787527i
$566$	6.81195	−	17.5957i	0.286327	−	0.739602i
$567$	2.35351	−	16.1871i	0.0988380	−	0.679794i
$568$	−23.1287	+	11.5367i	−0.970458	+	0.484067i
$569$	−8.28687	−	14.3533i	−0.347403	−	0.601720i	0.638384	−	0.769718i	$-0.279603\pi$
$569$	−8.28687	−	14.3533i	−0.347403	−	0.601720i	−0.985787	+	0.167998i	$0.946270\pi$
$570$	7.54296	−	1.77820i	0.315940	−	0.0744807i
$571$	32.2707	+	18.6315i	1.35048	+	0.779703i	0.988317	−	0.152410i	$-0.0487035\pi$
$571$	32.2707	+	18.6315i	1.35048	+	0.779703i	0.362167	+	0.932113i	$0.382037\pi$
$572$	14.8592	+	3.24704i	0.621293	+	0.135766i
$573$	−0.885950			−0.0370111
$574$	−0.759881	+	0.448752i	−0.0317168	+	0.0187306i
$575$	−11.0329	+	8.88854i	−0.460103	+	0.370678i
$576$	21.2432	+	2.60069i	0.885132	+	0.108362i
$577$	−14.0287	−	8.09946i	−0.584022	−	0.337185i	0.178708	−	0.983902i	$-0.442808\pi$
$577$	−14.0287	−	8.09946i	−0.584022	−	0.337185i	−0.762730	+	0.646717i	$0.776141\pi$
$578$	−27.1666	−	33.7442i	−1.12998	−	1.40357i
$579$	−6.45035	+	3.72411i	−0.268068	+	0.154769i
$580$	−11.9927	+	4.87011i	−0.497968	+	0.202220i
$581$	21.7472	−	8.66636i	0.902227	−	0.359541i
$582$	−4.29350	−	1.66217i	−0.177971	−	0.0688993i
$583$	5.19333	−	2.99837i	0.215086	−	0.124180i
$584$	4.80890	+	0.293269i	0.198994	+	0.0121356i
$585$	28.5638	−	19.5787i	1.18097	−	0.809478i
$586$	−8.21061	+	1.27646i	−0.339177	+	0.0527300i
$587$	6.37825			0.263259			0.131629	−	0.991299i	$-0.457979\pi$
$587$	6.37825			0.263259			0.131629	+	0.991299i	$0.457979\pi$
$588$	−4.12456	−	6.82969i	−0.170094	−	0.281652i
$589$		−	30.0315i		−	1.23743i
$590$	−3.28845	+	10.9366i	−0.135383	+	0.450254i
$591$	7.33360	−	12.7022i	0.301664	−	0.522497i
$592$	11.9993	+	5.50718i	0.493169	+	0.226344i
$593$	11.3484	−	6.55199i	0.466022	−	0.269058i	−0.248551	−	0.968619i	$-0.579954\pi$
$593$	11.3484	−	6.55199i	0.466022	−	0.269058i	0.714573	+	0.699561i	$0.246621\pi$
$594$	5.60346	+	2.16931i	0.229913	+	0.0890079i
$595$	2.73751	−	40.7387i	0.112227	−	1.67012i
$596$	27.2775	−	29.9497i	1.11733	−	1.22679i
$597$	−2.12479	−	3.68025i	−0.0869621	−	0.150623i
$598$	18.0700	−	14.5477i	0.738935	−	0.594899i
$599$	−1.62789	+	2.81959i	−0.0665139	+	0.115206i	−0.897365	−	0.441290i	$-0.854521\pi$
$599$	−1.62789	+	2.81959i	−0.0665139	+	0.115206i	0.830851	+	0.556496i	$0.187854\pi$
$600$	−0.753778	−	8.02418i	−0.0307729	−	0.327586i
$601$	−19.1578			−0.781462			−0.390731	−	0.920505i	$-0.627778\pi$
$601$	−19.1578			−0.781462			−0.390731	+	0.920505i	$0.627778\pi$
$602$	15.1176	−	8.92776i	0.616145	−	0.363868i
$603$	42.6209			1.73566
$604$	4.12311	−	18.8683i	0.167767	−	0.767739i
$605$	17.1053	−	11.7246i	0.695429	−	0.476673i
$606$	−7.34458	+	5.91295i	−0.298353	+	0.240197i
$607$	38.6873	−	22.3361i	1.57027	−	0.906596i	0.574136	−	0.818760i	$-0.305338\pi$
$607$	38.6873	−	22.3361i	1.57027	−	0.906596i	0.996135	−	0.0878358i	$-0.0279951\pi$
$608$	6.63014	−	23.4049i	0.268888	−	0.949192i
$609$	−4.31864	−	0.627905i	−0.175000	−	0.0254440i
$610$	−15.7130	−	16.6948i	−0.636202	−	0.675951i
$611$	−31.2001	+	18.0134i	−1.26222	+	0.728745i
$612$	11.2106	+	35.1839i	0.453164	+	1.42223i
$613$	−6.59656	+	11.4256i	−0.266433	+	0.461475i	−0.967938	−	0.251189i	$-0.919178\pi$
$613$	−6.59656	+	11.4256i	−0.266433	+	0.461475i	0.701505	+	0.712664i	$0.252512\pi$
$614$	−3.64063	+	0.565989i	−0.146924	+	0.0228415i
$615$	−0.271116	−	0.129733i	−0.0109325	−	0.00523134i
$616$	−9.33687	+	3.07661i	−0.376193	+	0.123960i
$617$		−	35.6232i		−	1.43414i	−0.697003	−	0.717068i	$-0.745484\pi$
$617$		−	35.6232i		−	1.43414i	0.697003	−	0.717068i	$-0.254516\pi$
$618$	−0.784592	−	5.04676i	−0.0315609	−	0.203010i
$619$	−28.2474	−	16.3087i	−1.13536	−	0.655500i	−0.190082	−	0.981768i	$-0.560876\pi$
$619$	−28.2474	−	16.3087i	−1.13536	−	0.655500i	−0.945277	+	0.326268i	$0.894209\pi$
$620$	−30.9357	−	4.29179i	−1.24241	−	0.172362i
$621$	7.93677	−	4.58230i	0.318492	−	0.183881i
$622$	−3.64372	+	9.41197i	−0.146100	+	0.377386i
$623$	−15.9430	−	12.5786i	−0.638744	−	0.503952i
$624$	1.22971	+	13.1390i	0.0492280	+	0.525982i
$625$	23.8148	−	7.60611i	0.952594	−	0.304245i
$626$	−10.5280	+	8.47586i	−0.420785	+	0.338764i
$627$	1.60971	−	2.78810i	0.0642855	−	0.111346i
$628$	0.176217	−	0.806408i	0.00703182	−	0.0321792i
$629$			22.7801i			0.908302i
$630$	−9.46195	+	20.2842i	−0.376973	+	0.808141i
$631$	−18.1967			−0.724398			−0.362199	−	0.932101i	$-0.617974\pi$
$631$	−18.1967			−0.724398			−0.362199	+	0.932101i	$0.617974\pi$
$632$	27.4073	+	18.1335i	1.09020	+	0.721311i
$633$	−0.623132	−	0.359766i	−0.0247673	−	0.0142994i
$634$	−10.9857	−	13.6456i	−0.436299	−	0.541934i
$635$	−19.1393	+	1.48216i	−0.759522	+	0.0588178i
$636$	3.84663	+	3.50342i	0.152529	+	0.138920i
$637$	−29.4162	+	27.8711i	−1.16551	+	1.10429i
$638$	−1.94130	+	5.01449i	−0.0768567	+	0.198526i
$639$	12.2231	+	21.1711i	0.483540	+	0.837516i
$640$	−23.1620	−	10.1745i	−0.915559	−	0.402184i
$641$	1.58468	−	2.74475i	0.0625911	−	0.108411i	−0.833032	−	0.553225i	$-0.813397\pi$
$641$	1.58468	−	2.74475i	0.0625911	−	0.108411i	0.895623	+	0.444814i	$0.146730\pi$
$642$	−3.48187	+	0.541308i	−0.137419	+	0.0213637i
$643$	36.1272			1.42472			0.712358	−	0.701816i	$-0.247627\pi$
$643$	36.1272			1.42472			0.712358	+	0.701816i	$0.247627\pi$
$644$	−5.27526	+	14.0353i	−0.207874	+	0.553069i
$645$	5.39375	+	2.58099i	0.212379	+	0.101626i
$646$	41.4738	−	6.44770i	1.63176	−	0.253681i
$647$	3.04348	+	1.75715i	0.119651	+	0.0690808i	0.558631	−	0.829416i	$-0.311327\pi$
$647$	3.04348	+	1.75715i	0.119651	+	0.0690808i	−0.438980	+	0.898497i	$0.644660\pi$
$648$	1.06444	−	17.4542i	0.0418152	−	0.685668i
$649$	2.37213	+	4.10865i	0.0931143	+	0.161279i
$650$	−38.9981	+	12.4407i	−1.52963	+	0.487964i
$651$	−8.26681	−	6.52229i	−0.324002	−	0.255629i
$652$	21.3567	+	19.4512i	0.836391	+	0.761766i
$653$	−8.44643	−	14.6296i	−0.330534	−	0.572502i	0.652082	−	0.758148i	$-0.273896\pi$
$653$	−8.44643	−	14.6296i	−0.330534	−	0.572502i	−0.982617	+	0.185646i	$0.940562\pi$
$654$	5.17303	−	4.16469i	0.202282	−	0.162852i
$655$	−10.5475	−	15.3879i	−0.412123	−	0.601256i
$656$	−0.769520	+	0.545796i	−0.0300447	+	0.0213098i
$657$		−	4.55687i		−	0.177780i
$658$	11.4436	−	20.2796i	0.446119	−	0.790579i
$659$		−	8.16696i		−	0.318140i	−0.987267	−	0.159070i	$-0.949151\pi$
$659$		−	8.16696i		−	0.318140i	0.987267	−	0.159070i	$-0.0508495\pi$
$660$	−2.64200	−	2.05662i	−0.102840	−	0.0800537i
$661$	1.16741	+	0.674004i	0.0454069	+	0.0262157i	0.522532	−	0.852620i	$-0.324988\pi$
$661$	1.16741	+	0.674004i	0.0454069	+	0.0262157i	−0.477125	+	0.878836i	$0.658321\pi$
$662$	22.6264	−	18.2160i	0.879399	−	0.707983i
$663$	−19.7187	+	11.3846i	−0.765813	+	0.442142i
$664$	22.3953	−	11.1709i	0.869108	−	0.433514i
$665$	21.1298	+	14.1688i	0.819377	+	0.549443i
$666$	4.50836	−	11.6454i	0.174695	−	0.451249i
$667$	4.10066	+	7.10255i	0.158778	+	0.275012i
$668$	11.3188	+	35.5235i	0.437939	+	1.37444i
$669$	−3.82754	−	2.20983i	−0.147981	−	0.0854371i
$670$	−48.2468	−	14.5070i	−1.86394	−	0.560453i
$671$	−9.52410			−0.367674
$672$	−5.00273	−	6.90819i	−0.192985	−	0.266489i
$673$		−	11.4143i		−	0.439989i	−0.975501	−	0.219995i	$-0.929396\pi$
$673$		−	11.4143i		−	0.439989i	0.975501	−	0.219995i	$-0.0706040\pi$
$674$	−6.02318	−	38.7432i	−0.232004	−	1.49233i
$675$	−15.9786	+	2.48971i	−0.615015	+	0.0958289i
$676$	39.0887	−	12.4548i	1.50341	−	0.479032i
$677$	4.47255	+	7.74669i	0.171894	+	0.297730i	0.939082	−	0.343693i	$-0.111678\pi$
$677$	4.47255	+	7.74669i	0.171894	+	0.297730i	−0.767188	+	0.641422i	$0.778345\pi$
$678$	8.14925	+	3.15488i	0.312970	+	0.121162i
$679$	−5.59506	−	14.0401i	−0.214719	−	0.538811i
$680$	−0.714825	−	43.6439i	−0.0274123	−	1.67367i
$681$	6.06406	+	10.5033i	0.232375	+	0.402486i
$682$	−10.1063	+	8.13634i	−0.386990	+	0.311557i
$683$	−14.4983	+	25.1118i	−0.554762	+	0.960876i	0.443160	+	0.896443i	$0.353857\pi$
$683$	−14.4983	+	25.1118i	−0.554762	+	0.960876i	−0.997922	+	0.0644337i	$0.979476\pi$
$684$	−22.4778	−	4.91186i	−0.859459	−	0.187810i
$685$	−3.68393	+	7.69866i	−0.140756	+	0.294151i
$686$	7.21093	−	25.1794i	0.275315	−	0.961354i
$687$		−	8.36869i		−	0.319286i
$688$	15.3093	−	10.8584i	0.583662	−	0.413973i
$689$	13.2129	−	22.8854i	0.503371	−	0.871864i
$690$	−4.97034	+	1.17172i	−0.189218	+	0.0446068i
$691$	17.5253	−	10.1183i	0.666696	−	0.384917i	−0.128128	−	0.991758i	$-0.540897\pi$
$691$	17.5253	−	10.1183i	0.666696	−	0.384917i	0.794823	+	0.606841i	$0.207563\pi$
$692$	−0.328492	−	0.299183i	−0.0124874	−	0.0113732i
$693$	3.44213	+	8.63762i	0.130756	+	0.328116i
$694$	2.92798	−	7.56314i	0.111144	−	0.287093i
$695$	−26.0479	+	2.01716i	−0.988052	+	0.0765153i
$696$	−4.65671	−	0.283988i	−0.176512	−	0.0107645i
$697$	−1.40971	−	0.813898i	−0.0533966	−	0.0308286i
$698$	4.35088	+	27.9863i	0.164683	+	1.05930i
$699$		−	2.83286i		−	0.107149i
$700$	17.6151	−	19.7411i	0.665787	−	0.746142i
$701$			38.7717i			1.46439i	0.681097	+	0.732193i	$0.261503\pi$
$701$			38.7717i			1.46439i	−0.681097	+	0.732193i	$0.738497\pi$
$702$	26.1643	−	4.06762i	0.987508	−	0.153522i
$703$	−12.2921	−	7.09687i	−0.463607	−	0.267664i
$704$	−9.67255	+	4.10980i	−0.364548	+	0.154894i
$705$	7.90684	−	0.612310i	0.297789	−	0.0230609i
$706$	−0.941894	−	0.364642i	−0.0354487	−	0.0137235i
$707$	−30.6311	−	4.45358i	−1.15200	−	0.167494i
$708$	−2.77170	+	3.04322i	−0.104167	+	0.114371i
$709$	−15.6009	+	9.00717i	−0.585903	+	0.338271i	−0.763476	−	0.645836i	$-0.776509\pi$
$709$	−15.6009	+	9.00717i	−0.585903	+	0.338271i	0.177573	+	0.984108i	$0.443175\pi$
$710$	−6.63052	−	28.1260i	−0.248839	−	1.05555i
$711$	15.5415	−	26.9187i	0.582852	−	1.00953i
$712$	−18.1056	−	11.9793i	−0.678538	−	0.448941i
$713$			19.7889i			0.741100i
$714$	7.23247	−	12.8168i	0.270668	−	0.479658i
$715$	−7.34011	+	15.3394i	−0.274505	+	0.573659i
$716$	39.5770	+	8.64839i	1.47906	+	0.323206i
$717$	−5.83674	+	10.1095i	−0.217977	+	0.377547i
$718$	−18.3459	−	22.7878i	−0.684662	−	0.850431i
$719$	10.7410	+	18.6039i	0.400571	+	0.693809i	0.993795	−	0.111229i	$-0.0354786\pi$
$719$	10.7410	+	18.6039i	0.400571	+	0.693809i	−0.593224	+	0.805037i	$0.702145\pi$
$720$	−8.27204	+	22.4526i	−0.308281	+	0.836758i
$721$	10.3851	−	13.1628i	0.386762	−	0.490209i
$722$	0.259331	−	0.669869i	0.00965131	−	0.0249299i
$723$	−1.06720	−	1.84845i	−0.0396897	−	0.0687445i
$724$	9.93607	+	31.1837i	0.369271	+	1.15893i
$725$	−2.22802	−	14.2991i	−0.0827465	−	0.531054i
$726$	7.38586	−	1.14824i	0.274115	−	0.0426151i
$727$			7.05501i			0.261656i	0.991405	+	0.130828i	$0.0417635\pi$
$727$			7.05501i			0.261656i	−0.991405	+	0.130828i	$0.958236\pi$
$728$	−28.8535	+	32.3137i	−1.06938	+	1.19762i
$729$	−11.0099			−0.407775
$730$	−1.55103	+	5.15837i	−0.0574062	+	0.190920i
$731$	28.0457	+	16.1922i	1.03731	+	0.598890i
$732$	−2.50869	−	7.87336i	−0.0927238	−	0.291008i
$733$	−0.922520	−	1.59785i	−0.0340741	−	0.0590180i	0.848485	−	0.529219i	$-0.177515\pi$
$733$	−0.922520	−	1.59785i	−0.0340741	−	0.0590180i	−0.882560	+	0.470201i	$0.844182\pi$
$734$	30.4099	+	11.7728i	1.12245	+	0.434542i
$735$	8.48926	−	2.73920i	0.313131	−	0.101037i
$736$	−4.36885	+	15.4223i	−0.161038	+	0.568475i
$737$	−18.1253	+	10.4646i	−0.667653	+	0.385470i
$738$	0.559580	+	0.695064i	0.0205984	+	0.0255857i
$739$	−34.5859	−	19.9682i	−1.27226	−	0.734541i	−0.296848	−	0.954925i	$-0.595936\pi$
$739$	−34.5859	−	19.9682i	−1.27226	−	0.734541i	−0.975413	+	0.220384i	$0.929269\pi$
$740$	−9.06720	+	11.6480i	−0.333317	+	0.428190i
$741$		−	14.1870i		−	0.521172i
$742$	0.168193	+	17.0792i	0.00617458	+	0.626997i
$743$		−	7.06288i		−	0.259112i	−0.991572	−	0.129556i	$-0.958645\pi$
$743$		−	7.06288i		−	0.259112i	0.991572	−	0.129556i	$-0.0413552\pi$
$744$	−9.38817	−	6.21150i	−0.344187	−	0.227725i
$745$	25.6065	+	37.3579i	0.938150	+	1.36869i
$746$	2.25796	+	2.80465i	0.0826697	+	0.102686i
$747$	−11.8356	−	20.4998i	−0.433041	−	0.750050i
$748$	−13.4061	−	12.2100i	−0.490177	−	0.446442i
$749$	−9.08133	−	7.16493i	−0.331825	−	0.261801i
$750$	8.92575	+	1.23517i	0.325922	+	0.0451022i
$751$	13.9010	+	24.0772i	0.507254	+	0.878590i	0.999965	+	0.00839697i	$0.00267287\pi$
$751$	13.9010	+	24.0772i	0.507254	+	0.878590i	−0.492710	+	0.870193i	$0.663994\pi$
$752$	10.3836	−	22.6243i	0.378650	−	0.825022i
$753$	7.97960	+	4.60702i	0.290793	+	0.167889i
$754$	3.64008	+	23.4142i	0.132564	+	0.852695i
$755$	19.4780	+	9.32052i	0.708877	+	0.339208i
$756$	−13.2245	+	10.8631i	−0.480971	+	0.395087i
$757$	−6.35430			−0.230951			−0.115475	−	0.993310i	$-0.536839\pi$
$757$	−6.35430			−0.230951			−0.115475	+	0.993310i	$0.536839\pi$
$758$	2.55437	+	16.4306i	0.0927791	+	0.596786i
$759$	−1.06070	+	1.83718i	−0.0385008	+	0.0666854i
$760$	23.7729	+	13.2110i	0.862335	+	0.479214i
$761$	24.4967	+	42.4295i	0.888004	+	1.53807i	0.842231	+	0.539117i	$0.181242\pi$
$761$	24.4967	+	42.4295i	0.888004	+	1.53807i	0.0457730	+	0.998952i	$0.485425\pi$
$762$	−6.45243	−	2.49798i	−0.233747	−	0.0904922i
$763$	21.5745	+	3.13681i	0.781050	+	0.113560i
$764$	−2.29867	−	2.09358i	−0.0831631	−	0.0757431i
$765$	−41.1621	+	3.18762i	−1.48822	+	0.115249i
$766$	5.35997	−	4.31519i	0.193664	−	0.155914i
$767$	18.1056	+	10.4533i	0.653754	+	0.377445i
$768$	−5.94527	−	6.91354i	−0.214532	−	0.249471i
$769$	−46.6400			−1.68188			−0.840941	−	0.541127i	$-0.817998\pi$
$769$	−46.6400			−1.68188			−0.840941	+	0.541127i	$0.817998\pi$
$770$	−0.956482	−	10.9494i	−0.0344692	−	0.394588i
$771$			2.43267i			0.0876106i
$772$	−25.5364	−	5.58024i	−0.919076	−	0.200837i
$773$	10.8364	−	18.7692i	0.389759	−	0.675082i	−0.602658	−	0.797999i	$-0.705892\pi$
$773$	10.8364	−	18.7692i	0.389759	−	0.675082i	0.992417	+	0.122918i	$0.0392251\pi$
$774$	−11.1326	−	13.8280i	−0.400154	−	0.497039i
$775$	12.5953	−	32.5677i	0.452438	−	1.16987i
$776$	−7.21198	−	14.4586i	−0.258895	−	0.519033i
$777$	−4.62319	+	1.84236i	−0.165856	+	0.0660943i
$778$	−0.672887	−	0.260499i	−0.0241242	−	0.00933936i
$779$	0.878358	−	0.507120i	0.0314704	−	0.0181695i
$780$	−14.6141	−	2.02745i	−0.523269	−	0.0725945i
$781$	−10.3962	−	6.00224i	−0.372005	−	0.214777i
$782$	−27.3286	+	4.24863i	−0.977269	+	0.151931i
$783$			9.36103i			0.334536i
$784$	5.43766	−	27.4669i	0.194202	−	0.980962i
$785$	0.832467	+	0.398348i	0.0297120	+	0.0142177i
$786$	−1.03296	−	6.64432i	−0.0368443	−	0.236995i
$787$	−11.4943	+	19.9088i	−0.409729	+	0.709672i	−0.994859	−	0.101268i	$-0.967710\pi$
$787$	−11.4943	+	19.9088i	−0.409729	+	0.709672i	0.585130	+	0.810940i	$0.301044\pi$
$788$	49.0440	−	15.6269i	1.74712	−	0.556685i
$789$	−0.605124	+	0.349368i	−0.0215430	+	0.0124378i
$790$	−26.7553	+	25.1820i	−0.951910	+	0.895935i
$791$	10.6197	+	26.6488i	0.377592	+	0.947523i
$792$	4.43687	+	8.89504i	0.157657	+	0.316072i
$793$	−36.3469	+	20.9849i	−1.29072	+	0.745196i
$794$	14.8582	+	18.4556i	0.527298	+	0.654966i
$795$	−4.79811	+	3.28880i	−0.170172	+	0.116642i
$796$	3.18381	−	14.5698i	0.112847	−	0.516414i
$797$	14.2453			0.504594			0.252297	−	0.967650i	$-0.418814\pi$
$797$	14.2453			0.504594			0.252297	+	0.967650i	$0.418814\pi$
$798$	4.66278	+	7.89558i	0.165061	+	0.279500i
$799$	42.9511			1.51950
$800$	17.0061	−	22.6007i	0.601258	−	0.799055i
$801$	−10.2669	+	17.7829i	−0.362765	+	0.628327i
$802$	9.42543	+	11.7075i	0.332824	+	0.413406i
$803$	1.11884	+	1.93789i	0.0394830	+	0.0683865i
$804$	−13.4251	−	12.2273i	−0.473468	−	0.431224i
$805$	−13.9232	−	9.33637i	−0.490728	−	0.329064i
$806$	−20.6416	+	53.3185i	−0.727068	+	1.87806i
$807$	−7.78695	+	4.49580i	−0.274114	+	0.158260i
$808$	−33.0290	−	2.01426i	−1.16196	−	0.0708614i
$809$	−10.5722	+	18.3115i	−0.371698	+	0.643799i	−0.989827	−	0.142277i	$-0.954558\pi$
$809$	−10.5722	+	18.3115i	−0.371698	+	0.643799i	0.618129	+	0.786077i	$0.287891\pi$
$810$	18.7227	+	5.62957i	0.657847	+	0.197803i
$811$		−	38.1114i		−	1.33827i	−0.743139	−	0.669137i	$-0.766664\pi$
$811$		−	38.1114i		−	1.33827i	0.743139	−	0.669137i	$-0.233336\pi$
$812$	−9.72129	−	11.8345i	−0.341150	−	0.415309i
$813$	10.3633			0.363457
$814$	0.942009	+	6.05932i	0.0330174	+	0.212379i
$815$	−26.6394	+	18.2596i	−0.933136	+	0.639606i
$816$	6.56251	−	14.2987i	0.229734	−	0.500555i
$817$	−17.4746	+	10.0890i	−0.611359	+	0.352969i
$818$	−17.6184	+	45.5095i	−0.616013	+	1.59120i
$819$	32.1679	+	25.3796i	1.12404	+	0.886835i
$820$	−0.396863	−	0.977276i	−0.0138590	−	0.0341279i
$821$	29.4742	−	17.0169i	1.02866	−	0.593895i	0.112057	−	0.993702i	$-0.464256\pi$
$821$	29.4742	−	17.0169i	1.02866	−	0.593895i	0.916600	+	0.399806i	$0.130923\pi$
$822$	−2.39614	+	1.92908i	−0.0835751	+	0.0672843i
$823$	45.5387	+	26.2918i	1.58738	+	0.916473i	0.993737	+	0.111743i	$0.0356433\pi$
$823$	45.5387	+	26.2918i	1.58738	+	0.916473i	0.593641	+	0.804730i	$0.297690\pi$
$824$	9.89026	−	14.9483i	0.344544	−	0.520749i
$825$	2.91498	−	2.34843i	0.101487	−	0.0817619i
$826$	−13.5120	+	0.133065i	−0.470144	+	0.00462991i
$827$	7.10577			0.247092			0.123546	−	0.992339i	$-0.460573\pi$
$827$	7.10577			0.247092			0.123546	+	0.992339i	$0.460573\pi$
$828$	14.8114	+	3.23661i	0.514733	+	0.112480i
$829$	−37.0911	−	21.4146i	−1.28823	−	0.743759i	−0.309890	−	0.950772i	$-0.600292\pi$
$829$	−37.0911	−	21.4146i	−1.28823	−	0.743759i	−0.978338	+	0.207014i	$0.933626\pi$
$830$	6.42029	+	27.2343i	0.222852	+	0.945315i
$831$	−4.67349	−	8.09472i	−0.162122	−	0.280803i
$832$	−27.8581	+	36.9963i	−0.965807	+	1.28262i
$833$	46.9854	−	11.2412i	1.62795	−	0.389484i
$834$	−8.78151	−	3.39965i	−0.304079	−	0.117720i
$835$	−41.5594	+	3.21838i	−1.43822	+	0.111377i
$836$	10.7651	−	3.43007i	0.372317	−	0.118631i
$837$	−11.2936	+	19.5610i	−0.390363	+	0.676128i
$838$	−5.67197	−	36.4841i	−0.195935	−	1.26032i
$839$	23.3527			0.806224			0.403112	−	0.915151i	$-0.367928\pi$
$839$	23.3527			0.806224			0.403112	+	0.915151i	$0.367928\pi$
$840$	8.79965	−	3.67481i	0.303617	−	0.126793i
$841$	20.6229			0.711134
$842$	−5.38023	−	34.6074i	−0.185415	−	1.19265i
$843$	−2.40465	+	4.16497i	−0.0828205	+	0.143449i
$844$	−0.766611	−	2.40596i	−0.0263879	−	0.0828166i
$845$	3.54139	+	45.7304i	0.121827	+	1.57317i
$846$	−21.9569	−	8.50035i	−0.754895	−	0.292248i
$847$	19.2636	+	15.1985i	0.661906	+	0.522226i
$848$	1.70150	+	18.1799i	0.0584297	+	0.624299i
$849$	3.80172	+	6.58477i	0.130475	+	0.225989i
$850$	47.6804	+	10.4020i	1.63542	+	0.356787i
$851$	8.09975	+	4.67639i	0.277656	+	0.160305i
$852$	2.22352	−	10.1753i	0.0761765	−	0.348600i
$853$	41.3658			1.41634			0.708169	−	0.706043i	$-0.249522\pi$
$853$	41.3658			1.41634			0.708169	+	0.706043i	$0.249522\pi$
$854$	13.3314	−	23.6249i	0.456190	−	0.808426i
$855$	11.1035	−	23.2042i	0.379733	−	0.793565i
$856$	−10.3132	−	6.82352i	−0.352497	−	0.233223i
$857$	−19.7406	−	11.3972i	−0.674324	−	0.389321i	0.123389	−	0.992358i	$-0.460624\pi$
$857$	−19.7406	−	11.3972i	−0.674324	−	0.389321i	−0.797713	+	0.603037i	$0.793957\pi$
$858$	−4.77424	+	3.84363i	−0.162990	+	0.131219i
$859$	−8.52951	+	4.92451i	−0.291023	+	0.168022i	−0.638403	−	0.769702i	$-0.720405\pi$
$859$	−8.52951	+	4.92451i	−0.291023	+	0.168022i	0.347380	+	0.937724i	$0.387071\pi$
$860$	7.89544	+	19.4425i	0.269232	+	0.662985i
$861$	0.0511676	−	0.351924i	0.00174379	−	0.0119935i
$862$	4.17303	−	10.7792i	0.142134	−	0.367141i
$863$	11.5024	−	6.64092i	0.391547	−	0.226060i	−0.291283	−	0.956637i	$-0.594082\pi$
$863$	11.5024	−	6.64092i	0.391547	−	0.226060i	0.682830	+	0.730577i	$0.260749\pi$
$864$	−13.1201	+	12.7514i	−0.446355	+	0.433813i
$865$	0.409747	−	0.280855i	0.0139318	−	0.00954937i
$866$	−1.20961	−	7.78064i	−0.0411043	−	0.264397i
$867$	17.4572			0.592879
$868$	−6.03618	−	36.4579i	−0.204881	−	1.23746i
$869$			15.2635i			0.517778i
$870$	1.50194	−	4.99512i	0.0509206	−	0.169350i
$871$	−46.1144	+	79.8725i	−1.56253	+	2.70638i
$872$	23.2634	+	1.41871i	0.787799	+	0.0480436i
$873$	−13.2348	+	7.64113i	−0.447931	+	0.258613i
$874$	6.22135	−	16.0701i	0.210440	−	0.543580i
$875$	16.9717	+	24.2273i	0.573749	+	0.819031i
$876$	−1.30730	+	1.43537i	−0.0441695	+	0.0484965i
$877$	−7.54809	−	13.0737i	−0.254881	−	0.441467i	0.709982	−	0.704220i	$-0.248703\pi$
$877$	−7.54809	−	13.0737i	−0.254881	−	0.441467i	−0.964863	+	0.262753i	$0.915370\pi$
$878$	14.7471	+	18.3176i	0.497690	+	0.618190i
$879$	1.67421	−	2.89982i	0.0564697	−	0.0978085i
$880$	−1.99491	−	11.5793i	−0.0672484	−	0.390340i
$881$	32.0538			1.07992			0.539959	−	0.841691i	$-0.318440\pi$
$881$	32.0538			1.07992			0.539959	+	0.841691i	$0.318440\pi$
$882$	−26.2440	−	3.55219i	−0.883683	−	0.119609i
$883$	−45.7582			−1.53988			−0.769942	−	0.638113i	$-0.779715\pi$
$883$	−45.7582			−1.53988			−0.769942	+	0.638113i	$0.779715\pi$
$884$	−78.0649	−	17.0588i	−2.62561	−	0.573750i
$885$	−2.60191	−	3.79598i	−0.0874621	−	0.127601i
$886$	31.6195	+	39.2751i	1.06228	+	1.31947i
$887$	−8.66707	+	5.00394i	−0.291012	+	0.168016i	−0.638398	−	0.769706i	$-0.720403\pi$
$887$	−8.66707	+	5.00394i	−0.291012	+	0.168016i	0.347386	+	0.937722i	$0.387069\pi$
$888$	−4.76097	+	2.37479i	−0.159768	+	0.0796926i
$889$	−8.40847	−	21.1001i	−0.282011	−	0.707674i
$890$	17.6749	−	16.6356i	0.592465	−	0.557626i
$891$	7.03369	−	4.06090i	0.235638	−	0.136045i
$892$	−4.70885	−	14.7784i	−0.157664	−	0.494819i
$893$	−13.3809	+	23.1764i	−0.447775	+	0.775569i
$894$	2.50775	+	16.1307i	0.0838717	+	0.539491i
$895$	−19.5502	+	40.8559i	−0.653490	+	1.36566i
$896$	3.34465	−	29.7458i	0.111737	−	0.993738i
$897$			9.34833i			0.312132i
$898$	−25.2989	+	3.93309i	−0.844236	+	0.131249i
$899$	−17.5050	−	10.1065i	−0.583824	−	0.337071i
$900$	−22.3160	−	14.7539i	−0.743866	−	0.491798i
$901$	−27.2839	+	15.7524i	−0.908959	+	0.524788i
$902$	−0.408628	−	0.158195i	−0.0136058	−	0.00526733i
$903$	−1.01796	+	7.00139i	−0.0338756	+	0.232992i
$904$	13.6887	+	27.4430i	0.455278	+	0.912742i
$905$	−36.4822	+	2.82521i	−1.21271	+	0.0939130i
$906$	4.88066	+	6.06236i	0.162149	+	0.201408i
$907$	−9.12794	+	15.8101i	−0.303088	+	0.524964i	−0.976834	−	0.213999i	$-0.931351\pi$
$907$	−9.12794	+	15.8101i	−0.303088	+	0.524964i	0.673746	+	0.738963i	$0.264684\pi$
$908$	−9.08644	+	41.5816i	−0.301544	+	1.37993i
$909$			31.2980i			1.03809i
$910$	−27.7755	−	39.6787i	−0.920748	−	1.31534i
$911$	17.5783			0.582394			0.291197	−	0.956663i	$-0.405947\pi$
$911$	17.5783			0.582394			0.291197	+	0.956663i	$0.405947\pi$
$912$	5.67112	+	7.99573i	0.187790	+	0.264765i
$913$	10.0666	+	5.81193i	0.333155	+	0.192347i
$914$	−10.4229	+	8.39123i	−0.344759	+	0.277557i
$915$	9.21115	−	0.713317i	0.304511	−	0.0235815i
$916$	19.7760	−	21.7133i	0.653417	−	0.717428i
$917$	13.6726	−	17.3296i	0.451508	−	0.572272i
$918$	−29.4386	−	11.3968i	−0.971620	−	0.376150i
$919$	8.86215	+	15.3497i	0.292335	+	0.506340i	0.974362	−	0.224988i	$-0.0722343\pi$
$919$	8.86215	+	15.3497i	0.292335	+	0.506340i	−0.682026	+	0.731328i	$0.738901\pi$
$920$	−15.6649	−	8.70523i	−0.516455	−	0.287003i
$921$	0.742355	−	1.28580i	0.0244614	−	0.0423684i
$922$	3.33732	+	21.4667i	0.109909	+	0.706970i
$923$	−52.9001			−1.74123
$924$	1.39377	−	3.70825i	0.0458517	−	0.121993i
$925$	−10.3538	−	12.8516i	−0.340429	−	0.422557i
$926$	−5.31485	−	34.1869i	−0.174657	−	1.12345i
$927$	−14.6818	−	8.47656i	−0.482215	−	0.278407i
$928$	−11.4112	−	11.7411i	−0.374590	−	0.385420i
$929$	−7.54130	−	13.0619i	−0.247422	−	0.428547i	0.715388	−	0.698728i	$-0.246250\pi$
$929$	−7.54130	−	13.0619i	−0.247422	−	0.428547i	−0.962810	+	0.270180i	$0.912917\pi$
$930$	9.16483	−	8.62591i	0.300527	−	0.282855i
$931$	−8.57200	+	28.8554i	−0.280936	+	0.945697i
$932$	6.69432	−	7.35011i	0.219280	−	0.240761i
$933$	−2.03355	−	3.52221i	−0.0665754	−	0.115312i
$934$	12.3672	+	15.3616i	0.404668	+	0.502645i
$935$	16.7222	−	11.4620i	0.546876	−	0.374849i
$936$	36.5313	+	24.1703i	1.19406	+	0.790029i
$937$		−	47.2563i		−	1.54380i	−0.635746	−	0.771899i	$-0.719307\pi$
$937$		−	47.2563i		−	1.54380i	0.635746	−	0.771899i	$-0.280693\pi$
$938$	−0.587013	−	59.6082i	−0.0191667	−	1.94628i
$939$		−	5.44658i		−	0.177742i
$940$	21.9619	+	17.0959i	0.716319	+	0.557607i
$941$	−4.55249	−	2.62838i	−0.148407	−	0.0856828i	0.423958	−	0.905682i	$-0.360641\pi$
$941$	−4.55249	−	2.62838i	−0.148407	−	0.0856828i	−0.572365	+	0.819999i	$0.693974\pi$
$942$	0.208594	+	0.259098i	0.00679636	+	0.00844188i
$943$	−0.578783	+	0.334160i	−0.0188478	+	0.0108818i
$944$	−14.3828	+	1.34612i	−0.468121	+	0.0438126i
$945$	−8.43458	−	17.1749i	−0.274377	−	0.558698i
$946$	8.12951	+	3.14724i	0.264313	+	0.102325i
$947$	−9.20138	−	15.9373i	−0.299005	−	0.517892i	0.676904	−	0.736072i	$-0.263321\pi$
$947$	−9.20138	−	15.9373i	−0.299005	−	0.517892i	−0.975909	+	0.218180i	$0.929988\pi$
$948$	−12.6180	+	4.02047i	−0.409813	+	0.130579i
$949$	8.53967	+	4.93038i	0.277209	+	0.160047i
$950$	−20.4672	+	22.4877i	−0.664044	+	0.729598i
$951$	7.05941			0.228917
$952$	49.0526	−	16.1634i	1.58981	−	0.523860i
$953$		−	46.9607i		−	1.52121i	−0.649216	−	0.760604i	$-0.724903\pi$
$953$		−	46.9607i		−	1.52121i	0.649216	−	0.760604i	$-0.275097\pi$
$954$	17.0653	−	2.65304i	0.552509	−	0.0858955i
$955$	2.86726	−	1.96533i	0.0927825	−	0.0635966i
$956$	−39.0337	+	12.4373i	−1.26244	+	0.402251i
$957$	−1.08343	−	1.87656i	−0.0350223	−	0.0606605i
$958$	−7.59934	+	19.6296i	−0.245524	+	0.634203i
$959$	−9.99329	−	1.45297i	−0.322700	−	0.0469187i
$960$	9.04692	−	4.69920i	0.291988	−	0.151666i
$961$	−8.88592	−	15.3909i	−0.286642	−	0.496479i
$962$	16.9458	+	21.0487i	0.546354	+	0.678636i
$963$	−5.84817	+	10.1293i	−0.188455	+	0.326413i
$964$	1.59910	−	7.31785i	0.0515037	−	0.235692i
$965$	12.6144	−	26.3616i	0.406073	−	0.848611i
$966$	−3.07248	−	5.20269i	−0.0988554	−	0.167394i
$967$			5.79729i			0.186428i	0.995646	+	0.0932142i	$0.0297141\pi$
$967$			5.79729i			0.186428i	−0.995646	+	0.0932142i	$0.970286\pi$
$968$	21.8766	+	14.4743i	0.703142	+	0.465220i
$969$	−8.45684	+	14.6477i	−0.271673	+	0.470551i
$970$	17.5826	−	4.14498i	0.564543	−	0.133087i
$971$	−31.4067	+	18.1326i	−1.00789	+	0.581904i	−0.910573	−	0.413349i	$-0.864359\pi$
$971$	−31.4067	+	18.1326i	−1.00789	+	0.581904i	−0.0973153	+	0.995254i	$0.531026\pi$
$972$	19.5567	+	17.8118i	0.627282	+	0.571314i
$973$	−11.4436	−	28.7164i	−0.366865	−	0.920604i
$974$	50.6165	+	19.5955i	1.62186	+	0.627881i
$975$	5.95007	−	15.3851i	0.190555	−	0.492716i
$976$	12.0965	−	26.3564i	0.387198	−	0.843647i
$977$	41.8750	+	24.1765i	1.33970	+	0.773475i	0.986763	−	0.162172i	$-0.0518499\pi$
$977$	41.8750	+	24.1765i	1.33970	+	0.773475i	0.352936	+	0.935647i	$0.385183\pi$
$978$	−11.5026	+	1.78824i	−0.367811	+	0.0571816i
$979$		−	10.0833i		−	0.322263i
$980$	28.4991	+	12.9538i	0.910371	+	0.413794i
$981$		−	22.0442i		−	0.703817i
$982$	7.68703	+	49.4456i	0.245303	+	1.57787i
$983$	−7.20732	−	4.16115i	−0.229878	−	0.132720i	0.380638	−	0.924724i	$-0.375704\pi$
$983$	−7.20732	−	4.16115i	−0.229878	−	0.132720i	−0.610516	+	0.792004i	$0.709038\pi$
$984$	0.0231420	−	0.379473i	0.000737741	−	0.0120972i
$985$	4.44333	+	57.3773i	0.141576	+	1.82819i
$986$	10.1989	−	26.3444i	0.324799	−	0.838976i
$987$	3.47371	+	8.71686i	0.110569	+	0.277461i
$988$	33.5251	−	36.8093i	1.06658	−	1.17106i
$989$	11.5147	−	6.64800i	0.366145	−	0.211394i
$990$	−10.8170	+	2.55003i	−0.343786	+	0.0810452i
$991$	−6.34893	+	10.9967i	−0.201680	+	0.349321i	−0.949070	−	0.315065i	$-0.897974\pi$
$991$	−6.34893	+	10.9967i	−0.201680	+	0.349321i	0.747390	+	0.664386i	$0.231307\pi$
$992$	−9.68007	−	38.3014i	−0.307343	−	1.21607i
$993$			11.7055i			0.371464i
$994$	29.4409	−	17.3865i	0.933807	−	0.551465i
$995$	15.0406	+	7.19718i	0.476820	+	0.228166i
$996$	−2.15302	+	9.85269i	−0.0682210	+	0.312194i
$997$	5.88824	−	10.1987i	0.186482	−	0.322997i	−0.757593	−	0.652728i	$-0.773625\pi$
$997$	5.88824	−	10.1987i	0.186482	−	0.322997i	0.944075	+	0.329731i	$0.106958\pi$
$998$	−35.1135	+	28.2690i	−1.11150	+	0.894840i
$999$	5.33766	+	9.24509i	0.168876	+	0.292502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bf.a.109.2	✓	88
4.3	odd	2		1120.2.bv.a.529.22		88
5.4	even	2	inner	280.2.bf.a.109.43	yes	88
7.2	even	3	inner	280.2.bf.a.149.32	yes	88
8.3	odd	2		1120.2.bv.a.529.23		88
8.5	even	2	inner	280.2.bf.a.109.13	yes	88
20.19	odd	2		1120.2.bv.a.529.24		88
28.23	odd	6		1120.2.bv.a.849.21		88
35.9	even	6	inner	280.2.bf.a.149.13	yes	88
40.19	odd	2		1120.2.bv.a.529.21		88
40.29	even	2	inner	280.2.bf.a.109.32	yes	88
56.37	even	6	inner	280.2.bf.a.149.43	yes	88
56.51	odd	6		1120.2.bv.a.849.24		88
140.79	odd	6		1120.2.bv.a.849.23		88
280.149	even	6	inner	280.2.bf.a.149.2	yes	88
280.219	odd	6		1120.2.bv.a.849.22		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bf.a.109.2	✓	88	1.1	even	1	trivial
280.2.bf.a.109.13	yes	88	8.5	even	2	inner
280.2.bf.a.109.32	yes	88	40.29	even	2	inner
280.2.bf.a.109.43	yes	88	5.4	even	2	inner
280.2.bf.a.149.2	yes	88	280.149	even	6	inner
280.2.bf.a.149.13	yes	88	35.9	even	6	inner
280.2.bf.a.149.32	yes	88	7.2	even	3	inner
280.2.bf.a.149.43	yes	88	56.37	even	6	inner
1120.2.bv.a.529.21		88	40.19	odd	2
1120.2.bv.a.529.22		88	4.3	odd	2
1120.2.bv.a.529.23		88	8.3	odd	2
1120.2.bv.a.529.24		88	20.19	odd	2
1120.2.bv.a.849.21		88	28.23	odd	6
1120.2.bv.a.849.22		88	280.219	odd	6
1120.2.bv.a.849.23		88	140.79	odd	6
1120.2.bv.a.849.24		88	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39743 + 0.217250i) q^{2} +(0.284947 - 0.493542i) q^{3} +(1.90560 - 0.607183i) q^{4} +(0.172645 + 2.22939i) q^{5} +(-0.290970 + 0.751594i) q^{6} +(-2.45778 + 0.979438i) q^{7} +(-2.53103 + 1.26249i) q^{8} +(1.33761 + 2.31681i) q^{9} +O(q^{10})\)	\(q+(-1.39743 + 0.217250i) q^{2} +(0.284947 - 0.493542i) q^{3} +(1.90560 - 0.607183i) q^{4} +(0.172645 + 2.22939i) q^{5} +(-0.290970 + 0.751594i) q^{6} +(-2.45778 + 0.979438i) q^{7} +(-2.53103 + 1.26249i) q^{8} +(1.33761 + 2.31681i) q^{9} +(-0.725596 - 3.07791i) q^{10} +(-1.13768 - 0.656841i) q^{11} +(0.243325 - 1.11351i) q^{12} -5.78900 q^{13} +(3.22179 - 1.90265i) q^{14} +(1.14949 + 0.550050i) q^{15} +(3.26266 - 2.31410i) q^{16} +(5.97698 + 3.45081i) q^{17} +(-2.37254 - 2.94698i) q^{18} +(-3.72412 + 2.15012i) q^{19} +(1.68264 + 4.14351i) q^{20} +(-0.216944 + 1.49211i) q^{21} +(1.73253 + 0.670726i) q^{22} +(2.45396 - 1.41679i) q^{23} +(-0.0981190 + 1.60891i) q^{24} +(-4.94039 + 0.769789i) q^{25} +(8.08970 - 1.25766i) q^{26} +3.23427 q^{27} +(-4.08887 + 3.35875i) q^{28} +2.89432i q^{29} +(-1.72583 - 0.518927i) q^{30} +(-3.49184 + 6.04805i) q^{31} +(-4.05659 + 3.94260i) q^{32} +(-0.648358 + 0.374330i) q^{33} +(-9.10209 - 3.52376i) q^{34} +(-2.60788 - 5.31027i) q^{35} +(3.95568 + 3.60275i) q^{36} +(1.65034 + 2.85848i) q^{37} +(4.73707 - 3.81370i) q^{38} +(-1.64956 + 2.85711i) q^{39} +(-3.25155 - 5.42470i) q^{40} -0.235857 q^{41} +(-0.0209980 - 2.13224i) q^{42} +4.69228 q^{43} +(-2.56680 - 0.560899i) q^{44} +(-4.93415 + 3.38205i) q^{45} +(-3.12143 + 2.51299i) q^{46} +(5.38956 - 3.11166i) q^{47} +(-0.212423 - 2.26966i) q^{48} +(5.08140 - 4.81449i) q^{49} +(6.73659 - 2.14902i) q^{50} +(3.40624 - 1.96660i) q^{51} +(-11.0315 + 3.51498i) q^{52} +(-2.28241 + 3.95326i) q^{53} +(-4.51966 + 0.702646i) q^{54} +(1.26794 - 2.64974i) q^{55} +(4.98420 - 5.58191i) q^{56} +2.45068i q^{57} +(-0.628792 - 4.04460i) q^{58} +(-3.12758 - 1.80571i) q^{59} +(2.52446 + 0.350225i) q^{60} +(6.27862 - 3.62496i) q^{61} +(3.56565 - 9.21031i) q^{62} +(-5.55673 - 4.38411i) q^{63} +(4.81225 - 6.39079i) q^{64} +(-0.999444 - 12.9060i) q^{65} +(0.824710 - 0.663954i) q^{66} +(7.96587 - 13.7973i) q^{67} +(13.4850 + 2.94676i) q^{68} -1.61484i q^{69} +(4.79798 + 6.85415i) q^{70} +9.13804 q^{71} +(-6.31048 - 4.17521i) q^{72} +(-1.47515 - 0.851681i) q^{73} +(-2.92724 - 3.63598i) q^{74} +(-1.02782 + 2.65764i) q^{75} +(-5.79118 + 6.35850i) q^{76} +(3.43951 + 0.500085i) q^{77} +(1.68443 - 4.35098i) q^{78} +(-5.80943 - 10.0622i) q^{79} +(5.72232 + 6.87423i) q^{80} +(-3.09124 + 5.35418i) q^{81} +(0.329593 - 0.0512399i) q^{82} -8.84830 q^{83} +(0.492574 + 2.97509i) q^{84} +(-6.66132 + 13.9208i) q^{85} +(-6.55712 + 1.01940i) q^{86} +(1.42847 + 0.824728i) q^{87} +(3.70877 + 0.226178i) q^{88} +(3.83779 + 6.64725i) q^{89} +(6.16036 - 5.79811i) q^{90} +(14.2281 - 5.66996i) q^{91} +(3.81602 - 4.18985i) q^{92} +(1.98998 + 3.44674i) q^{93} +(-6.85551 + 5.51921i) q^{94} +(-5.43642 - 7.93131i) q^{95} +(0.789928 + 3.12553i) q^{96} +5.71252i q^{97} +(-6.05494 + 7.83184i) q^{98} -3.51439i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) \) 88 * q - 2 * q^4 - 40 * q^9	\( 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) \) 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

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