LMFDB - Embedded newform 483.2.r.a.181.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.15
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0528826 - 0.367807i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(-1.16855 + 1.34858i) q^{5} +(-0.104689 + 0.356537i) q^{6} +(2.36025 - 1.19550i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.0528826 - 0.367807i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(-1.16855 + 1.34858i) q^{5} +(-0.104689 + 0.356537i) q^{6} +(2.36025 - 1.19550i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.557813 + 0.358485i) q^{10} +(2.52764 + 0.363420i) q^{11} +(-1.84297 - 0.264979i) q^{12} +(-1.29979 + 2.02252i) q^{13} +(-0.564528 - 0.804896i) q^{14} +(1.62317 - 0.741278i) q^{15} +(2.68410 - 1.72497i) q^{16} +(-2.41938 - 0.710394i) q^{17} +(0.243339 - 0.280828i) q^{18} +(4.98600 - 1.46402i) q^{19} +(-1.38020 + 3.02222i) q^{20} +(-2.64359 + 0.106978i) q^{21} -0.948903i q^{22} +(2.24432 - 4.23828i) q^{23} +1.43505i q^{24} +(0.258418 + 1.79734i) q^{25} +(0.812633 + 0.371117i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(3.58948 - 3.37386i) q^{28} +(-0.540320 - 0.158652i) q^{29} +(-0.358485 - 0.557813i) q^{30} +(6.42522 - 2.93430i) q^{31} +(-2.65591 - 3.06508i) q^{32} +(-2.14825 - 1.38060i) q^{33} +(-0.133345 + 0.927433i) q^{34} +(-1.14585 + 4.57999i) q^{35} +(1.56635 + 1.00663i) q^{36} +(0.723568 - 0.626975i) q^{37} +(-0.802150 - 1.75646i) q^{38} +(2.02252 - 1.29979i) q^{39} +(2.45701 + 0.721444i) q^{40} +(0.680684 + 0.589816i) q^{41} +(0.179147 + 0.966672i) q^{42} +(-6.82303 - 3.11597i) q^{43} +(4.70627 - 0.676660i) q^{44} -1.78443 q^{45} +(-1.67755 - 0.601344i) q^{46} -4.33216i q^{47} +(-3.15812 + 0.454069i) q^{48} +(4.14157 - 5.64335i) q^{49} +(0.647406 - 0.190096i) q^{50} +(1.90564 + 1.65124i) q^{51} +(-1.26114 + 4.29506i) q^{52} +(4.74091 + 7.37701i) q^{53} +(-0.338009 + 0.154364i) q^{54} +(-3.44378 + 2.98405i) q^{55} +(-2.96760 - 2.36831i) q^{56} +(-5.14360 - 0.739538i) q^{57} +(-0.0297799 + 0.207124i) q^{58} +(-4.20500 + 6.54311i) q^{59} +(2.51095 - 2.17575i) q^{60} +(-4.59307 - 10.0574i) q^{61} +(-1.41904 - 2.20807i) q^{62} +(2.44913 + 1.00087i) q^{63} +(3.19188 - 3.68363i) q^{64} +(-1.20865 - 4.11630i) q^{65} +(-0.394189 + 0.863153i) q^{66} +(-9.43925 + 1.35716i) q^{67} -4.69487 q^{68} +(-3.80215 + 2.92295i) q^{69} +(1.74515 + 0.179250i) q^{70} +(0.808859 + 5.62574i) q^{71} +(0.596140 - 1.30537i) q^{72} +(2.02760 + 6.90538i) q^{73} +(-0.268870 - 0.232977i) q^{74} +(0.511575 - 1.74226i) q^{75} +(8.13951 - 5.23095i) q^{76} +(6.40034 - 2.16403i) q^{77} +(-0.585030 - 0.675160i) q^{78} +(-6.76587 + 10.5279i) q^{79} +(-0.810253 + 5.63544i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.180942 - 0.281551i) q^{82} +(10.7055 + 12.3548i) q^{83} +(-4.66665 + 1.57785i) q^{84} +(3.78520 - 2.43260i) q^{85} +(-0.785257 + 2.67434i) q^{86} +(0.425586 + 0.368773i) q^{87} +(-1.03243 - 3.51615i) q^{88} +(2.99411 - 6.55618i) q^{89} +(0.0943653 + 0.656325i) q^{90} +(-0.649926 + 6.32756i) q^{91} +(1.78623 - 8.74898i) q^{92} -7.06354 q^{93} +(-1.59340 + 0.229096i) q^{94} +(-3.85205 + 8.43480i) q^{95} +(1.14262 + 3.89140i) q^{96} +(-0.0261853 + 0.0302194i) q^{97} +(-2.29468 - 1.22486i) q^{98} +(1.38060 + 2.14825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

Coefficient data

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

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

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

$2$	−0.0528826	−	0.367807i	−0.0373937	−	0.260079i	0.962545	−	0.271121i	$-0.0873943\pi$
$2$	−0.0528826	−	0.367807i	−0.0373937	−	0.260079i	−0.999939	+	0.0110420i	$0.996485\pi$
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	1.78650	−	0.524564i	0.893250	−	0.262282i
$5$	−1.16855	+	1.34858i	−0.522592	+	0.603104i	−0.954278	−	0.298920i	$-0.903373\pi$
$5$	−1.16855	+	1.34858i	−0.522592	+	0.603104i	0.431686	+	0.902024i	$0.357919\pi$
$6$	−0.104689	+	0.356537i	−0.0427390	+	0.145556i
$7$	2.36025	−	1.19550i	0.892091	−	0.451855i
$7$	2.36025	−	1.19550i	0.892091	−	0.451855i
$8$	−0.596140	−	1.30537i	−0.210767	−	0.461516i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	0.557813	+	0.358485i	0.176396	+	0.113363i
$11$	2.52764	+	0.363420i	0.762113	+	0.109575i	0.512403	−	0.858745i	$-0.328756\pi$
$11$	2.52764	+	0.363420i	0.762113	+	0.109575i	0.249710	+	0.968321i	$0.419665\pi$
$12$	−1.84297	−	0.264979i	−0.532020	−	0.0764929i
$13$	−1.29979	+	2.02252i	−0.360498	+	0.560946i	−0.973371	−	0.229235i	$-0.926377\pi$
$13$	−1.29979	+	2.02252i	−0.360498	+	0.560946i	0.612873	+	0.790182i	$0.290014\pi$
$14$	−0.564528	−	0.804896i	−0.150877	−	0.215117i
$15$	1.62317	−	0.741278i	0.419101	−	0.191397i
$16$	2.68410	−	1.72497i	0.671025	−	0.431241i
$17$	−2.41938	−	0.710394i	−0.586786	−	0.172296i	−0.0251548	−	0.999684i	$-0.508008\pi$
$17$	−2.41938	−	0.710394i	−0.586786	−	0.172296i	−0.561631	+	0.827388i	$0.689826\pi$
$18$	0.243339	−	0.280828i	0.0573556	−	0.0661919i
$19$	4.98600	−	1.46402i	1.14387	−	0.335869i	0.345723	−	0.938337i	$-0.387634\pi$
$19$	4.98600	−	1.46402i	1.14387	−	0.335869i	0.798144	+	0.602467i	$0.205816\pi$
$20$	−1.38020	+	3.02222i	−0.308622	+	0.675789i
$21$	−2.64359	+	0.106978i	−0.576878	+	0.0233446i
$22$		−	0.948903i		−	0.202307i
$23$	2.24432	−	4.23828i	0.467973	−	0.883743i
$23$	2.24432	−	4.23828i	0.467973	−	0.883743i
$24$			1.43505i			0.292928i
$25$	0.258418	+	1.79734i	0.0516836	+	0.359467i
$26$	0.812633	+	0.371117i	0.159370	+	0.0727821i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	3.58948	−	3.37386i	0.678347	−	0.637599i
$29$	−0.540320	−	0.158652i	−0.100335	−	0.0294610i	0.231180	−	0.972911i	$-0.425741\pi$
$29$	−0.540320	−	0.158652i	−0.100335	−	0.0294610i	−0.331515	+	0.943450i	$0.607560\pi$
$30$	−0.358485	−	0.557813i	−0.0654501	−	0.101842i
$31$	6.42522	−	2.93430i	1.15400	−	0.527016i	0.255858	−	0.966714i	$-0.417642\pi$
$31$	6.42522	−	2.93430i	1.15400	−	0.527016i	0.898145	+	0.439698i	$0.144915\pi$
$32$	−2.65591	−	3.06508i	−0.469503	−	0.541835i
$33$	−2.14825	−	1.38060i	−0.373963	−	0.240331i
$34$	−0.133345	+	0.927433i	−0.0228684	+	0.159053i
$35$	−1.14585	+	4.57999i	−0.193684	+	0.774159i
$36$	1.56635	+	1.00663i	0.261058	+	0.167772i
$37$	0.723568	−	0.626975i	0.118954	−	0.103074i	−0.593353	−	0.804943i	$-0.702196\pi$
$37$	0.723568	−	0.626975i	0.118954	−	0.103074i	0.712307	+	0.701868i	$0.247651\pi$
$38$	−0.802150	−	1.75646i	−0.130126	−	0.284936i
$39$	2.02252	−	1.29979i	0.323862	−	0.208134i
$40$	2.45701	+	0.721444i	0.388488	+	0.114070i
$41$	0.680684	+	0.589816i	0.106305	+	0.0921138i	0.706392	−	0.707821i	$-0.250322\pi$
$41$	0.680684	+	0.589816i	0.106305	+	0.0921138i	−0.600087	+	0.799935i	$0.704867\pi$
$42$	0.179147	+	0.966672i	0.0276430	+	0.149161i
$43$	−6.82303	−	3.11597i	−1.04050	−	0.475182i	−0.179487	−	0.983760i	$-0.557444\pi$
$43$	−6.82303	−	3.11597i	−1.04050	−	0.475182i	−0.861016	+	0.508579i	$0.830171\pi$
$44$	4.70627	−	0.676660i	0.709497	−	0.102010i
$45$	−1.78443			−0.266007
$46$	−1.67755	−	0.601344i	−0.247342	−	0.0886633i
$47$		−	4.33216i		−	0.631911i	−0.948774	−	0.315955i	$-0.897675\pi$
$47$		−	4.33216i		−	0.631911i	0.948774	−	0.315955i	$-0.102325\pi$
$48$	−3.15812	+	0.454069i	−0.455835	+	0.0655392i
$49$	4.14157	−	5.64335i	0.591653	−	0.806192i
$50$	0.647406	−	0.190096i	0.0915571	−	0.0268836i
$51$	1.90564	+	1.65124i	0.266843	+	0.231221i
$52$	−1.26114	+	4.29506i	−0.174889	+	0.595617i
$53$	4.74091	+	7.37701i	0.651215	+	1.01331i	0.997179	+	0.0750622i	$0.0239155\pi$
$53$	4.74091	+	7.37701i	0.651215	+	1.01331i	−0.345964	+	0.938248i	$0.612448\pi$
$54$	−0.338009	+	0.154364i	−0.0459972	+	0.0210062i
$55$	−3.44378	+	2.98405i	−0.464360	+	0.402370i
$56$	−2.96760	−	2.36831i	−0.396563	−	0.316478i
$57$	−5.14360	−	0.739538i	−0.681286	−	0.0979542i
$58$	−0.0297799	+	0.207124i	−0.00391029	+	0.0271967i
$59$	−4.20500	+	6.54311i	−0.547445	+	0.851841i	−0.999187	−	0.0403077i	$-0.987166\pi$
$59$	−4.20500	+	6.54311i	−0.547445	+	0.851841i	0.451743	+	0.892148i	$0.350803\pi$
$60$	2.51095	−	2.17575i	0.324162	−	0.280888i
$61$	−4.59307	−	10.0574i	−0.588083	−	1.28772i	−0.936594	−	0.350417i	$-0.886040\pi$
$61$	−4.59307	−	10.0574i	−0.588083	−	1.28772i	0.348511	−	0.937305i	$-0.386687\pi$
$62$	−1.41904	−	2.20807i	−0.180218	−	0.280425i
$63$	2.44913	+	1.00087i	0.308562	+	0.126098i
$64$	3.19188	−	3.68363i	0.398985	−	0.460454i
$65$	−1.20865	−	4.11630i	−0.149915	−	0.510564i
$66$	−0.394189	+	0.863153i	−0.0485213	+	0.106247i
$67$	−9.43925	+	1.35716i	−1.15319	+	0.165803i	−0.692270	−	0.721639i	$-0.743389\pi$
$67$	−9.43925	+	1.35716i	−1.15319	+	0.165803i	−0.460919	+	0.887442i	$0.652480\pi$
$68$	−4.69487			−0.569337
$69$	−3.80215	+	2.92295i	−0.457725	+	0.351882i
$70$	1.74515	+	0.179250i	0.208585	+	0.0214245i
$71$	0.808859	+	5.62574i	0.0959939	+	0.667652i	0.979827	+	0.199849i	$0.0640452\pi$
$71$	0.808859	+	5.62574i	0.0959939	+	0.667652i	−0.883833	+	0.467803i	$0.845046\pi$
$72$	0.596140	−	1.30537i	0.0702558	−	0.153839i
$73$	2.02760	+	6.90538i	0.237313	+	0.808214i	0.988900	+	0.148580i	$0.0474704\pi$
$73$	2.02760	+	6.90538i	0.237313	+	0.808214i	−0.751587	+	0.659634i	$0.770711\pi$
$74$	−0.268870	−	0.232977i	−0.0312555	−	0.0270831i
$75$	0.511575	−	1.74226i	0.0590716	−	0.201179i
$76$	8.13951	−	5.23095i	0.933666	−	0.600031i
$77$	6.40034	−	2.16403i	0.729386	−	0.246614i
$78$	−0.585030	−	0.675160i	−0.0662416	−	0.0764468i
$79$	−6.76587	+	10.5279i	−0.761220	+	1.18448i	0.216850	+	0.976205i	$0.430422\pi$
$79$	−6.76587	+	10.5279i	−0.761220	+	1.18448i	−0.978070	+	0.208276i	$0.933215\pi$
$80$	−0.810253	+	5.63544i	−0.0905891	+	0.630061i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	0.180942	−	0.281551i	0.0199817	−	0.0310921i
$83$	10.7055	+	12.3548i	1.17509	+	1.35612i	0.921296	+	0.388861i	$0.127131\pi$
$83$	10.7055	+	12.3548i	1.17509	+	1.35612i	0.253789	+	0.967260i	$0.418323\pi$
$84$	−4.66665	+	1.57785i	−0.509174	+	0.172157i
$85$	3.78520	−	2.43260i	0.410562	−	0.263852i
$86$	−0.785257	+	2.67434i	−0.0846764	+	0.288381i
$87$	0.425586	+	0.368773i	0.0456276	+	0.0395366i
$88$	−1.03243	−	3.51615i	−0.110058	−	0.374823i
$89$	2.99411	−	6.55618i	0.317375	−	0.694954i	−0.681961	−	0.731388i	$-0.738873\pi$
$89$	2.99411	−	6.55618i	0.317375	−	0.694954i	0.999336	+	0.0364342i	$0.0115999\pi$
$90$	0.0943653	+	0.656325i	0.00994697	+	0.0691827i
$91$	−0.649926	+	6.32756i	−0.0681307	+	0.663308i
$92$	1.78623	−	8.74898i	0.186227	−	0.912144i
$93$	−7.06354			−0.732455
$94$	−1.59340	+	0.229096i	−0.164347	+	0.0236295i
$95$	−3.85205	+	8.43480i	−0.395212	+	0.865393i
$96$	1.14262	+	3.89140i	0.116618	+	0.397165i
$97$	−0.0261853	+	0.0302194i	−0.00265871	+	0.00306832i	−0.757077	−	0.653325i	$-0.773373\pi$
$97$	−0.0261853	+	0.0302194i	−0.00265871	+	0.00306832i	0.754419	+	0.656394i	$0.227919\pi$
$98$	−2.29468	−	1.22486i	−0.231798	−	0.123730i
$99$	1.38060	+	2.14825i	0.138755	+	0.215908i
$100$	1.40448	+	3.07538i	0.140448	+	0.307538i
$101$	−8.11335	+	7.03026i	−0.807308	+	0.699537i	−0.957283	−	0.289153i	$-0.906626\pi$
$101$	−8.11335	+	7.03026i	−0.807308	+	0.699537i	0.149974	+	0.988690i	$0.452081\pi$
$102$	0.506564	−	0.788229i	0.0501573	−	0.0780463i
$103$	−0.300741	+	2.09170i	−0.0296329	+	0.206101i	−0.999259	−	0.0384909i	$-0.987745\pi$
$103$	−0.300741	+	2.09170i	−0.0296329	+	0.206101i	0.969626	+	0.244592i	$0.0786540\pi$
$104$	3.41499	+	0.491001i	0.334867	+	0.0481466i
$105$	2.94490	−	3.69010i	0.287393	−	0.360117i
$106$	2.46260	−	2.13386i	0.239189	−	0.207258i
$107$	−13.1144	+	5.98915i	−1.26782	+	0.578993i	−0.931838	−	0.362875i	$-0.881795\pi$
$107$	−13.1144	+	5.98915i	−1.26782	+	0.578993i	−0.335981	+	0.941869i	$0.609068\pi$
$108$	−1.00663	−	1.56635i	−0.0968631	−	0.150722i
$109$	−5.41552	+	18.4436i	−0.518713	+	1.76657i	0.115386	+	0.993321i	$0.463189\pi$
$109$	−5.41552	+	18.4436i	−0.518713	+	1.76657i	−0.634099	+	0.773252i	$0.718629\pi$
$110$	1.27967	+	1.10884i	0.122012	+	0.105724i
$111$	−0.918636	+	0.269736i	−0.0871931	+	0.0256022i
$112$	4.27296	−	7.28019i	0.403757	−	0.687913i
$113$	−9.67659	+	1.39128i	−0.910297	+	0.130881i	−0.581525	−	0.813528i	$-0.697544\pi$
$113$	−9.67659	+	1.39128i	−0.910297	+	0.130881i	−0.328772	+	0.944409i	$0.606635\pi$
$114$			1.93096i			0.180851i
$115$	3.09306	+	7.97930i	0.288430	+	0.744073i
$116$	−1.04851			−0.0973513
$117$	−2.37970	+	0.342150i	−0.220004	+	0.0316317i
$118$	2.62897	+	1.20061i	0.242017	+	0.110525i
$119$	−6.55962	+	1.21565i	−0.601320	+	0.111439i
$120$	−1.93528	−	1.67693i	−0.176666	−	0.153082i
$121$	−4.29752	−	1.26187i	−0.390684	−	0.114715i
$122$	−3.45630	+	2.22123i	−0.312918	+	0.201100i
$123$	−0.374153	−	0.819282i	−0.0337363	−	0.0738722i
$124$	9.93943	−	8.61257i	0.892587	−	0.773431i
$125$	−10.2316	−	6.57545i	−0.915143	−	0.588127i
$126$	0.238612	−	0.953737i	0.0212573	−	0.0849656i
$127$	−0.983659	+	6.84150i	−0.0872856	+	0.607085i	0.898487	+	0.439000i	$0.144667\pi$
$127$	−0.983659	+	6.84150i	−0.0872856	+	0.607085i	−0.985773	+	0.168085i	$0.946242\pi$
$128$	−8.34738	−	5.36454i	−0.737811	−	0.474162i
$129$	4.91203	+	5.66878i	0.432480	+	0.499108i
$130$	−1.45009	+	0.662232i	−0.127181	+	0.0580816i
$131$	−6.97012	−	10.8457i	−0.608982	−	0.947595i	−0.999634	−	0.0270560i	$-0.991387\pi$
$131$	−6.97012	−	10.8457i	−0.608982	−	0.947595i	0.390652	−	0.920538i	$-0.372250\pi$
$132$	−4.56207	−	1.33954i	−0.397077	−	0.116592i
$133$	10.0180	−	9.41620i	0.868669	−	0.816488i
$134$	0.998346	+	3.40005i	0.0862439	+	0.293720i
$135$	1.62317	+	0.741278i	0.139700	+	0.0637991i
$136$	0.514967	+	3.58167i	0.0441580	+	0.307126i
$137$		−	15.0547i		−	1.28621i	−0.765779	−	0.643104i	$-0.777646\pi$
$137$		−	15.0547i		−	1.28621i	0.765779	−	0.643104i	$-0.222354\pi$
$138$	1.27615	+	1.24388i	0.108633	+	0.105886i
$139$			0.0576594i			0.00489061i	0.999997	+	0.00244530i	$0.000778365\pi$
$139$			0.0576594i			0.00489061i	−0.999997	+	0.00244530i	$0.999222\pi$
$140$	0.355432	+	8.78323i	0.0300395	+	0.742318i
$141$	−1.79965	+	3.94067i	−0.151557	+	0.331865i
$142$	2.02641	−	0.595008i	0.170053	−	0.0499319i
$143$	−4.02044	+	4.63984i	−0.336206	+	0.388003i
$144$	3.06135	+	0.898894i	0.255113	+	0.0749079i
$145$	0.845348	−	0.543272i	0.0702023	−	0.0451163i
$146$	2.43262	−	1.11094i	0.201325	−	0.0919422i
$147$	−6.11164	+	3.41290i	−0.504080	+	0.281491i
$148$	0.963766	−	1.49965i	0.0792211	−	0.123270i
$149$	7.42062	+	1.06692i	0.607921	+	0.0874058i	0.439399	−	0.898292i	$-0.355191\pi$
$149$	7.42062	+	1.06692i	0.607921	+	0.0874058i	0.168522	+	0.985698i	$0.446101\pi$
$150$	−0.667870	−	0.0960252i	−0.0545314	−	0.00784043i
$151$	−0.981968	−	0.631072i	−0.0799114	−	0.0513559i	0.500075	−	0.865982i	$-0.333306\pi$
$151$	−0.981968	−	0.631072i	−0.0799114	−	0.0513559i	−0.579986	+	0.814626i	$0.696942\pi$
$152$	−4.88344	−	5.63579i	−0.396099	−	0.457123i
$153$	−1.04748	−	2.29366i	−0.0846835	−	0.185431i
$154$	−1.13441	−	2.23965i	−0.0914134	−	0.180476i
$155$	−3.55106	+	12.0938i	−0.285228	+	0.971398i
$156$	2.93141	−	3.38302i	0.234700	−	0.270859i
$157$	−16.6163	+	4.87899i	−1.32613	+	0.389386i	−0.866700	−	0.498829i	$-0.833763\pi$
$157$	−16.6163	+	4.87899i	−1.32613	+	0.389386i	−0.459427	+	0.888215i	$0.651945\pi$
$158$	4.23003	+	1.93179i	0.336523	+	0.153685i
$159$	−1.24797	−	8.67981i	−0.0989703	−	0.688354i
$160$	7.23708			0.572141
$161$	0.230301	−	12.6865i	0.0181502	−	0.999835i
$162$	0.371589			0.0291948
$163$	−0.0202717	−	0.140992i	−0.00158780	−	0.0110434i	0.989012	−	0.147834i	$-0.0472302\pi$
$163$	−0.0202717	−	0.140992i	−0.00158780	−	0.0110434i	−0.990600	+	0.136791i	$0.956321\pi$
$164$	1.52544	+	0.696644i	0.119117	+	0.0543988i
$165$	4.37220	−	1.28379i	0.340375	−	0.0999431i
$166$	3.97806	−	4.59093i	0.308757	−	0.356325i
$167$	−0.664497	+	2.26307i	−0.0514203	+	0.175122i	−0.981200	−	0.192996i	$-0.938179\pi$
$167$	−0.664497	+	2.26307i	−0.0514203	+	0.175122i	0.929779	+	0.368118i	$0.119998\pi$
$168$	1.71560	+	3.38707i	0.132361	+	0.261318i
$169$	2.99927	+	6.56750i	0.230713	+	0.505192i
$170$	−1.09490	−	1.26358i	−0.0839748	−	0.0969121i
$171$	4.37157	+	2.80944i	0.334302	+	0.214843i
$172$	−13.8239	−	1.98757i	−1.05406	−	0.151551i
$173$	23.6711	+	3.40340i	1.79968	+	0.258755i	0.959129	−	0.282970i	$-0.0913198\pi$
$173$	23.6711	+	3.40340i	1.79968	+	0.258755i	0.840555	+	0.541726i	$0.182229\pi$
$174$	0.113131	−	0.176035i	0.00857643	−	0.0133452i
$175$	2.75864	+	3.93323i	0.208534	+	0.297324i
$176$	7.41133	−	3.38464i	0.558650	−	0.255127i
$177$	6.54311	−	4.20500i	0.491810	−	0.316067i
$178$	−2.56975	−	0.754546i	−0.192611	−	0.0565556i
$179$	13.9524	−	16.1020i	1.04285	−	1.20352i	0.0642152	−	0.997936i	$-0.479546\pi$
$179$	13.9524	−	16.1020i	1.04285	−	1.20352i	0.978640	−	0.205583i	$-0.0659089\pi$
$180$	−3.18788	+	0.936046i	−0.237611	+	0.0697688i
$181$	−1.66306	+	3.64159i	−0.123614	+	0.270677i	−0.961315	−	0.275453i	$-0.911172\pi$
$181$	−1.66306	+	3.64159i	−0.123614	+	0.270677i	0.837701	+	0.546130i	$0.183899\pi$
$182$	2.36169	−	0.0955708i	0.175060	−	0.00708418i
$183$			11.0566i			0.817326i
$184$	−6.87044	−	0.403044i	−0.506495	−	0.0297128i
$185$			1.70844i			0.125607i
$186$	0.373539	+	2.59802i	0.0273892	+	0.190496i
$187$	−5.85716	−	2.67488i	−0.428318	−	0.195606i
$188$	−2.27250	−	7.73941i	−0.165739	−	0.564455i
$189$	−1.81203	−	1.92783i	−0.131806	−	0.140229i
$190$	3.30608	+	0.970754i	0.239849	+	0.0704259i
$191$	0.910791	+	1.41722i	0.0659025	+	0.102546i	0.872641	−	0.488363i	$-0.162406\pi$
$191$	0.910791	+	1.41722i	0.0659025	+	0.102546i	−0.806738	+	0.590909i	$0.798769\pi$
$192$	−4.43367	+	2.02479i	−0.319973	+	0.146127i
$193$	−8.44951	−	9.75126i	−0.608209	−	0.701911i	0.365214	−	0.930923i	$-0.380996\pi$
$193$	−8.44951	−	9.75126i	−0.608209	−	0.701911i	−0.973423	+	0.229013i	$0.926450\pi$
$194$	0.0124997	+	0.00803305i	0.000897424	+	0.000576739i
$195$	−0.610541	+	4.24641i	−0.0437218	+	0.304092i
$196$	4.43863	−	12.2544i	0.317045	−	0.875312i
$197$	−10.7390	−	6.90152i	−0.765120	−	0.491713i	0.0989452	−	0.995093i	$-0.468453\pi$
$197$	−10.7390	−	6.90152i	−0.765120	−	0.491713i	−0.864065	+	0.503380i	$0.832090\pi$
$198$	0.717133	−	0.621399i	0.0509644	−	0.0441609i
$199$	0.240381	+	0.526360i	0.0170401	+	0.0373127i	0.917961	−	0.396671i	$-0.129835\pi$
$199$	0.240381	+	0.526360i	0.0170401	+	0.0373127i	−0.900921	+	0.433984i	$0.857107\pi$
$200$	2.19213	−	1.40879i	0.155007	−	0.0996168i
$201$	9.15003	+	2.68669i	0.645394	+	0.189505i
$202$	3.01483	+	2.61237i	0.212123	+	0.183805i
$203$	−1.46496	+	0.271492i	−0.102820	+	0.0190550i
$204$	4.27061	+	1.95032i	0.299002	+	0.136550i
$205$	−1.59083	+	0.228727i	−0.111108	+	0.0159750i
$206$	0.785245			0.0547106
$207$	4.67280	−	1.07934i	0.324782	−	0.0750195i
$208$			7.67074i			0.531870i
$209$	13.1349	−	1.88851i	0.908558	−	0.130631i
$210$	−1.51298	−	0.888012i	−0.104405	−	0.0612787i
$211$	24.8927	−	7.30914i	1.71368	−	0.503182i	0.730052	−	0.683391i	$-0.239496\pi$
$211$	24.8927	−	7.30914i	1.71368	−	0.503182i	0.983628	+	0.180209i	$0.0576774\pi$
$212$	12.3394	+	10.6921i	0.847471	+	0.734338i
$213$	1.60125	−	5.45336i	0.109716	−	0.373658i
$214$	2.89638	+	4.50685i	0.197992	+	0.308082i
$215$	12.1752	−	5.56023i	0.830342	−	0.379205i
$216$	−1.08454	+	0.939757i	−0.0737934	+	0.0639423i
$217$	11.6572	−	14.6070i	0.791342	−	0.991589i
$218$	7.07005	+	1.01652i	0.478845	+	0.0688474i
$219$	1.02423	−	7.12366i	0.0692109	−	0.481372i
$220$	−4.58699	+	7.13750i	−0.309255	+	0.481210i
$221$	4.58149	−	3.96988i	0.308184	−	0.267043i
$222$	0.147791	+	0.323616i	0.00991905	+	0.0217197i
$223$	1.25692	+	1.95580i	0.0841696	+	0.130970i	0.880786	−	0.473515i	$-0.157015\pi$
$223$	1.25692	+	1.95580i	0.0841696	+	0.130970i	−0.796616	+	0.604486i	$0.793379\pi$
$224$	−9.93291	−	4.05924i	−0.663671	−	0.271219i
$225$	−1.18911	+	1.37230i	−0.0792738	+	0.0914869i
$226$	1.02345	+	3.48554i	0.0680787	+	0.231855i
$227$	−3.49471	+	7.65235i	−0.231952	+	0.507905i	−0.989440	−	0.144945i	$-0.953699\pi$
$227$	−3.49471	+	7.65235i	−0.231952	+	0.507905i	0.757487	+	0.652850i	$0.226427\pi$
$228$	−9.57698	+	1.37696i	−0.634251	+	0.0911915i
$229$	−2.80899			−0.185624			−0.0928118	−	0.995684i	$-0.529585\pi$
$229$	−2.80899			−0.185624			−0.0928118	+	0.995684i	$0.529585\pi$
$230$	2.77127	−	1.55962i	0.182732	−	0.102838i
$231$	−6.72092	−	0.690330i	−0.442204	−	0.0454204i
$232$	0.115008	+	0.799895i	0.00755061	+	0.0525157i
$233$	5.61198	−	12.2885i	0.367653	−	0.805048i	−0.631897	−	0.775052i	$-0.717724\pi$
$233$	5.61198	−	12.2885i	0.367653	−	0.805048i	0.999550	−	0.0299953i	$-0.00954923\pi$
$234$	0.251690	+	0.857177i	0.0164535	+	0.0560354i
$235$	5.84227	+	5.06236i	0.381108	+	0.330232i
$236$	−4.07996	+	13.8951i	−0.265583	+	0.904492i
$237$	10.5279	−	6.76587i	0.683860	−	0.439490i
$238$	0.794016	+	2.34839i	0.0514684	+	0.152223i
$239$	−13.9147	−	16.0585i	−0.900069	−	1.03874i	−0.999047	−	0.0436456i	$-0.986103\pi$
$239$	−13.9147	−	16.0585i	−0.900069	−	1.03874i	0.0989779	−	0.995090i	$-0.468443\pi$
$240$	3.07808	−	4.78958i	0.198689	−	0.309166i
$241$	−0.996136	+	6.92828i	−0.0641667	+	0.446289i	0.932257	+	0.361796i	$0.117836\pi$
$241$	−0.996136	+	6.92828i	−0.0641667	+	0.446289i	−0.996424	+	0.0844935i	$0.973073\pi$
$242$	−0.236859	+	1.64739i	−0.0152258	+	0.105898i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	−13.4813	−	15.5582i	−0.863051	−	0.996014i
$245$	2.77086	+	12.1798i	0.177024	+	0.778138i
$246$	−0.281551	+	0.180942i	−0.0179511	+	0.0115364i
$247$	−3.51976	+	11.9872i	−0.223957	+	0.762728i
$248$	−7.66067	−	6.63801i	−0.486453	−	0.421514i
$249$	−4.60571	−	15.6856i	−0.291875	−	0.994035i
$250$	−1.87742	+	4.11098i	−0.118739	+	0.260001i
$251$	0.699522	+	4.86528i	0.0441534	+	0.307094i	0.999916	+	0.0129549i	$0.00412379\pi$
$251$	0.699522	+	4.86528i	0.0441534	+	0.307094i	−0.955763	+	0.294139i	$0.904967\pi$
$252$	4.90040	+	0.503337i	0.308696	+	0.0317073i
$253$	7.21311	−	9.89723i	0.453484	−	0.622234i
$254$	2.56837			0.161154
$255$	−4.45367	+	0.640342i	−0.278900	+	0.0400997i
$256$	2.51790	−	5.51343i	0.157369	−	0.344590i
$257$	−6.02898	−	20.5328i	−0.376077	−	1.28080i	−0.902541	−	0.430604i	$-0.858301\pi$
$257$	−6.02898	−	20.5328i	−0.376077	−	1.28080i	0.526464	−	0.850198i	$-0.323518\pi$
$258$	1.82526	−	2.10646i	0.113635	−	0.131142i
$259$	0.958256	−	2.34484i	0.0595431	−	0.145701i
$260$	−4.31852	−	6.71975i	−0.267823	−	0.416741i
$261$	−0.233933	−	0.512242i	−0.0144801	−	0.0317070i
$262$	−3.62053	+	3.13721i	−0.223677	+	0.193817i
$263$	−5.13861	+	7.99583i	−0.316860	+	0.493044i	−0.962752	−	0.270385i	$-0.912849\pi$
$263$	−5.13861	+	7.99583i	−0.316860	+	0.493044i	0.645892	+	0.763428i	$0.276485\pi$
$264$	−0.521525	+	3.62729i	−0.0320977	+	0.223244i
$265$	−15.4885	−	2.22691i	−0.951450	−	0.136798i
$266$	−3.99312	−	3.18673i	−0.244834	−	0.195391i
$267$	−5.44708	+	4.71992i	−0.333356	+	0.288854i
$268$	−16.1513	+	7.37606i	−0.986599	+	0.450565i
$269$	6.73891	+	10.4859i	0.410878	+	0.639339i	0.983590	−	0.180418i	$-0.0577449\pi$
$269$	6.73891	+	10.4859i	0.410878	+	0.639339i	−0.572712	+	0.819757i	$0.694109\pi$
$270$	0.186810	−	0.636215i	0.0113689	−	0.0387188i
$271$	−15.7013	−	13.6053i	−0.953786	−	0.826460i	0.0311261	−	0.999515i	$-0.490091\pi$
$271$	−15.7013	−	13.6053i	−0.953786	−	0.826460i	−0.984912	+	0.173055i	$0.944636\pi$
$272$	−7.71927	+	2.26658i	−0.468049	+	0.137432i
$273$	3.21975	−	5.48576i	0.194868	−	0.332013i
$274$	−5.53721	+	0.796131i	−0.334515	+	0.0480960i
$275$			4.63694i			0.279618i
$276$	−5.25927	+	7.21633i	−0.316571	+	0.434372i
$277$	7.58961			0.456015			0.228008	−	0.973659i	$-0.426779\pi$
$277$	7.58961			0.456015			0.228008	+	0.973659i	$0.426779\pi$
$278$	0.0212075	−	0.00304918i	0.00127194	−	0.000182878i
$279$	6.42522	+	2.93430i	0.384668	+	0.175672i
$280$	6.66165	−	1.23456i	0.398110	−	0.0737792i
$281$	22.1086	+	19.1573i	1.31889	+	1.14283i	0.979336	+	0.202240i	$0.0648220\pi$
$281$	22.1086	+	19.1573i	1.31889	+	1.14283i	0.339555	+	0.940586i	$0.389723\pi$
$282$	1.54458	+	0.453529i	0.0919782	+	0.0270072i
$283$	−11.5659	+	7.43297i	−0.687523	+	0.441844i	−0.837204	−	0.546890i	$-0.815812\pi$
$283$	−11.5659	+	7.43297i	−0.687523	+	0.441844i	0.149681	+	0.988734i	$0.452175\pi$
$284$	4.39609	+	9.62608i	0.260860	+	0.571203i
$285$	7.00789	−	6.07237i	0.415111	−	0.359696i
$286$	1.91918	+	1.23338i	0.113483	+	0.0729312i
$287$	2.31171	+	0.578358i	0.136456	+	0.0341394i
$288$	0.577184	−	4.01441i	0.0340109	−	0.236551i
$289$	−8.95256	−	5.75346i	−0.526621	−	0.338439i
$290$	−0.244523	−	0.282195i	−0.0143589	−	0.0165711i
$291$	0.0363726	−	0.0166108i	0.00213220	−	0.000973743i
$292$	7.24463	+	11.2729i	0.423960	+	0.659695i
$293$	−14.7698	−	4.33681i	−0.862861	−	0.253359i	−0.179785	−	0.983706i	$-0.557540\pi$
$293$	−14.7698	−	4.33681i	−0.862861	−	0.253359i	−0.683076	+	0.730347i	$0.739358\pi$
$294$	1.57849	+	2.06742i	0.0920592	+	0.120574i
$295$	−3.91015	−	13.3167i	−0.227658	−	0.775331i
$296$	−1.24978	−	0.570756i	−0.0726420	−	0.0331745i
$297$	−0.363420	−	2.52764i	−0.0210878	−	0.146669i
$298$		−	2.78578i		−	0.161376i
$299$	5.65486	+	10.0481i	0.327029	+	0.581095i
$300$		−	3.38091i		−	0.195197i
$301$	−19.8292	+	0.802431i	−1.14294	+	0.0462514i
$302$	−0.180184	+	0.394547i	−0.0103684	+	0.0227036i
$303$	10.3006	−	3.02454i	0.591756	−	0.173755i
$304$	10.8575	−	12.5303i	0.622722	−	0.718659i
$305$	18.9305	+	5.55849i	1.08396	+	0.318278i
$306$	−0.788229	+	0.506564i	−0.0450601	+	0.0289583i
$307$	−17.6123	+	8.04326i	−1.00519	+	0.459053i	−0.848841	−	0.528649i	$-0.822699\pi$
$307$	−17.6123	+	8.04326i	−1.00519	+	0.459053i	−0.156346	+	0.987702i	$0.549972\pi$
$308$	10.2990	−	7.22342i	0.586842	−	0.411593i
$309$	1.14249	−	1.77774i	0.0649938	−	0.101132i
$310$	4.63598	+	0.666553i	0.263306	+	0.0378576i
$311$	−0.717999	−	0.103233i	−0.0407140	−	0.00585378i	0.121928	−	0.992539i	$-0.461092\pi$
$311$	−0.717999	−	0.103233i	−0.0407140	−	0.00585378i	−0.162642	+	0.986685i	$0.552001\pi$
$312$	−2.90241	−	1.86527i	−0.164317	−	0.105600i
$313$	−7.23714	−	8.35210i	−0.409067	−	0.472089i	0.513408	−	0.858144i	$-0.328383\pi$
$313$	−7.23714	−	8.35210i	−0.409067	−	0.472089i	−0.922475	+	0.386056i	$0.873837\pi$
$314$	2.67324	+	5.85359i	0.150860	+	0.330337i
$315$	−4.21170	+	2.13328i	−0.237302	+	0.120197i
$316$	−6.56467	+	22.3572i	−0.369292	+	1.25769i
$317$	17.1951	−	19.8443i	0.965776	−	1.11456i	−0.0275961	−	0.999619i	$-0.508785\pi$
$317$	17.1951	−	19.8443i	0.965776	−	1.11456i	0.993372	−	0.114945i	$-0.0366693\pi$
$318$	−3.12650	+	0.918023i	−0.175325	+	0.0514801i
$319$	−1.30808	−	0.597380i	−0.0732384	−	0.0334469i
$320$	1.23779	+	8.60902i	0.0691946	+	0.481259i
$321$	14.4173			0.804694
$322$	−4.67836	+	0.586189i	−0.260715	+	0.0326670i
$323$	−13.1031			−0.729074
$324$	0.264979	+	1.84297i	0.0147211	+	0.102387i
$325$	−3.97104	−	1.81351i	−0.220273	−	0.100596i
$326$	−0.0507860	+	0.0149121i	−0.00281278	+	0.000825905i
$327$	12.5879	−	14.5272i	0.696110	−	0.803354i
$328$	0.364142	−	1.24015i	0.0201064	−	0.0684761i
$329$	−5.17909	−	10.2250i	−0.285532	−	0.563722i
$330$	−0.703401	−	1.54023i	−0.0387209	−	0.0847871i
$331$	17.0796	+	19.7109i	0.938778	+	1.08341i	0.996375	+	0.0850681i	$0.0271108\pi$
$331$	17.0796	+	19.7109i	0.938778	+	1.08341i	−0.0575968	+	0.998340i	$0.518344\pi$
$332$	25.6064	+	16.4562i	1.40533	+	0.903151i
$333$	0.947673	+	0.136255i	0.0519322	+	0.00746672i
$334$	0.867513	+	0.124730i	0.0474682	+	0.00682490i
$335$	9.20002	−	14.3155i	0.502651	−	0.782140i
$336$	−6.91112	+	4.84724i	−0.377032	+	0.264439i
$337$	10.3077	−	4.70736i	0.561495	−	0.256426i	−0.114387	−	0.993436i	$-0.536490\pi$
$337$	10.3077	−	4.70736i	0.561495	−	0.256426i	0.675882	+	0.737010i	$0.263763\pi$
$338$	2.25696	−	1.45046i	0.122762	−	0.0788946i
$339$	9.38010	+	2.75424i	0.509457	+	0.149590i
$340$	5.48620	−	6.33141i	0.297531	−	0.343369i
$341$	17.3070	−	5.08181i	0.937229	−	0.275195i
$342$	0.802150	−	1.75646i	0.0433753	−	0.0949786i
$343$	3.02855	−	18.2710i	0.163526	−	0.986539i
$344$			10.7641i			0.580362i
$345$	0.501169	−	8.54313i	0.0269821	−	0.459947i
$346$		−	8.88639i		−	0.477735i
$347$	−1.17274	−	8.15661i	−0.0629562	−	0.437870i	−0.996783	−	0.0801449i	$-0.974462\pi$
$347$	−1.17274	−	8.15661i	−0.0629562	−	0.437870i	0.933827	−	0.357725i	$-0.116447\pi$
$348$	0.953755	+	0.435565i	0.0511266	+	0.0233487i
$349$	3.19107	+	10.8678i	0.170814	+	0.581739i	0.999749	+	0.0223944i	$0.00712896\pi$
$349$	3.19107	+	10.8678i	0.170814	+	0.581739i	−0.828935	+	0.559345i	$0.811053\pi$
$350$	1.30078	−	1.22265i	0.0695298	−	0.0653532i
$351$	2.30679	+	0.677334i	0.123127	+	0.0361534i
$352$	−5.59928	−	8.71265i	−0.298443	−	0.464386i
$353$	13.6324	−	6.22573i	0.725582	−	0.331362i	−0.0181545	−	0.999835i	$-0.505779\pi$
$353$	13.6324	−	6.22573i	0.725582	−	0.331362i	0.743736	+	0.668473i	$0.233052\pi$
$354$	−1.89265	−	2.18423i	−0.100593	−	0.116091i
$355$	−8.53195	−	5.48315i	−0.452829	−	0.291016i
$356$	1.90984	−	13.2832i	0.101221	−	0.704010i
$357$	6.47184	+	1.61917i	0.342526	+	0.0856955i
$358$	−6.66026	−	4.28029i	−0.352006	−	0.226220i
$359$	0.858571	−	0.743956i	0.0453136	−	0.0392645i	−0.631910	−	0.775042i	$-0.717729\pi$
$359$	0.858571	−	0.743956i	0.0453136	−	0.0392645i	0.677223	+	0.735778i	$0.263183\pi$
$360$	1.06377	+	2.32933i	0.0560656	+	0.122766i
$361$	6.73300	−	4.32703i	0.354368	−	0.227739i
$362$	1.42735	+	0.419107i	0.0750197	+	0.0220278i
$363$	3.38496	+	2.93309i	0.177664	+	0.153947i
$364$	2.15811	+	11.6451i	0.113116	+	0.610370i
$365$	−11.6818	−	5.33491i	−0.611455	−	0.279242i
$366$	4.06669	−	0.584701i	0.212569	−	0.0305628i
$367$	−10.9999			−0.574193			−0.287096	−	0.957902i	$-0.592690\pi$
$367$	−10.9999			−0.574193			−0.287096	+	0.957902i	$0.592690\pi$
$368$	−1.28692	−	15.2473i	−0.0670854	−	0.794823i
$369$			0.900674i			0.0468872i
$370$	0.628377	−	0.0903470i	0.0326678	−	0.00469692i
$371$	20.0089	+	11.7438i	1.03881	+	0.609710i
$372$	−12.6190	+	3.70528i	−0.654266	+	0.192110i
$373$	4.01889	+	3.48239i	0.208090	+	0.180311i	0.752670	−	0.658398i	$-0.228765\pi$
$373$	4.01889	+	3.48239i	0.208090	+	0.180311i	−0.544580	+	0.838709i	$0.683311\pi$
$374$	−0.674095	+	2.29576i	−0.0348566	+	0.118711i
$375$	6.57545	+	10.2316i	0.339555	+	0.528358i
$376$	−5.65506	+	2.58258i	−0.291637	+	0.133186i
$377$	1.02318	−	0.886593i	0.0526966	−	0.0456619i
$378$	−0.613246	+	0.768426i	−0.0315420	+	0.0395236i
$379$	3.63263	+	0.522294i	0.186596	+	0.0268284i	0.234979	−	0.972000i	$-0.424498\pi$
$379$	3.63263	+	0.522294i	0.186596	+	0.0268284i	−0.0483833	+	0.998829i	$0.515407\pi$
$380$	−2.45709	+	17.0894i	−0.126046	+	0.876669i
$381$	3.73683	−	5.81462i	0.191444	−	0.297892i
$382$	0.473097	−	0.409941i	0.0242058	−	0.0209744i
$383$	−3.90708	−	8.55531i	−0.199642	−	0.437156i	0.783159	−	0.621822i	$-0.213607\pi$
$383$	−3.90708	−	8.55531i	−0.199642	−	0.437156i	−0.982801	+	0.184666i	$0.940880\pi$
$384$	5.36454	+	8.34738i	0.273758	+	0.425975i
$385$	−4.56076	+	11.1602i	−0.232438	+	0.568774i
$386$	−3.13975	+	3.62346i	−0.159809	+	0.184429i
$387$	−2.11324	−	7.19703i	−0.107422	−	0.365846i
$388$	−0.0309280	+	0.0677229i	−0.00157013	+	0.00343811i
$389$	−26.3967	+	3.79528i	−1.33837	+	0.192428i	−0.774047	−	0.633128i	$-0.781771\pi$
$389$	−26.3967	+	3.79528i	−1.33837	+	0.192428i	−0.564320	+	0.825556i	$0.690862\pi$
$390$	1.59415			0.0807227
$391$	−8.44071	+	8.65967i	−0.426865	+	0.437938i
$392$	−9.83559	−	2.04204i	−0.496772	−	0.103139i
$393$	1.83477	+	12.7611i	0.0925519	+	0.643712i
$394$	−1.97052	+	4.31484i	−0.0992734	+	0.217378i
$395$	−6.29145	−	21.4267i	−0.316557	−	1.07809i
$396$	3.59334	+	3.11365i	0.180572	+	0.156467i
$397$	−5.70211	+	19.4196i	−0.286181	+	0.974642i	0.683436	+	0.730011i	$0.260485\pi$
$397$	−5.70211	+	19.4196i	−0.286181	+	0.974642i	−0.969616	+	0.244631i	$0.921333\pi$
$398$	0.180887	−	0.116249i	0.00906704	−	0.00582704i
$399$	−13.0243	+	4.40366i	−0.652031	+	0.220459i
$400$	3.79396	+	4.37846i	0.189698	+	0.218923i
$401$	15.3838	−	23.9377i	0.768231	−	1.19539i	−0.207887	−	0.978153i	$-0.566659\pi$
$401$	15.3838	−	23.9377i	0.768231	−	1.19539i	0.976119	−	0.217239i	$-0.0697050\pi$
$402$	0.504306	−	3.50752i	0.0251525	−	0.174939i
$403$	−2.41679	+	16.8091i	−0.120389	+	0.837322i
$404$	−10.8067	+	16.8155i	−0.537653	+	0.836604i
$405$	−1.16855	−	1.34858i	−0.0580658	−	0.0670115i
$406$	0.177328	+	0.524465i	0.00880062	+	0.0260288i
$407$	2.05678	−	1.32181i	0.101951	−	0.0655197i
$408$	1.01945	−	3.47193i	0.0504703	−	0.171886i
$409$	−1.84276	−	1.59676i	−0.0911187	−	0.0789548i	0.608110	−	0.793852i	$-0.291928\pi$
$409$	−1.84276	−	1.59676i	−0.0911187	−	0.0789548i	−0.699229	+	0.714898i	$0.746473\pi$
$410$	0.168254	+	0.573022i	0.00830950	+	0.0282995i
$411$	−6.25394	+	13.6942i	−0.308484	+	0.675486i
$412$	0.559956	+	3.89458i	0.0275870	+	0.191872i
$413$	−2.10259	+	20.4705i	−0.103462	+	1.00729i
$414$	−0.644099	−	1.66161i	−0.0316558	−	0.0816636i
$415$	−29.1715			−1.43197
$416$	9.65133	−	1.38765i	0.473195	−	0.0680352i
$417$	0.0239526	−	0.0524488i	0.00117296	−	0.00256843i
$418$	−1.38921	−	4.73123i	−0.0679487	−	0.231412i
$419$	−25.0345	+	28.8914i	−1.22302	+	1.41144i	−0.341104	+	0.940026i	$0.610801\pi$
$419$	−25.0345	+	28.8914i	−1.22302	+	1.41144i	−0.881913	+	0.471411i	$0.843745\pi$
$420$	3.32537	−	8.13715i	0.162262	−	0.397053i
$421$	−0.512484	−	0.797441i	−0.0249770	−	0.0388649i	0.828541	−	0.559929i	$-0.189172\pi$
$421$	−0.512484	−	0.797441i	−0.0249770	−	0.0388649i	−0.853518	+	0.521064i	$0.825535\pi$
$422$	−4.00474	−	8.76916i	−0.194948	−	0.426876i
$423$	3.27403	−	2.83696i	0.159189	−	0.137938i
$424$	6.80344	−	10.5864i	0.330404	−	0.514119i
$425$	0.651606	−	4.53202i	0.0316075	−	0.219835i
$426$	−2.09046	−	0.300563i	−0.101283	−	0.0145623i
$427$	−22.8644	−	18.2470i	−1.10649	−	0.883036i
$428$	−20.2872	+	17.5790i	−0.980620	+	0.849712i
$429$	5.58458	−	2.55039i	0.269626	−	0.123134i
$430$	−2.68895	−	4.18409i	−0.129673	−	0.201775i
$431$	−6.36192	+	21.6667i	−0.306443	+	1.04365i	0.651966	+	0.758249i	$0.273945\pi$
$431$	−6.36192	+	21.6667i	−0.306443	+	1.04365i	−0.958408	+	0.285400i	$0.907874\pi$
$432$	−2.41129	−	2.08940i	−0.116013	−	0.100526i
$433$	−17.6227	+	5.17450i	−0.846894	+	0.248671i	−0.676259	−	0.736664i	$-0.736400\pi$
$433$	−17.6227	+	5.17450i	−0.846894	+	0.248671i	−0.170635	+	0.985334i	$0.554582\pi$
$434$	−5.98902	−	3.51514i	−0.287482	−	0.168732i
$435$	−0.994639	+	0.143007i	−0.0476893	+	0.00685668i
$436$			35.7902i			1.71404i
$437$	4.98523	−	24.4178i	0.238476	−	1.16806i
$438$	−2.67429			−0.127783
$439$	11.4367	−	1.64435i	0.545844	−	0.0784806i	0.136124	−	0.990692i	$-0.456535\pi$
$439$	11.4367	−	1.64435i	0.545844	−	0.0784806i	0.409720	+	0.912211i	$0.365626\pi$
$440$	5.94826	+	2.71648i	0.283572	+	0.129503i
$441$	6.97711	−	0.565614i	0.332243	−	0.0269340i
$442$	−1.70243	−	1.47516i	−0.0809763	−	0.0701664i
$443$	21.5258	+	6.32053i	1.02272	+	0.300298i	0.749747	−	0.661724i	$-0.230175\pi$
$443$	21.5258	+	6.32053i	1.02272	+	0.300298i	0.272972	+	0.962022i	$0.411993\pi$
$444$	−1.49965	+	0.963766i	−0.0711702	+	0.0457383i
$445$	5.34277	+	11.6990i	0.253272	+	0.554588i
$446$	0.652889	−	0.565732i	0.0309152	−	0.0267882i
$447$	−6.30682	−	4.05315i	−0.298302	−	0.191707i
$448$	3.12988	−	12.5102i	0.147873	−	0.591050i
$449$	1.77506	−	12.3458i	0.0837702	−	0.582634i	−0.904096	−	0.427329i	$-0.859455\pi$
$449$	1.77506	−	12.3458i	0.0837702	−	0.582634i	0.987866	−	0.155306i	$-0.0496362\pi$
$450$	0.567626	+	0.364791i	0.0267581	+	0.0171964i
$451$	1.50617	+	1.73822i	0.0709230	+	0.0818495i
$452$	−16.5574	+	7.56152i	−0.778795	+	0.355664i
$453$	0.631072	+	0.981968i	0.0296504	+	0.0461369i
$454$	2.99940	+	0.880703i	0.140769	+	0.0413334i
$455$	−7.77375	−	8.27055i	−0.364439	−	0.387729i
$456$	2.10094	+	7.15515i	0.0983855	+	0.335070i
$457$	−36.0433	−	16.4604i	−1.68604	−	0.769987i	−0.999062	−	0.0433046i	$-0.986211\pi$
$457$	−36.0433	−	16.4604i	−1.68604	−	0.769987i	−0.686974	−	0.726682i	$-0.741061\pi$
$458$	0.148547	+	1.03317i	0.00694115	+	0.0482767i
$459$			2.52152i			0.117695i
$460$	9.71141	+	12.6325i	0.452797	+	0.588994i
$461$			30.8822i			1.43833i	0.694842	+	0.719163i	$0.255474\pi$
$461$			30.8822i			1.43833i	−0.694842	+	0.719163i	$0.744526\pi$
$462$	0.101512	+	2.50851i	0.00472277	+	0.116706i
$463$	3.02205	−	6.61736i	0.140446	−	0.307535i	−0.826318	−	0.563204i	$-0.809569\pi$
$463$	3.02205	−	6.61736i	0.140446	−	0.307535i	0.966764	+	0.255669i	$0.0822958\pi$
$464$	−1.72394	+	0.506196i	−0.0800321	+	0.0234995i
$465$	8.25411	−	9.52575i	0.382775	−	0.441746i
$466$	−4.81658	−	1.41427i	−0.223124	−	0.0655150i
$467$	−13.0534	+	8.38891i	−0.604039	+	0.388192i	−0.806618	−	0.591074i	$-0.798704\pi$
$467$	−13.0534	+	8.38891i	−0.604039	+	0.388192i	0.202578	+	0.979266i	$0.435068\pi$
$468$	−4.07186	+	1.85956i	−0.188222	+	0.0859580i
$469$	−20.6565	+	14.4878i	−0.953830	+	0.668986i
$470$	1.55301	−	2.41654i	0.0716352	−	0.111467i
$471$	17.1416	+	2.46458i	0.789841	+	0.113562i
$472$	11.0479	+	1.58845i	0.508522	+	0.0731144i
$473$	−16.1138	−	10.3557i	−0.740912	−	0.476155i
$474$	−3.04528	−	3.51444i	−0.139874	−	0.161423i
$475$	3.91981	+	8.58318i	0.179853	+	0.393823i
$476$	−11.0811	+	5.61271i	−0.507901	+	0.257258i
$477$	−2.47053	+	8.41386i	−0.113118	+	0.385244i
$478$	−5.17056	+	5.96715i	−0.236496	+	0.272931i
$479$	30.2691	−	8.88781i	1.38303	−	0.406094i	0.496208	−	0.868204i	$-0.334725\pi$
$479$	30.2691	−	8.88781i	1.38303	−	0.406094i	0.886823	+	0.462109i	$0.152907\pi$
$480$	−6.58308	−	3.00639i	−0.300475	−	0.137222i
$481$	0.327580	+	2.27837i	0.0149364	+	0.103885i
$482$	2.60095			0.118470
$483$	−5.47965	+	11.4444i	−0.249333	+	0.520737i
$484$	−8.33945			−0.379066
$485$	−0.0101545	−	0.0706260i	−0.000461091	−	0.00320696i
$486$	−0.338009	−	0.154364i	−0.0153324	−	0.00700208i
$487$	4.40411	−	1.29316i	0.199569	−	0.0585988i	−0.180420	−	0.983590i	$-0.557746\pi$
$487$	4.40411	−	1.29316i	0.199569	−	0.0585988i	0.379989	+	0.924991i	$0.375928\pi$
$488$	−10.3905	+	11.9913i	−0.470356	+	0.542820i
$489$	−0.0401306	+	0.136672i	−0.00181477	+	0.00618054i
$490$	4.33328	−	1.66324i	0.195758	−	0.0751376i
$491$	10.8460	+	23.7494i	0.489474	+	1.07180i	0.979749	+	0.200230i	$0.0641689\pi$
$491$	10.8460	+	23.7494i	0.489474	+	1.07180i	−0.490275	+	0.871568i	$0.663104\pi$
$492$	−1.09819	−	1.26738i	−0.0495103	−	0.0571379i
$493$	1.19454	+	0.767681i	0.0537992	+	0.0345746i
$494$	4.59511	+	0.660677i	0.206744	+	0.0297253i
$495$	−4.51040	−	0.648497i	−0.202727	−	0.0291478i
$496$	12.1844	−	18.9592i	0.547094	−	0.851295i
$497$	8.63466	+	12.3112i	0.387318	+	0.552231i
$498$	−5.52571	+	2.52351i	−0.247613	+	0.113081i
$499$	−35.2736	+	22.6690i	−1.57906	+	1.01480i	−0.602886	+	0.797827i	$0.705983\pi$
$499$	−35.2736	+	22.6690i	−1.57906	+	1.01480i	−0.976177	+	0.216975i	$0.930381\pi$
$500$	−21.7280	−	6.37992i	−0.971706	−	0.285319i
$501$	1.54456	−	1.78252i	0.0690059	−	0.0796370i
$502$	1.75249	−	0.514578i	0.0782176	−	0.0229667i
$503$	−8.07258	+	17.6765i	−0.359939	+	0.788155i	0.639868	+	0.768485i	$0.278989\pi$
$503$	−8.07258	+	17.6765i	−0.359939	+	0.788155i	−0.999807	+	0.0196706i	$0.993738\pi$
$504$	−0.153519	−	3.79368i	−0.00683829	−	0.168984i
$505$		−	19.1567i		−	0.852463i
$506$	−4.02172	−	2.12964i	−0.178787	−	0.0946740i
$507$		−	7.21995i		−	0.320649i
$508$	1.83150	+	12.7383i	0.0812595	+	0.565172i
$509$	−28.4261	−	12.9818i	−1.25996	−	0.575406i	−0.330321	−	0.943869i	$-0.607157\pi$
$509$	−28.4261	−	12.9818i	−1.25996	−	0.575406i	−0.929643	+	0.368463i	$0.879884\pi$
$510$	0.471044	+	1.60423i	0.0208582	+	0.0710364i
$511$	13.0410	+	13.8745i	0.576901	+	0.613770i
$512$	−21.2023	−	6.22555i	−0.937017	−	0.275133i
$513$	−2.80944	−	4.37157i	−0.124040	−	0.193009i
$514$	−7.23328	+	3.30333i	−0.319046	+	0.145704i
$515$	−2.46939	−	2.84983i	−0.108814	−	0.125578i
$516$	11.7490	+	7.55061i	0.517220	+	0.332397i
$517$	1.57440	−	10.9502i	0.0692418	−	0.481587i
$518$	−0.913125	−	0.228452i	−0.0401204	−	0.0100376i
$519$	−20.1182	−	12.9292i	−0.883091	−	0.567528i
$520$	−4.65274	+	4.03163i	−0.204036	+	0.176798i
$521$	12.7799	+	27.9840i	0.559897	+	1.22600i	0.952005	+	0.306084i	$0.0990188\pi$
$521$	12.7799	+	27.9840i	0.559897	+	1.22600i	−0.392108	+	0.919919i	$0.628254\pi$
$522$	−0.176035	+	0.113131i	−0.00770485	+	0.00495161i
$523$	39.9177	+	11.7209i	1.74548	+	0.512519i	0.989805	−	0.142430i	$-0.0454916\pi$
$523$	39.9177	+	11.7209i	1.74548	+	0.512519i	0.755673	+	0.654949i	$0.227310\pi$
$524$	−18.1414	−	15.7196i	−0.792510	−	0.686714i
$525$	−0.875426	−	4.72377i	−0.0382067	−	0.206162i
$526$	3.21266	+	1.46717i	0.140079	+	0.0639718i
$527$	−17.6296	+	2.53475i	−0.767956	+	0.110415i
$528$	−8.14761			−0.354579
$529$	−12.9261	−	19.0241i	−0.562003	−	0.827135i
$530$			5.81454i			0.252567i
$531$	−7.69865	+	1.10690i	−0.334093	+	0.0480353i
$532$	12.9577	−	22.0771i	0.561788	−	0.957165i
$533$	−2.07766	+	0.610057i	−0.0899936	+	0.0264245i
$534$	2.02407	+	1.75387i	0.0875902	+	0.0758974i
$535$	7.24802	−	24.6845i	0.313359	−	1.06720i
$536$	7.39871	+	11.5126i	0.319576	+	0.497269i
$537$	−19.3806	+	8.85082i	−0.836335	+	0.381941i
$538$	3.50043	−	3.03314i	0.150914	−	0.130768i
$539$	12.5193	−	12.7592i	0.539246	−	0.549579i
$540$	3.28865	+	0.472836i	0.141521	+	0.0203476i
$541$	−2.94050	+	20.4516i	−0.126422	+	0.879285i	0.823615	+	0.567149i	$0.191954\pi$
$541$	−2.94050	+	20.4516i	−0.126422	+	0.879285i	−0.950037	+	0.312136i	$0.898956\pi$
$542$	−4.17378	+	6.49453i	−0.179279	+	0.278964i
$543$	3.02554	−	2.62164i	0.129838	−	0.112506i
$544$	4.24824	+	9.30235i	0.182142	+	0.398835i
$545$	−18.5443	−	28.8555i	−0.794351	−	1.23603i
$546$	−2.18797	−	0.894147i	−0.0936364	−	0.0382659i
$547$	17.0697	−	19.6995i	0.729847	−	0.842288i	−0.262608	−	0.964903i	$-0.584582\pi$
$547$	17.0697	−	19.6995i	0.729847	−	0.842288i	0.992454	+	0.122615i	$0.0391279\pi$
$548$	−7.89714	−	26.8952i	−0.337349	−	1.14891i
$549$	4.59307	−	10.0574i	0.196028	−	0.429240i
$550$	1.70550	−	0.245213i	0.0727226	−	0.0104559i
$551$	−2.92631			−0.124665
$552$	6.08214	+	3.22070i	0.258873	+	0.137082i
$553$	−3.38308	+	32.9371i	−0.143863	+	1.40063i
$554$	−0.401359	−	2.79151i	−0.0170521	−	0.118600i
$555$	0.709713	−	1.55405i	0.0301256	−	0.0659659i
$556$	0.0302460	+	0.103009i	0.00128272	+	0.00436854i
$557$	7.32080	+	6.34351i	0.310192	+	0.268783i	0.796018	−	0.605272i	$-0.206936\pi$
$557$	7.32080	+	6.34351i	0.310192	+	0.268783i	−0.485826	+	0.874055i	$0.661481\pi$
$558$	0.739473	−	2.51841i	0.0313044	−	0.106613i
$559$	15.1707	−	9.74959i	0.641651	−	0.412364i
$560$	4.82474	+	14.2697i	0.203883	+	0.603005i
$561$	4.21668	+	4.86630i	0.178028	+	0.205456i
$562$	5.87700	−	9.14480i	0.247906	−	0.385750i
$563$	5.47881	−	38.1059i	0.230904	−	1.60597i	−0.463304	−	0.886200i	$-0.653336\pi$
$563$	5.47881	−	38.1059i	0.230904	−	1.60597i	0.694208	−	0.719775i	$-0.255755\pi$
$564$	−1.14793	+	7.98404i	−0.0483367	+	0.336189i
$565$	9.43134	−	14.6754i	0.396779	−	0.617401i
$566$	3.34554	+	3.86095i	0.140623	+	0.162288i
$567$	0.847430	+	2.50636i	0.0355887	+	0.105257i
$568$	6.86145	−	4.40959i	0.287900	−	0.185022i
$569$	6.52215	−	22.2124i	0.273423	−	0.931193i	−0.702244	−	0.711936i	$-0.747819\pi$
$569$	6.52215	−	22.2124i	0.273423	−	0.931193i	0.975667	−	0.219257i	$-0.0703632\pi$
$570$	−2.60405	−	2.25643i	−0.109072	−	0.0945113i
$571$	2.96711	+	10.1051i	0.124170	+	0.422884i	0.997990	−	0.0633649i	$-0.0201832\pi$
$571$	2.96711	+	10.1051i	0.124170	+	0.422884i	−0.873821	+	0.486248i	$0.838365\pi$
$572$	−4.74863	+	10.3980i	−0.198550	+	0.434764i
$573$	−0.239751	−	1.66750i	−0.0100157	−	0.0696609i
$574$	0.0904750	−	0.880847i	0.00377635	−	0.0367659i
$575$	8.19759	+	2.93854i	0.341863	+	0.122546i
$576$	4.87414			0.203089
$577$	16.6114	−	2.38836i	0.691543	−	0.0994289i	0.212422	−	0.977178i	$-0.431865\pi$
$577$	16.6114	−	2.38836i	0.691543	−	0.0994289i	0.479121	+	0.877749i	$0.340956\pi$
$578$	−1.64273	+	3.59707i	−0.0683285	+	0.149619i
$579$	3.63513	+	12.3801i	0.151071	+	0.514500i
$580$	1.22523	−	1.41399i	0.0508751	−	0.0587129i
$581$	40.0379	+	16.3621i	1.66105	+	0.678815i
$582$	−0.00803305	−	0.0124997i	−0.000332981	−	0.000518128i
$583$	9.30239	+	20.3694i	0.385265	+	0.843614i
$584$	7.80531	−	6.76334i	0.322986	−	0.279869i
$585$	2.31939	−	3.60904i	0.0958950	−	0.149215i
$586$	−0.814041	+	5.66178i	−0.0336277	+	0.233886i
$587$	7.90217	+	1.13616i	0.326157	+	0.0468944i	0.303449	−	0.952848i	$-0.401862\pi$
$587$	7.90217	+	1.13616i	0.326157	+	0.0468944i	0.0227087	+	0.999742i	$0.492771\pi$
$588$	−9.12816	+	9.30309i	−0.376439	+	0.383653i
$589$	27.7403	−	24.0371i	1.14302	−	0.990430i
$590$	−4.69121	+	2.14241i	−0.193134	+	0.0882014i
$591$	6.90152	+	10.7390i	0.283890	+	0.441742i
$592$	0.860618	−	2.93099i	0.0353712	−	0.120463i
$593$	22.2131	+	19.2478i	0.912184	+	0.790412i	0.978256	−	0.207403i	$-0.0665011\pi$
$593$	22.2131	+	19.2478i	0.912184	+	0.790412i	−0.0660716	+	0.997815i	$0.521047\pi$
$594$	−0.910466	+	0.267337i	−0.0373569	+	0.0109690i
$595$	6.02585	−	10.2667i	0.247036	−	0.420895i
$596$	13.8166	−	1.98653i	0.565951	−	0.0813714i
$597$		−	0.578652i		−	0.0236826i
$598$	3.39671	−	2.61126i	0.138902	−	0.106783i
$599$	−15.4770			−0.632373			−0.316187	−	0.948697i	$-0.602403\pi$
$599$	−15.4770			−0.632373			−0.316187	+	0.948697i	$0.602403\pi$
$600$	−2.57926	+	0.370842i	−0.105298	+	0.0151396i
$601$	0.0889384	+	0.0406168i	0.00362787	+	0.00165679i	0.417228	−	0.908802i	$-0.363002\pi$
$601$	0.0889384	+	0.0406168i	0.00362787	+	0.00165679i	−0.413600	+	0.910459i	$0.635729\pi$
$602$	1.34376	+	7.25088i	0.0547676	+	0.295524i
$603$	−7.20707	−	6.24496i	−0.293495	−	0.254315i
$604$	−2.08532	−	0.612306i	−0.0848506	−	0.0249144i
$605$	6.72360	−	4.32100i	0.273353	−	0.175673i
$606$	−1.65717	−	3.62870i	−0.0673180	−	0.147406i
$607$	−0.800830	+	0.693923i	−0.0325047	+	0.0281655i	−0.670962	−	0.741492i	$-0.734118\pi$
$607$	−0.800830	+	0.693923i	−0.0325047	+	0.0281655i	0.638457	+	0.769658i	$0.279573\pi$
$608$	−17.7297	−	11.3942i	−0.719034	−	0.462095i
$609$	1.44536	+	0.361609i	0.0585688	+	0.0146531i
$610$	1.04336	−	7.25671i	0.0422443	−	0.293816i
$611$	8.76188	+	5.63092i	0.354468	+	0.227803i
$612$	−3.07449	−	3.54815i	−0.124279	−	0.143425i
$613$	−15.9158	+	7.26850i	−0.642833	+	0.293572i	−0.710034	−	0.704167i	$-0.751320\pi$
$613$	−15.9158	+	7.26850i	−0.642833	+	0.293572i	0.0672008	+	0.997739i	$0.478593\pi$
$614$	3.88975	+	6.05257i	0.156978	+	0.244262i
$615$	1.54209	+	0.452797i	0.0621829	+	0.0182585i
$616$	−6.64035	−	7.06472i	−0.267547	−	0.284646i
$617$	−5.41310	−	18.4353i	−0.217923	−	0.742178i	−0.993789	−	0.111280i	$-0.964505\pi$
$617$	−5.41310	−	18.4353i	−0.217923	−	0.742178i	0.775866	−	0.630898i	$-0.217313\pi$
$618$	−0.714284	−	0.326202i	−0.0287327	−	0.0131218i
$619$	−5.05833	−	35.1815i	−0.203311	−	1.41406i	−0.794370	−	0.607434i	$-0.792199\pi$
$619$	−5.05833	−	35.1815i	−0.203311	−	1.41406i	0.591059	−	0.806628i	$-0.298710\pi$
$620$			23.4684i			0.942512i
$621$	−4.69890	−	0.959345i	−0.188560	−	0.0384972i
$622$			0.269544i			0.0108077i
$623$	−0.771049	−	19.0537i	−0.0308914	−	0.763370i
$624$	3.18654	−	6.97756i	0.127564	−	0.279326i
$625$	12.1124	−	3.55651i	0.484495	−	0.142260i
$626$	−2.68924	+	3.10355i	−0.107484	+	0.124043i
$627$	−12.7324	−	3.73858i	−0.508484	−	0.149304i
$628$	−27.1257	+	17.4327i	−1.08243	+	0.695639i
$629$	−2.19599	+	1.00287i	−0.0875598	+	0.0399872i
$630$	1.00736	+	1.43628i	0.0401342	+	0.0572227i
$631$	16.1381	−	25.1113i	0.642447	−	0.999667i	−0.355441	−	0.934699i	$-0.615669\pi$
$631$	16.1381	−	25.1113i	0.642447	−	0.999667i	0.997887	−	0.0649677i	$-0.0206944\pi$
$632$	17.7762	+	2.55583i	0.707098	+	0.101665i
$633$	−25.6795	−	3.69215i	−1.02067	−	0.146750i
$634$	−8.20818	−	5.27508i	−0.325988	−	0.209500i
$635$	−8.07686	−	9.32119i	−0.320520	−	0.369900i
$636$	−6.78261	−	14.8518i	−0.268948	−	0.588914i
$637$	6.03059	+	15.7116i	0.238941	+	0.622517i
$638$	−0.150546	+	0.512712i	−0.00596016	+	0.0202984i
$639$	−3.72196	+	4.29537i	−0.147238	+	0.169922i
$640$	16.9889	−	4.98838i	0.671543	−	0.197183i
$641$	7.26388	+	3.31730i	0.286906	+	0.131026i	0.553670	−	0.832736i	$-0.313227\pi$
$641$	7.26388	+	3.31730i	0.286906	+	0.131026i	−0.266764	+	0.963762i	$0.585954\pi$
$642$	−0.762424	−	5.30277i	−0.0300905	−	0.209284i
$643$	49.9189			1.96861			0.984305	−	0.176475i	$-0.0564696\pi$
$643$	49.9189			1.96861			0.984305	+	0.176475i	$0.0564696\pi$
$644$	−6.24344	−	22.7852i	−0.246026	−	0.897864i
$645$	−13.3848			−0.527024
$646$	0.692925	+	4.81940i	0.0272628	+	0.189617i
$647$	−31.2141	−	14.2550i	−1.22715	−	0.560422i	−0.306899	−	0.951742i	$-0.599291\pi$
$647$	−31.2141	−	14.2550i	−1.22715	−	0.560422i	−0.920255	+	0.391320i	$0.872019\pi$
$648$	1.37692	−	0.404300i	0.0540905	−	0.0158824i
$649$	−13.0066	+	15.0105i	−0.510555	+	0.589212i
$650$	−0.457023	+	1.55648i	−0.0179259	+	0.0610501i
$651$	−16.6717	+	8.44444i	−0.653417	+	0.330964i
$652$	−0.110175	−	0.241249i	−0.00431478	−	0.00944806i
$653$	18.8137	+	21.7122i	0.736237	+	0.849663i	0.993159	−	0.116769i	$-0.0372537\pi$
$653$	18.8137	+	21.7122i	0.736237	+	0.849663i	−0.256922	+	0.966432i	$0.582708\pi$
$654$	−6.00887	−	3.86167i	−0.234965	−	0.151003i
$655$	22.7713	+	3.27401i	0.889747	+	0.127926i
$656$	2.84444	+	0.408968i	0.111057	+	0.0159675i
$657$	−3.89094	+	6.05443i	−0.151800	+	0.236206i
$658$	−3.48694	+	2.44563i	−0.135935	+	0.0953405i
$659$	−16.2536	+	7.42277i	−0.633151	+	0.289150i	−0.706021	−	0.708191i	$-0.749511\pi$
$659$	−16.2536	+	7.42277i	−0.633151	+	0.289150i	0.0728700	+	0.997341i	$0.476784\pi$
$660$	7.13750	−	4.58699i	0.277827	−	0.178548i
$661$	16.7127	+	4.90728i	0.650047	+	0.190871i	0.590099	−	0.807331i	$-0.299089\pi$
$661$	16.7127	+	4.90728i	0.650047	+	0.190871i	0.0599474	+	0.998202i	$0.480907\pi$
$662$	6.34658	−	7.32435i	0.246667	−	0.284669i
$663$	−5.81661	+	1.70791i	−0.225899	+	0.0663298i
$664$	9.74559	−	21.3399i	0.378202	−	0.828147i
$665$	0.991986	+	24.5134i	0.0384676	+	0.950587i
$666$		−	0.355766i		−	0.0137857i
$667$	−1.88506	+	1.93396i	−0.0729900	+	0.0748834i
$668$			4.39155i			0.169914i
$669$	−0.330863	−	2.30121i	−0.0127919	−	0.0889698i
$670$	−5.75186	−	2.62679i	−0.222214	−	0.101482i
$671$	−7.95457	−	27.0908i	−0.307083	−	1.04583i
$672$	7.34903	+	7.81869i	0.283495	+	0.301613i
$673$	47.4059	+	13.9196i	1.82736	+	0.536563i	0.999696	−	0.0246546i	$-0.00784859\pi$
$673$	47.4059	+	13.9196i	1.82736	+	0.536563i	0.827669	+	0.561217i	$0.189667\pi$
$674$	−2.27650	−	3.54230i	−0.0876873	−	0.136444i
$675$	1.65173	−	0.754318i	0.0635750	−	0.0290337i
$676$	8.80328	+	10.1595i	0.338588	+	0.390751i
$677$	11.0679	+	7.11292i	0.425375	+	0.273372i	0.735764	−	0.677238i	$-0.236823\pi$
$677$	11.0679	+	7.11292i	0.425375	+	0.273372i	−0.310389	+	0.950609i	$0.600459\pi$
$678$	0.516986	−	3.59572i	0.0198547	−	0.138093i
$679$	−0.0256766	+	0.102630i	−0.000985379	+	0.00393858i
$680$	−5.43194	−	3.49089i	−0.208305	−	0.133870i
$681$	6.35781	−	5.50907i	0.243632	−	0.211108i
$682$	−2.78437	−	6.09691i	−0.106619	−	0.233463i
$683$	15.8821	−	10.2068i	0.607711	−	0.390552i	−0.200287	−	0.979737i	$-0.564188\pi$
$683$	15.8821	−	10.2068i	0.607711	−	0.390552i	0.807998	+	0.589185i	$0.200551\pi$
$684$	9.28354	+	2.72589i	0.354965	+	0.104227i
$685$	20.3024	+	17.5922i	0.775717	+	0.672162i
$686$	−6.88034	−	0.147705i	−0.262693	−	0.00563942i
$687$	2.55515	+	1.16690i	0.0974851	+	0.0445199i
$688$	−23.6886	+	3.40591i	−0.903121	+	0.129849i
$689$	−21.0824			−0.803174
$690$	−3.16872	+	0.267450i	−0.120631	+	0.0101816i
$691$		−	33.6433i		−	1.27985i	−0.768437	−	0.639925i	$-0.778965\pi$
$691$		−	33.6433i		−	1.27985i	0.768437	−	0.639925i	$-0.221035\pi$
$692$	44.0738	−	6.33686i	1.67544	−	0.240891i
$693$	5.82679	+	3.41992i	0.221342	+	0.129912i
$694$	−2.93804	+	0.862686i	−0.111526	+	0.0327471i
$695$	−0.0777583	−	0.0673780i	−0.00294954	−	0.00255579i
$696$	0.227674	−	0.775386i	0.00862995	−	0.0293909i
$697$	−1.22783	−	1.91054i	−0.0465075	−	0.0723670i
$698$	3.82849	−	1.74841i	0.144911	−	0.0661784i
$699$	−10.2097	+	8.84673i	−0.386165	+	0.334614i
$700$	6.99154	+	5.57963i	0.264255	+	0.210890i
$701$	2.11726	+	0.304416i	0.0799678	+	0.0114976i	0.182183	−	0.983265i	$-0.441684\pi$
$701$	2.11726	+	0.304416i	0.0799678	+	0.0114976i	−0.102215	+	0.994762i	$0.532593\pi$
$702$	0.127139	−	0.884272i	0.00479856	−	0.0333747i
$703$	2.68980	−	4.18542i	0.101448	−	0.157856i
$704$	9.40665	−	8.15091i	0.354526	−	0.307199i
$705$	−3.21134	−	7.03185i	−0.120946	−	0.264835i
$706$	−3.01079	−	4.68487i	−0.113312	−	0.176318i
$707$	−10.7449	+	26.2927i	−0.404103	+	0.988837i
$708$	9.48348	−	10.9445i	0.356411	−	0.411320i
$709$	−9.68905	−	32.9979i	−0.363880	−	1.23926i	−0.914528	−	0.404523i	$-0.867437\pi$
$709$	−9.68905	−	32.9979i	−0.363880	−	1.23926i	0.550648	−	0.834738i	$-0.314381\pi$
$710$	−1.56555	+	3.42807i	−0.0587540	+	0.128653i
$711$	−12.3872	+	1.78100i	−0.464555	+	0.0667929i
$712$	−10.3431			−0.387625
$713$	1.98385	−	33.8174i	0.0742956	−	1.26647i
$714$	0.253293	−	2.46601i	0.00947925	−	0.0922883i
$715$	−1.55910	−	10.8438i	−0.0583070	−	0.405534i
$716$	16.4795	−	36.0852i	0.615869	−	1.34857i
$717$	5.98636	+	20.3877i	0.223565	+	0.761392i
$718$	−0.319036	−	0.276446i	−0.0119063	−	0.0103169i
$719$	5.62214	−	19.1473i	0.209670	−	0.714072i	−0.785756	−	0.618537i	$-0.787726\pi$
$719$	5.62214	−	19.1473i	0.209670	−	0.714072i	0.995426	−	0.0955349i	$-0.0304562\pi$
$720$	−4.78958	+	3.07808i	−0.178497	+	0.114713i
$721$	1.79079	+	5.29647i	0.0666927	+	0.197251i
$722$	−1.94757	−	2.24762i	−0.0724811	−	0.0836476i
$723$	3.78423	−	5.88837i	0.140737	−	0.218991i
$724$	−1.06081	+	7.37807i	−0.0394246	+	0.274204i
$725$	0.145523	−	1.01214i	0.00540459	−	0.0375898i
$726$	0.899804	−	1.40012i	0.0333949	−	0.0519634i
$727$	15.5015	+	17.8897i	0.574918	+	0.663490i	0.966504	−	0.256651i	$-0.0826191\pi$
$727$	15.5015	+	17.8897i	0.574918	+	0.663490i	−0.391586	+	0.920141i	$0.628074\pi$
$728$	8.64722	−	2.92372i	0.320487	−	0.108360i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−1.34445	+	4.57878i	−0.0497604	+	0.169468i
$731$	14.2939	+	12.3858i	0.528681	+	0.458104i
$732$	5.79989	+	19.7526i	0.214370	+	0.730077i
$733$	−8.72201	+	19.0985i	−0.322155	+	0.705420i	−0.999544	−	0.0302045i	$-0.990384\pi$
$733$	−8.72201	+	19.0985i	−0.322155	+	0.705420i	0.677389	+	0.735625i	$0.263111\pi$
$734$	0.581706	+	4.04586i	0.0214712	+	0.149335i
$735$	2.53920	−	12.2302i	0.0936598	−	0.451117i
$736$	−18.9514	+	4.37747i	−0.698558	+	0.161356i
$737$	−24.3523			−0.897028
$738$	0.331274	−	0.0476300i	0.0121944	−	0.00175329i
$739$	13.5382	−	29.6445i	0.498011	−	1.09049i	−0.479100	−	0.877760i	$-0.659037\pi$
$739$	13.5382	−	29.6445i	0.498011	−	1.09049i	0.977111	−	0.212731i	$-0.0682359\pi$
$740$	0.896188	+	3.05213i	0.0329445	+	0.112199i
$741$	8.18135	−	9.44178i	0.300549	−	0.346853i
$742$	3.26134	−	7.98047i	0.119728	−	0.292972i
$743$	11.7472	+	18.2789i	0.430962	+	0.670589i	0.987028	−	0.160549i	$-0.0513263\pi$
$743$	11.7472	+	18.2789i	0.430962	+	0.670589i	−0.556066	+	0.831138i	$0.687690\pi$
$744$	4.21086	+	9.22050i	0.154378	+	0.338040i
$745$	−10.1102	+	8.76055i	−0.370410	+	0.320962i
$746$	1.06832	−	1.66233i	0.0391138	−	0.0608623i
$747$	−2.32654	+	16.1814i	−0.0851235	+	0.592047i
$748$	−11.8670	−	1.70621i	−0.433899	−	0.0623853i
$749$	−23.7933	+	29.8142i	−0.869389	+	1.08939i
$750$	3.41553	−	2.95957i	0.124717	−	0.108068i
$751$	−9.81327	+	4.48157i	−0.358091	+	0.163535i	−0.586334	−	0.810069i	$-0.699429\pi$
$751$	−9.81327	+	4.48157i	−0.358091	+	0.163535i	0.228243	+	0.973604i	$0.426702\pi$
$752$	−7.47283	−	11.6280i	−0.272506	−	0.424028i
$753$	1.38480	−	4.71621i	0.0504651	−	0.171868i
$754$	−0.380204	−	0.329448i	−0.0138462	−	0.0119978i
$755$	1.99853	−	0.586822i	0.0727340	−	0.0213566i
$756$	−4.24847	−	2.49355i	−0.154515	−	0.0906896i
$757$	2.93346	−	0.421767i	0.106618	−	0.0153294i	−0.0887992	−	0.996050i	$-0.528303\pi$
$757$	2.93346	−	0.421767i	0.106618	−	0.0153294i	0.195417	+	0.980720i	$0.437394\pi$
$758$		−	1.36373i		−	0.0495328i
$759$	−10.6727	+	6.00641i	−0.387396	+	0.218019i
$760$	13.3069			0.482691
$761$	−32.8714	+	4.72619i	−1.19159	+	0.171324i	−0.709440	−	0.704766i	$-0.751052\pi$
$761$	−32.8714	+	4.72619i	−1.19159	+	0.171324i	−0.482147	+	0.876090i	$0.660143\pi$
$762$	−2.33627	−	1.06694i	−0.0846341	−	0.0386511i
$763$	9.26724	+	50.0057i	0.335496	+	1.81033i
$764$	2.37055	+	2.05409i	0.0857635	+	0.0743145i
$765$	4.31721	+	1.26765i	0.156089	+	0.0458319i
$766$	−2.94009	+	1.88948i	−0.106230	+	0.0682696i
$767$	−7.76793	−	17.0094i	−0.280484	−	0.614174i
$768$	−4.58073	+	3.96922i	−0.165293	+	0.143227i
$769$	−30.4788	−	19.5875i	−1.09909	−	0.706344i	−0.140203	−	0.990123i	$-0.544775\pi$
$769$	−30.4788	−	19.5875i	−1.09909	−	0.706344i	−0.958890	+	0.283779i	$0.908412\pi$
$770$	4.34597	+	1.08730i	0.156618	+	0.0391837i
$771$	−3.04549	+	21.1818i	−0.109681	+	0.762845i
$772$	−20.2102	−	12.9883i	−0.727381	−	0.467460i
$773$	−24.0284	−	27.7302i	−0.864240	−	0.997387i	−0.999978	−	0.00664174i	$-0.997886\pi$
$773$	−24.0284	−	27.7302i	−0.864240	−	0.997387i	0.135738	−	0.990745i	$-0.456660\pi$
$774$	−2.53536	+	1.15786i	−0.0911318	+	0.0416185i
$775$	6.93431	+	10.7900i	0.249088	+	0.387588i
$776$	0.0550575	+	0.0161664i	0.00197645	+	0.000580338i
$777$	−1.84574	+	1.73487i	−0.0662157	+	0.0622381i
$778$	2.79186	+	9.50819i	0.100093	+	0.340885i
$779$	4.25739	+	1.94429i	0.152537	+	0.0696613i
$780$	1.13678	+	7.90648i	0.0407033	+	0.283097i
$781$			14.5138i			0.519345i
$782$	3.63145	+	2.64661i	0.129861	+	0.0946424i
$783$			0.563131i			0.0201247i
$784$	1.38181	−	22.2914i	0.0493505	−	0.796121i
$785$	12.8373	−	28.1098i	0.458184	−	1.00328i
$786$	4.59659	−	1.34968i	0.163955	−	0.0481415i
$787$	26.1210	−	30.1453i	0.931114	−	1.07456i	−0.0659377	−	0.997824i	$-0.521004\pi$
$787$	26.1210	−	30.1453i	0.931114	−	1.07456i	0.997051	−	0.0767386i	$-0.0244507\pi$
$788$	−22.8055	−	6.69629i	−0.812411	−	0.238545i
$789$	7.99583	−	5.13861i	0.284659	−	0.182939i
$790$	−7.54818	+	3.44714i	−0.268552	+	0.122644i
$791$	−21.1759	+	14.8521i	−0.752929	+	0.528080i
$792$	1.98123	−	3.08285i	0.0703998	−	0.109544i
$793$	26.3114	+	3.78301i	0.934345	+	0.134338i
$794$	7.44421	+	1.07032i	0.264185	+	0.0379841i
$795$	13.1637	+	8.45982i	0.466870	+	0.300039i
$796$	0.705550	+	0.814248i	0.0250076	+	0.0288603i
$797$	−1.15278	−	2.52424i	−0.0408336	−	0.0894131i	0.888116	−	0.459620i	$-0.152014\pi$
$797$	−1.15278	−	2.52424i	−0.0408336	−	0.0894131i	−0.928950	+	0.370206i	$0.879287\pi$
$798$	2.30846	+	4.55755i	0.0817185	+	0.161336i
$799$	−3.07754	+	10.4812i	−0.108876	+	0.370797i
$800$	4.82265	−	5.56563i	0.170506	−	0.196775i
$801$	6.91556	−	2.03059i	0.244349	−	0.0717474i
$802$	−9.61799	−	4.39239i	−0.339623	−	0.155101i
$803$	2.61550	+	18.1912i	0.0922991	+	0.641954i
$804$	17.7559			0.626202
$805$	16.8396	+	15.1354i	0.593519	+	0.533453i
$806$	6.31032			0.222271
$807$	−1.77391	−	12.3378i	−0.0624445	−	0.434311i
$808$	14.0138	+	6.39987i	0.493002	+	0.225146i
$809$	43.2081	−	12.6870i	1.51911	−	0.446052i	0.587416	−	0.809285i	$-0.300145\pi$
$809$	43.2081	−	12.6870i	1.51911	−	0.446052i	0.931698	+	0.363233i	$0.118327\pi$
$810$	−0.434221	+	0.501118i	−0.0152570	+	0.0176075i
$811$	13.4991	−	45.9737i	0.474017	−	1.61435i	−0.281732	−	0.959493i	$-0.590909\pi$
$811$	13.4991	−	45.9737i	0.474017	−	1.61435i	0.755749	−	0.654861i	$-0.227273\pi$
$812$	−2.47474	+	1.25349i	−0.0868463	+	0.0439887i
$813$	8.63058	+	18.8983i	0.302688	+	0.662793i
$814$	−0.594939	−	0.686596i	−0.0208526	−	0.0240652i
$815$	0.213828	+	0.137419i	0.00749008	+	0.00481358i
$816$	7.96326	+	1.14494i	0.278770	+	0.0400811i
$817$	−38.5815	−	5.54718i	−1.34979	−	0.194071i
$818$	−0.489850	+	0.762222i	−0.0171272	+	0.0266505i
$819$	−5.20766	+	3.65249i	−0.181970	+	0.127628i
$820$	−2.72203	+	1.24311i	−0.0950576	+	0.0434113i
$821$	−30.9829	+	19.9115i	−1.08131	+	0.694915i	−0.954860	−	0.297058i	$-0.903995\pi$
$821$	−30.9829	+	19.9115i	−1.08131	+	0.694915i	−0.126450	+	0.991973i	$0.540358\pi$
$822$	5.36755	+	1.57606i	0.187215	+	0.0549713i
$823$	7.66525	−	8.84618i	0.267194	−	0.308358i	−0.606259	−	0.795268i	$-0.707330\pi$
$823$	7.66525	−	8.84618i	0.267194	−	0.308358i	0.873453	+	0.486909i	$0.161876\pi$
$824$	2.90971	−	0.854369i	0.101365	−	0.0297634i
$825$	1.92625	−	4.21791i	0.0670635	−	0.146849i
$826$	7.64037	−	0.309184i	0.265842	−	0.0107579i
$827$			23.3448i			0.811778i	0.913922	+	0.405889i	$0.133038\pi$
$827$			23.3448i			0.811778i	−0.913922	+	0.405889i	$0.866962\pi$
$828$	7.78177	−	4.37943i	0.270435	−	0.152196i
$829$		−	34.7750i		−	1.20779i	−0.797065	−	0.603893i	$-0.793615\pi$
$829$		−	34.7750i		−	1.20779i	0.797065	−	0.603893i	$-0.206385\pi$
$830$	1.54266	+	10.7295i	0.0535467	+	0.372425i
$831$	−6.90375	−	3.15284i	−0.239488	−	0.109371i
$832$	3.30142	+	11.2436i	0.114456	+	0.389802i
$833$	−14.0290	+	10.7113i	−0.486078	+	0.371123i
$834$	−0.0205577	−	0.00603629i	−0.000711856	−	0.000209020i
$835$	−2.27543	−	3.54064i	−0.0787446	−	0.122529i
$836$	22.4748	−	10.2639i	0.777308	−	0.354985i
$837$	−4.62563	−	5.33827i	−0.159885	−	0.184517i
$838$	11.9503	+	7.68002i	0.412818	+	0.265302i
$839$	−8.19921	+	57.0267i	−0.283068	+	1.96878i	−0.0379919	+	0.999278i	$0.512096\pi$
$839$	−8.19921	+	57.0267i	−0.283068	+	1.96878i	−0.245076	+	0.969504i	$0.578813\pi$
$840$	−6.57250	−	1.64435i	−0.226773	−	0.0567355i
$841$	−24.1296	−	15.5071i	−0.832054	−	0.534729i
$842$	−0.266203	+	0.230666i	−0.00917395	+	0.00794928i
$843$	−12.1525	−	26.6103i	−0.418555	−	0.916508i
$844$	40.6366	−	26.1156i	1.39877	−	0.898935i
$845$	−12.3616	−	3.62969i	−0.425252	−	0.124865i
$846$	−1.21659	−	1.05418i	−0.0418274	−	0.0362436i
$847$	−11.6518	+	2.15935i	−0.400360	+	0.0741962i
$848$	25.4502	+	11.6227i	0.873962	+	0.399125i
$849$	13.6085	−	1.95661i	0.467043	−	0.0671506i
$850$	−1.70137			−0.0583564
$851$	−1.03338	−	4.47382i	−0.0354239	−	0.153361i
$852$		−	10.5824i		−	0.362547i
$853$	−12.5992	+	1.81149i	−0.431387	+	0.0620241i	−0.354588	−	0.935023i	$-0.615379\pi$
$853$	−12.5992	+	1.81149i	−0.431387	+	0.0620241i	−0.0767988	+	0.997047i	$0.524470\pi$
$854$	−5.50226	+	9.37464i	−0.188283	+	0.320794i
$855$	−8.89715	+	2.61244i	−0.304276	+	0.0893435i
$856$	15.6361	+	13.5487i	0.534430	+	0.463086i
$857$	−2.78650	+	9.48995i	−0.0951851	+	0.324171i	−0.993296	−	0.115598i	$-0.963121\pi$
$857$	−2.78650	+	9.48995i	−0.0951851	+	0.324171i	0.898111	+	0.439769i	$0.144940\pi$
$858$	−1.23338	−	1.91918i	−0.0421069	−	0.0655196i
$859$	28.5675	−	13.0464i	0.974712	−	0.445136i	0.136595	−	0.990627i	$-0.456384\pi$
$859$	28.5675	−	13.0464i	0.974712	−	0.445136i	0.838117	+	0.545491i	$0.183657\pi$
$860$	18.8343	−	16.3200i	0.642245	−	0.556508i
$861$	−1.86255	−	1.48641i	−0.0634754	−	0.0506568i
$862$	8.30560	+	1.19417i	0.282890	+	0.0406734i
$863$	−0.954534	+	6.63893i	−0.0324927	+	0.225992i	−0.999597	−	0.0283886i	$-0.990962\pi$
$863$	−0.954534	+	6.63893i	−0.0324927	+	0.225992i	0.967104	+	0.254380i	$0.0818715\pi$
$864$	−2.19267	+	3.41186i	−0.0745961	+	0.116074i
$865$	−32.2507	+	27.9454i	−1.09656	+	0.950172i
$866$	2.83515	+	6.20812i	0.0963424	+	0.210960i
$867$	5.75346	+	8.95256i	0.195398	+	0.304045i
$868$	13.1633	−	32.2104i	0.446790	−	1.09329i
$869$	−20.9278	+	24.1519i	−0.709925	+	0.819297i
$870$	0.105198	+	0.358272i	0.00356656	+	0.0121466i
$871$	9.52421	−	20.8551i	0.322716	−	0.706648i
$872$	27.3040	−	3.92572i	0.924630	−	0.132942i
$873$	−0.0399861			−0.00135332
$874$	−9.24466	−	0.542324i	−0.312705	−	0.0183444i
$875$	−32.0101	−	3.28787i	−1.08214	−	0.111150i
$876$	−1.90703	−	13.2637i	−0.0644326	−	0.448139i
$877$	−22.5424	+	49.3610i	−0.761203	+	1.66680i	−0.0160851	+	0.999871i	$0.505120\pi$
$877$	−22.5424	+	49.3610i	−0.761203	+	1.66680i	−0.745118	+	0.666932i	$0.767607\pi$
$878$	−1.20961	−	4.11954i	−0.0408222	−	0.139028i
$879$	11.6335	+	10.0805i	0.392389	+	0.340007i
$880$	−4.09606	+	13.9499i	−0.138078	+	0.470251i
$881$	34.1473	−	21.9451i	1.15045	−	0.739350i	0.180723	−	0.983534i	$-0.442156\pi$
$881$	34.1473	−	21.9451i	1.15045	−	0.739350i	0.969729	+	0.244184i	$0.0785200\pi$
$882$	−0.577005	−	2.53632i	−0.0194288	−	0.0854023i
$883$	−30.4986	−	35.1973i	−1.02636	−	1.18448i	−0.982656	−	0.185440i	$-0.940629\pi$
$883$	−30.4986	−	35.1973i	−1.02636	−	1.18448i	−0.0437056	−	0.999044i	$-0.513916\pi$
$884$	6.10237	−	9.49547i	0.205245	−	0.319367i
$885$	−1.97518	+	13.7377i	−0.0663949	+	0.461787i
$886$	1.18640	−	8.25157i	0.0398578	−	0.277217i
$887$	−12.8127	+	19.9370i	−0.430209	+	0.669419i	−0.986906	−	0.161297i	$-0.948432\pi$
$887$	−12.8127	+	19.9370i	−0.430209	+	0.669419i	0.556696	+	0.830716i	$0.312069\pi$
$888$	0.899740	+	1.03836i	0.0301933	+	0.0348449i
$889$	5.85731	+	17.3236i	0.196448	+	0.581016i
$890$	4.02045	−	2.58378i	0.134766	−	0.0866086i
$891$	−0.719442	+	2.45019i	−0.0241022	+	0.0820846i
$892$	3.27143	+	2.83471i	0.109536	+	0.0949132i
$893$	−6.34238	−	21.6001i	−0.212240	−	0.722821i
$894$	−1.15725	+	2.53403i	−0.0387044	+	0.0847507i
$895$	5.41066	+	37.6320i	0.180859	+	1.25790i
$896$	−26.1152	−	2.68238i	−0.872448	−	0.0896122i
$897$	−0.969719	−	11.4892i	−0.0323780	−	0.383612i
$898$	−4.63474			−0.154663
$899$	−3.93721	+	0.566086i	−0.131313	+	0.0188800i
$900$	−1.40448	+	3.07538i	−0.0468160	+	0.102513i
$901$	−6.22950	−	21.2157i	−0.207535	−	0.706798i
$902$	0.559678	−	0.645903i	0.0186352	−	0.0215062i
$903$	18.3706	+	7.50743i	0.611336	+	0.249832i
$904$	7.58474	+	11.8021i	0.252265	+	0.392532i
$905$	−2.96760	−	6.49815i	−0.0986465	−	0.216006i
$906$	0.327802	−	0.284042i	0.0108905	−	0.00943666i
$907$	−21.9707	+	34.1870i	−0.729524	+	1.13516i	0.256172	+	0.966631i	$0.417538\pi$
$907$	−21.9707	+	34.1870i	−0.729524	+	1.13516i	−0.985696	+	0.168530i	$0.946098\pi$
$908$	−2.22916	+	15.5041i	−0.0739772	+	0.514523i
$909$	−10.6262	−	1.52782i	−0.352450	−	0.0506746i
$910$	−2.63087	+	3.29661i	−0.0872125	+	0.109281i
$911$	6.18321	−	5.35778i	0.204859	−	0.177511i	−0.546389	−	0.837532i	$-0.683998\pi$
$911$	6.18321	−	5.35778i	0.204859	−	0.177511i	0.751248	+	0.660021i	$0.229452\pi$
$912$	−15.0816	+	6.88754i	−0.499402	+	0.228069i
$913$	22.5698	+	35.1192i	0.746950	+	1.16228i
$914$	−4.14820	+	14.1275i	−0.137210	+	0.467295i
$915$	−14.9107	−	12.9202i	−0.492932	−	0.427128i
$916$	−5.01827	+	1.47350i	−0.165808	+	0.0486857i
$917$	−29.4173	−	17.2659i	−0.971443	−	0.570169i
$918$	0.927433	−	0.133345i	0.0306098	−	0.00440103i
$919$		−	25.3955i		−	0.837720i	−0.908051	−	0.418860i	$-0.862430\pi$
$919$		−	25.3955i		−	0.837720i	0.908051	−	0.418860i	$-0.137570\pi$
$920$	8.57200	−	8.79436i	0.282610	−	0.289941i
$921$	19.3620			0.637999
$922$	11.3587	−	1.63313i	0.374078	−	0.0537843i
$923$	−12.4295	−	5.67637i	−0.409122	−	0.186840i
$924$	−12.3691	+	2.29228i	−0.406912	+	0.0754104i
$925$	1.31387	+	1.13847i	0.0431997	+	0.0374328i
$926$	−2.59372	−	0.761586i	−0.0852351	−	0.0250273i
$927$	−1.77774	+	1.14249i	−0.0583887	+	0.0375242i
$928$	0.948760	+	2.07749i	0.0311446	+	0.0681971i
$929$	35.8330	−	31.0495i	1.17564	−	1.01870i	0.176234	−	0.984348i	$-0.443609\pi$
$929$	35.8330	−	31.0495i	1.17564	−	1.01870i	0.999410	−	0.0343526i	$-0.0109369\pi$
$930$	−3.94014	−	2.53217i	−0.129202	−	0.0830332i
$931$	12.3879	−	34.2011i	0.405997	−	1.12089i
$932$	3.57969	−	24.8973i	0.117257	−	0.815538i
$933$	0.610230	+	0.392171i	0.0199780	+	0.0128391i
$934$	3.77580	+	4.35750i	0.123548	+	0.142582i
$935$	10.4517	−	4.77312i	0.341806	−	0.156098i
$936$	1.86527	+	2.90241i	0.0609682	+	0.0948683i
$937$	22.5848	+	6.63149i	0.737813	+	0.216641i	0.628983	−	0.777419i	$-0.283472\pi$
$937$	22.5848	+	6.63149i	0.737813	+	0.216641i	0.108830	+	0.994060i	$0.465290\pi$
$938$	6.42110	+	6.83146i	0.209656	+	0.223055i
$939$	3.11354	+	10.6038i	0.101607	+	0.346040i
$940$	13.0927	+	5.97926i	0.427038	+	0.195022i
$941$	−2.25615	−	15.6918i	−0.0735482	−	0.511539i	−0.992979	−	0.118288i	$-0.962259\pi$
$941$	−2.25615	−	15.6918i	−0.0735482	−	0.511539i	0.919431	−	0.393251i	$-0.128650\pi$
$942$		−	6.43511i		−	0.209667i
$943$	4.02748	−	1.56120i	0.131153	−	0.0508395i
$944$			24.8158i			0.807687i
$945$	4.71729	−	0.190895i	0.153453	−	0.00620982i
$946$	−2.95676	+	6.47440i	−0.0961325	+	0.210501i
$947$	54.7477	−	16.0754i	1.77906	−	0.522380i	0.783922	−	0.620859i	$-0.213216\pi$
$947$	54.7477	−	16.0754i	1.77906	−	0.522380i	0.995139	+	0.0984796i	$0.0313979\pi$
$948$	15.2590	−	17.6098i	0.495588	−	0.571939i
$949$	−16.6017	−	4.87471i	−0.538915	−	0.158240i
$950$	2.94966	−	1.89563i	0.0956997	−	0.0615025i
$951$	−23.8849	+	10.9078i	−0.774520	+	0.353711i
$952$	5.49733	+	7.83801i	0.178169	+	0.254031i
$953$	−8.08530	+	12.5810i	−0.261908	+	0.407538i	−0.947156	−	0.320772i	$-0.896058\pi$
$953$	−8.08530	+	12.5810i	−0.261908	+	0.407538i	0.685248	+	0.728310i	$0.259694\pi$
$954$	3.22532	+	0.463731i	0.104424	+	0.0150139i
$955$	−2.97554	−	0.427818i	−0.0962861	−	0.0138439i
$956$	−33.2824	−	21.3893i	−1.07643	−	0.691779i
$957$	0.941710	+	1.08679i	0.0304412	+	0.0351310i
$958$	−4.86971	−	10.6632i	−0.157333	−	0.344511i
$959$	−17.9978	−	35.5328i	−0.581180	−	1.14741i
$960$	2.45038	−	8.34524i	0.0790858	−	0.269341i
$961$	12.3727	−	14.2788i	0.399118	−	0.460607i
$962$	0.820677	−	0.240973i	0.0264597	−	0.00776927i
$963$	−13.1144	−	5.98915i	−0.422606	−	0.192998i
$964$	1.85473	+	12.8999i	0.0597367	+	0.415478i
$965$	23.0240			0.741170
$966$	4.49909	+	1.41024i	0.144756	+	0.0453738i
$967$	−14.4238			−0.463838			−0.231919	−	0.972735i	$-0.574500\pi$
$967$	−14.4238			−0.463838			−0.231919	+	0.972735i	$0.574500\pi$
$968$	0.914729	+	6.36208i	0.0294005	+	0.204485i
$969$	11.9190	+	5.44321i	0.382892	+	0.174861i
$970$	−0.0254397	+	0.00746978i	−0.000816820	+	0.000239840i
$971$	−33.7872	+	38.9925i	−1.08428	+	1.25133i	−0.118229	+	0.992986i	$0.537722\pi$
$971$	−33.7872	+	38.9925i	−1.08428	+	1.25133i	−0.966054	+	0.258342i	$0.916824\pi$
$972$	0.524564	−	1.78650i	0.0168254	−	0.0573020i
$973$	0.0689316	+	0.136091i	0.00220985	+	0.00436287i
$974$	−0.708535	−	1.55147i	−0.0227029	−	0.0497125i
$975$	2.85882	+	3.29926i	0.0915556	+	0.105661i
$976$	−29.6770	−	19.0722i	−0.949937	−	0.610487i
$977$	−56.4151	−	8.11127i	−1.80488	−	0.259502i	−0.843975	−	0.536383i	$-0.819790\pi$
$977$	−56.4151	−	8.11127i	−1.80488	−	0.259502i	−0.960904	+	0.276880i	$0.910699\pi$
$978$	0.0523913	+	0.00753273i	0.00167529	+	0.000240870i
$979$	9.95069	−	15.4836i	0.318025	−	0.494857i
$980$	11.3392	+	20.3057i	0.362218	+	0.648642i
$981$	−17.4851	+	7.98519i	−0.558257	+	0.254947i
$982$	8.16164	−	5.24517i	0.260449	−	0.167380i
$983$	−3.89741	−	1.14438i	−0.124308	−	0.0365001i	0.218987	−	0.975728i	$-0.429725\pi$
$983$	−3.89741	−	1.14438i	−0.124308	−	0.0365001i	−0.343295	+	0.939228i	$0.611543\pi$
$984$	−0.846414	+	0.976814i	−0.0269827	+	0.0311397i
$985$	21.8563	−	6.41759i	0.696399	−	0.204481i
$986$	0.219188	−	0.479955i	0.00698038	−	0.0152849i
$987$	0.463448	+	11.4525i	0.0147517	+	0.364536i
$988$			23.2615i			0.740047i
$989$	−28.5194	+	21.9247i	−0.906865	+	0.697165i
$990$			1.69325i			0.0538150i
$991$	4.65331	+	32.3645i	0.147817	+	1.02809i	0.919783	+	0.392428i	$0.128365\pi$
$991$	4.65331	+	32.3645i	0.147817	+	1.02809i	−0.771966	+	0.635664i	$0.780726\pi$
$992$	−26.0587	−	11.9006i	−0.827364	−	0.377844i
$993$	−7.34793	−	25.0248i	−0.233180	−	0.794137i
$994$	4.07151	−	3.82694i	0.129140	−	0.121383i
$995$	−0.990736	−	0.290906i	−0.0314085	−	0.00922236i
$996$	−16.4562	−	25.6064i	−0.521435	−	0.811368i
$997$	33.5013	−	15.2995i	1.06100	−	0.484541i	0.193046	−	0.981190i	$-0.438163\pi$
$997$	33.5013	−	15.2995i	1.06100	−	0.484541i	0.867952	+	0.496648i	$0.165436\pi$
$998$	10.2032	+	11.7751i	0.322976	+	0.372734i
$999$	−0.805431	−	0.517619i	−0.0254827	−	0.0163767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.15	✓	320
7.6	odd	2	inner	483.2.r.a.181.16	yes	320
23.15	odd	22	inner	483.2.r.a.475.16	yes	320
161.153	even	22	inner	483.2.r.a.475.15	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.15	✓	320	1.1	even	1	trivial
483.2.r.a.181.16	yes	320	7.6	odd	2	inner
483.2.r.a.475.15	yes	320	161.153	even	22	inner
483.2.r.a.475.16	yes	320	23.15	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0528826 - 0.367807i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(-1.16855 + 1.34858i) q^{5} +(-0.104689 + 0.356537i) q^{6} +(2.36025 - 1.19550i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.0528826 - 0.367807i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(1.78650 - 0.524564i) q^{4} +(-1.16855 + 1.34858i) q^{5} +(-0.104689 + 0.356537i) q^{6} +(2.36025 - 1.19550i) q^{7} +(-0.596140 - 1.30537i) q^{8} +(0.654861 + 0.755750i) q^{9} +(0.557813 + 0.358485i) q^{10} +(2.52764 + 0.363420i) q^{11} +(-1.84297 - 0.264979i) q^{12} +(-1.29979 + 2.02252i) q^{13} +(-0.564528 - 0.804896i) q^{14} +(1.62317 - 0.741278i) q^{15} +(2.68410 - 1.72497i) q^{16} +(-2.41938 - 0.710394i) q^{17} +(0.243339 - 0.280828i) q^{18} +(4.98600 - 1.46402i) q^{19} +(-1.38020 + 3.02222i) q^{20} +(-2.64359 + 0.106978i) q^{21} -0.948903i q^{22} +(2.24432 - 4.23828i) q^{23} +1.43505i q^{24} +(0.258418 + 1.79734i) q^{25} +(0.812633 + 0.371117i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(3.58948 - 3.37386i) q^{28} +(-0.540320 - 0.158652i) q^{29} +(-0.358485 - 0.557813i) q^{30} +(6.42522 - 2.93430i) q^{31} +(-2.65591 - 3.06508i) q^{32} +(-2.14825 - 1.38060i) q^{33} +(-0.133345 + 0.927433i) q^{34} +(-1.14585 + 4.57999i) q^{35} +(1.56635 + 1.00663i) q^{36} +(0.723568 - 0.626975i) q^{37} +(-0.802150 - 1.75646i) q^{38} +(2.02252 - 1.29979i) q^{39} +(2.45701 + 0.721444i) q^{40} +(0.680684 + 0.589816i) q^{41} +(0.179147 + 0.966672i) q^{42} +(-6.82303 - 3.11597i) q^{43} +(4.70627 - 0.676660i) q^{44} -1.78443 q^{45} +(-1.67755 - 0.601344i) q^{46} -4.33216i q^{47} +(-3.15812 + 0.454069i) q^{48} +(4.14157 - 5.64335i) q^{49} +(0.647406 - 0.190096i) q^{50} +(1.90564 + 1.65124i) q^{51} +(-1.26114 + 4.29506i) q^{52} +(4.74091 + 7.37701i) q^{53} +(-0.338009 + 0.154364i) q^{54} +(-3.44378 + 2.98405i) q^{55} +(-2.96760 - 2.36831i) q^{56} +(-5.14360 - 0.739538i) q^{57} +(-0.0297799 + 0.207124i) q^{58} +(-4.20500 + 6.54311i) q^{59} +(2.51095 - 2.17575i) q^{60} +(-4.59307 - 10.0574i) q^{61} +(-1.41904 - 2.20807i) q^{62} +(2.44913 + 1.00087i) q^{63} +(3.19188 - 3.68363i) q^{64} +(-1.20865 - 4.11630i) q^{65} +(-0.394189 + 0.863153i) q^{66} +(-9.43925 + 1.35716i) q^{67} -4.69487 q^{68} +(-3.80215 + 2.92295i) q^{69} +(1.74515 + 0.179250i) q^{70} +(0.808859 + 5.62574i) q^{71} +(0.596140 - 1.30537i) q^{72} +(2.02760 + 6.90538i) q^{73} +(-0.268870 - 0.232977i) q^{74} +(0.511575 - 1.74226i) q^{75} +(8.13951 - 5.23095i) q^{76} +(6.40034 - 2.16403i) q^{77} +(-0.585030 - 0.675160i) q^{78} +(-6.76587 + 10.5279i) q^{79} +(-0.810253 + 5.63544i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.180942 - 0.281551i) q^{82} +(10.7055 + 12.3548i) q^{83} +(-4.66665 + 1.57785i) q^{84} +(3.78520 - 2.43260i) q^{85} +(-0.785257 + 2.67434i) q^{86} +(0.425586 + 0.368773i) q^{87} +(-1.03243 - 3.51615i) q^{88} +(2.99411 - 6.55618i) q^{89} +(0.0943653 + 0.656325i) q^{90} +(-0.649926 + 6.32756i) q^{91} +(1.78623 - 8.74898i) q^{92} -7.06354 q^{93} +(-1.59340 + 0.229096i) q^{94} +(-3.85205 + 8.43480i) q^{95} +(1.14262 + 3.89140i) q^{96} +(-0.0261853 + 0.0302194i) q^{97} +(-2.29468 - 1.22486i) q^{98} +(1.38060 + 2.14825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more