LMFDB - Embedded newform 189.2.bd.a.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0147002 - 0.00259205i) q^{2} +(-1.71867 + 0.214901i) q^{3} +(-1.87918 - 0.683964i) q^{4} +(1.54651 + 0.562885i) q^{5} +(0.0258218 + 0.00129578i) q^{6} +(2.21011 + 1.45445i) q^{7} +(0.0517058 + 0.0298524i) q^{8} +(2.90764 - 0.738686i) q^{9} +O(q^{10})$	\(q+(-0.0147002 - 0.00259205i) q^{2} +(-1.71867 + 0.214901i) q^{3} +(-1.87918 - 0.683964i) q^{4} +(1.54651 + 0.562885i) q^{5} +(0.0258218 + 0.00129578i) q^{6} +(2.21011 + 1.45445i) q^{7} +(0.0517058 + 0.0298524i) q^{8} +(2.90764 - 0.738686i) q^{9} +(-0.0212751 - 0.0122832i) q^{10} +(1.57083 + 4.31582i) q^{11} +(3.37666 + 0.771671i) q^{12} +(-1.52751 + 4.19679i) q^{13} +(-0.0287191 - 0.0271094i) q^{14} +(-2.77891 - 0.635065i) q^{15} +(3.06315 + 2.57029i) q^{16} +(1.88705 - 3.26847i) q^{17} +(-0.0446576 + 0.00332212i) q^{18} +(-1.27160 + 0.734160i) q^{19} +(-2.52118 - 2.11552i) q^{20} +(-4.11100 - 2.02476i) q^{21} +(-0.0119048 - 0.0675152i) q^{22} +(7.31736 - 1.29025i) q^{23} +(-0.0952804 - 0.0401947i) q^{24} +(-1.75536 - 1.47292i) q^{25} +(0.0333330 - 0.0577345i) q^{26} +(-4.83851 + 1.89441i) q^{27} +(-3.15839 - 4.24480i) q^{28} +(-2.83246 - 7.78213i) q^{29} +(0.0392044 + 0.0165387i) q^{30} +(-2.87381 + 7.89573i) q^{31} +(-0.115122 - 0.137197i) q^{32} +(-3.62721 - 7.07988i) q^{33} +(-0.0362121 + 0.0431559i) q^{34} +(2.59927 + 3.49336i) q^{35} +(-5.96919 - 0.600598i) q^{36} -0.794639 q^{37} +(0.0205958 - 0.00749627i) q^{38} +(1.72338 - 7.54116i) q^{39} +(0.0631602 + 0.0752714i) q^{40} +(3.97658 + 1.44736i) q^{41} +(0.0551844 + 0.0404204i) q^{42} +(-0.303215 + 1.71962i) q^{43} -9.18457i q^{44} +(4.91249 + 0.494277i) q^{45} -0.110911 q^{46} +(-1.54917 + 0.563852i) q^{47} +(-5.81690 - 3.75920i) q^{48} +(2.76916 + 6.42898i) q^{49} +(0.0219863 + 0.0262023i) q^{50} +(-2.54082 + 6.02294i) q^{51} +(5.74091 - 6.84175i) q^{52} +(3.66888 - 2.11823i) q^{53} +(0.0760377 - 0.0153066i) q^{54} +7.55866i q^{55} +(0.0708567 + 0.141180i) q^{56} +(2.02769 - 1.53505i) q^{57} +(0.0214662 + 0.121741i) q^{58} +(-8.85828 + 7.43298i) q^{59} +(4.78769 + 3.09407i) q^{60} +(1.02900 + 2.82714i) q^{61} +(0.0627118 - 0.108620i) q^{62} +(7.50057 + 2.59643i) q^{63} +(-3.99733 - 6.92357i) q^{64} +(-4.72462 + 5.63058i) q^{65} +(0.0349694 + 0.113478i) q^{66} +(-1.88292 - 10.6785i) q^{67} +(-5.78162 + 4.85135i) q^{68} +(-12.2988 + 3.79001i) q^{69} +(-0.0291550 - 0.0580906i) q^{70} +(6.66808 - 3.84982i) q^{71} +(0.172393 + 0.0486054i) q^{72} -15.8281i q^{73} +(0.0116814 + 0.00205974i) q^{74} +(3.33341 + 2.15423i) q^{75} +(2.89171 - 0.509886i) q^{76} +(-2.80543 + 11.8231i) q^{77} +(-0.0448812 + 0.106390i) q^{78} +(0.276799 - 1.56981i) q^{79} +(3.29043 + 5.69919i) q^{80} +(7.90869 - 4.29566i) q^{81} +(-0.0547050 - 0.0315840i) q^{82} +(4.61667 - 1.68033i) q^{83} +(6.34044 + 6.61666i) q^{84} +(4.75812 - 3.99254i) q^{85} +(0.00891467 - 0.0244929i) q^{86} +(6.54045 + 12.7662i) q^{87} +(-0.0476164 + 0.270046i) q^{88} +(-3.59252 - 6.22243i) q^{89} +(-0.0709336 - 0.0199994i) q^{90} +(-9.47998 + 7.05369i) q^{91} +(-14.6331 - 2.58021i) q^{92} +(3.24233 - 14.1877i) q^{93} +(0.0242347 - 0.00427323i) q^{94} +(-2.37980 + 0.419623i) q^{95} +(0.227340 + 0.211056i) q^{96} +(-1.56544 - 0.276029i) q^{97} +(-0.0240431 - 0.101685i) q^{98} +(7.75543 + 11.3885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0147002	−	0.00259205i	−0.0103946	−	0.00183285i	0.168448	−	0.985710i	$-0.446124\pi$
$2$	−0.0147002	−	0.00259205i	−0.0103946	−	0.00183285i	−0.178843	+	0.983878i	$0.557235\pi$
$3$	−1.71867	+	0.214901i	−0.992273	+	0.124073i
$3$	−1.71867	+	0.214901i	−0.992273	+	0.124073i
$4$	−1.87918	−	0.683964i	−0.939588	−	0.341982i
$5$	1.54651	+	0.562885i	0.691622	+	0.251730i	0.663829	−	0.747884i	$-0.268930\pi$
$5$	1.54651	+	0.562885i	0.691622	+	0.251730i	0.0277922	+	0.999614i	$0.491152\pi$
$6$	0.0258218	+	0.00129578i	0.0105417	+	0.000528999i
$7$	2.21011	+	1.45445i	0.835342	+	0.549730i
$7$	2.21011	+	1.45445i	0.835342	+	0.549730i
$8$	0.0517058	+	0.0298524i	0.0182808	+	0.0105544i
$9$	2.90764	−	0.738686i	0.969212	−	0.246229i
$10$	−0.0212751	−	0.0122832i	−0.00672777	−	0.00388428i
$11$	1.57083	+	4.31582i	0.473623	+	1.30127i	0.914821	+	0.403859i	$0.132331\pi$
$11$	1.57083	+	4.31582i	0.473623	+	1.30127i	−0.441199	+	0.897409i	$0.645447\pi$
$12$	3.37666	+	0.771671i	0.974759	+	0.222762i
$13$	−1.52751	+	4.19679i	−0.423654	+	1.16398i	0.525946	+	0.850518i	$0.323711\pi$
$13$	−1.52751	+	4.19679i	−0.423654	+	1.16398i	−0.949600	+	0.313463i	$0.898511\pi$
$14$	−0.0287191	−	0.0271094i	−0.00767551	−	0.00724530i
$15$	−2.77891	−	0.635065i	−0.717510	−	0.163973i
$16$	3.06315	+	2.57029i	0.765788	+	0.642573i
$17$	1.88705	−	3.26847i	0.457677	−	0.792720i	−0.541160	−	0.840919i	$-0.682015\pi$
$17$	1.88705	−	3.26847i	0.457677	−	0.792720i	0.998838	+	0.0481990i	$0.0153482\pi$
$18$	−0.0446576	+	0.00332212i	−0.0105259	+	0.000783031i
$19$	−1.27160	+	0.734160i	−0.291726	+	0.168428i	−0.638720	−	0.769439i	$-0.720536\pi$
$19$	−1.27160	+	0.734160i	−0.291726	+	0.168428i	0.346994	+	0.937867i	$0.387202\pi$
$20$	−2.52118	−	2.11552i	−0.563752	−	0.473044i
$21$	−4.11100	−	2.02476i	−0.897094	−	0.441839i
$22$	−0.0119048	−	0.0675152i	−0.00253810	−	0.0143943i
$23$	7.31736	−	1.29025i	1.52578	−	0.269035i	0.653076	−	0.757293i	$-0.273478\pi$
$23$	7.31736	−	1.29025i	1.52578	−	0.269035i	0.872700	+	0.488257i	$0.162367\pi$
$24$	−0.0952804	−	0.0401947i	−0.0194490	−	0.00820470i
$25$	−1.75536	−	1.47292i	−0.351072	−	0.294584i
$26$	0.0333330	−	0.0577345i	0.00653714	−	0.0113227i
$27$	−4.83851	+	1.89441i	−0.931172	+	0.364579i
$28$	−3.15839	−	4.24480i	−0.596880	−	0.802192i
$29$	−2.83246	−	7.78213i	−0.525975	−	1.44511i	−0.863771	−	0.503885i	$-0.831903\pi$
$29$	−2.83246	−	7.78213i	−0.525975	−	1.44511i	0.337795	−	0.941220i	$-0.390319\pi$
$30$	0.0392044	+	0.0165387i	0.00715772	+	0.00301953i
$31$	−2.87381	+	7.89573i	−0.516152	+	1.41812i	0.358576	+	0.933501i	$0.383262\pi$
$31$	−2.87381	+	7.89573i	−0.516152	+	1.41812i	−0.874728	+	0.484615i	$0.838960\pi$
$32$	−0.115122	−	0.137197i	−0.0203508	−	0.0242532i
$33$	−3.62721	−	7.07988i	−0.631415	−	1.23245i
$34$	−0.0362121	+	0.0431559i	−0.00621033	+	0.00740118i
$35$	2.59927	+	3.49336i	0.439358	+	0.590485i
$36$	−5.96919	−	0.600598i	−0.994865	−	0.100100i
$37$	−0.794639			−0.130638			−0.0653190	−	0.997864i	$-0.520806\pi$
$37$	−0.794639			−0.130638			−0.0653190	+	0.997864i	$0.520806\pi$
$38$	0.0205958	−	0.00749627i	0.00334109	−	0.00121606i
$39$	1.72338	−	7.54116i	0.275962	−	1.20755i
$40$	0.0631602	+	0.0752714i	0.00998651	+	0.0119015i
$41$	3.97658	+	1.44736i	0.621037	+	0.226039i	0.633326	−	0.773885i	$-0.281689\pi$
$41$	3.97658	+	1.44736i	0.621037	+	0.226039i	−0.0122884	+	0.999924i	$0.503912\pi$
$42$	0.0551844	+	0.0404204i	0.00851514	+	0.00623700i
$43$	−0.303215	+	1.71962i	−0.0462399	+	0.262239i	−0.999160	−	0.0409825i	$-0.986951\pi$
$43$	−0.303215	+	1.71962i	−0.0462399	+	0.262239i	0.952920	+	0.303222i	$0.0980623\pi$
$44$		−	9.18457i		−	1.38463i
$45$	4.91249	+	0.494277i	0.732311	+	0.0736824i
$46$	−0.110911			−0.0163530
$47$	−1.54917	+	0.563852i	−0.225970	+	0.0822463i	−0.452524	−	0.891752i	$-0.649476\pi$
$47$	−1.54917	+	0.563852i	−0.225970	+	0.0822463i	0.226554	+	0.973999i	$0.427254\pi$
$48$	−5.81690	−	3.75920i	−0.839597	−	0.542594i
$49$	2.76916	+	6.42898i	0.395594	+	0.918425i
$50$	0.0219863	+	0.0262023i	0.00310933	+	0.00370556i
$51$	−2.54082	+	6.02294i	−0.355786	+	0.843380i
$52$	5.74091	−	6.84175i	0.796121	−	0.948780i
$53$	3.66888	−	2.11823i	0.503959	−	0.290961i	−0.226388	−	0.974037i	$-0.572692\pi$
$53$	3.66888	−	2.11823i	0.503959	−	0.290961i	0.730347	+	0.683076i	$0.239358\pi$
$54$	0.0760377	−	0.0153066i	0.0103474	−	0.00208296i
$55$			7.55866i			1.01921i
$56$	0.0708567	+	0.141180i	0.00946863	+	0.0188660i
$57$	2.02769	−	1.53505i	0.268574	−	0.203322i
$58$	0.0214662	+	0.121741i	0.00281865	+	0.0159854i
$59$	−8.85828	+	7.43298i	−1.15325	+	0.967691i	−0.999791	−	0.0204636i	$-0.993486\pi$
$59$	−8.85828	+	7.43298i	−1.15325	+	0.967691i	−0.153459	+	0.988155i	$0.549041\pi$
$60$	4.78769	+	3.09407i	0.618088	+	0.399443i
$61$	1.02900	+	2.82714i	0.131749	+	0.361978i	0.987973	−	0.154627i	$-0.0494176\pi$
$61$	1.02900	+	2.82714i	0.131749	+	0.361978i	−0.856224	+	0.516605i	$0.827195\pi$
$62$	0.0627118	−	0.108620i	0.00796441	−	0.0137948i
$63$	7.50057	+	2.59643i	0.944983	+	0.327120i
$64$	−3.99733	−	6.92357i	−0.499666	−	0.865447i
$65$	−4.72462	+	5.63058i	−0.586017	+	0.698388i
$66$	0.0349694	+	0.113478i	0.00430443	+	0.0139682i
$67$	−1.88292	−	10.6785i	−0.230035	−	1.30459i	−0.852823	−	0.522201i	$-0.825111\pi$
$67$	−1.88292	−	10.6785i	−0.230035	−	1.30459i	0.622788	−	0.782391i	$-0.286000\pi$
$68$	−5.78162	+	4.85135i	−0.701124	+	0.588313i
$69$	−12.2988	+	3.79001i	−1.48061	+	0.456264i
$70$	−0.0291550	−	0.0580906i	−0.00348469	−	0.00694316i
$71$	6.66808	−	3.84982i	0.791355	−	0.456889i	−0.0490844	−	0.998795i	$-0.515630\pi$
$71$	6.66808	−	3.84982i	0.791355	−	0.456889i	0.840439	+	0.541906i	$0.182297\pi$
$72$	0.172393	+	0.0486054i	0.0203167	+	0.00572821i
$73$		−	15.8281i		−	1.85254i	−0.376858	−	0.926271i	$-0.622995\pi$
$73$		−	15.8281i		−	1.85254i	0.376858	−	0.926271i	$-0.377005\pi$
$74$	0.0116814	+	0.00205974i	0.00135793	+	0.000239440i
$75$	3.33341	+	2.15423i	0.384909	+	0.248750i
$76$	2.89171	−	0.509886i	0.331701	−	0.0584879i
$77$	−2.80543	+	11.8231i	−0.319709	+	1.34737i
$78$	−0.0448812	+	0.106390i	−0.00508179	+	0.0120463i
$79$	0.276799	−	1.56981i	0.0311423	−	0.176617i	−0.965269	−	0.261257i	$-0.915863\pi$
$79$	0.276799	−	1.56981i	0.0311423	−	0.176617i	0.996412	+	0.0846402i	$0.0269741\pi$
$80$	3.29043	+	5.69919i	0.367881	+	0.637189i
$81$	7.90869	−	4.29566i	0.878743	−	0.477295i
$82$	−0.0547050	−	0.0315840i	−0.00604116	−	0.00348787i
$83$	4.61667	−	1.68033i	0.506745	−	0.184440i	−0.0759804	−	0.997109i	$-0.524209\pi$
$83$	4.61667	−	1.68033i	0.506745	−	0.184440i	0.582725	+	0.812669i	$0.301986\pi$
$84$	6.34044	+	6.61666i	0.691798	+	0.721937i
$85$	4.75812	−	3.99254i	0.516091	−	0.433051i
$86$	0.00891467	−	0.0244929i	0.000961293	−	0.00264113i
$87$	6.54045	+	12.7662i	0.701210	+	1.36868i
$88$	−0.0476164	+	0.270046i	−0.00507592	+	0.0287870i
$89$	−3.59252	−	6.22243i	−0.380807	−	0.659577i	0.610371	−	0.792116i	$-0.291020\pi$
$89$	−3.59252	−	6.22243i	−0.380807	−	0.659577i	−0.991178	+	0.132539i	$0.957687\pi$
$90$	−0.0709336	−	0.0199994i	−0.00747705	−	0.00210812i
$91$	−9.47998	+	7.05369i	−0.993772	+	0.739427i
$92$	−14.6331	−	2.58021i	−1.52561	−	0.269005i
$93$	3.24233	−	14.1877i	0.336214	−	1.47120i
$94$	0.0242347	−	0.00427323i	0.00249962	−	0.000440750i
$95$	−2.37980	+	0.419623i	−0.244162	+	0.0430524i
$96$	0.227340	+	0.211056i	0.0232027	+	0.0215408i
$97$	−1.56544	−	0.276029i	−0.158946	−	0.0280265i	0.0936086	−	0.995609i	$-0.470160\pi$
$97$	−1.56544	−	0.276029i	−0.158946	−	0.0280265i	−0.252555	+	0.967583i	$0.581271\pi$
$98$	−0.0240431	−	0.101685i	−0.00242872	−	0.0102718i
$99$	7.75543	+	11.3885i	0.779450	+	1.14458i
$100$	2.29120	+	3.96848i	0.229120	+	0.396848i
$101$	0.401328	−	2.27604i	0.0399336	−	0.226475i	−0.958309	−	0.285734i	$-0.907763\pi$
$101$	0.401328	−	2.27604i	0.0399336	−	0.226475i	0.998243	+	0.0592590i	$0.0188738\pi$
$102$	0.0529624	−	0.0819527i	0.00524406	−	0.00811453i
$103$	0.187058	−	0.513937i	0.0184313	−	0.0506397i	−0.930136	−	0.367216i	$-0.880311\pi$
$103$	0.187058	−	0.513937i	0.0184313	−	0.0506397i	0.948567	+	0.316576i	$0.102533\pi$
$104$	−0.204265	+	0.171399i	−0.0200299	+	0.0168070i
$105$	−5.21801	−	5.44534i	−0.509226	−	0.531410i
$106$	−0.0594239	+	0.0216285i	−0.00577176	+	0.00210075i
$107$	2.89299	+	1.67027i	0.279676	+	0.161471i	0.633277	−	0.773925i	$-0.281709\pi$
$107$	2.89299	+	1.67027i	0.279676	+	0.161471i	−0.353601	+	0.935397i	$0.615043\pi$
$108$	10.3881	−	0.250555i	0.999598	−	0.0241097i
$109$	1.92585	+	3.33567i	0.184463	+	0.319499i	0.943395	−	0.331670i	$-0.107612\pi$
$109$	1.92585	+	3.33567i	0.184463	+	0.319499i	−0.758932	+	0.651169i	$0.774279\pi$
$110$	0.0195924	−	0.111114i	0.00186806	−	0.0105943i
$111$	1.36572	−	0.170769i	0.129628	−	0.0162086i
$112$	3.03155	+	10.1358i	0.286454	+	0.957745i
$113$	4.52691	−	0.798216i	0.425856	−	0.0750899i	0.0433872	−	0.999058i	$-0.486185\pi$
$113$	4.52691	−	0.798216i	0.425856	−	0.0750899i	0.382469	+	0.923968i	$0.375074\pi$
$114$	−0.0337864	+	0.0173097i	−0.00316439	+	0.00162120i
$115$	12.0427	+	2.12344i	1.12298	+	0.198012i
$116$			16.5613i			1.53768i
$117$	−1.34133	+	13.3311i	−0.124006	+	1.23246i
$118$	0.149485	−	0.0863054i	0.0137612	−	0.00794506i
$119$	8.92441	−	4.47905i	0.818099	−	0.410594i
$120$	−0.124727	−	0.115793i	−0.0113860	−	0.0105704i
$121$	−7.73229	+	6.48816i	−0.702935	+	0.589833i
$122$	−0.00779839	−	0.0442268i	−0.000706033	−	0.00400411i
$123$	−7.14545	−	1.63295i	−0.644284	−	0.147239i
$124$	10.8008	−	12.8719i	0.969940	−	1.15593i
$125$	−6.00001	−	10.3923i	−0.536657	−	0.929518i
$126$	−0.103530	−	0.0576100i	−0.00922319	−	0.00513230i
$127$	2.63202	−	4.55879i	0.233554	−	0.404527i	−0.725298	−	0.688435i	$-0.758298\pi$
$127$	2.63202	−	4.55879i	0.233554	−	0.404527i	0.958851	+	0.283908i	$0.0916312\pi$
$128$	0.163325	+	0.448733i	0.0144361	+	0.0396627i
$129$	0.151579	−	3.02061i	0.0133458	−	0.265950i
$130$	0.0840478	−	0.0705245i	0.00737148	−	0.00618540i
$131$	−2.62848	−	14.9069i	−0.229652	−	1.30242i	−0.853590	−	0.520946i	$-0.825579\pi$
$131$	−2.62848	−	14.9069i	−0.229652	−	1.30242i	0.623938	−	0.781474i	$-0.285532\pi$
$132$	1.97377	+	15.7852i	0.171795	+	1.37393i
$133$	−3.87818	−	0.226907i	−0.336281	−	0.0196753i
$134$			0.161858i			0.0139824i
$135$	−8.54916	+	0.206200i	−0.735794	+	0.0177469i
$136$	0.195143	−	0.112666i	0.0167334	−	0.00966102i
$137$	−2.29638	+	2.73672i	−0.196193	+	0.233814i	−0.855168	−	0.518351i	$-0.826546\pi$
$137$	−2.29638	+	2.73672i	−0.196193	+	0.233814i	0.658975	+	0.752165i	$0.270990\pi$
$138$	0.190620	−	0.0238349i	0.0162266	−	0.00202896i
$139$	3.91305	+	4.66340i	0.331901	+	0.395544i	0.906025	−	0.423224i	$-0.139102\pi$
$139$	3.91305	+	4.66340i	0.331901	+	0.395544i	−0.574124	+	0.818768i	$0.694657\pi$
$140$	−2.49516	−	8.34245i	−0.210880	−	0.705065i
$141$	2.54134	−	1.30199i	0.214019	−	0.109648i
$142$	−0.108001	+	0.0393092i	−0.00906326	+	0.00329876i
$143$	−20.5121			−1.71530
$144$	10.8052	+	5.21076i	0.900431	+	0.434230i
$145$		−	13.6295i		−	1.13187i
$146$	−0.0410273	+	0.232677i	−0.00339544	+	0.0192565i
$147$	−6.14086	−	10.4542i	−0.506489	−	0.862246i
$148$	1.49327	+	0.543505i	0.122746	+	0.0446758i
$149$	12.9982	+	15.4906i	1.06485	+	1.26904i	0.961620	+	0.274383i	$0.0884738\pi$
$149$	12.9982	+	15.4906i	1.06485	+	1.26904i	0.103231	+	0.994657i	$0.467082\pi$
$150$	−0.0434180	−	0.0403081i	−0.00354507	−	0.00329114i
$151$	−17.9723	+	6.54137i	−1.46256	+	0.532329i	−0.946070	−	0.323963i	$-0.894985\pi$
$151$	−17.9723	+	6.54137i	−1.46256	+	0.532329i	−0.516492	+	0.856292i	$0.672762\pi$
$152$	−0.0876657			−0.00711062
$153$	3.07249	−	10.8975i	0.248396	−	0.881007i
$154$	0.0718866	−	0.166531i	0.00579279	−	0.0134194i
$155$	−8.88877	+	10.5932i	−0.713963	+	0.850868i
$156$	−8.39642	+	12.9924i	−0.672252	+	1.04023i
$157$	−10.2114	−	12.1695i	−0.814957	−	0.971228i	0.184977	−	0.982743i	$-0.440779\pi$
$157$	−10.2114	−	12.1695i	−0.814957	−	0.971228i	−0.999934	+	0.0115149i	$0.996335\pi$
$158$	−0.00813802	+	0.0223590i	−0.000647426	+	0.00177879i
$159$	−5.85037	+	4.42897i	−0.463965	+	0.351240i
$160$	−0.100811	−	0.276977i	−0.00796983	−	0.0218969i
$161$	18.0488	+	7.79114i	1.42244	+	0.614028i
$162$	−0.127394	+	0.0426475i	−0.0100090	+	0.00335070i
$163$	8.71884	−	15.1015i	0.682912	−	1.18284i	−0.291176	−	0.956670i	$-0.594046\pi$
$163$	8.71884	−	15.1015i	0.682912	−	1.18284i	0.974088	−	0.226169i	$-0.0726202\pi$
$164$	−6.48275	−	5.43967i	−0.506218	−	0.424767i
$165$	−1.62436	−	12.9908i	−0.126456	−	1.01133i
$166$	−0.0722216	+	0.0127346i	−0.00560548	+	0.000988397i
$167$	−1.64317	−	9.31890i	−0.127153	−	0.721118i	−0.980006	−	0.198968i	$-0.936241\pi$
$167$	−1.64317	−	9.31890i	−0.127153	−	0.721118i	0.852853	−	0.522150i	$-0.174870\pi$
$168$	−0.152119	−	0.227415i	−0.0117362	−	0.0175454i
$169$	−5.32122	−	4.46503i	−0.409325	−	0.343464i
$170$	−0.0802943	+	0.0463580i	−0.00615829	+	0.00355549i
$171$	−3.15504	+	3.07399i	−0.241272	+	0.235074i
$172$	1.74595	−	3.02408i	0.133128	−	0.230584i
$173$	1.16427	+	0.976939i	0.0885179	+	0.0742753i	0.685973	−	0.727627i	$-0.259377\pi$
$173$	1.16427	+	0.976939i	0.0885179	+	0.0742753i	−0.597455	+	0.801902i	$0.703821\pi$
$174$	−0.0630555	−	0.204619i	−0.00478023	−	0.0155121i
$175$	−1.73725	−	5.80840i	−0.131323	−	0.439074i
$176$	−6.28122	+	17.2575i	−0.473465	+	1.30083i
$177$	13.6271	−	14.6785i	1.02427	−	1.10330i
$178$	0.0366821	+	0.100783i	0.00274944	+	0.00755402i
$179$	−7.44216	−	4.29673i	−0.556253	−	0.321153i	0.195387	−	0.980726i	$-0.437404\pi$
$179$	−7.44216	−	4.29673i	−0.556253	−	0.321153i	−0.751640	+	0.659573i	$0.770737\pi$
$180$	−8.89337	−	4.28880i	−0.662872	−	0.319668i
$181$	9.18805	+	5.30472i	0.682942	+	0.394297i	0.800963	−	0.598714i	$-0.204322\pi$
$181$	9.18805	+	5.30472i	0.682942	+	0.394297i	−0.118021	+	0.993011i	$0.537655\pi$
$182$	0.157641	−	0.0791183i	0.0116852	−	0.00586464i
$183$	−2.37605	−	4.63778i	−0.175643	−	0.342835i
$184$	0.416867	+	0.151727i	0.0307318	+	0.0111855i
$185$	−1.22892	−	0.447290i	−0.0903520	−	0.0328854i
$186$	−0.0844382	+	0.200159i	−0.00619131	+	0.0146763i
$187$	17.0704	+	3.00996i	1.24831	+	0.220110i
$188$	3.29682			0.240445
$189$	−13.4490	−	2.85052i	−0.978268	−	0.207345i
$190$	0.0360713			0.00261688
$191$	−9.68268	−	1.70732i	−0.700614	−	0.123537i	−0.188016	−	0.982166i	$-0.560206\pi$
$191$	−9.68268	−	1.70732i	−0.700614	−	0.123537i	−0.512598	+	0.858629i	$0.671317\pi$
$192$	8.35796	+	11.0403i	0.603183	+	0.796764i
$193$	−18.3352	−	6.67347i	−1.31980	−	0.480367i	−0.416404	−	0.909180i	$-0.636710\pi$
$193$	−18.3352	−	6.67347i	−1.31980	−	0.480367i	−0.903393	+	0.428813i	$0.858932\pi$
$194$	0.0222969	+	0.00811539i	0.00160082	+	0.000582651i
$195$	6.91004	−	10.6924i	0.494838	−	0.765701i
$196$	−0.806547	−	13.9752i	−0.0576105	−	0.998228i
$197$	−3.74738	−	2.16355i	−0.266990	−	0.154147i	0.360529	−	0.932748i	$-0.382596\pi$
$197$	−3.74738	−	2.16355i	−0.266990	−	0.154147i	−0.627519	+	0.778601i	$0.715930\pi$
$198$	−0.0844872	−	0.187516i	−0.00600424	−	0.0133262i
$199$	1.46886	+	0.848046i	0.104125	+	0.0601164i	0.551158	−	0.834401i	$-0.314186\pi$
$199$	1.46886	+	0.848046i	0.104125	+	0.0601164i	−0.447033	+	0.894517i	$0.647519\pi$
$200$	−0.0467921	−	0.128560i	−0.00330870	−	0.00909058i
$201$	5.53093	+	17.9482i	0.390122	+	1.26597i
$202$	−0.0117992	+	0.0324181i	−0.000830191	+	0.00228093i
$203$	5.05865	−	21.3190i	0.355048	−	1.49630i
$204$	8.89412	−	9.58034i	0.622713	−	0.670758i
$205$	5.33514	+	4.47671i	0.372622	+	0.312667i
$206$	−0.00408194	+	0.00707013i	−0.000284402	+	0.000492599i
$207$	20.3231	−	9.15680i	1.41256	−	0.636442i
$208$	−15.4660	+	8.92928i	−1.07237	+	0.619134i
$209$	−5.16597	−	4.33477i	−0.357338	−	0.299842i
$210$	0.0625914	+	0.0935731i	0.00431922	+	0.00645716i
$211$	1.04647	+	5.93483i	0.0720420	+	0.408570i	0.999408	+	0.0344141i	$0.0109565\pi$
$211$	1.04647	+	5.93483i	0.0720420	+	0.408570i	−0.927366	+	0.374156i	$0.877932\pi$
$212$	−8.34326	+	1.47114i	−0.573017	+	0.101038i
$213$	−10.6329	+	8.04953i	−0.728553	+	0.551544i
$214$	−0.0381983	−	0.0320521i	−0.00261118	−	0.00219104i
$215$	−1.43687	+	2.48874i	−0.0979939	+	0.169730i
$216$	−0.306732	−	0.0464892i	−0.0208705	−	0.00316319i
$217$	−17.8354	+	13.2706i	−1.21074	+	0.900868i
$218$	−0.0196642	−	0.0540270i	−0.00133183	−	0.00365917i
$219$	3.40148	+	27.2033i	0.229850	+	1.83823i
$220$	5.16985	−	14.2041i	0.348551	−	0.957637i
$221$	10.8346	+	12.9122i	0.728814	+	0.868567i
$222$	−0.0205191	−	0.00102968i	−0.00137715	−	6.91074e-5i
$223$	0.590154	−	0.703318i	0.0395196	−	0.0470976i	−0.745923	−	0.666033i	$-0.767991\pi$
$223$	0.590154	−	0.703318i	0.0395196	−	0.0470976i	0.785442	+	0.618935i	$0.212436\pi$
$224$	−0.0548859	−	0.470658i	−0.00366722	−	0.0314472i
$225$	−6.19197	−	2.98606i	−0.412798	−	0.199071i
$226$	−0.0686157			−0.00456425
$227$	−12.5247	+	4.55861i	−0.831293	+	0.302566i	−0.722389	−	0.691487i	$-0.756956\pi$
$227$	−12.5247	+	4.55861i	−0.831293	+	0.302566i	−0.108903	+	0.994052i	$0.534734\pi$
$228$	−4.86030	+	1.49775i	−0.321882	+	0.0991911i
$229$	7.91645	+	9.43446i	0.523134	+	0.623447i	0.961319	−	0.275438i	$-0.0888229\pi$
$229$	7.91645	+	9.43446i	0.523134	+	0.623447i	−0.438185	+	0.898885i	$0.644378\pi$
$230$	−0.171526	−	0.0624303i	−0.0113101	−	0.00411653i
$231$	2.28081	−	20.9229i	0.150066	−	1.37663i
$232$	0.0858601	−	0.486937i	0.00563699	−	0.0319690i
$233$		−	24.9355i		−	1.63358i	−0.576937	−	0.816788i	$-0.695752\pi$
$233$		−	24.9355i		−	1.63358i	0.576937	−	0.816788i	$-0.304248\pi$
$234$	0.0542726	−	0.192493i	0.00354791	−	0.0125837i
$235$	−2.71320			−0.176989
$236$	21.7302	−	7.90913i	1.41451	−	0.514840i
$237$	−0.138373	+	2.75746i	−0.00898831	+	0.179116i
$238$	−0.142801	+	0.0427106i	−0.00925640	+	0.00276852i
$239$	7.34853	+	8.75764i	0.475337	+	0.566485i	0.949425	−	0.313993i	$-0.101667\pi$
$239$	7.34853	+	8.75764i	0.475337	+	0.566485i	−0.474088	+	0.880477i	$0.657222\pi$
$240$	−6.87991	−	9.08790i	−0.444096	−	0.586621i
$241$	−3.95464	+	4.71296i	−0.254741	+	0.303588i	−0.878225	−	0.478248i	$-0.841272\pi$
$241$	−3.95464	+	4.71296i	−0.254741	+	0.303588i	0.623484	+	0.781836i	$0.285717\pi$
$242$	0.130484	−	0.0753350i	0.00838784	−	0.00484272i
$243$	−12.6693	+	9.08239i	−0.812734	+	0.582635i
$244$		−	6.01649i		−	0.385166i
$245$	0.663767	+	11.5012i	0.0424065	+	0.734786i
$246$	0.100807	+	0.0425262i	0.00642723	+	0.00271137i
$247$	−1.13874	−	6.45809i	−0.0724560	−	0.410919i
$248$	−0.384299	+	0.322465i	−0.0244030	+	0.0204766i
$249$	−7.57341	+	3.88005i	−0.479945	+	0.245888i
$250$	0.0612642	+	0.168322i	0.00387469	+	0.0106456i
$251$	−6.31801	+	10.9431i	−0.398789	+	0.690724i	−0.993577	−	0.113160i	$-0.963903\pi$
$251$	−6.31801	+	10.9431i	−0.398789	+	0.690724i	0.594787	+	0.803883i	$0.297236\pi$
$252$	−12.3190	−	10.0093i	−0.776026	−	0.630525i
$253$	17.0628	+	29.5536i	1.07273	+	1.85802i
$254$	−0.0505079	+	0.0601929i	−0.00316915	+	0.00377684i
$255$	−7.31963	+	7.88437i	−0.458373	+	0.493738i
$256$	2.77528	+	15.7394i	0.173455	+	0.983711i
$257$	11.4631	−	9.61867i	0.715048	−	0.599996i	−0.210963	−	0.977494i	$-0.567660\pi$
$257$	11.4631	−	9.61867i	0.715048	−	0.599996i	0.926010	+	0.377498i	$0.123215\pi$
$258$	−0.0100578	+	0.0440108i	−0.000626173	+	0.00273999i
$259$	−1.75624	−	1.15576i	−0.109127	−	0.0718156i
$260$	12.7295	−	7.34939i	0.789451	−	0.455790i
$261$	−13.9843	−	20.5353i	−0.865607	−	1.27110i
$262$			0.225948i			0.0139591i
$263$	15.6917	+	2.76688i	0.967594	+	0.170613i	0.635047	−	0.772474i	$-0.280981\pi$
$263$	15.6917	+	2.76688i	0.967594	+	0.170613i	0.332547	+	0.943087i	$0.392092\pi$
$264$	0.0238037	−	0.474352i	0.00146501	−	0.0291943i
$265$	6.86628	−	1.21071i	0.421792	−	0.0743734i
$266$	0.0564220	+	0.0133880i	0.00345945	+	0.000820872i
$267$	7.51156	+	9.92226i	0.459700	+	0.607232i
$268$	−3.76541	+	21.3547i	−0.230009	+	1.30445i
$269$	4.94336	+	8.56215i	0.301402	+	0.522044i	0.976454	−	0.215727i	$-0.0692121\pi$
$269$	4.94336	+	8.56215i	0.301402	+	0.522044i	−0.675052	+	0.737770i	$0.735879\pi$
$270$	0.126209	+	0.0191286i	0.00768084	+	0.00116413i
$271$	1.92889	+	1.11364i	0.117171	+	0.0676490i	0.557440	−	0.830217i	$-0.311784\pi$
$271$	1.92889	+	1.11364i	0.117171	+	0.0676490i	−0.440269	+	0.897866i	$0.645117\pi$
$272$	14.1812	−	5.16155i	0.859864	−	0.312965i
$273$	14.7771	−	14.1602i	0.894350	−	0.857014i
$274$	0.0408511	−	0.0342782i	0.00246791	−	0.00207082i
$275$	3.59949	−	9.88952i	0.217057	−	0.596361i
$276$	25.7039	+	1.28986i	1.54719	+	0.0776404i
$277$	−1.50230	+	8.51996i	−0.0902644	+	0.511915i	0.905832	+	0.423638i	$0.139247\pi$
$277$	−1.50230	+	8.51996i	−0.0902644	+	0.511915i	−0.996096	+	0.0882769i	$0.971864\pi$
$278$	−0.0454351	−	0.0786958i	−0.00272501	−	0.00471986i
$279$	−2.52353	+	25.0808i	−0.151080	+	1.50155i
$280$	0.0301125	+	0.258221i	0.00179957	+	0.0154317i
$281$	29.4759	+	5.19740i	1.75839	+	0.310051i	0.957429	−	0.288670i	$-0.0932130\pi$
$281$	29.4759	+	5.19740i	1.75839	+	0.310051i	0.800958	+	0.598721i	$0.204324\pi$
$282$	−0.0407331	+	0.0125523i	−0.00242562	+	0.000747480i
$283$	9.64374	−	1.70045i	0.573261	−	0.101081i	0.120500	−	0.992713i	$-0.461550\pi$
$283$	9.64374	−	1.70045i	0.573261	−	0.101081i	0.452761	+	0.891632i	$0.350439\pi$
$284$	−15.1636	+	2.67376i	−0.899795	+	0.158658i
$285$	3.99990	−	1.23261i	0.236934	−	0.0730136i
$286$	0.301532	+	0.0531682i	0.0178300	+	0.00314390i
$287$	6.68357	+	8.98254i	0.394518	+	0.530223i
$288$	−0.436077	−	0.313879i	−0.0256961	−	0.0184955i
$289$	1.37807	+	2.38689i	0.0810630	+	0.140405i
$290$	−0.0353283	+	0.200357i	−0.00207455	+	0.0117654i
$291$	2.74979	+	0.137989i	0.161196	+	0.00808903i
$292$	−10.8259	+	29.7438i	−0.633536	+	1.74063i
$293$	7.96197	−	6.68088i	0.465143	−	0.390301i	−0.379876	−	0.925037i	$-0.624033\pi$
$293$	7.96197	−	6.68088i	0.465143	−	0.390301i	0.845019	+	0.534736i	$0.179589\pi$
$294$	0.0631743	+	0.169596i	0.00368440	+	0.00989106i
$295$	−17.8834	+	6.50901i	−1.04121	+	0.378969i
$296$	−0.0410875	−	0.0237219i	−0.00238816	−	0.00137881i
$297$	−15.7764	−	17.9064i	−0.915439	−	1.03903i
$298$	−0.150924	−	0.261408i	−0.00874278	−	0.0151429i
$299$	−5.76242	+	32.6803i	−0.333249	+	1.88995i
$300$	−4.79065	−	6.32812i	−0.276588	−	0.365354i
$301$	−3.17124	+	3.35953i	−0.182787	+	0.193640i
$302$	0.281152	−	0.0495747i	0.0161785	−	0.00285270i
$303$	−0.200626	+	3.99801i	−0.0115257	+	0.229680i
$304$	−5.78212	−	1.01954i	−0.331627	−	0.0584749i
$305$			4.95142i			0.283517i
$306$	−0.0734130	+	0.152231i	−0.00419674	+	0.00870247i
$307$	14.7821	−	8.53446i	0.843660	−	0.487087i	−0.0148465	−	0.999890i	$-0.504726\pi$
$307$	14.7821	−	8.53446i	0.843660	−	0.487087i	0.858507	+	0.512802i	$0.171393\pi$
$308$	13.3585	−	20.2989i	0.761170	−	1.15664i
$309$	−0.211045	+	0.923485i	−0.0120059	+	0.0525352i
$310$	0.158125	−	0.132683i	0.00898091	−	0.00753588i
$311$	−5.77607	−	32.7577i	−0.327531	−	1.85752i	−0.491260	−	0.871013i	$-0.663463\pi$
$311$	−5.77607	−	32.7577i	−0.327531	−	1.85752i	0.163729	−	0.986505i	$-0.447648\pi$
$312$	0.314230	−	0.338474i	0.0177898	−	0.0191623i
$313$	−0.628153	+	0.748603i	−0.0355053	+	0.0423135i	−0.783505	−	0.621386i	$-0.786570\pi$
$313$	−0.628153	+	0.748603i	−0.0355053	+	0.0423135i	0.748000	+	0.663699i	$0.231014\pi$
$314$	0.118566	+	0.205362i	0.00669106	+	0.0115893i
$315$	10.1382	+	8.23737i	0.571225	+	0.464123i
$316$	−1.59384	+	2.76062i	−0.0896608	+	0.155297i
$317$	1.15835	+	3.18255i	0.0650597	+	0.178750i	0.967963	−	0.251095i	$-0.0807905\pi$
$317$	1.15835	+	3.18255i	0.0650597	+	0.178750i	−0.902903	+	0.429845i	$0.858568\pi$
$318$	0.0974820	−	0.0499425i	0.00546652	−	0.00280064i
$319$	29.1369	−	24.4488i	1.63136	−	1.36887i
$320$	−2.28474	−	12.9574i	−0.127721	−	0.724342i
$321$	−5.33104	−	2.24893i	−0.297549	−	0.125523i
$322$	−0.245126	−	0.161315i	−0.0136603	−	0.00898972i
$323$			5.54159i			0.308343i
$324$	−17.7999	+	2.66304i	−0.988883	+	0.147946i
$325$	8.86287	−	5.11698i	0.491624	−	0.283839i
$326$	−0.167313	+	0.199396i	−0.00926660	+	0.0110435i
$327$	−4.02673	−	5.31904i	−0.222679	−	0.294144i
$328$	0.162405	+	0.193547i	0.00896733	+	0.0106868i
$329$	−4.24393	−	1.00702i	−0.233975	−	0.0555185i
$330$	−0.00979435	+	0.195179i	−0.000539161	+	0.0107442i
$331$	−5.71144	+	2.07879i	−0.313929	+	0.114261i	−0.494179	−	0.869360i	$-0.664531\pi$
$331$	−5.71144	+	2.07879i	−0.313929	+	0.114261i	0.180250	+	0.983621i	$0.442309\pi$
$332$	−9.82481			−0.539206
$333$	−2.31052	+	0.586989i	−0.126616	+	0.0321668i
$334$			0.141249i			0.00772881i
$335$	3.09883	−	17.5744i	0.169307	−	0.960190i
$336$	−7.38841	−	16.7686i	−0.403071	−	0.914803i
$337$	−16.0696	−	5.84885i	−0.875366	−	0.318607i	−0.135028	−	0.990842i	$-0.543112\pi$
$337$	−16.0696	−	5.84885i	−0.875366	−	0.318607i	−0.740338	+	0.672235i	$0.765335\pi$
$338$	0.0666496	+	0.0794299i	0.00362526	+	0.00432042i
$339$	−7.60872	+	2.34470i	−0.413249	+	0.127347i
$340$	−11.6721	+	4.24830i	−0.633008	+	0.230396i
$341$	−38.5908			−2.08981
$342$	0.0543478	−	0.0370103i	0.00293879	−	0.00200129i
$343$	−3.23048	+	18.2363i	−0.174429	+	0.984670i
$344$	−0.0670127	+	0.0798626i	−0.00361308	+	0.00430590i
$345$	−21.1536	−	1.06152i	−1.13887	−	0.0571504i
$346$	−0.0145828	−	0.0173791i	−0.000783975	−	0.000934305i
$347$	−7.20872	+	19.8058i	−0.386984	+	1.06323i	0.581367	+	0.813641i	$0.302518\pi$
$347$	−7.20872	+	19.8058i	−0.386984	+	1.06323i	−0.968352	+	0.249590i	$0.919704\pi$
$348$	−3.55903	−	28.4634i	−0.190784	−	1.52580i
$349$	2.22508	+	6.11336i	0.119106	+	0.327240i	0.984891	−	0.173175i	$-0.0554027\pi$
$349$	2.22508	+	6.11336i	0.119106	+	0.327240i	−0.865785	+	0.500416i	$0.833181\pi$
$350$	0.0104823	+	0.0898878i	0.000560302	+	0.00480471i
$351$	−0.559569	−	23.2000i	−0.0298676	−	1.23832i
$352$	0.411279	−	0.712357i	0.0219213	−	0.0379687i
$353$	14.6259	+	12.2726i	0.778459	+	0.653204i	0.942860	−	0.333189i	$-0.108125\pi$
$353$	14.6259	+	12.2726i	0.778459	+	0.653204i	−0.164401	+	0.986394i	$0.552569\pi$
$354$	−0.238369	+	0.180455i	−0.0126691	+	0.00959107i
$355$	12.4793	−	2.20043i	0.662331	−	0.116787i
$356$	2.49506	+	14.1502i	0.132238	+	0.749959i
$357$	−14.3755	+	9.61586i	−0.760834	+	0.508925i
$358$	0.0982642	+	0.0824534i	0.00519342	+	0.00435780i
$359$	−17.4085	+	10.0508i	−0.918784	+	0.530460i	−0.883247	−	0.468908i	$-0.844648\pi$
$359$	−17.4085	+	10.0508i	−0.918784	+	0.530460i	−0.0355371	+	0.999368i	$0.511314\pi$
$360$	0.239249	+	0.172206i	0.0126095	+	0.00907607i
$361$	−8.42202	+	14.5874i	−0.443264	+	0.767756i
$362$	−0.121316	−	0.101797i	−0.00637625	−	0.00535031i
$363$	11.8949	−	12.8127i	0.624322	−	0.672491i
$364$	22.6390	−	6.77115i	1.18661	−	0.354905i
$365$	8.90941	−	24.4784i	0.466340	−	1.28126i
$366$	0.0229072	+	0.0743354i	0.00119738	+	0.00388557i
$367$	−0.211500	−	0.581091i	−0.0110402	−	0.0303327i	0.934050	−	0.357142i	$-0.116249\pi$
$367$	−0.211500	−	0.581091i	−0.0110402	−	0.0303327i	−0.945090	+	0.326809i	$0.894027\pi$
$368$	25.7305	+	14.8555i	1.34130	+	0.774398i
$369$	12.6316	+	1.27094i	0.657574	+	0.0661627i
$370$	0.0169060	+	0.00976069i	0.000878902	+	0.000507434i
$371$	11.1895	+	0.654681i	0.580928	+	0.0339894i
$372$	−15.7968	+	24.4436i	−0.819026	+	1.26734i
$373$	−30.2831	−	11.0222i	−1.56800	−	0.570706i	−0.595450	−	0.803392i	$-0.703026\pi$
$373$	−30.2831	−	11.0222i	−1.56800	−	0.570706i	−0.972552	+	0.232686i	$0.925248\pi$
$374$	−0.243136	−	0.0884944i	−0.0125723	−	0.00457593i
$375$	12.5453	+	16.5715i	0.647839	+	0.855751i
$376$	−0.0969334	−	0.0170920i	−0.00499896	−	0.000881452i
$377$	36.9866			1.90491
$378$	0.190314	+	0.0767637i	0.00978870	+	0.00394830i
$379$	8.60323			0.441918			0.220959	−	0.975283i	$-0.429081\pi$
$379$	8.60323			0.441918			0.220959	+	0.975283i	$0.429081\pi$
$380$	4.75907	+	0.839152i	0.244135	+	0.0430476i
$381$	−3.54388	+	8.40066i	−0.181558	+	0.430379i
$382$	0.137912	+	0.0501960i	0.00705621	+	0.00256825i
$383$	11.4138	+	4.15427i	0.583216	+	0.212273i	0.616743	−	0.787164i	$-0.288452\pi$
$383$	11.4138	+	4.15427i	0.583216	+	0.212273i	−0.0335270	+	0.999438i	$0.510674\pi$
$384$	−0.377135	−	0.736123i	−0.0192456	−	0.0375651i
$385$	−10.9937	+	16.7055i	−0.560290	+	0.851389i
$386$	0.252234	+	0.145627i	0.0128384	+	0.00741224i
$387$	0.388618	+	5.22400i	0.0197546	+	0.265551i
$388$	2.75294	+	1.58941i	0.139760	+	0.0806902i
$389$	−11.0030	−	30.2306i	−0.557876	−	1.53275i	−0.822712	−	0.568459i	$-0.807540\pi$
$389$	−11.0030	−	30.2306i	−0.557876	−	1.53275i	0.264836	−	0.964294i	$-0.414682\pi$
$390$	−0.129294	+	0.139270i	−0.00654708	+	0.00705221i
$391$	9.59110	−	26.3513i	0.485043	−	1.33264i
$392$	−0.0487386	+	0.415081i	−0.00246167	+	0.0209648i
$393$	7.72099	+	25.0551i	0.389472	+	1.26386i
$394$	0.0494794	+	0.0415181i	0.00249274	+	0.00209165i
$395$	1.31169	−	2.27192i	0.0659984	−	0.114313i
$396$	−6.78451	−	26.7054i	−0.340934	−	1.34200i
$397$	10.0122	−	5.78053i	0.502496	−	0.290116i	−0.227247	−	0.973837i	$-0.572973\pi$
$397$	10.0122	−	5.78053i	0.502496	−	0.290116i	0.729744	+	0.683721i	$0.239639\pi$
$398$	−0.0193944	−	0.0162738i	−0.000972153	−	0.000815733i
$399$	6.71406	−	0.443445i	0.336124	−	0.0222000i
$400$	−1.59110	−	9.02357i	−0.0795549	−	0.451179i
$401$	0.101869	−	0.0179623i	0.00508710	−	0.000896994i	−0.171104	−	0.985253i	$-0.554733\pi$
$401$	0.101869	−	0.0179623i	0.00508710	−	0.000896994i	0.176191	+	0.984356i	$0.443622\pi$
$402$	−0.0347833	−	0.278180i	−0.00173483	−	0.0138743i
$403$	−28.7470	−	24.1216i	−1.43199	−	1.20158i
$404$	−2.31090	+	4.00259i	−0.114971	+	0.199136i
$405$	14.6488	−	2.19161i	0.727907	−	0.108902i
$406$	−0.129623	+	0.300282i	−0.00643310	+	0.0149028i
$407$	−1.24824	−	3.42952i	−0.0618731	−	0.169995i
$408$	−0.311174	+	0.235572i	−0.0154054	+	0.0116625i
$409$	−1.24227	+	3.41310i	−0.0614262	+	0.168767i	−0.966609	−	0.256255i	$-0.917511\pi$
$409$	−1.24227	+	3.41310i	−0.0614262	+	0.168767i	0.905183	+	0.425022i	$0.139734\pi$
$410$	−0.0668239	−	0.0796376i	−0.00330020	−	0.00393302i
$411$	3.35860	−	5.19701i	0.165667	−	0.256350i
$412$	−0.703029	+	0.837837i	−0.0346357	+	0.0412773i
$413$	−30.3886	+	3.54378i	−1.49533	+	0.174378i
$414$	−0.322490	+	0.0819286i	−0.0158495	+	0.00402657i
$415$	8.08556			0.396905
$416$	0.751635	−	0.273573i	0.0368520	−	0.0134130i
$417$	−7.72741	−	7.17391i	−0.378413	−	0.351308i
$418$	0.0647051	+	0.0771125i	0.00316483	+	0.00377170i
$419$	−37.3388	−	13.5902i	−1.82412	−	0.663926i	−0.994392	−	0.105761i	$-0.966272\pi$
$419$	−37.3388	−	13.5902i	−1.82412	−	0.663926i	−0.829730	−	0.558165i	$-0.811506\pi$
$420$	6.08115	+	13.8017i	0.296730	+	0.673453i
$421$	−1.45892	+	8.27397i	−0.0711036	+	0.403249i	0.928395	+	0.371594i	$0.121189\pi$
$421$	−1.45892	+	8.27397i	−0.0711036	+	0.403249i	−0.999499	+	0.0316544i	$0.989922\pi$
$422$		−	0.0899558i		−	0.00437898i
$423$	−4.08792	+	2.78383i	−0.198761	+	0.135354i
$424$	0.252936			0.0122837
$425$	−8.12665	+	2.95786i	−0.394201	+	0.143477i
$426$	0.177171	−	0.0907690i	0.00858394	−	0.00439777i
$427$	−1.83774	+	7.74491i	−0.0889345	+	0.374802i
$428$	−4.29404	−	5.11744i	−0.207560	−	0.247361i
$429$	35.2534	−	4.40805i	1.70205	−	0.212823i
$430$	0.0275733	−	0.0328606i	0.00132970	−	0.00158468i
$431$	4.45253	−	2.57067i	0.214471	−	0.123825i	−0.388917	−	0.921273i	$-0.627151\pi$
$431$	4.45253	−	2.57067i	0.214471	−	0.123825i	0.603387	+	0.797448i	$0.293817\pi$
$432$	−19.6903	−	6.63353i	−0.947350	−	0.319156i
$433$			19.5889i			0.941384i	0.882298	+	0.470692i	$0.155996\pi$
$433$			19.5889i			0.941384i	−0.882298	+	0.470692i	$0.844004\pi$
$434$	0.296582	−	0.148851i	0.0142364	−	0.00714508i
$435$	2.92899	+	23.4246i	0.140434	+	1.12312i
$436$	−1.33753	−	7.58552i	−0.0640562	−	0.363281i
$437$	−8.35753	+	7.01280i	−0.399795	+	0.335468i
$438$	0.0205097	−	0.408712i	0.000979993	−	0.0195290i
$439$	−11.0039	−	30.2330i	−0.525189	−	1.44294i	−0.864674	−	0.502333i	$-0.832475\pi$
$439$	−11.0039	−	30.2330i	−0.525189	−	1.44294i	0.339485	−	0.940611i	$-0.389747\pi$
$440$	−0.225644	+	0.390827i	−0.0107572	+	0.0186319i
$441$	12.8007	+	16.6476i	0.609557	+	0.792742i
$442$	−0.125802	−	0.217896i	−0.00598380	−	0.0103643i
$443$	−14.9004	+	17.7576i	−0.707939	+	0.843689i	−0.993400	−	0.114701i	$-0.963409\pi$
$443$	−14.9004	+	17.7576i	−0.707939	+	0.843689i	0.285461	+	0.958390i	$0.407853\pi$
$444$	−2.68323	−	0.613200i	−0.127340	−	0.0291012i
$445$	−2.05337	−	11.6453i	−0.0973392	−	0.552038i
$446$	−0.0104984	+	0.00880923i	−0.000497115	+	0.000417129i
$447$	−25.6685	−	23.8299i	−1.21408	−	1.12712i
$448$	1.23545	−	21.1158i	0.0583697	−	0.997626i
$449$	−16.3545	+	9.44229i	−0.771817	+	0.445609i	−0.833523	−	0.552485i	$-0.813679\pi$
$449$	−16.3545	+	9.44229i	−0.771817	+	0.445609i	0.0617051	+	0.998094i	$0.480346\pi$
$450$	0.0832834	+	0.0599457i	0.00392602	+	0.00282587i
$451$			19.4357i			0.915193i
$452$	−9.05281	−	1.59625i	−0.425808	−	0.0750815i
$453$	29.4826	−	15.1047i	1.38521	−	0.709680i
$454$	0.195932	−	0.0345481i	0.00919554	−	0.00162142i
$455$	−18.6313	+	5.57248i	−0.873450	+	0.261242i
$456$	0.150668	−	0.0188394i	0.00705568	−	0.000882236i
$457$	−3.19633	+	18.1273i	−0.149518	+	0.847960i	0.814109	+	0.580711i	$0.197226\pi$
$457$	−3.19633	+	18.1273i	−0.149518	+	0.847960i	−0.963628	+	0.267248i	$0.913886\pi$
$458$	−0.0919191	−	0.159209i	−0.00429510	−	0.00743933i
$459$	−2.93871	+	19.3894i	−0.137167	+	0.905019i
$460$	−21.1779	−	12.2271i	−0.987425	−	0.570090i
$461$	15.0689	−	5.48464i	0.701830	−	0.255445i	0.0336380	−	0.999434i	$-0.489291\pi$
$461$	15.0689	−	5.48464i	0.701830	−	0.255445i	0.668192	+	0.743989i	$0.267068\pi$
$462$	−0.0877616	+	0.301659i	−0.00408304	+	0.0140345i
$463$	27.7311	−	23.2691i	1.28877	−	1.08141i	0.296802	−	0.954939i	$-0.404080\pi$
$463$	27.7311	−	23.2691i	1.28877	−	1.08141i	0.991971	−	0.126469i	$-0.0403645\pi$
$464$	11.3261	−	31.1181i	0.525799	−	1.44462i
$465$	13.0004	−	20.1164i	0.602877	−	0.932877i
$466$	−0.0646339	+	0.366557i	−0.00299411	+	0.0169804i
$467$	−5.43272	−	9.40975i	−0.251396	−	0.435431i	0.712514	−	0.701658i	$-0.247556\pi$
$467$	−5.43272	−	9.40975i	−0.251396	−	0.435431i	−0.963911	+	0.266226i	$0.914223\pi$
$468$	11.6386	−	24.1341i	0.537993	−	1.11560i
$469$	11.3699	−	26.3393i	0.525015	−	1.21624i
$470$	0.0398846	+	0.00703274i	0.00183974	+	0.000324396i
$471$	20.1652	+	18.7208i	0.929163	+	0.862609i
$472$	−0.679916	+	0.119888i	−0.0312957	+	0.00551827i
$473$	−7.89786	+	1.39261i	−0.363144	+	0.0640321i
$474$	0.00918158	−	0.0401766i	0.000421724	−	0.00184537i
$475$	3.31348	+	0.584256i	0.152033	+	0.0268075i
$476$	−19.8340	+	2.31295i	−0.909092	+	0.106014i
$477$	9.10305	−	8.86918i	0.416800	−	0.406092i
$478$	−0.0853249	−	0.147787i	−0.00390267	−	0.00675962i
$479$	2.14052	−	12.1395i	0.0978027	−	0.554667i	−0.896050	−	0.443954i	$-0.853575\pi$
$479$	2.14052	−	12.1395i	0.0978027	−	0.554667i	0.993852	−	0.110713i	$-0.0353135\pi$
$480$	0.232783	+	0.454366i	0.0106251	+	0.0207389i
$481$	1.21382	−	3.33494i	0.0553453	−	0.152060i
$482$	0.0703504	−	0.0590310i	0.00320437	−	0.00268879i
$483$	−32.6941	−	9.51168i	−1.48763	−	0.432796i
$484$	18.9680	−	6.90379i	0.862182	−	0.313809i
$485$	−2.26560	−	1.30805i	−0.102876	−	0.0593953i
$486$	0.209783	−	0.100674i	0.00951596	−	0.00456666i
$487$	9.66499	+	16.7403i	0.437963	+	0.758574i	0.997532	−	0.0702097i	$-0.0223669\pi$
$487$	9.66499	+	16.7403i	0.437963	+	0.758574i	−0.559570	+	0.828783i	$0.689034\pi$
$488$	−0.0311918	+	0.176898i	−0.00141199	+	0.00800777i
$489$	−11.7395	+	27.8281i	−0.530877	+	1.25843i
$490$	0.0200542	−	0.170791i	0.000905955	−	0.00771555i
$491$	−32.7847	+	5.78082i	−1.47955	+	0.260885i	−0.854399	−	0.519617i	$-0.826074\pi$
$491$	−32.7847	+	5.78082i	−1.47955	+	0.260885i	−0.625153	+	0.780502i	$0.714963\pi$
$492$	12.3107	+	7.95584i	0.555008	+	0.358677i
$493$	−30.7807	−	5.42746i	−1.38629	−	0.244441i
$494$			0.0978871i			0.00440415i
$495$	5.58348	+	21.9778i	0.250959	+	0.987830i
$496$	−29.0973	+	16.7993i	−1.30651	+	0.754311i
$497$	20.3365	+	1.18986i	0.912218	+	0.0533727i
$498$	0.121388	−	0.0374070i	0.00543953	−	0.00167625i
$499$	−15.4221	+	12.9407i	−0.690389	+	0.579305i	−0.919021	−	0.394208i	$-0.871019\pi$
$499$	−15.4221	+	12.9407i	−0.690389	+	0.579305i	0.228633	+	0.973513i	$0.426575\pi$
$500$	4.16710	+	23.6328i	0.186358	+	1.05689i
$501$	4.82671	+	15.6630i	0.215641	+	0.699770i
$502$	0.121241	−	0.144490i	0.00541127	−	0.00644890i
$503$	5.39577	+	9.34574i	0.240585	+	0.416706i	0.960881	−	0.276961i	$-0.0893273\pi$
$503$	5.39577	+	9.34574i	0.240585	+	0.416706i	−0.720296	+	0.693667i	$0.755994\pi$
$504$	0.310313	+	0.358160i	0.0138225	+	0.0159537i
$505$	1.90181	−	3.29403i	0.0846294	−	0.146582i
$506$	−0.174223	−	0.478673i	−0.00774514	−	0.0212796i
$507$	10.1049	+	6.53037i	0.448776	+	0.290024i
$508$	−8.06407	+	6.76656i	−0.357785	+	0.300218i
$509$	−5.96937	−	33.8540i	−0.264588	−	1.50055i	−0.770207	−	0.637794i	$-0.779847\pi$
$509$	−5.96937	−	33.8540i	−0.264588	−	1.50055i	0.505619	−	0.862757i	$-0.331264\pi$
$510$	0.128037	−	0.0969292i	0.00566957	−	0.00429210i
$511$	23.0212	−	34.9819i	1.01840	−	1.54751i
$512$		−	1.19363i		−	0.0527514i
$513$	4.76187	−	5.96118i	0.210242	−	0.263193i
$514$	−0.193442	+	0.111684i	−0.00853237	+	0.00492616i
$515$	0.578574	−	0.689518i	0.0254950	−	0.0303838i
$516$	−2.35083	+	5.57259i	−0.103490	+	0.245320i
$517$	−4.86697	−	5.80022i	−0.214049	−	0.255094i
$518$	0.0228213	+	0.0215422i	0.00100271	+	0.000946511i
$519$	−2.21094	−	1.42883i	−0.0970495	−	0.0627187i
$520$	−0.412377	+	0.150093i	−0.0180839	+	0.00658200i
$521$	32.8374			1.43863			0.719317	−	0.694682i	$-0.244455\pi$
$521$	32.8374			1.43863			0.719317	+	0.694682i	$0.244455\pi$
$522$	0.152344	+	0.338122i	0.00666793	+	0.0147992i
$523$			2.32319i			0.101586i	0.998709	+	0.0507929i	$0.0161749\pi$
$523$			2.32319i			0.101586i	−0.998709	+	0.0507929i	$0.983825\pi$
$524$	−5.25638	+	29.8104i	−0.229626	+	1.30227i
$525$	4.23398	+	9.60937i	0.184786	+	0.419387i
$526$	−0.223500	−	0.0813475i	−0.00974508	−	0.00354692i
$527$	20.3839	+	24.2926i	0.887938	+	1.05820i
$528$	7.08667	−	31.0097i	0.308408	−	1.34953i
$529$	30.2661	−	11.0160i	1.31592	−	0.478955i
$530$	−0.104074			−0.00452069
$531$	−20.2660	+	28.1559i	−0.879470	+	1.22186i
$532$	7.13258	+	3.07893i	0.309237	+	0.133489i
$533$	−12.1485	+	14.4780i	−0.526210	+	0.627113i
$534$	−0.0847027	−	0.165330i	−0.00366544	−	0.00715452i
$535$	3.53388	+	4.21152i	0.152783	+	0.182080i
$536$	0.221422	−	0.608352i	0.00956397	−	0.0262768i
$537$	13.7140	+	5.78533i	0.591802	+	0.249655i
$538$	−0.0504750	−	0.138679i	−0.00217613	−	0.00597888i
$539$	−23.3964	+	22.0500i	−1.00776	+	0.949761i
$540$	16.2064	+	5.45983i	0.697413	+	0.234954i
$541$	9.54866	−	16.5388i	0.410529	−	0.711057i	−0.584419	−	0.811452i	$-0.698677\pi$
$541$	9.54866	−	16.5388i	0.410529	−	0.711057i	0.994948	+	0.100395i	$0.0320108\pi$
$542$	−0.0254685	−	0.0213706i	−0.00109396	−	0.000917945i
$543$	−16.9312	−	7.14253i	−0.726587	−	0.306515i
$544$	−0.665664	+	0.117374i	−0.0285401	+	0.00503239i
$545$	1.10075	+	6.24269i	0.0471511	+	0.267407i
$546$	−0.253931	+	0.169855i	−0.0108672	+	0.00726914i
$547$	18.5854	+	15.5950i	0.794655	+	0.666795i	0.946893	−	0.321549i	$-0.104204\pi$
$547$	18.5854	+	15.5950i	0.794655	+	0.666795i	−0.152238	+	0.988344i	$0.548648\pi$
$548$	6.18713	−	3.57214i	0.264301	−	0.152594i
$549$	5.08031	+	7.46019i	0.216822	+	0.318393i
$550$	−0.0785475	+	0.136048i	−0.00334928	+	0.00580112i
$551$	9.31510	+	7.81630i	0.396837	+	0.332985i
$552$	−0.749062	−	0.171184i	−0.0318822	−	0.00728606i
$553$	2.89496	−	3.06685i	0.123106	−	0.130416i
$554$	0.0441683	−	0.121351i	0.00187653	−	0.00515573i
$555$	2.20823	+	0.504648i	0.0937341	+	0.0214211i
$556$	−4.16372	−	11.4397i	−0.176581	−	0.485153i
$557$	14.3493	+	8.28455i	0.607998	+	0.351028i	0.772181	−	0.635402i	$-0.219166\pi$
$557$	14.3493	+	8.28455i	0.607998	+	0.351028i	−0.164184	+	0.986430i	$0.552499\pi$
$558$	0.102107	−	0.362152i	0.00432254	−	0.0153311i
$559$	−6.75372	−	3.89926i	−0.285652	−	0.164921i
$560$	−1.01697	+	17.3816i	−0.0429750	+	0.734506i
$561$	−29.9851	−	1.50470i	−1.26597	−	0.0635283i
$562$	−0.419831	−	0.152806i	−0.0177095	−	0.00644573i
$563$	37.2905	+	13.5726i	1.57161	+	0.572019i	0.973358	−	0.229290i	$-0.0736405\pi$
$563$	37.2905	+	13.5726i	1.57161	+	0.572019i	0.598251	+	0.801309i	$0.295863\pi$
$564$	−5.66614	+	0.708489i	−0.238587	+	0.0298328i
$565$	7.45023	+	1.31368i	0.313433	+	0.0552668i
$566$	−0.146173			−0.00614411
$567$	23.7269	+	2.00891i	0.996435	+	0.0843663i
$568$	0.459704			0.0192888
$569$	−6.95833	−	1.22694i	−0.291708	−	0.0514361i	0.0258789	−	0.999665i	$-0.491762\pi$
$569$	−6.95833	−	1.22694i	−0.291708	−	0.0514361i	−0.317587	+	0.948229i	$0.602873\pi$
$570$	−0.0619945	+	0.00775174i	−0.00259666	+	0.000324685i
$571$	20.5987	+	7.49733i	0.862030	+	0.313753i	0.734935	−	0.678137i	$-0.237212\pi$
$571$	20.5987	+	7.49733i	0.862030	+	0.313753i	0.127095	+	0.991891i	$0.459435\pi$
$572$	38.5458	+	14.0295i	1.61168	+	0.586603i
$573$	17.0082	+	0.853497i	0.710528	+	0.0356554i
$574$	−0.0749668	−	0.149370i	−0.00312905	−	0.00623457i
$575$	−14.7450	−	8.51305i	−0.614910	−	0.355019i
$576$	−16.7371	−	17.1785i	−0.697380	−	0.715769i
$577$	3.83091	+	2.21178i	0.159483	+	0.0920775i	0.577617	−	0.816308i	$-0.303983\pi$
$577$	3.83091	+	2.21178i	0.159483	+	0.0920775i	−0.418134	+	0.908385i	$0.637316\pi$
$578$	−0.0140710	−	0.0386599i	−0.000585278	−	0.00160804i
$579$	32.9463	+	7.52923i	1.36920	+	0.312904i
$580$	−9.32210	+	25.6122i	−0.387079	+	1.06349i
$581$	12.6473	+	3.00099i	0.524698	+	0.124502i
$582$	−0.0400649	−	0.00915605i	−0.00166074	−	0.000379531i
$583$	14.9051	+	12.5068i	0.617305	+	0.517980i
$584$	0.472507	−	0.818406i	0.0195525	−	0.0338659i
$585$	−9.57824	+	19.8617i	−0.396012	+	0.821180i
$586$	−0.134360	+	0.0775728i	−0.00555036	+	0.00320450i
$587$	−28.2005	−	23.6630i	−1.16396	−	0.976677i	−0.164007	−	0.986459i	$-0.552442\pi$
$587$	−28.2005	−	23.6630i	−1.16396	−	0.976677i	−0.999952	+	0.00978187i	$0.996886\pi$
$588$	4.38946	+	23.8454i	0.181018	+	0.983366i
$589$	−2.14239	−	12.1501i	−0.0882755	−	0.500635i
$590$	0.279761	−	0.0493294i	0.0115176	−	0.00203086i
$591$	6.90545	+	2.91311i	0.284052	+	0.119829i
$592$	−2.43410	−	2.04245i	−0.100041	−	0.0839444i
$593$	−15.9700	+	27.6608i	−0.655809	+	1.13589i	0.325882	+	0.945411i	$0.394339\pi$
$593$	−15.9700	+	27.6608i	−0.655809	+	1.13589i	−0.981690	+	0.190484i	$0.938994\pi$
$594$	0.185503	+	0.304121i	0.00761126	+	0.0124782i
$595$	16.3229	−	1.90350i	0.669174	−	0.0780359i
$596$	−13.8308	−	37.9999i	−0.566533	−	1.55654i
$597$	−2.70673	−	1.14185i	−0.110779	−	0.0467328i
$598$	0.169418	−	0.465472i	0.00692801	−	0.0190346i
$599$	−24.7052	−	29.4425i	−1.00943	−	1.20299i	−0.979086	−	0.203446i	$-0.934786\pi$
$599$	−24.7052	−	29.4425i	−1.00943	−	1.20299i	−0.0303390	−	0.999540i	$-0.509659\pi$
$600$	0.108048	+	0.210897i	0.00441103	+	0.00860982i
$601$	−11.7434	+	13.9953i	−0.479025	+	0.570880i	−0.950391	−	0.311058i	$-0.899317\pi$
$601$	−11.7434	+	13.9953i	−0.479025	+	0.570880i	0.471366	+	0.881938i	$0.343761\pi$
$602$	0.0553260	−	0.0411659i	0.00225492	−	0.00167780i
$603$	−13.3629	−	29.6584i	−0.544180	−	1.20778i
$604$	38.2471			1.55625
$605$	−15.6102	+	5.68164i	−0.634644	+	0.230991i
$606$	0.0133123	−	0.0582516i	0.000540774	−	0.00236631i
$607$	12.5091	+	14.9077i	0.507727	+	0.605085i	0.957633	−	0.287990i	$-0.0929871\pi$
$607$	12.5091	+	14.9077i	0.507727	+	0.605085i	−0.449906	+	0.893076i	$0.648543\pi$
$608$	0.247113	+	0.0899419i	0.0100218	+	0.00364763i
$609$	−4.11267	+	37.7274i	−0.166654	+	1.52879i
$610$	0.0128343	−	0.0727870i	0.000519646	−	0.00294706i
$611$		−	7.36284i		−	0.297869i
$612$	−13.2272	+	18.3768i	−0.534678	+	0.742837i
$613$	26.4037			1.06643			0.533217	−	0.845979i	$-0.320983\pi$
$613$	26.4037			1.06643			0.533217	+	0.845979i	$0.320983\pi$
$614$	−0.239422	+	0.0871426i	−0.00966230	+	0.00351679i
$615$	−10.1314	−	6.54745i	−0.408536	−	0.264019i
$616$	−0.498005	+	0.527575i	−0.0200652	+	0.0212566i
$617$	16.7822	+	20.0003i	0.675628	+	0.805182i	0.989538	−	0.144271i	$-0.0460836\pi$
$617$	16.7822	+	20.0003i	0.675628	+	0.805182i	−0.313910	+	0.949453i	$0.601639\pi$
$618$	0.00549612	−	0.0130284i	0.000221087	−	0.000524080i
$619$	−18.0250	+	21.4814i	−0.724486	+	0.863409i	−0.995058	−	0.0992909i	$-0.968343\pi$
$619$	−18.0250	+	21.4814i	−0.724486	+	0.863409i	0.270573	+	0.962700i	$0.412787\pi$
$620$	23.9489	−	13.8269i	0.961813	−	0.555303i
$621$	−32.9609	+	20.1049i	−1.32268	+	0.806784i
$622$			0.496518i			0.0199085i
$623$	1.11034	−	18.9774i	0.0444849	−	0.760313i
$624$	24.6620	−	18.6701i	0.987268	−	0.747403i
$625$	−1.43988	−	8.16595i	−0.0575951	−	0.326638i
$626$	0.0111744	−	0.00937644i	0.000446619	−	0.000374758i
$627$	9.81013	+	6.33985i	0.391779	+	0.253189i
$628$	10.8655	+	29.8528i	0.433581	+	1.19125i
$629$	−1.49953	+	2.59725i	−0.0597900	+	0.103559i
$630$	−0.127683	−	0.147370i	−0.00508700	−	0.00587136i
$631$	−19.6263	−	33.9938i	−0.781312	−	1.35327i	−0.931178	−	0.364565i	$-0.881218\pi$
$631$	−19.6263	−	33.9938i	−0.781312	−	1.35327i	0.149866	−	0.988706i	$-0.452116\pi$
$632$	0.0611745	−	0.0729050i	0.00243339	−	0.00290000i
$633$	−3.07393	−	9.97511i	−0.122178	−	0.396475i
$634$	−0.00877876	−	0.0497868i	−0.000348649	−	0.00197729i
$635$	6.63652	−	5.56870i	0.263362	−	0.220987i
$636$	14.0231	−	4.32137i	0.556054	−	0.171354i
$637$	−31.2110	+	1.80127i	−1.23663	+	0.0713691i
$638$	−0.491692	+	0.283879i	−0.0194663	+	0.0112389i
$639$	16.5445	−	16.1195i	0.654491	−	0.637676i
$640$			0.785904i			0.0310656i
$641$	−29.4709	−	5.19651i	−1.16403	−	0.205250i	−0.441937	−	0.897046i	$-0.645708\pi$
$641$	−29.4709	−	5.19651i	−1.16403	−	0.205250i	−0.722092	+	0.691797i	$0.756819\pi$
$642$	0.0725381	+	0.0468781i	0.00286285	+	0.00185013i
$643$	−1.69315	+	0.298548i	−0.0667714	+	0.0117736i	−0.206934	−	0.978355i	$-0.566349\pi$
$643$	−1.69315	+	0.298548i	−0.0667714	+	0.0117736i	0.140163	+	0.990128i	$0.455237\pi$
$644$	−28.5879	−	26.9856i	−1.12652	−	1.06338i
$645$	1.93468	−	4.58610i	0.0761778	−	0.180577i
$646$	0.0143641	−	0.0814627i	0.000565147	−	0.00320511i
$647$	−23.2767	−	40.3164i	−0.915102	−	1.58500i	−0.806752	−	0.590890i	$-0.798777\pi$
$647$	−23.2767	−	40.3164i	−0.915102	−	1.58500i	−0.108350	−	0.994113i	$-0.534557\pi$
$648$	0.537160	+	0.0139826i	0.0211017	+	0.000549288i
$649$	−45.9942	−	26.5548i	−1.80543	−	1.04237i
$650$	−0.143550	+	0.0522479i	−0.00563049	+	0.00204933i
$651$	27.8012	−	26.6406i	1.08962	−	1.04413i
$652$	−26.7131	+	22.4150i	−1.04617	+	0.877837i
$653$	−6.57724	+	18.0708i	−0.257387	+	0.707165i	0.741939	+	0.670467i	$0.233906\pi$
$653$	−6.57724	+	18.0708i	−0.257387	+	0.707165i	−0.999326	+	0.0366983i	$0.988316\pi$
$654$	0.0454067	+	0.0886286i	0.00177554	+	0.00346565i
$655$	4.32586	−	24.5332i	0.169026	−	0.958591i
$656$	8.46075	+	14.6544i	0.330337	+	0.572160i
$657$	−11.6920	−	46.0224i	−0.456149	−	1.79551i
$658$	0.0597765	+	0.0258038i	0.00233033	+	0.00100594i
$659$	20.4588	+	3.60744i	0.796962	+	0.140526i	0.557279	−	0.830325i	$-0.311845\pi$
$659$	20.4588	+	3.60744i	0.796962	+	0.140526i	0.239683	+	0.970851i	$0.422957\pi$
$660$	−5.83280	+	25.5231i	−0.227041	+	0.993484i
$661$	13.9006	−	2.45105i	0.540671	−	0.0953350i	0.103358	−	0.994644i	$-0.467041\pi$
$661$	13.9006	−	2.45105i	0.540671	−	0.0953350i	0.437313	+	0.899309i	$0.355930\pi$
$662$	0.0893478	−	0.0157544i	0.00347260	−	0.000612313i
$663$	−21.3959	−	19.8634i	−0.830949	−	0.771430i
$664$	0.288870	+	0.0509356i	0.0112103	+	0.00197668i
$665$	−5.86993	−	2.53388i	−0.227626	−	0.0982597i
$666$	0.0354867	−	0.00263989i	0.00137508	−	0.000102294i
$667$	−30.7670	−	53.2901i	−1.19130	−	2.06340i
$668$	−3.28598	+	18.6357i	−0.127138	+	0.721038i
$669$	−0.863134	+	1.33559i	−0.0333707	+	0.0516370i
$670$	−0.0911072	+	0.250315i	−0.00351978	+	0.00967051i
$671$	−10.5850	+	8.88191i	−0.408631	+	0.342882i
$672$	0.195475	+	0.797110i	0.00754062	+	0.0307492i
$673$	−6.36430	+	2.31642i	−0.245326	+	0.0892913i	−0.461757	−	0.887007i	$-0.652781\pi$
$673$	−6.36430	+	2.31642i	−0.245326	+	0.0892913i	0.216431	+	0.976298i	$0.430558\pi$
$674$	0.221066	+	0.127633i	0.00851515	+	0.00491623i
$675$	11.2836	+	3.80139i	0.434308	+	0.146315i
$676$	6.94558	+	12.0301i	0.267138	+	0.462696i
$677$	−5.48142	+	31.0867i	−0.210668	+	1.19476i	0.677599	+	0.735431i	$0.263020\pi$
$677$	−5.48142	+	31.0867i	−0.210668	+	1.19476i	−0.888267	+	0.459327i	$0.848091\pi$
$678$	0.117927	−	0.0147456i	0.00452898	−	0.000566299i
$679$	−3.05832	−	2.88691i	−0.117368	−	0.110789i
$680$	0.365209	−	0.0643962i	0.0140051	−	0.00246948i
$681$	20.5461	−	10.5263i	0.787329	−	0.403369i
$682$	0.567294	+	0.100029i	0.0217228	+	0.00383032i
$683$		−	24.5110i		−	0.937886i	−0.883229	−	0.468943i	$-0.844635\pi$
$683$		−	24.5110i		−	0.937886i	0.883229	−	0.468943i	$-0.155365\pi$
$684$	8.03138	−	3.61862i	0.307087	−	0.138361i
$685$	−5.09185	+	2.93978i	−0.194550	+	0.112323i
$686$	0.0947582	−	0.259705i	0.00361789	−	0.00991558i
$687$	−15.6332	−	14.5134i	−0.596445	−	0.553723i
$688$	−5.34872	+	4.48811i	−0.203918	+	0.171107i
$689$	3.28552	+	18.6331i	0.125168	+	0.709866i
$690$	0.308212	+	0.0704359i	0.0117334	+	0.00268145i
$691$	17.3675	−	20.6978i	0.660691	−	0.787381i	−0.326793	−	0.945096i	$-0.605968\pi$
$691$	17.3675	−	20.6978i	0.660691	−	0.787381i	0.987485	+	0.157714i	$0.0504125\pi$
$692$	−1.51968	−	2.63216i	−0.0577695	−	0.100060i
$693$	0.576392	+	36.4496i	0.0218953	+	1.38461i
$694$	0.157307	−	0.272465i	0.00597131	−	0.0103426i
$695$	3.42663	+	9.41460i	0.129980	+	0.357116i
$696$	−0.0429219	+	0.855334i	−0.00162695	+	0.0324213i
$697$	12.2347	−	10.2661i	0.463420	−	0.388856i
$698$	−0.0168631	−	0.0956353i	−0.000638277	−	0.00361985i
$699$	5.35865	+	42.8558i	0.202683	+	1.62095i
$700$	−0.708143	+	12.1032i	−0.0267653	+	0.457458i
$701$		−	28.6921i		−	1.08369i	−0.840479	−	0.541843i	$-0.817727\pi$
$701$		−	28.6921i		−	1.08369i	0.840479	−	0.541843i	$-0.182273\pi$
$702$	−0.0519096	+	0.342495i	−0.00195920	+	0.0129267i
$703$	1.01047	−	0.583393i	0.0381104	−	0.0220031i
$704$	23.6018	−	28.1275i	0.889525	−	1.06009i
$705$	4.66308	−	0.583068i	0.175622	−	0.0219596i
$706$	−0.183193	−	0.218321i	−0.00689457	−	0.00821662i
$707$	4.19737	−	4.44659i	0.157858	−	0.167231i
$708$	−35.6472	+	18.2630i	−1.33971	+	0.686365i
$709$	35.7630	−	13.0167i	1.34311	−	0.488852i	0.432319	−	0.901721i	$-0.357696\pi$
$709$	35.7630	−	13.0167i	1.34311	−	0.488852i	0.910790	+	0.412869i	$0.135473\pi$
$710$	−0.189152			−0.00709874
$711$	−0.354762	−	4.76889i	−0.0133046	−	0.178847i
$712$		−	0.428981i		−	0.0160768i
$713$	−10.8413	+	61.4838i	−0.406008	+	2.30259i
$714$	0.236249	−	0.104093i	0.00884138	−	0.00389560i
$715$	−31.7221	−	11.5459i	−1.18634	−	0.431793i
$716$	11.0463	+	13.1645i	0.412820	+	0.491980i
$717$	−14.5117	−	13.4723i	−0.541949	−	0.503131i
$718$	0.281961	−	0.102625i	0.0105227	−	0.00382994i
$719$	−12.3232			−0.459577			−0.229789	−	0.973241i	$-0.573803\pi$
$719$	−12.3232			−0.459577			−0.229789	+	0.973241i	$0.573803\pi$
$720$	13.7773	+	14.1406i	0.513449	+	0.526988i
$721$	1.16091	−	0.863790i	0.0432346	−	0.0321692i
$722$	0.161617	−	0.192607i	0.00601475	−	0.00716810i
$723$	5.78390	−	8.94986i	0.215105	−	0.332849i
$724$	−13.6377	−	16.2528i	−0.506842	−	0.604030i
$725$	−6.49047	+	17.8324i	−0.241050	+	0.662280i
$726$	−0.208069	+	0.157517i	−0.00772217	+	0.00584600i
$727$	−9.28805	−	25.5187i	−0.344475	−	0.946437i	−0.984079	−	0.177732i	$-0.943124\pi$
$727$	−9.28805	−	25.5187i	−0.344475	−	0.946437i	0.639604	−	0.768705i	$-0.279098\pi$
$728$	−0.700739	+	0.0817168i	−0.0259711	+	0.00302863i
$729$	19.8224	−	18.3322i	0.734164	−	0.678972i
$730$	−0.194420	+	0.336745i	−0.00719579	+	0.0124635i
$731$	5.04834	+	4.23606i	0.186720	+	0.156676i
$732$	1.29295	+	10.3403i	0.0477887	+	0.382190i
$733$	−45.2315	+	7.97554i	−1.67066	+	0.294583i	−0.927304	−	0.374308i	$-0.877880\pi$
$733$	−45.2315	+	7.97554i	−1.67066	+	0.294583i	−0.743360	+	0.668891i	$0.766769\pi$
$734$	0.00160288	+	0.00909040i	5.91635e−5	+	0.000335533i
$735$	−3.61241	−	19.6241i	−0.133246	−	0.723846i
$736$	−1.01940	−	0.855382i	−0.0375757	−	0.0315298i
$737$	43.1289	−	24.9005i	1.58867	−	0.917221i
$738$	−0.182393	−	0.0514248i	−0.00671398	−	0.00189297i
$739$	−13.8133	+	23.9253i	−0.508129	+	0.880106i	0.491826	+	0.870693i	$0.336330\pi$
$739$	−13.8133	+	23.9253i	−0.508129	+	0.880106i	−0.999956	+	0.00941271i	$0.997004\pi$
$740$	2.00343	+	1.68107i	0.0736474	+	0.0617975i
$741$	3.34496	+	10.8546i	0.122880	+	0.398754i
$742$	−0.162791	−	0.0386276i	−0.00597624	−	0.00141806i
$743$	3.93643	−	10.8153i	0.144414	−	0.396773i	−0.846306	−	0.532698i	$-0.821178\pi$
$743$	3.93643	−	10.8153i	0.144414	−	0.396773i	0.990719	+	0.135925i	$0.0434005\pi$
$744$	0.591184	−	0.636796i	0.0216739	−	0.0233461i
$745$	11.3824	+	31.2729i	0.417019	+	1.14575i
$746$	0.416599	+	0.240524i	0.0152528	+	0.00880620i
$747$	12.1823	−	8.29605i	0.445729	−	0.303536i
$748$	−30.0195	−	17.3318i	−1.09762	−	0.633712i
$749$	3.96451	+	7.89919i	0.144860	+	0.288630i
$750$	−0.141465	−	0.276124i	−0.00516558	−	0.0100826i
$751$	10.9144	+	3.97250i	0.398270	+	0.144959i	0.533387	−	0.845871i	$-0.320919\pi$
$751$	10.9144	+	3.97250i	0.398270	+	0.144959i	−0.135117	+	0.990830i	$0.543141\pi$
$752$	−6.19461	−	2.25465i	−0.225894	−	0.0822188i
$753$	8.50688	−	20.1653i	0.310008	−	0.734865i
$754$	−0.543712	−	0.0958710i	−0.0198008	−	0.00349142i
$755$	−31.4764			−1.14554
$756$	23.3233	+	14.5552i	0.848260	+	0.529369i
$757$	25.0813			0.911595			0.455798	−	0.890083i	$-0.349354\pi$
$757$	25.0813			0.911595			0.455798	+	0.890083i	$0.349354\pi$
$758$	−0.126470	−	0.0223000i	−0.00459358	−	0.000809972i
$759$	−35.6764	−	47.1261i	−1.29497	−	1.71057i
$760$	−0.135576	−	0.0493457i	−0.00491786	−	0.00178996i
$761$	−24.4966	−	8.91602i	−0.888000	−	0.323205i	−0.142566	−	0.989785i	$-0.545535\pi$
$761$	−24.4966	−	8.91602i	−0.888000	−	0.323205i	−0.745434	+	0.666580i	$0.767758\pi$
$762$	0.0738707	−	0.114306i	0.00267605	−	0.00414086i
$763$	−0.595223	+	10.1732i	−0.0215485	+	0.368296i
$764$	17.0277	+	9.83096i	0.616041	+	0.355672i
$765$	10.8857	−	15.1236i	0.393572	−	0.546795i
$766$	−0.157017	−	0.0906538i	−0.00567325	−	0.00327545i
$767$	−17.6636	−	48.5303i	−0.637795	−	1.75233i
$768$	−8.15218	−	26.4543i	−0.294166	−	0.954589i
$769$	3.57920	−	9.83378i	0.129069	−	0.354615i	−0.858279	−	0.513184i	$-0.828466\pi$
$769$	3.57920	−	9.83378i	0.129069	−	0.354615i	0.987348	+	0.158569i	$0.0506880\pi$
$770$	0.204911	−	0.217078i	0.00738448	−	0.00782295i
$771$	−17.6342	+	18.9947i	−0.635079	+	0.684078i
$772$	29.8907	+	25.0813i	1.07579	+	0.902694i
$773$	14.0939	−	24.4113i	0.506921	−	0.878013i	−0.493047	−	0.870003i	$-0.664117\pi$
$773$	14.0939	−	24.4113i	0.506921	−	0.878013i	0.999968	−	0.00801007i	$-0.00254971\pi$
$774$	0.00782809	−	0.0778014i	0.000281375	−	0.00279651i
$775$	16.6744	−	9.62695i	0.598961	−	0.345810i
$776$	−0.0727022	−	0.0610044i	−0.00260986	−	0.00218993i
$777$	3.26677	+	1.60895i	0.117195	+	0.0577209i
$778$	0.0833881	+	0.472917i	0.00298961	+	0.0169549i
$779$	−6.11922	+	1.07898i	−0.219244	+	0.0386586i
$780$	−20.2984	+	15.3667i	−0.726800	+	0.550217i
$781$	27.0895	+	22.7308i	0.969339	+	0.813372i
$782$	−0.209295	+	0.362510i	−0.00748439	+	0.0129633i
$783$	28.4474	+	32.2881i	1.01663	+	1.15388i
$784$	−8.04199	+	26.8105i	−0.287214	+	0.957518i
$785$	−8.94204	−	24.5680i	−0.319155	−	0.876871i
$786$	−0.0485563	−	0.388329i	−0.00173195	−	0.0138512i
$787$	−12.0231	+	33.0332i	−0.428577	+	1.17751i	0.518100	+	0.855320i	$0.326640\pi$
$787$	−12.0231	+	33.0332i	−0.428577	+	1.17751i	−0.946677	+	0.322185i	$0.895583\pi$
$788$	5.56220	+	6.62877i	0.198145	+	0.236140i
$789$	−27.5635	−	1.38318i	−0.981286	−	0.0492424i
$790$	−0.0251711	+	0.0299978i	−0.000895548	+	0.00106727i
$791$	11.1659	+	4.82001i	0.397015	+	0.171380i
$792$	0.0610279	+	0.820368i	0.00216853	+	0.0291505i
$793$	−13.4367			−0.477152
$794$	−0.162165	+	0.0590231i	−0.00575501	+	0.00209465i
$795$	−11.5407	+	3.55638i	−0.409306	+	0.126132i
$796$	−2.18021	−	2.59827i	−0.0772755	−	0.0920934i
$797$	−3.03842	−	1.10589i	−0.107626	−	0.0391728i	0.287646	−	0.957737i	$-0.407127\pi$
$797$	−3.03842	−	1.10589i	−0.107626	−	0.0391728i	−0.395272	+	0.918564i	$0.629350\pi$
$798$	−0.0998477	−	0.0108844i	−0.00353457	−	0.000385304i
$799$	−1.08043	+	6.12744i	−0.0382229	+	0.216773i
$800$			0.410395i			0.0145096i
$801$	−15.0422	−	15.4388i	−0.531489	−	0.545504i
$802$	−0.00154406			−5.45226e−5
$803$	68.3113	−	24.8633i	2.41065	−	0.877406i
$804$	1.88235	−	37.5108i	0.0663853	−	1.32290i
$805$	23.5271	+	22.2085i	0.829222	+	0.782745i
$806$	0.360063	+	0.429107i	0.0126827	+	0.0151146i
$807$	−10.3360	−	13.6532i	−0.363845	−	0.480614i
$808$	0.0886963	−	0.105704i	0.00312032	−	0.00371866i
$809$	−6.10355	+	3.52388i	−0.214589	+	0.123893i	−0.603442	−	0.797407i	$-0.706205\pi$
$809$	−6.10355	+	3.52388i	−0.214589	+	0.123893i	0.388853	+	0.921300i	$0.372871\pi$
$810$	−0.221022	−	0.00575333i	−0.00776593	−	0.000202152i
$811$		−	27.1164i		−	0.952186i	−0.879395	−	0.476093i	$-0.842053\pi$
$811$		−	27.1164i		−	0.952186i	0.879395	−	0.476093i	$-0.157947\pi$
$812$	−24.0875	+	36.6023i	−0.845307	+	1.28449i
$813$	−3.55444	−	1.49946i	−0.124660	−	0.0525885i
$814$	0.00945999	+	0.0536502i	0.000331572	+	0.00188044i
$815$	21.9842	−	18.4469i	0.770072	−	0.646167i
$816$	−23.2636	+	11.9186i	−0.814390	+	0.417233i
$817$	−0.876907	−	2.40928i	−0.0306791	−	0.0842901i
$818$	0.0271086	−	0.0469534i	0.000947829	−	0.00164169i
$819$	−22.3539	+	27.5123i	−0.781107	+	0.961357i
$820$	−6.96375	−	12.0616i	−0.243185	−	0.421208i
$821$	−24.7699	+	29.5196i	−0.864475	+	1.03024i	0.134750	+	0.990880i	$0.456977\pi$
$821$	−24.7699	+	29.5196i	−0.864475	+	1.03024i	−0.999225	+	0.0393621i	$0.987467\pi$
$822$	−0.0628431	+	0.0676917i	−0.00219190	+	0.00236102i
$823$	5.54143	+	31.4270i	0.193162	+	1.09548i	0.915012	+	0.403427i	$0.132181\pi$
$823$	5.54143	+	31.4270i	0.193162	+	1.09548i	−0.721850	+	0.692050i	$0.756708\pi$
$824$	0.0250142	−	0.0209894i	0.000871411	−	0.000731200i
$825$	−4.06106	+	17.7703i	−0.141388	+	0.618683i
$826$	0.455906	+	0.0266744i	0.0158630	+	0.000928123i
$827$	19.5503	−	11.2874i	0.679831	−	0.392501i	−0.119960	−	0.992779i	$-0.538277\pi$
$827$	19.5503	−	11.2874i	0.679831	−	0.392501i	0.799791	+	0.600278i	$0.204943\pi$
$828$	−44.4537	+	3.30695i	−1.54487	+	0.114924i
$829$			33.2803i			1.15587i	0.816082	+	0.577936i	$0.196142\pi$
$829$			33.2803i			1.15587i	−0.816082	+	0.577936i	$0.803858\pi$
$830$	−0.118860	−	0.0209582i	−0.00412568	−	0.000727469i
$831$	0.751007	−	14.9658i	0.0260522	−	0.519159i
$832$	35.1628	−	6.20014i	1.21905	−	0.214951i
$833$	26.2385	+	3.08090i	0.909109	+	0.106747i
$834$	0.0949996	+	0.125488i	0.00328957	+	0.00434529i
$835$	2.70428	−	15.3367i	0.0935854	−	0.530749i
$836$	6.74295	+	11.6791i	0.233210	+	0.403931i
$837$	−1.05276	−	43.6478i	−0.0363886	−	1.50869i
$838$	0.513663	+	0.296564i	0.0177442	+	0.0102446i
$839$	28.7046	−	10.4476i	0.990993	−	0.360692i	0.204888	−	0.978785i	$-0.434317\pi$
$839$	28.7046	−	10.4476i	0.990993	−	0.360692i	0.786105	+	0.618093i	$0.212095\pi$
$840$	−0.107245	−	0.437325i	−0.00370032	−	0.0150892i
$841$	−30.3234	+	25.4443i	−1.04563	+	0.877391i
$842$	0.0428930	−	0.117848i	0.00147819	−	0.00406130i
$843$	−51.7762	−	2.59821i	−1.78327	−	0.0894870i
$844$	2.09271	−	11.8683i	0.0720339	−	0.408525i
$845$	−5.71603	−	9.90046i	−0.196638	−	0.340586i
$846$	0.0673091	−	0.0303268i	0.00231414	−	0.00104266i
$847$	−26.5259	+	3.09332i	−0.911441	+	0.106288i
$848$	16.6828	+	2.94163i	0.572890	+	0.101016i
$849$	−16.2090	+	4.99496i	−0.556290	+	0.171427i
$850$	0.127131	−	0.0224166i	0.00436054	−	0.000768882i
$851$	−5.81466	+	1.02528i	−0.199324	+	0.0351462i
$852$	25.4866	−	7.85397i	0.873158	−	0.269073i
$853$	−39.5220	−	6.96880i	−1.35321	−	0.238607i	−0.550429	−	0.834882i	$-0.685536\pi$
$853$	−39.5220	−	6.96880i	−1.35321	−	0.238607i	−0.802780	+	0.596275i	$0.796647\pi$
$854$	0.0470904	−	0.109088i	0.00161140	−	0.00373293i
$855$	−6.60962	+	2.97803i	−0.226044	+	0.101847i
$856$	0.0997230	+	0.172725i	0.00340846	+	0.00590363i
$857$	5.17547	−	29.3515i	0.176791	−	1.00263i	−0.759266	−	0.650780i	$-0.774442\pi$
$857$	5.17547	−	29.3515i	0.176791	−	1.00263i	0.936057	−	0.351849i	$-0.114447\pi$
$858$	−0.529659	−	0.0265791i	−0.0180823	−	0.000907394i
$859$	−16.7620	+	46.0532i	−0.571912	+	1.57132i	0.229567	+	0.973293i	$0.426269\pi$
$859$	−16.7620	+	46.0532i	−0.571912	+	1.57132i	−0.801479	+	0.598023i	$0.795953\pi$
$860$	4.40234	−	3.69401i	0.150119	−	0.125965i
$861$	−13.4172	−	14.0017i	−0.457256	−	0.477177i
$862$	−0.0721165	+	0.0262483i	−0.00245630	+	0.000894019i
$863$	−16.1553	−	9.32725i	−0.549932	−	0.317503i	0.199163	−	0.979966i	$-0.436178\pi$
$863$	−16.1553	−	9.32725i	−0.549932	−	0.317503i	−0.749095	+	0.662463i	$0.769511\pi$
$864$	0.816924	+	0.445741i	0.0277923	+	0.0151644i
$865$	1.25066	+	2.16620i	0.0425236	+	0.0736530i
$866$	0.0507755	−	0.287962i	0.00172542	−	0.00978535i
$867$	−2.88139	−	3.80612i	−0.0978572	−	0.129263i
$868$	42.5924	−	12.7391i	1.44568	−	0.432392i
$869$	7.20980	−	1.27128i	0.244576	−	0.0431253i
$870$	0.0176608	−	0.351939i	0.000598758	−	0.0119319i
$871$	47.6918	+	8.40935i	1.61598	+	0.284940i
$872$			0.229965i			0.00778758i
$873$	−4.75563	+	0.353776i	−0.160954	+	0.0119735i
$874$	0.141035	−	0.0814267i	0.00477059	−	0.00275430i
$875$	1.85443	−	31.6949i	0.0626910	−	1.07148i
$876$	12.2141	−	53.4462i	0.412676	−	1.80578i
$877$	−0.469167	+	0.393678i	−0.0158427	+	0.0132936i	−0.650675	−	0.759357i	$-0.725514\pi$
$877$	−0.469167	+	0.393678i	−0.0158427	+	0.0132936i	0.634832	+	0.772650i	$0.281069\pi$
$878$	0.0833948	+	0.472956i	0.00281444	+	0.0159615i
$879$	−12.2482	+	13.1932i	−0.413123	+	0.444997i
$880$	−19.4280	+	23.1533i	−0.654917	+	0.780499i
$881$	24.2819	+	42.0575i	0.818079	+	1.41695i	0.907096	+	0.420924i	$0.138294\pi$
$881$	24.2819	+	42.0575i	0.818079	+	1.41695i	−0.0890174	+	0.996030i	$0.528373\pi$
$882$	−0.145022	−	0.277903i	−0.00488314	−	0.00935750i
$883$	−10.4471	+	18.0949i	−0.351573	+	0.608943i	−0.986525	−	0.163609i	$-0.947686\pi$
$883$	−10.4471	+	18.0949i	−0.351573	+	0.608943i	0.634952	+	0.772551i	$0.281020\pi$
$884$	−11.5287	−	31.6747i	−0.387751	−	1.06534i
$885$	29.3367	−	15.0300i	0.986144	−	0.505227i
$886$	0.265068	−	0.222418i	0.00890513	−	0.00747229i
$887$	1.97175	+	11.1824i	0.0662050	+	0.375467i	0.999851	+	0.0172696i	$0.00549737\pi$
$887$	1.97175	+	11.1824i	0.0662050	+	0.375467i	−0.933646	+	0.358197i	$0.883392\pi$
$888$	0.0757135	+	0.0319403i	0.00254078	+	0.00107185i
$889$	12.4476	−	6.24728i	0.417478	−	0.209527i
$890$			0.176510i			0.00591664i
$891$	30.9625	+	27.3847i	1.03728	+	0.917422i
$892$	−1.59005	+	0.918014i	−0.0532387	+	0.0307374i
$893$	1.55597	−	1.85434i	0.0520686	−	0.0620530i
$894$	0.315564	+	0.416839i	0.0105541	+	0.0139412i
$895$	−9.09083	−	10.8340i	−0.303873	−	0.362142i
$896$	−0.291692	+	1.22930i	−0.00974474	+	0.0410679i
$897$	2.88066	−	57.4049i	0.0961826	−	1.91670i
$898$	0.264890	−	0.0964121i	0.00883950	−	0.00321731i
$899$	69.5856			2.32081
$900$	9.59345	+	9.84642i	0.319782	+	0.328214i
$901$		−	15.9888i		−	0.532665i
$902$	0.0503784	−	0.285710i	0.00167742	−	0.00951310i
$903$	4.72833	−	6.45542i	0.157349	−	0.214823i
$904$	0.257896	+	0.0938665i	0.00857750	+	0.00312195i
$905$	11.2235	+	13.3756i	0.373081	+	0.444621i
$906$	−0.472553	+	0.145622i	−0.0156995	+	0.00483797i
$907$	−38.3161	+	13.9459i	−1.27227	+	0.463067i	−0.887867	−	0.460101i	$-0.847813\pi$
$907$	−38.3161	+	13.9459i	−1.27227	+	0.463067i	−0.384399	+	0.923167i	$0.625591\pi$
$908$	26.6540			0.884545
$909$	−0.514365	−	6.91436i	−0.0170604	−	0.229335i
$910$	0.288329	−	0.0336235i	0.00955801	−	0.00111461i
$911$	−22.9670	+	27.3710i	−0.760931	+	0.906843i	−0.997907	−	0.0646730i	$-0.979400\pi$
$911$	−22.9670	+	27.3710i	−0.760931	+	0.906843i	0.236975	+	0.971516i	$0.423844\pi$
$912$	10.1566	+	0.509675i	0.336320	+	0.0168770i
$913$	14.5040	+	17.2852i	0.480012	+	0.572056i
$914$	0.0939737	−	0.258191i	0.00310837	−	0.00854019i
$915$	−1.06406	−	8.50984i	−0.0351768	−	0.281326i
$916$	−8.42357	−	23.1436i	−0.278323	−	0.764685i
$917$	15.8720	−	36.7688i	0.524141	−	1.21421i
$918$	0.0934580	−	0.277411i	0.00308457	−	0.00915593i
$919$	−13.2691	+	22.9827i	−0.437706	+	0.758129i	−0.997512	−	0.0704945i	$-0.977542\pi$
$919$	−13.2691	+	22.9827i	−0.437706	+	0.758129i	0.559806	+	0.828624i	$0.310876\pi$
$920$	0.559285	+	0.469296i	0.0184391	+	0.0154722i
$921$	−23.5715	+	17.8446i	−0.776707	+	0.587999i
$922$	−0.235733	+	0.0415661i	−0.00776346	+	0.00136891i
$923$	5.97134	+	33.8652i	0.196549	+	1.11469i
$924$	−18.5965	+	37.7578i	−0.611782	+	1.24214i
$925$	1.39488	+	1.17044i	0.0458633	+	0.0384839i
$926$	−0.467968	+	0.270181i	−0.0153784	+	0.00887871i
$927$	0.164258	−	1.63252i	0.00539494	−	0.0536189i
$928$	−0.741604	+	1.28450i	−0.0243443	+	0.0421656i
$929$	−9.44219	−	7.92293i	−0.309788	−	0.259943i	0.474616	−	0.880193i	$-0.342587\pi$
$929$	−9.44219	−	7.92293i	−0.309788	−	0.259943i	−0.784404	+	0.620250i	$0.787031\pi$
$930$	−0.243251	+	0.262019i	−0.00797651	+	0.00859193i
$931$	−8.24117	−	6.14210i	−0.270094	−	0.201299i
$932$	−17.0550	+	46.8581i	−0.558654	+	1.53489i
$933$	16.9668	+	55.0583i	0.555468	+	1.80253i
$934$	0.0554718	+	0.152407i	0.00181509	+	0.00498692i
$935$	24.7053	+	14.2636i	0.807948	+	0.466469i
$936$	−0.467319	+	0.649253i	−0.0152748	+	0.0212215i
$937$	32.0189	+	18.4861i	1.04601	+	0.603915i	0.921530	−	0.388307i	$-0.126940\pi$
$937$	32.0189	+	18.4861i	1.04601	+	0.603915i	0.124481	+	0.992222i	$0.460273\pi$
$938$	−0.235414	+	0.357723i	−0.00768653	+	0.0116801i
$939$	0.918710	−	1.42159i	0.0299810	−	0.0463918i
$940$	5.09857	+	1.85573i	0.166297	+	0.0605272i
$941$	40.5370	+	14.7543i	1.32147	+	0.480975i	0.903928	−	0.427684i	$-0.140670\pi$
$941$	40.5370	+	14.7543i	1.32147	+	0.480975i	0.417539	+	0.908659i	$0.362893\pi$
$942$	−0.247908	−	0.327469i	−0.00807727	−	0.0106695i
$943$	30.9655	+	5.46006i	1.00838	+	0.177804i
$944$	−46.2392			−1.50496
$945$	−19.1945	−	11.9786i	−0.624396	−	0.389663i
$946$	0.119710			0.00389211
$947$	−32.3861	−	5.71054i	−1.05241	−	0.185567i	−0.379421	−	0.925224i	$-0.623877\pi$
$947$	−32.3861	−	5.71054i	−1.05241	−	0.185567i	−0.672984	+	0.739657i	$0.734988\pi$
$948$	2.14603	−	5.08711i	0.0696998	−	0.165222i
$949$	66.4274	+	24.1776i	2.15632	+	0.784838i
$950$	−0.0471945	−	0.0171774i	−0.00153119	−	0.000557309i
$951$	−2.67476	−	5.22082i	−0.0867350	−	0.169297i
$952$	0.595154	+	0.0348217i	0.0192891	+	0.00112858i
$953$	39.0374	+	22.5383i	1.26455	+	0.730086i	0.973951	−	0.226760i	$-0.0728134\pi$
$953$	39.0374	+	22.5383i	1.26455	+	0.730086i	0.290595	+	0.956846i	$0.406147\pi$
$954$	−0.156806	+	0.106783i	−0.00507679	+	0.00345724i
$955$	−14.0134	−	8.09062i	−0.453462	−	0.261806i
$956$	−7.81927	−	21.4833i	−0.252893	−	0.694819i
$957$	−44.8226	+	48.2809i	−1.44891	+	1.56070i
$958$	−0.0629322	+	0.172905i	−0.00203325	+	0.00558630i
$959$	−9.05568	+	2.70848i	−0.292423	+	0.0874615i
$960$	6.71127	+	21.7785i	0.216605	+	0.702899i
$961$	−30.3364	−	25.4553i	−0.978594	−	0.821138i
$962$	−0.0264877	+	0.0458781i	−0.000853999	+	0.00147917i
$963$	9.64557	+	2.71953i	0.310824	+	0.0876355i
$964$	10.6550	−	6.15165i	0.343173	−	0.198131i
$965$	−24.5992	−	20.6412i	−0.791878	−	0.664464i
$966$	0.455957	+	0.224569i	0.0146702	+	0.00722538i
$967$	0.795684	+	4.51255i	0.0255875	+	0.145114i	0.994925	−	0.100619i	$-0.0320824\pi$
$967$	0.795684	+	4.51255i	0.0255875	+	0.145114i	−0.969338	+	0.245733i	$0.920971\pi$
$968$	−0.593491	+	0.104648i	−0.0190755	+	0.00336353i
$969$	−1.19089	−	9.52416i	−0.0382570	−	0.305960i
$970$	0.0299144	+	0.0251011i	0.000960492	+	0.000805948i
$971$	8.12033	−	14.0648i	0.260594	−	0.451362i	−0.705806	−	0.708405i	$-0.749415\pi$
$971$	8.12033	−	14.0648i	0.260594	−	0.451362i	0.966400	+	0.257043i	$0.0827483\pi$
$972$	30.0198	−	8.40208i	0.962886	−	0.269497i
$973$	1.86560	+	15.9979i	0.0598085	+	0.512871i
$974$	−0.0986861	−	0.271138i	−0.00316211	−	0.00868782i
$975$	−14.1327	+	10.6990i	−0.452608	+	0.342643i
$976$	−4.11461	+	11.3048i	−0.131705	+	0.361857i
$977$	5.54097	+	6.60347i	0.177271	+	0.211264i	0.847362	−	0.531015i	$-0.178189\pi$
$977$	5.54097	+	6.60347i	0.177271	+	0.211264i	−0.670091	+	0.742279i	$0.733745\pi$
$978$	0.244705	−	0.378650i	0.00782479	−	0.0121079i
$979$	21.2117	−	25.2791i	0.677927	−	0.807922i
$980$	6.61908	−	22.0668i	0.211439	−	0.704898i
$981$	8.06368	+	8.27631i	0.257453	+	0.264242i
$982$	0.496927			0.0158576
$983$	−21.4542	+	7.80867i	−0.684281	+	0.249058i	−0.660685	−	0.750664i	$-0.729734\pi$
$983$	−21.4542	+	7.80867i	−0.684281	+	0.249058i	−0.0235966	+	0.999722i	$0.507512\pi$
$984$	−0.320714	−	0.297742i	−0.0102240	−	0.00949166i
$985$	−4.57755	−	5.45531i	−0.145853	−	0.173820i
$986$	0.438415	+	0.159570i	0.0139620	+	0.00508174i
$987$	7.51031	+	0.818701i	0.239056	+	0.0260595i
$988$	−2.27722	+	12.9147i	−0.0724480	+	0.410873i
$989$			12.9743i			0.412559i
$990$	−0.0251108	−	0.337552i	−0.000798073	−	0.0107281i
$991$	−14.9160			−0.473821			−0.236910	−	0.971531i	$-0.576135\pi$
$991$	−14.9160			−0.473821			−0.236910	+	0.971531i	$0.576135\pi$
$992$	1.41411	−	0.514692i	0.0448979	−	0.0163415i
$993$	9.36933	−	4.80015i	0.297327	−	0.152328i
$994$	−0.295868	−	0.0702045i	−0.00938435	−	0.00222675i
$995$	1.79426	+	2.13831i	0.0568818	+	0.0677891i
$996$	16.8856	−	2.11136i	0.535040	−	0.0669009i
$997$	−1.49123	+	1.77718i	−0.0472279	+	0.0562840i	−0.789141	−	0.614212i	$-0.789474\pi$
$997$	−1.49123	+	1.77718i	−0.0472279	+	0.0562840i	0.741913	+	0.670496i	$0.233919\pi$
$998$	0.260252	−	0.150256i	0.00823812	−	0.00475628i
$999$	3.84487	−	1.50537i	0.121646	−	0.0476278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.11	yes	132
3.2	odd	2		567.2.bd.a.467.12		132
7.3	odd	6		189.2.ba.a.101.12	✓	132
21.17	even	6		567.2.ba.a.143.11		132
27.4	even	9		567.2.ba.a.341.11		132
27.23	odd	18		189.2.ba.a.131.12	yes	132
189.31	odd	18		567.2.bd.a.17.12		132
189.185	even	18	inner	189.2.bd.a.185.11	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.12	✓	132	7.3	odd	6
189.2.ba.a.131.12	yes	132	27.23	odd	18
189.2.bd.a.47.11	yes	132	1.1	even	1	trivial
189.2.bd.a.185.11	yes	132	189.185	even	18	inner
567.2.ba.a.143.11		132	21.17	even	6
567.2.ba.a.341.11		132	27.4	even	9
567.2.bd.a.17.12		132	189.31	odd	18
567.2.bd.a.467.12		132	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0147002 - 0.00259205i) q^{2} +(-1.71867 + 0.214901i) q^{3} +(-1.87918 - 0.683964i) q^{4} +(1.54651 + 0.562885i) q^{5} +(0.0258218 + 0.00129578i) q^{6} +(2.21011 + 1.45445i) q^{7} +(0.0517058 + 0.0298524i) q^{8} +(2.90764 - 0.738686i) q^{9} +O(q^{10})\)	\(q+(-0.0147002 - 0.00259205i) q^{2} +(-1.71867 + 0.214901i) q^{3} +(-1.87918 - 0.683964i) q^{4} +(1.54651 + 0.562885i) q^{5} +(0.0258218 + 0.00129578i) q^{6} +(2.21011 + 1.45445i) q^{7} +(0.0517058 + 0.0298524i) q^{8} +(2.90764 - 0.738686i) q^{9} +(-0.0212751 - 0.0122832i) q^{10} +(1.57083 + 4.31582i) q^{11} +(3.37666 + 0.771671i) q^{12} +(-1.52751 + 4.19679i) q^{13} +(-0.0287191 - 0.0271094i) q^{14} +(-2.77891 - 0.635065i) q^{15} +(3.06315 + 2.57029i) q^{16} +(1.88705 - 3.26847i) q^{17} +(-0.0446576 + 0.00332212i) q^{18} +(-1.27160 + 0.734160i) q^{19} +(-2.52118 - 2.11552i) q^{20} +(-4.11100 - 2.02476i) q^{21} +(-0.0119048 - 0.0675152i) q^{22} +(7.31736 - 1.29025i) q^{23} +(-0.0952804 - 0.0401947i) q^{24} +(-1.75536 - 1.47292i) q^{25} +(0.0333330 - 0.0577345i) q^{26} +(-4.83851 + 1.89441i) q^{27} +(-3.15839 - 4.24480i) q^{28} +(-2.83246 - 7.78213i) q^{29} +(0.0392044 + 0.0165387i) q^{30} +(-2.87381 + 7.89573i) q^{31} +(-0.115122 - 0.137197i) q^{32} +(-3.62721 - 7.07988i) q^{33} +(-0.0362121 + 0.0431559i) q^{34} +(2.59927 + 3.49336i) q^{35} +(-5.96919 - 0.600598i) q^{36} -0.794639 q^{37} +(0.0205958 - 0.00749627i) q^{38} +(1.72338 - 7.54116i) q^{39} +(0.0631602 + 0.0752714i) q^{40} +(3.97658 + 1.44736i) q^{41} +(0.0551844 + 0.0404204i) q^{42} +(-0.303215 + 1.71962i) q^{43} -9.18457i q^{44} +(4.91249 + 0.494277i) q^{45} -0.110911 q^{46} +(-1.54917 + 0.563852i) q^{47} +(-5.81690 - 3.75920i) q^{48} +(2.76916 + 6.42898i) q^{49} +(0.0219863 + 0.0262023i) q^{50} +(-2.54082 + 6.02294i) q^{51} +(5.74091 - 6.84175i) q^{52} +(3.66888 - 2.11823i) q^{53} +(0.0760377 - 0.0153066i) q^{54} +7.55866i q^{55} +(0.0708567 + 0.141180i) q^{56} +(2.02769 - 1.53505i) q^{57} +(0.0214662 + 0.121741i) q^{58} +(-8.85828 + 7.43298i) q^{59} +(4.78769 + 3.09407i) q^{60} +(1.02900 + 2.82714i) q^{61} +(0.0627118 - 0.108620i) q^{62} +(7.50057 + 2.59643i) q^{63} +(-3.99733 - 6.92357i) q^{64} +(-4.72462 + 5.63058i) q^{65} +(0.0349694 + 0.113478i) q^{66} +(-1.88292 - 10.6785i) q^{67} +(-5.78162 + 4.85135i) q^{68} +(-12.2988 + 3.79001i) q^{69} +(-0.0291550 - 0.0580906i) q^{70} +(6.66808 - 3.84982i) q^{71} +(0.172393 + 0.0486054i) q^{72} -15.8281i q^{73} +(0.0116814 + 0.00205974i) q^{74} +(3.33341 + 2.15423i) q^{75} +(2.89171 - 0.509886i) q^{76} +(-2.80543 + 11.8231i) q^{77} +(-0.0448812 + 0.106390i) q^{78} +(0.276799 - 1.56981i) q^{79} +(3.29043 + 5.69919i) q^{80} +(7.90869 - 4.29566i) q^{81} +(-0.0547050 - 0.0315840i) q^{82} +(4.61667 - 1.68033i) q^{83} +(6.34044 + 6.61666i) q^{84} +(4.75812 - 3.99254i) q^{85} +(0.00891467 - 0.0244929i) q^{86} +(6.54045 + 12.7662i) q^{87} +(-0.0476164 + 0.270046i) q^{88} +(-3.59252 - 6.22243i) q^{89} +(-0.0709336 - 0.0199994i) q^{90} +(-9.47998 + 7.05369i) q^{91} +(-14.6331 - 2.58021i) q^{92} +(3.24233 - 14.1877i) q^{93} +(0.0242347 - 0.00427323i) q^{94} +(-2.37980 + 0.419623i) q^{95} +(0.227340 + 0.211056i) q^{96} +(-1.56544 - 0.276029i) q^{97} +(-0.0240431 - 0.101685i) q^{98} +(7.75543 + 11.3885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more