LMFDB - Embedded newform 135.2.k.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(16,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("135.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.k (of order $9$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	135.16
Dual form			135.2.k.b.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42971 + 1.19967i) q^{2} +(0.697646 + 1.58534i) q^{3} +(0.257569 + 1.46075i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.904448 + 3.10352i) q^{6} +(0.603654 - 3.42349i) q^{7} +(0.482190 - 0.835177i) q^{8} +(-2.02658 + 2.21201i) q^{9} +O(q^{10})$	\(q+(1.42971 + 1.19967i) q^{2} +(0.697646 + 1.58534i) q^{3} +(0.257569 + 1.46075i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.904448 + 3.10352i) q^{6} +(0.603654 - 3.42349i) q^{7} +(0.482190 - 0.835177i) q^{8} +(-2.02658 + 2.21201i) q^{9} +(-0.933178 - 1.61631i) q^{10} +(-3.21914 + 1.17167i) q^{11} +(-2.13608 + 1.42742i) q^{12} +(-2.29137 + 1.92269i) q^{13} +(4.97011 - 4.17042i) q^{14} +(-0.113356 - 1.72834i) q^{15} +(4.47899 - 1.63022i) q^{16} +(-0.915007 - 1.58484i) q^{17} +(-5.55110 + 0.731301i) q^{18} +(2.83150 - 4.90430i) q^{19} +(0.257569 - 1.46075i) q^{20} +(5.84852 - 1.43139i) q^{21} +(-6.00805 - 2.18675i) q^{22} +(1.47679 + 8.37528i) q^{23} +(1.66043 + 0.181775i) q^{24} +(0.766044 + 0.642788i) q^{25} -5.58258 q^{26} +(-4.92061 - 1.66961i) q^{27} +5.15634 q^{28} +(2.71852 + 2.28111i) q^{29} +(1.91137 - 2.60701i) q^{30} +(0.629929 + 3.57251i) q^{31} +(6.54694 + 2.38289i) q^{32} +(-4.10331 - 4.28600i) q^{33} +(0.593087 - 3.36357i) q^{34} +(-1.73815 + 3.01057i) q^{35} +(-3.75317 - 2.39058i) q^{36} +(-4.12531 - 7.14525i) q^{37} +(9.93177 - 3.61487i) q^{38} +(-4.64666 - 2.29123i) q^{39} +(-0.738757 + 0.619891i) q^{40} +(3.49560 - 2.93316i) q^{41} +(10.0789 + 4.96982i) q^{42} +(-6.40168 + 2.33002i) q^{43} +(-2.54066 - 4.40056i) q^{44} +(2.66091 - 1.38547i) q^{45} +(-7.93619 + 13.7459i) q^{46} +(-0.749097 + 4.24834i) q^{47} +(5.70919 + 5.96338i) q^{48} +(-4.77806 - 1.73907i) q^{49} +(0.324089 + 1.83800i) q^{50} +(1.87415 - 2.55625i) q^{51} +(-3.39874 - 2.85188i) q^{52} -6.55503 q^{53} +(-5.03206 - 8.29017i) q^{54} +3.42573 q^{55} +(-2.56815 - 2.15493i) q^{56} +(9.75035 + 1.06741i) q^{57} +(1.15012 + 6.52266i) q^{58} +(-3.06342 - 1.11500i) q^{59} +(2.49547 - 0.610751i) q^{60} +(0.589476 - 3.34309i) q^{61} +(-3.38521 + 5.86336i) q^{62} +(6.34943 + 8.27327i) q^{63} +(1.73511 + 3.00530i) q^{64} +(2.81078 - 1.02304i) q^{65} +(-0.724755 - 11.0504i) q^{66} +(-3.19129 + 2.67781i) q^{67} +(2.07937 - 1.74480i) q^{68} +(-12.2474 + 8.18418i) q^{69} +(-6.09675 + 2.21903i) q^{70} +(4.35406 + 7.54146i) q^{71} +(0.870220 + 2.75916i) q^{72} +(3.97200 - 6.87971i) q^{73} +(2.67394 - 15.1646i) q^{74} +(-0.484607 + 1.66288i) q^{75} +(7.89326 + 2.87291i) q^{76} +(2.06796 + 11.7280i) q^{77} +(-3.89466 - 8.85027i) q^{78} +(11.2271 + 9.42064i) q^{79} -4.76644 q^{80} +(-0.785942 - 8.96562i) q^{81} +8.51652 q^{82} +(-11.0597 - 9.28016i) q^{83} +(3.59730 + 8.17453i) q^{84} +(0.317778 + 1.80221i) q^{85} +(-11.9478 - 4.34865i) q^{86} +(-1.71976 + 5.90118i) q^{87} +(-0.573682 + 3.25351i) q^{88} +(1.78804 - 3.09697i) q^{89} +(5.46645 + 1.21139i) q^{90} +(5.19911 + 9.00512i) q^{91} +(-11.8538 + 4.31443i) q^{92} +(-5.22416 + 3.49099i) q^{93} +(-6.16760 + 5.17523i) q^{94} +(-4.33811 + 3.64011i) q^{95} +(0.789762 + 12.0415i) q^{96} +(3.43991 - 1.25203i) q^{97} +(-4.74493 - 8.21846i) q^{98} +(3.93210 - 9.49523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 6 q^{6} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 6 * q^6 - 9 * q^8 - 3 * q^9	\( 42 q - 3 q^{3} - 6 q^{6} - 9 q^{8} - 3 q^{9} - 3 q^{10} - 6 q^{11} - 39 q^{12} - 3 q^{13} - 27 q^{14} + 6 q^{15} - 12 q^{16} - 12 q^{17} + 6 q^{18} - 24 q^{19} + 12 q^{21} + 33 q^{22} + 18 q^{23} - 3 q^{24} - 18 q^{26} + 39 q^{27} + 60 q^{28} - 21 q^{30} - 12 q^{31} + 36 q^{32} - 33 q^{33} + 51 q^{34} - 12 q^{35} - 36 q^{36} - 24 q^{37} - 24 q^{38} - 30 q^{39} - 9 q^{40} + 33 q^{41} + 78 q^{42} - 24 q^{43} + 12 q^{44} - 12 q^{45} - 30 q^{46} + 27 q^{47} + 141 q^{48} + 18 q^{49} - 39 q^{51} - 84 q^{52} + 36 q^{53} + 30 q^{54} - 24 q^{56} - 81 q^{58} - 27 q^{59} - 6 q^{61} - 18 q^{62} - 6 q^{63} - 63 q^{64} + 6 q^{65} - 30 q^{66} + 12 q^{67} - 3 q^{68} + 51 q^{69} + 9 q^{70} + 12 q^{71} - 153 q^{72} - 39 q^{73} - 72 q^{74} + 138 q^{76} - 54 q^{77} - 48 q^{78} - 18 q^{79} + 78 q^{80} + 45 q^{81} + 48 q^{82} + 57 q^{83} - 51 q^{84} + 9 q^{85} + 18 q^{86} - 39 q^{87} + 126 q^{88} + 9 q^{89} + 54 q^{90} - 69 q^{91} + 24 q^{92} - 18 q^{93} - 33 q^{94} + 3 q^{95} + 153 q^{96} + 21 q^{97} - 15 q^{98} - 9 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 6 * q^6 - 9 * q^8 - 3 * q^9 - 3 * q^10 - 6 * q^11 - 39 * q^12 - 3 * q^13 - 27 * q^14 + 6 * q^15 - 12 * q^16 - 12 * q^17 + 6 * q^18 - 24 * q^19 + 12 * q^21 + 33 * q^22 + 18 * q^23 - 3 * q^24 - 18 * q^26 + 39 * q^27 + 60 * q^28 - 21 * q^30 - 12 * q^31 + 36 * q^32 - 33 * q^33 + 51 * q^34 - 12 * q^35 - 36 * q^36 - 24 * q^37 - 24 * q^38 - 30 * q^39 - 9 * q^40 + 33 * q^41 + 78 * q^42 - 24 * q^43 + 12 * q^44 - 12 * q^45 - 30 * q^46 + 27 * q^47 + 141 * q^48 + 18 * q^49 - 39 * q^51 - 84 * q^52 + 36 * q^53 + 30 * q^54 - 24 * q^56 - 81 * q^58 - 27 * q^59 - 6 * q^61 - 18 * q^62 - 6 * q^63 - 63 * q^64 + 6 * q^65 - 30 * q^66 + 12 * q^67 - 3 * q^68 + 51 * q^69 + 9 * q^70 + 12 * q^71 - 153 * q^72 - 39 * q^73 - 72 * q^74 + 138 * q^76 - 54 * q^77 - 48 * q^78 - 18 * q^79 + 78 * q^80 + 45 * q^81 + 48 * q^82 + 57 * q^83 - 51 * q^84 + 9 * q^85 + 18 * q^86 - 39 * q^87 + 126 * q^88 + 9 * q^89 + 54 * q^90 - 69 * q^91 + 24 * q^92 - 18 * q^93 - 33 * q^94 + 3 * q^95 + 153 * q^96 + 21 * q^97 - 15 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.42971	+	1.19967i	1.01096	+	0.848295i	0.988465	−	0.151452i	$-0.0483949\pi$
$2$	1.42971	+	1.19967i	1.01096	+	0.848295i	0.0224938	+	0.999747i	$0.492839\pi$
$3$	0.697646	+	1.58534i	0.402786	+	0.915294i
$3$	0.697646	+	1.58534i	0.402786	+	0.915294i
$4$	0.257569	+	1.46075i	0.128785	+	0.730374i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$	−0.904448	+	3.10352i	−0.369239	+	1.26701i
$7$	0.603654	−	3.42349i	0.228160	−	1.29396i	−0.628392	−	0.777897i	$-0.716286\pi$
$7$	0.603654	−	3.42349i	0.228160	−	1.29396i	0.856552	−	0.516062i	$-0.172602\pi$
$8$	0.482190	−	0.835177i	0.170480	−	0.295280i
$9$	−2.02658	+	2.21201i	−0.675527	+	0.737335i
$10$	−0.933178	−	1.61631i	−0.295097	−	0.511122i
$11$	−3.21914	+	1.17167i	−0.970606	+	0.353272i	−0.778181	−	0.628040i	$-0.783857\pi$
$11$	−3.21914	+	1.17167i	−0.970606	+	0.353272i	−0.192425	+	0.981312i	$0.561635\pi$
$12$	−2.13608	+	1.42742i	−0.616634	+	0.412060i
$13$	−2.29137	+	1.92269i	−0.635511	+	0.533257i	−0.902636	−	0.430405i	$-0.858371\pi$
$13$	−2.29137	+	1.92269i	−0.635511	+	0.533257i	0.267125	+	0.963662i	$0.413926\pi$
$14$	4.97011	−	4.17042i	1.32832	−	1.11459i
$15$	−0.113356	−	1.72834i	−0.0292683	−	0.446255i
$16$	4.47899	−	1.63022i	1.11975	−	0.407554i
$17$	−0.915007	−	1.58484i	−0.221922	−	0.384380i	0.733470	−	0.679722i	$-0.237900\pi$
$17$	−0.915007	−	1.58484i	−0.221922	−	0.384380i	−0.955391	+	0.295342i	$0.904566\pi$
$18$	−5.55110	+	0.731301i	−1.30841	+	0.172369i
$19$	2.83150	−	4.90430i	0.649591	−	1.12512i	−0.333630	−	0.942704i	$-0.608274\pi$
$19$	2.83150	−	4.90430i	0.649591	−	1.12512i	0.983221	−	0.182420i	$-0.0583931\pi$
$20$	0.257569	−	1.46075i	0.0575942	−	0.326633i
$21$	5.84852	−	1.43139i	1.27625	−	0.312355i
$22$	−6.00805	−	2.18675i	−1.28092	−	0.466217i
$23$	1.47679	+	8.37528i	0.307931	+	1.74637i	0.609375	+	0.792882i	$0.291420\pi$
$23$	1.47679	+	8.37528i	0.307931	+	1.74637i	−0.301444	+	0.953484i	$0.597468\pi$
$24$	1.66043	+	0.181775i	0.338935	+	0.0371046i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−5.58258			−1.09483
$27$	−4.92061	−	1.66961i	−0.946972	−	0.321317i
$28$	5.15634			0.974457
$29$	2.71852	+	2.28111i	0.504817	+	0.423592i	0.859301	−	0.511470i	$-0.170899\pi$
$29$	2.71852	+	2.28111i	0.504817	+	0.423592i	−0.354484	+	0.935062i	$0.615343\pi$
$30$	1.91137	−	2.60701i	0.348967	−	0.475973i
$31$	0.629929	+	3.57251i	0.113139	+	0.641641i	0.987655	+	0.156645i	$0.0500679\pi$
$31$	0.629929	+	3.57251i	0.113139	+	0.641641i	−0.874516	+	0.484996i	$0.838821\pi$
$32$	6.54694	+	2.38289i	1.15735	+	0.421240i
$33$	−4.10331	−	4.28600i	−0.714294	−	0.746097i
$34$	0.593087	−	3.36357i	0.101714	−	0.576847i
$35$	−1.73815	+	3.01057i	−0.293801	+	0.508879i
$36$	−3.75317	−	2.39058i	−0.625528	−	0.398430i
$37$	−4.12531	−	7.14525i	−0.678197	−	1.17467i	−0.975523	−	0.219895i	$-0.929428\pi$
$37$	−4.12531	−	7.14525i	−0.678197	−	1.17467i	0.297327	−	0.954776i	$-0.403905\pi$
$38$	9.93177	−	3.61487i	1.61115	−	0.586409i
$39$	−4.64666	−	2.29123i	−0.744062	−	0.366891i
$40$	−0.738757	+	0.619891i	−0.116808	+	0.0980134i
$41$	3.49560	−	2.93316i	0.545921	−	0.458082i	−0.327636	−	0.944804i	$-0.606252\pi$
$41$	3.49560	−	2.93316i	0.545921	−	0.458082i	0.873557	+	0.486722i	$0.161808\pi$
$42$	10.0789	+	4.96982i	1.55521	+	0.766860i
$43$	−6.40168	+	2.33002i	−0.976247	+	0.355325i	−0.780380	−	0.625306i	$-0.784974\pi$
$43$	−6.40168	+	2.33002i	−0.976247	+	0.355325i	−0.195867	+	0.980630i	$0.562752\pi$
$44$	−2.54066	−	4.40056i	−0.383019	−	0.663409i
$45$	2.66091	−	1.38547i	0.396666	−	0.206534i
$46$	−7.93619	+	13.7459i	−1.17013	+	2.02672i
$47$	−0.749097	+	4.24834i	−0.109267	+	0.619684i	0.880163	+	0.474672i	$0.157433\pi$
$47$	−0.749097	+	4.24834i	−0.109267	+	0.619684i	−0.989430	+	0.145012i	$0.953678\pi$
$48$	5.70919	+	5.96338i	0.824051	+	0.860740i
$49$	−4.77806	−	1.73907i	−0.682579	−	0.248439i
$50$	0.324089	+	1.83800i	0.0458331	+	0.259933i
$51$	1.87415	−	2.55625i	0.262433	−	0.357946i
$52$	−3.39874	−	2.85188i	−0.471321	−	0.395485i
$53$	−6.55503			−0.900403			−0.450201	−	0.892927i	$-0.648648\pi$
$53$	−6.55503			−0.900403			−0.450201	+	0.892927i	$0.648648\pi$
$54$	−5.03206	−	8.29017i	−0.684777	−	1.12815i
$55$	3.42573			0.461926
$56$	−2.56815	−	2.15493i	−0.343183	−	0.287965i
$57$	9.75035	+	1.06741i	1.29147	+	0.141382i
$58$	1.15012	+	6.52266i	0.151018	+	0.856467i
$59$	−3.06342	−	1.11500i	−0.398824	−	0.145160i	0.134818	−	0.990870i	$-0.456955\pi$
$59$	−3.06342	−	1.11500i	−0.398824	−	0.145160i	−0.533642	+	0.845710i	$0.679177\pi$
$60$	2.49547	−	0.610751i	0.322164	−	0.0788476i
$61$	0.589476	−	3.34309i	0.0754747	−	0.428038i	−0.923534	−	0.383517i	$-0.874713\pi$
$61$	0.589476	−	3.34309i	0.0754747	−	0.428038i	0.999008	−	0.0445212i	$-0.0141762\pi$
$62$	−3.38521	+	5.86336i	−0.429922	+	0.744648i
$63$	6.34943	+	8.27327i	0.799953	+	1.04233i
$64$	1.73511	+	3.00530i	0.216889	+	0.375663i
$65$	2.81078	−	1.02304i	0.348634	−	0.126892i
$66$	−0.724755	−	11.0504i	−0.0892112	−	1.36020i
$67$	−3.19129	+	2.67781i	−0.389878	+	0.327146i	−0.816566	−	0.577253i	$-0.804125\pi$
$67$	−3.19129	+	2.67781i	−0.389878	+	0.327146i	0.426688	+	0.904399i	$0.359680\pi$
$68$	2.07937	−	1.74480i	0.252161	−	0.211588i
$69$	−12.2474	+	8.18418i	−1.47441	+	0.985260i
$70$	−6.09675	+	2.21903i	−0.728701	+	0.265225i
$71$	4.35406	+	7.54146i	0.516732	+	0.895007i	0.999811	+	0.0194298i	$0.00618507\pi$
$71$	4.35406	+	7.54146i	0.516732	+	0.895007i	−0.483079	+	0.875577i	$0.660482\pi$
$72$	0.870220	+	2.75916i	0.102556	+	0.325170i
$73$	3.97200	−	6.87971i	0.464888	−	0.805210i	−0.534309	−	0.845290i	$-0.679428\pi$
$73$	3.97200	−	6.87971i	0.464888	−	0.805210i	0.999196	+	0.0400800i	$0.0127613\pi$
$74$	2.67394	−	15.1646i	0.310839	−	1.76285i
$75$	−0.484607	+	1.66288i	−0.0559576	+	0.192012i
$76$	7.89326	+	2.87291i	0.905419	+	0.329545i
$77$	2.06796	+	11.7280i	0.235666	+	1.33653i
$78$	−3.89466	−	8.85027i	−0.440984	−	1.00210i
$79$	11.2271	+	9.42064i	1.26315	+	1.05990i	0.995340	+	0.0964321i	$0.0307431\pi$
$79$	11.2271	+	9.42064i	1.26315	+	1.05990i	0.267806	+	0.963473i	$0.413701\pi$
$80$	−4.76644			−0.532904
$81$	−0.785942	−	8.96562i	−0.0873268	−	0.996180i
$82$	8.51652			0.940492
$83$	−11.0597	−	9.28016i	−1.21396	−	1.01863i	−0.999118	−	0.0419799i	$-0.986633\pi$
$83$	−11.0597	−	9.28016i	−1.21396	−	1.01863i	−0.214837	−	0.976650i	$-0.568922\pi$
$84$	3.59730	+	8.17453i	0.392498	+	0.891915i
$85$	0.317778	+	1.80221i	0.0344679	+	0.195477i
$86$	−11.9478	−	4.34865i	−1.28837	−	0.468927i
$87$	−1.71976	+	5.90118i	−0.184378	+	0.632673i
$88$	−0.573682	+	3.25351i	−0.0611547	+	0.346826i
$89$	1.78804	−	3.09697i	0.189531	−	0.328278i	−0.755563	−	0.655076i	$-0.772636\pi$
$89$	1.78804	−	3.09697i	0.189531	−	0.328278i	0.945094	+	0.326798i	$0.105970\pi$
$90$	5.46645	+	1.21139i	0.576214	+	0.127692i
$91$	5.19911	+	9.00512i	0.545014	+	0.943993i
$92$	−11.8538	+	4.31443i	−1.23584	+	0.449810i
$93$	−5.22416	+	3.49099i	−0.541720	+	0.361999i
$94$	−6.16760	+	5.17523i	−0.636139	+	0.533784i
$95$	−4.33811	+	3.64011i	−0.445081	+	0.373467i
$96$	0.789762	+	12.0415i	0.0806047	+	1.22898i
$97$	3.43991	−	1.25203i	0.349270	−	0.127124i	−0.161427	−	0.986885i	$-0.551610\pi$
$97$	3.43991	−	1.25203i	0.349270	−	0.127124i	0.510697	+	0.859761i	$0.329387\pi$
$98$	−4.74493	−	8.21846i	−0.479310	−	0.830190i
$99$	3.93210	−	9.49523i	0.395191	−	0.954306i
$100$	−0.741641	+	1.28456i	−0.0741641	+	0.128456i
$101$	0.0680401	−	0.385875i	0.00677025	−	0.0383960i	−0.981235	−	0.192813i	$-0.938239\pi$
$101$	0.0680401	−	0.385875i	0.00677025	−	0.0383960i	0.988006	+	0.154417i	$0.0493500\pi$
$102$	5.74615	−	1.40633i	0.568953	−	0.139248i
$103$	15.4578	+	5.62618i	1.52310	+	0.554364i	0.961920	−	0.273330i	$-0.0881249\pi$
$103$	15.4578	+	5.62618i	1.52310	+	0.554364i	0.561181	+	0.827693i	$0.310347\pi$
$104$	0.500909	+	2.84080i	0.0491182	+	0.278563i
$105$	−5.98538	−	0.655245i	−0.584113	−	0.0639454i
$106$	−9.37180	−	7.86388i	−0.910270	−	0.763807i
$107$	12.6842			1.22623			0.613113	−	0.789995i	$-0.289917\pi$
$107$	12.6842			1.22623			0.613113	+	0.789995i	$0.289917\pi$
$108$	1.17149	−	7.61781i	0.112727	−	0.733024i
$109$	14.0464			1.34540			0.672701	−	0.739914i	$-0.265134\pi$
$109$	14.0464			1.34540			0.672701	+	0.739914i	$0.265134\pi$
$110$	4.89781	+	4.10975i	0.466988	+	0.391849i
$111$	8.44961	−	11.5249i	0.802002	−	1.09389i
$112$	−2.87728	−	16.3179i	−0.271877	−	1.54189i
$113$	−7.00413	−	2.54930i	−0.658893	−	0.239818i	−0.00913486	−	0.999958i	$-0.502908\pi$
$113$	−7.00413	−	2.54930i	−0.658893	−	0.239818i	−0.649758	+	0.760141i	$0.725130\pi$
$114$	12.6596	+	13.2233i	1.18568	+	1.23848i
$115$	1.47679	−	8.37528i	0.137711	−	0.780999i
$116$	−2.63192	+	4.55862i	−0.244368	+	0.423257i
$117$	0.390649	−	8.96499i	0.0361155	−	0.828814i
$118$	−3.04218	−	5.26922i	−0.280056	−	0.485071i
$119$	−5.97803	+	2.17582i	−0.548005	+	0.199457i
$120$	−1.49813	−	0.738714i	−0.136760	−	0.0674351i
$121$	0.563534	−	0.472862i	0.0512304	−	0.0429874i
$122$	4.85338	−	4.07247i	0.439405	−	0.368704i
$123$	7.08873	+	3.49540i	0.639169	+	0.315169i
$124$	−5.05628	+	1.84034i	−0.454067	+	0.165267i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.847341	+	19.4456i	−0.0754871	+	1.73235i
$127$	−6.42637	+	11.1308i	−0.570248	+	0.987699i	0.426292	+	0.904586i	$0.359820\pi$
$127$	−6.42637	+	11.1308i	−0.570248	+	0.987699i	−0.996540	+	0.0831130i	$0.973514\pi$
$128$	1.29499	−	7.34425i	0.114462	−	0.649146i
$129$	−8.15997	−	8.52328i	−0.718445	−	0.750433i
$130$	5.24591	+	1.90936i	0.460097	+	0.167462i
$131$	−3.04490	−	17.2685i	−0.266034	−	1.50876i	−0.766074	−	0.642753i	$-0.777792\pi$
$131$	−3.04490	−	17.2685i	−0.266034	−	1.50876i	0.500040	−	0.866003i	$-0.333319\pi$
$132$	5.20388	−	7.09784i	0.452940	−	0.617787i
$133$	−15.0806	−	12.6541i	−1.30765	−	1.09725i
$134$	−7.77510			−0.671667
$135$	4.05282	+	3.25187i	0.348811	+	0.279877i
$136$	−1.76483			−0.151333
$137$	−7.61384	−	6.38877i	−0.650495	−	0.545830i	0.256726	−	0.966484i	$-0.417356\pi$
$137$	−7.61384	−	6.38877i	−0.650495	−	0.545830i	−0.907221	+	0.420654i	$0.861801\pi$
$138$	−27.3285	−	2.99177i	−2.32636	−	0.254676i
$139$	0.556612	+	3.15670i	0.0472112	+	0.267748i	0.999272	−	0.0381621i	$-0.0121503\pi$
$139$	0.556612	+	3.15670i	0.0472112	+	0.267748i	−0.952060	+	0.305910i	$0.901039\pi$
$140$	−4.84538	−	1.76357i	−0.409509	−	0.149049i
$141$	−7.25765	+	1.77627i	−0.611205	+	0.149589i
$142$	−2.82221	+	16.0055i	−0.236835	+	1.34316i
$143$	5.12347	−	8.87411i	0.428446	−	0.742090i
$144$	−5.47098	+	13.2113i	−0.455915	+	1.10094i
$145$	−1.77439	−	3.07333i	−0.147355	−	0.255226i
$146$	13.9322	−	5.07091i	1.15304	−	0.419671i
$147$	−0.576380	−	8.78808i	−0.0475390	−	0.724829i
$148$	9.37485	−	7.86643i	0.770608	−	0.646617i
$149$	0.773640	−	0.649161i	0.0633790	−	0.0531813i	−0.610548	−	0.791979i	$-0.709051\pi$
$149$	0.773640	−	0.649161i	0.0633790	−	0.0531813i	0.673927	+	0.738798i	$0.264606\pi$
$150$	−2.68775	+	1.79606i	−0.219454	+	0.146648i
$151$	11.1642	−	4.06345i	0.908533	−	0.330679i	0.154866	−	0.987936i	$-0.450505\pi$
$151$	11.1642	−	4.06345i	0.908533	−	0.330679i	0.753667	+	0.657257i	$0.228283\pi$
$152$	−2.73064	−	4.72961i	−0.221484	−	0.383622i
$153$	5.36001	+	1.18780i	0.433331	+	0.0960281i
$154$	−11.1131	+	19.2485i	−0.895520	+	1.55109i
$155$	0.629929	−	3.57251i	0.0505971	−	0.286951i
$156$	2.15008	−	7.37776i	0.172144	−	0.590693i
$157$	−18.3957	−	6.69550i	−1.46814	−	0.534359i	−0.520545	−	0.853834i	$-0.674271\pi$
$157$	−18.3957	−	6.69550i	−1.46814	−	0.534359i	−0.947595	+	0.319475i	$0.896493\pi$
$158$	4.74982	+	26.9376i	0.377876	+	2.14304i
$159$	−4.57309	−	10.3919i	−0.362670	−	0.824134i
$160$	−5.33712	−	4.47837i	−0.421936	−	0.354046i
$161$	29.5642			2.32998
$162$	9.63211	−	13.7611i	0.756770	−	1.08118i
$163$	9.26458			0.725658			0.362829	−	0.931856i	$-0.381811\pi$
$163$	9.26458			0.725658			0.362829	+	0.931856i	$0.381811\pi$
$164$	5.18496	+	4.35070i	0.404877	+	0.339732i
$165$	2.38995	+	5.43094i	0.186057	+	0.422798i
$166$	−4.67899	−	26.5359i	−0.363160	−	2.05958i
$167$	−9.58151	−	3.48738i	−0.741439	−	0.269862i	−0.0564405	−	0.998406i	$-0.517975\pi$
$167$	−9.58151	−	3.48738i	−0.741439	−	0.269862i	−0.684999	+	0.728544i	$0.740197\pi$
$168$	1.62463	−	5.57475i	0.125343	−	0.430102i
$169$	−0.703782	+	3.99135i	−0.0541371	+	0.307027i
$170$	−1.70773	+	2.95787i	−0.130977	+	0.226858i
$171$	5.11008	+	16.2023i	0.390778	+	1.23902i
$172$	−5.05245	−	8.75110i	−0.385246	−	0.667265i
$173$	10.6251	−	3.86724i	0.807815	−	0.294021i	0.0950941	−	0.995468i	$-0.469685\pi$
$173$	10.6251	−	3.86724i	0.807815	−	0.294021i	0.712721	+	0.701448i	$0.247463\pi$
$174$	−9.53823	+	6.37383i	−0.723091	+	0.483199i
$175$	2.66300	−	2.23453i	0.201304	−	0.168914i
$176$	−12.5084	+	10.4958i	−0.942855	+	0.791150i
$177$	−0.369543	−	5.63443i	−0.0277765	−	0.423510i
$178$	6.27171	−	2.28272i	0.470085	−	0.171097i
$179$	12.0316	+	20.8394i	0.899285	+	1.55761i	0.828410	+	0.560122i	$0.189246\pi$
$179$	12.0316	+	20.8394i	0.899285	+	1.55761i	0.0708754	+	0.997485i	$0.477421\pi$
$180$	2.70920	+	3.53007i	0.201932	+	0.263116i
$181$	−4.60686	+	7.97931i	−0.342425	+	0.593098i	−0.984882	−	0.173224i	$-0.944582\pi$
$181$	−4.60686	+	7.97931i	−0.342425	+	0.593098i	0.642457	+	0.766321i	$0.277915\pi$
$182$	−3.36995	+	19.1119i	−0.249797	+	1.41667i
$183$	5.71116	−	1.39777i	0.422181	−	0.103326i
$184$	7.70693	+	2.80509i	0.568162	+	0.206794i
$185$	1.43270	+	8.12527i	0.105335	+	0.597382i
$186$	−11.6571	−	1.27615i	−0.854738	−	0.0935719i
$187$	4.80244	+	4.02972i	0.351189	+	0.294682i
$188$	−6.39870			−0.466673
$189$	−8.68626	+	15.8378i	−0.631832	+	1.15203i
$190$	−10.5692			−0.766768
$191$	−1.50137	−	1.25980i	−0.108635	−	0.0911559i	0.586852	−	0.809694i	$-0.300367\pi$
$191$	−1.50137	−	1.25980i	−0.108635	−	0.0911559i	−0.695487	+	0.718538i	$0.744811\pi$
$192$	−3.55392	+	4.84737i	−0.256482	+	0.349829i
$193$	1.83340	+	10.3977i	0.131971	+	0.748446i	0.976921	+	0.213601i	$0.0685191\pi$
$193$	1.83340	+	10.3977i	0.131971	+	0.748446i	−0.844950	+	0.534846i	$0.820370\pi$
$194$	6.42010	+	2.33673i	0.460937	+	0.167767i
$195$	3.58279	+	3.74231i	0.256569	+	0.267992i
$196$	1.30966	−	7.42747i	0.0935473	−	0.530533i
$197$	0.984623	−	1.70542i	0.0701515	−	0.121506i	−0.828816	−	0.559521i	$-0.810985\pi$
$197$	0.984623	−	1.70542i	0.0701515	−	0.121506i	0.898968	+	0.438015i	$0.144318\pi$
$198$	17.0129	−	8.85822i	1.20905	−	0.629526i
$199$	−7.27018	−	12.5923i	−0.515369	−	0.892646i	−0.999841	−	0.0178388i	$-0.994321\pi$
$199$	−7.27018	−	12.5923i	−0.515369	−	0.892646i	0.484472	−	0.874807i	$-0.339012\pi$
$200$	0.906220	−	0.329837i	0.0640794	−	0.0233230i
$201$	−6.47161	−	3.19110i	−0.456472	−	0.225083i
$202$	0.560200	−	0.470064i	0.0394155	−	0.0330736i
$203$	9.45041	−	7.92984i	0.663289	−	0.556565i
$204$	4.21676	+	2.07925i	0.295232	+	0.145577i
$205$	−4.28799	+	1.56070i	−0.299486	+	0.109004i
$206$	15.3506	+	26.5881i	1.06953	+	1.85248i
$207$	−21.5190	−	13.7065i	−1.49567	−	0.952669i
$208$	−7.12861	+	12.3471i	−0.494280	+	0.856118i
$209$	−3.36876	+	19.1052i	−0.233022	+	1.32153i
$210$	−7.77128	−	8.11729i	−0.536270	−	0.560146i
$211$	−11.3530	−	4.13217i	−0.781575	−	0.284470i	−0.0797459	−	0.996815i	$-0.525411\pi$
$211$	−11.3530	−	4.13217i	−0.781575	−	0.284470i	−0.701829	+	0.712345i	$0.747633\pi$
$212$	−1.68837	−	9.57525i	−0.115958	−	0.657631i
$213$	−8.91815	+	12.1639i	−0.611062	+	0.833458i
$214$	18.1347	+	15.2168i	1.23966	+	1.04020i
$215$	6.81253			0.464610
$216$	−3.76709	+	3.30451i	−0.256318	+	0.224843i
$217$	12.6107			0.856071
$218$	20.0823	+	16.8511i	1.36015	+	1.14130i
$219$	13.6777	+	1.49736i	0.924254	+	0.101182i
$220$	0.882363	+	5.00413i	0.0594889	+	0.337378i
$221$	5.14376	+	1.87218i	0.346007	+	0.125936i
$222$	25.9065	−	6.34046i	1.73873	−	0.425544i
$223$	−3.61394	+	20.4957i	−0.242007	+	1.37249i	0.585334	+	0.810792i	$0.300963\pi$
$223$	−3.61394	+	20.4957i	−0.242007	+	1.37249i	−0.827342	+	0.561699i	$0.810148\pi$
$224$	12.1099	−	20.9750i	0.809127	−	1.40145i
$225$	−2.97430	+	0.391834i	−0.198287	+	0.0261223i
$226$	−6.95557	−	12.0474i	−0.462678	−	0.801381i
$227$	−8.01519	+	2.91729i	−0.531987	+	0.193627i	−0.594025	−	0.804446i	$-0.702462\pi$
$227$	−8.01519	+	2.91729i	−0.531987	+	0.193627i	0.0620383	+	0.998074i	$0.480240\pi$
$228$	0.952169	+	14.5177i	0.0630589	+	0.961461i
$229$	12.0900	−	10.1447i	0.798931	−	0.670383i	−0.149008	−	0.988836i	$-0.547608\pi$
$229$	12.0900	−	10.1447i	0.798931	−	0.670383i	0.947938	+	0.318453i	$0.103163\pi$
$230$	12.1589	−	10.2026i	0.801737	−	0.672738i
$231$	−17.1501	+	11.4604i	−1.12839	+	0.754037i
$232$	3.21597	−	1.17052i	0.211139	−	0.0768483i
$233$	−9.08918	−	15.7429i	−0.595452	−	1.03135i	−0.993483	−	0.113981i	$-0.963640\pi$
$233$	−9.08918	−	15.7429i	−0.595452	−	1.03135i	0.398031	−	0.917372i	$-0.369694\pi$
$234$	11.3136	−	12.3487i	0.739590	−	0.807260i
$235$	2.15694	−	3.73593i	0.140703	−	0.243705i
$236$	0.839683	−	4.76208i	0.0546587	−	0.309985i
$237$	−7.10235	+	24.3710i	−0.461348	+	1.58306i
$238$	−11.1571	−	4.06086i	−0.723209	−	0.263227i
$239$	−2.15258	−	12.2079i	−0.139239	−	0.789663i	−0.971814	−	0.235750i	$-0.924245\pi$
$239$	−2.15258	−	12.2079i	−0.139239	−	0.789663i	0.832575	−	0.553913i	$-0.186866\pi$
$240$	−3.32529	−	7.55641i	−0.214646	−	0.487764i
$241$	−6.87075	−	5.76524i	−0.442584	−	0.371372i	0.394091	−	0.919071i	$-0.371059\pi$
$241$	−6.87075	−	5.76524i	−0.442584	−	0.371372i	−0.836675	+	0.547699i	$0.815504\pi$
$242$	1.37297			0.0882578
$243$	13.6652	−	7.50081i	0.876623	−	0.481177i
$244$	5.03524			0.322348
$245$	3.89511	+	3.26838i	0.248849	+	0.208809i
$246$	5.94151	+	13.5015i	0.378817	+	0.860827i
$247$	2.94142	+	16.6816i	0.187158	+	1.06143i
$248$	3.28742	+	1.19652i	0.208751	+	0.0759793i
$249$	6.99644	−	24.0075i	0.443382	−	1.52142i
$250$	0.324089	−	1.83800i	0.0204972	−	0.116245i
$251$	−5.89181	+	10.2049i	−0.371888	+	0.644129i	−0.989856	−	0.142074i	$-0.954623\pi$
$251$	−5.89181	+	10.2049i	−0.371888	+	0.644129i	0.617968	+	0.786203i	$0.287956\pi$
$252$	−10.4497	+	11.4059i	−0.658272	+	0.718502i
$253$	−14.5670	−	25.2308i	−0.915822	−	1.58625i
$254$	−22.5411	+	8.20430i	−1.41436	+	0.514784i
$255$	−2.63541	+	1.76109i	−0.165036	+	0.110284i
$256$	15.9788	−	13.4078i	0.998677	−	0.837989i
$257$	−7.83057	+	6.57063i	−0.488458	+	0.409865i	−0.853473	−	0.521137i	$-0.825508\pi$
$257$	−7.83057	+	6.57063i	−0.488458	+	0.409865i	0.365015	+	0.931001i	$0.381064\pi$
$258$	−1.44127	−	21.9751i	−0.0897297	−	1.36811i
$259$	−26.9520	+	9.80971i	−1.67471	+	0.609546i
$260$	2.21837	+	3.84233i	0.137578	+	0.238291i
$261$	−10.5551	+	1.39053i	−0.653346	+	0.0860718i
$262$	16.3632	−	28.3418i	1.01092	−	1.75096i
$263$	−3.97496	+	22.5431i	−0.245107	+	1.39007i	0.575138	+	0.818056i	$0.304948\pi$
$263$	−3.97496	+	22.5431i	−0.245107	+	1.39007i	−0.820245	+	0.572013i	$0.806163\pi$
$264$	−5.55814	+	1.36032i	−0.342080	+	0.0837220i
$265$	6.15972	+	2.24195i	0.378388	+	0.137722i
$266$	−6.38013	−	36.1835i	−0.391191	−	2.21855i
$267$	6.15715	+	0.674050i	0.376811	+	0.0412512i
$268$	−4.73358	−	3.97194i	−0.289149	−	0.242625i
$269$	0.457689			0.0279058			0.0139529	−	0.999903i	$-0.495559\pi$
$269$	0.457689			0.0279058			0.0139529	+	0.999903i	$0.495559\pi$
$270$	1.89319	+	9.51128i	0.115216	+	0.578838i
$271$	−24.7898			−1.50588			−0.752938	−	0.658092i	$-0.771364\pi$
$271$	−24.7898			−1.50588			−0.752938	+	0.658092i	$0.771364\pi$
$272$	−6.68193	−	5.60681i	−0.405152	−	0.339963i
$273$	−10.6490	+	14.5247i	−0.644507	+	0.879076i
$274$	−3.22118	−	18.2682i	−0.194598	−	1.10362i
$275$	−3.21914	−	1.17167i	−0.194121	−	0.0706543i
$276$	−15.1096	−	15.7823i	−0.909489	−	0.949983i
$277$	−1.06913	+	6.06336i	−0.0642381	+	0.364312i	0.935696	+	0.352808i	$0.114773\pi$
$277$	−1.06913	+	6.06336i	−0.0642381	+	0.364312i	−0.999934	+	0.0115042i	$0.996338\pi$
$278$	−2.99121	+	5.18093i	−0.179401	+	0.310731i
$279$	−9.17901	−	5.84657i	−0.549533	−	0.350025i
$280$	1.67624	+	2.90333i	0.100174	+	0.173507i
$281$	17.0698	−	6.21288i	1.01830	−	0.370629i	0.221683	−	0.975119i	$-0.428845\pi$
$281$	17.0698	−	6.21288i	1.01830	−	0.370629i	0.796613	+	0.604489i	$0.206623\pi$
$282$	−12.5073	−	6.16724i	−0.744798	−	0.367254i
$283$	−5.38619	+	4.51955i	−0.320176	+	0.268659i	−0.788683	−	0.614800i	$-0.789237\pi$
$283$	−5.38619	+	4.51955i	−0.320176	+	0.268659i	0.468507	+	0.883460i	$0.344792\pi$
$284$	−9.89470	+	8.30264i	−0.587142	+	0.492671i
$285$	−8.79726	−	4.33786i	−0.521105	−	0.256953i
$286$	17.9711	−	6.54094i	1.06265	−	0.386774i
$287$	−7.93150	−	13.7378i	−0.468182	−	0.810915i
$288$	−18.5389	+	9.65275i	−1.09241	+	0.568794i
$289$	6.82553	−	11.8222i	0.401502	−	0.695421i
$290$	1.15012	−	6.52266i	0.0675374	−	0.383024i
$291$	4.38472	+	4.57995i	0.257037	+	0.268481i
$292$	11.0726	+	4.03009i	0.647974	+	0.235843i
$293$	−4.12441	−	23.3907i	−0.240951	−	1.36650i	−0.829712	−	0.558192i	$-0.811495\pi$
$293$	−4.12441	−	23.3907i	−0.240951	−	1.36650i	0.588761	−	0.808307i	$-0.299616\pi$
$294$	9.71874	−	13.2559i	0.566808	−	0.773099i
$295$	2.49733	+	2.09551i	0.145400	+	0.122005i
$296$	−7.95672			−0.462475
$297$	17.7963	−	0.390611i	1.03265	−	0.0226656i
$298$	1.88486			0.109187
$299$	−19.4869	−	16.3514i	−1.12696	−	0.945628i
$300$	−2.55386	−	0.279582i	−0.147447	−	0.0161417i
$301$	4.11241	+	23.3226i	0.237035	+	1.34429i
$302$	20.8364	+	7.58384i	1.19900	+	0.436401i
$303$	0.659209	−	0.161337i	0.0378706	−	0.00926859i
$304$	4.68717	−	26.5823i	0.268828	−	1.52460i
$305$	−1.69733	+	2.93986i	−0.0971888	+	0.168336i
$306$	6.23829	+	8.12845i	0.356619	+	0.464673i
$307$	9.31264	+	16.1300i	0.531500	+	0.920585i	0.999324	+	0.0367637i	$0.0117049\pi$
$307$	9.31264	+	16.1300i	0.531500	+	0.920585i	−0.467824	+	0.883822i	$0.654962\pi$
$308$	−16.5990	+	6.04153i	−0.945814	+	0.344248i
$309$	1.86468	+	28.4309i	0.106078	+	1.61738i
$310$	5.18645	−	4.35195i	0.294570	−	0.247174i
$311$	1.48464	−	1.24576i	0.0841860	−	0.0706404i	−0.599724	−	0.800207i	$-0.704723\pi$
$311$	1.48464	−	1.24576i	0.0841860	−	0.0706404i	0.683909	+	0.729567i	$0.260278\pi$
$312$	−4.15416	+	2.77598i	−0.235183	+	0.157159i
$313$	28.4277	−	10.3468i	1.60683	−	0.584838i	0.626021	−	0.779806i	$-0.284683\pi$
$313$	28.4277	−	10.3468i	1.60683	−	0.584838i	0.980810	+	0.194968i	$0.0624603\pi$
$314$	−18.2682	−	31.6414i	−1.03093	−	1.78563i
$315$	−3.13689	−	9.94597i	−0.176744	−	0.560392i
$316$	−10.8694	+	18.8264i	−0.611453	+	1.05907i
$317$	0.508892	−	2.88607i	0.0285822	−	0.162098i	−0.967176	−	0.254108i	$-0.918218\pi$
$317$	0.508892	−	2.88607i	0.0285822	−	0.162098i	0.995758	+	0.0920102i	$0.0293292\pi$
$318$	5.92869	−	20.3437i	0.332464	−	1.14082i
$319$	−11.4240	−	4.15799i	−0.639621	−	0.232803i
$320$	−0.602598	−	3.41750i	−0.0336863	−	0.191044i
$321$	8.84907	+	20.1087i	0.493907	+	1.12236i
$322$	42.2682	+	35.4673i	2.35552	+	1.97651i
$323$	−10.3634			−0.576633
$324$	12.8941	−	3.45733i	0.716337	−	0.192074i
$325$	−2.99117			−0.165920
$326$	13.2457	+	11.1144i	0.733610	+	0.615572i
$327$	9.79943	+	22.2683i	0.541909	+	1.23144i
$328$	−0.764162	−	4.33378i	−0.0421938	−	0.239293i
$329$	14.0920	+	5.12906i	0.776915	+	0.282774i
$330$	−3.09840	+	10.6318i	−0.170561	+	0.585262i
$331$	−1.87857	+	10.6539i	−0.103255	+	0.585590i	0.888648	+	0.458591i	$0.151646\pi$
$331$	−1.87857	+	10.6539i	−0.103255	+	0.585590i	−0.991903	+	0.126999i	$0.959465\pi$
$332$	10.7073	−	18.5457i	0.587642	−	1.01783i
$333$	24.1656	+	5.35521i	1.32427	+	0.293464i
$334$	−9.51508	−	16.4806i	−0.520642	−	0.901778i
$335$	3.91469	−	1.42483i	0.213883	−	0.0778469i
$336$	23.8620	−	15.9455i	1.30178	−	0.869901i
$337$	−10.4808	+	8.79442i	−0.570925	+	0.479063i	−0.881953	−	0.471338i	$-0.843771\pi$
$337$	−10.4808	+	8.79442i	−0.570925	+	0.479063i	0.311028	+	0.950401i	$0.399327\pi$
$338$	−5.79450	+	4.86216i	−0.315179	+	0.264467i
$339$	−0.844913	−	12.8824i	−0.0458894	−	0.699676i
$340$	−2.55073	+	0.928388i	−0.138333	+	0.0503489i
$341$	−6.21363	−	10.7623i	−0.336487	−	0.582812i
$342$	−12.1314	+	29.2950i	−0.655992	+	1.58409i
$343$	3.32908	−	5.76614i	0.179754	−	0.311342i
$344$	−1.14084	+	6.47005i	−0.0615102	+	0.348842i
$345$	14.3079	−	3.50177i	0.770312	−	0.188529i
$346$	19.8303	+	7.21764i	1.06608	+	0.388023i
$347$	−3.12373	−	17.7155i	−0.167691	−	0.951020i	−0.946247	−	0.323445i	$-0.895159\pi$
$347$	−3.12373	−	17.7155i	−0.167691	−	0.951020i	0.778556	−	0.627575i	$-0.215952\pi$
$348$	−9.06309	−	0.992176i	−0.485833	−	0.0531862i
$349$	2.87063	+	2.40875i	0.153661	+	0.128937i	0.716377	−	0.697713i	$-0.245799\pi$
$349$	2.87063	+	2.40875i	0.153661	+	0.128937i	−0.562716	+	0.826650i	$0.690243\pi$
$350$	6.48802			0.346799
$351$	14.4851	−	5.63508i	0.773156	−	0.300778i
$352$	−23.8675			−1.27214
$353$	−0.250470	−	0.210170i	−0.0133312	−	0.0111862i	0.636098	−	0.771609i	$-0.280548\pi$
$353$	−0.250470	−	0.210170i	−0.0133312	−	0.0111862i	−0.649429	+	0.760422i	$0.724992\pi$
$354$	6.23111	−	8.49893i	0.331180	−	0.451713i
$355$	−1.51215	−	8.57583i	−0.0802566	−	0.455158i
$356$	4.98443	+	1.81418i	0.264174	+	0.0961516i
$357$	−7.61996	−	7.95923i	−0.403291	−	0.421247i
$358$	−7.79863	+	44.2282i	−0.412171	+	2.33754i
$359$	3.20577	−	5.55255i	0.169194	−	0.293053i	−0.768943	−	0.639318i	$-0.779217\pi$
$359$	3.20577	−	5.55255i	0.169194	−	0.293053i	0.938137	+	0.346265i	$0.112550\pi$
$360$	0.125949	−	2.89039i	0.00663808	−	0.152337i
$361$	−6.53480	−	11.3186i	−0.343937	−	0.595716i
$362$	−16.1590	+	5.88140i	−0.849299	+	0.309120i
$363$	1.14279	+	0.563502i	0.0599810	+	0.0295762i
$364$	−11.8151	+	9.91402i	−0.619278	+	0.519636i
$365$	−6.08546	+	5.10631i	−0.318528	+	0.267277i
$366$	9.84218	+	4.85310i	0.514459	+	0.253676i
$367$	7.66491	−	2.78980i	0.400105	−	0.145626i	−0.134127	−	0.990964i	$-0.542823\pi$
$367$	7.66491	−	2.78980i	0.400105	−	0.145626i	0.534232	+	0.845338i	$0.320601\pi$
$368$	20.2680	+	35.1053i	1.05654	+	1.82999i
$369$	−0.595955	+	13.6766i	−0.0310242	+	0.711973i
$370$	−7.69929	+	13.3356i	−0.400267	+	0.693283i
$371$	−3.95697	+	22.4411i	−0.205436	+	1.16508i
$372$	−6.44504	−	6.73200i	−0.334160	−	0.349038i
$373$	−0.786850	−	0.286390i	−0.0407415	−	0.0148287i	0.321569	−	0.946886i	$-0.395790\pi$
$373$	−0.786850	−	0.286390i	−0.0407415	−	0.0148287i	−0.362311	+	0.932057i	$0.618012\pi$
$374$	2.03176	+	11.5227i	0.105060	+	0.595823i
$375$	1.02412	−	1.39685i	0.0528852	−	0.0721329i
$376$	3.18691	+	2.67413i	0.164352	+	0.137908i
$377$	−10.6150			−0.546700
$378$	−31.4190	+	12.2228i	−1.61602	+	0.628675i
$379$	−7.38310			−0.379245			−0.189622	−	0.981857i	$-0.560726\pi$
$379$	−7.38310			−0.379245			−0.189622	+	0.981857i	$0.560726\pi$
$380$	−6.43464	−	5.39931i	−0.330090	−	0.276979i
$381$	−22.1294	−	2.42260i	−1.13372	−	0.124114i
$382$	−0.635182	−	3.60230i	−0.0324988	−	0.184310i
$383$	−16.1122	−	5.86435i	−0.823293	−	0.299654i	−0.104190	−	0.994557i	$-0.533225\pi$
$383$	−16.1122	−	5.86435i	−0.823293	−	0.299654i	−0.719103	+	0.694903i	$0.755447\pi$
$384$	12.5465	−	3.07069i	0.640263	−	0.156701i
$385$	2.06796	−	11.7280i	0.105393	−	0.597713i
$386$	−9.85263	+	17.0653i	−0.501486	+	0.868599i
$387$	7.81950	−	18.8825i	0.397488	−	0.959853i
$388$	2.71491	+	4.70236i	0.137829	+	0.238726i
$389$	6.10545	−	2.22220i	0.309558	−	0.112670i	−0.182569	−	0.983193i	$-0.558441\pi$
$389$	6.10545	−	2.22220i	0.309558	−	0.112670i	0.492128	+	0.870523i	$0.336219\pi$
$390$	0.632818	+	9.64858i	0.0320440	+	0.488575i
$391$	11.9222	−	10.0039i	0.602931	−	0.505919i
$392$	−3.75636	+	3.15196i	−0.189725	+	0.159198i
$393$	25.2521	−	16.8745i	1.27380	−	0.851205i
$394$	3.45366	−	1.25703i	0.173993	−	0.0633283i
$395$	−7.32796	−	12.6924i	−0.368710	−	0.638624i
$396$	14.8829	+	3.29812i	0.747895	+	0.165737i
$397$	−3.60614	+	6.24602i	−0.180987	+	0.313479i	−0.942217	−	0.335003i	$-0.891263\pi$
$397$	−3.60614	+	6.24602i	−0.180987	+	0.313479i	0.761230	+	0.648482i	$0.224596\pi$
$398$	4.71237	−	26.7252i	0.236210	−	1.33961i
$399$	9.54012	−	32.7359i	0.477604	−	1.63885i
$400$	4.47899	+	1.63022i	0.223949	+	0.0815109i
$401$	−1.84693	−	10.4745i	−0.0922313	−	0.523070i	−0.995561	−	0.0941220i	$-0.969996\pi$
$401$	−1.84693	−	10.4745i	−0.0922313	−	0.523070i	0.903329	−	0.428948i	$-0.141115\pi$
$402$	−5.42427	−	12.3262i	−0.270538	−	0.614773i
$403$	−8.31221	−	6.97477i	−0.414060	−	0.347438i
$404$	0.581191			0.0289153
$405$	−2.32788	+	8.69373i	−0.115673	+	0.431995i
$406$	23.0245			1.14269
$407$	21.6518	+	18.1680i	1.07324	+	0.900555i
$408$	−1.23122	−	2.79784i	−0.0609547	−	0.138514i
$409$	1.72049	+	9.75737i	0.0850727	+	0.482471i	0.997341	+	0.0728778i	$0.0232183\pi$
$409$	1.72049	+	9.75737i	0.0850727	+	0.482471i	−0.912268	+	0.409593i	$0.865671\pi$
$410$	−8.00291	−	2.91282i	−0.395235	−	0.143854i
$411$	4.81659	−	16.5276i	0.237585	−	0.815246i
$412$	−4.23697	+	24.0291i	−0.208741	+	1.18383i
$413$	−5.66643	+	9.81454i	−0.278827	+	0.482942i
$414$	−14.3227	−	45.4120i	−0.703920	−	2.23188i
$415$	7.21868	+	12.5031i	0.354351	+	0.613754i
$416$	−19.5830	+	7.12763i	−0.960135	+	0.349461i
$417$	−4.61612	+	3.08468i	−0.226052	+	0.151057i
$418$	−27.7363	+	23.2735i	−1.35663	+	1.13834i
$419$	−8.15754	+	6.84499i	−0.398522	+	0.334400i	−0.819922	−	0.572475i	$-0.805983\pi$
$419$	−8.15754	+	6.84499i	−0.398522	+	0.334400i	0.421400	+	0.906875i	$0.361539\pi$
$420$	−0.584501	−	8.91190i	−0.0285207	−	0.434856i
$421$	−36.2626	+	13.1985i	−1.76733	+	0.643255i	−0.767331	+	0.641251i	$0.778416\pi$
$421$	−36.2626	+	13.1985i	−1.76733	+	0.643255i	−0.999998	+	0.00200391i	$0.999362\pi$
$422$	−11.2743	−	19.5277i	−0.548826	−	0.950594i
$423$	−7.87925	−	10.2666i	−0.383102	−	0.499180i
$424$	−3.16077	+	5.47461i	−0.153500	+	0.265871i
$425$	0.317778	−	1.80221i	0.0154145	−	0.0874201i
$426$	−27.3431	+	6.69205i	−1.32478	+	0.324231i
$427$	−11.0892	−	4.03614i	−0.536644	−	0.195322i
$428$	3.26706	+	18.5284i	0.157919	+	0.895604i
$429$	17.6428	+	1.93144i	0.851803	+	0.0932506i
$430$	9.73994	+	8.17278i	0.469702	+	0.394127i
$431$	−24.1205			−1.16184			−0.580922	−	0.813960i	$-0.697308\pi$
$431$	−24.1205			−1.16184			−0.580922	+	0.813960i	$0.697308\pi$
$432$	−24.7612	+	0.543482i	−1.19132	+	0.0261483i
$433$	−9.73516			−0.467842			−0.233921	−	0.972256i	$-0.575156\pi$
$433$	−9.73516			−0.467842			−0.233921	+	0.972256i	$0.575156\pi$
$434$	18.0297	+	15.1287i	0.865452	+	0.726201i
$435$	3.63437	−	4.95710i	0.174255	−	0.237675i
$436$	3.61793	+	20.5183i	0.173267	+	0.982647i
$437$	45.2564	+	16.4720i	2.16491	+	0.787962i
$438$	17.7588	+	18.5495i	0.848550	+	0.886331i
$439$	4.96370	−	28.1505i	0.236904	−	1.34355i	−0.601662	−	0.798751i	$-0.705494\pi$
$439$	4.96370	−	28.1505i	0.236904	−	1.34355i	0.838566	−	0.544800i	$-0.183394\pi$
$440$	1.65185	−	2.86109i	0.0787490	−	0.136397i
$441$	13.5299	−	7.04472i	0.644283	−	0.335463i
$442$	5.10810	+	8.84749i	0.242967	+	0.420832i
$443$	−27.5517	+	10.0280i	−1.30902	+	0.476444i	−0.899924	−	0.436048i	$-0.856378\pi$
$443$	−27.5517	+	10.0280i	−1.30902	+	0.476444i	−0.409096	+	0.912492i	$0.634156\pi$
$444$	19.0113	+	9.37430i	0.902235	+	0.444885i
$445$	−2.73943	+	2.29865i	−0.129861	+	0.108967i
$446$	−29.7549	+	24.9673i	−1.40894	+	1.18224i
$447$	1.56886	+	0.773594i	0.0742047	+	0.0365898i
$448$	11.3360	−	4.12598i	0.535578	−	0.194934i
$449$	13.6125	+	23.5775i	0.642413	+	1.11269i	0.984893	+	0.173167i	$0.0553999\pi$
$449$	13.6125	+	23.5775i	0.642413	+	1.11269i	−0.342480	+	0.939525i	$0.611267\pi$
$450$	−4.72246	−	3.00797i	−0.222619	−	0.141797i
$451$	−7.81612	+	13.5379i	−0.368047	+	0.637475i
$452$	1.91983	−	10.8879i	0.0903012	−	0.512123i
$453$	14.2306	+	14.8642i	0.668613	+	0.698382i
$454$	−14.9592	−	5.44470i	−0.702070	−	0.255533i
$455$	−1.80563	−	10.2402i	−0.0846493	−	0.480070i
$456$	5.59300	−	7.62857i	0.261916	−	0.357241i
$457$	−25.1380	−	21.0933i	−1.17591	−	0.986704i	−0.999997	−	0.00229800i	$-0.999269\pi$
$457$	−25.1380	−	21.0933i	−1.17591	−	0.986704i	−0.175911	−	0.984406i	$-0.556287\pi$
$458$	29.4556			1.37637
$459$	1.85632	+	9.32607i	0.0866456	+	0.435304i
$460$	12.6145			0.588156
$461$	4.81252	+	4.03819i	0.224142	+	0.188077i	0.747942	−	0.663764i	$-0.231042\pi$
$461$	4.81252	+	4.03819i	0.224142	+	0.188077i	−0.523801	+	0.851841i	$0.675486\pi$
$462$	−38.2683	−	4.18940i	−1.78040	−	0.194909i
$463$	−4.32044	−	24.5024i	−0.200788	−	1.13872i	−0.903932	−	0.427677i	$-0.859332\pi$
$463$	−4.32044	−	24.5024i	−0.200788	−	1.13872i	0.703144	−	0.711047i	$-0.251779\pi$
$464$	15.8949	+	5.78528i	0.737904	+	0.268575i
$465$	6.10309	−	1.49369i	0.283024	−	0.0692684i
$466$	5.89141	−	33.4118i	0.272914	−	1.54777i
$467$	15.1156	−	26.1809i	0.699464	−	1.21151i	−0.269188	−	0.963088i	$-0.586755\pi$
$467$	15.1156	−	26.1809i	0.699464	−	1.21151i	0.968652	−	0.248420i	$-0.0799114\pi$
$468$	13.1962	−	1.73847i	0.609995	−	0.0803607i
$469$	7.24102	+	12.5418i	0.334359	+	0.579127i
$470$	7.56568	−	2.75368i	0.348979	−	0.127018i
$471$	−2.21909	−	33.8345i	−0.102250	−	1.55901i
$472$	−2.40837	+	2.02086i	−0.110854	+	0.0930177i
$473$	17.8779	−	15.0013i	0.822025	−	0.689761i
$474$	−39.3914	+	26.3230i	−1.80931	+	1.20905i
$475$	5.32148	−	1.93686i	0.244166	−	0.0888693i
$476$	−4.71809	−	8.17197i	−0.216253	−	0.374561i
$477$	13.2843	−	14.4998i	0.608246	−	0.663899i
$478$	11.5679	−	20.0361i	0.529102	−	0.916432i
$479$	−1.45847	+	8.27140i	−0.0666392	+	0.377930i	0.933189	+	0.359386i	$0.117014\pi$
$479$	−1.45847	+	8.27140i	−0.0666392	+	0.377930i	−0.999828	+	0.0185434i	$0.994097\pi$
$480$	3.37631	−	11.5854i	0.154107	−	0.528800i
$481$	23.1907	+	8.44071i	1.05740	+	0.384863i
$482$	−2.90680	−	16.4853i	−0.132401	−	0.750883i
$483$	20.6253	+	46.8691i	0.938485	+	2.13262i
$484$	0.835881	+	0.701387i	0.0379946	+	0.0318812i
$485$	−3.66068			−0.166223
$486$	28.5358	+	5.66975i	1.29441	+	0.257185i
$487$	25.5873			1.15947			0.579735	−	0.814805i	$-0.303156\pi$
$487$	25.5873			1.15947			0.579735	+	0.814805i	$0.303156\pi$
$488$	−2.50783	−	2.10432i	−0.113524	−	0.0952580i
$489$	6.46340	+	14.6875i	0.292285	+	0.664191i
$490$	1.64790	+	9.34569i	0.0744444	+	0.422195i
$491$	2.22987	+	0.811607i	0.100633	+	0.0366273i	0.391846	−	0.920031i	$-0.371837\pi$
$491$	2.22987	+	0.811607i	0.100633	+	0.0366273i	−0.291213	+	0.956658i	$0.594059\pi$
$492$	−3.28005	+	11.2551i	−0.147876	+	0.507421i
$493$	1.12773	−	6.39565i	0.0507902	−	0.288045i
$494$	−15.8071	+	27.3787i	−0.711194	+	1.23182i
$495$	−6.94252	+	7.57774i	−0.312043	+	0.340594i
$496$	8.64541	+	14.9743i	0.388190	+	0.672366i
$497$	28.4465	−	10.3537i	1.27600	−	0.464426i
$498$	38.8040	−	25.9304i	1.73885	−	1.16197i
$499$	1.12305	−	0.942347i	0.0502744	−	0.0421853i	−0.617304	−	0.786725i	$-0.711775\pi$
$499$	1.12305	−	0.942347i	0.0502744	−	0.0421853i	0.667579	+	0.744539i	$0.267331\pi$
$500$	1.13626	−	0.953435i	0.0508151	−	0.0426389i
$501$	−1.15582	−	17.6229i	−0.0516384	−	0.787332i
$502$	−20.6661	+	7.52186i	−0.922374	+	0.335717i
$503$	13.6055	+	23.5654i	0.606640	+	1.05073i	0.991790	+	0.127877i	$0.0408164\pi$
$503$	13.6055	+	23.5654i	0.606640	+	1.05073i	−0.385150	+	0.922854i	$0.625850\pi$
$504$	9.97127	−	1.31361i	0.444156	−	0.0585130i
$505$	−0.195914	+	0.339333i	−0.00871805	+	0.0151001i
$506$	9.44204	−	53.5485i	0.419750	−	2.38052i
$507$	−6.81861	+	1.66881i	−0.302825	+	0.0741147i
$508$	−17.9145	−	6.52035i	−0.794828	−	0.289294i
$509$	−0.472987	−	2.68244i	−0.0209648	−	0.118897i	0.972529	−	0.232780i	$-0.0747822\pi$
$509$	−0.472987	−	2.68244i	−0.0209648	−	0.118897i	−0.993494	+	0.113883i	$0.963671\pi$
$510$	−5.88061	−	0.643776i	−0.260398	−	0.0285069i
$511$	−21.1549	−	17.7511i	−0.935839	−	0.785262i
$512$	24.0150			1.06132
$513$	−22.1210	+	19.4046i	−0.976666	+	0.856736i
$514$	−19.0781			−0.841497
$515$	−12.6013	−	10.5738i	−0.555280	−	0.465935i
$516$	10.3486	−	14.1150i	0.455572	−	0.621378i
$517$	−2.56621	−	14.5537i	−0.112862	−	0.640070i
$518$	−50.3019	−	18.3084i	−2.21014	−	0.804425i
$519$	13.5435	+	14.1465i	0.594492	+	0.620961i
$520$	0.500909	−	2.84080i	0.0219663	−	0.124577i
$521$	2.22878	−	3.86036i	0.0976447	−	0.169126i	−0.813065	−	0.582173i	$-0.802202\pi$
$521$	2.22878	−	3.86036i	0.0976447	−	0.169126i	0.910709	+	0.413048i	$0.135536\pi$
$522$	−16.7590	−	10.6746i	−0.733520	−	0.467215i
$523$	18.2523	+	31.6140i	0.798119	+	1.38238i	0.920840	+	0.389941i	$0.127505\pi$
$523$	18.2523	+	31.6140i	0.798119	+	1.38238i	−0.122721	+	0.992441i	$0.539162\pi$
$524$	24.4406	−	8.89566i	1.06769	−	0.388609i
$525$	5.40031	+	2.66285i	0.235689	+	0.116216i
$526$	−32.7274	+	27.4615i	−1.42698	+	1.19738i
$527$	5.08545	−	4.26720i	0.221526	−	0.185882i
$528$	−25.3658	−	12.5077i	−1.10390	−	0.544326i
$529$	−46.3514	+	16.8705i	−2.01528	+	0.733502i
$530$	6.11701	+	10.5950i	0.265706	+	0.460216i
$531$	8.67465	−	4.51668i	0.376448	−	0.196007i
$532$	14.6002	−	25.2883i	0.632998	−	1.09639i
$533$	−2.37016	+	13.4419i	−0.102663	+	0.582232i
$534$	7.99431	+	8.35024i	0.345948	+	0.361350i
$535$	−11.9192	−	4.33825i	−0.515314	−	0.187559i
$536$	0.697638	+	3.95650i	0.0301334	+	0.170895i
$537$	−24.6436	+	33.6127i	−1.06345	+	1.45049i
$538$	0.654364	+	0.549076i	0.0282116	+	0.0236724i
$539$	17.4188			0.750282
$540$	−3.70628	+	6.75773i	−0.159493	+	0.290806i
$541$	−5.40959			−0.232577			−0.116288	−	0.993216i	$-0.537100\pi$
$541$	−5.40959			−0.232577			−0.116288	+	0.993216i	$0.537100\pi$
$542$	−35.4423	−	29.7396i	−1.52238	−	1.27743i
$543$	−15.8638	−	1.73668i	−0.680783	−	0.0745283i
$544$	−2.21400	−	12.5562i	−0.0949243	−	0.538343i
$545$	−13.1993	−	4.80416i	−0.565397	−	0.205788i
$546$	−32.6499	+	7.99085i	−1.39728	+	0.341977i
$547$	3.75894	−	21.3180i	0.160721	−	0.911492i	−0.792647	−	0.609681i	$-0.791298\pi$
$547$	3.75894	−	21.3180i	0.160721	−	0.911492i	0.953368	−	0.301811i	$-0.0975912\pi$
$548$	7.37129	−	12.7675i	0.314886	−	0.545399i
$549$	6.20031	+	8.07896i	0.264623	+	0.344802i
$550$	−3.19682	−	5.53705i	−0.136313	−	0.236101i
$551$	18.8848	−	6.87349i	0.804518	−	0.292820i
$552$	0.929692	+	14.1750i	0.0395703	+	0.603330i
$553$	39.0288	−	32.7490i	1.65967	−	1.39263i
$554$	−8.80259	+	7.38625i	−0.373986	+	0.313812i
$555$	−11.8818	+	7.93988i	−0.504353	+	0.337029i
$556$	−4.46778	+	1.62614i	−0.189476	+	0.0689637i
$557$	2.62910	+	4.55373i	0.111399	+	0.192948i	0.916334	−	0.400414i	$-0.131134\pi$
$557$	2.62910	+	4.55373i	0.111399	+	0.192948i	−0.804936	+	0.593362i	$0.797800\pi$
$558$	−6.10938	−	19.3707i	−0.258631	−	0.820026i
$559$	10.1887	−	17.6473i	0.430936	−	0.746403i
$560$	−2.87728	+	16.3179i	−0.121587	+	0.689556i
$561$	−3.03806	+	10.4248i	−0.128267	+	0.440135i
$562$	31.8582	+	11.5954i	1.34386	+	0.489124i
$563$	4.12942	+	23.4191i	0.174034	+	0.986998i	0.939253	+	0.343227i	$0.111520\pi$
$563$	4.12942	+	23.4191i	0.174034	+	0.986998i	−0.765218	+	0.643771i	$0.777369\pi$
$564$	−4.46403	−	10.1441i	−0.187969	−	0.427143i
$565$	5.70982	+	4.79111i	0.240214	+	0.201563i
$566$	−13.1227			−0.551587
$567$	−31.1682	−	2.72147i	−1.30894	−	0.114291i
$568$	8.39794			0.352370
$569$	−23.3095	−	19.5590i	−0.977185	−	0.819955i	0.00647745	−	0.999979i	$-0.497938\pi$
$569$	−23.3095	−	19.5590i	−0.977185	−	0.819955i	−0.983662	+	0.180024i	$0.942383\pi$
$570$	−7.37354	−	16.7557i	−0.308844	−	0.701819i
$571$	3.24490	+	18.4027i	0.135795	+	0.770130i	0.974303	+	0.225241i	$0.0723170\pi$
$571$	3.24490	+	18.4027i	0.135795	+	0.770130i	−0.838508	+	0.544889i	$0.816572\pi$
$572$	14.2825	+	5.19840i	0.597181	+	0.217356i
$573$	0.949781	−	3.25907i	0.0396777	−	0.136150i
$574$	5.14103	−	29.1562i	0.214582	−	1.21696i
$575$	−4.25224	+	7.36510i	−0.177331	+	0.307146i
$576$	−10.1641	−	2.25241i	−0.423504	−	0.0938504i
$577$	−9.24093	−	16.0058i	−0.384705	−	0.666329i	0.607023	−	0.794684i	$-0.292363\pi$
$577$	−9.24093	−	16.0058i	−0.384705	−	0.666329i	−0.991728	+	0.128355i	$0.959030\pi$
$578$	23.9412	−	8.71389i	0.995823	−	0.362450i
$579$	−15.2049	+	10.1605i	−0.631892	+	0.422256i
$580$	4.03233	−	3.38353i	0.167434	−	0.140493i
$581$	−38.4468	+	32.2607i	−1.59504	+	1.33840i
$582$	0.774461	+	11.8082i	0.0321025	+	0.489467i
$583$	21.1015	−	7.68033i	0.873936	−	0.318087i
$584$	−3.83052	−	6.63465i	−0.158508	−	0.274544i
$585$	−3.43330	+	8.29073i	−0.141949	+	0.342779i
$586$	22.1644	−	38.3899i	0.915603	−	1.58587i
$587$	4.62650	−	26.2382i	0.190956	−	1.08297i	−0.727105	−	0.686527i	$-0.759135\pi$
$587$	4.62650	−	26.2382i	0.190956	−	1.08297i	0.918061	−	0.396440i	$-0.129754\pi$
$588$	12.6887	−	3.10548i	0.523274	−	0.128068i
$589$	19.3043	+	7.02619i	0.795420	+	0.289509i
$590$	1.05654	+	5.99193i	0.0434971	+	0.246684i
$591$	3.39058	+	0.371181i	0.139470	+	0.0152684i
$592$	−30.1255	−	25.2783i	−1.23815	−	1.03893i
$593$	−4.62357			−0.189867			−0.0949337	−	0.995484i	$-0.530264\pi$
$593$	−4.62357			−0.189867			−0.0949337	+	0.995484i	$0.530264\pi$
$594$	25.9122	+	20.7913i	1.06319	+	0.853076i
$595$	6.36168			0.260804
$596$	1.14753	+	0.962888i	0.0470045	+	0.0394414i
$597$	14.8910	−	20.3107i	0.609450	−	0.831260i
$598$	−8.24429	−	46.7557i	−0.337134	−	1.91198i
$599$	−7.29668	−	2.65577i	−0.298134	−	0.108512i	0.188622	−	0.982050i	$-0.439598\pi$
$599$	−7.29668	−	2.65577i	−0.298134	−	0.108512i	−0.486756	+	0.873538i	$0.661820\pi$
$600$	1.15512	+	1.20655i	0.0471577	+	0.0492573i
$601$	−2.59767	+	14.7321i	−0.105961	+	0.600936i	0.884871	+	0.465837i	$0.154247\pi$
$601$	−2.59767	+	14.7321i	−0.105961	+	0.600936i	−0.990832	+	0.135099i	$0.956865\pi$
$602$	−22.0999	+	38.2782i	−0.900725	+	1.56010i
$603$	0.544074	−	12.4859i	0.0221564	−	0.508467i
$604$	8.81124	+	15.2615i	0.358524	+	0.620982i
$605$	−0.691277	+	0.251604i	−0.0281044	+	0.0102292i
$606$	1.13603	+	0.560167i	0.0461481	+	0.0227552i
$607$	19.7122	−	16.5405i	0.800094	−	0.671359i	−0.148128	−	0.988968i	$-0.547325\pi$
$607$	19.7122	−	16.5405i	0.800094	−	0.671359i	0.948222	+	0.317610i	$0.102880\pi$
$608$	30.2241	−	25.3610i	1.22575	−	1.02853i
$609$	19.1645	+	9.44986i	0.776585	+	0.382928i
$610$	−5.95355	+	2.16692i	−0.241052	+	0.0877359i
$611$	−6.45177	−	11.1748i	−0.261011	−	0.452084i
$612$	−0.354506	+	8.13556i	−0.0143301	+	0.328860i
$613$	−14.5722	+	25.2399i	−0.588567	+	1.01943i	0.405853	+	0.913938i	$0.366974\pi$
$613$	−14.5722	+	25.2399i	−0.588567	+	1.01943i	−0.994420	+	0.105490i	$0.966359\pi$
$614$	−6.03625	+	34.2333i	−0.243603	+	1.38154i
$615$	−5.46573	−	5.70908i	−0.220399	−	0.230213i
$616$	10.7921	+	3.92799i	0.434825	+	0.158263i
$617$	1.48661	+	8.43098i	0.0598486	+	0.339418i	0.999999	−	0.00134119i	$-0.000426915\pi$
$617$	1.48661	+	8.43098i	0.0598486	+	0.339418i	−0.940150	+	0.340760i	$0.889316\pi$
$618$	−31.4417	+	42.8849i	−1.26477	+	1.72509i
$619$	16.6721	+	13.9895i	0.670108	+	0.562287i	0.913097	−	0.407741i	$-0.133684\pi$
$619$	16.6721	+	13.9895i	0.670108	+	0.562287i	−0.242989	+	0.970029i	$0.578128\pi$
$620$	5.38078			0.216097
$621$	6.71679	−	43.6771i	0.269536	−	1.75270i
$622$	3.61710			0.145032
$623$	−9.52309	−	7.99082i	−0.381535	−	0.320146i
$624$	−24.5476	−	2.68733i	−0.982689	−	0.107579i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	53.0562	+	19.3109i	2.12055	+	0.771819i
$627$	−32.6384	+	7.98804i	−1.30345	+	0.319012i
$628$	5.04226	−	28.5961i	0.201208	−	1.14111i
$629$	−7.54937	+	13.0759i	−0.301013	+	0.521370i
$630$	7.44703	−	17.9831i	0.296697	−	0.716463i
$631$	22.3730	+	38.7512i	0.890657	+	1.54266i	0.839090	+	0.543993i	$0.183088\pi$
$631$	22.3730	+	38.7512i	0.890657	+	1.54266i	0.0515673	+	0.998670i	$0.483578\pi$
$632$	13.2815	−	4.83407i	0.528309	−	0.192289i
$633$	−1.36952	−	20.8812i	−0.0544337	−	0.829952i
$634$	4.18990	−	3.51574i	0.166402	−	0.139628i
$635$	9.84577	−	8.26158i	0.390717	−	0.327851i
$636$	14.0021	−	9.35677i	0.555219	−	0.371020i
$637$	14.2920	−	5.20185i	0.566268	−	0.206105i
$638$	−11.3448	−	19.6498i	−0.449145	−	0.777941i
$639$	−25.5056	−	5.65216i	−1.00899	−	0.223596i
$640$	−3.72877	+	6.45842i	−0.147393	+	0.255292i
$641$	4.57420	−	25.9416i	0.180670	−	1.02463i	−0.750723	−	0.660617i	$-0.770295\pi$
$641$	4.57420	−	25.9416i	0.180670	−	1.02463i	0.931393	−	0.364014i	$-0.118594\pi$
$642$	−11.4722	+	39.3656i	−0.452771	+	1.55364i
$643$	−34.1452	−	12.4278i	−1.34656	−	0.490106i	−0.434684	−	0.900583i	$-0.643140\pi$
$643$	−34.1452	−	12.4278i	−1.34656	−	0.490106i	−0.911871	+	0.410477i	$0.865362\pi$
$644$	7.61482	+	43.1858i	0.300066	+	1.70176i
$645$	4.75273	+	10.8001i	0.187139	+	0.425255i
$646$	−14.8166	−	12.4326i	−0.582952	−	0.489155i
$647$	−39.1069			−1.53745			−0.768725	−	0.639580i	$-0.779108\pi$
$647$	−39.1069			−1.53745			−0.768725	+	0.639580i	$0.779108\pi$
$648$	−7.86685	−	3.66673i	−0.309039	−	0.144043i
$649$	11.1680			0.438382
$650$	−4.27651	−	3.58841i	−0.167738	−	0.140749i
$651$	8.79781	+	19.9922i	0.344813	+	0.783557i
$652$	2.38627	+	13.5332i	0.0934536	+	0.530002i
$653$	13.7430	+	5.00203i	0.537804	+	0.195744i	0.596619	−	0.802524i	$-0.296510\pi$
$653$	13.7430	+	5.00203i	0.537804	+	0.195744i	−0.0588158	+	0.998269i	$0.518732\pi$
$654$	−12.7043	+	43.5933i	−0.496776	+	1.70463i
$655$	−3.04490	+	17.2685i	−0.118974	+	0.674736i
$656$	10.8751	−	18.8362i	0.424600	−	0.735428i
$657$	7.16838	+	22.7284i	0.279665	+	0.886719i
$658$	13.9943	+	24.2388i	0.545553	+	0.944926i
$659$	19.5964	−	7.13252i	0.763369	−	0.277844i	0.0691489	−	0.997606i	$-0.477972\pi$
$659$	19.5964	−	7.13252i	0.763369	−	0.277844i	0.694220	+	0.719763i	$0.255749\pi$
$660$	−7.31765	+	4.88995i	−0.284839	+	0.190341i
$661$	13.5383	−	11.3600i	0.526580	−	0.441853i	−0.340339	−	0.940303i	$-0.610542\pi$
$661$	13.5383	−	11.3600i	0.526580	−	0.441853i	0.866918	+	0.498450i	$0.166097\pi$
$662$	−15.4669	+	12.9783i	−0.601140	+	0.504416i
$663$	0.620495	+	9.46070i	0.0240980	+	0.367423i
$664$	−13.0834	+	4.76198i	−0.507735	+	0.184801i
$665$	9.84316	+	17.0489i	0.381701	+	0.661126i
$666$	28.1253	+	36.6471i	1.08983	+	1.42005i
$667$	−15.0903	+	26.1371i	−0.584297	+	1.01203i
$668$	2.62629	−	14.8944i	0.101614	−	0.576282i
$669$	−35.0138	+	8.56941i	−1.35371	+	0.331312i
$670$	7.30621	+	2.65924i	0.282263	+	0.102735i
$671$	2.01939	+	11.4525i	0.0779576	+	0.442120i
$672$	41.7008	+	4.56517i	1.60864	+	0.176105i
$673$	−18.0270	−	15.1265i	−0.694890	−	0.583082i	0.225425	−	0.974261i	$-0.427623\pi$
$673$	−18.0270	−	15.1265i	−0.694890	−	0.583082i	−0.920315	+	0.391179i	$0.872067\pi$
$674$	−25.5349			−0.983567
$675$	−2.69620	−	4.44191i	−0.103777	−	0.170969i
$676$	−6.01162			−0.231216
$677$	29.2846	+	24.5727i	1.12550	+	0.944407i	0.998869	−	0.0475429i	$-0.0151391\pi$
$677$	29.2846	+	24.5727i	1.12550	+	0.944407i	0.126631	+	0.991950i	$0.459584\pi$
$678$	14.2467	−	19.4317i	0.547140	−	0.746271i
$679$	−2.20978	−	12.5323i	−0.0848038	−	0.480946i
$680$	1.65839	+	0.603606i	0.0635965	+	0.0231472i
$681$	−10.2167	−	10.6715i	−0.391503	−	0.408934i
$682$	4.02754	−	22.8413i	0.154222	−	0.874639i
$683$	−2.77501	+	4.80646i	−0.106183	+	0.183914i	−0.914221	−	0.405216i	$-0.867196\pi$
$683$	−2.77501	+	4.80646i	−0.106183	+	0.183914i	0.808038	+	0.589130i	$0.200530\pi$
$684$	−22.3512	+	11.6377i	−0.854620	+	0.444980i
$685$	4.96958	+	8.60757i	0.189878	+	0.328878i
$686$	11.6771	−	4.25011i	0.445833	−	0.162270i
$687$	24.5174	+	12.0893i	0.935395	+	0.461236i
$688$	−24.8746	+	20.8723i	−0.948335	+	0.795748i
$689$	15.0200	−	12.6033i	0.572216	−	0.480146i
$690$	24.6571	+	12.1582i	0.938681	+	0.462856i
$691$	28.6323	−	10.4213i	1.08922	−	0.396445i	0.265890	−	0.964003i	$-0.414334\pi$
$691$	28.6323	−	10.4213i	1.08922	−	0.396445i	0.823333	+	0.567559i	$0.192112\pi$
$692$	8.38577	+	14.5246i	0.318779	+	0.552142i
$693$	−30.1332	−	19.1933i	−1.14467	−	0.729095i
$694$	16.7868	−	29.0756i	0.637217	−	1.10369i
$695$	0.556612	−	3.15670i	0.0211135	−	0.119741i
$696$	4.09928	+	4.28179i	0.155383	+	0.162301i
$697$	−7.84707	−	2.85610i	−0.297229	−	0.108183i
$698$	1.21447	+	6.88762i	0.0459685	+	0.260700i
$699$	18.6168	−	25.3924i	0.704152	−	0.960428i
$700$	3.94999	+	3.31443i	0.149295	+	0.125274i
$701$	−9.84780			−0.371946			−0.185973	−	0.982555i	$-0.559544\pi$
$701$	−9.84780			−0.371946			−0.185973	+	0.982555i	$0.559544\pi$
$702$	27.4697	+	9.32076i	1.03678	+	0.351789i
$703$	−46.7233			−1.76220
$704$	−9.10678	−	7.64150i	−0.343225	−	0.288000i
$705$	7.42748	+	0.813119i	0.279735	+	0.0306238i
$706$	−0.105966	−	0.600964i	−0.00398809	−	0.0226176i
$707$	−1.27997	−	0.465870i	−0.0481381	−	0.0175208i
$708$	8.13529	−	1.99106i	0.305743	−	0.0748288i
$709$	−7.42637	+	42.1171i	−0.278903	+	1.58174i	0.447380	+	0.894344i	$0.352357\pi$
$709$	−7.42637	+	42.1171i	−0.278903	+	1.58174i	−0.726284	+	0.687395i	$0.758754\pi$
$710$	8.12623	−	14.0750i	0.304972	−	0.528227i
$711$	−43.5911	+	5.74269i	−1.63479	+	0.215368i
$712$	−1.72434	−	2.98665i	−0.0646225	−	0.111929i
$713$	−28.9905	+	10.5517i	−1.08570	+	0.395163i
$714$	−1.34589	−	20.5208i	−0.0503687	−	0.767973i
$715$	−7.84961	+	6.58661i	−0.293559	+	0.246325i
$716$	−27.3421	+	22.9427i	−1.02182	+	0.857410i
$717$	17.8519	−	11.9293i	0.666690	−	0.445510i
$718$	11.2446	−	4.09268i	0.419643	−	0.152738i
$719$	5.28698	+	9.15732i	0.197171	+	0.341510i	0.947610	−	0.319429i	$-0.103491\pi$
$719$	5.28698	+	9.15732i	0.197171	+	0.341510i	−0.750439	+	0.660940i	$0.770158\pi$
$720$	9.65957	−	10.5434i	0.359991	−	0.392929i
$721$	28.5923	−	49.5234i	1.06483	−	1.84435i
$722$	4.23571	−	24.0219i	0.157637	−	0.894004i
$723$	4.34650	−	14.9145i	0.161648	−	0.554678i
$724$	−12.8423	−	4.67423i	−0.477282	−	0.173716i
$725$	0.616239	+	3.49486i	0.0228865	+	0.129796i
$726$	0.957846	+	2.17662i	0.0355490	+	0.0807819i
$727$	30.8438	+	25.8811i	1.14393	+	0.959875i	0.999560	−	0.0296480i	$-0.00943865\pi$
$727$	30.8438	+	25.8811i	1.14393	+	0.959875i	0.144374	+	0.989523i	$0.453883\pi$
$728$	10.0278			0.371656
$729$	21.4248	+	16.4310i	0.793510	+	0.608557i
$730$	−14.8263			−0.548748
$731$	9.55028	+	8.01364i	0.353230	+	0.296395i
$732$	3.51281	+	7.98254i	0.129837	+	0.295043i
$733$	7.76303	+	44.0263i	0.286734	+	1.62615i	0.699025	+	0.715098i	$0.253618\pi$
$733$	7.76303	+	44.0263i	0.286734	+	1.62615i	−0.412290	+	0.911052i	$0.635271\pi$
$734$	14.3054	+	5.20676i	0.528024	+	0.192185i
$735$	−2.46408	+	8.45523i	−0.0908890	+	0.311876i
$736$	−10.2889	+	58.3515i	−0.379255	+	2.15086i
$737$	7.13568	−	12.3594i	0.262846	−	0.455263i
$738$	−17.2594	+	18.8386i	−0.635328	+	0.693458i
$739$	−7.15194	−	12.3875i	−0.263088	−	0.455682i	0.703973	−	0.710227i	$-0.251408\pi$
$739$	−7.15194	−	12.3875i	−0.263088	−	0.455682i	−0.967061	+	0.254545i	$0.918074\pi$
$740$	−11.5000	+	4.18564i	−0.422747	+	0.153867i
$741$	−24.3939	+	16.3010i	−0.896134	+	0.598833i
$742$	−32.5792	+	27.3372i	−1.19602	+	1.00358i
$743$	16.7804	−	14.0804i	0.615612	−	0.516560i	−0.280809	−	0.959764i	$-0.590603\pi$
$743$	16.7804	−	14.0804i	0.615612	−	0.516560i	0.896421	+	0.443204i	$0.146158\pi$
$744$	0.396564	+	6.04642i	0.0145387	+	0.221672i
$745$	−0.949009	+	0.345411i	−0.0347690	+	0.0126549i
$746$	−0.781395	−	1.35342i	−0.0286089	−	0.0495521i
$747$	42.9411	−	5.65705i	1.57113	−	0.206981i
$748$	−4.64945	+	8.05308i	−0.170001	+	0.294450i
$749$	7.65686	−	43.4242i	0.279776	−	1.58669i
$750$	3.13995	−	0.768484i	0.114655	−	0.0280611i
$751$	−2.77841	−	1.01126i	−0.101386	−	0.0369014i	0.290829	−	0.956775i	$-0.406069\pi$
$751$	−2.77841	−	1.01126i	−0.101386	−	0.0369014i	−0.392215	+	0.919874i	$0.628291\pi$
$752$	3.57053	+	20.2495i	0.130204	+	0.738422i
$753$	−20.2886	−	2.22108i	−0.739359	−	0.0809408i
$754$	−15.1764	−	12.7345i	−0.552691	−	0.463763i
$755$	−11.8807			−0.432384
$756$	−25.3723	−	8.60910i	−0.922783	−	0.313110i
$757$	31.6130			1.14899			0.574497	−	0.818507i	$-0.305198\pi$
$757$	31.6130			1.14899			0.574497	+	0.818507i	$0.305198\pi$
$758$	−10.5557	−	8.85729i	−0.383401	−	0.321711i
$759$	29.8367	−	40.6958i	1.08301	−	1.47717i
$760$	0.948342	+	5.37831i	0.0344000	+	0.195092i
$761$	15.9097	+	5.79066i	0.576727	+	0.209911i	0.613882	−	0.789398i	$-0.289607\pi$
$761$	15.9097	+	5.79066i	0.576727	+	0.209911i	−0.0371547	+	0.999310i	$0.511829\pi$
$762$	−28.7323	−	30.0116i	−1.04086	−	1.08720i
$763$	8.47918	−	48.0878i	0.306967	−	1.74090i
$764$	1.45354	−	2.51761i	0.0525873	−	0.0910839i
$765$	−4.63051	−	2.94940i	−0.167416	−	0.106636i
$766$	−16.0005	−	27.7136i	−0.578120	−	1.00133i
$767$	9.16321	−	3.33514i	0.330864	−	0.120425i
$768$	32.4035	+	15.9779i	1.16926	+	0.576553i
$769$	−15.8071	+	13.2638i	−0.570020	+	0.478303i	−0.881653	−	0.471899i	$-0.843569\pi$
$769$	−15.8071	+	13.2638i	−0.570020	+	0.478303i	0.311633	+	0.950203i	$0.399124\pi$
$770$	17.0263	−	14.2867i	0.613584	−	0.514858i
$771$	−15.8796	−	7.83012i	−0.571891	−	0.281995i
$772$	−14.7163	+	5.35628i	−0.529650	+	0.192777i
$773$	−7.16157	−	12.4042i	−0.257584	−	0.446148i	0.708010	−	0.706202i	$-0.249593\pi$
$773$	−7.16157	−	12.4042i	−0.257584	−	0.446148i	−0.965594	+	0.260054i	$0.916260\pi$
$774$	33.8324	−	17.6157i	1.21608	−	0.633185i
$775$	−1.81381	+	3.14161i	−0.0651540	+	0.112850i
$776$	0.613027	−	3.47665i	0.0220064	−	0.124804i
$777$	−34.3546	−	35.8842i	−1.23246	−	1.28734i
$778$	11.3949	+	4.14742i	0.408528	+	0.148692i
$779$	−4.48729	−	25.4487i	−0.160774	−	0.911795i
$780$	−4.54375	+	6.19745i	−0.162692	+	0.221904i
$781$	−22.8524	−	19.1755i	−0.817724	−	0.686152i
$782$	29.0467			1.03871
$783$	−9.56821	−	15.7633i	−0.341940	−	0.563336i
$784$	−24.2359			−0.865568
$785$	14.9963	+	12.5834i	0.535242	+	0.449122i
$786$	56.3470	+	6.16855i	2.00983	+	0.220025i
$787$	5.33548	+	30.2590i	0.190189	+	1.07862i	0.919105	+	0.394013i	$0.128914\pi$
$787$	5.33548	+	30.2590i	0.190189	+	1.07862i	−0.728916	+	0.684603i	$0.759975\pi$
$788$	2.74479	+	0.999023i	0.0977792	+	0.0355887i
$789$	−38.5116	+	9.42547i	−1.37105	+	0.335556i
$790$	4.74982	−	26.9376i	0.168991	−	0.958397i
$791$	−12.9556	+	22.4397i	−0.460647	+	0.797864i
$792$	−6.03418	−	7.86250i	−0.214415	−	0.279382i
$793$	5.07700	+	8.79362i	0.180289	+	0.312270i
$794$	−12.6489	+	4.60382i	−0.448893	+	0.163384i
$795$	0.743051	+	11.3293i	0.0263533	+	0.401809i
$796$	16.5216	−	13.8633i	0.585594	−	0.491371i
$797$	−23.7219	+	19.9050i	−0.840271	+	0.705071i	−0.957625	−	0.288019i	$-0.907003\pi$
$797$	−23.7219	+	19.9050i	−0.840271	+	0.705071i	0.117354	+	0.993090i	$0.462559\pi$
$798$	52.9119	−	35.3579i	1.87306	−	1.25166i
$799$	7.41836	−	2.70006i	0.262443	−	0.0955213i
$800$	3.48355	+	6.03369i	0.123162	+	0.213323i
$801$	3.22691	+	10.2314i	0.114017	+	0.361509i
$802$	9.92532	−	17.1912i	0.350475	−	0.607041i
$803$	−4.72567	+	26.8006i	−0.166765	+	0.945773i
$804$	2.99451	−	10.2753i	0.105608	−	0.362383i
$805$	−27.7812	−	10.1115i	−0.979160	−	0.356385i
$806$	−3.51663	−	19.9438i	−0.123868	−	0.702491i
$807$	0.319305	+	0.725591i	0.0112401	+	0.0255420i
$808$	−0.289465	−	0.242890i	−0.0101834	−	0.00854485i
$809$	−2.58326			−0.0908226			−0.0454113	−	0.998968i	$-0.514460\pi$
$809$	−2.58326			−0.0908226			−0.0454113	+	0.998968i	$0.514460\pi$
$810$	−13.7578	+	9.63684i	−0.483400	+	0.338604i
$811$	−24.6638			−0.866064			−0.433032	−	0.901379i	$-0.642556\pi$
$811$	−24.6638			−0.866064			−0.433032	+	0.901379i	$0.642556\pi$
$812$	14.0176	+	11.7622i	0.491922	+	0.412772i
$813$	−17.2945	−	39.3002i	−0.606546	−	1.37832i
$814$	9.16019	+	51.9500i	0.321065	+	1.82085i
$815$	−8.70586	−	3.16867i	−0.304953	−	0.110994i
$816$	4.22705	−	14.5047i	0.147976	−	0.507765i
$817$	−6.69923	+	37.9932i	−0.234376	+	1.32922i
$818$	−9.24583	+	16.0142i	−0.323273	+	0.559925i
$819$	−30.4558	−	6.74914i	−1.06421	−	0.235834i
$820$	−3.38424	−	5.86168i	−0.118183	−	0.204699i
$821$	−21.3469	+	7.76964i	−0.745013	+	0.271162i	−0.686505	−	0.727125i	$-0.740856\pi$
$821$	−21.3469	+	7.76964i	−0.745013	+	0.271162i	−0.0585070	+	0.998287i	$0.518634\pi$
$822$	26.7140	−	17.8514i	0.931758	−	0.622638i
$823$	20.4763	−	17.1816i	0.713758	−	0.598914i	−0.211893	−	0.977293i	$-0.567963\pi$
$823$	20.4763	−	17.1816i	0.713758	−	0.598914i	0.925651	+	0.378379i	$0.123518\pi$
$824$	12.1524	−	10.1971i	0.423350	−	0.355233i
$825$	−0.388326	−	5.92082i	−0.0135198	−	0.206137i
$826$	−19.8756	+	7.23411i	−0.691559	+	0.251707i
$827$	−7.72449	−	13.3792i	−0.268607	−	0.465241i	0.699895	−	0.714245i	$-0.253230\pi$
$827$	−7.72449	−	13.3792i	−0.268607	−	0.465241i	−0.968502	+	0.249005i	$0.919897\pi$
$828$	14.4791	−	34.9642i	0.503184	−	1.21509i
$829$	6.87832	−	11.9136i	0.238894	−	0.413776i	−0.721503	−	0.692411i	$-0.756549\pi$
$829$	6.87832	−	11.9136i	0.238894	−	0.413776i	0.960397	+	0.278635i	$0.0898819\pi$
$830$	−4.67899	+	26.5359i	−0.162410	+	0.921074i
$831$	−10.3583	+	2.53514i	−0.359327	+	0.0879431i
$832$	−9.75403	−	3.55018i	−0.338160	−	0.123080i
$833$	1.61581	+	9.16370i	0.0559844	+	0.317504i
$834$	−10.3003	−	1.12762i	−0.356671	−	0.0390463i
$835$	7.81092	+	6.55414i	0.270308	+	0.226815i
$836$	−28.7756			−0.995224
$837$	2.86507	−	18.6306i	0.0990315	−	0.643969i
$838$	−19.8747			−0.686559
$839$	7.36180	+	6.17729i	0.254158	+	0.213264i	0.760960	−	0.648799i	$-0.224728\pi$
$839$	7.36180	+	6.17729i	0.254158	+	0.213264i	−0.506803	+	0.862062i	$0.669173\pi$
$840$	−3.43333	+	4.68290i	−0.118461	+	0.161575i
$841$	−2.84890	−	16.1569i	−0.0982380	−	0.557135i
$842$	−67.6788	−	24.6331i	−2.33237	−	0.848912i
$843$	21.7581	+	22.7269i	0.749390	+	0.782756i
$844$	3.11186	−	17.6482i	0.107115	−	0.607477i
$845$	2.02646	−	3.50993i	0.0697123	−	0.120745i
$846$	1.05150	−	24.1308i	0.0361512	−	0.829634i
$847$	−1.27866	−	2.21470i	−0.0439352	−	0.0760980i
$848$	−29.3599	+	10.6861i	−1.00822	+	0.366963i
$849$	−10.9227	−	5.38588i	−0.374865	−	0.184843i
$850$	2.61639	−	2.19541i	0.0897414	−	0.0753020i
$851$	53.7512	−	45.1026i	1.84257	−	1.54610i
$852$	−20.0655	−	9.89412i	−0.687431	−	0.338967i
$853$	19.3174	−	7.03097i	0.661416	−	0.240736i	0.0105685	−	0.999944i	$-0.496636\pi$
$853$	19.3174	−	7.03097i	0.661416	−	0.240736i	0.650848	+	0.759208i	$0.274414\pi$
$854$	−11.0123	−	19.0739i	−0.376834	−	0.652695i
$855$	0.739592	−	16.9729i	0.0252935	−	0.580461i
$856$	6.11618	−	10.5935i	0.209047	−	0.362080i
$857$	−7.03369	+	39.8901i	−0.240266	+	1.36262i	0.590967	+	0.806695i	$0.298746\pi$
$857$	−7.03369	+	39.8901i	−0.240266	+	1.36262i	−0.831234	+	0.555923i	$0.812365\pi$
$858$	22.9070	+	23.9269i	0.782033	+	0.816853i
$859$	−23.7524	−	8.64516i	−0.810421	−	0.294969i	−0.0966234	−	0.995321i	$-0.530804\pi$
$859$	−23.7524	−	8.64516i	−0.810421	−	0.294969i	−0.713798	+	0.700352i	$0.753026\pi$
$860$	1.75470	+	9.95138i	0.0598347	+	0.339339i
$861$	16.2456	−	22.1582i	0.553649	−	0.755149i
$862$	−34.4853	−	28.9366i	−1.17458	−	0.985585i
$863$	47.4531			1.61532			0.807661	−	0.589648i	$-0.200733\pi$
$863$	47.4531			1.61532			0.807661	+	0.589648i	$0.200733\pi$
$864$	−28.2364	−	22.6561i	−0.960623	−	0.770778i
$865$	−11.3070			−0.384451
$866$	−13.9185	−	11.6790i	−0.472969	−	0.396868i
$867$	23.5039	+	2.57307i	0.798234	+	0.0873862i
$868$	3.24813	+	18.4211i	0.110249	+	0.625252i
$869$	−47.1794	−	17.1719i	−1.60045	−	0.582516i
$870$	11.1430	−	2.72718i	0.377782	−	0.0924600i
$871$	2.16383	−	12.2717i	0.0733185	−	0.415810i
$872$	6.77304	−	11.7312i	0.229364	−	0.397270i
$873$	−4.20177	+	10.1464i	−0.142209	+	0.343405i
$874$	44.9427	+	77.8430i	1.52021	+	2.63308i
$875$	−3.26666	+	1.18897i	−0.110433	+	0.0401944i
$876$	1.33569	+	20.3654i	0.0451289	+	0.688082i
$877$	−2.59201	+	2.17496i	−0.0875260	+	0.0734430i	−0.685501	−	0.728072i	$-0.740417\pi$
$877$	−2.59201	+	2.17496i	−0.0875260	+	0.0734430i	0.597975	+	0.801515i	$0.295972\pi$
$878$	40.8680	−	34.2923i	1.37923	−	1.15731i
$879$	34.2047	−	22.8570i	1.15370	−	0.770948i
$880$	15.3438	−	5.58469i	0.517240	−	0.188260i
$881$	−11.9030	−	20.6166i	−0.401022	−	0.694591i	0.592827	−	0.805330i	$-0.298012\pi$
$881$	−11.9030	−	20.6166i	−0.401022	−	0.694591i	−0.993850	+	0.110738i	$0.964678\pi$
$882$	27.7953	+	6.15956i	0.935915	+	0.207403i
$883$	−11.6829	+	20.2353i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$883$	−11.6829	+	20.2353i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$884$	−1.40990	+	7.99595i	−0.0474201	+	0.268933i
$885$	−1.57983	+	5.42102i	−0.0531054	+	0.182226i
$886$	−51.4212	−	18.7158i	−1.72753	−	0.628769i
$887$	5.36066	+	30.4018i	0.179993	+	1.02079i	0.932221	+	0.361890i	$0.117868\pi$
$887$	5.36066	+	30.4018i	0.179993	+	1.02079i	−0.752228	+	0.658903i	$0.771021\pi$
$888$	−5.55098	−	12.6141i	−0.186279	−	0.423301i
$889$	34.2269	+	28.7198i	1.14793	+	0.963231i
$890$	−6.67422			−0.223720
$891$	13.0348	+	27.9407i	0.436682	+	0.936048i
$892$	−30.8698			−1.03360
$893$	18.7141	+	15.7030i	0.626243	+	0.525480i
$894$	1.31496	+	2.98814i	0.0439790	+	0.0999382i
$895$	−4.17854	−	23.6977i	−0.139673	−	0.792125i
$896$	−24.3613	−	8.86677i	−0.813853	−	0.296218i
$897$	12.3276	−	42.3008i	0.411606	−	1.41238i
$898$	−8.82332	+	50.0395i	−0.294438	+	1.66984i
$899$	−6.43681	+	11.1489i	−0.214680	+	0.371836i
$900$	−1.33846	−	4.24378i	−0.0446153	−	0.141459i
$901$	5.99790	+	10.3887i	0.199819	+	0.346097i
$902$	−27.4158	+	9.97854i	−0.912847	+	0.332249i
$903$	−34.1052	+	22.7905i	−1.13495	+	0.758420i
$904$	−5.50643	+	4.62045i	−0.183141	+	0.153674i
$905$	7.05812	−	5.92246i	0.234620	−	0.196869i
$906$	2.51351	+	38.3236i	0.0835059	+	1.27322i
$907$	10.5268	−	3.83144i	0.349537	−	0.127221i	−0.161284	−	0.986908i	$-0.551564\pi$
$907$	10.5268	−	3.83144i	0.349537	−	0.127221i	0.510821	+	0.859687i	$0.329341\pi$
$908$	−6.32589	−	10.9568i	−0.209932	−	0.363613i
$909$	0.715668	+	0.932511i	0.0237372	+	0.0309295i
$910$	9.70338	−	16.8067i	0.321664	−	0.557138i
$911$	−4.51397	+	25.6000i	−0.149555	+	0.848166i	0.814042	+	0.580806i	$0.197262\pi$
$911$	−4.51397	+	25.6000i	−0.149555	+	0.848166i	−0.963597	+	0.267360i	$0.913849\pi$
$912$	45.4118	−	11.1143i	1.50374	−	0.368030i
$913$	46.4758	+	16.9158i	1.53813	+	0.559832i
$914$	−10.6351	−	60.3147i	−0.351778	−	1.99503i
$915$	−5.84480	−	0.639856i	−0.193223	−	0.0211530i
$916$	17.9329	+	15.0475i	0.592520	+	0.497183i
$917$	−60.9566			−2.01296
$918$	−8.53421	+	15.5606i	−0.281671	+	0.513575i
$919$	−9.14191			−0.301564			−0.150782	−	0.988567i	$-0.548179\pi$
$919$	−9.14191			−0.301564			−0.150782	+	0.988567i	$0.548179\pi$
$920$	−6.28275	−	5.27185i	−0.207136	−	0.173808i
$921$	−19.0745	+	26.0167i	−0.628526	+	0.857278i
$922$	2.03603	+	11.5469i	0.0670530	+	0.380276i
$923$	−24.4766	−	8.90876i	−0.805657	−	0.293235i
$924$	−21.1580	−	22.1001i	−0.696049	−	0.727039i
$925$	1.43270	−	8.12527i	0.0471070	−	0.267157i
$926$	23.2178	−	40.2145i	0.762986	−	1.32153i
$927$	−43.7716	+	22.7908i	−1.43765	+	0.748549i
$928$	12.3624	+	21.4122i	0.405814	+	0.702891i
$929$	51.0829	−	18.5927i	1.67598	−	0.610005i	0.683226	−	0.730207i	$-0.260576\pi$
$929$	51.0829	−	18.5927i	1.67598	−	0.610005i	0.992749	+	0.120202i	$0.0383541\pi$
$930$	10.5176	+	5.18614i	0.344886	+	0.170060i
$931$	−22.0580	+	18.5089i	−0.722922	+	0.606603i
$932$	20.6553	−	17.3319i	0.676588	−	0.567725i
$933$	3.01069	+	1.48455i	0.0985657	+	0.0486019i
$934$	53.0193	−	19.2975i	1.73485	−	0.631432i
$935$	−3.13457	−	5.42923i	−0.102511	−	0.177555i
$936$	−7.29899	−	4.64909i	−0.238575	−	0.151960i
$937$	0.513624	−	0.889623i	0.0167794	−	0.0290627i	−0.857514	−	0.514461i	$-0.827992\pi$
$937$	0.513624	−	0.889623i	0.0167794	−	0.0290627i	0.874293	+	0.485398i	$0.161325\pi$
$938$	−4.69347	+	26.6180i	−0.153247	+	0.869109i
$939$	36.2357	+	37.8491i	1.18251	+	1.23516i
$940$	6.01281	+	2.18848i	0.196116	+	0.0713805i
$941$	8.92999	+	50.6445i	0.291109	+	1.65096i	0.682608	+	0.730785i	$0.260846\pi$
$941$	8.92999	+	50.6445i	0.291109	+	1.65096i	−0.391499	+	0.920179i	$0.628043\pi$
$942$	37.4176	−	51.0357i	1.21913	−	1.66283i
$943$	29.7283	+	24.9450i	0.968085	+	0.812320i
$944$	−15.5387			−0.505742
$945$	13.5793	−	11.9118i	0.441733	−	0.387490i
$946$	43.5568			1.41615
$947$	−20.8637	−	17.5068i	−0.677980	−	0.568893i	0.237435	−	0.971403i	$-0.423693\pi$
$947$	−20.8637	−	17.5068i	−0.677980	−	0.568893i	−0.915415	+	0.402510i	$0.868138\pi$
$948$	−37.4292	−	4.09754i	−1.21564	−	0.133082i
$949$	4.12620	+	23.4009i	0.133942	+	0.759624i
$950$	9.93177	+	3.61487i	0.322229	+	0.117282i
$951$	4.93041	−	1.20669i	0.159880	−	0.0391296i
$952$	−1.06534	+	6.04187i	−0.0345280	+	0.195818i
$953$	6.60432	−	11.4390i	0.213935	−	0.370546i	−0.739008	−	0.673697i	$-0.764705\pi$
$953$	6.60432	−	11.4390i	0.213935	−	0.370546i	0.952943	+	0.303151i	$0.0980386\pi$
$954$	36.3877	−	4.79370i	1.17809	−	0.155202i
$955$	0.979950	+	1.69732i	0.0317104	+	0.0549241i
$956$	17.2782	−	6.28875i	0.558817	−	0.203393i
$957$	−1.37808	−	21.0117i	−0.0445471	−	0.679211i
$958$	−12.0081	+	10.0760i	−0.387965	+	0.325542i
$959$	−26.4680	+	22.2093i	−0.854698	+	0.717177i
$960$	4.99749	−	3.33953i	0.161293	−	0.107783i
$961$	16.7645	−	6.10177i	0.540790	−	0.196831i
$962$	23.0299	+	39.8889i	0.742513	+	1.28607i
$963$	−25.7055	+	28.0575i	−0.828349	+	0.904140i
$964$	6.65187	−	11.5214i	0.214242	−	0.371079i
$965$	1.83340	−	10.3977i	0.0590194	−	0.334715i
$966$	−26.7393	+	91.7529i	−0.860322	+	2.95210i
$967$	8.14181	+	2.96338i	0.261823	+	0.0952958i	0.469596	−	0.882881i	$-0.344399\pi$
$967$	8.14181	+	2.96338i	0.261823	+	0.0952958i	−0.207773	+	0.978177i	$0.566622\pi$
$968$	−0.123193	−	0.698660i	−0.00395956	−	0.0224558i
$969$	−7.22996	−	16.4294i	−0.232260	−	0.527789i
$970$	−5.23372	−	4.39161i	−0.168044	−	0.141006i
$971$	27.5409			0.883831			0.441915	−	0.897057i	$-0.354299\pi$
$971$	27.5409			0.883831			0.441915	+	0.897057i	$0.354299\pi$
$972$	14.4765	+	18.0294i	0.464335	+	0.578295i
$973$	11.1430			0.357227
$974$	36.5824	+	30.6963i	1.17218	+	0.983572i
$975$	−2.08678	−	4.74201i	−0.0668303	−	0.151866i
$976$	−2.80970	−	15.9346i	−0.0899364	−	0.510055i
$977$	−6.21685	−	2.26275i	−0.198895	−	0.0723917i	0.240652	−	0.970611i	$-0.422639\pi$
$977$	−6.21685	−	2.26275i	−0.198895	−	0.0723917i	−0.439547	+	0.898220i	$0.644861\pi$
$978$	−8.37933	+	28.7528i	−0.267942	+	0.919413i
$979$	−2.12730	+	12.0645i	−0.0679889	+	0.385584i
$980$	−3.77102	+	6.53160i	−0.120461	+	0.208644i
$981$	−28.4662	+	31.0708i	−0.908856	+	0.992013i
$982$	2.21441	+	3.83548i	0.0706648	+	0.122395i
$983$	−35.0558	+	12.7593i	−1.11811	+	0.406958i	−0.833961	−	0.551823i	$-0.813932\pi$
$983$	−35.0558	+	12.7593i	−1.11811	+	0.406958i	−0.284147	+	0.958781i	$0.591710\pi$
$984$	6.33738	−	4.23490i	0.202028	−	0.135004i
$985$	−1.50853	+	1.26581i	−0.0480658	+	0.0403320i
$986$	9.28499	−	7.79103i	0.295694	−	0.248117i
$987$	1.69992	+	25.9188i	0.0541092	+	0.825004i
$988$	−23.6101	+	8.59336i	−0.751136	+	0.273391i
$989$	−28.9685	−	50.1749i	−0.921144	−	1.59547i
$990$	−19.0166	+	2.50524i	−0.604387	+	0.0796219i
$991$	20.4866	−	35.4838i	0.650777	−	1.12718i	−0.332158	−	0.943224i	$-0.607777\pi$
$991$	20.4866	−	35.4838i	0.650777	−	1.12718i	0.982935	−	0.183955i	$-0.0588900\pi$
$992$	−4.38879	+	24.8900i	−0.139344	+	0.790260i
$993$	−18.2005	+	4.45447i	−0.577577	+	0.141358i
$994$	53.0912	+	19.3236i	1.68395	+	0.612908i
$995$	2.52491	+	14.3195i	0.0800449	+	0.453957i
$996$	36.8710	+	4.03643i	1.16830	+	0.127899i
$997$	−17.7398	−	14.8855i	−0.561826	−	0.471428i	0.317096	−	0.948393i	$-0.397292\pi$
$997$	−17.7398	−	14.8855i	−0.561826	−	0.471428i	−0.878922	+	0.476965i	$0.841737\pi$
$998$	2.73614			0.0866109
$999$	8.36923	+	42.0466i	0.264791	+	1.33030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.k.b.16.6	✓	42
3.2	odd	2		405.2.k.b.46.2		42
5.2	odd	4		675.2.u.d.124.3		84
5.3	odd	4		675.2.u.d.124.12		84
5.4	even	2		675.2.l.e.151.2		42
27.5	odd	18		405.2.k.b.361.2		42
27.7	even	9		3645.2.a.l.1.17		21
27.20	odd	18		3645.2.a.k.1.5		21
27.22	even	9	inner	135.2.k.b.76.6	yes	42
135.22	odd	36		675.2.u.d.49.12		84
135.49	even	18		675.2.l.e.76.2		42
135.103	odd	36		675.2.u.d.49.3		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.b.16.6	✓	42	1.1	even	1	trivial
135.2.k.b.76.6	yes	42	27.22	even	9	inner
405.2.k.b.46.2		42	3.2	odd	2
405.2.k.b.361.2		42	27.5	odd	18
675.2.l.e.76.2		42	135.49	even	18
675.2.l.e.151.2		42	5.4	even	2
675.2.u.d.49.3		84	135.103	odd	36
675.2.u.d.49.12		84	135.22	odd	36
675.2.u.d.124.3		84	5.2	odd	4
675.2.u.d.124.12		84	5.3	odd	4
3645.2.a.k.1.5		21	27.20	odd	18
3645.2.a.l.1.17		21	27.7	even	9

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42971 + 1.19967i) q^{2} +(0.697646 + 1.58534i) q^{3} +(0.257569 + 1.46075i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.904448 + 3.10352i) q^{6} +(0.603654 - 3.42349i) q^{7} +(0.482190 - 0.835177i) q^{8} +(-2.02658 + 2.21201i) q^{9} +O(q^{10})\)	\(q+(1.42971 + 1.19967i) q^{2} +(0.697646 + 1.58534i) q^{3} +(0.257569 + 1.46075i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(-0.904448 + 3.10352i) q^{6} +(0.603654 - 3.42349i) q^{7} +(0.482190 - 0.835177i) q^{8} +(-2.02658 + 2.21201i) q^{9} +(-0.933178 - 1.61631i) q^{10} +(-3.21914 + 1.17167i) q^{11} +(-2.13608 + 1.42742i) q^{12} +(-2.29137 + 1.92269i) q^{13} +(4.97011 - 4.17042i) q^{14} +(-0.113356 - 1.72834i) q^{15} +(4.47899 - 1.63022i) q^{16} +(-0.915007 - 1.58484i) q^{17} +(-5.55110 + 0.731301i) q^{18} +(2.83150 - 4.90430i) q^{19} +(0.257569 - 1.46075i) q^{20} +(5.84852 - 1.43139i) q^{21} +(-6.00805 - 2.18675i) q^{22} +(1.47679 + 8.37528i) q^{23} +(1.66043 + 0.181775i) q^{24} +(0.766044 + 0.642788i) q^{25} -5.58258 q^{26} +(-4.92061 - 1.66961i) q^{27} +5.15634 q^{28} +(2.71852 + 2.28111i) q^{29} +(1.91137 - 2.60701i) q^{30} +(0.629929 + 3.57251i) q^{31} +(6.54694 + 2.38289i) q^{32} +(-4.10331 - 4.28600i) q^{33} +(0.593087 - 3.36357i) q^{34} +(-1.73815 + 3.01057i) q^{35} +(-3.75317 - 2.39058i) q^{36} +(-4.12531 - 7.14525i) q^{37} +(9.93177 - 3.61487i) q^{38} +(-4.64666 - 2.29123i) q^{39} +(-0.738757 + 0.619891i) q^{40} +(3.49560 - 2.93316i) q^{41} +(10.0789 + 4.96982i) q^{42} +(-6.40168 + 2.33002i) q^{43} +(-2.54066 - 4.40056i) q^{44} +(2.66091 - 1.38547i) q^{45} +(-7.93619 + 13.7459i) q^{46} +(-0.749097 + 4.24834i) q^{47} +(5.70919 + 5.96338i) q^{48} +(-4.77806 - 1.73907i) q^{49} +(0.324089 + 1.83800i) q^{50} +(1.87415 - 2.55625i) q^{51} +(-3.39874 - 2.85188i) q^{52} -6.55503 q^{53} +(-5.03206 - 8.29017i) q^{54} +3.42573 q^{55} +(-2.56815 - 2.15493i) q^{56} +(9.75035 + 1.06741i) q^{57} +(1.15012 + 6.52266i) q^{58} +(-3.06342 - 1.11500i) q^{59} +(2.49547 - 0.610751i) q^{60} +(0.589476 - 3.34309i) q^{61} +(-3.38521 + 5.86336i) q^{62} +(6.34943 + 8.27327i) q^{63} +(1.73511 + 3.00530i) q^{64} +(2.81078 - 1.02304i) q^{65} +(-0.724755 - 11.0504i) q^{66} +(-3.19129 + 2.67781i) q^{67} +(2.07937 - 1.74480i) q^{68} +(-12.2474 + 8.18418i) q^{69} +(-6.09675 + 2.21903i) q^{70} +(4.35406 + 7.54146i) q^{71} +(0.870220 + 2.75916i) q^{72} +(3.97200 - 6.87971i) q^{73} +(2.67394 - 15.1646i) q^{74} +(-0.484607 + 1.66288i) q^{75} +(7.89326 + 2.87291i) q^{76} +(2.06796 + 11.7280i) q^{77} +(-3.89466 - 8.85027i) q^{78} +(11.2271 + 9.42064i) q^{79} -4.76644 q^{80} +(-0.785942 - 8.96562i) q^{81} +8.51652 q^{82} +(-11.0597 - 9.28016i) q^{83} +(3.59730 + 8.17453i) q^{84} +(0.317778 + 1.80221i) q^{85} +(-11.9478 - 4.34865i) q^{86} +(-1.71976 + 5.90118i) q^{87} +(-0.573682 + 3.25351i) q^{88} +(1.78804 - 3.09697i) q^{89} +(5.46645 + 1.21139i) q^{90} +(5.19911 + 9.00512i) q^{91} +(-11.8538 + 4.31443i) q^{92} +(-5.22416 + 3.49099i) q^{93} +(-6.16760 + 5.17523i) q^{94} +(-4.33811 + 3.64011i) q^{95} +(0.789762 + 12.0415i) q^{96} +(3.43991 - 1.25203i) q^{97} +(-4.74493 - 8.21846i) q^{98} +(3.93210 - 9.49523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 6 q^{6} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 6 * q^6 - 9 * q^8 - 3 * q^9	\( 42 q - 3 q^{3} - 6 q^{6} - 9 q^{8} - 3 q^{9} - 3 q^{10} - 6 q^{11} - 39 q^{12} - 3 q^{13} - 27 q^{14} + 6 q^{15} - 12 q^{16} - 12 q^{17} + 6 q^{18} - 24 q^{19} + 12 q^{21} + 33 q^{22} + 18 q^{23} - 3 q^{24} - 18 q^{26} + 39 q^{27} + 60 q^{28} - 21 q^{30} - 12 q^{31} + 36 q^{32} - 33 q^{33} + 51 q^{34} - 12 q^{35} - 36 q^{36} - 24 q^{37} - 24 q^{38} - 30 q^{39} - 9 q^{40} + 33 q^{41} + 78 q^{42} - 24 q^{43} + 12 q^{44} - 12 q^{45} - 30 q^{46} + 27 q^{47} + 141 q^{48} + 18 q^{49} - 39 q^{51} - 84 q^{52} + 36 q^{53} + 30 q^{54} - 24 q^{56} - 81 q^{58} - 27 q^{59} - 6 q^{61} - 18 q^{62} - 6 q^{63} - 63 q^{64} + 6 q^{65} - 30 q^{66} + 12 q^{67} - 3 q^{68} + 51 q^{69} + 9 q^{70} + 12 q^{71} - 153 q^{72} - 39 q^{73} - 72 q^{74} + 138 q^{76} - 54 q^{77} - 48 q^{78} - 18 q^{79} + 78 q^{80} + 45 q^{81} + 48 q^{82} + 57 q^{83} - 51 q^{84} + 9 q^{85} + 18 q^{86} - 39 q^{87} + 126 q^{88} + 9 q^{89} + 54 q^{90} - 69 q^{91} + 24 q^{92} - 18 q^{93} - 33 q^{94} + 3 q^{95} + 153 q^{96} + 21 q^{97} - 15 q^{98} - 9 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 6 * q^6 - 9 * q^8 - 3 * q^9 - 3 * q^10 - 6 * q^11 - 39 * q^12 - 3 * q^13 - 27 * q^14 + 6 * q^15 - 12 * q^16 - 12 * q^17 + 6 * q^18 - 24 * q^19 + 12 * q^21 + 33 * q^22 + 18 * q^23 - 3 * q^24 - 18 * q^26 + 39 * q^27 + 60 * q^28 - 21 * q^30 - 12 * q^31 + 36 * q^32 - 33 * q^33 + 51 * q^34 - 12 * q^35 - 36 * q^36 - 24 * q^37 - 24 * q^38 - 30 * q^39 - 9 * q^40 + 33 * q^41 + 78 * q^42 - 24 * q^43 + 12 * q^44 - 12 * q^45 - 30 * q^46 + 27 * q^47 + 141 * q^48 + 18 * q^49 - 39 * q^51 - 84 * q^52 + 36 * q^53 + 30 * q^54 - 24 * q^56 - 81 * q^58 - 27 * q^59 - 6 * q^61 - 18 * q^62 - 6 * q^63 - 63 * q^64 + 6 * q^65 - 30 * q^66 + 12 * q^67 - 3 * q^68 + 51 * q^69 + 9 * q^70 + 12 * q^71 - 153 * q^72 - 39 * q^73 - 72 * q^74 + 138 * q^76 - 54 * q^77 - 48 * q^78 - 18 * q^79 + 78 * q^80 + 45 * q^81 + 48 * q^82 + 57 * q^83 - 51 * q^84 + 9 * q^85 + 18 * q^86 - 39 * q^87 + 126 * q^88 + 9 * q^89 + 54 * q^90 - 69 * q^91 + 24 * q^92 - 18 * q^93 - 33 * q^94 + 3 * q^95 + 153 * q^96 + 21 * q^97 - 15 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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