LMFDB - Embedded newform 108.2.l.a.23.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,2,Mod(11,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	108.23
Dual form			108.2.l.a.47.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16185 + 0.806289i) q^{2} +(-1.33417 + 1.10453i) q^{3} +(0.699796 + 1.87358i) q^{4} +(0.297855 + 0.0525198i) q^{5} +(-2.44068 + 0.207573i) q^{6} +(-0.312070 - 0.371910i) q^{7} +(-0.697584 + 2.74105i) q^{8} +(0.560024 - 2.94727i) q^{9} +(0.303717 + 0.301177i) q^{10} +(-0.00722947 - 0.0410004i) q^{11} +(-3.00307 - 1.72672i) q^{12} +(4.05761 - 1.47685i) q^{13} +(-0.0627115 - 0.683722i) q^{14} +(-0.455399 + 0.258919i) q^{15} +(-3.02057 + 2.62224i) q^{16} +(-2.14427 - 1.23800i) q^{17} +(3.02701 - 2.97274i) q^{18} +(6.55326 - 3.78353i) q^{19} +(0.110038 + 0.594806i) q^{20} +(0.827140 + 0.151501i) q^{21} +(0.0246586 - 0.0534654i) q^{22} +(-5.03199 - 4.22234i) q^{23} +(-2.09688 - 4.42754i) q^{24} +(-4.61250 - 1.67881i) q^{25} +(5.90510 + 1.55572i) q^{26} +(2.50818 + 4.55072i) q^{27} +(0.478416 - 0.844947i) q^{28} +(-2.40260 + 6.60109i) q^{29} +(-0.737869 - 0.0663574i) q^{30} +(2.30836 - 2.75099i) q^{31} +(-5.62374 + 0.611204i) q^{32} +(0.0549315 + 0.0467164i) q^{33} +(-1.49314 - 3.16727i) q^{34} +(-0.0734187 - 0.127165i) q^{35} +(5.91383 - 1.01324i) q^{36} +(-3.36015 + 5.81994i) q^{37} +(10.6645 + 0.887926i) q^{38} +(-3.78232 + 6.45212i) q^{39} +(-0.351738 + 0.779799i) q^{40} +(2.16312 + 5.94312i) q^{41} +(0.838860 + 0.842936i) q^{42} +(-2.38200 + 0.420011i) q^{43} +(0.0717582 - 0.0422369i) q^{44} +(0.321596 - 0.848444i) q^{45} +(-2.44200 - 8.96296i) q^{46} +(-5.51016 + 4.62358i) q^{47} +(1.13361 - 6.83483i) q^{48} +(1.17461 - 6.66153i) q^{49} +(-4.00543 - 5.66954i) q^{50} +(4.22823 - 0.716716i) q^{51} +(5.60648 + 6.56874i) q^{52} -9.90799i q^{53} +(-0.755067 + 7.30957i) q^{54} -0.0125918i q^{55} +(1.23712 - 0.595961i) q^{56} +(-4.56415 + 12.2862i) q^{57} +(-8.11385 + 5.73229i) q^{58} +(0.755918 - 4.28703i) q^{59} +(-0.803791 - 0.672033i) q^{60} +(-5.77142 + 4.84280i) q^{61} +(4.90006 - 1.33504i) q^{62} +(-1.27088 + 0.711473i) q^{63} +(-7.02675 - 3.82423i) q^{64} +(1.28614 - 0.226781i) q^{65} +(0.0261554 + 0.0985681i) q^{66} +(3.80965 + 10.4669i) q^{67} +(0.818925 - 4.88380i) q^{68} +(11.3772 + 0.0753378i) q^{69} +(0.0172301 - 0.206943i) q^{70} +(1.68932 - 2.92598i) q^{71} +(7.68795 + 3.59102i) q^{72} +(0.315477 + 0.546421i) q^{73} +(-8.59654 + 4.05266i) q^{74} +(8.00817 - 2.85483i) q^{75} +(11.6747 + 9.63033i) q^{76} +(-0.0129924 + 0.0154837i) q^{77} +(-9.59676 + 4.44676i) q^{78} +(-1.03548 + 2.84496i) q^{79} +(-1.03741 + 0.622407i) q^{80} +(-8.37275 - 3.30108i) q^{81} +(-2.27865 + 8.64913i) q^{82} +(5.41059 + 1.96930i) q^{83} +(0.294981 + 1.65573i) q^{84} +(-0.573662 - 0.481360i) q^{85} +(-3.10618 - 1.43259i) q^{86} +(-4.08563 - 11.4607i) q^{87} +(0.117427 + 0.00878482i) q^{88} +(9.00521 - 5.19916i) q^{89} +(1.05774 - 0.726467i) q^{90} +(-1.81551 - 1.04819i) q^{91} +(4.38950 - 12.3826i) q^{92} +(-0.0411872 + 6.21994i) q^{93} +(-10.1299 + 0.929124i) q^{94} +(2.15063 - 0.782765i) q^{95} +(6.82793 - 7.02704i) q^{96} +(-0.578459 - 3.28061i) q^{97} +(6.73584 - 6.79263i) q^{98} +(-0.124888 - 0.00165404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	1.16185	+	0.806289i	0.821553	+	0.570132i
$2$	1.16185	+	0.806289i	0.821553	+	0.570132i
$3$	−1.33417	+	1.10453i	−0.770284	+	0.637701i
$3$	−1.33417	+	1.10453i	−0.770284	+	0.637701i
$4$	0.699796	+	1.87358i	0.349898	+	0.936788i
$5$	0.297855	+	0.0525198i	0.133205	+	0.0234876i	0.239853	−	0.970809i	$-0.422901\pi$
$5$	0.297855	+	0.0525198i	0.133205	+	0.0234876i	−0.106648	+	0.994297i	$0.534012\pi$
$6$	−2.44068	+	0.207573i	−0.996403	+	0.0847413i
$7$	−0.312070	−	0.371910i	−0.117951	−	0.140569i	0.703838	−	0.710361i	$-0.251468\pi$
$7$	−0.312070	−	0.371910i	−0.117951	−	0.140569i	−0.821789	+	0.569792i	$0.807024\pi$
$8$	−0.697584	+	2.74105i	−0.246633	+	0.969109i
$9$	0.560024	−	2.94727i	0.186675	−	0.982422i
$10$	0.303717	+	0.301177i	0.0960436	+	0.0952405i
$11$	−0.00722947	−	0.0410004i	−0.00217977	−	0.0123621i	0.983698	−	0.179826i	$-0.0575534\pi$
$11$	−0.00722947	−	0.0410004i	−0.00217977	−	0.0123621i	−0.985878	+	0.167464i	$0.946442\pi$
$12$	−3.00307	−	1.72672i	−0.866912	−	0.498462i
$13$	4.05761	−	1.47685i	1.12538	−	0.409604i	0.288765	−	0.957400i	$-0.406755\pi$
$13$	4.05761	−	1.47685i	1.12538	−	0.409604i	0.836612	+	0.547796i	$0.184533\pi$
$14$	−0.0627115	−	0.683722i	−0.0167604	−	0.182733i
$15$	−0.455399	+	0.258919i	−0.117583	+	0.0668526i
$16$	−3.02057	+	2.62224i	−0.755142	+	0.655561i
$17$	−2.14427	−	1.23800i	−0.520062	−	0.300258i	0.216898	−	0.976194i	$-0.430406\pi$
$17$	−2.14427	−	1.23800i	−0.520062	−	0.300258i	−0.736960	+	0.675936i	$0.763739\pi$
$18$	3.02701	−	2.97274i	0.713474	−	0.700682i
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.503430	−	0.864036i	$-0.332071\pi$
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.999992	−	0.00396479i	$-0.00126203\pi$
$20$	0.110038	+	0.594806i	0.0246052	+	0.133003i
$21$	0.827140	+	0.151501i	0.180497	+	0.0330603i
$22$	0.0246586	−	0.0534654i	0.00525723	−	0.0113989i
$23$	−5.03199	−	4.22234i	−1.04924	−	0.880418i	−0.0562281	−	0.998418i	$-0.517907\pi$
$23$	−5.03199	−	4.22234i	−1.04924	−	0.880418i	−0.993014	+	0.118000i	$0.962352\pi$
$24$	−2.09688	−	4.42754i	−0.428024	−	0.903767i
$25$	−4.61250	−	1.67881i	−0.922501	−	0.335763i
$26$	5.90510	+	1.55572i	1.15809	+	0.305103i
$27$	2.50818	+	4.55072i	0.482699	+	0.875786i
$28$	0.478416	−	0.844947i	0.0904122	−	0.159680i
$29$	−2.40260	+	6.60109i	−0.446152	+	1.22579i	0.489231	+	0.872154i	$0.337278\pi$
$29$	−2.40260	+	6.60109i	−0.446152	+	1.22579i	−0.935383	+	0.353637i	$0.884945\pi$
$30$	−0.737869	−	0.0663574i	−0.134716	−	0.0121151i
$31$	2.30836	−	2.75099i	0.414593	−	0.494092i	−0.517819	−	0.855490i	$-0.673256\pi$
$31$	2.30836	−	2.75099i	0.414593	−	0.494092i	0.932412	+	0.361398i	$0.117700\pi$
$32$	−5.62374	+	0.611204i	−0.994146	+	0.108047i
$33$	0.0549315	+	0.0467164i	0.00956235	+	0.00813227i
$34$	−1.49314	−	3.16727i	−0.256072	−	0.543182i
$35$	−0.0734187	−	0.127165i	−0.0124100	−	0.0214948i
$36$	5.91383	−	1.01324i	0.985638	−	0.168873i
$37$	−3.36015	+	5.81994i	−0.552405	+	0.956793i	0.445696	+	0.895184i	$0.352956\pi$
$37$	−3.36015	+	5.81994i	−0.552405	+	0.956793i	−0.998100	+	0.0616082i	$0.980377\pi$
$38$	10.6645	+	0.887926i	1.73002	+	0.144041i
$39$	−3.78232	+	6.45212i	−0.605655	+	1.03317i
$40$	−0.351738	+	0.779799i	−0.0556147	+	0.123297i
$41$	2.16312	+	5.94312i	0.337823	+	0.928160i	0.986011	+	0.166680i	$0.0533047\pi$
$41$	2.16312	+	5.94312i	0.337823	+	0.928160i	−0.648188	+	0.761480i	$0.724473\pi$
$42$	0.838860	+	0.842936i	0.129439	+	0.130068i
$43$	−2.38200	+	0.420011i	−0.363252	+	0.0640511i	−0.352295	−	0.935889i	$-0.614599\pi$
$43$	−2.38200	+	0.420011i	−0.363252	+	0.0640511i	−0.0109565	+	0.999940i	$0.503488\pi$
$44$	0.0717582	−	0.0422369i	0.0108179	−	0.00636745i
$45$	0.321596	−	0.848444i	0.0479406	−	0.126479i
$46$	−2.44200	−	8.96296i	−0.360053	−	1.32152i
$47$	−5.51016	+	4.62358i	−0.803740	+	0.674418i	−0.949105	−	0.314960i	$-0.898009\pi$
$47$	−5.51016	+	4.62358i	−0.803740	+	0.674418i	0.145365	+	0.989378i	$0.453564\pi$
$48$	1.13361	−	6.83483i	0.163622	−	0.986523i
$49$	1.17461	−	6.66153i	0.167801	−	0.951647i
$50$	−4.00543	−	5.66954i	−0.566454	−	0.801794i
$51$	4.22823	−	0.716716i	0.592071	−	0.100360i
$52$	5.60648	+	6.56874i	0.777479	+	0.910920i
$53$		−	9.90799i		−	1.36097i	−0.732763	−	0.680484i	$-0.761770\pi$
$53$		−	9.90799i		−	1.36097i	0.732763	−	0.680484i	$-0.238230\pi$
$54$	−0.755067	+	7.30957i	−0.102752	+	0.994707i
$55$		−	0.0125918i		−	0.00169788i
$56$	1.23712	−	0.595961i	0.165317	−	0.0796387i
$57$	−4.56415	+	12.2862i	−0.604537	+	1.62734i
$58$	−8.11385	+	5.73229i	−1.06540	+	0.752687i
$59$	0.755918	−	4.28703i	0.0984122	−	0.558123i	−0.895236	−	0.445592i	$-0.852993\pi$
$59$	0.755918	−	4.28703i	0.0984122	−	0.558123i	0.993648	−	0.112531i	$-0.0358958\pi$
$60$	−0.803791	−	0.672033i	−0.103769	−	0.0867591i
$61$	−5.77142	+	4.84280i	−0.738955	+	0.620057i	−0.932557	−	0.361024i	$-0.882427\pi$
$61$	−5.77142	+	4.84280i	−0.738955	+	0.620057i	0.193602	+	0.981080i	$0.437983\pi$
$62$	4.90006	−	1.33504i	0.622308	−	0.169550i
$63$	−1.27088	+	0.711473i	−0.160116	+	0.0896372i
$64$	−7.02675	−	3.82423i	−0.878344	−	0.478029i
$65$	1.28614	−	0.226781i	0.159526	−	0.0281287i
$66$	0.0261554	+	0.0985681i	0.00321951	+	0.0121329i
$67$	3.80965	+	10.4669i	0.465423	+	1.27874i	0.921354	+	0.388724i	$0.127084\pi$
$67$	3.80965	+	10.4669i	0.465423	+	1.27874i	−0.455932	+	0.890015i	$0.650694\pi$
$68$	0.818925	−	4.88380i	0.0993092	−	0.592248i
$69$	11.3772	+	0.0753378i	1.36966	+	0.00906960i
$70$	0.0172301	−	0.206943i	0.00205939	−	0.0247345i
$71$	1.68932	−	2.92598i	0.200485	−	0.347250i	−0.748200	−	0.663473i	$-0.769082\pi$
$71$	1.68932	−	2.92598i	0.200485	−	0.347250i	0.948685	+	0.316223i	$0.102415\pi$
$72$	7.68795	+	3.59102i	0.906034	+	0.423206i
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	0.883897	−	0.467682i	$-0.154911\pi$
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	−0.846973	+	0.531636i	$0.821577\pi$
$74$	−8.59654	+	4.05266i	−0.999328	+	0.471112i
$75$	8.00817	−	2.85483i	0.924704	−	0.329647i
$76$	11.6747	+	9.63033i	1.33918	+	1.10468i
$77$	−0.0129924	+	0.0154837i	−0.00148062	+	0.00176453i
$78$	−9.59676	+	4.44676i	−1.08662	+	0.503496i
$79$	−1.03548	+	2.84496i	−0.116501	+	0.320083i	−0.984214	−	0.176982i	$-0.943367\pi$
$79$	−1.03548	+	2.84496i	−0.116501	+	0.320083i	0.867714	+	0.497065i	$0.165589\pi$
$80$	−1.03741	+	0.622407i	−0.115986	+	0.0695873i
$81$	−8.37275	−	3.30108i	−0.930305	−	0.366787i
$82$	−2.27865	+	8.64913i	−0.251635	+	0.955136i
$83$	5.41059	+	1.96930i	0.593890	+	0.216158i	0.621439	−	0.783462i	$-0.286548\pi$
$83$	5.41059	+	1.96930i	0.593890	+	0.216158i	−0.0275495	+	0.999620i	$0.508770\pi$
$84$	0.294981	+	1.65573i	0.0321851	+	0.180655i
$85$	−0.573662	−	0.481360i	−0.0622224	−	0.0522108i
$86$	−3.10618	−	1.43259i	−0.334948	−	0.154480i
$87$	−4.08563	−	11.4607i	−0.438025	−	1.22872i
$88$	0.117427	+	0.00878482i	0.0125178	+	0.000936465i
$89$	9.00521	−	5.19916i	0.954550	−	0.551110i	0.0600588	−	0.998195i	$-0.480871\pi$
$89$	9.00521	−	5.19916i	0.954550	−	0.551110i	0.894491	+	0.447085i	$0.147538\pi$
$90$	1.05774	−	0.726467i	0.111495	−	0.0765763i
$91$	−1.81551	−	1.04819i	−0.190317	−	0.109880i
$92$	4.38950	−	12.3826i	0.457637	−	1.29097i
$93$	−0.0411872	+	6.21994i	−0.00427091	+	0.644978i
$94$	−10.1299	+	0.929124i	−1.04482	+	0.0958318i
$95$	2.15063	−	0.782765i	0.220650	−	0.0803100i
$96$	6.82793	−	7.02704i	0.696873	−	0.717194i
$97$	−0.578459	−	3.28061i	−0.0587337	−	0.333095i	0.941256	−	0.337694i	$-0.109647\pi$
$97$	−0.578459	−	3.28061i	−0.0587337	−	0.333095i	−0.999989	+	0.00459941i	$0.998536\pi$
$98$	6.73584	−	6.79263i	0.680422	−	0.686160i
$99$	−0.124888	−	0.00165404i	−0.0125517	−	0.000166237i
$100$	−0.0824291	−	9.81670i	−0.00824291	−	0.981670i
$101$	−10.7344	−	12.7927i	−1.06811	−	1.27292i	−0.960366	−	0.278743i	$-0.910082\pi$
$101$	−10.7344	−	12.7927i	−1.06811	−	1.27292i	−0.107742	−	0.994179i	$-0.534362\pi$
$102$	5.49045	+	2.57646i	0.543636	+	0.255107i
$103$	−15.6512	−	2.75973i	−1.54216	−	0.271924i	−0.663062	−	0.748565i	$-0.730743\pi$
$103$	−15.6512	−	2.75973i	−1.54216	−	0.271924i	−0.879098	+	0.476640i	$0.841854\pi$
$104$	1.21760	+	12.1523i	0.119395	+	1.19163i
$105$	0.238411	+	0.0885666i	0.0232665	+	0.00864321i
$106$	7.98871	−	11.5116i	0.775932	−	1.11811i
$107$	−1.00162			−0.0968302			−0.0484151	−	0.998827i	$-0.515417\pi$
$107$	−1.00162			−0.0968302			−0.0484151	+	0.998827i	$0.515417\pi$
$108$	−6.77090	+	7.88384i	−0.651531	+	0.758622i
$109$	7.26618			0.695973			0.347987	−	0.937499i	$-0.386865\pi$
$109$	7.26618			0.695973			0.347987	+	0.937499i	$0.386865\pi$
$110$	0.0101527	−	0.0146298i	0.000968019	−	0.00139490i
$111$	−1.94530	−	11.4762i	−0.184639	−	1.08927i
$112$	1.91787	+	0.305058i	0.181221	+	0.0288253i
$113$	14.2492	+	2.51252i	1.34045	+	0.236358i	0.797456	−	0.603377i	$-0.206179\pi$
$113$	14.2492	+	2.51252i	1.34045	+	0.236358i	0.542997	+	0.839735i	$0.317290\pi$
$114$	−15.2091	+	10.5947i	−1.42446	+	0.992281i
$115$	−1.27704	−	1.52192i	−0.119085	−	0.141920i
$116$	−14.0490	+	0.117967i	−1.30441	+	0.0109529i
$117$	−2.08030	−	12.7859i	−0.192324	−	1.18206i
$118$	4.33485	−	4.37140i	0.399055	−	0.402420i
$119$	0.208739	+	1.18382i	0.0191351	+	0.108520i
$120$	−0.392033	−	1.42889i	−0.0357875	−	0.130439i
$121$	10.3350	−	3.76163i	0.939545	−	0.341966i
$122$	−10.6102	+	0.973177i	−0.960605	+	0.0881073i
$123$	−9.45034	−	5.53991i	−0.852108	−	0.499517i
$124$	6.76957	+	2.39974i	0.607925	+	0.215503i
$125$	−2.59533	−	1.49841i	−0.232133	−	0.134022i
$126$	−2.05023	−	0.198074i	−0.182649	−	0.0176458i
$127$	−7.70348	+	4.44760i	−0.683573	+	0.394661i	−0.801200	−	0.598397i	$-0.795805\pi$
$127$	−7.70348	+	4.44760i	−0.683573	+	0.394661i	0.117627	+	0.993058i	$0.462471\pi$
$128$	−5.08061	−	10.1088i	−0.449067	−	0.893498i
$129$	2.71408	−	3.19136i	0.238962	−	0.280984i
$130$	1.67715	+	0.773514i	0.147096	+	0.0678417i
$131$	14.8870	+	12.4917i	1.30068	+	1.09140i	0.990027	+	0.140881i	$0.0449935\pi$
$131$	14.8870	+	12.4917i	1.30068	+	1.09140i	0.310657	+	0.950522i	$0.399451\pi$
$132$	−0.0490857	+	0.135610i	−0.00427236	+	0.0118034i
$133$	−3.45221	−	1.25650i	−0.299344	−	0.108952i
$134$	−4.01312	+	15.2327i	−0.346681	+	1.31590i
$135$	0.508069	+	1.48718i	0.0437276	+	0.127996i
$136$	4.88922	−	5.01396i	0.419247	−	0.429943i
$137$	−5.24564	+	14.4123i	−0.448165	+	1.23132i	0.485834	+	0.874051i	$0.338516\pi$
$137$	−5.24564	+	14.4123i	−0.448165	+	1.23132i	−0.934000	+	0.357274i	$0.883706\pi$
$138$	13.1579	+	9.26087i	1.12008	+	0.788337i
$139$	5.74324	−	6.84453i	0.487135	−	0.580545i	−0.465351	−	0.885126i	$-0.654072\pi$
$139$	5.74324	−	6.84453i	0.487135	−	0.580545i	0.952486	+	0.304581i	$0.0985164\pi$
$140$	0.186875	−	0.226545i	0.0157938	−	0.0191466i
$141$	2.24462	−	12.2548i	0.189031	−	1.03204i
$142$	4.32192	−	2.03748i	0.362688	−	0.170981i
$143$	−0.0898857	−	0.155687i	−0.00751662	−	0.0130192i
$144$	6.03685	+	10.3709i	0.503071	+	0.864245i
$145$	−1.06231	+	1.83998i	−0.0882203	+	0.152802i
$146$	−0.0740367	+	0.889226i	−0.00612732	+	0.0735928i
$147$	5.79074	+	10.1850i	0.477612	+	0.840046i
$148$	−13.2555	−	2.22271i	−1.08960	−	0.182706i
$149$	0.588938	+	1.61809i	0.0482477	+	0.132559i	0.961476	−	0.274889i	$-0.0886410\pi$
$149$	0.588938	+	1.61809i	0.0482477	+	0.132559i	−0.913228	+	0.407448i	$0.866419\pi$
$150$	11.6061	+	3.14002i	0.947636	+	0.256381i
$151$	0.593940	−	0.104728i	0.0483342	−	0.00852262i	−0.149429	−	0.988772i	$-0.547743\pi$
$151$	0.593940	−	0.104728i	0.0483342	−	0.00852262i	0.197763	+	0.980250i	$0.436632\pi$
$152$	5.79941	+	20.6022i	0.470394	+	1.67106i
$153$	−4.84955	+	5.62643i	−0.392063	+	0.454870i
$154$	−0.0275795	+	0.00751415i	−0.00222242	+	0.000605507i
$155$	0.832036	−	0.698161i	0.0668307	−	0.0560776i
$156$	−14.7354	−	2.57129i	−1.17977	−	0.205868i
$157$	−1.80133	+	10.2158i	−0.143762	+	0.815313i	0.824592	+	0.565729i	$0.191405\pi$
$157$	−1.80133	+	10.2158i	−0.143762	+	0.815313i	−0.968353	+	0.249584i	$0.919706\pi$
$158$	−3.49693	+	2.47052i	−0.278201	+	0.196544i
$159$	10.9437	+	13.2190i	0.867890	+	1.04833i
$160$	−1.70716	−	0.113308i	−0.134963	−	0.00895775i
$161$			3.18911i			0.251337i
$162$	−7.06626	−	10.5862i	−0.555178	−	0.831732i
$163$			5.70430i			0.446795i	0.974727	+	0.223397i	$0.0717148\pi$
$163$			5.70430i			0.446795i	−0.974727	+	0.223397i	$0.928285\pi$
$164$	−9.62115	+	8.21175i	−0.751285	+	0.641230i
$165$	0.0139081	+	0.0167997i	0.00108274	+	0.00130785i
$166$	4.69849	+	6.65053i	0.364673	+	0.516181i
$167$	−0.911752	+	5.17080i	−0.0705535	+	0.400129i	0.928995	+	0.370092i	$0.120674\pi$
$167$	−0.911752	+	5.17080i	−0.0705535	+	0.400129i	−0.999549	+	0.0300372i	$0.990437\pi$
$168$	−0.992273	+	2.16155i	−0.0765555	+	0.166767i
$169$	4.32450	−	3.62869i	0.332654	−	0.279130i
$170$	−0.278395	−	1.02181i	−0.0213519	−	0.0783689i
$171$	−7.48108	−	21.4331i	−0.572092	−	1.63903i
$172$	−2.45384	−	4.16894i	−0.187104	−	0.317879i
$173$	−1.36617	+	0.240893i	−0.103868	+	0.0183148i	−0.225341	−	0.974280i	$-0.572350\pi$
$173$	−1.36617	+	0.240893i	−0.103868	+	0.0183148i	0.121472	+	0.992595i	$0.461238\pi$
$174$	4.49377	−	16.6099i	0.340672	−	1.25919i
$175$	0.815054	+	2.23934i	0.0616123	+	0.169278i
$176$	0.129350	+	0.104887i	0.00975013	+	0.00790616i
$177$	3.72663	+	6.55456i	0.280110	+	0.492671i
$178$	14.6547	+	1.22015i	1.09842	+	0.0914541i
$179$	−5.77179	+	9.99703i	−0.431403	+	0.747213i	−0.996994	−	0.0774732i	$-0.975315\pi$
$179$	−5.77179	+	9.99703i	−0.431403	+	0.747213i	0.565591	+	0.824686i	$0.308648\pi$
$180$	1.81468	+	0.00879540i	0.135258	+	0.000655571i
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	0.986039	+	0.166514i	$0.0532510\pi$
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	−0.348814	+	0.937192i	$0.613416\pi$
$182$	−1.26421	−	2.68166i	−0.0937097	−	0.198778i
$183$	2.35104	−	12.8358i	0.173794	−	0.948852i
$184$	15.0839	−	10.8475i	1.11200	−	0.799689i
$185$	−1.30650	+	1.55702i	−0.0960556	+	0.114475i
$186$	−5.06292	+	7.19344i	−0.371231	+	0.527448i
$187$	−0.0352564	+	0.0968660i	−0.00257820	+	0.00708355i
$188$	−12.5186	−	7.08814i	−0.913014	−	0.516956i
$189$	0.909733	−	2.35296i	0.0661733	−	0.171152i
$190$	3.12985	+	0.824572i	0.227063	+	0.0598208i
$191$	15.5567	+	5.66216i	1.12564	+	0.409699i	0.836708	−	0.547650i	$-0.184477\pi$
$191$	15.5567	+	5.66216i	1.12564	+	0.409699i	0.288933	+	0.957349i	$0.406700\pi$
$192$	13.5989	−	2.65909i	0.981414	−	0.191903i
$193$	−6.74355	−	5.65851i	−0.485411	−	0.407308i	0.366967	−	0.930234i	$-0.380396\pi$
$193$	−6.74355	−	5.65851i	−0.485411	−	0.407308i	−0.852378	+	0.522925i	$0.824841\pi$
$194$	1.97303	−	4.27798i	0.141655	−	0.307141i
$195$	−1.46544	+	1.72315i	−0.104943	+	0.123397i
$196$	13.3029	−	2.46100i	0.950205	−	0.175786i
$197$	−10.8232	+	6.24879i	−0.771122	+	0.445208i	−0.833275	−	0.552859i	$-0.813537\pi$
$197$	−10.8232	+	6.24879i	−0.771122	+	0.445208i	0.0621526	+	0.998067i	$0.480203\pi$
$198$	−0.143767	−	0.102617i	−0.0102171	−	0.00729269i
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	0.355927	−	0.934514i	$-0.384165\pi$
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	−0.631349	+	0.775499i	$0.717499\pi$
$200$	7.81933	−	11.4720i	0.552910	−	0.811194i
$201$	−16.6438	−	9.75679i	−1.17396	−	0.688191i
$202$	−2.15711	−	23.5182i	−0.151773	−	1.65474i
$203$	3.20479	−	1.16645i	0.224932	−	0.0818686i
$204$	4.30172	+	7.42035i	0.301181	+	0.519529i
$205$	0.332164	+	1.88379i	0.0231993	+	0.131570i
$206$	−15.9592	−	15.8258i	−1.11193	−	1.10264i
$207$	−15.2624	+	12.4660i	−1.06081	+	0.866446i
$208$	−8.38363	+	15.1009i	−0.581300	+	1.04706i
$209$	−0.202503	−	0.241333i	−0.0140074	−	0.0166934i
$210$	0.205588	+	0.295129i	0.0141869	+	0.0203658i
$211$	−22.1033	−	3.89740i	−1.52165	−	0.268308i	−0.650570	−	0.759446i	$-0.725470\pi$
$211$	−22.1033	−	3.89740i	−1.52165	−	0.268308i	−0.871082	+	0.491138i	$0.836581\pi$
$212$	18.5634	−	6.93358i	1.27494	−	0.476200i
$213$	0.978000	+	5.76966i	0.0670114	+	0.395331i
$214$	−1.16373	−	0.807595i	−0.0795511	−	0.0552060i
$215$	−0.731549			−0.0498912
$216$	−14.2234	+	3.70054i	−0.967782	+	0.251790i
$217$	−1.74349			−0.118356
$218$	8.44222	+	5.85864i	0.571779	+	0.396797i
$219$	−1.02444	−	0.380566i	−0.0692252	−	0.0257163i
$220$	0.0235918	−	0.00881173i	0.00159056	−	0.000594087i
$221$	−10.5289	−	1.85654i	−0.708253	−	0.124884i
$222$	6.99297	−	14.9021i	0.469338	−	1.00016i
$223$	11.7737	+	14.0314i	0.788428	+	0.939612i	0.999281	−	0.0379061i	$-0.0120688\pi$
$223$	11.7737	+	14.0314i	0.788428	+	0.939612i	−0.210854	+	0.977518i	$0.567624\pi$
$224$	1.98231	+	1.90079i	0.132449	+	0.127002i
$225$	−7.53103	+	12.6541i	−0.502068	+	0.843606i
$226$	14.5296	+	14.4082i	0.966498	+	0.958416i
$227$	−3.40406	−	19.3054i	−0.225936	−	1.28134i	−0.860888	−	0.508794i	$-0.830092\pi$
$227$	−3.40406	−	19.3054i	−0.225936	−	1.28134i	0.634953	−	0.772551i	$-0.281020\pi$
$228$	−26.2130	+	0.0465261i	−1.73600	+	0.00308127i
$229$	−5.32626	+	1.93860i	−0.351969	+	0.128106i	−0.511953	−	0.859013i	$-0.671078\pi$
$229$	−5.32626	+	1.93860i	−0.351969	+	0.128106i	0.159984	+	0.987120i	$0.448856\pi$
$230$	−0.256627	−	2.79791i	−0.0169215	−	0.184489i
$231$	0.000231818	−	0.0350083i	1.52525e−5	−	0.00230338i
$232$	−16.4179	−	11.1905i	−1.07789	−	0.734690i
$233$	6.50499	+	3.75566i	0.426156	+	0.246041i	0.697708	−	0.716383i	$-0.254203\pi$
$233$	6.50499	+	3.75566i	0.426156	+	0.246041i	−0.271552	+	0.962424i	$0.587537\pi$
$234$	7.89213	−	16.5327i	0.515925	−	1.08077i
$235$	−1.88406	+	1.08776i	−0.122902	+	0.0709577i
$236$	8.56106	−	1.58378i	0.557277	−	0.103095i
$237$	−1.76083	−	4.93938i	−0.114379	−	0.320847i
$238$	−0.711975	+	1.54372i	−0.0461505	+	0.100065i
$239$	−4.95760	−	4.15992i	−0.320680	−	0.269083i	0.468209	−	0.883618i	$-0.344899\pi$
$239$	−4.95760	−	4.15992i	−0.320680	−	0.269083i	−0.788890	+	0.614535i	$0.789344\pi$
$240$	0.696615	−	1.97625i	0.0449663	−	0.127566i
$241$	0.652071	+	0.237335i	0.0420036	+	0.0152881i	0.362937	−	0.931814i	$-0.381774\pi$
$241$	0.652071	+	0.237335i	0.0420036	+	0.0152881i	−0.320933	+	0.947102i	$0.603996\pi$
$242$	15.0407	+	3.96253i	0.966852	+	0.254721i
$243$	14.8168	−	4.84375i	0.950499	−	0.310727i
$244$	−13.1122	−	7.42422i	−0.839420	−	0.475287i
$245$	0.699725	−	1.92248i	0.0447038	−	0.122823i
$246$	−6.51311	−	14.0563i	−0.415261	−	0.896194i
$247$	21.0029	−	25.0302i	1.33638	−	1.59264i
$248$	5.93034	+	8.24637i	0.376577	+	0.523645i
$249$	−9.39381	+	3.34879i	−0.595308	+	0.212221i
$250$	−1.80723	−	3.83352i	−0.114299	−	0.242453i
$251$	1.09113	+	1.88989i	0.0688715	+	0.119289i	0.898405	−	0.439168i	$-0.144727\pi$
$251$	1.09113	+	1.88989i	0.0688715	+	0.119289i	−0.829533	+	0.558457i	$0.811393\pi$
$252$	−2.22236	−	1.88321i	−0.139995	−	0.118631i
$253$	−0.136739	+	0.236839i	−0.00859670	+	0.0148899i
$254$	−12.5363	−	1.04377i	−0.786600	−	0.0654921i
$255$	1.29704	+	0.00858874i	0.0812238	+	0.000537848i
$256$	2.24768	−	15.8413i	0.140480	−	0.990083i
$257$	−4.92162	−	13.5220i	−0.307002	−	0.843481i	−0.993237	−	0.116102i	$-0.962960\pi$
$257$	−4.92162	−	13.5220i	−0.307002	−	0.843481i	0.686235	−	0.727380i	$-0.259262\pi$
$258$	5.72652	−	1.51955i	0.356518	−	0.0946032i
$259$	3.21309	−	0.566555i	0.199652	−	0.0352040i
$260$	1.32493	+	2.25098i	0.0821686	+	0.139600i
$261$	18.1096	+	10.7779i	1.12096	+	0.667133i
$262$	7.22458	+	26.5167i	0.446336	+	1.63821i
$263$	7.84733	−	6.58469i	0.483887	−	0.406029i	−0.367943	−	0.929849i	$-0.619938\pi$
$263$	7.84733	−	6.58469i	0.483887	−	0.406029i	0.851829	+	0.523819i	$0.175493\pi$
$264$	−0.166371	+	0.117982i	−0.0102395	+	0.00726127i
$265$	0.520366	−	2.95114i	0.0319658	−	0.181287i
$266$	−2.99785	−	4.24334i	−0.183810	−	0.260176i
$267$	−6.27186	+	16.8831i	−0.383831	+	1.03323i
$268$	−16.9446	+	14.4624i	−1.03506	+	0.883431i
$269$			3.15222i			0.192194i	0.995372	+	0.0960971i	$0.0306359\pi$
$269$			3.15222i			0.192194i	−0.995372	+	0.0960971i	$0.969364\pi$
$270$	−0.608798	+	2.13753i	−0.0370502	+	0.130086i
$271$			3.33151i			0.202375i	0.994867	+	0.101188i	$0.0322642\pi$
$271$			3.33151i			0.202375i	−0.994867	+	0.101188i	$0.967736\pi$
$272$	9.72325	−	1.88335i	0.589559	−	0.114195i
$273$	3.57995	−	0.606828i	0.216669	−	0.0367269i
$274$	−17.7151	+	12.5154i	−1.07021	+	0.756084i
$275$	−0.0354861	+	0.201251i	−0.00213989	+	0.0121359i
$276$	7.82060	+	21.3688i	0.470745	+	1.28625i
$277$	3.19860	−	2.68395i	0.192186	−	0.161263i	−0.541618	−	0.840625i	$-0.682188\pi$
$277$	3.19860	−	2.68395i	0.192186	−	0.161263i	0.733803	+	0.679362i	$0.237743\pi$
$278$	12.1915	−	3.32161i	0.731195	−	0.199217i
$279$	−6.81516	−	8.34396i	−0.408013	−	0.499540i
$280$	0.399782	−	0.112537i	0.0238915	−	0.00672534i
$281$	19.3295	−	3.40832i	1.15310	−	0.203323i	0.435773	−	0.900057i	$-0.356475\pi$
$281$	19.3295	−	3.40832i	1.15310	−	0.203323i	0.717330	+	0.696733i	$0.245364\pi$
$282$	12.4888	−	12.4284i	0.743698	−	0.740102i
$283$	5.26641	+	14.4693i	0.313055	+	0.860113i	0.992036	+	0.125956i	$0.0401999\pi$
$283$	5.26641	+	14.4693i	0.313055	+	0.860113i	−0.678980	+	0.734156i	$0.737578\pi$
$284$	6.66423	+	1.11747i	0.395449	+	0.0663096i
$285$	−2.00472	+	3.41978i	−0.118749	+	0.202570i
$286$	0.0210946	−	0.253358i	0.00124735	−	0.0149814i
$287$	1.53526	−	2.65916i	0.0906238	−	0.156965i
$288$	−1.34805	+	16.9169i	−0.0794345	+	0.996840i
$289$	−5.43473	−	9.41323i	−0.319690	−	0.553720i
$290$	−2.71781	+	1.28125i	−0.159595	+	0.0752377i
$291$	4.39529	+	3.73796i	0.257657	+	0.219123i
$292$	−0.802992	+	0.973453i	−0.0469916	+	0.0569670i
$293$	11.9699	−	14.2652i	0.699290	−	0.833382i	−0.293156	−	0.956065i	$-0.594705\pi$
$293$	11.9699	−	14.2652i	0.699290	−	0.833382i	0.992446	+	0.122683i	$0.0391498\pi$
$294$	−1.48409	+	16.5025i	−0.0865537	+	0.962444i
$295$	0.450307	−	1.23721i	0.0262179	−	0.0720331i
$296$	−13.6088	−	13.2702i	−0.790995	−	0.771317i
$297$	0.168448	−	0.135736i	0.00977437	−	0.00787617i
$298$	−0.620393	+	2.35484i	−0.0359384	+	0.136412i
$299$	−26.6536	−	9.70110i	−1.54142	−	0.561029i
$300$	10.9528	+	13.0061i	0.632362	+	0.750908i
$301$	0.899557	+	0.754818i	0.0518496	+	0.0435070i
$302$	0.774511	+	0.357209i	0.0445681	+	0.0205551i
$303$	28.4514	+	5.21123i	1.63449	+	0.299378i
$304$	−9.87326	+	28.6127i	−0.566270	+	1.64105i
$305$	−1.97339	+	1.13934i	−0.112996	+	0.0652382i
$306$	−10.1710	+	2.62694i	−0.581436	+	0.150172i
$307$	17.7533	+	10.2499i	1.01323	+	0.584990i	0.912136	−	0.409887i	$-0.134432\pi$
$307$	17.7533	+	10.2499i	1.01323	+	0.584990i	0.101096	+	0.994877i	$0.467765\pi$
$308$	−0.0381019	−	0.0135067i	−0.00217106	−	0.000769617i
$309$	23.9296	−	13.6053i	1.36131	−	0.773978i
$310$	1.52962	−	0.140298i	0.0868766	−	0.00796839i
$311$	−18.8205	+	6.85012i	−1.06722	+	0.388435i	−0.815135	−	0.579272i	$-0.803337\pi$
$311$	−18.8205	+	6.85012i	−1.06722	+	0.388435i	−0.252081	+	0.967706i	$0.581115\pi$
$312$	−15.0471	−	14.8684i	−0.851875	−	0.841759i
$313$	−3.06340	−	17.3734i	−0.173154	−	0.982003i	−0.940253	−	0.340475i	$-0.889412\pi$
$313$	−3.06340	−	17.3734i	−0.173154	−	0.982003i	0.767100	−	0.641528i	$-0.221699\pi$
$314$	−10.3298	+	10.4169i	−0.582944	+	0.587859i
$315$	−0.415905	+	0.145169i	−0.0234336	+	0.00817935i
$316$	−6.05487	+	0.0508417i	−0.340613	+	0.00286007i
$317$	2.76189	+	3.29149i	0.155123	+	0.184868i	0.838009	−	0.545657i	$-0.183720\pi$
$317$	2.76189	+	3.29149i	0.155123	+	0.184868i	−0.682886	+	0.730525i	$0.739275\pi$
$318$	2.05663	+	24.1822i	0.115330	+	1.35607i
$319$	0.288017	+	0.0507851i	0.0161258	+	0.00284342i
$320$	−1.89210	−	1.50811i	−0.105772	−	0.0843058i
$321$	1.33633	−	1.10632i	0.0745867	−	0.0617487i
$322$	−2.57134	+	3.70527i	−0.143295	+	0.206487i
$323$	−18.7360			−1.04250
$324$	0.325606	−	17.9971i	0.0180892	−	0.999836i
$325$	−21.1951			−1.17569
$326$	−4.59931	+	6.62754i	−0.254732	+	0.367066i
$327$	−9.69432	+	8.02571i	−0.536097	+	0.443823i
$328$	−17.7994	+	1.78340i	−0.982807	+	0.0984720i
$329$	3.43911	+	0.606408i	0.189604	+	0.0334323i
$330$	0.00261373	+	0.0307326i	0.000143881	+	0.00169178i
$331$	−12.9390	−	15.4201i	−0.711190	−	0.847563i	0.282554	−	0.959252i	$-0.408819\pi$
$331$	−12.9390	−	15.4201i	−0.711190	−	0.847563i	−0.993743	+	0.111689i	$0.964374\pi$
$332$	0.0966917	+	11.5153i	0.00530664	+	0.631982i
$333$	15.2712	+	13.1625i	0.836854	+	0.721303i
$334$	−5.22848	+	5.27257i	−0.286090	+	0.288502i
$335$	0.585001	+	3.31770i	0.0319620	+	0.181266i
$336$	−2.89571	+	1.71134i	−0.157974	+	0.0933614i
$337$	−12.4122	+	4.51765i	−0.676133	+	0.246092i	−0.657186	−	0.753728i	$-0.728254\pi$
$337$	−12.4122	+	4.51765i	−0.676133	+	0.246092i	−0.0189468	+	0.999820i	$0.506031\pi$
$338$	7.95020	−	0.729198i	0.432434	−	0.0396631i
$339$	−21.7860	+	12.3866i	−1.18326	+	0.672745i
$340$	0.500417	−	1.41165i	0.0271389	−	0.0765576i
$341$	−0.129480	−	0.0747552i	−0.00701173	−	0.00404822i
$342$	8.58935	−	30.9340i	0.464459	−	1.67272i
$343$	−5.78720	+	3.34124i	−0.312480	+	0.180410i
$344$	0.510372	−	6.82219i	0.0275174	−	0.367828i
$345$	3.38480	+	0.619970i	0.182232	+	0.0333780i
$346$	−1.78152	−	0.821648i	−0.0957751	−	0.0441721i
$347$	−13.6769	−	11.4763i	−0.734213	−	0.616078i	0.197064	−	0.980391i	$-0.436859\pi$
$347$	−13.6769	−	11.4763i	−0.734213	−	0.616078i	−0.931277	+	0.364313i	$0.881304\pi$
$348$	18.6134	−	15.6749i	0.997785	−	0.840263i
$349$	12.2841	+	4.47105i	0.657554	+	0.239330i	0.649180	−	0.760635i	$-0.275112\pi$
$349$	12.2841	+	4.47105i	0.657554	+	0.239330i	0.00837388	+	0.999965i	$0.497334\pi$
$350$	−0.858586	+	3.25895i	−0.0458933	+	0.174198i
$351$	16.8979	+	14.7608i	0.901944	+	0.787875i
$352$	0.0657163	+	0.226157i	0.00350269	+	0.0120542i
$353$	7.34903	−	20.1913i	0.391149	−	1.07467i	−0.575328	−	0.817923i	$-0.695126\pi$
$353$	7.34903	−	20.1913i	0.391149	−	1.07467i	0.966477	−	0.256751i	$-0.0826521\pi$
$354$	−0.955083	+	10.6202i	−0.0507621	+	0.564455i
$355$	0.656843	−	0.782795i	0.0348616	−	0.0415464i
$356$	16.0428	+	13.2336i	0.850268	+	0.701379i
$357$	−1.58606	−	1.34886i	−0.0839430	−	0.0713890i
$358$	−14.7664	+	6.96133i	−0.780431	+	0.367918i
$359$	−9.46695	−	16.3972i	−0.499647	−	0.865413i	0.500353	−	0.865821i	$-0.333203\pi$
$359$	−9.46695	−	16.3972i	−0.499647	−	0.865413i	−1.00000		0.000407927i	$0.999870\pi$
$360$	2.10129	+	1.47337i	0.110748	+	0.0776535i
$361$	19.1302	−	33.1344i	1.00685	−	1.74392i
$362$	−2.01193	+	24.1644i	−0.105744	+	1.27005i
$363$	−9.63381	+	16.4340i	−0.505644	+	0.862560i
$364$	0.693366	−	4.13501i	0.0363423	−	0.216733i
$365$	0.0652682	+	0.179323i	0.00341629	+	0.00938619i
$366$	13.0810	−	13.0177i	0.683752	−	0.680446i
$367$	23.4580	−	4.13627i	1.22450	−	0.215912i	0.476236	−	0.879317i	$-0.342001\pi$
$367$	23.4580	−	4.13627i	1.22450	−	0.215912i	0.748260	+	0.663406i	$0.230890\pi$
$368$	26.2715	−	0.441225i	1.36949	−	0.0230004i
$369$	18.7274	−	3.04700i	0.974908	−	0.158620i
$370$	−2.77337	+	0.755615i	−0.144180	+	0.0392825i
$371$	−3.68488	+	3.09198i	−0.191310	+	0.160528i
$372$	−11.6824	+	4.27553i	−0.605702	+	0.221676i
$373$	−3.76380	+	21.3456i	−0.194882	+	1.10523i	0.717705	+	0.696348i	$0.245193\pi$
$373$	−3.76380	+	21.3456i	−0.194882	+	1.10523i	−0.912587	+	0.408883i	$0.865918\pi$
$374$	−0.119065	+	0.0841171i	−0.00615669	+	0.00434959i
$375$	5.11766	−	0.867480i	0.264275	−	0.0447965i
$376$	−8.82967	−	18.3290i	−0.455356	−	0.945245i
$377$			30.3329i			1.56222i
$378$	2.95414	−	2.00028i	0.151944	−	0.102883i
$379$		−	33.6783i		−	1.72994i	−0.501825	−	0.864969i	$-0.667338\pi$
$379$		−	33.6783i		−	1.72994i	0.501825	−	0.864969i	$-0.332662\pi$
$380$	2.97157	+	3.48159i	0.152438	+	0.178602i
$381$	5.36524	−	14.4426i	0.274870	−	0.739916i
$382$	13.5092	+	19.1217i	0.691190	+	0.978354i
$383$	−0.261068	+	1.48059i	−0.0133400	+	0.0756548i	−0.990751	−	0.135693i	$-0.956674\pi$
$383$	−0.261068	+	1.48059i	−0.0133400	+	0.0756548i	0.977411	+	0.211347i	$0.0677851\pi$
$384$	17.9439	+	7.87515i	0.915694	+	0.401877i
$385$	−0.00468303	+	0.00392953i	−0.000238670	+	0.000200268i
$386$	−3.27261	−	12.0116i	−0.166571	−	0.611374i
$387$	−0.0960946	+	7.25561i	−0.00488476	+	0.368823i
$388$	5.74166	−	3.37954i	0.291489	−	0.171570i
$389$	−3.80299	+	0.670570i	−0.192819	+	0.0339993i	−0.269224	−	0.963078i	$-0.586767\pi$
$389$	−3.80299	+	0.670570i	−0.192819	+	0.0339993i	0.0764044	+	0.997077i	$0.475656\pi$
$390$	−3.09198	+	0.820468i	−0.156569	+	0.0415460i
$391$	5.56271	+	15.2834i	0.281318	+	0.772916i
$392$	17.4402	+	7.86664i	0.880865	+	0.397325i
$393$	−33.6593	−	0.222885i	−1.69788	−	0.0112431i
$394$	−17.6133	−	1.46648i	−0.887345	−	0.0738801i
$395$	−0.457839	+	0.793000i	−0.0230364	+	0.0399002i
$396$	−0.0842970	−	0.235144i	−0.00423608	−	0.0118164i
$397$	−9.80431	−	16.9816i	−0.492064	−	0.852280i	0.507894	−	0.861419i	$-0.330424\pi$
$397$	−9.80431	−	16.9816i	−0.492064	−	0.852280i	−0.999958	+	0.00913954i	$0.997091\pi$
$398$	−2.70550	−	5.73893i	−0.135614	−	0.287666i
$399$	5.99368	−	2.13668i	0.300059	−	0.106968i
$400$	18.3346	−	7.02413i	0.916732	−	0.351207i
$401$	−13.9437	+	16.6175i	−0.696316	+	0.829838i	−0.992104	−	0.125416i	$-0.959973\pi$
$401$	−13.9437	+	16.6175i	−0.696316	+	0.829838i	0.295788	+	0.955254i	$0.404418\pi$
$402$	−11.4708	−	24.7556i	−0.572111	−	1.23470i
$403$	5.30360	−	14.5715i	0.264191	−	0.725859i
$404$	16.4562	−	29.0639i	0.818728	−	1.44598i
$405$	−2.32049	−	1.42298i	−0.115306	−	0.0707083i
$406$	4.66398	+	1.22875i	0.231470	+	0.0609817i
$407$	0.262912	+	0.0956921i	0.0130321	+	0.00474328i
$408$	−0.984988	+	12.0898i	−0.0487641	+	0.598533i
$409$	−8.42462	−	7.06909i	−0.416570	−	0.349544i	0.410286	−	0.911957i	$-0.365429\pi$
$409$	−8.42462	−	7.06909i	−0.416570	−	0.349544i	−0.826857	+	0.562413i	$0.809873\pi$
$410$	−1.13296	+	2.45651i	−0.0559528	+	0.121318i
$411$	−8.92022	−	25.0224i	−0.440002	−	1.23426i
$412$	−5.78210	−	31.2550i	−0.284864	−	1.53982i
$413$	−1.83029	+	1.05672i	−0.0900626	+	0.0519976i
$414$	−27.7838	+	2.17773i	−1.36550	+	0.107030i
$415$	1.50814	+	0.870727i	0.0740319	+	0.0427423i
$416$	−21.9163	+	10.7854i	−1.07453	+	0.528799i
$417$	−0.102475	+	15.4754i	−0.00501821	+	0.757831i
$418$	−0.0406937	−	0.443669i	−0.00199039	−	0.0217006i
$419$	22.7569	−	8.28284i	1.11175	−	0.404643i	0.280114	−	0.959967i	$-0.409628\pi$
$419$	22.7569	−	8.28284i	1.11175	−	0.404643i	0.831635	+	0.555323i	$0.187405\pi$
$420$	0.000902832		0.508659i	4.40537e−5		0.0248200i
$421$	6.35770	+	36.0563i	0.309855	+	1.75728i	0.599721	+	0.800209i	$0.295278\pi$
$421$	6.35770	+	36.0563i	0.309855	+	1.75728i	−0.289866	+	0.957067i	$0.593611\pi$
$422$	−22.5383	−	22.3498i	−1.09715	−	1.08797i
$423$	10.5411	+	18.8292i	0.512525	+	0.915508i
$424$	27.1583	+	6.91165i	1.31893	+	0.335660i
$425$	7.81210	+	9.31010i	0.378942	+	0.451606i
$426$	−3.51572	+	7.49204i	−0.170337	+	0.362990i
$427$	3.60217	+	0.635160i	0.174321	+	0.0307375i
$428$	−0.700930	−	1.87661i	−0.0338807	−	0.0907093i
$429$	0.291883	+	0.108431i	0.0140923	+	0.00523510i
$430$	−0.849951	−	0.589840i	−0.0409883	−	0.0284446i
$431$	38.5608			1.85741			0.928705	−	0.370820i	$-0.120923\pi$
$431$	38.5608			1.85741			0.928705	+	0.370820i	$0.120923\pi$
$432$	−19.5092	−	7.16872i	−0.938638	−	0.344905i
$433$	−6.56251			−0.315374			−0.157687	−	0.987489i	$-0.550404\pi$
$433$	−6.56251			−0.315374			−0.157687	+	0.987489i	$0.550404\pi$
$434$	−2.02567	−	1.40576i	−0.0972355	−	0.0674784i
$435$	−0.615007	−	3.62821i	−0.0294873	−	0.173959i
$436$	5.08484	+	13.6137i	0.243520	+	0.651979i
$437$	−48.9513	−	8.63143i	−2.34166	−	0.412897i
$438$	−0.883399	−	1.26815i	−0.0422104	−	0.0605948i
$439$	1.17279	+	1.39768i	0.0559744	+	0.0667077i	0.793305	−	0.608824i	$-0.208359\pi$
$439$	1.17279	+	1.39768i	0.0559744	+	0.0667077i	−0.737331	+	0.675532i	$0.763914\pi$
$440$	0.0345149	+	0.00878386i	0.00164543	+	0.000418754i
$441$	−18.9755	−	7.19250i	−0.903595	−	0.342500i
$442$	−10.7362	−	10.6464i	−0.510667	−	0.506397i
$443$	0.302973	+	1.71824i	0.0143947	+	0.0816362i	0.991159	−	0.132681i	$-0.0423585\pi$
$443$	0.302973	+	1.71824i	0.0143947	+	0.0816362i	−0.976764	+	0.214317i	$0.931247\pi$
$444$	20.1402	−	11.6757i	0.955811	−	0.554102i
$445$	2.95530	−	1.07564i	0.140095	−	0.0509903i
$446$	2.36597	+	25.7954i	0.112032	+	1.22145i
$447$	−2.57298	−	1.50831i	−0.121698	−	0.0713408i
$448$	0.770567	+	3.80675i	0.0364059	+	0.179852i
$449$	8.00158	+	4.61971i	0.377618	+	0.218018i	0.676781	−	0.736184i	$-0.263374\pi$
$449$	8.00158	+	4.61971i	0.377618	+	0.218018i	−0.299164	+	0.954202i	$0.596708\pi$
$450$	−18.9528	+	8.63000i	−0.893443	+	0.406822i
$451$	0.228032	−	0.131654i	0.0107376	−	0.00619937i
$452$	5.26415	+	28.4552i	0.247605	+	1.33842i
$453$	−0.676743	+	0.795750i	−0.0317962	+	0.0373876i
$454$	11.6107	−	25.1747i	0.544918	−	1.18151i
$455$	−0.485708	−	0.407557i	−0.0227703	−	0.0191066i
$456$	−30.4931	−	21.0812i	−1.42797	−	0.987218i
$457$	25.9190	+	9.43376i	1.21244	+	0.441293i	0.867550	−	0.497350i	$-0.165694\pi$
$457$	25.9190	+	9.43376i	1.21244	+	0.441293i	0.344891	+	0.938643i	$0.387916\pi$
$458$	−7.75140	−	2.04214i	−0.362199	−	0.0954229i
$459$	0.255560	−	12.8631i	0.0119285	−	0.600398i
$460$	1.95776	−	3.45767i	0.0912812	−	0.161215i
$461$	7.09177	−	19.4845i	0.330297	−	0.907483i	−0.657737	−	0.753247i	$-0.728486\pi$
$461$	7.09177	−	19.4845i	0.330297	−	0.907483i	0.988034	−	0.154236i	$-0.0492915\pi$
$462$	0.0284962	−	0.0404876i	0.00132576	−	0.00188365i
$463$	6.16175	−	7.34328i	0.286361	−	0.341271i	−0.603618	−	0.797274i	$-0.706275\pi$
$463$	6.16175	−	7.34328i	0.286361	−	0.341271i	0.889979	+	0.456002i	$0.150719\pi$
$464$	−10.0524	−	26.2393i	−0.466673	−	1.21813i
$465$	−0.338938	+	1.85047i	−0.0157179	+	0.0858137i
$466$	4.52969	+	9.60842i	0.209834	+	0.445101i
$467$	8.74737	+	15.1509i	0.404780	+	0.701099i	0.994296	−	0.106657i	$-0.0340148\pi$
$467$	8.74737	+	15.1509i	0.404780	+	0.701099i	−0.589516	+	0.807757i	$0.700681\pi$
$468$	22.4996	−	12.8451i	1.04004	−	0.593767i
$469$	2.70388	−	4.68326i	0.124854	−	0.216253i
$470$	−3.06604	−	0.255278i	−0.141426	−	0.0117751i
$471$	−8.88042	−	15.6193i	−0.409188	−	0.719699i
$472$	11.2237	+	5.06257i	0.516610	+	0.233024i
$473$	0.0344412	+	0.0946266i	0.00158361	+	0.00435093i
$474$	1.93674	−	7.15856i	0.0889573	−	0.328804i
$475$	−36.5788	+	6.44983i	−1.67835	+	0.295938i
$476$	−2.07190	+	1.21952i	−0.0949652	+	0.0558966i
$477$	−29.2015	−	5.54872i	−1.33704	−	0.254058i
$478$	−2.40590	−	8.83047i	−0.110043	−	0.403896i
$479$	−20.0678	+	16.8388i	−0.916919	+	0.769386i	−0.973423	−	0.229016i	$-0.926449\pi$
$479$	−20.0678	+	16.8388i	−0.916919	+	0.769386i	0.0565037	+	0.998402i	$0.482005\pi$
$480$	2.40279	−	1.73444i	0.109672	−	0.0791658i
$481$	−5.03898	+	28.5775i	−0.229758	+	1.30302i
$482$	0.566250	+	0.801505i	0.0257920	+	0.0365076i
$483$	−3.52247	−	4.25482i	−0.160278	−	0.193601i
$484$	14.2801	+	16.7310i	0.649095	+	0.760500i
$485$		−	1.00752i		−	0.0457493i
$486$	21.1204	+	6.31892i	0.958041	+	0.286632i
$487$			7.10957i			0.322166i	0.986941	+	0.161083i	$0.0514986\pi$
$487$			7.10957i			0.322166i	−0.986941	+	0.161083i	$0.948501\pi$
$488$	−9.24832	−	19.1980i	−0.418652	−	0.869054i
$489$	−6.30057	−	7.61051i	−0.284922	−	0.344159i
$490$	2.36305	−	1.66945i	0.106752	−	0.0754182i
$491$	−3.43007	+	19.4529i	−0.154797	+	0.877897i	0.804174	+	0.594393i	$0.202608\pi$
$491$	−3.43007	+	19.4529i	−0.154797	+	0.877897i	−0.958971	+	0.283503i	$0.908503\pi$
$492$	3.76613	−	21.5827i	0.169790	−	0.973024i
$493$	13.3239	−	11.1801i	0.600081	−	0.503527i
$494$	44.5838	−	12.1470i	2.00592	−	0.546521i
$495$	−0.0371115	−	0.00705174i	−0.00166804	−	0.000316952i
$496$	0.241218	+	14.3626i	0.0108310	+	0.644901i
$497$	−1.61539	+	0.284836i	−0.0724600	+	0.0127767i
$498$	−13.6143	−	3.68332i	−0.610071	−	0.165054i
$499$	13.5189	+	37.1430i	0.605191	+	1.66275i	0.740591	+	0.671956i	$0.234546\pi$
$499$	13.5189	+	37.1430i	0.605191	+	1.66275i	−0.135400	+	0.990791i	$0.543232\pi$
$500$	0.991189	−	5.91113i	0.0443273	−	0.264354i
$501$	−4.49488	−	7.90579i	−0.200816	−	0.353205i
$502$	−0.256069	+	3.07554i	−0.0114289	+	0.137268i
$503$	19.5426	−	33.8489i	0.871364	−	1.50925i	0.0107769	−	0.999942i	$-0.496570\pi$
$503$	19.5426	−	33.8489i	0.871364	−	1.50925i	0.860587	−	0.509304i	$-0.170097\pi$
$504$	−1.06364	−	3.97987i	−0.0473782	−	0.177278i
$505$	−2.52541	−	4.37413i	−0.112379	−	0.194646i
$506$	−0.349831	+	0.164920i	−0.0155519	+	0.00733160i
$507$	−1.76163	+	9.61784i	−0.0782367	+	0.427143i
$508$	−13.7238	−	11.3206i	−0.608895	−	0.502271i
$509$	−9.47986	+	11.2977i	−0.420187	+	0.500760i	−0.934065	−	0.357104i	$-0.883764\pi$
$509$	−9.47986	+	11.2977i	−0.420187	+	0.500760i	0.513877	+	0.857864i	$0.328209\pi$
$510$	1.50004	+	1.05577i	0.0664230	+	0.0467502i
$511$	0.104769	−	0.287850i	0.00463471	−	0.0127338i
$512$	15.3842	−	16.5930i	0.679891	−	0.733314i
$513$	33.6545	+	20.3323i	1.48588	+	0.897693i
$514$	5.18448	−	19.6788i	0.228677	−	0.867996i
$515$	−4.51685	−	1.64400i	−0.199036	−	0.0724432i
$516$	7.87856	+	2.85174i	0.346834	+	0.125541i
$517$	0.229404	+	0.192493i	0.0100892	+	0.00846582i
$518$	4.18995	+	1.93243i	0.184096	+	0.0849061i
$519$	1.55663	−	1.83037i	0.0683287	−	0.0803444i
$520$	−0.275571	+	3.68358i	−0.0120846	+	0.161536i
$521$	−10.1293	+	5.84816i	−0.443773	+	0.256213i	−0.705197	−	0.709012i	$-0.749141\pi$
$521$	−10.1293	+	5.84816i	−0.443773	+	0.256213i	0.261424	+	0.965224i	$0.415808\pi$
$522$	12.3506	+	27.1239i	0.540573	+	1.18718i
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	0.341505	−	0.939880i	$-0.389063\pi$
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	−0.643207	+	0.765692i	$0.722397\pi$
$524$	−12.9862	+	36.6336i	−0.567306	+	1.60034i
$525$	−3.56085	−	2.08741i	−0.155408	−	0.0911023i
$526$	14.4266	−	1.32322i	0.629029	−	0.0576950i
$527$	−8.35546	+	3.04114i	−0.363969	+	0.132474i
$528$	−0.288426	+	0.00293384i	−0.0125521	+	0.000127679i
$529$	3.49884	+	19.8429i	0.152124	+	0.862736i
$530$	2.98406	−	3.00922i	0.129619	−	0.130712i
$531$	−12.2117	−	4.62873i	−0.529941	−	0.200870i
$532$	−0.0616937	−	7.34727i	−0.00267476	−	0.318544i
$533$	17.5542	+	20.9203i	0.760356	+	0.906157i
$534$	−20.8996	+	14.5587i	−0.904415	+	0.630017i
$535$	−0.298337	−	0.0526049i	−0.0128982	−	0.00227431i
$536$	−31.3480	+	3.14090i	−1.35403	+	0.135666i
$537$	−3.34147	−	19.7129i	−0.144195	−	0.850672i
$538$	−2.54160	+	3.66241i	−0.109576	+	0.157898i
$539$	−0.281617			−0.0121301
$540$	−2.43080	+	1.99263i	−0.104605	+	0.0857492i
$541$	8.41220			0.361669			0.180834	−	0.983514i	$-0.442120\pi$
$541$	8.41220			0.361669			0.180834	+	0.983514i	$0.442120\pi$
$542$	−2.68616	+	3.87072i	−0.115381	+	0.166262i
$543$	−27.8388	−	10.3418i	−1.19468	−	0.443808i
$544$	12.8155	+	5.65158i	0.549460	+	0.242309i
$545$	2.16426	+	0.381618i	0.0927069	+	0.0163467i
$546$	4.64865	+	2.18143i	0.198944	+	0.0933567i
$547$	−11.2369	−	13.3916i	−0.480453	−	0.572582i	0.470309	−	0.882502i	$-0.344142\pi$
$547$	−11.2369	−	13.3916i	−0.480453	−	0.572582i	−0.950763	+	0.309920i	$0.899698\pi$
$548$	−30.6734	+	0.257559i	−1.31030	+	0.0110024i
$549$	11.0409	+	19.7220i	0.471213	+	0.841714i
$550$	−0.203496	+	0.205212i	−0.00867711	+	0.00875028i
$551$	9.23054	+	52.3490i	0.393234	+	2.23014i
$552$	−8.14308	+	31.1331i	−0.346592	+	1.32511i
$553$	1.38121	−	0.502719i	0.0587350	−	0.0213778i
$554$	5.88034	−	0.539349i	0.249832	−	0.0229147i
$555$	0.0233114	−	3.52040i	0.000989513	−	0.149433i
$556$	16.8428	+	5.97062i	0.714295	+	0.253211i
$557$	0.688812	+	0.397686i	0.0291859	+	0.0168505i	0.514522	−	0.857477i	$-0.327969\pi$
$557$	0.688812	+	0.397686i	0.0291859	+	0.0168505i	−0.485336	+	0.874328i	$0.661303\pi$
$558$	−1.19057	−	15.1894i	−0.0504007	−	0.643020i
$559$	−9.04493	+	5.22209i	−0.382560	+	0.220871i
$560$	0.555224	+	0.191589i	0.0234625	+	0.00809611i
$561$	−0.0599535	−	0.168178i	−0.00253124	−	0.00710046i
$562$	25.2061	+	11.6252i	1.06326	+	0.490381i
$563$	4.79979	+	4.02750i	0.202287	+	0.169739i	0.738304	−	0.674468i	$-0.235627\pi$
$563$	4.79979	+	4.02750i	0.202287	+	0.169739i	−0.536017	+	0.844207i	$0.680072\pi$
$564$	24.5310	−	4.37039i	1.03294	−	0.184027i
$565$	4.11224	+	1.49673i	0.173003	+	0.0629680i
$566$	−5.54768	+	21.0575i	−0.233187	+	0.885111i
$567$	1.38517	+	4.14408i	0.0581719	+	0.174035i
$568$	6.84184	+	6.67163i	0.287077	+	0.279935i
$569$	1.85350	−	5.09244i	0.0777027	−	0.213486i	−0.894759	−	0.446550i	$-0.852653\pi$
$569$	1.85350	−	5.09244i	0.0777027	−	0.213486i	0.972462	+	0.233063i	$0.0748749\pi$
$570$	−5.08652	+	2.35689i	−0.213051	+	0.0987193i
$571$	−19.5951	+	23.3525i	−0.820029	+	0.977273i	−0.999979	−	0.00640314i	$-0.997962\pi$
$571$	−19.5951	+	23.3525i	−0.820029	+	0.977273i	0.179950	+	0.983676i	$0.442406\pi$
$572$	0.228789	−	0.277356i	0.00956614	−	0.0115969i
$573$	−27.0093	+	9.62851i	−1.12833	+	0.402237i
$574$	3.92780	−	1.85168i	0.163943	−	0.0772875i
$575$	16.1215	+	27.9233i	0.672315	+	1.16448i
$576$	−15.2062	+	18.5680i	−0.633590	+	0.773669i
$577$	−9.67484	+	16.7573i	−0.402769	+	0.697616i	−0.994059	−	0.108843i	$-0.965286\pi$
$577$	−9.67484	+	16.7573i	−0.402769	+	0.697616i	0.591290	+	0.806459i	$0.298619\pi$
$578$	1.27543	−	15.3187i	0.0530511	−	0.637176i
$579$	15.2470	+	0.100963i	0.633646	+	0.00419587i
$580$	−4.19075	−	0.702712i	−0.174011	−	0.0291785i
$581$	−0.956081	−	2.62681i	−0.0396649	−	0.108979i
$582$	2.09280	+	7.88683i	0.0867493	+	0.326920i
$583$	−0.406232	+	0.0716296i	−0.0168244	+	0.00296659i
$584$	−1.71784	+	0.483564i	−0.0710848	+	0.0200100i
$585$	0.0518854	−	3.91760i	0.00214520	−	0.161973i
$586$	25.4091	−	6.92282i	1.04964	−	0.285979i
$587$	33.1376	−	27.8057i	1.36773	−	1.14767i	0.394227	−	0.919013i	$-0.371012\pi$
$587$	33.1376	−	27.8057i	1.36773	−	1.14767i	0.973508	−	0.228653i	$-0.0734320\pi$
$588$	−15.0300	+	17.9768i	−0.619829	+	0.741351i
$589$	4.71881	−	26.7617i	0.194435	−	1.10270i
$590$	1.52074	−	1.07438i	0.0626078	−	0.0442313i
$591$	7.53804	−	20.2915i	0.310074	−	0.834682i
$592$	−5.11175	−	26.3907i	−0.210092	−	1.08465i
$593$		−	32.7916i		−	1.34659i	−0.739375	−	0.673294i	$-0.764879\pi$
$593$		−	32.7916i		−	1.34659i	0.739375	−	0.673294i	$-0.235121\pi$
$594$	0.305154	−	0.0218863i	0.0125206	−	0.000898008i
$595$			0.363568i			0.0149048i
$596$	−2.61948	+	2.23576i	−0.107298	+	0.0915801i
$597$	7.66133	−	1.29865i	0.313557	−	0.0531502i
$598$	−23.1456	−	32.7617i	−0.946493	−	1.33973i
$599$	6.52625	−	37.0122i	0.266655	−	1.51228i	−0.497624	−	0.867393i	$-0.665794\pi$
$599$	6.52625	−	37.0122i	0.266655	−	1.51228i	0.764279	−	0.644885i	$-0.223095\pi$
$600$	2.23887	+	23.9423i	0.0914013	+	0.977441i
$601$	7.65033	−	6.41939i	0.312063	−	0.261852i	−0.473281	−	0.880912i	$-0.656930\pi$
$601$	7.65033	−	6.41939i	0.312063	−	0.261852i	0.785344	+	0.619059i	$0.212486\pi$
$602$	0.436550	+	1.60229i	0.0177925	+	0.0653044i
$603$	32.9823	−	5.36631i	1.34314	−	0.218533i
$604$	0.611852	+	1.03950i	0.0248959	+	0.0422968i
$605$	3.27588	−	0.577627i	0.133184	−	0.0234839i
$606$	28.8545	+	28.9947i	1.17214	+	1.17783i
$607$	−9.92909	−	27.2799i	−0.403009	−	1.10726i	−0.960792	−	0.277271i	$-0.910570\pi$
$607$	−9.92909	−	27.2799i	−0.403009	−	1.10726i	0.557783	−	0.829987i	$-0.311652\pi$
$608$	−34.5413	+	25.2830i	−1.40084	+	1.02536i
$609$	−2.98736	+	5.09603i	−0.121054	+	0.206502i
$610$	−3.21142	−	0.267382i	−0.130026	−	0.0108260i
$611$	−15.5298	+	26.8983i	−0.628266	+	1.08819i
$612$	−13.9352	−	5.14864i	−0.563299	−	0.208121i
$613$	−10.6465	−	18.4402i	−0.430007	−	0.744794i	0.566866	−	0.823810i	$-0.308156\pi$
$613$	−10.6465	−	18.4402i	−0.430007	−	0.744794i	−0.996873	+	0.0790155i	$0.974822\pi$
$614$	12.3623	+	26.2231i	0.498902	+	1.05828i
$615$	−2.52387	−	2.14642i	−0.101772	−	0.0865519i
$616$	−0.0333784	−	0.0464139i	−0.00134485	−	0.00187007i
$617$	1.59822	−	1.90469i	0.0643420	−	0.0766798i	−0.732913	−	0.680322i	$-0.761840\pi$
$617$	1.59822	−	1.90469i	0.0643420	−	0.0766798i	0.797255	+	0.603642i	$0.206284\pi$
$618$	38.7724	+	3.48685i	1.55966	+	0.140262i
$619$	−4.56324	+	12.5374i	−0.183412	+	0.503921i	−0.996990	−	0.0775360i	$-0.975295\pi$
$619$	−4.56324	+	12.5374i	−0.183412	+	0.503921i	0.813577	+	0.581457i	$0.197517\pi$
$620$	1.89031	+	1.07031i	0.0759168	+	0.0429847i
$621$	6.59357	−	33.4895i	0.264591	−	1.34389i
$622$	−27.3899	−	7.21598i	−1.09823	−	0.289334i
$623$	−4.74387	−	1.72663i	−0.190059	−	0.0691759i
$624$	−5.49427	−	29.4072i	−0.219947	−	1.17723i
$625$	18.1064	+	15.1931i	0.724256	+	0.607723i
$626$	10.4488	−	22.6553i	0.417617	−	0.905488i
$627$	0.536733	+	0.0983095i	0.0214351	+	0.00392610i
$628$	−20.4007	+	3.77408i	−0.814077	+	0.150602i
$629$	14.4101	−	8.31969i	0.574570	−	0.331728i
$630$	−0.600268	−	0.166675i	−0.0239153	−	0.00664049i
$631$	−33.1235	−	19.1238i	−1.31862	−	0.761308i	−0.335117	−	0.942176i	$-0.608776\pi$
$631$	−33.1235	−	19.1238i	−1.31862	−	0.761308i	−0.983507	+	0.180868i	$0.942109\pi$
$632$	−7.07585	−	4.82290i	−0.281462	−	0.191845i
$633$	33.7943	−	19.2139i	1.34320	−	0.763685i
$634$	0.555011	+	6.05110i	0.0220423	+	0.240320i
$635$	−2.52810	+	0.920154i	−0.100325	+	0.0365152i
$636$	−17.1084	+	29.7544i	−0.678391	+	1.17984i
$637$	−5.07197	−	28.7646i	−0.200959	−	1.13969i
$638$	0.293685	+	0.291229i	0.0116271	+	0.0115299i
$639$	−7.67759	−	6.61749i	−0.303721	−	0.261784i
$640$	−0.982372	−	3.27778i	−0.0388317	−	0.129566i
$641$	9.13644	+	10.8884i	0.360868	+	0.430065i	0.915679	−	0.401911i	$-0.131654\pi$
$641$	9.13644	+	10.8884i	0.360868	+	0.430065i	−0.554811	+	0.831976i	$0.687209\pi$
$642$	2.44463	−	0.207909i	0.0964819	−	0.00820552i
$643$	−0.627325	−	0.110614i	−0.0247393	−	0.00436221i	0.161265	−	0.986911i	$-0.448443\pi$
$643$	−0.627325	−	0.110614i	−0.0247393	−	0.00436221i	−0.186004	+	0.982549i	$0.559554\pi$
$644$	−5.97504	+	2.23173i	−0.235450	+	0.0879424i
$645$	0.976012	−	0.808019i	0.0384304	−	0.0318157i
$646$	−21.7684	−	15.1066i	−0.856467	−	0.594361i
$647$	7.26586			0.285650			0.142825	−	0.989748i	$-0.454381\pi$
$647$	7.26586			0.285650			0.142825	+	0.989748i	$0.454381\pi$
$648$	14.8891	−	20.6474i	0.584900	−	0.811105i
$649$	−0.181235			−0.00711408
$650$	−24.6255	−	17.0894i	−0.965892	−	0.670300i
$651$	2.32611	−	1.92574i	0.0911675	−	0.0754756i
$652$	−10.6874	+	3.99185i	−0.418552	+	0.156333i
$653$	31.3669	+	5.53083i	1.22748	+	0.216438i	0.749543	−	0.661955i	$-0.230273\pi$
$653$	31.3669	+	5.53083i	1.22748	+	0.216438i	0.477938	+	0.878393i	$0.341384\pi$
$654$	−17.7344	+	1.50826i	−0.693470	+	0.0589777i
$655$	3.77810	+	4.50257i	0.147623	+	0.175930i
$656$	−22.1182	−	12.2794i	−0.863570	−	0.479430i
$657$	1.78712	−	0.623784i	0.0697223	−	0.0243361i
$658$	3.50679	+	3.47747i	0.136709	+	0.135566i
$659$	−2.56367	−	14.5393i	−0.0998663	−	0.566370i	−0.993147	−	0.116871i	$-0.962714\pi$
$659$	−2.56367	−	14.5393i	−0.0998663	−	0.566370i	0.893281	−	0.449499i	$-0.148397\pi$
$660$	−0.0217426	+	0.0378142i	−0.000846331	+	0.00147192i
$661$	−18.8308	+	6.85385i	−0.732433	+	0.266584i	−0.681194	−	0.732103i	$-0.738539\pi$
$661$	−18.8308	+	6.85385i	−0.732433	+	0.266584i	−0.0512388	+	0.998686i	$0.516317\pi$
$662$	−2.60013	−	28.3484i	−0.101057	−	1.10179i
$663$	16.0980	−	9.15260i	0.625195	−	0.355458i
$664$	−9.17229	+	13.4570i	−0.355954	+	0.522232i
$665$	−0.962265	−	0.555564i	−0.0373150	−	0.0215438i
$666$	7.12999	+	27.6059i	0.276281	+	1.06971i
$667$	39.9619	−	23.0720i	1.54733	−	0.893352i
$668$	−10.3259	+	1.91027i	−0.399522	+	0.0739107i
$669$	−31.2063	−	5.71582i	−1.20650	−	0.220987i
$670$	−1.99534	+	4.32636i	−0.0770869	+	0.167142i
$671$	0.240281	+	0.201620i	0.00927594	+	0.00778344i
$672$	−4.74422	−	0.346451i	−0.183012	−	0.0133646i
$673$	−32.6670	−	11.8898i	−1.25922	−	0.458319i	−0.375713	−	0.926736i	$-0.622602\pi$
$673$	−32.6670	−	11.8898i	−1.25922	−	0.458319i	−0.883508	+	0.468417i	$0.844825\pi$
$674$	−18.0636	−	4.75894i	−0.695784	−	0.183307i
$675$	−3.92916	−	25.2010i	−0.151233	−	0.969986i
$676$	9.82490	+	5.56294i	0.377881	+	0.213959i
$677$	11.4934	−	31.5778i	0.441726	−	1.21363i	−0.496630	−	0.867962i	$-0.665429\pi$
$677$	11.4934	−	31.5778i	0.441726	−	1.21363i	0.938356	−	0.345670i	$-0.112348\pi$
$678$	−35.2993	−	3.17450i	−1.35566	−	0.121916i
$679$	−1.03957	+	1.23891i	−0.0398951	+	0.0475451i
$680$	1.71961	−	1.23665i	0.0659440	−	0.0474234i
$681$	25.8650	+	21.9968i	0.991149	+	0.842920i
$682$	−0.0901620	−	0.191253i	−0.00345248	−	0.00732344i
$683$	−12.3153	−	21.3308i	−0.471233	−	0.816200i	0.528225	−	0.849104i	$-0.322858\pi$
$683$	−12.3153	−	21.3308i	−0.471233	−	0.816200i	−0.999459	+	0.0329044i	$0.989524\pi$
$684$	34.9213	−	29.0151i	1.33525	−	1.10942i
$685$	−2.31937	+	4.01726i	−0.0886185	+	0.153492i
$686$	−9.41787	−	0.784130i	−0.359576	−	0.0299382i
$687$	4.96490	−	8.46945i	0.189423	−	0.323129i
$688$	6.09363	−	7.51486i	0.232318	−	0.286501i
$689$	−14.6326	−	40.2027i	−0.557458	−	1.53160i
$690$	3.43276	+	3.44944i	0.130683	+	0.131318i
$691$	−14.4784	+	2.55293i	−0.550784	+	0.0971181i	−0.442113	−	0.896960i	$-0.645771\pi$
$691$	−14.4784	+	2.55293i	−0.550784	+	0.0971181i	−0.108672	+	0.994078i	$0.534660\pi$
$692$	−1.40737	−	2.39105i	−0.0535003	−	0.0908942i
$693$	0.0383585	+	0.0469632i	0.00145712	+	0.00178398i
$694$	−6.63731	−	24.3612i	−0.251949	−	0.924739i
$695$	2.07012	−	1.73704i	0.0785243	−	0.0658897i
$696$	34.2645	−	3.20411i	1.29879	−	0.121451i
$697$	2.71925	−	15.4216i	0.102999	−	0.584135i
$698$	10.6674	+	15.0992i	0.403765	+	0.571515i
$699$	−12.8270	+	2.17427i	−0.485162	+	0.0822385i
$700$	−3.62521	+	3.09415i	−0.137020	+	0.116948i
$701$			32.3443i			1.22163i	0.791775	+	0.610813i	$0.209157\pi$
$701$			32.3443i			1.22163i	−0.791775	+	0.610813i	$0.790843\pi$
$702$	7.73136	+	30.7745i	0.291801	+	1.16151i
$703$			50.8528i			1.91795i
$704$	−0.105995	+	0.315747i	−0.00399484	+	0.0119002i
$705$	1.31219	−	3.53226i	0.0494199	−	0.133032i
$706$	24.8185	−	17.5338i	0.934056	−	0.659895i
$707$	−1.40787	+	7.98443i	−0.0529484	+	0.300285i
$708$	−9.67258	+	11.5690i	−0.363518	+	0.434789i
$709$	−30.0746	+	25.2356i	−1.12947	+	0.947741i	−0.999044	−	0.0437162i	$-0.986080\pi$
$709$	−30.0746	+	25.2356i	−1.12947	+	0.947741i	−0.130430	+	0.991458i	$0.541636\pi$
$710$	1.39431	−	0.379886i	0.0523276	−	0.0142569i
$711$	7.80495	+	4.64508i	0.292708	+	0.174204i
$712$	7.96929	+	28.3106i	0.298662	+	1.06099i
$713$	−23.2312	+	4.09629i	−0.870016	+	0.153407i
$714$	−0.755193	−	2.84599i	−0.0282624	−	0.106508i
$715$	−0.0185962	−	0.0510927i	−0.000695460	−	0.00191076i
$716$	−22.7693	−	3.81799i	−0.850927	−	0.142685i
$717$	11.2090	+	0.0742241i	0.418609	+	0.00277195i
$718$	2.22172	−	26.6843i	0.0829140	−	0.995848i
$719$	0.482259	−	0.835298i	0.0179852	−	0.0311514i	−0.856893	−	0.515495i	$-0.827608\pi$
$719$	0.482259	−	0.835298i	0.0179852	−	0.0311514i	0.874878	+	0.484343i	$0.160941\pi$
$720$	1.25342	+	3.40609i	0.0467124	+	0.126937i
$721$	3.85790	+	6.68207i	0.143676	+	0.248853i
$722$	48.9423	−	23.0728i	1.82145	−	0.858682i
$723$	−1.13212	+	0.403588i	−0.0421039	+	0.0150096i
$724$	−21.8211	+	26.4533i	−0.810974	+	0.983129i
$725$	22.1640	−	26.4140i	0.823151	−	0.980993i
$726$	−24.4436	+	11.3262i	−0.907186	+	0.420354i
$727$	−7.16819	+	19.6944i	−0.265854	+	0.730427i	0.732892	+	0.680345i	$0.238170\pi$
$727$	−7.16819	+	19.6944i	−0.265854	+	0.730427i	−0.998745	+	0.0500812i	$0.984052\pi$
$728$	4.13960	−	4.24521i	0.153424	−	0.157338i
$729$	−14.4181	+	22.8280i	−0.534004	+	0.845482i
$730$	−0.0687541	+	0.260972i	−0.00254470	+	0.00965899i
$731$	5.62763	+	2.04829i	0.208146	+	0.0757588i
$732$	25.6941	−	4.57761i	0.949683	−	0.169193i
$733$	1.37507	+	1.15382i	0.0507892	+	0.0426172i	0.667829	−	0.744315i	$-0.267224\pi$
$733$	1.37507	+	1.15382i	0.0507892	+	0.0426172i	−0.617040	+	0.786932i	$0.711668\pi$
$734$	30.5897	+	14.1082i	1.12909	+	0.520742i
$735$	1.18988	+	3.33778i	0.0438895	+	0.123116i
$736$	30.8793	+	20.6698i	1.13823	+	0.761897i
$737$	0.401606	−	0.231867i	0.0147934	−	0.00854095i
$738$	24.2152	+	11.5595i	0.891373	+	0.425511i
$739$	17.1448	+	9.89858i	0.630683	+	0.364125i	0.781017	−	0.624510i	$-0.214701\pi$
$739$	17.1448	+	9.89858i	0.630683	+	0.364125i	−0.150333	+	0.988635i	$0.548035\pi$
$740$	−3.83148	−	1.35822i	−0.140848	−	0.0499292i
$741$	−0.374747	+	56.5929i	−0.0137667	+	2.07899i
$742$	−6.77432	+	0.621345i	−0.248693	+	0.0228103i
$743$	−36.3877	+	13.2440i	−1.33494	+	0.485877i	−0.908214	−	0.418507i	$-0.862554\pi$
$743$	−36.3877	+	13.2440i	−1.33494	+	0.485877i	−0.426721	+	0.904383i	$0.640331\pi$
$744$	−17.0205	−	4.45183i	−0.624000	−	0.163212i
$745$	0.0904359	+	0.512888i	0.00331332	+	0.0187907i
$746$	−21.5837	+	21.7656i	−0.790234	+	0.796897i
$747$	8.83410	−	14.8436i	0.323223	−	0.543099i
$748$	−0.206158	+	0.00173107i	−0.00753789	+	6.32943e-5i
$749$	0.312575	+	0.372512i	0.0114212	+	0.0136113i
$750$	6.64540	+	3.11843i	0.242656	+	0.113869i
$751$	−22.7048	−	4.00346i	−0.828508	−	0.146088i	−0.256716	−	0.966487i	$-0.582641\pi$
$751$	−22.7048	−	4.00346i	−0.828508	−	0.146088i	−0.571792	+	0.820398i	$0.693752\pi$
$752$	4.51969	−	28.4148i	0.164816	−	1.03618i
$753$	−3.54320	−	1.31625i	−0.129121	−	0.0479670i
$754$	−24.4571	+	35.2423i	−0.890674	+	1.28345i
$755$	0.182408			0.00663851
$756$	5.04507	+	0.0578619i	0.183487	+	0.00210442i
$757$	33.3070			1.21056			0.605281	−	0.796012i	$-0.293061\pi$
$757$	33.3070			1.21056			0.605281	+	0.796012i	$0.293061\pi$
$758$	27.1544	−	39.1292i	0.986294	−	1.42124i
$759$	−0.0791625	−	0.467016i	−0.00287342	−	0.0169516i
$760$	0.645358	+	6.44104i	0.0234096	+	0.233641i
$761$	15.6353	+	2.75693i	0.566780	+	0.0999386i	0.449693	−	0.893183i	$-0.351533\pi$
$761$	15.6353	+	2.75693i	0.566780	+	0.0999386i	0.117087	+	0.993122i	$0.462644\pi$
$762$	17.8785	−	12.4542i	0.647670	−	0.451168i
$763$	−2.26755	−	2.70236i	−0.0820909	−	0.0978322i
$764$	0.278010	+	33.1089i	0.0100580	+	1.19784i
$765$	−1.73996	+	1.42116i	−0.0629083	+	0.0513822i
$766$	−1.49711	+	1.50973i	−0.0540927	+	0.0545488i
$767$	−3.26407	−	18.5114i	−0.117859	−	0.668409i
$768$	14.4984	+	23.6177i	0.523168	+	0.852230i
$769$	20.7088	−	7.53738i	0.746777	−	0.271805i	0.0595284	−	0.998227i	$-0.481040\pi$
$769$	20.7088	−	7.53738i	0.746777	−	0.271805i	0.687249	+	0.726422i	$0.258818\pi$
$770$	−0.00860933		0.000789653i	−0.000310259		2.84571e-5i
$771$	21.5018	+	12.6046i	0.774368	+	0.453945i
$772$	5.88253	−	16.5944i	0.211717	−	0.597244i
$773$	−18.9410	−	10.9356i	−0.681261	−	0.393326i	0.119069	−	0.992886i	$-0.462009\pi$
$773$	−18.9410	−	10.9356i	−0.681261	−	0.393326i	−0.800330	+	0.599560i	$0.795342\pi$
$774$	−5.96176	+	8.35246i	−0.214291	+	0.300223i
$775$	−15.2657	+	8.81366i	−0.548360	+	0.316596i
$776$	9.39584	+	0.702909i	0.337291	+	0.0252330i
$777$	−3.66104	+	4.30484i	−0.131339	+	0.154435i
$778$	−4.95918	−	2.28721i	−0.177795	−	0.0820004i
$779$	36.6615	+	30.7626i	1.31353	+	1.10219i
$780$	−4.25396	−	1.53977i	−0.152316	−	0.0551326i
$781$	−0.132179	−	0.0481093i	−0.00472975	−	0.00172149i
$782$	−5.85981	+	22.2422i	−0.209546	+	0.795380i
$783$	−36.0659	+	5.62314i	−1.28889	+	0.200955i
$784$	13.9202	+	23.2017i	0.497149	+	0.828633i
$785$	−1.07307	+	2.94823i	−0.0382994	+	0.105227i
$786$	−38.9273	−	27.3980i	−1.38849	−	0.977256i
$787$	−2.17335	+	2.59010i	−0.0774716	+	0.0923271i	−0.803388	−	0.595456i	$-0.796971\pi$
$787$	−2.17335	+	2.59010i	−0.0774716	+	0.0923271i	0.725916	+	0.687783i	$0.241416\pi$
$788$	−19.2816	−	15.9052i	−0.686879	−	0.566600i
$789$	−3.19669	+	17.4527i	−0.113805	+	0.621333i
$790$	−1.17133	+	0.552198i	−0.0416740	+	0.0196463i
$791$	−3.51231	−	6.08351i	−0.124884	−	0.216305i
$792$	0.0916534	−	0.341170i	0.00325676	−	0.0121230i
$793$	−16.2661	+	28.1737i	−0.577625	+	1.00048i
$794$	2.30090	−	27.6351i	0.0816557	−	0.980735i
$795$	2.56537	+	4.51209i	0.0909843	+	0.160027i
$796$	1.48385	−	8.84919i	0.0525936	−	0.313651i
$797$	16.3658	+	44.9646i	0.579705	+	1.59273i	0.788679	+	0.614805i	$0.210765\pi$
$797$	16.3658	+	44.9646i	0.579705	+	1.59273i	−0.208974	+	0.977921i	$0.567012\pi$
$798$	8.68654	+	2.35013i	0.307500	+	0.0831937i
$799$	17.5393	−	3.09264i	0.620494	−	0.109410i
$800$	26.9656	+	6.62203i	0.953378	+	0.234124i
$801$	−10.2802	−	29.4524i	−0.363232	−	1.04065i
$802$	−29.5990	+	8.06437i	−1.04518	+	0.284763i
$803$	0.0201228	−	0.0168850i	0.000710117	−	0.000595859i
$804$	6.63284	−	38.0111i	0.233922	−	1.34055i
$805$	−0.167491	+	0.949891i	−0.00590330	+	0.0334793i
$806$	17.9109	−	12.6537i	0.630883	−	0.445708i
$807$	−3.48172	−	4.20560i	−0.122562	−	0.148044i
$808$	42.5536	−	20.4995i	1.49703	−	0.721169i
$809$		−	17.3637i		−	0.610473i	−0.952277	−	0.305237i	$-0.901264\pi$
$809$		−	17.3637i		−	0.610473i	0.952277	−	0.305237i	$-0.0987356\pi$
$810$	−1.54873	−	3.52427i	−0.0544169	−	0.123830i
$811$			13.7618i			0.483242i	0.970371	+	0.241621i	$0.0776791\pi$
$811$			13.7618i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$812$	4.42813	+	5.18814i	0.155397	+	0.182068i
$813$	−3.67976	−	4.44481i	−0.129055	−	0.155886i
$814$	0.228309	+	0.323163i	0.00800223	+	0.0113269i
$815$	−0.299589	+	1.69905i	−0.0104941	+	0.0595152i
$816$	−10.8923	+	13.2523i	−0.381305	+	0.463925i
$817$	−14.0208	+	11.7648i	−0.490524	+	0.411599i
$818$	−4.08842	−	15.0059i	−0.142948	−	0.524669i
$819$	−4.10601	+	4.76378i	−0.143476	+	0.166460i
$820$	−3.29698	+	1.94061i	−0.115136	+	0.0677689i
$821$	−26.2703	+	4.63216i	−0.916840	+	0.161664i	−0.612108	−	0.790774i	$-0.709678\pi$
$821$	−26.2703	+	4.63216i	−0.916840	+	0.161664i	−0.304732	+	0.952438i	$0.598567\pi$
$822$	9.81133	−	36.2646i	0.342209	−	1.26487i
$823$	−15.0879	−	41.4538i	−0.525932	−	1.44499i	−0.863820	−	0.503801i	$-0.831935\pi$
$823$	−15.0879	−	41.4538i	−0.525932	−	1.44499i	0.337888	−	0.941186i	$-0.390288\pi$
$824$	18.4826	−	40.9757i	0.643872	−	1.42746i
$825$	−0.174944	−	0.307699i	−0.00609076	−	0.0107127i
$826$	−2.97854	−	0.247993i	−0.103637	−	0.00862876i
$827$	−5.67028	+	9.82121i	−0.197175	+	0.341517i	−0.947611	−	0.319426i	$-0.896510\pi$
$827$	−5.67028	+	9.82121i	−0.197175	+	0.341517i	0.750436	+	0.660943i	$0.229843\pi$
$828$	−34.0365	−	19.8716i	−1.18285	−	0.690585i
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	0.999985	+	0.00549015i	$0.00174758\pi$
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	−0.495238	+	0.868757i	$0.664919\pi$
$830$	1.05018	+	2.22765i	0.0364523	+	0.0773230i
$831$	−1.30298	+	7.11380i	−0.0452000	+	0.246775i
$832$	−34.1596	−	5.13977i	−1.18427	−	0.178189i
$833$	−10.7656	+	12.8300i	−0.373007	+	0.444532i
$834$	−12.5967	+	17.8974i	−0.436187	+	0.619737i
$835$	−0.543139	+	1.49226i	−0.0187961	+	0.0516419i
$836$	0.310446	−	0.548289i	0.0107370	−	0.0189630i
$837$	18.3087	+	3.60471i	0.632843	+	0.124597i
$838$	33.1185	+	8.72523i	1.14406	+	0.301408i
$839$	11.0585	+	4.02496i	0.381781	+	0.138957i	0.525779	−	0.850621i	$-0.323774\pi$
$839$	11.0585	+	4.02496i	0.381781	+	0.138957i	−0.143998	+	0.989578i	$0.545996\pi$
$840$	−0.409077	+	0.591714i	−0.0141145	+	0.0204161i
$841$	−15.5866	−	13.0787i	−0.537469	−	0.450990i
$842$	−21.6851	+	47.0182i	−0.747318	+	1.62035i
$843$	−22.0243	+	25.8973i	−0.758558	+	0.891952i
$844$	−8.16571	−	44.1395i	−0.281075	−	1.51935i
$845$	1.47865	−	0.853700i	0.0508672	−	0.0293682i
$846$	−2.93463	+	30.3759i	−0.100895	+	1.04435i
$847$	−4.62422	−	2.66980i	−0.158890	−	0.0917353i
$848$	25.9812	+	29.9278i	0.892197	+	1.02772i
$849$	−23.0081	−	13.4877i	−0.789636	−	0.462895i
$850$	1.56987	+	17.1158i	0.0538461	+	0.587065i
$851$	41.4820	−	15.0982i	1.42198	−	0.517560i
$852$	−10.1255	+	5.86995i	−0.346894	+	0.201101i
$853$	−7.59288	−	43.0614i	−0.259975	−	1.47439i	−0.782971	−	0.622058i	$-0.786297\pi$
$853$	−7.59288	−	43.0614i	−0.259975	−	1.47439i	0.522996	−	0.852335i	$-0.324814\pi$
$854$	3.67306	+	3.64235i	0.125690	+	0.124639i
$855$	−1.10261	−	6.77684i	−0.0377085	−	0.231763i
$856$	0.698713	−	2.74549i	0.0238815	−	0.0938390i
$857$	−2.62091	−	3.12348i	−0.0895287	−	0.106696i	0.719420	−	0.694575i	$-0.244408\pi$
$857$	−2.62091	−	3.12348i	−0.0895287	−	0.106696i	−0.808949	+	0.587879i	$0.799963\pi$
$858$	0.251698	+	0.361323i	0.00859284	+	0.0123354i
$859$	38.3251	+	6.75775i	1.30764	+	0.230571i	0.783675	−	0.621171i	$-0.213343\pi$
$859$	38.3251	+	6.75775i	1.30764	+	0.230571i	0.523961	+	0.851743i	$0.324454\pi$
$860$	−0.511936	−	1.37061i	−0.0174569	−	0.0467375i
$861$	0.888814	+	5.24351i	0.0302907	+	0.178698i
$862$	44.8019	+	31.0912i	1.52596	+	1.05897i
$863$	−48.5663			−1.65322			−0.826608	−	0.562778i	$-0.809732\pi$
$863$	−48.5663			−1.65322			−0.826608	+	0.562778i	$0.809732\pi$
$864$	−16.8867	−	24.0590i	−0.574499	−	0.818505i
$865$	−0.419573			−0.0142659
$866$	−7.62466	−	5.29128i	−0.259097	−	0.179805i
$867$	17.6481	+	6.55603i	0.599360	+	0.222655i
$868$	−1.22009	−	3.26656i	−0.0414125	−	0.110874i
$869$	0.124130	+	0.0218875i	0.00421083	+	0.000742483i
$870$	2.21084	−	4.71131i	0.0749543	−	0.159728i
$871$	30.9161	+	36.8444i	1.04755	+	1.24842i
$872$	−5.06877	+	19.9170i	−0.171650	+	0.674474i
$873$	−9.99277	−	0.132346i	−0.338204	−	0.00447924i
$874$	−49.9147	−	49.4973i	−1.68839	−	1.67427i
$875$	0.252648	+	1.43284i	0.00854107	+	0.0484388i
$876$	−0.00387942	−	2.18568i	−0.000131074	−	0.0738474i
$877$	15.9919	−	5.82058i	0.540008	−	0.196547i	−0.0575935	−	0.998340i	$-0.518343\pi$
$877$	15.9919	−	5.82058i	0.540008	−	0.196547i	0.597602	+	0.801793i	$0.296120\pi$
$878$	0.235677	+	2.56951i	0.00795371	+	0.0867167i
$879$	−0.213575	+	32.2534i	−0.00720372	+	1.08788i
$880$	0.0330189	+	0.0380345i	0.00111307	+	0.00128214i
$881$	−2.59611	−	1.49886i	−0.0874651	−	0.0504980i	0.455630	−	0.890169i	$-0.349414\pi$
$881$	−2.59611	−	1.49886i	−0.0874651	−	0.0504980i	−0.543095	+	0.839672i	$0.682748\pi$
$882$	−16.2475	−	23.6563i	−0.547081	−	0.796550i
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	−0.184154	−	0.982897i	$-0.558954\pi$
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	0.759137	+	0.650931i	$0.225621\pi$
$884$	−3.88975	−	21.0260i	−0.130827	−	0.707180i
$885$	0.765749	+	2.14803i	0.0257404	+	0.0722052i
$886$	−1.03339	+	2.24063i	−0.0347175	+	0.0752754i
$887$	−35.6487	−	29.9128i	−1.19697	−	1.00437i	−0.999711	−	0.0240206i	$-0.992353\pi$
$887$	−35.6487	−	29.9128i	−1.19697	−	1.00437i	−0.197254	−	0.980352i	$-0.563202\pi$
$888$	32.8138	+	2.67343i	1.10116	+	0.0897146i
$889$	4.05813	+	1.47704i	0.136105	+	0.0495383i
$890$	4.30090	+	1.13309i	0.144166	+	0.0379813i
$891$	−0.0748150	+	0.367151i	−0.00250640	+	0.0123000i
$892$	−18.0497	+	31.8781i	−0.604347	+	1.06736i
$893$	−18.6161	+	51.1474i	−0.622965	+	1.71158i
$894$	−1.77328	−	3.82700i	−0.0593074	−	0.127994i
$895$	−2.24419	+	2.67453i	−0.0750152	+	0.0893996i
$896$	−2.17405	+	5.04417i	−0.0726300	+	0.168514i
$897$	46.2756	−	16.4967i	1.54510	−	0.550810i
$898$	5.57182	+	11.8190i	0.185934	+	0.394405i
$899$	12.6135	+	21.8472i	0.420683	+	0.728645i
$900$	−28.9786	−	5.25465i	−0.965953	−	0.175155i
$901$	−12.2661	+	21.2454i	−0.408642	+	0.707788i
$902$	0.371091	+	0.0308969i	0.0123560	+	0.00102876i
$903$	−2.03388	−	0.0134680i	−0.0676834	−	0.000448186i
$904$	−16.8270	+	37.3052i	−0.559657	+	1.24075i
$905$	1.77364	+	4.87305i	0.0589579	+	0.161986i
$906$	−1.42788	+	0.378893i	−0.0474381	+	0.0125879i
$907$	34.2556	−	6.04019i	1.13744	−	0.200561i	0.426954	−	0.904273i	$-0.359587\pi$
$907$	34.2556	−	6.04019i	1.13744	−	0.200561i	0.710485	+	0.703712i	$0.248476\pi$
$908$	33.7880	−	19.8876i	1.12129	−	0.659994i
$909$	−43.7150	+	24.4728i	−1.44993	+	0.811710i
$910$	−0.235711	−	0.865141i	−0.00781375	−	0.0286791i
$911$	22.9255	−	19.2368i	0.759557	−	0.637344i	−0.178454	−	0.983948i	$-0.557110\pi$
$911$	22.9255	−	19.2368i	0.759557	−	0.637344i	0.938012	+	0.346604i	$0.112665\pi$
$912$	−18.4309	−	49.0795i	−0.610310	−	1.62518i
$913$	0.0416261	−	0.236073i	0.00137762	−	0.00781289i
$914$	22.5077	+	31.8589i	0.744489	+	1.05380i
$915$	1.37440	−	3.69973i	0.0454364	−	0.122309i
$916$	−7.35942	−	8.62253i	−0.243162	−	0.284896i
$917$		−	9.43490i		−	0.311568i
$918$	10.6683	−	14.7389i	0.352106	−	0.486458i
$919$		−	52.7647i		−	1.74055i	−0.492569	−	0.870273i	$-0.663942\pi$
$919$		−	52.7647i		−	1.74055i	0.492569	−	0.870273i	$-0.336058\pi$
$920$	5.06252	−	2.43878i	0.166906	−	0.0804042i
$921$	−35.0072	+	5.93397i	−1.15353	+	0.195531i
$922$	23.9497	−	16.9201i	0.788742	−	0.557232i
$923$	2.53335	−	14.3673i	0.0833862	−	0.472907i
$924$	0.0657530	−	0.0240644i	0.00216312	−	0.000791660i
$925$	25.2693	−	21.2034i	0.830849	−	0.697165i
$926$	13.0798	−	3.56365i	0.429830	−	0.117109i
$927$	−16.8987	+	44.5828i	−0.555027	+	1.46429i
$928$	9.47698	−	38.5913i	0.311097	−	1.26682i
$929$	−54.7677	+	9.65703i	−1.79687	+	0.316837i	−0.969550	−	0.244892i	$-0.921247\pi$
$929$	−54.7677	+	9.65703i	−1.79687	+	0.316837i	−0.827321	+	0.561729i	$0.810136\pi$
$930$	−1.88581	+	1.87669i	−0.0618382	+	0.0615392i
$931$	−17.5066	−	48.0989i	−0.573755	−	1.57638i
$932$	−2.48434	+	14.8158i	−0.0813772	+	0.485307i
$933$	17.5437	−	29.9271i	0.574354	−	0.979769i
$934$	−2.05285	+	24.6560i	−0.0671713	+	0.806768i
$935$	−0.0155887	+	0.0270003i	−0.000509803	+	0.000883005i
$936$	36.4981	+	3.21702i	1.19298	+	0.105151i
$937$	9.12048	+	15.7971i	0.297953	+	0.516070i	0.975667	−	0.219255i	$-0.0703628\pi$
$937$	9.12048	+	15.7971i	0.297953	+	0.516070i	−0.677715	+	0.735325i	$0.737029\pi$
$938$	6.91756	−	3.26114i	0.225866	−	0.106480i
$939$	23.2766	+	19.7955i	0.759602	+	0.646001i
$940$	−3.35646	−	2.76871i	−0.109476	−	0.0903054i
$941$	11.2021	−	13.3502i	0.365179	−	0.435204i	−0.551899	−	0.833911i	$-0.686097\pi$
$941$	11.2021	−	13.3502i	0.365179	−	0.435204i	0.917078	+	0.398707i	$0.130541\pi$
$942$	2.27593	−	25.3075i	0.0741538	−	0.824562i
$943$	14.2091	−	39.0392i	0.462712	−	1.27129i
$944$	8.95832	+	14.9315i	0.291568	+	0.485978i
$945$	0.394545	−	0.653060i	0.0128346	−	0.0212441i
$946$	−0.0362807	+	0.137712i	−0.00117959	+	0.00447739i
$947$	−40.4292	−	14.7150i	−1.31377	−	0.478174i	−0.412315	−	0.911042i	$-0.635280\pi$
$947$	−40.4292	−	14.7150i	−1.31377	−	0.478174i	−0.901458	+	0.432868i	$0.857502\pi$
$948$	8.02207	−	6.75562i	0.260545	−	0.219412i
$949$	2.08706	+	1.75125i	0.0677488	+	0.0568480i
$950$	−47.6995	−	21.9993i	−1.54758	−	0.713753i
$951$	−7.32038	−	1.34082i	−0.237379	−	0.0434790i
$952$	−3.39052	−	0.253647i	−0.109887	−	0.00822074i
$953$	−17.5809	+	10.1503i	−0.569502	+	0.328802i	−0.756950	−	0.653472i	$-0.773312\pi$
$953$	−17.5809	+	10.1503i	−0.569502	+	0.328802i	0.187449	+	0.982274i	$0.439978\pi$
$954$	−29.4539	−	29.9916i	−0.953606	−	0.971015i
$955$	4.33625	+	2.50353i	0.140318	+	0.0810124i
$956$	4.32461	−	12.1995i	0.139868	−	0.394561i
$957$	−0.440357	+	0.250367i	−0.0142347	+	0.00809322i
$958$	−36.8927	+	3.38383i	−1.19195	+	0.109326i
$959$	6.99708	−	2.54673i	0.225947	−	0.0822382i
$960$	4.19014	−	0.0778122i	0.135236	−	0.00251138i
$961$	3.14365	+	17.8285i	0.101408	+	0.575113i
$962$	−28.8962	+	29.1399i	−0.931652	+	0.939507i
$963$	−0.560931	+	2.95204i	−0.0180758	+	0.0951281i
$964$	0.0116530	+	1.38779i	0.000375319	+	0.0446977i
$965$	−1.71141	−	2.03958i	−0.0550923	−	0.0656565i
$966$	−0.661973	−	7.78359i	−0.0212986	−	0.250433i
$967$	46.0060	+	8.11209i	1.47945	+	0.260867i	0.854359	−	0.519683i	$-0.173950\pi$
$967$	46.0060	+	8.11209i	1.47945	+	0.260867i	0.625093	+	0.780550i	$0.285061\pi$
$968$	3.10131	+	30.9528i	0.0996798	+	0.994861i
$969$	24.9970	−	20.6945i	0.803019	−	0.664802i
$970$	0.812356	−	1.17059i	0.0260832	−	0.0375855i
$971$	−29.3788			−0.942809			−0.471405	−	0.881917i	$-0.656253\pi$
$971$	−29.3788			−0.942809			−0.471405	+	0.881917i	$0.656253\pi$
$972$	19.4439	+	24.3708i	0.623663	+	0.781693i
$973$	−4.33784			−0.139065
$974$	−5.73237	+	8.26027i	−0.183677	+	0.264676i
$975$	28.2779	−	23.4106i	0.905616	−	0.749739i
$976$	4.73399	−	29.7621i	0.151531	−	0.952661i
$977$	18.3908	+	3.24280i	0.588375	+	0.103746i	0.459907	−	0.887967i	$-0.347883\pi$
$977$	18.3908	+	3.24280i	0.588375	+	0.103746i	0.128468	+	0.991714i	$0.458994\pi$
$978$	−1.18406	−	13.9224i	−0.0378620	−	0.445188i
$979$	−0.278270	−	0.331630i	−0.00889356	−	0.0105989i
$980$	4.09157	−	0.0343562i	0.130700	−	0.00109747i
$981$	4.06924	−	21.4153i	0.129921	−	0.683739i
$982$	−19.6699	+	19.8357i	−0.627691	+	0.632984i
$983$	4.54380	+	25.7692i	0.144925	+	0.821909i	0.967428	+	0.253148i	$0.0814660\pi$
$983$	4.54380	+	25.7692i	0.144925	+	0.821909i	−0.822503	+	0.568761i	$0.807423\pi$
$984$	21.7776	−	22.0393i	0.694244	−	0.702588i
$985$	−3.55193	+	1.29280i	−0.113174	+	0.0411919i
$986$	24.4949	−	2.24669i	0.780075	−	0.0715490i
$987$	−5.25816	+	2.98955i	−0.167369	+	0.0951584i
$988$	61.5938	+	21.8344i	1.95956	+	0.694644i
$989$	13.7596	+	7.94413i	0.437531	+	0.252609i
$990$	−0.0374323	−	0.0381157i	−0.00118968	−	0.00121140i
$991$	−25.5875	+	14.7730i	−0.812815	+	0.469279i	−0.847932	−	0.530105i	$-0.822153\pi$
$991$	−25.5875	+	14.7730i	−0.812815	+	0.469279i	0.0351178	+	0.999383i	$0.488819\pi$
$992$	−11.3002	+	16.8817i	−0.358781	+	0.535995i
$993$	34.2947	+	6.28151i	1.08831	+	0.199338i
$994$	−2.10650	−	0.971531i	−0.0668141	−	0.0308151i
$995$	−1.03945	−	0.872198i	−0.0329526	−	0.0276505i
$996$	−12.8480	−	15.2565i	−0.407103	−	0.483422i
$997$	−37.2095	−	13.5431i	−1.17844	−	0.428916i	−0.322787	−	0.946472i	$-0.604620\pi$
$997$	−37.2095	−	13.5431i	−1.17844	−	0.428916i	−0.855649	+	0.517556i	$0.826842\pi$
$998$	−14.2410	+	54.0548i	−0.450790	+	1.71107i
$999$	−34.9128	−	0.693637i	−1.10459	−	0.0219457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.23.14	yes	96
3.2	odd	2		324.2.l.a.179.3		96
4.3	odd	2	inner	108.2.l.a.23.1	✓	96
9.2	odd	6		972.2.l.b.215.9		96
9.4	even	3		972.2.l.d.863.3		96
9.5	odd	6		972.2.l.a.863.14		96
9.7	even	3		972.2.l.c.215.8		96
12.11	even	2		324.2.l.a.179.16		96
27.2	odd	18		972.2.l.d.107.12		96
27.7	even	9		324.2.l.a.143.16		96
27.11	odd	18		972.2.l.c.755.10		96
27.16	even	9		972.2.l.b.755.7		96
27.20	odd	18	inner	108.2.l.a.47.1	yes	96
27.25	even	9		972.2.l.a.107.5		96
36.7	odd	6		972.2.l.c.215.10		96
36.11	even	6		972.2.l.b.215.7		96
36.23	even	6		972.2.l.a.863.5		96
36.31	odd	6		972.2.l.d.863.12		96
108.7	odd	18		324.2.l.a.143.3		96
108.11	even	18		972.2.l.c.755.8		96
108.43	odd	18		972.2.l.b.755.9		96
108.47	even	18	inner	108.2.l.a.47.14	yes	96
108.79	odd	18		972.2.l.a.107.14		96
108.83	even	18		972.2.l.d.107.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	4.3	odd	2	inner
108.2.l.a.23.14	yes	96	1.1	even	1	trivial
108.2.l.a.47.1	yes	96	27.20	odd	18	inner
108.2.l.a.47.14	yes	96	108.47	even	18	inner
324.2.l.a.143.3		96	108.7	odd	18
324.2.l.a.143.16		96	27.7	even	9
324.2.l.a.179.3		96	3.2	odd	2
324.2.l.a.179.16		96	12.11	even	2
972.2.l.a.107.5		96	27.25	even	9
972.2.l.a.107.14		96	108.79	odd	18
972.2.l.a.863.5		96	36.23	even	6
972.2.l.a.863.14		96	9.5	odd	6
972.2.l.b.215.7		96	36.11	even	6
972.2.l.b.215.9		96	9.2	odd	6
972.2.l.b.755.7		96	27.16	even	9
972.2.l.b.755.9		96	108.43	odd	18
972.2.l.c.215.8		96	9.7	even	3
972.2.l.c.215.10		96	36.7	odd	6
972.2.l.c.755.8		96	108.11	even	18
972.2.l.c.755.10		96	27.11	odd	18
972.2.l.d.107.3		96	108.83	even	18
972.2.l.d.107.12		96	27.2	odd	18
972.2.l.d.863.3		96	9.4	even	3
972.2.l.d.863.12		96	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16185 + 0.806289i) q^{2} +(-1.33417 + 1.10453i) q^{3} +(0.699796 + 1.87358i) q^{4} +(0.297855 + 0.0525198i) q^{5} +(-2.44068 + 0.207573i) q^{6} +(-0.312070 - 0.371910i) q^{7} +(-0.697584 + 2.74105i) q^{8} +(0.560024 - 2.94727i) q^{9} +(0.303717 + 0.301177i) q^{10} +(-0.00722947 - 0.0410004i) q^{11} +(-3.00307 - 1.72672i) q^{12} +(4.05761 - 1.47685i) q^{13} +(-0.0627115 - 0.683722i) q^{14} +(-0.455399 + 0.258919i) q^{15} +(-3.02057 + 2.62224i) q^{16} +(-2.14427 - 1.23800i) q^{17} +(3.02701 - 2.97274i) q^{18} +(6.55326 - 3.78353i) q^{19} +(0.110038 + 0.594806i) q^{20} +(0.827140 + 0.151501i) q^{21} +(0.0246586 - 0.0534654i) q^{22} +(-5.03199 - 4.22234i) q^{23} +(-2.09688 - 4.42754i) q^{24} +(-4.61250 - 1.67881i) q^{25} +(5.90510 + 1.55572i) q^{26} +(2.50818 + 4.55072i) q^{27} +(0.478416 - 0.844947i) q^{28} +(-2.40260 + 6.60109i) q^{29} +(-0.737869 - 0.0663574i) q^{30} +(2.30836 - 2.75099i) q^{31} +(-5.62374 + 0.611204i) q^{32} +(0.0549315 + 0.0467164i) q^{33} +(-1.49314 - 3.16727i) q^{34} +(-0.0734187 - 0.127165i) q^{35} +(5.91383 - 1.01324i) q^{36} +(-3.36015 + 5.81994i) q^{37} +(10.6645 + 0.887926i) q^{38} +(-3.78232 + 6.45212i) q^{39} +(-0.351738 + 0.779799i) q^{40} +(2.16312 + 5.94312i) q^{41} +(0.838860 + 0.842936i) q^{42} +(-2.38200 + 0.420011i) q^{43} +(0.0717582 - 0.0422369i) q^{44} +(0.321596 - 0.848444i) q^{45} +(-2.44200 - 8.96296i) q^{46} +(-5.51016 + 4.62358i) q^{47} +(1.13361 - 6.83483i) q^{48} +(1.17461 - 6.66153i) q^{49} +(-4.00543 - 5.66954i) q^{50} +(4.22823 - 0.716716i) q^{51} +(5.60648 + 6.56874i) q^{52} -9.90799i q^{53} +(-0.755067 + 7.30957i) q^{54} -0.0125918i q^{55} +(1.23712 - 0.595961i) q^{56} +(-4.56415 + 12.2862i) q^{57} +(-8.11385 + 5.73229i) q^{58} +(0.755918 - 4.28703i) q^{59} +(-0.803791 - 0.672033i) q^{60} +(-5.77142 + 4.84280i) q^{61} +(4.90006 - 1.33504i) q^{62} +(-1.27088 + 0.711473i) q^{63} +(-7.02675 - 3.82423i) q^{64} +(1.28614 - 0.226781i) q^{65} +(0.0261554 + 0.0985681i) q^{66} +(3.80965 + 10.4669i) q^{67} +(0.818925 - 4.88380i) q^{68} +(11.3772 + 0.0753378i) q^{69} +(0.0172301 - 0.206943i) q^{70} +(1.68932 - 2.92598i) q^{71} +(7.68795 + 3.59102i) q^{72} +(0.315477 + 0.546421i) q^{73} +(-8.59654 + 4.05266i) q^{74} +(8.00817 - 2.85483i) q^{75} +(11.6747 + 9.63033i) q^{76} +(-0.0129924 + 0.0154837i) q^{77} +(-9.59676 + 4.44676i) q^{78} +(-1.03548 + 2.84496i) q^{79} +(-1.03741 + 0.622407i) q^{80} +(-8.37275 - 3.30108i) q^{81} +(-2.27865 + 8.64913i) q^{82} +(5.41059 + 1.96930i) q^{83} +(0.294981 + 1.65573i) q^{84} +(-0.573662 - 0.481360i) q^{85} +(-3.10618 - 1.43259i) q^{86} +(-4.08563 - 11.4607i) q^{87} +(0.117427 + 0.00878482i) q^{88} +(9.00521 - 5.19916i) q^{89} +(1.05774 - 0.726467i) q^{90} +(-1.81551 - 1.04819i) q^{91} +(4.38950 - 12.3826i) q^{92} +(-0.0411872 + 6.21994i) q^{93} +(-10.1299 + 0.929124i) q^{94} +(2.15063 - 0.782765i) q^{95} +(6.82793 - 7.02704i) q^{96} +(-0.578459 - 3.28061i) q^{97} +(6.73584 - 6.79263i) q^{98} +(-0.124888 - 0.00165404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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