LMFDB - Embedded newform 76.2.k.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	76.59
Dual form			76.2.k.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22869 - 0.700233i) q^{2} +(-1.98545 - 1.66599i) q^{3} +(1.01935 + 1.72074i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(1.27292 + 3.43726i) q^{6} +(-1.43753 + 0.829960i) q^{7} +(-0.0475435 - 2.82803i) q^{8} +(0.645546 + 3.66107i) q^{9} +O(q^{10})$	\(q+(-1.22869 - 0.700233i) q^{2} +(-1.98545 - 1.66599i) q^{3} +(1.01935 + 1.72074i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(1.27292 + 3.43726i) q^{6} +(-1.43753 + 0.829960i) q^{7} +(-0.0475435 - 2.82803i) q^{8} +(0.645546 + 3.66107i) q^{9} +(3.75379 + 0.640228i) q^{10} +(-2.94034 - 1.69761i) q^{11} +(0.842867 - 5.11466i) q^{12} +(-2.17565 - 2.59283i) q^{13} +(2.34744 - 0.0131536i) q^{14} +(6.55803 + 2.38693i) q^{15} +(-1.92186 + 3.50805i) q^{16} +(1.03855 - 5.88992i) q^{17} +(1.77043 - 4.95035i) q^{18} +(4.28990 - 0.772510i) q^{19} +(-4.16393 - 3.41517i) q^{20} +(4.23686 + 0.747073i) q^{21} +(2.42404 + 4.14475i) q^{22} +(-2.01148 + 5.52649i) q^{23} +(-4.61708 + 5.69412i) q^{24} +(1.72393 - 1.44655i) q^{25} +(0.857602 + 4.70924i) q^{26} +(0.929885 - 1.61061i) q^{27} +(-2.89349 - 1.62760i) q^{28} +(-2.92975 + 0.516594i) q^{29} +(-6.38636 - 7.52493i) q^{30} +(-2.91510 - 5.04911i) q^{31} +(4.81782 - 2.96455i) q^{32} +(3.00971 + 8.26910i) q^{33} +(-5.40038 + 6.50965i) q^{34} +(2.87301 - 3.42391i) q^{35} +(-5.64171 + 4.84272i) q^{36} -0.798908i q^{37} +(-5.81188 - 2.05476i) q^{38} +8.77256i q^{39} +(2.72475 + 7.11190i) q^{40} +(0.904276 - 1.07767i) q^{41} +(-4.68265 - 3.88471i) q^{42} +(-0.235045 - 0.645782i) q^{43} +(-0.0760962 - 6.79000i) q^{44} +(-5.00506 - 8.66901i) q^{45} +(6.34131 - 5.38183i) q^{46} +(6.47756 - 1.14217i) q^{47} +(9.66016 - 3.76327i) q^{48} +(-2.12233 + 3.67599i) q^{49} +(-3.13109 + 0.570203i) q^{50} +(-11.8746 + 9.96394i) q^{51} +(2.24384 - 6.38671i) q^{52} +(-2.91069 + 7.99704i) q^{53} +(-2.27034 + 1.32780i) q^{54} +(9.00327 + 1.58752i) q^{55} +(2.41550 + 4.02592i) q^{56} +(-9.80439 - 5.61316i) q^{57} +(3.96148 + 1.41677i) q^{58} +(0.838664 - 4.75630i) q^{59} +(2.57764 + 13.7177i) q^{60} +(3.56100 + 1.29610i) q^{61} +(0.0462000 + 8.24503i) q^{62} +(-3.96654 - 4.72714i) q^{63} +(-7.99548 + 0.268908i) q^{64} +(7.89284 + 4.55693i) q^{65} +(2.09231 - 12.2676i) q^{66} +(-1.76401 - 10.0042i) q^{67} +(11.1936 - 4.21680i) q^{68} +(13.2008 - 7.62148i) q^{69} +(-5.92757 + 2.19515i) q^{70} +(2.34943 - 0.855121i) q^{71} +(10.3229 - 1.99968i) q^{72} +(-8.03196 - 6.73961i) q^{73} +(-0.559422 + 0.981609i) q^{74} -5.83271 q^{75} +(5.70218 + 6.59433i) q^{76} +5.63578 q^{77} +(6.14284 - 10.7787i) q^{78} +(-6.98750 - 5.86321i) q^{79} +(1.63212 - 10.6463i) q^{80} +(5.95057 - 2.16583i) q^{81} +(-1.86570 + 0.690921i) q^{82} +(-6.78922 + 3.91976i) q^{83} +(3.03332 + 8.05204i) q^{84} +(2.79647 + 15.8596i) q^{85} +(-0.163400 + 0.958050i) q^{86} +(6.67752 + 3.85527i) q^{87} +(-4.66108 + 8.39607i) q^{88} +(-7.99275 - 9.52539i) q^{89} +(0.0793226 + 14.1562i) q^{90} +(5.27951 + 1.92159i) q^{91} +(-11.5600 + 2.17219i) q^{92} +(-2.62398 + 14.8813i) q^{93} +(-8.75868 - 3.13243i) q^{94} +(-10.1432 + 5.90542i) q^{95} +(-14.5045 - 2.14048i) q^{96} +(-8.40551 - 1.48212i) q^{97} +(5.18173 - 3.03051i) q^{98} +(4.31694 - 11.8607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−1.22869	−	0.700233i	−0.868813	−	0.495140i
$2$	−1.22869	−	0.700233i	−0.868813	−	0.495140i
$3$	−1.98545	−	1.66599i	−1.14630	−	0.961861i	−0.146675	−	0.989185i	$-0.546857\pi$
$3$	−1.98545	−	1.66599i	−1.14630	−	0.961861i	−0.999627	+	0.0273235i	$0.991302\pi$
$4$	1.01935	+	1.72074i	0.509674	+	0.860368i
$5$	−2.53027	+	0.920944i	−1.13157	+	0.411859i	−0.838863	−	0.544342i	$-0.816779\pi$
$5$	−2.53027	+	0.920944i	−1.13157	+	0.411859i	−0.292710	+	0.956201i	$0.594557\pi$
$6$	1.27292	+	3.43726i	0.519667	+	1.40326i
$7$	−1.43753	+	0.829960i	−0.543336	+	0.313695i	−0.746430	−	0.665464i	$-0.768234\pi$
$7$	−1.43753	+	0.829960i	−0.543336	+	0.313695i	0.203094	+	0.979159i	$0.434900\pi$
$8$	−0.0475435	−	2.82803i	−0.0168092	−	0.999859i
$9$	0.645546	+	3.66107i	0.215182	+	1.22036i
$10$	3.75379	+	0.640228i	1.18705	+	0.202458i
$11$	−2.94034	−	1.69761i	−0.886546	−	0.511848i	−0.0137349	−	0.999906i	$-0.504372\pi$
$11$	−2.94034	−	1.69761i	−0.886546	−	0.511848i	−0.872811	+	0.488058i	$0.837705\pi$
$12$	0.842867	−	5.11466i	0.243315	−	1.47648i
$13$	−2.17565	−	2.59283i	−0.603416	−	0.719123i	0.374709	−	0.927143i	$-0.377743\pi$
$13$	−2.17565	−	2.59283i	−0.603416	−	0.719123i	−0.978125	+	0.208020i	$0.933298\pi$
$14$	2.34744	−	0.0131536i	0.627381	−	0.00351545i
$15$	6.55803	+	2.38693i	1.69328	+	0.616302i
$16$	−1.92186	+	3.50805i	−0.480466	+	0.877014i
$17$	1.03855	−	5.88992i	0.251886	−	1.42852i	−0.552055	−	0.833808i	$-0.686156\pi$
$17$	1.03855	−	5.88992i	0.251886	−	1.42852i	0.803941	−	0.594709i	$-0.202733\pi$
$18$	1.77043	−	4.95035i	0.417295	−	1.16681i
$19$	4.28990	−	0.772510i	0.984170	−	0.177226i
$19$	4.28990	−	0.772510i	0.984170	−	0.177226i
$20$	−4.16393	−	3.41517i	−0.931083	−	0.763655i
$21$	4.23686	+	0.747073i	0.924559	+	0.163025i
$22$	2.42404	+	4.14475i	0.516807	+	0.883664i
$23$	−2.01148	+	5.52649i	−0.419422	+	1.15235i	0.532611	+	0.846360i	$0.321211\pi$
$23$	−2.01148	+	5.52649i	−0.419422	+	1.15235i	−0.952034	+	0.305993i	$0.901011\pi$
$24$	−4.61708	+	5.69412i	−0.942457	+	1.16231i
$25$	1.72393	−	1.44655i	0.344785	−	0.289309i
$26$	0.857602	+	4.70924i	0.168190	+	0.923559i
$27$	0.929885	−	1.61061i	0.178957	−	0.309962i
$28$	−2.89349	−	1.62760i	−0.546818	−	0.307587i
$29$	−2.92975	+	0.516594i	−0.544040	+	0.0959290i	−0.438913	−	0.898530i	$-0.644636\pi$
$29$	−2.92975	+	0.516594i	−0.544040	+	0.0959290i	−0.105128	+	0.994459i	$0.533525\pi$
$30$	−6.38636	−	7.52493i	−1.16598	−	1.37386i
$31$	−2.91510	−	5.04911i	−0.523568	−	0.906846i	−0.999624	−	0.0274312i	$-0.991267\pi$
$31$	−2.91510	−	5.04911i	−0.523568	−	0.906846i	0.476056	−	0.879415i	$-0.342066\pi$
$32$	4.81782	−	2.96455i	0.851679	−	0.524064i
$33$	3.00971	+	8.26910i	0.523923	+	1.43947i
$34$	−5.40038	+	6.50965i	−0.926157	+	1.11640i
$35$	2.87301	−	3.42391i	0.485627	−	0.578747i
$36$	−5.64171	+	4.84272i	−0.940284	+	0.807120i
$37$		−	0.798908i		−	0.131340i	−0.997841	−	0.0656699i	$-0.979082\pi$
$37$		−	0.798908i		−	0.131340i	0.997841	−	0.0656699i	$-0.0209184\pi$
$38$	−5.81188	−	2.05476i	−0.942812	−	0.333325i
$39$			8.77256i			1.40473i
$40$	2.72475	+	7.11190i	0.430821	+	1.12449i
$41$	0.904276	−	1.07767i	0.141224	−	0.168304i	−0.690796	−	0.723050i	$-0.742740\pi$
$41$	0.904276	−	1.07767i	0.141224	−	0.168304i	0.832020	+	0.554745i	$0.187184\pi$
$42$	−4.68265	−	3.88471i	−0.722549	−	0.599424i
$43$	−0.235045	−	0.645782i	−0.0358441	−	0.0984808i	0.920480	−	0.390791i	$-0.127798\pi$
$43$	−0.235045	−	0.645782i	−0.0358441	−	0.0984808i	−0.956324	+	0.292310i	$0.905576\pi$
$44$	−0.0760962	−	6.79000i	−0.0114719	−	1.02363i
$45$	−5.00506	−	8.66901i	−0.746110	−	1.29230i
$46$	6.34131	−	5.38183i	0.934975	−	0.793507i
$47$	6.47756	−	1.14217i	0.944849	−	0.166602i	0.320061	−	0.947397i	$-0.396296\pi$
$47$	6.47756	−	1.14217i	0.944849	−	0.166602i	0.624788	+	0.780794i	$0.285185\pi$
$48$	9.66016	−	3.76327i	1.39432	−	0.543181i
$49$	−2.12233	+	3.67599i	−0.303190	+	0.525141i
$50$	−3.13109	+	0.570203i	−0.442803	+	0.0806389i
$51$	−11.8746	+	9.96394i	−1.66277	+	1.39523i
$52$	2.24384	−	6.38671i	0.311165	−	0.885678i
$53$	−2.91069	+	7.99704i	−0.399813	+	1.09848i	0.562562	+	0.826755i	$0.309816\pi$
$53$	−2.91069	+	7.99704i	−0.399813	+	1.09848i	−0.962375	+	0.271723i	$0.912406\pi$
$54$	−2.27034	+	1.32780i	−0.308954	+	0.180690i
$55$	9.00327	+	1.58752i	1.21400	+	0.214061i
$56$	2.41550	+	4.02592i	0.322784	+	0.537987i
$57$	−9.80439	−	5.61316i	−1.29862	−	0.743481i
$58$	3.96148	+	1.41677i	0.520168	+	0.186032i
$59$	0.838664	−	4.75630i	0.109185	−	0.619218i	−0.880281	−	0.474452i	$-0.842646\pi$
$59$	0.838664	−	4.75630i	0.109185	−	0.619218i	0.989466	−	0.144765i	$-0.0462428\pi$
$60$	2.57764	+	13.7177i	0.332771	+	1.77095i
$61$	3.56100	+	1.29610i	0.455939	+	0.165948i	0.559772	−	0.828647i	$-0.310889\pi$
$61$	3.56100	+	1.29610i	0.455939	+	0.165948i	−0.103833	+	0.994595i	$0.533111\pi$
$62$	0.0462000	+	8.24503i	0.00586740	+	1.04712i
$63$	−3.96654	−	4.72714i	−0.499737	−	0.595563i
$64$	−7.99548	+	0.268908i	−0.999435	+	0.0336136i
$65$	7.89284	+	4.55693i	0.978986	+	0.565218i
$66$	2.09231	−	12.2676i	0.257545	−	1.51004i
$67$	−1.76401	−	10.0042i	−0.215509	−	1.22221i	−0.880022	−	0.474934i	$-0.842472\pi$
$67$	−1.76401	−	10.0042i	−0.215509	−	1.22221i	0.664513	−	0.747277i	$-0.268639\pi$
$68$	11.1936	−	4.21680i	1.35743	−	0.511363i
$69$	13.2008	−	7.62148i	1.58919	−	0.917518i
$70$	−5.92757	+	2.19515i	−0.708480	+	0.262370i
$71$	2.34943	−	0.855121i	0.278825	−	0.101484i	−0.198822	−	0.980036i	$-0.563712\pi$
$71$	2.34943	−	0.855121i	0.278825	−	0.101484i	0.477648	+	0.878551i	$0.341489\pi$
$72$	10.3229	−	1.99968i	1.21657	−	0.235665i
$73$	−8.03196	−	6.73961i	−0.940069	−	0.788812i	0.0375281	−	0.999296i	$-0.488052\pi$
$73$	−8.03196	−	6.73961i	−0.940069	−	0.788812i	−0.977597	+	0.210484i	$0.932496\pi$
$74$	−0.559422	+	0.981609i	−0.0650315	+	0.114110i
$75$	−5.83271			−0.673503
$76$	5.70218	+	6.59433i	0.654085	+	0.756421i
$77$	5.63578			0.642257
$78$	6.14284	−	10.7787i	0.695539	−	1.22045i
$79$	−6.98750	−	5.86321i	−0.786156	−	0.659663i	0.158635	−	0.987337i	$-0.449291\pi$
$79$	−6.98750	−	5.86321i	−0.786156	−	0.659663i	−0.944791	+	0.327674i	$0.893735\pi$
$80$	1.63212	−	10.6463i	0.182476	−	1.19029i
$81$	5.95057	−	2.16583i	0.661174	−	0.240648i
$82$	−1.86570	+	0.690921i	−0.206032	+	0.0762995i
$83$	−6.78922	+	3.91976i	−0.745213	+	0.430249i	−0.823962	−	0.566645i	$-0.808241\pi$
$83$	−6.78922	+	3.91976i	−0.745213	+	0.430249i	0.0787485	+	0.996895i	$0.474908\pi$
$84$	3.03332	+	8.05204i	0.330962	+	0.878550i
$85$	2.79647	+	15.8596i	0.303320	+	1.72021i
$86$	−0.163400	+	0.958050i	−0.0176199	+	0.103309i
$87$	6.67752	+	3.85527i	0.715905	+	0.413328i
$88$	−4.66108	+	8.39607i	−0.496873	+	0.895025i
$89$	−7.99275	−	9.52539i	−0.847230	−	1.00969i	−0.999771	−	0.0213925i	$-0.993190\pi$
$89$	−7.99275	−	9.52539i	−0.847230	−	1.00969i	0.152541	−	0.988297i	$-0.451254\pi$
$90$	0.0793226	+	14.1562i	0.00836133	+	1.49220i
$91$	5.27951	+	1.92159i	0.553443	+	0.201437i
$92$	−11.5600	+	2.17219i	−1.20522	+	0.226467i
$93$	−2.62398	+	14.8813i	−0.272094	+	1.54312i
$94$	−8.75868	−	3.13243i	−0.903389	−	0.323086i
$95$	−10.1432	+	5.90542i	−1.04067	+	0.605883i
$96$	−14.5045	−	2.14048i	−1.48036	−	0.218462i
$97$	−8.40551	−	1.48212i	−0.853451	−	0.150486i	−0.270226	−	0.962797i	$-0.587098\pi$
$97$	−8.40551	−	1.48212i	−0.853451	−	0.150486i	−0.583225	+	0.812311i	$0.698209\pi$
$98$	5.18173	−	3.03051i	0.523434	−	0.306128i
$99$	4.31694	−	11.8607i	0.433869	−	1.19204i
$100$	4.24640	+	1.49189i	0.424640	+	0.149189i
$101$	−0.0868957	+	0.0729142i	−0.00864645	+	0.00725523i	−0.647101	−	0.762405i	$-0.724019\pi$
$101$	−0.0868957	+	0.0729142i	−0.00864645	+	0.00725523i	0.638454	+	0.769660i	$0.279574\pi$
$102$	21.5672	−	3.92761i	2.13547	−	0.388892i
$103$	−3.35278	+	5.80718i	−0.330359	+	0.572199i	−0.982582	−	0.185828i	$-0.940503\pi$
$103$	−3.35278	+	5.80718i	−0.330359	+	0.572199i	0.652223	+	0.758027i	$0.273837\pi$
$104$	−7.22917	+	6.27606i	−0.708878	+	0.615418i
$105$	−11.4084	+	2.01161i	−1.11335	+	0.196313i
$106$	9.17612	−	7.78771i	0.891263	−	0.756409i
$107$	2.83864	+	4.91666i	0.274421	+	0.475312i	0.969989	−	0.243149i	$-0.0781804\pi$
$107$	2.83864	+	4.91666i	0.274421	+	0.475312i	−0.695568	+	0.718461i	$0.744847\pi$
$108$	3.71931	−	0.0416827i	0.357891	−	0.00401091i
$109$	−2.68819	−	7.38575i	−0.257482	−	0.707427i	−0.999321	−	0.0368484i	$-0.988268\pi$
$109$	−2.68819	−	7.38575i	−0.257482	−	0.707427i	0.741839	−	0.670579i	$-0.233954\pi$
$110$	−9.95057	−	8.25495i	−0.948750	−	0.787079i
$111$	−1.33098	+	1.58619i	−0.126331	+	0.150555i
$112$	−0.148804	−	6.63801i	−0.0140607	−	0.627233i
$113$			9.61911i			0.904890i	0.891792	+	0.452445i	$0.149448\pi$
$113$			9.61911i			0.904890i	−0.891792	+	0.452445i	$0.850552\pi$
$114$	8.11601	+	13.7622i	0.760134	+	1.28895i
$115$		−	15.8360i		−	1.47671i
$116$	−3.87535	−	4.51473i	−0.359817	−	0.419182i
$117$	8.08808	−	9.63900i	0.747743	−	0.891126i
$118$	−4.36098	+	5.25675i	−0.401460	+	0.483923i
$119$	3.39545	+	9.32892i	0.311260	+	0.855180i
$120$	6.43850	−	18.6598i	0.587752	−	1.70340i
$121$	0.263736	+	0.456803i	0.0239760	+	0.0415276i
$122$	−3.46778	−	4.08602i	−0.313958	−	0.369931i
$123$	−3.59079	+	0.633154i	−0.323771	+	0.0570896i
$124$	5.71668	−	10.1629i	0.513373	−	0.912657i
$125$	3.70184	−	6.41177i	0.331102	−	0.573486i
$126$	1.56354	+	8.58568i	0.139291	+	0.764873i
$127$	6.20191	−	5.20402i	0.550331	−	0.461782i	−0.324722	−	0.945809i	$-0.605271\pi$
$127$	6.20191	−	5.20402i	0.550331	−	0.461782i	0.875053	+	0.484027i	$0.160826\pi$
$128$	10.0122	+	5.26829i	0.884966	+	0.465656i
$129$	−0.609196	+	1.67375i	−0.0536367	+	0.147366i
$130$	−6.50692	−	11.1259i	−0.570695	−	0.975804i
$131$	−5.31618	−	0.937385i	−0.464476	−	0.0818997i	−0.0634875	−	0.997983i	$-0.520222\pi$
$131$	−5.31618	−	0.937385i	−0.464476	−	0.0818997i	−0.400989	+	0.916083i	$0.631333\pi$
$132$	−11.1610	+	13.6080i	−0.971441	+	1.18442i
$133$	−5.52572	+	4.67095i	−0.479141	+	0.405023i
$134$	−4.83787	+	13.5273i	−0.417928	+	1.16858i
$135$	−0.869584	+	4.93165i	−0.0748418	+	0.424449i
$136$	−16.7062	−	2.65703i	−1.43255	−	0.227838i
$137$	10.8411	+	3.94583i	0.926216	+	0.337115i	0.760709	−	0.649093i	$-0.224852\pi$
$137$	10.8411	+	3.94583i	0.926216	+	0.337115i	0.165507	+	0.986209i	$0.447074\pi$
$138$	−21.5565	+	0.120789i	−1.83501	+	0.0102822i
$139$	3.12723	+	3.72688i	0.265248	+	0.316110i	0.882186	−	0.470902i	$-0.156071\pi$
$139$	3.12723	+	3.72688i	0.265248	+	0.316110i	−0.616938	+	0.787012i	$0.711627\pi$
$140$	8.82024	+	1.45353i	0.745447	+	0.122845i
$141$	−14.7637	−	8.52385i	−1.24333	−	0.717837i
$142$	−3.48549	−	0.594469i	−0.292496	−	0.0498867i
$143$	1.99553	+	11.3172i	0.166875	+	0.946393i
$144$	−14.0839	−	4.77147i	−1.17366	−	0.397623i
$145$	6.93731	−	4.00526i	0.576112	−	0.332619i
$146$	5.14947	+	13.9051i	0.426173	+	1.15080i
$147$	10.3380	−	3.76271i	0.852660	−	0.310343i
$148$	1.37471	−	0.814365i	0.113000	−	0.0669404i
$149$	14.3556	+	12.0458i	1.17606	+	0.986831i	0.999997	+	0.00245146i	$0.000780324\pi$
$149$	14.3556	+	12.0458i	1.17606	+	0.986831i	0.176062	+	0.984379i	$0.443664\pi$
$150$	7.16658	+	4.08426i	0.585149	+	0.333478i
$151$	6.11110			0.497314			0.248657	−	0.968592i	$-0.420011\pi$
$151$	6.11110			0.497314			0.248657	+	0.968592i	$0.420011\pi$
$152$	−2.38864	−	12.0952i	−0.193744	−	0.981052i
$153$	22.2339			1.79750
$154$	−6.92462	−	3.94636i	−0.558002	−	0.318007i
$155$	12.0260	+	10.0910i	0.965948	+	0.810527i
$156$	−15.0953	+	8.94229i	−1.20859	+	0.715956i
$157$	3.67562	−	1.33782i	0.293347	−	0.106769i	−0.191155	−	0.981560i	$-0.561223\pi$
$157$	3.67562	−	1.33782i	0.293347	−	0.106769i	0.484501	+	0.874790i	$0.339001\pi$
$158$	4.47985	+	12.0969i	0.356397	+	0.962381i
$159$	19.1020	−	11.0286i	1.51489	−	0.874622i
$160$	−9.46023	+	11.9381i	−0.747897	+	0.943788i
$161$	−1.69520	−	9.61396i	−0.133601	−	0.757686i
$162$	−8.82797	−	1.50566i	−0.693591	−	0.118295i
$163$	3.89527	+	2.24893i	0.305101	+	0.176150i	0.644732	−	0.764409i	$-0.276969\pi$
$163$	3.89527	+	2.24893i	0.305101	+	0.176150i	−0.339631	+	0.940559i	$0.610302\pi$
$164$	2.77616	+	0.457496i	0.216782	+	0.0357244i
$165$	−15.2308	−	18.1513i	−1.18571	−	1.41308i
$166$	11.0866	−	0.0621222i	0.860485	−	0.00482162i
$167$	−14.9157	−	5.42887i	−1.15421	−	0.420099i	−0.307185	−	0.951650i	$-0.599387\pi$
$167$	−14.9157	−	5.42887i	−1.15421	−	0.420099i	−0.847026	+	0.531551i	$0.821609\pi$
$168$	1.91131	−	12.0175i	0.147461	−	0.927169i
$169$	0.268073	−	1.52032i	0.0206210	−	0.116948i
$170$	7.66941	−	21.4446i	0.588217	−	1.64473i
$171$	5.59754	+	15.2069i	0.428055	+	1.16290i
$172$	0.871627	−	1.06273i	0.0664609	−	0.0810321i
$173$	−4.51044	−	0.795312i	−0.342922	−	0.0604664i	−0.000465084	−	1.00000i	$-0.500148\pi$
$173$	−4.51044	−	0.795312i	−0.342922	−	0.0604664i	−0.342457	+	0.939533i	$0.611259\pi$
$174$	−5.50500	−	9.41274i	−0.417333	−	0.713578i
$175$	−1.27763	+	3.51025i	−0.0965794	+	0.265350i
$176$	11.6062	−	7.05231i	0.874852	−	0.531588i
$177$	−9.58909	+	8.04620i	−0.720760	+	0.604790i
$178$	3.15060	+	17.3005i	0.236148	+	1.29673i
$179$	−3.50718	+	6.07462i	−0.262139	+	0.454039i	−0.966810	−	0.255496i	$-0.917761\pi$
$179$	−3.50718	+	6.07462i	−0.262139	+	0.454039i	0.704671	+	0.709534i	$0.251095\pi$
$180$	9.81519	−	17.4491i	0.731581	−	1.30058i
$181$	2.24482	−	0.395823i	0.166856	−	0.0294213i	−0.0895957	−	0.995978i	$-0.528558\pi$
$181$	2.24482	−	0.395823i	0.166856	−	0.0294213i	0.256452	+	0.966557i	$0.417446\pi$
$182$	−5.14132	−	6.05792i	−0.381100	−	0.449043i
$183$	−4.91090	−	8.50593i	−0.363024	−	0.628776i
$184$	15.7247	+	5.42577i	1.15924	+	0.399993i
$185$	0.735750	+	2.02146i	0.0540934	+	0.148620i
$186$	13.6444	−	16.4471i	1.00046	−	1.20596i
$187$	−13.0525	+	15.5553i	−0.954491	+	1.13752i
$188$	8.56825	+	9.98190i	0.624904	+	0.728005i
$189$			3.08707i			0.224551i
$190$	16.5980	−	0.153327i	1.20414	−	0.0111235i
$191$		−	23.8531i		−	1.72595i	−0.505245	−	0.862976i	$-0.668598\pi$
$191$		−	23.8531i		−	1.72595i	0.505245	−	0.862976i	$-0.331402\pi$
$192$	16.3226	+	12.7865i	1.17799	+	0.922786i
$193$	10.3925	−	12.3853i	0.748066	−	0.891511i	−0.248965	−	0.968513i	$-0.580090\pi$
$193$	10.3925	−	12.3853i	0.748066	−	0.891511i	0.997031	+	0.0770018i	$0.0245347\pi$
$194$	9.28992	+	7.70688i	0.666978	+	0.553322i
$195$	−8.07904	−	22.1970i	−0.578552	−	1.58956i
$196$	−8.48880	+	0.0951348i	−0.606343	+	0.00679534i
$197$	−1.59411	−	2.76108i	−0.113576	−	0.196719i	0.803634	−	0.595124i	$-0.202897\pi$
$197$	−1.59411	−	2.76108i	−0.113576	−	0.196719i	−0.917209	+	0.398405i	$0.869564\pi$
$198$	−13.6094	+	11.5502i	−0.967179	+	0.820839i
$199$	11.2456	−	1.98291i	0.797183	−	0.140565i	0.239802	−	0.970822i	$-0.422917\pi$
$199$	11.2456	−	1.98291i	0.797183	−	0.140565i	0.557381	+	0.830257i	$0.311806\pi$
$200$	−4.17283	−	4.80654i	−0.295064	−	0.339874i
$201$	−13.1646	+	22.8018i	−0.928559	+	1.60831i
$202$	0.157825	−	0.0287415i	0.0111045	−	0.00202224i
$203$	3.78286	−	3.17419i	0.265505	−	0.222785i
$204$	−29.2496	−	10.2763i	−2.04788	−	0.719483i
$205$	−1.29559	+	3.55960i	−0.0904878	+	0.248613i
$206$	8.18590	−	4.78749i	0.570339	−	0.333560i
$207$	−21.5314	−	3.79657i	−1.49654	−	0.263880i
$208$	13.2771	−	2.64922i	0.920601	−	0.183690i
$209$	−13.9252	−	5.01112i	−0.963225	−	0.346626i
$210$	15.4260	+	5.51692i	1.06450	+	0.380703i
$211$	−0.664785	+	3.77018i	−0.0457657	+	0.259550i	−0.999102	−	0.0423589i	$-0.986513\pi$
$211$	−0.664785	+	3.77018i	−0.0457657	+	0.259550i	0.953337	+	0.301909i	$0.0976238\pi$
$212$	−16.7278	+	3.14324i	−1.14887	+	0.215879i
$213$	−6.08930	−	2.21632i	−0.417232	−	0.151860i
$214$	−0.0449881	−	8.02875i	−0.00307532	−	0.548834i
$215$	1.18946	+	1.41754i	0.0811204	+	0.0966755i
$216$	−4.59906	−	2.55317i	−0.312926	−	0.173721i
$217$	8.38111	+	4.83884i	0.568947	+	0.328482i
$218$	−1.86880	+	10.9571i	−0.126571	+	0.742112i
$219$	4.71893	+	26.7624i	0.318875	+	1.80843i
$220$	6.44576	+	17.1105i	0.434573	+	1.15359i
$221$	−17.5311	+	10.1216i	−1.17927	+	0.680852i
$222$	2.74606	−	1.01694i	0.184303	−	0.0682529i
$223$	−22.3608	+	8.13865i	−1.49739	+	0.545004i	−0.955382	−	0.295372i	$-0.904557\pi$
$223$	−22.3608	+	8.13865i	−1.49739	+	0.545004i	−0.542004	+	0.840376i	$0.682334\pi$
$224$	−4.46532	+	8.26024i	−0.298352	+	0.551911i
$225$	6.40879	+	5.37761i	0.427253	+	0.358507i
$226$	6.73562	−	11.8189i	0.448047	−	0.786180i
$227$	21.4255			1.42206			0.711031	−	0.703161i	$-0.248229\pi$
$227$	21.4255			1.42206			0.711031	+	0.703161i	$0.248229\pi$
$228$	−0.335314	−	22.5925i	−0.0222067	−	1.49623i
$229$	−17.6065			−1.16347			−0.581735	−	0.813378i	$-0.697626\pi$
$229$	−17.6065			−1.16347			−0.581735	+	0.813378i	$0.697626\pi$
$230$	−11.0889	+	19.4575i	−0.731180	+	1.28299i
$231$	−11.1896	−	9.38917i	−0.736220	−	0.617762i
$232$	1.60023	+	8.26085i	0.105060	+	0.542351i
$233$	10.9408	−	3.98214i	0.716758	−	0.260879i	0.0422092	−	0.999109i	$-0.486560\pi$
$233$	10.9408	−	3.98214i	0.716758	−	0.260879i	0.674549	+	0.738230i	$0.264338\pi$
$234$	−16.6873	+	6.17978i	−1.09088	+	0.403985i
$235$	−15.3381	+	8.85547i	−1.00055	+	0.577667i
$236$	9.03923	−	3.40520i	0.588404	−	0.221660i
$237$	4.10529	+	23.2823i	0.266667	+	1.51235i
$238$	2.36047	−	13.8399i	0.153007	−	0.897110i
$239$	−15.1464	−	8.74479i	−0.979741	−	0.565654i	−0.0775489	−	0.996989i	$-0.524709\pi$
$239$	−15.1464	−	8.74479i	−0.979741	−	0.565654i	−0.902192	+	0.431335i	$0.858043\pi$
$240$	−20.9771	+	18.4186i	−1.35407	+	1.18891i
$241$	17.4817	+	20.8339i	1.12610	+	1.34203i	0.932593	+	0.360930i	$0.117541\pi$
$241$	17.4817	+	20.8339i	1.12610	+	1.34203i	0.193504	+	0.981100i	$0.438015\pi$
$242$	−0.00417981	−	0.745945i	−0.000268688	−	0.0479512i
$243$	−20.6657	−	7.52168i	−1.32570	−	0.482516i
$244$	1.39965	+	7.44870i	0.0896035	+	0.476854i
$245$	1.98470	−	11.2558i	0.126798	−	0.719107i
$246$	4.85532	+	1.73644i	0.309564	+	0.110712i
$247$	−11.3363	−	9.44229i	−0.721311	−	0.600798i
$248$	−14.1404	+	8.48404i	−0.897918	+	0.538737i
$249$	20.0099	+	3.52829i	1.26808	+	0.223597i
$250$	−9.03813	+	5.28591i	−0.571622	+	0.334310i
$251$	7.93890	−	21.8120i	0.501099	−	1.37676i	−0.389103	−	0.921194i	$-0.627215\pi$
$251$	7.93890	−	21.8120i	0.501099	−	1.37676i	0.890203	−	0.455565i	$-0.150563\pi$
$252$	4.09087	−	11.6440i	0.257701	−	0.733501i
$253$	15.2962	−	12.8351i	0.961666	−	0.806934i
$254$	−11.2642	+	2.05133i	−0.706781	+	0.128712i
$255$	20.8697	−	36.1473i	1.30691	−	2.26363i
$256$	−8.61289	−	13.4840i	−0.538306	−	0.842750i
$257$	−8.80240	+	1.55210i	−0.549079	+	0.0968174i	−0.441303	−	0.897358i	$-0.645484\pi$
$257$	−8.80240	+	1.55210i	−0.549079	+	0.0968174i	−0.107775	+	0.994175i	$0.534373\pi$
$258$	1.92053	−	1.62994i	0.119567	−	0.101476i
$259$	0.663062	+	1.14846i	0.0412007	+	0.0713617i
$260$	0.204267	+	18.2266i	0.0126681	+	1.13036i
$261$	−3.78258	−	10.3925i	−0.234136	−	0.643282i
$262$	5.87553	+	4.87432i	0.362992	+	0.301136i
$263$	−0.382797	+	0.456200i	−0.0236043	+	0.0281305i	−0.777717	−	0.628614i	$-0.783623\pi$
$263$	−0.382797	+	0.456200i	−0.0236043	+	0.0281305i	0.754113	+	0.656744i	$0.228067\pi$
$264$	23.2422	−	8.90468i	1.43046	−	0.548045i
$265$		−	22.9153i		−	1.40768i
$266$	10.0601	−	1.86985i	0.616827	−	0.114648i
$267$			32.2281i			1.97233i
$268$	15.4165	−	13.2332i	0.941712	−	0.808345i
$269$	6.62803	−	7.89898i	0.404118	−	0.481609i	−0.525153	−	0.851008i	$-0.675992\pi$
$269$	6.62803	−	7.89898i	0.404118	−	0.481609i	0.929271	+	0.369399i	$0.120436\pi$
$270$	4.52175	−	5.45055i	0.275185	−	0.331710i
$271$	4.03735	+	11.0925i	0.245252	+	0.673823i	0.999845	+	0.0176301i	$0.00561214\pi$
$271$	4.03735	+	11.0925i	0.245252	+	0.673823i	−0.754593	+	0.656193i	$0.772166\pi$
$272$	18.6662	+	14.9629i	1.13181	+	0.907260i
$273$	−7.28088	−	12.6108i	−0.440659	−	0.763243i
$274$	−10.5573	−	12.4395i	−0.637790	−	0.751496i
$275$	−7.52460	+	1.32679i	−0.453750	+	0.0800084i
$276$	26.5707	+	14.9461i	1.59937	+	0.899652i
$277$	−14.1103	+	24.4398i	−0.847807	+	1.46844i	0.0353540	+	0.999375i	$0.488744\pi$
$277$	−14.1103	+	24.4398i	−0.847807	+	1.46844i	−0.883161	+	0.469070i	$0.844589\pi$
$278$	−1.23270	−	6.76896i	−0.0739323	−	0.405976i
$279$	16.6033	−	13.9318i	0.994015	−	0.834078i
$280$	−9.81952	−	7.96215i	−0.586828	−	0.475830i
$281$	1.73634	−	4.77054i	0.103581	−	0.284587i	−0.877066	−	0.480370i	$-0.840503\pi$
$281$	1.73634	−	4.77054i	0.103581	−	0.284587i	0.980647	+	0.195783i	$0.0627248\pi$
$282$	12.1713	+	20.8112i	0.724793	+	1.23929i
$283$	4.41352	+	0.778223i	0.262357	+	0.0462605i	0.303279	−	0.952902i	$-0.401919\pi$
$283$	4.41352	+	0.778223i	0.262357	+	0.0462605i	−0.0409225	+	0.999162i	$0.513030\pi$
$284$	3.86632	+	3.17107i	0.229424	+	0.188169i
$285$	29.9772	+	5.17353i	1.77570	+	0.306454i
$286$	5.47280	−	15.3027i	0.323614	−	0.904865i
$287$	−0.405500	+	2.29971i	−0.0239359	+	0.135747i
$288$	13.9636	+	15.7247i	0.822812	+	0.926584i
$289$	−17.6378	−	6.41965i	−1.03752	−	0.377626i
$290$	−11.3284	+	0.0634773i	−0.665227	+	0.00372751i
$291$	14.2195	+	16.9462i	0.833565	+	0.993404i
$292$	3.40974	−	20.6909i	0.199540	−	1.21084i
$293$	−19.7434	−	11.3988i	−1.15342	−	0.665928i	−0.203702	−	0.979033i	$-0.565298\pi$
$293$	−19.7434	−	11.3988i	−1.15342	−	0.665928i	−0.949719	+	0.313105i	$0.898631\pi$
$294$	−15.3369	−	2.61579i	−0.894466	−	0.152556i
$295$	2.25824	+	12.8071i	0.131480	+	0.745659i
$296$	−2.25933	+	0.0379829i	−0.131321	+	0.00220771i
$297$	−5.46836	+	3.15716i	−0.317306	+	0.183197i
$298$	−9.20372	−	24.8528i	−0.533157	−	1.43968i
$299$	18.7055	−	6.80826i	1.08177	−	0.393732i
$300$	−5.94556	−	10.0366i	−0.343267	−	0.579461i
$301$	0.873858	+	0.733254i	0.0503684	+	0.0422641i
$302$	−7.50863	−	4.27919i	−0.432073	−	0.246240i
$303$	0.294002			0.0168900
$304$	−5.53459	+	16.5339i	−0.317430	+	0.948282i
$305$	−10.2039			−0.584275
$306$	−27.3185	−	15.5689i	−1.56169	−	0.890015i
$307$	25.9825	+	21.8019i	1.48290	+	1.24430i	0.903019	+	0.429602i	$0.141346\pi$
$307$	25.9825	+	21.8019i	1.48290	+	1.24430i	0.579882	+	0.814700i	$0.303098\pi$
$308$	5.74482	+	9.69769i	0.327341	+	0.552577i
$309$	16.3315	−	5.94418i	0.929067	−	0.338153i
$310$	−7.71011	−	20.8196i	−0.437905	−	1.18248i
$311$	−15.6547	+	9.03827i	−0.887699	+	0.512513i	−0.873189	−	0.487382i	$-0.837952\pi$
$311$	−15.6547	+	9.03827i	−0.887699	+	0.512513i	−0.0145095	+	0.999895i	$0.504619\pi$
$312$	24.8090	−	0.417078i	1.40454	−	0.0236124i
$313$	0.100851	+	0.571953i	0.00570042	+	0.0323287i	0.987525	−	0.157460i	$-0.0503307\pi$
$313$	0.100851	+	0.571953i	0.00570042	+	0.0323287i	−0.981825	+	0.189789i	$0.939220\pi$
$314$	−5.45298	−	0.930033i	−0.307729	−	0.0524848i
$315$	14.3899	+	8.30799i	0.810777	+	0.468102i
$316$	2.96634	−	18.0003i	0.166870	−	1.01260i
$317$	−0.495890	−	0.590979i	−0.0278520	−	0.0331927i	0.751939	−	0.659233i	$-0.229119\pi$
$317$	−0.495890	−	0.590979i	−0.0278520	−	0.0331927i	−0.779791	+	0.626040i	$0.784674\pi$
$318$	−31.1930	+	0.174786i	−1.74922	+	0.00980152i
$319$	9.49143	+	3.45460i	0.531418	+	0.193420i
$320$	19.9831	−	8.04380i	1.11709	−	0.449662i
$321$	2.55515	−	14.4909i	0.142614	−	0.808806i
$322$	−4.64914	+	12.9996i	−0.259087	+	0.724439i
$323$	−0.0947395	−	26.0695i	−0.00527145	−	1.45054i
$324$	9.79251	+	8.03162i	0.544028	+	0.446201i
$325$	−7.50131	−	1.32268i	−0.416098	−	0.0733693i
$326$	−3.21129	−	5.49083i	−0.177857	−	0.304109i
$327$	−6.96733	+	19.1426i	−0.385294	+	1.05859i
$328$	−3.09068	−	2.50608i	−0.170655	−	0.138375i
$329$	−8.36375	+	7.01802i	−0.461109	+	0.386916i
$330$	6.00370	+	32.9674i	0.330493	+	1.81480i
$331$	−11.5517	+	20.0081i	−0.634937	+	1.09974i	0.351591	+	0.936154i	$0.385641\pi$
$331$	−11.5517	+	20.0081i	−0.634937	+	1.09974i	−0.986528	+	0.163590i	$0.947693\pi$
$332$	−13.6654	−	7.68685i	−0.749988	−	0.421871i
$333$	2.92486	−	0.515732i	0.160282	−	0.0282620i
$334$	14.5253	+	17.1149i	0.794787	+	0.936483i
$335$	13.6768	+	23.6889i	0.747242	+	1.29426i
$336$	−10.7634	+	13.4274i	−0.587194	+	0.732523i
$337$	−1.58775	−	4.36231i	−0.0864903	−	0.237630i	0.888906	−	0.458090i	$-0.151466\pi$
$337$	−1.58775	−	4.36231i	−0.0864903	−	0.237630i	−0.975396	+	0.220460i	$0.929244\pi$
$338$	−1.39395	+	1.68028i	−0.0758211	+	0.0913953i
$339$	16.0254	−	19.0983i	0.870378	−	1.03728i
$340$	−24.4396	+	20.9784i	−1.32542	+	1.13771i
$341$			19.7948i			1.07195i
$342$	3.77077	−	22.6042i	0.203900	−	1.22229i
$343$		−	18.6652i		−	1.00783i
$344$	−1.81511	+	0.695417i	−0.0978643	+	0.0374944i
$345$	−26.3827	+	31.4416i	−1.42039	+	1.69276i
$346$	4.98502	+	4.13555i	0.267996	+	0.222328i
$347$	−7.62858	−	20.9593i	−0.409524	−	1.12516i	−0.957442	−	0.288625i	$-0.906802\pi$
$347$	−7.62858	−	20.9593i	−0.409524	−	1.12516i	0.547919	−	0.836532i	$-0.315420\pi$
$348$	0.172815	+	15.4201i	0.00926383	+	0.826604i
$349$	6.79776	+	11.7741i	0.363876	+	0.630251i	0.988595	−	0.150598i	$-0.0481200\pi$
$349$	6.79776	+	11.7741i	0.363876	+	0.630251i	−0.624719	+	0.780849i	$0.714787\pi$
$350$	4.02779	−	3.41836i	0.215295	−	0.182719i
$351$	−6.19914	+	1.09308i	−0.330886	+	0.0583441i
$352$	−19.1987	+	0.538022i	−1.02329	+	0.0286767i
$353$	12.5636	−	21.7608i	0.668692	−	1.15821i	−0.309578	−	0.950874i	$-0.600188\pi$
$353$	12.5636	−	21.7608i	0.668692	−	1.15821i	0.978270	−	0.207335i	$-0.0664789\pi$
$354$	17.4162	−	3.17167i	0.925661	−	0.168572i
$355$	−5.15717	+	4.32738i	−0.273714	+	0.229674i
$356$	8.24329	−	23.4631i	0.436894	−	1.24354i
$357$	8.80041	−	24.1789i	0.465767	−	1.27968i
$358$	8.56289	−	5.00797i	0.452563	−	0.264679i
$359$	9.73513	+	1.71657i	0.513800	+	0.0905969i	0.424536	−	0.905411i	$-0.360437\pi$
$359$	9.73513	+	1.71657i	0.513800	+	0.0905969i	0.0892644	+	0.996008i	$0.471548\pi$
$360$	−24.2782	+	14.5666i	−1.27958	+	0.767727i
$361$	17.8065	−	6.62798i	0.937182	−	0.348841i
$362$	−3.03536	−	1.08556i	−0.159535	−	0.0570556i
$363$	0.237397	−	1.34634i	0.0124601	−	0.0706647i
$364$	2.07512	+	11.0434i	0.108766	+	0.578832i
$365$	26.5299	+	9.65608i	1.38864	+	0.505422i
$366$	0.0778303	+	13.8899i	0.00406826	+	0.726037i
$367$	−20.2739	−	24.1615i	−1.05829	−	1.26122i	−0.964064	−	0.265671i	$-0.914406\pi$
$367$	−20.2739	−	24.1615i	−1.05829	−	1.26122i	−0.0942270	−	0.995551i	$-0.530038\pi$
$368$	−15.5214	−	17.6775i	−0.809111	−	0.921505i
$369$	4.52920	+	2.61493i	0.235781	+	0.136128i
$370$	0.511484	−	2.99894i	0.0265908	−	0.155907i
$371$	−2.45302	−	13.9118i	−0.127354	−	0.722263i
$372$	−28.2815	+	10.6540i	−1.46633	+	0.552387i
$373$	17.2111	−	9.93681i	0.891155	−	0.514509i	0.0168350	−	0.999858i	$-0.494641\pi$
$373$	17.2111	−	9.93681i	0.891155	−	0.514509i	0.874320	+	0.485350i	$0.161308\pi$
$374$	26.9298	−	9.97287i	1.39251	−	0.515685i
$375$	−18.0318	+	6.56303i	−0.931157	+	0.338913i
$376$	−3.53805	−	18.2644i	−0.182461	−	0.941915i
$377$	7.71354	+	6.47243i	0.397267	+	0.333347i
$378$	2.16167	−	3.79305i	0.111184	−	0.195093i
$379$	−36.4793			−1.87382			−0.936909	−	0.349573i	$-0.886327\pi$
$379$	−36.4793			−1.87382			−0.936909	+	0.349573i	$0.886327\pi$
$380$	−20.5011	−	11.4341i	−1.05168	−	0.586555i
$381$	−20.9835			−1.07502
$382$	−16.7027	+	29.3080i	−0.854587	+	1.49953i
$383$	−14.8965	−	12.4996i	−0.761175	−	0.638702i	0.177258	−	0.984164i	$-0.443277\pi$
$383$	−14.8965	−	12.4996i	−0.761175	−	0.638702i	−0.938432	+	0.345463i	$0.887722\pi$
$384$	−11.1019	−	27.1403i	−0.566541	−	1.38500i
$385$	−14.2601	+	5.19024i	−0.726761	+	0.264519i
$386$	−21.4417	+	7.94047i	−1.09135	+	0.404159i
$387$	2.21252	−	1.27740i	0.112469	−	0.0649339i
$388$	−6.01780	−	15.9745i	−0.305508	−	0.810980i
$389$	−1.67034	−	9.47298i	−0.0846897	−	0.480299i	−0.997423	−	0.0717435i	$-0.977144\pi$
$389$	−1.67034	−	9.47298i	−0.0846897	−	0.480299i	0.912733	−	0.408556i	$-0.133967\pi$
$390$	−5.61644	+	32.9304i	−0.284400	+	1.66749i
$391$	30.4616	+	17.5870i	1.54051	+	0.889413i
$392$	10.4967	+	5.82725i	0.530163	+	0.294320i
$393$	8.99334	+	10.7178i	0.453654	+	0.540644i
$394$	0.0252642	+	4.50875i	0.00127279	+	0.227147i
$395$	23.0800	+	8.40043i	1.16128	+	0.422671i
$396$	24.8096	−	4.66185i	1.24673	−	0.234267i
$397$	−0.0229782	+	0.130316i	−0.00115324	+	0.00654036i	−0.985379	−	0.170377i	$-0.945501\pi$
$397$	−0.0229782	+	0.130316i	−0.00115324	+	0.00654036i	0.984226	+	0.176917i	$0.0566125\pi$
$398$	−15.2059	−	5.43820i	−0.762202	−	0.272592i
$399$	18.7528	−	0.0681499i	0.938815	−	0.00341176i
$400$	1.76141	+	8.82769i	0.0880706	+	0.441385i
$401$	−1.91187	−	0.337113i	−0.0954740	−	0.0168346i	0.125707	−	0.992067i	$-0.459880\pi$
$401$	−1.91187	−	0.337113i	−0.0954740	−	0.0168346i	−0.221181	+	0.975233i	$0.570991\pi$
$402$	32.1417	−	18.7979i	1.60308	−	0.937556i
$403$	−6.74926	+	18.5435i	−0.336205	+	0.923715i
$404$	−0.214043	−	0.0751997i	−0.0106490	−	0.00374132i
$405$	−13.0620	+	10.9603i	−0.649054	+	0.544621i
$406$	−6.87063	+	1.25121i	−0.340983	+	0.0620966i
$407$	−1.35623	+	2.34906i	−0.0672259	+	0.116439i
$408$	28.7429	+	33.1079i	1.42298	+	1.63908i
$409$	−27.0452	+	4.76879i	−1.33730	+	0.235802i	−0.796136	−	0.605117i	$-0.793126\pi$
$409$	−27.0452	+	4.76879i	−1.33730	+	0.235802i	−0.541161	+	0.840919i	$0.682015\pi$
$410$	4.08442	−	3.46642i	0.201715	−	0.171194i
$411$	−14.9507	−	25.8954i	−0.737465	−	1.27733i
$412$	−13.4103	+	0.150290i	−0.660677	+	0.00740427i
$413$	2.74193	+	7.53340i	0.134922	+	0.370694i
$414$	23.7969	+	19.7418i	1.16955	+	0.970256i
$415$	13.5687	−	16.1705i	0.666061	−	0.793781i
$416$	−18.1685	−	6.04200i	−0.890783	−	0.296234i
$417$		−	12.6095i		−	0.617489i
$418$	13.6007	+	15.9080i	0.665234	+	0.778084i
$419$			6.34043i			0.309750i	0.987934	+	0.154875i	$0.0494975\pi$
$419$			6.34043i			0.309750i	−0.987934	+	0.154875i	$0.950503\pi$
$420$	−15.0906	−	17.5804i	−0.736346	−	0.857834i
$421$	7.49154	−	8.92808i	0.365116	−	0.435128i	−0.551942	−	0.833882i	$-0.686113\pi$
$421$	7.49154	−	8.92808i	0.365116	−	0.435128i	0.917058	+	0.398755i	$0.130558\pi$
$422$	3.45682	−	4.16687i	0.168275	−	0.202840i
$423$	8.36313	+	22.9775i	0.406629	+	1.11720i
$424$	22.7542	+	7.85129i	1.10504	+	0.381292i
$425$	−6.72966	−	11.6561i	−0.326436	−	0.565404i
$426$	5.92990	+	6.98710i	0.287305	+	0.338526i
$427$	−6.19476	+	1.09230i	−0.299785	+	0.0528602i
$428$	−5.56672	+	9.89633i	−0.269078	+	0.478357i
$429$	14.8924	−	25.7943i	0.719010	−	1.24536i
$430$	−0.468863	−	2.57461i	−0.0226106	−	0.124159i
$431$	−17.1020	+	14.3503i	−0.823775	+	0.691229i	−0.953853	−	0.300275i	$-0.902922\pi$
$431$	−17.1020	+	14.3503i	−0.823775	+	0.691229i	0.130078	+	0.991504i	$0.458477\pi$
$432$	3.86299	+	6.35746i	0.185858	+	0.305873i
$433$	−6.55454	+	18.0085i	−0.314991	+	0.865431i	0.676638	+	0.736316i	$0.263436\pi$
$433$	−6.55454	+	18.0085i	−0.314991	+	0.865431i	−0.991630	+	0.129116i	$0.958786\pi$
$434$	−6.90946	−	11.8142i	−0.331665	−	0.567098i
$435$	−20.4464	−	3.60526i	−0.980331	−	0.172859i
$436$	9.96873	−	12.1543i	0.477415	−	0.582086i
$437$	−4.35977	+	25.2620i	−0.208556	+	1.20844i
$438$	12.9418	−	36.1869i	0.618383	−	1.72908i
$439$	−0.638308	+	3.62002i	−0.0304648	+	0.172774i	−0.996244	−	0.0865917i	$-0.972402\pi$
$439$	−0.638308	+	3.62002i	−0.0304648	+	0.172774i	0.965779	+	0.259366i	$0.0835136\pi$
$440$	4.06150	−	25.5370i	0.193624	−	1.21743i
$441$	−14.8281	−	5.39700i	−0.706101	−	0.257000i
$442$	28.6278	−	0.160412i	1.36168	−	0.00763002i
$443$	14.4156	+	17.1798i	0.684905	+	0.816237i	0.990729	−	0.135850i	$-0.0433766\pi$
$443$	14.4156	+	17.1798i	0.684905	+	0.816237i	−0.305825	+	0.952088i	$0.598932\pi$
$444$	−4.08615	−	0.673374i	−0.193920	−	0.0319569i
$445$	28.9962	+	16.7410i	1.37455	+	0.793598i
$446$	33.1733	+	5.65788i	1.57080	+	0.267908i
$447$	−8.43420	−	47.8327i	−0.398924	−	2.26241i
$448$	11.2706	−	7.02249i	0.532485	−	0.331782i
$449$	−32.5644	+	18.8011i	−1.53681	+	0.887278i	−0.537788	+	0.843080i	$0.680740\pi$
$449$	−32.5644	+	18.8011i	−1.53681	+	0.887278i	−0.999023	+	0.0441984i	$0.985927\pi$
$450$	−4.10882	−	11.0951i	−0.193692	−	0.523026i
$451$	−4.48835	+	1.63362i	−0.211348	+	0.0769244i
$452$	−16.5519	+	9.80521i	−0.778538	+	0.461198i
$453$	−12.1333	−	10.1810i	−0.570072	−	0.478347i
$454$	−26.3253	−	15.0029i	−1.23551	−	0.704119i
$455$	−15.1283			−0.709225
$456$	−15.4080	+	27.9939i	−0.721547	+	1.31094i
$457$	40.6482			1.90144			0.950721	−	0.310047i	$-0.100345\pi$
$457$	40.6482			1.90144			0.950721	+	0.310047i	$0.100345\pi$
$458$	21.6329	+	12.3287i	1.01084	+	0.576080i
$459$	−8.52063	−	7.14966i	−0.397709	−	0.333717i
$460$	27.2496	−	16.1424i	1.27052	−	0.752642i
$461$	−27.8951	+	10.1530i	−1.29920	+	0.472871i	−0.896737	−	0.442564i	$-0.854069\pi$
$461$	−27.8951	+	10.1530i	−1.29920	+	0.472871i	−0.402466	+	0.915435i	$0.631847\pi$
$462$	7.17389	+	19.3717i	0.333760	+	0.901252i
$463$	16.0546	−	9.26911i	0.746119	−	0.430772i	−0.0781706	−	0.996940i	$-0.524908\pi$
$463$	16.0546	−	9.26911i	0.746119	−	0.430772i	0.824290	+	0.566168i	$0.191575\pi$
$464$	3.81833	−	11.2705i	0.177262	−	0.523221i
$465$	−7.06548	−	40.0703i	−0.327654	−	1.85822i
$466$	−16.2313	−	2.76833i	−0.751900	−	0.128240i
$467$	−22.4178	−	12.9429i	−1.03737	−	0.598926i	−0.118283	−	0.992980i	$-0.537739\pi$
$467$	−22.4178	−	12.9429i	−1.03737	−	0.598926i	−0.919087	+	0.394054i	$0.871072\pi$
$468$	24.8307	+	4.09196i	1.14780	+	0.189151i
$469$	10.8389	+	12.9173i	0.500496	+	0.596467i
$470$	25.0467	−	0.140346i	1.15532	−	0.00647367i
$471$	−9.52657	−	3.46739i	−0.438961	−	0.159769i
$472$	−13.4908	−	2.14563i	−0.620966	−	0.0987608i
$473$	−0.405170	+	2.29783i	−0.0186297	+	0.105654i
$474$	11.2589	−	31.4813i	0.517138	−	1.44598i
$475$	6.27800	−	7.53729i	0.288054	−	0.345834i
$476$	−12.5915	+	15.3521i	−0.577129	+	0.703661i
$477$	−31.1568	−	5.49378i	−1.42657	−	0.251543i
$478$	12.4868	+	21.3506i	0.571134	+	0.976556i
$479$	−0.149158	+	0.409808i	−0.00681519	+	0.0187246i	−0.943054	−	0.332641i	$-0.892060\pi$
$479$	−0.149158	+	0.409808i	−0.00681519	+	0.0187246i	0.936238	+	0.351365i	$0.114283\pi$
$480$	38.6716	−	7.94182i	1.76511	−	0.362493i
$481$	−2.07144	+	1.73814i	−0.0944494	+	0.0792525i
$482$	−6.89099	−	37.8396i	−0.313876	−	1.72355i
$483$	−12.6510	+	21.9123i	−0.575643	+	0.997042i
$484$	−0.517200	+	0.919461i	−0.0235091	+	0.0417937i
$485$	22.6332	−	3.99084i	1.02772	−	0.181215i
$486$	20.1247	+	23.7126i	0.912875	+	1.07562i
$487$	2.67545	+	4.63401i	0.121236	+	0.209987i	0.920255	−	0.391318i	$-0.127981\pi$
$487$	2.67545	+	4.63401i	0.121236	+	0.209987i	−0.799019	+	0.601305i	$0.794648\pi$
$488$	3.49609	−	10.1322i	0.158261	−	0.458664i
$489$	−3.98716	−	10.9546i	−0.180306	−	0.495386i
$490$	−10.3203	+	12.4401i	−0.466222	+	0.561987i
$491$	17.1929	−	20.4898i	0.775907	−	0.924690i	−0.222834	−	0.974856i	$-0.571531\pi$
$491$	17.1929	−	20.4898i	0.775907	−	0.924690i	0.998741	+	0.0501666i	$0.0159752\pi$
$492$	−4.74976	−	5.53340i	−0.214136	−	0.249465i
$493$			17.7925i			0.801334i
$494$	7.31696	+	19.5397i	0.329206	+	0.879131i
$495$			33.9865i			1.52758i
$496$	23.3150	−	0.522652i	1.04687	−	0.0234678i
$497$	−2.66766	+	3.17919i	−0.119661	+	0.142606i
$498$	−22.1154	−	18.3468i	−0.991013	−	0.822140i
$499$	1.54362	+	4.24107i	0.0691021	+	0.189856i	0.969437	−	0.245342i	$-0.0789003\pi$
$499$	1.54362	+	4.24107i	0.0691021	+	0.189856i	−0.900334	+	0.435199i	$0.856678\pi$
$500$	14.8064	−	0.165937i	0.662163	−	0.00742093i
$501$	20.5700	+	35.6282i	0.918998	+	1.59175i
$502$	−25.0279	+	21.2410i	−1.11705	+	0.948033i
$503$	20.5559	−	3.62456i	0.916543	−	0.161611i	0.304570	−	0.952490i	$-0.401487\pi$
$503$	20.5559	−	3.62456i	0.916543	−	0.161611i	0.611973	+	0.790879i	$0.290376\pi$
$504$	−13.1799	+	11.4422i	−0.587079	+	0.509677i
$505$	0.152720	−	0.264519i	0.00679595	−	0.0117709i
$506$	−27.7818	+	5.05936i	−1.23505	+	0.224916i
$507$	−3.06508	+	2.57191i	−0.136125	+	0.114223i
$508$	15.2766	+	5.36714i	0.677791	+	0.238129i
$509$	11.3786	−	31.2625i	0.504348	−	1.38569i	−0.382642	−	0.923897i	$-0.624986\pi$
$509$	11.3786	−	31.2625i	0.504348	−	1.38569i	0.886990	−	0.461789i	$-0.152792\pi$
$510$	−50.9539	+	29.8001i	−2.25627	+	1.31957i
$511$	17.1398	+	3.02221i	0.758221	+	0.133695i
$512$	1.14061	+	22.5987i	0.0504085	+	0.998729i
$513$	2.74490	−	7.62769i	0.121190	−	0.336771i
$514$	11.9022	+	4.25668i	0.524985	+	0.187754i
$515$	3.13536	−	17.7815i	0.138160	−	0.783546i
$516$	−3.50107	+	0.657870i	−0.154126	+	0.0289611i
$517$	−20.9852	−	7.63798i	−0.922928	−	0.335918i
$518$	−0.0105085	−	1.87539i	−0.000461718	−	0.0824000i
$519$	7.63028	+	9.09341i	0.334932	+	0.399156i
$520$	12.5119	−	22.5378i	0.548682	−	0.988349i
$521$	18.8289	+	10.8709i	0.824911	+	0.476262i	0.852107	−	0.523368i	$-0.175325\pi$
$521$	18.8289	+	10.8709i	0.824911	+	0.476262i	−0.0271962	+	0.999630i	$0.508658\pi$
$522$	−2.62960	+	15.4179i	−0.115094	+	0.674822i
$523$	−3.60494	−	20.4446i	−0.157633	−	0.893981i	−0.956339	−	0.292260i	$-0.905593\pi$
$523$	−3.60494	−	20.4446i	−0.157633	−	0.893981i	0.798706	−	0.601722i	$-0.205518\pi$
$524$	−3.80604	−	10.1033i	−0.166267	−	0.441363i
$525$	8.38471	−	4.84092i	0.365939	−	0.211275i
$526$	0.789784	−	0.292480i	0.0344362	−	0.0127527i
$527$	−32.7663	+	11.9260i	−1.42732	+	0.519504i
$528$	−34.7927	−	5.33386i	−1.51416	−	0.232126i
$529$	−8.87704	−	7.44872i	−0.385958	−	0.323858i
$530$	−16.0460	+	28.1557i	−0.696996	+	1.22301i
$531$	17.9546			0.779162
$532$	−13.6701	−	4.74698i	−0.592674	−	0.205808i
$533$	−4.76162			−0.206248
$534$	22.5672	−	39.5983i	0.976577	−	1.71358i
$535$	−11.7105	−	9.82628i	−0.506289	−	0.424827i
$536$	−28.2084	+	5.46432i	−1.21842	+	0.236023i
$537$	17.0836	−	6.21793i	0.737213	−	0.268324i
$538$	−13.6749	+	5.06421i	−0.589567	+	0.218334i
$539$	12.4808	−	7.20577i	0.537584	−	0.310375i
$540$	−9.37248	+	3.53074i	−0.403327	+	0.151939i
$541$	−6.88874	−	39.0680i	−0.296170	−	1.67966i	−0.662408	−	0.749143i	$-0.730465\pi$
$541$	−6.88874	−	39.0680i	−0.296170	−	1.67966i	0.366238	−	0.930521i	$-0.380646\pi$
$542$	2.80671	−	16.4563i	0.120559	−	0.706861i
$543$	−5.11643	−	2.95397i	−0.219567	−	0.126767i
$544$	−12.4574	−	31.4555i	−0.534108	−	1.34864i
$545$	13.6037	+	16.2123i	0.582720	+	0.694459i
$546$	0.115391	+	20.5931i	0.00493827	+	0.881303i
$547$	14.4386	+	5.25520i	0.617348	+	0.224696i	0.631715	−	0.775200i	$-0.282351\pi$
$547$	14.4386	+	5.25520i	0.617348	+	0.224696i	−0.0143672	+	0.999897i	$0.504573\pi$
$548$	4.26110	+	22.6768i	0.182025	+	0.968705i
$549$	−2.44632	+	13.8738i	−0.104406	+	0.592118i
$550$	10.1744	+	3.63876i	0.433840	+	0.155157i
$551$	−12.1692	+	4.47939i	−0.518427	+	0.190829i
$552$	−22.1814	−	36.9698i	−0.944102	−	1.57354i
$553$	14.9110	+	2.62921i	0.634080	+	0.111805i
$554$	34.4507	−	20.1484i	1.46367	−	0.856022i
$555$	1.90694	−	5.23926i	0.0809449	−	0.222394i
$556$	−3.22525	+	9.18012i	−0.136781	+	0.389324i
$557$	0.878070	−	0.736789i	0.0372050	−	0.0312187i	−0.623996	−	0.781428i	$-0.714492\pi$
$557$	0.878070	−	0.736789i	0.0372050	−	0.0312187i	0.661201	+	0.750209i	$0.270047\pi$
$558$	−30.1558	+	5.49169i	−1.27660	+	0.232482i
$559$	−1.16303	+	2.01443i	−0.0491909	+	0.0852011i
$560$	6.48976	+	16.6590i	0.274242	+	0.703969i
$561$	51.8301	−	9.13905i	2.18827	−	0.385851i
$562$	−5.47391	+	4.64567i	−0.230903	+	0.195966i
$563$	13.2485	+	22.9471i	0.558358	+	0.967104i	0.997634	+	0.0687518i	$0.0219017\pi$
$563$	13.2485	+	22.9471i	0.558358	+	0.967104i	−0.439276	+	0.898352i	$0.644765\pi$
$564$	−0.382086	−	34.0932i	−0.0160887	−	1.43558i
$565$	−8.85867	−	24.3390i	−0.372687	−	1.02395i
$566$	−4.87790	−	4.04668i	−0.205033	−	0.170095i
$567$	−6.75658	+	8.05218i	−0.283750	+	0.338160i
$568$	−2.53001	−	6.60358i	−0.106157	−	0.277080i
$569$		−	9.00969i		−	0.377706i	−0.982005	−	0.188853i	$-0.939523\pi$
$569$		−	9.00969i		−	0.377706i	0.982005	−	0.188853i	$-0.0604769\pi$
$570$	−33.2099	−	27.3477i	−1.39101	−	1.14547i
$571$			12.9557i			0.542179i	0.962554	+	0.271089i	$0.0873839\pi$
$571$			12.9557i			0.542179i	−0.962554	+	0.271089i	$0.912616\pi$
$572$	−17.4398	+	14.9699i	−0.729194	+	0.625925i
$573$	−39.7391	+	47.3593i	−1.66013	+	1.97846i
$574$	2.10856	−	2.54168i	0.0880097	−	0.106087i
$575$	4.52668	+	12.4370i	0.188776	+	0.518657i
$576$	−6.14595	−	29.0985i	−0.256081	−	1.21244i
$577$	15.3414	+	26.5721i	0.638672	+	1.10621i	0.985725	+	0.168366i	$0.0538490\pi$
$577$	15.3414	+	26.5721i	0.638672	+	1.10621i	−0.347053	+	0.937846i	$0.612818\pi$
$578$	17.1761	+	20.2383i	0.714434	+	0.841804i
$579$	−41.2675	+	7.27658i	−1.71502	+	0.302404i
$580$	13.9635	+	7.85453i	0.579804	+	0.326142i
$581$	6.50648	−	11.2696i	0.269934	−	0.467540i
$582$	−5.60510	−	30.7786i	−0.232339	−	1.27581i
$583$	22.1342	−	18.5728i	0.916706	−	0.769208i
$584$	−18.6779	+	23.0350i	−0.772899	+	0.953196i
$585$	−11.5881	+	31.8380i	−0.479108	+	1.31634i
$586$	16.2766	+	27.8306i	0.672380	+	1.14967i
$587$	29.7939	+	5.25347i	1.22973	+	0.216834i	0.750508	−	0.660862i	$-0.229809\pi$
$587$	29.7939	+	5.25347i	1.22973	+	0.216834i	0.479218	+	0.877696i	$0.340920\pi$
$588$	17.0126	+	13.9534i	0.701588	+	0.575428i
$589$	−16.4060	−	19.4082i	−0.675997	−	0.799701i
$590$	6.19329	−	17.3172i	0.254974	−	0.712939i
$591$	−1.43491	+	8.13776i	−0.0590242	+	0.334743i
$592$	2.80261	+	1.53539i	0.115187	+	0.0631042i
$593$	−4.00540	−	1.45785i	−0.164482	−	0.0598666i	0.258467	−	0.966020i	$-0.416783\pi$
$593$	−4.00540	−	1.45785i	−0.164482	−	0.0598666i	−0.422949	+	0.906154i	$0.639005\pi$
$594$	8.92965	−	0.0500362i	0.366388	−	0.00205301i
$595$	−17.1828	−	20.4777i	−0.704427	−	0.839504i
$596$	−6.09427	+	36.9811i	−0.249631	+	1.51480i
$597$	−25.6312	−	14.7982i	−1.04902	−	0.605650i
$598$	−27.7506	−	4.73301i	−1.13481	−	0.193547i
$599$	0.748191	+	4.24320i	0.0305703	+	0.173373i	0.996270	−	0.0862879i	$-0.0275005\pi$
$599$	0.748191	+	4.24320i	0.0305703	+	0.173373i	−0.965700	+	0.259660i	$0.916389\pi$
$600$	0.277307	+	16.4951i	0.0113210	+	0.673408i
$601$	0.136310	−	0.0786987i	0.00556021	−	0.00321019i	−0.497217	−	0.867626i	$-0.665645\pi$
$601$	0.136310	−	0.0786987i	0.00556021	−	0.00321019i	0.502778	+	0.864416i	$0.332311\pi$
$602$	−0.560250	−	1.51284i	−0.0228341	−	0.0616590i
$603$	35.4875	−	12.9164i	1.44516	−	0.525996i
$604$	6.22933	+	10.5156i	0.253468	+	0.427873i
$605$	−1.08801	−	0.912952i	−0.0442341	−	0.0371168i
$606$	−0.361236	−	0.205870i	−0.0146742	−	0.00836289i
$607$	23.1610			0.940074			0.470037	−	0.882647i	$-0.344240\pi$
$607$	23.1610			0.940074			0.470037	+	0.882647i	$0.344240\pi$
$608$	18.3778	−	16.4394i	0.745320	−	0.666707i
$609$	−12.7989			−0.518636
$610$	12.5374	+	7.14513i	0.507626	+	0.289298i
$611$	−17.0543	−	14.3103i	−0.689945	−	0.578932i
$612$	22.6641	+	38.2586i	0.916140	+	1.54651i
$613$	−45.1542	+	16.4348i	−1.82376	+	0.663795i	−0.829286	+	0.558825i	$0.811252\pi$
$613$	−45.1542	+	16.4348i	−1.82376	+	0.663795i	−0.994475	+	0.104970i	$0.966525\pi$
$614$	−16.6580	−	44.9816i	−0.672261	−	1.81531i
$615$	8.50259	−	4.90898i	0.342858	−	0.197949i
$616$	−0.267945	−	15.9381i	−0.0107958	−	0.642166i
$617$	−2.55508	−	14.4906i	−0.102864	−	0.583369i	−0.992052	−	0.125828i	$-0.959841\pi$
$617$	−2.55508	−	14.4906i	−0.102864	−	0.583369i	0.889188	−	0.457541i	$-0.151270\pi$
$618$	−24.2286	−	4.13232i	−0.974619	−	0.166226i
$619$	−41.6191	−	24.0288i	−1.67281	−	0.965800i	−0.966052	−	0.258349i	$-0.916822\pi$
$619$	−41.6191	−	24.0288i	−1.67281	−	0.965800i	−0.706762	−	0.707451i	$-0.749845\pi$
$620$	−5.10528	+	30.9797i	−0.205033	+	1.24417i
$621$	7.03057	+	8.37871i	0.282127	+	0.336226i
$622$	25.5637	−	0.143243i	1.02501	−	0.00574351i
$623$	19.3955	+	7.05940i	0.777066	+	0.282829i
$624$	−30.7746	−	16.8597i	−1.23197	−	0.674926i
$625$	−5.41569	+	30.7139i	−0.216628	+	1.22856i
$626$	0.276586	−	0.773371i	0.0110546	−	0.0309101i
$627$	19.2993	+	33.1486i	0.770740	+	1.32383i
$628$	6.04877	+	4.96107i	0.241372	+	0.197968i
$629$	−4.70551	−	0.829708i	−0.187621	−	0.0330826i
$630$	−11.8631	−	20.2842i	−0.472638	−	0.808141i
$631$	−2.81681	+	7.73912i	−0.112135	+	0.308090i	−0.983048	−	0.183348i	$-0.941306\pi$
$631$	−2.81681	+	7.73912i	−0.112135	+	0.308090i	0.870913	+	0.491438i	$0.163529\pi$
$632$	−16.2491	+	20.0396i	−0.646355	+	0.797133i
$633$	7.60099	−	6.37799i	0.302112	−	0.253502i
$634$	0.195471	+	1.07337i	0.00776316	+	0.0426289i
$635$	−10.8999	+	18.8792i	−0.432550	+	0.749199i
$636$	38.4489	+	21.6276i	1.52460	+	0.857591i
$637$	14.1487	−	2.49479i	0.560591	−	0.0988473i
$638$	−9.24298	−	10.8908i	−0.365933	−	0.431172i
$639$	4.64732	+	8.04940i	0.183845	+	0.318429i
$640$	−30.1855	−	4.10951i	−1.19319	−	0.162443i
$641$	12.2993	+	33.7920i	0.485793	+	1.33471i	0.904457	+	0.426564i	$0.140276\pi$
$641$	12.2993	+	33.7920i	0.485793	+	1.33471i	−0.418664	+	0.908141i	$0.637502\pi$
$642$	−13.2865	+	16.0157i	−0.524377	+	0.632087i
$643$	−12.2592	+	14.6099i	−0.483454	+	0.576158i	−0.951540	−	0.307525i	$-0.900499\pi$
$643$	−12.2592	+	14.6099i	−0.483454	+	0.576158i	0.468086	+	0.883683i	$0.344944\pi$
$644$	14.8151	−	12.7170i	0.583796	−	0.501118i
$645$		−	4.79609i		−	0.188846i
$646$	−18.1383	+	32.0976i	−0.713642	+	1.26286i
$647$			44.0542i			1.73195i	0.500089	+	0.865974i	$0.333301\pi$
$647$			44.0542i			1.73195i	−0.500089	+	0.865974i	$0.666699\pi$
$648$	−6.40793	−	16.7254i	−0.251727	−	0.657035i
$649$	−10.5403	+	12.5614i	−0.413742	+	0.493079i
$650$	8.29058	+	6.87783i	0.325183	+	0.269771i
$651$	−8.57884	−	23.5702i	−0.336231	−	0.923787i
$652$	0.100810	+	8.99517i	0.00394802	+	0.352278i
$653$	−14.7359	−	25.5233i	−0.576660	−	0.998804i	−0.995859	−	0.0909095i	$-0.971023\pi$
$653$	−14.7359	−	25.5233i	−0.576660	−	0.998804i	0.419200	−	0.907894i	$-0.362311\pi$
$654$	21.9649	−	18.6415i	0.858897	−	0.728940i
$655$	14.3147	−	2.52406i	0.559320	−	0.0986232i
$656$	2.04265	+	5.24339i	0.0797519	+	0.204720i
$657$	19.4892	−	33.7563i	0.760347	−	1.31696i
$658$	15.1907	−	2.76638i	0.592195	−	0.107845i
$659$	−4.57370	+	3.83779i	−0.178166	+	0.149499i	−0.727510	−	0.686098i	$-0.759322\pi$
$659$	−4.57370	+	3.83779i	−0.178166	+	0.149499i	0.549344	+	0.835597i	$0.314878\pi$
$660$	15.7082	−	44.7106i	0.611440	−	1.74036i
$661$	14.8266	−	40.7359i	0.576690	−	1.58444i	−0.217034	−	0.976164i	$-0.569638\pi$
$661$	14.8266	−	40.7359i	0.576690	−	1.58444i	0.793724	−	0.608278i	$-0.208139\pi$
$662$	28.2037	−	16.4948i	1.09617	−	0.641089i
$663$	51.6697	+	9.11077i	2.00669	+	0.353833i
$664$	11.4080	+	19.0137i	0.442715	+	0.737876i
$665$	9.67989	−	16.9077i	0.375370	−	0.655651i
$666$	−3.95488	−	1.41441i	−0.153248	−	0.0548074i
$667$	3.03817	−	17.2303i	0.117639	−	0.667162i
$668$	−5.86263	−	31.1999i	−0.226832	−	1.20716i
$669$	57.9551	+	21.0939i	2.24067	+	0.815539i
$670$	−0.216756	−	38.6832i	−0.00837402	−	1.49446i
$671$	−8.27028	−	9.85613i	−0.319271	−	0.380492i
$672$	22.6272	−	8.96113i	0.872863	−	0.345683i
$673$	−29.6835	−	17.1378i	−1.14421	−	0.660613i	−0.196744	−	0.980455i	$-0.563037\pi$
$673$	−29.6835	−	17.1378i	−1.14421	−	0.660613i	−0.947471	+	0.319842i	$0.896370\pi$
$674$	−1.10378	+	6.47171i	−0.0425162	+	0.249281i
$675$	−0.726766	−	4.12169i	−0.0279732	−	0.158644i
$676$	2.88932	−	1.08845i	0.111128	−	0.0418634i
$677$	22.0117	−	12.7085i	0.845978	−	0.488425i	−0.0133139	−	0.999911i	$-0.504238\pi$
$677$	22.0117	−	12.7085i	0.845978	−	0.488425i	0.859292	+	0.511486i	$0.170905\pi$
$678$	−33.0634	+	12.2443i	−1.26979	+	0.470241i
$679$	13.3133	−	4.84565i	0.510918	−	0.185959i
$680$	44.7184	−	8.66251i	1.71487	−	0.332192i
$681$	−42.5393	−	35.6947i	−1.63011	−	1.36783i
$682$	13.8610	−	24.3216i	0.530764	−	0.931323i
$683$	−1.72512			−0.0660100			−0.0330050	−	0.999455i	$-0.510508\pi$
$683$	−1.72512			−0.0660100			−0.0330050	+	0.999455i	$0.510508\pi$
$684$	−20.4613	+	25.1331i	−0.782357	+	0.960986i
$685$	−31.0648			−1.18693
$686$	−13.0700	+	22.9338i	−0.499016	+	0.875615i
$687$	34.9569	+	29.3323i	1.33369	+	1.11910i
$688$	2.71716	+	0.416552i	0.103591	+	0.0158809i
$689$	27.0676	−	9.85181i	1.03119	−	0.375324i
$690$	54.4325	−	20.1579i	2.07221	−	0.767399i
$691$	14.5248	−	8.38589i	0.552549	−	0.319014i	−0.197601	−	0.980283i	$-0.563315\pi$
$691$	14.5248	−	8.38589i	0.552549	−	0.319014i	0.750149	+	0.661268i	$0.229982\pi$
$692$	−3.22918	−	8.57197i	−0.122755	−	0.325857i
$693$	3.63816	+	20.6330i	0.138202	+	0.783784i
$694$	−5.30329	+	31.0943i	−0.201310	+	1.18032i
$695$	−11.3450	−	6.55004i	−0.430340	−	0.248457i
$696$	10.5853	−	19.0675i	0.401236	−	0.722751i
$697$	−5.40828	−	6.44534i	−0.204853	−	0.244135i
$698$	−0.107734	−	19.2267i	−0.00407780	−	0.727740i
$699$	−28.3567	−	10.3210i	−1.07255	−	0.390376i
$700$	−7.34255	+	1.37971i	−0.277522	+	0.0521480i
$701$	1.08176	−	6.13496i	0.0408574	−	0.231714i	−0.957540	−	0.288299i	$-0.906910\pi$
$701$	1.08176	−	6.13496i	0.0408574	−	0.231714i	0.998398	+	0.0565853i	$0.0180213\pi$
$702$	8.38222	+	2.99780i	0.316366	+	0.113145i
$703$	−0.617165	−	3.42724i	−0.0232768	−	0.129261i
$704$	23.9659	+	12.7825i	0.903250	+	0.481758i
$705$	45.2063	+	7.97109i	1.70257	+	0.300209i
$706$	−30.6743	+	17.9397i	−1.15444	+	0.675171i
$707$	0.0643996	−	0.176936i	0.00242200	−	0.00665438i
$708$	−23.6200	−	8.29842i	−0.887694	−	0.311874i
$709$	34.9962	−	29.3653i	1.31431	−	1.10284i	0.326829	−	0.945083i	$-0.394020\pi$
$709$	34.9962	−	29.3653i	1.31431	−	1.10284i	0.987479	−	0.157752i	$-0.0504247\pi$
$710$	9.36673	−	1.70578i	0.351527	−	0.0640167i
$711$	16.9549	−	29.3667i	0.635858	−	1.10134i
$712$	−26.5581	+	23.0566i	−0.995306	+	0.864083i
$713$	33.7675	−	5.95412i	1.26460	−	0.222984i
$714$	−27.7438	+	23.5460i	−1.03829	+	0.881187i
$715$	−15.4718	−	26.7979i	−0.578611	−	1.00218i
$716$	−14.0279	+	0.157212i	−0.524246	+	0.00587527i
$717$	15.5037	+	42.5962i	0.578998	+	1.59078i
$718$	−10.7594	−	8.92598i	−0.401539	−	0.333115i
$719$	−30.0416	+	35.8022i	−1.12036	+	1.33520i	−0.184499	+	0.982833i	$0.559066\pi$
$719$	−30.0416	+	35.8022i	−1.12036	+	1.33520i	−0.935863	+	0.352363i	$0.885378\pi$
$720$	40.0304	−	0.897362i	1.49184	−	0.0334427i
$721$		−	11.1307i		−	0.414529i
$722$	−26.5197	−	4.32496i	−0.986961	−	0.160958i
$723$		−	70.4891i		−	2.62152i
$724$	2.96936	+	3.45927i	0.110355	+	0.128563i
$725$	−4.30339	+	5.12858i	−0.159824	+	0.190471i
$726$	−1.23444	+	1.48800i	−0.0458144	+	0.0552249i
$727$	−12.7241	−	34.9591i	−0.471910	−	1.29656i	−0.916215	−	0.400687i	$-0.868771\pi$
$727$	−12.7241	−	34.9591i	−0.471910	−	1.29656i	0.444305	−	0.895876i	$-0.353451\pi$
$728$	5.18329	−	15.0220i	0.192106	−	0.556751i
$729$	19.0009	+	32.9106i	0.703738	+	1.21891i
$730$	−25.8354	−	30.4414i	−0.956211	−	1.12669i
$731$	−4.04771	+	0.713721i	−0.149710	+	0.0263979i
$732$	9.63054	−	17.1209i	0.355955	−	0.632805i
$733$	−5.28816	+	9.15936i	−0.195323	+	0.338309i	−0.947006	−	0.321215i	$-0.895909\pi$
$733$	−5.28816	+	9.15936i	−0.195323	+	0.338309i	0.751684	+	0.659524i	$0.229242\pi$
$734$	7.99163	+	43.8835i	0.294976	+	1.61977i
$735$	−22.6926	+	19.0414i	−0.837030	+	0.702352i
$736$	6.69262	+	32.5888i	0.246693	+	1.20124i
$737$	−11.7964	+	32.4104i	−0.434527	+	1.19385i
$738$	−3.73391	−	6.38443i	−0.137447	−	0.235014i
$739$	−34.7564	−	6.12848i	−1.27853	−	0.225440i	−0.507176	−	0.861842i	$-0.669311\pi$
$739$	−34.7564	−	6.12848i	−1.27853	−	0.225440i	−0.771357	+	0.636402i	$0.780422\pi$
$740$	−2.72841	+	3.32660i	−0.100298	+	0.122288i
$741$	6.77689	+	37.6334i	0.248955	+	1.38250i
$742$	−6.72748	+	18.8109i	−0.246974	+	0.690570i
$743$	−3.19307	+	18.1088i	−0.117142	+	0.664348i	0.868525	+	0.495646i	$0.165069\pi$
$743$	−3.19307	+	18.1088i	−0.117142	+	0.664348i	−0.985667	+	0.168702i	$0.946043\pi$
$744$	42.2095	+	6.71317i	1.54747	+	0.246117i
$745$	−47.4172	−	17.2584i	−1.73723	−	0.632301i
$746$	−28.1051	+	0.157483i	−1.02900	+	0.00576588i
$747$	−18.7333	−	22.3254i	−0.685415	−	0.816845i
$748$	−40.0716	−	6.60357i	−1.46516	−	0.241450i
$749$	−8.16127	−	4.71191i	−0.298206	−	0.172169i
$750$	26.7511	+	4.56253i	0.976811	+	0.166600i
$751$	7.68759	+	43.5985i	0.280524	+	1.59093i	0.720848	+	0.693093i	$0.243752\pi$
$751$	7.68759	+	43.5985i	0.280524	+	1.59093i	−0.440324	+	0.897839i	$0.645137\pi$
$752$	−8.44219	+	24.9187i	−0.307855	+	0.908693i
$753$	−52.1009	+	30.0805i	−1.89866	+	1.09619i
$754$	−4.94532	−	13.3539i	−0.180098	−	0.486319i
$755$	−15.4628	+	5.62798i	−0.562747	+	0.204823i
$756$	−5.31203	+	3.14680i	−0.193197	+	0.114448i
$757$	−4.01307	−	3.36736i	−0.145857	−	0.122389i	0.566939	−	0.823760i	$-0.308127\pi$
$757$	−4.01307	−	3.36736i	−0.145857	−	0.122389i	−0.712797	+	0.701371i	$0.752572\pi$
$758$	44.8217	+	25.5440i	1.62800	+	0.927801i
$759$	−51.7531			−1.87852
$760$	17.1829	+	28.4044i	0.623290	+	1.03034i
$761$	−35.8399			−1.29919			−0.649597	−	0.760279i	$-0.725062\pi$
$761$	−35.8399			−1.29919			−0.649597	+	0.760279i	$0.725062\pi$
$762$	25.7821	+	14.6933i	0.933988	+	0.532283i
$763$	9.99425	+	8.38617i	0.361816	+	0.303600i
$764$	41.0449	−	24.3146i	1.48495	−	0.879672i
$765$	−56.2578	+	20.4762i	−2.03401	+	0.740318i
$766$	9.55047	+	25.7892i	0.345073	+	0.931800i
$767$	−14.1569	+	8.17351i	−0.511178	+	0.295128i
$768$	−5.36375	+	41.1208i	−0.193548	+	1.48382i
$769$	5.00228	+	28.3693i	0.180387	+	1.02302i	0.931740	+	0.363125i	$0.118290\pi$
$769$	5.00228	+	28.3693i	0.180387	+	1.02302i	−0.751354	+	0.659900i	$0.770599\pi$
$770$	21.1556	+	3.60819i	0.762393	+	0.130030i
$771$	20.0625	+	11.5831i	0.722535	+	0.417156i
$772$	31.9053	+	5.25781i	1.14830	+	0.189233i
$773$	1.14807	+	1.36822i	0.0412933	+	0.0492114i	0.786296	−	0.617850i	$-0.211996\pi$
$773$	1.14807	+	1.36822i	0.0412933	+	0.0492114i	−0.745003	+	0.667062i	$0.767552\pi$
$774$	−3.61298	+	0.0202449i	−0.129866	+	0.000727686i
$775$	−12.3292	−	4.48746i	−0.442878	−	0.161194i
$776$	−3.79185	+	23.8415i	−0.136119	+	0.855860i
$777$	0.596843	−	3.38486i	0.0214116	−	0.121431i
$778$	−4.58097	+	12.8090i	−0.164236	+	0.459224i
$779$	3.04674	−	5.32168i	0.109161	−	0.190669i
$780$	29.9598	−	36.5283i	1.07273	−	1.30792i
$781$	−8.35977	−	1.47405i	−0.299136	−	0.0527458i
$782$	−25.1128	−	42.9392i	−0.898031	−	1.53550i
$783$	−1.89230	+	5.19905i	−0.0676253	+	0.185799i
$784$	−8.81673	−	14.5100i	−0.314883	−	0.518214i
$785$	−8.06828	+	6.77009i	−0.287969	+	0.241635i
$786$	−3.54502	−	19.4663i	−0.126447	−	0.694340i
$787$	27.7835	−	48.1225i	0.990376	−	1.71538i	0.375327	−	0.926892i	$-0.377530\pi$
$787$	27.7835	−	48.1225i	0.990376	−	1.71538i	0.615049	−	0.788489i	$-0.289136\pi$
$788$	3.12613	−	5.55754i	0.111364	−	0.197979i
$789$	1.52005	−	0.268026i	0.0541152	−	0.00954198i
$790$	−22.4758	−	26.4829i	−0.799655	−	0.942219i
$791$	−7.98348	−	13.8278i	−0.283860	−	0.491660i
$792$	−33.7476	−	11.6445i	−1.19917	−	0.413770i
$793$	−4.38690	−	12.0529i	−0.155784	−	0.428012i
$794$	0.119484	−	0.144027i	0.00424034	−	0.00511134i
$795$	−38.1767	+	45.4972i	−1.35399	+	1.61362i
$796$	14.8753	+	17.3295i	0.527241	+	0.614228i
$797$		−	21.8514i		−	0.774016i	−0.922076	−	0.387008i	$-0.873509\pi$
$797$		−	21.8514i		−	0.774016i	0.922076	−	0.387008i	$-0.126491\pi$
$798$	−23.0891	−	13.0476i	−0.817345	−	0.461880i
$799$		−	39.3385i		−	1.39170i
$800$	4.01721	−	12.0799i	0.142030	−	0.427088i
$801$	29.7135	−	35.4112i	1.04987	−	1.25119i
$802$	2.11303	+	1.75296i	0.0746136	+	0.0618991i
$803$	12.1755	+	33.4519i	0.429663	+	1.18049i
$804$	−52.6551	+	0.590111i	−1.85700	+	0.0208116i
$805$	13.1432	+	22.7648i	0.463239	+	0.802353i
$806$	21.2775	−	18.0581i	0.749467	−	0.636068i
$807$	−26.3193	+	4.64080i	−0.926482	+	0.163364i
$808$	0.210335	+	0.242277i	0.00739954	+	0.00852327i
$809$	−1.75120	+	3.03317i	−0.0615690	+	0.106641i	−0.895167	−	0.445731i	$-0.852944\pi$
$809$	−1.75120	+	3.03317i	−0.0615690	+	0.106641i	0.833598	+	0.552372i	$0.186277\pi$
$810$	23.7238	−	4.32035i	0.833570	−	0.151802i
$811$	10.9054	−	9.15072i	0.382941	−	0.321325i	−0.430915	−	0.902393i	$-0.641809\pi$
$811$	10.9054	−	9.15072i	0.382941	−	0.321325i	0.813856	+	0.581067i	$0.197365\pi$
$812$	9.31799	+	3.27369i	0.326997	+	0.114884i
$813$	10.4641	−	28.7499i	0.366992	−	1.00830i
$814$	3.31128	−	1.93659i	0.116060	−	0.0678773i
$815$	−11.9272	−	2.10309i	−0.417793	−	0.0736682i
$816$	−12.1328	−	60.8060i	−0.424732	−	2.12863i
$817$	−1.50719	−	2.58876i	−0.0527300	−	0.0905693i
$818$	36.5693	+	13.0786i	1.27862	+	0.457281i
$819$	−3.62690	+	20.5692i	−0.126734	+	0.718745i
$820$	−7.44578	+	1.39910i	−0.260018	+	0.0488588i
$821$	7.20202	+	2.62132i	0.251352	+	0.0914847i	0.464624	−	0.885508i	$-0.346190\pi$
$821$	7.20202	+	2.62132i	0.251352	+	0.0914847i	−0.213271	+	0.976993i	$0.568412\pi$
$822$	0.236946	+	42.2864i	0.00826446	+	1.47491i
$823$	−0.679981	−	0.810370i	−0.0237027	−	0.0282477i	0.754063	−	0.656802i	$-0.228091\pi$
$823$	−0.679981	−	0.810370i	−0.0237027	−	0.0282477i	−0.777766	+	0.628554i	$0.783647\pi$
$824$	16.5823	+	9.20566i	0.577671	+	0.320694i
$825$	17.1502	+	9.90164i	0.597092	+	0.344731i
$826$	1.90616	−	11.1762i	0.0663236	−	0.388869i
$827$	−4.31460	−	24.4693i	−0.150033	−	0.850881i	−0.963187	−	0.268832i	$-0.913362\pi$
$827$	−4.31460	−	24.4693i	−0.150033	−	0.850881i	0.813154	−	0.582049i	$-0.197749\pi$
$828$	−15.4151	−	40.9199i	−0.535711	−	1.42206i
$829$	−7.34481	+	4.24053i	−0.255096	+	0.147280i	−0.622095	−	0.782941i	$-0.713718\pi$
$829$	−7.34481	+	4.24053i	−0.255096	+	0.147280i	0.367000	+	0.930221i	$0.380385\pi$
$830$	−27.9948	+	10.3673i	−0.971715	+	0.359854i
$831$	68.7319	−	25.0164i	2.38428	−	0.867808i
$832$	18.0926	+	20.1459i	0.627247	+	0.698434i
$833$	19.4471	+	16.3181i	0.673803	+	0.565388i
$834$	−8.82958	+	15.4931i	−0.305743	+	0.536483i
$835$	42.7405			1.47910
$836$	−5.57179	−	29.0696i	−0.192704	−	1.00539i
$837$	−10.8428			−0.374784
$838$	4.43978	−	7.79040i	0.153370	−	0.269115i
$839$	6.60696	+	5.54389i	0.228097	+	0.191396i	0.749673	−	0.661809i	$-0.230211\pi$
$839$	6.60696	+	5.54389i	0.228097	+	0.191396i	−0.521575	+	0.853205i	$0.674655\pi$
$840$	6.23130	+	32.1677i	0.215000	+	1.10989i
$841$	−18.9345	+	6.89161i	−0.652915	+	0.237642i
$842$	−15.4565	+	5.72399i	−0.532666	+	0.197262i
$843$	−11.3951	+	6.57897i	−0.392468	+	0.226592i
$844$	−7.16513	+	2.69920i	−0.246634	+	0.0929105i
$845$	0.721830	+	4.09370i	0.0248317	+	0.140828i
$846$	5.81394	−	34.0883i	0.199887	−	1.17198i
$847$	−0.758257	−	0.437780i	−0.0260540	−	0.0150423i
$848$	−22.4601	−	25.5801i	−0.771284	−	0.878423i
$849$	−7.46632	−	8.89801i	−0.256243	−	0.305379i
$850$	0.106655	+	19.0341i	0.00365823	+	0.652863i
$851$	4.41516	+	1.60699i	0.151350	+	0.0550868i
$852$	−2.39340	−	12.7373i	−0.0819966	−	0.436372i
$853$	1.20460	−	6.83164i	0.0412448	−	0.233911i	−0.957216	−	0.289375i	$-0.906553\pi$
$853$	1.20460	−	6.83164i	0.0412448	−	0.233911i	0.998461	+	0.0554639i	$0.0176638\pi$
$854$	8.37629	+	2.99567i	0.286631	+	0.102510i
$855$	−28.1681	−	33.3227i	−0.963328	−	1.13961i
$856$	13.7695	−	8.26150i	0.470632	−	0.282372i
$857$	−9.28874	−	1.63785i	−0.317297	−	0.0559481i	0.0127315	−	0.999919i	$-0.495947\pi$
$857$	−9.28874	−	1.63785i	−0.317297	−	0.0559481i	−0.330029	+	0.943971i	$0.607058\pi$
$858$	−36.3601	+	21.2650i	−1.24131	+	0.725977i
$859$	2.83749	−	7.79595i	0.0968140	−	0.265994i	−0.881826	−	0.471574i	$-0.843686\pi$
$859$	2.83749	−	7.79595i	0.0968140	−	0.265994i	0.978640	+	0.205580i	$0.0659081\pi$
$860$	−1.22674	+	3.49171i	−0.0418316	+	0.119066i
$861$	4.63639	−	3.89040i	0.158008	−	0.132584i
$862$	31.0616	−	5.65663i	1.05796	−	0.192666i
$863$	−11.3225	+	19.6112i	−0.385423	+	0.667573i	−0.991828	−	0.127584i	$-0.959278\pi$
$863$	−11.3225	+	19.6112i	−0.385423	+	0.667573i	0.606405	+	0.795156i	$0.292611\pi$
$864$	−0.294708	−	10.5163i	−0.0100262	−	0.357773i
$865$	12.1451	−	2.14151i	0.412945	−	0.0728134i
$866$	20.6636	−	17.5371i	0.702178	−	0.595934i
$867$	24.3240	+	42.1304i	0.826087	+	1.43082i
$868$	0.216904	+	19.3541i	0.00736219	+	0.656922i
$869$	10.5922	+	29.1019i	0.359316	+	0.987213i
$870$	22.5978	+	18.7470i	0.766136	+	0.635583i
$871$	−22.1014	+	26.3395i	−0.748878	+	0.892478i
$872$	−20.7593	+	7.95343i	−0.702999	+	0.269337i
$873$		−	31.7300i		−	1.07390i
$874$	23.0461	−	27.9862i	0.779545	−	0.946648i
$875$			12.2895i			0.415461i
$876$	−41.2407	+	35.4002i	−1.39339	+	1.19606i
$877$	12.8658	−	15.3329i	0.434448	−	0.517755i	−0.503752	−	0.863848i	$-0.668048\pi$
$877$	12.8658	−	15.3329i	0.434448	−	0.517755i	0.938200	+	0.346094i	$0.112492\pi$
$878$	3.31914	−	4.00091i	0.112016	−	0.135024i
$879$	20.2092	+	55.5242i	0.681638	+	1.87279i
$880$	−22.8721	+	28.5330i	−0.771020	+	0.961846i
$881$	−2.29906	−	3.98208i	−0.0774572	−	0.134160i	0.824695	−	0.565578i	$-0.191347\pi$
$881$	−2.29906	−	3.98208i	−0.0774572	−	0.134160i	−0.902152	+	0.431418i	$0.858013\pi$
$882$	14.4400	+	17.0144i	0.486220	+	0.572904i
$883$	24.2556	−	4.27692i	0.816266	−	0.143930i	0.250099	−	0.968220i	$-0.419537\pi$
$883$	24.2556	−	4.27692i	0.816266	−	0.143930i	0.566167	+	0.824291i	$0.308426\pi$
$884$	−35.2869	−	19.8490i	−1.18683	−	0.667594i
$885$	16.8529	−	29.1901i	0.566505	−	0.981215i
$886$	−5.68237	−	31.2029i	−0.190903	−	1.04828i
$887$	34.9136	−	29.2960i	1.17229	−	0.983664i	0.172286	−	0.985047i	$-0.444885\pi$
$887$	34.9136	−	29.2960i	1.17229	−	0.983664i	0.999999	+	0.00138259i	$0.000440093\pi$
$888$	4.54908	+	3.68862i	0.152657	+	0.123782i
$889$	−4.59632	+	12.6283i	−0.154156	+	0.423539i
$890$	−23.9047	−	40.8735i	−0.801288	−	1.37008i
$891$	−21.1734	−	3.73344i	−0.709336	−	0.125075i
$892$	−36.7978	−	30.1808i	−1.23208	−	1.01053i
$893$	26.9057	−	9.90377i	0.900366	−	0.331417i
$894$	−23.1311	+	64.6774i	−0.773619	+	2.16314i
$895$	3.27975	−	18.6004i	0.109630	−	0.621742i
$896$	−18.7654	+	0.736417i	−0.626908	+	0.0246020i
$897$	−48.4815	−	17.6458i	−1.61875	−	0.589177i
$898$	53.1767	−	0.297969i	1.77453	−	0.00994335i
$899$	11.1489	+	13.2867i	0.371835	+	0.443136i
$900$	−2.72067	+	16.5095i	−0.0906889	+	0.550316i
$901$	44.0791	+	25.4491i	1.46849	+	0.847831i
$902$	6.65869	+	1.13567i	0.221710	+	0.0378138i
$903$	−0.513408	−	2.91168i	−0.0170852	−	0.0968947i
$904$	27.2031	−	0.457326i	0.904762	−	0.0152104i
$905$	−5.31549	+	3.06890i	−0.176693	+	0.102014i
$906$	7.77893	+	21.0055i	0.258438	+	0.697860i
$907$	−5.54925	+	2.01976i	−0.184260	+	0.0670651i	−0.432502	−	0.901633i	$-0.642369\pi$
$907$	−5.54925	+	2.01976i	−0.184260	+	0.0670651i	0.248242	+	0.968698i	$0.420147\pi$
$908$	21.8400	+	36.8676i	0.724787	+	1.22350i
$909$	−0.323039	−	0.271062i	−0.0107145	−	0.00899057i
$910$	18.5879	+	10.5933i	0.616184	+	0.351165i
$911$	19.1178			0.633401			0.316700	−	0.948526i	$-0.397425\pi$
$911$	19.1178			0.633401			0.316700	+	0.948526i	$0.397425\pi$
$912$	38.5339	−	23.6066i	1.27599	−	0.781693i
$913$	26.6168			0.880888
$914$	−49.9439	−	28.4632i	−1.65200	−	0.941480i
$915$	20.2594	+	16.9997i	0.669756	+	0.561992i
$916$	−17.9471	−	30.2961i	−0.592990	−	1.00101i
$917$	8.42017	−	3.06469i	0.278059	−	0.101205i
$918$	5.46277	+	14.7511i	0.180298	+	0.486859i
$919$	31.2360	−	18.0341i	1.03038	−	0.594890i	0.113286	−	0.993562i	$-0.463862\pi$
$919$	31.2360	−	18.0341i	1.03038	−	0.594890i	0.917093	+	0.398673i	$0.130529\pi$
$920$	−44.7846	+	0.752898i	−1.47651	+	0.0248223i
$921$	−15.2652	−	86.5734i	−0.503006	−	2.85269i
$922$	41.3838	+	7.05821i	1.36290	+	0.232450i
$923$	−7.32871	−	4.23123i	−0.241227	−	0.139273i
$924$	4.75022	−	28.8251i	0.156271	−	0.948277i
$925$	−1.15566	−	1.37726i	−0.0379978	−	0.0452840i
$926$	−26.2166	+	0.146901i	−0.861531	+	0.00482748i
$927$	−23.4249	−	8.52597i	−0.769375	−	0.280030i
$928$	−12.5835	+	11.1742i	−0.413075	+	0.366813i
$929$	−2.58424	+	14.6560i	−0.0847862	+	0.480846i	0.912616	+	0.408817i	$0.134059\pi$
$929$	−2.58424	+	14.6560i	−0.0847862	+	0.480846i	−0.997403	+	0.0720292i	$0.977053\pi$
$930$	−19.3773	+	54.1814i	−0.635406	+	1.77668i
$931$	−6.26485	+	17.4091i	−0.205322	+	0.570561i
$932$	18.0047	+	14.7671i	0.589764	+	0.483713i
$933$	46.1394	+	8.13562i	1.51054	+	0.266348i
$934$	18.4814	+	31.6005i	0.604729	+	1.03400i
$935$	18.7007	−	51.3799i	0.611580	−	1.68030i
$936$	−27.6439	−	22.4150i	−0.903569	−	0.732659i
$937$	24.7907	−	20.8019i	0.809877	−	0.679568i	−0.140701	−	0.990052i	$-0.544936\pi$
$937$	24.7907	−	20.8019i	0.809877	−	0.679568i	0.950579	+	0.310484i	$0.100491\pi$
$938$	−4.27252	−	23.4612i	−0.139503	−	0.766034i
$939$	0.752635	−	1.30360i	0.0245613	−	0.0425414i
$940$	−30.8728	−	17.3661i	−1.00696	−	0.566419i
$941$	−22.0071	+	3.88045i	−0.717411	+	0.126499i	−0.520425	−	0.853907i	$-0.674226\pi$
$941$	−22.0071	+	3.88045i	−0.717411	+	0.126499i	−0.196986	+	0.980406i	$0.563115\pi$
$942$	9.27720	+	10.9312i	0.302267	+	0.356156i
$943$	4.13683	+	7.16519i	0.134714	+	0.233331i
$944$	15.0736	+	12.0830i	0.490603	+	0.393269i
$945$	−2.84302	−	7.81114i	−0.0924835	−	0.254096i
$946$	2.10685	−	2.53961i	0.0684995	−	0.0825697i
$947$	35.4036	−	42.1924i	1.15046	−	1.37107i	0.233374	−	0.972387i	$-0.425023\pi$
$947$	35.4036	−	42.1924i	1.15046	−	1.37107i	0.917089	−	0.398682i	$-0.130532\pi$
$948$	−35.8779	+	30.7968i	−1.16526	+	1.00023i
$949$			35.4885i			1.15201i
$950$	−12.9916	+	4.86491i	−0.421502	+	0.157838i
$951$			1.99951i			0.0648386i
$952$	26.2210	−	10.0460i	0.849828	−	0.325591i
$953$	−4.51618	+	5.38217i	−0.146293	+	0.174346i	−0.834215	−	0.551439i	$-0.814079\pi$
$953$	−4.51618	+	5.38217i	−0.146293	+	0.174346i	0.687922	+	0.725785i	$0.258523\pi$
$954$	34.4350	+	28.5671i	1.11487	+	0.924895i
$955$	21.9674	+	60.3550i	0.710849	+	1.95304i
$956$	−0.391990	−	34.9770i	−0.0126779	−	1.13124i
$957$	−13.0894	−	22.6716i	−0.423122	−	0.732868i
$958$	0.470229	−	0.399080i	0.0151924	−	0.0128937i
$959$	−18.8593	+	3.32540i	−0.608998	+	0.107383i
$960$	−53.0764	−	17.3211i	−1.71303	−	0.559036i
$961$	−1.49565	+	2.59055i	−0.0482469	+	0.0835661i
$962$	3.76225	−	0.685145i	0.121300	−	0.0220900i
$963$	−16.1678	+	13.5664i	−0.521000	+	0.437171i
$964$	−18.0297	+	51.3184i	−0.580697	+	1.65285i
$965$	−14.8897	+	40.9090i	−0.479315	+	1.31691i
$966$	30.8879	−	18.0646i	0.993801	−	0.581220i
$967$	−33.5782	−	5.92074i	−1.07980	−	0.190398i	−0.394674	−	0.918821i	$-0.629142\pi$
$967$	−33.5782	−	5.92074i	−1.07980	−	0.190398i	−0.685127	+	0.728423i	$0.740253\pi$
$968$	1.27931	−	0.767570i	0.0411187	−	0.0246706i
$969$	−43.2434	+	51.9175i	−1.38918	+	1.66783i
$970$	−30.6037	−	10.9450i	−0.982624	−	0.351423i
$971$	−0.272182	+	1.54362i	−0.00873472	+	0.0495371i	−0.988864	−	0.148825i	$-0.952451\pi$
$971$	−0.272182	+	1.54362i	−0.00873472	+	0.0495371i	0.980129	+	0.198362i	$0.0635621\pi$
$972$	−8.12265	−	43.2273i	−0.260534	−	1.38652i
$973$	−7.58866	−	2.76205i	−0.243281	−	0.0885471i
$974$	−0.0424018	−	7.56718i	−0.00135864	−	0.242468i
$975$	12.6899	+	15.1232i	0.406402	+	0.484332i
$976$	−11.3905	+	10.0012i	−0.364602	+	0.320132i
$977$	−15.5733	−	8.99124i	−0.498233	−	0.287655i	0.229750	−	0.973250i	$-0.426209\pi$
$977$	−15.5733	−	8.99124i	−0.498233	−	0.287655i	−0.727984	+	0.685594i	$0.759542\pi$
$978$	−2.77182	+	16.2518i	−0.0886331	+	0.519675i
$979$	7.33105	+	41.5765i	0.234301	+	1.32879i
$980$	21.3914	−	8.05843i	0.683322	−	0.257417i
$981$	25.3044	−	14.6095i	0.807909	−	0.466446i
$982$	−35.4724	+	13.1364i	−1.13197	+	0.419201i
$983$	47.5857	−	17.3198i	1.51775	−	0.552415i	0.557163	−	0.830403i	$-0.311890\pi$
$983$	47.5857	−	17.3198i	1.51775	−	0.552415i	0.960584	+	0.277988i	$0.0896677\pi$
$984$	1.96130	+	10.1248i	0.0625238	+	0.322766i
$985$	6.57633	+	5.51820i	0.209539	+	0.175824i
$986$	12.4589	−	21.8614i	0.396772	−	0.696210i
$987$	28.2978			0.900729
$988$	4.69206	−	29.1317i	0.149274	−	0.926804i
$989$	4.04170			0.128518
$990$	23.7984	−	41.7587i	0.756364	−	1.32718i
$991$	−3.54873	−	2.97774i	−0.112729	−	0.0945911i	0.584681	−	0.811264i	$-0.301220\pi$
$991$	−3.54873	−	2.97774i	−0.112729	−	0.0945911i	−0.697410	+	0.716672i	$0.745664\pi$
$992$	−29.0128	−	15.6837i	−0.921157	−	0.497959i
$993$	56.2686	−	20.4801i	1.78563	−	0.649916i
$994$	5.50390	−	2.03825i	0.174573	−	0.0646494i
$995$	−26.6284	+	15.3739i	−0.844178	+	0.487386i
$996$	14.3258	+	38.0284i	0.453931	+	1.20498i
$997$	8.73220	+	49.5228i	0.276551	+	1.56840i	0.733990	+	0.679160i	$0.237656\pi$
$997$	8.73220	+	49.5228i	0.276551	+	1.56840i	−0.457439	+	0.889241i	$0.651233\pi$
$998$	1.07311	−	6.29185i	0.0339686	−	0.199165i
$999$	−1.28673	−	0.742893i	−0.0407103	−	0.0235041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.59.2	yes	48
3.2	odd	2		684.2.cf.a.667.7		48
4.3	odd	2	inner	76.2.k.a.59.1	✓	48
12.11	even	2		684.2.cf.a.667.8		48
19.10	odd	18	inner	76.2.k.a.67.1	yes	48
57.29	even	18		684.2.cf.a.523.8		48
76.67	even	18	inner	76.2.k.a.67.2	yes	48
228.143	odd	18		684.2.cf.a.523.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.1	✓	48	4.3	odd	2	inner
76.2.k.a.59.2	yes	48	1.1	even	1	trivial
76.2.k.a.67.1	yes	48	19.10	odd	18	inner
76.2.k.a.67.2	yes	48	76.67	even	18	inner
684.2.cf.a.523.7		48	228.143	odd	18
684.2.cf.a.523.8		48	57.29	even	18
684.2.cf.a.667.7		48	3.2	odd	2
684.2.cf.a.667.8		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22869 - 0.700233i) q^{2} +(-1.98545 - 1.66599i) q^{3} +(1.01935 + 1.72074i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(1.27292 + 3.43726i) q^{6} +(-1.43753 + 0.829960i) q^{7} +(-0.0475435 - 2.82803i) q^{8} +(0.645546 + 3.66107i) q^{9} +O(q^{10})\)	\(q+(-1.22869 - 0.700233i) q^{2} +(-1.98545 - 1.66599i) q^{3} +(1.01935 + 1.72074i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(1.27292 + 3.43726i) q^{6} +(-1.43753 + 0.829960i) q^{7} +(-0.0475435 - 2.82803i) q^{8} +(0.645546 + 3.66107i) q^{9} +(3.75379 + 0.640228i) q^{10} +(-2.94034 - 1.69761i) q^{11} +(0.842867 - 5.11466i) q^{12} +(-2.17565 - 2.59283i) q^{13} +(2.34744 - 0.0131536i) q^{14} +(6.55803 + 2.38693i) q^{15} +(-1.92186 + 3.50805i) q^{16} +(1.03855 - 5.88992i) q^{17} +(1.77043 - 4.95035i) q^{18} +(4.28990 - 0.772510i) q^{19} +(-4.16393 - 3.41517i) q^{20} +(4.23686 + 0.747073i) q^{21} +(2.42404 + 4.14475i) q^{22} +(-2.01148 + 5.52649i) q^{23} +(-4.61708 + 5.69412i) q^{24} +(1.72393 - 1.44655i) q^{25} +(0.857602 + 4.70924i) q^{26} +(0.929885 - 1.61061i) q^{27} +(-2.89349 - 1.62760i) q^{28} +(-2.92975 + 0.516594i) q^{29} +(-6.38636 - 7.52493i) q^{30} +(-2.91510 - 5.04911i) q^{31} +(4.81782 - 2.96455i) q^{32} +(3.00971 + 8.26910i) q^{33} +(-5.40038 + 6.50965i) q^{34} +(2.87301 - 3.42391i) q^{35} +(-5.64171 + 4.84272i) q^{36} -0.798908i q^{37} +(-5.81188 - 2.05476i) q^{38} +8.77256i q^{39} +(2.72475 + 7.11190i) q^{40} +(0.904276 - 1.07767i) q^{41} +(-4.68265 - 3.88471i) q^{42} +(-0.235045 - 0.645782i) q^{43} +(-0.0760962 - 6.79000i) q^{44} +(-5.00506 - 8.66901i) q^{45} +(6.34131 - 5.38183i) q^{46} +(6.47756 - 1.14217i) q^{47} +(9.66016 - 3.76327i) q^{48} +(-2.12233 + 3.67599i) q^{49} +(-3.13109 + 0.570203i) q^{50} +(-11.8746 + 9.96394i) q^{51} +(2.24384 - 6.38671i) q^{52} +(-2.91069 + 7.99704i) q^{53} +(-2.27034 + 1.32780i) q^{54} +(9.00327 + 1.58752i) q^{55} +(2.41550 + 4.02592i) q^{56} +(-9.80439 - 5.61316i) q^{57} +(3.96148 + 1.41677i) q^{58} +(0.838664 - 4.75630i) q^{59} +(2.57764 + 13.7177i) q^{60} +(3.56100 + 1.29610i) q^{61} +(0.0462000 + 8.24503i) q^{62} +(-3.96654 - 4.72714i) q^{63} +(-7.99548 + 0.268908i) q^{64} +(7.89284 + 4.55693i) q^{65} +(2.09231 - 12.2676i) q^{66} +(-1.76401 - 10.0042i) q^{67} +(11.1936 - 4.21680i) q^{68} +(13.2008 - 7.62148i) q^{69} +(-5.92757 + 2.19515i) q^{70} +(2.34943 - 0.855121i) q^{71} +(10.3229 - 1.99968i) q^{72} +(-8.03196 - 6.73961i) q^{73} +(-0.559422 + 0.981609i) q^{74} -5.83271 q^{75} +(5.70218 + 6.59433i) q^{76} +5.63578 q^{77} +(6.14284 - 10.7787i) q^{78} +(-6.98750 - 5.86321i) q^{79} +(1.63212 - 10.6463i) q^{80} +(5.95057 - 2.16583i) q^{81} +(-1.86570 + 0.690921i) q^{82} +(-6.78922 + 3.91976i) q^{83} +(3.03332 + 8.05204i) q^{84} +(2.79647 + 15.8596i) q^{85} +(-0.163400 + 0.958050i) q^{86} +(6.67752 + 3.85527i) q^{87} +(-4.66108 + 8.39607i) q^{88} +(-7.99275 - 9.52539i) q^{89} +(0.0793226 + 14.1562i) q^{90} +(5.27951 + 1.92159i) q^{91} +(-11.5600 + 2.17219i) q^{92} +(-2.62398 + 14.8813i) q^{93} +(-8.75868 - 3.13243i) q^{94} +(-10.1432 + 5.90542i) q^{95} +(-14.5045 - 2.14048i) q^{96} +(-8.40551 - 1.48212i) q^{97} +(5.18173 - 3.03051i) q^{98} +(4.31694 - 11.8607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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