LMFDB - Embedded newform 76.2.k.a.67.2

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			67.2
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.2

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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	−0.999627	−	0.0273235i	$-0.991302\pi$
$3$	−1.98545	+	1.66599i	−1.14630	+	0.961861i	−0.146675	+	0.989185i	$0.546857\pi$
$4$	1.01935	−	1.72074i	0.509674	−	0.860368i
$5$	−2.53027	−	0.920944i	−1.13157	−	0.411859i	−0.292710	−	0.956201i	$-0.594557\pi$
$5$	−2.53027	−	0.920944i	−1.13157	−	0.411859i	−0.838863	+	0.544342i	$0.816779\pi$
$6$	1.27292	−	3.43726i	0.519667	−	1.40326i
$7$	−1.43753	−	0.829960i	−0.543336	−	0.313695i	0.203094	−	0.979159i	$-0.434900\pi$
$7$	−1.43753	−	0.829960i	−0.543336	−	0.313695i	−0.746430	+	0.665464i	$0.768234\pi$
$8$	−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	−0.872811	−	0.488058i	$-0.837705\pi$
$11$	−2.94034	+	1.69761i	−0.886546	+	0.511848i	−0.0137349	+	0.999906i	$0.504372\pi$
$12$	0.842867	+	5.11466i	0.243315	+	1.47648i
$13$	−2.17565	+	2.59283i	−0.603416	+	0.719123i	−0.978125	−	0.208020i	$-0.933298\pi$
$13$	−2.17565	+	2.59283i	−0.603416	+	0.719123i	0.374709	+	0.927143i	$0.377743\pi$
$14$	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	0.803941	+	0.594709i	$0.202733\pi$
$17$	1.03855	+	5.88992i	0.251886	+	1.42852i	−0.552055	+	0.833808i	$0.686156\pi$
$18$	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	−0.952034	−	0.305993i	$-0.901011\pi$
$23$	−2.01148	−	5.52649i	−0.419422	−	1.15235i	0.532611	−	0.846360i	$-0.321211\pi$
$24$	−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	−0.105128	−	0.994459i	$-0.533525\pi$
$29$	−2.92975	−	0.516594i	−0.544040	−	0.0959290i	−0.438913	+	0.898530i	$0.644636\pi$
$30$	−6.38636	+	7.52493i	−1.16598	+	1.37386i
$31$	−2.91510	+	5.04911i	−0.523568	+	0.906846i	0.476056	+	0.879415i	$0.342066\pi$
$31$	−2.91510	+	5.04911i	−0.523568	+	0.906846i	−0.999624	+	0.0274312i	$0.991267\pi$
$32$	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	$0.0209184\pi$
$37$			0.798908i			0.131340i	−0.997841	+	0.0656699i	$0.979082\pi$
$38$	−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	0.832020	−	0.554745i	$-0.187184\pi$
$41$	0.904276	+	1.07767i	0.141224	+	0.168304i	−0.690796	+	0.723050i	$0.742740\pi$
$42$	−4.68265	+	3.88471i	−0.722549	+	0.599424i
$43$	−0.235045	+	0.645782i	−0.0358441	+	0.0984808i	−0.956324	−	0.292310i	$-0.905576\pi$
$43$	−0.235045	+	0.645782i	−0.0358441	+	0.0984808i	0.920480	+	0.390791i	$0.127798\pi$
$44$	−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	0.624788	−	0.780794i	$-0.285185\pi$
$47$	6.47756	+	1.14217i	0.944849	+	0.166602i	0.320061	+	0.947397i	$0.396296\pi$
$48$	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	−0.962375	−	0.271723i	$-0.912406\pi$
$53$	−2.91069	−	7.99704i	−0.399813	−	1.09848i	0.562562	−	0.826755i	$-0.309816\pi$
$54$	−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	0.989466	+	0.144765i	$0.0462428\pi$
$59$	0.838664	+	4.75630i	0.109185	+	0.619218i	−0.880281	+	0.474452i	$0.842646\pi$
$60$	2.57764	−	13.7177i	0.332771	−	1.77095i
$61$	3.56100	−	1.29610i	0.455939	−	0.165948i	−0.103833	−	0.994595i	$-0.533111\pi$
$61$	3.56100	−	1.29610i	0.455939	−	0.165948i	0.559772	+	0.828647i	$0.310889\pi$
$62$	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	0.664513	+	0.747277i	$0.268639\pi$
$67$	−1.76401	+	10.0042i	−0.215509	+	1.22221i	−0.880022	+	0.474934i	$0.842472\pi$
$68$	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	0.477648	−	0.878551i	$-0.341489\pi$
$71$	2.34943	+	0.855121i	0.278825	+	0.101484i	−0.198822	+	0.980036i	$0.563712\pi$
$72$	10.3229	+	1.99968i	1.21657	+	0.235665i
$73$	−8.03196	+	6.73961i	−0.940069	+	0.788812i	−0.977597	−	0.210484i	$-0.932496\pi$
$73$	−8.03196	+	6.73961i	−0.940069	+	0.788812i	0.0375281	+	0.999296i	$0.488052\pi$
$74$	−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	−0.944791	−	0.327674i	$-0.893735\pi$
$79$	−6.98750	+	5.86321i	−0.786156	+	0.659663i	0.158635	+	0.987337i	$0.449291\pi$
$80$	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	0.0787485	−	0.996895i	$-0.474908\pi$
$83$	−6.78922	−	3.91976i	−0.745213	−	0.430249i	−0.823962	+	0.566645i	$0.808241\pi$
$84$	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	0.152541	+	0.988297i	$0.451254\pi$
$89$	−7.99275	+	9.52539i	−0.847230	+	1.00969i	−0.999771	+	0.0213925i	$0.993190\pi$
$90$	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	−0.583225	−	0.812311i	$-0.698209\pi$
$97$	−8.40551	+	1.48212i	−0.853451	+	0.150486i	−0.270226	+	0.962797i	$0.587098\pi$
$98$	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	0.638454	−	0.769660i	$-0.279574\pi$
$101$	−0.0868957	−	0.0729142i	−0.00864645	−	0.00725523i	−0.647101	+	0.762405i	$0.724019\pi$
$102$	21.5672	+	3.92761i	2.13547	+	0.388892i
$103$	−3.35278	−	5.80718i	−0.330359	−	0.572199i	0.652223	−	0.758027i	$-0.273837\pi$
$103$	−3.35278	−	5.80718i	−0.330359	−	0.572199i	−0.982582	+	0.185828i	$0.940503\pi$
$104$	−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	−0.695568	−	0.718461i	$-0.744847\pi$
$107$	2.83864	−	4.91666i	0.274421	−	0.475312i	0.969989	+	0.243149i	$0.0781804\pi$
$108$	3.71931	+	0.0416827i	0.357891	+	0.00401091i
$109$	−2.68819	+	7.38575i	−0.257482	+	0.707427i	0.741839	+	0.670579i	$0.233954\pi$
$109$	−2.68819	+	7.38575i	−0.257482	+	0.707427i	−0.999321	+	0.0368484i	$0.988268\pi$
$110$	−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	$-0.850552\pi$
$113$		−	9.61911i		−	0.904890i	0.891792	−	0.452445i	$-0.149448\pi$
$114$	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	0.875053	−	0.484027i	$-0.160826\pi$
$127$	6.20191	+	5.20402i	0.550331	+	0.461782i	−0.324722	+	0.945809i	$0.605271\pi$
$128$	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	−0.400989	−	0.916083i	$-0.631333\pi$
$131$	−5.31618	+	0.937385i	−0.464476	+	0.0818997i	−0.0634875	+	0.997983i	$0.520222\pi$
$132$	−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	0.165507	−	0.986209i	$-0.447074\pi$
$137$	10.8411	−	3.94583i	0.926216	−	0.337115i	0.760709	+	0.649093i	$0.224852\pi$
$138$	−21.5565	−	0.120789i	−1.83501	−	0.0102822i
$139$	3.12723	−	3.72688i	0.265248	−	0.316110i	−0.616938	−	0.787012i	$-0.711627\pi$
$139$	3.12723	−	3.72688i	0.265248	−	0.316110i	0.882186	+	0.470902i	$0.156071\pi$
$140$	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	0.176062	−	0.984379i	$-0.443664\pi$
$149$	14.3556	−	12.0458i	1.17606	−	0.986831i	0.999997	−	0.00245146i	$-0.000780324\pi$
$150$	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	0.484501	−	0.874790i	$-0.339001\pi$
$157$	3.67562	+	1.33782i	0.293347	+	0.106769i	−0.191155	+	0.981560i	$0.561223\pi$
$158$	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	−0.339631	−	0.940559i	$-0.610302\pi$
$163$	3.89527	−	2.24893i	0.305101	−	0.176150i	0.644732	+	0.764409i	$0.276969\pi$
$164$	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	−0.847026	−	0.531551i	$-0.821609\pi$
$167$	−14.9157	+	5.42887i	−1.15421	+	0.420099i	−0.307185	+	0.951650i	$0.599387\pi$
$168$	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	−0.342457	−	0.939533i	$-0.611259\pi$
$173$	−4.51044	+	0.795312i	−0.342922	+	0.0604664i	−0.000465084		1.00000i	$0.500148\pi$
$174$	−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	0.704671	−	0.709534i	$-0.251095\pi$
$179$	−3.50718	−	6.07462i	−0.262139	−	0.454039i	−0.966810	+	0.255496i	$0.917761\pi$
$180$	9.81519	+	17.4491i	0.731581	+	1.30058i
$181$	2.24482	+	0.395823i	0.166856	+	0.0294213i	0.256452	−	0.966557i	$-0.417446\pi$
$181$	2.24482	+	0.395823i	0.166856	+	0.0294213i	−0.0895957	+	0.995978i	$0.528558\pi$
$182$	−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	$0.331402\pi$
$191$			23.8531i			1.72595i	−0.505245	+	0.862976i	$0.668598\pi$
$192$	16.3226	−	12.7865i	1.17799	−	0.922786i
$193$	10.3925	+	12.3853i	0.748066	+	0.891511i	0.997031	−	0.0770018i	$-0.0245347\pi$
$193$	10.3925	+	12.3853i	0.748066	+	0.891511i	−0.248965	+	0.968513i	$0.580090\pi$
$194$	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	−0.917209	−	0.398405i	$-0.869564\pi$
$197$	−1.59411	+	2.76108i	−0.113576	+	0.196719i	0.803634	+	0.595124i	$0.202897\pi$
$198$	−13.6094	−	11.5502i	−0.967179	−	0.820839i
$199$	11.2456	+	1.98291i	0.797183	+	0.140565i	0.557381	−	0.830257i	$-0.311806\pi$
$199$	11.2456	+	1.98291i	0.797183	+	0.140565i	0.239802	+	0.970822i	$0.422917\pi$
$200$	−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	0.953337	−	0.301909i	$-0.0976238\pi$
$211$	−0.664785	−	3.77018i	−0.0457657	−	0.259550i	−0.999102	+	0.0423589i	$0.986513\pi$
$212$	−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	−0.542004	−	0.840376i	$-0.682334\pi$
$223$	−22.3608	−	8.13865i	−1.49739	−	0.545004i	−0.955382	+	0.295372i	$0.904557\pi$
$224$	−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	0.674549	−	0.738230i	$-0.264338\pi$
$233$	10.9408	+	3.98214i	0.716758	+	0.260879i	0.0422092	+	0.999109i	$0.486560\pi$
$234$	−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	−0.902192	−	0.431335i	$-0.858043\pi$
$239$	−15.1464	+	8.74479i	−0.979741	+	0.565654i	−0.0775489	+	0.996989i	$0.524709\pi$
$240$	−20.9771	−	18.4186i	−1.35407	−	1.18891i
$241$	17.4817	−	20.8339i	1.12610	−	1.34203i	0.193504	−	0.981100i	$-0.438015\pi$
$241$	17.4817	−	20.8339i	1.12610	−	1.34203i	0.932593	−	0.360930i	$-0.117541\pi$
$242$	−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	0.890203	+	0.455565i	$0.150563\pi$
$251$	7.93890	+	21.8120i	0.501099	+	1.37676i	−0.389103	+	0.921194i	$0.627215\pi$
$252$	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	−0.107775	−	0.994175i	$-0.534373\pi$
$257$	−8.80240	−	1.55210i	−0.549079	−	0.0968174i	−0.441303	+	0.897358i	$0.645484\pi$
$258$	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	0.754113	−	0.656744i	$-0.228067\pi$
$263$	−0.382797	−	0.456200i	−0.0236043	−	0.0281305i	−0.777717	+	0.628614i	$0.783623\pi$
$264$	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	0.929271	−	0.369399i	$-0.120436\pi$
$269$	6.62803	+	7.89898i	0.404118	+	0.481609i	−0.525153	+	0.851008i	$0.675992\pi$
$270$	4.52175	+	5.45055i	0.275185	+	0.331710i
$271$	4.03735	−	11.0925i	0.245252	−	0.673823i	−0.754593	−	0.656193i	$-0.772166\pi$
$271$	4.03735	−	11.0925i	0.245252	−	0.673823i	0.999845	−	0.0176301i	$-0.00561214\pi$
$272$	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	−0.883161	−	0.469070i	$-0.844589\pi$
$277$	−14.1103	−	24.4398i	−0.847807	−	1.46844i	0.0353540	−	0.999375i	$-0.488744\pi$
$278$	−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	0.980647	−	0.195783i	$-0.0627248\pi$
$281$	1.73634	+	4.77054i	0.103581	+	0.284587i	−0.877066	+	0.480370i	$0.840503\pi$
$282$	12.1713	−	20.8112i	0.724793	−	1.23929i
$283$	4.41352	−	0.778223i	0.262357	−	0.0462605i	−0.0409225	−	0.999162i	$-0.513030\pi$
$283$	4.41352	−	0.778223i	0.262357	−	0.0462605i	0.303279	+	0.952902i	$0.401919\pi$
$284$	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	−0.949719	−	0.313105i	$-0.898631\pi$
$293$	−19.7434	+	11.3988i	−1.15342	+	0.665928i	−0.203702	+	0.979033i	$0.565298\pi$
$294$	−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	0.579882	−	0.814700i	$-0.303098\pi$
$307$	25.9825	−	21.8019i	1.48290	−	1.24430i	0.903019	−	0.429602i	$-0.141346\pi$
$308$	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	−0.0145095	−	0.999895i	$-0.504619\pi$
$311$	−15.6547	−	9.03827i	−0.887699	−	0.512513i	−0.873189	+	0.487382i	$0.837952\pi$
$312$	24.8090	+	0.417078i	1.40454	+	0.0236124i
$313$	0.100851	−	0.571953i	0.00570042	−	0.0323287i	−0.981825	−	0.189789i	$-0.939220\pi$
$313$	0.100851	−	0.571953i	0.00570042	−	0.0323287i	0.987525	+	0.157460i	$0.0503307\pi$
$314$	−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	−0.779791	−	0.626040i	$-0.784674\pi$
$317$	−0.495890	+	0.590979i	−0.0278520	+	0.0331927i	0.751939	+	0.659233i	$0.229119\pi$
$318$	−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	−0.986528	−	0.163590i	$-0.947693\pi$
$331$	−11.5517	−	20.0081i	−0.634937	−	1.09974i	0.351591	−	0.936154i	$-0.385641\pi$
$332$	−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	−0.975396	−	0.220460i	$-0.929244\pi$
$337$	−1.58775	+	4.36231i	−0.0864903	+	0.237630i	0.888906	+	0.458090i	$0.151466\pi$
$338$	−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	0.547919	+	0.836532i	$0.315420\pi$
$347$	−7.62858	+	20.9593i	−0.409524	+	1.12516i	−0.957442	+	0.288625i	$0.906802\pi$
$348$	0.172815	−	15.4201i	0.00926383	−	0.826604i
$349$	6.79776	−	11.7741i	0.363876	−	0.630251i	−0.624719	−	0.780849i	$-0.714787\pi$
$349$	6.79776	−	11.7741i	0.363876	−	0.630251i	0.988595	+	0.150598i	$0.0481200\pi$
$350$	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	0.978270	+	0.207335i	$0.0664789\pi$
$353$	12.5636	+	21.7608i	0.668692	+	1.15821i	−0.309578	+	0.950874i	$0.600188\pi$
$354$	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	0.0892644	−	0.996008i	$-0.471548\pi$
$359$	9.73513	−	1.71657i	0.513800	−	0.0905969i	0.424536	+	0.905411i	$0.360437\pi$
$360$	−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	−0.0942270	+	0.995551i	$0.530038\pi$
$367$	−20.2739	+	24.1615i	−1.05829	+	1.26122i	−0.964064	+	0.265671i	$0.914406\pi$
$368$	−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	0.874320	−	0.485350i	$-0.161308\pi$
$373$	17.2111	+	9.93681i	0.891155	+	0.514509i	0.0168350	+	0.999858i	$0.494641\pi$
$374$	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	−0.938432	−	0.345463i	$-0.887722\pi$
$383$	−14.8965	+	12.4996i	−0.761175	+	0.638702i	0.177258	+	0.984164i	$0.443277\pi$
$384$	−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	0.912733	+	0.408556i	$0.133967\pi$
$389$	−1.67034	+	9.47298i	−0.0846897	+	0.480299i	−0.997423	+	0.0717435i	$0.977144\pi$
$390$	−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	0.984226	−	0.176917i	$-0.0566125\pi$
$397$	−0.0229782	−	0.130316i	−0.00115324	−	0.00654036i	−0.985379	+	0.170377i	$0.945501\pi$
$398$	−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	−0.221181	−	0.975233i	$-0.570991\pi$
$401$	−1.91187	+	0.337113i	−0.0954740	+	0.0168346i	0.125707	+	0.992067i	$0.459880\pi$
$402$	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	−0.541161	−	0.840919i	$-0.682015\pi$
$409$	−27.0452	−	4.76879i	−1.33730	−	0.235802i	−0.796136	+	0.605117i	$0.793126\pi$
$410$	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	$-0.950503\pi$
$419$		−	6.34043i		−	0.309750i	0.987934	−	0.154875i	$-0.0494975\pi$
$420$	−15.0906	+	17.5804i	−0.736346	+	0.857834i
$421$	7.49154	+	8.92808i	0.365116	+	0.435128i	0.917058	−	0.398755i	$-0.130558\pi$
$421$	7.49154	+	8.92808i	0.365116	+	0.435128i	−0.551942	+	0.833882i	$0.686113\pi$
$422$	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	0.130078	−	0.991504i	$-0.458477\pi$
$431$	−17.1020	−	14.3503i	−0.823775	−	0.691229i	−0.953853	+	0.300275i	$0.902922\pi$
$432$	3.86299	−	6.35746i	0.185858	−	0.305873i
$433$	−6.55454	−	18.0085i	−0.314991	−	0.865431i	−0.991630	−	0.129116i	$-0.958786\pi$
$433$	−6.55454	−	18.0085i	−0.314991	−	0.865431i	0.676638	−	0.736316i	$-0.263436\pi$
$434$	−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	0.965779	−	0.259366i	$-0.0835136\pi$
$439$	−0.638308	−	3.62002i	−0.0304648	−	0.172774i	−0.996244	+	0.0865917i	$0.972402\pi$
$440$	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	−0.305825	−	0.952088i	$-0.598932\pi$
$443$	14.4156	−	17.1798i	0.684905	−	0.816237i	0.990729	+	0.135850i	$0.0433766\pi$
$444$	−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	−0.999023	−	0.0441984i	$-0.985927\pi$
$449$	−32.5644	−	18.8011i	−1.53681	−	0.887278i	−0.537788	−	0.843080i	$-0.680740\pi$
$450$	−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	−0.402466	−	0.915435i	$-0.631847\pi$
$461$	−27.8951	−	10.1530i	−1.29920	−	0.472871i	−0.896737	+	0.442564i	$0.854069\pi$
$462$	7.17389	−	19.3717i	0.333760	−	0.901252i
$463$	16.0546	+	9.26911i	0.746119	+	0.430772i	0.824290	−	0.566168i	$-0.191575\pi$
$463$	16.0546	+	9.26911i	0.746119	+	0.430772i	−0.0781706	+	0.996940i	$0.524908\pi$
$464$	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	−0.919087	−	0.394054i	$-0.871072\pi$
$467$	−22.4178	+	12.9429i	−1.03737	+	0.598926i	−0.118283	+	0.992980i	$0.537739\pi$
$468$	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	0.936238	−	0.351365i	$-0.114283\pi$
$479$	−0.149158	−	0.409808i	−0.00681519	−	0.0187246i	−0.943054	+	0.332641i	$0.892060\pi$
$480$	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	−0.799019	−	0.601305i	$-0.794648\pi$
$487$	2.67545	−	4.63401i	0.121236	−	0.209987i	0.920255	+	0.391318i	$0.127981\pi$
$488$	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	0.998741	−	0.0501666i	$-0.0159752\pi$
$491$	17.1929	+	20.4898i	0.775907	+	0.924690i	−0.222834	+	0.974856i	$0.571531\pi$
$492$	−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	−0.900334	−	0.435199i	$-0.856678\pi$
$499$	1.54362	−	4.24107i	0.0691021	−	0.189856i	0.969437	+	0.245342i	$0.0789003\pi$
$500$	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	0.611973	−	0.790879i	$-0.290376\pi$
$503$	20.5559	+	3.62456i	0.916543	+	0.161611i	0.304570	+	0.952490i	$0.401487\pi$
$504$	−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	0.886990	+	0.461789i	$0.152792\pi$
$509$	11.3786	+	31.2625i	0.504348	+	1.38569i	−0.382642	+	0.923897i	$0.624986\pi$
$510$	−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	−0.0271962	−	0.999630i	$-0.508658\pi$
$521$	18.8289	−	10.8709i	0.824911	−	0.476262i	0.852107	+	0.523368i	$0.175325\pi$
$522$	−2.62960	−	15.4179i	−0.115094	−	0.674822i
$523$	−3.60494	+	20.4446i	−0.157633	+	0.893981i	0.798706	+	0.601722i	$0.205518\pi$
$523$	−3.60494	+	20.4446i	−0.157633	+	0.893981i	−0.956339	+	0.292260i	$0.905593\pi$
$524$	−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	0.366238	+	0.930521i	$0.380646\pi$
$541$	−6.88874	+	39.0680i	−0.296170	+	1.67966i	−0.662408	+	0.749143i	$0.730465\pi$
$542$	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	−0.0143672	−	0.999897i	$-0.504573\pi$
$547$	14.4386	−	5.25520i	0.617348	−	0.224696i	0.631715	+	0.775200i	$0.282351\pi$
$548$	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	0.661201	−	0.750209i	$-0.270047\pi$
$557$	0.878070	+	0.736789i	0.0372050	+	0.0312187i	−0.623996	+	0.781428i	$0.714492\pi$
$558$	−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	−0.439276	−	0.898352i	$-0.644765\pi$
$563$	13.2485	−	22.9471i	0.558358	−	0.967104i	0.997634	−	0.0687518i	$-0.0219017\pi$
$564$	−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	$0.0604769\pi$
$569$			9.00969i			0.377706i	−0.982005	+	0.188853i	$0.939523\pi$
$570$	−33.2099	+	27.3477i	−1.39101	+	1.14547i
$571$		−	12.9557i		−	0.542179i	−0.962554	−	0.271089i	$-0.912616\pi$
$571$		−	12.9557i		−	0.542179i	0.962554	−	0.271089i	$-0.0873839\pi$
$572$	−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	−0.347053	−	0.937846i	$-0.612818\pi$
$577$	15.3414	−	26.5721i	0.638672	−	1.10621i	0.985725	−	0.168366i	$-0.0538490\pi$
$578$	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	0.479218	−	0.877696i	$-0.340920\pi$
$587$	29.7939	−	5.25347i	1.22973	−	0.216834i	0.750508	+	0.660862i	$0.229809\pi$
$588$	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	−0.422949	−	0.906154i	$-0.639005\pi$
$593$	−4.00540	+	1.45785i	−0.164482	+	0.0598666i	0.258467	+	0.966020i	$0.416783\pi$
$594$	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	−0.965700	−	0.259660i	$-0.916389\pi$
$599$	0.748191	−	4.24320i	0.0305703	−	0.173373i	0.996270	+	0.0862879i	$0.0275005\pi$
$600$	0.277307	−	16.4951i	0.0113210	−	0.673408i
$601$	0.136310	+	0.0786987i	0.00556021	+	0.00321019i	0.502778	−	0.864416i	$-0.332311\pi$
$601$	0.136310	+	0.0786987i	0.00556021	+	0.00321019i	−0.497217	+	0.867626i	$0.665645\pi$
$602$	−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	−0.994475	−	0.104970i	$-0.966525\pi$
$613$	−45.1542	−	16.4348i	−1.82376	−	0.663795i	−0.829286	−	0.558825i	$-0.811252\pi$
$614$	−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	0.889188	+	0.457541i	$0.151270\pi$
$617$	−2.55508	+	14.4906i	−0.102864	+	0.583369i	−0.992052	+	0.125828i	$0.959841\pi$
$618$	−24.2286	+	4.13232i	−0.974619	+	0.166226i
$619$	−41.6191	+	24.0288i	−1.67281	+	0.965800i	−0.706762	+	0.707451i	$0.749845\pi$
$619$	−41.6191	+	24.0288i	−1.67281	+	0.965800i	−0.966052	+	0.258349i	$0.916822\pi$
$620$	−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	0.870913	−	0.491438i	$-0.163529\pi$
$631$	−2.81681	−	7.73912i	−0.112135	−	0.308090i	−0.983048	+	0.183348i	$0.941306\pi$
$632$	−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	−0.418664	−	0.908141i	$-0.637502\pi$
$641$	12.2993	−	33.7920i	0.485793	−	1.33471i	0.904457	−	0.426564i	$-0.140276\pi$
$642$	−13.2865	−	16.0157i	−0.524377	−	0.632087i
$643$	−12.2592	−	14.6099i	−0.483454	−	0.576158i	0.468086	−	0.883683i	$-0.344944\pi$
$643$	−12.2592	−	14.6099i	−0.483454	−	0.576158i	−0.951540	+	0.307525i	$0.900499\pi$
$644$	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	$-0.666699\pi$
$647$		−	44.0542i		−	1.73195i	0.500089	−	0.865974i	$-0.333301\pi$
$648$	−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	0.419200	+	0.907894i	$0.362311\pi$
$653$	−14.7359	+	25.5233i	−0.576660	+	0.998804i	−0.995859	+	0.0909095i	$0.971023\pi$
$654$	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	0.549344	−	0.835597i	$-0.314878\pi$
$659$	−4.57370	−	3.83779i	−0.178166	−	0.149499i	−0.727510	+	0.686098i	$0.759322\pi$
$660$	15.7082	+	44.7106i	0.611440	+	1.74036i
$661$	14.8266	+	40.7359i	0.576690	+	1.58444i	0.793724	+	0.608278i	$0.208139\pi$
$661$	14.8266	+	40.7359i	0.576690	+	1.58444i	−0.217034	+	0.976164i	$0.569638\pi$
$662$	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	−0.947471	−	0.319842i	$-0.896370\pi$
$673$	−29.6835	+	17.1378i	−1.14421	+	0.660613i	−0.196744	+	0.980455i	$0.563037\pi$
$674$	−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	0.859292	−	0.511486i	$-0.170905\pi$
$677$	22.0117	+	12.7085i	0.845978	+	0.488425i	−0.0133139	+	0.999911i	$0.504238\pi$
$678$	−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	0.750149	−	0.661268i	$-0.229982\pi$
$691$	14.5248	+	8.38589i	0.552549	+	0.319014i	−0.197601	+	0.980283i	$0.563315\pi$
$692$	−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	0.998398	−	0.0565853i	$-0.0180213\pi$
$701$	1.08176	+	6.13496i	0.0408574	+	0.231714i	−0.957540	+	0.288299i	$0.906910\pi$
$702$	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	0.987479	+	0.157752i	$0.0504247\pi$
$709$	34.9962	+	29.3653i	1.31431	+	1.10284i	0.326829	+	0.945083i	$0.394020\pi$
$710$	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	−0.935863	−	0.352363i	$-0.885378\pi$
$719$	−30.0416	−	35.8022i	−1.12036	−	1.33520i	−0.184499	−	0.982833i	$-0.559066\pi$
$720$	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	0.444305	+	0.895876i	$0.353451\pi$
$727$	−12.7241	+	34.9591i	−0.471910	+	1.29656i	−0.916215	+	0.400687i	$0.868771\pi$
$728$	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	0.751684	−	0.659524i	$-0.229242\pi$
$733$	−5.28816	−	9.15936i	−0.195323	−	0.338309i	−0.947006	+	0.321215i	$0.895909\pi$
$734$	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	−0.771357	−	0.636402i	$-0.780422\pi$
$739$	−34.7564	+	6.12848i	−1.27853	+	0.225440i	−0.507176	+	0.861842i	$0.669311\pi$
$740$	−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	−0.985667	−	0.168702i	$-0.946043\pi$
$743$	−3.19307	−	18.1088i	−0.117142	−	0.664348i	0.868525	−	0.495646i	$-0.165069\pi$
$744$	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	−0.440324	−	0.897839i	$-0.645137\pi$
$751$	7.68759	−	43.5985i	0.280524	−	1.59093i	0.720848	−	0.693093i	$-0.243752\pi$
$752$	−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	−0.712797	−	0.701371i	$-0.752572\pi$
$757$	−4.01307	+	3.36736i	−0.145857	+	0.122389i	0.566939	+	0.823760i	$0.308127\pi$
$758$	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	−0.751354	−	0.659900i	$-0.770599\pi$
$769$	5.00228	−	28.3693i	0.180387	−	1.02302i	0.931740	−	0.363125i	$-0.118290\pi$
$770$	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	−0.745003	−	0.667062i	$-0.767552\pi$
$773$	1.14807	−	1.36822i	0.0412933	−	0.0492114i	0.786296	+	0.617850i	$0.211996\pi$
$774$	−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	0.615049	+	0.788489i	$0.289136\pi$
$787$	27.7835	+	48.1225i	0.990376	+	1.71538i	0.375327	+	0.926892i	$0.377530\pi$
$788$	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	$0.126491\pi$
$797$			21.8514i			0.774016i	−0.922076	+	0.387008i	$0.873509\pi$
$798$	−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	0.833598	−	0.552372i	$-0.186277\pi$
$809$	−1.75120	−	3.03317i	−0.0615690	−	0.106641i	−0.895167	+	0.445731i	$0.852944\pi$
$810$	23.7238	+	4.32035i	0.833570	+	0.151802i
$811$	10.9054	+	9.15072i	0.382941	+	0.321325i	0.813856	−	0.581067i	$-0.197365\pi$
$811$	10.9054	+	9.15072i	0.382941	+	0.321325i	−0.430915	+	0.902393i	$0.641809\pi$
$812$	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	−0.213271	−	0.976993i	$-0.568412\pi$
$821$	7.20202	−	2.62132i	0.251352	−	0.0914847i	0.464624	+	0.885508i	$0.346190\pi$
$822$	0.236946	−	42.2864i	0.00826446	−	1.47491i
$823$	−0.679981	+	0.810370i	−0.0237027	+	0.0282477i	−0.777766	−	0.628554i	$-0.783647\pi$
$823$	−0.679981	+	0.810370i	−0.0237027	+	0.0282477i	0.754063	+	0.656802i	$0.228091\pi$
$824$	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	0.813154	+	0.582049i	$0.197749\pi$
$827$	−4.31460	+	24.4693i	−0.150033	+	0.850881i	−0.963187	+	0.268832i	$0.913362\pi$
$828$	−15.4151	+	40.9199i	−0.535711	+	1.42206i
$829$	−7.34481	−	4.24053i	−0.255096	−	0.147280i	0.367000	−	0.930221i	$-0.380385\pi$
$829$	−7.34481	−	4.24053i	−0.255096	−	0.147280i	−0.622095	+	0.782941i	$0.713718\pi$
$830$	−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	−0.521575	−	0.853205i	$-0.674655\pi$
$839$	6.60696	−	5.54389i	0.228097	−	0.191396i	0.749673	+	0.661809i	$0.230211\pi$
$840$	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	0.998461	−	0.0554639i	$-0.0176638\pi$
$853$	1.20460	+	6.83164i	0.0412448	+	0.233911i	−0.957216	+	0.289375i	$0.906553\pi$
$854$	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	−0.330029	−	0.943971i	$-0.607058\pi$
$857$	−9.28874	+	1.63785i	−0.317297	+	0.0559481i	0.0127315	+	0.999919i	$0.495947\pi$
$858$	−36.3601	−	21.2650i	−1.24131	−	0.725977i
$859$	2.83749	+	7.79595i	0.0968140	+	0.265994i	0.978640	−	0.205580i	$-0.0659081\pi$
$859$	2.83749	+	7.79595i	0.0968140	+	0.265994i	−0.881826	+	0.471574i	$0.843686\pi$
$860$	−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	0.606405	−	0.795156i	$-0.292611\pi$
$863$	−11.3225	−	19.6112i	−0.385423	−	0.667573i	−0.991828	+	0.127584i	$0.959278\pi$
$864$	−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	0.938200	−	0.346094i	$-0.112492\pi$
$877$	12.8658	+	15.3329i	0.434448	+	0.517755i	−0.503752	+	0.863848i	$0.668048\pi$
$878$	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	−0.902152	−	0.431418i	$-0.858013\pi$
$881$	−2.29906	+	3.98208i	−0.0774572	+	0.134160i	0.824695	+	0.565578i	$0.191347\pi$
$882$	14.4400	−	17.0144i	0.486220	−	0.572904i
$883$	24.2556	+	4.27692i	0.816266	+	0.143930i	0.566167	−	0.824291i	$-0.308426\pi$
$883$	24.2556	+	4.27692i	0.816266	+	0.143930i	0.250099	+	0.968220i	$0.419537\pi$
$884$	−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	0.999999	−	0.00138259i	$-0.000440093\pi$
$887$	34.9136	+	29.2960i	1.17229	+	0.983664i	0.172286	+	0.985047i	$0.444885\pi$
$888$	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	0.248242	−	0.968698i	$-0.420147\pi$
$907$	−5.54925	−	2.01976i	−0.184260	−	0.0670651i	−0.432502	+	0.901633i	$0.642369\pi$
$908$	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	0.917093	−	0.398673i	$-0.130529\pi$
$919$	31.2360	+	18.0341i	1.03038	+	0.594890i	0.113286	+	0.993562i	$0.463862\pi$
$920$	−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	−0.997403	−	0.0720292i	$-0.977053\pi$
$929$	−2.58424	−	14.6560i	−0.0847862	−	0.480846i	0.912616	−	0.408817i	$-0.134059\pi$
$930$	−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	0.950579	−	0.310484i	$-0.100491\pi$
$937$	24.7907	+	20.8019i	0.809877	+	0.679568i	−0.140701	+	0.990052i	$0.544936\pi$
$938$	−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	−0.196986	−	0.980406i	$-0.563115\pi$
$941$	−22.0071	−	3.88045i	−0.717411	−	0.126499i	−0.520425	+	0.853907i	$0.674226\pi$
$942$	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	0.917089	+	0.398682i	$0.130532\pi$
$947$	35.4036	+	42.1924i	1.15046	+	1.37107i	0.233374	+	0.972387i	$0.425023\pi$
$948$	−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	0.687922	−	0.725785i	$-0.258523\pi$
$953$	−4.51618	−	5.38217i	−0.146293	−	0.174346i	−0.834215	+	0.551439i	$0.814079\pi$
$954$	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	−0.685127	−	0.728423i	$-0.740253\pi$
$967$	−33.5782	+	5.92074i	−1.07980	+	0.190398i	−0.394674	+	0.918821i	$0.629142\pi$
$968$	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	0.980129	−	0.198362i	$-0.0635621\pi$
$971$	−0.272182	−	1.54362i	−0.00873472	−	0.0495371i	−0.988864	+	0.148825i	$0.952451\pi$
$972$	−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	−0.727984	−	0.685594i	$-0.759542\pi$
$977$	−15.5733	+	8.99124i	−0.498233	+	0.287655i	0.229750	+	0.973250i	$0.426209\pi$
$978$	−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	0.960584	−	0.277988i	$-0.0896677\pi$
$983$	47.5857	+	17.3198i	1.51775	+	0.552415i	0.557163	+	0.830403i	$0.311890\pi$
$984$	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	−0.697410	−	0.716672i	$-0.745664\pi$
$991$	−3.54873	+	2.97774i	−0.112729	+	0.0945911i	0.584681	+	0.811264i	$0.301220\pi$
$992$	−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	−0.457439	−	0.889241i	$-0.651233\pi$
$997$	8.73220	−	49.5228i	0.276551	−	1.56840i	0.733990	−	0.679160i	$-0.237656\pi$
$998$	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.67.2	yes	48
3.2	odd	2		684.2.cf.a.523.7		48
4.3	odd	2	inner	76.2.k.a.67.1	yes	48
12.11	even	2		684.2.cf.a.523.8		48
19.2	odd	18	inner	76.2.k.a.59.1	✓	48
57.2	even	18		684.2.cf.a.667.8		48
76.59	even	18	inner	76.2.k.a.59.2	yes	48
228.59	odd	18		684.2.cf.a.667.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.1	✓	48	19.2	odd	18	inner
76.2.k.a.59.2	yes	48	76.59	even	18	inner
76.2.k.a.67.1	yes	48	4.3	odd	2	inner
76.2.k.a.67.2	yes	48	1.1	even	1	trivial
684.2.cf.a.523.7		48	3.2	odd	2
684.2.cf.a.523.8		48	12.11	even	2
684.2.cf.a.667.7		48	228.59	odd	18
684.2.cf.a.667.8		48	57.2	even	18

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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