LMFDB - Embedded newform 76.2.k.a.67.1

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			67.1
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39408 - 0.237768i) q^{2} +(1.98545 - 1.66599i) q^{3} +(1.88693 + 0.662936i) q^{4} +(-2.53027 - 0.920944i) q^{5} +(-3.16400 + 1.85045i) q^{6} +(1.43753 + 0.829960i) q^{7} +(-2.47292 - 1.37284i) q^{8} +(0.645546 - 3.66107i) q^{9} +O(q^{10})$	\(q+(-1.39408 - 0.237768i) q^{2} +(1.98545 - 1.66599i) q^{3} +(1.88693 + 0.662936i) q^{4} +(-2.53027 - 0.920944i) q^{5} +(-3.16400 + 1.85045i) q^{6} +(1.43753 + 0.829960i) q^{7} +(-2.47292 - 1.37284i) q^{8} +(0.645546 - 3.66107i) q^{9} +(3.30844 + 1.88549i) q^{10} +(2.94034 - 1.69761i) q^{11} +(4.85086 - 1.82739i) q^{12} +(-2.17565 + 2.59283i) q^{13} +(-1.80670 - 1.49883i) q^{14} +(-6.55803 + 2.38693i) q^{15} +(3.12103 + 2.50183i) 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} +(-4.50271 + 1.66749i) q^{22} +(2.01148 + 5.52649i) q^{23} +(-7.19700 + 1.39415i) q^{24} +(1.72393 + 1.44655i) q^{25} +(3.64952 - 3.09733i) q^{26} +(-0.929885 - 1.61061i) q^{27} +(2.16232 + 2.51907i) q^{28} +(-2.92975 - 0.516594i) q^{29} +(9.70996 - 1.76828i) q^{30} +(2.91510 - 5.04911i) q^{31} +(-3.75612 - 4.22984i) q^{32} +(3.00971 - 8.26910i) q^{33} +(-0.0473932 - 8.45798i) q^{34} +(-2.87301 - 3.42391i) q^{35} +(3.64516 - 6.48025i) q^{36} +0.798908i q^{37} +(5.79679 + 2.09694i) q^{38} +8.77256i q^{39} +(4.99284 + 5.75108i) q^{40} +(0.904276 + 1.07767i) q^{41} +(-6.08416 + 0.0340918i) q^{42} +(0.235045 - 0.645782i) q^{43} +(6.67363 - 1.25401i) q^{44} +(-5.00506 + 8.66901i) q^{45} +(-1.49014 - 8.18265i) q^{46} +(-6.47756 - 1.14217i) q^{47} +(10.3647 - 0.232345i) q^{48} +(-2.12233 - 3.67599i) q^{49} +(-2.05935 - 2.42650i) q^{50} +(11.8746 + 9.96394i) q^{51} +(-5.82418 + 3.45019i) q^{52} +(-2.91069 - 7.99704i) q^{53} +(0.913386 + 2.46642i) 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} +(-13.9569 + 0.156417i) q^{60} +(3.56100 - 1.29610i) q^{61} +(-5.26441 + 6.34575i) q^{62} +(3.96654 - 4.72714i) q^{63} +(4.23062 + 6.78983i) q^{64} +(7.89284 - 4.55693i) q^{65} +(-6.16191 + 10.8122i) q^{66} +(1.76401 - 10.0042i) q^{67} +(-1.94497 + 11.8024i) q^{68} +(13.2008 + 7.62148i) q^{69} +(3.19111 + 5.45633i) q^{70} +(-2.34943 - 0.855121i) q^{71} +(-6.62245 + 8.16730i) q^{72} +(-8.03196 + 6.73961i) q^{73} +(0.189955 - 1.11374i) q^{74} +5.83271 q^{75} +(-7.58263 - 4.30160i) q^{76} +5.63578 q^{77} +(2.08583 - 12.2297i) q^{78} +(6.98750 - 5.86321i) q^{79} +(-5.59302 - 9.20462i) q^{80} +(5.95057 + 2.16583i) q^{81} +(-1.00440 - 1.71737i) q^{82} +(6.78922 + 3.91976i) q^{83} +(8.48993 + 1.39909i) q^{84} +(2.79647 - 15.8596i) q^{85} +(-0.481219 + 0.844387i) q^{86} +(-6.67752 + 3.85527i) q^{87} +(-9.60176 + 0.161420i) q^{88} +(-7.99275 + 9.52539i) q^{89} +(9.03867 - 10.8953i) q^{90} +(-5.27951 + 1.92159i) q^{91} +(0.131813 + 11.7616i) 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} +(2.08468 + 5.62925i) 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 $

$2$	−1.39408	−	0.237768i	−0.985765	−	0.168127i
$2$	−1.39408	−	0.237768i	−0.985765	−	0.168127i
$3$	1.98545	−	1.66599i	1.14630	−	0.961861i	0.146675	−	0.989185i	$-0.453143\pi$
$3$	1.98545	−	1.66599i	1.14630	−	0.961861i	0.999627	+	0.0273235i	$0.00869844\pi$
$4$	1.88693	+	0.662936i	0.943466	+	0.331468i
$5$	−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	$0.816779\pi$
$6$	−3.16400	+	1.85045i	−1.29170	+	0.755445i
$7$	1.43753	+	0.829960i	0.543336	+	0.313695i	0.746430	−	0.665464i	$-0.231766\pi$
$7$	1.43753	+	0.829960i	0.543336	+	0.313695i	−0.203094	+	0.979159i	$0.565100\pi$
$8$	−2.47292	−	1.37284i	−0.874308	−	0.485372i
$9$	0.645546	−	3.66107i	0.215182	−	1.22036i
$10$	3.30844	+	1.88549i	1.04622	+	0.596245i
$11$	2.94034	−	1.69761i	0.886546	−	0.511848i	0.0137349	−	0.999906i	$-0.495628\pi$
$11$	2.94034	−	1.69761i	0.886546	−	0.511848i	0.872811	+	0.488058i	$0.162295\pi$
$12$	4.85086	−	1.82739i	1.40032	−	0.527521i
$13$	−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	$0.377743\pi$
$14$	−1.80670	−	1.49883i	−0.482861	−	0.400580i
$15$	−6.55803	+	2.38693i	−1.69328	+	0.616302i
$16$	3.12103	+	2.50183i	0.780258	+	0.625458i
$17$	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
$22$	−4.50271	+	1.66749i	−0.959982	+	0.355509i
$23$	2.01148	+	5.52649i	0.419422	+	1.15235i	0.952034	+	0.305993i	$0.0989885\pi$
$23$	2.01148	+	5.52649i	0.419422	+	1.15235i	−0.532611	+	0.846360i	$0.678789\pi$
$24$	−7.19700	+	1.39415i	−1.46908	+	0.284580i
$25$	1.72393	+	1.44655i	0.344785	+	0.289309i
$26$	3.64952	−	3.09733i	0.715731	−	0.607436i
$27$	−0.929885	−	1.61061i	−0.178957	−	0.309962i
$28$	2.16232	+	2.51907i	0.408640	+	0.476060i
$29$	−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	$0.644636\pi$
$30$	9.70996	−	1.76828i	1.77279	−	0.322843i
$31$	2.91510	−	5.04911i	0.523568	−	0.906846i	−0.476056	−	0.879415i	$-0.657934\pi$
$31$	2.91510	−	5.04911i	0.523568	−	0.906846i	0.999624	−	0.0274312i	$-0.00873273\pi$
$32$	−3.75612	−	4.22984i	−0.663994	−	0.747737i
$33$	3.00971	−	8.26910i	0.523923	−	1.43947i
$34$	−0.0473932	−	8.45798i	−0.00812787	−	1.45053i
$35$	−2.87301	−	3.42391i	−0.485627	−	0.578747i
$36$	3.64516	−	6.48025i	0.607527	−	1.08004i
$37$			0.798908i			0.131340i	0.997841	+	0.0656699i	$0.0209184\pi$
$37$			0.798908i			0.131340i	−0.997841	+	0.0656699i	$0.979082\pi$
$38$	5.79679	+	2.09694i	0.940364	+	0.340169i
$39$			8.77256i			1.40473i
$40$	4.99284	+	5.75108i	0.789438	+	0.909325i
$41$	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	$0.742740\pi$
$42$	−6.08416	+	0.0340918i	−0.938807	+	0.00526049i
$43$	0.235045	−	0.645782i	0.0358441	−	0.0984808i	−0.920480	−	0.390791i	$-0.872202\pi$
$43$	0.235045	−	0.645782i	0.0358441	−	0.0984808i	0.956324	+	0.292310i	$0.0944239\pi$
$44$	6.67363	−	1.25401i	1.00609	−	0.189049i
$45$	−5.00506	+	8.66901i	−0.746110	+	1.29230i
$46$	−1.49014	−	8.18265i	−0.219710	−	1.20647i
$47$	−6.47756	−	1.14217i	−0.944849	−	0.166602i	−0.320061	−	0.947397i	$-0.603704\pi$
$47$	−6.47756	−	1.14217i	−0.944849	−	0.166602i	−0.624788	+	0.780794i	$0.714815\pi$
$48$	10.3647	−	0.232345i	1.49601	−	0.0335362i
$49$	−2.12233	−	3.67599i	−0.303190	−	0.525141i
$50$	−2.05935	−	2.42650i	−0.291237	−	0.343159i
$51$	11.8746	+	9.96394i	1.66277	+	1.39523i
$52$	−5.82418	+	3.45019i	−0.807669	+	0.478455i
$53$	−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	$-0.309816\pi$
$54$	0.913386	+	2.46642i	0.124296	+	0.335637i
$55$	−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	$-0.953757\pi$
$59$	−0.838664	−	4.75630i	−0.109185	−	0.619218i	0.880281	−	0.474452i	$-0.157354\pi$
$60$	−13.9569	+	0.156417i	−1.80183	+	0.0201933i
$61$	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	$0.310889\pi$
$62$	−5.26441	+	6.34575i	−0.668581	+	0.805912i
$63$	3.96654	−	4.72714i	0.499737	−	0.595563i
$64$	4.23062	+	6.78983i	0.528828	+	0.848729i
$65$	7.89284	−	4.55693i	0.978986	−	0.565218i
$66$	−6.16191	+	10.8122i	−0.758478	+	1.33089i
$67$	1.76401	−	10.0042i	0.215509	−	1.22221i	−0.664513	−	0.747277i	$-0.731361\pi$
$67$	1.76401	−	10.0042i	0.215509	−	1.22221i	0.880022	−	0.474934i	$-0.157528\pi$
$68$	−1.94497	+	11.8024i	−0.235862	+	1.43125i
$69$	13.2008	+	7.62148i	1.58919	+	0.917518i
$70$	3.19111	+	5.45633i	0.381411	+	0.652156i
$71$	−2.34943	−	0.855121i	−0.278825	−	0.101484i	0.198822	−	0.980036i	$-0.436288\pi$
$71$	−2.34943	−	0.855121i	−0.278825	−	0.101484i	−0.477648	+	0.878551i	$0.658511\pi$
$72$	−6.62245	+	8.16730i	−0.780463	+	0.962525i
$73$	−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	$0.488052\pi$
$74$	0.189955	−	1.11374i	0.0220818	−	0.129470i
$75$	5.83271			0.673503
$76$	−7.58263	−	4.30160i	−0.869787	−	0.493428i
$77$	5.63578			0.642257
$78$	2.08583	−	12.2297i	0.236174	−	1.38474i
$79$	6.98750	−	5.86321i	0.786156	−	0.659663i	−0.158635	−	0.987337i	$-0.550709\pi$
$79$	6.98750	−	5.86321i	0.786156	−	0.659663i	0.944791	+	0.327674i	$0.106265\pi$
$80$	−5.59302	−	9.20462i	−0.625318	−	1.02911i
$81$	5.95057	+	2.16583i	0.661174	+	0.240648i
$82$	−1.00440	−	1.71737i	−0.110917	−	0.189652i
$83$	6.78922	+	3.91976i	0.745213	+	0.430249i	0.823962	−	0.566645i	$-0.191759\pi$
$83$	6.78922	+	3.91976i	0.745213	+	0.430249i	−0.0787485	+	0.996895i	$0.525092\pi$
$84$	8.48993	+	1.39909i	0.926328	+	0.152653i
$85$	2.79647	−	15.8596i	0.303320	−	1.72021i
$86$	−0.481219	+	0.844387i	−0.0518911	+	0.0910526i
$87$	−6.67752	+	3.85527i	−0.715905	+	0.413328i
$88$	−9.60176	+	0.161420i	−1.02355	+	0.0172075i
$89$	−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	$0.993190\pi$
$90$	9.03867	−	10.8953i	0.952760	−	1.14846i
$91$	−5.27951	+	1.92159i	−0.553443	+	0.201437i
$92$	0.131813	+	11.7616i	0.0137425	+	1.22623i
$93$	−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	$0.587098\pi$
$98$	2.08468	+	5.62925i	0.210584	+	0.568640i
$99$	−4.31694	−	11.8607i	−0.433869	−	1.19204i
$100$	2.29397	+	3.87239i	0.229397	+	0.387239i
$101$	−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	$0.724019\pi$
$102$	−14.1850	−	16.7140i	−1.40453	−	1.65493i
$103$	3.35278	+	5.80718i	0.330359	+	0.572199i	0.982582	−	0.185828i	$-0.0594968\pi$
$103$	3.35278	+	5.80718i	0.330359	+	0.572199i	−0.652223	+	0.758027i	$0.726163\pi$
$104$	8.93974	−	3.42505i	0.876613	−	0.335853i
$105$	−11.4084	−	2.01161i	−1.11335	−	0.196313i
$106$	2.15630	+	11.8406i	0.209438	+	1.15006i
$107$	−2.83864	+	4.91666i	−0.274421	+	0.475312i	−0.969989	−	0.243149i	$-0.921820\pi$
$107$	−2.83864	+	4.91666i	−0.274421	+	0.475312i	0.695568	+	0.718461i	$0.255153\pi$
$108$	−0.686900	−	3.65556i	−0.0660970	−	0.351757i
$109$	−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	$0.988268\pi$
$110$	12.9288	−	0.0724447i	1.23271	−	0.00690733i
$111$	1.33098	+	1.58619i	0.126331	+	0.150555i
$112$	2.41016	+	6.18680i	0.227739	+	0.584597i
$113$		−	9.61911i		−	0.904890i	−0.891792	−	0.452445i	$-0.850552\pi$
$113$		−	9.61911i		−	0.904890i	0.891792	−	0.452445i	$-0.149448\pi$
$114$	15.0028	−	5.49404i	1.40514	−	0.514564i
$115$		−	15.8360i		−	1.47671i
$116$	−5.18577	−	2.91701i	−0.481487	−	0.270838i
$117$	8.08808	+	9.63900i	0.747743	+	0.891126i
$118$	0.0382715	+	6.83009i	0.00352318	+	0.628760i
$119$	−3.39545	+	9.32892i	−0.311260	+	0.855180i
$120$	19.4943	+	3.10045i	1.77958	+	0.283031i
$121$	0.263736	−	0.456803i	0.0239760	−	0.0415276i
$122$	−5.27249	+	0.960175i	−0.477349	+	0.0869302i
$123$	3.59079	+	0.633154i	0.323771	+	0.0570896i
$124$	8.84784	−	7.59480i	0.794559	−	0.682033i
$125$	3.70184	+	6.41177i	0.331102	+	0.573486i
$126$	−6.65365	+	5.64691i	−0.592754	+	0.503066i
$127$	−6.20191	−	5.20402i	−0.550331	−	0.461782i	0.324722	−	0.945809i	$-0.394729\pi$
$127$	−6.20191	−	5.20402i	−0.550331	−	0.461782i	−0.875053	+	0.484027i	$0.839174\pi$
$128$	−4.28343	−	10.4715i	−0.378605	−	0.925558i
$129$	−0.609196	−	1.67375i	−0.0536367	−	0.147366i
$130$	−12.0868	+	4.47608i	−1.06008	+	0.392578i
$131$	5.31618	−	0.937385i	0.464476	−	0.0818997i	0.0634875	−	0.997983i	$-0.479778\pi$
$131$	5.31618	−	0.937385i	0.464476	−	0.0818997i	0.400989	+	0.916083i	$0.368667\pi$
$132$	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
$136$	5.51767	−	15.9911i	0.473136	−	1.37122i
$137$	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	$0.224852\pi$
$138$	−16.5908	−	13.7637i	−1.41231	−	1.17164i
$139$	−3.12723	+	3.72688i	−0.265248	+	0.316110i	−0.882186	−	0.470902i	$-0.843929\pi$
$139$	−3.12723	+	3.72688i	−0.265248	+	0.316110i	0.616938	+	0.787012i	$0.288373\pi$
$140$	−3.15133	−	8.36532i	−0.266336	−	0.706998i
$141$	−14.7637	+	8.52385i	−1.24333	+	0.717837i
$142$	3.07197	+	1.75073i	0.257794	+	0.146918i
$143$	−1.99553	+	11.3172i	−0.166875	+	0.946393i
$144$	11.1742	−	9.81128i	0.931180	−	0.817607i
$145$	6.93731	+	4.00526i	0.576112	+	0.332619i
$146$	12.7997	−	7.48583i	1.05931	−	0.619532i
$147$	−10.3380	−	3.76271i	−0.852660	−	0.310343i
$148$	−0.529625	+	1.50749i	−0.0435349	+	0.123915i
$149$	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	$-0.000780324\pi$
$150$	−8.13128	−	1.38683i	−0.663916	−	0.113234i
$151$	−6.11110			−0.497314			−0.248657	−	0.968592i	$-0.579989\pi$
$151$	−6.11110			−0.497314			−0.248657	+	0.968592i	$0.579989\pi$
$152$	9.54802	+	7.79970i	0.774447	+	0.632639i
$153$	22.2339			1.79750
$154$	−7.85675	−	1.34001i	−0.633115	−	0.107981i
$155$	−12.0260	+	10.0910i	−0.965948	+	0.810527i
$156$	−5.81565	+	16.5532i	−0.465624	+	1.32532i
$157$	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	$0.561223\pi$
$158$	−11.1352	+	6.51240i	−0.885872	+	0.518099i
$159$	−19.1020	−	11.0286i	−1.51489	−	0.874622i
$160$	5.60856	+	14.1618i	0.443396	+	1.11959i
$161$	−1.69520	+	9.61396i	−0.133601	+	0.757686i
$162$	−7.78062	−	4.43420i	−0.611303	−	0.348383i
$163$	−3.89527	+	2.24893i	−0.305101	+	0.176150i	−0.644732	−	0.764409i	$-0.723031\pi$
$163$	−3.89527	+	2.24893i	−0.305101	+	0.176150i	0.339631	+	0.940559i	$0.389698\pi$
$164$	0.991879	+	2.63298i	0.0774527	+	0.205601i
$165$	−15.2308	+	18.1513i	−1.18571	+	1.41308i
$166$	−8.53274	−	7.07872i	−0.662269	−	0.549415i
$167$	14.9157	−	5.42887i	1.15421	−	0.420099i	0.307185	−	0.951650i	$-0.400613\pi$
$167$	14.9157	−	5.42887i	1.15421	−	0.420099i	0.847026	+	0.531551i	$0.178391\pi$
$168$	−11.5030	−	3.96908i	−0.887476	−	0.306221i
$169$	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	$0.500148\pi$
$174$	10.2257	−	3.78686i	0.775206	−	0.287081i
$175$	1.27763	+	3.51025i	0.0965794	+	0.265350i
$176$	13.4240	+	2.05796i	1.01187	+	0.155124i
$177$	−9.58909	−	8.04620i	−0.720760	−	0.604790i
$178$	13.4074	−	11.3788i	1.00493	−	0.852875i
$179$	3.50718	+	6.07462i	0.262139	+	0.454039i	0.966810	−	0.255496i	$-0.0822387\pi$
$179$	3.50718	+	6.07462i	0.262139	+	0.454039i	−0.704671	+	0.709534i	$0.748905\pi$
$180$	−15.1912	+	13.0398i	−1.13229	+	0.971930i
$181$	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	$0.528558\pi$
$182$	7.81697	−	1.42355i	0.579432	−	0.105521i
$183$	4.91090	−	8.50593i	0.363024	−	0.628776i
$184$	2.61277	−	16.4280i	0.192616	−	1.21109i
$185$	0.735750	−	2.02146i	0.0540934	−	0.148620i
$186$	0.119742	+	21.3697i	0.00877992	+	1.56690i
$187$	13.0525	+	15.5553i	0.954491	+	1.13752i
$188$	−11.4655	−	6.44941i	−0.836210	−	0.470371i
$189$		−	3.08707i		−	0.224551i
$190$	−12.7363	−	10.6444i	−0.923989	−	0.772223i
$191$		−	23.8531i		−	1.72595i	−0.505245	−	0.862976i	$-0.668598\pi$
$191$		−	23.8531i		−	1.72595i	0.505245	−	0.862976i	$-0.331402\pi$
$192$	19.7115	+	6.43271i	1.42256	+	0.464241i
$193$	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	$0.580090\pi$
$194$	12.0704	−	0.0676349i	0.866603	−	0.00485590i
$195$	8.07904	−	22.1970i	0.578552	−	1.58956i
$196$	−1.56775	−	8.34331i	−0.111982	−	0.595951i
$197$	−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	$0.202897\pi$
$198$	3.19808	+	17.5612i	0.227277	+	1.24802i
$199$	−11.2456	−	1.98291i	−0.797183	−	0.140565i	−0.239802	−	0.970822i	$-0.577083\pi$
$199$	−11.2456	−	1.98291i	−0.797183	−	0.140565i	−0.557381	+	0.830257i	$0.688194\pi$
$200$	−2.27725	−	5.94386i	−0.161026	−	0.420294i
$201$	−13.1646	−	22.8018i	−0.928559	−	1.60831i
$202$	0.103803	+	0.122309i	0.00730356	+	0.00860566i
$203$	−3.78286	−	3.17419i	−0.265505	−	0.222785i
$204$	15.8011	+	26.6734i	1.10629	+	1.86751i
$205$	−1.29559	−	3.55960i	−0.0904878	−	0.248613i
$206$	−3.29329	−	8.89288i	−0.229454	−	0.619596i
$207$	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	$-0.0134873\pi$
$211$	0.664785	+	3.77018i	0.0457657	+	0.259550i	−0.953337	+	0.301909i	$0.902376\pi$
$212$	−0.190739	−	17.0195i	−0.0131000	−	1.16890i
$213$	−6.08930	+	2.21632i	−0.417232	+	0.151860i
$214$	5.12632	−	6.17930i	0.350428	−	0.422408i
$215$	−1.18946	+	1.41754i	−0.0811204	+	0.0966755i
$216$	0.0884199	+	5.25948i	0.00601621	+	0.357862i
$217$	8.38111	−	4.83884i	0.568947	−	0.328482i
$218$	5.50366	−	9.65719i	0.372755	−	0.654067i
$219$	−4.71893	+	26.7624i	−0.318875	+	1.80843i
$220$	−18.0410	−	2.97305i	−1.21632	−	0.200443i
$221$	−17.5311	−	10.1216i	−1.17927	−	0.680852i
$222$	−1.47834	−	2.52775i	−0.0992199	−	0.169651i
$223$	22.3608	+	8.13865i	1.49739	+	0.545004i	0.955382	−	0.295372i	$-0.0954435\pi$
$223$	22.3608	+	8.13865i	1.49739	+	0.545004i	0.542004	+	0.840376i	$0.317666\pi$
$224$	−1.88895	−	9.19797i	−0.126211	−	0.614565i
$225$	6.40879	−	5.37761i	0.427253	−	0.358507i
$226$	−2.28712	+	13.4098i	−0.152137	+	0.892009i
$227$	−21.4255			−1.42206			−0.711031	−	0.703161i	$-0.751771\pi$
$227$	−21.4255			−1.42206			−0.711031	+	0.703161i	$0.751771\pi$
$228$	−22.2214	+	4.09197i	−1.47165	+	0.270997i
$229$	−17.6065			−1.16347			−0.581735	−	0.813378i	$-0.697626\pi$
$229$	−17.6065			−1.16347			−0.581735	+	0.813378i	$0.697626\pi$
$230$	−3.76529	+	22.0767i	−0.248276	+	1.45569i
$231$	11.1896	−	9.38917i	0.736220	−	0.617762i
$232$	6.53582	+	5.29957i	0.429097	+	0.347934i
$233$	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	$0.486560\pi$
$234$	−8.98361	−	15.3606i	−0.587277	−	1.00416i
$235$	15.3381	+	8.85547i	1.00055	+	0.577667i
$236$	1.57062	−	9.53080i	0.102239	−	0.620402i
$237$	4.10529	−	23.2823i	0.266667	−	1.51235i
$238$	6.95165	−	12.1980i	0.450609	−	0.790676i
$239$	15.1464	−	8.74479i	0.979741	−	0.565654i	0.0775489	−	0.996989i	$-0.475291\pi$
$239$	15.1464	−	8.74479i	0.979741	−	0.565654i	0.902192	+	0.431335i	$0.141957\pi$
$240$	−26.4395	−	8.95741i	−1.70666	−	0.578198i
$241$	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	$-0.117541\pi$
$242$	−0.476282	+	0.574114i	−0.0306166	+	0.0369054i
$243$	20.6657	−	7.52168i	1.32570	−	0.482516i
$244$	7.57859	−	0.0849340i	0.485169	−	0.00543734i
$245$	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
$250$	−3.63615	−	9.81871i	−0.229970	−	0.620990i
$251$	−7.93890	−	21.8120i	−0.501099	−	1.37676i	−0.890203	−	0.455565i	$-0.849437\pi$
$251$	−7.93890	−	21.8120i	−0.501099	−	1.37676i	0.389103	−	0.921194i	$-0.372785\pi$
$252$	10.6184	−	6.29023i	0.668895	−	0.396247i
$253$	15.2962	+	12.8351i	0.961666	+	0.806934i
$254$	7.40863	+	8.72945i	0.464859	+	0.547734i
$255$	−20.8697	−	36.1473i	−1.30691	−	2.26363i
$256$	3.48167	+	15.6166i	0.217604	+	0.976037i
$257$	−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	$0.645484\pi$
$258$	0.451305	+	2.47820i	0.0280970	+	0.154286i
$259$	−0.663062	+	1.14846i	−0.0412007	+	0.0713617i
$260$	17.9142	−	3.36618i	1.11099	−	0.208761i
$261$	−3.78258	+	10.3925i	−0.234136	+	0.643282i
$262$	−7.63407	+	0.0427765i	−0.471634	+	0.00264274i
$263$	0.382797	+	0.456200i	0.0236043	+	0.0281305i	0.777717	−	0.628614i	$-0.216377\pi$
$263$	0.382797	+	0.456200i	0.0236043	+	0.0281305i	−0.754113	+	0.656744i	$0.771933\pi$
$264$	−18.7949	+	16.3169i	−1.15675	+	1.00424i
$265$			22.9153i			1.40768i
$266$	6.59271	+	7.82553i	0.404225	+	0.479814i
$267$			32.2281i			1.97233i
$268$	9.96074	−	17.7079i	0.608449	−	1.08168i
$269$	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	$0.675992\pi$
$270$	−0.0396825	−	7.08189i	−0.00241500	−	0.430990i
$271$	−4.03735	+	11.0925i	−0.245252	+	0.673823i	0.754593	+	0.656193i	$0.227834\pi$
$271$	−4.03735	+	11.0925i	−0.245252	+	0.673823i	−0.999845	+	0.0176301i	$0.994388\pi$
$272$	−11.4942	+	20.9809i	−0.696941	+	1.27216i
$273$	−7.28088	+	12.6108i	−0.440659	+	0.763243i
$274$	−16.0516	+	2.92315i	−0.969710	+	0.176594i
$275$	7.52460	+	1.32679i	0.453750	+	0.0800084i
$276$	19.8564	+	23.1325i	1.19522	+	1.39241i
$277$	−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	$-0.488744\pi$
$278$	5.24575	−	4.45203i	0.314619	−	0.267015i
$279$	−16.6033	−	13.9318i	−0.994015	−	0.834078i
$280$	2.40421	+	12.4112i	0.143679	+	0.741713i
$281$	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	$0.840503\pi$
$282$	22.6086	−	8.37260i	1.34632	−	0.498581i
$283$	−4.41352	+	0.778223i	−0.262357	+	0.0462605i	−0.303279	−	0.952902i	$-0.598081\pi$
$283$	−4.41352	+	0.778223i	−0.262357	+	0.0462605i	0.0409225	+	0.999162i	$0.486970\pi$
$284$	−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
$288$	−17.9105	+	11.0209i	−1.05539	+	0.649411i
$289$	−17.6378	+	6.41965i	−1.03752	+	0.377626i
$290$	−8.71886	−	7.23313i	−0.511989	−	0.424744i
$291$	−14.2195	+	16.9462i	−0.833565	+	0.993404i
$292$	−19.6237	+	7.39252i	−1.14839	+	0.432614i
$293$	−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	$0.565298\pi$
$294$	13.5173	+	7.70356i	0.788346	+	0.449281i
$295$	−2.25824	+	12.8071i	−0.131480	+	0.745659i
$296$	1.09677	−	1.97563i	0.0637487	−	0.114831i
$297$	−5.46836	−	3.15716i	−0.317306	−	0.183197i
$298$	−22.8770	+	13.3795i	−1.32523	+	0.775056i
$299$	−18.7055	−	6.80826i	−1.08177	−	0.393732i
$300$	11.0059	+	3.86671i	0.635428	+	0.223245i
$301$	0.873858	−	0.733254i	0.0503684	−	0.0422641i
$302$	8.51938	+	1.45302i	0.490235	+	0.0836121i
$303$	−0.294002			−0.0168900
$304$	−11.4562	−	13.1436i	−0.657059	−	0.753839i
$305$	−10.2039			−0.584275
$306$	−30.9959	−	5.28650i	−1.77192	−	0.302209i
$307$	−25.9825	+	21.8019i	−1.48290	+	1.24430i	−0.579882	+	0.814700i	$0.696902\pi$
$307$	−25.9825	+	21.8019i	−1.48290	+	1.24430i	−0.903019	+	0.429602i	$0.858654\pi$
$308$	10.6343	+	3.73616i	0.605948	+	0.212888i
$309$	16.3315	+	5.94418i	0.929067	+	0.338153i
$310$	19.1645	−	11.2083i	1.08847	−	0.636587i
$311$	15.6547	+	9.03827i	0.887699	+	0.512513i	0.873189	−	0.487382i	$-0.162048\pi$
$311$	15.6547	+	9.03827i	0.887699	+	0.512513i	0.0145095	+	0.999895i	$0.495381\pi$
$312$	12.0433	−	21.6938i	0.681819	−	1.22817i
$313$	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	$0.0503307\pi$
$314$	−4.80603	−	2.73897i	−0.271220	−	0.154569i
$315$	−14.3899	+	8.30799i	−0.810777	+	0.468102i
$316$	17.0719	−	6.43122i	0.960369	−	0.361784i
$317$	−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	$0.229119\pi$
$318$	24.0076	+	19.9166i	1.34628	+	1.11687i
$319$	−9.49143	+	3.45460i	−0.531418	+	0.193420i
$320$	−4.45157	−	21.0763i	−0.248850	−	1.17820i
$321$	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
$326$	5.96505	−	2.20903i	0.330374	−	0.122347i
$327$	6.96733	+	19.1426i	0.385294	+	1.05859i
$328$	−0.756724	−	3.90642i	−0.0417831	−	0.215696i
$329$	−8.36375	−	7.01802i	−0.461109	−	0.386916i
$330$	25.5488	−	21.6831i	1.40641	−	1.19361i
$331$	11.5517	+	20.0081i	0.634937	+	1.09974i	0.986528	+	0.163590i	$0.0523073\pi$
$331$	11.5517	+	20.0081i	0.634937	+	1.09974i	−0.351591	+	0.936154i	$0.614359\pi$
$332$	10.2122	+	11.8971i	0.560470	+	0.652940i
$333$	2.92486	+	0.515732i	0.160282	+	0.0282620i
$334$	−22.0845	+	4.02182i	−1.20841	+	0.220064i
$335$	−13.6768	+	23.6889i	−0.747242	+	1.29426i
$336$	15.0924	+	8.26828i	0.823359	+	0.451071i
$337$	−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	$0.151466\pi$
$338$	−0.0122332	−	2.18319i	−0.000665399	−	0.118750i
$339$	−16.0254	−	19.0983i	−0.870378	−	1.03728i
$340$	15.7906	−	28.0721i	0.856368	−	1.52242i
$341$		−	19.7948i		−	1.07195i
$342$	11.4192	−	19.8688i	0.617478	−	1.07438i
$343$		−	18.6652i		−	1.00783i
$344$	−1.46780	+	1.27428i	−0.0791386	+	0.0687048i
$345$	−26.3827	−	31.4416i	−1.42039	−	1.69276i
$346$	6.47702	−	0.0362932i	0.348207	−	0.00195113i
$347$	7.62858	−	20.9593i	0.409524	−	1.12516i	−0.547919	−	0.836532i	$-0.684580\pi$
$347$	7.62858	−	20.9593i	0.409524	−	1.12516i	0.957442	−	0.288625i	$-0.0931981\pi$
$348$	−15.1558	+	2.84786i	−0.812437	+	0.152661i
$349$	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	$0.0481200\pi$
$350$	−0.946492	−	5.19735i	−0.0505921	−	0.277810i
$351$	6.19914	+	1.09308i	0.330886	+	0.0583441i
$352$	−18.2249	−	6.06076i	−0.971389	−	0.323040i
$353$	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	$0.600188\pi$
$354$	11.4549	+	13.4970i	0.608819	+	0.717360i
$355$	5.15717	+	4.32738i	0.273714	+	0.229674i
$356$	−21.3965	+	12.6751i	−1.13401	+	0.671779i
$357$	8.80041	+	24.1789i	0.465767	+	1.27968i
$358$	−3.44496	−	9.30242i	−0.182072	−	0.491648i
$359$	−9.73513	+	1.71657i	−0.513800	+	0.0905969i	−0.424536	−	0.905411i	$-0.639563\pi$
$359$	−9.73513	+	1.71657i	−0.513800	+	0.0905969i	−0.0892644	+	0.996008i	$0.528452\pi$
$360$	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
$364$	−11.2360	+	0.125923i	−0.588925	+	0.00660014i
$365$	26.5299	−	9.65608i	1.38864	−	0.505422i
$366$	−8.86864	+	10.6903i	−0.463571	+	0.558792i
$367$	20.2739	−	24.1615i	1.05829	−	1.26122i	0.0942270	−	0.995551i	$-0.469962\pi$
$367$	20.2739	−	24.1615i	1.05829	−	1.26122i	0.964064	−	0.265671i	$-0.0855935\pi$
$368$	−7.54847	+	22.2807i	−0.393491	+	1.16146i
$369$	4.52920	−	2.61493i	0.235781	−	0.136128i
$370$	−1.50633	+	2.64314i	−0.0783106	+	0.137410i
$371$	2.45302	−	13.9118i	0.127354	−	0.722263i
$372$	4.91409	−	29.8195i	0.254784	−	1.54607i
$373$	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	$0.494641\pi$
$374$	−14.4977	−	24.7889i	−0.749656	−	1.28180i
$375$	18.0318	+	6.56303i	0.931157	+	0.338913i
$376$	14.4504	+	11.7171i	0.745225	+	0.604265i
$377$	7.71354	−	6.47243i	0.397267	−	0.333347i
$378$	−0.734006	+	4.30363i	−0.0377532	+	0.221355i
$379$	36.4793			1.87382			0.936909	−	0.349573i	$-0.113673\pi$
$379$	36.4793			1.87382			0.936909	+	0.349573i	$0.113673\pi$
$380$	15.2246	+	17.8674i	0.781005	+	0.916579i
$381$	−20.9835			−1.07502
$382$	−5.67151	+	33.2532i	−0.290180	+	1.70138i
$383$	14.8965	−	12.4996i	0.761175	−	0.638702i	−0.177258	−	0.984164i	$-0.556723\pi$
$383$	14.8965	−	12.4996i	0.761175	−	0.638702i	0.938432	+	0.345463i	$0.112278\pi$
$384$	−25.9500	−	13.6545i	−1.32425	−	0.696803i
$385$	−14.2601	−	5.19024i	−0.726761	−	0.264519i
$386$	−11.5431	−	19.7371i	−0.587531	−	1.00459i
$387$	−2.21252	−	1.27740i	−0.112469	−	0.0649339i
$388$	−16.8432	−	2.77566i	−0.855083	−	0.140913i
$389$	−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	$0.977144\pi$
$390$	−16.5406	+	29.0235i	−0.837565	+	1.46966i
$391$	−30.4616	+	17.5870i	−1.54051	+	0.889413i
$392$	0.201806	+	12.0040i	0.0101927	+	0.606295i
$393$	8.99334	−	10.7178i	0.453654	−	0.540644i
$394$	2.87881	−	3.47014i	0.145033	−	0.174823i
$395$	−23.0800	+	8.40043i	−1.16128	+	0.422671i
$396$	−0.282892	−	25.2422i	−0.0142158	−	1.26847i
$397$	−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	$0.459880\pi$
$402$	12.9310	+	34.9176i	0.644940	+	1.74153i
$403$	6.74926	+	18.5435i	0.336205	+	0.923715i
$404$	−0.115629	−	0.195190i	−0.00575275	−	0.00971109i
$405$	−13.0620	−	10.9603i	−0.649054	−	0.544621i
$406$	4.51889	+	5.32453i	0.224269	+	0.264252i
$407$	1.35623	+	2.34906i	0.0672259	+	0.116439i
$408$	−15.6859	−	40.9419i	−0.776568	−	2.02692i
$409$	−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	$0.793126\pi$
$410$	0.959799	+	5.27042i	0.0474011	+	0.260288i
$411$	14.9507	−	25.8954i	0.737465	−	1.27733i
$412$	2.47668	+	13.1804i	0.122017	+	0.649354i
$413$	2.74193	−	7.53340i	0.134922	−	0.370694i
$414$	−30.9193	+	0.173252i	−1.51960	+	0.00851488i
$415$	−13.5687	−	16.1705i	−0.666061	−	0.793781i
$416$	19.1393	−	0.536357i	0.938380	−	0.0262971i
$417$			12.6095i			0.617489i
$418$	20.6043	−	3.67495i	1.00779	−	0.179748i
$419$			6.34043i			0.309750i	0.987934	+	0.154875i	$0.0494975\pi$
$419$			6.34043i			0.309750i	−0.987934	+	0.154875i	$0.950503\pi$
$420$	−20.1934	−	11.3588i	−0.985336	−	0.554255i
$421$	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	$0.686113\pi$
$422$	−0.0303367	−	5.41401i	−0.00147677	−	0.263550i
$423$	−8.36313	+	22.9775i	−0.406629	+	1.11720i
$424$	−3.78078	+	23.7719i	−0.183611	+	1.15447i
$425$	−6.72966	+	11.6561i	−0.326436	+	0.565404i
$426$	9.01595	−	1.64190i	0.436824	−	0.0795502i
$427$	6.19476	+	1.09230i	0.299785	+	0.0528602i
$428$	−8.61575	+	7.39558i	−0.416458	+	0.357479i
$429$	14.8924	+	25.7943i	0.719010	+	1.24536i
$430$	1.99525	−	1.69335i	0.0962194	−	0.0816608i
$431$	17.1020	+	14.3503i	0.823775	+	0.691229i	0.953853	−	0.300275i	$-0.0970784\pi$
$431$	17.1020	+	14.3503i	0.823775	+	0.691229i	−0.130078	+	0.991504i	$0.541523\pi$
$432$	1.12727	−	7.35318i	0.0542359	−	0.353780i
$433$	−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	$-0.263436\pi$
$434$	−12.8345	+	4.75298i	−0.616075	+	0.228150i
$435$	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	$-0.0275975\pi$
$439$	0.638308	+	3.62002i	0.0304648	+	0.172774i	−0.965779	+	0.259366i	$0.916486\pi$
$440$	24.4437	+	8.43425i	1.16531	+	0.402087i
$441$	−14.8281	+	5.39700i	−0.706101	+	0.257000i
$442$	22.0332	+	18.2787i	1.04801	+	0.869428i
$443$	−14.4156	+	17.1798i	−0.684905	+	0.816237i	−0.990729	−	0.135850i	$-0.956623\pi$
$443$	−14.4156	+	17.1798i	−0.684905	+	0.816237i	0.305825	+	0.952088i	$0.401068\pi$
$444$	1.45992	+	3.87539i	0.0692845	+	0.183918i
$445$	28.9962	−	16.7410i	1.37455	−	0.793598i
$446$	−29.2376	−	16.6626i	−1.38444	−	0.788998i
$447$	8.43420	−	47.8327i	0.398924	−	2.26241i
$448$	0.446367	+	13.2719i	0.0210888	+	0.627036i
$449$	−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	$-0.680740\pi$
$450$	−10.2130	+	5.97303i	−0.481446	+	0.281571i
$451$	4.48835	+	1.63362i	0.211348	+	0.0769244i
$452$	6.37686	−	18.1506i	0.299942	−	0.853733i
$453$	−12.1333	+	10.1810i	−0.570072	+	0.478347i
$454$	29.8689	+	5.09430i	1.40182	+	0.239087i
$455$	15.1283			0.709225
$456$	31.9514	−	0.421011i	1.49626	−	0.0197156i
$457$	40.6482			1.90144			0.950721	−	0.310047i	$-0.100345\pi$
$457$	40.6482			1.90144			0.950721	+	0.310047i	$0.100345\pi$
$458$	24.5449	+	4.18626i	1.14691	+	0.195611i
$459$	8.52063	−	7.14966i	0.397709	−	0.333717i
$460$	10.4983	−	29.8815i	0.489484	−	1.39323i
$461$	−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	$0.854069\pi$
$462$	−17.8316	+	10.4288i	−0.829603	+	0.485190i
$463$	−16.0546	−	9.26911i	−0.746119	−	0.430772i	0.0781706	−	0.996940i	$-0.475092\pi$
$463$	−16.0546	−	9.26911i	−0.746119	−	0.430772i	−0.824290	+	0.566168i	$0.808425\pi$
$464$	−7.85140	−	8.94204i	−0.364492	−	0.415124i
$465$	−7.06548	+	40.0703i	−0.327654	+	1.85822i
$466$	−14.3056	−	8.15281i	−0.662694	−	0.377672i
$467$	22.4178	−	12.9429i	1.03737	−	0.598926i	0.118283	−	0.992980i	$-0.462261\pi$
$467$	22.4178	−	12.9429i	1.03737	−	0.598926i	0.919087	+	0.394054i	$0.128928\pi$
$468$	8.87162	+	23.5500i	0.410091	+	1.08860i
$469$	10.8389	−	12.9173i	0.500496	−	0.596467i
$470$	−19.2771	−	15.9922i	−0.889185	−	0.737664i
$471$	9.52657	−	3.46739i	0.438961	−	0.159769i
$472$	−4.45569	+	12.9133i	−0.205090	+	0.594382i
$473$	−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
$478$	−23.1946	+	8.58963i	−1.06090	+	0.392881i
$479$	0.149158	+	0.409808i	0.00681519	+	0.0187246i	0.943054	−	0.332641i	$-0.107940\pi$
$479$	0.149158	+	0.409808i	0.00681519	+	0.0187246i	−0.936238	+	0.351365i	$0.885717\pi$
$480$	34.7291	+	18.7738i	1.58516	+	0.856904i
$481$	−2.07144	−	1.73814i	−0.0944494	−	0.0792525i
$482$	−29.3246	+	24.8876i	−1.33570	+	1.13360i
$483$	12.6510	+	21.9123i	0.575643	+	0.997042i
$484$	0.800483	−	0.687118i	0.0363856	−	0.0312326i
$485$	22.6332	+	3.99084i	1.02772	+	0.181215i
$486$	−30.5981	+	5.57222i	−1.38796	+	0.252761i
$487$	−2.67545	+	4.63401i	−0.121236	+	0.209987i	−0.920255	−	0.391318i	$-0.872019\pi$
$487$	−2.67545	+	4.63401i	−0.121236	+	0.209987i	0.799019	+	0.601305i	$0.205352\pi$
$488$	−10.5854	−	1.68354i	−0.479177	−	0.0762103i
$489$	−3.98716	+	10.9546i	−0.180306	+	0.495386i
$490$	−0.0905697	−	16.1634i	−0.00409152	−	0.730189i
$491$	−17.1929	−	20.4898i	−0.775907	−	0.924690i	0.222834	−	0.974856i	$-0.428469\pi$
$491$	−17.1929	−	20.4898i	−0.775907	−	0.924690i	−0.998741	+	0.0501666i	$0.984025\pi$
$492$	6.35585	+	3.57519i	0.286544	+	0.161182i
$493$		−	17.7925i		−	0.801334i
$494$	−18.0488	+	10.4679i	−0.812054	+	0.470974i
$495$			33.9865i			1.52758i
$496$	21.7301	−	8.46532i	0.975712	−	0.380104i
$497$	−2.66766	−	3.17919i	−0.119661	−	0.142606i
$498$	−28.7344	+	0.161010i	−1.28762	+	0.00721502i
$499$	−1.54362	+	4.24107i	−0.0691021	+	0.189856i	−0.969437	−	0.245342i	$-0.921100\pi$
$499$	−1.54362	+	4.24107i	−0.0691021	+	0.189856i	0.900334	+	0.435199i	$0.143322\pi$
$500$	2.73452	+	14.5527i	0.122292	+	0.650815i
$501$	20.5700	−	35.6282i	0.918998	−	1.59175i
$502$	5.88131	+	32.2953i	0.262495	+	1.44141i
$503$	−20.5559	−	3.62456i	−0.916543	−	0.161611i	−0.304570	−	0.952490i	$-0.598513\pi$
$503$	−20.5559	−	3.62456i	−0.916543	−	0.161611i	−0.611973	+	0.790879i	$0.709624\pi$
$504$	−16.2985	+	6.24439i	−0.725994	+	0.278147i
$505$	0.152720	+	0.264519i	0.00679595	+	0.0117709i
$506$	−18.2725	−	21.5301i	−0.812310	−	0.957130i
$507$	3.06508	+	2.57191i	0.136125	+	0.114223i
$508$	−8.25265	−	13.9311i	−0.366152	−	0.618093i
$509$	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	$0.624986\pi$
$510$	20.4994	+	55.3545i	0.907727	+	2.45114i
$511$	−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
$516$	−0.0399210	−	3.56212i	−0.00175742	−	0.156813i
$517$	−20.9852	+	7.63798i	−0.922928	+	0.335918i
$518$	1.19743	−	1.44339i	0.0526120	−	0.0634189i
$519$	−7.63028	+	9.09341i	−0.334932	+	0.399156i
$520$	−25.7743	+	0.433305i	−1.13028	+	0.0190017i
$521$	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	$0.175325\pi$
$522$	7.74423	−	13.5887i	0.338956	−	0.594761i
$523$	3.60494	−	20.4446i	0.157633	−	0.893981i	−0.798706	−	0.601722i	$-0.794482\pi$
$523$	3.60494	−	20.4446i	0.157633	−	0.893981i	0.956339	−	0.292260i	$-0.0944072\pi$
$524$	10.6527	+	1.75550i	0.465365	+	0.0766895i
$525$	8.38471	+	4.84092i	0.365939	+	0.211275i
$526$	−0.425181	−	0.726997i	−0.0185388	−	0.0316986i
$527$	32.7663	+	11.9260i	1.42732	+	0.519504i
$528$	30.0813	−	18.2783i	1.30912	−	0.795463i
$529$	−8.87704	+	7.44872i	−0.385958	+	0.323858i
$530$	5.44852	−	31.9458i	0.236669	−	1.38764i
$531$	−17.9546			−0.779162
$532$	−7.33012	−	12.4770i	−0.317801	−	0.540945i
$533$	−4.76162			−0.206248
$534$	7.66280	−	44.9286i	0.331602	−	1.94425i
$535$	11.7105	−	9.82628i	0.506289	−	0.424827i
$536$	−18.0965	+	22.3179i	−0.781648	+	0.963986i
$537$	17.0836	+	6.21793i	0.737213	+	0.268324i
$538$	−7.36190	−	12.5878i	−0.317394	−	0.542697i
$539$	−12.4808	−	7.20577i	−0.537584	−	0.310375i
$540$	−1.62853	+	9.88218i	−0.0700806	+	0.425261i
$541$	−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	$0.730465\pi$
$542$	8.26585	−	14.5040i	0.355049	−	0.622998i
$543$	5.11643	−	2.95397i	0.219567	−	0.126767i
$544$	21.0125	−	26.5162i	0.900904	−	1.13687i
$545$	13.6037	−	16.2123i	0.582720	−	0.694459i
$546$	13.1486	−	15.8494i	0.562708	−	0.678292i
$547$	−14.4386	+	5.25520i	−0.617348	+	0.224696i	−0.631715	−	0.775200i	$-0.717649\pi$
$547$	−14.4386	+	5.25520i	−0.617348	+	0.224696i	0.0143672	+	0.999897i	$0.495427\pi$
$548$	23.0722	−	0.258573i	0.985597	−	0.0110457i
$549$	−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
$554$	13.8600	+	37.4261i	0.588853	+	1.59008i
$555$	−1.90694	−	5.23926i	−0.0809449	−	0.222394i
$556$	−8.37155	+	4.95923i	−0.355033	+	0.210318i
$557$	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	$0.714492\pi$
$558$	19.8339	+	23.3699i	0.839634	+	0.989326i
$559$	1.16303	+	2.01443i	0.0491909	+	0.0852011i
$560$	−0.400680	−	17.8739i	−0.0169318	−	0.755311i
$561$	51.8301	+	9.13905i	2.18827	+	0.385851i
$562$	−1.28631	−	7.06338i	−0.0542599	−	0.297951i
$563$	−13.2485	+	22.9471i	−0.558358	+	0.967104i	0.439276	+	0.898352i	$0.355235\pi$
$563$	−13.2485	+	22.9471i	−0.558358	+	0.967104i	−0.997634	+	0.0687518i	$0.978098\pi$
$564$	−33.5089	+	6.29651i	−1.41098	+	0.265131i
$565$	−8.85867	+	24.3390i	−0.372687	+	1.02395i
$566$	6.33785	−	0.0355133i	0.266400	−	0.00149274i
$567$	6.75658	+	8.05218i	0.283750	+	0.338160i
$568$	4.63599	+	5.34003i	0.194522	+	0.224063i
$569$			9.00969i			0.377706i	0.982005	+	0.188853i	$0.0604769\pi$
$569$			9.00969i			0.377706i	−0.982005	+	0.188853i	$0.939523\pi$
$570$	−43.0208	+	0.0847173i	−1.80194	+	0.00354842i
$571$			12.9557i			0.542179i	0.962554	+	0.271089i	$0.0873839\pi$
$571$			12.9557i			0.542179i	−0.962554	+	0.271089i	$0.912616\pi$
$572$	−11.2680	+	20.0319i	−0.471139	+	0.837576i
$573$	−39.7391	−	47.3593i	−1.66013	−	1.97846i
$574$	−0.0185045	−	3.30239i	−0.000772365	−	0.137839i
$575$	−4.52668	+	12.4370i	−0.188776	+	0.518657i
$576$	27.5892	−	11.1055i	1.14955	−	0.462728i
$577$	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	$-0.0538490\pi$
$578$	26.1150	−	4.75581i	1.08624	−	0.197816i
$579$	41.2675	+	7.27658i	1.71502	+	0.302404i
$580$	10.4350	+	12.1566i	0.433290	+	0.504777i
$581$	6.50648	+	11.2696i	0.269934	+	0.467540i
$582$	23.8525	−	20.2434i	0.988717	−	0.839118i
$583$	−22.1342	−	18.5728i	−0.916706	−	0.769208i
$584$	29.1148	−	5.63990i	1.20478	−	0.233381i
$585$	−11.5881	−	31.8380i	−0.479108	−	1.31634i
$586$	30.2342	−	11.1966i	1.24896	−	0.462527i
$587$	−29.7939	+	5.25347i	−1.22973	+	0.216834i	−0.750508	−	0.660862i	$-0.770191\pi$
$587$	−29.7939	+	5.25347i	−1.22973	+	0.216834i	−0.479218	+	0.877696i	$0.659080\pi$
$588$	−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
$592$	−1.99873	+	2.49342i	−0.0821475	+	0.102479i
$593$	−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	$0.416783\pi$
$594$	6.87267	+	5.70154i	0.281989	+	0.233937i
$595$	17.1828	−	20.4777i	0.704427	−	0.839504i
$596$	35.0737	−	13.2128i	1.43667	−	0.541216i
$597$	−25.6312	+	14.7982i	−1.04902	+	0.605650i
$598$	24.4583	+	13.9389i	1.00017	+	0.570002i
$599$	−0.748191	+	4.24320i	−0.0305703	+	0.173373i	−0.996270	−	0.0862879i	$-0.972500\pi$
$599$	−0.748191	+	4.24320i	−0.0305703	+	0.173373i	0.965700	+	0.259660i	$0.0836106\pi$
$600$	−14.4238	−	8.00738i	−0.588849	−	0.326900i
$601$	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	$0.665645\pi$
$602$	−1.39257	+	0.814441i	−0.0567571	+	0.0331942i
$603$	−35.4875	−	12.9164i	−1.44516	−	0.525996i
$604$	−11.5312	−	4.05127i	−0.469199	−	0.164844i
$605$	−1.08801	+	0.912952i	−0.0442341	+	0.0371168i
$606$	0.409863	+	0.0699042i	0.0166495	+	0.00283966i
$607$	−23.1610			−0.940074			−0.470037	−	0.882647i	$-0.655760\pi$
$607$	−23.1610			−0.940074			−0.470037	+	0.882647i	$0.655760\pi$
$608$	12.8458	+	21.0472i	0.520965	+	0.853578i
$609$	−12.7989			−0.518636
$610$	14.2251	+	2.42617i	0.575958	+	0.0982326i
$611$	17.0543	−	14.3103i	0.689945	−	0.578932i
$612$	41.9539	+	14.7396i	1.69588	+	0.595815i
$613$	−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	$-0.811252\pi$
$614$	41.4056	−	24.2159i	1.67099	−	0.977273i
$615$	−8.50259	−	4.90898i	−0.342858	−	0.197949i
$616$	−13.9368	−	7.73703i	−0.561530	−	0.311734i
$617$	−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	$0.959841\pi$
$618$	−21.3541	−	12.1698i	−0.858989	−	0.489541i
$619$	41.6191	−	24.0288i	1.67281	−	0.965800i	0.706762	−	0.707451i	$-0.250155\pi$
$619$	41.6191	−	24.0288i	1.67281	−	0.965800i	0.966052	−	0.258349i	$-0.0831783\pi$
$620$	−29.3818	+	11.0686i	−1.18000	+	0.444524i
$621$	7.03057	−	8.37871i	0.282127	−	0.336226i
$622$	−19.6750	−	16.3223i	−0.788895	−	0.654464i
$623$	−19.3955	+	7.05940i	−0.777066	+	0.282829i
$624$	−21.9475	+	27.3794i	−0.878602	+	1.09605i
$625$	−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
$630$	22.0360	−	8.16058i	0.877937	−	0.325125i
$631$	2.81681	+	7.73912i	0.112135	+	0.308090i	0.983048	−	0.183348i	$-0.0586937\pi$
$631$	2.81681	+	7.73912i	0.112135	+	0.308090i	−0.870913	+	0.491438i	$0.836471\pi$
$632$	−25.3288	+	4.90650i	−1.00752	+	0.195170i
$633$	7.60099	+	6.37799i	0.302112	+	0.253502i
$634$	0.831828	−	0.705967i	0.0330361	−	0.0280375i
$635$	10.8999	+	18.8792i	0.432550	+	0.749199i
$636$	−28.7330	−	33.4736i	−1.13934	−	1.32731i
$637$	14.1487	+	2.49479i	0.560591	+	0.0988473i
$638$	14.0532	−	2.55924i	0.556373	−	0.101321i
$639$	−4.64732	+	8.04940i	−0.183845	+	0.318429i
$640$	1.19459	+	30.4406i	0.0472203	+	1.20327i
$641$	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	$-0.140276\pi$
$642$	−0.116601	−	20.8091i	−0.00460188	−	0.821270i
$643$	12.2592	+	14.6099i	0.483454	+	0.576158i	0.951540	−	0.307525i	$-0.0995008\pi$
$643$	12.2592	+	14.6099i	0.483454	+	0.576158i	−0.468086	+	0.883683i	$0.655056\pi$
$644$	−9.57217	+	17.0171i	−0.377196	+	0.670567i
$645$			4.79609i			0.188846i
$646$	−6.33056	+	36.3205i	−0.249072	+	1.42901i
$647$			44.0542i			1.73195i	0.500089	+	0.865974i	$0.333301\pi$
$647$			44.0542i			1.73195i	−0.500089	+	0.865974i	$0.666699\pi$
$648$	−11.7419	−	13.5251i	−0.461266	−	0.531316i
$649$	−10.5403	−	12.5614i	−0.413742	−	0.493079i
$650$	10.7719	−	0.0603592i	0.422510	−	0.00236748i
$651$	8.57884	−	23.5702i	0.336231	−	0.923787i
$652$	−8.84101	+	1.66127i	−0.346241	+	0.0650605i
$653$	−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	$0.971023\pi$
$654$	−5.16154	−	28.3429i	−0.201832	−	1.10830i
$655$	−14.3147	−	2.52406i	−0.559320	−	0.0986232i
$656$	0.126114	+	5.62580i	0.00492391	+	0.219651i
$657$	19.4892	+	33.7563i	0.760347	+	1.31696i
$658$	9.99110	+	11.7723i	0.389494	+	0.458933i
$659$	4.57370	+	3.83779i	0.178166	+	0.149499i	0.727510	−	0.686098i	$-0.240678\pi$
$659$	4.57370	+	3.83779i	0.178166	+	0.149499i	−0.549344	+	0.835597i	$0.685122\pi$
$660$	−40.7726	+	24.1533i	−1.58707	+	0.940166i
$661$	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	$0.569638\pi$
$662$	−11.3467	−	30.6395i	−0.441002	−	1.19084i
$663$	−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
$668$	31.7439	−	0.355757i	1.22821	−	0.0137647i
$669$	57.9551	−	21.0939i	2.24067	−	0.815539i
$670$	24.6990	−	29.7723i	0.954206	−	1.15021i
$671$	8.27028	−	9.85613i	0.319271	−	0.380492i
$672$	−19.0742	−	15.1152i	−0.735802	−	0.583080i
$673$	−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	$0.563037\pi$
$674$	3.25067	−	5.70390i	0.125211	−	0.219706i
$675$	0.726766	−	4.12169i	0.0279732	−	0.158644i
$676$	−0.502038	+	3.04645i	−0.0193091	+	0.117171i
$677$	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	$0.504238\pi$
$678$	17.7997	+	30.4349i	0.683594	+	1.16885i
$679$	−13.3133	−	4.84565i	−0.510918	−	0.185959i
$680$	−28.6881	+	35.3803i	−1.10014	+	1.35677i
$681$	−42.5393	+	35.6947i	−1.63011	+	1.36783i
$682$	−4.70657	+	27.5956i	−0.180224	+	1.05669i
$683$	1.72512			0.0660100			0.0330050	−	0.999455i	$-0.489492\pi$
$683$	1.72512			0.0660100			0.0330050	+	0.999455i	$0.489492\pi$
$684$	−20.6434	+	24.9837i	−0.789321	+	0.955275i
$685$	−31.0648			−1.18693
$686$	−4.43800	+	26.0209i	−0.169443	+	0.993482i
$687$	−34.9569	+	29.3323i	−1.33369	+	1.11910i
$688$	2.34922	−	1.42746i	0.0895632	−	0.0544214i
$689$	27.0676	+	9.85181i	1.03119	+	0.375324i
$690$	29.3038	+	50.1052i	1.11558	+	1.90747i
$691$	−14.5248	−	8.38589i	−0.552549	−	0.319014i	0.197601	−	0.980283i	$-0.436685\pi$
$691$	−14.5248	−	8.38589i	−0.552549	−	0.319014i	−0.750149	+	0.661268i	$0.770018\pi$
$692$	−9.03813	−	1.48943i	−0.343578	−	0.0566197i
$693$	3.63816	−	20.6330i	0.138202	−	0.783784i
$694$	−15.6183	+	27.4052i	−0.592864	+	1.04029i
$695$	11.3450	−	6.55004i	0.430340	−	0.248457i
$696$	21.8056	−	0.366585i	0.826539	−	0.0138954i
$697$	−5.40828	+	6.44534i	−0.204853	+	0.244135i
$698$	−12.2761	+	14.7977i	−0.464658	+	0.560102i
$699$	28.3567	−	10.3210i	1.07255	−	0.390376i
$700$	0.0837236	+	7.47059i	0.00316445	+	0.282362i
$701$	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
$706$	−12.3407	−	33.3235i	−0.464447	−	1.25415i
$707$	−0.0643996	−	0.176936i	−0.00242200	−	0.00665438i
$708$	−12.7599	−	21.5396i	−0.479545	−	0.809508i
$709$	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	$0.394020\pi$
$710$	−6.16061	−	7.25894i	−0.231204	−	0.272423i
$711$	−16.9549	−	29.3667i	−0.635858	−	1.10134i
$712$	32.8422	−	12.5827i	1.23082	−	0.471557i
$713$	33.7675	+	5.95412i	1.26460	+	0.222984i
$714$	−6.51952	−	35.7999i	−0.243987	−	1.33978i
$715$	15.4718	−	26.7979i	0.578611	−	1.00218i
$716$	2.59074	+	13.7874i	0.0968203	+	0.515261i
$717$	15.5037	−	42.5962i	0.578998	−	1.59078i
$718$	13.9797	−	0.0783336i	0.521718	−	0.00292338i
$719$	30.0416	+	35.8022i	1.12036	+	1.33520i	0.935863	+	0.352363i	$0.114622\pi$
$719$	30.0416	+	35.8022i	1.12036	+	1.33520i	0.184499	+	0.982833i	$0.440934\pi$
$720$	−37.3093	+	14.5344i	−1.39044	+	0.541667i
$721$			11.1307i			0.414529i
$722$	−23.2478	−	13.4738i	−0.865192	−	0.501441i
$723$		−	70.4891i		−	2.62152i
$724$	3.97343	+	2.23507i	0.147671	+	0.0830656i
$725$	−4.30339	−	5.12858i	−0.159824	−	0.190471i
$726$	0.0108333	+	1.93336i	0.000402063	+	0.0717537i
$727$	12.7241	−	34.9591i	0.471910	−	1.29656i	−0.444305	−	0.895876i	$-0.646549\pi$
$727$	12.7241	−	34.9591i	0.471910	−	1.29656i	0.916215	−	0.400687i	$-0.131229\pi$
$728$	15.6938	+	2.49601i	0.581652	+	0.0925082i
$729$	19.0009	−	32.9106i	0.703738	−	1.21891i
$730$	−39.2807	+	7.15342i	−1.45384	+	0.264760i
$731$	4.04771	+	0.713721i	0.149710	+	0.0263979i
$732$	14.9054	−	12.7945i	0.550921	−	0.472899i
$733$	−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	$0.895909\pi$
$734$	−34.0084	+	28.8627i	−1.25527	+	1.06534i
$735$	22.6926	+	19.0414i	0.837030	+	0.702352i
$736$	15.8208	−	29.2664i	0.583164	−	1.07877i
$737$	−11.7964	−	32.4104i	−0.434527	−	1.19385i
$738$	−6.93582	+	2.56854i	−0.255311	+	0.0945491i
$739$	34.7564	−	6.12848i	1.27853	−	0.225440i	0.507176	−	0.861842i	$-0.330689\pi$
$739$	34.7564	−	6.12848i	1.27853	−	0.225440i	0.771357	+	0.636402i	$0.219578\pi$
$740$	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	$0.0539575\pi$
$743$	3.19307	+	18.1088i	0.117142	+	0.664348i	−0.868525	+	0.495646i	$0.834931\pi$
$744$	−13.9408	+	40.4025i	−0.511094	+	1.48123i
$745$	−47.4172	+	17.2584i	−1.73723	+	0.632301i
$746$	−21.6310	−	17.9450i	−0.791967	−	0.657012i
$747$	18.7333	−	22.3254i	0.685415	−	0.816845i
$748$	14.3169	+	38.0048i	0.523479	+	1.38959i
$749$	−8.16127	+	4.71191i	−0.298206	+	0.172169i
$750$	−23.5773	−	13.4368i	−0.860922	−	0.490642i
$751$	−7.68759	+	43.5985i	−0.280524	+	1.59093i	0.440324	+	0.897839i	$0.354863\pi$
$751$	−7.68759	+	43.5985i	−0.280524	+	1.59093i	−0.720848	+	0.693093i	$0.756248\pi$
$752$	−17.3592	−	19.7705i	−0.633023	−	0.720957i
$753$	−52.1009	−	30.0805i	−1.89866	−	1.09619i
$754$	−12.2922	+	7.18907i	−0.447657	+	0.261810i
$755$	15.4628	+	5.62798i	0.562747	+	0.204823i
$756$	2.04653	−	5.82509i	0.0744316	−	0.211857i
$757$	−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	$0.308127\pi$
$758$	−50.8552	−	8.67362i	−1.84714	−	0.315040i
$759$	51.7531			1.87852
$760$	−16.9760	−	28.5286i	−0.615785	−	1.03484i
$761$	−35.8399			−1.29919			−0.649597	−	0.760279i	$-0.725062\pi$
$761$	−35.8399			−1.29919			−0.649597	+	0.760279i	$0.725062\pi$
$762$	29.2527	+	4.98919i	1.05971	+	0.180739i
$763$	−9.99425	+	8.38617i	−0.361816	+	0.303600i
$764$	15.8131	−	45.0093i	0.572098	−	1.62838i
$765$	−56.2578	−	20.4762i	−2.03401	−	0.740318i
$766$	−23.7389	+	13.8836i	−0.857723	+	0.501636i
$767$	14.1569	+	8.17351i	0.511178	+	0.295128i
$768$	32.9298	+	25.2056i	1.18825	+	0.909527i
$769$	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	$-0.118290\pi$
$770$	18.6456	+	10.6262i	0.671943	+	0.382942i
$771$	−20.0625	+	11.5831i	−0.722535	+	0.417156i
$772$	11.3993	+	30.2597i	0.410268	+	1.08907i
$773$	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	$0.211996\pi$
$774$	2.78071	+	2.30687i	0.0999507	+	0.0829187i
$775$	12.3292	−	4.48746i	0.442878	−	0.161194i
$776$	22.8208	+	7.87427i	0.819220	+	0.282670i
$777$	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
$782$	46.6476	−	17.2750i	1.66811	−	0.617751i
$783$	1.89230	+	5.19905i	0.0676253	+	0.185799i
$784$	2.57284	−	16.7826i	0.0918871	−	0.599378i
$785$	−8.06828	−	6.77009i	−0.287969	−	0.241635i
$786$	−15.0858	+	12.8032i	−0.538093	+	0.456676i
$787$	−27.7835	−	48.1225i	−0.990376	−	1.71538i	−0.615049	−	0.788489i	$-0.710864\pi$
$787$	−27.7835	−	48.1225i	−0.990376	−	1.71538i	−0.375327	−	0.926892i	$-0.622470\pi$
$788$	−4.83839	+	4.15317i	−0.172361	+	0.147951i
$789$	1.52005	+	0.268026i	0.0541152	+	0.00954198i
$790$	34.1728	−	6.22321i	1.21581	−	0.221412i
$791$	7.98348	−	13.8278i	0.283860	−	0.491660i
$792$	−5.60741	+	35.2569i	−0.199250	+	1.25280i
$793$	−4.38690	+	12.0529i	−0.155784	+	0.428012i
$794$	0.00104858	+	0.187134i	3.72129e−5	+	0.00664115i
$795$	38.1767	+	45.4972i	1.35399	+	1.61362i
$796$	−19.9052	−	11.1968i	−0.705523	−	0.396859i
$797$			21.8514i			0.774016i	0.922076	+	0.387008i	$0.126491\pi$
$797$			21.8514i			0.774016i	−0.922076	+	0.387008i	$0.873509\pi$
$798$	26.1268	+	4.55383i	0.924878	+	0.161204i
$799$		−	39.3385i		−	1.39170i
$800$	−0.356614	−	12.7253i	−0.0126082	−	0.449909i
$801$	29.7135	+	35.4112i	1.04987	+	1.25119i
$802$	2.74545	−	0.0153838i	0.0969453	−	0.000543221i
$803$	−12.1755	+	33.4519i	−0.429663	+	1.18049i
$804$	−9.72460	−	51.7527i	−0.342960	−	1.82518i
$805$	13.1432	−	22.7648i	0.463239	−	0.802353i
$806$	−5.00000	−	27.4559i	−0.176117	−	0.967092i
$807$	26.3193	+	4.64080i	0.926482	+	0.163364i
$808$	0.114786	+	0.299604i	0.00403817	+	0.0105400i
$809$	−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	$0.852944\pi$
$810$	15.6034	+	18.3853i	0.548249	+	0.645992i
$811$	−10.9054	−	9.15072i	−0.382941	−	0.321325i	0.430915	−	0.902393i	$-0.358191\pi$
$811$	−10.9054	−	9.15072i	−0.382941	−	0.321325i	−0.813856	+	0.581067i	$0.802635\pi$
$812$	−5.03371	−	8.49728i	−0.176649	−	0.298196i
$813$	10.4641	+	28.7499i	0.366992	+	1.00830i
$814$	−1.33217	−	3.59726i	−0.0466925	−	0.126084i
$815$	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
$820$	−0.0849007	−	7.57562i	−0.00296486	−	0.264552i
$821$	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	$0.346190\pi$
$822$	−26.9997	+	32.5456i	−0.941721	+	1.13516i
$823$	0.679981	−	0.810370i	0.0237027	−	0.0282477i	−0.754063	−	0.656802i	$-0.771909\pi$
$823$	0.679981	−	0.810370i	0.0237027	−	0.0282477i	0.777766	+	0.628554i	$0.216353\pi$
$824$	−0.318806	−	18.9635i	−0.0111061	−	0.660625i
$825$	17.1502	−	9.90164i	0.597092	−	0.344731i
$826$	−5.61368	+	9.85024i	−0.195325	+	0.342734i
$827$	4.31460	−	24.4693i	0.150033	−	0.850881i	−0.813154	−	0.582049i	$-0.802251\pi$
$827$	4.31460	−	24.4693i	0.150033	−	0.850881i	0.963187	−	0.268832i	$-0.0866377\pi$
$828$	43.1452	+	7.11008i	1.49940	+	0.247092i
$829$	−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	$0.713718\pi$
$830$	15.0711	+	25.7693i	0.523124	+	0.894465i
$831$	−68.7319	−	25.0164i	−2.38428	−	0.867808i
$832$	−26.8093	−	3.80298i	−0.929444	−	0.131845i
$833$	19.4471	−	16.3181i	0.673803	−	0.565388i
$834$	2.99813	−	17.5787i	0.103817	−	0.608699i
$835$	−42.7405			−1.47910
$836$	−29.5979	+	0.224136i	−1.02367	+	0.00775189i
$837$	−10.8428			−0.374784
$838$	1.50755	−	8.83908i	0.0520774	−	0.305341i
$839$	−6.60696	+	5.54389i	−0.228097	+	0.191396i	−0.749673	−	0.661809i	$-0.769789\pi$
$839$	−6.60696	+	5.54389i	−0.228097	+	0.191396i	0.521575	+	0.853205i	$0.325345\pi$
$840$	25.4505	+	20.6365i	0.878124	+	0.712027i
$841$	−18.9345	−	6.89161i	−0.652915	−	0.237642i
$842$	−8.32102	−	14.2277i	−0.286761	−	0.490320i
$843$	11.3951	+	6.57897i	0.392468	+	0.226592i
$844$	−1.24499	+	7.55479i	−0.0428542	+	0.260047i
$845$	0.721830	−	4.09370i	0.0248317	−	0.140828i
$846$	17.1222	−	30.0441i	0.588674	−	1.03294i
$847$	0.758257	−	0.437780i	0.0260540	−	0.0150423i
$848$	10.9229	−	32.2411i	0.375095	−	1.10716i
$849$	−7.46632	+	8.89801i	−0.256243	+	0.305379i
$850$	12.1531	−	14.6495i	0.416850	−	0.502473i
$851$	−4.41516	+	1.60699i	−0.151350	+	0.0550868i
$852$	−12.9594	+	0.145237i	−0.443981	+	0.00497574i
$853$	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	$0.495947\pi$
$858$	−14.6281	−	39.5003i	−0.499396	−	1.34852i
$859$	−2.83749	−	7.79595i	−0.0968140	−	0.265994i	0.881826	−	0.471574i	$-0.156314\pi$
$859$	−2.83749	−	7.79595i	−0.0968140	−	0.265994i	−0.978640	+	0.205580i	$0.934092\pi$
$860$	−3.18417	+	1.88627i	−0.108579	+	0.0643213i
$861$	4.63639	+	3.89040i	0.158008	+	0.132584i
$862$	−20.4296	−	24.0718i	−0.695834	−	0.819889i
$863$	11.3225	+	19.6112i	0.385423	+	0.667573i	0.991828	−	0.127584i	$-0.0407221\pi$
$863$	11.3225	+	19.6112i	0.385423	+	0.667573i	−0.606405	+	0.795156i	$0.707389\pi$
$864$	−3.31986	+	9.98291i	−0.112944	+	0.339625i
$865$	12.1451	+	2.14151i	0.412945	+	0.0728134i
$866$	4.85574	+	26.6637i	0.165005	+	0.906071i
$867$	−24.3240	+	42.1304i	−0.826087	+	1.43082i
$868$	19.0224	−	3.57442i	0.645664	−	0.121324i
$869$	10.5922	−	29.1019i	0.359316	−	0.987213i
$870$	−29.3612	+	0.164522i	−0.995439	+	0.00557782i
$871$	22.1014	+	26.3395i	0.748878	+	0.892478i
$872$	16.7871	−	14.5739i	0.568484	−	0.493534i
$873$			31.7300i			1.07390i
$874$	0.0713918	+	36.2539i	0.00241486	+	1.22631i
$875$			12.2895i			0.415461i
$876$	−26.6460	+	47.3704i	−0.900286	+	1.60050i
$877$	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	$0.668048\pi$
$878$	−0.0291285	−	5.19838i	−0.000983038	−	0.175437i
$879$	−20.2092	+	55.5242i	−0.681638	+	1.87279i
$880$	−32.0712	−	17.5700i	−1.08112	−	0.592284i
$881$	−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	$0.191347\pi$
$882$	21.9549	−	3.99821i	0.739259	−	0.134627i
$883$	−24.2556	−	4.27692i	−0.816266	−	0.143930i	−0.250099	−	0.968220i	$-0.580463\pi$
$883$	−24.2556	−	4.27692i	−0.816266	−	0.143930i	−0.566167	+	0.824291i	$0.691574\pi$
$884$	−26.3701	−	30.7208i	−0.886922	−	1.03325i
$885$	16.8529	+	29.1901i	0.566505	+	0.981215i
$886$	24.1813	−	20.5225i	0.812387	−	0.689467i
$887$	−34.9136	−	29.2960i	−1.17229	−	0.983664i	−0.172286	−	0.985047i	$-0.555115\pi$
$887$	−34.9136	−	29.2960i	−1.17229	−	0.983664i	−0.999999	+	0.00138259i	$0.999560\pi$
$888$	−1.11380	−	5.74974i	−0.0373766	−	0.192949i
$889$	−4.59632	−	12.6283i	−0.154156	−	0.423539i
$890$	−44.4036	+	16.4439i	−1.48841	+	0.551202i
$891$	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
$896$	2.53335	−	18.6082i	0.0846333	−	0.621656i
$897$	−48.4815	+	17.6458i	−1.61875	+	0.589177i
$898$	40.9272	+	33.9531i	1.36576	+	1.13303i
$899$	−11.1489	+	13.2867i	−0.371835	+	0.443136i
$900$	15.6580	−	5.89857i	0.521932	−	0.196619i
$901$	44.0791	−	25.4491i	1.46849	−	0.847831i
$902$	−5.86870	−	3.34459i	−0.195406	−	0.111363i
$903$	0.513408	−	2.91168i	0.0170852	−	0.0968947i
$904$	−13.2055	+	23.7872i	−0.439208	+	0.791152i
$905$	−5.31549	−	3.06890i	−0.176693	−	0.102014i
$906$	19.3355	−	11.3083i	0.642380	−	0.375693i
$907$	5.54925	+	2.01976i	0.184260	+	0.0670651i	0.432502	−	0.901633i	$-0.357631\pi$
$907$	5.54925	+	2.01976i	0.184260	+	0.0670651i	−0.248242	+	0.968698i	$0.579853\pi$
$908$	−40.4285	−	14.2037i	−1.34167	−	0.471368i
$909$	−0.323039	+	0.271062i	−0.0107145	+	0.00899057i
$910$	−21.0901	−	3.59702i	−0.699130	−	0.119240i
$911$	−19.1178			−0.633401			−0.316700	−	0.948526i	$-0.602575\pi$
$911$	−19.1178			−0.633401			−0.316700	+	0.948526i	$0.602575\pi$
$912$	−44.6430	−	7.01009i	−1.47828	−	0.232127i
$913$	26.6168			0.880888
$914$	−56.6670	−	9.66484i	−1.87438	−	0.319684i
$915$	−20.2594	+	16.9997i	−0.669756	+	0.561992i
$916$	−33.2223	−	11.6720i	−1.09770	−	0.385653i
$917$	8.42017	+	3.06469i	0.278059	+	0.101205i
$918$	−13.5784	+	7.94128i	−0.448155	+	0.262101i
$919$	−31.2360	−	18.0341i	−1.03038	−	0.594890i	−0.113286	−	0.993562i	$-0.536138\pi$
$919$	−31.2360	−	18.0341i	−1.03038	−	0.594890i	−0.917093	+	0.398673i	$0.869471\pi$
$920$	−21.7403	+	39.1611i	−0.716756	+	1.29110i
$921$	−15.2652	+	86.5734i	−0.503006	+	2.85269i
$922$	36.4740	+	20.7866i	1.20121	+	0.684571i
$923$	7.32871	−	4.23123i	0.241227	−	0.139273i
$924$	27.3384	−	10.2988i	0.899367	−	0.338804i
$925$	−1.15566	+	1.37726i	−0.0379978	+	0.0452840i
$926$	20.1775	+	16.7392i	0.663074	+	0.550083i
$927$	23.4249	−	8.52597i	0.769375	−	0.280030i
$928$	8.81937	+	14.3328i	0.289510	+	0.470496i
$929$	−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
$934$	−34.3296	+	12.7133i	−1.12330	+	0.415990i
$935$	−18.7007	−	51.3799i	−0.611580	−	1.68030i
$936$	−6.76834	−	34.9401i	−0.221230	−	1.14205i
$937$	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	$0.544936\pi$
$938$	−18.1817	+	15.4307i	−0.593654	+	0.503830i
$939$	−0.752635	−	1.30360i	−0.0245613	−	0.0425414i
$940$	23.0714	+	26.8779i	0.752506	+	0.876660i
$941$	−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	$0.674226\pi$
$942$	−14.1053	+	2.56871i	−0.459574	+	0.0836932i
$943$	−4.13683	+	7.16519i	−0.134714	+	0.233331i
$944$	9.28197	−	16.9428i	0.302102	−	0.551440i
$945$	−2.84302	+	7.81114i	−0.0924835	+	0.254096i
$946$	0.0184895	+	3.29970i	0.000601145	+	0.107283i
$947$	−35.4036	−	42.1924i	−1.15046	−	1.37107i	−0.917089	−	0.398682i	$-0.869468\pi$
$947$	−35.4036	−	42.1924i	−1.15046	−	1.37107i	−0.233374	−	0.972387i	$-0.574977\pi$
$948$	23.1811	−	41.2105i	0.752886	−	1.33846i
$949$		−	35.4885i		−	1.15201i
$950$	6.95992	+	12.0003i	0.225810	+	0.389341i
$951$			1.99951i			0.0648386i
$952$	21.2038	−	18.4082i	0.687218	−	0.596614i
$953$	−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	$0.814079\pi$
$954$	44.7413	−	0.250702i	1.44855	−	0.00811679i
$955$	−21.9674	+	60.3550i	−0.710849	+	1.95304i
$956$	34.3775	−	6.45972i	1.11185	−	0.208922i
$957$	−13.0894	+	22.6716i	−0.423122	+	0.732868i
$958$	−0.110499	−	0.606771i	−0.00357007	−	0.0196039i
$959$	18.8593	+	3.32540i	0.608998	+	0.107383i
$960$	−43.9514	−	34.4297i	−1.41852	−	1.11121i
$961$	−1.49565	−	2.59055i	−0.0482469	−	0.0835661i
$962$	2.47448	+	2.91564i	0.0797804	+	0.0940039i
$963$	16.1678	+	13.5664i	0.521000	+	0.437171i
$964$	46.7984	−	27.7229i	1.50727	−	0.892895i
$965$	−14.8897	−	40.9090i	−0.479315	−	1.31691i
$966$	−12.4266	−	33.5555i	−0.399818	−	1.07963i
$967$	33.5782	−	5.92074i	1.07980	−	0.190398i	0.394674	−	0.918821i	$-0.370858\pi$
$967$	33.5782	−	5.92074i	1.07980	−	0.190398i	0.685127	+	0.728423i	$0.259747\pi$
$968$	−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	$-0.0475490\pi$
$971$	0.272182	+	1.54362i	0.00873472	+	0.0495371i	−0.980129	+	0.198362i	$0.936438\pi$
$972$	43.9811	−	0.492901i	1.41069	−	0.0158098i
$973$	−7.58866	+	2.76205i	−0.243281	+	0.0885471i
$974$	4.83161	−	5.82405i	0.154815	−	0.186615i
$975$	−12.6899	+	15.1232i	−0.406402	+	0.484332i
$976$	14.3566	+	4.86386i	0.459543	+	0.155688i
$977$	−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	$0.426209\pi$
$978$	8.16310	−	14.3237i	0.261027	−	0.458020i
$979$	−7.33105	+	41.5765i	−0.234301	+	1.32879i
$980$	−3.71688	+	22.5547i	−0.118731	+	0.720483i
$981$	25.3044	+	14.6095i	0.807909	+	0.466446i
$982$	19.0966	+	32.6523i	0.609396	+	1.04198i
$983$	−47.5857	−	17.3198i	−1.51775	−	0.552415i	−0.557163	−	0.830403i	$-0.688110\pi$
$983$	−47.5857	−	17.3198i	−1.51775	−	0.552415i	−0.960584	+	0.277988i	$0.910332\pi$
$984$	−8.01051	−	6.49532i	−0.255366	−	0.207063i
$985$	6.57633	−	5.51820i	0.209539	−	0.175824i
$986$	−4.23049	+	24.8042i	−0.134726	+	0.789927i
$987$	−28.2978			−0.900729
$988$	27.6505	−	10.3017i	0.879678	−	0.327742i
$989$	4.04170			0.128518
$990$	8.08089	−	47.3799i	0.256828	−	1.50583i
$991$	3.54873	−	2.97774i	0.112729	−	0.0945911i	−0.584681	−	0.811264i	$-0.698780\pi$
$991$	3.54873	−	2.97774i	0.112729	−	0.0945911i	0.697410	+	0.716672i	$0.254336\pi$
$992$	−32.3064	+	6.63463i	−1.02573	+	0.210650i
$993$	56.2686	+	20.4801i	1.78563	+	0.649916i
$994$	2.96303	+	5.06634i	0.0939816	+	0.160695i
$995$	26.6284	+	15.3739i	0.844178	+	0.487386i
$996$	40.0965	+	6.60767i	1.27051	+	0.209372i
$997$	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	$-0.237656\pi$
$998$	3.16033	−	5.54538i	0.100039	−	0.175536i
$999$	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.67.1	yes	48
3.2	odd	2		684.2.cf.a.523.8		48
4.3	odd	2	inner	76.2.k.a.67.2	yes	48
12.11	even	2		684.2.cf.a.523.7		48
19.2	odd	18	inner	76.2.k.a.59.2	yes	48
57.2	even	18		684.2.cf.a.667.7		48
76.59	even	18	inner	76.2.k.a.59.1	✓	48
228.59	odd	18		684.2.cf.a.667.8		48

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

\(f(q)\)	\(=\)	\(q+(-1.39408 - 0.237768i) q^{2} +(1.98545 - 1.66599i) q^{3} +(1.88693 + 0.662936i) q^{4} +(-2.53027 - 0.920944i) q^{5} +(-3.16400 + 1.85045i) q^{6} +(1.43753 + 0.829960i) q^{7} +(-2.47292 - 1.37284i) q^{8} +(0.645546 - 3.66107i) q^{9} +O(q^{10})\)	\(q+(-1.39408 - 0.237768i) q^{2} +(1.98545 - 1.66599i) q^{3} +(1.88693 + 0.662936i) q^{4} +(-2.53027 - 0.920944i) q^{5} +(-3.16400 + 1.85045i) q^{6} +(1.43753 + 0.829960i) q^{7} +(-2.47292 - 1.37284i) q^{8} +(0.645546 - 3.66107i) q^{9} +(3.30844 + 1.88549i) q^{10} +(2.94034 - 1.69761i) q^{11} +(4.85086 - 1.82739i) q^{12} +(-2.17565 + 2.59283i) q^{13} +(-1.80670 - 1.49883i) q^{14} +(-6.55803 + 2.38693i) q^{15} +(3.12103 + 2.50183i) 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} +(-4.50271 + 1.66749i) q^{22} +(2.01148 + 5.52649i) q^{23} +(-7.19700 + 1.39415i) q^{24} +(1.72393 + 1.44655i) q^{25} +(3.64952 - 3.09733i) q^{26} +(-0.929885 - 1.61061i) q^{27} +(2.16232 + 2.51907i) q^{28} +(-2.92975 - 0.516594i) q^{29} +(9.70996 - 1.76828i) q^{30} +(2.91510 - 5.04911i) q^{31} +(-3.75612 - 4.22984i) q^{32} +(3.00971 - 8.26910i) q^{33} +(-0.0473932 - 8.45798i) q^{34} +(-2.87301 - 3.42391i) q^{35} +(3.64516 - 6.48025i) q^{36} +0.798908i q^{37} +(5.79679 + 2.09694i) q^{38} +8.77256i q^{39} +(4.99284 + 5.75108i) q^{40} +(0.904276 + 1.07767i) q^{41} +(-6.08416 + 0.0340918i) q^{42} +(0.235045 - 0.645782i) q^{43} +(6.67363 - 1.25401i) q^{44} +(-5.00506 + 8.66901i) q^{45} +(-1.49014 - 8.18265i) q^{46} +(-6.47756 - 1.14217i) q^{47} +(10.3647 - 0.232345i) q^{48} +(-2.12233 - 3.67599i) q^{49} +(-2.05935 - 2.42650i) q^{50} +(11.8746 + 9.96394i) q^{51} +(-5.82418 + 3.45019i) q^{52} +(-2.91069 - 7.99704i) q^{53} +(0.913386 + 2.46642i) 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} +(-13.9569 + 0.156417i) q^{60} +(3.56100 - 1.29610i) q^{61} +(-5.26441 + 6.34575i) q^{62} +(3.96654 - 4.72714i) q^{63} +(4.23062 + 6.78983i) q^{64} +(7.89284 - 4.55693i) q^{65} +(-6.16191 + 10.8122i) q^{66} +(1.76401 - 10.0042i) q^{67} +(-1.94497 + 11.8024i) q^{68} +(13.2008 + 7.62148i) q^{69} +(3.19111 + 5.45633i) q^{70} +(-2.34943 - 0.855121i) q^{71} +(-6.62245 + 8.16730i) q^{72} +(-8.03196 + 6.73961i) q^{73} +(0.189955 - 1.11374i) q^{74} +5.83271 q^{75} +(-7.58263 - 4.30160i) q^{76} +5.63578 q^{77} +(2.08583 - 12.2297i) q^{78} +(6.98750 - 5.86321i) q^{79} +(-5.59302 - 9.20462i) q^{80} +(5.95057 + 2.16583i) q^{81} +(-1.00440 - 1.71737i) q^{82} +(6.78922 + 3.91976i) q^{83} +(8.48993 + 1.39909i) q^{84} +(2.79647 - 15.8596i) q^{85} +(-0.481219 + 0.844387i) q^{86} +(-6.67752 + 3.85527i) q^{87} +(-9.60176 + 0.161420i) q^{88} +(-7.99275 + 9.52539i) q^{89} +(9.03867 - 10.8953i) q^{90} +(-5.27951 + 1.92159i) q^{91} +(0.131813 + 11.7616i) 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} +(2.08468 + 5.62925i) 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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