LMFDB - Embedded newform 112.2.v.a.75.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(3,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.v (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			75.7
Character	$\chi$	$=$	112.75
Dual form			112.2.v.a.3.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.252874 - 1.39142i) q^{2} +(-2.61463 - 0.700587i) q^{3} +(-1.87211 + 0.703710i) q^{4} +(0.120751 + 0.450647i) q^{5} +(-0.313640 + 3.81521i) q^{6} +(-2.37326 + 1.16946i) q^{7} +(1.45257 + 2.42694i) q^{8} +(3.74737 + 2.16355i) q^{9} +(0.596506 - 0.281972i) q^{10} +(-1.93537 - 0.518581i) q^{11} +(5.38787 - 0.528362i) q^{12} +(-4.51607 - 4.51607i) q^{13} +(2.22735 + 3.00648i) q^{14} -1.26287i q^{15} +(3.00959 - 2.63484i) q^{16} +(-4.68066 + 2.70238i) q^{17} +(2.06279 - 5.76128i) q^{18} +(-0.510379 - 1.90476i) q^{19} +(-0.543183 - 0.758687i) q^{20} +(7.02450 - 1.39503i) q^{21} +(-0.232159 + 2.82405i) q^{22} +(0.951245 - 1.64761i) q^{23} +(-2.09763 - 7.36320i) q^{24} +(4.14162 - 2.39117i) q^{25} +(-5.14176 + 7.42576i) q^{26} +(-2.54010 - 2.54010i) q^{27} +(3.62004 - 3.85944i) q^{28} +(-1.12415 + 1.12415i) q^{29} +(-1.75718 + 0.319347i) q^{30} +(-0.434075 - 0.751840i) q^{31} +(-4.42722 - 3.52132i) q^{32} +(4.69696 + 2.71179i) q^{33} +(4.94377 + 5.82941i) q^{34} +(-0.813586 - 0.928290i) q^{35} +(-8.53799 - 1.41333i) q^{36} +(-7.90732 + 2.11876i) q^{37} +(-2.52126 + 1.19182i) q^{38} +(8.64394 + 14.9717i) q^{39} +(-0.918297 + 0.947649i) q^{40} +3.24226 q^{41} +(-3.71738 - 9.42127i) q^{42} +(6.35727 - 6.35727i) q^{43} +(3.98816 - 0.391099i) q^{44} +(-0.522499 + 1.94999i) q^{45} +(-2.53306 - 0.906947i) q^{46} +(-1.49266 + 2.58536i) q^{47} +(-9.71488 + 4.78065i) q^{48} +(4.26473 - 5.55087i) q^{49} +(-4.37443 - 5.15808i) q^{50} +(14.1314 - 3.78650i) q^{51} +(11.6326 + 5.27658i) q^{52} +(-1.81663 + 6.77976i) q^{53} +(-2.89203 + 4.17668i) q^{54} -0.934789i q^{55} +(-6.28553 - 4.06105i) q^{56} +5.33780i q^{57} +(1.84843 + 1.27990i) q^{58} +(-2.22228 + 8.29366i) q^{59} +(0.888694 + 2.36423i) q^{60} +(0.469703 - 0.125856i) q^{61} +(-0.936361 + 0.794103i) q^{62} +(-11.4237 - 0.752254i) q^{63} +(-3.78011 + 7.05059i) q^{64} +(1.48984 - 2.58047i) q^{65} +(2.58551 - 7.22120i) q^{66} +(-1.03224 + 3.85238i) q^{67} +(6.86102 - 8.35298i) q^{68} +(-3.64144 + 3.64144i) q^{69} +(-1.08591 + 1.36678i) q^{70} -12.1916 q^{71} +(0.192498 + 12.2373i) q^{72} +(-7.79109 - 13.4946i) q^{73} +(4.94765 + 10.4666i) q^{74} +(-12.5040 + 3.35044i) q^{75} +(2.29588 + 3.20676i) q^{76} +(5.19960 - 1.03261i) q^{77} +(18.6462 - 15.8133i) q^{78} +(-1.07130 - 0.618516i) q^{79} +(1.55079 + 1.03810i) q^{80} +(-1.62878 - 2.82113i) q^{81} +(-0.819885 - 4.51136i) q^{82} +(9.03560 - 9.03560i) q^{83} +(-12.1689 + 7.55485i) q^{84} +(-1.78301 - 1.78301i) q^{85} +(-10.4532 - 7.23805i) q^{86} +(3.72680 - 2.15167i) q^{87} +(-1.55269 - 5.45031i) q^{88} +(-1.16364 + 2.01548i) q^{89} +(2.84539 + 0.233913i) q^{90} +(15.9992 + 5.43644i) q^{91} +(-0.621399 + 3.75390i) q^{92} +(0.608215 + 2.26989i) q^{93} +(3.97479 + 1.42315i) q^{94} +(0.796746 - 0.460002i) q^{95} +(9.10855 + 12.3086i) q^{96} +4.69704i q^{97} +(-8.80204 - 4.53036i) q^{98} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.252874	−	1.39142i	−0.178809	−	0.983884i
$2$	−0.252874	−	1.39142i	−0.178809	−	0.983884i
$3$	−2.61463	−	0.700587i	−1.50955	−	0.404484i	−0.593268	−	0.805005i	$-0.702162\pi$
$3$	−2.61463	−	0.700587i	−1.50955	−	0.404484i	−0.916287	+	0.400521i	$0.868829\pi$
$4$	−1.87211	+	0.703710i	−0.936055	+	0.351855i
$5$	0.120751	+	0.450647i	0.0540013	+	0.201536i	0.987656	−	0.156639i	$-0.0500659\pi$
$5$	0.120751	+	0.450647i	0.0540013	+	0.201536i	−0.933655	+	0.358175i	$0.883399\pi$
$6$	−0.313640	+	3.81521i	−0.128043	+	1.55755i
$7$	−2.37326	+	1.16946i	−0.897008	+	0.442014i
$7$	−2.37326	+	1.16946i	−0.897008	+	0.442014i
$8$	1.45257	+	2.42694i	0.513559	+	0.858054i
$9$	3.74737	+	2.16355i	1.24912	+	0.721182i
$10$	0.596506	−	0.281972i	0.188632	−	0.0891674i
$11$	−1.93537	−	0.518581i	−0.583536	−	0.156358i	−0.0450390	−	0.998985i	$-0.514341\pi$
$11$	−1.93537	−	0.518581i	−0.583536	−	0.156358i	−0.538497	+	0.842627i	$0.681008\pi$
$12$	5.38787	−	0.528362i	1.55535	−	0.152525i
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.954581	−	0.297952i	$-0.903696\pi$
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.297952	−	0.954581i	$-0.596304\pi$
$14$	2.22735	+	3.00648i	0.595284	+	0.803515i
$15$		−	1.26287i		−	0.326072i
$16$	3.00959	−	2.63484i	0.752396	−	0.658711i
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.945244	−	0.326364i	$-0.894177\pi$
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.189983	+	0.981787i	$0.560843\pi$
$18$	2.06279	−	5.76128i	0.486204	−	1.35795i
$19$	−0.510379	−	1.90476i	−0.117089	−	0.436982i	0.882346	−	0.470602i	$-0.155963\pi$
$19$	−0.510379	−	1.90476i	−0.117089	−	0.436982i	−0.999435	+	0.0336198i	$0.989296\pi$
$20$	−0.543183	−	0.758687i	−0.121459	−	0.169648i
$21$	7.02450	−	1.39503i	1.53287	−	0.304420i
$22$	−0.232159	+	2.82405i	−0.0494966	+	0.602090i
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	−0.749645	−	0.661841i	$-0.769776\pi$
$23$	0.951245	−	1.64761i	0.198348	−	0.343549i	0.947993	+	0.318291i	$0.103109\pi$
$24$	−2.09763	−	7.36320i	−0.428177	−	1.50301i
$25$	4.14162	−	2.39117i	0.828325	−	0.478234i
$26$	−5.14176	+	7.42576i	−1.00838	+	1.45631i
$27$	−2.54010	−	2.54010i	−0.488843	−	0.488843i
$28$	3.62004	−	3.85944i	0.684123	−	0.729366i
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	−0.803736	−	0.594986i	$-0.797157\pi$
$29$	−1.12415	+	1.12415i	−0.208749	+	0.208749i	0.594986	+	0.803736i	$0.297157\pi$
$30$	−1.75718	+	0.319347i	−0.320817	+	0.0583046i
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	0.824408	−	0.565995i	$-0.191508\pi$
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	−0.902371	+	0.430961i	$0.858175\pi$
$32$	−4.42722	−	3.52132i	−0.782630	−	0.622487i
$33$	4.69696	+	2.71179i	0.817636	+	0.472062i
$34$	4.94377	+	5.82941i	0.847849	+	0.999736i
$35$	−0.813586	−	0.928290i	−0.137521	−	0.156910i
$36$	−8.53799	−	1.41333i	−1.42300	−	0.235555i
$37$	−7.90732	+	2.11876i	−1.29996	+	0.348322i	−0.841433	−	0.540361i	$-0.818288\pi$
$37$	−7.90732	+	2.11876i	−1.29996	+	0.348322i	−0.458522	+	0.888683i	$0.651621\pi$
$38$	−2.52126	+	1.19182i	−0.409003	+	0.193338i
$39$	8.64394	+	14.9717i	1.38414	+	2.39740i
$40$	−0.918297	+	0.947649i	−0.145196	+	0.149836i
$41$	3.24226			0.506356			0.253178	−	0.967420i	$-0.418524\pi$
$41$	3.24226			0.506356			0.253178	+	0.967420i	$0.418524\pi$
$42$	−3.71738	−	9.42127i	−0.573605	−	1.45373i
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	−0.0300731	−	0.999548i	$-0.509574\pi$
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	0.999548	+	0.0300731i	$0.00957401\pi$
$44$	3.98816	−	0.391099i	0.601237	−	0.0589604i
$45$	−0.522499	+	1.94999i	−0.0778895	+	0.290688i
$46$	−2.53306	−	0.906947i	−0.373479	−	0.133722i
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	−0.954113	−	0.299448i	$-0.903198\pi$
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	0.736386	+	0.676562i	$0.236531\pi$
$48$	−9.71488	+	4.78065i	−1.40222	+	0.690028i
$49$	4.26473	−	5.55087i	0.609246	−	0.792981i
$50$	−4.37443	−	5.15808i	−0.618638	−	0.729463i
$51$	14.1314	−	3.78650i	1.97880	−	0.530217i
$52$	11.6326	+	5.27658i	1.61315	+	0.731729i
$53$	−1.81663	+	6.77976i	−0.249533	+	0.931272i	0.721517	+	0.692397i	$0.243445\pi$
$53$	−1.81663	+	6.77976i	−0.249533	+	0.931272i	−0.971050	+	0.238875i	$0.923221\pi$
$54$	−2.89203	+	4.17668i	−0.393555	+	0.568374i
$55$		−	0.934789i		−	0.126047i
$56$	−6.28553	−	4.06105i	−0.839939	−	0.542681i
$57$			5.33780i			0.707009i
$58$	1.84843	+	1.27990i	0.242711	+	0.168059i
$59$	−2.22228	+	8.29366i	−0.289316	+	1.07974i	0.656311	+	0.754491i	$0.272116\pi$
$59$	−2.22228	+	8.29366i	−0.289316	+	1.07974i	−0.945627	+	0.325253i	$0.894551\pi$
$60$	0.888694	+	2.36423i	0.114730	+	0.305221i
$61$	0.469703	−	0.125856i	0.0601393	−	0.0161143i	−0.228624	−	0.973515i	$-0.573423\pi$
$61$	0.469703	−	0.125856i	0.0601393	−	0.0161143i	0.288763	+	0.957401i	$0.406756\pi$
$62$	−0.936361	+	0.794103i	−0.118918	+	0.100851i
$63$	−11.4237	−	0.752254i	−1.43925	−	0.0947751i
$64$	−3.78011	+	7.05059i	−0.472513	+	0.881323i
$65$	1.48984	−	2.58047i	0.184792	−	0.320068i
$66$	2.58551	−	7.22120i	0.318254	−	0.888868i
$67$	−1.03224	+	3.85238i	−0.126108	+	0.470643i	−0.999877	−	0.0156996i	$-0.995002\pi$
$67$	−1.03224	+	3.85238i	−0.126108	+	0.470643i	0.873768	+	0.486342i	$0.161669\pi$
$68$	6.86102	−	8.35298i	0.832020	−	1.01295i
$69$	−3.64144	+	3.64144i	−0.438378	+	0.438378i
$70$	−1.08591	+	1.36678i	−0.129791	+	0.163362i
$71$	−12.1916			−1.44687			−0.723437	−	0.690390i	$-0.757439\pi$
$71$	−12.1916			−1.44687			−0.723437	+	0.690390i	$0.757439\pi$
$72$	0.192498	+	12.2373i	0.0226862	+	1.44219i
$73$	−7.79109	−	13.4946i	−0.911878	−	1.57942i	−0.811408	−	0.584480i	$-0.801299\pi$
$73$	−7.79109	−	13.4946i	−0.911878	−	1.57942i	−0.100470	−	0.994940i	$-0.532035\pi$
$74$	4.94765	+	10.4666i	0.575152	+	1.21672i
$75$	−12.5040	+	3.35044i	−1.44384	+	0.386876i
$76$	2.29588	+	3.20676i	0.263356	+	0.367841i
$77$	5.19960	−	1.03261i	0.592549	−	0.117677i
$78$	18.6462	−	15.8133i	2.11126	−	1.79051i
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	0.438522	−	0.898720i	$-0.355502\pi$
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	−0.559053	+	0.829132i	$0.688835\pi$
$80$	1.55079	+	1.03810i	0.173384	+	0.116063i
$81$	−1.62878	−	2.82113i	−0.180976	−	0.313459i
$82$	−0.819885	−	4.51136i	−0.0905412	−	0.498196i
$83$	9.03560	−	9.03560i	0.991786	−	0.991786i	−0.00818066	−	0.999967i	$-0.502604\pi$
$83$	9.03560	−	9.03560i	0.991786	−	0.991786i	0.999967	+	0.00818066i	$0.00260402\pi$
$84$	−12.1689	+	7.55485i	−1.32774	+	0.824301i
$85$	−1.78301	−	1.78301i	−0.193395	−	0.193395i
$86$	−10.4532	−	7.23805i	−1.12720	−	0.780499i
$87$	3.72680	−	2.15167i	0.399554	−	0.230683i
$88$	−1.55269	−	5.45031i	−0.165517	−	0.581005i
$89$	−1.16364	+	2.01548i	−0.123345	+	0.213640i	−0.921085	−	0.389362i	$-0.872696\pi$
$89$	−1.16364	+	2.01548i	−0.123345	+	0.213640i	0.797740	+	0.603002i	$0.206029\pi$
$90$	2.84539	+	0.233913i	0.299930	+	0.0246566i
$91$	15.9992	+	5.43644i	1.67717	+	0.569894i
$92$	−0.621399	+	3.75390i	−0.0647854	+	0.391371i
$93$	0.608215	+	2.26989i	0.0630689	+	0.235376i
$94$	3.97479	+	1.42315i	0.409968	+	0.146786i
$95$	0.796746	−	0.460002i	0.0817444	−	0.0471952i
$96$	9.10855	+	12.3086i	0.929637	+	1.25624i
$97$			4.69704i			0.476912i	0.971153	+	0.238456i	$0.0766414\pi$
$97$			4.69704i			0.476912i	−0.971153	+	0.238456i	$0.923359\pi$
$98$	−8.80204	−	4.53036i	−0.889140	−	0.457635i
$99$	−6.13058	−	6.13058i	−0.616146	−	0.616146i
$100$	−6.07089	+	7.39103i	−0.607089	+	0.739103i
$101$	5.35584	+	1.43509i	0.532926	+	0.142797i	0.515239	−	0.857047i	$-0.327703\pi$
$101$	5.35584	+	1.43509i	0.532926	+	0.142797i	0.0176866	+	0.999844i	$0.494370\pi$
$102$	−8.84210	−	18.7053i	−0.875498	−	1.85210i
$103$	−0.958115	−	0.553168i	−0.0944059	−	0.0545053i	0.452054	−	0.891991i	$-0.350692\pi$
$103$	−0.958115	−	0.553168i	−0.0944059	−	0.0545053i	−0.546460	+	0.837485i	$0.684025\pi$
$104$	4.40036	−	17.5201i	0.431491	−	1.71799i
$105$	1.47688	+	2.99712i	0.144128	+	0.292489i
$106$	9.89289	+	0.813273i	0.960882	+	0.0789921i
$107$	−1.60020	−	5.97202i	−0.154697	−	0.577337i	−0.999131	−	0.0416773i	$-0.986730\pi$
$107$	−1.60020	−	5.97202i	−0.154697	−	0.577337i	0.844434	−	0.535659i	$-0.179937\pi$
$108$	6.54284	+	2.96785i	0.629585	+	0.285582i
$109$	−10.5236	−	2.81979i	−1.00798	−	0.270087i	−0.283194	−	0.959063i	$-0.591394\pi$
$109$	−10.5236	−	2.81979i	−1.00798	−	0.270087i	−0.724785	+	0.688975i	$0.758061\pi$
$110$	−1.30069	+	0.236384i	−0.124015	+	0.0225383i
$111$	22.1591			2.10324
$112$	−4.06118	+	9.77276i	−0.383746	+	0.923439i
$113$	−2.81872			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$113$	−2.81872			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$114$	7.42713	−	1.34979i	0.695615	−	0.126420i
$115$	0.857352	+	0.229727i	0.0799485	+	0.0214221i
$116$	1.31346	−	2.89561i	0.121951	−	0.268850i
$117$	−7.15267	−	26.6941i	−0.661264	−	2.46787i
$118$	12.1019	+	0.994875i	1.11407	+	0.0915857i
$119$	7.94810	−	11.8873i	0.728601	−	1.08971i
$120$	3.06491	−	1.83440i	0.279787	−	0.167457i
$121$	−6.04954	−	3.49271i	−0.549958	−	0.317519i
$122$	−0.293895	−	0.621729i	−0.0266080	−	0.0562887i
$123$	−8.47731	−	2.27149i	−0.764373	−	0.204813i
$124$	1.34171	+	1.10206i	0.120489	+	0.0989683i
$125$	3.22716	+	3.22716i	0.288646	+	0.288646i
$126$	1.84205	+	16.0854i	0.164103	+	1.43300i
$127$			9.34725i			0.829434i	0.909950	+	0.414717i	$0.136119\pi$
$127$			9.34725i			0.829434i	−0.909950	+	0.414717i	$0.863881\pi$
$128$	10.7662	+	3.47681i	0.951610	+	0.307310i
$129$	−21.0757	+	12.1681i	−1.85561	+	1.07134i
$130$	−3.96727	−	1.42046i	−0.347952	−	0.124582i
$131$	4.80174	+	17.9203i	0.419530	+	1.56571i	0.775586	+	0.631242i	$0.217455\pi$
$131$	4.80174	+	17.9203i	0.419530	+	1.56571i	−0.356056	+	0.934465i	$0.615879\pi$
$132$	−10.7015	−	1.77147i	−0.931449	−	0.154187i
$133$	3.43880	+	3.92362i	0.298182	+	0.340221i
$134$	5.62131	+	0.462116i	0.485607	+	0.0399207i
$135$	0.837971	−	1.45141i	0.0721211	−	0.124917i
$136$	−13.3575	−	7.43431i	−1.14540	−	0.637487i
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.181455	−	0.983399i	$-0.441919\pi$
$137$	13.1541	−	7.59453i	1.12383	−	0.648844i	0.942376	+	0.334555i	$0.108586\pi$
$138$	5.98761	+	4.14595i	0.509699	+	0.352927i
$139$	1.13113	+	1.13113i	0.0959413	+	0.0959413i	0.753448	−	0.657507i	$-0.228389\pi$
$139$	1.13113	+	1.13113i	0.0959413	+	0.0959413i	−0.657507	+	0.753448i	$0.728389\pi$
$140$	2.17637	+	1.16533i	0.183937	+	0.0984885i
$141$	5.71402	−	5.71402i	0.481207	−	0.481207i
$142$	3.08294	+	16.9636i	0.258714	+	1.42356i
$143$	6.39833	+	11.0822i	0.535055	+	0.926742i
$144$	16.9786	−	3.36236i	1.41489	−	0.280196i
$145$	−0.642337	−	0.370853i	−0.0533431	−	0.0307977i
$146$	−16.8065	+	14.2531i	−1.39091	+	1.17960i
$147$	−15.0395	+	11.5256i	−1.24044	+	0.950618i
$148$	13.3124	−	9.53101i	1.09427	−	0.783444i
$149$	−9.81380	+	2.62960i	−0.803978	+	0.215425i	−0.637330	−	0.770591i	$-0.719961\pi$
$149$	−9.81380	+	2.62960i	−0.803978	+	0.215425i	−0.166648	+	0.986016i	$0.553294\pi$
$150$	7.82382	+	16.5511i	0.638813	+	1.35139i
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	0.524425	−	0.851457i	$-0.324280\pi$
$151$	−5.83900	−	10.1134i	−0.475171	−	0.823020i	−0.999596	+	0.0284368i	$0.990947\pi$
$152$	3.88139	−	4.00545i	0.314822	−	0.324885i
$153$	−23.3869			−1.89072
$154$	−2.75164	−	6.97372i	−0.221734	−	0.561958i
$155$	0.286400	−	0.286400i	0.0230042	−	0.0230042i
$156$	−26.7182	−	21.9459i	−2.13916	−	1.75708i
$157$	0.576431	−	2.15127i	0.0460042	−	0.171690i	−0.939101	−	0.343640i	$-0.888340\pi$
$157$	0.576431	−	2.15127i	0.0460042	−	0.171690i	0.985106	+	0.171950i	$0.0550067\pi$
$158$	−0.589712	+	1.64704i	−0.0469150	+	0.131031i
$159$	9.49962	−	16.4538i	0.753369	−	1.30487i
$160$	1.05228	−	2.42032i	0.0831902	−	0.191343i
$161$	−0.330743	+	5.02264i	−0.0260662	+	0.395839i
$162$	−3.51350	+	2.97971i	−0.276047	+	0.234108i
$163$	−14.1740	+	3.79792i	−1.11020	+	0.297476i	−0.766910	−	0.641755i	$-0.778207\pi$
$163$	−14.1740	+	3.79792i	−1.11020	+	0.297476i	−0.343286	+	0.939231i	$0.611540\pi$
$164$	−6.06987	+	2.28161i	−0.473977	+	0.178164i
$165$	−0.654901	+	2.44412i	−0.0509839	+	0.190275i
$166$	−14.8572	−	10.2875i	−1.15314	−	0.798462i
$167$		−	5.94995i		−	0.460421i	−0.973141	−	0.230210i	$-0.926059\pi$
$167$		−	5.94995i		−	0.460421i	0.973141	−	0.230210i	$-0.0739415\pi$
$168$	13.5892	+	15.0217i	1.04843	+	1.15895i
$169$			27.7898i			2.13768i
$170$	−2.03004	+	2.93180i	−0.155697	+	0.224859i
$171$	2.20846	−	8.24207i	0.168885	−	0.630287i
$172$	−7.42783	+	16.3752i	−0.566367	+	1.24860i
$173$	−8.87194	+	2.37723i	−0.674521	+	0.180737i	−0.579790	−	0.814766i	$-0.696866\pi$
$173$	−8.87194	+	2.37723i	−0.674521	+	0.180737i	−0.0947304	+	0.995503i	$0.530199\pi$
$174$	−3.93629	−	4.64144i	−0.298409	−	0.351867i
$175$	−7.03278	+	10.5183i	−0.531628	+	0.795111i
$176$	−7.19105	+	3.53868i	−0.542045	+	0.266738i
$177$	11.6209	−	20.1279i	0.873478	−	1.51291i
$178$	3.09863	+	1.10945i	0.232252	+	0.0831566i
$179$	−0.984716	+	3.67501i	−0.0736011	+	0.274683i	−0.992912	−	0.118848i	$-0.962080\pi$
$179$	−0.984716	+	3.67501i	−0.0736011	+	0.274683i	0.919311	+	0.393531i	$0.128747\pi$
$180$	−0.394053	−	4.01828i	−0.0293710	−	0.299505i
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	−0.490055	−	0.871691i	$-0.663023\pi$
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	0.871691	+	0.490055i	$0.163023\pi$
$182$	3.51861	−	23.6363i	0.260816	−	1.75204i
$183$	−1.31627			−0.0973015
$184$	5.38039	−	0.0846358i	0.396648	−	0.00623943i
$185$	−1.90963	−	3.30757i	−0.140398	−	0.243177i
$186$	3.00457	−	1.42028i	0.220306	−	0.104140i
$187$	10.4602	−	2.80281i	0.764927	−	0.204962i
$188$	0.975077	−	5.89048i	0.0711148	−	0.429607i
$189$	8.99887	+	3.05777i	0.654572	+	0.222420i
$190$	−0.841533	−	0.992287i	−0.0610512	−	0.0719881i
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.165791	−	0.986161i	$-0.553018\pi$
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.936936	+	0.349501i	$0.886351\pi$
$192$	14.8231	−	15.7864i	1.06977	−	1.13928i
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	0.959793	−	0.280708i	$-0.0905692\pi$
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	−0.722997	+	0.690851i	$0.757236\pi$
$194$	6.53557	−	1.18776i	0.469226	−	0.0852763i
$195$	−5.70321	+	5.70321i	−0.408415	+	0.408415i
$196$	−4.07783	+	13.3930i	−0.291274	+	0.956640i
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.998082	+	0.0619015i	$0.0197165\pi$
$197$	14.8776	+	14.8776i	1.05998	+	1.05998i	0.0619015	+	0.998082i	$0.480284\pi$
$198$	−6.97996	+	10.0805i	−0.496044	+	0.716389i
$199$	6.43322	−	3.71422i	0.456039	−	0.263294i	−0.254338	−	0.967115i	$-0.581858\pi$
$199$	6.43322	−	3.71422i	0.456039	−	0.263294i	0.710377	+	0.703821i	$0.248524\pi$
$200$	11.8192	+	6.57816i	0.835744	+	0.465146i
$201$	5.39785	−	9.34935i	0.380735	−	0.659452i
$202$	0.642465	−	7.81512i	0.0452037	−	0.549870i
$203$	1.35325	−	3.98255i	0.0949796	−	0.279520i
$204$	−23.7910	+	17.0332i	−1.66570	+	1.19256i
$205$	0.391505	+	1.46112i	0.0273439	+	0.102049i
$206$	−0.527407	+	1.47302i	−0.0367462	+	0.102630i
$207$	7.12934	−	4.11612i	0.495523	−	0.286090i
$208$	−25.4906	−	1.69236i	−1.76746	−	0.117344i
$209$			3.95109i			0.273303i
$210$	3.79679	−	2.81285i	0.262004	−	0.194105i
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	0.319820	−	0.947478i	$-0.396378\pi$
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	−0.947478	+	0.319820i	$0.896378\pi$
$212$	−1.37005	−	13.9708i	−0.0940955	−	0.959521i
$213$	31.8764	+	8.54126i	2.18414	+	0.585237i
$214$	−7.90494	+	3.73672i	−0.540371	+	0.255437i
$215$	3.63253	+	2.09724i	0.247736	+	0.143031i
$216$	2.47502	−	9.85435i	0.168404	−	0.670504i
$217$	1.90942	+	1.27668i	0.129620	+	0.0866666i
$218$	−1.26237	+	15.3558i	−0.0854985	+	1.04003i
$219$	10.9167	+	40.7416i	0.737681	+	2.75306i
$220$	0.657820	+	1.75003i	0.0443502	+	0.117987i
$221$	33.3423	+	8.93405i	2.24285	+	0.600969i
$222$	−5.60346	−	30.8326i	−0.376079	−	2.06935i
$223$	−6.72926			−0.450624			−0.225312	−	0.974287i	$-0.572340\pi$
$223$	−6.72926			−0.450624			−0.225312	+	0.974287i	$0.572340\pi$
$224$	14.6250	+	3.17954i	0.977174	+	0.212442i
$225$	20.6936			1.37957
$226$	0.712783	+	3.92203i	0.0474136	+	0.260890i
$227$	−7.46500	−	2.00024i	−0.495469	−	0.132761i	0.00242728	−	0.999997i	$-0.499227\pi$
$227$	−7.46500	−	2.00024i	−0.495469	−	0.132761i	−0.497896	+	0.867236i	$0.665894\pi$
$228$	−3.75626	−	9.99294i	−0.248765	−	0.661799i
$229$	−3.94509	−	14.7233i	−0.260699	−	0.972941i	−0.964831	−	0.262872i	$-0.915330\pi$
$229$	−3.94509	−	14.7233i	−0.260699	−	0.972941i	0.704132	−	0.710069i	$-0.251336\pi$
$230$	0.102845	−	1.25103i	0.00678137	−	0.0824905i
$231$	−14.3184	−	0.942877i	−0.942084	−	0.0620367i
$232$	−4.36115	−	1.09535i	−0.286323	−	0.0719130i
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	0.856670	−	0.515865i	$-0.172529\pi$
$233$	12.7954	+	7.38741i	0.838253	+	0.483965i	−0.0184173	+	0.999830i	$0.505863\pi$
$234$	−35.3340	+	16.7026i	−2.30986	+	1.09189i
$235$	−1.34533	−	0.360479i	−0.0877594	−	0.0235151i
$236$	−1.67598	−	17.0905i	−0.109097	−	1.11250i
$237$	2.36773	+	2.36773i	0.153800	+	0.153800i
$238$	−18.5501	−	8.05316i	−1.20243	−	0.522009i
$239$		−	28.5488i		−	1.84667i	−0.383998	−	0.923334i	$-0.625453\pi$
$239$		−	28.5488i		−	1.84667i	0.383998	−	0.923334i	$-0.374547\pi$
$240$	−3.32746	−	3.80072i	−0.214787	−	0.245335i
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.303584	−	0.952805i	$-0.401817\pi$
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.976945	+	0.213491i	$0.0684834\pi$
$242$	−3.33005	+	9.30068i	−0.214064	+	0.597870i
$243$	5.07143	+	18.9268i	0.325332	+	1.21416i
$244$	−0.790768	+	0.566151i	−0.0506238	+	0.0362441i
$245$	3.01645	+	1.25162i	0.192714	+	0.0799628i
$246$	−1.01690	+	12.3699i	−0.0648354	+	0.788677i
$247$	−6.29713	+	10.9069i	−0.400676	+	0.693992i
$248$	1.19415	−	2.14557i	0.0758287	−	0.136244i
$249$	−29.9549	+	17.2945i	−1.89832	+	1.09599i
$250$	3.67427	−	5.30641i	0.232382	−	0.335607i
$251$	−10.2808	−	10.2808i	−0.648918	−	0.648918i	0.303813	−	0.952732i	$-0.401740\pi$
$251$	−10.2808	−	10.2808i	−0.648918	−	0.648918i	−0.952732	+	0.303813i	$0.901740\pi$
$252$	21.9157	−	6.63064i	1.38056	−	0.417691i
$253$	−2.69543	+	2.69543i	−0.169460	+	0.169460i
$254$	13.0060	−	2.36368i	0.816067	−	0.148310i
$255$	3.41276	+	5.91107i	0.213715	+	0.370165i
$256$	2.11521	−	15.8596i	0.132200	−	0.991223i
$257$	2.17812	+	1.25754i	0.135867	+	0.0784431i	0.566393	−	0.824135i	$-0.308338\pi$
$257$	2.17812	+	1.25754i	0.135867	+	0.0784431i	−0.430526	+	0.902578i	$0.641672\pi$
$258$	22.2604	+	26.2482i	1.38587	+	1.63414i
$259$	16.2883	−	14.2757i	1.01211	−	0.887046i
$260$	−0.973233	+	5.87934i	−0.0603574	+	0.364621i
$261$	−6.64475	+	1.78046i	−0.411300	+	0.110207i
$262$	23.7205	−	11.2128i	1.46546	−	0.692731i
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	0.691061	−	0.722797i	$-0.257144\pi$
$263$	−4.54781	−	7.87703i	−0.280430	−	0.485718i	−0.971491	+	0.237078i	$0.923810\pi$
$264$	0.241278	+	15.3383i	0.0148496	+	0.944008i
$265$	−3.27464			−0.201159
$266$	4.58983	−	5.77701i	0.281420	−	0.354211i
$267$	4.45449	−	4.45449i	0.272611	−	0.272611i
$268$	−0.778486	−	7.93847i	−0.0475536	−	0.484919i
$269$	1.47548	−	5.50656i	0.0899615	−	0.335741i	−0.906246	−	0.422751i	$-0.861065\pi$
$269$	1.47548	−	5.50656i	0.0899615	−	0.335741i	0.996207	+	0.0870099i	$0.0277312\pi$
$270$	−2.23142	−	0.798947i	−0.135800	−	0.0486224i
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	−0.986231	−	0.165372i	$-0.947118\pi$
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	0.636332	+	0.771415i	$0.280451\pi$
$272$	−6.96650	+	20.4658i	−0.422406	+	1.24092i
$273$	−38.0232	−	25.4231i	−2.30127	−	1.53868i
$274$	−13.8935	−	16.3824i	−0.839338	−	0.989700i
$275$	−9.25560	+	2.48003i	−0.558134	+	0.149551i
$276$	4.25466	−	9.37969i	0.256100	−	0.564591i
$277$	5.40800	−	20.1829i	0.324935	−	1.21268i	−0.589442	−	0.807811i	$-0.700652\pi$
$277$	5.40800	−	20.1829i	0.324935	−	1.21268i	0.914377	−	0.404864i	$-0.132681\pi$
$278$	1.28785	−	1.85991i	0.0772399	−	0.111550i
$279$		−	3.75657i		−	0.224900i
$280$	1.07112	−	3.32293i	0.0640116	−	0.198583i
$281$		−	19.8360i		−	1.18331i	−0.806190	−	0.591657i	$-0.798474\pi$
$281$		−	19.8360i		−	1.18331i	0.806190	−	0.591657i	$-0.201526\pi$
$282$	−9.39554	−	6.50568i	−0.559496	−	0.387408i
$283$	5.26602	−	19.6531i	0.313033	−	1.16825i	−0.612775	−	0.790258i	$-0.709947\pi$
$283$	5.26602	−	19.6531i	0.313033	−	1.16825i	0.925807	−	0.377996i	$-0.123387\pi$
$284$	22.8240	−	8.57933i	1.35435	−	0.509090i
$285$	−2.40546	+	0.644542i	−0.142487	+	0.0381794i
$286$	13.8021	−	11.7052i	0.816134	−	0.692142i
$287$	−7.69473	+	3.79170i	−0.454206	+	0.223817i
$288$	−8.97192	−	22.7742i	−0.528675	−	1.34198i
$289$	6.10572	−	10.5754i	0.359160	−	0.622083i
$290$	−0.353583	+	0.987540i	−0.0207631	+	0.0579904i
$291$	3.29069	−	12.2810i	0.192903	−	0.719926i
$292$	24.0820	+	19.7806i	1.40929	+	1.15757i
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	−0.876336	−	0.481700i	$-0.840020\pi$
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	0.481700	+	0.876336i	$0.340020\pi$
$294$	19.8401	+	18.0118i	1.15710	+	1.05047i
$295$	−4.00586			−0.233230
$296$	−16.6280	−	16.1130i	−0.966483	−	0.936548i
$297$	3.59879	+	6.23329i	0.208823	+	0.361692i
$298$	6.14054	+	12.9902i	0.355712	+	0.752501i
$299$	−11.7366	+	3.14481i	−0.678745	+	0.181869i
$300$	21.0512	−	15.0716i	1.21539	−	0.870159i
$301$	−7.65288	+	22.5220i	−0.441105	+	1.29815i
$302$	−12.5955	+	10.6819i	−0.724791	+	0.614676i
$303$	−12.9981	−	7.50446i	−0.746721	−	0.431120i
$304$	−6.55477	−	4.38777i	−0.375942	−	0.251656i
$305$	0.113434	+	0.196473i	0.00649520	+	0.0112500i
$306$	5.91394	+	32.5410i	0.338078	+	1.86025i
$307$	2.36930	−	2.36930i	0.135223	−	0.135223i	−0.636255	−	0.771479i	$-0.719517\pi$
$307$	2.36930	−	2.36930i	0.135223	−	0.135223i	0.771479	+	0.636255i	$0.219517\pi$
$308$	−9.00756	+	5.59217i	−0.513253	+	0.318644i
$309$	2.11757	+	2.11757i	0.120464	+	0.120464i
$310$	−0.470926	−	0.326080i	−0.0267468	−	0.0185201i
$311$	−13.1239	+	7.57707i	−0.744186	+	0.429656i	−0.823589	−	0.567186i	$-0.808032\pi$
$311$	−13.1239	+	7.57707i	−0.744186	+	0.429656i	0.0794032	+	0.996843i	$0.474699\pi$
$312$	−23.7797	+	42.7258i	−1.34626	+	2.41887i
$313$	−3.32791	+	5.76411i	−0.188105	+	0.325807i	−0.944618	−	0.328171i	$-0.893568\pi$
$313$	−3.32791	+	5.76411i	−0.188105	+	0.325807i	0.756514	+	0.653978i	$0.226901\pi$
$314$	−3.13909	−	0.258058i	−0.177149	−	0.0145630i
$315$	−1.04041	−	5.23888i	−0.0586206	−	0.295177i
$316$	2.44085	+	0.404045i	0.137308	+	0.0227293i
$317$	6.86233	+	25.6106i	0.385427	+	1.43843i	0.837493	+	0.546449i	$0.184021\pi$
$317$	6.86233	+	25.6106i	0.385427	+	1.43843i	−0.452065	+	0.891985i	$0.649313\pi$
$318$	−25.2964	−	9.05723i	−1.41855	−	0.507904i
$319$	2.75861	−	1.59268i	0.154453	−	0.0891732i
$320$	−3.63378	−	0.852133i	−0.203134	−	0.0476357i
$321$			16.7357i			0.934094i
$322$	7.07225	−	0.809893i	0.394121	−	0.0451336i
$323$	7.53630	+	7.53630i	0.419331	+	0.419331i
$324$	5.03451	+	4.13527i	0.279695	+	0.229737i
$325$	−29.5026	−	7.90519i	−1.63651	−	0.438501i
$326$	8.86876	+	18.7617i	0.491195	+	1.03911i
$327$	25.5398	+	14.7454i	1.41235	+	0.815423i
$328$	4.70960	+	7.86879i	0.260044	+	0.434481i
$329$	0.518991	−	7.88134i	0.0286129	−	0.434513i
$330$	3.56641	+	0.293187i	0.196325	+	0.0161394i
$331$	2.45530	+	9.16331i	0.134956	+	0.503661i	0.999998	+	0.00196237i	$0.000624644\pi$
$331$	2.45530	+	9.16331i	0.134956	+	0.503661i	−0.865043	+	0.501699i	$0.832709\pi$
$332$	−10.5572	+	23.2741i	−0.579401	+	1.27733i
$333$	−34.2157	−	9.16806i	−1.87501	−	0.502407i
$334$	−8.27889	+	1.50459i	−0.453001	+	0.0823275i
$335$	−1.86071			−0.101661
$336$	17.4651	−	22.7069i	0.952802	−	1.23876i
$337$	−16.0354			−0.873502			−0.436751	−	0.899582i	$-0.643871\pi$
$337$	−16.0354			−0.873502			−0.436751	+	0.899582i	$0.643871\pi$
$338$	38.6673	−	7.02733i	2.10323	−	0.382236i
$339$	7.36991	+	1.97476i	0.400278	+	0.107254i
$340$	4.59272	+	2.08327i	0.249075	+	0.112981i
$341$	0.450207	+	1.68019i	0.0243801	+	0.0909876i
$342$	−12.0267	−	0.988686i	−0.650327	−	0.0534620i
$343$	−3.62978	+	18.1611i	−0.195990	+	0.980606i
$344$	24.6631	+	6.19438i	1.32974	+	0.333979i
$345$	−2.08071	−	1.20130i	−0.112022	−	0.0646758i
$346$	5.55121	+	11.7435i	0.298435	+	0.631333i
$347$	−3.06636	−	0.821629i	−0.164611	−	0.0441074i	0.175572	−	0.984467i	$-0.443822\pi$
$347$	−3.06636	−	0.821629i	−0.164611	−	0.0441074i	−0.340183	+	0.940359i	$0.610489\pi$
$348$	−5.46282	+	6.65074i	−0.292838	+	0.356517i
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	0.645378	−	0.763863i	$-0.276700\pi$
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	−0.763863	+	0.645378i	$0.776700\pi$
$350$	16.4138	+	7.12574i	0.877357	+	0.380887i
$351$			22.9426i			1.22458i
$352$	6.74223	+	9.11093i	0.359362	+	0.485614i
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	−0.677312	−	0.735696i	$-0.736855\pi$
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	0.298475	+	0.954417i	$0.403522\pi$
$354$	−30.9451	−	11.0797i	−1.64471	−	0.588879i
$355$	−1.47214	−	5.49410i	−0.0781331	−	0.291597i
$356$	0.760144	−	4.59206i	0.0402875	−	0.243379i
$357$	−29.1094	+	25.5125i	−1.54063	+	1.35026i
$358$	5.36250	+	0.440840i	0.283417	+	0.0232991i
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	−0.104245	−	0.994552i	$-0.533243\pi$
$359$	15.3319	−	26.5556i	0.809184	−	1.40155i	0.913430	−	0.406997i	$-0.133424\pi$
$360$	−5.49148	+	1.56442i	−0.289426	+	0.0824519i
$361$	13.0869	−	7.55570i	0.688782	−	0.397668i
$362$	−8.44245	−	5.84574i	−0.443725	−	0.307245i
$363$	13.3703	+	13.3703i	0.701761	+	0.701761i
$364$	−33.7779	+	1.08116i	−1.77044	+	0.0566681i
$365$	5.14051	−	5.14051i	0.269067	−	0.269067i
$366$	0.332851	+	1.83149i	0.0173984	+	0.0957334i
$367$	8.91168	+	15.4355i	0.465186	+	0.805726i	0.999210	−	0.0397435i	$-0.0126541\pi$
$367$	8.91168	+	15.4355i	0.465186	+	0.805726i	−0.534024	+	0.845469i	$0.679321\pi$
$368$	−1.47833	−	7.46499i	−0.0770631	−	0.389140i
$369$	12.1500	+	7.01478i	0.632502	+	0.365175i
$370$	−4.11933	+	3.49349i	−0.214154	+	0.181618i
$371$	−3.61732	−	18.2146i	−0.187802	−	0.945656i
$372$	−2.73599	−	3.82147i	−0.141854	−	0.198134i
$373$	2.39939	−	0.642914i	0.124236	−	0.0332888i	−0.196166	−	0.980571i	$-0.562849\pi$
$373$	2.39939	−	0.642914i	0.124236	−	0.0332888i	0.320401	+	0.947282i	$0.396182\pi$
$374$	−6.54501	−	13.8458i	−0.338434	−	0.715950i
$375$	−6.17691	−	10.6987i	−0.318974	−	0.552480i
$376$	−8.44272	+	0.132807i	−0.435400	+	0.00684902i
$377$	10.1535			0.522931
$378$	1.97907	−	13.2945i	0.101792	−	0.683793i
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	−0.720489	−	0.693466i	$-0.756083\pi$
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	0.693466	+	0.720489i	$0.256083\pi$
$380$	−1.16789	+	1.42185i	−0.0599114	+	0.0729394i
$381$	6.54856	−	24.4396i	0.335493	−	1.25208i
$382$	−8.38906	+	23.4303i	−0.429222	+	1.19880i
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	−0.383928	−	0.923363i	$-0.625429\pi$
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	0.991620	−	0.129190i	$-0.0412377\pi$
$384$	−25.7139	−	16.6332i	−1.31221	−	0.848812i
$385$	1.09320	+	2.21850i	0.0557145	+	0.113065i
$386$	7.09630	−	6.01819i	0.361192	−	0.306318i
$387$	37.5773	−	10.0688i	1.91016	−	0.511826i
$388$	−3.30535	−	8.79338i	−0.167804	−	0.446416i
$389$	6.27509	−	23.4190i	0.318160	−	1.18739i	−0.602852	−	0.797853i	$-0.705969\pi$
$389$	6.27509	−	23.4190i	0.318160	−	1.18739i	0.921012	−	0.389535i	$-0.127364\pi$
$390$	9.37777	+	6.49338i	0.474862	+	0.328805i
$391$			10.2825i			0.520009i
$392$	19.6664	+	2.28725i	0.993305	+	0.115524i
$393$		−	50.2190i		−	2.53321i
$394$	16.9388	−	24.4631i	0.853366	−	1.23244i
$395$	0.149372	−	0.557465i	0.00751574	−	0.0280491i
$396$	15.7913	+	7.16297i	0.793541	+	0.359953i
$397$	4.07659	−	1.09232i	0.204598	−	0.0548219i	−0.155064	−	0.987904i	$-0.549558\pi$
$397$	4.07659	−	1.09232i	0.204598	−	0.0548219i	0.359662	+	0.933082i	$0.382892\pi$
$398$	−6.79485	−	8.01209i	−0.340595	−	0.401610i
$399$	−6.24235	−	12.6680i	−0.312508	−	0.634193i
$400$	6.16422	−	18.1090i	0.308211	−	0.905448i
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	−0.998387	−	0.0567812i	$-0.981916\pi$
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	0.548367	+	0.836238i	$0.315250\pi$
$402$	−14.3739	−	5.14647i	−0.716903	−	0.256683i
$403$	−1.43505	+	5.35568i	−0.0714849	+	0.266785i
$404$	−11.0366	+	1.08230i	−0.549091	+	0.0538467i
$405$	1.07466	−	1.07466i	0.0534002	−	0.0534002i
$406$	−5.88361	−	0.875859i	−0.291998	−	0.0434681i
$407$	16.4023			0.813034
$408$	29.7165	+	28.7960i	1.47118	+	1.42562i
$409$	13.9843	+	24.2215i	0.691478	+	1.19768i	0.971354	+	0.237639i	$0.0763736\pi$
$409$	13.9843	+	24.2215i	0.691478	+	1.19768i	−0.279875	+	0.960036i	$0.590293\pi$
$410$	1.93403	−	0.914228i	0.0955149	−	0.0451505i
$411$	−39.7137	+	10.6412i	−1.95893	+	0.524894i
$412$	2.18297	+	0.361356i	0.107547	+	0.0178027i
$413$	−4.42506	−	22.2819i	−0.217743	−	1.09642i
$414$	−7.53009	−	8.87905i	−0.370084	−	0.436382i
$415$	5.16292	+	2.98081i	0.253438	+	0.146322i
$416$	4.09114	+	35.8962i	0.200584	+	1.75996i
$417$	−2.16503	−	3.74994i	−0.106022	−	0.183635i
$418$	5.49763	−	0.999130i	0.268898	−	0.0488690i
$419$	−10.4669	+	10.4669i	−0.511342	+	0.511342i	−0.914937	−	0.403596i	$-0.867760\pi$
$419$	−10.4669	+	10.4669i	−0.511342	+	0.511342i	0.403596	+	0.914937i	$0.367760\pi$
$420$	−4.87398	−	4.57164i	−0.237826	−	0.223073i
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	0.941103	−	0.338119i	$-0.109791\pi$
$421$	12.3722	+	12.3722i	0.602984	+	0.602984i	−0.338119	+	0.941103i	$0.609791\pi$
$422$	−10.3804	+	14.9915i	−0.505312	+	0.729775i
$423$	−11.1871	+	6.45887i	−0.543935	+	0.314041i
$424$	−19.0929	+	5.43918i	−0.927232	+	0.264150i
$425$	−12.9237	+	22.3845i	−0.626891	+	1.08581i
$426$	3.82377	−	46.5134i	0.185262	−	2.25358i
$427$	−0.967542	+	0.847989i	−0.0468227	+	0.0410370i
$428$	7.19831	+	10.0542i	0.347943	+	0.485988i
$429$	−8.96517	−	33.4585i	−0.432842	−	1.61539i
$430$	1.99957	−	5.58472i	0.0964281	−	0.269319i
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	−0.756675	−	0.653791i	$-0.773178\pi$
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	0.187862	+	0.982195i	$0.439844\pi$
$432$	−14.3374	−	0.951885i	−0.689810	−	0.0457976i
$433$			19.1575i			0.920649i	0.887751	+	0.460325i	$0.152267\pi$
$433$			19.1575i			0.920649i	−0.887751	+	0.460325i	$0.847733\pi$
$434$	1.29356	−	2.97965i	0.0620926	−	0.143028i
$435$	1.41965	+	1.41965i	0.0680672	+	0.0680672i
$436$	21.6857	−	2.12661i	1.03855	−	0.101846i
$437$	−3.62379	−	0.970991i	−0.173349	−	0.0464488i
$438$	53.9282	−	25.4922i	2.57679	−	1.21806i
$439$	7.42387	+	4.28617i	0.354322	+	0.204568i	0.666587	−	0.745427i	$-0.267754\pi$
$439$	7.42387	+	4.28617i	0.354322	+	0.204568i	−0.312265	+	0.949995i	$0.601088\pi$
$440$	2.26868	−	1.35784i	0.108155	−	0.0647326i
$441$	27.9911	−	11.5742i	1.33291	−	0.551154i
$442$	3.99961	−	48.6524i	0.190242	−	2.31416i
$443$	−5.42088	−	20.2310i	−0.257554	−	0.961204i	−0.966652	−	0.256094i	$-0.917564\pi$
$443$	−5.42088	−	20.2310i	−0.257554	−	0.961204i	0.709098	−	0.705110i	$-0.249102\pi$
$444$	−41.4842	+	15.5935i	−1.96875	+	0.740037i
$445$	−1.04878	−	0.281020i	−0.0497169	−	0.0133216i
$446$	1.70166	+	9.36324i	0.0805758	+	0.443362i
$447$	27.5017			1.30079
$448$	0.725796	−	21.1536i	0.0342906	−	0.999412i
$449$	−24.4270			−1.15278			−0.576391	−	0.817174i	$-0.695539\pi$
$449$	−24.4270			−1.15278			−0.576391	+	0.817174i	$0.695539\pi$
$450$	−5.23288	−	28.7935i	−0.246680	−	1.35734i
$451$	−6.27498	−	1.68138i	−0.295477	−	0.0791729i
$452$	5.27696	−	1.98356i	0.248207	−	0.0932990i
$453$	8.18145	+	30.5336i	0.384398	+	1.43459i
$454$	−0.895471	+	10.8928i	−0.0420265	+	0.511223i
$455$	−0.518009	+	7.86644i	−0.0242846	+	0.368784i
$456$	−12.9545	+	7.75350i	−0.606652	+	0.363091i
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	0.571370	−	0.820693i	$-0.306412\pi$
$457$	3.12783	+	1.80585i	0.146314	+	0.0844743i	−0.425056	+	0.905167i	$0.639746\pi$
$458$	−19.4887	+	9.21242i	−0.910645	+	0.430468i
$459$	18.7537	+	5.02503i	0.875347	+	0.234548i
$460$	−1.76672	+	0.173253i	−0.0823736	+	0.00807798i
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.980318	−	0.197423i	$-0.936743\pi$
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.197423	−	0.980318i	$-0.563257\pi$
$462$	2.30883	+	20.1614i	0.107416	+	0.937994i
$463$			8.01165i			0.372333i	0.982518	+	0.186166i	$0.0596064\pi$
$463$			8.01165i			0.372333i	−0.982518	+	0.186166i	$0.940394\pi$
$464$	−0.421267	+	6.34518i	−0.0195568	+	0.294568i
$465$	−0.949477	+	0.548181i	−0.0440309	+	0.0254213i
$466$	7.04338	−	19.6718i	0.326278	−	0.911281i
$467$	−4.79633	−	17.9002i	−0.221948	−	0.828321i	−0.983604	−	0.180340i	$-0.942280\pi$
$467$	−4.79633	−	17.9002i	−0.221948	−	0.828321i	0.761657	−	0.647981i	$-0.224386\pi$
$468$	32.1755	+	44.9409i	1.48731	+	2.07739i
$469$	−2.05542	−	10.3499i	−0.0949107	−	0.477912i
$470$	−0.161380	+	1.96307i	−0.00744390	+	0.0905498i
$471$	−3.01430	+	5.22093i	−0.138892	+	0.240568i
$472$	−23.3563	+	6.65374i	−1.07506	+	0.306263i
$473$	−15.6004	+	9.00692i	−0.717309	+	0.414139i
$474$	2.69577	−	3.89325i	0.123821	−	0.178823i
$475$	−6.66840	−	6.66840i	−0.305967	−	0.305967i
$476$	−6.51450	+	27.8475i	−0.298591	+	1.27639i
$477$	−21.4759	+	21.4759i	−0.983314	+	0.983314i
$478$	−39.7234	+	7.21926i	−1.81691	+	0.330201i
$479$	13.6882	+	23.7087i	0.625432	+	1.08328i	0.988457	+	0.151501i	$0.0484106\pi$
$479$	13.6882	+	23.7087i	0.625432	+	1.08328i	−0.363025	+	0.931779i	$0.618256\pi$
$480$	−4.44697	+	5.59101i	−0.202975	+	0.255193i
$481$	45.2785	+	26.1415i	2.06452	+	1.19195i
$482$	−20.9966	−	24.7580i	−0.956369	−	1.12770i
$483$	4.38357	−	12.9006i	0.199459	−	0.586998i
$484$	13.7833	+	2.28160i	0.626512	+	0.103709i
$485$	−2.11671	+	0.567171i	−0.0961148	+	0.0257539i
$486$	25.0528	−	11.8426i	1.13642	−	0.537192i
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	0.558938	−	0.829210i	$-0.311209\pi$
$487$	−9.68012	−	16.7665i	−0.438648	−	0.759761i	−0.997585	+	0.0694492i	$0.977876\pi$
$488$	0.987720	+	0.957127i	0.0447120	+	0.0433271i
$489$	39.7206			1.79623
$490$	0.978743	−	4.51366i	0.0442151	−	0.203906i
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	−0.979148	−	0.203149i	$-0.934882\pi$
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	0.203149	+	0.979148i	$0.434882\pi$
$492$	17.4689	−	1.71309i	0.787559	−	0.0772321i
$493$	2.22388	−	8.29964i	0.100159	−	0.373797i
$494$	16.7685	+	6.00387i	0.754452	+	0.270127i
$495$	2.02246	−	3.50300i	0.0909027	−	0.157448i
$496$	−3.28737	−	1.11901i	−0.147607	−	0.0502449i
$497$	28.9338	−	14.2576i	1.29786	−	0.639539i
$498$	31.6388	+	37.3066i	1.41777	+	1.67175i
$499$	2.92484	−	0.783708i	0.130934	−	0.0350836i	−0.192757	−	0.981247i	$-0.561743\pi$
$499$	2.92484	−	0.783708i	0.130934	−	0.0350836i	0.323691	+	0.946163i	$0.395076\pi$
$500$	−8.31258	−	3.77061i	−0.371750	−	0.168627i
$501$	−4.16846	+	15.5569i	−0.186233	+	0.695031i
$502$	−11.7052	+	16.9047i	−0.522428	+	0.754493i
$503$			34.5673i			1.54128i	0.637272	+	0.770639i	$0.280063\pi$
$503$			34.5673i			1.54128i	−0.637272	+	0.770639i	$0.719937\pi$
$504$	−14.7679	−	28.8173i	−0.657816	−	1.28362i
$505$			2.58688i			0.115115i
$506$	4.43209	+	3.06888i	0.197030	+	0.136428i
$507$	19.4692	−	72.6599i	0.864656	−	3.22694i
$508$	−6.57775	−	17.4991i	−0.291840	−	0.776396i
$509$	−15.2307	+	4.08105i	−0.675088	+	0.180889i	−0.580046	−	0.814584i	$-0.696965\pi$
$509$	−15.2307	+	4.08105i	−0.675088	+	0.180889i	−0.0950424	+	0.995473i	$0.530299\pi$
$510$	7.36179	−	6.24334i	0.325985	−	0.276460i
$511$	34.2717	+	22.9147i	1.51609	+	1.01369i
$512$	−22.6022	+	1.06733i	−0.998887	+	0.0471698i
$513$	−3.54187	+	6.13470i	−0.156377	+	0.270854i
$514$	1.19898	−	3.34869i	0.0528846	−	0.147704i
$515$	0.133591	−	0.498567i	0.00588671	−	0.0219695i
$516$	30.8932	−	37.6111i	1.36000	−	1.65574i
$517$	4.22957	−	4.22957i	0.186016	−	0.186016i
$518$	−23.9824	−	19.0540i	−1.05372	−	0.837183i
$519$	24.8623			1.09133
$520$	8.42675	−	0.132556i	0.369537	−	0.00581297i
$521$	−7.72095	−	13.3731i	−0.338261	−	0.585885i	0.645845	−	0.763469i	$-0.276505\pi$
$521$	−7.72095	−	13.3731i	−0.338261	−	0.585885i	−0.984106	+	0.177584i	$0.943172\pi$
$522$	4.15765	+	8.79542i	0.181976	+	0.384965i
$523$	1.96968	−	0.527773i	0.0861280	−	0.0230779i	−0.215498	−	0.976504i	$-0.569137\pi$
$523$	1.96968	−	0.527773i	0.0861280	−	0.0230779i	0.301626	+	0.953426i	$0.402471\pi$
$524$	−21.6001	−	30.1698i	−0.943604	−	1.31797i
$525$	25.7571	−	22.5744i	1.12413	−	0.985229i
$526$	−9.81025	+	8.31981i	−0.427747	+	0.362761i
$527$	4.06352	+	2.34607i	0.177010	+	0.102197i
$528$	21.2810	−	4.21439i	0.926139	−	0.183408i
$529$	9.69026	+	16.7840i	0.421316	+	0.729740i
$530$	0.828072	+	4.55640i	0.0359692	+	0.197918i
$531$	−26.2714	+	26.2714i	−1.14008	+	1.14008i
$532$	−9.19891	−	4.92553i	−0.398823	−	0.213549i
$533$	−14.6423	−	14.6423i	−0.634228	−	0.634228i
$534$	−7.32450	−	5.07165i	−0.316962	−	0.219472i
$535$	2.49805	−	1.44225i	0.108000	−	0.0623538i
$536$	−10.8489	+	3.09064i	−0.468601	+	0.133495i
$537$	5.14933	−	8.91890i	0.222210	−	0.384879i
$538$	−8.03506	−	0.660545i	−0.346416	−	0.0284781i
$539$	−11.1324	+	8.53138i	−0.479507	+	0.367473i
$540$	−0.547403	+	3.30688i	−0.0235565	+	0.142306i
$541$	5.40772	+	20.1819i	0.232496	+	0.867686i	0.979262	+	0.202599i	$0.0649389\pi$
$541$	5.40772	+	20.1819i	0.232496	+	0.867686i	−0.746766	+	0.665087i	$0.768394\pi$
$542$	15.3384	+	5.49183i	0.658841	+	0.235894i
$543$	−17.0216	+	9.82741i	−0.730466	+	0.421735i
$544$	30.2383	+	4.51805i	1.29646	+	0.193710i
$545$		−	5.08293i		−	0.217729i
$546$	−25.7592	+	59.3351i	−1.10239	+	2.53931i
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	0.928945	−	0.370217i	$-0.120717\pi$
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	−0.370217	+	0.928945i	$0.620717\pi$
$548$	−19.2816	+	23.4744i	−0.823668	+	1.00278i
$549$	2.03245	+	0.544592i	0.0867427	+	0.0232426i
$550$	5.79127	+	12.2513i	0.246941	+	0.522397i
$551$	2.71498	+	1.56749i	0.115662	+	0.0667775i
$552$	−14.1270	−	3.54814i	−0.601285	−	0.151019i
$553$	3.26581	+	0.215055i	0.138876	+	0.00914507i
$554$	−29.4505	−	2.42106i	−1.25123	−	0.102861i
$555$	2.67572	+	9.98591i	0.113578	+	0.423878i
$556$	−2.91359	−	1.32161i	−0.123564	−	0.0560489i
$557$	−11.6914	−	3.13271i	−0.495381	−	0.132737i	0.00247440	−	0.999997i	$-0.499212\pi$
$557$	−11.6914	−	3.13271i	−0.495381	−	0.132737i	−0.497856	+	0.867260i	$0.665879\pi$
$558$	−5.22697	+	0.949939i	−0.221275	+	0.0402141i
$559$	−57.4198			−2.42860
$560$	−4.89446	−	0.650095i	−0.206829	−	0.0274715i
$561$	−29.3132			−1.23760
$562$	−27.6002	+	5.01600i	−1.16424	+	0.211587i
$563$	27.2040	+	7.28930i	1.14651	+	0.307207i	0.781567	−	0.623821i	$-0.214421\pi$
$563$	27.2040	+	7.28930i	1.14651	+	0.307207i	0.364946	+	0.931029i	$0.381087\pi$
$564$	−6.67626	+	14.7183i	−0.281121	+	0.619751i
$565$	−0.340362	−	1.27025i	−0.0143192	−	0.0534398i
$566$	−28.6773	−	2.35750i	−1.20540	−	0.0990932i
$567$	7.16472	+	4.79048i	0.300890	+	0.201181i
$568$	−17.7091	−	29.5883i	−0.743056	−	1.24150i
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	0.00642167	−	0.999979i	$-0.497956\pi$
$569$	−20.4277	−	11.7940i	−0.856375	−	0.494428i	−0.862797	+	0.505551i	$0.831289\pi$
$570$	1.50511	+	3.18403i	0.0630421	+	0.133364i
$571$	21.7673	+	5.83253i	0.910933	+	0.244084i	0.683705	−	0.729758i	$-0.260367\pi$
$571$	21.7673	+	5.83253i	0.910933	+	0.244084i	0.227227	+	0.973842i	$0.427034\pi$
$572$	−19.7770	−	16.2446i	−0.826919	−	0.679220i
$573$	33.6826	+	33.6826i	1.40711	+	1.40711i
$574$	7.22165	+	9.74780i	0.301426	+	0.406865i
$575$		−	9.09835i		−	0.379427i
$576$	−29.4197	+	18.2427i	−1.22582	+	0.760114i
$577$	−16.2893	+	9.40463i	−0.678132	+	0.391520i	−0.799151	−	0.601130i	$-0.794717\pi$
$577$	−16.2893	+	9.40463i	−0.678132	+	0.391520i	0.121019	+	0.992650i	$0.461384\pi$
$578$	−16.2588	−	5.82138i	−0.676279	−	0.242137i
$579$	−4.60942	−	17.2026i	−0.191561	−	0.714915i
$580$	1.46350	+	0.242259i	0.0607684	+	0.0100593i
$581$	−10.8771	+	32.0106i	−0.451256	+	1.32802i
$582$	−17.9202	−	1.47318i	−0.742816	−	0.0610653i
$583$	7.03171	−	12.1793i	0.291224	−	0.504414i
$584$	21.4335	−	38.5103i	0.886924	−	1.59357i
$585$	11.1659	−	6.44666i	0.461655	−	0.266537i
$586$	11.1074	+	7.69099i	0.458841	+	0.317712i
$587$	12.6185	+	12.6185i	0.520820	+	0.520820i	0.917819	−	0.396999i	$-0.129948\pi$
$587$	12.6185	+	12.6185i	0.520820	+	0.520820i	−0.396999	+	0.917819i	$0.629948\pi$
$588$	20.0449	−	32.1607i	0.826639	−	1.32628i
$589$	−1.21053	+	1.21053i	−0.0498791	+	0.0498791i
$590$	1.01298	+	5.57384i	0.0417037	+	0.229471i
$591$	−28.4763	−	49.3223i	−1.17136	−	2.02885i
$592$	−18.2152	+	27.2111i	−0.748638	+	1.11837i
$593$	−22.0260	−	12.7167i	−0.904498	−	0.522212i	−0.0258409	−	0.999666i	$-0.508226\pi$
$593$	−22.0260	−	12.7167i	−0.904498	−	0.522212i	−0.878657	+	0.477454i	$0.841560\pi$
$594$	7.76310	−	6.58368i	0.318524	−	0.270132i
$595$	6.31671	+	2.14639i	0.258960	+	0.0879934i
$596$	16.5220	−	11.8290i	0.676769	−	0.484533i
$597$	−19.4226	+	5.20427i	−0.794914	+	0.212997i
$598$	7.34364	+	15.5353i	0.300304	+	0.635286i
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	0.869864	+	0.493292i	$0.164207\pi$
$599$	21.1003	+	36.5468i	0.862135	+	1.49326i	−0.00772853	+	0.999970i	$0.502460\pi$
$600$	−26.2942	−	25.4798i	−1.07346	−	1.04021i
$601$	−29.8695			−1.21840			−0.609202	−	0.793015i	$-0.708510\pi$
$601$	−29.8695			−1.21840			−0.609202	+	0.793015i	$0.708510\pi$
$602$	33.2729	+	4.95314i	1.35610	+	0.201875i
$603$	−12.2030	+	12.2030i	−0.496944	+	0.496944i
$604$	18.0482	+	14.8245i	0.734369	+	0.603200i
$605$	0.843492	−	3.14796i	0.0342928	−	0.127983i
$606$	−7.15498	+	19.9835i	−0.290651	+	0.811775i
$607$	14.7137	−	25.4850i	0.597212	−	1.03440i	−0.396018	−	0.918243i	$-0.629608\pi$
$607$	14.7137	−	25.4850i	0.597212	−	1.03440i	0.993231	−	0.116160i	$-0.0370584\pi$
$608$	−4.44771	+	10.2300i	−0.180378	+	0.414882i
$609$	−6.32837	+	9.46480i	−0.256438	+	0.383533i
$610$	0.244692	−	0.207517i	0.00990730	−	0.00840212i
$611$	18.4166	−	4.93472i	0.745058	−	0.199638i
$612$	43.7828	−	16.4576i	1.76982	−	0.665258i
$613$	5.94532	−	22.1882i	0.240129	−	0.896175i	−0.735640	−	0.677373i	$-0.763118\pi$
$613$	5.94532	−	22.1882i	0.240129	−	0.896175i	0.975769	−	0.218802i	$-0.0702149\pi$
$614$	−3.89584	−	2.69756i	−0.157223	−	0.108865i
$615$		−	4.09456i		−	0.165108i
$616$	10.0588	+	11.1192i	0.405283	+	0.448005i
$617$			31.2064i			1.25632i	0.778084	+	0.628161i	$0.216192\pi$
$617$			31.2064i			1.25632i	−0.778084	+	0.628161i	$0.783808\pi$
$618$	2.41095	−	3.48191i	0.0969828	−	0.140063i
$619$	−4.74503	+	17.7087i	−0.190719	+	0.711772i	0.802615	+	0.596498i	$0.203441\pi$
$619$	−4.74503	+	17.7087i	−0.190719	+	0.711772i	−0.993334	+	0.115275i	$0.963225\pi$
$620$	−0.334630	+	0.737714i	−0.0134390	+	0.0296273i
$621$	−6.60135	+	1.76883i	−0.264903	+	0.0709805i
$622$	13.8616	+	16.3448i	0.555799	+	0.655366i
$623$	0.404591	−	6.14408i	0.0162096	−	0.246157i
$624$	65.4628	+	22.2833i	2.62061	+	0.892046i
$625$	10.8912	−	18.8641i	0.435648	−	0.754565i
$626$	8.86185	+	3.17293i	0.354191	+	0.126816i
$627$	2.76808	−	10.3306i	0.110547	−	0.412565i
$628$	0.434728	+	4.43305i	0.0173475	+	0.176898i
$629$	31.2858	−	31.2858i	1.24745	−	1.24745i
$630$	−7.02639	+	2.77243i	−0.279938	+	0.110456i
$631$	8.10970			0.322842			0.161421	−	0.986886i	$-0.448392\pi$
$631$	8.10970			0.322842			0.161421	+	0.986886i	$0.448392\pi$
$632$	−0.0550316	−	3.49842i	−0.00218904	−	0.139160i
$633$	17.4508	+	30.2257i	0.693608	+	1.20136i
$634$	33.8998	−	16.0247i	1.34633	−	0.636421i
$635$	−4.21231	+	1.12869i	−0.167160	+	0.0447905i
$636$	−6.20561	+	37.4883i	−0.246068	+	1.48651i
$637$	−44.3279	+	5.80831i	−1.75634	+	0.230134i
$638$	−2.91368	−	3.43564i	−0.115354	−	0.136018i
$639$	−45.6864	−	26.3770i	−1.80732	−	1.04346i
$640$	−0.266787	+	5.27160i	−0.0105457	+	0.208378i
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	−0.997928	−	0.0643416i	$-0.979505\pi$
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	0.443242	−	0.896402i	$-0.353828\pi$
$642$	23.2864	−	4.23202i	0.919040	−	0.167024i
$643$	21.6759	−	21.6759i	0.854812	−	0.854812i	−0.135909	−	0.990721i	$-0.543395\pi$
$643$	21.6759	−	21.6759i	0.854812	−	0.854812i	0.990721	+	0.135909i	$0.0433955\pi$
$644$	−2.91529	−	9.63568i	−0.114879	−	0.379699i
$645$	−8.02841	−	8.02841i	−0.316118	−	0.316118i
$646$	8.58043	−	12.3919i	0.337593	−	0.487553i
$647$	−39.8543	+	23.0099i	−1.56683	+	0.904612i	−0.570299	+	0.821437i	$0.693173\pi$
$647$	−39.8543	+	23.0099i	−1.56683	+	0.904612i	−0.996535	+	0.0831749i	$0.973494\pi$
$648$	4.48081	−	8.05083i	0.176023	−	0.316267i
$649$	8.60188	−	14.8989i	0.337653	−	0.584833i
$650$	−3.53901	+	43.0495i	−0.138811	+	1.68854i
$651$	−4.09800	−	4.67575i	−0.160613	−	0.183257i
$652$	23.8627	−	17.0845i	0.934536	−	0.669082i
$653$	7.84001	+	29.2593i	0.306803	+	1.14501i	0.931382	+	0.364043i	$0.118604\pi$
$653$	7.84001	+	29.2593i	0.306803	+	1.14501i	−0.624579	+	0.780962i	$0.714729\pi$
$654$	14.0587	−	39.2654i	0.549740	−	1.53540i
$655$	−7.49594	+	4.32778i	−0.292890	+	0.169100i
$656$	9.75787	−	8.54285i	0.380981	−	0.333542i
$657$		−	67.4255i		−	2.63052i
$658$	−11.0975	+	1.27085i	−0.432626	+	0.0495431i
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	0.546096	−	0.837723i	$-0.316113\pi$
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	−0.837723	+	0.546096i	$0.816113\pi$
$660$	−0.493907	−	5.03652i	−0.0192253	−	0.196046i
$661$	10.2052	+	2.73446i	0.396934	+	0.106358i	0.451764	−	0.892137i	$-0.350795\pi$
$661$	10.2052	+	2.73446i	0.396934	+	0.106358i	−0.0548296	+	0.998496i	$0.517462\pi$
$662$	12.1291	−	5.73352i	0.471412	−	0.222840i
$663$	−80.9187	−	46.7184i	−3.14262	−	1.81439i
$664$	35.0537	+	8.80409i	1.36035	+	0.341665i
$665$	−1.35293	+	2.02347i	−0.0524645	+	0.0784667i
$666$	−4.10438	+	49.9268i	−0.159041	+	1.93462i
$667$	0.782813	+	2.92150i	0.0303106	+	0.113121i
$668$	4.18704	+	11.1390i	0.162001	+	0.430979i
$669$	17.5945	+	4.71443i	0.680242	+	0.182270i
$670$	0.470525	+	2.58903i	0.0181780	+	0.100023i
$671$	−0.974316			−0.0376130
$672$	−36.0113	−	18.5594i	−1.38917	−	0.715944i
$673$	17.2027			0.663115			0.331557	−	0.943435i	$-0.392426\pi$
$673$	17.2027			0.663115			0.331557	+	0.943435i	$0.392426\pi$
$674$	4.05493	+	22.3120i	0.156190	+	0.859425i
$675$	−16.5940	−	4.44634i	−0.638702	−	0.171140i
$676$	−19.5560	−	52.0255i	−0.752152	−	2.00098i
$677$	5.18323	+	19.3441i	0.199208	+	0.743453i	0.991137	+	0.132841i	$0.0424099\pi$
$677$	5.18323	+	19.3441i	0.199208	+	0.743453i	−0.791930	+	0.610612i	$0.790923\pi$
$678$	0.884065	−	10.7540i	0.0339523	−	0.413006i
$679$	−5.49301	−	11.1473i	−0.210802	−	0.427794i
$680$	1.73733	−	6.91721i	0.0666235	−	0.265263i
$681$	18.1168	+	10.4598i	0.694238	+	0.400819i
$682$	2.22401	−	1.05131i	0.0851618	−	0.0402566i
$683$	−0.930638	−	0.249364i	−0.0356099	−	0.00954164i	0.240970	−	0.970533i	$-0.422534\pi$
$683$	−0.930638	−	0.249364i	−0.0356099	−	0.00954164i	−0.276580	+	0.960991i	$0.589201\pi$
$684$	1.66555	+	16.9842i	0.0636840	+	0.649406i
$685$	5.01082	+	5.01082i	0.191453	+	0.191453i
$686$	26.1876	+	0.458089i	0.999847	+	0.0174899i
$687$			41.2597i			1.57416i
$688$	2.38234	−	35.8832i	0.0908259	−	1.36803i
$689$	38.8219	−	22.4138i	1.47900	−	0.853899i
$690$	−1.14536	+	3.19893i	−0.0436029	+	0.121781i
$691$	−8.97758	−	33.5048i	−0.341523	−	1.27458i	−0.896622	−	0.442797i	$-0.853986\pi$
$691$	−8.97758	−	33.5048i	−0.341523	−	1.27458i	0.555099	−	0.831784i	$-0.312680\pi$
$692$	14.9364	−	10.6937i	0.567795	−	0.406513i
$693$	21.7189	+	7.37999i	0.825034	+	0.280343i
$694$	−0.367829	+	4.47437i	−0.0139626	+	0.169845i
$695$	−0.373156	+	0.646326i	−0.0141546	+	0.0245165i
$696$	10.6354	+	5.91929i	0.403133	+	0.224370i
$697$	−15.1759	+	8.76183i	−0.574829	+	0.331878i
$698$	−2.52015	+	3.63961i	−0.0953891	+	0.137761i
$699$	−28.2796	−	28.2796i	−1.06963	−	1.06963i
$700$	5.76427	−	24.6405i	0.217869	−	0.931323i
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.262444	−	0.964947i	$-0.415471\pi$
$701$	32.4969	−	32.4969i	1.22739	−	1.22739i	0.964947	−	0.262444i	$-0.0845286\pi$
$702$	31.9228	−	5.80159i	1.20485	−	0.218967i
$703$	8.07146	+	13.9802i	0.304421	+	0.527272i
$704$	10.9722	−	11.6852i	0.413531	−	0.440403i
$705$	3.26498	+	1.88504i	0.122966	+	0.0709945i
$706$	7.51780	+	8.86456i	0.282936	+	0.333622i
$707$	−14.3891	+	2.85759i	−0.541157	+	0.107471i
$708$	−7.59131	+	45.8594i	−0.285299	+	1.72350i
$709$	4.54454	−	1.21770i	0.170674	−	0.0457319i	−0.172470	−	0.985015i	$-0.555175\pi$
$709$	4.54454	−	1.21770i	0.170674	−	0.0457319i	0.343144	+	0.939283i	$0.388508\pi$
$710$	−7.27234	+	3.43768i	−0.272926	+	0.129014i
$711$	−2.67638	−	4.63562i	−0.100372	−	0.173849i
$712$	−6.58171	+	0.103533i	−0.246660	+	0.00388006i
$713$	−1.65165			−0.0618547
$714$	42.8597	+	34.0520i	1.60398	+	1.27436i
$715$	−4.22157	+	4.22157i	−0.157878	+	0.157878i
$716$	−0.742644	−	7.57297i	−0.0277539	−	0.283015i
$717$	−20.0009	+	74.6444i	−0.746947	+	2.78765i
$718$	−40.8270	−	14.6179i	−1.52365	−	0.545534i
$719$	9.27548	−	16.0656i	0.345917	−	0.599146i	−0.639603	−	0.768706i	$-0.720901\pi$
$719$	9.27548	−	16.0656i	0.345917	−	0.599146i	0.985520	+	0.169559i	$0.0542345\pi$
$720$	3.56542	+	7.24537i	0.132875	+	0.270019i
$721$	2.92076	+	0.192334i	0.108775	+	0.00716289i
$722$	−13.8225	−	16.2987i	−0.514420	−	0.606575i
$723$	−60.0174	+	16.0816i	−2.23207	+	0.598081i
$724$	−5.99901	+	13.2252i	−0.222952	+	0.491512i
$725$	−1.96778	+	7.34384i	−0.0730813	+	0.272743i
$726$	15.2228	−	21.9848i	0.564970	−	0.815933i
$727$			5.96613i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$727$			5.96613i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$728$	10.0459	+	46.7259i	0.372326	+	1.73178i
$729$		−	43.2669i		−	1.60248i
$730$	−8.45252	−	5.85272i	−0.312842	−	0.216619i
$731$	−12.5765	+	46.9360i	−0.465157	+	1.73599i
$732$	2.46420	−	0.926272i	0.0910795	−	0.0342360i
$733$	20.8755	−	5.59358i	0.771055	−	0.206604i	0.148218	−	0.988955i	$-0.452646\pi$
$733$	20.8755	−	5.59358i	0.771055	−	0.206604i	0.622838	+	0.782351i	$0.285980\pi$
$734$	19.2237	−	16.3031i	0.709561	−	0.601760i
$735$	−7.01002	−	5.38579i	−0.258569	−	0.198658i
$736$	−10.0131	+	3.94468i	−0.369089	+	0.145403i
$737$	3.99554	−	6.92048i	0.147178	−	0.254919i
$738$	6.68811	−	18.6796i	0.246193	−	0.687605i
$739$	−9.37297	+	34.9804i	−0.344790	+	1.28677i	0.548067	+	0.836434i	$0.315364\pi$
$739$	−9.37297	+	34.9804i	−0.344790	+	1.28677i	−0.892857	+	0.450340i	$0.851303\pi$
$740$	5.90260	+	4.84831i	0.216984	+	0.178227i
$741$	24.1059	−	24.1059i	0.885552	−	0.885552i
$742$	−24.4295	+	9.63923i	−0.896834	+	0.353867i
$743$	16.2749			0.597067			0.298533	−	0.954399i	$-0.403503\pi$
$743$	16.2749			0.597067			0.298533	+	0.954399i	$0.403503\pi$
$744$	−4.62542	+	4.77326i	−0.169576	+	0.174996i
$745$	−2.37004	−	4.10504i	−0.0868317	−	0.150397i
$746$	−1.50131	−	3.17598i	−0.0549668	−	0.116281i
$747$	53.4087	−	14.3108i	1.95412	−	0.523605i
$748$	−17.6103	+	12.6081i	−0.643897	+	0.460998i
$749$	10.7817	+	12.3018i	0.393955	+	0.449497i
$750$	−13.3245	+	11.3001i	−0.486540	+	0.412622i
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	0.760504	−	0.649334i	$-0.224952\pi$
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	−0.182087	+	0.983282i	$0.558285\pi$
$752$	2.31974	+	11.7138i	0.0845921	+	0.427158i
$753$	19.6778	+	34.0830i	0.717101	+	1.24205i
$754$	−2.56755	−	14.1278i	−0.0935048	−	0.514503i
$755$	3.85253	−	3.85253i	0.140208	−	0.140208i
$756$	−18.9987	+	0.608107i	−0.690975	+	0.0221166i
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	0.335333	−	0.942100i	$-0.391151\pi$
$757$	−16.6944	−	16.6944i	−0.606767	−	0.606767i	−0.942100	+	0.335333i	$0.891151\pi$
$758$	0.865015	+	0.598956i	0.0314188	+	0.0217551i
$759$	8.93593	−	5.15916i	0.324354	−	0.187266i
$760$	2.27372	+	1.26548i	0.0824766	+	0.0459036i
$761$	−4.43390	+	7.67974i	−0.160729	+	0.278390i	−0.935130	−	0.354304i	$-0.884718\pi$
$761$	−4.43390	+	7.67974i	−0.160729	+	0.278390i	0.774401	+	0.632695i	$0.218051\pi$
$762$	−35.6617	−	2.93167i	−1.29189	−	0.106203i
$763$	28.2729	−	5.61484i	1.02355	−	0.203271i
$764$	34.7228	+	5.74781i	1.25623	+	0.207949i
$765$	−2.82398	−	10.5392i	−0.102101	−	0.381047i
$766$	−31.6691	−	11.3389i	−1.14425	−	0.409692i
$767$	47.4908	−	27.4188i	1.71479	−	0.990036i
$768$	−16.6415	+	39.9849i	−0.600498	+	1.44283i
$769$			1.14344i			0.0412335i	0.999787	+	0.0206167i	$0.00656298\pi$
$769$			1.14344i			0.0412335i	−0.999787	+	0.0206167i	$0.993437\pi$
$770$	2.81042	−	2.08210i	0.101281	−	0.0750337i
$771$	−4.81396	−	4.81396i	−0.173370	−	0.173370i
$772$	−10.1683	−	8.35210i	−0.365966	−	0.300599i
$773$	−5.25103	−	1.40701i	−0.188866	−	0.0506066i	0.163146	−	0.986602i	$-0.447836\pi$
$773$	−5.25103	−	1.40701i	−0.188866	−	0.0506066i	−0.352012	+	0.935995i	$0.614503\pi$
$774$	−23.5123	−	49.7397i	−0.845132	−	1.78786i
$775$	−3.59555	−	2.07589i	−0.129156	−	0.0745683i
$776$	−11.3995	+	6.82276i	−0.409217	+	0.244923i
$777$	−52.5892	+	25.9141i	−1.88663	+	0.929664i
$778$	−34.1725	−	2.80925i	−1.22514	−	0.100716i
$779$	−1.65478	−	6.17573i	−0.0592888	−	0.221269i
$780$	6.66363	−	14.6904i	0.238596	−	0.526002i
$781$	23.5952	+	6.32232i	0.844304	+	0.226231i
$782$	14.3073	−	2.60018i	0.511628	−	0.0929823i
$783$	5.71091			0.204091
$784$	−1.79061	−	27.9427i	−0.0639502	−	0.997953i
$785$	1.03907			0.0370859
$786$	−69.8758	+	12.6991i	−2.49239	+	0.452962i
$787$	−49.2659	−	13.2008i	−1.75614	−	0.470556i	−0.770220	−	0.637778i	$-0.779854\pi$
$787$	−49.2659	−	13.2008i	−1.75614	−	0.470556i	−0.985919	+	0.167221i	$0.946521\pi$
$788$	−38.3220	−	17.3830i	−1.36516	−	0.619242i
$789$	6.37227	+	23.7816i	0.226859	+	0.846648i
$790$	−0.813442	−	0.0668713i	−0.0289410	−	0.00237917i
$791$	6.68956	−	3.29639i	0.237854	−	0.117206i
$792$	5.97350	−	23.7836i	0.212259	−	0.845115i
$793$	−2.68959	−	1.55283i	−0.0955101	−	0.0551428i
$794$	−2.55074	−	5.39604i	−0.0905224	−	0.191498i
$795$	8.56196	+	2.29417i	0.303661	+	0.0813658i
$796$	−9.42996	+	11.4806i	−0.334236	+	0.406917i
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	0.0581002	−	0.998311i	$-0.481496\pi$
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	−0.998311	+	0.0581002i	$0.981496\pi$
$798$	−16.0480	+	11.8891i	−0.568092	+	0.420871i
$799$		−	16.1349i		−	0.570813i
$800$	−26.7560	−	3.99774i	−0.945966	−	0.141342i
$801$	−8.72116	+	5.03516i	−0.308147	+	0.177909i
$802$	23.9970	+	8.59196i	0.847362	+	0.303393i
$803$	8.08063	+	30.1573i	0.285159	+	1.06423i
$804$	−3.52613	+	21.3015i	−0.124357	+	0.751247i
$805$	−2.30338	+	0.457438i	−0.0811833	+	0.0161226i
$806$	7.81490	+	0.642446i	0.275268	+	0.0226292i
$807$	−7.71565	+	13.3639i	−0.271604	+	0.470432i
$808$	4.29681	+	15.0829i	0.151161	+	0.530614i
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	−0.776869	−	0.629662i	$-0.783193\pi$
$809$	−17.6346	+	10.1813i	−0.620000	+	0.357957i	0.156869	+	0.987619i	$0.449860\pi$
$810$	−1.76706	−	1.22355i	−0.0620880	−	0.0429911i
$811$	−31.8932	−	31.8932i	−1.11992	−	1.11992i	−0.991752	−	0.128171i	$-0.959089\pi$
$811$	−31.8932	−	31.8932i	−1.11992	−	1.11992i	−0.128171	−	0.991752i	$-0.540911\pi$
$812$	0.269124	+	8.40806i	0.00944441	+	0.295065i
$813$	22.0500	−	22.0500i	0.773327	−	0.773327i
$814$	−4.14773	−	22.8226i	−0.145378	−	0.799931i
$815$	−3.42304	−	5.92889i	−0.119904	−	0.207680i
$816$	32.5529	−	48.6299i	1.13958	−	1.70239i
$817$	−15.3537	−	8.86446i	−0.537158	−	0.310128i
$818$	30.1660	−	25.5830i	1.05473	−	0.894490i
$819$	48.1928	+	54.9873i	1.68399	+	1.92141i
$820$	−1.76114	−	2.45986i	−0.0615018	−	0.0859022i
$821$	23.6777	−	6.34443i	0.826359	−	0.221422i	0.179234	−	0.983806i	$-0.442638\pi$
$821$	23.6777	−	6.34443i	0.826359	−	0.221422i	0.647125	+	0.762384i	$0.275971\pi$
$822$	24.8490	+	52.5676i	0.866710	+	1.83351i
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	0.761744	−	0.647878i	$-0.224343\pi$
$823$	−5.16976	−	8.95429i	−0.180207	−	0.312127i	−0.941951	+	0.335751i	$0.891010\pi$
$824$	−0.0492174	−	3.12880i	−0.00171457	−	0.108997i
$825$	25.9374			0.903024
$826$	−29.8845	+	11.7916i	−1.03982	+	0.410284i
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.161581	−	0.986859i	$-0.448341\pi$
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.986859	−	0.161581i	$-0.0516594\pi$
$828$	−10.4503	+	12.7228i	−0.363174	+	0.442149i
$829$	9.70111	−	36.2050i	0.336934	−	1.25745i	−0.564824	−	0.825211i	$-0.691056\pi$
$829$	9.70111	−	36.2050i	0.336934	−	1.25745i	0.901758	−	0.432242i	$-0.142277\pi$
$830$	2.84200	−	7.93757i	0.0986472	−	0.275517i
$831$	−28.2798	+	48.9821i	−0.981015	+	1.69917i
$832$	48.9122	−	14.7697i	1.69573	−	0.512048i
$833$	−4.96118	+	37.5066i	−0.171895	+	1.29953i
$834$	−4.67027	+	3.96073i	−0.161718	+	0.137149i
$835$	2.68133	−	0.718460i	0.0927912	−	0.0248633i
$836$	−2.78042	−	7.39687i	−0.0961629	−	0.255826i
$837$	−0.807156	+	3.01235i	−0.0278994	+	0.104122i
$838$	17.2107	+	11.9171i	0.594534	+	0.411668i
$839$		−	41.5802i		−	1.43551i	−0.696296	−	0.717754i	$-0.745170\pi$
$839$		−	41.5802i		−	1.43551i	0.696296	−	0.717754i	$-0.254830\pi$
$840$	−5.12858	+	7.93781i	−0.176953	+	0.273880i
$841$			26.4726i			0.912847i
$842$	14.0863	−	20.3436i	0.485447	−	0.701085i
$843$	−13.8968	+	51.8636i	−0.478632	+	1.78628i
$844$	23.4844	+	10.6526i	0.808368	+	0.366678i
$845$	−12.5234	+	3.35563i	−0.430818	+	0.115437i
$846$	11.8159	+	13.9327i	0.406241	+	0.479016i
$847$	18.4417	+	1.21440i	0.633665	+	0.0417272i
$848$	12.3963	+	25.1908i	0.425691	+	0.865056i
$849$	−27.5374	+	47.6961i	−0.945080	+	1.63693i
$850$	34.4143	+	12.3218i	1.18040	+	0.422636i
$851$	−4.03092	+	15.0436i	−0.138178	+	0.515688i
$852$	−65.6867	+	6.44157i	−2.25039	+	0.220685i
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	−0.768950	−	0.639309i	$-0.779221\pi$
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	0.639309	+	0.768950i	$0.279221\pi$
$854$	1.42458	+	1.13182i	0.0487480	+	0.0387303i
$855$	3.98094			0.136145
$856$	12.1694	−	12.5583i	0.415940	−	0.429235i
$857$	−9.93943	−	17.2156i	−0.339524	−	0.588073i	0.644819	−	0.764335i	$-0.276933\pi$
$857$	−9.93943	−	17.2156i	−0.339524	−	0.588073i	−0.984343	+	0.176262i	$0.943599\pi$
$858$	−44.2878	+	20.9351i	−1.51196	+	0.714713i
$859$	−12.3699	+	3.31449i	−0.422054	+	0.113089i	−0.463594	−	0.886048i	$-0.653440\pi$
$859$	−12.3699	+	3.31449i	−0.422054	+	0.113089i	0.0415399	+	0.999137i	$0.486774\pi$
$860$	−8.27634	−	1.37002i	−0.282221	−	0.0467173i
$861$	22.7753	−	4.52304i	0.776179	−	0.154145i
$862$	12.4727	+	14.7071i	0.424821	+	0.500925i
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	0.812778	−	0.582574i	$-0.197954\pi$
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	−0.0981346	+	0.995173i	$0.531288\pi$
$864$	2.30109	+	20.1901i	0.0782848	+	0.686882i
$865$	−2.14258	−	3.71106i	−0.0728500	−	0.126180i
$866$	26.6561	−	4.84443i	0.905812	−	0.164620i
$867$	−23.3732	+	23.3732i	−0.793794	+	0.793794i
$868$	−4.47306	−	1.04640i	−0.151825	−	0.0355173i
$869$	1.75262	+	1.75262i	0.0594534	+	0.0594534i
$870$	1.61634	−	2.33433i	0.0547992	−	0.0791413i
$871$	22.0593	−	12.7359i	0.747450	−	0.431541i
$872$	−8.44275	−	29.6361i	−0.285908	−	1.00361i
$873$	−10.1623	+	17.6016i	−0.343941	+	0.595723i
$874$	−0.434695	+	5.28776i	−0.0147038	+	0.178861i
$875$	−11.4329	−	3.88485i	−0.386503	−	0.131332i
$876$	−49.1075	−	68.5905i	−1.65919	−	2.31746i
$877$	−5.60738	−	20.9270i	−0.189348	−	0.706656i	−0.993658	−	0.112446i	$-0.964132\pi$
$877$	−5.60738	−	20.9270i	−0.189348	−	0.706656i	0.804310	−	0.594210i	$-0.202535\pi$
$878$	4.08657	−	11.4136i	0.137915	−	0.385190i
$879$	22.3946	−	12.9295i	0.755349	−	0.436101i
$880$	−2.46302	−	2.81333i	−0.0830284	−	0.0948372i
$881$			15.3375i			0.516733i	0.966047	+	0.258367i	$0.0831842\pi$
$881$			15.3375i			0.516733i	−0.966047	+	0.258367i	$0.916816\pi$
$882$	−23.1829	−	36.0205i	−0.780607	−	1.21287i
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.973124	+	0.230282i	$0.0739648\pi$
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.230282	+	0.973124i	$0.426035\pi$
$884$	−68.7075	+	6.73781i	−2.31088	+	0.226617i
$885$	10.4738	+	2.80645i	0.352074	+	0.0943378i
$886$	−26.7790	+	12.6586i	−0.899660	+	0.425275i
$887$	28.0000	+	16.1658i	0.940148	+	0.542795i	0.890007	−	0.455947i	$-0.150699\pi$
$887$	28.0000	+	16.1658i	0.940148	+	0.542795i	0.0501414	+	0.998742i	$0.484033\pi$
$888$	32.1875	+	53.7788i	1.08014	+	1.80470i
$889$	−10.9312	−	22.1835i	−0.366622	−	0.744009i
$890$	−0.125807	+	1.53036i	−0.00421707	+	0.0512977i
$891$	1.68931	+	6.30459i	0.0565940	+	0.211212i
$892$	12.5979	−	4.73544i	0.421809	−	0.158554i
$893$	5.68632	+	1.52364i	0.190285	+	0.0509868i
$894$	−6.95447	−	38.2664i	−0.232592	−	1.27982i
$895$	−1.77504			−0.0593330
$896$	−29.6171	+	4.33930i	−0.989437	+	0.144966i
$897$	32.8900			1.09817
$898$	6.17696	+	33.9883i	0.206128	+	1.13420i
$899$	1.33315	+	0.357216i	0.0444629	+	0.0119138i
$900$	−38.7407	+	14.5623i	−1.29136	+	0.485410i
$901$	−9.81846	−	36.6430i	−0.327100	−	1.22075i
$902$	−0.752722	+	9.15633i	−0.0250629	+	0.304872i
$903$	35.7881	−	53.5252i	1.19095	−	1.78121i
$904$	−4.09438	−	6.84088i	−0.136177	−	0.227524i
$905$	2.93378	+	1.69382i	0.0975220	+	0.0563044i
$906$	40.4162	−	19.1050i	1.34274	−	0.634721i
$907$	−30.5807	−	8.19408i	−1.01542	−	0.272080i	−0.287525	−	0.957773i	$-0.592832\pi$
$907$	−30.5807	−	8.19408i	−1.01542	−	0.272080i	−0.727891	+	0.685693i	$0.759499\pi$
$908$	15.3829	−	1.50852i	0.510499	−	0.0500621i
$909$	16.9654	+	16.9654i	0.562707	+	0.562707i
$910$	11.0765	−	1.26845i	0.367183	−	0.0420487i
$911$			7.17911i			0.237854i	0.992903	+	0.118927i	$0.0379455\pi$
$911$			7.17911i			0.237854i	−0.992903	+	0.118927i	$0.962054\pi$
$912$	14.0643	+	16.0646i	0.465714	+	0.531951i
$913$	−22.1729	+	12.8015i	−0.733817	+	0.423669i
$914$	1.72176	−	4.80878i	0.0569506	−	0.159060i
$915$	−0.158940	−	0.593173i	−0.00525441	−	0.0196097i
$916$	17.7465	+	24.7874i	0.586362	+	0.818998i
$917$	−32.3529	−	36.9142i	−1.06839	−	1.21901i
$918$	2.24962	−	27.3650i	0.0742484	−	0.903179i
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	−0.884869	−	0.465841i	$-0.845752\pi$
$919$	−1.18242	+	2.04801i	−0.0390044	+	0.0675576i	0.845864	+	0.533398i	$0.179085\pi$
$920$	0.687826	+	2.41444i	0.0226770	+	0.0796017i
$921$	−7.85475	+	4.53494i	−0.258823	+	0.149431i
$922$	−28.7907	+	41.5796i	−0.948170	+	1.36935i
$923$	55.0580	+	55.0580i	1.81226	+	1.81226i
$924$	27.4692	−	8.31086i	0.903670	−	0.273407i
$925$	−27.6828	+	27.6828i	−0.910206	+	0.910206i
$926$	11.1476	−	2.02594i	0.366332	−	0.0665765i
$927$	−2.39361	−	4.14585i	−0.0786164	−	0.136168i
$928$	8.93535	−	1.01837i	0.293317	−	0.0334298i
$929$	−50.6476	−	29.2414i	−1.66169	−	0.959379i	−0.971906	−	0.235367i	$-0.924371\pi$
$929$	−50.6476	−	29.2414i	−1.66169	−	0.959379i	−0.689787	−	0.724012i	$-0.742296\pi$
$930$	1.00285	+	1.18250i	0.0328847	+	0.0387758i
$931$	−12.7497	−	5.29023i	−0.417854	−	0.173380i
$932$	−29.1529	−	4.82581i	−0.954936	−	0.158075i
$933$	39.6224	−	10.6168i	1.29718	−	0.347578i
$934$	−23.6938	+	11.2002i	−0.775285	+	0.366482i
$935$	2.52615	+	4.37543i	0.0826141	+	0.143092i
$936$	54.3954	−	56.1341i	1.77797	−	1.83480i
$937$	−13.4613			−0.439761			−0.219881	−	0.975527i	$-0.570567\pi$
$937$	−13.4613			−0.439761			−0.219881	+	0.975527i	$0.570567\pi$
$938$	−13.8812	+	5.47717i	−0.453239	+	0.178836i
$939$	12.7395	−	12.7395i	0.415738	−	0.415738i
$940$	2.77227	−	0.271863i	0.0904215	−	0.00886719i
$941$	−3.99761	+	14.9193i	−0.130318	+	0.486355i	−0.999973	−	0.00730539i	$-0.997675\pi$
$941$	−3.99761	+	14.9193i	−0.130318	+	0.486355i	0.869655	+	0.493660i	$0.164341\pi$
$942$	8.02675	+	2.87393i	0.261526	+	0.0936377i
$943$	3.08419	−	5.34197i	0.100435	−	0.173959i
$944$	15.1644	+	30.8159i	0.493558	+	1.00297i
$945$	−0.291359	+	4.42454i	−0.00947790	+	0.143930i
$946$	16.4774	+	19.4292i	0.535726	+	0.631697i
$947$	−30.1683	+	8.08357i	−0.980338	+	0.262681i	−0.713187	−	0.700974i	$-0.752749\pi$
$947$	−30.1683	+	8.08357i	−0.980338	+	0.262681i	−0.267151	+	0.963655i	$0.586082\pi$
$948$	−6.09884	−	2.76645i	−0.198081	−	0.0898502i
$949$	−25.7573	+	96.1276i	−0.836118	+	3.12043i
$950$	−7.59229	+	10.9648i	−0.246326	+	0.355746i
$951$		−	71.7697i		−	2.32729i
$952$	40.3949	+	2.02250i	1.30921	+	0.0655497i
$953$		−	15.7802i		−	0.511170i	−0.966787	−	0.255585i	$-0.917732\pi$
$953$		−	15.7802i		−	0.511170i	0.966787	−	0.255585i	$-0.0822680\pi$
$954$	35.3128	+	24.4513i	1.14329	+	0.791641i
$955$	2.12492	−	7.93032i	0.0687609	−	0.256619i
$956$	20.0901	+	53.4464i	0.649759	+	1.72858i
$957$	−8.32855	+	2.23163i	−0.269224	+	0.0721383i
$958$	29.5275	−	25.0415i	0.953989	−	0.809053i
$959$	−22.3366	+	33.4070i	−0.721287	+	1.07877i
$960$	8.90398	+	4.77378i	0.287375	+	0.154073i
$961$	15.1232	−	26.1941i	0.487844	−	0.844970i
$962$	24.9241	−	69.6120i	0.803587	−	2.24438i
$963$	6.92420	−	25.8415i	0.223129	−	0.832729i
$964$	−29.1393	+	35.4758i	−0.938514	+	1.14260i
$965$	−2.17051	+	2.17051i	−0.0698712	+	0.0698712i
$966$	−19.0587	−	2.83716i	−0.613203	−	0.0912840i
$967$	−44.7046			−1.43760			−0.718801	−	0.695216i	$-0.755309\pi$
$967$	−44.7046			−1.43760			−0.718801	+	0.695216i	$0.755309\pi$
$968$	−0.310759	−	19.7553i	−0.00998816	−	0.634959i
$969$	−14.4248	−	24.9844i	−0.463390	−	0.802615i
$970$	1.32443	+	2.80181i	0.0425250	+	0.0899608i
$971$	56.2271	−	15.0660i	1.80441	−	0.483491i	0.809761	−	0.586761i	$-0.199597\pi$
$971$	56.2271	−	15.0660i	1.80441	−	0.483491i	0.994653	+	0.103269i	$0.0329303\pi$
$972$	−22.8133	−	31.8643i	−0.731736	−	1.02205i
$973$	−4.00728	−	1.36166i	−0.128468	−	0.0436527i
$974$	−20.8814	+	17.7089i	−0.669082	+	0.567431i
$975$	71.5999	+	41.3382i	2.29303	+	1.32388i
$976$	1.08200	−	1.61637i	0.0346339	−	0.0517387i
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	0.983259	−	0.182215i	$-0.0583267\pi$
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	−0.649432	+	0.760420i	$0.724993\pi$
$978$	−10.0443	−	55.2681i	−0.321182	−	1.76728i
$979$	3.29726	−	3.29726i	0.105381	−	0.105381i
$980$	−6.52790	−	0.220457i	−0.208526	−	0.00704223i
$981$	−33.3351	−	33.3351i	−1.06431	−	1.06431i
$982$	28.2736	+	19.5773i	0.902248	+	0.624737i
$983$	36.5230	−	21.0866i	1.16490	−	0.672558i	0.212430	−	0.977176i	$-0.431862\pi$
$983$	36.5230	−	21.0866i	1.16490	−	0.672558i	0.952474	+	0.304619i	$0.0985291\pi$
$984$	−6.80107	−	23.8734i	−0.216810	−	0.761057i
$985$	−4.90806	+	8.50102i	−0.156384	+	0.270865i
$986$	−12.1107	−	0.995592i	−0.385682	−	0.0317061i
$987$	−6.87853	+	20.2432i	−0.218946	+	0.644347i
$988$	4.11359	−	24.8503i	0.130871	−	0.790594i
$989$	−4.42695	−	16.5216i	−0.140769	−	0.525356i
$990$	−5.38558	−	1.92827i	−0.171165	−	0.0612845i
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	−0.716280	−	0.697813i	$-0.754156\pi$
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	0.246184	+	0.969223i	$0.420823\pi$
$992$	−0.725721	+	4.85708i	−0.0230417	+	0.154213i
$993$		−	25.6788i		−	0.814891i
$994$	−27.1549	−	36.6537i	−0.861301	−	1.16259i
$995$	2.45062	+	2.45062i	0.0776898	+	0.0776898i
$996$	43.9086	−	53.4567i	1.39130	−	1.69384i
$997$	−27.4427	−	7.35325i	−0.869119	−	0.232880i	−0.203412	−	0.979093i	$-0.565203\pi$
$997$	−27.4427	−	7.35325i	−0.869119	−	0.232880i	−0.665707	+	0.746214i	$0.731870\pi$
$998$	−1.83008	−	3.87150i	−0.0579303	−	0.122550i
$999$	25.4673	+	14.7035i	0.805749	+	0.465199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.v.a.75.7	yes	56
4.3	odd	2		448.2.z.a.271.13		56
7.2	even	3		784.2.j.a.587.8		56
7.3	odd	6	inner	112.2.v.a.59.13	yes	56
7.4	even	3		784.2.w.f.619.13		56
7.5	odd	6		784.2.j.a.587.7		56
7.6	odd	2		784.2.w.f.411.7		56
8.3	odd	2		896.2.z.a.159.2		56
8.5	even	2		896.2.z.b.159.13		56
16.3	odd	4	inner	112.2.v.a.19.13	yes	56
16.5	even	4		896.2.z.a.607.2		56
16.11	odd	4		896.2.z.b.607.13		56
16.13	even	4		448.2.z.a.47.13		56
28.3	even	6		448.2.z.a.143.13		56
56.3	even	6		896.2.z.a.31.2		56
56.45	odd	6		896.2.z.b.31.13		56
112.3	even	12	inner	112.2.v.a.3.7	✓	56
112.19	even	12		784.2.j.a.195.8		56
112.45	odd	12		448.2.z.a.367.13		56
112.51	odd	12		784.2.j.a.195.7		56
112.59	even	12		896.2.z.b.479.13		56
112.67	odd	12		784.2.w.f.227.7		56
112.83	even	4		784.2.w.f.19.13		56
112.101	odd	12		896.2.z.a.479.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	112.3	even	12	inner
112.2.v.a.19.13	yes	56	16.3	odd	4	inner
112.2.v.a.59.13	yes	56	7.3	odd	6	inner
112.2.v.a.75.7	yes	56	1.1	even	1	trivial
448.2.z.a.47.13		56	16.13	even	4
448.2.z.a.143.13		56	28.3	even	6
448.2.z.a.271.13		56	4.3	odd	2
448.2.z.a.367.13		56	112.45	odd	12
784.2.j.a.195.7		56	112.51	odd	12
784.2.j.a.195.8		56	112.19	even	12
784.2.j.a.587.7		56	7.5	odd	6
784.2.j.a.587.8		56	7.2	even	3
784.2.w.f.19.13		56	112.83	even	4
784.2.w.f.227.7		56	112.67	odd	12
784.2.w.f.411.7		56	7.6	odd	2
784.2.w.f.619.13		56	7.4	even	3
896.2.z.a.31.2		56	56.3	even	6
896.2.z.a.159.2		56	8.3	odd	2
896.2.z.a.479.2		56	112.101	odd	12
896.2.z.a.607.2		56	16.5	even	4
896.2.z.b.31.13		56	56.45	odd	6
896.2.z.b.159.13		56	8.5	even	2
896.2.z.b.479.13		56	112.59	even	12
896.2.z.b.607.13		56	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.252874 - 1.39142i) q^{2} +(-2.61463 - 0.700587i) q^{3} +(-1.87211 + 0.703710i) q^{4} +(0.120751 + 0.450647i) q^{5} +(-0.313640 + 3.81521i) q^{6} +(-2.37326 + 1.16946i) q^{7} +(1.45257 + 2.42694i) q^{8} +(3.74737 + 2.16355i) q^{9} +(0.596506 - 0.281972i) q^{10} +(-1.93537 - 0.518581i) q^{11} +(5.38787 - 0.528362i) q^{12} +(-4.51607 - 4.51607i) q^{13} +(2.22735 + 3.00648i) q^{14} -1.26287i q^{15} +(3.00959 - 2.63484i) q^{16} +(-4.68066 + 2.70238i) q^{17} +(2.06279 - 5.76128i) q^{18} +(-0.510379 - 1.90476i) q^{19} +(-0.543183 - 0.758687i) q^{20} +(7.02450 - 1.39503i) q^{21} +(-0.232159 + 2.82405i) q^{22} +(0.951245 - 1.64761i) q^{23} +(-2.09763 - 7.36320i) q^{24} +(4.14162 - 2.39117i) q^{25} +(-5.14176 + 7.42576i) q^{26} +(-2.54010 - 2.54010i) q^{27} +(3.62004 - 3.85944i) q^{28} +(-1.12415 + 1.12415i) q^{29} +(-1.75718 + 0.319347i) q^{30} +(-0.434075 - 0.751840i) q^{31} +(-4.42722 - 3.52132i) q^{32} +(4.69696 + 2.71179i) q^{33} +(4.94377 + 5.82941i) q^{34} +(-0.813586 - 0.928290i) q^{35} +(-8.53799 - 1.41333i) q^{36} +(-7.90732 + 2.11876i) q^{37} +(-2.52126 + 1.19182i) q^{38} +(8.64394 + 14.9717i) q^{39} +(-0.918297 + 0.947649i) q^{40} +3.24226 q^{41} +(-3.71738 - 9.42127i) q^{42} +(6.35727 - 6.35727i) q^{43} +(3.98816 - 0.391099i) q^{44} +(-0.522499 + 1.94999i) q^{45} +(-2.53306 - 0.906947i) q^{46} +(-1.49266 + 2.58536i) q^{47} +(-9.71488 + 4.78065i) q^{48} +(4.26473 - 5.55087i) q^{49} +(-4.37443 - 5.15808i) q^{50} +(14.1314 - 3.78650i) q^{51} +(11.6326 + 5.27658i) q^{52} +(-1.81663 + 6.77976i) q^{53} +(-2.89203 + 4.17668i) q^{54} -0.934789i q^{55} +(-6.28553 - 4.06105i) q^{56} +5.33780i q^{57} +(1.84843 + 1.27990i) q^{58} +(-2.22228 + 8.29366i) q^{59} +(0.888694 + 2.36423i) q^{60} +(0.469703 - 0.125856i) q^{61} +(-0.936361 + 0.794103i) q^{62} +(-11.4237 - 0.752254i) q^{63} +(-3.78011 + 7.05059i) q^{64} +(1.48984 - 2.58047i) q^{65} +(2.58551 - 7.22120i) q^{66} +(-1.03224 + 3.85238i) q^{67} +(6.86102 - 8.35298i) q^{68} +(-3.64144 + 3.64144i) q^{69} +(-1.08591 + 1.36678i) q^{70} -12.1916 q^{71} +(0.192498 + 12.2373i) q^{72} +(-7.79109 - 13.4946i) q^{73} +(4.94765 + 10.4666i) q^{74} +(-12.5040 + 3.35044i) q^{75} +(2.29588 + 3.20676i) q^{76} +(5.19960 - 1.03261i) q^{77} +(18.6462 - 15.8133i) q^{78} +(-1.07130 - 0.618516i) q^{79} +(1.55079 + 1.03810i) q^{80} +(-1.62878 - 2.82113i) q^{81} +(-0.819885 - 4.51136i) q^{82} +(9.03560 - 9.03560i) q^{83} +(-12.1689 + 7.55485i) q^{84} +(-1.78301 - 1.78301i) q^{85} +(-10.4532 - 7.23805i) q^{86} +(3.72680 - 2.15167i) q^{87} +(-1.55269 - 5.45031i) q^{88} +(-1.16364 + 2.01548i) q^{89} +(2.84539 + 0.233913i) q^{90} +(15.9992 + 5.43644i) q^{91} +(-0.621399 + 3.75390i) q^{92} +(0.608215 + 2.26989i) q^{93} +(3.97479 + 1.42315i) q^{94} +(0.796746 - 0.460002i) q^{95} +(9.10855 + 12.3086i) q^{96} +4.69704i q^{97} +(-8.80204 - 4.53036i) q^{98} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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