LMFDB - Embedded newform 112.2.v.a.75.6

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)

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);

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")

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			75.6
Character	$\chi$	$=$	112.75
Dual form			112.2.v.a.3.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.799555 + 1.16650i) q^{2} +(-0.763582 - 0.204601i) q^{3} +(-0.721425 - 1.86535i) q^{4} +(-1.02188 - 3.81370i) q^{5} +(0.849192 - 0.727125i) q^{6} +(-2.64575 - 0.00379639i) q^{7} +(2.75275 + 0.649913i) q^{8} +(-2.05688 - 1.18754i) q^{9} +(5.26571 + 1.85724i) q^{10} +(4.35958 + 1.16815i) q^{11} +(0.169214 + 1.57195i) q^{12} +(-1.34913 - 1.34913i) q^{13} +(2.11985 - 3.08322i) q^{14} +3.12115i q^{15} +(-2.95909 + 2.69143i) q^{16} +(0.989178 - 0.571102i) q^{17} +(3.02985 - 1.44984i) q^{18} +(-0.808212 - 3.01629i) q^{19} +(-6.37669 + 4.65746i) q^{20} +(2.01947 + 0.544222i) q^{21} +(-4.84836 + 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(-1.96897 - 1.05948i) q^{24} +(-9.16994 + 5.29427i) q^{25} +(2.65246 - 0.495052i) q^{26} +(3.00457 + 3.00457i) q^{27} +(1.90163 + 4.93800i) q^{28} +(5.30239 - 5.30239i) q^{29} +(-3.64081 - 2.49553i) q^{30} +(-2.07171 - 3.58830i) q^{31} +(-0.773583 - 5.60371i) q^{32} +(-3.08989 - 1.78395i) q^{33} +(-0.124713 + 1.61050i) q^{34} +(2.68915 + 10.0940i) q^{35} +(-0.731298 + 4.69353i) q^{36} +(2.99943 - 0.803695i) q^{37} +(4.16470 + 1.46891i) q^{38} +(0.754139 + 1.30621i) q^{39} +(-0.334398 - 11.1623i) q^{40} +8.08732 q^{41} +(-2.24951 + 1.92057i) q^{42} +(-3.82205 + 3.82205i) q^{43} +(-0.966105 - 8.97489i) q^{44} +(-2.42704 + 9.05785i) q^{45} +(-1.25008 - 2.61239i) q^{46} +(-0.814305 + 1.41042i) q^{47} +(2.81018 - 1.44969i) q^{48} +(6.99997 + 0.0200886i) q^{49} +(1.15613 - 14.9298i) q^{50} +(-0.872167 + 0.233696i) q^{51} +(-1.54331 + 3.48991i) q^{52} +(0.783749 - 2.92499i) q^{53} +(-5.90713 + 1.10250i) q^{54} -17.8198i q^{55} +(-7.28061 - 1.72996i) q^{56} +2.46854i q^{57} +(1.94567 + 10.4248i) q^{58} +(1.86863 - 6.97383i) q^{59} +(5.82205 - 2.25168i) q^{60} +(6.30611 - 1.68972i) q^{61} +(5.84218 + 0.452405i) q^{62} +(5.43748 + 3.14974i) q^{63} +(7.15523 + 3.57809i) q^{64} +(-3.76654 + 6.52383i) q^{65} +(4.55151 - 2.17798i) q^{66} +(-0.165120 + 0.616236i) q^{67} +(-1.77893 - 1.43316i) q^{68} +(1.14470 - 1.14470i) q^{69} +(-13.9247 - 4.93379i) q^{70} -2.40482 q^{71} +(-4.89027 - 4.60579i) q^{72} +(-1.47966 - 2.56284i) q^{73} +(-1.46070 + 4.14142i) q^{74} +(8.08521 - 2.16643i) q^{75} +(-5.04338 + 3.68363i) q^{76} +(-11.5299 - 3.10717i) q^{77} +(-2.12666 - 0.164684i) q^{78} +(-1.06303 - 0.613742i) q^{79} +(13.2881 + 8.53478i) q^{80} +(1.88313 + 3.26167i) q^{81} +(-6.46626 + 9.43383i) q^{82} +(2.29910 - 2.29910i) q^{83} +(-0.441729 - 4.15964i) q^{84} +(-3.18883 - 3.18883i) q^{85} +(-1.40247 - 7.51435i) q^{86} +(-5.13369 + 2.96394i) q^{87} +(11.2416 + 6.04896i) q^{88} +(-4.36654 + 7.56307i) q^{89} +(-8.62539 - 10.0734i) q^{90} +(3.56434 + 3.57459i) q^{91} +(4.04685 + 0.630538i) q^{92} +(0.847747 + 3.16383i) q^{93} +(-0.994165 - 2.07759i) q^{94} +(-10.6773 + 6.16455i) q^{95} +(-0.555832 + 4.43717i) q^{96} +8.42967i q^{97} +(-5.62029 + 8.14938i) q^{98} +(-7.57992 - 7.57992i) 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 $

$2$	−0.799555	+	1.16650i	−0.565370	+	0.824837i
$2$	−0.799555	+	1.16650i	−0.565370	+	0.824837i
$3$	−0.763582	−	0.204601i	−0.440854	−	0.118127i	0.0315627	−	0.999502i	$-0.489952\pi$
$3$	−0.763582	−	0.204601i	−0.440854	−	0.118127i	−0.472417	+	0.881375i	$0.656618\pi$
$4$	−0.721425	−	1.86535i	−0.360713	−	0.932677i
$5$	−1.02188	−	3.81370i	−0.456998	−	1.70554i	−0.682148	−	0.731214i	$-0.738954\pi$
$5$	−1.02188	−	3.81370i	−0.456998	−	1.70554i	0.225150	−	0.974324i	$-0.427713\pi$
$6$	0.849192	−	0.727125i	0.346681	−	0.296848i
$7$	−2.64575	−	0.00379639i	−0.999999	−	0.00143490i
$7$	−2.64575	−	0.00379639i	−0.999999	−	0.00143490i
$8$	2.75275	+	0.649913i	0.973243	+	0.229779i
$9$	−2.05688	−	1.18754i	−0.685627	−	0.395847i
$10$	5.26571	+	1.85724i	1.66516	+	0.587312i
$11$	4.35958	+	1.16815i	1.31446	+	0.352209i	0.846901	−	0.531751i	$-0.178466\pi$
$11$	4.35958	+	1.16815i	1.31446	+	0.352209i	0.467562	+	0.883960i	$0.345132\pi$
$12$	0.169214	+	1.57195i	0.0488477	+	0.453784i
$13$	−1.34913	−	1.34913i	−0.374182	−	0.374182i	0.494816	−	0.868998i	$-0.335236\pi$
$13$	−1.34913	−	1.34913i	−0.374182	−	0.374182i	−0.868998	+	0.494816i	$0.835236\pi$
$14$	2.11985	−	3.08322i	0.566553	−	0.824025i
$15$			3.12115i			0.805877i
$16$	−2.95909	+	2.69143i	−0.739773	+	0.672857i
$17$	0.989178	−	0.571102i	0.239911	−	0.138513i	−0.375225	−	0.926934i	$-0.622435\pi$
$17$	0.989178	−	0.571102i	0.239911	−	0.138513i	0.615136	+	0.788421i	$0.289101\pi$
$18$	3.02985	−	1.44984i	0.714142	−	0.341730i
$19$	−0.808212	−	3.01629i	−0.185416	−	0.691984i	−0.994541	−	0.104346i	$-0.966725\pi$
$19$	−0.808212	−	3.01629i	−0.185416	−	0.691984i	0.809125	−	0.587637i	$-0.199942\pi$
$20$	−6.37669	+	4.65746i	−1.42587	+	1.04144i
$21$	2.01947	+	0.544222i	0.440684	+	0.118759i
$22$	−4.84836	+	4.15144i	−1.03367	+	0.885089i
$23$	−1.02392	+	1.77348i	−0.213502	+	0.369796i	−0.952808	−	0.303573i	$-0.901820\pi$
$23$	−1.02392	+	1.77348i	−0.213502	+	0.369796i	0.739306	+	0.673369i	$0.235154\pi$
$24$	−1.96897	−	1.05948i	−0.401915	−	0.216265i
$25$	−9.16994	+	5.29427i	−1.83399	+	1.05885i
$26$	2.65246	−	0.495052i	0.520191	−	0.0970878i
$27$	3.00457	+	3.00457i	0.578229	+	0.578229i
$28$	1.90163	+	4.93800i	0.359374	+	0.933194i
$29$	5.30239	−	5.30239i	0.984630	−	0.984630i	−0.0152539	−	0.999884i	$-0.504856\pi$
$29$	5.30239	−	5.30239i	0.984630	−	0.984630i	0.999884	+	0.0152539i	$0.00485565\pi$
$30$	−3.64081	−	2.49553i	−0.664717	−	0.455619i
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	0.617797	−	0.786337i	$-0.288025\pi$
$31$	−2.07171	−	3.58830i	−0.372089	−	0.644478i	−0.989887	+	0.141860i	$0.954692\pi$
$32$	−0.773583	−	5.60371i	−0.136751	−	0.990605i
$33$	−3.08989	−	1.78395i	−0.537881	−	0.310546i
$34$	−0.124713	+	1.61050i	−0.0213882	+	0.276198i
$35$	2.68915	+	10.0940i	0.454550	+	1.70619i
$36$	−0.731298	+	4.69353i	−0.121883	+	0.782255i
$37$	2.99943	−	0.803695i	0.493103	−	0.132127i	−0.00369416	−	0.999993i	$-0.501176\pi$
$37$	2.99943	−	0.803695i	0.493103	−	0.132127i	0.496797	+	0.867867i	$0.334509\pi$
$38$	4.16470	+	1.46891i	0.675603	+	0.238289i
$39$	0.754139	+	1.30621i	0.120759	+	0.209161i
$40$	−0.334398	−	11.1623i	−0.0528730	−	1.76491i
$41$	8.08732			1.26303			0.631514	−	0.775365i	$-0.282434\pi$
$41$	8.08732			1.26303			0.631514	+	0.775365i	$0.282434\pi$
$42$	−2.24951	+	1.92057i	−0.347107	+	0.296350i
$43$	−3.82205	+	3.82205i	−0.582858	+	0.582858i	−0.935688	−	0.352830i	$-0.885220\pi$
$43$	−3.82205	+	3.82205i	−0.582858	+	0.582858i	0.352830	+	0.935688i	$0.385220\pi$
$44$	−0.966105	−	8.97489i	−0.145646	−	1.35302i
$45$	−2.42704	+	9.05785i	−0.361802	+	1.35026i
$46$	−1.25008	−	2.61239i	−0.184314	−	0.385176i
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	−0.919284	−	0.393595i	$-0.871231\pi$
$47$	−0.814305	+	1.41042i	−0.118779	+	0.205731i	0.800505	+	0.599326i	$0.204565\pi$
$48$	2.81018	−	1.44969i	0.405614	−	0.209245i
$49$	6.99997	+	0.0200886i	0.999996	+	0.00286980i
$50$	1.15613	−	14.9298i	0.163501	−	2.11139i
$51$	−0.872167	+	0.233696i	−0.122128	+	0.0327240i
$52$	−1.54331	+	3.48991i	−0.214019	+	0.483963i
$53$	0.783749	−	2.92499i	0.107656	−	0.401779i	−0.890977	−	0.454049i	$-0.849979\pi$
$53$	0.783749	−	2.92499i	0.107656	−	0.401779i	0.998633	+	0.0522704i	$0.0166458\pi$
$54$	−5.90713	+	1.10250i	−0.803858	+	0.150031i
$55$		−	17.8198i		−	2.40283i
$56$	−7.28061	−	1.72996i	−0.972912	−	0.231175i
$57$			2.46854i			0.326966i
$58$	1.94567	+	10.4248i	0.255479	+	1.36884i
$59$	1.86863	−	6.97383i	0.243275	−	0.907915i	−0.730967	−	0.682412i	$-0.760931\pi$
$59$	1.86863	−	6.97383i	0.243275	−	0.907915i	0.974243	−	0.225503i	$-0.0724025\pi$
$60$	5.82205	−	2.25168i	0.751623	−	0.290690i
$61$	6.30611	−	1.68972i	0.807414	−	0.216346i	0.168578	−	0.985688i	$-0.446083\pi$
$61$	6.30611	−	1.68972i	0.807414	−	0.216346i	0.638837	+	0.769342i	$0.279416\pi$
$62$	5.84218	+	0.452405i	0.741958	+	0.0574555i
$63$	5.43748	+	3.14974i	0.685058	+	0.396830i
$64$	7.15523	+	3.57809i	0.894403	+	0.447261i
$65$	−3.76654	+	6.52383i	−0.467181	+	0.809182i
$66$	4.55151	−	2.17798i	0.560252	−	0.268091i
$67$	−0.165120	+	0.616236i	−0.0201726	+	0.0752852i	−0.975278	−	0.220980i	$-0.929074\pi$
$67$	−0.165120	+	0.616236i	−0.0201726	+	0.0752852i	0.955106	+	0.296265i	$0.0957412\pi$
$68$	−1.77893	−	1.43316i	−0.215726	−	0.173796i
$69$	1.14470	−	1.14470i	0.137806	−	0.137806i
$70$	−13.9247	−	4.93379i	−1.66432	−	0.589701i
$71$	−2.40482			−0.285400			−0.142700	−	0.989766i	$-0.545578\pi$
$71$	−2.40482			−0.285400			−0.142700	+	0.989766i	$0.545578\pi$
$72$	−4.89027	−	4.60579i	−0.576324	−	0.542798i
$73$	−1.47966	−	2.56284i	−0.173181	−	0.299958i	0.766349	−	0.642424i	$-0.222071\pi$
$73$	−1.47966	−	2.56284i	−0.173181	−	0.299958i	−0.939530	+	0.342466i	$0.888738\pi$
$74$	−1.46070	+	4.14142i	−0.169803	+	0.481430i
$75$	8.08521	−	2.16643i	0.933600	−	0.250157i
$76$	−5.04338	+	3.68363i	−0.578515	+	0.422541i
$77$	−11.5299	−	3.10717i	−1.31396	−	0.354095i
$78$	−2.12666	−	0.164684i	−0.240797	−	0.0186468i
$79$	−1.06303	−	0.613742i	−0.119601	−	0.0690514i	0.439006	−	0.898484i	$-0.355331\pi$
$79$	−1.06303	−	0.613742i	−0.119601	−	0.0690514i	−0.558607	+	0.829433i	$0.688664\pi$
$80$	13.2881	+	8.53478i	1.48566	+	0.954217i
$81$	1.88313	+	3.26167i	0.209236	+	0.362408i
$82$	−6.46626	+	9.43383i	−0.714078	+	1.04179i
$83$	2.29910	−	2.29910i	0.252359	−	0.252359i	−0.569578	−	0.821937i	$-0.692893\pi$
$83$	2.29910	−	2.29910i	0.252359	−	0.252359i	0.821937	+	0.569578i	$0.192893\pi$
$84$	−0.441729	−	4.15964i	−0.0481966	−	0.453854i
$85$	−3.18883	−	3.18883i	−0.345877	−	0.345877i
$86$	−1.40247	−	7.51435i	−0.151232	−	0.810293i
$87$	−5.13369	+	2.96394i	−0.550389	+	0.317767i
$88$	11.2416	+	6.04896i	1.19836	+	0.644821i
$89$	−4.36654	+	7.56307i	−0.462852	+	0.801684i	−0.999102	−	0.0423758i	$-0.986507\pi$
$89$	−4.36654	+	7.56307i	−0.462852	+	0.801684i	0.536249	+	0.844060i	$0.319841\pi$
$90$	−8.62539	−	10.0734i	−0.909196	−	1.06183i
$91$	3.56434	+	3.57459i	0.373645	+	0.374719i
$92$	4.04685	+	0.630538i	0.421913	+	0.0657381i
$93$	0.847747	+	3.16383i	0.0879073	+	0.328074i
$94$	−0.994165	−	2.07759i	−0.102540	−	0.214287i
$95$	−10.6773	+	6.16455i	−1.09547	+	0.632470i
$96$	−0.555832	+	4.43717i	−0.0567293	+	0.452866i
$97$			8.42967i			0.855903i	0.903802	+	0.427952i	$0.140765\pi$
$97$			8.42967i			0.855903i	−0.903802	+	0.427952i	$0.859235\pi$
$98$	−5.62029	+	8.14938i	−0.567735	+	0.823211i
$99$	−7.57992	−	7.57992i	−0.761810	−	0.761810i
$100$	16.4911	+	13.2858i	1.64911	+	1.32858i
$101$	−14.2323	−	3.81352i	−1.41616	−	0.379460i	−0.532042	−	0.846718i	$-0.678575\pi$
$101$	−14.2323	−	3.81352i	−1.41616	−	0.379460i	−0.884121	+	0.467258i	$0.845242\pi$
$102$	0.424739	−	1.20423i	0.0420554	−	0.119237i
$103$	6.87358	+	3.96846i	0.677274	+	0.391024i	0.798827	−	0.601561i	$-0.205454\pi$
$103$	6.87358	+	3.96846i	0.677274	+	0.391024i	−0.121553	+	0.992585i	$0.538787\pi$
$104$	−2.83700	−	4.59064i	−0.278191	−	0.450149i
$105$	0.0118491	−	8.25777i	0.00115635	−	0.805876i
$106$	2.78534	+	3.25293i	0.270536	+	0.315953i
$107$	−2.40287	−	8.96762i	−0.232294	−	0.866932i	−0.979350	−	0.202172i	$-0.935200\pi$
$107$	−2.40287	−	8.96762i	−0.232294	−	0.866932i	0.747056	−	0.664761i	$-0.231467\pi$
$108$	3.43701	−	7.77215i	0.330726	−	0.747875i
$109$	−0.849736	−	0.227686i	−0.0813900	−	0.0218084i	0.217894	−	0.975972i	$-0.430081\pi$
$109$	−0.849736	−	0.227686i	−0.0813900	−	0.0218084i	−0.299284	+	0.954164i	$0.596748\pi$
$110$	20.7868	+	14.2479i	1.98194	+	1.35849i
$111$	−2.45475			−0.232994
$112$	7.83923	−	7.10960i	0.740738	−	0.671794i
$113$	1.91230			0.179894			0.0899469	−	0.995947i	$-0.471330\pi$
$113$	1.91230			0.179894			0.0899469	+	0.995947i	$0.471330\pi$
$114$	−2.87954	−	1.97373i	−0.269694	−	0.184857i
$115$	7.80983	+	2.09264i	0.728271	+	0.195140i
$116$	−13.7161	−	6.06556i	−1.27351	−	0.563173i
$117$	1.17285	+	4.37715i	0.108430	+	0.404668i
$118$	6.64087	+	7.75571i	0.611342	+	0.713971i
$119$	−2.61928	+	1.50724i	−0.240109	+	0.138168i
$120$	−2.02847	+	8.59173i	−0.185174	+	0.784314i
$121$	8.11511	+	4.68526i	0.737737	+	0.425933i
$122$	−3.07103	+	8.70707i	−0.278038	+	0.788301i
$123$	−6.17533	−	1.65468i	−0.556811	−	0.149197i
$124$	−5.19887	+	6.45316i	−0.466872	+	0.579511i
$125$	15.6022	+	15.6022i	1.39550	+	1.39550i
$126$	−8.02172	+	3.82441i	−0.714632	+	0.340705i
$127$		−	11.9607i		−	1.06134i	−0.847578	−	0.530671i	$-0.821940\pi$
$127$		−	11.9607i		−	1.06134i	0.847578	−	0.530671i	$-0.178060\pi$
$128$	−9.89482	+	5.48566i	−0.874587	+	0.484869i
$129$	3.70045	−	2.13645i	0.325806	−	0.188104i
$130$	−4.59847	−	9.60981i	−0.403313	−	0.842836i
$131$	−1.43700	−	5.36296i	−0.125551	−	0.468564i	0.874307	−	0.485372i	$-0.161316\pi$
$131$	−1.43700	−	5.36296i	−0.125551	−	0.468564i	−0.999859	+	0.0168089i	$0.994649\pi$
$132$	−1.09857	+	7.05073i	−0.0956185	+	0.613687i
$133$	2.12687	+	7.98340i	0.184423	+	0.692249i
$134$	−0.586814	−	0.685325i	−0.0506930	−	0.0592031i
$135$	8.38821	−	14.5288i	0.721943	−	1.25044i
$136$	3.09412	−	0.929220i	0.265319	−	0.0796800i
$137$	12.4195	−	7.17038i	1.06107	−	0.612607i	0.135339	−	0.990799i	$-0.456788\pi$
$137$	12.4195	−	7.17038i	1.06107	−	0.612607i	0.925727	+	0.378192i	$0.123454\pi$
$138$	0.420038	+	2.25054i	0.0357560	+	0.191579i
$139$	−14.6088	−	14.6088i	−1.23910	−	1.23910i	−0.960369	−	0.278731i	$-0.910086\pi$
$139$	−14.6088	−	14.6088i	−1.23910	−	1.23910i	−0.278731	−	0.960369i	$-0.589914\pi$
$140$	16.8888	−	12.2983i	1.42736	−	1.03939i
$141$	0.910361	−	0.910361i	0.0766663	−	0.0766663i
$142$	1.92279	−	2.80521i	0.161357	−	0.235408i
$143$	−4.30567	−	7.45764i	−0.360058	−	0.623639i
$144$	9.28268	−	2.02190i	0.773556	−	0.168492i
$145$	−25.6401	−	14.8033i	−2.12930	−	1.22935i
$146$	4.17262	+	0.323118i	0.345328	+	0.0267414i
$147$	−5.34094	−	1.44754i	−0.440513	−	0.119391i
$148$	−3.66304	−	5.01519i	−0.301100	−	0.412246i
$149$	11.3862	−	3.05093i	0.932797	−	0.249942i	0.239750	−	0.970835i	$-0.422934\pi$
$149$	11.3862	−	3.05093i	0.932797	−	0.249942i	0.693047	+	0.720892i	$0.256268\pi$
$150$	−3.93744	+	11.1635i	−0.321491	+	0.911500i
$151$	6.85381	+	11.8712i	0.557755	+	0.966061i	0.997683	+	0.0680276i	$0.0216706\pi$
$151$	6.85381	+	11.8712i	0.557755	+	0.966061i	−0.439928	+	0.898033i	$0.644996\pi$
$152$	−0.264478	−	8.82834i	−0.0214520	−	0.716073i
$153$	−2.71283			−0.219319
$154$	12.8433	−	10.9653i	1.03494	−	0.883605i
$155$	−11.5677	+	11.5677i	−0.929138	+	0.929138i
$156$	1.89248	−	2.34907i	0.151520	−	0.188076i
$157$	0.539359	−	2.01291i	0.0430455	−	0.160648i	−0.941058	−	0.338247i	$-0.890166\pi$
$157$	0.539359	−	2.01291i	0.0430455	−	0.160648i	0.984103	+	0.177599i	$0.0568329\pi$
$158$	1.56588	−	0.749303i	0.124575	−	0.0596113i
$159$	−1.19691	+	2.07311i	−0.0949214	+	0.164409i
$160$	−20.5804	+	8.67652i	−1.62702	+	0.685939i
$161$	2.71576	−	4.68829i	0.214032	−	0.369489i
$162$	−5.31039	−	0.411225i	−0.417224	−	0.0323089i
$163$	−1.74222	+	0.466826i	−0.136461	+	0.0365647i	−0.326403	−	0.945231i	$-0.605837\pi$
$163$	−1.74222	+	0.466826i	−0.136461	+	0.0365647i	0.189942	+	0.981795i	$0.439170\pi$
$164$	−5.83440	−	15.0857i	−0.455590	−	1.17800i
$165$	−3.64596	+	13.6069i	−0.283837	+	1.05930i
$166$	0.843635	+	4.52015i	0.0654788	+	0.350831i
$167$			21.6002i			1.67147i	0.549132	+	0.835735i	$0.314958\pi$
$167$			21.6002i			1.67147i	−0.549132	+	0.835735i	$0.685042\pi$
$168$	5.20539	+	2.81058i	0.401604	+	0.216841i
$169$		−	9.35968i		−	0.719976i
$170$	6.26940	−	1.17011i	0.480841	−	0.0897437i
$171$	−1.91957	+	7.16393i	−0.146793	+	0.547839i
$172$	9.88681	+	4.37216i	0.753862	+	0.333374i
$173$	−8.48775	+	2.27429i	−0.645312	+	0.172911i	−0.566608	−	0.823987i	$-0.691745\pi$
$173$	−8.48775	+	2.27429i	−0.645312	+	0.172911i	−0.0787035	+	0.996898i	$0.525078\pi$
$174$	0.647244	−	8.35825i	0.0490674	−	0.633637i
$175$	24.2815	−	13.9725i	1.83551	−	1.05622i
$176$	−16.0444	+	8.27684i	−1.20939	+	0.623890i
$177$	−2.85371	+	4.94277i	−0.214498	+	0.371521i
$178$	−5.33100	−	11.1406i	−0.399575	−	0.835026i
$179$	0.452081	−	1.68719i	0.0337901	−	0.126106i	−0.946971	−	0.321320i	$-0.895873\pi$
$179$	0.452081	−	1.68719i	0.0337901	−	0.126106i	0.980761	+	0.195214i	$0.0625401\pi$
$180$	18.6470	−	2.00726i	1.38987	−	0.149613i
$181$	−5.29547	+	5.29547i	−0.393609	+	0.393609i	−0.875972	−	0.482362i	$-0.839779\pi$
$181$	−5.29547	+	5.29547i	−0.393609	+	0.393609i	0.482362	+	0.875972i	$0.339779\pi$
$182$	−7.01963	+	1.29971i	−0.520329	+	0.0963413i
$183$	−5.16095			−0.381508
$184$	−3.97119	+	4.21648i	−0.292760	+	0.310843i
$185$	−6.13010	−	10.6176i	−0.450694	−	0.780625i
$186$	−4.36842	−	1.54076i	−0.320308	−	0.112974i
$187$	4.97953	−	1.33426i	0.364140	−	0.0975709i
$188$	3.21839	+	0.501456i	0.234725	+	0.0365725i
$189$	−7.93792	−	7.96073i	−0.577399	−	0.579058i
$190$	1.34617	−	17.3839i	0.0976617	−	1.26116i
$191$	23.5567	+	13.6004i	1.70450	+	0.984093i	0.941076	+	0.338195i	$0.109816\pi$
$191$	23.5567	+	13.6004i	1.70450	+	0.984093i	0.763423	+	0.645899i	$0.223517\pi$
$192$	−4.73152	−	4.19613i	−0.341468	−	0.302830i
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	0.743477	−	0.668762i	$-0.233175\pi$
$193$	−2.88165	−	4.99117i	−0.207426	−	0.359272i	−0.950903	+	0.309489i	$0.899842\pi$
$194$	−9.83318	−	6.73998i	−0.705981	−	0.483902i
$195$	4.21084	−	4.21084i	0.301545	−	0.301545i
$196$	−5.01248	−	13.0719i	−0.358034	−	0.933708i
$197$	12.7740	+	12.7740i	0.910107	+	0.910107i	0.996280	−	0.0861731i	$-0.0274638\pi$
$197$	12.7740	+	12.7740i	0.910107	+	0.910107i	−0.0861731	+	0.996280i	$0.527464\pi$
$198$	14.9025	−	2.78139i	1.05907	−	0.197664i
$199$	−4.76949	+	2.75367i	−0.338100	+	0.195202i	−0.659432	−	0.751764i	$-0.729203\pi$
$199$	−4.76949	+	2.75367i	−0.338100	+	0.195202i	0.321331	+	0.946967i	$0.395870\pi$
$200$	−28.6833	+	8.61412i	−2.02822	+	0.609110i
$201$	0.252165	−	0.436763i	0.0177863	−	0.0308069i
$202$	15.8279	−	13.5528i	1.11365	−	0.953569i
$203$	−14.0489	+	14.0087i	−0.986042	+	0.983216i
$204$	1.06513	+	1.45831i	0.0745740	+	0.102102i
$205$	−8.26425	−	30.8426i	−0.577201	−	2.15414i
$206$	−10.1250	+	4.84500i	−0.705442	+	0.337567i
$207$	4.21216	−	2.43189i	0.292765	−	0.169028i
$208$	7.62330	+	0.361115i	0.528581	+	0.0250388i
$209$		−	14.0939i		−	0.974893i
$210$	9.62319	+	6.61636i	0.664063	+	0.456572i
$211$	19.3846	+	19.3846i	1.33449	+	1.33449i	0.901302	+	0.433192i	$0.142613\pi$
$211$	19.3846	+	19.3846i	1.33449	+	1.33449i	0.433192	+	0.901302i	$0.357387\pi$
$212$	−6.02156	+	0.648193i	−0.413563	+	0.0445181i
$213$	1.83628	+	0.492029i	0.125820	+	0.0337133i
$214$	12.3819	+	4.36717i	0.846410	+	0.298533i
$215$	18.4818	+	10.6705i	1.26045	+	0.727722i
$216$	6.31810	+	10.2235i	0.429892	+	0.695622i
$217$	5.46759	+	9.50161i	0.371164	+	0.645011i
$218$	0.945005	−	0.809166i	0.0640038	−	0.0548036i
$219$	0.605480	+	2.25968i	0.0409145	+	0.152695i
$220$	−33.2403	+	12.8557i	−2.24106	+	0.866730i
$221$	−2.10503	−	0.564040i	−0.141599	−	0.0379414i
$222$	1.96270	−	2.86345i	0.131728	−	0.192182i
$223$	−22.1379			−1.48247			−0.741233	−	0.671248i	$-0.765759\pi$
$223$	−22.1379			−1.48247			−0.741233	+	0.671248i	$0.765759\pi$
$224$	2.02543	+	14.8289i	0.135330	+	0.990801i
$225$	25.1486			1.67658
$226$	−1.52899	+	2.23069i	−0.101707	+	0.148383i
$227$	8.31664	+	2.22844i	0.551995	+	0.147907i	0.524026	−	0.851702i	$-0.324429\pi$
$227$	8.31664	+	2.22844i	0.551995	+	0.147907i	0.0279688	+	0.999609i	$0.491096\pi$
$228$	4.60471	−	1.78087i	0.304954	−	0.117941i
$229$	6.55130	+	24.4498i	0.432922	+	1.61569i	0.745990	+	0.665957i	$0.231977\pi$
$229$	6.55130	+	24.4498i	0.432922	+	1.61569i	−0.313067	+	0.949731i	$0.601357\pi$
$230$	−8.68544	+	7.43696i	−0.572701	+	0.490379i
$231$	8.16831	+	4.73162i	0.537435	+	0.311317i
$232$	18.0422	−	11.1501i	1.18453	−	0.732037i
$233$	13.4837	+	7.78481i	0.883346	+	0.510000i	0.871760	−	0.489933i	$-0.162979\pi$
$233$	13.4837	+	7.78481i	0.883346	+	0.510000i	0.0115857	+	0.999933i	$0.496312\pi$
$234$	−6.04369	−	2.13164i	−0.395089	−	0.139350i
$235$	6.21103	+	1.66424i	0.405163	+	0.108563i
$236$	−14.3567	+	1.54544i	−0.934544	+	0.100599i
$237$	0.686140	+	0.686140i	0.0445696	+	0.0445696i
$238$	0.336074	−	4.26050i	0.0217845	−	0.276167i
$239$			11.6230i			0.751832i	0.926654	+	0.375916i	$0.122672\pi$
$239$			11.6230i			0.751832i	−0.926654	+	0.375916i	$0.877328\pi$
$240$	−8.40034	−	9.23576i	−0.542240	−	0.596166i
$241$	2.43625	−	1.40657i	0.156933	−	0.0906051i	−0.419477	−	0.907766i	$-0.637787\pi$
$241$	2.43625	−	1.40657i	0.156933	−	0.0906051i	0.576410	+	0.817161i	$0.304453\pi$
$242$	−11.9538	+	5.72012i	−0.768420	+	0.367703i
$243$	−4.06982	−	15.1888i	−0.261079	−	0.974361i
$244$	−7.70131	−	10.5441i	−0.493026	−	0.675018i
$245$	−7.07650	−	26.7163i	−0.452101	−	1.70684i
$246$	6.86769	−	5.88050i	0.437868	−	0.374927i
$247$	−2.97899	+	5.15975i	−0.189548	+	0.328307i
$248$	−3.37080	−	11.2241i	−0.214046	−	0.712732i
$249$	−2.22595	+	1.28515i	−0.141064	+	0.0814432i
$250$	−30.6747	+	5.72509i	−1.94004	+	0.362087i
$251$	1.99507	+	1.99507i	0.125928	+	0.125928i	0.767262	−	0.641334i	$-0.221619\pi$
$251$	1.99507	+	1.99507i	0.125928	+	0.125928i	−0.641334	+	0.767262i	$0.721619\pi$
$252$	1.95265	−	12.4151i	0.123005	−	0.782080i
$253$	−6.53554	+	6.53554i	−0.410886	+	0.410886i
$254$	13.9521	+	9.56324i	0.875434	+	0.600051i
$255$	1.78250	+	3.08737i	0.111624	+	0.193339i
$256$	1.51245	−	15.9284i	0.0945278	−	0.995522i
$257$	12.9550	+	7.47955i	0.808108	+	0.466561i	0.846298	−	0.532709i	$-0.178826\pi$
$257$	12.9550	+	7.47955i	0.808108	+	0.466561i	−0.0381904	+	0.999270i	$0.512159\pi$
$258$	−0.466544	+	6.02477i	−0.0290458	+	0.375086i
$259$	−7.93879	+	2.11499i	−0.493292	+	0.131419i
$260$	14.8865	+	2.31947i	0.923224	+	0.143847i
$261$	−17.2032	+	4.60958i	−1.06485	+	0.285326i
$262$	7.40482	+	2.61172i	0.457472	+	0.161353i
$263$	−7.39409	−	12.8069i	−0.455939	−	0.789710i	0.542802	−	0.839860i	$-0.317363\pi$
$263$	−7.39409	−	12.8069i	−0.455939	−	0.789710i	−0.998742	+	0.0501505i	$0.984030\pi$
$264$	−7.34628	−	6.91892i	−0.452132	−	0.425830i
$265$	−11.9559			−0.734447
$266$	−11.0132	−	3.90218i	−0.675260	−	0.239258i
$267$	4.88162	−	4.88162i	0.298750	−	0.298750i
$268$	1.26862	−	0.136561i	0.0774932	−	0.00834178i
$269$	−6.20182	+	23.1455i	−0.378132	+	1.41121i	0.470583	+	0.882356i	$0.344044\pi$
$269$	−6.20182	+	23.1455i	−0.378132	+	1.41121i	−0.848715	+	0.528851i	$0.822623\pi$
$270$	10.2410	+	21.4014i	0.623245	+	1.30245i
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	−0.998264	−	0.0588906i	$-0.981244\pi$
$271$	−7.37718	+	12.7776i	−0.448131	+	0.776186i	0.550133	+	0.835077i	$0.314577\pi$
$272$	−1.38999	+	4.35224i	−0.0842805	+	0.263894i
$273$	−1.99030	−	3.45876i	−0.120459	−	0.209334i
$274$	−1.56582	+	20.2204i	−0.0945946	+	1.22156i
$275$	−46.1616	+	12.3690i	−2.78365	+	0.745877i
$276$	−2.96109	−	1.30946i	−0.178237	−	0.0788200i
$277$	4.76091	−	17.7680i	0.286055	−	1.06757i	−0.662009	−	0.749496i	$-0.730296\pi$
$277$	4.76091	−	17.7680i	0.286055	−	1.06757i	0.948065	−	0.318077i	$-0.103037\pi$
$278$	28.7216	−	5.36056i	1.72261	−	0.321505i
$279$			9.84094i			0.589162i
$280$	0.842357	+	29.5339i	0.0503404	+	1.76499i
$281$		−	31.9694i		−	1.90713i	−0.301185	−	0.953566i	$-0.597382\pi$
$281$		−	31.9694i		−	1.90713i	0.301185	−	0.953566i	$-0.402618\pi$
$282$	0.334049	+	1.78982i	0.0198923	+	0.106582i
$283$	−0.851136	+	3.17648i	−0.0505948	+	0.188822i	−0.986598	−	0.163169i	$-0.947829\pi$
$283$	−0.851136	+	3.17648i	−0.0505948	+	0.188822i	0.936003	+	0.351991i	$0.114495\pi$
$284$	1.73490	+	4.48584i	0.102947	+	0.266186i
$285$	9.41428	−	2.52255i	0.557654	−	0.149423i
$286$	12.1419	+	0.940243i	0.717967	+	0.0555977i
$287$	−21.3970	−	0.0307026i	−1.26303	−	0.00181232i
$288$	−5.06347	+	12.4448i	−0.298368	+	0.733318i
$289$	−7.84768	+	13.5926i	−0.461628	+	0.799564i
$290$	37.7687	−	18.0730i	2.21786	−	1.06129i
$291$	1.72472	−	6.43674i	0.101105	−	0.377329i
$292$	−3.71315	+	4.60899i	−0.217296	+	0.269721i
$293$	−6.98254	+	6.98254i	−0.407925	+	0.407925i	−0.881014	−	0.473090i	$-0.843139\pi$
$293$	−6.98254	+	6.98254i	−0.407925	+	0.407925i	0.473090	+	0.881014i	$0.343139\pi$
$294$	5.95892	−	5.07280i	0.347531	−	0.295851i
$295$	−28.5056			−1.65966
$296$	8.77900	−	0.263000i	0.510269	−	0.0152866i
$297$	9.58888	+	16.6084i	0.556403	+	0.963719i
$298$	−5.54502	+	15.7214i	−0.321214	+	0.910716i
$299$	3.77406	−	1.01126i	0.218259	−	0.0584824i
$300$	−9.87403	−	13.5189i	−0.570077	−	0.780513i
$301$	10.1267	−	10.0977i	0.583694	−	0.582021i
$302$	−19.3276	−	1.49669i	−1.11218	−	0.0861248i
$303$	10.0872	+	5.82388i	0.579497	+	0.334573i
$304$	10.5097	+	6.75023i	0.602772	+	0.387152i
$305$	−12.8881	−	22.3229i	−0.737973	−	1.27821i
$306$	2.16905	−	3.16450i	0.123997	−	0.180903i
$307$	23.3885	−	23.3885i	1.33485	−	1.33485i	0.433888	−	0.900967i	$-0.357141\pi$
$307$	23.3885	−	23.3885i	1.33485	−	1.33485i	0.900967	−	0.433888i	$-0.142859\pi$
$308$	2.52200	+	23.7490i	0.143704	+	1.35322i
$309$	−4.43659	−	4.43659i	−0.252389	−	0.252389i
$310$	−4.24466	−	22.7426i	−0.241080	−	1.29169i
$311$	21.8118	−	12.5931i	1.23684	−	0.714087i	0.268390	−	0.963310i	$-0.413509\pi$
$311$	21.8118	−	12.5931i	1.23684	−	0.714087i	0.968446	+	0.249223i	$0.0801752\pi$
$312$	1.22703	+	4.08578i	0.0694670	+	0.231312i
$313$	−4.22602	+	7.31969i	−0.238869	+	0.413733i	−0.960390	−	0.278659i	$-0.910110\pi$
$313$	−4.22602	+	7.31969i	−0.238869	+	0.413733i	0.721521	+	0.692393i	$0.243443\pi$
$314$	1.91681	+	2.23859i	0.108172	+	0.126331i
$315$	6.45573	−	23.9556i	0.363739	−	1.34974i
$316$	−0.377948	+	2.42570i	−0.0212612	+	0.136456i
$317$	−4.95323	−	18.4857i	−0.278201	−	1.03826i	−0.953666	−	0.300868i	$-0.902724\pi$
$317$	−4.95323	−	18.4857i	−0.278201	−	1.03826i	0.675464	−	0.737393i	$-0.263943\pi$
$318$	−1.46128	−	3.05376i	−0.0819446	−	0.171246i
$319$	29.3102	−	16.9222i	1.64106	−	0.947464i
$320$	6.33400	−	30.9443i	0.354081	−	1.72984i
$321$			7.33914i			0.409631i
$322$	3.29747	+	6.91647i	0.183761	+	0.385440i
$323$	−2.52207	−	2.52207i	−0.140332	−	0.140332i
$324$	4.72564	−	5.86575i	0.262535	−	0.325875i
$325$	19.5141	+	5.22880i	1.08245	+	0.290041i
$326$	0.848448	−	2.40554i	0.0469912	−	0.133231i
$327$	0.602258	+	0.347714i	0.0333050	+	0.0192286i
$328$	22.2623	+	5.25606i	1.22923	+	0.290217i
$329$	2.15980	−	3.72852i	0.119074	−	0.205560i
$330$	−12.9573	−	15.1325i	−0.713273	−	0.833014i
$331$	3.74100	+	13.9616i	0.205624	+	0.767399i	0.989258	+	0.146177i	$0.0466968\pi$
$331$	3.74100	+	13.9616i	0.205624	+	0.767399i	−0.783635	+	0.621222i	$0.786636\pi$
$332$	−5.94726	−	2.63001i	−0.326399	−	0.144340i
$333$	−7.12389	−	1.90884i	−0.390387	−	0.104604i
$334$	−25.1965	−	17.2705i	−1.37869	−	0.945000i
$335$	2.51887			0.137621
$336$	−7.44053	+	3.82485i	−0.405914	+	0.208663i
$337$	−13.7159			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$337$	−13.7159			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$338$	10.9180	+	7.48358i	0.593863	+	0.407053i
$339$	−1.46020	−	0.391258i	−0.0793069	−	0.0212502i
$340$	−3.64780	+	8.24880i	−0.197830	+	0.447354i
$341$	−4.84011	−	18.0635i	−0.262107	−	0.978196i
$342$	−6.82189	−	7.96712i	−0.368886	−	0.430812i
$343$	−18.5201	−	0.0797240i	−0.999991	−	0.00430469i
$344$	−13.0052	+	8.03715i	−0.701191	+	0.433334i
$345$	−5.53529	−	3.19580i	−0.298010	−	0.172056i
$346$	4.13347	−	11.7193i	0.222217	−	0.630036i
$347$	9.07603	+	2.43191i	0.487227	+	0.130552i	0.494066	−	0.869425i	$-0.335510\pi$
$347$	9.07603	+	2.43191i	0.487227	+	0.130552i	−0.00683892	+	0.999977i	$0.502177\pi$
$348$	9.23236	+	7.43789i	0.494906	+	0.398713i
$349$	8.35069	+	8.35069i	0.447002	+	0.447002i	0.894357	−	0.447355i	$-0.147634\pi$
$349$	8.35069	+	8.35069i	0.447002	+	0.447002i	−0.447355	+	0.894357i	$0.647634\pi$
$350$	−3.11550	+	39.4960i	−0.166530	+	2.11115i
$351$		−	8.10712i		−	0.432726i
$352$	3.17346	−	25.3335i	0.169146	−	1.35028i
$353$	16.9374	−	9.77882i	0.901488	−	0.520474i	0.0238051	−	0.999717i	$-0.492422\pi$
$353$	16.9374	−	9.77882i	0.901488	−	0.520474i	0.877683	+	0.479242i	$0.159089\pi$
$354$	−3.48402	−	7.28085i	−0.185174	−	0.386973i
$355$	2.45743	+	9.17127i	0.130427	+	0.486760i
$356$	17.2579	+	2.68895i	0.914669	+	0.142514i
$357$	2.30842	−	0.614991i	0.122175	−	0.0325488i
$358$	1.60663	+	1.87635i	0.0849133	+	0.0991681i
$359$	8.80385	−	15.2487i	0.464650	−	0.804797i	−0.534536	−	0.845146i	$-0.679514\pi$
$359$	8.80385	−	15.2487i	0.464650	−	0.804797i	0.999186	+	0.0403489i	$0.0128469\pi$
$360$	−12.5678	+	23.3566i	−0.662384	+	1.23100i
$361$	8.00970	−	4.62440i	0.421563	−	0.243390i
$362$	−1.94313	−	10.4112i	−0.102128	−	0.547199i
$363$	−5.23794	−	5.23794i	−0.274920	−	0.274920i
$364$	4.09646	−	9.22756i	0.214713	−	0.483656i
$365$	−8.26189	+	8.26189i	−0.432447	+	0.432447i
$366$	4.12646	−	6.02022i	0.215693	−	0.314682i
$367$	−16.4811	−	28.5462i	−0.860309	−	1.49010i	−0.871631	−	0.490163i	$-0.836937\pi$
$367$	−16.4811	−	28.5462i	−0.860309	−	1.49010i	0.0113220	−	0.999936i	$-0.496396\pi$
$368$	−1.74332	−	8.00369i	−0.0908768	−	0.417221i
$369$	−16.6347	−	9.60402i	−0.865966	−	0.499966i
$370$	17.2868	+	1.33865i	0.898697	+	0.0695931i
$371$	−2.08471	+	7.73582i	−0.108233	+	0.401624i
$372$	5.29009	−	3.86382i	0.274278	−	0.200330i
$373$	−12.9747	+	3.47655i	−0.671802	+	0.180009i	−0.578566	−	0.815635i	$-0.696388\pi$
$373$	−12.9747	+	3.47655i	−0.671802	+	0.180009i	−0.0932356	+	0.995644i	$0.529721\pi$
$374$	−2.42500	+	6.87542i	−0.125394	+	0.355520i
$375$	−8.72133	−	15.1058i	−0.450368	−	0.780059i
$376$	−3.15822	+	3.35329i	−0.162873	+	0.172933i
$377$	−14.3073			−0.736861
$378$	15.6330	−	2.89451i	0.804073	−	0.148878i
$379$	0.617225	−	0.617225i	0.0317047	−	0.0317047i	−0.691077	−	0.722781i	$-0.742863\pi$
$379$	0.617225	−	0.617225i	0.0317047	−	0.0317047i	0.722781	+	0.691077i	$0.242863\pi$
$380$	19.2020	+	15.4697i	0.985040	+	0.793580i
$381$	−2.44718	+	9.13298i	−0.125373	+	0.467897i
$382$	−34.6997	+	16.6044i	−1.77539	+	0.849557i
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	−0.871451	−	0.490483i	$-0.836821\pi$
$383$	−0.214398	+	0.371348i	−0.0109552	+	0.0189750i	0.860496	+	0.509457i	$0.170154\pi$
$384$	8.67788	−	2.16426i	0.442841	−	0.110444i
$385$	−0.0676511	+	47.1468i	−0.00344782	+	2.40282i
$386$	8.12622	+	0.629276i	0.413614	+	0.0320293i
$387$	12.4004	−	3.32267i	0.630346	−	0.168901i
$388$	15.7243	−	6.08138i	0.798281	−	0.308735i
$389$	−2.70883	+	10.1095i	−0.137343	+	0.512571i	0.862634	+	0.505828i	$0.168813\pi$
$389$	−2.70883	+	10.1095i	−0.137343	+	0.512571i	−0.999977	+	0.00674269i	$0.997854\pi$
$390$	1.54513	+	8.27873i	0.0782408	+	0.419210i
$391$			2.33905i			0.118291i
$392$	19.2561	+	4.60467i	0.972579	+	0.232571i
$393$			4.38907i			0.221399i
$394$	−25.1143	+	4.68729i	−1.26524	+	0.236142i
$395$	−1.25434	+	4.68126i	−0.0631126	+	0.235540i
$396$	−8.67089	+	19.6076i	−0.435729	+	0.985318i
$397$	26.9635	−	7.22485i	1.35326	−	0.362605i	0.491922	−	0.870639i	$-0.336294\pi$
$397$	26.9635	−	7.22485i	1.35326	−	0.362605i	0.861337	+	0.508034i	$0.169628\pi$
$398$	0.601327	−	7.76530i	0.0301418	−	0.389239i
$399$	0.00937155	−	6.53114i	0.000469165	−	0.326966i
$400$	12.8856	−	40.3465i	0.644278	−	2.01732i
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	0.322410	+	0.946600i	$0.395507\pi$
$401$	−13.1880	+	22.8422i	−0.658575	+	1.14069i	−0.980985	+	0.194085i	$0.937826\pi$
$402$	0.307862	+	0.643365i	0.0153548	+	0.0320881i
$403$	−2.04609	+	7.63610i	−0.101923	+	0.380381i
$404$	3.15394	+	29.2994i	0.156914	+	1.45770i
$405$	10.5147	−	10.5147i	0.522480	−	0.522480i
$406$	−5.10817	−	27.5887i	−0.253514	−	1.36920i
$407$	14.0151			0.694702
$408$	−2.55274	+	0.0764745i	−0.126379	+	0.00378605i
$409$	8.91434	+	15.4401i	0.440786	+	0.763463i	0.997748	−	0.0670744i	$-0.0213665\pi$
$409$	8.91434	+	15.4401i	0.440786	+	0.763463i	−0.556962	+	0.830538i	$0.688033\pi$
$410$	42.5855	+	15.0201i	2.10315	+	0.741792i
$411$	−10.9503	+	2.93414i	−0.540141	+	0.144730i
$412$	2.44382	−	15.6846i	0.120398	−	0.772725i
$413$	−4.97041	+	18.4439i	−0.244578	+	0.907565i
$414$	−0.531059	+	6.85789i	−0.0261001	+	0.337047i
$415$	−11.1175	−	6.41868i	−0.545735	−	0.315081i
$416$	−6.51648	+	8.60381i	−0.319497	+	0.421837i
$417$	8.16602	+	14.1440i	0.399892	+	0.692633i
$418$	16.4404	+	11.2688i	0.804128	+	0.551175i
$419$	−19.6171	+	19.6171i	−0.958358	+	0.958358i	−0.999167	−	0.0408093i	$-0.987006\pi$
$419$	−19.6171	+	19.6171i	−0.958358	+	0.958358i	0.0408093	+	0.999167i	$0.487006\pi$
$420$	−15.4122	+	5.93526i	−0.752039	+	0.289611i
$421$	−5.25405	−	5.25405i	−0.256067	−	0.256067i	0.567385	−	0.823452i	$-0.307955\pi$
$421$	−5.25405	−	5.25405i	−0.256067	−	0.256067i	−0.823452	+	0.567385i	$0.807955\pi$
$422$	−38.1112	+	7.11303i	−1.85522	+	0.346257i
$423$	3.34986	−	1.93404i	0.162876	−	0.0940363i
$424$	4.05845	−	7.54239i	0.197096	−	0.366291i
$425$	−6.04714	+	10.4740i	−0.293329	+	0.508061i
$426$	−2.04215	+	1.74861i	−0.0989427	+	0.0847202i
$427$	−16.6908	+	4.44663i	−0.807724	+	0.215187i
$428$	−14.9943	+	10.9517i	−0.724777	+	0.529369i
$429$	1.76189	+	6.57546i	0.0850648	+	0.317466i
$430$	−27.2243	+	13.0273i	−1.31287	+	0.628234i
$431$	−23.2543	+	13.4259i	−1.12012	+	0.646701i	−0.941431	−	0.337205i	$-0.890518\pi$
$431$	−23.2543	+	13.4259i	−1.12012	+	0.646701i	−0.178687	+	0.983906i	$0.557185\pi$
$432$	−16.9774	−	0.804217i	−0.816823	−	0.0386929i
$433$		−	18.6517i		−	0.896344i	−0.893947	−	0.448172i	$-0.852075\pi$
$433$		−	18.6517i		−	0.896344i	0.893947	−	0.448172i	$-0.147925\pi$
$434$	−15.4552	−	1.21913i	−0.741874	−	0.0585201i
$435$	16.5496	+	16.5496i	0.793491	+	0.793491i
$436$	0.188306	+	1.74932i	0.00901821	+	0.0837771i
$437$	6.17686	+	1.65509i	0.295479	+	0.0791735i
$438$	−3.12002	−	1.10045i	−0.149080	−	0.0525815i
$439$	−17.5460	−	10.1302i	−0.837427	−	0.483488i	0.0189621	−	0.999820i	$-0.493964\pi$
$439$	−17.5460	−	10.1302i	−0.837427	−	0.483488i	−0.856389	+	0.516332i	$0.827297\pi$
$440$	11.5813	−	49.0535i	0.552119	−	2.33853i
$441$	−14.3742	−	8.35407i	−0.684488	−	0.397813i
$442$	2.34103	−	2.00452i	0.111352	−	0.0953454i
$443$	−9.15149	−	34.1538i	−0.434800	−	1.62270i	−0.741544	−	0.670904i	$-0.765906\pi$
$443$	−9.15149	−	34.1538i	−0.434800	−	1.62270i	0.306744	−	0.951792i	$-0.400761\pi$
$444$	1.77092	+	4.57897i	0.0840440	+	0.217308i
$445$	33.3053	+	8.92414i	1.57882	+	0.423045i
$446$	17.7005	−	25.8238i	0.838142	−	1.22279i
$447$	−9.31855			−0.440752
$448$	−18.9173	−	9.49389i	−0.893761	−	0.448544i
$449$	14.0702			0.664012			0.332006	−	0.943277i	$-0.392275\pi$
$449$	14.0702			0.664012			0.332006	+	0.943277i	$0.392275\pi$
$450$	−20.1077	+	29.3358i	−0.947886	+	1.38290i
$451$	35.2573	+	9.44718i	1.66020	+	0.444850i
$452$	−1.37958	−	3.56711i	−0.0648899	−	0.167783i
$453$	−2.80460	−	10.4669i	−0.131771	−	0.491777i
$454$	−9.24907	+	7.91957i	−0.434080	+	0.371684i
$455$	9.99008	−	17.2461i	0.468342	−	0.808511i
$456$	−1.60434	+	6.79527i	−0.0751300	+	0.318218i
$457$	4.61613	+	2.66512i	0.215933	+	0.124669i	0.604066	−	0.796934i	$-0.293546\pi$
$457$	4.61613	+	2.66512i	0.215933	+	0.124669i	−0.388133	+	0.921604i	$0.626880\pi$
$458$	−33.7587	−	11.9069i	−1.57744	−	0.556372i
$459$	4.68797	+	1.25614i	0.218816	+	0.0586314i
$460$	−1.73070	−	16.0778i	−0.0806942	−	0.749631i
$461$	2.32075	+	2.32075i	0.108088	+	0.108088i	0.759082	−	0.650995i	$-0.225648\pi$
$461$	2.32075	+	2.32075i	0.108088	+	0.108088i	−0.650995	+	0.759082i	$0.725648\pi$
$462$	−12.0504	+	5.74511i	−0.560636	+	0.267287i
$463$			15.2932i			0.710736i	0.934727	+	0.355368i	$0.115644\pi$
$463$			15.2932i			0.710736i	−0.934727	+	0.355368i	$0.884356\pi$
$464$	−1.41926	+	29.9613i	−0.0658877	+	1.39092i
$465$	11.1996	−	6.46610i	0.519370	−	0.299858i
$466$	−19.8619	+	9.50429i	−0.920084	+	0.440278i
$467$	−7.77086	−	29.0012i	−0.359592	−	1.34202i	−0.874606	−	0.484835i	$-0.838880\pi$
$467$	−7.77086	−	29.0012i	−0.359592	−	1.34202i	0.515014	−	0.857182i	$-0.327787\pi$
$468$	7.31882	−	5.34558i	0.338312	−	0.247099i
$469$	0.439205	−	1.62978i	0.0202806	−	0.0752561i
$470$	−6.90739	+	5.91449i	−0.318614	+	0.272815i
$471$	−0.823689	+	1.42667i	−0.0379536	+	0.0657375i
$472$	9.67625	−	17.9827i	0.445386	−	0.827723i
$473$	−21.1273	+	12.1978i	−0.971433	+	0.560857i
$474$	−1.34899	+	0.251773i	−0.0619610	+	0.0115643i
$475$	23.3803	+	23.3803i	1.07276	+	1.07276i
$476$	4.70115	+	3.79853i	0.215477	+	0.174106i
$477$	−5.08563	+	5.08563i	−0.232855	+	0.232855i
$478$	−13.5582	−	9.29326i	−0.620139	−	0.425064i
$479$	17.2367	+	29.8548i	0.787564	+	1.36410i	0.927456	+	0.373933i	$0.121991\pi$
$479$	17.2367	+	29.8548i	0.787564	+	1.36410i	−0.139892	+	0.990167i	$0.544676\pi$
$480$	17.4900	−	2.41447i	0.798306	−	0.110205i
$481$	−5.13092	−	2.96234i	−0.233950	−	0.135071i
$482$	−0.307157	+	3.96651i	−0.0139906	+	0.180669i
$483$	−3.03294	+	3.02425i	−0.138003	+	0.137608i
$484$	2.88523	−	18.5176i	0.131147	−	0.841710i
$485$	32.1482	−	8.61409i	1.45978	−	0.391146i
$486$	20.9717	+	7.39683i	0.951296	+	0.335527i
$487$	7.45142	+	12.9062i	0.337656	+	0.584837i	0.983991	−	0.178216i	$-0.0570326\pi$
$487$	7.45142	+	12.9062i	0.337656	+	0.584837i	−0.646335	+	0.763053i	$0.723699\pi$
$488$	18.4573	−	0.552941i	0.835522	−	0.0250305i
$489$	1.42584			0.0644787
$490$	36.8225	+	13.1064i	1.66347	+	0.592089i
$491$	30.5248	−	30.5248i	1.37756	−	1.37756i	0.528844	−	0.848719i	$-0.322626\pi$
$491$	30.5248	−	30.5248i	1.37756	−	1.37756i	0.848719	−	0.528844i	$-0.177374\pi$
$492$	1.36848	+	12.7129i	0.0616961	+	0.573142i
$493$	2.21680	−	8.27322i	0.0998398	−	0.372607i
$494$	−3.63697	−	7.60048i	−0.163635	−	0.341962i
$495$	−21.1618	+	36.6533i	−0.951151	+	1.64744i
$496$	15.7880	+	5.04226i	0.708903	+	0.226404i
$497$	6.36255	+	0.00912964i	0.285399	+	0.000409520i
$498$	0.280643	−	3.62411i	0.0125759	−	0.162400i
$499$	−10.6899	+	2.86434i	−0.478544	+	0.128225i	−0.490025	−	0.871709i	$-0.663012\pi$
$499$	−10.6899	+	2.86434i	−0.478544	+	0.128225i	0.0114806	+	0.999934i	$0.496346\pi$
$500$	17.8478	−	40.3595i	0.798178	−	1.80493i
$501$	4.41942	−	16.4935i	0.197445	−	0.736875i
$502$	−3.92241	+	0.732074i	−0.175066	+	0.0326741i
$503$		−	25.6811i		−	1.14507i	−0.819882	−	0.572533i	$-0.805961\pi$
$503$		−	25.6811i		−	1.14507i	0.819882	−	0.572533i	$-0.194039\pi$
$504$	12.9209	+	12.2043i	0.575545	+	0.543624i
$505$			58.1745i			2.58873i
$506$	−2.39816	−	12.8492i	−0.106611	−	0.571216i
$507$	−1.91500	+	7.14688i	−0.0850482	+	0.317404i
$508$	−22.3110	+	8.62876i	−0.989889	+	0.382839i
$509$	14.8346	−	3.97493i	0.657534	−	0.176186i	0.0854009	−	0.996347i	$-0.472783\pi$
$509$	14.8346	−	3.97493i	0.657534	−	0.176186i	0.572133	+	0.820161i	$0.306116\pi$
$510$	−5.02661	−	0.389249i	−0.222582	−	0.0172362i
$511$	3.90508	+	6.78626i	0.172750	+	0.300206i
$512$	17.3711	+	14.4998i	0.767700	+	0.640809i
$513$	6.63431	−	11.4910i	0.292912	−	0.507338i
$514$	−19.0831	+	9.13160i	−0.841718	+	0.402777i
$515$	8.11057	−	30.2691i	0.357394	−	1.33381i
$516$	−6.65484	−	5.36135i	−0.292963	−	0.236020i
$517$	−5.19760	+	5.19760i	−0.228590	+	0.228590i
$518$	3.88037	−	10.9516i	0.170494	−	0.481186i
$519$	6.94641			0.304914
$520$	−14.6082	+	15.5105i	−0.640614	+	0.680182i
$521$	−14.9189	−	25.8403i	−0.653609	−	1.13208i	−0.982241	−	0.187626i	$-0.939921\pi$
$521$	−14.9189	−	25.8403i	−0.653609	−	1.13208i	0.328632	−	0.944458i	$-0.393412\pi$
$522$	8.37784	−	23.7531i	0.366688	−	1.03964i
$523$	34.8063	−	9.32633i	1.52198	−	0.407812i	0.601583	−	0.798810i	$-0.294537\pi$
$523$	34.8063	−	9.32633i	1.52198	−	0.407812i	0.920392	+	0.390998i	$0.127870\pi$
$524$	−8.96712	+	6.54948i	−0.391731	+	0.286116i
$525$	−21.3997	+	5.70113i	−0.933958	+	0.248818i
$526$	20.8512	+	1.61467i	0.909157	+	0.0704030i
$527$	−4.09857	−	2.36631i	−0.178537	−	0.103078i
$528$	13.9446	−	3.03735i	0.606863	−	0.132184i
$529$	9.40318	+	16.2868i	0.408834	+	0.708121i
$530$	9.55942	−	13.9465i	0.415235	−	0.605799i
$531$	−12.1253	+	12.1253i	−0.526191	+	0.526191i
$532$	13.3575	−	9.72680i	0.579121	−	0.421710i
$533$	−10.9109	−	10.9109i	−0.472602	−	0.472602i
$534$	1.79127	+	9.59752i	0.0775158	+	0.415325i
$535$	−31.7444	+	18.3276i	−1.37243	+	0.792372i
$536$	−0.855032	+	1.58903i	−0.0369318	+	0.0686355i
$537$	−0.690401	+	1.19581i	−0.0297930	+	0.0516030i
$538$	−22.0405	−	25.7405i	−0.950231	−	1.10975i
$539$	30.4935	+	8.26457i	1.31345	+	0.355980i
$540$	−33.1528	−	5.16554i	−1.42667	−	0.222289i
$541$	3.50141	+	13.0674i	0.150537	+	0.561813i	0.999446	+	0.0332740i	$0.0105934\pi$
$541$	3.50141	+	13.0674i	0.150537	+	0.561813i	−0.848909	+	0.528539i	$0.822740\pi$
$542$	−9.00661	−	18.8219i	−0.386867	−	0.808468i
$543$	5.12698	−	2.96007i	0.220020	−	0.127029i
$544$	−3.96550	−	5.10127i	−0.170020	−	0.218715i
$545$			3.47331i			0.148780i
$546$	5.62598	+	0.443785i	0.240770	+	0.0189923i
$547$	−19.9064	−	19.9064i	−0.851134	−	0.851134i	0.139139	−	0.990273i	$-0.455567\pi$
$547$	−19.9064	−	19.9064i	−0.851134	−	0.851134i	−0.990273	+	0.139139i	$0.955567\pi$
$548$	−22.3350	−	17.9938i	−0.954104	−	0.768657i
$549$	−14.9775	−	4.01321i	−0.639225	−	0.171280i
$550$	22.4804	−	63.7370i	0.958566	−	2.71775i
$551$	−20.2790	−	11.7081i	−0.863914	−	0.498781i
$552$	3.89503	−	2.40712i	0.165783	−	0.102454i
$553$	2.81019	+	1.62784i	0.119501	+	0.0692229i
$554$	16.9196	+	19.7600i	0.718847	+	0.839523i
$555$	2.50845	+	9.36167i	0.106478	+	0.397381i
$556$	−16.7114	+	37.7897i	−0.708721	+	1.60264i
$557$	−12.8968	−	3.45569i	−0.546456	−	0.146422i	−0.0249794	−	0.999688i	$-0.507952\pi$
$557$	−12.8968	−	3.45569i	−0.546456	−	0.146422i	−0.521477	+	0.853265i	$0.674619\pi$
$558$	−11.4794	−	7.86837i	−0.485962	−	0.333095i
$559$	10.3129			0.436190
$560$	−35.1246	−	22.6313i	−1.48429	−	0.956348i
$561$	−4.07527			−0.172058
$562$	37.2921	+	25.5612i	1.57307	+	1.07824i
$563$	24.4041	+	6.53907i	1.02851	+	0.275589i	0.733345	−	0.679857i	$-0.237958\pi$
$563$	24.4041	+	6.53907i	1.02851	+	0.275589i	0.295167	+	0.955446i	$0.404625\pi$
$564$	−2.35490	−	1.04139i	−0.0991594	−	0.0438504i
$565$	−1.95413	−	7.29293i	−0.0822110	−	0.306816i
$566$	−3.02482	−	3.53262i	−0.127143	−	0.148487i
$567$	−4.96990	−	8.63671i	−0.208716	−	0.362708i
$568$	−6.61986	−	1.56292i	−0.277763	−	0.0655788i
$569$	−10.8718	−	6.27682i	−0.455768	−	0.263138i	0.254495	−	0.967074i	$-0.418091\pi$
$569$	−10.8718	−	6.27682i	−0.455768	−	0.263138i	−0.710263	+	0.703936i	$0.751424\pi$
$570$	−4.58469	+	12.9986i	−0.192031	+	0.544453i
$571$	−38.1427	−	10.2203i	−1.59622	−	0.427706i	−0.652322	−	0.757942i	$-0.726205\pi$
$571$	−38.1427	−	10.2203i	−1.59622	−	0.427706i	−0.943899	+	0.330235i	$0.892872\pi$
$572$	−10.8049	+	13.4117i	−0.451776	+	0.560772i
$573$	−15.2048	−	15.2048i	−0.635188	−	0.635188i
$574$	17.1439	−	24.9350i	0.715573	−	1.04077i
$575$		−	21.6836i		−	0.904268i
$576$	−10.4683	−	15.8568i	−0.436180	−	0.660701i
$577$	−20.1944	+	11.6592i	−0.840702	+	0.485380i	−0.857503	−	0.514479i	$-0.827985\pi$
$577$	−20.1944	+	11.6592i	−0.840702	+	0.485380i	0.0168006	+	0.999859i	$0.494652\pi$
$578$	−9.58105	−	20.0223i	−0.398519	−	0.832818i
$579$	1.17918	+	4.40076i	0.0490050	+	0.182889i
$580$	−9.11603	+	58.5074i	−0.378523	+	2.42939i
$581$	−6.09157	+	6.07411i	−0.252721	+	0.251997i
$582$	6.12943	+	7.15841i	0.254073	+	0.296725i
$583$	6.83364	−	11.8362i	0.283020	−	0.490206i
$584$	−2.40750	−	8.01651i	−0.0996231	−	0.331726i
$585$	15.4946	−	8.94583i	0.640624	−	0.369865i
$586$	−2.56218	−	13.7280i	−0.105843	−	0.567100i
$587$	24.2488	+	24.2488i	1.00085	+	1.00085i	1.00000		0.000853494i	$0.000271676\pi$
$587$	24.2488	+	24.2488i	1.00085	+	1.00085i	0.000853494		1.00000i	$0.499728\pi$
$588$	1.15291	+	11.0070i	0.0475453	+	0.453923i
$589$	−9.14897	+	9.14897i	−0.376977	+	0.376977i
$590$	22.7918	−	33.2517i	0.938323	−	1.36895i
$591$	−7.14040	−	12.3675i	−0.293717	−	0.508732i
$592$	−6.71250	+	10.4510i	−0.275882	+	0.429531i
$593$	33.2134	+	19.1758i	1.36391	+	0.787454i	0.990142	−	0.140068i	$-0.0447322\pi$
$593$	33.2134	+	19.1758i	1.36391	+	0.787454i	0.373768	+	0.927522i	$0.378066\pi$
$594$	−27.0405	−	2.09395i	−1.10948	−	0.0859160i
$595$	8.42474	+	8.44895i	0.345381	+	0.346373i
$596$	−13.9054	−	19.0384i	−0.569587	−	0.779841i
$597$	4.20530	−	1.12681i	0.172112	−	0.0461171i
$598$	−1.83794	+	5.21098i	−0.0751589	+	0.213093i
$599$	−0.398968	−	0.691033i	−0.0163014	−	0.0282348i	0.857760	−	0.514051i	$-0.171856\pi$
$599$	−0.398968	−	0.691033i	−0.0163014	−	0.0282348i	−0.874061	+	0.485816i	$0.838522\pi$
$600$	23.6645	−	0.708939i	0.966101	−	0.0289423i
$601$	−4.37578			−0.178492			−0.0892459	−	0.996010i	$-0.528446\pi$
$601$	−4.37578			−0.178492			−0.0892459	+	0.996010i	$0.528446\pi$
$602$	3.68206	+	19.8864i	0.150069	+	0.810510i
$603$	1.07144	−	1.07144i	0.0436323	−	0.0436323i
$604$	17.1994	−	21.3489i	0.699833	−	0.868676i
$605$	9.57552	−	35.7363i	0.389300	−	1.45289i
$606$	−14.8588	+	7.11023i	−0.603599	+	0.288833i
$607$	3.27685	−	5.67568i	0.133003	−	0.230369i	−0.791830	−	0.610742i	$-0.790871\pi$
$607$	3.27685	−	5.67568i	0.133003	−	0.230369i	0.924833	+	0.380373i	$0.124205\pi$
$608$	−16.2772	+	6.86233i	−0.660127	+	0.278304i
$609$	13.5937	−	7.82234i	0.550844	−	0.316977i
$610$	36.3444	+	2.81443i	1.47154	+	0.113953i
$611$	3.00145	−	0.804235i	0.121425	−	0.0325359i
$612$	1.95710	+	5.06039i	0.0791112	+	0.204554i
$613$	4.86583	−	18.1595i	0.196529	−	0.733457i	−0.795337	−	0.606168i	$-0.792706\pi$
$613$	4.86583	−	18.1595i	0.196529	−	0.733457i	0.991866	−	0.127289i	$-0.0406274\pi$
$614$	8.58222	+	45.9831i	0.346350	+	1.85573i
$615$			25.2417i			1.01785i
$616$	−29.7196	−	16.0467i	−1.19744	−	0.646540i
$617$			22.2202i			0.894552i	0.894396	+	0.447276i	$0.147606\pi$
$617$			22.2202i			0.894552i	−0.894396	+	0.447276i	$0.852394\pi$
$618$	8.72256	−	1.62797i	0.350873	−	0.0654865i
$619$	−2.20771	+	8.23929i	−0.0887354	+	0.331165i	−0.995995	−	0.0894053i	$-0.971503\pi$
$619$	−2.20771	+	8.23929i	−0.0887354	+	0.331165i	0.907260	+	0.420570i	$0.138170\pi$
$620$	29.9230	+	13.2326i	1.20174	+	0.531434i
$621$	−8.40496	+	2.25210i	−0.337280	+	0.0903738i
$622$	−2.74999	+	35.5123i	−0.110264	+	1.42391i
$623$	11.5815	−	19.9934i	0.464002	−	0.801019i
$624$	−5.74713	−	1.83548i	−0.230069	−	0.0734779i
$625$	17.0872	−	29.5959i	0.683489	−	1.18384i
$626$	−5.15945	−	10.7821i	−0.206213	−	0.430941i
$627$	−2.88362	+	10.7618i	−0.115161	+	0.429785i
$628$	−4.14390	+	0.446072i	−0.165360	+	0.0178002i
$629$	2.50798	−	2.50798i	0.0999997	−	0.0999997i
$630$	22.7824	+	26.6844i	0.907671	+	1.06313i
$631$	45.0684			1.79415			0.897073	−	0.441882i	$-0.145689\pi$
$631$	45.0684			1.79415			0.897073	+	0.441882i	$0.145689\pi$
$632$	−2.52738	−	2.38036i	−0.100534	−	0.0946855i
$633$	−10.8356	−	18.7679i	−0.430678	−	0.745956i
$634$	25.5239	+	9.00241i	1.01368	+	0.357531i
$635$	−45.6146	+	12.2224i	−1.81016	+	0.485031i
$636$	4.73058	+	0.737070i	0.187580	+	0.0292267i
$637$	−9.41679	−	9.47099i	−0.373107	−	0.375254i
$638$	−3.69537	+	47.7205i	−0.146301	+	1.88927i
$639$	4.94643	+	2.85582i	0.195678	+	0.112975i
$640$	31.0320	+	32.1302i	1.22665	+	1.27006i
$641$	−14.4649	−	25.0540i	−0.571329	−	0.989572i	−0.996430	−	0.0844254i	$-0.973095\pi$
$641$	−14.4649	−	25.0540i	−0.571329	−	0.989572i	0.425100	−	0.905146i	$-0.360239\pi$
$642$	−8.56108	−	5.86804i	−0.337879	−	0.231593i
$643$	−27.4126	+	27.4126i	−1.08105	+	1.08105i	−0.0846366	+	0.996412i	$0.526973\pi$
$643$	−27.4126	+	27.4126i	−1.08105	+	1.08105i	−0.996412	+	0.0846366i	$0.973027\pi$
$644$	−10.7045	−	1.68361i	−0.421818	−	0.0663435i
$645$	−11.9292	−	11.9292i	−0.469712	−	0.469712i
$646$	4.95852	−	0.925453i	0.195091	−	0.0364115i
$647$	−25.8281	+	14.9119i	−1.01541	+	0.586247i	−0.912771	−	0.408472i	$-0.866062\pi$
$647$	−25.8281	+	14.9119i	−1.01541	+	0.586247i	−0.102638	+	0.994719i	$0.532728\pi$
$648$	3.06397	+	10.2024i	0.120364	+	0.400789i
$649$	16.2929	−	28.2201i	0.639553	−	1.10774i
$650$	−21.7020	+	18.5825i	−0.851222	+	0.728864i
$651$	−2.23091	−	8.37393i	−0.0874364	−	0.328200i
$652$	2.12768	+	2.91308i	0.0833263	+	0.114085i
$653$	3.37562	+	12.5980i	0.132098	+	0.492997i	0.999993	−	0.00375078i	$-0.00119391\pi$
$653$	3.37562	+	12.5980i	0.132098	+	0.492997i	−0.867895	+	0.496748i	$0.834527\pi$
$654$	−0.887145	+	0.424515i	−0.0346901	+	0.0165999i
$655$	−18.9843	+	10.9606i	−0.741776	+	0.428265i
$656$	−23.9311	+	21.7664i	−0.934354	+	0.849837i
$657$			7.02862i			0.274213i
$658$	2.62242	+	5.50055i	0.102233	+	0.214434i
$659$	−15.1555	−	15.1555i	−0.590375	−	0.590375i	0.347358	−	0.937733i	$-0.387079\pi$
$659$	−15.1555	−	15.1555i	−0.590375	−	0.590375i	−0.937733	+	0.347358i	$0.887079\pi$
$660$	28.0120	−	3.01536i	1.09036	−	0.117373i
$661$	2.13447	+	0.571930i	0.0830213	+	0.0222455i	0.300091	−	0.953911i	$-0.402983\pi$
$661$	2.13447	+	0.571930i	0.0830213	+	0.0222455i	−0.217069	+	0.976156i	$0.569650\pi$
$662$	−19.2773	−	6.79920i	−0.749233	−	0.264258i
$663$	1.49196	+	0.861381i	0.0579428	+	0.0334533i
$664$	7.82305	−	4.83463i	0.303593	−	0.187620i
$665$	28.2729	−	16.2693i	1.09638	−	0.630897i
$666$	7.92259	−	6.78377i	0.306994	−	0.262866i
$667$	3.97446	+	14.8329i	0.153892	+	0.574332i
$668$	40.2920	−	15.5829i	1.55894	−	0.602921i
$669$	16.9041	+	4.52945i	0.653551	+	0.175118i
$670$	−2.01397	+	2.93825i	−0.0778066	+	0.113515i
$671$	29.4658			1.13752
$672$	1.48744	−	11.7375i	0.0573791	−	0.452785i
$673$	−50.4864			−1.94611			−0.973054	−	0.230577i	$-0.925939\pi$
$673$	−50.4864			−1.94611			−0.973054	+	0.230577i	$0.925939\pi$
$674$	10.9666	−	15.9995i	0.422418	−	0.616279i
$675$	−43.4587	−	11.6447i	−1.67273	−	0.448205i
$676$	−17.4591	+	6.75231i	−0.671505	+	0.259704i
$677$	7.66899	+	28.6211i	0.294743	+	1.10000i	0.941421	+	0.337234i	$0.109491\pi$
$677$	7.66899	+	28.6211i	0.294743	+	1.10000i	−0.646678	+	0.762763i	$0.723842\pi$
$678$	1.62391	−	1.39048i	0.0623658	−	0.0534010i
$679$	0.0320023	−	22.3028i	0.00122814	−	0.855903i
$680$	−6.70558	−	10.8505i	−0.257147	−	0.416098i
$681$	−5.89450	−	3.40319i	−0.225878	−	0.130410i
$682$	24.9410	+	8.79682i	0.955040	+	0.336848i
$683$	3.63037	+	0.972755i	0.138912	+	0.0372214i	0.327605	−	0.944815i	$-0.393758\pi$
$683$	3.63037	+	0.972755i	0.138912	+	0.0372214i	−0.188693	+	0.982036i	$0.560425\pi$
$684$	14.7481	−	1.58756i	0.563907	−	0.0607020i
$685$	−40.0368	−	40.0368i	−1.52973	−	1.52973i
$686$	14.9008	−	21.5399i	0.568916	−	0.822396i
$687$		−	20.0098i		−	0.763423i
$688$	1.02303	−	21.5966i	0.0390027	−	0.823362i
$689$	−5.00358	+	2.88882i	−0.190621	+	0.110055i
$690$	8.15366	−	3.90168i	0.310404	−	0.148534i
$691$	3.71391	+	13.8605i	0.141284	+	0.527278i	0.999893	+	0.0146470i	$0.00466244\pi$
$691$	3.71391	+	13.8605i	0.141284	+	0.527278i	−0.858609	+	0.512631i	$0.828671\pi$
$692$	10.3656	+	14.1919i	0.394042	+	0.539496i
$693$	20.0258	+	20.0833i	0.760717	+	0.762903i
$694$	−10.0936	+	8.64270i	−0.383148	+	0.328072i
$695$	−40.7851	+	70.6418i	−1.54707	+	2.67960i
$696$	−16.0580	+	4.82251i	−0.608678	+	0.182797i
$697$	7.99980	−	4.61869i	0.303014	−	0.174945i
$698$	−16.4179	+	3.06421i	−0.621426	+	0.115982i
$699$	−8.70312	−	8.70312i	−0.329182	−	0.329182i
$700$	−43.5809	−	35.2134i	−1.64720	−	1.33094i
$701$	12.9519	−	12.9519i	0.489187	−	0.489187i	−0.418863	−	0.908050i	$-0.637571\pi$
$701$	12.9519	−	12.9519i	0.489187	−	0.489187i	0.908050	+	0.418863i	$0.137571\pi$
$702$	9.45692	+	6.48208i	0.356928	+	0.244650i
$703$	−4.84835	−	8.39758i	−0.182859	−	0.316721i
$704$	27.0141	+	23.9573i	1.01813	+	0.902926i
$705$	−4.40212	−	2.54157i	−0.165794	−	0.0957210i
$706$	−2.13543	+	27.5761i	−0.0803681	+	1.03784i
$707$	37.6405	+	10.1437i	1.41562	+	0.381492i
$708$	11.2787	+	1.75734i	0.423881	+	0.0660448i
$709$	0.623389	−	0.167036i	0.0234119	−	0.00627319i	−0.247094	−	0.968991i	$-0.579476\pi$
$709$	0.623389	−	0.167036i	0.0234119	−	0.00627319i	0.270506	+	0.962718i	$0.412809\pi$
$710$	−12.6631	−	4.46634i	−0.475238	−	0.167619i
$711$	1.45769	+	2.52479i	0.0546676	+	0.0946870i
$712$	−16.9353	+	17.9813i	−0.634678	+	0.673879i
$713$	8.48503			0.317767
$714$	−1.12832	+	3.18448i	−0.0422265	+	0.119176i
$715$	−24.0413	+	24.0413i	−0.899094	+	0.899094i
$716$	−3.47334	+	0.373889i	−0.129805	+	0.0139729i
$717$	2.37809	−	8.87514i	0.0888113	−	0.331448i
$718$	10.7484	+	22.4618i	0.401127	+	0.838269i
$719$	15.4833	−	26.8178i	0.577429	−	1.00014i	−0.418344	−	0.908289i	$-0.637389\pi$
$719$	15.4833	−	26.8178i	0.577429	−	1.00014i	0.995773	−	0.0918476i	$-0.0292772\pi$
$720$	−17.1967	−	33.3352i	−0.640883	−	1.24233i
$721$	−18.1707	−	10.5257i	−0.676712	−	0.391996i
$722$	−1.00985	+	13.0407i	−0.0375826	+	0.485326i
$723$	−2.14806	+	0.575572i	−0.0798873	+	0.0214057i
$724$	13.6982	+	6.05764i	0.509090	+	0.225130i
$725$	−20.5503	+	76.6949i	−0.763221	+	2.84838i
$726$	10.2981	−	1.92202i	0.382197	−	0.0713327i
$727$		−	16.7744i		−	0.622128i	−0.950389	−	0.311064i	$-0.899315\pi$
$727$		−	16.7744i		−	0.622128i	0.950389	−	0.311064i	$-0.100685\pi$
$728$	7.48856	+	12.1564i	0.277545	+	0.450548i
$729$			1.13181i			0.0419187i
$730$	−3.03163	−	16.2433i	−0.112206	−	0.601191i
$731$	−1.59791	+	5.96348i	−0.0591008	+	0.220567i
$732$	3.72324	+	9.62699i	0.137615	+	0.355824i
$733$	29.4110	−	7.88067i	1.08632	−	0.291079i	0.329139	−	0.944282i	$-0.393242\pi$
$733$	29.4110	−	7.88067i	1.08632	−	0.291079i	0.757183	+	0.653203i	$0.226575\pi$
$734$	46.4766	+	3.59904i	1.71548	+	0.132843i
$735$	−0.0626995	+	21.8480i	−0.00231271	+	0.805874i
$736$	10.7301	+	4.36581i	0.395518	+	0.160926i
$737$	−1.43971	+	2.49365i	−0.0530323	+	0.0918546i
$738$	24.5034	−	11.7253i	0.901982	−	0.431615i
$739$	−6.69098	+	24.9711i	−0.246132	+	0.918577i	0.726679	+	0.686977i	$0.241063\pi$
$739$	−6.69098	+	24.9711i	−0.246132	+	0.918577i	−0.972811	+	0.231600i	$0.925604\pi$
$740$	−15.3833	+	19.0946i	−0.565500	+	0.701933i
$741$	3.33039	−	3.33039i	0.122345	−	0.122345i
$742$	−7.35696	−	8.61701i	−0.270083	−	0.316340i
$743$	16.7597			0.614855			0.307427	−	0.951572i	$-0.400532\pi$
$743$	16.7597			0.614855			0.307427	+	0.951572i	$0.400532\pi$
$744$	0.277416	+	9.26020i	0.0101706	+	0.339495i
$745$	−23.2707	−	40.3060i	−0.852572	−	1.47670i
$746$	6.31856	−	17.9146i	0.231339	−	0.655899i
$747$	−7.45925	+	1.99870i	−0.272920	+	0.0731286i
$748$	−6.08123	−	8.32602i	−0.222352	−	0.304430i
$749$	6.32334	+	23.7352i	0.231050	+	0.867265i
$750$	24.5940	+	1.90450i	0.898046	+	0.0695427i
$751$	19.4065	+	11.2044i	0.708154	+	0.408853i	0.810377	−	0.585909i	$-0.199262\pi$
$751$	19.4065	+	11.2044i	0.708154	+	0.408853i	−0.102223	+	0.994761i	$0.532596\pi$
$752$	−1.38643	−	6.36520i	−0.0505580	−	0.232115i
$753$	−1.11521	−	1.93159i	−0.0406404	−	0.0703912i
$754$	11.4394	−	16.6894i	0.416600	−	0.607791i
$755$	38.2692	−	38.2692i	1.39276	−	1.39276i
$756$	−9.12297	+	20.5501i	−0.331799	+	0.747400i
$757$	10.1520	+	10.1520i	0.368982	+	0.368982i	0.867106	−	0.498124i	$-0.165978\pi$
$757$	10.1520	+	10.1520i	0.368982	+	0.368982i	−0.498124	+	0.867106i	$0.665978\pi$
$758$	0.226485	+	1.21349i	0.00822632	+	0.0440761i
$759$	6.32760	−	3.65324i	0.229677	−	0.132604i
$760$	−33.3984	+	10.0301i	−1.21149	+	0.363831i
$761$	−10.0149	+	17.3464i	−0.363041	+	0.628805i	−0.988460	−	0.151484i	$-0.951595\pi$
$761$	−10.0149	+	17.3464i	−0.363041	+	0.628805i	0.625419	+	0.780289i	$0.284928\pi$
$762$	−8.69694	−	10.1569i	−0.315057	−	0.367947i
$763$	2.24732	+	0.605626i	0.0813586	+	0.0219251i
$764$	8.37527	−	53.7532i	0.303007	−	1.94472i
$765$	2.77218	+	10.3459i	0.100228	+	0.374057i
$766$	−0.261753	−	0.547007i	−0.00945752	−	0.0197642i
$767$	−11.9297	+	6.88759i	−0.430755	+	0.248696i
$768$	−4.41384	+	11.8532i	−0.159271	+	0.427714i
$769$		−	50.7365i		−	1.82960i	−0.403902	−	0.914802i	$-0.632346\pi$
$769$		−	50.7365i		−	1.82960i	0.403902	−	0.914802i	$-0.367654\pi$
$770$	−54.9425	−	37.7754i	−1.97999	−	1.36133i
$771$	−8.36185	−	8.36185i	−0.301144	−	0.301144i
$772$	−7.23141	+	8.97606i	−0.260264	+	0.323056i
$773$	−28.8514	−	7.73070i	−1.03771	−	0.278054i	−0.300547	−	0.953767i	$-0.597169\pi$
$773$	−28.8514	−	7.73070i	−1.03771	−	0.278054i	−0.737165	+	0.675713i	$0.763836\pi$
$774$	−6.03889	+	17.1216i	−0.217063	+	0.615424i
$775$	37.9949	+	21.9363i	1.36482	+	0.787977i
$776$	−5.47855	+	23.2047i	−0.196669	+	0.833002i
$777$	6.49464	+	0.00931918i	0.232994	+	0.000334324i
$778$	−9.62681	−	11.2429i	−0.345138	−	0.403078i
$779$	−6.53627	−	24.3937i	−0.234186	−	0.873994i
$780$	−10.8925	−	4.81691i	−0.390015	−	0.172473i
$781$	−10.4840	−	2.80918i	−0.375148	−	0.100520i
$782$	−2.72849	−	1.87020i	−0.0975706	−	0.0668781i
$783$	31.8628			1.13868
$784$	−20.7676	+	18.7805i	−0.741701	+	0.670731i
$785$	−8.22781			−0.293663
$786$	−5.11983	−	3.50930i	−0.182618	−	0.125173i
$787$	−37.0302	−	9.92221i	−1.31998	−	0.353688i	−0.471012	−	0.882127i	$-0.656111\pi$
$787$	−37.0302	−	9.92221i	−1.31998	−	0.353688i	−0.848972	+	0.528438i	$0.822778\pi$
$788$	14.6125	−	33.0434i	0.520549	−	1.17712i
$789$	3.02568	+	11.2920i	0.107717	+	0.402005i
$790$	−4.45775	−	5.20610i	−0.158600	−	0.185225i
$791$	−5.05946	−	0.00725983i	−0.179894	−	0.000258130i
$792$	−15.9393	−	25.7919i	−0.566379	−	0.916475i
$793$	−10.7874	−	6.22812i	−0.383073	−	0.221167i
$794$	−13.1310	+	37.2295i	−0.466003	+	1.32122i
$795$	9.12933	+	2.44620i	0.323784	+	0.0867577i
$796$	8.57740	+	6.91023i	0.304018	+	0.244927i
$797$	−18.8328	−	18.8328i	−0.667092	−	0.667092i	0.289949	−	0.957042i	$-0.406361\pi$
$797$	−18.8328	−	18.8328i	−0.667092	−	0.667092i	−0.957042	+	0.289949i	$0.906361\pi$
$798$	7.61106	+	5.23294i	0.269429	+	0.185244i
$799$			1.86021i			0.0658094i
$800$	36.7613	+	47.2901i	1.29971	+	1.67196i
$801$	17.9629	−	10.3709i	0.634688	−	0.366437i
$802$	−16.1008	−	33.6473i	−0.568541	−	1.18813i
$803$	−3.45692	−	12.9014i	−0.121992	−	0.455280i
$804$	−0.996635	−	0.155285i	−0.0351486	−	0.00547650i
$805$	−20.6549	−	5.56624i	−0.727990	−	0.196184i
$806$	−7.27152	−	8.49223i	−0.256128	−	0.299126i
$807$	9.47120	−	16.4046i	0.333402	−	0.577469i
$808$	−36.6994	−	19.7474i	−1.29108	−	0.694711i
$809$	−17.1772	+	9.91725i	−0.603918	+	0.348672i	−0.770581	−	0.637342i	$-0.780034\pi$
$809$	−17.1772	+	9.91725i	−0.603918	+	0.348672i	0.166663	+	0.986014i	$0.446701\pi$
$810$	3.85828	+	20.6725i	0.135566	+	0.726356i
$811$	−3.89894	−	3.89894i	−0.136910	−	0.136910i	0.635330	−	0.772240i	$-0.280864\pi$
$811$	−3.89894	−	3.89894i	−0.136910	−	0.136910i	−0.772240	+	0.635330i	$0.780864\pi$
$812$	36.2664	+	16.1000i	1.27270	+	0.565000i
$813$	8.24740	−	8.24740i	0.289249	−	0.289249i
$814$	−11.2058	+	16.3485i	−0.392764	+	0.573016i
$815$	3.56067	+	6.16726i	0.124725	+	0.216030i
$816$	1.95184	−	3.03890i	0.0683282	−	0.106383i
$817$	14.6174	+	8.43938i	0.511400	+	0.295257i
$818$	−25.1383	−	1.94665i	−0.878940	−	0.0680631i
$819$	−3.08646	−	11.5853i	−0.107850	−	0.404823i
$820$	−51.5704	+	37.6664i	−1.80092	+	1.31537i
$821$	18.6923	−	5.00859i	0.652366	−	0.174801i	0.0825677	−	0.996585i	$-0.473688\pi$
$821$	18.6923	−	5.00859i	0.652366	−	0.174801i	0.569798	+	0.821784i	$0.307021\pi$
$822$	5.33274	−	15.1195i	0.186001	−	0.527354i
$823$	20.0886	+	34.7944i	0.700243	+	1.21286i	0.968381	+	0.249476i	$0.0802583\pi$
$823$	20.0886	+	34.7944i	0.700243	+	1.21286i	−0.268138	+	0.963381i	$0.586408\pi$
$824$	16.3421	+	15.3914i	0.569303	+	0.536185i
$825$	37.7789			1.31529
$826$	−17.5406	−	20.5449i	−0.610317	−	0.714847i
$827$	11.2802	−	11.2802i	0.392250	−	0.392250i	−0.483239	−	0.875489i	$-0.660540\pi$
$827$	11.2802	−	11.2802i	0.392250	−	0.392250i	0.875489	+	0.483239i	$0.160540\pi$
$828$	−7.57509	−	6.10274i	−0.263253	−	0.212085i
$829$	−10.9094	+	40.7143i	−0.378898	+	1.41407i	0.468668	+	0.883375i	$0.344734\pi$
$829$	−10.9094	+	40.7143i	−0.378898	+	1.41407i	−0.847565	+	0.530691i	$0.821933\pi$
$830$	16.3764	−	7.83641i	0.568433	−	0.272006i
$831$	−7.27069	+	12.5932i	−0.252217	+	0.436853i
$832$	−4.82603	−	14.4807i	−0.167312	−	0.502027i
$833$	6.93569	−	3.97783i	0.240307	−	0.137824i
$834$	−23.0281	−	1.78324i	−0.797396	−	0.0617486i
$835$	82.3765	−	22.0727i	2.85076	−	0.763858i
$836$	−26.2900	+	10.1677i	−0.909260	+	0.351656i
$837$	4.55671	−	17.0059i	0.157503	−	0.587809i
$838$	−7.19832	−	38.5682i	−0.248662	−	1.33232i
$839$			27.4328i			0.947087i	0.880771	+	0.473543i	$0.157025\pi$
$839$			27.4328i			0.947087i	−0.880771	+	0.473543i	$0.842975\pi$
$840$	5.39945	−	22.7239i	0.186299	−	0.784048i
$841$		−	27.2308i		−	0.938992i
$842$	10.3297	−	1.92793i	0.355986	−	0.0664408i
$843$	−6.54097	+	24.4112i	−0.225283	+	0.840767i
$844$	22.1747	−	50.1438i	0.763283	−	1.72602i
$845$	−35.6950	+	9.56445i	−1.22795	+	0.329027i
$846$	−0.422343	+	5.45396i	−0.0145204	+	0.187511i
$847$	−21.4527	−	12.4268i	−0.737125	−	0.426991i
$848$	5.55322	+	10.7647i	0.190698	+	0.369662i
$849$	1.29982	−	2.25136i	0.0446098	−	0.0772665i
$850$	−7.38280	−	15.4285i	−0.253228	−	0.529192i
$851$	−1.64584	+	6.14234i	−0.0564185	+	0.210557i
$852$	−0.406928	−	3.78027i	−0.0139411	−	0.129510i
$853$	8.95019	−	8.95019i	0.306449	−	0.306449i	−0.537082	−	0.843530i	$-0.680473\pi$
$853$	8.95019	−	8.95019i	0.306449	−	0.306449i	0.843530	+	0.537082i	$0.180473\pi$
$854$	8.15823	−	23.0251i	0.279169	−	0.787901i
$855$	29.2826			1.00144
$856$	−0.786311	−	26.2472i	−0.0268756	−	0.897112i
$857$	26.8241	+	46.4607i	0.916294	+	1.58707i	0.804995	+	0.593281i	$0.202168\pi$
$857$	26.8241	+	46.4607i	0.916294	+	1.58707i	0.111299	+	0.993787i	$0.464499\pi$
$858$	−9.07897	−	3.20220i	−0.309951	−	0.109321i
$859$	−12.7333	+	3.41188i	−0.434455	+	0.116412i	−0.469417	−	0.882977i	$-0.655536\pi$
$859$	−12.7333	+	3.41188i	−0.434455	+	0.116412i	0.0349617	+	0.999389i	$0.488869\pi$
$860$	6.57099	−	42.1731i	0.224069	−	1.43809i
$861$	16.3321	+	4.40130i	0.556596	+	0.149996i
$862$	2.93185	−	37.8607i	0.0998591	−	1.28954i
$863$	−6.64111	−	3.83425i	−0.226066	−	0.130519i	0.382690	−	0.923877i	$-0.374998\pi$
$863$	−6.64111	−	3.83425i	−0.226066	−	0.130519i	−0.608756	+	0.793358i	$0.708331\pi$
$864$	14.5124	−	19.1610i	0.493723	−	0.651871i
$865$	17.3469	+	30.0457i	0.589812	+	1.02158i
$866$	21.7571	+	14.9131i	0.739338	+	0.506766i
$867$	8.77341	−	8.77341i	0.297961	−	0.297961i
$868$	13.7794	−	17.0537i	0.467703	−	0.578840i
$869$	−3.91744	−	3.91744i	−0.132890	−	0.132890i
$870$	−32.5373	+	6.07272i	−1.10312	+	0.205884i
$871$	1.05415	−	0.608615i	0.0357186	−	0.0206221i
$872$	−2.19113	−	1.17902i	−0.0742011	−	0.0399265i
$873$	10.0106	−	17.3388i	0.338807	−	0.586830i
$874$	−6.86939	+	5.88195i	−0.232361	+	0.198960i
$875$	−41.2203	−	41.3387i	−1.39350	−	1.39750i
$876$	3.77830	−	2.75962i	0.127657	−	0.0932391i
$877$	−3.97908	−	14.8501i	−0.134364	−	0.501453i	−1.00000		0.000778781i	$-0.999752\pi$
$877$	−3.97908	−	14.8501i	−0.134364	−	0.501453i	0.865636	−	0.500674i	$-0.166915\pi$
$878$	25.8459	−	12.3677i	0.872255	−	0.417390i
$879$	6.76038	−	3.90311i	0.228022	−	0.131649i
$880$	47.9608	+	52.7305i	1.61676	+	1.77755i
$881$			21.5605i			0.726392i	0.931713	+	0.363196i	$0.118314\pi$
$881$			21.5605i			0.726392i	−0.931713	+	0.363196i	$0.881686\pi$
$882$	21.2380	−	10.0880i	0.715120	−	0.339680i
$883$	3.61325	+	3.61325i	0.121596	+	0.121596i	0.765286	−	0.643690i	$-0.222598\pi$
$883$	3.61325	+	3.61325i	0.121596	+	0.121596i	−0.643690	+	0.765286i	$0.722598\pi$
$884$	0.466484	+	4.33353i	0.0156896	+	0.145752i
$885$	21.7664	+	5.83228i	0.731668	+	0.196050i
$886$	47.1574	+	16.6327i	1.58428	+	0.558785i
$887$	−31.1537	−	17.9866i	−1.04604	−	0.603930i	−0.124500	−	0.992220i	$-0.539733\pi$
$887$	−31.1537	−	17.9866i	−1.04604	−	0.603930i	−0.921537	+	0.388290i	$0.873066\pi$
$888$	−6.75730	−	1.59537i	−0.226760	−	0.0535372i
$889$	−0.0454076	+	31.6450i	−0.00152292	+	1.06134i
$890$	−37.0394	+	31.7152i	−1.24156	+	1.06310i
$891$	4.39954	+	16.4193i	0.147390	+	0.550067i
$892$	15.9709	+	41.2951i	0.534744	+	1.38266i
$893$	4.91235	+	1.31626i	0.164386	+	0.0440470i
$894$	7.45069	−	10.8701i	0.249188	−	0.363549i
$895$	−6.89640			−0.230521
$896$	26.2000	−	14.4761i	0.875282	−	0.483613i
$897$	−3.08871			−0.103129
$898$	−11.2499	+	16.4128i	−0.375413	+	0.547702i
$899$	−30.0116	−	8.04158i	−1.00094	−	0.268202i
$900$	−18.1429	−	46.9111i	−0.604762	−	1.56370i
$901$	−0.895202	−	3.34094i	−0.0298235	−	0.111303i
$902$	−39.2103	+	33.5740i	−1.30556	+	1.11789i
$903$	−9.79857	+	5.63847i	−0.326076	+	0.187637i
$904$	5.26407	+	1.24283i	0.175080	+	0.0413358i
$905$	25.6067	+	14.7840i	0.851194	+	0.491437i
$906$	14.4520	+	5.09730i	0.480136	+	0.169347i
$907$	−18.5085	−	4.95935i	−0.614566	−	0.164672i	−0.0619098	−	0.998082i	$-0.519719\pi$
$907$	−18.5085	−	4.95935i	−0.614566	−	0.164672i	−0.552656	+	0.833409i	$0.686386\pi$
$908$	−1.84301	−	17.1211i	−0.0611624	−	0.568185i
$909$	24.7454	+	24.7454i	0.820752	+	0.820752i
$910$	12.1299	+	25.4426i	0.402103	+	0.843414i
$911$			16.9566i			0.561797i	0.959737	+	0.280899i	$0.0906325\pi$
$911$			16.9566i			0.561797i	−0.959737	+	0.280899i	$0.909368\pi$
$912$	−6.64390	−	7.30464i	−0.220002	−	0.241881i
$913$	12.7088	−	7.33743i	0.420600	−	0.242833i
$914$	−6.79970	+	3.25378i	−0.224914	+	0.107626i
$915$	5.27386	+	19.6823i	0.174348	+	0.650677i
$916$	40.8813	−	29.8592i	1.35075	−	0.986576i
$917$	3.78158	+	14.1945i	0.124879	+	0.468743i
$918$	−5.21356	+	4.46414i	−0.172073	+	0.147339i
$919$	19.0403	−	32.9788i	0.628083	−	1.08787i	−0.359853	−	0.933009i	$-0.617173\pi$
$919$	19.0403	−	32.9788i	0.628083	−	1.08787i	0.987936	−	0.154863i	$-0.0494935\pi$
$920$	20.1385	+	10.8362i	0.663945	+	0.357259i
$921$	−22.6444	+	13.0737i	−0.746158	+	0.430794i
$922$	−4.56270	+	0.851577i	−0.150265	+	0.0280452i
$923$	3.24442	+	3.24442i	0.106791	+	0.106791i
$924$	2.93332	−	18.6503i	0.0964990	−	0.613550i
$925$	−23.2496	+	23.2496i	−0.764443	+	0.764443i
$926$	−17.8395	−	12.2278i	−0.586241	−	0.401829i
$927$	−9.42543	−	16.3253i	−0.309572	−	0.536194i
$928$	−33.8149	−	25.6112i	−1.11003	−	0.840730i
$929$	−3.92408	−	2.26557i	−0.128745	−	0.0743309i	0.434244	−	0.900795i	$-0.357015\pi$
$929$	−3.92408	−	2.26557i	−0.128745	−	0.0743309i	−0.562989	+	0.826464i	$0.690349\pi$
$930$	−1.41202	+	18.2343i	−0.0463021	+	0.597927i
$931$	−5.59686	−	21.1302i	−0.183430	−	0.692513i
$932$	4.79396	−	30.7680i	0.157031	−	1.00784i
$933$	−19.2317	+	5.15311i	−0.629617	+	0.168705i
$934$	40.0430	+	14.1234i	1.31025	+	0.462131i
$935$	−10.1770	−	17.6270i	−0.332822	−	0.576464i
$936$	0.383804	+	12.8114i	0.0125450	+	0.418755i
$937$	37.0969			1.21190			0.605952	−	0.795501i	$-0.292792\pi$
$937$	37.0969			1.21190			0.605952	+	0.795501i	$0.292792\pi$
$938$	1.54996	+	1.81543i	0.0506080	+	0.0592758i
$939$	4.72453	−	4.72453i	0.154179	−	0.154179i
$940$	−1.37640	−	12.7864i	−0.0448931	−	0.417046i
$941$	0.583589	−	2.17799i	0.0190245	−	0.0710003i	−0.955761	−	0.294144i	$-0.904965\pi$
$941$	0.583589	−	2.17799i	0.0190245	−	0.0710003i	0.974785	+	0.223144i	$0.0716320\pi$
$942$	−1.00562	−	2.10153i	−0.0327649	−	0.0684716i
$943$	−8.28076	+	14.3427i	−0.269659	+	0.467062i
$944$	13.2401	+	25.6655i	0.430928	+	0.835340i
$945$	−22.2483	+	38.4077i	−0.723736	+	1.24940i
$946$	2.66368	−	34.3977i	0.0866038	−	1.11837i
$947$	15.7523	−	4.22082i	0.511882	−	0.137158i	0.00637300	−	0.999980i	$-0.497971\pi$
$947$	15.7523	−	4.22082i	0.511882	−	0.137158i	0.505509	+	0.862821i	$0.331305\pi$
$948$	0.784895	−	1.77489i	0.0254922	−	0.0576458i
$949$	−1.46136	+	5.45387i	−0.0474378	+	0.177040i
$950$	−45.9668	+	8.57919i	−1.49136	+	0.278346i
$951$			15.1288i			0.490585i
$952$	−8.18980	+	2.44674i	−0.265433	+	0.0792992i
$953$		−	27.9419i		−	0.905126i	−0.891733	−	0.452563i	$-0.850510\pi$
$953$		−	27.9419i		−	0.905126i	0.891733	−	0.452563i	$-0.149490\pi$
$954$	−1.86613	−	9.99860i	−0.0604181	−	0.323716i
$955$	27.7960	−	103.736i	0.899456	−	3.35682i
$956$	21.6811	−	8.38515i	0.701216	−	0.271195i
$957$	−25.8430	+	6.92462i	−0.835387	+	0.223841i
$958$	−48.6071	−	3.76403i	−1.57043	−	0.121610i
$959$	−32.8860	+	18.9239i	−1.06194	+	0.611084i
$960$	−11.1678	+	22.3325i	−0.360438	+	0.720779i
$961$	6.91607	−	11.9790i	0.223099	−	0.386419i
$962$	7.55800	−	3.61665i	0.243680	−	0.116605i
$963$	−5.70700	+	21.2988i	−0.183906	+	0.686345i
$964$	−4.38132	−	3.52974i	−0.141113	−	0.113685i
$965$	−16.0901	+	16.0901i	−0.517960	+	0.517960i
$966$	−1.10277	−	5.95596i	−0.0354811	−	0.191630i
$967$	−47.4478			−1.52582			−0.762910	−	0.646505i	$-0.776230\pi$
$967$	−47.4478			−1.52582			−0.762910	+	0.646505i	$0.776230\pi$
$968$	19.2938	+	18.1714i	0.620127	+	0.584052i
$969$	1.40979	+	2.44183i	0.0452890	+	0.0784428i
$970$	−15.6560	+	44.3882i	−0.502683	+	1.42522i
$971$	−31.6308	+	8.47546i	−1.01508	+	0.271990i	−0.727751	−	0.685841i	$-0.759434\pi$
$971$	−31.6308	+	8.47546i	−1.01508	+	0.271990i	−0.287330	+	0.957832i	$0.592768\pi$
$972$	−25.3964	+	18.5492i	−0.814590	+	0.594967i
$973$	38.5957	+	38.7066i	1.23732	+	1.24088i
$974$	−21.0129	−	1.62719i	−0.673296	−	0.0521385i
$975$	−13.8308	−	7.98523i	−0.442941	−	0.255732i
$976$	−14.1126	+	21.9725i	−0.451733	+	0.703321i
$977$	15.9234	+	27.5802i	0.509435	+	0.882368i	0.999940	+	0.0109296i	$0.00347908\pi$
$977$	15.9234	+	27.5802i	0.509435	+	0.882368i	−0.490505	+	0.871438i	$0.663188\pi$
$978$	−1.14004	+	1.66324i	−0.0364544	+	0.0531844i
$979$	−27.8711	+	27.8711i	−0.890763	+	0.890763i
$980$	−44.7302	+	32.4740i	−1.42885	+	1.03734i
$981$	1.47742	+	1.47742i	0.0471704	+	0.0471704i
$982$	11.2008	+	60.0132i	0.357432	+	1.91510i
$983$	37.4979	−	21.6494i	1.19600	−	0.690509i	0.236337	−	0.971671i	$-0.424053\pi$
$983$	37.4979	−	21.6494i	1.19600	−	0.690509i	0.959660	+	0.281162i	$0.0907198\pi$
$984$	−15.9237	−	8.56833i	−0.507630	−	0.273148i
$985$	35.6626	−	61.7695i	1.13631	−	1.96814i
$986$	7.87822	+	9.20078i	0.250894	+	0.293013i
$987$	−2.41204	+	2.40513i	−0.0767762	+	0.0765562i
$988$	11.7739	+	1.83449i	0.374577	+	0.0583628i
$989$	−2.86486	−	10.6918i	−0.0910973	−	0.339980i
$990$	−25.8359	−	53.9914i	−0.821119	−	1.71596i
$991$	16.4220	−	9.48127i	0.521663	−	0.301183i	−0.215952	−	0.976404i	$-0.569285\pi$
$991$	16.4220	−	9.48127i	0.521663	−	0.301183i	0.737615	+	0.675222i	$0.235952\pi$
$992$	−18.5052	+	14.3851i	−0.587539	+	0.456727i
$993$		−	11.4262i		−	0.362601i
$994$	−5.09786	+	7.41459i	−0.161694	+	0.235177i
$995$	15.3755	+	15.3755i	0.487436	+	0.487436i
$996$	4.00312	+	3.22504i	0.126844	+	0.102189i
$997$	29.2330	+	7.83295i	0.925818	+	0.248072i	0.690070	−	0.723742i	$-0.257580\pi$
$997$	29.2330	+	7.83295i	0.925818	+	0.248072i	0.235747	+	0.971814i	$0.424246\pi$
$998$	5.20589	−	14.7599i	0.164789	−	0.467216i
$999$	11.4267	+	6.59723i	0.361526	+	0.208727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.v.a.75.6	yes	56
4.3	odd	2		448.2.z.a.271.8		56
7.2	even	3		784.2.j.a.587.28		56
7.3	odd	6	inner	112.2.v.a.59.5	yes	56
7.4	even	3		784.2.w.f.619.5		56
7.5	odd	6		784.2.j.a.587.27		56
7.6	odd	2		784.2.w.f.411.6		56
8.3	odd	2		896.2.z.a.159.7		56
8.5	even	2		896.2.z.b.159.8		56
16.3	odd	4	inner	112.2.v.a.19.5	yes	56
16.5	even	4		896.2.z.a.607.7		56
16.11	odd	4		896.2.z.b.607.8		56
16.13	even	4		448.2.z.a.47.8		56
28.3	even	6		448.2.z.a.143.8		56
56.3	even	6		896.2.z.a.31.7		56
56.45	odd	6		896.2.z.b.31.8		56
112.3	even	12	inner	112.2.v.a.3.6	✓	56
112.19	even	12		784.2.j.a.195.28		56
112.45	odd	12		448.2.z.a.367.8		56
112.51	odd	12		784.2.j.a.195.27		56
112.59	even	12		896.2.z.b.479.8		56
112.67	odd	12		784.2.w.f.227.6		56
112.83	even	4		784.2.w.f.19.5		56
112.101	odd	12		896.2.z.a.479.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	112.3	even	12	inner
112.2.v.a.19.5	yes	56	16.3	odd	4	inner
112.2.v.a.59.5	yes	56	7.3	odd	6	inner
112.2.v.a.75.6	yes	56	1.1	even	1	trivial
448.2.z.a.47.8		56	16.13	even	4
448.2.z.a.143.8		56	28.3	even	6
448.2.z.a.271.8		56	4.3	odd	2
448.2.z.a.367.8		56	112.45	odd	12
784.2.j.a.195.27		56	112.51	odd	12
784.2.j.a.195.28		56	112.19	even	12
784.2.j.a.587.27		56	7.5	odd	6
784.2.j.a.587.28		56	7.2	even	3
784.2.w.f.19.5		56	112.83	even	4
784.2.w.f.227.6		56	112.67	odd	12
784.2.w.f.411.6		56	7.6	odd	2
784.2.w.f.619.5		56	7.4	even	3
896.2.z.a.31.7		56	56.3	even	6
896.2.z.a.159.7		56	8.3	odd	2
896.2.z.a.479.7		56	112.101	odd	12
896.2.z.a.607.7		56	16.5	even	4
896.2.z.b.31.8		56	56.45	odd	6
896.2.z.b.159.8		56	8.5	even	2
896.2.z.b.479.8		56	112.59	even	12
896.2.z.b.607.8		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+(-0.799555 + 1.16650i) q^{2} +(-0.763582 - 0.204601i) q^{3} +(-0.721425 - 1.86535i) q^{4} +(-1.02188 - 3.81370i) q^{5} +(0.849192 - 0.727125i) q^{6} +(-2.64575 - 0.00379639i) q^{7} +(2.75275 + 0.649913i) q^{8} +(-2.05688 - 1.18754i) q^{9} +(5.26571 + 1.85724i) q^{10} +(4.35958 + 1.16815i) q^{11} +(0.169214 + 1.57195i) q^{12} +(-1.34913 - 1.34913i) q^{13} +(2.11985 - 3.08322i) q^{14} +3.12115i q^{15} +(-2.95909 + 2.69143i) q^{16} +(0.989178 - 0.571102i) q^{17} +(3.02985 - 1.44984i) q^{18} +(-0.808212 - 3.01629i) q^{19} +(-6.37669 + 4.65746i) q^{20} +(2.01947 + 0.544222i) q^{21} +(-4.84836 + 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(-1.96897 - 1.05948i) q^{24} +(-9.16994 + 5.29427i) q^{25} +(2.65246 - 0.495052i) q^{26} +(3.00457 + 3.00457i) q^{27} +(1.90163 + 4.93800i) q^{28} +(5.30239 - 5.30239i) q^{29} +(-3.64081 - 2.49553i) q^{30} +(-2.07171 - 3.58830i) q^{31} +(-0.773583 - 5.60371i) q^{32} +(-3.08989 - 1.78395i) q^{33} +(-0.124713 + 1.61050i) q^{34} +(2.68915 + 10.0940i) q^{35} +(-0.731298 + 4.69353i) q^{36} +(2.99943 - 0.803695i) q^{37} +(4.16470 + 1.46891i) q^{38} +(0.754139 + 1.30621i) q^{39} +(-0.334398 - 11.1623i) q^{40} +8.08732 q^{41} +(-2.24951 + 1.92057i) q^{42} +(-3.82205 + 3.82205i) q^{43} +(-0.966105 - 8.97489i) q^{44} +(-2.42704 + 9.05785i) q^{45} +(-1.25008 - 2.61239i) q^{46} +(-0.814305 + 1.41042i) q^{47} +(2.81018 - 1.44969i) q^{48} +(6.99997 + 0.0200886i) q^{49} +(1.15613 - 14.9298i) q^{50} +(-0.872167 + 0.233696i) q^{51} +(-1.54331 + 3.48991i) q^{52} +(0.783749 - 2.92499i) q^{53} +(-5.90713 + 1.10250i) q^{54} -17.8198i q^{55} +(-7.28061 - 1.72996i) q^{56} +2.46854i q^{57} +(1.94567 + 10.4248i) q^{58} +(1.86863 - 6.97383i) q^{59} +(5.82205 - 2.25168i) q^{60} +(6.30611 - 1.68972i) q^{61} +(5.84218 + 0.452405i) q^{62} +(5.43748 + 3.14974i) q^{63} +(7.15523 + 3.57809i) q^{64} +(-3.76654 + 6.52383i) q^{65} +(4.55151 - 2.17798i) q^{66} +(-0.165120 + 0.616236i) q^{67} +(-1.77893 - 1.43316i) q^{68} +(1.14470 - 1.14470i) q^{69} +(-13.9247 - 4.93379i) q^{70} -2.40482 q^{71} +(-4.89027 - 4.60579i) q^{72} +(-1.47966 - 2.56284i) q^{73} +(-1.46070 + 4.14142i) q^{74} +(8.08521 - 2.16643i) q^{75} +(-5.04338 + 3.68363i) q^{76} +(-11.5299 - 3.10717i) q^{77} +(-2.12666 - 0.164684i) q^{78} +(-1.06303 - 0.613742i) q^{79} +(13.2881 + 8.53478i) q^{80} +(1.88313 + 3.26167i) q^{81} +(-6.46626 + 9.43383i) q^{82} +(2.29910 - 2.29910i) q^{83} +(-0.441729 - 4.15964i) q^{84} +(-3.18883 - 3.18883i) q^{85} +(-1.40247 - 7.51435i) q^{86} +(-5.13369 + 2.96394i) q^{87} +(11.2416 + 6.04896i) q^{88} +(-4.36654 + 7.56307i) q^{89} +(-8.62539 - 10.0734i) q^{90} +(3.56434 + 3.57459i) q^{91} +(4.04685 + 0.630538i) q^{92} +(0.847747 + 3.16383i) q^{93} +(-0.994165 - 2.07759i) q^{94} +(-10.6773 + 6.16455i) q^{95} +(-0.555832 + 4.43717i) q^{96} +8.42967i q^{97} +(-5.62029 + 8.14938i) q^{98} +(-7.57992 - 7.57992i) 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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