LMFDB - Embedded newform 112.2.v.a.19.5

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			19.5
Character	$\chi$	$=$	112.19
Dual form			112.2.v.a.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.610438 + 1.27568i) q^{2} +(-0.204601 + 0.763582i) q^{3} +(-1.25473 - 1.55745i) q^{4} +(-3.81370 + 1.02188i) 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} +(1.02443 - 5.48886i) q^{10} +(-1.16815 + 4.35958i) q^{11} +(1.44596 - 0.639434i) q^{12} +(1.34913 - 1.34913i) q^{13} +(1.61991 - 3.37282i) q^{14} -3.12115i q^{15} +(-0.851298 + 3.90836i) q^{16} +(0.989178 - 0.571102i) q^{17} +(-2.77052 + 1.89901i) q^{18} +(-3.01629 + 0.808212i) q^{19} +(6.37669 + 4.65746i) q^{20} +(0.544222 - 2.01947i) q^{21} +(-4.84836 - 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(-0.0669534 + 2.23492i) q^{24} +(9.16994 - 5.29427i) q^{25} +(0.897503 + 2.54463i) q^{26} +(-3.00457 + 3.00457i) q^{27} +(3.31379 + 4.12538i) q^{28} +(5.30239 + 5.30239i) q^{29} +(3.98159 + 1.90527i) q^{30} +(2.07171 + 3.58830i) q^{31} +(-4.46616 - 3.47180i) q^{32} +(-3.08989 - 1.78395i) q^{33} +(0.124713 + 1.61050i) q^{34} +(10.0940 - 2.68915i) q^{35} +(-0.731298 - 4.69353i) q^{36} +(-0.803695 - 2.99943i) q^{37} +(0.810234 - 4.34119i) q^{38} +(0.754139 + 1.30621i) q^{39} +(-9.83402 + 5.29154i) q^{40} -8.08732 q^{41} +(2.24399 + 1.92701i) q^{42} +(-3.82205 - 3.82205i) q^{43} +(8.25554 - 3.65078i) q^{44} +(-9.05785 - 2.42704i) q^{45} +(-1.63736 - 2.38879i) 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} +(0.233696 + 0.872167i) q^{51} +(-3.79400 - 0.408407i) q^{52} +(-2.92499 - 0.783749i) q^{53} +(-1.99877 - 5.66697i) q^{54} -17.8198i q^{55} +(-7.28554 + 1.70906i) q^{56} -2.46854i q^{57} +(-10.0010 + 3.52739i) q^{58} +(6.97383 + 1.86863i) q^{59} +(-4.86103 + 3.91620i) q^{60} +(1.68972 + 6.30611i) 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} +(4.16194 - 2.85273i) q^{66} +(0.616236 + 0.165120i) q^{67} +(-2.13062 - 0.824015i) q^{68} +(-1.14470 - 1.14470i) q^{69} +(-2.73123 + 14.5183i) q^{70} -2.40482 q^{71} +(6.43387 + 1.93221i) q^{72} +(1.47966 + 2.56284i) q^{73} +(4.31693 + 0.805706i) q^{74} +(2.16643 + 8.08521i) q^{75} +(5.04338 + 3.68363i) q^{76} +(3.10717 - 11.5299i) q^{77} +(-2.12666 + 0.164684i) q^{78} +(1.06303 + 0.613742i) q^{79} +(-0.747273 - 15.7752i) q^{80} +(1.88313 + 3.26167i) q^{81} +(4.93681 - 10.3169i) q^{82} +(-2.29910 - 2.29910i) q^{83} +(-3.82807 + 1.68629i) q^{84} +(-3.18883 + 3.18883i) q^{85} +(7.20885 - 2.54260i) q^{86} +(-5.13369 + 2.96394i) q^{87} +(-0.382263 + 12.7600i) q^{88} +(4.36654 - 7.56307i) q^{89} +(8.62539 - 10.0734i) q^{90} +(-3.57459 + 3.56434i) q^{91} +(4.04685 - 0.630538i) q^{92} +(-3.16383 + 0.847747i) q^{93} +(1.30216 + 1.89977i) q^{94} +(10.6773 - 6.16455i) q^{95} +(3.56478 - 2.69995i) q^{96} +8.42967i q^{97} +(-4.29867 + 8.91748i) 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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.610438	+	1.27568i	−0.431645	+	0.902044i
$2$	−0.610438	+	1.27568i	−0.431645	+	0.902044i
$3$	−0.204601	+	0.763582i	−0.118127	+	0.440854i	−0.999502	−	0.0315627i	$-0.989952\pi$
$3$	−0.204601	+	0.763582i	−0.118127	+	0.440854i	0.881375	+	0.472417i	$0.156618\pi$
$4$	−1.25473	−	1.55745i	−0.627366	−	0.778725i
$5$	−3.81370	+	1.02188i	−1.70554	+	0.456998i	−0.974324	−	0.225150i	$-0.927713\pi$
$5$	−3.81370	+	1.02188i	−1.70554	+	0.456998i	−0.731214	+	0.682148i	$0.761046\pi$
$6$	−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
$10$	1.02443	−	5.48886i	0.323955	−	1.73573i
$11$	−1.16815	+	4.35958i	−0.352209	+	1.31446i	0.531751	+	0.846901i	$0.321534\pi$
$11$	−1.16815	+	4.35958i	−0.352209	+	1.31446i	−0.883960	+	0.467562i	$0.845132\pi$
$12$	1.44596	−	0.639434i	0.417413	−	0.184589i
$13$	1.34913	−	1.34913i	0.374182	−	0.374182i	−0.494816	−	0.868998i	$-0.664764\pi$
$13$	1.34913	−	1.34913i	0.374182	−	0.374182i	0.868998	+	0.494816i	$0.164764\pi$
$14$	1.61991	−	3.37282i	0.432939	−	0.901423i
$15$		−	3.12115i		−	0.805877i
$16$	−0.851298	+	3.90836i	−0.212825	+	0.977090i
$17$	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	$0.289101\pi$
$18$	−2.77052	+	1.89901i	−0.653018	+	0.447600i
$19$	−3.01629	+	0.808212i	−0.691984	+	0.185416i	−0.587637	−	0.809125i	$-0.699942\pi$
$19$	−3.01629	+	0.808212i	−0.691984	+	0.185416i	−0.104346	+	0.994541i	$0.533275\pi$
$20$	6.37669	+	4.65746i	1.42587	+	1.04144i
$21$	0.544222	−	2.01947i	0.118759	−	0.440684i
$22$	−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	$0.235154\pi$
$24$	−0.0669534	+	2.23492i	−0.0136668	+	0.456201i
$25$	9.16994	−	5.29427i	1.83399	−	1.05885i
$26$	0.897503	+	2.54463i	0.176015	+	0.499042i
$27$	−3.00457	+	3.00457i	−0.578229	+	0.578229i
$28$	3.31379	+	4.12538i	0.626248	+	0.779624i
$29$	5.30239	+	5.30239i	0.984630	+	0.984630i	0.999884	−	0.0152539i	$-0.00485565\pi$
$29$	5.30239	+	5.30239i	0.984630	+	0.984630i	−0.0152539	+	0.999884i	$0.504856\pi$
$30$	3.98159	+	1.90527i	0.726936	+	0.347853i
$31$	2.07171	+	3.58830i	0.372089	+	0.644478i	0.989887	−	0.141860i	$-0.0453081\pi$
$31$	2.07171	+	3.58830i	0.372089	+	0.644478i	−0.617797	+	0.786337i	$0.711975\pi$
$32$	−4.46616	−	3.47180i	−0.789514	−	0.613733i
$33$	−3.08989	−	1.78395i	−0.537881	−	0.310546i
$34$	0.124713	+	1.61050i	0.0213882	+	0.276198i
$35$	10.0940	−	2.68915i	1.70619	−	0.454550i
$36$	−0.731298	−	4.69353i	−0.121883	−	0.782255i
$37$	−0.803695	−	2.99943i	−0.132127	−	0.493103i	0.867867	−	0.496797i	$-0.165491\pi$
$37$	−0.803695	−	2.99943i	−0.132127	−	0.493103i	−0.999993	+	0.00369416i	$0.998824\pi$
$38$	0.810234	−	4.34119i	0.131437	−	0.704234i
$39$	0.754139	+	1.30621i	0.120759	+	0.209161i
$40$	−9.83402	+	5.29154i	−1.55489	+	0.836666i
$41$	−8.08732			−1.26303			−0.631514	−	0.775365i	$-0.717566\pi$
$41$	−8.08732			−1.26303			−0.631514	+	0.775365i	$0.717566\pi$
$42$	2.24399	+	1.92701i	0.346255	+	0.297345i
$43$	−3.82205	−	3.82205i	−0.582858	−	0.582858i	0.352830	−	0.935688i	$-0.385220\pi$
$43$	−3.82205	−	3.82205i	−0.582858	−	0.582858i	−0.935688	+	0.352830i	$0.885220\pi$
$44$	8.25554	−	3.65078i	1.24457	−	0.550375i
$45$	−9.05785	−	2.42704i	−1.35026	−	0.361802i
$46$	−1.63736	−	2.38879i	−0.241415	−	0.352208i
$47$	0.814305	−	1.41042i	0.118779	−	0.205731i	−0.800505	−	0.599326i	$-0.795435\pi$
$47$	0.814305	−	1.41042i	0.118779	−	0.205731i	0.919284	+	0.393595i	$0.128769\pi$
$48$	−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
$51$	0.233696	+	0.872167i	0.0327240	+	0.122128i
$52$	−3.79400	−	0.408407i	−0.526134	−	0.0566358i
$53$	−2.92499	−	0.783749i	−0.401779	−	0.107656i	0.0522704	−	0.998633i	$-0.483354\pi$
$53$	−2.92499	−	0.783749i	−0.401779	−	0.107656i	−0.454049	+	0.890977i	$0.650021\pi$
$54$	−1.99877	−	5.66697i	−0.271998	−	0.771177i
$55$		−	17.8198i		−	2.40283i
$56$	−7.28554	+	1.70906i	−0.973572	+	0.228382i
$57$		−	2.46854i		−	0.326966i
$58$	−10.0010	+	3.52739i	−1.31319	+	0.463169i
$59$	6.97383	+	1.86863i	0.907915	+	0.243275i	0.682412	−	0.730967i	$-0.260931\pi$
$59$	6.97383	+	1.86863i	0.907915	+	0.243275i	0.225503	+	0.974243i	$0.427597\pi$
$60$	−4.86103	+	3.91620i	−0.627556	+	0.505580i
$61$	1.68972	+	6.30611i	0.216346	+	0.807414i	0.985688	+	0.168578i	$0.0539174\pi$
$61$	1.68972	+	6.30611i	0.216346	+	0.807414i	−0.769342	+	0.638837i	$0.779416\pi$
$62$	−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
$66$	4.16194	−	2.85273i	0.512300	−	0.351147i
$67$	0.616236	+	0.165120i	0.0752852	+	0.0201726i	0.296265	−	0.955106i	$-0.404259\pi$
$67$	0.616236	+	0.165120i	0.0752852	+	0.0201726i	−0.220980	+	0.975278i	$0.570926\pi$
$68$	−2.13062	−	0.824015i	−0.258375	−	0.0999265i
$69$	−1.14470	−	1.14470i	−0.137806	−	0.137806i
$70$	−2.73123	+	14.5183i	−0.326445	+	1.73526i
$71$	−2.40482			−0.285400			−0.142700	−	0.989766i	$-0.545578\pi$
$71$	−2.40482			−0.285400			−0.142700	+	0.989766i	$0.545578\pi$
$72$	6.43387	+	1.93221i	0.758239	+	0.227713i
$73$	1.47966	+	2.56284i	0.173181	+	0.299958i	0.939530	−	0.342466i	$-0.111262\pi$
$73$	1.47966	+	2.56284i	0.173181	+	0.299958i	−0.766349	+	0.642424i	$0.777929\pi$
$74$	4.31693	+	0.805706i	0.501832	+	0.0936614i
$75$	2.16643	+	8.08521i	0.250157	+	0.933600i
$76$	5.04338	+	3.68363i	0.578515	+	0.422541i
$77$	3.10717	−	11.5299i	0.354095	−	1.31396i
$78$	−2.12666	+	0.164684i	−0.240797	+	0.0186468i
$79$	1.06303	+	0.613742i	0.119601	+	0.0690514i	0.558607	−	0.829433i	$-0.311336\pi$
$79$	1.06303	+	0.613742i	0.119601	+	0.0690514i	−0.439006	+	0.898484i	$0.644669\pi$
$80$	−0.747273	−	15.7752i	−0.0835476	−	1.76373i
$81$	1.88313	+	3.26167i	0.209236	+	0.362408i
$82$	4.93681	−	10.3169i	0.545179	−	1.13931i
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	0.569578	−	0.821937i	$-0.307107\pi$
$83$	−2.29910	−	2.29910i	−0.252359	−	0.252359i	−0.821937	+	0.569578i	$0.807107\pi$
$84$	−3.82807	+	1.68629i	−0.417677	+	0.183990i
$85$	−3.18883	+	3.18883i	−0.345877	+	0.345877i
$86$	7.20885	−	2.54260i	0.777351	−	0.274176i
$87$	−5.13369	+	2.96394i	−0.550389	+	0.317767i
$88$	−0.382263	+	12.7600i	−0.0407493	+	1.36022i
$89$	4.36654	−	7.56307i	0.462852	−	0.801684i	−0.536249	−	0.844060i	$-0.680159\pi$
$89$	4.36654	−	7.56307i	0.462852	−	0.801684i	0.999102	+	0.0423758i	$0.0134927\pi$
$90$	8.62539	−	10.0734i	0.909196	−	1.06183i
$91$	−3.57459	+	3.56434i	−0.374719	+	0.373645i
$92$	4.04685	−	0.630538i	0.421913	−	0.0657381i
$93$	−3.16383	+	0.847747i	−0.328074	+	0.0879073i
$94$	1.30216	+	1.89977i	0.134308	+	0.195946i
$95$	10.6773	−	6.16455i	1.09547	−	0.632470i
$96$	3.56478	−	2.69995i	0.363829	−	0.275562i
$97$			8.42967i			0.855903i	0.903802	+	0.427952i	$0.140765\pi$
$97$			8.42967i			0.855903i	−0.903802	+	0.427952i	$0.859235\pi$
$98$	−4.29867	+	8.91748i	−0.434232	+	0.900801i
$99$	−7.57992	+	7.57992i	−0.761810	+	0.761810i
$100$	−19.7514	−	7.63884i	−1.97514	−	0.763884i
$101$	−3.81352	+	14.2323i	−0.379460	+	1.41616i	0.467258	+	0.884121i	$0.345242\pi$
$101$	−3.81352	+	14.2323i	−0.379460	+	1.41616i	−0.846718	+	0.532042i	$0.821425\pi$
$102$	−1.25526	−	0.234281i	−0.124290	−	0.0231973i
$103$	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
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.202172	−	0.979350i	$-0.435200\pi$
$107$	8.96762	−	2.40287i	0.866932	−	0.232294i	0.664761	+	0.747056i	$0.268533\pi$
$108$	8.44938	+	0.909537i	0.813042	+	0.0875202i
$109$	0.227686	−	0.849736i	0.0218084	−	0.0813900i	−0.954164	−	0.299284i	$-0.903252\pi$
$109$	0.227686	−	0.849736i	0.0218084	−	0.0813900i	0.975972	+	0.217894i	$0.0699188\pi$
$110$	22.7325	+	10.8779i	2.16745	+	1.03717i
$111$	2.45475			0.232994
$112$	2.26716	−	10.3373i	0.214226	−	0.976784i
$113$	1.91230			0.179894			0.0899469	−	0.995947i	$-0.471330\pi$
$113$	1.91230			0.179894			0.0899469	+	0.995947i	$0.471330\pi$
$114$	3.14908	+	1.50689i	0.294938	+	0.141133i
$115$	2.09264	−	7.80983i	0.195140	−	0.728271i
$116$	1.60513	−	14.9113i	0.149033	−	1.38448i
$117$	4.37715	−	1.17285i	0.404668	−	0.108430i
$118$	−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
$122$	−9.07606	−	1.69395i	−0.821708	−	0.153363i
$123$	1.65468	−	6.17533i	0.149197	−	0.556811i
$124$	2.98916	−	7.72893i	0.268435	−	0.694079i
$125$	−15.6022	+	15.6022i	−1.39550	+	1.39550i
$126$	7.33732	−	5.01378i	0.653660	−	0.446663i
$127$			11.9607i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$127$			11.9607i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$128$	0.196687	+	11.3120i	0.0173848	+	0.999849i
$129$	3.70045	−	2.13645i	0.325806	−	0.188104i
$130$	−6.02310	−	8.78730i	−0.528261	−	0.770697i
$131$	−5.36296	+	1.43700i	−0.468564	+	0.125551i	−0.485372	−	0.874307i	$-0.661316\pi$
$131$	−5.36296	+	1.43700i	−0.468564	+	0.125551i	0.0168089	+	0.999859i	$0.494649\pi$
$132$	1.09857	+	7.05073i	0.0956185	+	0.613687i
$133$	7.98340	−	2.12687i	0.692249	−	0.184423i
$134$	−0.586814	+	0.685325i	−0.0506930	+	0.0592031i
$135$	8.38821	−	14.5288i	0.721943	−	1.25044i
$136$	2.35179	−	2.21498i	0.201664	−	0.189933i
$137$	−12.4195	+	7.17038i	−1.06107	+	0.612607i	−0.925727	−	0.378192i	$-0.876546\pi$
$137$	−12.4195	+	7.17038i	−1.06107	+	0.612607i	−0.135339	+	0.990799i	$0.543212\pi$
$138$	2.15904	−	0.761506i	0.183790	−	0.0648237i
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.278731	−	0.960369i	$-0.410086\pi$
$139$	14.6088	−	14.6088i	1.23910	−	1.23910i	0.960369	−	0.278731i	$-0.0899137\pi$
$140$	−16.8534	−	12.3467i	−1.42438	−	1.04349i
$141$	0.910361	+	0.910361i	0.0766663	+	0.0766663i
$142$	1.46799	−	3.06779i	0.123191	−	0.257443i
$143$	4.30567	+	7.45764i	0.360058	+	0.623639i
$144$	−6.39236	+	7.02808i	−0.532696	+	0.585674i
$145$	−25.6401	−	14.8033i	−2.12930	−	1.22935i
$146$	−4.17262	+	0.323118i	−0.345328	+	0.0267414i
$147$	−1.44754	+	5.34094i	−0.119391	+	0.440513i
$148$	−3.66304	+	5.01519i	−0.301100	+	0.412246i
$149$	−3.05093	−	11.3862i	−0.249942	−	0.932797i	−0.970835	−	0.239750i	$-0.922934\pi$
$149$	−3.05093	−	11.3862i	−0.249942	−	0.932797i	0.720892	−	0.693047i	$-0.243732\pi$
$150$	−11.6366	−	2.17185i	−0.950127	−	0.177331i
$151$	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	$0.644996\pi$
$152$	−7.77781	+	4.18513i	−0.630863	+	0.339458i
$153$	2.71283			0.219319
$154$	12.8118	+	11.0021i	1.03240	+	0.886572i
$155$	−11.5677	−	11.5677i	−0.929138	−	0.929138i
$156$	1.08811	−	2.81347i	0.0871185	−	0.225258i
$157$	2.01291	+	0.539359i	0.160648	+	0.0430455i	0.338247	−	0.941058i	$-0.390166\pi$
$157$	2.01291	+	0.539359i	0.160648	+	0.0430455i	−0.177599	+	0.984103i	$0.556833\pi$
$158$	−1.43186	+	0.981441i	−0.113912	+	0.0780792i
$159$	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
$163$	0.466826	+	1.74222i	0.0365647	+	0.136461i	0.981795	−	0.189942i	$-0.0608300\pi$
$163$	0.466826	+	1.74222i	0.0365647	+	0.136461i	−0.945231	+	0.326403i	$0.894163\pi$
$164$	10.1474	+	12.5956i	0.792380	+	0.983551i
$165$	13.6069	+	3.64596i	1.05930	+	0.283837i
$166$	4.33638	−	1.52946i	0.336568	−	0.118709i
$167$			21.6002i			1.67147i	0.549132	+	0.835735i	$0.314958\pi$
$167$			21.6002i			1.67147i	−0.549132	+	0.835735i	$0.685042\pi$
$168$	0.185627	−	5.91278i	0.0143214	−	0.456181i
$169$			9.35968i			0.719976i
$170$	−2.12135	−	6.01452i	−0.162700	−	0.461293i
$171$	−7.16393	−	1.91957i	−0.547839	−	0.146793i
$172$	−1.15701	+	10.7483i	−0.0882208	+	0.819551i
$173$	−2.27429	−	8.48775i	−0.172911	−	0.645312i	−0.996898	−	0.0787035i	$-0.974922\pi$
$173$	−2.27429	−	8.48775i	−0.172911	−	0.645312i	0.823987	−	0.566608i	$-0.191745\pi$
$174$	−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
$178$	6.98257	+	10.1871i	0.523366	+	0.763556i
$179$	−1.68719	−	0.452081i	−0.126106	−	0.0337901i	0.195214	−	0.980761i	$-0.437460\pi$
$179$	−1.68719	−	0.452081i	−0.126106	−	0.0337901i	−0.321320	+	0.946971i	$0.604127\pi$
$180$	7.58517	+	17.1524i	0.565365	+	1.27847i
$181$	5.29547	+	5.29547i	0.393609	+	0.393609i	0.875972	−	0.482362i	$-0.160221\pi$
$181$	5.29547	+	5.29547i	0.393609	+	0.393609i	−0.482362	+	0.875972i	$0.660221\pi$
$182$	−2.36491	−	6.73585i	−0.175299	−	0.499294i
$183$	−5.16095			−0.381508
$184$	−1.66598	+	5.54739i	−0.122818	+	0.408959i
$185$	6.13010	+	10.6176i	0.450694	+	0.780625i
$186$	0.849868	−	4.55354i	0.0623154	−	0.333882i
$187$	1.33426	+	4.97953i	0.0975709	+	0.364140i
$188$	−3.21839	+	0.501456i	−0.234725	+	0.0365725i
$189$	7.96073	−	7.93792i	0.579058	−	0.577399i
$190$	1.34617	+	17.3839i	0.0976617	+	1.26116i
$191$	−23.5567	−	13.6004i	−1.70450	−	0.984093i	−0.941076	−	0.338195i	$-0.890184\pi$
$191$	−23.5567	−	13.6004i	−1.70450	−	0.984093i	−0.763423	−	0.645899i	$-0.776483\pi$
$192$	1.26820	+	6.19568i	0.0915243	+	0.447135i
$193$	−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	$0.899842\pi$
$194$	−10.7536	−	5.14579i	−0.772062	−	0.369446i
$195$	−4.21084	−	4.21084i	−0.301545	−	0.301545i
$196$	−8.75180	−	10.9273i	−0.625128	−	0.780522i
$197$	12.7740	−	12.7740i	0.910107	−	0.910107i	−0.0861731	−	0.996280i	$-0.527464\pi$
$197$	12.7740	−	12.7740i	0.910107	−	0.910107i	0.996280	+	0.0861731i	$0.0274638\pi$
$198$	−5.04250	−	14.2966i	−0.358355	−	1.01602i
$199$	−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	$0.395870\pi$
$200$	21.8017	−	20.5334i	1.54161	−	1.45193i
$201$	−0.252165	+	0.436763i	−0.0177863	+	0.0308069i
$202$	−15.8279	−	13.5528i	−1.11365	−	0.953569i
$203$	−14.0087	−	14.0489i	−0.983216	−	0.986042i
$204$	1.06513	−	1.45831i	0.0745740	−	0.102102i
$205$	30.8426	−	8.26425i	2.15414	−	0.577201i
$206$	−9.25839	+	6.34601i	−0.645063	+	0.442147i
$207$	−4.21216	+	2.43189i	−0.292765	+	0.169028i
$208$	4.12438	+	6.42141i	0.285975	+	0.445245i
$209$		−	14.0939i		−	0.974893i
$210$	−10.5271	−	5.05597i	−0.726437	−	0.348895i
$211$	19.3846	−	19.3846i	1.33449	−	1.33449i	0.433192	−	0.901302i	$-0.357387\pi$
$211$	19.3846	−	19.3846i	1.33449	−	1.33449i	0.901302	−	0.433192i	$-0.142613\pi$
$212$	2.44943	+	5.53892i	0.168227	+	0.380415i
$213$	0.492029	−	1.83628i	0.0337133	−	0.125820i
$214$	−2.40888	+	12.9066i	−0.164668	+	0.882279i
$215$	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
$219$	−2.25968	+	0.605480i	−0.152695	+	0.0409145i
$220$	−27.7535	+	22.3591i	−1.87114	+	1.50745i
$221$	0.564040	−	2.10503i	0.0379414	−	0.141599i
$222$	−1.49847	+	3.13148i	−0.100571	+	0.210171i
$223$	22.1379			1.48247			0.741233	−	0.671248i	$-0.234241\pi$
$223$	22.1379			1.48247			0.741233	+	0.671248i	$0.234241\pi$
$224$	11.8032	+	9.20246i	0.788632	+	0.614865i
$225$	25.1486			1.67658
$226$	−1.16734	+	2.43948i	−0.0776502	+	0.162272i
$227$	2.22844	−	8.31664i	0.147907	−	0.551995i	−0.851702	−	0.524026i	$-0.824429\pi$
$227$	2.22844	−	8.31664i	0.147907	−	0.551995i	0.999609	−	0.0279688i	$-0.00890392\pi$
$228$	−3.84463	+	3.09736i	−0.254617	+	0.205128i
$229$	24.4498	−	6.55130i	1.61569	−	0.432922i	0.665957	−	0.745990i	$-0.268023\pi$
$229$	24.4498	−	6.55130i	1.61569	−	0.432922i	0.949731	+	0.313067i	$0.101357\pi$
$230$	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	−0.0115857	−	0.999933i	$-0.503688\pi$
$233$	−13.4837	−	7.78481i	−0.883346	−	0.510000i	−0.871760	+	0.489933i	$0.837021\pi$
$234$	−1.17579	+	6.29981i	−0.0768638	+	0.411832i
$235$	−1.66424	+	6.21103i	−0.108563	+	0.405163i
$236$	−5.83998	−	13.2060i	−0.380151	−	0.859639i
$237$	−0.686140	+	0.686140i	−0.0445696	+	0.0445696i
$238$	−0.323846	−	4.26145i	−0.0209918	−	0.276229i
$239$		−	11.6230i		−	0.751832i	−0.926654	−	0.375916i	$-0.877328\pi$
$239$		−	11.6230i		−	0.751832i	0.926654	−	0.375916i	$-0.122672\pi$
$240$	12.1986	+	2.65703i	0.787415	+	0.171510i
$241$	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	$0.304453\pi$
$242$	10.9307	−	7.49224i	0.702650	−	0.481619i
$243$	−15.1888	+	4.06982i	−0.974361	+	0.261079i
$244$	7.70131	−	10.5441i	0.493026	−	0.675018i
$245$	−26.7163	+	7.07650i	−1.70684	+	0.452101i
$246$	6.86769	+	5.88050i	0.437868	+	0.374927i
$247$	−2.97899	+	5.15975i	−0.189548	+	0.328307i
$248$	8.03496	+	8.53125i	0.510221	+	0.541735i
$249$	2.22595	−	1.28515i	0.141064	−	0.0814432i
$250$	−10.3793	−	29.4276i	−0.656443	−	1.86117i
$251$	−1.99507	+	1.99507i	−0.125928	+	0.125928i	−0.767262	−	0.641334i	$-0.778381\pi$
$251$	−1.99507	+	1.99507i	−0.125928	+	0.125928i	0.641334	+	0.767262i	$0.278381\pi$
$252$	1.91701	+	12.4207i	0.120760	+	0.782429i
$253$	−6.53554	−	6.53554i	−0.410886	−	0.410886i
$254$	−15.2581	−	7.30127i	−0.957377	−	0.458123i
$255$	−1.78250	−	3.08737i	−0.111624	−	0.193339i
$256$	−14.5506	−	6.65436i	−0.909411	−	0.415898i
$257$	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
$259$	2.11499	+	7.93879i	0.131419	+	0.493292i
$260$	14.8865	−	2.31947i	0.923224	−	0.143847i
$261$	4.60958	+	17.2032i	0.285326	+	1.06485i
$262$	1.44060	−	7.71863i	0.0890003	−	0.476858i
$263$	−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	$0.984030\pi$
$264$	−9.66510	−	2.90260i	−0.594846	−	0.178643i
$265$	11.9559			0.734447
$266$	−2.16016	+	11.4826i	−0.132448	+	0.704044i
$267$	4.88162	+	4.88162i	0.298750	+	0.298750i
$268$	−0.516044	−	1.16694i	−0.0315224	−	0.0712820i
$269$	−23.1455	−	6.20182i	−1.41121	−	0.378132i	−0.528851	−	0.848715i	$-0.677377\pi$
$269$	−23.1455	−	6.20182i	−1.41121	−	0.378132i	−0.882356	+	0.470583i	$0.844044\pi$
$270$	13.4137	+	19.5696i	0.816330	+	1.19097i
$271$	7.37718	−	12.7776i	0.448131	−	0.776186i	−0.550133	−	0.835077i	$-0.685423\pi$
$271$	7.37718	−	12.7776i	0.448131	−	0.776186i	0.998264	+	0.0588906i	$0.0187563\pi$
$272$	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
$275$	12.3690	+	46.1616i	0.745877	+	2.78365i
$276$	−0.346522	+	3.21911i	−0.0208582	+	0.193767i
$277$	−17.7680	−	4.76091i	−1.06757	−	0.286055i	−0.318077	−	0.948065i	$-0.603037\pi$
$277$	−17.7680	−	4.76091i	−1.06757	−	0.286055i	−0.749496	+	0.662009i	$0.769704\pi$
$278$	9.71841	+	27.5539i	0.582871	+	1.65257i
$279$			9.84094i			0.589162i
$280$	26.0384	−	13.9628i	1.55609	−	0.834434i
$281$			31.9694i			1.90713i	0.301185	+	0.953566i	$0.402618\pi$
$281$			31.9694i			1.90713i	−0.301185	+	0.953566i	$0.597382\pi$
$282$	−1.71705	+	0.605613i	−0.102249	+	0.0360637i
$283$	−3.17648	−	0.851136i	−0.188822	−	0.0505948i	0.163169	−	0.986598i	$-0.447829\pi$
$283$	−3.17648	−	0.851136i	−0.188822	−	0.0505948i	−0.351991	+	0.936003i	$0.614495\pi$
$284$	3.01740	+	3.74539i	0.179050	+	0.222248i
$285$	2.52255	+	9.41428i	0.149423	+	0.557654i
$286$	−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
$290$	34.5361	−	23.6722i	2.02803	−	1.39008i
$291$	−6.43674	−	1.72472i	−0.377329	−	0.101105i
$292$	2.13493	−	5.52018i	0.124937	−	0.323044i
$293$	6.98254	+	6.98254i	0.407925	+	0.407925i	0.881014	−	0.473090i	$-0.156861\pi$
$293$	6.98254	+	6.98254i	0.407925	+	0.407925i	−0.473090	+	0.881014i	$0.656861\pi$
$294$	−5.92971	−	5.10691i	−0.345828	−	0.297841i
$295$	−28.5056			−1.65966
$296$	−4.16174	−	7.73434i	−0.241896	−	0.449549i
$297$	−9.58888	−	16.6084i	−0.556403	−	0.963719i
$298$	16.3876	+	3.05857i	0.949310	+	0.177178i
$299$	1.01126	+	3.77406i	0.0584824	+	0.218259i
$300$	9.87403	−	13.5189i	0.570077	−	0.780513i
$301$	10.0977	+	10.1267i	0.582021	+	0.583694i
$302$	−19.3276	+	1.49669i	−1.11218	+	0.0861248i
$303$	−10.0872	−	5.82388i	−0.579497	−	0.334573i
$304$	−0.591024	−	12.4768i	−0.0338976	−	0.715592i
$305$	−12.8881	−	22.3229i	−0.737973	−	1.27821i
$306$	−1.65601	+	3.46071i	−0.0946680	+	0.197836i
$307$	−23.3885	−	23.3885i	−1.33485	−	1.33485i	−0.900967	−	0.433888i	$-0.857141\pi$
$307$	−23.3885	−	23.3885i	−1.33485	−	1.33485i	−0.433888	−	0.900967i	$-0.642859\pi$
$308$	−21.8559	+	9.62769i	−1.24536	+	0.548589i
$309$	−4.43659	+	4.43659i	−0.252389	+	0.252389i
$310$	21.8180	−	7.69533i	1.23918	−	0.437065i
$311$	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	$0.0801752\pi$
$312$	2.92487	+	3.10553i	0.165588	+	0.175816i
$313$	4.22602	−	7.31969i	0.238869	−	0.413733i	−0.721521	−	0.692393i	$-0.756557\pi$
$313$	4.22602	−	7.31969i	0.238869	−	0.413733i	0.960390	+	0.278659i	$0.0898900\pi$
$314$	−1.91681	+	2.23859i	−0.108172	+	0.126331i
$315$	23.9556	+	6.45573i	1.34974	+	0.363739i
$316$	−0.377948	−	2.42570i	−0.0212612	−	0.136456i
$317$	18.4857	−	4.95323i	1.03826	−	0.278201i	0.300868	−	0.953666i	$-0.402724\pi$
$317$	18.4857	−	4.95323i	1.03826	−	0.278201i	0.737393	+	0.675464i	$0.236057\pi$
$318$	1.91399	+	2.79239i	0.107331	+	0.156589i
$319$	−29.3102	+	16.9222i	−1.64106	+	0.947464i
$320$	−23.6315	+	20.9575i	−1.32104	+	1.17156i
$321$			7.33914i			0.409631i
$322$	4.32297	+	6.32636i	0.240909	+	0.352554i
$323$	−2.52207	+	2.52207i	−0.140332	+	0.140332i
$324$	2.71707	−	7.02540i	0.150948	−	0.390300i
$325$	5.22880	−	19.5141i	0.290041	−	1.08245i
$326$	−2.50749	−	0.467994i	−0.138877	−	0.0259198i
$327$	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
$331$	−13.9616	+	3.74100i	−0.767399	+	0.205624i	−0.621222	−	0.783635i	$-0.713364\pi$
$331$	−13.9616	+	3.74100i	−0.767399	+	0.205624i	−0.146177	+	0.989258i	$0.546697\pi$
$332$	−0.695979	+	6.46549i	−0.0381968	+	0.354840i
$333$	1.90884	−	7.12389i	0.104604	−	0.390387i
$334$	−27.5549	−	13.1856i	−1.50774	−	0.721482i
$335$	−2.51887			−0.137621
$336$	7.42952	+	3.84619i	0.405313	+	0.209827i
$337$	−13.7159			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$337$	−13.7159			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$338$	−11.9400	−	5.71350i	−0.649449	−	0.310774i
$339$	−0.391258	+	1.46020i	−0.0212502	+	0.0793069i
$340$	8.96757	+	0.965317i	0.486335	+	0.0523517i
$341$	−18.0635	+	4.84011i	−0.978196	+	0.262107i
$342$	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
$346$	12.2160	+	2.27998i	0.656736	+	0.122572i
$347$	−2.43191	+	9.07603i	−0.130552	+	0.487227i	−0.999977	−	0.00683892i	$-0.997823\pi$
$347$	−2.43191	+	9.07603i	−0.130552	+	0.487227i	0.869425	+	0.494066i	$0.164490\pi$
$348$	11.0576	+	4.27651i	0.592748	+	0.229245i
$349$	−8.35069	+	8.35069i	−0.447002	+	0.447002i	−0.894357	−	0.447355i	$-0.852366\pi$
$349$	−8.35069	+	8.35069i	−0.447002	+	0.447002i	0.447355	+	0.894357i	$0.352366\pi$
$350$	−3.00214	−	39.5048i	−0.160471	−	2.11162i
$351$			8.10712i			0.432726i
$352$	20.3527	−	15.4150i	1.08480	−	0.821624i
$353$	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	$0.159089\pi$
$354$	−4.56339	−	6.65767i	−0.242541	−	0.353851i
$355$	9.17127	−	2.45743i	0.486760	−	0.130427i
$356$	−17.2579	+	2.68895i	−0.914669	+	0.142514i
$357$	−0.614991	−	2.30842i	−0.0325488	−	0.122175i
$358$	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	$0.0128469\pi$
$360$	−26.5113	−	0.794222i	−1.39727	−	0.0418592i
$361$	−8.00970	+	4.62440i	−0.421563	+	0.243390i
$362$	−9.98789	+	3.52278i	−0.524952	+	0.185153i
$363$	5.23794	−	5.23794i	0.274920	−	0.274920i
$364$	10.0364	+	1.09495i	0.526052	+	0.0573907i
$365$	−8.26189	−	8.26189i	−0.432447	−	0.432447i
$366$	3.15044	−	6.58373i	0.164676	−	0.344137i
$367$	16.4811	+	28.5462i	0.860309	+	1.49010i	0.871631	+	0.490163i	$0.163063\pi$
$367$	16.4811	+	28.5462i	0.860309	+	1.49010i	−0.0113220	+	0.999936i	$0.503604\pi$
$368$	−6.05974	−	5.51160i	−0.315886	−	0.287312i
$369$	−16.6347	−	9.60402i	−0.865966	−	0.499966i
$370$	−17.2868	+	1.33865i	−0.898697	+	0.0695931i
$371$	7.73582	+	2.08471i	0.401624	+	0.108233i
$372$	5.29009	+	3.86382i	0.274278	+	0.200330i
$373$	3.47655	+	12.9747i	0.180009	+	0.671802i	0.995644	+	0.0932356i	$0.0297210\pi$
$373$	3.47655	+	12.9747i	0.180009	+	0.671802i	−0.815635	+	0.578566i	$0.803612\pi$
$374$	−7.16679	−	1.33760i	−0.370586	−	0.0691657i
$375$	−8.72133	−	15.1058i	−0.450368	−	0.780059i
$376$	1.32493	−	4.41175i	0.0683279	−	0.227519i
$377$	14.3073			0.736861
$378$	5.26673	+	15.0010i	0.270892	+	0.771567i
$379$	0.617225	+	0.617225i	0.0317047	+	0.0317047i	0.722781	−	0.691077i	$-0.242863\pi$
$379$	0.617225	+	0.617225i	0.0317047	+	0.0317047i	−0.691077	+	0.722781i	$0.742863\pi$
$380$	−22.9981	−	8.89453i	−1.17978	−	0.456280i
$381$	−9.13298	−	2.44718i	−0.467897	−	0.125373i
$382$	31.7297	−	21.7486i	1.62343	−	1.11275i
$383$	0.214398	−	0.371348i	0.0109552	−	0.0189750i	−0.860496	−	0.509457i	$-0.829846\pi$
$383$	0.214398	−	0.371348i	0.0109552	−	0.0189750i	0.871451	+	0.490483i	$0.163179\pi$
$384$	−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
$387$	−3.32267	−	12.4004i	−0.168901	−	0.630346i
$388$	13.1288	−	10.5770i	0.666513	−	0.536964i
$389$	10.1095	+	2.70883i	0.512571	+	0.137343i	0.505828	−	0.862634i	$-0.331187\pi$
$389$	10.1095	+	2.70883i	0.512571	+	0.137343i	0.00674269	+	0.999977i	$0.497854\pi$
$390$	7.94216	−	2.80124i	0.402167	−	0.141846i
$391$			2.33905i			0.118291i
$392$	19.2822	−	4.49407i	0.973898	−	0.226985i
$393$		−	4.38907i		−	0.221399i
$394$	8.49781	+	24.0932i	0.428113	+	1.21380i
$395$	−4.68126	−	1.25434i	−0.235540	−	0.0631126i
$396$	21.3161	+	2.29458i	1.07117	+	0.115307i
$397$	7.22485	+	26.9635i	0.362605	+	1.35326i	0.870639	+	0.491922i	$0.163706\pi$
$397$	7.22485	+	26.9635i	0.362605	+	1.35326i	−0.508034	+	0.861337i	$0.669628\pi$
$398$	−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	$0.937826\pi$
$402$	−0.403239	−	0.588299i	−0.0201117	−	0.0293417i
$403$	7.63610	+	2.04609i	0.380381	+	0.101923i
$404$	26.9510	−	11.9183i	1.34086	−	0.592958i
$405$	−10.5147	−	10.5147i	−0.522480	−	0.522480i
$406$	26.4734	−	9.29462i	1.31385	−	0.461284i
$407$	14.0151			0.694702
$408$	1.21014	+	2.24897i	0.0599108	+	0.111341i
$409$	−8.91434	−	15.4401i	−0.440786	−	0.763463i	0.556962	−	0.830538i	$-0.311967\pi$
$409$	−8.91434	−	15.4401i	−0.440786	−	0.763463i	−0.997748	+	0.0670744i	$0.978634\pi$
$410$	−8.28494	+	44.3902i	−0.409164	+	2.19228i
$411$	−2.93414	−	10.9503i	−0.144730	−	0.540141i
$412$	−2.44382	−	15.6846i	−0.120398	−	0.772725i
$413$	−18.4439	−	4.97041i	−0.907565	−	0.244578i
$414$	−0.531059	−	6.85789i	−0.0261001	−	0.337047i
$415$	11.1175	+	6.41868i	0.545735	+	0.315081i
$416$	−10.7094	+	1.34153i	−0.525070	+	0.0657740i
$417$	8.16602	+	14.1440i	0.399892	+	0.692633i
$418$	17.9793	+	8.60342i	0.879396	+	0.420807i
$419$	19.6171	+	19.6171i	0.958358	+	0.958358i	0.999167	−	0.0408093i	$-0.0129936\pi$
$419$	19.6171	+	19.6171i	0.958358	+	0.958358i	−0.0408093	+	0.999167i	$0.512994\pi$
$420$	12.8759	−	10.3428i	0.628281	−	0.504679i
$421$	−5.25405	+	5.25405i	−0.256067	+	0.256067i	−0.823452	−	0.567385i	$-0.807955\pi$
$421$	−5.25405	+	5.25405i	−0.256067	+	0.256067i	0.567385	+	0.823452i	$0.307955\pi$
$422$	12.8955	+	36.5618i	0.627745	+	1.77980i
$423$	3.34986	−	1.93404i	0.162876	−	0.0940363i
$424$	−8.56113	−	0.256473i	−0.415765	−	0.0124554i
$425$	6.04714	−	10.4740i	0.293329	−	0.508061i
$426$	2.04215	+	1.74861i	0.0989427	+	0.0847202i
$427$	−4.44663	−	16.6908i	−0.215187	−	0.807724i
$428$	−14.9943	−	10.9517i	−0.724777	−	0.529369i
$429$	−6.57546	+	1.76189i	−0.317466	+	0.0850648i
$430$	−24.8942	+	17.0633i	−1.20050	+	0.822865i
$431$	23.2543	−	13.4259i	1.12012	−	0.646701i	0.178687	−	0.983906i	$-0.442815\pi$
$431$	23.2543	−	13.4259i	1.12012	−	0.646701i	0.941431	+	0.337205i	$0.109482\pi$
$432$	−9.18515	−	14.3007i	−0.441921	−	0.688043i
$433$		−	18.6517i		−	0.896344i	−0.893947	−	0.448172i	$-0.852075\pi$
$433$		−	18.6517i		−	0.896344i	0.893947	−	0.448172i	$-0.147925\pi$
$434$	15.4587	−	1.17477i	0.742039	−	0.0563908i
$435$	16.5496	−	16.5496i	0.793491	−	0.793491i
$436$	−1.60911	+	0.711581i	−0.0770622	+	0.0340785i
$437$	1.65509	−	6.17686i	0.0791735	−	0.295479i
$438$	0.606995	−	3.25224i	0.0290033	−	0.155398i
$439$	−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
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.670904	−	0.741544i	$-0.265906\pi$
$443$	34.1538	−	9.15149i	1.62270	−	0.434800i	0.951792	+	0.306744i	$0.0992394\pi$
$444$	−3.08005	−	3.82314i	−0.146173	−	0.181438i
$445$	−8.92414	+	33.3053i	−0.423045	+	1.57882i
$446$	−13.5138	+	28.2410i	−0.639898	+	1.33725i
$447$	9.31855			0.440752
$448$	−18.9445	+	9.43956i	−0.895044	+	0.445977i
$449$	14.0702			0.664012			0.332006	−	0.943277i	$-0.392275\pi$
$449$	14.0702			0.664012			0.332006	+	0.943277i	$0.392275\pi$
$450$	−15.3517	+	32.0817i	−0.723685	+	1.51234i
$451$	9.44718	−	35.2573i	0.444850	−	1.66020i
$452$	−2.39942	−	2.97831i	−0.112859	−	0.140088i
$453$	−10.4669	+	2.80460i	−0.491777	+	0.131771i
$454$	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	0.388133	−	0.921604i	$-0.373120\pi$
$457$	−4.61613	−	2.66512i	−0.215933	−	0.124669i	−0.604066	+	0.796934i	$0.706454\pi$
$458$	−6.56770	+	35.1893i	−0.306888	+	1.64429i
$459$	−1.25614	+	4.68797i	−0.0586314	+	0.218816i
$460$	−14.7891	+	6.54006i	−0.689546	+	0.304932i
$461$	−2.32075	+	2.32075i	−0.108088	+	0.108088i	−0.759082	−	0.650995i	$-0.774352\pi$
$461$	−2.32075	+	2.32075i	−0.108088	+	0.108088i	0.650995	+	0.759082i	$0.274352\pi$
$462$	−11.0223	+	7.53181i	−0.512803	+	0.350412i
$463$		−	15.2932i		−	0.710736i	−0.934727	−	0.355368i	$-0.884356\pi$
$463$		−	15.2932i		−	0.710736i	0.934727	−	0.355368i	$-0.115644\pi$
$464$	−25.2376	+	16.2098i	−1.17163	+	0.752519i
$465$	11.1996	−	6.46610i	0.519370	−	0.299858i
$466$	18.1619	−	12.4488i	0.841334	−	0.576678i
$467$	−29.0012	+	7.77086i	−1.34202	+	0.359592i	−0.857182	−	0.515014i	$-0.827787\pi$
$467$	−29.0012	+	7.77086i	−1.34202	+	0.359592i	−0.484835	+	0.874606i	$0.661120\pi$
$468$	−7.31882	−	5.34558i	−0.338312	−	0.247099i
$469$	−1.62978	−	0.439205i	−0.0752561	−	0.0202806i
$470$	−6.90739	−	5.91449i	−0.318614	−	0.272815i
$471$	−0.823689	+	1.42667i	−0.0379536	+	0.0657375i
$472$	20.4116	+	0.611489i	0.939522	+	0.0281461i
$473$	21.1273	−	12.1978i	0.971433	−	0.560857i
$474$	−0.456451	−	1.29414i	−0.0209655	−	0.0594419i
$475$	−23.3803	+	23.3803i	−1.07276	+	1.07276i
$476$	5.63395	+	2.18823i	0.258231	+	0.100297i
$477$	−5.08563	−	5.08563i	−0.232855	−	0.232855i
$478$	14.8273	+	7.09514i	0.678185	+	0.324524i
$479$	−17.2367	−	29.8548i	−0.787564	−	1.36410i	−0.927456	−	0.373933i	$-0.878009\pi$
$479$	−17.2367	−	29.8548i	−0.787564	−	1.36410i	0.139892	−	0.990167i	$-0.455324\pi$
$480$	−10.8360	+	13.9396i	−0.494593	+	0.636251i
$481$	−5.13092	−	2.96234i	−0.233950	−	0.135071i
$482$	0.307157	+	3.96651i	0.0139906	+	0.180669i
$483$	3.02425	+	3.03294i	0.137608	+	0.138003i
$484$	2.88523	+	18.5176i	0.131147	+	0.841710i
$485$	−8.61409	−	32.1482i	−0.391146	−	1.45978i
$486$	4.08001	−	21.8604i	0.185073	−	0.991610i
$487$	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	$0.723699\pi$
$488$	8.74978	+	16.2610i	0.396084	+	0.736099i
$489$	−1.42584			−0.0644787
$490$	7.28128	−	38.4013i	0.328935	−	1.73479i
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.848719	+	0.528844i	$0.177374\pi$
$491$	30.5248	+	30.5248i	1.37756	+	1.37756i	0.528844	+	0.848719i	$0.322626\pi$
$492$	−11.6939	+	5.17131i	−0.527204	+	0.233141i
$493$	8.27322	+	2.21680i	0.372607	+	0.0998398i
$494$	−4.76372	−	6.94995i	−0.214330	−	0.312693i
$495$	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
$499$	2.86434	+	10.6899i	0.128225	+	0.478544i	0.999934	−	0.0114806i	$-0.00365448\pi$
$499$	2.86434	+	10.6899i	0.128225	+	0.478544i	−0.871709	+	0.490025i	$0.836988\pi$
$500$	43.8762	+	4.72307i	1.96220	+	0.211222i
$501$	−16.4935	−	4.41942i	−0.736875	−	0.197445i
$502$	−1.32721	−	3.76294i	−0.0592363	−	0.167948i
$503$		−	25.6811i		−	1.14507i	−0.819882	−	0.572533i	$-0.805961\pi$
$503$		−	25.6811i		−	1.14507i	0.819882	−	0.572533i	$-0.194039\pi$
$504$	−17.0151	−	5.13655i	−0.757911	−	0.228800i
$505$		−	58.1745i		−	2.58873i
$506$	12.3268	−	4.34773i	0.547994	−	0.193280i
$507$	−7.14688	−	1.91500i	−0.317404	−	0.0850482i
$508$	18.6282	−	15.0075i	0.826493	−	0.665849i
$509$	3.97493	+	14.8346i	0.176186	+	0.657534i	0.996347	+	0.0854009i	$0.0272171\pi$
$509$	3.97493	+	14.8346i	0.176186	+	0.657534i	−0.820161	+	0.572133i	$0.806116\pi$
$510$	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
$514$	−17.4497	+	11.9606i	−0.769674	+	0.527560i
$515$	−30.2691	−	8.11057i	−1.33381	−	0.357394i
$516$	−7.97049	−	3.08258i	−0.350881	−	0.135703i
$517$	5.19760	+	5.19760i	0.228590	+	0.228590i
$518$	−11.4184	−	2.14808i	−0.501697	−	0.0943814i
$519$	6.94641			0.304914
$520$	−6.12840	+	20.4064i	−0.268748	+	0.894879i
$521$	14.9189	+	25.8403i	0.653609	+	1.13208i	0.982241	+	0.187626i	$0.0600792\pi$
$521$	14.9189	+	25.8403i	0.653609	+	1.13208i	−0.328632	+	0.944458i	$0.606588\pi$
$522$	−24.7597	−	4.62112i	−1.08370	−	0.202261i
$523$	9.32633	+	34.8063i	0.407812	+	1.52198i	0.798810	+	0.601583i	$0.205463\pi$
$523$	9.32633	+	34.8063i	0.407812	+	1.52198i	−0.390998	+	0.920392i	$0.627870\pi$
$524$	8.96712	+	6.54948i	0.391731	+	0.286116i
$525$	−5.70113	−	21.3997i	−0.248818	−	0.933958i
$526$	20.8512	−	1.61467i	0.909157	−	0.0704030i
$527$	4.09857	+	2.36631i	0.178537	+	0.103078i
$528$	9.60274	−	10.5577i	0.417906	−	0.459467i
$529$	9.40318	+	16.2868i	0.408834	+	0.708121i
$530$	−7.29835	+	15.2520i	−0.317020	+	0.662504i
$531$	12.1253	+	12.1253i	0.526191	+	0.526191i
$532$	−13.3295	−	9.76509i	−0.577908	−	0.423371i
$533$	−10.9109	+	10.9109i	−0.472602	+	0.472602i
$534$	−9.20733	+	3.24747i	−0.398440	+	0.140532i
$535$	−31.7444	+	18.3276i	−1.37243	+	0.792372i
$536$	1.80365	+	0.0540336i	0.0779060	+	0.00233390i
$537$	0.690401	−	1.19581i	0.0297930	−	0.0516030i
$538$	22.0405	−	25.7405i	0.950231	−	1.10975i
$539$	−8.26457	+	30.4935i	−0.355980	+	1.31345i
$540$	−33.1528	+	5.16554i	−1.42667	+	0.222289i
$541$	−13.0674	+	3.50141i	−0.561813	+	0.150537i	−0.528539	−	0.848909i	$-0.677260\pi$
$541$	−13.0674	+	3.50141i	−0.561813	+	0.150537i	−0.0332740	+	0.999446i	$0.510593\pi$
$542$	11.7969	+	17.2109i	0.506721	+	0.739271i
$543$	−5.12698	+	2.96007i	−0.220020	+	0.127029i
$544$	−6.40058	−	0.883590i	−0.274423	−	0.0378836i
$545$			3.47331i			0.148780i
$546$	5.62723	−	0.427638i	0.240823	−	0.0183012i
$547$	−19.9064	+	19.9064i	−0.851134	+	0.851134i	−0.990273	−	0.139139i	$-0.955567\pi$
$547$	−19.9064	+	19.9064i	−0.851134	+	0.851134i	0.139139	+	0.990273i	$0.455567\pi$
$548$	26.7506	+	10.3458i	1.14273	+	0.441950i
$549$	−4.01321	+	14.9775i	−0.171280	+	0.639225i
$550$	−66.4380	−	12.3999i	−2.83293	−	0.528734i
$551$	−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
$555$	−9.36167	+	2.50845i	−0.397381	+	0.106478i
$556$	−41.0825	−	4.42234i	−1.74229	−	0.187549i
$557$	3.45569	−	12.8968i	0.146422	−	0.546456i	−0.853265	−	0.521477i	$-0.825381\pi$
$557$	3.45569	−	12.8968i	0.146422	−	0.546456i	0.999688	−	0.0249794i	$-0.00795201\pi$
$558$	−12.5539	−	6.00728i	−0.531450	−	0.254309i
$559$	−10.3129			−0.436190
$560$	1.91721	+	41.7402i	0.0810168	+	1.76384i
$561$	−4.07527			−0.172058
$562$	−40.7827	−	19.5153i	−1.72032	−	0.823203i
$563$	6.53907	−	24.4041i	0.275589	−	1.02851i	−0.679857	−	0.733345i	$-0.737958\pi$
$563$	6.53907	−	24.4041i	0.275589	−	1.02851i	0.955446	−	0.295167i	$-0.0953751\pi$
$564$	0.275583	−	2.56010i	0.0116041	−	0.107800i
$565$	−7.29293	+	1.95413i	−0.306816	+	0.0822110i
$566$	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	0.710263	−	0.703936i	$-0.248576\pi$
$569$	10.8718	+	6.27682i	0.455768	+	0.263138i	−0.254495	+	0.967074i	$0.581909\pi$
$570$	−13.5495	−	2.52886i	−0.567526	−	0.105922i
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	−0.330235	−	0.943899i	$-0.607128\pi$
$571$	10.2203	−	38.1427i	0.427706	−	1.59622i	0.757942	−	0.652322i	$-0.226205\pi$
$572$	6.21244	−	16.0632i	0.259755	−	0.671636i
$573$	15.2048	−	15.2048i	0.635188	−	0.635188i
$574$	−13.1007	+	27.2771i	−0.546813	+	1.13852i
$575$			21.6836i			0.904268i
$576$	18.9666	+	1.13742i	0.790274	+	0.0473924i
$577$	−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	$0.494652\pi$
$578$	−12.5493	−	18.3086i	−0.521982	−	0.761537i
$579$	4.40076	−	1.17918i	0.182889	−	0.0490050i
$580$	9.11603	+	58.5074i	0.378523	+	2.42939i
$581$	6.07411	+	6.09157i	0.251997	+	0.252721i
$582$	6.12943	−	7.15841i	0.254073	−	0.296725i
$583$	6.83364	−	11.8362i	0.283020	−	0.490206i
$584$	5.73875	+	6.09321i	0.237471	+	0.252139i
$585$	−15.4946	+	8.94583i	−0.640624	+	0.369865i
$586$	−13.1699	+	4.64510i	−0.544044	+	0.191887i
$587$	−24.2488	+	24.2488i	−1.00085	+	1.00085i	−0.000853494		1.00000i	$0.500272\pi$
$587$	−24.2488	+	24.2488i	−1.00085	+	1.00085i	−1.00000		0.000853494i	$0.999728\pi$
$588$	10.1345	−	4.44697i	0.417941	−	0.183390i
$589$	−9.14897	−	9.14897i	−0.376977	−	0.376977i
$590$	17.4009	−	36.3641i	0.716384	−	1.49709i
$591$	7.14040	+	12.3675i	0.293717	+	0.508732i
$592$	12.4070	−	0.587721i	0.509926	−	0.0241552i
$593$	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
$595$	8.44895	−	8.42474i	0.346373	−	0.345381i
$596$	−13.9054	+	19.0384i	−0.569587	+	0.779841i
$597$	−1.12681	−	4.20530i	−0.0461171	−	0.172112i
$598$	−5.43181	−	1.01379i	−0.222123	−	0.0414568i
$599$	−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	$0.838522\pi$
$600$	11.2183	+	20.8486i	0.457986	+	0.851139i
$601$	4.37578			0.178492			0.0892459	−	0.996010i	$-0.471554\pi$
$601$	4.37578			0.178492			0.0892459	+	0.996010i	$0.471554\pi$
$602$	−19.0825	+	6.69972i	−0.777743	+	0.273060i
$603$	1.07144	+	1.07144i	0.0436323	+	0.0436323i
$604$	9.88902	−	25.5696i	0.402379	−	1.04041i
$605$	35.7363	+	9.57552i	1.45289	+	0.389300i
$606$	13.5871	−	9.31301i	0.551936	−	0.378315i
$607$	−3.27685	+	5.67568i	−0.133003	+	0.230369i	−0.924833	−	0.380373i	$-0.875795\pi$
$607$	−3.27685	+	5.67568i	−0.133003	+	0.230369i	0.791830	+	0.610742i	$0.209129\pi$
$608$	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
$611$	−0.804235	−	3.00145i	−0.0325359	−	0.121425i
$612$	−3.40387	−	4.22509i	−0.137593	−	0.170789i
$613$	−18.1595	−	4.86583i	−0.733457	−	0.196529i	−0.127289	−	0.991866i	$-0.540627\pi$
$613$	−18.1595	−	4.86583i	−0.733457	−	0.196529i	−0.606168	+	0.795337i	$0.707294\pi$
$614$	44.1136	−	15.5591i	1.78028	−	0.627914i
$615$			25.2417i			1.01785i
$616$	1.05981	−	33.7583i	0.0427011	−	1.36016i
$617$		−	22.2202i		−	0.894552i	−0.894396	−	0.447276i	$-0.852394\pi$
$617$		−	22.2202i		−	0.894552i	0.894396	−	0.447276i	$-0.147606\pi$
$618$	−2.95142	−	8.36794i	−0.118723	−	0.336608i
$619$	−8.23929	−	2.20771i	−0.331165	−	0.0887354i	0.0894053	−	0.995995i	$-0.471503\pi$
$619$	−8.23929	−	2.20771i	−0.331165	−	0.0887354i	−0.420570	+	0.907260i	$0.638170\pi$
$620$	−3.50174	+	32.5304i	−0.140633	+	1.30645i
$621$	−2.25210	−	8.40496i	−0.0903738	−	0.337280i
$622$	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
$626$	6.75787	+	9.85928i	0.270099	+	0.394056i
$627$	10.7618	+	2.88362i	0.429785	+	0.115161i
$628$	−1.68564	−	3.81176i	−0.0672645	−	0.152106i
$629$	−2.50798	−	2.50798i	−0.0999997	−	0.0999997i
$630$	−22.8588	+	26.6189i	−0.910718	+	1.06052i
$631$	45.0684			1.79415			0.897073	−	0.441882i	$-0.145689\pi$
$631$	45.0684			1.79415			0.897073	+	0.441882i	$0.145689\pi$
$632$	3.32514	+	0.998598i	0.132267	+	0.0397221i
$633$	10.8356	+	18.7679i	0.430678	+	0.745956i
$634$	−4.96563	+	26.6055i	−0.197210	+	1.05664i
$635$	−12.2224	−	45.6146i	−0.485031	−	1.81016i
$636$	−4.73058	+	0.737070i	−0.187580	+	0.0292267i
$637$	9.47099	−	9.41679i	0.375254	−	0.373107i
$638$	−3.69537	−	47.7205i	−0.146301	−	1.88927i
$639$	−4.94643	−	2.85582i	−0.195678	−	0.112975i
$640$	−12.3096	−	42.9396i	−0.486579	−	1.69734i
$641$	−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	$-0.360239\pi$
$642$	−9.36241	−	4.48009i	−0.369505	−	0.176815i
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.996412	+	0.0846366i	$0.0269729\pi$
$643$	27.4126	+	27.4126i	1.08105	+	1.08105i	0.0846366	+	0.996412i	$0.473027\pi$
$644$	−10.7093	+	1.65288i	−0.422007	+	0.0651327i
$645$	−11.9292	+	11.9292i	−0.469712	+	0.469712i
$646$	−1.67780	−	4.75693i	−0.0660120	−	0.187159i
$647$	−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	$0.532728\pi$
$648$	7.30358	+	7.75469i	0.286912	+	0.304633i
$649$	−16.2929	+	28.2201i	−0.639553	+	1.10774i
$650$	21.7020	+	18.5825i	0.851222	+	0.728864i
$651$	8.37393	−	2.23091i	0.328200	−	0.0874364i
$652$	2.12768	−	2.91308i	0.0833263	−	0.114085i
$653$	−12.5980	+	3.37562i	−0.492997	+	0.132098i	−0.496748	−	0.867895i	$-0.665473\pi$
$653$	−12.5980	+	3.37562i	−0.492997	+	0.132098i	0.00375078	+	0.999993i	$0.498806\pi$
$654$	−0.811214	+	0.556032i	−0.0317210	+	0.0217426i
$655$	18.9843	−	10.9606i	0.741776	−	0.428265i
$656$	6.88472	−	31.6082i	0.268803	−	1.23409i
$657$			7.02862i			0.274213i
$658$	−3.43798	−	5.03125i	−0.134027	−	0.196139i
$659$	−15.1555	+	15.1555i	−0.590375	+	0.590375i	−0.937733	−	0.347358i	$-0.887079\pi$
$659$	−15.1555	+	15.1555i	−0.590375	+	0.590375i	0.347358	+	0.937733i	$0.387079\pi$
$660$	−11.3946	−	25.7668i	−0.443535	−	1.00297i
$661$	0.571930	−	2.13447i	0.0222455	−	0.0830213i	−0.953911	−	0.300091i	$-0.902983\pi$
$661$	0.571930	−	2.13447i	0.0222455	−	0.0830213i	0.976156	+	0.217069i	$0.0696498\pi$
$662$	3.75036	−	20.0942i	0.145762	−	0.780984i
$663$	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
$667$	−14.8329	+	3.97446i	−0.574332	+	0.153892i
$668$	33.6412	−	27.1024i	1.30162	−	1.04862i
$669$	−4.52945	+	16.9041i	−0.175118	+	0.653551i
$670$	1.53761	−	3.21328i	0.0594032	−	0.124140i
$671$	−29.4658			−1.13752
$672$	−9.44177	+	7.12985i	−0.364224	+	0.275040i
$673$	−50.4864			−1.94611			−0.973054	−	0.230577i	$-0.925939\pi$
$673$	−50.4864			−1.94611			−0.973054	+	0.230577i	$0.925939\pi$
$674$	8.37270	−	17.4971i	0.322504	−	0.673964i
$675$	−11.6447	+	43.4587i	−0.448205	+	1.67273i
$676$	14.5772	−	11.7439i	0.560663	−	0.451688i
$677$	28.6211	−	7.66899i	1.10000	−	0.294743i	0.337234	−	0.941421i	$-0.390509\pi$
$677$	28.6211	−	7.66899i	1.10000	−	0.294743i	0.762763	+	0.646678i	$0.223842\pi$
$678$	−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
$682$	4.85222	−	25.9979i	0.185801	−	0.995512i
$683$	−0.972755	+	3.63037i	−0.0372214	+	0.138912i	−0.982036	−	0.188693i	$-0.939575\pi$
$683$	−0.972755	+	3.63037i	−0.0372214	+	0.138912i	0.944815	+	0.327605i	$0.106242\pi$
$684$	5.99917	+	13.5660i	0.229384	+	0.518709i
$685$	40.0368	−	40.0368i	1.52973	−	1.52973i
$686$	11.4071	−	23.5771i	0.435524	−	0.900177i
$687$			20.0098i			0.763423i
$688$	18.1917	−	11.6843i	0.693551	−	0.445458i
$689$	−5.00358	+	2.88882i	−0.190621	+	0.110055i
$690$	−7.45578	+	5.11043i	−0.283837	+	0.194551i
$691$	13.8605	−	3.71391i	0.527278	−	0.141284i	0.0146470	−	0.999893i	$-0.495338\pi$
$691$	13.8605	−	3.71391i	0.527278	−	0.141284i	0.512631	+	0.858609i	$0.328671\pi$
$692$	−10.3656	+	14.1919i	−0.394042	+	0.539496i
$693$	20.0833	−	20.0258i	0.762903	−	0.760717i
$694$	−10.0936	−	8.64270i	−0.383148	−	0.328072i
$695$	−40.7851	+	70.6418i	−1.54707	+	2.67960i
$696$	−12.2054	+	11.4954i	−0.462646	+	0.435732i
$697$	−7.99980	+	4.61869i	−0.303014	+	0.174945i
$698$	−5.55525	−	15.7504i	−0.210269	−	0.596162i
$699$	8.70312	−	8.70312i	0.329182	−	0.329182i
$700$	52.2282	+	20.2854i	1.97404	+	0.766717i
$701$	12.9519	+	12.9519i	0.489187	+	0.489187i	0.908050	−	0.418863i	$-0.137571\pi$
$701$	12.9519	+	12.9519i	0.489187	+	0.489187i	−0.418863	+	0.908050i	$0.637571\pi$
$702$	−10.3421	−	4.94889i	−0.390338	−	0.186784i
$703$	4.84835	+	8.39758i	0.182859	+	0.316721i
$704$	7.24063	+	35.3735i	0.272891	+	1.33319i
$705$	−4.40212	−	2.54157i	−0.165794	−	0.0957210i
$706$	2.13543	+	27.5761i	0.0803681	+	1.03784i
$707$	10.1437	−	37.6405i	0.381492	−	1.41562i
$708$	11.2787	−	1.75734i	0.423881	−	0.0660448i
$709$	−0.167036	−	0.623389i	−0.00627319	−	0.0234119i	0.962718	−	0.270506i	$-0.0871910\pi$
$709$	−0.167036	−	0.623389i	−0.00627319	−	0.0234119i	−0.968991	+	0.247094i	$0.920524\pi$
$710$	−2.46358	+	13.1997i	−0.0924566	+	0.495377i
$711$	1.45769	+	2.52479i	0.0546676	+	0.0946870i
$712$	7.10464	−	23.6571i	0.266258	−	0.886587i
$713$	−8.48503			−0.317767
$714$	3.32023	+	0.624614i	0.124256	+	0.0233756i
$715$	−24.0413	−	24.0413i	−0.899094	−	0.899094i
$716$	1.41287	+	3.19495i	0.0528016	+	0.119401i
$717$	8.87514	+	2.37809i	0.331448	+	0.0888113i
$718$	14.0783	+	20.5393i	0.525398	+	0.766521i
$719$	−15.4833	+	26.8178i	−0.577429	+	1.00014i	0.418344	+	0.908289i	$0.362611\pi$
$719$	−15.4833	+	26.8178i	−0.577429	+	1.00014i	−0.995773	+	0.0918476i	$0.970723\pi$
$720$	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
$723$	0.575572	+	2.14806i	0.0214057	+	0.0798873i
$724$	1.60303	−	14.8918i	0.0595763	−	0.553450i
$725$	76.6949	+	20.5503i	2.84838	+	0.763221i
$726$	3.48451	+	9.87938i	0.129322	+	0.366658i
$727$		−	16.7744i		−	0.622128i	−0.950389	−	0.311064i	$-0.899315\pi$
$727$		−	16.7744i		−	0.622128i	0.950389	−	0.311064i	$-0.100685\pi$
$728$	−7.52342	+	12.1349i	−0.278836	+	0.449749i
$729$		−	1.13181i		−	0.0419187i
$730$	15.5829	−	5.49618i	0.576750	−	0.203423i
$731$	−5.96348	−	1.59791i	−0.220567	−	0.0591008i
$732$	6.47560	+	8.03792i	0.239345	+	0.297090i
$733$	7.88067	+	29.4110i	0.291079	+	1.08632i	0.944282	+	0.329139i	$0.106758\pi$
$733$	7.88067	+	29.4110i	0.291079	+	1.08632i	−0.653203	+	0.757183i	$0.726575\pi$
$734$	−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
$738$	22.4061	−	15.3579i	0.824780	−	0.565331i
$739$	24.9711	+	6.69098i	0.918577	+	0.246132i	0.686977	−	0.726679i	$-0.258937\pi$
$739$	24.9711	+	6.69098i	0.918577	+	0.246132i	0.231600	+	0.972811i	$0.425604\pi$
$740$	8.84482	−	22.8696i	0.325142	−	0.840704i
$741$	−3.33039	−	3.33039i	−0.122345	−	0.122345i
$742$	−7.38166	+	8.59586i	−0.270989	+	0.315564i
$743$	16.7597			0.614855			0.307427	−	0.951572i	$-0.400532\pi$
$743$	16.7597			0.614855			0.307427	+	0.951572i	$0.400532\pi$
$744$	−8.15827	+	4.38985i	−0.299097	+	0.160940i
$745$	23.2707	+	40.3060i	0.852572	+	1.47670i
$746$	−18.6738	−	3.48525i	−0.683695	−	0.127604i
$747$	−1.99870	−	7.45925i	−0.0731286	−	0.272920i
$748$	6.08123	−	8.32602i	0.222352	−	0.304430i
$749$	−23.7352	+	6.32334i	−0.867265	+	0.231050i
$750$	24.5940	−	1.90450i	0.898046	−	0.0695427i
$751$	−19.4065	−	11.2044i	−0.708154	−	0.408853i	0.102223	−	0.994761i	$-0.467404\pi$
$751$	−19.4065	−	11.2044i	−0.708154	−	0.408853i	−0.810377	+	0.585909i	$0.800738\pi$
$752$	4.81921	+	4.38328i	0.175738	+	0.159842i
$753$	−1.11521	−	1.93159i	−0.0406404	−	0.0703912i
$754$	−8.73369	+	18.2515i	−0.318062	+	0.664681i
$755$	−38.2692	−	38.2692i	−1.39276	−	1.39276i
$756$	−22.3515	−	2.43848i	−0.812916	−	0.0886867i
$757$	10.1520	−	10.1520i	0.368982	−	0.368982i	−0.498124	−	0.867106i	$-0.665978\pi$
$757$	10.1520	−	10.1520i	0.368982	−	0.368982i	0.867106	+	0.498124i	$0.165978\pi$
$758$	−1.16416	+	0.410605i	−0.0422842	+	0.0149139i
$759$	6.32760	−	3.65324i	0.229677	−	0.132604i
$760$	25.3855	−	23.9088i	0.920830	−	0.867262i
$761$	10.0149	−	17.3464i	0.363041	−	0.628805i	−0.625419	−	0.780289i	$-0.715072\pi$
$761$	10.0149	−	17.3464i	0.363041	−	0.628805i	0.988460	+	0.151484i	$0.0484053\pi$
$762$	8.69694	−	10.1569i	0.315057	−	0.367947i
$763$	−0.605626	+	2.24732i	−0.0219251	+	0.0813586i
$764$	8.37527	+	53.7532i	0.303007	+	1.94472i
$765$	−10.3459	+	2.77218i	−0.374057	+	0.100228i
$766$	0.342845	+	0.500188i	0.0123875	+	0.0180725i
$767$	11.9297	−	6.88759i	0.430755	−	0.248696i
$768$	8.05821	−	9.74907i	0.290776	−	0.351789i
$769$		−	50.7365i		−	1.82960i	−0.403902	−	0.914802i	$-0.632346\pi$
$769$		−	50.7365i		−	1.82960i	0.403902	−	0.914802i	$-0.367654\pi$
$770$	−60.1031	−	28.8665i	−2.16596	−	1.04028i
$771$	−8.36185	+	8.36185i	−0.301144	+	0.301144i
$772$	−4.15780	+	10.7506i	−0.149642	+	0.386923i
$773$	−7.73070	+	28.8514i	−0.278054	+	1.03771i	0.675713	+	0.737165i	$0.263836\pi$
$773$	−7.73070	+	28.8514i	−0.278054	+	1.03771i	−0.953767	+	0.300547i	$0.902831\pi$
$774$	17.8472	+	3.33098i	0.641504	+	0.119730i
$775$	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
$779$	24.3937	−	6.53627i	0.873994	−	0.234186i
$780$	−1.27470	+	11.8417i	−0.0456415	+	0.423999i
$781$	2.80918	−	10.4840i	0.100520	−	0.375148i
$782$	−2.98388	−	1.42784i	−0.106703	−	0.0510596i
$783$	−31.8628			−1.13868
$784$	−6.03758	+	27.3413i	−0.215628	+	0.976476i
$785$	−8.22781			−0.293663
$786$	5.59905	+	2.67925i	0.199712	+	0.0955658i
$787$	−9.92221	+	37.0302i	−0.353688	+	1.31998i	0.528438	+	0.848972i	$0.322778\pi$
$787$	−9.92221	+	37.0302i	−0.353688	+	1.31998i	−0.882127	+	0.471012i	$0.843889\pi$
$788$	−35.9227	−	3.86691i	−1.27969	−	0.137753i
$789$	11.2920	−	3.02568i	0.402005	−	0.107717i
$790$	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
$794$	−38.8072	−	7.24293i	−1.37722	−	0.257042i
$795$	−2.44620	+	9.12933i	−0.0867577	+	0.323784i
$796$	10.2731	+	3.97313i	0.364121	+	0.140824i
$797$	18.8328	−	18.8328i	0.667092	−	0.667092i	−0.289949	−	0.957042i	$-0.593639\pi$
$797$	18.8328	−	18.8328i	0.667092	−	0.667092i	0.957042	+	0.289949i	$0.0936385\pi$
$798$	−8.32594	−	3.99881i	−0.294735	−	0.141556i
$799$		−	1.86021i		−	0.0658094i
$800$	−59.3351	−	8.19111i	−2.09781	−	0.289600i
$801$	17.9629	−	10.3709i	0.634688	−	0.366437i
$802$	−21.0890	−	30.7674i	−0.744678	−	1.08643i
$803$	−12.9014	+	3.45692i	−0.455280	+	0.121992i
$804$	0.996635	−	0.155285i	0.0351486	−	0.00547650i
$805$	−5.56624	+	20.6549i	−0.196184	+	0.727990i
$806$	−7.27152	+	8.49223i	−0.256128	+	0.299126i
$807$	9.47120	−	16.4046i	0.333402	−	0.577469i
$808$	−1.24793	+	41.6563i	−0.0439021	+	1.46546i
$809$	17.1772	−	9.91725i	0.603918	−	0.348672i	−0.166663	−	0.986014i	$-0.553299\pi$
$809$	17.1772	−	9.91725i	0.603918	−	0.348672i	0.770581	+	0.637342i	$0.219966\pi$
$810$	19.8320	−	6.99486i	0.696826	−	0.245774i
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	−0.635330	−	0.772240i	$-0.719136\pi$
$811$	3.89894	−	3.89894i	0.136910	−	0.136910i	0.772240	+	0.635330i	$0.219136\pi$
$812$	−4.30338	+	39.4454i	−0.151019	+	1.38426i
$813$	8.24740	+	8.24740i	0.289249	+	0.289249i
$814$	−8.55534	+	17.8788i	−0.299865	+	0.626652i
$815$	−3.56067	−	6.16726i	−0.124725	−	0.216030i
$816$	−3.60769	+	0.170896i	−0.126294	+	0.00598256i
$817$	14.6174	+	8.43938i	0.511400	+	0.295257i
$818$	25.1383	−	1.94665i	0.878940	−	0.0680631i
$819$	−11.5853	+	3.08646i	−0.404823	+	0.107850i
$820$	−51.5704	−	37.6664i	−1.80092	−	1.31537i
$821$	−5.00859	−	18.6923i	−0.174801	−	0.652366i	−0.996585	−	0.0825677i	$-0.973688\pi$
$821$	−5.00859	−	18.6923i	−0.174801	−	0.652366i	0.821784	−	0.569798i	$-0.192979\pi$
$822$	15.7603	+	2.94148i	0.549702	+	0.102596i
$823$	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	$0.586408\pi$
$824$	21.5004	+	6.45695i	0.749001	+	0.224938i
$825$	−37.7789			−1.31529
$826$	17.5995	−	20.4944i	0.612366	−	0.713093i
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	0.875489	−	0.483239i	$-0.160540\pi$
$827$	11.2802	+	11.2802i	0.392250	+	0.392250i	−0.483239	+	0.875489i	$0.660540\pi$
$828$	9.07267	+	3.50885i	0.315297	+	0.121941i
$829$	−40.7143	−	10.9094i	−1.41407	−	0.378898i	−0.530691	−	0.847565i	$-0.678067\pi$
$829$	−40.7143	−	10.9094i	−1.41407	−	0.378898i	−0.883375	+	0.468668i	$0.844734\pi$
$830$	−14.9747	+	10.2642i	−0.519780	+	0.356274i
$831$	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
$835$	−22.0727	−	82.3765i	−0.763858	−	2.85076i
$836$	−21.9505	+	17.6840i	−0.759173	+	0.611614i
$837$	−17.0059	−	4.55671i	−0.587809	−	0.157503i
$838$	−37.0002	+	13.0502i	−1.27815	+	0.450811i
$839$			27.4328i			0.947087i	0.880771	+	0.473543i	$0.157025\pi$
$839$			27.4328i			0.947087i	−0.880771	+	0.473543i	$0.842975\pi$
$840$	5.33422	+	22.7393i	0.184048	+	0.784579i
$841$			27.2308i			0.938992i
$842$	−3.49523	−	9.90977i	−0.120454	−	0.341513i
$843$	−24.4112	−	6.54097i	−0.840767	−	0.225283i
$844$	−54.5131	−	5.86808i	−1.87642	−	0.201988i
$845$	−9.56445	−	35.6950i	−0.329027	−	1.22795i
$846$	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
$850$	9.67003	+	14.1079i	0.331679	+	0.483898i
$851$	6.14234	+	1.64584i	0.210557	+	0.0564185i
$852$	−3.47727	+	1.53772i	−0.119129	+	0.0526816i
$853$	−8.95019	−	8.95019i	−0.306449	−	0.306449i	0.537082	−	0.843530i	$-0.319527\pi$
$853$	−8.95019	−	8.95019i	−0.306449	−	0.306449i	−0.843530	+	0.537082i	$0.819527\pi$
$854$	24.0065	+	4.51621i	0.821487	+	0.154541i
$855$	29.2826			1.00144
$856$	23.1239	−	12.4427i	0.790360	−	0.425281i
$857$	−26.8241	−	46.4607i	−0.916294	−	1.58707i	−0.804995	−	0.593281i	$-0.797832\pi$
$857$	−26.8241	−	46.4607i	−0.916294	−	1.58707i	−0.111299	−	0.993787i	$-0.535501\pi$
$858$	1.76630	−	9.46372i	0.0603004	−	0.323086i
$859$	−3.41188	−	12.7333i	−0.116412	−	0.434455i	0.882977	−	0.469417i	$-0.155536\pi$
$859$	−3.41188	−	12.7333i	−0.116412	−	0.434455i	−0.999389	+	0.0349617i	$0.988869\pi$
$860$	−6.57099	−	42.1731i	−0.224069	−	1.43809i
$861$	−4.40130	+	16.3321i	−0.149996	+	0.556596i
$862$	2.93185	+	37.8607i	0.0998591	+	1.28954i
$863$	6.64111	+	3.83425i	0.226066	+	0.130519i	0.608756	−	0.793358i	$-0.291669\pi$
$863$	6.64111	+	3.83425i	0.226066	+	0.130519i	−0.382690	+	0.923877i	$0.625002\pi$
$864$	23.8501	−	2.98764i	0.811398	−	0.101642i
$865$	17.3469	+	30.0457i	0.589812	+	1.02158i
$866$	23.7937	+	11.3857i	0.808541	+	0.386902i
$867$	−8.77341	−	8.77341i	−0.297961	−	0.297961i
$868$	−7.93791	+	20.4375i	−0.269430	+	0.693693i
$869$	−3.91744	+	3.91744i	−0.132890	+	0.132890i
$870$	11.0095	+	31.2145i	0.373257	+	1.05827i
$871$	1.05415	−	0.608615i	0.0357186	−	0.0206221i
$872$	0.0745077	−	2.48708i	0.00252315	−	0.0842233i
$873$	−10.0106	+	17.3388i	−0.338807	+	0.586830i
$874$	6.86939	+	5.88195i	0.232361	+	0.198960i
$875$	41.3387	−	41.2203i	1.39750	−	1.39350i
$876$	3.77830	+	2.75962i	0.127657	+	0.0932391i
$877$	14.8501	−	3.97908i	0.501453	−	0.134364i	0.000778781	−	1.00000i	$-0.499752\pi$
$877$	14.8501	−	3.97908i	0.501453	−	0.134364i	0.500674	+	0.865636i	$0.333085\pi$
$878$	23.6337	−	16.1993i	0.797598	−	0.546700i
$879$	−6.76038	+	3.90311i	−0.228022	+	0.131649i
$880$	69.6464	+	15.1700i	2.34778	+	0.511380i
$881$			21.5605i			0.726392i	0.931713	+	0.363196i	$0.118314\pi$
$881$			21.5605i			0.726392i	−0.931713	+	0.363196i	$0.881686\pi$
$882$	−19.4317	+	13.2373i	−0.654300	+	0.445724i
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	−0.643690	−	0.765286i	$-0.722598\pi$
$883$	3.61325	−	3.61325i	0.121596	−	0.121596i	0.765286	+	0.643690i	$0.222598\pi$
$884$	−3.98619	+	1.76278i	−0.134070	+	0.0592886i
$885$	5.83228	−	21.7664i	0.196050	−	0.731668i
$886$	−9.17439	+	49.1558i	−0.308220	+	1.65142i
$887$	−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
$891$	−16.4193	+	4.39954i	−0.550067	+	0.147390i
$892$	−27.7772	−	34.4787i	−0.930048	−	1.15443i
$893$	−1.31626	+	4.91235i	−0.0440470	+	0.164386i
$894$	−5.68840	+	11.8875i	−0.190248	+	0.397578i
$895$	6.89640			0.230521
$896$	−0.477439	−	29.9295i	−0.0159501	−	0.999873i
$897$	−3.08871			−0.103129
$898$	−8.58896	+	17.9491i	−0.286617	+	0.598968i
$899$	−8.04158	+	30.0116i	−0.268202	+	1.00094i
$900$	−31.5548	−	39.1677i	−1.05183	−	1.30559i
$901$	−3.34094	+	0.895202i	−0.111303	+	0.0298235i
$902$	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
$906$	2.81161	−	15.0645i	0.0934096	−	0.500483i
$907$	4.95935	−	18.5085i	0.164672	−	0.614566i	−0.833409	−	0.552656i	$-0.813614\pi$
$907$	4.95935	−	18.5085i	0.164672	−	0.614566i	0.998082	−	0.0619098i	$-0.0197191\pi$
$908$	−15.7488	+	6.96447i	−0.522644	+	0.231124i
$909$	−24.7454	+	24.7454i	−0.820752	+	0.820752i
$910$	15.9023	+	23.2719i	0.527155	+	0.771454i
$911$		−	16.9566i		−	0.561797i	−0.959737	−	0.280899i	$-0.909368\pi$
$911$		−	16.9566i		−	0.561797i	0.959737	−	0.280899i	$-0.0906325\pi$
$912$	9.64796	+	2.10147i	0.319476	+	0.0695865i
$913$	12.7088	−	7.33743i	0.420600	−	0.242833i
$914$	6.21771	−	4.26182i	0.205664	−	0.140969i
$915$	19.6823	−	5.27386i	0.650677	−	0.174348i
$916$	−40.8813	−	29.8592i	−1.35075	−	0.986576i
$917$	14.1945	−	3.78158i	0.468743	−	0.124879i
$918$	−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	$-0.0494935\pi$
$920$	0.684792	−	22.8585i	0.0225769	−	0.753623i
$921$	22.6444	−	13.0737i	0.746158	−	0.430794i
$922$	−1.54386	−	4.37720i	−0.0508444	−	0.144156i
$923$	−3.24442	+	3.24442i	−0.106791	+	0.106791i
$924$	−2.87978	−	18.6586i	−0.0947378	−	0.613824i
$925$	−23.2496	−	23.2496i	−0.764443	−	0.764443i
$926$	19.5093	+	9.33555i	0.641115	+	0.306785i
$927$	9.42543	+	16.3253i	0.309572	+	0.536194i
$928$	−5.27252	−	42.0902i	−0.173079	−	1.38168i
$929$	−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
$931$	−21.1302	+	5.59686i	−0.692513	+	0.183430i
$932$	4.79396	+	30.7680i	0.157031	+	1.00784i
$933$	5.15311	+	19.2317i	0.168705	+	0.629617i
$934$	7.79030	−	41.7400i	0.254906	−	1.36577i
$935$	−10.1770	−	17.6270i	−0.332822	−	0.576464i
$936$	11.2869	−	6.07334i	0.368925	−	0.198513i
$937$	−37.0969			−1.21190			−0.605952	−	0.795501i	$-0.707208\pi$
$937$	−37.0969			−1.21190			−0.605952	+	0.795501i	$0.707208\pi$
$938$	1.55516	−	1.81097i	0.0507779	−	0.0591303i
$939$	4.72453	+	4.72453i	0.154179	+	0.154179i
$940$	11.7615	−	5.20120i	0.383619	−	0.169645i
$941$	2.17799	+	0.583589i	0.0710003	+	0.0190245i	0.294144	−	0.955761i	$-0.404965\pi$
$941$	2.17799	+	0.583589i	0.0710003	+	0.0190245i	−0.223144	+	0.974785i	$0.571632\pi$
$942$	−1.31717	−	1.92166i	−0.0429157	−	0.0626111i
$943$	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
$947$	−4.22082	−	15.7523i	−0.137158	−	0.511882i	−0.999980	−	0.00637300i	$-0.997971\pi$
$947$	−4.22082	−	15.7523i	−0.137158	−	0.511882i	0.862821	−	0.505509i	$-0.168695\pi$
$948$	1.92955	+	0.207707i	0.0626689	+	0.00674601i
$949$	5.45387	+	1.46136i	0.177040	+	0.0474378i
$950$	−15.5536	−	44.0980i	−0.504626	−	1.43073i
$951$			15.1288i			0.490585i
$952$	−6.23065	+	5.85135i	−0.201937	+	0.189643i
$953$			27.9419i			0.905126i	0.891733	+	0.452563i	$0.149490\pi$
$953$			27.9419i			0.905126i	−0.891733	+	0.452563i	$0.850510\pi$
$954$	9.59210	−	3.38319i	0.310556	−	0.109535i
$955$	103.736	+	27.7960i	3.35682	+	0.899456i
$956$	−18.1023	+	14.5838i	−0.585470	+	0.471674i
$957$	−6.92462	−	25.8430i	−0.223841	−	0.835387i
$958$	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
$962$	6.91111	−	4.73710i	0.222823	−	0.152730i
$963$	21.2988	+	5.70700i	0.686345	+	0.183906i
$964$	−5.24750	−	2.02947i	−0.169011	−	0.0653648i
$965$	16.0901	+	16.0901i	0.517960	+	0.517960i
$966$	−5.71518	+	2.00656i	−0.183883	+	0.0645599i
$967$	−47.4478			−1.52582			−0.762910	−	0.646505i	$-0.776230\pi$
$967$	−47.4478			−1.52582			−0.762910	+	0.646505i	$0.776230\pi$
$968$	−25.3838	−	7.62322i	−0.815868	−	0.245020i
$969$	−1.40979	−	2.44183i	−0.0452890	−	0.0784428i
$970$	46.2693	+	8.63565i	1.48562	+	0.277274i
$971$	−8.47546	−	31.6308i	−0.271990	−	1.01508i	−0.957832	−	0.287330i	$-0.907232\pi$
$971$	−8.47546	−	31.6308i	−0.271990	−	1.01508i	0.685841	−	0.727751i	$-0.259434\pi$
$972$	25.3964	+	18.5492i	0.814590	+	0.594967i
$973$	−38.7066	+	38.5957i	−1.24088	+	1.23732i
$974$	−21.0129	+	1.62719i	−0.673296	+	0.0521385i
$975$	13.8308	+	7.98523i	0.442941	+	0.255732i
$976$	−26.0850	+	1.23565i	−0.834961	+	0.0395521i
$977$	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	$0.663188\pi$
$978$	0.870387	−	1.81892i	0.0278319	−	0.0581626i
$979$	27.8711	+	27.8711i	0.890763	+	0.890763i
$980$	44.5431	+	32.7302i	1.42288	+	1.04553i
$981$	1.47742	−	1.47742i	0.0471704	−	0.0471704i
$982$	−57.5734	+	20.3064i	−1.83724	+	0.648004i
$983$	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	$0.0907198\pi$
$984$	0.541474	−	18.0745i	0.0172616	−	0.576195i
$985$	−35.6626	+	61.7695i	−1.13631	+	1.96814i
$986$	−7.87822	+	9.20078i	−0.250894	+	0.293013i
$987$	−2.40513	−	2.41204i	−0.0765562	−	0.0767762i
$988$	11.7739	−	1.83449i	0.374577	−	0.0583628i
$989$	10.6918	−	2.86486i	0.339980	−	0.0910973i
$990$	33.8400	+	49.3703i	1.07551	+	1.56909i
$991$	−16.4220	+	9.48127i	−0.521663	+	0.301183i	−0.737615	−	0.675222i	$-0.764048\pi$
$991$	−16.4220	+	9.48127i	−0.521663	+	0.301183i	0.215952	+	0.976404i	$0.430715\pi$
$992$	3.20527	−	23.2185i	0.101768	−	0.737188i
$993$		−	11.4262i		−	0.362601i
$994$	−3.89559	+	8.11102i	−0.123561	+	0.257266i
$995$	15.3755	−	15.3755i	0.487436	−	0.487436i
$996$	−4.79453	−	1.85428i	−0.151920	−	0.0587552i
$997$	7.83295	−	29.2330i	0.248072	−	0.925818i	−0.723742	−	0.690070i	$-0.757580\pi$
$997$	7.83295	−	29.2330i	0.248072	−	0.925818i	0.971814	−	0.235747i	$-0.0757538\pi$
$998$	−15.3854	−	2.87151i	−0.487015	−	0.0908960i
$999$	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.19.5	yes	56
4.3	odd	2		448.2.z.a.47.8		56
7.2	even	3		784.2.j.a.195.27		56
7.3	odd	6	inner	112.2.v.a.3.6	✓	56
7.4	even	3		784.2.w.f.227.6		56
7.5	odd	6		784.2.j.a.195.28		56
7.6	odd	2		784.2.w.f.19.5		56
8.3	odd	2		896.2.z.a.607.7		56
8.5	even	2		896.2.z.b.607.8		56
16.3	odd	4		896.2.z.b.159.8		56
16.5	even	4		448.2.z.a.271.8		56
16.11	odd	4	inner	112.2.v.a.75.6	yes	56
16.13	even	4		896.2.z.a.159.7		56
28.3	even	6		448.2.z.a.367.8		56
56.3	even	6		896.2.z.a.479.7		56
56.45	odd	6		896.2.z.b.479.8		56
112.3	even	12		896.2.z.b.31.8		56
112.11	odd	12		784.2.w.f.619.5		56
112.27	even	4		784.2.w.f.411.6		56
112.45	odd	12		896.2.z.a.31.7		56
112.59	even	12	inner	112.2.v.a.59.5	yes	56
112.75	even	12		784.2.j.a.587.27		56
112.101	odd	12		448.2.z.a.143.8		56
112.107	odd	12		784.2.j.a.587.28		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.6	✓	56	7.3	odd	6	inner
112.2.v.a.19.5	yes	56	1.1	even	1	trivial
112.2.v.a.59.5	yes	56	112.59	even	12	inner
112.2.v.a.75.6	yes	56	16.11	odd	4	inner
448.2.z.a.47.8		56	4.3	odd	2
448.2.z.a.143.8		56	112.101	odd	12
448.2.z.a.271.8		56	16.5	even	4
448.2.z.a.367.8		56	28.3	even	6
784.2.j.a.195.27		56	7.2	even	3
784.2.j.a.195.28		56	7.5	odd	6
784.2.j.a.587.27		56	112.75	even	12
784.2.j.a.587.28		56	112.107	odd	12
784.2.w.f.19.5		56	7.6	odd	2
784.2.w.f.227.6		56	7.4	even	3
784.2.w.f.411.6		56	112.27	even	4
784.2.w.f.619.5		56	112.11	odd	12
896.2.z.a.31.7		56	112.45	odd	12
896.2.z.a.159.7		56	16.13	even	4
896.2.z.a.479.7		56	56.3	even	6
896.2.z.a.607.7		56	8.3	odd	2
896.2.z.b.31.8		56	112.3	even	12
896.2.z.b.159.8		56	16.3	odd	4
896.2.z.b.479.8		56	56.45	odd	6
896.2.z.b.607.8		56	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-0.610438 + 1.27568i) q^{2} +(-0.204601 + 0.763582i) q^{3} +(-1.25473 - 1.55745i) q^{4} +(-3.81370 + 1.02188i) 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} +(1.02443 - 5.48886i) q^{10} +(-1.16815 + 4.35958i) q^{11} +(1.44596 - 0.639434i) q^{12} +(1.34913 - 1.34913i) q^{13} +(1.61991 - 3.37282i) q^{14} -3.12115i q^{15} +(-0.851298 + 3.90836i) q^{16} +(0.989178 - 0.571102i) q^{17} +(-2.77052 + 1.89901i) q^{18} +(-3.01629 + 0.808212i) q^{19} +(6.37669 + 4.65746i) q^{20} +(0.544222 - 2.01947i) q^{21} +(-4.84836 - 4.15144i) q^{22} +(-1.02392 + 1.77348i) q^{23} +(-0.0669534 + 2.23492i) q^{24} +(9.16994 - 5.29427i) q^{25} +(0.897503 + 2.54463i) q^{26} +(-3.00457 + 3.00457i) q^{27} +(3.31379 + 4.12538i) q^{28} +(5.30239 + 5.30239i) q^{29} +(3.98159 + 1.90527i) q^{30} +(2.07171 + 3.58830i) q^{31} +(-4.46616 - 3.47180i) q^{32} +(-3.08989 - 1.78395i) q^{33} +(0.124713 + 1.61050i) q^{34} +(10.0940 - 2.68915i) q^{35} +(-0.731298 - 4.69353i) q^{36} +(-0.803695 - 2.99943i) q^{37} +(0.810234 - 4.34119i) q^{38} +(0.754139 + 1.30621i) q^{39} +(-9.83402 + 5.29154i) q^{40} -8.08732 q^{41} +(2.24399 + 1.92701i) q^{42} +(-3.82205 - 3.82205i) q^{43} +(8.25554 - 3.65078i) q^{44} +(-9.05785 - 2.42704i) q^{45} +(-1.63736 - 2.38879i) 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} +(0.233696 + 0.872167i) q^{51} +(-3.79400 - 0.408407i) q^{52} +(-2.92499 - 0.783749i) q^{53} +(-1.99877 - 5.66697i) q^{54} -17.8198i q^{55} +(-7.28554 + 1.70906i) q^{56} -2.46854i q^{57} +(-10.0010 + 3.52739i) q^{58} +(6.97383 + 1.86863i) q^{59} +(-4.86103 + 3.91620i) q^{60} +(1.68972 + 6.30611i) 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} +(4.16194 - 2.85273i) q^{66} +(0.616236 + 0.165120i) q^{67} +(-2.13062 - 0.824015i) q^{68} +(-1.14470 - 1.14470i) q^{69} +(-2.73123 + 14.5183i) q^{70} -2.40482 q^{71} +(6.43387 + 1.93221i) q^{72} +(1.47966 + 2.56284i) q^{73} +(4.31693 + 0.805706i) q^{74} +(2.16643 + 8.08521i) q^{75} +(5.04338 + 3.68363i) q^{76} +(3.10717 - 11.5299i) q^{77} +(-2.12666 + 0.164684i) q^{78} +(1.06303 + 0.613742i) q^{79} +(-0.747273 - 15.7752i) q^{80} +(1.88313 + 3.26167i) q^{81} +(4.93681 - 10.3169i) q^{82} +(-2.29910 - 2.29910i) q^{83} +(-3.82807 + 1.68629i) q^{84} +(-3.18883 + 3.18883i) q^{85} +(7.20885 - 2.54260i) q^{86} +(-5.13369 + 2.96394i) q^{87} +(-0.382263 + 12.7600i) q^{88} +(4.36654 - 7.56307i) q^{89} +(8.62539 - 10.0734i) q^{90} +(-3.57459 + 3.56434i) q^{91} +(4.04685 - 0.630538i) q^{92} +(-3.16383 + 0.847747i) q^{93} +(1.30216 + 1.89977i) q^{94} +(10.6773 - 6.16455i) q^{95} +(3.56478 - 2.69995i) q^{96} +8.42967i q^{97} +(-4.29867 + 8.91748i) 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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