LMFDB - Embedded newform 74.2.f.b.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.2
Root			$2.14169 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	74.9
Dual form			74.2.f.b.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.504922 - 2.86356i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.266044 + 0.223238i) q^{5} +2.90773 q^{6} +(0.773586 + 0.649116i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-5.12593 - 1.86569i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.504922 - 2.86356i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.266044 + 0.223238i) q^{5} +2.90773 q^{6} +(0.773586 + 0.649116i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-5.12593 - 1.86569i) q^{9} +(-0.173648 + 0.300767i) q^{10} +(2.73237 + 4.73261i) q^{11} +(0.504922 + 2.86356i) q^{12} +(-5.97892 + 2.17615i) q^{13} +(-0.504922 + 0.874551i) q^{14} +(0.773586 - 0.649116i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.490749 - 0.178618i) q^{17} +(0.947234 - 5.37203i) q^{18} +(0.869950 - 4.93373i) q^{19} +(-0.326352 - 0.118782i) q^{20} +(2.24938 - 1.88745i) q^{21} +(-4.18624 + 3.51267i) q^{22} +(-0.721492 + 1.24966i) q^{23} +(-2.73237 + 0.994503i) q^{24} +(-0.847296 - 4.80526i) q^{25} +(-3.18132 - 5.51020i) q^{26} +(-3.56910 + 6.18186i) q^{27} +(-0.948944 - 0.345387i) q^{28} +(3.16714 + 5.48565i) q^{29} +(0.773586 + 0.649116i) q^{30} +3.30777 q^{31} +(0.766044 + 0.642788i) q^{32} +(14.9317 - 5.43471i) q^{33} +(0.0906868 - 0.514310i) q^{34} +(0.0609011 + 0.345387i) q^{35} +5.45490 q^{36} +(-5.88521 + 1.53765i) q^{37} +5.00984 q^{38} +(3.21264 + 18.2198i) q^{39} +(0.0603074 - 0.342020i) q^{40} +(1.03412 - 0.376390i) q^{41} +(2.24938 + 1.88745i) q^{42} -6.27037 q^{43} +(-4.18624 - 3.51267i) q^{44} +(-0.947234 - 1.64066i) q^{45} +(-1.35596 - 0.493529i) q^{46} +(5.71910 - 9.90577i) q^{47} +(-1.45387 - 2.51817i) q^{48} +(-1.03845 - 5.88936i) q^{49} +(4.58512 - 1.66885i) q^{50} +(-0.759273 + 1.31510i) q^{51} +(4.87406 - 4.08982i) q^{52} +(0.0706817 - 0.0593090i) q^{53} +(-6.70771 - 2.44141i) q^{54} +(-0.329565 + 1.86905i) q^{55} +(0.175358 - 0.994503i) q^{56} +(-13.6888 - 4.98230i) q^{57} +(-4.85235 + 4.07160i) q^{58} +(2.29059 - 1.92203i) q^{59} +(-0.504922 + 0.874551i) q^{60} +(-3.58571 + 1.30509i) q^{61} +(0.574388 + 3.25751i) q^{62} +(-2.75430 - 4.77059i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.07646 - 0.755769i) q^{65} +(7.94501 + 13.7612i) q^{66} +(-0.892251 - 0.748687i) q^{67} +0.522244 q^{68} +(3.21418 + 2.69701i) q^{69} +(-0.329565 + 0.119952i) q^{70} +(0.0543332 - 0.308139i) q^{71} +(0.947234 + 5.37203i) q^{72} +13.2325 q^{73} +(-2.53624 - 5.52879i) q^{74} -14.1879 q^{75} +(0.869950 + 4.93373i) q^{76} +(-0.958285 + 5.43471i) q^{77} +(-17.3851 + 6.32766i) q^{78} +(7.12939 + 5.98227i) q^{79} +0.347296 q^{80} +(3.36390 + 2.82265i) q^{81} +(0.550245 + 0.953052i) q^{82} +(-8.89395 - 3.23713i) q^{83} +(-1.46818 + 2.54296i) q^{84} +(-0.0906868 - 0.157074i) q^{85} +(-1.08884 - 6.17511i) q^{86} +(17.3076 - 6.29947i) q^{87} +(2.73237 - 4.73261i) q^{88} +(-12.0788 + 10.1354i) q^{89} +(1.45125 - 1.21774i) q^{90} +(-6.03778 - 2.19757i) q^{91} +(0.250571 - 1.42106i) q^{92} +(1.67017 - 9.47198i) q^{93} +(10.7484 + 3.91209i) q^{94} +(1.33284 - 1.11839i) q^{95} +(2.22745 - 1.86905i) q^{96} +(0.464564 - 0.804648i) q^{97} +(5.61956 - 2.04535i) q^{98} +(-5.17640 - 29.3568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.504922	−	2.86356i	0.291517	−	1.65328i	−0.389514	−	0.921021i	$-0.627357\pi$
$3$	0.504922	−	2.86356i	0.291517	−	1.65328i	0.681031	−	0.732255i	$-0.261532\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.266044	+	0.223238i	0.118979	+	0.0998350i	0.700336	−	0.713814i	$-0.253034\pi$
$5$	0.266044	+	0.223238i	0.118979	+	0.0998350i	−0.581357	+	0.813649i	$0.697478\pi$
$6$	2.90773			1.18708
$7$	0.773586	+	0.649116i	0.292388	+	0.245343i	0.777168	−	0.629294i	$-0.216656\pi$
$7$	0.773586	+	0.649116i	0.292388	+	0.245343i	−0.484780	+	0.874636i	$0.661100\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−5.12593	−	1.86569i	−1.70864	−	0.621896i
$10$	−0.173648	+	0.300767i	−0.0549124	+	0.0951110i
$11$	2.73237	+	4.73261i	0.823842	+	1.42694i	0.902801	+	0.430058i	$0.141507\pi$
$11$	2.73237	+	4.73261i	0.823842	+	1.42694i	−0.0789595	+	0.996878i	$0.525160\pi$
$12$	0.504922	+	2.86356i	0.145759	+	0.826638i
$13$	−5.97892	+	2.17615i	−1.65825	+	0.603555i	−0.990087	−	0.140456i	$-0.955143\pi$
$13$	−5.97892	+	2.17615i	−1.65825	+	0.603555i	−0.668167	+	0.744011i	$0.732921\pi$
$14$	−0.504922	+	0.874551i	−0.134946	+	0.233734i
$15$	0.773586	−	0.649116i	0.199739	−	0.167601i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.490749	−	0.178618i	−0.119024	−	0.0433212i	0.281821	−	0.959467i	$-0.409061\pi$
$17$	−0.490749	−	0.178618i	−0.119024	−	0.0433212i	−0.400846	+	0.916146i	$0.631284\pi$
$18$	0.947234	−	5.37203i	0.223265	−	1.26620i
$19$	0.869950	−	4.93373i	0.199580	−	1.13188i	−0.706163	−	0.708049i	$-0.749575\pi$
$19$	0.869950	−	4.93373i	0.199580	−	1.13188i	0.905743	−	0.423827i	$-0.139313\pi$
$20$	−0.326352	−	0.118782i	−0.0729745	−	0.0265605i
$21$	2.24938	−	1.88745i	0.490855	−	0.411876i
$22$	−4.18624	+	3.51267i	−0.892509	+	0.748904i
$23$	−0.721492	+	1.24966i	−0.150441	+	0.260572i	−0.931390	−	0.364023i	$-0.881403\pi$
$23$	−0.721492	+	1.24966i	−0.150441	+	0.260572i	0.780948	+	0.624596i	$0.214736\pi$
$24$	−2.73237	+	0.994503i	−0.557744	+	0.203002i
$25$	−0.847296	−	4.80526i	−0.169459	−	0.961051i
$26$	−3.18132	−	5.51020i	−0.623908	−	1.08064i
$27$	−3.56910	+	6.18186i	−0.686874	+	1.18970i
$28$	−0.948944	−	0.345387i	−0.179333	−	0.0652720i
$29$	3.16714	+	5.48565i	0.588124	+	1.01866i	0.994478	+	0.104945i	$0.0334666\pi$
$29$	3.16714	+	5.48565i	0.588124	+	1.01866i	−0.406354	+	0.913716i	$0.633200\pi$
$30$	0.773586	+	0.649116i	0.141237	+	0.118512i
$31$	3.30777			0.594092			0.297046	−	0.954863i	$-0.403998\pi$
$31$	3.30777			0.594092			0.297046	+	0.954863i	$0.403998\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	14.9317	−	5.43471i	2.59928	−	0.946061i
$34$	0.0906868	−	0.514310i	0.0155527	−	0.0882035i
$35$	0.0609011	+	0.345387i	0.0102942	+	0.0583811i
$36$	5.45490			0.909151
$37$	−5.88521	+	1.53765i	−0.967522	+	0.252787i
$37$	−5.88521	+	1.53765i	−0.967522	+	0.252787i
$38$	5.00984			0.812704
$39$	3.21264	+	18.2198i	0.514434	+	2.91750i
$40$	0.0603074	−	0.342020i	0.00953543	−	0.0540781i
$41$	1.03412	−	0.376390i	0.161503	−	0.0587822i	−0.260004	−	0.965608i	$-0.583724\pi$
$41$	1.03412	−	0.376390i	0.161503	−	0.0587822i	0.421506	+	0.906825i	$0.361502\pi$
$42$	2.24938	+	1.88745i	0.347087	+	0.291240i
$43$	−6.27037			−0.956222			−0.478111	−	0.878299i	$-0.658678\pi$
$43$	−6.27037			−0.956222			−0.478111	+	0.878299i	$0.658678\pi$
$44$	−4.18624	−	3.51267i	−0.631099	−	0.529555i
$45$	−0.947234	−	1.64066i	−0.141205	−	0.244575i
$46$	−1.35596	−	0.493529i	−0.199926	−	0.0727670i
$47$	5.71910	−	9.90577i	0.834216	−	1.44491i	−0.0604506	−	0.998171i	$-0.519254\pi$
$47$	5.71910	−	9.90577i	0.834216	−	1.44491i	0.894667	−	0.446734i	$-0.147413\pi$
$48$	−1.45387	−	2.51817i	−0.209847	−	0.363466i
$49$	−1.03845	−	5.88936i	−0.148350	−	0.841337i
$50$	4.58512	−	1.66885i	0.648434	−	0.236011i
$51$	−0.759273	+	1.31510i	−0.106320	+	0.184151i
$52$	4.87406	−	4.08982i	0.675911	−	0.567156i
$53$	0.0706817	−	0.0593090i	0.00970887	−	0.00814671i	−0.637920	−	0.770102i	$-0.720205\pi$
$53$	0.0706817	−	0.0593090i	0.00970887	−	0.00814671i	0.647629	+	0.761956i	$0.275761\pi$
$54$	−6.70771	−	2.44141i	−0.912804	−	0.332234i
$55$	−0.329565	+	1.86905i	−0.0444385	+	0.252023i
$56$	0.175358	−	0.994503i	0.0234332	−	0.132896i
$57$	−13.6888	−	4.98230i	−1.81312	−	0.659922i
$58$	−4.85235	+	4.07160i	−0.637144	+	0.534628i
$59$	2.29059	−	1.92203i	0.298210	−	0.250228i	−0.481389	−	0.876507i	$-0.659868\pi$
$59$	2.29059	−	1.92203i	0.298210	−	0.250228i	0.779599	+	0.626279i	$0.215423\pi$
$60$	−0.504922	+	0.874551i	−0.0651852	+	0.112904i
$61$	−3.58571	+	1.30509i	−0.459103	+	0.167100i	−0.561210	−	0.827674i	$-0.689664\pi$
$61$	−3.58571	+	1.30509i	−0.459103	+	0.167100i	0.102107	+	0.994773i	$0.467442\pi$
$62$	0.574388	+	3.25751i	0.0729473	+	0.413705i
$63$	−2.75430	−	4.77059i	−0.347009	−	0.601038i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.07646	−	0.755769i	−0.257553	−	0.0937416i
$66$	7.94501	+	13.7612i	0.977963	+	1.69388i
$67$	−0.892251	−	0.748687i	−0.109006	−	0.0914667i	0.586656	−	0.809836i	$-0.300444\pi$
$67$	−0.892251	−	0.748687i	−0.109006	−	0.0914667i	−0.695662	+	0.718370i	$0.744889\pi$
$68$	0.522244			0.0633314
$69$	3.21418	+	2.69701i	0.386941	+	0.324682i
$70$	−0.329565	+	0.119952i	−0.0393905	+	0.0143370i
$71$	0.0543332	−	0.308139i	0.00644816	−	0.0365693i	−0.981414	−	0.191903i	$-0.938534\pi$
$71$	0.0543332	−	0.308139i	0.00644816	−	0.0365693i	0.987862	+	0.155334i	$0.0496452\pi$
$72$	0.947234	+	5.37203i	0.111633	+	0.633100i
$73$	13.2325			1.54875			0.774376	−	0.632726i	$-0.218064\pi$
$73$	13.2325			1.54875			0.774376	+	0.632726i	$0.218064\pi$
$74$	−2.53624	−	5.52879i	−0.294832	−	0.642708i
$75$	−14.1879			−1.63828
$76$	0.869950	+	4.93373i	0.0997902	+	0.565938i
$77$	−0.958285	+	5.43471i	−0.109207	+	0.619342i
$78$	−17.3851	+	6.32766i	−1.96847	+	0.716466i
$79$	7.12939	+	5.98227i	0.802119	+	0.673058i	0.948713	−	0.316139i	$-0.102387\pi$
$79$	7.12939	+	5.98227i	0.802119	+	0.673058i	−0.146594	+	0.989197i	$0.546831\pi$
$80$	0.347296			0.0388289
$81$	3.36390	+	2.82265i	0.373767	+	0.313628i
$82$	0.550245	+	0.953052i	0.0607644	+	0.105247i
$83$	−8.89395	−	3.23713i	−0.976238	−	0.355322i	−0.195862	−	0.980632i	$-0.562750\pi$
$83$	−8.89395	−	3.23713i	−0.976238	−	0.355322i	−0.780377	+	0.625310i	$0.784973\pi$
$84$	−1.46818	+	2.54296i	−0.160191	+	0.277460i
$85$	−0.0906868	−	0.157074i	−0.00983636	−	0.0170371i
$86$	−1.08884	−	6.17511i	−0.117412	−	0.665879i
$87$	17.3076	−	6.29947i	1.85557	−	0.675374i
$88$	2.73237	−	4.73261i	0.291272	−	0.504498i
$89$	−12.0788	+	10.1354i	−1.28035	+	1.07435i	−0.287160	+	0.957883i	$0.592711\pi$
$89$	−12.0788	+	10.1354i	−1.28035	+	1.07435i	−0.993195	+	0.116463i	$0.962844\pi$
$90$	1.45125	−	1.21774i	0.152975	−	0.128361i
$91$	−6.03778	−	2.19757i	−0.632931	−	0.230368i
$92$	0.250571	−	1.42106i	0.0261239	−	0.148156i
$93$	1.67017	−	9.47198i	0.173188	−	0.982198i
$94$	10.7484	+	3.91209i	1.10861	+	0.403502i
$95$	1.33284	−	1.11839i	0.136747	−	0.114744i
$96$	2.22745	−	1.86905i	0.227338	−	0.190760i
$97$	0.464564	−	0.804648i	0.0471693	−	0.0816997i	−0.841477	−	0.540293i	$-0.818313\pi$
$97$	0.464564	−	0.804648i	0.0471693	−	0.0816997i	0.888646	+	0.458594i	$0.151647\pi$
$98$	5.61956	−	2.04535i	0.567662	−	0.206612i
$99$	−5.17640	−	29.3568i	−0.520247	−	2.95047i
$100$	2.43969	+	4.22567i	0.243969	+	0.422567i
$101$	−4.28093	+	7.41479i	−0.425969	+	0.737799i	−0.996510	−	0.0834694i	$-0.973400\pi$
$101$	−4.28093	+	7.41479i	−0.425969	+	0.737799i	0.570542	+	0.821269i	$0.306733\pi$
$102$	−1.42697	−	0.519373i	−0.141291	−	0.0514256i
$103$	−2.47956	−	4.29473i	−0.244319	−	0.423172i	0.717621	−	0.696434i	$-0.245231\pi$
$103$	−2.47956	−	4.29473i	−0.244319	−	0.423172i	−0.961940	+	0.273261i	$0.911898\pi$
$104$	4.87406	+	4.08982i	0.477941	+	0.401040i
$105$	1.01979			0.0995209
$106$	0.0706817	+	0.0593090i	0.00686521	+	0.00576059i
$107$	3.35307	−	1.22042i	0.324153	−	0.117982i	−0.174818	−	0.984601i	$-0.555934\pi$
$107$	3.35307	−	1.22042i	0.324153	−	0.117982i	0.498971	+	0.866619i	$0.333711\pi$
$108$	1.23954	−	7.02975i	0.119274	−	0.676438i
$109$	−0.169947	−	0.963819i	−0.0162780	−	0.0923171i	0.975586	−	0.219616i	$-0.0704804\pi$
$109$	−0.169947	−	0.963819i	−0.0162780	−	0.0923171i	−0.991864	+	0.127299i	$0.959369\pi$
$110$	−1.89789			−0.180956
$111$	1.43157	+	17.6290i	0.135878	+	1.67327i
$112$	1.00984			0.0954213
$113$	1.60399	+	9.09669i	0.150891	+	0.855745i	0.962447	+	0.271470i	$0.0875098\pi$
$113$	1.60399	+	9.09669i	0.150891	+	0.855745i	−0.811556	+	0.584275i	$0.801379\pi$
$114$	2.52958	−	14.3460i	0.236917	−	1.34362i
$115$	−0.470920	+	0.171401i	−0.0439136	+	0.0159832i
$116$	−4.85235	−	4.07160i	−0.450529	−	0.378039i
$117$	34.7076			3.20871
$118$	2.29059	+	1.92203i	0.210866	+	0.176938i
$119$	−0.263693	−	0.456729i	−0.0241727	−	0.0418683i
$120$	−0.948944	−	0.345387i	−0.0866263	−	0.0315294i
$121$	−9.43174	+	16.3362i	−0.857430	+	1.48511i
$122$	−1.90792	−	3.30461i	−0.172735	−	0.299185i
$123$	−0.555662	−	3.15132i	−0.0501023	−	0.284145i
$124$	−3.10828	+	1.13132i	−0.279132	+	0.101596i
$125$	1.71554	−	2.97140i	0.153442	−	0.265770i
$126$	4.21984	−	3.54086i	0.375933	−	0.315445i
$127$	5.18728	−	4.35264i	0.460296	−	0.386235i	−0.382944	−	0.923772i	$-0.625090\pi$
$127$	5.18728	−	4.35264i	0.460296	−	0.386235i	0.843240	+	0.537537i	$0.180645\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−3.16605	+	17.9556i	−0.278755	+	1.58090i
$130$	0.383714	−	2.17615i	0.0336539	−	0.190861i
$131$	14.2349	+	5.18108i	1.24371	+	0.452673i	0.878271	−	0.478163i	$-0.158697\pi$
$131$	14.2349	+	5.18108i	1.24371	+	0.452673i	0.365438	+	0.930836i	$0.380919\pi$
$132$	−12.1725	+	10.2139i	−1.05948	+	0.889007i
$133$	3.87554	−	3.25197i	0.336052	−	0.281981i
$134$	0.582375	−	1.00870i	0.0503096	−	0.0871387i
$135$	−2.32956	+	0.847892i	−0.200497	+	0.0729749i
$136$	0.0906868	+	0.514310i	0.00777633	+	0.0441017i
$137$	4.24086	+	7.34539i	0.362321	+	0.627559i	0.988342	−	0.152247i	$-0.0486510\pi$
$137$	4.24086	+	7.34539i	0.362321	+	0.627559i	−0.626021	+	0.779806i	$0.715318\pi$
$138$	−2.09790	+	3.63368i	−0.178586	+	0.309319i
$139$	17.2324	+	6.27209i	1.46164	+	0.531992i	0.945815	−	0.324705i	$-0.105265\pi$
$139$	17.2324	+	6.27209i	1.46164	+	0.531992i	0.515820	+	0.856697i	$0.327487\pi$
$140$	−0.175358	−	0.303728i	−0.0148204	−	0.0256697i
$141$	−25.4780	−	21.3786i	−2.14564	−	1.80040i
$142$	0.312892			0.0262573
$143$	−26.6355	−	22.3499i	−2.22737	−	1.86899i
$144$	−5.12593	+	1.86569i	−0.427161	+	0.155474i
$145$	−0.382004	+	2.16645i	−0.0317237	+	0.179914i
$146$	2.29781	+	13.0315i	0.190168	+	1.07850i
$147$	−17.3889			−1.43421
$148$	5.00438	−	3.45777i	0.411357	−	0.284227i
$149$	5.45291			0.446720			0.223360	−	0.974736i	$-0.428297\pi$
$149$	5.45291			0.446720			0.223360	+	0.974736i	$0.428297\pi$
$150$	−2.46371	−	13.9724i	−0.201161	−	1.14084i
$151$	−2.70116	+	15.3190i	−0.219817	+	1.24665i	0.652531	+	0.757762i	$0.273707\pi$
$151$	−2.70116	+	15.3190i	−0.219817	+	1.24665i	−0.872349	+	0.488884i	$0.837404\pi$
$152$	−4.70771	+	1.71347i	−0.381846	+	0.138981i
$153$	2.18230	+	1.83117i	0.176429	+	0.148041i
$154$	−5.51855			−0.444697
$155$	0.880013	+	0.738419i	0.0706843	+	0.0593112i
$156$	−9.25042	−	16.0222i	−0.740626	−	1.28280i
$157$	3.76650	+	1.37089i	0.300599	+	0.109409i	0.487916	−	0.872890i	$-0.337757\pi$
$157$	3.76650	+	1.37089i	0.300599	+	0.109409i	−0.187317	+	0.982299i	$0.559979\pi$
$158$	−4.65338	+	8.05989i	−0.370203	+	0.641211i
$159$	−0.134146	−	0.232347i	−0.0106385	−	0.0184263i
$160$	0.0603074	+	0.342020i	0.00476772	+	0.0270391i
$161$	−1.36931	+	0.498388i	−0.107917	+	0.0392785i
$162$	−2.19563	+	3.80294i	−0.172505	+	0.298787i
$163$	3.59446	−	3.01611i	0.281540	−	0.236240i	−0.491072	−	0.871119i	$-0.663395\pi$
$163$	3.59446	−	3.01611i	0.281540	−	0.236240i	0.772611	+	0.634879i	$0.218950\pi$
$164$	−0.843024	+	0.707381i	−0.0658291	+	0.0552372i
$165$	5.18574	+	1.88745i	0.403709	+	0.146938i
$166$	1.64354	−	9.32096i	0.127563	−	0.723447i
$167$	−0.134923	+	0.765189i	−0.0104407	+	0.0592121i	−0.989583	−	0.143964i	$-0.954015\pi$
$167$	−0.134923	+	0.765189i	−0.0104407	+	0.0592121i	0.979142	+	0.203176i	$0.0651263\pi$
$168$	−2.75927	−	1.00429i	−0.212883	−	0.0774829i
$169$	21.0533	−	17.6658i	1.61948	−	1.35891i
$170$	0.138940	−	0.116585i	0.0106562	−	0.00894164i
$171$	−13.6641	+	23.6669i	−1.04492	+	1.80986i
$172$	5.89222	−	2.14459i	0.449277	−	0.163524i
$173$	1.86383	+	10.5703i	0.141704	+	0.803644i	0.969955	+	0.243286i	$0.0782253\pi$
$173$	1.86383	+	10.5703i	0.141704	+	0.803644i	−0.828251	+	0.560358i	$0.810664\pi$
$174$	9.20921	+	15.9508i	0.698148	+	1.20923i
$175$	2.46371	−	4.26727i	0.186239	−	0.322575i
$176$	5.13518	+	1.86905i	0.387079	+	0.140885i
$177$	−4.34728	−	7.52972i	−0.326762	−	0.565968i
$178$	−12.0788	−	10.1354i	−0.905348	−	0.759677i
$179$	−11.8976			−0.889267			−0.444633	−	0.895713i	$-0.646666\pi$
$179$	−11.8976			−0.889267			−0.444633	+	0.895713i	$0.646666\pi$
$180$	1.45125	+	1.21774i	0.108170	+	0.0907650i
$181$	−4.12213	+	1.50033i	−0.306395	+	0.111519i	−0.490642	−	0.871361i	$-0.663238\pi$
$181$	−4.12213	+	1.50033i	−0.306395	+	0.111519i	0.184247	+	0.982880i	$0.441015\pi$
$182$	1.11574	−	6.32766i	0.0827039	−	0.469037i
$183$	1.92670	+	10.9268i	0.142426	+	0.807736i
$184$	1.44298			0.106378
$185$	−1.90899	−	0.904718i	−0.140352	−	0.0665162i
$186$	9.61810			0.705233
$187$	−0.495580	−	2.81058i	−0.0362404	−	0.205530i
$188$	−1.98622	+	11.2644i	−0.144860	+	0.821543i
$189$	−6.77375	+	2.46544i	−0.492718	+	0.179335i
$190$	1.33284	+	1.11839i	0.0966945	+	0.0811363i
$191$	−10.4903			−0.759053			−0.379527	−	0.925181i	$-0.623913\pi$
$191$	−10.4903			−0.759053			−0.379527	+	0.925181i	$0.623913\pi$
$192$	2.22745	+	1.86905i	0.160752	+	0.134887i
$193$	−4.91474	−	8.51259i	−0.353771	−	0.612749i	0.633136	−	0.774041i	$-0.281767\pi$
$193$	−4.91474	−	8.51259i	−0.353771	−	0.612749i	−0.986907	+	0.161291i	$0.948434\pi$
$194$	0.873095	+	0.317780i	0.0626845	+	0.0228153i
$195$	−3.21264	+	5.56445i	−0.230062	+	0.398478i
$196$	2.99011	+	5.17902i	0.213579	+	0.369930i
$197$	−2.09473	−	11.8798i	−0.149244	−	0.846402i	−0.963861	−	0.266404i	$-0.914164\pi$
$197$	−2.09473	−	11.8798i	−0.149244	−	0.846402i	0.814618	−	0.579998i	$-0.196947\pi$
$198$	28.0119	−	10.1955i	1.99072	−	0.724563i
$199$	4.64995	−	8.05395i	0.329626	−	0.570929i	−0.652811	−	0.757520i	$-0.726411\pi$
$199$	4.64995	−	8.05395i	0.329626	−	0.570929i	0.982438	+	0.186591i	$0.0597439\pi$
$200$	−3.73783	+	3.13641i	−0.264304	+	0.221778i
$201$	−2.59443	+	2.17698i	−0.182997	+	0.153552i
$202$	−8.04552	−	2.92833i	−0.566081	−	0.206037i
$203$	−1.11077	+	6.29947i	−0.0779605	+	0.442136i
$204$	0.263693	−	1.49548i	0.0184622	−	0.104704i
$205$	0.359147	+	0.130719i	0.0250839	+	0.00912980i
$206$	3.79891	−	3.18767i	0.264683	−	0.222095i
$207$	6.02979	−	5.05960i	0.419100	−	0.351666i
$208$	−3.18132	+	5.51020i	−0.220585	+	0.382064i
$209$	25.7265	−	9.36367i	1.77954	−	0.647699i
$210$	0.177084	+	1.00429i	0.0122200	+	0.0693028i
$211$	2.20002	+	3.81054i	0.151455	+	0.262329i	0.931763	−	0.363068i	$-0.118271\pi$
$211$	2.20002	+	3.81054i	0.151455	+	0.262329i	−0.780307	+	0.625396i	$0.784937\pi$
$212$	−0.0461342	+	0.0799067i	−0.00316851	+	0.00548802i
$213$	−0.854939	−	0.311172i	−0.0585794	−	0.0213212i
$214$	1.78413	+	3.09020i	0.121961	+	0.211242i
$215$	−1.66820	−	1.39978i	−0.113770	−	0.0954644i
$216$	7.13820			0.485693
$217$	2.55884	+	2.14712i	0.173705	+	0.145756i
$218$	0.919666	−	0.334731i	0.0622876	−	0.0226708i
$219$	6.68141	−	37.8921i	0.451488	−	2.56051i
$220$	−0.329565	−	1.86905i	−0.0222192	−	0.126012i
$221$	3.32285			0.223519
$222$	−17.1126	+	4.47106i	−1.14852	+	0.300078i
$223$	11.2311			0.752092			0.376046	−	0.926601i	$-0.377283\pi$
$223$	11.2311			0.752092			0.376046	+	0.926601i	$0.377283\pi$
$224$	0.175358	+	0.994503i	0.0117166	+	0.0664480i
$225$	−4.62192	+	26.2122i	−0.308128	+	1.74748i
$226$	−8.67996	+	3.15925i	−0.577382	+	0.210150i
$227$	−11.6086	−	9.74076i	−0.770489	−	0.646517i	0.170345	−	0.985384i	$-0.445512\pi$
$227$	−11.6086	−	9.74076i	−0.770489	−	0.646517i	−0.940834	+	0.338868i	$0.889956\pi$
$228$	14.5673			0.964742
$229$	−11.9210	−	10.0029i	−0.787759	−	0.661008i	0.157431	−	0.987530i	$-0.449679\pi$
$229$	−11.9210	−	10.0029i	−0.787759	−	0.661008i	−0.945190	+	0.326522i	$0.894123\pi$
$230$	−0.250571	−	0.434003i	−0.0165222	−	0.0286173i
$231$	15.0787	+	5.48821i	0.992108	+	0.361098i
$232$	3.16714	−	5.48565i	0.207933	−	0.360151i
$233$	−6.79356	−	11.7668i	−0.445061	−	0.770868i	0.552995	−	0.833184i	$-0.313485\pi$
$233$	−6.79356	−	11.7668i	−0.445061	−	0.770868i	−0.998056	+	0.0623159i	$0.980151\pi$
$234$	6.02690	+	34.1803i	0.393991	+	2.23443i
$235$	3.73288	−	1.35866i	0.243506	−	0.0886289i
$236$	−1.49508	+	2.58955i	−0.0973213	+	0.168565i
$237$	20.7304	−	17.3948i	1.34658	−	1.12992i
$238$	0.404001	−	0.338997i	0.0261875	−	0.0219739i
$239$	18.3188	+	6.66750i	1.18494	+	0.431285i	0.857946	−	0.513740i	$-0.171740\pi$
$239$	18.3188	+	6.66750i	1.18494	+	0.431285i	0.326999	+	0.945025i	$0.393963\pi$
$240$	0.175358	−	0.994503i	0.0113193	−	0.0641949i
$241$	0.250684	−	1.42170i	0.0161480	−	0.0915797i	−0.975669	−	0.219250i	$-0.929639\pi$
$241$	0.250684	−	1.42170i	0.0161480	−	0.0915797i	0.991817	+	0.127671i	$0.0407500\pi$
$242$	−17.7259	−	6.45169i	−1.13946	−	0.414730i
$243$	−6.62322	+	5.55754i	−0.424879	+	0.356516i
$244$	2.92310	−	2.45277i	0.187132	−	0.157022i
$245$	1.03845	−	1.79865i	0.0663443	−	0.114912i
$246$	3.00695	−	1.09444i	0.191716	−	0.0697790i
$247$	5.53518	+	31.3915i	0.352195	+	1.99740i
$248$	−1.65388	−	2.86461i	−0.105022	−	0.181903i
$249$	−13.7605	+	23.8338i	−0.872035	+	1.51041i
$250$	3.22416	+	1.17350i	0.203913	+	0.0742184i
$251$	−5.03646	−	8.72340i	−0.317898	−	0.550616i	0.662151	−	0.749371i	$-0.269644\pi$
$251$	−5.03646	−	8.72340i	−0.317898	−	0.550616i	−0.980049	+	0.198754i	$0.936310\pi$
$252$	4.21984	+	3.54086i	0.265825	+	0.223053i
$253$	−7.88554			−0.495760
$254$	5.18728	+	4.35264i	0.325479	+	0.273109i
$255$	−0.495580	+	0.180376i	−0.0310344	+	0.0112956i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.21293	−	6.87888i	−0.0756607	−	0.429093i	−0.998984	−	0.0450692i	$-0.985649\pi$
$257$	−1.21293	−	6.87888i	−0.0756607	−	0.429093i	0.923323	−	0.384024i	$-0.125462\pi$
$258$	−18.2325			−1.13511
$259$	−5.55082	−	2.63068i	−0.344911	−	0.163462i
$260$	2.20972			0.137041
$261$	−6.00005	−	34.0280i	−0.371394	−	2.10628i
$262$	−2.63050	+	14.9183i	−0.162513	+	0.921657i
$263$	−2.50225	+	0.910746i	−0.154296	+	0.0561590i	−0.418013	−	0.908441i	$-0.637273\pi$
$263$	−2.50225	+	0.910746i	−0.154296	+	0.0561590i	0.263718	+	0.964600i	$0.415051\pi$
$264$	−12.1725	−	10.2139i	−0.749163	−	0.628623i
$265$	0.0320445			0.00196848
$266$	3.87554	+	3.25197i	0.237625	+	0.199391i
$267$	22.9243	+	39.7060i	1.40294	+	2.42997i
$268$	1.09451	+	0.398368i	0.0668577	+	0.0243342i
$269$	−1.20752	+	2.09148i	−0.0736236	+	0.127520i	−0.900487	−	0.434883i	$-0.856790\pi$
$269$	−1.20752	+	2.09148i	−0.0736236	+	0.127520i	0.826863	+	0.562403i	$0.190123\pi$
$270$	−1.23954	−	2.14694i	−0.0754357	−	0.130659i
$271$	−4.38472	−	24.8670i	−0.266353	−	1.51056i	−0.765156	−	0.643845i	$-0.777338\pi$
$271$	−4.38472	−	24.8670i	−0.266353	−	1.51056i	0.498803	−	0.866715i	$-0.333773\pi$
$272$	−0.490749	+	0.178618i	−0.0297560	+	0.0108303i
$273$	−9.34148	+	16.1799i	−0.565372	+	0.979254i
$274$	−6.49738	+	5.45195i	−0.392521	+	0.329364i
$275$	20.4263	−	17.1397i	1.23175	−	1.03356i
$276$	−3.94277	−	1.43505i	−0.237327	−	0.0863799i
$277$	−3.07913	+	17.4626i	−0.185007	+	1.04923i	0.740940	+	0.671571i	$0.234380\pi$
$277$	−3.07913	+	17.4626i	−0.185007	+	1.04923i	−0.925947	+	0.377654i	$0.876731\pi$
$278$	−3.18442	+	18.0598i	−0.190989	+	1.08315i
$279$	−16.9554	−	6.17126i	−1.01509	−	0.369464i
$280$	0.268664	−	0.225435i	0.0160557	−	0.0134723i
$281$	15.1288	−	12.6946i	0.902511	−	0.757297i	−0.0681682	−	0.997674i	$-0.521715\pi$
$281$	15.1288	−	12.6946i	0.902511	−	0.757297i	0.970680	+	0.240377i	$0.0772710\pi$
$282$	16.6296	−	28.8033i	0.990279	−	1.71521i
$283$	−22.8810	+	8.32799i	−1.36013	+	0.495047i	−0.916095	−	0.400961i	$-0.868676\pi$
$283$	−22.8810	+	8.32799i	−1.36013	+	0.495047i	−0.444037	+	0.896009i	$0.646454\pi$
$284$	0.0543332	+	0.308139i	0.00322408	+	0.0182847i
$285$	−2.52958	−	4.38137i	−0.149840	−	0.259530i
$286$	17.3851	−	30.1119i	1.02800	−	1.78055i
$287$	1.04430	+	0.380095i	0.0616432	+	0.0224363i
$288$	−2.72745	−	4.72408i	−0.160717	−	0.278369i
$289$	−12.8138	−	10.7521i	−0.753754	−	0.632475i
$290$	−2.19988			−0.129181
$291$	−2.06959	−	1.73659i	−0.121321	−	0.101801i
$292$	−12.4345	+	4.52580i	−0.727675	+	0.264852i
$293$	−4.03707	+	22.8954i	−0.235848	+	1.33756i	0.604972	+	0.796247i	$0.293184\pi$
$293$	−4.03707	+	22.8954i	−0.235848	+	1.33756i	−0.840820	+	0.541315i	$0.817927\pi$
$294$	−3.01954	−	17.1247i	−0.176103	−	0.998732i
$295$	1.03847			0.0604621
$296$	4.27424	+	4.32791i	0.248435	+	0.251555i
$297$	−39.0085			−2.26350
$298$	0.946888	+	5.37007i	0.0548518	+	0.311080i
$299$	1.59429	−	9.04170i	0.0922005	−	0.522895i
$300$	13.3323	−	4.85256i	0.769741	−	0.280163i
$301$	−4.85067	−	4.07019i	−0.279588	−	0.234602i
$302$	−15.5554			−0.895111
$303$	19.0711	+	16.0026i	1.09561	+	0.919324i
$304$	−2.50492	−	4.33865i	−0.143667	−	0.248839i
$305$	−1.24530	−	0.453253i	−0.0713059	−	0.0259532i
$306$	−1.42440	+	2.46713i	−0.0814273	+	0.141036i
$307$	5.33508	+	9.24063i	0.304489	+	0.527391i	0.977147	−	0.212563i	$-0.0681809\pi$
$307$	5.33508	+	9.24063i	0.304489	+	0.527391i	−0.672658	+	0.739953i	$0.734848\pi$
$308$	−0.958285	−	5.43471i	−0.0546034	−	0.309671i
$309$	−13.5502	+	4.93187i	−0.770843	+	0.280564i
$310$	−0.574388	+	0.994869i	−0.0326230	+	0.0565047i
$311$	13.0382	−	10.9403i	0.739326	−	0.620368i	−0.193330	−	0.981134i	$-0.561929\pi$
$311$	13.0382	−	10.9403i	0.739326	−	0.620368i	0.932657	+	0.360765i	$0.117484\pi$
$312$	14.1725	−	11.8921i	0.802358	−	0.673258i
$313$	−10.2525	−	3.73159i	−0.579503	−	0.210922i	0.0356035	−	0.999366i	$-0.488665\pi$
$313$	−10.2525	−	3.73159i	−0.579503	−	0.210922i	−0.615106	+	0.788444i	$0.710887\pi$
$314$	−0.696020	+	3.94733i	−0.0392787	+	0.222761i
$315$	0.332210	−	1.88405i	0.0187179	−	0.106154i
$316$	−8.74550	−	3.18310i	−0.491973	−	0.179063i
$317$	−22.0930	+	18.5382i	−1.24086	+	1.04121i	−0.243409	+	0.969924i	$0.578266\pi$
$317$	−22.0930	+	18.5382i	−1.24086	+	1.04121i	−0.997456	+	0.0712854i	$0.977290\pi$
$318$	0.205523	−	0.172455i	0.0115252	−	0.00967077i
$319$	−17.3076	+	29.9777i	−0.969042	+	1.67843i
$320$	−0.326352	+	0.118782i	−0.0182436	+	0.00664014i
$321$	−1.80169	−	10.2179i	−0.100561	−	0.570308i
$322$	−0.728595	−	1.26196i	−0.0406030	−	0.0703264i
$323$	−1.30818	+	2.26584i	−0.0727892	+	0.126075i
$324$	−4.12644	−	1.50190i	−0.229246	−	0.0834389i
$325$	15.5229	+	26.8864i	0.861054	+	1.49139i
$326$	3.59446	+	3.01611i	0.199079	+	0.167047i
$327$	−2.84576			−0.157371
$328$	−0.843024	−	0.707381i	−0.0465482	−	0.0390586i
$329$	10.8542	−	3.95061i	0.598412	−	0.217804i
$330$	−0.958285	+	5.43471i	−0.0527519	+	0.299171i
$331$	0.687569	+	3.89939i	0.0377922	+	0.214330i	0.997856	−	0.0654519i	$-0.0208489\pi$
$331$	0.687569	+	3.89939i	0.0377922	+	0.214330i	−0.960064	+	0.279782i	$0.909738\pi$
$332$	9.46475			0.519446
$333$	33.0359	+	3.09808i	1.81036	+	0.169774i
$334$	−0.776993			−0.0425152
$335$	−0.0702431	−	0.398368i	−0.00383779	−	0.0217652i
$336$	0.509893	−	2.89175i	0.0278169	−	0.157758i
$337$	4.01886	−	1.46274i	0.218921	−	0.0796807i	−0.230231	−	0.973136i	$-0.573948\pi$
$337$	4.01886	−	1.46274i	0.218921	−	0.0796807i	0.449152	+	0.893455i	$0.351726\pi$
$338$	21.0533	+	17.6658i	1.14515	+	0.960893i
$339$	26.8588			1.45877
$340$	0.138940	+	0.116585i	0.00753509	+	0.00632269i
$341$	9.03806	+	15.6544i	0.489438	+	0.847732i
$342$	−25.6801	−	9.34680i	−1.38862	−	0.505417i
$343$	6.55400	−	11.3519i	0.353883	−	0.612943i
$344$	3.13518	+	5.43030i	0.169038	+	0.292782i
$345$	0.253038	+	1.43505i	0.0136231	+	0.0772606i
$346$	−10.0860	+	3.67102i	−0.542229	+	0.197355i
$347$	5.06401	−	8.77113i	0.271850	−	0.470859i	−0.697485	−	0.716599i	$-0.745698\pi$
$347$	5.06401	−	8.77113i	0.271850	−	0.470859i	0.969336	+	0.245740i	$0.0790310\pi$
$348$	−14.1093	+	11.8391i	−0.756339	+	0.634644i
$349$	−5.50852	+	4.62220i	−0.294864	+	0.247421i	−0.778203	−	0.628013i	$-0.783869\pi$
$349$	−5.50852	+	4.62220i	−0.294864	+	0.247421i	0.483338	+	0.875434i	$0.339424\pi$
$350$	4.63026	+	1.68528i	0.247498	+	0.0900819i
$351$	7.88671	−	44.7278i	0.420962	−	2.38739i
$352$	−0.948944	+	5.38173i	−0.0505789	+	0.286847i
$353$	32.0012	+	11.6475i	1.70325	+	0.619933i	0.996189	−	0.0872167i	$-0.0277972\pi$
$353$	32.0012	+	11.6475i	1.70325	+	0.619933i	0.707064	+	0.707150i	$0.250019\pi$
$354$	6.66043	−	5.58876i	0.353998	−	0.297039i
$355$	0.0832432	−	0.0698494i	0.00441809	−	0.00370722i
$356$	7.88391	−	13.6553i	0.417846	−	0.723731i
$357$	−1.44101	+	0.524486i	−0.0762666	+	0.0277588i
$358$	−2.06599	−	11.7168i	−0.109191	−	0.619254i
$359$	−4.93976	−	8.55592i	−0.260711	−	0.451564i	0.705720	−	0.708491i	$-0.250624\pi$
$359$	−4.93976	−	8.55592i	−0.260711	−	0.451564i	−0.966431	+	0.256926i	$0.917290\pi$
$360$	−0.947234	+	1.64066i	−0.0499236	+	0.0864702i
$361$	−5.73076	−	2.08582i	−0.301619	−	0.109780i
$362$	−2.19334	−	3.79897i	−0.115279	−	0.199670i
$363$	42.0175	+	35.2568i	2.20535	+	1.85050i
$364$	6.42527			0.336776
$365$	3.52044	+	2.95400i	0.184268	+	0.154620i
$366$	−10.4263	+	3.79485i	−0.544990	+	0.198360i
$367$	−5.88735	+	33.3888i	−0.307317	+	1.74288i	0.305074	+	0.952329i	$0.401319\pi$
$367$	−5.88735	+	33.3888i	−0.307317	+	1.74288i	−0.612391	+	0.790555i	$0.709792\pi$
$368$	0.250571	+	1.42106i	0.0130619	+	0.0740780i
$369$	−6.00307			−0.312507
$370$	0.559481	−	2.03709i	0.0290860	−	0.105903i
$371$	0.0931767			0.00483749
$372$	1.67017	+	9.47198i	0.0865940	+	0.491099i
$373$	5.44457	−	30.8777i	0.281909	−	1.59879i	−0.434212	−	0.900811i	$-0.642973\pi$
$373$	5.44457	−	30.8777i	0.281909	−	1.59879i	0.716121	−	0.697976i	$-0.245916\pi$
$374$	2.68182	−	0.976103i	0.138674	−	0.0504731i
$375$	−7.64255	−	6.41286i	−0.394660	−	0.331159i
$376$	−11.4382			−0.589880
$377$	−30.8737	−	25.9061i	−1.59008	−	1.33423i
$378$	−3.60424	−	6.24272i	−0.185382	−	0.321091i
$379$	−10.0119	−	3.64403i	−0.514276	−	0.187181i	0.0718279	−	0.997417i	$-0.477117\pi$
$379$	−10.0119	−	3.64403i	−0.514276	−	0.187181i	−0.586104	+	0.810236i	$0.699339\pi$
$380$	−0.869950	+	1.50680i	−0.0446275	+	0.0772971i
$381$	−9.84487	−	17.0518i	−0.504368	−	0.873591i
$382$	−1.82163	−	10.3310i	−0.0932025	−	0.528577i
$383$	−18.2315	+	6.63571i	−0.931585	+	0.339069i	−0.762838	−	0.646590i	$-0.776194\pi$
$383$	−18.2315	+	6.63571i	−0.931585	+	0.339069i	−0.168747	+	0.985659i	$0.553972\pi$
$384$	−1.45387	+	2.51817i	−0.0741923	+	0.128505i
$385$	−1.46818	+	1.23195i	−0.0748253	+	0.0627859i
$386$	7.52982	−	6.31827i	0.383258	−	0.321592i
$387$	32.1415	+	11.6985i	1.63384	+	0.594670i
$388$	−0.161341	+	0.915012i	−0.00819087	+	0.0464527i
$389$	3.24705	−	18.4149i	0.164632	−	0.933674i	−0.784811	−	0.619735i	$-0.787240\pi$
$389$	3.24705	−	18.4149i	0.164632	−	0.933674i	0.949443	−	0.313939i	$-0.101649\pi$
$390$	−6.03778	−	2.19757i	−0.305735	−	0.111278i
$391$	0.577283	−	0.484398i	0.0291945	−	0.0244971i
$392$	−4.58111	+	3.84401i	−0.231381	+	0.194152i
$393$	22.0238	−	38.1464i	1.11096	−	1.92423i
$394$	11.3356	−	4.12582i	0.571079	−	0.207856i
$395$	0.561266	+	3.18310i	0.0282404	+	0.160159i
$396$	14.9048	+	25.8159i	0.748996	+	1.29730i
$397$	11.9316	−	20.6661i	0.598829	−	1.03720i	−0.394165	−	0.919040i	$-0.628966\pi$
$397$	11.9316	−	20.6661i	0.598829	−	1.03720i	0.992994	−	0.118163i	$-0.0377005\pi$
$398$	8.73905	+	3.18075i	0.438049	+	0.159437i
$399$	−7.35535	−	12.7398i	−0.368228	−	0.637789i
$400$	−3.73783	−	3.13641i	−0.186891	−	0.156820i
$401$	17.8350			0.890638			0.445319	−	0.895372i	$-0.353090\pi$
$401$	17.8350			0.890638			0.445319	+	0.895372i	$0.353090\pi$
$402$	−2.59443	−	2.17698i	−0.129398	−	0.108578i
$403$	−19.7769	+	7.19819i	−0.985156	+	0.358568i
$404$	1.48675	−	8.43179i	0.0739687	−	0.419497i
$405$	0.264825	+	1.50190i	0.0131593	+	0.0746300i
$406$	−6.39665			−0.317460
$407$	−23.3577	−	23.6510i	−1.15780	−	1.17233i
$408$	1.51855			0.0751792
$409$	−1.73417	−	9.83496i	−0.0857492	−	0.486308i	−0.997192	−	0.0748818i	$-0.976142\pi$
$409$	−1.73417	−	9.83496i	−0.0857492	−	0.486308i	0.911443	−	0.411426i	$-0.134969\pi$
$410$	−0.0663677	+	0.376390i	−0.00327767	+	0.0185886i
$411$	23.1752	−	8.43510i	1.14315	−	0.416073i
$412$	3.79891	+	3.18767i	0.187159	+	0.157045i
$413$	3.01959			0.148584
$414$	6.02979	+	5.05960i	0.296348	+	0.248666i
$415$	−1.64354	−	2.84669i	−0.0806780	−	0.139738i
$416$	−5.97892	−	2.17615i	−0.293141	−	0.106694i
$417$	26.6615	−	46.1791i	1.30562	−	2.26140i
$418$	13.6888	+	23.7096i	0.669540	+	1.15968i
$419$	6.25638	+	35.4817i	0.305644	+	1.73340i	0.620456	+	0.784241i	$0.286948\pi$
$419$	6.25638	+	35.4817i	0.305644	+	1.73340i	−0.314812	+	0.949154i	$0.601941\pi$
$420$	−0.958285	+	0.348787i	−0.0467595	+	0.0170191i
$421$	−11.1668	+	19.3414i	−0.544235	+	0.942643i	0.454419	+	0.890788i	$0.349847\pi$
$421$	−11.1668	+	19.3414i	−0.544235	+	0.942643i	−0.998655	+	0.0518555i	$0.983486\pi$
$422$	−3.37062	+	2.82829i	−0.164079	+	0.137679i
$423$	−47.7968	+	40.1063i	−2.32396	+	1.95003i
$424$	−0.0867039	−	0.0315576i	−0.00421071	−	0.00153257i
$425$	−0.442496	+	2.50952i	−0.0214642	+	0.121729i
$426$	0.157986	−	0.895985i	0.00765446	−	0.0434106i
$427$	−3.62101	−	1.31794i	−0.175233	−	0.0637796i
$428$	−2.73344	+	2.29363i	−0.132126	+	0.110867i
$429$	−77.4489	+	64.9874i	−3.73927	+	3.13762i
$430$	1.08884	−	1.88592i	0.0525084	−	0.0909472i
$431$	−29.3710	+	10.6902i	−1.41475	+	0.514928i	−0.932521	−	0.361116i	$-0.882396\pi$
$431$	−29.3710	+	10.6902i	−1.41475	+	0.514928i	−0.482231	+	0.876044i	$0.660173\pi$
$432$	1.23954	+	7.02975i	0.0596372	+	0.338219i
$433$	−2.71093	−	4.69547i	−0.130279	−	0.225650i	0.793505	−	0.608564i	$-0.208254\pi$
$433$	−2.71093	−	4.69547i	−0.130279	−	0.225650i	−0.923784	+	0.382914i	$0.874921\pi$
$434$	−1.67017	+	2.89281i	−0.0801705	+	0.138859i
$435$	6.01088	+	2.18778i	0.288200	+	0.104896i
$436$	0.489344	+	0.847568i	0.0234353	+	0.0405912i
$437$	5.53783	+	4.64679i	0.264910	+	0.222286i
$438$	38.4767			1.83849
$439$	−11.8195	−	9.91772i	−0.564113	−	0.473347i	0.315573	−	0.948901i	$-0.397803\pi$
$439$	−11.8195	−	9.91772i	−0.564113	−	0.473347i	−0.879687	+	0.475554i	$0.842248\pi$
$440$	1.78343	−	0.649116i	0.0850217	−	0.0309454i
$441$	−5.66466	+	32.1259i	−0.269746	+	1.52980i
$442$	0.577007	+	3.27237i	0.0274454	+	0.155651i
$443$	−8.45523			−0.401720			−0.200860	−	0.979620i	$-0.564374\pi$
$443$	−8.45523			−0.401720			−0.200860	+	0.979620i	$0.564374\pi$
$444$	−7.37471	−	16.0762i	−0.349988	−	0.762944i
$445$	−5.47610			−0.259592
$446$	1.95027	+	11.0605i	0.0923478	+	0.523730i
$447$	2.75330	−	15.6147i	0.130226	−	0.738551i
$448$	−0.948944	+	0.345387i	−0.0448334	+	0.0163180i
$449$	27.8798	+	23.3939i	1.31573	+	1.10403i	0.987192	+	0.159538i	$0.0510004\pi$
$449$	27.8798	+	23.3939i	1.31573	+	1.10403i	0.328538	+	0.944491i	$0.393444\pi$
$450$	−26.6166			−1.25472
$451$	4.60691	+	3.86566i	0.216931	+	0.182027i
$452$	−4.61851	−	7.99950i	−0.217236	−	0.376265i
$453$	42.5031	+	15.4699i	1.99697	+	0.726837i
$454$	7.57697	−	13.1237i	0.355605	−	0.615925i
$455$	−1.11574	−	1.93251i	−0.0523066	−	0.0905976i
$456$	2.52958	+	14.3460i	0.118459	+	0.671812i
$457$	−12.2550	+	4.46044i	−0.573263	+	0.208651i	−0.612352	−	0.790585i	$-0.709777\pi$
$457$	−12.2550	+	4.46044i	−0.573263	+	0.208651i	0.0390893	+	0.999236i	$0.487554\pi$
$458$	7.78085	−	13.4768i	0.363575	−	0.629731i
$459$	2.85572	−	2.39624i	0.133294	−	0.111847i
$460$	0.383898	−	0.322128i	0.0178993	−	0.0150193i
$461$	−16.5840	−	6.03608i	−0.772393	−	0.281128i	−0.0743962	−	0.997229i	$-0.523703\pi$
$461$	−16.5840	−	6.03608i	−0.772393	−	0.281128i	−0.697997	+	0.716101i	$0.745925\pi$
$462$	−2.78644	+	15.8027i	−0.129637	+	0.735207i
$463$	4.60063	−	26.0915i	0.213809	−	1.21257i	−0.669151	−	0.743126i	$-0.733342\pi$
$463$	4.60063	−	26.0915i	0.213809	−	1.21257i	0.882961	−	0.469447i	$-0.155547\pi$
$464$	5.95228	+	2.16645i	0.276328	+	0.100575i
$465$	2.55884	−	2.14712i	0.118663	−	0.0995705i
$466$	10.4083	−	8.73363i	0.482157	−	0.404578i
$467$	9.54875	−	16.5389i	0.441864	−	0.765330i	−0.555964	−	0.831206i	$-0.687651\pi$
$467$	9.54875	−	16.5389i	0.441864	−	0.765330i	0.997828	+	0.0658760i	$0.0209842\pi$
$468$	−32.6144	+	11.8707i	−1.50760	+	0.548723i
$469$	−0.204248	−	1.15835i	−0.00943129	−	0.0534875i
$470$	1.98622	+	3.44024i	0.0916176	+	0.158686i
$471$	5.82742	−	10.0934i	0.268513	−	0.465078i
$472$	−2.80983	−	1.02269i	−0.129333	−	0.0470733i
$473$	−17.1330	−	29.6752i	−0.787776	−	1.36447i
$474$	20.7304	+	17.3948i	0.952177	+	0.798971i
$475$	−24.4450			−1.12161
$476$	0.404001	+	0.338997i	0.0185173	+	0.0155379i
$477$	−0.472961	+	0.172144i	−0.0216554	+	0.00788193i
$478$	−3.38518	+	19.1983i	−0.154834	+	0.878110i
$479$	3.33101	+	18.8911i	0.152198	+	0.863156i	0.961303	+	0.275492i	$0.0888409\pi$
$479$	3.33101	+	18.8911i	0.152198	+	0.863156i	−0.809106	+	0.587663i	$0.800048\pi$
$480$	1.00984			0.0460929
$481$	31.8410	−	22.0006i	1.45183	−	1.00314i
$482$	1.44363			0.0657556
$483$	0.735767	+	4.17274i	0.0334786	+	0.189866i
$484$	3.27561	−	18.5769i	0.148891	−	0.844404i
$485$	0.303223	−	0.110364i	0.0137686	−	0.00501137i
$486$	−6.62322	−	5.55754i	−0.300435	−	0.252095i
$487$	−35.7577			−1.62034			−0.810168	−	0.586197i	$-0.800624\pi$
$487$	−35.7577			−1.62034			−0.810168	+	0.586197i	$0.800624\pi$
$488$	2.92310	+	2.45277i	0.132322	+	0.111032i
$489$	−6.82188	−	11.8158i	−0.308496	−	0.534331i
$490$	1.95165	+	0.710344i	0.0881667	+	0.0320901i
$491$	−14.8866	+	25.7843i	−0.671822	+	1.16363i	0.305565	+	0.952171i	$0.401155\pi$
$491$	−14.8866	+	25.7843i	−0.671822	+	1.16363i	−0.977387	+	0.211459i	$0.932179\pi$
$492$	1.59996	+	2.77122i	0.0721320	+	0.124936i
$493$	−0.574436	−	3.25779i	−0.0258713	−	0.146723i
$494$	−29.9535	+	10.9022i	−1.34767	+	0.490512i
$495$	5.17640	−	8.96578i	0.232662	−	0.402982i
$496$	2.53390	−	2.12619i	0.113775	−	0.0954688i
$497$	0.242049	−	0.203103i	0.0108574	−	0.00911043i
$498$	−25.8612	−	9.41272i	−1.15887	−	0.421794i
$499$	4.30958	−	24.4409i	0.192923	−	1.09412i	−0.722422	−	0.691453i	$-0.756971\pi$
$499$	4.30958	−	24.4409i	0.192923	−	1.09412i	0.915345	−	0.402670i	$-0.131918\pi$
$500$	−0.595800	+	3.37895i	−0.0266450	+	0.151111i
$501$	2.12304	+	0.772722i	0.0948503	+	0.0345227i
$502$	7.71630	−	6.47475i	0.344395	−	0.288982i
$503$	10.4375	−	8.75811i	0.465386	−	0.390505i	−0.379722	−	0.925100i	$-0.623981\pi$
$503$	10.4375	−	8.75811i	0.465386	−	0.390505i	0.845108	+	0.534596i	$0.179536\pi$
$504$	−2.75430	+	4.77059i	−0.122686	+	0.212499i
$505$	−2.79418	+	1.01700i	−0.124339	+	0.0452558i
$506$	−1.36931	−	7.76574i	−0.0608733	−	0.345229i
$507$	−39.9568	−	69.2072i	−1.77454	−	3.07360i
$508$	−3.38575	+	5.86430i	−0.150219	+	0.260186i
$509$	−19.8285	−	7.21697i	−0.878881	−	0.319886i	−0.137123	−	0.990554i	$-0.543785\pi$
$509$	−19.8285	−	7.21697i	−0.878881	−	0.319886i	−0.741758	+	0.670668i	$0.766008\pi$
$510$	−0.263693	−	0.456729i	−0.0116765	−	0.0202243i
$511$	10.2365	+	8.58945i	0.452836	+	0.379975i
$512$	1.00000			0.0441942
$513$	27.3947	+	22.9869i	1.20951	+	1.01490i
$514$	6.56375	−	2.38901i	0.289515	−	0.105375i
$515$	0.299072	−	1.69612i	0.0131787	−	0.0747400i
$516$	−3.16605	−	17.9556i	−0.139377	−	0.790449i
$517$	62.5069			2.74905
$518$	1.62682	−	5.92330i	0.0714784	−	0.260255i
$519$	31.2097			1.36995
$520$	0.383714	+	2.17615i	0.0168270	+	0.0954305i
$521$	0.510798	−	2.89688i	0.0223784	−	0.126914i	−0.971572	−	0.236745i	$-0.923920\pi$
$521$	0.510798	−	2.89688i	0.0223784	−	0.126914i	0.993950	+	0.109830i	$0.0350307\pi$
$522$	32.4691	−	11.8178i	1.42114	−	0.517251i
$523$	8.30708	+	6.97047i	0.363243	+	0.304797i	0.806082	−	0.591804i	$-0.201584\pi$
$523$	8.30708	+	6.97047i	0.363243	+	0.304797i	−0.442839	+	0.896601i	$0.646029\pi$
$524$	−15.1485			−0.661764
$525$	−10.9756	−	9.20962i	−0.479014	−	0.401941i
$526$	−1.33142	−	2.30609i	−0.0580527	−	0.100550i
$527$	−1.62328	−	0.590827i	−0.0707113	−	0.0257368i
$528$	7.94501	−	13.7612i	0.345762	−	0.598878i
$529$	10.4589	+	18.1153i	0.454735	+	0.787624i
$530$	0.00556446	+	0.0315576i	0.000241705	+	0.00137078i
$531$	−15.3273	+	5.57869i	−0.665150	+	0.242095i
$532$	−2.52958	+	4.38137i	−0.109671	+	0.189956i
$533$	−5.36386	+	4.50081i	−0.232334	+	0.194952i
$534$	−35.1220	+	29.4709i	−1.51988	+	1.27533i
$535$	1.16451	+	0.423846i	0.0503461	+	0.0183245i
$536$	−0.202257	+	1.14706i	−0.00873616	+	0.0495452i
$537$	−6.00735	+	34.0694i	−0.259236	+	1.47020i
$538$	−2.26939	−	0.825991i	−0.0978404	−	0.0356110i
$539$	25.0346	−	21.0065i	1.07832	−	0.904815i
$540$	1.89908	−	1.59352i	0.0817233	−	0.0685740i
$541$	−4.43868	+	7.68801i	−0.190834	+	0.330534i	−0.945527	−	0.325544i	$-0.894452\pi$
$541$	−4.43868	+	7.68801i	−0.190834	+	0.330534i	0.754693	+	0.656078i	$0.227786\pi$
$542$	23.7278	−	8.63621i	1.01920	−	0.370957i
$543$	2.21493	+	12.5615i	0.0950517	+	0.539065i
$544$	−0.261122	−	0.452277i	−0.0111955	−	0.0193912i
$545$	0.169947	−	0.294357i	0.00727974	−	0.0126089i
$546$	−17.5562	−	6.38995i	−0.751338	−	0.273465i
$547$	18.2649	+	31.6358i	0.780952	+	1.35265i	0.931388	+	0.364028i	$0.118599\pi$
$547$	18.2649	+	31.6358i	0.780952	+	1.35265i	−0.150436	+	0.988620i	$0.548068\pi$
$548$	−6.49738	−	5.45195i	−0.277554	−	0.232896i
$549$	20.8150			0.888362
$550$	20.4263	+	17.1397i	0.870979	+	0.730838i
$551$	29.8200	−	10.8536i	1.27038	−	0.462379i
$552$	0.728595	−	4.13207i	0.0310110	−	0.175872i
$553$	1.63201	+	9.25560i	0.0694002	+	0.393588i
$554$	−17.7320			−0.753360
$555$	−3.55460	+	5.00968i	−0.150884	+	0.212649i
$556$	−18.3384			−0.777720
$557$	6.37699	+	36.1657i	0.270202	+	1.53239i	0.753803	+	0.657101i	$0.228217\pi$
$557$	6.37699	+	36.1657i	0.270202	+	1.53239i	−0.483601	+	0.875288i	$0.660671\pi$
$558$	3.13323	−	17.7694i	0.132640	−	0.752240i
$559$	37.4900	−	13.6453i	1.58566	−	0.577133i
$560$	0.268664	+	0.225435i	0.0113531	+	0.00952639i
$561$	−8.29847			−0.350362
$562$	15.1288	+	12.6946i	0.638172	+	0.535490i
$563$	−0.238456	−	0.413018i	−0.0100497	−	0.0174066i	0.860957	−	0.508678i	$-0.169866\pi$
$563$	−0.238456	−	0.413018i	−0.0100497	−	0.0174066i	−0.871007	+	0.491271i	$0.836532\pi$
$564$	31.2534	+	11.3753i	1.31601	+	0.478987i
$565$	−1.60399	+	2.77820i	−0.0674805	+	0.116880i
$566$	−12.1747	−	21.0872i	−0.511741	−	0.886361i
$567$	0.770041	+	4.36712i	0.0323387	+	0.183402i
$568$	−0.294023	+	0.107015i	−0.0123369	+	0.00449027i
$569$	−4.54906	+	7.87920i	−0.190706	+	0.330313i	−0.945485	−	0.325667i	$-0.894411\pi$
$569$	−4.54906	+	7.87920i	−0.190706	+	0.330313i	0.754778	+	0.655980i	$0.227745\pi$
$570$	3.87554	−	3.25197i	0.162329	−	0.136210i
$571$	19.6081	−	16.4532i	0.820574	−	0.688543i	−0.132532	−	0.991179i	$-0.542311\pi$
$571$	19.6081	−	16.4532i	0.820574	−	0.688543i	0.953106	+	0.302635i	$0.0978664\pi$
$572$	32.6733	+	11.8921i	1.36614	+	0.497234i
$573$	−5.29680	+	30.0396i	−0.221277	+	1.25492i
$574$	−0.192979	+	1.09444i	−0.00805480	+	0.0456811i
$575$	6.61626	+	2.40812i	0.275917	+	0.100426i
$576$	4.17870	−	3.50634i	0.174112	−	0.146098i
$577$	11.8194	−	9.91764i	0.492048	−	0.412877i	−0.362712	−	0.931901i	$-0.618149\pi$
$577$	11.8194	−	9.91764i	0.492048	−	0.412877i	0.854759	+	0.519024i	$0.173705\pi$
$578$	8.36363	−	14.4862i	0.347881	−	0.602548i
$579$	−26.8578	+	9.77545i	−1.11617	+	0.406254i
$580$	−0.382004	−	2.16645i	−0.0158619	−	0.0899571i
$581$	−4.77896	−	8.27741i	−0.198265	−	0.343405i
$582$	1.35083	−	2.33970i	0.0559936	−	0.0969838i
$583$	0.473815	+	0.172455i	0.0196234	+	0.00714234i
$584$	−6.61627	−	11.4597i	−0.273783	−	0.474207i
$585$	9.23375	+	7.74804i	0.381769	+	0.320342i
$586$	−23.2486			−0.960390
$587$	12.4394	+	10.4379i	0.513430	+	0.430819i	0.862334	−	0.506340i	$-0.169002\pi$
$587$	12.4394	+	10.4379i	0.513430	+	0.430819i	−0.348904	+	0.937158i	$0.613446\pi$
$588$	16.3402	−	5.94734i	0.673858	−	0.245264i
$589$	2.87759	−	16.3196i	0.118569	−	0.672439i
$590$	0.180328	+	1.02269i	0.00742400	+	0.0421036i
$591$	−35.0762			−1.44284
$592$	−3.51995	+	4.96084i	−0.144669	+	0.203889i
$593$	−27.0626			−1.11133			−0.555663	−	0.831407i	$-0.687536\pi$
$593$	−27.0626			−1.11133			−0.555663	+	0.831407i	$0.687536\pi$
$594$	−6.77375	−	38.4158i	−0.277930	−	1.57622i
$595$	0.0318052	−	0.180376i	0.00130389	−	0.00739472i
$596$	−5.12406	+	1.86501i	−0.209890	+	0.0763936i
$597$	−20.7151	−	17.3820i	−0.847812	−	0.711399i
$598$	9.18118			0.375446
$599$	−30.5258	−	25.6142i	−1.24725	−	1.04657i	−0.996922	−	0.0784059i	$-0.975017\pi$
$599$	−30.5258	−	25.6142i	−1.24725	−	1.04657i	−0.250328	−	0.968161i	$-0.580539\pi$
$600$	7.09397	+	12.2871i	0.289610	+	0.501620i
$601$	−33.5222	−	12.2011i	−1.36740	−	0.497692i	−0.449065	−	0.893499i	$-0.648243\pi$
$601$	−33.5222	−	12.2011i	−1.36740	−	0.497692i	−0.918334	+	0.395807i	$0.870465\pi$
$602$	3.16605	−	5.48376i	0.129038	−	0.223501i
$603$	3.17680	+	5.50238i	0.129369	+	0.224074i
$604$	−2.70116	−	15.3190i	−0.109909	−	0.623323i
$605$	−6.15613	+	2.24065i	−0.250282	+	0.0910953i
$606$	−12.4478	+	21.5602i	−0.505657	+	0.875824i
$607$	−9.76538	+	8.19413i	−0.396365	+	0.332589i	−0.819086	−	0.573670i	$-0.805519\pi$
$607$	−9.76538	+	8.19413i	−0.396365	+	0.332589i	0.422722	+	0.906259i	$0.361075\pi$
$608$	3.83776	−	3.22027i	0.155642	−	0.130599i
$609$	17.4780	+	6.36148i	0.708246	+	0.257780i
$610$	0.230123	−	1.30509i	0.00931740	−	0.0528416i
$611$	−12.6376	+	71.6714i	−0.511263	+	2.89952i
$612$	−2.67699	−	0.974344i	−0.108211	−	0.0393855i
$613$	−3.13519	+	2.63074i	−0.126629	+	0.106255i	−0.703903	−	0.710296i	$-0.748561\pi$
$613$	−3.13519	+	2.63074i	−0.126629	+	0.106255i	0.577274	+	0.816551i	$0.304117\pi$
$614$	−8.17382	+	6.85865i	−0.329868	+	0.276792i
$615$	0.555662	−	0.962435i	0.0224065	−	0.0388091i
$616$	5.18574	−	1.88745i	0.208939	−	0.0760477i
$617$	8.20856	+	46.5531i	0.330464	+	1.87416i	0.468104	+	0.883673i	$0.344937\pi$
$617$	8.20856	+	46.5531i	0.330464	+	1.87416i	−0.137640	+	0.990482i	$0.543952\pi$
$618$	−7.20990	−	12.4879i	−0.290025	−	0.502338i
$619$	10.5169	−	18.2157i	0.422708	−	0.732152i	−0.573495	−	0.819209i	$-0.694413\pi$
$619$	10.5169	−	18.2157i	0.422708	−	0.732152i	0.996203	+	0.0870571i	$0.0277463\pi$
$620$	−1.07950	−	0.392904i	−0.0433536	−	0.0157794i
$621$	−5.15015	−	8.92033i	−0.206669	−	0.357960i
$622$	13.0382	+	10.9403i	0.522783	+	0.438667i
$623$	−15.9230			−0.637943
$624$	14.1725	+	11.8921i	0.567353	+	0.476065i
$625$	−21.8059	+	7.93669i	−0.872235	+	0.317468i
$626$	1.89458	−	10.7447i	0.0757225	−	0.429444i
$627$	−13.8235	−	78.3971i	−0.552059	−	3.13088i
$628$	−4.00822			−0.159945
$629$	3.16281	+	0.296606i	0.126110	+	0.0118264i
$630$	1.91312			0.0762205
$631$	−5.68830	−	32.2599i	−0.226448	−	1.28425i	−0.859898	−	0.510465i	$-0.829473\pi$
$631$	−5.68830	−	32.2599i	−0.226448	−	1.28425i	0.633451	−	0.773783i	$-0.281638\pi$
$632$	1.61610	−	9.16537i	0.0642851	−	0.364579i
$633$	12.0225	−	4.37585i	0.477853	−	0.173924i
$634$	−22.0930	−	18.5382i	−0.877424	−	0.736246i
$635$	2.35172			0.0933252
$636$	0.205523	+	0.172455i	0.00814953	+	0.00683827i
$637$	19.0250	+	32.9522i	0.753796	+	1.30561i
$638$	−32.5277	−	11.8391i	−1.28779	−	0.468716i
$639$	−0.853398	+	1.47813i	−0.0337599	+	0.0584739i
$640$	−0.173648	−	0.300767i	−0.00686405	−	0.0118889i
$641$	3.47857	+	19.7280i	0.137395	+	0.779208i	0.973162	+	0.230123i	$0.0739127\pi$
$641$	3.47857	+	19.7280i	0.137395	+	0.779208i	−0.835766	+	0.549085i	$0.814976\pi$
$642$	9.74982	−	3.54864i	0.384795	−	0.140054i
$643$	6.69618	−	11.5981i	0.264071	−	0.457385i	−0.703249	−	0.710944i	$-0.748268\pi$
$643$	6.69618	−	11.5981i	0.264071	−	0.457385i	0.967320	+	0.253559i	$0.0816012\pi$
$644$	1.11627	−	0.936663i	0.0439873	−	0.0369097i
$645$	−4.85067	+	4.07019i	−0.190995	+	0.160264i
$646$	−2.45858	−	0.894849i	−0.0967314	−	0.0352074i
$647$	2.56647	−	14.5551i	0.100898	−	0.572222i	−0.891881	−	0.452269i	$-0.850615\pi$
$647$	2.56647	−	14.5551i	0.100898	−	0.572222i	0.992780	−	0.119953i	$-0.0382743\pi$
$648$	0.762534	−	4.32455i	0.0299552	−	0.169884i
$649$	15.3550	+	5.58876i	0.602736	+	0.219378i
$650$	−23.7824	+	19.9558i	−0.932823	+	0.782732i
$651$	7.44042	−	6.24326i	0.291613	−	0.244693i
$652$	−2.34612	+	4.06359i	−0.0918810	+	0.159143i
$653$	25.4991	−	9.28092i	0.997857	−	0.363190i	0.209099	−	0.977894i	$-0.432947\pi$
$653$	25.4991	−	9.28092i	0.997857	−	0.363190i	0.788758	+	0.614704i	$0.210725\pi$
$654$	−0.494161	−	2.80253i	−0.0193232	−	0.109588i
$655$	2.63050	+	4.55617i	0.102782	+	0.178024i
$656$	0.550245	−	0.953052i	0.0214835	−	0.0372104i
$657$	−67.8291	−	24.6878i	−2.64627	−	0.963162i
$658$	5.77540	+	10.0033i	0.225149	+	0.389969i
$659$	24.2414	+	20.3409i	0.944311	+	0.792371i	0.978330	−	0.207050i	$-0.0663864\pi$
$659$	24.2414	+	20.3409i	0.944311	+	0.792371i	−0.0340197	+	0.999421i	$0.510831\pi$
$660$	−5.51855			−0.214809
$661$	26.0376	+	21.8481i	1.01274	+	0.849793i	0.988698	−	0.149918i	$-0.0479009\pi$
$661$	26.0376	+	21.8481i	1.01274	+	0.849793i	0.0240454	+	0.999711i	$0.492345\pi$
$662$	−3.72076	+	1.35425i	−0.144611	+	0.0526343i
$663$	1.67778	−	9.51517i	0.0651596	−	0.369539i
$664$	1.64354	+	9.32096i	0.0637816	+	0.361723i
$665$	1.75703			0.0681347
$666$	2.68562	+	33.0720i	0.104066	+	1.28151i
$667$	−9.14028			−0.353913
$668$	−0.134923	−	0.765189i	−0.00522035	−	0.0296060i
$669$	5.67085	−	32.1610i	0.219248	−	1.24342i
$670$	0.380118	−	0.138352i	0.0146853	−	0.00534500i
$671$	−15.9740	−	13.4038i	−0.616669	−	0.517447i
$672$	2.93636			0.113272
$673$	30.3717	+	25.4849i	1.17074	+	0.982372i	0.999996	−	0.00294292i	$-0.000936763\pi$
$673$	30.3717	+	25.4849i	1.17074	+	0.982372i	0.170749	+	0.985315i	$0.445381\pi$
$674$	2.13839	+	3.70380i	0.0823676	+	0.142665i
$675$	32.7295	+	11.9126i	1.25976	+	0.458515i
$676$	−13.7416	+	23.8011i	−0.528522	+	0.915426i
$677$	−9.65303	−	16.7195i	−0.370996	−	0.642584i	0.618723	−	0.785609i	$-0.287650\pi$
$677$	−9.65303	−	16.7195i	−0.370996	−	0.642584i	−0.989719	+	0.143025i	$0.954317\pi$
$678$	4.66398	+	26.4507i	0.179119	+	1.01583i
$679$	0.881690	−	0.320909i	0.0338362	−	0.0123154i
$680$	−0.0906868	+	0.157074i	−0.00347768	+	0.00602352i
$681$	−33.7546	+	28.3235i	−1.29348	+	1.08536i
$682$	−13.8471	+	11.6191i	−0.530233	+	0.444918i
$683$	−1.90109	−	0.691940i	−0.0727432	−	0.0264764i	0.305392	−	0.952227i	$-0.401212\pi$
$683$	−1.90109	−	0.691940i	−0.0727432	−	0.0264764i	−0.378135	+	0.925750i	$0.623435\pi$
$684$	4.74550	−	26.9130i	0.181449	−	1.02905i
$685$	−0.511511	+	2.90092i	−0.0195438	+	0.110838i
$686$	12.3175	+	4.48320i	0.470284	+	0.171169i
$687$	−34.6629	+	29.0857i	−1.32247	+	1.10969i
$688$	−4.80338	+	4.03051i	−0.183127	+	0.153662i
$689$	−0.293535	+	0.508417i	−0.0111828	+	0.0193692i
$690$	−1.36931	+	0.498388i	−0.0521287	+	0.0189733i
$691$	−0.242292	−	1.37410i	−0.00921721	−	0.0522734i	0.979852	−	0.199724i	$-0.0640045\pi$
$691$	−0.242292	−	1.37410i	−0.00921721	−	0.0522734i	−0.989069	+	0.147450i	$0.952893\pi$
$692$	−5.36667	−	9.29535i	−0.204010	−	0.353356i
$693$	15.0516	−	26.0701i	0.571762	−	0.990320i
$694$	9.51723	+	3.46399i	0.361269	+	0.131491i
$695$	3.18442	+	5.51559i	0.120792	+	0.209218i
$696$	−14.1093	−	11.8391i	−0.534812	−	0.448761i
$697$	−0.574725			−0.0217692
$698$	−5.50852	−	4.62220i	−0.208501	−	0.174953i
$699$	−37.1251	+	13.5124i	−1.40420	+	0.511087i
$700$	−0.855638	+	4.85256i	−0.0323401	+	0.183410i
$701$	−7.84895	−	44.5136i	−0.296451	−	1.68126i	−0.661247	−	0.750168i	$-0.729973\pi$
$701$	−7.84895	−	44.5136i	−0.296451	−	1.68126i	0.364797	−	0.931087i	$-0.381138\pi$
$702$	45.4178			1.71418
$703$	2.46650	+	30.3737i	0.0930258	+	1.14557i
$704$	−5.46475			−0.205960
$705$	−2.00578	−	11.3753i	−0.0755419	−	0.428419i
$706$	−5.91359	+	33.5376i	−0.222561	+	1.26220i
$707$	−8.12472	+	2.95716i	−0.305562	+	0.111215i
$708$	6.66043	+	5.58876i	0.250314	+	0.210039i
$709$	−28.5445			−1.07201			−0.536005	−	0.844215i	$-0.680067\pi$
$709$	−28.5445			−1.07201			−0.536005	+	0.844215i	$0.680067\pi$
$710$	0.0832432	+	0.0698494i	0.00312406	+	0.00262140i
$711$	−25.3837	−	43.9659i	−0.951965	−	1.64885i
$712$	14.8169	+	5.39291i	0.555287	+	0.202108i
$713$	−2.38653	+	4.13359i	−0.0893761	+	0.154804i
$714$	−0.766748	−	1.32805i	−0.0286948	−	0.0497009i
$715$	−2.09690	−	11.8921i	−0.0784196	−	0.444740i
$716$	11.1801	−	4.06921i	0.417819	−	0.152074i
$717$	28.3423	−	49.0904i	1.05846	−	1.83331i
$718$	7.56816	−	6.35044i	0.282441	−	0.236996i
$719$	−13.6923	+	11.4892i	−0.510637	+	0.428475i	−0.861353	−	0.508007i	$-0.830383\pi$
$719$	−13.6923	+	11.4892i	−0.510637	+	0.428475i	0.350717	+	0.936482i	$0.385938\pi$
$720$	−1.78022	−	0.647946i	−0.0663448	−	0.0241475i
$721$	0.869621	−	4.93187i	0.0323864	−	0.183672i
$722$	1.05900	−	6.00589i	0.0394119	−	0.223516i
$723$	−3.94454	−	1.43569i	−0.146699	−	0.0533941i
$724$	3.36039	−	2.81970i	0.124888	−	0.104793i
$725$	23.6765	−	19.8669i	0.879322	−	0.737839i
$726$	−27.4250	+	47.5014i	−1.01784	+	1.76294i
$727$	16.3955	−	5.96747i	0.608075	−	0.221321i	−0.0195860	−	0.999808i	$-0.506235\pi$
$727$	16.3955	−	5.96747i	0.608075	−	0.221321i	0.627661	+	0.778487i	$0.284013\pi$
$728$	1.11574	+	6.32766i	0.0413520	+	0.234519i
$729$	19.1570	+	33.1809i	0.709519	+	1.22892i
$730$	−2.29781	+	3.97992i	−0.0850457	+	0.147303i
$731$	3.07718	+	1.12000i	0.113813	+	0.0414247i
$732$	−5.54771	−	9.60891i	−0.205049	−	0.355156i
$733$	−33.6087	−	28.2011i	−1.24137	−	1.04163i	−0.997416	−	0.0718424i	$-0.977112\pi$
$733$	−33.6087	−	28.2011i	−1.24137	−	1.04163i	−0.243950	−	0.969788i	$-0.578443\pi$
$734$	−33.9039			−1.25142
$735$	−4.62621	−	3.88185i	−0.170640	−	0.143184i
$736$	−1.35596	+	0.493529i	−0.0499814	+	0.0181917i
$737$	1.10528	−	6.26837i	0.0407136	−	0.230898i
$738$	−1.04242	−	5.91187i	−0.0383721	−	0.217619i
$739$	39.5017			1.45309			0.726546	−	0.687118i	$-0.241124\pi$
$739$	39.5017			1.45309			0.726546	+	0.687118i	$0.241124\pi$
$740$	2.10329	+	0.197245i	0.0773186	+	0.00725087i
$741$	92.6863			3.40492
$742$	0.0161800	+	0.0917611i	0.000593985	+	0.00336866i
$743$	3.45404	−	19.5888i	0.126716	−	0.718644i	−0.853557	−	0.520999i	$-0.825560\pi$
$743$	3.45404	−	19.5888i	0.126716	−	0.718644i	0.980274	−	0.197645i	$-0.0633293\pi$
$744$	−9.03806	+	3.28958i	−0.331351	+	0.120602i
$745$	1.45072	+	1.21730i	0.0531502	+	0.0445983i
$746$	31.3540			1.14795
$747$	39.5503	+	33.1867i	1.44707	+	1.21424i
$748$	1.42697	+	2.47158i	0.0521751	+	0.0903699i
$749$	3.38608	+	1.23243i	0.123725	+	0.0450320i
$750$	4.98832	−	8.64003i	0.182148	−	0.315489i
$751$	16.6184	+	28.7839i	0.606413	+	1.05034i	0.991826	+	0.127594i	$0.0407255\pi$
$751$	16.6184	+	28.7839i	0.606413	+	1.05034i	−0.385413	+	0.922744i	$0.625941\pi$
$752$	−1.98622	−	11.2644i	−0.0724301	−	0.410771i
$753$	−27.5230	+	10.0175i	−1.00299	+	0.365060i
$754$	20.1514	−	34.9032i	0.733870	−	1.27110i
$755$	−4.13842	+	3.47255i	−0.150612	+	0.126379i
$756$	5.52201	−	4.63352i	0.200834	−	0.168519i
$757$	−40.7915	−	14.8469i	−1.48259	−	0.539620i	−0.531105	−	0.847306i	$-0.678223\pi$
$757$	−40.7915	−	14.8469i	−1.48259	−	0.539620i	−0.951488	+	0.307686i	$0.900445\pi$
$758$	1.85012	−	10.4926i	0.0671994	−	0.381107i
$759$	−3.98159	+	22.5807i	−0.144522	+	0.819627i
$760$	−1.63497	−	0.595081i	−0.0593067	−	0.0215859i
$761$	19.3702	−	16.2536i	0.702171	−	0.589191i	−0.220220	−	0.975450i	$-0.570677\pi$
$761$	19.3702	−	16.2536i	0.702171	−	0.589191i	0.922390	+	0.386259i	$0.126233\pi$
$762$	15.0832	−	12.6563i	0.546407	−	0.458490i
$763$	0.494161	−	0.855912i	0.0178898	−	0.0309861i
$764$	9.85768	−	3.58790i	0.356638	−	0.129806i
$765$	0.171803	+	0.974344i	0.00621156	+	0.0352275i
$766$	−9.70076	−	16.8022i	−0.350503	−	0.607089i
$767$	−9.51263	+	16.4764i	−0.343481	+	0.594927i
$768$	−2.73237	−	0.994503i	−0.0985961	−	0.0358860i
$769$	−13.8992	−	24.0740i	−0.501216	−	0.868132i	−0.999999	−	0.00140492i	$-0.999553\pi$
$769$	−13.8992	−	24.0740i	−0.501216	−	0.868132i	0.498783	−	0.866727i	$-0.333781\pi$
$770$	−1.46818	−	1.23195i	−0.0529095	−	0.0443963i
$771$	−20.3105			−0.731465
$772$	7.52982	+	6.31827i	0.271004	+	0.227400i
$773$	0.927201	−	0.337474i	0.0333491	−	0.0121381i	−0.325292	−	0.945614i	$-0.605463\pi$
$773$	0.927201	−	0.337474i	0.0333491	−	0.0121381i	0.358641	+	0.933476i	$0.383240\pi$
$774$	−5.93950	+	33.6846i	−0.213491	+	1.21077i
$775$	−2.80266	−	15.8947i	−0.100674	−	0.570953i
$776$	−0.929128			−0.0333538
$777$	−10.3358	+	14.5668i	−0.370796	+	0.522581i
$778$	18.6990			0.670392
$779$	−0.957372	−	5.42952i	−0.0343014	−	0.194533i
$780$	1.11574	−	6.32766i	0.0399498	−	0.226567i
$781$	1.60676	−	0.584812i	0.0574944	−	0.0209262i
$782$	0.577283	+	0.484398i	0.0206436	+	0.0173220i
$783$	−45.2154			−1.61587
$784$	−4.58111	−	3.84401i	−0.163611	−	0.137286i
$785$	0.696020	+	1.20554i	0.0248420	+	0.0430277i
$786$	41.3913	+	15.0652i	1.47638	+	0.537358i
$787$	−12.8990	+	22.3417i	−0.459799	+	0.796394i	−0.998950	−	0.0458144i	$-0.985412\pi$
$787$	−12.8990	+	22.3417i	−0.459799	+	0.796394i	0.539151	+	0.842209i	$0.318745\pi$
$788$	6.03154	+	10.4469i	0.214865	+	0.372157i
$789$	1.34453	+	7.62520i	0.0478665	+	0.271464i
$790$	−3.03728	+	1.10548i	−0.108062	+	0.0393312i
$791$	−4.66398	+	8.07825i	−0.165832	+	0.287229i
$792$	−22.8355	+	19.1613i	−0.811425	+	0.680867i
$793$	18.5986	−	15.6061i	0.660455	−	0.554188i
$794$	22.4240	+	8.16169i	0.795800	+	0.289647i
$795$	0.0161800	−	0.0917611i	0.000573844	−	0.00325443i
$796$	−1.61491	+	9.15861i	−0.0572390	+	0.324618i
$797$	−14.1958	−	5.16684i	−0.502841	−	0.183019i	0.0781306	−	0.996943i	$-0.475105\pi$
$797$	−14.1958	−	5.16684i	−0.502841	−	0.183019i	−0.580971	+	0.813924i	$0.697327\pi$
$798$	11.2690	−	9.45585i	0.398920	−	0.334734i
$799$	−4.57599	+	3.83971i	−0.161887	+	0.135839i
$800$	2.43969	−	4.22567i	0.0862562	−	0.149400i
$801$	80.8247	−	29.4178i	2.85580	−	1.03943i
$802$	3.09702	+	17.5641i	0.109359	+	0.620208i
$803$	36.1563	+	62.6245i	1.27593	+	2.20997i
$804$	1.69339	−	2.93304i	0.0597213	−	0.103440i
$805$	−0.475556	−	0.173088i	−0.0167612	−	0.00610056i
$806$	−10.5231	−	18.2265i	−0.370659	−	0.642000i
$807$	5.37937	+	4.51383i	0.189363	+	0.158894i
$808$	8.56186			0.301205
$809$	−32.7023	−	27.4405i	−1.14975	−	0.964757i	−0.150039	−	0.988680i	$-0.547940\pi$
$809$	−32.7023	−	27.4405i	−1.14975	−	0.964757i	−0.999714	+	0.0239226i	$0.992384\pi$
$810$	−1.43310	+	0.521604i	−0.0503539	+	0.0183273i
$811$	3.54555	−	20.1078i	0.124501	−	0.706081i	−0.857102	−	0.515147i	$-0.827737\pi$
$811$	3.54555	−	20.1078i	0.124501	−	0.706081i	0.981603	−	0.190934i	$-0.0611517\pi$
$812$	−1.11077	−	6.29947i	−0.0389802	−	0.221068i
$813$	−73.4219			−2.57502
$814$	19.2356	−	27.1098i	0.674209	−	0.950196i
$815$	1.62960			0.0570822
$816$	0.263693	+	1.49548i	0.00923109	+	0.0523521i
$817$	−5.45491	+	30.9363i	−0.190843	+	1.08232i
$818$	9.38441	−	3.41565i	0.328118	−	0.119425i
$819$	26.8493	+	22.5292i	0.938190	+	0.787235i
$820$	−0.382196			−0.0133469
$821$	10.3004	+	8.64304i	0.359485	+	0.301644i	0.804586	−	0.593837i	$-0.202387\pi$
$821$	10.3004	+	8.64304i	0.359485	+	0.301644i	−0.445100	+	0.895481i	$0.646832\pi$
$822$	12.3313	+	21.3584i	0.430103	+	0.744961i
$823$	38.3237	+	13.9487i	1.33588	+	0.486221i	0.908513	−	0.417857i	$-0.137219\pi$
$823$	38.3237	+	13.9487i	1.33588	+	0.486221i	0.427368	+	0.904078i	$0.359441\pi$
$824$	−2.47956	+	4.29473i	−0.0863797	+	0.149614i
$825$	−38.7668	−	67.1460i	−1.34969	−	2.33772i
$826$	0.524347	+	2.97372i	0.0182444	+	0.103469i
$827$	38.0037	−	13.8322i	1.32152	−	0.480993i	0.417574	−	0.908643i	$-0.362880\pi$
$827$	38.0037	−	13.8322i	1.32152	−	0.480993i	0.903945	+	0.427650i	$0.140658\pi$
$828$	−3.93567	+	6.81678i	−0.136774	+	0.236899i
$829$	2.03399	−	1.70672i	0.0706435	−	0.0592770i	−0.606782	−	0.794868i	$-0.707540\pi$
$829$	2.03399	−	1.70672i	0.0706435	−	0.0592770i	0.677426	+	0.735591i	$0.263096\pi$
$830$	2.51804	−	2.11289i	0.0874026	−	0.0733395i
$831$	48.4504	+	17.6345i	1.68073	+	0.611734i
$832$	1.10486	−	6.26597i	0.0383041	−	0.217234i
$833$	−0.542326	+	3.07569i	−0.0187905	+	0.106566i
$834$	50.1073	+	18.2376i	1.73507	+	0.631515i
$835$	−0.206715	+	0.173454i	−0.00715366	+	0.00600263i
$836$	−20.9724	+	17.5979i	−0.725346	+	0.608638i
$837$	−11.8058	+	20.4482i	−0.408066	+	0.706792i
$838$	−33.8563	+	12.3227i	−1.16955	+	0.425680i
$839$	−7.48912	−	42.4729i	−0.258553	−	1.46633i	−0.786785	−	0.617228i	$-0.788256\pi$
$839$	−7.48912	−	42.4729i	−0.258553	−	1.46633i	0.528231	−	0.849101i	$-0.322855\pi$
$840$	−0.509893	−	0.883161i	−0.0175930	−	0.0304719i
$841$	−5.56161	+	9.63298i	−0.191780	+	0.332172i
$842$	−20.9867	−	7.63853i	−0.723249	−	0.263241i
$843$	−28.7128	−	49.7321i	−0.988923	−	1.71286i
$844$	−3.37062	−	2.82829i	−0.116022	−	0.0973537i
$845$	9.54479			0.328351
$846$	−47.7968	−	40.1063i	−1.64329	−	1.37888i
$847$	−17.9004	+	6.51520i	−0.615064	+	0.223865i
$848$	0.0160222	−	0.0908666i	0.000550206	−	0.00312037i
$849$	12.2946	+	69.7259i	0.421948	+	2.39299i
$850$	−2.54823			−0.0874036
$851$	2.32459	−	8.46391i	0.0796860	−	0.290139i
$852$	0.909807			0.0311695
$853$	−7.79993	−	44.2356i	−0.267064	−	1.51460i	−0.763092	−	0.646290i	$-0.776319\pi$
$853$	−7.79993	−	44.2356i	−0.267064	−	1.51460i	0.496027	−	0.868307i	$-0.334792\pi$
$854$	0.669135	−	3.79485i	0.0228973	−	0.129857i
$855$	−8.91861	+	3.24611i	−0.305010	+	0.111015i
$856$	−2.73344	−	2.29363i	−0.0934272	−	0.0783947i
$857$	−1.14287			−0.0390395			−0.0195198	−	0.999809i	$-0.506214\pi$
$857$	−1.14287			−0.0390395			−0.0195198	+	0.999809i	$0.506214\pi$
$858$	−77.4489	−	64.9874i	−2.64406	−	2.21863i
$859$	−10.3483	−	17.9238i	−0.353080	−	0.611552i	0.633708	−	0.773573i	$-0.281532\pi$
$859$	−10.3483	−	17.9238i	−0.353080	−	0.611552i	−0.986787	+	0.162020i	$0.948199\pi$
$860$	2.04635	+	0.744809i	0.0697798	+	0.0253978i
$861$	1.61572	−	2.79850i	0.0550634	−	0.0953727i
$862$	−15.6280	−	27.0685i	−0.532291	−	0.921956i
$863$	−1.91838	−	10.8797i	−0.0653023	−	0.370348i	−0.999893	−	0.0146230i	$-0.995345\pi$
$863$	−1.91838	−	10.8797i	−0.0653023	−	0.370348i	0.934591	−	0.355725i	$-0.115766\pi$
$864$	−6.70771	+	2.44141i	−0.228201	+	0.0830584i
$865$	−1.86383	+	3.22824i	−0.0633720	+	0.109764i
$866$	4.15339	−	3.48511i	0.141138	−	0.118429i
$867$	−37.2592	+	31.2642i	−1.26539	+	1.06179i
$868$	−3.13888	−	1.14246i	−0.106541	−	0.0387776i
$869$	−8.83159	+	50.0864i	−0.299591	+	1.69907i
$870$	−1.11077	+	6.29947i	−0.0376585	+	0.213572i
$871$	6.96395	+	2.53467i	0.235965	+	0.0858841i
$872$	−0.749718	+	0.629088i	−0.0253887	+	0.0213036i
$873$	−3.88255	+	3.25784i	−0.131404	+	0.110261i
$874$	−3.61456	+	6.26061i	−0.122264	+	0.211768i
$875$	3.25590	−	1.18505i	0.110069	−	0.0400620i
$876$	6.68141	+	37.8921i	0.225744	+	1.28026i
$877$	6.18401	+	10.7110i	0.208819	+	0.361686i	0.951343	−	0.308134i	$-0.0997046\pi$
$877$	6.18401	+	10.7110i	0.208819	+	0.361686i	−0.742524	+	0.669820i	$0.766371\pi$
$878$	7.71462	−	13.3621i	0.260356	−	0.450950i
$879$	63.5238	+	23.1208i	2.14260	+	0.779844i
$880$	0.948944	+	1.64362i	0.0319889	+	0.0554064i
$881$	13.7758	+	11.5593i	0.464120	+	0.389443i	0.844644	−	0.535328i	$-0.179812\pi$
$881$	13.7758	+	11.5593i	0.464120	+	0.389443i	−0.380524	+	0.924771i	$0.624256\pi$
$882$	−32.6215			−1.09842
$883$	−8.21722	−	6.89507i	−0.276532	−	0.232038i	0.493965	−	0.869482i	$-0.335547\pi$
$883$	−8.21722	−	6.89507i	−0.276532	−	0.232038i	−0.770496	+	0.637444i	$0.779992\pi$
$884$	−3.12246	+	1.13648i	−0.105020	+	0.0382240i
$885$	0.524347	−	2.97372i	0.0176257	−	0.0999604i
$886$	−1.46824	−	8.32678i	−0.0493263	−	0.279744i
$887$	−16.7444			−0.562222			−0.281111	−	0.959675i	$-0.590703\pi$
$887$	−16.7444			−0.562222			−0.281111	+	0.959675i	$0.590703\pi$
$888$	14.5514	−	10.0543i	0.488313	−	0.337399i
$889$	6.83817			0.229345
$890$	−0.950915	−	5.39291i	−0.0318748	−	0.180771i
$891$	−4.16706	+	23.6326i	−0.139602	+	0.791721i
$892$	−10.5538	+	3.84127i	−0.353368	+	0.128615i
$893$	−43.8971	−	36.8340i	−1.46896	−	1.23260i
$894$	15.8556			0.530291
$895$	−3.16528	−	2.65599i	−0.105804	−	0.0887799i
$896$	−0.504922	−	0.874551i	−0.0168683	−	0.0292167i
$897$	−25.0864	−	9.13071i	−0.837611	−	0.304865i
$898$	−18.1973	+	31.5186i	−0.607250	+	1.05179i
$899$	10.4762	+	18.1453i	0.349400	+	0.605179i
$900$	−4.62192	−	26.2122i	−0.154064	−	0.873740i
$901$	−0.0452806	+	0.0164808i	−0.00150852	+	0.000549055i
$902$	−3.00695	+	5.20819i	−0.100120	+	0.173414i
$903$	−14.1044	+	11.8350i	−0.469366	+	0.393845i
$904$	7.07597	−	5.93744i	0.235343	−	0.197476i
$905$	−1.43160	−	0.521060i	−0.0475880	−	0.0173206i
$906$	−7.85425	+	44.5437i	−0.260940	+	1.47986i
$907$	7.53327	−	42.7233i	0.250138	−	1.41860i	−0.558113	−	0.829765i	$-0.688474\pi$
$907$	7.53327	−	42.7233i	0.250138	−	1.41860i	0.808251	−	0.588838i	$-0.200415\pi$
$908$	14.2400	+	5.18295i	0.472572	+	0.172002i
$909$	35.7774	−	30.0208i	1.18666	−	0.995728i
$910$	1.70941	−	1.43436i	0.0566663	−	0.0475487i
$911$	−5.05307	+	8.75217i	−0.167416	+	0.289972i	−0.937510	−	0.347957i	$-0.886876\pi$
$911$	−5.05307	+	8.75217i	−0.167416	+	0.289972i	0.770095	+	0.637929i	$0.220209\pi$
$912$	−13.6888	+	4.98230i	−0.453280	+	0.164981i
$913$	−8.98151	−	50.9367i	−0.297245	−	1.68576i
$914$	−6.52073	−	11.2942i	−0.215687	−	0.373580i
$915$	−1.92670	+	3.33714i	−0.0636947	+	0.110322i
$916$	14.6232	+	5.32242i	0.483165	+	0.175858i
$917$	7.64880	+	13.2481i	0.252586	+	0.437491i
$918$	2.85572	+	2.39624i	0.0942530	+	0.0790876i
$919$	2.82736			0.0932661			0.0466330	−	0.998912i	$-0.485151\pi$
$919$	2.82736			0.0932661			0.0466330	+	0.998912i	$0.485151\pi$
$920$	0.383898	+	0.322128i	0.0126567	+	0.0106203i
$921$	29.1549	−	10.6115i	0.960686	−	0.349661i
$922$	3.06460	−	17.3802i	0.100927	−	0.572386i
$923$	0.345702	+	1.96057i	0.0113789	+	0.0645331i
$924$	−16.0465			−0.527889
$925$	12.3753	+	26.9771i	0.406897	+	0.887001i
$926$	26.4940			0.870646
$927$	4.69745	+	26.6406i	0.154285	+	0.874992i
$928$	−1.09994	+	6.23806i	−0.0361072	+	0.204774i
$929$	−31.4473	+	11.4459i	−1.03175	+	0.375528i	−0.801748	−	0.597662i	$-0.796097\pi$
$929$	−31.4473	+	11.4459i	−1.03175	+	0.375528i	−0.230005	+	0.973189i	$0.573874\pi$
$930$	2.55884	+	2.14712i	0.0839077	+	0.0704069i
$931$	−29.9599			−0.981897
$932$	10.4083	+	8.73363i	0.340937	+	0.286080i
$933$	−24.7450	−	42.8595i	−0.810114	−	1.40316i
$934$	17.9458	+	6.53173i	0.587204	+	0.213725i
$935$	0.495580	−	0.858370i	0.0162072	−	0.0280717i
$936$	−17.3538	−	30.0576i	−0.567226	−	0.982464i
$937$	7.99787	+	45.3582i	0.261279	+	1.48179i	0.779425	+	0.626495i	$0.215511\pi$
$937$	7.99787	+	45.3582i	0.261279	+	1.48179i	−0.518146	+	0.855292i	$0.673378\pi$
$938$	1.10528	−	0.402290i	0.0360888	−	0.0131352i
$939$	−15.8623	+	27.4743i	−0.517647	+	0.896590i
$940$	−3.04307	+	2.55344i	−0.0992540	+	0.0832840i
$941$	−13.4316	+	11.2705i	−0.437858	+	0.367406i	−0.834907	−	0.550391i	$-0.814479\pi$
$941$	−13.4316	+	11.2705i	−0.437858	+	0.367406i	0.397049	+	0.917797i	$0.370034\pi$
$942$	10.9520	+	3.98619i	0.356834	+	0.129877i
$943$	−0.275751	+	1.56386i	−0.00897970	+	0.0509264i
$944$	0.519235	−	2.94473i	0.0168997	−	0.0958427i
$945$	−2.35250	−	0.856239i	−0.0765268	−	0.0278535i
$946$	26.2493	−	22.0257i	0.853437	−	0.716119i
$947$	20.0641	−	16.8357i	0.651994	−	0.547088i	−0.255681	−	0.966761i	$-0.582300\pi$
$947$	20.0641	−	16.8357i	0.651994	−	0.547088i	0.907675	+	0.419673i	$0.137855\pi$
$948$	−13.5308	+	23.4360i	−0.439459	+	0.761166i
$949$	−79.1163	+	28.7960i	−2.56822	+	0.934757i
$950$	−4.24482	−	24.0736i	−0.137720	−	0.781050i
$951$	41.9300	+	72.6248i	1.35967	+	2.35502i
$952$	−0.263693	+	0.456729i	−0.00854633	+	0.0148027i
$953$	24.4034	+	8.88209i	0.790502	+	0.287719i	0.705545	−	0.708665i	$-0.250702\pi$
$953$	24.4034	+	8.88209i	0.790502	+	0.287719i	0.0849574	+	0.996385i	$0.472925\pi$
$954$	−0.251657	−	0.435884i	−0.00814771	−	0.0141123i
$955$	−2.79089	−	2.34184i	−0.0903112	−	0.0757801i
$956$	−19.4945			−0.630496
$957$	77.1039	+	64.6978i	2.49241	+	2.09138i
$958$	−18.0257	+	6.56080i	−0.582383	+	0.211970i
$959$	−1.48734	+	8.43510i	−0.0480286	+	0.272384i
$960$	0.175358	+	0.994503i	0.00565964	+	0.0320974i
$961$	−20.0587			−0.647054
$962$	27.1955	+	27.5369i	0.876817	+	0.887827i
$963$	−19.4645			−0.627235
$964$	0.250684	+	1.42170i	0.00807398	+	0.0457898i
$965$	0.592791	−	3.36188i	0.0190826	−	0.108223i
$966$	−3.98159	+	1.44918i	−0.128105	+	0.0466266i
$967$	25.8686	+	21.7064i	0.831879	+	0.698029i	0.955722	−	0.294273i	$-0.0950773\pi$
$967$	25.8686	+	21.7064i	0.831879	+	0.698029i	−0.123843	+	0.992302i	$0.539522\pi$
$968$	18.8635			0.606295
$969$	5.82782	+	4.89012i	0.187217	+	0.157093i
$970$	0.161341	+	0.279451i	0.00518036	+	0.00897265i
$971$	12.9625	+	4.71796i	0.415986	+	0.151407i	0.541530	−	0.840682i	$-0.317845\pi$
$971$	12.9625	+	4.71796i	0.415986	+	0.151407i	−0.125544	+	0.992088i	$0.540068\pi$
$972$	4.32300	−	7.48765i	0.138660	−	0.240166i
$973$	9.25945	+	16.0378i	0.296844	+	0.514150i
$974$	−6.20926	−	35.2145i	−0.198958	−	1.12834i
$975$	84.8286	−	30.8751i	2.71669	−	0.988794i
$976$	−1.90792	+	3.30461i	−0.0610709	+	0.105778i
$977$	−29.8644	+	25.0592i	−0.955448	+	0.801716i	−0.980207	−	0.197978i	$-0.936563\pi$
$977$	−29.8644	+	25.0592i	−0.955448	+	0.801716i	0.0247589	+	0.999693i	$0.492118\pi$
$978$	10.4517	−	8.77004i	0.334209	−	0.280435i
$979$	−80.9706	−	29.4709i	−2.58783	−	0.941894i
$980$	−0.360651	+	2.04535i	−0.0115206	+	0.0653364i
$981$	−0.927046	+	5.25754i	−0.0295983	+	0.167860i
$982$	−27.9776	−	10.1830i	−0.892802	−	0.324953i
$983$	9.34290	−	7.83963i	0.297992	−	0.250045i	−0.481516	−	0.876437i	$-0.659914\pi$
$983$	9.34290	−	7.83963i	0.297992	−	0.250045i	0.779508	+	0.626392i	$0.215469\pi$
$984$	−2.45129	+	2.05687i	−0.0781442	+	0.0655708i
$985$	2.09473	−	3.62818i	0.0667438	−	0.115604i
$986$	3.10855	−	1.13142i	0.0989963	−	0.0360317i
$987$	−5.83226	−	33.0764i	−0.185643	−	1.05283i
$988$	−15.9379	−	27.6053i	−0.507052	−	0.878240i
$989$	4.52402	−	7.83583i	0.143855	−	0.249165i
$990$	9.72844	+	3.54086i	0.309190	+	0.112536i
$991$	−13.2303	−	22.9156i	−0.420275	−	0.727937i	0.575691	−	0.817667i	$-0.304733\pi$
$991$	−13.2303	−	22.9156i	−0.420275	−	0.727937i	−0.995966	+	0.0897299i	$0.971400\pi$
$992$	2.53390	+	2.12619i	0.0804513	+	0.0675067i
$993$	11.5133			0.365364
$994$	0.242049	+	0.203103i	0.00767733	+	0.00644204i
$995$	3.03504	−	1.10466i	0.0962172	−	0.0350202i
$996$	4.77896	−	27.1028i	0.151427	−	0.858786i
$997$	−2.31702	−	13.1405i	−0.0733809	−	0.416164i	−0.999264	−	0.0383540i	$-0.987789\pi$
$997$	−2.31702	−	13.1405i	−0.0733809	−	0.416164i	0.925883	−	0.377809i	$-0.123323\pi$
$998$	24.8179			0.785597
$999$	11.4994	−	41.8695i	0.363824	−	1.32469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.9.2	✓	12
3.2	odd	2		666.2.x.g.379.2		12
4.3	odd	2		592.2.bc.d.305.1		12
37.12	even	9		2738.2.a.t.1.6		6
37.25	even	18		2738.2.a.q.1.6		6
37.33	even	9	inner	74.2.f.b.33.2	yes	12
111.107	odd	18		666.2.x.g.181.2		12
148.107	odd	18		592.2.bc.d.33.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.2	✓	12	1.1	even	1	trivial
74.2.f.b.33.2	yes	12	37.33	even	9	inner
592.2.bc.d.33.1		12	148.107	odd	18
592.2.bc.d.305.1		12	4.3	odd	2
666.2.x.g.181.2		12	111.107	odd	18
666.2.x.g.379.2		12	3.2	odd	2
2738.2.a.q.1.6		6	37.25	even	18
2738.2.a.t.1.6		6	37.12	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.504922 - 2.86356i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.266044 + 0.223238i) q^{5} +2.90773 q^{6} +(0.773586 + 0.649116i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-5.12593 - 1.86569i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.504922 - 2.86356i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.266044 + 0.223238i) q^{5} +2.90773 q^{6} +(0.773586 + 0.649116i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-5.12593 - 1.86569i) q^{9} +(-0.173648 + 0.300767i) q^{10} +(2.73237 + 4.73261i) q^{11} +(0.504922 + 2.86356i) q^{12} +(-5.97892 + 2.17615i) q^{13} +(-0.504922 + 0.874551i) q^{14} +(0.773586 - 0.649116i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.490749 - 0.178618i) q^{17} +(0.947234 - 5.37203i) q^{18} +(0.869950 - 4.93373i) q^{19} +(-0.326352 - 0.118782i) q^{20} +(2.24938 - 1.88745i) q^{21} +(-4.18624 + 3.51267i) q^{22} +(-0.721492 + 1.24966i) q^{23} +(-2.73237 + 0.994503i) q^{24} +(-0.847296 - 4.80526i) q^{25} +(-3.18132 - 5.51020i) q^{26} +(-3.56910 + 6.18186i) q^{27} +(-0.948944 - 0.345387i) q^{28} +(3.16714 + 5.48565i) q^{29} +(0.773586 + 0.649116i) q^{30} +3.30777 q^{31} +(0.766044 + 0.642788i) q^{32} +(14.9317 - 5.43471i) q^{33} +(0.0906868 - 0.514310i) q^{34} +(0.0609011 + 0.345387i) q^{35} +5.45490 q^{36} +(-5.88521 + 1.53765i) q^{37} +5.00984 q^{38} +(3.21264 + 18.2198i) q^{39} +(0.0603074 - 0.342020i) q^{40} +(1.03412 - 0.376390i) q^{41} +(2.24938 + 1.88745i) q^{42} -6.27037 q^{43} +(-4.18624 - 3.51267i) q^{44} +(-0.947234 - 1.64066i) q^{45} +(-1.35596 - 0.493529i) q^{46} +(5.71910 - 9.90577i) q^{47} +(-1.45387 - 2.51817i) q^{48} +(-1.03845 - 5.88936i) q^{49} +(4.58512 - 1.66885i) q^{50} +(-0.759273 + 1.31510i) q^{51} +(4.87406 - 4.08982i) q^{52} +(0.0706817 - 0.0593090i) q^{53} +(-6.70771 - 2.44141i) q^{54} +(-0.329565 + 1.86905i) q^{55} +(0.175358 - 0.994503i) q^{56} +(-13.6888 - 4.98230i) q^{57} +(-4.85235 + 4.07160i) q^{58} +(2.29059 - 1.92203i) q^{59} +(-0.504922 + 0.874551i) q^{60} +(-3.58571 + 1.30509i) q^{61} +(0.574388 + 3.25751i) q^{62} +(-2.75430 - 4.77059i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.07646 - 0.755769i) q^{65} +(7.94501 + 13.7612i) q^{66} +(-0.892251 - 0.748687i) q^{67} +0.522244 q^{68} +(3.21418 + 2.69701i) q^{69} +(-0.329565 + 0.119952i) q^{70} +(0.0543332 - 0.308139i) q^{71} +(0.947234 + 5.37203i) q^{72} +13.2325 q^{73} +(-2.53624 - 5.52879i) q^{74} -14.1879 q^{75} +(0.869950 + 4.93373i) q^{76} +(-0.958285 + 5.43471i) q^{77} +(-17.3851 + 6.32766i) q^{78} +(7.12939 + 5.98227i) q^{79} +0.347296 q^{80} +(3.36390 + 2.82265i) q^{81} +(0.550245 + 0.953052i) q^{82} +(-8.89395 - 3.23713i) q^{83} +(-1.46818 + 2.54296i) q^{84} +(-0.0906868 - 0.157074i) q^{85} +(-1.08884 - 6.17511i) q^{86} +(17.3076 - 6.29947i) q^{87} +(2.73237 - 4.73261i) q^{88} +(-12.0788 + 10.1354i) q^{89} +(1.45125 - 1.21774i) q^{90} +(-6.03778 - 2.19757i) q^{91} +(0.250571 - 1.42106i) q^{92} +(1.67017 - 9.47198i) q^{93} +(10.7484 + 3.91209i) q^{94} +(1.33284 - 1.11839i) q^{95} +(2.22745 - 1.86905i) q^{96} +(0.464564 - 0.804648i) q^{97} +(5.61956 - 2.04535i) q^{98} +(-5.17640 - 29.3568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

L-functions

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