LMFDB - Embedded newform 117.2.bc.a.110.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(20,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 11]))

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

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

chi := DirichletCharacter("117.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			110.1
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641647 + 2.39466i) q^{2} +(0.658999 + 1.60179i) q^{3} +(-3.59064 - 2.07306i) q^{4} +(-0.145266 + 0.542141i) q^{5} +(-4.25858 + 0.550296i) q^{6} +(-0.396138 - 0.396138i) q^{7} +(3.76217 - 3.76217i) q^{8} +(-2.13144 + 2.11115i) q^{9} +O(q^{10})$	\(q+(-0.641647 + 2.39466i) q^{2} +(0.658999 + 1.60179i) q^{3} +(-3.59064 - 2.07306i) q^{4} +(-0.145266 + 0.542141i) q^{5} +(-4.25858 + 0.550296i) q^{6} +(-0.396138 - 0.396138i) q^{7} +(3.76217 - 3.76217i) q^{8} +(-2.13144 + 2.11115i) q^{9} +(-1.20503 - 0.695727i) q^{10} +(5.09416 + 1.36498i) q^{11} +(0.954368 - 7.11758i) q^{12} +(-1.60889 - 3.22668i) q^{13} +(1.20280 - 0.694436i) q^{14} +(-0.964125 + 0.124585i) q^{15} +(2.44901 + 4.24182i) q^{16} +(1.39921 + 2.42351i) q^{17} +(-3.68786 - 6.45869i) q^{18} +(3.31532 + 0.888337i) q^{19} +(1.64549 - 1.64549i) q^{20} +(0.373474 - 0.895584i) q^{21} +(-6.53731 + 11.3229i) q^{22} -7.55830 q^{23} +(8.50545 + 3.54692i) q^{24} +(4.05731 + 2.34249i) q^{25} +(8.75915 - 1.78235i) q^{26} +(-4.78623 - 2.02287i) q^{27} +(0.601173 + 2.24361i) q^{28} +(-0.775891 + 0.447961i) q^{29} +(0.320290 - 2.38869i) q^{30} +(5.88269 + 1.57626i) q^{31} +(-1.45069 + 0.388711i) q^{32} +(1.17064 + 9.05927i) q^{33} +(-6.70128 + 1.79560i) q^{34} +(0.272308 - 0.157217i) q^{35} +(12.0298 - 3.16178i) q^{36} +(-0.0565841 + 0.0151617i) q^{37} +(-4.25453 + 7.36906i) q^{38} +(4.10820 - 4.70347i) q^{39} +(1.49311 + 2.58614i) q^{40} +(4.11801 + 4.11801i) q^{41} +(1.90498 + 1.46899i) q^{42} -10.4345i q^{43} +(-15.4616 - 15.4616i) q^{44} +(-0.834915 - 1.46222i) q^{45} +(4.84977 - 18.0996i) q^{46} +(-2.84732 - 10.6264i) q^{47} +(-5.18059 + 6.71815i) q^{48} -6.68615i q^{49} +(-8.21283 + 8.21283i) q^{50} +(-2.95986 + 3.83833i) q^{51} +(-0.912164 + 14.9212i) q^{52} +5.68410i q^{53} +(7.91516 - 10.1634i) q^{54} +(-1.48002 + 2.56347i) q^{55} -2.98068 q^{56} +(0.761864 + 5.89584i) q^{57} +(-0.574866 - 2.14543i) q^{58} +(-1.32335 - 4.93881i) q^{59} +(3.72010 + 1.55135i) q^{60} -4.16982 q^{61} +(-7.54922 + 13.0756i) q^{62} +(1.68065 + 0.00803816i) q^{63} +6.07273i q^{64} +(1.98303 - 0.403516i) q^{65} +(-22.4450 - 3.00956i) q^{66} +(4.65866 - 4.65866i) q^{67} -11.6026i q^{68} +(-4.98091 - 12.1068i) q^{69} +(0.201756 + 0.752964i) q^{70} +(0.573694 - 2.14106i) q^{71} +(-0.0763393 + 15.9613i) q^{72} +(2.68642 + 2.68642i) q^{73} -0.145228i q^{74} +(-1.07841 + 8.04265i) q^{75} +(-10.0625 - 10.0625i) q^{76} +(-1.47727 - 2.55871i) q^{77} +(8.62721 + 12.8557i) q^{78} +(2.61166 - 4.52353i) q^{79} +(-2.65542 + 0.711518i) q^{80} +(0.0860878 - 8.99959i) q^{81} +(-12.5035 + 7.21893i) q^{82} +(0.139959 - 0.0375018i) q^{83} +(-3.19761 + 2.44148i) q^{84} +(-1.51714 + 0.406517i) q^{85} +(24.9870 + 6.69526i) q^{86} +(-1.22885 - 0.947606i) q^{87} +(24.3003 - 14.0298i) q^{88} +(-2.14168 - 7.99287i) q^{89} +(4.03725 - 1.06111i) q^{90} +(-0.640871 + 1.91555i) q^{91} +(27.1391 + 15.6688i) q^{92} +(1.35185 + 10.4616i) q^{93} +27.2735 q^{94} +(-0.963208 + 1.66832i) q^{95} +(-1.57863 - 2.06753i) q^{96} +(-0.650247 + 0.650247i) q^{97} +(16.0111 + 4.29015i) q^{98} +(-13.7396 + 7.84517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.641647	+	2.39466i	−0.453713	+	1.69328i	0.238130	+	0.971233i	$0.423466\pi$
$2$	−0.641647	+	2.39466i	−0.453713	+	1.69328i	−0.691843	+	0.722048i	$0.743201\pi$
$3$	0.658999	+	1.60179i	0.380473	+	0.924792i
$3$	0.658999	+	1.60179i	0.380473	+	0.924792i
$4$	−3.59064	−	2.07306i	−1.79532	−	1.03653i
$5$	−0.145266	+	0.542141i	−0.0649651	+	0.242453i	−0.990771	−	0.135546i	$-0.956721\pi$
$5$	−0.145266	+	0.542141i	−0.0649651	+	0.242453i	0.925806	+	0.377999i	$0.123388\pi$
$6$	−4.25858	+	0.550296i	−1.73856	+	0.224657i
$7$	−0.396138	−	0.396138i	−0.149726	−	0.149726i	0.628270	−	0.777996i	$-0.283764\pi$
$7$	−0.396138	−	0.396138i	−0.149726	−	0.149726i	−0.777996	+	0.628270i	$0.783764\pi$
$8$	3.76217	−	3.76217i	1.33013	−	1.33013i
$9$	−2.13144	+	2.11115i	−0.710481	+	0.703717i
$10$	−1.20503	−	0.695727i	−0.381065	−	0.220008i
$11$	5.09416	+	1.36498i	1.53595	+	0.411555i	0.924953	−	0.380081i	$-0.124104\pi$
$11$	5.09416	+	1.36498i	1.53595	+	0.411555i	0.610993	+	0.791636i	$0.290770\pi$
$12$	0.954368	−	7.11758i	0.275502	−	2.05467i
$13$	−1.60889	−	3.22668i	−0.446225	−	0.894921i
$13$	−1.60889	−	3.22668i	−0.446225	−	0.894921i
$14$	1.20280	−	0.694436i	0.321461	−	0.185596i
$15$	−0.964125	+	0.124585i	−0.248936	+	0.0321676i
$16$	2.44901	+	4.24182i	0.612253	+	1.06045i
$17$	1.39921	+	2.42351i	0.339359	+	0.587787i	0.984312	−	0.176435i	$-0.0564565\pi$
$17$	1.39921	+	2.42351i	0.339359	+	0.587787i	−0.644953	+	0.764222i	$0.723123\pi$
$18$	−3.68786	−	6.45869i	−0.869236	−	1.52233i
$19$	3.31532	+	0.888337i	0.760586	+	0.203798i	0.618209	−	0.786014i	$-0.287859\pi$
$19$	3.31532	+	0.888337i	0.760586	+	0.203798i	0.142377	+	0.989812i	$0.454525\pi$
$20$	1.64549	−	1.64549i	0.367942	−	0.367942i
$21$	0.373474	−	0.895584i	0.0814988	−	0.195432i
$22$	−6.53731	+	11.3229i	−1.39376	+	2.41406i
$23$	−7.55830			−1.57602			−0.788008	−	0.615666i	$-0.788887\pi$
$23$	−7.55830			−1.57602			−0.788008	+	0.615666i	$0.788887\pi$
$24$	8.50545	+	3.54692i	1.73617	+	0.724013i
$25$	4.05731	+	2.34249i	0.811462	+	0.468498i
$26$	8.75915	−	1.78235i	1.71781	−	0.349547i
$27$	−4.78623	−	2.02287i	−0.921110	−	0.389302i
$28$	0.601173	+	2.24361i	0.113611	+	0.424002i
$29$	−0.775891	+	0.447961i	−0.144079	+	0.0831842i	−0.570307	−	0.821432i	$-0.693176\pi$
$29$	−0.775891	+	0.447961i	−0.144079	+	0.0831842i	0.426227	+	0.904616i	$0.359842\pi$
$30$	0.320290	−	2.38869i	0.0584767	−	0.436113i
$31$	5.88269	+	1.57626i	1.05656	+	0.283105i	0.744961	−	0.667108i	$-0.232468\pi$
$31$	5.88269	+	1.57626i	1.05656	+	0.283105i	0.311601	+	0.950213i	$0.399135\pi$
$32$	−1.45069	+	0.388711i	−0.256448	+	0.0687150i
$33$	1.17064	+	9.05927i	0.203783	+	1.57702i
$34$	−6.70128	+	1.79560i	−1.14926	+	0.307943i
$35$	0.272308	−	0.157217i	0.0460285	−	0.0265746i
$36$	12.0298	−	3.16178i	2.00496	−	0.526963i
$37$	−0.0565841	+	0.0151617i	−0.00930236	+	0.00249256i	−0.263467	−	0.964668i	$-0.584866\pi$
$37$	−0.0565841	+	0.0151617i	−0.00930236	+	0.00249256i	0.254165	+	0.967161i	$0.418199\pi$
$38$	−4.25453	+	7.36906i	−0.690176	+	1.19542i
$39$	4.10820	−	4.70347i	0.657839	−	0.753158i
$40$	1.49311	+	2.58614i	0.236081	+	0.408905i
$41$	4.11801	+	4.11801i	0.643125	+	0.643125i	0.951322	−	0.308197i	$-0.0997257\pi$
$41$	4.11801	+	4.11801i	0.643125	+	0.643125i	−0.308197	+	0.951322i	$0.599726\pi$
$42$	1.90498	+	1.46899i	0.293945	+	0.226671i
$43$		−	10.4345i		−	1.59124i	−0.605794	−	0.795621i	$-0.707145\pi$
$43$		−	10.4345i		−	1.59124i	0.605794	−	0.795621i	$-0.292855\pi$
$44$	−15.4616	−	15.4616i	−2.33093	−	2.33093i
$45$	−0.834915	−	1.46222i	−0.124462	−	0.217975i
$46$	4.84977	−	18.0996i	0.715059	−	2.66864i
$47$	−2.84732	−	10.6264i	−0.415325	−	1.55001i	−0.784184	−	0.620528i	$-0.786918\pi$
$47$	−2.84732	−	10.6264i	−0.415325	−	1.55001i	0.368859	−	0.929485i	$-0.379748\pi$
$48$	−5.18059	+	6.71815i	−0.747754	+	0.969681i
$49$		−	6.68615i		−	0.955164i
$50$	−8.21283	+	8.21283i	−1.16147	+	1.16147i
$51$	−2.95986	+	3.83833i	−0.414464	+	0.537474i
$52$	−0.912164	+	14.9212i	−0.126494	+	2.06919i
$53$			5.68410i			0.780771i	0.920652	+	0.390385i	$0.127658\pi$
$53$			5.68410i			0.780771i	−0.920652	+	0.390385i	$0.872342\pi$
$54$	7.91516	−	10.1634i	1.07712	−	1.38307i
$55$	−1.48002	+	2.56347i	−0.199566	+	0.345658i
$56$	−2.98068			−0.398309
$57$	0.761864	+	5.89584i	0.100911	+	0.780924i
$58$	−0.574866	−	2.14543i	−0.0754836	−	0.281709i
$59$	−1.32335	−	4.93881i	−0.172285	−	0.642978i	−0.996998	−	0.0774259i	$-0.975330\pi$
$59$	−1.32335	−	4.93881i	−0.172285	−	0.642978i	0.824713	−	0.565552i	$-0.191337\pi$
$60$	3.72010	+	1.55135i	0.480262	+	0.200278i
$61$	−4.16982			−0.533890			−0.266945	−	0.963712i	$-0.586014\pi$
$61$	−4.16982			−0.533890			−0.266945	+	0.963712i	$0.586014\pi$
$62$	−7.54922	+	13.0756i	−0.958752	+	1.66061i
$63$	1.68065	+	0.00803816i	0.211742	+	0.00101271i
$64$			6.07273i			0.759091i
$65$	1.98303	−	0.403516i	0.245965	−	0.0500499i
$66$	−22.4450	−	3.00956i	−2.76279	−	0.370452i
$67$	4.65866	−	4.65866i	0.569146	−	0.569146i	−0.362743	−	0.931889i	$-0.618160\pi$
$67$	4.65866	−	4.65866i	0.569146	−	0.569146i	0.931889	+	0.362743i	$0.118160\pi$
$68$		−	11.6026i		−	1.40702i
$69$	−4.98091	−	12.1068i	−0.599631	−	1.45749i
$70$	0.201756	+	0.752964i	0.0241145	+	0.0899965i
$71$	0.573694	−	2.14106i	0.0680850	−	0.254097i	−0.923492	−	0.383619i	$-0.874678\pi$
$71$	0.573694	−	2.14106i	0.0680850	−	0.254097i	0.991577	+	0.129522i	$0.0413443\pi$
$72$	−0.0763393	+	15.9613i	−0.00899667	+	1.88106i
$73$	2.68642	+	2.68642i	0.314422	+	0.314422i	0.846620	−	0.532198i	$-0.178634\pi$
$73$	2.68642	+	2.68642i	0.314422	+	0.314422i	−0.532198	+	0.846620i	$0.678634\pi$
$74$		−	0.145228i		−	0.0168824i
$75$	−1.07841	+	8.04265i	−0.124524	+	0.928685i
$76$	−10.0625	−	10.0625i	−1.15425	−	1.15425i
$77$	−1.47727	−	2.55871i	−0.168351	−	0.291592i
$78$	8.62721	+	12.8557i	0.976839	+	1.45562i
$79$	2.61166	−	4.52353i	0.293835	−	0.508937i	−0.680878	−	0.732397i	$-0.738402\pi$
$79$	2.61166	−	4.52353i	0.293835	−	0.508937i	0.974713	+	0.223459i	$0.0717350\pi$
$80$	−2.65542	+	0.711518i	−0.296885	+	0.0795502i
$81$	0.0860878	−	8.99959i	0.00956531	−	0.999954i
$82$	−12.5035	+	7.21893i	−1.38079	+	0.797197i
$83$	0.139959	−	0.0375018i	0.0153625	−	0.00411636i	−0.251130	−	0.967953i	$-0.580802\pi$
$83$	0.139959	−	0.0375018i	0.0153625	−	0.00411636i	0.266492	+	0.963837i	$0.414135\pi$
$84$	−3.19761	+	2.44148i	−0.348888	+	0.266388i
$85$	−1.51714	+	0.406517i	−0.164557	+	0.0440930i
$86$	24.9870	+	6.69526i	2.69442	+	0.721968i
$87$	−1.22885	−	0.947606i	−0.131746	−	0.101594i
$88$	24.3003	−	14.0298i	2.59042	−	1.49558i
$89$	−2.14168	−	7.99287i	−0.227018	−	0.847242i	−0.981586	−	0.191020i	$-0.938820\pi$
$89$	−2.14168	−	7.99287i	−0.227018	−	0.847242i	0.754568	−	0.656222i	$-0.227846\pi$
$90$	4.03725	−	1.06111i	0.425563	−	0.111851i
$91$	−0.640871	+	1.91555i	−0.0671815	+	0.200805i
$92$	27.1391	+	15.6688i	2.82945	+	1.63358i
$93$	1.35185	+	10.4616i	0.140180	+	1.08481i
$94$	27.2735			2.81305
$95$	−0.963208	+	1.66832i	−0.0988230	+	0.171167i
$96$	−1.57863	−	2.06753i	−0.161119	−	0.211017i
$97$	−0.650247	+	0.650247i	−0.0660226	+	0.0660226i	−0.739347	−	0.673325i	$-0.764866\pi$
$97$	−0.650247	+	0.650247i	−0.0660226	+	0.0660226i	0.673325	+	0.739347i	$0.264866\pi$
$98$	16.0111	+	4.29015i	1.61736	+	0.433371i
$99$	−13.7396	+	7.84517i	−1.38088	+	0.788469i
$100$	−9.71223	−	16.8221i	−0.971223	−	1.68221i
$101$	6.92119	+	11.9878i	0.688684	+	1.19284i	0.972264	+	0.233887i	$0.0751445\pi$
$101$	6.92119	+	11.9878i	0.688684	+	1.19284i	−0.283580	+	0.958949i	$0.591522\pi$
$102$	−7.29231	−	9.55073i	−0.722046	−	0.945663i
$103$	−0.558610	+	0.322514i	−0.0550415	+	0.0317782i	−0.527268	−	0.849699i	$-0.676784\pi$
$103$	−0.558610	+	0.322514i	−0.0550415	+	0.0317782i	0.472227	+	0.881477i	$0.343450\pi$
$104$	−18.1922	−	6.08642i	−1.78389	−	0.596822i
$105$	0.431279	+	0.332574i	0.0420886	+	0.0324559i
$106$	−13.6115	−	3.64719i	−1.32206	−	0.354246i
$107$	−9.64434	−	5.56816i	−0.932354	−	0.538295i	−0.0447985	−	0.998996i	$-0.514265\pi$
$107$	−9.64434	−	5.56816i	−0.932354	−	0.538295i	−0.887555	+	0.460701i	$0.847598\pi$
$108$	12.9921	+	17.1855i	1.25017	+	1.65368i
$109$	−12.1108	+	12.1108i	−1.16000	+	1.16000i	−0.175526	+	0.984475i	$0.556163\pi$
$109$	−12.1108	+	12.1108i	−1.16000	+	1.16000i	−0.984475	+	0.175526i	$0.943837\pi$
$110$	−5.18898	−	5.18898i	−0.494750	−	0.494750i
$111$	−0.0615745	−	0.0806441i	−0.00584440	−	0.00765440i
$112$	0.710198	−	2.65049i	0.0671074	−	0.250448i
$113$	−5.73325	−	3.31009i	−0.539339	−	0.311387i	0.205472	−	0.978663i	$-0.434127\pi$
$113$	−5.73325	−	3.31009i	−0.539339	−	0.311387i	−0.744811	+	0.667276i	$0.767460\pi$
$114$	−14.6074	−	1.95865i	−1.36811	−	0.183444i
$115$	1.09797	−	4.09767i	0.102386	−	0.382109i
$116$	3.71459			0.344891
$117$	10.2413	+	3.48088i	0.946805	+	0.321808i
$118$	12.6759			1.16691
$119$	0.405763	−	1.51433i	0.0371962	−	0.138818i
$120$	−3.15849	+	4.09590i	−0.288329	+	0.373903i
$121$	14.5610	+	8.40679i	1.32373	+	0.764254i
$122$	2.67555	−	9.98530i	0.242233	−	0.904026i
$123$	−3.88241	+	9.30994i	−0.350065	+	0.839449i
$124$	−17.8549	−	17.8549i	−1.60342	−	1.60342i
$125$	−3.84373	+	3.84373i	−0.343793	+	0.343793i
$126$	−1.09764	+	4.01944i	−0.0977851	+	0.358080i
$127$	−4.61182	−	2.66264i	−0.409233	−	0.236271i	0.281227	−	0.959641i	$-0.409259\pi$
$127$	−4.61182	−	2.66264i	−0.409233	−	0.236271i	−0.690460	+	0.723370i	$0.742592\pi$
$128$	−17.4435	−	4.67397i	−1.54180	−	0.413125i
$129$	16.7138	−	6.87631i	1.47157	−	0.605425i
$130$	−0.306126	+	5.00761i	−0.0268491	+	0.439197i
$131$	−10.5429	+	6.08694i	−0.921137	+	0.531819i	−0.883998	−	0.467491i	$-0.845158\pi$
$131$	−10.5429	+	6.08694i	−0.921137	+	0.531819i	−0.0371394	+	0.999310i	$0.511825\pi$
$132$	14.5770	−	34.9554i	1.26877	−	3.04247i
$133$	−0.961420	−	1.66523i	−0.0833657	−	0.144394i
$134$	8.16670	+	14.1451i	0.705495	+	1.22195i
$135$	1.79196	−	2.30096i	0.154227	−	0.198035i
$136$	14.3817	+	3.85357i	1.23322	+	0.330441i
$137$	−4.64769	+	4.64769i	−0.397079	+	0.397079i	−0.877201	−	0.480122i	$-0.840592\pi$
$137$	−4.64769	+	4.64769i	−0.397079	+	0.397079i	0.480122	+	0.877201i	$0.340592\pi$
$138$	32.1876	−	4.15930i	2.73999	−	0.354063i
$139$	−1.44255	+	2.49856i	−0.122355	+	0.211925i	−0.920696	−	0.390281i	$-0.872378\pi$
$139$	−1.44255	+	2.49856i	−0.122355	+	0.211925i	0.798341	+	0.602206i	$0.205711\pi$
$140$	−1.30368			−0.110181
$141$	15.1448	−	11.5636i	1.27542	−	0.973827i
$142$	4.75900	+	2.74761i	0.399366	+	0.230574i
$143$	−3.79158	−	18.6333i	−0.317068	−	1.55820i
$144$	−14.1750	−	3.87095i	−1.18125	−	0.322579i
$145$	−0.130147	−	0.485716i	−0.0108081	−	0.0403365i
$146$	−8.15681	+	4.70934i	−0.675062	+	0.389747i
$147$	10.7098	−	4.40616i	0.883328	−	0.363414i
$148$	0.234604	+	0.0628619i	0.0192843	+	0.00516722i
$149$	−0.293107	+	0.0785378i	−0.0240123	+	0.00643407i	−0.270805	−	0.962634i	$-0.587290\pi$
$149$	−0.293107	+	0.0785378i	−0.0240123	+	0.00643407i	0.246793	+	0.969068i	$0.420623\pi$
$150$	−18.5675	−	7.74296i	−1.51603	−	0.632210i
$151$	−14.6230	+	3.91822i	−1.19000	+	0.318860i	−0.798887	−	0.601481i	$-0.794578\pi$
$151$	−14.6230	+	3.91822i	−1.19000	+	0.318860i	−0.391116	+	0.920341i	$0.627911\pi$
$152$	15.8148	−	9.13070i	1.28275	−	0.740598i
$153$	−8.09873	−	2.21162i	−0.654744	−	0.178799i
$154$	7.07513	−	1.89577i	0.570130	−	0.152766i
$155$	−1.70911	+	2.96027i	−0.137279	+	0.237775i
$156$	−24.5016	+	8.37194i	−1.96170	+	0.670291i
$157$	2.96185	+	5.13007i	0.236381	+	0.409424i	0.959673	−	0.281118i	$-0.0907053\pi$
$157$	2.96185	+	5.13007i	0.236381	+	0.409424i	−0.723292	+	0.690542i	$0.757372\pi$
$158$	9.15656	+	9.15656i	0.728457	+	0.728457i
$159$	−9.10471	+	3.74581i	−0.722050	+	0.297062i
$160$		−	0.842945i		−	0.0666406i
$161$	2.99413	+	2.99413i	0.235971	+	0.235971i
$162$	21.4957	+	5.98071i	1.68886	+	0.469889i
$163$	−3.97922	+	14.8506i	−0.311676	+	1.16319i	0.615368	+	0.788240i	$0.289007\pi$
$163$	−3.97922	+	14.8506i	−0.311676	+	1.16319i	−0.927044	+	0.374952i	$0.877659\pi$
$164$	−6.24942	−	23.3232i	−0.487998	−	1.82123i
$165$	−5.08146	−	0.681353i	−0.395591	−	0.0530432i
$166$			0.359216i			0.0278806i
$167$	1.38680	−	1.38680i	0.107314	−	0.107314i	−0.651411	−	0.758725i	$-0.725823\pi$
$167$	1.38680	−	1.38680i	0.107314	−	0.107314i	0.758725	+	0.651411i	$0.225823\pi$
$168$	−1.96426	−	4.77441i	−0.151546	−	0.368353i
$169$	−7.82297	+	10.3827i	−0.601767	+	0.798672i
$170$		−	3.89388i		−	0.298647i
$171$	−8.94182	+	5.10570i	−0.683798	+	0.390442i
$172$	−21.6313	+	37.4664i	−1.64937	+	2.85679i
$173$	−11.7902			−0.896389			−0.448194	−	0.893936i	$-0.647933\pi$
$173$	−11.7902			−0.896389			−0.448194	+	0.893936i	$0.647933\pi$
$174$	3.05768	−	2.33465i	0.231802	−	0.176989i
$175$	−0.679307	−	2.53521i	−0.0513507	−	0.191644i
$176$	6.68569	+	24.9513i	0.503952	+	1.88078i
$177$	7.03883	−	5.37439i	0.529071	−	0.403964i
$178$	20.5144			1.53762
$179$	7.29437	−	12.6342i	0.545207	−	0.944326i	−0.453387	−	0.891314i	$-0.649784\pi$
$179$	7.29437	−	12.6342i	0.545207	−	0.944326i	0.998594	−	0.0530122i	$-0.0168822\pi$
$180$	−0.0333891	+	6.98113i	−0.00248868	+	0.520343i
$181$		−	3.05362i		−	0.226974i	−0.993539	−	0.113487i	$-0.963798\pi$
$181$		−	3.05362i		−	0.226974i	0.993539	−	0.113487i	$-0.0362020\pi$
$182$	−4.17589	−	2.76378i	−0.309538	−	0.204865i
$183$	−2.74790	−	6.67916i	−0.203131	−	0.493738i
$184$	−28.4356	+	28.4356i	−2.09630	+	2.09630i
$185$		−	0.0328790i		−	0.00241731i
$186$	−25.9193	−	3.47542i	−1.90050	−	0.254830i
$187$	3.81978	+	14.2556i	0.279330	+	1.04247i
$188$	−11.8053	+	44.0581i	−0.860992	+	3.21327i
$189$	1.09467	+	2.69734i	0.0796257	+	0.196203i
$190$	−3.37703	−	3.37703i	−0.244996	−	0.244996i
$191$		−	13.4213i		−	0.971129i	−0.874201	−	0.485564i	$-0.838614\pi$
$191$		−	13.4213i		−	0.971129i	0.874201	−	0.485564i	$-0.161386\pi$
$192$	−9.72722	+	4.00192i	−0.702002	+	0.288814i
$193$	−2.53424	−	2.53424i	−0.182418	−	0.182418i	0.609990	−	0.792409i	$-0.291173\pi$
$193$	−2.53424	−	2.53424i	−0.182418	−	0.182418i	−0.792409	+	0.609990i	$0.791173\pi$
$194$	−1.13989	−	1.97435i	−0.0818394	−	0.141750i
$195$	1.95316	+	2.91048i	0.139869	+	0.208424i
$196$	−13.8608	+	24.0075i	−0.990055	+	1.71482i
$197$	12.7045	−	3.40415i	0.905155	−	0.242536i	0.223926	−	0.974606i	$-0.428113\pi$
$197$	12.7045	−	3.40415i	0.905155	−	0.242536i	0.681229	+	0.732071i	$0.261446\pi$
$198$	−9.97055	−	37.9354i	−0.708576	−	2.69595i
$199$	17.2174	−	9.94049i	1.22051	−	0.704662i	0.255484	−	0.966813i	$-0.417765\pi$
$199$	17.2174	−	9.94049i	1.22051	−	0.704662i	0.965027	+	0.262151i	$0.0844318\pi$
$200$	24.0771	−	6.45144i	1.70251	−	0.456186i
$201$	10.5322	+	4.39213i	0.742886	+	0.309797i
$202$	−33.1478	+	8.88192i	−2.33227	+	0.624930i
$203$	0.484814	+	0.129906i	0.0340273	+	0.00911759i
$204$	18.5849	−	7.64609i	1.30120	−	0.535334i
$205$	−2.83075	+	1.63433i	−0.197708	+	0.114147i
$206$	−0.413880	−	1.54462i	−0.0288364	−	0.107619i
$207$	16.1101	−	15.9567i	1.11973	−	1.10907i
$208$	9.74681	−	14.7268i	0.675820	−	1.02112i
$209$	15.6762	+	9.05065i	1.08434	+	0.626047i
$210$	−1.07313	+	0.819373i	−0.0740531	+	0.0565421i
$211$	−5.58902			−0.384764			−0.192382	−	0.981320i	$-0.561621\pi$
$211$	−5.58902			−0.384764			−0.192382	+	0.981320i	$0.561621\pi$
$212$	11.7835	−	20.4095i	0.809291	−	1.40173i
$213$	3.80758	−	0.492017i	0.260891	−	0.0337125i
$214$	19.5221	−	19.5221i	1.33451	−	1.33451i
$215$	5.65696	+	1.51578i	0.385801	+	0.103375i
$216$	−25.6170	+	10.3962i	−1.74301	+	0.707373i
$217$	−1.70594	−	2.95478i	−0.115807	−	0.200583i
$218$	−21.2303	−	36.7720i	−1.43790	−	2.49051i
$219$	−2.53273	+	6.07343i	−0.171146	+	0.410404i
$220$	10.6284	−	6.13632i	0.716568	−	0.413711i
$221$	5.56872	−	8.41397i	0.374593	−	0.565985i
$222$	0.232624	−	0.0957051i	0.0156127	−	0.00642330i
$223$	15.9523	+	4.27441i	1.06825	+	0.286236i	0.749773	−	0.661696i	$-0.230163\pi$
$223$	15.9523	+	4.27441i	1.06825	+	0.286236i	0.318474	+	0.947931i	$0.396830\pi$
$224$	0.728656	+	0.420690i	0.0486854	+	0.0281085i
$225$	−13.5933	+	3.57271i	−0.906218	+	0.238181i
$226$	11.6053	−	11.6053i	0.771971	−	0.771971i
$227$	−2.39191	−	2.39191i	−0.158757	−	0.158757i	0.623259	−	0.782016i	$-0.285808\pi$
$227$	−2.39191	−	2.39191i	−0.158757	−	0.158757i	−0.782016	+	0.623259i	$0.785808\pi$
$228$	9.48684	−	22.7492i	0.628281	−	1.50661i
$229$	4.44029	−	16.5714i	0.293423	−	1.09507i	−0.649039	−	0.760755i	$-0.724829\pi$
$229$	4.44029	−	16.5714i	0.293423	−	1.09507i	0.942462	−	0.334313i	$-0.108504\pi$
$230$	9.10802	+	5.25852i	0.600565	+	0.346736i
$231$	3.12499	−	4.05246i	0.205609	−	0.266632i
$232$	−1.23373	+	4.60433i	−0.0809981	+	0.302289i
$233$	−2.96268			−0.194092			−0.0970459	−	0.995280i	$-0.530939\pi$
$233$	−2.96268			−0.194092			−0.0970459	+	0.995280i	$0.530939\pi$
$234$	−14.9068	+	22.2908i	−0.974489	+	1.45720i
$235$	6.17460			0.402787
$236$	−5.48675	+	20.4768i	−0.357157	+	1.33293i
$237$	8.96682	+	1.20233i	0.582457	+	0.0780994i
$238$	3.36594	+	1.94333i	0.218182	+	0.125967i
$239$	−6.69421	+	24.9831i	−0.433012	+	1.61602i	0.312766	+	0.949830i	$0.398744\pi$
$239$	−6.69421	+	24.9831i	−0.433012	+	1.61602i	−0.745778	+	0.666194i	$0.767922\pi$
$240$	−2.88962	−	3.78453i	−0.186524	−	0.244290i
$241$	−4.17557	−	4.17557i	−0.268972	−	0.268972i	0.559714	−	0.828686i	$-0.310911\pi$
$241$	−4.17557	−	4.17557i	−0.268972	−	0.268972i	−0.828686	+	0.559714i	$0.810911\pi$
$242$	−29.4744	+	29.4744i	−1.89469	+	1.89469i
$243$	14.4722	−	5.79282i	0.928389	−	0.371610i
$244$	14.9723	+	8.64427i	0.958504	+	0.553392i
$245$	3.62484	+	0.971272i	0.231582	+	0.0620523i
$246$	−19.8030	−	15.2708i	−1.26259	−	0.973628i
$247$	−2.46759	−	12.1267i	−0.157009	−	0.771604i
$248$	28.0618	−	16.2015i	1.78193	−	1.02880i
$249$	0.152302	+	0.199470i	0.00965177	+	0.0126409i
$250$	−6.73810	−	11.6707i	−0.426155	−	0.738122i
$251$	−1.51755	−	2.62847i	−0.0957869	−	0.165908i	0.814150	−	0.580655i	$-0.197203\pi$
$251$	−1.51755	−	2.62847i	−0.0957869	−	0.165908i	−0.909937	+	0.414747i	$0.863870\pi$
$252$	−6.01796	−	3.51295i	−0.379096	−	0.221295i
$253$	−38.5032	−	10.3169i	−2.42067	−	0.648618i
$254$	9.33528	−	9.33528i	0.585747	−	0.585747i
$255$	−1.65095	−	2.16224i	−0.103386	−	0.135405i
$256$	16.3124	−	28.2540i	1.01953	−	1.76587i
$257$	19.3209			1.20521			0.602603	−	0.798041i	$-0.294130\pi$
$257$	19.3209			1.20521			0.602603	+	0.798041i	$0.294130\pi$
$258$	5.74205	+	44.4361i	0.357484	+	2.76647i
$259$	0.0284212	+	0.0164090i	0.00176601	+	0.00101961i
$260$	−7.95687	−	2.66206i	−0.493464	−	0.165094i
$261$	0.708053	−	2.59282i	0.0438274	−	0.160492i
$262$	−7.81134	−	29.1523i	−0.482586	−	1.80104i
$263$	7.98587	−	4.61064i	0.492430	−	0.284304i	−0.233152	−	0.972440i	$-0.574904\pi$
$263$	7.98587	−	4.61064i	0.492430	−	0.284304i	0.725582	+	0.688136i	$0.241571\pi$
$264$	38.4866	+	29.6783i	2.36869	+	1.82657i
$265$	−3.08158	−	0.825708i	−0.189300	−	0.0507228i
$266$	4.60455	−	1.23379i	0.282323	−	0.0756482i
$267$	11.3915	−	8.69781i	0.697149	−	0.532297i
$268$	−26.3852	+	7.06990i	−1.61173	+	0.431863i
$269$	−21.9375	+	12.6656i	−1.33755	+	0.772236i	−0.986444	−	0.164099i	$-0.947528\pi$
$269$	−21.9375	+	12.6656i	−1.33755	+	0.772236i	−0.351108	+	0.936335i	$0.614195\pi$
$270$	4.36021	+	5.76754i	0.265354	+	0.351001i
$271$	21.4503	−	5.74758i	1.30301	−	0.349141i	0.460423	−	0.887700i	$-0.347698\pi$
$271$	21.4503	−	5.74758i	1.30301	−	0.349141i	0.842588	+	0.538559i	$0.181031\pi$
$272$	−6.85338	+	11.8704i	−0.415548	+	0.719749i
$273$	−3.49064	+	0.235809i	−0.211263	+	0.0142718i
$274$	−8.14747	−	14.1118i	−0.492206	−	0.852526i
$275$	17.4711	+	17.4711i	1.05355	+	1.05355i
$276$	−7.21340	+	53.7968i	−0.434196	+	3.23819i
$277$		−	20.5727i		−	1.23609i	−0.786142	−	0.618046i	$-0.787924\pi$
$277$		−	20.5727i		−	1.23609i	0.786142	−	0.618046i	$-0.212076\pi$
$278$	−5.05760	−	5.05760i	−0.303335	−	0.303335i
$279$	−15.8663	+	9.05953i	−0.949893	+	0.542380i
$280$	0.432992	−	1.61595i	0.0258762	−	0.0965713i
$281$	−0.359183	−	1.34049i	−0.0214271	−	0.0799670i	0.954384	−	0.298581i	$-0.0965132\pi$
$281$	−0.359183	−	1.34049i	−0.0214271	−	0.0799670i	−0.975811	+	0.218614i	$0.929847\pi$
$282$	17.9732	+	43.6863i	1.07029	+	2.60148i
$283$			33.2869i			1.97870i	0.145554	+	0.989350i	$0.453503\pi$
$283$			33.2869i			1.97870i	−0.145554	+	0.989350i	$0.546497\pi$
$284$	−6.49846	+	6.49846i	−0.385613	+	0.385613i
$285$	−3.30705	−	0.443430i	−0.195893	−	0.0262665i
$286$	47.0533	+	2.87648i	2.78232	+	0.170090i
$287$		−	3.26260i		−	0.192585i
$288$	2.27143	−	3.89114i	0.133845	−	0.229287i
$289$	4.58440	−	7.94042i	0.269671	−	0.467084i
$290$	1.24663			0.0732048
$291$	−1.47007	−	0.613045i	−0.0861769	−	0.0359373i
$292$	−4.07687	−	15.2151i	−0.238581	−	0.890395i
$293$	2.47350	+	9.23122i	0.144503	+	0.539294i	0.999777	+	0.0211172i	$0.00672230\pi$
$293$	2.47350	+	9.23122i	0.144503	+	0.539294i	−0.855274	+	0.518177i	$0.826611\pi$
$294$	3.67936	+	28.4735i	0.214585	+	1.66061i
$295$	2.86977			0.167084
$296$	−0.155838	+	0.269919i	−0.00905789	+	0.0156887i
$297$	−21.6206	−	16.8379i	−1.25456	−	0.977034i
$298$		−	0.752285i		−	0.0435787i
$299$	12.1605	+	24.3882i	0.703257	+	1.41041i
$300$	20.5450	−	26.6426i	1.18617	−	1.53821i
$301$	−4.13350	+	4.13350i	−0.238251	+	0.238251i
$302$		−	37.5313i		−	2.15968i
$303$	−14.6409	+	18.9862i	−0.841099	+	1.09073i
$304$	4.35110	+	16.2385i	0.249553	+	0.931343i
$305$	0.605734	−	2.26063i	0.0346842	−	0.129443i
$306$	10.4926	−	17.9746i	0.599822	−	1.02754i
$307$	22.8954	+	22.8954i	1.30671	+	1.30671i	0.923774	+	0.382938i	$0.125088\pi$
$307$	22.8954	+	22.8954i	1.30671	+	1.30671i	0.382938	+	0.923774i	$0.374912\pi$
$308$			12.2499i			0.698001i
$309$	−0.884722	−	0.682238i	−0.0503301	−	0.0388112i
$310$	−5.99220	−	5.99220i	−0.340334	−	0.340334i
$311$	−8.44356	−	14.6247i	−0.478790	−	0.829289i	0.520914	−	0.853609i	$-0.325591\pi$
$311$	−8.44356	−	14.6247i	−0.478790	−	0.829289i	−0.999704	+	0.0243201i	$0.992258\pi$
$312$	−2.23950	−	33.1510i	−0.126787	−	1.87680i
$313$	−8.64294	+	14.9700i	−0.488528	+	0.846155i	−0.999913	−	0.0131968i	$-0.995799\pi$
$313$	−8.64294	+	14.9700i	−0.488528	+	0.846155i	0.511385	+	0.859352i	$0.329133\pi$
$314$	−14.1852	+	3.80092i	−0.800519	+	0.214498i
$315$	−0.248500	+	0.909984i	−0.0140014	+	0.0512718i
$316$	−18.7551	+	10.8282i	−1.05506	+	0.609137i
$317$	11.2652	−	3.01849i	0.632715	−	0.169535i	0.0718135	−	0.997418i	$-0.477121\pi$
$317$	11.2652	−	3.01849i	0.632715	−	0.169535i	0.560901	+	0.827883i	$0.310455\pi$
$318$	−3.12793	−	24.2062i	−0.175406	−	1.35742i
$319$	−4.56396	+	1.22291i	−0.255533	+	0.0684698i
$320$	−3.29228	−	0.882163i	−0.184044	−	0.0493144i
$321$	2.56340	−	19.1176i	0.143075	−	1.06704i
$322$	−9.09111	+	5.24876i	−0.506628	+	0.292502i
$323$	2.48595	+	9.27767i	0.138322	+	0.516224i
$324$	−18.9658	+	32.1358i	−1.05365	+	1.78532i
$325$	1.03072	−	16.8605i	0.0571739	−	0.935250i
$326$	−33.0090	−	19.0577i	−1.82820	−	1.05551i
$327$	−27.3798	−	11.4179i	−1.51411	−	0.631410i
$328$	30.9853			1.71087
$329$	−3.08157	+	5.33744i	−0.169893	+	0.294263i
$330$	4.89211	−	11.7312i	0.269302	−	0.645780i
$331$	5.21823	−	5.21823i	0.286820	−	0.286820i	−0.549001	−	0.835821i	$-0.684992\pi$
$331$	5.21823	−	5.21823i	0.286820	−	0.286820i	0.835821	+	0.549001i	$0.184992\pi$
$332$	−0.580284	−	0.155487i	−0.0318472	−	0.00853344i
$333$	0.0885971	−	0.151774i	0.00485509	−	0.00831714i
$334$	2.43109	+	4.21076i	0.133023	+	0.230403i
$335$	1.84891	+	3.20240i	0.101016	+	0.174966i
$336$	4.71354	−	0.609086i	0.257145	−	0.0332284i
$337$	−20.3501	+	11.7491i	−1.10854	+	0.640015i	−0.938450	−	0.345414i	$-0.887738\pi$
$337$	−20.3501	+	11.7491i	−1.10854	+	0.640015i	−0.170088	+	0.985429i	$0.554405\pi$
$338$	−19.8435	−	25.3954i	−1.07935	−	1.38133i
$339$	1.52386	−	11.3648i	0.0827647	−	0.617251i
$340$	6.29024	+	1.68547i	0.341136	+	0.0914072i
$341$	27.8158	+	16.0594i	1.50631	+	0.869668i
$342$	−6.48892	−	24.6887i	−0.350880	−	1.33501i
$343$	−5.42161	+	5.42161i	−0.292739	+	0.292739i
$344$	−39.2562	−	39.2562i	−2.11655	−	2.11655i
$345$	7.28715	−	0.941648i	0.392327	−	0.0506966i
$346$	7.56512	−	28.2334i	0.406704	−	1.51784i
$347$	−20.4167	−	11.7876i	−1.09603	−	0.632790i	−0.160851	−	0.986979i	$-0.551424\pi$
$347$	−20.4167	−	11.7876i	−1.09603	−	0.632790i	−0.935174	+	0.354188i	$0.884757\pi$
$348$	2.44791	+	5.94998i	0.131222	+	0.318953i
$349$	−4.05824	+	15.1456i	−0.217233	+	0.810724i	0.768136	+	0.640287i	$0.221185\pi$
$349$	−4.05824	+	15.1456i	−0.217233	+	0.810724i	−0.985369	+	0.170437i	$0.945482\pi$
$350$	6.50684			0.347805
$351$	1.17334	+	18.6982i	0.0626284	+	0.998037i
$352$	−7.92061			−0.422170
$353$	−0.433147	+	1.61652i	−0.0230541	+	0.0860389i	−0.976494	−	0.215543i	$-0.930848\pi$
$353$	−0.433147	+	1.61652i	−0.0230541	+	0.0860389i	0.953440	+	0.301582i	$0.0975146\pi$
$354$	8.35339	+	20.3041i	0.443978	+	1.07915i
$355$	1.07742	+	0.622047i	0.0571833	+	0.0330148i
$356$	−8.87966	+	33.1393i	−0.470621	+	1.75638i
$357$	2.69302	−	0.347994i	0.142530	−	0.0184178i
$358$	25.5743	+	25.5743i	1.35164	+	1.35164i
$359$	3.23316	−	3.23316i	0.170640	−	0.170640i	−0.616621	−	0.787260i	$-0.711499\pi$
$359$	3.23316	−	3.23316i	0.170640	−	0.170640i	0.787260	+	0.616621i	$0.211499\pi$
$360$	−8.64221	−	2.36003i	−0.455484	−	0.124385i
$361$	−6.25229	−	3.60976i	−0.329068	−	0.189988i
$362$	7.31239	+	1.95935i	0.384330	+	0.102981i
$363$	−3.87022	+	28.8637i	−0.203134	+	1.51495i
$364$	6.27219	−	5.54950i	0.328752	−	0.290873i
$365$	−1.84667	+	1.06617i	−0.0966590	+	0.0558061i
$366$	17.7575	−	2.29463i	0.928200	−	0.119942i
$367$	0.929853	+	1.61055i	0.0485379	+	0.0840701i	0.889274	−	0.457376i	$-0.151210\pi$
$367$	0.929853	+	1.61055i	0.0485379	+	0.0840701i	−0.840736	+	0.541446i	$0.817877\pi$
$368$	−18.5104	−	32.0609i	−0.964921	−	1.67129i
$369$	−17.4710	−	0.0835598i	−0.909506	−	0.00434995i
$370$	0.0787341	+	0.0210967i	0.00409319	+	0.00109677i
$371$	2.25169	−	2.25169i	0.116902	−	0.116902i
$372$	16.8334	−	40.3662i	0.872772	−	2.09289i
$373$	−12.9172	+	22.3732i	−0.668826	+	1.15844i	0.309406	+	0.950930i	$0.399870\pi$
$373$	−12.9172	+	22.3732i	−0.668826	+	1.15844i	−0.978233	+	0.207511i	$0.933464\pi$
$374$	−36.5883			−1.89194
$375$	−8.68984	−	3.62382i	−0.448741	−	0.187133i
$376$	−50.6902	−	29.2660i	−2.61415	−	1.50928i
$377$	2.69375	+	1.78284i	0.138735	+	0.0918207i
$378$	−7.16162	+	0.890625i	−0.368354	+	0.0458088i
$379$	−9.87280	−	36.8458i	−0.507132	−	1.89264i	−0.447190	−	0.894439i	$-0.647575\pi$
$379$	−9.87280	−	36.8458i	−0.507132	−	1.89264i	−0.0599419	−	0.998202i	$-0.519092\pi$
$380$	6.91706	−	3.99357i	0.354838	−	0.204866i
$381$	1.22579	−	9.14183i	0.0627992	−	0.468350i
$382$	32.1394	+	8.61172i	1.64439	+	0.440614i
$383$	14.3643	−	3.84890i	0.733981	−	0.196669i	0.127579	−	0.991828i	$-0.459279\pi$
$383$	14.3643	−	3.84890i	0.733981	−	0.196669i	0.606401	+	0.795159i	$0.292613\pi$
$384$	−4.00854	−	31.0209i	−0.204560	−	1.58303i
$385$	1.60178	−	0.429195i	0.0816342	−	0.0218738i
$386$	7.69473	−	4.44255i	0.391651	−	0.226120i
$387$	22.0288	+	22.2405i	1.11978	+	1.13055i
$388$	3.68280	−	0.986803i	0.186966	−	0.0500973i
$389$	−7.77391	+	13.4648i	−0.394153	+	0.682692i	−0.992993	−	0.118176i	$-0.962295\pi$
$389$	−7.77391	+	13.4648i	−0.394153	+	0.682692i	0.598840	+	0.800869i	$0.295629\pi$
$390$	−8.22286	+	2.80966i	−0.416381	+	0.142273i
$391$	−10.5757	−	18.3176i	−0.534835	−	0.926361i
$392$	−25.1544	−	25.1544i	−1.27049	−	1.27049i
$393$	−16.6977	−	12.8762i	−0.842289	−	0.649518i
$394$			32.6071i			1.64272i
$395$	2.07301	+	2.07301i	0.104304	+	0.104304i
$396$	65.5973	+	0.313736i	3.29639	+	0.0157658i
$397$	−0.481208	+	1.79589i	−0.0241511	+	0.0901332i	−0.976949	−	0.213471i	$-0.931523\pi$
$397$	−0.481208	+	1.79589i	−0.0241511	+	0.0901332i	0.952798	+	0.303604i	$0.0981899\pi$
$398$	12.7566	+	47.6082i	0.639429	+	2.38638i
$399$	2.03377	−	2.63737i	0.101816	−	0.132034i
$400$			22.9472i			1.14736i
$401$	−2.01062	+	2.01062i	−0.100406	+	0.100406i	−0.755525	−	0.655120i	$-0.772618\pi$
$401$	−2.01062	+	2.01062i	−0.100406	+	0.100406i	0.655120	+	0.755525i	$0.272618\pi$
$402$	−17.2756	+	22.4029i	−0.861631	+	1.11736i
$403$	−4.37848	−	21.5176i	−0.218108	−	1.07187i
$404$		−	57.3920i		−	2.85536i
$405$	4.86654	+	1.35401i	0.241820	+	0.0672812i
$406$	−0.622160	+	1.07761i	−0.0308773	+	0.0534810i
$407$	−0.308943			−0.0153137
$408$	3.30493	+	25.5759i	0.163619	+	1.26620i
$409$	3.05436	+	11.3990i	0.151029	+	0.563646i	0.999413	+	0.0342653i	$0.0109091\pi$
$409$	3.05436	+	11.3990i	0.151029	+	0.563646i	−0.848384	+	0.529381i	$0.822424\pi$
$410$	−2.09733	−	7.82735i	−0.103580	−	0.386565i
$411$	−10.5074	−	4.38179i	−0.518293	−	0.216138i
$412$	2.67436			0.131756
$413$	−1.43222	+	2.48068i	−0.0704750	+	0.122066i
$414$	27.8739	+	48.8168i	1.36993	+	2.39921i
$415$			0.0813251i			0.00399209i
$416$	3.58824	+	4.05552i	0.175928	+	0.198838i
$417$	−4.95280	−	0.664102i	−0.242540	−	0.0325212i
$418$	−31.7318	+	31.7318i	−1.55205	+	1.55205i
$419$			22.6065i			1.10440i	0.833711	+	0.552201i	$0.186212\pi$
$419$			22.6065i			1.10440i	−0.833711	+	0.552201i	$0.813788\pi$
$420$	−0.859124	−	2.08822i	−0.0419210	−	0.101895i
$421$	−5.04668	−	18.8345i	−0.245960	−	0.917936i	−0.972898	−	0.231233i	$-0.925724\pi$
$421$	−5.04668	−	18.8345i	−0.245960	−	0.917936i	0.726938	−	0.686703i	$-0.240943\pi$
$422$	3.58618	−	13.3838i	0.174573	−	0.651514i
$423$	28.5027	+	16.6383i	1.38585	+	0.808983i
$424$	21.3845	+	21.3845i	1.03852	+	1.03852i
$425$			13.1106i			0.635956i
$426$	−1.26491	+	9.43357i	−0.0612851	+	0.457058i
$427$	1.65182	+	1.65182i	0.0799374	+	0.0799374i
$428$	23.0862	+	39.9865i	1.11592	+	1.93282i
$429$	27.3480	−	18.3526i	1.32037	−	0.886073i
$430$	−7.25955	+	12.5739i	−0.350086	+	0.606368i
$431$	11.0205	−	2.95294i	0.530840	−	0.142238i	0.0165641	−	0.999863i	$-0.494727\pi$
$431$	11.0205	−	2.95294i	0.530840	−	0.142238i	0.514276	+	0.857625i	$0.328061\pi$
$432$	−3.14090	−	25.2563i	−0.151117	−	1.21515i
$433$	24.9555	−	14.4081i	1.19929	−	0.692408i	0.238890	−	0.971047i	$-0.423217\pi$
$433$	24.9555	−	14.4081i	1.19929	−	0.692408i	0.960396	+	0.278639i	$0.0898832\pi$
$434$	8.17030	−	2.18922i	0.392187	−	0.105086i
$435$	0.692247	−	0.528554i	0.0331907	−	0.0253422i
$436$	68.5917	−	18.3791i	3.28495	−	0.880198i
$437$	−25.0582	−	6.71432i	−1.19870	−	0.321189i
$438$	−12.9187	−	9.96202i	−0.617278	−	0.476004i
$439$	20.1714	−	11.6460i	0.962730	−	0.555833i	0.0657179	−	0.997838i	$-0.479066\pi$
$439$	20.1714	−	11.6460i	0.962730	−	0.555833i	0.897012	+	0.442006i	$0.145733\pi$
$440$	4.07611	+	15.2123i	0.194321	+	0.725216i
$441$	14.1155	+	14.2511i	0.672165	+	0.678626i
$442$	16.5754	+	18.7340i	0.788414	+	0.891085i
$443$	−15.9997	−	9.23744i	−0.760170	−	0.438884i	0.0691871	−	0.997604i	$-0.477959\pi$
$443$	−15.9997	−	9.23744i	−0.760170	−	0.438884i	−0.829357	+	0.558720i	$0.811293\pi$
$444$	0.0539122	+	0.417211i	0.00255856	+	0.0198000i
$445$	4.64438			0.220165
$446$	−20.4715	+	35.4578i	−0.969356	+	1.67897i
$447$	−0.318958	−	0.417739i	−0.0150862	−	0.0197584i
$448$	2.40564	−	2.40564i	0.113656	−	0.113656i
$449$	−34.2960	−	9.18959i	−1.61853	−	0.433684i	−0.667960	−	0.744197i	$-0.732832\pi$
$449$	−34.2960	−	9.18959i	−1.61853	−	0.433684i	−0.950569	+	0.310513i	$0.899499\pi$
$450$	0.166649	−	34.8437i	0.00785592	−	1.64255i
$451$	15.3568	+	26.5988i	0.723124	+	1.25249i
$452$	13.7240	+	23.7707i	0.645524	+	1.11808i
$453$	−15.9127	−	20.8408i	−0.747644	−	0.979188i
$454$	7.26258	−	4.19305i	0.340850	−	0.196790i
$455$	−0.945404	−	0.625708i	−0.0443212	−	0.0293336i
$456$	25.0474	+	19.3149i	1.17295	+	0.904502i
$457$	−16.8725	−	4.52097i	−0.789262	−	0.211482i	−0.158398	−	0.987375i	$-0.550633\pi$
$457$	−16.8725	−	4.52097i	−0.789262	−	0.211482i	−0.630864	+	0.775893i	$0.717300\pi$
$458$	36.8337	+	21.2660i	1.72113	+	0.993694i
$459$	−1.79451	−	14.4299i	−0.0837607	−	0.673530i
$460$	−12.4371	+	12.4371i	−0.579883	+	0.579883i
$461$	3.34883	+	3.34883i	0.155971	+	0.155971i	0.780779	−	0.624808i	$-0.214823\pi$
$461$	3.34883	+	3.34883i	0.155971	+	0.155971i	−0.624808	+	0.780779i	$0.714823\pi$
$462$	7.69913	+	10.0835i	0.358196	+	0.469128i
$463$	−0.585260	+	2.18422i	−0.0271993	+	0.101509i	−0.978191	−	0.207707i	$-0.933400\pi$
$463$	−0.585260	+	2.18422i	−0.0271993	+	0.101509i	0.950992	+	0.309216i	$0.100067\pi$
$464$	−3.80033	−	2.19412i	−0.176426	−	0.101860i
$465$	−5.86802	−	0.786820i	−0.272123	−	0.0364879i
$466$	1.90100	−	7.09462i	0.0880620	−	0.328652i
$467$	−13.8388			−0.640383			−0.320192	−	0.947353i	$-0.603747\pi$
$467$	−13.8388			−0.640383			−0.320192	+	0.947353i	$0.603747\pi$
$468$	−29.5566	−	33.7293i	−1.36625	−	1.55914i
$469$	−3.69095			−0.170432
$470$	−3.96192	+	14.7861i	−0.182750	+	0.682031i
$471$	−6.26542	+	8.12495i	−0.288695	+	0.374378i
$472$	−23.5593	−	13.6019i	−1.08440	−	0.626080i
$473$	14.2428	−	53.1549i	0.654885	−	2.44406i
$474$	−8.63270	+	20.7010i	−0.396513	+	0.950829i
$475$	11.3704	+	11.3704i	0.521708	+	0.521708i
$476$	−4.59623	+	4.59623i	−0.210668	+	0.210668i
$477$	−12.0000	−	12.1153i	−0.549441	−	0.554722i
$478$	−55.5308	−	32.0607i	−2.53992	−	1.46642i
$479$	6.05369	+	1.62208i	0.276600	+	0.0741148i	0.394452	−	0.918916i	$-0.370934\pi$
$479$	6.05369	+	1.62208i	0.276600	+	0.0741148i	−0.117852	+	0.993031i	$0.537601\pi$
$480$	1.35022	−	0.555499i	0.0616287	−	0.0253550i
$481$	0.139959	+	0.158185i	0.00638159	+	0.00721263i
$482$	12.6783	−	7.31984i	0.577482	−	0.333409i
$483$	−2.82283	+	6.76909i	−0.128443	+	0.308004i
$484$	−34.8555	−	60.3715i	−1.58434	−	2.74416i
$485$	−0.258067	−	0.446984i	−0.0117182	−	0.0202965i
$486$	4.58582	+	38.3729i	0.208017	+	1.74063i
$487$	−17.1218	−	4.58779i	−0.775865	−	0.207892i	−0.150904	−	0.988548i	$-0.548218\pi$
$487$	−17.1218	−	4.58779i	−0.775865	−	0.207892i	−0.624961	+	0.780656i	$0.714885\pi$
$488$	−15.6875	+	15.6875i	−0.710142	+	0.710142i
$489$	−26.4098	+	3.41269i	−1.19429	+	0.154327i
$490$	−4.65173	+	8.05704i	−0.210144	+	0.363980i
$491$	24.1634			1.09048			0.545239	−	0.838281i	$-0.316439\pi$
$491$	24.1634			1.09048			0.545239	+	0.838281i	$0.316439\pi$
$492$	33.2404	−	25.3802i	1.49859	−	1.14423i
$493$	−2.17127	−	1.25359i	−0.0977892	−	0.0564586i
$494$	30.6227	+	1.87203i	1.37778	+	0.0842268i
$495$	−2.25729	−	8.58842i	−0.101458	−	0.386021i
$496$	7.72057	+	28.8136i	0.346664	+	1.29377i
$497$	−1.07542	+	0.620892i	−0.0482390	+	0.0278508i
$498$	−0.575388	+	0.236723i	−0.0257838	+	0.0106078i
$499$	−9.32320	−	2.49814i	−0.417364	−	0.111832i	0.0440247	−	0.999030i	$-0.485982\pi$
$499$	−9.32320	−	2.49814i	−0.417364	−	0.111832i	−0.461389	+	0.887198i	$0.652649\pi$
$500$	21.7697	−	5.83317i	0.973570	−	0.260867i
$501$	3.13526	+	1.30746i	0.140073	+	0.0584131i
$502$	7.26804	−	1.94746i	0.324388	−	0.0869196i
$503$	16.6315	−	9.60220i	0.741562	−	0.428141i	−0.0810753	−	0.996708i	$-0.525835\pi$
$503$	16.6315	−	9.60220i	0.741562	−	0.428141i	0.822637	+	0.568567i	$0.192502\pi$
$504$	6.35314	−	6.29265i	0.282991	−	0.280297i
$505$	−7.50452	+	2.01083i	−0.333947	+	0.0894808i
$506$	49.4109	−	85.5822i	2.19658	−	3.80459i
$507$	−21.7863	−	5.68852i	−0.967561	−	0.252636i
$508$	11.0396	+	19.1211i	0.489803	+	0.848363i
$509$	4.19890	+	4.19890i	0.186113	+	0.186113i	0.794013	−	0.607900i	$-0.207988\pi$
$509$	4.19890	+	4.19890i	0.186113	+	0.186113i	−0.607900	+	0.794013i	$0.707988\pi$
$510$	6.23717	−	2.56606i	0.276186	−	0.113627i
$511$		−	2.12839i		−	0.0941544i
$512$	31.6528	+	31.6528i	1.39887	+	1.39887i
$513$	−14.0709	−	10.9582i	−0.621245	−	0.483818i
$514$	−12.3972	+	46.2671i	−0.546818	+	2.04075i
$515$	−0.0937008	−	0.349696i	−0.00412895	−	0.0154094i
$516$	−74.2682	−	9.95833i	−3.26948	−	0.438391i
$517$		−	58.0188i		−	2.55167i
$518$	−0.0575304	+	0.0575304i	−0.00252774	+	0.00252774i
$519$	−7.76970	−	18.8853i	−0.341052	−	0.828973i
$520$	5.94241	−	8.97860i	0.260592	−	0.393737i
$521$			13.0320i			0.570942i	0.958387	+	0.285471i	$0.0921500\pi$
$521$			13.0320i			0.570942i	−0.958387	+	0.285471i	$0.907850\pi$
$522$	5.75461	+	3.35923i	0.251873	+	0.147029i
$523$	6.02410	−	10.4340i	0.263415	−	0.456249i	−0.703732	−	0.710466i	$-0.748484\pi$
$523$	6.02410	−	10.4340i	0.263415	−	0.456249i	0.967147	+	0.254217i	$0.0818177\pi$
$524$	50.4743			2.20498
$525$	3.61320	−	2.75880i	0.157693	−	0.120404i
$526$	5.91682	+	22.0819i	0.257985	+	0.962815i
$527$	4.41105	+	16.4623i	0.192148	+	0.717108i
$528$	−35.5608	+	27.1519i	−1.54759	+	1.18164i
$529$	34.1279			1.48382
$530$	3.95458	−	6.84953i	0.171776	−	0.297525i
$531$	13.2472	+	7.73299i	0.574880	+	0.335583i
$532$			7.97231i			0.345644i
$533$	6.66210	−	19.9129i	0.288568	−	0.862524i
$534$	13.5190	+	32.8597i	0.585023	+	1.42198i
$535$	4.41973	−	4.41973i	0.191082	−	0.191082i
$536$		−	35.0533i		−	1.51407i
$537$	25.0443	+	3.35809i	1.08074	+	0.144912i
$538$	−16.2537	−	60.6597i	−0.700747	−	2.61522i
$539$	9.12643	−	34.0603i	0.393103	−	1.46708i
$540$	−11.2043	+	4.54708i	−0.482156	+	0.195675i
$541$	5.96251	+	5.96251i	0.256348	+	0.256348i	0.823567	−	0.567219i	$-0.191981\pi$
$541$	5.96251	+	5.96251i	0.256348	+	0.256348i	−0.567219	+	0.823567i	$0.691981\pi$
$542$			55.0540i			2.36477i
$543$	4.89125	−	2.01233i	0.209904	−	0.0863574i
$544$	−2.97187	−	2.97187i	−0.127418	−	0.127418i
$545$	−4.80646	−	8.32503i	−0.205886	−	0.356605i
$546$	1.67508	−	8.51021i	0.0716868	−	0.364203i
$547$	−14.3308	+	24.8217i	−0.612740	+	1.06130i	0.378036	+	0.925791i	$0.376600\pi$
$547$	−14.3308	+	24.8217i	−0.612740	+	1.06130i	−0.990776	+	0.135507i	$0.956734\pi$
$548$	26.3231	−	7.05326i	1.12447	−	0.301300i
$549$	8.88772	−	8.80311i	0.379319	−	0.375708i
$550$	−53.0478	+	30.6271i	−2.26196	+	1.30595i
$551$	−2.97026	+	0.795880i	−0.126538	+	0.0339056i
$552$	−64.2868	−	26.8087i	−2.73623	−	1.14106i
$553$	−2.82652	+	0.757365i	−0.120196	+	0.0322064i
$554$	49.2646	+	13.2004i	2.09305	+	0.560832i
$555$	0.0526652	−	0.0216672i	0.00223551	−	0.000919723i
$556$	10.3593	−	5.98096i	0.439333	−	0.253649i
$557$	11.3445	+	42.3384i	0.480683	+	1.79393i	0.598759	+	0.800930i	$0.295661\pi$
$557$	11.3445	+	42.3384i	0.480683	+	1.79393i	−0.118075	+	0.993005i	$0.537672\pi$
$558$	−11.5139	−	43.8075i	−0.487423	−	1.85452i
$559$	−33.6687	+	16.7879i	−1.42404	+	0.710052i
$560$	1.33377	+	0.770055i	0.0563622	+	0.0325408i
$561$	−20.3172	+	15.5129i	−0.857794	+	0.654956i
$562$	3.44049			0.145128
$563$	−17.0301	+	29.4970i	−0.717732	+	1.24315i	0.244164	+	0.969734i	$0.421486\pi$
$563$	−17.0301	+	29.4970i	−0.717732	+	1.24315i	−0.961896	+	0.273415i	$0.911847\pi$
$564$	−78.3513	+	10.1246i	−3.29919	+	0.426322i
$565$	2.62739	−	2.62739i	0.110535	−	0.110535i
$566$	−79.7108	−	21.3585i	−3.35050	−	0.897763i
$567$	−3.59918	+	3.53098i	−0.151152	+	0.148287i
$568$	−5.89668	−	10.2133i	−0.247419	−	0.428542i
$569$	−9.31633	−	16.1364i	−0.390561	−	0.676471i	0.601963	−	0.798524i	$-0.294386\pi$
$569$	−9.31633	−	16.1364i	−0.390561	−	0.676471i	−0.992524	+	0.122053i	$0.961052\pi$
$570$	3.18383	−	7.63475i	0.133356	−	0.319784i
$571$	−15.0722	+	8.70193i	−0.630751	+	0.364164i	−0.781043	−	0.624477i	$-0.785312\pi$
$571$	−15.0722	+	8.70193i	−0.630751	+	0.364164i	0.150292	+	0.988642i	$0.451979\pi$
$572$	−25.0137	+	74.7657i	−1.04588	+	3.12611i
$573$	21.4980	−	8.84460i	0.898092	−	0.369488i
$574$	7.81283	+	2.09344i	0.326101	+	0.0873785i
$575$	−30.6664	−	17.7053i	−1.27888	−	0.738360i
$576$	−12.8205	−	12.9437i	−0.534185	−	0.539320i
$577$	7.58470	−	7.58470i	0.315755	−	0.315755i	−0.531379	−	0.847134i	$-0.678326\pi$
$577$	7.58470	−	7.58470i	0.315755	−	0.315755i	0.847134	+	0.531379i	$0.178326\pi$
$578$	16.0730	+	16.0730i	0.668551	+	0.668551i
$579$	2.38925	−	5.72937i	0.0992938	−	0.238104i
$580$	−0.539605	+	2.01383i	−0.0224059	+	0.0836199i
$581$	−0.0702989	−	0.0405871i	−0.00291649	−	0.00168383i
$582$	2.41130	−	3.12696i	0.0999516	−	0.129617i
$583$	−7.75865	+	28.9557i	−0.321330	+	1.19922i
$584$	20.2135			0.836442
$585$	−3.37484	+	5.04655i	−0.139533	+	0.208649i
$586$	−23.6928			−0.978739
$587$	8.74408	−	32.6334i	0.360907	−	1.34692i	−0.511979	−	0.858998i	$-0.671087\pi$
$587$	8.74408	−	32.6334i	0.360907	−	1.34692i	0.872886	−	0.487925i	$-0.162246\pi$
$588$	−47.5892	−	6.38105i	−1.96255	−	0.263150i
$589$	18.1027	+	10.4516i	0.745910	+	0.430651i
$590$	−1.84138	+	6.87212i	−0.0758084	+	0.282921i
$591$	13.8249	+	18.1065i	0.568682	+	0.744802i
$592$	−0.202888	−	0.202888i	−0.00833865	−	0.00833865i
$593$	21.2686	−	21.2686i	0.873399	−	0.873399i	−0.119443	−	0.992841i	$-0.538111\pi$
$593$	21.2686	−	21.2686i	0.873399	−	0.873399i	0.992841	+	0.119443i	$0.0381107\pi$
$594$	54.1939	−	40.9701i	2.22360	−	1.68102i
$595$	0.762035	+	0.439961i	0.0312404	+	0.0180366i
$596$	1.21525	+	0.325627i	0.0497788	+	0.0133382i
$597$	27.2688	+	21.0279i	1.11604	+	0.860614i
$598$	−66.2043	+	13.4715i	−2.70730	+	0.550891i
$599$	3.06596	−	1.77013i	0.125272	−	0.0723256i	−0.436055	−	0.899920i	$-0.643625\pi$
$599$	3.06596	−	1.77013i	0.125272	−	0.0723256i	0.561326	+	0.827595i	$0.310291\pi$
$600$	26.2006	+	34.3149i	1.06964	+	1.40090i
$601$	14.1832	+	24.5660i	0.578544	+	1.00207i	0.995647	+	0.0932081i	$0.0297122\pi$
$601$	14.1832	+	24.5660i	0.578544	+	1.00207i	−0.417103	+	0.908859i	$0.636954\pi$
$602$	−7.24607	−	12.5506i	−0.295328	−	0.511523i
$603$	−0.0945303	+	19.7648i	−0.00384957	+	0.804885i
$604$	60.6286	+	16.2454i	2.46694	+	0.661016i
$605$	−6.67289	+	6.67289i	−0.271292	+	0.271292i
$606$	−36.0713	−	47.2425i	−1.46530	−	1.91910i
$607$	5.08006	−	8.79892i	0.206193	−	0.357137i	−0.744319	−	0.667824i	$-0.767226\pi$
$607$	5.08006	−	8.79892i	0.206193	−	0.357137i	0.950512	+	0.310687i	$0.100559\pi$
$608$	−5.15480			−0.209055
$609$	0.111411	+	0.862177i	0.00451460	+	0.0349372i
$610$	5.02477	+	2.90105i	0.203447	+	0.117460i
$611$	−29.7069	+	26.2840i	−1.20181	+	1.06334i
$612$	24.4948	+	24.7303i	0.990144	+	0.999661i
$613$	5.13413	+	19.1608i	0.207365	+	0.773898i	0.988716	+	0.149805i	$0.0478647\pi$
$613$	5.13413	+	19.1608i	0.207365	+	0.773898i	−0.781350	+	0.624093i	$0.785469\pi$
$614$	−69.5176	+	40.1360i	−2.80550	+	1.61976i
$615$	−4.48332	−	3.45723i	−0.180785	−	0.139409i
$616$	−15.1840	−	4.06855i	−0.611782	−	0.163926i
$617$	5.46601	−	1.46461i	0.220053	−	0.0589631i	−0.147108	−	0.989120i	$-0.546996\pi$
$617$	5.46601	−	1.46461i	0.220053	−	0.0589631i	0.367161	+	0.930157i	$0.380330\pi$
$618$	2.20141	−	1.68085i	0.0885537	−	0.0676138i
$619$	21.9131	−	5.87159i	0.880761	−	0.235999i	0.210025	−	0.977696i	$-0.432645\pi$
$619$	21.9131	−	5.87159i	0.880761	−	0.235999i	0.670735	+	0.741697i	$0.265979\pi$
$620$	12.2736	−	7.08617i	0.492920	−	0.284588i
$621$	36.1758	+	15.2895i	1.45168	+	0.613545i
$622$	40.4389	−	10.8356i	1.62145	−	0.434467i
$623$	−2.31788	+	4.01468i	−0.0928638	+	0.160845i
$624$	30.0123	+	5.90738i	1.20145	+	0.236484i
$625$	10.1870	+	17.6444i	0.407479	+	0.705774i
$626$	−30.3024	−	30.3024i	−1.21113	−	1.21113i
$627$	−4.16663	+	31.0743i	−0.166399	+	1.24099i
$628$		−	24.5603i		−	0.980062i
$629$	−0.115918	−	0.115918i	−0.00462194	−	0.00462194i
$630$	−2.01965	−	1.17896i	−0.0804649	−	0.0469710i
$631$	5.55205	−	20.7205i	0.221024	−	0.824872i	−0.762935	−	0.646475i	$-0.776242\pi$
$631$	5.55205	−	20.7205i	0.221024	−	0.824872i	0.983959	−	0.178397i	$-0.0570910\pi$
$632$	−7.19277	−	26.8438i	−0.286113	−	1.06779i
$633$	−3.68316	−	8.95242i	−0.146392	−	0.355827i
$634$			28.9131i			1.14828i
$635$	2.11347	−	2.11347i	0.0838704	−	0.0838704i
$636$	40.4570	+	5.42472i	1.60422	+	0.215104i
$637$	−21.5741	+	10.7573i	−0.854796	+	0.426218i
$638$		−	11.7138i		−	0.463755i
$639$	3.29730	+	5.77469i	0.130439	+	0.228443i
$640$	5.06791	−	8.77787i	0.200327	−	0.346976i
$641$	−28.2882			−1.11732			−0.558658	−	0.829398i	$-0.688684\pi$
$641$	−28.2882			−1.11732			−0.558658	+	0.829398i	$0.688684\pi$
$642$	44.1353	+	18.4052i	1.74188	+	0.726397i
$643$	7.40547	+	27.6376i	0.292043	+	1.08992i	0.943537	+	0.331266i	$0.107476\pi$
$643$	7.40547	+	27.6376i	0.292043	+	1.08992i	−0.651494	+	0.758654i	$0.725857\pi$
$644$	−4.54384	−	16.9579i	−0.179053	−	0.668233i
$645$	1.29998	+	10.0601i	0.0511865	+	0.396118i
$646$	−23.8120			−0.936870
$647$	0.317553	−	0.550019i	0.0124843	−	0.0216235i	−0.859716	−	0.510773i	$-0.829359\pi$
$647$	0.317553	−	0.550019i	0.0124843	−	0.0216235i	0.872200	+	0.489149i	$0.162693\pi$
$648$	−33.5341	−	34.1818i	−1.31734	−	1.34279i
$649$		−	26.9654i		−	1.05848i
$650$	39.7137	+	13.2867i	1.55770	+	0.521147i
$651$	3.60871	−	4.67975i	0.141436	−	0.183414i
$652$	45.0741	−	45.0741i	1.76524	−	1.76524i
$653$			5.83510i			0.228345i	0.993461	+	0.114172i	$0.0364216\pi$
$653$			5.83510i			0.228345i	−0.993461	+	0.114172i	$0.963578\pi$
$654$	44.9102	−	58.2392i	1.75613	−	2.27733i
$655$	−1.76846	−	6.59997i	−0.0690993	−	0.257882i
$656$	−7.38278	+	27.5529i	−0.288249	+	1.07576i
$657$	−11.3974	−	0.0545110i	−0.444655	−	0.00212668i
$658$	−10.8041	−	10.8041i	−0.421187	−	0.421187i
$659$		−	0.0891900i		−	0.00347435i	−0.999998	−	0.00173718i	$-0.999447\pi$
$659$		−	0.0891900i		−	0.00347435i	0.999998	−	0.00173718i	$-0.000552960\pi$
$660$	16.8332	+	12.9806i	0.655231	+	0.505271i
$661$	−25.7422	−	25.7422i	−1.00126	−	1.00126i	−0.999999	−	0.00125729i	$-0.999600\pi$
$661$	−25.7422	−	25.7422i	−1.00126	−	1.00126i	−0.00125729	−	0.999999i	$-0.500400\pi$
$662$	9.14764	+	15.8442i	0.355533	+	0.615801i
$663$	17.1472	+	3.37511i	0.665941	+	0.131078i
$664$	0.385459	−	0.667635i	0.0149587	−	0.0259093i
$665$	1.04245	−	0.279324i	0.0404245	−	0.0108317i
$666$	0.306598	+	0.309545i	0.0118804	+	0.0119946i
$667$	5.86442	−	3.38582i	0.227071	−	0.131100i
$668$	−7.85443	+	2.10459i	−0.303897	+	0.0814290i
$669$	3.66586	+	28.3691i	0.141730	+	1.09681i
$670$	−8.85500	+	2.37269i	−0.342099	+	0.0916651i
$671$	−21.2417	−	5.69170i	−0.820027	−	0.219725i
$672$	−0.193672	+	1.44439i	−0.00747106	+	0.0557184i
$673$	−17.5073	+	10.1079i	−0.674858	+	0.389630i	−0.797915	−	0.602770i	$-0.794064\pi$
$673$	−17.5073	+	10.1079i	−0.674858	+	0.389630i	0.123057	+	0.992400i	$0.460730\pi$
$674$	−15.0776	−	56.2703i	−0.580766	−	2.16745i
$675$	−14.6807	−	19.4191i	−0.565059	−	0.747442i
$676$	49.6134	−	21.0632i	1.90821	−	0.810123i
$677$	−11.6860	−	6.74691i	−0.449129	−	0.259305i	0.258333	−	0.966056i	$-0.416827\pi$
$677$	−11.6860	−	6.74691i	−0.449129	−	0.259305i	−0.707462	+	0.706751i	$0.750160\pi$
$678$	26.2370	+	10.9413i	1.00763	+	0.420199i
$679$	0.515175			0.0197706
$680$	−4.17836	+	7.23712i	−0.160233	+	0.277531i
$681$	2.25507	−	5.40760i	0.0864143	−	0.207220i
$682$	−56.3049	+	56.3049i	−2.15602	+	2.15602i
$683$	−32.8276	−	8.79612i	−1.25611	−	0.336574i	−0.431417	−	0.902153i	$-0.641986\pi$
$683$	−32.8276	−	8.79612i	−1.25611	−	0.336574i	−0.824695	+	0.565578i	$0.808653\pi$
$684$	42.6912	+	0.204182i	1.63234	+	0.00780710i
$685$	−1.84455	−	3.19486i	−0.0704767	−	0.122069i
$686$	−9.50415	−	16.4617i	−0.362870	−	0.628510i
$687$	29.4700	−	3.80812i	1.12435	−	0.145289i
$688$	44.2611	−	25.5542i	1.68744	−	0.974244i
$689$	18.3408	−	9.14507i	0.698728	−	0.348399i
$690$	−2.42085	+	18.0545i	−0.0921602	+	0.687321i
$691$	−9.92881	−	2.66042i	−0.377710	−	0.101207i	0.0649690	−	0.997887i	$-0.479305\pi$
$691$	−9.92881	−	2.66042i	−0.377710	−	0.101207i	−0.442679	+	0.896680i	$0.645972\pi$
$692$	42.3342	+	24.4417i	1.60930	+	0.929132i
$693$	8.55054	+	2.33500i	0.324808	+	0.0886992i
$694$	41.3276	−	41.3276i	1.56877	−	1.56877i
$695$	−1.14502	−	1.14502i	−0.0434331	−	0.0434331i
$696$	−8.18818	+	1.05808i	−0.310372	+	0.0401064i
$697$	−4.21806	+	15.7420i	−0.159770	+	0.596271i
$698$	−33.6646	−	19.4362i	−1.27422	−	0.735672i
$699$	−1.95240	−	4.74558i	−0.0738467	−	0.179494i
$700$	−2.81648	+	10.5113i	−0.106453	+	0.397288i
$701$	2.07594			0.0784071			0.0392036	−	0.999231i	$-0.487518\pi$
$701$	2.07594			0.0784071			0.0392036	+	0.999231i	$0.487518\pi$
$702$	−45.5288	−	9.18791i	−1.71837	−	0.346775i
$703$	−0.201063			−0.00758323
$704$	−8.28913	+	30.9354i	−0.312408	+	1.16592i
$705$	4.06906	+	9.89040i	0.153250	+	0.372494i
$706$	−3.59310	−	2.07448i	−0.135228	−	0.0780740i
$707$	2.00710	−	7.49059i	0.0754847	−	0.281713i
$708$	−36.4153	+	4.70560i	−1.36857	+	0.176847i
$709$	34.9739	+	34.9739i	1.31347	+	1.31347i	0.918839	+	0.394633i	$0.129128\pi$
$709$	34.9739	+	34.9739i	1.31347	+	1.31347i	0.394633	+	0.918839i	$0.370872\pi$
$710$	−2.18091	+	2.18091i	−0.0818482	+	0.0818482i
$711$	3.98325	+	15.1553i	0.149384	+	0.568367i
$712$	−38.1278	−	22.0131i	−1.42890	−	0.824977i
$713$	−44.4631	−	11.9139i	−1.66516	−	0.446178i
$714$	−0.894645	+	6.67217i	−0.0334813	+	0.249700i
$715$	10.6527	+	0.651222i	0.398388	+	0.0243543i
$716$	−52.3829	+	30.2433i	−1.95764	+	1.13024i
$717$	−44.4291	+	5.74115i	−1.65924	+	0.214407i
$718$	5.66778	+	9.81688i	0.211520	+	0.366363i
$719$	16.4531	+	28.4976i	0.613597	+	1.06278i	0.990629	+	0.136581i	$0.0436112\pi$
$719$	16.4531	+	28.4976i	0.613597	+	1.06278i	−0.377032	+	0.926200i	$0.623055\pi$
$720$	4.15776	−	7.12256i	0.154950	−	0.265442i
$721$	0.349047	+	0.0935268i	0.0129992	+	0.00348312i
$722$	12.6559	−	12.6559i	0.471005	−	0.471005i
$723$	3.93668	−	9.44007i	0.146407	−	0.351080i
$724$	−6.33033	+	10.9644i	−0.235265	+	0.407491i
$725$	−4.19737			−0.155887
$726$	−66.6354	−	27.7882i	−2.47307	−	1.03132i
$727$	14.8096	+	8.55034i	0.549258	+	0.317115i	0.748823	−	0.662770i	$-0.230619\pi$
$727$	14.8096	+	8.55034i	0.549258	+	0.317115i	−0.199564	+	0.979885i	$0.563953\pi$
$728$	4.79557	+	9.61769i	0.177736	+	0.356455i
$729$	18.8160	+	19.3638i	0.696889	+	0.717179i
$730$	−1.36822	−	5.10625i	−0.0506399	−	0.188991i
$731$	25.2880	−	14.6001i	0.935312	−	0.540003i
$732$	−3.97954	+	29.6790i	−0.147088	+	1.09697i
$733$	22.7169	+	6.08699i	0.839070	+	0.224828i	0.652667	−	0.757645i	$-0.273650\pi$
$733$	22.7169	+	6.08699i	0.839070	+	0.224828i	0.186403	+	0.982473i	$0.440317\pi$
$734$	−4.45336	+	1.19328i	−0.164377	+	0.0440446i
$735$	0.832991	+	6.44628i	0.0307254	+	0.237775i
$736$	10.9647	−	2.93799i	0.404166	−	0.108296i
$737$	30.0909	−	17.3730i	1.10841	−	0.639942i
$738$	11.4103	−	41.7836i	0.420021	−	1.53808i
$739$	−23.5898	+	6.32087i	−0.867766	+	0.232517i	−0.665121	−	0.746735i	$-0.731620\pi$
$739$	−23.5898	+	6.32087i	−0.867766	+	0.232517i	−0.202644	+	0.979252i	$0.564954\pi$
$740$	−0.0681601	+	0.118057i	−0.00250561	+	0.00433985i
$741$	17.7983	−	11.9440i	0.653836	−	0.438775i
$742$	3.94724	+	6.83682i	0.144908	+	0.250988i
$743$	−25.2565	−	25.2565i	−0.926569	−	0.926569i	0.0709132	−	0.997482i	$-0.477409\pi$
$743$	−25.2565	−	25.2565i	−0.926569	−	0.926569i	−0.997482	+	0.0709132i	$0.977409\pi$
$744$	44.4440	+	34.2723i	1.62940	+	1.25648i
$745$		−	0.170314i		−	0.00623983i
$746$	−45.2880	−	45.2880i	−1.65811	−	1.65811i
$747$	−0.219142	+	0.375407i	−0.00801797	+	0.0137354i
$748$	15.8373	−	59.1054i	0.579067	−	2.16111i
$749$	1.61473	+	6.02625i	0.0590010	+	0.220195i
$750$	14.2536	−	18.4840i	0.520469	−	0.674940i
$751$		−	2.42500i		−	0.0884897i	−0.999021	−	0.0442448i	$-0.985912\pi$
$751$		−	2.42500i		−	0.0884897i	0.999021	−	0.0442448i	$-0.0140882\pi$
$752$	38.1019	−	38.1019i	1.38943	−	1.38943i
$753$	3.21019	−	4.16295i	0.116986	−	0.151706i
$754$	−5.99772	+	5.30666i	−0.218424	+	0.193257i
$755$		−	8.49692i		−	0.309235i
$756$	1.66117	−	11.9545i	0.0604163	−	0.434781i
$757$	−13.9450	+	24.1534i	−0.506838	+	0.877869i	0.493131	+	0.869955i	$0.335852\pi$
$757$	−13.9450	+	24.1534i	−0.506838	+	0.877869i	−0.999969	+	0.00791399i	$0.997481\pi$
$758$	94.5680			3.43487
$759$	−8.84807	−	68.4727i	−0.321165	−	2.48540i
$760$	2.65277	+	9.90026i	0.0962260	+	0.359120i
$761$	−8.65092	−	32.2857i	−0.313595	−	1.17035i	−0.925290	−	0.379260i	$-0.876179\pi$
$761$	−8.65092	−	32.2857i	−0.313595	−	1.17035i	0.611695	−	0.791094i	$-0.290488\pi$
$762$	21.1051	+	8.80119i	0.764556	+	0.318833i
$763$	9.59507			0.347365
$764$	−27.8230	+	48.1909i	−1.00660	+	1.74349i
$765$	2.37548	−	4.06938i	0.0858857	−	0.147129i
$766$			36.8672i			1.33207i
$767$	−13.8068	+	12.2160i	−0.498536	+	0.441094i
$768$	56.0067	+	7.50972i	2.02097	+	0.270984i
$769$	19.5474	−	19.5474i	0.704899	−	0.704899i	−0.260559	−	0.965458i	$-0.583907\pi$
$769$	19.5474	−	19.5474i	0.704899	−	0.704899i	0.965458	+	0.260559i	$0.0839069\pi$
$770$			4.11111i			0.148154i
$771$	12.7325	+	30.9480i	0.458548	+	1.11457i
$772$	3.84592	+	14.3532i	0.138418	+	0.516581i
$773$	−9.46654	+	35.3296i	−0.340488	+	1.27072i	0.557308	+	0.830306i	$0.311834\pi$
$773$	−9.46654	+	35.3296i	−0.340488	+	1.27072i	−0.897796	+	0.440412i	$0.854833\pi$
$774$	−67.3931	+	38.4808i	−2.42240	+	1.38317i
$775$	20.1755	+	20.1755i	0.724726	+	0.724726i
$776$			4.89267i			0.175637i
$777$	−0.00755417	+	0.0563382i	−0.000271004	+	0.00202112i
$778$	−27.2555	−	27.2555i	−0.977158	−	0.977158i
$779$	9.99433	+	17.3107i	0.358084	+	0.620220i
$780$	−0.979508	−	14.4995i	−0.0350720	−	0.519166i
$781$	5.84498	−	10.1238i	0.209150	−	0.362258i
$782$	50.6503	−	13.5717i	1.81125	−	0.485324i
$783$	4.61976	−	0.574517i	0.165097	−	0.0205316i
$784$	28.3614	−	16.3745i	1.01291	−	0.584803i
$785$	−3.21148	+	0.860512i	−0.114623	+	0.0307130i
$786$	41.5482	−	31.7235i	1.48197	−	1.13154i
$787$	2.10996	−	0.565362i	0.0752119	−	0.0201530i	−0.221017	−	0.975270i	$-0.570938\pi$
$787$	2.10996	−	0.565362i	0.0752119	−	0.0201530i	0.296229	+	0.955117i	$0.404271\pi$
$788$	−52.6741	−	14.1140i	−1.87644	−	0.502790i
$789$	12.6479	+	9.75325i	0.450279	+	0.347225i
$790$	−6.29429	+	3.63401i	−0.223941	+	0.129292i
$791$	0.959905	+	3.58241i	0.0341303	+	0.127376i
$792$	−22.1757	+	81.2053i	−0.787979	+	2.88551i
$793$	6.70876	+	13.4547i	0.238235	+	0.477790i
$794$	−3.99179	−	2.30466i	−0.141663	−	0.0817893i
$795$	−0.708151	−	5.48018i	−0.0251155	−	0.194362i
$796$	−82.4288			−2.92161
$797$	−5.80017	+	10.0462i	−0.205452	+	0.355854i	−0.950277	−	0.311406i	$-0.899200\pi$
$797$	−5.80017	+	10.0462i	−0.205452	+	0.355854i	0.744824	+	0.667261i	$0.232533\pi$
$798$	5.01065	+	6.56244i	0.177375	+	0.232308i
$799$	21.7691	−	21.7691i	0.770134	−	0.770134i
$800$	−6.79645	−	1.82110i	−0.240291	−	0.0643857i
$801$	21.4390	+	12.5149i	0.757510	+	0.442193i
$802$	−3.52465	−	6.10487i	−0.124460	−	0.215570i
$803$	10.0182	+	17.3520i	0.353533	+	0.612337i
$804$	−28.7123	−	37.6045i	−1.01261	−	1.32621i
$805$	−2.05819	+	1.18830i	−0.0725416	+	0.0418819i
$806$	54.3368	+	3.32173i	1.91393	+	0.117003i
$807$	−34.7444	−	26.7925i	−1.22306	−	0.943142i
$808$	71.1389	+	19.0616i	2.50266	+	0.670585i
$809$	15.4191	+	8.90221i	0.542106	+	0.312985i	0.745932	−	0.666022i	$-0.232004\pi$
$809$	15.4191	+	8.90221i	0.542106	+	0.312985i	−0.203826	+	0.979007i	$0.565338\pi$
$810$	−6.36500	+	10.7849i	−0.223643	+	0.378944i
$811$	−28.5606	+	28.5606i	−1.00290	+	1.00290i	−0.00290204	+	0.999996i	$0.500924\pi$
$811$	−28.5606	+	28.5606i	−1.00290	+	1.00290i	−0.999996	+	0.00290204i	$0.999076\pi$
$812$	−1.47149	−	1.47149i	−0.0516392	−	0.0516392i
$813$	23.3421	+	30.5711i	0.818643	+	1.07217i
$814$	0.198233	−	0.739814i	0.00694805	−	0.0259305i
$815$	−7.47309	−	4.31459i	−0.261771	−	0.151134i
$816$	−23.5302	−	3.15508i	−0.823723	−	0.110450i
$817$	9.26933	−	34.5936i	0.324293	−	1.21028i
$818$	−29.2567			−1.02294
$819$	−2.67804	−	5.43587i	−0.0935784	−	0.189945i
$820$	13.5523			0.473266
$821$	−4.14386	+	15.4651i	−0.144622	+	0.539735i	0.855150	+	0.518380i	$0.173465\pi$
$821$	−4.14386	+	15.4651i	−0.144622	+	0.539735i	−0.999772	+	0.0213553i	$0.993202\pi$
$822$	17.2350	−	22.3502i	0.601138	−	0.779552i
$823$	22.9874	+	13.2718i	0.801290	+	0.462625i	0.843922	−	0.536466i	$-0.180241\pi$
$823$	22.9874	+	13.2718i	0.801290	+	0.462625i	−0.0426318	+	0.999091i	$0.513574\pi$
$824$	−0.888234	+	3.31493i	−0.0309431	+	0.115481i
$825$	−16.4716	+	39.4985i	−0.573467	+	1.37516i
$826$	−5.02140	−	5.02140i	−0.174717	−	0.174717i
$827$	9.10200	−	9.10200i	0.316508	−	0.316508i	−0.530916	−	0.847424i	$-0.678152\pi$
$827$	9.10200	−	9.10200i	0.316508	−	0.316508i	0.847424	+	0.530916i	$0.178152\pi$
$828$	−90.9247	+	23.8977i	−3.15985	+	0.830502i
$829$	15.4318	+	8.90953i	0.535967	+	0.309441i	0.743443	−	0.668799i	$-0.233191\pi$
$829$	15.4318	+	8.90953i	0.535967	+	0.309441i	−0.207476	+	0.978240i	$0.566525\pi$
$830$	−0.194746	−	0.0521820i	−0.00675973	−	0.00181126i
$831$	32.9530	−	13.5574i	1.14313	−	0.470300i
$832$	19.5948	−	9.77034i	0.679327	−	0.338726i
$833$	16.2039	−	9.35535i	0.561433	−	0.324144i
$834$	4.76825	−	11.4342i	0.165111	−	0.395933i
$835$	0.550387	+	0.953299i	0.0190469	+	0.0329903i
$836$	−37.5250	−	64.9953i	−1.29783	−	2.24791i
$837$	−24.9673	−	19.4443i	−0.862997	−	0.672092i
$838$	−54.1350	−	14.5054i	−1.87006	−	0.501081i
$839$	13.5710	−	13.5710i	0.468523	−	0.468523i	−0.432913	−	0.901436i	$-0.642514\pi$
$839$	13.5710	−	13.5710i	0.468523	−	0.468523i	0.901436	+	0.432913i	$0.142514\pi$
$840$	2.87374	−	0.371346i	0.0991535	−	0.0128127i
$841$	−14.0987	+	24.4196i	−0.486161	+	0.842055i
$842$	48.3404			1.66592
$843$	1.91048	−	1.45872i	0.0658004	−	0.0502409i
$844$	20.0682	+	11.5864i	0.690774	+	0.398819i
$845$	−4.49250	−	5.74941i	−0.154547	−	0.197786i
$846$	−58.1319	+	57.5785i	−1.99861	+	1.97959i
$847$	−2.43791	−	9.09842i	−0.0837677	−	0.312625i
$848$	−24.1109	+	13.9204i	−0.827971	+	0.478029i
$849$	−53.3185	+	21.9360i	−1.82989	+	0.752842i
$850$	−31.3954	−	8.41237i	−1.07685	−	0.288542i
$851$	0.427679	−	0.114596i	0.0146607	−	0.00392831i
$852$	−14.6916	−	6.12667i	−0.503327	−	0.209896i
$853$	16.2603	−	4.35692i	0.556741	−	0.149178i	0.0305321	−	0.999534i	$-0.490280\pi$
$853$	16.2603	−	4.35692i	0.556741	−	0.149178i	0.526208	+	0.850356i	$0.323613\pi$
$854$	−5.01545	+	2.89567i	−0.171625	+	0.0990878i
$855$	−1.46906	−	5.58941i	−0.0502409	−	0.191154i
$856$	−57.2320	+	15.3353i	−1.95615	+	0.524148i
$857$	−11.2337	+	19.4574i	−0.383737	+	0.664653i	−0.991593	−	0.129395i	$-0.958697\pi$
$857$	−11.2337	+	19.4574i	−0.383737	+	0.664653i	0.607856	+	0.794047i	$0.292030\pi$
$858$	26.4006	+	77.2650i	0.901301	+	2.63778i
$859$	−12.8127	−	22.1923i	−0.437165	−	0.757193i	0.560304	−	0.828287i	$-0.310684\pi$
$859$	−12.8127	−	22.1923i	−0.437165	−	0.757193i	−0.997470	+	0.0710943i	$0.977351\pi$
$860$	−17.1698	−	17.1698i	−0.585486	−	0.585486i
$861$	5.22599	−	2.15005i	0.178101	−	0.0732735i
$862$			28.2852i			0.963398i
$863$	9.56910	+	9.56910i	0.325736	+	0.325736i	0.850962	−	0.525226i	$-0.176019\pi$
$863$	9.56910	+	9.56910i	0.325736	+	0.325736i	−0.525226	+	0.850962i	$0.676019\pi$
$864$	7.72964	+	1.07409i	0.262968	+	0.0365415i
$865$	1.71271	−	6.39193i	0.0582340	−	0.217332i
$866$	18.4898	+	69.0049i	0.628309	+	2.34488i
$867$	15.7400	+	2.11051i	0.534558	+	0.0716767i
$868$			14.1460i			0.480148i
$869$	19.4787	−	19.4787i	0.660771	−	0.660771i
$870$	0.821530	+	1.99684i	0.0278525	+	0.0676993i
$871$	−22.5273	−	7.53676i	−0.763308	−	0.255373i
$872$			91.1254i			3.08589i
$873$	0.0131944	−	2.75873i	0.000446561	−	0.0933689i
$874$	32.1570	−	55.6976i	1.08773	−	1.88400i
$875$	3.04529			0.102950
$876$	21.6847	−	16.5570i	0.732657	−	0.559409i
$877$	−14.0606	−	52.4750i	−0.474794	−	1.77195i	−0.622178	−	0.782875i	$-0.713752\pi$
$877$	−14.0606	−	52.4750i	−0.474794	−	1.77195i	0.147385	−	0.989079i	$-0.452915\pi$
$878$	14.9452	+	55.7764i	0.504377	+	1.88236i
$879$	−13.1564	+	10.0454i	−0.443755	+	0.338822i
$880$	−14.4983			−0.488739
$881$	13.0677	−	22.6339i	0.440261	−	0.762554i	−0.557448	−	0.830212i	$-0.688219\pi$
$881$	13.0677	−	22.6339i	0.440261	−	0.762554i	0.997709	+	0.0676577i	$0.0215526\pi$
$882$	−43.1838	+	24.6576i	−1.45407	+	0.830263i
$883$		−	47.1984i		−	1.58835i	−0.607687	−	0.794177i	$-0.707903\pi$
$883$		−	47.1984i		−	1.58835i	0.607687	−	0.794177i	$-0.292097\pi$
$884$	−37.4379	+	18.6673i	−1.25917	+	0.627848i
$885$	1.89117	+	4.59676i	0.0635711	+	0.154518i
$886$	32.3867	−	32.3867i	1.08805	−	1.08805i
$887$		−	14.1641i		−	0.475585i	−0.971316	−	0.237793i	$-0.923576\pi$
$887$		−	14.1641i		−	0.475585i	0.971316	−	0.237793i	$-0.0764238\pi$
$888$	−0.535050	−	0.0717427i	−0.0179551	−	0.00240753i
$889$	0.772147	+	2.88169i	0.0258970	+	0.0966488i
$890$	−2.98005	+	11.1217i	−0.0998916	+	0.372800i
$891$	12.7228	−	45.7278i	0.426228	−	1.53194i
$892$	−48.4180	−	48.4180i	−1.62115	−	1.62115i
$893$		−	37.7591i		−	1.26356i
$894$	1.20500	−	0.495755i	0.0403013	−	0.0165805i
$895$	5.78990	+	5.78990i	0.193535	+	0.193535i
$896$	5.05850	+	8.76158i	0.168993	+	0.292704i
$897$	−31.0510	+	35.5503i	−1.03676	+	1.18699i
$898$	44.0119	−	76.2309i	1.46870	−	2.54386i
$899$	−5.27043	+	1.41221i	−0.175779	+	0.0470997i
$900$	56.2150	+	15.3513i	1.87383	+	0.511710i
$901$	−13.7755	+	7.95326i	−0.458927	+	0.264962i
$902$	−73.5487	+	19.7073i	−2.44890	+	0.656182i
$903$	−9.34495	−	3.89701i	−0.310980	−	0.129684i
$904$	−34.0225	+	9.11631i	−1.13157	+	0.303204i
$905$	1.65549	+	0.443588i	0.0550305	+	0.0147454i
$906$	60.1171	−	24.7331i	1.99726	−	0.821701i
$907$	−30.6411	+	17.6906i	−1.01742	+	0.587408i	−0.913356	−	0.407163i	$-0.866518\pi$
$907$	−30.6411	+	17.6906i	−1.01742	+	0.587408i	−0.104065	+	0.994571i	$0.533185\pi$
$908$	3.62992	+	13.5471i	0.120463	+	0.449575i
$909$	−40.0602	−	10.9397i	−1.32871	−	0.362848i
$910$	2.10497	−	1.86244i	0.0697792	−	0.0617392i
$911$	19.1166	+	11.0370i	0.633362	+	0.365672i	0.782053	−	0.623212i	$-0.214173\pi$
$911$	19.1166	+	11.0370i	0.633362	+	0.365672i	−0.148691	+	0.988884i	$0.547506\pi$
$912$	−23.1433	+	17.6707i	−0.766350	+	0.585135i
$913$	0.764160			0.0252900
$914$	21.6524	−	37.5030i	0.716198	−	1.24049i
$915$	4.02022	−	0.519495i	0.132905	−	0.0171740i
$916$	−50.2969	+	50.2969i	−1.66186	+	1.66186i
$917$	6.58772	+	1.76517i	0.217546	+	0.0582911i
$918$	35.7062	+	4.96165i	1.17848	+	0.163759i
$919$	−19.0623	−	33.0168i	−0.628807	−	1.08913i	−0.987791	−	0.155782i	$-0.950210\pi$
$919$	−19.0623	−	33.0168i	−0.628807	−	1.08913i	0.358985	−	0.933343i	$-0.383123\pi$
$920$	−11.2854	−	19.5468i	−0.372068	−	0.644440i
$921$	−21.5856	+	51.7617i	−0.711268	+	1.70561i
$922$	−10.1681	+	5.87055i	−0.334868	+	0.193336i
$923$	−7.83152	+	1.59359i	−0.257778	+	0.0524536i
$924$	−19.6217	+	8.07265i	−0.645506	+	0.265571i
$925$	−0.265095	−	0.0710320i	−0.00871628	−	0.00233552i
$926$	−4.85493	−	2.80300i	−0.159543	−	0.0921122i
$927$	0.509770	−	1.86673i	0.0167430	−	0.0613114i
$928$	0.951449	−	0.951449i	0.0312328	−	0.0312328i
$929$	−35.5030	−	35.5030i	−1.16481	−	1.16481i	−0.983408	−	0.181406i	$-0.941935\pi$
$929$	−35.5030	−	35.5030i	−1.16481	−	1.16481i	−0.181406	−	0.983408i	$-0.558065\pi$
$930$	5.64937	−	13.5471i	0.185250	−	0.444226i
$931$	5.93955	−	22.1667i	0.194661	−	0.726485i
$932$	10.6379	+	6.14181i	0.348457	+	0.201182i
$933$	17.8613	−	23.1624i	0.584753	−	0.758304i
$934$	8.87963	−	33.1392i	0.290550	−	1.08435i
$935$	−8.28345			−0.270898
$936$	51.6250	−	25.4337i	1.68742	−	0.831325i
$937$	51.0153			1.66660			0.833299	−	0.552822i	$-0.186449\pi$
$937$	51.0153			1.66660			0.833299	+	0.552822i	$0.186449\pi$
$938$	2.36829	−	8.83857i	0.0773273	−	0.288589i
$939$	−29.6744	−	3.97893i	−0.968389	−	0.129847i
$940$	−22.1708	−	12.8003i	−0.723131	−	0.417500i
$941$	−6.90418	+	25.7667i	−0.225070	+	0.839972i	0.757307	+	0.653059i	$0.226515\pi$
$941$	−6.90418	+	25.7667i	−0.225070	+	0.839972i	−0.982377	+	0.186912i	$0.940152\pi$
$942$	−15.4363	−	20.2169i	−0.502942	−	0.658703i
$943$	−31.1252	−	31.1252i	−1.01357	−	1.01357i
$944$	17.7086	−	17.7086i	0.576366	−	0.576366i
$945$	−1.62136	+	0.201634i	−0.0527429	+	0.00655915i
$946$	118.149	+	68.2134i	3.84136	+	2.21781i
$947$	16.6114	+	4.45102i	0.539800	+	0.144639i	0.518410	−	0.855132i	$-0.326524\pi$
$947$	16.6114	+	4.45102i	0.539800	+	0.144639i	0.0213898	+	0.999771i	$0.493191\pi$
$948$	−29.7041	−	22.9058i	−0.964745	−	0.743947i
$949$	4.34608	−	12.9904i	0.141080	−	0.421686i
$950$	−34.5239	+	19.9324i	−1.12010	+	0.646692i
$951$	12.2587	+	16.0552i	0.397516	+	0.520626i
$952$	−4.17060	−	7.22369i	−0.135170	−	0.234121i
$953$	−23.1429	−	40.0846i	−0.749671	−	1.29847i	−0.947981	−	0.318328i	$-0.896879\pi$
$953$	−23.1429	−	40.0846i	−0.749671	−	1.29847i	0.198310	−	0.980139i	$-0.436455\pi$
$954$	36.7118	−	20.9621i	1.18859	−	0.678674i
$955$	7.27622	+	1.94966i	0.235453	+	0.0630894i
$956$	75.8279	−	75.8279i	2.45245	−	2.45245i
$957$	−4.96649	−	6.50460i	−0.160544	−	0.210264i
$958$	−7.76867	+	13.4557i	−0.250994	+	0.434735i
$959$	3.68226			0.118906
$960$	−0.756569	−	5.85487i	−0.0244182	−	0.188965i
$961$	5.27464	+	3.04531i	0.170150	+	0.0982359i
$962$	−0.468605	+	0.233656i	−0.0151084	+	0.00753336i
$963$	32.3116	−	8.49244i	1.04123	−	0.273665i
$964$	6.33678	+	23.6492i	0.204094	+	0.761689i
$965$	1.74205	−	1.00578i	0.0560787	−	0.0323771i
$966$	−14.3984	−	11.1031i	−0.463261	−	0.357236i
$967$	−10.6628	−	2.85708i	−0.342892	−	0.0918776i	0.0832636	−	0.996528i	$-0.473466\pi$
$967$	−10.6628	−	2.85708i	−0.342892	−	0.0918776i	−0.426155	+	0.904650i	$0.640132\pi$
$968$	86.4086	−	23.1531i	2.77728	−	0.744169i
$969$	−13.2226	+	10.0959i	−0.424772	+	0.324328i
$970$	1.23596	−	0.331176i	0.0396844	−	0.0106334i
$971$	−43.7777	+	25.2751i	−1.40489	+	0.811116i	−0.994890	−	0.100968i	$-0.967806\pi$
$971$	−43.7777	+	25.2751i	−1.40489	+	0.811116i	−0.410004	+	0.912084i	$0.634473\pi$
$972$	−63.9731	−	9.20166i	−2.05194	−	0.295143i
$973$	1.56122	−	0.418329i	0.0500505	−	0.0134110i
$974$	21.9724	−	38.0573i	0.704041	−	1.21943i
$975$	27.6861	−	9.46003i	0.886665	−	0.302963i
$976$	−10.2119	−	17.6876i	−0.326876	−	0.566166i
$977$	23.5749	+	23.5749i	0.754227	+	0.754227i	0.975265	−	0.221038i	$-0.0709445\pi$
$977$	23.5749	+	23.5749i	0.754227	+	0.754227i	−0.221038	+	0.975265i	$0.570945\pi$
$978$	8.77357	−	65.4324i	0.280548	−	2.09230i
$979$		−	43.6403i		−	1.39475i
$980$	−11.0020	−	11.0020i	−0.351445	−	0.351445i
$981$	0.245743	−	51.3810i	0.00784598	−	1.64047i
$982$	−15.5044	+	57.8631i	−0.494764	+	1.84649i
$983$	−7.33255	−	27.3655i	−0.233872	−	0.872823i	−0.978654	−	0.205515i	$-0.934113\pi$
$983$	−7.33255	−	27.3655i	−0.233872	−	0.872823i	0.744782	−	0.667308i	$-0.232554\pi$
$984$	20.4192	+	49.6318i	0.650942	+	1.58220i
$985$			7.38212i			0.235214i
$986$	4.39510	−	4.39510i	0.139969	−	0.139969i
$987$	−10.5802	−	1.41866i	−0.336771	−	0.0451563i
$988$	−16.2791	+	48.6581i	−0.517908	+	1.54802i
$989$			78.8669i			2.50782i
$990$	22.0147	+	0.105291i	0.699675	+	0.00334638i
$991$	−1.60816	+	2.78541i	−0.0510848	+	0.0884814i	−0.890437	−	0.455106i	$-0.849601\pi$
$991$	−1.60816	+	2.78541i	−0.0510848	+	0.0884814i	0.839352	+	0.543588i	$0.182935\pi$
$992$	−9.14666			−0.290407
$993$	11.7973	+	4.91969i	0.374376	+	0.156122i
$994$	−0.796788	−	2.97365i	−0.0252726	−	0.0943185i
$995$	2.88803	+	10.7783i	0.0915569	+	0.341695i
$996$	−0.133350	−	1.03196i	−0.00422535	−	0.0326988i
$997$	6.63495			0.210131			0.105065	−	0.994465i	$-0.466495\pi$
$997$	6.63495			0.210131			0.105065	+	0.994465i	$0.466495\pi$
$998$	11.9644	−	20.7230i	0.378727	−	0.655975i
$999$	0.301494	+	0.0418950i	0.00953886	+	0.00132550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.110.1	yes	48
3.2	odd	2		351.2.bf.a.305.12		48
9.4	even	3		351.2.ba.a.71.1		48
9.5	odd	6		117.2.x.a.32.12	yes	48
13.11	odd	12		117.2.x.a.11.12	✓	48
39.11	even	12		351.2.ba.a.89.1		48
117.50	even	12	inner	117.2.bc.a.50.1	yes	48
117.76	odd	12		351.2.bf.a.206.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.12	✓	48	13.11	odd	12
117.2.x.a.32.12	yes	48	9.5	odd	6
117.2.bc.a.50.1	yes	48	117.50	even	12	inner
117.2.bc.a.110.1	yes	48	1.1	even	1	trivial
351.2.ba.a.71.1		48	9.4	even	3
351.2.ba.a.89.1		48	39.11	even	12
351.2.bf.a.206.12		48	117.76	odd	12
351.2.bf.a.305.12		48	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.641647 + 2.39466i) q^{2} +(0.658999 + 1.60179i) q^{3} +(-3.59064 - 2.07306i) q^{4} +(-0.145266 + 0.542141i) q^{5} +(-4.25858 + 0.550296i) q^{6} +(-0.396138 - 0.396138i) q^{7} +(3.76217 - 3.76217i) q^{8} +(-2.13144 + 2.11115i) q^{9} +O(q^{10})\)	\(q+(-0.641647 + 2.39466i) q^{2} +(0.658999 + 1.60179i) q^{3} +(-3.59064 - 2.07306i) q^{4} +(-0.145266 + 0.542141i) q^{5} +(-4.25858 + 0.550296i) q^{6} +(-0.396138 - 0.396138i) q^{7} +(3.76217 - 3.76217i) q^{8} +(-2.13144 + 2.11115i) q^{9} +(-1.20503 - 0.695727i) q^{10} +(5.09416 + 1.36498i) q^{11} +(0.954368 - 7.11758i) q^{12} +(-1.60889 - 3.22668i) q^{13} +(1.20280 - 0.694436i) q^{14} +(-0.964125 + 0.124585i) q^{15} +(2.44901 + 4.24182i) q^{16} +(1.39921 + 2.42351i) q^{17} +(-3.68786 - 6.45869i) q^{18} +(3.31532 + 0.888337i) q^{19} +(1.64549 - 1.64549i) q^{20} +(0.373474 - 0.895584i) q^{21} +(-6.53731 + 11.3229i) q^{22} -7.55830 q^{23} +(8.50545 + 3.54692i) q^{24} +(4.05731 + 2.34249i) q^{25} +(8.75915 - 1.78235i) q^{26} +(-4.78623 - 2.02287i) q^{27} +(0.601173 + 2.24361i) q^{28} +(-0.775891 + 0.447961i) q^{29} +(0.320290 - 2.38869i) q^{30} +(5.88269 + 1.57626i) q^{31} +(-1.45069 + 0.388711i) q^{32} +(1.17064 + 9.05927i) q^{33} +(-6.70128 + 1.79560i) q^{34} +(0.272308 - 0.157217i) q^{35} +(12.0298 - 3.16178i) q^{36} +(-0.0565841 + 0.0151617i) q^{37} +(-4.25453 + 7.36906i) q^{38} +(4.10820 - 4.70347i) q^{39} +(1.49311 + 2.58614i) q^{40} +(4.11801 + 4.11801i) q^{41} +(1.90498 + 1.46899i) q^{42} -10.4345i q^{43} +(-15.4616 - 15.4616i) q^{44} +(-0.834915 - 1.46222i) q^{45} +(4.84977 - 18.0996i) q^{46} +(-2.84732 - 10.6264i) q^{47} +(-5.18059 + 6.71815i) q^{48} -6.68615i q^{49} +(-8.21283 + 8.21283i) q^{50} +(-2.95986 + 3.83833i) q^{51} +(-0.912164 + 14.9212i) q^{52} +5.68410i q^{53} +(7.91516 - 10.1634i) q^{54} +(-1.48002 + 2.56347i) q^{55} -2.98068 q^{56} +(0.761864 + 5.89584i) q^{57} +(-0.574866 - 2.14543i) q^{58} +(-1.32335 - 4.93881i) q^{59} +(3.72010 + 1.55135i) q^{60} -4.16982 q^{61} +(-7.54922 + 13.0756i) q^{62} +(1.68065 + 0.00803816i) q^{63} +6.07273i q^{64} +(1.98303 - 0.403516i) q^{65} +(-22.4450 - 3.00956i) q^{66} +(4.65866 - 4.65866i) q^{67} -11.6026i q^{68} +(-4.98091 - 12.1068i) q^{69} +(0.201756 + 0.752964i) q^{70} +(0.573694 - 2.14106i) q^{71} +(-0.0763393 + 15.9613i) q^{72} +(2.68642 + 2.68642i) q^{73} -0.145228i q^{74} +(-1.07841 + 8.04265i) q^{75} +(-10.0625 - 10.0625i) q^{76} +(-1.47727 - 2.55871i) q^{77} +(8.62721 + 12.8557i) q^{78} +(2.61166 - 4.52353i) q^{79} +(-2.65542 + 0.711518i) q^{80} +(0.0860878 - 8.99959i) q^{81} +(-12.5035 + 7.21893i) q^{82} +(0.139959 - 0.0375018i) q^{83} +(-3.19761 + 2.44148i) q^{84} +(-1.51714 + 0.406517i) q^{85} +(24.9870 + 6.69526i) q^{86} +(-1.22885 - 0.947606i) q^{87} +(24.3003 - 14.0298i) q^{88} +(-2.14168 - 7.99287i) q^{89} +(4.03725 - 1.06111i) q^{90} +(-0.640871 + 1.91555i) q^{91} +(27.1391 + 15.6688i) q^{92} +(1.35185 + 10.4616i) q^{93} +27.2735 q^{94} +(-0.963208 + 1.66832i) q^{95} +(-1.57863 - 2.06753i) q^{96} +(-0.650247 + 0.650247i) q^{97} +(16.0111 + 4.29015i) q^{98} +(-13.7396 + 7.84517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

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