LMFDB - Embedded newform 180.2.x.a.103.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(7,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	180.103
Dual form			180.2.x.a.7.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0534584 - 1.41320i) q^{2} +(-0.133985 + 1.72686i) q^{3} +(-1.99428 - 0.151095i) q^{4} +(0.795868 + 2.08964i) q^{5} +(2.43324 + 0.281664i) q^{6} +(-0.659597 + 2.46165i) q^{7} +(-0.320139 + 2.81025i) q^{8} +(-2.96410 - 0.462748i) q^{9} +(2.99563 - 1.01301i) q^{10} +(-3.01796 + 1.74242i) q^{11} +(0.528125 - 3.42361i) q^{12} +(5.09493 - 1.36518i) q^{13} +(3.44355 + 1.06374i) q^{14} +(-3.71515 + 1.09437i) q^{15} +(3.95434 + 0.602653i) q^{16} +(2.16382 - 2.16382i) q^{17} +(-0.812413 + 4.16413i) q^{18} +3.88577 q^{19} +(-1.27145 - 4.28759i) q^{20} +(-4.16255 - 1.46886i) q^{21} +(2.30106 + 4.35813i) q^{22} +(-0.991920 - 3.70190i) q^{23} +(-4.81002 - 0.929369i) q^{24} +(-3.73319 + 3.32615i) q^{25} +(-1.65691 - 7.27315i) q^{26} +(1.19625 - 5.05658i) q^{27} +(1.68737 - 4.80957i) q^{28} +(-3.85118 + 2.22348i) q^{29} +(1.34796 + 5.30877i) q^{30} +(1.86992 + 1.07960i) q^{31} +(1.06306 - 5.55607i) q^{32} +(-2.60455 - 5.44505i) q^{33} +(-2.94224 - 3.17359i) q^{34} +(-5.66891 + 0.580828i) q^{35} +(5.84133 + 1.37071i) q^{36} +(3.67542 - 3.67542i) q^{37} +(0.207727 - 5.49138i) q^{38} +(1.67483 + 8.98115i) q^{39} +(-6.12720 + 1.56761i) q^{40} +(-4.04792 + 7.01121i) q^{41} +(-2.29832 + 5.80400i) q^{42} +(5.08248 + 1.36185i) q^{43} +(6.28194 - 3.01888i) q^{44} +(-1.39205 - 6.56218i) q^{45} +(-5.28456 + 1.20389i) q^{46} +(0.0620436 - 0.231550i) q^{47} +(-1.57052 + 6.74785i) q^{48} +(0.437526 + 0.252606i) q^{49} +(4.50096 + 5.45356i) q^{50} +(3.44669 + 4.02653i) q^{51} +(-10.3670 + 1.95274i) q^{52} +(0.265818 + 0.265818i) q^{53} +(-7.08202 - 1.96086i) q^{54} +(-6.04292 - 4.91971i) q^{55} +(-6.70669 - 2.64170i) q^{56} +(-0.520636 + 6.71018i) q^{57} +(2.93635 + 5.56137i) q^{58} +(5.69158 - 9.85810i) q^{59} +(7.57442 - 1.62115i) q^{60} +(-4.61792 - 7.99848i) q^{61} +(1.62566 - 2.58487i) q^{62} +(3.09423 - 6.99134i) q^{63} +(-7.79502 - 1.79934i) q^{64} +(6.90763 + 9.56007i) q^{65} +(-7.83420 + 3.38968i) q^{66} +(-0.719566 + 0.192807i) q^{67} +(-4.64221 + 3.98832i) q^{68} +(6.52556 - 1.21691i) q^{69} +(0.517777 + 8.04237i) q^{70} +2.06980i q^{71} +(2.24936 - 8.18171i) q^{72} +(8.97449 + 8.97449i) q^{73} +(-4.99763 - 5.39060i) q^{74} +(-5.24361 - 6.89235i) q^{75} +(-7.74933 - 0.587121i) q^{76} +(-2.29859 - 8.57845i) q^{77} +(12.7817 - 1.88676i) q^{78} +(-7.56173 - 13.0973i) q^{79} +(1.88780 + 8.74278i) q^{80} +(8.57173 + 2.74326i) q^{81} +(9.69186 + 6.09534i) q^{82} +(14.9925 + 4.01723i) q^{83} +(8.07937 + 3.55826i) q^{84} +(6.24371 + 2.79948i) q^{85} +(2.19627 - 7.10978i) q^{86} +(-3.32364 - 6.94837i) q^{87} +(-3.93047 - 9.03903i) q^{88} +3.61495i q^{89} +(-9.34811 + 1.61645i) q^{90} +13.4424i q^{91} +(1.41883 + 7.53251i) q^{92} +(-2.11486 + 3.08444i) q^{93} +(-0.323910 - 0.100059i) q^{94} +(3.09256 + 8.11986i) q^{95} +(9.45212 + 2.58020i) q^{96} +(3.05651 + 0.818990i) q^{97} +(0.380373 - 0.604809i) q^{98} +(9.75182 - 3.76814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{16} - 16 q^{17} - 36 q^{18} - 18 q^{20} - 24 q^{21} - 10 q^{22} - 4 q^{25} - 48 q^{26} + 8 q^{28} - 14 q^{30} + 18 q^{32}+ \cdots + 164 q^{98}+O(q^{100}) $ 128 * q - 2 * q^2 - 4 * q^5 - 8 * q^6 - 8 * q^8 - 8 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^16 - 16 * q^17 - 36 * q^18 - 18 * q^20 - 24 * q^21 - 10 * q^22 - 4 * q^25 - 48 * q^26 + 8 * q^28 - 14 * q^30 + 18 * q^32 - 20 * q^33 - 40 * q^36 - 16 * q^37 - 34 * q^38 - 2 * q^40 - 8 * q^41 + 34 * q^42 - 28 * q^45 - 40 * q^46 - 22 * q^48 + 38 * q^50 - 18 * q^52 - 64 * q^53 - 32 * q^56 - 48 * q^57 - 10 * q^58 + 74 * q^60 - 8 * q^61 + 44 * q^62 + 12 * q^65 - 36 * q^66 + 58 * q^68 - 22 * q^70 + 78 * q^72 - 16 * q^73 - 32 * q^76 - 60 * q^77 + 114 * q^78 + 132 * q^80 + 24 * q^81 - 4 * q^85 + 32 * q^86 - 10 * q^88 + 138 * q^90 + 52 * q^92 - 68 * q^93 + 52 * q^96 - 4 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.0534584	−	1.41320i	0.0378008	−	0.999285i
$2$	0.0534584	−	1.41320i	0.0378008	−	0.999285i
$3$	−0.133985	+	1.72686i	−0.0773565	+	0.997003i
$3$	−0.133985	+	1.72686i	−0.0773565	+	0.997003i
$4$	−1.99428	−	0.151095i	−0.997142	−	0.0755476i
$5$	0.795868	+	2.08964i	0.355923	+	0.934515i
$5$	0.795868	+	2.08964i	0.355923	+	0.934515i
$6$	2.43324	+	0.281664i	0.993367	+	0.114989i
$7$	−0.659597	+	2.46165i	−0.249304	+	0.930416i	0.721867	+	0.692032i	$0.243284\pi$
$7$	−0.659597	+	2.46165i	−0.249304	+	0.930416i	−0.971171	+	0.238384i	$0.923382\pi$
$8$	−0.320139	+	2.81025i	−0.113186	+	0.993574i
$9$	−2.96410	−	0.462748i	−0.988032	−	0.154249i
$10$	2.99563	−	1.01301i	0.947302	−	0.320343i
$11$	−3.01796	+	1.74242i	−0.909948	+	0.525359i	−0.880415	−	0.474205i	$-0.842736\pi$
$11$	−3.01796	+	1.74242i	−0.909948	+	0.525359i	−0.0295338	+	0.999564i	$0.509402\pi$
$12$	0.528125	−	3.42361i	0.152457	−	0.988310i
$13$	5.09493	−	1.36518i	1.41308	−	0.378634i	0.530057	−	0.847962i	$-0.322171\pi$
$13$	5.09493	−	1.36518i	1.41308	−	0.378634i	0.883024	+	0.469329i	$0.155504\pi$
$14$	3.44355	+	1.06374i	0.920327	+	0.284297i
$15$	−3.71515	+	1.09437i	−0.959248	+	0.282566i
$16$	3.95434	+	0.602653i	0.988585	+	0.150663i
$17$	2.16382	−	2.16382i	0.524802	−	0.524802i	−0.394216	−	0.919018i	$-0.628984\pi$
$17$	2.16382	−	2.16382i	0.524802	−	0.524802i	0.919018	+	0.394216i	$0.128984\pi$
$18$	−0.812413	+	4.16413i	−0.191488	+	0.981495i
$19$	3.88577			0.891456			0.445728	−	0.895168i	$-0.352945\pi$
$19$	3.88577			0.891456			0.445728	+	0.895168i	$0.352945\pi$
$20$	−1.27145	−	4.28759i	−0.284305	−	0.958734i
$21$	−4.16255	−	1.46886i	−0.908343	−	0.320531i
$22$	2.30106	+	4.35813i	0.490587	+	0.929157i
$23$	−0.991920	−	3.70190i	−0.206830	−	0.771899i	−0.988884	−	0.148689i	$-0.952495\pi$
$23$	−0.991920	−	3.70190i	−0.206830	−	0.771899i	0.782054	−	0.623210i	$-0.214172\pi$
$24$	−4.81002	−	0.929369i	−0.981841	−	0.189707i
$25$	−3.73319	+	3.32615i	−0.746638	+	0.665231i
$26$	−1.65691	−	7.27315i	−0.324947	−	1.42638i
$27$	1.19625	−	5.05658i	0.230218	−	0.973139i
$28$	1.68737	−	4.80957i	0.318883	−	0.908923i
$29$	−3.85118	+	2.22348i	−0.715147	+	0.412890i	−0.812964	−	0.582314i	$-0.802147\pi$
$29$	−3.85118	+	2.22348i	−0.715147	+	0.412890i	0.0978169	+	0.995204i	$0.468814\pi$
$30$	1.34796	+	5.30877i	0.246103	+	0.969244i
$31$	1.86992	+	1.07960i	0.335848	+	0.193902i	0.658434	−	0.752638i	$-0.271219\pi$
$31$	1.86992	+	1.07960i	0.335848	+	0.193902i	−0.322586	+	0.946540i	$0.604552\pi$
$32$	1.06306	−	5.55607i	0.187925	−	0.982183i
$33$	−2.60455	−	5.44505i	−0.453394	−	0.947862i
$34$	−2.94224	−	3.17359i	−0.504589	−	0.544265i
$35$	−5.66891	+	0.580828i	−0.958221	+	0.0981779i
$36$	5.84133	+	1.37071i	0.973555	+	0.228452i
$37$	3.67542	−	3.67542i	0.604235	−	0.604235i	−0.337198	−	0.941434i	$-0.609479\pi$
$37$	3.67542	−	3.67542i	0.604235	−	0.604235i	0.941434	+	0.337198i	$0.109479\pi$
$38$	0.207727	−	5.49138i	0.0336978	−	0.890819i
$39$	1.67483	+	8.98115i	0.268188	+	1.43814i
$40$	−6.12720	+	1.56761i	−0.968796	+	0.247861i
$41$	−4.04792	+	7.01121i	−0.632179	+	1.09497i	0.354926	+	0.934894i	$0.384506\pi$
$41$	−4.04792	+	7.01121i	−0.632179	+	1.09497i	−0.987105	+	0.160072i	$0.948827\pi$
$42$	−2.29832	+	5.80400i	−0.354638	+	0.895577i
$43$	5.08248	+	1.36185i	0.775071	+	0.207680i	0.624611	−	0.780936i	$-0.285258\pi$
$43$	5.08248	+	1.36185i	0.775071	+	0.207680i	0.150461	+	0.988616i	$0.451924\pi$
$44$	6.28194	−	3.01888i	0.947037	−	0.455113i
$45$	−1.39205	−	6.56218i	−0.207515	−	0.978232i
$46$	−5.28456	+	1.20389i	−0.779165	+	0.177503i
$47$	0.0620436	−	0.231550i	0.00904999	−	0.0337750i	−0.961253	−	0.275667i	$-0.911101\pi$
$47$	0.0620436	−	0.231550i	0.00904999	−	0.0337750i	0.970303	+	0.241892i	$0.0777680\pi$
$48$	−1.57052	+	6.74785i	−0.226685	+	0.973968i
$49$	0.437526	+	0.252606i	0.0625037	+	0.0360865i
$50$	4.50096	+	5.45356i	0.636532	+	0.771250i
$51$	3.44669	+	4.02653i	0.482633	+	0.563827i
$52$	−10.3670	+	1.95274i	−1.43765	+	0.270797i
$53$	0.265818	+	0.265818i	0.0365129	+	0.0365129i	0.725127	−	0.688615i	$-0.241781\pi$
$53$	0.265818	+	0.265818i	0.0365129	+	0.0365129i	−0.688615	+	0.725127i	$0.741781\pi$
$54$	−7.08202	−	1.96086i	−0.963741	−	0.266839i
$55$	−6.04292	−	4.91971i	−0.814827	−	0.663373i
$56$	−6.70669	−	2.64170i	−0.896219	−	0.353013i
$57$	−0.520636	+	6.71018i	−0.0689600	+	0.888785i
$58$	2.93635	+	5.56137i	0.385562	+	0.730243i
$59$	5.69158	−	9.85810i	0.740980	−	1.28342i	−0.211069	−	0.977471i	$-0.567695\pi$
$59$	5.69158	−	9.85810i	0.740980	−	1.28342i	0.952049	−	0.305944i	$-0.0989722\pi$
$60$	7.57442	−	1.62115i	0.977854	−	0.209289i
$61$	−4.61792	−	7.99848i	−0.591264	−	1.02410i	−0.994062	−	0.108811i	$-0.965296\pi$
$61$	−4.61792	−	7.99848i	−0.591264	−	1.02410i	0.402798	−	0.915289i	$-0.368038\pi$
$62$	1.62566	−	2.58487i	0.206459	−	0.328278i
$63$	3.09423	−	6.99134i	0.389837	−	0.880826i
$64$	−7.79502	−	1.79934i	−0.974378	−	0.224918i
$65$	6.90763	+	9.56007i	0.856787	+	1.18578i
$66$	−7.83420	+	3.38968i	−0.964323	+	0.417240i
$67$	−0.719566	+	0.192807i	−0.0879089	+	0.0235551i	−0.302505	−	0.953148i	$-0.597823\pi$
$67$	−0.719566	+	0.192807i	−0.0879089	+	0.0235551i	0.214596	+	0.976703i	$0.431156\pi$
$68$	−4.64221	+	3.98832i	−0.562950	+	0.483655i
$69$	6.52556	−	1.21691i	0.785585	−	0.146498i
$70$	0.517777	+	8.04237i	0.0618862	+	0.961248i
$71$			2.06980i			0.245640i	0.992429	+	0.122820i	$0.0391938\pi$
$71$			2.06980i			0.245640i	−0.992429	+	0.122820i	$0.960806\pi$
$72$	2.24936	−	8.18171i	0.265090	−	0.964224i
$73$	8.97449	+	8.97449i	1.05038	+	1.05038i	0.998661	+	0.0517232i	$0.0164714\pi$
$73$	8.97449	+	8.97449i	1.05038	+	1.05038i	0.0517232	+	0.998661i	$0.483529\pi$
$74$	−4.99763	−	5.39060i	−0.580963	−	0.626644i
$75$	−5.24361	−	6.89235i	−0.605480	−	0.795860i
$76$	−7.74933	−	0.587121i	−0.888909	−	0.0673474i
$77$	−2.29859	−	8.57845i	−0.261948	−	0.977605i
$78$	12.7817	−	1.88676i	1.44725	−	0.213634i
$79$	−7.56173	−	13.0973i	−0.850761	−	1.47356i	−0.880523	−	0.474004i	$-0.842808\pi$
$79$	−7.56173	−	13.0973i	−0.850761	−	1.47356i	0.0297623	−	0.999557i	$-0.490525\pi$
$80$	1.88780	+	8.74278i	0.211063	+	0.977472i
$81$	8.57173	+	2.74326i	0.952414	+	0.304807i
$82$	9.69186	+	6.09534i	1.07029	+	0.673118i
$83$	14.9925	+	4.01723i	1.64564	+	0.440949i	0.958388	−	0.285468i	$-0.0921490\pi$
$83$	14.9925	+	4.01723i	1.64564	+	0.440949i	0.687255	+	0.726417i	$0.258816\pi$
$84$	8.07937	+	3.55826i	0.881532	+	0.388238i
$85$	6.24371	+	2.79948i	0.677225	+	0.303647i
$86$	2.19627	−	7.10978i	0.236830	−	0.766667i
$87$	−3.32364	−	6.94837i	−0.356332	−	0.744944i
$88$	−3.93047	−	9.03903i	−0.418989	−	0.963564i
$89$			3.61495i			0.383184i	0.981475	+	0.191592i	$0.0613650\pi$
$89$			3.61495i			0.383184i	−0.981475	+	0.191592i	$0.938635\pi$
$90$	−9.34811	+	1.61645i	−0.985377	+	0.170389i
$91$			13.4424i			1.40915i
$92$	1.41883	+	7.53251i	0.147923	+	0.785318i
$93$	−2.11486	+	3.08444i	−0.219301	+	0.319842i
$94$	−0.323910	−	0.100059i	−0.0334088	−	0.0103203i
$95$	3.09256	+	8.11986i	0.317290	+	0.833080i
$96$	9.45212	+	2.58020i	0.964703	+	0.263340i
$97$	3.05651	+	0.818990i	0.310342	+	0.0831559i	0.410629	−	0.911803i	$-0.365309\pi$
$97$	3.05651	+	0.818990i	0.310342	+	0.0831559i	−0.100287	+	0.994959i	$0.531976\pi$
$98$	0.380373	−	0.604809i	0.0384234	−	0.0610949i
$99$	9.75182	−	3.76814i	0.980094	−	0.378712i
$100$	7.94760	−	6.06923i	0.794760	−	0.606923i
$101$	2.15969	+	3.74069i	0.214897	+	0.372213i	0.953241	−	0.302212i	$-0.0977250\pi$
$101$	2.15969	+	3.74069i	0.214897	+	0.372213i	−0.738344	+	0.674425i	$0.764392\pi$
$102$	5.87456	−	4.65562i	0.581668	−	0.460975i
$103$	−0.353529	−	1.31939i	−0.0348342	−	0.130003i	0.946319	−	0.323234i	$-0.104770\pi$
$103$	−0.353529	−	1.31939i	−0.0348342	−	0.130003i	−0.981153	+	0.193231i	$0.938103\pi$
$104$	2.20542	+	14.7551i	0.216259	+	1.44686i
$105$	−0.243457	−	9.86725i	−0.0237590	−	0.962945i
$106$	0.389864	−	0.361444i	0.0378670	−	0.0351065i
$107$	−5.32781	−	5.32781i	−0.515059	−	0.515059i	0.401013	−	0.916072i	$-0.368658\pi$
$107$	−5.32781	−	5.32781i	−0.515059	−	0.515059i	−0.916072	+	0.401013i	$0.868658\pi$
$108$	−3.14968	+	9.90351i	−0.303078	+	0.952966i
$109$		−	14.1851i		−	1.35869i	−0.733820	−	0.679344i	$-0.762264\pi$
$109$		−	14.1851i		−	1.35869i	0.733820	−	0.679344i	$-0.237736\pi$
$110$	−7.27559	+	8.27687i	−0.693700	+	0.789169i
$111$	5.85449	+	6.83939i	0.555683	+	0.649166i
$112$	−4.09179	+	9.33669i	−0.386638	+	0.882235i
$113$	0.437551	−	0.117242i	0.0411614	−	0.0110292i	−0.238180	−	0.971221i	$-0.576551\pi$
$113$	0.437551	−	0.117242i	0.0411614	−	0.0110292i	0.279341	+	0.960192i	$0.409884\pi$
$114$	9.45501	+	1.09448i	0.885543	+	0.102507i
$115$	6.94619	−	5.01898i	0.647736	−	0.468022i
$116$	8.01631	−	3.85236i	0.744296	−	0.357683i
$117$	−15.7336	+	1.68886i	−1.45457	+	0.156135i
$118$	−13.6272	−	8.57035i	−1.25449	−	0.788965i
$119$	3.89931	+	6.75380i	0.357449	+	0.619120i
$120$	−1.88609	−	10.7909i	−0.172176	−	0.985066i
$121$	0.572043	−	0.990808i	0.0520040	−	0.0900735i
$122$	−11.5503	+	6.09848i	−1.04572	+	0.552130i
$123$	−11.5650	−	7.92960i	−1.04278	−	0.714988i
$124$	−3.56603	−	2.43557i	−0.320239	−	0.218720i
$125$	−9.92159	−	5.15384i	−0.887414	−	0.460973i
$126$	−9.71477	−	4.74653i	−0.865460	−	0.422854i
$127$	2.66261	+	2.66261i	0.236269	+	0.236269i	0.815303	−	0.579034i	$-0.196570\pi$
$127$	2.66261	+	2.66261i	0.236269	+	0.236269i	−0.579034	+	0.815303i	$0.696570\pi$
$128$	−2.95955	+	10.9198i	−0.261590	+	0.965179i
$129$	−3.03270	+	8.59427i	−0.267014	+	0.756683i
$130$	13.8796	−	9.25082i	1.21732	−	0.811351i
$131$	−10.6177	−	6.13011i	−0.927670	−	0.535590i	−0.0415959	−	0.999135i	$-0.513244\pi$
$131$	−10.6177	−	6.13011i	−0.927670	−	0.535590i	−0.886074	+	0.463544i	$0.846578\pi$
$132$	4.37150	+	11.2525i	0.380490	+	0.979406i
$133$	−2.56304	+	9.56540i	−0.222244	+	0.829425i
$134$	0.234009	+	1.02720i	0.0202153	+	0.0887365i
$135$	11.5185	−	1.52464i	0.991353	−	0.131220i
$136$	5.38814	+	6.77359i	0.462029	+	0.580830i
$137$	−8.93538	−	2.39423i	−0.763401	−	0.204553i	−0.143947	−	0.989585i	$-0.545979\pi$
$137$	−8.93538	−	2.39423i	−0.763401	−	0.204553i	−0.619454	+	0.785033i	$0.712646\pi$
$138$	−1.37089	−	9.28700i	−0.116698	−	0.790562i
$139$	−8.95460	+	15.5098i	−0.759520	+	1.31553i	0.183576	+	0.983005i	$0.441233\pi$
$139$	−8.95460	+	15.5098i	−0.759520	+	1.31553i	−0.943096	+	0.332521i	$0.892101\pi$
$140$	11.3932	−	0.301791i	0.962900	−	0.0255060i
$141$	0.391542	+	0.138165i	0.0329738	+	0.0116356i
$142$	2.92504	+	0.110648i	0.245464	+	0.00928539i
$143$	−12.9976	+	12.9976i	−1.08691	+	1.08691i
$144$	−11.4422	−	3.61619i	−0.953514	−	0.301349i
$145$	−7.71131	−	6.27799i	−0.640389	−	0.521359i
$146$	13.1625	−	12.2030i	1.08934	−	1.00993i
$147$	−0.494837	+	0.721701i	−0.0408135	+	0.0595249i
$148$	−7.88517	+	6.77450i	−0.648157	+	0.556860i
$149$	2.39752	+	1.38421i	0.196413	+	0.113399i	0.594981	−	0.803740i	$-0.297160\pi$
$149$	2.39752	+	1.38421i	0.196413	+	0.113399i	−0.398568	+	0.917139i	$0.630493\pi$
$150$	−10.0206	+	7.04183i	−0.818179	+	0.574963i
$151$	−6.51667	+	3.76240i	−0.530319	+	0.306180i	−0.741146	−	0.671343i	$-0.765718\pi$
$151$	−6.51667	+	3.76240i	−0.530319	+	0.306180i	0.210827	+	0.977523i	$0.432384\pi$
$152$	−1.24399	+	10.9200i	−0.100901	+	0.885728i
$153$	−7.41506	+	5.41246i	−0.599472	+	0.437571i
$154$	−12.2460	+	2.78978i	−0.986808	+	0.224807i
$155$	−0.767764	+	4.76668i	−0.0616683	+	0.382869i
$156$	−1.98309	−	18.1640i	−0.158774	−	1.45429i
$157$	0.969291	+	3.61744i	0.0773578	+	0.288703i	0.993758	−	0.111561i	$-0.0355850\pi$
$157$	0.969291	+	3.61744i	0.0773578	+	0.288703i	−0.916400	+	0.400264i	$0.868918\pi$
$158$	−18.9134	+	9.98609i	−1.50467	+	0.794451i
$159$	−0.494646	+	0.423414i	−0.0392279	+	0.0335789i
$160$	12.4562	−	2.20048i	0.984752	−	0.173963i
$161$	9.76704			0.769751
$162$	4.33502	−	11.9669i	0.340591	−	0.940212i
$163$	6.76935	−	6.76935i	0.530216	−	0.530216i	−0.390420	−	0.920637i	$-0.627670\pi$
$163$	6.76935	−	6.76935i	0.530216	−	0.530216i	0.920637	+	0.390420i	$0.127670\pi$
$164$	9.13207	−	13.3707i	0.713095	−	1.04408i
$165$	9.30531	−	9.77612i	0.724418	−	0.761070i
$166$	6.47864	−	20.9727i	0.502840	−	1.62780i
$167$	−3.57315	+	0.957423i	−0.276499	+	0.0740876i	−0.394404	−	0.918937i	$-0.629049\pi$
$167$	−3.57315	+	0.957423i	−0.276499	+	0.0740876i	0.117905	+	0.993025i	$0.462382\pi$
$168$	5.46045	−	11.2276i	0.421283	−	0.866226i
$169$	12.8363	−	7.41103i	0.987406	−	0.570079i
$170$	4.29002	−	8.67397i	0.329029	−	0.665263i
$171$	−11.5178	−	1.79813i	−0.880787	−	0.137507i
$172$	−9.93015	−	3.48385i	−0.757167	−	0.265641i
$173$	6.00167	−	22.3985i	0.456299	−	1.70293i	−0.227943	−	0.973674i	$-0.573200\pi$
$173$	6.00167	−	22.3985i	0.456299	−	1.70293i	0.684242	−	0.729255i	$-0.260133\pi$
$174$	−9.99714	+	4.32553i	−0.757881	+	0.327918i
$175$	−5.72543	−	11.3837i	−0.432802	−	0.860529i
$176$	−12.9841	+	5.07133i	−0.978714	+	0.382266i
$177$	16.2610	+	11.1494i	1.22225	+	0.838041i
$178$	5.10866	+	0.193249i	0.382910	+	0.0144847i
$179$	10.0185			0.748819			0.374410	−	0.927263i	$-0.377845\pi$
$179$	10.0185			0.748819			0.374410	+	0.927263i	$0.377845\pi$
$180$	1.78463	+	13.2972i	0.133019	+	0.991114i
$181$	−19.9811			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$181$	−19.9811			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$182$	18.9969	+	0.718610i	1.40814	+	0.0532669i
$183$	14.4310	−	6.90283i	1.06677	−	0.510272i
$184$	10.7208	−	1.60242i	0.790349	−	0.118132i
$185$	10.6055	+	4.75515i	0.779728	+	0.349606i
$186$	4.24589	+	3.15362i	0.311324	+	0.231234i
$187$	−2.76003	+	10.3006i	−0.201833	+	0.753253i
$188$	−0.158719	+	0.452402i	−0.0115758	+	0.0329948i
$189$	11.6585	+	6.28005i	0.848030	+	0.456806i
$190$	11.6403	−	3.93634i	0.844478	−	0.285572i
$191$	13.5705	−	7.83490i	0.981923	−	0.566914i	0.0790731	−	0.996869i	$-0.474804\pi$
$191$	13.5705	−	7.83490i	0.981923	−	0.566914i	0.902850	+	0.429955i	$0.141471\pi$
$192$	4.15164	−	13.2198i	0.299619	−	0.954059i
$193$	−20.8469	+	5.58592i	−1.50060	+	0.402083i	−0.913299	−	0.407289i	$-0.866474\pi$
$193$	−20.8469	+	5.58592i	−1.50060	+	0.402083i	−0.587296	+	0.809372i	$0.699807\pi$
$194$	1.32080	−	4.27569i	0.0948276	−	0.306977i
$195$	−17.4344	+	10.6476i	−1.24851	+	0.762491i
$196$	−0.834384	−	0.569876i	−0.0595988	−	0.0407054i
$197$	−9.44630	+	9.44630i	−0.673021	+	0.673021i	−0.958411	−	0.285390i	$-0.907877\pi$
$197$	−9.44630	+	9.44630i	−0.673021	+	0.673021i	0.285390	+	0.958411i	$0.407877\pi$
$198$	−4.80383	−	13.9827i	−0.341393	−	0.993709i
$199$	2.06079			0.146085			0.0730427	−	0.997329i	$-0.476729\pi$
$199$	2.06079			0.146085			0.0730427	+	0.997329i	$0.476729\pi$
$200$	−8.15219	−	11.5560i	−0.576447	−	0.817135i
$201$	−0.236540	−	1.26842i	−0.0166842	−	0.0894677i
$202$	5.40181	−	2.85211i	0.380070	−	0.200674i
$203$	−2.93320	−	10.9469i	−0.205871	−	0.768320i
$204$	−6.26529	−	8.55082i	−0.438658	−	0.598677i
$205$	−17.8725	−	2.87870i	−1.24827	−	0.201057i
$206$	−1.88346	+	0.429076i	−0.131227	+	0.0298951i
$207$	1.22710	+	11.4318i	0.0852893	+	0.794564i
$208$	20.9698	−	2.32792i	1.45400	−	0.161412i
$209$	−11.7271	+	6.77063i	−0.811179	+	0.468335i
$210$	−13.9574	−	0.183433i	−0.963155	−	0.0126581i
$211$	−1.99458	−	1.15157i	−0.137313	−	0.0792776i	0.429770	−	0.902938i	$-0.358595\pi$
$211$	−1.99458	−	1.15157i	−0.137313	−	0.0792776i	−0.567083	+	0.823661i	$0.691928\pi$
$212$	−0.489952	−	0.570280i	−0.0336500	−	0.0391670i
$213$	−3.57425	−	0.277323i	−0.244904	−	0.0190019i
$214$	−7.81409	+	7.24446i	−0.534161	+	0.495221i
$215$	1.19922	+	11.7044i	0.0817858	+	0.798234i
$216$	13.8273	+	4.98057i	0.940828	+	0.338885i
$217$	−3.89099	+	3.89099i	−0.264138	+	0.264138i
$218$	−20.0465	−	0.758314i	−1.35772	−	0.0513595i
$219$	−16.7001	+	14.2952i	−1.12849	+	0.965983i
$220$	11.3080	+	10.7244i	0.762383	+	0.723036i
$221$	8.07049	−	13.9785i	0.542880	−	0.940296i
$222$	9.97842	−	7.90795i	0.669708	−	0.530747i
$223$	−16.1225	−	4.32002i	−1.07964	−	0.289290i	−0.325194	−	0.945647i	$-0.605430\pi$
$223$	−16.1225	−	4.32002i	−1.07964	−	0.289290i	−0.754450	+	0.656357i	$0.772096\pi$
$224$	12.9759	+	6.28166i	0.866989	+	0.419711i
$225$	12.6047	−	8.13151i	0.840313	−	0.542101i
$226$	−0.142295	−	0.624617i	−0.00946534	−	0.0415489i
$227$	−1.30473	+	4.86933i	−0.0865981	+	0.323189i	−0.995612	−	0.0935772i	$-0.970170\pi$
$227$	−1.30473	+	4.86933i	−0.0865981	+	0.323189i	0.909014	+	0.416766i	$0.136836\pi$
$228$	2.05217	−	13.3033i	0.135908	−	0.881035i
$229$	−6.71866	−	3.87902i	−0.443981	−	0.256333i	0.261304	−	0.965257i	$-0.415848\pi$
$229$	−6.71866	−	3.87902i	−0.443981	−	0.256333i	−0.705285	+	0.708924i	$0.749181\pi$
$230$	−6.72150	−	10.0847i	−0.443203	−	0.664964i
$231$	15.1218	−	2.81995i	0.994939	−	0.185539i
$232$	−5.01563	−	11.5346i	−0.329292	−	0.757285i
$233$	−4.15335	−	4.15335i	−0.272095	−	0.272095i	0.557848	−	0.829943i	$-0.311627\pi$
$233$	−4.15335	−	4.15335i	−0.272095	−	0.272095i	−0.829943	+	0.557848i	$0.811627\pi$
$234$	1.54561	+	22.3251i	0.101040	+	1.45943i
$235$	0.533235	−	0.0546344i	0.0347844	−	0.00356396i
$236$	−12.8401	+	18.7999i	−0.835822	+	1.22377i
$237$	23.6304	−	11.3032i	1.53496	−	0.734222i
$238$	9.75295	−	5.14947i	0.632190	−	0.333791i
$239$	1.28058	−	2.21802i	0.0828335	−	0.143472i	−0.821632	−	0.570018i	$-0.806936\pi$
$239$	1.28058	−	2.21802i	0.0828335	−	0.143472i	0.904466	+	0.426546i	$0.140270\pi$
$240$	−15.3505	+	2.08857i	−0.990871	+	0.134817i
$241$	6.89420	+	11.9411i	0.444094	+	0.769194i	0.997989	−	0.0633929i	$-0.0201921\pi$
$241$	6.89420	+	11.9411i	0.444094	+	0.769194i	−0.553894	+	0.832587i	$0.686859\pi$
$242$	−1.36963	−	0.861381i	−0.0880433	−	0.0553716i
$243$	−5.88572	+	14.4346i	−0.377569	+	0.925981i
$244$	8.00092	+	16.6490i	0.512206	+	1.06584i
$245$	−0.179642	+	1.11531i	−0.0114769	+	0.0712547i
$246$	−11.8244	+	15.9198i	−0.753895	+	1.01501i
$247$	19.7977	−	5.30478i	1.25970	−	0.337535i
$248$	−3.63258	+	4.90933i	−0.230669	+	0.311743i
$249$	−8.94598	+	25.3517i	−0.566929	+	1.60660i
$250$	−7.81381	+	13.7457i	−0.494189	+	0.869355i
$251$			11.4799i			0.724602i	0.932061	+	0.362301i	$0.118009\pi$
$251$			11.4799i			0.724602i	−0.932061	+	0.362301i	$0.881991\pi$
$252$	−7.22714	+	13.4752i	−0.455267	+	0.848857i
$253$	9.44382	+	9.44382i	0.593728	+	0.593728i
$254$	3.90515	−	3.62047i	0.245031	−	0.227169i
$255$	−5.67088	+	10.4069i	−0.355125	+	0.651707i
$256$	15.2736	+	4.76619i	0.954601	+	0.297887i
$257$	−3.79760	−	14.1728i	−0.236888	−	0.884077i	−0.977289	−	0.211912i	$-0.932031\pi$
$257$	−3.79760	−	14.1728i	−0.236888	−	0.884077i	0.740401	−	0.672165i	$-0.234636\pi$
$258$	11.9833	+	4.74525i	0.746049	+	0.295427i
$259$	6.62330	+	11.4719i	0.411552	+	0.712829i
$260$	−12.3313	−	20.1092i	−0.764755	−	1.24712i
$261$	12.4442	−	4.80848i	0.770276	−	0.297638i
$262$	−9.23070	+	14.6772i	−0.570274	+	0.906761i
$263$	1.77189	+	0.474777i	0.109259	+	0.0292760i	0.313034	−	0.949742i	$-0.398654\pi$
$263$	1.77189	+	0.474777i	0.109259	+	0.0292760i	−0.203775	+	0.979018i	$0.565321\pi$
$264$	16.1358	−	5.57627i	0.993088	−	0.343196i
$265$	−0.343907	+	0.767019i	−0.0211261	+	0.0471176i
$266$	13.3808	+	4.13345i	0.820432	+	0.253438i
$267$	−6.24252	−	0.484351i	−0.382036	−	0.0296418i
$268$	1.46415	−	0.275789i	0.0894372	−	0.0168465i
$269$		−	13.4031i		−	0.817201i	−0.912713	−	0.408600i	$-0.866017\pi$
$269$		−	13.4031i		−	0.817201i	0.912713	−	0.408600i	$-0.133983\pi$
$270$	−1.53887	−	16.3595i	−0.0936526	−	0.995605i
$271$		−	19.1919i		−	1.16582i	−0.812536	−	0.582911i	$-0.801914\pi$
$271$		−	19.1919i		−	1.16582i	0.812536	−	0.582911i	$-0.198086\pi$
$272$	9.86050	−	7.25243i	0.597880	−	0.439743i
$273$	−23.2132	−	1.80109i	−1.40493	−	0.109007i
$274$	−3.86120	+	12.4995i	−0.233264	+	0.755123i
$275$	5.47105	−	16.5430i	0.329917	−	0.997579i
$276$	−13.1977	+	1.44088i	−0.794408	+	0.0867307i
$277$	7.21889	+	1.93430i	0.433741	+	0.116221i	0.469082	−	0.883155i	$-0.344585\pi$
$277$	7.21889	+	1.93430i	0.433741	+	0.116221i	−0.0353406	+	0.999375i	$0.511252\pi$
$278$	21.4398	+	13.4838i	1.28588	+	0.808705i
$279$	−5.04305	−	4.06534i	−0.301919	−	0.243386i
$280$	0.182570	−	16.1170i	0.0109106	−	0.963176i
$281$	−6.99536	−	12.1163i	−0.417308	−	0.722799i	0.578360	−	0.815782i	$-0.303693\pi$
$281$	−6.99536	−	12.1163i	−0.417308	−	0.722799i	−0.995668	+	0.0929831i	$0.970360\pi$
$282$	0.216186	−	0.545942i	0.0128737	−	0.0325104i
$283$	0.480944	+	1.79491i	0.0285891	+	0.106696i	0.978746	−	0.205076i	$-0.0657441\pi$
$283$	0.480944	+	1.79491i	0.0285891	+	0.106696i	−0.950157	+	0.311772i	$0.899077\pi$
$284$	0.312737	−	4.12777i	0.0185575	−	0.244938i
$285$	−14.4362	+	4.25248i	−0.855128	+	0.251895i
$286$	17.6734	+	19.0630i	1.04505	+	1.12722i
$287$	−14.5891	−	14.5891i	−0.861170	−	0.861170i
$288$	−5.72209	+	15.9768i	−0.337177	+	0.941441i
$289$			7.63580i			0.449165i
$290$	−9.28431	+	10.5620i	−0.545193	+	0.620224i
$291$	−1.82381	+	5.16844i	−0.106914	+	0.302979i
$292$	−16.5417	−	19.2537i	−0.968029	−	1.12674i
$293$	25.4808	−	6.82756i	1.48860	−	0.398870i	0.579339	−	0.815087i	$-0.303311\pi$
$293$	25.4808	−	6.82756i	1.48860	−	0.398870i	0.909266	+	0.416217i	$0.136644\pi$
$294$	0.993456	+	0.737886i	0.0579396	+	0.0430344i
$295$	25.1296	+	4.04760i	1.46310	+	0.235660i
$296$	9.15221	+	11.5055i	0.531961	+	0.668744i
$297$	5.20045	+	17.3449i	0.301761	+	1.00645i
$298$	2.08434	−	3.31419i	0.120742	−	0.191986i
$299$	−10.1075	−	17.5068i	−0.584534	−	1.01244i
$300$	9.41585	+	14.5376i	0.543625	+	0.839328i
$301$	−6.70478	+	11.6130i	−0.386457	+	0.669363i
$302$	4.96867	+	9.41051i	0.285915	+	0.541514i
$303$	−6.74902	+	3.22828i	−0.387721	+	0.185460i
$304$	15.3657	+	2.34177i	0.881280	+	0.134310i
$305$	13.0387	−	16.0155i	0.746593	−	0.917046i
$306$	7.25250	+	10.7683i	0.414598	+	0.615584i
$307$	−13.9421	−	13.9421i	−0.795717	−	0.795717i	0.186700	−	0.982417i	$-0.440221\pi$
$307$	−13.9421	−	13.9421i	−0.795717	−	0.795717i	−0.982417	+	0.186700i	$0.940221\pi$
$308$	3.28788	+	17.4552i	0.187344	+	0.994601i
$309$	2.32577	−	0.433717i	0.132308	−	0.0246733i
$310$	6.69525	+	1.33983i	0.380264	+	0.0760970i
$311$	−0.701482	−	0.405001i	−0.0397774	−	0.0229655i	0.479979	−	0.877280i	$-0.340644\pi$
$311$	−0.701482	−	0.405001i	−0.0397774	−	0.0229655i	−0.519757	+	0.854314i	$0.673977\pi$
$312$	−25.7755	+	1.83148i	−1.45925	+	0.103687i
$313$	−1.63805	+	6.11329i	−0.0925882	+	0.345544i	−0.996643	−	0.0818732i	$-0.973910\pi$
$313$	−1.63805	+	6.11329i	−0.0925882	+	0.345544i	0.904055	+	0.427417i	$0.140576\pi$
$314$	5.16400	−	1.17642i	0.291421	−	0.0663893i
$315$	17.0720	+	0.901651i	0.961897	+	0.0508023i
$316$	13.1013	+	27.2623i	0.737005	+	1.53362i
$317$	19.5297	+	5.23297i	1.09690	+	0.293913i	0.761501	−	0.648164i	$-0.224463\pi$
$317$	19.5297	+	5.23297i	1.09690	+	0.293913i	0.335397	+	0.942077i	$0.391129\pi$
$318$	0.571927	+	0.721670i	0.0320721	+	0.0404692i
$319$	7.74847	−	13.4207i	0.433831	−	0.751418i
$320$	−2.44383	−	17.7208i	−0.136614	−	0.990624i
$321$	9.91424	−	8.48654i	0.553359	−	0.473672i
$322$	0.522130	−	13.8028i	0.0290972	−	0.769200i
$323$	8.40809	−	8.40809i	0.467838	−	0.467838i
$324$	−16.6800	−	6.76599i	−0.926665	−	0.375888i
$325$	−14.4795	+	22.0430i	−0.803180	+	1.22273i
$326$	−9.20458	−	9.92834i	−0.509795	−	0.549880i
$327$	24.4957	+	1.90060i	1.35462	+	0.105103i
$328$	−18.4073	−	13.6202i	−1.01638	−	0.752052i
$329$	0.529071	+	0.305459i	0.0291686	+	0.0168405i
$330$	−13.3182	−	13.6729i	−0.733142	−	0.752669i
$331$	16.9166	−	9.76680i	0.929821	−	0.536832i	0.0430657	−	0.999072i	$-0.486288\pi$
$331$	16.9166	−	9.76680i	0.929821	−	0.536832i	0.886755	+	0.462240i	$0.152954\pi$
$332$	−29.2924	−	10.2768i	−1.60763	−	0.564013i
$333$	−12.5951	+	9.19350i	−0.690207	+	0.503801i
$334$	1.16202	+	5.10077i	0.0635828	+	0.279102i
$335$	−0.975577	−	1.35018i	−0.0533014	−	0.0737684i
$336$	−15.5749	−	8.31694i	−0.849682	−	0.453726i
$337$	−2.61793	−	9.77024i	−0.142608	−	0.532219i	−0.999850	−	0.0173061i	$-0.994491\pi$
$337$	−2.61793	−	9.77024i	−0.142608	−	0.532219i	0.857243	−	0.514913i	$-0.172176\pi$
$338$	−9.78708	−	18.5365i	−0.532347	−	1.00825i
$339$	0.143834	+	0.771299i	0.00781201	+	0.0418912i
$340$	−12.0287	−	6.52636i	−0.652350	−	0.353942i
$341$	−7.52446			−0.407472
$342$	−3.15685	+	16.1808i	−0.170703	+	0.874960i
$343$	−13.5248	+	13.5248i	−0.730270	+	0.730270i
$344$	−5.45423	+	13.8471i	−0.294073	+	0.746584i
$345$	7.73638	+	12.6676i	0.416513	+	0.681999i
$346$	−31.3328	−	9.67897i	−1.68446	−	0.520345i
$347$	24.2713	−	6.50347i	1.30295	−	0.349125i	0.460386	−	0.887719i	$-0.347711\pi$
$347$	24.2713	−	6.50347i	1.30295	−	0.349125i	0.842565	+	0.538594i	$0.181044\pi$
$348$	5.57842	+	14.3592i	0.299035	+	0.769735i
$349$	15.0315	−	8.67844i	0.804617	−	0.464546i	−0.0404658	−	0.999181i	$-0.512884\pi$
$349$	15.0315	−	8.67844i	0.804617	−	0.464546i	0.845083	+	0.534635i	$0.179551\pi$
$350$	−16.3936	+	7.48264i	−0.876274	+	0.399964i
$351$	−0.808354	−	27.3960i	−0.0431467	−	1.46229i
$352$	6.47271	+	18.6203i	0.344997	+	0.992464i
$353$	7.72886	−	28.8445i	0.411366	−	1.53524i	−0.380640	−	0.924723i	$-0.624296\pi$
$353$	7.72886	−	28.8445i	0.411366	−	1.53524i	0.792006	−	0.610514i	$-0.209037\pi$
$354$	16.6257	−	22.3840i	0.883644	−	1.18970i
$355$	−4.32513	+	1.64729i	−0.229554	+	0.0874289i
$356$	0.546201	−	7.20924i	0.0289486	−	0.382089i
$357$	−12.1853	+	5.82865i	−0.644916	+	0.308485i
$358$	0.535574	−	14.1582i	0.0283060	−	0.748284i
$359$	−26.1394			−1.37959			−0.689794	−	0.724006i	$-0.742299\pi$
$359$	−26.1394			−1.37959			−0.689794	+	0.724006i	$0.742299\pi$
$360$	18.8870	−	1.81120i	0.995433	−	0.0954587i
$361$	−3.90081			−0.205306
$362$	−1.06816	+	28.2373i	−0.0561410	+	1.48412i
$363$	1.63434	+	1.12059i	0.0857807	+	0.0588159i
$364$	2.03108	−	26.8080i	0.106458	−	1.40512i
$365$	−11.6109	+	25.8960i	−0.607744	+	1.35546i
$366$	−8.98364	−	20.7629i	−0.469582	−	1.08530i
$367$	−5.95191	+	22.2128i	−0.310687	+	1.15950i	0.617251	+	0.786766i	$0.288246\pi$
$367$	−5.95191	+	22.2128i	−0.310687	+	1.15950i	−0.927938	+	0.372734i	$0.878420\pi$
$368$	−1.69143	−	15.2363i	−0.0881718	−	0.794249i
$369$	15.2429	−	18.9087i	0.793511	−	0.984348i
$370$	7.28695	−	14.7335i	0.378830	−	0.765956i
$371$	−0.829682	+	0.479017i	−0.0430750	+	0.0248693i
$372$	4.68368	−	5.83172i	0.242838	−	0.302360i
$373$	12.8388	−	3.44016i	0.664770	−	0.178125i	0.0893722	−	0.995998i	$-0.471514\pi$
$373$	12.8388	−	3.44016i	0.664770	−	0.178125i	0.575398	+	0.817874i	$0.304847\pi$
$374$	14.4093	+	4.45114i	0.745085	+	0.230163i
$375$	10.2293	−	16.4427i	0.528239	−	0.849096i
$376$	0.630851	+	0.248486i	0.0325337	+	0.0128147i
$377$	−16.5861	+	16.5861i	−0.854226	+	0.854226i
$378$	9.49823	−	16.1401i	0.488536	−	0.830156i
$379$	12.7657			0.655730			0.327865	−	0.944725i	$-0.393671\pi$
$379$	12.7657			0.655730			0.327865	+	0.944725i	$0.393671\pi$
$380$	−4.94057	−	16.6606i	−0.253446	−	0.854669i
$381$	−4.95471	+	4.24121i	−0.253838	+	0.217284i
$382$	−10.3469	−	19.5966i	−0.529391	−	1.00265i
$383$	9.09327	+	33.9365i	0.464644	+	1.73408i	0.658066	+	0.752960i	$0.271375\pi$
$383$	9.09327	+	33.9365i	0.464644	+	1.73408i	−0.193422	+	0.981116i	$0.561959\pi$
$384$	−18.4604	−	6.57381i	−0.942051	−	0.335469i
$385$	16.0965	−	11.6305i	0.820353	−	0.592747i
$386$	6.77959	+	29.7596i	0.345072	+	1.51472i
$387$	−14.4348	−	6.38856i	−0.733761	−	0.324749i
$388$	−5.97181	−	2.09512i	−0.303173	−	0.106364i
$389$	−15.4675	+	8.93019i	−0.784236	+	0.452779i	−0.837929	−	0.545779i	$-0.816234\pi$
$389$	−15.4675	+	8.93019i	−0.784236	+	0.452779i	0.0536937	+	0.998557i	$0.482901\pi$
$390$	14.1152	+	25.2076i	0.714752	+	1.27644i
$391$	−10.1566	−	5.86389i	−0.513639	−	0.296550i
$392$	−0.849955	+	1.14869i	−0.0429292	+	0.0580175i
$393$	12.0085	−	17.5139i	0.605747	−	0.883459i
$394$	12.8446	+	13.8545i	0.647099	+	0.697981i
$395$	21.3505	−	26.2250i	1.07426	−	1.31952i
$396$	−20.0172	+	6.04129i	−1.00590	+	0.303586i
$397$	22.9050	−	22.9050i	1.14957	−	1.14957i	0.162934	−	0.986637i	$-0.447904\pi$
$397$	22.9050	−	22.9050i	1.14957	−	1.14957i	0.986637	−	0.162934i	$-0.0520959\pi$
$398$	0.110166	−	2.91231i	0.00552215	−	0.145981i
$399$	−16.1747	−	5.70764i	−0.809748	−	0.285739i
$400$	−16.7668	+	10.9029i	−0.838341	+	0.545147i
$401$	−15.2608	+	26.4324i	−0.762087	+	1.31997i	0.179686	+	0.983724i	$0.442492\pi$
$401$	−15.2608	+	26.4324i	−0.762087	+	1.31997i	−0.941773	+	0.336249i	$0.890841\pi$
$402$	−1.80518	+	0.266471i	−0.0900344	+	0.0132903i
$403$	11.0010	+	2.94770i	0.547998	+	0.146836i
$404$	−3.74183	−	7.78632i	−0.186163	−	0.387384i
$405$	1.08954	+	20.0951i	0.0541395	+	0.998533i
$406$	−15.6270	+	3.56001i	−0.775553	+	0.176680i
$407$	−4.68814	+	17.4964i	−0.232383	+	0.867263i
$408$	−12.4190	+	8.39701i	−0.614831	+	0.415714i
$409$	−14.2191	−	8.20942i	−0.703091	−	0.405930i	0.105407	−	0.994429i	$-0.466386\pi$
$409$	−14.2191	−	8.20942i	−0.703091	−	0.405930i	−0.808498	+	0.588499i	$0.799719\pi$
$410$	−5.02363	+	25.1036i	−0.248099	+	1.23978i
$411$	5.33171	−	15.1094i	0.262994	−	0.745290i
$412$	0.505684	+	2.68465i	0.0249133	+	0.132263i
$413$	20.5130	+	20.5130i	1.00938	+	1.00938i
$414$	16.2210	−	1.12302i	0.797220	−	0.0551932i
$415$	3.53750	+	34.5262i	0.173649	+	1.69482i
$416$	−2.16881	−	29.7591i	−0.106335	−	1.45906i
$417$	−25.5835	−	17.5414i	−1.25283	−	0.859008i
$418$	8.94137	+	16.9347i	0.437337	+	0.828303i
$419$	−5.01036	+	8.67820i	−0.244772	+	0.423958i	−0.962068	−	0.272811i	$-0.912047\pi$
$419$	−5.01036	+	8.67820i	−0.244772	+	0.423958i	0.717295	+	0.696769i	$0.245380\pi$
$420$	−1.00537	+	19.7149i	−0.0490570	+	0.961988i
$421$	−3.68335	−	6.37975i	−0.179515	−	0.310930i	0.762199	−	0.647342i	$-0.224120\pi$
$421$	−3.68335	−	6.37975i	−0.179515	−	0.310930i	−0.941715	+	0.336413i	$0.890786\pi$
$422$	−1.73403	+	2.75719i	−0.0844115	+	0.134218i
$423$	−0.291053	+	0.657626i	−0.0141515	+	0.0319749i
$424$	−0.832113	+	0.661915i	−0.0404110	+	0.0321455i
$425$	−0.880745	+	15.2751i	−0.0427224	+	0.740952i
$426$	−0.582987	+	5.03632i	−0.0282458	+	0.244010i
$427$	22.7354	−	6.09194i	1.10024	−	0.294810i
$428$	9.82017	+	11.4302i	0.474676	+	0.552499i
$429$	−20.7035	−	24.1865i	−0.999575	−	1.16773i
$430$	16.6048	−	1.06904i	0.800755	−	0.0515535i
$431$		−	16.4473i		−	0.792237i	−0.918199	−	0.396119i	$-0.870357\pi$
$431$		−	16.4473i		−	0.792237i	0.918199	−	0.396119i	$-0.129643\pi$
$432$	7.77774	−	19.2745i	0.374206	−	0.927345i
$433$	−3.78112	−	3.78112i	−0.181709	−	0.181709i	0.610391	−	0.792100i	$-0.291012\pi$
$433$	−3.78112	−	3.78112i	−0.181709	−	0.181709i	−0.792100	+	0.610391i	$0.791012\pi$
$434$	5.29076	+	5.70677i	0.253964	+	0.273934i
$435$	11.8744	−	12.4752i	0.569335	−	0.598140i
$436$	−2.14330	+	28.2892i	−0.102646	+	1.35481i
$437$	−3.85437	−	14.3847i	−0.184380	−	0.688114i
$438$	19.3093	+	24.3649i	0.922635	+	1.16420i
$439$	−18.4104	−	31.8878i	−0.878683	−	1.52192i	−0.852787	−	0.522258i	$-0.825090\pi$
$439$	−18.4104	−	31.8878i	−0.878683	−	1.52192i	−0.0258954	−	0.999665i	$-0.508244\pi$
$440$	15.7602	−	15.4071i	0.751338	−	0.734506i
$441$	−1.17998	−	0.951212i	−0.0561893	−	0.0452958i
$442$	−19.3230	−	12.1525i	−0.919102	−	0.578036i
$443$	−11.6926	−	3.13302i	−0.555532	−	0.148854i	−0.0298790	−	0.999554i	$-0.509512\pi$
$443$	−11.6926	−	3.13302i	−0.555532	−	0.148854i	−0.525653	+	0.850699i	$0.676179\pi$
$444$	−10.6421	−	14.5243i	−0.505052	−	0.689292i
$445$	−7.55394	+	2.87702i	−0.358091	+	0.136384i
$446$	−6.96695	+	22.5535i	−0.329895	+	1.06794i
$447$	−2.71157	+	3.95472i	−0.128253	+	0.187052i
$448$	9.57093	−	18.0018i	0.452184	−	0.850504i
$449$			1.04828i			0.0494715i	0.999694	+	0.0247357i	$0.00787443\pi$
$449$			1.04828i			0.0494715i	−0.999694	+	0.0247357i	$0.992126\pi$
$450$	−10.8177	−	18.2477i	−0.509949	−	0.860205i
$451$		−	28.2127i		−	1.32848i
$452$	−0.890317	+	0.167701i	−0.0418770	+	0.00788800i
$453$	−5.62401	−	11.7575i	−0.264239	−	0.552415i
$454$	6.81160	+	2.10416i	0.319684	+	0.0987530i
$455$	−28.0898	+	10.6984i	−1.31687	+	0.501548i
$456$	−18.6906	−	3.61131i	−0.875268	−	0.169115i
$457$	−13.1438	−	3.52188i	−0.614843	−	0.164747i	−0.0620609	−	0.998072i	$-0.519767\pi$
$457$	−13.1438	−	3.52188i	−0.614843	−	0.164747i	−0.552782	+	0.833326i	$0.686434\pi$
$458$	−5.84101	+	9.28746i	−0.272932	+	0.433974i
$459$	−8.35305	−	13.5300i	−0.389887	−	0.631525i
$460$	−14.6110	+	8.95973i	−0.681242	+	0.417750i
$461$	5.72422	+	9.91464i	0.266604	+	0.461771i	0.967983	−	0.251018i	$-0.0807652\pi$
$461$	5.72422	+	9.91464i	0.266604	+	0.461771i	−0.701379	+	0.712789i	$0.747432\pi$
$462$	−3.17678	−	21.5209i	−0.147797	−	1.00124i
$463$	−1.21606	−	4.53841i	−0.0565153	−	0.210918i	0.931894	−	0.362731i	$-0.118156\pi$
$463$	−1.21606	−	4.53841i	−0.0565153	−	0.210918i	−0.988409	+	0.151813i	$0.951489\pi$
$464$	−16.5689	+	6.47148i	−0.769191	+	0.300431i
$465$	−8.12853	−	1.96449i	−0.376952	−	0.0911009i
$466$	−6.09155	+	5.64749i	−0.282186	+	0.261615i
$467$	25.5411	+	25.5411i	1.18190	+	1.18190i	0.979251	+	0.202651i	$0.0649557\pi$
$467$	25.5411	+	25.5411i	1.18190	+	1.18190i	0.202651	+	0.979251i	$0.435044\pi$
$468$	31.6325	−	0.990798i	1.46221	−	0.0457997i
$469$		−	1.89849i		−	0.0876643i
$470$	−0.0487036	−	0.756489i	−0.00224653	−	0.0348943i
$471$	−6.37669	+	1.18915i	−0.293822	+	0.0547929i
$472$	25.8816	+	19.1507i	1.19130	+	0.881484i
$473$	−17.7116	+	4.74581i	−0.814381	+	0.218213i
$474$	−14.7105	−	33.9987i	−0.675674	−	1.56161i
$475$	−14.5063	+	12.9247i	−0.665595	+	0.593024i
$476$	−6.75587	−	14.0582i	−0.309655	−	0.644355i
$477$	−0.664902	−	0.910915i	−0.0304438	−	0.0417080i
$478$	−3.06606	−	1.92828i	−0.140238	−	0.0881977i
$479$	6.06234	+	10.5003i	0.276995	+	0.479770i	0.970637	−	0.240551i	$-0.0773280\pi$
$479$	6.06234	+	10.5003i	0.276995	+	0.479770i	−0.693641	+	0.720321i	$0.743995\pi$
$480$	2.13096	+	21.8050i	0.0972646	+	0.995259i
$481$	13.7084	−	23.7436i	0.625049	−	1.08262i
$482$	17.2438	−	9.10455i	0.785431	−	0.414701i
$483$	−1.30864	+	16.8663i	−0.0595452	+	0.767444i
$484$	−1.29052	+	1.88952i	−0.0586602	+	0.0858873i
$485$	0.721187	+	7.03882i	0.0327474	+	0.319616i
$486$	20.0844	+	9.08936i	0.911047	+	0.412302i
$487$	−12.5621	−	12.5621i	−0.569243	−	0.569243i	0.362673	−	0.931916i	$-0.381864\pi$
$487$	−12.5621	−	12.5621i	−0.569243	−	0.569243i	−0.931916	+	0.362673i	$0.881864\pi$
$488$	23.9561	−	10.4169i	1.08444	−	0.471551i
$489$	10.7827	+	12.5967i	0.487612	+	0.569643i
$490$	1.56656	+	0.313493i	0.0707699	+	0.0141622i
$491$	0.109289	+	0.0630982i	0.00493215	+	0.00284758i	0.502464	−	0.864598i	$-0.332427\pi$
$491$	0.109289	+	0.0630982i	0.00493215	+	0.00284758i	−0.497532	+	0.867446i	$0.665760\pi$
$492$	21.8658	+	17.5613i	0.985786	+	0.791724i
$493$	−3.52205	+	13.1445i	−0.158625	+	0.591997i
$494$	−6.43838	−	28.2618i	−0.289677	−	1.27156i
$495$	15.6352	+	17.3788i	0.702751	+	0.781121i
$496$	6.74369	+	5.39602i	0.302800	+	0.242289i
$497$	−5.09512	−	1.36523i	−0.228547	−	0.0612391i
$498$	35.3489	+	13.9978i	1.58402	+	0.627254i
$499$	−20.2868	+	35.1377i	−0.908161	+	1.57298i	−0.0915430	+	0.995801i	$0.529180\pi$
$499$	−20.2868	+	35.1377i	−0.908161	+	1.57298i	−0.816618	+	0.577179i	$0.804153\pi$
$500$	19.0078	+	11.7773i	0.850053	+	0.526698i
$501$	−1.17459	−	6.29862i	−0.0524766	−	0.281401i
$502$	16.2234	+	0.613695i	0.724084	+	0.0273905i
$503$	−6.97397	+	6.97397i	−0.310954	+	0.310954i	−0.845279	−	0.534325i	$-0.820566\pi$
$503$	−6.97397	+	6.97397i	−0.310954	+	0.310954i	0.534325	+	0.845279i	$0.320566\pi$
$504$	18.6568	+	10.9338i	0.831041	+	0.487029i
$505$	−6.09787	+	7.49007i	−0.271352	+	0.333304i
$506$	13.8509	−	12.8412i	0.615747	−	0.570860i
$507$	11.0779	+	23.1594i	0.491989	+	1.02855i
$508$	−4.90770	−	5.71231i	−0.217744	−	0.253443i
$509$	−27.6387	−	15.9572i	−1.22507	−	0.707292i	−0.259072	−	0.965858i	$-0.583417\pi$
$509$	−27.6387	−	15.9572i	−1.22507	−	0.707292i	−0.965994	+	0.258566i	$0.916750\pi$
$510$	14.4039	+	8.57045i	0.637817	+	0.379506i
$511$	−28.0116	+	16.1725i	−1.23916	+	0.715430i
$512$	7.55210	−	21.3299i	0.333759	−	0.942658i
$513$	4.64834	−	19.6487i	0.205229	−	0.867511i
$514$	−20.2321	+	4.60912i	−0.892400	+	0.203300i
$515$	2.47568	−	1.78881i	0.109092	−	0.0788243i
$516$	7.34662	−	16.6812i	0.323417	−	0.734349i
$517$	0.216212	+	0.806914i	0.00950899	+	0.0354880i
$518$	16.5662	−	8.74680i	0.727876	−	0.384312i
$519$	37.8750	+	13.3651i	1.66253	+	0.586664i
$520$	−29.0776	+	16.3516i	−1.27514	+	0.717067i
$521$	34.5815			1.51504			0.757521	−	0.652811i	$-0.226410\pi$
$521$	34.5815			1.51504			0.757521	+	0.652811i	$0.226410\pi$
$522$	−6.13012	−	17.8432i	−0.268308	−	0.780977i
$523$	−31.6445	+	31.6445i	−1.38372	+	1.38372i	−0.545801	+	0.837915i	$0.683775\pi$
$523$	−31.6445	+	31.6445i	−1.38372	+	1.38372i	−0.837915	+	0.545801i	$0.816225\pi$
$524$	20.2484	+	13.8295i	0.884556	+	0.604143i
$525$	20.4252	−	8.36176i	0.891430	−	0.364937i
$526$	0.765678	−	2.47866i	0.0333851	−	0.108075i
$527$	6.38222	−	1.71011i	0.278014	−	0.0744936i
$528$	−7.01780	−	23.1012i	−0.305411	−	1.00535i
$529$	7.19846	−	4.15603i	0.312976	−	0.180697i
$530$	1.06557	+	0.527014i	0.0462853	+	0.0228920i
$531$	−21.4322	+	26.5866i	−0.930078	+	1.15376i
$532$	6.55672	−	18.6889i	0.284270	−	0.810265i
$533$	−11.0523	+	41.2478i	−0.478729	+	1.78664i
$534$	−1.01820	+	8.79605i	−0.0440619	+	0.380642i
$535$	6.89297	−	15.3734i	0.298009	−	0.664652i
$536$	−0.311475	−	2.08389i	−0.0134537	−	0.0900101i
$537$	−1.34234	+	17.3006i	−0.0579261	+	0.746575i
$538$	−18.9413	−	0.716508i	−0.816617	−	0.0308908i
$539$	−1.76058			−0.0758335
$540$	−23.2015	+	1.30018i	−0.998434	+	0.0559510i
$541$	35.6814			1.53407			0.767033	−	0.641608i	$-0.221732\pi$
$541$	35.6814			1.53407			0.767033	+	0.641608i	$0.221732\pi$
$542$	−27.1220	−	1.02597i	−1.16499	−	0.0440690i
$543$	2.67717	−	34.5045i	0.114888	−	1.48073i
$544$	−9.72203	−	14.3226i	−0.416829	−	0.614076i
$545$	29.6418	−	11.2895i	1.26972	−	0.483588i
$546$	−3.78624	+	32.7086i	−0.162036	+	1.39980i
$547$	4.27345	−	15.9487i	0.182720	−	0.681919i	−0.812388	−	0.583118i	$-0.801833\pi$
$547$	4.27345	−	15.9487i	0.182720	−	0.681919i	0.995107	−	0.0988010i	$-0.0315007\pi$
$548$	17.4579	+	6.12487i	0.745766	+	0.261641i
$549$	9.98668	+	25.8452i	0.426221	+	1.10305i
$550$	−23.0861	−	8.61606i	−0.984394	−	0.367390i
$551$	−14.9648	+	8.63994i	−0.637522	+	0.368074i
$552$	1.33073	+	18.7280i	0.0566395	+	0.797119i
$553$	37.2286	−	9.97538i	1.58312	−	0.424197i
$554$	3.11946	−	10.0984i	0.132533	−	0.429038i
$555$	−9.63247	+	17.6770i	−0.408875	+	0.750348i
$556$	20.2015	−	29.5780i	0.856734	−	1.25439i
$557$	1.96120	−	1.96120i	0.0830989	−	0.0830989i	−0.664336	−	0.747434i	$-0.731285\pi$
$557$	1.96120	−	1.96120i	0.0830989	−	0.0830989i	0.747434	+	0.664336i	$0.231285\pi$
$558$	−6.01475	+	6.90952i	−0.254625	+	0.292503i
$559$	27.7541			1.17387
$560$	−22.7669	−	1.11960i	−0.962075	−	0.0473116i
$561$	−17.4179	−	6.14632i	−0.735383	−	0.259498i
$562$	−17.4968	+	9.23814i	−0.738057	+	0.389687i
$563$	−3.43039	−	12.8024i	−0.144574	−	0.539557i	−0.999774	−	0.0212589i	$-0.993233\pi$
$563$	−3.43039	−	12.8024i	−0.144574	−	0.539557i	0.855200	−	0.518298i	$-0.173434\pi$
$564$	−0.759969	−	0.334700i	−0.0320005	−	0.0140934i
$565$	0.593226	+	0.821016i	0.0249572	+	0.0345404i
$566$	2.56228	−	0.583718i	0.107701	−	0.0245355i
$567$	−12.4068	+	19.2911i	−0.521038	+	0.810152i
$568$	−5.81665	−	0.662624i	−0.244061	−	0.0278031i
$569$	9.89594	−	5.71342i	0.414859	−	0.239519i	−0.278016	−	0.960576i	$-0.589677\pi$
$569$	9.89594	−	5.71342i	0.414859	−	0.239519i	0.692876	+	0.721057i	$0.256344\pi$
$570$	5.23787	+	20.6286i	0.219390	+	0.864038i
$571$	32.2228	+	18.6038i	1.34848	+	0.778546i	0.988034	−	0.154234i	$-0.0492908\pi$
$571$	32.2228	+	18.6038i	1.34848	+	0.778546i	0.360447	+	0.932780i	$0.382624\pi$
$572$	27.8847	−	23.9570i	1.16592	−	1.00169i
$573$	11.7115	+	24.4840i	0.489257	+	1.02284i
$574$	−21.3973	+	19.8375i	−0.893107	+	0.828001i
$575$	16.0161	+	10.5206i	0.667918	+	0.438739i
$576$	22.2725	+	8.94056i	0.928023	+	0.372523i
$577$	−8.63696	+	8.63696i	−0.359561	+	0.359561i	−0.863651	−	0.504090i	$-0.831828\pi$
$577$	−8.63696	+	8.63696i	−0.359561	+	0.359561i	0.504090	+	0.863651i	$0.331828\pi$
$578$	10.7909	+	0.408198i	0.448844	+	0.0169788i
$579$	−6.85292	−	36.7482i	−0.284798	−	1.52720i
$580$	14.4300	+	13.6852i	0.599172	+	0.568249i
$581$	−19.7780	+	34.2566i	−0.820532	+	1.42120i
$582$	7.20655	+	2.85371i	0.298721	+	0.118290i
$583$	−1.26539	−	0.339061i	−0.0524072	−	0.0140425i
$584$	−28.0937	+	22.3475i	−1.16252	+	0.924745i
$585$	−16.0510	−	31.5335i	−0.663627	−	1.30375i
$586$	−8.28656	−	36.3745i	−0.342315	−	1.50262i
$587$	2.05297	−	7.66180i	0.0847352	−	0.316236i	−0.910529	−	0.413446i	$-0.864325\pi$
$587$	2.05297	−	7.66180i	0.0847352	−	0.316236i	0.995264	+	0.0972097i	$0.0309917\pi$
$588$	1.09589	−	1.36451i	0.0451938	−	0.0562714i
$589$	7.26609	+	4.19508i	0.299394	+	0.172855i
$590$	7.06347	−	35.2969i	0.290798	−	1.45315i
$591$	−15.0468	−	17.5781i	−0.618942	−	0.723067i
$592$	16.7489	−	12.3189i	0.688374	−	0.506302i
$593$	−17.4824	−	17.4824i	−0.717918	−	0.717918i	0.250261	−	0.968178i	$-0.419484\pi$
$593$	−17.4824	−	17.4824i	−0.717918	−	0.717918i	−0.968178	+	0.250261i	$0.919484\pi$
$594$	24.7899	−	6.42206i	1.01714	−	0.263500i
$595$	−11.0097	+	13.5233i	−0.451353	+	0.554401i
$596$	−4.57219	−	3.12276i	−0.187284	−	0.127913i
$597$	−0.276116	+	3.55869i	−0.0113007	+	0.145648i
$598$	−25.2809	+	13.3481i	−1.03381	+	0.545845i
$599$	−15.1365	+	26.2172i	−0.618461	+	1.07121i	0.371305	+	0.928511i	$0.378910\pi$
$599$	−15.1365	+	26.2172i	−0.618461	+	1.07121i	−0.989767	+	0.142696i	$0.954423\pi$
$600$	21.0479	−	12.5294i	0.859278	−	0.511509i
$601$	−1.15030	−	1.99238i	−0.0469219	−	0.0812710i	0.841611	−	0.540085i	$-0.181608\pi$
$601$	−1.15030	−	1.99238i	−0.0469219	−	0.0812710i	−0.888532	+	0.458814i	$0.848275\pi$
$602$	16.0531	+	10.0960i	0.654277	+	0.411483i
$603$	2.22208	−	0.238521i	0.0904902	−	0.00971331i
$604$	13.5646	−	6.51866i	0.551935	−	0.265241i
$605$	2.52570	+	0.406812i	0.102684	+	0.0165393i
$606$	4.20143	+	9.71031i	0.170671	+	0.394455i
$607$	−42.3071	+	11.3362i	−1.71719	+	0.460120i	−0.977170	−	0.212461i	$-0.931852\pi$
$607$	−42.3071	+	11.3362i	−1.71719	+	0.460120i	−0.740023	+	0.672581i	$0.765185\pi$
$608$	4.13082	−	21.5896i	0.167527	−	0.875574i
$609$	19.2967	−	3.59851i	0.781943	−	0.145819i
$610$	−21.9362	−	19.2825i	−0.888169	−	0.780724i
$611$		−	1.26443i		−	0.0511535i
$612$	15.6055	−	9.67360i	0.630816	−	0.391032i
$613$	5.01756	+	5.01756i	0.202657	+	0.202657i	0.801138	−	0.598480i	$-0.204228\pi$
$613$	5.01756	+	5.01756i	0.202657	+	0.202657i	−0.598480	+	0.801138i	$0.704228\pi$
$614$	−20.4483	+	18.9577i	−0.825227	+	0.765070i
$615$	7.36578	−	30.4776i	0.297017	−	1.22898i
$616$	24.8435	−	3.71331i	1.00097	−	0.149614i
$617$	1.85628	+	6.92773i	0.0747310	+	0.278900i	0.993172	−	0.116658i	$-0.0372181\pi$
$617$	1.85628	+	6.92773i	0.0747310	+	0.278900i	−0.918441	+	0.395558i	$0.870551\pi$
$618$	−0.488598	−	3.30997i	−0.0196543	−	0.133146i
$619$	6.11352	+	10.5889i	0.245723	+	0.425605i	0.962335	−	0.271868i	$-0.0876413\pi$
$619$	6.11352	+	10.5889i	0.245723	+	0.425605i	−0.716612	+	0.697473i	$0.754308\pi$
$620$	2.25136	−	9.39012i	0.0904169	−	0.377116i
$621$	−19.9055	+	0.587337i	−0.798781	+	0.0235690i
$622$	−0.609848	+	0.969686i	−0.0244527	+	0.0388809i
$623$	−8.89874	−	2.38441i	−0.356521	−	0.0955294i
$624$	1.21034	+	36.5239i	0.0484524	+	1.46213i
$625$	2.87339	−	24.8343i	0.114936	−	0.993373i
$626$	8.55176	+	2.64171i	0.341797	+	0.105584i
$627$	−10.1207	−	21.1582i	−0.404181	−	0.844977i
$628$	−1.38646	−	7.36066i	−0.0553259	−	0.293723i
$629$		−	15.9059i		−	0.634208i
$630$	2.18686	−	24.0780i	0.0871264	−	0.959289i
$631$		−	8.53598i		−	0.339812i	−0.985460	−	0.169906i	$-0.945654\pi$
$631$		−	8.53598i		−	0.339812i	0.985460	−	0.169906i	$-0.0543464\pi$
$632$	39.2275	−	17.0574i	1.56039	−	0.678506i
$633$	2.25585	−	3.29008i	0.0896621	−	0.130769i
$634$	8.43928	−	27.3197i	0.335167	−	1.08500i
$635$	−3.44481	+	7.68299i	−0.136703	+	0.304890i
$636$	1.05044	−	0.769670i	0.0416527	−	0.0305194i
$637$	2.57402	+	0.689706i	0.101986	+	0.0273272i
$638$	−18.5520	−	11.6676i	−0.734481	−	0.461925i
$639$	0.957796	−	6.13508i	0.0378898	−	0.242700i
$640$	−25.1738	+	2.50630i	−0.995080	+	0.0990701i
$641$	5.32828	+	9.22886i	0.210454	+	0.364518i	0.951857	−	0.306543i	$-0.0991723\pi$
$641$	5.32828	+	9.22886i	0.210454	+	0.364518i	−0.741402	+	0.671061i	$0.765839\pi$
$642$	−11.4632	−	14.4645i	−0.452416	−	0.570869i
$643$	0.0850425	+	0.317383i	0.00335375	+	0.0125164i	0.967582	−	0.252555i	$-0.0812710\pi$
$643$	0.0850425	+	0.317383i	0.00335375	+	0.0125164i	−0.964229	+	0.265072i	$0.914604\pi$
$644$	−19.4783	−	1.47575i	−0.767551	−	0.0581528i
$645$	−20.3726	+	0.502658i	−0.802169	+	0.0197921i
$646$	−11.4328	−	12.3318i	−0.449819	−	0.485189i
$647$	1.08970	+	1.08970i	0.0428405	+	0.0428405i	0.728203	−	0.685362i	$-0.240356\pi$
$647$	1.08970	+	1.08970i	0.0428405	+	0.0428405i	−0.685362	+	0.728203i	$0.740356\pi$
$648$	−10.4534	+	23.2105i	−0.410648	+	0.911794i
$649$			39.6684i			1.55712i
$650$	30.3772	+	21.6409i	1.19149	+	0.848826i
$651$	−6.19787	−	7.24054i	−0.242914	−	0.283779i
$652$	−14.5228	+	12.4772i	−0.568758	+	0.488644i
$653$	−22.1285	+	5.92931i	−0.865954	+	0.232032i	−0.664337	−	0.747433i	$-0.731286\pi$
$653$	−22.1285	+	5.92931i	−0.865954	+	0.232032i	−0.201617	+	0.979465i	$0.564620\pi$
$654$	3.99544	−	34.5158i	0.156234	−	1.34968i
$655$	4.35947	−	27.0659i	0.170338	−	1.05755i
$656$	−20.2322	+	25.2852i	−0.789934	+	0.987221i
$657$	−22.4483	−	30.7542i	−0.875792	−	1.19983i
$658$	0.459959	−	0.731356i	0.0179311	−	0.0285112i
$659$	−6.24819	−	10.8222i	−0.243395	−	0.421572i	0.718284	−	0.695750i	$-0.244928\pi$
$659$	−6.24819	−	10.8222i	−0.243395	−	0.421572i	−0.961679	+	0.274177i	$0.911594\pi$
$660$	−20.0346	+	18.0904i	−0.779844	+	0.704167i
$661$	−2.84081	+	4.92043i	−0.110495	+	0.191382i	−0.915970	−	0.401247i	$-0.868577\pi$
$661$	−2.84081	+	4.92043i	−0.110495	+	0.191382i	0.805475	+	0.592630i	$0.201910\pi$
$662$	−12.8981	−	24.4287i	−0.501300	−	0.949449i
$663$	23.0576	+	15.8095i	0.895483	+	0.613991i
$664$	−16.0891	+	40.8467i	−0.624379	+	1.58516i
$665$	−22.0281	+	2.25696i	−0.854212	+	0.0875213i
$666$	12.3190	+	18.2909i	0.477350	+	0.708758i
$667$	12.0512	+	12.0512i	0.466623	+	0.466623i
$668$	7.27054	−	1.36949i	0.281306	−	0.0529871i
$669$	9.62026	−	27.2625i	0.371941	−	1.05403i
$670$	−1.96024	+	1.30651i	−0.0757306	+	0.0504748i
$671$	27.8734	+	16.0927i	1.07604	+	0.621252i
$672$	−12.5861	+	21.5659i	−0.485521	+	0.831924i
$673$	7.75138	−	28.9286i	0.298794	−	1.11511i	−0.639363	−	0.768905i	$-0.720802\pi$
$673$	7.75138	−	28.9286i	0.298794	−	1.11511i	0.938157	−	0.346209i	$-0.112531\pi$
$674$	−13.9473	+	3.17736i	−0.537229	+	0.122387i
$675$	12.3531	+	22.8561i	0.475473	+	0.879730i
$676$	−26.7190	+	12.8402i	−1.02765	+	0.493854i
$677$	2.56951	+	0.688499i	0.0987544	+	0.0264612i	0.307858	−	0.951432i	$-0.400388\pi$
$677$	2.56951	+	0.688499i	0.0987544	+	0.0264612i	−0.209103	+	0.977894i	$0.567055\pi$
$678$	1.09769	−	0.162035i	0.0421566	−	0.00622290i
$679$	−4.03213	+	6.98386i	−0.154739	+	0.268016i
$680$	−9.86611	+	16.6502i	−0.378348	+	0.638505i
$681$	−8.23384	−	2.90551i	−0.315521	−	0.111339i
$682$	−0.402246	+	10.6336i	−0.0154028	+	0.407181i
$683$	31.3443	−	31.3443i	1.19936	−	1.19936i	0.224999	−	0.974359i	$-0.427762\pi$
$683$	31.3443	−	31.3443i	1.19936	−	1.19936i	0.974359	−	0.224999i	$-0.0722379\pi$
$684$	22.6981	+	5.32627i	0.867882	+	0.203655i
$685$	−2.10831	−	20.5772i	−0.0805544	−	0.786215i
$686$	18.3903	+	19.8363i	0.702143	+	0.757353i
$687$	7.59873	−	11.0825i	0.289909	−	0.422822i
$688$	19.2771	+	8.44818i	0.734934	+	0.322084i
$689$	1.71721	+	0.991433i	0.0654206	+	0.0377706i
$690$	18.3154	−	10.2559i	0.697256	−	0.390435i
$691$	−1.44150	+	0.832251i	−0.0548373	+	0.0316603i	−0.527168	−	0.849761i	$-0.676746\pi$
$691$	−1.44150	+	0.832251i	−0.0548373	+	0.0316603i	0.472331	+	0.881421i	$0.343413\pi$
$692$	−15.3534	+	43.7622i	−0.583647	+	1.66359i
$693$	2.84357	+	26.4910i	0.108018	+	1.00631i
$694$	−7.89322	−	34.6479i	−0.299623	−	1.31522i
$695$	−39.5366	−	6.36812i	−1.49971	−	0.241557i
$696$	20.5907	−	7.11582i	0.780488	−	0.269724i
$697$	6.41200	+	23.9299i	0.242872	+	0.906410i
$698$	−11.4608	−	21.7065i	−0.433799	−	0.821603i
$699$	7.72874	−	6.61576i	0.292328	−	0.250231i
$700$	9.69811	+	23.5675i	0.366554	+	0.890767i
$701$	−6.95642			−0.262740			−0.131370	−	0.991333i	$-0.541938\pi$
$701$	−6.95642			−0.262740			−0.131370	+	0.991333i	$0.541938\pi$
$702$	−38.7594	−	0.322180i	−1.46288	−	0.0121599i
$703$	14.2818	−	14.2818i	0.538649	−	0.538649i
$704$	26.6603	−	8.15185i	1.00480	−	0.307234i
$705$	0.0229003	+	0.928142i	0.000862476	+	0.0349559i
$706$	−40.3499	−	12.4644i	−1.51859	−	0.469105i
$707$	−10.6328	+	2.84905i	−0.399888	+	0.107150i
$708$	−30.7444	−	24.6920i	−1.15545	−	0.927984i
$709$	−41.5369	+	23.9814i	−1.55995	+	0.900639i	−0.562693	+	0.826666i	$0.690235\pi$
$709$	−41.5369	+	23.9814i	−1.55995	+	0.900639i	−0.997260	+	0.0739729i	$0.976432\pi$
$710$	2.09673	+	6.20035i	0.0786891	+	0.232695i
$711$	16.3529	+	42.3208i	0.613283	+	1.58715i
$712$	−10.1589	−	1.15729i	−0.380722	−	0.0433712i
$713$	2.14175	−	7.99314i	0.0802093	−	0.299345i
$714$	7.58566	+	17.5319i	0.283886	+	0.656116i
$715$	−37.5046	−	16.8159i	−1.40259	−	0.628878i
$716$	−19.9798	−	1.51375i	−0.746679	−	0.0565715i
$717$	3.65864	+	2.50856i	0.136634	+	0.0936838i
$718$	−1.39737	+	36.9403i	−0.0521495	+	1.37860i
$719$	27.9555			1.04257			0.521283	−	0.853384i	$-0.325454\pi$
$719$	27.9555			1.04257			0.521283	+	0.853384i	$0.325454\pi$
$720$	−1.54993	−	26.7880i	−0.0577623	−	0.998330i
$721$	3.48106			0.129641
$722$	−0.208531	+	5.51263i	−0.00776072	+	0.205159i
$723$	−21.5443	+	10.3054i	−0.801243	+	0.383261i
$724$	39.8479	+	3.01904i	1.48094	+	0.112202i
$725$	6.98155	−	21.1103i	0.259288	−	0.784017i
$726$	1.67100	−	2.24975i	0.0620164	−	0.0834961i
$727$	8.62843	−	32.2018i	0.320011	−	1.19430i	−0.599222	−	0.800583i	$-0.704523\pi$
$727$	8.62843	−	32.2018i	0.320011	−	1.19430i	0.919233	−	0.393714i	$-0.128810\pi$
$728$	−37.7766	−	4.30345i	−1.40009	−	0.159496i
$729$	−24.1380	−	12.0978i	−0.893999	−	0.448068i
$730$	35.9755	+	17.7930i	1.33151	+	0.658547i
$731$	13.9443	−	8.05077i	0.515750	−	0.297768i
$732$	−29.8225	+	11.5858i	−1.10227	+	0.428222i
$733$	1.63983	−	0.439391i	0.0605685	−	0.0162293i	−0.228408	−	0.973566i	$-0.573352\pi$
$733$	1.63983	−	0.439391i	0.0605685	−	0.0162293i	0.288976	+	0.957336i	$0.406685\pi$
$734$	31.0731	+	9.59872i	1.14693	+	0.354295i
$735$	−1.90192	−	0.459652i	−0.0701534	−	0.0169545i
$736$	−21.6225	+	1.57582i	−0.797014	+	0.0580856i
$737$	1.83567	−	1.83567i	0.0676177	−	0.0676177i
$738$	−25.9070	−	22.5521i	−0.953650	−	0.830153i
$739$	48.7588			1.79362			0.896811	−	0.442414i	$-0.145878\pi$
$739$	48.7588			1.79362			0.896811	+	0.442414i	$0.145878\pi$
$740$	−20.4318	−	11.0856i	−0.751088	−	0.407513i
$741$	6.50802	+	34.8987i	0.239078	+	1.28204i
$742$	0.632595	+	1.19812i	0.0232233	+	0.0439843i
$743$	−5.51322	−	20.5756i	−0.202260	−	0.754846i	−0.990267	−	0.139179i	$-0.955554\pi$
$743$	−5.51322	−	20.5756i	−0.202260	−	0.754846i	0.788007	−	0.615667i	$-0.211113\pi$
$744$	−7.99101	−	6.93074i	−0.292965	−	0.254093i
$745$	−0.984389	+	6.11161i	−0.0360652	+	0.223912i
$746$	−4.17530	−	18.3278i	−0.152868	−	0.671028i
$747$	−42.5803	−	18.8452i	−1.55793	−	0.689511i
$748$	7.06065	−	20.1253i	0.258163	−	0.735852i
$749$	16.6294	−	9.60100i	0.607626	−	0.350813i
$750$	−22.6900	−	15.3351i	−0.828521	−	0.559958i
$751$	30.0558	+	17.3527i	1.09675	+	0.633209i	0.935366	−	0.353682i	$-0.115071\pi$
$751$	30.0558	+	17.3527i	1.09675	+	0.633209i	0.161385	+	0.986892i	$0.448404\pi$
$752$	0.384886	−	0.878237i	0.0140354	−	0.0320260i
$753$	−19.8241	−	1.53813i	−0.722431	−	0.0560527i
$754$	22.5528	+	24.3261i	0.821325	+	0.885906i
$755$	−13.0485	−	10.6231i	−0.474883	−	0.386615i
$756$	−22.3015	−	14.2857i	−0.811096	−	0.519567i
$757$	21.6732	−	21.6732i	0.787727	−	0.787727i	−0.193394	−	0.981121i	$-0.561950\pi$
$757$	21.6732	−	21.6732i	0.787727	−	0.787727i	0.981121	+	0.193394i	$0.0619496\pi$
$758$	0.682434	−	18.0405i	0.0247871	−	0.655262i
$759$	−17.5735	+	15.0428i	−0.637878	+	0.546020i
$760$	−23.8089	+	6.09138i	−0.863639	+	0.220958i
$761$	13.2539	−	22.9564i	0.480452	−	0.832167i	−0.519297	−	0.854594i	$-0.673806\pi$
$761$	13.2539	−	22.9564i	0.480452	−	0.832167i	0.999748	+	0.0224270i	$0.00713933\pi$
$762$	5.72882	+	7.22874i	0.207533	+	0.261870i
$763$	34.9188	+	9.35647i	1.26415	+	0.338727i
$764$	−28.2472	+	13.5746i	−1.02195	+	0.491112i
$765$	−17.2115	−	11.1872i	−0.622283	−	0.404474i
$766$	48.4453	−	11.0364i	1.75040	−	0.398763i
$767$	15.5401	−	57.9964i	0.561120	−	2.09413i
$768$	−10.2770	+	25.7368i	−0.370839	+	0.928697i
$769$	−10.2142	−	5.89716i	−0.368333	−	0.212657i	0.304397	−	0.952545i	$-0.401545\pi$
$769$	−10.2142	−	5.89716i	−0.368333	−	0.212657i	−0.672730	+	0.739888i	$0.734878\pi$
$770$	−15.5758	−	23.3694i	−0.561313	−	0.842173i
$771$	24.9833	−	4.65897i	0.899753	−	0.167789i
$772$	42.4187	−	7.99004i	1.52668	−	0.287568i
$773$	7.36402	+	7.36402i	0.264865	+	0.264865i	0.827027	−	0.562162i	$-0.190030\pi$
$773$	7.36402	+	7.36402i	0.264865	+	0.264865i	−0.562162	+	0.827027i	$0.690030\pi$
$774$	−9.79998	+	20.0577i	−0.352253	+	0.720960i
$775$	−10.5717	+	2.18930i	−0.379746	+	0.0786420i
$776$	−3.28008	+	8.32738i	−0.117748	+	0.298935i
$777$	−20.6978	+	9.90045i	−0.742529	+	0.355177i
$778$	11.7933	+	22.3362i	0.422810	+	0.800791i
$779$	−15.7293	+	27.2439i	−0.563560	+	0.976115i
$780$	36.3780	−	18.6001i	1.30254	−	0.665991i
$781$	−3.60645	−	6.24656i	−0.129049	−	0.223520i
$782$	−8.82982	+	14.0398i	−0.315754	+	0.502062i
$783$	6.63624	+	22.1337i	0.237160	+	0.790992i
$784$	1.57789	+	1.26257i	0.0563533	+	0.0450916i
$785$	−6.78772	+	4.90448i	−0.242264	+	0.175048i
$786$	−24.1087	−	17.9067i	−0.859929	−	0.638709i
$787$	29.6943	−	7.95656i	1.05849	−	0.283621i	0.312733	−	0.949841i	$-0.398756\pi$
$787$	29.6943	−	7.95656i	1.05849	−	0.283621i	0.745755	+	0.666220i	$0.232089\pi$
$788$	20.2659	−	17.4113i	0.721943	−	0.620253i
$789$	−1.05728	+	2.99619i	−0.0376402	+	0.106667i
$790$	−35.9199	−	31.5745i	−1.27797	−	1.12337i
$791$			1.15443i			0.0410468i
$792$	7.46748	+	28.6114i	0.265345	+	1.01666i
$793$	−34.4474	−	34.4474i	−1.22326	−	1.22326i
$794$	−31.1450	−	33.5939i	−1.10529	−	1.19220i
$795$	−1.27846	−	0.696649i	−0.0453422	−	0.0247076i
$796$	−4.10980	−	0.311375i	−0.145668	−	0.0110364i
$797$	4.77511	+	17.8210i	0.169143	+	0.631251i	0.997475	+	0.0710135i	$0.0226233\pi$
$797$	4.77511	+	17.8210i	0.169143	+	0.631251i	−0.828332	+	0.560237i	$0.810710\pi$
$798$	−8.93073	+	22.5530i	−0.316144	+	0.798368i
$799$	−0.366781	−	0.635283i	−0.0129758	−	0.0224747i
$800$	14.5117	+	24.2778i	0.513067	+	0.858349i
$801$	1.67281	−	10.7151i	0.0591059	−	0.378598i
$802$	36.5386	+	22.9796i	1.29022	+	0.811438i
$803$	−42.7219	−	11.4473i	−1.50762	−	0.403967i
$804$	0.280075	+	2.56534i	0.00987747	+	0.0904724i
$805$	7.77327	+	20.4096i	0.273972	+	0.719344i
$806$	4.75380	−	15.3890i	0.167445	−	0.542056i
$807$	23.1453	+	1.79582i	0.814752	+	0.0632158i
$808$	−11.2037	+	4.87173i	−0.394144	+	0.171387i
$809$			45.3459i			1.59428i	0.603798	+	0.797138i	$0.293653\pi$
$809$			45.3459i			1.59428i	−0.603798	+	0.797138i	$0.706347\pi$
$810$	28.4567	−	0.465483i	0.999866	−	0.0163554i
$811$		−	32.6505i		−	1.14652i	−0.819375	−	0.573258i	$-0.805679\pi$
$811$		−	32.6505i		−	1.14652i	0.819375	−	0.573258i	$-0.194321\pi$
$812$	4.19563	+	22.2744i	0.147238	+	0.781677i
$813$	33.1417	+	2.57143i	1.16233	+	0.0901840i
$814$	24.4753	+	7.56062i	0.857859	+	0.265000i
$815$	19.5330	+	8.75799i	0.684211	+	0.306779i
$816$	11.2028	+	17.9994i	0.392176	+	0.630106i
$817$	19.7493	+	5.29182i	0.690942	+	0.185137i
$818$	−12.3617	+	19.6557i	−0.432217	+	0.687244i
$819$	6.22045	−	39.8446i	0.217360	−	1.39228i
$820$	35.2079	+	8.44140i	1.22951	+	0.294787i
$821$	−14.0278	−	24.2968i	−0.489572	−	0.847964i	0.510356	−	0.859963i	$-0.329514\pi$
$821$	−14.0278	−	24.2968i	−0.489572	−	0.847964i	−0.999928	+	0.0119995i	$0.996180\pi$
$822$	−21.0676	−	8.34251i	−0.734816	−	0.290978i
$823$	−8.98407	−	33.5290i	−0.313165	−	1.16875i	−0.925686	−	0.378293i	$-0.876511\pi$
$823$	−8.98407	−	33.5290i	−0.313165	−	1.16875i	0.612521	−	0.790454i	$-0.290156\pi$
$824$	3.82099	−	0.571117i	0.133111	−	0.0198958i
$825$	27.8344	+	11.6643i	0.969068	+	0.406097i
$826$	30.0857	−	27.8925i	1.04682	−	0.970504i
$827$	0.244245	+	0.244245i	0.00849323	+	0.00849323i	0.711341	−	0.702847i	$-0.248088\pi$
$827$	0.244245	+	0.244245i	0.00849323	+	0.00849323i	−0.702847	+	0.711341i	$0.748088\pi$
$828$	−0.719898	−	22.9836i	−0.0250182	−	0.798737i
$829$		−	24.5821i		−	0.853771i	−0.904306	−	0.426885i	$-0.859611\pi$
$829$		−	24.5821i		−	0.853771i	0.904306	−	0.426885i	$-0.140389\pi$
$830$	48.9816	−	3.15349i	1.70017	−	0.109459i
$831$	−4.30749	+	12.2069i	−0.149425	+	0.423451i
$832$	−42.1715	+	1.47409i	−1.46204	+	0.0511050i
$833$	1.49332	−	0.400133i	0.0517404	−	0.0138638i
$834$	−26.1573	+	35.2170i	−0.905752	+	1.21946i
$835$	−4.84443	−	6.70462i	−0.167648	−	0.232023i
$836$	24.4101	−	11.7307i	0.844243	−	0.405713i
$837$	7.69597	−	8.16394i	0.266012	−	0.282187i
$838$	11.9962	+	7.54458i	0.414402	+	0.260623i
$839$	−4.08967	−	7.08351i	−0.141191	−	0.244550i	0.786754	−	0.617266i	$-0.211760\pi$
$839$	−4.08967	−	7.08351i	−0.141191	−	0.244550i	−0.927945	+	0.372716i	$0.878426\pi$
$840$	27.8074	+	2.47472i	0.959446	+	0.0853859i
$841$	−4.61225	+	7.98866i	−0.159043	+	0.275471i
$842$	−9.21278	+	4.86427i	−0.317493	+	0.167634i
$843$	21.8605	−	10.4566i	0.752914	−	0.360144i
$844$	3.80377	+	2.59794i	0.130931	+	0.0894247i
$845$	25.7024	+	20.9250i	0.884189	+	0.719842i
$846$	0.913799	+	0.446472i	0.0314171	+	0.0153500i
$847$	2.06171	+	2.06171i	0.0708410	+	0.0708410i
$848$	0.890937	+	1.21133i	0.0305949	+	0.0415972i
$849$	−3.16399	+	0.590032i	−0.108588	+	0.0202498i
$850$	21.5398	+	2.06126i	0.738808	+	0.0707005i
$851$	−17.2517	−	9.96030i	−0.591382	−	0.341435i
$852$	7.08618	+	1.09311i	0.242768	+	0.0374494i
$853$	−7.21700	+	26.9342i	−0.247105	+	0.922210i	0.725208	+	0.688530i	$0.241743\pi$
$853$	−7.21700	+	26.9342i	−0.247105	+	0.922210i	−0.972314	+	0.233680i	$0.924923\pi$
$854$	−7.39374	−	32.4554i	−0.253009	−	1.11060i
$855$	−5.40919	−	25.4991i	−0.184990	−	0.872051i
$856$	16.6781	−	13.2668i	0.570047	−	0.453451i
$857$	42.5245	+	11.3944i	1.45261	+	0.389226i	0.896931	−	0.442171i	$-0.145792\pi$
$857$	42.5245	+	11.3944i	1.45261	+	0.389226i	0.555679	+	0.831397i	$0.312458\pi$
$858$	−35.2872	+	27.9653i	−1.20468	+	0.954719i
$859$	−1.47011	+	2.54630i	−0.0501593	+	0.0868785i	−0.890015	−	0.455931i	$-0.849306\pi$
$859$	−1.47011	+	2.54630i	−0.0501593	+	0.0868785i	0.839856	+	0.542810i	$0.182640\pi$
$860$	−0.623098	−	23.5231i	−0.0212474	−	0.802131i
$861$	27.1481	−	23.2387i	0.925206	−	0.791972i
$862$	−23.2433	−	0.879245i	−0.791671	−	0.0299472i
$863$	7.13386	−	7.13386i	0.242839	−	0.242839i	−0.575184	−	0.818024i	$-0.695070\pi$
$863$	7.13386	−	7.13386i	0.242839	−	0.242839i	0.818024	+	0.575184i	$0.195070\pi$
$864$	−26.8230	−	12.0219i	−0.912537	−	0.408993i
$865$	51.5814	−	5.28495i	1.75382	−	0.179694i
$866$	−5.54562	+	5.14136i	−0.188448	+	0.174710i
$867$	−13.1860	−	1.02309i	−0.447819	−	0.0347458i
$868$	8.34766	−	7.17184i	0.283338	−	0.243428i
$869$	45.6419	+	26.3514i	1.54830	+	0.893909i
$870$	−16.9952	−	17.4479i	−0.576191	−	0.591538i
$871$	−3.40292	+	1.96468i	−0.115304	+	0.0665706i
$872$	39.8638	+	4.54122i	1.34996	+	0.153785i
$873$	−8.68081	−	3.84196i	−0.293801	−	0.130031i
$874$	−20.5346	+	4.67802i	−0.694592	+	0.158237i
$875$	19.2312	−	21.0240i	0.650133	−	0.710742i
$876$	35.4648	−	25.9855i	1.19824	−	0.877968i
$877$	6.03921	+	22.5386i	0.203930	+	0.761076i	0.989773	+	0.142650i	$0.0455625\pi$
$877$	6.03921	+	22.5386i	0.203930	+	0.761076i	−0.785843	+	0.618426i	$0.787771\pi$
$878$	−46.0482	+	24.3130i	−1.55405	+	0.820525i
$879$	8.37619	+	44.9166i	0.282522	+	1.51500i
$880$	−20.9309	−	23.0960i	−0.705580	−	0.778566i
$881$	−42.4590			−1.43048			−0.715241	−	0.698878i	$-0.753683\pi$
$881$	−42.4590			−1.43048			−0.715241	+	0.698878i	$0.753683\pi$
$882$	−1.40734	+	1.61669i	−0.0473874	+	0.0544370i
$883$	7.64008	−	7.64008i	0.257109	−	0.257109i	−0.566768	−	0.823877i	$-0.691807\pi$
$883$	7.64008	−	7.64008i	0.257109	−	0.257109i	0.823877	+	0.566768i	$0.191807\pi$
$884$	−18.2069	+	26.6577i	−0.612366	+	0.896595i
$885$	−10.3566	+	42.8530i	−0.348135	+	1.44049i
$886$	−5.05266	+	16.3565i	−0.169747	+	0.549508i
$887$	−4.69064	+	1.25685i	−0.157496	+	0.0422010i	−0.336706	−	0.941610i	$-0.609313\pi$
$887$	−4.69064	+	1.25685i	−0.157496	+	0.0422010i	0.179209	+	0.983811i	$0.442646\pi$
$888$	−21.0947	+	14.2630i	−0.707890	+	0.478636i
$889$	−8.31067	+	4.79817i	−0.278731	+	0.160925i
$890$	3.66200	+	10.8291i	0.122750	+	0.362991i
$891$	−30.6490	+	6.65649i	−1.02678	+	0.223001i
$892$	31.5002	+	11.0514i	1.05470	+	0.370028i
$893$	0.241087	−	0.899750i	0.00806768	−	0.0301090i
$894$	5.44387	+	4.04341i	0.182070	+	0.135232i
$895$	7.97342	+	20.9351i	0.266522	+	0.699783i
$896$	−24.9285	−	14.4880i	−0.832803	−	0.484010i
$897$	31.5860	−	15.1086i	1.05463	−	0.504463i
$898$	1.48143	+	0.0560395i	0.0494361	+	0.00187006i
$899$	−9.60189			−0.320241
$900$	−26.3660	+	14.3120i	−0.878866	+	0.477068i
$901$	1.15036			0.0383241
$902$	−39.8703	−	1.50821i	−1.32753	−	0.0502178i
$903$	−19.1557	−	13.1342i	−0.637463	−	0.437079i
$904$	0.189401	+	1.26716i	0.00629938	+	0.0421452i
$905$	−15.9023	−	41.7532i	−0.528610	−	1.38792i
$906$	−16.9164	+	7.31932i	−0.562009	+	0.243168i
$907$	−15.5709	+	58.1113i	−0.517022	+	1.92955i	−0.211402	+	0.977399i	$0.567803\pi$
$907$	−15.5709	+	58.1113i	−0.517022	+	1.92955i	−0.305620	+	0.952154i	$0.598864\pi$
$908$	3.33774	−	9.51369i	0.110767	−	0.315723i
$909$	−4.67053	−	12.0872i	−0.154912	−	0.400906i
$910$	13.6174	+	40.2685i	0.451411	+	1.33489i
$911$	−2.72513	+	1.57335i	−0.0902875	+	0.0521275i	−0.544464	−	0.838784i	$-0.683267\pi$
$911$	−2.72513	+	1.57335i	−0.0902875	+	0.0521275i	0.454176	+	0.890912i	$0.349934\pi$
$912$	−6.10269	+	26.2206i	−0.202080	+	0.868250i
$913$	−52.2465	+	13.9994i	−1.72911	+	0.463313i
$914$	−5.67979	+	18.3867i	−0.187871	+	0.608176i
$915$	25.9096	+	24.6618i	0.856545	+	0.815295i
$916$	12.8128	+	8.75102i	0.423347	+	0.289142i
$917$	22.0936	−	22.0936i	0.729594	−	0.729594i
$918$	−19.5671	+	11.0813i	−0.645811	+	0.365736i
$919$	−31.3326			−1.03357			−0.516783	−	0.856116i	$-0.672871\pi$
$919$	−31.3326			−1.03357			−0.516783	+	0.856116i	$0.672871\pi$
$920$	11.8808	+	21.1273i	0.391699	+	0.696547i
$921$	25.9441	−	22.2080i	0.854887	−	0.731779i
$922$	14.3174	−	7.55947i	0.471519	−	0.248958i
$923$	2.82565	+	10.5455i	0.0930075	+	0.347109i
$924$	−30.5832	+	3.33897i	−1.00611	+	0.109844i
$925$	−1.49602	+	25.9461i	−0.0491888	+	0.853101i
$926$	−6.47871	+	1.47593i	−0.212904	+	0.0485020i
$927$	0.437349	+	4.07439i	0.0143644	+	0.133820i
$928$	8.25976	+	23.7611i	0.271140	+	0.779998i
$929$	10.8495	−	6.26399i	0.355962	−	0.205515i	−0.311346	−	0.950297i	$-0.600780\pi$
$929$	10.8495	−	6.26399i	0.355962	−	0.205515i	0.667308	+	0.744782i	$0.267446\pi$
$930$	−3.21076	+	11.3822i	−0.105285	+	0.373238i
$931$	1.70012	+	0.981567i	0.0557193	+	0.0321696i
$932$	7.65540	+	8.91050i	0.250761	+	0.291873i
$933$	0.793368	−	1.15710i	0.0259737	−	0.0378817i
$934$	37.4602	−	34.7294i	1.22573	−	1.13638i
$935$	−23.7211	+	2.43043i	−0.775763	+	0.0794835i
$936$	0.290822	−	44.7561i	0.00950583	−	1.46290i
$937$	−27.1824	+	27.1824i	−0.888011	+	0.888011i	−0.994332	−	0.106321i	$-0.966093\pi$
$937$	−27.1824	+	27.1824i	−0.888011	+	0.888011i	0.106321	+	0.994332i	$0.466093\pi$
$938$	−2.68296	−	0.101490i	−0.0876016	−	0.00331378i
$939$	−10.3373	−	3.64778i	−0.337346	−	0.119041i
$940$	−1.07168	+	0.0283874i	−0.0349542	+	0.000925894i
$941$	12.5030	−	21.6558i	0.407585	−	0.705957i	−0.587034	−	0.809562i	$-0.699704\pi$
$941$	12.5030	−	21.6558i	0.407585	−	0.705957i	0.994619	+	0.103605i	$0.0330378\pi$
$942$	1.33962	+	9.07513i	0.0436471	+	0.295684i
$943$	29.9700	+	8.03043i	0.975956	+	0.261507i
$944$	28.4475	−	35.5522i	0.925886	−	1.15713i
$945$	−3.84442	+	29.3601i	−0.125059	+	0.955085i
$946$	5.75996	+	25.2838i	0.187273	+	0.822048i
$947$	−15.5957	+	58.2038i	−0.506791	+	1.89137i	−0.0566928	+	0.998392i	$0.518056\pi$
$947$	−15.5957	+	58.2038i	−0.506791	+	1.89137i	−0.450098	+	0.892979i	$0.648611\pi$
$948$	−48.8335	+	18.9714i	−1.58604	+	0.616161i
$949$	57.9762	+	33.4726i	1.88199	+	1.08657i
$950$	17.4897	+	21.1913i	0.567441	+	0.687536i
$951$	−11.6533	+	33.0240i	−0.377885	+	1.07088i
$952$	−20.2282	+	8.79588i	−0.655600	+	0.285076i
$953$	7.86673	+	7.86673i	0.254828	+	0.254828i	0.822947	−	0.568118i	$-0.192328\pi$
$953$	7.86673	+	7.86673i	0.254828	+	0.254828i	−0.568118	+	0.822947i	$0.692328\pi$
$954$	−1.32285	+	0.890945i	−0.0428289	+	0.0288454i
$955$	27.1724	+	22.1218i	0.879279	+	0.715845i
$956$	−2.88896	+	4.22988i	−0.0934357	+	0.136804i
$957$	22.1376	+	15.1787i	0.715606	+	0.490658i
$958$	15.1631	−	8.00599i	0.489898	−	0.258662i
$959$	11.7875	−	20.4166i	0.380638	−	0.659285i
$960$	30.9288	−	1.84582i	0.998224	−	0.0595735i
$961$	−13.1689	−	22.8092i	−0.424804	−	0.735782i
$962$	−32.8218	−	20.6420i	−1.05822	−	0.665526i
$963$	13.3267	+	18.2576i	0.429447	+	0.588342i
$964$	−11.9448	−	24.8556i	−0.384715	−	0.800546i
$965$	−28.2640	−	39.1169i	−0.909849	−	1.25922i
$966$	23.7656	+	2.75102i	0.764645	+	0.0885127i
$967$	−15.5687	+	4.17163i	−0.500657	+	0.134151i	−0.500305	−	0.865849i	$-0.666779\pi$
$967$	−15.5687	+	4.17163i	−0.500657	+	0.134151i	−0.000352232		1.00000i	$0.500112\pi$
$968$	2.60129	+	1.92478i	0.0836085	+	0.0618649i
$969$	13.3930	+	15.6462i	0.430246	+	0.502627i
$970$	9.98583	−	0.642899i	0.320626	−	0.0206422i
$971$			51.3038i			1.64642i	0.567739	+	0.823209i	$0.307818\pi$
$971$			51.3038i			1.64642i	−0.567739	+	0.823209i	$0.692182\pi$
$972$	13.9188	−	27.8974i	0.446446	−	0.894811i
$973$	−32.2733	−	32.2733i	−1.03464	−	1.03464i
$974$	−18.4243	+	17.0812i	−0.590354	+	0.547318i
$975$	−36.1252	−	27.9576i	−1.15693	−	0.895359i
$976$	−13.4405	−	34.4117i	−0.430221	−	1.10149i
$977$	−0.369048	−	1.37730i	−0.0118069	−	0.0440639i	0.959771	−	0.280784i	$-0.0905943\pi$
$977$	−0.369048	−	1.37730i	−0.0118069	−	0.0440639i	−0.971578	+	0.236720i	$0.923928\pi$
$978$	18.3781	−	14.5648i	0.587668	−	0.465730i
$979$	−6.29876	−	10.9098i	−0.201309	−	0.348678i
$980$	0.526776	−	2.19711i	0.0168272	−	0.0701840i
$981$	−6.56414	+	42.0461i	−0.209577	+	1.34243i
$982$	0.0950129	−	0.151075i	0.00303198	−	0.00482099i
$983$	44.4088	+	11.8993i	1.41642	+	0.379529i	0.884212	−	0.467085i	$-0.154696\pi$
$983$	44.4088	+	11.8993i	1.41642	+	0.379529i	0.532208	+	0.846614i	$0.321362\pi$
$984$	25.9866	−	29.9620i	0.828422	−	0.955154i
$985$	−27.2574	−	12.2214i	−0.868492	−	0.389405i
$986$	18.3875	+	5.68005i	0.585577	+	0.180890i
$987$	−0.598374	+	0.872705i	−0.0190464	+	0.0277785i
$988$	−40.2838	+	7.58791i	−1.28160	+	0.241404i
$989$		−	20.1657i		−	0.641231i
$990$	25.3957	−	21.1667i	0.807127	−	0.672721i
$991$			47.4822i			1.50832i	0.656689	+	0.754161i	$0.271956\pi$
$991$			47.4822i			1.50832i	−0.656689	+	0.754161i	$0.728044\pi$
$992$	7.98618	−	9.24173i	0.253561	−	0.293425i
$993$	14.5993	+	30.5212i	0.463296	+	0.968562i
$994$	−2.20173	+	7.12745i	−0.0698346	+	0.226069i
$995$	1.64012	+	4.30631i	0.0519952	+	0.136519i
$996$	21.6714	−	49.2069i	0.686683	−	1.55918i
$997$	−54.8142	−	14.6874i	−1.73598	−	0.465156i	−0.754436	−	0.656373i	$-0.772090\pi$
$997$	−54.8142	−	14.6874i	−1.73598	−	0.465156i	−0.981548	+	0.191218i	$0.938756\pi$
$998$	48.5722	+	30.5477i	1.53753	+	0.966971i
$999$	−14.1883	−	22.9818i	−0.448899	−	0.727111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.x.a.103.18	yes	128
3.2	odd	2		540.2.y.a.523.15		128
4.3	odd	2	inner	180.2.x.a.103.12	yes	128
5.2	odd	4	inner	180.2.x.a.67.32	yes	128
5.3	odd	4		900.2.bf.e.607.1		128
5.4	even	2		900.2.bf.e.643.15		128
9.2	odd	6		540.2.y.a.343.28		128
9.7	even	3	inner	180.2.x.a.43.5	yes	128
12.11	even	2		540.2.y.a.523.21		128
15.2	even	4		540.2.y.a.307.1		128
20.3	even	4		900.2.bf.e.607.28		128
20.7	even	4	inner	180.2.x.a.67.5	yes	128
20.19	odd	2		900.2.bf.e.643.21		128
36.7	odd	6	inner	180.2.x.a.43.32	yes	128
36.11	even	6		540.2.y.a.343.1		128
45.2	even	12		540.2.y.a.127.21		128
45.7	odd	12	inner	180.2.x.a.7.12	✓	128
45.34	even	6		900.2.bf.e.43.28		128
45.43	odd	12		900.2.bf.e.7.21		128
60.47	odd	4		540.2.y.a.307.28		128
180.7	even	12	inner	180.2.x.a.7.18	yes	128
180.43	even	12		900.2.bf.e.7.15		128
180.47	odd	12		540.2.y.a.127.15		128
180.79	odd	6		900.2.bf.e.43.1		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.12	✓	128	45.7	odd	12	inner
180.2.x.a.7.18	yes	128	180.7	even	12	inner
180.2.x.a.43.5	yes	128	9.7	even	3	inner
180.2.x.a.43.32	yes	128	36.7	odd	6	inner
180.2.x.a.67.5	yes	128	20.7	even	4	inner
180.2.x.a.67.32	yes	128	5.2	odd	4	inner
180.2.x.a.103.12	yes	128	4.3	odd	2	inner
180.2.x.a.103.18	yes	128	1.1	even	1	trivial
540.2.y.a.127.15		128	180.47	odd	12
540.2.y.a.127.21		128	45.2	even	12
540.2.y.a.307.1		128	15.2	even	4
540.2.y.a.307.28		128	60.47	odd	4
540.2.y.a.343.1		128	36.11	even	6
540.2.y.a.343.28		128	9.2	odd	6
540.2.y.a.523.15		128	3.2	odd	2
540.2.y.a.523.21		128	12.11	even	2
900.2.bf.e.7.15		128	180.43	even	12
900.2.bf.e.7.21		128	45.43	odd	12
900.2.bf.e.43.1		128	180.79	odd	6
900.2.bf.e.43.28		128	45.34	even	6
900.2.bf.e.607.1		128	5.3	odd	4
900.2.bf.e.607.28		128	20.3	even	4
900.2.bf.e.643.15		128	5.4	even	2
900.2.bf.e.643.21		128	20.19	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0534584 - 1.41320i) q^{2} +(-0.133985 + 1.72686i) q^{3} +(-1.99428 - 0.151095i) q^{4} +(0.795868 + 2.08964i) q^{5} +(2.43324 + 0.281664i) q^{6} +(-0.659597 + 2.46165i) q^{7} +(-0.320139 + 2.81025i) q^{8} +(-2.96410 - 0.462748i) q^{9} +(2.99563 - 1.01301i) q^{10} +(-3.01796 + 1.74242i) q^{11} +(0.528125 - 3.42361i) q^{12} +(5.09493 - 1.36518i) q^{13} +(3.44355 + 1.06374i) q^{14} +(-3.71515 + 1.09437i) q^{15} +(3.95434 + 0.602653i) q^{16} +(2.16382 - 2.16382i) q^{17} +(-0.812413 + 4.16413i) q^{18} +3.88577 q^{19} +(-1.27145 - 4.28759i) q^{20} +(-4.16255 - 1.46886i) q^{21} +(2.30106 + 4.35813i) q^{22} +(-0.991920 - 3.70190i) q^{23} +(-4.81002 - 0.929369i) q^{24} +(-3.73319 + 3.32615i) q^{25} +(-1.65691 - 7.27315i) q^{26} +(1.19625 - 5.05658i) q^{27} +(1.68737 - 4.80957i) q^{28} +(-3.85118 + 2.22348i) q^{29} +(1.34796 + 5.30877i) q^{30} +(1.86992 + 1.07960i) q^{31} +(1.06306 - 5.55607i) q^{32} +(-2.60455 - 5.44505i) q^{33} +(-2.94224 - 3.17359i) q^{34} +(-5.66891 + 0.580828i) q^{35} +(5.84133 + 1.37071i) q^{36} +(3.67542 - 3.67542i) q^{37} +(0.207727 - 5.49138i) q^{38} +(1.67483 + 8.98115i) q^{39} +(-6.12720 + 1.56761i) q^{40} +(-4.04792 + 7.01121i) q^{41} +(-2.29832 + 5.80400i) q^{42} +(5.08248 + 1.36185i) q^{43} +(6.28194 - 3.01888i) q^{44} +(-1.39205 - 6.56218i) q^{45} +(-5.28456 + 1.20389i) q^{46} +(0.0620436 - 0.231550i) q^{47} +(-1.57052 + 6.74785i) q^{48} +(0.437526 + 0.252606i) q^{49} +(4.50096 + 5.45356i) q^{50} +(3.44669 + 4.02653i) q^{51} +(-10.3670 + 1.95274i) q^{52} +(0.265818 + 0.265818i) q^{53} +(-7.08202 - 1.96086i) q^{54} +(-6.04292 - 4.91971i) q^{55} +(-6.70669 - 2.64170i) q^{56} +(-0.520636 + 6.71018i) q^{57} +(2.93635 + 5.56137i) q^{58} +(5.69158 - 9.85810i) q^{59} +(7.57442 - 1.62115i) q^{60} +(-4.61792 - 7.99848i) q^{61} +(1.62566 - 2.58487i) q^{62} +(3.09423 - 6.99134i) q^{63} +(-7.79502 - 1.79934i) q^{64} +(6.90763 + 9.56007i) q^{65} +(-7.83420 + 3.38968i) q^{66} +(-0.719566 + 0.192807i) q^{67} +(-4.64221 + 3.98832i) q^{68} +(6.52556 - 1.21691i) q^{69} +(0.517777 + 8.04237i) q^{70} +2.06980i q^{71} +(2.24936 - 8.18171i) q^{72} +(8.97449 + 8.97449i) q^{73} +(-4.99763 - 5.39060i) q^{74} +(-5.24361 - 6.89235i) q^{75} +(-7.74933 - 0.587121i) q^{76} +(-2.29859 - 8.57845i) q^{77} +(12.7817 - 1.88676i) q^{78} +(-7.56173 - 13.0973i) q^{79} +(1.88780 + 8.74278i) q^{80} +(8.57173 + 2.74326i) q^{81} +(9.69186 + 6.09534i) q^{82} +(14.9925 + 4.01723i) q^{83} +(8.07937 + 3.55826i) q^{84} +(6.24371 + 2.79948i) q^{85} +(2.19627 - 7.10978i) q^{86} +(-3.32364 - 6.94837i) q^{87} +(-3.93047 - 9.03903i) q^{88} +3.61495i q^{89} +(-9.34811 + 1.61645i) q^{90} +13.4424i q^{91} +(1.41883 + 7.53251i) q^{92} +(-2.11486 + 3.08444i) q^{93} +(-0.323910 - 0.100059i) q^{94} +(3.09256 + 8.11986i) q^{95} +(9.45212 + 2.58020i) q^{96} +(3.05651 + 0.818990i) q^{97} +(0.380373 - 0.604809i) q^{98} +(9.75182 - 3.76814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{16} - 16 q^{17} - 36 q^{18} - 18 q^{20} - 24 q^{21} - 10 q^{22} - 4 q^{25} - 48 q^{26} + 8 q^{28} - 14 q^{30} + 18 q^{32}+ \cdots + 164 q^{98}+O(q^{100}) \) 128 * q - 2 * q^2 - 4 * q^5 - 8 * q^6 - 8 * q^8 - 8 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^16 - 16 * q^17 - 36 * q^18 - 18 * q^20 - 24 * q^21 - 10 * q^22 - 4 * q^25 - 48 * q^26 + 8 * q^28 - 14 * q^30 + 18 * q^32 - 20 * q^33 - 40 * q^36 - 16 * q^37 - 34 * q^38 - 2 * q^40 - 8 * q^41 + 34 * q^42 - 28 * q^45 - 40 * q^46 - 22 * q^48 + 38 * q^50 - 18 * q^52 - 64 * q^53 - 32 * q^56 - 48 * q^57 - 10 * q^58 + 74 * q^60 - 8 * q^61 + 44 * q^62 + 12 * q^65 - 36 * q^66 + 58 * q^68 - 22 * q^70 + 78 * q^72 - 16 * q^73 - 32 * q^76 - 60 * q^77 + 114 * q^78 + 132 * q^80 + 24 * q^81 - 4 * q^85 + 32 * q^86 - 10 * q^88 + 138 * q^90 + 52 * q^92 - 68 * q^93 + 52 * q^96 - 4 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more