LMFDB - Embedded newform 150.2.l.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.1
Character	$\chi$	$=$	150.113
Dual form			150.2.l.a.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-1.70980 - 0.276758i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.89132 + 1.19286i) q^{5} +(-0.00587961 + 1.73204i) q^{6} +(-1.11983 + 1.11983i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.84681 + 0.946400i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-1.70980 - 0.276758i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.89132 + 1.19286i) q^{5} +(-0.00587961 + 1.73204i) q^{6} +(-1.11983 + 1.11983i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.84681 + 0.946400i) q^{9} +(1.47404 + 1.68143i) q^{10} +(-2.56196 + 3.52624i) q^{11} +(1.71164 - 0.265144i) q^{12} +(-5.38535 - 0.852956i) q^{13} +(1.28122 + 0.930864i) q^{14} +(3.56390 - 1.51611i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.44561 - 2.26515i) q^{17} +(0.489409 - 2.95981i) q^{18} +(-1.25836 - 0.408866i) q^{19} +(1.43014 - 1.71893i) q^{20} +(2.22461 - 1.60476i) q^{21} +(3.88360 + 1.97879i) q^{22} +(-8.85228 + 1.40206i) q^{23} +(-0.529638 - 1.64909i) q^{24} +(2.15418 - 4.51215i) q^{25} +5.45248i q^{26} +(-4.60554 - 2.40603i) q^{27} +(0.718976 - 1.41107i) q^{28} +(1.25026 + 3.84789i) q^{29} +(-2.05496 - 3.28286i) q^{30} +(0.895777 - 2.75692i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.35635 - 5.32010i) q^{33} +(-2.93271 - 4.03653i) q^{34} +(0.782158 - 3.45376i) q^{35} +(-2.99993 - 0.0203674i) q^{36} +(0.0106771 - 0.0674126i) q^{37} +(-0.206981 + 1.30683i) q^{38} +(8.97179 + 2.94882i) q^{39} +(-1.92149 - 1.14363i) q^{40} +(0.0469455 + 0.0646149i) q^{41} +(-1.93301 - 1.94618i) q^{42} +(1.06892 + 1.06892i) q^{43} +(1.34690 - 4.14534i) q^{44} +(-6.51315 + 1.60590i) q^{45} +(2.76960 + 8.52397i) q^{46} +(0.351249 - 0.689364i) q^{47} +(-1.54593 + 0.781091i) q^{48} +4.49196i q^{49} +(-4.79359 - 1.42180i) q^{50} +(-8.22800 + 2.64259i) q^{51} +(5.38535 - 0.852956i) q^{52} +(7.22974 + 3.68374i) q^{53} +(-1.65594 + 4.92523i) q^{54} +(0.639185 - 9.72530i) q^{55} +(-1.50617 - 0.489384i) q^{56} +(2.03838 + 1.04734i) q^{57} +(3.60493 - 1.83681i) q^{58} +(0.576184 - 0.418622i) q^{59} +(-2.92097 + 2.54321i) q^{60} +(-5.17620 - 3.76073i) q^{61} +(-2.86311 - 0.453472i) q^{62} +(-4.24775 + 2.12814i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(11.2029 - 4.81075i) q^{65} +(-6.09252 - 4.45815i) q^{66} +(5.56612 + 10.9241i) q^{67} +(-3.52806 + 3.52806i) q^{68} +(15.5236 + 0.0526967i) q^{69} +(-3.53359 - 0.232242i) q^{70} +(-1.05328 + 0.342232i) q^{71} +(0.449176 + 2.96618i) q^{72} +(2.62862 + 16.5964i) q^{73} -0.0682529 q^{74} +(-4.93198 + 7.11868i) q^{75} +1.32312 q^{76} +(-1.07983 - 6.81775i) q^{77} +(1.50902 - 9.32263i) q^{78} +(-7.08470 + 2.30196i) q^{79} +(-0.828965 + 2.07673i) q^{80} +(7.20865 + 5.38844i) q^{81} +(0.0564755 - 0.0564755i) q^{82} +(-2.09751 - 4.11659i) q^{83} +(-1.61983 + 2.21366i) q^{84} +(-5.70607 + 9.58712i) q^{85} +(0.888543 - 1.22297i) q^{86} +(-1.07275 - 6.92513i) q^{87} +(-4.30501 - 0.681846i) q^{88} +(-5.12153 - 3.72101i) q^{89} +(2.60501 + 6.18174i) q^{90} +(6.98585 - 5.07552i) q^{91} +(7.98576 - 4.06895i) q^{92} +(-2.29460 + 4.46586i) q^{93} +(-0.735824 - 0.239084i) q^{94} +(2.86768 - 0.727750i) q^{95} +(1.01331 + 1.40471i) q^{96} +(-10.5981 - 5.40000i) q^{97} +(4.43665 - 0.702697i) q^{98} +(-10.6306 + 7.61389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−1.70980	−	0.276758i	−0.987152	−	0.159786i
$3$	−1.70980	−	0.276758i	−0.987152	−	0.159786i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−1.89132	+	1.19286i	−0.845824	+	0.533462i
$5$	−1.89132	+	1.19286i	−0.845824	+	0.533462i
$6$	−0.00587961	+	1.73204i	−0.00240034	+	0.707103i
$7$	−1.11983	+	1.11983i	−0.423256	+	0.423256i	−0.886323	−	0.463067i	$-0.846749\pi$
$7$	−1.11983	+	1.11983i	−0.423256	+	0.423256i	0.463067	+	0.886323i	$0.346749\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	2.84681	+	0.946400i	0.948937	+	0.315467i
$10$	1.47404	+	1.68143i	0.466132	+	0.531715i
$11$	−2.56196	+	3.52624i	−0.772460	+	1.06320i	0.223614	+	0.974678i	$0.428215\pi$
$11$	−2.56196	+	3.52624i	−0.772460	+	1.06320i	−0.996074	+	0.0885226i	$0.971785\pi$
$12$	1.71164	−	0.265144i	0.494107	−	0.0765404i
$13$	−5.38535	−	0.852956i	−1.49363	−	0.236567i	−0.644438	−	0.764656i	$-0.722909\pi$
$13$	−5.38535	−	0.852956i	−1.49363	−	0.236567i	−0.849189	+	0.528089i	$0.822909\pi$
$14$	1.28122	+	0.930864i	0.342422	+	0.248784i
$15$	3.56390	−	1.51611i	0.920196	−	0.391457i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.44561	−	2.26515i	1.07822	−	0.549380i	0.177651	−	0.984094i	$-0.443150\pi$
$17$	4.44561	−	2.26515i	1.07822	−	0.549380i	0.900569	+	0.434713i	$0.143150\pi$
$18$	0.489409	−	2.95981i	0.115355	−	0.697634i
$19$	−1.25836	−	0.408866i	−0.288688	−	0.0938003i	0.161093	−	0.986939i	$-0.448498\pi$
$19$	−1.25836	−	0.408866i	−0.288688	−	0.0938003i	−0.449781	+	0.893139i	$0.648498\pi$
$20$	1.43014	−	1.71893i	0.319789	−	0.384363i
$21$	2.22461	−	1.60476i	0.485449	−	0.350188i
$22$	3.88360	+	1.97879i	0.827987	+	0.421880i
$23$	−8.85228	+	1.40206i	−1.84583	+	0.292351i	−0.978633	−	0.205617i	$-0.934080\pi$
$23$	−8.85228	+	1.40206i	−1.84583	+	0.292351i	−0.867196	+	0.497967i	$0.834080\pi$
$24$	−0.529638	−	1.64909i	−0.108112	−	0.336618i
$25$	2.15418	−	4.51215i	0.430836	−	0.902430i
$26$			5.45248i			1.06932i
$27$	−4.60554	−	2.40603i	−0.886337	−	0.463041i
$28$	0.718976	−	1.41107i	0.135874	−	0.266667i
$29$	1.25026	+	3.84789i	0.232167	+	0.714536i	0.997485	+	0.0708831i	$0.0225817\pi$
$29$	1.25026	+	3.84789i	0.232167	+	0.714536i	−0.765318	+	0.643652i	$0.777418\pi$
$30$	−2.05496	−	3.28286i	−0.375183	−	0.599365i
$31$	0.895777	−	2.75692i	0.160886	−	0.495157i	−0.837823	−	0.545941i	$-0.816172\pi$
$31$	0.895777	−	2.75692i	0.160886	−	0.495157i	0.998710	+	0.0507843i	$0.0161721\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.35635	−	5.32010i	0.932420	−	0.926111i
$34$	−2.93271	−	4.03653i	−0.502956	−	0.692260i
$35$	0.782158	−	3.45376i	0.132209	−	0.583792i
$36$	−2.99993	−	0.0203674i	−0.499988	−	0.00339457i
$37$	0.0106771	−	0.0674126i	0.00175531	−	0.0110826i	−0.986795	−	0.161973i	$-0.948214\pi$
$37$	0.0106771	−	0.0674126i	0.00175531	−	0.0110826i	0.988550	+	0.150891i	$0.0482142\pi$
$38$	−0.206981	+	1.30683i	−0.0335768	+	0.211996i
$39$	8.97179	+	2.94882i	1.43664	+	0.472189i
$40$	−1.92149	−	1.14363i	−0.303814	−	0.180824i
$41$	0.0469455	+	0.0646149i	0.00733165	+	0.0100911i	0.812667	−	0.582728i	$-0.198015\pi$
$41$	0.0469455	+	0.0646149i	0.00733165	+	0.0100911i	−0.805335	+	0.592819i	$0.798015\pi$
$42$	−1.93301	−	1.94618i	−0.298270	−	0.300302i
$43$	1.06892	+	1.06892i	0.163009	+	0.163009i	0.783898	−	0.620890i	$-0.213228\pi$
$43$	1.06892	+	1.06892i	0.163009	+	0.163009i	−0.620890	+	0.783898i	$0.713228\pi$
$44$	1.34690	−	4.14534i	0.203053	−	0.624933i
$45$	−6.51315	+	1.60590i	−0.970923	+	0.239393i
$46$	2.76960	+	8.52397i	0.408356	+	1.25679i
$47$	0.351249	−	0.689364i	0.0512349	−	0.100554i	−0.863969	−	0.503544i	$-0.832029\pi$
$47$	0.351249	−	0.689364i	0.0512349	−	0.100554i	0.915204	+	0.402990i	$0.132029\pi$
$48$	−1.54593	+	0.781091i	−0.223136	+	0.112741i
$49$			4.49196i			0.641708i
$50$	−4.79359	−	1.42180i	−0.677916	−	0.201073i
$51$	−8.22800	+	2.64259i	−1.15215	+	0.370037i
$52$	5.38535	−	0.852956i	0.746814	−	0.118284i
$53$	7.22974	+	3.68374i	0.993082	+	0.506000i	0.873500	−	0.486824i	$-0.161845\pi$
$53$	7.22974	+	3.68374i	0.993082	+	0.506000i	0.119582	+	0.992824i	$0.461845\pi$
$54$	−1.65594	+	4.92523i	−0.225345	+	0.670238i
$55$	0.639185	−	9.72530i	0.0861877	−	1.31136i
$56$	−1.50617	−	0.489384i	−0.201270	−	0.0653967i
$57$	2.03838	+	1.04734i	0.269991	+	0.138723i
$58$	3.60493	−	1.83681i	0.473351	−	0.241184i
$59$	0.576184	−	0.418622i	0.0750127	−	0.0544999i	−0.549647	−	0.835397i	$-0.685238\pi$
$59$	0.576184	−	0.418622i	0.0750127	−	0.0544999i	0.624660	+	0.780897i	$0.285238\pi$
$60$	−2.92097	+	2.54321i	−0.377096	+	0.328327i
$61$	−5.17620	−	3.76073i	−0.662745	−	0.481512i	0.204844	−	0.978795i	$-0.434331\pi$
$61$	−5.17620	−	3.76073i	−0.662745	−	0.481512i	−0.867589	+	0.497282i	$0.834331\pi$
$62$	−2.86311	−	0.453472i	−0.363615	−	0.0575909i
$63$	−4.24775	+	2.12814i	−0.535167	+	0.268120i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	11.2029	−	4.81075i	1.38955	−	0.596700i
$66$	−6.09252	−	4.45815i	−0.749938	−	0.548761i
$67$	5.56612	+	10.9241i	0.680010	+	1.33459i	0.930435	+	0.366458i	$0.119430\pi$
$67$	5.56612	+	10.9241i	0.680010	+	1.33459i	−0.250425	+	0.968136i	$0.580570\pi$
$68$	−3.52806	+	3.52806i	−0.427840	+	0.427840i
$69$	15.5236	+	0.0526967i	1.86883	+	0.00634394i
$70$	−3.53359	−	0.232242i	−0.422345	−	0.0277582i
$71$	−1.05328	+	0.342232i	−0.125002	+	0.0406155i	−0.370850	−	0.928693i	$-0.620934\pi$
$71$	−1.05328	+	0.342232i	−0.125002	+	0.0406155i	0.245848	+	0.969308i	$0.420934\pi$
$72$	0.449176	+	2.96618i	0.0529359	+	0.349568i
$73$	2.62862	+	16.5964i	0.307656	+	1.94247i	0.333371	+	0.942796i	$0.391814\pi$
$73$	2.62862	+	16.5964i	0.307656	+	1.94247i	−0.0257147	+	0.999669i	$0.508186\pi$
$74$	−0.0682529			−0.00793424
$75$	−4.93198	+	7.11868i	−0.569496	+	0.821994i
$76$	1.32312			0.151772
$77$	−1.07983	−	6.81775i	−0.123058	−	0.776955i
$78$	1.50902	−	9.32263i	0.170863	−	1.05558i
$79$	−7.08470	+	2.30196i	−0.797091	+	0.258990i	−0.679121	−	0.734027i	$-0.737639\pi$
$79$	−7.08470	+	2.30196i	−0.797091	+	0.258990i	−0.117970	+	0.993017i	$0.537639\pi$
$80$	−0.828965	+	2.07673i	−0.0926811	+	0.232186i
$81$	7.20865	+	5.38844i	0.800961	+	0.598716i
$82$	0.0564755	−	0.0564755i	0.00623667	−	0.00623667i
$83$	−2.09751	−	4.11659i	−0.230231	−	0.451854i	0.746772	−	0.665081i	$-0.231603\pi$
$83$	−2.09751	−	4.11659i	−0.230231	−	0.451854i	−0.977003	+	0.213226i	$0.931603\pi$
$84$	−1.61983	+	2.21366i	−0.176738	+	0.241530i
$85$	−5.70607	+	9.58712i	−0.618910	+	1.03987i
$86$	0.888543	−	1.22297i	0.0958140	−	0.131877i
$87$	−1.07275	−	6.92513i	−0.115011	−	0.742452i
$88$	−4.30501	−	0.681846i	−0.458915	−	0.0726850i
$89$	−5.12153	−	3.72101i	−0.542881	−	0.394426i	0.282273	−	0.959334i	$-0.408912\pi$
$89$	−5.12153	−	3.72101i	−0.542881	−	0.394426i	−0.825154	+	0.564908i	$0.808912\pi$
$90$	2.60501	+	6.18174i	0.274592	+	0.651613i
$91$	6.98585	−	5.07552i	0.732316	−	0.532059i
$92$	7.98576	−	4.06895i	0.832573	−	0.424217i
$93$	−2.29460	+	4.46586i	−0.237939	+	0.463088i
$94$	−0.735824	−	0.239084i	−0.0758945	−	0.0246596i
$95$	2.86768	−	0.727750i	0.294218	−	0.0746655i
$96$	1.01331	+	1.40471i	0.103421	+	0.143367i
$97$	−10.5981	−	5.40000i	−1.07607	−	0.548287i	−0.176163	−	0.984361i	$-0.556369\pi$
$97$	−10.5981	−	5.40000i	−1.07607	−	0.548287i	−0.899911	+	0.436074i	$0.856369\pi$
$98$	4.43665	−	0.702697i	0.448170	−	0.0709831i
$99$	−10.6306	+	7.61389i	−1.06842	+	0.765224i
$100$	−0.654413	+	4.95699i	−0.0654413	+	0.495699i
$101$		−	7.28037i		−	0.724424i	−0.932096	−	0.362212i	$-0.882022\pi$
$101$		−	7.28037i		−	0.724424i	0.932096	−	0.362212i	$-0.117978\pi$
$102$	3.89720	+	7.71330i	0.385880	+	0.763731i
$103$	−1.84465	+	3.62033i	−0.181759	+	0.356722i	−0.963851	−	0.266440i	$-0.914152\pi$
$103$	−1.84465	+	3.62033i	−0.181759	+	0.356722i	0.782092	+	0.623162i	$0.214152\pi$
$104$	−1.68491	−	5.18562i	−0.165219	−	0.508492i
$105$	−2.29319	+	5.68876i	−0.223792	+	0.555166i
$106$	2.50740	−	7.71700i	0.243541	−	0.749541i
$107$	8.83022	+	8.83022i	0.853650	+	0.853650i	0.990581	−	0.136931i	$-0.0437238\pi$
$107$	8.83022	+	8.83022i	0.853650	+	0.853650i	−0.136931	+	0.990581i	$0.543724\pi$
$108$	5.12364	+	0.865079i	0.493022	+	0.0832423i
$109$	−4.97517	−	6.84773i	−0.476535	−	0.655894i	0.501300	−	0.865274i	$-0.332855\pi$
$109$	−4.97517	−	6.84773i	−0.476535	−	0.655894i	−0.977834	+	0.209380i	$0.932855\pi$
$110$	−9.70555	+	0.890056i	−0.925388	+	0.0848635i
$111$	−0.0369127	+	0.112307i	−0.00350359	+	0.0106597i
$112$	−0.247742	+	1.56418i	−0.0234094	+	0.147801i
$113$	0.444366	−	2.80561i	0.0418024	−	0.263930i	−0.957932	−	0.286997i	$-0.907343\pi$
$113$	0.444366	−	2.80561i	0.0418024	−	0.263930i	0.999734	+	0.0230668i	$0.00734306\pi$
$114$	0.715571	−	2.17713i	0.0670194	−	0.203907i
$115$	15.0700	−	13.2113i	1.40529	−	1.23196i
$116$	−2.37813	−	3.27321i	−0.220804	−	0.303910i
$117$	−14.5238	−	7.52490i	−1.34273	−	0.695677i
$118$	−0.503603	−	0.503603i	−0.0463604	−	0.0463604i
$119$	−2.44175	+	7.51492i	−0.223835	+	0.688892i
$120$	2.96884	+	2.48716i	0.271017	+	0.227046i
$121$	−2.47151	−	7.60654i	−0.224683	−	0.691504i
$122$	−2.90469	+	5.70078i	−0.262979	+	0.516125i
$123$	−0.0623845	−	0.123471i	−0.00562502	−	0.0111330i
$124$			2.89880i			0.260320i
$125$	1.30812	+	11.1035i	0.117002	+	0.993132i
$126$	2.76643	+	3.86254i	0.246453	+	0.344103i
$127$	0.720445	−	0.114107i	0.0639292	−	0.0101254i	−0.124388	−	0.992234i	$-0.539697\pi$
$127$	0.720445	−	0.114107i	0.0639292	−	0.0101254i	0.188317	+	0.982108i	$0.439697\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	−1.53180	−	2.12347i	−0.134868	−	0.186961i
$130$	−6.50404	−	10.3124i	−0.570442	−	0.904456i
$131$	−7.16884	−	2.32930i	−0.626345	−	0.203512i	−0.0213895	−	0.999771i	$-0.506809\pi$
$131$	−7.16884	−	2.32930i	−0.626345	−	0.203512i	−0.604955	+	0.796259i	$0.706809\pi$
$132$	−3.45019	+	6.71492i	−0.300300	+	0.584459i
$133$	1.86701	−	0.951290i	0.161890	−	0.0824873i
$134$	9.91890	−	7.20650i	0.856862	−	0.622547i
$135$	11.5806	−	0.943189i	0.996700	−	0.0811768i
$136$	4.03653	+	2.93271i	0.346130	+	0.251478i
$137$	−9.15207	−	1.44955i	−0.781914	−	0.123843i	−0.247300	−	0.968939i	$-0.579543\pi$
$137$	−9.15207	−	1.44955i	−0.781914	−	0.123843i	−0.534615	+	0.845096i	$0.679543\pi$
$138$	−2.37638	−	15.3408i	−0.202291	−	1.30589i
$139$	3.83373	−	5.27668i	0.325173	−	0.447562i	−0.614865	−	0.788633i	$-0.710789\pi$
$139$	3.83373	−	5.27668i	0.325173	−	0.447562i	0.940038	+	0.341070i	$0.110789\pi$
$140$	0.323393	+	3.52642i	0.0273317	+	0.298037i
$141$	−0.791351	+	1.08146i	−0.0666438	+	0.0910755i
$142$	0.502789	+	0.986779i	0.0421931	+	0.0828086i
$143$	16.8048	−	16.8048i	1.40529	−	1.40529i
$144$	2.85940	−	0.907659i	0.238283	−	0.0756383i
$145$	−6.95462	−	5.78621i	−0.577550	−	0.480519i
$146$	15.9809	−	5.19251i	1.32259	−	0.429735i
$147$	1.24319	−	7.68033i	0.102536	−	0.633463i
$148$	0.0106771	+	0.0674126i	0.000877653	+	0.00554128i
$149$	−17.4830			−1.43226			−0.716132	−	0.697964i	$-0.754089\pi$
$149$	−17.4830			−1.43226			−0.716132	+	0.697964i	$0.754089\pi$
$150$	7.80257	+	3.75765i	0.637077	+	0.306811i
$151$	15.0419			1.22409			0.612046	−	0.790822i	$-0.290347\pi$
$151$	15.0419			1.22409			0.612046	+	0.790822i	$0.290347\pi$
$152$	−0.206981	−	1.30683i	−0.0167884	−	0.105998i
$153$	14.7996	−	2.24113i	1.19647	−	0.181185i
$154$	−6.56489	+	2.13306i	−0.529014	+	0.171887i
$155$	1.59441	+	6.28275i	0.128066	+	0.504643i
$156$	−9.44392	−	0.0320584i	−0.756119	−	0.00256673i
$157$	10.8749	−	10.8749i	0.867911	−	0.867911i	−0.124330	−	0.992241i	$-0.539678\pi$
$157$	10.8749	−	10.8749i	0.867911	−	0.867911i	0.992241	+	0.124330i	$0.0396780\pi$
$158$	3.38191	+	6.63737i	0.269050	+	0.528041i
$159$	−11.3419	−	8.29933i	−0.899470	−	0.658180i
$160$	2.18084	+	0.493886i	0.172411	+	0.0390452i
$161$	8.34299	−	11.4831i	0.657519	−	0.904998i
$162$	4.19442	−	7.96284i	0.329545	−	0.625620i
$163$	−23.9735	−	3.79703i	−1.87775	−	0.297407i	−0.890305	−	0.455365i	$-0.849509\pi$
$163$	−23.9735	−	3.79703i	−1.87775	−	0.297407i	−0.987446	+	0.157958i	$0.949509\pi$
$164$	−0.0646149	−	0.0469455i	−0.00504557	−	0.00366582i
$165$	−3.78443	+	16.4514i	−0.294618	+	1.28074i
$166$	−3.73778	+	2.71566i	−0.290108	+	0.210776i
$167$	−8.70863	+	4.43727i	−0.673894	+	0.343366i	−0.757223	−	0.653156i	$-0.773445\pi$
$167$	−8.70863	+	4.43727i	−0.673894	+	0.343366i	0.0833296	+	0.996522i	$0.473445\pi$
$168$	2.43980	+	1.25359i	0.188235	+	0.0967167i
$169$	15.9107	+	5.16971i	1.22390	+	0.397670i
$170$	10.3617	+	4.13606i	0.794707	+	0.317221i
$171$	−3.19536	−	2.35488i	−0.244355	−	0.180082i
$172$	−1.34692	−	0.686288i	−0.102701	−	0.0523290i
$173$	1.33648	−	0.211678i	0.101611	−	0.0160936i	−0.105422	−	0.994428i	$-0.533619\pi$
$173$	1.33648	−	0.211678i	0.101611	−	0.0160936i	0.207033	+	0.978334i	$0.433619\pi$
$174$	−6.67206	+	2.14287i	−0.505807	+	0.162451i
$175$	2.64053	+	7.46516i	0.199606	+	0.564313i
$176$			4.35867i			0.328547i
$177$	−1.10101	+	0.556295i	−0.0827573	+	0.0418137i
$178$	−2.87401	+	5.64057i	−0.215417	+	0.422779i
$179$	−1.80244	−	5.54735i	−0.134721	−	0.414629i	0.860826	−	0.508900i	$-0.169948\pi$
$179$	−1.80244	−	5.54735i	−0.134721	−	0.414629i	−0.995547	+	0.0942716i	$0.969948\pi$
$180$	5.69812	−	3.53997i	0.424713	−	0.263854i
$181$	−2.49922	+	7.69182i	−0.185766	+	0.571729i	−0.999961	−	0.00886318i	$-0.997179\pi$
$181$	−2.49922	+	7.69182i	−0.185766	+	0.571729i	0.814195	+	0.580592i	$0.197179\pi$
$182$	−6.10586	−	6.10586i	−0.452596	−	0.452596i
$183$	7.80944	+	7.86264i	0.577291	+	0.581223i
$184$	−5.26810	−	7.25092i	−0.388369	−	0.534545i
$185$	0.0602199	+	0.140235i	0.00442745	+	0.0103103i
$186$	4.76983	+	1.56773i	0.349741	+	0.114952i
$187$	−3.40202	+	21.4795i	−0.248780	+	1.57074i
$188$	−0.121032	+	0.764166i	−0.00882717	+	0.0557325i
$189$	7.85178	−	2.46308i	0.571133	−	0.179163i
$190$	−1.16739	−	2.71853i	−0.0846917	−	0.197223i
$191$	7.75927	+	10.6797i	0.561441	+	0.772757i	0.991509	−	0.130039i	$-0.0415103\pi$
$191$	7.75927	+	10.6797i	0.561441	+	0.772757i	−0.430068	+	0.902797i	$0.641510\pi$
$192$	1.22890	−	1.22058i	0.0886879	−	0.0880878i
$193$	5.85434	+	5.85434i	0.421404	+	0.421404i	0.885687	−	0.464283i	$-0.153688\pi$
$193$	5.85434	+	5.85434i	0.421404	+	0.421404i	−0.464283	+	0.885687i	$0.653688\pi$
$194$	−3.67561	+	11.3124i	−0.263894	+	0.812181i
$195$	−20.4861	+	5.12492i	−1.46704	+	0.367003i
$196$	−1.38809	−	4.27211i	−0.0991494	−	0.305150i
$197$	−10.7134	+	21.0262i	−0.763298	+	1.49806i	0.100895	+	0.994897i	$0.467830\pi$
$197$	−10.7134	+	21.0262i	−0.763298	+	1.49806i	−0.864193	+	0.503160i	$0.832170\pi$
$198$	9.18315	+	9.30869i	0.652618	+	0.661540i
$199$		−	11.9416i		−	0.846519i	−0.906008	−	0.423260i	$-0.860886\pi$
$199$		−	11.9416i		−	0.846519i	0.906008	−	0.423260i	$-0.139114\pi$
$200$	4.99833	−	0.129088i	0.353436	−	0.00912789i
$201$	−6.49359	−	20.2185i	−0.458023	−	1.42610i
$202$	−7.19074	+	1.13890i	−0.505939	+	0.0801328i
$203$	−5.70906	−	2.90891i	−0.400698	−	0.204166i
$204$	7.00868	−	5.05584i	0.490706	−	0.353980i
$205$	−0.165865	−	0.0662081i	−0.0115845	−	0.00462417i
$206$	3.86433	+	1.25560i	0.269241	+	0.0874816i
$207$	−26.5277	−	4.38639i	−1.84380	−	0.304875i
$208$	−4.85820	+	2.47537i	−0.336855	+	0.171636i
$209$	4.66563	−	3.38978i	0.322728	−	0.234476i
$210$	5.97745	+	1.37504i	0.412483	+	0.0948865i
$211$	17.6913	+	12.8535i	1.21792	+	0.884868i	0.995925	−	0.0901803i	$-0.0287443\pi$
$211$	17.6913	+	12.8535i	1.21792	+	0.884868i	0.221991	+	0.975049i	$0.428744\pi$
$212$	−8.01423	−	1.26933i	−0.550420	−	0.0871779i
$213$	1.89562	−	0.293643i	0.129885	−	0.0201201i
$214$	7.34016	−	10.1029i	0.501763	−	0.690617i
$215$	−3.29673	−	0.746598i	−0.224835	−	0.0509176i
$216$	0.0529156	−	5.19588i	0.00360045	−	0.353535i
$217$	2.08416	+	4.09040i	0.141482	+	0.277675i
$218$	−5.98514	+	5.98514i	−0.405365	+	0.405365i
$219$	0.0987968	−	29.1040i	0.00667607	−	1.96667i
$220$	2.39738	+	9.44683i	0.161631	+	0.636905i
$221$	−25.8733	+	8.40673i	−1.74042	+	0.565498i
$222$	0.116699	+	0.0188895i	0.00783230	+	0.00126778i
$223$	3.61275	+	22.8100i	0.241928	+	1.52747i	0.747251	+	0.664542i	$0.231373\pi$
$223$	3.61275	+	22.8100i	0.241928	+	1.52747i	−0.505323	+	0.862930i	$0.668627\pi$
$224$	1.58368			0.105814
$225$	10.4028	−	10.8065i	0.693522	−	0.720435i
$226$	−2.84059			−0.188953
$227$	2.38471	+	15.0565i	0.158279	+	0.999334i	0.931114	+	0.364727i	$0.118838\pi$
$227$	2.38471	+	15.0565i	0.158279	+	0.999334i	−0.772835	+	0.634606i	$0.781162\pi$
$228$	−2.26226	−	0.366184i	−0.149822	−	0.0242511i
$229$	−18.0834	+	5.87564i	−1.19498	+	0.388273i	−0.837913	−	0.545804i	$-0.816224\pi$
$229$	−18.0834	+	5.87564i	−1.19498	+	0.388273i	−0.357070	+	0.934078i	$0.616224\pi$
$230$	−15.4061	−	12.8178i	−1.01585	−	0.845180i
$231$	−0.0405854	+	11.9558i	−0.00267032	+	0.786635i
$232$	−2.86089	+	2.86089i	−0.187827	+	0.187827i
$233$	0.567423	+	1.11363i	0.0371731	+	0.0729563i	0.908846	−	0.417132i	$-0.136965\pi$
$233$	0.567423	+	1.11363i	0.0371731	+	0.0729563i	−0.871673	+	0.490088i	$0.836965\pi$
$234$	−5.16023	+	15.5222i	−0.337335	+	1.01472i
$235$	0.157991	+	1.72280i	0.0103062	+	0.112383i
$236$	−0.418622	+	0.576184i	−0.0272500	+	0.0375064i
$237$	12.7505	−	1.97513i	0.828233	−	0.128299i
$238$	7.80438	+	1.23609i	0.505883	+	0.0801239i
$239$	−0.0867791	−	0.0630487i	−0.00561328	−	0.00407828i	0.584975	−	0.811051i	$-0.301104\pi$
$239$	−0.0867791	−	0.0630487i	−0.00561328	−	0.00407828i	−0.590588	+	0.806973i	$0.701104\pi$
$240$	1.99211	−	3.32137i	0.128590	−	0.214393i
$241$	−9.47730	+	6.88566i	−0.610486	+	0.443544i	−0.849586	−	0.527451i	$-0.823148\pi$
$241$	−9.47730	+	6.88566i	−0.610486	+	0.443544i	0.239099	+	0.970995i	$0.423148\pi$
$242$	−7.12626	+	3.63101i	−0.458093	+	0.233410i
$243$	−10.8340	−	11.2082i	−0.695004	−	0.719006i
$244$	6.08499	+	1.97713i	0.389552	+	0.126573i
$245$	−5.35827	−	8.49573i	−0.342327	−	0.542772i
$246$	−0.112192	+	0.0809315i	−0.00715308	+	0.00516001i
$247$	6.42797	+	3.27521i	0.409002	+	0.208397i
$248$	2.86311	−	0.453472i	0.181807	−	0.0287955i
$249$	2.44701	+	7.61903i	0.155073	+	0.482837i
$250$	10.7622	−	3.02899i	0.680662	−	0.191570i
$251$		−	30.0045i		−	1.89387i	−0.321431	−	0.946933i	$-0.604164\pi$
$251$		−	30.0045i		−	1.89387i	0.321431	−	0.946933i	$-0.395836\pi$
$252$	3.38222	−	3.33661i	0.213060	−	0.210187i
$253$	17.7352	−	34.8073i	1.11500	−	2.18831i
$254$	−0.225405	−	0.693725i	−0.0141432	−	0.0435282i
$255$	12.4095	−	14.8128i	0.777115	−	0.927615i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	10.3109	+	10.3109i	0.643174	+	0.643174i	0.951334	−	0.308161i	$-0.0997134\pi$
$257$	10.3109	+	10.3109i	0.643174	+	0.643174i	−0.308161	+	0.951334i	$0.599713\pi$
$258$	−1.85770	+	1.84513i	−0.115655	+	0.114873i
$259$	0.0635342	+	0.0874473i	0.00394782	+	0.00543371i
$260$	−9.16796	+	8.03717i	−0.568573	+	0.498444i
$261$	−0.0824049	+	12.1375i	−0.00510073	+	0.751290i
$262$	−1.17917	+	7.44497i	−0.0728492	+	0.459951i
$263$	0.896435	−	5.65987i	0.0552765	−	0.349002i	−0.944513	−	0.328475i	$-0.893465\pi$
$263$	0.896435	−	5.65987i	0.0552765	−	0.349002i	0.999789	−	0.0205276i	$-0.00653459\pi$
$264$	7.17198	+	2.35726i	0.441405	+	0.145080i
$265$	−18.0679	+	1.65693i	−1.10990	+	0.101785i
$266$	−1.23164	−	1.69521i	−0.0755169	−	0.103940i
$267$	7.72696	+	7.77960i	0.472882	+	0.476104i
$268$	−8.66943	−	8.66943i	−0.529570	−	0.529570i
$269$	−8.89631	+	27.3800i	−0.542418	+	1.66939i	0.184634	+	0.982807i	$0.440890\pi$
$269$	−8.89631	+	27.3800i	−0.542418	+	1.66939i	−0.727051	+	0.686583i	$0.759110\pi$
$270$	−2.74318	−	11.2905i	−0.166945	−	0.687117i
$271$	2.94335	+	9.05871i	0.178796	+	0.550277i	0.999786	−	0.0206645i	$-0.00657819\pi$
$271$	2.94335	+	9.05871i	0.178796	+	0.550277i	−0.820991	+	0.570942i	$0.806578\pi$
$272$	2.26515	−	4.44561i	0.137345	−	0.269555i
$273$	−13.3491	+	6.74471i	−0.807923	+	0.408209i
$274$			9.26615i			0.559789i
$275$	10.3920	+	19.1561i	0.626661	+	1.15516i
$276$	−14.7801	+	4.74695i	−0.889660	+	0.285733i
$277$	1.32775	−	0.210294i	0.0797766	−	0.0126354i	−0.116419	−	0.993200i	$-0.537141\pi$
$277$	1.32775	−	0.210294i	0.0797766	−	0.0126354i	0.196195	+	0.980565i	$0.437141\pi$
$278$	−5.81144	−	2.96108i	−0.348547	−	0.177594i
$279$	5.15926	−	7.00066i	0.308877	−	0.419119i
$280$	3.43241	−	0.871065i	0.205126	−	0.0520561i
$281$	3.45870	+	1.12380i	0.206329	+	0.0670403i	0.410358	−	0.911925i	$-0.365404\pi$
$281$	3.45870	+	1.12380i	0.206329	+	0.0670403i	−0.204029	+	0.978965i	$0.565404\pi$
$282$	1.19194	+	0.612430i	0.0709791	+	0.0364697i
$283$	23.2662	−	11.8547i	1.38303	−	0.704689i	0.405226	−	0.914216i	$-0.367193\pi$
$283$	23.2662	−	11.8547i	1.38303	−	0.704689i	0.977803	+	0.209528i	$0.0671927\pi$
$284$	0.895976	−	0.650965i	0.0531664	−	0.0386277i
$285$	−5.10456	+	0.450650i	−0.302368	+	0.0266942i
$286$	−19.2267	−	13.9690i	−1.13690	−	0.826007i
$287$	−0.124929	−	0.0197868i	−0.00737431	−	0.00116798i
$288$	−1.34379	−	2.68220i	−0.0791837	−	0.158050i
$289$	4.64021	−	6.38670i	0.272954	−	0.375688i
$290$	−4.62703	+	7.77416i	−0.271709	+	0.456515i
$291$	16.6261	+	12.1660i	0.974640	+	0.713185i
$292$	−7.62854	−	14.9719i	−0.446427	−	0.876162i
$293$	−7.70940	+	7.70940i	−0.450388	+	0.450388i	−0.895483	−	0.445095i	$-0.853170\pi$
$293$	−7.70940	+	7.70940i	−0.450388	+	0.450388i	0.445095	+	0.895483i	$0.353170\pi$
$294$	−7.78025	−	0.0264109i	−0.453754	−	0.00154032i
$295$	−0.590391	+	1.47905i	−0.0343739	+	0.0861138i
$296$	0.0649124	−	0.0210913i	0.00377295	−	0.00122591i
$297$	20.2834	−	10.0761i	1.17697	−	0.584673i
$298$	2.73495	+	17.2678i	0.158431	+	1.00030i
$299$	48.8685			2.82614
$300$	2.49080	−	8.29433i	0.143806	−	0.478873i
$301$	−2.39402			−0.137989
$302$	−2.35307	−	14.8567i	−0.135404	−	0.854908i
$303$	−2.01490	+	12.4480i	−0.115753	+	0.715117i
$304$	−1.25836	+	0.408866i	−0.0721719	+	0.0234501i
$305$	14.2759	+	0.938267i	0.817434	+	0.0537250i
$306$	−4.52870	−	14.2668i	−0.258889	−	0.815576i
$307$	12.2859	−	12.2859i	0.701191	−	0.701191i	−0.263476	−	0.964666i	$-0.584869\pi$
$307$	12.2859	−	12.2859i	0.701191	−	0.701191i	0.964666	+	0.263476i	$0.0848688\pi$
$308$	3.13378	+	6.15038i	0.178564	+	0.350451i
$309$	4.15594	−	5.67951i	0.236423	−	0.323096i
$310$	5.95598	−	2.55762i	0.338277	−	0.145263i
$311$	3.02551	−	4.16426i	0.171561	−	0.236134i	−0.714575	−	0.699559i	$-0.753380\pi$
$311$	3.02551	−	4.16426i	0.171561	−	0.236134i	0.886136	+	0.463425i	$0.153380\pi$
$312$	1.44569	+	9.33266i	0.0818461	+	0.528358i
$313$	−10.3075	−	1.63255i	−0.582617	−	0.0922774i	−0.141833	−	0.989891i	$-0.545300\pi$
$313$	−10.3075	−	1.63255i	−0.582617	−	0.0922774i	−0.440784	+	0.897613i	$0.645300\pi$
$314$	−12.4422	−	9.03980i	−0.702155	−	0.510146i
$315$	5.49529	−	9.09196i	0.309625	−	0.512274i
$316$	6.02660	−	4.37858i	0.339023	−	0.246315i
$317$	24.5645	−	12.5162i	1.37968	−	0.702981i	0.402503	−	0.915419i	$-0.368140\pi$
$317$	24.5645	−	12.5162i	1.37968	−	0.702981i	0.977175	+	0.212438i	$0.0681404\pi$
$318$	−6.42289	+	12.5006i	−0.360178	+	0.700996i
$319$	−16.7717	−	5.44945i	−0.939034	−	0.305111i
$320$	0.146647	−	2.23125i	0.00819781	−	0.124731i
$321$	−12.6540	−	17.5417i	−0.706280	−	0.979083i
$322$	−12.6469	−	6.44391i	−0.704784	−	0.359105i
$323$	−6.52033	+	1.03272i	−0.362801	+	0.0574620i
$324$	−8.52096	−	2.89712i	−0.473387	−	0.160951i
$325$	−15.4497	+	22.4621i	−0.856993	+	1.24597i
$326$			24.2723i			1.34432i
$327$	6.61136	+	13.0851i	0.365609	+	0.723610i
$328$	−0.0362595	+	0.0711632i	−0.00200210	+	0.00392933i
$329$	0.378632	+	1.16531i	0.0208747	+	0.0642456i
$330$	16.8409	+	1.16428i	0.927058	+	0.0640913i
$331$	4.85839	−	14.9526i	0.267042	−	0.821869i	−0.724175	−	0.689617i	$-0.757779\pi$
$331$	4.85839	−	14.9526i	0.267042	−	0.821869i	0.991216	−	0.132253i	$-0.0422210\pi$
$332$	3.26694	+	3.26694i	0.179297	+	0.179297i
$333$	0.0941950	−	0.181806i	0.00516185	−	0.00996291i
$334$	5.74497	+	7.90727i	0.314351	+	0.432666i
$335$	−23.5582	−	14.0214i	−1.28712	−	0.766072i
$336$	0.856489	−	2.60587i	0.0467253	−	0.142162i
$337$	3.27427	−	20.6729i	0.178361	−	1.12613i	−0.722292	−	0.691588i	$-0.756912\pi$
$337$	3.27427	−	20.6729i	0.178361	−	1.12613i	0.900653	−	0.434538i	$-0.143088\pi$
$338$	2.61708	−	16.5236i	0.142350	−	0.898764i
$339$	−1.53625	+	4.67405i	−0.0834377	+	0.253860i
$340$	2.46421	−	10.8812i	0.133641	−	0.590114i
$341$	7.42660	+	10.2218i	0.402173	+	0.553544i
$342$	−1.82602	+	3.52441i	−0.0987398	+	0.190578i
$343$	−12.8690	−	12.8690i	−0.694863	−	0.694863i
$344$	−0.467135	+	1.43769i	−0.0251862	+	0.0775152i
$345$	−29.4230	+	18.4178i	−1.58408	+	0.991583i
$346$	−0.418144	−	1.28691i	−0.0224796	−	0.0691850i
$347$	4.78862	−	9.39820i	0.257067	−	0.504522i	−0.726018	−	0.687676i	$-0.758631\pi$
$347$	4.78862	−	9.39820i	0.257067	−	0.504522i	0.983084	+	0.183155i	$0.0586309\pi$
$348$	3.16023	+	6.25469i	0.169406	+	0.335287i
$349$			26.2133i			1.40316i	0.712588	+	0.701582i	$0.247523\pi$
$349$			26.2133i			1.40316i	−0.712588	+	0.701582i	$0.752477\pi$
$350$	6.96018	−	3.77583i	0.372037	−	0.201827i
$351$	22.7502	+	16.8856i	1.21432	+	0.901289i
$352$	4.30501	−	0.681846i	0.229458	−	0.0363425i
$353$	3.70269	+	1.88662i	0.197074	+	0.100414i	0.549743	−	0.835334i	$-0.314726\pi$
$353$	3.70269	+	1.88662i	0.197074	+	0.100414i	−0.352669	+	0.935748i	$0.614726\pi$
$354$	0.721683	+	1.00044i	0.0383570	+	0.0531725i
$355$	1.58386	−	1.90369i	0.0840626	−	0.101037i
$356$	6.02072	+	1.95625i	0.319098	+	0.103681i
$357$	6.25471	−	12.1732i	0.331034	−	0.644275i
$358$	−5.19709	+	2.64805i	−0.274675	+	0.139954i
$359$	−4.75359	+	3.45368i	−0.250885	+	0.182279i	−0.706119	−	0.708093i	$-0.749556\pi$
$359$	−4.75359	+	3.45368i	−0.250885	+	0.182279i	0.455234	+	0.890372i	$0.349556\pi$
$360$	−4.38777	−	5.07420i	−0.231256	−	0.267434i
$361$	−13.9550	−	10.1389i	−0.734475	−	0.533627i
$362$	7.98809	+	1.26519i	0.419844	+	0.0664968i
$363$	2.12062	+	13.6896i	0.111303	+	0.718520i
$364$	−5.07552	+	6.98585i	−0.266029	+	0.366158i
$365$	−24.7687	−	28.2536i	−1.29646	−	1.47886i
$366$	6.54418	−	8.94329i	0.342070	−	0.467473i
$367$	−7.71561	−	15.1427i	−0.402751	−	0.790444i	0.597181	−	0.802107i	$-0.296288\pi$
$367$	−7.71561	−	15.1427i	−0.402751	−	0.790444i	−0.999932	+	0.0116626i	$0.996288\pi$
$368$	−6.33753	+	6.33753i	−0.330367	+	0.330367i
$369$	0.0724933	+	0.228375i	0.00377385	+	0.0118888i
$370$	0.129088	−	0.0814160i	0.00671097	−	0.00423262i
$371$	−12.2213	+	3.97093i	−0.634496	+	0.206160i
$372$	0.802265	−	4.95635i	0.0415955	−	0.256975i
$373$	−4.29420	−	27.1125i	−0.222345	−	1.40383i	−0.806041	−	0.591859i	$-0.798394\pi$
$373$	−4.29420	−	27.1125i	−0.222345	−	1.40383i	0.583696	−	0.811972i	$-0.301606\pi$
$374$	21.7473			1.12452
$375$	0.836377	−	19.3468i	0.0431903	−	0.999067i
$376$	0.773692			0.0399001
$377$	−3.45098	−	21.7887i	−0.177735	−	1.12217i
$378$	−3.66105	−	7.36980i	−0.188304	−	0.379061i
$379$	14.0563	−	4.56718i	0.722026	−	0.234600i	0.0751246	−	0.997174i	$-0.476065\pi$
$379$	14.0563	−	4.56718i	0.722026	−	0.234600i	0.646901	+	0.762574i	$0.276065\pi$
$380$	−2.50244	+	1.57829i	−0.128372	+	0.0809647i
$381$	−1.26339	−	0.00428874i	−0.0647257	−	0.000219719i
$382$	9.33442	−	9.33442i	0.477590	−	0.477590i
$383$	−7.56228	−	14.8418i	−0.386414	−	0.758381i	0.613085	−	0.790017i	$-0.289928\pi$
$383$	−7.56228	−	14.8418i	−0.386414	−	0.758381i	−0.999499	+	0.0316359i	$0.989928\pi$
$384$	−1.39779	−	1.02282i	−0.0713309	−	0.0521958i
$385$	10.1749	+	11.6065i	0.518561	+	0.591520i
$386$	4.86644	−	6.69808i	0.247695	−	0.340923i
$387$	2.03138	+	4.05463i	0.103261	+	0.206109i
$388$	11.7481	+	1.86071i	0.596419	+	0.0944635i
$389$	−19.7696	−	14.3635i	−1.00236	−	0.728257i	−0.0397671	−	0.999209i	$-0.512662\pi$
$389$	−19.7696	−	14.3635i	−1.00236	−	0.728257i	−0.962593	+	0.270952i	$0.912662\pi$
$390$	8.26655	+	19.4321i	0.418593	+	0.983984i
$391$	−36.1779	+	26.2848i	−1.82960	+	1.32928i
$392$	−4.00236	+	2.03931i	−0.202150	+	0.103001i
$393$	11.6126	+	5.96666i	0.585779	+	0.300978i
$394$	22.4433	+	7.29228i	1.13068	+	0.367380i
$395$	10.6535	−	12.8048i	0.536037	−	0.644278i
$396$	7.75753	−	10.5263i	0.389830	−	0.528966i
$397$	−6.08913	−	3.10257i	−0.305605	−	0.155713i	0.294462	−	0.955663i	$-0.404859\pi$
$397$	−6.08913	−	3.10257i	−0.305605	−	0.155713i	−0.600067	+	0.799950i	$0.704859\pi$
$398$	−11.7946	+	1.86808i	−0.591210	+	0.0936384i
$399$	−3.45549	+	1.10980i	−0.172991	+	0.0555596i
$400$	−0.909410	−	4.91660i	−0.0454705	−	0.245830i
$401$			22.7020i			1.13368i	0.823826	+	0.566842i	$0.191835\pi$
$401$			22.7020i			1.13368i	−0.823826	+	0.566842i	$0.808165\pi$
$402$	−18.9538	+	9.57652i	−0.945327	+	0.477633i
$403$	−7.17560	+	14.0829i	−0.357442	+	0.701520i
$404$	2.24976	+	6.92405i	0.111930	+	0.344484i
$405$	−20.0615	−	1.59236i	−0.996865	−	0.0791252i
$406$	−1.98001	+	6.09383i	−0.0982660	+	0.302432i
$407$	0.210358	+	0.210358i	0.0104271	+	0.0104271i
$408$	−6.09000	−	6.13149i	−0.301500	−	0.303554i
$409$	8.27872	+	11.3947i	0.409357	+	0.563431i	0.963061	−	0.269282i	$-0.0867864\pi$
$409$	8.27872	+	11.3947i	0.409357	+	0.563431i	−0.553705	+	0.832713i	$0.686786\pi$
$410$	−0.0394459	+	0.174180i	−0.00194809	+	0.00860216i
$411$	15.2470	+	5.01134i	0.752079	+	0.247191i
$412$	0.635624	−	4.01317i	0.0313149	−	0.197715i
$413$	−0.176443	+	1.11401i	−0.00868217	+	0.0548171i
$414$	−0.182546	+	26.8873i	−0.00897163	+	1.32144i
$415$	8.87756	+	5.28376i	0.435782	+	0.259369i
$416$	3.20489	+	4.41115i	0.157133	+	0.216274i
$417$	−8.01527	+	7.96104i	−0.392509	+	0.389854i
$418$	−4.07791	−	4.07791i	−0.199457	−	0.199457i
$419$	−5.00642	+	15.4082i	−0.244579	+	0.752738i	0.751126	+	0.660159i	$0.229511\pi$
$419$	−5.00642	+	15.4082i	−0.244579	+	0.752738i	−0.995705	+	0.0925792i	$0.970489\pi$
$420$	0.423028	−	6.11896i	0.0206417	−	0.298575i
$421$	0.809743	+	2.49213i	0.0394645	+	0.121459i	0.968848	−	0.247657i	$-0.0796605\pi$
$421$	0.809743	+	2.49213i	0.0394645	+	0.121459i	−0.929383	+	0.369116i	$0.879661\pi$
$422$	9.92768	−	19.4842i	0.483272	−	0.948475i
$423$	1.65235	−	1.63007i	0.0803401	−	0.0792566i
$424$			8.11413i			0.394057i
$425$	−0.644075	−	24.9388i	−0.0312422	−	1.20971i
$426$	−0.586568	−	1.82634i	−0.0284193	−	0.0884865i
$427$	10.0079	−	1.58509i	0.484314	−	0.0767078i
$428$	−11.1267	−	5.66935i	−0.537831	−	0.274038i
$429$	−33.3836	+	24.0819i	−1.61178	+	1.16269i
$430$	−0.221683	+	3.37294i	−0.0106905	+	0.162658i
$431$	21.5704	+	7.00864i	1.03901	+	0.337594i	0.778346	−	0.627835i	$-0.216059\pi$
$431$	21.5704	+	7.00864i	1.03901	+	0.337594i	0.260663	+	0.965430i	$0.416059\pi$
$432$	−5.14019	+	0.760551i	−0.247308	+	0.0365920i
$433$	15.3259	−	7.80892i	0.736514	−	0.375273i	−0.0451434	−	0.998981i	$-0.514374\pi$
$433$	15.3259	−	7.80892i	0.736514	−	0.375273i	0.781658	+	0.623708i	$0.214374\pi$
$434$	3.71401	−	2.69838i	0.178278	−	0.129527i
$435$	10.2896	+	11.8180i	0.493349	+	0.566630i
$436$	6.84773	+	4.97517i	0.327947	+	0.238267i
$437$	11.7126	+	1.85510i	0.560291	+	0.0887413i
$438$	−28.7611	+	4.45529i	−1.37426	+	0.212882i
$439$	−9.32959	+	12.8411i	−0.445277	+	0.612872i	−0.971375	−	0.237553i	$-0.923655\pi$
$439$	−9.32959	+	12.8411i	−0.445277	+	0.612872i	0.526097	+	0.850424i	$0.323655\pi$
$440$	8.95549	−	3.84567i	0.426936	−	0.183335i
$441$	−4.25119	+	12.7877i	−0.202438	+	0.608940i
$442$	12.3507	+	24.2396i	0.587463	+	1.15296i
$443$	−6.25112	+	6.25112i	−0.297000	+	0.297000i	−0.839838	−	0.542838i	$-0.817350\pi$
$443$	−6.25112	+	6.25112i	−0.297000	+	0.297000i	0.542838	+	0.839838i	$0.317350\pi$
$444$	0.000401300	−	0.118217i	1.90449e−5	−	0.00561032i
$445$	14.1251	+	0.928357i	0.669594	+	0.0440084i
$446$	21.9640	−	7.13655i	1.04003	−	0.337925i
$447$	29.8924	+	4.83857i	1.41386	+	0.228856i
$448$	−0.247742	−	1.56418i	−0.0117047	−	0.0739007i
$449$	4.48699			0.211754			0.105877	−	0.994379i	$-0.466235\pi$
$449$	4.48699			0.211754			0.105877	+	0.994379i	$0.466235\pi$
$450$	−12.3008	−	8.58425i	−0.579867	−	0.404665i
$451$	−0.348120			−0.0163923
$452$	0.444366	+	2.80561i	0.0209012	+	0.131965i
$453$	−25.7186	−	4.16297i	−1.20837	−	0.195593i
$454$	14.4981	−	4.71070i	0.680428	−	0.221084i
$455$	−7.15810	+	17.9326i	−0.335577	+	0.840691i
$456$	−0.00777942	+	2.29170i	−0.000364305	+	0.107318i
$457$	−21.3476	+	21.3476i	−0.998599	+	0.998599i	−0.999999	−	0.00140011i	$-0.999554\pi$
$457$	−21.3476	+	21.3476i	−0.998599	+	0.998599i	0.00140011	+	0.999999i	$0.499554\pi$
$458$	8.63217	+	16.9416i	0.403355	+	0.791628i
$459$	−25.9245	−	0.264019i	−1.21005	−	0.0123233i
$460$	−10.2499	+	17.2216i	−0.477906	+	0.802959i
$461$	−15.2106	+	20.9356i	−0.708430	+	0.975070i	0.291400	+	0.956601i	$0.405879\pi$
$461$	−15.2106	+	20.9356i	−0.708430	+	0.975070i	−0.999829	+	0.0184685i	$0.994121\pi$
$462$	11.8150	−	1.83022i	0.549682	−	0.0851494i
$463$	10.1474	+	1.60719i	0.471590	+	0.0746925i	0.387706	−	0.921783i	$-0.373268\pi$
$463$	10.1474	+	1.60719i	0.471590	+	0.0746925i	0.0838837	+	0.996476i	$0.473268\pi$
$464$	3.27321	+	2.37813i	0.151955	+	0.110402i
$465$	−0.987320	−	11.1835i	−0.0457859	−	0.518622i
$466$	1.01116	−	0.734647i	0.0468409	−	0.0340319i
$467$	−13.5652	+	6.91180i	−0.627722	+	0.319840i	−0.738753	−	0.673977i	$-0.764585\pi$
$467$	−13.5652	+	6.91180i	−0.627722	+	0.319840i	0.111031	+	0.993817i	$0.464585\pi$
$468$	16.1383	+	2.66849i	0.745994	+	0.123351i
$469$	−18.4663	−	6.00006i	−0.852694	−	0.277057i
$470$	1.67687	−	0.425550i	0.0773483	−	0.0196292i
$471$	−21.6036	+	15.5842i	−0.995441	+	0.718080i
$472$	0.634577	+	0.323333i	0.0292088	+	0.0148826i
$473$	−6.50779	+	1.03073i	−0.299228	+	0.0473931i
$474$	−3.94543	−	12.2845i	−0.181220	−	0.564247i
$475$	−4.55560	+	4.79714i	−0.209025	+	0.220108i
$476$		−	7.90166i		−	0.362172i
$477$	17.0954	+	17.3291i	0.782745	+	0.793447i
$478$	−0.0486972	+	0.0955737i	−0.00222736	+	0.00437144i
$479$	−5.66185	−	17.4254i	−0.258697	−	0.796186i	−0.993079	−	0.117450i	$-0.962528\pi$
$479$	−5.66185	−	17.4254i	−0.258697	−	0.796186i	0.734382	−	0.678736i	$-0.237472\pi$
$480$	−3.59211	−	1.44801i	−0.163957	−	0.0660924i
$481$	−0.115000	+	0.353933i	−0.00524355	+	0.0161380i
$482$	8.28346	+	8.28346i	0.377301	+	0.377301i
$483$	−17.4429	+	17.3248i	−0.793678	+	0.788307i
$484$	4.70110	+	6.47051i	0.213686	+	0.294114i
$485$	26.4858	−	2.42891i	1.20266	−	0.110291i
$486$	−9.37539	+	12.4540i	−0.425276	+	0.564925i
$487$	−0.621987	+	3.92707i	−0.0281849	+	0.177953i	−0.997765	−	0.0668221i	$-0.978714\pi$
$487$	−0.621987	+	3.92707i	−0.0281849	+	0.177953i	0.969580	+	0.244775i	$0.0787140\pi$
$488$	1.00089	−	6.31937i	0.0453081	−	0.286064i
$489$	39.9390	+	13.1270i	1.80610	+	0.593624i
$490$	−7.55291	+	6.62132i	−0.341206	+	0.299121i
$491$	−11.8356	−	16.2903i	−0.534132	−	0.735170i	0.453621	−	0.891195i	$-0.350132\pi$
$491$	−11.8356	−	16.2903i	−0.534132	−	0.735170i	−0.987753	+	0.156025i	$0.950132\pi$
$492$	0.0974858	+	0.0981499i	0.00439500	+	0.00442494i
$493$	14.2742	+	14.2742i	0.642878	+	0.642878i
$494$	2.22933	−	6.86119i	0.100302	−	0.308699i
$495$	11.0237	−	27.0811i	0.495477	−	1.21721i
$496$	−0.895777	−	2.75692i	−0.0402216	−	0.123789i
$497$	0.796257	−	1.56274i	0.0357170	−	0.0700985i
$498$	7.14243	−	3.60876i	0.320060	−	0.161713i
$499$		−	26.9424i		−	1.20611i	−0.797700	−	0.603054i	$-0.793950\pi$
$499$		−	26.9424i		−	1.20611i	0.797700	−	0.603054i	$-0.206050\pi$
$500$	−4.67528	−	10.1559i	−0.209085	−	0.454184i
$501$	16.1180	−	5.17664i	0.720101	−	0.231275i
$502$	−29.6351	+	4.69374i	−1.32268	+	0.209492i
$503$	10.7060	+	5.45499i	0.477358	+	0.243226i	0.676078	−	0.736830i	$-0.263678\pi$
$503$	10.7060	+	5.45499i	0.477358	+	0.243226i	−0.198720	+	0.980056i	$0.563678\pi$
$504$	−3.82462	−	2.81862i	−0.170362	−	0.125551i
$505$	8.68445	+	13.7695i	0.386453	+	0.612735i
$506$	−37.1531	−	12.0718i	−1.65166	−	0.536656i
$507$	−25.7734	−	13.2426i	−1.14464	−	0.588124i
$508$	−0.649923	+	0.331152i	−0.0288357	+	0.0146925i
$509$	33.2088	−	24.1276i	1.47196	−	1.06944i	0.491914	−	0.870644i	$-0.336297\pi$
$509$	33.2088	−	24.1276i	1.47196	−	1.06944i	0.980041	−	0.198794i	$-0.0637025\pi$
$510$	−16.5717	−	9.93951i	−0.733808	−	0.440129i
$511$	−21.5288	−	15.6416i	−0.952378	−	0.691943i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	4.81169	+	4.91070i	0.212441	+	0.216813i
$514$	8.57094	−	11.7969i	0.378048	−	0.520339i
$515$	−0.829719	−	9.04762i	−0.0365618	−	0.398686i
$516$	2.11302	+	1.54618i	0.0930204	+	0.0680669i
$517$	1.53098	+	3.00471i	0.0673323	+	0.132147i
$518$	0.0764317	−	0.0764317i	0.00335822	−	0.00335822i
$519$	−2.34370	−	0.00795594i	−0.102877	−	0.000349227i
$520$	9.37241	+	7.79780i	0.411007	+	0.341956i
$521$	−11.9997	+	3.89893i	−0.525715	+	0.170815i	−0.559837	−	0.828602i	$-0.689136\pi$
$521$	−11.9997	+	3.89893i	−0.525715	+	0.170815i	0.0341223	+	0.999418i	$0.489136\pi$
$522$	12.0009	−	1.81733i	0.525266	−	0.0795422i
$523$	−4.31549	−	27.2469i	−0.188703	−	1.19142i	−0.882168	−	0.470934i	$-0.843917\pi$
$523$	−4.31549	−	27.2469i	−0.188703	−	1.19142i	0.693465	−	0.720490i	$-0.256083\pi$
$524$	7.53777			0.329289
$525$	−2.44873	−	13.4947i	−0.106871	−	0.588957i
$526$	−5.73042			−0.249858
$527$	−2.26256	−	14.2853i	−0.0985588	−	0.622276i
$528$	1.20630	−	7.45244i	0.0524973	−	0.324326i
$529$	54.5228	−	17.7155i	2.37056	−	0.770241i
$530$	4.46298	+	17.5863i	0.193860	+	0.763899i
$531$	2.03647	−	0.646437i	0.0883752	−	0.0280530i
$532$	−1.48167	+	1.48167i	−0.0642385	+	0.0642385i
$533$	−0.197704	−	0.388016i	−0.00856352	−	0.0168068i
$534$	6.47506	−	8.84882i	0.280203	−	0.382926i
$535$	−27.2340	−	6.16756i	−1.17743	−	0.266647i
$536$	−7.20650	+	9.91890i	−0.311273	+	0.428431i
$537$	1.54654	+	9.98369i	0.0667380	+	0.430828i
$538$	28.4346	+	4.50360i	1.22590	+	0.194164i
$539$	−15.8397	−	11.5082i	−0.682264	−	0.495694i
$540$	−10.7223	+	4.47563i	−0.461416	+	0.192600i
$541$	9.58802	−	6.96610i	0.412221	−	0.299496i	−0.362279	−	0.932070i	$-0.618001\pi$
$541$	9.58802	−	6.96610i	0.412221	−	0.299496i	0.774500	+	0.632573i	$0.218001\pi$
$542$	8.48674	−	4.32421i	0.364537	−	0.185741i
$543$	6.40194	−	12.4598i	0.274733	−	0.534700i
$544$	−4.74523	−	1.54182i	−0.203450	−	0.0661049i
$545$	17.5780	+	7.01657i	0.752959	+	0.300557i
$546$	8.74993	+	12.1296i	0.374462	+	0.519100i
$547$	−11.2529	−	5.73365i	−0.481140	−	0.245153i	0.196560	−	0.980492i	$-0.437023\pi$
$547$	−11.2529	−	5.73365i	−0.481140	−	0.245153i	−0.677700	+	0.735339i	$0.737023\pi$
$548$	9.15207	−	1.44955i	0.390957	−	0.0619215i
$549$	−11.1765	−	15.6049i	−0.477002	−	0.665999i
$550$	17.2946	−	13.2607i	0.737444	−	0.565439i
$551$		−	5.35322i		−	0.228055i
$552$	7.00063	+	13.8556i	0.297967	+	0.589733i
$553$	5.35586	−	10.5115i	0.227754	−	0.446993i
$554$	−0.415411	−	1.27850i	−0.0176491	−	0.0543184i
$555$	−0.0641525	−	0.256440i	−0.00272312	−	0.0108853i
$556$	−2.01551	+	6.20311i	−0.0854768	+	0.263070i
$557$	−14.4201	−	14.4201i	−0.611000	−	0.611000i	0.332207	−	0.943207i	$-0.392207\pi$
$557$	−14.4201	−	14.4201i	−0.611000	−	0.611000i	−0.943207	+	0.332207i	$0.892207\pi$
$558$	−7.72156	−	4.00059i	−0.326879	−	0.169359i
$559$	−4.84476	−	6.66824i	−0.204912	−	0.282037i
$560$	−1.39729	−	3.25389i	−0.0590462	−	0.137502i
$561$	11.7614	−	35.7841i	0.496567	−	1.51080i
$562$	0.568904	−	3.59192i	0.0239978	−	0.151516i
$563$	−3.91368	+	24.7100i	−0.164942	+	1.04140i	0.756814	+	0.653631i	$0.226755\pi$
$563$	−3.91368	+	24.7100i	−0.164942	+	1.04140i	−0.921756	+	0.387771i	$0.873245\pi$
$564$	0.418429	−	1.27307i	0.0176191	−	0.0536060i
$565$	2.50626	+	5.83638i	0.105439	+	0.245538i
$566$	−15.3484	−	21.1252i	−0.645140	−	0.887959i
$567$	−14.1066	+	2.03833i	−0.592422	+	0.0856017i
$568$	−0.783112	−	0.783112i	−0.0328586	−	0.0328586i
$569$	−11.3127	+	34.8170i	−0.474254	+	1.45960i	0.372706	+	0.927949i	$0.378430\pi$
$569$	−11.3127	+	34.8170i	−0.474254	+	1.45960i	−0.846961	+	0.531655i	$0.821570\pi$
$570$	1.24363	+	4.97122i	0.0520900	+	0.208221i
$571$	6.22100	+	19.1463i	0.260341	+	0.801246i	0.992730	+	0.120361i	$0.0384051\pi$
$571$	6.22100	+	19.1463i	0.260341	+	0.801246i	−0.732389	+	0.680886i	$0.761595\pi$
$572$	−10.7893	+	21.1753i	−0.451125	+	0.885382i
$573$	−10.3111	−	20.4076i	−0.430751	−	0.852539i
$574$			0.126486i			0.00527942i
$575$	−12.7431	+	42.9631i	−0.531423	+	1.79169i
$576$	−2.43897	+	1.74684i	−0.101624	+	0.0727849i
$577$	−4.58006	+	0.725410i	−0.190670	+	0.0301992i	−0.251039	−	0.967977i	$-0.580772\pi$
$577$	−4.58006	+	0.725410i	−0.190670	+	0.0301992i	0.0603688	+	0.998176i	$0.480772\pi$
$578$	−7.03396	−	3.58398i	−0.292574	−	0.149074i
$579$	−8.38949	−	11.6300i	−0.348655	−	0.483325i
$580$	8.40228	+	3.35392i	0.348886	+	0.139264i
$581$	6.95874	+	2.26103i	0.288697	+	0.0938034i
$582$	9.41534	−	18.3246i	0.390278	−	0.759579i
$583$	−31.5121	+	16.0562i	−1.30510	+	0.664980i
$584$	−13.5942	+	9.87674i	−0.562530	+	0.408702i
$585$	36.4453	−	3.09289i	1.50683	−	0.127875i
$586$	8.82050	+	6.40847i	0.364372	+	0.264731i
$587$	−3.32343	−	0.526380i	−0.137173	−	0.0217260i	0.0874705	−	0.996167i	$-0.472122\pi$
$587$	−3.32343	−	0.526380i	−0.137173	−	0.0217260i	−0.224643	+	0.974441i	$0.572122\pi$
$588$	1.19101	+	7.68860i	0.0491166	+	0.317072i
$589$	−2.25442	+	3.10294i	−0.0928918	+	0.127855i
$590$	1.55320	+	0.351747i	0.0639443	+	0.0144812i
$591$	24.1369	−	32.9856i	0.992861	−	1.35685i
$592$	−0.0309862	−	0.0608138i	−0.00127352	−	0.00249943i
$593$	14.1294	−	14.1294i	0.580225	−	0.580225i	−0.354740	−	0.934965i	$-0.615431\pi$
$593$	14.1294	−	14.1294i	0.580225	−	0.580225i	0.934965	+	0.354740i	$0.115431\pi$
$594$	−13.1251	−	18.4575i	−0.538528	−	0.757320i
$595$	−4.34612	−	17.1258i	−0.178173	−	0.702089i
$596$	16.6273	−	5.40255i	0.681082	−	0.221297i
$597$	−3.30494	+	20.4177i	−0.135262	+	0.835643i
$598$	−7.64473	−	48.2669i	−0.312616	−	1.97378i
$599$	9.39141			0.383723			0.191861	−	0.981422i	$-0.438548\pi$
$599$	9.39141			0.383723			0.191861	+	0.981422i	$0.438548\pi$
$600$	−8.58186	−	1.16262i	−0.350353	−	0.0474636i
$601$	−33.0912			−1.34982			−0.674908	−	0.737901i	$-0.735817\pi$
$601$	−33.0912			−1.34982			−0.674908	+	0.737901i	$0.735817\pi$
$602$	0.374507	+	2.36454i	0.0152638	+	0.0963715i
$603$	5.50709	+	36.3667i	0.224266	+	1.48097i
$604$	−14.3057	+	4.64820i	−0.582091	+	0.189133i
$605$	13.7479	+	11.4382i	0.558934	+	0.465030i
$606$	12.6099	+	0.0428057i	0.512242	+	0.00173886i
$607$	−6.13790	+	6.13790i	−0.249130	+	0.249130i	−0.820613	−	0.571484i	$-0.806368\pi$
$607$	−6.13790	+	6.13790i	−0.249130	+	0.249130i	0.571484	+	0.820613i	$0.306368\pi$
$608$	0.600683	+	1.17891i	0.0243609	+	0.0478110i
$609$	8.95627	+	6.55368i	0.362926	+	0.265569i
$610$	−1.30652	−	14.2469i	−0.0528996	−	0.576840i
$611$	−2.47959	+	3.41287i	−0.100314	+	0.138070i
$612$	−13.3827	+	6.70476i	−0.540962	+	0.271024i
$613$	−0.210830	−	0.0333923i	−0.00851536	−	0.00134870i	0.152175	−	0.988354i	$-0.451372\pi$
$613$	−0.210830	−	0.0333923i	−0.00851536	−	0.00134870i	−0.160691	+	0.987005i	$0.551372\pi$
$614$	−14.0565	−	10.2127i	−0.567275	−	0.412149i
$615$	0.265272	+	0.159107i	0.0106968	+	0.00641581i
$616$	5.58443	−	4.05733i	0.225003	−	0.163474i
$617$	25.4122	−	12.9482i	1.02306	−	0.521274i	0.139808	−	0.990179i	$-0.455351\pi$
$617$	25.4122	−	12.9482i	1.02306	−	0.521274i	0.883249	+	0.468905i	$0.155351\pi$
$618$	−6.25972	−	3.21630i	−0.251803	−	0.129379i
$619$	20.8855	+	6.78613i	0.839461	+	0.272757i	0.697025	−	0.717047i	$-0.254507\pi$
$619$	20.8855	+	6.78613i	0.839461	+	0.272757i	0.142436	+	0.989804i	$0.454507\pi$
$620$	−3.45785	−	5.48255i	−0.138871	−	0.220184i
$621$	44.1430	+	14.8416i	1.77140	+	0.595573i
$622$	−4.58629	−	2.33683i	−0.183893	−	0.0936984i
$623$	9.90215	−	1.56835i	0.396721	−	0.0628345i
$624$	8.99161	−	2.88784i	0.359952	−	0.115606i
$625$	−15.7190	−	19.4400i	−0.628761	−	0.777598i
$626$			10.4360i			0.417108i
$627$	−8.91543	+	4.50458i	−0.356048	+	0.179896i
$628$	−6.98212	+	13.7032i	−0.278617	+	0.546816i
$629$	−0.105234	−	0.323876i	−0.00419594	−	0.0129138i
$630$	−9.83967	−	4.00534i	−0.392022	−	0.159577i
$631$	−6.16753	+	18.9817i	−0.245526	+	0.755650i	0.750024	+	0.661411i	$0.230042\pi$
$631$	−6.16753	+	18.9817i	−0.245526	+	0.755650i	−0.995550	+	0.0942396i	$0.969958\pi$
$632$	−5.26744	−	5.26744i	−0.209528	−	0.209528i
$633$	−26.6912	−	26.8730i	−1.06088	−	1.06811i
$634$	−16.2048	−	22.3041i	−0.643577	−	0.885807i
$635$	−1.22648	+	1.07520i	−0.0486713	+	0.0426681i
$636$	13.3514	+	4.38830i	0.529418	+	0.174007i
$637$	3.83144	−	24.1908i	0.151807	−	0.958473i
$638$	−2.75869	+	17.4177i	−0.109218	+	0.689572i
$639$	−3.32239	−	0.0225567i	−0.131432	−	0.000892329i
$640$	−2.22672	+	0.204204i	−0.0880190	+	0.00807186i
$641$	−11.5288	−	15.8680i	−0.455359	−	0.626748i	0.518179	−	0.855272i	$-0.326610\pi$
$641$	−11.5288	−	15.8680i	−0.455359	−	0.626748i	−0.973538	+	0.228524i	$0.926610\pi$
$642$	−15.3462	+	15.2424i	−0.605667	+	0.601569i
$643$	10.1389	+	10.1389i	0.399838	+	0.399838i	0.878176	−	0.478338i	$-0.158760\pi$
$643$	10.1389	+	10.1389i	0.399838	+	0.399838i	−0.478338	+	0.878176i	$0.658760\pi$
$644$	−4.38617	+	13.4992i	−0.172839	+	0.531944i
$645$	5.43012	+	2.18893i	0.213811	+	0.0861890i
$646$	2.04001	+	6.27850i	0.0802631	+	0.247024i
$647$	−19.4543	+	38.1812i	−0.764827	+	1.50106i	0.0977930	+	0.995207i	$0.468822\pi$
$647$	−19.4543	+	38.1812i	−0.764827	+	1.50106i	−0.862620	+	0.505852i	$0.831178\pi$
$648$	−1.52848	+	8.86926i	−0.0600443	+	0.348417i
$649$			3.10425i			0.121853i
$650$	24.6024	+	11.7456i	0.964986	+	0.460701i
$651$	−2.43144	−	7.57057i	−0.0952958	−	0.296714i
$652$	23.9735	−	3.79703i	0.938875	−	0.148703i
$653$	43.2254	+	22.0245i	1.69154	+	0.861884i	0.988587	+	0.150649i	$0.0481362\pi$
$653$	43.2254	+	22.0245i	1.69154	+	0.861884i	0.702954	+	0.711235i	$0.251864\pi$
$654$	11.8898	−	8.57693i	0.464928	−	0.335385i
$655$	16.3371	−	4.14597i	0.638343	−	0.161996i
$656$	0.0759593	+	0.0246807i	0.00296571	+	0.000963619i
$657$	−8.22369	+	49.7346i	−0.320837	+	1.94033i
$658$	1.09173	−	0.556265i	0.0425602	−	0.0216855i
$659$	−12.3351	+	8.96198i	−0.480508	+	0.349109i	−0.801522	−	0.597965i	$-0.795976\pi$
$659$	−12.3351	+	8.96198i	−0.480508	+	0.349109i	0.321015	+	0.947074i	$0.395976\pi$
$660$	−1.48455	−	16.8156i	−0.0577860	−	0.654548i
$661$	8.69836	+	6.31973i	0.338327	+	0.245809i	0.743956	−	0.668229i	$-0.232947\pi$
$661$	8.69836	+	6.31973i	0.338327	+	0.245809i	−0.405629	+	0.914038i	$0.632947\pi$
$662$	−15.5285	−	2.45948i	−0.603533	−	0.0955903i
$663$	46.5647	−	7.21317i	1.80842	−	0.280136i
$664$	2.71566	−	3.73778i	0.105388	−	0.145054i
$665$	−2.39636	+	4.02627i	−0.0929269	+	0.156132i
$666$	−0.194303	−	0.0645946i	−0.00752909	−	0.00250299i
$667$	−16.4626	−	32.3097i	−0.637435	−	1.25104i
$668$	6.91121	−	6.91121i	0.267403	−	0.267403i
$669$	0.135786	−	40.0004i	0.00524978	−	1.54650i
$670$	−10.1635	+	25.4616i	−0.392649	+	0.983669i
$671$	26.5225	−	8.61767i	1.02389	−	0.332682i
$672$	−2.70777	−	0.438296i	−0.104455	−	0.0169076i
$673$	3.23263	+	20.4100i	0.124609	+	0.786748i	0.968276	+	0.249882i	$0.0803919\pi$
$673$	3.23263	+	20.4100i	0.124609	+	0.786748i	−0.843668	+	0.536866i	$0.819608\pi$
$674$	−20.9306			−0.806217
$675$	−20.7775	+	15.5979i	−0.799727	+	0.600363i
$676$	−16.7295			−0.643444
$677$	0.268244	+	1.69362i	0.0103094	+	0.0650913i	0.992307	−	0.123804i	$-0.0395094\pi$
$677$	0.268244	+	1.69362i	0.0103094	+	0.0650913i	−0.981997	+	0.188895i	$0.939509\pi$
$678$	4.85683	+	0.786156i	0.186525	+	0.0301921i
$679$	17.9152	−	5.82099i	0.687521	−	0.223389i
$680$	−11.1327	−	0.731684i	−0.426919	−	0.0280588i
$681$	0.0896297	−	26.4035i	0.00343462	−	1.01178i
$682$	8.93422	−	8.93422i	0.342109	−	0.342109i
$683$	−13.0207	−	25.5547i	−0.498225	−	0.977822i	−0.994001	−	0.109371i	$-0.965116\pi$
$683$	−13.0207	−	25.5547i	−0.498225	−	0.977822i	0.495776	−	0.868450i	$-0.334884\pi$
$684$	3.76667	+	1.25220i	0.144022	+	0.0478791i
$685$	19.0386	−	8.17557i	0.727427	−	0.312373i
$686$	−10.6974	+	14.7238i	−0.408430	+	0.562156i
$687$	32.5450	−	5.04144i	1.24167	−	0.192343i
$688$	1.49307	+	0.236479i	0.0569227	+	0.00901567i
$689$	−35.7926	−	26.0049i	−1.36359	−	0.990707i
$690$	22.7939	+	26.1796i	0.867747	+	0.996640i
$691$	26.7982	−	19.4700i	1.01945	−	0.740675i	0.0532811	−	0.998580i	$-0.483032\pi$
$691$	26.7982	−	19.4700i	1.01945	−	0.740675i	0.966170	+	0.257905i	$0.0830321\pi$
$692$	−1.20566	+	0.614314i	−0.0458323	+	0.0233527i
$693$	3.37826	−	20.4308i	0.128330	−	0.776102i
$694$	−10.0316	−	3.25946i	−0.380794	−	0.123728i
$695$	−0.956480	+	14.5530i	−0.0362814	+	0.552026i
$696$	5.68332	−	4.09977i	0.215426	−	0.155401i
$697$	0.355064	+	0.180914i	0.0134490	+	0.00685261i
$698$	25.8905	−	4.10066i	0.979972	−	0.155212i
$699$	−0.661972	−	2.06112i	−0.0250381	−	0.0779587i
$700$	−4.81816	−	6.28382i	−0.182109	−	0.237506i
$701$		−	15.0225i		−	0.567393i	−0.958914	−	0.283696i	$-0.908439\pi$
$701$		−	15.0225i		−	0.567393i	0.958914	−	0.283696i	$-0.0915608\pi$
$702$	13.1188	−	25.1116i	0.495138	−	0.947777i
$703$	−0.0409984	+	0.0804638i	−0.00154628	+	0.00303475i
$704$	−1.34690	−	4.14534i	−0.0507633	−	0.156233i
$705$	0.206666	−	2.98936i	0.00778351	−	0.112586i
$706$	1.28416	−	3.95224i	0.0483300	−	0.148744i
$707$	8.15279	+	8.15279i	0.306617	+	0.306617i
$708$	0.875222	−	0.869300i	0.0328929	−	0.0326703i
$709$	26.1516	+	35.9945i	0.982142	+	1.35180i	0.935667	+	0.352884i	$0.114799\pi$
$709$	26.1516	+	35.9945i	0.982142	+	1.35180i	0.0464751	+	0.998919i	$0.485201\pi$
$710$	−2.12802	−	1.26656i	−0.0798632	−	0.0475331i
$711$	−22.3474	−	0.151723i	−0.838091	−	0.00569006i
$712$	0.990318	−	6.25262i	0.0371137	−	0.234327i
$713$	−4.06430	+	25.6610i	−0.152209	+	0.961010i
$714$	−13.0018	−	4.27339i	−0.486580	−	0.159928i
$715$	−11.7375	+	51.8289i	−0.438957	+	1.93829i
$716$	3.42845	+	4.71886i	0.128127	+	0.176352i
$717$	0.130925	+	0.131817i	0.00488950	+	0.00492281i
$718$	4.15479	+	4.15479i	0.155055	+	0.155055i
$719$	6.98735	−	21.5049i	0.260584	−	0.801996i	−0.732094	−	0.681204i	$-0.761457\pi$
$719$	6.98735	−	21.5049i	0.260584	−	0.801996i	0.992678	−	0.120792i	$-0.0385433\pi$
$720$	−4.32533	+	5.12753i	−0.161195	+	0.191092i
$721$	−1.98846	−	6.11986i	−0.0740543	−	0.227916i
$722$	−7.83104	+	15.3693i	−0.291441	+	0.571986i
$723$	18.1099	−	9.15016i	0.673515	−	0.340298i
$724$		−	8.08766i		−	0.300575i
$725$	20.0555	+	2.64770i	0.744844	+	0.0983330i
$726$	13.1894	−	4.23604i	0.489503	−	0.157214i
$727$	−44.9536	+	7.11996i	−1.66724	+	0.264065i	−0.917519	−	0.397692i	$-0.869811\pi$
$727$	−44.9536	+	7.11996i	−1.66724	+	0.264065i	−0.749719	+	0.661756i	$0.769811\pi$
$728$	7.69383	+	3.92020i	0.285152	+	0.145292i
$729$	15.4220	+	22.1621i	0.571187	+	0.820820i
$730$	−24.0310	+	28.8836i	−0.889429	+	1.06903i
$731$	7.17326	+	2.33073i	0.265313	+	0.0862053i
$732$	−9.85691	−	5.06457i	−0.364322	−	0.187192i
$733$	−25.0784	+	12.7781i	−0.926293	+	0.471970i	−0.850985	−	0.525191i	$-0.823994\pi$
$733$	−25.0784	+	12.7781i	−0.926293	+	0.471970i	−0.0753080	+	0.997160i	$0.523994\pi$
$734$	−13.7493	+	9.98946i	−0.507496	+	0.368718i
$735$	6.81029	+	16.0089i	0.251201	+	0.590497i
$736$	7.25092	+	5.26810i	0.267272	+	0.194185i
$737$	−52.7812	−	8.35972i	−1.94422	−	0.307934i
$738$	0.214223	−	0.107327i	0.00788567	−	0.00395074i
$739$	−22.4956	+	30.9626i	−0.827515	+	1.13898i	0.160865	+	0.986976i	$0.448572\pi$
$739$	−22.4956	+	30.9626i	−0.827515	+	1.13898i	−0.988380	+	0.152001i	$0.951428\pi$
$740$	−0.100607	−	0.114762i	−0.00369841	−	0.00421875i
$741$	−10.0841	−	7.37894i	−0.370448	−	0.271072i
$742$	5.83386	+	11.4496i	0.214168	+	0.420328i
$743$	−13.5540	+	13.5540i	−0.497249	+	0.497249i	−0.910581	−	0.413332i	$-0.864365\pi$
$743$	−13.5540	+	13.5540i	−0.497249	+	0.497249i	0.413332	+	0.910581i	$0.364365\pi$
$744$	−5.02083	−	0.0170438i	−0.184073	−	0.000624855i
$745$	33.0660	−	20.8548i	1.21144	−	0.764060i
$746$	−26.1069	+	8.48265i	−0.955842	+	0.310572i
$747$	−2.07526	−	13.7042i	−0.0759299	−	0.501411i
$748$	−3.40202	−	21.4795i	−0.124390	−	0.785369i
$749$	−19.7767			−0.722625
$750$	−19.2395	+	2.20043i	−0.702527	+	0.0803485i
$751$	29.1530			1.06381			0.531904	−	0.846805i	$-0.321477\pi$
$751$	29.1530			1.06381			0.531904	+	0.846805i	$0.321477\pi$
$752$	−0.121032	−	0.764166i	−0.00441358	−	0.0278663i
$753$	−8.30398	+	51.3016i	−0.302614	+	1.86953i
$754$	−20.9806	+	6.81699i	−0.764067	+	0.248260i
$755$	−28.4490	+	17.9429i	−1.03537	+	0.653008i
$756$	−6.70635	+	4.76886i	−0.243908	+	0.173442i
$757$	12.7694	−	12.7694i	0.464113	−	0.464113i	−0.435888	−	0.900001i	$-0.643566\pi$
$757$	12.7694	−	12.7694i	0.464113	−	0.464113i	0.900001	+	0.435888i	$0.143566\pi$
$758$	−6.70985	−	13.1688i	−0.243713	−	0.478313i
$759$	−39.9568	+	54.6050i	−1.45034	+	1.98204i
$760$	1.95033	+	2.22473i	0.0707459	+	0.0806995i
$761$	1.38914	−	1.91199i	0.0503564	−	0.0693097i	−0.783096	−	0.621901i	$-0.786361\pi$
$761$	1.38914	−	1.91199i	0.0503564	−	0.0693097i	0.833453	+	0.552591i	$0.186361\pi$
$762$	0.193403	+	1.24851i	0.00700624	+	0.0452288i
$763$	13.2396	+	2.09695i	0.479307	+	0.0759148i
$764$	−10.6797	−	7.75927i	−0.386379	−	0.280721i
$765$	−25.3173	+	21.8925i	−0.915350	+	0.791524i
$766$	−13.4761	+	9.79095i	−0.486911	+	0.353761i
$767$	−3.46002	+	1.76297i	−0.124934	+	0.0636570i
$768$	−0.791569	+	1.54059i	−0.0285633	+	0.0555913i
$769$	−15.6427	−	5.08261i	−0.564089	−	0.183284i	0.0130714	−	0.999915i	$-0.495839\pi$
$769$	−15.6427	−	5.08261i	−0.564089	−	0.183284i	−0.577160	+	0.816631i	$0.695839\pi$
$770$	9.87187	−	11.8653i	0.355757	−	0.427595i
$771$	−14.7759	−	20.4831i	−0.532140	−	0.737680i
$772$	−7.37690	−	3.75872i	−0.265500	−	0.135279i
$773$	18.5483	−	2.93775i	0.667134	−	0.105664i	0.186324	−	0.982488i	$-0.440343\pi$
$773$	18.5483	−	2.93775i	0.667134	−	0.105664i	0.480810	+	0.876825i	$0.340343\pi$
$774$	3.68693	−	2.64066i	0.132524	−	0.0949165i
$775$	−10.5100	−	9.98078i	−0.377529	−	0.358520i
$776$		−	11.8945i		−	0.426989i
$777$	−0.0844288	−	0.167101i	−0.00302886	−	0.00599470i
$778$	−11.0940	+	21.7732i	−0.397739	+	0.780606i
$779$	−0.0326555	−	0.100503i	−0.00117000	−	0.00360090i
$780$	17.8997	−	11.2046i	0.640912	−	0.401190i
$781$	1.49168	−	4.59091i	0.0533764	−	0.164276i
$782$	31.6207	+	31.6207i	1.13075	+	1.13075i
$783$	3.50004	−	20.7298i	0.125081	−	0.740822i
$784$	2.64031	+	3.63407i	0.0942966	+	0.129788i
$785$	−7.59569	+	33.5401i	−0.271102	+	1.19710i
$786$	4.07659	−	12.4030i	0.145407	−	0.442402i
$787$	−3.72349	+	23.5092i	−0.132728	+	0.838013i	0.828042	+	0.560666i	$0.189455\pi$
$787$	−3.72349	+	23.5092i	−0.132728	+	0.838013i	−0.960770	+	0.277347i	$0.910545\pi$
$788$	3.69159	−	23.3078i	0.131507	−	0.830305i
$789$	−3.09914	+	9.42913i	−0.110332	+	0.335686i
$790$	−14.3137	−	8.51924i	−0.509259	−	0.303101i
$791$	2.64420	+	3.63943i	0.0940169	+	0.129403i
$792$	−11.6102	−	6.01534i	−0.412552	−	0.213746i
$793$	24.6679	+	24.6679i	0.875984	+	0.875984i
$794$	−2.11182	+	6.49951i	−0.0749456	+	0.230659i
$795$	31.3511	+	2.16742i	1.11191	+	0.0768706i
$796$	3.69016	+	11.3572i	0.130794	+	0.402544i
$797$	8.27146	−	16.2336i	0.292990	−	0.575025i	−0.696849	−	0.717218i	$-0.745415\pi$
$797$	8.27146	−	16.2336i	0.292990	−	0.575025i	0.989839	+	0.142193i	$0.0454152\pi$
$798$	1.63670	+	3.23933i	0.0579384	+	0.114671i
$799$		−	3.86028i		−	0.136567i
$800$	−4.71381	+	1.66734i	−0.166658	+	0.0589494i
$801$	−11.0585	−	15.4400i	−0.390732	−	0.545547i
$802$	22.4225	−	3.55138i	0.791767	−	0.125404i
$803$	−65.2573	−	33.2503i	−2.30288	−	1.17338i
$804$	12.4236	+	17.2223i	0.438148	+	0.607384i
$805$	−2.08150	+	31.6703i	−0.0733631	+	1.11623i
$806$	15.0320	+	4.88421i	0.529481	+	0.172039i
$807$	22.7885	−	44.3522i	0.802194	−	1.56127i
$808$	6.48686	−	3.30522i	0.228207	−	0.116277i
$809$	0.465989	−	0.338561i	0.0163833	−	0.0119032i	−0.579563	−	0.814927i	$-0.696777\pi$
$809$	0.465989	−	0.338561i	0.0163833	−	0.0119032i	0.595947	+	0.803024i	$0.296777\pi$
$810$	1.56555	+	20.0636i	0.0550079	+	0.704964i
$811$	−16.4035	−	11.9178i	−0.576004	−	0.418491i	0.261277	−	0.965264i	$-0.415856\pi$
$811$	−16.4035	−	11.9178i	−0.576004	−	0.418491i	−0.837281	+	0.546772i	$0.815856\pi$
$812$	6.32855	+	1.00234i	0.222088	+	0.0351753i
$813$	−2.52546	−	16.3031i	−0.0885719	−	0.571776i
$814$	0.174861	−	0.240676i	0.00612888	−	0.00843569i
$815$	49.8709	−	21.4156i	1.74690	−	0.750156i
$816$	−5.10331	+	6.97420i	−0.178652	+	0.244146i
$817$	−0.908040	−	1.78213i	−0.0317683	−	0.0623488i
$818$	9.95932	−	9.95932i	0.348219	−	0.348219i
$819$	24.6909	−	7.83762i	0.862768	−	0.273869i
$820$	0.178207	+	0.0117125i	0.00622325	+	0.000409017i
$821$	31.2665	−	10.1591i	1.09121	−	0.354555i	0.292495	−	0.956267i	$-0.405515\pi$
$821$	31.2665	−	10.1591i	1.09121	−	0.354555i	0.798713	+	0.601712i	$0.205515\pi$
$822$	2.56448	−	15.8432i	0.0894466	−	0.552596i
$823$	−5.34295	−	33.7341i	−0.186244	−	1.17590i	−0.886750	−	0.462249i	$-0.847043\pi$
$823$	−5.34295	−	33.7341i	−0.186244	−	1.17590i	0.700507	−	0.713646i	$-0.252957\pi$
$824$	−4.06320			−0.141548
$825$	−12.4666	−	35.6291i	−0.434031	−	1.24045i
$826$	1.12790			0.0392447
$827$	4.48852	+	28.3394i	0.156081	+	0.985457i	0.934047	+	0.357151i	$0.116252\pi$
$827$	4.48852	+	28.3394i	0.156081	+	0.985457i	−0.777966	+	0.628307i	$0.783748\pi$
$828$	26.5848	−	4.02580i	0.923885	−	0.139906i
$829$	−17.3783	+	5.64654i	−0.603572	+	0.196113i	−0.594833	−	0.803849i	$-0.702782\pi$
$829$	−17.3783	+	5.64654i	−0.603572	+	0.196113i	−0.00873938	+	0.999962i	$0.502782\pi$
$830$	3.82995	−	9.59483i	0.132939	−	0.333041i
$831$	−2.32838	−	0.00790394i	−0.0807705	−	0.000274185i
$832$	3.85549	−	3.85549i	0.133665	−	0.133665i
$833$	10.1750	+	19.9695i	0.352542	+	0.691902i
$834$	9.11689	+	6.67121i	0.315692	+	0.231005i
$835$	11.1778	−	18.7804i	0.386822	−	0.649924i
$836$	−3.38978	+	4.66563i	−0.117238	+	0.161364i
$837$	−10.7588	+	10.5418i	−0.371877	+	0.364379i
$838$	16.0016	+	2.53441i	0.552768	+	0.0875498i
$839$	25.5591	+	18.5698i	0.882398	+	0.641099i	0.933885	−	0.357574i	$-0.116396\pi$
$839$	25.5591	+	18.5698i	0.882398	+	0.641099i	−0.0514870	+	0.998674i	$0.516396\pi$
$840$	−6.10980	+	0.539396i	−0.210808	+	0.0186109i
$841$	10.2184	−	7.42407i	0.352357	−	0.256003i
$842$	2.33478	−	1.18963i	0.0804618	−	0.0409973i
$843$	−5.60265	−	2.87869i	−0.192966	−	0.0991474i
$844$	−20.7973	−	6.75746i	−0.715874	−	0.232601i
$845$	−36.2590	+	9.20168i	−1.24735	+	0.316547i
$846$	−1.86848	−	1.37701i	−0.0642398	−	0.0473426i
$847$	11.2857	+	5.75036i	0.387782	+	0.197585i
$848$	8.01423	−	1.26933i	0.275210	−	0.0435890i
$849$	−43.0613	+	13.8300i	−1.47786	+	0.474645i
$850$	−24.5310	+	4.53744i	−0.841408	+	0.155633i
$851$			0.611725i			0.0209697i
$852$	−1.71210	+	0.865049i	−0.0586555	+	0.0296361i
$853$	−9.15038	+	17.9586i	−0.313303	+	0.614892i	−0.992935	−	0.118662i	$-0.962140\pi$
$853$	−9.15038	+	17.9586i	−0.313303	+	0.614892i	0.679632	+	0.733553i	$0.262140\pi$
$854$	−3.13115	−	9.63668i	−0.107146	−	0.329760i
$855$	8.85248	+	0.642209i	0.302749	+	0.0219631i
$856$	−3.85895	+	11.8766i	−0.131896	+	0.405935i
$857$	−0.835861	−	0.835861i	−0.0285525	−	0.0285525i	0.692686	−	0.721239i	$-0.256427\pi$
$857$	−0.835861	−	0.835861i	−0.0285525	−	0.0285525i	−0.721239	+	0.692686i	$0.756427\pi$
$858$	29.0078	+	29.2054i	0.990309	+	0.997055i
$859$	23.4268	+	32.2443i	0.799313	+	1.10016i	0.992885	+	0.119074i	$0.0379926\pi$
$859$	23.4268	+	32.2443i	0.799313	+	1.10016i	−0.193572	+	0.981086i	$0.562007\pi$
$860$	3.36609	−	0.308690i	0.114783	−	0.0105263i
$861$	0.208127	+	0.0684064i	0.00709293	+	0.00233128i
$862$	3.54800	−	22.4012i	0.120845	−	0.762988i
$863$	−1.59543	+	10.0731i	−0.0543089	+	0.342893i	0.945540	+	0.325506i	$0.105535\pi$
$863$	−1.59543	+	10.0731i	−0.0543089	+	0.342893i	−0.999849	+	0.0173869i	$0.994465\pi$
$864$	1.55529	+	4.95793i	0.0529121	+	0.168672i
$865$	−2.27521	+	1.99459i	−0.0773596	+	0.0678180i
$866$	−10.1103	−	13.9156i	−0.343561	−	0.472871i
$867$	−9.70139	+	9.63575i	−0.329477	+	0.327247i
$868$	−3.24616	−	3.24616i	−0.110182	−	0.110182i
$869$	10.0335	−	30.8798i	0.340362	−	1.04753i
$870$	10.0628	−	12.0117i	0.341163	−	0.407234i
$871$	−20.6577	−	63.5779i	−0.699960	−	2.15425i
$872$	3.84269	−	7.54171i	0.130130	−	0.255395i
$873$	−25.0602	−	25.4028i	−0.848160	−	0.859756i
$874$		−	11.8586i		−	0.401124i
$875$	−13.8990	−	10.9692i	−0.469871	−	0.370827i
$876$	8.89967	+	27.7101i	0.300692	+	0.936237i
$877$	28.7259	−	4.54973i	0.970003	−	0.153633i	0.348726	−	0.937225i	$-0.386614\pi$
$877$	28.7259	−	4.54973i	0.970003	−	0.153633i	0.621277	+	0.783591i	$0.286614\pi$
$878$	14.1425	+	7.20594i	0.477285	+	0.243189i
$879$	15.3151	−	11.0479i	0.516567	−	0.372635i
$880$	−5.19927	−	8.24363i	−0.175267	−	0.277893i
$881$	−8.28622	−	2.69236i	−0.279170	−	0.0907078i	0.166086	−	0.986111i	$-0.446887\pi$
$881$	−8.28622	−	2.69236i	−0.279170	−	0.0907078i	−0.445256	+	0.895404i	$0.646887\pi$
$882$	13.2953	+	2.19841i	0.447677	+	0.0740242i
$883$	10.3084	−	5.25241i	0.346906	−	0.176758i	−0.271852	−	0.962339i	$-0.587636\pi$
$883$	10.3084	−	5.25241i	0.346906	−	0.176758i	0.618758	+	0.785581i	$0.287636\pi$
$884$	22.0091	−	15.9906i	0.740247	−	0.537821i
$885$	1.41879	−	2.36549i	0.0476920	−	0.0795149i
$886$	7.15205	+	5.19627i	0.240278	+	0.174572i
$887$	3.17898	+	0.503502i	0.106740	+	0.0169059i	0.209576	−	0.977792i	$-0.432792\pi$
$887$	3.17898	+	0.503502i	0.106740	+	0.0169059i	−0.102836	+	0.994698i	$0.532792\pi$
$888$	−0.116824	+	0.0180968i	−0.00392036	+	0.000607290i
$889$	−0.678996	+	0.934558i	−0.0227728	+	0.0313441i
$890$	−1.29272	−	14.0964i	−0.0433322	−	0.472513i
$891$	−37.4692	+	11.6144i	−1.25527	+	0.389098i
$892$	−10.4846	−	20.5772i	−0.351051	−	0.688977i
$893$	−0.723855	+	0.723855i	−0.0242229	+	0.0242229i
$894$	0.102793	−	30.2813i	0.00343792	−	1.01276i
$895$	10.0262	+	8.34175i	0.335139	+	0.278834i
$896$	−1.50617	+	0.489384i	−0.0503176	+	0.0163492i
$897$	−83.5553	−	13.5248i	−2.78983	−	0.451579i
$898$	−0.701920	−	4.43175i	−0.0234234	−	0.147889i
$899$	11.7283			0.391160
$900$	−6.55429	+	13.4923i	−0.218476	+	0.449742i
$901$	40.4849			1.34875
$902$	0.0544579	+	0.343834i	0.00181325	+	0.0114484i
$903$	4.09328	+	0.662563i	0.136216	+	0.0220487i
$904$	2.70156	−	0.877790i	0.0898525	−	0.0291949i
$905$	−4.44842	−	17.5289i	−0.147871	−	0.582681i
$906$	−0.0884405	+	26.0532i	−0.00293824	+	0.865559i
$907$	−7.25177	+	7.25177i	−0.240791	+	0.240791i	−0.817177	−	0.576386i	$-0.804462\pi$
$907$	−7.25177	+	7.25177i	−0.240791	+	0.240791i	0.576386	+	0.817177i	$0.304462\pi$
$908$	−6.92070	−	13.5826i	−0.229672	−	0.450756i
$909$	6.89015	−	20.7258i	0.228532	−	0.687433i
$910$	18.8315	+	4.26470i	0.624260	+	0.141373i
$911$	21.4007	−	29.4555i	0.709035	−	0.975903i	−0.290782	−	0.956789i	$-0.593915\pi$
$911$	21.4007	−	29.4555i	0.709035	−	0.975903i	0.999817	−	0.0191141i	$-0.00608458\pi$
$912$	2.26470	−	0.350816i	0.0749916	−	0.0116167i
$913$	19.8898	+	3.15023i	0.658256	+	0.104258i
$914$	24.4243	+	17.7453i	0.807883	+	0.586962i
$915$	−24.1492	−	5.55521i	−0.798347	−	0.183650i
$916$	15.3826	−	11.1761i	0.508256	−	0.369270i
$917$	10.6363	−	5.41947i	0.351242	−	0.178967i
$918$	3.79472	+	25.6466i	0.125244	+	0.846464i
$919$	−12.8805	−	4.18512i	−0.424887	−	0.138054i	0.0887651	−	0.996053i	$-0.471708\pi$
$919$	−12.8805	−	4.18512i	−0.424887	−	0.138054i	−0.513653	+	0.857998i	$0.671708\pi$
$920$	18.6130	+	7.42970i	0.613652	+	0.244950i
$921$	−24.4065	+	17.6061i	−0.804222	+	0.580141i
$922$	23.0574	+	11.7483i	0.759354	+	0.386910i
$923$	5.96421	−	0.944638i	0.196314	−	0.0310931i
$924$	−3.65595	−	11.3832i	−0.120272	−	0.374480i
$925$	−0.281176	−	0.193395i	−0.00924499	−	0.00635880i
$926$		−	10.2739i		−	0.337621i
$927$	−8.67766	+	8.56063i	−0.285012	+	0.281168i
$928$	1.83681	−	3.60493i	0.0602961	−	0.118338i
$929$	9.27450	+	28.5440i	0.304286	+	0.936497i	0.979943	+	0.199280i	$0.0638604\pi$
$929$	9.27450	+	28.5440i	0.304286	+	0.936497i	−0.675656	+	0.737217i	$0.736140\pi$
$930$	−10.8914	+	2.72465i	−0.357142	+	0.0893447i
$931$	1.83661	−	5.65250i	0.0601924	−	0.185253i
$932$	−0.883782	−	0.883782i	−0.0289492	−	0.0289492i
$933$	−6.32551	+	6.28271i	−0.207088	+	0.205687i
$934$	8.94877	+	12.3169i	0.292813	+	0.403022i
$935$	−19.1877	−	44.6828i	−0.627505	−	1.46128i
$936$	0.111053	−	16.3571i	0.00362988	−	0.534647i
$937$	−4.50748	+	28.4591i	−0.147253	+	0.929718i	0.797829	+	0.602884i	$0.205982\pi$
$937$	−4.50748	+	28.4591i	−0.147253	+	0.929718i	−0.945082	+	0.326834i	$0.894018\pi$
$938$	−3.03743	+	19.1776i	−0.0991755	+	0.626169i
$939$	17.1720	+	5.64403i	0.560387	+	0.184186i
$940$	−0.682632	−	1.58966i	−0.0222650	−	0.0518489i
$941$	7.80628	+	10.7444i	0.254478	+	0.350258i	0.917073	−	0.398719i	$-0.130545\pi$
$941$	7.80628	+	10.7444i	0.254478	+	0.350258i	−0.662596	+	0.748977i	$0.730545\pi$
$942$	18.7718	+	18.8997i	0.611619	+	0.615786i
$943$	−0.506169	−	0.506169i	−0.0164831	−	0.0164831i
$944$	0.220083	−	0.677345i	0.00716308	−	0.0220457i
$945$	−11.9121	+	14.0245i	−0.387501	+	0.456218i
$946$	2.03608	+	6.26642i	0.0661988	+	0.203739i
$947$	10.9048	−	21.4019i	0.354359	−	0.695469i	−0.643170	−	0.765724i	$-0.722381\pi$
$947$	10.9048	−	21.4019i	0.354359	−	0.695469i	0.997529	+	0.0702542i	$0.0223810\pi$
$948$	−11.5161	+	5.81858i	−0.374025	+	0.188979i
$949$		−	91.6197i		−	2.97410i
$950$	5.45074	+	3.74907i	0.176845	+	0.121636i
$951$	−45.4642	+	14.6018i	−1.47428	+	0.473495i
$952$	−7.80438	+	1.23609i	−0.252941	+	0.0400620i
$953$	−17.3120	−	8.82088i	−0.560789	−	0.285736i	0.150530	−	0.988605i	$-0.451902\pi$
$953$	−17.3120	−	8.82088i	−0.560789	−	0.285736i	−0.711319	+	0.702869i	$0.751902\pi$
$954$	14.4415	−	19.5958i	0.467560	−	0.634438i
$955$	−27.4147	−	10.9430i	−0.887117	−	0.354109i
$956$	0.102015	+	0.0331467i	0.00329940	+	0.00107204i
$957$	27.1680	+	13.9592i	0.878216	+	0.451235i
$958$	−16.3251	+	8.31808i	−0.527441	+	0.268745i
$959$	11.8720	−	8.62553i	0.383368	−	0.278533i
$960$	−0.868254	+	3.77441i	−0.0280228	+	0.121818i
$961$	18.2813	+	13.2822i	0.589721	+	0.428457i
$962$	0.367566	+	0.0582167i	0.0118508	+	0.00187698i
$963$	16.7810	+	33.4949i	0.540761	+	1.07936i
$964$	6.88566	−	9.47730i	0.221772	−	0.305243i
$965$	−18.0558	−	4.08903i	−0.581237	−	0.131630i
$966$	19.8402	+	14.5179i	0.638348	+	0.467106i
$967$	5.93841	+	11.6548i	0.190966	+	0.374793i	0.966560	−	0.256440i	$-0.0825495\pi$
$967$	5.93841	+	11.6548i	0.190966	+	0.374793i	−0.775594	+	0.631232i	$0.782550\pi$
$968$	5.65543	−	5.65543i	0.181772	−	0.181772i
$969$	11.4343	+	0.0388148i	0.367321	+	0.00124691i
$970$	−6.54230	−	25.7798i	−0.210061	−	0.827739i
$971$	7.00547	−	2.27622i	0.224816	−	0.0730472i	−0.194443	−	0.980914i	$-0.562290\pi$
$971$	7.00547	−	2.27622i	0.224816	−	0.0730472i	0.419259	+	0.907867i	$0.362290\pi$
$972$	13.7673	+	7.31173i	0.441586	+	0.234524i
$973$	1.61586	+	10.2021i	0.0518020	+	0.327065i
$974$	3.97602			0.127400
$975$	32.6324	−	34.1298i	1.04507	−	1.09303i
$976$	−6.39814			−0.204799
$977$	−6.51715	−	41.1477i	−0.208502	−	1.31643i	−0.840648	−	0.541582i	$-0.817826\pi$
$977$	−6.51715	−	41.1477i	−0.208502	−	1.31643i	0.632146	−	0.774849i	$-0.282174\pi$
$978$	6.71757	−	41.5008i	0.214804	−	1.32705i
$979$	26.2423	−	8.52665i	0.838708	−	0.272513i
$980$	7.72134	+	6.42412i	0.246649	+	0.205211i
$981$	−7.68266	−	24.2027i	−0.245289	−	0.772732i
$982$	−14.2382	+	14.2382i	−0.454360	+	0.454360i
$983$	27.1685	+	53.3212i	0.866541	+	1.70068i	0.699377	+	0.714753i	$0.253461\pi$
$983$	27.1685	+	53.3212i	0.866541	+	1.70068i	0.167164	+	0.985929i	$0.446539\pi$
$984$	0.0816914	−	0.111640i	0.00260423	−	0.00355894i
$985$	−4.81886	−	52.5469i	−0.153542	−	1.67428i
$986$	11.8655	−	16.3315i	0.377874	−	0.520100i
$987$	−0.324875	−	2.09723i	−0.0103409	−	0.0667557i
$988$	−7.12546	−	1.12856i	−0.226691	−	0.0359043i
$989$	−10.9611	−	7.96368i	−0.348541	−	0.253230i
$990$	−28.4722	−	6.65152i	−0.904906	−	0.211399i
$991$	−25.5455	+	18.5599i	−0.811478	+	0.589573i	−0.914259	−	0.405131i	$-0.867226\pi$
$991$	−25.5455	+	18.5599i	−0.811478	+	0.589573i	0.102781	+	0.994704i	$0.467226\pi$
$992$	−2.58285	+	1.31603i	−0.0820054	+	0.0417839i
$993$	−12.4451	+	24.2213i	−0.394934	+	0.768640i
$994$	−1.66806	−	0.541987i	−0.0529078	−	0.0171908i
$995$	14.2447	+	22.5854i	0.451586	+	0.716006i
$996$	−4.68166	−	6.48996i	−0.148344	−	0.205642i
$997$	30.4001	+	15.4896i	0.962780	+	0.490561i	0.863417	−	0.504490i	$-0.168320\pi$
$997$	30.4001	+	15.4896i	0.962780	+	0.490561i	0.0993629	+	0.995051i	$0.468320\pi$
$998$	−26.6107	+	4.21472i	−0.842348	+	0.133415i
$999$	−0.211371	+	0.284782i	−0.00668747	+	0.00901011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.113.1	yes	80
3.2	odd	2	inner	150.2.l.a.113.10	yes	80
5.2	odd	4		750.2.l.c.707.7		80
5.3	odd	4		750.2.l.a.707.4		80
5.4	even	2		750.2.l.b.293.10		80
15.2	even	4		750.2.l.c.707.4		80
15.8	even	4		750.2.l.a.707.7		80
15.14	odd	2		750.2.l.b.293.1		80
25.2	odd	20	inner	150.2.l.a.77.10	yes	80
25.11	even	5		750.2.l.c.593.4		80
25.14	even	10		750.2.l.a.593.7		80
25.23	odd	20		750.2.l.b.407.1		80
75.2	even	20	inner	150.2.l.a.77.1	✓	80
75.11	odd	10		750.2.l.c.593.7		80
75.14	odd	10		750.2.l.a.593.4		80
75.23	even	20		750.2.l.b.407.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.1	✓	80	75.2	even	20	inner
150.2.l.a.77.10	yes	80	25.2	odd	20	inner
150.2.l.a.113.1	yes	80	1.1	even	1	trivial
150.2.l.a.113.10	yes	80	3.2	odd	2	inner
750.2.l.a.593.4		80	75.14	odd	10
750.2.l.a.593.7		80	25.14	even	10
750.2.l.a.707.4		80	5.3	odd	4
750.2.l.a.707.7		80	15.8	even	4
750.2.l.b.293.1		80	15.14	odd	2
750.2.l.b.293.10		80	5.4	even	2
750.2.l.b.407.1		80	25.23	odd	20
750.2.l.b.407.10		80	75.23	even	20
750.2.l.c.593.4		80	25.11	even	5
750.2.l.c.593.7		80	75.11	odd	10
750.2.l.c.707.4		80	15.2	even	4
750.2.l.c.707.7		80	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-1.70980 - 0.276758i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.89132 + 1.19286i) q^{5} +(-0.00587961 + 1.73204i) q^{6} +(-1.11983 + 1.11983i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.84681 + 0.946400i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-1.70980 - 0.276758i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.89132 + 1.19286i) q^{5} +(-0.00587961 + 1.73204i) q^{6} +(-1.11983 + 1.11983i) q^{7} +(0.453990 + 0.891007i) q^{8} +(2.84681 + 0.946400i) q^{9} +(1.47404 + 1.68143i) q^{10} +(-2.56196 + 3.52624i) q^{11} +(1.71164 - 0.265144i) q^{12} +(-5.38535 - 0.852956i) q^{13} +(1.28122 + 0.930864i) q^{14} +(3.56390 - 1.51611i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.44561 - 2.26515i) q^{17} +(0.489409 - 2.95981i) q^{18} +(-1.25836 - 0.408866i) q^{19} +(1.43014 - 1.71893i) q^{20} +(2.22461 - 1.60476i) q^{21} +(3.88360 + 1.97879i) q^{22} +(-8.85228 + 1.40206i) q^{23} +(-0.529638 - 1.64909i) q^{24} +(2.15418 - 4.51215i) q^{25} +5.45248i q^{26} +(-4.60554 - 2.40603i) q^{27} +(0.718976 - 1.41107i) q^{28} +(1.25026 + 3.84789i) q^{29} +(-2.05496 - 3.28286i) q^{30} +(0.895777 - 2.75692i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.35635 - 5.32010i) q^{33} +(-2.93271 - 4.03653i) q^{34} +(0.782158 - 3.45376i) q^{35} +(-2.99993 - 0.0203674i) q^{36} +(0.0106771 - 0.0674126i) q^{37} +(-0.206981 + 1.30683i) q^{38} +(8.97179 + 2.94882i) q^{39} +(-1.92149 - 1.14363i) q^{40} +(0.0469455 + 0.0646149i) q^{41} +(-1.93301 - 1.94618i) q^{42} +(1.06892 + 1.06892i) q^{43} +(1.34690 - 4.14534i) q^{44} +(-6.51315 + 1.60590i) q^{45} +(2.76960 + 8.52397i) q^{46} +(0.351249 - 0.689364i) q^{47} +(-1.54593 + 0.781091i) q^{48} +4.49196i q^{49} +(-4.79359 - 1.42180i) q^{50} +(-8.22800 + 2.64259i) q^{51} +(5.38535 - 0.852956i) q^{52} +(7.22974 + 3.68374i) q^{53} +(-1.65594 + 4.92523i) q^{54} +(0.639185 - 9.72530i) q^{55} +(-1.50617 - 0.489384i) q^{56} +(2.03838 + 1.04734i) q^{57} +(3.60493 - 1.83681i) q^{58} +(0.576184 - 0.418622i) q^{59} +(-2.92097 + 2.54321i) q^{60} +(-5.17620 - 3.76073i) q^{61} +(-2.86311 - 0.453472i) q^{62} +(-4.24775 + 2.12814i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(11.2029 - 4.81075i) q^{65} +(-6.09252 - 4.45815i) q^{66} +(5.56612 + 10.9241i) q^{67} +(-3.52806 + 3.52806i) q^{68} +(15.5236 + 0.0526967i) q^{69} +(-3.53359 - 0.232242i) q^{70} +(-1.05328 + 0.342232i) q^{71} +(0.449176 + 2.96618i) q^{72} +(2.62862 + 16.5964i) q^{73} -0.0682529 q^{74} +(-4.93198 + 7.11868i) q^{75} +1.32312 q^{76} +(-1.07983 - 6.81775i) q^{77} +(1.50902 - 9.32263i) q^{78} +(-7.08470 + 2.30196i) q^{79} +(-0.828965 + 2.07673i) q^{80} +(7.20865 + 5.38844i) q^{81} +(0.0564755 - 0.0564755i) q^{82} +(-2.09751 - 4.11659i) q^{83} +(-1.61983 + 2.21366i) q^{84} +(-5.70607 + 9.58712i) q^{85} +(0.888543 - 1.22297i) q^{86} +(-1.07275 - 6.92513i) q^{87} +(-4.30501 - 0.681846i) q^{88} +(-5.12153 - 3.72101i) q^{89} +(2.60501 + 6.18174i) q^{90} +(6.98585 - 5.07552i) q^{91} +(7.98576 - 4.06895i) q^{92} +(-2.29460 + 4.46586i) q^{93} +(-0.735824 - 0.239084i) q^{94} +(2.86768 - 0.727750i) q^{95} +(1.01331 + 1.40471i) q^{96} +(-10.5981 - 5.40000i) q^{97} +(4.43665 - 0.702697i) q^{98} +(-10.6306 + 7.61389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more