LMFDB - Embedded newform 150.2.l.a.77.10

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			77.10
Character	$\chi$	$=$	150.77
Dual form			150.2.l.a.113.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(1.22890 - 1.22058i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.89132 + 1.19286i) q^{5} +(-1.01331 - 1.40471i) q^{6} +(-1.11983 - 1.11983i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0203674 - 2.99993i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(1.22890 - 1.22058i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.89132 + 1.19286i) q^{5} +(-1.01331 - 1.40471i) q^{6} +(-1.11983 - 1.11983i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0203674 - 2.99993i) q^{9} +(1.47404 - 1.68143i) q^{10} +(2.56196 + 3.52624i) q^{11} +(-1.54593 + 0.781091i) q^{12} +(-5.38535 + 0.852956i) q^{13} +(-1.28122 + 0.930864i) q^{14} +(3.78021 - 0.842609i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.44561 - 2.26515i) q^{17} +(-2.95981 - 0.489409i) q^{18} +(-1.25836 + 0.408866i) q^{19} +(-1.43014 - 1.71893i) q^{20} +(-2.74300 - 0.00931142i) 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} +(-3.63663 - 3.71146i) q^{27} +(0.718976 + 1.41107i) q^{28} +(-1.25026 + 3.84789i) q^{29} +(-0.240880 - 3.86549i) q^{30} +(0.895777 + 2.75692i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.45244 + 1.20630i) q^{33} +(-2.93271 + 4.03653i) q^{34} +(-0.782158 - 3.45376i) q^{35} +(-0.946400 + 2.84681i) q^{36} +(0.0106771 + 0.0674126i) q^{37} +(0.206981 + 1.30683i) q^{38} +(-5.57693 + 7.62145i) q^{39} +(-1.92149 + 1.14363i) q^{40} +(-0.0469455 + 0.0646149i) q^{41} +(-0.438296 + 2.70777i) q^{42} +(1.06892 - 1.06892i) q^{43} +(-1.34690 - 4.14534i) q^{44} +(3.61701 - 5.64953i) q^{45} +(2.76960 - 8.52397i) q^{46} +(-0.351249 - 0.689364i) q^{47} +(1.71164 - 0.265144i) 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} +(-4.23466 + 3.01125i) q^{54} +(0.639185 + 9.72530i) q^{55} +(1.50617 - 0.489384i) q^{56} +(-1.04734 + 2.03838i) q^{57} +(3.60493 + 1.83681i) q^{58} +(-0.576184 - 0.418622i) q^{59} +(-3.85558 - 0.366781i) q^{60} +(-5.17620 + 3.76073i) q^{61} +(2.86311 - 0.453472i) q^{62} +(-3.38222 + 3.33661i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-11.2029 - 4.81075i) q^{65} +(2.35726 - 7.17198i) q^{66} +(5.56612 - 10.9241i) q^{67} +(3.52806 + 3.52806i) q^{68} +(12.5899 - 9.08193i) q^{69} +(-3.53359 + 0.232242i) q^{70} +(1.05328 + 0.342232i) q^{71} +(2.66371 + 1.38009i) q^{72} +(2.62862 - 16.5964i) q^{73} +0.0682529 q^{74} +(8.15470 + 2.91562i) q^{75} +1.32312 q^{76} +(1.07983 - 6.81775i) q^{77} +(6.65519 + 6.70053i) q^{78} +(-7.08470 - 2.30196i) q^{79} +(0.828965 + 2.07673i) q^{80} +(-8.99917 - 0.122202i) q^{81} +(0.0564755 + 0.0564755i) q^{82} +(2.09751 - 4.11659i) q^{83} +(2.60587 + 0.856489i) q^{84} +(-5.70607 - 9.58712i) q^{85} +(-0.888543 - 1.22297i) q^{86} +(3.16023 + 6.25469i) q^{87} +(-4.30501 + 0.681846i) q^{88} +(5.12153 - 3.72101i) q^{89} +(-5.01415 - 4.45626i) q^{90} +(6.98585 + 5.07552i) q^{91} +(-7.98576 - 4.06895i) q^{92} +(4.46586 + 2.29460i) q^{93} +(-0.735824 + 0.239084i) q^{94} +(-2.86768 - 0.727750i) q^{95} +(0.00587961 - 1.73204i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	1.22890	−	1.22058i	0.709503	−	0.704702i
$3$	1.22890	−	1.22058i	0.709503	−	0.704702i
$4$	−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
$6$	−1.01331	−	1.40471i	−0.413683	−	0.573469i
$7$	−1.11983	−	1.11983i	−0.423256	−	0.423256i	0.463067	−	0.886323i	$-0.346749\pi$
$7$	−1.11983	−	1.11983i	−0.423256	−	0.423256i	−0.886323	+	0.463067i	$0.846749\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	0.0203674	−	2.99993i	0.00678915	−	0.999977i
$10$	1.47404	−	1.68143i	0.466132	−	0.531715i
$11$	2.56196	+	3.52624i	0.772460	+	1.06320i	0.996074	+	0.0885226i	$0.0282145\pi$
$11$	2.56196	+	3.52624i	0.772460	+	1.06320i	−0.223614	+	0.974678i	$0.571785\pi$
$12$	−1.54593	+	0.781091i	−0.446271	+	0.225482i
$13$	−5.38535	+	0.852956i	−1.49363	+	0.236567i	−0.849189	−	0.528089i	$-0.822909\pi$
$13$	−5.38535	+	0.852956i	−1.49363	+	0.236567i	−0.644438	+	0.764656i	$0.722909\pi$
$14$	−1.28122	+	0.930864i	−0.342422	+	0.248784i
$15$	3.78021	−	0.842609i	0.976047	−	0.217561i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−4.44561	−	2.26515i	−1.07822	−	0.549380i	−0.177651	−	0.984094i	$-0.556850\pi$
$17$	−4.44561	−	2.26515i	−1.07822	−	0.549380i	−0.900569	+	0.434713i	$0.856850\pi$
$18$	−2.95981	−	0.489409i	−0.697634	−	0.115355i
$19$	−1.25836	+	0.408866i	−0.288688	+	0.0938003i	−0.449781	−	0.893139i	$-0.648498\pi$
$19$	−1.25836	+	0.408866i	−0.288688	+	0.0938003i	0.161093	+	0.986939i	$0.448498\pi$
$20$	−1.43014	−	1.71893i	−0.319789	−	0.384363i
$21$	−2.74300	−	0.00931142i	−0.598571	−	0.00203192i
$22$	3.88360	−	1.97879i	0.827987	−	0.421880i
$23$	8.85228	+	1.40206i	1.84583	+	0.292351i	0.978633	−	0.205617i	$-0.0659200\pi$
$23$	8.85228	+	1.40206i	1.84583	+	0.292351i	0.867196	+	0.497967i	$0.165920\pi$
$24$	0.529638	+	1.64909i	0.108112	+	0.336618i
$25$	2.15418	+	4.51215i	0.430836	+	0.902430i
$26$			5.45248i			1.06932i
$27$	−3.63663	−	3.71146i	−0.699869	−	0.714271i
$28$	0.718976	+	1.41107i	0.135874	+	0.266667i
$29$	−1.25026	+	3.84789i	−0.232167	+	0.714536i	0.765318	+	0.643652i	$0.222582\pi$
$29$	−1.25026	+	3.84789i	−0.232167	+	0.714536i	−0.997485	+	0.0708831i	$0.977418\pi$
$30$	−0.240880	−	3.86549i	−0.0439784	−	0.705738i
$31$	0.895777	+	2.75692i	0.160886	+	0.495157i	0.998710	−	0.0507843i	$-0.0161721\pi$
$31$	0.895777	+	2.75692i	0.160886	+	0.495157i	−0.837823	+	0.545941i	$0.816172\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	7.45244	+	1.20630i	1.29730	+	0.209989i
$34$	−2.93271	+	4.03653i	−0.502956	+	0.692260i
$35$	−0.782158	−	3.45376i	−0.132209	−	0.583792i
$36$	−0.946400	+	2.84681i	−0.157733	+	0.474468i
$37$	0.0106771	+	0.0674126i	0.00175531	+	0.0110826i	0.988550	−	0.150891i	$-0.0482142\pi$
$37$	0.0106771	+	0.0674126i	0.00175531	+	0.0110826i	−0.986795	+	0.161973i	$0.948214\pi$
$38$	0.206981	+	1.30683i	0.0335768	+	0.211996i
$39$	−5.57693	+	7.62145i	−0.893024	+	1.22041i
$40$	−1.92149	+	1.14363i	−0.303814	+	0.180824i
$41$	−0.0469455	+	0.0646149i	−0.00733165	+	0.0100911i	−0.812667	−	0.582728i	$-0.801985\pi$
$41$	−0.0469455	+	0.0646149i	−0.00733165	+	0.0100911i	0.805335	+	0.592819i	$0.201985\pi$
$42$	−0.438296	+	2.70777i	−0.0676306	+	0.417818i
$43$	1.06892	−	1.06892i	0.163009	−	0.163009i	−0.620890	−	0.783898i	$-0.713228\pi$
$43$	1.06892	−	1.06892i	0.163009	−	0.163009i	0.783898	+	0.620890i	$0.213228\pi$
$44$	−1.34690	−	4.14534i	−0.203053	−	0.624933i
$45$	3.61701	−	5.64953i	0.539193	−	0.842182i
$46$	2.76960	−	8.52397i	0.408356	−	1.25679i
$47$	−0.351249	−	0.689364i	−0.0512349	−	0.100554i	0.863969	−	0.503544i	$-0.167971\pi$
$47$	−0.351249	−	0.689364i	−0.0512349	−	0.100554i	−0.915204	+	0.402990i	$0.867971\pi$
$48$	1.71164	−	0.265144i	0.247053	−	0.0382702i
$49$		−	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	$-0.838155\pi$
$53$	−7.22974	+	3.68374i	−0.993082	+	0.506000i	−0.119582	+	0.992824i	$0.538155\pi$
$54$	−4.23466	+	3.01125i	−0.576264	+	0.409780i
$55$	0.639185	+	9.72530i	0.0861877	+	1.31136i
$56$	1.50617	−	0.489384i	0.201270	−	0.0653967i
$57$	−1.04734	+	2.03838i	−0.138723	+	0.269991i
$58$	3.60493	+	1.83681i	0.473351	+	0.241184i
$59$	−0.576184	−	0.418622i	−0.0750127	−	0.0544999i	0.549647	−	0.835397i	$-0.314762\pi$
$59$	−0.576184	−	0.418622i	−0.0750127	−	0.0544999i	−0.624660	+	0.780897i	$0.714762\pi$
$60$	−3.85558	−	0.366781i	−0.497753	−	0.0473513i
$61$	−5.17620	+	3.76073i	−0.662745	+	0.481512i	−0.867589	−	0.497282i	$-0.834331\pi$
$61$	−5.17620	+	3.76073i	−0.662745	+	0.481512i	0.204844	+	0.978795i	$0.434331\pi$
$62$	2.86311	−	0.453472i	0.363615	−	0.0575909i
$63$	−3.38222	+	3.33661i	−0.426120	+	0.420373i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−11.2029	−	4.81075i	−1.38955	−	0.596700i
$66$	2.35726	−	7.17198i	0.290159	−	0.882810i
$67$	5.56612	−	10.9241i	0.680010	−	1.33459i	−0.250425	−	0.968136i	$-0.580570\pi$
$67$	5.56612	−	10.9241i	0.680010	−	1.33459i	0.930435	−	0.366458i	$-0.119430\pi$
$68$	3.52806	+	3.52806i	0.427840	+	0.427840i
$69$	12.5899	−	9.08193i	1.51564	−	1.09334i
$70$	−3.53359	+	0.232242i	−0.422345	+	0.0277582i
$71$	1.05328	+	0.342232i	0.125002	+	0.0406155i	0.370850	−	0.928693i	$-0.379066\pi$
$71$	1.05328	+	0.342232i	0.125002	+	0.0406155i	−0.245848	+	0.969308i	$0.579066\pi$
$72$	2.66371	+	1.38009i	0.313921	+	0.162645i
$73$	2.62862	−	16.5964i	0.307656	−	1.94247i	−0.0257147	−	0.999669i	$-0.508186\pi$
$73$	2.62862	−	16.5964i	0.307656	−	1.94247i	0.333371	−	0.942796i	$-0.391814\pi$
$74$	0.0682529			0.00793424
$75$	8.15470	+	2.91562i	0.941624	+	0.336666i
$76$	1.32312			0.151772
$77$	1.07983	−	6.81775i	0.123058	−	0.776955i
$78$	6.65519	+	6.70053i	0.753552	+	0.758685i
$79$	−7.08470	−	2.30196i	−0.797091	−	0.258990i	−0.117970	−	0.993017i	$-0.537639\pi$
$79$	−7.08470	−	2.30196i	−0.797091	−	0.258990i	−0.679121	+	0.734027i	$0.737639\pi$
$80$	0.828965	+	2.07673i	0.0926811	+	0.232186i
$81$	−8.99917	−	0.122202i	−0.999908	−	0.0135780i
$82$	0.0564755	+	0.0564755i	0.00623667	+	0.00623667i
$83$	2.09751	−	4.11659i	0.230231	−	0.451854i	−0.746772	−	0.665081i	$-0.768397\pi$
$83$	2.09751	−	4.11659i	0.230231	−	0.451854i	0.977003	+	0.213226i	$0.0683972\pi$
$84$	2.60587	+	0.856489i	0.284324	+	0.0934506i
$85$	−5.70607	−	9.58712i	−0.618910	−	1.03987i
$86$	−0.888543	−	1.22297i	−0.0958140	−	0.131877i
$87$	3.16023	+	6.25469i	0.338812	+	0.670574i
$88$	−4.30501	+	0.681846i	−0.458915	+	0.0726850i
$89$	5.12153	−	3.72101i	0.542881	−	0.394426i	−0.282273	−	0.959334i	$-0.591088\pi$
$89$	5.12153	−	3.72101i	0.542881	−	0.394426i	0.825154	+	0.564908i	$0.191088\pi$
$90$	−5.01415	−	4.45626i	−0.528538	−	0.469731i
$91$	6.98585	+	5.07552i	0.732316	+	0.532059i
$92$	−7.98576	−	4.06895i	−0.832573	−	0.424217i
$93$	4.46586	+	2.29460i	0.463088	+	0.237939i
$94$	−0.735824	+	0.239084i	−0.0758945	+	0.0246596i
$95$	−2.86768	−	0.727750i	−0.294218	−	0.0746655i
$96$	0.00587961	−	1.73204i	0.000600085	−	0.176776i
$97$	−10.5981	+	5.40000i	−1.07607	+	0.548287i	−0.899911	−	0.436074i	$-0.856369\pi$
$97$	−10.5981	+	5.40000i	−1.07607	+	0.548287i	−0.176163	+	0.984361i	$0.556369\pi$
$98$	−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	$-0.117978\pi$
$102$	1.32292	+	8.54009i	0.130988	+	0.845595i
$103$	−1.84465	−	3.62033i	−0.181759	−	0.356722i	0.782092	−	0.623162i	$-0.214152\pi$
$103$	−1.84465	−	3.62033i	−0.181759	−	0.356722i	−0.963851	+	0.266440i	$0.914152\pi$
$104$	1.68491	−	5.18562i	0.165219	−	0.508492i
$105$	−5.17678	−	3.28962i	−0.505202	−	0.321034i
$106$	2.50740	+	7.71700i	0.243541	+	0.749541i
$107$	−8.83022	+	8.83022i	−0.853650	+	0.853650i	−0.990581	−	0.136931i	$-0.956276\pi$
$107$	−8.83022	+	8.83022i	−0.853650	+	0.853650i	0.136931	+	0.990581i	$0.456276\pi$
$108$	2.31173	+	4.65359i	0.222447	+	0.447792i
$109$	−4.97517	+	6.84773i	−0.476535	+	0.655894i	−0.977834	−	0.209380i	$-0.932855\pi$
$109$	−4.97517	+	6.84773i	−0.476535	+	0.655894i	0.501300	+	0.865274i	$0.332855\pi$
$110$	9.70555	+	0.890056i	0.925388	+	0.0848635i
$111$	0.0954035	+	0.0698108i	0.00905530	+	0.00662614i
$112$	−0.247742	−	1.56418i	−0.0234094	−	0.147801i
$113$	−0.444366	−	2.80561i	−0.0418024	−	0.263930i	0.957932	−	0.286997i	$-0.0926569\pi$
$113$	−0.444366	−	2.80561i	−0.0418024	−	0.263930i	−0.999734	+	0.0230668i	$0.992657\pi$
$114$	1.84945	+	1.35332i	0.173217	+	0.126750i
$115$	15.0700	+	13.2113i	1.40529	+	1.23196i
$116$	2.37813	−	3.27321i	0.220804	−	0.303910i
$117$	2.44912	+	16.1731i	0.226421	+	1.49520i
$118$	−0.503603	+	0.503603i	−0.0463604	+	0.0463604i
$119$	2.44175	+	7.51492i	0.223835	+	0.688892i
$120$	−0.965411	+	3.75073i	−0.0881295	+	0.342393i
$121$	−2.47151	+	7.60654i	−0.224683	+	0.691504i
$122$	2.90469	+	5.70078i	0.262979	+	0.516125i
$123$	0.0211766	+	0.136706i	0.00190943	+	0.0123263i
$124$		−	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	0.188317	−	0.982108i	$-0.439697\pi$
$127$	0.720445	+	0.114107i	0.0639292	+	0.0101254i	−0.124388	+	0.992234i	$0.539697\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	0.00888808	−	2.61829i	0.000782552	−	0.230528i
$130$	−6.50404	+	10.3124i	−0.570442	+	0.904456i
$131$	7.16884	−	2.32930i	0.626345	−	0.203512i	0.0213895	−	0.999771i	$-0.493191\pi$
$131$	7.16884	−	2.32930i	0.626345	−	0.203512i	0.604955	+	0.796259i	$0.293191\pi$
$132$	−6.71492	−	3.45019i	−0.584459	−	0.300300i
$133$	1.86701	+	0.951290i	0.161890	+	0.0824873i
$134$	−9.91890	−	7.20650i	−0.856862	−	0.622547i
$135$	−2.45078	−	11.3575i	−0.210929	−	0.977501i
$136$	4.03653	−	2.93271i	0.346130	−	0.251478i
$137$	9.15207	−	1.44955i	0.781914	−	0.123843i	0.247300	−	0.968939i	$-0.420457\pi$
$137$	9.15207	−	1.44955i	0.781914	−	0.123843i	0.534615	+	0.845096i	$0.320457\pi$
$138$	−7.00063	−	13.8556i	−0.595933	−	1.17947i
$139$	3.83373	+	5.27668i	0.325173	+	0.447562i	0.940038	−	0.341070i	$-0.110789\pi$
$139$	3.83373	+	5.27668i	0.325173	+	0.447562i	−0.614865	+	0.788633i	$0.710789\pi$
$140$	−0.323393	+	3.52642i	−0.0273317	+	0.298037i
$141$	−1.27307	−	0.418429i	−0.107212	−	0.0352381i
$142$	0.502789	−	0.986779i	0.0421931	−	0.0828086i
$143$	−16.8048	−	16.8048i	−1.40529	−	1.40529i
$144$	1.77979	−	2.41502i	0.148316	−	0.201252i
$145$	−6.95462	+	5.78621i	−0.577550	+	0.480519i
$146$	−15.9809	−	5.19251i	−1.32259	−	0.429735i
$147$	−5.48279	−	5.52015i	−0.452213	−	0.455294i
$148$	0.0106771	−	0.0674126i	0.000877653	−	0.00554128i
$149$	17.4830			1.43226			0.716132	−	0.697964i	$-0.245911\pi$
$149$	17.4830			1.43226			0.716132	+	0.697964i	$0.245911\pi$
$150$	4.15540	−	7.59820i	0.339287	−	0.620391i
$151$	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
$153$	−6.88585	+	13.2904i	−0.556688	+	1.07446i
$154$	−6.56489	−	2.13306i	−0.529014	−	0.171887i
$155$	−1.59441	+	6.28275i	−0.128066	+	0.504643i
$156$	7.65913	−	5.52506i	0.613221	−	0.442359i
$157$	10.8749	+	10.8749i	0.867911	+	0.867911i	0.992241	−	0.124330i	$-0.0396780\pi$
$157$	10.8749	+	10.8749i	0.867911	+	0.867911i	−0.124330	+	0.992241i	$0.539678\pi$
$158$	−3.38191	+	6.63737i	−0.269050	+	0.528041i
$159$	−4.38830	+	13.3514i	−0.348015	+	1.05884i
$160$	2.18084	−	0.493886i	0.172411	−	0.0390452i
$161$	−8.34299	−	11.4831i	−0.657519	−	0.904998i
$162$	−1.52848	+	8.86926i	−0.120089	+	0.696835i
$163$	−23.9735	+	3.79703i	−1.87775	+	0.297407i	−0.987446	−	0.157958i	$-0.949509\pi$
$163$	−23.9735	+	3.79703i	−1.87775	+	0.297407i	−0.890305	+	0.455365i	$0.849509\pi$
$164$	0.0646149	−	0.0469455i	0.00504557	−	0.00366582i
$165$	12.6560	+	11.1712i	0.985268	+	0.869676i
$166$	−3.73778	−	2.71566i	−0.290108	−	0.210776i
$167$	8.70863	+	4.43727i	0.673894	+	0.343366i	0.757223	−	0.653156i	$-0.226555\pi$
$167$	8.70863	+	4.43727i	0.673894	+	0.343366i	−0.0833296	+	0.996522i	$0.526555\pi$
$168$	1.25359	−	2.43980i	0.0967167	−	0.188235i
$169$	15.9107	−	5.16971i	1.22390	−	0.397670i
$170$	−10.3617	+	4.13606i	−0.794707	+	0.317221i
$171$	1.20094	+	3.78332i	0.0918382	+	0.289318i
$172$	−1.34692	+	0.686288i	−0.102701	+	0.0523290i
$173$	−1.33648	−	0.211678i	−0.101611	−	0.0160936i	0.105422	−	0.994428i	$-0.466381\pi$
$173$	−1.33648	−	0.211678i	−0.101611	−	0.0160936i	−0.207033	+	0.978334i	$0.566381\pi$
$174$	6.67206	−	2.14287i	0.505807	−	0.162451i
$175$	2.64053	−	7.46516i	0.199606	−	0.564313i
$176$			4.35867i			0.328547i
$177$	−1.21903	+	0.188836i	−0.0916280	+	0.0141938i
$178$	−2.87401	−	5.64057i	−0.215417	−	0.422779i
$179$	1.80244	−	5.54735i	0.134721	−	0.414629i	−0.860826	−	0.508900i	$-0.830052\pi$
$179$	1.80244	−	5.54735i	0.134721	−	0.414629i	0.995547	+	0.0942716i	$0.0300522\pi$
$180$	−5.18579	+	4.25531i	−0.386526	+	0.317172i
$181$	−2.49922	−	7.69182i	−0.185766	−	0.571729i	0.814195	−	0.580592i	$-0.197179\pi$
$181$	−2.49922	−	7.69182i	−0.185766	−	0.571729i	−0.999961	+	0.00886318i	$0.997179\pi$
$182$	6.10586	−	6.10586i	0.452596	−	0.452596i
$183$	−1.77074	+	10.9395i	−0.130897	+	0.808673i
$184$	−5.26810	+	7.25092i	−0.388369	+	0.534545i
$185$	−0.0602199	+	0.140235i	−0.00442745	+	0.0103103i
$186$	2.96496	−	4.05192i	0.217401	−	0.297101i
$187$	−3.40202	−	21.4795i	−0.248780	−	1.57074i
$188$	0.121032	+	0.764166i	0.00882717	+	0.0557325i
$189$	−0.0838015	+	8.22862i	−0.00609566	+	0.598544i
$190$	−1.16739	+	2.71853i	−0.0846917	+	0.197223i
$191$	−7.75927	+	10.6797i	−0.561441	+	0.772757i	−0.991509	−	0.130039i	$-0.958490\pi$
$191$	−7.75927	+	10.6797i	−0.561441	+	0.772757i	0.430068	+	0.902797i	$0.358490\pi$
$192$	−1.70980	−	0.276758i	−0.123394	−	0.0199733i
$193$	5.85434	−	5.85434i	0.421404	−	0.421404i	−0.464283	−	0.885687i	$-0.653688\pi$
$193$	5.85434	−	5.85434i	0.421404	−	0.421404i	0.885687	+	0.464283i	$0.153688\pi$
$194$	3.67561	+	11.3124i	0.263894	+	0.812181i
$195$	−19.6391	+	7.76210i	−1.40638	+	0.555856i
$196$	−1.38809	+	4.27211i	−0.0991494	+	0.305150i
$197$	10.7134	+	21.0262i	0.763298	+	1.49806i	0.864193	+	0.503160i	$0.167830\pi$
$197$	10.7134	+	21.0262i	0.763298	+	1.49806i	−0.100895	+	0.994897i	$0.532170\pi$
$198$	−5.85715	−	11.6908i	−0.416249	−	0.830832i
$199$			11.9416i			0.846519i	0.906008	+	0.423260i	$0.139114\pi$
$199$			11.9416i			0.846519i	−0.906008	+	0.423260i	$0.860886\pi$
$200$	−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
$204$	8.64189	+	0.0293359i	0.605054	+	0.00205392i
$205$	−0.165865	+	0.0662081i	−0.0115845	+	0.00462417i
$206$	−3.86433	+	1.25560i	−0.269241	+	0.0874816i
$207$	4.38639	−	26.5277i	0.304875	−	1.84380i
$208$	−4.85820	−	2.47537i	−0.336855	−	0.171636i
$209$	−4.66563	−	3.38978i	−0.322728	−	0.234476i
$210$	−4.05895	+	4.59843i	−0.280094	+	0.317322i
$211$	17.6913	−	12.8535i	1.21792	−	0.884868i	0.221991	−	0.975049i	$-0.428744\pi$
$211$	17.6913	−	12.8535i	1.21792	−	0.884868i	0.995925	+	0.0901803i	$0.0287443\pi$
$212$	8.01423	−	1.26933i	0.550420	−	0.0871779i
$213$	1.71210	−	0.865049i	0.117311	−	0.0592722i
$214$	7.34016	+	10.1029i	0.501763	+	0.690617i
$215$	3.29673	−	0.746598i	0.224835	−	0.0509176i
$216$	4.95793	−	1.55529i	0.337344	−	0.105824i
$217$	2.08416	−	4.09040i	0.141482	−	0.277675i
$218$	5.98514	+	5.98514i	0.405365	+	0.405365i
$219$	−17.0270	−	23.6037i	−1.15058	−	1.59499i
$220$	2.39738	−	9.44683i	0.161631	−	0.636905i
$221$	25.8733	+	8.40673i	1.74042	+	0.565498i
$222$	0.0838757	−	0.0833081i	0.00562937	−	0.00559128i
$223$	3.61275	−	22.8100i	0.241928	−	1.52747i	−0.505323	−	0.862930i	$-0.668627\pi$
$223$	3.61275	−	22.8100i	0.241928	−	1.52747i	0.747251	−	0.664542i	$-0.231373\pi$
$224$	−1.58368			−0.105814
$225$	13.5800	−	6.37048i	0.905335	−	0.424699i
$226$	−2.84059			−0.188953
$227$	−2.38471	+	15.0565i	−0.158279	+	0.999334i	0.772835	+	0.634606i	$0.218838\pi$
$227$	−2.38471	+	15.0565i	−0.158279	+	0.999334i	−0.931114	+	0.364727i	$0.881162\pi$
$228$	1.62597	−	1.61497i	0.107683	−	0.106954i
$229$	−18.0834	−	5.87564i	−1.19498	−	0.388273i	−0.357070	−	0.934078i	$-0.616224\pi$
$229$	−18.0834	−	5.87564i	−1.19498	−	0.388273i	−0.837913	+	0.545804i	$0.816224\pi$
$230$	15.4061	−	12.8178i	1.01585	−	0.845180i
$231$	−6.99462	−	9.69632i	−0.460212	−	0.637971i
$232$	−2.86089	−	2.86089i	−0.187827	−	0.187827i
$233$	−0.567423	+	1.11363i	−0.0371731	+	0.0729563i	−0.908846	−	0.417132i	$-0.863035\pi$
$233$	−0.567423	+	1.11363i	−0.0371731	+	0.0729563i	0.871673	+	0.490088i	$0.163035\pi$
$234$	16.3571	+	0.111053i	1.06929	+	0.00725976i
$235$	0.157991	−	1.72280i	0.0103062	−	0.112383i
$236$	0.418622	+	0.576184i	0.0272500	+	0.0375064i
$237$	−11.5161	+	5.81858i	−0.748050	+	0.377957i
$238$	7.80438	−	1.23609i	0.505883	−	0.0801239i
$239$	0.0867791	−	0.0630487i	0.00561328	−	0.00407828i	−0.584975	−	0.811051i	$-0.698896\pi$
$239$	0.0867791	−	0.0630487i	0.00561328	−	0.00407828i	0.590588	+	0.806973i	$0.298896\pi$
$240$	3.55353	+	1.54027i	0.229379	+	0.0994239i
$241$	−9.47730	−	6.88566i	−0.610486	−	0.443544i	0.239099	−	0.970995i	$-0.423148\pi$
$241$	−9.47730	−	6.88566i	−0.610486	−	0.443544i	−0.849586	+	0.527451i	$0.823148\pi$
$242$	7.12626	+	3.63101i	0.458093	+	0.233410i
$243$	−11.2082	+	10.8340i	−0.719006	+	0.695004i
$244$	6.08499	−	1.97713i	0.389552	−	0.126573i
$245$	5.35827	−	8.49573i	0.342327	−	0.542772i
$246$	0.138335		0.000469595i	0.00881994		2.99403e-5i
$247$	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	$-0.395836\pi$
$252$	4.24775	−	2.12814i	0.267583	−	0.134060i
$253$	17.7352	+	34.8073i	1.11500	+	2.18831i
$254$	0.225405	−	0.693725i	0.0141432	−	0.0435282i
$255$	−18.7140	−	4.81685i	−1.17192	−	0.301643i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−10.3109	+	10.3109i	−0.643174	+	0.643174i	−0.951334	−	0.308161i	$-0.900287\pi$
$257$	−10.3109	+	10.3109i	−0.643174	+	0.643174i	0.308161	+	0.951334i	$0.400287\pi$
$258$	−2.58466	−	0.418369i	−0.160914	−	0.0260465i
$259$	0.0635342	−	0.0874473i	0.00394782	−	0.00543371i
$260$	9.16796	+	8.03717i	0.568573	+	0.498444i
$261$	11.5179	+	3.82905i	0.712943	+	0.237012i
$262$	−1.17917	−	7.44497i	−0.0728492	−	0.459951i
$263$	−0.896435	−	5.65987i	−0.0552765	−	0.349002i	−0.999789	−	0.0205276i	$-0.993465\pi$
$263$	−0.896435	−	5.65987i	−0.0552765	−	0.349002i	0.944513	−	0.328475i	$-0.106535\pi$
$264$	−4.45815	+	6.09252i	−0.274380	+	0.374969i
$265$	−18.0679	−	1.65693i	−1.10990	−	0.101785i
$266$	1.23164	−	1.69521i	0.0755169	−	0.103940i
$267$	1.75203	−	10.8240i	0.107223	−	0.662416i
$268$	−8.66943	+	8.66943i	−0.529570	+	0.529570i
$269$	8.89631	+	27.3800i	0.542418	+	1.66939i	0.727051	+	0.686583i	$0.240890\pi$
$269$	8.89631	+	27.3800i	0.542418	+	1.66939i	−0.184634	+	0.982807i	$0.559110\pi$
$270$	−11.6011	+	0.643892i	−0.706020	+	0.0391860i
$271$	2.94335	−	9.05871i	0.178796	−	0.550277i	−0.820991	−	0.570942i	$-0.806578\pi$
$271$	2.94335	−	9.05871i	0.178796	−	0.550277i	0.999786	+	0.0206645i	$0.00657819\pi$
$272$	−2.26515	−	4.44561i	−0.137345	−	0.269555i
$273$	14.7800	−	2.28951i	0.894523	−	0.138568i
$274$		−	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	0.196195	−	0.980565i	$-0.437141\pi$
$277$	1.32775	+	0.210294i	0.0797766	+	0.0126354i	−0.116419	+	0.993200i	$0.537141\pi$
$278$	5.81144	−	2.96108i	0.348547	−	0.177594i
$279$	8.28881	−	2.63112i	0.496238	−	0.157521i
$280$	3.43241	+	0.871065i	0.205126	+	0.0520561i
$281$	−3.45870	+	1.12380i	−0.206329	+	0.0670403i	−0.410358	−	0.911925i	$-0.634596\pi$
$281$	−3.45870	+	1.12380i	−0.206329	+	0.0670403i	0.204029	+	0.978965i	$0.434596\pi$
$282$	−0.612430	+	1.19194i	−0.0364697	+	0.0709791i
$283$	23.2662	+	11.8547i	1.38303	+	0.704689i	0.977803	−	0.209528i	$-0.0671927\pi$
$283$	23.2662	+	11.8547i	1.38303	+	0.704689i	0.405226	+	0.914216i	$0.367193\pi$
$284$	−0.895976	−	0.650965i	−0.0531664	−	0.0386277i
$285$	−4.41236	+	2.60591i	−0.261365	+	0.154361i
$286$	−19.2267	+	13.9690i	−1.13690	+	0.826007i
$287$	0.124929	−	0.0197868i	0.00737431	−	0.00116798i
$288$	−2.10687	−	2.13567i	−0.124148	−	0.125846i
$289$	4.64021	+	6.38670i	0.272954	+	0.375688i
$290$	4.62703	+	7.77416i	0.271709	+	0.456515i
$291$	−6.43282	+	19.5719i	−0.377099	+	1.14732i
$292$	−7.62854	+	14.9719i	−0.446427	+	0.876162i
$293$	7.70940	+	7.70940i	0.450388	+	0.450388i	0.895483	−	0.445095i	$-0.146830\pi$
$293$	7.70940	+	7.70940i	0.450388	+	0.450388i	−0.445095	+	0.895483i	$0.646830\pi$
$294$	−6.30988	+	4.55175i	−0.368000	+	0.265464i
$295$	−0.590391	−	1.47905i	−0.0343739	−	0.0861138i
$296$	−0.0649124	−	0.0210913i	−0.00377295	−	0.00122591i
$297$	3.77059	−	22.3322i	0.218792	−	1.29585i
$298$	2.73495	−	17.2678i	0.158431	−	1.00030i
$299$	−48.8685			−2.82614
$300$	−6.85461	−	5.29286i	−0.395751	−	0.305583i
$301$	−2.39402			−0.137989
$302$	2.35307	−	14.8567i	0.135404	−	0.854908i
$303$	−8.88628	−	8.94682i	−0.510503	−	0.513981i
$304$	−1.25836	−	0.408866i	−0.0721719	−	0.0234501i
$305$	−14.2759	+	0.938267i	−0.817434	+	0.0537250i
$306$	12.0496	+	8.88015i	0.688829	+	0.507644i
$307$	12.2859	+	12.2859i	0.701191	+	0.701191i	0.964666	−	0.263476i	$-0.0848688\pi$
$307$	12.2859	+	12.2859i	0.701191	+	0.701191i	−0.263476	+	0.964666i	$0.584869\pi$
$308$	−3.13378	+	6.15038i	−0.178564	+	0.350451i
$309$	−6.68579	−	2.19747i	−0.380342	−	0.125009i
$310$	5.95598	+	2.55762i	0.338277	+	0.145263i
$311$	−3.02551	−	4.16426i	−0.171561	−	0.236134i	0.714575	−	0.699559i	$-0.246620\pi$
$311$	−3.02551	−	4.16426i	−0.171561	−	0.236134i	−0.886136	+	0.463425i	$0.846620\pi$
$312$	−4.25888	−	8.42915i	−0.241112	−	0.477206i
$313$	−10.3075	+	1.63255i	−0.582617	+	0.0922774i	−0.440784	−	0.897613i	$-0.645300\pi$
$313$	−10.3075	+	1.63255i	−0.582617	+	0.0922774i	−0.141833	+	0.989891i	$0.545300\pi$
$314$	12.4422	−	9.03980i	0.702155	−	0.510146i
$315$	−10.3770	+	2.27608i	−0.584676	+	0.128242i
$316$	6.02660	+	4.37858i	0.339023	+	0.246315i
$317$	−24.5645	−	12.5162i	−1.37968	−	0.702981i	−0.402503	−	0.915419i	$-0.631860\pi$
$317$	−24.5645	−	12.5162i	−1.37968	−	0.702981i	−0.977175	+	0.212438i	$0.931860\pi$
$318$	12.5006	+	6.42289i	0.700996	+	0.360178i
$319$	−16.7717	+	5.44945i	−0.939034	+	0.305111i
$320$	−0.146647	−	2.23125i	−0.00819781	−	0.124731i
$321$	−0.0734235	+	21.6294i	−0.00409810	+	1.20724i
$322$	−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
$327$	2.24424	+	14.4877i	0.124107	+	0.801174i
$328$	−0.0362595	−	0.0711632i	−0.00200210	−	0.00392933i
$329$	−0.378632	+	1.16531i	−0.0208747	+	0.0642456i
$330$	13.0135	−	10.7526i	0.716369	−	0.591912i
$331$	4.85839	+	14.9526i	0.267042	+	0.821869i	0.991216	+	0.132253i	$0.0422210\pi$
$331$	4.85839	+	14.9526i	0.267042	+	0.821869i	−0.724175	+	0.689617i	$0.757779\pi$
$332$	−3.26694	+	3.26694i	−0.179297	+	0.179297i
$333$	0.202451	−	0.0306576i	0.0110942	−	0.00168002i
$334$	5.74497	−	7.90727i	0.314351	−	0.432666i
$335$	23.5582	−	14.0214i	1.28712	−	0.766072i
$336$	−2.21366	−	1.61983i	−0.120765	−	0.0883688i
$337$	3.27427	+	20.6729i	0.178361	+	1.12613i	0.900653	+	0.434538i	$0.143088\pi$
$337$	3.27427	+	20.6729i	0.178361	+	1.12613i	−0.722292	+	0.691588i	$0.756912\pi$
$338$	−2.61708	−	16.5236i	−0.142350	−	0.898764i
$339$	−3.97056	−	2.90542i	−0.215651	−	0.157801i
$340$	2.46421	+	10.8812i	0.133641	+	0.590114i
$341$	−7.42660	+	10.2218i	−0.402173	+	0.553544i
$342$	3.92461	−	0.594313i	0.212219	−	0.0321368i
$343$	−12.8690	+	12.8690i	−0.694863	+	0.694863i
$344$	0.467135	+	1.43769i	0.0251862	+	0.0775152i
$345$	34.6449	−	2.15891i	1.86522	−	0.116232i
$346$	−0.418144	+	1.28691i	−0.0224796	+	0.0691850i
$347$	−4.78862	−	9.39820i	−0.257067	−	0.504522i	0.726018	−	0.687676i	$-0.241369\pi$
$347$	−4.78862	−	9.39820i	−0.257067	−	0.504522i	−0.983084	+	0.183155i	$0.941369\pi$
$348$	−1.07275	−	6.92513i	−0.0575053	−	0.371226i
$349$		−	26.2133i		−	1.40316i	−0.712588	−	0.701582i	$-0.752477\pi$
$349$		−	26.2133i		−	1.40316i	0.712588	−	0.701582i	$-0.247523\pi$
$350$	−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	$-0.685274\pi$
$353$	−3.70269	+	1.88662i	−0.197074	+	0.100414i	0.352669	+	0.935748i	$0.385274\pi$
$354$	−0.00418747	+	1.23356i	−0.000222561	+	0.0655631i
$355$	1.58386	+	1.90369i	0.0840626	+	0.101037i
$356$	−6.02072	+	1.95625i	−0.319098	+	0.103681i
$357$	12.1732	+	6.25471i	0.644275	+	0.331034i
$358$	−5.19709	−	2.64805i	−0.274675	−	0.139954i
$359$	4.75359	+	3.45368i	0.250885	+	0.182279i	0.706119	−	0.708093i	$-0.250444\pi$
$359$	4.75359	+	3.45368i	0.250885	+	0.182279i	−0.455234	+	0.890372i	$0.650444\pi$
$360$	3.39168	+	5.78762i	0.178757	+	0.305034i
$361$	−13.9550	+	10.1389i	−0.734475	+	0.533627i
$362$	−7.98809	+	1.26519i	−0.419844	+	0.0664968i
$363$	6.24716	+	12.3643i	0.327891	+	0.648959i
$364$	−5.07552	−	6.98585i	−0.266029	−	0.366158i
$365$	24.7687	−	28.2536i	1.29646	−	1.47886i
$366$	10.5278	+	3.46025i	0.550299	+	0.180870i
$367$	−7.71561	+	15.1427i	−0.402751	+	0.790444i	−0.999932	−	0.0116626i	$-0.996288\pi$
$367$	−7.71561	+	15.1427i	−0.402751	+	0.790444i	0.597181	+	0.802107i	$0.296288\pi$
$368$	6.33753	+	6.33753i	0.330367	+	0.330367i
$369$	0.192884	+	0.142149i	0.0100411	+	0.00739999i
$370$	0.129088	+	0.0814160i	0.00671097	+	0.00423262i
$371$	12.2213	+	3.97093i	0.634496	+	0.206160i
$372$	−3.53821	−	3.56232i	−0.183448	−	0.184698i
$373$	−4.29420	+	27.1125i	−0.222345	+	1.40383i	0.583696	+	0.811972i	$0.301606\pi$
$373$	−4.29420	+	27.1125i	−0.222345	+	1.40383i	−0.806041	+	0.591859i	$0.798394\pi$
$374$	−21.7473			−1.12452
$375$	11.9452	+	15.2418i	0.616849	+	0.787081i
$376$	0.773692			0.0399001
$377$	3.45098	−	21.7887i	0.177735	−	1.12217i
$378$	8.11420	+	1.37001i	0.417349	+	0.0704657i
$379$	14.0563	+	4.56718i	0.722026	+	0.234600i	0.646901	−	0.762574i	$-0.276065\pi$
$379$	14.0563	+	4.56718i	0.722026	+	0.234600i	0.0751246	+	0.997174i	$0.476065\pi$
$380$	2.50244	+	1.57829i	0.128372	+	0.0809647i
$381$	1.02463	−	0.739135i	0.0524933	−	0.0378670i
$382$	9.33442	+	9.33442i	0.477590	+	0.477590i
$383$	7.56228	−	14.8418i	0.386414	−	0.758381i	−0.613085	−	0.790017i	$-0.710072\pi$
$383$	7.56228	−	14.8418i	0.386414	−	0.758381i	0.999499	+	0.0316359i	$0.0100717\pi$
$384$	−0.540822	+	1.64545i	−0.0275987	+	0.0839691i
$385$	10.1749	−	11.6065i	0.518561	−	0.591520i
$386$	−4.86644	−	6.69808i	−0.247695	−	0.340923i
$387$	−3.18491	−	3.22845i	−0.161898	−	0.164111i
$388$	11.7481	−	1.86071i	0.596419	−	0.0944635i
$389$	19.7696	−	14.3635i	1.00236	−	0.728257i	0.0397671	−	0.999209i	$-0.487338\pi$
$389$	19.7696	−	14.3635i	1.00236	−	0.728257i	0.962593	+	0.270952i	$0.0873384\pi$
$390$	4.59431	+	20.6115i	0.232642	+	1.04371i
$391$	−36.1779	−	26.2848i	−1.82960	−	1.32928i
$392$	4.00236	+	2.03931i	0.202150	+	0.103001i
$393$	5.96666	−	11.6126i	0.300978	−	0.585779i
$394$	22.4433	−	7.29228i	1.13068	−	0.367380i
$395$	−10.6535	−	12.8048i	−0.536037	−	0.644278i
$396$	−12.4632	+	3.95618i	−0.626298	+	0.198806i
$397$	−6.08913	+	3.10257i	−0.305605	+	0.155713i	−0.600067	−	0.799950i	$-0.704859\pi$
$397$	−6.08913	+	3.10257i	−0.305605	+	0.155713i	0.294462	+	0.955663i	$0.404859\pi$
$398$	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	$0.808165\pi$
$402$	−20.9854	+	3.25078i	−1.04666	+	0.162134i
$403$	−7.17560	−	14.0829i	−0.357442	−	0.701520i
$404$	−2.24976	+	6.92405i	−0.111930	+	0.344484i
$405$	−16.8745	−	10.9659i	−0.838502	−	0.544898i
$406$	−1.98001	−	6.09383i	−0.0982660	−	0.302432i
$407$	−0.210358	+	0.210358i	−0.0104271	+	0.0104271i
$408$	1.38086	−	8.53091i	0.0683630	−	0.422343i
$409$	8.27872	−	11.3947i	0.409357	−	0.563431i	−0.553705	−	0.832713i	$-0.686786\pi$
$409$	8.27872	−	11.3947i	0.409357	−	0.563431i	0.963061	+	0.269282i	$0.0867864\pi$
$410$	0.0394459	+	0.174180i	0.00194809	+	0.00860216i
$411$	9.47765	−	12.9522i	0.467498	−	0.638884i
$412$	0.635624	+	4.01317i	0.0313149	+	0.197715i
$413$	0.176443	+	1.11401i	0.00868217	+	0.0548171i
$414$	−25.5149	−	8.48223i	−1.25399	−	0.416879i
$415$	8.87756	−	5.28376i	0.435782	−	0.259369i
$416$	−3.20489	+	4.41115i	−0.157133	+	0.216274i
$417$	11.1519	+	1.80511i	0.546109	+	0.0883966i
$418$	−4.07791	+	4.07791i	−0.199457	+	0.199457i
$419$	5.00642	+	15.4082i	0.244579	+	0.752738i	0.995705	+	0.0925792i	$0.0295111\pi$
$419$	5.00642	+	15.4082i	0.244579	+	0.752738i	−0.751126	+	0.660159i	$0.770489\pi$
$420$	3.90686	+	4.72833i	0.190635	+	0.230719i
$421$	0.809743	−	2.49213i	0.0394645	−	0.121459i	−0.929383	−	0.369116i	$-0.879661\pi$
$421$	0.809743	−	2.49213i	0.0394645	−	0.121459i	0.968848	+	0.247657i	$0.0796605\pi$
$422$	−9.92768	−	19.4842i	−0.483272	−	0.948475i
$423$	−2.07520	+	1.03968i	−0.100900	+	0.0505510i
$424$		−	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
$429$	−41.1629	−	0.139732i	−1.98736	−	0.00674633i
$430$	−0.221683	−	3.37294i	−0.0106905	−	0.162658i
$431$	−21.5704	+	7.00864i	−1.03901	+	0.337594i	−0.778346	−	0.627835i	$-0.783941\pi$
$431$	−21.5704	+	7.00864i	−1.03901	+	0.337594i	−0.260663	+	0.965430i	$0.583941\pi$
$432$	−0.760551	−	5.14019i	−0.0365920	−	0.247308i
$433$	15.3259	+	7.80892i	0.736514	+	0.375273i	0.781658	−	0.623708i	$-0.214374\pi$
$433$	15.3259	+	7.80892i	0.736514	+	0.375273i	−0.0451434	+	0.998981i	$0.514374\pi$
$434$	−3.71401	−	2.69838i	−0.178278	−	0.129527i
$435$	−1.48396	+	15.5993i	−0.0711507	+	0.747930i
$436$	6.84773	−	4.97517i	0.327947	−	0.238267i
$437$	−11.7126	+	1.85510i	−0.560291	+	0.0887413i
$438$	−25.9767	+	13.1249i	−1.24122	+	0.627133i
$439$	−9.32959	−	12.8411i	−0.445277	−	0.612872i	0.526097	−	0.850424i	$-0.323655\pi$
$439$	−9.32959	−	12.8411i	−0.445277	−	0.612872i	−0.971375	+	0.237553i	$0.923655\pi$
$440$	−8.95549	−	3.84567i	−0.426936	−	0.183335i
$441$	−13.4756	−	0.0914897i	−0.641693	−	0.00435665i
$442$	12.3507	−	24.2396i	0.587463	−	1.15296i
$443$	6.25112	+	6.25112i	0.297000	+	0.297000i	0.839838	−	0.542838i	$-0.182650\pi$
$443$	6.25112	+	6.25112i	0.297000	+	0.297000i	−0.542838	+	0.839838i	$0.682650\pi$
$444$	−0.0691614	−	0.0958753i	−0.00328226	−	0.00455004i
$445$	14.1251	−	0.928357i	0.669594	−	0.0440084i
$446$	−21.9640	−	7.13655i	−1.04003	−	0.337925i
$447$	21.4848	−	21.3394i	1.01620	−	1.00932i
$448$	−0.247742	+	1.56418i	−0.0117047	+	0.0739007i
$449$	−4.48699			−0.211754			−0.105877	−	0.994379i	$-0.533765\pi$
$449$	−4.48699			−0.211754			−0.105877	+	0.994379i	$0.533765\pi$
$450$	−4.16767	−	14.4094i	−0.196466	−	0.679265i
$451$	−0.348120			−0.0163923
$452$	−0.444366	+	2.80561i	−0.0209012	+	0.131965i
$453$	18.4849	−	18.3599i	0.868498	−	0.862621i
$454$	14.4981	+	4.71070i	0.680428	+	0.221084i
$455$	7.15810	+	17.9326i	0.335577	+	0.840691i
$456$	−1.34073	−	1.85859i	−0.0627855	−	0.0870366i
$457$	−21.3476	−	21.3476i	−0.998599	−	0.998599i	0.00140011	−	0.999999i	$-0.499554\pi$
$457$	−21.3476	−	21.3476i	−0.998599	−	0.998599i	−0.999999	+	0.00140011i	$0.999554\pi$
$458$	−8.63217	+	16.9416i	−0.403355	+	0.791628i
$459$	7.76001	+	24.7372i	0.362206	+	1.15464i
$460$	−10.2499	−	17.2216i	−0.477906	−	0.802959i
$461$	15.2106	+	20.9356i	0.708430	+	0.975070i	0.999829	+	0.0184685i	$0.00587905\pi$
$461$	15.2106	+	20.9356i	0.708430	+	0.975070i	−0.291400	+	0.956601i	$0.594121\pi$
$462$	−10.6711	+	5.39167i	−0.496466	+	0.250843i
$463$	10.1474	−	1.60719i	0.471590	−	0.0746925i	0.0838837	−	0.996476i	$-0.473268\pi$
$463$	10.1474	−	1.60719i	0.471590	−	0.0746925i	0.387706	+	0.921783i	$0.373268\pi$
$464$	−3.27321	+	2.37813i	−0.151955	+	0.110402i
$465$	5.70923	+	9.66695i	0.264759	+	0.448294i
$466$	1.01116	+	0.734647i	0.0468409	+	0.0340319i
$467$	13.5652	+	6.91180i	0.627722	+	0.319840i	0.738753	−	0.673977i	$-0.235415\pi$
$467$	13.5652	+	6.91180i	0.627722	+	0.319840i	−0.111031	+	0.993817i	$0.535415\pi$
$468$	2.66849	−	16.1383i	0.123351	−	0.745994i
$469$	−18.4663	+	6.00006i	−0.852694	+	0.277057i
$470$	−1.67687	−	0.425550i	−0.0773483	−	0.0196292i
$471$	26.6378	+	0.0904250i	1.22741	+	0.00416656i
$472$	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
$477$	10.9037	+	21.7638i	0.499247	+	0.996494i
$478$	−0.0486972	−	0.0955737i	−0.00222736	−	0.00437144i
$479$	5.66185	−	17.4254i	0.258697	−	0.796186i	−0.734382	−	0.678736i	$-0.762528\pi$
$479$	5.66185	−	17.4254i	0.258697	−	0.796186i	0.993079	−	0.117450i	$-0.0374720\pi$
$480$	2.07720	−	3.26883i	0.0948108	−	0.149201i
$481$	−0.115000	−	0.353933i	−0.00524355	−	0.0161380i
$482$	−8.28346	+	8.28346i	−0.377301	+	0.377301i
$483$	−24.2687	−	3.92829i	−1.10427	−	0.178743i
$484$	4.70110	−	6.47051i	0.213686	−	0.294114i
$485$	−26.4858	−	2.42891i	−1.20266	−	0.110291i
$486$	8.94730	+	12.7650i	0.405858	+	0.579033i
$487$	−0.621987	−	3.92707i	−0.0281849	−	0.177953i	0.969580	−	0.244775i	$-0.0787140\pi$
$487$	−0.621987	−	3.92707i	−0.0281849	−	0.177953i	−0.997765	+	0.0668221i	$0.978714\pi$
$488$	−1.00089	−	6.31937i	−0.0453081	−	0.286064i
$489$	−24.8264	+	33.9278i	−1.12269	+	1.53427i
$490$	−7.55291	−	6.62132i	−0.341206	−	0.299121i
$491$	11.8356	−	16.2903i	0.534132	−	0.735170i	−0.453621	−	0.891195i	$-0.649868\pi$
$491$	11.8356	−	16.2903i	0.534132	−	0.735170i	0.987753	+	0.156025i	$0.0498680\pi$
$492$	0.0221042	−	0.136559i	0.000996535	−	0.00615654i
$493$	14.2742	−	14.2742i	0.642878	−	0.642878i
$494$	−2.22933	−	6.86119i	−0.100302	−	0.308699i
$495$	29.1882	−	1.71943i	1.31191	−	0.0772827i
$496$	−0.895777	+	2.75692i	−0.0402216	+	0.123789i
$497$	−0.796257	−	1.56274i	−0.0357170	−	0.0700985i
$498$	−7.90803	+	1.22501i	−0.354367	+	0.0548938i
$499$			26.9424i			1.20611i	0.797700	+	0.603054i	$0.206050\pi$
$499$			26.9424i			1.20611i	−0.797700	+	0.603054i	$0.793950\pi$
$500$	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	$-0.736322\pi$
$503$	−10.7060	+	5.45499i	−0.477358	+	0.243226i	0.198720	+	0.980056i	$0.436322\pi$
$504$	−1.43744	−	4.52837i	−0.0640287	−	0.201710i
$505$	8.68445	−	13.7695i	0.386453	−	0.612735i
$506$	37.1531	−	12.0718i	1.65166	−	0.536656i
$507$	13.2426	−	25.7734i	0.588124	−	1.14464i
$508$	−0.649923	−	0.331152i	−0.0288357	−	0.0146925i
$509$	−33.2088	−	24.1276i	−1.47196	−	1.06944i	−0.980041	−	0.198794i	$-0.936297\pi$
$509$	−33.2088	−	24.1276i	−1.47196	−	1.06944i	−0.491914	−	0.870644i	$-0.663703\pi$
$510$	−7.68506	+	17.7301i	−0.340300	+	0.785101i
$511$	−21.5288	+	15.6416i	−0.952378	+	0.691943i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	6.09368	+	3.18346i	0.269042	+	0.140553i
$514$	8.57094	+	11.7969i	0.378048	+	0.520339i
$515$	0.829719	−	9.04762i	0.0365618	−	0.398686i
$516$	−0.817549	+	2.48740i	−0.0359906	+	0.109501i
$517$	1.53098	−	3.00471i	0.0673323	−	0.132147i
$518$	−0.0764317	−	0.0764317i	−0.00335822	−	0.00335822i
$519$	−1.90077	+	1.37115i	−0.0834344	+	0.0601870i
$520$	9.37241	−	7.79780i	0.411007	−	0.341956i
$521$	11.9997	+	3.89893i	0.525715	+	0.170815i	0.559837	−	0.828602i	$-0.310864\pi$
$521$	11.9997	+	3.89893i	0.525715	+	0.170815i	−0.0341223	+	0.999418i	$0.510864\pi$
$522$	5.58371	−	10.7771i	0.244393	−	0.471703i
$523$	−4.31549	+	27.2469i	−0.188703	+	1.19142i	0.693465	+	0.720490i	$0.256083\pi$
$523$	−4.31549	+	27.2469i	−0.188703	+	1.19142i	−0.882168	+	0.470934i	$0.843917\pi$
$524$	−7.53777			−0.329289
$525$	−5.86689	−	12.3969i	−0.256052	−	0.541044i
$526$	−5.73042			−0.249858
$527$	2.26256	−	14.2853i	0.0985588	−	0.622276i
$528$	5.32010	+	5.35635i	0.231528	+	0.233105i
$529$	54.5228	+	17.7155i	2.37056	+	0.770241i
$530$	−4.46298	+	17.5863i	−0.193860	+	0.763899i
$531$	−1.26757	+	1.71998i	−0.0550080	+	0.0746410i
$532$	−1.48167	−	1.48167i	−0.0642385	−	0.0642385i
$533$	0.197704	−	0.388016i	0.00856352	−	0.0168068i
$534$	−10.4166	−	3.42371i	−0.450772	−	0.148158i
$535$	−27.2340	+	6.16756i	−1.17743	+	0.266647i
$536$	7.20650	+	9.91890i	0.311273	+	0.428431i
$537$	−4.55597	−	9.01714i	−0.196605	−	0.389118i
$538$	28.4346	−	4.50360i	1.22590	−	0.194164i
$539$	15.8397	−	11.5082i	0.682264	−	0.495694i
$540$	−1.17885	+	11.5590i	−0.0507295	+	0.497420i
$541$	9.58802	+	6.96610i	0.412221	+	0.299496i	0.774500	−	0.632573i	$-0.218001\pi$
$541$	9.58802	+	6.96610i	0.412221	+	0.299496i	−0.362279	+	0.932070i	$0.618001\pi$
$542$	−8.48674	−	4.32421i	−0.364537	−	0.185741i
$543$	−12.4598	−	6.40194i	−0.534700	−	0.274733i
$544$	−4.74523	+	1.54182i	−0.203450	+	0.0661049i
$545$	−17.5780	+	7.01657i	−0.752959	+	0.300557i
$546$	0.0507703	−	14.9561i	0.00217277	−	0.640064i
$547$	−11.2529	+	5.73365i	−0.481140	+	0.245153i	−0.677700	−	0.735339i	$-0.737023\pi$
$547$	−11.2529	+	5.73365i	−0.481140	+	0.245153i	0.196560	+	0.980492i	$0.437023\pi$
$548$	−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
$552$	2.37638	+	15.3408i	0.101146	+	0.652946i
$553$	5.35586	+	10.5115i	0.227754	+	0.446993i
$554$	0.415411	−	1.27850i	0.0176491	−	0.0543184i
$555$	0.0971642	+	0.245837i	0.00412439	+	0.0104352i
$556$	−2.01551	−	6.20311i	−0.0854768	−	0.263070i
$557$	14.4201	−	14.4201i	0.611000	−	0.611000i	−0.332207	−	0.943207i	$-0.607793\pi$
$557$	14.4201	−	14.4201i	0.611000	−	0.611000i	0.943207	+	0.332207i	$0.107793\pi$
$558$	−1.30207	−	8.59836i	−0.0551210	−	0.363998i
$559$	−4.84476	+	6.66824i	−0.204912	+	0.282037i
$560$	1.39729	−	3.25389i	0.0590462	−	0.137502i
$561$	−30.3982	−	22.2436i	−1.28341	−	0.939127i
$562$	0.568904	+	3.59192i	0.0239978	+	0.151516i
$563$	3.91368	+	24.7100i	0.164942	+	1.04140i	0.921756	+	0.387771i	$0.126755\pi$
$563$	3.91368	+	24.7100i	0.164942	+	1.04140i	−0.756814	+	0.653631i	$0.773245\pi$
$564$	1.08146	+	0.791351i	0.0455378	+	0.0333219i
$565$	2.50626	−	5.83638i	0.105439	−	0.245538i
$566$	15.3484	−	21.1252i	0.645140	−	0.887959i
$567$	9.94070	+	10.2144i	0.417470	+	0.428964i
$568$	−0.783112	+	0.783112i	−0.0328586	+	0.0328586i
$569$	11.3127	+	34.8170i	0.474254	+	1.45960i	0.846961	+	0.531655i	$0.178430\pi$
$569$	11.3127	+	34.8170i	0.474254	+	1.45960i	−0.372706	+	0.927949i	$0.621570\pi$
$570$	1.88358	+	4.76569i	0.0788945	+	0.199613i
$571$	6.22100	−	19.1463i	0.260341	−	0.801246i	−0.732389	−	0.680886i	$-0.761595\pi$
$571$	6.22100	−	19.1463i	0.260341	−	0.801246i	0.992730	−	0.120361i	$-0.0384051\pi$
$572$	10.7893	+	21.1753i	0.451125	+	0.885382i
$573$	3.50012	+	22.5951i	0.146220	+	0.943923i
$574$		−	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	0.0603688	−	0.998176i	$-0.480772\pi$
$577$	−4.58006	−	0.725410i	−0.190670	−	0.0301992i	−0.251039	+	0.967977i	$0.580772\pi$
$578$	7.03396	−	3.58398i	0.292574	−	0.149074i
$579$	0.0486789	−	14.3401i	0.00202303	−	0.595953i
$580$	8.40228	−	3.35392i	0.348886	−	0.139264i
$581$	−6.95874	+	2.26103i	−0.288697	+	0.0938034i
$582$	18.3246	+	9.41534i	0.759579	+	0.390278i
$583$	−31.5121	−	16.0562i	−1.30510	−	0.664980i
$584$	13.5942	+	9.87674i	0.562530	+	0.408702i
$585$	−14.6601	+	33.5099i	−0.606120	+	1.38546i
$586$	8.82050	−	6.40847i	0.364372	−	0.264731i
$587$	3.32343	−	0.526380i	0.137173	−	0.0217260i	−0.0874705	−	0.996167i	$-0.527878\pi$
$587$	3.32343	−	0.526380i	0.137173	−	0.0217260i	0.224643	+	0.974441i	$0.427878\pi$
$588$	3.50863	+	6.94425i	0.144693	+	0.286376i
$589$	−2.25442	−	3.10294i	−0.0928918	−	0.127855i
$590$	−1.55320	+	0.351747i	−0.0639443	+	0.0144812i
$591$	38.8299	+	12.7625i	1.59725	+	0.524978i
$592$	−0.0309862	+	0.0608138i	−0.00127352	+	0.00249943i
$593$	−14.1294	−	14.1294i	−0.580225	−	0.580225i	0.354740	−	0.934965i	$-0.384569\pi$
$593$	−14.1294	−	14.1294i	−0.580225	−	0.580225i	−0.934965	+	0.354740i	$0.884569\pi$
$594$	−21.4674	−	7.21770i	−0.880819	−	0.296146i
$595$	−4.34612	+	17.1258i	−0.178173	+	0.702089i
$596$	−16.6273	−	5.40255i	−0.681082	−	0.221297i
$597$	14.5757	+	14.6750i	0.596544	+	0.600608i
$598$	−7.64473	+	48.2669i	−0.312616	+	1.97378i
$599$	−9.39141			−0.383723			−0.191861	−	0.981422i	$-0.561452\pi$
$599$	−9.39141			−0.383723			−0.191861	+	0.981422i	$0.561452\pi$
$600$	−6.29999	+	5.94223i	−0.257196	+	0.242591i
$601$	−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
$603$	−32.6582	−	16.9205i	−1.32995	−	0.689055i
$604$	−14.3057	−	4.64820i	−0.582091	−	0.189133i
$605$	−13.7479	+	11.4382i	−0.558934	+	0.465030i
$606$	−10.2268	+	7.37729i	−0.415435	+	0.299682i
$607$	−6.13790	−	6.13790i	−0.249130	−	0.249130i	0.571484	−	0.820613i	$-0.306368\pi$
$607$	−6.13790	−	6.13790i	−0.249130	−	0.249130i	−0.820613	+	0.571484i	$0.806368\pi$
$608$	−0.600683	+	1.17891i	−0.0243609	+	0.0478110i
$609$	3.46528	−	10.5431i	0.140420	−	0.427229i
$610$	−1.30652	+	14.2469i	−0.0528996	+	0.576840i
$611$	2.47959	+	3.41287i	0.100314	+	0.138070i
$612$	10.6558	−	10.5121i	0.430735	−	0.424925i
$613$	−0.210830	+	0.0333923i	−0.00851536	+	0.00134870i	−0.160691	−	0.987005i	$-0.551372\pi$
$613$	−0.210830	+	0.0333923i	−0.00851536	+	0.00134870i	0.152175	+	0.988354i	$0.451372\pi$
$614$	14.0565	−	10.2127i	0.567275	−	0.412149i
$615$	−0.123019	+	0.283815i	−0.00496059	+	0.0114445i
$616$	5.58443	+	4.05733i	0.225003	+	0.163474i
$617$	−25.4122	−	12.9482i	−1.02306	−	0.521274i	−0.139808	−	0.990179i	$-0.544649\pi$
$617$	−25.4122	−	12.9482i	−1.02306	−	0.521274i	−0.883249	+	0.468905i	$0.844649\pi$
$618$	−3.21630	+	6.25972i	−0.129379	+	0.251803i
$619$	20.8855	−	6.78613i	0.839461	−	0.272757i	0.142436	−	0.989804i	$-0.454507\pi$
$619$	20.8855	−	6.78613i	0.839461	−	0.272757i	0.697025	+	0.717047i	$0.254507\pi$
$620$	3.45785	−	5.48255i	0.138871	−	0.220184i
$621$	−26.9887	−	37.9537i	−1.08302	−	1.52303i
$622$	−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
$627$	−9.87107	+	1.52909i	−0.394212	+	0.0610661i
$628$	−6.98212	−	13.7032i	−0.278617	−	0.546816i
$629$	0.105234	−	0.323876i	0.00419594	−	0.0129138i
$630$	0.624739	+	10.6053i	0.0248902	+	0.422524i
$631$	−6.16753	−	18.9817i	−0.245526	−	0.755650i	−0.995550	−	0.0942396i	$-0.969958\pi$
$631$	−6.16753	−	18.9817i	−0.245526	−	0.755650i	0.750024	−	0.661411i	$-0.230042\pi$
$632$	5.26744	−	5.26744i	0.209528	−	0.209528i
$633$	6.05204	−	37.3892i	0.240547	−	1.48609i
$634$	−16.2048	+	22.3041i	−0.643577	+	0.885807i
$635$	1.22648	+	1.07520i	0.0486713	+	0.0426681i
$636$	8.29933	−	11.3419i	0.329090	−	0.449735i
$637$	3.83144	+	24.1908i	0.151807	+	0.958473i
$638$	2.75869	+	17.4177i	0.109218	+	0.689572i
$639$	1.04813	−	3.15281i	0.0414632	−	0.124723i
$640$	−2.22672	−	0.204204i	−0.0880190	−	0.00807186i
$641$	11.5288	−	15.8680i	0.455359	−	0.626748i	−0.518179	−	0.855272i	$-0.673390\pi$
$641$	11.5288	−	15.8680i	0.455359	−	0.626748i	0.973538	+	0.228524i	$0.0733899\pi$
$642$	21.3516	+	3.45611i	0.842682	+	0.136402i
$643$	10.1389	−	10.1389i	0.399838	−	0.399838i	−0.478338	−	0.878176i	$-0.658760\pi$
$643$	10.1389	−	10.1389i	0.399838	−	0.399838i	0.878176	+	0.478338i	$0.158760\pi$
$644$	4.38617	+	13.4992i	0.172839	+	0.531944i
$645$	3.14006	−	4.94142i	0.123640	−	0.194568i
$646$	2.04001	−	6.27850i	0.0802631	−	0.247024i
$647$	19.4543	+	38.1812i	0.764827	+	1.50106i	0.862620	+	0.505852i	$0.168822\pi$
$647$	19.4543	+	38.1812i	0.764827	+	1.50106i	−0.0977930	+	0.995207i	$0.531178\pi$
$648$	4.19442	−	7.96284i	0.164772	−	0.312810i
$649$		−	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	−0.702954	+	0.711235i	$0.748136\pi$
$653$	−43.2254	+	22.0245i	−1.69154	+	0.861884i	−0.988587	+	0.150649i	$0.951864\pi$
$654$	14.6604	+	0.0497665i	0.573269	+	0.00194602i
$655$	16.3371	+	4.14597i	0.638343	+	0.161996i
$656$	−0.0759593	+	0.0246807i	−0.00296571	+	0.000963619i
$657$	−49.7346	−	8.22369i	−1.94033	−	0.320837i
$658$	1.09173	+	0.556265i	0.0425602	+	0.0216855i
$659$	12.3351	+	8.96198i	0.480508	+	0.349109i	0.801522	−	0.597965i	$-0.204024\pi$
$659$	12.3351	+	8.96198i	0.480508	+	0.349109i	−0.321015	+	0.947074i	$0.604024\pi$
$660$	−8.58448	−	14.5354i	−0.334150	−	0.565788i
$661$	8.69836	−	6.31973i	0.338327	−	0.245809i	−0.405629	−	0.914038i	$-0.632947\pi$
$661$	8.69836	−	6.31973i	0.338327	−	0.245809i	0.743956	+	0.668229i	$0.232947\pi$
$662$	15.5285	−	2.45948i	0.603533	−	0.0955903i
$663$	42.0566	−	21.2494i	1.63334	−	0.825258i
$664$	2.71566	+	3.73778i	0.105388	+	0.145054i
$665$	2.39636	+	4.02627i	0.0929269	+	0.156132i
$666$	0.00139014	−	0.204754i	5.38667e−5	−	0.00793406i
$667$	−16.4626	+	32.3097i	−0.637435	+	1.25104i
$668$	−6.91121	−	6.91121i	−0.267403	−	0.267403i
$669$	−23.4018	−	32.4408i	−0.904765	−	1.25423i
$670$	−10.1635	−	25.4616i	−0.392649	−	0.983669i
$671$	−26.5225	−	8.61767i	−1.02389	−	0.332682i
$672$	−1.94618	+	1.93301i	−0.0750754	+	0.0745674i
$673$	3.23263	−	20.4100i	0.124609	−	0.786748i	−0.843668	−	0.536866i	$-0.819608\pi$
$673$	3.23263	−	20.4100i	0.124609	−	0.786748i	0.968276	−	0.249882i	$-0.0803919\pi$
$674$	20.9306			0.806217
$675$	8.91274	−	24.4042i	0.343051	−	0.939317i
$676$	−16.7295			−0.643444
$677$	−0.268244	+	1.69362i	−0.0103094	+	0.0650913i	−0.992307	−	0.123804i	$-0.960491\pi$
$677$	−0.268244	+	1.69362i	−0.0103094	+	0.0650913i	0.981997	+	0.188895i	$0.0604906\pi$
$678$	−3.49078	+	3.46716i	−0.134063	+	0.133156i
$679$	17.9152	+	5.82099i	0.687521	+	0.223389i
$680$	11.1327	−	0.731684i	0.426919	−	0.0280588i
$681$	15.4471	+	21.4136i	0.591933	+	0.820570i
$682$	8.93422	+	8.93422i	0.342109	+	0.342109i
$683$	13.0207	−	25.5547i	0.498225	−	0.977822i	−0.495776	−	0.868450i	$-0.665116\pi$
$683$	13.0207	−	25.5547i	0.498225	−	0.977822i	0.994001	−	0.109371i	$-0.0348837\pi$
$684$	0.0269485	−	3.96926i	0.00103040	−	0.151769i
$685$	19.0386	+	8.17557i	0.727427	+	0.312373i
$686$	10.6974	+	14.7238i	0.408430	+	0.562156i
$687$	−29.3943	+	14.8517i	−1.12146	+	0.566626i
$688$	1.49307	−	0.236479i	0.0569227	−	0.00901567i
$689$	35.7926	−	26.0049i	1.36359	−	0.990707i
$690$	3.28732	−	34.5561i	0.125146	−	1.31553i
$691$	26.7982	+	19.4700i	1.01945	+	0.740675i	0.966170	−	0.257905i	$-0.0830321\pi$
$691$	26.7982	+	19.4700i	1.01945	+	0.740675i	0.0532811	+	0.998580i	$0.483032\pi$
$692$	1.20566	+	0.614314i	0.0458323	+	0.0233527i
$693$	−20.4308	−	3.37826i	−0.776102	−	0.128330i
$694$	−10.0316	+	3.25946i	−0.380794	+	0.123728i
$695$	0.956480	+	14.5530i	0.0362814	+	0.552026i
$696$	−7.00769	−	0.0237884i	−0.265626	−	0.000901696i
$697$	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	$-0.0915608\pi$
$702$	20.2367	−	19.8286i	0.763784	−	0.748384i
$703$	−0.0409984	−	0.0804638i	−0.00154628	−	0.00303475i
$704$	1.34690	−	4.14534i	0.0507633	−	0.156233i
$705$	−1.90866	−	2.30998i	−0.0718843	−	0.0869988i
$706$	1.28416	+	3.95224i	0.0483300	+	0.148744i
$707$	−8.15279	+	8.15279i	−0.306617	+	0.306617i
$708$	1.21772	+	0.197108i	0.0457648	+	0.00740776i
$709$	26.1516	−	35.9945i	0.982142	−	1.35180i	0.0464751	−	0.998919i	$-0.485201\pi$
$709$	26.1516	−	35.9945i	0.982142	−	1.35180i	0.935667	−	0.352884i	$-0.114799\pi$
$710$	2.12802	−	1.26656i	0.0798632	−	0.0475331i
$711$	−7.05001	+	21.2067i	−0.264396	+	0.795314i
$712$	0.990318	+	6.25262i	0.0371137	+	0.234327i
$713$	4.06430	+	25.6610i	0.152209	+	0.961010i
$714$	8.08201	−	11.0449i	0.302462	−	0.413345i
$715$	−11.7375	−	51.8289i	−0.438957	−	1.93829i
$716$	−3.42845	+	4.71886i	−0.128127	+	0.176352i
$717$	0.0296864	−	0.183401i	0.00110866	−	0.00684924i
$718$	4.15479	−	4.15479i	0.155055	−	0.155055i
$719$	−6.98735	−	21.5049i	−0.260584	−	0.801996i	−0.992678	−	0.120792i	$-0.961457\pi$
$719$	−6.98735	−	21.5049i	−0.260584	−	0.801996i	0.732094	−	0.681204i	$-0.238543\pi$
$720$	6.24694	−	2.44454i	0.232810	−	0.0911026i
$721$	−1.98846	+	6.11986i	−0.0740543	+	0.227916i
$722$	7.83104	+	15.3693i	0.291441	+	0.571986i
$723$	−20.0511	+	3.10605i	−0.745709	+	0.115515i
$724$			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	−0.749719	−	0.661756i	$-0.769811\pi$
$727$	−44.9536	−	7.11996i	−1.66724	−	0.264065i	−0.917519	+	0.397692i	$0.869811\pi$
$728$	−7.69383	+	3.92020i	−0.285152	+	0.145292i
$729$	−0.549887	+	26.9944i	−0.0203662	+	0.999793i
$730$	−24.0310	−	28.8836i	−0.889429	−	1.06903i
$731$	−7.17326	+	2.33073i	−0.265313	+	0.0862053i
$732$	5.06457	−	9.85691i	0.187192	−	0.364322i
$733$	−25.0784	−	12.7781i	−0.926293	−	0.471970i	−0.0753080	−	0.997160i	$-0.523994\pi$
$733$	−25.0784	−	12.7781i	−0.926293	−	0.471970i	−0.850985	+	0.525191i	$0.823994\pi$
$734$	13.7493	+	9.98946i	0.507496	+	0.368718i
$735$	−3.78496	−	16.9806i	−0.139610	−	0.626337i
$736$	7.25092	−	5.26810i	0.267272	−	0.194185i
$737$	52.7812	−	8.35972i	1.94422	−	0.307934i
$738$	0.170573	−	0.168272i	0.00627887	−	0.00619419i
$739$	−22.4956	−	30.9626i	−0.827515	−	1.13898i	−0.988380	−	0.152001i	$-0.951428\pi$
$739$	−22.4956	−	30.9626i	−0.827515	−	1.13898i	0.160865	−	0.986976i	$-0.448572\pi$
$740$	0.100607	−	0.114762i	0.00369841	−	0.00421875i
$741$	3.90164	−	11.8707i	0.143330	−	0.436083i
$742$	5.83386	−	11.4496i	0.214168	−	0.420328i
$743$	13.5540	+	13.5540i	0.497249	+	0.497249i	0.910581	−	0.413332i	$-0.135635\pi$
$743$	13.5540	+	13.5540i	0.497249	+	0.497249i	−0.413332	+	0.910581i	$0.635635\pi$
$744$	−4.07196	+	2.93738i	−0.149285	+	0.107690i
$745$	33.0660	+	20.8548i	1.21144	+	0.764060i
$746$	26.1069	+	8.48265i	0.955842	+	0.310572i
$747$	−12.3068	−	6.37622i	−0.450281	−	0.233294i
$748$	−3.40202	+	21.4795i	−0.124390	+	0.785369i
$749$	19.7767			0.722625
$750$	16.9228	−	9.41383i	0.617932	−	0.343744i
$751$	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
$753$	−36.6229	−	36.8724i	−1.33461	−	1.34370i
$754$	−20.9806	−	6.81699i	−0.764067	−	0.248260i
$755$	28.4490	+	17.9429i	1.03537	+	0.653008i
$756$	2.62248	−	7.79998i	0.0953788	−	0.283683i
$757$	12.7694	+	12.7694i	0.464113	+	0.464113i	0.900001	−	0.435888i	$-0.143566\pi$
$757$	12.7694	+	12.7694i	0.464113	+	0.464113i	−0.435888	+	0.900001i	$0.643566\pi$
$758$	6.70985	−	13.1688i	0.243713	−	0.478313i
$759$	64.2798	+	21.1273i	2.33321	+	0.766871i
$760$	1.95033	−	2.22473i	0.0707459	−	0.0806995i
$761$	−1.38914	−	1.91199i	−0.0503564	−	0.0693097i	0.783096	−	0.621901i	$-0.213639\pi$
$761$	−1.38914	−	1.91199i	−0.0503564	−	0.0693097i	−0.833453	+	0.552591i	$0.813639\pi$
$762$	−0.569748	−	1.12764i	−0.0206398	−	0.0408501i
$763$	13.2396	−	2.09695i	0.479307	−	0.0759148i
$764$	10.6797	−	7.75927i	0.386379	−	0.280721i
$765$	−28.8769	+	16.9225i	−1.04405	+	0.611836i
$766$	−13.4761	−	9.79095i	−0.486911	−	0.353761i
$767$	3.46002	+	1.76297i	0.124934	+	0.0636570i
$768$	1.54059	+	0.791569i	0.0555913	+	0.0285633i
$769$	−15.6427	+	5.08261i	−0.564089	+	0.183284i	−0.577160	−	0.816631i	$-0.695839\pi$
$769$	−15.6427	+	5.08261i	−0.564089	+	0.183284i	0.0130714	+	0.999915i	$0.495839\pi$
$770$	−9.87187	−	11.8653i	−0.355757	−	0.427595i
$771$	−0.0857350	+	25.2562i	−0.00308767	+	0.909580i
$772$	−7.37690	+	3.75872i	−0.265500	+	0.135279i
$773$	−18.5483	−	2.93775i	−0.667134	−	0.105664i	−0.186324	−	0.982488i	$-0.559657\pi$
$773$	−18.5483	−	2.93775i	−0.667134	−	0.105664i	−0.480810	+	0.876825i	$0.659657\pi$
$774$	−3.68693	+	2.64066i	−0.132524	+	0.0949165i
$775$	−10.5100	+	9.98078i	−0.377529	+	0.358520i
$776$		−	11.8945i		−	0.426989i
$777$	−0.0286596	−	0.185012i	−0.00102816	−	0.00663727i
$778$	−11.0940	−	21.7732i	−0.397739	−	0.780606i
$779$	0.0326555	−	0.100503i	0.00117000	−	0.00360090i
$780$	21.0765	−	1.31339i	0.754659	−	0.0470269i
$781$	1.49168	+	4.59091i	0.0533764	+	0.164276i
$782$	−31.6207	+	31.6207i	−1.13075	+	1.13075i
$783$	18.8280	−	9.35307i	0.672858	−	0.334251i
$784$	2.64031	−	3.63407i	0.0942966	−	0.129788i
$785$	7.59569	+	33.5401i	0.271102	+	1.19710i
$786$	−10.5363	−	7.70982i	−0.375816	−	0.275000i
$787$	−3.72349	−	23.5092i	−0.132728	−	0.838013i	−0.960770	−	0.277347i	$-0.910545\pi$
$787$	−3.72349	−	23.5092i	−0.132728	−	0.838013i	0.828042	−	0.560666i	$-0.189455\pi$
$788$	−3.69159	−	23.3078i	−0.131507	−	0.830305i
$789$	−8.00995	−	5.86121i	−0.285162	−	0.208665i
$790$	−14.3137	+	8.51924i	−0.509259	+	0.303101i
$791$	−2.64420	+	3.63943i	−0.0940169	+	0.129403i
$792$	1.95781	+	12.9286i	0.0695677	+	0.459398i
$793$	24.6679	−	24.6679i	0.875984	−	0.875984i
$794$	2.11182	+	6.49951i	0.0749456	+	0.230659i
$795$	−24.2260	+	20.0172i	−0.859208	+	0.709936i
$796$	3.69016	−	11.3572i	0.130794	−	0.402544i
$797$	−8.27146	−	16.2336i	−0.292990	−	0.575025i	0.696849	−	0.717218i	$-0.254585\pi$
$797$	−8.27146	−	16.2336i	−0.292990	−	0.575025i	−0.989839	+	0.142193i	$0.954585\pi$
$798$	−0.555581	−	3.58656i	−0.0196674	−	0.126963i
$799$			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
$804$	−0.0720865	+	21.2356i	−0.00254230	+	0.748921i
$805$	−2.08150	−	31.6703i	−0.0733631	−	1.11623i
$806$	−15.0320	+	4.88421i	−0.529481	+	0.172039i
$807$	44.3522	+	22.7885i	1.56127	+	0.802194i
$808$	6.48686	+	3.30522i	0.228207	+	0.116277i
$809$	−0.465989	−	0.338561i	−0.0163833	−	0.0119032i	0.579563	−	0.814927i	$-0.303223\pi$
$809$	−0.465989	−	0.338561i	−0.0163833	−	0.0119032i	−0.595947	+	0.803024i	$0.703223\pi$
$810$	−13.4706	+	14.9513i	−0.473309	+	0.525337i
$811$	−16.4035	+	11.9178i	−0.576004	+	0.418491i	−0.837281	−	0.546772i	$-0.815856\pi$
$811$	−16.4035	+	11.9178i	−0.576004	+	0.418491i	0.261277	+	0.965264i	$0.415856\pi$
$812$	−6.32855	+	1.00234i	−0.222088	+	0.0351753i
$813$	−7.43981	−	14.7248i	−0.260925	−	0.516421i
$814$	0.174861	+	0.240676i	0.00612888	+	0.00843569i
$815$	−49.8709	−	21.4156i	−1.74690	−	0.750156i
$816$	−8.20986	−	2.69839i	−0.287403	−	0.0944626i
$817$	−0.908040	+	1.78213i	−0.0317683	+	0.0623488i
$818$	−9.95932	−	9.95932i	−0.348219	−	0.348219i
$819$	15.3685	−	20.8537i	0.537018	−	0.728687i
$820$	0.178207	−	0.0117125i	0.00622325	−	0.000409017i
$821$	−31.2665	−	10.1591i	−1.09121	−	0.354555i	−0.292495	−	0.956267i	$-0.594485\pi$
$821$	−31.2665	−	10.1591i	−1.09121	−	0.354555i	−0.798713	+	0.601712i	$0.794485\pi$
$822$	−11.3101	−	11.3871i	−0.394484	−	0.397172i
$823$	−5.34295	+	33.7341i	−0.186244	+	1.17590i	0.700507	+	0.713646i	$0.252957\pi$
$823$	−5.34295	+	33.7341i	−0.186244	+	1.17590i	−0.886750	+	0.462249i	$0.847043\pi$
$824$	4.06320			0.141548
$825$	10.6109	+	36.2251i	0.369423	+	1.26120i
$826$	1.12790			0.0392447
$827$	−4.48852	+	28.3394i	−0.156081	+	0.985457i	0.777966	+	0.628307i	$0.216252\pi$
$827$	−4.48852	+	28.3394i	−0.156081	+	0.985457i	−0.934047	+	0.357151i	$0.883748\pi$
$828$	−12.3692	+	23.8739i	−0.429860	+	0.829674i
$829$	−17.3783	−	5.64654i	−0.603572	−	0.196113i	−0.00873938	−	0.999962i	$-0.502782\pi$
$829$	−17.3783	−	5.64654i	−0.603572	−	0.196113i	−0.594833	+	0.803849i	$0.702782\pi$
$830$	−3.82995	−	9.59483i	−0.132939	−	0.333041i
$831$	1.88834	−	1.36219i	0.0655059	−	0.0472539i
$832$	3.85549	+	3.85549i	0.133665	+	0.133665i
$833$	−10.1750	+	19.9695i	−0.352542	+	0.691902i
$834$	3.52742	−	10.7322i	0.122145	−	0.371625i
$835$	11.1778	+	18.7804i	0.386822	+	0.649924i
$836$	3.38978	+	4.66563i	0.117238	+	0.161364i
$837$	6.97459	−	13.3505i	0.241077	−	0.461462i
$838$	16.0016	−	2.53441i	0.552768	−	0.0875498i
$839$	−25.5591	+	18.5698i	−0.882398	+	0.641099i	−0.933885	−	0.357574i	$-0.883604\pi$
$839$	−25.5591	+	18.5698i	−0.882398	+	0.641099i	0.0514870	+	0.998674i	$0.483604\pi$
$840$	5.28128	−	3.11909i	0.182222	−	0.107619i
$841$	10.2184	+	7.42407i	0.352357	+	0.256003i
$842$	−2.33478	−	1.18963i	−0.0804618	−	0.0409973i
$843$	−2.87869	+	5.60265i	−0.0991474	+	0.192966i
$844$	−20.7973	+	6.75746i	−0.715874	+	0.232601i
$845$	36.2590	+	9.20168i	1.24735	+	0.316547i
$846$	0.702248	+	2.21229i	0.0241438	+	0.0760602i
$847$	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
$852$	−1.89562	+	0.293643i	−0.0649427	+	0.0100601i
$853$	−9.15038	−	17.9586i	−0.313303	−	0.614892i	0.679632	−	0.733553i	$-0.262140\pi$
$853$	−9.15038	−	17.9586i	−0.313303	−	0.614892i	−0.992935	+	0.118662i	$0.962140\pi$
$854$	3.13115	−	9.63668i	0.107146	−	0.329760i
$855$	−2.24161	+	8.58802i	−0.0766613	+	0.293704i
$856$	−3.85895	−	11.8766i	−0.131896	−	0.405935i
$857$	0.835861	−	0.835861i	0.0285525	−	0.0285525i	−0.692686	−	0.721239i	$-0.743573\pi$
$857$	0.835861	−	0.835861i	0.0285525	−	0.0285525i	0.721239	+	0.692686i	$0.243573\pi$
$858$	−6.57731	+	40.6343i	−0.224546	+	1.38723i
$859$	23.4268	−	32.2443i	0.799313	−	1.10016i	−0.193572	−	0.981086i	$-0.562007\pi$
$859$	23.4268	−	32.2443i	0.799313	−	1.10016i	0.992885	−	0.119074i	$-0.0379926\pi$
$860$	−3.36609	−	0.308690i	−0.114783	−	0.0105263i
$861$	0.129373	−	0.176801i	0.00440902	−	0.00602538i
$862$	3.54800	+	22.4012i	0.120845	+	0.762988i
$863$	1.59543	+	10.0731i	0.0543089	+	0.342893i	0.999849	+	0.0173869i	$0.00553470\pi$
$863$	1.59543	+	10.0731i	0.0543089	+	0.342893i	−0.945540	+	0.325506i	$0.894465\pi$
$864$	−5.19588	−	0.0529156i	−0.176768	−	0.00180023i
$865$	−2.27521	−	1.99459i	−0.0773596	−	0.0678180i
$866$	10.1103	−	13.9156i	0.343561	−	0.472871i
$867$	13.4978	+	2.18484i	0.458410	+	0.0742010i
$868$	−3.24616	+	3.24616i	−0.110182	+	0.110182i
$869$	−10.0335	−	30.8798i	−0.340362	−	1.04753i
$870$	15.1751	+	3.90597i	0.514485	+	0.132425i
$871$	−20.6577	+	63.5779i	−0.699960	+	2.15425i
$872$	−3.84269	−	7.54171i	−0.130130	−	0.255395i
$873$	15.9838	+	31.9036i	0.540969	+	1.07977i
$874$			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	0.621277	−	0.783591i	$-0.286614\pi$
$877$	28.7259	+	4.54973i	0.970003	+	0.153633i	0.348726	+	0.937225i	$0.386614\pi$
$878$	−14.1425	+	7.20594i	−0.477285	+	0.243189i
$879$	18.8840	+	0.0641038i	0.636941	+	0.00216217i
$880$	−5.19927	+	8.24363i	−0.175267	+	0.277893i
$881$	8.28622	−	2.69236i	0.279170	−	0.0907078i	−0.166086	−	0.986111i	$-0.553113\pi$
$881$	8.28622	−	2.69236i	0.279170	−	0.0907078i	0.445256	+	0.895404i	$0.353113\pi$
$882$	−2.19841	+	13.2953i	−0.0740242	+	0.447677i
$883$	10.3084	+	5.25241i	0.346906	+	0.176758i	0.618758	−	0.785581i	$-0.287636\pi$
$883$	10.3084	+	5.25241i	0.346906	+	0.176758i	−0.271852	+	0.962339i	$0.587636\pi$
$884$	−22.0091	−	15.9906i	−0.740247	−	0.537821i
$885$	−2.53083	−	1.09698i	−0.0850730	−	0.0368747i
$886$	7.15205	−	5.19627i	0.240278	−	0.174572i
$887$	−3.17898	+	0.503502i	−0.106740	+	0.0169059i	−0.209576	−	0.977792i	$-0.567208\pi$
$887$	−3.17898	+	0.503502i	−0.106740	+	0.0169059i	0.102836	+	0.994698i	$0.467208\pi$
$888$	−0.105514	+	0.0533117i	−0.00354082	+	0.00178903i
$889$	−0.678996	−	0.934558i	−0.0227728	−	0.0313441i
$890$	1.29272	−	14.0964i	0.0433322	−	0.472513i
$891$	−22.6246	−	32.0463i	−0.757953	−	1.07359i
$892$	−10.4846	+	20.5772i	−0.351051	+	0.688977i
$893$	0.723855	+	0.723855i	0.0242229	+	0.0242229i
$894$	−17.7157	−	24.5585i	−0.592503	−	0.821359i
$895$	10.0262	−	8.34175i	0.335139	−	0.278834i
$896$	1.50617	+	0.489384i	0.0503176	+	0.0163492i
$897$	−60.0543	+	59.6480i	−2.00516	+	1.99159i
$898$	−0.701920	+	4.43175i	−0.0234234	+	0.147889i
$899$	−11.7283			−0.391160
$900$	−14.8840	+	1.86223i	−0.496132	+	0.0620744i
$901$	40.4849			1.34875
$902$	−0.0544579	+	0.343834i	−0.00181325	+	0.0114484i
$903$	−2.94200	+	2.92209i	−0.0979035	+	0.0972410i
$904$	2.70156	+	0.877790i	0.0898525	+	0.0291949i
$905$	4.44842	−	17.5289i	0.147871	−	0.582681i
$906$	−15.2421	−	21.1295i	−0.506386	−	0.701979i
$907$	−7.25177	−	7.25177i	−0.240791	−	0.240791i	0.576386	−	0.817177i	$-0.304462\pi$
$907$	−7.25177	−	7.25177i	−0.240791	−	0.240791i	−0.817177	+	0.576386i	$0.804462\pi$
$908$	6.92070	−	13.5826i	0.229672	−	0.450756i
$909$	−21.8406	−	0.148283i	−0.724408	−	0.00491822i
$910$	18.8315	−	4.26470i	0.624260	−	0.141373i
$911$	−21.4007	−	29.4555i	−0.709035	−	0.975903i	−0.999817	−	0.0191141i	$-0.993915\pi$
$911$	−21.4007	−	29.4555i	−0.709035	−	0.975903i	0.290782	−	0.956789i	$-0.406085\pi$
$912$	−2.04545	+	1.03348i	−0.0677315	+	0.0342218i
$913$	19.8898	−	3.15023i	0.658256	−	0.104258i
$914$	−24.4243	+	17.7453i	−0.807883	+	0.586962i
$915$	−16.3983	+	18.5779i	−0.542112	+	0.614166i
$916$	15.3826	+	11.1761i	0.508256	+	0.369270i
$917$	−10.6363	−	5.41947i	−0.351242	−	0.178967i
$918$	25.6466	−	3.79472i	0.846464	−	0.125244i
$919$	−12.8805	+	4.18512i	−0.424887	+	0.138054i	−0.513653	−	0.857998i	$-0.671708\pi$
$919$	−12.8805	+	4.18512i	−0.424887	+	0.138054i	0.0887651	+	0.996053i	$0.471708\pi$
$920$	−18.6130	+	7.42970i	−0.613652	+	0.244950i
$921$	30.0939	+	0.102157i	0.991627	+	0.00336619i
$922$	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
$927$	−10.8983	+	5.46009i	−0.357948	+	0.179333i
$928$	1.83681	+	3.60493i	0.0602961	+	0.118338i
$929$	−9.27450	+	28.5440i	−0.304286	+	0.936497i	0.675656	+	0.737217i	$0.263860\pi$
$929$	−9.27450	+	28.5440i	−0.304286	+	0.936497i	−0.979943	+	0.199280i	$0.936140\pi$
$930$	10.4411	−	4.12670i	0.342376	−	0.135320i
$931$	1.83661	+	5.65250i	0.0601924	+	0.185253i
$932$	0.883782	−	0.883782i	0.0289492	−	0.0289492i
$933$	−8.80086	−	1.42456i	−0.288127	−	0.0466380i
$934$	8.94877	−	12.3169i	0.292813	−	0.403022i
$935$	19.1877	−	44.6828i	0.627505	−	1.46128i
$936$	−15.5222	−	5.16023i	−0.507358	−	0.168667i
$937$	−4.50748	−	28.4591i	−0.147253	−	0.929718i	−0.945082	−	0.326834i	$-0.894018\pi$
$937$	−4.50748	−	28.4591i	−0.147253	−	0.929718i	0.797829	−	0.602884i	$-0.205982\pi$
$938$	3.03743	+	19.1776i	0.0991755	+	0.626169i
$939$	−10.6742	+	14.5874i	−0.348340	+	0.476043i
$940$	−0.682632	+	1.58966i	−0.0222650	+	0.0518489i
$941$	−7.80628	+	10.7444i	−0.254478	+	0.350258i	−0.917073	−	0.398719i	$-0.869455\pi$
$941$	−7.80628	+	10.7444i	−0.254478	+	0.350258i	0.662596	+	0.748977i	$0.269455\pi$
$942$	4.25638	−	26.2957i	0.138680	−	0.856760i
$943$	−0.506169	+	0.506169i	−0.0164831	+	0.0164831i
$944$	−0.220083	−	0.677345i	−0.00716308	−	0.0220457i
$945$	−9.97407	+	15.4630i	−0.324457	+	0.503011i
$946$	2.03608	−	6.26642i	0.0661988	−	0.203739i
$947$	−10.9048	−	21.4019i	−0.354359	−	0.695469i	0.643170	−	0.765724i	$-0.277619\pi$
$947$	−10.9048	−	21.4019i	−0.354359	−	0.695469i	−0.997529	+	0.0702542i	$0.977619\pi$
$948$	12.7505	−	1.97513i	0.414116	−	0.0641493i
$949$			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	$-0.548098\pi$
$953$	17.3120	−	8.82088i	0.560789	−	0.285736i	0.711319	+	0.702869i	$0.248098\pi$
$954$	23.2015	−	7.36486i	0.751177	−	0.238446i
$955$	−27.4147	+	10.9430i	−0.887117	+	0.354109i
$956$	−0.102015	+	0.0331467i	−0.00329940	+	0.00107204i
$957$	−13.9592	+	27.1680i	−0.451235	+	0.878216i
$958$	−16.3251	−	8.31808i	−0.527441	−	0.268745i
$959$	−11.8720	−	8.62553i	−0.383368	−	0.278533i
$960$	−2.90364	−	2.56298i	−0.0937145	−	0.0827199i
$961$	18.2813	−	13.2822i	0.589721	−	0.428457i
$962$	−0.367566	+	0.0582167i	−0.0118508	+	0.00187698i
$963$	26.3102	+	26.6699i	0.847835	+	0.859426i
$964$	6.88566	+	9.47730i	0.221772	+	0.305243i
$965$	18.0558	−	4.08903i	0.581237	−	0.131630i
$966$	−7.67639	+	23.3554i	−0.246984	+	0.751449i
$967$	5.93841	−	11.6548i	0.190966	−	0.374793i	−0.775594	−	0.631232i	$-0.782550\pi$
$967$	5.93841	−	11.6548i	0.190966	−	0.374793i	0.966560	+	0.256440i	$0.0825495\pi$
$968$	−5.65543	−	5.65543i	−0.181772	−	0.181772i
$969$	9.27332	−	6.68948i	0.297902	−	0.214897i
$970$	−6.54230	+	25.7798i	−0.210061	+	0.827739i
$971$	−7.00547	−	2.27622i	−0.224816	−	0.0730472i	0.194443	−	0.980914i	$-0.437710\pi$
$971$	−7.00547	−	2.27622i	−0.224816	−	0.0730472i	−0.419259	+	0.907867i	$0.637710\pi$
$972$	14.0075	−	6.84026i	0.449292	−	0.219401i
$973$	1.61586	−	10.2021i	0.0518020	−	0.327065i
$974$	−3.97602			−0.127400
$975$	−46.4028	−	8.74601i	−1.48608	−	0.280097i
$976$	−6.39814			−0.204799
$977$	6.51715	−	41.1477i	0.208502	−	1.31643i	−0.632146	−	0.774849i	$-0.717826\pi$
$977$	6.51715	−	41.1477i	0.208502	−	1.31643i	0.840648	−	0.541582i	$-0.182174\pi$
$978$	29.6264	+	29.8282i	0.947346	+	0.953800i
$979$	26.2423	+	8.52665i	0.838708	+	0.272513i
$980$	−7.72134	+	6.42412i	−0.246649	+	0.205211i
$981$	20.4414	+	15.0646i	0.652643	+	0.480977i
$982$	−14.2382	−	14.2382i	−0.454360	−	0.454360i
$983$	−27.1685	+	53.3212i	−0.866541	+	1.70068i	−0.167164	+	0.985929i	$0.553461\pi$
$983$	−27.1685	+	53.3212i	−0.866541	+	1.70068i	−0.699377	+	0.714753i	$0.746539\pi$
$984$	−0.131420	−	0.0431946i	−0.00418950	−	0.00137699i
$985$	−4.81886	+	52.5469i	−0.153542	+	1.67428i
$986$	−11.8655	−	16.3315i	−0.377874	−	0.520100i
$987$	0.957056	+	1.89420i	0.0304634	+	0.0602929i
$988$	−7.12546	+	1.12856i	−0.226691	+	0.0359043i
$989$	10.9611	−	7.96368i	0.348541	−	0.253230i
$990$	2.86778	−	29.0979i	0.0911441	−	0.924791i
$991$	−25.5455	−	18.5599i	−0.811478	−	0.589573i	0.102781	−	0.994704i	$-0.467226\pi$
$991$	−25.5455	−	18.5599i	−0.811478	−	0.589573i	−0.914259	+	0.405131i	$0.867226\pi$
$992$	2.58285	+	1.31603i	0.0820054	+	0.0417839i
$993$	24.2213	+	12.4451i	0.768640	+	0.394934i
$994$	−1.66806	+	0.541987i	−0.0529078	+	0.0171908i
$995$	−14.2447	+	22.5854i	−0.451586	+	0.716006i
$996$	−0.0271647	+	8.00230i	−0.000860746	+	0.253563i
$997$	30.4001	−	15.4896i	0.962780	−	0.490561i	0.0993629	−	0.995051i	$-0.468320\pi$
$997$	30.4001	−	15.4896i	0.962780	−	0.490561i	0.863417	+	0.504490i	$0.168320\pi$
$998$	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.77.10	yes	80
3.2	odd	2	inner	150.2.l.a.77.1	✓	80
5.2	odd	4		750.2.l.a.593.7		80
5.3	odd	4		750.2.l.c.593.4		80
5.4	even	2		750.2.l.b.407.1		80
15.2	even	4		750.2.l.a.593.4		80
15.8	even	4		750.2.l.c.593.7		80
15.14	odd	2		750.2.l.b.407.10		80
25.9	even	10		750.2.l.a.707.4		80
25.12	odd	20		750.2.l.b.293.10		80
25.13	odd	20	inner	150.2.l.a.113.1	yes	80
25.16	even	5		750.2.l.c.707.7		80
75.38	even	20	inner	150.2.l.a.113.10	yes	80
75.41	odd	10		750.2.l.c.707.4		80
75.59	odd	10		750.2.l.a.707.7		80
75.62	even	20		750.2.l.b.293.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.1	✓	80	3.2	odd	2	inner
150.2.l.a.77.10	yes	80	1.1	even	1	trivial
150.2.l.a.113.1	yes	80	25.13	odd	20	inner
150.2.l.a.113.10	yes	80	75.38	even	20	inner
750.2.l.a.593.4		80	15.2	even	4
750.2.l.a.593.7		80	5.2	odd	4
750.2.l.a.707.4		80	25.9	even	10
750.2.l.a.707.7		80	75.59	odd	10
750.2.l.b.293.1		80	75.62	even	20
750.2.l.b.293.10		80	25.12	odd	20
750.2.l.b.407.1		80	5.4	even	2
750.2.l.b.407.10		80	15.14	odd	2
750.2.l.c.593.4		80	5.3	odd	4
750.2.l.c.593.7		80	15.8	even	4
750.2.l.c.707.4		80	75.41	odd	10
750.2.l.c.707.7		80	25.16	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(1.22890 - 1.22058i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.89132 + 1.19286i) q^{5} +(-1.01331 - 1.40471i) q^{6} +(-1.11983 - 1.11983i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0203674 - 2.99993i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(1.22890 - 1.22058i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.89132 + 1.19286i) q^{5} +(-1.01331 - 1.40471i) q^{6} +(-1.11983 - 1.11983i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.0203674 - 2.99993i) q^{9} +(1.47404 - 1.68143i) q^{10} +(2.56196 + 3.52624i) q^{11} +(-1.54593 + 0.781091i) q^{12} +(-5.38535 + 0.852956i) q^{13} +(-1.28122 + 0.930864i) q^{14} +(3.78021 - 0.842609i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.44561 - 2.26515i) q^{17} +(-2.95981 - 0.489409i) q^{18} +(-1.25836 + 0.408866i) q^{19} +(-1.43014 - 1.71893i) q^{20} +(-2.74300 - 0.00931142i) 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} +(-3.63663 - 3.71146i) q^{27} +(0.718976 + 1.41107i) q^{28} +(-1.25026 + 3.84789i) q^{29} +(-0.240880 - 3.86549i) q^{30} +(0.895777 + 2.75692i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.45244 + 1.20630i) q^{33} +(-2.93271 + 4.03653i) q^{34} +(-0.782158 - 3.45376i) q^{35} +(-0.946400 + 2.84681i) q^{36} +(0.0106771 + 0.0674126i) q^{37} +(0.206981 + 1.30683i) q^{38} +(-5.57693 + 7.62145i) q^{39} +(-1.92149 + 1.14363i) q^{40} +(-0.0469455 + 0.0646149i) q^{41} +(-0.438296 + 2.70777i) q^{42} +(1.06892 - 1.06892i) q^{43} +(-1.34690 - 4.14534i) q^{44} +(3.61701 - 5.64953i) q^{45} +(2.76960 - 8.52397i) q^{46} +(-0.351249 - 0.689364i) q^{47} +(1.71164 - 0.265144i) 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} +(-4.23466 + 3.01125i) q^{54} +(0.639185 + 9.72530i) q^{55} +(1.50617 - 0.489384i) q^{56} +(-1.04734 + 2.03838i) q^{57} +(3.60493 + 1.83681i) q^{58} +(-0.576184 - 0.418622i) q^{59} +(-3.85558 - 0.366781i) q^{60} +(-5.17620 + 3.76073i) q^{61} +(2.86311 - 0.453472i) q^{62} +(-3.38222 + 3.33661i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-11.2029 - 4.81075i) q^{65} +(2.35726 - 7.17198i) q^{66} +(5.56612 - 10.9241i) q^{67} +(3.52806 + 3.52806i) q^{68} +(12.5899 - 9.08193i) q^{69} +(-3.53359 + 0.232242i) q^{70} +(1.05328 + 0.342232i) q^{71} +(2.66371 + 1.38009i) q^{72} +(2.62862 - 16.5964i) q^{73} +0.0682529 q^{74} +(8.15470 + 2.91562i) q^{75} +1.32312 q^{76} +(1.07983 - 6.81775i) q^{77} +(6.65519 + 6.70053i) q^{78} +(-7.08470 - 2.30196i) q^{79} +(0.828965 + 2.07673i) q^{80} +(-8.99917 - 0.122202i) q^{81} +(0.0564755 + 0.0564755i) q^{82} +(2.09751 - 4.11659i) q^{83} +(2.60587 + 0.856489i) q^{84} +(-5.70607 - 9.58712i) q^{85} +(-0.888543 - 1.22297i) q^{86} +(3.16023 + 6.25469i) q^{87} +(-4.30501 + 0.681846i) q^{88} +(5.12153 - 3.72101i) q^{89} +(-5.01415 - 4.45626i) q^{90} +(6.98585 + 5.07552i) q^{91} +(-7.98576 - 4.06895i) q^{92} +(4.46586 + 2.29460i) q^{93} +(-0.735824 + 0.239084i) q^{94} +(-2.86768 - 0.727750i) q^{95} +(0.00587961 - 1.73204i) 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

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