LMFDB - Embedded newform 930.2.bt.b.13.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(13,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([0, 45, 22])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bt (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [256,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	930.13
Dual form			930.2.bt.b.787.10

$q$-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} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.14184 + 1.92255i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.0309572 - 0.00162240i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +(1.72026 + 1.42854i) q^{10} +(-0.858109 - 4.03708i) q^{11} +(-0.629320 + 0.777146i) q^{12} +(0.374047 + 0.461909i) q^{13} +(-0.00644519 + 0.0303222i) q^{14} +(1.38565 + 1.75498i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.22902 - 3.43239i) q^{17} +(-0.777146 + 0.629320i) q^{18} +(-2.09187 + 0.219864i) q^{19} +(1.68006 - 1.47560i) q^{20} +(-0.0126087 + 0.0283196i) q^{21} +(-4.12162 + 0.216005i) q^{22} +(-3.85281 - 1.96311i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-2.39239 - 4.39050i) q^{25} +(0.514736 - 0.297183i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(0.0289407 + 0.0111093i) q^{28} +(-4.38491 + 3.18582i) q^{29} +(1.95014 - 1.09405i) q^{30} +(-2.86075 + 4.77662i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.07646 - 0.645648i) q^{33} +(-3.73882 + 1.66463i) q^{34} +(0.0384674 - 0.0576642i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.49336 + 0.936044i) q^{37} +(-0.110083 + 2.10051i) q^{38} +(0.565275 - 0.183669i) q^{39} +(-1.19462 - 1.89021i) q^{40} +(-3.98282 - 1.77326i) q^{41} +(0.0259985 + 0.0168836i) q^{42} +(-0.248318 - 0.201084i) q^{43} +(-0.431418 + 4.10466i) q^{44} +(2.13499 - 0.664690i) q^{45} +(-2.54165 + 3.49828i) q^{46} +(3.73784 - 0.592016i) q^{47} +(0.838671 - 0.544639i) q^{48} +(-6.96070 - 0.731599i) q^{49} +(-4.71070 + 1.67611i) q^{50} +(-4.00322 + 0.850910i) q^{51} +(-0.213002 - 0.554888i) q^{52} +(0.0643963 + 1.22875i) q^{53} +(0.309017 + 0.951057i) q^{54} +(8.74132 + 2.95996i) q^{55} +(0.0154998 - 0.0268465i) q^{56} +(-0.544398 + 2.03172i) q^{57} +(2.46065 + 4.82929i) q^{58} +(-2.76413 - 6.20833i) q^{59} +(-0.775516 - 2.09728i) q^{60} -9.30660i q^{61} +(4.27029 + 3.57276i) q^{62} +(0.0219201 + 0.0219201i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.31515 + 0.191695i) q^{65} +(-1.27540 + 3.92527i) q^{66} +(3.06099 + 0.820189i) q^{67} +(1.05926 + 3.95320i) q^{68} +(-3.21344 + 2.89340i) q^{69} +(-0.0509366 - 0.0470144i) q^{70} +(8.03180 - 8.92021i) q^{71} +(0.933580 - 0.358368i) q^{72} +(-4.47712 + 6.89416i) q^{73} +(0.378037 + 3.59678i) q^{74} +(-4.95624 + 0.660075i) q^{75} +(2.05743 + 0.437320i) q^{76} +(0.0200149 + 0.126369i) q^{77} +(-0.0929793 - 0.587048i) q^{78} +(15.8885 + 3.37722i) q^{79} +(-2.05382 + 0.884217i) q^{80} +(0.104528 + 0.994522i) q^{81} +(-2.37448 + 3.65638i) q^{82} +(-6.37114 + 2.44565i) q^{83} +(0.0207428 - 0.0230372i) q^{84} +(9.14412 - 0.366150i) q^{85} +(-0.237454 + 0.213804i) q^{86} +(1.40281 + 5.23536i) q^{87} +(3.98664 + 1.06822i) q^{88} +(0.716054 - 2.20379i) q^{89} +(-0.322521 - 2.21269i) q^{90} +(-0.0108300 - 0.0149063i) q^{91} +(3.05761 + 3.05761i) q^{92} +(3.43416 + 4.38253i) q^{93} -3.78443i q^{94} +(1.96589 - 4.27277i) q^{95} +(-0.406737 - 0.913545i) q^{96} +(6.39024 + 12.5416i) q^{97} +(-1.81148 + 6.76055i) q^{98} +(-2.06364 + 3.57432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 16 q^{7} + 4 q^{10} + 24 q^{14} + 8 q^{15} + 64 q^{16} - 36 q^{17} + 40 q^{19} - 12 q^{20} - 16 q^{21} + 44 q^{22} + 32 q^{24} - 28 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35}+ \cdots - 4 q^{99}+O(q^{100}) $ 256 * q + 16 * q^7 + 4 * q^10 + 24 * q^14 + 8 * q^15 + 64 * q^16 - 36 * q^17 + 40 * q^19 - 12 * q^20 - 16 * q^21 + 44 * q^22 + 32 * q^24 - 28 * q^25 - 8 * q^28 + 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 - 76 * q^37 + 28 * q^38 + 48 * q^41 - 4 * q^42 + 120 * q^43 - 4 * q^44 + 12 * q^45 - 20 * q^46 + 72 * q^47 + 40 * q^49 + 48 * q^50 - 16 * q^53 - 64 * q^54 + 36 * q^55 - 4 * q^57 - 68 * q^58 + 24 * q^59 - 20 * q^62 + 4 * q^63 + 156 * q^65 + 12 * q^66 + 44 * q^67 + 4 * q^68 - 12 * q^69 + 104 * q^70 - 48 * q^71 - 84 * q^73 - 68 * q^74 - 48 * q^75 + 48 * q^76 - 124 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 112 * q^83 + 132 * q^85 + 24 * q^86 + 32 * q^87 + 52 * q^88 + 224 * q^89 + 40 * q^91 + 64 * q^93 - 204 * q^95 + 8 * q^97 - 32 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{11}{30}\right)$

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
$3$	0.358368	−	0.933580i	0.206904	−	0.539003i
$3$	0.358368	−	0.933580i	0.206904	−	0.539003i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−1.14184	+	1.92255i	−0.510648	+	0.859790i
$5$	−1.14184	+	1.92255i	−0.510648	+	0.859790i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−0.0309572	−	0.00162240i	−0.0117007	−	0.000613208i	0.0464847	−	0.998919i	$-0.485198\pi$
$7$	−0.0309572	−	0.00162240i	−0.0117007	−	0.000613208i	−0.0581854	+	0.998306i	$0.518531\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−0.743145	−	0.669131i	−0.247715	−	0.223044i
$10$	1.72026	+	1.42854i	0.543993	+	0.451743i
$11$	−0.858109	−	4.03708i	−0.258729	−	1.21723i	−0.895108	−	0.445850i	$-0.852902\pi$
$11$	−0.858109	−	4.03708i	−0.258729	−	1.21723i	0.636378	−	0.771377i	$-0.280432\pi$
$12$	−0.629320	+	0.777146i	−0.181669	+	0.224343i
$13$	0.374047	+	0.461909i	0.103742	+	0.128111i	0.826373	−	0.563124i	$-0.190401\pi$
$13$	0.374047	+	0.461909i	0.103742	+	0.128111i	−0.722631	+	0.691234i	$0.757067\pi$
$14$	−0.00644519	+	0.0303222i	−0.00172255	+	0.00810396i
$15$	1.38565	+	1.75498i	0.357774	+	0.453134i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−2.22902	−	3.43239i	−0.540616	−	0.832476i	0.457781	−	0.889065i	$-0.348644\pi$
$17$	−2.22902	−	3.43239i	−0.540616	−	0.832476i	−0.998398	+	0.0565889i	$0.981978\pi$
$18$	−0.777146	+	0.629320i	−0.183175	+	0.148332i
$19$	−2.09187	+	0.219864i	−0.479908	+	0.0504403i	−0.341394	−	0.939920i	$-0.610899\pi$
$19$	−2.09187	+	0.219864i	−0.479908	+	0.0504403i	−0.138513	+	0.990361i	$0.544232\pi$
$20$	1.68006	−	1.47560i	0.375672	−	0.329955i
$21$	−0.0126087	+	0.0283196i	−0.00275144	+	0.00617984i
$22$	−4.12162	+	0.216005i	−0.878732	+	0.0460524i
$23$	−3.85281	−	1.96311i	−0.803367	−	0.409336i	0.00355535	−	0.999994i	$-0.498868\pi$
$23$	−3.85281	−	1.96311i	−0.803367	−	0.409336i	−0.806922	+	0.590658i	$0.798868\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−2.39239	−	4.39050i	−0.478478	−	0.878100i
$26$	0.514736	−	0.297183i	0.100948	−	0.0582824i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	0.0289407	+	0.0111093i	0.00546927	+	0.00209946i
$29$	−4.38491	+	3.18582i	−0.814256	+	0.591592i	−0.915062	−	0.403314i	$-0.867858\pi$
$29$	−4.38491	+	3.18582i	−0.814256	+	0.591592i	0.100805	+	0.994906i	$0.467858\pi$
$30$	1.95014	−	1.09405i	0.356045	−	0.199746i
$31$	−2.86075	+	4.77662i	−0.513806	+	0.857906i
$31$	−2.86075	+	4.77662i	−0.513806	+	0.857906i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.07646	−	0.645648i	−0.709621	−	0.112393i
$34$	−3.73882	+	1.66463i	−0.641203	+	0.285482i
$35$	0.0384674	−	0.0576642i	0.00650217	−	0.00974702i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.49336	+	0.936044i	−0.574305	+	0.153885i	−0.534270	−	0.845314i	$-0.679414\pi$
$37$	−3.49336	+	0.936044i	−0.574305	+	0.153885i	−0.0400349	+	0.999198i	$0.512747\pi$
$38$	−0.110083	+	2.10051i	−0.0178578	+	0.340748i
$39$	0.565275	−	0.183669i	0.0905165	−	0.0294106i
$40$	−1.19462	−	1.89021i	−0.188886	−	0.298868i
$41$	−3.98282	−	1.77326i	−0.622012	−	0.276937i	0.0714352	−	0.997445i	$-0.477242\pi$
$41$	−3.98282	−	1.77326i	−0.622012	−	0.276937i	−0.693447	+	0.720508i	$0.743909\pi$
$42$	0.0259985	+	0.0168836i	0.00401166	+	0.00260520i
$43$	−0.248318	−	0.201084i	−0.0378681	−	0.0306650i	0.610200	−	0.792248i	$-0.291089\pi$
$43$	−0.248318	−	0.201084i	−0.0378681	−	0.0306650i	−0.648068	+	0.761583i	$0.724423\pi$
$44$	−0.431418	+	4.10466i	−0.0650387	+	0.618802i
$45$	2.13499	−	0.664690i	0.318266	−	0.0990862i
$46$	−2.54165	+	3.49828i	−0.374746	+	0.515793i
$47$	3.73784	−	0.592016i	0.545220	−	0.0863543i	0.122252	−	0.992499i	$-0.460988\pi$
$47$	3.73784	−	0.592016i	0.545220	−	0.0863543i	0.422968	+	0.906145i	$0.360988\pi$
$48$	0.838671	−	0.544639i	0.121052	−	0.0786119i
$49$	−6.96070	−	0.731599i	−0.994385	−	0.104514i
$50$	−4.71070	+	1.67611i	−0.666193	+	0.237038i
$51$	−4.00322	+	0.850910i	−0.560562	+	0.119151i
$52$	−0.213002	−	0.554888i	−0.0295380	−	0.0769492i
$53$	0.0643963	+	1.22875i	0.00884551	+	0.168782i	0.999480	+	0.0322424i	$0.0102649\pi$
$53$	0.0643963	+	1.22875i	0.00884551	+	0.168782i	−0.990635	+	0.136540i	$0.956402\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	8.74132	+	2.95996i	1.17868	+	0.399121i
$56$	0.0154998	−	0.0268465i	0.00207125	−	0.00358751i
$57$	−0.544398	+	2.03172i	−0.0721072	+	0.269108i
$58$	2.46065	+	4.82929i	0.323099	+	0.634117i
$59$	−2.76413	−	6.20833i	−0.359859	−	0.808256i	−0.999225	−	0.0393537i	$-0.987470\pi$
$59$	−2.76413	−	6.20833i	−0.359859	−	0.808256i	0.639367	−	0.768902i	$-0.279197\pi$
$60$	−0.775516	−	2.09728i	−0.100119	−	0.270757i
$61$		−	9.30660i		−	1.19159i	−0.803137	−	0.595794i	$-0.796837\pi$
$61$		−	9.30660i		−	1.19159i	0.803137	−	0.595794i	$-0.203163\pi$
$62$	4.27029	+	3.57276i	0.542328	+	0.453741i
$63$	0.0219201	+	0.0219201i	0.00276167	+	0.00276167i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−1.31515	+	0.191695i	−0.163124	+	0.0237769i
$66$	−1.27540	+	3.92527i	−0.156991	+	0.483167i
$67$	3.06099	+	0.820189i	0.373959	+	0.100202i	0.440903	−	0.897555i	$-0.354658\pi$
$67$	3.06099	+	0.820189i	0.373959	+	0.100202i	−0.0669441	+	0.997757i	$0.521325\pi$
$68$	1.05926	+	3.95320i	0.128454	+	0.479396i
$69$	−3.21344	+	2.89340i	−0.386853	+	0.348324i
$70$	−0.0509366	−	0.0470144i	−0.00608809	−	0.00561930i
$71$	8.03180	−	8.92021i	0.953199	−	1.05863i	−0.0450205	−	0.998986i	$-0.514335\pi$
$71$	8.03180	−	8.92021i	0.953199	−	1.05863i	0.998219	−	0.0596486i	$-0.0189980\pi$
$72$	0.933580	−	0.358368i	0.110024	−	0.0422341i
$73$	−4.47712	+	6.89416i	−0.524007	+	0.806900i	−0.997256	−	0.0740283i	$-0.976414\pi$
$73$	−4.47712	+	6.89416i	−0.524007	+	0.806900i	0.473249	+	0.880929i	$0.343081\pi$
$74$	0.378037	+	3.59678i	0.0439459	+	0.418118i
$75$	−4.95624	+	0.660075i	−0.572297	+	0.0762189i
$76$	2.05743	+	0.437320i	0.236003	+	0.0501640i
$77$	0.0200149	+	0.126369i	0.00228091	+	0.0144011i
$78$	−0.0929793	−	0.587048i	−0.0105278	−	0.0664701i
$79$	15.8885	+	3.37722i	1.78760	+	0.379966i	0.978262	−	0.207374i	$-0.0664918\pi$
$79$	15.8885	+	3.37722i	1.78760	+	0.379966i	0.809340	+	0.587341i	$0.199825\pi$
$80$	−2.05382	+	0.884217i	−0.229624	+	0.0988584i
$81$	0.104528	+	0.994522i	0.0116143	+	0.110502i
$82$	−2.37448	+	3.65638i	−0.262218	+	0.403780i
$83$	−6.37114	+	2.44565i	−0.699324	+	0.268445i	−0.681945	−	0.731404i	$-0.738866\pi$
$83$	−6.37114	+	2.44565i	−0.699324	+	0.268445i	−0.0173790	+	0.999849i	$0.505532\pi$
$84$	0.0207428	−	0.0230372i	0.00226323	−	0.00251357i
$85$	9.14412	−	0.366150i	0.991819	−	0.0397146i
$86$	−0.237454	+	0.213804i	−0.0256053	+	0.0230551i
$87$	1.40281	+	5.23536i	0.150397	+	0.561289i
$88$	3.98664	+	1.06822i	0.424977	+	0.113872i
$89$	0.716054	−	2.20379i	0.0759016	−	0.233601i	−0.905906	−	0.423478i	$-0.860809\pi$
$89$	0.716054	−	2.20379i	0.0759016	−	0.233601i	0.981808	+	0.189877i	$0.0608090\pi$
$90$	−0.322521	−	2.21269i	−0.0339967	−	0.233238i
$91$	−0.0108300	−	0.0149063i	−0.00113530	−	0.00156260i
$92$	3.05761	+	3.05761i	0.318778	+	0.318778i
$93$	3.43416	+	4.38253i	0.356106	+	0.454447i
$94$		−	3.78443i		−	0.390334i
$95$	1.96589	−	4.27277i	0.201696	−	0.438377i
$96$	−0.406737	−	0.913545i	−0.0415124	−	0.0932383i
$97$	6.39024	+	12.5416i	0.648831	+	1.27340i	0.947717	+	0.319113i	$0.103385\pi$
$97$	6.39024	+	12.5416i	0.648831	+	1.27340i	−0.298886	+	0.954289i	$0.596615\pi$
$98$	−1.81148	+	6.76055i	−0.182988	+	0.682919i
$99$	−2.06364	+	3.57432i	−0.207403	+	0.359233i
$100$	0.918560	+	4.91490i	0.0918560	+	0.491490i
$101$	−2.29786	−	7.07209i	−0.228646	−	0.703699i	−0.997901	−	0.0647578i	$-0.979373\pi$
$101$	−2.29786	−	7.07209i	−0.228646	−	0.703699i	0.769255	−	0.638942i	$-0.220627\pi$
$102$	0.214193	+	4.08704i	0.0212082	+	0.404677i
$103$	−0.107706	−	0.280583i	−0.0106126	−	0.0276467i	0.928172	−	0.372152i	$-0.121380\pi$
$103$	−0.107706	−	0.280583i	−0.0106126	−	0.0276467i	−0.938784	+	0.344505i	$0.888047\pi$
$104$	−0.581378	+	0.123576i	−0.0570088	+	0.0121176i
$105$	−0.0400487	−	0.0565774i	−0.00390835	−	0.00552139i
$106$	1.22370	+	0.128616i	0.118856	+	0.0124923i
$107$	−1.78436	+	1.15878i	−0.172500	+	0.112023i	−0.628001	−	0.778212i	$-0.716127\pi$
$107$	−1.78436	+	1.15878i	−0.172500	+	0.112023i	0.455501	+	0.890235i	$0.349460\pi$
$108$	0.987688	−	0.156434i	0.0950404	−	0.0150529i
$109$	8.50501	−	11.7061i	0.814632	−	1.12124i	−0.175960	−	0.984397i	$-0.556303\pi$
$109$	8.50501	−	11.7061i	0.814632	−	1.12124i	0.990592	−	0.136847i	$-0.0436970\pi$
$110$	4.29096	−	8.17066i	0.409127	−	0.779042i
$111$	−0.378037	+	3.59678i	−0.0358817	+	0.341392i
$112$	−0.0240913	−	0.0195087i	−0.00227641	−	0.00184340i
$113$	−14.9429	−	9.70405i	−1.40571	−	0.912880i	−0.405713	−	0.914001i	$-0.632977\pi$
$113$	−14.9429	−	9.70405i	−1.40571	−	0.912880i	−0.999999	+	0.00112034i	$0.999643\pi$
$114$	1.92154	+	0.855526i	0.179969	+	0.0801274i
$115$	8.17347	−	5.16566i	0.762180	−	0.481700i
$116$	5.15477	−	1.67488i	0.478608	−	0.155509i
$117$	0.0311067	−	0.593551i	0.00287582	−	0.0548738i
$118$	−6.56430	+	1.75890i	−0.604293	+	0.161920i
$119$	0.0634354	+	0.109873i	0.00581511	+	0.0100721i
$120$	−2.19277	+	0.437882i	−0.200172	+	0.0399730i
$121$	−5.51269	+	2.45441i	−0.501154	+	0.223128i
$122$	−9.19202	−	1.45587i	−0.832207	−	0.131809i
$123$	−3.08280	+	3.08280i	−0.277967	+	0.277967i
$124$	4.19679	−	3.65882i	0.376883	−	0.328571i
$125$	11.1727	+	0.413771i	0.999315	+	0.0370088i
$126$	0.0250793	−	0.0182211i	0.00223424	−	0.00162327i
$127$	11.2193	+	4.30667i	0.995549	+	0.382155i	0.800952	−	0.598728i	$-0.204327\pi$
$127$	11.2193	+	4.30667i	0.995549	+	0.382155i	0.194596	+	0.980883i	$0.437660\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	−0.276717	+	0.159763i	−0.0243636	+	0.0140663i
$130$	−0.0163988	+	1.32894i	−0.00143827	+	0.116556i
$131$	−8.60206	−	9.55356i	−0.751565	−	0.834698i	0.239103	−	0.970994i	$-0.423147\pi$
$131$	−8.60206	−	9.55356i	−0.751565	−	0.834698i	−0.990668	+	0.136296i	$0.956480\pi$
$132$	3.67743	+	1.87374i	0.320079	+	0.163088i
$133$	0.0651151	−	0.00341254i	0.00564619	−	0.000295904i
$134$	1.28893	−	2.89499i	0.111347	−	0.250089i
$135$	0.144570	−	2.23139i	0.0124426	−	0.192047i
$136$	4.07023	−	0.427799i	0.349019	−	0.0366834i
$137$	8.87168	−	7.18415i	0.757959	−	0.613783i	−0.170440	−	0.985368i	$-0.554519\pi$
$137$	8.87168	−	7.18415i	0.757959	−	0.613783i	0.928399	+	0.371585i	$0.121186\pi$
$138$	2.35508	+	3.62651i	0.200478	+	0.308709i
$139$	17.8869	+	12.9956i	1.51715	+	1.10227i	0.962880	+	0.269931i	$0.0870010\pi$
$139$	17.8869	+	12.9956i	1.51715	+	1.10227i	0.554266	+	0.832339i	$0.312999\pi$
$140$	−0.0544038	+	0.0429548i	−0.00459796	+	0.00363034i
$141$	0.786828	−	3.70173i	0.0662628	−	0.311742i
$142$	−7.55394	−	9.32834i	−0.633913	−	0.782817i
$143$	1.54379	−	1.90643i	0.129098	−	0.159423i
$144$	−0.207912	−	0.978148i	−0.0173260	−	0.0815123i
$145$	−1.11802	−	12.0679i	−0.0928468	−	1.00218i
$146$	6.10891	+	5.50048i	0.505577	+	0.455223i
$147$	−3.17750	+	6.23619i	−0.262076	+	0.514352i
$148$	3.61164	+	0.189278i	0.296875	+	0.0155586i
$149$	−12.4778	−	7.20407i	−1.02222	−	0.590181i	−0.107476	−	0.994208i	$-0.534277\pi$
$149$	−12.4778	−	7.20407i	−1.02222	−	0.590181i	−0.914747	+	0.404027i	$0.867610\pi$
$150$	−0.123378	+	4.99848i	−0.0100738	+	0.408124i
$151$	−18.0221	−	5.85574i	−1.46662	−	0.476533i	−0.536534	−	0.843879i	$-0.680267\pi$
$151$	−18.0221	−	5.85574i	−1.46662	−	0.476533i	−0.930085	+	0.367345i	$0.880267\pi$
$152$	0.753788	−	1.96369i	0.0611403	−	0.159276i
$153$	−0.640232	+	4.04226i	−0.0517597	+	0.326798i
$154$	0.127944			0.0103100
$155$	−5.91676	−	10.9541i	−0.475246	−	0.879853i
$156$	−0.594366			−0.0475874
$157$	−3.22926	+	20.3887i	−0.257723	+	1.62720i	0.431126	+	0.902292i	$0.358116\pi$
$157$	−3.22926	+	20.3887i	−0.257723	+	1.62720i	−0.688849	+	0.724905i	$0.741884\pi$
$158$	5.82115	−	15.1646i	0.463106	−	1.20643i
$159$	1.17022	+	0.380227i	0.0928043	+	0.0301540i
$160$	0.552043	+	2.16685i	0.0436428	+	0.171305i
$161$	0.116087	+	0.0670230i	0.00914896	+	0.00528215i
$162$	0.998630	+	0.0523360i	0.0784597	+	0.00411190i
$163$	−1.89209	+	3.71343i	−0.148200	+	0.290858i	−0.953158	−	0.302473i	$-0.902188\pi$
$163$	−1.89209	+	3.71343i	−0.148200	+	0.290858i	0.804958	+	0.593332i	$0.202188\pi$
$164$	3.23992	+	2.91723i	0.252995	+	0.227798i
$165$	5.89597	−	7.09997i	0.459000	−	0.552732i
$166$	1.41888	+	6.67529i	0.110126	+	0.518103i
$167$	−2.21521	+	2.73555i	−0.171418	+	0.211683i	−0.855614	−	0.517615i	$-0.826820\pi$
$167$	−2.21521	+	2.73555i	−0.171418	+	0.211683i	0.684196	+	0.729298i	$0.260153\pi$
$168$	−0.0195087	−	0.0240913i	−0.00150513	−	0.00185868i
$169$	2.62940	−	12.3704i	0.202262	−	0.951567i
$170$	1.06881	−	9.08882i	0.0819742	−	0.697080i
$171$	1.70168	+	1.23634i	0.130131	+	0.0945455i
$172$	0.174026	+	0.267977i	0.0132694	+	0.0204330i
$173$	−9.44992	+	7.65240i	−0.718464	+	0.581801i	−0.917283	−	0.398235i	$-0.869623\pi$
$173$	−9.44992	+	7.65240i	−0.718464	+	0.581801i	0.198819	+	0.980036i	$0.436289\pi$
$174$	5.39035	−	0.566549i	0.408641	−	0.0429499i
$175$	0.0669385	+	0.139799i	0.00506008	+	0.0105678i
$176$	1.67871	−	3.77045i	0.126538	−	0.284209i
$177$	−6.78655	+	0.355668i	−0.510108	+	0.0267336i
$178$	−2.06464	−	1.05199i	−0.154751	−	0.0788498i
$179$	3.07502	+	3.41516i	0.229838	+	0.255261i	0.847022	−	0.531558i	$-0.178393\pi$
$179$	3.07502	+	3.41516i	0.229838	+	0.255261i	−0.617184	+	0.786819i	$0.711727\pi$
$180$	−2.23590	−	0.0275903i	−0.166654	−	0.00205646i
$181$	−1.51877	+	0.876865i	−0.112890	+	0.0651769i	−0.555382	−	0.831596i	$-0.687428\pi$
$181$	−1.51877	+	0.876865i	−0.112890	+	0.0651769i	0.442492	+	0.896772i	$0.354094\pi$
$182$	−0.0164169	+	0.00836484i	−0.00121690	+	0.000620043i
$183$	−8.68846	−	3.33519i	−0.642269	−	0.246544i
$184$	3.49828	−	2.54165i	0.257897	−	0.187373i
$185$	2.18928	−	7.78498i	0.160959	−	0.572363i
$186$	4.86579	−	2.70630i	0.356777	−	0.198436i
$187$	−11.9441	+	11.9441i	−0.873438	+	0.873438i
$188$	−3.73784	−	0.592016i	−0.272610	−	0.0431772i
$189$	0.0283196	−	0.0126087i	0.00205995	−	0.000917148i
$190$	−3.91263	−	2.61009i	−0.283852	−	0.189356i
$191$	−1.73409	−	3.00354i	−0.125475	−	0.217329i	0.796444	−	0.604713i	$-0.206712\pi$
$191$	−1.73409	−	3.00354i	−0.125475	−	0.217329i	−0.921918	+	0.387384i	$0.873379\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	1.20270	−	22.9490i	0.0865725	−	1.65190i	−0.518021	−	0.855368i	$-0.673331\pi$
$193$	1.20270	−	22.9490i	0.0865725	−	1.65190i	0.604593	−	0.796534i	$-0.293336\pi$
$194$	13.3868	−	4.34964i	0.961116	−	0.312286i
$195$	−0.292343	+	1.29649i	−0.0209351	+	0.0928437i
$196$	6.39394	+	2.84677i	0.456710	+	0.203340i
$197$	15.1702	+	9.85165i	1.08083	+	0.701901i	0.956908	−	0.290391i	$-0.0937853\pi$
$197$	15.1702	+	9.85165i	1.08083	+	0.701901i	0.123924	+	0.992292i	$0.460452\pi$
$198$	3.20749	+	2.59738i	0.227947	+	0.184588i
$199$	0.678657	−	6.45699i	0.0481087	−	0.457724i	−0.943776	−	0.330585i	$-0.892754\pi$
$199$	0.678657	−	6.45699i	0.0481087	−	0.457724i	0.991885	−	0.127139i	$-0.0405793\pi$
$200$	4.99808	−	0.138391i	0.353418	−	0.00978571i
$201$	1.86267	−	2.56375i	0.131383	−	0.180833i
$202$	−7.34449	+	1.16325i	−0.516756	+	0.0818462i
$203$	0.140913	−	0.0915099i	0.00989015	−	0.00642274i
$204$	4.07023	+	0.427799i	0.284973	+	0.0299519i
$205$	7.95694	−	5.63237i	0.555737	−	0.393382i
$206$	−0.293978	+	0.0624869i	−0.0204824	+	0.00435367i
$207$	1.54962	+	4.03691i	0.107706	+	0.280584i
$208$	0.0311067	+	0.593551i	0.00215686	+	0.0411554i
$209$	2.68266	+	8.25638i	0.185564	+	0.571106i
$210$	−0.0621458	+	0.0307050i	−0.00428847	+	0.00211884i
$211$	−1.86364	+	3.22792i	−0.128298	+	0.222219i	−0.923017	−	0.384758i	$-0.874285\pi$
$211$	−1.86364	+	3.22792i	−0.128298	+	0.222219i	0.794719	+	0.606977i	$0.207618\pi$
$212$	0.318461	−	1.18851i	0.0218720	−	0.0816275i
$213$	−5.44940	−	10.6950i	−0.373387	−	0.732813i
$214$	0.865374	+	1.94366i	0.0591557	+	0.132866i
$215$	0.670134	−	0.247797i	0.0457028	−	0.0168996i
$216$		−	1.00000i		−	0.0680414i
$217$	0.0963103	−	0.143229i	0.00653797	−	0.00972305i
$218$	−10.2315	−	10.2315i	−0.692967	−	0.692967i
$219$	4.83180	+	6.65040i	0.326503	+	0.449392i
$220$	−7.39881	−	5.51630i	−0.498828	−	0.371909i
$221$	0.751694	−	2.31348i	0.0505644	−	0.155621i
$222$	3.49336	+	0.936044i	0.234459	+	0.0628231i
$223$	−0.197817	−	0.738261i	−0.0132468	−	0.0494376i	0.958986	−	0.283453i	$-0.0914800\pi$
$223$	−0.197817	−	0.738261i	−0.0132468	−	0.0494376i	−0.972233	+	0.234015i	$0.924813\pi$
$224$	−0.0230372	+	0.0207428i	−0.00153924	+	0.00138594i
$225$	−1.15992	+	4.86360i	−0.0773283	+	0.324240i
$226$	−11.9222	+	13.2409i	−0.793051	+	0.880772i
$227$	16.1631	−	6.20442i	1.07278	−	0.411802i	0.243078	−	0.970007i	$-0.421843\pi$
$227$	16.1631	−	6.20442i	1.07278	−	0.411802i	0.829703	+	0.558205i	$0.188510\pi$
$228$	1.14559	−	1.76405i	0.0758685	−	0.116827i
$229$	−0.300156	−	2.85579i	−0.0198349	−	0.188716i	0.980118	−	0.198415i	$-0.0635794\pi$
$229$	−0.300156	−	2.85579i	−0.0198349	−	0.188716i	−0.999953	+	0.00969891i	$0.996913\pi$
$230$	−3.82345	−	8.88093i	−0.252111	−	0.585591i
$231$	0.125148	+	0.0266011i	0.00823415	+	0.00175022i
$232$	−0.847881	−	5.35331i	−0.0556661	−	0.351462i
$233$	−1.06900	−	6.74942i	−0.0700327	−	0.442169i	−0.997643	−	0.0686195i	$-0.978141\pi$
$233$	−1.06900	−	6.74942i	−0.0700327	−	0.442169i	0.927610	−	0.373550i	$-0.121859\pi$
$234$	−0.581378	−	0.123576i	−0.0380058	−	0.00807839i
$235$	−3.12985	+	7.86217i	−0.204169	+	0.512871i
$236$	0.710361	+	6.75863i	0.0462406	+	0.439950i
$237$	8.84685	−	13.6230i	0.574665	−	0.884906i
$238$	0.118444	−	0.0454664i	0.00767759	−	0.00294715i
$239$	−9.85439	+	10.9444i	−0.637428	+	0.707935i	−0.972144	−	0.234384i	$-0.924693\pi$
$239$	−9.85439	+	10.9444i	−0.637428	+	0.707935i	0.334716	+	0.942319i	$0.391359\pi$
$240$	0.0894653	+	2.23428i	0.00577496	+	0.144222i
$241$	14.7153	−	13.2497i	0.947896	−	0.853489i	−0.0414402	−	0.999141i	$-0.513195\pi$
$241$	14.7153	−	13.2497i	0.947896	−	0.853489i	0.989336	+	0.145652i	$0.0465279\pi$
$242$	1.56182	+	5.82878i	0.100397	+	0.374688i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−2.87590	+	8.85110i	−0.184110	+	0.566634i
$245$	9.35456	−	12.5469i	0.597641	−	0.801593i
$246$	2.56259	+	3.52710i	0.163385	+	0.224880i
$247$	−0.884014	−	0.884014i	−0.0562484	−	0.0562484i
$248$	−2.95725	−	4.71749i	−0.187785	−	0.299561i
$249$			6.82442i			0.432480i
$250$	2.15647	−	10.9704i	0.136387	−	0.693829i
$251$	2.85013	+	6.40151i	0.179899	+	0.404059i	0.980876	−	0.194636i	$-0.0623526\pi$
$251$	2.85013	+	6.40151i	0.179899	+	0.404059i	−0.800977	+	0.598696i	$0.795686\pi$
$252$	−0.0140736	−	0.0276209i	−0.000886550	−	0.00173995i
$253$	−4.61909	+	17.2387i	−0.290400	+	1.08379i
$254$	6.00873	−	10.4074i	0.377021	−	0.653020i
$255$	2.93513	−	8.66799i	0.183805	−	0.542810i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.567880	−	10.8358i	−0.0354234	−	0.675919i	−0.957416	−	0.288712i	$-0.906773\pi$
$257$	−0.567880	−	10.8358i	−0.0354234	−	0.675919i	0.921993	−	0.387207i	$-0.126560\pi$
$258$	0.114508	+	0.298303i	0.00712894	+	0.0185715i
$259$	0.109663	−	0.0233096i	0.00681414	−	0.00144839i
$260$	1.31001	+	0.224089i	0.0812436	+	0.0138974i
$261$	5.39035	+	0.566549i	0.333654	+	0.0350685i
$262$	−10.7816	+	7.00165i	−0.666089	+	0.432563i
$263$	11.2422	−	1.78059i	0.693223	−	0.109796i	0.200126	−	0.979770i	$-0.435865\pi$
$263$	11.2422	−	1.78059i	0.693223	−	0.109796i	0.493097	+	0.869974i	$0.335865\pi$
$264$	2.42595	−	3.33904i	0.149307	−	0.205503i
$265$	−2.43587	−	1.27924i	−0.149634	−	0.0785830i
$266$	0.00681572	−	0.0648472i	0.000417898	−	0.00397604i
$267$	−1.80080	−	1.45826i	−0.110207	−	0.0892442i
$268$	−2.65772	−	1.72594i	−0.162346	−	0.105429i
$269$	2.31068	+	1.02878i	0.140884	+	0.0627258i	0.475968	−	0.879463i	$-0.342098\pi$
$269$	2.31068	+	1.02878i	0.140884	+	0.0627258i	−0.335083	+	0.942188i	$0.608765\pi$
$270$	−2.18130	−	0.491857i	−0.132750	−	0.0299334i
$271$	16.2073	−	5.26606i	0.984521	−	0.319890i	0.227857	−	0.973695i	$-0.426828\pi$
$271$	16.2073	−	5.26606i	0.984521	−	0.319890i	0.756664	+	0.653804i	$0.226828\pi$
$272$	0.214193	−	4.08704i	0.0129873	−	0.247813i
$273$	−0.0177973	+	0.00476878i	−0.00107714	+	0.000288619i
$274$	−5.70786	−	9.88631i	−0.344825	−	0.597254i
$275$	−15.6719	+	13.4258i	−0.945050	+	0.809606i
$276$	3.95027	−	1.75877i	0.237778	−	0.105866i
$277$	−7.74804	−	1.22717i	−0.465535	−	0.0737335i	−0.0807391	−	0.996735i	$-0.525728\pi$
$277$	−7.74804	−	1.22717i	−0.465535	−	0.0737335i	−0.384796	+	0.923002i	$0.625728\pi$
$278$	15.6337	−	15.6337i	0.937648	−	0.937648i
$279$	5.32214	−	1.63551i	0.318628	−	0.0979151i
$280$	0.0339153	+	0.0604537i	0.00202683	+	0.00361280i
$281$	7.07352	−	5.13921i	0.421971	−	0.306580i	−0.356460	−	0.934311i	$-0.616016\pi$
$281$	7.07352	−	5.13921i	0.421971	−	0.306580i	0.778430	+	0.627731i	$0.216016\pi$
$282$	−3.53307	−	1.35622i	−0.210391	−	0.0807617i
$283$	−16.3347	+	8.32294i	−0.970997	+	0.494747i	−0.866173	−	0.499743i	$-0.833428\pi$
$283$	−16.3347	+	8.32294i	−0.970997	+	0.494747i	−0.104823	+	0.994491i	$0.533428\pi$
$284$	−10.3952	+	6.00167i	−0.616841	+	0.356133i
$285$	−3.28446	−	3.36654i	−0.194555	−	0.199416i
$286$	−1.64145	−	1.82302i	−0.0970611	−	0.107797i
$287$	0.120420	+	0.0613570i	0.00710816	+	0.00362179i
$288$	−0.998630	+	0.0523360i	−0.0588448	+	0.00308393i
$289$	0.101769	−	0.228576i	0.00598639	−	0.0134457i
$290$	−12.0942	−	0.783577i	−0.710197	−	0.0460132i
$291$	13.9986	−	1.47131i	0.820613	−	0.0862499i
$292$	6.38841	−	5.17323i	0.373853	−	0.302740i
$293$	12.5799	+	19.3713i	0.734924	+	1.13168i	0.986487	+	0.163843i	$0.0523889\pi$
$293$	12.5799	+	19.3713i	0.734924	+	1.13168i	−0.251563	+	0.967841i	$0.580944\pi$
$294$	5.66234	+	4.11393i	0.330234	+	0.239929i
$295$	15.0920	+	1.77477i	0.878691	+	0.103331i
$296$	0.751932	−	3.53756i	0.0437052	−	0.205617i
$297$	2.59738	+	3.20749i	0.150715	+	0.186118i
$298$	−9.06734	+	11.1972i	−0.525257	+	0.648638i
$299$	−0.534355	−	2.51394i	−0.0309025	−	0.145385i
$300$	4.91764	+	0.903794i	0.283920	+	0.0521805i
$301$	0.00736099	+	0.00662786i	0.000424280	+	0.000382024i
$302$	−8.60292	+	16.8842i	−0.495043	+	0.971576i
$303$	−7.42585	−	0.389172i	−0.426604	−	0.0223574i
$304$	−1.82159	−	1.05170i	−0.104475	−	0.0603189i
$305$	17.8924	+	10.6267i	1.02452	+	0.608482i
$306$	3.89234	+	1.26470i	0.222510	+	0.0722980i
$307$	−4.78534	+	12.4662i	−0.273114	+	0.711485i	0.726588	+	0.687073i	$0.241105\pi$
$307$	−4.78534	+	12.4662i	−0.273114	+	0.711485i	−0.999702	+	0.0244122i	$0.992229\pi$
$308$	0.0200149	−	0.126369i	0.00114045	−	0.00720054i
$309$	−0.300545			−0.0170974
$310$	−11.7448	+	4.13032i	−0.667060	+	0.234586i
$311$	10.1547			0.575822			0.287911	−	0.957657i	$-0.407039\pi$
$311$	10.1547			0.575822			0.287911	+	0.957657i	$0.407039\pi$
$312$	−0.0929793	+	0.587048i	−0.00526392	+	0.0332351i
$313$	1.25628	−	3.27271i	0.0710089	−	0.184985i	−0.893483	−	0.449097i	$-0.851746\pi$
$313$	1.25628	−	3.27271i	0.0710089	−	0.184985i	0.964492	+	0.264113i	$0.0850790\pi$
$314$	19.6325	+	6.37900i	1.10793	+	0.359988i
$315$	−0.0671717	+	0.0171131i	−0.00378470	+	0.000964216i
$316$	−14.0673	−	8.12175i	−0.791347	−	0.456884i
$317$	−2.97617	−	0.155974i	−0.167158	−	0.00876040i	−0.0314268	−	0.999506i	$-0.510005\pi$
$317$	−2.97617	−	0.155974i	−0.167158	−	0.00876040i	−0.135732	+	0.990746i	$0.543338\pi$
$318$	0.558608	−	1.09633i	0.0313252	−	0.0614792i
$319$	16.6241	+	14.9684i	0.930774	+	0.838072i
$320$	2.22653	−	0.206276i	0.124467	−	0.0115312i
$321$	0.442353	+	2.08111i	0.0246898	+	0.116156i
$322$	0.0843579	−	0.104173i	0.00470108	−	0.00580535i
$323$	5.41747	+	6.69002i	0.301436	+	0.372243i
$324$	0.207912	−	0.978148i	0.0115506	−	0.0543415i
$325$	1.13315	−	2.74732i	0.0628556	−	0.152394i
$326$	3.37173	+	2.44970i	0.186743	+	0.135676i
$327$	−7.88070	−	12.1352i	−0.435804	−	0.671079i
$328$	3.38815	−	2.74367i	0.187079	−	0.151494i
$329$	−0.116673	+	0.0122629i	−0.00643241	+	0.000676074i
$330$	−6.09022	−	6.93406i	−0.335256	−	0.381707i
$331$	2.36410	−	5.30985i	0.129943	−	0.291856i	−0.836844	−	0.547442i	$-0.815602\pi$
$331$	2.36410	−	5.30985i	0.129943	−	0.291856i	0.966786	+	0.255586i	$0.0822684\pi$
$332$	6.81506	−	0.357162i	0.374025	−	0.0196018i
$333$	3.22241	+	1.64190i	0.176587	+	0.0899755i
$334$	2.35534	+	2.61587i	0.128878	+	0.143134i
$335$	−5.07202	+	4.94837i	−0.277114	+	0.270358i
$336$	−0.0268465	+	0.0154998i	−0.00146460	+	0.000845585i
$337$	−24.9086	+	12.6916i	−1.35686	+	0.691354i	−0.972733	−	0.231926i	$-0.925497\pi$
$337$	−24.9086	+	12.6916i	−1.35686	+	0.691354i	−0.384126	+	0.923281i	$0.625497\pi$
$338$	−11.8067	−	4.53218i	−0.642202	−	0.246518i
$339$	−14.4146	+	10.4728i	−0.782892	+	0.568805i
$340$	−8.80972	−	2.47746i	−0.477774	−	0.134359i
$341$	21.7385	+	7.45023i	1.17720	+	0.403453i
$342$	1.48732	−	1.48732i	0.0804252	−	0.0804252i
$343$	0.428623	+	0.0678872i	0.0231434	+	0.00366556i
$344$	0.291901	−	0.129963i	0.0157383	−	0.00700712i
$345$	−1.89345	−	9.48180i	−0.101940	−	0.510483i
$346$	6.07989	+	10.5307i	0.326857	+	0.566133i
$347$	20.2607	−	5.42883i	1.08765	−	0.291435i	0.329924	−	0.944008i	$-0.392977\pi$
$347$	20.2607	−	5.42883i	1.08765	−	0.291435i	0.757726	+	0.652573i	$0.226310\pi$
$348$	0.283663	−	5.41261i	0.0152059	−	0.290147i
$349$	11.5396	−	3.74944i	0.617700	−	0.200703i	0.0165814	−	0.999863i	$-0.494722\pi$
$349$	11.5396	−	3.74944i	0.617700	−	0.200703i	0.601119	+	0.799159i	$0.294722\pi$
$350$	0.148549	−	0.0442450i	0.00794029	−	0.00236500i
$351$	−0.542980	−	0.241750i	−0.0289821	−	0.0129037i
$352$	−3.46142	−	2.24787i	−0.184494	−	0.119812i
$353$	0.720760	+	0.583660i	0.0383622	+	0.0310651i	0.648310	−	0.761377i	$-0.275476\pi$
$353$	0.720760	+	0.583660i	0.0383622	+	0.0310651i	−0.609948	+	0.792442i	$0.708810\pi$
$354$	−0.710361	+	6.75863i	−0.0377553	+	0.359217i
$355$	7.97850	+	25.6270i	0.423455	+	1.36014i
$356$	−1.36202	+	1.87465i	−0.0721867	+	0.0993565i
$357$	0.125309	−	0.0198470i	0.00663204	−	0.00105041i
$358$	3.85415	−	2.50292i	0.203698	−	0.132283i
$359$	−27.9868	−	2.94153i	−1.47709	−	0.155248i	−0.668538	−	0.743678i	$-0.733079\pi$
$359$	−27.9868	−	2.94153i	−1.47709	−	0.155248i	−0.808548	+	0.588430i	$0.799746\pi$
$360$	−0.377022	+	2.20405i	−0.0198708	+	0.116164i
$361$	−14.2572	+	3.03047i	−0.750381	+	0.159498i
$362$	0.628481	+	1.63725i	0.0330322	+	0.0860518i
$363$	0.315816	+	6.02612i	0.0165760	+	0.316290i
$364$	0.00569368	+	0.0175233i	0.000298430	+	0.000918473i
$365$	−8.14219	−	16.4795i	−0.426182	−	0.862578i
$366$	−4.65330	+	8.05975i	−0.243232	+	0.421290i
$367$	0.0851691	−	0.317855i	0.00444579	−	0.0165919i	−0.963667	−	0.267105i	$-0.913933\pi$
$367$	0.0851691	−	0.317855i	0.00444579	−	0.0165919i	0.968113	+	0.250514i	$0.0805995\pi$
$368$	−1.96311	−	3.85281i	−0.102334	−	0.200842i
$369$	1.77326	+	3.98282i	0.0923125	+	0.207337i
$370$	−7.34665	−	3.38017i	−0.381934	−	0.175726i
$371$		−	0.0381432i		−	0.00198030i
$372$	−1.91180	−	5.22925i	−0.0991224	−	0.271124i
$373$	−1.97534	−	1.97534i	−0.102279	−	0.102279i	0.654116	−	0.756395i	$-0.273041\pi$
$373$	−1.97534	−	1.97534i	−0.102279	−	0.102279i	−0.756395	+	0.654116i	$0.773041\pi$
$374$	9.92857	+	13.6655i	0.513394	+	0.706626i
$375$	4.39022	−	10.2823i	0.226710	−	0.530976i
$376$	−1.16945	+	3.59921i	−0.0603100	+	0.185615i
$377$	−3.11172	−	0.833782i	−0.160262	−	0.0429420i
$378$	−0.00802330	−	0.0299434i	−0.000412674	−	0.00154012i
$379$	12.1445	−	10.9350i	0.623823	−	0.561692i	−0.295428	−	0.955365i	$-0.595462\pi$
$379$	12.1445	−	10.9350i	0.623823	−	0.561692i	0.919251	+	0.393673i	$0.128796\pi$
$380$	−3.19003	+	3.45615i	−0.163645	+	0.177297i
$381$	8.04125	−	8.93071i	0.411966	−	0.457534i
$382$	−3.23783	+	1.24289i	−0.165662	+	0.0635917i
$383$	−7.12108	+	10.9655i	−0.363870	+	0.560311i	−0.972429	−	0.233198i	$-0.925081\pi$
$383$	−7.12108	+	10.9655i	−0.363870	+	0.560311i	0.608559	+	0.793508i	$0.291748\pi$
$384$	0.104528	+	0.994522i	0.00533420	+	0.0507515i
$385$	−0.265804	−	0.105814i	−0.0135466	−	0.00539277i
$386$	−22.4783	−	4.77791i	−1.14411	−	0.243189i
$387$	0.0499848	+	0.315592i	0.00254087	+	0.0160424i
$388$	−2.20193	−	13.9024i	−0.111786	−	0.705789i
$389$	−7.70060	−	1.63681i	−0.390436	−	0.0829898i	0.00851078	−	0.999964i	$-0.497291\pi$
$389$	−7.70060	−	1.63681i	−0.390436	−	0.0829898i	−0.398947	+	0.916974i	$0.630624\pi$
$390$	1.23480	+	0.491559i	0.0625264	+	0.0248911i
$391$	1.84985	+	17.6001i	0.0935509	+	0.890077i
$392$	3.81195	−	5.86989i	0.192533	−	0.296474i
$393$	−12.0017	+	4.60703i	−0.605406	+	0.232394i
$394$	12.1035	−	13.4423i	0.609766	−	0.677213i
$395$	−24.6351	+	26.6903i	−1.23953	+	1.34293i
$396$	3.06716	−	2.76169i	0.154131	−	0.138780i
$397$	−7.47413	−	27.8938i	−0.375116	−	1.39995i	−0.853176	−	0.521624i	$-0.825327\pi$
$397$	−7.47413	−	27.8938i	−0.375116	−	1.39995i	0.478060	−	0.878327i	$-0.341340\pi$
$398$	−6.27132	−	1.68040i	−0.314353	−	0.0842307i
$399$	0.0201493	−	0.0620131i	0.00100873	−	0.00310454i
$400$	0.645186	−	4.95820i	0.0322593	−	0.247910i
$401$	1.60392	+	2.20761i	0.0800961	+	0.110243i	0.847185	−	0.531298i	$-0.178296\pi$
$401$	1.60392	+	2.20761i	0.0800961	+	0.110243i	−0.767089	+	0.641541i	$0.778296\pi$
$402$	−2.24080	−	2.24080i	−0.111761	−	0.111761i
$403$	−3.27642	+	0.465272i	−0.163210	+	0.0231768i
$404$			7.43604i			0.369957i
$405$	−2.03137	−	0.934627i	−0.100940	−	0.0464420i
$406$	−0.0683397	−	0.153493i	−0.00339164	−	0.00761775i
$407$	6.77657	+	13.2998i	0.335902	+	0.659245i
$408$	1.05926	−	3.95320i	0.0524410	−	0.195712i
$409$	18.0152	−	31.2033i	0.890795	−	1.54290i	0.0518704	−	0.998654i	$-0.483482\pi$
$409$	18.0152	−	31.2033i	0.890795	−	1.54290i	0.838924	−	0.544248i	$-0.183185\pi$
$410$	−4.31829	−	8.74007i	−0.213265	−	0.431641i
$411$	−3.52765	−	10.8570i	−0.174006	−	0.535536i
$412$	0.0157293	+	0.300133i	0.000774928	+	0.0147865i
$413$	0.0754972	+	0.196677i	0.00371497	+	0.00967783i
$414$	4.22962	−	0.899033i	0.207874	−	0.0441851i
$415$	2.57296	−	15.0414i	0.126301	−	0.738352i
$416$	0.591110	+	0.0621281i	0.0289815	+	0.00304608i
$417$	18.5425	−	12.0416i	0.908030	−	0.589682i
$418$	8.57439	−	1.35805i	0.419387	−	0.0664244i
$419$	−3.68565	+	5.07286i	−0.180056	+	0.247825i	−0.889499	−	0.456937i	$-0.848946\pi$
$419$	−3.68565	+	5.07286i	−0.180056	+	0.247825i	0.709443	+	0.704763i	$0.248946\pi$
$420$	0.0206052	+	0.0661840i	0.00100543	+	0.00322945i
$421$	2.97418	−	28.2975i	0.144953	−	1.37913i	−0.644163	−	0.764889i	$-0.722794\pi$
$421$	2.97418	−	28.2975i	0.144953	−	1.37913i	0.789115	−	0.614245i	$-0.210539\pi$
$422$	2.89664	+	2.34565i	0.141006	+	0.114185i
$423$	−3.17389	−	2.06115i	−0.154320	−	0.100217i
$424$	−1.12406	−	0.500465i	−0.0545893	−	0.0243047i
$425$	−9.73720	+	17.9981i	−0.472324	+	0.873036i
$426$	−11.4158	+	3.70923i	−0.553100	+	0.179713i
$427$	−0.0150990	+	0.288106i	−0.000730692	+	0.0139424i
$428$	2.05511	−	0.550664i	0.0993373	−	0.0266173i
$429$	−1.22656	−	2.12446i	−0.0592187	−	0.102570i
$430$	−0.139914	−	0.700647i	−0.00674727	−	0.0337882i
$431$	−8.40083	+	3.74029i	−0.404654	+	0.180163i	−0.598963	−	0.800777i	$-0.704420\pi$
$431$	−8.40083	+	3.74029i	−0.404654	+	0.180163i	0.194309	+	0.980940i	$0.437754\pi$
$432$	−0.987688	−	0.156434i	−0.0475202	−	0.00752646i
$433$	−23.5582	+	23.5582i	−1.13213	+	1.13213i	−0.142312	+	0.989822i	$0.545454\pi$
$433$	−23.5582	+	23.5582i	−1.13213	+	1.13213i	−0.989822	+	0.142312i	$0.954546\pi$
$434$	−0.126400	−	0.117531i	−0.00606738	−	0.00564165i
$435$	−11.6670	−	3.28098i	−0.559391	−	0.157311i
$436$	−11.7061	+	8.50501i	−0.560622	+	0.407316i
$437$	8.49119	+	3.25946i	0.406189	+	0.155921i
$438$	7.32438	−	3.73196i	0.349972	−	0.178320i
$439$	−14.8809	+	8.59152i	−0.710229	+	0.410051i	−0.811146	−	0.584844i	$-0.801156\pi$
$439$	−14.8809	+	8.59152i	−0.710229	+	0.410051i	0.100917	+	0.994895i	$0.467822\pi$
$440$	−6.60582	+	6.44478i	−0.314920	+	0.307243i
$441$	4.68327	+	5.20130i	0.223013	+	0.247681i
$442$	−2.16740	−	1.10435i	−0.103093	−	0.0525284i
$443$	−12.6280	+	0.661803i	−0.599972	+	0.0314432i	−0.349905	−	0.936785i	$-0.613786\pi$
$443$	−12.6280	+	0.661803i	−0.599972	+	0.0314432i	−0.250067	+	0.968228i	$0.580453\pi$
$444$	1.47100	−	3.30392i	0.0698106	−	0.156797i
$445$	3.41927	+	3.89303i	0.162089	+	0.184547i
$446$	−0.760117	+	0.0798916i	−0.0359926	+	0.00378297i
$447$	−11.1972	+	9.06734i	−0.529611	+	0.428870i
$448$	0.0168836	+	0.0259985i	0.000797676	+	0.00122831i
$449$	−1.76036	−	1.27898i	−0.0830765	−	0.0603586i	0.545472	−	0.838129i	$-0.316351\pi$
$449$	−1.76036	−	1.27898i	−0.0830765	−	0.0603586i	−0.628548	+	0.777771i	$0.716351\pi$
$450$	4.62227	+	1.90648i	0.217896	+	0.0898722i
$451$	−3.74113	+	17.6006i	−0.176163	+	0.828781i
$452$	11.2129	+	13.8467i	0.527408	+	0.651295i
$453$	−11.9254	+	14.7266i	−0.560302	+	0.691915i
$454$	−3.59958	−	16.9347i	−0.168936	−	0.794783i
$455$	0.0410242	−	0.00380066i	0.00192324	−	0.000178178i
$456$	−1.56312	−	1.40744i	−0.0732000	−	0.0659096i
$457$	−13.4515	+	26.4000i	−0.629232	+	1.23494i	0.327742	+	0.944767i	$0.393712\pi$
$457$	−13.4515	+	26.4000i	−0.629232	+	1.23494i	−0.956975	+	0.290171i	$0.906288\pi$
$458$	−2.86759	−	0.150284i	−0.133994	−	0.00702230i
$459$	3.54434	+	2.04633i	0.165436	+	0.0955143i
$460$	−9.36971	+	2.38709i	−0.436865	+	0.111299i
$461$	−14.6245	−	4.75178i	−0.681130	−	0.221313i	−0.0520402	−	0.998645i	$-0.516572\pi$
$461$	−14.6245	−	4.75178i	−0.681130	−	0.221313i	−0.629090	+	0.777332i	$0.716572\pi$
$462$	0.0458511	−	0.119446i	0.00213318	−	0.00555714i
$463$	0.331745	−	2.09455i	0.0154175	−	0.0973421i	−0.978780	−	0.204915i	$-0.934308\pi$
$463$	0.331745	−	2.09455i	0.0154175	−	0.0973421i	0.994197	+	0.107573i	$0.0343081\pi$
$464$	−5.42004			−0.251619
$465$	−12.3469	+	1.59818i	−0.572574	+	0.0741138i
$466$	−6.83355			−0.316558
$467$	−2.71714	+	17.1553i	−0.125734	+	0.793854i	0.841554	+	0.540173i	$0.181641\pi$
$467$	−2.71714	+	17.1553i	−0.125734	+	0.793854i	−0.967288	+	0.253681i	$0.918359\pi$
$468$	−0.213002	+	0.554888i	−0.00984601	+	0.0256497i
$469$	−0.0934288	−	0.0303569i	−0.00431414	−	0.00140175i
$470$	7.27576	+	4.32123i	0.335606	+	0.199323i
$471$	17.8772	+	10.3214i	0.823740	+	0.475586i
$472$	6.78655	+	0.355668i	0.312376	+	0.0163709i
$473$	−0.598709	+	1.17503i	−0.0275287	+	0.0540280i
$474$	−12.0713	−	10.8690i	−0.554452	−	0.499231i
$475$	5.96988	+	8.65834i	0.273917	+	0.397272i
$476$	−0.0263779	−	0.124098i	−0.00120903	−	0.00568804i
$477$	0.774341	−	0.956232i	0.0354546	−	0.0437828i
$478$	9.26810	+	11.4452i	0.423913	+	0.523489i
$479$	−5.16188	+	24.2847i	−0.235852	+	1.10960i	0.687662	+	0.726031i	$0.258637\pi$
$479$	−5.16188	+	24.2847i	−0.235852	+	1.10960i	−0.923514	+	0.383566i	$0.874696\pi$
$480$	2.22077	+	0.261154i	0.101364	+	0.0119200i
$481$	−1.73905	−	1.26349i	−0.0792937	−	0.0576103i
$482$	−10.7846	−	16.6068i	−0.491225	−	0.756421i
$483$	0.104173	−	0.0843579i	0.00474005	−	0.00383842i
$484$	6.00134	−	0.630766i	0.272788	−	0.0286712i
$485$	−31.4084	−	2.03493i	−1.42618	−	0.0924015i
$486$	0.406737	−	0.913545i	0.0184499	−	0.0414393i
$487$	15.4679	−	0.810636i	0.700916	−	0.0367334i	0.301450	−	0.953482i	$-0.402529\pi$
$487$	15.4679	−	0.810636i	0.700916	−	0.0367334i	0.399465	+	0.916748i	$0.369196\pi$
$488$	8.29224	+	4.22511i	0.375372	+	0.191262i
$489$	2.78872	+	3.09719i	0.126110	+	0.140060i
$490$	−10.9291	−	11.2022i	−0.493725	−	0.506062i
$491$	−8.66595	+	5.00329i	−0.391089	+	0.225795i	−0.682632	−	0.730763i	$-0.739165\pi$
$491$	−8.66595	+	5.00329i	−0.391089	+	0.225795i	0.291543	+	0.956558i	$0.405831\pi$
$492$	3.88455	−	1.97928i	0.175129	−	0.0892328i
$493$	20.7090	+	7.94944i	0.932686	+	0.358025i
$494$	−1.01142	+	0.734840i	−0.0455059	+	0.0330620i
$495$	−4.51547	−	8.04876i	−0.202955	−	0.361765i
$496$	−5.12202	+	2.18286i	−0.229986	+	0.0980133i
$497$	−0.263114	+	0.263114i	−0.0118023	+	0.0118023i
$498$	6.74040	+	1.06757i	0.302044	+	0.0478391i
$499$	−39.8458	+	17.7405i	−1.78374	+	0.794174i	−0.803801	+	0.594898i	$0.797192\pi$
$499$	−39.8458	+	17.7405i	−1.78374	+	0.794174i	−0.979943	+	0.199276i	$0.936141\pi$
$500$	−10.4980	−	3.84607i	−0.469484	−	0.172001i
$501$	1.76000	+	3.04841i	0.0786309	+	0.136193i
$502$	6.76855	−	1.81363i	0.302095	−	0.0809462i
$503$	2.33585	−	44.5707i	0.104151	−	1.98731i	−0.0474773	−	0.998872i	$-0.515118\pi$
$503$	2.33585	−	44.5707i	0.104151	−	1.98731i	0.151628	−	0.988438i	$-0.451548\pi$
$504$	−0.0294824	+	0.00957942i	−0.00131325	+	0.000426701i
$505$	16.2202	+	3.65747i	0.721791	+	0.162755i
$506$	16.3039	+	7.25895i	0.724795	+	0.322699i
$507$	−10.6064	−	6.88790i	−0.471049	−	0.305902i
$508$	−9.33932	−	7.56283i	−0.414365	−	0.335546i
$509$	−3.52588	+	33.5465i	−0.156282	+	1.48692i	0.582419	+	0.812889i	$0.302106\pi$
$509$	−3.52588	+	33.5465i	−0.156282	+	1.48692i	−0.738701	+	0.674033i	$0.764560\pi$
$510$	−8.10211	−	4.25496i	−0.358768	−	0.188413i
$511$	0.149784	−	0.206160i	0.00662606	−	0.00911999i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	1.76405	−	1.14559i	0.0778848	−	0.0505790i
$514$	−10.7912	−	1.13420i	−0.475981	−	0.0500276i
$515$	0.662418	+	0.113312i	0.0291896	+	0.00499313i
$516$	0.312543	−	0.0664331i	0.0137589	−	0.00292455i
$517$	−5.59749	−	14.5820i	−0.246177	−	0.641314i
$518$	−0.00586755	−	0.111960i	−0.000257805	−	0.00491922i
$519$	3.75758	+	11.5646i	0.164939	+	0.507631i
$520$	0.426262	−	1.25883i	0.0186928	−	0.0552034i
$521$	11.3189	−	19.6048i	0.495888	−	0.858904i	−0.504101	−	0.863645i	$-0.668176\pi$
$521$	11.3189	−	19.6048i	0.495888	−	0.858904i	0.999989	+	0.00474136i	$0.00150923\pi$
$522$	1.40281	−	5.23536i	0.0613993	−	0.229145i
$523$	12.4738	+	24.4812i	0.545441	+	1.07049i	0.985045	+	0.172296i	$0.0551186\pi$
$523$	12.4738	+	24.4812i	0.545441	+	1.07049i	−0.439605	+	0.898191i	$0.644881\pi$
$524$	5.22883	+	11.7442i	0.228423	+	0.513046i
$525$	0.154502	−	0.0123931i	0.00674302	−	0.000540878i
$526$		−	11.3823i		−	0.496293i
$527$	22.7719	−	0.827971i	0.991958	−	0.0360670i
$528$	−2.91842	−	2.91842i	−0.127008	−	0.127008i
$529$	−2.52869	−	3.48044i	−0.109943	−	0.151323i
$530$	−1.64454	+	2.20576i	−0.0714344	+	0.0958122i
$531$	−2.10004	+	6.46325i	−0.0911338	+	0.280481i
$532$	−0.0629826	−	0.0168761i	−0.00273064	−	0.000731674i
$533$	−0.670672	−	2.50298i	−0.0290500	−	0.108416i
$534$	−1.72202	+	1.55051i	−0.0745189	+	0.0670971i
$535$	−0.190347	−	4.75365i	−0.00822940	−	0.205518i
$536$	−2.12045	+	2.35500i	−0.0915896	+	0.101721i
$537$	4.29031	−	1.64690i	0.185141	−	0.0710689i
$538$	1.37758	−	2.12129i	0.0593918	−	0.0914553i
$539$	3.01951	+	28.7287i	0.130059	+	1.23743i
$540$	−0.827032	+	2.07750i	−0.0355898	+	0.0894015i
$541$	−6.23271	−	1.32480i	−0.267965	−	0.0569578i	0.0719694	−	0.997407i	$-0.477072\pi$
$541$	−6.23271	−	1.32480i	−0.267965	−	0.0569578i	−0.339935	+	0.940449i	$0.610405\pi$
$542$	−2.66585	−	16.8315i	−0.114508	−	0.722975i
$543$	0.274344	+	1.73214i	0.0117732	+	0.0743332i
$544$	−4.00322	−	0.850910i	−0.171637	−	0.0364825i
$545$	12.7942	+	29.7179i	0.548045	+	1.27297i
$546$	0.00192595	+	0.0183242i	8.24231e−5	+	0.000784204i
$547$	−7.67212	+	11.8140i	−0.328036	+	0.505131i	−0.963755	−	0.266789i	$-0.914037\pi$
$547$	−7.67212	+	11.8140i	−0.328036	+	0.505131i	0.635719	+	0.771921i	$0.280704\pi$
$548$	−10.6575	+	4.09103i	−0.455266	+	0.174760i
$549$	−6.22733	+	6.91615i	−0.265776	+	0.295174i
$550$	10.8089	+	17.5792i	0.460892	+	0.749579i
$551$	8.47220	−	7.62840i	0.360928	−	0.324981i
$552$	−1.11916	−	4.17677i	−0.0476347	−	0.177775i
$553$	−0.486385	−	0.130327i	−0.0206832	−	0.00554205i
$554$	−2.42412	+	7.46068i	−0.102991	+	0.316974i
$555$	−6.48333	−	4.83376i	−0.275202	−	0.205181i
$556$	−12.9956	−	17.8869i	−0.551135	−	0.758573i
$557$	0.137590	+	0.137590i	0.00582989	+	0.00582989i	0.710016	−	0.704186i	$-0.248688\pi$
$557$	0.137590	+	0.137590i	0.00582989	+	0.00582989i	−0.704186	+	0.710016i	$0.748688\pi$
$558$	−0.782804	−	5.51246i	−0.0331387	−	0.233361i
$559$		−	0.189915i		−	0.00803255i
$560$	0.0650149	−	0.0240407i	0.00274738	−	0.00101591i
$561$	6.87039	+	15.4311i	0.290068	+	0.651504i
$562$	−3.96940	−	7.79038i	−0.167439	−	0.328617i
$563$	−6.04825	+	22.5724i	−0.254904	+	0.951313i	0.713241	+	0.700919i	$0.247227\pi$
$563$	−6.04825	+	22.5724i	−0.254904	+	0.951313i	−0.968144	+	0.250394i	$0.919440\pi$
$564$	−1.89222	+	3.27741i	−0.0796767	+	0.138004i
$565$	35.7190	−	17.6480i	1.50271	−	0.742457i
$566$	5.66516	+	17.4356i	0.238125	+	0.732872i
$567$	−0.00162240	−	0.0309572i	−6.81343e−5	−	0.00130008i
$568$	4.30161	+	11.2061i	0.180492	+	0.470197i
$569$	21.2768	−	4.52253i	0.891971	−	0.189594i	0.260943	−	0.965354i	$-0.415967\pi$
$569$	21.2768	−	4.52253i	0.891971	−	0.189594i	0.631028	+	0.775760i	$0.282633\pi$
$570$	−3.83889	+	2.71739i	−0.160793	+	0.113819i
$571$	14.2536	+	1.49811i	0.596493	+	0.0626940i	0.397964	−	0.917401i	$-0.369717\pi$
$571$	14.2536	+	1.49811i	0.596493	+	0.0626940i	0.198529	+	0.980095i	$0.436383\pi$
$572$	−2.05735	+	1.33606i	−0.0860222	+	0.0558635i
$573$	−3.42549	+	0.542544i	−0.143102	+	0.0226651i
$574$	0.0794394	−	0.109339i	0.00331574	−	0.00456372i
$575$	0.598417	+	21.6123i	0.0249557	+	0.901294i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−18.1318	−	14.6829i	−0.754838	−	0.611255i	0.172705	−	0.984974i	$-0.444749\pi$
$577$	−18.1318	−	14.6829i	−0.754838	−	0.611255i	−0.927542	+	0.373718i	$0.878083\pi$
$578$	−0.209842	−	0.136273i	−0.00872827	−	0.00566821i
$579$	−20.9937	−	9.34699i	−0.872468	−	0.388448i
$580$	−2.66588	+	11.8227i	−0.110695	+	0.490913i
$581$	0.201200	−	0.0653740i	0.00834720	−	0.00271217i
$582$	0.736666	−	14.0564i	0.0305358	−	0.582658i
$583$	4.90532	−	1.31438i	0.203158	−	0.0544360i
$584$	−4.11017	−	7.11903i	−0.170080	−	0.294587i
$585$	1.10561	+	0.737546i	0.0457115	+	0.0304938i
$586$	21.1007	−	9.39465i	0.871663	−	0.388090i
$587$	−9.27006	−	1.46823i	−0.382616	−	0.0606005i	−0.0378362	−	0.999284i	$-0.512047\pi$
$587$	−9.27006	−	1.46823i	−0.382616	−	0.0606005i	−0.344780	+	0.938683i	$0.612047\pi$
$588$	4.94907	−	4.94907i	0.204096	−	0.204096i
$589$	4.93411	−	10.6210i	0.203306	−	0.437632i
$590$	4.11383	−	14.6286i	0.169364	−	0.602249i
$591$	14.6338	−	10.6321i	0.601955	−	0.437346i
$592$	−3.37638	−	1.29607i	−0.138768	−	0.0532682i
$593$	−6.06338	+	3.08944i	−0.248993	+	0.126868i	−0.574033	−	0.818832i	$-0.694622\pi$
$593$	−6.06338	+	3.08944i	−0.248993	+	0.126868i	0.325040	+	0.945700i	$0.394622\pi$
$594$	3.57432	−	2.06364i	0.146656	−	0.0846721i
$595$	−0.283670	−	0.00350041i	−0.0116293	−	0.000143503i
$596$	9.64093	+	10.7073i	0.394908	+	0.438590i
$597$	−5.78491	−	2.94756i	−0.236760	−	0.120635i
$598$	−2.56658	+	0.134509i	−0.104955	+	0.00550048i
$599$	0.660601	−	1.48373i	0.0269914	−	0.0606237i	−0.899547	−	0.436825i	$-0.856103\pi$
$599$	0.660601	−	1.48373i	0.0269914	−	0.0606237i	0.926538	+	0.376201i	$0.122770\pi$
$600$	1.66195	−	4.71571i	0.0678490	−	0.192518i
$601$	11.1847	−	1.17556i	0.456234	−	0.0479521i	0.126375	−	0.991982i	$-0.459666\pi$
$601$	11.1847	−	1.17556i	0.456234	−	0.0479521i	0.329859	+	0.944030i	$0.392999\pi$
$602$	0.00769777	−	0.00623353i	0.000313738	−	0.000254060i
$603$	−1.72594	−	2.65772i	−0.0702858	−	0.108231i
$604$	15.3305	+	11.1383i	0.623790	+	0.453210i
$605$	1.57591	−	13.4010i	0.0640697	−	0.544827i
$606$	−1.54604	+	7.27354i	−0.0628035	+	0.295467i
$607$	−17.4269	−	21.5205i	−0.707337	−	0.873489i	0.289146	−	0.957285i	$-0.406629\pi$
$607$	−17.4269	−	21.5205i	−0.707337	−	0.873489i	−0.996483	+	0.0837965i	$0.973295\pi$
$608$	−1.32371	+	1.63464i	−0.0536834	+	0.0662935i
$609$	−0.0349332	−	0.164348i	−0.00141556	−	0.00665971i
$610$	13.2948	−	16.0097i	0.538292	−	0.648215i
$611$	1.67158	+	1.50510i	0.0676250	+	0.0608898i
$612$	1.85802	−	3.64658i	0.0751062	−	0.147404i
$613$	−38.4613	−	2.01567i	−1.55344	−	0.0814123i	−0.743824	−	0.668375i	$-0.766990\pi$
$613$	−38.4613	−	2.01567i	−1.55344	−	0.0814123i	−0.809614	+	0.586963i	$0.800323\pi$
$614$	11.5642	+	6.67657i	0.466691	+	0.269444i
$615$	−2.40676	−	9.44690i	−0.0970500	−	0.380936i
$616$	−0.121682	−	0.0395369i	−0.00490271	−	0.00159299i
$617$	0.440435	−	1.14737i	0.0177312	−	0.0461914i	−0.924429	−	0.381354i	$-0.875458\pi$
$617$	0.440435	−	1.14737i	0.0177312	−	0.0461914i	0.942160	+	0.335163i	$0.108791\pi$
$618$	−0.0470156	+	0.296845i	−0.00189125	+	0.0119409i
$619$	−26.0338			−1.04639			−0.523193	−	0.852214i	$-0.675259\pi$
$619$	−26.0338			−1.04639			−0.523193	+	0.852214i	$0.675259\pi$
$620$	2.24218	+	12.2463i	0.0900479	+	0.491825i
$621$	4.32411			0.173521
$622$	1.58855	−	10.0297i	0.0636951	−	0.402155i
$623$	−0.0257424	+	0.0670613i	−0.00103135	+	0.00268676i
$624$	0.565275	+	0.183669i	0.0226291	+	0.00735265i
$625$	−13.5529	+	21.0076i	−0.542118	+	0.840303i
$626$	−3.03589	−	1.75277i	−0.121339	−	0.0700549i
$627$	8.66938	+	0.454343i	0.346222	+	0.0181447i
$628$	9.37166	−	18.3929i	0.373970	−	0.733958i
$629$	10.9996	+	9.90411i	0.438584	+	0.394903i
$630$	0.00639448	+	0.0690218i	0.000254762	+	0.00274989i
$631$	−5.14050	−	24.1841i	−0.204640	−	0.962755i	−0.953818	−	0.300386i	$-0.902884\pi$
$631$	−5.14050	−	24.1841i	−0.204640	−	0.962755i	0.749178	−	0.662369i	$-0.230449\pi$
$632$	−10.2224	+	12.6236i	−0.406624	+	0.502139i
$633$	2.34565	+	2.89664i	0.0932313	+	0.115131i
$634$	−0.619630	+	2.91513i	−0.0246086	+	0.115775i
$635$	−21.0904	+	16.6520i	−0.836948	+	0.660816i
$636$	−0.995447	−	0.723235i	−0.0394720	−	0.0286781i
$637$	−2.26569	−	3.48886i	−0.0897700	−	0.138234i
$638$	17.3848	−	14.0779i	0.688269	−	0.557349i
$639$	−11.9376	+	1.25469i	−0.472243	+	0.0496348i
$640$	0.144570	−	2.23139i	0.00571465	−	0.0882034i
$641$	−5.81862	+	13.0688i	−0.229822	+	0.516188i	−0.991240	−	0.132073i	$-0.957837\pi$
$641$	−5.81862	+	13.0688i	−0.229822	+	0.516188i	0.761418	+	0.648261i	$0.224503\pi$
$642$	2.12469	−	0.111350i	0.0838547	−	0.00439464i
$643$	18.5335	+	9.44329i	0.730890	+	0.372407i	0.779493	−	0.626411i	$-0.215477\pi$
$643$	18.5335	+	9.44329i	0.730890	+	0.372407i	−0.0486028	+	0.998818i	$0.515477\pi$
$644$	−0.0896943	−	0.0996156i	−0.00353445	−	0.00392540i
$645$	0.00881582	−	0.714426i	0.000347122	−	0.0281305i
$646$	7.45513	−	4.30422i	0.293318	−	0.169347i
$647$	−26.1577	+	13.3280i	−1.02836	+	0.523978i	−0.884950	−	0.465685i	$-0.845808\pi$
$647$	−26.1577	+	13.3280i	−1.02836	+	0.523978i	−0.143414	+	0.989663i	$0.545808\pi$
$648$	−0.933580	−	0.358368i	−0.0366745	−	0.0140780i
$649$	−22.6916	+	16.4864i	−0.890724	+	0.647149i
$650$	−2.53623	−	1.54897i	−0.0994791	−	0.0607556i
$651$	−0.0992016	−	0.141242i	−0.00388802	−	0.00553572i
$652$	2.94700	−	2.94700i	0.115413	−	0.115413i
$653$	−10.3474	−	1.63887i	−0.404926	−	0.0641340i	−0.0493505	−	0.998782i	$-0.515715\pi$
$653$	−10.3474	−	1.63887i	−0.404926	−	0.0641340i	−0.355576	+	0.934648i	$0.615715\pi$
$654$	−13.2186	+	5.88531i	−0.516889	+	0.230134i
$655$	28.1894	−	5.62922i	1.10145	−	0.219952i
$656$	−2.17987	−	3.77564i	−0.0851096	−	0.147414i
$657$	7.94024	−	2.12758i	0.309778	−	0.0830049i
$658$	−0.00613985	+	0.117155i	−0.000239356	+	0.00456719i
$659$	−18.3567	+	5.96445i	−0.715075	+	0.232342i	−0.643886	−	0.765121i	$-0.722679\pi$
$659$	−18.3567	+	5.96445i	−0.715075	+	0.232342i	−0.0711881	+	0.997463i	$0.522679\pi$
$660$	−7.80141	+	4.93052i	−0.303669	+	0.191920i
$661$	−6.36459	−	2.83370i	−0.247554	−	0.110218i	0.279209	−	0.960230i	$-0.409928\pi$
$661$	−6.36459	−	2.83370i	−0.247554	−	0.110218i	−0.526763	+	0.850012i	$0.676594\pi$
$662$	−4.87465	−	3.16563i	−0.189459	−	0.123036i
$663$	−1.89043	−	1.53084i	−0.0734183	−	0.0594530i
$664$	0.713346	−	6.78703i	0.0276832	−	0.263388i
$665$	−0.0677904	+	0.129083i	−0.00262880	+	0.00500564i
$666$	2.12578	−	2.92589i	0.0823723	−	0.113376i
$667$	23.1483	−	3.66633i	0.896306	−	0.141961i
$668$	2.95212	−	1.91713i	0.114221	−	0.0741759i
$669$	−0.760117	−	0.0798916i	−0.0293878	−	0.00308879i
$670$	4.09401	+	5.78367i	0.158165	+	0.223443i
$671$	−37.5715	+	7.98607i	−1.45043	+	0.308299i
$672$	0.0111093	+	0.0289407i	0.000428550	+	0.00111641i
$673$	−0.812705	−	15.5073i	−0.0313275	−	0.597764i	−0.968518	−	0.248945i	$-0.919916\pi$
$673$	−0.812705	−	15.5073i	−0.0313275	−	0.597764i	0.937190	−	0.348819i	$-0.113417\pi$
$674$	8.63876	+	26.5874i	0.332752	+	1.02411i
$675$	4.12488	+	2.82584i	0.158767	+	0.108767i
$676$	−6.32336	+	10.9524i	−0.243206	+	0.421246i
$677$	9.34888	−	34.8905i	0.359307	−	1.34095i	−0.515671	−	0.856787i	$-0.672457\pi$
$677$	9.34888	−	34.8905i	0.359307	−	1.34095i	0.874977	−	0.484164i	$-0.160876\pi$
$678$	8.08893	+	15.8754i	0.310653	+	0.609692i
$679$	−0.177476	−	0.398619i	−0.00681092	−	0.0152976i
$680$	−3.82510	+	8.31370i	−0.146686	+	0.318816i
$681$		−	17.3130i		−	0.663436i
$682$	10.7591	−	20.3053i	0.411989	−	0.777532i
$683$	−16.5971	−	16.5971i	−0.635069	−	0.635069i	0.314266	−	0.949335i	$-0.398242\pi$
$683$	−16.5971	−	16.5971i	−0.635069	−	0.635069i	−0.949335	+	0.314266i	$0.898242\pi$
$684$	−1.23634	−	1.70168i	−0.0472727	−	0.0650653i
$685$	3.68181	+	25.2594i	0.140675	+	0.965113i
$686$	0.134103	−	0.412726i	0.00512006	−	0.0157579i
$687$	−2.77368	−	0.743205i	−0.105822	−	0.0283550i
$688$	−0.0826993	−	0.308638i	−0.00315288	−	0.0117667i
$689$	−0.543485	+	0.489356i	−0.0207051	+	0.0186430i
$690$	−9.66127	+	0.386858i	−0.367798	+	0.0147274i
$691$	17.1216	−	19.0154i	0.651336	−	0.723382i	−0.323519	−	0.946222i	$-0.604866\pi$
$691$	17.1216	−	19.0154i	0.651336	−	0.723382i	0.974855	+	0.222840i	$0.0715328\pi$
$692$	11.3521	−	4.35768i	0.431543	−	0.165654i
$693$	0.0696834	−	0.107303i	0.00264705	−	0.00407610i
$694$	−2.19253	−	20.8605i	−0.0832271	−	0.791853i
$695$	−45.4087	+	19.5495i	−1.72245	+	0.741555i
$696$	−5.30160	−	1.12689i	−0.200957	−	0.0427147i
$697$	2.79124	+	17.6232i	0.105726	+	0.667526i
$698$	−1.89809	−	11.9841i	−0.0718438	−	0.453604i
$699$	−6.68422	−	1.42077i	−0.252820	−	0.0537386i
$700$	−0.0204621	−	0.153642i	−0.000773394	−	0.00580711i
$701$	−1.44343	−	13.7333i	−0.0545176	−	0.518700i	−0.987369	−	0.158438i	$-0.949354\pi$
$701$	−1.44343	−	13.7333i	−0.0545176	−	0.518700i	0.932851	−	0.360262i	$-0.117313\pi$
$702$	−0.323715	+	0.498477i	−0.0122178	+	0.0188138i
$703$	7.10185	−	2.72615i	0.267851	−	0.102819i
$704$	−2.76169	+	3.06716i	−0.104085	+	0.115598i
$705$	6.21833	+	5.73951i	0.234196	+	0.216163i
$706$	0.689226	−	0.620582i	0.0259394	−	0.0233559i
$707$	0.0596616	+	0.222660i	0.00224380	+	0.00837399i
$708$	6.56430	+	1.75890i	0.246701	+	0.0661035i
$709$	4.72103	−	14.5298i	0.177302	−	0.545680i	−0.822429	−	0.568868i	$-0.807382\pi$
$709$	4.72103	−	14.5298i	0.177302	−	0.545680i	0.999731	+	0.0231881i	$0.00738166\pi$
$710$	26.5596	−	3.87132i	0.996764	−	0.145288i
$711$	−9.54769	−	13.1413i	−0.358067	−	0.492836i
$712$	1.63851	+	1.63851i	0.0614057	+	0.0614057i
$713$	20.3989	−	12.7875i	0.763946	−	0.478894i
$714$		−	0.126871i		−	0.00474802i
$715$	1.90243	+	5.14486i	0.0711468	+	0.192407i
$716$	−1.86918	−	4.19824i	−0.0698545	−	0.156896i
$717$	6.68599	+	13.1220i	0.249693	+	0.490050i
$718$	−7.28341	+	27.1821i	−0.271814	+	1.01443i
$719$	21.5745	−	37.3682i	0.804594	−	1.39360i	−0.111972	−	0.993711i	$-0.535717\pi$
$719$	21.5745	−	37.3682i	0.804594	−	1.39360i	0.916565	−	0.399886i	$-0.130950\pi$
$720$	2.11794	+	0.717170i	0.0789309	+	0.0267274i
$721$	0.00287905	+	0.00886080i	0.000107221	+	0.000329994i
$722$	0.762836	+	14.5558i	0.0283898	+	0.541710i
$723$	−7.09618	−	18.4862i	−0.263910	−	0.687509i
$724$	1.71541	−	0.364621i	0.0637526	−	0.0135510i
$725$	24.4777	+	11.6302i	0.909080	+	0.431935i
$726$	6.00134	+	0.630766i	0.222731	+	0.0234099i
$727$	33.6977	−	21.8836i	1.24978	−	0.811616i	0.261639	−	0.965166i	$-0.415737\pi$
$727$	33.6977	−	21.8836i	1.24978	−	0.811616i	0.988141	+	0.153550i	$0.0490705\pi$
$728$	0.0181983	−	0.00288233i	0.000674474	−	0.000106826i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−17.5504	+	5.46398i	−0.649568	+	0.202231i
$731$	−0.136693	+	1.30054i	−0.00505576	+	0.0481023i
$732$	7.23259	+	5.85683i	0.267324	+	0.216475i
$733$	32.2615	+	20.9509i	1.19161	+	0.773839i	0.979112	−	0.203324i	$-0.0651743\pi$
$733$	32.2615	+	20.9509i	1.19161	+	0.773839i	0.212495	+	0.977162i	$0.431841\pi$
$734$	−0.300619	−	0.133844i	−0.0110960	−	0.00494027i
$735$	−8.36118	−	13.2296i	−0.308407	−	0.487983i
$736$	−4.11247	+	1.33622i	−0.151588	+	0.0492539i
$737$	0.684512	−	13.0613i	0.0252143	−	0.481118i
$738$	4.21118	−	1.12838i	0.155016	−	0.0415363i
$739$	−14.8583	−	25.7353i	−0.546571	−	0.946689i	−0.998506	−	0.0546380i	$-0.982600\pi$
$739$	−14.8583	−	25.7353i	−0.546571	−	0.946689i	0.451935	−	0.892051i	$-0.350734\pi$
$740$	−4.48782	+	6.72743i	−0.164976	+	0.247305i
$741$	−1.14210	+	0.508496i	−0.0419561	+	0.0186801i
$742$	−0.0376736	−	0.00596692i	−0.00138304	−	0.000219052i
$743$	16.9825	−	16.9825i	0.623029	−	0.623029i	−0.323276	−	0.946305i	$-0.604784\pi$
$743$	16.9825	−	16.9825i	0.623029	−	0.623029i	0.946305	+	0.323276i	$0.104784\pi$
$744$	−5.46394	+	1.07023i	−0.200318	+	0.0392366i
$745$	28.0979	−	15.7633i	1.02943	−	0.577523i
$746$	−2.26003	+	1.64201i	−0.0827456	+	0.0601182i
$747$	6.37114	+	2.44565i	0.233108	+	0.0894817i
$748$	15.0504	−	7.66858i	0.550298	−	0.280391i
$749$	0.0571187	−	0.0329775i	0.00208707	−	0.00120497i
$750$	−9.46894	−	5.94468i	−0.345757	−	0.217069i
$751$	−15.3046	−	16.9975i	−0.558475	−	0.620249i	0.396105	−	0.918205i	$-0.370362\pi$
$751$	−15.3046	−	16.9975i	−0.558475	−	0.620249i	−0.954579	+	0.297956i	$0.903695\pi$
$752$	3.37195	+	1.71810i	0.122962	+	0.0626525i
$753$	6.99772	−	0.366735i	0.255011	−	0.0133646i
$754$	−1.31030	+	2.94298i	−0.0477182	+	0.107177i
$755$	31.8364	−	27.9621i	1.15864	−	1.01764i
$756$	−0.0308298	+	0.00324035i	−0.00112127	+	0.000117850i
$757$	−10.2177	+	8.27411i	−0.371368	+	0.300727i	−0.796777	−	0.604274i	$-0.793463\pi$
$757$	−10.2177	+	8.27411i	−0.371368	+	0.300727i	0.425409	+	0.905001i	$0.360130\pi$
$758$	−8.90053	−	13.7056i	−0.323282	−	0.497811i
$759$	14.4384	+	10.4901i	0.524079	+	0.380766i
$760$	2.91457	+	3.69141i	0.105723	+	0.133902i
$761$	−0.213988	+	1.00673i	−0.00775705	+	0.0364941i	−0.981856	−	0.189628i	$-0.939272\pi$
$761$	−0.213988	+	1.00673i	−0.00775705	+	0.0364941i	0.974099	+	0.226123i	$0.0726050\pi$
$762$	−7.56283	−	9.33932i	−0.273972	−	0.338328i
$763$	−0.282283	+	0.348590i	−0.0102193	+	0.0126198i
$764$	0.721077	+	3.39240i	0.0260877	+	0.122733i
$765$	−7.04041	−	5.84651i	−0.254546	−	0.211381i
$766$	9.71651	+	8.74879i	0.351072	+	0.316107i
$767$	1.83377	−	3.59898i	0.0662136	−	0.129952i
$768$	0.998630	+	0.0523360i	0.0360349	+	0.00188851i
$769$	−23.0723	−	13.3208i	−0.832010	−	0.480361i	0.0225303	−	0.999746i	$-0.492828\pi$
$769$	−23.0723	−	13.3208i	−0.832010	−	0.480361i	−0.854540	+	0.519385i	$0.826161\pi$
$770$	−0.146092	+	0.245979i	−0.00526479	+	0.00886446i
$771$	−10.3196	−	3.35304i	−0.371651	−	0.120757i
$772$	−8.23546	+	21.4541i	−0.296401	+	0.772150i
$773$	−5.79357	+	36.5792i	−0.208380	+	1.31566i	0.632551	+	0.774519i	$0.282008\pi$
$773$	−5.79357	+	36.5792i	−0.208380	+	1.31566i	−0.840931	+	0.541142i	$0.817992\pi$
$774$	0.319526			0.0114851
$775$	27.8158	+	1.13258i	0.999172	+	0.0406834i
$776$	−14.0757			−0.505289
$777$	0.0175384	−	0.110733i	0.000629186	−	0.00397252i
$778$	−2.82130	+	7.34974i	−0.101149	+	0.263501i
$779$	8.72141	+	2.83376i	0.312477	+	0.101530i
$780$	0.678672	−	1.14270i	0.0243004	−	0.0409151i
$781$	−42.9038	−	24.7705i	−1.53522	−	0.886359i
$782$	17.6728	+	0.926194i	0.631979	+	0.0331206i
$783$	2.46065	−	4.82929i	0.0879364	−	0.172585i
$784$	−5.20130	−	4.68327i	−0.185761	−	0.167260i
$785$	−35.5110	−	29.4891i	−1.26744	−	1.05251i
$786$	2.67282	+	12.5747i	0.0953365	+	0.448523i
$787$	22.6900	−	28.0198i	0.808811	−	0.998799i	−0.191041	−	0.981582i	$-0.561186\pi$
$787$	22.6900	−	28.0198i	0.808811	−	0.998799i	0.999852	−	0.0172164i	$-0.00548042\pi$
$788$	−11.3834	−	14.0573i	−0.405517	−	0.500771i
$789$	2.36652	−	11.1336i	0.0842503	−	0.396366i
$790$	22.5079	+	28.5071i	0.800795	+	1.01424i
$791$	0.446847	+	0.324653i	0.0158880	+	0.0115433i
$792$	−2.24787	−	3.46142i	−0.0798748	−	0.122996i
$793$	4.29880	−	3.48110i	0.152655	−	0.123618i
$794$	−28.7196	+	3.01855i	−1.01922	+	0.107124i
$795$	−2.06721	+	1.81564i	−0.0733164	+	0.0643942i
$796$	−2.64076	+	5.93124i	−0.0935992	+	0.210227i
$797$	2.15610	−	0.112997i	0.0763731	−	0.00400255i	−0.0141111	−	0.999900i	$-0.504492\pi$
$797$	2.15610	−	0.112997i	0.0763731	−	0.00400255i	0.0904842	+	0.995898i	$0.471159\pi$
$798$	−0.0580976	−	0.0296022i	−0.00205663	−	0.00104791i
$799$	−10.3637	−	11.5101i	−0.366643	−	0.407198i
$800$	−4.79623	−	1.41288i	−0.169572	−	0.0499527i
$801$	−2.00675	+	1.15860i	−0.0709052	+	0.0409371i
$802$	2.43134	−	1.23883i	0.0858536	−	0.0437446i
$803$	31.6742	+	12.1586i	1.11776	+	0.429067i
$804$	−2.56375	+	1.86267i	−0.0904164	+	0.0656913i
$805$	−0.261408	+	0.146654i	−0.00921343	+	0.00516886i
$806$	−0.0530010	+	3.30886i	−0.00186688	+	0.116550i
$807$	1.78852	−	1.78852i	0.0629589	−	0.0629589i
$808$	7.34449	+	1.16325i	0.258378	+	0.0409231i
$809$	33.1393	−	14.7546i	1.16512	−	0.518744i	0.269252	−	0.963070i	$-0.413223\pi$
$809$	33.1393	−	14.7546i	1.16512	−	0.518744i	0.895865	+	0.444326i	$0.146557\pi$
$810$	−1.24090	+	1.86015i	−0.0436007	+	0.0653592i
$811$	14.4915	+	25.1001i	0.508867	+	0.881384i	0.999947	+	0.0102692i	$0.00326885\pi$
$811$	14.4915	+	25.1001i	0.508867	+	0.881384i	−0.491080	+	0.871114i	$0.663398\pi$
$812$	−0.162294	+	0.0434866i	−0.00569541	+	0.00152608i
$813$	0.891874	−	17.0180i	0.0312794	−	0.596846i
$814$	14.1961	−	4.61260i	0.497574	−	0.161671i
$815$	−4.97879	−	7.87779i	−0.174399	−	0.275947i
$816$	−3.73882	−	1.66463i	−0.130885	−	0.0582737i
$817$	0.563660	+	0.366045i	0.0197200	+	0.0128063i
$818$	−28.0009	−	22.6747i	−0.979028	−	0.792801i
$819$	−0.00192595	+	0.0183242i	−6.72982e−5	+	0.000640299i
$820$	−9.30800	+	2.89788i	−0.325049	+	0.101198i
$821$	−5.90888	+	8.13287i	−0.206221	+	0.283839i	−0.899582	−	0.436751i	$-0.856129\pi$
$821$	−5.90888	+	8.13287i	−0.206221	+	0.283839i	0.693361	+	0.720590i	$0.256129\pi$
$822$	−11.2752	+	1.78581i	−0.393267	+	0.0622874i
$823$	27.2552	−	17.6997i	0.950055	−	0.616973i	0.0261761	−	0.999657i	$-0.491667\pi$
$823$	27.2552	−	17.6997i	0.950055	−	0.616973i	0.923879	+	0.382684i	$0.125000\pi$
$824$	0.298899	+	0.0314155i	0.0104126	+	0.00109441i
$825$	6.91777	+	19.4423i	0.240846	+	0.676895i
$826$	0.206066	−	0.0438006i	0.00716995	−	0.00152402i
$827$	6.94409	+	18.0900i	0.241470	+	0.629050i	0.999738	−	0.0228927i	$-0.00728760\pi$
$827$	6.94409	+	18.0900i	0.241470	+	0.629050i	−0.758268	+	0.651943i	$0.773954\pi$
$828$	−0.226307	−	4.31819i	−0.00786469	−	0.150067i
$829$	−0.162650	−	0.500585i	−0.00564907	−	0.0173860i	0.948192	−	0.317697i	$-0.102910\pi$
$829$	−0.162650	−	0.500585i	−0.00564907	−	0.0173860i	−0.953841	+	0.300311i	$0.902910\pi$
$830$	−14.4537	−	4.89427i	−0.501695	−	0.169883i
$831$	−3.92231	+	6.79364i	−0.136063	+	0.235669i
$832$	0.153833	−	0.574113i	0.00533321	−	0.0199038i
$833$	13.0044	+	25.5225i	0.450575	+	0.884304i
$834$	−8.99271	−	20.1979i	−0.311392	−	0.699398i
$835$	−2.72981	−	7.38241i	−0.0944691	−	0.255479i
$836$		−	8.68127i		−	0.300248i
$837$	0.380407	−	5.55475i	0.0131488	−	0.192000i
$838$	4.43384	+	4.43384i	0.153165	+	0.153165i
$839$	25.4645	+	35.0489i	0.879132	+	1.21002i	0.976661	+	0.214788i	$0.0689062\pi$
$839$	25.4645	+	35.0489i	0.879132	+	1.21002i	−0.0975289	+	0.995233i	$0.531094\pi$
$840$	0.0685925	−	0.00999804i	0.00236667	−	0.000344965i
$841$	0.116452	−	0.358401i	0.00401557	−	0.0123587i
$842$	−27.4838	−	7.36426i	−0.947154	−	0.253789i
$843$	−2.26295	−	8.44543i	−0.0779400	−	0.290876i
$844$	2.76991	−	2.49404i	0.0953442	−	0.0858483i
$845$	20.7803	+	19.1802i	0.714863	+	0.659818i
$846$	−2.53228	+	2.81238i	−0.0870616	+	0.0966917i
$847$	0.174639	−	0.0670378i	0.00600068	−	0.00230345i
$848$	−0.670146	+	1.03193i	−0.0230129	+	0.0354368i
$849$	1.91630	+	18.2324i	0.0657674	+	0.625735i
$850$	16.2533	+	12.4328i	0.557483	+	0.426443i
$851$	15.2968	+	3.25144i	0.524368	+	0.111458i
$852$	1.87773	+	11.8556i	0.0643301	+	0.406164i
$853$	−3.78918	−	23.9240i	−0.129739	−	0.819141i	−0.963636	−	0.267220i	$-0.913895\pi$
$853$	−3.78918	−	23.9240i	−0.129739	−	0.819141i	0.833896	−	0.551921i	$-0.186105\pi$
$854$	0.282197	+	0.0599828i	0.00965658	+	0.00205257i
$855$	−4.31998	+	1.85985i	−0.147740	+	0.0636056i
$856$	−0.222395	−	2.11595i	−0.00760130	−	0.0723216i
$857$	15.8520	−	24.4100i	0.541495	−	0.833829i	−0.456955	−	0.889490i	$-0.651060\pi$
$857$	15.8520	−	24.4100i	0.541495	−	0.833829i	0.998450	+	0.0556607i	$0.0177265\pi$
$858$	−2.29018	+	0.879116i	−0.0781853	+	0.0300125i
$859$	14.1667	−	15.7337i	0.483361	−	0.536826i	−0.451298	−	0.892373i	$-0.649039\pi$
$859$	14.1667	−	15.7337i	0.483361	−	0.536826i	0.934658	+	0.355547i	$0.115705\pi$
$860$	−0.713909	+	0.0285865i	−0.0243441	+	0.000974790i
$861$	0.100436	−	0.0904332i	0.00342286	−	0.00308196i
$862$	2.38006	+	8.88251i	0.0810652	+	0.302540i
$863$	44.3136	+	11.8738i	1.50845	+	0.404189i	0.915921	−	0.401358i	$-0.131462\pi$
$863$	44.3136	+	11.8738i	1.50845	+	0.404189i	0.592532	+	0.805547i	$0.298128\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−3.92178	−	26.9058i	−0.133345	−	0.914824i
$866$	19.5828	+	26.9535i	0.665452	+	0.915916i
$867$	−0.176924	−	0.176924i	−0.00600864	−	0.00600864i
$868$	−0.135857	+	0.106458i	−0.00461128	+	0.00361341i
$869$		−	67.0414i		−	2.27422i
$870$	−5.06571	+	11.0101i	−0.171744	+	0.373278i
$871$	0.766099	+	1.72069i	0.0259583	+	0.0583032i
$872$	6.56905	+	12.8925i	0.222456	+	0.436595i
$873$	3.64306	−	13.5961i	0.123299	−	0.460158i
$874$	4.54765	−	7.87676i	0.153827	−	0.266435i
$875$	−0.345203	−	0.0309357i	−0.0116700	−	0.00104582i
$876$	−2.54023	−	7.81801i	−0.0858263	−	0.264146i
$877$	2.36218	+	45.0731i	0.0797651	+	1.52201i	0.686515	+	0.727116i	$0.259140\pi$
$877$	2.36218	+	45.0731i	0.0797651	+	1.52201i	−0.606750	+	0.794893i	$0.707527\pi$
$878$	6.15785	+	16.0417i	0.207817	+	0.541383i
$879$	22.5929	−	4.80227i	0.762039	−	0.161976i
$880$	5.33205	+	7.53267i	0.179743	+	0.253926i
$881$	−52.0723	−	5.47301i	−1.75436	−	0.184391i	−0.827923	−	0.560842i	$-0.810477\pi$
$881$	−52.0723	−	5.47301i	−1.75436	−	0.184391i	−0.926436	+	0.376452i	$0.877144\pi$
$882$	5.86989	−	3.81195i	0.197649	−	0.128355i
$883$	−36.0595	+	5.71127i	−1.21350	+	0.192199i	−0.730186	−	0.683248i	$-0.760567\pi$
$883$	−36.0595	+	5.71127i	−1.21350	+	0.192199i	−0.483313	+	0.875448i	$0.660567\pi$
$884$	−1.42981	+	1.96796i	−0.0480896	+	0.0661896i
$885$	7.06538	−	13.4536i	0.237500	−	0.452237i
$886$	−1.32179	+	12.5760i	−0.0444065	+	0.422500i
$887$	−22.8413	−	18.4965i	−0.766936	−	0.621053i	0.163905	−	0.986476i	$-0.447591\pi$
$887$	−22.8413	−	18.4965i	−0.766936	−	0.621053i	−0.930841	+	0.365423i	$0.880924\pi$
$888$	−3.03313	−	1.96974i	−0.101785	−	0.0661001i
$889$	−0.340330	−	0.151525i	−0.0114143	−	0.00508197i
$890$	4.37999	−	2.76817i	0.146818	−	0.0927893i
$891$	3.92527	−	1.27540i	0.131502	−	0.0427274i
$892$	−0.0400006	+	0.763257i	−0.00133932	+	0.0255557i
$893$	−7.68891	+	2.06024i	−0.257299	+	0.0689432i
$894$	7.20407	+	12.4778i	0.240940	+	0.417321i
$895$	−10.0770	+	2.01231i	−0.336837	+	0.0672640i
$896$	0.0283196	−	0.0126087i	0.000946091	−	0.000421227i
$897$	−2.53846	−	0.402053i	−0.0847568	−	0.0134242i
$898$	−1.53861	+	1.53861i	−0.0513441	+	0.0513441i
$899$	−2.67333	−	30.0589i	−0.0891607	−	1.00252i
$900$	2.60609	−	4.26712i	0.0868696	−	0.142237i
$901$	4.07402	−	2.95995i	0.135725	−	0.0986101i
$902$	16.7987	+	6.44841i	0.559335	+	0.214709i
$903$	0.00882558	−	0.00449686i	0.000293697	−	0.000149646i
$904$	15.4303	−	8.90870i	0.513205	−	0.296299i
$905$	0.0483860	−	3.92116i	0.00160840	−	0.130344i
$906$	12.6797	+	14.0823i	0.421256	+	0.467852i
$907$	11.7763	+	6.00031i	0.391025	+	0.199237i	0.638438	−	0.769673i	$-0.279581\pi$
$907$	11.7763	+	6.00031i	0.391025	+	0.199237i	−0.247414	+	0.968910i	$0.579581\pi$
$908$	−17.2893	+	0.906092i	−0.573765	+	0.0300697i
$909$	−3.02451	+	6.79316i	−0.100317	+	0.225315i
$910$	0.00266373	−	0.0411137i	8.83018e−5	−	0.00136290i
$911$	−42.2636	+	4.44209i	−1.40026	+	0.147173i	−0.774366	−	0.632738i	$-0.781931\pi$
$911$	−42.2636	+	4.44209i	−1.40026	+	0.147173i	−0.625891	+	0.779911i	$0.715264\pi$
$912$	−1.63464	+	1.32371i	−0.0541284	+	0.0438323i
$913$	15.3404	+	23.6222i	0.507694	+	0.781781i
$914$	23.9707	+	17.4157i	0.792879	+	0.576060i
$915$	16.3329	−	12.8957i	0.539950	−	0.426320i
$916$	−0.597023	+	2.80877i	−0.0197262	+	0.0928045i
$917$	0.250796	+	0.309707i	0.00828201	+	0.0102274i
$918$	2.57559	−	3.18059i	0.0850071	−	0.104975i
$919$	−4.69449	−	22.0858i	−0.154857	−	0.728544i	−0.985216	−	0.171316i	$-0.945198\pi$
$919$	−4.69449	−	22.0858i	−0.154857	−	0.728544i	0.830359	−	0.557228i	$-0.188135\pi$
$920$	0.891959	+	9.62778i	0.0294070	+	0.317418i
$921$	9.92332	+	8.93499i	0.326984	+	0.294418i
$922$	−6.98106	+	13.7011i	−0.229909	+	0.451221i
$923$	7.12459	+	0.373384i	0.234509	+	0.0122901i
$924$	−0.110803	−	0.0639721i	−0.00364515	−	0.00210453i
$925$	12.4672	+	13.0982i	0.409918	+	0.430667i
$926$	−2.01687	−	0.655320i	−0.0662784	−	0.0215352i
$927$	−0.107706	+	0.280583i	−0.00353752	+	0.00921556i
$928$	−0.847881	+	5.35331i	−0.0278331	+	0.175731i
$929$	−4.60824			−0.151191			−0.0755957	−	0.997139i	$-0.524086\pi$
$929$	−4.60824			−0.151191			−0.0755957	+	0.997139i	$0.524086\pi$
$930$	−0.352977	+	12.4449i	−0.0115746	+	0.408084i
$931$	14.7217			0.482485
$932$	−1.06900	+	6.74942i	−0.0350163	+	0.221085i
$933$	3.63913	−	9.48027i	0.119140	−	0.310370i
$934$	16.5191	+	5.36737i	0.540520	+	0.175626i
$935$	−9.32483	−	36.6014i	−0.304954	−	1.19699i
$936$	0.514736	+	0.297183i	0.0168247	+	0.00971373i
$937$	−28.9412	−	1.51674i	−0.945468	−	0.0495499i	−0.426633	−	0.904425i	$-0.640301\pi$
$937$	−28.9412	−	1.51674i	−0.945468	−	0.0495499i	−0.518834	+	0.854875i	$0.673634\pi$
$938$	−0.0445986	+	0.0875297i	−0.00145620	+	0.00285795i
$939$	−2.60513	−	2.34567i	−0.0850152	−	0.0765480i
$940$	5.40620	−	6.51019i	0.176331	−	0.212339i
$941$	1.85309	+	8.71808i	0.0604089	+	0.284201i	0.997975	−	0.0636053i	$-0.0202599\pi$
$941$	1.85309	+	8.71808i	0.0604089	+	0.284201i	−0.937566	+	0.347807i	$0.886927\pi$
$942$	12.9910	−	16.0425i	0.423269	−	0.522694i
$943$	11.8639	+	14.6507i	0.386343	+	0.477094i
$944$	1.41294	−	6.64736i	0.0459873	−	0.216353i
$945$	−0.00809569	+	0.0688430i	−0.000263353	+	0.00223946i
$946$	1.06691	+	0.775153i	0.0346881	+	0.0252024i
$947$	8.44065	+	12.9975i	0.274284	+	0.422361i	0.948789	−	0.315909i	$-0.102310\pi$
$947$	8.44065	+	12.9975i	0.274284	+	0.422361i	−0.674505	+	0.738270i	$0.735643\pi$
$948$	−12.6236	+	10.2224i	−0.409995	+	0.332007i
$949$	−4.85913	+	0.510715i	−0.157734	+	0.0165785i
$950$	9.48564	−	4.54192i	0.307755	−	0.147359i
$951$	−1.21218	+	2.72260i	−0.0393076	+	0.0882863i
$952$	−0.126697	+	0.00663990i	−0.00410627	+	0.000215201i
$953$	30.2013	+	15.3883i	0.978317	+	0.498477i	0.868615	−	0.495487i	$-0.165010\pi$
$953$	30.2013	+	15.3883i	0.978317	+	0.498477i	0.109702	+	0.993965i	$0.465010\pi$
$954$	−0.823325	−	0.914395i	−0.0266561	−	0.0296046i
$955$	7.75452	+	0.0956885i	0.250930	+	0.00309641i
$956$	12.7541	−	7.36358i	0.412497	−	0.238155i
$957$	19.9318	−	10.1558i	0.644304	−	0.328289i
$958$	23.1782	+	8.89729i	0.748855	+	0.287458i
$959$	−0.286298	+	0.208008i	−0.00924504	+	0.00671691i
$960$	0.605343	−	2.15257i	0.0195374	−	0.0694739i
$961$	−14.6322	−	27.3294i	−0.472007	−	0.881595i
$962$	−1.51998	+	1.51998i	−0.0490062	+	0.0490062i
$963$	2.10141	+	0.332830i	0.0677169	+	0.0107253i
$964$	−18.0895	+	8.05395i	−0.582622	+	0.259400i
$965$	42.7472	+	28.5164i	1.37608	+	0.917974i
$966$	−0.0670230	−	0.116087i	−0.00215643	−	0.00373505i
$967$	−1.46849	+	0.393481i	−0.0472235	+	0.0126535i	−0.282353	−	0.959310i	$-0.591115\pi$
$967$	−1.46849	+	0.393481i	−0.0472235	+	0.0126535i	0.235130	+	0.971964i	$0.424448\pi$
$968$	0.315816	−	6.02612i	0.0101507	−	0.193687i
$969$	8.18712	−	2.66016i	0.263008	−	0.0854565i
$970$	−6.92324	+	30.7034i	−0.222292	+	0.985826i
$971$	28.1405	+	12.5290i	0.903073	+	0.402074i	0.805117	−	0.593117i	$-0.202103\pi$
$971$	28.1405	+	12.5290i	0.903073	+	0.402074i	0.0979565	+	0.995191i	$0.468769\pi$
$972$	−0.838671	−	0.544639i	−0.0269004	−	0.0174693i
$973$	−0.532643	−	0.431326i	−0.0170758	−	0.0138277i
$974$	1.61905	−	15.4042i	0.0518777	−	0.493583i
$975$	−2.15876	−	2.04243i	−0.0691356	−	0.0654102i
$976$	5.47028	−	7.52920i	0.175099	−	0.241004i
$977$	31.2899	−	4.95583i	1.00105	−	0.158551i	0.365666	−	0.930746i	$-0.380841\pi$
$977$	31.2899	−	4.95583i	1.00105	−	0.158551i	0.635385	+	0.772195i	$0.280841\pi$
$978$	3.49531	−	2.26988i	0.111768	−	0.0725828i
$979$	−9.51133	−	0.999681i	−0.303983	−	0.0319500i
$980$	−12.7739	+	9.04211i	−0.408048	+	0.288839i
$981$	−14.1534	+	3.00840i	−0.451883	+	0.0960507i
$982$	3.58604	+	9.34194i	0.114435	+	0.298113i
$983$	−2.24276	−	42.7944i	−0.0715328	−	1.36493i	−0.764810	−	0.644256i	$-0.777167\pi$
$983$	−2.24276	−	42.7944i	−0.0715328	−	1.36493i	0.693277	−	0.720671i	$-0.256166\pi$
$984$	−1.34723	−	4.14636i	−0.0429482	−	0.132181i
$985$	−36.2623	+	17.9164i	−1.15541	+	0.570865i
$986$	11.0912	−	19.2105i	0.353215	−	0.611786i
$987$	−0.0303636	+	0.113319i	−0.000966485	+	0.00360697i
$988$	0.567572	+	1.11392i	0.0180569	+	0.0354386i
$989$	0.561973	+	1.26221i	0.0178697	+	0.0401360i
$990$	−8.65604	+	3.20077i	−0.275107	+	0.101727i
$991$			38.9192i			1.23631i	0.786057	+	0.618154i	$0.212119\pi$
$991$			38.9192i			1.23631i	−0.786057	+	0.618154i	$0.787881\pi$
$992$	1.35472	+	5.40044i	0.0430126	+	0.171464i
$993$	−4.10995	−	4.10995i	−0.130425	−	0.130425i
$994$	0.218714	+	0.301035i	0.00693720	+	0.00954824i
$995$	11.6390	+	8.67761i	0.368980	+	0.275099i
$996$	2.10886	−	6.49041i	0.0668218	−	0.205656i
$997$	−41.1409	−	11.0237i	−1.30295	−	0.349123i	−0.460382	−	0.887721i	$-0.652288\pi$
$997$	−41.1409	−	11.0237i	−1.30295	−	0.349123i	−0.842563	+	0.538597i	$0.818954\pi$
$998$	11.2888	+	42.1305i	0.357342	+	1.33362i
$999$	2.68765	−	2.41997i	0.0850336	−	0.0765646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bt.b.13.10	yes	256
5.2	odd	4		930.2.bt.a.757.16	yes	256
31.12	odd	30		930.2.bt.a.43.16	✓	256
155.12	even	60	inner	930.2.bt.b.787.10	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bt.a.43.16	✓	256	31.12	odd	30
930.2.bt.a.757.16	yes	256	5.2	odd	4
930.2.bt.b.13.10	yes	256	1.1	even	1	trivial
930.2.bt.b.787.10	yes	256	155.12	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bt (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(0.358368 - 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.14184 + 1.92255i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.0309572 - 0.00162240i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +(1.72026 + 1.42854i) q^{10} +(-0.858109 - 4.03708i) q^{11} +(-0.629320 + 0.777146i) q^{12} +(0.374047 + 0.461909i) q^{13} +(-0.00644519 + 0.0303222i) q^{14} +(1.38565 + 1.75498i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.22902 - 3.43239i) q^{17} +(-0.777146 + 0.629320i) q^{18} +(-2.09187 + 0.219864i) q^{19} +(1.68006 - 1.47560i) q^{20} +(-0.0126087 + 0.0283196i) q^{21} +(-4.12162 + 0.216005i) q^{22} +(-3.85281 - 1.96311i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-2.39239 - 4.39050i) q^{25} +(0.514736 - 0.297183i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(0.0289407 + 0.0111093i) q^{28} +(-4.38491 + 3.18582i) q^{29} +(1.95014 - 1.09405i) q^{30} +(-2.86075 + 4.77662i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.07646 - 0.645648i) q^{33} +(-3.73882 + 1.66463i) q^{34} +(0.0384674 - 0.0576642i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.49336 + 0.936044i) q^{37} +(-0.110083 + 2.10051i) q^{38} +(0.565275 - 0.183669i) q^{39} +(-1.19462 - 1.89021i) q^{40} +(-3.98282 - 1.77326i) q^{41} +(0.0259985 + 0.0168836i) q^{42} +(-0.248318 - 0.201084i) q^{43} +(-0.431418 + 4.10466i) q^{44} +(2.13499 - 0.664690i) q^{45} +(-2.54165 + 3.49828i) q^{46} +(3.73784 - 0.592016i) q^{47} +(0.838671 - 0.544639i) q^{48} +(-6.96070 - 0.731599i) q^{49} +(-4.71070 + 1.67611i) q^{50} +(-4.00322 + 0.850910i) q^{51} +(-0.213002 - 0.554888i) q^{52} +(0.0643963 + 1.22875i) q^{53} +(0.309017 + 0.951057i) q^{54} +(8.74132 + 2.95996i) q^{55} +(0.0154998 - 0.0268465i) q^{56} +(-0.544398 + 2.03172i) q^{57} +(2.46065 + 4.82929i) q^{58} +(-2.76413 - 6.20833i) q^{59} +(-0.775516 - 2.09728i) q^{60} -9.30660i q^{61} +(4.27029 + 3.57276i) q^{62} +(0.0219201 + 0.0219201i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.31515 + 0.191695i) q^{65} +(-1.27540 + 3.92527i) q^{66} +(3.06099 + 0.820189i) q^{67} +(1.05926 + 3.95320i) q^{68} +(-3.21344 + 2.89340i) q^{69} +(-0.0509366 - 0.0470144i) q^{70} +(8.03180 - 8.92021i) q^{71} +(0.933580 - 0.358368i) q^{72} +(-4.47712 + 6.89416i) q^{73} +(0.378037 + 3.59678i) q^{74} +(-4.95624 + 0.660075i) q^{75} +(2.05743 + 0.437320i) q^{76} +(0.0200149 + 0.126369i) q^{77} +(-0.0929793 - 0.587048i) q^{78} +(15.8885 + 3.37722i) q^{79} +(-2.05382 + 0.884217i) q^{80} +(0.104528 + 0.994522i) q^{81} +(-2.37448 + 3.65638i) q^{82} +(-6.37114 + 2.44565i) q^{83} +(0.0207428 - 0.0230372i) q^{84} +(9.14412 - 0.366150i) q^{85} +(-0.237454 + 0.213804i) q^{86} +(1.40281 + 5.23536i) q^{87} +(3.98664 + 1.06822i) q^{88} +(0.716054 - 2.20379i) q^{89} +(-0.322521 - 2.21269i) q^{90} +(-0.0108300 - 0.0149063i) q^{91} +(3.05761 + 3.05761i) q^{92} +(3.43416 + 4.38253i) q^{93} -3.78443i q^{94} +(1.96589 - 4.27277i) q^{95} +(-0.406737 - 0.913545i) q^{96} +(6.39024 + 12.5416i) q^{97} +(-1.81148 + 6.76055i) q^{98} +(-2.06364 + 3.57432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 16 q^{7} + 4 q^{10} + 24 q^{14} + 8 q^{15} + 64 q^{16} - 36 q^{17} + 40 q^{19} - 12 q^{20} - 16 q^{21} + 44 q^{22} + 32 q^{24} - 28 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35}+ \cdots - 4 q^{99}+O(q^{100}) \) 256 * q + 16 * q^7 + 4 * q^10 + 24 * q^14 + 8 * q^15 + 64 * q^16 - 36 * q^17 + 40 * q^19 - 12 * q^20 - 16 * q^21 + 44 * q^22 + 32 * q^24 - 28 * q^25 - 8 * q^28 + 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 - 76 * q^37 + 28 * q^38 + 48 * q^41 - 4 * q^42 + 120 * q^43 - 4 * q^44 + 12 * q^45 - 20 * q^46 + 72 * q^47 + 40 * q^49 + 48 * q^50 - 16 * q^53 - 64 * q^54 + 36 * q^55 - 4 * q^57 - 68 * q^58 + 24 * q^59 - 20 * q^62 + 4 * q^63 + 156 * q^65 + 12 * q^66 + 44 * q^67 + 4 * q^68 - 12 * q^69 + 104 * q^70 - 48 * q^71 - 84 * q^73 - 68 * q^74 - 48 * q^75 + 48 * q^76 - 124 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 112 * q^83 + 132 * q^85 + 24 * q^86 + 32 * q^87 + 52 * q^88 + 224 * q^89 + 40 * q^91 + 64 * q^93 - 204 * q^95 + 8 * q^97 - 32 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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