LMFDB - Embedded newform 720.2.cf.a.11.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.25
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995082 - 1.00489i) q^{2} +(1.72693 + 0.133152i) q^{3} +(-0.0196241 + 1.99990i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.58463 - 1.86787i) q^{6} +(-0.393114 + 0.680893i) q^{7} +(2.02922 - 1.97035i) q^{8} +(2.96454 + 0.459886i) q^{9} +O(q^{10})$	\(q+(-0.995082 - 1.00489i) q^{2} +(1.72693 + 0.133152i) q^{3} +(-0.0196241 + 1.99990i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.58463 - 1.86787i) q^{6} +(-0.393114 + 0.680893i) q^{7} +(2.02922 - 1.97035i) q^{8} +(2.96454 + 0.459886i) q^{9} +(0.701090 + 1.22820i) q^{10} +(-3.54899 + 0.950948i) q^{11} +(-0.300180 + 3.45107i) q^{12} +(6.60966 + 1.77105i) q^{13} +(1.07541 - 0.282507i) q^{14} +(-1.63362 - 0.575576i) q^{15} +(-3.99923 - 0.0784926i) q^{16} +2.55663i q^{17} +(-2.48782 - 3.43667i) q^{18} +(1.51313 + 1.51313i) q^{19} +(0.536569 - 1.92668i) q^{20} +(-0.769540 + 1.12351i) q^{21} +(4.48713 + 2.62008i) q^{22} +(-2.20315 + 1.27199i) q^{23} +(3.76666 - 3.13245i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.79743 - 8.40435i) q^{26} +(5.05831 + 1.18892i) q^{27} +(-1.35401 - 0.799552i) q^{28} +(2.94071 - 0.787960i) q^{29} +(1.04719 + 2.21436i) q^{30} +(4.66615 - 2.69400i) q^{31} +(3.90068 + 4.09691i) q^{32} +(-6.25546 + 1.16966i) q^{33} +(2.56914 - 2.54406i) q^{34} +(0.555947 - 0.555947i) q^{35} +(-0.977905 + 5.91977i) q^{36} +(-3.16968 - 3.16968i) q^{37} +(0.0148470 - 3.02621i) q^{38} +(11.1786 + 3.93856i) q^{39} +(-2.47004 + 1.37801i) q^{40} +(3.90371 + 6.76142i) q^{41} +(1.89476 - 0.344676i) q^{42} +(1.59211 + 5.94185i) q^{43} +(-1.83216 - 7.11629i) q^{44} +(-2.74450 - 1.21150i) q^{45} +(3.47053 + 0.948199i) q^{46} +(3.71556 - 6.43554i) q^{47} +(-6.89592 - 0.668056i) q^{48} +(3.19092 + 5.52684i) q^{49} +(-0.359319 - 1.36780i) q^{50} +(-0.340420 + 4.41511i) q^{51} +(-3.67164 + 13.1839i) q^{52} +(-3.08554 + 3.08554i) q^{53} +(-3.83869 - 6.26614i) q^{54} +3.67418 q^{55} +(0.543882 + 2.15625i) q^{56} +(2.41158 + 2.81453i) q^{57} +(-3.71806 - 2.17101i) q^{58} +(2.12786 - 7.94129i) q^{59} +(1.18315 - 3.25579i) q^{60} +(-0.236293 - 0.881857i) q^{61} +(-7.35038 - 2.00823i) q^{62} +(-1.47854 + 1.83775i) q^{63} +(0.235459 - 7.99653i) q^{64} +(-5.92606 - 3.42141i) q^{65} +(7.40008 + 5.12216i) q^{66} +(-3.71237 + 13.8548i) q^{67} +(-5.11301 - 0.0501716i) q^{68} +(-3.97404 + 1.90328i) q^{69} +(-1.11188 - 0.00545504i) q^{70} -2.01079i q^{71} +(6.92184 - 4.90797i) q^{72} -2.76008i q^{73} +(-0.0311014 + 6.33928i) q^{74} +(1.42899 + 0.978775i) q^{75} +(-3.05580 + 2.99641i) q^{76} +(0.747662 - 2.79031i) q^{77} +(-7.16575 - 15.1525i) q^{78} +(-6.86402 - 3.96294i) q^{79} +(3.84264 + 1.11089i) q^{80} +(8.57701 + 2.72670i) q^{81} +(2.91000 - 10.6510i) q^{82} +(-0.390797 - 1.45847i) q^{83} +(-2.23181 - 1.56105i) q^{84} +(0.661705 - 2.46952i) q^{85} +(4.38665 - 7.51253i) q^{86} +(5.18330 - 0.969187i) q^{87} +(-5.32797 + 8.92242i) q^{88} +15.3156 q^{89} +(1.51358 + 3.96347i) q^{90} +(-3.80425 + 3.80425i) q^{91} +(-2.50062 - 4.43105i) q^{92} +(8.41680 - 4.03103i) q^{93} +(-10.1643 + 2.67014i) q^{94} +(-1.06994 - 1.85319i) q^{95} +(6.19068 + 7.59444i) q^{96} +(1.98896 - 3.44498i) q^{97} +(2.37866 - 8.70620i) q^{98} +(-10.9584 + 1.18699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.995082	−	1.00489i	−0.703629	−	0.710567i
$2$	−0.995082	−	1.00489i	−0.703629	−	0.710567i
$3$	1.72693	+	0.133152i	0.997041	+	0.0768752i
$3$	1.72693	+	0.133152i	0.997041	+	0.0768752i
$4$	−0.0196241	+	1.99990i	−0.00981205	+	0.999952i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−1.58463	−	1.86787i	−0.646922	−	0.762556i
$7$	−0.393114	+	0.680893i	−0.148583	+	0.257353i	−0.930704	−	0.365773i	$-0.880805\pi$
$7$	−0.393114	+	0.680893i	−0.148583	+	0.257353i	0.782121	+	0.623127i	$0.214138\pi$
$8$	2.02922	−	1.97035i	0.717437	−	0.696623i
$9$	2.96454	+	0.459886i	0.988180	+	0.153295i
$10$	0.701090	+	1.22820i	0.221704	+	0.388391i
$11$	−3.54899	+	0.950948i	−1.07006	+	0.286722i	−0.750518	−	0.660850i	$-0.770196\pi$
$11$	−3.54899	+	0.950948i	−1.07006	+	0.286722i	−0.319542	+	0.947572i	$0.603529\pi$
$12$	−0.300180	+	3.45107i	−0.0866545	+	0.996238i
$13$	6.60966	+	1.77105i	1.83319	+	0.491202i	0.998250	−	0.0591393i	$-0.0188356\pi$
$13$	6.60966	+	1.77105i	1.83319	+	0.491202i	0.834940	+	0.550341i	$0.185502\pi$
$14$	1.07541	−	0.282507i	0.287414	−	0.0755031i
$15$	−1.63362	−	0.575576i	−0.421799	−	0.148613i
$16$	−3.99923	−	0.0784926i	−0.999807	−	0.0196232i
$17$			2.55663i			0.620074i	0.950725	+	0.310037i	$0.100341\pi$
$17$			2.55663i			0.620074i	−0.950725	+	0.310037i	$0.899659\pi$
$18$	−2.48782	−	3.43667i	−0.586386	−	0.810032i
$19$	1.51313	+	1.51313i	0.347135	+	0.347135i	0.859041	−	0.511906i	$-0.171061\pi$
$19$	1.51313	+	1.51313i	0.347135	+	0.347135i	−0.511906	+	0.859041i	$0.671061\pi$
$20$	0.536569	−	1.92668i	0.119980	−	0.430819i
$21$	−0.769540	+	1.12351i	−0.167927	+	0.245169i
$22$	4.48713	+	2.62008i	0.956660	+	0.558604i
$23$	−2.20315	+	1.27199i	−0.459389	+	0.265228i	−0.711787	−	0.702395i	$-0.752114\pi$
$23$	−2.20315	+	1.27199i	−0.459389	+	0.265228i	0.252398	+	0.967623i	$0.418781\pi$
$24$	3.76666	−	3.13245i	0.768867	−	0.639408i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−4.79743	−	8.40435i	−0.940854	−	1.64823i
$27$	5.05831	+	1.18892i	0.973471	+	0.228808i
$28$	−1.35401	−	0.799552i	−0.255883	−	0.151101i
$29$	2.94071	−	0.787960i	0.546075	−	0.146320i	0.0247740	−	0.999693i	$-0.492113\pi$
$29$	2.94071	−	0.787960i	0.546075	−	0.146320i	0.521301	+	0.853373i	$0.325447\pi$
$30$	1.04719	+	2.21436i	0.191190	+	0.404285i
$31$	4.66615	−	2.69400i	0.838065	−	0.483857i	−0.0185413	−	0.999828i	$-0.505902\pi$
$31$	4.66615	−	2.69400i	0.838065	−	0.483857i	0.856606	+	0.515971i	$0.172569\pi$
$32$	3.90068	+	4.09691i	0.689550	+	0.724238i
$33$	−6.25546	+	1.16966i	−1.08893	+	0.203612i
$34$	2.56914	−	2.54406i	0.440604	−	0.436302i
$35$	0.555947	−	0.555947i	0.0939722	−	0.0939722i
$36$	−0.977905	+	5.91977i	−0.162984	+	0.986629i
$37$	−3.16968	−	3.16968i	−0.521092	−	0.521092i	0.396809	−	0.917901i	$-0.370117\pi$
$37$	−3.16968	−	3.16968i	−0.521092	−	0.521092i	−0.917901	+	0.396809i	$0.870117\pi$
$38$	0.0148470	−	3.02621i	0.00240851	−	0.490917i
$39$	11.1786	+	3.93856i	1.79000	+	0.630675i
$40$	−2.47004	+	1.37801i	−0.390547	+	0.217882i
$41$	3.90371	+	6.76142i	0.609657	+	1.05596i	0.991297	+	0.131645i	$0.0420260\pi$
$41$	3.90371	+	6.76142i	0.609657	+	1.05596i	−0.381640	+	0.924311i	$0.624641\pi$
$42$	1.89476	−	0.344676i	0.292368	−	0.0531846i
$43$	1.59211	+	5.94185i	0.242795	+	0.906123i	0.974479	+	0.224479i	$0.0720681\pi$
$43$	1.59211	+	5.94185i	0.242795	+	0.906123i	−0.731684	+	0.681644i	$0.761265\pi$
$44$	−1.83216	−	7.11629i	−0.276208	−	1.07282i
$45$	−2.74450	−	1.21150i	−0.409126	−	0.180599i
$46$	3.47053	+	0.948199i	0.511702	+	0.139804i
$47$	3.71556	−	6.43554i	0.541970	−	0.938719i	−0.456821	−	0.889559i	$-0.651012\pi$
$47$	3.71556	−	6.43554i	0.541970	−	0.938719i	0.998791	−	0.0491607i	$-0.0156546\pi$
$48$	−6.89592	−	0.668056i	−0.995340	−	0.0964255i
$49$	3.19092	+	5.52684i	0.455846	+	0.789549i
$50$	−0.359319	−	1.36780i	−0.0508154	−	0.193437i
$51$	−0.340420	+	4.41511i	−0.0476683	+	0.618239i
$52$	−3.67164	+	13.1839i	−0.509165	+	1.82828i
$53$	−3.08554	+	3.08554i	−0.423832	+	0.423832i	−0.886521	−	0.462689i	$-0.846885\pi$
$53$	−3.08554	+	3.08554i	−0.423832	+	0.423832i	0.462689	+	0.886521i	$0.346885\pi$
$54$	−3.83869	−	6.26614i	−0.522379	−	0.852713i
$55$	3.67418			0.495427
$56$	0.543882	+	2.15625i	0.0726793	+	0.288141i
$57$	2.41158	+	2.81453i	0.319421	+	0.372794i
$58$	−3.71806	−	2.17101i	−0.488205	−	0.285068i
$59$	2.12786	−	7.94129i	0.277024	−	1.03387i	−0.677449	−	0.735570i	$-0.736914\pi$
$59$	2.12786	−	7.94129i	0.277024	−	1.03387i	0.954473	−	0.298298i	$-0.0964190\pi$
$60$	1.18315	−	3.25579i	0.152745	−	0.420320i
$61$	−0.236293	−	0.881857i	−0.0302542	−	0.112910i	0.949148	−	0.314832i	$-0.101948\pi$
$61$	−0.236293	−	0.881857i	−0.0302542	−	0.112910i	−0.979402	+	0.201922i	$0.935281\pi$
$62$	−7.35038	−	2.00823i	−0.933500	−	0.255046i
$63$	−1.47854	+	1.83775i	−0.186278	+	0.231534i
$64$	0.235459	−	7.99653i	0.0294324	−	0.999567i
$65$	−5.92606	−	3.42141i	−0.735037	−	0.424374i
$66$	7.40008	+	5.12216i	0.910886	+	0.630494i
$67$	−3.71237	+	13.8548i	−0.453539	+	1.69263i	0.238810	+	0.971066i	$0.423243\pi$
$67$	−3.71237	+	13.8548i	−0.453539	+	1.69263i	−0.692349	+	0.721563i	$0.743424\pi$
$68$	−5.11301	−	0.0501716i	−0.620044	−	0.00608420i
$69$	−3.97404	+	1.90328i	−0.478419	+	0.229128i
$70$	−1.11188	−	0.00545504i	−0.132895	−	0.000652003i
$71$		−	2.01079i		−	0.238637i	−0.992856	−	0.119318i	$-0.961929\pi$
$71$		−	2.01079i		−	0.238637i	0.992856	−	0.119318i	$-0.0380709\pi$
$72$	6.92184	−	4.90797i	0.815747	−	0.578409i
$73$		−	2.76008i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$73$		−	2.76008i		−	0.323042i	0.986869	−	0.161521i	$-0.0516400\pi$
$74$	−0.0311014	+	6.33928i	−0.00361547	+	0.736926i
$75$	1.42899	+	0.978775i	0.165005	+	0.113019i
$76$	−3.05580	+	2.99641i	−0.350524	+	0.343712i
$77$	0.747662	−	2.79031i	0.0852040	−	0.317985i
$78$	−7.16575	−	15.1525i	−0.811362	−	1.71568i
$79$	−6.86402	−	3.96294i	−0.772263	−	0.445866i	0.0614185	−	0.998112i	$-0.480438\pi$
$79$	−6.86402	−	3.96294i	−0.772263	−	0.445866i	−0.833681	+	0.552246i	$0.813771\pi$
$80$	3.84264	+	1.11089i	0.429621	+	0.124202i
$81$	8.57701	+	2.72670i	0.953001	+	0.302967i
$82$	2.91000	−	10.6510i	0.321356	−	1.17620i
$83$	−0.390797	−	1.45847i	−0.0428955	−	0.160088i	0.941156	−	0.337973i	$-0.109741\pi$
$83$	−0.390797	−	1.45847i	−0.0428955	−	0.160088i	−0.984051	+	0.177885i	$0.943075\pi$
$84$	−2.23181	−	1.56105i	−0.243510	−	0.170325i
$85$	0.661705	−	2.46952i	0.0717719	−	0.267857i
$86$	4.38665	−	7.51253i	0.473024	−	0.810097i
$87$	5.18330	−	0.969187i	0.555708	−	0.103908i
$88$	−5.32797	+	8.92242i	−0.567964	+	0.951133i
$89$	15.3156			1.62345			0.811723	−	0.584042i	$-0.198530\pi$
$89$	15.3156			1.62345			0.811723	+	0.584042i	$0.198530\pi$
$90$	1.51358	+	3.96347i	0.159545	+	0.417786i
$91$	−3.80425	+	3.80425i	−0.398793	+	0.398793i
$92$	−2.50062	−	4.43105i	−0.260708	−	0.461969i
$93$	8.41680	−	4.03103i	0.872781	−	0.417999i
$94$	−10.1643	+	2.67014i	−1.04837	+	0.275404i
$95$	−1.06994	−	1.85319i	−0.109774	−	0.190134i
$96$	6.19068	+	7.59444i	0.631834	+	0.775104i
$97$	1.98896	−	3.44498i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$97$	1.98896	−	3.44498i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$98$	2.37866	−	8.70620i	0.240281	−	0.879459i
$99$	−10.9584	+	1.18699i	−1.10137	+	0.119297i
$100$	−1.01695	+	1.72216i	−0.101695	+	0.172216i
$101$	−4.40298	−	16.4322i	−0.438113	−	1.63506i	−0.733505	−	0.679684i	$-0.762117\pi$
$101$	−4.40298	−	16.4322i	−0.438113	−	1.63506i	0.295391	−	0.955376i	$-0.404550\pi$
$102$	4.77546	−	4.05131i	0.472841	−	0.401139i
$103$	−7.57081	−	13.1130i	−0.745974	−	1.29207i	−0.949738	−	0.313046i	$-0.898651\pi$
$103$	−7.57081	−	13.1130i	−0.745974	−	1.29207i	0.203764	−	0.979020i	$-0.434683\pi$
$104$	16.9020	−	9.42947i	1.65738	−	0.924636i
$105$	1.03410	−	0.886053i	0.100918	−	0.0864699i
$106$	6.17101	+	0.0302759i	0.599381	+	0.00294065i
$107$	−2.73587	−	2.73587i	−0.264487	−	0.264487i	0.562387	−	0.826874i	$-0.309883\pi$
$107$	−2.73587	−	2.73587i	−0.264487	−	0.264487i	−0.826874	+	0.562387i	$0.809883\pi$
$108$	−2.47700	+	10.0928i	−0.238349	+	0.971180i
$109$	6.61766	−	6.61766i	0.633857	−	0.633857i	−0.315176	−	0.949033i	$-0.602064\pi$
$109$	6.61766	−	6.61766i	0.633857	−	0.633857i	0.949033	+	0.315176i	$0.102064\pi$
$110$	−3.65611	−	3.69216i	−0.348597	−	0.352034i
$111$	−5.05175	−	5.89585i	−0.479491	−	0.559609i
$112$	1.62560	−	2.69219i	0.153605	−	0.254388i
$113$	−13.4086	+	7.74147i	−1.26138	+	0.728256i	−0.973341	−	0.229364i	$-0.926335\pi$
$113$	−13.4086	+	7.74147i	−1.26138	+	0.728256i	−0.288036	+	0.957620i	$0.593002\pi$
$114$	0.428586	−	5.22407i	0.0401407	−	0.489279i
$115$	2.45730	−	0.658430i	0.229144	−	0.0613990i
$116$	1.51814	+	5.89659i	0.140955	+	0.547485i
$117$	18.7801	+	8.29005i	1.73622	+	0.766416i
$118$	−10.0976	+	5.76396i	−0.929555	+	0.530615i
$119$	−1.74079	−	1.00505i	−0.159578	−	0.0921325i
$120$	−4.44906	+	2.05083i	−0.406141	+	0.187214i
$121$	2.16473	−	1.24980i	0.196793	−	0.113619i
$122$	−0.651042	+	1.11497i	−0.0589426	+	0.100945i
$123$	5.84112	+	12.1963i	0.526676	+	1.09970i
$124$	5.29617	+	9.38471i	0.475610	+	0.842772i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	3.31801	−	0.342938i	0.295591	−	0.0305514i
$127$			6.83544i			0.606547i	0.952904	+	0.303274i	$0.0980796\pi$
$127$			6.83544i			0.606547i	−0.952904	+	0.303274i	$0.901920\pi$
$128$	−8.26997	+	7.72059i	−0.730969	+	0.682411i
$129$	1.95829	+	10.4731i	0.172418	+	0.922107i
$130$	2.45876	+	9.35965i	0.215647	+	0.820895i
$131$	−11.4390	−	3.06506i	−0.999426	−	0.267795i	−0.278221	−	0.960517i	$-0.589745\pi$
$131$	−11.4390	−	3.06506i	−0.999426	−	0.267795i	−0.721205	+	0.692722i	$0.756411\pi$
$132$	−2.21645	−	12.5333i	−0.192918	−	1.09088i
$133$	−1.62511	+	0.435446i	−0.140915	+	0.0377580i
$134$	17.6167	−	10.0561i	1.52185	−	0.868714i
$135$	−4.57823	−	2.45760i	−0.394032	−	0.211516i
$136$	5.03745	+	5.18796i	0.431958	+	0.444864i
$137$	−1.76316	+	3.05388i	−0.150637	+	0.260911i	−0.931462	−	0.363839i	$-0.881466\pi$
$137$	−1.76316	+	3.05388i	−0.150637	+	0.260911i	0.780825	+	0.624750i	$0.214799\pi$
$138$	5.86709	+	2.09958i	0.499440	+	0.178728i
$139$	−8.85445	−	2.37254i	−0.751024	−	0.201236i	−0.137052	−	0.990564i	$-0.543763\pi$
$139$	−8.85445	−	2.37254i	−0.751024	−	0.201236i	−0.613972	+	0.789327i	$0.710429\pi$
$140$	1.10093	+	1.12275i	0.0930456	+	0.0948897i
$141$	7.27339	−	10.6190i	0.612530	−	0.894277i
$142$	−2.02063	+	2.00090i	−0.169567	+	0.167912i
$143$	−25.1418			−2.10246
$144$	−11.8198	−	2.07189i	−0.984982	−	0.172657i
$145$	−3.04444			−0.252827
$146$	−2.77358	+	2.74650i	−0.229543	+	0.227302i
$147$	4.77458	+	9.96932i	0.393800	+	0.822255i
$148$	6.40125	−	6.27685i	0.526180	−	0.515954i
$149$	18.6774	+	5.00461i	1.53012	+	0.409993i	0.923057	−	0.384663i	$-0.125682\pi$
$149$	18.6774	+	5.00461i	1.53012	+	0.409993i	0.607059	+	0.794657i	$0.292349\pi$
$150$	−0.438392	−	2.40994i	−0.0357945	−	0.196771i
$151$	1.56334	−	2.70778i	0.127222	−	0.220356i	−0.795377	−	0.606115i	$-0.792727\pi$
$151$	1.56334	−	2.70778i	0.127222	−	0.220356i	0.922600	+	0.385759i	$0.126060\pi$
$152$	6.05185	+	0.0890794i	0.490870	+	0.00722529i
$153$	−1.17576	+	7.57924i	−0.0950545	+	0.612745i
$154$	−3.54795	+	2.02527i	−0.285902	+	0.163201i
$155$	−5.20441	+	1.39452i	−0.418028	+	0.112010i
$156$	−8.09612	+	22.2788i	−0.648208	+	1.78373i
$157$	−7.14565	−	1.91467i	−0.570285	−	0.152807i	−0.0378578	−	0.999283i	$-0.512053\pi$
$157$	−7.14565	−	1.91467i	−0.570285	−	0.152807i	−0.532427	+	0.846476i	$0.678720\pi$
$158$	2.84792	+	10.8411i	0.226569	+	0.862469i
$159$	−5.73934	+	4.91765i	−0.455160	+	0.389995i
$160$	−2.70741	−	4.96688i	−0.214040	−	0.392666i
$161$		−	2.00015i		−	0.157634i
$162$	−5.79478	−	11.3323i	−0.455281	−	0.890348i
$163$	−9.76889	−	9.76889i	−0.765158	−	0.765158i	0.212091	−	0.977250i	$-0.431973\pi$
$163$	−9.76889	−	9.76889i	−0.765158	−	0.765158i	−0.977250	+	0.212091i	$0.931973\pi$
$164$	−13.5988	+	7.67435i	−1.06189	+	0.599266i
$165$	6.34504	+	0.489224i	0.493960	+	0.0380860i
$166$	−1.07674	+	1.84401i	−0.0835709	+	0.143123i
$167$	1.11159	−	0.641775i	0.0860171	−	0.0496620i	−0.456374	−	0.889788i	$-0.650852\pi$
$167$	1.11159	−	0.641775i	0.0860171	−	0.0496620i	0.542392	+	0.840126i	$0.317519\pi$
$168$	0.652135	+	3.79610i	0.0503133	+	0.292876i
$169$	29.2926	+	16.9121i	2.25328	+	1.30093i
$170$	−3.14005	+	1.79243i	−0.240831	+	0.137473i
$171$	3.78986	+	5.18159i	0.289818	+	0.396246i
$172$	−11.9144	+	3.06747i	−0.908462	+	0.233892i
$173$	−10.4042	+	2.78780i	−0.791018	+	0.211953i	−0.631637	−	0.775265i	$-0.717616\pi$
$173$	−10.4042	+	2.78780i	−0.791018	+	0.211953i	−0.159381	+	0.987217i	$0.550950\pi$
$174$	−6.13174	−	4.24424i	−0.464846	−	0.321755i
$175$	−0.680893	+	0.393114i	−0.0514707	+	0.0297166i
$176$	14.2679	−	3.52449i	1.07548	−	0.265668i
$177$	4.73206	−	13.4307i	0.355683	−	1.00951i
$178$	−15.2402	−	15.3905i	−1.14230	−	1.15357i
$179$	−17.1437	+	17.1437i	−1.28138	+	1.28138i	−0.341500	+	0.939882i	$0.610935\pi$
$179$	−17.1437	+	17.1437i	−1.28138	+	1.28138i	−0.939882	+	0.341500i	$0.889065\pi$
$180$	2.47673	−	5.46496i	0.184605	−	0.407334i
$181$	−11.7104	−	11.7104i	−0.870423	−	0.870423i	0.122095	−	0.992518i	$-0.461039\pi$
$181$	−11.7104	−	11.7104i	−0.870423	−	0.870423i	−0.992518	+	0.122095i	$0.961039\pi$
$182$	7.60840	+	0.0373279i	0.563972	+	0.00276693i
$183$	−0.290639	−	1.55436i	−0.0214847	−	0.114902i
$184$	−1.96441	+	6.92212i	−0.144818	+	0.510305i
$185$	2.24130	+	3.88205i	0.164784	+	0.285414i
$186$	−12.4262	−	4.44678i	−0.911130	−	0.326054i
$187$	−2.43122	−	9.07345i	−0.177789	−	0.663516i
$188$	12.7975	+	7.55705i	0.933356	+	0.551155i
$189$	−2.79802	+	2.97678i	−0.203526	+	0.216529i
$190$	−0.797583	+	2.91926i	−0.0578628	+	0.211785i
$191$	3.59782	−	6.23160i	0.260329	−	0.450903i	−0.706000	−	0.708211i	$-0.749502\pi$
$191$	3.59782	−	6.23160i	0.260329	−	0.450903i	0.966329	+	0.257309i	$0.0828357\pi$
$192$	1.47137	−	13.7781i	0.106187	−	0.994346i
$193$	−10.9771	−	19.0128i	−0.790146	−	1.36857i	−0.925876	−	0.377827i	$-0.876672\pi$
$193$	−10.9771	−	19.0128i	−0.790146	−	1.36857i	0.135731	−	0.990746i	$-0.456662\pi$
$194$	−5.44101	+	1.42934i	−0.390642	+	0.102621i
$195$	−9.77829	−	6.69759i	−0.700238	−	0.479624i
$196$	−11.1158	+	6.27308i	−0.793983	+	0.448077i
$197$	−17.0380	+	17.0380i	−1.21391	+	1.21391i	−0.244173	+	0.969732i	$0.578517\pi$
$197$	−17.0380	+	17.0380i	−1.21391	+	1.21391i	−0.969732	+	0.244173i	$0.921483\pi$
$198$	12.0974	+	9.83092i	0.859722	+	0.698653i
$199$	−22.8230			−1.61788			−0.808941	−	0.587890i	$-0.799959\pi$
$199$	−22.8230			−1.61788			−0.808941	+	0.587890i	$0.799959\pi$
$200$	2.74253	−	0.691762i	0.193926	−	0.0489149i
$201$	−8.25578	+	23.4318i	−0.582318	+	1.65275i
$202$	−12.1312	+	20.7759i	−0.853552	+	1.46179i
$203$	−0.619516	+	2.31206i	−0.0434815	+	0.162275i
$204$	−8.82311	−	0.767450i	−0.617741	−	0.0537322i
$205$	−2.02071	−	7.54138i	−0.141132	−	0.526713i
$206$	−5.64363	+	20.6564i	−0.393210	+	1.43920i
$207$	−7.11630	+	2.75767i	−0.494617	+	0.191671i
$208$	−26.2945	−	7.60166i	−1.82320	−	0.527080i
$209$	−6.80897	−	3.93116i	−0.470986	−	0.271924i
$210$	−1.91941	−	0.157469i	−0.132452	−	0.0108664i
$211$	0.850303	−	3.17337i	0.0585372	−	0.218464i	−0.930461	−	0.366391i	$-0.880593\pi$
$211$	0.850303	−	3.17337i	0.0585372	−	0.218464i	0.988998	+	0.147927i	$0.0472600\pi$
$212$	−6.11023	−	6.23134i	−0.419653	−	0.427970i
$213$	0.267740	−	3.47248i	0.0183452	−	0.237930i
$214$	−0.0268448	+	5.47167i	−0.00183507	+	0.374036i
$215$		−	6.15145i		−	0.419526i
$216$	12.6070	−	7.55404i	0.857798	−	0.513987i
$217$			4.23620i			0.287572i
$218$	−13.2352	−	0.0649336i	−0.896398	−	0.00439786i
$219$	0.367509	−	4.76644i	0.0248340	−	0.322086i
$220$	−0.0721025	+	7.34801i	−0.00486115	+	0.495403i
$221$	−4.52793	+	16.8985i	−0.304581	+	1.13671i
$222$	−0.897796	+	10.9433i	−0.0602561	+	0.734468i
$223$	17.3837	+	10.0365i	1.16410	+	0.672094i	0.952283	−	0.305216i	$-0.0987286\pi$
$223$	17.3837	+	10.0365i	1.16410	+	0.672094i	0.211817	+	0.977309i	$0.432062\pi$
$224$	−4.32297	+	1.04540i	−0.288841	+	0.0698486i
$225$	2.33742	+	1.88054i	0.155828	+	0.125370i
$226$	21.1220	+	5.77084i	1.40502	+	0.383871i
$227$	−6.39086	−	23.8510i	−0.424176	−	1.58305i	−0.765715	−	0.643180i	$-0.777615\pi$
$227$	−6.39086	−	23.8510i	−0.424176	−	1.58305i	0.341539	−	0.939868i	$-0.389052\pi$
$228$	−5.67611	+	4.76769i	−0.375910	+	0.315748i
$229$	−1.84254	+	6.87647i	−0.121759	+	0.454410i	−0.999703	−	0.0243522i	$-0.992248\pi$
$229$	−1.84254	+	6.87647i	−0.121759	+	0.454410i	0.877945	+	0.478762i	$0.158914\pi$
$230$	−3.10686	−	1.81413i	−0.204860	−	0.119620i
$231$	1.66269	−	4.71911i	0.109397	−	0.310494i
$232$	4.41478	−	7.39316i	0.289845	−	0.485385i
$233$	−0.683549			−0.0447808			−0.0223904	−	0.999749i	$-0.507128\pi$
$233$	−0.683549			−0.0447808			−0.0223904	+	0.999749i	$0.507128\pi$
$234$	−10.3571	−	27.1213i	−0.677067	−	1.77298i
$235$	−5.25459	+	5.25459i	−0.342772	+	0.342772i
$236$	15.8401	+	4.41136i	1.03110	+	0.287155i
$237$	−11.3260	−	7.75767i	−0.735701	−	0.503915i
$238$	0.722265	+	2.74942i	0.0468175	+	0.178218i
$239$	4.62511	+	8.01092i	0.299173	+	0.518183i	0.975947	−	0.218008i	$-0.0699558\pi$
$239$	4.62511	+	8.01092i	0.299173	+	0.518183i	−0.676774	+	0.736191i	$0.736622\pi$
$240$	6.48804	+	2.43009i	0.418801	+	0.156861i
$241$	12.0918	−	20.9437i	0.778904	−	1.34910i	−0.153670	−	0.988122i	$-0.549109\pi$
$241$	12.0918	−	20.9437i	0.778904	−	1.34910i	0.932574	−	0.360979i	$-0.117557\pi$
$242$	−3.41000	−	0.931662i	−0.219203	−	0.0598895i
$243$	14.4488	+	5.85086i	0.926890	+	0.375333i
$244$	1.76827	−	0.455257i	0.113202	−	0.0291449i
$245$	−1.65174	−	6.16439i	−0.105526	−	0.393828i
$246$	6.44355	−	18.0060i	0.410826	−	1.14802i
$247$	7.32142	+	12.6811i	0.465851	+	0.806877i
$248$	4.16051	−	14.6606i	0.264193	−	0.930952i
$249$	−0.480678	−	2.57071i	−0.0304617	−	0.162912i
$250$	−0.00693825	+	1.41420i	−0.000438814	+	0.0894416i
$251$	−3.53384	−	3.53384i	−0.223054	−	0.223054i	0.586729	−	0.809783i	$-0.300415\pi$
$251$	−3.53384	−	3.53384i	−0.223054	−	0.223054i	−0.809783	+	0.586729i	$0.800415\pi$
$252$	−3.64630	−	2.99299i	−0.229696	−	0.188541i
$253$	6.60936	−	6.60936i	0.415527	−	0.415527i
$254$	6.86889	−	6.80182i	0.430993	−	0.426784i
$255$	1.47153	−	4.17656i	0.0921511	−	0.261546i
$256$	15.9877	+	0.627820i	0.999230	+	0.0392388i
$257$	0.544391	−	0.314305i	0.0339582	−	0.0196058i	−0.482925	−	0.875662i	$-0.660426\pi$
$257$	0.544391	−	0.314305i	0.0339582	−	0.0196058i	0.516883	+	0.856056i	$0.327092\pi$
$258$	8.57572	−	12.3895i	0.533901	−	0.771336i
$259$	3.40426	−	0.912168i	0.211530	−	0.0566793i
$260$	6.95879	−	11.7844i	0.431566	−	0.730838i
$261$	9.08022	−	0.983549i	0.562051	−	0.0608801i
$262$	8.30263	+	14.5449i	0.512938	+	0.898588i
$263$	16.7552	+	9.67361i	1.03317	+	0.596500i	0.917891	−	0.396833i	$-0.129891\pi$
$263$	16.7552	+	9.67361i	1.03317	+	0.596500i	0.115278	+	0.993333i	$0.463224\pi$
$264$	−10.3890	+	14.6989i	−0.639402	+	0.904656i
$265$	3.77900	−	2.18181i	0.232142	−	0.134027i
$266$	2.05469	+	1.19976i	0.125981	+	0.0735618i
$267$	26.4488	+	2.03929i	1.61864	+	0.124803i
$268$	−27.6354	−	7.69628i	−1.68810	−	0.470125i
$269$	17.9414	+	17.9414i	1.09391	+	1.09391i	0.995107	+	0.0987997i	$0.0315003\pi$
$269$	17.9414	+	17.9414i	1.09391	+	1.09391i	0.0987997	+	0.995107i	$0.468500\pi$
$270$	2.08609	+	7.04615i	0.126955	+	0.428815i
$271$			18.8674i			1.14611i	0.819516	+	0.573056i	$0.194242\pi$
$271$			18.8674i			1.14611i	−0.819516	+	0.573056i	$0.805758\pi$
$272$	0.200677	−	10.2246i	0.0121678	−	0.619955i
$273$	−7.07619	+	6.06311i	−0.428271	+	0.366956i
$274$	4.82331	−	1.26707i	0.291387	−	0.0765467i
$275$	−3.54899	−	0.950948i	−0.214012	−	0.0573443i
$276$	−3.72839	−	7.98506i	−0.224422	−	0.480644i
$277$	0.472965	−	0.126731i	0.0284177	−	0.00761450i	−0.244582	−	0.969629i	$-0.578651\pi$
$277$	0.472965	−	0.126731i	0.0284177	−	0.00761450i	0.273000	+	0.962014i	$0.411984\pi$
$278$	6.42675	+	11.2587i	0.385451	+	0.675249i
$279$	15.0719	−	5.84058i	0.902332	−	0.349666i
$280$	0.0327292	−	2.22355i	0.00195594	−	0.132882i
$281$	16.1646	−	27.9979i	0.964300	−	1.67022i	0.252814	−	0.967515i	$-0.418644\pi$
$281$	16.1646	−	27.9979i	0.964300	−	1.67022i	0.711485	−	0.702701i	$-0.248023\pi$
$282$	−17.9085	+	3.25774i	−1.06644	+	0.193996i
$283$	−8.26823	−	2.21546i	−0.491495	−	0.131696i	0.00455503	−	0.999990i	$-0.498550\pi$
$283$	−8.26823	−	2.21546i	−0.491495	−	0.131696i	−0.496050	+	0.868294i	$0.665217\pi$
$284$	4.02138	+	0.0394599i	0.238625	+	0.00234151i
$285$	−1.60095	−	3.34279i	−0.0948323	−	0.198010i
$286$	25.0181	+	25.2648i	1.47935	+	1.49394i
$287$	−6.13840			−0.362339
$288$	9.67963	+	13.9393i	0.570377	+	0.821383i
$289$	10.4636			0.615508
$290$	3.02947	+	3.05934i	0.177897	+	0.179651i
$291$	3.89349	−	5.68438i	0.228240	−	0.333224i
$292$	5.51989	+	0.0541640i	0.323027	+	0.00316971i
$293$	1.71619	+	0.459850i	0.100261	+	0.0268647i	0.308601	−	0.951192i	$-0.400139\pi$
$293$	1.71619	+	0.459850i	0.100261	+	0.0268647i	−0.208340	+	0.978056i	$0.566806\pi$
$294$	5.26701	−	14.7182i	0.307178	−	0.858385i
$295$	−4.11072	+	7.11997i	−0.239335	+	0.414541i
$296$	−12.6773	−	0.186603i	−0.736855	−	0.0108461i
$297$	−19.0825	+	0.590713i	−1.10728	+	0.0342767i
$298$	−13.5565	−	23.7488i	−0.785306	−	1.37573i
$299$	−16.8148	+	4.50552i	−0.972427	+	0.260561i
$300$	−1.98550	+	2.83863i	−0.114633	+	0.163888i
$301$	−4.67165	−	1.25176i	−0.269269	−	0.0721505i
$302$	−4.27668	+	1.12347i	−0.246095	+	0.0646486i
$303$	−5.41565	−	28.9634i	−0.311121	−	1.66390i
$304$	−5.93257	−	6.17011i	−0.340256	−	0.353880i
$305$			0.912965i			0.0522762i
$306$	8.78631	−	6.36045i	0.502280	−	0.363603i
$307$	−11.9725	−	11.9725i	−0.683309	−	0.683309i	0.277436	−	0.960744i	$-0.410515\pi$
$307$	−11.9725	−	11.9725i	−0.683309	−	0.683309i	−0.960744	+	0.277436i	$0.910515\pi$
$308$	5.56568	+	1.55001i	0.317134	+	0.0883199i
$309$	−11.3282	−	23.6533i	−0.644439	−	1.34559i
$310$	6.58016	+	3.84222i	0.373728	+	0.218224i
$311$	17.5376	−	10.1253i	0.994464	−	0.574154i	0.0878580	−	0.996133i	$-0.471998\pi$
$311$	17.5376	−	10.1253i	0.994464	−	0.574154i	0.906606	+	0.421979i	$0.138664\pi$
$312$	30.4441	−	14.0335i	1.72356	−	0.794488i
$313$	13.3063	+	7.68237i	0.752114	+	0.434233i	0.826457	−	0.562999i	$-0.190353\pi$
$313$	13.3063	+	7.68237i	0.752114	+	0.434233i	−0.0743430	+	0.997233i	$0.523686\pi$
$314$	5.18647	+	9.08588i	0.292689	+	0.512746i
$315$	1.90380	−	1.39245i	0.107267	−	0.0784559i
$316$	8.06021	−	13.6496i	0.453422	−	0.767851i
$317$	−3.11988	+	0.835971i	−0.175230	+	0.0469528i	−0.345367	−	0.938468i	$-0.612246\pi$
$317$	−3.11988	+	0.835971i	−0.175230	+	0.0469528i	0.170137	+	0.985420i	$0.445579\pi$
$318$	10.6528	+	0.873965i	0.597381	+	0.0490095i
$319$	−9.68722	+	5.59292i	−0.542380	+	0.313143i
$320$	−2.29709	+	7.66312i	−0.128411	+	0.428381i
$321$	−4.36036	−	5.08893i	−0.243371	−	0.284036i
$322$	−2.00994	+	1.99031i	−0.112009	+	0.110916i
$323$	−3.86850	+	3.86850i	−0.215249	+	0.215249i
$324$	−5.62146	+	17.0997i	−0.312303	+	0.949982i
$325$	4.83861	+	4.83861i	0.268398	+	0.268398i
$326$	−0.0958540	+	19.5375i	−0.00530886	+	1.08208i
$327$	12.3094	−	10.5470i	0.680709	−	0.583253i
$328$	21.2438	+	6.02874i	1.17299	+	0.332881i
$329$	2.92127	+	5.05980i	0.161055	+	0.278956i
$330$	−5.82221	−	6.86291i	−0.320502	−	0.377791i
$331$	−5.38295	−	20.0894i	−0.295874	−	1.10422i	−0.940521	−	0.339735i	$-0.889662\pi$
$331$	−5.38295	−	20.0894i	−0.295874	−	1.10422i	0.644647	−	0.764480i	$-0.277004\pi$
$332$	2.92447	−	0.752934i	0.160501	−	0.0413226i
$333$	−7.93895	−	10.8543i	−0.435052	−	0.594814i
$334$	−1.75104	−	0.478408i	−0.0958124	−	0.0261773i
$335$	7.17176	−	12.4218i	0.391835	−	0.678678i
$336$	3.16576	−	4.43276i	0.172706	−	0.241827i
$337$	9.00027	+	15.5889i	0.490276	+	0.849183i	0.999937	−	0.0111920i	$-0.00356259\pi$
$337$	9.00027	+	15.5889i	0.490276	+	0.849183i	−0.509661	+	0.860375i	$0.670229\pi$
$338$	−12.1537	−	46.2649i	−0.661074	−	2.51648i
$339$	−24.1865	+	11.5836i	−1.31363	+	0.629132i
$340$	4.92581	+	1.37181i	0.267139	+	0.0743967i
$341$	−13.9982	+	13.9982i	−0.758047	+	0.758047i
$342$	1.43573	−	8.96451i	0.0776354	−	0.484745i
$343$	−10.5212			−0.568090
$344$	14.9383	+	8.92029i	0.805417	+	0.480950i
$345$	4.33124	−	0.809867i	0.233186	−	0.0436018i
$346$	13.1545	+	7.68104i	0.707190	+	0.412935i
$347$	−6.44401	+	24.0494i	−0.345933	+	1.29104i	0.545586	+	0.838055i	$0.316307\pi$
$347$	−6.44401	+	24.0494i	−0.345933	+	1.29104i	−0.891519	+	0.452984i	$0.850359\pi$
$348$	1.83656	+	10.3851i	0.0984502	+	0.556701i
$349$	−7.51635	−	28.0514i	−0.402341	−	1.50156i	−0.808908	−	0.587936i	$-0.799941\pi$
$349$	−7.51635	−	28.0514i	−0.402341	−	1.50156i	0.406567	−	0.913621i	$-0.366726\pi$
$350$	1.07258	+	0.293045i	0.0573319	+	0.0156639i
$351$	31.3280	+	16.8169i	1.67217	+	0.897620i
$352$	−17.7394	−	10.8305i	−0.945515	−	0.577269i
$353$	16.6088	+	9.58909i	0.883997	+	0.510376i	0.871974	−	0.489552i	$-0.162840\pi$
$353$	16.6088	+	9.58909i	0.883997	+	0.510376i	0.0120228	+	0.999928i	$0.496173\pi$
$354$	−18.2052	+	8.60942i	−0.967596	+	0.457585i
$355$	−0.520430	+	1.94227i	−0.0276216	+	0.103085i
$356$	−0.300554	+	30.6297i	−0.0159293	+	1.62337i
$357$	−2.87239	−	1.96743i	−0.152023	−	0.104127i
$358$	34.2870	+	0.168217i	1.81213	+	0.00889055i
$359$		−	29.6488i		−	1.56480i	−0.622774	−	0.782402i	$-0.713994\pi$
$359$		−	29.6488i		−	1.56480i	0.622774	−	0.782402i	$-0.286006\pi$
$360$	−7.95626	+	2.94923i	−0.419332	+	0.155438i
$361$		−	14.4209i		−	0.758995i
$362$	−0.114904	+	23.4204i	−0.00603922	+	1.23095i
$363$	3.90473	−	1.87008i	0.204945	−	0.0981539i
$364$	−7.53347	−	7.68278i	−0.394861	−	0.402687i
$365$	−0.714360	+	2.66603i	−0.0373913	+	0.139546i
$366$	−1.27276	+	1.83878i	−0.0665283	+	0.0961146i
$367$	15.7082	+	9.06912i	0.819960	+	0.473404i	0.850403	−	0.526132i	$-0.176358\pi$
$367$	15.7082	+	9.06912i	0.819960	+	0.473404i	−0.0304424	+	0.999537i	$0.509692\pi$
$368$	8.91075	−	4.91405i	0.464505	−	0.256162i
$369$	8.46322	+	21.8398i	0.440577	+	1.13693i
$370$	1.67077	−	6.11522i	0.0868591	−	0.317915i
$371$	−0.887955	−	3.31389i	−0.0461003	−	0.172049i
$372$	7.89650	+	16.9119i	0.409415	+	0.876840i
$373$	5.48619	−	20.4747i	0.284064	−	1.06014i	−0.665456	−	0.746437i	$-0.731763\pi$
$373$	5.48619	−	20.4747i	0.284064	−	1.06014i	0.949520	−	0.313705i	$-0.101570\pi$
$374$	−6.69859	+	11.4719i	−0.346376	+	0.593200i
$375$	−1.12697	−	1.31527i	−0.0581964	−	0.0679204i
$376$	−5.14056	−	20.3801i	−0.265104	−	1.05102i
$377$	20.8326			1.07293
$378$	5.77561	−	0.150430i	0.297065	−	0.00773728i
$379$	7.67878	−	7.67878i	0.394433	−	0.394433i	−0.481831	−	0.876264i	$-0.660028\pi$
$379$	7.67878	−	7.67878i	0.394433	−	0.394433i	0.876264	+	0.481831i	$0.160028\pi$
$380$	3.72720	−	2.10341i	0.191202	−	0.107903i
$381$	−0.910151	+	11.8043i	−0.0466285	+	0.604752i
$382$	−9.84222	+	2.58553i	−0.503572	+	0.132287i
$383$	−5.91516	−	10.2454i	−0.302250	−	0.523513i	0.674395	−	0.738371i	$-0.264405\pi$
$383$	−5.91516	−	10.2454i	−0.302250	−	0.523513i	−0.976645	+	0.214858i	$0.931071\pi$
$384$	−15.3096	+	12.2317i	−0.781266	+	0.624198i
$385$	−1.44437	+	2.50172i	−0.0736120	+	0.127500i
$386$	−8.18280	+	29.9501i	−0.416493	+	1.52442i
$387$	1.98731	+	18.3470i	0.101021	+	0.932633i
$388$	6.85059	+	4.04533i	0.347786	+	0.205370i
$389$	1.40336	+	5.23742i	0.0711533	+	0.265548i	0.992334	−	0.123588i	$-0.0394403\pi$
$389$	1.40336	+	5.23742i	0.0711533	+	0.265548i	−0.921180	+	0.389136i	$0.872774\pi$
$390$	2.99984	+	16.4908i	0.151903	+	0.835044i
$391$	−3.25201	−	5.63264i	−0.164461	−	0.284855i
$392$	17.3649	+	4.92794i	0.877059	+	0.248899i
$393$	−19.3461	−	6.81624i	−0.975881	−	0.343834i
$394$	34.0755	+	0.167179i	1.71670	+	0.00842238i
$395$	5.60445	+	5.60445i	0.281990	+	0.281990i
$396$	−2.15882	−	21.9391i	−0.108485	−	1.10248i
$397$	17.8933	−	17.8933i	0.898038	−	0.898038i	−0.0972243	−	0.995262i	$-0.530996\pi$
$397$	17.8933	−	17.8933i	0.898038	−	0.898038i	0.995262	+	0.0972243i	$0.0309964\pi$
$398$	22.7108	+	22.9347i	1.13839	+	1.14961i
$399$	−2.86442	+	0.535597i	−0.143400	+	0.0268134i
$400$	−3.42419	−	2.06759i	−0.171209	−	0.103380i
$401$	−7.68203	+	4.43522i	−0.383622	+	0.221485i	−0.679393	−	0.733774i	$-0.737757\pi$
$401$	−7.68203	+	4.43522i	−0.383622	+	0.221485i	0.295771	+	0.955259i	$0.404424\pi$
$402$	31.7617	−	15.0204i	1.58413	−	0.749150i
$403$	35.6129	−	9.54244i	1.77400	−	0.475343i
$404$	32.9491	−	8.48308i	1.63928	−	0.422049i
$405$	−7.57903	−	4.85369i	−0.376605	−	0.241182i
$406$	2.93985	−	1.67815i	0.145902	−	0.0832850i
$407$	14.2633	+	8.23495i	0.707008	+	0.408191i
$408$	8.00851	+	9.62997i	0.396481	+	0.476755i
$409$	7.66456	−	4.42513i	0.378988	−	0.218809i	−0.298390	−	0.954444i	$-0.596450\pi$
$409$	7.66456	−	4.42513i	0.378988	−	0.218809i	0.677378	+	0.735635i	$0.263116\pi$
$410$	−5.56752	+	9.53489i	−0.274960	+	0.470895i
$411$	−3.45147	+	5.03905i	−0.170249	+	0.248558i
$412$	26.3734	−	14.8836i	1.29932	−	0.733261i
$413$	4.57068	+	4.57068i	0.224908	+	0.224908i
$414$	9.85247	+	4.40703i	0.484222	+	0.216594i
$415$			1.50992i			0.0741192i
$416$	18.5264	+	33.9875i	0.908329	+	1.66637i
$417$	−14.9751	−	5.27619i	−0.733332	−	0.258376i
$418$	2.82508	+	10.7541i	0.138179	+	0.526001i
$419$	−7.61125	−	2.03943i	−0.371834	−	0.0996326i	0.0680627	−	0.997681i	$-0.478318\pi$
$419$	−7.61125	−	2.03943i	−0.371834	−	0.0996326i	−0.439896	+	0.898048i	$0.644985\pi$
$420$	1.75173	+	2.08550i	0.0854756	+	0.101762i
$421$	−34.3360	+	9.20031i	−1.67344	+	0.448396i	−0.966034	−	0.258415i	$-0.916800\pi$
$421$	−34.3360	+	9.20031i	−1.67344	+	0.448396i	−0.707402	+	0.706811i	$0.750133\pi$
$422$	−4.03502	+	2.30330i	−0.196422	+	0.112123i
$423$	13.9745	−	17.3697i	0.679465	−	0.844542i
$424$	−0.181649	+	12.3408i	−0.00882167	+	0.599324i
$425$	−1.27832	+	2.21411i	−0.0620074	+	0.107400i
$426$	−3.75590	+	3.18635i	−0.181974	+	0.154379i
$427$	0.693340	+	0.185780i	0.0335531	+	0.00899052i
$428$	5.52517	−	5.41779i	0.267069	−	0.261879i
$429$	−43.4180	−	3.34767i	−2.09624	−	0.161627i
$430$	−6.18156	+	6.12120i	−0.298101	+	0.295191i
$431$	−9.32415			−0.449129			−0.224564	−	0.974459i	$-0.572096\pi$
$431$	−9.32415			−0.449129			−0.224564	+	0.974459i	$0.572096\pi$
$432$	−20.1360	−	5.15182i	−0.968794	−	0.247867i
$433$	32.9835			1.58509			0.792543	−	0.609816i	$-0.208757\pi$
$433$	32.9835			1.58509			0.792543	+	0.609816i	$0.208757\pi$
$434$	4.25693	−	4.21536i	0.204339	−	0.202344i
$435$	−5.25753	−	0.405373i	−0.252079	−	0.0194362i
$436$	13.1048	+	13.3645i	0.627607	+	0.640046i
$437$	−5.25832	−	1.40896i	−0.251540	−	0.0673999i
$438$	−5.15547	+	4.37370i	−0.246338	+	0.208983i
$439$	17.6002	−	30.4845i	0.840013	−	1.45495i	−0.0498693	−	0.998756i	$-0.515880\pi$
$439$	17.6002	−	30.4845i	0.840013	−	1.45495i	0.889882	−	0.456190i	$-0.150786\pi$
$440$	7.45572	−	7.23942i	0.355437	−	0.345126i
$441$	6.91790	+	17.8520i	0.329424	+	0.850096i
$442$	21.4868	−	12.2653i	1.02202	−	0.583399i
$443$	−31.1213	+	8.33892i	−1.47862	+	0.396194i	−0.905876	−	0.423543i	$-0.860786\pi$
$443$	−31.1213	+	8.33892i	−1.47862	+	0.396194i	−0.572741	+	0.819737i	$0.694120\pi$
$444$	11.8903	−	9.98731i	0.564287	−	0.473977i
$445$	−14.7937	−	3.96396i	−0.701289	−	0.187910i
$446$	−7.21261	−	27.4559i	−0.341527	−	1.30008i
$447$	31.5882	+	11.1295i	1.49407	+	0.526408i
$448$	5.35222	+	3.30387i	0.252869	+	0.156093i
$449$		−	1.30829i		−	0.0617418i	−0.999523	−	0.0308709i	$-0.990172\pi$
$449$		−	1.30829i		−	0.0617418i	0.999523	−	0.0308709i	$-0.00982807\pi$
$450$	−0.436182	−	4.22016i	−0.0205618	−	0.198940i
$451$	−20.2840	−	20.2840i	−0.955135	−	0.955135i
$452$	−15.2191	−	26.9679i	−0.715844	−	1.26846i
$453$	3.06031	−	4.46797i	0.143786	−	0.209923i
$454$	−17.6083	+	30.1559i	−0.826399	+	1.41528i
$455$	4.65923	−	2.69001i	0.218428	−	0.126110i
$456$	10.4392	+	0.959648i	0.488862	+	0.0449396i
$457$	−25.9634	−	14.9900i	−1.21452	−	0.701201i	−0.250776	−	0.968045i	$-0.580686\pi$
$457$	−25.9634	−	14.9900i	−1.21452	−	0.701201i	−0.963740	+	0.266844i	$0.914019\pi$
$458$	8.74361	−	4.99109i	0.408562	−	0.233218i
$459$	−3.03964	+	12.9322i	−0.141878	+	0.603624i
$460$	1.26858	+	4.92728i	0.0591476	+	0.229735i
$461$	−4.38224	+	1.17422i	−0.204101	+	0.0546887i	−0.359421	−	0.933175i	$-0.617026\pi$
$461$	−4.38224	+	1.17422i	−0.204101	+	0.0546887i	0.155320	+	0.987864i	$0.450359\pi$
$462$	−6.39672	+	3.02507i	−0.297602	+	0.140739i
$463$	−9.82544	+	5.67272i	−0.456627	+	0.263634i	−0.710625	−	0.703571i	$-0.751588\pi$
$463$	−9.82544	+	5.67272i	−0.456627	+	0.263634i	0.253998	+	0.967205i	$0.418254\pi$
$464$	−11.8224	+	2.92041i	−0.548842	+	0.135577i
$465$	−9.17331	+	1.71525i	−0.425402	+	0.0795428i
$466$	0.680187	+	0.686894i	0.0315091	+	0.0318198i
$467$	−12.7227	+	12.7227i	−0.588734	+	0.588734i	−0.937289	−	0.348554i	$-0.886673\pi$
$467$	−12.7227	+	12.7227i	−0.588734	+	0.588734i	0.348554	+	0.937289i	$0.386673\pi$
$468$	−16.9478	+	37.3958i	−0.783415	+	1.72862i
$469$	−7.97423	−	7.97423i	−0.368216	−	0.368216i
$470$	10.5091	+	0.0515590i	0.484747	+	0.00237824i
$471$	−12.0851	−	4.25795i	−0.556850	−	0.196196i
$472$	−11.3292	−	20.3073i	−0.521469	−	0.934717i
$473$	−11.3008	−	19.5735i	−0.519610	−	0.899992i
$474$	3.47464	+	19.1009i	0.159596	+	0.877334i
$475$	0.553842	+	2.06697i	0.0254120	+	0.0948390i
$476$	2.04416	−	3.46169i	0.0936938	−	0.158666i
$477$	−10.5662	+	7.72822i	−0.483794	+	0.353851i
$478$	3.44777	−	12.6193i	0.157697	−	0.577192i
$479$	9.74830	−	16.8845i	0.445411	−	0.771475i	−0.552670	−	0.833400i	$-0.686391\pi$
$479$	9.74830	−	16.8845i	0.445411	−	0.771475i	0.998081	+	0.0619258i	$0.0197242\pi$
$480$	−4.01415	−	8.93793i	−0.183220	−	0.407959i
$481$	−15.3368	−	26.5642i	−0.699299	−	1.21122i
$482$	−33.0785	+	8.68966i	−1.50669	+	0.395803i
$483$	0.266323	−	3.45410i	0.0121181	−	0.157167i
$484$	2.45701	+	4.35377i	0.111682	+	0.197899i
$485$	−2.81281	+	2.81281i	−0.127723	+	0.127723i
$486$	−8.49823	−	20.3416i	−0.385488	−	0.922713i
$487$	8.87316			0.402081			0.201041	−	0.979583i	$-0.435568\pi$
$487$	8.87316			0.402081			0.201041	+	0.979583i	$0.435568\pi$
$488$	−2.21705	−	1.32390i	−0.100361	−	0.0599302i
$489$	−15.5694	−	18.1709i	−0.704072	−	0.821716i
$490$	−4.55094	+	7.79390i	−0.205590	+	0.352093i
$491$	6.87882	−	25.6721i	0.310437	−	1.15857i	−0.617727	−	0.786393i	$-0.711946\pi$
$491$	6.87882	−	25.6721i	0.310437	−	1.15857i	0.928163	−	0.372173i	$-0.121387\pi$
$492$	−24.5060	+	11.4423i	−1.10481	+	0.515860i
$493$	2.01452	+	7.51830i	0.0907295	+	0.338607i
$494$	5.45772	−	19.9760i	0.245554	−	0.898761i
$495$	10.8923	+	1.68971i	0.489571	+	0.0759466i
$496$	−18.8724	+	10.4077i	−0.847398	+	0.467318i
$497$	1.36913	+	0.790468i	0.0614139	+	0.0354573i
$498$	−2.10498	+	3.04110i	−0.0943262	+	0.136275i
$499$	−6.70050	+	25.0066i	−0.299955	+	1.11945i	0.637246	+	0.770661i	$0.280074\pi$
$499$	−6.70050	+	25.0066i	−0.299955	+	1.11945i	−0.937201	+	0.348789i	$0.886593\pi$
$500$	1.42802	−	1.40027i	0.0638631	−	0.0626219i
$501$	2.00508	−	0.960287i	0.0895804	−	0.0429025i
$502$	−0.0346746	+	7.06760i	−0.00154761	+	0.315442i
$503$			22.1646i			0.988269i	0.869386	+	0.494134i	$0.164515\pi$
$503$			22.1646i			0.988269i	−0.869386	+	0.494134i	$0.835485\pi$
$504$	0.620730	+	6.64242i	0.0276495	+	0.295877i
$505$			17.0118i			0.757016i
$506$	−13.2186	−	0.0648521i	−0.587636	−	0.00288303i
$507$	48.3343	+	33.1063i	2.14660	+	1.47030i
$508$	−13.6702	−	0.134139i	−0.606518	−	0.00595147i
$509$	3.24657	−	12.1164i	0.143902	−	0.537048i	−0.855900	−	0.517141i	$-0.826996\pi$
$509$	3.24657	−	12.1164i	0.143902	−	0.537048i	0.999802	−	0.0199070i	$-0.00633702\pi$
$510$	−5.66130	+	2.67728i	−0.250687	+	0.118552i
$511$	1.87932	+	1.08502i	0.0831361	+	0.0479986i
$512$	−15.2782	−	16.6907i	−0.675205	−	0.737630i
$513$	5.85486	+	9.45284i	0.258498	+	0.417353i
$514$	−0.857557	−	0.234297i	−0.0378252	−	0.0103344i
$515$	3.91894	+	14.6257i	0.172689	+	0.644485i
$516$	−20.9837	+	3.71087i	−0.923754	+	0.163362i
$517$	−7.06661	+	26.3729i	−0.310789	+	1.15988i
$518$	−4.30415	−	2.51324i	−0.189113	−	0.110425i
$519$	−18.3385	+	3.42898i	−0.804971	+	0.150516i
$520$	−18.7666	+	4.73360i	−0.822972	+	0.207582i
$521$	−9.17436			−0.401936			−0.200968	−	0.979598i	$-0.564409\pi$
$521$	−9.17436			−0.401936			−0.200968	+	0.979598i	$0.564409\pi$
$522$	−10.0239	−	8.14594i	−0.438735	−	0.356538i
$523$	−3.51867	+	3.51867i	−0.153861	+	0.153861i	−0.779840	−	0.625979i	$-0.784700\pi$
$523$	−3.51867	+	3.51867i	−0.153861	+	0.153861i	0.625979	+	0.779840i	$0.284700\pi$
$524$	6.35430	−	22.8167i	0.277589	−	0.996750i
$525$	−1.22820	+	0.588216i	−0.0536028	+	0.0256718i
$526$	−6.95183	−	26.4632i	−0.303114	−	1.15385i
$527$	6.88756	+	11.9296i	0.300027	+	0.519662i
$528$	25.1088	−	4.18674i	1.09272	−	0.182205i
$529$	−8.26408	+	14.3138i	−0.359308	+	0.622340i
$530$	−5.95290	−	1.62642i	−0.258577	−	0.0706471i
$531$	9.96023	−	22.5637i	0.432237	−	0.979182i
$532$	−0.838959	−	3.25860i	−0.0363735	−	0.141278i
$533$	13.8273	+	51.6044i	0.598929	+	2.23523i
$534$	−24.2695	−	28.6075i	−1.05024	−	1.23797i
$535$	1.93455	+	3.35074i	0.0836380	+	0.144865i
$536$	19.7655	+	35.4290i	0.853739	+	1.53030i
$537$	−31.8886	+	27.3232i	−1.37610	+	1.17908i
$538$	0.176044	−	35.8824i	0.00758980	−	1.54700i
$539$	−16.5803	−	16.5803i	−0.714163	−	0.714163i
$540$	5.00480	−	9.10780i	0.215372	−	0.391937i
$541$	10.0625	−	10.0625i	0.432620	−	0.432620i	−0.456899	−	0.889519i	$-0.651040\pi$
$541$	10.0625	−	10.0625i	0.432620	−	0.432620i	0.889519	+	0.456899i	$0.151040\pi$
$542$	18.9597	−	18.7746i	0.814390	−	0.806438i
$543$	−18.6636	−	21.7822i	−0.800934	−	0.934762i
$544$	−10.4743	+	9.97261i	−0.449081	+	0.427572i
$545$	−8.10494	+	4.67939i	−0.347178	+	0.200443i
$546$	13.1342	+	1.07753i	0.562090	+	0.0461142i
$547$	20.8505	−	5.58689i	0.891505	−	0.238878i	0.216141	−	0.976362i	$-0.430653\pi$
$547$	20.8505	−	5.58689i	0.891505	−	0.238878i	0.675364	+	0.737484i	$0.263986\pi$
$548$	−6.07286	−	3.58608i	−0.259420	−	0.153190i
$549$	−0.294946	−	2.72297i	−0.0125880	−	0.116213i
$550$	2.57593	+	4.51263i	0.109838	+	0.192419i
$551$	5.64194	+	3.25738i	0.240355	+	0.138769i
$552$	−4.31409	+	11.6924i	−0.183620	+	0.497662i
$553$	5.39668	−	3.11578i	0.229490	−	0.132496i
$554$	−0.597990	−	0.349172i	−0.0254061	−	0.0148349i
$555$	3.35366	+	7.00244i	0.142355	+	0.297237i
$556$	4.91862	−	17.6615i	0.208596	−	0.749014i
$557$	−19.4625	−	19.4625i	−0.824651	−	0.824651i	0.162120	−	0.986771i	$-0.448167\pi$
$557$	−19.4625	−	19.4625i	−0.824651	−	0.824651i	−0.986771	+	0.162120i	$0.948167\pi$
$558$	−20.8670	−	9.33382i	−0.883369	−	0.395132i
$559$			42.0933i			1.78036i
$560$	−2.26700	+	2.17972i	−0.0957981	+	0.0921100i
$561$	−2.99039	−	15.9929i	−0.126255	−	0.675220i
$562$	−44.2201	+	11.6165i	−1.86531	+	0.490013i
$563$	15.8173	+	4.23823i	0.666619	+	0.178620i	0.576231	−	0.817287i	$-0.304523\pi$
$563$	15.8173	+	4.23823i	0.666619	+	0.178620i	0.0903876	+	0.995907i	$0.471189\pi$
$564$	21.0942	+	14.7545i	0.888224	+	0.621275i
$565$	14.9554	−	4.00728i	0.629177	−	0.168587i
$566$	6.00125	+	10.5133i	0.252252	+	0.441905i
$567$	−5.22833	+	4.76812i	−0.219569	+	0.200242i
$568$	−3.96195	−	4.08033i	−0.166240	−	0.171207i
$569$	8.38538	−	14.5239i	0.351533	−	0.608874i	−0.634985	−	0.772524i	$-0.718994\pi$
$569$	8.38538	−	14.5239i	0.351533	−	0.608874i	0.986518	+	0.163651i	$0.0523271\pi$
$570$	−1.76607	+	4.93514i	−0.0739726	+	0.206710i
$571$	32.0360	+	8.58401i	1.34066	+	0.359230i	0.856680	−	0.515848i	$-0.172523\pi$
$571$	32.0360	+	8.58401i	1.34066	+	0.359230i	0.483983	+	0.875078i	$0.339190\pi$
$572$	0.493385	−	50.2811i	0.0206295	−	2.10236i
$573$	7.04291	−	10.2824i	0.294222	−	0.429555i
$574$	6.10822	+	6.16845i	0.254952	+	0.257466i
$575$	−2.54398			−0.106091
$576$	4.37553	−	23.5978i	0.182314	−	0.983240i
$577$	27.6936			1.15290			0.576450	−	0.817132i	$-0.304438\pi$
$577$	27.6936			1.15290			0.576450	+	0.817132i	$0.304438\pi$
$578$	−10.4122	−	10.5149i	−0.433090	−	0.437360i
$579$	−16.4250	−	34.2953i	−0.682598	−	1.42527i
$580$	0.0597445	−	6.08859i	0.00248075	−	0.252815i
$581$	1.14669	+	0.307255i	0.0475728	+	0.0127471i
$582$	−9.58654	+	1.74389i	−0.397375	+	0.0722864i
$583$	8.01636	−	13.8847i	0.332004	−	0.575047i
$584$	−5.43831	−	5.60080i	−0.225039	−	0.231763i
$585$	−15.9946	−	12.8682i	−0.661295	−	0.532036i
$586$	−1.24564	−	2.18217i	−0.0514571	−	0.0901447i
$587$	23.9606	−	6.42021i	0.988958	−	0.264990i	0.272145	−	0.962256i	$-0.412267\pi$
$587$	23.9606	−	6.42021i	0.988958	−	0.264990i	0.716813	+	0.697266i	$0.245600\pi$
$588$	−20.0314	+	9.35305i	−0.826080	+	0.385713i
$589$	11.1368	+	2.98410i	0.458885	+	0.122958i
$590$	11.2453	−	2.95412i	0.462962	−	0.121619i
$591$	−31.6919	+	27.1547i	−1.30363	+	1.11699i
$592$	12.4275	+	12.9251i	0.510766	+	0.531217i
$593$			11.4796i			0.471412i	0.971824	+	0.235706i	$0.0757403\pi$
$593$			11.4796i			0.471412i	−0.971824	+	0.235706i	$0.924260\pi$
$594$	19.5822	+	18.5880i	0.803468	+	0.762677i
$595$	1.42135	+	1.42135i	0.0582697	+	0.0582697i
$596$	−10.3753	+	37.2549i	−0.424987	+	1.52602i
$597$	−39.4137	−	3.03893i	−1.61309	−	0.124375i
$598$	21.2597	+	12.4138i	0.869374	+	0.507637i
$599$	28.2475	−	16.3087i	1.15416	−	0.666356i	0.204264	−	0.978916i	$-0.434520\pi$
$599$	28.2475	−	16.3087i	1.15416	−	0.666356i	0.949898	+	0.312560i	$0.101186\pi$
$600$	4.82825	−	0.829448i	0.197113	−	0.0338621i
$601$	−4.35810	−	2.51615i	−0.177770	−	0.102636i	0.408474	−	0.912770i	$-0.366061\pi$
$601$	−4.35810	−	2.51615i	−0.177770	−	0.102636i	−0.586245	+	0.810134i	$0.699394\pi$
$602$	3.39078	+	5.94012i	0.138198	+	0.242101i
$603$	−17.3771	+	39.3658i	−0.707650	+	1.60310i
$604$	5.38462	+	3.17966i	0.219097	+	0.129379i
$605$	−2.41444	+	0.646947i	−0.0981608	+	0.0263021i
$606$	−23.7161	+	34.2631i	−0.963401	+	1.39184i
$607$	15.9708	−	9.22073i	0.648234	−	0.374258i	−0.139545	−	0.990216i	$-0.544564\pi$
$607$	15.9708	−	9.22073i	0.648234	−	0.374258i	0.787779	+	0.615958i	$0.211231\pi$
$608$	−0.296912	+	12.1014i	−0.0120414	+	0.490775i
$609$	−1.37771	+	3.91027i	−0.0558277	+	0.158452i
$610$	0.917433	−	0.908475i	0.0371458	−	0.0367831i
$611$	35.9562	−	35.9562i	1.45463	−	1.45463i
$612$	−15.1347	−	2.50014i	−0.611783	−	0.101062i
$613$	−6.11687	−	6.11687i	−0.247058	−	0.247058i	0.572704	−	0.819762i	$-0.305894\pi$
$613$	−6.11687	−	6.11687i	−0.247058	−	0.247058i	−0.819762	+	0.572704i	$0.805894\pi$
$614$	−0.117477	+	23.9448i	−0.00474097	+	0.966333i
$615$	−2.48546	−	13.2925i	−0.100224	−	0.536004i
$616$	−3.98071	−	7.13531i	−0.160388	−	0.287490i
$617$	15.2653	+	26.4402i	0.614557	+	1.06444i	0.990462	+	0.137786i	$0.0439985\pi$
$617$	15.2653	+	26.4402i	0.614557	+	1.06444i	−0.375905	+	0.926658i	$0.622668\pi$
$618$	−12.4966	+	34.9206i	−0.502686	+	1.40471i
$619$	−2.10172	−	7.84372i	−0.0844752	−	0.315266i	0.910739	−	0.412982i	$-0.135513\pi$
$619$	−2.10172	−	7.84372i	−0.0844752	−	0.315266i	−0.995214	+	0.0977165i	$0.968846\pi$
$620$	−2.68677	−	10.4357i	−0.107903	−	0.419107i
$621$	−12.6565	+	3.81474i	−0.507888	+	0.153080i
$622$	−27.6262	−	7.54787i	−1.10771	−	0.302642i
$623$	−6.02076	+	10.4283i	−0.241217	+	0.417799i
$624$	−44.3965	−	16.6287i	−1.77728	−	0.665679i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−5.52085	−	21.0160i	−0.220657	−	0.839967i
$627$	−11.2351	−	7.69544i	−0.448688	−	0.307326i
$628$	3.96939	−	14.2530i	0.158396	−	0.568758i
$629$	8.10370	−	8.10370i	0.323115	−	0.323115i
$630$	−3.29371	−	0.527510i	−0.131224	−	0.0210165i
$631$	−39.2428			−1.56223			−0.781115	−	0.624388i	$-0.785349\pi$
$631$	−39.2428			−1.56223			−0.781115	+	0.624388i	$0.785349\pi$
$632$	−21.7370	+	5.48283i	−0.864651	+	0.218095i
$633$	1.89095	−	5.36696i	0.0751585	−	0.213317i
$634$	3.94460	+	2.30329i	0.156660	+	0.0914755i
$635$	1.76914	−	6.60253i	0.0702063	−	0.262013i
$636$	−9.72220	−	11.5746i	−0.385510	−	0.458964i
$637$	11.3026	+	42.1818i	0.447825	+	1.67130i
$638$	15.2599	+	4.16922i	0.604144	+	0.165061i
$639$	0.924734	−	5.96106i	0.0365819	−	0.235816i
$640$	9.98642	−	5.31710i	0.394748	−	0.210177i
$641$	−32.5708	−	18.8047i	−1.28647	−	0.742743i	−0.308445	−	0.951242i	$-0.599809\pi$
$641$	−32.5708	−	18.8047i	−1.28647	−	0.742743i	−0.978022	+	0.208499i	$0.933142\pi$
$642$	−0.774922	+	9.44560i	−0.0305837	+	0.372788i
$643$	0.771205	−	2.87818i	0.0304134	−	0.113504i	−0.949050	−	0.315124i	$-0.897954\pi$
$643$	0.771205	−	2.87818i	0.0304134	−	0.113504i	0.979464	+	0.201620i	$0.0646205\pi$
$644$	4.00010	+	0.0392511i	0.157626	+	0.00154671i
$645$	0.819077	−	10.6231i	0.0322511	−	0.418284i
$646$	7.73691	+	0.0379584i	0.304405	+	0.00149345i
$647$			45.5577i			1.79106i	0.445002	+	0.895530i	$0.353203\pi$
$647$			45.5577i			1.79106i	−0.445002	+	0.895530i	$0.646797\pi$
$648$	22.7772	−	11.3666i	0.894772	−	0.446523i
$649$			30.2070i			1.18573i
$650$	0.0474772	−	9.67710i	0.00186221	−	0.379567i
$651$	−0.564057	+	7.31559i	−0.0221071	+	0.286721i
$652$	19.7285	−	19.3451i	0.772629	−	0.757614i
$653$	−0.0723613	+	0.270056i	−0.00283172	+	0.0105681i	−0.967327	−	0.253531i	$-0.918408\pi$
$653$	−0.0723613	+	0.270056i	−0.00283172	+	0.0105681i	0.964496	+	0.264099i	$0.0850746\pi$
$654$	−22.8475	−	1.87442i	−0.893407	−	0.0732956i
$655$	10.2559	+	5.92124i	0.400731	+	0.231362i
$656$	−15.0811	−	27.3469i	−0.588818	−	1.06772i
$657$	1.26932	−	8.18236i	0.0495209	−	0.319224i
$658$	2.17765	−	7.97048i	0.0848937	−	0.310722i
$659$	0.725194	+	2.70646i	0.0282495	+	0.105429i	0.978611	−	0.205719i	$-0.0659533\pi$
$659$	0.725194	+	2.70646i	0.0282495	+	0.105429i	−0.950362	+	0.311148i	$0.899287\pi$
$660$	−1.10292	+	12.6799i	−0.0429310	+	0.493563i
$661$	5.45071	−	20.3423i	0.212008	−	0.791225i	−0.775190	−	0.631728i	$-0.782346\pi$
$661$	5.45071	−	20.3423i	0.212008	−	0.791225i	0.987198	−	0.159497i	$-0.0509872\pi$
$662$	−14.8313	+	25.3999i	−0.576434	+	0.987196i
$663$	−10.0695	+	28.5795i	−0.391065	+	1.10993i
$664$	−3.66671	−	2.18956i	−0.142296	−	0.0849712i
$665$	1.68243			0.0652420
$666$	−3.00755	+	18.7788i	−0.116540	+	0.727662i
$667$	−5.47654	+	5.47654i	−0.212053	+	0.212053i
$668$	1.26167	+	2.23566i	0.0488156	+	0.0865003i
$669$	28.6840	+	19.6470i	1.10899	+	0.759595i
$670$	−19.6191	+	5.15390i	−0.757953	+	0.199112i
$671$	1.67720	+	2.90500i	0.0647476	+	0.112146i
$672$	−7.60464	+	1.22971i	−0.293355	+	0.0474372i
$673$	2.03414	−	3.52324i	0.0784105	−	0.135811i	−0.824154	−	0.566366i	$-0.808349\pi$
$673$	2.03414	−	3.52324i	0.0784105	−	0.135811i	0.902564	+	0.430555i	$0.141682\pi$
$674$	6.70921	−	24.5566i	0.258429	−	0.945884i
$675$	3.78616	+	3.55879i	0.145729	+	0.136978i
$676$	−34.3974	+	58.2506i	−1.32298	+	2.24041i
$677$	−0.727070	−	2.71346i	−0.0279436	−	0.104287i	0.950546	−	0.310585i	$-0.100525\pi$
$677$	−0.727070	−	2.71346i	−0.0279436	−	0.104287i	−0.978489	+	0.206298i	$0.933858\pi$
$678$	35.7078	+	12.7783i	1.37135	+	0.490746i
$679$	1.56377	+	2.70854i	0.0600121	+	0.103944i
$680$	−3.52306	−	6.31498i	−0.135103	−	0.242168i
$681$	−7.86073	−	42.0399i	−0.301224	−	1.61097i
$682$	27.9961	+	0.137353i	1.07203	+	0.00525952i
$683$	−2.61236	−	2.61236i	−0.0999593	−	0.0999593i	0.655359	−	0.755318i	$-0.272518\pi$
$683$	−2.61236	−	2.61236i	−0.0999593	−	0.0999593i	−0.755318	+	0.655359i	$0.772518\pi$
$684$	−10.4371	+	7.47767i	−0.399071	+	0.285916i
$685$	2.49348	−	2.49348i	0.0952711	−	0.0952711i
$686$	10.4694	+	10.5727i	0.399725	+	0.403666i
$687$	−4.09755	+	11.6298i	−0.156331	+	0.443705i
$688$	−5.90084	−	23.8878i	−0.224967	−	0.910713i
$689$	−25.8590	+	14.9297i	−0.985151	+	0.568777i
$690$	−5.12377	−	3.54655i	−0.195058	−	0.135015i
$691$	−35.5635	+	9.52921i	−1.35290	+	0.362508i	−0.861204	−	0.508260i	$-0.830289\pi$
$691$	−35.5635	+	9.52921i	−1.35290	+	0.362508i	−0.491695	+	0.870768i	$0.663622\pi$
$692$	−5.37116	−	20.8621i	−0.204181	−	0.793059i
$693$	3.49970	−	7.92815i	0.132943	−	0.301166i
$694$	30.5794	−	17.4556i	1.16078	−	0.662604i
$695$	7.93868	+	4.58340i	0.301131	+	0.173858i
$696$	8.60841	−	12.1796i	0.326301	−	0.461666i
$697$	−17.2865	+	9.98034i	−0.654771	+	0.378032i
$698$	−20.7093	+	35.4666i	−0.783859	+	1.34243i
$699$	−1.18044	−	0.0910158i	−0.0446483	−	0.00344253i
$700$	−0.772828	−	1.36944i	−0.0292101	−	0.0517598i
$701$	21.3468	+	21.3468i	0.806257	+	0.806257i	0.984065	−	0.177808i	$-0.0569007\pi$
$701$	21.3468	+	21.3468i	0.806257	+	0.806257i	−0.177808	+	0.984065i	$0.556901\pi$
$702$	−14.2748	−	48.2156i	−0.538766	−	1.81978i
$703$		−	9.59224i		−	0.361778i
$704$	6.76865	+	28.6035i	0.255103	+	1.07804i
$705$	−9.77395	+	8.37463i	−0.368108	+	0.315407i
$706$	−6.89109	−	26.2320i	−0.259350	−	0.987255i
$707$	12.9194	+	3.46175i	0.485885	+	0.130192i
$708$	26.7672	+	9.72722i	1.00597	+	0.365571i
$709$	−46.9406	+	12.5777i	−1.76289	+	0.472366i	−0.987300	−	0.158868i	$-0.949216\pi$
$709$	−46.9406	+	12.5777i	−1.76289	+	0.472366i	−0.775593	+	0.631234i	$0.782549\pi$
$710$	2.46965	−	1.40974i	0.0926842	−	0.0529067i
$711$	−18.5262	−	14.9050i	−0.694786	−	0.558980i
$712$	31.0786	−	30.1770i	1.16472	−	1.13093i
$713$	−6.85348	+	11.8706i	−0.256665	+	0.444557i
$714$	0.881208	+	4.84420i	0.0329784	+	0.181290i
$715$	24.2851	+	6.50717i	0.908211	+	0.243354i
$716$	−33.9494	−	34.6222i	−1.26875	−	1.29389i
$717$	6.92054	+	14.4501i	0.258452	+	0.539649i
$718$	−29.7939	+	29.5030i	−1.11190	+	1.10104i
$719$	50.6532			1.88905			0.944523	−	0.328446i	$-0.106525\pi$
$719$	50.6532			1.88905			0.944523	+	0.328446i	$0.106525\pi$
$720$	10.8808	+	5.06047i	0.405503	+	0.188593i
$721$	11.9048			0.443357
$722$	−14.4915	+	14.3500i	−0.539317	+	0.534051i
$723$	23.6704	−	34.5581i	0.880311	−	1.28523i
$724$	23.6494	−	23.1898i	0.878922	−	0.861841i
$725$	2.94071	+	0.787960i	0.109215	+	0.0292641i
$726$	−5.76476	−	2.06296i	−0.213950	−	0.0765635i
$727$	−8.72624	+	15.1143i	−0.323638	+	0.560558i	−0.981236	−	0.192811i	$-0.938239\pi$
$727$	−8.72624	+	15.1143i	−0.323638	+	0.560558i	0.657597	+	0.753370i	$0.271573\pi$
$728$	−0.223960	+	15.2153i	−0.00830052	+	0.563918i
$729$	24.1729	+	12.0279i	0.895293	+	0.445477i
$730$	3.38992	−	1.93506i	0.125467	−	0.0716198i
$731$	−15.1911	+	4.07045i	−0.561864	+	0.150551i
$732$	3.11428	−	0.550747i	0.115107	−	0.0203562i
$733$	24.1719	+	6.47685i	0.892811	+	0.239228i	0.675926	−	0.736969i	$-0.263744\pi$
$733$	24.1719	+	6.47685i	0.892811	+	0.239228i	0.216885	+	0.976197i	$0.430410\pi$
$734$	−6.51742	−	24.8096i	−0.240562	−	0.915738i
$735$	−2.03164	−	10.8654i	−0.0749381	−	0.400775i
$736$	−13.8050	−	4.06448i	−0.508860	−	0.149819i
$737$		−	52.7007i		−	1.94125i
$738$	13.5251	−	30.2370i	0.497864	−	1.11304i
$739$	35.3109	+	35.3109i	1.29893	+	1.29893i	0.929098	+	0.369835i	$0.120586\pi$
$739$	35.3109	+	35.3109i	1.29893	+	1.29893i	0.369835	+	0.929098i	$0.379414\pi$
$740$	−7.80770	+	4.40620i	−0.287017	+	0.161975i
$741$	10.9550	+	22.8741i	0.402443	+	0.840302i
$742$	−2.44652	+	4.18989i	−0.0898147	+	0.153816i
$743$	20.2664	−	11.7008i	0.743500	−	0.429260i	−0.0798402	−	0.996808i	$-0.525441\pi$
$743$	20.2664	−	11.7008i	0.743500	−	0.429260i	0.823341	+	0.567547i	$0.192108\pi$
$744$	9.13699	−	24.7639i	0.334978	−	0.907887i
$745$	−16.7457	−	9.66816i	−0.613516	−	0.354214i
$746$	−26.0341	+	14.8610i	−0.953178	+	0.544100i
$747$	−0.487801	−	4.50343i	−0.0178477	−	0.164772i
$748$	18.1937	−	4.68415i	0.665229	−	0.171270i
$749$	2.93834	−	0.787327i	0.107365	−	0.0287683i
$750$	−0.200285	+	2.44129i	−0.00731336	+	0.0891432i
$751$	−20.1859	+	11.6543i	−0.736593	+	0.425272i	−0.820829	−	0.571174i	$-0.806488\pi$
$751$	−20.1859	+	11.6543i	−0.736593	+	0.425272i	0.0842362	+	0.996446i	$0.473155\pi$
$752$	−15.3645	+	25.4455i	−0.560286	+	0.927903i
$753$	−5.63214	−	6.57322i	−0.205247	−	0.239541i
$754$	−20.7301	−	20.9345i	−0.754947	−	0.762391i
$755$	−2.21089	+	2.21089i	−0.0804626	+	0.0804626i
$756$	−5.89837	−	5.65419i	−0.214522	−	0.205641i
$757$	−14.2591	−	14.2591i	−0.518255	−	0.518255i	0.398788	−	0.917043i	$-0.369431\pi$
$757$	−14.2591	−	14.2591i	−0.518255	−	0.518255i	−0.917043	+	0.398788i	$0.869431\pi$
$758$	−15.3574	−	0.0753455i	−0.557805	−	0.00273667i
$759$	12.2939	−	10.5338i	0.446241	−	0.382353i
$760$	−5.82258	−	1.65238i	−0.211207	−	0.0599380i
$761$	12.2151	+	21.1572i	0.442798	+	0.766949i	0.997896	−	0.0648359i	$-0.0206524\pi$
$761$	12.2151	+	21.1572i	0.442798	+	0.766949i	−0.555097	+	0.831785i	$0.687319\pi$
$762$	12.7677	−	10.8316i	0.462526	−	0.392389i
$763$	1.90442	+	7.10741i	0.0689448	+	0.257306i
$764$	12.3920	+	7.31757i	0.448327	+	0.264741i
$765$	3.09735	−	7.01667i	0.111985	−	0.253688i
$766$	−4.40943	+	16.1391i	−0.159319	+	0.583128i
$767$	28.1289	−	48.7207i	1.01568	−	1.75920i
$768$	27.5259	+	3.21299i	0.993256	+	0.115939i
$769$	20.9293	+	36.2506i	0.754729	+	1.30723i	0.945509	+	0.325596i	$0.105565\pi$
$769$	20.9293	+	36.2506i	0.754729	+	1.30723i	−0.190780	+	0.981633i	$0.561102\pi$
$770$	3.95124	−	1.03798i	0.142393	−	0.0374062i
$771$	0.981974	−	0.470294i	0.0353649	−	0.0169372i
$772$	38.2392	−	21.5799i	1.37626	−	0.776679i
$773$	−17.8859	+	17.8859i	−0.643311	+	0.643311i	−0.951368	−	0.308057i	$-0.900321\pi$
$773$	−17.8859	+	17.8859i	−0.643311	+	0.643311i	0.308057	+	0.951368i	$0.400321\pi$
$774$	16.4593	−	20.2539i	0.591617	−	0.728010i
$775$	5.38800			0.193543
$776$	−2.75177	−	10.9096i	−0.0987828	−	0.391630i
$777$	6.00035	−	1.12196i	0.215261	−	0.0402502i
$778$	3.86659	−	6.62189i	0.138624	−	0.237406i
$779$	−4.32408	+	16.1377i	−0.154926	+	0.578192i
$780$	13.5864	−	19.4242i	0.486472	−	0.695498i
$781$	1.91215	+	7.13626i	0.0684223	+	0.255355i
$782$	−2.42420	+	8.87286i	−0.0866890	+	0.317293i
$783$	15.8118	−	0.489468i	0.565068	−	0.0174922i
$784$	−12.3274	−	22.3536i	−0.440265	−	0.798342i
$785$	6.40662	+	3.69886i	0.228662	+	0.132018i
$786$	12.4013	+	26.2235i	0.442341	+	0.935361i
$787$	5.11137	−	19.0759i	0.182201	−	0.679983i	−0.813012	−	0.582247i	$-0.802174\pi$
$787$	5.11137	−	19.0759i	0.182201	−	0.679983i	0.995212	−	0.0977352i	$-0.0311598\pi$
$788$	−33.7399	−	34.4087i	−1.20194	−	1.22576i
$789$	27.6469	+	18.9366i	0.984255	+	0.674160i
$790$	0.0549918	−	11.2088i	0.00195652	−	0.398790i
$791$		−	12.1731i		−	0.432826i
$792$	−19.8983	+	24.0006i	−0.707055	+	0.852825i
$793$		−	6.24726i		−	0.221847i
$794$	−35.7861	−	0.175572i	−1.27000	−	0.00623081i
$795$	6.81656	−	3.26464i	0.241759	−	0.115785i
$796$	0.447881	−	45.6439i	0.0158747	−	1.61780i
$797$	7.88037	−	29.4099i	0.279137	−	1.04175i	−0.673881	−	0.738840i	$-0.735374\pi$
$797$	7.88037	−	29.4099i	0.279137	−	1.04175i	0.953018	−	0.302914i	$-0.0979594\pi$
$798$	3.38855	+	2.34547i	0.119953	+	0.0830289i
$799$	16.4533	+	9.49931i	0.582075	+	0.336061i
$800$	1.32964	+	5.49837i	0.0470098	+	0.194397i
$801$	45.4036	+	7.04342i	1.60426	+	0.248867i
$802$	12.1012	+	3.30622i	0.427308	+	0.116747i
$803$	2.62469	+	9.79547i	0.0926233	+	0.345675i
$804$	−46.6994	−	16.9706i	−1.64696	−	0.598507i
$805$	−0.517676	+	1.93199i	−0.0182457	+	0.0680938i
$806$	−45.0268	−	26.2916i	−1.58600	−	0.926084i
$807$	28.5945	+	33.3724i	1.00658	+	1.17476i
$808$	−41.3117	−	24.6690i	−1.45334	−	0.867854i
$809$	2.92888			0.102974			0.0514870	−	0.998674i	$-0.483604\pi$
$809$	2.92888			0.102974			0.0514870	+	0.998674i	$0.483604\pi$
$810$	2.66432	+	12.4459i	0.0936145	+	0.437306i
$811$	2.93813	−	2.93813i	0.103172	−	0.103172i	−0.653637	−	0.756808i	$-0.726758\pi$
$811$	2.93813	−	2.93813i	0.103172	−	0.103172i	0.756808	+	0.653637i	$0.226758\pi$
$812$	−4.61175	−	1.28434i	−0.161841	−	0.0450716i
$813$	−2.51223	+	32.5826i	−0.0881076	+	1.14272i
$814$	−5.91795	−	22.5276i	−0.207424	−	0.789592i
$815$	6.90765	+	11.9644i	0.241964	+	0.419094i
$816$	1.70797	−	17.6303i	0.0597909	−	0.617185i
$817$	−6.58170	+	11.3998i	−0.230264	+	0.398830i
$818$	−12.0737	−	3.29870i	−0.422145	−	0.115336i
$819$	−13.0274	+	9.52832i	−0.455213	+	0.332947i
$820$	15.1217	−	3.89323i	0.528073	−	0.135957i
$821$	4.67546	+	17.4491i	0.163175	+	0.608976i	0.998266	+	0.0588649i	$0.0187481\pi$
$821$	4.67546	+	17.4491i	0.163175	+	0.608976i	−0.835091	+	0.550111i	$0.814585\pi$
$822$	8.49821	−	1.54591i	0.296409	−	0.0539197i
$823$	21.5753	+	37.3694i	0.752066	+	1.30262i	0.946820	+	0.321764i	$0.104276\pi$
$823$	21.5753	+	37.3694i	0.752066	+	1.30262i	−0.194754	+	0.980852i	$0.562391\pi$
$824$	−41.2001	−	11.6921i	−1.43527	−	0.407313i
$825$	−6.00221	−	2.11477i	−0.208970	−	0.0736269i
$826$	0.0448483	−	9.14125i	0.00156047	−	0.318065i
$827$	−10.4539	−	10.4539i	−0.363519	−	0.363519i	0.501588	−	0.865107i	$-0.332750\pi$
$827$	−10.4539	−	10.4539i	−0.363519	−	0.363519i	−0.865107	+	0.501588i	$0.832750\pi$
$828$	−5.37542	−	14.2860i	−0.186809	−	0.496474i
$829$	19.3699	−	19.3699i	0.672746	−	0.672746i	−0.285602	−	0.958348i	$-0.592194\pi$
$829$	19.3699	−	19.3699i	0.672746	−	0.672746i	0.958348	+	0.285602i	$0.0921936\pi$
$830$	1.51731	−	1.50250i	0.0526667	−	0.0521524i
$831$	0.833649	−	0.155878i	0.0289190	−	0.00540735i
$832$	15.7186	−	52.4374i	0.544944	−	1.81794i
$833$	−14.1301	+	8.15801i	−0.489579	+	0.282658i
$834$	9.59940	+	20.2986i	0.332400	+	0.702883i
$835$	−1.23981	+	0.332207i	−0.0429055	+	0.0114965i
$836$	7.99556	−	13.5401i	0.276532	−	0.468295i
$837$	26.8058	−	8.07939i	0.926542	−	0.279265i
$838$	5.52441	+	9.67789i	0.190837	+	0.334317i
$839$	−14.6540	−	8.46048i	−0.505912	−	0.292088i	0.225240	−	0.974303i	$-0.427683\pi$
$839$	−14.6540	−	8.46048i	−0.505912	−	0.292088i	−0.731152	+	0.682215i	$0.761017\pi$
$840$	0.352590	−	3.83554i	0.0121655	−	0.132339i
$841$	−17.0879	+	9.86568i	−0.589237	+	0.340196i
$842$	43.4125	+	25.3490i	1.49609	+	0.873585i
$843$	31.6430	−	46.1980i	1.08984	−	1.59114i
$844$	6.32975	+	1.76280i	0.217879	+	0.0606780i
$845$	−23.9173	−	23.9173i	−0.822782	−	0.822782i
$846$	−31.3605	+	3.24132i	−1.07820	+	0.111439i
$847$			1.96526i			0.0675272i
$848$	12.5820	−	12.0976i	0.432067	−	0.415433i
$849$	−13.9836	−	4.92687i	−0.479916	−	0.169090i
$850$	3.49697	−	0.918646i	0.119945	−	0.0315093i
$851$	11.0151	+	2.95148i	0.377592	+	0.101175i
$852$	6.93937	+	0.603598i	0.237739	+	0.0206789i
$853$	−11.4619	+	3.07120i	−0.392447	+	0.105156i	−0.449646	−	0.893207i	$-0.648450\pi$
$853$	−11.4619	+	3.07120i	−0.392447	+	0.105156i	0.0571987	+	0.998363i	$0.481783\pi$
$854$	−0.503241	−	0.881600i	−0.0172206	−	0.0301677i
$855$	−2.31963	−	5.98592i	−0.0793296	−	0.204714i
$856$	−10.9423	−	0.161064i	−0.374000	−	0.00550505i
$857$	20.3851	−	35.3079i	0.696340	−	1.20610i	−0.273387	−	0.961904i	$-0.588144\pi$
$857$	20.3851	−	35.3079i	0.696340	−	1.20610i	0.969727	−	0.244192i	$-0.0785228\pi$
$858$	39.8404	+	46.9617i	1.36013	+	1.60324i
$859$	−13.2649	−	3.55431i	−0.452592	−	0.121272i	0.0253201	−	0.999679i	$-0.491939\pi$
$859$	−13.2649	−	3.55431i	−0.452592	−	0.121272i	−0.477912	+	0.878408i	$0.658606\pi$
$860$	12.3023	+	0.120717i	0.419506	+	0.00411641i
$861$	−10.6006	−	0.817340i	−0.361266	−	0.0278549i
$862$	9.27830	+	9.36979i	0.316020	+	0.319136i
$863$	−47.0763			−1.60249			−0.801247	−	0.598333i	$-0.795830\pi$
$863$	−47.0763			−1.60249			−0.801247	+	0.598333i	$0.795830\pi$
$864$	14.8599	+	25.3610i	0.505546	+	0.862800i
$865$	10.7712			0.366233
$866$	−32.8213	−	33.1449i	−1.11531	−	1.12631i
$867$	18.0699	+	1.39325i	0.613687	+	0.0473173i
$868$	−8.47198	−	0.0831315i	−0.287558	−	0.00282167i
$869$	28.1289	+	7.53711i	0.954207	+	0.255679i
$870$	4.82431	+	5.68664i	0.163559	+	0.192795i
$871$	−49.0751	+	85.0005i	−1.66284	+	2.88013i
$872$	0.389589	−	26.4678i	0.0131931	−	0.896312i
$873$	7.48065	−	9.29808i	0.253182	−	0.314692i
$874$	3.81660	+	6.68609i	0.129099	+	0.226160i
$875$	0.759438	−	0.203491i	0.0256737	−	0.00687924i
$876$	9.52522	+	0.828520i	0.321827	+	0.0279931i
$877$	−55.0209	−	14.7428i	−1.85792	−	0.497829i	−0.858048	−	0.513569i	$-0.828323\pi$
$877$	−55.0209	−	14.7428i	−1.85792	−	0.497829i	−0.999876	+	0.0157394i	$0.994990\pi$
$878$	−48.1474	+	12.6482i	−1.62489	+	0.426856i
$879$	2.90249	+	1.02264i	0.0978987	+	0.0344928i
$880$	−14.6939	−	0.288396i	−0.495331	−	0.00972183i
$881$			28.1967i			0.949971i	0.879994	+	0.474986i	$0.157547\pi$
$881$			28.1967i			0.949971i	−0.879994	+	0.474986i	$0.842453\pi$
$882$	11.0555	−	24.7160i	0.372258	−	0.832230i
$883$	27.9056	+	27.9056i	0.939099	+	0.939099i	0.998249	−	0.0591501i	$-0.0188391\pi$
$883$	27.9056	+	27.9056i	0.939099	+	0.939099i	−0.0591501	+	0.998249i	$0.518839\pi$
$884$	−33.7064	−	9.38704i	−1.13367	−	0.315720i
$885$	−8.04693	+	11.7483i	−0.270495	+	0.394915i
$886$	39.3480	+	22.9757i	1.32192	+	0.771883i
$887$	−32.1128	+	18.5403i	−1.07824	+	0.622524i	−0.930422	−	0.366490i	$-0.880559\pi$
$887$	−32.1128	+	18.5403i	−1.07824	+	0.622524i	−0.147821	+	0.989014i	$0.547226\pi$
$888$	−21.8680	−	2.01026i	−0.733841	−	0.0674599i
$889$	−4.65420	−	2.68711i	−0.156097	−	0.0901226i
$890$	10.7376	+	18.8106i	0.359925	+	0.630532i
$891$	−33.0326	−	1.52075i	−1.10664	−	0.0509469i
$892$	−20.4132	+	34.5688i	−0.683483	+	1.15745i
$893$	15.3599	−	4.11567i	0.513999	−	0.137726i
$894$	−20.2488	−	42.8176i	−0.677223	−	1.43203i
$895$	20.9967	−	12.1224i	0.701842	−	0.405209i
$896$	−2.00586	−	8.66604i	−0.0670111	−	0.289512i
$897$	−29.6379	+	5.54177i	−0.989580	+	0.185034i
$898$	−1.31469	+	1.30185i	−0.0438717	+	0.0434433i
$899$	11.5990	−	11.5990i	0.386848	−	0.386848i
$900$	−3.80678	+	4.63772i	−0.126893	+	0.154591i
$901$	−7.88859	−	7.88859i	−0.262807	−	0.262807i
$902$	−0.199030	+	40.5674i	−0.00662696	+	1.35075i
$903$	−7.90091	−	2.78374i	−0.262926	−	0.0926371i
$904$	−11.9556	+	42.1288i	−0.397638	+	1.40118i
$905$	8.28047	+	14.3422i	0.275252	+	0.476751i
$906$	−7.53509	+	1.37071i	−0.250337	+	0.0455387i
$907$	−7.00872	−	26.1569i	−0.232721	−	0.868526i	−0.979163	−	0.203076i	$-0.934906\pi$
$907$	−7.00872	−	26.1569i	−0.232721	−	0.868526i	0.746442	−	0.665450i	$-0.231760\pi$
$908$	47.8252	−	12.3131i	1.58713	−	0.408623i
$909$	−5.49590	−	50.7387i	−0.182287	−	1.68290i
$910$	−7.33949	−	2.00525i	−0.243302	−	0.0664736i
$911$	23.7855	−	41.1977i	0.788049	−	1.36494i	−0.139111	−	0.990277i	$-0.544425\pi$
$911$	23.7855	−	41.1977i	0.788049	−	1.36494i	0.927161	−	0.374664i	$-0.122242\pi$
$912$	−9.42354	−	11.4452i	−0.312045	−	0.378990i
$913$	2.77386	+	4.80447i	0.0918015	+	0.159005i
$914$	10.7724	+	41.0067i	0.356318	+	1.35638i
$915$	−0.121563	+	1.57662i	−0.00401875	+	0.0521215i
$916$	−13.7161	−	3.81986i	−0.453193	−	0.126212i
$917$	6.58379	−	6.58379i	0.217416	−	0.217416i
$918$	16.0202	−	9.81410i	0.528745	−	0.323914i
$919$	−37.4477			−1.23529			−0.617643	−	0.786458i	$-0.711912\pi$
$919$	−37.4477			−1.23529			−0.617643	+	0.786458i	$0.711912\pi$
$920$	3.68905	−	6.17783i	0.121625	−	0.203677i
$921$	−19.0815	−	22.2698i	−0.628757	−	0.733816i
$922$	5.54065	+	3.23524i	0.182471	+	0.106547i
$923$	3.56121	−	13.2906i	0.117219	−	0.437466i
$924$	9.40513	+	3.41783i	0.309406	+	0.112438i
$925$	−1.16018	−	4.32986i	−0.0381466	−	0.142365i
$926$	15.4776	+	4.22871i	0.508626	+	0.138964i
$927$	−16.4135	−	42.3558i	−0.539090	−	1.39115i
$928$	14.6990	+	8.97422i	0.482517	+	0.294593i
$929$	33.0329	+	19.0716i	1.08378	+	0.625718i	0.931912	−	0.362683i	$-0.118139\pi$
$929$	33.0329	+	19.0716i	1.08378	+	0.625718i	0.151863	+	0.988402i	$0.451473\pi$
$930$	10.8518	+	7.51139i	0.355846	+	0.246308i
$931$	−3.53454	+	13.1911i	−0.115840	+	0.432320i
$932$	0.0134140	−	1.36703i	0.000439391	−	0.0447786i
$933$	31.6342	−	15.1505i	1.03566	−	0.496005i
$934$	25.4450	+	0.124837i	0.832586	+	0.00408479i
$935$			9.39352i			0.307201i
$936$	54.4433	−	20.1810i	1.77953	−	0.659638i
$937$		−	15.2548i		−	0.498353i	−0.968458	−	0.249177i	$-0.919840\pi$
$937$		−	15.2548i		−	0.498353i	0.968458	−	0.249177i	$-0.0801600\pi$
$938$	−0.0782445	+	15.9483i	−0.00255477	+	0.520729i
$939$	21.9560	+	15.0386i	0.716507	+	0.490767i
$940$	−10.4056	−	10.6118i	−0.339392	−	0.346119i
$941$	−9.93300	+	37.0705i	−0.323806	+	1.20846i	0.591700	+	0.806158i	$0.298457\pi$
$941$	−9.93300	+	37.0705i	−0.323806	+	1.20846i	−0.915506	+	0.402304i	$0.868210\pi$
$942$	7.74684	+	16.3812i	0.252406	+	0.533729i
$943$	−17.2009	−	9.93095i	−0.560139	−	0.323396i
$944$	−9.13315	+	31.5920i	−0.297259	+	1.02823i
$945$	3.47313	−	2.15117i	0.112981	−	0.0699776i
$946$	−8.42412	+	30.8333i	−0.273892	+	1.00248i
$947$	3.82450	+	14.2732i	0.124280	+	0.463818i	0.999813	−	0.0193398i	$-0.00615645\pi$
$947$	3.82450	+	14.2732i	0.124280	+	0.463818i	−0.875533	+	0.483158i	$0.839490\pi$
$948$	15.7368	−	22.4986i	0.511109	−	0.730721i
$949$	4.88824	−	18.2432i	0.158679	−	0.592198i
$950$	1.52597	−	2.61336i	0.0495089	−	0.0847884i
$951$	−5.49912	+	1.02824i	−0.178321	+	0.0333430i
$952$	−5.51274	+	1.39051i	−0.178669	+	0.0450665i
$953$	−28.9123			−0.936560			−0.468280	−	0.883580i	$-0.655126\pi$
$953$	−28.9123			−0.936560			−0.468280	+	0.883580i	$0.655126\pi$
$954$	18.2803	+	2.92772i	0.591846	+	0.0947883i
$955$	−5.08808	+	5.08808i	−0.164646	+	0.164646i
$956$	−16.1118	+	9.09256i	−0.521094	+	0.294074i
$957$	−17.4738	+	8.36868i	−0.564848	+	0.270521i
$958$	−26.6675	+	7.00550i	−0.861589	+	0.226337i
$959$	−1.38624	−	2.40104i	−0.0447641	−	0.0775338i
$960$	−4.98726	+	12.9278i	−0.160963	+	0.417242i
$961$	−0.984721	+	1.70559i	−0.0317652	+	0.0550189i
$962$	−11.4328	+	41.8454i	−0.368607	+	1.34915i
$963$	−6.85241	−	9.36879i	−0.220816	−	0.301905i
$964$	41.6481	+	24.5935i	1.34139	+	0.792104i
$965$	5.68214	+	21.2060i	0.182915	+	0.682647i
$966$	−3.73602	+	3.16949i	−0.120205	+	0.101977i
$967$	−16.5439	−	28.6548i	−0.532015	−	0.921476i	−0.999301	−	0.0373705i	$-0.988102\pi$
$967$	−16.5439	−	28.6548i	−0.532015	−	0.921476i	0.467287	−	0.884106i	$-0.345232\pi$
$968$	1.93015	−	6.80139i	0.0620374	−	0.218605i
$969$	−7.19571	+	6.16552i	−0.231160	+	0.198065i
$970$	5.62556	+	0.0275998i	0.180626	+	0.000886176i
$971$	−5.48676	−	5.48676i	−0.176078	−	0.176078i	0.613565	−	0.789644i	$-0.289735\pi$
$971$	−5.48676	−	5.48676i	−0.176078	−	0.176078i	−0.789644	+	0.613565i	$0.789735\pi$
$972$	−11.9847	+	28.7814i	−0.384409	+	0.923163i
$973$	5.09625	−	5.09625i	0.163378	−	0.163378i
$974$	−8.82952	−	8.91659i	−0.282916	−	0.285706i
$975$	7.71164	+	9.00018i	0.246970	+	0.288236i
$976$	0.875770	+	3.54530i	0.0280327	+	0.113482i
$977$	19.9543	−	11.5206i	0.638394	−	0.368577i	−0.145602	−	0.989343i	$-0.546512\pi$
$977$	19.9543	−	11.5206i	0.638394	−	0.368577i	0.783996	+	0.620766i	$0.213178\pi$
$978$	−2.76699	+	33.7271i	−0.0884786	+	1.07847i
$979$	−54.3547	+	14.5643i	−1.73718	+	0.465477i
$980$	12.3606	−	3.18236i	0.394845	−	0.101657i
$981$	22.6617	−	16.5749i	0.723532	−	0.529197i
$982$	−32.6427	+	18.6334i	−1.04167	+	0.594615i
$983$	0.808921	+	0.467031i	0.0258006	+	0.0148960i	0.512845	−	0.858481i	$-0.328592\pi$
$983$	0.808921	+	0.467031i	0.0258006	+	0.0148960i	−0.487044	+	0.873377i	$0.661925\pi$
$984$	35.8838	+	13.2398i	1.14393	+	0.422071i
$985$	20.8672	−	12.0477i	0.664883	−	0.383870i
$986$	5.55048	−	9.50570i	0.176763	−	0.302723i
$987$	4.37110	+	9.12686i	0.139134	+	0.290511i
$988$	−25.5046	+	14.3933i	−0.811409	+	0.457911i
$989$	−11.0656	−	11.0656i	−0.351867	−	0.351867i
$990$	−9.14072	−	12.6270i	−0.290511	−	0.401311i
$991$		−	24.3313i		−	0.772908i	−0.922309	−	0.386454i	$-0.873700\pi$
$991$		−	24.3313i		−	0.772908i	0.922309	−	0.386454i	$-0.126300\pi$
$992$	29.2382	+	8.60833i	0.928315	+	0.273315i
$993$	−6.62100	−	35.4097i	−0.210111	−	1.12369i
$994$	−0.568061	−	2.16241i	−0.0180178	−	0.0685876i
$995$	22.0453	+	5.90703i	0.698885	+	0.187266i
$996$	5.15060	−	0.910862i	0.163203	−	0.0288618i
$997$	−44.9076	+	12.0330i	−1.42224	+	0.381088i	−0.886278	−	0.463154i	$-0.846718\pi$
$997$	−44.9076	+	12.0330i	−1.42224	+	0.381088i	−0.535962	+	0.844242i	$0.680051\pi$
$998$	31.7965	−	18.1503i	1.00650	−	0.574538i
$999$	−12.2647	−	19.8017i	−0.388038	−	0.626498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.25	✓	384
9.5	odd	6	inner	720.2.cf.a.491.7	yes	384
16.3	odd	4	inner	720.2.cf.a.371.7	yes	384
144.131	even	12	inner	720.2.cf.a.131.25	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.25	✓	384	1.1	even	1	trivial
720.2.cf.a.131.25	yes	384	144.131	even	12	inner
720.2.cf.a.371.7	yes	384	16.3	odd	4	inner
720.2.cf.a.491.7	yes	384	9.5	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995082 - 1.00489i) q^{2} +(1.72693 + 0.133152i) q^{3} +(-0.0196241 + 1.99990i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.58463 - 1.86787i) q^{6} +(-0.393114 + 0.680893i) q^{7} +(2.02922 - 1.97035i) q^{8} +(2.96454 + 0.459886i) q^{9} +O(q^{10})\)	\(q+(-0.995082 - 1.00489i) q^{2} +(1.72693 + 0.133152i) q^{3} +(-0.0196241 + 1.99990i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.58463 - 1.86787i) q^{6} +(-0.393114 + 0.680893i) q^{7} +(2.02922 - 1.97035i) q^{8} +(2.96454 + 0.459886i) q^{9} +(0.701090 + 1.22820i) q^{10} +(-3.54899 + 0.950948i) q^{11} +(-0.300180 + 3.45107i) q^{12} +(6.60966 + 1.77105i) q^{13} +(1.07541 - 0.282507i) q^{14} +(-1.63362 - 0.575576i) q^{15} +(-3.99923 - 0.0784926i) q^{16} +2.55663i q^{17} +(-2.48782 - 3.43667i) q^{18} +(1.51313 + 1.51313i) q^{19} +(0.536569 - 1.92668i) q^{20} +(-0.769540 + 1.12351i) q^{21} +(4.48713 + 2.62008i) q^{22} +(-2.20315 + 1.27199i) q^{23} +(3.76666 - 3.13245i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.79743 - 8.40435i) q^{26} +(5.05831 + 1.18892i) q^{27} +(-1.35401 - 0.799552i) q^{28} +(2.94071 - 0.787960i) q^{29} +(1.04719 + 2.21436i) q^{30} +(4.66615 - 2.69400i) q^{31} +(3.90068 + 4.09691i) q^{32} +(-6.25546 + 1.16966i) q^{33} +(2.56914 - 2.54406i) q^{34} +(0.555947 - 0.555947i) q^{35} +(-0.977905 + 5.91977i) q^{36} +(-3.16968 - 3.16968i) q^{37} +(0.0148470 - 3.02621i) q^{38} +(11.1786 + 3.93856i) q^{39} +(-2.47004 + 1.37801i) q^{40} +(3.90371 + 6.76142i) q^{41} +(1.89476 - 0.344676i) q^{42} +(1.59211 + 5.94185i) q^{43} +(-1.83216 - 7.11629i) q^{44} +(-2.74450 - 1.21150i) q^{45} +(3.47053 + 0.948199i) q^{46} +(3.71556 - 6.43554i) q^{47} +(-6.89592 - 0.668056i) q^{48} +(3.19092 + 5.52684i) q^{49} +(-0.359319 - 1.36780i) q^{50} +(-0.340420 + 4.41511i) q^{51} +(-3.67164 + 13.1839i) q^{52} +(-3.08554 + 3.08554i) q^{53} +(-3.83869 - 6.26614i) q^{54} +3.67418 q^{55} +(0.543882 + 2.15625i) q^{56} +(2.41158 + 2.81453i) q^{57} +(-3.71806 - 2.17101i) q^{58} +(2.12786 - 7.94129i) q^{59} +(1.18315 - 3.25579i) q^{60} +(-0.236293 - 0.881857i) q^{61} +(-7.35038 - 2.00823i) q^{62} +(-1.47854 + 1.83775i) q^{63} +(0.235459 - 7.99653i) q^{64} +(-5.92606 - 3.42141i) q^{65} +(7.40008 + 5.12216i) q^{66} +(-3.71237 + 13.8548i) q^{67} +(-5.11301 - 0.0501716i) q^{68} +(-3.97404 + 1.90328i) q^{69} +(-1.11188 - 0.00545504i) q^{70} -2.01079i q^{71} +(6.92184 - 4.90797i) q^{72} -2.76008i q^{73} +(-0.0311014 + 6.33928i) q^{74} +(1.42899 + 0.978775i) q^{75} +(-3.05580 + 2.99641i) q^{76} +(0.747662 - 2.79031i) q^{77} +(-7.16575 - 15.1525i) q^{78} +(-6.86402 - 3.96294i) q^{79} +(3.84264 + 1.11089i) q^{80} +(8.57701 + 2.72670i) q^{81} +(2.91000 - 10.6510i) q^{82} +(-0.390797 - 1.45847i) q^{83} +(-2.23181 - 1.56105i) q^{84} +(0.661705 - 2.46952i) q^{85} +(4.38665 - 7.51253i) q^{86} +(5.18330 - 0.969187i) q^{87} +(-5.32797 + 8.92242i) q^{88} +15.3156 q^{89} +(1.51358 + 3.96347i) q^{90} +(-3.80425 + 3.80425i) q^{91} +(-2.50062 - 4.43105i) q^{92} +(8.41680 - 4.03103i) q^{93} +(-10.1643 + 2.67014i) q^{94} +(-1.06994 - 1.85319i) q^{95} +(6.19068 + 7.59444i) q^{96} +(1.98896 - 3.44498i) q^{97} +(2.37866 - 8.70620i) q^{98} +(-10.9584 + 1.18699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more