LMFDB - Embedded newform 570.2.bc.a.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.a.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.66692 - 1.49043i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.49117 - 1.43828i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.66692 - 1.49043i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.49117 - 1.43828i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(-1.38279 - 1.75724i) q^{10} +(1.55090 - 2.68623i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-2.90007 - 3.45617i) q^{13} +(2.70308 - 0.983840i) q^{14} +(2.21321 - 0.318910i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.49399 + 0.968738i) q^{17} -1.00000i q^{18} +(-1.21338 + 4.18661i) q^{19} +(-1.05664 - 1.97066i) q^{20} +(-0.499509 + 2.83285i) q^{21} +(1.99380 - 2.37611i) q^{22} +(3.18560 - 8.75236i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(0.557263 + 4.96885i) q^{25} +(-2.25585 - 3.90726i) q^{26} +(0.866025 + 0.500000i) q^{27} +(2.83285 - 0.499509i) q^{28} +(-0.440638 - 2.49898i) q^{29} +(2.23496 + 0.0702550i) q^{30} +(4.41386 + 7.64503i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.06088 + 2.91473i) q^{33} +(5.24230 + 1.90804i) q^{34} +(-6.29623 - 1.31541i) q^{35} +(0.173648 - 0.984808i) q^{36} +2.27367i q^{37} +(-1.92195 + 3.91230i) q^{38} +4.51171 q^{39} +(-0.698385 - 2.12421i) q^{40} +(-0.333723 - 0.280027i) q^{41} +(-0.983840 + 2.70308i) q^{42} +(-2.93987 - 8.07723i) q^{43} +(2.37611 - 1.99380i) q^{44} +(-1.17832 + 1.90041i) q^{45} +(4.65703 - 8.06622i) q^{46} +(2.24182 - 0.395294i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(0.637287 - 1.10381i) q^{49} +(-0.314035 + 4.99013i) q^{50} +(-4.27356 + 3.58595i) q^{51} +(-1.54310 - 4.23962i) q^{52} +(0.710592 - 1.95234i) q^{53} +(0.766044 + 0.642788i) q^{54} +(-6.58886 + 2.16625i) q^{55} +2.87656 q^{56} +(-2.42718 - 3.62061i) q^{57} -2.53753i q^{58} +(0.356922 - 2.02421i) q^{59} +(2.18881 + 0.457285i) q^{60} +(0.0144765 + 0.00526902i) q^{61} +(3.01926 + 8.29535i) q^{62} +(-1.84901 - 2.20357i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.316970 + 10.0835i) q^{65} +(0.538621 + 3.05467i) q^{66} +(-3.16330 + 0.557775i) q^{67} +(4.83133 + 2.78937i) q^{68} +(4.65703 + 8.06622i) q^{69} +(-5.97216 - 2.38875i) q^{70} +(-11.4145 + 4.15453i) q^{71} +(0.342020 - 0.939693i) q^{72} +(-9.94919 + 11.8570i) q^{73} +(-0.394819 + 2.23913i) q^{74} +(-4.16456 - 2.76703i) q^{75} +(-2.57211 + 3.51912i) q^{76} -8.92249i q^{77} +(4.44317 + 0.783450i) q^{78} +(4.42341 + 3.71168i) q^{79} +(-0.318910 - 2.21321i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.280027 - 0.333723i) q^{82} +(-10.3069 + 5.95067i) q^{83} +(-1.43828 + 2.49117i) q^{84} +(-7.71422 - 9.80319i) q^{85} +(-1.49261 - 8.46502i) q^{86} +(2.19757 + 1.26877i) q^{87} +(2.68623 - 1.55090i) q^{88} +(-2.57903 + 2.16406i) q^{89} +(-1.49043 + 1.66692i) q^{90} +(-12.1955 - 4.43880i) q^{91} +(5.98697 - 7.13499i) q^{92} +(-8.69361 - 1.53292i) q^{93} +2.27641 q^{94} +(8.26245 - 5.17029i) q^{95} -1.00000 q^{96} +(18.9274 + 3.33742i) q^{97} +(0.819280 - 0.976380i) q^{98} +(-2.91473 - 1.06088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{5}+O(q^{10}) $ 60 * q - 6 * q^5	$ 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.642788	+	0.766044i	−0.371114	+	0.442276i
$3$	−0.642788	+	0.766044i	−0.371114	+	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−1.66692	−	1.49043i	−0.745471	−	0.666539i
$5$	−1.66692	−	1.49043i	−0.745471	−	0.666539i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	2.49117	−	1.43828i	0.941574	−	0.543618i	0.0511206	−	0.998692i	$-0.483721\pi$
$7$	2.49117	−	1.43828i	0.941574	−	0.543618i	0.890453	+	0.455075i	$0.150387\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	−1.38279	−	1.75724i	−0.437276	−	0.555688i
$11$	1.55090	−	2.68623i	0.467613	−	0.809930i	−0.531702	−	0.846932i	$-0.678447\pi$
$11$	1.55090	−	2.68623i	0.467613	−	0.809930i	0.999315	+	0.0370015i	$0.0117806\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−2.90007	−	3.45617i	−0.804335	−	0.958569i	0.195420	−	0.980720i	$-0.437393\pi$
$13$	−2.90007	−	3.45617i	−0.804335	−	0.958569i	−0.999755	+	0.0221506i	$0.992949\pi$
$14$	2.70308	−	0.983840i	0.722428	−	0.262942i
$15$	2.21321	−	0.318910i	0.571448	−	0.0823421i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	5.49399	+	0.968738i	1.33249	+	0.234954i	0.794122	−	0.607758i	$-0.207931\pi$
$17$	5.49399	+	0.968738i	1.33249	+	0.234954i	0.538366	+	0.842711i	$0.319042\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.21338	+	4.18661i	−0.278370	+	0.960474i
$19$	−1.21338	+	4.18661i	−0.278370	+	0.960474i
$20$	−1.05664	−	1.97066i	−0.236272	−	0.440654i
$21$	−0.499509	+	2.83285i	−0.109002	+	0.618180i
$22$	1.99380	−	2.37611i	0.425079	−	0.506589i
$23$	3.18560	−	8.75236i	0.664243	−	1.82499i	0.107685	−	0.994185i	$-0.465656\pi$
$23$	3.18560	−	8.75236i	0.664243	−	1.82499i	0.556559	−	0.830808i	$-0.312122\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	0.557263	+	4.96885i	0.111453	+	0.993770i
$26$	−2.25585	−	3.90726i	−0.442410	−	0.766276i
$27$	0.866025	+	0.500000i	0.166667	+	0.0962250i
$28$	2.83285	−	0.499509i	0.535359	−	0.0943983i
$29$	−0.440638	−	2.49898i	−0.0818245	−	0.464050i	−0.997997	−	0.0632650i	$-0.979849\pi$
$29$	−0.440638	−	2.49898i	−0.0818245	−	0.464050i	0.916172	−	0.400785i	$-0.131262\pi$
$30$	2.23496	+	0.0702550i	0.408047	+	0.0128267i
$31$	4.41386	+	7.64503i	0.792753	+	1.37309i	0.924256	+	0.381773i	$0.124686\pi$
$31$	4.41386	+	7.64503i	0.792753	+	1.37309i	−0.131503	+	0.991316i	$0.541980\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	1.06088	+	2.91473i	0.184675	+	0.507390i
$34$	5.24230	+	1.90804i	0.899048	+	0.327227i
$35$	−6.29623	−	1.31541i	−1.06426	−	0.222344i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$			2.27367i			0.373790i	0.982380	+	0.186895i	$0.0598424\pi$
$37$			2.27367i			0.373790i	−0.982380	+	0.186895i	$0.940158\pi$
$38$	−1.92195	+	3.91230i	−0.311781	+	0.634659i
$39$	4.51171			0.722452
$40$	−0.698385	−	2.12421i	−0.110424	−	0.335867i
$41$	−0.333723	−	0.280027i	−0.0521188	−	0.0437329i	0.616356	−	0.787467i	$-0.288608\pi$
$41$	−0.333723	−	0.280027i	−0.0521188	−	0.0437329i	−0.668475	+	0.743735i	$0.733053\pi$
$42$	−0.983840	+	2.70308i	−0.151810	+	0.417094i
$43$	−2.93987	−	8.07723i	−0.448326	−	1.23177i	−0.933889	−	0.357564i	$-0.883607\pi$
$43$	−2.93987	−	8.07723i	−0.448326	−	1.23177i	0.485562	−	0.874202i	$-0.338615\pi$
$44$	2.37611	−	1.99380i	0.358213	−	0.300576i
$45$	−1.17832	+	1.90041i	−0.175654	+	0.283296i
$46$	4.65703	−	8.06622i	0.686642	−	1.18930i
$47$	2.24182	−	0.395294i	0.327003	−	0.0576595i	−0.00773655	−	0.999970i	$-0.502463\pi$
$47$	2.24182	−	0.395294i	0.327003	−	0.0576595i	0.334740	+	0.942311i	$0.391352\pi$
$48$	−0.984808	+	0.173648i	−0.142145	+	0.0250640i
$49$	0.637287	−	1.10381i	0.0910410	−	0.157688i
$50$	−0.314035	+	4.99013i	−0.0444112	+	0.705711i
$51$	−4.27356	+	3.58595i	−0.598419	+	0.502133i
$52$	−1.54310	−	4.23962i	−0.213989	−	0.587930i
$53$	0.710592	−	1.95234i	0.0976073	−	0.268174i	−0.881273	−	0.472607i	$-0.843313\pi$
$53$	0.710592	−	1.95234i	0.0976073	−	0.268174i	0.978880	+	0.204433i	$0.0655352\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	−6.58886	+	2.16625i	−0.888442	+	0.292097i
$56$	2.87656			0.384396
$57$	−2.42718	−	3.62061i	−0.321488	−	0.479561i
$58$		−	2.53753i		−	0.333195i
$59$	0.356922	−	2.02421i	0.0464673	−	0.263529i	−0.952719	−	0.303852i	$-0.901727\pi$
$59$	0.356922	−	2.02421i	0.0464673	−	0.263529i	0.999187	+	0.0403222i	$0.0128384\pi$
$60$	2.18881	+	0.457285i	0.282574	+	0.0590353i
$61$	0.0144765	+	0.00526902i	0.00185353	+	0.000674629i	0.342947	−	0.939355i	$-0.388575\pi$
$61$	0.0144765	+	0.00526902i	0.00185353	+	0.000674629i	−0.341093	+	0.940029i	$0.610797\pi$
$62$	3.01926	+	8.29535i	0.383446	+	1.05351i
$63$	−1.84901	−	2.20357i	−0.232954	−	0.277624i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.316970	+	10.0835i	−0.0393153	+	1.25071i
$66$	0.538621	+	3.05467i	0.0662997	+	0.376004i
$67$	−3.16330	+	0.557775i	−0.386459	+	0.0681431i	−0.363502	−	0.931593i	$-0.618419\pi$
$67$	−3.16330	+	0.557775i	−0.386459	+	0.0681431i	−0.0229566	+	0.999736i	$0.507308\pi$
$68$	4.83133	+	2.78937i	0.585885	+	0.338261i
$69$	4.65703	+	8.06622i	0.560641	+	0.971059i
$70$	−5.97216	−	2.38875i	−0.713810	−	0.285510i
$71$	−11.4145	+	4.15453i	−1.35465	+	0.493052i	−0.914395	−	0.404822i	$-0.867333\pi$
$71$	−11.4145	+	4.15453i	−1.35465	+	0.493052i	−0.440253	+	0.897874i	$0.645111\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	−9.94919	+	11.8570i	−1.16446	+	1.38776i	−0.257644	+	0.966240i	$0.582946\pi$
$73$	−9.94919	+	11.8570i	−1.16446	+	1.38776i	−0.906821	+	0.421515i	$0.861498\pi$
$74$	−0.394819	+	2.23913i	−0.0458968	+	0.260294i
$75$	−4.16456	−	2.76703i	−0.480882	−	0.319509i
$76$	−2.57211	+	3.51912i	−0.295042	+	0.403671i
$77$		−	8.92249i		−	1.01681i
$78$	4.44317	+	0.783450i	0.503090	+	0.0887083i
$79$	4.42341	+	3.71168i	0.497673	+	0.417597i	0.856767	−	0.515705i	$-0.172470\pi$
$79$	4.42341	+	3.71168i	0.497673	+	0.417597i	−0.359094	+	0.933301i	$0.616914\pi$
$80$	−0.318910	−	2.21321i	−0.0356552	−	0.247444i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−0.280027	−	0.333723i	−0.0309238	−	0.0368535i
$83$	−10.3069	+	5.95067i	−1.13132	+	0.653171i	−0.944268	−	0.329178i	$-0.893228\pi$
$83$	−10.3069	+	5.95067i	−1.13132	+	0.653171i	−0.187057	+	0.982349i	$0.559895\pi$
$84$	−1.43828	+	2.49117i	−0.156929	+	0.271809i
$85$	−7.71422	−	9.80319i	−0.836725	−	1.06331i
$86$	−1.49261	−	8.46502i	−0.160952	−	0.912807i
$87$	2.19757	+	1.26877i	0.235604	+	0.136026i
$88$	2.68623	−	1.55090i	0.286354	−	0.165326i
$89$	−2.57903	+	2.16406i	−0.273376	+	0.229390i	−0.769160	−	0.639056i	$-0.779325\pi$
$89$	−2.57903	+	2.16406i	−0.273376	+	0.229390i	0.495784	+	0.868446i	$0.334881\pi$
$90$	−1.49043	+	1.66692i	−0.157105	+	0.175709i
$91$	−12.1955	−	4.43880i	−1.27844	−	0.465313i
$92$	5.98697	−	7.13499i	0.624185	−	0.743874i
$93$	−8.69361	−	1.53292i	−0.901486	−	0.158956i
$94$	2.27641			0.234793
$95$	8.26245	−	5.17029i	0.847709	−	0.530461i
$96$	−1.00000			−0.102062
$97$	18.9274	+	3.33742i	1.92179	+	0.338863i	0.998929	−	0.0462733i	$-0.0147345\pi$
$97$	18.9274	+	3.33742i	1.92179	+	0.338863i	0.922860	+	0.385136i	$0.125846\pi$
$98$	0.819280	−	0.976380i	0.0827598	−	0.0986293i
$99$	−2.91473	−	1.06088i	−0.292942	−	0.106622i
$100$	−1.17579	+	4.85979i	−0.117579	+	0.485979i
$101$	7.17155	−	6.01765i	0.713596	−	0.598778i	−0.212009	−	0.977268i	$-0.568001\pi$
$101$	7.17155	−	6.01765i	0.713596	−	0.598778i	0.925606	+	0.378489i	$0.123556\pi$
$102$	−4.83133	+	2.78937i	−0.478373	+	0.276189i
$103$	−1.59094	−	0.918531i	−0.156760	−	0.0905056i	0.419568	−	0.907724i	$-0.362182\pi$
$103$	−1.59094	−	0.918531i	−0.156760	−	0.0905056i	−0.576328	+	0.817218i	$0.695515\pi$
$104$	−0.783450	−	4.44317i	−0.0768236	−	0.435688i
$105$	5.05480	−	3.97767i	0.493298	−	0.388181i
$106$	1.03882	−	1.79928i	0.100899	−	0.174762i
$107$	−12.5290	+	7.23363i	−1.21123	+	0.699301i	−0.963026	−	0.269408i	$-0.913172\pi$
$107$	−12.5290	+	7.23363i	−1.21123	+	0.699301i	−0.248199	+	0.968709i	$0.579839\pi$
$108$	0.642788	+	0.766044i	0.0618523	+	0.0737127i
$109$	6.62231	−	2.41032i	0.634302	−	0.230867i	−0.00480053	−	0.999988i	$-0.501528\pi$
$109$	6.62231	−	2.41032i	0.634302	−	0.230867i	0.639103	+	0.769121i	$0.279306\pi$
$110$	−6.86492	+	0.989193i	−0.654545	+	0.0943159i
$111$	−1.74174	−	1.46149i	−0.165318	−	0.138718i
$112$	2.83285	+	0.499509i	0.267680	+	0.0471991i
$113$		−	1.99521i		−	0.187694i	−0.995587	−	0.0938470i	$-0.970084\pi$
$113$		−	1.99521i		−	0.187694i	0.995587	−	0.0938470i	$-0.0299165\pi$
$114$	−1.76159	−	3.98708i	−0.164988	−	0.373424i
$115$	−18.3549	+	9.84161i	−1.71160	+	0.917735i
$116$	0.440638	−	2.49898i	0.0409122	−	0.232025i
$117$	−2.90007	+	3.45617i	−0.268112	+	0.319523i
$118$	0.703000	−	1.93148i	0.0647164	−	0.177807i
$119$	15.0798	−	5.48859i	1.38236	−	0.503138i
$120$	2.07615	+	0.830421i	0.189526	+	0.0758067i
$121$	0.689431	+	1.19413i	0.0626755	+	0.108557i
$122$	0.0133416	+	0.00770279i	0.00120789	+	0.000697378i
$123$	0.429026	−	0.0756489i	0.0386840	−	0.00682103i
$124$	1.53292	+	8.69361i	0.137660	+	0.780709i
$125$	6.47679	−	9.11325i	0.579301	−	0.815113i
$126$	−1.43828	−	2.49117i	−0.128132	−	0.221931i
$127$	−10.4526	−	12.4569i	−0.927516	−	1.10537i	−0.994195	−	0.107596i	$-0.965685\pi$
$127$	−10.4526	−	12.4569i	−0.927516	−	1.10537i	0.0666783	−	0.997775i	$-0.478760\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	8.07723	+	2.93987i	0.711161	+	0.258841i
$130$	−2.06314	+	9.87528i	−0.180949	+	0.866119i
$131$	−0.330789	+	1.87600i	−0.0289012	+	0.163907i	−0.995842	−	0.0910925i	$-0.970964\pi$
$131$	−0.330789	+	1.87600i	−0.0289012	+	0.163907i	0.966941	+	0.254999i	$0.0820752\pi$
$132$			3.10180i			0.269977i
$133$	2.99876	+	12.1747i	0.260025	+	1.05568i
$134$	−3.21210			−0.277483
$135$	−0.698385	−	2.12421i	−0.0601074	−	0.182823i
$136$	4.27356	+	3.58595i	0.366455	+	0.307492i
$137$	2.08341	−	5.72411i	0.177997	−	0.489044i	−0.818322	−	0.574760i	$-0.805096\pi$
$137$	2.08341	−	5.72411i	0.177997	−	0.489044i	0.996320	+	0.0857159i	$0.0273177\pi$
$138$	3.18560	+	8.75236i	0.271176	+	0.745050i
$139$	6.16568	−	5.17362i	0.522967	−	0.438821i	−0.342698	−	0.939446i	$-0.611341\pi$
$139$	6.16568	−	5.17362i	0.522967	−	0.438821i	0.865664	+	0.500625i	$0.166896\pi$
$140$	−5.46663	−	3.38952i	−0.462015	−	0.286466i
$141$	−1.13820	+	1.97143i	−0.0958540	+	0.166024i
$142$	−11.9625	+	2.10931i	−1.00387	+	0.177009i
$143$	−13.7818	+	2.43010i	−1.15249	+	0.203215i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−2.99004	+	4.82235i	−0.248309	+	0.400474i
$146$	−11.8570	+	9.94919i	−0.981291	+	0.823401i
$147$	0.435930	+	1.19771i	0.0359549	+	0.0987852i
$148$	−0.777642	+	2.13655i	−0.0639218	+	0.175624i
$149$	6.05471	+	5.08050i	0.496021	+	0.416211i	0.856178	−	0.516681i	$-0.172833\pi$
$149$	6.05471	+	5.08050i	0.496021	+	0.416211i	−0.360157	+	0.932892i	$0.617277\pi$
$150$	−3.62080	−	3.44816i	−0.295637	−	0.281541i
$151$	−19.7088			−1.60388			−0.801939	−	0.597406i	$-0.796198\pi$
$151$	−19.7088			−1.60388			−0.801939	+	0.597406i	$0.796198\pi$
$152$	−3.14413	+	3.01902i	−0.255022	+	0.244875i
$153$		−	5.57874i		−	0.451015i
$154$	1.54937	−	8.78694i	0.124852	−	0.708072i
$155$	4.03679	−	19.3222i	0.324243	−	1.55200i
$156$	4.23962	+	1.54310i	0.339441	+	0.123547i
$157$	8.25953	+	22.6929i	0.659182	+	1.81109i	0.580612	+	0.814180i	$0.302813\pi$
$157$	8.25953	+	22.6929i	0.659182	+	1.81109i	0.0785706	+	0.996909i	$0.474964\pi$
$158$	3.71168	+	4.42341i	0.295286	+	0.351908i
$159$	1.03882	+	1.79928i	0.0823835	+	0.142692i
$160$	0.0702550	−	2.23496i	0.00555414	−	0.176689i
$161$	−4.65246	−	26.3854i	−0.366665	−	2.07946i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	13.0752	+	7.54898i	1.02413	+	0.591282i	0.915297	−	0.402778i	$-0.131956\pi$
$163$	13.0752	+	7.54898i	1.02413	+	0.591282i	0.108832	+	0.994060i	$0.465289\pi$
$164$	−0.217822	−	0.377279i	−0.0170091	−	0.0294606i
$165$	2.57580	−	6.43980i	0.200525	−	0.501337i
$166$	−11.1836	+	4.07050i	−0.868016	+	0.315932i
$167$	−7.72393	+	21.2213i	−0.597696	+	1.64216i	0.158158	+	0.987414i	$0.449445\pi$
$167$	−7.72393	+	21.2213i	−0.597696	+	1.64216i	−0.755853	+	0.654741i	$0.772778\pi$
$168$	−1.84901	+	2.20357i	−0.142655	+	0.170009i
$169$	−1.27727	+	7.24378i	−0.0982518	+	0.557214i
$170$	−5.89472	−	10.9938i	−0.452104	−	0.843188i
$171$	4.33371	+	0.467954i	0.331407	+	0.0357853i
$172$		−	8.59561i		−	0.655409i
$173$	19.1625	+	3.37887i	1.45690	+	0.256891i	0.845307	−	0.534281i	$-0.179417\pi$
$173$	19.1625	+	3.37887i	1.45690	+	0.256891i	0.611594	+	0.791172i	$0.290529\pi$
$174$	1.94386	+	1.63110i	0.147364	+	0.123653i
$175$	8.53482	+	11.5768i	0.645172	+	0.875120i
$176$	2.91473	−	1.06088i	0.219706	−	0.0799666i
$177$	1.32121	+	1.57455i	0.0993080	+	0.118351i
$178$	−2.91563	+	1.68334i	−0.218536	+	0.126172i
$179$	−7.51486	+	13.0161i	−0.561687	+	0.972871i	0.435662	+	0.900110i	$0.356514\pi$
$179$	−7.51486	+	13.0161i	−0.561687	+	0.972871i	−0.997349	+	0.0727606i	$0.976819\pi$
$180$	−1.75724	+	1.38279i	−0.130977	+	0.103067i
$181$	1.88610	+	10.6966i	0.140192	+	0.795071i	0.971102	+	0.238664i	$0.0767094\pi$
$181$	1.88610	+	10.6966i	0.140192	+	0.795071i	−0.830910	+	0.556407i	$0.812179\pi$
$182$	−11.2394	−	6.48909i	−0.833123	−	0.481004i
$183$	−0.0133416	+	0.00770279i	−0.000986242	+	0.000569407i
$184$	7.13499	−	5.98697i	0.525998	−	0.441365i
$185$	3.38874	−	3.79004i	0.249145	−	0.278649i
$186$	−8.29535	−	3.01926i	−0.608244	−	0.221383i
$187$	11.1229	−	13.2557i	0.813385	−	0.969355i
$188$	2.24182	+	0.395294i	0.163502	+	0.0288298i
$189$	2.87656			0.209239
$190$	9.03474	−	3.65699i	0.655449	−	0.265306i
$191$	18.1221			1.31127			0.655636	−	0.755077i	$-0.272401\pi$
$191$	18.1221			1.31127			0.655636	+	0.755077i	$0.272401\pi$
$192$	−0.984808	−	0.173648i	−0.0710724	−	0.0125320i
$193$	−5.64743	+	6.73034i	−0.406511	+	0.484461i	−0.929994	−	0.367575i	$-0.880188\pi$
$193$	−5.64743	+	6.73034i	−0.406511	+	0.484461i	0.523483	+	0.852036i	$0.324632\pi$
$194$	18.0603	+	6.57342i	1.29666	+	0.471944i
$195$	−7.52067	−	6.72437i	−0.538566	−	0.481542i
$196$	0.976380	−	0.819280i	0.0697414	−	0.0585200i
$197$	−7.09065	+	4.09379i	−0.505188	+	0.291670i	−0.730853	−	0.682534i	$-0.760878\pi$
$197$	−7.09065	+	4.09379i	−0.505188	+	0.291670i	0.225665	+	0.974205i	$0.427544\pi$
$198$	−2.68623	−	1.55090i	−0.190902	−	0.110218i
$199$	−2.91057	−	16.5067i	−0.206325	−	1.17013i	−0.895341	−	0.445380i	$-0.853068\pi$
$199$	−2.91057	−	16.5067i	−0.206325	−	1.17013i	0.689017	−	0.724745i	$-0.258043\pi$
$200$	−2.00182	+	4.58178i	−0.141550	+	0.323981i
$201$	1.60605	−	2.78176i	0.113282	−	0.196210i
$202$	8.10756	−	4.68090i	0.570446	−	0.329347i
$203$	−4.69194	−	5.59163i	−0.329310	−	0.392456i
$204$	−5.24230	+	1.90804i	−0.367035	+	0.133590i
$205$	0.138931	+	0.964173i	0.00970338	+	0.0673407i
$206$	−1.40727	−	1.18084i	−0.0980492	−	0.0822731i
$207$	−9.17257	−	1.61737i	−0.637537	−	0.112415i
$208$		−	4.51171i		−	0.312831i
$209$	9.36438	+	9.75244i	0.647747	+	0.674590i
$210$	5.66872	−	3.03948i	0.391179	−	0.209744i
$211$	−3.25836	+	18.4791i	−0.224315	+	1.27215i	0.639676	+	0.768645i	$0.279069\pi$
$211$	−3.25836	+	18.4791i	−0.224315	+	1.27215i	−0.863991	+	0.503508i	$0.832043\pi$
$212$	1.33548	−	1.59156i	0.0917209	−	0.109309i
$213$	4.15453	−	11.4145i	0.284663	−	0.782106i
$214$	−13.5948	+	4.94809i	−0.929320	+	0.338245i
$215$	−7.13797	+	17.8458i	−0.486806	+	1.21707i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	21.9914	+	12.6967i	1.49287	+	0.861910i
$218$	6.94025	−	1.22375i	0.470053	−	0.0828830i
$219$	−2.68776	−	15.2430i	−0.181622	−	1.03003i
$220$	−6.93240	−	0.217917i	−0.467382	−	0.0146919i
$221$	−12.5848	−	21.7976i	−0.846547	−	1.46626i
$222$	−1.46149	−	1.74174i	−0.0980888	−	0.116898i
$223$	1.58948	+	4.36707i	0.106440	+	0.292441i	0.981466	−	0.191634i	$-0.0613786\pi$
$223$	1.58948	+	4.36707i	0.106440	+	0.292441i	−0.875027	+	0.484074i	$0.839156\pi$
$224$	2.70308	+	0.983840i	0.180607	+	0.0657356i
$225$	4.79659	−	1.41163i	0.319773	−	0.0941086i
$226$	0.346465	−	1.96490i	0.0230465	−	0.130703i
$227$		−	9.45349i		−	0.627450i	−0.949514	−	0.313725i	$-0.898423\pi$
$227$		−	9.45349i		−	0.627450i	0.949514	−	0.313725i	$-0.101577\pi$
$228$	−1.04248	−	4.23240i	−0.0690401	−	0.280298i
$229$	14.1280			0.933603			0.466802	−	0.884362i	$-0.345406\pi$
$229$	14.1280			0.933603			0.466802	+	0.884362i	$0.345406\pi$
$230$	−19.7850	+	6.50480i	−1.30459	+	0.428914i
$231$	6.83502	+	5.73527i	0.449712	+	0.377353i
$232$	0.867888	−	2.38450i	0.0569796	−	0.156550i
$233$	−1.22486	−	3.36527i	−0.0802432	−	0.220466i	0.893083	−	0.449892i	$-0.148538\pi$
$233$	−1.22486	−	3.36527i	−0.0802432	−	0.220466i	−0.973326	+	0.229425i	$0.926315\pi$
$234$	−3.45617	+	2.90007i	−0.225937	+	0.189584i
$235$	−4.32610	−	2.68235i	−0.282204	−	0.174977i
$236$	1.02772	−	1.78006i	0.0668987	−	0.115872i
$237$	−5.68663	+	1.00271i	−0.369386	+	0.0651328i
$238$	15.8038	−	2.78663i	1.02441	−	0.180630i
$239$	1.56990	−	2.71915i	0.101548	−	0.175887i	−0.810774	−	0.585359i	$-0.800954\pi$
$239$	1.56990	−	2.71915i	0.101548	−	0.175887i	0.912323	+	0.409472i	$0.134287\pi$
$240$	1.90041	+	1.17832i	0.122671	+	0.0760605i
$241$	7.69139	−	6.45384i	0.495446	−	0.415729i	−0.360527	−	0.932749i	$-0.617403\pi$
$241$	7.69139	−	6.45384i	0.495446	−	0.415729i	0.855973	+	0.517020i	$0.172959\pi$
$242$	0.471599	+	1.29571i	0.0303155	+	0.0832912i
$243$	0.342020	−	0.939693i	0.0219406	−	0.0602813i
$244$	0.0118014	+	0.00990252i	0.000755505	+	0.000633944i
$245$	−2.70746	+	0.890143i	−0.172973	+	0.0568691i
$246$	0.435644			0.0277757
$247$	17.9885	−	7.94780i	1.14458	−	0.505706i
$248$			8.82772i			0.560561i
$249$	2.06665	−	11.7205i	0.130968	−	0.742758i
$250$	7.96089	−	7.85011i	0.503491	−	0.496485i
$251$	7.61227	+	2.77064i	0.480483	+	0.174881i	0.570895	−	0.821023i	$-0.306596\pi$
$251$	7.61227	+	2.77064i	0.480483	+	0.174881i	−0.0904125	+	0.995904i	$0.528819\pi$
$252$	−0.983840	−	2.70308i	−0.0619761	−	0.170278i
$253$	−18.5704	−	22.1313i	−1.16751	−	1.39138i
$254$	−8.13066	−	14.0827i	−0.510163	−	0.883628i
$255$	12.4683	+	0.391935i	0.780795	+	0.0245439i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.35126	+	0.414591i	−0.146668	+	0.0258615i	−0.246500	−	0.969143i	$-0.579280\pi$
$257$	−2.35126	+	0.414591i	−0.146668	+	0.0258615i	0.0998322	+	0.995004i	$0.468169\pi$
$258$	7.44402	+	4.29780i	0.463444	+	0.267570i
$259$	3.27018	+	5.66411i	0.203199	+	0.351951i
$260$	−3.74662	+	9.36699i	−0.232355	+	0.580916i
$261$	−2.38450	+	0.867888i	−0.147597	+	0.0537209i
$262$	−0.651527	+	1.79006i	−0.0402515	+	0.110590i
$263$	14.3463	−	17.0973i	0.884633	−	1.05426i	−0.113521	−	0.993536i	$-0.536213\pi$
$263$	14.3463	−	17.0973i	0.884633	−	1.05426i	0.998154	−	0.0607290i	$-0.0193425\pi$
$264$	−0.538621	+	3.05467i	−0.0331498	+	0.188002i
$265$	−4.09431	+	2.19531i	−0.251512	+	0.134857i
$266$	0.839080	+	12.5105i	0.0514473	+	0.767069i
$267$		−	3.36668i		−	0.206038i
$268$	−3.16330	−	0.557775i	−0.193229	−	0.0340715i
$269$	2.66580	+	2.23687i	0.162537	+	0.136384i	0.720428	−	0.693529i	$-0.243945\pi$
$269$	2.66580	+	2.23687i	0.162537	+	0.136384i	−0.557892	+	0.829914i	$0.688390\pi$
$270$	−0.318910	−	2.21321i	−0.0194082	−	0.134692i
$271$	−7.14339	+	2.59998i	−0.433930	+	0.157938i	−0.549744	−	0.835333i	$-0.685275\pi$
$271$	−7.14339	+	2.59998i	−0.433930	+	0.157938i	0.115814	+	0.993271i	$0.463052\pi$
$272$	3.58595	+	4.27356i	0.217430	+	0.259123i
$273$	11.2394	−	6.48909i	0.680242	−	0.392738i
$274$	3.04574	−	5.27537i	0.184000	−	0.318697i
$275$	14.2117	+	6.20924i	0.857001	+	0.374431i
$276$	1.61737	+	9.17257i	0.0973543	+	0.552124i
$277$	−7.19711	−	4.15525i	−0.432432	−	0.249665i	0.267950	−	0.963433i	$-0.413654\pi$
$277$	−7.19711	−	4.15525i	−0.432432	−	0.249665i	−0.700382	+	0.713768i	$0.746987\pi$
$278$	6.97040	−	4.02436i	0.418057	−	0.241365i
$279$	6.76243	−	5.67435i	0.404856	−	0.339715i
$280$	−4.79500	−	4.28729i	−0.286556	−	0.256215i
$281$	29.7114	+	10.8141i	1.77244	+	0.645114i	0.999949	+	0.0100820i	$0.00320925\pi$
$281$	29.7114	+	10.8141i	1.77244	+	0.645114i	0.772486	+	0.635032i	$0.219013\pi$
$282$	−1.46325	+	1.74383i	−0.0871350	+	0.103843i
$283$	−2.88467	−	0.508646i	−0.171476	−	0.0302359i	0.0872508	−	0.996186i	$-0.472192\pi$
$283$	−2.88467	−	0.508646i	−0.171476	−	0.0302359i	−0.258727	+	0.965951i	$0.583303\pi$
$284$	−12.1470			−0.720793
$285$	−1.35032	+	9.65280i	−0.0799863	+	0.571783i
$286$	−13.9944			−0.827506
$287$	−1.23412	−	0.217608i	−0.0728477	−	0.0128450i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	13.2707	+	4.83013i	0.780628	+	0.284125i
$290$	−3.78201	+	4.22987i	−0.222087	+	0.248387i
$291$	−14.7229	+	12.3540i	−0.863073	+	0.724204i
$292$	−13.4045	+	7.73910i	−0.784440	+	0.452896i
$293$	−13.9019	−	8.02629i	−0.812160	−	0.468901i	0.0355451	−	0.999368i	$-0.488683\pi$
$293$	−13.9019	−	8.02629i	−0.812160	−	0.468901i	−0.847706	+	0.530467i	$0.822017\pi$
$294$	0.221327	+	1.25521i	0.0129081	+	0.0732053i
$295$	−3.61189	+	2.84223i	−0.210292	+	0.165481i
$296$	−1.13684	+	1.96906i	−0.0660773	+	0.114449i
$297$	2.68623	−	1.55090i	0.155871	−	0.0899922i
$298$	5.08050	+	6.05471i	0.294306	+	0.350740i
$299$	−39.4881	+	14.3725i	−2.28366	+	0.831183i
$300$	−2.96703	−	4.02452i	−0.171301	−	0.232356i
$301$	−18.9410	−	15.8934i	−1.09174	−	0.916081i
$302$	−19.4094	−	3.42239i	−1.11688	−	0.196937i
$303$			9.36180i			0.537821i
$304$	−3.62061	+	2.42718i	−0.207656	+	0.139208i
$305$	−0.0162782	−	0.0303592i	−0.000932084	−	0.00173836i
$306$	0.968738	−	5.49399i	0.0553791	−	0.314070i
$307$	13.8955	−	16.5600i	0.793060	−	0.945132i	−0.206384	−	0.978471i	$-0.566170\pi$
$307$	13.8955	−	16.5600i	0.793060	−	0.945132i	0.999444	+	0.0333393i	$0.0106142\pi$
$308$	3.05167	−	8.38440i	0.173885	−	0.477745i
$309$	1.72627	−	0.628312i	0.0982043	−	0.0357434i
$310$	7.33073	−	18.3277i	0.416357	−	1.04094i
$311$	10.6034	+	18.3656i	0.601261	+	1.04142i	0.992630	+	0.121181i	$0.0386682\pi$
$311$	10.6034	+	18.3656i	0.601261	+	1.04142i	−0.391369	+	0.920234i	$0.627998\pi$
$312$	3.90726	+	2.25585i	0.221205	+	0.127713i
$313$	−24.7696	+	4.36755i	−1.40006	+	0.246868i	−0.822168	−	0.569245i	$-0.807236\pi$
$313$	−24.7696	+	4.36755i	−1.40006	+	0.246868i	−0.577892	+	0.816113i	$0.696125\pi$
$314$	4.19347	+	23.7824i	0.236651	+	1.34212i
$315$	−0.202092	+	6.42900i	−0.0113866	+	0.362233i
$316$	2.88718	+	5.00074i	0.162416	+	0.281313i
$317$	−11.8230	−	14.0901i	−0.664048	−	0.791381i	0.323913	−	0.946087i	$-0.395002\pi$
$317$	−11.8230	−	14.0901i	−0.664048	−	0.791381i	−0.987961	+	0.154706i	$0.950557\pi$
$318$	0.710592	+	1.95234i	0.0398480	+	0.109482i
$319$	−7.39624	−	2.69201i	−0.414110	−	0.150724i
$320$	0.457285	−	2.18881i	0.0255630	−	0.122358i
$321$	2.51221	−	14.2475i	0.140218	−	0.795216i
$322$		−	26.7924i		−	1.49308i
$323$	−10.7221	+	21.8257i	−0.596591	+	1.21442i
$324$	−1.00000			−0.0555556
$325$	15.5571	−	16.3360i	0.862952	−	0.906159i
$326$	11.5657	+	9.70478i	0.640565	+	0.537498i
$327$	−2.41032	+	6.62231i	−0.133291	+	0.366215i
$328$	−0.148999	−	0.409372i	−0.00822710	−	0.0226038i
$329$	5.01622	−	4.20911i	0.276553	−	0.232056i
$330$	3.65492	−	5.89468i	0.201197	−	0.324491i
$331$	0.719268	−	1.24581i	0.0395345	−	0.0684758i	−0.845581	−	0.533847i	$-0.820746\pi$
$331$	0.719268	−	1.24581i	0.0395345	−	0.0684758i	0.885116	+	0.465371i	$0.154079\pi$
$332$	−11.7205	+	2.06665i	−0.643248	+	0.113422i
$333$	2.23913	−	0.394819i	0.122704	−	0.0216360i
$334$	−11.2916	+	19.5577i	−0.617850	+	1.07015i
$335$	6.10430	+	3.78490i	0.333514	+	0.206791i
$336$	−2.20357	+	1.84901i	−0.120215	+	0.100872i
$337$	−3.10381	−	8.52764i	−0.169075	−	0.464530i	0.825998	−	0.563673i	$-0.190612\pi$
$337$	−3.10381	−	8.52764i	−0.169075	−	0.464530i	−0.995073	+	0.0991428i	$0.968390\pi$
$338$	−2.51574	+	6.91193i	−0.136838	+	0.375960i
$339$	1.52842	+	1.28250i	0.0830125	+	0.0696558i
$340$	−3.89611	−	11.8504i	−0.211296	−	0.642679i
$341$	27.3818			1.48281
$342$	4.18661	+	1.21338i	0.226386	+	0.0656123i
$343$			16.4695i			0.889270i
$344$	1.49261	−	8.46502i	0.0804762	−	0.456403i
$345$	4.25918	−	20.3867i	0.229307	−	1.09758i
$346$	18.2847	+	6.65508i	0.982991	+	0.357779i
$347$	−3.08897	−	8.48689i	−0.165825	−	0.455600i	0.828751	−	0.559618i	$-0.189052\pi$
$347$	−3.08897	−	8.48689i	−0.165825	−	0.455600i	−0.994575	+	0.104018i	$0.966830\pi$
$348$	1.63110	+	1.94386i	0.0874359	+	0.104202i
$349$	3.07889	+	5.33280i	0.164809	+	0.285458i	0.936588	−	0.350434i	$-0.113966\pi$
$349$	3.07889	+	5.33280i	0.164809	+	0.285458i	−0.771778	+	0.635892i	$0.780632\pi$
$350$	6.39488	+	12.8829i	0.341821	+	0.688622i
$351$	−0.783450	−	4.44317i	−0.0418175	−	0.237159i
$352$	3.05467	−	0.538621i	0.162815	−	0.0287086i
$353$	12.1356	+	7.00648i	0.645912	+	0.372917i	0.786888	−	0.617096i	$-0.211691\pi$
$353$	12.1356	+	7.00648i	0.645912	+	0.372917i	−0.140976	+	0.990013i	$0.545024\pi$
$354$	1.02772	+	1.78006i	0.0546225	+	0.0946090i
$355$	25.2190	+	10.0871i	1.33849	+	0.535370i
$356$	−3.16365	+	1.15147i	−0.167673	+	0.0610279i
$357$	−5.48859	+	15.0798i	−0.290487	+	0.798106i
$358$	−9.66092	+	11.5134i	−0.510596	+	0.608504i
$359$	−1.22769	+	6.96257i	−0.0647949	+	0.367470i	0.935119	+	0.354334i	$0.115293\pi$
$359$	−1.22769	+	6.96257i	−0.0647949	+	0.367470i	−0.999914	+	0.0131359i	$0.995819\pi$
$360$	−1.97066	+	1.05664i	−0.103863	+	0.0556898i
$361$	−16.0554	−	10.1599i	−0.845021	−	0.534733i
$362$			10.8616i			0.570873i
$363$	−1.35791	−	0.239437i	−0.0712720	−	0.0125672i
$364$	−9.94187	−	8.34222i	−0.521095	−	0.437251i
$365$	34.2565	−	4.93615i	1.79307	−	0.258370i
$366$	−0.0144765	+	0.00526902i	−0.000756700	+	0.000275416i
$367$	−23.9660	−	28.5616i	−1.25102	−	1.49090i	−0.801932	−	0.597415i	$-0.796194\pi$
$367$	−23.9660	−	28.5616i	−1.25102	−	1.49090i	−0.449085	−	0.893489i	$-0.648250\pi$
$368$	8.06622	−	4.65703i	0.420481	−	0.242765i
$369$	−0.217822	+	0.377279i	−0.0113394	+	0.0196404i
$370$	3.99539	−	3.14401i	0.207711	−	0.163449i
$371$	−1.03780	−	5.88563i	−0.0538797	−	0.305567i
$372$	−7.64503	−	4.41386i	−0.396377	−	0.228848i
$373$	8.58785	−	4.95820i	0.444662	−	0.256726i	−0.260911	−	0.965363i	$-0.584023\pi$
$373$	8.58785	−	4.95820i	0.444662	−	0.256726i	0.705573	+	0.708637i	$0.250690\pi$
$374$	13.2557	−	11.1229i	0.685437	−	0.575150i
$375$	2.81795	+	10.8194i	0.145519	+	0.558711i
$376$	2.13912	+	0.778577i	0.110317	+	0.0401520i
$377$	−7.35903	+	8.77015i	−0.379009	+	0.451686i
$378$	2.83285	+	0.499509i	0.145706	+	0.0256920i
$379$	19.6457			1.00913			0.504567	−	0.863373i	$-0.331652\pi$
$379$	19.6457			1.00913			0.504567	+	0.863373i	$0.331652\pi$
$380$	9.53251	−	2.03256i	0.489007	−	0.104268i
$381$	16.2613			0.833093
$382$	17.8468	+	3.14688i	0.913123	+	0.161008i
$383$	7.93869	−	9.46096i	0.405648	−	0.483432i	−0.524085	−	0.851666i	$-0.675593\pi$
$383$	7.93869	−	9.46096i	0.405648	−	0.483432i	0.929733	+	0.368233i	$0.120037\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	−13.2983	+	14.8731i	−0.677744	+	0.758003i
$386$	−6.73034	+	5.64743i	−0.342566	+	0.287447i
$387$	−7.44402	+	4.29780i	−0.378401	+	0.218470i
$388$	16.6445	+	9.60970i	0.844996	+	0.487859i
$389$	1.21738	+	6.90410i	0.0617235	+	0.350052i	0.999991	+	0.00414206i	$0.00131846\pi$
$389$	1.21738	+	6.90410i	0.0617235	+	0.350052i	−0.938268	+	0.345909i	$0.887570\pi$
$390$	−6.23874	−	7.92816i	−0.315911	−	0.401458i
$391$	25.9804	−	44.9994i	1.31388	−	2.27572i
$392$	1.10381	−	0.637287i	0.0557510	−	0.0321878i
$393$	−1.22447	−	1.45927i	−0.0617664	−	0.0736103i
$394$	−7.69381	+	2.80032i	−0.387608	+	0.141078i
$395$	−1.84150	−	12.7799i	−0.0926558	−	0.643024i
$396$	−2.37611	−	1.99380i	−0.119404	−	0.100192i
$397$	−3.35345	−	0.591304i	−0.168305	−	0.0296767i	0.0888607	−	0.996044i	$-0.471677\pi$
$397$	−3.35345	−	0.591304i	−0.168305	−	0.0296767i	−0.257165	+	0.966367i	$0.582789\pi$
$398$		−	16.7613i		−	0.840168i
$399$	−11.2540	−	5.52859i	−0.563403	−	0.276776i
$400$	−2.76703	+	4.16456i	−0.138351	+	0.208228i
$401$	−3.04648	+	17.2774i	−0.152134	+	0.862794i	0.809226	+	0.587498i	$0.199887\pi$
$401$	−3.04648	+	17.2774i	−0.152134	+	0.862794i	−0.961359	+	0.275296i	$0.911224\pi$
$402$	2.06470	−	2.46061i	0.102978	−	0.122724i
$403$	13.6220	−	37.4262i	0.678561	−	1.86433i
$404$	8.79721	−	3.20192i	0.437678	−	0.159302i
$405$	2.07615	+	0.830421i	0.103165	+	0.0412639i
$406$	−3.64968	−	6.32143i	−0.181131	−	0.313727i
$407$	6.10762	+	3.52624i	0.302744	+	0.174789i
$408$	−5.49399	+	0.968738i	−0.271993	+	0.0479597i
$409$	−2.37090	−	13.4460i	−0.117233	−	0.664863i	−0.985620	−	0.168976i	$-0.945954\pi$
$409$	−2.37090	−	13.4460i	−0.117233	−	0.664863i	0.868387	−	0.495887i	$-0.165157\pi$
$410$	−0.0306062	+	0.973650i	−0.00151153	+	0.0480851i
$411$	3.04574	+	5.27537i	0.150235	+	0.260215i
$412$	−1.18084	−	1.40727i	−0.0581759	−	0.0693313i
$413$	−2.02222	−	5.55600i	−0.0995068	−	0.273393i
$414$	−8.75236	−	3.18560i	−0.430155	−	0.156564i
$415$	26.0498	+	5.44230i	1.27873	+	0.267152i
$416$	0.783450	−	4.44317i	0.0384118	−	0.217844i
$417$			8.04873i			0.394148i
$418$	7.52862	+	11.2304i	0.368237	+	0.549296i
$419$	−32.1105			−1.56870			−0.784351	−	0.620317i	$-0.787004\pi$
$419$	−32.1105			−1.56870			−0.784351	+	0.620317i	$0.787004\pi$
$420$	6.11040	−	2.00894i	0.298157	−	0.0980264i
$421$	2.61137	+	2.19120i	0.127270	+	0.106792i	0.704201	−	0.710001i	$-0.251305\pi$
$421$	2.61137	+	2.19120i	0.127270	+	0.106792i	−0.576931	+	0.816793i	$0.695750\pi$
$422$	−6.41772	+	17.6325i	−0.312410	+	0.858338i
$423$	−0.778577	−	2.13912i	−0.0378557	−	0.104008i
$424$	1.59156	−	1.33548i	0.0772929	−	0.0648565i
$425$	−1.75192	+	27.8386i	−0.0849806	+	1.35037i
$426$	6.07351	−	10.5196i	0.294263	−	0.509678i
$427$	0.0436418	−	0.00769522i	0.00211197	−	0.000372398i
$428$	−14.2475	+	2.51221i	−0.688677	+	0.121432i
$429$	6.99720	−	12.1195i	0.337828	−	0.585135i
$430$	−10.1284	+	16.3352i	−0.488436	+	0.787752i
$431$	13.2914	−	11.1528i	0.640226	−	0.537214i	−0.263861	−	0.964561i	$-0.584996\pi$
$431$	13.2914	−	11.1528i	0.640226	−	0.537214i	0.904088	+	0.427347i	$0.140552\pi$
$432$	0.342020	+	0.939693i	0.0164555	+	0.0452110i
$433$	−9.28298	+	25.5048i	−0.446112	+	1.22568i	0.489298	+	0.872117i	$0.337253\pi$
$433$	−9.28298	+	25.5048i	−0.446112	+	1.22568i	−0.935410	+	0.353565i	$0.884969\pi$
$434$	19.4525	+	16.3226i	0.933750	+	0.783509i
$435$	−1.77218	−	5.39025i	−0.0849693	−	0.258443i
$436$	7.04732			0.337505
$437$	32.7774	+	23.9568i	1.56795	+	1.14601i
$438$		−	15.4782i		−	0.739577i
$439$	2.88220	−	16.3458i	0.137560	−	0.780140i	−0.835483	−	0.549516i	$-0.814812\pi$
$439$	2.88220	−	16.3458i	0.137560	−	0.780140i	0.973043	−	0.230624i	$-0.0740768\pi$
$440$	−6.78924	−	1.41841i	−0.323664	−	0.0676198i
$441$	−1.19771	−	0.435930i	−0.0570337	−	0.0207586i
$442$	−8.60853	−	23.6517i	−0.409466	−	1.12500i
$443$	2.58875	+	3.08516i	0.122995	+	0.146580i	0.824028	−	0.566549i	$-0.191722\pi$
$443$	2.58875	+	3.08516i	0.122995	+	0.146580i	−0.701033	+	0.713129i	$0.747277\pi$
$444$	−1.13684	−	1.96906i	−0.0539519	−	0.0934474i
$445$	7.52441	+	0.236526i	0.356691	+	0.0112124i
$446$	0.807002	+	4.57673i	0.0382126	+	0.216715i
$447$	−7.78378	+	1.37249i	−0.368160	+	0.0649166i
$448$	2.49117	+	1.43828i	0.117697	+	0.0679522i
$449$	2.39872	+	4.15471i	0.113203	+	0.196073i	0.917060	−	0.398750i	$-0.130556\pi$
$449$	2.39872	+	4.15471i	0.113203	+	0.196073i	−0.803857	+	0.594822i	$0.797222\pi$
$450$	4.96885	−	0.557263i	0.234234	−	0.0262696i
$451$	−1.26979	+	0.462165i	−0.0597920	+	0.0217625i
$452$	0.682404	−	1.87489i	0.0320976	−	0.0881873i
$453$	12.6686	−	15.0978i	0.595221	−	0.709357i
$454$	1.64158	−	9.30987i	0.0770432	−	0.436934i
$455$	13.7133	+	25.5756i	0.642888	+	1.19900i
$456$	−0.291696	−	4.34913i	−0.0136599	−	0.203667i
$457$			20.0888i			0.939713i	0.882743	+	0.469856i	$0.155694\pi$
$457$			20.0888i			0.939713i	−0.882743	+	0.469856i	$0.844306\pi$
$458$	13.9133	+	2.45330i	0.650128	+	0.114635i
$459$	4.27356	+	3.58595i	0.199473	+	0.167378i
$460$	−20.6140	+	2.97035i	−0.961132	+	0.138493i
$461$	−39.5005	+	14.3770i	−1.83972	+	0.669604i	−0.849966	+	0.526837i	$0.823378\pi$
$461$	−39.5005	+	14.3770i	−1.83972	+	0.669604i	−0.989756	+	0.142767i	$0.954400\pi$
$462$	5.73527	+	6.83502i	0.266829	+	0.317994i
$463$	−2.53448	+	1.46328i	−0.117787	+	0.0680045i	−0.557736	−	0.830018i	$-0.688330\pi$
$463$	−2.53448	+	1.46328i	−0.117787	+	0.0680045i	0.439949	+	0.898023i	$0.354997\pi$
$464$	1.26877	−	2.19757i	0.0589010	−	0.102020i
$465$	12.2069	+	15.5124i	0.566080	+	0.719372i
$466$	−0.621878	−	3.52684i	−0.0288079	−	0.163378i
$467$	−29.9493	−	17.2912i	−1.38589	−	0.800143i	−0.393039	−	0.919522i	$-0.628576\pi$
$467$	−29.9493	−	17.2912i	−1.38589	−	0.800143i	−0.992849	+	0.119379i	$0.961910\pi$
$468$	−3.90726	+	2.25585i	−0.180613	+	0.104277i
$469$	−7.07809	+	5.93922i	−0.326836	+	0.274248i
$470$	−3.79459	−	3.39281i	−0.175032	−	0.156499i
$471$	−22.6929	−	8.25953i	−1.04563	−	0.380579i
$472$	1.32121	−	1.57455i	0.0608135	−	0.0724747i
$473$	−26.2568	−	4.62978i	−1.20729	−	0.212877i
$474$	−5.77435			−0.265225
$475$	−21.4788	−	3.69608i	−0.985515	−	0.169588i
$476$	16.0476			0.735539
$477$	−2.04607	−	0.360777i	−0.0936830	−	0.0165188i
$478$	2.01822	−	2.40523i	0.0923114	−	0.110012i
$479$	−8.82999	−	3.21385i	−0.403453	−	0.146845i	0.132320	−	0.991207i	$-0.457757\pi$
$479$	−8.82999	−	3.21385i	−0.403453	−	0.146845i	−0.535773	+	0.844362i	$0.679980\pi$
$480$	1.66692	+	1.49043i	0.0760843	+	0.0680283i
$481$	7.85820	−	6.59382i	0.358303	−	0.300652i
$482$	8.69524	−	5.02020i	0.396057	−	0.228664i
$483$	23.2029	+	13.3962i	1.05577	+	0.609549i
$484$	0.239437	+	1.35791i	0.0108835	+	0.0617234i
$485$	−26.5764	−	33.7731i	−1.20677	−	1.53356i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	30.3579	−	17.5272i	1.37565	−	0.794231i	0.384017	−	0.923326i	$-0.374541\pi$
$487$	30.3579	−	17.5272i	1.37565	−	0.794231i	0.991632	+	0.129095i	$0.0412072\pi$
$488$	0.00990252	+	0.0118014i	0.000448266	+	0.000534223i
$489$	−14.1874	+	5.16381i	−0.641578	+	0.233515i
$490$	−2.82090	+	0.406474i	−0.127435	+	0.0183626i
$491$	−11.2923	−	9.47540i	−0.509616	−	0.427619i	0.351378	−	0.936234i	$-0.385713\pi$
$491$	−11.2923	−	9.47540i	−0.509616	−	0.427619i	−0.860994	+	0.508615i	$0.830158\pi$
$492$	0.429026	+	0.0756489i	0.0193420	+	0.00341051i
$493$		−	14.1563i		−	0.637566i
$494$	19.0954	−	4.70338i	0.859141	−	0.211615i
$495$	3.27748	+	6.11259i	0.147312	+	0.274741i
$496$	−1.53292	+	8.69361i	−0.0688301	+	0.390355i
$497$	−22.4600	+	26.7668i	−1.00747	+	1.20066i
$498$	4.07050	−	11.1836i	0.182403	−	0.501149i
$499$	−4.50951	+	1.64133i	−0.201873	+	0.0734759i	−0.440978	−	0.897518i	$-0.645368\pi$
$499$	−4.50951	+	1.64133i	−0.201873	+	0.0734759i	0.239105	+	0.970994i	$0.423146\pi$
$500$	9.20310	−	6.34846i	0.411575	−	0.283912i
$501$	−11.2916	−	19.5577i	−0.504473	−	0.873772i
$502$	7.01551	+	4.05041i	0.313118	+	0.180778i
$503$	−37.5943	+	6.62889i	−1.67625	+	0.295568i	−0.929303	−	0.369318i	$-0.879591\pi$
$503$	−37.5943	+	6.62889i	−1.67625	+	0.295568i	−0.746945	+	0.664886i	$0.768480\pi$
$504$	−0.499509	−	2.83285i	−0.0222499	−	0.126185i
$505$	−20.9233	−	0.657713i	−0.931074	−	0.0292679i
$506$	−14.4452	−	25.0198i	−0.642166	−	1.11226i
$507$	−4.72804	−	5.63466i	−0.209980	−	0.250244i
$508$	−5.56170	−	15.2806i	−0.246761	−	0.677969i
$509$	−29.8641	−	10.8696i	−1.32370	−	0.481788i	−0.419059	−	0.907959i	$-0.637640\pi$
$509$	−29.8641	−	10.8696i	−1.32370	−	0.481788i	−0.904642	+	0.426171i	$0.859862\pi$
$510$	12.2108	+	2.55108i	0.540704	+	0.112964i
$511$	−7.73149	+	43.8475i	−0.342021	+	1.93970i
$512$			1.00000i			0.0441942i
$513$	−3.14413	+	3.01902i	−0.138817	+	0.133293i
$514$	−2.38753			−0.105310
$515$	1.28298	+	3.90230i	0.0565347	+	0.171956i
$516$	6.58462	+	5.52515i	0.289872	+	0.243231i
$517$	2.41499	−	6.63512i	0.106211	−	0.291812i
$518$	2.23693	+	6.14592i	0.0982851	+	0.270036i
$519$	−14.9058	+	12.5075i	−0.654293	+	0.549017i
$520$	−5.31626	+	8.57409i	−0.233133	+	0.375999i
$521$	−16.3139	+	28.2565i	−0.714725	+	1.23794i	0.248341	+	0.968673i	$0.420115\pi$
$521$	−16.3139	+	28.2565i	−0.714725	+	1.23794i	−0.963066	+	0.269267i	$0.913219\pi$
$522$	−2.49898	+	0.440638i	−0.109378	+	0.0192862i
$523$	−31.2208	+	5.50506i	−1.36519	+	0.240720i	−0.807763	−	0.589507i	$-0.799322\pi$
$523$	−31.2208	+	5.50506i	−1.36519	+	0.240720i	−0.557426	+	0.830227i	$0.688211\pi$
$524$	−0.952469	+	1.64973i	−0.0416088	+	0.0720686i
$525$	−14.3544	−	0.903339i	−0.626477	−	0.0394249i
$526$	17.0973	−	14.3463i	0.745478	−	0.625530i
$527$	16.8437	+	46.2776i	0.733722	+	2.01588i
$528$	−1.06088	+	2.91473i	−0.0461687	+	0.126848i
$529$	−48.8368	−	40.9789i	−2.12334	−	1.78169i
$530$	−4.41332	+	1.45099i	−0.191702	+	0.0630268i
$531$	−2.05543			−0.0891982
$532$	−1.34610	+	12.4662i	−0.0583606	+	0.540476i
$533$			1.96550i			0.0851353i
$534$	0.584618	−	3.31553i	0.0252989	−	0.143477i
$535$	31.6661	+	6.61566i	1.36904	+	0.286020i
$536$	−3.01839	−	1.09860i	−0.130374	−	0.0474524i
$537$	−5.14047	−	14.1233i	−0.221828	−	0.609466i
$538$	2.23687	+	2.66580i	0.0964383	+	0.114931i
$539$	−1.97673	−	3.42380i	−0.0851439	−	0.147474i
$540$	0.0702550	−	2.23496i	0.00302329	−	0.0961775i
$541$	2.63012	+	14.9161i	0.113078	+	0.641294i	0.987684	+	0.156461i	$0.0500086\pi$
$541$	2.63012	+	14.9161i	0.113078	+	0.641294i	−0.874607	+	0.484833i	$0.838880\pi$
$542$	−7.48635	+	1.32004i	−0.321566	+	0.0567008i
$543$	−9.40642	−	5.43080i	−0.403668	−	0.233058i
$544$	2.78937	+	4.83133i	0.119593	+	0.207142i
$545$	−14.6313	−	5.85224i	−0.626735	−	0.250682i
$546$	12.1955	−	4.43880i	0.521919	−	0.189963i
$547$	0.0698638	−	0.191949i	0.00298716	−	0.00820716i	−0.938190	−	0.346120i	$-0.887499\pi$
$547$	0.0698638	−	0.191949i	0.00298716	−	0.00820716i	0.941177	+	0.337913i	$0.109721\pi$
$548$	3.91552	−	4.66634i	0.167263	−	0.199336i
$549$	0.00267515	−	0.0151715i	0.000114173	−	0.000647506i
$550$	12.9176	+	8.58275i	0.550809	+	0.365970i
$551$	10.9969	+	1.18745i	0.468485	+	0.0505870i
$552$			9.31407i			0.396433i
$553$	16.3579	+	2.88434i	0.695609	+	0.122655i
$554$	−6.36622	−	5.34189i	−0.270475	−	0.226955i
$555$	0.725097	+	5.03212i	0.0307786	+	0.213601i
$556$	7.56333	−	2.75283i	0.320757	−	0.116746i
$557$	21.0157	+	25.0455i	0.890463	+	1.06121i	0.997754	+	0.0669849i	$0.0213379\pi$
$557$	21.0157	+	25.0455i	0.890463	+	1.06121i	−0.107291	+	0.994228i	$0.534218\pi$
$558$	7.64503	−	4.41386i	0.323640	−	0.186854i
$559$	−19.3904	+	33.5852i	−0.820129	+	1.42050i
$560$	−3.97767	−	5.05480i	−0.168087	−	0.213604i
$561$	3.00483	+	17.0412i	0.126864	+	0.719481i
$562$	27.3822	+	15.8091i	1.15505	+	0.666868i
$563$	11.5464	−	6.66630i	0.486621	−	0.280951i	−0.236550	−	0.971619i	$-0.576017\pi$
$563$	11.5464	−	6.66630i	0.486621	−	0.280951i	0.723172	+	0.690668i	$0.242684\pi$
$564$	−1.74383	+	1.46325i	−0.0734284	+	0.0616138i
$565$	−2.97372	+	3.32587i	−0.125105	+	0.139920i
$566$	−2.75252	−	1.00184i	−0.115697	−	0.0421103i
$567$	−1.84901	+	2.20357i	−0.0776513	+	0.0925412i
$568$	−11.9625	−	2.10931i	−0.501935	−	0.0885046i
$569$	−3.05631			−0.128127			−0.0640636	−	0.997946i	$-0.520406\pi$
$569$	−3.05631			−0.128127			−0.0640636	+	0.997946i	$0.520406\pi$
$570$	−3.00600	+	9.27167i	−0.125908	+	0.388348i
$571$	39.6574			1.65961			0.829805	−	0.558053i	$-0.188451\pi$
$571$	39.6574			1.65961			0.829805	+	0.558053i	$0.188451\pi$
$572$	−13.7818	−	2.43010i	−0.576246	−	0.101608i
$573$	−11.6487	+	13.8824i	−0.486631	+	0.579944i
$574$	−1.17758	−	0.428604i	−0.0491513	−	0.0178896i
$575$	45.2644	+	10.9514i	1.88765	+	0.456705i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	19.7822	−	11.4213i	0.823544	−	0.475474i	−0.0280928	−	0.999605i	$-0.508943\pi$
$577$	19.7822	−	11.4213i	0.823544	−	0.475474i	0.851637	+	0.524132i	$0.175610\pi$
$578$	12.2303	+	7.06118i	0.508715	+	0.293706i
$579$	−1.52565	−	8.65236i	−0.0634037	−	0.359580i
$580$	−4.45906	+	3.50887i	−0.185152	+	0.145698i
$581$	−17.1174	+	29.6483i	−0.710151	+	1.23002i
$582$	−16.6445	+	9.60970i	−0.689937	+	0.398335i
$583$	−4.14238	−	4.93669i	−0.171560	−	0.204457i
$584$	−14.5447	+	5.29385i	−0.601866	+	0.219061i
$585$	9.98536	−	1.43883i	0.412844	−	0.0594882i
$586$	−12.2970	−	10.3184i	−0.507984	−	0.426249i
$587$	−28.5295	−	5.03052i	−1.17754	−	0.207632i	−0.449572	−	0.893244i	$-0.648423\pi$
$587$	−28.5295	−	5.03052i	−1.17754	−	0.207632i	−0.727967	+	0.685612i	$0.759535\pi$
$588$			1.27457i			0.0525625i
$589$	−37.3625	+	9.20275i	−1.53949	+	0.379193i
$590$	−4.05057	+	2.17185i	−0.166759	+	0.0894137i
$591$	1.42176	−	8.06319i	0.0584833	−	0.331675i
$592$	−1.46149	+	1.74174i	−0.0600669	+	0.0715849i
$593$	−0.0613065	+	0.168438i	−0.00251756	+	0.00691693i	−0.940945	−	0.338559i	$-0.890060\pi$
$593$	−0.0613065	+	0.168438i	−0.00251756	+	0.00691693i	0.938427	+	0.345476i	$0.112283\pi$
$594$	2.91473	−	1.06088i	0.119593	−	0.0435283i
$595$	−33.3172	−	13.3262i	−1.36587	−	0.546322i
$596$	3.95193	+	6.84494i	0.161877	+	0.280380i
$597$	14.5157	+	8.38065i	0.594088	+	0.342997i
$598$	−41.3840	+	7.29711i	−1.69232	+	0.298401i
$599$	−1.22047	−	6.92166i	−0.0498672	−	0.282811i	0.949669	−	0.313254i	$-0.101419\pi$
$599$	−1.22047	−	6.92166i	−0.0498672	−	0.282811i	−0.999536	+	0.0304432i	$0.990308\pi$
$600$	−2.22310	−	4.47860i	−0.0907578	−	0.182838i
$601$	1.22063	+	2.11420i	0.0497907	+	0.0862401i	0.889847	−	0.456260i	$-0.150811\pi$
$601$	1.22063	+	2.11420i	0.0497907	+	0.0862401i	−0.840056	+	0.542500i	$0.817478\pi$
$602$	−15.8934	−	18.9410i	−0.647767	−	0.771979i
$603$	1.09860	+	3.01839i	0.0447386	+	0.122918i
$604$	−18.5202	−	6.74080i	−0.753576	−	0.274279i
$605$	0.630533	−	3.01807i	0.0256348	−	0.122702i
$606$	−1.62566	+	9.21957i	−0.0660379	+	0.374520i
$607$			17.7470i			0.720330i	0.932889	+	0.360165i	$0.117280\pi$
$607$			17.7470i			0.720330i	−0.932889	+	0.360165i	$0.882720\pi$
$608$	−3.98708	+	1.76159i	−0.161697	+	0.0714421i
$609$	7.29936			0.295785
$610$	−0.0107590	−	0.0327247i	−0.000435620	−	0.00132498i
$611$	−7.86765	−	6.60174i	−0.318291	−	0.267078i
$612$	1.90804	−	5.24230i	0.0771280	−	0.211908i
$613$	6.83583	+	18.7813i	0.276097	+	0.758569i	0.997796	+	0.0663621i	$0.0211392\pi$
$613$	6.83583	+	18.7813i	0.276097	+	0.758569i	−0.721699	+	0.692207i	$0.756639\pi$
$614$	16.5600	−	13.8955i	0.668309	−	0.560778i
$615$	−0.827902	−	0.513331i	−0.0333842	−	0.0206995i
$616$	4.46124	−	7.72710i	0.179749	−	0.311334i
$617$	19.3059	−	3.40414i	0.777225	−	0.137046i	0.229056	−	0.973413i	$-0.426436\pi$
$617$	19.3059	−	3.40414i	0.777225	−	0.137046i	0.548169	+	0.836368i	$0.315325\pi$
$618$	1.80915	−	0.319002i	0.0727748	−	0.0128322i
$619$	−1.17449	+	2.03427i	−0.0472066	+	0.0817642i	−0.888663	−	0.458560i	$-0.848365\pi$
$619$	−1.17449	+	2.03427i	−0.0472066	+	0.0817642i	0.841457	+	0.540325i	$0.181699\pi$
$620$	10.4019	−	16.7763i	0.417751	−	0.673752i
$621$	7.13499	−	5.98697i	0.286317	−	0.240249i
$622$	7.25312	+	19.9278i	0.290824	+	0.799032i
$623$	−3.31228	+	9.10040i	−0.132704	+	0.364600i
$624$	3.45617	+	2.90007i	0.138358	+	0.116096i
$625$	−24.3789	+	5.53791i	−0.975157	+	0.221516i
$626$	−25.1517			−1.00526
$627$	−13.4901	+	0.904781i	−0.538743	+	0.0361335i
$628$			24.1493i			0.963660i
$629$	−2.20260	+	12.4915i	−0.0878232	+	0.498070i
$630$	−1.31541	+	6.29623i	−0.0524070	+	0.250848i
$631$	5.91933	+	2.15446i	0.235645	+	0.0857677i	0.457143	−	0.889393i	$-0.348873\pi$
$631$	5.91933	+	2.15446i	0.235645	+	0.0857677i	−0.221499	+	0.975161i	$0.571095\pi$
$632$	1.97495	+	5.42612i	0.0785591	+	0.215839i
$633$	−12.0614	−	14.3742i	−0.479396	−	0.571322i
$634$	−9.19669	−	15.9291i	−0.365247	−	0.632627i
$635$	−1.14244	+	36.3435i	−0.0453363	+	1.44225i
$636$	0.360777	+	2.04607i	0.0143057	+	0.0811319i
$637$	−5.66314	+	0.998565i	−0.224382	+	0.0395646i
$638$	−6.81641	−	3.93546i	−0.269864	−	0.155806i
$639$	6.07351	+	10.5196i	0.240264	+	0.416150i
$640$	0.830421	−	2.07615i	0.0328253	−	0.0820671i
$641$	18.5567	−	6.75408i	0.732944	−	0.266770i	0.0515338	−	0.998671i	$-0.483589\pi$
$641$	18.5567	−	6.75408i	0.732944	−	0.266770i	0.681411	+	0.731901i	$0.261367\pi$
$642$	4.94809	−	13.5948i	0.195286	−	0.536543i
$643$	−4.98493	+	5.94080i	−0.196586	+	0.234282i	−0.855328	−	0.518087i	$-0.826644\pi$
$643$	−4.98493	+	5.94080i	−0.196586	+	0.234282i	0.658742	+	0.752369i	$0.271089\pi$
$644$	4.65246	−	26.3854i	0.183333	−	1.03973i
$645$	−9.08246	−	16.9391i	−0.357622	−	0.666974i
$646$	−14.3492	+	19.6323i	−0.564560	+	0.772422i
$647$		−	30.1849i		−	1.18669i	−0.804948	−	0.593345i	$-0.797807\pi$
$647$		−	30.1849i		−	1.18669i	0.804948	−	0.593345i	$-0.202193\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	−4.88394	−	4.09812i	−0.191712	−	0.160865i
$650$	18.1575	−	13.3864i	0.712194	−	0.525057i
$651$	−23.8620	+	8.68507i	−0.935227	+	0.340395i
$652$	9.70478	+	11.5657i	0.380069	+	0.452948i
$653$	−18.8899	+	10.9061i	−0.739220	+	0.426789i	−0.821786	−	0.569797i	$-0.807022\pi$
$653$	−18.8899	+	10.9061i	−0.739220	+	0.426789i	0.0825656	+	0.996586i	$0.473689\pi$
$654$	−3.52366	+	6.10315i	−0.137786	+	0.238652i
$655$	3.34744	−	2.63413i	0.130795	−	0.102924i
$656$	−0.0756489	−	0.429026i	−0.00295359	−	0.0167507i
$657$	13.4045	+	7.73910i	0.522960	+	0.301931i
$658$	5.67092	−	3.27410i	0.221075	−	0.127638i
$659$	−12.2489	+	10.2781i	−0.477151	+	0.400377i	−0.849395	−	0.527758i	$-0.823033\pi$
$659$	−12.2489	+	10.2781i	−0.477151	+	0.400377i	0.372244	+	0.928135i	$0.378588\pi$
$660$	4.62300	−	5.17045i	0.179950	−	0.201260i
$661$	33.1600	+	12.0693i	1.28978	+	0.469440i	0.893653	−	0.448758i	$-0.148133\pi$
$661$	33.1600	+	12.0693i	1.28978	+	0.469440i	0.396122	+	0.918198i	$0.370356\pi$
$662$	0.924673	−	1.10198i	0.0359384	−	0.0428298i
$663$	24.7873	+	4.37067i	0.962658	+	0.169743i
$664$	−11.9013			−0.461861
$665$	13.1468	−	24.7638i	0.509813	−	0.960298i
$666$	2.27367			0.0881031
$667$	−23.2757	−	4.10413i	−0.901239	−	0.158913i
$668$	−14.5162	+	17.2998i	−0.561650	+	0.669349i
$669$	−4.36707	−	1.58948i	−0.168841	−	0.0614530i
$670$	5.35432	+	4.78740i	0.206856	+	0.184953i
$671$	0.0366054	−	0.0307156i	0.00141314	−	0.00118576i
$672$	−2.49117	+	1.43828i	−0.0960990	+	0.0554828i
$673$	−43.0655	−	24.8639i	−1.66005	−	0.958432i	−0.972687	−	0.232120i	$-0.925434\pi$
$673$	−43.0655	−	24.8639i	−1.66005	−	0.958432i	−0.687365	−	0.726312i	$-0.741233\pi$
$674$	−1.57584	−	8.93706i	−0.0606992	−	0.344243i
$675$	−2.00182	+	4.58178i	−0.0770501	+	0.176353i
$676$	−3.67776	+	6.37007i	−0.141452	+	0.245003i
$677$	34.8924	−	20.1452i	1.34103	−	0.774242i	0.354068	−	0.935220i	$-0.384798\pi$
$677$	34.8924	−	20.1452i	1.34103	−	0.774242i	0.986958	+	0.160978i	$0.0514649\pi$
$678$	1.28250	+	1.52842i	0.0492541	+	0.0586987i
$679$	51.9516	−	18.9088i	1.99372	−	0.725654i
$680$	−1.77912	−	12.3469i	−0.0682260	−	0.473483i
$681$	7.24179	+	6.07659i	0.277506	+	0.232855i
$682$	26.9658	+	4.75480i	1.03257	+	0.182071i
$683$		−	35.8941i		−	1.37345i	−0.726917	−	0.686725i	$-0.759047\pi$
$683$		−	35.8941i		−	1.37345i	0.726917	−	0.686725i	$-0.240953\pi$
$684$	3.91230	+	1.92195i	0.149591	+	0.0734875i
$685$	−12.0042	+	6.43649i	−0.458658	+	0.245926i
$686$	−2.85990	+	16.2193i	−0.109191	+	0.619256i
$687$	−9.08129	+	10.8227i	−0.346473	+	0.412910i
$688$	2.93987	−	8.07723i	0.112082	−	0.307942i
$689$	−8.80837	+	3.20599i	−0.335572	+	0.122138i
$690$	7.73460	−	19.3374i	0.294451	−	0.736163i
$691$	−15.8942	−	27.5296i	−0.604645	−	1.04728i	−0.992107	−	0.125390i	$-0.959982\pi$
$691$	−15.8942	−	27.5296i	−0.604645	−	1.04728i	0.387462	−	0.921885i	$-0.373352\pi$
$692$	16.8513	+	9.72908i	0.640589	+	0.369844i
$693$	−8.78694	+	1.54937i	−0.333788	+	0.0588559i
$694$	−1.56831	−	8.89435i	−0.0595324	−	0.337625i
$695$	−17.9886	−	0.565463i	−0.682347	−	0.0214493i
$696$	1.26877	+	2.19757i	0.0480925	+	0.0832987i
$697$	−1.56220	−	1.86175i	−0.0591725	−	0.0705190i
$698$	2.10609	+	5.78642i	0.0797165	+	0.219019i
$699$	3.36527	+	1.22486i	0.127286	+	0.0463284i
$700$	4.06063	+	13.7977i	0.153477	+	0.521503i
$701$	3.60337	−	20.4358i	0.136098	−	0.771848i	−0.837992	−	0.545683i	$-0.816270\pi$
$701$	3.60337	−	20.4358i	0.136098	−	0.771848i	0.974089	−	0.226165i	$-0.0726187\pi$
$702$		−	4.51171i		−	0.170284i
$703$	−9.51899	−	2.75884i	−0.359015	−	0.104052i
$704$	3.10180			0.116903
$705$	4.83556	−	1.58981i	0.182118	−	0.0598756i
$706$	10.7346	+	9.00736i	0.404000	+	0.338996i
$707$	9.21051	−	25.3057i	0.346397	−	0.951718i
$708$	0.703000	+	1.93148i	0.0264203	+	0.0725893i
$709$	−3.09135	+	2.59395i	−0.116098	+	0.0974179i	−0.698988	−	0.715133i	$-0.746366\pi$
$709$	−3.09135	+	2.59395i	−0.116098	+	0.0974179i	0.582890	+	0.812551i	$0.301922\pi$
$710$	23.0843	+	14.3131i	0.866338	+	0.537162i
$711$	2.88718	−	5.00074i	0.108278	−	0.187542i
$712$	−3.31553	+	0.584618i	−0.124255	+	0.0219095i
$713$	80.9729	−	14.2777i	3.03246	−	0.534704i
$714$	−8.02378	+	13.8976i	−0.300282	+	0.520105i
$715$	26.5951	+	16.4899i	0.994599	+	0.616689i
$716$	−11.5134	+	9.66092i	−0.430277	+	0.361046i
$717$	1.07387	+	2.95045i	0.0401046	+	0.110186i
$718$	−2.41807	+	6.64360i	−0.0902417	+	0.247937i
$719$	−26.6630	−	22.3729i	−0.994361	−	0.834368i	−0.00816764	−	0.999967i	$-0.502600\pi$
$719$	−26.6630	−	22.3729i	−0.994361	−	0.834368i	−0.986193	+	0.165599i	$0.947044\pi$
$720$	−2.12421	+	0.698385i	−0.0791646	+	0.0260273i
$721$	−5.28441			−0.196802
$722$	−14.0472	−	12.7936i	−0.522783	−	0.476128i
$723$			10.0404i			0.373406i
$724$	−1.88610	+	10.6966i	−0.0700962	+	0.397536i
$725$	12.1715	−	3.58206i	0.452039	−	0.133034i
$726$	−1.29571	−	0.471599i	−0.0480882	−	0.0175027i
$727$	−6.23263	−	17.1240i	−0.231155	−	0.635094i	0.768835	−	0.639447i	$-0.220837\pi$
$727$	−6.23263	−	17.1240i	−0.231155	−	0.635094i	−0.999991	+	0.00435295i	$0.998614\pi$
$728$	−8.34222	−	9.94187i	−0.309183	−	0.368470i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	34.5932	+	1.08742i	1.28035	+	0.0402472i
$731$	−8.32690	−	47.2242i	−0.307981	−	1.74665i
$732$	−0.0151715	+	0.00267515i	−0.000560756	+	9.88765e-5i
$733$	13.0142	+	7.51373i	0.480689	+	0.277526i	0.720704	−	0.693243i	$-0.243819\pi$
$733$	13.0142	+	7.51373i	0.480689	+	0.277526i	−0.240015	+	0.970769i	$0.577152\pi$
$734$	−18.6423	−	32.2894i	−0.688099	−	1.19182i
$735$	1.05843	−	2.64621i	0.0390409	−	0.0976068i
$736$	8.75236	−	3.18560i	0.322616	−	0.117423i
$737$	−3.40764	+	9.36242i	−0.125522	+	0.344869i
$738$	−0.280027	+	0.333723i	−0.0103079	+	0.0122845i
$739$	3.70941	−	21.0371i	0.136453	−	0.773863i	−0.837384	−	0.546615i	$-0.815916\pi$
$739$	3.70941	−	21.0371i	0.136453	−	0.773863i	0.973837	−	0.227248i	$-0.0729728\pi$
$740$	4.48065	−	2.40245i	0.164712	−	0.0883160i
$741$	−5.47444	+	18.8888i	−0.201109	+	0.693896i
$742$		−	5.97643i		−	0.219401i
$743$	−6.97366	−	1.22965i	−0.255839	−	0.0451113i	0.0442576	−	0.999020i	$-0.485908\pi$
$743$	−6.97366	−	1.22965i	−0.255839	−	0.0451113i	−0.300096	+	0.953909i	$0.597019\pi$
$744$	−6.76243	−	5.67435i	−0.247923	−	0.208032i
$745$	−2.52062	−	17.4929i	−0.0923483	−	0.640890i
$746$	9.31836	−	3.39161i	0.341169	−	0.124176i
$747$	7.65003	+	9.11695i	0.279900	+	0.333572i
$748$	14.9858	−	8.65206i	0.547935	−	0.316351i
$749$	−20.8079	+	36.0404i	−0.760306	+	1.31689i
$750$	0.896376	+	11.1443i	0.0327310	+	0.406934i
$751$	−5.06645	−	28.7333i	−0.184877	−	1.04849i	−0.926113	−	0.377247i	$-0.876871\pi$
$751$	−5.06645	−	28.7333i	−0.184877	−	1.04849i	0.741235	−	0.671245i	$-0.234240\pi$
$752$	1.97143	+	1.13820i	0.0718905	+	0.0415060i
$753$	−7.01551	+	4.05041i	−0.255659	+	0.147605i
$754$	−8.77015	+	7.35903i	−0.319390	+	0.268000i
$755$	32.8530	+	29.3745i	1.19564	+	1.06905i
$756$	2.70308	+	0.983840i	0.0983100	+	0.0357819i
$757$	19.5828	−	23.3379i	0.711751	−	0.848231i	−0.282051	−	0.959399i	$-0.591015\pi$
$757$	19.5828	−	23.3379i	0.711751	−	0.848231i	0.993802	+	0.111168i	$0.0354592\pi$
$758$	19.3473	+	3.41145i	0.702724	+	0.123909i
$759$	28.8903			1.04865
$760$	9.74064	−	0.346382i	0.353330	−	0.0125646i
$761$	4.29035			0.155525			0.0777625	−	0.996972i	$-0.475222\pi$
$761$	4.29035			0.155525			0.0777625	+	0.996972i	$0.475222\pi$
$762$	16.0143	+	2.82375i	0.580136	+	0.102294i
$763$	13.0306	−	15.5292i	0.471739	−	0.562197i
$764$	17.0292	+	6.19813i	0.616096	+	0.224241i
$765$	−8.31470	+	9.29933i	−0.300619	+	0.336218i
$766$	9.46096	−	7.93869i	0.341838	−	0.286836i
$767$	−8.03110	+	4.63676i	−0.289986	+	0.167424i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	4.71311	+	26.7293i	0.169959	+	0.963885i	0.943803	+	0.330509i	$0.107220\pi$
$769$	4.71311	+	26.7293i	0.169959	+	0.963885i	−0.773844	+	0.633376i	$0.781669\pi$
$770$	−15.6790	+	12.3379i	−0.565031	+	0.444628i
$771$	1.19377	−	2.06766i	0.0429925	−	0.0744651i
$772$	−7.60876	+	4.39292i	−0.273845	+	0.158105i
$773$	−30.1356	−	35.9142i	−1.08390	−	1.29174i	−0.953866	−	0.300234i	$-0.902935\pi$
$773$	−30.1356	−	35.9142i	−1.08390	−	1.29174i	−0.130036	−	0.991509i	$-0.541509\pi$
$774$	−8.07723	+	2.93987i	−0.290330	+	0.105672i
$775$	−35.5273	+	26.1921i	−1.27618	+	0.940848i
$776$	14.7229	+	12.3540i	0.528522	+	0.443483i
$777$	−6.44099	−	1.13572i	−0.231069	−	0.0407437i
$778$			7.01060i			0.251342i
$779$	1.57730	−	1.05739i	0.0565126	−	0.0378848i
$780$	−4.76725	−	8.89106i	−0.170695	−	0.318351i
$781$	−6.54264	+	37.1052i	−0.234114	+	1.32773i
$782$	33.3998	−	39.8043i	1.19437	−	1.42340i
$783$	0.867888	−	2.38450i	0.0310158	−	0.0852152i
$784$	1.19771	−	0.435930i	0.0427753	−	0.0155689i
$785$	20.0540	−	50.1375i	0.715760	−	1.78948i
$786$	−0.952469	−	1.64973i	−0.0339735	−	0.0588438i
$787$	−3.91796	−	2.26203i	−0.139660	−	0.0806327i	0.428542	−	0.903522i	$-0.359027\pi$
$787$	−3.91796	−	2.26203i	−0.139660	−	0.0806327i	−0.568202	+	0.822889i	$0.692361\pi$
$788$	−8.06319	+	1.42176i	−0.287239	+	0.0506480i
$789$	3.87564	+	21.9799i	0.137977	+	0.782504i
$790$	0.405677	−	12.9055i	0.0144333	−	0.459156i
$791$	−2.86967	−	4.97042i	−0.102034	−	0.176728i
$792$	−1.99380	−	2.37611i	−0.0708465	−	0.0844315i
$793$	−0.0237723	−	0.0653138i	−0.000844179	−	0.00231936i
$794$	−3.19982	−	1.16464i	−0.113558	−	0.0413316i
$795$	0.950070	−	4.54754i	0.0336955	−	0.161285i
$796$	2.91057	−	16.5067i	0.103162	−	0.585063i
$797$			10.7651i			0.381319i	0.981656	+	0.190660i	$0.0610627\pi$
$797$			10.7651i			0.381319i	−0.981656	+	0.190660i	$0.938937\pi$
$798$	−10.1230	−	7.39883i	−0.358349	−	0.261916i
$799$	12.6995			0.449275
$800$	−3.44816	+	3.62080i	−0.121911	+	0.128015i
$801$	2.57903	+	2.16406i	0.0911255	+	0.0764633i
$802$	−6.00039	+	16.4859i	−0.211881	+	0.582139i
$803$	16.4205	+	45.1148i	0.579465	+	1.59207i
$804$	2.46061	−	2.06470i	0.0867791	−	0.0728163i
$805$	−31.5702	+	50.9166i	−1.11270	+	1.79457i
$806$	19.9141	−	34.4922i	0.701443	−	1.21493i
$807$	−3.42708	+	0.604287i	−0.120639	+	0.0212719i
$808$	9.21957	−	1.62566i	0.324343	−	0.0571905i
$809$	3.71142	−	6.42837i	0.130487	−	0.226009i	−0.793378	−	0.608730i	$-0.791679\pi$
$809$	3.71142	−	6.42837i	0.130487	−	0.226009i	0.923864	+	0.382720i	$0.125013\pi$
$810$	1.90041	+	1.17832i	0.0667735	+	0.0414021i
$811$	−14.6493	+	12.2922i	−0.514407	+	0.431639i	−0.862677	−	0.505756i	$-0.831214\pi$
$811$	−14.6493	+	12.2922i	−0.514407	+	0.431639i	0.348270	+	0.937394i	$0.386769\pi$
$812$	−2.49653	−	6.85915i	−0.0876110	−	0.240709i
$813$	2.59998	−	7.14339i	0.0911853	−	0.250530i
$814$	5.40251	+	4.53324i	0.189358	+	0.158890i
$815$	−10.5442	−	32.0712i	−0.369347	−	1.12341i
$816$	−5.57874			−0.195295
$817$	37.3834	−	2.50730i	1.30788	−	0.0877195i
$818$		−	13.6534i		−	0.477381i
$819$	−2.25364	+	12.7810i	−0.0787485	+	0.446605i
$820$	−0.199214	+	0.953543i	−0.00695685	+	0.0332992i
$821$	19.8257	+	7.21598i	0.691923	+	0.251839i	0.663958	−	0.747769i	$-0.268875\pi$
$821$	19.8257	+	7.21598i	0.691923	+	0.251839i	0.0279647	+	0.999609i	$0.491097\pi$
$822$	2.08341	+	5.72411i	0.0726671	+	0.199651i
$823$	16.1895	+	19.2939i	0.564331	+	0.672544i	0.970457	−	0.241273i	$-0.0775651\pi$
$823$	16.1895	+	19.2939i	0.564331	+	0.672544i	−0.406126	+	0.913817i	$0.633121\pi$
$824$	−0.918531	−	1.59094i	−0.0319985	−	0.0554231i
$825$	−13.8917	+	6.89561i	−0.483647	+	0.240074i
$826$	−1.02671	−	5.82274i	−0.0357237	−	0.202599i
$827$	0.0113676	−	0.00200441i	0.000395290	−	6.97002e-5i	−0.173451	−	0.984843i	$-0.555492\pi$
$827$	0.0113676	−	0.00200441i	0.000395290	−	6.97002e-5i	0.173846	+	0.984773i	$0.444381\pi$
$828$	−8.06622	−	4.65703i	−0.280321	−	0.161843i
$829$	12.5840	+	21.7961i	0.437059	+	0.757008i	0.997461	−	0.0712123i	$-0.0226868\pi$
$829$	12.5840	+	21.7961i	0.437059	+	0.757008i	−0.560402	+	0.828221i	$0.689353\pi$
$830$	24.7090	+	9.88312i	0.857661	+	0.343048i
$831$	7.80932	−	2.84236i	0.270902	−	0.0986004i
$832$	1.54310	−	4.23962i	0.0534972	−	0.146982i
$833$	4.57055	−	5.44697i	0.158360	−	0.188726i
$834$	−1.39765	+	7.92645i	−0.0483966	+	0.274471i
$835$	44.5040	−	23.8624i	1.54012	−	0.825791i
$836$	5.46410	+	12.3671i	0.188980	+	0.427725i
$837$			8.82772i			0.305131i
$838$	−31.6227	−	5.57594i	−1.09239	−	0.192618i
$839$	7.93997	+	6.66242i	0.274118	+	0.230012i	0.769475	−	0.638677i	$-0.220518\pi$
$839$	7.93997	+	6.66242i	0.274118	+	0.230012i	−0.495357	+	0.868690i	$0.664963\pi$
$840$	6.36642	−	0.917362i	0.219662	−	0.0316520i
$841$	21.2003	−	7.71629i	0.731046	−	0.266079i
$842$	2.19120	+	2.61137i	0.0755136	+	0.0899936i
$843$	−27.3822	+	15.8091i	−0.943093	+	0.544495i
$844$	−9.38207	+	16.2502i	−0.322944	+	0.559356i
$845$	12.9254	−	10.1711i	0.444648	−	0.349898i
$846$	−0.395294	−	2.24182i	−0.0135905	−	0.0770754i
$847$	3.43498	+	1.98319i	0.118027	+	0.0681431i
$848$	1.79928	−	1.03882i	0.0617876	−	0.0356731i
$849$	2.24388	−	1.88284i	0.0770097	−	0.0646188i
$850$	−6.55943	+	27.1115i	−0.224987	+	0.929916i
$851$	19.9000	+	7.24301i	0.682164	+	0.248287i
$852$	7.80795	−	9.30516i	0.267496	−	0.318789i
$853$	20.1166	+	3.54710i	0.688780	+	0.121451i	0.507074	−	0.861902i	$-0.330727\pi$
$853$	20.1166	+	3.54710i	0.688780	+	0.121451i	0.181706	+	0.983353i	$0.441838\pi$
$854$	0.0443150			0.00151643
$855$	−6.52651	−	7.23911i	−0.223202	−	0.247572i
$856$	−14.4673			−0.494481
$857$	−24.5325	−	4.32574i	−0.838015	−	0.147765i	−0.261861	−	0.965106i	$-0.584336\pi$
$857$	−24.5325	−	4.32574i	−0.838015	−	0.147765i	−0.576154	+	0.817341i	$0.695447\pi$
$858$	8.99543	−	10.7203i	0.307099	−	0.365986i
$859$	−46.4016	−	16.8888i	−1.58320	−	0.576238i	−0.607304	−	0.794470i	$-0.707749\pi$
$859$	−46.4016	−	16.8888i	−1.58320	−	0.576238i	−0.975897	+	0.218232i	$0.929971\pi$
$860$	−12.8111	+	14.3282i	−0.436855	+	0.488588i
$861$	0.959973	−	0.805513i	0.0327158	−	0.0274518i
$862$	15.0262	−	8.67538i	0.511794	−	0.295484i
$863$	20.3004	+	11.7204i	0.691033	+	0.398968i	0.803999	−	0.594631i	$-0.202702\pi$
$863$	20.3004	+	11.7204i	0.691033	+	0.398968i	−0.112966	+	0.993599i	$0.536035\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	−26.9065	−	34.1927i	−0.914849	−	1.16259i
$866$	−13.5708	+	23.5053i	−0.461155	+	0.798744i
$867$	−12.2303	+	7.06118i	−0.415364	+	0.239810i
$868$	16.3226	+	19.4525i	0.554025	+	0.660261i
$869$	16.8307	−	6.12588i	0.570943	−	0.207806i
$870$	−0.809245	−	5.61610i	−0.0274360	−	0.190403i
$871$	11.1016	+	9.31532i	0.376162	+	0.315638i
$872$	6.94025	+	1.22375i	0.235027	+	0.0414415i
$873$		−	19.2194i		−	0.650478i
$874$	28.1193	+	29.2846i	0.951151	+	0.990567i
$875$	3.02740	−	32.0181i	0.102345	−	1.08241i
$876$	2.68776	−	15.2430i	0.0908110	−	0.515015i
$877$	16.4685	−	19.6264i	0.556103	−	0.662738i	−0.412614	−	0.910906i	$-0.635384\pi$
$877$	16.4685	−	19.6264i	0.556103	−	0.662738i	0.968717	+	0.248168i	$0.0798286\pi$
$878$	5.67682	−	15.5969i	0.191583	−	0.526371i
$879$	15.0845	−	5.49031i	0.508787	−	0.185183i
$880$	−6.43980	−	2.57580i	−0.217085	−	0.0868301i
$881$	−20.4257	−	35.3783i	−0.688159	−	1.19193i	−0.972433	−	0.233183i	$-0.925086\pi$
$881$	−20.4257	−	35.3783i	−0.688159	−	1.19193i	0.284274	−	0.958743i	$-0.408248\pi$
$882$	−1.10381	−	0.637287i	−0.0371673	−	0.0214586i
$883$	16.9151	−	2.98258i	0.569237	−	0.100372i	0.118381	−	0.992968i	$-0.462230\pi$
$883$	16.9151	−	2.98258i	0.569237	−	0.100372i	0.450857	+	0.892596i	$0.351119\pi$
$884$	−4.37067	−	24.7873i	−0.147001	−	0.833686i
$885$	0.144404	−	4.59382i	0.00485410	−	0.154420i
$886$	2.01369	+	3.48782i	0.0676514	+	0.117176i
$887$	4.76555	+	5.67936i	0.160012	+	0.190694i	0.840093	−	0.542442i	$-0.182500\pi$
$887$	4.76555	+	5.67936i	0.160012	+	0.190694i	−0.680082	+	0.733136i	$0.738056\pi$
$888$	−0.777642	−	2.13655i	−0.0260960	−	0.0716981i
$889$	−43.9556	−	15.9985i	−1.47422	−	0.536574i
$890$	7.36903	+	1.53953i	0.247010	+	0.0516053i
$891$	−0.538621	+	3.05467i	−0.0180445	+	0.102335i
$892$			4.64734i			0.155604i
$893$	−1.06525	+	9.86528i	−0.0356473	+	0.330129i
$894$	−7.90386			−0.264345
$895$	31.9263	−	10.4965i	1.06718	−	0.350860i
$896$	2.20357	+	1.84901i	0.0736161	+	0.0617712i
$897$	14.3725	−	39.4881i	0.479884	−	1.31847i
$898$	1.64082	+	4.50812i	0.0547550	+	0.150438i
$899$	17.1599	−	14.3989i	0.572315	−	0.480229i
$900$	4.99013	+	0.314035i	0.166338	+	0.0104678i
$901$	5.79529	−	10.0377i	0.193069	−	0.334405i
$902$	−1.33075	+	0.234647i	−0.0443092	+	0.00781290i
$903$	24.3501	−	4.29358i	0.810321	−	0.142881i
$904$	0.997607	−	1.72791i	0.0331799	−	0.0574693i
$905$	12.7985	−	20.6415i	0.425436	−	0.686146i
$906$	15.0978	−	12.6686i	0.501591	−	0.420885i
$907$	−7.57887	−	20.8228i	−0.251652	−	0.691409i	−0.999617	−	0.0276707i	$-0.991191\pi$
$907$	−7.57887	−	20.8228i	−0.251652	−	0.691409i	0.747965	−	0.663738i	$-0.231031\pi$
$908$	3.23328	−	8.88338i	0.107300	−	0.294805i
$909$	−7.17155	−	6.01765i	−0.237865	−	0.199593i
$910$	9.06376	+	27.5684i	0.300461	+	0.913882i
$911$	−21.8110			−0.722631			−0.361316	−	0.932444i	$-0.617672\pi$
$911$	−21.8110			−0.722631			−0.361316	+	0.932444i	$0.617672\pi$
$912$	0.467954	−	4.33371i	0.0154955	−	0.143503i
$913$			36.9155i			1.22173i
$914$	−3.48838	+	19.7836i	−0.115385	+	0.654382i
$915$	0.0337199	+	0.00704475i	0.00111475	+	0.000232892i
$916$	13.2760	+	4.83205i	0.438650	+	0.159656i
$917$	1.87416	+	5.14920i	0.0618901	+	0.170042i
$918$	3.58595	+	4.27356i	0.118354	+	0.141049i
$919$	20.6102	+	35.6979i	0.679867	+	1.17756i	0.975021	+	0.222114i	$0.0712958\pi$
$919$	20.6102	+	35.6979i	0.679867	+	1.17756i	−0.295154	+	0.955450i	$0.595371\pi$
$920$	−20.8166	−	0.654360i	−0.686303	−	0.0215736i
$921$	3.75386	+	21.2892i	0.123694	+	0.701502i
$922$	−41.3970	+	7.29940i	−1.36334	+	0.240393i
$923$	47.4615	+	27.4019i	1.56221	+	0.901945i
$924$	4.46124	+	7.72710i	0.146764	+	0.254203i
$925$	−11.2975	+	1.26703i	−0.371461	+	0.0416598i
$926$	−2.75007	+	1.00094i	−0.0903730	+	0.0328931i
$927$	−0.628312	+	1.72627i	−0.0206365	+	0.0566983i
$928$	1.63110	−	1.94386i	0.0535433	−	0.0638105i
$929$	7.53575	−	42.7374i	0.247240	−	1.40217i	−0.567992	−	0.823034i	$-0.692280\pi$
$929$	7.53575	−	42.7374i	0.247240	−	1.40217i	0.815232	−	0.579134i	$-0.196609\pi$
$930$	9.32772	+	17.3965i	0.305868	+	0.570453i
$931$	3.84796	+	4.00742i	0.126112	+	0.131338i
$932$		−	3.58125i		−	0.117308i
$933$	−20.8845	−	3.68251i	−0.683729	−	0.120560i
$934$	−26.4917	−	22.2292i	−0.866835	−	0.727361i
$935$	−38.2976	+	5.51845i	−1.25247	+	0.180473i
$936$	−4.23962	+	1.54310i	−0.138576	+	0.0504377i
$937$	8.40977	+	10.0224i	0.274735	+	0.327417i	0.885715	−	0.464230i	$-0.153669\pi$
$937$	8.40977	+	10.0224i	0.274735	+	0.327417i	−0.610980	+	0.791646i	$0.709224\pi$
$938$	−8.00189	+	4.61989i	−0.261271	+	0.150845i
$939$	12.5759	−	21.7820i	0.410397	−	0.710829i
$940$	−3.14779	−	4.00019i	−0.102670	−	0.130472i
$941$	2.69039	+	15.2580i	0.0877043	+	0.497396i	0.996740	+	0.0806781i	$0.0257086\pi$
$941$	2.69039	+	15.2580i	0.0877043	+	0.497396i	−0.909036	+	0.416718i	$0.863180\pi$
$942$	−20.9139	−	12.0746i	−0.681411	−	0.393413i
$943$	−3.51400	+	2.02881i	−0.114432	+	0.0660672i
$944$	1.57455	−	1.32121i	0.0512474	−	0.0430016i
$945$	−4.79500	−	4.28729i	−0.155981	−	0.139466i
$946$	−25.0539	−	9.11888i	−0.814573	−	0.296480i
$947$	3.61086	−	4.30326i	0.117337	−	0.139837i	−0.704178	−	0.710023i	$-0.748684\pi$
$947$	3.61086	−	4.30326i	0.117337	−	0.139837i	0.821516	+	0.570186i	$0.193129\pi$
$948$	−5.68663	−	1.00271i	−0.184693	−	0.0325664i
$949$	69.8331			2.26688
$950$	−20.5107	−	7.36969i	−0.665454	−	0.239104i
$951$	18.3934			0.596446
$952$	15.8038	+	2.78663i	0.512203	+	0.0903152i
$953$	1.61828	−	1.92859i	0.0524213	−	0.0624733i	−0.739197	−	0.673490i	$-0.764795\pi$
$953$	1.61828	−	1.92859i	0.0524213	−	0.0624733i	0.791618	+	0.611016i	$0.209239\pi$
$954$	−1.95234	−	0.710592i	−0.0632092	−	0.0230063i
$955$	−30.2082	−	27.0097i	−0.977514	−	0.874013i
$956$	2.40523	−	2.01822i	0.0777906	−	0.0652740i
$957$	6.81641	−	3.93546i	0.220343	−	0.127215i
$958$	−8.13776	−	4.69834i	−0.262919	−	0.151796i
$959$	−3.04274	−	17.2563i	−0.0982553	−	0.557233i
$960$	1.38279	+	1.75724i	0.0446293	+	0.0567147i
$961$	−23.4644	+	40.6415i	−0.756915	+	1.31102i
$962$	8.88383	−	5.12908i	0.286426	−	0.165368i
$963$	9.29937	+	11.0826i	0.299668	+	0.357131i
$964$	9.43489	−	3.43402i	0.303877	−	0.110602i
$965$	19.4449	−	2.80189i	0.625954	−	0.0901960i
$966$	20.5242	+	17.2218i	0.660355	+	0.554104i
$967$	23.3930	+	4.12481i	0.752267	+	0.132645i	0.536617	−	0.843826i	$-0.319702\pi$
$967$	23.3930	+	4.12481i	0.752267	+	0.132645i	0.215650	+	0.976471i	$0.430813\pi$
$968$			1.37886i			0.0443183i
$969$	−9.82748	−	22.2429i	−0.315704	−	0.714544i
$970$	−20.3080	−	37.8750i	−0.652050	−	1.21609i
$971$	−9.87502	+	56.0040i	−0.316904	+	1.79725i	0.244432	+	0.969666i	$0.421399\pi$
$971$	−9.87502	+	56.0040i	−0.316904	+	1.79725i	−0.561336	+	0.827588i	$0.689713\pi$
$972$	0.642788	−	0.766044i	0.0206174	−	0.0245709i
$973$	7.91866	−	21.7563i	0.253861	−	0.697476i
$974$	32.9403	−	11.9893i	1.05547	−	0.384161i
$975$	2.51421	+	22.4180i	0.0805191	+	0.717951i
$976$	0.00770279	+	0.0133416i	0.000246560	+	0.000427055i
$977$	−28.9471	−	16.7126i	−0.926101	−	0.534685i	−0.0405245	−	0.999179i	$-0.512903\pi$
$977$	−28.9471	−	16.7126i	−0.926101	−	0.534685i	−0.885576	+	0.464494i	$0.846236\pi$
$978$	−14.8686	+	2.62173i	−0.475445	+	0.0838338i
$979$	1.81337	+	10.2841i	0.0579554	+	0.328682i
$980$	−2.84863	−	0.0895452i	−0.0909960	−	0.00286042i
$981$	−3.52366	−	6.10315i	−0.112502	−	0.194859i
$982$	−9.47540	−	11.2923i	−0.302372	−	0.360353i
$983$	−3.68538	−	10.1255i	−0.117545	−	0.322953i	0.866942	−	0.498409i	$-0.166082\pi$
$983$	−3.68538	−	10.1255i	−0.117545	−	0.322953i	−0.984487	+	0.175456i	$0.943860\pi$
$984$	0.409372	+	0.148999i	0.0130503	+	0.00474992i
$985$	17.9211	+	3.74406i	0.571012	+	0.119296i
$986$	2.45821	−	13.9412i	0.0782853	−	0.443978i
$987$			6.54821i			0.208432i
$988$	19.6220	−	1.31605i	0.624259	−	0.0418690i
$989$	−80.0601			−2.54576
$990$	2.16625	+	6.58886i	0.0688478	+	0.209408i
$991$	14.7339	+	12.3632i	0.468038	+	0.392731i	0.846078	−	0.533058i	$-0.178957\pi$
$991$	14.7339	+	12.3632i	0.468038	+	0.392731i	−0.378040	+	0.925789i	$0.623402\pi$
$992$	−3.01926	+	8.29535i	−0.0958616	+	0.263378i
$993$	0.492008	+	1.35178i	0.0156134	+	0.0428975i
$994$	−26.7668	+	22.4600i	−0.848992	+	0.712388i
$995$	−19.7502	+	31.8533i	−0.626125	+	1.00982i
$996$	5.95067	−	10.3069i	0.188554	−	0.326585i
$997$	−32.0347	+	5.64859i	−1.01455	+	0.178892i	−0.656114	−	0.754662i	$-0.727801\pi$
$997$	−32.0347	+	5.64859i	−1.01455	+	0.178892i	−0.358436	+	0.933554i	$0.616690\pi$
$998$	−4.72601	+	0.833324i	−0.149599	+	0.0263784i
$999$	−1.13684	+	1.96906i	−0.0359679	+	0.0622983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.169.6	yes	60
5.4	even	2	inner	570.2.bc.a.169.2	✓	60
19.9	even	9	inner	570.2.bc.a.199.2	yes	60
95.9	even	18	inner	570.2.bc.a.199.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.169.2	✓	60	5.4	even	2	inner
570.2.bc.a.169.6	yes	60	1.1	even	1	trivial
570.2.bc.a.199.2	yes	60	19.9	even	9	inner
570.2.bc.a.199.6	yes	60	95.9	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.66692 - 1.49043i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.49117 - 1.43828i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.66692 - 1.49043i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(2.49117 - 1.43828i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(-1.38279 - 1.75724i) q^{10} +(1.55090 - 2.68623i) q^{11} +(-0.866025 + 0.500000i) q^{12} +(-2.90007 - 3.45617i) q^{13} +(2.70308 - 0.983840i) q^{14} +(2.21321 - 0.318910i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.49399 + 0.968738i) q^{17} -1.00000i q^{18} +(-1.21338 + 4.18661i) q^{19} +(-1.05664 - 1.97066i) q^{20} +(-0.499509 + 2.83285i) q^{21} +(1.99380 - 2.37611i) q^{22} +(3.18560 - 8.75236i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(0.557263 + 4.96885i) q^{25} +(-2.25585 - 3.90726i) q^{26} +(0.866025 + 0.500000i) q^{27} +(2.83285 - 0.499509i) q^{28} +(-0.440638 - 2.49898i) q^{29} +(2.23496 + 0.0702550i) q^{30} +(4.41386 + 7.64503i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.06088 + 2.91473i) q^{33} +(5.24230 + 1.90804i) q^{34} +(-6.29623 - 1.31541i) q^{35} +(0.173648 - 0.984808i) q^{36} +2.27367i q^{37} +(-1.92195 + 3.91230i) q^{38} +4.51171 q^{39} +(-0.698385 - 2.12421i) q^{40} +(-0.333723 - 0.280027i) q^{41} +(-0.983840 + 2.70308i) q^{42} +(-2.93987 - 8.07723i) q^{43} +(2.37611 - 1.99380i) q^{44} +(-1.17832 + 1.90041i) q^{45} +(4.65703 - 8.06622i) q^{46} +(2.24182 - 0.395294i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(0.637287 - 1.10381i) q^{49} +(-0.314035 + 4.99013i) q^{50} +(-4.27356 + 3.58595i) q^{51} +(-1.54310 - 4.23962i) q^{52} +(0.710592 - 1.95234i) q^{53} +(0.766044 + 0.642788i) q^{54} +(-6.58886 + 2.16625i) q^{55} +2.87656 q^{56} +(-2.42718 - 3.62061i) q^{57} -2.53753i q^{58} +(0.356922 - 2.02421i) q^{59} +(2.18881 + 0.457285i) q^{60} +(0.0144765 + 0.00526902i) q^{61} +(3.01926 + 8.29535i) q^{62} +(-1.84901 - 2.20357i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.316970 + 10.0835i) q^{65} +(0.538621 + 3.05467i) q^{66} +(-3.16330 + 0.557775i) q^{67} +(4.83133 + 2.78937i) q^{68} +(4.65703 + 8.06622i) q^{69} +(-5.97216 - 2.38875i) q^{70} +(-11.4145 + 4.15453i) q^{71} +(0.342020 - 0.939693i) q^{72} +(-9.94919 + 11.8570i) q^{73} +(-0.394819 + 2.23913i) q^{74} +(-4.16456 - 2.76703i) q^{75} +(-2.57211 + 3.51912i) q^{76} -8.92249i q^{77} +(4.44317 + 0.783450i) q^{78} +(4.42341 + 3.71168i) q^{79} +(-0.318910 - 2.21321i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.280027 - 0.333723i) q^{82} +(-10.3069 + 5.95067i) q^{83} +(-1.43828 + 2.49117i) q^{84} +(-7.71422 - 9.80319i) q^{85} +(-1.49261 - 8.46502i) q^{86} +(2.19757 + 1.26877i) q^{87} +(2.68623 - 1.55090i) q^{88} +(-2.57903 + 2.16406i) q^{89} +(-1.49043 + 1.66692i) q^{90} +(-12.1955 - 4.43880i) q^{91} +(5.98697 - 7.13499i) q^{92} +(-8.69361 - 1.53292i) q^{93} +2.27641 q^{94} +(8.26245 - 5.17029i) q^{95} -1.00000 q^{96} +(18.9274 + 3.33742i) q^{97} +(0.819280 - 0.976380i) q^{98} +(-2.91473 - 1.06088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{5}+O(q^{10}) \) 60 * q - 6 * q^5	\( 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more