LMFDB - Embedded newform 570.2.bf.a.59.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (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:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.24
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-1.43202 - 0.974336i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.35867 - 1.77595i) q^{5} +(-1.24107 - 1.20820i) q^{6} +(-1.28021 + 0.739129i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.10134 + 2.79053i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-1.43202 - 0.974336i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.35867 - 1.77595i) q^{5} +(-1.24107 - 1.20820i) q^{6} +(-1.28021 + 0.739129i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.10134 + 2.79053i) q^{9} +(1.64642 - 1.51304i) q^{10} +(2.81878 + 1.62742i) q^{11} +(-1.01241 - 1.40535i) q^{12} +(3.29541 - 2.76518i) q^{13} +(-1.38911 + 0.505594i) q^{14} +(-3.67601 + 1.21939i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.748773 - 4.24650i) q^{17} +(0.600038 + 2.93938i) q^{18} +(1.45278 - 4.10968i) q^{19} +(1.88415 - 1.20416i) q^{20} +(2.55344 + 0.188909i) q^{21} +(2.49335 + 2.09217i) q^{22} +(-7.23936 - 2.63491i) q^{23} +(-0.752994 - 1.55981i) q^{24} +(-1.30803 - 4.82587i) q^{25} +(3.72551 - 2.15093i) q^{26} +(1.14177 - 5.06916i) q^{27} +(-1.45580 + 0.256697i) q^{28} +(0.791685 + 4.48987i) q^{29} +(-3.83191 + 0.562535i) q^{30} +(2.19798 - 1.26901i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-2.45088 - 5.07693i) q^{33} +(1.47480 - 4.05197i) q^{34} +(-0.426723 + 3.27783i) q^{35} +(0.0805041 + 2.99892i) q^{36} +4.11020 q^{37} +(2.14434 - 3.79497i) q^{38} +(-7.41329 + 0.748943i) q^{39} +(2.06462 - 0.858686i) q^{40} +(-1.02830 - 0.862846i) q^{41} +(2.48184 + 0.629439i) q^{42} +(-2.81406 - 7.73157i) q^{43} +(2.09217 + 2.49335i) q^{44} +(6.45221 + 1.83548i) q^{45} +(-6.67183 - 3.85198i) q^{46} +(2.06260 + 11.6976i) q^{47} +(-0.470697 - 1.66687i) q^{48} +(-2.40738 + 4.16970i) q^{49} +(-0.450151 - 4.97970i) q^{50} +(-5.20978 + 5.35151i) q^{51} +(4.04242 - 1.47132i) q^{52} +(-0.503212 + 1.38256i) q^{53} +(2.00468 - 4.79388i) q^{54} +(6.72001 - 2.79489i) q^{55} -1.47826 q^{56} +(-6.08460 + 4.46963i) q^{57} +4.55913i q^{58} +(-2.10421 + 11.9336i) q^{59} +(-3.87138 - 0.111416i) q^{60} +(8.53541 + 3.10664i) q^{61} +(2.38495 - 0.868051i) q^{62} +(-3.47251 - 2.75843i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.433451 - 9.60947i) q^{65} +(-1.53204 - 5.42539i) q^{66} +(2.31594 + 13.1344i) q^{67} +(2.15601 - 3.73431i) q^{68} +(7.79959 + 10.8268i) q^{69} +(-0.989429 + 3.15393i) q^{70} +(-2.08000 + 0.757058i) q^{71} +(-0.441476 + 2.96734i) q^{72} +(7.62144 - 9.08287i) q^{73} +(4.04776 + 0.713729i) q^{74} +(-2.82891 + 8.18519i) q^{75} +(2.77076 - 3.36495i) q^{76} -4.81150 q^{77} +(-7.43072 - 0.549740i) q^{78} +(4.55951 - 5.43381i) q^{79} +(2.18236 - 0.487123i) q^{80} +(-6.57410 + 6.14664i) q^{81} +(-0.862846 - 1.02830i) q^{82} +(-1.29300 - 2.23955i) q^{83} +(2.33484 + 1.05084i) q^{84} +(-6.52426 - 7.09939i) q^{85} +(-1.42874 - 8.10277i) q^{86} +(3.24093 - 7.20093i) q^{87} +(1.62742 + 2.81878i) q^{88} +(3.44561 - 2.89121i) q^{89} +(6.03546 + 2.92801i) q^{90} +(-2.17499 + 5.97574i) q^{91} +(-5.90158 - 4.95202i) q^{92} +(-4.38398 - 0.324336i) q^{93} +11.8780i q^{94} +(-5.32475 - 8.16376i) q^{95} +(-0.174098 - 1.72328i) q^{96} +(-1.63353 + 9.26423i) q^{97} +(-3.09486 + 3.68831i) q^{98} +(-1.43693 + 9.65822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{18}\right)$	$-1$

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
$3$	−1.43202	−	0.974336i	−0.826775	−	0.562533i
$3$	−1.43202	−	0.974336i	−0.826775	−	0.562533i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.35867	−	1.77595i	0.607616	−	0.794231i
$5$	1.35867	−	1.77595i	0.607616	−	0.794231i
$6$	−1.24107	−	1.20820i	−0.506664	−	0.493246i
$7$	−1.28021	+	0.739129i	−0.483874	+	0.279365i	−0.722029	−	0.691862i	$-0.756790\pi$
$7$	−1.28021	+	0.739129i	−0.483874	+	0.279365i	0.238156	+	0.971227i	$0.423457\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	1.10134	+	2.79053i	0.367113	+	0.930176i
$10$	1.64642	−	1.51304i	0.520644	−	0.478466i
$11$	2.81878	+	1.62742i	0.849893	+	0.490686i	0.860615	−	0.509257i	$-0.170080\pi$
$11$	2.81878	+	1.62742i	0.849893	+	0.490686i	−0.0107218	+	0.999943i	$0.503413\pi$
$12$	−1.01241	−	1.40535i	−0.292258	−	0.405691i
$13$	3.29541	−	2.76518i	0.913982	−	0.766922i	−0.0588900	−	0.998264i	$-0.518756\pi$
$13$	3.29541	−	2.76518i	0.913982	−	0.766922i	0.972872	+	0.231342i	$0.0743117\pi$
$14$	−1.38911	+	0.505594i	−0.371255	+	0.135126i
$15$	−3.67601	+	1.21939i	−0.949143	+	0.314846i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.748773	−	4.24650i	0.181604	−	1.02993i	−0.748637	−	0.662980i	$-0.769291\pi$
$17$	0.748773	−	4.24650i	0.181604	−	1.02993i	0.930241	−	0.366949i	$-0.119597\pi$
$18$	0.600038	+	2.93938i	0.141430	+	0.692818i
$19$	1.45278	−	4.10968i	0.333290	−	0.942824i
$19$	1.45278	−	4.10968i	0.333290	−	0.942824i
$20$	1.88415	−	1.20416i	0.421308	−	0.269258i
$21$	2.55344	+	0.188909i	0.557206	+	0.0412233i
$22$	2.49335	+	2.09217i	0.531585	+	0.446053i
$23$	−7.23936	−	2.63491i	−1.50951	−	0.549417i	−0.551008	−	0.834500i	$-0.685757\pi$
$23$	−7.23936	−	2.63491i	−1.50951	−	0.549417i	−0.958503	+	0.285083i	$0.907979\pi$
$24$	−0.752994	−	1.55981i	−0.153704	−	0.318394i
$25$	−1.30803	−	4.82587i	−0.261605	−	0.965175i
$26$	3.72551	−	2.15093i	0.730633	−	0.421831i
$27$	1.14177	−	5.06916i	0.219735	−	0.975560i
$28$	−1.45580	+	0.256697i	−0.275120	+	0.0485112i
$29$	0.791685	+	4.48987i	0.147012	+	0.833748i	0.965729	+	0.259551i	$0.0835745\pi$
$29$	0.791685	+	4.48987i	0.147012	+	0.833748i	−0.818717	+	0.574197i	$0.805314\pi$
$30$	−3.83191	+	0.562535i	−0.699608	+	0.102704i
$31$	2.19798	−	1.26901i	0.394769	−	0.227920i	−0.289455	−	0.957192i	$-0.593474\pi$
$31$	2.19798	−	1.26901i	0.394769	−	0.227920i	0.684225	+	0.729271i	$0.260141\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−2.45088	−	5.07693i	−0.426643	−	0.883780i
$34$	1.47480	−	4.05197i	0.252925	−	0.694907i
$35$	−0.426723	+	3.27783i	−0.0721294	+	0.554054i
$36$	0.0805041	+	2.99892i	0.0134173	+	0.499820i
$37$	4.11020			0.675713			0.337857	−	0.941198i	$-0.390298\pi$
$37$	4.11020			0.675713			0.337857	+	0.941198i	$0.390298\pi$
$38$	2.14434	−	3.79497i	0.347858	−	0.615625i
$39$	−7.41329	+	0.748943i	−1.18708	+	0.119927i
$40$	2.06462	−	0.858686i	0.326445	−	0.135770i
$41$	−1.02830	−	0.862846i	−0.160593	−	0.134754i	0.558950	−	0.829201i	$-0.311204\pi$
$41$	−1.02830	−	0.862846i	−0.160593	−	0.134754i	−0.719543	+	0.694448i	$0.755649\pi$
$42$	2.48184	+	0.629439i	0.382957	+	0.0971246i
$43$	−2.81406	−	7.73157i	−0.429140	−	1.17905i	−0.946335	−	0.323186i	$-0.895246\pi$
$43$	−2.81406	−	7.73157i	−0.429140	−	1.17905i	0.517195	−	0.855867i	$-0.326976\pi$
$44$	2.09217	+	2.49335i	0.315407	+	0.375887i
$45$	6.45221	+	1.83548i	0.961839	+	0.273617i
$46$	−6.67183	−	3.85198i	−0.983708	−	0.567944i
$47$	2.06260	+	11.6976i	0.300861	+	1.70627i	0.642374	+	0.766391i	$0.277949\pi$
$47$	2.06260	+	11.6976i	0.300861	+	1.70627i	−0.341513	+	0.939877i	$0.610939\pi$
$48$	−0.470697	−	1.66687i	−0.0679393	−	0.240591i
$49$	−2.40738	+	4.16970i	−0.343911	+	0.595671i
$50$	−0.450151	−	4.97970i	−0.0636610	−	0.704235i
$51$	−5.20978	+	5.35151i	−0.729515	+	0.749361i
$52$	4.04242	−	1.47132i	0.560583	−	0.204035i
$53$	−0.503212	+	1.38256i	−0.0691214	+	0.189910i	−0.969443	−	0.245315i	$-0.921109\pi$
$53$	−0.503212	+	1.38256i	−0.0691214	+	0.189910i	0.900322	+	0.435224i	$0.143331\pi$
$54$	2.00468	−	4.79388i	0.272802	−	0.652364i
$55$	6.72001	−	2.79489i	0.906126	−	0.376863i
$56$	−1.47826			−0.197541
$57$	−6.08460	+	4.46963i	−0.805925	+	0.592017i
$58$			4.55913i			0.598643i
$59$	−2.10421	+	11.9336i	−0.273945	+	1.55362i	0.468349	+	0.883544i	$0.344849\pi$
$59$	−2.10421	+	11.9336i	−0.273945	+	1.55362i	−0.742293	+	0.670075i	$0.766262\pi$
$60$	−3.87138	−	0.111416i	−0.499793	−	0.0143837i
$61$	8.53541	+	3.10664i	1.09285	+	0.397764i	0.824675	−	0.565607i	$-0.191358\pi$
$61$	8.53541	+	3.10664i	1.09285	+	0.397764i	0.268173	+	0.963371i	$0.413580\pi$
$62$	2.38495	−	0.868051i	0.302889	−	0.110243i
$63$	−3.47251	−	2.75843i	−0.437495	−	0.347529i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.433451	−	9.60947i	−0.0537630	−	1.19191i
$66$	−1.53204	−	5.42539i	−0.188582	−	0.667819i
$67$	2.31594	+	13.1344i	0.282937	+	1.60462i	0.712562	+	0.701609i	$0.247535\pi$
$67$	2.31594	+	13.1344i	0.282937	+	1.60462i	−0.429625	+	0.903008i	$0.641354\pi$
$68$	2.15601	−	3.73431i	0.261454	−	0.452852i
$69$	7.79959	+	10.8268i	0.938961	+	1.30339i
$70$	−0.989429	+	3.15393i	−0.118259	+	0.376967i
$71$	−2.08000	+	0.757058i	−0.246850	+	0.0898462i	−0.462482	−	0.886629i	$-0.653041\pi$
$71$	−2.08000	+	0.757058i	−0.246850	+	0.0898462i	0.215632	+	0.976475i	$0.430819\pi$
$72$	−0.441476	+	2.96734i	−0.0520284	+	0.349704i
$73$	7.62144	−	9.08287i	0.892022	−	1.06307i	−0.105618	−	0.994407i	$-0.533682\pi$
$73$	7.62144	−	9.08287i	0.892022	−	1.06307i	0.997640	−	0.0686633i	$-0.0218734\pi$
$74$	4.04776	+	0.713729i	0.470542	+	0.0829693i
$75$	−2.82891	+	8.18519i	−0.326654	+	0.945144i
$76$	2.77076	−	3.36495i	0.317827	−	0.385987i
$77$	−4.81150			−0.548321
$78$	−7.43072	−	0.549740i	−0.841363	−	0.0622458i
$79$	4.55951	−	5.43381i	0.512985	−	0.611351i	−0.445922	−	0.895072i	$-0.647124\pi$
$79$	4.55951	−	5.43381i	0.512985	−	0.611351i	0.958907	+	0.283720i	$0.0915687\pi$
$80$	2.18236	−	0.487123i	0.243996	−	0.0544620i
$81$	−6.57410	+	6.14664i	−0.730456	+	0.682960i
$82$	−0.862846	−	1.02830i	−0.0952854	−	0.113557i
$83$	−1.29300	−	2.23955i	−0.141926	−	0.245823i	0.786296	−	0.617850i	$-0.211996\pi$
$83$	−1.29300	−	2.23955i	−0.141926	−	0.245823i	−0.928222	+	0.372027i	$0.878663\pi$
$84$	2.33484	+	1.05084i	0.254752	+	0.114657i
$85$	−6.52426	−	7.09939i	−0.707655	−	0.770037i
$86$	−1.42874	−	8.10277i	−0.154065	−	0.873744i
$87$	3.24093	−	7.20093i	0.347465	−	0.772021i
$88$	1.62742	+	2.81878i	0.173484	+	0.300483i
$89$	3.44561	−	2.89121i	0.365234	−	0.306467i	−0.441639	−	0.897193i	$-0.645603\pi$
$89$	3.44561	−	2.89121i	0.365234	−	0.306467i	0.806873	+	0.590725i	$0.201158\pi$
$90$	6.03546	+	2.92801i	0.636193	+	0.308639i
$91$	−2.17499	+	5.97574i	−0.228001	+	0.626428i
$92$	−5.90158	−	4.95202i	−0.615282	−	0.516283i
$93$	−4.38398	−	0.324336i	−0.454598	−	0.0336321i
$94$			11.8780i			1.22513i
$95$	−5.32475	−	8.16376i	−0.546308	−	0.837584i
$96$	−0.174098	−	1.72328i	−0.0177688	−	0.175881i
$97$	−1.63353	+	9.26423i	−0.165860	+	0.940640i	0.782313	+	0.622886i	$0.214040\pi$
$97$	−1.63353	+	9.26423i	−0.165860	+	0.940640i	−0.948173	+	0.317754i	$0.897071\pi$
$98$	−3.09486	+	3.68831i	−0.312628	+	0.372576i
$99$	−1.43693	+	9.65822i	−0.144417	+	0.970688i
$100$	0.421403	−	4.98221i	0.0421403	−	0.498221i
$101$	−6.36950	−	7.59088i	−0.633789	−	0.755321i	0.349586	−	0.936904i	$-0.386322\pi$
$101$	−6.36950	−	7.59088i	−0.633789	−	0.755321i	−0.983376	+	0.181584i	$0.941878\pi$
$102$	−6.05991	+	4.36554i	−0.600020	+	0.432253i
$103$	−8.07822	+	13.9919i	−0.795971	+	1.37866i	0.126250	+	0.991998i	$0.459706\pi$
$103$	−8.07822	+	13.9919i	−0.795971	+	1.37866i	−0.922221	+	0.386663i	$0.873628\pi$
$104$	4.23650	−	0.747009i	0.415423	−	0.0732503i
$105$	3.80478	−	4.27813i	0.371308	−	0.417503i
$106$	−0.735646	+	1.27418i	−0.0714523	+	0.123759i
$107$	−9.45606	+	5.45946i	−0.914152	+	0.527786i	−0.881765	−	0.471689i	$-0.843644\pi$
$107$	−9.45606	+	5.45946i	−0.914152	+	0.527786i	−0.0323873	+	0.999475i	$0.510311\pi$
$108$	2.80667	−	4.37294i	0.270072	−	0.420786i
$109$	−1.84788	−	5.07700i	−0.176995	−	0.486289i	0.819194	−	0.573517i	$-0.194421\pi$
$109$	−1.84788	−	5.07700i	−0.176995	−	0.486289i	−0.996188	+	0.0872281i	$0.972199\pi$
$110$	7.10325	−	1.58551i	0.677268	−	0.151172i
$111$	−5.88588	−	4.00472i	−0.558663	−	0.380111i
$112$	−1.45580	−	0.256697i	−0.137560	−	0.0242556i
$113$			12.3088i			1.15792i	0.815357	+	0.578959i	$0.196541\pi$
$113$			12.3088i			1.15792i	−0.815357	+	0.578959i	$0.803459\pi$
$114$	−6.76831	+	3.34515i	−0.633910	+	0.313302i
$115$	−14.5154	+	9.27680i	−1.35357	+	0.865066i
$116$	−0.791685	+	4.48987i	−0.0735061	+	0.416874i
$117$	11.3457	+	6.15054i	1.04891	+	0.568617i
$118$	−4.14449	+	11.3869i	−0.381531	+	1.04825i
$119$	2.18013	+	5.98986i	0.199852	+	0.549089i
$120$	−3.79322	−	0.781981i	−0.346272	−	0.0713848i
$121$	−0.203002	−	0.351609i	−0.0184547	−	0.0319645i
$122$	7.86628	+	4.54160i	0.712180	+	0.411177i
$123$	0.631840	+	2.23752i	0.0569711	+	0.201750i
$124$	2.49945	−	0.440721i	0.224457	−	0.0395779i
$125$	−10.3477	−	4.23378i	−0.925527	−	0.378681i
$126$	−2.94076	−	3.31952i	−0.261983	−	0.295726i
$127$	0.979491	−	0.821891i	0.0869158	−	0.0729310i	−0.598295	−	0.801276i	$-0.704155\pi$
$127$	0.979491	−	0.821891i	0.0869158	−	0.0729310i	0.685210	+	0.728345i	$0.259710\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−3.50336	+	13.8136i	−0.308454	+	1.21622i
$130$	1.24180	−	9.53874i	0.108913	−	0.836603i
$131$	−10.3496	−	1.82492i	−0.904252	−	0.159444i	−0.297860	−	0.954610i	$-0.596273\pi$
$131$	−10.3496	−	1.82492i	−0.904252	−	0.159444i	−0.606392	+	0.795166i	$0.707384\pi$
$132$	−0.566661	−	5.60900i	−0.0493215	−	0.488201i
$133$	1.17772	+	6.33504i	0.102122	+	0.549317i
$134$			13.3370i			1.15214i
$135$	−7.45129	−	8.91506i	−0.641305	−	0.767286i
$136$	2.77171	−	3.30319i	0.237672	−	0.283247i
$137$	−6.87090	−	2.50080i	−0.587021	−	0.213658i	0.0313977	−	0.999507i	$-0.490004\pi$
$137$	−6.87090	−	2.50080i	−0.587021	−	0.213658i	−0.618419	+	0.785849i	$0.712226\pi$
$138$	5.80105	+	12.0167i	0.493818	+	1.02293i
$139$	−0.409647	+	0.343735i	−0.0347458	+	0.0291552i	−0.659995	−	0.751270i	$-0.729442\pi$
$139$	−0.409647	+	0.343735i	−0.0347458	+	0.0291552i	0.625249	+	0.780425i	$0.284997\pi$
$140$	−1.52207	+	2.93420i	−0.128639	+	0.247985i
$141$	8.44370	−	18.7608i	0.711088	−	1.57994i
$142$	−2.17986	+	0.384368i	−0.182930	+	0.0322555i
$143$	13.7891	−	2.43140i	1.15311	−	0.203324i
$144$	−0.950042	+	2.84560i	−0.0791702	+	0.237133i
$145$	9.04944	+	4.69426i	0.751515	+	0.389837i
$146$	9.08287	−	7.62144i	0.751704	−	0.630755i
$147$	7.51009	−	3.62548i	0.619421	−	0.299025i
$148$	3.86233	+	1.40577i	0.317481	+	0.115554i
$149$	2.54088	−	3.02810i	0.208157	−	0.248072i	−0.651857	−	0.758342i	$-0.726010\pi$
$149$	2.54088	−	3.02810i	0.208157	−	0.248072i	0.860014	+	0.510270i	$0.170454\pi$
$150$	−4.20727	+	7.56960i	−0.343522	+	0.618055i
$151$			4.79732i			0.390400i	0.980763	+	0.195200i	$0.0625356\pi$
$151$			4.79732i			0.390400i	−0.980763	+	0.195200i	$0.937464\pi$
$152$	3.31298	−	2.83270i	0.268718	−	0.229762i
$153$	12.6746	−	2.58737i	1.02468	−	0.209177i
$154$	−4.73840	−	0.835508i	−0.381831	−	0.0673271i
$155$	0.732638	−	5.62768i	0.0588469	−	0.452026i
$156$	−7.22237	−	1.83172i	−0.578252	−	0.146655i
$157$	1.75281	+	4.81581i	0.139890	+	0.384344i	0.989778	−	0.142620i	$-0.0455527\pi$
$157$	1.75281	+	4.81581i	0.139890	+	0.384344i	−0.849888	+	0.526963i	$0.823330\pi$
$158$	5.43381	−	4.55951i	0.432291	−	0.362735i
$159$	2.06769	−	1.48955i	0.163978	−	0.118129i
$160$	2.23380	−	0.100759i	0.176597	−	0.00796571i
$161$	11.2154	−	1.97758i	0.883901	−	0.155856i
$162$	−7.54158	+	4.91168i	−0.592522	+	0.385898i
$163$	−5.20311	−	3.00402i	−0.407539	−	0.235293i	0.282193	−	0.959358i	$-0.408938\pi$
$163$	−5.20311	−	3.00402i	−0.407539	−	0.235293i	−0.689732	+	0.724065i	$0.742272\pi$
$164$	−0.671175	−	1.16251i	−0.0524100	−	0.0907767i
$165$	−12.3463	−	2.54523i	−0.961160	−	0.198145i
$166$	−0.884467	−	2.43005i	−0.0686480	−	0.188609i
$167$	−4.24497	+	11.6630i	−0.328486	+	0.902508i	0.660009	+	0.751257i	$0.270552\pi$
$167$	−4.24497	+	11.6630i	−0.328486	+	0.902508i	−0.988495	+	0.151251i	$0.951670\pi$
$168$	2.11689	+	1.44032i	0.163322	+	0.111123i
$169$	0.956097	−	5.42229i	0.0735459	−	0.417099i
$170$	−5.19235	−	8.12446i	−0.398235	−	0.623118i
$171$	13.0682	−	0.472137i	0.999348	−	0.0361052i
$172$		−	8.22777i		−	0.627361i
$173$	4.05361	+	0.714761i	0.308190	+	0.0543423i	0.325604	−	0.945506i	$-0.394432\pi$
$173$	4.05361	+	0.714761i	0.308190	+	0.0543423i	−0.0174140	+	0.999848i	$0.505543\pi$
$174$	4.44212	−	6.52875i	0.336757	−	0.494943i
$175$	5.24149	+	5.21133i	0.396220	+	0.393939i
$176$	1.11322	+	3.05855i	0.0839122	+	0.230547i
$177$	14.6406	−	15.0389i	1.10045	−	1.13039i
$178$	3.89531	−	2.24896i	0.291966	−	0.168567i
$179$	−2.65771	+	4.60328i	−0.198646	+	0.344066i	−0.948090	−	0.318003i	$-0.896988\pi$
$179$	−2.65771	+	4.60328i	−0.198646	+	0.344066i	0.749443	+	0.662068i	$0.230321\pi$
$180$	5.43532	+	3.93157i	0.405125	+	0.293042i
$181$	−25.3198	+	4.46457i	−1.88201	+	0.331849i	−0.992217	−	0.124520i	$-0.960261\pi$
$181$	−25.3198	+	4.46457i	−1.88201	+	0.331849i	−0.889791	+	0.456369i	$0.849150\pi$
$182$	−3.17963	+	5.50727i	−0.235690	+	0.408226i
$183$	−9.19594	−	12.7651i	−0.679784	−	0.943624i
$184$	−4.95202	−	5.90158i	−0.365067	−	0.435070i
$185$	5.58441	−	7.29953i	0.410574	−	0.536672i
$186$	−4.26106	−	1.08068i	−0.312436	−	0.0792392i
$187$	9.02147	−	10.7514i	0.659716	−	0.786218i
$188$	−2.06260	+	11.6976i	−0.150431	+	0.853134i
$189$	2.28505	+	7.33350i	0.166213	+	0.533434i
$190$	−3.82624	−	8.96437i	−0.277584	−	0.650344i
$191$		−	11.5816i		−	0.838015i	−0.907983	−	0.419007i	$-0.862378\pi$
$191$		−	11.5816i		−	0.838015i	0.907983	−	0.419007i	$-0.137622\pi$
$192$	0.127791	−	1.72733i	0.00922255	−	0.124659i
$193$	0.0914143	+	0.0767057i	0.00658015	+	0.00552140i	0.646072	−	0.763277i	$-0.276411\pi$
$193$	0.0914143	+	0.0767057i	0.00658015	+	0.00552140i	−0.639492	+	0.768798i	$0.720855\pi$
$194$	−3.21743	+	8.83982i	−0.230998	+	0.634662i
$195$	−8.74214	+	14.1832i	−0.626037	+	1.01568i
$196$	−3.68831	+	3.09486i	−0.263451	+	0.221062i
$197$	10.0727	+	17.4464i	0.717649	+	1.24301i	0.961929	+	0.273300i	$0.0881152\pi$
$197$	10.0727	+	17.4464i	0.717649	+	1.24301i	−0.244279	+	0.969705i	$0.578551\pi$
$198$	−3.09224	+	9.26197i	−0.219756	+	0.658219i
$199$	−4.04530	−	22.9420i	−0.286764	−	1.62632i	−0.698917	−	0.715203i	$-0.746334\pi$
$199$	−4.04530	−	22.9420i	−0.286764	−	1.62632i	0.412153	−	0.911115i	$-0.364777\pi$
$200$	1.28015	−	4.83334i	0.0905204	−	0.341769i
$201$	9.48081	−	21.0651i	0.668724	−	1.48582i
$202$	−4.95459	−	8.58161i	−0.348604	−	0.603800i
$203$	−4.33212	−	5.16281i	−0.304055	−	0.362359i
$204$	−6.72591	+	3.24692i	−0.470908	+	0.227330i
$205$	−2.92950	+	0.653890i	−0.204605	+	0.0456696i
$206$	−10.3852	+	12.3766i	−0.723568	+	0.862315i
$207$	−0.620201	−	23.1036i	−0.0431069	−	1.60581i
$208$	4.30185			0.298280
$209$	10.7832	−	9.21998i	0.745891	−	0.637759i
$210$	4.48986	−	3.55244i	0.309830	−	0.245142i
$211$	24.9212	+	4.39428i	1.71565	+	0.302515i	0.943116	−	0.332463i	$-0.107880\pi$
$211$	24.9212	+	4.39428i	1.71565	+	0.302515i	0.772530	+	0.634978i	$0.218991\pi$
$212$	−0.945728	+	1.12708i	−0.0649529	+	0.0774078i
$213$	3.71622	+	0.942498i	0.254631	+	0.0645789i
$214$	−10.2604	+	3.73449i	−0.701388	+	0.255285i
$215$	−17.5543	−	5.50701i	−1.19719	−	0.375575i
$216$	3.52338	−	3.81913i	0.239736	−	0.259859i
$217$	−1.87592	+	3.24919i	−0.127346	+	0.220569i
$218$	−0.938193	−	5.32075i	−0.0635424	−	0.360367i
$219$	−19.7638	+	5.58098i	−1.33551	+	0.377128i
$220$	7.27066	−	0.327955i	0.490187	−	0.0221107i
$221$	−9.27482	−	16.0645i	−0.623892	−	1.08061i
$222$	−5.10104	−	4.96595i	−0.342360	−	0.333293i
$223$	22.3261	−	8.12604i	1.49507	−	0.544160i	0.540289	−	0.841479i	$-0.318315\pi$
$223$	22.3261	−	8.12604i	1.49507	−	0.544160i	0.954778	+	0.297319i	$0.0960925\pi$
$224$	−1.38911	−	0.505594i	−0.0928137	−	0.0337814i
$225$	12.0262	−	8.96502i	0.801744	−	0.597668i
$226$	−2.13741	+	12.1218i	−0.142178	+	0.806333i
$227$		−	12.6657i		−	0.840650i	−0.907374	−	0.420325i	$-0.861916\pi$
$227$		−	12.6657i		−	0.840650i	0.907374	−	0.420325i	$-0.138084\pi$
$228$	−7.24636	+	2.11902i	−0.479902	+	0.140336i
$229$	14.4298			0.953547			0.476773	−	0.879026i	$-0.341806\pi$
$229$	14.4298			0.953547			0.476773	+	0.879026i	$0.341806\pi$
$230$	−15.9058	+	6.61529i	−1.04880	+	0.436199i
$231$	6.89014	+	4.68801i	0.453338	+	0.308449i
$232$	−1.55931	+	4.28418i	−0.102374	+	0.281270i
$233$	2.30660	−	0.839533i	0.151110	−	0.0549996i	−0.265358	−	0.964150i	$-0.585490\pi$
$233$	2.30660	−	0.839533i	0.151110	−	0.0549996i	0.416468	+	0.909150i	$0.363268\pi$
$234$	10.1053	+	8.02725i	0.660603	+	0.524758i
$235$	23.5768	+	12.2301i	1.53798	+	0.797803i
$236$	−6.05883	+	10.4942i	−0.394396	+	0.683115i
$237$	−11.8236	+	3.33881i	−0.768028	+	0.216879i
$238$	1.10688	+	6.27743i	0.0717484	+	0.406905i
$239$	26.6345	+	15.3774i	1.72284	+	0.994682i	0.912917	+	0.408145i	$0.133824\pi$
$239$	26.6345	+	15.3774i	1.72284	+	0.994682i	0.809922	+	0.586537i	$0.199509\pi$
$240$	−3.59980	−	1.42879i	−0.232366	−	0.0922278i
$241$	3.73432	+	4.45039i	0.240549	+	0.286675i	0.872789	−	0.488097i	$-0.162309\pi$
$241$	3.73432	+	4.45039i	0.240549	+	0.286675i	−0.632240	+	0.774772i	$0.717864\pi$
$242$	−0.138861	−	0.381518i	−0.00892634	−	0.0245249i
$243$	15.4031	−	2.39671i	0.988110	−	0.153749i
$244$	6.95813	+	5.83857i	0.445449	+	0.373776i
$245$	4.13436	+	9.94064i	0.264135	+	0.635084i
$246$	0.233700	+	2.31324i	0.0149002	+	0.147487i
$247$	−6.57649	−	17.5603i	−0.418452	−	1.11733i
$248$	2.53801			0.161164
$249$	−0.330470	+	4.46689i	−0.0209427	+	0.283078i
$250$	−9.45532	−	5.96632i	−0.598007	−	0.377343i
$251$	−6.20880	+	17.0585i	−0.391896	+	1.07672i	0.574239	+	0.818688i	$0.305298\pi$
$251$	−6.20880	+	17.0585i	−0.391896	+	1.07672i	−0.966135	+	0.258037i	$0.916924\pi$
$252$	−2.31965	−	3.77974i	−0.146124	−	0.238101i
$253$	−16.1180	−	19.2087i	−1.01333	−	1.20764i
$254$	1.10733	−	0.639317i	0.0694801	−	0.0401143i
$255$	2.42566	+	16.5233i	0.151901	+	1.03473i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−29.4280	+	5.18895i	−1.83567	+	0.323678i	−0.980777	−	0.195132i	$-0.937487\pi$
$257$	−29.4280	+	5.18895i	−1.83567	+	0.323678i	−0.854890	+	0.518809i	$0.826376\pi$
$258$	−5.84884	+	12.9954i	−0.364133	+	0.809056i
$259$	−5.26192	+	3.03797i	−0.326960	+	0.188770i
$260$	2.87932	−	9.17819i	0.178568	−	0.569207i
$261$	−11.6572	+	7.15409i	−0.721562	+	0.442827i
$262$	−9.87551	−	3.59439i	−0.610111	−	0.222062i
$263$	6.37410	+	5.34851i	0.393044	+	0.329803i	0.817798	−	0.575506i	$-0.195195\pi$
$263$	6.37410	+	5.34851i	0.393044	+	0.329803i	−0.424754	+	0.905309i	$0.639639\pi$
$264$	0.415941	−	5.62219i	0.0255994	−	0.346022i
$265$	1.77167	+	2.77213i	0.108833	+	0.170290i
$266$	0.0597642	+	6.44330i	0.00366438	+	0.395064i
$267$	−7.75117	+	0.783078i	−0.474364	+	0.0479236i
$268$	−2.31594	+	13.1344i	−0.141469	+	0.802308i
$269$	−12.4453	−	10.4428i	−0.758802	−	0.636711i	0.179013	−	0.983847i	$-0.442710\pi$
$269$	−12.4453	−	10.4428i	−0.758802	−	0.636711i	−0.937815	+	0.347136i	$0.887154\pi$
$270$	−5.79001	−	10.0735i	−0.352369	−	0.613055i
$271$	−10.5460	+	3.83843i	−0.640624	+	0.233168i	−0.641849	−	0.766831i	$-0.721832\pi$
$271$	−10.5460	+	3.83843i	−0.640624	+	0.233168i	0.00122479	+	0.999999i	$0.499610\pi$
$272$	3.30319	−	2.77171i	0.200286	−	0.168060i
$273$	8.93700	−	6.43819i	0.540892	−	0.389657i
$274$	−6.33226	−	3.65593i	−0.382546	−	0.220863i
$275$	4.16669	−	15.7318i	0.251261	−	0.948661i
$276$	3.62624	+	12.8415i	0.218274	+	0.772967i
$277$	−16.8897	−	9.75128i	−1.01480	−	0.585898i	−0.102210	−	0.994763i	$-0.532591\pi$
$277$	−16.8897	−	9.75128i	−1.01480	−	0.585898i	−0.912595	+	0.408865i	$0.865925\pi$
$278$	−0.463113	+	0.267378i	−0.0277757	+	0.0160363i
$279$	5.96192	+	4.73592i	0.356931	+	0.283532i
$280$	−2.00847	+	2.62532i	−0.120029	+	0.156893i
$281$	0.926183	+	0.337103i	0.0552515	+	0.0201099i	0.369498	−	0.929232i	$-0.379530\pi$
$281$	0.926183	+	0.337103i	0.0552515	+	0.0201099i	−0.314247	+	0.949341i	$0.601752\pi$
$282$	11.5732	−	17.0095i	0.689174	−	1.01290i
$283$	−9.06457	−	1.59833i	−0.538833	−	0.0950107i	−0.102393	−	0.994744i	$-0.532650\pi$
$283$	−9.06457	−	1.59833i	−0.538833	−	0.0950107i	−0.436440	+	0.899733i	$0.643761\pi$
$284$	−2.21349			−0.131346
$285$	−0.329113	+	16.8787i	−0.0194950	+	0.999810i
$286$	14.0019			0.827947
$287$	1.95419	+	0.344577i	0.115352	+	0.0203397i
$288$	−1.42974	+	2.63739i	−0.0842483	+	0.155410i
$289$	−1.49736	−	0.544996i	−0.0880802	−	0.0320586i
$290$	8.09681	+	6.19436i	0.475461	+	0.363745i
$291$	11.3657	−	11.6749i	0.666270	−	0.684395i
$292$	10.2683	−	5.92843i	0.600909	−	0.346935i
$293$	10.4808	+	6.05108i	0.612294	+	0.353508i	0.773863	−	0.633354i	$-0.218322\pi$
$293$	10.4808	+	6.05108i	0.612294	+	0.353508i	−0.161569	+	0.986861i	$0.551655\pi$
$294$	8.02555	−	2.26629i	0.468060	−	0.132173i
$295$	18.3345	+	19.9508i	1.06748	+	1.16158i
$296$	3.55954	+	2.05510i	0.206894	+	0.119450i
$297$	11.4681	−	12.4307i	0.665444	−	0.721301i
$298$	3.02810	−	2.54088i	0.175413	−	0.147189i
$299$	−31.1427	+	11.3350i	−1.80103	+	0.655520i
$300$	−5.45780	+	6.72402i	−0.315106	+	0.388211i
$301$	9.31722	+	7.81807i	0.537036	+	0.450626i
$302$	−0.833045	+	4.72443i	−0.0479364	+	0.271861i
$303$	1.72517	+	17.0763i	0.0991083	+	0.981007i
$304$	3.75454	−	2.21437i	0.215338	−	0.127003i
$305$	17.1141	−	10.9376i	0.979948	−	0.626286i
$306$	12.9314	−	0.347135i	0.739238	−	0.0198444i
$307$	−5.37432	−	4.50959i	−0.306729	−	0.257376i	0.476410	−	0.879223i	$-0.341938\pi$
$307$	−5.37432	−	4.50959i	−0.306729	−	0.257376i	−0.783138	+	0.621848i	$0.786382\pi$
$308$	−4.52133	−	1.64563i	−0.257627	−	0.0937684i
$309$	25.2009	−	12.1657i	1.43363	−	0.692083i
$310$	1.69874	−	5.41496i	0.0964821	−	0.307549i
$311$	5.59973	−	3.23301i	0.317532	−	0.183327i	−0.332760	−	0.943011i	$-0.607980\pi$
$311$	5.59973	−	3.23301i	0.317532	−	0.183327i	0.650292	+	0.759685i	$0.274647\pi$
$312$	−6.79457	−	3.05804i	−0.384667	−	0.173128i
$313$	−13.0662	+	2.30393i	−0.738546	+	0.130226i	−0.530251	−	0.847841i	$-0.677902\pi$
$313$	−13.0662	+	2.30393i	−0.738546	+	0.130226i	−0.208295	+	0.978066i	$0.566791\pi$
$314$	0.889926	+	5.04702i	0.0502214	+	0.284820i
$315$	−9.61684	+	2.41922i	−0.541847	+	0.136307i
$316$	6.14301	−	3.54667i	0.345571	−	0.199516i
$317$	17.7824	+	21.1922i	0.998758	+	1.19027i	0.981703	+	0.190419i	$0.0609845\pi$
$317$	17.7824	+	21.1922i	0.998758	+	1.19027i	0.0170548	+	0.999855i	$0.494571\pi$
$318$	2.29493	−	1.10787i	0.128693	−	0.0621265i
$319$	−5.07532	+	13.9443i	−0.284164	+	0.780733i
$320$	2.21736	+	0.288666i	0.123954	+	0.0161369i
$321$	18.8606	+	1.39534i	1.05269	+	0.0778805i
$322$	11.3885			0.634654
$323$	−16.3640	−	9.24644i	−0.910515	−	0.514486i
$324$	−8.27991	+	3.52748i	−0.459995	+	0.195971i
$325$	−17.6549	−	12.2863i	−0.979317	−	0.681522i
$326$	−4.60242	−	3.86189i	−0.254905	−	0.213890i
$327$	−2.30051	+	9.07081i	−0.127219	+	0.501617i
$328$	−0.459111	−	1.26140i	−0.0253502	−	0.0696490i
$329$	−11.2866	−	13.4508i	−0.622250	−	0.741568i
$330$	−11.7168	−	4.65047i	−0.644988	−	0.256000i
$331$	−19.1889	−	11.0787i	−1.05472	−	0.608941i	−0.130750	−	0.991415i	$-0.541739\pi$
$331$	−19.1889	−	11.0787i	−1.05472	−	0.608941i	−0.923966	+	0.382475i	$0.875072\pi$
$332$	−0.449056	−	2.54672i	−0.0246451	−	0.139770i
$333$	4.52673	+	11.4696i	0.248063	+	0.628532i
$334$	−6.20574	+	10.7487i	−0.339563	+	0.588140i
$335$	26.4726	+	13.7323i	1.44635	+	0.750273i
$336$	1.83462	+	1.78603i	0.100087	+	0.0974361i
$337$	0.337706	−	0.122915i	0.0183960	−	0.00669561i	−0.332806	−	0.942995i	$-0.607995\pi$
$337$	0.337706	−	0.122915i	0.0183960	−	0.00669561i	0.351202	+	0.936300i	$0.385773\pi$
$338$	1.88314	−	5.17389i	0.102429	−	0.281423i
$339$	11.9929	−	17.6264i	0.651367	−	0.957337i
$340$	−3.70267	−	8.90267i	−0.200805	−	0.482815i
$341$	8.26082			0.447349
$342$	12.9516	+	1.80430i	0.700343	+	0.0975654i
$343$		−	17.4653i		−	0.943035i
$344$	1.42874	−	8.10277i	0.0770323	−	0.436872i
$345$	29.8250	+	0.858342i	1.60572	+	0.0462116i
$346$	3.86791	+	1.40780i	0.207940	+	0.0756840i
$347$	−9.09244	+	3.30938i	−0.488108	+	0.177657i	−0.574338	−	0.818619i	$-0.694740\pi$
$347$	−9.09244	+	3.30938i	−0.488108	+	0.177657i	0.0862298	+	0.996275i	$0.472518\pi$
$348$	5.50834	−	5.65820i	0.295278	−	0.303311i
$349$	12.0168	+	20.8137i	0.643245	+	1.11413i	0.984704	+	0.174236i	$0.0557456\pi$
$349$	12.0168	+	20.8137i	0.643245	+	1.11413i	−0.341459	+	0.939897i	$0.610921\pi$
$350$	4.25693	+	6.04233i	0.227542	+	0.322976i
$351$	−10.2545	−	19.8622i	−0.547345	−	1.06016i
$352$	0.565197	+	3.20539i	0.0301251	+	0.170848i
$353$	−6.31913	+	10.9451i	−0.336333	+	0.582546i	−0.983740	−	0.179598i	$-0.942520\pi$
$353$	−6.31913	+	10.9451i	−0.336333	+	0.582546i	0.647407	+	0.762145i	$0.275854\pi$
$354$	17.0296	−	12.2681i	0.905114	−	0.652041i
$355$	−1.48153	+	4.72258i	−0.0786317	+	0.250648i
$356$	4.22666	−	1.53838i	0.224013	−	0.0815339i
$357$	2.71415	−	10.7017i	0.143648	−	0.566397i
$358$	−3.41668	+	4.07184i	−0.180577	+	0.215204i
$359$	9.62079	+	1.69640i	0.507766	+	0.0895328i	0.421662	−	0.906753i	$-0.361447\pi$
$359$	9.62079	+	1.69640i	0.507766	+	0.0895328i	0.0861044	+	0.996286i	$0.472558\pi$
$360$	4.67004	+	4.81568i	0.246133	+	0.253808i
$361$	−14.7789	−	11.9409i	−0.777836	−	0.628468i
$362$	−25.7104			−1.35131
$363$	−0.0518837	+	0.701301i	−0.00272319	+	0.0368088i
$364$	−4.08765	+	4.87147i	−0.214251	+	0.255334i
$365$	−5.77575	−	25.8760i	−0.302316	−	1.35441i
$366$	−6.83960	−	14.1680i	−0.357512	−	0.740575i
$367$	−17.3910	−	20.7258i	−0.907802	−	1.08188i	−0.996312	−	0.0858013i	$-0.972655\pi$
$367$	−17.3910	−	20.7258i	−0.907802	−	1.08188i	0.0885101	−	0.996075i	$-0.471789\pi$
$368$	−3.85198	−	6.67183i	−0.200799	−	0.347793i
$369$	1.27529	−	3.81979i	0.0663889	−	0.198850i
$370$	6.76712	−	6.21891i	0.351806	−	0.323306i
$371$	−0.377676	−	2.14191i	−0.0196080	−	0.111202i
$372$	−4.00867	−	1.80419i	−0.207840	−	0.0935427i
$373$	−14.7375	−	25.5261i	−0.763079	−	1.32169i	−0.941256	−	0.337693i	$-0.890353\pi$
$373$	−14.7375	−	25.5261i	−0.763079	−	1.32169i	0.178178	−	0.983998i	$-0.442980\pi$
$374$	10.7514	−	9.02147i	0.555940	−	0.466489i
$375$	10.6930	+	16.1450i	0.552182	+	0.833723i
$376$	−4.06253	+	11.1617i	−0.209509	+	0.575621i
$377$	15.0242	+	12.6068i	0.773786	+	0.649284i
$378$	0.976887	+	7.61888i	0.0502456	+	0.391873i
$379$		−	9.76267i		−	0.501475i	−0.968055	−	0.250737i	$-0.919327\pi$
$379$		−	9.76267i		−	0.501475i	0.968055	−	0.250737i	$-0.0806730\pi$
$380$	−2.21146	−	9.49260i	−0.113445	−	0.486960i
$381$	−2.20344	+	0.222607i	−0.112886	+	0.0114045i
$382$	2.01112	−	11.4056i	0.102898	−	0.583563i
$383$	13.5937	−	16.2003i	0.694604	−	0.827797i	−0.297300	−	0.954784i	$-0.596086\pi$
$383$	13.5937	−	16.2003i	0.694604	−	0.827797i	0.991904	+	0.126987i	$0.0405306\pi$
$384$	0.425798	−	1.67890i	0.0217289	−	0.0856759i
$385$	−6.53724	+	8.54500i	−0.333169	+	0.435494i
$386$	0.0767057	+	0.0914143i	0.00390422	+	0.00465287i
$387$	18.4759	−	16.3678i	0.939184	−	0.832022i
$388$	−4.70357	+	8.14682i	−0.238788	+	0.413592i
$389$	−16.3233	+	2.87824i	−0.827625	+	0.145933i	−0.571387	−	0.820681i	$-0.693594\pi$
$389$	−16.3233	+	2.87824i	−0.827625	+	0.145933i	−0.256238	+	0.966614i	$0.582483\pi$
$390$	−11.0722	+	12.4497i	−0.560663	+	0.630415i
$391$	−16.6098	+	28.7690i	−0.839994	+	1.45491i
$392$	−4.16970	+	2.40738i	−0.210602	+	0.121591i
$393$	13.0428	+	12.6973i	0.657920	+	0.640496i
$394$	6.89012	+	18.9305i	0.347119	+	0.953703i
$395$	−3.45533	−	15.4802i	−0.173856	−	0.778895i
$396$	−4.65358	+	8.58430i	−0.233851	+	0.431377i
$397$	28.9935	+	5.11234i	1.45514	+	0.256581i	0.844598	−	0.535401i	$-0.179839\pi$
$397$	28.9935	+	5.11234i	1.45514	+	0.256581i	0.610545	+	0.791982i	$0.290951\pi$
$398$		−	23.2959i		−	1.16772i
$399$	4.48593	−	10.2194i	0.224578	−	0.511609i
$400$	2.10001	−	4.53762i	0.105000	−	0.226881i
$401$	0.524009	−	2.97180i	0.0261678	−	0.148405i	−0.968924	−	0.247357i	$-0.920438\pi$
$401$	0.524009	−	2.97180i	0.0261678	−	0.148405i	0.995092	+	0.0989522i	$0.0315491\pi$
$402$	12.9947	−	19.0988i	0.648116	−	0.952560i
$403$	3.73423	−	10.2597i	0.186015	−	0.511072i
$404$	−3.38914	−	9.31159i	−0.168616	−	0.463269i
$405$	1.98412	+	20.0266i	0.0985916	+	0.995128i
$406$	−3.36979	−	5.83664i	−0.167240	−	0.289668i
$407$	11.5857	+	6.68903i	0.574284	+	0.331563i
$408$	−7.18755	+	2.02965i	−0.355837	+	0.100483i
$409$	2.11348	−	0.372663i	0.104505	−	0.0184270i	−0.121151	−	0.992634i	$-0.538659\pi$
$409$	2.11348	−	0.372663i	0.104505	−	0.0184270i	0.225656	+	0.974207i	$0.427547\pi$
$410$	−2.99854	+	0.135254i	−0.148087	+	0.00667972i
$411$	7.40262	+	10.2758i	0.365144	+	0.506866i
$412$	−12.3766	+	10.3852i	−0.609749	+	0.511640i
$413$	−6.12662	−	16.8328i	−0.301471	−	0.828286i
$414$	3.40112	−	22.8603i	0.167156	−	1.12352i
$415$	−5.73411	−	0.746494i	−0.281476	−	0.0366439i
$416$	4.23650	+	0.747009i	0.207711	+	0.0366251i
$417$	0.921535	−	0.0930999i	0.0451278	−	0.00455912i
$418$	12.2204	−	7.20742i	0.597721	−	0.352526i
$419$		−	23.8617i		−	1.16572i	−0.812573	−	0.582859i	$-0.801934\pi$
$419$		−	23.8617i		−	1.16572i	0.812573	−	0.582859i	$-0.198066\pi$
$420$	5.03853	−	2.71882i	0.245855	−	0.132665i
$421$	−5.91970	+	7.05483i	−0.288509	+	0.343831i	−0.890759	−	0.454476i	$-0.849827\pi$
$421$	−5.91970	+	7.05483i	−0.288509	+	0.343831i	0.602250	+	0.798307i	$0.294271\pi$
$422$	23.7795	+	8.65504i	1.15757	+	0.421321i
$423$	−30.3708	+	18.6388i	−1.47668	+	0.906247i
$424$	−1.12708	+	0.945728i	−0.0547356	+	0.0459286i
$425$	−21.4725	+	1.94106i	−1.04157	+	0.0941551i
$426$	3.49610	+	1.57349i	0.169387	+	0.0762361i
$427$	−13.2233	+	2.33163i	−0.639922	+	0.112835i
$428$	−10.7530	+	1.89605i	−0.519768	+	0.0916491i
$429$	−22.1153	−	9.95345i	−1.06773	−	0.480557i
$430$	−16.3313	−	8.47162i	−0.787566	−	0.408538i
$431$	−5.05850	+	4.24459i	−0.243660	+	0.204455i	−0.756436	−	0.654067i	$-0.773061\pi$
$431$	−5.05850	+	4.24459i	−0.243660	+	0.204455i	0.512777	+	0.858522i	$0.328617\pi$
$432$	4.13304	−	3.14928i	0.198851	−	0.151520i
$433$	15.0200	+	5.46683i	0.721815	+	0.262719i	0.676696	−	0.736262i	$-0.263411\pi$
$433$	15.0200	+	5.46683i	0.721815	+	0.262719i	0.0451190	+	0.998982i	$0.485633\pi$
$434$	−2.41163	+	2.87407i	−0.115762	+	0.137960i
$435$	−8.38516	−	15.5394i	−0.402038	−	0.745059i
$436$		−	5.40284i		−	0.258749i
$437$	−21.3458	+	25.9235i	−1.02111	+	1.24009i
$438$	−20.4327	+	2.06425i	−0.976310	+	0.0986337i
$439$	13.4451	+	2.37074i	0.641701	+	0.113149i	0.485024	−	0.874501i	$-0.338811\pi$
$439$	13.4451	+	2.37074i	0.641701	+	0.113149i	0.156677	+	0.987650i	$0.449922\pi$
$440$	7.21715	+	0.939563i	0.344064	+	0.0447919i
$441$	−14.2870	−	2.12560i	−0.680333	−	0.101219i
$442$	−6.34435	−	17.4310i	−0.301770	−	0.829107i
$443$	8.77593	−	7.36388i	0.416957	−	0.349869i	−0.410047	−	0.912064i	$-0.634488\pi$
$443$	8.77593	−	7.36388i	0.416957	−	0.349869i	0.827004	+	0.562196i	$0.190043\pi$
$444$	−4.16122	−	5.77629i	−0.197483	−	0.274131i
$445$	−0.453207	−	10.0474i	−0.0214841	−	0.476294i
$446$	23.3980	−	4.12570i	1.10793	−	0.195358i
$447$	−6.58897	+	1.86062i	−0.311648	+	0.0880044i
$448$	−1.28021	−	0.739129i	−0.0604842	−	0.0349206i
$449$	12.0850	+	20.9319i	0.570328	+	0.987836i	0.996532	+	0.0832095i	$0.0265171\pi$
$449$	12.0850	+	20.9319i	0.570328	+	0.987836i	−0.426204	+	0.904627i	$0.640150\pi$
$450$	13.4002	−	6.74050i	0.631692	−	0.317750i
$451$	−1.49433	−	4.10565i	−0.0703654	−	0.193327i
$452$	−4.20987	+	11.5665i	−0.198016	+	0.544043i
$453$	4.67420	−	6.86983i	0.219613	−	0.322773i
$454$	2.19937	−	12.4733i	0.103222	−	0.585399i
$455$	7.65755	+	11.9818i	0.358991	+	0.561713i
$456$	−7.50424	+	0.828512i	−0.351418	+	0.0387986i
$457$			31.4742i			1.47230i	0.676818	+	0.736150i	$0.263358\pi$
$457$			31.4742i			1.47230i	−0.676818	+	0.736150i	$0.736642\pi$
$458$	14.2106	+	2.50570i	0.664016	+	0.117084i
$459$	−20.6713	−	8.64420i	−0.964852	−	0.403477i
$460$	−16.8129	+	3.75278i	−0.783904	+	0.174974i
$461$	11.7029	+	32.1534i	0.545058	+	1.49753i	0.840305	+	0.542113i	$0.182376\pi$
$461$	11.7029	+	32.1534i	0.545058	+	1.49753i	−0.295248	+	0.955421i	$0.595402\pi$
$462$	5.97140	+	5.81325i	0.277815	+	0.270457i
$463$	−15.9360	+	9.20064i	−0.740608	+	0.427590i	−0.822290	−	0.569068i	$-0.807304\pi$
$463$	−15.9360	+	9.20064i	−0.740608	+	0.427590i	0.0816824	+	0.996658i	$0.473971\pi$
$464$	−2.27957	+	3.94832i	−0.105826	+	0.183296i
$465$	−6.53239	+	7.34509i	−0.302933	+	0.340620i
$466$	2.41734	−	0.426242i	0.111981	−	0.0197453i
$467$	15.9343	−	27.5990i	0.737351	−	1.27713i	−0.216333	−	0.976320i	$-0.569410\pi$
$467$	15.9343	−	27.5990i	0.737351	−	1.27713i	0.953684	−	0.300810i	$-0.0972570\pi$
$468$	8.55784	+	9.66006i	0.395586	+	0.446537i
$469$	−12.6729	−	15.1029i	−0.585179	−	0.697389i
$470$	21.0949	+	16.1383i	0.973033	+	0.744406i
$471$	2.18216	−	8.60414i	0.100549	−	0.396458i
$472$	−7.78909	+	9.28267i	−0.358522	+	0.427270i
$473$	4.65031	−	26.3732i	0.213822	−	1.21264i
$474$	−12.2238	+	1.23493i	−0.561457	+	0.0567224i
$475$	−21.7331	−	1.63535i	−0.997181	−	0.0750349i
$476$			6.37427i			0.292164i
$477$	−4.41229	+	0.118445i	−0.202025	+	0.00542323i
$478$	23.5596	+	19.7688i	1.07759	+	0.904205i
$479$	8.97820	−	24.6674i	0.410224	−	1.12708i	−0.546848	−	0.837232i	$-0.684172\pi$
$479$	8.97820	−	24.6674i	0.410224	−	1.12708i	0.957072	−	0.289850i	$-0.0936055\pi$
$480$	−3.29701	−	2.03218i	−0.150487	−	0.0927559i
$481$	13.5448	−	11.3654i	0.617590	−	0.518220i
$482$	2.90479	+	5.03124i	0.132309	+	0.229167i
$483$	−17.9875	−	8.09567i	−0.818461	−	0.368366i
$484$	−0.0705017	−	0.399835i	−0.00320462	−	0.0181743i
$485$	14.2334	+	15.4881i	0.646306	+	0.703279i
$486$	15.5853	+	0.314424i	0.706963	+	0.0142626i
$487$	−7.30221	−	12.6478i	−0.330895	−	0.573126i	0.651793	−	0.758397i	$-0.274017\pi$
$487$	−7.30221	−	12.6478i	−0.330895	−	0.573126i	−0.982688	+	0.185271i	$0.940684\pi$
$488$	5.83857	+	6.95813i	0.264300	+	0.314980i
$489$	4.52402	+	9.37138i	0.204583	+	0.423788i
$490$	2.34538	+	10.5075i	0.105953	+	0.474682i
$491$	0.299707	−	0.357177i	0.0135256	−	0.0161192i	−0.759239	−	0.650812i	$-0.774429\pi$
$491$	0.299707	−	0.357177i	0.0135256	−	0.0161192i	0.772765	+	0.634692i	$0.218873\pi$
$492$	−0.171541	+	2.31868i	−0.00773366	+	0.104534i
$493$	19.6590			0.885399
$494$	−3.42727	−	18.4355i	−0.154200	−	0.829451i
$495$	15.2002	+	15.6743i	0.683200	+	0.704506i
$496$	2.49945	+	0.440721i	0.112229	+	0.0197890i
$497$	2.10327	−	2.50658i	0.0943446	−	0.112436i
$498$	−1.10112	+	4.34164i	−0.0493422	+	0.194554i
$499$	−7.85290	+	2.85822i	−0.351544	+	0.127952i	−0.511756	−	0.859131i	$-0.671005\pi$
$499$	−7.85290	+	2.85822i	−0.351544	+	0.127952i	0.160211	+	0.987083i	$0.448782\pi$
$500$	−8.27563	−	7.51758i	−0.370097	−	0.336196i
$501$	17.4425	−	12.5655i	0.779274	−	0.561387i
$502$	−9.07666	+	15.7212i	−0.405111	+	0.701673i
$503$	−1.95218	−	11.0714i	−0.0870436	−	0.493649i	−0.996897	−	0.0787187i	$-0.974917\pi$
$503$	−1.95218	−	11.0714i	−0.0870436	−	0.493649i	0.909853	−	0.414930i	$-0.136194\pi$
$504$	−1.62807	−	4.12512i	−0.0725198	−	0.183748i
$505$	−22.1351	+	0.998442i	−0.984999	+	0.0444301i
$506$	−12.5376	−	21.7158i	−0.557364	−	0.965383i
$507$	−6.65228	+	6.83325i	−0.295438	+	0.303475i
$508$	1.20152	−	0.437319i	0.0533090	−	0.0194029i
$509$	2.39322	+	0.871062i	0.106078	+	0.0386091i	0.394514	−	0.918890i	$-0.370913\pi$
$509$	2.39322	+	0.871062i	0.106078	+	0.0386091i	−0.288436	+	0.957499i	$0.593135\pi$
$510$	−0.480426	+	16.6934i	−0.0212736	+	0.739198i
$511$	−3.04362	+	17.2612i	−0.134642	+	0.763591i
$512$			1.00000i			0.0441942i
$513$	−19.1739	−	12.0567i	−0.846546	−	0.532315i
$514$	−29.8820			−1.31804
$515$	13.8733	+	33.3569i	0.611331	+	1.46988i
$516$	−8.01660	+	11.7823i	−0.352911	+	0.518686i
$517$	−13.2229	+	36.3296i	−0.581542	+	1.59777i
$518$	−5.70952	+	2.07809i	−0.250862	+	0.0913062i
$519$	−5.10842	−	4.97313i	−0.224235	−	0.218296i
$520$	4.42935	−	8.53877i	0.194240	−	0.374450i
$521$	5.34154	−	9.25182i	0.234017	−	0.405330i	−0.724969	−	0.688781i	$-0.758146\pi$
$521$	5.34154	−	9.25182i	0.234017	−	0.405330i	0.958987	+	0.283451i	$0.0914795\pi$
$522$	−12.7224	+	5.02115i	−0.556844	+	0.219770i
$523$	6.46521	+	36.6660i	0.282704	+	1.60329i	0.713374	+	0.700784i	$0.247166\pi$
$523$	6.46521	+	36.6660i	0.282704	+	1.60329i	−0.430670	+	0.902510i	$0.641723\pi$
$524$	−9.10132	−	5.25465i	−0.397593	−	0.229550i
$525$	−2.42832	−	12.5697i	−0.105981	−	0.548586i
$526$	5.34851	+	6.37410i	0.233206	+	0.277924i
$527$	−3.74305	−	10.2839i	−0.163050	−	0.447975i
$528$	1.38590	−	5.46455i	0.0603137	−	0.237814i
$529$	27.8466	+	23.3661i	1.21072	+	1.01592i
$530$	1.26338	+	3.03766i	0.0548776	+	0.131948i
$531$	−35.6184	+	7.27106i	−1.54571	+	0.315537i
$532$	−1.06001	+	6.35579i	−0.0459573	+	0.275559i
$533$	−5.77459			−0.250125
$534$	−7.76939	−	0.574795i	−0.336214	−	0.0248738i
$535$	−3.15192	+	24.2111i	−0.136270	+	1.04674i
$536$	−4.56151	+	12.5327i	−0.197027	+	0.541328i
$537$	8.29102	−	4.00248i	0.357784	−	0.172720i
$538$	−10.4428	−	12.4453i	−0.450222	−	0.536554i
$539$	−13.5717	+	7.83563i	−0.584575	+	0.337504i
$540$	−3.95280	−	10.9259i	−0.170101	−	0.470176i
$541$	1.13016	+	6.40946i	0.0485894	+	0.275564i	0.999416	−	0.0341582i	$-0.0108750\pi$
$541$	1.13016	+	6.40946i	0.0485894	+	0.275564i	−0.950827	+	0.309722i	$0.899764\pi$
$542$	−11.0523	+	1.94882i	−0.474738	+	0.0837091i
$543$	40.6084	+	18.2767i	1.74267	+	0.784327i
$544$	3.73431	−	2.15601i	0.160107	−	0.0924380i
$545$	−11.5272	−	3.61623i	−0.493770	−	0.154902i
$546$	9.91921	−	4.78848i	0.424503	−	0.204928i
$547$	15.1317	+	5.50749i	0.646985	+	0.235483i	0.644607	−	0.764514i	$-0.277021\pi$
$547$	15.1317	+	5.50749i	0.646985	+	0.235483i	0.00237778	+	0.999997i	$0.499243\pi$
$548$	−5.60121	−	4.69998i	−0.239272	−	0.200773i
$549$	0.731235	+	27.2398i	0.0312083	+	1.16257i
$550$	6.83519	−	14.7692i	0.291453	−	0.629762i
$551$	19.6020	+	3.26921i	0.835075	+	0.139273i
$552$	1.34124	+	13.2761i	0.0570871	+	0.565068i
$553$	−1.82084	+	10.3265i	−0.0774299	+	0.439127i
$554$	−14.9398	−	12.5360i	−0.634733	−	0.532604i
$555$	−15.1092	+	5.01196i	−0.641348	+	0.212746i
$556$	−0.502507	+	0.182898i	−0.0213110	+	0.00775658i
$557$	−14.6705	+	12.3100i	−0.621609	+	0.521592i	−0.898309	−	0.439365i	$-0.855204\pi$
$557$	−14.6705	+	12.3100i	−0.621609	+	0.521592i	0.276700	+	0.960956i	$0.410759\pi$
$558$	5.04896	+	5.69925i	0.213740	+	0.241269i
$559$	−30.6527	−	17.6973i	−1.29647	−	0.748517i
$560$	−2.43384	+	2.23667i	−0.102848	+	0.0945165i
$561$	−23.3943	+	6.60620i	−0.987710	+	0.278914i
$562$	0.853575	+	0.492812i	0.0360059	+	0.0207880i
$563$	−5.79723	+	3.34703i	−0.244324	+	0.141061i	−0.617163	−	0.786836i	$-0.711718\pi$
$563$	−5.79723	+	3.34703i	−0.244324	+	0.141061i	0.372838	+	0.927896i	$0.378385\pi$
$564$	14.3510	−	14.7415i	0.604288	−	0.620728i
$565$	21.8599	+	16.7237i	0.919654	+	0.703569i
$566$	−8.64931	−	3.14809i	−0.363558	−	0.132324i
$567$	3.87306	−	12.7281i	0.162653	−	0.534530i
$568$	−2.17986	−	0.384368i	−0.0914649	−	0.0161277i
$569$	8.36559			0.350704			0.175352	−	0.984506i	$-0.443894\pi$
$569$	8.36559			0.350704			0.175352	+	0.984506i	$0.443894\pi$
$570$	−3.25507	+	16.5652i	−0.136340	+	0.693838i
$571$	−20.1454			−0.843060			−0.421530	−	0.906814i	$-0.638507\pi$
$571$	−20.1454			−0.843060			−0.421530	+	0.906814i	$0.638507\pi$
$572$	13.7891	+	2.43140i	0.576553	+	0.101662i
$573$	−11.2844	+	16.5850i	−0.471411	+	0.692850i
$574$	1.86467	+	0.678684i	0.0778298	+	0.0283277i
$575$	−3.24647	+	38.3828i	−0.135387	+	1.60067i
$576$	−1.86600	+	2.34905i	−0.0777499	+	0.0978772i
$577$	6.73746	−	3.88988i	0.280484	−	0.161938i	−0.353158	−	0.935564i	$-0.614892\pi$
$577$	6.73746	−	3.88988i	0.280484	−	0.161938i	0.633643	+	0.773626i	$0.281559\pi$
$578$	−1.37998	−	0.796731i	−0.0573995	−	0.0331396i
$579$	−0.0561697	−	0.198912i	−0.00233433	−	0.00826651i
$580$	6.89816	+	7.50625i	0.286431	+	0.311680i
$581$	3.31063	+	1.91140i	0.137348	+	0.0792980i
$582$	13.2204	−	9.52391i	0.548002	−	0.394779i
$583$	−3.66845	+	3.07820i	−0.151932	+	0.127486i
$584$	11.1418	−	4.05528i	0.461051	−	0.167809i
$585$	26.3381	−	11.7928i	1.08895	−	0.487574i
$586$	9.27079	+	7.77912i	0.382973	+	0.321352i
$587$	−1.97128	+	11.1797i	−0.0813632	+	0.461434i	0.916719	+	0.399533i	$0.130828\pi$
$587$	−1.97128	+	11.1797i	−0.0813632	+	0.461434i	−0.998082	+	0.0619014i	$0.980284\pi$
$588$	8.29716	−	0.838237i	0.342169	−	0.0345683i
$589$	−2.02203	−	10.8766i	−0.0833161	−	0.448161i
$590$	14.5916	+	22.8314i	0.600726	+	0.939956i
$591$	2.57441	−	34.7977i	0.105897	−	1.43139i
$592$	3.14860	+	2.64199i	0.129407	+	0.108585i
$593$	−24.3330	−	8.85648i	−0.999236	−	0.363692i	−0.209946	−	0.977713i	$-0.567329\pi$
$593$	−24.3330	−	8.85648i	−0.999236	−	0.363692i	−0.789290	+	0.614021i	$0.789551\pi$
$594$	13.4524	−	10.2504i	0.551959	−	0.420579i
$595$	13.5998	+	4.26643i	0.557537	+	0.174907i
$596$	3.42332	−	1.97645i	0.140225	−	0.0809587i
$597$	−16.5603	+	36.7948i	−0.677768	+	1.50591i
$598$	−32.6378	+	5.75493i	−1.33466	+	0.235337i
$599$	−4.49458	−	25.4900i	−0.183643	−	1.04149i	−0.927686	−	0.373361i	$-0.878205\pi$
$599$	−4.49458	−	25.4900i	−0.183643	−	1.04149i	0.744043	−	0.668132i	$-0.232906\pi$
$600$	−6.54250	+	5.67413i	−0.267096	+	0.231645i
$601$	24.4980	−	14.1439i	0.999294	−	0.576943i	0.0912547	−	0.995828i	$-0.470912\pi$
$601$	24.4980	−	14.1439i	0.999294	−	0.576943i	0.908039	+	0.418885i	$0.137579\pi$
$602$	7.81807	+	9.31722i	0.318641	+	0.379741i
$603$	−34.1012	+	20.9281i	−1.38871	+	0.852258i
$604$	−1.64078	+	4.50800i	−0.0667623	+	0.183428i
$605$	−0.900254	−	0.117199i	−0.0366005	−	0.00476483i
$606$	−1.26631	+	17.1164i	−0.0514403	+	0.695308i
$607$	42.0994			1.70876			0.854381	−	0.519647i	$-0.173937\pi$
$607$	42.0994			1.70876			0.854381	+	0.519647i	$0.173937\pi$
$608$	4.08202	−	1.52876i	0.165548	−	0.0619993i
$609$	1.17334	+	11.6142i	0.0475463	+	0.470630i
$610$	18.7534	−	7.79962i	0.759301	−	0.315797i
$611$	39.1430	+	32.8449i	1.58356	+	1.32876i
$612$	12.7952	+	1.90365i	0.517216	+	0.0769505i
$613$	−9.34878	−	25.6856i	−0.377594	−	1.03743i	−0.972351	−	0.233525i	$-0.924974\pi$
$613$	−9.34878	−	25.6856i	−0.377594	−	1.03743i	0.594757	−	0.803906i	$-0.297248\pi$
$614$	−4.50959	−	5.37432i	−0.181992	−	0.216890i
$615$	4.83219	+	1.91793i	0.194853	+	0.0773385i
$616$	−4.16688	−	2.40575i	−0.167888	−	0.0969304i
$617$	−5.70210	−	32.3382i	−0.229558	−	1.30189i	−0.853778	−	0.520638i	$-0.825694\pi$
$617$	−5.70210	−	32.3382i	−0.229558	−	1.30189i	0.624220	−	0.781249i	$-0.285417\pi$
$618$	26.9306	−	7.60479i	1.08331	−	0.305909i
$619$	16.3880	−	28.3849i	0.658690	−	1.14088i	−0.322265	−	0.946649i	$-0.604444\pi$
$619$	16.3880	−	28.3849i	0.658690	−	1.14088i	0.980955	−	0.194235i	$-0.0622225\pi$
$620$	2.61323	−	5.03771i	0.104950	−	0.202319i
$621$	−21.6225	+	33.6890i	−0.867681	+	1.35189i
$622$	6.07606	−	2.21151i	0.243628	−	0.0886733i
$623$	−2.27412	+	6.24810i	−0.0911108	+	0.250325i
$624$	−6.16032	−	4.19145i	−0.246610	−	0.167792i
$625$	−21.5781	+	12.6248i	−0.863125	+	0.504990i
$626$	−13.2678			−0.530287
$627$	−24.4251	+	2.69668i	−0.975445	+	0.107695i
$628$			5.12488i			0.204505i
$629$	3.07761	−	17.4540i	0.122712	−	0.695936i
$630$	−9.89083	+	0.712518i	−0.394060	+	0.0283874i
$631$	−14.5454	−	5.29409i	−0.579042	−	0.210754i	0.0358608	−	0.999357i	$-0.488583\pi$
$631$	−14.5454	−	5.29409i	−0.579042	−	0.210754i	−0.614903	+	0.788603i	$0.710805\pi$
$632$	6.66555	−	2.42606i	0.265141	−	0.0965036i
$633$	−31.4061	−	30.5743i	−1.24828	−	1.21522i
$634$	13.8322	+	23.9581i	0.549348	+	0.951499i
$635$	−0.128834	−	2.85621i	−0.00511263	−	0.113345i
$636$	2.45245	−	0.692533i	0.0972459	−	0.0274607i
$637$	3.59666	+	20.3977i	0.142505	+	0.808186i
$638$	−7.41963	+	12.8512i	−0.293746	+	0.508783i
$639$	−4.40338	−	4.97052i	−0.174195	−	0.196631i
$640$	2.13354	+	0.669321i	0.0843357	+	0.0264572i
$641$	−35.9483	+	13.0841i	−1.41987	+	0.516791i	−0.934010	−	0.357246i	$-0.883716\pi$
$641$	−35.9483	+	13.0841i	−1.41987	+	0.516791i	−0.485860	+	0.874037i	$0.661494\pi$
$642$	18.3317	+	4.64925i	0.723496	+	0.183491i
$643$	−6.24965	+	7.44804i	−0.246462	+	0.293722i	−0.875066	−	0.484003i	$-0.839182\pi$
$643$	−6.24965	+	7.44804i	−0.246462	+	0.293722i	0.628604	+	0.777726i	$0.283627\pi$
$644$	11.2154	+	1.97758i	0.441950	+	0.0779278i
$645$	19.7724	+	24.9899i	0.778536	+	0.983977i
$646$	−14.5097	−	11.9475i	−0.570878	−	0.470069i
$647$	11.4994			0.452090			0.226045	−	0.974117i	$-0.427420\pi$
$647$	11.4994			0.452090			0.226045	+	0.974117i	$0.427420\pi$
$648$	−8.76666	+	2.03610i	−0.344387	+	0.0799855i
$649$	−25.3522	+	30.2136i	−0.995163	+	1.18599i
$650$	−15.2532	−	15.1654i	−0.598279	−	0.594836i
$651$	5.85214	−	2.82511i	0.229364	−	0.110725i
$652$	−3.86189	−	4.60242i	−0.151243	−	0.180245i
$653$	−13.7942	−	23.8922i	−0.539807	−	0.934973i	−0.998914	−	0.0465920i	$-0.985164\pi$
$653$	−13.7942	−	23.8922i	−0.539807	−	0.934973i	0.459107	−	0.888381i	$-0.348169\pi$
$654$	−3.84069	+	8.53352i	−0.150183	+	0.333687i
$655$	−17.3027	+	15.9010i	−0.676073	+	0.621304i
$656$	−0.233097	−	1.32196i	−0.00910089	−	0.0516137i
$657$	33.7398	+	11.2645i	1.31632	+	0.439470i
$658$	−8.77941	−	15.2064i	−0.342257	−	0.592806i
$659$	−20.6532	+	17.3301i	−0.804533	+	0.675083i	−0.949296	−	0.314383i	$-0.898202\pi$
$659$	−20.6532	+	17.3301i	−0.804533	+	0.675083i	0.144763	+	0.989466i	$0.453758\pi$
$660$	−10.7312	−	6.61442i	−0.417713	−	0.257466i
$661$	11.9285	−	32.7733i	0.463965	−	1.27473i	−0.458514	−	0.888687i	$-0.651618\pi$
$661$	11.9285	−	32.7733i	0.463965	−	1.27473i	0.922479	−	0.386046i	$-0.126160\pi$
$662$	−16.9736	−	14.2425i	−0.659696	−	0.553551i
$663$	−2.37049	+	32.0414i	−0.0920620	+	1.24438i
$664$		−	2.58601i		−	0.100357i
$665$	12.8509	+	6.51564i	0.498336	+	0.252666i
$666$	2.46628	+	12.0814i	0.0955663	+	0.468147i
$667$	6.09912	−	34.5898i	0.236159	−	1.33932i
$668$	−7.97794	+	9.50774i	−0.308676	+	0.367866i
$669$	−39.8889	−	10.1165i	−1.54219	−	0.391127i
$670$	23.6859	+	18.1206i	0.915064	+	0.700058i
$671$	19.0036	+	22.6476i	0.733626	+	0.874302i
$672$	1.49661	+	2.07748i	0.0577329	+	0.0801404i
$673$	−7.40599	+	12.8275i	−0.285480	+	0.494466i	−0.972725	−	0.231960i	$-0.925486\pi$
$673$	−7.40599	+	12.8275i	−0.285480	+	0.494466i	0.687246	+	0.726425i	$0.258820\pi$
$674$	0.353920	−	0.0624056i	0.0136325	−	0.00240377i
$675$	−25.9566	+	1.12053i	−0.999069	+	0.0431293i
$676$	2.75297	−	4.76828i	0.105883	−	0.183396i
$677$	−18.6874	+	10.7891i	−0.718213	+	0.414661i	−0.814095	−	0.580732i	$-0.802766\pi$
$677$	−18.6874	+	10.7891i	−0.718213	+	0.414661i	0.0958814	+	0.995393i	$0.469433\pi$
$678$	14.8715	−	15.2761i	0.571138	−	0.586676i
$679$	−4.75620	−	13.0675i	−0.182526	−	0.501486i
$680$	−2.10048	−	9.41038i	−0.0805498	−	0.360872i
$681$	−12.3406	+	18.1374i	−0.472894	+	0.695029i
$682$	8.13532	+	1.43448i	0.311518	+	0.0549290i
$683$			17.1907i			0.657782i	0.944368	+	0.328891i	$0.106675\pi$
$683$			17.1907i			0.657782i	−0.944368	+	0.328891i	$0.893325\pi$
$684$	12.4415	+	4.02591i	0.475714	+	0.153935i
$685$	−13.7766	+	8.80464i	−0.526377	+	0.336408i
$686$	3.03281	−	17.1999i	0.115793	−	0.656696i
$687$	−20.6637	−	14.0594i	−0.788368	−	0.536401i
$688$	2.81406	−	7.73157i	0.107285	−	0.294763i
$689$	2.16474	+	5.94758i	0.0824701	+	0.226585i
$690$	29.2228	+	6.02436i	1.11249	+	0.229343i
$691$	−1.18086	−	2.04531i	−0.0449220	−	0.0778072i	0.842690	−	0.538399i	$-0.180971\pi$
$691$	−1.18086	−	2.04531i	−0.0449220	−	0.0778072i	−0.887612	+	0.460592i	$0.847637\pi$
$692$	3.56469	+	2.05807i	0.135509	+	0.0782362i
$693$	−5.29910	−	13.4266i	−0.201296	−	0.510035i
$694$	−9.52897	+	1.68021i	−0.361715	+	0.0637801i
$695$	0.0538817	+	1.19454i	0.00204385	+	0.0453114i
$696$	6.40720	−	4.61572i	0.242864	−	0.174958i
$697$	−4.43404	+	3.72060i	−0.167951	+	0.140928i
$698$	8.21998	+	22.5842i	0.311131	+	0.854825i
$699$	−4.12107	−	1.04518i	−0.155873	−	0.0395322i
$700$	3.14301	+	6.68974i	0.118795	+	0.252849i
$701$	−26.2374	−	4.62636i	−0.990972	−	0.174735i	−0.345417	−	0.938449i	$-0.612263\pi$
$701$	−26.2374	−	4.62636i	−0.990972	−	0.174735i	−0.645555	+	0.763714i	$0.723374\pi$
$702$	−6.64969	−	21.3411i	−0.250976	−	0.805468i
$703$	5.97121	−	16.8916i	0.225208	−	0.637079i
$704$			3.25484i			0.122671i
$705$	−21.8461	−	40.4854i	−0.822772	−	1.52477i
$706$	−8.12372	+	9.68147i	−0.305740	+	0.364367i
$707$	13.7649	+	5.01003i	0.517684	+	0.188421i
$708$	18.9012	−	9.12454i	0.710352	−	0.342921i
$709$	33.7315	−	28.3041i	1.26681	−	1.06298i	0.271891	−	0.962328i	$-0.412351\pi$
$709$	33.7315	−	28.3041i	1.26681	−	1.06298i	0.994922	−	0.100654i	$-0.0320935\pi$
$710$	−2.27909	+	4.39356i	−0.0855328	+	0.164888i
$711$	20.1848	+	6.73896i	0.756988	+	0.252731i
$712$	4.42959	−	0.781056i	0.166006	−	0.0292713i
$713$	−19.2557	+	3.39530i	−0.721132	+	0.127155i
$714$	4.53125	−	10.0679i	0.169578	−	0.376780i
$715$	14.4168	−	27.7923i	0.539159	−	1.03937i
$716$	−4.07184	+	3.41668i	−0.152172	+	0.127687i
$717$	−23.1582	−	47.9716i	−0.864859	−	1.79153i
$718$	9.18005	+	3.34127i	0.342596	+	0.124695i
$719$	24.3135	−	28.9757i	0.906741	−	1.08061i	−0.0896708	−	0.995971i	$-0.528582\pi$
$719$	24.3135	−	28.9757i	0.906741	−	1.08061i	0.996412	−	0.0846401i	$-0.0269741\pi$
$720$	3.76286	+	5.55346i	0.140233	+	0.206965i
$721$		−	23.8834i		−	0.889464i
$722$	−12.4808	−	14.3258i	−0.464489	−	0.533151i
$723$	−1.01143	−	10.0115i	−0.0376156	−	0.372332i
$724$	−25.3198	−	4.46457i	−0.941004	−	0.165924i
$725$	20.6320	−	9.69344i	0.766253	−	0.360005i
$726$	−0.172875	+	0.681637i	−0.00641600	+	0.0252979i
$727$	3.86750	+	10.6259i	0.143438	+	0.394092i	0.990520	−	0.137370i	$-0.0438650\pi$
$727$	3.86750	+	10.6259i	0.143438	+	0.394092i	−0.847082	+	0.531462i	$0.821643\pi$
$728$	−4.87147	+	4.08765i	−0.180549	+	0.151498i
$729$	−24.3927	−	11.5757i	−0.903433	−	0.428729i
$730$	−1.19469	−	26.4858i	−0.0442173	−	0.980283i
$731$	−34.9392	+	6.16073i	−1.29227	+	0.227863i
$732$	−4.27543	−	15.1405i	−0.158025	−	0.559608i
$733$	29.1108	+	16.8071i	1.07523	+	0.620786i	0.929606	−	0.368554i	$-0.120147\pi$
$733$	29.1108	+	16.8071i	1.07523	+	0.620786i	0.145626	+	0.989340i	$0.453480\pi$
$734$	−13.5278	−	23.4308i	−0.499320	−	0.864847i
$735$	3.76504	−	18.2634i	0.138876	−	0.673656i
$736$	−2.63491	−	7.23936i	−0.0971242	−	0.266846i
$737$	−14.8470	+	40.7918i	−0.546896	+	1.50259i
$738$	1.91921	−	3.54030i	0.0706472	−	0.130320i
$739$	4.15936	−	23.5889i	0.153005	−	0.867732i	−0.807583	−	0.589754i	$-0.799225\pi$
$739$	4.15936	−	23.5889i	0.153005	−	0.867732i	0.960588	−	0.277978i	$-0.0896642\pi$
$740$	7.74422	−	4.94934i	0.284683	−	0.181941i
$741$	−7.69194	+	31.5543i	−0.282571	+	1.15918i
$742$		−	2.17495i		−	0.0798449i
$743$	37.1845	+	6.55664i	1.36417	+	0.240540i	0.807339	−	0.590087i	$-0.200907\pi$
$743$	37.1845	+	6.55664i	1.36417	+	0.240540i	0.556829	+	0.830627i	$0.312018\pi$
$744$	−3.63447	−	2.47287i	−0.133246	−	0.0906600i
$745$	−1.92555	−	8.62668i	−0.0705468	−	0.316057i
$746$	−10.0810	−	27.6974i	−0.369093	−	1.01408i
$747$	4.82549	−	6.07467i	0.176555	−	0.222261i
$748$	12.1546	−	7.01746i	0.444416	−	0.256584i
$749$	8.07049	−	13.9785i	0.294889	−	0.510763i
$750$	7.72697	+	17.7565i	0.282149	+	0.648376i
$751$	14.6978	−	2.59162i	0.536331	−	0.0945696i	0.101079	−	0.994878i	$-0.467771\pi$
$751$	14.6978	−	2.59162i	0.536331	−	0.0945696i	0.435252	+	0.900309i	$0.356659\pi$
$752$	−5.93902	+	10.2867i	−0.216574	+	0.375117i
$753$	25.5118	−	18.3786i	0.929703	−	0.669755i
$754$	12.6068	+	15.0242i	0.459113	+	0.547149i
$755$	8.51982	+	6.51797i	0.310068	+	0.237213i
$756$	−0.360960	+	7.67277i	−0.0131280	+	0.279056i
$757$	1.36076	−	1.62169i	0.0494576	−	0.0589413i	−0.740749	−	0.671782i	$-0.765529\pi$
$757$	1.36076	−	1.62169i	0.0494576	−	0.0589413i	0.790206	+	0.612841i	$0.209973\pi$
$758$	1.69527	−	9.61435i	0.0615750	−	0.349209i
$759$	4.36554	+	43.2116i	0.158459	+	1.56848i
$760$	−0.529490	−	9.73240i	−0.0192066	−	0.353031i
$761$		−	33.4174i		−	1.21138i	−0.795701	−	0.605690i	$-0.792897\pi$
$761$		−	33.4174i		−	1.21138i	0.795701	−	0.605690i	$-0.207103\pi$
$762$	−2.20862	−	0.163399i	−0.0800100	−	0.00591930i
$763$	6.11823	+	5.13381i	0.221495	+	0.185856i
$764$	3.96114	−	10.8831i	0.143309	−	0.393738i
$765$	12.6256	−	26.0250i	0.456480	−	0.940935i
$766$	16.2003	−	13.5937i	0.585341	−	0.491159i
$767$	26.0642	+	45.1445i	0.941124	+	1.63007i
$768$	0.710866	−	1.57945i	0.0256512	−	0.0569936i
$769$	2.70890	+	15.3629i	0.0976855	+	0.554002i	0.993891	+	0.110363i	$0.0352015\pi$
$769$	2.70890	+	15.3629i	0.0976855	+	0.554002i	−0.896206	+	0.443639i	$0.853687\pi$
$770$	−7.92175	+	7.28000i	−0.285480	+	0.262353i
$771$	47.1971	+	21.2421i	1.69976	+	0.765015i
$772$	0.0596665	+	0.103345i	0.00214744	+	0.00371948i
$773$	−9.91263	−	11.8134i	−0.356533	−	0.424899i	0.557729	−	0.830023i	$-0.311673\pi$
$773$	−9.91263	−	11.8134i	−0.356533	−	0.424899i	−0.914262	+	0.405124i	$0.867228\pi$
$774$	21.0375	−	12.9108i	0.756177	−	0.464070i
$775$	−8.99908	−	8.94729i	−0.323257	−	0.321396i
$776$	−6.04679	+	7.20629i	−0.217067	+	0.258691i
$777$	10.4952	+	0.776453i	0.376512	+	0.0278551i
$778$	−16.5751			−0.594247
$779$	−5.03991	+	2.97246i	−0.180573	+	0.106499i
$780$	−13.0659	+	10.3379i	−0.467833	+	0.370156i
$781$	−7.09510	−	1.25106i	−0.253883	−	0.0447664i
$782$	−21.3532	+	25.4477i	−0.763587	+	0.910008i
$783$	23.6638	+	1.11324i	0.845674	+	0.0397841i
$784$	−4.52439	+	1.64674i	−0.161585	+	0.0588122i
$785$	10.9342	+	3.43019i	0.390257	+	0.122429i
$786$	10.6397	+	14.7693i	0.379507	+	0.526803i
$787$	13.1009	−	22.6914i	0.466997	−	0.808862i	−0.532292	−	0.846561i	$-0.678669\pi$
$787$	13.1009	−	22.6914i	0.466997	−	0.808862i	0.999289	+	0.0376985i	$0.0120026\pi$
$788$	3.49821	+	19.8393i	0.124618	+	0.706747i
$789$	−3.91658	−	13.8697i	−0.139434	−	0.493773i
$790$	−0.714719	−	15.8451i	−0.0254285	−	0.563742i
$791$	−9.09782	−	15.7579i	−0.323481	−	0.560286i
$792$	−6.07353	+	7.64580i	−0.215814	+	0.271682i
$793$	36.7181	−	13.3643i	1.30390	−	0.474580i
$794$	27.6653	+	10.0693i	0.981804	+	0.357348i
$795$	0.163925	−	5.69593i	0.00581382	−	0.202014i
$796$	4.04530	−	22.9420i	0.143382	−	0.813159i
$797$		−	28.0217i		−	0.992578i	−0.868157	−	0.496289i	$-0.834696\pi$
$797$		−	28.0217i		−	0.992578i	0.868157	−	0.496289i	$-0.165304\pi$
$798$	6.19236	−	9.28514i	0.219207	−	0.328691i
$799$	51.2183			1.81197
$800$	2.85605	−	4.10402i	0.100977	−	0.145099i
$801$	11.8628	+	6.43086i	0.419151	+	0.227223i
$802$	1.03210	−	2.83566i	0.0364446	−	0.100131i
$803$	36.2648	−	13.1993i	1.27976	−	0.465793i
$804$	16.1137	−	16.5521i	0.568288	−	0.583748i
$805$	11.7260	−	22.6050i	0.413287	−	0.796721i
$806$	5.45907	−	9.45540i	0.192288	−	0.333052i
$807$	7.64702	+	27.0802i	0.269188	+	0.953267i
$808$	−1.72071	−	9.75864i	−0.0605345	−	0.343308i
$809$	−44.9366	−	25.9441i	−1.57989	−	0.912147i	−0.994874	−	0.101122i	$-0.967757\pi$
$809$	−44.9366	−	25.9441i	−1.57989	−	0.912147i	−0.585011	−	0.811025i	$-0.698910\pi$
$810$	−1.52360	+	20.0669i	−0.0535339	+	0.705077i
$811$	−14.4295	−	17.1965i	−0.506690	−	0.603849i	0.450690	−	0.892680i	$-0.351178\pi$
$811$	−14.4295	−	17.1965i	−0.506690	−	0.603849i	−0.957380	+	0.288831i	$0.906733\pi$
$812$	−2.30507	−	6.33313i	−0.0808921	−	0.222249i
$813$	18.8420	+	4.77865i	0.660817	+	0.167595i
$814$	10.2482	+	8.59925i	0.359199	+	0.301404i
$815$	−12.4043	+	5.15902i	−0.434504	+	0.180712i
$816$	−7.43080	+	0.750712i	−0.260130	+	0.0262802i
$817$	−35.8625	+	0.332639i	−1.25467	+	0.0116375i
$818$	2.14608			0.0750359
$819$	−19.0709	+	0.511946i	−0.666391	+	0.0178888i
$820$	−2.97647	−	0.387491i	−0.103943	−	0.0135318i
$821$	−7.32798	+	20.1335i	−0.255748	+	0.702662i	0.743670	+	0.668547i	$0.233084\pi$
$821$	−7.32798	+	20.1335i	−0.255748	+	0.702662i	−0.999418	+	0.0341151i	$0.989139\pi$
$822$	5.50579	+	11.4051i	0.192037	+	0.397799i
$823$	−6.19125	−	7.37844i	−0.215813	−	0.257196i	0.647267	−	0.762264i	$-0.275912\pi$
$823$	−6.19125	−	7.37844i	−0.215813	−	0.257196i	−0.863080	+	0.505067i	$0.831468\pi$
$824$	−13.9919	+	8.07822i	−0.487430	+	0.281418i
$825$	−21.2948	+	18.4684i	−0.741390	+	0.642987i
$826$	−3.11057	−	17.6409i	−0.108230	−	0.613806i
$827$	18.9143	−	3.33510i	0.657715	−	0.115973i	0.165177	−	0.986264i	$-0.447180\pi$
$827$	18.9143	−	3.33510i	0.657715	−	0.115973i	0.492538	+	0.870291i	$0.336069\pi$
$828$	7.31909	−	21.9224i	0.254356	−	0.761856i
$829$	5.11519	−	2.95325i	0.177658	−	0.102571i	−0.408534	−	0.912743i	$-0.633960\pi$
$829$	5.11519	−	2.95325i	0.177658	−	0.102571i	0.586192	+	0.810172i	$0.300627\pi$
$830$	−5.51736	−	1.73087i	−0.191511	−	0.0600794i
$831$	14.6853	+	30.4202i	0.509428	+	1.05527i
$832$	4.04242	+	1.47132i	0.140146	+	0.0510089i
$833$	15.9041	+	13.3451i	0.551043	+	0.462380i
$834$	0.923701	+	0.0683373i	0.0319852	+	0.00236633i
$835$	14.9454	+	23.3850i	0.517206	+	0.809272i
$836$	13.2863	−	4.97587i	0.459518	−	0.172094i
$837$	−3.92319	−	12.5908i	−0.135605	−	0.435203i
$838$	4.14353	−	23.4991i	0.143136	−	0.811764i
$839$	−15.2081	−	12.7611i	−0.525042	−	0.440563i	0.341343	−	0.939939i	$-0.389118\pi$
$839$	−15.2081	−	12.7611i	−0.525042	−	0.440563i	−0.866385	+	0.499376i	$0.833563\pi$
$840$	5.43410	−	1.80258i	0.187494	−	0.0621949i
$841$	7.71894	−	2.80946i	0.266170	−	0.0968780i
$842$	−7.05483	+	5.91970i	−0.243125	+	0.204006i
$843$	−0.997858	−	1.38515i	−0.0343680	−	0.0477071i
$844$	21.9153	+	12.6528i	0.754357	+	0.435528i
$845$	−8.33072	−	9.06509i	−0.286586	−	0.311849i
$846$	−33.1460	+	13.0818i	−1.13958	+	0.449760i
$847$	0.519769	+	0.300089i	0.0178595	+	0.0103112i
$848$	−1.27418	+	0.735646i	−0.0437554	+	0.0252622i
$849$	11.4233	+	11.1208i	0.392047	+	0.381664i
$850$	−21.4834	−	1.81709i	−0.736873	−	0.0623258i
$851$	−29.7552	−	10.8300i	−1.02000	−	0.371248i
$852$	3.16975	+	2.15668i	0.108594	+	0.0738867i
$853$	−9.20696	−	1.62344i	−0.315240	−	0.0555854i	0.0137894	−	0.999905i	$-0.495611\pi$
$853$	−9.20696	−	1.62344i	−0.315240	−	0.0555854i	−0.329030	+	0.944320i	$0.606722\pi$
$854$	−13.4273			−0.459473
$855$	16.9168	−	23.8500i	0.578544	−	0.815651i
$856$	−10.9189			−0.373201
$857$	−23.2313	−	4.09630i	−0.793565	−	0.139927i	−0.237852	−	0.971301i	$-0.576443\pi$
$857$	−23.2313	−	4.09630i	−0.793565	−	0.139927i	−0.555713	+	0.831374i	$0.687555\pi$
$858$	−20.0509	−	13.6425i	−0.684526	−	0.465747i
$859$	2.12716	+	0.774223i	0.0725778	+	0.0264161i	0.378054	−	0.925784i	$-0.376593\pi$
$859$	2.12716	+	0.774223i	0.0725778	+	0.0264161i	−0.305476	+	0.952200i	$0.598816\pi$
$860$	−14.6121	−	11.1788i	−0.498270	−	0.381195i
$861$	−2.46270	−	2.39748i	−0.0839287	−	0.0817059i
$862$	−5.71872	+	3.30170i	−0.194780	+	0.112456i
$863$	−3.08356	−	1.78029i	−0.104966	−	0.0606019i	0.446598	−	0.894735i	$-0.352635\pi$
$863$	−3.08356	−	1.78029i	−0.104966	−	0.0606019i	−0.551564	+	0.834133i	$0.685969\pi$
$864$	4.61712	−	2.38374i	0.157078	−	0.0810965i
$865$	6.77691	−	6.22790i	0.230422	−	0.211755i
$866$	13.8425	+	7.99198i	0.470388	+	0.271578i
$867$	1.61324	+	2.23938i	0.0547885	+	0.0760533i
$868$	−2.87407	+	2.41163i	−0.0975524	+	0.0818562i
$869$	21.6953	−	7.89645i	0.735963	−	0.267869i
$870$	−5.55938	−	16.7594i	−0.188481	−	0.568198i
$871$	43.9508	+	36.8791i	1.48922	+	1.24960i
$872$	0.938193	−	5.32075i	0.0317712	−	0.180183i
$873$	−27.6512	+	5.64464i	−0.935850	+	0.191042i
$874$	−25.5231	+	21.8230i	−0.863331	+	0.738174i
$875$	16.3765	−	2.22817i	0.553628	−	0.0753260i
$876$	−20.4807	−	1.51520i	−0.691979	−	0.0511940i
$877$	−2.68068	−	2.24935i	−0.0905200	−	0.0759553i	0.596405	−	0.802684i	$-0.296595\pi$
$877$	−2.68068	−	2.24935i	−0.0905200	−	0.0759553i	−0.686925	+	0.726729i	$0.741040\pi$
$878$	12.8292	+	4.66944i	0.432964	+	0.157586i
$879$	−9.11286	−	18.8770i	−0.307369	−	0.636707i
$880$	6.94435	+	2.17853i	0.234094	+	0.0734383i
$881$	46.7149	−	26.9708i	1.57386	−	0.908671i	0.578175	−	0.815913i	$-0.303765\pi$
$881$	46.7149	−	26.9708i	1.57386	−	0.908671i	0.995689	−	0.0927579i	$-0.0295683\pi$
$882$	−13.7008	−	4.57422i	−0.461331	−	0.154022i
$883$	−51.1621	+	9.02126i	−1.72174	+	0.303589i	−0.945204	−	0.326481i	$-0.894137\pi$
$883$	−51.1621	+	9.02126i	−1.72174	+	0.303589i	−0.776538	+	0.630071i	$0.783026\pi$
$884$	−3.22111	−	18.2678i	−0.108338	−	0.614414i
$885$	−6.81661	−	46.4338i	−0.229138	−	1.56086i
$886$	9.92133	−	5.72808i	0.333314	−	0.192439i
$887$	−22.4066	−	26.7032i	−0.752341	−	0.896605i	0.244997	−	0.969524i	$-0.421213\pi$
$887$	−22.4066	−	26.7032i	−0.752341	−	0.896605i	−0.997338	+	0.0729185i	$0.976769\pi$
$888$	−3.09496	−	6.41113i	−0.103860	−	0.215143i
$889$	−0.646470	+	1.77616i	−0.0216819	+	0.0595706i
$890$	1.29840	−	9.97349i	0.0435224	−	0.334312i
$891$	−28.5341	+	6.62718i	−0.955928	+	0.222019i
$892$	23.7590			0.795509
$893$	51.0698	+	8.51736i	1.70898	+	0.285022i
$894$	−6.81196	+	0.688192i	−0.227826	+	0.0230166i
$895$	4.56427	+	10.9743i	0.152567	+	0.366831i
$896$	−1.13241	−	0.950206i	−0.0378312	−	0.0317442i
$897$	55.6409	+	14.1115i	1.85780	+	0.471169i
$898$	8.26664	+	22.7124i	0.275861	+	0.757923i
$899$	7.43778	+	8.86400i	0.248064	+	0.295631i
$900$	14.3671	−	4.31117i	0.478904	−	0.143706i
$901$	5.49427	+	3.17212i	0.183041	+	0.105678i
$902$	−0.758693	−	4.30276i	−0.0252617	−	0.143266i
$903$	−5.72498	−	20.2737i	−0.190515	−	0.674667i
$904$	−6.15442	+	10.6598i	−0.204693	+	0.354538i
$905$	−26.4724	+	51.0327i	−0.879974	+	1.69639i
$906$	5.79612	−	5.95380i	0.192563	−	0.197802i
$907$	6.49266	−	2.36314i	0.215585	−	0.0784666i	−0.231970	−	0.972723i	$-0.574517\pi$
$907$	6.49266	−	2.36314i	0.215585	−	0.0784666i	0.447555	+	0.894256i	$0.352295\pi$
$908$	4.33192	−	11.9018i	0.143760	−	0.394976i
$909$	14.1676	−	26.1344i	0.469909	−	0.866824i
$910$	5.46060	+	13.1294i	0.181017	+	0.435237i
$911$	56.3500			1.86696			0.933479	−	0.358633i	$-0.116757\pi$
$911$	56.3500			1.86696			0.933479	+	0.358633i	$0.116757\pi$
$912$	−7.53410	−	0.487172i	−0.249479	−	0.0161319i
$913$		−	8.41705i		−	0.278564i
$914$	−5.46543	+	30.9960i	−0.180781	+	1.02526i
$915$	−35.1645	−	1.01201i	−1.16250	−	0.0334560i
$916$	13.5596	+	4.93528i	0.448020	+	0.163066i
$917$	14.5986	−	5.31344i	0.482087	−	0.175465i
$918$	−18.8562	−	12.1024i	−0.622346	−	0.399439i
$919$	2.36992	+	4.10482i	0.0781764	+	0.135406i	0.902463	−	0.430767i	$-0.141757\pi$
$919$	2.36992	+	4.10482i	0.0781764	+	0.135406i	−0.824287	+	0.566173i	$0.808424\pi$
$920$	−17.2091	+	0.776246i	−0.567367	+	0.0255921i
$921$	3.30226	+	11.6942i	0.108813	+	0.385337i
$922$	5.94171	+	33.6971i	0.195680	+	1.10976i
$923$	−4.76105	+	8.24638i	−0.156712	+	0.271433i
$924$	4.87122	+	6.76186i	0.160251	+	0.222449i
$925$	−5.37626	−	19.8353i	−0.176770	−	0.652181i
$926$	−17.2916	+	6.29361i	−0.568236	+	0.206821i
$927$	−47.9416	−	7.13268i	−1.57461	−	0.234268i
$928$	−2.93055	+	3.49250i	−0.0962001	+	0.114647i
$929$	−40.4290	−	7.12872i	−1.32643	−	0.233886i	−0.534849	−	0.844948i	$-0.679631\pi$
$929$	−40.4290	−	7.12872i	−1.32643	−	0.233886i	−0.791582	+	0.611062i	$0.790742\pi$
$930$	−7.70861	+	6.09916i	−0.252775	+	0.199999i
$931$	13.6387	+	15.9512i	0.446991	+	0.522779i
$932$	2.45463			0.0804040
$933$	−11.1689	−	0.826301i	−0.365655	−	0.0270519i
$934$	20.4847	−	24.4128i	0.670281	−	0.798810i
$935$	−6.83674	−	30.6293i	−0.223585	−	1.00169i
$936$	6.75038	+	10.9994i	0.220643	+	0.359525i
$937$	21.9810	+	26.1960i	0.718089	+	0.855785i	0.994444	−	0.105270i	$-0.0335708\pi$
$937$	21.9810	+	26.1960i	0.718089	+	0.855785i	−0.276354	+	0.961056i	$0.589126\pi$
$938$	−9.85775	−	17.0741i	−0.321867	−	0.557490i
$939$	20.9558	+	9.43162i	0.683867	+	0.307789i
$940$	17.9720	+	19.5562i	0.586181	+	0.637854i
$941$	7.68867	+	43.6046i	0.250644	+	1.42147i	0.807012	+	0.590535i	$0.201083\pi$
$941$	7.68867	+	43.6046i	0.250644	+	1.42147i	−0.556369	+	0.830936i	$0.687806\pi$
$942$	3.64310	−	8.09450i	0.118699	−	0.263733i
$943$	5.17071	+	8.95593i	0.168382	+	0.291645i
$944$	−9.28267	+	7.78909i	−0.302125	+	0.253513i
$945$	16.1286	+	5.90567i	0.524663	+	0.192111i
$946$	9.15933	−	25.1650i	0.297795	−	0.818186i
$947$	14.1159	+	11.8447i	0.458706	+	0.384900i	0.842655	−	0.538454i	$-0.180991\pi$
$947$	14.1159	+	11.8447i	0.458706	+	0.384900i	−0.383948	+	0.923355i	$0.625436\pi$
$948$	−12.2525	−	0.906467i	−0.397944	−	0.0294407i
$949$		−	51.0064i		−	1.65574i
$950$	−21.1189	−	5.38441i	−0.685188	−	0.174693i
$951$	−4.81632	−	47.6736i	−0.156180	−	1.54592i
$952$	−1.10688	+	6.27743i	−0.0358742	+	0.203453i
$953$	0.970531	−	1.15663i	0.0314386	−	0.0374671i	−0.750096	−	0.661329i	$-0.769993\pi$
$953$	0.970531	−	1.15663i	0.0314386	−	0.0374671i	0.781535	+	0.623862i	$0.214437\pi$
$954$	−4.36582	−	0.649540i	−0.141349	−	0.0210296i
$955$	−20.5684	−	15.7356i	−0.665577	−	0.509191i
$956$	19.7688	+	23.5596i	0.639369	+	0.761971i
$957$	20.8544	−	15.0234i	0.674127	−	0.485639i
$958$	13.1253	−	22.7336i	0.424058	−	0.734489i
$959$	10.6446	−	1.87693i	0.343733	−	0.0606093i
$960$	−2.89403	−	2.57382i	−0.0934045	−	0.0830698i
$961$	−12.2793	+	21.2683i	−0.396105	+	0.686074i
$962$	15.3126	−	8.84074i	0.493699	−	0.285037i
$963$	−25.6491	−	20.3747i	−0.826531	−	0.656565i
$964$	1.98699	+	5.45921i	0.0639967	+	0.175829i
$965$	0.260428	−	0.0581298i	0.00838347	−	0.00187127i
$966$	−16.3085	−	11.0962i	−0.524716	−	0.357014i
$967$	−12.4716	−	2.19909i	−0.401061	−	0.0707179i	−0.0305203	−	0.999534i	$-0.509716\pi$
$967$	−12.4716	−	2.19909i	−0.401061	−	0.0707179i	−0.370541	+	0.928816i	$0.620828\pi$
$968$		−	0.406003i		−	0.0130494i
$969$	14.4243	+	29.1850i	0.463376	+	0.937558i
$970$	11.3277	+	17.7244i	0.363710	+	0.569097i
$971$	4.46581	−	25.3269i	0.143315	−	0.812778i	−0.825390	−	0.564563i	$-0.809045\pi$
$971$	4.46581	−	25.3269i	0.143315	−	0.812778i	0.968705	−	0.248216i	$-0.0798441\pi$
$972$	15.2939	+	3.01600i	0.490552	+	0.0967384i
$973$	0.270370	−	0.742835i	0.00866766	−	0.0238142i
$974$	−4.99500	−	13.7237i	−0.160050	−	0.439734i
$975$	13.3111	+	34.7960i	0.426296	+	1.11436i
$976$	4.54160	+	7.86628i	0.145373	+	0.251793i
$977$	−21.2084	−	12.2447i	−0.678516	−	0.391741i	0.120780	−	0.992679i	$-0.461461\pi$
$977$	−21.2084	−	12.2447i	−0.678516	−	0.391741i	−0.799296	+	0.600938i	$0.794794\pi$
$978$	2.82796	+	10.0146i	0.0904283	+	0.320231i
$979$	14.4176	−	2.54221i	0.460789	−	0.0812495i
$980$	0.485131	+	10.7552i	0.0154969	+	0.343561i
$981$	12.1324	−	10.7481i	0.387357	−	0.343159i
$982$	0.357177	−	0.299707i	0.0113980	−	0.00956403i
$983$	17.5558	+	48.2342i	0.559944	+	1.53843i	0.819720	+	0.572764i	$0.194129\pi$
$983$	17.5558	+	48.2342i	0.559944	+	1.53843i	−0.259776	+	0.965669i	$0.583649\pi$
$984$	−0.571570	+	2.25367i	−0.0182210	+	0.0718443i
$985$	44.6695	+	5.81529i	1.42329	+	0.185291i
$986$	19.3604	+	3.41376i	0.616560	+	0.108716i
$987$	3.05695	+	30.2587i	0.0973038	+	0.963146i
$988$	−0.173919	−	18.7505i	−0.00553309	−	0.596534i
$989$			63.3864i			2.01557i
$990$	12.2475	+	18.0756i	0.389251	+	0.574481i
$991$	10.9756	−	13.0802i	0.348651	−	0.415506i	−0.563009	−	0.826451i	$-0.690356\pi$
$991$	10.9756	−	13.0802i	0.348651	−	0.415506i	0.911660	+	0.410944i	$0.134801\pi$
$992$	2.38495	+	0.868051i	0.0757222	+	0.0275606i
$993$	16.6844	+	34.5613i	0.529464	+	1.09677i
$994$	2.50658	−	2.10327i	0.0795039	−	0.0667117i
$995$	−46.2402	−	23.9864i	−1.46591	−	0.760420i
$996$	−1.83831	+	4.08448i	−0.0582490	+	0.129422i
$997$	−0.296241	+	0.0522353i	−0.00938205	+	0.00165431i	−0.178337	−	0.983969i	$-0.557072\pi$
$997$	−0.296241	+	0.0522353i	−0.00938205	+	0.00165431i	0.168955	+	0.985624i	$0.445961\pi$
$998$	−8.22992	+	1.45116i	−0.260514	+	0.0459356i
$999$	4.69293	−	20.8353i	0.148478	−	0.659199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.59.24	yes	240
3.2	odd	2	inner	570.2.bf.a.59.6	yes	240
5.4	even	2	inner	570.2.bf.a.59.17	yes	240
15.14	odd	2	inner	570.2.bf.a.59.35	yes	240
19.10	odd	18	inner	570.2.bf.a.29.35	yes	240
57.29	even	18	inner	570.2.bf.a.29.17	yes	240
95.29	odd	18	inner	570.2.bf.a.29.6	✓	240
285.29	even	18	inner	570.2.bf.a.29.24	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.6	✓	240	95.29	odd	18	inner
570.2.bf.a.29.17	yes	240	57.29	even	18	inner
570.2.bf.a.29.24	yes	240	285.29	even	18	inner
570.2.bf.a.29.35	yes	240	19.10	odd	18	inner
570.2.bf.a.59.6	yes	240	3.2	odd	2	inner
570.2.bf.a.59.17	yes	240	5.4	even	2	inner
570.2.bf.a.59.24	yes	240	1.1	even	1	trivial
570.2.bf.a.59.35	yes	240	15.14	odd	2	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.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-1.43202 - 0.974336i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.35867 - 1.77595i) q^{5} +(-1.24107 - 1.20820i) q^{6} +(-1.28021 + 0.739129i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.10134 + 2.79053i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-1.43202 - 0.974336i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.35867 - 1.77595i) q^{5} +(-1.24107 - 1.20820i) q^{6} +(-1.28021 + 0.739129i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.10134 + 2.79053i) q^{9} +(1.64642 - 1.51304i) q^{10} +(2.81878 + 1.62742i) q^{11} +(-1.01241 - 1.40535i) q^{12} +(3.29541 - 2.76518i) q^{13} +(-1.38911 + 0.505594i) q^{14} +(-3.67601 + 1.21939i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.748773 - 4.24650i) q^{17} +(0.600038 + 2.93938i) q^{18} +(1.45278 - 4.10968i) q^{19} +(1.88415 - 1.20416i) q^{20} +(2.55344 + 0.188909i) q^{21} +(2.49335 + 2.09217i) q^{22} +(-7.23936 - 2.63491i) q^{23} +(-0.752994 - 1.55981i) q^{24} +(-1.30803 - 4.82587i) q^{25} +(3.72551 - 2.15093i) q^{26} +(1.14177 - 5.06916i) q^{27} +(-1.45580 + 0.256697i) q^{28} +(0.791685 + 4.48987i) q^{29} +(-3.83191 + 0.562535i) q^{30} +(2.19798 - 1.26901i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-2.45088 - 5.07693i) q^{33} +(1.47480 - 4.05197i) q^{34} +(-0.426723 + 3.27783i) q^{35} +(0.0805041 + 2.99892i) q^{36} +4.11020 q^{37} +(2.14434 - 3.79497i) q^{38} +(-7.41329 + 0.748943i) q^{39} +(2.06462 - 0.858686i) q^{40} +(-1.02830 - 0.862846i) q^{41} +(2.48184 + 0.629439i) q^{42} +(-2.81406 - 7.73157i) q^{43} +(2.09217 + 2.49335i) q^{44} +(6.45221 + 1.83548i) q^{45} +(-6.67183 - 3.85198i) q^{46} +(2.06260 + 11.6976i) q^{47} +(-0.470697 - 1.66687i) q^{48} +(-2.40738 + 4.16970i) q^{49} +(-0.450151 - 4.97970i) q^{50} +(-5.20978 + 5.35151i) q^{51} +(4.04242 - 1.47132i) q^{52} +(-0.503212 + 1.38256i) q^{53} +(2.00468 - 4.79388i) q^{54} +(6.72001 - 2.79489i) q^{55} -1.47826 q^{56} +(-6.08460 + 4.46963i) q^{57} +4.55913i q^{58} +(-2.10421 + 11.9336i) q^{59} +(-3.87138 - 0.111416i) q^{60} +(8.53541 + 3.10664i) q^{61} +(2.38495 - 0.868051i) q^{62} +(-3.47251 - 2.75843i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.433451 - 9.60947i) q^{65} +(-1.53204 - 5.42539i) q^{66} +(2.31594 + 13.1344i) q^{67} +(2.15601 - 3.73431i) q^{68} +(7.79959 + 10.8268i) q^{69} +(-0.989429 + 3.15393i) q^{70} +(-2.08000 + 0.757058i) q^{71} +(-0.441476 + 2.96734i) q^{72} +(7.62144 - 9.08287i) q^{73} +(4.04776 + 0.713729i) q^{74} +(-2.82891 + 8.18519i) q^{75} +(2.77076 - 3.36495i) q^{76} -4.81150 q^{77} +(-7.43072 - 0.549740i) q^{78} +(4.55951 - 5.43381i) q^{79} +(2.18236 - 0.487123i) q^{80} +(-6.57410 + 6.14664i) q^{81} +(-0.862846 - 1.02830i) q^{82} +(-1.29300 - 2.23955i) q^{83} +(2.33484 + 1.05084i) q^{84} +(-6.52426 - 7.09939i) q^{85} +(-1.42874 - 8.10277i) q^{86} +(3.24093 - 7.20093i) q^{87} +(1.62742 + 2.81878i) q^{88} +(3.44561 - 2.89121i) q^{89} +(6.03546 + 2.92801i) q^{90} +(-2.17499 + 5.97574i) q^{91} +(-5.90158 - 4.95202i) q^{92} +(-4.38398 - 0.324336i) q^{93} +11.8780i q^{94} +(-5.32475 - 8.16376i) q^{95} +(-0.174098 - 1.72328i) q^{96} +(-1.63353 + 9.26423i) q^{97} +(-3.09486 + 3.68831i) q^{98} +(-1.43693 + 9.65822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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