LMFDB - Embedded newform 570.2.bf.a.29.24

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			29.24
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.24

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

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	0.238156	−	0.971227i	$-0.423457\pi$
$7$	−1.28021	−	0.739129i	−0.483874	−	0.279365i	−0.722029	+	0.691862i	$0.756790\pi$
$8$	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	−0.0107218	−	0.999943i	$-0.503413\pi$
$11$	2.81878	−	1.62742i	0.849893	−	0.490686i	0.860615	+	0.509257i	$0.170080\pi$
$12$	−1.01241	+	1.40535i	−0.292258	+	0.405691i
$13$	3.29541	+	2.76518i	0.913982	+	0.766922i	0.972872	−	0.231342i	$-0.0743117\pi$
$13$	3.29541	+	2.76518i	0.913982	+	0.766922i	−0.0588900	+	0.998264i	$0.518756\pi$
$14$	−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	0.930241	+	0.366949i	$0.119597\pi$
$17$	0.748773	+	4.24650i	0.181604	+	1.02993i	−0.748637	+	0.662980i	$0.769291\pi$
$18$	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	−0.958503	−	0.285083i	$-0.907979\pi$
$23$	−7.23936	+	2.63491i	−1.50951	+	0.549417i	−0.551008	+	0.834500i	$0.685757\pi$
$24$	−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	−0.818717	−	0.574197i	$-0.805314\pi$
$29$	0.791685	−	4.48987i	0.147012	−	0.833748i	0.965729	−	0.259551i	$-0.0835745\pi$
$30$	−3.83191	−	0.562535i	−0.699608	−	0.102704i
$31$	2.19798	+	1.26901i	0.394769	+	0.227920i	0.684225	−	0.729271i	$-0.260141\pi$
$31$	2.19798	+	1.26901i	0.394769	+	0.227920i	−0.289455	+	0.957192i	$0.593474\pi$
$32$	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	−0.719543	−	0.694448i	$-0.755649\pi$
$41$	−1.02830	+	0.862846i	−0.160593	+	0.134754i	0.558950	+	0.829201i	$0.311204\pi$
$42$	2.48184	−	0.629439i	0.382957	−	0.0971246i
$43$	−2.81406	+	7.73157i	−0.429140	+	1.17905i	0.517195	+	0.855867i	$0.326976\pi$
$43$	−2.81406	+	7.73157i	−0.429140	+	1.17905i	−0.946335	+	0.323186i	$0.895246\pi$
$44$	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	−0.341513	−	0.939877i	$-0.610939\pi$
$47$	2.06260	−	11.6976i	0.300861	−	1.70627i	0.642374	−	0.766391i	$-0.277949\pi$
$48$	−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	0.900322	−	0.435224i	$-0.143331\pi$
$53$	−0.503212	−	1.38256i	−0.0691214	−	0.189910i	−0.969443	+	0.245315i	$0.921109\pi$
$54$	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	−0.742293	−	0.670075i	$-0.766262\pi$
$59$	−2.10421	−	11.9336i	−0.273945	−	1.55362i	0.468349	−	0.883544i	$-0.344849\pi$
$60$	−3.87138	+	0.111416i	−0.499793	+	0.0143837i
$61$	8.53541	−	3.10664i	1.09285	−	0.397764i	0.268173	−	0.963371i	$-0.413580\pi$
$61$	8.53541	−	3.10664i	1.09285	−	0.397764i	0.824675	+	0.565607i	$0.191358\pi$
$62$	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	−0.429625	−	0.903008i	$-0.641354\pi$
$67$	2.31594	−	13.1344i	0.282937	−	1.60462i	0.712562	−	0.701609i	$-0.247535\pi$
$68$	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	0.215632	−	0.976475i	$-0.430819\pi$
$71$	−2.08000	−	0.757058i	−0.246850	−	0.0898462i	−0.462482	+	0.886629i	$0.653041\pi$
$72$	−0.441476	−	2.96734i	−0.0520284	−	0.349704i
$73$	7.62144	+	9.08287i	0.892022	+	1.06307i	0.997640	+	0.0686633i	$0.0218734\pi$
$73$	7.62144	+	9.08287i	0.892022	+	1.06307i	−0.105618	+	0.994407i	$0.533682\pi$
$74$	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	0.958907	−	0.283720i	$-0.0915687\pi$
$79$	4.55951	+	5.43381i	0.512985	+	0.611351i	−0.445922	+	0.895072i	$0.647124\pi$
$80$	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	−0.928222	−	0.372027i	$-0.878663\pi$
$83$	−1.29300	+	2.23955i	−0.141926	+	0.245823i	0.786296	+	0.617850i	$0.211996\pi$
$84$	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	0.806873	−	0.590725i	$-0.201158\pi$
$89$	3.44561	+	2.89121i	0.365234	+	0.306467i	−0.441639	+	0.897193i	$0.645603\pi$
$90$	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	−0.948173	−	0.317754i	$-0.897071\pi$
$97$	−1.63353	−	9.26423i	−0.165860	−	0.940640i	0.782313	−	0.622886i	$-0.214040\pi$
$98$	−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	−0.983376	−	0.181584i	$-0.941878\pi$
$101$	−6.36950	+	7.59088i	−0.633789	+	0.755321i	0.349586	+	0.936904i	$0.386322\pi$
$102$	−6.05991	−	4.36554i	−0.600020	−	0.432253i
$103$	−8.07822	−	13.9919i	−0.795971	−	1.37866i	−0.922221	−	0.386663i	$-0.873628\pi$
$103$	−8.07822	−	13.9919i	−0.795971	−	1.37866i	0.126250	−	0.991998i	$-0.459706\pi$
$104$	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	−0.0323873	−	0.999475i	$-0.510311\pi$
$107$	−9.45606	−	5.45946i	−0.914152	−	0.527786i	−0.881765	+	0.471689i	$0.843644\pi$
$108$	2.80667	+	4.37294i	0.270072	+	0.420786i
$109$	−1.84788	+	5.07700i	−0.176995	+	0.486289i	−0.996188	−	0.0872281i	$-0.972199\pi$
$109$	−1.84788	+	5.07700i	−0.176995	+	0.486289i	0.819194	+	0.573517i	$0.194421\pi$
$110$	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	$-0.803459\pi$
$113$		−	12.3088i		−	1.15792i	0.815357	−	0.578959i	$-0.196541\pi$
$114$	−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	0.685210	−	0.728345i	$-0.259710\pi$
$127$	0.979491	+	0.821891i	0.0869158	+	0.0729310i	−0.598295	+	0.801276i	$0.704155\pi$
$128$	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	−0.606392	−	0.795166i	$-0.707384\pi$
$131$	−10.3496	+	1.82492i	−0.904252	+	0.159444i	−0.297860	+	0.954610i	$0.596273\pi$
$132$	−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	−0.618419	−	0.785849i	$-0.712226\pi$
$137$	−6.87090	+	2.50080i	−0.587021	+	0.213658i	0.0313977	+	0.999507i	$0.490004\pi$
$138$	5.80105	−	12.0167i	0.493818	−	1.02293i
$139$	−0.409647	−	0.343735i	−0.0347458	−	0.0291552i	0.625249	−	0.780425i	$-0.284997\pi$
$139$	−0.409647	−	0.343735i	−0.0347458	−	0.0291552i	−0.659995	+	0.751270i	$0.729442\pi$
$140$	−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	0.860014	−	0.510270i	$-0.170454\pi$
$149$	2.54088	+	3.02810i	0.208157	+	0.248072i	−0.651857	+	0.758342i	$0.726010\pi$
$150$	−4.20727	−	7.56960i	−0.343522	−	0.618055i
$151$		−	4.79732i		−	0.390400i	−0.980763	−	0.195200i	$-0.937464\pi$
$151$		−	4.79732i		−	0.390400i	0.980763	−	0.195200i	$-0.0625356\pi$
$152$	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	−0.849888	−	0.526963i	$-0.823330\pi$
$157$	1.75281	−	4.81581i	0.139890	−	0.384344i	0.989778	+	0.142620i	$0.0455527\pi$
$158$	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	−0.689732	−	0.724065i	$-0.742272\pi$
$163$	−5.20311	+	3.00402i	−0.407539	+	0.235293i	0.282193	+	0.959358i	$0.408938\pi$
$164$	−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	−0.988495	−	0.151251i	$-0.951670\pi$
$167$	−4.24497	−	11.6630i	−0.328486	−	0.902508i	0.660009	−	0.751257i	$-0.270552\pi$
$168$	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	−0.0174140	−	0.999848i	$-0.505543\pi$
$173$	4.05361	−	0.714761i	0.308190	−	0.0543423i	0.325604	+	0.945506i	$0.394432\pi$
$174$	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	0.749443	−	0.662068i	$-0.230321\pi$
$179$	−2.65771	−	4.60328i	−0.198646	−	0.344066i	−0.948090	+	0.318003i	$0.896988\pi$
$180$	5.43532	−	3.93157i	0.405125	−	0.293042i
$181$	−25.3198	−	4.46457i	−1.88201	−	0.331849i	−0.889791	−	0.456369i	$-0.849150\pi$
$181$	−25.3198	−	4.46457i	−1.88201	−	0.331849i	−0.992217	+	0.124520i	$0.960261\pi$
$182$	−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	$0.137622\pi$
$191$			11.5816i			0.838015i	−0.907983	+	0.419007i	$0.862378\pi$
$192$	0.127791	+	1.72733i	0.00922255	+	0.124659i
$193$	0.0914143	−	0.0767057i	0.00658015	−	0.00552140i	−0.639492	−	0.768798i	$-0.720855\pi$
$193$	0.0914143	−	0.0767057i	0.00658015	−	0.00552140i	0.646072	+	0.763277i	$0.276411\pi$
$194$	−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	−0.244279	−	0.969705i	$-0.578551\pi$
$197$	10.0727	−	17.4464i	0.717649	−	1.24301i	0.961929	−	0.273300i	$-0.0881152\pi$
$198$	−3.09224	−	9.26197i	−0.219756	−	0.658219i
$199$	−4.04530	+	22.9420i	−0.286764	+	1.62632i	0.412153	+	0.911115i	$0.364777\pi$
$199$	−4.04530	+	22.9420i	−0.286764	+	1.62632i	−0.698917	+	0.715203i	$0.746334\pi$
$200$	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	0.772530	−	0.634978i	$-0.218991\pi$
$211$	24.9212	−	4.39428i	1.71565	−	0.302515i	0.943116	+	0.332463i	$0.107880\pi$
$212$	−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	0.954778	−	0.297319i	$-0.0960925\pi$
$223$	22.3261	+	8.12604i	1.49507	+	0.544160i	0.540289	+	0.841479i	$0.318315\pi$
$224$	−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	$0.138084\pi$
$227$			12.6657i			0.840650i	−0.907374	+	0.420325i	$0.861916\pi$
$228$	−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	0.416468	−	0.909150i	$-0.363268\pi$
$233$	2.30660	+	0.839533i	0.151110	+	0.0549996i	−0.265358	+	0.964150i	$0.585490\pi$
$234$	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	0.809922	−	0.586537i	$-0.199509\pi$
$239$	26.6345	−	15.3774i	1.72284	−	0.994682i	0.912917	−	0.408145i	$-0.133824\pi$
$240$	−3.59980	+	1.42879i	−0.232366	+	0.0922278i
$241$	3.73432	−	4.45039i	0.240549	−	0.286675i	−0.632240	−	0.774772i	$-0.717864\pi$
$241$	3.73432	−	4.45039i	0.240549	−	0.286675i	0.872789	+	0.488097i	$0.162309\pi$
$242$	−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	−0.966135	−	0.258037i	$-0.916924\pi$
$251$	−6.20880	−	17.0585i	−0.391896	−	1.07672i	0.574239	−	0.818688i	$-0.305298\pi$
$252$	−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	−0.854890	−	0.518809i	$-0.826376\pi$
$257$	−29.4280	−	5.18895i	−1.83567	−	0.323678i	−0.980777	+	0.195132i	$0.937487\pi$
$258$	−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	−0.424754	−	0.905309i	$-0.639639\pi$
$263$	6.37410	−	5.34851i	0.393044	−	0.329803i	0.817798	+	0.575506i	$0.195195\pi$
$264$	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	−0.937815	−	0.347136i	$-0.887154\pi$
$269$	−12.4453	+	10.4428i	−0.758802	+	0.636711i	0.179013	+	0.983847i	$0.442710\pi$
$270$	−5.79001	+	10.0735i	−0.352369	+	0.613055i
$271$	−10.5460	−	3.83843i	−0.640624	−	0.233168i	0.00122479	−	0.999999i	$-0.499610\pi$
$271$	−10.5460	−	3.83843i	−0.640624	−	0.233168i	−0.641849	+	0.766831i	$0.721832\pi$
$272$	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	−0.912595	−	0.408865i	$-0.865925\pi$
$277$	−16.8897	+	9.75128i	−1.01480	+	0.585898i	−0.102210	+	0.994763i	$0.532591\pi$
$278$	−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	−0.314247	−	0.949341i	$-0.601752\pi$
$281$	0.926183	−	0.337103i	0.0552515	−	0.0201099i	0.369498	+	0.929232i	$0.379530\pi$
$282$	11.5732	+	17.0095i	0.689174	+	1.01290i
$283$	−9.06457	+	1.59833i	−0.538833	+	0.0950107i	−0.436440	−	0.899733i	$-0.643761\pi$
$283$	−9.06457	+	1.59833i	−0.538833	+	0.0950107i	−0.102393	+	0.994744i	$0.532650\pi$
$284$	−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	−0.161569	−	0.986861i	$-0.551655\pi$
$293$	10.4808	−	6.05108i	0.612294	−	0.353508i	0.773863	+	0.633354i	$0.218322\pi$
$294$	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	−0.783138	−	0.621848i	$-0.786382\pi$
$307$	−5.37432	+	4.50959i	−0.306729	+	0.257376i	0.476410	+	0.879223i	$0.341938\pi$
$308$	−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	0.650292	−	0.759685i	$-0.274647\pi$
$311$	5.59973	+	3.23301i	0.317532	+	0.183327i	−0.332760	+	0.943011i	$0.607980\pi$
$312$	−6.79457	+	3.05804i	−0.384667	+	0.173128i
$313$	−13.0662	−	2.30393i	−0.738546	−	0.130226i	−0.208295	−	0.978066i	$-0.566791\pi$
$313$	−13.0662	−	2.30393i	−0.738546	−	0.130226i	−0.530251	+	0.847841i	$0.677902\pi$
$314$	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	0.0170548	−	0.999855i	$-0.494571\pi$
$317$	17.7824	−	21.1922i	0.998758	−	1.19027i	0.981703	−	0.190419i	$-0.0609845\pi$
$318$	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	−0.923966	−	0.382475i	$-0.875072\pi$
$331$	−19.1889	+	11.0787i	−1.05472	+	0.608941i	−0.130750	+	0.991415i	$0.541739\pi$
$332$	−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	0.351202	−	0.936300i	$-0.385773\pi$
$337$	0.337706	+	0.122915i	0.0183960	+	0.00669561i	−0.332806	+	0.942995i	$0.607995\pi$
$338$	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	0.0862298	−	0.996275i	$-0.472518\pi$
$347$	−9.09244	−	3.30938i	−0.488108	−	0.177657i	−0.574338	+	0.818619i	$0.694740\pi$
$348$	5.50834	+	5.65820i	0.295278	+	0.303311i
$349$	12.0168	−	20.8137i	0.643245	−	1.11413i	−0.341459	−	0.939897i	$-0.610921\pi$
$349$	12.0168	−	20.8137i	0.643245	−	1.11413i	0.984704	−	0.174236i	$-0.0557456\pi$
$350$	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	0.647407	−	0.762145i	$-0.275854\pi$
$353$	−6.31913	−	10.9451i	−0.336333	−	0.582546i	−0.983740	+	0.179598i	$0.942520\pi$
$354$	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	0.0861044	−	0.996286i	$-0.472558\pi$
$359$	9.62079	−	1.69640i	0.507766	−	0.0895328i	0.421662	+	0.906753i	$0.361447\pi$
$360$	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	0.0885101	+	0.996075i	$0.471789\pi$
$367$	−17.3910	+	20.7258i	−0.907802	+	1.08188i	−0.996312	+	0.0858013i	$0.972655\pi$
$368$	−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	0.178178	+	0.983998i	$0.442980\pi$
$373$	−14.7375	+	25.5261i	−0.763079	+	1.32169i	−0.941256	+	0.337693i	$0.890353\pi$
$374$	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	$0.0806730\pi$
$379$			9.76267i			0.501475i	−0.968055	+	0.250737i	$0.919327\pi$
$380$	−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	0.991904	−	0.126987i	$-0.0405306\pi$
$383$	13.5937	+	16.2003i	0.694604	+	0.827797i	−0.297300	+	0.954784i	$0.596086\pi$
$384$	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	−0.256238	−	0.966614i	$-0.582483\pi$
$389$	−16.3233	−	2.87824i	−0.827625	−	0.145933i	−0.571387	+	0.820681i	$0.693594\pi$
$390$	−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	0.610545	−	0.791982i	$-0.290951\pi$
$397$	28.9935	−	5.11234i	1.45514	−	0.256581i	0.844598	+	0.535401i	$0.179839\pi$
$398$			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	0.995092	−	0.0989522i	$-0.0315491\pi$
$401$	0.524009	+	2.97180i	0.0261678	+	0.148405i	−0.968924	+	0.247357i	$0.920438\pi$
$402$	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	0.225656	−	0.974207i	$-0.427547\pi$
$409$	2.11348	+	0.372663i	0.104505	+	0.0184270i	−0.121151	+	0.992634i	$0.538659\pi$
$410$	−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	$0.198066\pi$
$419$			23.8617i			1.16572i	−0.812573	+	0.582859i	$0.801934\pi$
$420$	5.03853	+	2.71882i	0.245855	+	0.132665i
$421$	−5.91970	−	7.05483i	−0.288509	−	0.343831i	0.602250	−	0.798307i	$-0.294271\pi$
$421$	−5.91970	−	7.05483i	−0.288509	−	0.343831i	−0.890759	+	0.454476i	$0.849827\pi$
$422$	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	0.512777	−	0.858522i	$-0.328617\pi$
$431$	−5.05850	−	4.24459i	−0.243660	−	0.204455i	−0.756436	+	0.654067i	$0.773061\pi$
$432$	4.13304	+	3.14928i	0.198851	+	0.151520i
$433$	15.0200	−	5.46683i	0.721815	−	0.262719i	0.0451190	−	0.998982i	$-0.485633\pi$
$433$	15.0200	−	5.46683i	0.721815	−	0.262719i	0.676696	+	0.736262i	$0.263411\pi$
$434$	−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	0.156677	−	0.987650i	$-0.449922\pi$
$439$	13.4451	−	2.37074i	0.641701	−	0.113149i	0.485024	+	0.874501i	$0.338811\pi$
$440$	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	0.827004	−	0.562196i	$-0.190043\pi$
$443$	8.77593	+	7.36388i	0.416957	+	0.349869i	−0.410047	+	0.912064i	$0.634488\pi$
$444$	−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	−0.426204	−	0.904627i	$-0.640150\pi$
$449$	12.0850	−	20.9319i	0.570328	−	0.987836i	0.996532	−	0.0832095i	$-0.0265171\pi$
$450$	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	$-0.736642\pi$
$457$		−	31.4742i		−	1.47230i	0.676818	−	0.736150i	$-0.263358\pi$
$458$	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	−0.295248	−	0.955421i	$-0.595402\pi$
$461$	11.7029	−	32.1534i	0.545058	−	1.49753i	0.840305	−	0.542113i	$-0.182376\pi$
$462$	5.97140	−	5.81325i	0.277815	−	0.270457i
$463$	−15.9360	−	9.20064i	−0.740608	−	0.427590i	0.0816824	−	0.996658i	$-0.473971\pi$
$463$	−15.9360	−	9.20064i	−0.740608	−	0.427590i	−0.822290	+	0.569068i	$0.807304\pi$
$464$	−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	0.953684	+	0.300810i	$0.0972570\pi$
$467$	15.9343	+	27.5990i	0.737351	+	1.27713i	−0.216333	+	0.976320i	$0.569410\pi$
$468$	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	0.957072	+	0.289850i	$0.0936055\pi$
$479$	8.97820	+	24.6674i	0.410224	+	1.12708i	−0.546848	+	0.837232i	$0.684172\pi$
$480$	−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	−0.982688	−	0.185271i	$-0.940684\pi$
$487$	−7.30221	+	12.6478i	−0.330895	+	0.573126i	0.651793	+	0.758397i	$0.274017\pi$
$488$	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	0.772765	−	0.634692i	$-0.218873\pi$
$491$	0.299707	+	0.357177i	0.0135256	+	0.0161192i	−0.759239	+	0.650812i	$0.774429\pi$
$492$	−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	0.160211	−	0.987083i	$-0.448782\pi$
$499$	−7.85290	−	2.85822i	−0.351544	−	0.127952i	−0.511756	+	0.859131i	$0.671005\pi$
$500$	−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	0.909853	+	0.414930i	$0.136194\pi$
$503$	−1.95218	+	11.0714i	−0.0870436	+	0.493649i	−0.996897	+	0.0787187i	$0.974917\pi$
$504$	−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	−0.288436	−	0.957499i	$-0.593135\pi$
$509$	2.39322	−	0.871062i	0.106078	−	0.0386091i	0.394514	+	0.918890i	$0.370913\pi$
$510$	−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	0.958987	−	0.283451i	$-0.0914795\pi$
$521$	5.34154	+	9.25182i	0.234017	+	0.405330i	−0.724969	+	0.688781i	$0.758146\pi$
$522$	−12.7224	−	5.02115i	−0.556844	−	0.219770i
$523$	6.46521	−	36.6660i	0.282704	−	1.60329i	−0.430670	−	0.902510i	$-0.641723\pi$
$523$	6.46521	−	36.6660i	0.282704	−	1.60329i	0.713374	−	0.700784i	$-0.247166\pi$
$524$	−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	−0.950827	−	0.309722i	$-0.899764\pi$
$541$	1.13016	−	6.40946i	0.0485894	−	0.275564i	0.999416	+	0.0341582i	$0.0108750\pi$
$542$	−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	0.00237778	−	0.999997i	$-0.499243\pi$
$547$	15.1317	−	5.50749i	0.646985	−	0.235483i	0.644607	+	0.764514i	$0.277021\pi$
$548$	−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	0.276700	−	0.960956i	$-0.410759\pi$
$557$	−14.6705	−	12.3100i	−0.621609	−	0.521592i	−0.898309	+	0.439365i	$0.855204\pi$
$558$	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	0.372838	−	0.927896i	$-0.378385\pi$
$563$	−5.79723	−	3.34703i	−0.244324	−	0.141061i	−0.617163	+	0.786836i	$0.711718\pi$
$564$	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	0.633643	−	0.773626i	$-0.281559\pi$
$577$	6.73746	+	3.88988i	0.280484	+	0.161938i	−0.353158	+	0.935564i	$0.614892\pi$
$578$	−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	−0.998082	−	0.0619014i	$-0.980284\pi$
$587$	−1.97128	−	11.1797i	−0.0813632	−	0.461434i	0.916719	−	0.399533i	$-0.130828\pi$
$588$	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	−0.789290	−	0.614021i	$-0.789551\pi$
$593$	−24.3330	+	8.85648i	−0.999236	+	0.363692i	−0.209946	+	0.977713i	$0.567329\pi$
$594$	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	0.744043	+	0.668132i	$0.232906\pi$
$599$	−4.49458	+	25.4900i	−0.183643	+	1.04149i	−0.927686	+	0.373361i	$0.878205\pi$
$600$	−6.54250	−	5.67413i	−0.267096	−	0.231645i
$601$	24.4980	+	14.1439i	0.999294	+	0.576943i	0.908039	−	0.418885i	$-0.137579\pi$
$601$	24.4980	+	14.1439i	0.999294	+	0.576943i	0.0912547	+	0.995828i	$0.470912\pi$
$602$	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	0.594757	+	0.803906i	$0.297248\pi$
$613$	−9.34878	+	25.6856i	−0.377594	+	1.03743i	−0.972351	+	0.233525i	$0.924974\pi$
$614$	−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	0.624220	+	0.781249i	$0.285417\pi$
$617$	−5.70210	+	32.3382i	−0.229558	+	1.30189i	−0.853778	+	0.520638i	$0.825694\pi$
$618$	26.9306	+	7.60479i	1.08331	+	0.305909i
$619$	16.3880	+	28.3849i	0.658690	+	1.14088i	0.980955	+	0.194235i	$0.0622225\pi$
$619$	16.3880	+	28.3849i	0.658690	+	1.14088i	−0.322265	+	0.946649i	$0.604444\pi$
$620$	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	−0.614903	−	0.788603i	$-0.710805\pi$
$631$	−14.5454	+	5.29409i	−0.579042	+	0.210754i	0.0358608	+	0.999357i	$0.488583\pi$
$632$	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	−0.485860	−	0.874037i	$-0.661494\pi$
$641$	−35.9483	−	13.0841i	−1.41987	−	0.516791i	−0.934010	+	0.357246i	$0.883716\pi$
$642$	18.3317	−	4.64925i	0.723496	−	0.183491i
$643$	−6.24965	−	7.44804i	−0.246462	−	0.293722i	0.628604	−	0.777726i	$-0.283627\pi$
$643$	−6.24965	−	7.44804i	−0.246462	−	0.293722i	−0.875066	+	0.484003i	$0.839182\pi$
$644$	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	0.459107	+	0.888381i	$0.348169\pi$
$653$	−13.7942	+	23.8922i	−0.539807	+	0.934973i	−0.998914	+	0.0465920i	$0.985164\pi$
$654$	−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	0.144763	−	0.989466i	$-0.453758\pi$
$659$	−20.6532	−	17.3301i	−0.804533	−	0.675083i	−0.949296	+	0.314383i	$0.898202\pi$
$660$	−10.7312	+	6.61442i	−0.417713	+	0.257466i
$661$	11.9285	+	32.7733i	0.463965	+	1.27473i	0.922479	+	0.386046i	$0.126160\pi$
$661$	11.9285	+	32.7733i	0.463965	+	1.27473i	−0.458514	+	0.888687i	$0.651618\pi$
$662$	−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	0.687246	−	0.726425i	$-0.258820\pi$
$673$	−7.40599	−	12.8275i	−0.285480	−	0.494466i	−0.972725	+	0.231960i	$0.925486\pi$
$674$	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	0.0958814	−	0.995393i	$-0.469433\pi$
$677$	−18.6874	−	10.7891i	−0.718213	−	0.414661i	−0.814095	+	0.580732i	$0.802766\pi$
$678$	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	$-0.893325\pi$
$683$		−	17.1907i		−	0.657782i	0.944368	−	0.328891i	$-0.106675\pi$
$684$	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	−0.887612	−	0.460592i	$-0.847637\pi$
$691$	−1.18086	+	2.04531i	−0.0449220	+	0.0778072i	0.842690	+	0.538399i	$0.180971\pi$
$692$	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	−0.645555	−	0.763714i	$-0.723374\pi$
$701$	−26.2374	+	4.62636i	−0.990972	+	0.174735i	−0.345417	+	0.938449i	$0.612263\pi$
$702$	−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	0.994922	+	0.100654i	$0.0320935\pi$
$709$	33.7315	+	28.3041i	1.26681	+	1.06298i	0.271891	+	0.962328i	$0.412351\pi$
$710$	−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	0.996412	+	0.0846401i	$0.0269741\pi$
$719$	24.3135	+	28.9757i	0.906741	+	1.08061i	−0.0896708	+	0.995971i	$0.528582\pi$
$720$	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	−0.847082	−	0.531462i	$-0.821643\pi$
$727$	3.86750	−	10.6259i	0.143438	−	0.394092i	0.990520	+	0.137370i	$0.0438650\pi$
$728$	−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	0.145626	−	0.989340i	$-0.453480\pi$
$733$	29.1108	−	16.8071i	1.07523	−	0.620786i	0.929606	+	0.368554i	$0.120147\pi$
$734$	−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	0.960588	+	0.277978i	$0.0896642\pi$
$739$	4.15936	+	23.5889i	0.153005	+	0.867732i	−0.807583	+	0.589754i	$0.799225\pi$
$740$	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	0.556829	−	0.830627i	$-0.312018\pi$
$743$	37.1845	−	6.55664i	1.36417	−	0.240540i	0.807339	+	0.590087i	$0.200907\pi$
$744$	−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	0.435252	−	0.900309i	$-0.356659\pi$
$751$	14.6978	+	2.59162i	0.536331	+	0.0945696i	0.101079	+	0.994878i	$0.467771\pi$
$752$	−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	0.790206	−	0.612841i	$-0.209973\pi$
$757$	1.36076	+	1.62169i	0.0494576	+	0.0589413i	−0.740749	+	0.671782i	$0.765529\pi$
$758$	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	$0.207103\pi$
$761$			33.4174i			1.21138i	−0.795701	+	0.605690i	$0.792897\pi$
$762$	−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	−0.896206	−	0.443639i	$-0.853687\pi$
$769$	2.70890	−	15.3629i	0.0976855	−	0.554002i	0.993891	−	0.110363i	$-0.0352015\pi$
$770$	−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	−0.914262	−	0.405124i	$-0.867228\pi$
$773$	−9.91263	+	11.8134i	−0.356533	+	0.424899i	0.557729	+	0.830023i	$0.311673\pi$
$774$	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	0.999289	−	0.0376985i	$-0.0120026\pi$
$787$	13.1009	+	22.6914i	0.466997	+	0.808862i	−0.532292	+	0.846561i	$0.678669\pi$
$788$	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	$0.165304\pi$
$797$			28.0217i			0.992578i	−0.868157	+	0.496289i	$0.834696\pi$
$798$	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	−0.585011	+	0.811025i	$0.698910\pi$
$809$	−44.9366	+	25.9441i	−1.57989	+	0.912147i	−0.994874	+	0.101122i	$0.967757\pi$
$810$	−1.52360	−	20.0669i	−0.0535339	−	0.705077i
$811$	−14.4295	+	17.1965i	−0.506690	+	0.603849i	−0.957380	−	0.288831i	$-0.906733\pi$
$811$	−14.4295	+	17.1965i	−0.506690	+	0.603849i	0.450690	+	0.892680i	$0.351178\pi$
$812$	−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	−0.999418	−	0.0341151i	$-0.989139\pi$
$821$	−7.32798	−	20.1335i	−0.255748	−	0.702662i	0.743670	−	0.668547i	$-0.233084\pi$
$822$	5.50579	−	11.4051i	0.192037	−	0.397799i
$823$	−6.19125	+	7.37844i	−0.215813	+	0.257196i	−0.863080	−	0.505067i	$-0.831468\pi$
$823$	−6.19125	+	7.37844i	−0.215813	+	0.257196i	0.647267	+	0.762264i	$0.275912\pi$
$824$	−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	0.492538	−	0.870291i	$-0.336069\pi$
$827$	18.9143	+	3.33510i	0.657715	+	0.115973i	0.165177	+	0.986264i	$0.447180\pi$
$828$	7.31909	+	21.9224i	0.254356	+	0.761856i
$829$	5.11519	+	2.95325i	0.177658	+	0.102571i	0.586192	−	0.810172i	$-0.300627\pi$
$829$	5.11519	+	2.95325i	0.177658	+	0.102571i	−0.408534	+	0.912743i	$0.633960\pi$
$830$	−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	−0.866385	−	0.499376i	$-0.833563\pi$
$839$	−15.2081	+	12.7611i	−0.525042	+	0.440563i	0.341343	+	0.939939i	$0.389118\pi$
$840$	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	−0.329030	−	0.944320i	$-0.606722\pi$
$853$	−9.20696	+	1.62344i	−0.315240	+	0.0555854i	0.0137894	+	0.999905i	$0.495611\pi$
$854$	−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	−0.555713	−	0.831374i	$-0.687555\pi$
$857$	−23.2313	+	4.09630i	−0.793565	+	0.139927i	−0.237852	+	0.971301i	$0.576443\pi$
$858$	−20.0509	+	13.6425i	−0.684526	+	0.465747i
$859$	2.12716	−	0.774223i	0.0725778	−	0.0264161i	−0.305476	−	0.952200i	$-0.598816\pi$
$859$	2.12716	−	0.774223i	0.0725778	−	0.0264161i	0.378054	+	0.925784i	$0.376593\pi$
$860$	−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	−0.551564	−	0.834133i	$-0.685969\pi$
$863$	−3.08356	+	1.78029i	−0.104966	+	0.0606019i	0.446598	+	0.894735i	$0.352635\pi$
$864$	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	−0.686925	−	0.726729i	$-0.741040\pi$
$877$	−2.68068	+	2.24935i	−0.0905200	+	0.0759553i	0.596405	+	0.802684i	$0.296595\pi$
$878$	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	0.995689	+	0.0927579i	$0.0295683\pi$
$881$	46.7149	+	26.9708i	1.57386	+	0.908671i	0.578175	+	0.815913i	$0.303765\pi$
$882$	−13.7008	+	4.57422i	−0.461331	+	0.154022i
$883$	−51.1621	−	9.02126i	−1.72174	−	0.303589i	−0.776538	−	0.630071i	$-0.783026\pi$
$883$	−51.1621	−	9.02126i	−1.72174	−	0.303589i	−0.945204	+	0.326481i	$0.894137\pi$
$884$	−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	−0.997338	−	0.0729185i	$-0.976769\pi$
$887$	−22.4066	+	26.7032i	−0.752341	+	0.896605i	0.244997	+	0.969524i	$0.421213\pi$
$888$	−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	0.447555	−	0.894256i	$-0.352295\pi$
$907$	6.49266	+	2.36314i	0.215585	+	0.0784666i	−0.231970	+	0.972723i	$0.574517\pi$
$908$	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	−0.824287	−	0.566173i	$-0.808424\pi$
$919$	2.36992	−	4.10482i	0.0781764	−	0.135406i	0.902463	+	0.430767i	$0.141757\pi$
$920$	−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	−0.791582	−	0.611062i	$-0.790742\pi$
$929$	−40.4290	+	7.12872i	−1.32643	+	0.233886i	−0.534849	+	0.844948i	$0.679631\pi$
$930$	−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	−0.276354	−	0.961056i	$-0.589126\pi$
$937$	21.9810	−	26.1960i	0.718089	−	0.855785i	0.994444	+	0.105270i	$0.0335708\pi$
$938$	−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	−0.556369	−	0.830936i	$-0.687806\pi$
$941$	7.68867	−	43.6046i	0.250644	−	1.42147i	0.807012	−	0.590535i	$-0.201083\pi$
$942$	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	−0.383948	−	0.923355i	$-0.625436\pi$
$947$	14.1159	−	11.8447i	0.458706	−	0.384900i	0.842655	+	0.538454i	$0.180991\pi$
$948$	−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	0.781535	−	0.623862i	$-0.214437\pi$
$953$	0.970531	+	1.15663i	0.0314386	+	0.0374671i	−0.750096	+	0.661329i	$0.769993\pi$
$954$	−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	−0.370541	−	0.928816i	$-0.620828\pi$
$967$	−12.4716	+	2.19909i	−0.401061	+	0.0707179i	−0.0305203	+	0.999534i	$0.509716\pi$
$968$			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	0.968705	+	0.248216i	$0.0798441\pi$
$971$	4.46581	+	25.3269i	0.143315	+	0.812778i	−0.825390	+	0.564563i	$0.809045\pi$
$972$	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	−0.799296	−	0.600938i	$-0.794794\pi$
$977$	−21.2084	+	12.2447i	−0.678516	+	0.391741i	0.120780	+	0.992679i	$0.461461\pi$
$978$	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	−0.259776	−	0.965669i	$-0.583649\pi$
$983$	17.5558	−	48.2342i	0.559944	−	1.53843i	0.819720	−	0.572764i	$-0.194129\pi$
$984$	−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	0.911660	−	0.410944i	$-0.134801\pi$
$991$	10.9756	+	13.0802i	0.348651	+	0.415506i	−0.563009	+	0.826451i	$0.690356\pi$
$992$	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	0.168955	−	0.985624i	$-0.445961\pi$
$997$	−0.296241	−	0.0522353i	−0.00938205	−	0.00165431i	−0.178337	+	0.983969i	$0.557072\pi$
$998$	−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.29.24	yes	240
3.2	odd	2	inner	570.2.bf.a.29.6	✓	240
5.4	even	2	inner	570.2.bf.a.29.17	yes	240
15.14	odd	2	inner	570.2.bf.a.29.35	yes	240
19.2	odd	18	inner	570.2.bf.a.59.35	yes	240
57.2	even	18	inner	570.2.bf.a.59.17	yes	240
95.59	odd	18	inner	570.2.bf.a.59.6	yes	240
285.59	even	18	inner	570.2.bf.a.59.24	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.6	✓	240	3.2	odd	2	inner
570.2.bf.a.29.17	yes	240	5.4	even	2	inner
570.2.bf.a.29.24	yes	240	1.1	even	1	trivial
570.2.bf.a.29.35	yes	240	15.14	odd	2	inner
570.2.bf.a.59.6	yes	240	95.59	odd	18	inner
570.2.bf.a.59.17	yes	240	57.2	even	18	inner
570.2.bf.a.59.24	yes	240	285.59	even	18	inner
570.2.bf.a.59.35	yes	240	19.2	odd	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.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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