LMFDB - Embedded newform 882.2.bk.a.131.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(5,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("882.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bk (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			131.40
Character	$\chi$	$=$	882.131
Dual form			882.2.bk.a.101.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(-0.552148 - 1.64169i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.0566430 - 0.755848i) q^{5} +(0.591888 - 1.62778i) q^{6} +(-0.221618 + 2.63645i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-2.39026 + 1.81291i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(-0.552148 - 1.64169i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.0566430 - 0.755848i) q^{5} +(0.591888 - 1.62778i) q^{6} +(-0.221618 + 2.63645i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-2.39026 + 1.81291i) q^{9} +(0.426978 - 0.626262i) q^{10} +(-2.16683 + 0.850419i) q^{11} +(1.47766 - 0.903614i) q^{12} +(-2.81526 + 1.10491i) q^{13} +(-1.81707 + 1.92309i) q^{14} +(-1.20959 + 0.510330i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-5.74022 + 1.77062i) q^{17} +(-2.99911 - 0.0729175i) q^{18} +(-7.05190 - 4.07141i) q^{19} +(0.724293 - 0.223415i) q^{20} +(4.45059 - 1.09189i) q^{21} +(-2.22432 - 0.686113i) q^{22} +(5.61479 + 6.05131i) q^{23} +(1.71868 + 0.214833i) q^{24} +(4.37606 - 0.659584i) q^{25} +(-2.88995 - 0.891433i) q^{26} +(4.29601 + 2.92307i) q^{27} +(-2.61967 + 0.370604i) q^{28} +(0.808321 + 2.62051i) q^{29} +(-1.26388 - 0.355175i) q^{30} -3.31724i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.59253 + 3.08770i) q^{33} +(-5.59185 - 2.19464i) q^{34} +(2.00531 + 0.0181731i) q^{35} +(-2.29934 - 1.92693i) q^{36} +(-2.59367 - 2.40658i) q^{37} +(-2.97491 - 7.57994i) q^{38} +(3.36835 + 4.01169i) q^{39} +(0.705572 + 0.276917i) q^{40} +(-2.33954 + 1.59507i) q^{41} +(4.16039 + 1.92123i) q^{42} +(5.50666 + 3.75437i) q^{43} +(-1.31126 - 1.92327i) q^{44} +(1.50567 + 1.70399i) q^{45} +(0.616893 + 8.23187i) q^{46} +(-5.03860 + 6.31820i) q^{47} +(1.20977 + 1.23954i) q^{48} +(-6.90177 - 1.16857i) q^{49} +(3.83258 + 2.21274i) q^{50} +(6.07626 + 8.44599i) q^{51} +(-1.70366 - 2.49881i) q^{52} +(-5.47511 - 5.90077i) q^{53} +(1.53625 + 4.96386i) q^{54} +(0.765523 + 1.58963i) q^{55} +(-2.27921 - 1.34359i) q^{56} +(-2.79029 + 13.8250i) q^{57} +(-1.00189 + 2.55278i) q^{58} +(-8.16951 + 3.93423i) q^{59} +(-0.766694 - 1.06570i) q^{60} +(0.141574 + 0.0323133i) q^{61} +(2.06826 - 2.59352i) q^{62} +(-4.24992 - 6.70359i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(0.994606 + 2.06532i) q^{65} +(0.101774 + 4.03048i) q^{66} -6.79534 q^{67} +(-3.00355 - 5.20230i) q^{68} +(6.83415 - 12.5589i) q^{69} +(1.55649 + 1.26450i) q^{70} +(4.55532 - 1.03972i) q^{71} +(-0.596276 - 2.94015i) q^{72} +(15.5077 + 6.08632i) q^{73} +(-0.527339 - 3.49867i) q^{74} +(-3.49906 - 6.81992i) q^{75} +(2.40014 - 7.78106i) q^{76} +(-1.76188 - 5.90122i) q^{77} +(0.132230 + 5.23660i) q^{78} +6.80768 q^{79} +(0.378984 + 0.656419i) q^{80} +(2.42673 - 8.66666i) q^{81} +(-2.82364 - 0.211603i) q^{82} +(0.0599028 - 0.152630i) q^{83} +(2.05486 + 4.09604i) q^{84} +(1.66347 + 4.23844i) q^{85} +(1.96446 + 6.36863i) q^{86} +(3.85574 - 2.77392i) q^{87} +(0.173952 - 2.32123i) q^{88} +(-7.92304 + 1.19421i) q^{89} +(0.114764 + 2.27101i) q^{90} +(-2.28912 - 7.66716i) q^{91} +(-4.65018 + 6.82056i) q^{92} +(-5.44586 + 1.83161i) q^{93} +(-7.87867 + 1.79826i) q^{94} +(-2.67793 + 5.56078i) q^{95} +(0.172995 + 1.72339i) q^{96} +(7.07221 - 4.08315i) q^{97} +(-4.66743 - 5.21681i) q^{98} +(3.63757 - 5.96099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9	$ 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) $ 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^15 - 112 * q^16 + 18 * q^17 + 8 * q^18 + 12 * q^21 + 18 * q^23 + 56 * q^25 - 12 * q^26 + 48 * q^27 + 2 * q^28 - 6 * q^29 + 4 * q^30 - 30 * q^35 - 10 * q^36 - 26 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^42 + 2 * q^43 + 58 * q^45 + 78 * q^46 - 90 * q^47 + 8 * q^49 + 24 * q^50 + 6 * q^51 - 22 * q^52 + 12 * q^53 - 18 * q^54 - 42 * q^55 - 6 * q^56 - 28 * q^57 + 78 * q^58 - 60 * q^59 - 6 * q^60 + 98 * q^61 - 36 * q^62 - 36 * q^63 + 112 * q^64 - 24 * q^66 + 28 * q^67 - 18 * q^68 + 14 * q^69 + 18 * q^70 + 126 * q^71 - 8 * q^72 - 18 * q^74 - 102 * q^75 + 42 * q^77 - 8 * q^78 - 8 * q^79 + 26 * q^81 + 30 * q^84 + 80 * q^87 - 186 * q^89 - 102 * q^90 + 12 * q^91 - 18 * q^92 - 224 * q^93 - 6 * q^97 + 24 * q^98 + 194 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−0.552148	−	1.64169i	−0.318783	−	0.947828i
$3$	−0.552148	−	1.64169i	−0.318783	−	0.947828i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−0.0566430	−	0.755848i	−0.0253315	−	0.338026i	−0.995442	−	0.0953639i	$-0.969599\pi$
$5$	−0.0566430	−	0.755848i	−0.0253315	−	0.338026i	0.970111	−	0.242662i	$-0.0780205\pi$
$6$	0.591888	−	1.62778i	0.241637	−	0.664539i
$7$	−0.221618	+	2.63645i	−0.0837638	+	0.996486i
$7$	−0.221618	+	2.63645i	−0.0837638	+	0.996486i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	−2.39026	+	1.81291i	−0.796755	+	0.604303i
$10$	0.426978	−	0.626262i	0.135022	−	0.198042i
$11$	−2.16683	+	0.850419i	−0.653324	+	0.256411i	−0.668769	−	0.743470i	$-0.733179\pi$
$11$	−2.16683	+	0.850419i	−0.653324	+	0.256411i	0.0154453	+	0.999881i	$0.495083\pi$
$12$	1.47766	−	0.903614i	0.426564	−	0.260851i
$13$	−2.81526	+	1.10491i	−0.780812	+	0.306446i	−0.722063	−	0.691827i	$-0.756806\pi$
$13$	−2.81526	+	1.10491i	−0.780812	+	0.306446i	−0.0587481	+	0.998273i	$0.518711\pi$
$14$	−1.81707	+	1.92309i	−0.485632	+	0.513966i
$15$	−1.20959	+	0.510330i	−0.312315	+	0.131767i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−5.74022	+	1.77062i	−1.39221	+	0.429439i	−0.898035	−	0.439925i	$-0.855005\pi$
$17$	−5.74022	+	1.77062i	−1.39221	+	0.429439i	−0.494173	+	0.869364i	$0.664529\pi$
$18$	−2.99911	−	0.0729175i	−0.706898	−	0.0171868i
$19$	−7.05190	−	4.07141i	−1.61782	−	0.934046i	−0.987484	−	0.157721i	$-0.949585\pi$
$19$	−7.05190	−	4.07141i	−1.61782	−	0.934046i	−0.630332	−	0.776326i	$-0.717081\pi$
$20$	0.724293	−	0.223415i	0.161957	−	0.0499571i
$21$	4.45059	−	1.09189i	0.971199	−	0.238269i
$22$	−2.22432	−	0.686113i	−0.474227	−	0.146280i
$23$	5.61479	+	6.05131i	1.17076	+	1.26178i	0.958665	+	0.284536i	$0.0918396\pi$
$23$	5.61479	+	6.05131i	1.17076	+	1.26178i	0.212100	+	0.977248i	$0.431970\pi$
$24$	1.71868	+	0.214833i	0.350823	+	0.0438525i
$25$	4.37606	−	0.659584i	0.875211	−	0.131917i
$26$	−2.88995	−	0.891433i	−0.566767	−	0.174824i
$27$	4.29601	+	2.92307i	0.826767	+	0.562545i
$28$	−2.61967	+	0.370604i	−0.495070	+	0.0700376i
$29$	0.808321	+	2.62051i	0.150101	+	0.486617i	0.999129	−	0.0417320i	$-0.0132876\pi$
$29$	0.808321	+	2.62051i	0.150101	+	0.486617i	−0.849027	+	0.528349i	$0.822811\pi$
$30$	−1.26388	−	0.355175i	−0.230752	−	0.0648458i
$31$		−	3.31724i		−	0.595793i	−0.954598	−	0.297897i	$-0.903715\pi$
$31$		−	3.31724i		−	0.595793i	0.954598	−	0.297897i	$-0.0962851\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	2.59253	+	3.08770i	0.451302	+	0.537499i
$34$	−5.59185	−	2.19464i	−0.958994	−	0.376378i
$35$	2.00531	+	0.0181731i	0.338960	+	0.00307182i
$36$	−2.29934	−	1.92693i	−0.383223	−	0.321154i
$37$	−2.59367	−	2.40658i	−0.426397	−	0.395639i	0.437572	−	0.899183i	$-0.355838\pi$
$37$	−2.59367	−	2.40658i	−0.426397	−	0.395639i	−0.863969	+	0.503545i	$0.832029\pi$
$38$	−2.97491	−	7.57994i	−0.482594	−	1.22963i
$39$	3.36835	+	4.01169i	0.539367	+	0.642385i
$40$	0.705572	+	0.276917i	0.111561	+	0.0437844i
$41$	−2.33954	+	1.59507i	−0.365375	+	0.249109i	−0.732065	−	0.681235i	$-0.761443\pi$
$41$	−2.33954	+	1.59507i	−0.365375	+	0.249109i	0.366690	+	0.930343i	$0.380491\pi$
$42$	4.16039	+	1.92123i	0.641963	+	0.296452i
$43$	5.50666	+	3.75437i	0.839757	+	0.572537i	0.905038	−	0.425330i	$-0.139842\pi$
$43$	5.50666	+	3.75437i	0.839757	+	0.572537i	−0.0652811	+	0.997867i	$0.520794\pi$
$44$	−1.31126	−	1.92327i	−0.197680	−	0.289944i
$45$	1.50567	+	1.70399i	0.224453	+	0.254016i
$46$	0.616893	+	8.23187i	0.0909559	+	1.21372i
$47$	−5.03860	+	6.31820i	−0.734955	+	0.921605i	−0.999080	−	0.0428838i	$-0.986345\pi$
$47$	−5.03860	+	6.31820i	−0.734955	+	0.921605i	0.264125	+	0.964489i	$0.414917\pi$
$48$	1.20977	+	1.23954i	0.174615	+	0.178912i
$49$	−6.90177	−	1.16857i	−0.985967	−	0.166939i
$50$	3.83258	+	2.21274i	0.542009	+	0.312929i
$51$	6.07626	+	8.44599i	0.850846	+	1.18268i
$52$	−1.70366	−	2.49881i	−0.236255	−	0.346522i
$53$	−5.47511	−	5.90077i	−0.752064	−	0.810533i	0.234807	−	0.972042i	$-0.424554\pi$
$53$	−5.47511	−	5.90077i	−0.752064	−	0.810533i	−0.986871	+	0.161509i	$0.948364\pi$
$54$	1.53625	+	4.96386i	0.209057	+	0.675496i
$55$	0.765523	+	1.58963i	0.103223	+	0.214345i
$56$	−2.27921	−	1.34359i	−0.304572	−	0.179544i
$57$	−2.79029	+	13.8250i	−0.369583	+	1.83117i
$58$	−1.00189	+	2.55278i	−0.131555	+	0.335196i
$59$	−8.16951	+	3.93423i	−1.06358	+	0.512193i	−0.882032	−	0.471189i	$-0.843825\pi$
$59$	−8.16951	+	3.93423i	−1.06358	+	0.512193i	−0.181547	+	0.983382i	$0.558111\pi$
$60$	−0.766694	−	1.06570i	−0.0989798	−	0.137582i
$61$	0.141574	+	0.0323133i	0.0181266	+	0.00413729i	0.231575	−	0.972817i	$-0.425612\pi$
$61$	0.141574	+	0.0323133i	0.0181266	+	0.00413729i	−0.213448	+	0.976954i	$0.568469\pi$
$62$	2.06826	−	2.59352i	0.262670	−	0.329377i
$63$	−4.24992	−	6.70359i	−0.535440	−	0.844574i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	0.994606	+	2.06532i	0.123366	+	0.256172i
$66$	0.101774	+	4.03048i	0.0125275	+	0.496117i
$67$	−6.79534			−0.830183			−0.415091	−	0.909780i	$-0.636250\pi$
$67$	−6.79534			−0.830183			−0.415091	+	0.909780i	$0.636250\pi$
$68$	−3.00355	−	5.20230i	−0.364234	−	0.630871i
$69$	6.83415	−	12.5589i	0.822734	−	1.51192i
$70$	1.55649	+	1.26450i	0.186036	+	0.151137i
$71$	4.55532	−	1.03972i	0.540617	−	0.123392i	0.0565116	−	0.998402i	$-0.482002\pi$
$71$	4.55532	−	1.03972i	0.540617	−	0.123392i	0.484106	+	0.875010i	$0.339145\pi$
$72$	−0.596276	−	2.94015i	−0.0702718	−	0.346499i
$73$	15.5077	+	6.08632i	1.81504	+	0.712350i	0.988842	+	0.148969i	$0.0475954\pi$
$73$	15.5077	+	6.08632i	1.81504	+	0.712350i	0.826197	+	0.563381i	$0.190500\pi$
$74$	−0.527339	−	3.49867i	−0.0613019	−	0.406712i
$75$	−3.49906	−	6.81992i	−0.404037	−	0.787497i
$76$	2.40014	−	7.78106i	0.275315	−	0.892549i
$77$	−1.76188	−	5.90122i	−0.200785	−	0.672506i
$78$	0.132230	+	5.23660i	0.0149721	+	0.592928i
$79$	6.80768			0.765924			0.382962	−	0.923764i	$-0.374904\pi$
$79$	6.80768			0.765924			0.382962	+	0.923764i	$0.374904\pi$
$80$	0.378984	+	0.656419i	0.0423717	+	0.0733899i
$81$	2.42673	−	8.66666i	0.269637	−	0.962962i
$82$	−2.82364	−	0.211603i	−0.311819	−	0.0233676i
$83$	0.0599028	−	0.152630i	0.00657518	−	0.0167533i	−0.927548	−	0.373703i	$-0.878088\pi$
$83$	0.0599028	−	0.152630i	0.00657518	−	0.0167533i	0.934124	+	0.356950i	$0.116183\pi$
$84$	2.05486	+	4.09604i	0.224204	+	0.446915i
$85$	1.66347	+	4.23844i	0.180428	+	0.459724i
$86$	1.96446	+	6.36863i	0.211833	+	0.686747i
$87$	3.85574	−	2.77392i	0.413379	−	0.297395i
$88$	0.173952	−	2.32123i	0.0185434	−	0.247444i
$89$	−7.92304	+	1.19421i	−0.839840	+	0.126586i	−0.554856	−	0.831947i	$-0.687227\pi$
$89$	−7.92304	+	1.19421i	−0.839840	+	0.126586i	−0.284985	+	0.958532i	$0.591988\pi$
$90$	0.114764	+	2.27101i	0.0120972	+	0.239385i
$91$	−2.28912	−	7.66716i	−0.239965	−	0.803737i
$92$	−4.65018	+	6.82056i	−0.484815	+	0.711092i
$93$	−5.44586	+	1.83161i	−0.564710	+	0.189929i
$94$	−7.87867	+	1.79826i	−0.812623	+	0.185476i
$95$	−2.67793	+	5.56078i	−0.274750	+	0.570524i
$96$	0.172995	+	1.72339i	0.0176562	+	0.175893i
$97$	7.07221	−	4.08315i	0.718075	−	0.414581i	−0.0959690	−	0.995384i	$-0.530595\pi$
$97$	7.07221	−	4.08315i	0.718075	−	0.414581i	0.814044	+	0.580804i	$0.197262\pi$
$98$	−4.66743	−	5.21681i	−0.471482	−	0.526977i
$99$	3.63757	−	5.96099i	0.365590	−	0.599102i
$100$	1.61681	+	4.11957i	0.161681	+	0.411957i
$101$	3.34087	−	2.27777i	0.332429	−	0.226646i	−0.385589	−	0.922671i	$-0.626002\pi$
$101$	3.34087	−	2.27777i	0.332429	−	0.226646i	0.718018	+	0.696024i	$0.245049\pi$
$102$	−0.515379	+	10.3918i	−0.0510301	+	1.02894i
$103$	11.6088	−	0.869957i	1.14385	−	0.0857194i	0.510705	−	0.859756i	$-0.329384\pi$
$103$	11.6088	−	0.869957i	1.14385	−	0.0857194i	0.633141	+	0.774037i	$0.281765\pi$
$104$	0.226007	−	3.01586i	0.0221618	−	0.295729i
$105$	−1.07739	−	3.30213i	−0.105143	−	0.322255i
$106$	−0.601547	−	8.02708i	−0.0584274	−	0.779659i
$107$	1.00147	+	6.64429i	0.0968154	+	0.642328i	0.983630	+	0.180202i	$0.0576751\pi$
$107$	1.00147	+	6.64429i	0.0968154	+	0.642328i	−0.886814	+	0.462126i	$0.847087\pi$
$108$	−1.89383	+	4.83874i	−0.182234	+	0.465608i
$109$	−10.1249	−	1.52608i	−0.969786	−	0.146172i	−0.355000	−	0.934866i	$-0.615519\pi$
$109$	−10.1249	−	1.52608i	−0.969786	−	0.146172i	−0.614785	+	0.788694i	$0.710757\pi$
$110$	−0.392605	+	1.72012i	−0.0374334	+	0.164007i
$111$	−2.51875	+	5.58678i	−0.239069	+	0.530274i
$112$	−0.944243	−	2.47152i	−0.0892226	−	0.233537i
$113$	0.530080	+	3.51685i	0.0498657	+	0.330837i	0.999829	+	0.0184766i	$0.00588163\pi$
$113$	0.530080	+	3.51685i	0.0498657	+	0.330837i	−0.949964	+	0.312361i	$0.898880\pi$
$114$	−10.8013	+	9.06912i	−1.01163	+	0.849401i
$115$	4.25583	−	4.58669i	0.396858	−	0.427711i
$116$	−2.37494	+	1.37117i	−0.220508	+	0.127310i
$117$	4.72611	−	7.74482i	0.436929	−	0.716009i
$118$	−8.84013	−	2.01770i	−0.813800	−	0.185745i
$119$	−3.39603	−	15.5262i	−0.311313	−	1.42329i
$120$	0.0650298	−	1.31123i	0.00593638	−	0.119698i
$121$	−4.09163	+	3.79647i	−0.371966	+	0.345134i
$122$	0.0905397	+	0.113533i	0.00819708	+	0.0102788i
$123$	3.91039	+	2.96008i	0.352588	+	0.266901i
$124$	3.23407	−	0.738155i	0.290428	−	0.0662883i
$125$	−1.58974	−	6.96509i	−0.142190	−	0.622977i
$126$	0.856902	−	7.89086i	0.0763389	−	0.702974i
$127$	1.53286	−	6.71590i	0.136019	−	0.595940i	−0.860267	−	0.509843i	$-0.829703\pi$
$127$	1.53286	−	6.71590i	0.136019	−	0.595940i	0.996287	−	0.0860968i	$-0.0274394\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.12301	−	11.1132i	0.274966	−	0.978460i
$130$	−0.510092	+	2.23486i	−0.0447380	+	0.196010i
$131$	1.05196	+	0.717213i	0.0919100	+	0.0626632i	0.608403	−	0.793628i	$-0.291810\pi$
$131$	1.05196	+	0.717213i	0.0919100	+	0.0626632i	−0.516493	+	0.856291i	$0.672763\pi$
$132$	−2.43339	+	3.21461i	−0.211800	+	0.279796i
$133$	12.2969	−	17.6897i	1.06628	−	1.53389i
$134$	−5.31281	−	4.23682i	−0.458957	−	0.366006i
$135$	1.96606	−	3.41270i	0.169211	−	0.293718i
$136$	0.895311	−	5.94000i	0.0767723	−	0.509351i
$137$	−16.5165	−	1.23774i	−1.41110	−	0.105748i	−0.652741	−	0.757581i	$-0.726381\pi$
$137$	−16.5165	−	1.23774i	−1.41110	−	0.105748i	−0.758362	+	0.651833i	$0.774000\pi$
$138$	13.1735	−	5.55795i	1.12140	−	0.473124i
$139$	9.83226	+	14.4213i	0.833962	+	1.22320i	0.972515	+	0.232842i	$0.0748025\pi$
$139$	9.83226	+	14.4213i	0.833962	+	1.22320i	−0.138553	+	0.990355i	$0.544245\pi$
$140$	0.428506	+	1.95908i	0.0362154	+	0.165572i
$141$	13.1546	+	4.78321i	1.10781	+	0.402819i
$142$	4.20975	+	2.02731i	0.353274	+	0.170128i
$143$	5.16055	−	4.78829i	0.431547	−	0.400417i
$144$	1.36696	−	2.67047i	0.113914	−	0.222539i
$145$	1.93492	−	0.759401i	0.160687	−	0.0630649i
$146$	8.32965	+	14.4274i	0.689366	+	1.19402i
$147$	1.89237	+	11.9758i	0.156080	+	0.987744i
$148$	1.76909	−	3.06416i	0.145418	−	0.251872i
$149$	1.91158	−	12.6825i	0.156603	−	1.03899i	−0.763072	−	0.646313i	$-0.776310\pi$
$149$	1.91158	−	12.6825i	0.156603	−	1.03899i	0.919675	−	0.392680i	$-0.128452\pi$
$150$	1.51647	−	7.51366i	0.123820	−	0.613488i
$151$	5.85594	+	1.80632i	0.476550	+	0.146996i	0.523719	−	0.851891i	$-0.324544\pi$
$151$	5.85594	+	1.80632i	0.476550	+	0.146996i	−0.0471698	+	0.998887i	$0.515020\pi$
$152$	6.72792	−	4.58702i	0.545706	−	0.372056i
$153$	10.5107	−	14.6387i	0.849737	−	1.18347i
$154$	2.30186	−	5.71227i	0.185489	−	0.460308i
$155$	−2.50733	+	0.187898i	−0.201393	+	0.0150924i
$156$	−3.16158	+	4.17658i	−0.253129	+	0.334394i
$157$	−9.57425	−	19.8811i	−0.764108	−	1.58669i	−0.809080	−	0.587699i	$-0.800034\pi$
$157$	−9.57425	−	19.8811i	−0.764108	−	1.58669i	0.0449719	−	0.998988i	$-0.485680\pi$
$158$	5.32246	+	4.24452i	0.423432	+	0.337676i
$159$	−6.66413	+	12.2465i	−0.528500	+	0.971212i
$160$	−0.112969	+	0.749502i	−0.00893100	+	0.0592533i
$161$	−17.1983	+	13.4621i	−1.35542	+	1.06096i
$162$	7.30087	−	5.26282i	0.573610	−	0.413486i
$163$	0.0208690	−	0.278477i	0.00163459	−	0.0218120i	−0.996327	−	0.0856316i	$-0.972709\pi$
$163$	0.0208690	−	0.278477i	0.00163459	−	0.0218120i	0.997961	+	0.0638196i	$0.0203282\pi$
$164$	−2.07568	−	1.92595i	−0.162083	−	0.150391i
$165$	2.18698	−	2.13446i	0.170256	−	0.166167i
$166$	0.141997	−	0.0819820i	0.0110211	−	0.00636304i
$167$	14.7406	+	13.6773i	1.14066	+	1.05838i	0.997640	+	0.0686579i	$0.0218717\pi$
$167$	14.7406	+	13.6773i	1.14066	+	1.05838i	0.143020	+	0.989720i	$0.454319\pi$
$168$	−0.947286	+	4.48360i	−0.0730847	+	0.345917i
$169$	−2.82483	+	2.62106i	−0.217294	+	0.201620i
$170$	−1.34208	+	4.35090i	−0.102932	+	0.333699i
$171$	24.2370	−	3.05268i	1.85345	−	0.233444i
$172$	−2.43490	+	6.20402i	−0.185659	+	0.473052i
$173$	−4.40080	−	19.2811i	−0.334586	−	1.46592i	−0.810142	−	0.586233i	$-0.800610\pi$
$173$	−4.40080	−	19.2811i	−0.334586	−	1.46592i	0.475556	−	0.879685i	$-0.342247\pi$
$174$	4.74405	+	0.235280i	0.359646	+	0.0178365i
$175$	0.769149	+	11.6834i	0.0581422	+	0.883185i
$176$	1.58326	−	1.70635i	0.119343	−	0.128621i
$177$	10.9695	+	11.2395i	0.824522	+	0.844812i
$178$	−6.93906	−	4.00627i	−0.520104	−	0.300282i
$179$	−2.35962	−	7.64969i	−0.176366	−	0.571764i	−0.999989	−	0.00462721i	$-0.998527\pi$
$179$	−2.35962	−	7.64969i	−0.176366	−	0.571764i	0.823623	−	0.567137i	$-0.191949\pi$
$180$	−1.32622	+	1.84710i	−0.0988508	+	0.137675i
$181$	5.58898	−	4.45706i	0.415426	−	0.331291i	−0.393370	−	0.919380i	$-0.628691\pi$
$181$	5.58898	−	4.45706i	0.415426	−	0.331291i	0.808796	+	0.588089i	$0.200120\pi$
$182$	2.99069	−	7.42167i	0.221684	−	0.550131i
$183$	−0.0251214	−	0.250261i	−0.00185703	−	0.0184998i
$184$	−7.88820	+	2.43319i	−0.581526	+	0.179377i
$185$	−1.67209	+	2.09674i	−0.122935	+	0.154155i
$186$	−5.39973	−	1.96343i	−0.395928	−	0.143966i
$187$	10.9323	−	8.71823i	0.799450	−	0.637540i
$188$	−7.28099	−	3.50634i	−0.531021	−	0.255726i
$189$	−8.65861	+	10.6784i	−0.629821	+	0.776740i
$190$	−5.56078	+	2.67793i	−0.403421	+	0.194278i
$191$	−7.91920	+	16.4444i	−0.573013	+	1.18987i	0.390099	+	0.920773i	$0.372441\pi$
$191$	−7.91920	+	16.4444i	−0.573013	+	1.18987i	−0.963112	+	0.269101i	$0.913273\pi$
$192$	−0.939263	+	1.45526i	−0.0677855	+	0.105024i
$193$	−19.9355	−	9.60041i	−1.43499	−	0.691053i	−0.455068	−	0.890457i	$-0.650385\pi$
$193$	−19.9355	−	9.60041i	−1.43499	−	0.691053i	−0.979917	+	0.199404i	$0.936099\pi$
$194$	8.07508	+	1.21712i	0.579757	+	0.0873843i
$195$	2.84144	−	2.77319i	0.203480	−	0.198593i
$196$	−0.396515	−	6.98876i	−0.0283225	−	0.499197i
$197$			13.3108i			0.948357i	0.880429	+	0.474179i	$0.157255\pi$
$197$			13.3108i			0.948357i	−0.880429	+	0.474179i	$0.842745\pi$
$198$	6.56058	−	2.39250i	0.466240	−	0.170028i
$199$	9.73851	−	0.729800i	0.690345	−	0.0517342i	0.275062	−	0.961427i	$-0.411302\pi$
$199$	9.73851	−	0.729800i	0.690345	−	0.0517342i	0.415283	+	0.909692i	$0.363683\pi$
$200$	−1.30443	+	4.22887i	−0.0922375	+	0.299026i
$201$	3.75203	+	11.1558i	0.264648	+	0.786870i
$202$	4.03216	+	0.302169i	0.283702	+	0.0212605i
$203$	−7.08799	+	1.55035i	−0.497480	+	0.108813i
$204$	−6.88214	+	7.80332i	−0.481846	+	0.546342i
$205$	1.33815	+	1.67799i	0.0934607	+	0.117196i
$206$	9.61851	+	6.55779i	0.670153	+	0.456903i
$207$	−24.3913	−	4.28513i	−1.69531	−	0.297837i
$208$	2.05706	−	2.21698i	0.142631	−	0.153720i
$209$	18.7427	+	2.82500i	1.29646	+	0.195410i
$210$	1.21650	−	3.25345i	0.0839465	−	0.224509i
$211$	5.66101	−	0.853259i	0.389720	−	0.0587408i	0.0487401	−	0.998811i	$-0.484479\pi$
$211$	5.66101	−	0.853259i	0.389720	−	0.0587408i	0.340980	+	0.940071i	$0.389241\pi$
$212$	4.53450	−	6.65088i	0.311430	−	0.456785i
$213$	−4.22211	−	6.90432i	−0.289294	−	0.473077i
$214$	−3.35967	+	5.81912i	−0.229662	+	0.397787i
$215$	2.52582	−	4.37486i	0.172260	−	0.298363i
$216$	−4.49756	+	2.60229i	−0.306020	+	0.177064i
$217$	8.74574	+	0.735160i	0.593700	+	0.0499059i
$218$	−6.96444	−	7.50588i	−0.471692	−	0.508363i
$219$	1.42928	−	28.8193i	0.0965820	−	1.94743i
$220$	−1.37943	+	1.10005i	−0.0930008	+	0.0741657i
$221$	14.2038	−	11.3272i	0.955452	−	0.761947i
$222$	−5.45254	+	2.79751i	−0.365951	+	0.187756i
$223$	−4.98775	−	5.37552i	−0.334004	−	0.359971i	0.543610	−	0.839338i	$-0.317057\pi$
$223$	−4.98775	−	5.37552i	−0.334004	−	0.359971i	−0.877615	+	0.479367i	$0.840866\pi$
$224$	0.802728	−	2.52104i	0.0536345	−	0.168444i
$225$	−9.26417	+	9.50997i	−0.617611	+	0.633998i
$226$	−1.77829	+	3.08008i	−0.118290	+	0.204884i
$227$	−9.70406	+	16.8079i	−0.644081	+	1.11558i	0.340432	+	0.940269i	$0.389427\pi$
$227$	−9.70406	+	16.8079i	−0.644081	+	1.11558i	−0.984513	+	0.175312i	$0.943907\pi$
$228$	−14.0993	+	0.356024i	−0.933749	+	0.0235782i
$229$	−11.7804	+	17.2786i	−0.778469	+	1.14180i	0.208044	+	0.978119i	$0.433290\pi$
$229$	−11.7804	+	17.2786i	−0.778469	+	1.14180i	−0.986513	+	0.163685i	$0.947662\pi$
$230$	6.18710	−	0.932555i	0.407965	−	0.0614909i
$231$	−8.71513	+	6.15080i	−0.573413	+	0.404693i
$232$	−2.71172	−	0.408725i	−0.178033	−	0.0268341i
$233$	10.5047	−	11.3213i	0.688184	−	0.741686i	−0.288237	−	0.957559i	$-0.593069\pi$
$233$	10.5047	−	11.3213i	0.688184	−	0.741686i	0.976422	+	0.215873i	$0.0692596\pi$
$234$	8.52384	−	3.10846i	0.557221	−	0.203206i
$235$	5.06101	+	3.45053i	0.330144	+	0.225088i
$236$	−5.65348	−	7.08924i	−0.368010	−	0.461470i
$237$	−3.75885	−	11.1761i	−0.244164	−	0.725964i
$238$	7.02532	−	14.2563i	0.455384	−	0.924097i
$239$	−2.96320	−	0.222061i	−0.191674	−	0.0143639i	−0.0214526	−	0.999770i	$-0.506829\pi$
$239$	−2.96320	−	0.222061i	−0.191674	−	0.0143639i	−0.170221	+	0.985406i	$0.554448\pi$
$240$	0.868379	−	0.984613i	0.0560536	−	0.0635565i
$241$	5.97489	−	19.3701i	0.384876	−	1.24774i	−0.531376	−	0.847136i	$-0.678325\pi$
$241$	5.97489	−	19.3701i	0.384876	−	1.24774i	0.916252	−	0.400602i	$-0.131199\pi$
$242$	−5.56602	+	0.417116i	−0.357798	+	0.0268132i
$243$	−15.5678	+	0.801348i	−0.998678	+	0.0514065i
$244$			0.145214i			0.00929640i
$245$	−0.492326	+	5.28288i	−0.0314536	+	0.337511i
$246$	1.21168	+	4.75237i	0.0772541	+	0.303000i
$247$	24.3514	+	3.67039i	1.54944	+	0.233541i
$248$	2.98873	+	1.43930i	0.189784	+	0.0913954i
$249$	−0.283645	−	0.0140673i	−0.0179753	−	0.000891478i
$250$	3.09976	−	6.43671i	0.196046	−	0.407094i
$251$	3.62109	−	1.74383i	0.228561	−	0.110069i	−0.316099	−	0.948726i	$-0.602373\pi$
$251$	3.62109	−	1.74383i	0.228561	−	0.110069i	0.544660	+	0.838657i	$0.316659\pi$
$252$	5.58983	−	5.63506i	0.352126	−	0.354975i
$253$	−17.3124	−	8.33723i	−1.08842	−	0.524157i
$254$	5.38573	−	4.29498i	0.337931	−	0.269491i
$255$	6.03971	−	5.07114i	0.378221	−	0.317567i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−7.12885	+	2.19896i	−0.444686	+	0.137167i	−0.509008	−	0.860762i	$-0.669988\pi$
$257$	−7.12885	+	2.19896i	−0.444686	+	0.137167i	0.0643222	+	0.997929i	$0.479511\pi$
$258$	9.37062	−	6.74146i	0.583389	−	0.419705i
$259$	6.91963	−	6.30476i	0.429965	−	0.391758i
$260$	−1.79222	+	1.42925i	−0.111149	+	0.0886381i
$261$	−6.68285	−	4.79831i	−0.413658	−	0.297008i
$262$	0.375279	+	1.21663i	0.0231848	+	0.0751634i
$263$	20.5368	+	11.8569i	1.26635	+	0.731128i	0.974296	−	0.225273i	$-0.0723274\pi$
$263$	20.5368	+	11.8569i	1.26635	+	0.731128i	0.292056	+	0.956401i	$0.405661\pi$
$264$	−3.90678	+	0.996088i	−0.240446	+	0.0613050i
$265$	−4.14996	+	4.47259i	−0.254930	+	0.274749i
$266$	20.6435	−	6.16335i	1.26573	−	0.377899i
$267$	6.33520	+	12.3478i	0.387708	+	0.755671i
$268$	−1.51211	−	6.62497i	−0.0923665	−	0.404684i
$269$	−8.81325	+	22.4558i	−0.537353	+	1.36915i	0.362101	+	0.932139i	$0.382060\pi$
$269$	−8.81325	+	22.4558i	−0.537353	+	1.36915i	−0.899454	+	0.437015i	$0.856036\pi$
$270$	3.66491	−	1.44234i	0.223039	−	0.0877779i
$271$	−8.59910	+	27.8776i	−0.522358	+	1.69344i	0.181745	+	0.983346i	$0.441825\pi$
$271$	−8.59910	+	27.8776i	−0.522358	+	1.69344i	−0.704103	+	0.710097i	$0.748651\pi$
$272$	4.40351	−	4.08586i	0.267002	−	0.247742i
$273$	−11.3231	+	7.99143i	−0.685307	+	0.483663i
$274$	−12.1414	−	11.2656i	−0.733491	−	0.680580i
$275$	−8.92125	+	5.15069i	−0.537972	+	0.310598i
$276$	13.7648	+	3.86817i	0.828544	+	0.232837i
$277$	−3.43644	−	3.18855i	−0.206476	−	0.191581i	0.570156	−	0.821537i	$-0.306883\pi$
$277$	−3.43644	−	3.18855i	−0.206476	−	0.191581i	−0.776632	+	0.629955i	$0.783073\pi$
$278$	−1.30435	+	17.4053i	−0.0782297	+	1.04390i
$279$	6.01385	+	7.92908i	0.360040	+	0.474701i
$280$	−0.886446	+	1.79884i	−0.0529753	+	0.107501i
$281$	−3.96325	+	26.2944i	−0.236428	+	1.56859i	0.484003	+	0.875067i	$0.339183\pi$
$281$	−3.96325	+	26.2944i	−0.236428	+	1.56859i	−0.720430	+	0.693528i	$0.756056\pi$
$282$	7.30236	+	11.9414i	0.434849	+	0.711100i
$283$	−11.7493	−	9.36973i	−0.698421	−	0.556972i	0.208629	−	0.977995i	$-0.433100\pi$
$283$	−11.7493	−	9.36973i	−0.698421	−	0.556972i	−0.907050	+	0.421023i	$0.861671\pi$
$284$	2.02731	+	4.20975i	0.120299	+	0.249803i
$285$	10.6077	+	1.32595i	0.628344	+	0.0785423i
$286$	7.02013	−	0.526086i	0.415109	−	0.0311081i
$287$	−3.68685	−	6.52160i	−0.217628	−	0.384958i
$288$	2.73375	−	1.23557i	0.161088	−	0.0728067i
$289$	15.7689	−	10.7511i	0.927585	−	0.632417i
$290$	1.98626	+	0.612681i	0.116637	+	0.0359779i
$291$	−10.6082	−	9.35585i	−0.621861	−	0.548450i
$292$	−2.48294	+	16.4732i	−0.145303	+	0.964022i
$293$	−12.0770	+	20.9179i	−0.705544	+	1.22204i	0.260950	+	0.965352i	$0.415964\pi$
$293$	−12.0770	+	20.9179i	−0.705544	+	1.22204i	−0.966495	+	0.256686i	$0.917369\pi$
$294$	−5.98725	+	10.5429i	−0.349184	+	0.614875i
$295$	3.43643	+	5.95206i	0.200076	+	0.346543i
$296$	3.29360	−	1.29264i	0.191437	−	0.0751334i
$297$	−11.7946	−	2.68040i	−0.684389	−	0.155532i
$298$	9.40196	−	8.72374i	0.544641	−	0.505353i
$299$	−22.4932	−	10.8322i	−1.30082	−	0.626440i
$300$	5.87032	−	4.92891i	0.338923	−	0.284571i
$301$	−11.1186	+	13.6860i	−0.640866	+	0.788848i
$302$	3.45214	+	5.06336i	0.198648	+	0.291363i
$303$	−5.58403	−	4.22699i	−0.320794	−	0.242834i
$304$	8.12006	+	0.608514i	0.465717	+	0.0349007i
$305$	0.0164048	−	0.108839i	0.000939334	−	0.00623208i
$306$	17.3447	−	4.89174i	0.991529	−	0.279642i
$307$	15.8131	+	12.6105i	0.902500	+	0.719720i	0.960407	−	0.278602i	$-0.0898711\pi$
$307$	15.8131	+	12.6105i	0.902500	+	0.719720i	−0.0579066	+	0.998322i	$0.518443\pi$
$308$	5.36121	−	3.03085i	0.305483	−	0.172699i
$309$	−7.83796	−	18.5776i	−0.445886	−	1.05684i
$310$	−2.07746	−	1.41639i	−0.117992	−	0.0804455i
$311$	−4.90222	+	21.4780i	−0.277979	+	1.21791i	0.622365	+	0.782727i	$0.286172\pi$
$311$	−4.90222	+	21.4780i	−0.277979	+	1.21791i	−0.900344	+	0.435179i	$0.856685\pi$
$312$	−5.07588	+	1.29417i	−0.287365	+	0.0732678i
$313$		−	6.56074i		−	0.370835i	−0.982660	−	0.185417i	$-0.940636\pi$
$313$		−	6.56074i		−	0.370835i	0.982660	−	0.185417i	$-0.0593637\pi$
$314$	4.91023	−	21.5131i	0.277100	−	1.21406i
$315$	−4.82617	+	3.59201i	−0.271924	+	0.202387i
$316$	1.51485	+	6.63700i	0.0852171	+	0.373360i
$317$	13.5600	−	3.09498i	0.761604	−	0.173831i	0.175958	−	0.984398i	$-0.443698\pi$
$317$	13.5600	−	3.09498i	0.761604	−	0.173831i	0.585647	+	0.810567i	$0.300841\pi$
$318$	−12.8458	+	5.41969i	−0.720357	+	0.303921i
$319$	−3.98003	−	4.99079i	−0.222839	−	0.279431i
$320$	−0.555630	+	0.515549i	−0.0310606	+	0.0288201i
$321$	10.3549	−	5.31273i	0.577953	−	0.296527i
$322$	−21.8396	−	0.197922i	−1.21708	−	0.0110297i
$323$	47.6884	+	10.8846i	2.65345	+	0.605633i
$324$	8.98937	+	0.437376i	0.499409	+	0.0242987i
$325$	−11.5909	+	6.69203i	−0.642950	+	0.371207i
$326$	0.189944	−	0.204711i	0.0105200	−	0.0113379i
$327$	3.08508	+	17.4645i	0.170606	+	0.965787i
$328$	−0.422022	−	2.79993i	−0.0233023	−	0.154600i
$329$	−15.5410	−	14.6843i	−0.856803	−	0.809569i
$330$	3.04066	−	0.305224i	0.167383	−	0.0168020i
$331$	0.309908	−	1.35780i	0.0170341	−	0.0746312i	−0.965696	−	0.259673i	$-0.916385\pi$
$331$	0.309908	−	1.35780i	0.0170341	−	0.0746312i	0.982731	+	0.185042i	$0.0592422\pi$
$332$	0.162133	+	0.0244376i	0.00889818	+	0.00134119i
$333$	10.5625	+	1.05027i	0.578820	+	0.0575542i
$334$	2.99702	+	19.8839i	0.163989	+	1.08800i
$335$	0.384908	+	5.13625i	0.0210298	+	0.280623i
$336$	−3.53610	+	2.91479i	−0.192910	+	0.159015i
$337$	2.24937	−	30.0157i	0.122531	−	1.63506i	−0.509752	−	0.860322i	$-0.670263\pi$
$337$	2.24937	−	30.0157i	0.122531	−	1.63506i	0.632282	−	0.774738i	$-0.282118\pi$
$338$	−3.84274	+	0.287974i	−0.209018	+	0.0156637i
$339$	5.48088	−	2.81205i	0.297680	−	0.152729i
$340$	−3.76202	+	2.56490i	−0.204024	+	0.139101i
$341$	2.82104	+	7.18789i	0.152768	+	0.389246i
$342$	20.8526	+	12.7248i	1.12758	+	0.688081i
$343$	4.61044	−	17.9372i	0.248941	−	0.968519i
$344$	−5.77182	+	3.33236i	−0.311196	+	0.179669i
$345$	−9.87976	−	4.45420i	−0.531908	−	0.239806i
$346$	8.58092	−	17.8185i	0.461313	−	0.957926i
$347$	−11.2861	+	2.57597i	−0.605868	+	0.138285i	−0.514440	−	0.857526i	$-0.672000\pi$
$347$	−11.2861	+	2.57597i	−0.605868	+	0.138285i	−0.0914276	+	0.995812i	$0.529143\pi$
$348$	3.56235	+	3.14182i	0.190962	+	0.168419i
$349$	−2.55146	+	3.74231i	−0.136577	+	0.200321i	−0.888434	−	0.459005i	$-0.848206\pi$
$349$	−2.55146	+	3.74231i	−0.136577	+	0.200321i	0.751857	+	0.659326i	$0.229158\pi$
$350$	−6.68316	+	9.61404i	−0.357230	+	0.513892i
$351$	−15.3241	−	3.48251i	−0.817939	−	0.185882i
$352$	2.30174	−	0.346931i	0.122683	−	0.0184915i
$353$	1.91165	−	25.5092i	0.101747	−	1.35772i	−0.679582	−	0.733600i	$-0.737839\pi$
$353$	1.91165	−	25.5092i	0.101747	−	1.35772i	0.781329	−	0.624120i	$-0.214542\pi$
$354$	1.56863	+	15.6268i	0.0833717	+	0.830555i
$355$	−1.04390	−	3.38424i	−0.0554044	−	0.179617i
$356$	−2.92731	−	7.45866i	−0.155147	−	0.395308i
$357$	−23.6141	+	14.1480i	−1.24979	+	0.748791i
$358$	2.92468	−	7.45196i	0.154574	−	0.393848i
$359$	10.2552	+	0.768521i	0.541248	+	0.0405610i	0.342550	−	0.939500i	$-0.388709\pi$
$359$	10.2552	+	0.768521i	0.541248	+	0.0405610i	0.198699	+	0.980061i	$0.436328\pi$
$360$	−2.18853	+	0.617233i	−0.115346	+	0.0325310i
$361$	23.6528	+	40.9679i	1.24489	+	2.15620i
$362$	7.14858			0.375721
$363$	8.49180	+	4.62095i	0.445704	+	0.242537i
$364$	6.96555	−	3.93783i	0.365094	−	0.206399i
$365$	3.72193	−	12.0662i	0.194815	−	0.631575i
$366$	0.136395	−	0.211325i	0.00712946	−	0.0110461i
$367$	−1.05344	−	6.98915i	−0.0549894	−	0.364831i	−0.999354	−	0.0359311i	$-0.988560\pi$
$367$	−1.05344	−	6.98915i	−0.0549894	−	0.364831i	0.944365	−	0.328900i	$-0.106678\pi$
$368$	−7.68431	−	3.01587i	−0.400573	−	0.157213i
$369$	2.70041	−	8.05403i	0.140578	−	0.419276i
$370$	−2.61459	+	0.596763i	−0.135926	+	0.0310242i
$371$	16.7705	−	13.1272i	0.870680	−	0.681528i
$372$	−2.99750	−	4.90175i	−0.155413	−	0.254144i
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	0.987869	+	0.155292i	$0.0496318\pi$
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	−0.359448	+	0.933165i	$0.617035\pi$
$374$	13.9830			0.723041
$375$	−10.5567	+	6.45561i	−0.545147	+	0.333366i
$376$	−3.50634	−	7.28099i	−0.180826	−	0.375488i
$377$	−5.17105	−	6.48429i	−0.266323	−	0.333958i
$378$	−13.4275	+	2.95016i	−0.690634	+	0.151740i
$379$	−3.55630	+	4.45945i	−0.182675	+	0.229067i	−0.864734	−	0.502230i	$-0.832513\pi$
$379$	−3.55630	+	4.45945i	−0.182675	+	0.229067i	0.682059	+	0.731297i	$0.261085\pi$
$380$	−6.01726	−	1.37340i	−0.308679	−	0.0704539i
$381$	−11.8718	+	1.19170i	−0.608209	+	0.0610525i
$382$	−16.4444	+	7.91920i	−0.841368	+	0.405181i
$383$	−4.72168	+	12.0307i	−0.241267	+	0.614738i	−0.999297	−	0.0374813i	$-0.988067\pi$
$383$	−4.72168	+	12.0307i	−0.241267	+	0.614738i	0.758031	+	0.652219i	$0.226162\pi$
$384$	−1.64169	+	0.552148i	−0.0837769	+	0.0281767i
$385$	−4.36063	+	1.66598i	−0.222238	+	0.0849060i
$386$	−9.60041	−	19.9355i	−0.488648	−	1.01469i
$387$	−19.9687	+	1.00911i	−1.01507	+	0.0512959i
$388$	5.55449	+	5.98631i	0.281986	+	0.303909i
$389$	−9.97853	−	14.6358i	−0.505931	−	0.742065i	0.485279	−	0.874359i	$-0.338718\pi$
$389$	−9.97853	−	14.6358i	−0.505931	−	0.742065i	−0.991210	+	0.132294i	$0.957766\pi$
$390$	3.95058	−	0.396563i	0.200046	−	0.0200807i
$391$	−42.9447	−	24.7941i	−2.17181	−	1.25389i
$392$	4.04741	−	5.71126i	0.204425	−	0.288462i
$393$	0.596602	−	2.12299i	0.0300946	−	0.107091i
$394$	−8.29917	+	10.4068i	−0.418106	+	0.524288i
$395$	−0.385608	−	5.14558i	−0.0194020	−	0.258902i
$396$	6.62097	+	2.21992i	0.332716	+	0.111555i
$397$	13.7334	+	20.1433i	0.689262	+	1.01096i	0.998206	+	0.0598807i	$0.0190720\pi$
$397$	13.7334	+	20.1433i	0.689262	+	1.01096i	−0.308944	+	0.951080i	$0.599976\pi$
$398$	8.06890	+	5.50128i	0.404457	+	0.275754i
$399$	−35.8306	−	10.4203i	−1.79378	−	0.521670i
$400$	−3.65651	+	2.49296i	−0.182825	+	0.124648i
$401$	25.9315	+	10.1774i	1.29496	+	0.508233i	0.909964	−	0.414687i	$-0.136109\pi$
$401$	25.9315	+	10.1774i	1.29496	+	0.508233i	0.384992	+	0.922920i	$0.374204\pi$
$402$	−4.02208	+	11.0613i	−0.200603	+	0.551689i
$403$	3.66524	+	9.33887i	0.182578	+	0.465202i
$404$	2.96407	+	2.75026i	0.147468	+	0.136830i
$405$	−6.68814	−	1.34334i	−0.332336	−	0.0667509i
$406$	−6.50824	−	3.20718i	−0.322999	−	0.159170i
$407$	7.66665	+	3.00894i	0.380022	+	0.149147i
$408$	−10.2460	+	1.80994i	−0.507251	+	0.0896055i
$409$	27.5499	+	6.28809i	1.36226	+	0.310926i	0.840335	−	0.542067i	$-0.182358\pi$
$409$	27.5499	+	6.28809i	1.36226	+	0.310926i	0.521922	+	0.852993i	$0.325215\pi$
$410$			2.14623i			0.105995i
$411$	7.08759	+	27.7984i	0.349605	+	1.37119i
$412$	3.43134	+	11.1241i	0.169050	+	0.548046i
$413$	−8.56190	−	22.4104i	−0.421303	−	1.10275i
$414$	−16.3981	−	18.5580i	−0.805925	−	0.912074i
$415$	−0.118758	−	0.0366320i	−0.00582960	−	0.00179819i
$416$	2.99054	−	0.450751i	0.146623	−	0.0220999i
$417$	18.2463	−	24.1042i	0.893527	−	1.18039i
$418$	12.8922	+	13.8945i	0.630581	+	0.679604i
$419$	−2.93561	−	0.905515i	−0.143414	−	0.0442373i	0.222217	−	0.974997i	$-0.428671\pi$
$419$	−2.93561	−	0.905515i	−0.143414	−	0.0442373i	−0.365631	+	0.930760i	$0.619147\pi$
$420$	2.97959	−	1.78517i	0.145389	−	0.0871076i
$421$	−21.1713	+	6.53048i	−1.03183	+	0.318276i	−0.764017	−	0.645196i	$-0.776776\pi$
$421$	−21.1713	+	6.53048i	−1.03183	+	0.318276i	−0.267809	+	0.963472i	$0.586299\pi$
$422$	4.95795	+	2.86247i	0.241349	+	0.139343i
$423$	0.589267	−	24.2367i	0.0286512	−	1.17843i
$424$	7.69197	−	2.37266i	0.373555	−	0.115226i
$425$	−23.9516	+	11.5345i	−1.16183	+	0.559506i
$426$	1.00380	−	8.03046i	0.0486342	−	0.389077i
$427$	−0.116568	+	0.366091i	−0.00564111	+	0.0177164i
$428$	−6.25486	+	2.45485i	−0.302340	+	0.118660i
$429$	−10.7103	−	5.82816i	−0.517096	−	0.281386i
$430$	4.70245	−	1.84557i	0.226772	−	0.0890015i
$431$	−7.89183	+	11.5752i	−0.380136	+	0.557557i	−0.967855	−	0.251508i	$-0.919074\pi$
$431$	−7.89183	+	11.5752i	−0.380136	+	0.557557i	0.587719	+	0.809065i	$0.300026\pi$
$432$	−5.13884	−	0.769629i	−0.247243	−	0.0370288i
$433$	−11.6042	+	24.0964i	−0.557664	+	1.15800i	0.411461	+	0.911428i	$0.365019\pi$
$433$	−11.6042	+	24.0964i	−0.557664	+	1.15800i	−0.969124	+	0.246573i	$0.920695\pi$
$434$	6.37933	+	6.02765i	0.306218	+	0.289337i
$435$	−2.31506	−	2.75723i	−0.110999	−	0.132199i
$436$	−0.765178	−	10.2106i	−0.0366454	−	0.488999i
$437$	−14.9575	−	65.5333i	−0.715517	−	3.13488i
$438$	19.0860	−	21.6407i	0.911965	−	1.03403i
$439$	−15.8588	−	12.6470i	−0.756899	−	0.603607i	0.167128	−	0.985935i	$-0.446551\pi$
$439$	−15.8588	−	12.6470i	−0.756899	−	0.603607i	−0.924026	+	0.382329i	$0.875122\pi$
$440$	−1.76435			−0.0841121
$441$	18.6156	−	9.71908i	0.886456	−	0.462813i
$442$	18.1674			0.864133
$443$	10.1638	+	8.10534i	0.482895	+	0.385096i	0.834461	−	0.551067i	$-0.185779\pi$
$443$	10.1638	+	8.10534i	0.482895	+	0.385096i	−0.351566	+	0.936163i	$0.614351\pi$
$444$	−6.00718	−	1.21242i	−0.285088	−	0.0575391i
$445$	1.35142	+	5.92097i	0.0640636	+	0.280681i
$446$	−0.548000	−	7.31256i	−0.0259486	−	0.346260i
$447$	−21.8762	+	3.86441i	−1.03471	+	0.182780i
$448$	2.19944	−	1.47053i	0.103914	−	0.0694762i
$449$	−14.3993	+	29.9005i	−0.679545	+	1.41109i	0.220541	+	0.975378i	$0.429218\pi$
$449$	−14.3993	+	29.9005i	−0.679545	+	1.41109i	−0.900086	+	0.435712i	$0.856496\pi$
$450$	−13.1724	+	1.65908i	−0.620952	+	0.0782096i
$451$	3.71292	−	5.44585i	0.174834	−	0.256435i
$452$	−3.31072	+	1.29936i	−0.155723	+	0.0611168i
$453$	−0.267939	−	10.6110i	−0.0125889	−	0.498547i
$454$	−18.0665	+	7.09058i	−0.847903	+	0.332777i
$455$	−5.66555	+	2.16452i	−0.265605	+	0.101474i
$456$	−11.2453	−	8.51242i	−0.526607	−	0.398630i
$457$	26.7124	−	12.8640i	1.24955	−	0.601753i	0.312161	−	0.950029i	$-0.398947\pi$
$457$	26.7124	−	12.8640i	1.24955	−	0.601753i	0.937392	+	0.348276i	$0.113233\pi$
$458$	−19.9833	+	6.16404i	−0.933759	+	0.288026i
$459$	−29.8357	−	9.17246i	−1.39261	−	0.428134i
$460$	5.41871	+	3.12849i	0.252649	+	0.145867i
$461$	−3.11163	+	0.959810i	−0.144923	+	0.0447028i	−0.366368	−	0.930470i	$-0.619399\pi$
$461$	−3.11163	+	0.959810i	−0.144923	+	0.0447028i	0.221445	+	0.975173i	$0.428923\pi$
$462$	−10.6487	−	0.624904i	−0.495423	−	0.0290732i
$463$	−33.3108	−	10.2750i	−1.54808	−	0.477520i	−0.601199	−	0.799099i	$-0.705310\pi$
$463$	−33.3108	−	10.2750i	−1.54808	−	0.477520i	−0.946883	+	0.321579i	$0.895786\pi$
$464$	−1.86527	−	2.01028i	−0.0865929	−	0.0933250i
$465$	1.69289	+	4.01250i	0.0785057	+	0.186075i
$466$	15.2716	−	2.30183i	0.707445	−	0.106630i
$467$	0.360797	+	0.111291i	0.0166957	+	0.00514994i	0.303092	−	0.952961i	$-0.401981\pi$
$467$	0.360797	+	0.111291i	0.0166957	+	0.00514994i	−0.286396	+	0.958111i	$0.592457\pi$
$468$	8.60230	+	2.88424i	0.397641	+	0.133324i
$469$	1.50597	−	17.9156i	0.0695393	−	0.827265i
$470$	1.80548	+	5.85322i	0.0832806	+	0.269989i
$471$	−27.3522	+	26.6952i	−1.26032	+	1.23005i
$472$		−	9.06747i		−	0.417364i
$473$	−15.1248	−	3.45213i	−0.695438	−	0.158729i
$474$	4.02938	−	11.0814i	0.185076	−	0.508986i
$475$	−33.5449	−	13.1654i	−1.53915	−	0.604071i
$476$	14.3813	−	6.76579i	0.659164	−	0.310110i
$477$	23.7845	+	4.17852i	1.08902	+	0.191322i
$478$	−2.17827	−	2.02114i	−0.0996318	−	0.0924448i
$479$	12.8695	+	32.7910i	0.588024	+	1.49826i	0.846578	+	0.532264i	$0.178659\pi$
$479$	12.8695	+	32.7910i	0.588024	+	1.49826i	−0.258554	+	0.965997i	$0.583246\pi$
$480$	1.29282	−	0.228376i	0.0590090	−	0.0104239i
$481$	9.96089	+	3.90936i	0.454178	+	0.178252i
$482$	16.7484	−	11.4189i	0.762870	−	0.520116i
$483$	31.5965	+	20.8012i	1.43769	+	0.946487i
$484$	−4.61176	−	3.14424i	−0.209625	−	0.142920i
$485$	−3.48683	−	5.11424i	−0.158329	−	0.232226i
$486$	−12.6711	−	9.07987i	−0.574771	−	0.411871i
$487$	−2.46001	−	32.8265i	−0.111474	−	1.48751i	−0.719998	−	0.693977i	$-0.755857\pi$
$487$	−2.46001	−	32.8265i	−0.111474	−	1.48751i	0.608524	−	0.793536i	$-0.291762\pi$
$488$	−0.0905397	+	0.113533i	−0.00409854	+	0.00513941i
$489$	−0.468695	+	0.119500i	−0.0211951	+	0.00540400i
$490$	−3.67874	+	3.82336i	−0.166189	+	0.172722i
$491$	−19.6747	−	11.3592i	−0.887905	−	0.512632i	−0.0146485	−	0.999893i	$-0.504663\pi$
$491$	−19.6747	−	11.3592i	−0.887905	−	0.512632i	−0.873257	+	0.487260i	$0.837996\pi$
$492$	−2.01572	+	4.47102i	−0.0908757	+	0.201569i
$493$	−9.27988	−	13.6111i	−0.417945	−	0.613012i
$494$	16.7503	+	18.0525i	0.753630	+	0.812220i
$495$	−4.71165	−	2.41180i	−0.211773	−	0.108402i
$496$	1.43930	+	2.98873i	0.0646263	+	0.134198i
$497$	1.73164	+	12.2403i	0.0776745	+	0.549053i
$498$	−0.212992	−	0.187848i	−0.00954440	−	0.00841768i
$499$	2.21251	−	5.63739i	0.0990457	−	0.252364i	−0.872759	−	0.488151i	$-0.837671\pi$
$499$	2.21251	−	5.63739i	0.0990457	−	0.252364i	0.971805	+	0.235787i	$0.0757667\pi$
$500$	6.43671	−	3.09976i	0.287859	−	0.138625i
$501$	14.3148	−	31.7513i	0.639537	−	1.41854i
$502$	3.91834	+	0.894336i	0.174884	+	0.0399162i
$503$	3.15045	−	3.95054i	0.140472	−	0.176146i	−0.706619	−	0.707594i	$-0.749781\pi$
$503$	3.15045	−	3.95054i	0.140472	−	0.176146i	0.847091	+	0.531448i	$0.178352\pi$
$504$	7.88370	−	0.920465i	0.351168	−	0.0410008i
$505$	−1.91088	−	2.39617i	−0.0850331	−	0.106628i
$506$	−8.33723	−	17.3124i	−0.370635	−	0.769632i
$507$	5.86267	+	3.19027i	0.260370	+	0.141685i
$508$	6.88861			0.305633
$509$	9.85646	+	17.0719i	0.436880	+	0.756698i	0.997447	−	0.0714109i	$-0.0227502\pi$
$509$	9.85646	+	17.0719i	0.436880	+	0.756698i	−0.560567	+	0.828109i	$0.689417\pi$
$510$	7.88384	−	0.199076i	0.349102	−	0.00881523i
$511$	−19.4831	+	39.5365i	−0.861881	+	1.74899i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−18.3939	−	38.1040i	−0.812113	−	1.68233i
$514$	−6.94459	−	2.72555i	−0.306313	−	0.120219i
$515$	−1.31511	−	8.72519i	−0.0579507	−	0.384478i
$516$	11.5295	+	0.571800i	0.507557	+	0.0251721i
$517$	5.54468	−	17.9754i	0.243855	−	0.790557i
$518$	9.34094	−	0.614937i	0.410417	−	0.0270188i
$519$	−29.2237	+	17.8708i	−1.28278	+	0.784440i
$520$	−2.29233			−0.100525
$521$	−8.01029	−	13.8742i	−0.350937	−	0.607841i	0.635477	−	0.772120i	$-0.280804\pi$
$521$	−8.01029	−	13.8742i	−0.350937	−	0.607841i	−0.986414	+	0.164279i	$0.947470\pi$
$522$	−2.23316	−	7.91815i	−0.0977429	−	0.346568i
$523$	23.8100	+	1.78432i	1.04114	+	0.0780227i	0.584310	−	0.811531i	$-0.301365\pi$
$523$	23.8100	+	1.78432i	1.04114	+	0.0780227i	0.456831	+	0.889553i	$0.348984\pi$
$524$	−0.465148	+	1.18518i	−0.0203201	+	0.0517748i
$525$	18.7559	−	7.71369i	0.818573	−	0.336653i
$526$	8.66363	+	22.0746i	0.377752	+	0.962497i
$527$	5.87358	+	19.0417i	0.255857	+	0.829468i
$528$	−3.67549	−	1.65706i	−0.159955	−	0.0721144i
$529$	−3.37363	+	45.0179i	−0.146679	+	1.95730i
$530$	−6.03318	+	0.909356i	−0.262065	+	0.0394999i
$531$	12.3949	−	24.2144i	0.537893	−	1.05082i
$532$	19.9825	+	8.05228i	0.866351	+	0.349111i
$533$	4.82401	−	7.07552i	0.208951	−	0.306475i
$534$	−2.74564	+	13.6038i	−0.118816	+	0.588694i
$535$	4.96535	−	1.13331i	0.214671	−	0.0489972i
$536$	2.94839	−	6.12239i	0.127351	−	0.264447i
$537$	−11.2555	+	8.09751i	−0.485712	+	0.349433i
$538$	−20.8914	+	12.0617i	−0.900694	+	0.520016i
$539$	15.9487	−	3.33730i	0.686961	−	0.143747i
$540$	3.76463	+	1.15737i	0.162004	+	0.0498052i
$541$	0.760231	+	1.93704i	0.0326849	+	0.0832798i	0.946284	−	0.323335i	$-0.104804\pi$
$541$	0.760231	+	1.93704i	0.0326849	+	0.0832798i	−0.913600	+	0.406615i	$0.866709\pi$
$542$	−24.1044	+	16.4341i	−1.03537	+	0.705906i
$543$	−10.4030	−	6.71439i	−0.446437	−	0.288142i
$544$	5.99030	−	0.448911i	0.256832	−	0.0192469i
$545$	−0.579980	+	7.73930i	−0.0248436	+	0.331515i
$546$	−13.8354	−	0.811907i	−0.592098	−	0.0347464i
$547$	1.65517	+	22.0867i	0.0707699	+	0.944359i	0.913714	+	0.406358i	$0.133201\pi$
$547$	1.65517	+	22.0867i	0.0707699	+	0.944359i	−0.842944	+	0.538001i	$0.819180\pi$
$548$	−2.46857	−	16.3779i	−0.105452	−	0.699628i
$549$	−0.396979	+	0.179423i	−0.0169427	+	0.00765757i
$550$	−10.1863	−	1.53534i	−0.434346	−	0.0654671i
$551$	4.96899	−	21.7706i	0.211686	−	0.927458i
$552$	8.34999	+	11.6065i	0.355399	+	0.494004i
$553$	−1.50871	+	17.9481i	−0.0641567	+	0.763233i
$554$	−0.698688	−	4.63549i	−0.0296844	−	0.196943i
$555$	4.36543	+	1.58734i	0.185302	+	0.0673789i
$556$	−11.8718	+	12.7948i	−0.503478	+	0.542620i
$557$	−3.35834	+	1.93894i	−0.142297	+	0.0821555i	−0.569459	−	0.822020i	$-0.692847\pi$
$557$	−3.35834	+	1.93894i	−0.142297	+	0.0821555i	0.427161	+	0.904176i	$0.359514\pi$
$558$	−0.241885	+	9.94877i	−0.0102398	+	0.421165i
$559$	−19.6509	−	4.48518i	−0.831144	−	0.189703i
$560$	−1.81461	+	0.853699i	−0.0766812	+	0.0360754i
$561$	−20.3489	−	13.1337i	−0.859129	−	0.554504i
$562$	−19.4929	+	18.0868i	−0.822258	+	0.762944i
$563$	−10.0463	−	12.5976i	−0.423399	−	0.530926i	0.523684	−	0.851912i	$-0.324557\pi$
$563$	−10.0463	−	12.5976i	−0.423399	−	0.530926i	−0.947084	+	0.320986i	$0.895986\pi$
$564$	−1.73612	+	13.8891i	−0.0731040	+	0.584837i
$565$	2.62818	−	0.599865i	0.110568	−	0.0252365i
$566$	−3.34402	−	14.6511i	−0.140559	−	0.615831i
$567$	22.3114	+	8.31866i	0.936992	+	0.349351i
$568$	−1.03972	+	4.55532i	−0.0436258	+	0.191137i
$569$		−	37.2699i		−	1.56244i	−0.624258	−	0.781218i	$-0.714599\pi$
$569$		−	37.2699i		−	1.56244i	0.624258	−	0.781218i	$-0.285401\pi$
$570$	7.46670	+	7.65044i	0.312745	+	0.320442i
$571$	−5.33915	+	23.3923i	−0.223436	+	0.978939i	0.731433	+	0.681913i	$0.238852\pi$
$571$	−5.33915	+	23.3923i	−0.223436	+	0.978939i	−0.954870	+	0.297026i	$0.904005\pi$
$572$	5.81657	+	3.96567i	0.243203	+	0.165813i
$573$	31.3691	+	3.92110i	1.31046	+	0.163806i
$574$	1.18365	−	7.39750i	0.0494046	−	0.308766i
$575$	28.5620	+	22.7774i	1.19112	+	0.949884i
$576$	2.90769	+	0.738455i	0.121154	+	0.0307690i
$577$	−3.88949	+	25.8051i	−0.161922	+	1.07428i	0.749260	+	0.662276i	$0.230409\pi$
$577$	−3.88949	+	25.8051i	−0.161922	+	1.07428i	−0.911182	+	0.412004i	$0.864829\pi$
$578$	19.0319	+	1.42624i	0.791621	+	0.0593238i
$579$	−4.75353	+	38.0286i	−0.197550	+	1.58042i
$580$	1.17092	+	1.71743i	0.0486199	+	0.0713123i
$581$	0.389126	+	0.191756i	0.0161437	+	0.00795539i
$582$	−2.46051	−	13.9288i	−0.101991	−	0.577366i
$583$	16.8818	+	8.12983i	0.699171	+	0.336703i
$584$	−12.2121	+	11.3312i	−0.505341	+	0.468888i
$585$	−6.12161	−	3.13354i	−0.253097	−	0.129556i
$586$	−22.4843	+	8.82443i	−0.928817	+	0.364534i
$587$	12.9814	+	22.4844i	0.535798	+	0.928030i	0.999124	+	0.0418420i	$0.0133226\pi$
$587$	12.9814	+	22.4844i	0.535798	+	0.928030i	−0.463326	+	0.886188i	$0.653344\pi$
$588$	−11.2544	+	4.50978i	−0.464124	+	0.185980i
$589$	−13.5058	+	23.3928i	−0.556499	+	0.963884i
$590$	−1.02435	+	6.79609i	−0.0421716	+	0.279791i
$591$	21.8522	−	7.34955i	0.898880	−	0.302320i
$592$	3.38099	+	1.04290i	0.138958	+	0.0428628i
$593$	9.05699	−	6.17495i	0.371926	−	0.253575i	−0.362904	−	0.931827i	$-0.618215\pi$
$593$	9.05699	−	6.17495i	0.371926	−	0.253575i	0.734829	+	0.678252i	$0.237262\pi$
$594$	−7.55015	−	9.44940i	−0.309786	−	0.387714i
$595$	−11.5431	+	3.44633i	−0.473221	+	0.141286i
$596$	12.7899	−	0.958471i	0.523895	−	0.0392605i
$597$	−6.57520	−	15.5846i	−0.269105	−	0.637836i
$598$	−10.8322	−	22.4932i	−0.442960	−	0.919815i
$599$	−5.21352	−	4.15764i	−0.213019	−	0.169877i	0.511168	−	0.859481i	$-0.329213\pi$
$599$	−5.21352	−	4.15764i	−0.213019	−	0.169877i	−0.724186	+	0.689604i	$0.757785\pi$
$600$	7.66272	−	0.193493i	0.312829	−	0.00789930i
$601$	−5.14697	+	34.1479i	−0.209949	+	1.39292i	0.596971	+	0.802263i	$0.296371\pi$
$601$	−5.14697	+	34.1479i	−0.209949	+	1.39292i	−0.806921	+	0.590660i	$0.798867\pi$
$602$	−17.2260	+	3.76781i	−0.702078	+	0.153564i
$603$	16.2427	−	12.3193i	0.661452	−	0.501682i
$604$	−0.457961	+	6.11106i	−0.0186342	+	0.248656i
$605$	3.10132	+	2.87760i	0.126087	+	0.116991i
$606$	−1.73028	−	6.78638i	−0.0702880	−	0.275678i
$607$	−10.7225	+	6.19063i	−0.435212	+	0.251270i	−0.701565	−	0.712606i	$-0.747515\pi$
$607$	−10.7225	+	6.19063i	−0.435212	+	0.251270i	0.266353	+	0.963876i	$0.414181\pi$
$608$	5.96911	+	5.53853i	0.242080	+	0.224617i
$609$	6.45880	+	10.7802i	0.261724	+	0.436837i
$610$	0.0806855	−	0.0748652i	0.00326686	−	0.00303120i
$611$	7.20392	−	23.3545i	0.291439	−	0.944824i
$612$	16.6106	+	6.98972i	0.671442	+	0.282543i
$613$	−5.96241	+	15.1920i	−0.240819	+	0.613598i	−0.999273	−	0.0381296i	$-0.987860\pi$
$613$	−5.96241	+	15.1920i	−0.240819	+	0.613598i	0.758453	+	0.651727i	$0.225955\pi$
$614$	4.50064	+	19.7186i	0.181631	+	0.795777i
$615$	2.01587	−	3.12333i	0.0812879	−	0.125945i
$616$	6.08126	+	0.973044i	0.245021	+	0.0392050i
$617$	−25.0540	+	27.0018i	−1.00864	+	1.08705i	−0.0124400	+	0.999923i	$0.503960\pi$
$617$	−25.0540	+	27.0018i	−1.00864	+	1.08705i	−0.996197	+	0.0871296i	$0.972231\pi$
$618$	5.45499	−	19.4114i	0.219432	−	0.780843i
$619$	15.6569	+	9.03954i	0.629306	+	0.363330i	0.780483	−	0.625177i	$-0.214973\pi$
$619$	15.6569	+	9.03954i	0.629306	+	0.363330i	−0.151177	+	0.988507i	$0.548306\pi$
$620$	−0.741120	−	2.40265i	−0.0297641	−	0.0964929i
$621$	6.43278	+	42.4089i	0.258138	+	1.70181i
$622$	−17.2240	+	13.7357i	−0.690621	+	0.550752i
$623$	−1.39258	−	21.1534i	−0.0557925	−	0.847492i
$624$	−4.77539	−	2.15294i	−0.191168	−	0.0861866i
$625$	15.9699	−	4.92605i	0.638794	−	0.197042i
$626$	4.09055	−	5.12939i	0.163491	−	0.205012i
$627$	−5.71096	−	32.3294i	−0.228074	−	1.29111i
$628$	17.2522	−	13.7582i	0.688438	−	0.549011i
$629$	19.1494	+	9.22186i	0.763536	+	0.367700i
$630$	−6.01283	−	0.200726i	−0.239557	−	0.00799710i
$631$	−24.3288	+	11.7161i	−0.968513	+	0.466411i	−0.850139	−	0.526558i	$-0.823482\pi$
$631$	−24.3288	+	11.7161i	−0.968513	+	0.466411i	−0.118373	+	0.992969i	$0.537768\pi$
$632$	−2.95374	+	6.13351i	−0.117494	+	0.243978i
$633$	−4.52650	−	8.82247i	−0.179912	−	0.350662i
$634$	12.5313	+	6.03476i	0.497682	+	0.239671i
$635$	−5.16303	−	0.778201i	−0.204889	−	0.0308820i
$636$	−13.4224	−	3.77194i	−0.532232	−	0.149567i
$637$	20.7214	−	4.33598i	0.821012	−	0.171798i
$638$		−	6.38347i		−	0.252724i
$639$	−9.00350	+	10.7436i	−0.356173	+	0.425010i
$640$	−0.755848	+	0.0566430i	−0.0298775	+	0.00223901i
$641$	8.53785	−	27.6790i	0.337225	−	1.09326i	−0.615171	−	0.788394i	$-0.710913\pi$
$641$	8.53785	−	27.6790i	0.337225	−	1.09326i	0.952396	−	0.304863i	$-0.0986107\pi$
$642$	11.4082	+	2.30251i	0.450246	+	0.0908727i
$643$	−10.7814	−	0.807953i	−0.425176	−	0.0318625i	−0.139576	−	0.990211i	$-0.544574\pi$
$643$	−10.7814	−	0.807953i	−0.425176	−	0.0318625i	−0.285600	+	0.958349i	$0.592193\pi$
$644$	−16.9515	−	13.7715i	−0.667983	−	0.542675i
$645$	−8.57677	−	1.73104i	−0.337710	−	0.0681597i
$646$	30.4979	+	38.2431i	1.19992	+	1.50465i
$647$	17.3203	+	11.8088i	0.680933	+	0.464252i	0.853737	−	0.520704i	$-0.174330\pi$
$647$	17.3203	+	11.8088i	0.680933	+	0.464252i	−0.172804	+	0.984956i	$0.555283\pi$
$648$	6.75547	+	5.94673i	0.265380	+	0.233610i
$649$	14.3562	−	15.4723i	0.563530	−	0.607341i
$650$	−13.2346	−	1.99479i	−0.519103	−	0.0782421i
$651$	−3.62204	−	14.7637i	−0.141959	−	0.578634i
$652$	0.276139	−	0.0416213i	0.0108144	−	0.00163002i
$653$	−6.44566	+	9.45405i	−0.252238	+	0.369966i	−0.931384	−	0.364038i	$-0.881398\pi$
$653$	−6.44566	+	9.45405i	−0.252238	+	0.369966i	0.679146	+	0.734003i	$0.262350\pi$
$654$	−8.47690	+	15.5778i	−0.331473	+	0.609140i
$655$	0.482518	−	0.835746i	0.0188535	−	0.0326553i
$656$	1.41578	−	2.45220i	0.0552769	−	0.0957424i
$657$	−48.1014	+	13.5661i	−1.87662	+	0.529264i
$658$	−2.99496	−	21.1703i	−0.116756	−	0.825303i
$659$	8.38655	+	9.03855i	0.326694	+	0.352092i	0.874946	−	0.484221i	$-0.160897\pi$
$659$	8.38655	+	9.03855i	0.326694	+	0.352092i	−0.548252	+	0.836313i	$0.684707\pi$
$660$	2.56759	+	1.65719i	0.0999434	+	0.0645060i
$661$	27.3814	−	21.8359i	1.06501	−	0.849318i	0.0759925	−	0.997108i	$-0.475788\pi$
$661$	27.3814	−	21.8359i	1.06501	−	0.849318i	0.989019	+	0.147790i	$0.0472161\pi$
$662$	1.08887	−	0.868343i	0.0423201	−	0.0337491i
$663$	−26.4383	−	17.0639i	−1.02678	−	0.662708i
$664$	0.111524	+	0.120194i	0.00432796	+	0.00466443i
$665$	−14.0673	−	8.29261i	−0.545505	−	0.321574i
$666$	7.60324	+	7.40672i	0.294619	+	0.287005i
$667$	−11.3190	+	19.6050i	−0.438272	+	0.759109i
$668$	−10.0543	+	17.4145i	−0.389011	+	0.673786i
$669$	−6.07093	+	11.1564i	−0.234716	+	0.431331i
$670$	−2.90146	+	4.25567i	−0.112093	+	0.164411i
$671$	−0.334246	+	0.0503795i	−0.0129034	+	0.00194488i
$672$	−4.58198	+	0.0741591i	−0.176754	+	0.00286075i
$673$	−18.0383	−	2.71884i	−0.695326	−	0.104804i	−0.208136	−	0.978100i	$-0.566740\pi$
$673$	−18.0383	−	2.71884i	−0.695326	−	0.104804i	−0.487189	+	0.873296i	$0.661978\pi$
$674$	20.4731	−	22.0648i	0.788595	−	0.849903i
$675$	20.7276	+	9.95794i	0.797805	+	0.383281i
$676$	−3.18392	−	2.17076i	−0.122459	−	0.0834909i
$677$	5.04341	+	6.32424i	0.193834	+	0.243060i	0.869245	−	0.494381i	$-0.164605\pi$
$677$	5.04341	+	6.32424i	0.193834	+	0.243060i	−0.675411	+	0.737441i	$0.736034\pi$
$678$	6.03840	+	1.21873i	0.231904	+	0.0468049i
$679$	9.19769	+	19.5505i	0.352975	+	0.750278i
$680$	−4.54045	−	0.340260i	−0.174118	−	0.0130484i
$681$	32.9514	+	6.65055i	1.26270	+	0.254850i
$682$	−2.27600	+	7.37861i	−0.0871526	+	0.282542i
$683$	42.6578	−	3.19676i	1.63226	−	0.122321i	0.773187	−	0.634178i	$-0.218661\pi$
$683$	42.6578	−	3.19676i	1.63226	−	0.122321i	0.859070	+	0.511857i	$0.171042\pi$
$684$	8.36938	+	22.9500i	0.320011	+	0.877517i
$685$			12.5541i			0.479668i
$686$	14.7883	−	11.1493i	0.564618	−	0.425683i
$687$	34.8706	+	9.79930i	1.33040	+	0.373867i
$688$	−6.59029	−	0.993326i	−0.251252	−	0.0378702i
$689$	21.9336	+	10.5627i	0.835605	+	0.402406i
$690$	−4.94716	−	9.64236i	−0.188335	−	0.367079i
$691$	7.91146	−	16.4283i	0.300966	−	0.624963i	−0.694562	−	0.719433i	$-0.744402\pi$
$691$	7.91146	−	16.4283i	0.300966	−	0.624963i	0.995528	+	0.0944708i	$0.0301159\pi$
$692$	17.8185	−	8.58092i	0.677356	−	0.326198i
$693$	14.9097	+	10.9113i	0.566373	+	0.414488i
$694$	−10.4299	−	5.02277i	−0.395913	−	0.190662i
$695$	10.3434	−	8.24856i	0.392346	−	0.312886i
$696$	0.826270	+	4.67746i	0.0313197	+	0.177299i
$697$	10.6052	−	13.2985i	0.401701	−	0.503718i
$698$	−4.32810	+	1.33504i	−0.163821	+	0.0505321i
$699$	−24.3862	−	10.9943i	−0.922372	−	0.415843i
$700$	−11.2194	+	3.34968i	−0.424052	+	0.126606i
$701$	24.5628	−	19.5882i	0.927725	−	0.739836i	−0.0380338	−	0.999276i	$-0.512109\pi$
$701$	24.5628	−	19.5882i	0.927725	−	0.739836i	0.965759	+	0.259440i	$0.0835380\pi$
$702$	−9.80954	−	12.2771i	−0.370237	−	0.463371i
$703$	8.49214	+	27.5308i	0.320287	+	1.03835i
$704$	2.01588	+	1.16387i	0.0759764	+	0.0438650i
$705$	2.87027	−	10.2138i	0.108101	−	0.384673i
$706$	17.3993	−	18.7520i	0.654833	−	0.705742i
$707$	5.26483	+	9.31284i	0.198004	+	0.350245i
$708$	−8.51674	+	13.1955i	−0.320079	+	0.495919i
$709$	8.99975	+	39.4305i	0.337993	+	1.48084i	0.803237	+	0.595660i	$0.203109\pi$
$709$	8.99975	+	39.4305i	0.337993	+	1.48084i	−0.465244	+	0.885182i	$0.654034\pi$
$710$	1.29388	−	3.29676i	0.0485586	−	0.123725i
$711$	−16.2722	+	12.3417i	−0.610254	+	0.462850i
$712$	2.36174	−	7.65656i	0.0885098	−	0.286942i
$713$	20.0736	−	18.6256i	0.751763	−	0.697534i
$714$	−27.2833	−	3.66179i	−1.02105	−	0.137039i
$715$	−3.91153	−	3.62937i	−0.146283	−	0.135731i
$716$	6.93283	−	4.00267i	0.259092	−	0.149587i
$717$	1.27157	+	4.98726i	0.0474877	+	0.186252i
$718$	7.53867	+	6.99486i	0.281341	+	0.261046i
$719$	−0.339129	+	4.52536i	−0.0126474	+	0.168768i	0.987303	+	0.158846i	$0.0507773\pi$
$719$	−0.339129	+	4.52536i	−0.0126474	+	0.168768i	−0.999951	+	0.00992176i	$0.996842\pi$
$720$	−2.09590	−	0.881953i	−0.0781096	−	0.0328685i
$721$	−0.279114	+	30.7988i	−0.0103947	+	1.14701i
$722$	−7.05054	+	46.7773i	−0.262394	+	1.74087i
$723$	−35.0987	+	0.886282i	−1.30533	+	0.0329612i
$724$	5.58898	+	4.45706i	0.207713	+	0.165645i
$725$	5.26570	+	10.9343i	0.195563	+	0.406091i
$726$	3.75804	+	8.90735i	0.139474	+	0.330583i
$727$	4.86011	−	0.364215i	0.180251	−	0.0135080i	0.0157014	−	0.999877i	$-0.495002\pi$
$727$	4.86011	−	0.364215i	0.180251	−	0.0135080i	0.164550	+	0.986369i	$0.447383\pi$
$728$	7.90108	+	1.26423i	0.292834	+	0.0468554i
$729$	9.91132	+	25.1151i	0.367086	+	0.930187i
$730$	10.4331	−	7.11316i	0.386146	−	0.263270i
$731$	−38.2570	−	11.8007i	−1.41499	−	0.436465i
$732$	0.238397	−	0.0801799i	0.00881139	−	0.00296353i
$733$	4.07729	−	27.0510i	0.150598	−	0.999152i	−0.778053	−	0.628198i	$-0.783793\pi$
$733$	4.07729	−	27.0510i	0.150598	−	0.999152i	0.928651	−	0.370954i	$-0.120969\pi$
$734$	3.53405	−	6.12115i	0.130444	−	0.225936i
$735$	8.94467	−	2.10869i	0.329929	−	0.0777802i
$736$	−4.12747	−	7.14899i	−0.152141	−	0.263515i
$737$	14.7244	−	5.77888i	0.542378	−	0.212868i
$738$	7.13287	−	4.61321i	0.262564	−	0.169815i
$739$	15.6879	−	14.5563i	0.577090	−	0.535462i	−0.336719	−	0.941605i	$-0.609317\pi$
$739$	15.6879	−	14.5563i	0.577090	−	0.535462i	0.913809	+	0.406144i	$0.133127\pi$
$740$	−2.41625	−	1.16360i	−0.0888229	−	0.0427749i
$741$	−7.41997	−	42.0040i	−0.272579	−	1.54305i
$742$	21.2963	+	0.192998i	0.781813	+	0.00708518i
$743$	−28.2035	−	41.3670i	−1.03469	−	1.51761i	−0.844280	−	0.535903i	$-0.819971\pi$
$743$	−28.2035	−	41.3670i	−1.03469	−	1.51761i	−0.190408	−	0.981705i	$-0.560981\pi$
$744$	0.712651	−	5.70126i	0.0261270	−	0.209018i
$745$	−9.69434	−	0.726490i	−0.355173	−	0.0266165i
$746$	−3.61780	+	24.0025i	−0.132457	+	0.878795i
$747$	0.133520	+	0.473424i	0.00488525	+	0.0173217i
$748$	10.9323	+	8.71823i	0.399725	+	0.318770i
$749$	−17.7393	+	1.16782i	−0.648180	+	0.0426713i
$750$	−12.2786	−	1.53481i	−0.448351	−	0.0560433i
$751$	−20.6310	−	14.0660i	−0.752837	−	0.513276i	0.125046	−	0.992151i	$-0.460092\pi$
$751$	−20.6310	−	14.0660i	−0.752837	−	0.513276i	−0.877883	+	0.478875i	$0.841045\pi$
$752$	1.79826	−	7.87867i	0.0655756	−	0.287306i
$753$	−4.86220	−	4.98185i	−0.177188	−	0.181549i
$754$		−	8.29372i		−	0.302039i
$755$	1.03360	−	4.52852i	0.0376167	−	0.164810i
$756$	−12.3374	−	6.06535i	−0.448707	−	0.220595i
$757$	−6.26954	−	27.4686i	−0.227870	−	0.998364i	−0.951373	−	0.308042i	$-0.900326\pi$
$757$	−6.26954	−	27.4686i	−0.227870	−	0.998364i	0.723502	−	0.690322i	$-0.242531\pi$
$758$	−5.56085	+	1.26923i	−0.201979	+	0.0461004i
$759$	−4.12808	+	33.0250i	−0.149840	+	1.19873i
$760$	−3.84818	−	4.82546i	−0.139588	−	0.175038i
$761$	12.7031	−	11.7867i	0.460485	−	0.427268i	−0.415509	−	0.909589i	$-0.636397\pi$
$761$	12.7031	−	11.7867i	0.460485	−	0.427268i	0.875995	+	0.482321i	$0.160206\pi$
$762$	−10.0247	−	6.47022i	−0.363158	−	0.234391i
$763$	6.26729	−	26.3555i	0.226891	−	0.954134i
$764$	−17.7943	−	4.06143i	−0.643774	−	0.146937i
$765$	−11.6600	−	7.11529i	−0.421569	−	0.257254i
$766$	−11.1926	+	6.46202i	−0.404403	+	0.233482i
$767$	18.6523	−	20.1024i	0.673496	−	0.725856i
$768$	−1.62778	−	0.591888i	−0.0587375	−	0.0213579i
$769$	7.88955	+	52.3438i	0.284505	+	1.88756i	0.437314	+	0.899309i	$0.355930\pi$
$769$	7.88955	+	52.3438i	0.284505	+	1.88756i	−0.152810	+	0.988256i	$0.548832\pi$
$770$	−4.44799	−	1.41629i	−0.160295	−	0.0510397i
$771$	7.54619	+	10.4892i	0.271769	+	0.377759i
$772$	4.92365	−	21.5719i	0.177206	−	0.776391i
$773$	−9.33728	−	1.40737i	−0.335839	−	0.0506195i	−0.0210418	−	0.999779i	$-0.506698\pi$
$773$	−9.33728	−	1.40737i	−0.335839	−	0.0506195i	−0.314797	+	0.949159i	$0.601936\pi$
$774$	−16.2413	−	11.6613i	−0.583782	−	0.419158i
$775$	−2.18800	−	14.5164i	−0.0785952	−	0.521445i
$776$	0.610268	+	8.14346i	0.0219073	+	0.292333i
$777$	−14.1711	−	7.87870i	−0.508385	−	0.282647i
$778$	1.32375	−	17.6642i	0.0474588	−	0.633294i
$779$	22.9924	−	1.72304i	0.823789	−	0.0617345i
$780$	3.33594	+	2.15310i	0.119446	+	0.0770935i
$781$	−8.98641	+	6.12683i	−0.321559	+	0.219235i
$782$	−18.1166	−	46.1604i	−0.647849	−	1.65069i
$783$	−4.18739	+	13.6205i	−0.149645	+	0.486757i
$784$	6.72530	−	1.94172i	0.240189	−	0.0693471i
$785$	−14.4848	+	8.36281i	−0.516985	+	0.298481i
$786$	1.79011	−	1.28785i	0.0638510	−	0.0459360i
$787$	−1.34912	+	2.80148i	−0.0480910	+	0.0998619i	−0.923630	−	0.383286i	$-0.874792\pi$
$787$	−1.34912	+	2.80148i	−0.0480910	+	0.0998619i	0.875539	+	0.483148i	$0.160507\pi$
$788$	−12.9771	+	2.96194i	−0.462290	+	0.105515i
$789$	8.12598	−	40.2617i	0.289293	−	1.43335i
$790$	2.90673	−	4.26340i	0.103417	−	0.151685i
$791$	−9.38948	+	0.618132i	−0.333851	+	0.0219783i
$792$	3.79238	+	5.86371i	0.134756	+	0.208358i
$793$	−0.434269	+	0.0654555i	−0.0154213	+	0.00232439i
$794$	−1.82188	+	24.3113i	−0.0646561	+	0.862775i
$795$	9.63398	+	4.34339i	0.341682	+	0.154044i
$796$	2.87852	+	9.33195i	0.102027	+	0.330762i
$797$	−15.3362	−	39.0759i	−0.543234	−	1.38414i	−0.894165	−	0.447737i	$-0.852230\pi$
$797$	−15.3362	−	39.0759i	−0.543234	−	1.38414i	0.350931	−	0.936401i	$-0.385865\pi$
$798$	−21.5165	−	30.4870i	−0.761677	−	1.07923i
$799$	17.7355	−	45.1893i	0.627437	−	1.59868i
$800$	−4.41311	−	0.330717i	−0.156027	−	0.0116926i
$801$	16.7732	−	17.2182i	0.592651	−	0.608375i
$802$	13.9286	+	24.1250i	0.491835	+	0.851883i
$803$	−38.7785			−1.36846
$804$	−10.0412	+	6.14036i	−0.354126	+	0.216554i
$805$	11.1494	+	12.2368i	0.392966	+	0.431290i
$806$	−2.95709	+	9.58666i	−0.104159	+	0.337676i
$807$	41.7316	+	2.06966i	1.46902	+	0.0728556i
$808$	0.602647	+	3.99830i	0.0212011	+	0.140660i
$809$	3.77236	+	1.48054i	0.132629	+	0.0520531i	0.430727	−	0.902482i	$-0.358257\pi$
$809$	3.77236	+	1.48054i	0.132629	+	0.0520531i	−0.298098	+	0.954535i	$0.596352\pi$
$810$	−4.39144	−	5.22025i	−0.154299	−	0.183421i
$811$	2.93209	−	0.669230i	0.102960	−	0.0234999i	−0.170731	−	0.985318i	$-0.554613\pi$
$811$	2.93209	−	0.669230i	0.102960	−	0.0234999i	0.273690	+	0.961818i	$0.411756\pi$
$812$	−3.08870	−	6.56530i	−0.108392	−	0.230397i
$813$	50.5142	−	1.27554i	1.77161	−	0.0447352i
$814$	4.11798	+	7.13256i	0.144335	+	0.249996i
$815$	−0.211669			−0.00741443
$816$	−9.13910	−	4.97318i	−0.319932	−	0.174096i
$817$	−23.5467	−	48.8953i	−0.823796	−	1.71063i
$818$	17.6188	+	22.0933i	0.616029	+	0.772475i
$819$	19.3715	+	14.1766i	0.676894	+	0.495369i
$820$	−1.33815	+	1.67799i	−0.0467303	+	0.0585980i
$821$	−18.1411	−	4.14058i	−0.633128	−	0.144507i	−0.106100	−	0.994355i	$-0.533836\pi$
$821$	−18.1411	−	4.14058i	−0.633128	−	0.144507i	−0.527028	+	0.849848i	$0.676694\pi$
$822$	−11.7907	+	26.1527i	−0.411248	+	0.912180i
$823$	−35.3428	+	17.0202i	−1.23197	+	0.593286i	−0.932621	−	0.360857i	$-0.882484\pi$
$823$	−35.3428	+	17.0202i	−1.23197	+	0.593286i	−0.299351	+	0.954143i	$0.596770\pi$
$824$	−4.25305	+	10.8366i	−0.148162	+	0.377511i
$825$	13.3817	+	11.8019i	0.465890	+	0.410891i
$826$	7.27871	−	22.8594i	0.253259	−	0.795381i
$827$	3.25752	+	6.76431i	0.113275	+	0.235218i	0.949897	−	0.312562i	$-0.101187\pi$
$827$	3.25752	+	6.76431i	0.113275	+	0.235218i	−0.836622	+	0.547780i	$0.815473\pi$
$828$	−1.24988	−	24.7333i	−0.0434365	−	0.859541i
$829$	−2.90306	−	3.12875i	−0.100827	−	0.108666i	0.680622	−	0.732635i	$-0.261710\pi$
$829$	−2.90306	−	3.12875i	−0.100827	−	0.108666i	−0.781449	+	0.623969i	$0.785519\pi$
$830$	−0.0700091	−	0.102684i	−0.00243005	−	0.00356423i
$831$	−3.33717	+	7.40211i	−0.115765	+	0.256776i
$832$	2.61913	+	1.51216i	0.0908021	+	0.0524246i
$833$	41.6868	−	5.51257i	1.44436	−	0.190999i
$834$	29.2943	−	7.46899i	1.01438	−	0.258630i
$835$	9.50298	−	11.9164i	0.328864	−	0.412383i
$836$	1.41646	+	18.9014i	0.0489894	+	0.653718i
$837$	9.69652	−	14.2509i	0.335161	−	0.492582i
$838$	−1.73057	−	2.53828i	−0.0597816	−	0.0876834i
$839$	−18.5350	−	12.6370i	−0.639900	−	0.436277i	0.199420	−	0.979914i	$-0.436094\pi$
$839$	−18.5350	−	12.6370i	−0.639900	−	0.436277i	−0.839320	+	0.543638i	$0.817047\pi$
$840$	3.44258	+	0.462040i	0.118780	+	0.0159419i
$841$	17.7472	−	12.0999i	0.611973	−	0.417236i
$842$	−20.6241	−	8.09435i	−0.710752	−	0.278950i
$843$	45.3555	−	8.01201i	1.56213	−	0.275948i
$844$	2.09156	+	5.32920i	0.0719944	+	0.183439i
$845$	2.14113	+	1.98668i	0.0736570	+	0.0683437i
$846$	15.5720	−	18.5816i	0.535378	−	0.638849i
$847$	−9.10245	−	11.6287i	−0.312764	−	0.399568i
$848$	7.49315	+	2.94085i	0.257316	+	0.100989i
$849$	−8.89481	+	24.4621i	−0.305269	+	0.839536i
$850$	−25.9178	−	5.91557i	−0.888973	−	0.202902i
$851$		−	29.2075i		−	1.00122i
$852$	5.79171	−	5.65261i	0.198421	−	0.193655i
$853$	3.13683	+	10.1694i	0.107403	+	0.348192i	0.993281	−	0.115726i	$-0.0369194\pi$
$853$	3.13683	+	10.1694i	0.107403	+	0.348192i	−0.885878	+	0.463918i	$0.846443\pi$
$854$	−0.319390	+	0.213543i	−0.0109293	+	0.00730728i
$855$	−3.68022	−	18.1466i	−0.125861	−	0.620600i
$856$	−6.42082	−	1.98056i	−0.219459	−	0.0676942i
$857$	12.9983	−	1.95917i	0.444012	−	0.0669240i	0.0767687	−	0.997049i	$-0.475540\pi$
$857$	12.9983	−	1.95917i	0.444012	−	0.0669240i	0.367243	+	0.930125i	$0.380302\pi$
$858$	−4.73982	−	11.2344i	−0.161815	−	0.383535i
$859$	−18.2047	−	19.6200i	−0.621137	−	0.669427i	0.341606	−	0.939843i	$-0.389029\pi$
$859$	−18.2047	−	19.6200i	−0.621137	−	0.669427i	−0.962743	+	0.270416i	$0.912839\pi$
$860$	4.82722	+	1.48900i	0.164607	+	0.0507745i
$861$	−8.67072	+	9.65354i	−0.295497	+	0.328992i
$862$	−13.3871	+	4.12937i	−0.455966	+	0.140647i
$863$	5.11163	+	2.95120i	0.174002	+	0.100460i	0.584471	−	0.811414i	$-0.301302\pi$
$863$	5.11163	+	2.95120i	0.174002	+	0.100460i	−0.410470	+	0.911874i	$0.634635\pi$
$864$	−3.53785	−	3.80573i	−0.120360	−	0.129474i
$865$	−14.3244	+	4.41848i	−0.487043	+	0.150233i
$866$	−24.0964	+	11.6042i	−0.818830	+	0.394328i
$867$	−26.3567	−	19.9515i	−0.895121	−	0.677587i
$868$	1.22938	+	8.69006i	0.0417280	+	0.294960i
$869$	−14.7511	+	5.78938i	−0.500397	+	0.196391i
$870$	−0.0908817	−	3.59911i	−0.00308118	−	0.122021i
$871$	19.1306	−	7.50822i	0.648216	−	0.254406i
$872$	5.76796	−	8.46004i	0.195328	−	0.286493i
$873$	−9.50210	+	22.5811i	−0.321597	+	0.764253i
$874$	29.1651	−	60.5619i	0.986523	−	2.04854i
$875$	18.7155	−	2.64768i	0.632698	−	0.0895078i
$876$	28.4148	−	5.01945i	0.960047	−	0.169592i
$877$	−0.941786	−	12.5673i	−0.0318019	−	0.424366i	−0.990269	−	0.139164i	$-0.955558\pi$
$877$	−0.941786	−	12.5673i	−0.0318019	−	0.424366i	0.958467	−	0.285202i	$-0.0920607\pi$
$878$	−4.51365	−	19.7756i	−0.152328	−	0.667394i
$879$	41.0090	+	8.27680i	1.38320	+	0.279170i
$880$	−1.37943	−	1.10005i	−0.0465004	−	0.0370828i
$881$	−19.5438			−0.658448			−0.329224	−	0.944252i	$-0.606787\pi$
$881$	−19.5438			−0.658448			−0.329224	+	0.944252i	$0.606787\pi$
$882$	20.6140	+	4.00794i	0.694109	+	0.134954i
$883$	40.8366			1.37426			0.687130	−	0.726534i	$-0.258870\pi$
$883$	40.8366			1.37426			0.687130	+	0.726534i	$0.258870\pi$
$884$	14.2038	+	11.3272i	0.477726	+	0.380974i
$885$	7.87400	−	8.92795i	0.264682	−	0.300110i
$886$	2.89276	+	12.6740i	0.0971842	+	0.425792i
$887$	−1.67459	−	22.3458i	−0.0562271	−	0.750298i	−0.952061	−	0.305909i	$-0.901040\pi$
$887$	−1.67459	−	22.3458i	−0.0562271	−	0.750298i	0.895834	−	0.444389i	$-0.146579\pi$
$888$	−3.94067	−	4.69333i	−0.132240	−	0.157498i
$889$	17.3665	+	5.52968i	0.582452	+	0.185460i
$890$	−2.63508	+	5.47180i	−0.0883281	+	0.183415i
$891$	2.11197	+	20.8429i	0.0707536	+	0.698264i
$892$	4.13086	−	6.05886i	0.138311	−	0.202866i
$893$	61.2557	−	24.0411i	2.04984	−	0.804504i
$894$	−19.5129	−	10.6183i	−0.652610	−	0.355128i
$895$	−5.64835	+	2.21681i	−0.188803	+	0.0740999i
$896$	2.63645	+	0.221618i	0.0880777	+	0.00740374i
$897$	−5.36342	+	42.9077i	−0.179079	+	1.43265i
$898$	−29.9005	+	14.3993i	−0.997791	+	0.480511i
$899$	8.69286	−	2.68139i	0.289923	−	0.0894294i
$900$	−11.3330	−	6.91573i	−0.377767	−	0.230524i
$901$	41.8764	+	24.1773i	1.39510	+	0.805464i
$902$	6.29831	−	1.94277i	0.209711	−	0.0646872i
$903$	28.6072	+	10.6966i	0.951989	+	0.355959i
$904$	−3.39856	−	1.04832i	−0.113035	−	0.0348665i
$905$	−3.68544	−	3.97196i	−0.122508	−	0.132032i
$906$	6.40635	−	8.46305i	0.212837	−	0.281166i
$907$	−12.4961	+	1.88348i	−0.414926	+	0.0625400i	−0.353188	−	0.935552i	$-0.614902\pi$
$907$	−12.4961	+	1.88348i	−0.414926	+	0.0625400i	−0.0617377	+	0.998092i	$0.519664\pi$
$908$	−18.5459	−	5.72064i	−0.615466	−	0.189846i
$909$	−3.85618	+	11.5011i	−0.127901	+	0.381469i
$910$	−5.77906	−	1.84012i	−0.191574	−	0.0609994i
$911$	−9.70177	−	31.4524i	−0.321434	−	1.04206i	−0.961745	−	0.273948i	$-0.911671\pi$
$911$	−9.70177	−	31.4524i	−0.321434	−	1.04206i	0.640311	−	0.768116i	$-0.278806\pi$
$912$	−3.48449	−	13.6666i	−0.115383	−	0.452546i
$913$			0.381665i			0.0126313i
$914$	28.9052	+	6.59742i	0.956098	+	0.218223i
$915$	−0.187737	+	0.0331635i	−0.00620638	+	0.00109635i
$916$	−19.4668	−	7.64015i	−0.643201	−	0.252438i
$917$	−2.12403	+	2.61449i	−0.0701417	+	0.0863381i
$918$	−17.6075	−	25.7736i	−0.581135	−	0.850654i
$919$	9.28236	+	8.61277i	0.306197	+	0.284109i	0.818272	−	0.574832i	$-0.194933\pi$
$919$	9.28236	+	8.61277i	0.306197	+	0.284109i	−0.512075	+	0.858941i	$0.671123\pi$
$920$	2.28593	+	5.82446i	0.0753650	+	0.192027i
$921$	11.9713	−	32.9230i	0.394469	−	1.08485i
$922$	−3.03120	−	1.18966i	−0.0998272	−	0.0391793i
$923$	−11.6756	+	7.96029i	−0.384307	+	0.262016i
$924$	−7.93588	−	7.12794i	−0.261071	−	0.234492i
$925$	−12.9374	−	8.82057i	−0.425379	−	0.290018i
$926$	−19.6370	−	28.8022i	−0.645313	−	0.946500i
$927$	−26.1709	+	23.1251i	−0.859564	+	0.759526i
$928$	−0.204936	−	2.73468i	−0.00672735	−	0.0897702i
$929$	15.0661	−	18.8923i	0.494302	−	0.619836i	−0.470631	−	0.882330i	$-0.655974\pi$
$929$	15.0661	−	18.8923i	0.494302	−	0.619836i	0.964934	+	0.262494i	$0.0845451\pi$
$930$	−1.17820	+	4.19260i	−0.0386347	+	0.137481i
$931$	43.9128	+	36.3406i	1.43918	+	1.19102i
$932$	13.3750	+	7.72207i	0.438113	+	0.252945i
$933$	37.9669	−	3.81115i	1.24298	−	0.124771i
$934$	0.212694	+	0.311964i	0.00695955	+	0.0102078i
$935$	−7.20890	−	7.76934i	−0.235756	−	0.254085i
$936$	4.92726	+	7.61843i	0.161052	+	0.249016i
$937$	−4.96554	−	10.3111i	−0.162217	−	0.336848i	0.803978	−	0.594659i	$-0.202713\pi$
$937$	−4.96554	−	10.3111i	−0.162217	−	0.336848i	−0.966195	+	0.257811i	$0.916999\pi$
$938$	12.3476	−	13.0680i	0.403164	−	0.426686i
$939$	−10.7707	+	3.62250i	−0.351488	+	0.118216i
$940$	−2.23784	+	5.70193i	−0.0729904	+	0.185976i
$941$	−44.7525	+	21.5516i	−1.45889	+	0.702564i	−0.984113	−	0.177543i	$-0.943185\pi$
$941$	−44.7525	+	21.5516i	−1.45889	+	0.702564i	−0.474775	+	0.880107i	$0.657471\pi$
$942$	−38.0290	+	3.81738i	−1.23905	+	0.124377i
$943$	−22.7883	−	5.20129i	−0.742090	−	0.169377i
$944$	5.65348	−	7.08924i	0.184005	−	0.230735i
$945$	8.56171	+	5.93974i	0.278512	+	0.193220i
$946$	−9.67266	−	12.1291i	−0.314485	−	0.394352i
$947$	6.81030	+	14.1417i	0.221305	+	0.459544i	0.981830	−	0.189765i	$-0.0607725\pi$
$947$	6.81030	+	14.1417i	0.221305	+	0.459544i	−0.760525	+	0.649309i	$0.775058\pi$
$948$	10.0594	−	6.15152i	0.326716	−	0.199792i
$949$	−50.3830			−1.63550
$950$	−18.0180	−	31.2081i	−0.584580	−	1.01252i
$951$	−12.5681	−	20.5523i	−0.407548	−	0.666455i
$952$	15.4621	+	3.67686i	0.501130	+	0.119168i
$953$	26.1288	−	5.96373i	0.846395	−	0.193184i	0.222734	−	0.974879i	$-0.428502\pi$
$953$	26.1288	−	5.96373i	0.846395	−	0.193184i	0.623661	+	0.781695i	$0.285645\pi$
$954$	15.9902	+	18.0963i	0.517702	+	0.585889i
$955$	12.8780	+	5.05425i	0.416723	+	0.163552i
$956$	−0.442881	−	2.93832i	−0.0143238	−	0.0950321i
$957$	−5.99575	+	9.28961i	−0.193815	+	0.300290i
$958$	−10.3831	+	33.6611i	−0.335462	+	1.08754i
$959$	6.92362	−	43.2708i	0.223575	−	1.39729i
$960$	1.15316	+	0.627510i	0.0372181	+	0.0202528i
$961$	19.9959			0.645030
$962$	5.35029	+	9.26698i	0.172500	+	0.298779i
$963$	−14.4393	−	14.0661i	−0.465299	−	0.453272i
$964$	20.2140	+	1.51483i	0.651049	+	0.0487894i
$965$	−6.12725	+	15.6120i	−0.197243	+	0.502567i
$966$	11.7338	+	35.9631i	0.377529	+	1.15709i
$967$	−9.47665	−	24.1461i	−0.304748	−	0.776486i	−0.998420	−	0.0561946i	$-0.982103\pi$
$967$	−9.47665	−	24.1461i	−0.304748	−	0.776486i	0.693671	−	0.720292i	$-0.255992\pi$
$968$	−1.64521	−	5.33366i	−0.0528792	−	0.171430i
$969$	−8.46202	−	84.2992i	−0.271839	−	2.70808i
$970$	0.462563	−	6.17248i	0.0148520	−	0.198186i
$971$	−3.54656	+	0.534558i	−0.113814	+	0.0171548i	−0.205702	−	0.978615i	$-0.565948\pi$
$971$	−3.54656	+	0.534558i	−0.113814	+	0.0171548i	0.0918880	+	0.995769i	$0.470710\pi$
$972$	−4.24543	−	14.9992i	−0.136172	−	0.481100i
$973$	−40.2000	+	22.7263i	−1.28875	+	0.728571i
$974$	18.5437	−	27.1986i	0.594178	−	0.871500i
$975$	17.3861	+	15.3337i	0.556802	+	0.491071i
$976$	−0.141574	+	0.0323133i	−0.00453166	+	0.00103432i
$977$	−15.5079	+	32.2024i	−0.496140	+	1.03025i	0.491114	+	0.871095i	$0.336590\pi$
$977$	−15.5079	+	32.2024i	−0.496140	+	1.03025i	−0.987254	+	0.159151i	$0.949124\pi$
$978$	−0.440948	−	0.198797i	−0.0141000	−	0.00635684i
$979$	16.1523	−	9.32554i	0.516230	−	0.298046i
$980$	−5.25998	+	0.695570i	−0.168024	+	0.0222192i
$981$	26.9677	−	14.7077i	0.861014	−	0.469581i
$982$	−8.29994	−	21.1479i	−0.264862	−	0.674857i
$983$	−3.55134	+	2.42126i	−0.113270	+	0.0772263i	−0.618630	−	0.785682i	$-0.712312\pi$
$983$	−3.55134	+	2.42126i	−0.113270	+	0.0772263i	0.505360	+	0.862909i	$0.331360\pi$
$984$	−4.36359	+	2.23881i	−0.139106	+	0.0713705i
$985$	10.0610	−	0.753965i	0.320569	−	0.0240233i
$986$	1.23107	−	16.4275i	0.0392052	−	0.523157i
$987$	−15.5260	+	33.6213i	−0.494198	+	1.07018i
$988$	1.84034	+	24.5576i	0.0585490	+	0.781282i
$989$	8.19985	+	54.4025i	0.260740	+	1.72990i
$990$	−2.17998	−	4.82329i	−0.0692843	−	0.153294i
$991$	−30.9625	−	4.66684i	−0.983555	−	0.148247i	−0.362475	−	0.931994i	$-0.618068\pi$
$991$	−30.9625	−	4.66684i	−0.983555	−	0.148247i	−0.621081	+	0.783747i	$0.713306\pi$
$992$	−0.738155	+	3.23407i	−0.0234364	+	0.102682i
$993$	−2.40019	+	0.240933i	−0.0761677	+	0.00764577i
$994$	−6.27786	+	10.6495i	−0.199122	+	0.337782i
$995$	−1.10324	−	7.31950i	−0.0349750	−	0.232044i
$996$	−0.0494024	−	0.279664i	−0.00156538	−	0.00886149i
$997$	15.8513	−	17.0836i	0.502015	−	0.541043i	−0.430302	−	0.902685i	$-0.641593\pi$
$997$	15.8513	−	17.0836i	0.502015	−	0.541043i	0.932317	+	0.361641i	$0.117784\pi$
$998$	5.24467	−	3.02801i	0.166017	−	0.0958500i
$999$	−4.10784	−	17.9202i	−0.129966	−	0.566969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bk.a.131.40	yes	672
9.2	odd	6		882.2.bc.a.425.14	✓	672
49.3	odd	42		882.2.bc.a.689.14	yes	672
441.101	even	42	inner	882.2.bk.a.101.40	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bc.a.425.14	✓	672	9.2	odd	6
882.2.bc.a.689.14	yes	672	49.3	odd	42
882.2.bk.a.101.40	yes	672	441.101	even	42	inner
882.2.bk.a.131.40	yes	672	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bk (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-0.552148 - 1.64169i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.0566430 - 0.755848i) q^{5} +(0.591888 - 1.62778i) q^{6} +(-0.221618 + 2.63645i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-2.39026 + 1.81291i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(-0.552148 - 1.64169i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.0566430 - 0.755848i) q^{5} +(0.591888 - 1.62778i) q^{6} +(-0.221618 + 2.63645i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-2.39026 + 1.81291i) q^{9} +(0.426978 - 0.626262i) q^{10} +(-2.16683 + 0.850419i) q^{11} +(1.47766 - 0.903614i) q^{12} +(-2.81526 + 1.10491i) q^{13} +(-1.81707 + 1.92309i) q^{14} +(-1.20959 + 0.510330i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-5.74022 + 1.77062i) q^{17} +(-2.99911 - 0.0729175i) q^{18} +(-7.05190 - 4.07141i) q^{19} +(0.724293 - 0.223415i) q^{20} +(4.45059 - 1.09189i) q^{21} +(-2.22432 - 0.686113i) q^{22} +(5.61479 + 6.05131i) q^{23} +(1.71868 + 0.214833i) q^{24} +(4.37606 - 0.659584i) q^{25} +(-2.88995 - 0.891433i) q^{26} +(4.29601 + 2.92307i) q^{27} +(-2.61967 + 0.370604i) q^{28} +(0.808321 + 2.62051i) q^{29} +(-1.26388 - 0.355175i) q^{30} -3.31724i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.59253 + 3.08770i) q^{33} +(-5.59185 - 2.19464i) q^{34} +(2.00531 + 0.0181731i) q^{35} +(-2.29934 - 1.92693i) q^{36} +(-2.59367 - 2.40658i) q^{37} +(-2.97491 - 7.57994i) q^{38} +(3.36835 + 4.01169i) q^{39} +(0.705572 + 0.276917i) q^{40} +(-2.33954 + 1.59507i) q^{41} +(4.16039 + 1.92123i) q^{42} +(5.50666 + 3.75437i) q^{43} +(-1.31126 - 1.92327i) q^{44} +(1.50567 + 1.70399i) q^{45} +(0.616893 + 8.23187i) q^{46} +(-5.03860 + 6.31820i) q^{47} +(1.20977 + 1.23954i) q^{48} +(-6.90177 - 1.16857i) q^{49} +(3.83258 + 2.21274i) q^{50} +(6.07626 + 8.44599i) q^{51} +(-1.70366 - 2.49881i) q^{52} +(-5.47511 - 5.90077i) q^{53} +(1.53625 + 4.96386i) q^{54} +(0.765523 + 1.58963i) q^{55} +(-2.27921 - 1.34359i) q^{56} +(-2.79029 + 13.8250i) q^{57} +(-1.00189 + 2.55278i) q^{58} +(-8.16951 + 3.93423i) q^{59} +(-0.766694 - 1.06570i) q^{60} +(0.141574 + 0.0323133i) q^{61} +(2.06826 - 2.59352i) q^{62} +(-4.24992 - 6.70359i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(0.994606 + 2.06532i) q^{65} +(0.101774 + 4.03048i) q^{66} -6.79534 q^{67} +(-3.00355 - 5.20230i) q^{68} +(6.83415 - 12.5589i) q^{69} +(1.55649 + 1.26450i) q^{70} +(4.55532 - 1.03972i) q^{71} +(-0.596276 - 2.94015i) q^{72} +(15.5077 + 6.08632i) q^{73} +(-0.527339 - 3.49867i) q^{74} +(-3.49906 - 6.81992i) q^{75} +(2.40014 - 7.78106i) q^{76} +(-1.76188 - 5.90122i) q^{77} +(0.132230 + 5.23660i) q^{78} +6.80768 q^{79} +(0.378984 + 0.656419i) q^{80} +(2.42673 - 8.66666i) q^{81} +(-2.82364 - 0.211603i) q^{82} +(0.0599028 - 0.152630i) q^{83} +(2.05486 + 4.09604i) q^{84} +(1.66347 + 4.23844i) q^{85} +(1.96446 + 6.36863i) q^{86} +(3.85574 - 2.77392i) q^{87} +(0.173952 - 2.32123i) q^{88} +(-7.92304 + 1.19421i) q^{89} +(0.114764 + 2.27101i) q^{90} +(-2.28912 - 7.66716i) q^{91} +(-4.65018 + 6.82056i) q^{92} +(-5.44586 + 1.83161i) q^{93} +(-7.87867 + 1.79826i) q^{94} +(-2.67793 + 5.56078i) q^{95} +(0.172995 + 1.72339i) q^{96} +(7.07221 - 4.08315i) q^{97} +(-4.66743 - 5.21681i) q^{98} +(3.63757 - 5.96099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9	\( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) \) 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^15 - 112 * q^16 + 18 * q^17 + 8 * q^18 + 12 * q^21 + 18 * q^23 + 56 * q^25 - 12 * q^26 + 48 * q^27 + 2 * q^28 - 6 * q^29 + 4 * q^30 - 30 * q^35 - 10 * q^36 - 26 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^42 + 2 * q^43 + 58 * q^45 + 78 * q^46 - 90 * q^47 + 8 * q^49 + 24 * q^50 + 6 * q^51 - 22 * q^52 + 12 * q^53 - 18 * q^54 - 42 * q^55 - 6 * q^56 - 28 * q^57 + 78 * q^58 - 60 * q^59 - 6 * q^60 + 98 * q^61 - 36 * q^62 - 36 * q^63 + 112 * q^64 - 24 * q^66 + 28 * q^67 - 18 * q^68 + 14 * q^69 + 18 * q^70 + 126 * q^71 - 8 * q^72 - 18 * q^74 - 102 * q^75 + 42 * q^77 - 8 * q^78 - 8 * q^79 + 26 * q^81 + 30 * q^84 + 80 * q^87 - 186 * q^89 - 102 * q^90 + 12 * q^91 - 18 * q^92 - 224 * q^93 - 6 * q^97 + 24 * q^98 + 194 * q^99

Introduction

L-functions

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