LMFDB - Embedded newform 570.2.bb.a.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (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:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.a.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.70290 + 0.316445i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.49197 - 0.879786i) q^{6} +(-1.40312 - 2.43028i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.79973 - 1.07775i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70290 + 0.316445i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.49197 - 0.879786i) q^{6} +(-1.40312 - 2.43028i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.79973 - 1.07775i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(2.54956 + 1.47199i) q^{11} +(-1.10109 + 1.33701i) q^{12} +(-3.36962 + 0.594154i) q^{13} +(2.14971 + 1.80382i) q^{14} +(-0.852191 + 1.50790i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.0612457 - 0.168271i) q^{17} +(-2.26227 + 1.97031i) q^{18} +(-4.29273 - 0.756593i) q^{19} -1.00000i q^{20} +(3.15842 + 3.69451i) q^{21} +(-2.89925 - 0.511216i) q^{22} +(0.509670 + 0.607401i) q^{23} +(0.577400 - 1.63298i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(2.96319 - 1.71080i) q^{26} +(-4.42660 + 2.72125i) q^{27} +(-2.63701 - 0.959792i) q^{28} +(-0.910982 - 0.331570i) q^{29} +(0.285065 - 1.70843i) q^{30} +(-6.29928 + 3.63689i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.80744 - 1.69985i) q^{33} +(0.115104 + 0.137176i) q^{34} +(-2.76361 - 0.487299i) q^{35} +(1.45195 - 2.62523i) q^{36} -6.44330i q^{37} +(4.29262 - 0.757237i) q^{38} +(5.55010 - 2.07808i) q^{39} +(0.342020 + 0.939693i) q^{40} +(1.59026 - 9.01881i) q^{41} +(-4.23154 - 2.39146i) q^{42} +(-8.49079 - 7.12462i) q^{43} +(2.89925 - 0.511216i) q^{44} +(0.974027 - 2.83748i) q^{45} +(-0.686676 - 0.396453i) q^{46} +(0.0674464 - 0.185308i) q^{47} +(0.0159322 + 1.73198i) q^{48} +(-0.437502 + 0.757775i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.157544 + 0.267168i) q^{51} +(-2.19936 + 2.62110i) q^{52} +(-4.35018 + 3.65024i) q^{53} +(3.22892 - 4.07113i) q^{54} +(2.76643 - 1.00690i) q^{55} +2.80624 q^{56} +(7.54951 - 0.0700129i) q^{57} +0.969446 q^{58} +(-13.0683 + 4.75646i) q^{59} +(0.316445 + 1.70290i) q^{60} +(-0.563021 + 0.472431i) q^{61} +(4.67549 - 5.57204i) q^{62} +(-6.54758 - 5.29190i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.71080 + 2.96319i) q^{65} +(5.09890 - 0.0469041i) q^{66} +(1.87423 - 5.14941i) q^{67} +(-0.155080 - 0.0895352i) q^{68} +(-1.06012 - 0.873060i) q^{69} +(2.76361 - 0.487299i) q^{70} +(-7.97550 - 6.69224i) q^{71} +(-0.466506 + 2.96351i) q^{72} +(-0.0632772 + 0.358863i) q^{73} +(2.20374 + 6.05472i) q^{74} +(0.607343 + 1.62208i) q^{75} +(-3.77475 + 2.17973i) q^{76} -8.26151i q^{77} +(-4.50464 + 3.85100i) q^{78} +(-5.27331 - 0.929827i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(6.67692 - 6.03479i) q^{81} +(1.59026 + 9.01881i) q^{82} +(-11.2590 + 6.50039i) q^{83} +(4.79428 + 0.799961i) q^{84} +(-0.168271 - 0.0612457i) q^{85} +(10.4155 + 3.79093i) q^{86} +(1.65623 + 0.276355i) q^{87} +(-2.54956 + 1.47199i) q^{88} +(2.29593 + 13.0209i) q^{89} +(0.0551885 + 2.99949i) q^{90} +(6.17194 + 7.35543i) q^{91} +(0.780860 + 0.137687i) q^{92} +(9.57615 - 8.18663i) q^{93} +0.197200i q^{94} +(-3.33890 + 2.80210i) q^{95} +(-0.607343 - 1.62208i) q^{96} +(3.38911 + 9.31151i) q^{97} +(0.151943 - 0.861710i) q^{98} +(8.72449 + 1.37338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−1.70290	+	0.316445i	−0.983169	+	0.182700i
$3$	−1.70290	+	0.316445i	−0.983169	+	0.182700i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$6$	1.49197	−	0.879786i	0.609094	−	0.359171i
$7$	−1.40312	−	2.43028i	−0.530330	−	0.918559i	−0.999374	−	0.0353838i	$-0.988735\pi$
$7$	−1.40312	−	2.43028i	−0.530330	−	0.918559i	0.469044	−	0.883175i	$-0.344599\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.79973	−	1.07775i	0.933242	−	0.359249i
$10$	−0.342020	+	0.939693i	−0.108156	+	0.297157i
$11$	2.54956	+	1.47199i	0.768721	+	0.443821i	0.832418	−	0.554148i	$-0.186956\pi$
$11$	2.54956	+	1.47199i	0.768721	+	0.443821i	−0.0636974	+	0.997969i	$0.520289\pi$
$12$	−1.10109	+	1.33701i	−0.317857	+	0.385962i
$13$	−3.36962	+	0.594154i	−0.934563	+	0.164789i	−0.620137	−	0.784493i	$-0.712923\pi$
$13$	−3.36962	+	0.594154i	−0.934563	+	0.164789i	−0.314426	+	0.949282i	$0.601812\pi$
$14$	2.14971	+	1.80382i	0.574533	+	0.482091i
$15$	−0.852191	+	1.50790i	−0.220035	+	0.389339i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.0612457	−	0.168271i	−0.0148543	−	0.0408117i	0.932044	−	0.362345i	$-0.118024\pi$
$17$	−0.0612457	−	0.168271i	−0.0148543	−	0.0408117i	−0.946898	+	0.321534i	$0.895802\pi$
$18$	−2.26227	+	1.97031i	−0.533222	+	0.464407i
$19$	−4.29273	−	0.756593i	−0.984821	−	0.173574i
$19$	−4.29273	−	0.756593i	−0.984821	−	0.173574i
$20$		−	1.00000i		−	0.223607i
$21$	3.15842	+	3.69451i	0.689224	+	0.806207i
$22$	−2.89925	−	0.511216i	−0.618122	−	0.108992i
$23$	0.509670	+	0.607401i	0.106274	+	0.126652i	0.816559	−	0.577262i	$-0.195879\pi$
$23$	0.509670	+	0.607401i	0.106274	+	0.126652i	−0.710286	+	0.703913i	$0.751434\pi$
$24$	0.577400	−	1.63298i	0.117861	−	0.333330i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	2.96319	−	1.71080i	0.581129	−	0.335515i
$27$	−4.42660	+	2.72125i	−0.851900	+	0.523705i
$28$	−2.63701	−	0.959792i	−0.498347	−	0.181384i
$29$	−0.910982	−	0.331570i	−0.169165	−	0.0615710i	0.256049	−	0.966664i	$-0.417579\pi$
$29$	−0.910982	−	0.331570i	−0.169165	−	0.0615710i	−0.425214	+	0.905093i	$0.639801\pi$
$30$	0.285065	−	1.70843i	0.0520454	−	0.311915i
$31$	−6.29928	+	3.63689i	−1.13138	+	0.653205i	−0.944282	−	0.329136i	$-0.893242\pi$
$31$	−6.29928	+	3.63689i	−1.13138	+	0.653205i	−0.187101	+	0.982341i	$0.559909\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−4.80744	−	1.69985i	−0.836868	−	0.295906i
$34$	0.115104	+	0.137176i	0.0197402	+	0.0235255i
$35$	−2.76361	−	0.487299i	−0.467135	−	0.0823686i
$36$	1.45195	−	2.62523i	0.241992	−	0.437538i
$37$		−	6.44330i		−	1.05927i	−0.848225	−	0.529636i	$-0.822329\pi$
$37$		−	6.44330i		−	1.05927i	0.848225	−	0.529636i	$-0.177671\pi$
$38$	4.29262	−	0.757237i	0.696355	−	0.122840i
$39$	5.55010	−	2.07808i	0.888727	−	0.332759i
$40$	0.342020	+	0.939693i	0.0540781	+	0.148578i
$41$	1.59026	−	9.01881i	0.248357	−	1.40850i	−0.564209	−	0.825632i	$-0.690819\pi$
$41$	1.59026	−	9.01881i	0.248357	−	1.40850i	0.812566	−	0.582869i	$-0.198070\pi$
$42$	−4.23154	−	2.39146i	−0.652941	−	0.369010i
$43$	−8.49079	−	7.12462i	−1.29483	−	1.08649i	−0.991013	−	0.133765i	$-0.957293\pi$
$43$	−8.49079	−	7.12462i	−1.29483	−	1.08649i	−0.303820	−	0.952729i	$-0.598262\pi$
$44$	2.89925	−	0.511216i	0.437078	−	0.0770687i
$45$	0.974027	−	2.83748i	0.145199	−	0.422986i
$46$	−0.686676	−	0.396453i	−0.101245	−	0.0584538i
$47$	0.0674464	−	0.185308i	0.00983807	−	0.0270299i	−0.934676	−	0.355500i	$-0.884311\pi$
$47$	0.0674464	−	0.185308i	0.00983807	−	0.0270299i	0.944514	+	0.328470i	$0.106533\pi$
$48$	0.0159322	+	1.73198i	0.00229962	+	0.249989i
$49$	−0.437502	+	0.757775i	−0.0625003	+	0.108254i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.157544	+	0.267168i	0.0220605	+	0.0374110i
$52$	−2.19936	+	2.62110i	−0.304996	+	0.363481i
$53$	−4.35018	+	3.65024i	−0.597544	+	0.501399i	−0.890655	−	0.454680i	$-0.849754\pi$
$53$	−4.35018	+	3.65024i	−0.597544	+	0.501399i	0.293111	+	0.956078i	$0.405309\pi$
$54$	3.22892	−	4.07113i	0.439400	−	0.554010i
$55$	2.76643	−	1.00690i	0.373026	−	0.135770i
$56$	2.80624			0.375000
$57$	7.54951	−	0.0700129i	0.999957	−	0.00927343i
$58$	0.969446			0.127295
$59$	−13.0683	+	4.75646i	−1.70134	+	0.619238i	−0.995977	−	0.0896064i	$-0.971439\pi$
$59$	−13.0683	+	4.75646i	−1.70134	+	0.619238i	−0.705365	+	0.708844i	$0.749217\pi$
$60$	0.316445	+	1.70290i	0.0408529	+	0.219843i
$61$	−0.563021	+	0.472431i	−0.0720874	+	0.0604885i	−0.678119	−	0.734952i	$-0.737205\pi$
$61$	−0.563021	+	0.472431i	−0.0720874	+	0.0604885i	0.606032	+	0.795440i	$0.292760\pi$
$62$	4.67549	−	5.57204i	0.593788	−	0.707649i
$63$	−6.54758	−	5.29190i	−0.824918	−	0.666717i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.71080	+	2.96319i	−0.212198	+	0.367539i
$66$	5.09890	−	0.0469041i	0.627631	−	0.00577349i
$67$	1.87423	−	5.14941i	0.228974	−	0.629101i	−0.770996	−	0.636840i	$-0.780241\pi$
$67$	1.87423	−	5.14941i	0.228974	−	0.629101i	0.999970	+	0.00773916i	$0.00246348\pi$
$68$	−0.155080	−	0.0895352i	−0.0188062	−	0.0108577i
$69$	−1.06012	−	0.873060i	−0.127624	−	0.105104i
$70$	2.76361	−	0.487299i	0.330315	−	0.0582434i
$71$	−7.97550	−	6.69224i	−0.946518	−	0.794223i	0.0321896	−	0.999482i	$-0.489752\pi$
$71$	−7.97550	−	6.69224i	−0.946518	−	0.794223i	−0.978708	+	0.205259i	$0.934196\pi$
$72$	−0.466506	+	2.96351i	−0.0549783	+	0.349253i
$73$	−0.0632772	+	0.358863i	−0.00740603	+	0.0420017i	−0.988287	−	0.152608i	$-0.951233\pi$
$73$	−0.0632772	+	0.358863i	−0.00740603	+	0.0420017i	0.980881	+	0.194610i	$0.0623440\pi$
$74$	2.20374	+	6.05472i	0.256179	+	0.703847i
$75$	0.607343	+	1.62208i	0.0701299	+	0.187301i
$76$	−3.77475	+	2.17973i	−0.432994	+	0.250032i
$77$		−	8.26151i		−	0.941487i
$78$	−4.50464	+	3.85100i	−0.510050	+	0.436040i
$79$	−5.27331	−	0.929827i	−0.593294	−	0.104614i	−0.131064	−	0.991374i	$-0.541839\pi$
$79$	−5.27331	−	0.929827i	−0.593294	−	0.104614i	−0.462230	+	0.886760i	$0.652950\pi$
$80$	−0.642788	−	0.766044i	−0.0718658	−	0.0856464i
$81$	6.67692	−	6.03479i	0.741880	−	0.670532i
$82$	1.59026	+	9.01881i	0.175615	+	0.995960i
$83$	−11.2590	+	6.50039i	−1.23584	+	0.713510i	−0.968240	−	0.250021i	$-0.919563\pi$
$83$	−11.2590	+	6.50039i	−1.23584	+	0.713510i	−0.267596	+	0.963531i	$0.586229\pi$
$84$	4.79428	+	0.799961i	0.523098	+	0.0872829i
$85$	−0.168271	−	0.0612457i	−0.0182516	−	0.00664303i
$86$	10.4155	+	3.79093i	1.12313	+	0.408787i
$87$	1.65623	+	0.276355i	0.177567	+	0.0296283i
$88$	−2.54956	+	1.47199i	−0.271784	+	0.156914i
$89$	2.29593	+	13.0209i	0.243368	+	1.38021i	0.824253	+	0.566222i	$0.191595\pi$
$89$	2.29593	+	13.0209i	0.243368	+	1.38021i	−0.580885	+	0.813986i	$0.697293\pi$
$90$	0.0551885	+	2.99949i	0.00581738	+	0.316174i
$91$	6.17194	+	7.35543i	0.646995	+	0.771059i
$92$	0.780860	+	0.137687i	0.0814102	+	0.0143548i
$93$	9.57615	−	8.18663i	0.993001	−	0.848914i
$94$			0.197200i			0.0203396i
$95$	−3.33890	+	2.80210i	−0.342564	+	0.287489i
$96$	−0.607343	−	1.62208i	−0.0619866	−	0.165553i
$97$	3.38911	+	9.31151i	0.344112	+	0.945440i	0.984188	+	0.177128i	$0.0566808\pi$
$97$	3.38911	+	9.31151i	0.344112	+	0.945440i	−0.640076	+	0.768312i	$0.721097\pi$
$98$	0.151943	−	0.861710i	0.0153485	−	0.0870459i
$99$	8.72449	+	1.37338i	0.876845	+	0.138030i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	7.59289	−	1.33883i	0.755521	−	0.133219i	0.217395	−	0.976084i	$-0.430244\pi$
$101$	7.59289	−	1.33883i	0.755521	−	0.133219i	0.538125	+	0.842865i	$0.319133\pi$
$102$	−0.239419	−	0.197172i	−0.0237061	−	0.0195230i
$103$	−2.73049	−	1.57645i	−0.269043	−	0.155332i	0.359410	−	0.933180i	$-0.382978\pi$
$103$	−2.73049	−	1.57645i	−0.269043	−	0.155332i	−0.628453	+	0.777848i	$0.716311\pi$
$104$	1.17026	−	3.21525i	0.114753	−	0.315281i
$105$	4.86035	−	0.0447097i	0.474322	−	0.00436322i
$106$	2.83938	−	4.91795i	0.275785	−	0.477674i
$107$	4.83981	+	8.38280i	0.467882	+	0.810396i	0.999326	−	0.0366974i	$-0.0116838\pi$
$107$	4.83981	+	8.38280i	0.467882	+	0.810396i	−0.531444	+	0.847093i	$0.678350\pi$
$108$	−1.64178	+	4.92996i	−0.157981	+	0.474386i
$109$	10.6759	−	12.7231i	1.02257	−	1.21865i	0.0470125	−	0.998894i	$-0.485030\pi$
$109$	10.6759	−	12.7231i	1.02257	−	1.21865i	0.975555	−	0.219754i	$-0.0705256\pi$
$110$	−2.25522	+	1.89235i	−0.215026	+	0.180429i
$111$	2.03895	+	10.9723i	0.193528	+	1.04144i
$112$	−2.63701	+	0.959792i	−0.249174	+	0.0906918i
$113$	1.29530			0.121852			0.0609259	−	0.998142i	$-0.480595\pi$
$113$	1.29530			0.121852			0.0609259	+	0.998142i	$0.480595\pi$
$114$	−7.07027	+	2.64787i	−0.662192	+	0.247996i
$115$	0.792906			0.0739388
$116$	−0.910982	+	0.331570i	−0.0845825	+	0.0307855i
$117$	−8.79365	+	5.29506i	−0.812973	+	0.489529i
$118$	10.6533	−	8.93921i	0.980720	−	0.822921i
$119$	−0.323011	+	0.384949i	−0.0296103	+	0.0352882i
$120$	−0.879786	−	1.49197i	−0.0803131	−	0.136198i
$121$	−1.16650	−	2.02044i	−0.106046	−	0.183677i
$122$	0.367486	−	0.636504i	0.0332706	−	0.0576264i
$123$	0.145906	+	15.8613i	0.0131559	+	1.43017i
$124$	−2.48778	+	6.83512i	−0.223409	+	0.613811i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	7.96265	+	2.73336i	0.709369	+	0.243507i
$127$	18.9670	−	3.34439i	1.68305	−	0.296766i	0.751323	−	0.659935i	$-0.229416\pi$
$127$	18.9670	−	3.34439i	1.68305	−	0.296766i	0.931723	+	0.363169i	$0.118305\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	16.7135	+	9.44564i	1.47154	+	0.831642i
$130$	0.594154	−	3.36962i	0.0521108	−	0.295535i
$131$	−0.673684	−	1.85093i	−0.0588601	−	0.161717i	0.906777	−	0.421610i	$-0.138535\pi$
$131$	−0.673684	−	1.85093i	−0.0588601	−	0.161717i	−0.965637	+	0.259893i	$0.916313\pi$
$132$	−4.77536	+	1.78800i	−0.415641	+	0.155626i
$133$	4.18450	+	11.4941i	0.362842	+	0.996668i
$134$			5.47989i			0.473390i
$135$	−0.760763	+	5.14016i	−0.0654761	+	0.442394i
$136$	0.176350	+	0.0310953i	0.0151219	+	0.00266640i
$137$	5.59120	+	6.66334i	0.477689	+	0.569287i	0.950042	−	0.312122i	$-0.101040\pi$
$137$	5.59120	+	6.66334i	0.477689	+	0.569287i	−0.472353	+	0.881409i	$0.656595\pi$
$138$	1.29480	+	0.457824i	0.110220	+	0.0389725i
$139$	0.188870	+	1.07114i	0.0160198	+	0.0908526i	0.991769	−	0.128037i	$-0.0408676\pi$
$139$	0.188870	+	1.07114i	0.0160198	+	0.0908526i	−0.975750	+	0.218890i	$0.929757\pi$
$140$	−2.43028	+	1.40312i	−0.205396	+	0.118585i
$141$	−0.0562148	+	0.336903i	−0.00473414	+	0.0283724i
$142$	9.78340	+	3.56087i	0.821005	+	0.298821i
$143$	−9.46562	−	3.44520i	−0.791555	−	0.288102i
$144$	−0.575206	−	2.94434i	−0.0479339	−	0.245362i
$145$	−0.839565	+	0.484723i	−0.0697221	+	0.0402541i
$146$	−0.0632772	−	0.358863i	−0.00523686	−	0.0296997i
$147$	0.505227	−	1.42886i	0.0416704	−	0.117850i
$148$	−4.14167	−	4.93585i	−0.340443	−	0.405724i
$149$	−2.34227	−	0.413006i	−0.191886	−	0.0338347i	0.0768790	−	0.997040i	$-0.475504\pi$
$149$	−2.34227	−	0.413006i	−0.191886	−	0.0338347i	−0.268765	+	0.963206i	$0.586616\pi$
$150$	−1.12550	−	1.31653i	−0.0918966	−	0.107494i
$151$		−	5.17855i		−	0.421424i	−0.977548	−	0.210712i	$-0.932422\pi$
$151$		−	5.17855i		−	0.421424i	0.977548	−	0.210712i	$-0.0675782\pi$
$152$	2.80160	−	3.33932i	0.227239	−	0.270855i
$153$	−0.352825	−	0.405106i	−0.0285242	−	0.0327508i
$154$	2.82560	+	7.76328i	0.227694	+	0.625583i
$155$	−1.26308	+	7.16327i	−0.101453	+	0.575368i
$156$	2.91585	−	5.15944i	0.233455	−	0.413085i
$157$	−9.72181	−	8.15757i	−0.775885	−	0.651045i	0.166324	−	0.986071i	$-0.446810\pi$
$157$	−9.72181	−	8.15757i	−0.775885	−	0.651045i	−0.942209	+	0.335027i	$0.891255\pi$
$158$	5.27331	−	0.929827i	0.419522	−	0.0739730i
$159$	6.25282	−	7.59258i	0.495881	−	0.602130i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	0.761024	−	2.09090i	0.0599771	−	0.164786i
$162$	−4.21023	+	7.95449i	−0.330787	+	0.624964i
$163$	−8.60944	+	14.9120i	−0.674344	+	1.16800i	0.302316	+	0.953208i	$0.402240\pi$
$163$	−8.60944	+	14.9120i	−0.674344	+	1.16800i	−0.976660	+	0.214790i	$0.931093\pi$
$164$	−4.57897	−	7.93100i	−0.357557	−	0.619307i
$165$	−4.39233	+	2.59007i	−0.341942	+	0.201637i
$166$	8.35674	−	9.95917i	0.648609	−	0.772982i
$167$	12.0274	−	10.0922i	0.930708	−	0.780957i	−0.0452362	−	0.998976i	$-0.514404\pi$
$167$	12.0274	−	10.0922i	0.930708	−	0.780957i	0.975944	+	0.218019i	$0.0699596\pi$
$168$	−4.77875	+	0.888022i	−0.368688	+	0.0685123i
$169$	−1.21471	+	0.442120i	−0.0934396	+	0.0340092i
$170$	0.179070			0.0137341
$171$	−12.8339	+	2.50823i	−0.981432	+	0.191809i
$172$	−11.0839			−0.845143
$173$	−12.6328	+	4.59796i	−0.960453	+	0.349576i	−0.774211	−	0.632927i	$-0.781853\pi$
$173$	−12.6328	+	4.59796i	−0.960453	+	0.349576i	−0.186242	+	0.982504i	$0.559631\pi$
$174$	−1.65087	+	0.306776i	−0.125152	+	0.0232567i
$175$	−2.14971	+	1.80382i	−0.162503	+	0.136356i
$176$	1.89235	−	2.25522i	0.142641	−	0.169993i
$177$	20.7488	−	12.2351i	1.55957	−	0.919650i
$178$	−6.61086	−	11.4503i	−0.495505	−	0.858240i
$179$	7.62595	−	13.2085i	0.569990	−	0.987252i	−0.426576	−	0.904452i	$-0.640280\pi$
$179$	7.62595	−	13.2085i	0.569990	−	0.987252i	0.996566	−	0.0828000i	$-0.0263863\pi$
$180$	−1.07775	−	2.79973i	−0.0803305	−	0.208679i
$181$	−7.89648	+	21.6954i	−0.586940	+	1.61261i	0.189125	+	0.981953i	$0.439435\pi$
$181$	−7.89648	+	21.6954i	−0.586940	+	1.61261i	−0.776065	+	0.630653i	$0.782787\pi$
$182$	−8.31543	−	4.80092i	−0.616381	−	0.355868i
$183$	0.809269	−	0.982666i	0.0598229	−	0.0726408i
$184$	−0.780860	+	0.137687i	−0.0575657	+	0.0101504i
$185$	−4.93585	−	4.14167i	−0.362891	−	0.304502i
$186$	−6.19865	+	10.9681i	−0.454507	+	0.804224i
$187$	0.0915437	−	0.519170i	0.00669434	−	0.0379655i
$188$	−0.0674464	−	0.185308i	−0.00491904	−	0.0135149i
$189$	12.8245	+	6.93962i	0.932842	+	0.504783i
$190$	2.17917	−	3.77508i	0.158093	−	0.273873i
$191$		−	13.1408i		−	0.950835i	−0.879760	−	0.475417i	$-0.842297\pi$
$191$		−	13.1408i		−	0.950835i	0.879760	−	0.475417i	$-0.157703\pi$
$192$	1.12550	+	1.31653i	0.0812259	+	0.0950124i
$193$	−12.3983	−	2.18615i	−0.892448	−	0.157363i	−0.291424	−	0.956594i	$-0.594129\pi$
$193$	−12.3983	−	2.18615i	−0.892448	−	0.157363i	−0.601024	+	0.799231i	$0.705240\pi$
$194$	−6.36945	−	7.59081i	−0.457300	−	0.544989i
$195$	1.97563	−	5.58738i	0.141478	−	0.400121i
$196$	0.151943	+	0.861710i	0.0108531	+	0.0615507i
$197$	5.82696	−	3.36419i	0.415153	−	0.239689i	−0.277848	−	0.960625i	$-0.589621\pi$
$197$	5.82696	−	3.36419i	0.415153	−	0.239689i	0.693002	+	0.720936i	$0.256288\pi$
$198$	−8.66807	+	1.69339i	−0.616013	+	0.120344i
$199$	7.53380	+	2.74208i	0.534057	+	0.194381i	0.594949	−	0.803764i	$-0.297172\pi$
$199$	7.53380	+	2.74208i	0.534057	+	0.194381i	−0.0608920	+	0.998144i	$0.519395\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	−1.56212	+	9.36201i	−0.110184	+	0.660346i
$202$	−6.67707	+	3.85501i	−0.469797	+	0.271238i
$203$	0.472410	+	2.67917i	0.0331567	+	0.188041i
$204$	0.292418	+	0.103395i	0.0204733	+	0.00723911i
$205$	−5.88661	−	7.01539i	−0.411138	−	0.489976i
$206$	3.10499	+	0.547494i	0.216335	+	0.0381457i
$207$	2.08156	+	1.15126i	0.144678	+	0.0800181i
$208$			3.42160i			0.237245i
$209$	−9.83088	−	8.24783i	−0.680016	−	0.570514i
$210$	−4.55194	+	1.70435i	−0.314114	+	0.117611i
$211$	−3.66588	−	10.0719i	−0.252370	−	0.693380i	−0.999585	−	0.0287981i	$-0.990832\pi$
$211$	−3.66588	−	10.0719i	−0.252370	−	0.693380i	0.747216	−	0.664582i	$-0.231390\pi$
$212$	−0.986106	+	5.59249i	−0.0677261	+	0.384094i
$213$	15.6992	+	8.87240i	1.07569	+	0.607927i
$214$	−7.41502	−	6.22194i	−0.506881	−	0.425323i
$215$	−10.9156	+	1.92471i	−0.744434	+	0.131264i
$216$	−0.143374	−	5.19417i	−0.00975535	−	0.353419i
$217$	17.6773	+	10.2060i	1.20001	+	0.692828i
$218$	−5.68054	+	15.6072i	−0.384735	+	1.05705i
$219$	−0.00580568	−	0.631130i	−0.000392312	−	0.0426478i
$220$	1.47199	−	2.54956i	0.0992414	−	0.171891i
$221$	0.306353	+	0.530620i	0.0206076	+	0.0356933i
$222$	−5.66872	−	9.61321i	−0.380460	−	0.645196i
$223$	4.96798	−	5.92061i	0.332681	−	0.396473i	−0.573610	−	0.819129i	$-0.694457\pi$
$223$	4.96798	−	5.92061i	0.332681	−	0.396473i	0.906290	+	0.422655i	$0.138902\pi$
$224$	2.14971	−	1.80382i	0.143633	−	0.120523i
$225$	−1.54754	−	2.57004i	−0.103169	−	0.171336i
$226$	−1.21719	+	0.443020i	−0.0809661	+	0.0294692i
$227$	28.5580			1.89546			0.947731	−	0.319071i	$-0.103371\pi$
$227$	28.5580			1.89546			0.947731	+	0.319071i	$0.103371\pi$
$228$	5.73826	−	4.90636i	0.380025	−	0.324932i
$229$	−15.1214			−0.999251			−0.499625	−	0.866242i	$-0.666529\pi$
$229$	−15.1214			−0.999251			−0.499625	+	0.866242i	$0.666529\pi$
$230$	−0.745088	+	0.271190i	−0.0491296	+	0.0178817i
$231$	2.61431	+	14.0685i	0.172009	+	0.925641i
$232$	0.742639	−	0.623148i	0.0487566	−	0.0409117i
$233$	8.95592	−	10.6733i	0.586722	−	0.699228i	−0.388250	−	0.921554i	$-0.626920\pi$
$233$	8.95592	−	10.6733i	0.586722	−	0.699228i	0.974972	+	0.222326i	$0.0713649\pi$
$234$	6.45231	−	7.98334i	0.421801	−	0.521887i
$235$	−0.0986001	−	0.170780i	−0.00643196	−	0.0111405i
$236$	−6.95347	+	12.0438i	−0.452633	+	0.783983i
$237$	9.27415	−	0.0853116i	0.602421	−	0.00554158i
$238$	0.171870	−	0.472210i	0.0111407	−	0.0306088i
$239$	−21.7776	−	12.5733i	−1.40867	−	0.813299i	−0.413414	−	0.910543i	$-0.635664\pi$
$239$	−21.7776	−	12.5733i	−1.40867	−	0.813299i	−0.995261	+	0.0972441i	$0.968997\pi$
$240$	1.33701	+	1.10109i	0.0863038	+	0.0710750i
$241$	13.0786	−	2.30611i	0.842468	−	0.148550i	0.264273	−	0.964448i	$-0.414868\pi$
$241$	13.0786	−	2.30611i	0.842468	−	0.148550i	0.578196	+	0.815898i	$0.303757\pi$
$242$	1.78719	+	1.49963i	0.114885	+	0.0963997i
$243$	−9.46044	+	12.3895i	−0.606888	+	0.794788i
$244$	−0.127626	+	0.723806i	−0.00817045	+	0.0463369i
$245$	0.299269	+	0.822235i	0.0191196	+	0.0525306i
$246$	−5.56200	−	14.8549i	−0.354620	−	0.947113i
$247$	14.9144	−	0.00111801i	0.948980	−	7.11375e-5i
$248$		−	7.27378i		−	0.461885i
$249$	17.1159	−	14.6324i	1.08468	−	0.927288i
$250$	0.984808	+	0.173648i	0.0622847	+	0.0109825i
$251$	15.7882	+	18.8156i	0.996541	+	1.18763i	0.982220	+	0.187734i	$0.0601144\pi$
$251$	15.7882	+	18.8156i	0.996541	+	1.18763i	0.0143215	+	0.999897i	$0.495441\pi$
$252$	−8.41731	+	0.154872i	−0.530240	+	0.00975604i
$253$	0.405346	+	2.29883i	0.0254839	+	0.144526i
$254$	−16.6793	+	9.62978i	−1.04655	+	0.604226i
$255$	0.305930	+	0.0510466i	0.0191581	+	0.00319666i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−16.3671	−	5.95713i	−1.02095	−	0.371596i	−0.223322	−	0.974745i	$-0.571690\pi$
$257$	−16.3671	−	5.95713i	−1.02095	−	0.371596i	−0.797628	+	0.603149i	$0.793912\pi$
$258$	−18.9362	−	3.15964i	−1.17891	−	0.196711i
$259$	−15.6590	+	9.04073i	−0.973003	+	0.561764i
$260$	0.594154	+	3.36962i	0.0368479	+	0.208975i
$261$	−2.90785	+	0.0535023i	−0.179991	+	0.00331171i
$262$	1.26611	+	1.50889i	0.0782207	+	0.0932198i
$263$	21.6013	+	3.80890i	1.33199	+	0.234867i	0.793916	−	0.608028i	$-0.208039\pi$
$263$	21.6013	+	3.80890i	1.33199	+	0.234867i	0.538079	+	0.842895i	$0.319150\pi$
$264$	3.87583	−	3.31344i	0.238541	−	0.203928i
$265$			5.67876i			0.348843i
$266$	−7.86337	−	9.36977i	−0.482134	−	0.574497i
$267$	−8.03011	−	21.4467i	−0.491435	−	1.31251i
$268$	−1.87423	−	5.14941i	−0.114487	−	0.314550i
$269$	−0.185203	+	1.05034i	−0.0112920	+	0.0640402i	−0.989933	−	0.141536i	$-0.954796\pi$
$269$	−0.185203	+	1.05034i	−0.0112920	+	0.0640402i	0.978641	+	0.205576i	$0.0659069\pi$
$270$	−1.04315	−	5.09037i	−0.0634844	−	0.309790i
$271$	−20.1368	−	16.8968i	−1.22322	−	1.02641i	−0.998650	−	0.0519488i	$-0.983457\pi$
$271$	−20.1368	−	16.8968i	−1.22322	−	1.02641i	−0.224573	−	0.974457i	$-0.572099\pi$
$272$	−0.176350	+	0.0310953i	−0.0106928	+	0.00188543i
$273$	−12.8378	−	10.5725i	−0.776978	−	0.639875i
$274$	−7.53301	−	4.34919i	−0.455086	−	0.262744i
$275$	1.00690	−	2.76643i	0.0607183	−	0.166822i
$276$	−1.37329	+	0.0126327i	−0.0826626	+	0.000760402i
$277$	−2.17313	+	3.76397i	−0.130571	+	0.226155i	−0.923897	−	0.382642i	$-0.875014\pi$
$277$	−2.17313	+	3.76397i	−0.130571	+	0.226155i	0.793326	+	0.608797i	$0.208348\pi$
$278$	−0.543830	−	0.941941i	−0.0326167	−	0.0564939i
$279$	−13.7166	+	16.9713i	−0.821191	+	1.01605i
$280$	1.80382	−	2.14971i	0.107799	−	0.128470i
$281$	−4.32981	+	3.63314i	−0.258295	+	0.216735i	−0.762734	−	0.646712i	$-0.776144\pi$
$281$	−4.32981	+	3.63314i	−0.258295	+	0.216735i	0.504439	+	0.863447i	$0.331699\pi$
$282$	−0.0624030	−	0.335812i	−0.00371604	−	0.0199973i
$283$	23.8741	−	8.68946i	1.41917	−	0.516535i	0.485362	−	0.874313i	$-0.338688\pi$
$283$	23.8741	−	8.68946i	1.41917	−	0.516535i	0.933806	+	0.357779i	$0.116466\pi$
$284$	−10.4113			−0.617796
$285$	4.79910	−	5.82826i	0.284274	−	0.345237i
$286$	10.0731			0.595635
$287$	−24.1495	+	8.78971i	−1.42550	+	0.518840i
$288$	1.54754	+	2.57004i	0.0911897	+	0.151441i
$289$	12.9982	−	10.9068i	0.764599	−	0.641575i
$290$	0.623148	−	0.742639i	0.0365925	−	0.0436093i
$291$	−8.71789	−	14.7841i	−0.511052	−	0.866658i
$292$	0.182199	+	0.315579i	0.0106624	+	0.0184678i
$293$	15.8426	−	27.4403i	0.925537	−	1.60308i	0.134842	−	0.990867i	$-0.456947\pi$
$293$	15.8426	−	27.4403i	0.925537	−	1.60308i	0.790695	−	0.612210i	$-0.209719\pi$
$294$	0.0139407	+	1.51549i	0.000813041	+	0.0883850i
$295$	−4.75646	+	13.0683i	−0.276932	+	0.760863i
$296$	5.58006	+	3.22165i	0.324334	+	0.187254i
$297$	−15.2915	+	0.422089i	−0.887304	+	0.0244921i
$298$	2.34227	−	0.413006i	0.135684	−	0.0239248i
$299$	−2.07828	−	1.74389i	−0.120190	−	0.100851i
$300$	1.50790	+	0.852191i	0.0870588	+	0.0492013i
$301$	−5.40119	+	30.6317i	−0.311320	+	1.76558i
$302$	1.77117	+	4.86624i	0.101919	+	0.280021i
$303$	−12.5062	+	4.68262i	−0.718465	+	0.269010i
$304$	−1.49052	+	4.09614i	−0.0854874	+	0.234930i
$305$			0.734972i			0.0420844i
$306$	0.470101	+	0.260002i	0.0268739	+	0.0148633i
$307$	12.4947	+	2.20315i	0.713111	+	0.125741i	0.518423	−	0.855125i	$-0.326519\pi$
$307$	12.4947	+	2.20315i	0.713111	+	0.125741i	0.194688	+	0.980865i	$0.437631\pi$
$308$	−5.31040	−	6.32869i	−0.302588	−	0.360610i
$309$	5.14860	+	1.82048i	0.292894	+	0.103564i
$310$	−1.26308	−	7.16327i	−0.0717380	−	0.406847i
$311$	17.2759	−	9.97425i	0.979627	−	0.565588i	0.0774695	−	0.996995i	$-0.475316\pi$
$311$	17.2759	−	9.97425i	0.979627	−	0.565588i	0.902158	+	0.431407i	$0.141983\pi$
$312$	−0.975376	+	5.84556i	−0.0552198	+	0.330940i
$313$	−9.66646	−	3.51830i	−0.546381	−	0.198866i	0.0540570	−	0.998538i	$-0.482785\pi$
$313$	−9.66646	−	3.51830i	−0.546381	−	0.198866i	−0.600438	+	0.799672i	$0.705007\pi$
$314$	11.9256	+	4.34055i	0.672999	+	0.244951i
$315$	−8.26254	+	1.61417i	−0.465541	+	0.0909481i
$316$	−4.63727	+	2.67733i	−0.260867	+	0.150612i
$317$	−0.657185	−	3.72708i	−0.0369112	−	0.209334i	0.960774	−	0.277331i	$-0.0894500\pi$
$317$	−0.657185	−	3.72708i	−0.0369112	−	0.209334i	−0.997685	+	0.0679978i	$0.978339\pi$
$318$	−3.27892	+	9.27328i	−0.183872	+	0.520020i
$319$	−1.83453	−	2.18631i	−0.102714	−	0.122410i
$320$	−0.984808	−	0.173648i	−0.0550524	−	0.00970723i
$321$	−10.8944	−	12.7435i	−0.608066	−	0.711274i
$322$			2.22509i			0.123999i
$323$	0.135599	+	0.768681i	0.00754491	+	0.0427706i
$324$	1.23573	−	8.91476i	0.0686517	−	0.495265i
$325$	1.17026	+	3.21525i	0.0649141	+	0.178350i
$326$	2.99003	−	16.9573i	0.165602	−	0.939178i
$327$	−14.1539	+	25.0444i	−0.782710	+	1.38496i
$328$	7.01539	+	5.88661i	0.387360	+	0.325034i
$329$	−0.544984	+	0.0960955i	−0.0300460	+	0.00529791i
$330$	3.24158	−	3.93613i	0.178443	−	0.216677i
$331$	−2.66004	−	1.53578i	−0.146209	−	0.0844138i	0.425111	−	0.905141i	$-0.360235\pi$
$331$	−2.66004	−	1.53578i	−0.146209	−	0.0844138i	−0.571320	+	0.820727i	$0.693568\pi$
$332$	−4.44653	+	12.2167i	−0.244035	+	0.670480i
$333$	−6.94424	−	18.0395i	−0.380542	−	0.988556i
$334$	−7.85033	+	13.5972i	−0.429551	+	0.744004i
$335$	−2.73994	−	4.74572i	−0.149699	−	0.259287i
$336$	4.18683	−	2.46890i	0.228410	−	0.134689i
$337$	19.6752	−	23.4480i	1.07178	−	1.27730i	0.112861	−	0.993611i	$-0.463999\pi$
$337$	19.6752	−	23.4480i	1.07178	−	1.27730i	0.958918	−	0.283685i	$-0.0915570\pi$
$338$	0.990244	−	0.830914i	0.0538622	−	0.0451958i
$339$	−2.20577	+	0.409892i	−0.119801	+	0.0222623i
$340$	−0.168271	+	0.0612457i	−0.00912578	+	0.00332151i
$341$	−21.4138			−1.15962
$342$	11.2020	−	6.74641i	0.605737	−	0.364804i
$343$	−17.1882			−0.928077
$344$	10.4155	−	3.79093i	0.561566	−	0.204393i
$345$	−1.35024	+	0.250911i	−0.0726943	+	0.0135086i
$346$	10.2983	−	8.64134i	0.553643	−	0.464561i
$347$	−21.6050	+	25.7478i	−1.15982	+	1.38222i	−0.249462	+	0.968385i	$0.580254\pi$
$347$	−21.6050	+	25.7478i	−1.15982	+	1.38222i	−0.910354	+	0.413831i	$0.864191\pi$
$348$	1.44639	−	0.852906i	0.0775344	−	0.0457205i
$349$	−11.3512	−	19.6609i	−0.607618	−	1.05243i	−0.991632	−	0.129098i	$-0.958792\pi$
$349$	−11.3512	−	19.6609i	−0.607618	−	1.05243i	0.384014	−	0.923327i	$-0.374542\pi$
$350$	1.40312	−	2.43028i	0.0750000	−	0.129904i
$351$	13.2991	−	11.7997i	0.709853	−	0.629819i
$352$	−1.00690	+	2.76643i	−0.0536679	+	0.147451i
$353$	23.4493	+	13.5385i	1.24808	+	0.720580i	0.970727	−	0.240187i	$-0.0772088\pi$
$353$	23.4493	+	13.5385i	1.24808	+	0.720580i	0.277355	+	0.960767i	$0.410542\pi$
$354$	−15.3128	+	18.5938i	−0.813865	+	0.988248i
$355$	−10.2531	+	1.80790i	−0.544179	+	0.0959534i
$356$	10.1284	+	8.49876i	0.536805	+	0.450433i
$357$	0.428239	−	0.757744i	0.0226648	−	0.0401041i
$358$	−2.64846	+	15.0202i	−0.139976	+	0.793841i
$359$	10.6511	+	29.2638i	0.562146	+	1.54448i	0.816484	+	0.577368i	$0.195920\pi$
$359$	10.6511	+	29.2638i	0.562146	+	1.54448i	−0.254338	+	0.967115i	$0.581858\pi$
$360$	1.97031	+	2.26227i	0.103845	+	0.119232i
$361$	17.8551	+	6.49571i	0.939744	+	0.341879i
$362$		−	23.0878i		−	1.21347i
$363$	2.62579	+	3.07147i	0.137818	+	0.161211i
$364$	9.45596	+	1.66734i	0.495627	+	0.0873924i
$365$	0.234231	+	0.279146i	0.0122602	+	0.0146112i
$366$	−0.424372	+	1.20019i	−0.0221823	+	0.0627350i
$367$	−2.97589	−	16.8771i	−0.155340	−	0.880979i	−0.958474	−	0.285180i	$-0.907947\pi$
$367$	−2.97589	−	16.8771i	−0.155340	−	0.880979i	0.803134	−	0.595799i	$-0.203164\pi$
$368$	0.686676	−	0.396453i	0.0357955	−	0.0206665i
$369$	−5.26770	−	26.9641i	−0.274226	−	1.40369i
$370$	6.05472	+	2.20374i	0.314770	+	0.114567i
$371$	14.9749	+	5.45043i	0.777460	+	0.282972i
$372$	2.07350	−	12.4268i	0.107506	−	0.644297i
$373$	5.84370	−	3.37386i	0.302575	−	0.174692i	−0.341024	−	0.940055i	$-0.610774\pi$
$373$	5.84370	−	3.37386i	0.302575	−	0.174692i	0.643599	+	0.765363i	$0.277440\pi$
$374$	0.0915437	+	0.519170i	0.00473361	+	0.0268456i
$375$	1.63298	+	0.577400i	0.0843265	+	0.0298168i
$376$	0.126758	+	0.151064i	0.00653704	+	0.00779054i
$377$	3.26666	+	0.576001i	0.168242	+	0.0296655i
$378$	−14.4245	−	2.13489i	−0.741918	−	0.109807i
$379$			26.5182i			1.36215i	0.732214	+	0.681075i	$0.238487\pi$
$379$			26.5182i			1.36215i	−0.732214	+	0.681075i	$0.761513\pi$
$380$	−0.756593	+	4.29273i	−0.0388124	+	0.220213i
$381$	−31.2405	+	11.6972i	−1.60050	+	0.599263i
$382$	4.49442	+	12.3483i	0.229954	+	0.631795i
$383$	3.26632	−	18.5242i	0.166901	−	0.946542i	−0.780182	−	0.625553i	$-0.784873\pi$
$383$	3.26632	−	18.5242i	0.166901	−	0.946542i	0.947083	−	0.320990i	$-0.104015\pi$
$384$	−1.50790	−	0.852191i	−0.0769498	−	0.0434882i
$385$	−6.32869	−	5.31040i	−0.322540	−	0.270643i
$386$	12.3983	−	2.18615i	0.631056	−	0.111272i
$387$	−31.4504	−	10.7961i	−1.59871	−	0.548794i
$388$	8.58153	+	4.95455i	0.435661	+	0.251529i
$389$	−4.25051	+	11.6782i	−0.215510	+	0.592108i	−0.999592	−	0.0285485i	$-0.990911\pi$
$389$	−4.25051	+	11.6782i	−0.215510	+	0.592108i	0.784083	+	0.620656i	$0.213134\pi$
$390$	0.0545136	+	5.92613i	0.00276041	+	0.300081i
$391$	0.0709930	−	0.122963i	0.00359027	−	0.00621853i
$392$	−0.437502	−	0.757775i	−0.0220972	−	0.0382734i
$393$	1.73293	+	2.93877i	0.0874149	+	0.148241i
$394$	−4.32492	+	5.15424i	−0.217887	+	0.259667i
$395$	−4.10191	+	3.44191i	−0.206389	+	0.173181i
$396$	7.56614	−	4.55592i	0.380213	−	0.228944i
$397$	−10.5281	+	3.83190i	−0.528388	+	0.192318i	−0.592419	−	0.805630i	$-0.701827\pi$
$397$	−10.5281	+	3.83190i	−0.528388	+	0.192318i	0.0640302	+	0.997948i	$0.479605\pi$
$398$	−8.01730			−0.401871
$399$	−10.7630	−	18.2492i	−0.538826	−	0.913601i
$400$	−1.00000			−0.0500000
$401$	−25.9263	+	9.43641i	−1.29470	+	0.471232i	−0.895266	−	0.445531i	$-0.853015\pi$
$401$	−25.9263	+	9.43641i	−1.29470	+	0.471232i	−0.399432	+	0.916763i	$0.630793\pi$
$402$	−1.73408	−	9.33169i	−0.0864882	−	0.465423i
$403$	19.0653	−	15.9977i	0.949709	−	0.796900i
$404$	4.95591	−	5.90622i	0.246566	−	0.293845i
$405$	−0.331075	−	8.99391i	−0.0164512	−	0.446911i
$406$	−1.36025	−	2.35602i	−0.0675081	−	0.116928i
$407$	9.48445	−	16.4276i	0.470127	−	0.814284i
$408$	−0.310146	+	0.00285299i	−0.0153545	+	0.000141244i
$409$	4.81000	−	13.2154i	0.237839	−	0.653457i	−0.762143	−	0.647409i	$-0.775853\pi$
$409$	4.81000	−	13.2154i	0.237839	−	0.653457i	0.999982	−	0.00604828i	$-0.00192524\pi$
$410$	7.93100	+	4.57897i	0.391684	+	0.226139i
$411$	−11.6298	−	9.57768i	−0.573657	−	0.472432i
$412$	−3.10499	+	0.547494i	−0.152972	+	0.0269731i
$413$	29.8959	+	25.0856i	1.47108	+	1.23438i
$414$	−2.34978	−	0.369895i	−0.115485	−	0.0181794i
$415$	−2.25756	+	12.8033i	−0.110819	+	0.628488i
$416$	−1.17026	−	3.21525i	−0.0573765	−	0.157641i
$417$	−0.660582	−	1.76427i	−0.0323488	−	0.0863966i
$418$	12.0589	+	4.38807i	0.589821	+	0.214627i
$419$			4.27639i			0.208915i	0.994529	+	0.104458i	$0.0333107\pi$
$419$			4.27639i			0.208915i	−0.994529	+	0.104458i	$0.966689\pi$
$420$	3.69451	−	3.15842i	0.180273	−	0.154115i
$421$	13.8112	+	2.43528i	0.673115	+	0.118688i	0.499751	−	0.866169i	$-0.333425\pi$
$421$	13.8112	+	2.43528i	0.673115	+	0.118688i	0.173365	+	0.984858i	$0.444536\pi$
$422$	6.88960	+	8.21071i	0.335381	+	0.399691i
$423$	−0.0108832	−	0.591500i	−0.000529158	−	0.0287597i
$424$	−0.986106	−	5.59249i	−0.0478896	−	0.271595i
$425$	−0.155080	+	0.0895352i	−0.00752246	+	0.00434310i
$426$	−17.7870	−	2.96789i	−0.861781	−	0.143795i
$427$	1.93812	+	0.705420i	0.0937924	+	0.0341377i
$428$	9.09587	+	3.31063i	0.439666	+	0.160025i
$429$	17.2092	+	2.87148i	0.830868	+	0.138637i
$430$	9.59897	−	5.54197i	0.462904	−	0.267258i
$431$	−1.95988	−	11.1150i	−0.0944040	−	0.535392i	−0.994928	−	0.100586i	$-0.967928\pi$
$431$	−1.95988	−	11.1150i	−0.0944040	−	0.535392i	0.900524	−	0.434806i	$-0.143183\pi$
$432$	1.91124	+	4.83189i	0.0919546	+	0.232474i
$433$	11.0002	+	13.1095i	0.528634	+	0.630002i	0.962600	−	0.270928i	$-0.0873305\pi$
$433$	11.0002	+	13.1095i	0.528634	+	0.630002i	−0.433965	+	0.900929i	$0.642886\pi$
$434$	−20.1019	−	3.54451i	−0.964922	−	0.170142i
$435$	1.27631	−	1.09111i	0.0611942	−	0.0523147i
$436$		−	16.6088i		−	0.795416i
$437$	−1.72832	−	2.99302i	−0.0826769	−	0.143176i
$438$	0.221315	+	0.591083i	0.0105748	+	0.0282430i
$439$	11.5054	+	31.6107i	0.549121	+	1.50870i	0.834900	+	0.550402i	$0.185525\pi$
$439$	11.5054	+	31.6107i	0.549121	+	1.50870i	−0.285779	+	0.958296i	$0.592252\pi$
$440$	−0.511216	+	2.89925i	−0.0243713	+	0.138216i
$441$	−0.408195	+	2.59308i	−0.0194378	+	0.123480i
$442$	−0.469361	−	0.393840i	−0.0223252	−	0.0187331i
$443$	12.8000	−	2.25699i	0.608148	−	0.107233i	0.138910	−	0.990305i	$-0.455640\pi$
$443$	12.8000	−	2.25699i	0.608148	−	0.107233i	0.469237	+	0.883072i	$0.344529\pi$
$444$	8.61477	+	7.09464i	0.408839	+	0.336697i
$445$	11.4503	+	6.61086i	0.542798	+	0.313385i
$446$	−2.64341	+	7.26270i	−0.125169	+	0.343899i
$447$	4.11934	−	0.0378933i	0.194838	−	0.00179229i
$448$	−1.40312	+	2.43028i	−0.0662913	+	0.114820i
$449$	−0.773141	−	1.33912i	−0.0364868	−	0.0631970i	0.847205	−	0.531266i	$-0.178283\pi$
$449$	−0.773141	−	1.33912i	−0.0364868	−	0.0631970i	−0.883692	+	0.468069i	$0.844950\pi$
$450$	2.33322	+	1.88576i	0.109989	+	0.0888956i
$451$	17.3300	−	20.6531i	0.816039	−	0.972518i
$452$	0.992260	−	0.832605i	0.0466720	−	0.0391624i
$453$	1.63872	+	8.81854i	0.0769940	+	0.414331i
$454$	−26.8357	+	9.76741i	−1.25946	+	0.458407i
$455$	9.60184			0.450141
$456$	−3.71412	+	6.57307i	−0.173930	+	0.307812i
$457$	−20.8759			−0.976535			−0.488267	−	0.872694i	$-0.662371\pi$
$457$	−20.8759			−0.976535			−0.488267	+	0.872694i	$0.662371\pi$
$458$	14.2095	−	5.17183i	0.663965	−	0.241664i
$459$	0.729018	+	0.578204i	0.0340277	+	0.0269883i
$460$	0.607401	−	0.509670i	0.0283202	−	0.0237635i
$461$	8.05570	−	9.60041i	0.375191	−	0.447136i	−0.545099	−	0.838372i	$-0.683508\pi$
$461$	8.05570	−	9.60041i	0.375191	−	0.447136i	0.920290	+	0.391236i	$0.127952\pi$
$462$	−7.26837	−	12.3259i	−0.338155	−	0.573454i
$463$	3.41626	+	5.91713i	0.158767	+	0.274992i	0.934424	−	0.356162i	$-0.115915\pi$
$463$	3.41626	+	5.91713i	0.158767	+	0.274992i	−0.775657	+	0.631154i	$0.782582\pi$
$464$	−0.484723	+	0.839565i	−0.0225027	+	0.0389758i
$465$	−0.115887	−	12.5980i	−0.00537415	−	0.584219i
$466$	−4.76535	+	13.0927i	−0.220750	+	0.606507i
$467$	−14.4045	−	8.31642i	−0.666559	−	0.384838i	0.128212	−	0.991747i	$-0.459076\pi$
$467$	−14.4045	−	8.31642i	−0.666559	−	0.384838i	−0.794772	+	0.606909i	$0.792409\pi$
$468$	−3.33273	+	9.70870i	−0.154055	+	0.448785i
$469$	−15.1443	+	2.67034i	−0.699298	+	0.123305i
$470$	0.151064	+	0.126758i	0.00696807	+	0.00584690i
$471$	19.1367	+	10.8151i	0.881771	+	0.498333i
$472$	2.41492	−	13.6957i	0.111156	−	0.630394i
$473$	−11.1604	−	30.6630i	−0.513156	−	1.40989i
$474$	−8.68567	+	3.25211i	−0.398946	+	0.149374i
$475$	0.000326752		4.35890i	1.49924e−5		0.200000i
$476$			0.502515i			0.0230327i
$477$	−8.24529	+	14.9081i	−0.377526	+	0.682593i
$478$	24.7646	+	4.36666i	1.13270	+	0.199726i
$479$	4.24505	+	5.05905i	0.193961	+	0.231154i	0.854256	−	0.519853i	$-0.174013\pi$
$479$	4.24505	+	5.05905i	0.193961	+	0.231154i	−0.660295	+	0.751006i	$0.729569\pi$
$480$	−1.63298	−	0.577400i	−0.0745348	−	0.0263546i
$481$	3.82831	+	21.7114i	0.174556	+	0.989956i
$482$	−11.5012	+	6.64019i	−0.523863	+	0.302452i
$483$	−0.634293	+	3.80141i	−0.0288613	+	0.172970i
$484$	−2.19231	−	0.797935i	−0.0996503	−	0.0362698i
$485$	9.31151	+	3.38911i	0.422814	+	0.153892i
$486$	4.65244	−	14.8780i	0.211039	−	0.674880i
$487$	−7.72455	+	4.45977i	−0.350033	+	0.202091i	−0.664700	−	0.747111i	$-0.731441\pi$
$487$	−7.72455	+	4.45977i	−0.350033	+	0.202091i	0.314667	+	0.949202i	$0.398107\pi$
$488$	−0.127626	−	0.723806i	−0.00577738	−	0.0327651i
$489$	9.94218	−	28.1180i	0.449601	−	1.27154i
$490$	−0.562442	−	0.670292i	−0.0254085	−	0.0302807i
$491$	5.37581	+	0.947900i	0.242607	+	0.0427781i	0.293629	−	0.955919i	$-0.405137\pi$
$491$	5.37581	+	0.947900i	0.242607	+	0.0427781i	−0.0510224	+	0.998698i	$0.516248\pi$
$492$	10.3072	+	12.0567i	0.464686	+	0.543558i
$493$			0.173599i			0.00781851i
$494$	−14.0146	+	5.10207i	−0.630545	+	0.229553i
$495$	6.66007	−	5.80056i	0.299348	−	0.260716i
$496$	2.48778	+	6.83512i	0.111705	+	0.306906i
$497$	−5.07341	+	28.7727i	−0.227573	+	1.29063i
$498$	−11.0791	+	19.6039i	−0.496468	+	0.878472i
$499$	7.98337	+	6.69884i	0.357385	+	0.299881i	0.803747	−	0.594971i	$-0.202836\pi$
$499$	7.98337	+	6.69884i	0.357385	+	0.299881i	−0.446363	+	0.894852i	$0.647281\pi$
$500$	−0.984808	+	0.173648i	−0.0440419	+	0.00776578i
$501$	−17.2878	+	20.9920i	−0.772363	+	0.937852i
$502$	−21.2714	−	12.2810i	−0.949387	−	0.548129i
$503$	9.06015	−	24.8926i	0.403972	−	1.10990i	−0.556334	−	0.830958i	$-0.687793\pi$
$503$	9.06015	−	24.8926i	0.403972	−	1.10990i	0.960307	−	0.278946i	$-0.0899851\pi$
$504$	7.85671	−	3.02442i	0.349966	−	0.134718i
$505$	3.85501	−	6.67707i	0.171546	−	0.297126i
$506$	−1.16715	−	2.02156i	−0.0518860	−	0.0898693i
$507$	1.92863	−	1.13728i	0.0856534	−	0.0505082i
$508$	12.3798	−	14.7537i	0.549265	−	0.654589i
$509$	−25.9622	+	21.7849i	−1.15075	+	0.965598i	−0.999737	−	0.0229330i	$-0.992700\pi$
$509$	−25.9622	+	21.7849i	−1.15075	+	0.965598i	−0.151018	+	0.988531i	$0.548255\pi$
$510$	−0.304939	+	0.0566659i	−0.0135029	+	0.00250921i
$511$	0.960922	−	0.349747i	0.0425087	−	0.0154719i
$512$	1.00000			0.0441942
$513$	21.0611	−	8.33248i	0.929870	−	0.367888i
$514$	17.4175			0.768252
$515$	−2.96275	+	1.07835i	−0.130554	+	0.0475179i
$516$	18.8748	−	3.50746i	0.830918	−	0.154407i
$517$	0.444729	−	0.373172i	0.0195592	−	0.0164121i
$518$	11.6225	−	13.8512i	0.510665	−	0.608587i
$519$	20.0574	−	11.8274i	0.880420	−	0.519167i
$520$	−1.71080	−	2.96319i	−0.0750235	−	0.129944i
$521$	−10.2298	+	17.7185i	−0.448174	+	0.776260i	−0.998267	−	0.0588429i	$-0.981259\pi$
$521$	−10.2298	+	17.7185i	−0.448174	+	0.776260i	0.550093	+	0.835103i	$0.314592\pi$
$522$	2.71418	−	1.04482i	0.118797	−	0.0457304i
$523$	−4.52671	+	12.4370i	−0.197939	+	0.543834i	−0.998460	−	0.0554708i	$-0.982334\pi$
$523$	−4.52671	+	12.4370i	−0.197939	+	0.543834i	0.800521	+	0.599305i	$0.204556\pi$
$524$	−1.70583	−	0.984860i	−0.0745195	−	0.0430238i
$525$	3.08992	−	3.75198i	0.134855	−	0.163750i
$526$	−21.6013	+	3.80890i	−0.941862	+	0.166076i
$527$	0.997787	+	0.837243i	0.0434643	+	0.0364709i
$528$	−2.50883	+	4.43923i	−0.109183	+	0.193193i
$529$	3.88474	−	22.0314i	0.168902	−	0.957888i
$530$	−1.94225	−	5.33629i	−0.0843660	−	0.231794i
$531$	−31.4613	+	27.4010i	−1.36530	+	1.18910i
$532$	10.5938	+	6.11527i	0.459299	+	0.265131i
$533$			31.3348i			1.35726i
$534$	14.8810	+	17.4068i	0.643965	+	0.753266i
$535$	9.53257	+	1.68085i	0.412129	+	0.0726694i
$536$	3.52240	+	4.19784i	0.152145	+	0.181319i
$537$	−8.80644	+	24.9060i	−0.380026	+	1.07477i
$538$	−0.185203	−	1.05034i	−0.00798467	−	0.0452833i
$539$	−2.23087	+	1.28799i	−0.0960905	+	0.0554779i
$540$	2.72125	+	4.42660i	0.117104	+	0.190491i
$541$	6.07530	+	2.21123i	0.261198	+	0.0950681i	0.469300	−	0.883039i	$-0.344506\pi$
$541$	6.07530	+	2.21123i	0.261198	+	0.0950681i	−0.208102	+	0.978107i	$0.566729\pi$
$542$	24.7014	+	8.99059i	1.06102	+	0.386179i
$543$	6.58150	−	39.4438i	0.282439	−	1.69270i
$544$	0.155080	−	0.0895352i	0.00664898	−	0.00383879i
$545$	−2.88409	−	16.3565i	−0.123541	−	0.700634i
$546$	15.6796	+	5.54410i	0.671023	+	0.237265i
$547$	1.96092	+	2.33693i	0.0838428	+	0.0999200i	0.806335	−	0.591459i	$-0.201448\pi$
$547$	1.96092	+	2.33693i	0.0838428	+	0.0999200i	−0.722492	+	0.691379i	$0.757003\pi$
$548$	8.56622	+	1.51046i	0.365931	+	0.0645235i
$549$	−1.06714	+	1.92947i	−0.0455446	+	0.0823478i
$550$			2.94398i			0.125532i
$551$	3.65974	+	2.11258i	0.155910	+	0.0899991i
$552$	1.28615	−	0.481565i	0.0547424	−	0.0204968i
$553$	5.13936	+	14.1203i	0.218548	+	0.600455i
$554$	0.754720	−	4.28023i	0.0320650	−	0.181850i
$555$	9.71586	+	5.49092i	0.412415	+	0.233077i
$556$	0.833196	+	0.699134i	0.0353354	+	0.0296499i
$557$	−24.3271	+	4.28952i	−1.03077	+	0.181753i	−0.663356	−	0.748304i	$-0.730869\pi$
$557$	−24.3271	+	4.28952i	−1.03077	+	0.181753i	−0.367416	+	0.930057i	$0.619757\pi$
$558$	7.08485	−	20.6392i	0.299926	−	0.873726i
$559$	32.8438	+	18.9624i	1.38915	+	0.802024i
$560$	−0.959792	+	2.63701i	−0.0405586	+	0.111434i
$561$	0.00839913	+	0.913062i	0.000354612	+	0.0385495i
$562$	2.82608	−	4.89492i	0.119211	−	0.206480i
$563$	8.69829	+	15.0659i	0.366589	+	0.634951i	0.989030	−	0.147716i	$-0.0471921\pi$
$563$	8.69829	+	15.0659i	0.366589	+	0.634951i	−0.622440	+	0.782667i	$0.713859\pi$
$564$	0.173494	+	0.294217i	0.00730542	+	0.0123888i
$565$	0.832605	−	0.992260i	0.0350280	−	0.0417447i
$566$	−19.4623	+	16.3308i	−0.818063	+	0.686437i
$567$	−24.0348	−	7.75923i	−1.00936	−	0.325857i
$568$	9.78340	−	3.56087i	0.410502	−	0.149411i
$569$	−15.6399			−0.655660			−0.327830	−	0.944737i	$-0.606317\pi$
$569$	−15.6399			−0.655660			−0.327830	+	0.944737i	$0.606317\pi$
$570$	−2.51629	+	7.11816i	−0.105396	+	0.298147i
$571$	−20.0758			−0.840144			−0.420072	−	0.907491i	$-0.637995\pi$
$571$	−20.0758			−0.840144			−0.420072	+	0.907491i	$0.637995\pi$
$572$	−9.46562	+	3.44520i	−0.395777	+	0.144051i
$573$	4.15834	+	22.3774i	0.173717	+	0.934831i
$574$	19.6869	−	16.5193i	0.821715	−	0.689500i
$575$	0.509670	−	0.607401i	0.0212547	−	0.0253304i
$576$	−2.33322	−	1.88576i	−0.0972175	−	0.0785733i
$577$	14.5779	+	25.2497i	0.606887	+	1.05116i	0.991750	+	0.128185i	$0.0409152\pi$
$577$	14.5779	+	25.2497i	0.606887	+	1.05116i	−0.384864	+	0.922973i	$0.625751\pi$
$578$	−8.48397	+	14.6947i	−0.352887	+	0.611217i
$579$	21.8048	−	0.200579i	0.906177	−	0.00833580i
$580$	−0.331570	+	0.910982i	−0.0137677	+	0.0378264i
$581$	31.5955	+	18.2417i	1.31080	+	0.756792i
$582$	13.2486	+	10.9108i	0.549172	+	0.452267i
$583$	−16.4641	+	2.90307i	−0.681875	+	0.120233i
$584$	−0.279146	−	0.234231i	−0.0115511	−	0.00969255i
$585$	−1.59620	+	10.1399i	−0.0659946	+	0.419234i
$586$	−5.50209	+	31.2039i	−0.227289	+	1.28902i
$587$	4.05379	+	11.1377i	0.167318	+	0.459702i	0.994807	−	0.101780i	$-0.0324537\pi$
$587$	4.05379	+	11.1377i	0.167318	+	0.459702i	−0.827489	+	0.561482i	$0.810231\pi$
$588$	−0.531427	−	1.41932i	−0.0219157	−	0.0585319i
$589$	29.7928	−	10.8462i	1.22759	−	0.446910i
$590$		−	13.9069i		−	0.572540i
$591$	−8.85813	+	7.57279i	−0.364375	+	0.311503i
$592$	−6.34541	−	1.11887i	−0.260795	−	0.0459851i
$593$	−4.57942	−	5.45754i	−0.188054	−	0.224114i	0.663777	−	0.747930i	$-0.268952\pi$
$593$	−4.57942	−	5.45754i	−0.188054	−	0.224114i	−0.851831	+	0.523816i	$0.824508\pi$
$594$	14.2250	−	5.62664i	0.583658	−	0.230864i
$595$	0.0872609	+	0.494881i	0.00357735	+	0.0202881i
$596$	−2.05976	+	1.18920i	−0.0843710	+	0.0487116i
$597$	−13.6970	−	2.28545i	−0.560581	−	0.0935372i
$598$	2.54939	+	0.927902i	0.104252	+	0.0379447i
$599$	−15.8651	−	5.77443i	−0.648232	−	0.235937i	−0.00308427	−	0.999995i	$-0.500982\pi$
$599$	−15.8651	−	5.77443i	−0.648232	−	0.235937i	−0.645147	+	0.764058i	$0.723204\pi$
$600$	−1.70843	−	0.285065i	−0.0697464	−	0.0116377i
$601$	25.5919	−	14.7755i	1.04392	−	0.602705i	0.122976	−	0.992410i	$-0.460756\pi$
$601$	25.5919	−	14.7755i	1.04392	−	0.602705i	0.920940	+	0.389704i	$0.127423\pi$
$602$	−5.40119	−	30.6317i	−0.220136	−	1.24845i
$603$	−0.302427	−	16.4369i	−0.0123158	−	0.669362i
$604$	−3.32871	−	3.96700i	−0.135443	−	0.161415i
$605$	−2.29756	−	0.405122i	−0.0934092	−	0.0164706i
$606$	10.1505	−	8.67762i	0.412335	−	0.352504i
$607$		−	18.8869i		−	0.766596i	−0.923625	−	0.383298i	$-0.874788\pi$
$607$		−	18.8869i		−	0.766596i	0.923625	−	0.383298i	$-0.125212\pi$
$608$	−0.000326752	−	4.35890i	−1.32516e−5	−	0.176777i
$609$	−1.65228	−	4.41287i	−0.0669536	−	0.178818i
$610$	−0.251375	−	0.690647i	−0.0101779	−	0.0279635i
$611$	−0.117167	+	0.664489i	−0.00474008	+	0.0268823i
$612$	−0.530676	−	0.0835375i	−0.0214513	−	0.00337680i
$613$	14.1014	+	11.8325i	0.569551	+	0.477910i	0.881497	−	0.472190i	$-0.156536\pi$
$613$	14.1014	+	11.8325i	0.569551	+	0.477910i	−0.311946	+	0.950100i	$0.600981\pi$
$614$	−12.4947	+	2.20315i	−0.504245	+	0.0889121i
$615$	12.2443	+	10.0837i	0.493737	+	0.406614i
$616$	7.15468	+	4.13076i	0.288270	+	0.166433i
$617$	0.676460	−	1.85856i	0.0272333	−	0.0748228i	−0.925331	−	0.379160i	$-0.876213\pi$
$617$	0.676460	−	1.85856i	0.0272333	−	0.0748228i	0.952564	+	0.304338i	$0.0984351\pi$
$618$	−5.46074	+	0.0502326i	−0.219663	+	0.00202065i
$619$	11.7377	−	20.3303i	0.471779	−	0.817145i	−0.527700	−	0.849431i	$-0.676945\pi$
$619$	11.7377	−	20.3303i	0.471779	−	0.817145i	0.999479	+	0.0322857i	$0.0102786\pi$
$620$	3.63689	+	6.29928i	0.146061	+	0.252985i
$621$	−3.90900	−	1.30178i	−0.156863	−	0.0522386i
$622$	−12.8227	+	15.2814i	−0.514141	+	0.612730i
$623$	28.4228	−	23.8496i	1.13874	−	0.955513i
$624$	−1.08275	−	5.82663i	−0.0433446	−	0.233252i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	10.2868			0.411145
$627$	19.3510	+	10.9343i	0.772803	+	0.436673i
$628$	−12.6909			−0.506423
$629$	−1.08422	+	0.394624i	−0.0432307	+	0.0157347i
$630$	7.21217	−	4.34278i	0.287340	−	0.173020i
$631$	29.0205	−	24.3511i	1.15529	−	0.969402i	0.155458	−	0.987843i	$-0.450315\pi$
$631$	29.0205	−	24.3511i	1.15529	−	0.969402i	0.999830	+	0.0184410i	$0.00587028\pi$
$632$	3.44191	−	4.10191i	0.136912	−	0.163165i
$633$	9.42983	+	15.9914i	0.374802	+	0.635602i
$634$	1.89229	+	3.27754i	0.0751524	+	0.130168i
$635$	9.62978	−	16.6793i	0.382146	−	0.661897i
$636$	−0.0904753	−	9.83549i	−0.00358758	−	0.390002i
$637$	1.02398	−	2.81336i	0.0405715	−	0.111469i
$638$	2.47166	+	1.42701i	0.0978539	+	0.0564960i
$639$	−29.5418	−	10.1409i	−1.16865	−	0.401166i
$640$	0.984808	−	0.173648i	0.0389279	−	0.00686405i
$641$	−24.5465	−	20.5970i	−0.969530	−	0.813532i	0.0129474	−	0.999916i	$-0.495879\pi$
$641$	−24.5465	−	20.5970i	−0.969530	−	0.813532i	−0.982477	+	0.186384i	$0.940323\pi$
$642$	14.5959	+	8.24889i	0.576055	+	0.325558i
$643$	−1.49452	+	8.47583i	−0.0589380	+	0.334254i	−0.999992	−	0.00400231i	$-0.998726\pi$
$643$	−1.49452	+	8.47583i	−0.0589380	+	0.334254i	0.941054	+	0.338256i	$0.109837\pi$
$644$	−0.761024	−	2.09090i	−0.0299886	−	0.0823929i
$645$	17.9790	−	6.73175i	0.707923	−	0.265062i
$646$	−0.390326	−	0.675947i	−0.0153572	−	0.0265948i
$647$			1.68767i			0.0663490i	0.999450	+	0.0331745i	$0.0105617\pi$
$647$			1.68767i			0.0663490i	−0.999450	+	0.0331745i	$0.989438\pi$
$648$	1.88782	+	8.79978i	0.0741606	+	0.345688i
$649$	−40.3197	−	7.10946i	−1.58269	−	0.279071i
$650$	−2.19936	−	2.62110i	−0.0862660	−	0.102808i
$651$	−33.3323	−	11.7859i	−1.30640	−	0.461925i
$652$	2.99003	+	16.9573i	0.117099	+	0.664099i
$653$	−11.2100	+	6.47211i	−0.438682	+	0.253273i	−0.703038	−	0.711152i	$-0.748174\pi$
$653$	−11.2100	+	6.47211i	−0.438682	+	0.253273i	0.264356	+	0.964425i	$0.414841\pi$
$654$	4.73458	−	28.3750i	0.185137	−	1.10955i
$655$	−1.85093	−	0.673684i	−0.0723219	−	0.0263230i
$656$	−8.60564	−	3.13220i	−0.335994	−	0.122292i
$657$	0.209605	+	1.07291i	0.00817745	+	0.0418584i
$658$	0.479251	−	0.276696i	0.0186832	−	0.0107867i
$659$	5.64156	+	31.9949i	0.219764	+	1.24634i	0.872446	+	0.488711i	$0.162533\pi$
$659$	5.64156	+	31.9949i	0.219764	+	1.24634i	−0.652682	+	0.757632i	$0.726356\pi$
$660$	−1.69985	+	4.80744i	−0.0661666	+	0.187129i
$661$	−19.3267	−	23.0326i	−0.751720	−	0.895866i	0.245574	−	0.969378i	$-0.421024\pi$
$661$	−19.3267	−	23.0326i	−0.751720	−	0.895866i	−0.997294	+	0.0735123i	$0.976579\pi$
$662$	3.02489	+	0.533369i	0.117566	+	0.0207300i
$663$	−0.689601	−	0.806647i	−0.0267819	−	0.0313276i
$664$		−	13.0008i		−	0.504528i
$665$	11.4948	+	4.18277i	0.445748	+	0.162201i
$666$	12.6953	+	14.5765i	0.491933	+	0.564827i
$667$	−0.262904	−	0.722322i	−0.0101797	−	0.0279684i
$668$	2.72639	−	15.4621i	0.105487	−	0.598248i
$669$	−6.58642	+	11.6543i	−0.254646	+	0.450581i
$670$	4.19784	+	3.52240i	0.162177	+	0.136082i
$671$	−2.13087	+	0.375729i	−0.0822612	+	0.0145049i
$672$	−3.08992	+	3.75198i	−0.119196	+	0.144736i
$673$	−38.3746	−	22.1556i	−1.47923	−	0.854035i	−0.479508	−	0.877537i	$-0.659185\pi$
$673$	−38.3746	−	22.1556i	−1.47923	−	0.854035i	−0.999724	+	0.0235022i	$0.992518\pi$
$674$	−10.4690	+	28.7633i	−0.403250	+	1.10792i
$675$	3.44858	+	3.88681i	0.132736	+	0.149603i
$676$	−0.646336	+	1.11949i	−0.0248591	+	0.0430572i
$677$	−10.9227	−	18.9187i	−0.419793	−	0.727103i	0.576125	−	0.817361i	$-0.304564\pi$
$677$	−10.9227	−	18.9187i	−0.419793	−	0.727103i	−0.995918	+	0.0902585i	$0.971231\pi$
$678$	1.93255	−	1.13959i	0.0742193	−	0.0437657i
$679$	17.8742	−	21.3017i	0.685950	−	0.817483i
$680$	0.137176	−	0.115104i	0.00526046	−	0.00441405i
$681$	−48.6314	+	9.03704i	−1.86356	+	0.346300i
$682$	20.1224	−	7.32396i	0.770527	−	0.280449i
$683$	−2.28287			−0.0873516			−0.0436758	−	0.999046i	$-0.513907\pi$
$683$	−2.28287			−0.0873516			−0.0436758	+	0.999046i	$0.513907\pi$
$684$	−8.21907	+	10.1709i	−0.314264	+	0.388893i
$685$	8.69837			0.332348
$686$	16.1517	−	5.87872i	0.616673	−	0.224451i
$687$	25.7502	−	4.78509i	0.982432	−	0.182563i
$688$	−8.49079	+	7.12462i	−0.323708	+	0.271624i
$689$	12.4896	−	14.8846i	0.475817	−	0.567057i
$690$	1.18299	−	0.697588i	0.0450357	−	0.0265567i
$691$	−13.8739	−	24.0303i	−0.527788	−	0.914155i	−0.999475	−	0.0323896i	$-0.989688\pi$
$691$	−13.8739	−	24.0303i	−0.527788	−	0.914155i	0.471687	−	0.881766i	$-0.343645\pi$
$692$	−6.72177	+	11.6424i	−0.255523	+	0.442579i
$693$	−8.90382	−	23.1300i	−0.338228	−	0.878635i
$694$	11.4958	−	31.5844i	0.436373	−	1.19893i
$695$	0.941941	+	0.543830i	0.0357299	+	0.0206286i
$696$	−1.06745	+	1.29616i	−0.0404615	+	0.0491309i
$697$	−1.61500	+	0.284768i	−0.0611725	+	0.0107864i
$698$	17.3911	+	14.5929i	0.658263	+	0.552349i
$699$	−11.8735	+	21.0095i	−0.449098	+	0.794653i
$700$	−0.487299	+	2.76361i	−0.0184182	+	0.104455i
$701$	−3.37874	−	9.28302i	−0.127613	−	0.350615i	0.859389	−	0.511323i	$-0.170844\pi$
$701$	−3.37874	−	9.28302i	−0.127613	−	0.350615i	−0.987002	+	0.160708i	$0.948622\pi$
$702$	−8.46134	+	15.6366i	−0.319353	+	0.590166i
$703$	−4.87495	+	27.6594i	−0.183862	+	1.04319i
$704$		−	2.94398i		−	0.110955i
$705$	0.221948	+	0.259620i	0.00835906	+	0.00977786i
$706$	−26.6656	−	4.70186i	−1.00357	−	0.176957i
$707$	−13.9075	−	16.5743i	−0.523045	−	0.623340i
$708$	8.02987	−	22.7097i	0.301781	−	0.853483i
$709$	1.06981	+	6.06722i	0.0401777	+	0.227859i	0.998284	−	0.0585526i	$-0.0186485\pi$
$709$	1.06981	+	6.06722i	0.0401777	+	0.227859i	−0.958107	+	0.286412i	$0.907537\pi$
$710$	9.01643	−	5.20564i	0.338381	−	0.195364i
$711$	−15.7659	+	3.08003i	−0.591269	+	0.115510i
$712$	−12.4244	−	4.52209i	−0.465622	−	0.169473i
$713$	−5.41960	−	1.97257i	−0.202966	−	0.0738735i
$714$	−0.143249	+	0.858513i	−0.00536097	+	0.0321290i
$715$	−8.72356	+	5.03655i	−0.326243	+	0.188356i
$716$	−2.64846	−	15.0202i	−0.0989777	−	0.561331i
$717$	41.0638	+	14.5196i	1.53355	+	0.542246i
$718$	−20.0176	−	23.8561i	−0.747050	−	0.890300i
$719$	−45.4518	−	8.01438i	−1.69507	−	0.298886i	−0.759100	−	0.650974i	$-0.774361\pi$
$719$	−45.4518	−	8.01438i	−1.69507	−	0.298886i	−0.935967	+	0.352088i	$0.885472\pi$
$720$	−2.62523	−	1.45195i	−0.0978366	−	0.0541110i
$721$			8.84779i			0.329509i
$722$	−19.0000	+	0.00284856i	−0.707107	+	0.000106012i
$723$	−21.5418	+	8.06574i	−0.801149	+	0.299968i
$724$	7.89648	+	21.6954i	0.293470	+	0.806303i
$725$	−0.168343	+	0.954718i	−0.00625209	+	0.0354573i
$726$	−3.51794	−	1.98817i	−0.130563	−	0.0737878i
$727$	−38.7414	−	32.5079i	−1.43684	−	1.20565i	−0.941528	−	0.336934i	$-0.890610\pi$
$727$	−38.7414	−	32.5079i	−1.43684	−	1.20565i	−0.495310	−	0.868716i	$-0.664946\pi$
$728$	−9.45596	+	1.66734i	−0.350461	+	0.0617958i
$729$	12.1896	−	24.0918i	0.451466	−	0.892289i
$730$	−0.315579	−	0.182199i	−0.0116801	−	0.00674350i
$731$	−0.678844	+	1.86511i	−0.0251079	+	0.0689835i
$732$	−0.0117097	−	1.27295i	−0.000432804	−	0.0470497i
$733$	−9.55223	+	16.5449i	−0.352820	+	0.611101i	−0.986742	−	0.162295i	$-0.948110\pi$
$733$	−9.55223	+	16.5449i	−0.352820	+	0.611101i	0.633923	+	0.773396i	$0.281444\pi$
$734$	8.56874	+	14.8415i	0.316278	+	0.547809i
$735$	−0.769816	−	1.30548i	−0.0283951	−	0.0481533i
$736$	−0.509670	+	0.607401i	−0.0187867	+	0.0223891i
$737$	12.3583	−	10.3699i	0.455225	−	0.381979i
$738$	14.1723	+	23.5363i	0.521689	+	0.866382i
$739$	−32.6058	+	11.8675i	−1.19942	+	0.436554i	−0.863023	−	0.505165i	$-0.831432\pi$
$739$	−32.6058	+	11.8675i	−1.19942	+	0.436554i	−0.336400	+	0.941719i	$0.609209\pi$
$740$	−6.44330			−0.236860
$741$	−25.3973	+	4.72149i	−0.932995	+	0.173448i
$742$	−15.9360			−0.585028
$743$	−4.24197	+	1.54395i	−0.155623	+	0.0566421i	−0.418657	−	0.908144i	$-0.637499\pi$
$743$	−4.24197	+	1.54395i	−0.155623	+	0.0566421i	0.263034	+	0.964787i	$0.415277\pi$
$744$	2.30175	+	12.3865i	0.0843862	+	0.454111i
$745$	−1.82196	+	1.52881i	−0.0667516	+	0.0560112i
$746$	−4.33735	+	5.16906i	−0.158802	+	0.189253i
$747$	−24.5163	+	30.3337i	−0.897006	+	1.10985i
$748$	−0.263590	−	0.456550i	−0.00963779	−	0.0166931i
$749$	13.5817	−	23.5242i	0.496264	−	0.859555i
$750$	−1.73198	+	0.0159322i	−0.0632429	+	0.000581762i
$751$	9.49119	−	26.0768i	0.346339	−	0.951557i	−0.637174	−	0.770720i	$-0.719897\pi$
$751$	9.49119	−	26.0768i	0.346339	−	0.951557i	0.983513	−	0.180838i	$-0.0578809\pi$
$752$	−0.170780	−	0.0986001i	−0.00622772	−	0.00359558i
$753$	−32.8398	−	27.0450i	−1.19675	−	0.985575i
$754$	−3.26666	+	0.576001i	−0.118965	+	0.0209767i
$755$	−3.96700	−	3.32871i	−0.144374	−	0.121144i
$756$	14.2848	−	2.92735i	0.519533	−	0.106467i
$757$	−1.17463	+	6.66166i	−0.0426927	+	0.242122i	−0.998685	−	0.0512701i	$-0.983673\pi$
$757$	−1.17463	+	6.66166i	−0.0426927	+	0.242122i	0.955992	+	0.293392i	$0.0947842\pi$
$758$	−9.06976	−	24.9190i	−0.329429	−	0.905098i
$759$	−1.41772	−	3.78641i	−0.0514599	−	0.137438i
$760$	−0.757237	−	4.29262i	−0.0274679	−	0.155710i
$761$			32.9367i			1.19395i	0.802259	+	0.596977i	$0.203632\pi$
$761$			32.9367i			1.19395i	−0.802259	+	0.596977i	$0.796368\pi$
$762$	25.3558	−	21.6766i	0.918544	−	0.785261i
$763$	−45.9002	−	8.09345i	−1.66170	−	0.293002i
$764$	−8.44674	−	10.0664i	−0.305592	−	0.364191i
$765$	−0.537120	+	0.00988263i	−0.0194196	+	0.000357307i
$766$	3.26632	+	18.5242i	0.118017	+	0.669307i
$767$	41.2089	−	23.7920i	1.48797	−	0.859079i
$768$	1.70843	+	0.285065i	0.0616477	+	0.0102864i
$769$	20.4283	+	7.43530i	0.736664	+	0.268124i	0.682983	−	0.730434i	$-0.260682\pi$
$769$	20.4283	+	7.43530i	0.736664	+	0.268124i	0.0536813	+	0.998558i	$0.482904\pi$
$770$	7.76328	+	2.82560i	0.279769	+	0.101828i
$771$	29.7566	+	4.96511i	1.07166	+	0.178814i
$772$	−10.9029	+	6.29477i	−0.392403	+	0.226554i
$773$	−6.43318	−	36.4844i	−0.231386	−	1.31225i	−0.850094	−	0.526632i	$-0.823455\pi$
$773$	−6.43318	−	36.4844i	−0.231386	−	1.31225i	0.618708	−	0.785621i	$-0.287656\pi$
$774$	33.2462	−	0.611706i	1.19501	−	0.0219873i
$775$	4.67549	+	5.57204i	0.167949	+	0.200153i
$776$	−9.75856	−	1.72070i	−0.350312	−	0.0617694i
$777$	23.8048	−	20.3507i	0.853992	−	0.730076i
$778$		−	12.4277i		−	0.445554i
$779$	−13.6501	+	37.5122i	−0.489066	+	1.34401i
$780$	−2.07808	−	5.55010i	−0.0744073	−	0.198725i
$781$	−10.4831	−	28.8021i	−0.375115	−	1.03062i
$782$	−0.0246556	+	0.139829i	−0.000881682	+	0.00500027i
$783$	4.93484	−	1.01128i	0.176357	−	0.0361403i
$784$	0.670292	+	0.562442i	0.0239390	+	0.0200872i
$785$	−12.4981	+	2.20376i	−0.446077	+	0.0786554i
$786$	−2.63354	−	2.16884i	−0.0939353	−	0.0773599i
$787$	−30.6109	−	17.6732i	−1.09116	−	0.629982i	−0.157276	−	0.987555i	$-0.550271\pi$
$787$	−30.6109	−	17.6732i	−1.09116	−	0.629982i	−0.933885	+	0.357572i	$0.883605\pi$
$788$	2.30124	−	6.32262i	0.0819784	−	0.225234i
$789$	−37.9902	+	0.349466i	−1.35249	+	0.0124413i
$790$	2.67733	−	4.63727i	0.0952551	−	0.164987i
$791$	−1.81747	−	3.14795i	−0.0646217	−	0.111928i
$792$	−5.55163	+	6.86894i	−0.197269	+	0.244077i
$793$	1.61647	−	1.92643i	0.0574024	−	0.0684096i
$794$	8.58256	−	7.20162i	0.304584	−	0.255576i
$795$	−1.79701	−	9.67035i	−0.0637336	−	0.342972i
$796$	7.53380	−	2.74208i	0.267028	−	0.0971904i
$797$	33.2298			1.17706			0.588530	−	0.808475i	$-0.299707\pi$
$797$	33.2298			1.17706			0.588530	+	0.808475i	$0.299707\pi$
$798$	16.3555	+	13.4674i	0.578979	+	0.476742i
$799$	−0.0353127			−0.00124927
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	20.4611	+	33.9804i	0.722959	+	1.20064i
$802$	21.1353	−	17.7346i	0.746314	−	0.626232i
$803$	−0.689570	+	0.821798i	−0.0243344	+	0.0290006i
$804$	4.82113	+	8.17583i	0.170028	+	0.288339i
$805$	−1.11254	−	1.92698i	−0.0392120	−	0.0679172i
$806$	−12.4440	+	21.5536i	−0.438320	+	0.759193i
$807$	−0.0169924	−	1.84723i	−0.000598160	−	0.0650254i
$808$	−2.63698	+	7.24505i	−0.0927687	+	0.254880i
$809$	43.3260	+	25.0143i	1.52326	+	0.879455i	0.999621	+	0.0275152i	$0.00875948\pi$
$809$	43.3260	+	25.0143i	1.52326	+	0.879455i	0.523640	+	0.851940i	$0.324574\pi$
$810$	3.38721	+	8.33828i	0.119014	+	0.292977i
$811$	−52.4680	+	9.25152i	−1.84240	+	0.324865i	−0.982595	−	0.185759i	$-0.940526\pi$
$811$	−52.4680	+	9.25152i	−1.84240	+	0.324865i	−0.859804	+	0.510623i	$0.829415\pi$
$812$	2.08403	+	1.74871i	0.0731350	+	0.0613675i
$813$	39.6378	+	22.4013i	1.39016	+	0.785648i
$814$	−3.29392	+	18.6807i	−0.115452	+	0.654759i
$815$	5.88921	+	16.1805i	0.206290	+	0.566777i
$816$	0.290466	−	0.108757i	0.0101683	−	0.00380726i
$817$	31.0583	+	37.0082i	1.08659	+	1.29475i
$818$			14.0635i			0.491718i
$819$	25.2070	+	13.9414i	0.880805	+	0.487152i
$820$	−9.01881	−	1.59026i	−0.314950	−	0.0555342i
$821$	2.84151	+	3.38638i	0.0991693	+	0.118185i	0.813346	−	0.581780i	$-0.197643\pi$
$821$	2.84151	+	3.38638i	0.0991693	+	0.118185i	−0.714177	+	0.699965i	$0.753199\pi$
$822$	14.2042	+	5.02244i	0.495429	+	0.175178i
$823$	3.00453	+	17.0395i	0.104731	+	0.593960i	0.991327	+	0.131416i	$0.0419523\pi$
$823$	3.00453	+	17.0395i	0.104731	+	0.593960i	−0.886596	+	0.462544i	$0.846937\pi$
$824$	2.73049	−	1.57645i	0.0951210	−	0.0549181i
$825$	−0.839223	+	5.02958i	−0.0292180	+	0.175108i
$826$	−36.6727	−	13.3478i	−1.27601	−	0.464429i
$827$	47.8075	+	17.4005i	1.66243	+	0.605075i	0.990742	−	0.135759i	$-0.0433472\pi$
$827$	47.8075	+	17.4005i	1.66243	+	0.605075i	0.671688	+	0.740834i	$0.265569\pi$
$828$	2.33458	−	0.456084i	0.0811324	−	0.0158500i
$829$	40.6182	−	23.4509i	1.41073	−	0.814485i	0.415272	−	0.909697i	$-0.363686\pi$
$829$	40.6182	−	23.4509i	1.41073	−	0.814485i	0.995457	+	0.0952126i	$0.0303531\pi$
$830$	−2.25756	−	12.8033i	−0.0783611	−	0.444408i
$831$	2.50953	−	7.09734i	0.0870546	−	0.246204i
$832$	2.19936	+	2.62110i	0.0762491	+	0.0908701i
$833$	0.154307	+	0.0272085i	0.00534642	+	0.000942717i
$834$	1.22416	+	1.43194i	0.0423892	+	0.0495839i
$835$		−	15.7007i		−	0.543344i
$836$	−12.8325		0.000961951i	−0.443821		3.32698e-5i
$837$	17.9875	−	33.2410i	0.621738	−	1.14898i
$838$	−1.46261	−	4.01849i	−0.0505251	−	0.138816i
$839$	8.90715	−	50.5150i	0.307509	−	1.74397i	−0.303944	−	0.952690i	$-0.598304\pi$
$839$	8.90715	−	50.5150i	0.307509	−	1.74397i	0.611453	−	0.791281i	$-0.290585\pi$
$840$	−2.39146	+	4.23154i	−0.0825131	+	0.146002i
$841$	−21.4953	−	18.0367i	−0.741219	−	0.621956i
$842$	−13.8112	+	2.43528i	−0.475964	+	0.0839253i
$843$	6.22354	−	7.55702i	0.214350	−	0.260278i
$844$	−9.28233	−	5.35916i	−0.319511	−	0.184470i
$845$	−0.442120	+	1.21471i	−0.0152094	+	0.0417875i
$846$	0.212532	+	0.552106i	0.00730700	+	0.0189818i
$847$	−3.27349	+	5.66985i	−0.112478	+	0.194818i
$848$	2.83938	+	4.91795i	0.0975047	+	0.168883i
$849$	−37.9054	+	22.3521i	−1.30091	+	0.767122i
$850$	0.115104	−	0.137176i	0.00394804	−	0.00470509i
$851$	3.91366	−	3.28395i	0.134159	−	0.112572i
$852$	17.7294	−	3.29460i	0.607398	−	0.112871i
$853$	−9.52240	+	3.46587i	−0.326041	+	0.118669i	−0.499854	−	0.866109i	$-0.666613\pi$
$853$	−9.52240	+	3.46587i	−0.326041	+	0.118669i	0.173814	+	0.984779i	$0.444391\pi$
$854$	−2.06251			−0.0705776
$855$	−6.32805	+	11.4436i	−0.216415	+	0.391363i
$856$	−9.67962			−0.330843
$857$	−35.6104	+	12.9611i	−1.21643	+	0.442744i	−0.868929	−	0.494936i	$-0.835192\pi$
$857$	−35.6104	+	12.9611i	−1.21643	+	0.442744i	−0.347500	+	0.937680i	$0.612969\pi$
$858$	−17.1535	+	3.18758i	−0.585610	+	0.108822i
$859$	−7.45174	+	6.25275i	−0.254250	+	0.213341i	−0.761000	−	0.648752i	$-0.775291\pi$
$859$	−7.45174	+	6.25275i	−0.254250	+	0.213341i	0.506750	+	0.862093i	$0.330847\pi$
$860$	−7.12462	+	8.49079i	−0.242948	+	0.289534i
$861$	38.3427	−	22.6100i	1.30672	−	0.770546i
$862$	5.64325	+	9.77439i	0.192210	+	0.332917i
$863$	27.8105	−	48.1692i	0.946681	−	1.63970i	0.194331	−	0.980936i	$-0.437746\pi$
$863$	27.8105	−	48.1692i	0.946681	−	1.63970i	0.752350	−	0.658764i	$-0.228920\pi$
$864$	−3.44858	−	3.88681i	−0.117323	−	0.132232i
$865$	−4.59796	+	12.6328i	−0.156335	+	0.429528i
$866$	−14.8205	−	8.55661i	−0.503620	−	0.290765i
$867$	−18.6832	+	22.6863i	−0.634515	+	0.770469i
$868$	20.1019	−	3.54451i	0.682303	−	0.120308i
$869$	−12.0759	−	10.1329i	−0.409647	−	0.343735i
$870$	−0.826153	+	1.46183i	−0.0280092	+	0.0495607i
$871$	−3.25590	+	18.4651i	−0.110322	+	0.625667i
$872$	5.68054	+	15.6072i	0.192367	+	0.528525i
$873$	19.5240	+	22.4171i	0.660788	+	0.758703i
$874$	2.64777	+	2.22140i	0.0895620	+	0.0751400i
$875$			2.80624i			0.0948684i
$876$	−0.410130	−	0.479742i	−0.0138570	−	0.0162090i
$877$	−55.5785	−	9.80000i	−1.87675	−	0.330922i	−0.885687	−	0.464284i	$-0.846312\pi$
$877$	−55.5785	−	9.80000i	−1.87675	−	0.330922i	−0.991068	+	0.133361i	$0.957423\pi$
$878$	−21.6230	−	25.7693i	−0.729741	−	0.869672i
$879$	−18.2951	+	51.7413i	−0.617078	+	1.74519i
$880$	−0.511216	−	2.89925i	−0.0172331	−	0.0977337i
$881$	−22.8706	+	13.2043i	−0.770529	+	0.444865i	−0.833063	−	0.553178i	$-0.813415\pi$
$881$	−22.8706	+	13.2043i	−0.770529	+	0.444865i	0.0625344	+	0.998043i	$0.480082\pi$
$882$	−0.503308	−	2.57631i	−0.0169473	−	0.0867488i
$883$	37.9166	+	13.8005i	1.27600	+	0.464425i	0.889106	−	0.457701i	$-0.151327\pi$
$883$	37.9166	+	13.8005i	1.27600	+	0.464425i	0.386890	+	0.922126i	$0.373549\pi$
$884$	0.575756	+	0.209558i	0.0193648	+	0.00704820i
$885$	3.96438	−	23.7591i	0.133261	−	0.798652i
$886$	−11.2562	+	6.49874i	−0.378158	+	0.218330i
$887$	−8.74325	−	49.5854i	−0.293569	−	1.66492i	−0.672960	−	0.739679i	$-0.734978\pi$
$887$	−8.74325	−	49.5854i	−0.293569	−	1.66492i	0.379391	−	0.925237i	$-0.376134\pi$
$888$	−10.5217	−	3.72036i	−0.353087	−	0.124847i
$889$	−34.7408	−	41.4024i	−1.16517	−	1.38859i
$890$	−13.0209	−	2.29593i	−0.436460	−	0.0769597i
$891$	25.9063	−	5.55770i	0.867895	−	0.186190i
$892$		−	7.72880i		−	0.258779i
$893$	−0.429732	+	0.744447i	−0.0143804	+	0.0249120i
$894$	−3.85796	+	1.44451i	−0.129029	+	0.0483115i
$895$	−5.21645	−	14.3321i	−0.174367	−	0.479069i
$896$	0.487299	−	2.76361i	0.0162795	−	0.0923257i
$897$	4.09095	+	2.31200i	0.136593	+	0.0771953i
$898$	1.18452	+	0.993931i	0.0395280	+	0.0331679i
$899$	6.94441	−	1.22449i	0.231609	−	0.0408389i
$900$	−2.83748	−	0.974027i	−0.0945825	−	0.0324676i
$901$	0.880660	+	0.508449i	0.0293390	+	0.0169389i
$902$	−9.22112	+	25.3348i	−0.307030	+	0.843557i
$903$	−0.495560	−	53.8718i	−0.0164912	−	1.79274i
$904$	−0.647652	+	1.12177i	−0.0215406	+	0.0373094i
$905$	11.5439	+	19.9946i	0.383731	+	0.664642i
$906$	−4.55601	−	7.72624i	−0.151363	−	0.256687i
$907$	1.31411	−	1.56610i	0.0436344	−	0.0520015i	−0.743786	−	0.668418i	$-0.766972\pi$
$907$	1.31411	−	1.56610i	0.0436344	−	0.0520015i	0.787420	+	0.616416i	$0.211416\pi$
$908$	21.8767	−	18.3567i	0.726004	−	0.609190i
$909$	19.8151	−	11.9316i	0.657225	−	0.395745i
$910$	−9.02277	+	3.28402i	−0.299102	+	0.108864i
$911$	5.99399			0.198590			0.0992948	−	0.995058i	$-0.468341\pi$
$911$	5.99399			0.198590			0.0992948	+	0.995058i	$0.468341\pi$
$912$	1.24201	−	7.44697i	0.0411270	−	0.246594i
$913$	−38.2740			−1.26668
$914$	19.6170	−	7.13999i	0.648871	−	0.236170i
$915$	−0.232578	−	1.25158i	−0.00768879	−	0.0413760i
$916$	−11.5837	+	9.71986i	−0.382735	+	0.321153i
$917$	−3.55302	+	4.23432i	−0.117331	+	0.139830i
$918$	−0.882811	−	0.293995i	−0.0291371	−	0.00970328i
$919$	24.2042	+	41.9230i	0.798424	+	1.38291i	0.920642	+	0.390408i	$0.127666\pi$
$919$	24.2042	+	41.9230i	0.798424	+	1.38291i	−0.122218	+	0.992503i	$0.539001\pi$
$920$	−0.396453	+	0.686676i	−0.0130707	+	0.0226390i
$921$	−21.9744	+	0.202139i	−0.724081	+	0.00666072i
$922$	−4.28635	+	11.7766i	−0.141163	+	0.387843i
$923$	30.8506	+	17.8116i	1.01546	+	0.586276i
$924$	11.0458	+	9.09666i	0.363379	+	0.299258i
$925$	−6.34541	+	1.11887i	−0.208636	+	0.0367881i
$926$	−5.23401	−	4.39185i	−0.172000	−	0.144325i
$927$	−9.34362	−	1.47085i	−0.306885	−	0.0483089i
$928$	0.168343	−	0.954718i	0.00552612	−	0.0313402i
$929$	15.9528	+	43.8299i	0.523393	+	1.43801i	0.866720	+	0.498795i	$0.166224\pi$
$929$	15.9528	+	43.8299i	0.523393	+	1.43801i	−0.343327	+	0.939216i	$0.611554\pi$
$930$	4.41767	+	11.7986i	0.144861	+	0.386892i
$931$	2.45141	−	2.92192i	0.0803416	−	0.0957620i
$932$		−	13.9329i		−	0.456389i
$933$	−26.2628	+	22.4520i	−0.859806	+	0.735046i
$934$	16.3802	+	2.88826i	0.535975	+	0.0945069i
$935$	−0.338864	−	0.403843i	−0.0110820	−	0.0132071i
$936$	−0.188833	−	10.2631i	−0.00617219	−	0.335458i
$937$	−2.07938	−	11.7927i	−0.0679302	−	0.385252i	−0.999751	−	0.0223317i	$-0.992891\pi$
$937$	−2.07938	−	11.7927i	−0.0679302	−	0.385252i	0.931820	−	0.362920i	$-0.118220\pi$
$938$	13.3177	−	7.68895i	0.434837	−	0.251053i
$939$	17.5744	+	2.93241i	0.573517	+	0.0956957i
$940$	−0.185308	−	0.0674464i	−0.00604407	−	0.00219986i
$941$	−46.9123	−	17.0747i	−1.52930	−	0.556619i	−0.565849	−	0.824509i	$-0.691451\pi$
$941$	−46.9123	−	17.0747i	−1.52930	−	0.556619i	−0.963450	+	0.267890i	$0.913674\pi$
$942$	−21.6816	−	3.61773i	−0.706424	−	0.117872i
$943$	6.28854	−	3.63069i	0.204783	−	0.118232i
$944$	2.41492	+	13.6957i	0.0785988	+	0.445756i
$945$	13.5595	−	5.36340i	0.441089	−	0.174472i
$946$	20.9747	+	24.9967i	0.681947	+	0.812712i
$947$	0.296171	+	0.0522230i	0.00962427	+	0.00169702i	0.178458	−	0.983947i	$-0.442889\pi$
$947$	0.296171	+	0.0522230i	0.00962427	+	0.00169702i	−0.168834	+	0.985645i	$0.554000\pi$
$948$	7.04957	−	6.02666i	0.228959	−	0.195737i
$949$		−	1.24683i		−	0.0404737i
$950$	−1.49114	−	4.09591i	−0.0483789	−	0.132889i
$951$	2.29853	+	6.13888i	0.0745351	+	0.199067i
$952$	−0.171870	−	0.472210i	−0.00557035	−	0.0153044i
$953$	−1.12852	+	6.40013i	−0.0365562	+	0.207321i	−0.997615	−	0.0690233i	$-0.978012\pi$
$953$	−1.12852	+	6.40013i	−0.0365562	+	0.207321i	0.961059	+	0.276344i	$0.0891228\pi$
$954$	2.64918	−	16.8290i	0.0857703	−	0.544860i
$955$	−10.0664	−	8.44674i	−0.325742	−	0.273330i
$956$	−24.7646	+	4.36666i	−0.800943	+	0.141228i
$957$	3.81587	+	3.14254i	0.123350	+	0.101584i
$958$	−5.71933	−	3.30206i	−0.184783	−	0.106685i
$959$	8.34863	−	22.9377i	0.269591	−	0.740696i
$960$	1.73198	−	0.0159322i	0.0558993	−	0.000514210i
$961$	10.9539	−	18.9727i	0.353352	−	0.612024i
$962$	−11.0232	−	19.0927i	−0.355402	−	0.615574i
$963$	22.5847	+	18.2534i	0.727781	+	0.588209i
$964$	8.53647	−	10.1734i	0.274941	−	0.327662i
$965$	−9.64415	+	8.09240i	−0.310456	+	0.260504i
$966$	−0.704117	−	3.78910i	−0.0226546	−	0.121912i
$967$	−36.2786	+	13.2043i	−1.16664	+	0.424622i	−0.851465	−	0.524412i	$-0.824285\pi$
$967$	−36.2786	+	13.2043i	−1.16664	+	0.424622i	−0.315175	+	0.949034i	$0.602063\pi$
$968$	2.33301			0.0749856
$969$	−0.474156	−	1.26608i	−0.0152321	−	0.0406722i
$970$	−9.90910			−0.318162
$971$	−18.9098	+	6.88262i	−0.606845	+	0.220874i	−0.627122	−	0.778921i	$-0.715767\pi$
$971$	−18.9098	+	6.88262i	−0.606845	+	0.220874i	0.0202770	+	0.999794i	$0.493545\pi$
$972$	0.716707	+	15.5720i	0.0229884	+	0.499471i
$973$	2.33815	−	1.96194i	0.0749577	−	0.0628969i
$974$	5.73337	−	6.83276i	0.183709	−	0.218936i
$975$	−3.01027	−	5.10492i	−0.0964060	−	0.163488i
$976$	0.367486	+	0.636504i	0.0117629	+	0.0203740i
$977$	−27.8764	+	48.2833i	−0.891845	+	1.54472i	−0.0541839	+	0.998531i	$0.517256\pi$
$977$	−27.8764	+	48.2833i	−0.891845	+	1.54472i	−0.837661	+	0.546190i	$0.816078\pi$
$978$	0.274335	+	29.8227i	0.00877227	+	0.953626i
$979$	−13.3129	+	36.5770i	−0.425483	+	1.16901i
$980$	0.757775	+	0.437502i	0.0242062	+	0.0139755i
$981$	16.1774	−	47.1270i	0.516505	−	1.50465i
$982$	−5.37581	+	0.947900i	−0.171549	+	0.0302487i
$983$	31.1696	+	26.1544i	0.994157	+	0.834197i	0.986164	−	0.165772i	$-0.0530114\pi$
$983$	31.1696	+	26.1544i	0.994157	+	0.834197i	0.00799255	+	0.999968i	$0.497456\pi$
$984$	−13.8093	−	7.80431i	−0.440224	−	0.248792i
$985$	1.16837	−	6.62617i	0.0372274	−	0.211127i
$986$	−0.0593744	−	0.163130i	−0.00189087	−	0.00519511i
$987$	0.897644	−	0.336098i	0.0285723	−	0.0106981i
$988$	11.4244	−	9.58765i	0.363458	−	0.305024i
$989$		−	8.78852i		−	0.279459i
$990$	−4.27451	+	7.72862i	−0.135853	+	0.245632i
$991$	32.4742	+	5.72607i	1.03158	+	0.181895i	0.663714	−	0.747986i	$-0.268979\pi$
$991$	32.4742	+	5.72607i	1.03158	+	0.181895i	0.367861	+	0.929881i	$0.380090\pi$
$992$	−4.67549	−	5.57204i	−0.148447	−	0.176912i
$993$	5.01577	+	1.77351i	0.159171	+	0.0562807i
$994$	−5.07341	−	28.7727i	−0.160919	−	0.912615i
$995$	6.94319	−	4.00865i	0.220114	−	0.127083i
$996$	3.70606	−	22.2109i	0.117431	−	0.703781i
$997$	−0.991469	−	0.360865i	−0.0314001	−	0.0114287i	0.326272	−	0.945276i	$-0.394207\pi$
$997$	−0.991469	−	0.360865i	−0.0314001	−	0.0114287i	−0.357672	+	0.933847i	$0.616430\pi$
$998$	−9.79305	−	3.56438i	−0.309994	−	0.112828i
$999$	17.5338	+	28.5219i	0.554746	+	0.902393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.71.2	✓	84
3.2	odd	2		570.2.bb.b.71.3	yes	84
19.15	odd	18		570.2.bb.b.281.3	yes	84
57.53	even	18	inner	570.2.bb.a.281.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.2	✓	84	1.1	even	1	trivial
570.2.bb.a.281.2	yes	84	57.53	even	18	inner
570.2.bb.b.71.3	yes	84	3.2	odd	2
570.2.bb.b.281.3	yes	84	19.15	odd	18

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.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70290 + 0.316445i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.49197 - 0.879786i) q^{6} +(-1.40312 - 2.43028i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.79973 - 1.07775i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70290 + 0.316445i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(1.49197 - 0.879786i) q^{6} +(-1.40312 - 2.43028i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.79973 - 1.07775i) q^{9} +(-0.342020 + 0.939693i) q^{10} +(2.54956 + 1.47199i) q^{11} +(-1.10109 + 1.33701i) q^{12} +(-3.36962 + 0.594154i) q^{13} +(2.14971 + 1.80382i) q^{14} +(-0.852191 + 1.50790i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.0612457 - 0.168271i) q^{17} +(-2.26227 + 1.97031i) q^{18} +(-4.29273 - 0.756593i) q^{19} -1.00000i q^{20} +(3.15842 + 3.69451i) q^{21} +(-2.89925 - 0.511216i) q^{22} +(0.509670 + 0.607401i) q^{23} +(0.577400 - 1.63298i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(2.96319 - 1.71080i) q^{26} +(-4.42660 + 2.72125i) q^{27} +(-2.63701 - 0.959792i) q^{28} +(-0.910982 - 0.331570i) q^{29} +(0.285065 - 1.70843i) q^{30} +(-6.29928 + 3.63689i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.80744 - 1.69985i) q^{33} +(0.115104 + 0.137176i) q^{34} +(-2.76361 - 0.487299i) q^{35} +(1.45195 - 2.62523i) q^{36} -6.44330i q^{37} +(4.29262 - 0.757237i) q^{38} +(5.55010 - 2.07808i) q^{39} +(0.342020 + 0.939693i) q^{40} +(1.59026 - 9.01881i) q^{41} +(-4.23154 - 2.39146i) q^{42} +(-8.49079 - 7.12462i) q^{43} +(2.89925 - 0.511216i) q^{44} +(0.974027 - 2.83748i) q^{45} +(-0.686676 - 0.396453i) q^{46} +(0.0674464 - 0.185308i) q^{47} +(0.0159322 + 1.73198i) q^{48} +(-0.437502 + 0.757775i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.157544 + 0.267168i) q^{51} +(-2.19936 + 2.62110i) q^{52} +(-4.35018 + 3.65024i) q^{53} +(3.22892 - 4.07113i) q^{54} +(2.76643 - 1.00690i) q^{55} +2.80624 q^{56} +(7.54951 - 0.0700129i) q^{57} +0.969446 q^{58} +(-13.0683 + 4.75646i) q^{59} +(0.316445 + 1.70290i) q^{60} +(-0.563021 + 0.472431i) q^{61} +(4.67549 - 5.57204i) q^{62} +(-6.54758 - 5.29190i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.71080 + 2.96319i) q^{65} +(5.09890 - 0.0469041i) q^{66} +(1.87423 - 5.14941i) q^{67} +(-0.155080 - 0.0895352i) q^{68} +(-1.06012 - 0.873060i) q^{69} +(2.76361 - 0.487299i) q^{70} +(-7.97550 - 6.69224i) q^{71} +(-0.466506 + 2.96351i) q^{72} +(-0.0632772 + 0.358863i) q^{73} +(2.20374 + 6.05472i) q^{74} +(0.607343 + 1.62208i) q^{75} +(-3.77475 + 2.17973i) q^{76} -8.26151i q^{77} +(-4.50464 + 3.85100i) q^{78} +(-5.27331 - 0.929827i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(6.67692 - 6.03479i) q^{81} +(1.59026 + 9.01881i) q^{82} +(-11.2590 + 6.50039i) q^{83} +(4.79428 + 0.799961i) q^{84} +(-0.168271 - 0.0612457i) q^{85} +(10.4155 + 3.79093i) q^{86} +(1.65623 + 0.276355i) q^{87} +(-2.54956 + 1.47199i) q^{88} +(2.29593 + 13.0209i) q^{89} +(0.0551885 + 2.99949i) q^{90} +(6.17194 + 7.35543i) q^{91} +(0.780860 + 0.137687i) q^{92} +(9.57615 - 8.18663i) q^{93} +0.197200i q^{94} +(-3.33890 + 2.80210i) q^{95} +(-0.607343 - 1.62208i) q^{96} +(3.38911 + 9.31151i) q^{97} +(0.151943 - 0.861710i) q^{98} +(8.72449 + 1.37338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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