LMFDB - Embedded newform 430.2.q.d.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	430.81
Dual form			430.2.q.d.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(-0.366458 - 0.113037i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.191748 + 0.332117i) q^{6} +(-0.0855632 - 0.148200i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.35720 - 1.60711i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(-0.366458 - 0.113037i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.191748 + 0.332117i) q^{6} +(-0.0855632 - 0.148200i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.35720 - 1.60711i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(-3.23934 + 1.55998i) q^{11} +(0.281122 + 0.260843i) q^{12} +(-3.65202 - 0.550454i) q^{13} +(-0.163524 + 0.0504404i) q^{14} +(0.0286586 + 0.382423i) q^{15} +(0.623490 + 0.781831i) q^{16} +(0.504890 - 1.28644i) q^{17} +(-2.09135 + 1.94049i) q^{18} +(3.36543 - 2.29451i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(0.0146032 + 0.0639808i) q^{21} +(0.800050 + 3.50525i) q^{22} +(0.269393 - 3.59480i) q^{23} +(0.316859 - 0.216031i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.34931 + 3.43797i) q^{26} +(1.39947 + 1.75488i) q^{27} +(0.0127883 + 0.170648i) q^{28} +(-9.47220 + 2.92179i) q^{29} +(0.379212 + 0.0571570i) q^{30} +(-3.06062 - 2.83984i) q^{31} +(0.900969 - 0.433884i) q^{32} +(1.36342 - 0.205502i) q^{33} +(-1.14184 - 0.778492i) q^{34} +(-0.106696 + 0.133792i) q^{35} +(1.42647 + 2.47071i) q^{36} +(-2.14762 + 3.71979i) q^{37} +(-1.48810 - 3.79162i) q^{38} +(1.27609 + 0.614533i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-0.980995 + 4.29802i) q^{41} +0.0656262 q^{42} +(-4.36167 - 4.89651i) q^{43} +3.59539 q^{44} +(-0.634837 + 2.78140i) q^{45} +(-3.44473 - 1.06256i) q^{46} +(8.85959 + 4.26655i) q^{47} +(-0.140107 - 0.356986i) q^{48} +(3.48536 - 6.03682i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.330437 + 0.414354i) q^{51} +(3.05153 + 2.08050i) q^{52} +(8.35339 - 1.25907i) q^{53} +(2.02229 - 0.973883i) q^{54} +(2.63561 + 2.44549i) q^{55} +(0.169215 + 0.0255051i) q^{56} +(-1.49265 + 0.460422i) q^{57} +(0.740768 + 9.88487i) q^{58} +(-8.38122 - 10.5097i) q^{59} +(0.140107 - 0.356986i) q^{60} +(5.61012 - 5.20543i) q^{61} +(-3.44969 + 2.35196i) q^{62} +(-0.0364841 + 0.486847i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.821831 + 3.60068i) q^{65} +(0.103039 - 1.37496i) q^{66} +(10.2758 - 7.00593i) q^{67} +(-1.01306 + 0.939979i) q^{68} +(-0.505068 + 1.28689i) q^{69} +(0.106696 + 0.133792i) q^{70} +(-0.453881 - 6.05662i) q^{71} +(2.72618 - 0.840916i) q^{72} +(11.4818 + 1.73061i) q^{73} +(3.14863 + 2.92150i) q^{74} +(0.345517 - 0.166392i) q^{75} +(-4.02769 + 0.607077i) q^{76} +(0.508357 + 0.346592i) q^{77} +(0.883082 - 1.10735i) q^{78} +(-3.05423 - 5.29007i) q^{79} +(0.500000 - 0.866025i) q^{80} +(2.81240 + 7.16588i) q^{81} +(3.97197 + 1.91280i) q^{82} +(-0.108118 - 0.0333499i) q^{83} +(0.0146032 - 0.0639808i) q^{84} -1.38197 q^{85} +(-5.74431 + 3.16274i) q^{86} +3.80143 q^{87} +(0.800050 - 3.50525i) q^{88} +(-13.1872 - 4.06770i) q^{89} +(2.57040 + 1.23784i) q^{90} +(0.230902 + 0.588328i) q^{91} +(-1.80244 + 3.12192i) q^{92} +(0.800580 + 1.38664i) q^{93} +(6.13103 - 7.68806i) q^{94} +(-3.36543 - 2.29451i) q^{95} +(-0.379212 + 0.0571570i) q^{96} +(-0.224152 + 0.107946i) q^{97} +(-5.10990 - 4.74129i) q^{98} +(10.1428 + 1.52879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	−0.366458	−	0.113037i	−0.211574	−	0.0652621i	0.187156	−	0.982330i	$-0.440073\pi$
$3$	−0.366458	−	0.113037i	−0.211574	−	0.0652621i	−0.398731	+	0.917068i	$0.630549\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$6$	−0.191748	+	0.332117i	−0.0782807	+	0.135586i
$7$	−0.0855632	−	0.148200i	−0.0323399	−	0.0560143i	0.849402	−	0.527746i	$-0.176963\pi$
$7$	−0.0855632	−	0.148200i	−0.0323399	−	0.0560143i	−0.881742	+	0.471731i	$0.843629\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	−2.35720	−	1.60711i	−0.785734	−	0.535704i
$10$	−0.988831	+	0.149042i	−0.312696	+	0.0471313i
$11$	−3.23934	+	1.55998i	−0.976697	+	0.470352i	−0.852968	−	0.521964i	$-0.825200\pi$
$11$	−3.23934	+	1.55998i	−0.976697	+	0.470352i	−0.123729	+	0.992316i	$0.539485\pi$
$12$	0.281122	+	0.260843i	0.0811529	+	0.0752989i
$13$	−3.65202	−	0.550454i	−1.01289	−	0.152669i	−0.378434	−	0.925628i	$-0.623537\pi$
$13$	−3.65202	−	0.550454i	−1.01289	−	0.152669i	−0.634455	+	0.772960i	$0.718775\pi$
$14$	−0.163524	+	0.0504404i	−0.0437036	+	0.0134808i
$15$	0.0286586	+	0.382423i	0.00739963	+	0.0987412i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	0.504890	−	1.28644i	0.122454	−	0.312007i	−0.856481	−	0.516178i	$-0.827354\pi$
$17$	0.504890	−	1.28644i	0.122454	−	0.312007i	0.978935	+	0.204170i	$0.0654496\pi$
$18$	−2.09135	+	1.94049i	−0.492935	+	0.457377i
$19$	3.36543	−	2.29451i	0.772082	−	0.526396i	−0.112012	−	0.993707i	$-0.535729\pi$
$19$	3.36543	−	2.29451i	0.772082	−	0.526396i	0.884093	+	0.467311i	$0.154777\pi$
$20$	−0.0747301	+	0.997204i	−0.0167102	+	0.222982i
$21$	0.0146032	+	0.0639808i	0.00318668	+	0.0139618i
$22$	0.800050	+	3.50525i	0.170571	+	0.747322i
$23$	0.269393	−	3.59480i	0.0561724	−	0.749568i	−0.896009	−	0.444035i	$-0.853546\pi$
$23$	0.269393	−	3.59480i	0.0561724	−	0.749568i	0.952182	−	0.305533i	$-0.0988345\pi$
$24$	0.316859	−	0.216031i	0.0646785	−	0.0440971i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	−1.34931	+	3.43797i	−0.264620	+	0.674242i
$27$	1.39947	+	1.75488i	0.269328	+	0.337726i
$28$	0.0127883	+	0.170648i	0.00241676	+	0.0322494i
$29$	−9.47220	+	2.92179i	−1.75894	+	0.542562i	−0.994742	−	0.102416i	$-0.967343\pi$
$29$	−9.47220	+	2.92179i	−1.75894	+	0.542562i	−0.764201	+	0.644978i	$0.776867\pi$
$30$	0.379212	+	0.0571570i	0.0692343	+	0.0104354i
$31$	−3.06062	−	2.83984i	−0.549703	−	0.510050i	0.355701	−	0.934600i	$-0.384242\pi$
$31$	−3.06062	−	2.83984i	−0.549703	−	0.510050i	−0.905405	+	0.424550i	$0.860432\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	1.36342	−	0.205502i	0.237340	−	0.0357733i
$34$	−1.14184	−	0.778492i	−0.195824	−	0.133510i
$35$	−0.106696	+	0.133792i	−0.0180348	+	0.0226150i
$36$	1.42647	+	2.47071i	0.237744	+	0.411785i
$37$	−2.14762	+	3.71979i	−0.353066	+	0.611529i	−0.986785	−	0.162035i	$-0.948194\pi$
$37$	−2.14762	+	3.71979i	−0.353066	+	0.611529i	0.633719	+	0.773564i	$0.281528\pi$
$38$	−1.48810	−	3.79162i	−0.241402	−	0.615083i
$39$	1.27609	+	0.614533i	0.204338	+	0.0984040i
$40$	0.955573	+	0.294755i	0.151089	+	0.0466049i
$41$	−0.980995	+	4.29802i	−0.153206	+	0.671238i	0.838736	+	0.544539i	$0.183295\pi$
$41$	−0.980995	+	4.29802i	−0.153206	+	0.671238i	−0.991941	+	0.126699i	$0.959562\pi$
$42$	0.0656262			0.0101263
$43$	−4.36167	−	4.89651i	−0.665149	−	0.746711i
$43$	−4.36167	−	4.89651i	−0.665149	−	0.746711i
$44$	3.59539			0.542026
$45$	−0.634837	+	2.78140i	−0.0946359	+	0.414627i
$46$	−3.44473	−	1.06256i	−0.507897	−	0.156666i
$47$	8.85959	+	4.26655i	1.29230	+	0.622341i	0.948523	−	0.316709i	$-0.102578\pi$
$47$	8.85959	+	4.26655i	1.29230	+	0.622341i	0.343781	+	0.939050i	$0.388292\pi$
$48$	−0.140107	−	0.356986i	−0.0202226	−	0.0515264i
$49$	3.48536	−	6.03682i	0.497908	−	0.862402i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.330437	+	0.414354i	−0.0462704	+	0.0580212i
$52$	3.05153	+	2.08050i	0.423171	+	0.288513i
$53$	8.35339	−	1.25907i	1.14743	−	0.172947i	0.452322	−	0.891855i	$-0.350596\pi$
$53$	8.35339	−	1.25907i	1.14743	−	0.172947i	0.695105	+	0.718908i	$0.255358\pi$
$54$	2.02229	−	0.973883i	0.275199	−	0.132529i
$55$	2.63561	+	2.44549i	0.355386	+	0.329750i
$56$	0.169215	+	0.0255051i	0.0226123	+	0.00340826i
$57$	−1.49265	+	0.460422i	−0.197706	+	0.0609844i
$58$	0.740768	+	9.88487i	0.0972677	+	1.29795i
$59$	−8.38122	−	10.5097i	−1.09114	−	1.36825i	−0.924034	−	0.382310i	$-0.875128\pi$
$59$	−8.38122	−	10.5097i	−1.09114	−	1.36825i	−0.167108	−	0.985939i	$-0.553443\pi$
$60$	0.140107	−	0.356986i	0.0180877	−	0.0460867i
$61$	5.61012	−	5.20543i	0.718303	−	0.666488i	−0.233793	−	0.972286i	$-0.575114\pi$
$61$	5.61012	−	5.20543i	0.718303	−	0.666488i	0.952096	+	0.305799i	$0.0989235\pi$
$62$	−3.44969	+	2.35196i	−0.438111	+	0.298699i
$63$	−0.0364841	+	0.486847i	−0.00459657	+	0.0613369i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.821831	+	3.60068i	0.101936	+	0.446609i
$66$	0.103039	−	1.37496i	0.0126832	−	0.169246i
$67$	10.2758	−	7.00593i	1.25539	−	0.855911i	0.261384	−	0.965235i	$-0.415821\pi$
$67$	10.2758	−	7.00593i	1.25539	−	0.855911i	0.994006	+	0.109324i	$0.0348687\pi$
$68$	−1.01306	+	0.939979i	−0.122851	+	0.113989i
$69$	−0.505068	+	1.28689i	−0.0608030	+	0.154924i
$70$	0.106696	+	0.133792i	0.0127526	+	0.0159912i
$71$	−0.453881	−	6.05662i	−0.0538657	−	0.718788i	−0.957122	−	0.289686i	$-0.906449\pi$
$71$	−0.453881	−	6.05662i	−0.0538657	−	0.718788i	0.903256	−	0.429102i	$-0.141170\pi$
$72$	2.72618	−	0.840916i	0.321284	−	0.0991029i
$73$	11.4818	+	1.73061i	1.34385	+	0.202552i	0.781270	−	0.624194i	$-0.214572\pi$
$73$	11.4818	+	1.73061i	1.34385	+	0.202552i	0.562576	+	0.826746i	$0.309811\pi$
$74$	3.14863	+	2.92150i	0.366021	+	0.339618i
$75$	0.345517	−	0.166392i	0.0398969	−	0.0192133i
$76$	−4.02769	+	0.607077i	−0.462008	+	0.0696365i
$77$	0.508357	+	0.346592i	0.0579327	+	0.0394978i
$78$	0.883082	−	1.10735i	0.0999894	−	0.125383i
$79$	−3.05423	−	5.29007i	−0.343627	−	0.595180i	0.641476	−	0.767143i	$-0.278322\pi$
$79$	−3.05423	−	5.29007i	−0.343627	−	0.595180i	−0.985103	+	0.171963i	$0.944989\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	2.81240	+	7.16588i	0.312489	+	0.796209i
$82$	3.97197	+	1.91280i	0.438630	+	0.211233i
$83$	−0.108118	−	0.0333499i	−0.0118675	−	0.00366063i	0.288816	−	0.957385i	$-0.406738\pi$
$83$	−0.108118	−	0.0333499i	−0.0118675	−	0.00366063i	−0.300683	+	0.953724i	$0.597215\pi$
$84$	0.0146032	−	0.0639808i	0.00159334	−	0.00698088i
$85$	−1.38197			−0.149896
$86$	−5.74431	+	3.16274i	−0.619425	+	0.341047i
$87$	3.80143			0.407556
$88$	0.800050	−	3.50525i	0.0852856	−	0.373661i
$89$	−13.1872	−	4.06770i	−1.39784	−	0.431176i	−0.497915	−	0.867226i	$-0.665901\pi$
$89$	−13.1872	−	4.06770i	−1.39784	−	0.431176i	−0.899922	+	0.436050i	$0.856377\pi$
$90$	2.57040	+	1.23784i	0.270944	+	0.130480i
$91$	0.230902	+	0.588328i	0.0242051	+	0.0616735i
$92$	−1.80244	+	3.12192i	−0.187917	+	0.325483i
$93$	0.800580	+	1.38664i	0.0830162	+	0.143788i
$94$	6.13103	−	7.68806i	0.632367	−	0.792963i
$95$	−3.36543	−	2.29451i	−0.345285	−	0.235412i
$96$	−0.379212	+	0.0571570i	−0.0387032	+	0.00583356i
$97$	−0.224152	+	0.107946i	−0.0227592	+	0.0109603i	−0.445229	−	0.895417i	$-0.646878\pi$
$97$	−0.224152	+	0.107946i	−0.0227592	+	0.0109603i	0.422470	+	0.906377i	$0.361163\pi$
$98$	−5.10990	−	4.74129i	−0.516177	−	0.478943i
$99$	10.1428	+	1.52879i	1.01939	+	0.153649i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	0.498872	+	6.65698i	0.0496396	+	0.662394i	0.965417	+	0.260709i	$0.0839564\pi$
$101$	0.498872	+	6.65698i	0.0496396	+	0.662394i	−0.915778	+	0.401685i	$0.868425\pi$
$102$	0.330437	+	0.414354i	0.0327181	+	0.0410272i
$103$	2.88588	−	7.35310i	0.284354	−	0.724522i	−0.715315	−	0.698802i	$-0.753717\pi$
$103$	2.88588	−	7.35310i	0.284354	−	0.724522i	0.999669	−	0.0257203i	$-0.00818792\pi$
$104$	2.70736	−	2.51207i	0.265479	−	0.246328i
$105$	0.0542229	−	0.0369686i	0.00529161	−	0.00360776i
$106$	0.631301	−	8.42413i	0.0613174	−	0.818223i
$107$	2.25234	+	9.86812i	0.217741	+	0.953988i	0.959142	+	0.282925i	$0.0913047\pi$
$107$	2.25234	+	9.86812i	0.217741	+	0.953988i	−0.741401	+	0.671063i	$0.765838\pi$
$108$	−0.499464	−	2.18830i	−0.0480610	−	0.210569i
$109$	−0.407899	+	5.44303i	−0.0390696	+	0.521348i	0.942996	+	0.332805i	$0.107995\pi$
$109$	−0.407899	+	5.44303i	−0.0390696	+	0.521348i	−0.982065	+	0.188542i	$0.939624\pi$
$110$	2.97065	−	2.02536i	0.283241	−	0.193110i
$111$	1.20749	−	1.12038i	0.114610	−	0.106342i
$112$	0.0625195	−	0.159297i	0.00590754	−	0.0150522i
$113$	−7.37620	−	9.24946i	−0.693894	−	0.870116i	0.302657	−	0.953100i	$-0.402126\pi$
$113$	−7.37620	−	9.24946i	−0.693894	−	0.870116i	−0.996551	+	0.0829838i	$0.973555\pi$
$114$	0.116732	+	1.55768i	0.0109330	+	0.145890i
$115$	−3.44473	+	1.06256i	−0.321223	+	0.0990840i
$116$	9.80187	+	1.47739i	0.910081	+	0.137173i
$117$	7.72392	+	7.16675i	0.714077	+	0.662566i
$118$	−12.1112	+	5.83245i	−1.11493	+	0.536921i
$119$	−0.233850	+	0.0352473i	−0.0214370	+	0.00323111i
$120$	−0.316859	−	0.216031i	−0.0289251	−	0.0197208i
$121$	1.20137	−	1.50647i	0.109216	−	0.136952i
$122$	−3.82655	−	6.62778i	−0.346440	−	0.600051i
$123$	0.845329	−	1.46415i	0.0762208	−	0.132018i
$124$	1.52536	+	3.88656i	0.136982	+	0.349023i
$125$	0.900969	+	0.433884i	0.0805851	+	0.0388077i
$126$	0.466522	+	0.143903i	0.0415611	+	0.0128199i
$127$	3.23520	−	14.1744i	0.287078	−	1.25777i	−0.601436	−	0.798921i	$-0.705405\pi$
$127$	3.23520	−	14.1744i	0.287078	−	1.25777i	0.888514	−	0.458849i	$-0.151738\pi$
$128$	−1.00000			−0.0883883
$129$	1.04488	+	2.28740i	0.0919966	+	0.201394i
$130$	3.69328			0.323922
$131$	−0.124286	+	0.544535i	−0.0108590	+	0.0475762i	−0.980067	−	0.198667i	$-0.936339\pi$
$131$	−0.124286	+	0.544535i	−0.0108590	+	0.0475762i	0.969208	+	0.246243i	$0.0791961\pi$
$132$	−1.31756	−	0.406413i	−0.114679	−	0.0353737i
$133$	−0.628003	−	0.302430i	−0.0544547	−	0.0262240i
$134$	−4.54369	−	11.5771i	−0.392515	−	1.00011i
$135$	1.12229	−	1.94386i	0.0965910	−	0.167300i
$136$	0.690985	+	1.19682i	0.0592515	+	0.102627i
$137$	−4.14684	+	5.19998i	−0.354289	+	0.444264i	−0.926756	−	0.375663i	$-0.877415\pi$
$137$	−4.14684	+	5.19998i	−0.354289	+	0.444264i	0.572467	+	0.819927i	$0.305986\pi$
$138$	1.14224	+	0.778765i	0.0972338	+	0.0662929i
$139$	−10.7777	+	1.62447i	−0.914151	+	0.137786i	−0.589240	−	0.807958i	$-0.700573\pi$
$139$	−10.7777	+	1.62447i	−0.914151	+	0.137786i	−0.324911	+	0.945744i	$0.605334\pi$
$140$	0.154180	−	0.0742490i	0.0130306	−	0.00627518i
$141$	−2.76439	−	2.56497i	−0.232803	−	0.216010i
$142$	−6.00576	−	0.905223i	−0.503993	−	0.0759647i
$143$	12.6888	−	3.91399i	1.06109	−	0.327304i
$144$	−0.213200	−	2.84495i	−0.0177667	−	0.237079i
$145$	6.18040	+	7.74997i	0.513254	+	0.643600i
$146$	4.24216	−	10.8088i	0.351084	−	0.894547i
$147$	−1.95962	+	1.81826i	−0.161627	+	0.149968i
$148$	3.54889	−	2.41959i	0.291717	−	0.198889i
$149$	−0.344135	+	4.59216i	−0.0281926	+	0.376205i	0.965206	+	0.261491i	$0.0842141\pi$
$149$	−0.344135	+	4.59216i	−0.0281926	+	0.376205i	−0.993399	+	0.114714i	$0.963405\pi$
$150$	−0.0853357	−	0.373880i	−0.00696763	−	0.0305272i
$151$	−2.88544	−	12.6420i	−0.234814	−	1.02879i	−0.945588	−	0.325367i	$-0.894512\pi$
$151$	−2.88544	−	12.6420i	−0.234814	−	1.02879i	0.710774	−	0.703421i	$-0.248345\pi$
$152$	−0.304390	+	4.06180i	−0.0246893	+	0.329455i
$153$	−3.25758	+	2.22098i	−0.263360	+	0.179556i
$154$	0.451023	−	0.418488i	0.0363444	−	0.0337227i
$155$	−1.52536	+	3.88656i	−0.122520	+	0.312176i
$156$	−0.883082	−	1.10735i	−0.0707032	−	0.0886590i
$157$	0.144984	+	1.93467i	0.0115710	+	0.154404i	0.999996	+	0.00269603i	$0.000858175\pi$
$157$	0.144984	+	1.93467i	0.0115710	+	0.154404i	−0.988425	+	0.151708i	$0.951523\pi$
$158$	−5.83707	+	1.80050i	−0.464372	+	0.143240i
$159$	−3.20349	−	0.482848i	−0.254053	−	0.0382923i
$160$	−0.733052	−	0.680173i	−0.0579528	−	0.0537724i
$161$	−0.555799	+	0.267659i	−0.0438031	+	0.0210945i
$162$	7.61203	−	1.14733i	0.598058	−	0.0901427i
$163$	16.1733	+	11.0267i	1.26679	+	0.863681i	0.995116	−	0.0987093i	$-0.0314714\pi$
$163$	16.1733	+	11.0267i	1.26679	+	0.863681i	0.271671	+	0.962390i	$0.412424\pi$
$164$	2.74869	−	3.44674i	0.214636	−	0.269146i
$165$	−0.689408	−	1.19409i	−0.0536704	−	0.0929598i
$166$	−0.0565722	+	0.0979860i	−0.00439086	+	0.00760519i
$167$	5.29264	+	13.4854i	0.409557	+	1.04353i	0.975677	+	0.219211i	$0.0703484\pi$
$167$	5.29264	+	13.4854i	0.409557	+	1.04353i	−0.566121	+	0.824322i	$0.691556\pi$
$168$	−0.0591272	−	0.0284741i	−0.00456176	−	0.00219683i
$169$	0.611837	+	0.188727i	0.0470644	+	0.0145174i
$170$	−0.307517	+	1.34732i	−0.0235855	+	0.103335i
$171$	−11.6205			−0.888644
$172$	1.80521	+	6.30406i	0.137646	+	0.480680i
$173$	−22.7948			−1.73306			−0.866529	−	0.499126i	$-0.833654\pi$
$173$	−22.7948			−1.73306			−0.866529	+	0.499126i	$0.833654\pi$
$174$	0.845898	−	3.70612i	0.0641273	−	0.280960i
$175$	0.163524	+	0.0504404i	0.0123612	+	0.00381294i
$176$	−3.23934	−	1.55998i	−0.244174	−	0.117588i
$177$	1.88337	+	4.79876i	0.141563	+	0.360697i
$178$	−6.90014	+	11.9514i	−0.517187	+	0.895794i
$179$	−4.69549	−	8.13284i	−0.350958	−	0.607877i	0.635460	−	0.772134i	$-0.280811\pi$
$179$	−4.69549	−	8.13284i	−0.350958	−	0.607877i	−0.986418	+	0.164257i	$0.947477\pi$
$180$	1.77877	−	2.23051i	0.132582	−	0.166253i
$181$	5.56515	+	3.79426i	0.413655	+	0.282025i	0.752212	−	0.658921i	$-0.228987\pi$
$181$	5.56515	+	3.79426i	0.413655	+	0.282025i	−0.338558	+	0.940946i	$0.609939\pi$
$182$	0.624958	−	0.0941973i	0.0463250	−	0.00698237i
$183$	−2.64428	+	1.27342i	−0.195471	+	0.0941338i
$184$	2.64257	+	2.45194i	0.194813	+	0.180760i
$185$	4.24726	+	0.640172i	0.312265	+	0.0470664i
$186$	1.53002	−	0.471950i	0.112187	−	0.0346051i
$187$	0.371313	+	4.95483i	0.0271531	+	0.362333i
$188$	−6.13103	−	7.68806i	−0.447151	−	0.560710i
$189$	0.140330	−	0.357554i	0.0102075	−	0.0260082i
$190$	−2.98586	+	2.77047i	−0.216617	+	0.200991i
$191$	1.57022	−	1.07056i	0.113617	−	0.0774628i	−0.505178	−	0.863015i	$-0.668573\pi$
$191$	1.57022	−	1.07056i	0.113617	−	0.0774628i	0.618796	+	0.785552i	$0.287621\pi$
$192$	−0.0286586	+	0.382423i	−0.00206826	+	0.0275990i
$193$	0.567924	+	2.48824i	0.0408801	+	0.179107i	0.991246	−	0.132027i	$-0.0421484\pi$
$193$	0.567924	+	2.48824i	0.0408801	+	0.179107i	−0.950366	+	0.311134i	$0.899291\pi$
$194$	0.0553610	+	0.242552i	0.00397469	+	0.0174142i
$195$	0.105844	−	1.41239i	0.00757966	−	0.101144i
$196$	−5.75948	+	3.92674i	−0.411391	+	0.280482i
$197$	−14.3291	+	13.2955i	−1.02091	+	0.947264i	−0.998622	−	0.0524871i	$-0.983285\pi$
$197$	−14.3291	+	13.2955i	−1.02091	+	0.947264i	−0.0222867	+	0.999752i	$0.507095\pi$
$198$	3.74745	−	9.54835i	0.266320	−	0.678572i
$199$	6.09488	+	7.64274i	0.432055	+	0.541779i	0.949430	−	0.313979i	$-0.101662\pi$
$199$	6.09488	+	7.64274i	0.432055	+	0.541779i	−0.517375	+	0.855759i	$0.673091\pi$
$200$	−0.0747301	−	0.997204i	−0.00528422	−	0.0705130i
$201$	−4.55758	+	1.40583i	−0.321467	+	0.0991594i
$202$	6.60109	+	0.994954i	0.464451	+	0.0700047i
$203$	1.24348	+	1.15378i	0.0872752	+	0.0809795i
$204$	0.477495	−	0.229949i	0.0334313	−	0.0160997i
$205$	4.35931	−	0.657061i	0.304468	−	0.0458911i
$206$	−6.52657	−	4.44974i	−0.454728	−	0.310028i
$207$	−6.41227	+	8.04073i	−0.445684	+	0.558869i
$208$	−1.84664	−	3.19847i	−0.128041	−	0.221774i
$209$	−7.32236	+	12.6827i	−0.506498	+	0.877280i
$210$	−0.0239759	−	0.0610897i	−0.00165450	−	0.00421559i
$211$	19.1172	+	9.20637i	1.31608	+	0.633792i	0.954406	−	0.298511i	$-0.0964900\pi$
$211$	19.1172	+	9.20637i	1.31608	+	0.633792i	0.361677	+	0.932303i	$0.382204\pi$
$212$	−8.07244	−	2.49002i	−0.554417	−	0.171015i
$213$	−0.518295	+	2.27080i	−0.0355130	+	0.155593i
$214$	10.1219			0.691919
$215$	−2.96454	+	5.84906i	−0.202180	+	0.398903i
$216$	−2.24457			−0.152724
$217$	−0.158987	+	0.696569i	−0.0107928	+	0.0472862i
$218$	5.21579	+	1.60886i	0.353258	+	0.108966i
$219$	−4.01198	−	1.93207i	−0.271104	−	0.130557i
$220$	−1.31354	−	3.34686i	−0.0885592	−	0.225645i
$221$	−2.55200	+	4.42019i	−0.171666	+	0.297334i
$222$	−0.823602	−	1.42652i	−0.0552765	−	0.0957418i
$223$	−9.74858	+	12.2243i	−0.652813	+	0.818602i	−0.992540	−	0.121923i	$-0.961094\pi$
$223$	−9.74858	+	12.2243i	−0.652813	+	0.818602i	0.339726	+	0.940524i	$0.389665\pi$
$224$	−0.141391	−	0.0963990i	−0.00944710	−	0.00644093i
$225$	2.82107	−	0.425207i	0.188071	−	0.0283472i
$226$	−10.6589	+	5.13306i	−0.709020	+	0.341446i
$227$	−16.2852	−	15.1105i	−1.08089	−	1.00292i	−0.999981	−	0.00619589i	$-0.998028\pi$
$227$	−16.2852	−	15.1105i	−1.08089	−	1.00292i	−0.0809072	−	0.996722i	$-0.525782\pi$
$228$	1.54460	+	0.232811i	0.102294	+	0.0154183i
$229$	−23.4919	+	7.24629i	−1.55239	+	0.478848i	−0.948114	−	0.317929i	$-0.897012\pi$
$229$	−23.4919	+	7.24629i	−1.55239	+	0.478848i	−0.604273	+	0.796777i	$0.706536\pi$
$230$	0.269393	+	3.59480i	0.0177633	+	0.237034i
$231$	−0.147114	−	0.184475i	−0.00967937	−	0.0121375i
$232$	3.62147	−	9.22737i	0.237761	−	0.605806i
$233$	12.4803	−	11.5800i	0.817611	−	0.758632i	−0.155778	−	0.987792i	$-0.549788\pi$
$233$	12.4803	−	11.5800i	0.817611	−	0.758632i	0.973389	+	0.229160i	$0.0735979\pi$
$234$	8.70580	−	5.93551i	0.569116	−	0.388017i
$235$	0.734851	−	9.80591i	0.0479364	−	0.639667i
$236$	2.99122	+	13.1054i	0.194712	+	0.853089i
$237$	0.521269	+	2.28383i	0.0338601	+	0.148351i
$238$	−0.0176730	+	0.235830i	−0.00114557	+	0.0152866i
$239$	−0.374482	+	0.255318i	−0.0242233	+	0.0165151i	−0.575371	−	0.817892i	$-0.695142\pi$
$239$	−0.374482	+	0.255318i	−0.0242233	+	0.0165151i	0.551148	+	0.834408i	$0.314190\pi$
$240$	−0.281122	+	0.260843i	−0.0181463	+	0.0168373i
$241$	5.26262	−	13.4089i	0.338995	−	0.863746i	−0.655130	−	0.755516i	$-0.727386\pi$
$241$	5.26262	−	13.4089i	0.338995	−	0.863746i	0.994126	−	0.108230i	$-0.0345184\pi$
$242$	−1.20137	−	1.50647i	−0.0772271	−	0.0968398i
$243$	−0.723826	−	9.65878i	−0.0464334	−	0.619611i
$244$	−7.31310	+	2.25579i	−0.468173	+	0.144412i
$245$	−6.89286	−	1.03893i	−0.440369	−	0.0663749i
$246$	−1.23934	−	1.14994i	−0.0790175	−	0.0733175i
$247$	−13.5536	+	6.52709i	−0.862397	+	0.415309i
$248$	4.12854	−	0.622277i	0.262163	−	0.0395146i
$249$	0.0358508	+	0.0244427i	0.00227195	+	0.00154899i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−4.64681	−	8.04850i	−0.293304	−	0.508017i	0.681285	−	0.732018i	$-0.261421\pi$
$251$	−4.64681	−	8.04850i	−0.293304	−	0.508017i	−0.974589	+	0.224001i	$0.928088\pi$
$252$	0.244106	−	0.422804i	0.0153772	−	0.0266342i
$253$	4.73517	+	12.0650i	0.297698	+	0.758522i
$254$	−13.0991	−	6.30818i	−0.821909	−	0.395810i
$255$	0.506434	+	0.156214i	0.0317141	+	0.00978251i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	10.7030			0.667633			0.333817	−	0.942638i	$-0.391663\pi$
$257$	10.7030			0.667633			0.333817	+	0.942638i	$0.391663\pi$
$258$	2.46255	−	0.509690i	0.153312	−	0.0317319i
$259$	0.735029			0.0456725
$260$	0.821831	−	3.60068i	0.0509678	−	0.223305i
$261$	27.0235	+	8.33565i	1.67271	+	0.515964i
$262$	0.503226	+	0.242341i	0.0310894	+	0.0149719i
$263$	−3.27831	−	8.35300i	−0.202149	−	0.515068i	0.793466	−	0.608615i	$-0.208275\pi$
$263$	−3.27831	−	8.35300i	−0.202149	−	0.515068i	−0.995615	+	0.0935472i	$0.970179\pi$
$264$	−0.689408	+	1.19409i	−0.0424301	+	0.0734912i
$265$	−4.22387	−	7.31596i	−0.259470	−	0.449416i
$266$	−0.434591	+	0.544960i	−0.0266465	+	0.0334137i
$267$	4.37274	+	2.98128i	0.267607	+	0.182451i
$268$	−12.2979	+	1.85362i	−0.751217	+	0.113228i
$269$	−21.5112	+	10.3592i	−1.31156	+	0.631613i	−0.953305	−	0.302011i	$-0.902342\pi$
$269$	−21.5112	+	10.3592i	−1.31156	+	0.631613i	−0.358254	+	0.933624i	$0.616628\pi$
$270$	−1.64539	−	1.52670i	−0.100135	−	0.0929118i
$271$	−0.522286	−	0.0787219i	−0.0317266	−	0.00478202i	0.133160	−	0.991095i	$-0.457488\pi$
$271$	−0.522286	−	0.0787219i	−0.0317266	−	0.00478202i	−0.164886	+	0.986313i	$0.552726\pi$
$272$	1.32057	−	0.407343i	0.0800715	−	0.0246988i
$273$	−0.0181128	−	0.241698i	−0.00109623	−	0.0146282i
$274$	4.14684	+	5.19998i	0.250520	+	0.314142i
$275$	1.31354	−	3.34686i	0.0792097	−	0.201823i
$276$	1.01341	−	0.940309i	0.0610002	−	0.0565999i
$277$	−7.01500	+	4.78275i	−0.421490	+	0.287367i	−0.755433	−	0.655226i	$-0.772573\pi$
$277$	−7.01500	+	4.78275i	−0.421490	+	0.287367i	0.333942	+	0.942594i	$0.391621\pi$
$278$	−0.814515	+	10.8689i	−0.0488513	+	0.651876i
$279$	2.65055	+	11.6128i	0.158685	+	0.695242i
$280$	−0.0380792	−	0.166836i	−0.00227567	−	0.00997036i
$281$	1.97521	−	26.3574i	0.117831	−	1.57235i	−0.554555	−	0.832147i	$-0.687111\pi$
$281$	1.97521	−	26.3574i	0.117831	−	1.57235i	0.672386	−	0.740201i	$-0.265270\pi$
$282$	−3.11580	+	2.12432i	−0.185543	+	0.126501i
$283$	2.29806	−	2.13229i	0.136606	−	0.126751i	−0.608911	−	0.793239i	$-0.708393\pi$
$283$	2.29806	−	2.13229i	0.136606	−	0.126751i	0.745517	+	0.666487i	$0.232203\pi$
$284$	−2.21894	+	5.65376i	−0.131670	+	0.335489i
$285$	0.973921	+	1.22126i	0.0576901	+	0.0723411i
$286$	−0.992324	−	13.2416i	−0.0586774	−	0.782995i
$287$	0.720903	−	0.222369i	0.0425536	−	0.0131260i
$288$	−2.82107	−	0.425207i	−0.166233	−	0.0250556i
$289$	11.0619	+	10.2639i	0.650698	+	0.603760i
$290$	8.93093	−	4.30091i	0.524442	−	0.252558i
$291$	0.0943442	−	0.0142201i	0.00553055	−	0.000833597i
$292$	−9.59388	−	6.54100i	−0.561439	−	0.382783i
$293$	−7.95926	+	9.98060i	−0.464985	+	0.583073i	−0.957935	−	0.286985i	$-0.907347\pi$
$293$	−7.95926	+	9.98060i	−0.464985	+	0.583073i	0.492950	+	0.870058i	$0.335918\pi$
$294$	1.33662	+	2.31509i	0.0779532	+	0.135019i
$295$	−6.72122	+	11.6415i	−0.391324	+	0.677794i
$296$	−1.56923	−	3.99833i	−0.0912095	−	0.232398i
$297$	−7.27092	−	3.50149i	−0.421902	−	0.203177i
$298$	4.40045	+	1.35736i	0.254911	+	0.0786297i
$299$	−2.96260	+	12.9800i	−0.171332	+	0.750654i
$300$	−0.383495			−0.0221411
$301$	−0.352463	+	1.06536i	−0.0203157	+	0.0614064i
$302$	−12.9671			−0.746171
$303$	0.569671	−	2.49589i	0.0327268	−	0.143385i
$304$	3.89223	+	1.20059i	0.223235	+	0.0688587i
$305$	−6.89521	−	3.32056i	−0.394819	−	0.190135i
$306$	1.44042	+	3.67012i	0.0823432	+	0.209807i
$307$	12.9798	−	22.4817i	0.740798	−	1.28310i	−0.211334	−	0.977414i	$-0.567781\pi$
$307$	12.9798	−	22.4817i	0.740798	−	1.28310i	0.952132	−	0.305686i	$-0.0988858\pi$
$308$	−0.307633	−	0.532837i	−0.0175290	−	0.0303612i
$309$	−1.88873	+	2.36839i	−0.107446	+	0.134733i
$310$	3.44969	+	2.35196i	0.195929	+	0.133582i
$311$	−16.9359	+	2.55268i	−0.960348	+	0.144749i	−0.610464	−	0.792044i	$-0.709017\pi$
$311$	−16.9359	+	2.55268i	−0.960348	+	0.144749i	−0.349884	+	0.936793i	$0.613779\pi$
$312$	−1.27609	+	0.614533i	−0.0722444	+	0.0347911i
$313$	2.13737	+	1.98319i	0.120811	+	0.112096i	0.738265	−	0.674511i	$-0.235645\pi$
$313$	2.13737	+	1.98319i	0.120811	+	0.112096i	−0.617454	+	0.786607i	$0.711836\pi$
$314$	1.91843	+	0.289157i	0.108263	+	0.0163180i
$315$	0.466522	−	0.143903i	0.0262855	−	0.00810802i
$316$	0.456485	+	6.09137i	0.0256793	+	0.342666i
$317$	−7.80764	−	9.79047i	−0.438521	−	0.549888i	0.512632	−	0.858609i	$-0.328671\pi$
$317$	−7.80764	−	9.79047i	−0.438521	−	0.549888i	−0.951153	+	0.308721i	$0.900099\pi$
$318$	−1.18358	+	3.01572i	−0.0663721	+	0.169113i
$319$	26.1257	−	24.2411i	1.46276	−	1.35724i
$320$	−0.826239	+	0.563320i	−0.0461882	+	0.0314905i
$321$	0.290080	−	3.87085i	0.0161907	−	0.216050i
$322$	0.137271	+	0.601424i	0.00764982	+	0.0335161i
$323$	−1.25258	−	5.48789i	−0.0696952	−	0.305355i
$324$	0.575273	−	7.67649i	0.0319596	−	0.426471i
$325$	3.05153	−	2.08050i	0.169268	−	0.115405i
$326$	14.3492	−	13.3141i	0.794727	−	0.737399i
$327$	0.764742	−	1.94853i	0.0422904	−	0.107754i
$328$	−2.74869	−	3.44674i	−0.151771	−	0.190315i
$329$	−0.125752	−	1.67805i	−0.00693296	−	0.0925139i
$330$	−1.31756	+	0.406413i	−0.0725293	+	0.0223723i
$331$	25.4816	+	3.84073i	1.40059	+	0.211106i	0.805522	−	0.592566i	$-0.201885\pi$
$331$	25.4816	+	3.84073i	1.40059	+	0.211106i	0.595073	+	0.803672i	$0.297123\pi$
$332$	0.0829408	+	0.0769578i	0.00455197	+	0.00422361i
$333$	11.0405	−	5.31682i	0.605015	−	0.291360i
$334$	14.3250	−	2.15915i	0.783832	−	0.118144i
$335$	−10.2758	−	7.00593i	−0.561428	−	0.382775i
$336$	−0.0409173	+	0.0513086i	−0.00223222	+	0.00279911i
$337$	−10.7043	−	18.5405i	−0.583103	−	1.00996i	−0.995109	−	0.0987829i	$-0.968505\pi$
$337$	−10.7043	−	18.5405i	−0.583103	−	1.00996i	0.412006	−	0.911181i	$-0.364828\pi$
$338$	0.320142	−	0.554502i	0.0174134	−	0.0301609i
$339$	1.65753	+	4.22332i	0.0900247	+	0.229379i
$340$	1.24511	+	0.599614i	0.0675257	+	0.0325187i
$341$	14.3445	+	4.42468i	0.776797	+	0.239610i
$342$	−2.58581	+	11.3292i	−0.139825	+	0.612612i
$343$	−2.39076			−0.129089
$344$	6.54770	−	0.357168i	0.353029	−	0.0192572i
$345$	1.38246			0.0744289
$346$	−5.07233	+	22.2233i	−0.272690	+	1.19473i
$347$	−1.34063	−	0.413531i	−0.0719690	−	0.0221995i	0.258562	−	0.965995i	$-0.416751\pi$
$347$	−1.34063	−	0.413531i	−0.0719690	−	0.0221995i	−0.330531	+	0.943795i	$0.607228\pi$
$348$	−3.42497	−	1.64938i	−0.183598	−	0.0884160i
$349$	−5.74146	−	14.6290i	−0.307333	−	0.783072i	−0.998193	−	0.0600837i	$-0.980863\pi$
$349$	−5.74146	−	14.6290i	−0.307333	−	0.783072i	0.690860	−	0.722988i	$-0.257232\pi$
$350$	0.0855632	−	0.148200i	0.00457355	−	0.00792162i
$351$	−4.14491	−	7.17920i	−0.221239	−	0.383197i
$352$	−2.24169	+	2.81099i	−0.119483	+	0.149826i
$353$	−2.08082	−	1.41868i	−0.110751	−	0.0755087i	0.506678	−	0.862135i	$-0.330873\pi$
$353$	−2.08082	−	1.41868i	−0.110751	−	0.0755087i	−0.617429	+	0.786627i	$0.711826\pi$
$354$	5.09753	−	0.768329i	0.270931	−	0.0408363i
$355$	−5.47213	+	2.63524i	−0.290430	+	0.139864i
$356$	10.1163	+	9.38657i	0.536164	+	0.497487i
$357$	0.0896805	+	0.0135172i	0.00474639	+	0.000715404i
$358$	−8.97377	+	2.76804i	−0.474279	+	0.146296i
$359$	1.91683	+	25.5783i	0.101166	+	1.34997i	0.784620	+	0.619978i	$0.212858\pi$
$359$	1.91683	+	25.5783i	0.101166	+	1.34997i	−0.683453	+	0.729994i	$0.739523\pi$
$360$	−1.77877	−	2.23051i	−0.0937496	−	0.117558i
$361$	−0.880158	+	2.24261i	−0.0463241	+	0.118032i
$362$	4.93749	−	4.58132i	0.259509	−	0.240789i
$363$	−0.610540	+	0.416259i	−0.0320450	+	0.0218479i
$364$	0.0472307	−	0.630250i	0.00247556	−	0.0330341i
$365$	−2.58380	−	11.3204i	−0.135242	−	0.592536i
$366$	0.653083	+	2.86135i	0.0341372	+	0.149565i
$367$	1.47336	−	19.6607i	0.0769090	−	1.02628i	−0.816591	−	0.577216i	$-0.804139\pi$
$367$	1.47336	−	19.6607i	0.0769090	−	1.02628i	0.893500	−	0.449063i	$-0.148242\pi$
$368$	2.97849	−	2.03070i	0.155265	−	0.105858i
$369$	9.21981	−	8.55473i	0.479964	−	0.445342i
$370$	1.56923	−	3.99833i	0.0815802	−	0.207863i
$371$	−0.901337	−	1.13024i	−0.0467951	−	0.0586792i
$372$	−0.119655	−	1.59668i	−0.00620381	−	0.0827841i
$373$	−11.5606	+	3.56598i	−0.598586	+	0.184639i	−0.579218	−	0.815173i	$-0.696642\pi$
$373$	−11.5606	+	3.56598i	−0.598586	+	0.184639i	−0.0193688	+	0.999812i	$0.506166\pi$
$374$	4.91323	+	0.740550i	0.254057	+	0.0382929i
$375$	−0.281122	−	0.260843i	−0.0145171	−	0.0134699i
$376$	−8.85959	+	4.26655i	−0.456898	+	0.220031i
$377$	36.2010	−	5.45642i	1.86445	−	0.281020i
$378$	−0.317363	−	0.216374i	−0.0163234	−	0.0111291i
$379$	3.31422	−	4.15590i	0.170240	−	0.213474i	−0.689391	−	0.724389i	$-0.742122\pi$
$379$	3.31422	−	4.15590i	0.170240	−	0.213474i	0.859631	+	0.510915i	$0.170693\pi$
$380$	2.03659	+	3.52748i	0.104475	+	0.180956i
$381$	−2.78779	+	4.82860i	−0.142823	+	0.247377i
$382$	−0.694310	−	1.76907i	−0.0355240	−	0.0905136i
$383$	13.6961	+	6.59571i	0.699840	+	0.337025i	0.749743	−	0.661729i	$-0.230177\pi$
$383$	13.6961	+	6.59571i	0.699840	+	0.337025i	−0.0499031	+	0.998754i	$0.515891\pi$
$384$	0.366458	+	0.113037i	0.0187007	+	0.00576841i
$385$	0.136910	−	0.599841i	0.00697757	−	0.0305707i
$386$	2.55223			0.129905
$387$	2.41210	+	18.5518i	0.122614	+	0.943039i
$388$	0.248790			0.0126304
$389$	5.92737	−	25.9695i	0.300529	−	1.31671i	−0.568802	−	0.822475i	$-0.692593\pi$
$389$	5.92737	−	25.9695i	0.300529	−	1.31671i	0.869331	−	0.494230i	$-0.164550\pi$
$390$	−1.35343	−	0.417478i	−0.0685335	−	0.0211398i
$391$	−4.48848	−	2.16154i	−0.226992	−	0.109314i
$392$	2.54669	+	6.48886i	0.128627	+	0.327737i
$393$	0.107098	−	0.185500i	0.00540240	−	0.00935723i
$394$	9.77361	+	16.9284i	0.492388	+	0.852840i
$395$	−3.80856	+	4.77578i	−0.191629	+	0.240296i
$396$	−8.47507	−	5.77820i	−0.425888	−	0.290366i
$397$	−6.05833	+	0.913146i	−0.304059	+	0.0458295i	−0.299300	−	0.954159i	$-0.596753\pi$
$397$	−6.05833	+	0.913146i	−0.304059	+	0.0458295i	−0.00475918	+	0.999989i	$0.501515\pi$
$398$	8.80736	−	4.24140i	0.441473	−	0.212602i
$399$	0.195950	+	0.181815i	0.00980979	+	0.00910216i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−4.10652	+	1.26669i	−0.205070	+	0.0632556i	−0.395588	−	0.918428i	$-0.629459\pi$
$401$	−4.10652	+	1.26669i	−0.205070	+	0.0632556i	0.190519	+	0.981684i	$0.438983\pi$
$402$	0.356423	+	4.75614i	0.0177768	+	0.237215i
$403$	9.61425	+	12.0559i	0.478920	+	0.600547i
$404$	2.43889	−	6.21419i	0.121339	−	0.309167i
$405$	5.64304	−	5.23598i	0.280405	−	0.260178i
$406$	1.40155	−	0.955563i	0.0695579	−	0.0474238i
$407$	1.15406	−	15.3999i	0.0572047	−	0.763344i
$408$	−0.117931	−	0.516691i	−0.00583848	−	0.0255800i
$409$	4.71974	+	20.6785i	0.233376	+	1.02249i	0.946817	+	0.321772i	$0.104278\pi$
$409$	4.71974	+	20.6785i	0.233376	+	1.02249i	−0.713441	+	0.700715i	$0.752864\pi$
$410$	0.329451	−	4.39622i	0.0162704	−	0.217114i
$411$	2.10743	−	1.43682i	0.103952	−	0.0708733i
$412$	−5.79048	+	5.37278i	−0.285276	+	0.264698i
$413$	−0.840415	+	2.14134i	−0.0413541	+	0.105369i
$414$	6.41227	+	8.04073i	0.315146	+	0.395180i
$415$	0.00845530	+	0.112828i	0.000415054	+	0.00553851i
$416$	−3.52919	+	1.08861i	−0.173033	+	0.0533736i
$417$	4.13319	+	0.622978i	0.202403	+	0.0305074i
$418$	10.7353	+	9.96093i	0.525082	+	0.487205i
$419$	−13.2609	+	6.38609i	−0.647835	+	0.311981i	−0.728790	−	0.684737i	$-0.759917\pi$
$419$	−13.2609	+	6.38609i	−0.647835	+	0.311981i	0.0809554	+	0.996718i	$0.474203\pi$
$420$	−0.0648932	+	0.00978108i	−0.00316646	+	0.000477268i
$421$	12.8583	+	8.76666i	0.626677	+	0.427261i	0.834579	−	0.550889i	$-0.185711\pi$
$421$	12.8583	+	8.76666i	0.626677	+	0.427261i	−0.207902	+	0.978150i	$0.566663\pi$
$422$	13.2295	−	16.5893i	0.644003	−	0.807554i
$423$	−14.0270	−	24.2955i	−0.682017	−	1.18129i
$424$	−4.22387	+	7.31596i	−0.205129	+	0.355295i
$425$	0.504890	+	1.28644i	0.0244908	+	0.0624015i
$426$	2.09853	+	1.01060i	0.101674	+	0.0489638i
$427$	−1.25146	−	0.386026i	−0.0605626	−	0.0186811i
$428$	2.25234	−	9.86812i	0.108871	−	0.476994i
$429$	−5.09235			−0.245861
$430$	5.04274	+	4.19175i	0.243183	+	0.202144i
$431$	4.39950			0.211916			0.105958	−	0.994371i	$-0.466209\pi$
$431$	4.39950			0.211916			0.105958	+	0.994371i	$0.466209\pi$
$432$	−0.499464	+	2.18830i	−0.0240305	+	0.105284i
$433$	6.76099	+	2.08549i	0.324913	+	0.100222i	0.452921	−	0.891551i	$-0.350382\pi$
$433$	6.76099	+	2.08549i	0.324913	+	0.100222i	−0.128008	+	0.991773i	$0.540858\pi$
$434$	0.643727	+	0.310002i	0.0308999	+	0.0148806i
$435$	−1.38882	−	3.53865i	−0.0665887	−	0.169665i
$436$	2.72915	−	4.72702i	0.130702	−	0.226383i
$437$	−7.34168	−	12.7162i	−0.351200	−	0.608297i
$438$	−2.77637	+	3.48146i	−0.132660	+	0.166351i
$439$	5.53971	+	3.77691i	0.264396	+	0.180262i	0.688261	−	0.725463i	$-0.258374\pi$
$439$	5.53971	+	3.77691i	0.264396	+	0.180262i	−0.423865	+	0.905725i	$0.639327\pi$
$440$	−3.55524	+	0.535866i	−0.169489	+	0.0255464i
$441$	−17.9175	+	8.62863i	−0.853216	+	0.410887i
$442$	3.74149	+	3.47160i	0.177965	+	0.165127i
$443$	27.6139	+	4.16213i	1.31198	+	0.197749i	0.767512	−	0.641035i	$-0.221495\pi$
$443$	27.6139	+	4.16213i	1.31198	+	0.197749i	0.544465	+	0.838783i	$0.316733\pi$
$444$	−1.57402	+	0.485522i	−0.0746998	+	0.0230419i
$445$	1.03130	+	13.7617i	0.0488881	+	0.652367i
$446$	9.74858	+	12.2243i	0.461609	+	0.578839i
$447$	0.645196	−	1.64393i	0.0305167	−	0.0777554i
$448$	−0.125445	+	0.116396i	−0.00592670	+	0.00549917i
$449$	28.4237	−	19.3790i	1.34140	−	0.914550i	0.341717	−	0.939803i	$-0.388992\pi$
$449$	28.4237	−	19.3790i	1.34140	−	0.914550i	0.999681	+	0.0252535i	$0.00803929\pi$
$450$	0.213200	−	2.84495i	0.0100503	−	0.134112i
$451$	−3.52706	−	15.4531i	−0.166083	−	0.727657i
$452$	2.63253	+	11.5339i	0.123824	+	0.542508i
$453$	−0.371619	+	4.95890i	−0.0174602	+	0.232990i
$454$	−18.3554	+	12.5145i	−0.861463	+	0.587335i
$455$	0.463301	−	0.429881i	0.0217199	−	0.0201531i
$456$	0.570680	−	1.45407i	0.0267246	−	0.0680931i
$457$	−16.6410	−	20.8671i	−0.778433	−	0.976124i	−1.00000		0.000978702i	$-0.999688\pi$
$457$	−16.6410	−	20.8671i	−0.778433	−	0.976124i	0.221567	−	0.975145i	$-0.428883\pi$
$458$	1.83717	+	24.5153i	0.0858454	+	1.14553i
$459$	2.96412	−	0.914310i	0.138353	−	0.0426764i
$460$	3.56462	+	0.537280i	0.166201	+	0.0250508i
$461$	19.0445	+	17.6707i	0.886990	+	0.823006i	0.985067	−	0.172173i	$-0.0550787\pi$
$461$	19.0445	+	17.6707i	0.886990	+	0.823006i	−0.0980772	+	0.995179i	$0.531269\pi$
$462$	−0.212585	+	0.102376i	−0.00989037	+	0.00476295i
$463$	32.7523	−	4.93662i	1.52213	−	0.229424i	0.665908	−	0.746034i	$-0.268044\pi$
$463$	32.7523	−	4.93662i	1.52213	−	0.229424i	0.856221	+	0.516609i	$0.172806\pi$
$464$	−8.19016	−	5.58396i	−0.380219	−	0.259229i
$465$	0.998306	−	1.25184i	0.0462954	−	0.0580525i
$466$	−8.51255	−	14.7442i	−0.394336	−	0.683011i
$467$	2.66944	−	4.62361i	0.123527	−	0.213955i	−0.797629	−	0.603148i	$-0.793913\pi$
$467$	2.66944	−	4.62361i	0.123527	−	0.213955i	0.921156	+	0.389193i	$0.127246\pi$
$468$	−3.84947	−	9.80830i	−0.177942	−	0.453389i
$469$	−1.91751	−	0.923424i	−0.0885424	−	0.0426398i
$470$	−9.39653	−	2.89845i	−0.433430	−	0.133695i
$471$	0.165560	−	0.725364i	0.00762859	−	0.0334230i
$472$	13.4424			0.618738
$473$	21.7674	+	9.05732i	1.00087	+	0.416456i
$474$	2.34256			0.107597
$475$	−0.906370	+	3.97106i	−0.0415871	+	0.182205i
$476$	0.225985	+	0.0697071i	0.0103580	+	0.00319502i
$477$	−21.7141	−	10.4570i	−0.994221	−	0.478791i
$478$	0.165586	+	0.421907i	0.00757374	+	0.0192976i
$479$	−2.52861	+	4.37968i	−0.115535	+	0.200113i	−0.917994	−	0.396595i	$-0.870192\pi$
$479$	−2.52861	+	4.37968i	−0.115535	+	0.200113i	0.802458	+	0.596708i	$0.203525\pi$
$480$	0.191748	+	0.332117i	0.00875204	+	0.0151590i
$481$	9.89073	−	12.4026i	0.450979	−	0.565509i
$482$	−11.9017	−	8.11445i	−0.542108	−	0.369603i
$483$	0.233932	−	0.0352596i	0.0106443	−	0.00160437i
$484$	−1.73603	+	0.836030i	−0.0789106	+	0.0380013i
$485$	0.182376	+	0.169220i	0.00828127	+	0.00768389i
$486$	−9.57768	−	1.44360i	−0.434453	−	0.0654832i
$487$	11.1737	−	3.44664i	0.506330	−	0.156182i	−0.0310572	−	0.999518i	$-0.509887\pi$
$487$	11.1737	−	3.44664i	0.506330	−	0.156182i	0.537388	+	0.843335i	$0.319411\pi$
$488$	0.571917	+	7.63171i	0.0258895	+	0.345471i
$489$	−4.68038	−	5.86901i	−0.211654	−	0.265406i
$490$	−2.54669	+	6.48886i	−0.115048	+	0.293137i
$491$	−24.4915	+	22.7248i	−1.10529	+	1.02556i	−0.105773	+	0.994390i	$0.533732\pi$
$491$	−24.4915	+	22.7248i	−1.10529	+	1.02556i	−0.999514	+	0.0311668i	$0.990078\pi$
$492$	−1.39689	+	0.952382i	−0.0629766	+	0.0429367i
$493$	−1.02372	+	13.6606i	−0.0461060	+	0.615242i
$494$	3.34747	+	14.6662i	0.150610	+	0.659865i
$495$	−2.28249	−	10.0002i	−0.102590	−	0.449477i
$496$	0.312011	−	4.16350i	0.0140097	−	0.186947i
$497$	−0.858755	+	0.585489i	−0.0385204	+	0.0262628i
$498$	0.0318074	−	0.0295130i	0.00142532	−	0.00132251i
$499$	8.56720	−	21.8289i	0.383521	−	0.977195i	−0.600577	−	0.799567i	$-0.705062\pi$
$499$	8.56720	−	21.8289i	0.383521	−	0.977195i	0.984098	−	0.177628i	$-0.0568423\pi$
$500$	−0.623490	−	0.781831i	−0.0278833	−	0.0349646i
$501$	−0.415173	−	5.54010i	−0.0185486	−	0.247514i
$502$	−8.88072	+	2.73934i	−0.396366	+	0.122263i
$503$	1.39646	+	0.210482i	0.0622649	+	0.00938492i	0.180101	−	0.983648i	$-0.442358\pi$
$503$	1.39646	+	0.210482i	0.0622649	+	0.00938492i	−0.117836	+	0.993033i	$0.537596\pi$
$504$	−0.357885	−	0.332069i	−0.0159415	−	0.0147915i
$505$	6.01455	−	2.89646i	0.267644	−	0.128891i
$506$	12.8162	−	1.93173i	0.569750	−	0.0858760i
$507$	−0.202879	−	0.138321i	−0.00901019	−	0.00614304i
$508$	−9.06484	+	11.3669i	−0.402187	+	0.504327i
$509$	16.0702	+	27.8343i	0.712298	+	1.23374i	0.963993	+	0.265929i	$0.0856787\pi$
$509$	16.0702	+	27.8343i	0.712298	+	1.23374i	−0.251695	+	0.967807i	$0.580988\pi$
$510$	0.264990	−	0.458975i	0.0117339	−	0.0203238i
$511$	−0.725946	−	1.84968i	−0.0321140	−	0.0818250i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	8.73638	+	2.69482i	0.385721	+	0.118979i
$514$	2.38164	−	10.4346i	0.105049	−	0.460252i
$515$	−7.89914			−0.348078
$516$	0.0510591	−	2.51423i	0.00224775	−	0.110683i
$517$	−35.3549			−1.55491
$518$	0.163559	−	0.716600i	0.00718639	−	0.0314856i
$519$	8.35334	+	2.57666i	0.366671	+	0.113103i
$520$	−3.32753	−	1.60245i	−0.145922	−	0.0702722i
$521$	−9.36769	−	23.8685i	−0.410406	−	1.04570i	−0.975369	−	0.220581i	$-0.929205\pi$
$521$	−9.36769	−	23.8685i	−0.410406	−	1.04570i	0.564963	−	0.825117i	$-0.308891\pi$
$522$	14.1400	−	24.4911i	0.618889	−	1.07195i
$523$	−3.15578	−	5.46598i	−0.137993	−	0.239011i	0.788744	−	0.614722i	$-0.210732\pi$
$523$	−3.15578	−	5.46598i	−0.137993	−	0.239011i	−0.926737	+	0.375711i	$0.877398\pi$
$524$	0.348243	−	0.436683i	0.0152131	−	0.0190766i
$525$	−0.0542229	−	0.0369686i	−0.00236648	−	0.00161344i
$526$	−8.87306	+	1.33740i	−0.386884	+	0.0583134i
$527$	−5.19856	+	2.50349i	−0.226453	+	0.109054i
$528$	1.01074	+	0.937833i	0.0439870	+	0.0408140i
$529$	9.89308	+	1.49114i	0.430134	+	0.0648322i
$530$	−8.07244	+	2.49002i	−0.350644	+	0.108159i
$531$	2.86593	+	38.2431i	0.124371	+	1.65961i
$532$	0.434591	+	0.544960i	0.0188419	+	0.0236270i
$533$	5.94848	−	15.1565i	0.257657	−	0.656500i
$534$	3.87956	−	3.59971i	0.167885	−	0.155775i
$535$	8.36311	−	5.70187i	0.361569	−	0.246513i
$536$	−0.929407	+	12.4021i	−0.0401443	+	0.535688i
$537$	0.801387	+	3.51111i	0.0345824	+	0.151515i
$538$	5.31282	+	23.2770i	0.229052	+	1.00354i
$539$	−1.87292	+	24.9924i	−0.0806724	+	1.07650i
$540$	−1.85455	+	1.26441i	−0.0798072	+	0.0544116i
$541$	−13.1493	+	12.2008i	−0.565333	+	0.524552i	−0.910238	−	0.414085i	$-0.864101\pi$
$541$	−13.1493	+	12.2008i	−0.565333	+	0.524552i	0.344905	+	0.938637i	$0.387911\pi$
$542$	−0.192968	+	0.491674i	−0.00828867	+	0.0211192i
$543$	−1.61050	−	2.01950i	−0.0691132	−	0.0866652i
$544$	−0.103275	−	1.37811i	−0.00442787	−	0.0590858i
$545$	5.21579	−	1.60886i	0.223420	−	0.0689160i
$546$	−0.239668	−	0.0361242i	−0.0102569	−	0.00154597i
$547$	5.58065	+	5.17808i	0.238611	+	0.221399i	0.790410	−	0.612579i	$-0.209868\pi$
$547$	5.58065	+	5.17808i	0.238611	+	0.221399i	−0.551798	+	0.833978i	$0.686058\pi$
$548$	5.99236	−	2.88577i	0.255981	−	0.123274i
$549$	−21.5899	+	3.25416i	−0.921435	+	0.138884i
$550$	−2.97065	−	2.02536i	−0.126669	−	0.0863615i
$551$	−25.1739	+	31.5671i	−1.07244	+	1.34480i
$552$	−0.691228	−	1.19724i	−0.0294206	−	0.0509580i
$553$	−0.522659	+	0.905272i	−0.0222257	+	0.0384961i
$554$	3.10185	+	7.90338i	0.131785	+	0.335782i
$555$	−1.48408	−	0.714695i	−0.0629957	−	0.0303371i
$556$	10.4152	+	3.21266i	0.441702	+	0.136247i
$557$	7.93934	−	34.7845i	0.336401	−	1.47387i	−0.470088	−	0.882619i	$-0.655778\pi$
$557$	7.93934	−	34.7845i	0.336401	−	1.47387i	0.806489	−	0.591249i	$-0.201365\pi$
$558$	11.9115			0.504253
$559$	13.2336	+	20.2831i	0.559723	+	0.857883i
$560$	−0.171126			−0.00723141
$561$	0.424010	−	1.85771i	0.0179017	−	0.0784325i
$562$	−25.2570	−	7.79075i	−1.06540	−	0.328633i
$563$	13.8746	+	6.68165i	0.584744	+	0.281598i	0.702775	−	0.711412i	$-0.251944\pi$
$563$	13.8746	+	6.68165i	0.584744	+	0.281598i	−0.118031	+	0.993010i	$0.537658\pi$
$564$	1.37772	+	3.51038i	0.0580127	+	0.147814i
$565$	−5.91525	+	10.2455i	−0.248856	+	0.431032i
$566$	−1.56746	−	2.71492i	−0.0658853	−	0.114117i
$567$	0.821344	−	1.02993i	0.0344932	−	0.0432531i
$568$	5.01825	+	3.42138i	0.210561	+	0.143558i
$569$	31.4573	−	4.74143i	1.31876	−	0.198771i	0.548312	−	0.836274i	$-0.315271\pi$
$569$	31.4573	−	4.74143i	1.31876	−	0.198771i	0.770448	+	0.637503i	$0.220033\pi$
$570$	1.40736	−	0.677747i	0.0589477	−	0.0283877i
$571$	−27.2207	−	25.2571i	−1.13915	−	1.05698i	−0.997751	−	0.0670252i	$-0.978649\pi$
$571$	−27.2207	−	25.2571i	−1.13915	−	1.05698i	−0.141400	−	0.989953i	$-0.545160\pi$
$572$	−13.1305	−	1.97910i	−0.549012	−	0.0827503i
$573$	−0.696432	+	0.214821i	−0.0290939	+	0.00897427i
$574$	−0.0563779	−	0.752310i	−0.00235317	−	0.0314008i
$575$	2.24761	+	2.81841i	0.0937317	+	0.117536i
$576$	−1.04229	+	2.65572i	−0.0434289	+	0.110655i
$577$	25.0888	−	23.2790i	1.04446	−	0.969116i	0.0449049	−	0.998991i	$-0.485702\pi$
$577$	25.0888	−	23.2790i	1.04446	−	0.969116i	0.999554	+	0.0298753i	$0.00951103\pi$
$578$	12.4681	−	8.50059i	0.518604	−	0.353578i
$579$	0.0731433	−	0.976030i	0.00303973	−	0.0405624i
$580$	−2.20576	−	9.66406i	−0.0915891	−	0.401278i
$581$	0.00430845	+	0.0188766i	0.000178745	+	0.000783132i
$582$	0.00712998	−	0.0951430i	0.000295547	−	0.00394381i
$583$	−25.0953	+	17.1097i	−1.03934	+	0.708612i
$584$	−8.51184	+	7.89783i	−0.352222	+	0.326815i
$585$	3.84947	−	9.80830i	0.159156	−	0.405523i
$586$	7.95926	+	9.98060i	0.328794	+	0.412295i
$587$	−1.14437	−	15.2705i	−0.0472331	−	0.630282i	−0.969715	−	0.244241i	$-0.921461\pi$
$587$	−1.14437	−	15.2705i	−0.0472331	−	0.630282i	0.922481	−	0.386041i	$-0.126158\pi$
$588$	2.55447	−	0.787950i	0.105345	−	0.0324945i
$589$	−16.8163	−	2.53465i	−0.692904	−	0.104439i
$590$	9.85400	+	9.14318i	0.405683	+	0.376419i
$591$	6.75391	−	3.25251i	0.277819	−	0.133790i
$592$	−4.24726	+	0.640172i	−0.174562	+	0.0263109i
$593$	−20.0370	−	13.6610i	−0.822819	−	0.560989i	0.0771111	−	0.997023i	$-0.475430\pi$
$593$	−20.0370	−	13.6610i	−0.822819	−	0.560989i	−0.899930	+	0.436034i	$0.856383\pi$
$594$	−5.03164	+	6.30947i	−0.206451	+	0.258881i
$595$	0.118246	+	0.204808i	0.00484761	+	0.00839630i
$596$	2.30252	−	3.98808i	0.0943149	−	0.163358i
$597$	−1.36960	−	3.48969i	−0.0560541	−	0.142823i
$598$	11.9953	+	5.77665i	0.490526	+	0.236225i
$599$	−31.2765	−	9.64752i	−1.27792	−	0.394187i	−0.419793	−	0.907620i	$-0.637897\pi$
$599$	−31.2765	−	9.64752i	−1.27792	−	0.394187i	−0.858130	+	0.513433i	$0.828374\pi$
$600$	−0.0853357	+	0.373880i	−0.00348382	+	0.0152636i
$601$	−28.7764			−1.17381			−0.586907	−	0.809655i	$-0.699654\pi$
$601$	−28.7764			−1.17381			−0.586907	+	0.809655i	$0.699654\pi$
$602$	0.960219	+	0.580691i	0.0391356	+	0.0236672i
$603$	−35.4815			−1.44492
$604$	−2.88544	+	12.6420i	−0.117407	+	0.514394i
$605$	−1.84125	−	0.567950i	−0.0748573	−	0.0230904i
$606$	−2.30655	−	1.11078i	−0.0936973	−	0.0451222i
$607$	−11.3513	−	28.9226i	−0.460735	−	1.17393i	−0.952860	−	0.303409i	$-0.901875\pi$
$607$	−11.3513	−	28.9226i	−0.460735	−	1.17393i	0.492126	−	0.870524i	$-0.336220\pi$
$608$	2.03659	−	3.52748i	0.0825948	−	0.143058i
$609$	−0.325263	−	0.563371i	−0.0131803	−	0.0228290i
$610$	−4.77163	+	5.98344i	−0.193198	+	0.242262i
$611$	−30.0069	−	20.4584i	−1.21395	−	0.827656i
$612$	3.89863	−	0.587624i	0.157593	−	0.0237533i
$613$	−36.9515	+	17.7949i	−1.49246	+	0.718730i	−0.989358	−	0.145499i	$-0.953521\pi$
$613$	−36.9515	+	17.7949i	−1.49246	+	0.718730i	−0.503099	+	0.864229i	$0.667807\pi$
$614$	−19.0298	−	17.6571i	−0.767979	−	0.712581i
$615$	−1.67178	−	0.251980i	−0.0674125	−	0.0101608i
$616$	−0.587932	+	0.181353i	−0.0236885	+	0.00730692i
$617$	0.0249264	+	0.332620i	0.00100350	+	0.0133908i	0.997683	−	0.0680330i	$-0.0216723\pi$
$617$	0.0249264	+	0.332620i	0.00100350	+	0.0133908i	−0.996680	+	0.0814238i	$0.974053\pi$
$618$	1.88873	+	2.36839i	0.0759757	+	0.0952705i
$619$	7.69569	−	19.6083i	0.309316	−	0.788124i	−0.688693	−	0.725053i	$-0.741815\pi$
$619$	7.69569	−	19.6083i	0.309316	−	0.788124i	0.998009	−	0.0630709i	$-0.0200894\pi$
$620$	3.06062	−	2.83984i	0.122917	−	0.114051i
$621$	6.68544	−	4.55806i	0.268278	−	0.182909i
$622$	−1.27992	+	17.0793i	−0.0513200	+	0.684818i
$623$	0.525504	+	2.30238i	0.0210539	+	0.0922430i
$624$	0.315168	+	1.38084i	0.0126168	+	0.0552780i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	2.40908	−	1.64248i	0.0962860	−	0.0656467i
$627$	4.11695	−	3.81997i	0.164415	−	0.152555i
$628$	0.708797	−	1.80599i	0.0282841	−	0.0720667i
$629$	3.70097	+	4.64087i	0.147567	+	0.185044i
$630$	−0.0364841	−	0.486847i	−0.00145356	−	0.0193964i
$631$	−8.83919	+	2.72653i	−0.351883	+	0.108541i	−0.465657	−	0.884965i	$-0.654182\pi$
$631$	−8.83919	+	2.72653i	−0.351883	+	0.108541i	0.113775	+	0.993507i	$0.463706\pi$
$632$	6.04023	+	0.910418i	0.240267	+	0.0362145i
$633$	−5.96499	−	5.53470i	−0.237087	−	0.219985i
$634$	−11.2824	+	5.43330i	−0.448080	+	0.215784i
$635$	−14.3765	+	2.16691i	−0.570513	+	0.0859911i
$636$	2.67674	+	1.82497i	0.106140	+	0.0723648i
$637$	−16.0516	+	20.1281i	−0.635988	+	0.797503i
$638$	−17.8198	−	30.8648i	−0.705493	−	1.22195i
$639$	−8.66378	+	15.0061i	−0.342734	+	0.593633i
$640$	0.365341	+	0.930874i	0.0144414	+	0.0367960i
$641$	39.2115	+	18.8833i	1.54876	+	0.745845i	0.996156	−	0.0875972i	$-0.0279188\pi$
$641$	39.2115	+	18.8833i	1.54876	+	0.745845i	0.552607	+	0.833442i	$0.313633\pi$
$642$	−3.70925	−	1.14415i	−0.146392	−	0.0451561i
$643$	−10.8001	+	47.3182i	−0.425913	+	1.86605i	0.0697996	+	0.997561i	$0.477764\pi$
$643$	−10.8001	+	47.3182i	−0.425913	+	1.86605i	−0.495713	+	0.868487i	$0.665093\pi$
$644$	0.616891			0.0243089
$645$	1.74754	−	1.80833i	0.0688093	−	0.0712030i
$646$	−5.62902			−0.221471
$647$	−0.405182	+	1.77522i	−0.0159294	+	0.0697911i	−0.982268	−	0.187483i	$-0.939967\pi$
$647$	−0.405182	+	1.77522i	−0.0159294	+	0.0697911i	0.966339	+	0.257274i	$0.0828243\pi$
$648$	−7.35601	−	2.26903i	−0.288971	−	0.0891359i
$649$	43.5446	+	20.9700i	1.70927	+	0.823143i
$650$	−1.34931	−	3.43797i	−0.0529241	−	0.134848i
$651$	0.137000	−	0.237292i	0.00536947	−	0.00930019i
$652$	−9.78728	−	16.9521i	−0.383299	−	0.663894i
$653$	6.46822	−	8.11089i	0.253121	−	0.317403i	−0.638994	−	0.769211i	$-0.720649\pi$
$653$	6.46822	−	8.11089i	0.253121	−	0.317403i	0.892115	+	0.451808i	$0.149221\pi$
$654$	−1.72951	−	1.17916i	−0.0676291	−	0.0461087i
$655$	0.552300	−	0.0832458i	0.0215801	−	0.00325268i
$656$	−3.97197	+	1.91280i	−0.155079	+	0.0746823i
$657$	−24.2837	−	22.5320i	−0.947397	−	0.879056i
$658$	−1.66396	−	0.250802i	−0.0648679	−	0.00977727i
$659$	40.1274	−	12.3777i	1.56314	−	0.482165i	0.611983	−	0.790871i	$-0.290372\pi$
$659$	40.1274	−	12.3777i	1.56314	−	0.482165i	0.951158	+	0.308706i	$0.0998958\pi$
$660$	0.103039	+	1.37496i	0.00401079	+	0.0535203i
$661$	−26.4701	−	33.1924i	−1.02957	−	1.29104i	−0.955881	−	0.293754i	$-0.905095\pi$
$661$	−26.4701	−	33.1924i	−1.02957	−	1.29104i	−0.0736857	−	0.997282i	$-0.523476\pi$
$662$	9.41462	−	23.9881i	0.365910	−	0.932323i
$663$	1.43485	−	1.33134i	0.0557248	−	0.0517050i
$664$	0.0934844	−	0.0637366i	0.00362790	−	0.00247346i
$665$	−0.0520891	+	0.695081i	−0.00201993	+	0.0269541i
$666$	−2.72678	−	11.9468i	−0.105660	−	0.462929i
$667$	7.95150	+	34.8378i	0.307883	+	1.34892i
$668$	1.08260	−	14.4463i	0.0418872	−	0.558946i
$669$	4.95425	−	3.37775i	0.191542	−	0.130591i
$670$	−9.11686	+	8.45921i	−0.352215	+	0.326808i
$671$	−10.0527	+	25.6139i	−0.388080	+	0.988812i
$672$	0.0409173	+	0.0513086i	0.00157842	+	0.00197927i
$673$	−3.19015	−	42.5696i	−0.122971	−	1.64094i	−0.628272	−	0.777994i	$-0.716238\pi$
$673$	−3.19015	−	42.5696i	−0.122971	−	1.64094i	0.505301	−	0.862943i	$-0.331381\pi$
$674$	−20.4576	+	6.31032i	−0.787996	+	0.243065i
$675$	−2.21950	−	0.334536i	−0.0854287	−	0.0128763i
$676$	−0.469361	−	0.435503i	−0.0180523	−	0.0167501i
$677$	−22.3656	+	10.7707i	−0.859580	+	0.413952i	−0.811124	−	0.584874i	$-0.801144\pi$
$677$	−22.3656	+	10.7707i	−0.859580	+	0.413952i	−0.0484552	+	0.998825i	$0.515430\pi$
$678$	4.48627	−	0.676196i	0.172294	−	0.0259692i
$679$	0.0351767	+	0.0239831i	0.00134996	+	0.000920387i
$680$	0.861644	−	1.08047i	0.0330426	−	0.0414341i
$681$	4.25980	+	7.37819i	0.163236	+	0.282733i
$682$	7.50569	−	13.0002i	0.287408	−	0.497805i
$683$	−11.5894	−	29.5292i	−0.443454	−	1.12990i	−0.961562	−	0.274588i	$-0.911459\pi$
$683$	−11.5894	−	29.5292i	−0.443454	−	1.12990i	0.518108	−	0.855315i	$-0.326637\pi$
$684$	10.4697	+	5.04196i	0.400320	+	0.192784i
$685$	6.35553	+	1.96042i	0.242833	+	0.0749039i
$686$	−0.531994	+	2.33082i	−0.0203116	+	0.0889910i
$687$	9.42788			0.359696
$688$	1.10879	−	6.46302i	0.0422722	−	0.246400i
$689$	−31.1999			−1.18862
$690$	0.307625	−	1.34779i	0.0117111	−	0.0513097i
$691$	−15.1486	−	4.67273i	−0.576280	−	0.177759i	−0.00710436	−	0.999975i	$-0.502261\pi$
$691$	−15.1486	−	4.67273i	−0.576280	−	0.177759i	−0.569176	+	0.822216i	$0.692738\pi$
$692$	20.5374	+	9.89030i	0.780716	+	0.375973i
$693$	−0.641288	−	1.63398i	−0.0243605	−	0.0620696i
$694$	−0.701482	+	1.21500i	−0.0266279	+	0.0461209i
$695$	5.44971	+	9.43917i	0.206719	+	0.358048i
$696$	−2.37015	+	2.97208i	−0.0898404	+	0.112656i
$697$	5.03385	+	3.43202i	0.190671	+	0.129997i
$698$	−15.5398	+	2.34225i	−0.588190	+	0.0886554i
$699$	−5.88247	+	2.83285i	−0.222495	+	0.107148i
$700$	−0.125445	−	0.116396i	−0.00474136	−	0.00439934i
$701$	41.7258	+	6.28915i	1.57596	+	0.237538i	0.878023	−	0.478619i	$-0.158862\pi$
$701$	41.7258	+	6.28915i	1.57596	+	0.237538i	0.697939	+	0.716157i	$0.254101\pi$
$702$	−7.92153	+	2.44347i	−0.298979	+	0.0922227i
$703$	1.30743	+	17.4464i	0.0493105	+	0.658003i
$704$	2.24169	+	2.81099i	0.0844869	+	0.105943i
$705$	−1.37772	+	3.51038i	−0.0518881	+	0.132209i
$706$	−1.84614	+	1.71296i	−0.0694803	+	0.0644683i
$707$	0.943879	−	0.643526i	0.0354982	−	0.0242023i
$708$	0.385242	−	5.14070i	0.0144783	−	0.193199i
$709$	−4.55628	−	19.9623i	−0.171115	−	0.749702i	−0.985541	−	0.169435i	$-0.945806\pi$
$709$	−4.55628	−	19.9623i	−0.171115	−	0.749702i	0.814427	−	0.580266i	$-0.197052\pi$
$710$	1.35150	+	5.92132i	0.0507210	+	0.222223i
$711$	−1.30232	+	17.3783i	−0.0488409	+	0.651736i
$712$	11.4023	−	7.77397i	0.427320	−	0.291342i
$713$	−11.0332	+	10.2373i	−0.413195	+	0.383389i
$714$	0.0331340	−	0.0844242i	0.00124001	−	0.00315949i
$715$	−8.27918	−	10.3818i	−0.309624	−	0.388256i
$716$	0.701790	+	9.36473i	0.0262271	+	0.349976i
$717$	0.166092	−	0.0512327i	0.00620283	−	0.00191332i
$718$	25.3636	+	3.82294i	0.946559	+	0.142671i
$719$	17.2502	+	16.0059i	0.643325	+	0.596919i	0.932856	−	0.360250i	$-0.117309\pi$
$719$	17.2502	+	16.0059i	0.643325	+	0.596919i	−0.289530	+	0.957169i	$0.593499\pi$
$720$	−2.57040	+	1.23784i	−0.0957932	+	0.0461316i
$721$	−1.33665	+	0.201468i	−0.0497796	+	0.00750306i
$722$	1.99053	+	1.35712i	0.0740797	+	0.0505067i
$723$	−3.44424	+	4.31894i	−0.128093	+	0.160623i
$724$	−3.36776	−	5.83314i	−0.125162	−	0.216787i
$725$	4.95629	−	8.58455i	0.184072	−	0.318822i
$726$	0.269965	+	0.687859i	0.0100193	+	0.0255288i
$727$	2.39672	+	1.15420i	0.0888893	+	0.0428068i	0.477800	−	0.878469i	$-0.341434\pi$
$727$	2.39672	+	1.15420i	0.0888893	+	0.0428068i	−0.388911	+	0.921275i	$0.627149\pi$
$728$	−0.603938	−	0.186290i	−0.0223834	−	0.00690438i
$729$	4.31236	−	18.8937i	0.159717	−	0.699765i
$730$	−11.6115			−0.429761
$731$	−8.50123	+	3.13883i	−0.314429	+	0.116094i
$732$	2.93493			0.108478
$733$	3.03058	−	13.2778i	0.111937	−	0.490428i	−0.887618	−	0.460581i	$-0.847641\pi$
$733$	3.03058	−	13.2778i	0.111937	−	0.490428i	0.999554	−	0.0298466i	$-0.00950189\pi$
$734$	−18.8399	−	5.81134i	−0.695393	−	0.214500i
$735$	2.40850	+	1.15987i	0.0888390	+	0.0427826i
$736$	−1.31701	−	3.35569i	−0.0485457	−	0.123692i
$737$	−22.3577	+	38.7247i	−0.823556	+	1.42644i
$738$	−6.28865	−	10.8923i	−0.231488	−	0.400950i
$739$	−26.3192	+	33.0032i	−0.968168	+	1.21404i	0.00864792	+	0.999963i	$0.497247\pi$
$739$	−26.3192	+	33.0032i	−0.968168	+	1.21404i	−0.976816	+	0.214082i	$0.931324\pi$
$740$	−3.54889	−	2.41959i	−0.130460	−	0.0889461i
$741$	5.70464	−	0.859836i	0.209565	−	0.0315869i
$742$	−1.30247	+	0.627237i	−0.0478152	+	0.0230266i
$743$	−2.48319	−	2.30406i	−0.0910994	−	0.0845279i	0.633309	−	0.773899i	$-0.281696\pi$
$743$	−2.48319	−	2.30406i	−0.0910994	−	0.0845279i	−0.724408	+	0.689371i	$0.757887\pi$
$744$	−1.58328	−	0.238640i	−0.0580457	−	0.00874898i
$745$	4.40045	−	1.35736i	0.161220	−	0.0497298i
$746$	0.904093	+	12.0643i	0.0331012	+	0.441705i
$747$	0.201258	+	0.252370i	0.00736366	+	0.00923374i
$748$	1.81528	−	4.62526i	0.0663732	−	0.169116i
$749$	1.26974	−	1.17814i	0.0463952	−	0.0430485i
$750$	−0.316859	+	0.216031i	−0.0115700	+	0.00788832i
$751$	2.25422	−	30.0805i	0.0822576	−	1.09765i	−0.791461	−	0.611220i	$-0.790679\pi$
$751$	2.25422	−	30.0805i	0.0822576	−	1.09765i	0.873718	−	0.486432i	$-0.161702\pi$
$752$	2.18814	+	9.58686i	0.0797932	+	0.349597i
$753$	0.793077	+	3.47470i	0.0289013	+	0.126625i
$754$	2.73586	−	36.5075i	0.0996342	−	1.32953i
$755$	−10.7139	+	7.30461i	−0.389919	+	0.265842i
$756$	−0.281569	+	0.261258i	−0.0102406	+	0.00950187i
$757$	−6.62568	+	16.8820i	−0.240815	+	0.613585i	−0.999273	−	0.0381365i	$-0.987858\pi$
$757$	−6.62568	+	16.8820i	−0.240815	+	0.613585i	0.758458	+	0.651722i	$0.225953\pi$
$758$	−3.31422	−	4.15590i	−0.120378	−	0.150949i
$759$	−0.371444	−	4.95657i	−0.0134826	−	0.179912i
$760$	3.89223	−	1.20059i	0.141186	−	0.0435501i
$761$	44.8334	+	6.75755i	1.62521	+	0.244961i	0.897529	−	0.440955i	$-0.145360\pi$
$761$	44.8334	+	6.75755i	1.62521	+	0.244961i	0.727681	+	0.685916i	$0.240598\pi$
$762$	4.08720	+	3.79236i	0.148063	+	0.137383i
$763$	0.841557	−	0.405273i	0.0304664	−	0.0146719i
$764$	−1.87922	+	0.283246i	−0.0679877	+	0.0102475i
$765$	3.25758	+	2.22098i	0.117778	+	0.0802998i
$766$	9.47802	−	11.8851i	0.342455	−	0.429425i
$767$	24.8233	+	42.9952i	0.896318	+	1.55247i
$768$	0.191748	−	0.332117i	0.00691910	−	0.0119842i
$769$	3.91690	+	9.98010i	0.141247	+	0.359892i	0.983939	−	0.178504i	$-0.0571258\pi$
$769$	3.91690	+	9.98010i	0.141247	+	0.359892i	−0.842692	+	0.538396i	$0.819031\pi$
$770$	−0.554336	−	0.266954i	−0.0199769	−	0.00962037i
$771$	−3.92219	−	1.20983i	−0.141254	−	0.0435711i
$772$	0.567924	−	2.48824i	0.0204400	−	0.0895536i
$773$	30.9801			1.11428			0.557139	−	0.830419i	$-0.311899\pi$
$773$	30.9801			1.11428			0.557139	+	0.830419i	$0.311899\pi$
$774$	18.6234	+	1.77654i	0.669404	+	0.0638563i
$775$	4.17517			0.149977
$776$	0.0553610	−	0.242552i	0.00198734	−	0.00870712i
$777$	−0.269357	−	0.0830856i	−0.00966313	−	0.00298068i
$778$	−23.9994	−	11.5575i	−0.860421	−	0.414357i
$779$	6.56038	+	16.7156i	0.235050	+	0.598897i
$780$	−0.708177	+	1.22660i	−0.0253568	+	0.0439193i
$781$	10.9185	+	18.9114i	0.390694	+	0.676703i
$782$	−3.10613	+	3.89496i	−0.111075	+	0.139283i
$783$	−18.3834	−	12.5336i	−0.656969	−	0.447914i
$784$	6.89286	−	1.03893i	0.246174	−	0.0371047i
$785$	1.74797	−	0.841777i	0.0623876	−	0.0300443i
$786$	−0.157017	−	0.145691i	−0.00560062	−	0.00519662i
$787$	22.3689	+	3.37157i	0.797365	+	0.120183i	0.535074	−	0.844805i	$-0.320284\pi$
$787$	22.3689	+	3.37157i	0.797365	+	0.120183i	0.262291	+	0.964989i	$0.415522\pi$
$788$	18.6788	−	5.76165i	0.665405	−	0.205250i
$789$	0.257162	+	3.43159i	0.00915522	+	0.122168i
$790$	3.80856	+	4.77578i	0.135502	+	0.169915i
$791$	−0.739637	+	1.88456i	−0.0262985	+	0.0670074i
$792$	−7.51921	+	6.97681i	−0.267184	+	0.247910i
$793$	−23.3537	+	15.9223i	−0.829313	+	0.565416i
$794$	−0.457853	+	6.10963i	−0.0162486	+	0.216823i
$795$	0.720895	+	3.15845i	0.0255675	+	0.112019i
$796$	−2.17524	−	9.53034i	−0.0770993	−	0.337794i
$797$	−3.20620	+	42.7838i	−0.113570	+	1.51548i	0.591478	+	0.806321i	$0.298544\pi$
$797$	−3.20620	+	42.7838i	−0.113570	+	1.51548i	−0.705048	+	0.709160i	$0.749075\pi$
$798$	0.220860	−	0.150580i	0.00781836	−	0.00533047i
$799$	9.96179	−	9.24319i	0.352423	−	0.327000i
$800$	−0.365341	+	0.930874i	−0.0129168	+	0.0329114i
$801$	24.5476	+	30.7817i	0.867346	+	1.08762i
$802$	0.321148	+	4.28542i	0.0113401	+	0.151324i
$803$	−39.8932	+	12.3054i	−1.40780	+	0.434249i
$804$	4.71621	+	0.710854i	0.166328	+	0.0250699i
$805$	0.452213	+	0.419592i	0.0159384	+	0.0147887i
$806$	13.8930	−	6.69051i	0.489360	−	0.235663i
$807$	9.05391	−	1.36466i	0.318713	−	0.0480382i
$808$	−5.51568	−	3.76053i	−0.194041	−	0.132295i
$809$	21.7668	−	27.2947i	0.765281	−	0.959632i	−0.234642	−	0.972082i	$-0.575392\pi$
$809$	21.7668	−	27.2947i	0.765281	−	0.959632i	0.999922	+	0.0124503i	$0.00396317\pi$
$810$	−3.84901	−	6.66667i	−0.135240	−	0.234243i
$811$	−1.57202	+	2.72282i	−0.0552011	+	0.0956111i	−0.892305	−	0.451432i	$-0.850913\pi$
$811$	−1.57202	+	2.72282i	−0.0552011	+	0.0956111i	0.837104	+	0.547043i	$0.184247\pi$
$812$	−0.619730	−	1.57905i	−0.0217483	−	0.0554137i
$813$	0.182497	+	0.0878860i	0.00640045	+	0.00308230i
$814$	−14.7570	−	4.55193i	−0.517232	−	0.159545i
$815$	4.35575	−	19.0838i	0.152575	−	0.668476i
$816$	−0.529979			−0.0185530
$817$	−25.9140	−	6.47095i	−0.906615	−	0.226390i
$818$	21.2103			0.741601
$819$	0.401228	−	1.75789i	0.0140200	−	0.0614258i
$820$	−4.21269	−	1.29944i	−0.147114	−	0.0453785i
$821$	−29.7398	−	14.3219i	−1.03793	−	0.499838i	−0.164286	−	0.986413i	$-0.552532\pi$
$821$	−29.7398	−	14.3219i	−1.03793	−	0.499838i	−0.873639	+	0.486574i	$0.838246\pi$
$822$	−0.931852	−	2.37432i	−0.0325021	−	0.0828139i
$823$	−11.2949	+	19.5633i	−0.393715	+	0.681934i	−0.992936	−	0.118649i	$-0.962144\pi$
$823$	−11.2949	+	19.5633i	−0.393715	+	0.681934i	0.599221	+	0.800583i	$0.295477\pi$
$824$	3.94957	+	6.84085i	0.137590	+	0.238312i
$825$	−0.859678	+	1.07800i	−0.0299301	+	0.0375312i
$826$	1.90064	+	1.29584i	0.0661319	+	0.0450879i
$827$	14.4461	−	2.17740i	0.502341	−	0.0757157i	0.107016	−	0.994257i	$-0.465870\pi$
$827$	14.4461	−	2.17740i	0.502341	−	0.0757157i	0.395324	+	0.918542i	$0.370632\pi$
$828$	9.26600	−	4.46227i	0.322016	−	0.155075i
$829$	−38.4706	−	35.6955i	−1.33614	−	1.23975i	−0.948046	−	0.318134i	$-0.896944\pi$
$829$	−38.4706	−	35.6955i	−1.33614	−	1.23975i	−0.388092	−	0.921621i	$-0.626866\pi$
$830$	0.111881	+	0.0168633i	0.00388344	+	0.000585334i
$831$	3.11133	−	0.959718i	0.107931	−	0.0332922i
$832$	0.275999	+	3.68295i	0.00956854	+	0.127683i
$833$	−6.00628	−	7.53163i	−0.208105	−	0.260956i
$834$	1.52708	−	3.89094i	0.0528785	−	0.134732i
$835$	10.6196	−	9.85356i	0.367507	−	0.340997i
$836$	12.1000	−	8.24966i	0.418488	−	0.285320i
$837$	0.700331	−	9.34527i	0.0242070	−	0.323020i
$838$	3.27516	+	14.3494i	0.113139	+	0.495692i
$839$	−11.0632	−	48.4712i	−0.381945	−	1.67341i	−0.691382	−	0.722490i	$-0.742998\pi$
$839$	−11.0632	−	48.4712i	−0.381945	−	1.67341i	0.309437	−	0.950920i	$-0.399860\pi$
$840$	−0.00490425	+	0.0654427i	−0.000169213	+	0.00225799i
$841$	57.2248	−	39.0152i	1.97327	−	1.34535i
$842$	11.4081	−	10.5852i	0.393150	−	0.364790i
$843$	−3.70319	+	9.43558i	−0.127545	+	0.324979i
$844$	−13.2295	−	16.5893i	−0.455379	−	0.571027i
$845$	−0.0478484	−	0.638493i	−0.00164604	−	0.0219648i
$846$	−26.8077	+	8.26907i	−0.921666	+	0.284296i
$847$	−0.326052	−	0.0491445i	−0.0112033	−	0.00168863i
$848$	6.19264	+	5.74593i	0.212656	+	0.197316i
$849$	−1.08317	+	0.521627i	−0.0371743	+	0.0179022i
$850$	1.36653	−	0.205972i	0.0468718	−	0.00706478i
$851$	12.7933	+	8.72235i	0.438550	+	0.298998i
$852$	1.45223	−	1.82104i	0.0497526	−	0.0623878i
$853$	19.6333	+	34.0059i	0.672232	+	1.16434i	0.977270	+	0.212000i	$0.0679977\pi$
$853$	19.6333	+	34.0059i	0.672232	+	1.16434i	−0.305037	+	0.952340i	$0.598669\pi$
$854$	−0.654824	+	1.13419i	−0.0224076	+	0.0388112i
$855$	4.24545	+	10.8172i	0.145191	+	0.369942i
$856$	−9.11952	−	4.39173i	−0.311699	−	0.150106i
$857$	20.6361	+	6.36540i	0.704916	+	0.217438i	0.626430	−	0.779477i	$-0.284515\pi$
$857$	20.6361	+	6.36540i	0.704916	+	0.217438i	0.0784859	+	0.996915i	$0.474991\pi$
$858$	−1.13315	+	4.96467i	−0.0386852	+	0.169491i
$859$	−6.47737			−0.221005			−0.110503	−	0.993876i	$-0.535246\pi$
$859$	−6.47737			−0.221005			−0.110503	+	0.993876i	$0.535246\pi$
$860$	5.20877	−	3.98356i	0.177617	−	0.135838i
$861$	−0.289316			−0.00985988
$862$	0.978980	−	4.28919i	0.0333442	−	0.146091i
$863$	42.0218	+	12.9620i	1.43044	+	0.441231i	0.910691	−	0.413089i	$-0.135550\pi$
$863$	42.0218	+	12.9620i	1.43044	+	0.441231i	0.519747	+	0.854321i	$0.326026\pi$
$864$	2.02229	+	0.973883i	0.0687997	+	0.0331322i
$865$	8.32788	+	21.2191i	0.283157	+	0.721471i
$866$	3.53767	−	6.12742i	0.120215	−	0.208218i
$867$	−2.89350	−	5.01169i	−0.0982685	−	0.170206i
$868$	0.445473	−	0.558605i	0.0151203	−	0.0189603i
$869$	18.1461	+	12.3718i	0.615564	+	0.419684i
$870$	−3.75897	+	0.566574i	−0.127441	+	0.0192086i
$871$	−41.3840	+	19.9295i	−1.40224	+	0.675284i
$872$	−4.00121	−	3.71258i	−0.135498	−	0.125724i
$873$	0.701853	+	0.105787i	0.0237541	+	0.00358036i
$874$	−14.0310	+	4.32800i	−0.474606	+	0.146397i
$875$	−0.0127883	−	0.170648i	−0.000432323	−	0.00576895i
$876$	2.77637	+	3.48146i	0.0938050	+	0.117628i
$877$	16.1905	−	41.2528i	0.546715	−	1.39301i	−0.344225	−	0.938887i	$-0.611858\pi$
$877$	16.1905	−	41.2528i	0.546715	−	1.39301i	0.890940	−	0.454121i	$-0.150047\pi$
$878$	4.91491	−	4.56037i	0.165870	−	0.153905i
$879$	4.04491	−	2.75777i	0.136431	−	0.0930174i
$880$	−0.268684	+	3.58534i	−0.00905734	+	0.120862i
$881$	5.68129	+	24.8914i	0.191408	+	0.838611i	0.975856	+	0.218417i	$0.0700892\pi$
$881$	5.68129	+	24.8914i	0.191408	+	0.838611i	−0.784448	+	0.620195i	$0.787054\pi$
$882$	4.42527	+	19.3884i	0.149007	+	0.652840i
$883$	0.159373	−	2.12668i	0.00536332	−	0.0715686i	−0.993880	−	0.110466i	$-0.964766\pi$
$883$	0.159373	−	2.12668i	0.00536332	−	0.0715686i	0.999243	+	0.0388977i	$0.0123846\pi$
$884$	4.21712	−	2.87518i	0.141837	−	0.0967029i
$885$	3.77896	−	3.50637i	0.127028	−	0.117865i
$886$	10.2025	−	25.9954i	0.342758	−	0.873333i
$887$	26.2624	+	32.9320i	0.881806	+	1.10575i	0.993705	+	0.112030i	$0.0357353\pi$
$887$	26.2624	+	32.9320i	0.881806	+	1.10575i	−0.111899	+	0.993720i	$0.535693\pi$
$888$	0.123096	+	1.64260i	0.00413082	+	0.0551220i
$889$	−2.37745	+	0.733347i	−0.0797372	+	0.0245957i
$890$	13.6461	+	2.05682i	0.457420	+	0.0689449i
$891$	−20.2890	−	18.8254i	−0.679706	−	0.630675i
$892$	14.0871	−	6.78399i	0.471671	−	0.227145i
$893$	39.6059	−	5.96963i	1.32536	−	0.199766i
$894$	−1.45915	−	0.994829i	−0.0488012	−	0.0332721i
$895$	−5.85519	+	7.34217i	−0.195717	+	0.245422i
$896$	0.0855632	+	0.148200i	0.00285847	+	0.00495101i
$897$	2.55289	−	4.42174i	0.0852387	−	0.147638i
$898$	−12.5682	−	32.0233i	−0.419407	−	1.06863i
$899$	37.2882	+	17.9570i	1.24363	+	0.598901i
$900$	−2.72618	−	0.840916i	−0.0908728	−	0.0280305i
$901$	2.59783	−	11.3818i	0.0865462	−	0.379184i
$902$	−15.8505			−0.527763
$903$	0.249588	−	0.350568i	0.00830578	−	0.0116662i
$904$	11.8305			0.393477
$905$	1.49880	−	6.56665i	0.0498216	−	0.218283i
$906$	4.75188	+	1.46576i	0.157871	+	0.0486967i
$907$	10.3137	+	4.96683i	0.342461	+	0.164921i	0.597207	−	0.802088i	$-0.296277\pi$
$907$	10.3137	+	4.96683i	0.342461	+	0.164921i	−0.254745	+	0.967008i	$0.581992\pi$
$908$	8.11629	+	20.6800i	0.269348	+	0.686289i
$909$	9.52258	−	16.4936i	0.315844	−	0.547058i
$910$	−0.316009	−	0.547343i	−0.0104756	−	0.0181442i
$911$	−12.3184	+	15.4468i	−0.408128	+	0.511777i	−0.942834	−	0.333261i	$-0.891851\pi$
$911$	−12.3184	+	15.4468i	−0.408128	+	0.511777i	0.534706	+	0.845038i	$0.320422\pi$
$912$	−1.29062	−	0.879933i	−0.0427369	−	0.0291375i
$913$	0.402255	−	0.0606302i	0.0133127	−	0.00200657i
$914$	−24.0469	+	11.5804i	−0.795402	+	0.383045i
$915$	2.15146	+	1.99626i	0.0711249	+	0.0659943i
$916$	24.3095	+	3.66407i	0.803208	+	0.121064i
$917$	0.0913343	−	0.0281729i	0.00301612	−	0.000930351i
$918$	−0.231808	−	3.09326i	−0.00765079	−	0.102093i
$919$	12.8020	+	16.0533i	0.422301	+	0.529548i	0.946783	−	0.321873i	$-0.104313\pi$
$919$	12.8020	+	16.0533i	0.422301	+	0.529548i	−0.524482	+	0.851421i	$0.675741\pi$
$920$	1.31701	−	3.35569i	0.0434206	−	0.110634i
$921$	−7.29783	+	6.77140i	−0.240472	+	0.223125i
$922$	21.4654	−	14.6349i	0.706927	−	0.481974i
$923$	−1.67631	+	22.3688i	−0.0551763	+	0.736277i
$924$	0.0525043	+	0.230036i	0.00172726	+	0.00756763i
$925$	−0.955781	−	4.18755i	−0.0314259	−	0.137686i
$926$	2.47523	−	33.0297i	0.0813411	−	1.08542i
$927$	−18.6199	+	12.6948i	−0.611557	+	0.416952i
$928$	−7.26644	+	6.74227i	−0.238533	+	0.221326i
$929$	−8.00612	+	20.3993i	−0.262672	+	0.669278i	−0.999980	−	0.00627875i	$-0.998001\pi$
$929$	−8.00612	+	20.3993i	−0.262672	+	0.669278i	0.737308	+	0.675557i	$0.236097\pi$
$930$	−0.998306	−	1.25184i	−0.0327358	−	0.0410493i
$931$	−2.12181	−	28.3136i	−0.0695396	−	0.927942i
$932$	−16.2687	+	5.01824i	−0.532900	+	0.164378i
$933$	6.49484	+	0.978940i	0.212632	+	0.0320491i
$934$	−3.91368	−	3.63136i	−0.128059	−	0.118822i
$935$	4.47667	−	2.15585i	0.146403	−	0.0705038i
$936$	−10.4190	+	1.57041i	−0.340555	+	0.0513304i
$937$	9.84205	+	6.71019i	0.321526	+	0.219213i	0.713317	−	0.700842i	$-0.247192\pi$
$937$	9.84205	+	6.71019i	0.321526	+	0.219213i	−0.391791	+	0.920054i	$0.628144\pi$
$938$	−1.32696	+	1.66395i	−0.0433267	+	0.0543300i
$939$	−0.559081	−	0.968357i	−0.0182449	−	0.0316011i
$940$	−4.91670	+	8.51598i	−0.160365	+	0.277761i
$941$	5.42445	+	13.8213i	0.176832	+	0.450561i	0.991619	−	0.129200i	$-0.0412410\pi$
$941$	5.42445	+	13.8213i	0.176832	+	0.450561i	−0.814786	+	0.579761i	$0.803146\pi$
$942$	−0.670337	−	0.322817i	−0.0218408	−	0.0105180i
$943$	15.1863	+	4.68434i	0.494533	+	0.152543i
$944$	2.99122	−	13.1054i	0.0973560	−	0.426545i
$945$	−0.384106			−0.0124950
$946$	13.6739	−	19.2062i	0.444578	−	0.624447i
$947$	11.4289			0.371388			0.185694	−	0.982608i	$-0.440547\pi$
$947$	11.4289			0.371388			0.185694	+	0.982608i	$0.440547\pi$
$948$	0.521269	−	2.28383i	0.0169300	−	0.0741753i
$949$	−40.9793	−	12.6404i	−1.33024	−	0.410326i
$950$	3.66982	+	1.76729i	0.119065	+	0.0573385i
$951$	1.75448	+	4.47035i	0.0568930	+	0.144961i
$952$	0.118246	−	0.204808i	0.00383237	−	0.00663786i
$953$	−22.8187	−	39.5231i	−0.739169	−	1.28028i	−0.952870	−	0.303379i	$-0.901885\pi$
$953$	−22.8187	−	39.5231i	−0.739169	−	1.28028i	0.213701	−	0.976899i	$-0.431448\pi$
$954$	−15.0266	+	18.8428i	−0.486505	+	0.610058i
$955$	−1.57022	−	1.07056i	−0.0508111	−	0.0346424i
$956$	0.448175	−	0.0675515i	0.0144950	−	0.00218477i
$957$	−12.3141	+	5.93016i	−0.398059	+	0.191695i
$958$	3.70721	+	3.43979i	0.119774	+	0.111134i
$959$	1.12545	+	0.169635i	0.0363428	+	0.00547779i
$960$	0.366458	−	0.113037i	0.0118274	−	0.00364826i
$961$	−1.01393	−	13.5300i	−0.0327075	−	0.436451i
$962$	−9.89073	−	12.4026i	−0.318890	−	0.399875i
$963$	10.5500	−	26.8809i	0.339969	−	0.866226i
$964$	−10.5594	+	9.79768i	−0.340095	+	0.315562i
$965$	2.10875	−	1.43772i	0.0678830	−	0.0462819i
$966$	0.0176793	−	0.235913i	0.000568821	−	0.00759038i
$967$	9.45478	+	41.4241i	0.304045	+	1.33211i	0.863961	+	0.503559i	$0.167976\pi$
$967$	9.45478	+	41.4241i	0.304045	+	1.33211i	−0.559916	+	0.828550i	$0.689166\pi$
$968$	0.428765	+	1.87854i	0.0137810	+	0.0603786i
$969$	−0.161320	+	2.15267i	−0.00518235	+	0.0691537i
$970$	0.205560	−	0.140148i	0.00660013	−	0.00449989i
$971$	−16.9750	+	15.7505i	−0.544754	+	0.505458i	−0.903854	−	0.427841i	$-0.859274\pi$
$971$	−16.9750	+	15.7505i	−0.544754	+	0.505458i	0.359100	+	0.933299i	$0.383084\pi$
$972$	−3.53864	+	9.01632i	−0.113502	+	0.289199i
$973$	1.16292	+	1.45826i	0.0372815	+	0.0467495i
$974$	−0.873837	−	11.6605i	−0.0279995	−	0.373628i
$975$	−1.35343	+	0.417478i	−0.0433444	+	0.0133700i
$976$	7.56763	+	1.14064i	0.242234	+	0.0365109i
$977$	−24.7923	−	23.0039i	−0.793177	−	0.735961i	0.175447	−	0.984489i	$-0.443863\pi$
$977$	−24.7923	−	23.0039i	−0.793177	−	0.735961i	−0.968625	+	0.248528i	$0.920053\pi$
$978$	−6.76335	+	3.25706i	−0.216268	+	0.104149i
$979$	49.0632	−	7.39509i	1.56807	−	0.236348i
$980$	5.75948	+	3.92674i	0.183980	+	0.125435i
$981$	9.70906	−	12.1748i	0.309987	−	0.388711i
$982$	16.7052	+	28.9342i	0.533084	+	0.923328i
$983$	8.47556	−	14.6801i	0.270328	−	0.468222i	−0.698618	−	0.715495i	$-0.746201\pi$
$983$	8.47556	−	14.6801i	0.270328	−	0.468222i	0.968946	+	0.247273i	$0.0795344\pi$
$984$	0.617667	+	1.57379i	0.0196905	+	0.0501706i
$985$	17.6114	+	8.48122i	0.561147	+	0.270234i
$986$	13.0903	+	4.03782i	0.416880	+	0.128590i
$987$	−0.143599	+	0.629149i	−0.00457081	+	0.0200260i
$988$	15.0434			0.478594
$989$	−18.7770	+	14.3603i	−0.597074	+	0.456630i
$990$	−10.2574			−0.326002
$991$	0.387117	−	1.69607i	0.0122972	−	0.0538774i	−0.968407	−	0.249375i	$-0.919775\pi$
$991$	0.387117	−	1.69607i	0.0122972	−	0.0538774i	0.980704	+	0.195497i	$0.0626321\pi$
$992$	−3.98968	−	1.23065i	−0.126673	−	0.0390733i
$993$	−8.90378	−	4.28783i	−0.282553	−	0.136070i
$994$	0.379719	+	0.967507i	0.0120439	+	0.0306875i
$995$	4.88771	−	8.46577i	0.154951	−	0.268383i
$996$	−0.0216952	−	0.0375772i	−0.000687438	−	0.00119068i
$997$	−14.3072	+	17.9407i	−0.453114	+	0.568187i	−0.954946	−	0.296778i	$-0.904088\pi$
$997$	−14.3072	+	17.9407i	−0.453114	+	0.568187i	0.501833	+	0.864965i	$0.332659\pi$
$998$	−19.3752	−	13.2098i	−0.613311	−	0.418148i
$999$	−9.53329	+	1.43691i	−0.301620	+	0.0454619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.81.3	✓	60
43.17	even	21	inner	430.2.q.d.361.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.81.3	✓	60	1.1	even	1	trivial
430.2.q.d.361.3	yes	60	43.17	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.366458 - 0.113037i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.191748 + 0.332117i) q^{6} +(-0.0855632 - 0.148200i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.35720 - 1.60711i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.366458 - 0.113037i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(-0.191748 + 0.332117i) q^{6} +(-0.0855632 - 0.148200i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-2.35720 - 1.60711i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(-3.23934 + 1.55998i) q^{11} +(0.281122 + 0.260843i) q^{12} +(-3.65202 - 0.550454i) q^{13} +(-0.163524 + 0.0504404i) q^{14} +(0.0286586 + 0.382423i) q^{15} +(0.623490 + 0.781831i) q^{16} +(0.504890 - 1.28644i) q^{17} +(-2.09135 + 1.94049i) q^{18} +(3.36543 - 2.29451i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(0.0146032 + 0.0639808i) q^{21} +(0.800050 + 3.50525i) q^{22} +(0.269393 - 3.59480i) q^{23} +(0.316859 - 0.216031i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.34931 + 3.43797i) q^{26} +(1.39947 + 1.75488i) q^{27} +(0.0127883 + 0.170648i) q^{28} +(-9.47220 + 2.92179i) q^{29} +(0.379212 + 0.0571570i) q^{30} +(-3.06062 - 2.83984i) q^{31} +(0.900969 - 0.433884i) q^{32} +(1.36342 - 0.205502i) q^{33} +(-1.14184 - 0.778492i) q^{34} +(-0.106696 + 0.133792i) q^{35} +(1.42647 + 2.47071i) q^{36} +(-2.14762 + 3.71979i) q^{37} +(-1.48810 - 3.79162i) q^{38} +(1.27609 + 0.614533i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-0.980995 + 4.29802i) q^{41} +0.0656262 q^{42} +(-4.36167 - 4.89651i) q^{43} +3.59539 q^{44} +(-0.634837 + 2.78140i) q^{45} +(-3.44473 - 1.06256i) q^{46} +(8.85959 + 4.26655i) q^{47} +(-0.140107 - 0.356986i) q^{48} +(3.48536 - 6.03682i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.330437 + 0.414354i) q^{51} +(3.05153 + 2.08050i) q^{52} +(8.35339 - 1.25907i) q^{53} +(2.02229 - 0.973883i) q^{54} +(2.63561 + 2.44549i) q^{55} +(0.169215 + 0.0255051i) q^{56} +(-1.49265 + 0.460422i) q^{57} +(0.740768 + 9.88487i) q^{58} +(-8.38122 - 10.5097i) q^{59} +(0.140107 - 0.356986i) q^{60} +(5.61012 - 5.20543i) q^{61} +(-3.44969 + 2.35196i) q^{62} +(-0.0364841 + 0.486847i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.821831 + 3.60068i) q^{65} +(0.103039 - 1.37496i) q^{66} +(10.2758 - 7.00593i) q^{67} +(-1.01306 + 0.939979i) q^{68} +(-0.505068 + 1.28689i) q^{69} +(0.106696 + 0.133792i) q^{70} +(-0.453881 - 6.05662i) q^{71} +(2.72618 - 0.840916i) q^{72} +(11.4818 + 1.73061i) q^{73} +(3.14863 + 2.92150i) q^{74} +(0.345517 - 0.166392i) q^{75} +(-4.02769 + 0.607077i) q^{76} +(0.508357 + 0.346592i) q^{77} +(0.883082 - 1.10735i) q^{78} +(-3.05423 - 5.29007i) q^{79} +(0.500000 - 0.866025i) q^{80} +(2.81240 + 7.16588i) q^{81} +(3.97197 + 1.91280i) q^{82} +(-0.108118 - 0.0333499i) q^{83} +(0.0146032 - 0.0639808i) q^{84} -1.38197 q^{85} +(-5.74431 + 3.16274i) q^{86} +3.80143 q^{87} +(0.800050 - 3.50525i) q^{88} +(-13.1872 - 4.06770i) q^{89} +(2.57040 + 1.23784i) q^{90} +(0.230902 + 0.588328i) q^{91} +(-1.80244 + 3.12192i) q^{92} +(0.800580 + 1.38664i) q^{93} +(6.13103 - 7.68806i) q^{94} +(-3.36543 - 2.29451i) q^{95} +(-0.379212 + 0.0571570i) q^{96} +(-0.224152 + 0.107946i) q^{97} +(-5.10990 - 4.74129i) q^{98} +(10.1428 + 1.52879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

L-functions

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