LMFDB - Embedded newform 841.2.d.a.645.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-5,-2,5,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			645.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	841.645
Dual form			841.2.d.a.605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0990311 - 0.433884i) q^{2} +(-1.12349 - 0.541044i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.153989 - 0.674671i) q^{5} +(-0.123490 + 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.900969 - 1.12978i) q^{9} +(-0.277479 + 0.133627i) q^{10} +(-3.07942 + 3.86147i) q^{11} -2.24698 q^{12} +(-3.52446 + 4.41953i) q^{13} +(-0.0353438 + 0.154851i) q^{14} +(-0.192021 + 0.841301i) q^{15} +(1.77748 - 2.22889i) q^{16} -4.49396 q^{17} +(-0.400969 + 0.502799i) q^{18} +(-2.12349 + 1.02262i) q^{19} +(-0.777479 - 0.974928i) q^{20} +(0.277479 + 0.347948i) q^{21} +(1.98039 + 0.953703i) q^{22} +(-0.510885 + 2.23833i) q^{23} +(0.469501 + 2.05702i) q^{24} +(4.07338 - 1.96163i) q^{25} +(2.26659 + 1.09153i) q^{26} +(1.23341 + 5.40391i) q^{27} -0.643104 q^{28} +0.384043 q^{30} +(-1.48911 - 6.52424i) q^{31} +(-4.19202 - 2.01877i) q^{32} +(5.54892 - 2.67222i) q^{33} +(0.445042 + 1.94986i) q^{34} +(-0.0549581 + 0.240787i) q^{35} +(-2.34601 - 1.12978i) q^{36} +(3.07942 + 3.86147i) q^{37} +(0.653989 + 0.820077i) q^{38} +(6.35086 - 3.05841i) q^{39} +(-0.730054 + 0.915458i) q^{40} -3.10992 q^{41} +(0.123490 - 0.154851i) q^{42} +(-0.757865 + 3.32042i) q^{43} +(-1.98039 + 8.67664i) q^{44} +(-0.623490 + 0.781831i) q^{45} +1.02177 q^{46} +(4.01842 - 5.03894i) q^{47} +(-3.20291 + 1.54244i) q^{48} +(-4.28501 - 5.37323i) q^{49} +(-1.25451 - 1.57311i) q^{50} +(5.04892 + 2.43143i) q^{51} +(-2.26659 + 9.93060i) q^{52} +(1.04407 + 4.57438i) q^{53} +(2.22252 - 1.07031i) q^{54} +(3.07942 + 1.48297i) q^{55} +(0.134375 + 0.588735i) q^{56} +2.93900 q^{57} -12.4940 q^{59} +(0.346011 + 1.51597i) q^{60} +(-1.48039 - 0.712916i) q^{61} +(-2.68329 + 1.29221i) q^{62} +(0.114761 + 0.502799i) q^{63} +(0.807979 - 3.53999i) q^{64} +(3.52446 + 1.69729i) q^{65} +(-1.70895 - 2.14295i) q^{66} +(-1.44839 - 1.81623i) q^{67} +(-7.29590 + 3.51352i) q^{68} +(1.78501 - 2.23833i) q^{69} +0.109916 q^{70} +(-4.57338 + 5.73483i) q^{71} +(-0.544073 + 2.38374i) q^{72} +(1.25182 - 5.48460i) q^{73} +(1.37047 - 1.71851i) q^{74} -5.63773 q^{75} +(-2.64795 + 3.32042i) q^{76} +(1.58815 - 0.764811i) q^{77} +(-1.95593 - 2.45265i) q^{78} +(2.90850 + 3.64715i) q^{79} +(-1.77748 - 0.855989i) q^{80} +(0.573376 - 2.51212i) q^{81} +(0.307979 + 1.34934i) q^{82} +(-4.01357 + 1.93284i) q^{83} +(0.722521 + 0.347948i) q^{84} +(0.692021 + 3.03194i) q^{85} +1.51573 q^{86} +8.35690 q^{88} +(-1.26391 - 5.53753i) q^{89} +(0.400969 + 0.193096i) q^{90} +(1.81767 - 0.875342i) q^{91} +(0.920583 + 4.03334i) q^{92} +(-1.85690 + 8.13559i) q^{93} +(-2.58426 - 1.24451i) q^{94} +(1.01693 + 1.27518i) q^{95} +(3.61745 + 4.53614i) q^{96} +(-0.162718 + 0.0783611i) q^{97} +(-1.90701 + 2.39131i) q^{98} +7.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} - 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} - 7 q^{8} - q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} + 9 q^{15} + 11 q^{16} - 8 q^{17} + 2 q^{18} - 8 q^{19} - 5 q^{20}+ \cdots + 32 q^{99}+O(q^{100}) $ 6 * q - 5 * q^2 - 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 - 7 * q^8 - q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 + 9 * q^15 + 11 * q^16 - 8 * q^17 + 2 * q^18 - 8 * q^19 - 5 * q^20 + 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 + 17 * q^26 + 4 * q^27 - 12 * q^28 - 18 * q^30 - 12 * q^31 - 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 + 10 * q^37 + 9 * q^38 + 11 * q^39 + 21 * q^40 - 20 * q^41 - 4 * q^42 + 8 * q^43 + q^44 + q^45 - 4 * q^47 - 6 * q^48 - q^49 + 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 + 10 * q^55 - 7 * q^56 - 2 * q^57 - 56 * q^59 - 3 * q^60 + 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 - 16 * q^66 - 30 * q^67 - 16 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^72 - 24 * q^73 - 6 * q^74 - 48 * q^75 - 2 * q^76 + 17 * q^77 - 8 * q^78 - 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 + 4 * q^84 - 6 * q^85 - 16 * q^86 + 42 * q^88 - 14 * q^89 - 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 + 22 * q^95 - 2 * q^96 - 22 * q^97 - 26 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.0990311	−	0.433884i	−0.0700256	−	0.306802i	0.927771	−	0.373150i	$-0.121722\pi$
$2$	−0.0990311	−	0.433884i	−0.0700256	−	0.306802i	−0.997797	+	0.0663480i	$0.978865\pi$
$3$	−1.12349	−	0.541044i	−0.648647	−	0.312372i	0.0804740	−	0.996757i	$-0.474357\pi$
$3$	−1.12349	−	0.541044i	−0.648647	−	0.312372i	−0.729121	+	0.684385i	$0.760071\pi$
$4$	1.62349	−	0.781831i	0.811745	−	0.390916i
$5$	−0.153989	−	0.674671i	−0.0688661	−	0.301722i	0.928752	−	0.370702i	$-0.120883\pi$
$5$	−0.153989	−	0.674671i	−0.0688661	−	0.301722i	−0.997618	+	0.0689797i	$0.978026\pi$
$6$	−0.123490	+	0.541044i	−0.0504145	+	0.220880i
$7$	−0.321552	−	0.154851i	−0.121535	−	0.0585283i	0.372128	−	0.928181i	$-0.378628\pi$
$7$	−0.321552	−	0.154851i	−0.121535	−	0.0585283i	−0.493663	+	0.869653i	$0.664342\pi$
$8$	−1.05496	−	1.32288i	−0.372984	−	0.467707i
$9$	−0.900969	−	1.12978i	−0.300323	−	0.376593i
$10$	−0.277479	+	0.133627i	−0.0877466	+	0.0422565i
$11$	−3.07942	+	3.86147i	−0.928479	+	1.16428i	0.0576568	+	0.998336i	$0.481637\pi$
$11$	−3.07942	+	3.86147i	−0.928479	+	1.16428i	−0.986136	+	0.165940i	$0.946934\pi$
$12$	−2.24698			−0.648647
$13$	−3.52446	+	4.41953i	−0.977509	+	1.22576i	−0.00332670	+	0.999994i	$0.501059\pi$
$13$	−3.52446	+	4.41953i	−0.977509	+	1.22576i	−0.974182	+	0.225763i	$0.927513\pi$
$14$	−0.0353438	+	0.154851i	−0.00944603	+	0.0413858i
$15$	−0.192021	+	0.841301i	−0.0495797	+	0.217223i
$16$	1.77748	−	2.22889i	0.444370	−	0.557222i
$17$	−4.49396			−1.08995			−0.544973	−	0.838454i	$-0.683460\pi$
$17$	−4.49396			−1.08995			−0.544973	+	0.838454i	$0.683460\pi$
$18$	−0.400969	+	0.502799i	−0.0945093	+	0.118511i
$19$	−2.12349	+	1.02262i	−0.487162	+	0.234605i	−0.661307	−	0.750115i	$-0.729998\pi$
$19$	−2.12349	+	1.02262i	−0.487162	+	0.234605i	0.174145	+	0.984720i	$0.444284\pi$
$20$	−0.777479	−	0.974928i	−0.173850	−	0.218001i
$21$	0.277479	+	0.347948i	0.0605509	+	0.0759284i
$22$	1.98039	+	0.953703i	0.422220	+	0.203330i
$23$	−0.510885	+	2.23833i	−0.106527	+	0.466725i	0.893323	+	0.449415i	$0.148367\pi$
$23$	−0.510885	+	2.23833i	−0.106527	+	0.466725i	−0.999850	+	0.0173102i	$0.994490\pi$
$24$	0.469501	+	2.05702i	0.0958364	+	0.419887i
$25$	4.07338	−	1.96163i	0.814675	−	0.392327i
$26$	2.26659	+	1.09153i	0.444516	+	0.214067i
$27$	1.23341	+	5.40391i	0.237369	+	1.03998i
$28$	−0.643104			−0.121535
$29$		0			0
$29$		0			0
$30$	0.384043			0.0701163
$31$	−1.48911	−	6.52424i	−0.267453	−	1.17179i	−0.912965	−	0.408038i	$-0.866213\pi$
$31$	−1.48911	−	6.52424i	−0.267453	−	1.17179i	0.645512	−	0.763750i	$-0.276644\pi$
$32$	−4.19202	−	2.01877i	−0.741052	−	0.356872i
$33$	5.54892	−	2.67222i	0.965943	−	0.465173i
$34$	0.445042	+	1.94986i	0.0763241	+	0.334398i
$35$	−0.0549581	+	0.240787i	−0.00928962	+	0.0407005i
$36$	−2.34601	−	1.12978i	−0.391002	−	0.188297i
$37$	3.07942	+	3.86147i	0.506253	+	0.634821i	0.967627	−	0.252385i	$-0.0812148\pi$
$37$	3.07942	+	3.86147i	0.506253	+	0.634821i	−0.461374	+	0.887206i	$0.652643\pi$
$38$	0.653989	+	0.820077i	0.106091	+	0.133034i
$39$	6.35086	−	3.05841i	1.01695	−	0.489738i
$40$	−0.730054	+	0.915458i	−0.115432	+	0.144747i
$41$	−3.10992			−0.485687			−0.242844	−	0.970065i	$-0.578080\pi$
$41$	−3.10992			−0.485687			−0.242844	+	0.970065i	$0.578080\pi$
$42$	0.123490	−	0.154851i	0.0190549	−	0.0238941i
$43$	−0.757865	+	3.32042i	−0.115573	+	0.506360i	0.883693	+	0.468066i	$0.155049\pi$
$43$	−0.757865	+	3.32042i	−0.115573	+	0.506360i	−0.999267	+	0.0382932i	$0.987808\pi$
$44$	−1.98039	+	8.67664i	−0.298554	+	1.30805i
$45$	−0.623490	+	0.781831i	−0.0929444	+	0.116549i
$46$	1.02177			0.150652
$47$	4.01842	−	5.03894i	0.586146	−	0.735004i	−0.397001	−	0.917818i	$-0.629949\pi$
$47$	4.01842	−	5.03894i	0.586146	−	0.735004i	0.983148	+	0.182814i	$0.0585205\pi$
$48$	−3.20291	+	1.54244i	−0.462300	+	0.222632i
$49$	−4.28501	−	5.37323i	−0.612145	−	0.767605i
$50$	−1.25451	−	1.57311i	−0.177415	−	0.222471i
$51$	5.04892	+	2.43143i	0.706990	+	0.340468i
$52$	−2.26659	+	9.93060i	−0.314320	+	1.37713i
$53$	1.04407	+	4.57438i	0.143414	+	0.628340i	0.994627	+	0.103519i	$0.0330104\pi$
$53$	1.04407	+	4.57438i	0.143414	+	0.628340i	−0.851213	+	0.524820i	$0.824132\pi$
$54$	2.22252	−	1.07031i	0.302447	−	0.145651i
$55$	3.07942	+	1.48297i	0.415228	+	0.199963i
$56$	0.134375	+	0.588735i	0.0179566	+	0.0786730i
$57$	2.93900			0.389280
$58$		0			0
$59$	−12.4940			−1.62657			−0.813287	−	0.581862i	$-0.802324\pi$
$59$	−12.4940			−1.62657			−0.813287	+	0.581862i	$0.802324\pi$
$60$	0.346011	+	1.51597i	0.0446698	+	0.195711i
$61$	−1.48039	−	0.712916i	−0.189544	−	0.0912796i	0.336705	−	0.941610i	$-0.390688\pi$
$61$	−1.48039	−	0.712916i	−0.189544	−	0.0912796i	−0.526249	+	0.850331i	$0.676402\pi$
$62$	−2.68329	+	1.29221i	−0.340778	+	0.164110i
$63$	0.114761	+	0.502799i	0.0144585	+	0.0633467i
$64$	0.807979	−	3.53999i	0.100997	−	0.442498i
$65$	3.52446	+	1.69729i	0.437155	+	0.210523i
$66$	−1.70895	−	2.14295i	−0.210357	−	0.263779i
$67$	−1.44839	−	1.81623i	−0.176950	−	0.221888i	0.685445	−	0.728124i	$-0.259608\pi$
$67$	−1.44839	−	1.81623i	−0.176950	−	0.221888i	−0.862395	+	0.506237i	$0.831036\pi$
$68$	−7.29590	+	3.51352i	−0.884757	+	0.426077i
$69$	1.78501	−	2.23833i	0.214890	−	0.269464i
$70$	0.109916			0.0131375
$71$	−4.57338	+	5.73483i	−0.542760	+	0.680599i	−0.975267	−	0.221031i	$-0.929058\pi$
$71$	−4.57338	+	5.73483i	−0.542760	+	0.680599i	0.432507	+	0.901631i	$0.357629\pi$
$72$	−0.544073	+	2.38374i	−0.0641196	+	0.280926i
$73$	1.25182	−	5.48460i	0.146515	−	0.641924i	−0.847323	−	0.531078i	$-0.821787\pi$
$73$	1.25182	−	5.48460i	0.146515	−	0.641924i	0.993838	−	0.110845i	$-0.0353559\pi$
$74$	1.37047	−	1.71851i	0.159314	−	0.199773i
$75$	−5.63773			−0.650989
$76$	−2.64795	+	3.32042i	−0.303741	+	0.380879i
$77$	1.58815	−	0.764811i	0.180986	−	0.0871583i
$78$	−1.95593	−	2.45265i	−0.221465	−	0.277708i
$79$	2.90850	+	3.64715i	0.327232	+	0.410336i	0.918047	−	0.396471i	$-0.129765\pi$
$79$	2.90850	+	3.64715i	0.327232	+	0.410336i	−0.590815	+	0.806807i	$0.701194\pi$
$80$	−1.77748	−	0.855989i	−0.198728	−	0.0957025i
$81$	0.573376	−	2.51212i	0.0637084	−	0.279125i
$82$	0.307979	+	1.34934i	0.0340105	+	0.149010i
$83$	−4.01357	+	1.93284i	−0.440547	+	0.212156i	−0.640990	−	0.767549i	$-0.721476\pi$
$83$	−4.01357	+	1.93284i	−0.440547	+	0.212156i	0.200443	+	0.979705i	$0.435762\pi$
$84$	0.722521	+	0.347948i	0.0788335	+	0.0379642i
$85$	0.692021	+	3.03194i	0.0750603	+	0.328861i
$86$	1.51573			0.163445
$87$		0			0
$88$	8.35690			0.890848
$89$	−1.26391	−	5.53753i	−0.133974	−	0.586977i	−0.996691	−	0.0812898i	$-0.974096\pi$
$89$	−1.26391	−	5.53753i	−0.133974	−	0.586977i	0.862717	−	0.505687i	$-0.168761\pi$
$90$	0.400969	+	0.193096i	0.0422658	+	0.0203542i
$91$	1.81767	−	0.875342i	0.190543	−	0.0917608i
$92$	0.920583	+	4.03334i	0.0959774	+	0.420505i
$93$	−1.85690	+	8.13559i	−0.192551	+	0.843622i
$94$	−2.58426	−	1.24451i	−0.266546	−	0.128362i
$95$	1.01693	+	1.27518i	0.104334	+	0.130831i
$96$	3.61745	+	4.53614i	0.369204	+	0.462968i
$97$	−0.162718	+	0.0783611i	−0.0165216	+	0.00795636i	−0.442126	−	0.896953i	$-0.645776\pi$
$97$	−0.162718	+	0.0783611i	−0.0165216	+	0.00795636i	0.425605	+	0.904909i	$0.360061\pi$
$98$	−1.90701	+	2.39131i	−0.192637	+	0.241559i
$99$	7.13706			0.717302
$100$	5.07942	−	6.36939i	0.507942	−	0.636939i
$101$	0.718636	−	3.14855i	0.0715070	−	0.313292i	−0.926508	−	0.376276i	$-0.877204\pi$
$101$	0.718636	−	3.14855i	0.0715070	−	0.313292i	0.998015	+	0.0629836i	$0.0200616\pi$
$102$	0.554958	−	2.43143i	0.0549490	−	0.240747i
$103$	−8.51238	+	10.6742i	−0.838749	+	1.05176i	0.159168	+	0.987252i	$0.449119\pi$
$103$	−8.51238	+	10.6742i	−0.838749	+	1.05176i	−0.997917	+	0.0645070i	$0.979453\pi$
$104$	9.56465			0.937891
$105$	0.192021	−	0.240787i	0.0187394	−	0.0234984i
$106$	1.88135	−	0.906013i	0.182733	−	0.0879997i
$107$	10.1283	+	12.7005i	0.979143	+	1.22781i	0.973703	+	0.227821i	$0.0731602\pi$
$107$	10.1283	+	12.7005i	0.979143	+	1.22781i	0.00544006	+	0.999985i	$0.498268\pi$
$108$	6.22737	+	7.80887i	0.599229	+	0.751409i
$109$	−4.92543	−	2.37196i	−0.471770	−	0.227193i	0.182864	−	0.983138i	$-0.441463\pi$
$109$	−4.92543	−	2.37196i	−0.471770	−	0.227193i	−0.654634	+	0.755946i	$0.727177\pi$
$110$	0.338478	−	1.48297i	0.0322726	−	0.141396i
$111$	−1.37047	−	6.00442i	−0.130079	−	0.569914i
$112$	−0.916698	+	0.441459i	−0.0866199	+	0.0417139i
$113$	−9.61745	−	4.63152i	−0.904733	−	0.435697i	−0.0771372	−	0.997020i	$-0.524578\pi$
$113$	−9.61745	−	4.63152i	−0.904733	−	0.435697i	−0.827596	+	0.561324i	$0.810292\pi$
$114$	−0.291053	−	1.27518i	−0.0272596	−	0.119432i
$115$	1.58881			0.148157
$116$		0			0
$117$	8.16852			0.755180
$118$	1.23729	+	5.42093i	0.113902	+	0.499037i
$119$	1.44504	+	0.695895i	0.132467	+	0.0637926i
$120$	1.31551	−	0.633517i	0.120089	−	0.0578319i
$121$	−2.98039	−	13.0579i	−0.270944	−	1.18708i
$122$	−0.162718	+	0.712916i	−0.0147318	+	0.0645444i
$123$	3.49396	+	1.68260i	0.315040	+	0.151715i
$124$	−7.51842	−	9.42780i	−0.675174	−	0.846641i
$125$	−4.10806	−	5.15134i	−0.367436	−	0.460750i
$126$	0.206791	−	0.0995855i	0.0184224	−	0.00887178i
$127$	0.646457	−	0.810631i	0.0573637	−	0.0719319i	−0.752322	−	0.658796i	$-0.771066\pi$
$127$	0.646457	−	0.810631i	0.0573637	−	0.0719319i	0.809686	+	0.586864i	$0.199638\pi$
$128$	−10.9215			−0.965337
$129$	2.64795	−	3.32042i	0.233139	−	0.292347i
$130$	0.387395	−	1.69729i	0.0339768	−	0.148862i
$131$	1.78501	−	7.82065i	0.155957	−	0.683293i	−0.835127	−	0.550057i	$-0.814606\pi$
$131$	1.78501	−	7.82065i	0.155957	−	0.683293i	0.991084	−	0.133236i	$-0.0425369\pi$
$132$	6.91939	−	8.67664i	0.602255	−	0.755204i
$133$	0.841166			0.0729384
$134$	−0.644596	+	0.808298i	−0.0556846	+	0.0698263i
$135$	3.45593	−	1.66429i	0.297439	−	0.143239i
$136$	4.74094	+	5.94495i	0.406532	+	0.509775i
$137$	−10.7443	−	13.4729i	−0.917947	−	1.15107i	−0.988143	−	0.153536i	$-0.950934\pi$
$137$	−10.7443	−	13.4729i	−0.917947	−	1.15107i	0.0701964	−	0.997533i	$-0.477637\pi$
$138$	−1.14795	−	0.552823i	−0.0977199	−	0.0470594i
$139$	3.70895	−	16.2500i	0.314589	−	1.37830i	−0.532310	−	0.846550i	$-0.678676\pi$
$139$	3.70895	−	16.2500i	0.314589	−	1.37830i	0.846899	−	0.531754i	$-0.178467\pi$
$140$	0.0990311	+	0.433884i	0.00836966	+	0.0366699i
$141$	−7.24094	+	3.48705i	−0.609797	+	0.293663i
$142$	2.94116	+	1.41639i	0.246816	+	0.118861i
$143$	−6.21260	−	27.2192i	−0.519523	−	2.27618i
$144$	−4.11960			−0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	1.90701	+	8.35516i	0.157288	+	0.689122i
$148$	8.01842	+	3.86147i	0.659110	+	0.317411i
$149$	−16.7642	+	8.07321i	−1.37338	+	0.661383i	−0.967576	−	0.252578i	$-0.918721\pi$
$149$	−16.7642	+	8.07321i	−1.37338	+	0.661383i	−0.405800	+	0.913962i	$0.633007\pi$
$150$	0.558311	+	2.44612i	0.0455859	+	0.199725i
$151$	1.67510	−	7.33907i	0.136317	−	0.597245i	−0.859909	−	0.510448i	$-0.829480\pi$
$151$	1.67510	−	7.33907i	0.136317	−	0.597245i	0.996226	−	0.0867973i	$-0.0276633\pi$
$152$	3.59299	+	1.73029i	0.291430	+	0.140345i
$153$	4.04892	+	5.07718i	0.327336	+	0.410466i
$154$	−0.489115	−	0.613331i	−0.0394140	−	0.0494236i
$155$	−4.17241	+	2.00933i	−0.335136	+	0.161393i
$156$	7.91939	−	9.93060i	0.634058	−	0.795084i
$157$	18.2392			1.45565			0.727824	−	0.685764i	$-0.240532\pi$
$157$	18.2392			1.45565			0.727824	+	0.685764i	$0.240532\pi$
$158$	1.29440	−	1.62313i	0.102977	−	0.129129i
$159$	1.30194	−	5.70416i	0.103250	−	0.452369i
$160$	−0.716480	+	3.13910i	−0.0566427	+	0.248168i
$161$	0.510885	−	0.640630i	0.0402634	−	0.0504887i
$162$	−1.14675			−0.0900973
$163$	−7.88135	+	9.88291i	−0.617315	+	0.774089i	−0.987964	−	0.154684i	$-0.950564\pi$
$163$	−7.88135	+	9.88291i	−0.617315	+	0.774089i	0.370649	+	0.928773i	$0.379135\pi$
$164$	−5.04892	+	2.43143i	−0.394254	+	0.189863i
$165$	−2.65734	−	3.33220i	−0.206874	−	0.259411i
$166$	1.23609	+	1.55001i	0.0959395	+	0.120304i
$167$	0.717677	+	0.345615i	0.0555355	+	0.0267445i	0.461445	−	0.887169i	$-0.347331\pi$
$167$	0.717677	+	0.345615i	0.0555355	+	0.0267445i	−0.405910	+	0.913913i	$0.633045\pi$
$168$	0.167563	−	0.734141i	0.0129278	−	0.0566402i
$169$	−4.21768	−	18.4788i	−0.324437	−	1.42145i
$170$	1.24698	−	0.600514i	0.0956390	−	0.0460573i
$171$	3.06853	+	1.47773i	0.234656	+	0.113005i
$172$	1.36563	+	5.98319i	0.104128	+	0.456214i
$173$	−9.15346			−0.695924			−0.347962	−	0.937509i	$-0.613126\pi$
$173$	−9.15346			−0.695924			−0.347962	+	0.937509i	$0.613126\pi$
$174$		0			0
$175$	−1.61356			−0.121974
$176$	3.13318	+	13.7274i	0.236172	+	1.03474i
$177$	14.0368	+	6.75978i	1.05507	+	0.508096i
$178$	−2.27748	+	1.09678i	−0.170704	+	0.0822068i
$179$	−0.757865	−	3.32042i	−0.0566455	−	0.248180i	0.938676	−	0.344801i	$-0.112054\pi$
$179$	−0.757865	−	3.32042i	−0.0566455	−	0.248180i	−0.995321	+	0.0966211i	$0.969196\pi$
$180$	−0.400969	+	1.75676i	−0.0298865	+	0.130941i
$181$	−11.4194	−	5.49929i	−0.848796	−	0.408759i	−0.0416657	−	0.999132i	$-0.513266\pi$
$181$	−11.4194	−	5.49929i	−0.848796	−	0.408759i	−0.807131	+	0.590373i	$0.798981\pi$
$182$	−0.559802	−	0.701970i	−0.0414953	−	0.0520335i
$183$	1.27748	+	1.60191i	0.0944340	+	0.118416i
$184$	3.50000	−	1.68551i	0.258023	−	0.124258i
$185$	2.13102	−	2.67222i	0.156676	−	0.196465i
$186$	3.71379			0.272308
$187$	13.8388	−	17.3533i	1.01199	−	1.26900i
$188$	2.58426	−	11.3224i	0.188477	−	0.825770i
$189$	0.440198	−	1.92863i	0.0320197	−	0.140287i
$190$	0.452575	−	0.567511i	0.0328332	−	0.0411715i
$191$	10.6703			0.772072			0.386036	−	0.922484i	$-0.373844\pi$
$191$	10.6703			0.772072			0.386036	+	0.922484i	$0.373844\pi$
$192$	−2.82304	+	3.53999i	−0.203736	+	0.255476i
$193$	20.4780	−	9.86168i	1.47404	−	0.709859i	0.487459	−	0.873146i	$-0.337924\pi$
$193$	20.4780	−	9.86168i	1.47404	−	0.709859i	0.986579	+	0.163286i	$0.0522094\pi$
$194$	0.0501138	+	0.0628407i	0.00359796	+	0.00451170i
$195$	−3.04138	−	3.81378i	−0.217798	−	0.273110i
$196$	−11.1576	−	5.37323i	−0.796974	−	0.383802i
$197$	4.35205	−	19.0676i	0.310071	−	1.35851i	−0.544320	−	0.838878i	$-0.683212\pi$
$197$	4.35205	−	19.0676i	0.310071	−	1.35851i	0.854391	−	0.519631i	$-0.173931\pi$
$198$	−0.706791	−	3.09666i	−0.0502295	−	0.220070i
$199$	0.788364	−	0.379656i	0.0558857	−	0.0269131i	−0.405732	−	0.913992i	$-0.632983\pi$
$199$	0.788364	−	0.379656i	0.0558857	−	0.0269131i	0.461618	+	0.887079i	$0.347269\pi$
$200$	−6.89224	−	3.31913i	−0.487355	−	0.234698i
$201$	0.644596	+	2.82416i	0.0454663	+	0.199201i
$202$	−1.43727			−0.101126
$203$		0			0
$204$	10.0978			0.706990
$205$	0.478894	+	2.09817i	0.0334474	+	0.146543i
$206$	5.47434	+	2.63631i	0.381416	+	0.183680i
$207$	2.98911	−	1.43948i	0.207758	−	0.100051i
$208$	3.58599	+	15.7112i	0.248644	+	1.08938i
$209$	2.59030	−	11.3489i	0.179175	−	0.785017i
$210$	−0.123490	−	0.0594696i	−0.00852161	−	0.00410379i
$211$	11.3904	+	14.2831i	0.784146	+	0.983288i	0.999976	+	0.00685718i	$0.00218273\pi$
$211$	11.3904	+	14.2831i	0.784146	+	0.983288i	−0.215830	+	0.976431i	$0.569246\pi$
$212$	5.27144	+	6.61017i	0.362044	+	0.453989i
$213$	8.24094	−	3.96863i	0.564660	−	0.271926i
$214$	4.50753	−	5.65227i	0.308129	−	0.386381i
$215$	2.35690			0.160739
$216$	5.84750	−	7.33254i	0.397872	−	0.498916i
$217$	−0.531459	+	2.32847i	−0.0360778	+	0.158067i
$218$	−0.541385	+	2.37196i	−0.0366672	+	0.160649i
$219$	−4.37382	+	5.48460i	−0.295555	+	0.370615i
$220$	6.15883			0.415228
$221$	15.8388	−	19.8612i	1.06543	−	1.33601i
$222$	−2.46950	+	1.18925i	−0.165742	+	0.0798172i
$223$	−1.13371	−	1.42163i	−0.0759189	−	0.0951993i	0.742422	−	0.669933i	$-0.233677\pi$
$223$	−1.13371	−	1.42163i	−0.0759189	−	0.0951993i	−0.818341	+	0.574734i	$0.805106\pi$
$224$	1.03534	+	1.29828i	0.0691768	+	0.0867450i
$225$	−5.88620	−	2.83464i	−0.392413	−	0.188976i
$226$	−1.05711	+	4.63152i	−0.0703182	+	0.308084i
$227$	3.08330	+	13.5088i	0.204646	+	0.896612i	0.968063	+	0.250707i	$0.0806630\pi$
$227$	3.08330	+	13.5088i	0.204646	+	0.896612i	−0.763417	+	0.645906i	$0.776480\pi$
$228$	4.77144	−	2.29780i	0.315996	−	0.152176i
$229$	−11.5075	−	5.54174i	−0.760439	−	0.366208i	0.0131352	−	0.999914i	$-0.495819\pi$
$229$	−11.5075	−	5.54174i	−0.760439	−	0.366208i	−0.773574	+	0.633706i	$0.781533\pi$
$230$	−0.157342	−	0.689359i	−0.0103748	−	0.0454550i
$231$	−2.19806			−0.144622
$232$		0			0
$233$	−8.86592			−0.580826			−0.290413	−	0.956901i	$-0.593793\pi$
$233$	−8.86592			−0.580826			−0.290413	+	0.956901i	$0.593793\pi$
$234$	−0.808938	−	3.54419i	−0.0528819	−	0.231691i
$235$	−4.01842	−	1.93517i	−0.262133	−	0.126236i
$236$	−20.2838	+	9.76817i	−1.32036	+	0.635854i
$237$	−1.29440	−	5.67116i	−0.0840806	−	0.368381i
$238$	0.158834	−	0.695895i	0.0102957	−	0.0451082i
$239$	23.0330	+	11.0921i	1.48988	+	0.717487i	0.988984	−	0.148022i	$-0.0472905\pi$
$239$	23.0330	+	11.0921i	1.48988	+	0.717487i	0.500894	+	0.865509i	$0.333005\pi$
$240$	1.53385	+	1.92339i	0.0990097	+	0.124154i
$241$	6.06734	+	7.60820i	0.390831	+	0.490087i	0.937854	−	0.347031i	$-0.112810\pi$
$241$	6.06734	+	7.60820i	0.390831	+	0.490087i	−0.547022	+	0.837118i	$0.684239\pi$
$242$	−5.37047	+	2.58628i	−0.345227	+	0.166252i
$243$	8.36443	−	10.4887i	0.536578	−	0.672848i
$244$	−2.96077			−0.189544
$245$	−2.96532	+	3.71839i	−0.189447	+	0.237559i
$246$	0.384043	−	1.68260i	0.0244857	−	0.107279i
$247$	2.96466	−	12.9890i	0.188637	−	0.826471i
$248$	−7.05980	+	8.85271i	−0.448298	+	0.562148i
$249$	5.55496			0.352031
$250$	−1.82826	+	2.29256i	−0.115629	+	0.144994i
$251$	−8.79374	+	4.23484i	−0.555056	+	0.267301i	−0.690314	−	0.723509i	$-0.742528\pi$
$251$	−8.79374	+	4.23484i	−0.555056	+	0.267301i	0.135258	+	0.990810i	$0.456814\pi$
$252$	0.579417	+	0.726566i	0.0364998	+	0.0457693i
$253$	−7.07002	−	8.86553i	−0.444489	−	0.557371i
$254$	−0.415739	−	0.200209i	−0.0260858	−	0.0125622i
$255$	0.862937	−	3.78077i	0.0540392	−	0.236761i
$256$	−0.534384	−	2.34129i	−0.0333990	−	0.146331i
$257$	−14.7371	+	7.09699i	−0.919272	+	0.442698i	−0.832811	−	0.553557i	$-0.813270\pi$
$257$	−14.7371	+	7.09699i	−0.919272	+	0.442698i	−0.0864609	+	0.996255i	$0.527556\pi$
$258$	−1.70291	−	0.820077i	−0.106018	−	0.0510557i
$259$	−0.392240	−	1.71851i	−0.0243726	−	0.106783i
$260$	7.04892			0.437155
$261$		0			0
$262$	−3.57002			−0.220557
$263$	5.27897	+	23.1287i	0.325515	+	1.42618i	0.827581	+	0.561346i	$0.189716\pi$
$263$	5.27897	+	23.1287i	0.325515	+	1.42618i	−0.502066	+	0.864829i	$0.667426\pi$
$264$	−9.38889	−	4.52145i	−0.577846	−	0.278276i
$265$	2.92543	−	1.40881i	0.179708	−	0.0865426i
$266$	−0.0833017	−	0.364968i	−0.00510755	−	0.0223776i
$267$	−1.57606	+	6.90519i	−0.0964536	+	0.422591i
$268$	−3.77144	−	1.81623i	−0.230377	−	0.110944i
$269$	−15.8083	−	19.8229i	−0.963847	−	1.20863i	−0.977974	−	0.208726i	$-0.933068\pi$
$269$	−15.8083	−	19.8229i	−0.963847	−	1.20863i	0.0141266	−	0.999900i	$-0.495503\pi$
$270$	−1.06435	−	1.33465i	−0.0647744	−	0.0812245i
$271$	−1.08426	+	0.522153i	−0.0658642	+	0.0317185i	−0.466526	−	0.884508i	$-0.654495\pi$
$271$	−1.08426	+	0.522153i	−0.0658642	+	0.0317185i	0.400662	+	0.916226i	$0.368780\pi$
$272$	−7.98792	+	10.0165i	−0.484339	+	0.607342i
$273$	−2.51573			−0.152259
$274$	−4.78166	+	5.99601i	−0.288871	+	0.362232i
$275$	−4.96884	+	21.7699i	−0.299632	+	1.31277i
$276$	1.14795	−	5.02949i	0.0690984	−	0.302740i
$277$	6.64944	−	8.33813i	0.399526	−	0.500990i	−0.540853	−	0.841117i	$-0.681899\pi$
$277$	6.64944	−	8.33813i	0.399526	−	0.500990i	0.940380	+	0.340127i	$0.110470\pi$
$278$	−7.41789			−0.444896
$279$	−6.02930	+	7.56051i	−0.360965	+	0.452636i
$280$	0.376510	−	0.181318i	0.0225008	−	0.0108358i
$281$	−10.1501	−	12.7278i	−0.605504	−	0.759279i	0.380720	−	0.924690i	$-0.375676\pi$
$281$	−10.1501	−	12.7278i	−0.605504	−	0.759279i	−0.986225	+	0.165412i	$0.947105\pi$
$282$	2.23005	+	2.79640i	0.132798	+	0.166523i
$283$	4.72737	+	2.27658i	0.281013	+	0.135329i	0.569081	−	0.822281i	$-0.307299\pi$
$283$	4.72737	+	2.27658i	0.281013	+	0.135329i	−0.288069	+	0.957610i	$0.593013\pi$
$284$	−2.94116	+	12.8861i	−0.174526	+	0.764646i
$285$	−0.452575	−	1.98286i	−0.0268082	−	0.117454i
$286$	−11.1947	+	5.39109i	−0.661957	+	0.318782i
$287$	1.00000	+	0.481575i	0.0590281	+	0.0284265i
$288$	1.49612	+	6.55491i	0.0881594	+	0.386252i
$289$	3.19567			0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−2.25571	−	9.88291i	−0.132005	−	0.578353i
$293$	6.09395	+	2.93469i	0.356012	+	0.171447i	0.603337	−	0.797486i	$-0.293837\pi$
$293$	6.09395	+	2.93469i	0.356012	+	0.171447i	−0.247325	+	0.968933i	$0.579552\pi$
$294$	3.43631	−	1.65484i	0.200410	−	0.0965123i
$295$	1.92394	+	8.42931i	0.112016	+	0.490774i
$296$	1.85958	−	8.14737i	0.108086	−	0.473556i
$297$	−24.6652	−	11.8781i	−1.43122	−	0.689238i
$298$	5.16301	+	6.47421i	0.299085	+	0.375041i
$299$	−8.09179	−	10.1468i	−0.467961	−	0.586804i
$300$	−9.15279	+	4.40775i	−0.528437	+	0.254482i
$301$	0.757865	−	0.950332i	0.0436826	−	0.0547762i
$302$	−3.35019			−0.192782
$303$	−2.51089	+	3.14855i	−0.144247	+	0.180879i
$304$	−1.49516	+	6.55070i	−0.0857531	+	0.375709i
$305$	−0.253020	+	1.10855i	−0.0144879	+	0.0634757i
$306$	1.80194	−	2.25956i	0.103010	−	0.129170i
$307$	−4.51812			−0.257863			−0.128931	−	0.991654i	$-0.541155\pi$
$307$	−4.51812			−0.257863			−0.128931	+	0.991654i	$0.541155\pi$
$308$	1.98039	−	2.48333i	0.112843	−	0.141501i
$309$	15.3388	−	7.38676i	0.872592	−	0.420218i
$310$	1.28501	+	1.61135i	0.0729838	+	0.0915187i
$311$	7.86629	+	9.86401i	0.446056	+	0.559337i	0.953128	−	0.302567i	$-0.0978436\pi$
$311$	7.86629	+	9.86401i	0.446056	+	0.559337i	−0.507072	+	0.861904i	$0.669272\pi$
$312$	−10.7458	−	5.17490i	−0.608360	−	0.292971i
$313$	−4.28136	+	18.7579i	−0.241997	+	1.06026i	0.697199	+	0.716877i	$0.254429\pi$
$313$	−4.28136	+	18.7579i	−0.241997	+	1.06026i	−0.939196	+	0.343381i	$0.888428\pi$
$314$	−1.80625	−	7.91370i	−0.101933	−	0.446596i
$315$	0.321552	−	0.154851i	0.0181174	−	0.00872488i
$316$	7.57338	+	3.64715i	0.426036	+	0.205168i
$317$	0.638260	+	2.79640i	0.0358482	+	0.157061i	0.989684	−	0.143267i	$-0.0457608\pi$
$317$	0.638260	+	2.79640i	0.0358482	+	0.157061i	−0.953836	+	0.300329i	$0.902904\pi$
$318$	−2.60388			−0.146018
$319$		0			0
$320$	−2.51275			−0.140467
$321$	−4.50753	−	19.7488i	−0.251586	−	1.10227i
$322$	−0.328552	−	0.158222i	−0.0183095	−	0.00881739i
$323$	9.54288	−	4.59561i	0.530980	−	0.255706i
$324$	−1.03319	−	4.52669i	−0.0573993	−	0.251483i
$325$	−5.68694	+	24.9161i	−0.315455	+	1.38210i
$326$	5.06853	+	2.44088i	0.280720	+	0.135188i
$327$	4.25033	+	5.32975i	0.235044	+	0.294736i
$328$	3.28083	+	4.11403i	0.181154	+	0.227159i
$329$	−2.07242	+	0.998023i	−0.114256	+	0.0550228i
$330$	−1.18263	+	1.48297i	−0.0651015	+	0.0816348i
$331$	−3.13408			−0.172265			−0.0861323	−	0.996284i	$-0.527451\pi$
$331$	−3.13408			−0.172265			−0.0861323	+	0.996284i	$0.527451\pi$
$332$	−5.00484	+	6.27588i	−0.274677	+	0.344433i
$333$	1.58815	−	6.95812i	0.0870299	−	0.381303i
$334$	0.0788843	−	0.345615i	0.00431636	−	0.0189112i
$335$	−1.00232	+	1.25687i	−0.0547626	+	0.0686701i
$336$	1.26875			0.0692160
$337$	−3.10656	+	3.89551i	−0.169225	+	0.212202i	−0.859211	−	0.511621i	$-0.829045\pi$
$337$	−3.10656	+	3.89551i	−0.169225	+	0.212202i	0.689986	+	0.723823i	$0.257617\pi$
$338$	−7.59999	+	3.65996i	−0.413385	+	0.199076i
$339$	8.29925	+	10.4069i	0.450753	+	0.565227i
$340$	3.49396	+	4.38129i	0.189487	+	0.237609i
$341$	29.7787	+	14.3407i	1.61261	+	0.776591i
$342$	0.337282	−	1.47773i	0.0182381	−	0.0799063i
$343$	1.10172	+	4.82695i	0.0594873	+	0.260631i
$344$	5.19202	−	2.50035i	0.279935	−	0.134810i
$345$	−1.78501	−	0.859616i	−0.0961018	−	0.0462802i
$346$	0.906477	+	3.97154i	0.0487325	+	0.213511i
$347$	20.1172			1.07995			0.539974	−	0.841682i	$-0.318434\pi$
$347$	20.1172			1.07995			0.539974	+	0.841682i	$0.318434\pi$
$348$		0			0
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	0.159793	+	0.700099i	0.00854130	+	0.0374219i
$351$	−28.2298	−	13.5948i	−1.50680	−	0.725635i
$352$	20.7044	−	9.97071i	1.10355	−	0.531441i
$353$	−4.00484	−	17.5464i	−0.213156	−	0.933899i	−0.962407	−	0.271612i	$-0.912443\pi$
$353$	−4.00484	−	17.5464i	−0.213156	−	0.933899i	0.749250	−	0.662287i	$-0.230414\pi$
$354$	1.54288	−	6.75978i	0.0820030	−	0.359278i
$355$	4.57338	+	2.20242i	0.242730	+	0.116892i
$356$	−6.38135	−	8.00197i	−0.338211	−	0.424103i
$357$	−1.24698	−	1.56366i	−0.0659972	−	0.0827578i
$358$	−1.36563	+	0.657650i	−0.0721755	+	0.0347579i
$359$	−14.7322	+	18.4736i	−0.777536	+	0.975000i	0.222464	+	0.974941i	$0.428590\pi$
$359$	−14.7322	+	18.4736i	−0.777536	+	0.975000i	−1.00000		5.86917e-5i	$0.999981\pi$
$360$	1.69202			0.0891774
$361$	−8.38285	+	10.5118i	−0.441202	+	0.553250i
$362$	−1.25518	+	5.49929i	−0.0659706	+	0.289036i
$363$	−3.71648	+	16.2830i	−0.195065	+	0.854634i
$364$	2.26659	−	2.84222i	0.118802	−	0.148973i
$365$	−3.89307			−0.203772
$366$	0.568532	−	0.712916i	0.0297176	−	0.0372647i
$367$	−26.7075	+	12.8617i	−1.39412	+	0.671373i	−0.971960	−	0.235148i	$-0.924443\pi$
$367$	−26.7075	+	12.8617i	−1.39412	+	0.671373i	−0.422161	+	0.906521i	$0.638728\pi$
$368$	4.08091	+	5.11730i	0.212732	+	0.266758i
$369$	2.80194	+	3.51352i	0.145863	+	0.182906i
$370$	−1.37047	−	0.659983i	−0.0712473	−	0.0343109i
$371$	0.372625	−	1.63258i	0.0193457	−	0.0847592i
$372$	3.34601	+	14.6598i	0.173483	+	0.760077i
$373$	22.6935	−	10.9286i	1.17503	−	0.565862i	0.258567	−	0.965993i	$-0.416750\pi$
$373$	22.6935	−	10.9286i	1.17503	−	0.565862i	0.916458	+	0.400131i	$0.131035\pi$
$374$	−8.89977	−	4.28590i	−0.460196	−	0.221619i
$375$	1.82826	+	8.01012i	0.0944108	+	0.413641i
$376$	−10.9051			−0.562390
$377$		0			0
$378$	−0.880395			−0.0452826
$379$	−5.98739	−	26.2325i	−0.307551	−	1.34747i	−0.858450	−	0.512898i	$-0.828572\pi$
$379$	−5.98739	−	26.2325i	−0.307551	−	1.34747i	0.550898	−	0.834572i	$-0.314285\pi$
$380$	2.64795	+	1.27518i	0.135837	+	0.0654156i
$381$	−1.16487	+	0.560974i	−0.0596783	+	0.0287396i
$382$	−1.05669	−	4.62965i	−0.0540648	−	0.236873i
$383$	4.37681	−	19.1760i	0.223644	−	0.979850i	−0.731065	−	0.682308i	$-0.760976\pi$
$383$	4.37681	−	19.1760i	0.223644	−	0.979850i	0.954709	−	0.297542i	$-0.0961667\pi$
$384$	12.2702	+	5.90904i	0.626163	+	0.301544i
$385$	−0.760553	−	0.953703i	−0.0387614	−	0.0486052i
$386$	−6.30678	−	7.90845i	−0.321007	−	0.402530i
$387$	4.43416	−	2.13538i	0.225401	−	0.108547i
$388$	−0.202907	+	0.254437i	−0.0103010	+	0.0129171i
$389$	−24.8552			−1.26021			−0.630103	−	0.776511i	$-0.716988\pi$
$389$	−24.8552			−1.26021			−0.630103	+	0.776511i	$0.716988\pi$
$390$	−1.35354	+	1.69729i	−0.0685393	+	0.0859456i
$391$	2.29590	−	10.0590i	0.116108	−	0.508705i
$392$	−2.58761	+	11.3371i	−0.130694	+	0.572609i
$393$	−6.23676	+	7.82065i	−0.314603	+	0.394499i
$394$	−8.70410			−0.438506
$395$	2.01275	−	2.52390i	0.101272	−	0.126991i
$396$	11.5869	−	5.57998i	0.582266	−	0.280405i
$397$	−2.49061	−	3.12312i	−0.125000	−	0.156745i	0.715393	−	0.698722i	$-0.246247\pi$
$397$	−2.49061	−	3.12312i	−0.125000	−	0.156745i	−0.840393	+	0.541977i	$0.817676\pi$
$398$	−0.242799	−	0.304461i	−0.0121704	−	0.0152612i
$399$	−0.945042	−	0.455108i	−0.0473113	−	0.0227839i
$400$	2.86808	−	12.5659i	0.143404	−	0.628293i
$401$	5.54234	+	24.2826i	0.276771	+	1.21261i	0.901849	+	0.432052i	$0.142210\pi$
$401$	5.54234	+	24.2826i	0.276771	+	1.21261i	−0.625077	+	0.780563i	$0.714933\pi$
$402$	1.16152	−	0.559360i	0.0579315	−	0.0278983i
$403$	34.0824	+	16.4132i	1.69777	+	0.817601i
$404$	−1.29494	−	5.67349i	−0.0644255	−	0.282267i
$405$	−1.78315			−0.0886055
$406$		0			0
$407$	−24.3937			−1.20915
$408$	−2.10992	−	9.24415i	−0.104456	−	0.457653i
$409$	0.255176	+	0.122886i	0.0126177	+	0.00607634i	0.440182	−	0.897909i	$-0.354914\pi$
$409$	0.255176	+	0.122886i	0.0126177	+	0.00607634i	−0.427564	+	0.903985i	$0.640628\pi$
$410$	0.862937	−	0.415568i	0.0426174	−	0.0205235i
$411$	4.78166	+	20.9498i	0.235862	+	1.03338i
$412$	−5.47434	+	23.9847i	−0.269702	+	1.18164i
$413$	4.01746	+	1.93471i	0.197686	+	0.0952007i
$414$	−0.920583	−	1.15437i	−0.0452442	−	0.0567344i
$415$	1.92208	+	2.41021i	0.0943510	+	0.118312i
$416$	23.6966	−	11.4117i	1.16182	−	0.559504i
$417$	−12.9589	+	16.2500i	−0.634601	+	0.795764i
$418$	−5.18060			−0.253392
$419$	−16.5154	+	20.7096i	−0.806828	+	1.01173i	0.192707	+	0.981256i	$0.438273\pi$
$419$	−16.5154	+	20.7096i	−0.806828	+	1.01173i	−0.999536	+	0.0304743i	$0.990298\pi$
$420$	0.123490	−	0.541044i	0.00602569	−	0.0264003i
$421$	−3.91239	+	17.1413i	−0.190678	+	0.835415i	0.785572	+	0.618770i	$0.212369\pi$
$421$	−3.91239	+	17.1413i	−0.190678	+	0.835415i	−0.976250	+	0.216645i	$0.930488\pi$
$422$	5.06920	−	6.35657i	0.246765	−	0.309433i
$423$	−9.31336			−0.452831
$424$	4.94989	−	6.20696i	0.240388	−	0.301437i
$425$	−18.3056	+	8.81551i	−0.887951	+	0.427615i
$426$	−2.53803	−	3.18259i	−0.122968	−	0.154197i
$427$	0.365625	+	0.458479i	0.0176938	+	0.0221874i
$428$	26.3729	+	12.7005i	1.27478	+	0.613903i
$429$	−7.74698	+	33.9417i	−0.374028	+	1.63872i
$430$	−0.233406	−	1.02262i	−0.0112558	−	0.0493151i
$431$	25.0426	−	12.0599i	1.20626	−	0.580905i	0.280807	−	0.959764i	$-0.409398\pi$
$431$	25.0426	−	12.0599i	1.20626	−	0.580905i	0.925454	+	0.378859i	$0.123684\pi$
$432$	14.2371	+	6.85620i	0.684981	+	0.329869i
$433$	1.30745	+	5.72830i	0.0628318	+	0.275284i	0.996579	−	0.0826499i	$-0.0263383\pi$
$433$	1.30745	+	5.72830i	0.0628318	+	0.275284i	−0.933747	+	0.357934i	$0.883481\pi$
$434$	1.06292			0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−1.20410	−	5.27552i	−0.0576001	−	0.252362i
$438$	2.81282	+	1.35458i	0.134402	+	0.0647245i
$439$	14.1821	−	6.82974i	0.676875	−	0.325966i	−0.0636718	−	0.997971i	$-0.520281\pi$
$439$	14.1821	−	6.82974i	0.676875	−	0.325966i	0.740546	+	0.672005i	$0.234567\pi$
$440$	−1.28687	−	5.63816i	−0.0613492	−	0.268789i
$441$	−2.20991	+	9.68223i	−0.105234	+	0.461059i
$442$	−10.1860	−	4.90531i	−0.484498	−	0.233322i
$443$	−4.20141	−	5.26841i	−0.199615	−	0.250310i	0.671942	−	0.740604i	$-0.265461\pi$
$443$	−4.20141	−	5.26841i	−0.199615	−	0.250310i	−0.871557	+	0.490295i	$0.836889\pi$
$444$	−6.91939	−	8.67664i	−0.328380	−	0.411775i
$445$	−3.54138	+	1.70544i	−0.167878	+	0.0808457i
$446$	−0.504549	+	0.632684i	−0.0238911	+	0.0299585i
$447$	23.2024			1.09743
$448$	−0.807979	+	1.01317i	−0.0381734	+	0.0478679i
$449$	2.74147	−	12.0112i	0.129378	−	0.566842i	−0.868133	−	0.496332i	$-0.834680\pi$
$449$	2.74147	−	12.0112i	0.129378	−	0.566842i	0.997511	−	0.0705106i	$-0.0224628\pi$
$450$	−0.646989	+	2.83464i	−0.0304994	+	0.133626i
$451$	9.57673	−	12.0088i	0.450951	−	0.565474i
$452$	−19.2349			−0.904733
$453$	−5.85272	+	7.33907i	−0.274985	+	0.344820i
$454$	5.55592	−	2.67559i	0.260752	−	0.125572i
$455$	−0.870469	−	1.09153i	−0.0408082	−	0.0511719i
$456$	−3.10052	−	3.88793i	−0.145195	−	0.182069i
$457$	−12.3095	−	5.92793i	−0.575813	−	0.277297i	0.123228	−	0.992378i	$-0.460675\pi$
$457$	−12.3095	−	5.92793i	−0.575813	−	0.277297i	−0.699041	+	0.715082i	$0.746390\pi$
$458$	−1.26487	+	5.54174i	−0.0591033	+	0.258948i
$459$	−5.54288	−	24.2849i	−0.258719	−	1.13352i
$460$	2.57942	−	1.24218i	0.120266	−	0.0579170i
$461$	10.4586	+	5.03660i	0.487106	+	0.234578i	0.661283	−	0.750136i	$-0.270012\pi$
$461$	10.4586	+	5.03660i	0.487106	+	0.234578i	−0.174177	+	0.984714i	$0.555726\pi$
$462$	0.217677	+	0.953703i	0.0101272	+	0.0443703i
$463$	−7.24267			−0.336595			−0.168298	−	0.985736i	$-0.553827\pi$
$463$	−7.24267			−0.336595			−0.168298	+	0.985736i	$0.553827\pi$
$464$		0			0
$465$	5.77479			0.267800
$466$	0.878002	+	3.84678i	0.0406727	+	0.178199i
$467$	−1.85905	−	0.895272i	−0.0860267	−	0.0414283i	0.390376	−	0.920656i	$-0.372345\pi$
$467$	−1.85905	−	0.895272i	−0.0860267	−	0.0414283i	−0.476402	+	0.879227i	$0.658059\pi$
$468$	13.2615	−	6.38641i	0.613014	−	0.295212i
$469$	0.184489	+	0.808298i	0.00851890	+	0.0373237i
$470$	−0.441689	+	1.93517i	−0.0203736	+	0.0892626i
$471$	−20.4916	−	9.86822i	−0.944202	−	0.454703i
$472$	13.1806	+	16.5280i	0.606686	+	0.760761i
$473$	−10.4879	−	13.1514i	−0.482235	−	0.604704i
$474$	−2.33244	+	1.12324i	−0.107132	+	0.0515922i
$475$	−6.64377	+	8.33102i	−0.304837	+	0.382253i
$476$	2.89008			0.132467
$477$	4.22737	−	5.30095i	0.193558	−	0.242714i
$478$	2.53170	−	11.0921i	0.115797	−	0.507340i
$479$	−0.865388	+	3.79151i	−0.0395406	+	0.173239i	−0.990843	−	0.135022i	$-0.956890\pi$
$479$	−0.865388	+	3.79151i	−0.0395406	+	0.173239i	0.951302	+	0.308260i	$0.0997468\pi$
$480$	2.50335	−	3.13910i	0.114262	−	0.143280i
$481$	−27.9191			−1.27300
$482$	2.70022	−	3.38597i	0.122992	−	0.154227i
$483$	−0.920583	+	0.443330i	−0.0418880	+	0.0201722i
$484$	−15.0477	−	18.8692i	−0.683987	−	0.857693i
$485$	0.0779248	+	0.0977147i	0.00353839	+	0.00443699i
$486$	−5.37920	−	2.59049i	−0.244005	−	0.117507i
$487$	−2.19083	+	9.59863i	−0.0992758	+	0.434956i	0.900724	+	0.434392i	$0.143037\pi$
$487$	−2.19083	+	9.59863i	−0.0992758	+	0.434956i	−1.00000		0.000563841i	$0.999821\pi$
$488$	0.618645	+	2.71046i	0.0280048	+	0.122697i
$489$	14.2017	−	6.83918i	0.642224	−	0.309279i
$490$	1.90701	+	0.918367i	0.0861499	+	0.0414876i
$491$	1.73370	+	7.59584i	0.0782409	+	0.342796i	0.998864	−	0.0476574i	$-0.0151756\pi$
$491$	1.73370	+	7.59584i	0.0782409	+	0.342796i	−0.920623	+	0.390453i	$0.872318\pi$
$492$	6.98792			0.315040
$493$		0			0
$494$	−5.92931			−0.266772
$495$	−1.09903	−	4.81517i	−0.0493978	−	0.216426i
$496$	−17.1887	−	8.27763i	−0.771794	−	0.371676i
$497$	2.35862	−	1.13585i	0.105799	−	0.0509500i
$498$	−0.550114	−	2.41021i	−0.0246512	−	0.108004i
$499$	4.57620	−	20.0496i	0.204859	−	0.897544i	−0.763069	−	0.646317i	$-0.776309\pi$
$499$	4.57620	−	20.0496i	0.204859	−	0.897544i	0.967928	−	0.251228i	$-0.0808343\pi$
$500$	−10.6969	−	5.15134i	−0.478378	−	0.230375i
$501$	−0.619309	−	0.776589i	−0.0276687	−	0.0346955i
$502$	2.70828	+	3.39608i	0.120877	+	0.151574i
$503$	7.41939	−	3.57299i	0.330814	−	0.159312i	−0.261102	−	0.965311i	$-0.584086\pi$
$503$	7.41939	−	3.57299i	0.330814	−	0.159312i	0.591916	+	0.806000i	$0.298372\pi$
$504$	0.544073	−	0.682246i	0.0242349	−	0.0303897i
$505$	−2.23490			−0.0994517
$506$	−3.14646	+	3.94553i	−0.139877	+	0.175400i
$507$	−5.25936	+	23.0427i	−0.233576	+	1.02336i
$508$	0.415739	−	1.82147i	0.0184454	−	0.0808147i
$509$	4.93565	−	6.18911i	0.218769	−	0.274327i	−0.660321	−	0.750983i	$-0.729580\pi$
$509$	4.93565	−	6.18911i	0.218769	−	0.274327i	0.879090	+	0.476656i	$0.158151\pi$
$510$	−1.72587			−0.0764230
$511$	−1.25182	+	1.56974i	−0.0553774	+	0.0694411i
$512$	−20.6429	+	9.94108i	−0.912294	+	0.439338i
$513$	−8.14526	−	10.2138i	−0.359622	−	0.450952i
$514$	4.53870	+	5.69135i	0.200193	+	0.251034i
$515$	8.51238	+	4.09934i	0.375100	+	0.180639i
$516$	1.70291	−	7.46092i	0.0749663	−	0.328449i
$517$	7.08330	+	31.0340i	0.311523	+	1.36487i
$518$	−0.706791	+	0.340373i	−0.0310546	+	0.0149551i
$519$	10.2838	+	4.95242i	0.451409	+	0.217387i
$520$	−1.47285	−	6.45299i	−0.0645889	−	0.282982i
$521$	−3.52542			−0.154451			−0.0772257	−	0.997014i	$-0.524606\pi$
$521$	−3.52542			−0.154451			−0.0772257	+	0.997014i	$0.524606\pi$
$522$		0			0
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	−3.21648	−	14.0923i	−0.140513	−	0.615626i
$525$	1.81282	+	0.873009i	0.0791181	+	0.0381013i
$526$	9.51238	−	4.58092i	0.414759	−	0.199738i
$527$	6.69202	+	29.3197i	0.291509	+	1.27718i
$528$	3.90701	−	17.1177i	0.170031	−	0.744953i
$529$	15.9731	+	7.69226i	0.694485	+	0.334446i
$530$	−0.900969	−	1.12978i	−0.0391356	−	0.0490745i
$531$	11.2567	+	14.1154i	0.488498	+	0.612557i
$532$	1.36563	−	0.657650i	0.0592074	−	0.0285128i
$533$	10.9608	−	13.7444i	0.474764	−	0.595335i
$534$	3.15213			0.136406
$535$	7.00902	−	8.78904i	0.303027	−	0.379983i
$536$	−0.874650	+	3.83209i	−0.0377791	+	0.165521i
$537$	−0.945042	+	4.14050i	−0.0407816	+	0.178676i
$538$	−7.03534	+	8.82204i	−0.303315	+	0.380345i
$539$	33.9439			1.46207
$540$	4.30947	−	5.40391i	0.185450	−	0.232547i
$541$	7.40970	−	3.56832i	0.318568	−	0.153414i	−0.267765	−	0.963484i	$-0.586285\pi$
$541$	7.40970	−	3.56832i	0.318568	−	0.153414i	0.586333	+	0.810070i	$0.300571\pi$
$542$	0.333929	+	0.418734i	0.0143435	+	0.0179862i
$543$	9.85421	+	12.3568i	0.422885	+	0.530280i
$544$	18.8388	+	9.07228i	0.807706	+	0.388971i
$545$	−0.841830	+	3.68830i	−0.0360601	+	0.157989i
$546$	0.249136	+	1.09153i	0.0106620	+	0.0467133i
$547$	−23.3017	+	11.2215i	−0.996309	+	0.479797i	−0.859684	−	0.510826i	$-0.829340\pi$
$547$	−23.3017	+	11.2215i	−0.996309	+	0.479797i	−0.136625	+	0.990623i	$0.543625\pi$
$548$	−27.9768	−	13.4729i	−1.19511	−	0.575534i
$549$	0.528344	+	2.31482i	0.0225492	+	0.0987943i
$550$	9.93767			0.423744
$551$		0			0
$552$	−4.84415			−0.206181
$553$	−0.370469	−	1.62313i	−0.0157540	−	0.0690226i
$554$	−4.27628	−	2.05935i	−0.181682	−	0.0874934i
$555$	−3.83997	+	1.84923i	−0.162998	+	0.0784955i
$556$	−6.68329	−	29.2814i	−0.283435	−	1.24181i
$557$	−5.12014	+	22.4328i	−0.216947	+	0.950508i	0.742771	+	0.669545i	$0.233511\pi$
$557$	−5.12014	+	22.4328i	−0.216947	+	0.950508i	−0.959719	+	0.280963i	$0.909346\pi$
$558$	3.87747	+	1.86729i	0.164146	+	0.0790487i
$559$	−12.0036	−	15.0521i	−0.507700	−	0.636636i
$560$	0.439001	+	0.550490i	0.0185512	+	0.0232624i
$561$	−24.9366	+	12.0088i	−1.05282	+	0.507014i
$562$	−4.51722	+	5.66442i	−0.190547	+	0.238939i
$563$	−43.1159			−1.81712			−0.908559	−	0.417757i	$-0.862816\pi$
$563$	−43.1159			−1.81712			−0.908559	+	0.417757i	$0.862816\pi$
$564$	−9.02930	+	11.3224i	−0.380202	+	0.476759i
$565$	−1.64377	+	7.20182i	−0.0691538	+	0.302983i
$566$	0.519614	−	2.27658i	0.0218410	−	0.0956918i
$567$	−0.573376	+	0.718991i	−0.0240795	+	0.0301948i
$568$	12.4112			0.520762
$569$	15.1585	−	19.0081i	0.635476	−	0.796862i	−0.354953	−	0.934884i	$-0.615503\pi$
$569$	15.1585	−	19.0081i	0.635476	−	0.796862i	0.990429	+	0.138022i	$0.0440746\pi$
$570$	−0.815511	+	0.392730i	−0.0341580	+	0.0164496i
$571$	11.5274	+	14.4550i	0.482408	+	0.604921i	0.962161	−	0.272483i	$-0.0878448\pi$
$571$	11.5274	+	14.4550i	0.482408	+	0.604921i	−0.479752	+	0.877404i	$0.659273\pi$
$572$	−31.3669	−	39.3328i	−1.31152	−	1.64459i
$573$	−11.9879	−	5.77308i	−0.500802	−	0.241174i
$574$	0.109916	−	0.481575i	0.00458782	−	0.0201005i
$575$	2.30977	+	10.1197i	0.0963239	+	0.422023i
$576$	−4.72737	+	2.27658i	−0.196974	+	0.0948575i
$577$	−34.1090	−	16.4260i	−1.41998	−	0.683825i	−0.442872	−	0.896585i	$-0.646041\pi$
$577$	−34.1090	−	16.4260i	−1.41998	−	0.683825i	−0.977105	+	0.212760i	$0.931755\pi$
$578$	−0.316471	−	1.38655i	−0.0131634	−	0.0576728i
$579$	−28.3424			−1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0223027	−	0.0977147i	−0.000924478	−	0.00405040i
$583$	−20.8790	−	10.0548i	−0.864718	−	0.416426i
$584$	−8.57606	+	4.13001i	−0.354880	+	0.170901i
$585$	−1.25786	−	5.51107i	−0.0520063	−	0.227855i
$586$	0.669824	−	2.93469i	0.0276702	−	0.121231i
$587$	13.0058	+	6.26327i	0.536807	+	0.258513i	0.682587	−	0.730804i	$-0.260855\pi$
$587$	13.0058	+	6.26327i	0.536807	+	0.258513i	−0.145780	+	0.989317i	$0.546569\pi$
$588$	9.62833	+	12.0735i	0.397066	+	0.497905i
$589$	9.83393	+	12.3314i	0.405200	+	0.508105i
$590$	3.46681	−	1.66953i	0.142726	−	0.0687334i
$591$	−15.2059	+	19.0676i	−0.625487	+	0.784336i
$592$	14.0804			0.578700
$593$	−8.10656	+	10.1653i	−0.332897	+	0.417439i	−0.919905	−	0.392142i	$-0.871734\pi$
$593$	−8.10656	+	10.1653i	−0.332897	+	0.417439i	0.587008	+	0.809581i	$0.300306\pi$
$594$	−2.71110	+	11.8781i	−0.111238	+	0.487365i
$595$	0.246980	−	1.08209i	0.0101252	−	0.0443613i
$596$	−20.9046	+	26.2136i	−0.856286	+	1.07375i
$597$	−1.09113			−0.0446570
$598$	−3.60119	+	4.51575i	−0.147263	+	0.184663i
$599$	10.8959	−	5.24718i	0.445194	−	0.214394i	−0.197836	−	0.980235i	$-0.563391\pi$
$599$	10.8959	−	5.24718i	0.445194	−	0.214394i	0.643030	+	0.765841i	$0.277677\pi$
$600$	5.94757	+	7.45801i	0.242808	+	0.304472i
$601$	13.9333	+	17.4718i	0.568349	+	0.712688i	0.980077	−	0.198620i	$-0.0636458\pi$
$601$	13.9333	+	17.4718i	0.568349	+	0.712688i	−0.411727	+	0.911307i	$0.635074\pi$
$602$	−0.487386	−	0.234713i	−0.0198644	−	0.00956618i
$603$	−0.746980	+	3.27273i	−0.0304194	+	0.133276i
$604$	−3.01842	−	13.2246i	−0.122818	−	0.538099i
$605$	−8.35086	+	4.02156i	−0.339511	+	0.163500i
$606$	1.61476	+	0.777628i	0.0655952	+	0.0315890i
$607$	9.22766	+	40.4290i	0.374539	+	1.64096i	0.713857	+	0.700292i	$0.246947\pi$
$607$	9.22766	+	40.4290i	0.374539	+	1.64096i	−0.339318	+	0.940672i	$0.610196\pi$
$608$	10.9661			0.444736
$609$		0			0
$610$	0.506041			0.0204890
$611$	8.10699	+	35.5190i	0.327974	+	1.43695i
$612$	10.5429	+	5.07718i	0.426171	+	0.205233i
$613$	−23.2310	+	11.1875i	−0.938292	+	0.451858i	−0.839566	−	0.543257i	$-0.817191\pi$
$613$	−23.2310	+	11.1875i	−0.938292	+	0.451858i	−0.0987255	+	0.995115i	$0.531477\pi$
$614$	0.447435	+	1.96034i	0.0180570	+	0.0791129i
$615$	0.597171	−	2.61638i	0.0240802	−	0.105502i
$616$	−2.68718	−	1.29408i	−0.108269	−	0.0521398i
$617$	−5.52744	−	6.93119i	−0.222526	−	0.279039i	0.658019	−	0.753002i	$-0.271395\pi$
$617$	−5.52744	−	6.93119i	−0.222526	−	0.279039i	−0.880545	+	0.473962i	$0.842823\pi$
$618$	−4.72401	−	5.92372i	−0.190028	−	0.238287i
$619$	26.5347	−	12.7784i	1.06652	−	0.513608i	0.183536	−	0.983013i	$-0.441246\pi$
$619$	26.5347	−	12.7784i	1.06652	−	0.513608i	0.882983	+	0.469405i	$0.155531\pi$
$620$	−5.20291	+	6.52424i	−0.208954	+	0.262020i
$621$	−12.7259			−0.510672
$622$	3.50083	−	4.38990i	0.140370	−	0.176019i
$623$	−0.451083	+	1.97632i	−0.0180722	+	0.0791797i
$624$	4.47166	−	19.5916i	0.179010	−	0.784292i
$625$	11.2515	−	14.1089i	0.450058	−	0.564355i
$626$	8.56273			0.342235
$627$	−9.05041	+	11.3489i	−0.361439	+	0.453230i
$628$	29.6112	−	14.2600i	1.18161	−	0.569035i
$629$	−13.8388	−	17.3533i	−0.551788	−	0.691920i
$630$	−0.0990311	−	0.124181i	−0.00394549	−	0.00494749i
$631$	−21.4170	−	10.3139i	−0.852597	−	0.410589i	−0.0440561	−	0.999029i	$-0.514028\pi$
$631$	−21.4170	−	10.3139i	−0.852597	−	0.410589i	−0.808541	+	0.588440i	$0.799742\pi$
$632$	1.75637	−	7.69517i	0.0698648	−	0.306098i
$633$	−5.06920	−	22.2096i	−0.201482	−	0.882752i
$634$	1.15010	−	0.553861i	0.0456765	−	0.0219966i
$635$	−0.646457	−	0.311317i	−0.0256538	−	0.0123542i
$636$	−2.34601	−	10.2785i	−0.0930254	−	0.407571i
$637$	38.8495			1.53927
$638$		0			0
$639$	10.5996			0.419312
$640$	1.68180	+	7.36845i	0.0664790	+	0.291264i
$641$	25.6465	+	12.3507i	1.01298	+	0.487824i	0.865323	−	0.501215i	$-0.167114\pi$
$641$	25.6465	+	12.3507i	1.01298	+	0.487824i	0.147654	+	0.989039i	$0.452828\pi$
$642$	−8.12229	+	3.91149i	−0.320561	+	0.154374i
$643$	4.30505	+	18.8617i	0.169775	+	0.743832i	0.986088	+	0.166223i	$0.0531570\pi$
$643$	4.30505	+	18.8617i	0.169775	+	0.743832i	−0.816314	+	0.577609i	$0.803986\pi$
$644$	0.328552	−	1.43948i	0.0129468	−	0.0567235i
$645$	−2.64795	−	1.27518i	−0.104263	−	0.0502104i
$646$	−2.93900	−	3.68539i	−0.115633	−	0.145000i
$647$	14.1622	+	17.7588i	0.556773	+	0.698171i	0.977958	−	0.208804i	$-0.0669570\pi$
$647$	14.1622	+	17.7588i	0.556773	+	0.698171i	−0.421185	+	0.906975i	$0.638386\pi$
$648$	−3.92812	+	1.89168i	−0.154311	+	0.0743122i
$649$	38.4741	−	48.2450i	1.51024	−	1.89378i
$650$	11.3739			0.446120
$651$	1.85690	−	2.32847i	0.0727775	−	0.0912601i
$652$	−5.06853	+	22.2067i	−0.198499	+	0.869681i
$653$	5.10268	−	22.3563i	0.199683	−	0.874870i	−0.771442	−	0.636300i	$-0.780464\pi$
$653$	5.10268	−	22.3563i	0.199683	−	0.874870i	0.971125	−	0.238570i	$-0.0766786\pi$
$654$	1.89158	−	2.37196i	0.0739665	−	0.0927510i
$655$	−5.55124			−0.216905
$656$	−5.52781	+	6.93166i	−0.215825	+	0.270636i
$657$	−7.32424	+	3.52717i	−0.285746	+	0.137608i
$658$	0.638260	+	0.800352i	0.0248820	+	0.0312010i
$659$	11.9574	+	14.9941i	0.465795	+	0.584088i	0.958136	−	0.286314i	$-0.0924301\pi$
$659$	11.9574	+	14.9941i	0.465795	+	0.584088i	−0.492341	+	0.870402i	$0.663859\pi$
$660$	−6.91939	−	3.33220i	−0.269337	−	0.129706i
$661$	0.753553	−	3.30153i	0.0293098	−	0.128415i	−0.958156	−	0.286245i	$-0.907593\pi$
$661$	0.753553	−	3.30153i	0.0293098	−	0.128415i	0.987466	+	0.157831i	$0.0504500\pi$
$662$	0.310371	+	1.35983i	0.0120629	+	0.0528511i
$663$	−28.5405	+	13.7444i	−1.10842	+	0.533787i
$664$	6.79105	+	3.27040i	0.263544	+	0.126916i
$665$	−0.129531	−	0.567511i	−0.00502298	−	0.0220071i
$666$	−3.17629			−0.123079
$667$		0			0
$668$	1.43535			0.0555355
$669$	0.504549	+	2.21057i	0.0195070	+	0.0854657i
$670$	0.644596	+	0.310421i	0.0249029	+	0.0119926i
$671$	7.31163	−	3.52109i	0.282262	−	0.135930i
$672$	−0.460771	−	2.01877i	−0.0177746	−	0.0778758i
$673$	−1.06153	+	4.65087i	−0.0409190	+	0.179278i	−0.991258	−	0.131939i	$-0.957880\pi$
$673$	−1.06153	+	4.65087i	−0.0409190	+	0.179278i	0.950339	+	0.311217i	$0.100737\pi$
$674$	1.99784	+	0.962111i	0.0769541	+	0.0370591i
$675$	15.6246	+	19.5926i	0.601392	+	0.754121i
$676$	−21.2947	−	26.7027i	−0.819027	−	1.02703i
$677$	−38.8228	+	18.6961i	−1.49208	+	0.718549i	−0.989304	−	0.145867i	$-0.953403\pi$
$677$	−38.8228	+	18.6961i	−1.49208	+	0.718549i	−0.502778	+	0.864416i	$0.667688\pi$
$678$	3.69351	−	4.63152i	0.141849	−	0.177872i
$679$	0.0644568			0.00247362
$680$	3.28083	−	4.11403i	0.125814	−	0.157766i
$681$	3.84481	−	16.8452i	0.147334	−	0.645511i
$682$	3.27317	−	14.3407i	0.125336	−	0.549133i
$683$	14.6102	−	18.3206i	0.559044	−	0.701019i	−0.419337	−	0.907831i	$-0.637737\pi$
$683$	14.6102	−	18.3206i	0.559044	−	0.701019i	0.978381	+	0.206812i	$0.0663087\pi$
$684$	6.13706			0.234656
$685$	−7.43528	+	9.32355i	−0.284087	+	0.356234i
$686$	1.98523	−	0.956036i	0.0757964	−	0.0365016i
$687$	9.93027	+	12.4522i	0.378864	+	0.475080i
$688$	6.05376	+	7.59118i	0.230798	+	0.289411i
$689$	−23.8964	−	11.5079i	−0.910381	−	0.438416i
$690$	−0.196202	+	0.859616i	−0.00746928	+	0.0327250i
$691$	−9.59903	−	42.0561i	−0.365164	−	1.59989i	−0.739873	−	0.672747i	$-0.765114\pi$
$691$	−9.59903	−	42.0561i	−0.365164	−	1.59989i	0.374708	−	0.927143i	$-0.377743\pi$
$692$	−14.8605	+	7.15646i	−0.564913	+	0.272048i
$693$	−2.29494	−	1.10518i	−0.0871775	−	0.0419825i
$694$	−1.99223	−	8.72853i	−0.0756240	−	0.331331i
$695$	−11.5345			−0.437529
$696$		0			0
$697$	13.9758			0.529373
$698$	−2.02907	−	8.88992i	−0.0768013	−	0.336488i
$699$	9.96077	+	4.79685i	0.376751	+	0.181434i
$700$	−2.61960	+	1.26154i	−0.0990118	+	0.0476816i
$701$	−0.941453	−	4.12477i	−0.0355582	−	0.155791i	0.954032	−	0.299705i	$-0.0968882\pi$
$701$	−0.941453	−	4.12477i	−0.0355582	−	0.155791i	−0.989590	+	0.143914i	$0.954031\pi$
$702$	−3.10292	+	13.5948i	−0.117112	+	0.513101i
$703$	−10.4879	−	5.05072i	−0.395559	−	0.190491i
$704$	11.1814	+	14.0211i	0.421416	+	0.528439i
$705$	3.46764	+	4.34828i	0.130599	+	0.163766i
$706$	−7.21648	+	3.47527i	−0.271596	+	0.130794i
$707$	−0.718636	+	0.901141i	−0.0270271	+	0.0338909i
$708$	28.0737			1.05507
$709$	8.91819	−	11.1831i	0.334930	−	0.419989i	−0.585637	−	0.810573i	$-0.699156\pi$
$709$	8.91819	−	11.1831i	0.334930	−	0.419989i	0.920567	+	0.390585i	$0.127727\pi$
$710$	0.502688	−	2.20242i	0.0188656	−	0.0826554i
$711$	1.50000	−	6.57193i	0.0562544	−	0.246467i
$712$	−5.99210	+	7.51385i	−0.224563	+	0.281594i
$713$	15.3642			0.575393
$714$	−0.554958	+	0.695895i	−0.0207688	+	0.0260432i
$715$	−17.4073	+	8.38292i	−0.650996	+	0.313503i
$716$	−3.82640	−	4.79815i	−0.142999	−	0.179315i
$717$	−19.8760	−	24.9237i	−0.742282	−	0.930792i
$718$	9.47434	+	4.56260i	0.353579	+	0.170275i
$719$	5.21605	−	22.8530i	0.194526	−	0.852274i	−0.779602	−	0.626276i	$-0.784578\pi$
$719$	5.21605	−	22.8530i	0.194526	−	0.852274i	0.974128	−	0.225998i	$-0.0725644\pi$
$720$	0.634375	+	2.77938i	0.0236418	+	0.103581i
$721$	4.39008	−	2.11415i	0.163495	−	0.0787352i
$722$	5.39104	+	2.59619i	0.200634	+	0.0966202i
$723$	−2.70022	−	11.8304i	−0.100422	−	0.439978i
$724$	−22.8388			−0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	11.5706	+	50.6939i	0.429128	+	1.88013i	0.472942	+	0.881094i	$0.343192\pi$
$727$	11.5706	+	50.6939i	0.429128	+	1.88013i	−0.0438137	+	0.999040i	$0.513951\pi$
$728$	−3.07553	−	1.48110i	−0.113987	−	0.0548931i
$729$	−22.0368	+	10.6124i	−0.816179	+	0.393051i
$730$	0.385535	+	1.68914i	0.0142693	+	0.0625178i
$731$	3.40581	−	14.9218i	0.125969	−	0.551904i
$732$	3.32640	+	1.60191i	0.122947	+	0.0592082i
$733$	−21.3173	−	26.7310i	−0.787372	−	0.987334i	−0.999948	−	0.0101892i	$-0.996757\pi$
$733$	−21.3173	−	26.7310i	−0.787372	−	0.987334i	0.212576	−	0.977145i	$-0.431815\pi$
$734$	8.22534	+	10.3143i	0.303603	+	0.380706i
$735$	5.34332	−	2.57321i	0.197091	−	0.0949142i
$736$	6.66033	−	8.35178i	0.245503	−	0.307851i
$737$	11.4735			0.422632
$738$	1.24698	−	1.56366i	0.0459020	−	0.0575592i
$739$	8.85032	−	38.7758i	0.325564	−	1.42639i	−0.501926	−	0.864911i	$-0.667375\pi$
$739$	8.85032	−	38.7758i	0.325564	−	1.42639i	0.827490	−	0.561480i	$-0.189768\pi$
$740$	1.37047	−	6.00442i	0.0503795	−	0.220727i
$741$	−10.3584	+	12.9890i	−0.380525	+	0.477163i
$742$	−0.745251			−0.0273590
$743$	−4.47554	+	5.61215i	−0.164192	+	0.205890i	−0.857120	−	0.515116i	$-0.827749\pi$
$743$	−4.47554	+	5.61215i	−0.164192	+	0.205890i	0.692929	+	0.721006i	$0.256320\pi$
$744$	12.7213	−	6.12627i	0.466386	−	0.224600i
$745$	8.02827	+	10.0671i	0.294133	+	0.368831i
$746$	−6.98911	−	8.76407i	−0.255890	−	0.320876i
$747$	5.79978	+	2.79303i	0.212203	+	0.102192i
$748$	8.89977	−	38.9925i	0.325408	−	1.42571i
$749$	−1.29009	−	5.65227i	−0.0471390	−	0.206529i
$750$	3.29440	−	1.58650i	0.120295	−	0.0579309i
$751$	−24.4780	−	11.7880i	−0.893215	−	0.430150i	−0.0697812	−	0.997562i	$-0.522230\pi$
$751$	−24.4780	−	11.7880i	−0.893215	−	0.430150i	−0.823433	+	0.567413i	$0.807944\pi$
$752$	−4.08857	−	17.9132i	−0.149095	−	0.653228i
$753$	12.1709			0.443533
$754$		0			0
$755$	−5.20941			−0.189590
$756$	−0.793209	−	3.47527i	−0.0288487	−	0.126394i
$757$	21.3463	+	10.2798i	0.775845	+	0.373627i	0.779529	−	0.626366i	$-0.215458\pi$
$757$	21.3463	+	10.2798i	0.775845	+	0.373627i	−0.00368433	+	0.999993i	$0.501173\pi$
$758$	−10.7889	+	5.19566i	−0.391870	+	0.188715i
$759$	3.14646	+	13.7855i	0.114209	+	0.500383i
$760$	0.614097	−	2.69053i	0.0222756	−	0.0975959i
$761$	12.8427	+	6.18470i	0.465546	+	0.224195i	0.651926	−	0.758283i	$-0.273961\pi$
$761$	12.8427	+	6.18470i	0.465546	+	0.224195i	−0.186380	+	0.982478i	$0.559676\pi$
$762$	0.358756	+	0.449866i	0.0129964	+	0.0162969i
$763$	1.21648	+	1.52542i	0.0440395	+	0.0552238i
$764$	17.3230	−	8.34234i	0.626726	−	0.301815i
$765$	2.80194	−	3.51352i	0.101304	−	0.127032i
$766$	−8.75361			−0.316281
$767$	44.0344	−	55.2174i	1.58999	−	1.99379i
$768$	−0.666366	+	2.91954i	−0.0240454	+	0.105350i
$769$	−9.94816	+	43.5857i	−0.358740	+	1.57174i	0.397598	+	0.917560i	$0.369844\pi$
$769$	−9.94816	+	43.5857i	−0.358740	+	1.57174i	−0.756337	+	0.654182i	$0.773013\pi$
$770$	−0.338478	+	0.424438i	−0.0121979	+	0.0152957i
$771$	20.3967			0.734570
$772$	25.5356	−	32.0207i	0.919048	−	1.15245i
$773$	20.6761	−	9.95706i	0.743666	−	0.358131i	−0.0233767	−	0.999727i	$-0.507442\pi$
$773$	20.6761	−	9.95706i	0.743666	−	0.358131i	0.767043	+	0.641596i	$0.221727\pi$
$774$	−1.36563	−	1.71244i	−0.0490864	−	0.0615524i
$775$	−18.8639	−	23.6546i	−0.677611	−	0.849698i
$776$	0.275323	+	0.132589i	0.00988352	+	0.00475965i
$777$	−0.489115	+	2.14295i	−0.0175469	+	0.0768780i
$778$	2.46144	+	10.7843i	0.0882467	+	0.386634i
$779$	6.60388	−	3.18026i	0.236608	−	0.113945i
$780$	−7.91939	−	3.81378i	−0.283560	−	0.136555i
$781$	−8.06153	−	35.3199i	−0.288464	−	1.26384i
$782$	−4.59179			−0.164202
$783$		0			0
$784$	−19.5929			−0.699745
$785$	−2.80864	−	12.3055i	−0.100245	−	0.439201i
$786$	4.01089	+	1.93154i	0.143064	+	0.0688958i
$787$	−12.9133	+	6.21874i	−0.460311	+	0.221674i	−0.649644	−	0.760239i	$-0.725082\pi$
$787$	−12.9133	+	6.21874i	−0.460311	+	0.221674i	0.189333	+	0.981913i	$0.439368\pi$
$788$	−7.84213	−	34.3586i	−0.279364	−	1.22397i
$789$	6.58277	−	28.8410i	0.234353	−	1.02677i
$790$	−1.29440	−	0.623353i	−0.0460529	−	0.0221779i
$791$	2.37531	+	2.97855i	0.0844564	+	0.105905i
$792$	−7.52930	−	9.44145i	−0.267542	−	0.335487i
$793$	8.36831	−	4.02997i	0.297168	−	0.143108i
$794$	−1.10842	+	1.38992i	−0.0393365	+	0.0493264i
$795$	−4.04892			−0.143600
$796$	0.983074	−	1.23274i	0.0348441	−	0.0436932i
$797$	2.26822	−	9.93771i	0.0803444	−	0.352012i	−0.918737	−	0.394871i	$-0.870789\pi$
$797$	2.26822	−	9.93771i	0.0803444	−	0.352012i	0.999081	+	0.0428588i	$0.0136466\pi$
$798$	−0.103875	+	0.455108i	−0.00367715	+	0.0161107i
$799$	−18.0586	+	22.6448i	−0.638868	+	0.801115i
$800$	−21.0358			−0.743727
$801$	−5.11745	+	6.41708i	−0.180816	+	0.226736i
$802$	9.98696	−	4.80947i	0.352652	−	0.169828i
$803$	17.3237	+	21.7232i	0.611340	+	0.766597i
$804$	3.25451	+	4.08103i	0.114778	+	0.143927i
$805$	−0.510885	−	0.246029i	−0.0180063	−	0.00867139i
$806$	3.74621	−	16.4132i	0.131955	−	0.578131i
$807$	7.03534	+	30.8239i	0.247656	+	1.08505i
$808$	−4.92327	+	2.37092i	−0.173200	+	0.0834088i
$809$	8.08426	+	3.89317i	0.284227	+	0.136877i	0.570566	−	0.821252i	$-0.306724\pi$
$809$	8.08426	+	3.89317i	0.284227	+	0.136877i	−0.286338	+	0.958129i	$0.592438\pi$
$810$	0.176587	+	0.773680i	0.00620465	+	0.0271844i
$811$	−28.5628			−1.00298			−0.501489	−	0.865164i	$-0.667214\pi$
$811$	−28.5628			−1.00298			−0.501489	+	0.865164i	$0.667214\pi$
$812$		0			0
$813$	1.50066			0.0526306
$814$	2.41574	+	10.5840i	0.0846716	+	0.370971i
$815$	7.88135	+	3.79546i	0.276072	+	0.132949i
$816$	14.3937	−	6.93166i	0.503881	−	0.242656i
$817$	−1.78621	−	7.82589i	−0.0624915	−	0.273793i
$818$	0.0280480	−	0.122886i	0.000980676	−	0.00429662i
$819$	−2.62661	−	1.26491i	−0.0917810	−	0.0441994i
$820$	2.41789	+	3.03194i	0.0844365	+	0.105880i
$821$	7.06734	+	8.86216i	0.246652	+	0.309291i	0.889710	−	0.456526i	$-0.150906\pi$
$821$	7.06734	+	8.86216i	0.246652	+	0.309291i	−0.643059	+	0.765817i	$0.722335\pi$
$822$	8.61625	−	4.14937i	0.300526	−	0.144726i
$823$	−3.53654	+	4.43468i	−0.123276	+	0.154583i	−0.839640	−	0.543144i	$-0.817234\pi$
$823$	−3.53654	+	4.43468i	−0.123276	+	0.154583i	0.716364	+	0.697727i	$0.245805\pi$
$824$	23.1008			0.804755
$825$	17.3609	−	21.7699i	0.604429	−	0.757930i
$826$	0.441584	−	1.93471i	0.0153647	−	0.0673170i
$827$	−0.646030	+	2.83044i	−0.0224646	+	0.0984241i	−0.984917	−	0.173025i	$-0.944646\pi$
$827$	−0.646030	+	2.83044i	−0.0224646	+	0.0984241i	0.962453	+	0.271449i	$0.0875029\pi$
$828$	3.72737	−	4.67397i	0.129535	−	0.162432i
$829$	45.2137			1.57034			0.785169	−	0.619282i	$-0.212576\pi$
$829$	45.2137			1.57034			0.785169	+	0.619282i	$0.212576\pi$
$830$	0.855404	−	1.07264i	0.0296915	−	0.0372320i
$831$	−11.9819	+	5.77017i	−0.415647	+	0.200165i
$832$	12.7974	+	16.0474i	0.443670	+	0.556344i
$833$	19.2567	+	24.1471i	0.667204	+	0.836647i
$834$	8.33393	+	4.01341i	0.288580	+	0.138973i
$835$	0.122662	−	0.537417i	0.00424489	−	0.0185981i
$836$	−4.66756	−	20.4499i	−0.161431	−	0.707276i
$837$	33.4197	−	16.0941i	1.15515	−	0.556292i
$838$	10.6211	+	5.11485i	0.366900	+	0.176690i
$839$	−10.1527	−	44.4817i	−0.350509	−	1.53568i	−0.776009	−	0.630721i	$-0.782759\pi$
$839$	−10.1527	−	44.4817i	−0.350509	−	1.53568i	0.425501	−	0.904958i	$-0.360098\pi$
$840$	−0.521106			−0.0179799
$841$		0			0
$842$	7.82477			0.269659
$843$	4.51722	+	19.7912i	0.155581	+	0.681647i
$844$	29.6591	+	14.2831i	1.02091	+	0.491644i
$845$	−11.8177	+	5.69109i	−0.406540	+	0.195779i
$846$	0.922312	+	4.04091i	0.0317097	+	0.138929i
$847$	−1.06369	+	4.66032i	−0.0365487	+	0.160130i
$848$	12.0516	+	5.80375i	0.413854	+	0.199302i
$849$	−4.07942	−	5.11543i	−0.140005	−	0.175561i
$850$	5.63773	+	7.06949i	0.193372	+	0.242481i
$851$	−10.2165	+	4.92000i	−0.350216	+	0.168655i
$852$	10.2763	−	12.8861i	0.352060	−	0.441469i
$853$	36.9288			1.26442			0.632210	−	0.774797i	$-0.282148\pi$
$853$	36.9288			1.26442			0.632210	+	0.774797i	$0.282148\pi$
$854$	0.162718	−	0.204042i	0.00556811	−	0.00698219i
$855$	0.524459	−	2.29780i	0.0179361	−	0.0785832i
$856$	6.11625	−	26.7971i	0.209049	−	0.915904i
$857$	22.1652	−	27.7942i	0.757148	−	0.949433i	−0.242638	−	0.970117i	$-0.578013\pi$
$857$	22.1652	−	27.7942i	0.757148	−	0.949433i	0.999786	+	0.0206835i	$0.00658425\pi$
$858$	15.4940			0.528955
$859$	−26.4242	+	33.1349i	−0.901583	+	1.13055i	0.0893241	+	0.996003i	$0.471529\pi$
$859$	−26.4242	+	33.1349i	−0.901583	+	1.13055i	−0.990907	+	0.134547i	$0.957042\pi$
$860$	3.82640	−	1.84270i	0.130479	−	0.0628354i
$861$	−0.862937	−	1.08209i	−0.0294088	−	0.0368775i
$862$	−7.71260	−	9.67129i	−0.262692	−	0.329405i
$863$	−44.8500	−	21.5986i	−1.52671	−	0.735225i	−0.532886	−	0.846187i	$-0.678892\pi$
$863$	−44.8500	−	21.5986i	−1.52671	−	0.735225i	−0.993825	+	0.110962i	$0.964607\pi$
$864$	5.73878	−	25.1433i	0.195237	−	0.855391i
$865$	1.40953	+	6.17557i	0.0479256	+	0.209976i
$866$	2.35594	−	1.13456i	0.0800580	−	0.0385539i
$867$	−3.59030	−	1.72900i	−0.121933	−	0.0587199i
$868$	0.957656	+	4.19576i	0.0325050	+	0.142414i
$869$	−23.0398			−0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	2.05831	+	9.01805i	0.0697032	+	0.305390i
$873$	0.235135	+	0.113235i	0.00795811	+	0.00383243i
$874$	−2.16972	+	1.04488i	−0.0733918	+	0.0353436i
$875$	0.523262	+	2.29256i	0.0176895	+	0.0775027i
$876$	−2.81282	+	12.3238i	−0.0950365	+	0.416382i
$877$	−19.7250	−	9.49905i	−0.666065	−	0.320760i	0.0701218	−	0.997538i	$-0.477661\pi$
$877$	−19.7250	−	9.49905i	−0.666065	−	0.320760i	−0.736187	+	0.676778i	$0.763376\pi$
$878$	−4.36778	−	5.47702i	−0.147405	−	0.184841i
$879$	−5.25869	−	6.59419i	−0.177371	−	0.222417i
$880$	8.77897	−	4.22773i	0.295939	−	0.142517i
$881$	20.9061	−	26.2154i	0.704345	−	0.883220i	−0.292995	−	0.956114i	$-0.594652\pi$
$881$	20.9061	−	26.2154i	0.704345	−	0.883220i	0.997340	+	0.0728937i	$0.0232234\pi$
$882$	4.41981			0.148823
$883$	−10.0553	+	12.6089i	−0.338386	+	0.424323i	−0.921688	−	0.387933i	$-0.873189\pi$
$883$	−10.0553	+	12.6089i	−0.338386	+	0.424323i	0.583301	+	0.812256i	$0.301761\pi$
$884$	10.1860	−	44.6277i	0.342592	−	1.50099i
$885$	2.39911	−	10.5112i	0.0806451	−	0.353329i
$886$	−1.86981	+	2.34466i	−0.0628173	+	0.0787705i
$887$	−52.7391			−1.77081			−0.885403	−	0.464823i	$-0.846118\pi$
$887$	−52.7391			−1.77081			−0.885403	+	0.464823i	$0.846118\pi$
$888$	−6.49731	+	8.14737i	−0.218036	+	0.273408i
$889$	−0.333397	+	0.160555i	−0.0111818	+	0.00538485i
$890$	1.09067	+	1.36766i	0.0365594	+	0.0458440i
$891$	7.93482	+	9.94995i	0.265826	+	0.333336i
$892$	−2.95204	−	1.42163i	−0.0988417	−	0.0475996i
$893$	−3.38016	+	14.8094i	−0.113113	+	0.495579i
$894$	−2.29776	−	10.0671i	−0.0768485	−	0.336695i
$895$	−2.12349	+	1.02262i	−0.0709804	+	0.0341824i
$896$	3.51184	+	1.69122i	0.117322	+	0.0564995i
$897$	3.60119	+	15.7778i	0.120240	+	0.526806i
$898$	−5.48294			−0.182968
$899$		0			0
$900$	−11.7724			−0.392413
$901$	−4.69202	−	20.5571i	−0.156314	−	0.684856i
$902$	−6.15883	−	2.96594i	−0.205067	−	0.0987549i
$903$	−1.36563	+	0.657650i	−0.0454452	+	0.0218852i
$904$	4.01908	+	17.6087i	0.133673	+	0.585658i
$905$	−1.95175	+	8.55116i	−0.0648783	+	0.284250i
$906$	3.76391	+	1.81260i	0.125047	+	0.0602196i
$907$	18.6072	+	23.3327i	0.617843	+	0.774750i	0.988039	−	0.154203i	$-0.0492810\pi$
$907$	18.6072	+	23.3327i	0.617843	+	0.774750i	−0.370196	+	0.928954i	$0.620710\pi$
$908$	15.5673	+	19.5208i	0.516620	+	0.647821i
$909$	−4.20464	+	2.02485i	−0.139459	+	0.0671599i
$910$	−0.387395	+	0.485778i	−0.0128420	+	0.0161034i
$911$	9.34050			0.309465			0.154732	−	0.987956i	$-0.450548\pi$
$911$	9.34050			0.309465			0.154732	+	0.987956i	$0.450548\pi$
$912$	5.22401	−	6.55070i	0.172984	−	0.216916i
$913$	4.89589	−	21.4503i	0.162030	−	0.709901i
$914$	−1.35301	+	5.92793i	−0.0447536	+	0.196078i
$915$	0.884043	−	1.10855i	0.0292256	−	0.0366477i
$916$	−23.0151			−0.760439
$917$	−1.78501	+	2.23833i	−0.0589463	+	0.0739163i
$918$	−9.98792	+	4.80993i	−0.329650	+	0.158751i
$919$	−11.4852	−	14.4020i	−0.378863	−	0.475079i	0.555441	−	0.831556i	$-0.312549\pi$
$919$	−11.4852	−	14.4020i	−0.378863	−	0.475079i	−0.934304	+	0.356477i	$0.883978\pi$
$920$	−1.67613	−	2.10180i	−0.0552603	−	0.0692942i
$921$	5.07606	+	2.44450i	0.167262	+	0.0805491i
$922$	1.14957	−	5.03660i	0.0378591	−	0.165872i
$923$	−9.22660	−	40.4244i	−0.303697	−	1.33058i
$924$	−3.56853	+	1.71851i	−0.117396	+	0.0565350i
$925$	20.1184	+	9.68851i	0.661489	+	0.318556i
$926$	0.717250	+	3.14248i	0.0235703	+	0.103268i
$927$	19.7289			0.647981
$928$		0			0
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$	−0.571884	−	2.50559i	−0.0187528	−	0.0821615i
$931$	14.5939	+	7.02808i	0.478297	+	0.230336i
$932$	−14.3937	+	6.93166i	−0.471482	+	0.227054i
$933$	−3.50083	−	15.3381i	−0.114612	−	0.502148i
$934$	−0.204340	+	0.895272i	−0.00668621	+	0.0292942i
$935$	−13.8388	−	6.66440i	−0.452576	−	0.217949i
$936$	−8.61745	−	10.8059i	−0.281670	−	0.353203i
$937$	−27.8790	−	34.9591i	−0.910766	−	1.14206i	−0.989408	−	0.145161i	$-0.953630\pi$
$937$	−27.8790	−	34.9591i	−0.910766	−	1.14206i	0.0786420	−	0.996903i	$-0.474942\pi$
$938$	0.332437	−	0.160093i	0.0108545	−	0.00522723i
$939$	14.9589	−	18.7579i	0.488166	−	0.612140i
$940$	−8.03684			−0.262133
$941$	8.47016	−	10.6213i	0.276119	−	0.346243i	−0.624364	−	0.781134i	$-0.714642\pi$
$941$	8.47016	−	10.6213i	0.276119	−	0.346243i	0.900483	+	0.434891i	$0.143213\pi$
$942$	−2.25236	+	9.86822i	−0.0733857	+	0.321524i
$943$	1.58881	−	6.96103i	0.0517388	−	0.226682i
$944$	−22.2078	+	27.8476i	−0.722801	+	0.906363i
$945$	−1.36898			−0.0445328
$946$	−4.66756	+	5.85294i	−0.151756	+	0.190295i
$947$	13.5250	−	6.51329i	0.439503	−	0.211654i	−0.201028	−	0.979585i	$-0.564428\pi$
$947$	13.5250	−	6.51329i	0.439503	−	0.211654i	0.640532	+	0.767932i	$0.278714\pi$
$948$	−6.53534	−	8.19506i	−0.212258	−	0.266163i
$949$	19.8274	+	24.8627i	0.643623	+	0.807078i
$950$	4.27263	+	2.05759i	0.138623	+	0.0667571i
$951$	0.795897	−	3.48705i	0.0258087	−	0.113075i
$952$	−0.603875	−	2.64575i	−0.0195717	−	0.0857493i
$953$	−46.7105	+	22.4946i	−1.51310	+	0.728671i	−0.992166	−	0.124925i	$-0.960131\pi$
$953$	−46.7105	+	22.4946i	−1.51310	+	0.728671i	−0.520935	+	0.853596i	$0.674417\pi$
$954$	−2.71864	−	1.30923i	−0.0880191	−	0.0423878i
$955$	−1.64310	−	7.19891i	−0.0531696	−	0.232951i
$956$	46.0659			1.48988
$957$		0			0
$958$	1.73078			0.0559188
$959$	1.36855	+	5.99601i	0.0441928	+	0.193621i
$960$	2.82304	+	1.35951i	0.0911134	+	0.0438779i
$961$	−12.4182	+	5.98029i	−0.400587	+	0.192912i
$962$	2.76487	+	12.1137i	0.0891428	+	0.390560i
$963$	5.22348	−	22.8856i	0.168324	−	0.737477i
$964$	15.7986	+	7.60820i	0.508838	+	0.245044i
$965$	−9.80678	−	12.2973i	−0.315691	−	0.395865i
$966$	0.283520	+	0.355523i	0.00912210	+	0.0114388i
$967$	−37.5027	+	18.0604i	−1.20601	+	0.580782i	−0.925382	−	0.379035i	$-0.876256\pi$
$967$	−37.5027	+	18.0604i	−1.20601	+	0.580782i	−0.280625	+	0.959818i	$0.590542\pi$
$968$	−14.1298	+	17.7182i	−0.454150	+	0.569486i
$969$	−13.2078			−0.424294
$970$	0.0346798	−	0.0434871i	0.00111350	−	0.00139629i
$971$	−12.4107	+	54.3746i	−0.398277	+	1.74497i	0.235900	+	0.971777i	$0.424196\pi$
$971$	−12.4107	+	54.3746i	−0.398277	+	1.74497i	−0.634177	+	0.773188i	$0.718661\pi$
$972$	5.37920	−	23.5678i	0.172538	−	0.755938i
$973$	−3.70895	+	4.65087i	−0.118903	+	0.149100i
$974$	4.38165			0.140397
$975$	19.8699	−	24.9161i	0.636347	−	0.797954i
$976$	−4.22037	+	2.03242i	−0.135091	+	0.0650562i
$977$	30.5250	+	38.2772i	0.976583	+	1.22460i	0.974451	+	0.224598i	$0.0721070\pi$
$977$	30.5250	+	38.2772i	0.976583	+	1.22460i	0.00213146	+	0.999998i	$0.499322\pi$
$978$	−4.37382	−	5.48460i	−0.139859	−	0.175378i
$979$	25.2751	+	12.1718i	0.807795	+	0.389014i
$980$	−1.90701	+	8.35516i	−0.0609172	+	0.266896i
$981$	1.75786	+	7.70171i	0.0561243	+	0.245897i
$982$	3.12402	−	1.50445i	0.0996916	−	0.0480089i
$983$	4.66099	+	2.24461i	0.148662	+	0.0715921i	0.506736	−	0.862101i	$-0.330852\pi$
$983$	4.66099	+	2.24461i	0.148662	+	0.0715921i	−0.358073	+	0.933693i	$0.616566\pi$
$984$	−1.46011	−	6.39715i	−0.0465465	−	0.203934i
$985$	−13.5345			−0.431246
$986$		0			0
$987$	2.86831			0.0912994
$988$	−5.34213	−	23.4054i	−0.169956	−	0.744624i
$989$	−7.04503	−	3.39271i	−0.224019	−	0.107882i
$990$	−1.98039	+	0.953703i	−0.0629408	+	0.0303107i
$991$	3.75010	+	16.4302i	0.119126	+	0.521924i	0.998915	+	0.0465608i	$0.0148261\pi$
$991$	3.75010	+	16.4302i	0.119126	+	0.521924i	−0.879790	+	0.475363i	$0.842317\pi$
$992$	−6.92854	+	30.3559i	−0.219981	+	0.963802i
$993$	3.52111	+	1.69568i	0.111739	+	0.0538106i
$994$	−0.726406	−	0.910884i	−0.0230402	−	0.0288915i
$995$	−0.377543	−	0.473424i	−0.0119689	−	0.0150085i
$996$	9.01842	−	4.34304i	0.285760	−	0.137615i
$997$	−23.8233	+	29.8735i	−0.754493	+	0.946104i	−0.999727	−	0.0233599i	$-0.992564\pi$
$997$	−23.8233	+	29.8735i	−0.754493	+	0.946104i	0.245234	+	0.969464i	$0.421135\pi$
$998$	−9.15239			−0.289714
$999$	−17.0688	+	21.4036i	−0.540034	+	0.677181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.a.645.1		6
29.2	odd	28		841.2.b.c.840.3		6
29.3	odd	28		841.2.e.c.63.2		12
29.4	even	14		841.2.d.e.605.1		6
29.5	even	14		841.2.a.e.1.2		3
29.6	even	14		29.2.d.a.20.1	yes	6
29.7	even	7		841.2.d.c.778.1		6
29.8	odd	28		841.2.e.d.651.2		12
29.9	even	14		29.2.d.a.16.1	✓	6
29.10	odd	28		841.2.e.b.236.1		12
29.11	odd	28		841.2.e.c.267.1		12
29.12	odd	4		841.2.e.b.196.2		12
29.13	even	14		841.2.d.b.574.1		6
29.14	odd	28		841.2.e.d.270.2		12
29.15	odd	28		841.2.e.d.270.1		12
29.16	even	7		841.2.d.c.574.1		6
29.17	odd	4		841.2.e.b.196.1		12
29.18	odd	28		841.2.e.c.267.2		12
29.19	odd	28		841.2.e.b.236.2		12
29.20	even	7		841.2.d.d.190.1		6
29.21	odd	28		841.2.e.d.651.1		12
29.22	even	14		841.2.d.b.778.1		6
29.23	even	7		841.2.d.d.571.1		6
29.24	even	7		841.2.a.f.1.2		3
29.25	even	7	inner	841.2.d.a.605.1		6
29.26	odd	28		841.2.e.c.63.1		12
29.27	odd	28		841.2.b.c.840.4		6
29.28	even	2		841.2.d.e.645.1		6
87.5	odd	14		7569.2.a.r.1.2		3
87.35	odd	14		261.2.k.a.136.1		6
87.38	odd	14		261.2.k.a.190.1		6
87.53	odd	14		7569.2.a.p.1.2		3
116.35	odd	14		464.2.u.f.49.1		6
116.67	odd	14		464.2.u.f.161.1		6
145.9	even	14		725.2.l.b.451.1		6
145.38	odd	28		725.2.r.b.74.2		12
145.64	even	14		725.2.l.b.426.1		6
145.67	odd	28		725.2.r.b.74.1		12
145.93	odd	28		725.2.r.b.49.1		12
145.122	odd	28		725.2.r.b.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	29.9	even	14
29.2.d.a.20.1	yes	6	29.6	even	14
261.2.k.a.136.1		6	87.35	odd	14
261.2.k.a.190.1		6	87.38	odd	14
464.2.u.f.49.1		6	116.35	odd	14
464.2.u.f.161.1		6	116.67	odd	14
725.2.l.b.426.1		6	145.64	even	14
725.2.l.b.451.1		6	145.9	even	14
725.2.r.b.49.1		12	145.93	odd	28
725.2.r.b.49.2		12	145.122	odd	28
725.2.r.b.74.1		12	145.67	odd	28
725.2.r.b.74.2		12	145.38	odd	28
841.2.a.e.1.2		3	29.5	even	14
841.2.a.f.1.2		3	29.24	even	7
841.2.b.c.840.3		6	29.2	odd	28
841.2.b.c.840.4		6	29.27	odd	28
841.2.d.a.605.1		6	29.25	even	7	inner
841.2.d.a.645.1		6	1.1	even	1	trivial
841.2.d.b.574.1		6	29.13	even	14
841.2.d.b.778.1		6	29.22	even	14
841.2.d.c.574.1		6	29.16	even	7
841.2.d.c.778.1		6	29.7	even	7
841.2.d.d.190.1		6	29.20	even	7
841.2.d.d.571.1		6	29.23	even	7
841.2.d.e.605.1		6	29.4	even	14
841.2.d.e.645.1		6	29.28	even	2
841.2.e.b.196.1		12	29.17	odd	4
841.2.e.b.196.2		12	29.12	odd	4
841.2.e.b.236.1		12	29.10	odd	28
841.2.e.b.236.2		12	29.19	odd	28
841.2.e.c.63.1		12	29.26	odd	28
841.2.e.c.63.2		12	29.3	odd	28
841.2.e.c.267.1		12	29.11	odd	28
841.2.e.c.267.2		12	29.18	odd	28
841.2.e.d.270.1		12	29.15	odd	28
841.2.e.d.270.2		12	29.14	odd	28
841.2.e.d.651.1		12	29.21	odd	28
841.2.e.d.651.2		12	29.8	odd	28
7569.2.a.p.1.2		3	87.53	odd	14
7569.2.a.r.1.2		3	87.5	odd	14

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0990311 - 0.433884i) q^{2} +(-1.12349 - 0.541044i) q^{3} +(1.62349 - 0.781831i) q^{4} +(-0.153989 - 0.674671i) q^{5} +(-0.123490 + 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(-1.05496 - 1.32288i) q^{8} +(-0.900969 - 1.12978i) q^{9} +(-0.277479 + 0.133627i) q^{10} +(-3.07942 + 3.86147i) q^{11} -2.24698 q^{12} +(-3.52446 + 4.41953i) q^{13} +(-0.0353438 + 0.154851i) q^{14} +(-0.192021 + 0.841301i) q^{15} +(1.77748 - 2.22889i) q^{16} -4.49396 q^{17} +(-0.400969 + 0.502799i) q^{18} +(-2.12349 + 1.02262i) q^{19} +(-0.777479 - 0.974928i) q^{20} +(0.277479 + 0.347948i) q^{21} +(1.98039 + 0.953703i) q^{22} +(-0.510885 + 2.23833i) q^{23} +(0.469501 + 2.05702i) q^{24} +(4.07338 - 1.96163i) q^{25} +(2.26659 + 1.09153i) q^{26} +(1.23341 + 5.40391i) q^{27} -0.643104 q^{28} +0.384043 q^{30} +(-1.48911 - 6.52424i) q^{31} +(-4.19202 - 2.01877i) q^{32} +(5.54892 - 2.67222i) q^{33} +(0.445042 + 1.94986i) q^{34} +(-0.0549581 + 0.240787i) q^{35} +(-2.34601 - 1.12978i) q^{36} +(3.07942 + 3.86147i) q^{37} +(0.653989 + 0.820077i) q^{38} +(6.35086 - 3.05841i) q^{39} +(-0.730054 + 0.915458i) q^{40} -3.10992 q^{41} +(0.123490 - 0.154851i) q^{42} +(-0.757865 + 3.32042i) q^{43} +(-1.98039 + 8.67664i) q^{44} +(-0.623490 + 0.781831i) q^{45} +1.02177 q^{46} +(4.01842 - 5.03894i) q^{47} +(-3.20291 + 1.54244i) q^{48} +(-4.28501 - 5.37323i) q^{49} +(-1.25451 - 1.57311i) q^{50} +(5.04892 + 2.43143i) q^{51} +(-2.26659 + 9.93060i) q^{52} +(1.04407 + 4.57438i) q^{53} +(2.22252 - 1.07031i) q^{54} +(3.07942 + 1.48297i) q^{55} +(0.134375 + 0.588735i) q^{56} +2.93900 q^{57} -12.4940 q^{59} +(0.346011 + 1.51597i) q^{60} +(-1.48039 - 0.712916i) q^{61} +(-2.68329 + 1.29221i) q^{62} +(0.114761 + 0.502799i) q^{63} +(0.807979 - 3.53999i) q^{64} +(3.52446 + 1.69729i) q^{65} +(-1.70895 - 2.14295i) q^{66} +(-1.44839 - 1.81623i) q^{67} +(-7.29590 + 3.51352i) q^{68} +(1.78501 - 2.23833i) q^{69} +0.109916 q^{70} +(-4.57338 + 5.73483i) q^{71} +(-0.544073 + 2.38374i) q^{72} +(1.25182 - 5.48460i) q^{73} +(1.37047 - 1.71851i) q^{74} -5.63773 q^{75} +(-2.64795 + 3.32042i) q^{76} +(1.58815 - 0.764811i) q^{77} +(-1.95593 - 2.45265i) q^{78} +(2.90850 + 3.64715i) q^{79} +(-1.77748 - 0.855989i) q^{80} +(0.573376 - 2.51212i) q^{81} +(0.307979 + 1.34934i) q^{82} +(-4.01357 + 1.93284i) q^{83} +(0.722521 + 0.347948i) q^{84} +(0.692021 + 3.03194i) q^{85} +1.51573 q^{86} +8.35690 q^{88} +(-1.26391 - 5.53753i) q^{89} +(0.400969 + 0.193096i) q^{90} +(1.81767 - 0.875342i) q^{91} +(0.920583 + 4.03334i) q^{92} +(-1.85690 + 8.13559i) q^{93} +(-2.58426 - 1.24451i) q^{94} +(1.01693 + 1.27518i) q^{95} +(3.61745 + 4.53614i) q^{96} +(-0.162718 + 0.0783611i) q^{97} +(-1.90701 + 2.39131i) q^{98} +7.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} - 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} - 7 q^{8} - q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} + 9 q^{15} + 11 q^{16} - 8 q^{17} + 2 q^{18} - 8 q^{19} - 5 q^{20}+ \cdots + 32 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 - 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 - 7 * q^8 - q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 + 9 * q^15 + 11 * q^16 - 8 * q^17 + 2 * q^18 - 8 * q^19 - 5 * q^20 + 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 + 17 * q^26 + 4 * q^27 - 12 * q^28 - 18 * q^30 - 12 * q^31 - 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 + 10 * q^37 + 9 * q^38 + 11 * q^39 + 21 * q^40 - 20 * q^41 - 4 * q^42 + 8 * q^43 + q^44 + q^45 - 4 * q^47 - 6 * q^48 - q^49 + 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 + 10 * q^55 - 7 * q^56 - 2 * q^57 - 56 * q^59 - 3 * q^60 + 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 - 16 * q^66 - 30 * q^67 - 16 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^72 - 24 * q^73 - 6 * q^74 - 48 * q^75 - 2 * q^76 + 17 * q^77 - 8 * q^78 - 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 + 4 * q^84 - 6 * q^85 - 16 * q^86 + 42 * q^88 - 14 * q^89 - 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 + 22 * q^95 - 2 * q^96 - 22 * q^97 - 26 * q^98 + 32 * q^99

Introduction

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