LMFDB - Embedded newform 731.2.k.a.35.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(35,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("731.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.k (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			35.14
Character	$\chi$	$=$	731.35
Dual form			731.2.k.a.188.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104116 + 0.456161i) q^{2} +(-0.128875 - 0.564637i) q^{3} +(1.60469 + 0.772780i) q^{4} +(-2.20664 + 2.76704i) q^{5} +0.270983 q^{6} +0.0588619 q^{7} +(-1.10304 + 1.38317i) q^{8} +(2.40070 - 1.15612i) q^{9} +O(q^{10})$	\(q+(-0.104116 + 0.456161i) q^{2} +(-0.128875 - 0.564637i) q^{3} +(1.60469 + 0.772780i) q^{4} +(-2.20664 + 2.76704i) q^{5} +0.270983 q^{6} +0.0588619 q^{7} +(-1.10304 + 1.38317i) q^{8} +(2.40070 - 1.15612i) q^{9} +(-1.03247 - 1.29468i) q^{10} +(-0.929192 + 0.447475i) q^{11} +(0.229536 - 1.00566i) q^{12} +(-0.588272 + 0.737670i) q^{13} +(-0.00612846 + 0.0268505i) q^{14} +(1.84675 + 0.889350i) q^{15} +(1.70486 + 2.13783i) q^{16} +(0.623490 + 0.781831i) q^{17} +(0.277424 + 1.21548i) q^{18} +(2.85635 + 1.37554i) q^{19} +(-5.67930 + 2.73501i) q^{20} +(-0.00758581 - 0.0332356i) q^{21} +(-0.107377 - 0.470450i) q^{22} +(-6.68129 + 3.21754i) q^{23} +(0.923140 + 0.444561i) q^{24} +(-1.67465 - 7.33710i) q^{25} +(-0.275248 - 0.345150i) q^{26} +(-2.04547 - 2.56494i) q^{27} +(0.0944555 + 0.0454874i) q^{28} +(-2.30095 + 10.0811i) q^{29} +(-0.597963 + 0.749822i) q^{30} +(-0.157212 + 0.688790i) q^{31} +(-4.34057 + 2.09031i) q^{32} +(0.372410 + 0.466988i) q^{33} +(-0.421556 + 0.203011i) q^{34} +(-0.129887 + 0.162873i) q^{35} +4.74582 q^{36} -3.30551 q^{37} +(-0.924860 + 1.15974i) q^{38} +(0.492329 + 0.237093i) q^{39} +(-1.39327 - 6.10431i) q^{40} +(1.80556 - 7.91067i) q^{41} +0.0159506 q^{42} +(-3.93062 - 5.24883i) q^{43} -1.83687 q^{44} +(-2.09846 + 9.19397i) q^{45} +(-0.772089 - 3.38274i) q^{46} +(4.53602 + 2.18443i) q^{47} +(0.987385 - 1.23814i) q^{48} -6.99654 q^{49} +3.52126 q^{50} +(0.361099 - 0.452804i) q^{51} +(-1.51405 + 0.729130i) q^{52} +(1.54659 + 1.93936i) q^{53} +(1.38299 - 0.666014i) q^{54} +(0.812211 - 3.55853i) q^{55} +(-0.0649270 + 0.0814158i) q^{56} +(0.408572 - 1.79007i) q^{57} +(-4.35904 - 2.09920i) q^{58} +(5.58499 + 7.00335i) q^{59} +(2.27620 + 2.85427i) q^{60} +(2.87874 + 12.6126i) q^{61} +(-0.297831 - 0.143428i) q^{62} +(0.141310 - 0.0680513i) q^{63} +(0.715322 + 3.13403i) q^{64} +(-0.743057 - 3.25555i) q^{65} +(-0.251795 + 0.121258i) q^{66} +(8.90339 + 4.28765i) q^{67} +(0.396327 + 1.73642i) q^{68} +(2.67779 + 3.35784i) q^{69} +(-0.0607732 - 0.0762072i) q^{70} +(-3.28246 - 1.58075i) q^{71} +(-1.04896 + 4.59581i) q^{72} +(1.69384 - 2.12401i) q^{73} +(0.344156 - 1.50785i) q^{74} +(-3.92698 + 1.89113i) q^{75} +(3.52057 + 4.41466i) q^{76} +(-0.0546940 + 0.0263393i) q^{77} +(-0.159412 + 0.199896i) q^{78} +12.3199 q^{79} -9.67749 q^{80} +(3.79936 - 4.76425i) q^{81} +(3.42055 + 1.64725i) q^{82} +(-2.61454 - 11.4550i) q^{83} +(0.0135109 - 0.0591952i) q^{84} -3.53918 q^{85} +(2.80355 - 1.24651i) q^{86} +5.98870 q^{87} +(0.406002 - 1.77881i) q^{88} +(-2.77502 - 12.1581i) q^{89} +(-3.97545 - 1.91448i) q^{90} +(-0.0346268 + 0.0434207i) q^{91} -13.2079 q^{92} +0.409177 q^{93} +(-1.46872 + 1.84172i) q^{94} +(-10.1091 + 4.86830i) q^{95} +(1.73966 + 2.18146i) q^{96} +(-0.801582 + 0.386021i) q^{97} +(0.728450 - 3.19155i) q^{98} +(-1.71338 + 2.14851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) $ 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.104116	+	0.456161i	−0.0736210	+	0.322555i	−0.998306	−	0.0581778i	$-0.981471\pi$
$2$	−0.104116	+	0.456161i	−0.0736210	+	0.322555i	0.924685	+	0.380732i	$0.124328\pi$
$3$	−0.128875	−	0.564637i	−0.0744058	−	0.325993i	0.924003	−	0.382386i	$-0.124897\pi$
$3$	−0.128875	−	0.564637i	−0.0744058	−	0.325993i	−0.998409	+	0.0563923i	$0.982040\pi$
$4$	1.60469	+	0.772780i	0.802347	+	0.386390i
$5$	−2.20664	+	2.76704i	−0.986840	+	1.23746i	−0.0154719	+	0.999880i	$0.504925\pi$
$5$	−2.20664	+	2.76704i	−0.986840	+	1.23746i	−0.971368	+	0.237578i	$0.923646\pi$
$6$	0.270983			0.110628
$7$	0.0588619			0.0222477			0.0111239	−	0.999938i	$-0.496459\pi$
$7$	0.0588619			0.0222477			0.0111239	+	0.999938i	$0.496459\pi$
$8$	−1.10304	+	1.38317i	−0.389983	+	0.489023i
$9$	2.40070	−	1.15612i	0.800234	−	0.385372i
$10$	−1.03247	−	1.29468i	−0.326496	−	0.409413i
$11$	−0.929192	+	0.447475i	−0.280162	+	0.134919i	−0.568688	−	0.822553i	$-0.692549\pi$
$11$	−0.929192	+	0.447475i	−0.280162	+	0.134919i	0.288526	+	0.957472i	$0.406835\pi$
$12$	0.229536	−	1.00566i	0.0662612	−	0.290309i
$13$	−0.588272	+	0.737670i	−0.163157	+	0.204593i	−0.856689	−	0.515833i	$-0.827482\pi$
$13$	−0.588272	+	0.737670i	−0.163157	+	0.204593i	0.693532	+	0.720426i	$0.256054\pi$
$14$	−0.00612846	+	0.0268505i	−0.00163790	+	0.00717610i
$15$	1.84675	+	0.889350i	0.476830	+	0.229629i
$16$	1.70486	+	2.13783i	0.426216	+	0.534458i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$18$	0.277424	+	1.21548i	0.0653896	+	0.286490i
$19$	2.85635	+	1.37554i	0.655291	+	0.315571i	0.731822	−	0.681496i	$-0.238670\pi$
$19$	2.85635	+	1.37554i	0.655291	+	0.315571i	−0.0765313	+	0.997067i	$0.524385\pi$
$20$	−5.67930	+	2.73501i	−1.26993	+	0.611566i
$21$	−0.00758581	−	0.0332356i	−0.00165536	−	0.00725261i
$22$	−0.107377	−	0.470450i	−0.0228929	−	0.100300i
$23$	−6.68129	+	3.21754i	−1.39315	+	0.670903i	−0.971759	−	0.235977i	$-0.924171\pi$
$23$	−6.68129	+	3.21754i	−1.39315	+	0.670903i	−0.421387	+	0.906881i	$0.638457\pi$
$24$	0.923140	+	0.444561i	0.188435	+	0.0907456i
$25$	−1.67465	−	7.33710i	−0.334929	−	1.46742i
$26$	−0.275248	−	0.345150i	−0.0539805	−	0.0676895i
$27$	−2.04547	−	2.56494i	−0.393651	−	0.493623i
$28$	0.0944555	+	0.0454874i	0.0178504	+	0.00859630i
$29$	−2.30095	+	10.0811i	−0.427275	+	1.87201i	0.0590809	+	0.998253i	$0.481183\pi$
$29$	−2.30095	+	10.0811i	−0.427275	+	1.87201i	−0.486356	+	0.873761i	$0.661674\pi$
$30$	−0.597963	+	0.749822i	−0.109173	+	0.136898i
$31$	−0.157212	+	0.688790i	−0.0282361	+	0.123710i	−0.987082	−	0.160217i	$-0.948780\pi$
$31$	−0.157212	+	0.688790i	−0.0282361	+	0.123710i	0.958846	+	0.283928i	$0.0916376\pi$
$32$	−4.34057	+	2.09031i	−0.767312	+	0.369518i
$33$	0.372410	+	0.466988i	0.0648283	+	0.0812921i
$34$	−0.421556	+	0.203011i	−0.0722963	+	0.0348161i
$35$	−0.129887	+	0.162873i	−0.0219549	+	0.0275306i
$36$	4.74582			0.790969
$37$	−3.30551			−0.543423			−0.271711	−	0.962379i	$-0.587590\pi$
$37$	−3.30551			−0.543423			−0.271711	+	0.962379i	$0.587590\pi$
$38$	−0.924860	+	1.15974i	−0.150032	+	0.188134i
$39$	0.492329	+	0.237093i	0.0788357	+	0.0379653i
$40$	−1.39327	−	6.10431i	−0.220295	−	0.965175i
$41$	1.80556	−	7.91067i	0.281981	−	1.23544i	−0.613269	−	0.789874i	$-0.710146\pi$
$41$	1.80556	−	7.91067i	0.281981	−	1.23544i	0.895250	−	0.445565i	$-0.146997\pi$
$42$	0.0159506			0.00246123
$43$	−3.93062	−	5.24883i	−0.599413	−	0.800440i
$43$	−3.93062	−	5.24883i	−0.599413	−	0.800440i
$44$	−1.83687			−0.276919
$45$	−2.09846	+	9.19397i	−0.312821	+	1.37056i
$46$	−0.772089	−	3.38274i	−0.113838	−	0.498758i
$47$	4.53602	+	2.18443i	0.661646	+	0.318632i	0.734399	−	0.678718i	$-0.237464\pi$
$47$	4.53602	+	2.18443i	0.661646	+	0.318632i	−0.0727528	+	0.997350i	$0.523178\pi$
$48$	0.987385	−	1.23814i	0.142517	−	0.178710i
$49$	−6.99654			−0.999505
$50$	3.52126			0.497981
$51$	0.361099	−	0.452804i	0.0505639	−	0.0634052i
$52$	−1.51405	+	0.729130i	−0.209962	+	0.101112i
$53$	1.54659	+	1.93936i	0.212440	+	0.266392i	0.876622	−	0.481179i	$-0.159791\pi$
$53$	1.54659	+	1.93936i	0.212440	+	0.266392i	−0.664182	+	0.747571i	$0.731220\pi$
$54$	1.38299	−	0.666014i	0.188201	−	0.0906330i
$55$	0.812211	−	3.55853i	0.109519	−	0.479832i
$56$	−0.0649270	+	0.0814158i	−0.00867623	+	0.0108797i
$57$	0.408572	−	1.79007i	0.0541167	−	0.237101i
$58$	−4.35904	−	2.09920i	−0.572370	−	0.275639i
$59$	5.58499	+	7.00335i	0.727104	+	0.911759i	0.998717	−	0.0506476i	$-0.0161285\pi$
$59$	5.58499	+	7.00335i	0.727104	+	0.911759i	−0.271613	+	0.962407i	$0.587557\pi$
$60$	2.27620	+	2.85427i	0.293857	+	0.368485i
$61$	2.87874	+	12.6126i	0.368585	+	1.61488i	0.730670	+	0.682731i	$0.239208\pi$
$61$	2.87874	+	12.6126i	0.368585	+	1.61488i	−0.362085	+	0.932145i	$0.617935\pi$
$62$	−0.297831	−	0.143428i	−0.0378246	−	0.0182154i
$63$	0.141310	−	0.0680513i	0.0178034	−	0.00857365i
$64$	0.715322	+	3.13403i	0.0894153	+	0.391754i
$65$	−0.743057	−	3.25555i	−0.0921649	−	0.403801i
$66$	−0.251795	+	0.121258i	−0.0309939	+	0.0149259i
$67$	8.90339	+	4.28765i	1.08772	+	0.523820i	0.889778	−	0.456394i	$-0.150859\pi$
$67$	8.90339	+	4.28765i	1.08772	+	0.523820i	0.197945	+	0.980213i	$0.436573\pi$
$68$	0.396327	+	1.73642i	0.0480617	+	0.210572i
$69$	2.67779	+	3.35784i	0.322368	+	0.404237i
$70$	−0.0607732	−	0.0762072i	−0.00726379	−	0.00910850i
$71$	−3.28246	−	1.58075i	−0.389556	−	0.187600i	0.228845	−	0.973463i	$-0.426505\pi$
$71$	−3.28246	−	1.58075i	−0.389556	−	0.187600i	−0.618401	+	0.785863i	$0.712219\pi$
$72$	−1.04896	+	4.59581i	−0.123622	+	0.541621i
$73$	1.69384	−	2.12401i	0.198249	−	0.248596i	−0.672763	−	0.739858i	$-0.734893\pi$
$73$	1.69384	−	2.12401i	0.198249	−	0.248596i	0.871012	+	0.491262i	$0.163464\pi$
$74$	0.344156	−	1.50785i	0.0400073	−	0.175284i
$75$	−3.92698	+	1.89113i	−0.453448	+	0.218369i
$76$	3.52057	+	4.41466i	0.403837	+	0.506396i
$77$	−0.0546940	+	0.0263393i	−0.00623296	+	0.00300164i
$78$	−0.159412	+	0.199896i	−0.0180498	+	0.0226338i
$79$	12.3199			1.38609			0.693047	−	0.720892i	$-0.256268\pi$
$79$	12.3199			1.38609			0.693047	+	0.720892i	$0.256268\pi$
$80$	−9.67749			−1.08198
$81$	3.79936	−	4.76425i	0.422151	−	0.529361i
$82$	3.42055	+	1.64725i	0.377737	+	0.181908i
$83$	−2.61454	−	11.4550i	−0.286983	−	1.25735i	−0.888643	−	0.458600i	$-0.848351\pi$
$83$	−2.61454	−	11.4550i	−0.286983	−	1.25735i	0.601660	−	0.798752i	$-0.294506\pi$
$84$	0.0135109	−	0.0591952i	0.00147416	−	0.00645873i
$85$	−3.53918			−0.383878
$86$	2.80355	−	1.24651i	0.302315	−	0.134414i
$87$	5.98870			0.642056
$88$	0.406002	−	1.77881i	0.0432799	−	0.189622i
$89$	−2.77502	−	12.1581i	−0.294151	−	1.28876i	−0.878689	−	0.477394i	$-0.841581\pi$
$89$	−2.77502	−	12.1581i	−0.294151	−	1.28876i	0.584538	−	0.811366i	$-0.301276\pi$
$90$	−3.97545	−	1.91448i	−0.419049	−	0.201803i
$91$	−0.0346268	+	0.0434207i	−0.00362988	+	0.00455172i
$92$	−13.2079			−1.37702
$93$	0.409177			0.0424297
$94$	−1.46872	+	1.84172i	−0.151487	+	0.189959i
$95$	−10.1091	+	4.86830i	−1.03717	+	0.499477i
$96$	1.73966	+	2.18146i	0.177553	+	0.222644i
$97$	−0.801582	+	0.386021i	−0.0813883	+	0.0391945i	−0.474135	−	0.880452i	$-0.657239\pi$
$97$	−0.801582	+	0.386021i	−0.0813883	+	0.0391945i	0.392747	+	0.919647i	$0.371525\pi$
$98$	0.728450	−	3.19155i	0.0735845	−	0.322395i
$99$	−1.71338	+	2.14851i	−0.172201	+	0.215933i
$100$	2.98267	−	13.0679i	0.298267	−	1.30679i
$101$	12.4063	+	5.97454i	1.23447	+	0.594489i	0.933305	−	0.359083i	$-0.116911\pi$
$101$	12.4063	+	5.97454i	1.23447	+	0.594489i	0.301164	+	0.953572i	$0.402625\pi$
$102$	0.168955	+	0.211863i	0.0167291	+	0.0209776i
$103$	−7.55170	−	9.46953i	−0.744091	−	0.933061i	0.255338	−	0.966852i	$-0.417813\pi$
$103$	−7.55170	−	9.46953i	−0.744091	−	0.933061i	−0.999429	+	0.0337910i	$0.989242\pi$
$104$	−0.371433	−	1.62736i	−0.0364220	−	0.159575i
$105$	0.108704	+	0.0523488i	0.0106084	+	0.00510872i
$106$	−1.04569	+	0.503576i	−0.101566	+	0.0489116i
$107$	2.10621	+	9.22790i	0.203615	+	0.892095i	0.968713	+	0.248182i	$0.0798331\pi$
$107$	2.10621	+	9.22790i	0.203615	+	0.892095i	−0.765099	+	0.643913i	$0.777310\pi$
$108$	−1.30022	−	5.69665i	−0.125114	−	0.548160i
$109$	15.9719	−	7.69164i	1.52983	−	0.736725i	0.535645	−	0.844443i	$-0.320069\pi$
$109$	15.9719	−	7.69164i	1.52983	−	0.736725i	0.994181	+	0.107718i	$0.0343544\pi$
$110$	1.53870	+	0.740998i	0.146709	+	0.0706514i
$111$	0.425997	+	1.86641i	0.0404338	+	0.177152i
$112$	0.100352	+	0.125837i	0.00948233	+	0.0118905i
$113$	12.0971	+	15.1692i	1.13800	+	1.42700i	0.888650	+	0.458587i	$0.151644\pi$
$113$	12.0971	+	15.1692i	1.13800	+	1.42700i	0.249346	+	0.968414i	$0.419784\pi$
$114$	0.774022	+	0.372749i	0.0724938	+	0.0349112i
$115$	5.84015	−	25.5874i	0.544597	−	2.38603i
$116$	−11.4828	+	14.3990i	−1.06615	+	1.33691i
$117$	−0.559433	+	2.45104i	−0.0517196	+	0.226598i
$118$	−3.77614	+	1.81849i	−0.347622	+	0.167406i
$119$	0.0366998	+	0.0460201i	0.00336427	+	0.00421866i
$120$	−3.26716	+	1.57338i	−0.298249	+	0.143629i
$121$	−6.19522	+	7.76857i	−0.563202	+	0.706233i
$122$	−6.05309			−0.548021
$123$	−4.69934			−0.423726
$124$	−0.784561	+	0.983808i	−0.0704556	+	0.0883486i
$125$	8.05395	+	3.87858i	0.720368	+	0.346911i
$126$	0.0163297	+	0.0715453i	0.00145477	+	0.00637376i
$127$	2.03176	−	8.90173i	0.180290	−	0.789900i	−0.801202	−	0.598394i	$-0.795806\pi$
$127$	2.03176	−	8.90173i	0.180290	−	0.789900i	0.981491	−	0.191506i	$-0.0613372\pi$
$128$	−11.1394			−0.984597
$129$	−2.45713	+	2.89581i	−0.216338	+	0.254962i
$130$	1.56242			0.137033
$131$	3.05526	−	13.3860i	0.266940	−	1.16954i	−0.646613	−	0.762818i	$-0.723815\pi$
$131$	3.05526	−	13.3860i	0.266940	−	1.16954i	0.913553	−	0.406721i	$-0.133328\pi$
$132$	0.236726	+	1.03716i	0.0206043	+	0.0902735i
$133$	0.168130	+	0.0809672i	0.0145787	+	0.00702074i
$134$	−2.88284	+	3.61497i	−0.249040	+	0.312286i
$135$	11.6109			0.999309
$136$	−1.76914			−0.151702
$137$	−0.177470	+	0.222540i	−0.0151623	+	0.0190129i	−0.789355	−	0.613937i	$-0.789585\pi$
$137$	−0.177470	+	0.222540i	−0.0151623	+	0.0190129i	0.774193	+	0.632950i	$0.218156\pi$
$138$	−1.81052	+	0.871899i	−0.154121	+	0.0742210i
$139$	−8.73729	−	10.9562i	−0.741087	−	0.929294i	0.258236	−	0.966082i	$-0.416859\pi$
$139$	−8.73729	−	10.9562i	−0.741087	−	0.929294i	−0.999323	+	0.0367880i	$0.988287\pi$
$140$	−0.334295	+	0.160988i	−0.0282531	+	0.0136060i
$141$	0.648832	−	2.84272i	0.0546415	−	0.239400i
$142$	1.06283	−	1.33275i	0.0891908	−	0.111842i
$143$	0.216529	−	0.948674i	0.0181070	−	0.0793321i
$144$	6.56445	+	3.16127i	0.547038	+	0.263439i
$145$	−22.8175	−	28.6122i	−1.89489	−	2.37611i
$146$	0.792534	+	0.993806i	0.0655905	+	0.0822479i
$147$	0.901676	+	3.95050i	0.0743690	+	0.325832i
$148$	−5.30434	−	2.55443i	−0.436014	−	0.209973i
$149$	−9.46072	+	4.55604i	−0.775052	+	0.373246i	−0.779224	−	0.626746i	$-0.784386\pi$
$149$	−9.46072	+	4.55604i	−0.775052	+	0.373246i	0.00417149	+	0.999991i	$0.498672\pi$
$150$	−0.453801	−	1.98823i	−0.0370527	−	0.162338i
$151$	1.67058	+	7.31930i	0.135950	+	0.595636i	0.996301	+	0.0859339i	$0.0273874\pi$
$151$	1.67058	+	7.31930i	0.135950	+	0.595636i	−0.860351	+	0.509702i	$0.829755\pi$
$152$	−5.05326	+	2.43352i	−0.409874	+	0.197385i
$153$	2.40070	+	1.15612i	0.194085	+	0.0934665i
$154$	−0.00632043	−	0.0276916i	−0.000509315	−	0.00223145i
$155$	−1.55900	−	1.95493i	−0.125222	−	0.157023i
$156$	0.606817	+	0.760924i	0.0485842	+	0.0609227i
$157$	19.4352	+	9.35951i	1.55110	+	0.746970i	0.996375	−	0.0850647i	$-0.0271097\pi$
$157$	19.4352	+	9.35951i	1.55110	+	0.746970i	0.554724	+	0.832035i	$0.312824\pi$
$158$	−1.28269	+	5.61985i	−0.102046	+	0.447091i
$159$	0.895719	−	1.12320i	0.0710351	−	0.0890752i
$160$	3.79412	−	16.6231i	0.299951	−	1.31417i
$161$	−0.393274	+	0.189391i	−0.0309943	+	0.0149261i
$162$	1.77769	+	2.22915i	0.139669	+	0.175139i
$163$	16.1006	−	7.75362i	1.26109	−	0.607310i	0.320629	−	0.947205i	$-0.396106\pi$
$163$	16.1006	−	7.75362i	1.26109	−	0.607310i	0.940464	+	0.339894i	$0.110391\pi$
$164$	9.01058	−	11.2989i	0.703608	−	0.882297i
$165$	−2.11395			−0.164571
$166$	5.49755			0.426693
$167$	12.5731	−	15.7662i	0.972935	−	1.22002i	−0.00255962	−	0.999997i	$-0.500815\pi$
$167$	12.5731	−	15.7662i	0.972935	−	1.22002i	0.975494	−	0.220025i	$-0.0706138\pi$
$168$	0.0543378	+	0.0261677i	0.00419225	+	0.00201888i
$169$	2.69468	+	11.8062i	0.207283	+	0.908166i
$170$	0.368484	−	1.61444i	0.0282615	−	0.123822i
$171$	8.44752			0.645998
$172$	−2.25124	−	11.4603i	−0.171656	−	0.873838i
$173$	−6.44320			−0.489867			−0.244934	−	0.969540i	$-0.578766\pi$
$173$	−6.44320			−0.489867			−0.244934	+	0.969540i	$0.578766\pi$
$174$	−0.623518	+	2.73181i	−0.0472688	+	0.207098i
$175$	−0.0985729	−	0.431876i	−0.00745141	−	0.0326468i
$176$	−2.54077	−	1.22357i	−0.191518	−	0.0922302i
$177$	3.23459	−	4.05604i	0.243126	−	0.304871i
$178$	5.83499			0.437351
$179$	21.3548			1.59613			0.798067	−	0.602569i	$-0.205856\pi$
$179$	21.3548			1.59613			0.798067	+	0.602569i	$0.205856\pi$
$180$	−10.4723	+	13.1319i	−0.780560	+	0.978792i
$181$	0.555537	−	0.267533i	0.0412928	−	0.0198855i	−0.413123	−	0.910675i	$-0.635562\pi$
$181$	0.555537	−	0.267533i	0.0412928	−	0.0198855i	0.454416	+	0.890789i	$0.349848\pi$
$182$	−0.0162016	−	0.0203162i	−0.00120094	−	0.00150594i
$183$	6.75053	−	3.25089i	0.499014	−	0.240312i
$184$	2.91933	−	12.7904i	0.215216	−	0.942921i
$185$	7.29408	−	9.14649i	0.536272	−	0.672463i
$186$	−0.0426018	+	0.186651i	−0.00312371	+	0.0136859i
$187$	−0.929192	−	0.447475i	−0.0679492	−	0.0327226i
$188$	5.59084	+	7.01069i	0.407754	+	0.511307i
$189$	−0.120400	−	0.150977i	−0.00875784	−	0.0109820i
$190$	−1.16821	−	5.11825i	−0.0847507	−	0.371317i
$191$	−13.8688	−	6.67886i	−1.00351	−	0.483265i	−0.141382	−	0.989955i	$-0.545155\pi$
$191$	−13.8688	−	6.67886i	−1.00351	−	0.483265i	−0.862129	+	0.506690i	$0.830869\pi$
$192$	1.67740	−	0.807794i	0.121056	−	0.0582975i
$193$	1.48176	+	6.49202i	0.106660	+	0.467306i	0.999845	+	0.0176171i	$0.00560798\pi$
$193$	1.48176	+	6.49202i	0.106660	+	0.467306i	−0.893185	+	0.449689i	$0.851535\pi$
$194$	−0.0926306	−	0.405841i	−0.00665049	−	0.0291377i
$195$	−1.74244	+	0.839115i	−0.124779	+	0.0600903i
$196$	−11.2273	−	5.40679i	−0.801950	−	0.386199i
$197$	−5.68420	−	24.9041i	−0.404983	−	1.77435i	−0.606730	−	0.794908i	$-0.707519\pi$
$197$	−5.68420	−	24.9041i	−0.404983	−	1.77435i	0.201747	−	0.979438i	$-0.435338\pi$
$198$	−0.801676	−	1.00527i	−0.0569726	−	0.0714414i
$199$	−0.913043	−	1.14492i	−0.0647239	−	0.0811612i	0.748416	−	0.663230i	$-0.230815\pi$
$199$	−0.913043	−	1.14492i	−0.0647239	−	0.0811612i	−0.813140	+	0.582069i	$0.802243\pi$
$200$	11.9956	+	5.77679i	0.848219	+	0.408481i
$201$	1.27354	−	5.57975i	0.0898287	−	0.393565i
$202$	−4.01704	+	5.03721i	−0.282638	+	0.354417i
$203$	−0.135438	+	0.593393i	−0.00950590	+	0.0416480i
$204$	0.929371	−	0.447562i	0.0650690	−	0.0313356i
$205$	17.9049	+	22.4521i	1.25053	+	1.56812i
$206$	5.10588	−	2.45886i	0.355744	−	0.171317i
$207$	−12.3199	+	15.4487i	−0.856294	+	1.07376i
$208$	−2.57994			−0.178886
$209$	−3.26961			−0.226164
$210$	−0.0351973	+	0.0441360i	−0.00242884	+	0.00304567i
$211$	6.47125	+	3.11639i	0.445499	+	0.214541i	0.643164	−	0.765729i	$-0.277621\pi$
$211$	6.47125	+	3.11639i	0.445499	+	0.214541i	−0.197665	+	0.980270i	$0.563336\pi$
$212$	0.983103	+	4.30726i	0.0675198	+	0.295824i
$213$	−0.469523	+	2.05711i	−0.0321712	+	0.140951i
$214$	−4.42870			−0.302740
$215$	23.1972	+	0.706118i	1.58204	+	0.0481568i
$216$	5.80397			0.394910
$217$	−0.00925380	+	0.0405435i	−0.000628189	+	0.00275227i
$218$	1.84570	+	8.08656i	0.125007	+	0.547691i
$219$	−1.41758	−	0.682673i	−0.0957915	−	0.0461308i
$220$	4.05331	−	5.08269i	0.273274	−	0.342675i
$221$	−0.943515			−0.0634677
$222$	−0.895738			−0.0601180
$223$	1.66757	−	2.09106i	0.111668	−	0.140028i	−0.722856	−	0.690999i	$-0.757171\pi$
$223$	1.66757	−	2.09106i	0.111668	−	0.140028i	0.834524	+	0.550971i	$0.185742\pi$
$224$	−0.255494	+	0.123040i	−0.0170709	+	0.00822093i
$225$	−12.5029	−	15.6781i	−0.833524	−	1.04521i
$226$	−8.17911	+	3.93885i	−0.544066	+	0.262008i
$227$	1.90071	−	8.32756i	0.126155	−	0.552719i	−0.871861	−	0.489753i	$-0.837087\pi$
$227$	1.90071	−	8.32756i	0.126155	−	0.552719i	0.998016	−	0.0629660i	$-0.0200560\pi$
$228$	2.03896	−	2.55678i	0.135034	−	0.169327i
$229$	2.70956	−	11.8714i	0.179053	−	0.784482i	−0.803016	−	0.595958i	$-0.796773\pi$
$229$	2.70956	−	11.8714i	0.179053	−	0.784482i	0.982069	−	0.188524i	$-0.0603703\pi$
$230$	11.0639	+	5.32810i	0.729533	+	0.351324i
$231$	0.0219208	+	0.0274878i	0.00144228	+	0.00180856i
$232$	−11.4058	−	14.3024i	−0.748828	−	0.939001i
$233$	4.11316	+	18.0209i	0.269462	+	1.18059i	0.910641	+	0.413198i	$0.135588\pi$
$233$	4.11316	+	18.0209i	0.269462	+	1.18059i	−0.641179	+	0.767391i	$0.721554\pi$
$234$	−1.05982	−	0.510383i	−0.0692827	−	0.0333648i
$235$	−16.0538	+	7.73109i	−1.04723	+	0.504321i
$236$	3.55015	+	15.5542i	0.231095	+	1.01249i
$237$	−1.58772	−	6.95626i	−0.103133	−	0.451857i
$238$	−0.0248136	+	0.0119496i	−0.00160843	+	0.000774578i
$239$	14.6031	+	7.03248i	0.944596	+	0.454894i	0.841788	−	0.539808i	$-0.181503\pi$
$239$	14.6031	+	7.03248i	0.944596	+	0.454894i	0.102808	+	0.994701i	$0.467217\pi$
$240$	1.24718	+	5.46427i	0.0805054	+	0.352717i
$241$	5.16124	+	6.47199i	0.332465	+	0.416897i	0.919764	−	0.392473i	$-0.128380\pi$
$241$	5.16124	+	6.47199i	0.332465	+	0.416897i	−0.587299	+	0.809370i	$0.699809\pi$
$242$	−2.89870	−	3.63485i	−0.186335	−	0.233657i
$243$	−12.0471	−	5.80157i	−0.772821	−	0.372171i
$244$	−5.12726	+	22.4640i	−0.328239	+	1.43811i
$245$	15.4388	−	19.3597i	0.986352	−	1.23685i
$246$	0.489276	−	2.14366i	0.0311951	−	0.136675i
$247$	−2.69501	+	1.29785i	−0.171479	+	0.0825800i
$248$	−0.779301	−	0.977212i	−0.0494857	−	0.0620530i
$249$	−6.13098	+	2.95253i	−0.388535	+	0.187109i
$250$	−2.60780	+	3.27008i	−0.164932	+	0.206818i
$251$	15.2616			0.963307			0.481653	−	0.876362i	$-0.340036\pi$
$251$	15.2616			0.963307			0.481653	+	0.876362i	$0.340036\pi$
$252$	0.279348			0.0175973
$253$	4.76843	−	5.97942i	0.299789	−	0.375923i
$254$	3.84908	+	1.85362i	0.241513	+	0.116306i
$255$	0.456110	+	1.99835i	0.0285627	+	0.125142i
$256$	−0.270853	+	1.18668i	−0.0169283	+	0.0741677i
$257$	1.16632			0.0727528			0.0363764	−	0.999338i	$-0.488418\pi$
$257$	1.16632			0.0727528			0.0363764	+	0.999338i	$0.488418\pi$
$258$	−1.06513	−	1.42235i	−0.0663122	−	0.0885514i
$259$	−0.194569			−0.0120899
$260$	1.32344	−	5.79838i	0.0820764	−	0.359600i
$261$	6.13105	+	26.8619i	0.379502	+	1.66271i
$262$	5.78806	+	2.78738i	0.357588	+	0.172205i
$263$	−7.09558	+	8.89757i	−0.437532	+	0.548648i	−0.950891	−	0.309526i	$-0.899830\pi$
$263$	−7.09558	+	8.89757i	−0.437532	+	0.548648i	0.513359	+	0.858174i	$0.328401\pi$
$264$	−1.05670			−0.0650357
$265$	−8.77906			−0.539294
$266$	−0.0544391	+	0.0682644i	−0.00333787	+	0.00418556i
$267$	−6.50730	+	3.13375i	−0.398240	+	0.191782i
$268$	10.9738	+	13.7607i	0.670333	+	0.840571i
$269$	6.43083	−	3.09693i	0.392095	−	0.188823i	−0.227440	−	0.973792i	$-0.573036\pi$
$269$	6.43083	−	3.09693i	0.392095	−	0.188823i	0.619535	+	0.784969i	$0.287321\pi$
$270$	−1.20888	+	5.29645i	−0.0735701	+	0.322332i
$271$	15.4121	−	19.3262i	0.936218	−	1.17398i	−0.0483242	−	0.998832i	$-0.515388\pi$
$271$	15.4121	−	19.3262i	0.936218	−	1.17398i	0.984542	−	0.175148i	$-0.0560405\pi$
$272$	−0.608459	+	2.66583i	−0.0368932	+	0.161640i
$273$	0.0289794	+	0.0139558i	0.00175392	+	0.000844641i
$274$	−0.0830368	−	0.104125i	−0.00501644	−	0.00629041i
$275$	4.83924	+	6.06821i	0.291817	+	0.365927i
$276$	1.70216	+	7.45766i	0.102458	+	0.448898i
$277$	−26.8397	−	12.9253i	−1.61264	−	0.776607i	−0.612735	−	0.790289i	$-0.709931\pi$
$277$	−26.8397	−	12.9253i	−1.61264	−	0.776607i	−0.999906	+	0.0136816i	$0.995645\pi$
$278$	5.90749	−	2.84490i	0.354308	−	0.170626i
$279$	0.418903	+	1.83533i	0.0250791	+	0.109879i
$280$	−0.0820104	−	0.359311i	−0.00490106	−	0.0214730i
$281$	−29.1314	+	14.0289i	−1.73783	+	0.836896i	−0.754214	+	0.656628i	$0.771982\pi$
$281$	−29.1314	+	14.0289i	−1.73783	+	0.836896i	−0.983618	+	0.180267i	$0.942304\pi$
$282$	1.22918	+	0.591944i	0.0731969	+	0.0352498i
$283$	2.27544	+	9.96937i	0.135261	+	0.592618i	0.996439	+	0.0843143i	$0.0268700\pi$
$283$	2.27544	+	9.96937i	0.135261	+	0.592618i	−0.861178	+	0.508303i	$0.830273\pi$
$284$	−4.04577	−	5.07324i	−0.240072	−	0.301041i
$285$	4.05163	+	5.08058i	0.239998	+	0.300948i
$286$	0.410204	+	0.197544i	0.0242559	+	0.0116810i
$287$	0.106279	−	0.465637i	0.00627343	−	0.0274857i
$288$	−8.00377	+	10.0364i	−0.471627	+	0.591401i
$289$	−0.222521	+	0.974928i	−0.0130895	+	0.0573487i
$290$	15.4274	−	7.42946i	0.905930	−	0.436273i
$291$	0.321265	+	0.402854i	0.0188329	+	0.0236157i
$292$	4.35948	−	2.09942i	0.255120	−	0.122859i
$293$	−12.5911	+	15.7887i	−0.735579	+	0.922387i	−0.999106	−	0.0422652i	$-0.986543\pi$
$293$	−12.5911	+	15.7887i	−0.735579	+	0.922387i	0.263528	+	0.964652i	$0.415114\pi$
$294$	−1.89594			−0.110574
$295$	−31.7026			−1.84580
$296$	3.64611	−	4.57207i	0.211926	−	0.265746i
$297$	3.04838	+	1.46802i	0.176885	+	0.0851834i
$298$	−1.09328	−	4.78997i	−0.0633319	−	0.277475i
$299$	1.55693	−	6.82138i	0.0900398	−	0.394490i
$300$	−7.76303			−0.448199
$301$	−0.231364	−	0.308957i	−0.0133356	−	0.0178080i
$302$	−3.51271			−0.202134
$303$	1.77459	−	7.77500i	0.101948	−	0.446662i
$304$	1.92900	+	8.45150i	0.110636	+	0.484727i
$305$	−41.2519	−	19.8659i	−2.36208	−	1.13752i
$306$	−0.777326	+	0.974736i	−0.0444368	+	0.0557220i
$307$	−9.78098			−0.558230			−0.279115	−	0.960258i	$-0.590041\pi$
$307$	−9.78098			−0.558230			−0.279115	+	0.960258i	$0.590041\pi$
$308$	−0.108122			−0.00616081
$309$	−4.37362	+	5.48435i	−0.248807	+	0.311994i
$310$	1.05408	−	0.507617i	0.0598676	−	0.0288307i
$311$	−3.30124	−	4.13963i	−0.187196	−	0.234737i	0.679373	−	0.733793i	$-0.262252\pi$
$311$	−3.30124	−	4.13963i	−0.187196	−	0.234737i	−0.866570	+	0.499056i	$0.833680\pi$
$312$	−0.870997	+	0.419450i	−0.0493105	+	0.0237467i
$313$	−1.44453	+	6.32892i	−0.0816499	+	0.357732i	−0.999205	−	0.0398780i	$-0.987303\pi$
$313$	−1.44453	+	6.32892i	−0.0816499	+	0.357732i	0.917555	+	0.397610i	$0.130160\pi$
$314$	−6.29295	+	7.89112i	−0.355132	+	0.445321i
$315$	−0.123520	+	0.541175i	−0.00695955	+	0.0304918i
$316$	19.7696	+	9.52056i	1.11213	+	0.535573i
$317$	−8.08627	−	10.1399i	−0.454170	−	0.569512i	0.501046	−	0.865421i	$-0.332949\pi$
$317$	−8.08627	−	10.1399i	−0.454170	−	0.569512i	−0.955216	+	0.295909i	$0.904377\pi$
$318$	0.419100	+	0.525534i	0.0235019	+	0.0294705i
$319$	−2.37302	−	10.3969i	−0.132864	−	0.582114i
$320$	−10.2505	−	4.93636i	−0.573018	−	0.275951i
$321$	4.93898	−	2.37849i	0.275667	−	0.132754i
$322$	−0.0454466	−	0.199115i	−0.00253264	−	0.0110962i
$323$	0.705459	+	3.09082i	0.0392528	+	0.171978i
$324$	9.77853	−	4.70909i	0.543252	−	0.261616i
$325$	6.39750	+	3.08088i	0.354870	+	0.170896i
$326$	1.86058	+	8.15172i	0.103048	+	0.451482i
$327$	−6.40135	−	8.02704i	−0.353995	−	0.443896i
$328$	8.95017	+	11.2232i	0.494190	+	0.619695i
$329$	0.266999	+	0.128580i	0.0147201	+	0.00708884i
$330$	0.220096	−	0.964302i	0.0121159	−	0.0530831i
$331$	−10.0529	+	12.6059i	−0.552558	+	0.692885i	−0.977162	−	0.212494i	$-0.931842\pi$
$331$	−10.0529	+	12.6059i	−0.552558	+	0.692885i	0.424605	+	0.905379i	$0.360413\pi$
$332$	4.65669	−	20.4023i	0.255569	−	1.11972i
$333$	−7.93554	+	3.82156i	−0.434865	+	0.209420i
$334$	5.88285	+	7.37686i	0.321895	+	0.403644i
$335$	−31.5107	+	15.1748i	−1.72161	+	0.829085i
$336$	0.0581194	−	0.0728794i	0.00317067	−	0.00397590i
$337$	−12.6006			−0.686396			−0.343198	−	0.939263i	$-0.611510\pi$
$337$	−12.6006			−0.686396			−0.343198	+	0.939263i	$0.611510\pi$
$338$	−5.66607			−0.308194
$339$	7.00610	−	8.78537i	0.380519	−	0.477156i
$340$	−5.67930	−	2.73501i	−0.308003	−	0.148327i
$341$	−0.162137	−	0.710367i	−0.00878019	−	0.0384685i
$342$	−0.879520	+	3.85343i	−0.0475590	+	0.208370i
$343$	−0.823863			−0.0444844
$344$	11.5956	+	0.352968i	0.625194	+	0.0190308i
$345$	−15.2002			−0.818352
$346$	0.670839	−	2.93914i	0.0360645	−	0.158009i
$347$	7.23799	+	31.7117i	0.388556	+	1.70237i	0.669636	+	0.742690i	$0.266450\pi$
$347$	7.23799	+	31.7117i	0.388556	+	1.70237i	−0.281080	+	0.959684i	$0.590693\pi$
$348$	9.61003	+	4.62795i	0.515152	+	0.248084i
$349$	−10.0170	+	12.5610i	−0.536200	+	0.672374i	−0.973960	−	0.226718i	$-0.927200\pi$
$349$	−10.0170	+	12.5610i	−0.536200	+	0.672374i	0.437760	+	0.899092i	$0.355772\pi$
$350$	0.207268			0.0110789
$351$	3.09537			0.165219
$352$	3.09786	−	3.88460i	0.165117	−	0.207050i
$353$	−1.97846	+	0.952776i	−0.105303	+	0.0507111i	−0.485794	−	0.874074i	$-0.661469\pi$
$353$	−1.97846	+	0.952776i	−0.105303	+	0.0507111i	0.380491	+	0.924785i	$0.375755\pi$
$354$	1.51344	+	1.89779i	0.0804383	+	0.100866i
$355$	11.6172	−	5.59455i	0.616577	−	0.296928i
$356$	4.94252	−	21.6546i	0.261953	−	1.14769i
$357$	0.0212550	−	0.0266529i	0.00112493	−	0.00141062i
$358$	−2.22337	+	9.74124i	−0.117509	+	0.514840i
$359$	22.3741	+	10.7748i	1.18086	+	0.568672i	0.918162	−	0.396206i	$-0.129673\pi$
$359$	22.3741	+	10.7748i	1.18086	+	0.568672i	0.262698	+	0.964878i	$0.415388\pi$
$360$	−10.4021	−	13.0438i	−0.548239	−	0.687470i
$361$	−5.57972	−	6.99674i	−0.293669	−	0.368250i
$362$	0.0641978	+	0.281269i	0.00337416	+	0.0147832i
$363$	5.18483	+	2.49688i	0.272133	+	0.131052i
$364$	−0.0891202	+	0.0429180i	−0.00467117	+	0.00224951i
$365$	2.13952	+	9.37384i	0.111988	+	0.490649i
$366$	0.780090	+	3.41780i	0.0407760	+	0.178651i
$367$	−13.0344	+	6.27705i	−0.680392	+	0.327659i	−0.741961	−	0.670443i	$-0.766104\pi$
$367$	−13.0344	+	6.27705i	−0.680392	+	0.327659i	0.0615689	+	0.998103i	$0.480390\pi$
$368$	−18.2693	−	8.79801i	−0.952350	−	0.458628i
$369$	−4.81105	−	21.0786i	−0.250453	−	1.09731i
$370$	3.41284	+	4.27957i	0.177425	+	0.222484i
$371$	0.0910353	+	0.114155i	0.00472631	+	0.00592661i
$372$	0.656604	+	0.316204i	0.0340433	+	0.0163944i
$373$	−3.18301	+	13.9457i	−0.164810	+	0.722081i	0.823208	+	0.567741i	$0.192182\pi$
$373$	−3.18301	+	13.9457i	−0.164810	+	0.722081i	−0.988018	+	0.154340i	$0.950675\pi$
$374$	0.300864	−	0.377272i	0.0155573	−	0.0195083i
$375$	1.15204	−	5.04741i	0.0594910	−	0.260647i
$376$	−8.02483	+	3.86456i	−0.413849	+	0.199299i
$377$	−6.08294	−	7.62777i	−0.313288	−	0.392850i
$378$	0.0814056	−	0.0392029i	0.00418705	−	0.00201638i
$379$	−3.83499	+	4.80893i	−0.196990	+	0.247018i	−0.870509	−	0.492152i	$-0.836211\pi$
$379$	−3.83499	+	4.80893i	−0.196990	+	0.247018i	0.673519	+	0.739170i	$0.264782\pi$
$380$	−19.9842			−1.02517
$381$	−5.28808			−0.270917
$382$	4.49060	−	5.63103i	0.229759	−	0.288109i
$383$	−8.46022	−	4.07423i	−0.432297	−	0.208183i	0.205064	−	0.978749i	$-0.434260\pi$
$383$	−8.46022	−	4.07423i	−0.432297	−	0.208183i	−0.637361	+	0.770565i	$0.719974\pi$
$384$	1.43559	+	6.28974i	0.0732597	+	0.320972i
$385$	0.0478083	−	0.209462i	0.00243654	−	0.0106752i
$386$	−3.11568			−0.158584
$387$	−15.5045	−	8.05663i	−0.788138	−	0.409541i
$388$	−1.58460			−0.0804461
$389$	2.98527	−	13.0793i	0.151359	−	0.663149i	−0.841131	−	0.540831i	$-0.818110\pi$
$389$	2.98527	−	13.0793i	0.151359	−	0.663149i	0.992491	−	0.122318i	$-0.0390329\pi$
$390$	−0.201356	−	0.882198i	−0.0101961	−	0.0446718i
$391$	−6.68129	−	3.21754i	−0.337887	−	0.162718i
$392$	7.71745	−	9.67737i	0.389790	−	0.488781i
$393$	−7.95197			−0.401124
$394$	11.9521			0.602139
$395$	−27.1856	+	34.0896i	−1.36785	+	1.71523i
$396$	−4.40977	+	2.12364i	−0.221599	+	0.106717i
$397$	3.47732	+	4.36042i	0.174522	+	0.218843i	0.861397	−	0.507932i	$-0.169590\pi$
$397$	3.47732	+	4.36042i	0.174522	+	0.218843i	−0.686876	+	0.726775i	$0.741018\pi$
$398$	0.617330	−	0.297290i	0.0309439	−	0.0149018i
$399$	0.0240493	−	0.105367i	0.00120397	−	0.00527495i
$400$	12.8304	−	16.0889i	0.641522	−	0.804443i
$401$	6.37487	−	27.9301i	0.318346	−	1.39476i	−0.522108	−	0.852880i	$-0.674854\pi$
$401$	6.37487	−	27.9301i	0.318346	−	1.39476i	0.840453	−	0.541884i	$-0.182289\pi$
$402$	2.41267	+	1.16188i	0.120333	+	0.0579493i
$403$	−0.415617	−	0.521167i	−0.0207033	−	0.0259612i
$404$	15.2913	+	19.1746i	0.760768	+	0.953973i
$405$	4.79904	+	21.0260i	0.238466	+	1.04479i
$406$	−0.256582	−	0.123563i	−0.0127339	−	0.00613234i
$407$	3.07145	−	1.47913i	0.152246	−	0.0733180i
$408$	0.227997	+	0.998919i	0.0112875	+	0.0494539i
$409$	−5.90427	−	25.8683i	−0.291947	−	1.27911i	−0.881811	−	0.471603i	$-0.843676\pi$
$409$	−5.90427	−	25.8683i	−0.291947	−	1.27911i	0.589864	−	0.807503i	$-0.299181\pi$
$410$	−12.1059	+	5.82992i	−0.597870	+	0.287919i
$411$	0.148526	+	0.0715263i	0.00732624	+	0.00352813i
$412$	−4.80031	−	21.0315i	−0.236494	−	1.03615i
$413$	0.328743	+	0.412231i	0.0161764	+	0.0202846i
$414$	−5.76440	−	7.22832i	−0.283305	−	0.355253i
$415$	37.4659	+	18.0426i	1.83913	+	0.885677i
$416$	1.01148	−	4.43158i	0.0495918	−	0.217276i
$417$	−5.06027	+	6.34537i	−0.247802	+	0.310734i
$418$	0.340419	−	1.49147i	0.0166504	−	0.0729502i
$419$	−11.5050	+	5.54053i	−0.562058	+	0.270673i	−0.693266	−	0.720682i	$-0.743829\pi$
$419$	−11.5050	+	5.54053i	−0.562058	+	0.270673i	0.131208	+	0.991355i	$0.458114\pi$
$420$	0.133982	+	0.168008i	0.00653764	+	0.00819794i
$421$	2.88359	−	1.38866i	0.140538	−	0.0676793i	−0.362293	−	0.932064i	$-0.618006\pi$
$421$	2.88359	−	1.38866i	0.140538	−	0.0676793i	0.502831	+	0.864385i	$0.332292\pi$
$422$	−2.09533	+	2.62747i	−0.101999	+	0.127903i
$423$	13.4151			0.652263
$424$	−4.38841			−0.213120
$425$	4.69225	−	5.88390i	0.227608	−	0.285411i
$426$	−0.889490	−	0.428356i	−0.0430960	−	0.0207539i
$427$	0.169448	+	0.742401i	0.00820018	+	0.0359273i
$428$	−3.75132	+	16.4356i	−0.181327	+	0.794445i
$429$	−0.563561			−0.0272090
$430$	−2.73730	+	10.5081i	−0.132004	+	0.506748i
$431$	2.96238			0.142693			0.0713465	−	0.997452i	$-0.477270\pi$
$431$	2.96238			0.142693			0.0713465	+	0.997452i	$0.477270\pi$
$432$	1.99616	−	8.74575i	0.0960403	−	0.420780i
$433$	−2.91930	−	12.7903i	−0.140293	−	0.614662i	−0.995366	−	0.0961558i	$-0.969345\pi$
$433$	−2.91930	−	12.7903i	−0.140293	−	0.614662i	0.855074	−	0.518507i	$-0.173512\pi$
$434$	−0.0175309	−	0.00844244i	−0.000841511	−	0.000405250i
$435$	−13.2149	+	16.5710i	−0.633606	+	0.794517i
$436$	31.5739			1.51212
$437$	−23.5099			−1.12463
$438$	0.459002	−	0.575570i	0.0219320	−	0.0275018i
$439$	7.74345	−	3.72905i	0.369575	−	0.177978i	−0.239872	−	0.970804i	$-0.577106\pi$
$439$	7.74345	−	3.72905i	0.369575	−	0.177978i	0.609447	+	0.792827i	$0.291391\pi$
$440$	4.02614	+	5.04862i	0.191939	+	0.240683i
$441$	−16.7966	+	8.08881i	−0.799837	+	0.385181i
$442$	0.0982348	−	0.430395i	0.00467255	−	0.0204718i
$443$	16.1031	−	20.1926i	0.765079	−	0.959379i	−0.234840	−	0.972034i	$-0.575457\pi$
$443$	16.1031	−	20.1926i	0.765079	−	0.959379i	0.999920	+	0.0126546i	$0.00402819\pi$
$444$	−0.758733	+	3.32423i	−0.0360079	+	0.157761i
$445$	39.7655	+	19.1501i	1.88507	+	0.907801i
$446$	0.780241	+	0.978391i	0.0369455	+	0.0463281i
$447$	3.79176	+	4.75471i	0.179344	+	0.224890i
$448$	0.0421053	+	0.184475i	0.00198929	+	0.00871563i
$449$	24.3576	+	11.7300i	1.14951	+	0.553573i	0.908886	−	0.417046i	$-0.136934\pi$
$449$	24.3576	+	11.7300i	1.14951	+	0.553573i	0.240621	+	0.970619i	$0.422649\pi$
$450$	8.45348	−	4.07098i	0.398501	−	0.191908i
$451$	1.86212	+	8.15847i	0.0876837	+	0.384167i
$452$	7.68960	+	33.6904i	0.361689	+	1.58466i
$453$	3.91745	−	1.88655i	0.184058	−	0.0886376i
$454$	3.60081	+	1.73406i	0.168994	+	0.0813835i
$455$	−0.0437378	−	0.191628i	−0.00205046	−	0.00898365i
$456$	2.02529	+	2.53964i	0.0948431	+	0.118930i
$457$	10.5117	+	13.1812i	0.491715	+	0.616592i	0.964338	−	0.264673i	$-0.0852641\pi$
$457$	10.5117	+	13.1812i	0.491715	+	0.616592i	−0.472623	+	0.881265i	$0.656693\pi$
$458$	5.13314	+	2.47199i	0.239856	+	0.115509i
$459$	0.730020	−	3.19843i	0.0340744	−	0.149290i
$460$	29.1451	−	36.5468i	1.35890	−	1.70400i
$461$	−1.25495	+	5.49830i	−0.0584489	+	0.256081i	−0.995708	−	0.0925528i	$-0.970497\pi$
$461$	−1.25495	+	5.49830i	−0.0584489	+	0.256081i	0.937259	+	0.348634i	$0.113354\pi$
$462$	−0.0148212	+	0.00713750i	−0.000689543	+	0.000332066i
$463$	−2.06328	−	2.58727i	−0.0958885	−	0.120240i	0.731572	−	0.681764i	$-0.238787\pi$
$463$	−2.06328	−	2.58727i	−0.0958885	−	0.120240i	−0.827461	+	0.561523i	$0.810215\pi$
$464$	−25.4745	+	12.2679i	−1.18262	+	0.569522i
$465$	−0.902907	+	1.13221i	−0.0418713	+	0.0525050i
$466$	−8.64869			−0.400643
$467$	31.1173			1.43994			0.719968	−	0.694007i	$-0.244156\pi$
$467$	31.1173			1.43994			0.719968	+	0.694007i	$0.244156\pi$
$468$	−2.79183	+	3.50085i	−0.129052	+	0.161827i
$469$	0.524071	+	0.252379i	0.0241994	+	0.0116538i
$470$	−1.85517	−	8.12804i	−0.0855727	−	0.374918i
$471$	2.78001	−	12.1800i	0.128096	−	0.561227i
$472$	−15.8473			−0.729429
$473$	6.00102	+	3.11832i	0.275927	+	0.143381i
$474$	3.33848			0.153341
$475$	5.30914	−	23.2608i	0.243600	−	1.06728i
$476$	0.0233286	+	0.102209i	0.00106926	+	0.00468475i
$477$	5.95503	+	2.86779i	0.272662	+	0.131307i
$478$	−4.72836	+	5.92917i	−0.216270	+	0.271194i
$479$	13.8274			0.631791			0.315895	−	0.948794i	$-0.397695\pi$
$479$	13.8274			0.631791			0.315895	+	0.948794i	$0.397695\pi$
$480$	−9.87498			−0.450729
$481$	1.94454	−	2.43838i	0.0886634	−	0.111180i
$482$	−3.48964	+	1.68052i	−0.158949	+	0.0765456i
$483$	0.157620	+	0.197649i	0.00717196	+	0.00899335i
$484$	−15.9448	+	7.67863i	−0.724765	+	0.349029i
$485$	0.700667	−	3.06982i	0.0318156	−	0.139393i
$486$	3.90074	−	4.89138i	0.176941	−	0.221877i
$487$	−1.86181	+	8.15710i	−0.0843665	+	0.369634i	−0.999433	−	0.0336692i	$-0.989281\pi$
$487$	−1.86181	+	8.15710i	−0.0843665	+	0.369634i	0.915067	+	0.403303i	$0.132138\pi$
$488$	−20.6207	−	9.93039i	−0.933454	−	0.449528i
$489$	−6.45293	−	8.09172i	−0.291812	−	0.365920i
$490$	7.22371	+	9.05825i	0.326334	+	0.409210i
$491$	1.22218	+	5.35474i	0.0551564	+	0.241656i	0.994990	−	0.0999775i	$-0.0318771\pi$
$491$	1.22218	+	5.35474i	0.0551564	+	0.241656i	−0.939833	+	0.341633i	$0.889020\pi$
$492$	−7.54101	−	3.63156i	−0.339975	−	0.163723i
$493$	−9.31634	+	4.48651i	−0.419587	+	0.202062i
$494$	−0.311434	−	1.36448i	−0.0140121	−	0.0613910i
$495$	−2.16420	−	9.48198i	−0.0972735	−	0.426183i
$496$	−1.74054	+	0.838201i	−0.0781527	+	0.0376363i
$497$	−0.193212	−	0.0930459i	−0.00866673	−	0.00417368i
$498$	−0.708495	−	3.10412i	−0.0317484	−	0.139099i
$499$	6.00725	+	7.53285i	0.268921	+	0.337217i	0.897895	−	0.440210i	$-0.145096\pi$
$499$	6.00725	+	7.53285i	0.268921	+	0.337217i	−0.628973	+	0.777427i	$0.716525\pi$
$500$	9.92685	+	12.4479i	0.443942	+	0.556686i
$501$	−10.5225	−	5.06737i	−0.470111	−	0.226393i
$502$	−1.58898	+	6.96177i	−0.0709196	+	0.310719i
$503$	−6.54572	+	8.20807i	−0.291859	+	0.365980i	−0.906045	−	0.423182i	$-0.860913\pi$
$503$	−6.54572	+	8.20807i	−0.291859	+	0.365980i	0.614186	+	0.789162i	$0.289485\pi$
$504$	−0.0617440	+	0.270518i	−0.00275030	+	0.0120498i
$505$	−43.9080	+	21.1450i	−1.95388	+	0.940939i
$506$	2.23111	+	2.79773i	0.0991850	+	0.124374i
$507$	6.31892	−	3.04303i	0.280633	−	0.135146i
$508$	10.1394	−	12.7144i	0.449865	−	0.564112i
$509$	−7.94408			−0.352115			−0.176057	−	0.984380i	$-0.556334\pi$
$509$	−7.94408			−0.352115			−0.176057	+	0.984380i	$0.556334\pi$
$510$	−0.959058			−0.0424678
$511$	0.0997026	−	0.125023i	0.00441058	−	0.00553070i
$512$	−20.5857	−	9.91355i	−0.909768	−	0.438121i
$513$	−2.31439	−	10.1400i	−0.102183	−	0.447692i
$514$	−0.121432	+	0.532028i	−0.00535613	+	0.0234667i
$515$	42.8665			1.88892
$516$	−6.18077	+	2.74808i	−0.272093	+	0.120977i
$517$	−5.19231			−0.228358
$518$	0.0202577	−	0.0887547i	0.000890072	−	0.00389966i
$519$	0.830365	+	3.63807i	0.0364490	+	0.159693i
$520$	5.32258	+	2.56322i	0.233411	+	0.112405i
$521$	1.80744	−	2.26645i	0.0791853	−	0.0992952i	−0.740661	−	0.671879i	$-0.765487\pi$
$521$	1.80744	−	2.26645i	0.0791853	−	0.0992952i	0.819846	+	0.572584i	$0.194059\pi$
$522$	−12.8917			−0.564253
$523$	24.4323			1.06835			0.534174	−	0.845374i	$-0.320623\pi$
$523$	24.4323			1.06835			0.534174	+	0.845374i	$0.320623\pi$
$524$	15.2472	−	19.1194i	0.666077	−	0.835234i
$525$	−0.231150	+	0.111316i	−0.0100882	+	0.00485822i
$526$	−3.31996	−	4.16310i	−0.144757	−	0.181520i
$527$	−0.636538	+	0.306541i	−0.0277280	+	0.0133531i
$528$	−0.363432	+	1.59230i	−0.0158164	+	0.0692960i
$529$	19.9468	−	25.0125i	0.867253	−	1.08750i
$530$	0.914039	−	4.00467i	0.0397033	−	0.173952i
$531$	21.5046	+	10.3561i	0.933219	+	0.449415i
$532$	0.207228	+	0.259855i	0.00898446	+	0.0112662i
$533$	4.77330	+	5.98553i	0.206755	+	0.259262i
$534$	−0.751983	−	3.29465i	−0.0325415	−	0.142573i
$535$	−30.1816	−	14.5347i	−1.30487	−	0.628391i
$536$	−15.7513	+	7.58543i	−0.680353	+	0.327641i
$537$	−2.75210	−	12.0577i	−0.118762	−	0.520329i
$538$	0.743146	+	3.25593i	0.0320393	+	0.140373i
$539$	6.50112	−	3.13078i	0.280023	−	0.134852i
$540$	18.6320	+	8.97269i	0.801793	+	0.386123i
$541$	−0.222166	−	0.973373i	−0.00955167	−	0.0418486i	0.969928	−	0.243394i	$-0.0782608\pi$
$541$	−0.222166	−	0.973373i	−0.00955167	−	0.0418486i	−0.979479	+	0.201545i	$0.935404\pi$
$542$	7.21120	+	9.04255i	0.309747	+	0.388411i
$543$	−0.222653	−	0.279199i	−0.00955498	−	0.0119816i
$544$	−4.34057	−	2.09031i	−0.186100	−	0.0896213i
$545$	−13.9611	+	61.1675i	−0.598027	+	2.62013i
$546$	−0.00938329	+	0.0117663i	−0.000401568	+	0.000503550i
$547$	−1.18056	+	5.17239i	−0.0504773	+	0.221155i	−0.993875	−	0.110507i	$-0.964752\pi$
$547$	−1.18056	+	5.17239i	−0.0504773	+	0.221155i	0.943398	+	0.331663i	$0.107610\pi$
$548$	−0.456760	+	0.219964i	−0.0195118	+	0.00939640i
$549$	21.4926	+	26.9509i	0.917282	+	1.15024i
$550$	−3.27192	+	1.57567i	−0.139515	+	0.0671870i
$551$	−20.4393	+	25.6301i	−0.870743	+	1.09188i
$552$	−7.59816			−0.323399
$553$	0.725172			0.0308374
$554$	8.69046	−	10.8975i	0.369222	−	0.462990i
$555$	−6.10447	−	2.93976i	−0.259120	−	0.124786i
$556$	−5.55394	−	24.3334i	−0.235539	−	1.03197i
$557$	0.120369	−	0.527369i	0.00510018	−	0.0223453i	−0.972314	−	0.233679i	$-0.924924\pi$
$557$	0.120369	−	0.527369i	0.00510018	−	0.0223453i	0.977414	+	0.211334i	$0.0677807\pi$
$558$	−0.880823			−0.0372882
$559$	6.18418	+	0.188245i	0.261563	+	0.00796191i
$560$	−0.569636			−0.0240715
$561$	−0.132912	+	0.582324i	−0.00561154	+	0.0245857i
$562$	−3.36642	−	14.7492i	−0.142004	−	0.622159i
$563$	33.1632	+	15.9706i	1.39766	+	0.673080i	0.972686	−	0.232124i	$-0.0745675\pi$
$563$	33.1632	+	15.9706i	1.39766	+	0.673080i	0.424978	+	0.905204i	$0.360282\pi$
$564$	3.23798	−	4.06029i	0.136343	−	0.170969i
$565$	−68.6678			−2.88887
$566$	−4.78455			−0.201110
$567$	0.223638	−	0.280433i	0.00939190	−	0.0117771i
$568$	5.80711	−	2.79656i	0.243661	−	0.117341i
$569$	−1.10801	−	1.38940i	−0.0464503	−	0.0582468i	0.758064	−	0.652180i	$-0.226146\pi$
$569$	−1.10801	−	1.38940i	−0.0464503	−	0.0582468i	−0.804514	+	0.593934i	$0.797574\pi$
$570$	−2.73940	+	1.31923i	−0.114741	+	0.0552563i
$571$	−3.32855	+	14.5833i	−0.139296	+	0.610294i	0.856295	+	0.516487i	$0.172761\pi$
$571$	−3.32855	+	14.5833i	−0.139296	+	0.610294i	−0.995590	+	0.0938065i	$0.970097\pi$
$572$	1.08058	−	1.35500i	0.0451813	−	0.0566555i
$573$	−1.98379	+	8.69157i	−0.0828742	+	0.363096i
$574$	0.201340	+	0.0969604i	0.00840378	+	0.00404705i
$575$	34.7962	+	43.6331i	1.45110	+	1.81962i
$576$	5.34058	+	6.69687i	0.222524	+	0.279036i
$577$	0.650297	+	2.84914i	0.0270722	+	0.118611i	0.986659	−	0.162803i	$-0.0520536\pi$
$577$	0.650297	+	2.84914i	0.0270722	+	0.118611i	−0.959586	+	0.281414i	$0.909196\pi$
$578$	−0.421556	−	0.203011i	−0.0175344	−	0.00844413i
$579$	3.47467	−	1.67331i	0.144402	−	0.0695406i
$580$	−14.5041	−	63.5467i	−0.602251	−	2.63864i
$581$	−0.153897	−	0.674265i	−0.00638471	−	0.0279732i
$582$	−0.217215	+	0.104605i	−0.00900386	+	0.00433603i
$583$	−2.30489	−	1.10998i	−0.0954590	−	0.0459706i
$584$	1.06949	+	4.68572i	0.0442556	+	0.193896i
$585$	−5.54765	−	6.95653i	−0.229367	−	0.287617i
$586$	−5.89127	−	7.38742i	−0.243366	−	0.305171i
$587$	−31.3910	−	15.1171i	−1.29564	−	0.623949i	−0.346281	−	0.938131i	$-0.612555\pi$
$587$	−31.3910	−	15.1171i	−1.29564	−	0.623949i	−0.949363	+	0.314182i	$0.898270\pi$
$588$	−1.60595	+	7.03615i	−0.0662285	+	0.290166i
$589$	−1.39651	+	1.75117i	−0.0575423	+	0.0721558i
$590$	3.30074	−	14.4615i	0.135890	−	0.595371i
$591$	−13.3292	+	6.41902i	−0.548292	+	0.264043i
$592$	−5.63545	−	7.06663i	−0.231615	−	0.290437i
$593$	9.46044	−	4.55591i	0.388494	−	0.187089i	−0.229433	−	0.973324i	$-0.573687\pi$
$593$	9.46044	−	4.55591i	0.388494	−	0.187089i	0.617927	+	0.786236i	$0.287973\pi$
$594$	−0.987040	+	1.23771i	−0.0404987	+	0.0507838i
$595$	−0.208323			−0.00854041
$596$	−18.7024			−0.766080
$597$	−0.528796	+	0.663089i	−0.0216422	+	0.0271384i
$598$	2.94954	+	1.42043i	0.120616	+	0.0580855i
$599$	−3.62508	−	15.8825i	−0.148117	−	0.648942i	−0.993408	−	0.114635i	$-0.963430\pi$
$599$	−3.62508	−	15.8825i	−0.148117	−	0.648942i	0.845291	−	0.534306i	$-0.179427\pi$
$600$	1.71586	−	7.51765i	0.0700495	−	0.306907i
$601$	−8.04798			−0.328284			−0.164142	−	0.986437i	$-0.552486\pi$
$601$	−8.04798			−0.328284			−0.164142	+	0.986437i	$0.552486\pi$
$602$	0.165023	−	0.0733719i	0.00672582	−	0.00299041i
$603$	26.3314			1.07230
$604$	−2.97544	+	13.0362i	−0.121069	+	0.530437i
$605$	−7.82530	−	34.2849i	−0.318144	−	1.39388i
$606$	3.36189	+	1.61900i	0.136567	+	0.0657674i
$607$	−13.4723	+	16.8938i	−0.546825	+	0.685696i	−0.976061	−	0.217496i	$-0.930211\pi$
$607$	−13.4723	+	16.8938i	−0.546825	+	0.685696i	0.429237	+	0.903192i	$0.358783\pi$
$608$	−15.2735			−0.619422
$609$	0.352506			0.0142843
$610$	13.3570	−	16.7492i	0.540809	−	0.678154i
$611$	−4.27980	+	2.06104i	−0.173142	+	0.0833809i
$612$	2.95897	+	3.71043i	0.119609	+	0.149985i
$613$	4.58975	−	2.21031i	0.185378	−	0.0892735i	−0.338892	−	0.940825i	$-0.610052\pi$
$613$	4.58975	−	2.21031i	0.185378	−	0.0892735i	0.524271	+	0.851552i	$0.324338\pi$
$614$	1.01835	−	4.46170i	0.0410974	−	0.180060i
$615$	10.3698	−	13.0033i	0.418150	−	0.524343i
$616$	0.0238980	−	0.104704i	0.000962879	−	0.00421865i
$617$	−42.7278	−	20.5766i	−1.72016	−	0.828384i	−0.989307	−	0.145846i	$-0.953410\pi$
$617$	−42.7278	−	20.5766i	−1.72016	−	0.828384i	−0.730850	−	0.682538i	$-0.760876\pi$
$618$	−2.04638	−	2.56608i	−0.0823176	−	0.103223i
$619$	17.0349	+	21.3611i	0.684690	+	0.858574i	0.995777	−	0.0918079i	$-0.0292646\pi$
$619$	17.0349	+	21.3611i	0.684690	+	0.858574i	−0.311087	+	0.950381i	$0.600693\pi$
$620$	−0.990993	−	4.34182i	−0.0397992	−	0.174372i
$621$	21.9192	+	10.5557i	0.879587	+	0.423587i
$622$	2.23205	−	1.07490i	0.0894970	−	0.0430995i
$623$	−0.163343	−	0.715652i	−0.00654419	−	0.0286720i
$624$	0.332489	+	1.45673i	0.0133102	+	0.0583158i
$625$	5.39812	−	2.59960i	0.215925	−	0.103984i
$626$	−2.73661	−	1.31788i	−0.109377	−	0.0526731i
$627$	0.421371	+	1.84614i	0.0168279	+	0.0737279i
$628$	23.9547	+	30.0383i	0.955899	+	1.19866i
$629$	−2.06095	−	2.58435i	−0.0821756	−	0.103045i
$630$	−0.234003	−	0.112690i	−0.00932289	−	0.00448967i
$631$	−8.84995	+	38.7742i	−0.352311	+	1.54358i	0.419519	+	0.907747i	$0.362199\pi$
$631$	−8.84995	+	38.7742i	−0.352311	+	1.54358i	−0.771830	+	0.635829i	$0.780658\pi$
$632$	−13.5893	+	17.0404i	−0.540553	+	0.677832i
$633$	0.925648	−	4.05553i	0.0367912	−	0.161193i
$634$	5.46732	−	2.63292i	0.217135	−	0.104567i
$635$	20.1481	+	25.2649i	0.799552	+	1.00261i
$636$	2.30534	−	1.11019i	0.0914126	−	0.0440220i
$637$	4.11587	−	5.16113i	0.163077	−	0.204492i
$638$	4.98973			0.197545
$639$	−9.70772			−0.384032
$640$	24.5808	−	30.8233i	0.971640	−	1.21840i
$641$	−34.4679	−	16.5989i	−1.36140	−	0.655615i	−0.396451	−	0.918056i	$-0.629758\pi$
$641$	−34.4679	−	16.5989i	−1.36140	−	0.655615i	−0.964948	+	0.262440i	$0.915473\pi$
$642$	0.570747	+	2.50061i	0.0225256	+	0.0986911i
$643$	6.41401	−	28.1016i	0.252944	−	1.10822i	−0.675679	−	0.737196i	$-0.736149\pi$
$643$	6.41401	−	28.1016i	0.252944	−	1.10822i	0.928623	−	0.371024i	$-0.120993\pi$
$644$	−0.777442			−0.0306355
$645$	−2.59083	−	13.1890i	−0.102014	−	0.519316i
$646$	−1.48336			−0.0583620
$647$	9.23040	−	40.4410i	0.362885	−	1.58990i	−0.382950	−	0.923769i	$-0.625092\pi$
$647$	9.23040	−	40.4410i	0.362885	−	1.58990i	0.745834	−	0.666132i	$-0.232051\pi$
$648$	2.39890	+	10.5103i	0.0942379	+	0.412883i
$649$	−8.32335	−	4.00832i	−0.326720	−	0.157340i
$650$	−2.07146	+	2.59752i	−0.0812492	+	0.101883i
$651$	0.0240850			0.000943964
$652$	31.8283			1.24649
$653$	−1.49821	+	1.87870i	−0.0586296	+	0.0735192i	−0.810282	−	0.586041i	$-0.800686\pi$
$653$	−1.49821	+	1.87870i	−0.0586296	+	0.0735192i	0.751652	+	0.659560i	$0.229257\pi$
$654$	4.32810	−	2.08430i	0.169242	−	0.0815028i
$655$	30.2977	+	37.9921i	1.18383	+	1.48447i
$656$	19.9899	−	9.62663i	0.780475	−	0.375857i
$657$	1.61080	−	7.05738i	0.0628433	−	0.275335i
$658$	−0.0864519	+	0.108407i	−0.00337025	+	0.00422616i
$659$	−3.33286	+	14.6022i	−0.129830	+	0.568822i	0.867606	+	0.497253i	$0.165658\pi$
$659$	−3.33286	+	14.6022i	−0.129830	+	0.568822i	−0.997436	+	0.0715691i	$0.977199\pi$
$660$	−3.39225	−	1.63362i	−0.132043	−	0.0635885i
$661$	5.94755	+	7.45800i	0.231333	+	0.290082i	0.883927	−	0.467626i	$-0.154890\pi$
$661$	5.94755	+	7.45800i	0.231333	+	0.290082i	−0.652594	+	0.757708i	$0.726319\pi$
$662$	−4.70367	−	5.89822i	−0.182813	−	0.229241i
$663$	0.121595	+	0.532743i	0.00472237	+	0.0206900i
$664$	18.7281	+	9.01900i	0.726793	+	0.350005i
$665$	−0.595042	+	0.286557i	−0.0230748	+	0.0111122i
$666$	−0.917030	−	4.01777i	−0.0355342	−	0.155685i
$667$	−17.0631	−	74.7582i	−0.660685	−	2.89465i
$668$	32.3597	−	15.5836i	1.25204	−	0.602949i
$669$	−1.39560	−	0.672084i	−0.0539569	−	0.0259843i
$670$	−3.64137	−	15.9539i	−0.140678	−	0.616352i
$671$	−8.31872	−	10.4313i	−0.321141	−	0.402698i
$672$	0.102399	+	0.128405i	0.00395015	+	0.00495333i
$673$	−2.98168	−	1.43590i	−0.114935	−	0.0553499i	0.375533	−	0.926809i	$-0.377460\pi$
$673$	−2.98168	−	1.43590i	−0.114935	−	0.0553499i	−0.490468	+	0.871459i	$0.663174\pi$
$674$	1.31192	−	5.74788i	0.0505332	−	0.221400i
$675$	−15.3938	+	19.3032i	−0.592507	+	0.742980i
$676$	−4.79943	+	21.0277i	−0.184594	+	0.808757i
$677$	18.3088	−	8.81705i	0.703664	−	0.338867i	−0.0476017	−	0.998866i	$-0.515158\pi$
$677$	18.3088	−	8.81705i	0.703664	−	0.338867i	0.751266	+	0.660000i	$0.229444\pi$
$678$	3.27810	+	4.11061i	0.125895	+	0.157867i
$679$	−0.0471827	+	0.0227220i	−0.00181070	+	0.000871989i
$680$	3.90385	−	4.89527i	0.149706	−	0.187725i
$681$	−4.94700			−0.189569
$682$	0.340923			0.0130546
$683$	14.7869	−	18.5422i	0.565804	−	0.709496i	−0.413815	−	0.910361i	$-0.635804\pi$
$683$	14.7869	−	18.5422i	0.565804	−	0.709496i	0.979619	+	0.200865i	$0.0643752\pi$
$684$	13.5557	+	6.52808i	0.518315	+	0.249607i
$685$	−0.224166	−	0.982134i	−0.00856493	−	0.0375254i
$686$	0.0857772	−	0.375814i	0.00327499	−	0.0143487i
$687$	−7.05220			−0.269058
$688$	4.51996	−	17.3515i	0.172322	−	0.661521i
$689$	−2.34042			−0.0891631
$690$	1.58258	−	6.93375i	0.0602479	−	0.263963i
$691$	−7.72382	−	33.8403i	−0.293828	−	1.28735i	−0.879150	−	0.476544i	$-0.841889\pi$
$691$	−7.72382	−	33.8403i	−0.293828	−	1.28735i	0.585322	−	0.810801i	$-0.300968\pi$
$692$	−10.3394	−	4.97918i	−0.393044	−	0.189280i
$693$	−0.100853	+	0.126465i	−0.00383108	+	0.00480402i
$694$	−15.2192			−0.577714
$695$	49.5964			1.88130
$696$	−6.60576	+	8.28336i	−0.250391	+	0.313980i
$697$	7.31056	−	3.52058i	0.276907	−	0.133351i
$698$	−4.68690	−	5.87718i	−0.177402	−	0.222455i
$699$	9.64519	−	4.64488i	0.364815	−	0.175685i
$700$	0.175566	−	0.769204i	0.00663577	−	0.0290732i
$701$	−19.6057	+	24.5847i	−0.740496	+	0.928552i	−0.999301	−	0.0373771i	$-0.988100\pi$
$701$	−19.6057	+	24.5847i	−0.740496	+	0.928552i	0.258805	+	0.965929i	$0.416671\pi$
$702$	−0.322277	+	1.41199i	−0.0121636	+	0.0532921i
$703$	−9.44169	−	4.54688i	−0.356100	−	0.171489i
$704$	−2.06707	−	2.59203i	−0.0779057	−	0.0976907i
$705$	6.43418	+	8.06821i	0.242325	+	0.303866i
$706$	−0.228630	−	1.00170i	−0.00860462	−	0.0376993i
$707$	0.730257	+	0.351673i	0.0274641	+	0.0132260i
$708$	8.32496	−	4.00909i	0.312871	−	0.150671i
$709$	−1.17228	−	5.13610i	−0.0440260	−	0.192890i	0.948133	−	0.317875i	$-0.102969\pi$
$709$	−1.17228	−	5.13610i	−0.0440260	−	0.192890i	−0.992159	+	0.124984i	$0.960112\pi$
$710$	1.34248	+	5.88179i	0.0503824	+	0.220740i
$711$	29.5763	−	14.2432i	1.10920	−	0.534162i
$712$	19.8777	+	9.57258i	0.744947	+	0.358748i
$713$	−1.16583	−	5.10784i	−0.0436608	−	0.191290i
$714$	0.00994503	+	0.0124707i	0.000372184	+	0.000466703i
$715$	2.14722	+	2.69253i	0.0803014	+	0.100695i
$716$	34.2680	+	16.5026i	1.28065	+	0.616731i
$717$	2.08883	−	9.15176i	0.0780088	−	0.341779i
$718$	−7.24454	+	9.08437i	−0.270364	+	0.339026i
$719$	4.64952	−	20.3709i	0.173398	−	0.759706i	−0.811185	−	0.584789i	$-0.801177\pi$
$719$	4.64952	−	20.3709i	0.173398	−	0.759706i	0.984583	−	0.174917i	$-0.0559656\pi$
$720$	−23.2328	+	11.1883i	−0.865834	+	0.416964i
$721$	−0.444508	−	0.557395i	−0.0165543	−	0.0207585i
$722$	3.77258	−	1.81678i	0.140401	−	0.0676135i
$723$	2.98917	−	3.74830i	0.111168	−	0.139401i
$724$	1.09821			0.0408147
$725$	77.8193			2.89014
$726$	−1.67880	+	2.10515i	−0.0623062	+	0.0781295i
$727$	21.7672	+	10.4825i	0.807302	+	0.388776i	0.791553	−	0.611100i	$-0.209273\pi$
$727$	21.7672	+	10.4825i	0.807302	+	0.388776i	0.0157482	+	0.999876i	$0.494987\pi$
$728$	−0.0218633	−	0.0957893i	−0.000810307	−	0.00355019i
$729$	2.34471	−	10.2728i	0.0868411	−	0.380476i
$730$	−4.49874			−0.166506
$731$	1.65300	−	6.34567i	0.0611386	−	0.234703i
$732$	13.3448			0.493237
$733$	0.717659	−	3.14427i	0.0265073	−	0.116136i	−0.959943	−	0.280194i	$-0.909601\pi$
$733$	0.717659	−	3.14427i	0.0265073	−	0.116136i	0.986451	+	0.164058i	$0.0524583\pi$
$734$	−1.50626	−	6.59934i	−0.0555969	−	0.243586i
$735$	−12.9209	−	6.22237i	−0.476594	−	0.229515i
$736$	22.2750	−	27.9319i	0.821066	−	1.02958i
$737$	−10.1916			−0.375412
$738$	10.1161			0.372380
$739$	−9.45714	+	11.8589i	−0.347886	+	0.436236i	−0.924733	−	0.380617i	$-0.875712\pi$
$739$	−9.45714	+	11.8589i	−0.347886	+	0.436236i	0.576846	+	0.816853i	$0.304283\pi$
$740$	18.7730	−	9.04060i	0.690109	−	0.332339i
$741$	1.08013	+	1.35444i	0.0396796	+	0.0497566i
$742$	−0.0615511	+	0.0296414i	−0.00225961	+	0.00108817i
$743$	−3.31703	+	14.5328i	−0.121690	+	0.533158i	0.876929	+	0.480620i	$0.159588\pi$
$743$	−3.31703	+	14.5328i	−0.121690	+	0.533158i	−0.998619	+	0.0525383i	$0.983269\pi$
$744$	−0.451338	+	0.565960i	−0.0165468	+	0.0207491i
$745$	8.26966	−	36.2318i	0.302977	−	1.32743i
$746$	−6.03008	−	2.90393i	−0.220777	−	0.106321i
$747$	−19.5201	−	24.4774i	−0.714202	−	0.895581i
$748$	−1.14527	−	1.43612i	−0.0418752	−	0.0525098i
$749$	0.123976	+	0.543172i	0.00452997	+	0.0198471i
$750$	2.18249	+	1.05103i	0.0796931	+	0.0383782i
$751$	−6.03482	+	2.90622i	−0.220214	+	0.106049i	−0.540738	−	0.841191i	$-0.681855\pi$
$751$	−6.03482	+	2.90622i	−0.220214	+	0.106049i	0.320525	+	0.947240i	$0.396141\pi$
$752$	3.06335	+	13.4214i	0.111709	+	0.489428i
$753$	−1.96684	−	8.61729i	−0.0716756	−	0.314031i
$754$	4.11282	−	1.98063i	0.149780	−	0.0721303i
$755$	−23.9392	−	11.5285i	−0.871236	−	0.419565i
$756$	−0.0765336	−	0.335316i	−0.00278350	−	0.0121953i
$757$	−14.6468	−	18.3665i	−0.532348	−	0.667544i	0.440831	−	0.897590i	$-0.354684\pi$
$757$	−14.6468	−	18.3665i	−0.532348	−	0.667544i	−0.973180	+	0.230046i	$0.926112\pi$
$758$	−1.79436	−	2.25006i	−0.0651742	−	0.0817259i
$759$	−3.99073	−	1.92184i	−0.144854	−	0.0697582i
$760$	4.41708	−	19.3525i	0.160224	−	0.701989i
$761$	23.9149	−	29.9883i	0.866913	−	1.08707i	−0.128529	−	0.991706i	$-0.541026\pi$
$761$	23.9149	−	29.9883i	0.866913	−	1.08707i	0.995442	−	0.0953687i	$-0.0304030\pi$
$762$	0.550573	−	2.41222i	0.0199452	−	0.0873854i
$763$	0.940134	−	0.452745i	0.0340351	−	0.0163905i
$764$	−17.0939	−	21.4351i	−0.618436	−	0.775494i
$765$	−8.49651	+	4.09170i	−0.307192	+	0.147936i
$766$	2.73935	−	3.43503i	0.0989766	−	0.124113i
$767$	−8.45166			−0.305172
$768$	0.704951			0.0254377
$769$	−2.44088	+	3.06077i	−0.0880204	+	0.110374i	−0.823892	−	0.566748i	$-0.808201\pi$
$769$	−2.44088	+	3.06077i	−0.0880204	+	0.110374i	0.735871	+	0.677122i	$0.236773\pi$
$770$	0.0905708	+	0.0436166i	0.00326394	+	0.00157183i
$771$	−0.150309	−	0.658545i	−0.00541323	−	0.0237169i
$772$	−2.63913	+	11.5628i	−0.0949844	+	0.416154i
$773$	−25.8793			−0.930814			−0.465407	−	0.885097i	$-0.654092\pi$
$773$	−25.8793			−0.930814			−0.465407	+	0.885097i	$0.654092\pi$
$774$	5.28938	−	6.23373i	0.190123	−	0.224067i
$775$	5.31700			0.190992
$776$	0.350243	−	1.53452i	0.0125730	−	0.0550859i
$777$	0.0250750	+	0.109861i	0.000899560	+	0.00394123i
$778$	5.65547	+	2.72353i	0.202759	+	0.0976434i
$779$	16.0388	−	20.1120i	0.574649	−	0.720586i
$780$	−3.44454			−0.123334
$781$	3.75738			0.134450
$782$	2.16334	−	2.71275i	0.0773610	−	0.0970077i
$783$	30.5640	−	14.7188i	1.09227	−	0.526008i
$784$	−11.9281	−	14.9574i	−0.426005	−	0.534193i
$785$	−68.7847	+	33.1250i	−2.45503	+	1.18228i
$786$	0.827925	−	3.62738i	0.0295311	−	0.129384i
$787$	−28.1955	+	35.3560i	−1.00506	+	1.26031i	−0.0397475	+	0.999210i	$0.512655\pi$
$787$	−28.1955	+	35.3560i	−1.00506	+	1.26031i	−0.965313	+	0.261096i	$0.915916\pi$
$788$	10.1240	−	44.3562i	0.360653	−	1.58012i
$789$	5.93834	+	2.85975i	0.211410	+	0.101810i
$790$	−12.7199	−	15.9503i	−0.452554	−	0.567485i
$791$	0.712056	+	0.892890i	0.0253178	+	0.0317475i
$792$	−1.08182	−	4.73977i	−0.0384409	−	0.168420i
$793$	−10.9974	−	5.29607i	−0.390529	−	0.188069i
$794$	−2.35110	+	1.13223i	−0.0834374	+	0.0401813i
$795$	1.13140	+	4.95698i	0.0401266	+	0.175806i
$796$	−0.580384	−	2.54283i	−0.0205712	−	0.0901282i
$797$	−49.2271	+	23.7065i	−1.74371	+	0.839729i	−0.762455	+	0.647042i	$0.776006\pi$
$797$	−49.2271	+	23.7065i	−1.74371	+	0.839729i	−0.981260	+	0.192687i	$0.938280\pi$
$798$	0.0455604	+	0.0219407i	0.00161282	+	0.000776694i
$799$	1.12030	+	4.90837i	0.0396335	+	0.173646i
$800$	22.6057	+	28.3467i	0.799233	+	1.00221i
$801$	−20.7182	−	25.9798i	−0.732042	−	0.917951i
$802$	12.0769	+	5.81593i	0.426450	+	0.205368i
$803$	−0.623461	+	2.73156i	−0.0220015	+	0.0963947i
$804$	6.35557	−	7.96963i	0.224144	−	0.281067i
$805$	0.343763	−	1.50612i	0.0121160	−	0.0530838i
$806$	0.281008	−	0.135326i	0.00989809	−	0.00476667i
$807$	−2.57741	−	3.23197i	−0.0907291	−	0.113771i
$808$	−21.9484	+	10.5698i	−0.772141	+	0.371843i
$809$	−5.51189	+	6.91169i	−0.193788	+	0.243002i	−0.869227	−	0.494414i	$-0.835383\pi$
$809$	−5.51189	+	6.91169i	−0.193788	+	0.243002i	0.675439	+	0.737416i	$0.263954\pi$
$810$	−10.0909			−0.354557
$811$	42.6606			1.49802			0.749009	−	0.662560i	$-0.230530\pi$
$811$	42.6606			1.49802			0.749009	+	0.662560i	$0.230530\pi$
$812$	−0.675900	+	0.847551i	−0.0237194	+	0.0297432i
$813$	−12.8985	−	6.21158i	−0.452370	−	0.217850i
$814$	0.354937	+	1.55508i	0.0124405	+	0.0545055i
$815$	−14.0736	+	61.6604i	−0.492976	+	2.15987i
$816$	1.58364			0.0554386
$817$	−4.00720	−	20.3992i	−0.140194	−	0.713678i
$818$	12.4148			0.434075
$819$	−0.0329293	+	0.144273i	−0.00115064	+	0.00504130i
$820$	11.3814	+	49.8653i	0.397457	+	1.74137i
$821$	17.0634	+	8.21729i	0.595516	+	0.286786i	0.707262	−	0.706951i	$-0.249930\pi$
$821$	17.0634	+	8.21729i	0.595516	+	0.286786i	−0.111746	+	0.993737i	$0.535644\pi$
$822$	−0.0480914	+	0.0603047i	−0.00167738	+	0.00210337i
$823$	37.4004			1.30370			0.651848	−	0.758350i	$-0.273994\pi$
$823$	37.4004			1.30370			0.651848	+	0.758350i	$0.273994\pi$
$824$	21.4278			0.746471
$825$	2.80268	−	3.51445i	0.0975768	−	0.122357i
$826$	−0.222271	+	0.107040i	−0.00773380	+	0.00372440i
$827$	−2.95605	−	3.70678i	−0.102792	−	0.128897i	0.727775	−	0.685816i	$-0.240555\pi$
$827$	−2.95605	−	3.70678i	−0.102792	−	0.128897i	−0.830567	+	0.556919i	$0.811983\pi$
$828$	−31.7082	+	15.2699i	−1.10194	+	0.530664i
$829$	−5.57111	+	24.4086i	−0.193493	+	0.847746i	0.781215	+	0.624262i	$0.214600\pi$
$829$	−5.57111	+	24.4086i	−0.193493	+	0.847746i	−0.974708	+	0.223484i	$0.928257\pi$
$830$	−12.1311	+	15.2120i	−0.421078	+	0.528015i
$831$	−3.83915	+	16.8204i	−0.133179	+	0.583494i
$832$	−2.73268	−	1.31599i	−0.0947388	−	0.0456238i
$833$	−4.36227	−	5.47011i	−0.151144	−	0.189528i
$834$	−2.36766	−	2.96895i	−0.0819853	−	0.102806i
$835$	15.8813	+	69.5805i	0.549595	+	2.40793i
$836$	−5.24673	−	2.52669i	−0.181462	−	0.0873875i
$837$	2.08828	−	1.00566i	0.0721815	−	0.0347608i
$838$	−1.32952	−	5.82501i	−0.0459275	−	0.201221i
$839$	−11.5762	−	50.7189i	−0.399657	−	1.75101i	−0.628752	−	0.777606i	$-0.716434\pi$
$839$	−11.5762	−	50.7189i	−0.399657	−	1.75101i	0.229096	−	0.973404i	$-0.426423\pi$
$840$	−0.192311	+	0.0926122i	−0.00663537	+	0.00319543i
$841$	−70.2062	−	33.8095i	−2.42090	−	1.16585i
$842$	0.333227	+	1.45996i	0.0114838	+	0.0503136i
$843$	11.6755	+	14.6407i	0.402127	+	0.504251i
$844$	7.97610	+	10.0017i	0.274549	+	0.344273i
$845$	−38.6143	−	18.5957i	−1.32837	−	0.639711i
$846$	−1.39672	+	6.11944i	−0.0480203	+	0.210391i
$847$	−0.364663	+	0.457273i	−0.0125300	+	0.0157121i
$848$	−1.50930	+	6.61270i	−0.0518297	+	0.227081i
$849$	5.33583	−	2.56960i	0.183125	−	0.0881884i
$850$	2.19547	+	2.75303i	0.0753039	+	0.0944281i
$851$	22.0851	−	10.6356i	0.757067	−	0.364584i
$852$	−2.34314	+	2.93820i	−0.0802746	+	0.100661i
$853$	18.7101			0.640622			0.320311	−	0.947312i	$-0.396213\pi$
$853$	18.7101			0.640622			0.320311	+	0.947312i	$0.396213\pi$
$854$	−0.356297			−0.0121922
$855$	−18.6407	+	23.3746i	−0.637497	+	0.799396i
$856$	−15.0870	−	7.26549i	−0.515662	−	0.248329i
$857$	−0.989474	−	4.33517i	−0.0337998	−	0.148087i	0.955212	−	0.295922i	$-0.0956267\pi$
$857$	−0.989474	−	4.33517i	−0.0337998	−	0.148087i	−0.989012	+	0.147835i	$0.952770\pi$
$858$	0.0586756	−	0.257075i	0.00200315	−	0.00877639i
$859$	−14.4543			−0.493176			−0.246588	−	0.969120i	$-0.579309\pi$
$859$	−14.4543			−0.493176			−0.246588	+	0.969120i	$0.579309\pi$
$860$	36.6788	+	19.0594i	1.25074	+	0.649922i
$861$	−0.276613			−0.00942693
$862$	−0.308431	+	1.35132i	−0.0105052	+	0.0460263i
$863$	−7.54698	−	33.0655i	−0.256902	−	1.12556i	−0.924543	−	0.381078i	$-0.875553\pi$
$863$	−7.54698	−	33.0655i	−0.256902	−	1.12556i	0.667640	−	0.744484i	$-0.267304\pi$
$864$	14.2400	+	6.85764i	0.484456	+	0.233302i
$865$	14.2178	−	17.8286i	0.483421	−	0.606191i
$866$	6.13838			0.208591
$867$	0.579157			0.0196692
$868$	−0.0461808	+	0.0579089i	−0.00156748	+	0.00196555i
$869$	−11.4475	+	5.51284i	−0.388331	+	0.187010i
$870$	−6.18315	−	7.75343i	−0.209628	−	0.262866i
$871$	−8.40049	+	4.04546i	−0.284640	+	0.137075i
$872$	−6.97875	+	30.5759i	−0.236330	+	1.03543i
$873$	−1.47807	+	1.85344i	−0.0500252	+	0.0627296i
$874$	2.44776	−	10.7243i	0.0827966	−	0.362756i
$875$	0.474071	+	0.228301i	0.0160265	+	0.00771797i
$876$	−1.74724	−	2.19096i	−0.0590336	−	0.0740258i
$877$	−6.91596	−	8.67234i	−0.233535	−	0.292844i	0.651230	−	0.758880i	$-0.274253\pi$
$877$	−6.91596	−	8.67234i	−0.233535	−	0.292844i	−0.884766	+	0.466036i	$0.845682\pi$
$878$	0.894832	+	3.92052i	0.0301991	+	0.132311i
$879$	10.5376	+	5.07462i	0.355423	+	0.171163i
$880$	8.99225	−	4.33044i	0.303129	−	0.145979i
$881$	1.95532	+	8.56681i	0.0658763	+	0.288623i	0.997126	−	0.0757581i	$-0.0241377\pi$
$881$	1.95532	+	8.56681i	0.0658763	+	0.288623i	−0.931250	+	0.364381i	$0.881281\pi$
$882$	−1.94101	−	8.50412i	−0.0653572	−	0.286349i
$883$	−5.71600	+	2.75268i	−0.192359	+	0.0926351i	−0.527584	−	0.849503i	$-0.676902\pi$
$883$	−5.71600	+	2.75268i	−0.192359	+	0.0926351i	0.335225	+	0.942138i	$0.391188\pi$
$884$	−1.51405	−	0.729130i	−0.0509231	−	0.0245233i
$885$	4.08567	+	17.9005i	0.137338	+	0.601718i
$886$	7.53449	+	9.44796i	0.253126	+	0.317410i
$887$	4.85510	+	6.08810i	0.163018	+	0.204418i	0.856631	−	0.515930i	$-0.172553\pi$
$887$	4.85510	+	6.08810i	0.163018	+	0.204418i	−0.693613	+	0.720348i	$0.743982\pi$
$888$	−3.05145	−	1.46950i	−0.102400	−	0.0493132i
$889$	0.119593	−	0.523973i	0.00401103	−	0.0175735i
$890$	−12.8757	+	16.1457i	−0.431596	+	0.541204i
$891$	−1.39845	+	6.12702i	−0.0468499	+	0.205263i
$892$	4.29186	−	2.06685i	0.143702	−	0.0692033i
$893$	9.95166	+	12.4790i	0.333019	+	0.417593i
$894$	−2.56370	+	1.23461i	−0.0857428	+	0.0412916i
$895$	−47.1224	+	59.0897i	−1.57513	+	1.97515i
$896$	−0.655689			−0.0219050
$897$	−4.05225			−0.135301
$898$	−7.88679	+	9.88972i	−0.263185	+	0.330024i
$899$	−6.58203	−	3.16974i	−0.219523	−	0.105717i
$900$	−7.94756	−	34.8205i	−0.264919	−	1.16068i
$901$	−0.551971	+	2.41834i	−0.0183888	+	0.0805667i
$902$	−3.91545			−0.130370
$903$	−0.144631	+	0.170453i	−0.00481303	+	0.00567233i
$904$	−34.3251			−1.14164
$905$	−0.485598	+	2.12754i	−0.0161418	+	0.0707220i
$906$	0.452700	+	1.98341i	0.0150399	+	0.0658943i
$907$	−53.9629	−	25.9872i	−1.79181	−	0.862890i	−0.941843	−	0.336052i	$-0.890908\pi$
$907$	−53.9629	−	25.9872i	−1.79181	−	0.862890i	−0.849966	−	0.526838i	$-0.823377\pi$
$908$	9.48543	−	11.8944i	0.314785	−	0.394728i
$909$	36.6910			1.21696
$910$	0.0919669			0.00304867
$911$	−12.2389	+	15.3470i	−0.405491	+	0.508470i	−0.942087	−	0.335370i	$-0.891139\pi$
$911$	−12.2389	+	15.3470i	−0.405491	+	0.508470i	0.536595	+	0.843840i	$0.319710\pi$
$912$	4.52343	−	2.17837i	0.149786	−	0.0721330i
$913$	7.55525	+	9.47398i	0.250042	+	0.313543i
$914$	−7.10719	+	3.42264i	−0.235085	+	0.113211i
$915$	−5.90068	+	25.8525i	−0.195070	+	0.854659i
$916$	13.5220	−	16.9560i	0.446779	−	0.560243i
$917$	0.179839	−	0.787925i	0.00593880	−	0.0260196i
$918$	1.38299	+	0.666014i	0.0456455	+	0.0219817i
$919$	−1.77344	−	2.22383i	−0.0585005	−	0.0733573i	0.751720	−	0.659482i	$-0.229224\pi$
$919$	−1.77344	−	2.22383i	−0.0585005	−	0.0733573i	−0.810221	+	0.586125i	$0.800653\pi$
$920$	28.9497	+	36.3017i	0.954442	+	1.19683i
$921$	1.26052	+	5.52270i	0.0415356	+	0.181979i
$922$	−2.37745	−	1.14492i	−0.0782971	−	0.0377059i
$923$	3.09705	−	1.49146i	0.101941	−	0.0490920i
$924$	0.0139341	+	0.0610495i	0.000458400	+	0.00200838i
$925$	5.53556	+	24.2529i	0.182008	+	0.797430i
$926$	1.39503	−	0.671811i	0.0458435	−	0.0220771i
$927$	−29.0773	−	14.0029i	−0.955023	−	0.459915i
$928$	−11.0852	−	48.5674i	−0.363890	−	1.59430i
$929$	−29.3202	−	36.7664i	−0.961966	−	1.20627i	−0.978467	−	0.206403i	$-0.933824\pi$
$929$	−29.3202	−	36.7664i	−0.961966	−	1.20627i	0.0165012	−	0.999864i	$-0.494747\pi$
$930$	−0.422463	−	0.529752i	−0.0138531	−	0.0173713i
$931$	−19.9845	−	9.62404i	−0.654966	−	0.315415i
$932$	−7.32585	+	32.0966i	−0.239966	+	1.05136i
$933$	−1.91194	+	2.39750i	−0.0625941	+	0.0784905i
$934$	−3.23980	+	14.1945i	−0.106010	+	0.464458i
$935$	3.28858	−	1.58369i	0.107548	−	0.0517924i
$936$	−2.77311	−	3.47737i	−0.0906421	−	0.113662i
$937$	33.0045	−	15.8941i	1.07821	−	0.519238i	0.191465	−	0.981499i	$-0.438676\pi$
$937$	33.0045	−	15.8941i	1.07821	−	0.519238i	0.886744	+	0.462261i	$0.152962\pi$
$938$	−0.169690	+	0.212784i	−0.00554056	+	0.00694765i
$939$	3.75970			0.122693
$940$	−31.7359			−1.03511
$941$	−25.3340	+	31.7678i	−0.825865	+	1.03560i	0.172852	+	0.984948i	$0.444702\pi$
$941$	−25.3340	+	31.7678i	−0.825865	+	1.03560i	−0.998716	+	0.0506536i	$0.983870\pi$
$942$	5.26662	+	2.53627i	0.171596	+	0.0826361i
$943$	13.3894	+	58.6629i	0.436020	+	1.91033i
$944$	−5.45035	+	23.8795i	−0.177394	+	0.777212i
$945$	0.683441			0.0222323
$946$	−2.04726	+	2.41277i	−0.0665621	+	0.0784458i
$947$	−51.0017			−1.65733			−0.828666	−	0.559743i	$-0.810900\pi$
$947$	−51.0017			−1.65733			−0.828666	+	0.559743i	$0.810900\pi$
$948$	2.82785	−	12.3896i	0.0918443	−	0.402396i
$949$	0.570378	+	2.49899i	0.0185152	+	0.0811206i
$950$	10.0579	+	4.84364i	0.326322	+	0.157148i
$951$	−4.68323	+	5.87258i	−0.151864	+	0.190431i
$952$	−0.104135			−0.00337503
$953$	10.9261			0.353930			0.176965	−	0.984217i	$-0.443372\pi$
$953$	10.9261			0.353930			0.176965	+	0.984217i	$0.443372\pi$
$954$	−1.92819	+	2.41787i	−0.0624273	+	0.0782814i
$955$	49.0842	−	23.6377i	1.58833	−	0.764898i
$956$	17.9990	+	22.5700i	0.582128	+	0.729965i
$957$	−5.56465	+	2.67979i	−0.179879	+	0.0866254i
$958$	−1.43965	+	6.30753i	−0.0465130	+	0.203787i
$959$	−0.0104462	+	0.0130992i	−0.000337326	+	0.000422994i
$960$	−1.46623	+	6.42396i	−0.0473222	+	0.207332i
$961$	27.4803	+	13.2338i	0.886462	+	0.426898i
$962$	0.909835	+	1.14090i	0.0293343	+	0.0367840i
$963$	15.7249	+	19.7184i	0.506728	+	0.635417i
$964$	3.28079	+	14.3741i	0.105667	+	0.462958i
$965$	−21.2334	−	10.2255i	−0.683528	−	0.329170i
$966$	−0.106571	+	0.0513217i	−0.00342885	+	0.00165125i
$967$	−11.5434	−	50.5749i	−0.371210	−	1.62638i	−0.723386	−	0.690444i	$-0.757415\pi$
$967$	−11.5434	−	50.5749i	−0.371210	−	1.62638i	0.352176	−	0.935934i	$-0.385442\pi$
$968$	−3.91165	−	17.1380i	−0.125725	−	0.550838i
$969$	1.65427	−	0.796656i	0.0531429	−	0.0255923i
$970$	1.32738	+	0.639234i	0.0426197	+	0.0205246i
$971$	−10.3381	−	45.2944i	−0.331767	−	1.45357i	−0.815707	−	0.578465i	$-0.803652\pi$
$971$	−10.3381	−	45.2944i	−0.331767	−	1.45357i	0.483940	−	0.875101i	$-0.339205\pi$
$972$	−14.8486	−	18.6195i	−0.476268	−	0.597221i
$973$	−0.514294	−	0.644904i	−0.0164875	−	0.0206747i
$974$	−3.52711	−	1.69857i	−0.113016	−	0.0544256i
$975$	0.915100	−	4.00931i	0.0293066	−	0.128401i
$976$	−22.0557	+	27.6570i	−0.705987	+	0.885279i
$977$	−5.60064	+	24.5380i	−0.179180	+	0.785040i	0.802829	+	0.596209i	$0.203327\pi$
$977$	−5.60064	+	24.5380i	−0.179180	+	0.785040i	−0.982010	+	0.188831i	$0.939530\pi$
$978$	4.36298	−	2.10110i	0.139513	−	0.0671858i
$979$	8.01899	+	10.0555i	0.256288	+	0.321375i
$980$	39.7354	−	19.1356i	1.26930	−	0.611264i
$981$	29.4512	−	36.9306i	0.940305	−	1.17910i
$982$	−2.56987			−0.0820079
$983$	15.2307			0.485784			0.242892	−	0.970053i	$-0.421904\pi$
$983$	15.2307			0.485784			0.242892	+	0.970053i	$0.421904\pi$
$984$	5.18356	−	6.49997i	0.165246	−	0.207212i
$985$	81.4538	+	39.2261i	2.59533	+	1.24985i
$986$	−1.07659	−	4.71687i	−0.0342858	−	0.150216i
$987$	0.0381915	−	0.167328i	0.00121565	−	0.00532611i
$988$	−5.32761			−0.169494
$989$	43.1499	+	22.4221i	1.37209	+	0.712980i
$990$	4.55064			0.144629
$991$	11.5267	−	50.5016i	0.366156	−	1.60424i	−0.371080	−	0.928601i	$-0.621012\pi$
$991$	11.5267	−	50.5016i	0.366156	−	1.60424i	0.737236	−	0.675635i	$-0.236130\pi$
$992$	−0.757395	−	3.31837i	−0.0240473	−	0.105358i
$993$	8.41334	+	4.05165i	0.266989	+	0.128575i
$994$	0.0625603	−	0.0784481i	0.00198429	−	0.00248822i
$995$	5.18280			0.164306
$996$	−12.1200			−0.384037
$997$	−14.2814	+	17.9083i	−0.452296	+	0.567162i	−0.954738	−	0.297450i	$-0.903864\pi$
$997$	−14.2814	+	17.9083i	−0.452296	+	0.567162i	0.502441	+	0.864611i	$0.332435\pi$
$998$	−4.06164	+	1.95598i	−0.128569	+	0.0619156i
$999$	6.76133	+	8.47844i	0.213919	+	0.268246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.k.a.35.14	✓	180
43.16	even	7	inner	731.2.k.a.188.14	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.k.a.35.14	✓	180	1.1	even	1	trivial
731.2.k.a.188.14	yes	180	43.16	even	7	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104116 + 0.456161i) q^{2} +(-0.128875 - 0.564637i) q^{3} +(1.60469 + 0.772780i) q^{4} +(-2.20664 + 2.76704i) q^{5} +0.270983 q^{6} +0.0588619 q^{7} +(-1.10304 + 1.38317i) q^{8} +(2.40070 - 1.15612i) q^{9} +O(q^{10})\)	\(q+(-0.104116 + 0.456161i) q^{2} +(-0.128875 - 0.564637i) q^{3} +(1.60469 + 0.772780i) q^{4} +(-2.20664 + 2.76704i) q^{5} +0.270983 q^{6} +0.0588619 q^{7} +(-1.10304 + 1.38317i) q^{8} +(2.40070 - 1.15612i) q^{9} +(-1.03247 - 1.29468i) q^{10} +(-0.929192 + 0.447475i) q^{11} +(0.229536 - 1.00566i) q^{12} +(-0.588272 + 0.737670i) q^{13} +(-0.00612846 + 0.0268505i) q^{14} +(1.84675 + 0.889350i) q^{15} +(1.70486 + 2.13783i) q^{16} +(0.623490 + 0.781831i) q^{17} +(0.277424 + 1.21548i) q^{18} +(2.85635 + 1.37554i) q^{19} +(-5.67930 + 2.73501i) q^{20} +(-0.00758581 - 0.0332356i) q^{21} +(-0.107377 - 0.470450i) q^{22} +(-6.68129 + 3.21754i) q^{23} +(0.923140 + 0.444561i) q^{24} +(-1.67465 - 7.33710i) q^{25} +(-0.275248 - 0.345150i) q^{26} +(-2.04547 - 2.56494i) q^{27} +(0.0944555 + 0.0454874i) q^{28} +(-2.30095 + 10.0811i) q^{29} +(-0.597963 + 0.749822i) q^{30} +(-0.157212 + 0.688790i) q^{31} +(-4.34057 + 2.09031i) q^{32} +(0.372410 + 0.466988i) q^{33} +(-0.421556 + 0.203011i) q^{34} +(-0.129887 + 0.162873i) q^{35} +4.74582 q^{36} -3.30551 q^{37} +(-0.924860 + 1.15974i) q^{38} +(0.492329 + 0.237093i) q^{39} +(-1.39327 - 6.10431i) q^{40} +(1.80556 - 7.91067i) q^{41} +0.0159506 q^{42} +(-3.93062 - 5.24883i) q^{43} -1.83687 q^{44} +(-2.09846 + 9.19397i) q^{45} +(-0.772089 - 3.38274i) q^{46} +(4.53602 + 2.18443i) q^{47} +(0.987385 - 1.23814i) q^{48} -6.99654 q^{49} +3.52126 q^{50} +(0.361099 - 0.452804i) q^{51} +(-1.51405 + 0.729130i) q^{52} +(1.54659 + 1.93936i) q^{53} +(1.38299 - 0.666014i) q^{54} +(0.812211 - 3.55853i) q^{55} +(-0.0649270 + 0.0814158i) q^{56} +(0.408572 - 1.79007i) q^{57} +(-4.35904 - 2.09920i) q^{58} +(5.58499 + 7.00335i) q^{59} +(2.27620 + 2.85427i) q^{60} +(2.87874 + 12.6126i) q^{61} +(-0.297831 - 0.143428i) q^{62} +(0.141310 - 0.0680513i) q^{63} +(0.715322 + 3.13403i) q^{64} +(-0.743057 - 3.25555i) q^{65} +(-0.251795 + 0.121258i) q^{66} +(8.90339 + 4.28765i) q^{67} +(0.396327 + 1.73642i) q^{68} +(2.67779 + 3.35784i) q^{69} +(-0.0607732 - 0.0762072i) q^{70} +(-3.28246 - 1.58075i) q^{71} +(-1.04896 + 4.59581i) q^{72} +(1.69384 - 2.12401i) q^{73} +(0.344156 - 1.50785i) q^{74} +(-3.92698 + 1.89113i) q^{75} +(3.52057 + 4.41466i) q^{76} +(-0.0546940 + 0.0263393i) q^{77} +(-0.159412 + 0.199896i) q^{78} +12.3199 q^{79} -9.67749 q^{80} +(3.79936 - 4.76425i) q^{81} +(3.42055 + 1.64725i) q^{82} +(-2.61454 - 11.4550i) q^{83} +(0.0135109 - 0.0591952i) q^{84} -3.53918 q^{85} +(2.80355 - 1.24651i) q^{86} +5.98870 q^{87} +(0.406002 - 1.77881i) q^{88} +(-2.77502 - 12.1581i) q^{89} +(-3.97545 - 1.91448i) q^{90} +(-0.0346268 + 0.0434207i) q^{91} -13.2079 q^{92} +0.409177 q^{93} +(-1.46872 + 1.84172i) q^{94} +(-10.1091 + 4.86830i) q^{95} +(1.73966 + 2.18146i) q^{96} +(-0.801582 + 0.386021i) q^{97} +(0.728450 - 3.19155i) q^{98} +(-1.71338 + 2.14851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Introduction

L-functions

Modular forms

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