LMFDB - Embedded newform 847.2.n.i.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	847.9
Dual form			847.2.n.i.753.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49691 + 1.66249i) q^{2} +(1.21952 + 0.542967i) q^{3} +(-0.314069 + 2.98816i) q^{4} +(0.847402 + 0.180121i) q^{5} +(0.922843 + 2.84022i) q^{6} +(2.23951 - 1.40876i) q^{7} +(-1.81822 + 1.32101i) q^{8} +(-0.814967 - 0.905113i) q^{9} +O(q^{10})$	\(q+(1.49691 + 1.66249i) q^{2} +(1.21952 + 0.542967i) q^{3} +(-0.314069 + 2.98816i) q^{4} +(0.847402 + 0.180121i) q^{5} +(0.922843 + 2.84022i) q^{6} +(2.23951 - 1.40876i) q^{7} +(-1.81822 + 1.32101i) q^{8} +(-0.814967 - 0.905113i) q^{9} +(0.969038 + 1.67842i) q^{10} +(-2.00549 + 3.47361i) q^{12} +(-1.04483 + 3.21565i) q^{13} +(5.69440 + 1.61436i) q^{14} +(0.935627 + 0.679773i) q^{15} +(0.960039 + 0.204063i) q^{16} +(-1.46920 + 1.63171i) q^{17} +(0.284806 - 2.70975i) q^{18} +(0.375108 + 3.56891i) q^{19} +(-0.804373 + 2.47560i) q^{20} +(3.49604 - 0.502041i) q^{21} +(-0.834837 + 1.44598i) q^{23} +(-2.93463 + 0.623775i) q^{24} +(-3.88208 - 1.72841i) q^{25} +(-6.90999 + 3.07653i) q^{26} +(-1.73998 - 5.35510i) q^{27} +(3.50625 + 7.13446i) q^{28} +(-1.23968 - 0.900684i) q^{29} +(0.270436 + 2.57303i) q^{30} +(8.68291 - 1.84561i) q^{31} +(3.34529 + 5.79421i) q^{32} -4.91197 q^{34} +(2.15151 - 0.790406i) q^{35} +(2.96058 - 2.15099i) q^{36} +(2.81857 - 1.25491i) q^{37} +(-5.37178 + 5.96597i) q^{38} +(-3.02018 + 3.35425i) q^{39} +(-1.77870 + 0.791930i) q^{40} +(-0.532009 + 0.386527i) q^{41} +(6.06791 + 5.06062i) q^{42} -9.76359 q^{43} +(-0.527575 - 0.913787i) q^{45} +(-3.65361 + 0.776598i) q^{46} +(-1.37931 - 13.1232i) q^{47} +(1.05999 + 0.770128i) q^{48} +(3.03078 - 6.30986i) q^{49} +(-2.93767 - 9.04121i) q^{50} +(-2.67769 + 1.19218i) q^{51} +(-9.28073 - 4.13205i) q^{52} +(-6.42032 + 1.36468i) q^{53} +(6.29821 - 10.9088i) q^{54} +(-2.21092 + 5.51986i) q^{56} +(-1.48035 + 4.55604i) q^{57} +(-0.358322 - 3.40921i) q^{58} +(1.52289 - 14.4894i) q^{59} +(-2.32512 + 2.58231i) q^{60} +(-5.66971 - 1.20513i) q^{61} +(16.0659 + 11.6725i) q^{62} +(-3.10021 - 0.878911i) q^{63} +(-4.01862 + 12.3680i) q^{64} +(-1.46459 + 2.53675i) q^{65} +(-2.64188 - 4.57587i) q^{67} +(-4.41439 - 4.90267i) q^{68} +(-1.80322 + 1.31012i) q^{69} +(4.53466 + 2.39369i) q^{70} +(2.42090 + 7.45077i) q^{71} +(2.67746 + 0.569111i) q^{72} +(0.618530 - 5.88492i) q^{73} +(6.30542 + 2.80735i) q^{74} +(-3.79582 - 4.21568i) q^{75} -10.7823 q^{76} -10.0974 q^{78} +(7.86523 + 8.73522i) q^{79} +(0.776783 + 0.345846i) q^{80} +(0.403767 - 3.84159i) q^{81} +(-1.43897 - 0.305862i) q^{82} +(-0.174158 - 0.536005i) q^{83} +(0.402185 + 10.6044i) q^{84} +(-1.53891 + 1.11808i) q^{85} +(-14.6152 - 16.2319i) q^{86} +(-1.02278 - 1.77151i) q^{87} +(-1.76101 + 3.05016i) q^{89} +(0.729428 - 2.24495i) q^{90} +(2.19019 + 8.67337i) q^{91} +(-4.05863 - 2.94877i) q^{92} +(11.5911 + 2.46377i) q^{93} +(19.7525 - 21.9374i) q^{94} +(-0.324968 + 3.09187i) q^{95} +(0.933594 + 8.88255i) q^{96} +(-4.29963 + 13.2329i) q^{97} +(15.0269 - 4.40668i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} + 34 q^{6} + 13 q^{7} + 32 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 + 34 * q^6 + 13 * q^7 + 32 * q^8 + 2 * q^9	\( 40 q + 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} + 34 q^{6} + 13 q^{7} + 32 q^{8} + 2 q^{9} + 14 q^{10} - 18 q^{12} - 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} - 12 q^{17} - 41 q^{18} - 24 q^{19} + 40 q^{20} - 2 q^{21} - 14 q^{23} - 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} - 24 q^{28} - 30 q^{29} + 6 q^{30} + 3 q^{31} - 30 q^{32} + 48 q^{34} + 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} - 32 q^{39} - 20 q^{40} + 10 q^{41} + 45 q^{42} - 72 q^{43} - 16 q^{45} - 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} + 6 q^{50} + 28 q^{51} + 2 q^{52} - 42 q^{53} + 34 q^{54} + 24 q^{56} - 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} - 20 q^{61} + 128 q^{62} - 36 q^{63} - 36 q^{64} - 40 q^{65} - 38 q^{67} - 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} + 42 q^{72} - 14 q^{73} - q^{74} - 16 q^{75} - 96 q^{76} - 100 q^{78} + 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} + 104 q^{83} - 44 q^{84} + 32 q^{85} + 2 q^{86} + 48 q^{87} - 10 q^{89} + 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} - 18 q^{94} - 8 q^{95} + 7 q^{96} + 46 q^{97} + 116 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 + 34 * q^6 + 13 * q^7 + 32 * q^8 + 2 * q^9 + 14 * q^10 - 18 * q^12 - 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 - 12 * q^17 - 41 * q^18 - 24 * q^19 + 40 * q^20 - 2 * q^21 - 14 * q^23 - 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 - 24 * q^28 - 30 * q^29 + 6 * q^30 + 3 * q^31 - 30 * q^32 + 48 * q^34 + 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 - 32 * q^39 - 20 * q^40 + 10 * q^41 + 45 * q^42 - 72 * q^43 - 16 * q^45 - 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 + 6 * q^50 + 28 * q^51 + 2 * q^52 - 42 * q^53 + 34 * q^54 + 24 * q^56 - 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 - 20 * q^61 + 128 * q^62 - 36 * q^63 - 36 * q^64 - 40 * q^65 - 38 * q^67 - 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 + 42 * q^72 - 14 * q^73 - q^74 - 16 * q^75 - 96 * q^76 - 100 * q^78 + 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 + 104 * q^83 - 44 * q^84 + 32 * q^85 + 2 * q^86 + 48 * q^87 - 10 * q^89 + 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 - 18 * q^94 - 8 * q^95 + 7 * q^96 + 46 * q^97 + 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.49691	+	1.66249i	1.05848	+	1.17556i	0.983969	+	0.178338i	$0.0570720\pi$
$2$	1.49691	+	1.66249i	1.05848	+	1.17556i	0.0745080	+	0.997220i	$0.476261\pi$
$3$	1.21952	+	0.542967i	0.704092	+	0.313482i	0.727369	−	0.686247i	$-0.240743\pi$
$3$	1.21952	+	0.542967i	0.704092	+	0.313482i	−0.0232764	+	0.999729i	$0.507410\pi$
$4$	−0.314069	+	2.98816i	−0.157034	+	1.49408i
$5$	0.847402	+	0.180121i	0.378970	+	0.0805525i	0.393458	−	0.919343i	$-0.371279\pi$
$5$	0.847402	+	0.180121i	0.378970	+	0.0805525i	−0.0144885	+	0.999895i	$0.504612\pi$
$6$	0.922843	+	2.84022i	0.376749	+	1.15951i
$7$	2.23951	−	1.40876i	0.846454	−	0.532462i
$7$	2.23951	−	1.40876i	0.846454	−	0.532462i
$8$	−1.81822	+	1.32101i	−0.642838	+	0.467049i
$9$	−0.814967	−	0.905113i	−0.271656	−	0.301704i
$10$	0.969038	+	1.67842i	0.306437	+	0.530764i
$11$		0			0
$11$		0			0
$12$	−2.00549	+	3.47361i	−0.578934	+	1.00274i
$13$	−1.04483	+	3.21565i	−0.289783	+	0.891860i	0.695141	+	0.718873i	$0.255342\pi$
$13$	−1.04483	+	3.21565i	−0.289783	+	0.891860i	−0.984924	+	0.172987i	$0.944658\pi$
$14$	5.69440	+	1.61436i	1.52189	+	0.431457i
$15$	0.935627	+	0.679773i	0.241578	+	0.175517i
$16$	0.960039	+	0.204063i	0.240010	+	0.0510157i
$17$	−1.46920	+	1.63171i	−0.356333	+	0.395748i	−0.894484	−	0.447101i	$-0.852457\pi$
$17$	−1.46920	+	1.63171i	−0.356333	+	0.395748i	0.538151	+	0.842849i	$0.319123\pi$
$18$	0.284806	−	2.70975i	0.0671295	−	0.638694i
$19$	0.375108	+	3.56891i	0.0860557	+	0.818765i	0.949383	+	0.314121i	$0.101710\pi$
$19$	0.375108	+	3.56891i	0.0860557	+	0.818765i	−0.863327	+	0.504644i	$0.831624\pi$
$20$	−0.804373	+	2.47560i	−0.179863	+	0.553562i
$21$	3.49604	−	0.502041i	0.762899	−	0.109554i
$22$		0			0
$23$	−0.834837	+	1.44598i	−0.174076	+	0.301508i	−0.939841	−	0.341612i	$-0.889027\pi$
$23$	−0.834837	+	1.44598i	−0.174076	+	0.301508i	0.765765	+	0.643120i	$0.222360\pi$
$24$	−2.93463	+	0.623775i	−0.599029	+	0.127327i
$25$	−3.88208	−	1.72841i	−0.776416	−	0.345683i
$26$	−6.90999	+	3.07653i	−1.35516	+	0.603357i
$27$	−1.73998	−	5.35510i	−0.334859	−	1.03059i
$28$	3.50625	+	7.13446i	0.662620	+	1.34829i
$29$	−1.23968	−	0.900684i	−0.230204	−	0.167253i	0.466704	−	0.884414i	$-0.345441\pi$
$29$	−1.23968	−	0.900684i	−0.230204	−	0.167253i	−0.696908	+	0.717161i	$0.745441\pi$
$30$	0.270436	+	2.57303i	0.0493747	+	0.469769i
$31$	8.68291	−	1.84561i	1.55950	−	0.331481i	0.654221	−	0.756304i	$-0.272997\pi$
$31$	8.68291	−	1.84561i	1.55950	−	0.331481i	0.905277	+	0.424822i	$0.139663\pi$
$32$	3.34529	+	5.79421i	0.591369	+	1.02428i
$33$		0			0
$34$	−4.91197			−0.842395
$35$	2.15151	−	0.790406i	0.363671	−	0.133603i
$36$	2.96058	−	2.15099i	0.493430	−	0.358498i
$37$	2.81857	−	1.25491i	0.463370	−	0.206305i	−0.161754	−	0.986831i	$-0.551715\pi$
$37$	2.81857	−	1.25491i	0.463370	−	0.206305i	0.625124	+	0.780526i	$0.285049\pi$
$38$	−5.37178	+	5.96597i	−0.871418	+	0.967808i
$39$	−3.02018	+	3.35425i	−0.483616	+	0.537110i
$40$	−1.77870	+	0.791930i	−0.281238	+	0.125215i
$41$	−0.532009	+	0.386527i	−0.0830858	+	0.0603654i	−0.628553	−	0.777767i	$-0.716352\pi$
$41$	−0.532009	+	0.386527i	−0.0830858	+	0.0603654i	0.545467	+	0.838132i	$0.316352\pi$
$42$	6.06791	+	5.06062i	0.936299	+	0.780871i
$43$	−9.76359			−1.48893			−0.744467	−	0.667660i	$-0.767296\pi$
$43$	−9.76359			−1.48893			−0.744467	+	0.667660i	$0.767296\pi$
$44$		0			0
$45$	−0.527575	−	0.913787i	−0.0786463	−	0.136219i
$46$	−3.65361	+	0.776598i	−0.538695	+	0.114503i
$47$	−1.37931	−	13.1232i	−0.201193	−	1.91422i	−0.370809	−	0.928709i	$-0.620920\pi$
$47$	−1.37931	−	13.1232i	−0.201193	−	1.91422i	0.169616	−	0.985510i	$-0.445747\pi$
$48$	1.05999	+	0.770128i	0.152997	+	0.111158i
$49$	3.03078	−	6.30986i	0.432968	−	0.901409i
$50$	−2.93767	−	9.04121i	−0.415449	−	1.27862i
$51$	−2.67769	+	1.19218i	−0.374951	+	0.166939i
$52$	−9.28073	−	4.13205i	−1.28701	−	0.573012i
$53$	−6.42032	+	1.36468i	−0.881899	+	0.187454i	−0.626537	−	0.779392i	$-0.715528\pi$
$53$	−6.42032	+	1.36468i	−0.881899	+	0.187454i	−0.255363	+	0.966845i	$0.582195\pi$
$54$	6.29821	−	10.9088i	0.857078	−	1.48450i
$55$		0			0
$56$	−2.21092	+	5.51986i	−0.295447	+	0.737622i
$57$	−1.48035	+	4.55604i	−0.196077	+	0.603463i
$58$	−0.358322	−	3.40921i	−0.0470500	−	0.447651i
$59$	1.52289	−	14.4894i	0.198264	−	1.88636i	−0.216287	−	0.976330i	$-0.569395\pi$
$59$	1.52289	−	14.4894i	0.198264	−	1.88636i	0.414551	−	0.910026i	$-0.363939\pi$
$60$	−2.32512	+	2.58231i	−0.300172	+	0.333375i
$61$	−5.66971	−	1.20513i	−0.725932	−	0.154302i	−0.169899	−	0.985462i	$-0.554344\pi$
$61$	−5.66971	−	1.20513i	−0.725932	−	0.154302i	−0.556034	+	0.831160i	$0.687677\pi$
$62$	16.0659	+	11.6725i	2.04037	+	1.48241i
$63$	−3.10021	−	0.878911i	−0.390590	−	0.110732i
$64$	−4.01862	+	12.3680i	−0.502327	+	1.54600i
$65$	−1.46459	+	2.53675i	−0.181660	+	0.314645i
$66$		0			0
$67$	−2.64188	−	4.57587i	−0.322757	−	0.559032i	0.658299	−	0.752757i	$-0.271276\pi$
$67$	−2.64188	−	4.57587i	−0.322757	−	0.559032i	−0.981056	+	0.193725i	$0.937943\pi$
$68$	−4.41439	−	4.90267i	−0.535323	−	0.594537i
$69$	−1.80322	+	1.31012i	−0.217082	+	0.157720i
$70$	4.53466	+	2.39369i	0.541996	+	0.286101i
$71$	2.42090	+	7.45077i	0.287308	+	0.884244i	0.985697	+	0.168525i	$0.0539005\pi$
$71$	2.42090	+	7.45077i	0.287308	+	0.884244i	−0.698389	+	0.715718i	$0.746099\pi$
$72$	2.67746	+	0.569111i	0.315541	+	0.0670704i
$73$	0.618530	−	5.88492i	0.0723935	−	0.688778i	−0.896793	−	0.442450i	$-0.854109\pi$
$73$	0.618530	−	5.88492i	0.0723935	−	0.688778i	0.969187	−	0.246328i	$-0.0792240\pi$
$74$	6.30542	+	2.80735i	0.732990	+	0.326348i
$75$	−3.79582	−	4.21568i	−0.438303	−	0.486785i
$76$	−10.7823			−1.23682
$77$		0			0
$78$	−10.0974			−1.14330
$79$	7.86523	+	8.73522i	0.884908	+	0.982789i	0.999944	−	0.0105718i	$-0.00336517\pi$
$79$	7.86523	+	8.73522i	0.884908	+	0.982789i	−0.115037	+	0.993361i	$0.536699\pi$
$80$	0.776783	+	0.345846i	0.0868470	+	0.0386668i
$81$	0.403767	−	3.84159i	0.0448630	−	0.426843i
$82$	−1.43897	−	0.305862i	−0.158907	−	0.0337768i
$83$	−0.174158	−	0.536005i	−0.0191164	−	0.0588341i	0.941043	−	0.338286i	$-0.109847\pi$
$83$	−0.174158	−	0.536005i	−0.0191164	−	0.0588341i	−0.960160	+	0.279452i	$0.909847\pi$
$84$	0.402185	+	10.6044i	0.0438820	+	1.15704i
$85$	−1.53891	+	1.11808i	−0.166918	+	0.121273i
$86$	−14.6152	−	16.2319i	−1.57600	−	1.75033i
$87$	−1.02278	−	1.77151i	−0.109654	−	0.189926i
$88$		0			0
$89$	−1.76101	+	3.05016i	−0.186667	+	0.323317i	−0.944137	−	0.329553i	$-0.893102\pi$
$89$	−1.76101	+	3.05016i	−0.186667	+	0.323317i	0.757470	+	0.652870i	$0.226435\pi$
$90$	0.729428	−	2.24495i	0.0768884	−	0.236638i
$91$	2.19019	+	8.67337i	0.229594	+	0.909216i
$92$	−4.05863	−	2.94877i	−0.423141	−	0.307430i
$93$	11.5911	+	2.46377i	1.20194	+	0.255481i
$94$	19.7525	−	21.9374i	2.03732	−	2.26267i
$95$	−0.324968	+	3.09187i	−0.0333411	+	0.317219i
$96$	0.933594	+	8.88255i	0.0952845	+	0.906571i
$97$	−4.29963	+	13.2329i	−0.436561	+	1.34360i	0.454918	+	0.890534i	$0.349669\pi$
$97$	−4.29963	+	13.2329i	−0.436561	+	1.34360i	−0.891479	+	0.453063i	$0.850331\pi$
$98$	15.0269	−	4.40668i	1.51795	−	0.445142i
$99$		0			0
$100$	6.38402	−	11.0575i	0.638402	−	1.10575i
$101$	11.8727	−	2.52361i	1.18137	−	0.251109i	0.424967	−	0.905209i	$-0.360286\pi$
$101$	11.8727	−	2.52361i	1.18137	−	0.251109i	0.756408	+	0.654100i	$0.226953\pi$
$102$	−5.99026	−	2.66703i	−0.593124	−	0.264076i
$103$	2.63187	−	1.17178i	0.259326	−	0.115459i	−0.272956	−	0.962027i	$-0.588001\pi$
$103$	2.63187	−	1.17178i	0.259326	−	0.115459i	0.532282	+	0.846567i	$0.321335\pi$
$104$	−2.34819	−	7.22698i	−0.230259	−	0.708664i
$105$	3.05298	+	0.204279i	0.297940	+	0.0199356i
$106$	−11.8794	−	8.63092i	−1.15383	−	0.838309i
$107$	0.0975766	+	0.928379i	0.00943309	+	0.0897498i	0.998225	−	0.0595471i	$-0.0189656\pi$
$107$	0.0975766	+	0.928379i	0.00943309	+	0.0897498i	−0.988792	+	0.149297i	$0.952299\pi$
$108$	16.5484	−	3.51747i	1.59237	−	0.338469i
$109$	−6.08365	−	10.5372i	−0.582708	−	1.00928i	−0.995157	−	0.0982988i	$-0.968660\pi$
$109$	−6.08365	−	10.5372i	−0.582708	−	1.00928i	0.412449	−	0.910981i	$-0.364673\pi$
$110$		0			0
$111$	4.11868			0.390928
$112$	2.43749	−	0.895468i	0.230321	−	0.0846137i
$113$	−10.3511	+	7.52051i	−0.973748	+	0.707470i	−0.956303	−	0.292378i	$-0.905553\pi$
$113$	−10.3511	+	7.52051i	−0.973748	+	0.707470i	−0.0174457	+	0.999848i	$0.505553\pi$
$114$	−9.79033	+	4.35894i	−0.916949	+	0.408252i
$115$	−0.967894	+	1.07495i	−0.0902565	+	0.100240i
$116$	3.08074	−	3.42150i	0.286039	−	0.317679i
$117$	3.76202	−	1.67496i	0.347799	−	0.154850i
$118$	26.3681	−	19.1575i	2.42738	−	1.76359i
$119$	−0.991587	+	5.72398i	−0.0908986	+	0.524716i
$120$	−2.59916			−0.237270
$121$		0			0
$122$	−6.48354	−	11.2298i	−0.586992	−	1.01670i
$123$	−0.858668	+	0.182516i	−0.0774235	+	0.0164569i
$124$	2.78795	+	26.5256i	0.250366	+	2.38207i
$125$	−6.48275	−	4.70999i	−0.579835	−	0.421275i
$126$	−3.17957	−	6.46973i	−0.283259	−	0.576369i
$127$	0.685645	+	2.11020i	0.0608411	+	0.187250i	0.976858	−	0.213891i	$-0.0686138\pi$
$127$	0.685645	+	2.11020i	0.0608411	+	0.187250i	−0.916016	+	0.401141i	$0.868614\pi$
$128$	−14.3530	+	6.39035i	−1.26863	+	0.564833i
$129$	−11.9069	−	5.30130i	−1.04835	−	0.466754i
$130$	−6.40969	+	1.36242i	−0.562167	+	0.119492i
$131$	−0.633382	+	1.09705i	−0.0553388	+	0.0958497i	−0.892368	−	0.451309i	$-0.850957\pi$
$131$	−0.633382	+	1.09705i	−0.0553388	+	0.0958497i	0.837029	+	0.547159i	$0.184291\pi$
$132$		0			0
$133$	5.86781	+	7.46417i	0.508804	+	0.647225i
$134$	3.65268	−	11.2418i	0.315543	−	0.971143i
$135$	−0.509895	−	4.85133i	−0.0438848	−	0.417536i
$136$	0.515814	−	4.90764i	0.0442307	−	0.420827i
$137$	4.36466	−	4.84744i	0.372898	−	0.414145i	−0.527263	−	0.849702i	$-0.676782\pi$
$137$	4.36466	−	4.84744i	0.372898	−	0.414145i	0.900161	+	0.435557i	$0.143449\pi$
$138$	−4.87733	−	1.03671i	−0.415186	−	0.0882504i
$139$	11.5011	+	8.35605i	0.975512	+	0.708751i	0.956701	−	0.291072i	$-0.0940119\pi$
$139$	11.5011	+	8.35605i	0.975512	+	0.708751i	0.0188112	+	0.999823i	$0.494012\pi$
$140$	1.68614	+	6.67730i	0.142505	+	0.564335i
$141$	5.44338	−	16.7530i	0.458415	−	1.41086i
$142$	−8.76295	+	15.1779i	−0.735371	+	1.27370i
$143$		0			0
$144$	−0.597701	−	1.03525i	−0.0498084	−	0.0862707i
$145$	−0.888279	−	0.986534i	−0.0737676	−	0.0819272i
$146$	10.7095	−	7.78091i	0.886325	−	0.643953i
$147$	7.12215	−	6.04942i	0.587425	−	0.498948i
$148$	2.86464	+	8.81647i	0.235472	+	0.724709i
$149$	−3.59580	−	0.764311i	−0.294579	−	0.0626148i	0.0582513	−	0.998302i	$-0.481448\pi$
$149$	−3.59580	−	0.764311i	−0.294579	−	0.0626148i	−0.352831	+	0.935687i	$0.614781\pi$
$150$	1.32652	−	12.6210i	0.108310	−	1.03050i
$151$	−8.08256	−	3.59859i	−0.657750	−	0.292849i	0.0505913	−	0.998719i	$-0.483889\pi$
$151$	−8.08256	−	3.59859i	−0.657750	−	0.292849i	−0.708341	+	0.705870i	$0.750556\pi$
$152$	−5.39661	−	5.99355i	−0.437723	−	0.486141i
$153$	2.67423			0.216199
$154$		0			0
$155$	7.69035			0.617704
$156$	−9.07450	−	10.0783i	−0.726541	−	0.806906i
$157$	2.10725	+	0.938209i	0.168177	+	0.0748772i	0.489098	−	0.872229i	$-0.337326\pi$
$157$	2.10725	+	0.938209i	0.168177	+	0.0748772i	−0.320921	+	0.947106i	$0.603993\pi$
$158$	−2.74866	+	26.1517i	−0.218672	+	2.08052i
$159$	−8.57071	−	1.82176i	−0.679702	−	0.144475i
$160$	1.79114	+	5.51258i	0.141602	+	0.435807i
$161$	0.167420	+	4.41437i	0.0131945	+	0.347901i
$162$	6.99101	−	5.07927i	0.549266	−	0.399065i
$163$	−3.83555	−	4.25981i	−0.300424	−	0.333654i	0.573966	−	0.818879i	$-0.305404\pi$
$163$	−3.83555	−	4.25981i	−0.300424	−	0.333654i	−0.874389	+	0.485225i	$0.838738\pi$
$164$	−0.987918	−	1.71112i	−0.0771435	−	0.133616i
$165$		0			0
$166$	0.630402	−	1.09189i	0.0489287	−	0.0847470i
$167$	0.996382	−	3.06655i	0.0771023	−	0.237297i	−0.905075	−	0.425251i	$-0.860186\pi$
$167$	0.996382	−	3.06655i	0.0771023	−	0.237297i	0.982178	+	0.187955i	$0.0601858\pi$
$168$	−5.69337	+	5.53114i	−0.439253	+	0.426737i
$169$	1.26851	+	0.921624i	0.0975774	+	0.0708941i
$170$	−4.16241	−	0.884747i	−0.319242	−	0.0678570i
$171$	2.92457	−	3.24806i	0.223647	−	0.248386i
$172$	3.06644	−	29.1752i	0.233814	−	2.22459i
$173$	0.878080	+	8.35438i	0.0667592	+	0.635172i	0.975830	+	0.218530i	$0.0701262\pi$
$173$	0.878080	+	8.35438i	0.0667592	+	0.635172i	−0.909071	+	0.416641i	$0.863207\pi$
$174$	1.41410	−	4.35217i	0.107203	−	0.329937i
$175$	−11.1289	+	1.59814i	−0.841263	+	0.120808i
$176$		0			0
$177$	9.72446	−	16.8433i	0.730935	−	1.26602i
$178$	−7.70695	+	1.63816i	−0.577660	+	0.122786i
$179$	−2.34584	−	1.04444i	−0.175336	−	0.0780648i	0.317191	−	0.948362i	$-0.397260\pi$
$179$	−2.34584	−	1.04444i	−0.175336	−	0.0780648i	−0.492528	+	0.870297i	$0.663927\pi$
$180$	2.89624	−	1.28949i	0.215873	−	0.0961128i
$181$	0.547997	+	1.68656i	0.0407323	+	0.125361i	0.969355	−	0.245665i	$-0.0790062\pi$
$181$	0.547997	+	1.68656i	0.0407323	+	0.125361i	−0.928623	+	0.371026i	$0.879006\pi$
$182$	−11.1409	+	16.6244i	−0.825817	+	1.23229i
$183$	−6.26000	−	4.54816i	−0.462752	−	0.336209i
$184$	−0.392243	−	3.73194i	−0.0289165	−	0.275122i
$185$	2.61449	−	0.555728i	0.192221	−	0.0408579i
$186$	13.2549	+	22.9582i	0.971897	+	1.68338i
$187$		0			0
$188$	39.6475			2.89159
$189$	−11.4408	−	9.54157i	−0.832193	−	0.694047i
$190$	−5.62665	+	4.08800i	−0.408200	+	0.296575i
$191$	−7.56494	+	3.36813i	−0.547380	+	0.243709i	−0.661744	−	0.749730i	$-0.730184\pi$
$191$	−7.56494	+	3.36813i	−0.547380	+	0.243709i	0.114364	+	0.993439i	$0.463517\pi$
$192$	−11.6162	+	12.9011i	−0.838329	+	0.931059i
$193$	−12.7308	+	14.1389i	−0.916380	+	1.01774i	0.0833944	+	0.996517i	$0.473424\pi$
$193$	−12.7308	+	14.1389i	−0.916380	+	1.01774i	−0.999775	+	0.0212268i	$0.993243\pi$
$194$	−28.4357	+	12.6604i	−2.04157	+	0.908964i
$195$	−3.16348	+	2.29840i	−0.226541	+	0.164592i
$196$	17.9030	+	11.0382i	1.27879	+	0.788442i
$197$	15.1831			1.08175			0.540877	−	0.841102i	$-0.318093\pi$
$197$	15.1831			1.08175			0.540877	+	0.841102i	$0.318093\pi$
$198$		0			0
$199$	12.3023	+	21.3082i	0.872086	+	1.51050i	0.859835	+	0.510573i	$0.170567\pi$
$199$	12.3023	+	21.3082i	0.872086	+	1.51050i	0.0122517	+	0.999925i	$0.496100\pi$
$200$	9.34174	−	1.98565i	0.660561	−	0.140406i
$201$	−0.737289	−	7.01484i	−0.0520044	−	0.494789i
$202$	21.9678	+	15.9606i	1.54565	+	1.12298i
$203$	−4.04513	−	0.270665i	−0.283913	−	0.0189970i
$204$	−2.72146	−	8.37579i	−0.190540	−	0.586423i
$205$	−0.520447	+	0.231718i	−0.0363496	+	0.0161839i
$206$	5.88776	+	2.62140i	0.410219	+	0.182641i
$207$	1.98914	−	0.422805i	0.138255	−	0.0293870i
$208$	−1.65927	+	2.87394i	−0.115049	+	0.199272i
$209$		0			0
$210$	4.23043	+	5.38134i	0.291928	+	0.371348i
$211$	−5.37599	+	16.5456i	−0.370098	+	1.13905i	0.576628	+	0.817007i	$0.304368\pi$
$211$	−5.37599	+	16.5456i	−0.370098	+	1.13905i	−0.946726	+	0.322039i	$0.895632\pi$
$212$	−2.06147	−	19.6136i	−0.141582	−	1.34707i
$213$	−1.09317	+	10.4009i	−0.0749031	+	0.712655i
$214$	−1.39736	+	1.55192i	−0.0955214	+	0.106087i
$215$	−8.27368	−	1.75863i	−0.564260	−	0.119937i
$216$	10.2378	+	7.43822i	0.696596	+	0.506107i
$217$	16.8454	−	16.3654i	1.14354	−	1.11096i
$218$	8.41128	−	25.8873i	0.569684	−	1.75331i
$219$	3.94963	−	6.84096i	0.266891	−	0.462269i
$220$		0			0
$221$	−3.71194	−	6.42928i	−0.249692	−	0.432480i
$222$	6.16531	+	6.84727i	0.413788	+	0.459559i
$223$	−2.17841	+	1.58270i	−0.145877	+	0.105986i	−0.658330	−	0.752729i	$-0.728737\pi$
$223$	−2.17841	+	1.58270i	−0.145877	+	0.105986i	0.512453	+	0.858715i	$0.328737\pi$
$224$	15.6544	+	8.26345i	1.04596	+	0.552125i
$225$	1.59936	+	4.92232i	0.106624	+	0.328155i
$226$	−27.9974	−	5.95104i	−1.86236	−	0.395857i
$227$	2.40466	−	22.8788i	0.159603	−	1.51852i	−0.562538	−	0.826771i	$-0.690175\pi$
$227$	2.40466	−	22.8788i	0.159603	−	1.51852i	0.722141	−	0.691746i	$-0.243158\pi$
$228$	−13.1493	−	5.85443i	−0.870832	−	0.387719i
$229$	11.9826	+	13.3080i	0.791829	+	0.879416i	0.995015	−	0.0997246i	$-0.0317962\pi$
$229$	11.9826	+	13.3080i	0.791829	+	0.879416i	−0.203186	+	0.979140i	$0.565130\pi$
$230$	−3.23595			−0.213372
$231$		0			0
$232$	3.44384			0.226099
$233$	−13.6929	−	15.2075i	−0.897053	−	0.996279i	−0.999999	−	0.00159165i	$-0.999493\pi$
$233$	−13.6929	−	15.2075i	−0.897053	−	0.996279i	0.102945	−	0.994687i	$-0.467173\pi$
$234$	8.41603	+	3.74706i	0.550173	+	0.244953i
$235$	1.19494	−	11.3691i	0.0779492	−	0.741637i
$236$	42.8183	+	9.10132i	2.78724	+	0.592445i
$237$	4.84890	+	14.9234i	0.314970	+	0.969377i
$238$	−11.0004	+	6.91979i	−0.713049	+	0.448544i
$239$	−5.67652	+	4.12423i	−0.367184	+	0.266775i	−0.756042	−	0.654523i	$-0.772870\pi$
$239$	−5.67652	+	4.12423i	−0.367184	+	0.266775i	0.388858	+	0.921297i	$0.372870\pi$
$240$	0.759522	+	0.843535i	0.0490269	+	0.0544499i
$241$	−5.56584	−	9.64031i	−0.358527	−	0.620987i	0.629188	−	0.777253i	$-0.283388\pi$
$241$	−5.56584	−	9.64031i	−0.358527	−	0.620987i	−0.987715	+	0.156266i	$0.950054\pi$
$242$		0			0
$243$	−5.86777	+	10.1633i	−0.376418	+	0.651975i
$244$	5.38182	−	16.5635i	0.344536	−	1.06037i
$245$	3.70482	−	4.80108i	0.236692	−	0.306730i
$246$	−1.58878	−	1.15432i	−0.101297	−	0.0735966i
$247$	−11.8683	−	2.52268i	−0.755161	−	0.160514i
$248$	−13.3494	+	14.8260i	−0.847686	+	0.941450i
$249$	0.0786424	−	0.748232i	0.00498376	−	0.0474173i
$250$	−1.87379	−	17.8280i	−0.118509	−	1.12754i
$251$	3.27255	−	10.0719i	0.206562	−	0.635732i	−0.793084	−	0.609113i	$-0.791526\pi$
$251$	3.27255	−	10.0719i	0.206562	−	0.635732i	0.999646	−	0.0266194i	$-0.00847423\pi$
$252$	3.60001	−	8.98791i	0.226779	−	0.566185i
$253$		0			0
$254$	−2.48183	+	4.29866i	−0.155724	+	0.269722i
$255$	−2.48381	+	0.527951i	−0.155542	+	0.0330616i
$256$	−8.34861	−	3.71704i	−0.521788	−	0.232315i
$257$	0.549319	−	0.244573i	0.0342656	−	0.0152560i	−0.389532	−	0.921013i	$-0.627363\pi$
$257$	0.549319	−	0.244573i	0.0342656	−	0.0152560i	0.423798	+	0.905757i	$0.360697\pi$
$258$	−9.01026	−	27.7307i	−0.560954	−	1.72644i
$259$	4.54433	−	6.78106i	0.282371	−	0.421355i
$260$	−7.12024	−	5.17315i	−0.441578	−	0.320825i
$261$	0.195082	+	1.85608i	0.0120753	+	0.114889i
$262$	−2.77195	+	0.589197i	−0.171252	+	0.0364007i
$263$	8.60688	+	14.9076i	0.530723	+	0.919240i	0.999357	+	0.0358472i	$0.0114130\pi$
$263$	8.60688	+	14.9076i	0.530723	+	0.919240i	−0.468634	+	0.883392i	$0.655254\pi$
$264$		0			0
$265$	−5.68640			−0.349313
$266$	−3.62551	+	20.9284i	−0.222294	+	1.28320i
$267$	−3.80373	+	2.76357i	−0.232785	+	0.169128i
$268$	14.5032	−	6.45724i	0.885923	−	0.394438i
$269$	13.9367	−	15.4782i	0.849733	−	0.943724i	−0.149250	−	0.988799i	$-0.547686\pi$
$269$	13.9367	−	15.4782i	0.849733	−	0.943724i	0.998984	+	0.0450750i	$0.0143527\pi$
$270$	7.30202	−	8.10971i	0.444387	−	0.493541i
$271$	−21.2167	+	9.44627i	−1.28882	+	0.573820i	−0.932711	−	0.360624i	$-0.882564\pi$
$271$	−21.2167	+	9.44627i	−1.28882	+	0.573820i	−0.356110	+	0.934444i	$0.615897\pi$
$272$	−1.74346	+	1.26670i	−0.105713	+	0.0768048i
$273$	−2.03837	+	11.7666i	−0.123368	+	0.712146i
$274$	14.5923			0.881556
$275$		0			0
$276$	−3.34851	−	5.79979i	−0.201557	−	0.349106i
$277$	−7.75291	+	1.64793i	−0.465827	+	0.0990147i	−0.434845	−	0.900505i	$-0.643197\pi$
$277$	−7.75291	+	1.64793i	−0.465827	+	0.0990147i	−0.0309823	+	0.999520i	$0.509864\pi$
$278$	3.32432	+	31.6288i	0.199379	+	1.89697i
$279$	−8.74678	−	6.35491i	−0.523656	−	0.380458i
$280$	−2.86778	+	4.27931i	−0.171383	+	0.255737i
$281$	2.99866	+	9.22892i	0.178885	+	0.550551i	0.999790	−	0.0205139i	$-0.00653025\pi$
$281$	2.99866	+	9.22892i	0.178885	+	0.550551i	−0.820905	+	0.571065i	$0.806530\pi$
$282$	36.0000	−	16.0282i	2.14377	−	0.954466i
$283$	11.4579	+	5.10139i	0.681101	+	0.303246i	0.717970	−	0.696074i	$-0.245072\pi$
$283$	11.4579	+	5.10139i	0.681101	+	0.303246i	−0.0368684	+	0.999320i	$0.511738\pi$
$284$	−23.0244	+	4.89400i	−1.36625	+	0.290405i
$285$	−2.07509	+	3.59416i	−0.122918	+	0.212900i
$286$		0			0
$287$	−0.646912	+	1.61510i	−0.0381860	+	0.0953365i
$288$	2.51811	−	7.74995i	0.148381	−	0.456670i
$289$	1.27305	+	12.1123i	0.0748853	+	0.712486i
$290$	0.310426	−	2.95351i	0.0182289	−	0.173436i
$291$	−12.4285	+	13.8033i	−0.728572	+	0.809162i
$292$	17.3908	+	3.69654i	1.01772	+	0.216323i
$293$	5.38951	+	3.91571i	0.314858	+	0.228758i	0.733978	−	0.679173i	$-0.237661\pi$
$293$	5.38951	+	3.91571i	0.314858	+	0.228758i	−0.419120	+	0.907931i	$0.637661\pi$
$294$	20.7183	+	2.78505i	1.20832	+	0.162428i
$295$	3.90034	−	12.0040i	0.227087	−	0.698901i
$296$	−3.46702	+	6.00506i	−0.201517	+	0.349037i
$297$		0			0
$298$	−4.11194	−	7.12209i	−0.238198	−	0.412572i
$299$	−3.77750	−	4.19534i	−0.218458	−	0.242623i
$300$	13.7893	−	10.0185i	0.796125	−	0.578419i
$301$	−21.8656	+	13.7546i	−1.26031	+	0.792801i
$302$	−6.11627	−	18.8240i	−0.351952	−	1.08320i
$303$	15.8492	+	3.36886i	0.910515	+	0.193536i
$304$	−0.368164	+	3.50284i	−0.0211156	+	0.200902i
$305$	−4.58745	−	2.04247i	−0.262677	−	0.116951i
$306$	4.00309	+	4.44588i	0.228842	+	0.254154i
$307$	−2.06252			−0.117714			−0.0588572	−	0.998266i	$-0.518746\pi$
$307$	−2.06252			−0.117714			−0.0588572	+	0.998266i	$0.518746\pi$
$308$		0			0
$309$	3.84586			0.218784
$310$	11.5118	+	12.7851i	0.653825	+	0.726147i
$311$	3.23771	+	1.44152i	0.183593	+	0.0817411i	0.496475	−	0.868051i	$-0.334628\pi$
$311$	3.23771	+	1.44152i	0.183593	+	0.0817411i	−0.312881	+	0.949792i	$0.601294\pi$
$312$	1.06034	−	10.0885i	0.0600299	−	0.571147i
$313$	15.2155	+	3.23416i	0.860033	+	0.182806i	0.616759	−	0.787152i	$-0.288445\pi$
$313$	15.2155	+	3.23416i	0.860033	+	0.182806i	0.243274	+	0.969958i	$0.421779\pi$
$314$	1.59461	+	4.90770i	0.0899890	+	0.276958i
$315$	−2.46882	−	1.30320i	−0.139102	−	0.0734272i
$316$	−28.5725	+	20.7591i	−1.60733	+	1.16779i
$317$	−11.1217	−	12.3519i	−0.624656	−	0.693751i	0.344895	−	0.938641i	$-0.387915\pi$
$317$	−11.1217	−	12.3519i	−0.624656	−	0.693751i	−0.969551	+	0.244891i	$0.921248\pi$
$318$	−9.80095	−	16.9757i	−0.549610	−	0.951953i
$319$		0			0
$320$	−5.63312	+	9.75685i	−0.314901	+	0.545425i
$321$	−0.385082	+	1.18516i	−0.0214932	+	0.0661493i
$322$	−7.08823	+	6.88626i	−0.395012	+	0.383756i
$323$	−6.37454	−	4.63138i	−0.354689	−	0.257697i
$324$	11.3525	+	2.41305i	0.630694	+	0.134058i
$325$	9.61407	−	10.6775i	0.533293	−	0.592281i
$326$	1.34041	−	12.7531i	0.0742383	−	0.706331i
$327$	−1.69781	−	16.1536i	−0.0938890	−	0.893294i
$328$	0.456701	−	1.40558i	0.0252171	−	0.0776103i
$329$	−21.5765	−	27.4464i	−1.18955	−	1.51317i
$330$		0			0
$331$	−10.5203	+	18.2217i	−0.578249	+	1.00156i	0.417431	+	0.908709i	$0.362930\pi$
$331$	−10.5203	+	18.2217i	−0.578249	+	1.00156i	−0.995680	+	0.0928482i	$0.970403\pi$
$332$	1.65637	−	0.352072i	0.0909049	−	0.0193224i
$333$	−3.43287	−	1.52841i	−0.188120	−	0.0837565i
$334$	6.58960	−	2.93388i	0.360567	−	0.160535i
$335$	−1.41453	−	4.35346i	−0.0772838	−	0.237855i
$336$	3.45878	+	0.231432i	0.188692	+	0.0126257i
$337$	24.4873	+	17.7910i	1.33391	+	0.969139i	0.999645	+	0.0266588i	$0.00848677\pi$
$337$	24.4873	+	17.7910i	1.33391	+	0.969139i	0.334261	+	0.942480i	$0.391513\pi$
$338$	0.366653	+	3.48847i	0.0199433	+	0.189748i
$339$	−16.7068	+	3.55114i	−0.907388	+	0.192871i
$340$	−2.85769	−	4.94966i	−0.154980	−	0.268433i
$341$		0			0
$342$	9.77770			0.528717
$343$	−2.10166	−	18.4006i	−0.113479	−	0.993540i
$344$	17.7523	−	12.8978i	0.957142	−	0.695405i
$345$	−1.76403	+	0.785398i	−0.0949724	+	0.0422844i
$346$	−12.5747	+	13.9656i	−0.676018	+	0.750794i
$347$	17.5446	−	19.4853i	0.941846	−	1.04603i	−0.0570178	−	0.998373i	$-0.518159\pi$
$347$	17.5446	−	19.4853i	0.941846	−	1.04603i	0.998864	−	0.0476529i	$-0.0151741\pi$
$348$	5.61479	−	2.49987i	0.300984	−	0.134007i
$349$	8.63934	−	6.27685i	0.462453	−	0.335992i	−0.332040	−	0.943265i	$-0.607737\pi$
$349$	8.63934	−	6.27685i	0.462453	−	0.335992i	0.794493	+	0.607273i	$0.207737\pi$
$350$	−19.3158	−	16.1094i	−1.03247	−	0.861082i
$351$	19.0381			1.01618
$352$		0			0
$353$	−1.94930	−	3.37628i	−0.103751	−	0.179701i	0.809476	−	0.587152i	$-0.199751\pi$
$353$	−1.94930	−	3.37628i	−0.103751	−	0.179701i	−0.913227	+	0.407451i	$0.866418\pi$
$354$	42.5584	−	9.04607i	2.26195	−	0.480793i
$355$	0.709438	+	6.74985i	0.0376531	+	0.358245i
$356$	−8.56131	−	6.22016i	−0.453748	−	0.329668i
$357$	−4.31719	+	6.44213i	−0.228490	+	0.340953i
$358$	−1.77516	−	5.46337i	−0.0938199	−	0.288748i
$359$	−19.4896	+	8.67734i	−1.02862	+	0.457973i	−0.850466	−	0.526029i	$-0.823680\pi$
$359$	−19.4896	+	8.67734i	−1.02862	+	0.457973i	−0.178157	+	0.984002i	$0.557014\pi$
$360$	2.16637	+	0.964531i	0.114178	+	0.0508353i
$361$	5.98837	−	1.27287i	0.315177	−	0.0669930i
$362$	−1.98359	+	3.43568i	−0.104255	+	0.180575i
$363$		0			0
$364$	−26.6053	+	3.82060i	−1.39450	+	0.200254i
$365$	1.58414	−	4.87548i	0.0829177	−	0.255194i
$366$	−1.80941	−	17.2154i	−0.0945794	−	0.899862i
$367$	−0.0614645	+	0.584795i	−0.00320842	+	0.0305261i	−0.996009	−	0.0892531i	$-0.971552\pi$
$367$	−0.0614645	+	0.584795i	−0.00320842	+	0.0305261i	0.992801	+	0.119779i	$0.0382187\pi$
$368$	−1.09655	+	1.21784i	−0.0571614	+	0.0634842i
$369$	0.783420	+	0.166521i	0.0407832	+	0.00866874i
$370$	4.83756	+	3.51469i	0.251493	+	0.182720i
$371$	−12.4558	+	12.1009i	−0.646675	+	0.628249i
$372$	−11.0026	+	33.8624i	−0.570456	+	1.75568i
$373$	6.65785	−	11.5317i	0.344730	−	0.597090i	−0.640575	−	0.767896i	$-0.721304\pi$
$373$	6.65785	−	11.5317i	0.344730	−	0.597090i	0.985305	+	0.170806i	$0.0546371\pi$
$374$		0			0
$375$	−5.34850	−	9.26387i	−0.276195	−	0.478384i
$376$	19.8439	+	22.0388i	1.02337	+	1.13657i
$377$	4.19153	−	3.04533i	0.215875	−	0.156842i
$378$	−1.26306	−	33.3030i	−0.0649646	−	1.71292i
$379$	2.68691	+	8.26947i	0.138017	+	0.424774i	0.996047	−	0.0888260i	$-0.0283115\pi$
$379$	2.68691	+	8.26947i	0.138017	+	0.424774i	−0.858030	+	0.513600i	$0.828311\pi$
$380$	−9.13694	−	1.94212i	−0.468715	−	0.0996285i
$381$	−0.309607	+	2.94572i	−0.0158617	+	0.150914i
$382$	−16.9235	−	7.53484i	−0.865883	−	0.385516i
$383$	20.6511	+	22.9354i	1.05522	+	1.17194i	0.984669	+	0.174435i	$0.0558098\pi$
$383$	20.6511	+	22.9354i	1.05522	+	1.17194i	0.0705534	+	0.997508i	$0.477523\pi$
$384$	−20.9735			−1.07030
$385$		0			0
$386$	−42.5627			−2.16638
$387$	7.95700	+	8.83715i	0.404477	+	0.449218i
$388$	−38.1917	−	17.0040i	−1.93889	−	0.863248i
$389$	−0.536001	+	5.09971i	−0.0271763	+	0.258565i	0.972495	+	0.232924i	$0.0748294\pi$
$389$	−0.536001	+	5.09971i	−0.0271763	+	0.258565i	−0.999671	+	0.0256412i	$0.991837\pi$
$390$	−8.55651	−	1.81874i	−0.433276	−	0.0920956i
$391$	−1.13288	−	3.48664i	−0.0572922	−	0.176327i
$392$	2.82480	+	15.4764i	0.142674	+	0.781677i
$393$	−1.36809	+	0.993972i	−0.0690108	+	0.0501393i
$394$	22.7278	+	25.2418i	1.14501	+	1.27166i
$395$	5.09161	+	8.81894i	0.256187	+	0.443729i
$396$		0			0
$397$	14.6266	−	25.3340i	0.734088	−	1.27148i	−0.221034	−	0.975266i	$-0.570943\pi$
$397$	14.6266	−	25.3340i	0.734088	−	1.27148i	0.955122	−	0.296212i	$-0.0957234\pi$
$398$	−17.0092	+	52.3490i	−0.852594	+	2.62402i
$399$	3.10314	+	12.2888i	0.155351	+	0.615207i
$400$	−3.37424	−	2.45153i	−0.168712	−	0.122577i
$401$	−14.2054	−	3.01946i	−0.709385	−	0.150784i	−0.160932	−	0.986966i	$-0.551450\pi$
$401$	−14.2054	−	3.01946i	−0.709385	−	0.150784i	−0.548454	+	0.836181i	$0.684783\pi$
$402$	10.5584	−	11.7263i	0.526607	−	0.584857i
$403$	−3.13731	+	29.8495i	−0.156281	+	1.48691i
$404$	3.81214	+	36.2701i	0.189661	+	1.80450i
$405$	1.03410	−	3.18264i	0.0513850	−	0.158147i
$406$	−5.60523	−	7.13015i	−0.278183	−	0.353864i
$407$		0			0
$408$	3.29373	−	5.70491i	0.163064	−	0.282435i
$409$	−11.6740	+	2.48138i	−0.577240	+	0.122696i	−0.487275	−	0.873249i	$-0.662009\pi$
$409$	−11.6740	+	2.48138i	−0.577240	+	0.122696i	−0.0899655	+	0.995945i	$0.528676\pi$
$410$	−1.16429	−	0.518376i	−0.0575003	−	0.0256008i
$411$	7.95481	−	3.54171i	0.392382	−	0.174700i
$412$	2.67489	+	8.23247i	0.131783	+	0.405585i
$413$	−17.0016	−	34.5944i	−0.836592	−	1.70228i
$414$	3.68048	+	2.67402i	0.180886	+	0.131421i
$415$	−0.0510366	−	0.485581i	−0.00250529	−	0.0238362i
$416$	−22.1274	+	4.70332i	−1.08488	+	0.230599i
$417$	9.48883	+	16.4351i	0.464670	+	0.804832i
$418$		0			0
$419$	−15.3521			−0.749999			−0.374999	−	0.927025i	$-0.622357\pi$
$419$	−15.3521			−0.749999			−0.374999	+	0.927025i	$0.622357\pi$
$420$	−1.56926	+	9.05864i	−0.0765723	+	0.442017i
$421$	6.14320	−	4.46330i	0.299401	−	0.217528i	−0.427934	−	0.903810i	$-0.640758\pi$
$421$	6.14320	−	4.46330i	0.299401	−	0.217528i	0.727335	+	0.686282i	$0.240758\pi$
$422$	−35.5543	+	15.8298i	−1.73076	+	0.770582i
$423$	−10.7539	+	11.9434i	−0.522873	+	0.580709i
$424$	9.87080	−	10.9626i	0.479368	−	0.532392i
$425$	8.52382	−	3.79505i	0.413466	−	0.184087i
$426$	−18.9277	+	13.7518i	−0.917051	+	0.666276i
$427$	−14.3951	+	5.28837i	−0.696628	+	0.255922i
$428$	−2.80480			−0.135575
$429$		0			0
$430$	−9.46128	−	16.3874i	−0.456264	−	0.790272i
$431$	−25.7717	+	5.47794i	−1.24138	+	0.263863i	−0.781379	−	0.624056i	$-0.785484\pi$
$431$	−25.7717	+	5.47794i	−1.24138	+	0.263863i	−0.459999	+	0.887919i	$0.652150\pi$
$432$	−0.577671	−	5.49617i	−0.0277932	−	0.264435i
$433$	−6.01186	−	4.36787i	−0.288912	−	0.209907i	0.433883	−	0.900969i	$-0.357143\pi$
$433$	−6.01186	−	4.36787i	−0.288912	−	0.209907i	−0.722795	+	0.691062i	$0.757143\pi$
$434$	52.4235	+	3.50773i	2.51641	+	0.168376i
$435$	−0.547622	−	1.68541i	−0.0262565	−	0.0808091i
$436$	33.3975	−	14.8695i	1.59945	−	0.712121i
$437$	−5.47373	−	2.43706i	−0.261844	−	0.116581i
$438$	17.2853	−	3.67410i	0.825922	−	0.175555i
$439$	−9.49372	+	16.4436i	−0.453111	+	0.784811i	−0.998577	−	0.0533218i	$-0.983019\pi$
$439$	−9.49372	+	16.4436i	−0.453111	+	0.784811i	0.545467	+	0.838133i	$0.316352\pi$
$440$		0			0
$441$	−8.18112	+	2.39914i	−0.389577	+	0.114245i
$442$	5.13215	−	15.7951i	0.244112	−	0.751298i
$443$	0.546698	+	5.20148i	0.0259744	+	0.247130i	0.999803	+	0.0198464i	$0.00631773\pi$
$443$	0.546698	+	5.20148i	0.0259744	+	0.247130i	−0.973829	+	0.227283i	$0.927016\pi$
$444$	−1.29355	+	12.3073i	−0.0613891	+	0.584078i
$445$	−2.04168	+	2.26752i	−0.0967851	+	0.107491i
$446$	−5.89211	−	1.25241i	−0.279000	−	0.0593032i
$447$	−3.97017	−	2.88450i	−0.187782	−	0.136432i
$448$	8.42390	+	33.3596i	0.397992	+	1.57609i
$449$	−4.39039	+	13.5122i	−0.207195	+	0.637681i	0.792421	+	0.609975i	$0.208820\pi$
$449$	−4.39039	+	13.5122i	−0.207195	+	0.637681i	−0.999616	+	0.0277065i	$0.991180\pi$
$450$	−5.78921	+	10.0272i	−0.272906	+	0.472687i
$451$		0			0
$452$	−19.2215	−	33.2927i	−0.904106	−	1.56596i
$453$	−7.90296	−	8.77713i	−0.371313	−	0.412385i
$454$	41.6353	−	30.2498i	1.95404	−	1.41969i
$455$	0.293713	+	7.74433i	0.0137695	+	0.363060i
$456$	−3.32700	−	10.2395i	−0.155801	−	0.479506i
$457$	30.5614	+	6.49603i	1.42960	+	0.303872i	0.856727	−	0.515770i	$-0.172494\pi$
$457$	30.5614	+	6.49603i	1.42960	+	0.303872i	0.572876	+	0.819642i	$0.305828\pi$
$458$	−4.18754	+	39.8418i	−0.195671	+	1.86168i
$459$	11.2943	+	5.02857i	0.527175	+	0.234713i
$460$	−2.90816	−	3.22983i	−0.135593	−	0.150592i
$461$	−24.4883			−1.14053			−0.570266	−	0.821460i	$-0.693160\pi$
$461$	−24.4883			−1.14053			−0.570266	+	0.821460i	$0.693160\pi$
$462$		0			0
$463$	−4.68038			−0.217516			−0.108758	−	0.994068i	$-0.534687\pi$
$463$	−4.68038			−0.217516			−0.108758	+	0.994068i	$0.534687\pi$
$464$	−1.00635	−	1.11766i	−0.0467186	−	0.0518863i
$465$	9.37856	+	4.17560i	0.434920	+	0.193639i
$466$	4.78526	−	45.5287i	0.221673	−	2.10908i
$467$	−34.2333	−	7.27651i	−1.58413	−	0.336717i	−0.670068	−	0.742299i	$-0.733735\pi$
$467$	−34.2333	−	7.27651i	−1.58413	−	0.336717i	−0.914058	+	0.405583i	$0.867069\pi$
$468$	3.82352	+	11.7676i	0.176742	+	0.543957i
$469$	−12.3628	−	6.52591i	−0.570862	−	0.301339i
$470$	20.6897	−	15.0320i	0.954345	−	0.693373i
$471$	2.06043	+	2.28834i	0.0949395	+	0.105441i
$472$	16.3717	+	28.3566i	0.753569	+	1.30522i
$473$		0			0
$474$	−17.5516	+	30.4002i	−0.806171	+	1.39633i
$475$	4.71236	−	14.5032i	0.216218	−	0.665450i
$476$	−16.7928	−	4.76075i	−0.769695	−	0.218208i
$477$	6.46755	+	4.69895i	0.296129	+	0.215150i
$478$	−15.3538	−	3.26354i	−0.702265	−	0.149271i
$479$	−28.4688	+	31.6178i	−1.30077	+	1.44465i	−0.475717	+	0.879598i	$0.657811\pi$
$479$	−28.4688	+	31.6178i	−1.30077	+	1.44465i	−0.825054	+	0.565054i	$0.808855\pi$
$480$	−0.808803	+	7.69525i	−0.0369166	+	0.351238i
$481$	1.09042	+	10.3747i	0.0497190	+	0.473044i
$482$	7.69535	−	23.6839i	0.350514	−	1.07877i
$483$	−2.19268	+	5.47433i	−0.0997705	+	0.249091i
$484$		0			0
$485$	−6.02703	+	10.4391i	−0.273673	+	0.474016i
$486$	−25.6799	+	5.45843i	−1.16486	+	0.247599i
$487$	−19.1025	−	8.50497i	−0.865615	−	0.385397i	−0.0746149	−	0.997212i	$-0.523773\pi$
$487$	−19.1025	−	8.50497i	−0.865615	−	0.385397i	−0.791000	+	0.611816i	$0.790439\pi$
$488$	11.9008	−	5.29857i	0.538723	−	0.239855i
$489$	−2.36461	−	7.27752i	−0.106931	−	0.329101i
$490$	13.5276	−	1.02757i	0.611113	−	0.0464211i
$491$	−9.72869	−	7.06831i	−0.439050	−	0.318988i	0.346207	−	0.938158i	$-0.387469\pi$
$491$	−9.72869	−	7.06831i	−0.439050	−	0.318988i	−0.785257	+	0.619170i	$0.787469\pi$
$492$	−0.275706	−	2.62316i	−0.0124298	−	0.118261i
$493$	3.29100	−	0.699523i	0.148219	−	0.0315049i
$494$	−13.5719	−	23.5071i	−0.610627	−	1.05764i
$495$		0			0
$496$	8.71256			0.391205
$497$	15.9180	+	13.2756i	0.714019	+	0.595491i
$498$	1.36165	−	0.989296i	0.0610170	−	0.0443314i
$499$	18.4269	−	8.20418i	0.824901	−	0.367269i	0.0495275	−	0.998773i	$-0.484228\pi$
$499$	18.4269	−	8.20418i	0.824901	−	0.367269i	0.775373	+	0.631503i	$0.217562\pi$
$500$	16.1103	−	17.8923i	0.720473	−	0.800166i
$501$	2.88015	−	3.19873i	0.128675	−	0.142908i
$502$	21.6431	−	9.63615i	0.965981	−	0.430082i
$503$	−2.71060	+	1.96937i	−0.120860	+	0.0878098i	−0.646573	−	0.762852i	$-0.723798\pi$
$503$	−2.71060	+	1.96937i	−0.120860	+	0.0878098i	0.525713	+	0.850662i	$0.323798\pi$
$504$	6.79792	−	2.49737i	0.302804	−	0.111242i
$505$	10.5155			0.467932
$506$		0			0
$507$	1.04656	+	1.81270i	0.0464795	+	0.0805048i
$508$	−6.52095	+	1.38607i	−0.289321	+	0.0614970i
$509$	−3.05366	−	29.0537i	−0.135351	−	1.28778i	−0.825619	−	0.564228i	$-0.809174\pi$
$509$	−3.05366	−	29.0537i	−0.135351	−	1.28778i	0.690268	−	0.723554i	$-0.257493\pi$
$510$	−4.59577	−	3.33902i	−0.203504	−	0.147854i
$511$	−6.90525	−	14.0507i	−0.305470	−	0.621565i
$512$	3.39251	+	10.4411i	0.149929	+	0.461434i
$513$	18.4592	−	8.21857i	0.814994	−	0.362859i
$514$	1.22888	+	0.547134i	0.0542037	+	0.0241330i
$515$	2.44131	−	0.518917i	0.107577	−	0.0228662i
$516$	19.5808	−	33.9149i	0.861995	−	1.49302i
$517$		0			0
$518$	18.0759	−	2.59575i	0.794210	−	0.114051i
$519$	−3.46531	+	10.6651i	−0.152110	+	0.468147i
$520$	−0.688129	−	6.54711i	−0.0301765	−	0.287110i
$521$	−3.97259	+	37.7967i	−0.174042	+	1.65590i	0.463951	+	0.885861i	$0.346431\pi$
$521$	−3.97259	+	37.7967i	−0.174042	+	1.65590i	−0.637994	+	0.770041i	$0.720235\pi$
$522$	−2.79370	+	3.10272i	−0.122277	+	0.135802i
$523$	−0.589749	−	0.125355i	−0.0257879	−	0.00548139i	0.195000	−	0.980803i	$-0.437529\pi$
$523$	−0.589749	−	0.125355i	−0.0257879	−	0.00548139i	−0.220788	+	0.975322i	$0.570863\pi$
$524$	−3.07924	−	2.23720i	−0.134517	−	0.0977324i
$525$	−14.4397	−	4.09364i	−0.630198	−	0.178661i
$526$	−11.8999	+	36.6242i	−0.518861	+	1.59689i
$527$	−9.74542	+	16.8796i	−0.424517	+	0.735286i
$528$		0			0
$529$	10.1061	+	17.5043i	0.439395	+	0.761055i
$530$	−8.51205	−	9.45359i	−0.369740	−	0.410638i
$531$	−14.3556	+	10.4300i	−0.622981	+	0.452622i
$532$	−24.1470	+	15.1897i	−1.04691	+	0.658557i
$533$	−0.687077	−	2.11461i	−0.0297606	−	0.0915937i
$534$	−10.2883	−	2.18684i	−0.445217	−	0.0946339i
$535$	−0.0845339	+	0.804286i	−0.00365472	+	0.0347723i
$536$	10.8483	+	4.82998i	0.468576	+	0.208623i
$537$	−2.29371	−	2.54743i	−0.0989811	−	0.109930i
$538$	46.5944			2.00883
$539$		0			0
$540$	14.6567			0.630724
$541$	−4.20727	−	4.67265i	−0.180885	−	0.200893i	0.645883	−	0.763437i	$-0.276489\pi$
$541$	−4.20727	−	4.67265i	−0.180885	−	0.200893i	−0.826768	+	0.562544i	$0.809823\pi$
$542$	−47.4638	−	21.1323i	−2.03875	−	0.907708i
$543$	−0.247452	+	2.35435i	−0.0106192	+	0.101035i
$544$	−14.3694	−	3.05430i	−0.616081	−	0.130952i
$545$	−3.25733	−	10.0250i	−0.139529	−	0.429425i
$546$	−22.6131	+	14.2248i	−0.967751	+	0.608764i
$547$	−2.46573	+	1.79146i	−0.105427	+	0.0765972i	−0.639250	−	0.768999i	$-0.720755\pi$
$547$	−2.46573	+	1.79146i	−0.105427	+	0.0765972i	0.533823	+	0.845596i	$0.320755\pi$
$548$	13.1142	+	14.5647i	0.560209	+	0.622175i
$549$	3.52985	+	6.11388i	0.150650	+	0.260934i
$550$		0			0
$551$	2.74945	−	4.76218i	0.117130	−	0.202876i
$552$	1.54797	−	4.76417i	0.0658860	−	0.202776i
$553$	29.9201	+	8.48235i	1.27233	+	0.360706i
$554$	−14.3451	−	10.4223i	−0.609465	−	0.442802i
$555$	3.49018	+	0.741860i	0.148150	+	0.0314902i
$556$	−28.5814	+	31.7429i	−1.21212	+	1.34620i
$557$	3.55232	−	33.7981i	0.150517	−	1.43207i	−0.614935	−	0.788578i	$-0.710818\pi$
$557$	3.55232	−	33.7981i	0.150517	−	1.43207i	0.765452	−	0.643494i	$-0.222516\pi$
$558$	−2.52820	−	24.0542i	−0.107027	−	1.01829i
$559$	10.2013	−	31.3962i	0.431467	−	1.32792i
$560$	2.22682	−	0.319778i	0.0941005	−	0.0135131i
$561$		0			0
$562$	−10.8543	+	18.8001i	−0.457860	+	0.793036i
$563$	41.2073	−	8.75889i	1.73668	−	0.369143i	0.772630	−	0.634856i	$-0.218941\pi$
$563$	41.2073	−	8.75889i	1.73668	−	0.369143i	0.964052	+	0.265713i	$0.0856074\pi$
$564$	48.3511	+	21.5273i	2.03595	+	0.906463i
$565$	−10.1261	+	4.50844i	−0.426009	+	0.189672i
$566$	8.67048	+	26.6850i	0.364447	+	1.12165i
$567$	−4.50765	−	9.17207i	−0.189303	−	0.385191i
$568$	−14.2443	−	10.3491i	−0.597678	−	0.434238i
$569$	−2.33715	−	22.2365i	−0.0979785	−	0.932203i	−0.927524	−	0.373764i	$-0.878067\pi$
$569$	−2.33715	−	22.2365i	−0.0979785	−	0.932203i	0.829545	−	0.558439i	$-0.188600\pi$
$570$	−9.08148	+	1.93033i	−0.380381	+	0.0808526i
$571$	−9.49191	−	16.4405i	−0.397224	−	0.688012i	0.596158	−	0.802867i	$-0.296693\pi$
$571$	−9.49191	−	16.4405i	−0.397224	−	0.688012i	−0.993382	+	0.114855i	$0.963360\pi$
$572$		0			0
$573$	−11.0544			−0.461804
$574$	−3.65347	+	1.34218i	−0.152493	+	0.0560217i
$575$	5.74016	−	4.17047i	0.239381	−	0.173921i
$576$	14.4695	−	6.44224i	0.602896	−	0.268427i
$577$	18.5074	−	20.5545i	0.770473	−	0.855697i	−0.222390	−	0.974958i	$-0.571386\pi$
$577$	18.5074	−	20.5545i	0.770473	−	0.855697i	0.992863	+	0.119261i	$0.0380526\pi$
$578$	−18.2309	+	20.2474i	−0.758304	+	0.842182i
$579$	−23.2024	+	10.3304i	−0.964261	+	0.429316i
$580$	3.22690	−	2.34448i	0.133990	−	0.0973494i
$581$	−1.14513	−	0.955038i	−0.0475081	−	0.0396216i
$582$	−41.5522			−1.72239
$583$		0			0
$584$	6.64944	+	11.5172i	0.275156	+	0.476584i
$585$	3.48964	−	0.741746i	0.144279	−	0.0306674i
$586$	1.55780	+	14.8215i	0.0643521	+	0.612270i
$587$	17.9242	+	13.0227i	0.739812	+	0.537505i	0.892652	−	0.450746i	$-0.148842\pi$
$587$	17.9242	+	13.0227i	0.739812	+	0.537505i	−0.152840	+	0.988251i	$0.548842\pi$
$588$	15.8398	+	23.1821i	0.653222	+	0.956013i
$589$	9.84385	+	30.2963i	0.405609	+	1.24834i
$590$	25.7950	−	11.4847i	1.06196	−	0.472817i
$591$	18.5162	+	8.24394i	0.761654	+	0.339110i
$592$	2.96201	−	0.629596i	0.121738	−	0.0258762i
$593$	6.11706	−	10.5951i	0.251198	−	0.435087i	−0.712658	−	0.701511i	$-0.752509\pi$
$593$	6.11706	−	10.5951i	0.251198	−	0.435087i	0.963856	+	0.266424i	$0.0858422\pi$
$594$		0			0
$595$	−1.87128	+	4.67190i	−0.0767150	+	0.191529i
$596$	3.41321	−	10.5048i	0.139811	−	0.430293i
$597$	3.43329	+	32.6656i	0.140515	+	1.33691i
$598$	1.32012	−	12.5601i	0.0539838	−	0.513621i
$599$	−5.11903	+	5.68526i	−0.209158	+	0.232293i	−0.838591	−	0.544761i	$-0.816620\pi$
$599$	−5.11903	+	5.68526i	−0.209158	+	0.232293i	0.629433	+	0.777054i	$0.283287\pi$
$600$	12.4706	+	2.65071i	0.509110	+	0.108215i
$601$	2.23189	+	1.62156i	0.0910405	+	0.0661448i	0.632374	−	0.774663i	$-0.282080\pi$
$601$	2.23189	+	1.62156i	0.0910405	+	0.0661448i	−0.541334	+	0.840808i	$0.682080\pi$
$602$	−55.5978	−	15.7620i	−2.26600	−	0.642410i
$603$	−1.98863	+	6.12039i	−0.0809835	+	0.249242i
$604$	13.2917	−	23.0218i	0.540830	−	0.936744i
$605$		0			0
$606$	18.1242	+	31.3921i	0.736247	+	1.27522i
$607$	1.98929	+	2.20933i	0.0807428	+	0.0896740i	0.782162	−	0.623075i	$-0.214117\pi$
$607$	1.98929	+	2.20933i	0.0807428	+	0.0896740i	−0.701420	+	0.712749i	$0.747450\pi$
$608$	−19.4242	+	14.1125i	−0.787754	+	0.572337i
$609$	−4.78617	−	2.52645i	−0.193945	−	0.102377i
$610$	−3.47144	−	10.6840i	−0.140554	−	0.432582i
$611$	43.6408	+	9.27613i	1.76552	+	0.375272i
$612$	−0.839892	+	7.99104i	−0.0339506	+	0.323019i
$613$	−13.3510	−	5.94426i	−0.539243	−	0.240086i	0.118997	−	0.992895i	$-0.462032\pi$
$613$	−13.3510	−	5.94426i	−0.539243	−	0.240086i	−0.658240	+	0.752808i	$0.728699\pi$
$614$	−3.08742	−	3.42893i	−0.124598	−	0.138380i
$615$	−0.760512			−0.0306668
$616$		0			0
$617$	−8.43040			−0.339395			−0.169697	−	0.985496i	$-0.554279\pi$
$617$	−8.43040			−0.339395			−0.169697	+	0.985496i	$0.554279\pi$
$618$	5.75693	+	6.39371i	0.231577	+	0.257193i
$619$	40.5594	+	18.0582i	1.63022	+	0.725821i	0.998769	−	0.0495936i	$-0.0157926\pi$
$619$	40.5594	+	18.0582i	1.63022	+	0.725821i	0.631452	+	0.775415i	$0.282459\pi$
$620$	−2.41530	+	22.9800i	−0.0970007	+	0.922900i
$621$	9.19597	+	1.95466i	0.369022	+	0.0784379i
$622$	2.45005	+	7.54049i	0.0982381	+	0.302346i
$623$	0.353157	+	9.31171i	0.0141489	+	0.373066i
$624$	−3.58397	+	2.60390i	−0.143474	+	0.104240i
$625$	9.57212	+	10.6309i	0.382885	+	0.425236i
$626$	17.3996	+	30.1369i	0.695427	+	1.20451i
$627$		0			0
$628$	−3.46534	+	6.00215i	−0.138282	+	0.239512i
$629$	−2.09339	+	6.44279i	−0.0834689	+	0.256891i
$630$	−1.52904	−	6.05517i	−0.0609184	−	0.241244i
$631$	31.5083	+	22.8921i	1.25433	+	0.911322i	0.998465	−	0.0553916i	$-0.0176407\pi$
$631$	31.5083	+	22.8921i	1.25433	+	0.911322i	0.255862	+	0.966713i	$0.417641\pi$
$632$	−25.8401	−	5.49248i	−1.02786	−	0.218479i
$633$	−15.5399	+	17.2588i	−0.617654	+	0.685974i
$634$	3.88669	−	36.9794i	0.154360	−	1.46864i
$635$	0.200926	+	1.91168i	0.00797351	+	0.0758629i
$636$	8.13551	−	25.0385i	0.322594	−	0.992842i
$637$	17.1237	+	16.3386i	0.678464	+	0.647360i
$638$		0			0
$639$	4.77083	−	8.26332i	0.188731	−	0.326892i
$640$	−13.3138	+	2.82993i	−0.526273	+	0.111863i
$641$	−10.3998	−	4.63030i	−0.410769	−	0.182886i	0.190940	−	0.981602i	$-0.438846\pi$
$641$	−10.3998	−	4.63030i	−0.410769	−	0.182886i	−0.601709	+	0.798716i	$0.705513\pi$
$642$	−2.54675	+	1.13389i	−0.100512	+	0.0447510i
$643$	5.89109	+	18.1309i	0.232322	+	0.715013i	0.997465	+	0.0711535i	$0.0226680\pi$
$643$	5.89109	+	18.1309i	0.232322	+	0.715013i	−0.765143	+	0.643860i	$0.777332\pi$
$644$	−13.2434	−	0.886136i	−0.521865	−	0.0349187i
$645$	−9.13507	−	6.63702i	−0.359693	−	0.261332i
$646$	−1.84252	−	17.5304i	−0.0724929	−	0.689724i
$647$	−26.9805	+	5.73488i	−1.06071	+	0.225462i	−0.705054	−	0.709154i	$-0.749077\pi$
$647$	−26.9805	+	5.73488i	−1.06071	+	0.225462i	−0.355659	+	0.934616i	$0.615744\pi$
$648$	4.34066	+	7.51824i	0.170517	+	0.295344i
$649$		0			0
$650$	32.1427			1.26074
$651$	29.4293	−	10.8115i	1.15342	−	0.423737i
$652$	13.9336	−	10.1234i	0.545683	−	0.396462i
$653$	−3.13403	+	1.39536i	−0.122644	+	0.0546046i	−0.467141	−	0.884183i	$-0.654716\pi$
$653$	−3.13403	+	1.39536i	−0.122644	+	0.0546046i	0.344497	+	0.938787i	$0.388049\pi$
$654$	24.3137	−	27.0031i	0.950740	−	1.05590i
$655$	−0.734330	+	0.815557i	−0.0286927	+	0.0318664i
$656$	−0.589625	+	0.262518i	−0.0230210	+	0.0102496i
$657$	−5.83060	+	4.23618i	−0.227473	+	0.165269i
$658$	13.3313	−	76.9556i	0.519709	−	3.00004i
$659$	12.7090			0.495073			0.247536	−	0.968879i	$-0.420379\pi$
$659$	12.7090			0.495073			0.247536	+	0.968879i	$0.420379\pi$
$660$		0			0
$661$	1.25158	+	2.16780i	0.0486808	+	0.0843177i	0.889339	−	0.457248i	$-0.151165\pi$
$661$	1.25158	+	2.16780i	0.0486808	+	0.0843177i	−0.840658	+	0.541566i	$0.817832\pi$
$662$	−46.0415	+	9.78641i	−1.78945	+	0.380360i
$663$	−1.03592	−	9.85612i	−0.0402318	−	0.382780i
$664$	1.02473	+	0.744508i	0.0397672	+	0.0288925i
$665$	3.62794	+	7.38206i	0.140685	+	0.286264i
$666$	−2.59774	−	7.99502i	−0.100660	−	0.309801i
$667$	2.33731	−	1.04064i	0.0905008	−	0.0402936i
$668$	8.85041	+	3.94046i	0.342433	+	0.152461i
$669$	−3.51597	+	0.747343i	−0.135935	+	0.0288939i
$670$	5.12017	−	8.86839i	0.197809	−	0.342616i
$671$		0			0
$672$	14.6042	+	18.5773i	0.563369	+	0.716635i
$673$	−8.77218	+	26.9980i	−0.338143	+	1.04070i	0.627011	+	0.779011i	$0.284278\pi$
$673$	−8.77218	+	26.9980i	−0.338143	+	1.04070i	−0.965153	+	0.261685i	$0.915722\pi$
$674$	7.07787	+	67.3415i	0.272629	+	2.59390i
$675$	−2.50110	+	23.7963i	−0.0962672	+	0.915922i
$676$	−3.15236	+	3.50105i	−0.121245	+	0.134656i
$677$	−26.0934	−	5.54632i	−1.00285	−	0.213162i	−0.322910	−	0.946430i	$-0.604661\pi$
$677$	−26.0934	−	5.54632i	−1.00285	−	0.213162i	−0.679940	+	0.733268i	$0.737994\pi$
$678$	−30.9123	−	22.4591i	−1.18718	−	0.862537i
$679$	9.01296	+	35.6923i	0.345886	+	1.36974i
$680$	1.32107	−	4.06583i	0.0506607	−	0.155918i
$681$	15.3549	−	26.5955i	0.588403	−	1.01914i
$682$		0			0
$683$	−2.30840	−	3.99827i	−0.0883286	−	0.152990i	0.818476	−	0.574541i	$-0.194819\pi$
$683$	−2.30840	−	3.99827i	−0.0883286	−	0.152990i	−0.906805	+	0.421551i	$0.861486\pi$
$684$	8.78723	+	9.75921i	0.335988	+	0.373153i
$685$	4.57175	−	3.32157i	0.174677	−	0.126911i
$686$	27.4449	−	31.0381i	1.04785	−	1.18504i
$687$	7.38722	+	22.7355i	0.281840	+	0.867414i
$688$	−9.37342	−	1.99238i	−0.357358	−	0.0759589i
$689$	2.31979	−	22.0713i	0.0883770	−	0.840851i
$690$	−3.94632	−	1.75702i	−0.150234	−	0.0668884i
$691$	−13.6325	−	15.1405i	−0.518606	−	0.575971i	0.425773	−	0.904830i	$-0.360002\pi$
$691$	−13.6325	−	15.1405i	−0.518606	−	0.575971i	−0.944379	+	0.328860i	$0.893336\pi$
$692$	−25.2400			−0.959482
$693$		0			0
$694$	58.6570			2.22659
$695$	8.24097	+	9.15253i	0.312598	+	0.347175i
$696$	4.19984	+	1.86989i	0.159194	+	0.0708779i
$697$	0.150926	−	1.43597i	0.00571675	−	0.0543912i
$698$	23.3675	+	4.96692i	0.884474	+	0.188001i
$699$	−8.44166	−	25.9807i	−0.319293	−	0.982682i
$700$	−1.28027	−	33.7568i	−0.0483895	−	1.27589i
$701$	34.8613	−	25.3282i	1.31669	−	0.956634i	0.316727	−	0.948517i	$-0.397416\pi$
$701$	34.8613	−	25.3282i	1.31669	−	0.956634i	0.999967	−	0.00811779i	$-0.00258400\pi$
$702$	28.4984	+	31.6506i	1.07560	+	1.19458i
$703$	5.53592	+	9.58850i	0.208791	+	0.361637i
$704$		0			0
$705$	7.63029	−	13.2161i	0.287373	−	0.497745i
$706$	2.69511	−	8.29469i	0.101432	−	0.312175i
$707$	23.0337	−	22.3774i	0.866273	−	0.841589i
$708$	47.2762	+	34.3482i	1.77675	+	1.29088i
$709$	19.2189	+	4.08510i	0.721780	+	0.153419i	0.554133	−	0.832428i	$-0.313050\pi$
$709$	19.2189	+	4.08510i	0.721780	+	0.153419i	0.167647	+	0.985847i	$0.446383\pi$
$710$	−10.1596	+	11.2834i	−0.381283	+	0.423457i
$711$	1.49646	−	14.2378i	0.0561216	−	0.533961i
$712$	−0.827401	−	7.87219i	−0.0310082	−	0.295023i
$713$	−4.58010	+	14.0961i	−0.171526	+	0.527903i
$714$	−17.1724	+	2.46601i	−0.642662	+	0.0922881i
$715$		0			0
$716$	3.85770	−	6.68173i	0.144169	−	0.249708i
$717$	−9.16197	+	1.94744i	−0.342160	+	0.0727284i
$718$	−43.6003	−	19.4121i	−1.62715	−	0.724453i
$719$	15.4861	−	6.89483i	0.577532	−	0.257134i	−0.0971163	−	0.995273i	$-0.530962\pi$
$719$	15.4861	−	6.89483i	0.577532	−	0.257134i	0.674649	+	0.738139i	$0.264295\pi$
$720$	−0.320023	−	0.984929i	−0.0119266	−	0.0367062i
$721$	4.24332	−	6.33189i	0.158030	−	0.235812i
$722$	11.0802	+	8.05023i	0.412362	+	0.299599i
$723$	−1.55330	−	14.7786i	−0.0577678	−	0.549624i
$724$	−5.21183	+	1.10781i	−0.193696	+	0.0411714i
$725$	3.25580	+	5.63921i	0.120917	+	0.209435i
$726$		0			0
$727$	−4.90596			−0.181952			−0.0909760	−	0.995853i	$-0.528999\pi$
$727$	−4.90596			−0.181952			−0.0909760	+	0.995853i	$0.528999\pi$
$728$	−15.4399	−	12.8768i	−0.572240	−	0.477247i
$729$	−22.0493	+	16.0198i	−0.816641	+	0.593324i
$730$	10.4768	−	4.66455i	0.387762	−	0.172643i
$731$	14.3446	−	15.9313i	0.530556	−	0.589242i
$732$	15.5567	−	17.2775i	0.574992	−	0.638594i
$733$	14.1784	−	6.31265i	0.523693	−	0.233163i	−0.127824	−	0.991797i	$-0.540799\pi$
$733$	14.1784	−	6.31265i	0.523693	−	0.233163i	0.651517	+	0.758634i	$0.274133\pi$
$734$	−1.06422	+	0.773204i	−0.0392812	+	0.0285395i
$735$	7.12495	−	3.84344i	0.262808	−	0.141767i
$736$	−11.1711			−0.411771
$737$		0			0
$738$	0.895872	+	1.55170i	0.0329775	+	0.0571187i
$739$	14.4699	−	3.07568i	0.532285	−	0.113141i	0.0660751	−	0.997815i	$-0.478952\pi$
$739$	14.4699	−	3.07568i	0.532285	−	0.113141i	0.466210	+	0.884674i	$0.345619\pi$
$740$	0.839475	+	7.98707i	0.0308597	+	0.293611i
$741$	−13.1039	−	9.52055i	−0.481384	−	0.349746i
$742$	−38.7630	−	2.59368i	−1.42303	−	0.0952172i
$743$	−0.468468	−	1.44180i	−0.0171864	−	0.0528944i	0.942095	−	0.335345i	$-0.108853\pi$
$743$	−0.468468	−	1.44180i	−0.0171864	−	0.0528944i	−0.959282	+	0.282450i	$0.908853\pi$
$744$	−24.3299	+	10.8324i	−0.891977	+	0.397134i
$745$	−2.90942	−	1.29536i	−0.106593	−	0.0474582i
$746$	29.1376	−	6.19339i	1.06680	−	0.226756i
$747$	−0.343211	+	0.594459i	−0.0125574	+	0.0217501i
$748$		0			0
$749$	1.52639	+	1.94165i	0.0557731	+	0.0709463i
$750$	7.39486	−	22.7590i	0.270022	−	0.831042i
$751$	−4.39876	−	41.8514i	−0.160513	−	1.52718i	−0.717442	−	0.696618i	$-0.754687\pi$
$751$	−4.39876	−	41.8514i	−0.160513	−	1.52718i	0.556929	−	0.830560i	$-0.311979\pi$
$752$	1.35377	−	12.8803i	0.0493670	−	0.469695i
$753$	9.45966	−	10.5060i	0.344729	−	0.382860i
$754$	11.3372	+	2.40979i	0.412876	+	0.0877595i
$755$	−6.20100	−	4.50529i	−0.225677	−	0.163964i
$756$	32.1049	−	31.1901i	1.16765	−	1.13437i
$757$	13.2633	−	40.8203i	0.482064	−	1.48364i	−0.354125	−	0.935198i	$-0.615221\pi$
$757$	13.2633	−	40.8203i	0.482064	−	1.48364i	0.836189	−	0.548442i	$-0.184779\pi$
$758$	−9.72584	+	16.8456i	−0.353258	+	0.611861i
$759$		0			0
$760$	−3.49354	−	6.05098i	−0.126724	−	0.219492i
$761$	−27.7661	−	30.8374i	−1.00652	−	1.11786i	−0.993020	−	0.117947i	$-0.962369\pi$
$761$	−27.7661	−	30.8374i	−1.00652	−	1.11786i	−0.0135019	−	0.999909i	$-0.504298\pi$
$762$	−5.36068	+	3.89476i	−0.194197	+	0.141092i
$763$	−28.4688	−	15.0277i	−1.03064	−	0.544039i
$764$	−7.68861	−	23.6631i	−0.278164	−	0.856101i
$765$	2.26615	+	0.481685i	0.0819328	+	0.0174153i
$766$	−7.21693	+	68.6645i	−0.260758	+	2.48095i
$767$	45.0015	+	20.0360i	1.62491	+	0.723457i
$768$	−8.16309	−	9.06603i	−0.294560	−	0.327142i
$769$	36.1695			1.30430			0.652152	−	0.758088i	$-0.273866\pi$
$769$	36.1695			1.30430			0.652152	+	0.758088i	$0.273866\pi$
$770$		0			0
$771$	0.802702			0.0289086
$772$	−38.2511	−	42.4822i	−1.37669	−	1.52897i
$773$	1.23138	+	0.548248i	0.0442898	+	0.0197191i	0.428762	−	0.903417i	$-0.358950\pi$
$773$	1.23138	+	0.548248i	0.0442898	+	0.0197191i	−0.384472	+	0.923137i	$0.625617\pi$
$774$	−2.78073	+	26.4569i	−0.0999513	+	0.950973i
$775$	−36.8978	−	7.84286i	−1.32541	−	0.281724i
$776$	−9.66317	−	29.7402i	−0.346888	−	1.06761i
$777$	9.22381	−	5.80224i	0.330902	−	0.208154i
$778$	−9.28056	+	6.74272i	−0.332724	+	0.241738i
$779$	−1.57904	−	1.75370i	−0.0565751	−	0.0628330i
$780$	−5.87444	−	10.1748i	−0.210339	−	0.364318i
$781$		0			0
$782$	4.10069	−	7.10260i	0.146640	−	0.253989i
$783$	−2.66623	+	8.20581i	−0.0952832	+	0.293252i
$784$	4.19727	−	5.43925i	0.149903	−	0.194259i
$785$	1.61670	+	1.17460i	0.0577024	+	0.0419233i
$786$	−3.70037	−	0.786539i	−0.131988	−	0.0280549i
$787$	−13.6519	+	15.1620i	−0.486639	+	0.540468i	−0.935590	−	0.353089i	$-0.885131\pi$
$787$	−13.6519	+	15.1620i	−0.486639	+	0.540468i	0.448950	+	0.893557i	$0.351798\pi$
$788$	−4.76855	+	45.3697i	−0.169872	+	1.61623i
$789$	2.40199	+	22.8534i	0.0855130	+	0.813602i
$790$	−7.03969	+	21.6659i	−0.250461	+	0.770840i
$791$	−12.5867	+	31.4244i	−0.447532	+	1.11732i
$792$		0			0
$793$	9.79915	−	16.9726i	0.347978	−	0.602716i
$794$	64.0123	−	13.6062i	2.27171	−	0.482867i
$795$	−6.93470	−	3.08753i	−0.245948	−	0.109503i
$796$	−67.5361	+	30.0690i	−2.39375	+	1.06577i
$797$	16.9319	+	52.1110i	0.599758	+	1.84587i	0.529451	+	0.848340i	$0.322398\pi$
$797$	16.9319	+	52.1110i	0.599758	+	1.84587i	0.0703069	+	0.997525i	$0.477602\pi$
$798$	−15.7848	+	23.5541i	−0.558776	+	0.833807i
$799$	23.4398	+	17.0300i	0.829240	+	0.602478i
$800$	−2.97189	−	28.2756i	−0.105072	−	0.999694i
$801$	4.19591	−	0.891868i	0.148255	−	0.0315126i
$802$	−16.2445	−	28.1363i	−0.573612	−	0.993526i
$803$		0			0
$804$	21.1930			0.747421
$805$	−0.653248	+	3.77090i	−0.0230240	+	0.132907i
$806$	−54.3208	+	39.4664i	−1.91337	+	1.39014i
$807$	25.4003	−	11.3089i	0.894131	−	0.398093i
$808$	−18.2534	+	20.2724i	−0.642152	+	0.713182i
$809$	15.8948	−	17.6530i	0.558832	−	0.620646i	−0.395835	−	0.918322i	$-0.629545\pi$
$809$	15.8948	−	17.6530i	0.558832	−	0.620646i	0.954667	+	0.297676i	$0.0962115\pi$
$810$	6.83907	−	3.04495i	0.240301	−	0.106989i
$811$	23.6296	−	17.1679i	0.829747	−	0.602846i	−0.0897410	−	0.995965i	$-0.528604\pi$
$811$	23.6296	−	17.1679i	0.829747	−	0.602846i	0.919488	+	0.393119i	$0.128604\pi$
$812$	2.07924	−	12.0025i	0.0729670	−	0.421205i
$813$	−31.0032			−1.08733
$814$		0			0
$815$	−2.48297	−	4.30063i	−0.0869747	−	0.150645i
$816$	−2.81396	+	0.598126i	−0.0985084	+	0.0209386i
$817$	−3.66240	−	34.8454i	−0.128131	−	1.21909i
$818$	−21.6002	−	15.6934i	−0.755232	−	0.548708i
$819$	6.06545	−	9.05088i	0.211944	−	0.316263i
$820$	−0.528955	−	1.62795i	−0.0184719	−	0.0568506i
$821$	−10.4500	+	4.65264i	−0.364707	+	0.162378i	−0.580905	−	0.813971i	$-0.697301\pi$
$821$	−10.4500	+	4.65264i	−0.364707	+	0.162378i	0.216197	+	0.976350i	$0.430635\pi$
$822$	17.7957	+	7.92316i	0.620697	+	0.276352i
$823$	11.3311	−	2.40850i	0.394977	−	0.0839550i	−0.00614144	−	0.999981i	$-0.501955\pi$
$823$	11.3311	−	2.40850i	0.394977	−	0.0839550i	0.401118	+	0.916026i	$0.368622\pi$
$824$	−3.23737	+	5.60730i	−0.112779	+	0.195339i
$825$		0			0
$826$	32.0631	−	80.0498i	1.11562	−	2.78529i
$827$	−8.60927	+	26.4966i	−0.299374	+	0.921377i	0.682344	+	0.731032i	$0.260961\pi$
$827$	−8.60927	+	26.4966i	−0.299374	+	0.921377i	−0.981717	+	0.190346i	$0.939039\pi$
$828$	0.638683	+	6.07667i	0.0221958	+	0.211179i
$829$	−1.33119	+	12.6655i	−0.0462343	+	0.439890i	0.946779	+	0.321885i	$0.104317\pi$
$829$	−1.33119	+	12.6655i	−0.0462343	+	0.439890i	−0.993013	+	0.118005i	$0.962350\pi$
$830$	0.730876	−	0.811720i	0.0253691	−	0.0281752i
$831$	−10.3496	−	2.19988i	−0.359025	−	0.0763131i
$832$	−35.5724	−	25.8449i	−1.23325	−	0.896010i
$833$	5.84306	+	14.2158i	0.202450	+	0.492548i
$834$	−13.1193	+	40.3770i	−0.454284	+	1.39814i
$835$	1.39668	−	2.41913i	0.0483343	−	0.0837174i
$836$		0			0
$837$	−24.9915	−	43.2866i	−0.863833	−	1.49620i
$838$	−22.9807	−	25.5227i	−0.793856	−	0.881667i
$839$	−2.92838	+	2.12760i	−0.101099	+	0.0734528i	−0.637186	−	0.770710i	$-0.719902\pi$
$839$	−2.92838	+	2.12760i	−0.101099	+	0.0734528i	0.536087	+	0.844163i	$0.319902\pi$
$840$	−5.82084	+	3.66161i	−0.200838	+	0.126337i
$841$	−8.23591	−	25.3475i	−0.283997	−	0.874052i
$842$	16.6160	+	3.53185i	0.572626	+	0.121715i
$843$	−1.35406	+	12.8831i	−0.0466365	+	0.443716i
$844$	−47.7525	−	21.2608i	−1.64371	−	0.731826i
$845$	0.908931	+	1.00947i	0.0312682	+	0.0347268i
$846$	−35.9535			−1.23611
$847$		0			0
$848$	−6.44224			−0.221228
$849$	11.2033	+	12.4425i	0.384496	+	0.427026i
$850$	19.0686	+	8.48991i	0.654049	+	0.291201i
$851$	−0.538474	+	5.12323i	−0.0184586	+	0.175622i
$852$	−30.7361	−	6.53317i	−1.05300	−	0.223823i
$853$	−15.2157	−	46.8291i	−0.520976	−	1.60340i	−0.772139	−	0.635454i	$-0.780813\pi$
$853$	−15.2157	−	46.8291i	−0.520976	−	1.60340i	0.251163	−	0.967945i	$-0.419187\pi$
$854$	−30.3401	−	16.0155i	−1.03822	−	0.548039i
$855$	3.06333	−	2.22564i	0.104764	−	0.0761152i
$856$	−1.40382	−	1.55910i	−0.0479815	−	0.0532889i
$857$	12.0693	+	20.9046i	0.412278	+	0.714087i	0.995138	−	0.0984857i	$-0.0313999\pi$
$857$	12.0693	+	20.9046i	0.412278	+	0.714087i	−0.582860	+	0.812572i	$0.698067\pi$
$858$		0			0
$859$	0.0926485	−	0.160472i	0.00316113	−	0.00547523i	−0.864441	−	0.502735i	$-0.832327\pi$
$859$	0.0926485	−	0.160472i	0.00316113	−	0.00547523i	0.867602	+	0.497260i	$0.165660\pi$
$860$	7.85356	−	24.1708i	0.267804	−	0.824217i
$861$	−1.66587	+	1.61840i	−0.0567728	+	0.0551551i
$862$	−47.6850	−	34.6452i	−1.62416	−	1.18002i
$863$	−37.4906	−	7.96887i	−1.27619	−	0.271263i	−0.480518	−	0.876985i	$-0.659551\pi$
$863$	−37.4906	−	7.96887i	−1.27619	−	0.271263i	−0.795677	+	0.605722i	$0.792885\pi$
$864$	25.2078	−	27.9961i	0.857588	−	0.952448i
$865$	−0.760710	+	7.23767i	−0.0258649	+	0.246088i
$866$	−1.73769	−	16.5330i	−0.0590490	−	0.561814i
$867$	−5.02404	+	15.4624i	−0.170625	+	0.525131i
$868$	43.6119	+	55.4767i	1.48029	+	1.88300i
$869$		0			0
$870$	1.98223	−	3.43332i	0.0672039	−	0.116401i
$871$	17.4747	−	3.71436i	0.592107	−	0.125856i
$872$	24.9812	+	11.1223i	0.845970	+	0.376650i
$873$	15.4813	−	6.89273i	0.523963	−	0.233283i
$874$	−4.14211	−	12.7481i	−0.140109	−	0.431211i
$875$	−21.1534	−	1.41540i	−0.715116	−	0.0478494i
$876$	19.2014	+	13.9507i	0.648757	+	0.471349i
$877$	2.77990	+	26.4490i	0.0938707	+	0.893120i	0.935562	+	0.353161i	$0.114893\pi$
$877$	2.77990	+	26.4490i	0.0938707	+	0.893120i	−0.841692	+	0.539958i	$0.818440\pi$
$878$	−41.5486	+	8.83143i	−1.40220	+	0.298046i
$879$	4.44653	+	7.70162i	0.149978	+	0.259769i
$880$		0			0
$881$	1.78266			0.0600595			0.0300297	−	0.999549i	$-0.490440\pi$
$881$	1.78266			0.0600595			0.0300297	+	0.999549i	$0.490440\pi$
$882$	−16.2350	−	10.0097i	−0.546660	−	0.337045i
$883$	−36.4768	+	26.5020i	−1.22754	+	0.891862i	−0.996704	−	0.0811293i	$-0.974147\pi$
$883$	−36.4768	+	26.5020i	−1.22754	+	0.891862i	−0.230840	+	0.972992i	$0.574147\pi$
$884$	20.3775	−	9.07266i	0.685371	−	0.305147i
$885$	11.2743	−	12.5214i	0.378983	−	0.420903i
$886$	−7.82906	+	8.69505i	−0.263022	+	0.292116i
$887$	−16.9072	+	7.52756i	−0.567688	+	0.252751i	−0.670449	−	0.741955i	$-0.733899\pi$
$887$	−16.9072	+	7.52756i	−0.567688	+	0.252751i	0.102762	+	0.994706i	$0.467232\pi$
$888$	−7.48867	+	5.44084i	−0.251303	+	0.182582i
$889$	4.50827	+	3.75989i	0.151203	+	0.126103i
$890$	−6.82595			−0.228806
$891$		0			0
$892$	−4.04521	−	7.00651i	−0.135444	−	0.234595i
$893$	46.3183	−	9.84525i	1.54998	−	0.329459i
$894$	−1.14755	−	10.9182i	−0.0383798	−	0.365159i
$895$	−1.79974	−	1.30759i	−0.0601588	−	0.0437080i
$896$	−23.1411	+	34.5312i	−0.773089	+	1.15360i
$897$	−2.32882	−	7.16737i	−0.0777570	−	0.239312i
$898$	−29.0360	+	12.9276i	−0.968943	+	0.431401i
$899$	−12.4264	−	5.53258i	−0.414443	−	0.184522i
$900$	−15.2110	+	3.23320i	−0.507034	+	0.107773i
$901$	7.20597	−	12.4811i	0.240066	−	0.415806i
$902$		0			0
$903$	−34.1339	+	4.90172i	−1.13591	+	0.163119i
$904$	8.88586	−	27.3479i	0.295539	−	0.909577i
$905$	0.160589	+	1.52790i	0.00533816	+	0.0507892i
$906$	2.76184	−	26.2772i	0.0917561	−	0.873001i
$907$	10.1556	−	11.2790i	0.337212	−	0.374512i	−0.550560	−	0.834796i	$-0.685586\pi$
$907$	10.1556	−	11.2790i	0.337212	−	0.374512i	0.887772	+	0.460284i	$0.152252\pi$
$908$	67.6103	+	14.3710i	2.24373	+	0.476919i
$909$	−11.9600	−	8.68944i	−0.396688	−	0.288211i
$910$	−12.4352	+	12.0809i	−0.412223	+	0.400477i
$911$	−9.82660	+	30.2432i	−0.325570	+	1.00200i	0.645613	+	0.763665i	$0.276602\pi$
$911$	−9.82660	+	30.2432i	−0.325570	+	1.00200i	−0.971183	+	0.238336i	$0.923398\pi$
$912$	−2.35091	+	4.07190i	−0.0778464	+	0.134834i
$913$		0			0
$914$	34.9482	+	60.5321i	1.15598	+	2.00222i
$915$	−4.48552	−	4.98167i	−0.148287	−	0.164689i
$916$	−43.5297	+	31.6262i	−1.43826	+	1.04496i
$917$	0.127020	+	3.34913i	0.00419456	+	0.110598i
$918$	8.54671	+	26.3041i	0.282084	+	0.868164i
$919$	−21.3899	−	4.54656i	−0.705587	−	0.149977i	−0.158876	−	0.987299i	$-0.550787\pi$
$919$	−21.3899	−	4.54656i	−0.705587	−	0.149977i	−0.546711	+	0.837321i	$0.684120\pi$
$920$	0.339813	−	3.23310i	0.0112033	−	0.106592i
$921$	−2.51530	−	1.11988i	−0.0828818	−	0.0369014i
$922$	−36.6568	−	40.7115i	−1.20723	−	1.34076i
$923$	−26.4885			−0.871878
$924$		0			0
$925$	−13.1109			−0.431084
$926$	−7.00612	−	7.78109i	−0.230236	−	0.255702i
$927$	−3.20548	−	1.42717i	−0.105282	−	0.0468745i
$928$	1.07165	−	10.1960i	0.0351785	−	0.334701i
$929$	30.0517	+	6.38769i	0.985964	+	0.209573i	0.672557	−	0.740046i	$-0.265196\pi$
$929$	30.0517	+	6.38769i	0.985964	+	0.209573i	0.313408	+	0.949619i	$0.398529\pi$
$930$	7.09699	+	21.8423i	0.232719	+	0.716237i
$931$	23.6562	+	8.44970i	0.775302	+	0.276928i
$932$	49.7431	−	36.1405i	1.62939	−	1.18382i
$933$	3.16576	+	3.51593i	0.103642	+	0.115107i
$934$	−39.1471	−	67.8048i	−1.28093	−	2.21864i
$935$		0			0
$936$	−4.62754	+	8.01513i	−0.151256	+	0.261983i
$937$	13.6952	−	42.1495i	0.447403	−	1.37696i	−0.432425	−	0.901670i	$-0.642342\pi$
$937$	13.6952	−	42.1495i	0.447403	−	1.37696i	0.879827	−	0.475293i	$-0.157658\pi$
$938$	−7.65681	−	30.3218i	−0.250004	−	0.990042i
$939$	16.7997	+	12.2057i	0.548236	+	0.398317i
$940$	33.5974	+	7.14135i	1.09583	+	0.232925i
$941$	16.3342	−	18.1410i	0.532480	−	0.591379i	−0.415546	−	0.909572i	$-0.636409\pi$
$941$	16.3342	−	18.1410i	0.532480	−	0.591379i	0.948026	+	0.318193i	$0.103076\pi$
$942$	−0.720056	+	6.85088i	−0.0234607	+	0.223214i
$943$	−0.114770	−	1.09196i	−0.00373742	−	0.0355591i
$944$	4.41878	−	13.5996i	0.143819	−	0.442629i
$945$	−7.97628	−	10.1463i	−0.259469	−	0.330058i
$946$		0			0
$947$	26.4671	−	45.8424i	0.860066	−	1.48968i	−0.0117992	−	0.999930i	$-0.503756\pi$
$947$	26.4671	−	45.8424i	0.860066	−	1.48968i	0.871865	−	0.489747i	$-0.162911\pi$
$948$	−46.1164	+	9.80233i	−1.49779	+	0.318365i
$949$	18.2776	+	8.13769i	0.593315	+	0.264161i
$950$	31.1653	−	13.8757i	1.01114	−	0.450187i
$951$	−6.85649	−	21.1021i	−0.222337	−	0.684283i
$952$	−5.75853	−	11.7174i	−0.186635	−	0.379762i
$953$	3.88488	+	2.82253i	0.125844	+	0.0914307i	0.648927	−	0.760851i	$-0.275218\pi$
$953$	3.88488	+	2.82253i	0.125844	+	0.0914307i	−0.523083	+	0.852282i	$0.675218\pi$
$954$	1.86940	+	17.7862i	0.0605241	+	0.575848i
$955$	−7.01721	+	1.49155i	−0.227072	+	0.0482656i
$956$	−10.5411	−	18.2577i	−0.340922	−	0.590495i
$957$		0			0
$958$	−95.1795			−3.07511
$959$	2.94578	−	17.0047i	0.0951243	−	0.549109i
$960$	−12.1674	+	8.84011i	−0.392700	+	0.285313i
$961$	43.6668	−	19.4417i	1.40861	−	0.627152i
$962$	−15.6155	+	17.3428i	−0.503465	+	0.559154i
$963$	0.760767	−	0.844917i	0.0245154	−	0.0272271i
$964$	30.5549	−	13.6039i	0.984106	−	0.438152i
$965$	−13.3348	+	9.68829i	−0.429262	+	0.311877i
$966$	−12.3833	+	4.54928i	−0.398425	+	0.146371i
$967$	10.0231			0.322320			0.161160	−	0.986928i	$-0.448477\pi$
$967$	10.0231			0.322320			0.161160	+	0.986928i	$0.448477\pi$
$968$		0			0
$969$	−5.25922	−	9.10924i	−0.168950	−	0.292631i
$970$	−26.3769	+	5.60658i	−0.846911	+	0.180016i
$971$	−0.158145	−	1.50465i	−0.00507511	−	0.0482864i	0.991691	−	0.128641i	$-0.0410614\pi$
$971$	−0.158145	−	1.50465i	−0.00507511	−	0.0482864i	−0.996766	+	0.0803545i	$0.974395\pi$
$972$	−28.5267	−	20.7258i	−0.914993	−	0.664781i
$973$	37.5285	+	2.51109i	1.20311	+	0.0805017i
$974$	−14.4553	−	44.4889i	−0.463178	−	1.42551i
$975$	17.5221	−	7.80135i	0.561157	−	0.249843i
$976$	−5.19722	−	2.31395i	−0.166359	−	0.0740678i
$977$	17.9324	−	3.81165i	0.573708	−	0.121945i	0.0880837	−	0.996113i	$-0.471926\pi$
$977$	17.9324	−	3.81165i	0.573708	−	0.121945i	0.485624	+	0.874168i	$0.338592\pi$
$978$	8.55919	−	14.8249i	0.273693	−	0.474050i
$979$		0			0
$980$	13.1829	+	12.5785i	0.421111	+	0.401805i
$981$	−4.57937	+	14.0939i	−0.146208	+	0.449982i
$982$	−2.81201	−	26.7545i	−0.0897349	−	0.853771i
$983$	3.05374	−	29.0544i	0.0973993	−	0.926692i	−0.831291	−	0.555837i	$-0.812398\pi$
$983$	3.05374	−	29.0544i	0.0973993	−	0.926692i	0.928691	−	0.370855i	$-0.120935\pi$
$984$	1.32014	−	1.46617i	0.0420846	−	0.0467397i
$985$	12.8662	+	2.73480i	0.409952	+	0.0871379i
$986$	6.08929	+	4.42413i	0.193922	+	0.140893i
$987$	−11.4105	−	45.1869i	−0.363201	−	1.43831i
$988$	11.2656	−	34.6721i	0.358408	−	1.10307i
$989$	8.15100	−	14.1180i	0.259187	−	0.448925i
$990$		0			0
$991$	22.6187	+	39.1768i	0.718508	+	1.24449i	0.961591	+	0.274487i	$0.0885079\pi$
$991$	22.6187	+	39.1768i	0.718508	+	1.24449i	−0.243083	+	0.970005i	$0.578159\pi$
$992$	39.7407	+	44.1365i	1.26177	+	1.40134i
$993$	−22.7236	+	16.5096i	−0.721111	+	0.523918i
$994$	1.75734	+	46.3359i	0.0557395	+	1.46968i
$995$	6.58693	+	20.2725i	0.208820	+	0.642681i
$996$	2.21114	+	0.469993i	0.0700627	+	0.0148923i
$997$	1.47188	−	14.0040i	0.0466150	−	0.443512i	−0.946176	−	0.323653i	$-0.895089\pi$
$997$	1.47188	−	14.0040i	0.0466150	−	0.443512i	0.992791	−	0.119859i	$-0.0382443\pi$
$998$	41.2228	+	18.3536i	1.30489	+	0.580972i
$999$	−11.6244	−	12.9102i	−0.367780	−	0.408461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.i.9.5		40
7.4	even	3	inner	847.2.n.i.130.1		40
11.2	odd	10		847.2.n.j.366.5		40
11.3	even	5		77.2.m.b.37.5	yes	40
11.4	even	5		847.2.e.i.485.2		20
11.5	even	5	inner	847.2.n.i.632.1		40
11.6	odd	10		847.2.n.h.632.5		40
11.7	odd	10		847.2.e.h.485.9		20
11.8	odd	10		847.2.n.j.807.1		40
11.9	even	5		77.2.m.b.58.1	yes	40
11.10	odd	2		847.2.n.h.9.1		40
33.14	odd	10		693.2.by.b.37.1		40
33.20	odd	10		693.2.by.b.289.5		40
77.3	odd	30		539.2.q.h.312.1		40
77.4	even	15		847.2.e.i.606.2		20
77.9	even	15		539.2.f.h.344.1		20
77.18	odd	30		847.2.e.h.606.9		20
77.20	odd	10		539.2.q.h.520.1		40
77.25	even	15		77.2.m.b.4.1	✓	40
77.26	odd	30		5929.2.a.bx.1.9		10
77.31	odd	30		539.2.q.h.410.5		40
77.32	odd	6		847.2.n.h.130.5		40
77.37	even	15		5929.2.a.bw.1.9		10
77.39	odd	30		847.2.n.h.753.1		40
77.40	even	30		5929.2.a.bz.1.2		10
77.46	odd	30		847.2.n.j.487.1		40
77.47	odd	30		539.2.f.g.246.1		20
77.51	odd	30		5929.2.a.by.1.2		10
77.53	even	15		77.2.m.b.25.5	yes	40
77.58	even	15		539.2.f.h.246.1		20
77.60	even	15	inner	847.2.n.i.753.5		40
77.69	odd	10		539.2.q.h.422.5		40
77.74	odd	30		847.2.n.j.81.5		40
77.75	odd	30		539.2.f.g.344.1		20
231.53	odd	30		693.2.by.b.487.1		40
231.179	odd	30		693.2.by.b.235.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.1	✓	40	77.25	even	15
77.2.m.b.25.5	yes	40	77.53	even	15
77.2.m.b.37.5	yes	40	11.3	even	5
77.2.m.b.58.1	yes	40	11.9	even	5
539.2.f.g.246.1		20	77.47	odd	30
539.2.f.g.344.1		20	77.75	odd	30
539.2.f.h.246.1		20	77.58	even	15
539.2.f.h.344.1		20	77.9	even	15
539.2.q.h.312.1		40	77.3	odd	30
539.2.q.h.410.5		40	77.31	odd	30
539.2.q.h.422.5		40	77.69	odd	10
539.2.q.h.520.1		40	77.20	odd	10
693.2.by.b.37.1		40	33.14	odd	10
693.2.by.b.235.5		40	231.179	odd	30
693.2.by.b.289.5		40	33.20	odd	10
693.2.by.b.487.1		40	231.53	odd	30
847.2.e.h.485.9		20	11.7	odd	10
847.2.e.h.606.9		20	77.18	odd	30
847.2.e.i.485.2		20	11.4	even	5
847.2.e.i.606.2		20	77.4	even	15
847.2.n.h.9.1		40	11.10	odd	2
847.2.n.h.130.5		40	77.32	odd	6
847.2.n.h.632.5		40	11.6	odd	10
847.2.n.h.753.1		40	77.39	odd	30
847.2.n.i.9.5		40	1.1	even	1	trivial
847.2.n.i.130.1		40	7.4	even	3	inner
847.2.n.i.632.1		40	11.5	even	5	inner
847.2.n.i.753.5		40	77.60	even	15	inner
847.2.n.j.81.5		40	77.74	odd	30
847.2.n.j.366.5		40	11.2	odd	10
847.2.n.j.487.1		40	77.46	odd	30
847.2.n.j.807.1		40	11.8	odd	10
5929.2.a.bw.1.9		10	77.37	even	15
5929.2.a.bx.1.9		10	77.26	odd	30
5929.2.a.by.1.2		10	77.51	odd	30
5929.2.a.bz.1.2		10	77.40	even	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.49691 + 1.66249i) q^{2} +(1.21952 + 0.542967i) q^{3} +(-0.314069 + 2.98816i) q^{4} +(0.847402 + 0.180121i) q^{5} +(0.922843 + 2.84022i) q^{6} +(2.23951 - 1.40876i) q^{7} +(-1.81822 + 1.32101i) q^{8} +(-0.814967 - 0.905113i) q^{9} +O(q^{10})\)	\(q+(1.49691 + 1.66249i) q^{2} +(1.21952 + 0.542967i) q^{3} +(-0.314069 + 2.98816i) q^{4} +(0.847402 + 0.180121i) q^{5} +(0.922843 + 2.84022i) q^{6} +(2.23951 - 1.40876i) q^{7} +(-1.81822 + 1.32101i) q^{8} +(-0.814967 - 0.905113i) q^{9} +(0.969038 + 1.67842i) q^{10} +(-2.00549 + 3.47361i) q^{12} +(-1.04483 + 3.21565i) q^{13} +(5.69440 + 1.61436i) q^{14} +(0.935627 + 0.679773i) q^{15} +(0.960039 + 0.204063i) q^{16} +(-1.46920 + 1.63171i) q^{17} +(0.284806 - 2.70975i) q^{18} +(0.375108 + 3.56891i) q^{19} +(-0.804373 + 2.47560i) q^{20} +(3.49604 - 0.502041i) q^{21} +(-0.834837 + 1.44598i) q^{23} +(-2.93463 + 0.623775i) q^{24} +(-3.88208 - 1.72841i) q^{25} +(-6.90999 + 3.07653i) q^{26} +(-1.73998 - 5.35510i) q^{27} +(3.50625 + 7.13446i) q^{28} +(-1.23968 - 0.900684i) q^{29} +(0.270436 + 2.57303i) q^{30} +(8.68291 - 1.84561i) q^{31} +(3.34529 + 5.79421i) q^{32} -4.91197 q^{34} +(2.15151 - 0.790406i) q^{35} +(2.96058 - 2.15099i) q^{36} +(2.81857 - 1.25491i) q^{37} +(-5.37178 + 5.96597i) q^{38} +(-3.02018 + 3.35425i) q^{39} +(-1.77870 + 0.791930i) q^{40} +(-0.532009 + 0.386527i) q^{41} +(6.06791 + 5.06062i) q^{42} -9.76359 q^{43} +(-0.527575 - 0.913787i) q^{45} +(-3.65361 + 0.776598i) q^{46} +(-1.37931 - 13.1232i) q^{47} +(1.05999 + 0.770128i) q^{48} +(3.03078 - 6.30986i) q^{49} +(-2.93767 - 9.04121i) q^{50} +(-2.67769 + 1.19218i) q^{51} +(-9.28073 - 4.13205i) q^{52} +(-6.42032 + 1.36468i) q^{53} +(6.29821 - 10.9088i) q^{54} +(-2.21092 + 5.51986i) q^{56} +(-1.48035 + 4.55604i) q^{57} +(-0.358322 - 3.40921i) q^{58} +(1.52289 - 14.4894i) q^{59} +(-2.32512 + 2.58231i) q^{60} +(-5.66971 - 1.20513i) q^{61} +(16.0659 + 11.6725i) q^{62} +(-3.10021 - 0.878911i) q^{63} +(-4.01862 + 12.3680i) q^{64} +(-1.46459 + 2.53675i) q^{65} +(-2.64188 - 4.57587i) q^{67} +(-4.41439 - 4.90267i) q^{68} +(-1.80322 + 1.31012i) q^{69} +(4.53466 + 2.39369i) q^{70} +(2.42090 + 7.45077i) q^{71} +(2.67746 + 0.569111i) q^{72} +(0.618530 - 5.88492i) q^{73} +(6.30542 + 2.80735i) q^{74} +(-3.79582 - 4.21568i) q^{75} -10.7823 q^{76} -10.0974 q^{78} +(7.86523 + 8.73522i) q^{79} +(0.776783 + 0.345846i) q^{80} +(0.403767 - 3.84159i) q^{81} +(-1.43897 - 0.305862i) q^{82} +(-0.174158 - 0.536005i) q^{83} +(0.402185 + 10.6044i) q^{84} +(-1.53891 + 1.11808i) q^{85} +(-14.6152 - 16.2319i) q^{86} +(-1.02278 - 1.77151i) q^{87} +(-1.76101 + 3.05016i) q^{89} +(0.729428 - 2.24495i) q^{90} +(2.19019 + 8.67337i) q^{91} +(-4.05863 - 2.94877i) q^{92} +(11.5911 + 2.46377i) q^{93} +(19.7525 - 21.9374i) q^{94} +(-0.324968 + 3.09187i) q^{95} +(0.933594 + 8.88255i) q^{96} +(-4.29963 + 13.2329i) q^{97} +(15.0269 - 4.40668i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} + 34 q^{6} + 13 q^{7} + 32 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 + 34 * q^6 + 13 * q^7 + 32 * q^8 + 2 * q^9	\( 40 q + 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} + 34 q^{6} + 13 q^{7} + 32 q^{8} + 2 q^{9} + 14 q^{10} - 18 q^{12} - 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} - 12 q^{17} - 41 q^{18} - 24 q^{19} + 40 q^{20} - 2 q^{21} - 14 q^{23} - 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} - 24 q^{28} - 30 q^{29} + 6 q^{30} + 3 q^{31} - 30 q^{32} + 48 q^{34} + 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} - 32 q^{39} - 20 q^{40} + 10 q^{41} + 45 q^{42} - 72 q^{43} - 16 q^{45} - 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} + 6 q^{50} + 28 q^{51} + 2 q^{52} - 42 q^{53} + 34 q^{54} + 24 q^{56} - 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} - 20 q^{61} + 128 q^{62} - 36 q^{63} - 36 q^{64} - 40 q^{65} - 38 q^{67} - 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} + 42 q^{72} - 14 q^{73} - q^{74} - 16 q^{75} - 96 q^{76} - 100 q^{78} + 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} + 104 q^{83} - 44 q^{84} + 32 q^{85} + 2 q^{86} + 48 q^{87} - 10 q^{89} + 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} - 18 q^{94} - 8 q^{95} + 7 q^{96} + 46 q^{97} + 116 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 + 34 * q^6 + 13 * q^7 + 32 * q^8 + 2 * q^9 + 14 * q^10 - 18 * q^12 - 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 - 12 * q^17 - 41 * q^18 - 24 * q^19 + 40 * q^20 - 2 * q^21 - 14 * q^23 - 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 - 24 * q^28 - 30 * q^29 + 6 * q^30 + 3 * q^31 - 30 * q^32 + 48 * q^34 + 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 - 32 * q^39 - 20 * q^40 + 10 * q^41 + 45 * q^42 - 72 * q^43 - 16 * q^45 - 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 + 6 * q^50 + 28 * q^51 + 2 * q^52 - 42 * q^53 + 34 * q^54 + 24 * q^56 - 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 - 20 * q^61 + 128 * q^62 - 36 * q^63 - 36 * q^64 - 40 * q^65 - 38 * q^67 - 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 + 42 * q^72 - 14 * q^73 - q^74 - 16 * q^75 - 96 * q^76 - 100 * q^78 + 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 + 104 * q^83 - 44 * q^84 + 32 * q^85 + 2 * q^86 + 48 * q^87 - 10 * q^89 + 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 - 18 * q^94 - 8 * q^95 + 7 * q^96 + 46 * q^97 + 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more