LMFDB - Embedded newform 49.2.e.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.e (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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.2
Root			$0.365341 + 0.930874i$ of defining polynomial
Character	$\chi$	$=$	49.43
Dual form			49.2.e.b.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.914101 - 1.14625i) q^{2} +(-0.880843 - 0.424191i) q^{3} +(-0.0332580 - 0.145713i) q^{4} +(-0.830509 - 0.399952i) q^{5} +(-1.29141 + 0.621909i) q^{6} +(-0.938402 + 2.47374i) q^{7} +(2.44440 + 1.17716i) q^{8} +(-1.27452 - 1.59820i) q^{9} +O(q^{10})$	\(q+(0.914101 - 1.14625i) q^{2} +(-0.880843 - 0.424191i) q^{3} +(-0.0332580 - 0.145713i) q^{4} +(-0.830509 - 0.399952i) q^{5} +(-1.29141 + 0.621909i) q^{6} +(-0.938402 + 2.47374i) q^{7} +(2.44440 + 1.17716i) q^{8} +(-1.27452 - 1.59820i) q^{9} +(-1.21761 + 0.586371i) q^{10} +(-0.128892 + 0.161626i) q^{11} +(-0.0325151 + 0.142458i) q^{12} +(-1.07906 + 1.35310i) q^{13} +(1.97772 + 3.33689i) q^{14} +(0.561892 + 0.704590i) q^{15} +(3.85307 - 1.85554i) q^{16} +(1.14223 - 5.00446i) q^{17} -2.99698 q^{18} -3.25172 q^{19} +(-0.0306571 + 0.134318i) q^{20} +(1.87592 - 1.78092i) q^{21} +(0.0674425 + 0.295485i) q^{22} +(0.238377 + 1.04440i) q^{23} +(-1.65379 - 2.07379i) q^{24} +(-2.58767 - 3.24483i) q^{25} +(0.564616 + 2.47374i) q^{26} +(1.09736 + 4.80786i) q^{27} +(0.391666 + 0.0544655i) q^{28} +(1.32490 - 5.80477i) q^{29} +1.32126 q^{30} +8.38984 q^{31} +(0.187751 - 0.822592i) q^{32} +(0.182094 - 0.0876920i) q^{33} +(-4.69222 - 5.88386i) q^{34} +(1.76873 - 1.67915i) q^{35} +(-0.190491 + 0.238868i) q^{36} +(-1.82444 + 7.99340i) q^{37} +(-2.97240 + 3.72727i) q^{38} +(1.52446 - 0.734141i) q^{39} +(-1.55929 - 1.95529i) q^{40} +(10.9727 + 5.28418i) q^{41} +(-0.326584 - 3.77821i) q^{42} +(-8.14530 + 3.92257i) q^{43} +(0.0278377 + 0.0134059i) q^{44} +(0.419299 + 1.83707i) q^{45} +(1.41504 + 0.681446i) q^{46} +(-3.34737 + 4.19747i) q^{47} -4.18105 q^{48} +(-5.23880 - 4.64273i) q^{49} -6.08476 q^{50} +(-3.12898 + 3.92361i) q^{51} +(0.233052 + 0.112232i) q^{52} +(0.184264 + 0.807315i) q^{53} +(6.51409 + 3.13702i) q^{54} +(0.171689 - 0.0826810i) q^{55} +(-5.20583 + 4.94217i) q^{56} +(2.86425 + 1.37935i) q^{57} +(-5.44260 - 6.82480i) q^{58} +(-4.44313 + 2.13970i) q^{59} +(0.0839804 - 0.105308i) q^{60} +(1.96619 - 8.61445i) q^{61} +(7.66916 - 9.61682i) q^{62} +(5.14956 - 1.65309i) q^{63} +(4.56154 + 5.71999i) q^{64} +(1.43735 - 0.692190i) q^{65} +(0.0659359 - 0.288884i) q^{66} +5.82557 q^{67} -0.767203 q^{68} +(0.233052 - 1.02107i) q^{69} +(-0.307922 - 3.56231i) q^{70} +(-2.33108 - 10.2131i) q^{71} +(-1.23411 - 5.40697i) q^{72} +(5.82595 + 7.30552i) q^{73} +(7.49468 + 9.39803i) q^{74} +(0.902897 + 3.95585i) q^{75} +(0.108146 + 0.473817i) q^{76} +(-0.278868 - 0.470517i) q^{77} +(0.552003 - 2.41848i) q^{78} +4.55282 q^{79} -3.94213 q^{80} +(-0.291768 + 1.27832i) q^{81} +(16.0871 - 7.74716i) q^{82} +(-10.0118 - 12.5543i) q^{83} +(-0.321892 - 0.214117i) q^{84} +(-2.95018 + 3.69941i) q^{85} +(-2.94939 + 12.9221i) q^{86} +(-3.62936 + 4.55107i) q^{87} +(-0.505325 + 0.243352i) q^{88} +(-4.72383 - 5.92350i) q^{89} +(2.48902 + 1.19865i) q^{90} +(-2.33463 - 3.93908i) q^{91} +(0.144254 - 0.0694692i) q^{92} +(-7.39013 - 3.55890i) q^{93} +(1.75150 + 7.67381i) q^{94} +(2.70058 + 1.30053i) q^{95} +(-0.514316 + 0.644931i) q^{96} -5.84138 q^{97} +(-10.1105 + 1.76104i) q^{98} +0.422587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.914101	−	1.14625i	0.646367	−	0.810518i	−0.345416	−	0.938450i	$-0.612262\pi$
$2$	0.914101	−	1.14625i	0.646367	−	0.810518i	0.991783	+	0.127931i	$0.0408337\pi$
$3$	−0.880843	−	0.424191i	−0.508555	−	0.244907i	0.161968	−	0.986796i	$-0.448216\pi$
$3$	−0.880843	−	0.424191i	−0.508555	−	0.244907i	−0.670523	+	0.741889i	$0.733930\pi$
$4$	−0.0332580	−	0.145713i	−0.0166290	−	0.0728565i
$5$	−0.830509	−	0.399952i	−0.371415	−	0.178864i	0.238859	−	0.971054i	$-0.423226\pi$
$5$	−0.830509	−	0.399952i	−0.371415	−	0.178864i	−0.610274	+	0.792190i	$0.708941\pi$
$6$	−1.29141	+	0.621909i	−0.527215	+	0.253893i
$7$	−0.938402	+	2.47374i	−0.354683	+	0.934987i
$7$	−0.938402	+	2.47374i	−0.354683	+	0.934987i
$8$	2.44440	+	1.17716i	0.864227	+	0.416190i
$9$	−1.27452	−	1.59820i	−0.424841	−	0.532734i
$10$	−1.21761	+	0.586371i	−0.385043	+	0.185427i
$11$	−0.128892	+	0.161626i	−0.0388625	+	0.0487320i	−0.800883	−	0.598821i	$-0.795636\pi$
$11$	−0.128892	+	0.161626i	−0.0388625	+	0.0487320i	0.762020	+	0.647553i	$0.224208\pi$
$12$	−0.0325151	+	0.142458i	−0.00938630	+	0.0411241i
$13$	−1.07906	+	1.35310i	−0.299278	+	0.375283i	−0.908619	−	0.417625i	$-0.862863\pi$
$13$	−1.07906	+	1.35310i	−0.299278	+	0.375283i	0.609341	+	0.792908i	$0.291434\pi$
$14$	1.97772	+	3.33689i	0.528569	+	0.891821i
$15$	0.561892	+	0.704590i	0.145080	+	0.181924i
$16$	3.85307	−	1.85554i	0.963267	−	0.463885i
$17$	1.14223	−	5.00446i	0.277033	−	1.21376i	−0.624492	−	0.781031i	$-0.714694\pi$
$17$	1.14223	−	5.00446i	0.277033	−	1.21376i	0.901525	−	0.432728i	$-0.142449\pi$
$18$	−2.99698			−0.706394
$19$	−3.25172			−0.745996			−0.372998	−	0.927832i	$-0.621670\pi$
$19$	−3.25172			−0.745996			−0.372998	+	0.927832i	$0.621670\pi$
$20$	−0.0306571	+	0.134318i	−0.00685513	+	0.0300343i
$21$	1.87592	−	1.78092i	0.409360	−	0.388628i
$22$	0.0674425	+	0.295485i	0.0143788	+	0.0629976i
$23$	0.238377	+	1.04440i	0.0497050	+	0.217772i	0.993681	−	0.112243i	$-0.0358034\pi$
$23$	0.238377	+	1.04440i	0.0497050	+	0.217772i	−0.943976	+	0.330015i	$0.892946\pi$
$24$	−1.65379	−	2.07379i	−0.337579	−	0.423311i
$25$	−2.58767	−	3.24483i	−0.517533	−	0.648966i
$26$	0.564616	+	2.47374i	0.110730	+	0.485141i
$27$	1.09736	+	4.80786i	0.211187	+	0.925272i
$28$	0.391666	+	0.0544655i	0.0740178	+	0.0102930i
$29$	1.32490	−	5.80477i	0.246028	−	1.07792i	−0.689395	−	0.724386i	$-0.742123\pi$
$29$	1.32490	−	5.80477i	0.246028	−	1.07792i	0.935422	−	0.353532i	$-0.115019\pi$
$30$	1.32126			0.241228
$31$	8.38984			1.50686			0.753430	−	0.657528i	$-0.228398\pi$
$31$	8.38984			1.50686			0.753430	+	0.657528i	$0.228398\pi$
$32$	0.187751	−	0.822592i	0.0331900	−	0.145415i
$33$	0.182094	−	0.0876920i	0.0316985	−	0.0152652i
$34$	−4.69222	−	5.88386i	−0.804709	−	1.00907i
$35$	1.76873	−	1.67915i	0.298970	−	0.283828i
$36$	−0.190491	+	0.238868i	−0.0317484	+	0.0398113i
$37$	−1.82444	+	7.99340i	−0.299936	+	1.31411i	0.570286	+	0.821447i	$0.306833\pi$
$37$	−1.82444	+	7.99340i	−0.299936	+	1.31411i	−0.870222	+	0.492660i	$0.836025\pi$
$38$	−2.97240	+	3.72727i	−0.482187	+	0.604643i
$39$	1.52446	−	0.734141i	0.244109	−	0.117557i
$40$	−1.55929	−	1.95529i	−0.246545	−	0.309158i
$41$	10.9727	+	5.28418i	1.71365	+	0.825250i	0.990973	+	0.134065i	$0.0428031\pi$
$41$	10.9727	+	5.28418i	1.71365	+	0.825250i	0.722678	+	0.691185i	$0.242911\pi$
$42$	−0.326584	−	3.77821i	−0.0503930	−	0.582990i
$43$	−8.14530	+	3.92257i	−1.24215	+	0.598186i	−0.935395	−	0.353603i	$-0.884956\pi$
$43$	−8.14530	+	3.92257i	−1.24215	+	0.598186i	−0.306751	+	0.951790i	$0.599242\pi$
$44$	0.0278377	+	0.0134059i	0.00419669	+	0.00202102i
$45$	0.419299	+	1.83707i	0.0625054	+	0.273854i
$46$	1.41504	+	0.681446i	0.208636	+	0.100474i
$47$	−3.34737	+	4.19747i	−0.488264	+	0.612263i	−0.963537	−	0.267575i	$-0.913778\pi$
$47$	−3.34737	+	4.19747i	−0.488264	+	0.612263i	0.475273	+	0.879838i	$0.342349\pi$
$48$	−4.18105			−0.603483
$49$	−5.23880	−	4.64273i	−0.748401	−	0.663247i
$50$	−6.08476			−0.860515
$51$	−3.12898	+	3.92361i	−0.438144	+	0.549416i
$52$	0.233052	+	0.112232i	0.0323185	+	0.0155638i
$53$	0.184264	+	0.807315i	0.0253107	+	0.110893i	0.986005	−	0.166714i	$-0.0533157\pi$
$53$	0.184264	+	0.807315i	0.0253107	+	0.110893i	−0.960695	+	0.277607i	$0.910459\pi$
$54$	6.51409	+	3.13702i	0.886455	+	0.426894i
$55$	0.171689	−	0.0826810i	0.0231505	−	0.0111487i
$56$	−5.20583	+	4.94217i	−0.695658	+	0.660426i
$57$	2.86425	+	1.37935i	0.379380	+	0.182700i
$58$	−5.44260	−	6.82480i	−0.714648	−	0.896141i
$59$	−4.44313	+	2.13970i	−0.578446	+	0.278565i	−0.700143	−	0.714002i	$-0.746881\pi$
$59$	−4.44313	+	2.13970i	−0.578446	+	0.278565i	0.121697	+	0.992567i	$0.461166\pi$
$60$	0.0839804	−	0.105308i	0.0108418	−	0.0135952i
$61$	1.96619	−	8.61445i	0.251745	−	1.10297i	−0.678087	−	0.734982i	$-0.737191\pi$
$61$	1.96619	−	8.61445i	0.251745	−	1.10297i	0.929832	−	0.367985i	$-0.119952\pi$
$62$	7.66916	−	9.61682i	0.973984	−	1.22134i
$63$	5.14956	−	1.65309i	0.648783	−	0.208270i
$64$	4.56154	+	5.71999i	0.570193	+	0.714999i
$65$	1.43735	−	0.692190i	0.178281	−	0.0858556i
$66$	0.0659359	−	0.288884i	0.00811615	−	0.0355592i
$67$	5.82557			0.711707			0.355853	−	0.934542i	$-0.384190\pi$
$67$	5.82557			0.711707			0.355853	+	0.934542i	$0.384190\pi$
$68$	−0.767203			−0.0930370
$69$	0.233052	−	1.02107i	0.0280561	−	0.122922i
$70$	−0.307922	−	3.56231i	−0.0368037	−	0.425778i
$71$	−2.33108	−	10.2131i	−0.276648	−	1.21208i	−0.902001	−	0.431734i	$-0.857902\pi$
$71$	−2.33108	−	10.2131i	−0.276648	−	1.21208i	0.625353	−	0.780342i	$-0.284955\pi$
$72$	−1.23411	−	5.40697i	−0.145441	−	0.637218i
$73$	5.82595	+	7.30552i	0.681876	+	0.855046i	0.995526	−	0.0944930i	$-0.0301230\pi$
$73$	5.82595	+	7.30552i	0.681876	+	0.855046i	−0.313649	+	0.949539i	$0.601552\pi$
$74$	7.49468	+	9.39803i	0.871239	+	1.09250i
$75$	0.902897	+	3.95585i	0.104258	+	0.456782i
$76$	0.108146	+	0.473817i	0.0124052	+	0.0543506i
$77$	−0.278868	−	0.470517i	−0.0317800	−	0.0536203i
$78$	0.552003	−	2.41848i	0.0625020	−	0.273839i
$79$	4.55282			0.512232			0.256116	−	0.966646i	$-0.417557\pi$
$79$	4.55282			0.512232			0.256116	+	0.966646i	$0.417557\pi$
$80$	−3.94213			−0.440744
$81$	−0.291768	+	1.27832i	−0.0324187	+	0.142036i
$82$	16.0871	−	7.74716i	1.77653	−	0.855530i
$83$	−10.0118	−	12.5543i	−1.09893	−	1.37802i	−0.918962	−	0.394346i	$-0.870971\pi$
$83$	−10.0118	−	12.5543i	−1.09893	−	1.37802i	−0.179970	−	0.983672i	$-0.557600\pi$
$84$	−0.321892	−	0.214117i	−0.0351213	−	0.0233621i
$85$	−2.95018	+	3.69941i	−0.319992	+	0.401257i
$86$	−2.94939	+	12.9221i	−0.318041	+	1.39343i
$87$	−3.62936	+	4.55107i	−0.389108	+	0.487926i
$88$	−0.505325	+	0.243352i	−0.0538678	+	0.0259414i
$89$	−4.72383	−	5.92350i	−0.500725	−	0.627890i	0.465667	−	0.884960i	$-0.345814\pi$
$89$	−4.72383	−	5.92350i	−0.500725	−	0.627890i	−0.966393	+	0.257070i	$0.917243\pi$
$90$	2.48902	+	1.19865i	0.262365	+	0.126348i
$91$	−2.33463	−	3.93908i	−0.244736	−	0.412927i
$92$	0.144254	−	0.0694692i	0.0150395	−	0.00724266i
$93$	−7.39013	−	3.55890i	−0.766321	−	0.369041i
$94$	1.75150	+	7.67381i	0.180653	+	0.791493i
$95$	2.70058	+	1.30053i	0.277074	+	0.133432i
$96$	−0.514316	+	0.644931i	−0.0524921	+	0.0658230i
$97$	−5.84138			−0.593102			−0.296551	−	0.955017i	$-0.595836\pi$
$97$	−5.84138			−0.593102			−0.296551	+	0.955017i	$0.595836\pi$
$98$	−10.1105	+	1.76104i	−1.02132	+	0.177892i
$99$	0.422587			0.0424716
$100$	−0.386753	+	0.484973i	−0.0386753	+	0.0484973i
$101$	−7.60919	−	3.66439i	−0.757142	−	0.364621i	0.0151522	−	0.999885i	$-0.495177\pi$
$101$	−7.60919	−	3.66439i	−0.757142	−	0.364621i	−0.772294	+	0.635265i	$0.780891\pi$
$102$	1.63723	+	7.17316i	0.162110	+	0.710248i
$103$	8.49114	+	4.08912i	0.836657	+	0.402913i	0.802607	−	0.596508i	$-0.203445\pi$
$103$	8.49114	+	4.08912i	0.836657	+	0.402913i	0.0340491	+	0.999420i	$0.489160\pi$
$104$	−4.23049	+	2.03729i	−0.414833	+	0.199773i
$105$	−2.27025	+	0.728787i	−0.221554	+	0.0711223i
$106$	1.09382	+	0.526755i	0.106241	+	0.0511630i
$107$	−3.62532	−	4.54601i	−0.350473	−	0.439479i	0.575080	−	0.818097i	$-0.304971\pi$
$107$	−3.62532	−	4.54601i	−0.350473	−	0.439479i	−0.925553	+	0.378618i	$0.876399\pi$
$108$	0.664071	−	0.319800i	0.0639002	−	0.0307727i
$109$	−2.85886	+	3.58490i	−0.273829	+	0.343371i	−0.899663	−	0.436586i	$-0.856187\pi$
$109$	−2.85886	+	3.58490i	−0.273829	+	0.343371i	0.625834	+	0.779957i	$0.284759\pi$
$110$	0.0621682	−	0.272376i	0.00592750	−	0.0259701i
$111$	4.99778	−	6.26701i	0.474368	−	0.594839i
$112$	0.974402	+	11.2727i	0.0920723	+	1.06517i
$113$	−2.63884	−	3.30900i	−0.248241	−	0.311284i	0.642062	−	0.766653i	$-0.278079\pi$
$113$	−2.63884	−	3.30900i	−0.248241	−	0.311284i	−0.890303	+	0.455368i	$0.849508\pi$
$114$	4.19929	−	2.02227i	0.393300	−	0.189403i
$115$	0.219735	−	0.962721i	0.0204904	−	0.0897742i
$116$	−0.889893			−0.0826245
$117$	3.53782			0.327072
$118$	−1.60885	+	7.04882i	−0.148106	+	0.648896i
$119$	11.3079	+	7.52179i	1.03659	+	0.689521i
$120$	0.544073	+	2.38374i	0.0496668	+	0.217605i
$121$	2.43822	+	10.6825i	0.221656	+	0.971140i
$122$	−8.07698	−	10.1282i	−0.731255	−	0.916965i
$123$	−7.42373	−	9.30906i	−0.669375	−	0.839370i
$124$	−0.279029	−	1.22251i	−0.0250576	−	0.109784i
$125$	1.87690	+	8.22322i	0.167875	+	0.735507i
$126$	2.81237	−	7.41375i	0.250546	−	0.660469i
$127$	−1.41883	+	6.21629i	−0.125901	+	0.551607i	0.872152	+	0.489234i	$0.162724\pi$
$127$	−1.41883	+	6.21629i	−0.125901	+	0.551607i	−0.998053	+	0.0623723i	$0.980133\pi$
$128$	12.4137			1.09723
$129$	8.83865			0.778200
$130$	0.520460	−	2.28028i	0.0456474	−	0.199994i
$131$	−13.9077	+	6.69760i	−1.21512	+	0.585172i	−0.927949	−	0.372707i	$-0.878430\pi$
$131$	−13.9077	+	6.69760i	−1.21512	+	0.585172i	−0.287173	+	0.957879i	$0.592716\pi$
$132$	−0.0188339	−	0.0236170i	−0.00163928	−	0.00205560i
$133$	3.05142	−	8.04392i	0.264592	−	0.697496i
$134$	5.32516	−	6.67754i	0.460024	−	0.576851i
$135$	1.01154	−	4.43186i	0.0870598	−	0.381434i
$136$	8.68314	−	10.8883i	0.744573	−	0.933666i
$137$	0.841588	−	0.405288i	0.0719017	−	0.0346261i	−0.397587	−	0.917564i	$-0.630152\pi$
$137$	0.841588	−	0.405288i	0.0719017	−	0.0346261i	0.469489	+	0.882938i	$0.344438\pi$
$138$	−0.957361	−	1.20049i	−0.0814960	−	0.102193i
$139$	1.98261	+	0.954776i	0.168163	+	0.0809830i	0.516072	−	0.856545i	$-0.327394\pi$
$139$	1.98261	+	0.954776i	0.168163	+	0.0809830i	−0.347909	+	0.937528i	$0.613108\pi$
$140$	−0.303498	−	0.201882i	−0.0256503	−	0.0170621i
$141$	4.72903	−	2.27738i	0.398256	−	0.191790i
$142$	−13.8376	−	6.66384i	−1.16123	−	0.559217i
$143$	−0.0796134	−	0.348809i	−0.00665760	−	0.0291689i
$144$	−7.87635	−	3.79305i	−0.656363	−	0.316088i
$145$	−3.42197	+	4.29101i	−0.284179	+	0.356349i
$146$	13.6994			1.13377
$147$	2.64516	+	6.31177i	0.218169	+	0.520586i
$148$	1.22542			0.100729
$149$	−2.09684	+	2.62936i	−0.171780	+	0.215406i	−0.860268	−	0.509843i	$-0.829704\pi$
$149$	−2.09684	+	2.62936i	−0.171780	+	0.215406i	0.688487	+	0.725248i	$0.258275\pi$
$150$	5.35972	+	2.58110i	0.437619	+	0.210746i
$151$	−2.86969	−	12.5729i	−0.233532	−	1.02317i	−0.946685	−	0.322161i	$-0.895591\pi$
$151$	−2.86969	−	12.5729i	−0.233532	−	1.02317i	0.713153	−	0.701008i	$-0.247266\pi$
$152$	−7.94851	−	3.82780i	−0.644710	−	0.310476i
$153$	−9.45394	+	4.55278i	−0.764306	+	0.368070i
$154$	−0.794241	−	0.110448i	−0.0640018	−	0.00890016i
$155$	−6.96784	−	3.35553i	−0.559670	−	0.269523i
$156$	−0.157674	−	0.197717i	−0.0126240	−	0.0158300i
$157$	3.74918	−	1.80551i	0.299217	−	0.144095i	−0.278252	−	0.960508i	$-0.589755\pi$
$157$	3.74918	−	1.80551i	0.299217	−	0.144095i	0.577469	+	0.816413i	$0.304041\pi$
$158$	4.16173	−	5.21865i	0.331090	−	0.415173i
$159$	0.180148	−	0.789281i	0.0142867	−	0.0625941i
$160$	−0.484926	+	0.608078i	−0.0383368	+	0.0480728i
$161$	−2.80726	−	0.390381i	−0.221243	−	0.0307663i
$162$	1.19856	+	1.50295i	0.0941681	+	0.118083i
$163$	18.7194	−	9.01479i	1.46622	−	0.706093i	0.480891	−	0.876780i	$-0.340313\pi$
$163$	18.7194	−	9.01479i	1.46622	−	0.706093i	0.985325	+	0.170688i	$0.0545990\pi$
$164$	0.405043	−	1.77461i	0.0316285	−	0.138574i
$165$	−0.186303			−0.0145037
$166$	−23.5421			−1.82722
$167$	−0.435414	+	1.90767i	−0.0336933	+	0.147620i	−0.988977	−	0.148072i	$-0.952693\pi$
$167$	−0.435414	+	1.90767i	−0.0336933	+	0.147620i	0.955283	+	0.295692i	$0.0955503\pi$
$168$	6.68195	−	2.14501i	0.515523	−	0.165491i
$169$	2.22626	+	9.75390i	0.171251	+	0.750300i
$170$	1.54367	+	6.76326i	0.118394	+	0.518719i
$171$	4.14439	+	5.19691i	0.316930	+	0.397417i
$172$	0.842466	+	1.05642i	0.0642374	+	0.0805512i
$173$	2.98155	+	13.0630i	0.226683	+	0.993165i	0.952323	+	0.305090i	$0.0986866\pi$
$173$	2.98155	+	13.0630i	0.226683	+	0.993165i	−0.725640	+	0.688074i	$0.758456\pi$
$174$	1.89905	+	8.32028i	0.143967	+	0.630759i
$175$	10.4551	−	3.35626i	0.790335	−	0.253710i
$176$	−0.196728	+	0.861920i	−0.0148289	+	0.0649697i
$177$	4.82134			0.362394
$178$	−11.1078			−0.832568
$179$	0.186316	−	0.816302i	0.0139259	−	0.0610133i	−0.967488	−	0.252919i	$-0.918610\pi$
$179$	0.186316	−	0.816302i	0.0139259	−	0.0610133i	0.981413	+	0.191905i	$0.0614667\pi$
$180$	0.253740	−	0.122195i	0.0189126	−	0.00910785i
$181$	6.47192	+	8.11553i	0.481054	+	0.603222i	0.961839	−	0.273616i	$-0.0882198\pi$
$181$	6.47192	+	8.11553i	0.481054	+	0.603222i	−0.480785	+	0.876838i	$0.659648\pi$
$182$	−6.64924	−	0.924651i	−0.492874	−	0.0685397i
$183$	−5.38608	+	6.75393i	−0.398151	+	0.499265i
$184$	−0.646736	+	2.83354i	−0.0476780	+	0.208891i
$185$	4.71219	−	5.90890i	0.346447	−	0.434431i
$186$	−10.8347	+	5.21771i	−0.794438	+	0.382581i
$187$	0.661625	+	0.829651i	0.0483828	+	0.0606701i
$188$	0.722952	+	0.348155i	0.0527267	+	0.0253918i
$189$	−12.9232	−	1.79711i	−0.940022	−	0.130721i
$190$	3.95933	−	1.90671i	0.287240	−	0.138328i
$191$	7.42773	+	3.57700i	0.537451	+	0.258823i	0.682861	−	0.730549i	$-0.260736\pi$
$191$	7.42773	+	3.57700i	0.537451	+	0.258823i	−0.145409	+	0.989372i	$0.546450\pi$
$192$	−1.59163	−	6.97338i	−0.114866	−	0.503260i
$193$	−9.77596	−	4.70785i	−0.703689	−	0.338879i	0.0475870	−	0.998867i	$-0.484847\pi$
$193$	−9.77596	−	4.70785i	−0.703689	−	0.338879i	−0.751276	+	0.659988i	$0.770561\pi$
$194$	−5.33961	+	6.69565i	−0.383361	+	0.480720i
$195$	−1.55970			−0.111692
$196$	−0.502273	+	0.917769i	−0.0358767	+	0.0655550i
$197$	22.4336			1.59833			0.799164	−	0.601113i	$-0.205276\pi$
$197$	22.4336			1.59833			0.799164	+	0.601113i	$0.205276\pi$
$198$	0.386287	−	0.484389i	0.0274522	−	0.0344240i
$199$	−8.28086	−	3.98785i	−0.587015	−	0.282691i	0.116708	−	0.993166i	$-0.462766\pi$
$199$	−8.28086	−	3.98785i	−0.587015	−	0.282691i	−0.703723	+	0.710475i	$0.748480\pi$
$200$	−2.50561	−	10.9778i	−0.177173	−	0.776246i
$201$	−5.13141	−	2.47116i	−0.361942	−	0.174302i
$202$	−11.1559	+	5.37238i	−0.784923	+	0.377999i
$203$	13.1162	+	8.72466i	0.920577	+	0.612351i
$204$	0.675785	+	0.325441i	0.0473144	+	0.0227854i
$205$	−6.99952	−	8.77712i	−0.488868	−	0.613021i
$206$	12.4489	−	5.99507i	0.867355	−	0.417696i
$207$	1.36534	−	1.71208i	0.0948978	−	0.118998i
$208$	−1.64697	+	7.21584i	−0.114197	+	0.500328i
$209$	0.419122	−	0.525562i	0.0289913	−	0.0363539i
$210$	−1.23987	+	3.26845i	−0.0855593	+	0.225545i
$211$	−8.71768	−	10.9316i	−0.600150	−	0.752564i	0.385251	−	0.922812i	$-0.374115\pi$
$211$	−8.71768	−	10.9316i	−0.600150	−	0.752564i	−0.985401	+	0.170247i	$0.945543\pi$
$212$	0.111508	−	0.0536994i	0.00765840	−	0.00368809i
$213$	−2.27901	+	9.98499i	−0.156155	+	0.684160i
$214$	−8.52476			−0.582740
$215$	8.33359			0.568346
$216$	−2.97723	+	13.0441i	−0.202575	+	0.887540i
$217$	−7.87304	+	20.7543i	−0.534457	+	1.40889i
$218$	1.49589	+	6.55391i	0.101314	+	0.443887i
$219$	−2.03281	−	8.90633i	−0.137365	−	0.601834i
$220$	−0.0177577	−	0.0222675i	−0.00119723	−	0.00150127i
$221$	5.53900	+	6.94568i	0.372593	+	0.467217i
$222$	−2.61507	−	11.4574i	−0.175512	−	0.768968i
$223$	−3.42093	−	14.9881i	−0.229082	−	1.00368i	−0.950390	−	0.311061i	$-0.899316\pi$
$223$	−3.42093	−	14.9881i	−0.229082	−	1.00368i	0.721308	−	0.692615i	$-0.243541\pi$
$224$	1.85869	+	1.23637i	0.124189	+	0.0826084i
$225$	−1.88785	+	8.27123i	−0.125857	+	0.551415i
$226$	−6.20509			−0.412756
$227$	−27.0896			−1.79800			−0.899002	−	0.437945i	$-0.855706\pi$
$227$	−27.0896			−1.79800			−0.899002	+	0.437945i	$0.855706\pi$
$228$	0.105730	−	0.463233i	0.00700214	−	0.0306784i
$229$	9.04248	−	4.35463i	0.597544	−	0.287762i	−0.110561	−	0.993869i	$-0.535265\pi$
$229$	9.04248	−	4.35463i	0.597544	−	0.287762i	0.708105	+	0.706107i	$0.249550\pi$
$230$	−0.902655	−	1.13189i	−0.0595193	−	0.0746348i
$231$	0.0460498	+	0.532745i	0.00302985	+	0.0350520i
$232$	10.0717	−	12.6296i	0.661242	−	0.829172i
$233$	1.28517	−	5.63070i	0.0841943	−	0.368879i	−0.915225	−	0.402942i	$-0.867988\pi$
$233$	1.28517	−	5.63070i	0.0841943	−	0.368879i	0.999420	+	0.0340630i	$0.0108447\pi$
$234$	3.23393	−	4.05521i	0.211408	−	0.265098i
$235$	4.45880	−	2.14725i	0.290860	−	0.140071i
$236$	0.459551	+	0.576259i	0.0299142	+	0.0375113i
$237$	−4.01032	−	1.93127i	−0.260498	−	0.125449i
$238$	18.9583	−	6.08592i	1.22889	−	0.394492i
$239$	13.2227	−	6.36770i	0.855303	−	0.411892i	0.0457600	−	0.998952i	$-0.485429\pi$
$239$	13.2227	−	6.36770i	0.855303	−	0.411892i	0.809543	+	0.587060i	$0.199715\pi$
$240$	3.47240	+	1.67222i	0.224142	+	0.107941i
$241$	−4.79840	−	21.0231i	−0.309092	−	1.35422i	−0.855978	−	0.517013i	$-0.827044\pi$
$241$	−4.79840	−	21.0231i	−0.309092	−	1.35422i	0.546886	−	0.837207i	$-0.315813\pi$
$242$	14.4736	+	6.97012i	0.930398	+	0.448056i
$243$	10.0235	−	12.5690i	0.643006	−	0.806304i
$244$	−1.32063			−0.0845445
$245$	2.49401	+	5.95110i	0.159336	+	0.380202i
$246$	−17.4565			−1.11299
$247$	3.50881	−	4.39991i	0.223260	−	0.279959i
$248$	20.5082	+	9.87621i	1.30227	+	0.627140i
$249$	3.49333	+	15.3053i	0.221381	+	0.969934i
$250$	11.1415	+	5.36547i	0.704651	+	0.339342i
$251$	0.705402	−	0.339704i	0.0445246	−	0.0214419i	−0.411489	−	0.911415i	$-0.634991\pi$
$251$	0.705402	−	0.339704i	0.0445246	−	0.0214419i	0.456014	+	0.889973i	$0.349277\pi$
$252$	−0.412140	−	0.695378i	−0.0259624	−	0.0438047i
$253$	−0.199527	−	0.0960869i	−0.0125441	−	0.00604093i
$254$	5.82845	+	7.30864i	0.365709	+	0.458585i
$255$	4.16790	−	2.00716i	0.261004	−	0.125693i
$256$	2.22431	−	2.78919i	0.139019	−	0.174325i
$257$	5.11267	−	22.4001i	0.318920	−	1.39728i	−0.520531	−	0.853843i	$-0.674266\pi$
$257$	5.11267	−	22.4001i	0.318920	−	1.39728i	0.839451	−	0.543436i	$-0.182877\pi$
$258$	8.07942	−	10.1313i	0.503002	−	0.630745i
$259$	−18.0616	−	12.0142i	−1.12229	−	0.746527i
$260$	−0.148664	−	0.186419i	−0.00921977	−	0.0115612i
$261$	−10.9658	+	5.28086i	−0.678767	+	0.326877i
$262$	−5.03595	+	22.0639i	−0.311122	+	1.36311i
$263$	10.7806			0.664761			0.332380	−	0.943145i	$-0.392148\pi$
$263$	10.7806			0.664761			0.332380	+	0.943145i	$0.392148\pi$
$264$	0.548340			0.0337480
$265$	0.169854	−	0.744180i	0.0104341	−	0.0457146i
$266$	−6.43100	−	10.8506i	−0.394310	−	0.665295i
$267$	1.64826	+	7.22148i	0.100872	+	0.441948i
$268$	−0.193747	−	0.848861i	−0.0118350	−	0.0518524i
$269$	0.428422	+	0.537225i	0.0261214	+	0.0327552i	0.794721	−	0.606975i	$-0.207617\pi$
$269$	0.428422	+	0.537225i	0.0261214	+	0.0327552i	−0.768599	+	0.639731i	$0.779046\pi$
$270$	−4.15535	−	5.21064i	−0.252887	−	0.317110i
$271$	3.10448	+	13.6016i	0.188584	+	0.826238i	0.977364	+	0.211564i	$0.0678556\pi$
$271$	3.10448	+	13.6016i	0.188584	+	0.826238i	−0.788781	+	0.614675i	$0.789287\pi$
$272$	−4.88486	−	21.4020i	−0.296188	−	1.29769i
$273$	0.385520	+	4.46004i	0.0233327	+	0.269934i
$274$	0.304737	−	1.33514i	0.0184098	−	0.0806588i
$275$	0.857979			0.0517381
$276$	−0.156533			−0.00942221
$277$	−7.18224	+	31.4675i	−0.431539	+	1.89070i	0.0225602	+	0.999745i	$0.492818\pi$
$277$	−7.18224	+	31.4675i	−0.431539	+	1.89070i	−0.454099	+	0.890951i	$0.650039\pi$
$278$	2.90672	−	1.39980i	0.174333	−	0.0839545i
$279$	−10.6931	−	13.4087i	−0.640176	−	0.802756i
$280$	6.30012	−	2.02244i	0.376504	−	0.120864i
$281$	−4.83757	+	6.06612i	−0.288585	+	0.361875i	−0.904899	−	0.425626i	$-0.860054\pi$
$281$	−4.83757	+	6.06612i	−0.288585	+	0.361875i	0.616314	+	0.787501i	$0.288625\pi$
$282$	1.71237	−	7.50239i	0.101970	−	0.446761i
$283$	−9.06817	+	11.3711i	−0.539047	+	0.675943i	−0.974531	−	0.224253i	$-0.928006\pi$
$283$	−9.06817	+	11.3711i	−0.539047	+	0.675943i	0.435484	+	0.900196i	$0.356577\pi$
$284$	−1.41066	+	0.679337i	−0.0837072	+	0.0403113i
$285$	−1.82711	−	2.29113i	−0.108229	−	0.135715i
$286$	−0.472596	−	0.227590i	−0.0279452	−	0.0134577i
$287$	−23.3685	+	22.1850i	−1.37940	+	1.30954i
$288$	−1.55396	+	0.748348i	−0.0915681	+	0.0440969i
$289$	−8.42342	−	4.05651i	−0.495496	−	0.238618i
$290$	1.79053	+	7.84484i	0.105144	+	0.460665i
$291$	5.14533	+	2.47786i	0.301625	+	0.145255i
$292$	0.870748	−	1.09188i	0.0509567	−	0.0638977i
$293$	2.97748			0.173946			0.0869731	−	0.996211i	$-0.472281\pi$
$293$	2.97748			0.173946			0.0869731	+	0.996211i	$0.472281\pi$
$294$	9.65278	+	2.73759i	0.562962	+	0.159660i
$295$	4.54583			0.264669
$296$	−13.8692	+	17.3914i	−0.806131	+	1.01086i
$297$	−0.918516	−	0.442334i	−0.0532977	−	0.0256668i
$298$	1.09717	+	4.80700i	0.0635571	+	0.278462i
$299$	−1.67040	−	0.804422i	−0.0966017	−	0.0465209i
$300$	0.546390	−	0.263128i	0.0315458	−	0.0151917i
$301$	−2.05986	−	23.8303i	−0.118729	−	1.37356i
$302$	−17.0348	−	8.20355i	−0.980245	−	0.472061i
$303$	5.14809	+	6.45550i	0.295750	+	0.370859i
$304$	−12.5291	+	6.03369i	−0.718593	+	0.346056i
$305$	−5.07831	+	6.36799i	−0.290783	+	0.364630i
$306$	−3.42325	+	14.9982i	−0.195694	+	0.857392i
$307$	−4.16843	+	5.22704i	−0.237905	+	0.298323i	−0.886423	−	0.462876i	$-0.846818\pi$
$307$	−4.16843	+	5.22704i	−0.237905	+	0.298323i	0.648518	+	0.761199i	$0.275389\pi$
$308$	−0.0592857	+	0.0562831i	−0.00337812	+	0.00320703i
$309$	−5.74479	−	7.20374i	−0.326810	−	0.409806i
$310$	−10.2156	+	4.91956i	−0.580206	+	0.279412i
$311$	−0.604467	+	2.64835i	−0.0342762	+	0.150174i	−0.989170	−	0.146773i	$-0.953111\pi$
$311$	−0.604467	+	2.64835i	−0.0342762	+	0.150174i	0.954894	+	0.296947i	$0.0959684\pi$
$312$	4.59060			0.259891
$313$	9.37105			0.529683			0.264842	−	0.964292i	$-0.414680\pi$
$313$	9.37105			0.529683			0.264842	+	0.964292i	$0.414680\pi$
$314$	1.35757	−	5.94790i	0.0766120	−	0.335659i
$315$	−4.93791	−	0.686671i	−0.278220	−	0.0386896i
$316$	−0.151418	−	0.663404i	−0.00851791	−	0.0373194i
$317$	−3.01490	−	13.2091i	−0.169334	−	0.741899i	−0.986266	−	0.165166i	$-0.947184\pi$
$317$	−3.01490	−	13.2091i	−0.169334	−	0.741899i	0.816932	−	0.576734i	$-0.195673\pi$
$318$	−0.740037	−	0.927977i	−0.0414992	−	0.0520384i
$319$	0.767431	+	0.962328i	0.0429679	+	0.0538800i
$320$	−1.50068	−	6.57490i	−0.0838905	−	0.367548i
$321$	1.26496	+	5.54215i	0.0706032	+	0.309333i
$322$	−3.01359	+	2.86097i	−0.167941	+	0.159435i
$323$	−3.71423	+	16.2731i	−0.206665	+	0.905459i
$324$	0.195972			0.0108873
$325$	7.18284			0.398432
$326$	6.77825	−	29.6975i	0.375413	−	1.64479i
$327$	4.03889	−	1.94503i	0.223351	−	0.107560i
$328$	20.6014	+	25.8333i	1.13752	+	1.42641i
$329$	−7.24227	−	12.2194i	−0.399279	−	0.673679i
$330$	−0.170300	+	0.213550i	−0.00937471	+	0.0117555i
$331$	−1.72805	+	7.57106i	−0.0949820	+	0.416143i	−0.999957	−	0.00932249i	$-0.997033\pi$
$331$	−1.72805	+	7.57106i	−0.0949820	+	0.416143i	0.904975	+	0.425466i	$0.139890\pi$
$332$	−1.49636	+	1.87637i	−0.0821233	+	0.102979i
$333$	15.1004	−	7.27195i	0.827495	−	0.398501i
$334$	1.78865	+	2.24290i	0.0978706	+	0.122726i
$335$	−4.83819	−	2.32995i	−0.264339	−	0.127299i
$336$	3.92350	−	10.3428i	0.214045	−	0.564248i
$337$	12.9008	−	6.21268i	0.702749	−	0.338426i	−0.0481528	−	0.998840i	$-0.515333\pi$
$337$	12.9008	−	6.21268i	0.702749	−	0.338426i	0.750902	+	0.660414i	$0.229619\pi$
$338$	13.2154	+	6.36420i	0.718823	+	0.346167i
$339$	0.920752	+	4.03408i	0.0500084	+	0.219101i
$340$	0.637169	+	0.306844i	0.0345553	+	0.0166410i
$341$	−1.08139	+	1.35602i	−0.0585603	+	0.0734324i
$342$	9.74533			0.526967
$343$	16.4010	−	8.60271i	0.885572	−	0.464503i
$344$	−24.5279			−1.32246
$345$	−0.601930	+	0.754796i	−0.0324068	+	0.0406368i
$346$	17.6989	+	8.52334i	0.951499	+	0.458218i
$347$	−0.0856481	−	0.375249i	−0.00459783	−	0.0201444i	0.972577	−	0.232581i	$-0.0747172\pi$
$347$	−0.0856481	−	0.375249i	−0.00459783	−	0.0201444i	−0.977175	+	0.212437i	$0.931860\pi$
$348$	0.783856	+	0.377485i	0.0420191	+	0.0202353i
$349$	29.0232	−	13.9769i	1.55358	−	0.748164i	0.556976	−	0.830528i	$-0.311961\pi$
$349$	29.0232	−	13.9769i	1.55358	−	0.748164i	0.996602	+	0.0823643i	$0.0262471\pi$
$350$	5.70995	−	15.0521i	0.305210	−	0.804570i
$351$	−7.68964	−	3.70314i	−0.410443	−	0.197659i
$352$	0.108752	+	0.136371i	0.00579652	+	0.00726861i
$353$	6.28815	−	3.02821i	0.334685	−	0.161176i	−0.258992	−	0.965880i	$-0.583390\pi$
$353$	6.28815	−	3.02821i	0.334685	−	0.161176i	0.593676	+	0.804704i	$0.297676\pi$
$354$	4.40719	−	5.52644i	0.234239	−	0.293727i
$355$	−2.14878	+	9.41442i	−0.114045	+	0.499666i
$356$	−0.706025	+	0.885327i	−0.0374193	+	0.0469223i
$357$	−6.76977	−	11.4222i	−0.358294	−	0.604528i
$358$	−0.765372	−	0.959746i	−0.0404512	−	0.0507242i
$359$	−17.6413	+	8.49559i	−0.931071	+	0.448380i	−0.837011	−	0.547187i	$-0.815699\pi$
$359$	−17.6413	+	8.49559i	−0.931071	+	0.448380i	−0.0940599	+	0.995567i	$0.529985\pi$
$360$	−1.13759	+	4.98412i	−0.0599565	+	0.262686i
$361$	−8.42632			−0.443491
$362$	15.2184			0.799860
$363$	2.38375	−	10.4439i	0.125115	−	0.548163i
$364$	−0.496329	+	0.471192i	−0.0260147	+	0.0246972i
$365$	−1.91665	−	8.39740i	−0.100322	−	0.439540i
$366$	2.81825	+	12.3475i	0.147312	+	0.645417i
$367$	3.54539	+	4.44578i	0.185068	+	0.232068i	0.865707	−	0.500551i	$-0.166869\pi$
$367$	3.54539	+	4.44578i	0.185068	+	0.232068i	−0.680639	+	0.732619i	$0.738298\pi$
$368$	2.85640	+	3.58181i	0.148900	+	0.186715i
$369$	−5.53980	−	24.2714i	−0.288390	−	1.26352i
$370$	−2.46564	−	10.8027i	−0.128182	−	0.561604i
$371$	−2.17000	−	0.301763i	−0.112661	−	0.0156668i
$372$	−0.272796	+	1.19520i	−0.0141438	+	0.0619682i
$373$	−22.9182			−1.18666			−0.593331	−	0.804959i	$-0.702187\pi$
$373$	−22.9182			−1.18666			−0.593331	+	0.804959i	$0.702187\pi$
$374$	1.55578			0.0804473
$375$	1.83497	−	8.03953i	0.0947575	−	0.415160i
$376$	−13.1234	+	6.31990i	−0.676788	+	0.325924i
$377$	6.42479	+	8.05643i	0.330893	+	0.414927i
$378$	−13.8730	+	13.1704i	−0.713550	+	0.677412i
$379$	−5.85485	+	7.34175i	−0.300743	+	0.377120i	−0.909124	−	0.416525i	$-0.863248\pi$
$379$	−5.85485	+	7.34175i	−0.300743	+	0.377120i	0.608381	+	0.793645i	$0.291819\pi$
$380$	0.0996883	−	0.436763i	0.00511390	−	0.0224055i
$381$	3.88666	−	4.87372i	0.199120	−	0.249688i
$382$	10.8898	−	5.24426i	0.557172	−	0.268320i
$383$	7.74026	+	9.70598i	0.395509	+	0.495952i	0.939218	−	0.343321i	$-0.111552\pi$
$383$	7.74026	+	9.70598i	0.395509	+	0.495952i	−0.543709	+	0.839274i	$0.682981\pi$
$384$	−10.9345	−	5.26579i	−0.558001	−	0.268719i
$385$	0.0434184	+	0.502302i	0.00221281	+	0.0255997i
$386$	−14.3326	+	6.90220i	−0.729508	+	0.351313i
$387$	16.6504	+	8.01843i	0.846389	+	0.407600i
$388$	0.194273	+	0.851164i	0.00986270	+	0.0432113i
$389$	4.12533	+	1.98666i	0.209163	+	0.100727i	0.535532	−	0.844515i	$-0.320111\pi$
$389$	4.12533	+	1.98666i	0.209163	+	0.100727i	−0.326369	+	0.945242i	$0.605825\pi$
$390$	−1.42572	+	1.78780i	−0.0721942	+	0.0905286i
$391$	5.49892			0.278092
$392$	−7.34050	−	17.5156i	−0.370751	−	0.884673i
$393$	15.0916			0.761269
$394$	20.5066	−	25.7144i	1.03311	−	1.29547i
$395$	−3.78116	−	1.82091i	−0.190251	−	0.0916199i
$396$	−0.0140544	−	0.0615764i	−0.000706261	−	0.00309433i
$397$	−4.43563	−	2.13609i	−0.222618	−	0.107207i	0.319251	−	0.947670i	$-0.396569\pi$
$397$	−4.43563	−	2.13609i	−0.222618	−	0.107207i	−0.541869	+	0.840463i	$0.682283\pi$
$398$	−12.1406	+	5.84661i	−0.608553	+	0.293064i
$399$	−6.09998	+	5.79104i	−0.305381	+	0.289915i
$400$	−15.9914	−	7.70103i	−0.799568	−	0.385052i
$401$	9.67967	+	12.1379i	0.483380	+	0.606139i	0.962390	−	0.271670i	$-0.0875760\pi$
$401$	9.67967	+	12.1379i	0.483380	+	0.606139i	−0.479011	+	0.877809i	$0.659005\pi$
$402$	−7.52318	+	3.62297i	−0.375222	+	0.180697i
$403$	−9.05316	+	11.3523i	−0.450970	+	0.565499i
$404$	−0.280883	+	1.23063i	−0.0139744	+	0.0612260i
$405$	0.753584	−	0.944964i	0.0374459	−	0.0469556i
$406$	21.9901	−	7.05918i	1.09135	−	0.350341i
$407$	−1.05678	−	1.32517i	−0.0523828	−	0.0656860i
$408$	−12.2672	+	5.90758i	−0.607318	+	0.292469i
$409$	4.13971	−	18.1373i	0.204696	−	0.896830i	−0.763336	−	0.646002i	$-0.776440\pi$
$409$	4.13971	−	18.1373i	0.204696	−	0.896830i	0.968032	−	0.250829i	$-0.0807031\pi$
$410$	−16.4590			−0.812852
$411$	−0.913227			−0.0450461
$412$	0.313439	−	1.37326i	0.0154420	−	0.0676559i
$413$	−1.12362	−	12.9990i	−0.0552898	−	0.639641i
$414$	−0.714410	−	3.13003i	−0.0351113	−	0.153833i
$415$	3.29372	+	14.4307i	0.161682	+	0.708376i
$416$	0.910455	+	1.14167i	0.0446387	+	0.0559752i
$417$	−1.34136	−	1.68201i	−0.0656868	−	0.0823686i
$418$	−0.219304	−	0.960833i	−0.0107265	−	0.0469959i
$419$	2.23803	+	9.80543i	0.109335	+	0.479027i	0.999716	+	0.0238121i	$0.00758033\pi$
$419$	2.23803	+	9.80543i	0.109335	+	0.479027i	−0.890382	+	0.455215i	$0.849563\pi$
$420$	0.181698	+	0.306567i	0.00886594	+	0.0149590i
$421$	−0.204650	+	0.896632i	−0.00997405	+	0.0436992i	−0.979670	−	0.200615i	$-0.935706\pi$
$421$	−0.204650	+	0.896632i	−0.00997405	+	0.0436992i	0.969696	+	0.244315i	$0.0785630\pi$
$422$	−20.4992			−0.997884
$423$	10.9747			0.533608
$424$	−0.499925	+	2.19031i	−0.0242785	+	0.106371i
$425$	−19.1943	+	9.24350i	−0.931062	+	0.448376i
$426$	9.36201	+	11.7396i	0.453591	+	0.568785i
$427$	19.4648	+	12.9477i	0.941970	+	0.626581i
$428$	−0.541841	+	0.679447i	−0.0261909	+	0.0328423i
$429$	−0.0778349	+	0.341017i	−0.00375791	+	0.0164645i
$430$	7.61774	−	9.55234i	0.367360	−	0.460655i
$431$	−28.0354	+	13.5011i	−1.35042	+	0.650326i	−0.962478	−	0.271360i	$-0.912527\pi$
$431$	−28.0354	+	13.5011i	−1.35042	+	0.650326i	−0.387938	+	0.921686i	$0.626812\pi$
$432$	13.1494	+	16.4888i	0.632650	+	0.793318i
$433$	−18.9377	−	9.11991i	−0.910087	−	0.438275i	−0.0805654	−	0.996749i	$-0.525673\pi$
$433$	−18.9377	−	9.11991i	−0.910087	−	0.438275i	−0.829522	+	0.558474i	$0.811387\pi$
$434$	16.5928	+	27.9960i	0.796479	+	1.34385i
$435$	4.83443	−	2.32814i	0.231793	−	0.111626i
$436$	0.617445	+	0.297346i	0.0295703	+	0.0142403i
$437$	−0.775134	−	3.39609i	−0.0370797	−	0.162457i
$438$	−12.0670	−	5.81118i	−0.576586	−	0.277669i
$439$	3.08071	−	3.86309i	0.147034	−	0.184375i	−0.702860	−	0.711328i	$-0.748094\pi$
$439$	3.08071	−	3.86309i	0.147034	−	0.184375i	0.849895	+	0.526953i	$0.176665\pi$
$440$	0.517006			0.0246473
$441$	−0.743039	+	14.2899i	−0.0353828	+	0.680473i
$442$	13.0247			0.619520
$443$	13.1395	−	16.4764i	0.624274	−	0.782815i	−0.364665	−	0.931139i	$-0.618816\pi$
$443$	13.1395	−	16.4764i	0.624274	−	0.782815i	0.988939	+	0.148324i	$0.0473878\pi$
$444$	−1.07940	−	0.519812i	−0.0512261	−	0.0246692i
$445$	1.55407	+	6.80883i	0.0736700	+	0.322769i
$446$	−20.3071	−	9.77938i	−0.961569	−	0.463067i
$447$	2.96234	−	1.42659i	0.140114	−	0.0674753i
$448$	−18.4303	+	5.91643i	−0.870752	+	0.279525i
$449$	29.0362	+	13.9831i	1.37030	+	0.659903i	0.966909	−	0.255123i	$-0.0821161\pi$
$449$	29.0362	+	13.9831i	1.37030	+	0.659903i	0.403394	+	0.915026i	$0.367830\pi$
$450$	7.75517	+	9.72468i	0.365582	+	0.458426i
$451$	−2.26836	+	1.09238i	−0.106813	+	0.0514384i
$452$	−0.394401	+	0.494563i	−0.0185511	+	0.0232623i
$453$	−2.80558	+	12.2921i	−0.131818	+	0.577531i
$454$	−24.7627	+	31.0514i	−1.16217	+	1.45731i
$455$	0.363490	+	4.20518i	0.0170407	+	0.197142i
$456$	5.37767	+	6.74338i	0.251832	+	0.315788i
$457$	11.9568	−	5.75811i	0.559317	−	0.269353i	−0.132794	−	0.991144i	$-0.542395\pi$
$457$	11.9568	−	5.75811i	0.559317	−	0.269353i	0.692111	+	0.721791i	$0.256681\pi$
$458$	3.27426	−	14.3455i	0.152996	−	0.670320i
$459$	25.3142			1.18156
$460$	−0.147589			−0.00688136
$461$	1.40560	−	6.15832i	0.0654651	−	0.286821i	−0.931590	−	0.363511i	$-0.881578\pi$
$461$	1.40560	−	6.15832i	0.0654651	−	0.286821i	0.997055	+	0.0766896i	$0.0244351\pi$
$462$	0.652750	+	0.434198i	0.0303687	+	0.0202007i
$463$	−4.56276	−	19.9908i	−0.212050	−	0.929050i	−0.963172	−	0.268887i	$-0.913344\pi$
$463$	−4.56276	−	19.9908i	−0.212050	−	0.929050i	0.751122	−	0.660163i	$-0.229513\pi$
$464$	−5.66604	−	24.8246i	−0.263039	−	1.15245i
$465$	4.71418	+	5.91140i	0.218615	+	0.274134i
$466$	−5.27939	−	6.62015i	−0.244563	−	0.306672i
$467$	−2.43747	−	10.6793i	−0.112793	−	0.494178i	−0.999493	−	0.0318332i	$-0.989865\pi$
$467$	−2.43747	−	10.6793i	−0.112793	−	0.494178i	0.886700	−	0.462345i	$-0.152992\pi$
$468$	−0.117661	−	0.515506i	−0.00543888	−	0.0238293i
$469$	−5.46673	+	14.4110i	−0.252430	+	0.665436i
$470$	1.61452	−	7.07369i	0.0744724	−	0.326285i
$471$	−4.06832			−0.187458
$472$	−13.3796			−0.615845
$473$	0.415878	−	1.82208i	0.0191221	−	0.0837794i
$474$	−5.87954	+	2.83144i	−0.270056	+	0.130052i
$475$	8.41436	+	10.5513i	0.386077	+	0.484126i
$476$	0.719944	−	1.89786i	0.0329986	−	0.0869883i
$477$	1.05540	−	1.32343i	0.0483236	−	0.0605959i
$478$	4.78790	−	20.9772i	0.218993	−	0.959473i
$479$	−19.9143	+	24.9718i	−0.909909	+	1.14099i	0.0796447	+	0.996823i	$0.474621\pi$
$479$	−19.9143	+	24.9718i	−0.909909	+	1.14099i	−0.989553	+	0.144166i	$0.953950\pi$
$480$	0.685086	−	0.329920i	0.0312697	−	0.0150587i
$481$	−8.84720	−	11.0940i	−0.403397	−	0.505844i
$482$	−28.4839	−	13.7171i	−1.29741	−	0.624798i
$483$	2.30716	+	1.53468i	0.104979	+	0.0698304i
$484$	1.47549	−	0.710560i	0.0670679	−	0.0322982i
$485$	4.85132	+	2.33627i	0.220287	+	0.106085i
$486$	−5.24475	−	22.9787i	−0.237907	−	1.04234i
$487$	−10.0452	−	4.83749i	−0.455190	−	0.219208i	0.192217	−	0.981352i	$-0.438432\pi$
$487$	−10.0452	−	4.83749i	−0.455190	−	0.219208i	−0.647407	+	0.762145i	$0.724146\pi$
$488$	14.9468	−	18.7427i	0.676609	−	0.848440i
$489$	−20.3128			−0.918578
$490$	9.10120	+	2.58116i	0.411150	+	0.116605i
$491$	10.1397			0.457599			0.228799	−	0.973474i	$-0.426520\pi$
$491$	10.1397			0.457599			0.228799	+	0.973474i	$0.426520\pi$
$492$	−1.10955	+	1.39133i	−0.0500225	+	0.0627262i
$493$	−27.5364	−	13.2608i	−1.24018	−	0.597237i
$494$	−1.83597	−	8.04392i	−0.0826043	−	0.361913i
$495$	−0.350963	−	0.169015i	−0.0157746	−	0.00759664i
$496$	32.3266	−	15.5677i	1.45151	−	0.699009i
$497$	27.4522	+	3.81753i	1.23140	+	0.171240i
$498$	20.7369	+	9.98636i	0.929242	+	0.447500i
$499$	8.41361	+	10.5503i	0.376645	+	0.472298i	0.933637	−	0.358220i	$-0.116616\pi$
$499$	8.41361	+	10.5503i	0.376645	+	0.472298i	−0.556992	+	0.830518i	$0.688045\pi$
$500$	1.13581	−	0.546976i	0.0507949	−	0.0244615i
$501$	1.19275	−	1.49566i	0.0532881	−	0.0668212i
$502$	0.255425	−	1.11909i	0.0114002	−	0.0499473i
$503$	−23.3081	+	29.2275i	−1.03926	+	1.30319i	−0.0875585	+	0.996159i	$0.527906\pi$
$503$	−23.3081	+	29.2275i	−1.03926	+	1.30319i	−0.951700	+	0.307030i	$0.900665\pi$
$504$	14.5335	+	2.02105i	0.647376	+	0.0900248i
$505$	4.85392	+	6.08662i	0.215996	+	0.270851i
$506$	−0.292527	+	0.140873i	−0.0130044	+	0.00626259i
$507$	2.17653	−	9.53601i	0.0966632	−	0.423509i
$508$	0.952981			0.0422817
$509$	34.7630			1.54084			0.770422	−	0.637534i	$-0.220045\pi$
$509$	34.7630			1.54084			0.770422	+	0.637534i	$0.220045\pi$
$510$	1.50919	−	6.61218i	0.0668280	−	0.292792i
$511$	−23.5391	+	7.55640i	−1.04131	+	0.334276i
$512$	4.36076	+	19.1058i	0.192720	+	0.844363i
$513$	−3.56831	−	15.6338i	−0.157545	−	0.690249i
$514$	−21.0025	−	26.3363i	−0.926381	−	1.16165i
$515$	−5.41652	−	6.79210i	−0.238680	−	0.299295i
$516$	−0.293956	−	1.28791i	−0.0129407	−	0.0566969i
$517$	−0.246969	−	1.08204i	−0.0108617	−	0.0475882i
$518$	−30.2813	+	9.72078i	−1.33049	+	0.427106i
$519$	2.91495	−	12.7712i	0.127952	−	0.560595i
$520$	4.32828			0.189807
$521$	35.6527			1.56197			0.780986	−	0.624548i	$-0.214717\pi$
$521$	35.6527			1.56197			0.780986	+	0.624548i	$0.214717\pi$
$522$	−3.97069	+	17.3967i	−0.173793	+	0.761435i
$523$	−4.79740	+	2.31031i	−0.209776	+	0.101023i	−0.535821	−	0.844331i	$-0.679998\pi$
$523$	−4.79740	+	2.31031i	−0.209776	+	0.101023i	0.326046	+	0.945354i	$0.394284\pi$
$524$	1.43847	+	1.80378i	0.0628398	+	0.0787987i
$525$	−10.6330	−	1.47864i	−0.464064	−	0.0645332i
$526$	9.85456	−	12.3572i	0.429679	−	0.538801i
$527$	9.58317	−	41.9866i	0.417449	−	1.82896i
$528$	0.538905	−	0.675766i	0.0234528	−	0.0294089i
$529$	19.6883	−	9.48141i	0.856015	−	0.412235i
$530$	−0.697749	−	0.874950i	−0.0303083	−	0.0380054i
$531$	9.08254	+	4.37392i	0.394149	+	0.189812i
$532$	−1.27359	−	0.177106i	−0.0552170	−	0.00767854i
$533$	−18.9903	+	9.14524i	−0.822560	+	0.396124i
$534$	9.78427	+	4.71185i	0.423407	+	0.203902i
$535$	1.19268	+	5.22546i	0.0515639	+	0.225916i
$536$	14.2400	+	6.85765i	0.615076	+	0.296205i
$537$	−0.510383	+	0.640001i	−0.0220247	+	0.0276181i
$538$	1.00741			0.0434327
$539$	1.42563	−	0.248314i	0.0614061	−	0.0106957i
$540$	−0.679421			−0.0292376
$541$	3.47819	−	4.36151i	0.149539	−	0.187516i	−0.701420	−	0.712748i	$-0.747450\pi$
$541$	3.47819	−	4.36151i	0.149539	−	0.187516i	0.850959	+	0.525232i	$0.176022\pi$
$542$	18.4286	+	8.87474i	0.791576	+	0.381203i
$543$	−2.25820	−	9.89383i	−0.0969088	−	0.424585i
$544$	−3.90217	−	1.87919i	−0.167304	−	0.0805694i
$545$	3.80809	−	1.83388i	0.163121	−	0.0785549i
$546$	5.46470	+	3.63502i	0.233868	+	0.155565i
$547$	16.7858	+	8.08361i	0.717708	+	0.345630i	0.756837	−	0.653604i	$-0.226744\pi$
$547$	16.7858	+	8.08361i	0.717708	+	0.345630i	−0.0391283	+	0.999234i	$0.512458\pi$
$548$	−0.0870452	−	0.109151i	−0.00371839	−	0.00466271i
$549$	−16.2736	+	7.83695i	−0.694540	+	0.334473i
$550$	0.784279	−	0.983455i	0.0334418	−	0.0419347i
$551$	−4.30820	+	18.8755i	−0.183536	+	0.804122i
$552$	1.77163	−	2.22156i	0.0754058	−	0.0945559i
$553$	−4.27237	+	11.2625i	−0.181680	+	0.478930i
$554$	29.5042	+	36.9970i	1.25351	+	1.57185i
$555$	−6.65721	+	3.20594i	−0.282583	+	0.136085i
$556$	0.0731854	−	0.320646i	0.00310375	−	0.0135984i
$557$	−34.3660			−1.45613			−0.728067	−	0.685506i	$-0.759581\pi$
$557$	−34.3660			−1.45613			−0.728067	+	0.685506i	$0.759581\pi$
$558$	−25.1442			−1.06444
$559$	3.48165	−	15.2541i	0.147258	−	0.645180i
$560$	3.69931	−	9.75182i	0.156324	−	0.412090i
$561$	−0.230856	−	1.01145i	−0.00974676	−	0.0427034i
$562$	2.53124	+	11.0901i	0.106774	+	0.467807i
$563$	−6.00127	−	7.52535i	−0.252923	−	0.317156i	0.639119	−	0.769108i	$-0.279299\pi$
$563$	−6.00127	−	7.52535i	−0.252923	−	0.317156i	−0.892042	+	0.451952i	$0.850728\pi$
$564$	−0.489122	−	0.613340i	−0.0205958	−	0.0258263i
$565$	0.868138	+	3.80356i	0.0365228	+	0.160017i
$566$	4.74489	+	20.7887i	0.199442	+	0.873814i
$567$	−2.88844	−	1.92134i	−0.121303	−	0.0806886i
$568$	6.32442	−	27.7091i	0.265367	−	1.16265i
$569$	−6.05156			−0.253695			−0.126847	−	0.991922i	$-0.540486\pi$
$569$	−6.05156			−0.253695			−0.126847	+	0.991922i	$0.540486\pi$
$570$	−4.29636			−0.179955
$571$	7.05185	−	30.8962i	0.295111	−	1.29296i	−0.582202	−	0.813044i	$-0.697809\pi$
$571$	7.05185	−	30.8962i	0.295111	−	1.29296i	0.877312	−	0.479920i	$-0.159334\pi$
$572$	−0.0481782	+	0.0232014i	−0.00201443	+	0.000970099i
$573$	−5.02532	−	6.30156i	−0.209936	−	0.263251i
$574$	4.06827	+	47.0654i	0.169806	+	1.96447i
$575$	2.77205	−	3.47604i	0.115603	−	0.144961i
$576$	3.32791	−	14.5805i	0.138663	−	0.607522i
$577$	−6.91755	+	8.67433i	−0.287981	+	0.361117i	−0.904687	−	0.426077i	$-0.859895\pi$
$577$	−6.91755	+	8.67433i	−0.287981	+	0.361117i	0.616706	+	0.787194i	$0.288467\pi$
$578$	−12.3496	+	5.94726i	−0.513676	+	0.247373i
$579$	6.61405	+	8.29375i	0.274870	+	0.344677i
$580$	0.739064	+	0.355915i	0.0306880	+	0.0147785i
$581$	40.4512	−	12.9855i	1.67820	−	0.538728i
$582$	7.54359	−	3.63280i	0.312692	−	0.150585i
$583$	−0.154233	−	0.0742749i	−0.00638769	−	0.00307615i
$584$	5.64120	+	24.7157i	0.233435	+	1.02274i
$585$	−2.93819	−	1.41496i	−0.121479	−	0.0585014i
$586$	2.72171	−	3.41292i	0.112433	−	0.140987i
$587$	−25.0861			−1.03541			−0.517707	−	0.855558i	$-0.673214\pi$
$587$	−25.0861			−1.03541			−0.517707	+	0.855558i	$0.673214\pi$
$588$	0.831734	−	0.595350i	0.0343001	−	0.0245518i
$589$	−27.2814			−1.12411
$590$	4.15535	−	5.21064i	0.171073	−	0.214519i
$591$	−19.7605	−	9.51615i	−0.812838	−	0.391442i
$592$	7.80237	+	34.1844i	0.320676	+	1.40497i
$593$	−34.0859	−	16.4149i	−1.39974	−	0.674079i	−0.426630	−	0.904426i	$-0.640299\pi$
$593$	−34.0859	−	16.4149i	−1.39974	−	0.674079i	−0.973108	+	0.230347i	$0.926014\pi$
$594$	−1.34664	+	0.648507i	−0.0552533	+	0.0266086i
$595$	−6.38293	−	10.7695i	−0.261675	−	0.441507i
$596$	0.452869	+	0.218090i	0.0185502	+	0.00893331i
$597$	5.60252	+	7.02534i	0.229296	+	0.287528i
$598$	−2.44898	+	1.17937i	−0.100146	+	0.0482279i
$599$	−7.79727	+	9.77746i	−0.318588	+	0.399496i	−0.915178	−	0.403050i	$-0.867950\pi$
$599$	−7.79727	+	9.77746i	−0.318588	+	0.399496i	0.596591	+	0.802546i	$0.296522\pi$
$600$	−2.44963	+	10.7326i	−0.100006	+	0.438155i
$601$	−19.8326	+	24.8693i	−0.808990	+	1.01444i	0.190474	+	0.981692i	$0.438997\pi$
$601$	−19.8326	+	24.8693i	−0.808990	+	1.01444i	−0.999464	+	0.0327485i	$0.989574\pi$
$602$	−29.1983	−	19.4222i	−1.19004	−	0.791590i
$603$	−7.42483	−	9.31044i	−0.302362	−	0.379151i
$604$	−1.73660	+	0.836301i	−0.0706611	+	0.0340286i
$605$	2.24754	−	9.84712i	0.0913755	−	0.400342i
$606$	12.1055			0.491751
$607$	−41.0529			−1.66629			−0.833143	−	0.553057i	$-0.813461\pi$
$607$	−41.0529			−1.66629			−0.833143	+	0.553057i	$0.813461\pi$
$608$	−0.610514	+	2.67484i	−0.0247596	+	0.108479i
$609$	−7.85239	−	13.2488i	−0.318195	−	0.536870i
$610$	2.65720	+	11.6420i	0.107587	+	0.471370i
$611$	−2.06758	−	9.05866i	−0.0836453	−	0.366474i
$612$	0.977818	+	1.22615i	0.0395260	+	0.0495640i
$613$	5.71158	+	7.16210i	0.230689	+	0.289274i	0.883681	−	0.468091i	$-0.155058\pi$
$613$	5.71158	+	7.16210i	0.230689	+	0.289274i	−0.652992	+	0.757365i	$0.726486\pi$
$614$	2.18112	+	9.55609i	0.0880226	+	0.385652i
$615$	2.44230	+	10.7004i	0.0984829	+	0.431482i
$616$	−0.127792	−	1.47841i	−0.00514887	−	0.0595667i
$617$	−1.32918	+	5.82353i	−0.0535109	+	0.234447i	−0.994610	−	0.103683i	$-0.966937\pi$
$617$	−1.32918	+	5.82353i	−0.0535109	+	0.234447i	0.941099	+	0.338130i	$0.109794\pi$
$618$	−13.5086			−0.543394
$619$	22.5594			0.906737			0.453369	−	0.891323i	$-0.350222\pi$
$619$	22.5594			0.906737			0.453369	+	0.891323i	$0.350222\pi$
$620$	−0.257208	+	1.12690i	−0.0103297	+	0.0452575i
$621$	−4.75973	+	2.29216i	−0.191001	+	0.0919813i
$622$	2.48311	+	3.11372i	0.0995637	+	0.124849i
$623$	19.0861	−	6.12693i	0.764667	−	0.245470i
$624$	4.51161	−	5.65739i	0.180609	−	0.226477i
$625$	−2.88752	+	12.6511i	−0.115501	+	0.506042i
$626$	8.56608	−	10.7415i	0.342370	−	0.429318i
$627$	−0.592119	+	0.285150i	−0.0236470	+	0.0113878i
$628$	−0.387776	−	0.486256i	−0.0154740	−	0.0194037i
$629$	37.9187	+	18.2607i	1.51192	+	0.728101i
$630$	−5.30084	+	5.03237i	−0.211191	+	0.200495i
$631$	−43.0635	+	20.7383i	−1.71433	+	0.825579i	−0.723525	+	0.690298i	$0.757479\pi$
$631$	−43.0635	+	20.7383i	−1.71433	+	0.825579i	−0.990807	+	0.135281i	$0.956806\pi$
$632$	11.1289	+	5.35941i	0.442685	+	0.213186i
$633$	3.04180	+	13.3270i	0.120901	+	0.529701i
$634$	−17.8969	−	8.61867i	−0.710775	−	0.342291i
$635$	3.66457	−	4.59522i	0.145424	−	0.182356i
$636$	−0.121000			−0.00479796
$637$	11.9351	−	2.07884i	0.472885	−	0.0823666i
$638$	1.80457			0.0714438
$639$	−13.3516	+	16.7424i	−0.528183	+	0.662320i
$640$	−10.3097	−	4.96489i	−0.407527	−	0.196255i
$641$	−11.0248	−	48.3030i	−0.435455	−	1.90785i	−0.418995	−	0.907989i	$-0.637617\pi$
$641$	−11.0248	−	48.3030i	−0.435455	−	1.90785i	−0.0164602	−	0.999865i	$-0.505240\pi$
$642$	7.50897	+	3.61613i	0.296355	+	0.142717i
$643$	34.2638	−	16.5006i	1.35123	−	0.650719i	0.388569	−	0.921420i	$-0.372970\pi$
$643$	34.2638	−	16.5006i	1.35123	−	0.650719i	0.962664	+	0.270700i	$0.0872553\pi$
$644$	0.0364804	+	0.422038i	0.00143753	+	0.0166306i
$645$	−7.34058	−	3.53504i	−0.289035	−	0.139192i
$646$	15.2578	+	19.1327i	0.600310	+	0.752765i
$647$	21.6705	−	10.4360i	0.851954	−	0.410280i	0.0436517	−	0.999047i	$-0.486101\pi$
$647$	21.6705	−	10.4360i	0.851954	−	0.410280i	0.808303	+	0.588767i	$0.200387\pi$
$648$	−2.21799	+	2.78127i	−0.0871309	+	0.109259i
$649$	0.226855	−	0.993915i	0.00890482	−	0.0390146i
$650$	6.56584	−	8.23330i	0.257533	−	0.322937i
$651$	15.7387	−	14.9416i	0.616849	−	0.585607i
$652$	−1.93614	−	2.42784i	−0.0758251	−	0.0950817i
$653$	−32.5085	+	15.6553i	−1.27216	+	0.612638i	−0.943363	−	0.331763i	$-0.892357\pi$
$653$	−32.5085	+	15.6553i	−1.27216	+	0.612638i	−0.328794	+	0.944402i	$0.606642\pi$
$654$	1.46247	−	6.40751i	0.0571872	−	0.250553i
$655$	14.2292			0.555981
$656$	52.0836			2.03352
$657$	4.25038	−	18.6221i	0.165823	−	0.726518i
$658$	−20.6266	−	2.86836i	−0.804110	−	0.111821i
$659$	−6.35320	−	27.8352i	−0.247486	−	1.08430i	−0.934024	−	0.357211i	$-0.883728\pi$
$659$	−6.35320	−	27.8352i	−0.247486	−	1.08430i	0.686538	−	0.727094i	$-0.259129\pi$
$660$	0.00619609	+	0.0271468i	0.000241182	+	0.00105669i
$661$	26.6870	+	33.4645i	1.03800	+	1.30162i	0.952256	+	0.305300i	$0.0987567\pi$
$661$	26.6870	+	33.4645i	1.03800	+	1.30162i	0.0857485	+	0.996317i	$0.472672\pi$
$662$	7.09869	+	8.90148i	0.275898	+	0.345966i
$663$	−1.93269	−	8.46765i	−0.0750593	−	0.328856i
$664$	−9.69426	−	42.4733i	−0.376210	−	1.64828i
$665$	−5.75141	+	5.46012i	−0.223030	+	0.211735i
$666$	5.46781	−	23.9560i	0.211873	−	0.928277i
$667$	6.37831			0.246969
$668$	0.292454			0.0113154
$669$	−3.34451	+	14.6533i	−0.129306	+	0.566528i
$670$	−7.09329	+	3.41595i	−0.274038	+	0.131970i
$671$	1.13889	+	1.42812i	0.0439664	+	0.0551321i
$672$	−1.11276	−	1.87749i	−0.0429256	−	0.0724257i
$673$	−13.0617	+	16.3788i	−0.503490	+	0.631357i	−0.967013	−	0.254728i	$-0.918014\pi$
$673$	−13.0617	+	16.3788i	−0.503490	+	0.631357i	0.463522	+	0.886085i	$0.346585\pi$
$674$	4.67133	−	20.4665i	0.179933	−	0.788338i
$675$	12.7611	−	16.0019i	0.491174	−	0.615912i
$676$	1.34723	−	0.648791i	0.0518165	−	0.0249535i
$677$	23.7303	+	29.7569i	0.912031	+	1.14365i	0.989191	+	0.146632i	$0.0468433\pi$
$677$	23.7303	+	29.7569i	0.912031	+	1.14365i	−0.0771603	+	0.997019i	$0.524585\pi$
$678$	5.46571	+	2.63215i	0.209909	+	0.101087i
$679$	5.48156	−	14.4501i	0.210363	−	0.554542i
$680$	−11.5662	+	5.57001i	−0.443545	+	0.213600i
$681$	23.8617	+	11.4912i	0.914383	+	0.440344i
$682$	0.565831	+	2.47907i	0.0216668	+	0.0949285i
$683$	20.7210	+	9.97869i	0.792866	+	0.381824i	0.786058	−	0.618153i	$-0.212119\pi$
$683$	20.7210	+	9.97869i	0.792866	+	0.381824i	0.00680795	+	0.999977i	$0.497833\pi$
$684$	0.619422	−	0.776731i	0.0236842	−	0.0296990i
$685$	−0.861042			−0.0328987
$686$	5.13136	−	26.6633i	0.195916	−	1.01801i
$687$	−9.81220			−0.374359
$688$	−24.1059	+	30.2279i	−0.919029	+	1.15243i
$689$	−1.29121	−	0.621815i	−0.0491913	−	0.0236893i
$690$	0.314957	+	1.37992i	0.0119902	+	0.0525326i
$691$	32.1744	+	15.4944i	1.22397	+	0.589434i	0.930415	−	0.366508i	$-0.119447\pi$
$691$	32.1744	+	15.4944i	1.22397	+	0.589434i	0.293557	+	0.955942i	$0.405161\pi$
$692$	1.80429	−	0.868902i	0.0685889	−	0.0330307i
$693$	−0.396557	+	1.04537i	−0.0150639	+	0.0397104i
$694$	−0.508419	−	0.244842i	−0.0192993	−	0.00929406i
$695$	−1.26471	−	1.58590i	−0.0479733	−	0.0601566i
$696$	−14.2290	+	6.85232i	−0.539348	+	0.259736i
$697$	38.9779	−	48.8767i	1.47639	−	1.85134i
$698$	10.5093	−	46.0440i	0.397781	−	1.74279i
$699$	−3.52053	+	4.41460i	−0.133159	+	0.166976i
$700$	−0.836768	−	1.41183i	−0.0316269	−	0.0533620i
$701$	−18.8301	−	23.6121i	−0.711201	−	0.891818i	0.286603	−	0.958049i	$-0.407474\pi$
$701$	−18.8301	−	23.6121i	−0.711201	−	0.891818i	−0.997804	+	0.0662312i	$0.978902\pi$
$702$	−11.2738	+	5.42918i	−0.425503	+	0.204911i
$703$	5.93257	−	25.9923i	0.223751	−	0.980318i
$704$	−1.51245			−0.0570025
$705$	−4.83835			−0.182223
$706$	2.27693	−	9.97586i	0.0856932	−	0.375447i
$707$	16.2052	−	15.3845i	0.609460	−	0.578594i
$708$	−0.160348	−	0.702531i	−0.00602625	−	0.0264027i
$709$	5.05428	+	22.1442i	0.189817	+	0.831644i	0.976712	+	0.214556i	$0.0688305\pi$
$709$	5.05428	+	22.1442i	0.189817	+	0.831644i	−0.786894	+	0.617088i	$0.788312\pi$
$710$	8.82704	+	11.0688i	0.331273	+	0.415403i
$711$	−5.80268	−	7.27633i	−0.217617	−	0.272884i
$712$	−4.57403	−	20.0401i	−0.171419	−	0.751036i
$713$	1.99994	+	8.76232i	0.0748985	+	0.328152i
$714$	−19.2809	−	2.68123i	−0.721570	−	0.100342i
$715$	−0.0733872	+	0.321531i	−0.00274453	+	0.0120246i
$716$	−0.125142			−0.00467679
$717$	−14.3482			−0.535844
$718$	−6.38786	+	27.9871i	−0.238393	+	1.04447i
$719$	17.9546	−	8.64646i	0.669592	−	0.322458i	−0.0680194	−	0.997684i	$-0.521668\pi$
$719$	17.9546	−	8.64646i	0.669592	−	0.322458i	0.737611	+	0.675226i	$0.235954\pi$
$720$	5.02434	+	6.30033i	0.187246	+	0.234799i
$721$	−18.0835	+	17.1677i	−0.673465	+	0.639357i
$722$	−7.70251	+	9.65864i	−0.286658	+	0.359457i
$723$	−4.69121	+	20.5535i	−0.174468	+	0.764394i
$724$	0.967294	−	1.21295i	0.0359492	−	0.0450789i
$725$	−22.2639	+	10.7217i	−0.826860	+	0.398195i
$726$	−9.79230	−	12.2792i	−0.363426	−	0.455722i
$727$	−16.7610	−	8.07166i	−0.621630	−	0.299361i	0.0964329	−	0.995339i	$-0.469257\pi$
$727$	−16.7610	−	8.07166i	−0.621630	−	0.299361i	−0.718063	+	0.695978i	$0.754971\pi$
$728$	−1.06985	−	12.3769i	−0.0396512	−	0.458720i
$729$	−10.6167	+	5.11275i	−0.393213	+	0.189361i
$730$	−11.3775	−	5.47911i	−0.421100	−	0.202791i
$731$	10.3265	+	45.2433i	0.381939	+	1.67338i
$732$	1.16327	+	0.560199i	0.0429955	+	0.0207056i
$733$	−7.54573	+	9.46205i	−0.278708	+	0.349489i	−0.901407	−	0.432973i	$-0.857465\pi$
$733$	−7.54573	+	9.46205i	−0.278708	+	0.349489i	0.622699	+	0.782461i	$0.286036\pi$
$734$	8.33680			0.307717
$735$	0.327579	−	6.29992i	0.0120829	−	0.232376i
$736$	0.903868			0.0333170
$737$	−0.750872	+	0.941563i	−0.0276587	+	0.0346829i
$738$	−32.8850	−	15.8366i	−1.21051	−	0.582952i
$739$	3.49103	+	15.2952i	0.128420	+	0.562644i	0.997667	+	0.0682663i	$0.0217468\pi$
$739$	3.49103	+	15.2952i	0.128420	+	0.562644i	−0.869247	+	0.494377i	$0.835396\pi$
$740$	−1.01772	−	0.490109i	−0.0374122	−	0.0180168i
$741$	−4.95711	+	2.38722i	−0.182104	+	0.0876967i
$742$	−2.32950	+	2.21152i	−0.0855186	+	0.0811873i
$743$	5.41915	+	2.60973i	0.198809	+	0.0957416i	0.530640	−	0.847598i	$-0.321952\pi$
$743$	5.41915	+	2.60973i	0.198809	+	0.0957416i	−0.331830	+	0.943339i	$0.607666\pi$
$744$	−13.8751	−	17.3988i	−0.508684	−	0.637870i
$745$	2.79307	−	1.34507i	0.102330	−	0.0492795i
$746$	−20.9496	+	26.2700i	−0.767019	+	0.961811i
$747$	−7.30416	+	32.0016i	−0.267245	+	1.17088i
$748$	0.0988865	−	0.124000i	0.00361565	−	0.00453388i
$749$	14.6477	−	4.70213i	0.535214	−	0.171812i
$750$	−7.53793	−	9.45227i	−0.275246	−	0.345148i
$751$	−8.03284	+	3.86841i	−0.293122	+	0.141160i	−0.574666	−	0.818388i	$-0.694868\pi$
$751$	−8.03284	+	3.86841i	−0.293122	+	0.141160i	0.281543	+	0.959549i	$0.409154\pi$
$752$	−5.10907	+	22.3843i	−0.186309	+	0.816271i
$753$	−0.765448			−0.0278945
$754$	15.1076			0.550185
$755$	−2.64526	+	11.5897i	−0.0962710	+	0.421791i
$756$	0.167937	+	1.94284i	0.00610780	+	0.0706604i
$757$	−5.22014	−	22.8709i	−0.189729	−	0.831259i	−0.976758	−	0.214343i	$-0.931239\pi$
$757$	−5.22014	−	22.8709i	−0.189729	−	0.831259i	0.787029	−	0.616916i	$-0.211618\pi$
$758$	3.06353	+	13.4222i	0.111272	+	0.487516i
$759$	0.134992	+	0.169275i	0.00489991	+	0.00614429i
$760$	5.07038	+	6.35805i	0.183922	+	0.230631i
$761$	7.69499	+	33.7140i	0.278943	+	1.22213i	0.899132	+	0.437678i	$0.144199\pi$
$761$	7.69499	+	33.7140i	0.278943	+	1.22213i	−0.620189	+	0.784453i	$0.712944\pi$
$762$	−2.03368	−	8.91014i	−0.0736725	−	0.322780i
$763$	−6.18535	−	10.4362i	−0.223925	−	0.377814i
$764$	0.274184	−	1.20128i	0.00991964	−	0.0434608i
$765$	9.67248			0.349709
$766$	18.2008			0.657622
$767$	1.89918	−	8.32087i	0.0685756	−	0.300449i
$768$	−3.14242	+	1.51331i	−0.113392	+	0.0546068i
$769$	−3.30592	−	4.14549i	−0.119215	−	0.149490i	0.718643	−	0.695379i	$-0.244764\pi$
$769$	−3.30592	−	4.14549i	−0.119215	−	0.149490i	−0.837858	+	0.545889i	$0.816192\pi$
$770$	0.615451	+	0.409387i	0.0221793	+	0.0147533i
$771$	−14.0054	+	17.5622i	−0.504392	+	0.632487i
$772$	−0.360866	+	1.58106i	−0.0129878	+	0.0569035i
$773$	−15.9860	+	20.0459i	−0.574978	+	0.721000i	−0.981247	−	0.192754i	$-0.938258\pi$
$773$	−15.9860	+	20.0459i	−0.574978	+	0.721000i	0.406269	+	0.913753i	$0.366830\pi$
$774$	24.4113	−	11.7558i	0.877445	−	0.422555i
$775$	−21.7101	−	27.2236i	−0.779850	−	0.977901i
$776$	−14.2787	−	6.87625i	−0.512575	−	0.246843i
$777$	10.8131	+	18.2442i	0.387916	+	0.654507i
$778$	6.04817	−	2.91264i	0.216837	−	0.104423i
$779$	−35.6802	−	17.1827i	−1.27838	−	0.615633i
$780$	0.0518725	+	0.227268i	0.00185733	+	0.00813750i
$781$	1.95117	+	0.939632i	0.0698182	+	0.0336227i
$782$	5.02657	−	6.30312i	0.179750	−	0.225399i
$783$	29.3624			1.04933
$784$	−28.8002	−	8.16794i	−1.02858	−	0.291712i
$785$	−3.83584			−0.136907
$786$	13.7952	−	17.2987i	0.492059	−	0.617023i
$787$	22.5828	+	10.8753i	0.804989	+	0.387662i	0.790676	−	0.612235i	$-0.209729\pi$
$787$	22.5828	+	10.8753i	0.804989	+	0.387662i	0.0143135	+	0.999898i	$0.495444\pi$
$788$	−0.746097	−	3.26887i	−0.0265786	−	0.116449i
$789$	−9.49602	−	4.57304i	−0.338067	−	0.162805i
$790$	−5.54357	+	2.66964i	−0.197231	+	0.0949816i
$791$	10.6619	−	3.42264i	0.379094	−	0.121695i
$792$	1.03297	+	0.497454i	0.0367051	+	0.0176763i
$793$	9.53458	+	11.9560i	0.338583	+	0.424569i
$794$	−6.50309	+	3.13172i	−0.230786	+	0.111141i
$795$	−0.465289	+	0.583455i	−0.0165021	+	0.0206930i
$796$	−0.305677	+	1.33926i	−0.0108344	+	0.0474687i
$797$	8.46506	−	10.6149i	0.299848	−	0.375997i	−0.608968	−	0.793195i	$-0.708416\pi$
$797$	8.46506	−	10.6149i	0.299848	−	0.375997i	0.908816	+	0.417197i	$0.136988\pi$
$798$	1.06196	+	12.2857i	0.0375929	+	0.434908i
$799$	17.1826	+	21.5462i	0.607875	+	0.762251i
$800$	−3.15501	+	1.51937i	−0.111546	+	0.0537179i
$801$	−3.44631	+	15.0993i	−0.121769	+	0.533507i
$802$	22.7612			0.803727
$803$	−1.93168			−0.0681676
$804$	−0.189419	+	0.829899i	−0.00668029	+	0.0292683i
$805$	2.17532	+	1.44699i	0.0766701	+	0.0509995i
$806$	4.73703	+	20.7543i	0.166855	+	0.731039i
$807$	−0.149487	−	0.654944i	−0.00526218	−	0.0230551i
$808$	−14.2863	−	17.9145i	−0.502592	−	0.630230i
$809$	9.19822	+	11.5342i	0.323392	+	0.405521i	0.916778	−	0.399397i	$-0.130781\pi$
$809$	9.19822	+	11.5342i	0.323392	+	0.405521i	−0.593386	+	0.804918i	$0.702209\pi$
$810$	−0.394310	−	1.72758i	−0.0138546	−	0.0607011i
$811$	−3.30283	−	14.4706i	−0.115978	−	0.508133i	−0.999230	−	0.0392344i	$-0.987508\pi$
$811$	−3.30283	−	14.4706i	−0.115978	−	0.508133i	0.883252	−	0.468899i	$-0.155349\pi$
$812$	0.835077	−	2.20137i	0.0293055	−	0.0772528i
$813$	3.03513	−	13.2978i	0.106447	−	0.466373i
$814$	−2.48497			−0.0870982
$815$	−19.1521			−0.670869
$816$	−4.77574	+	20.9239i	−0.167184	+	0.732483i
$817$	26.4862	−	12.7551i	0.926636	−	0.446244i
$818$	−17.0057	−	21.3244i	−0.594589	−	0.745591i
$819$	−3.31990	+	8.75166i	−0.116007	+	0.305808i
$820$	−1.04615	+	1.31183i	−0.0365331	+	0.0458111i
$821$	6.24421	−	27.3577i	0.217924	−	0.954789i	−0.741084	−	0.671412i	$-0.765688\pi$
$821$	6.24421	−	27.3577i	0.217924	−	0.954789i	0.959009	−	0.283377i	$-0.0914547\pi$
$822$	−0.834781	+	1.04678i	−0.0291163	+	0.0365107i
$823$	6.90961	−	3.32749i	0.240854	−	0.115989i	−0.309563	−	0.950879i	$-0.600183\pi$
$823$	6.90961	−	3.32749i	0.240854	−	0.115989i	0.550417	+	0.834890i	$0.314469\pi$
$824$	15.9422	+	19.9909i	0.555373	+	0.696416i
$825$	−0.755744	−	0.363947i	−0.0263116	−	0.0126710i
$826$	−15.9272	−	10.5945i	−0.554179	−	0.368630i
$827$	37.9199	−	18.2612i	1.31860	−	0.635006i	0.363587	−	0.931560i	$-0.381552\pi$
$827$	37.9199	−	18.2612i	1.31860	−	0.635006i	0.955016	+	0.296555i	$0.0958377\pi$
$828$	−0.294881	−	0.142007i	−0.0102478	−	0.00493509i
$829$	3.40531	+	14.9196i	0.118271	+	0.518180i	0.999006	+	0.0445707i	$0.0141920\pi$
$829$	3.40531	+	14.9196i	0.118271	+	0.518180i	−0.880735	+	0.473609i	$0.842951\pi$
$830$	19.5519	+	9.41572i	0.678658	+	0.326824i
$831$	19.6747	−	24.6712i	0.682506	−	0.855836i
$832$	−12.6619			−0.438973
$833$	−29.2183	+	20.9143i	−1.01235	+	0.724637i
$834$	−3.15414			−0.109219
$835$	1.12459	−	1.41020i	0.0389181	−	0.0488018i
$836$	−0.0905203	−	0.0435923i	−0.00313071	−	0.00150767i
$837$	9.20669	+	40.3371i	0.318230	+	1.39426i
$838$	13.2852	+	6.39782i	0.458930	+	0.221009i
$839$	−5.06600	+	2.43966i	−0.174898	+	0.0842264i	−0.519284	−	0.854602i	$-0.673801\pi$
$839$	−5.06600	+	2.43966i	−0.174898	+	0.0842264i	0.344386	+	0.938828i	$0.388087\pi$
$840$	−6.40732	−	0.891009i	−0.221073	−	0.0307427i
$841$	−5.81186	−	2.79884i	−0.200409	−	0.0965118i
$842$	0.840690	+	1.05419i	0.0289721	+	0.0363298i
$843$	6.83434	−	3.29124i	0.235387	−	0.113356i
$844$	−1.30295	+	1.63384i	−0.0448493	+	0.0562392i
$845$	2.05216	−	8.99110i	0.0705965	−	0.309303i
$846$	10.0320	−	12.5797i	0.344907	−	0.432499i
$847$	−28.7139	−	3.99299i	−0.986621	−	0.137201i
$848$	2.20799	+	2.76873i	0.0758226	+	0.0950786i
$849$	12.8112	−	6.16953i	0.439678	−	0.211738i
$850$	−6.95022	+	30.4509i	−0.238391	+	1.04446i
$851$	−8.78319			−0.301084
$852$	1.53074			0.0524422
$853$	4.94709	−	21.6746i	0.169385	−	0.742124i	−0.816860	−	0.576836i	$-0.804287\pi$
$853$	4.94709	−	21.6746i	0.169385	−	0.742124i	0.986245	−	0.165289i	$-0.0528555\pi$
$854$	32.6340	−	10.4760i	1.11671	−	0.358483i
$855$	−1.36344	−	5.97364i	−0.0466288	−	0.204294i
$856$	−3.51036	−	15.3799i	−0.119982	−	0.525673i
$857$	−16.6972	−	20.9377i	−0.570367	−	0.715217i	0.410069	−	0.912054i	$-0.365504\pi$
$857$	−16.6972	−	20.9377i	−0.570367	−	0.715217i	−0.980436	+	0.196837i	$0.936933\pi$
$858$	0.319741	+	0.400942i	0.0109158	+	0.0136879i
$859$	−11.2057	−	49.0953i	−0.382333	−	1.67511i	−0.690151	−	0.723666i	$-0.742456\pi$
$859$	−11.2057	−	49.0953i	−0.382333	−	1.67511i	0.307817	−	0.951445i	$-0.400401\pi$
$860$	−0.277159	−	1.21431i	−0.00945103	−	0.0414077i
$861$	29.9947	−	9.62876i	1.02222	−	0.328147i
$862$	−10.1515	+	44.4768i	−0.345763	+	1.51489i
$863$	−14.0737			−0.479074			−0.239537	−	0.970887i	$-0.576996\pi$
$863$	−14.0737			−0.479074			−0.239537	+	0.970887i	$0.576996\pi$
$864$	4.16093			0.141558
$865$	2.74838	−	12.0415i	0.0934478	−	0.409422i
$866$	−27.7646	+	13.3707i	−0.943480	+	0.454356i
$867$	5.69898	+	7.14629i	0.193547	+	0.242701i
$868$	3.28601	+	0.456957i	0.111535	+	0.0155101i
$869$	−0.586823	+	0.735853i	−0.0199066	+	0.0249621i
$870$	1.75054	−	7.66960i	0.0593487	−	0.260024i
$871$	−6.28616	+	7.88259i	−0.212998	+	0.267091i
$872$	−11.2082	+	5.39759i	−0.379558	+	0.182785i
$873$	7.44497	+	9.33570i	0.251974	+	0.315966i
$874$	−4.60130	−	2.21587i	−0.155641	−	0.0749529i
$875$	−22.1034	−	3.07373i	−0.747232	−	0.103911i
$876$	−1.23016	+	0.592414i	−0.0415633	+	0.0200158i
$877$	−22.7201	−	10.9414i	−0.767204	−	0.369466i	0.00899019	−	0.999960i	$-0.497138\pi$
$877$	−22.7201	−	10.9414i	−0.767204	−	0.369466i	−0.776195	+	0.630493i	$0.782853\pi$
$878$	−1.61197	−	7.06251i	−0.0544014	−	0.238348i
$879$	−2.62269	−	1.26302i	−0.0884611	−	0.0426006i
$880$	0.508111	−	0.637151i	0.0171284	−	0.0214784i
$881$	−12.2945			−0.414211			−0.207106	−	0.978319i	$-0.566404\pi$
$881$	−12.2945			−0.414211			−0.207106	+	0.978319i	$0.566404\pi$
$882$	15.7006	+	13.9141i	0.528666	+	0.468514i
$883$	10.5061			0.353557			0.176779	−	0.984251i	$-0.443432\pi$
$883$	10.5061			0.353557			0.176779	+	0.984251i	$0.443432\pi$
$884$	0.827860	−	1.03810i	0.0278439	−	0.0349152i
$885$	−4.00416	−	1.92830i	−0.134599	−	0.0648192i
$886$	−6.87517	−	30.1221i	−0.230976	−	1.01197i
$887$	−3.04547	−	1.46662i	−0.102257	−	0.0492443i	0.382056	−	0.924139i	$-0.375216\pi$
$887$	−3.04547	−	1.46662i	−0.102257	−	0.0492443i	−0.484313	+	0.874895i	$0.660930\pi$
$888$	19.5939	−	9.43592i	0.657528	−	0.316649i
$889$	−14.0461	−	9.34319i	−0.471090	−	0.313361i
$890$	9.22517	+	4.44261i	0.309228	+	0.148917i
$891$	−0.169003	−	0.211923i	−0.00566182	−	0.00709969i
$892$	−2.07018	+	0.996947i	−0.0693148	+	0.0333803i
$893$	10.8847	−	13.6490i	0.364242	−	0.456746i
$894$	1.07266	−	4.69962i	0.0358750	−	0.157179i
$895$	−0.481219	+	0.603429i	−0.0160854	+	0.0201704i
$896$	−11.6491	+	30.7083i	−0.389168	+	1.02589i
$897$	1.13013	+	1.41714i	0.0377339	+	0.0473169i
$898$	42.5701	−	20.5007i	1.42058	−	0.684116i
$899$	11.1157	−	48.7011i	0.370729	−	1.62427i
$900$	1.26801			0.0422670
$901$	4.25065			0.141610
$902$	−0.821368	+	3.59865i	−0.0273486	+	0.119822i
$903$	−8.29420	+	21.8645i	−0.276014	+	0.727606i
$904$	−2.55516	−	11.1949i	−0.0849832	−	0.372336i
$905$	−2.12916	−	9.32847i	−0.0707758	−	0.310089i
$906$	11.5251	+	14.4521i	0.382897	+	0.480138i
$907$	−1.06769	−	1.33884i	−0.0354520	−	0.0444554i	0.763789	−	0.645465i	$-0.223337\pi$
$907$	−1.06769	−	1.33884i	−0.0354520	−	0.0444554i	−0.799241	+	0.601010i	$0.794765\pi$
$908$	0.900948	+	3.94731i	0.0298990	+	0.130996i
$909$	3.84165	+	16.8314i	0.127420	+	0.558261i
$910$	5.15244	+	3.42731i	0.170802	+	0.113614i
$911$	−3.31326	+	14.5163i	−0.109773	+	0.480947i	0.889919	+	0.456119i	$0.150761\pi$
$911$	−3.31326	+	14.5163i	−0.109773	+	0.480947i	−0.999692	+	0.0248280i	$0.992096\pi$
$912$	13.5956			0.450195
$913$	3.31954			0.109861
$914$	4.32954	−	18.9690i	0.143209	−	0.627438i
$915$	7.17444	−	3.45503i	0.237180	−	0.114220i
$916$	−0.935261	−	1.17278i	−0.0309019	−	0.0387497i
$917$	−3.51712	−	40.6891i	−0.116146	−	1.34367i
$918$	23.1397	−	29.0163i	0.763724	−	0.957679i
$919$	−7.89881	+	34.6069i	−0.260558	+	1.14158i	0.660091	+	0.751186i	$0.270518\pi$
$919$	−7.89881	+	34.6069i	−0.260558	+	1.14158i	−0.920649	+	0.390392i	$0.872339\pi$
$920$	1.67040	−	2.09461i	0.0550714	−	0.0690574i
$921$	5.88900	−	2.83599i	0.194049	−	0.0934491i
$922$	−5.77409	−	7.24048i	−0.190160	−	0.238453i
$923$	16.3348	+	7.86642i	0.537666	+	0.258926i
$924$	0.0760962	−	0.0244281i	0.00250338	−	0.000803625i
$925$	30.6583	−	14.7642i	1.00804	−	0.485445i
$926$	−27.0852	−	13.0435i	−0.890074	−	0.428637i
$927$	−4.28692	−	18.7822i	−0.140801	−	0.616889i
$928$	−4.52620	−	2.17970i	−0.148580	−	0.0715523i
$929$	−30.8737	+	38.7144i	−1.01293	+	1.27018i	−0.0504807	+	0.998725i	$0.516075\pi$
$929$	−30.8737	+	38.7144i	−1.01293	+	1.27018i	−0.962452	+	0.271452i	$0.912496\pi$
$930$	11.0851			0.363496
$931$	17.0351	+	15.0969i	0.558304	+	0.494779i
$932$	−0.863208			−0.0282753
$933$	1.65585	−	2.07637i	0.0542100	−	0.0679772i
$934$	−14.4692	−	6.96798i	−0.473446	−	0.227999i
$935$	−0.217665	−	0.953651i	−0.00711839	−	0.0311877i
$936$	8.64786	+	4.16459i	0.282664	+	0.136124i
$937$	−41.3963	+	19.9354i	−1.35236	+	0.651261i	−0.962919	−	0.269792i	$-0.913045\pi$
$937$	−41.3963	+	19.9354i	−1.35236	+	0.651261i	−0.389438	+	0.921053i	$0.627331\pi$
$938$	11.5214	+	19.4393i	0.376186	+	0.634715i
$939$	−8.25442	−	3.97512i	−0.269373	−	0.129723i
$940$	−0.461172	−	0.578292i	−0.0150418	−	0.0188618i
$941$	−11.6016	+	5.58706i	−0.378203	+	0.182133i	−0.613321	−	0.789834i	$-0.710167\pi$
$941$	−11.6016	+	5.58706i	−0.378203	+	0.182133i	0.235118	+	0.971967i	$0.424452\pi$
$942$	−3.71885	+	4.66329i	−0.121167	+	0.151938i
$943$	−2.90314	+	12.7195i	−0.0945393	+	0.414204i
$944$	−13.1494	+	16.4888i	−0.427976	+	0.536665i
$945$	10.0140	+	6.66116i	0.325757	+	0.216688i
$946$	−1.70840	−	2.14226i	−0.0555448	−	0.0696510i
$947$	15.9596	−	7.68572i	0.518616	−	0.249752i	−0.156217	−	0.987723i	$-0.549930\pi$
$947$	15.9596	−	7.68572i	0.518616	−	0.249752i	0.674833	+	0.737970i	$0.264216\pi$
$948$	−0.148035	+	0.648585i	−0.00480796	+	0.0210651i
$949$	−16.1717			−0.524955
$950$	19.7859			0.641940
$951$	−2.94755	+	12.9141i	−0.0955810	+	0.418768i
$952$	18.7866	+	31.6975i	0.608878	+	1.02732i
$953$	6.73077	+	29.4894i	0.218031	+	0.955256i	0.958931	+	0.283641i	$0.0915423\pi$
$953$	6.73077	+	29.4894i	0.218031	+	0.955256i	−0.740900	+	0.671616i	$0.765601\pi$
$954$	−0.552236	−	2.41951i	−0.0178793	−	0.0783344i
$955$	−4.73816	−	5.94147i	−0.153323	−	0.192261i
$956$	−1.36762	−	1.71494i	−0.0442319	−	0.0554650i
$957$	−0.267775	−	1.17320i	−0.00865593	−	0.0379241i
$958$	10.4201	+	45.6534i	0.336658	+	1.47500i
$959$	0.212829	+	2.46220i	0.00687261	+	0.0795084i
$960$	−1.46716	+	6.42803i	−0.0473523	+	0.207464i
$961$	39.3894			1.27063
$962$	−20.8037			−0.670739
$963$	−2.64488	+	11.5880i	−0.0852302	+	0.373418i
$964$	−2.90376	+	1.39838i	−0.0935238	+	0.0450387i
$965$	6.23610	+	7.81983i	0.200747	+	0.251729i
$966$	3.86810	−	1.24172i	0.124454	−	0.0399517i
$967$	20.6172	−	25.8531i	0.663003	−	0.831380i	−0.330663	−	0.943749i	$-0.607272\pi$
$967$	20.6172	−	25.8531i	0.663003	−	0.831380i	0.993667	+	0.112369i	$0.0358438\pi$
$968$	−6.61510	+	28.9826i	−0.212617	+	0.931537i
$969$	10.1746	−	12.7585i	0.326854	−	0.409862i
$970$	7.11253	−	3.42521i	0.228370	−	0.109977i
$971$	−27.2182	−	34.1306i	−0.873474	−	1.09530i	−0.994715	−	0.102679i	$-0.967259\pi$
$971$	−27.2182	−	34.1306i	−0.873474	−	1.09530i	0.121241	−	0.992623i	$-0.461313\pi$
$972$	−2.16483	−	1.04253i	−0.0694370	−	0.0334391i
$973$	−4.22236	+	4.00851i	−0.135363	+	0.128507i
$974$	−14.7272	+	7.09227i	−0.471891	+	0.227251i
$975$	−6.32695	−	3.04690i	−0.202625	−	0.0975789i
$976$	−8.40858	−	36.8404i	−0.269152	−	1.17923i
$977$	−52.5303	−	25.2972i	−1.68059	−	0.809331i	−0.996824	−	0.0796312i	$-0.974626\pi$
$977$	−52.5303	−	25.2972i	−1.68059	−	0.809331i	−0.683768	−	0.729699i	$-0.739660\pi$
$978$	−18.5680	+	23.2835i	−0.593739	+	0.744525i
$979$	1.56626			0.0500578
$980$	0.784206	−	0.561331i	0.0250505	−	0.0179310i
$981$	9.37307			0.299259
$982$	9.26872	−	11.6226i	0.295777	−	0.370892i
$983$	42.3783	+	20.4083i	1.35166	+	0.650924i	0.962760	−	0.270357i	$-0.0871416\pi$
$983$	42.3783	+	20.4083i	1.35166	+	0.650924i	0.388898	+	0.921281i	$0.372856\pi$
$984$	−7.18831	−	31.4940i	−0.229155	−	1.00399i
$985$	−18.6313	−	8.97237i	−0.593643	−	0.285883i
$986$	−40.3712	+	19.4417i	−1.28568	+	0.619151i
$987$	1.19592	+	13.8355i	0.0380667	+	0.440389i
$988$	−0.757819	−	0.364947i	−0.0241094	−	0.0116105i
$989$	−6.03837	−	7.57188i	−0.192009	−	0.240772i
$990$	−0.514548	+	0.247793i	−0.0163534	+	0.00787538i
$991$	−19.4556	+	24.3965i	−0.618027	+	0.774982i	−0.988065	−	0.154035i	$-0.950773\pi$
$991$	−19.4556	+	24.3965i	−0.618027	+	0.774982i	0.370038	+	0.929017i	$0.379345\pi$
$992$	1.57520	−	6.90141i	0.0500127	−	0.219120i
$993$	4.73372	−	5.93589i	0.150220	−	0.188370i
$994$	29.4699	−	27.9773i	0.934727	−	0.887387i
$995$	5.28238	+	6.62389i	0.167463	+	0.209992i
$996$	2.11400	−	1.01805i	0.0669846	−	0.0322581i
$997$	−7.75659	+	33.9839i	−0.245654	+	1.07628i	0.690124	+	0.723691i	$0.257556\pi$
$997$	−7.75659	+	33.9839i	−0.245654	+	1.07628i	−0.935778	+	0.352589i	$0.885301\pi$
$998$	19.7842			0.626257
$999$	−40.4332			−1.27925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.b.43.2	yes	12
3.2	odd	2		441.2.u.b.190.1		12
4.3	odd	2		784.2.u.b.337.2		12
7.2	even	3		343.2.g.b.165.1		12
7.3	odd	6		343.2.g.a.226.1		12
7.4	even	3		343.2.g.d.226.1		12
7.5	odd	6		343.2.g.c.165.1		12
7.6	odd	2		343.2.e.b.295.2		12
49.3	odd	42		343.2.g.c.79.1		12
49.5	odd	42		343.2.g.a.214.1		12
49.8	even	7	inner	49.2.e.b.8.2	✓	12
49.20	odd	14		2401.2.a.d.1.5		6
49.29	even	7		2401.2.a.c.1.5		6
49.41	odd	14		343.2.e.b.50.2		12
49.44	even	21		343.2.g.d.214.1		12
49.46	even	21		343.2.g.b.79.1		12
147.8	odd	14		441.2.u.b.253.1		12
196.155	odd	14		784.2.u.b.449.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.8.2	✓	12	49.8	even	7	inner
49.2.e.b.43.2	yes	12	1.1	even	1	trivial
343.2.e.b.50.2		12	49.41	odd	14
343.2.e.b.295.2		12	7.6	odd	2
343.2.g.a.214.1		12	49.5	odd	42
343.2.g.a.226.1		12	7.3	odd	6
343.2.g.b.79.1		12	49.46	even	21
343.2.g.b.165.1		12	7.2	even	3
343.2.g.c.79.1		12	49.3	odd	42
343.2.g.c.165.1		12	7.5	odd	6
343.2.g.d.214.1		12	49.44	even	21
343.2.g.d.226.1		12	7.4	even	3
441.2.u.b.190.1		12	3.2	odd	2
441.2.u.b.253.1		12	147.8	odd	14
784.2.u.b.337.2		12	4.3	odd	2
784.2.u.b.449.2		12	196.155	odd	14
2401.2.a.c.1.5		6	49.29	even	7
2401.2.a.d.1.5		6	49.20	odd	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.914101 - 1.14625i) q^{2} +(-0.880843 - 0.424191i) q^{3} +(-0.0332580 - 0.145713i) q^{4} +(-0.830509 - 0.399952i) q^{5} +(-1.29141 + 0.621909i) q^{6} +(-0.938402 + 2.47374i) q^{7} +(2.44440 + 1.17716i) q^{8} +(-1.27452 - 1.59820i) q^{9} +O(q^{10})\)	\(q+(0.914101 - 1.14625i) q^{2} +(-0.880843 - 0.424191i) q^{3} +(-0.0332580 - 0.145713i) q^{4} +(-0.830509 - 0.399952i) q^{5} +(-1.29141 + 0.621909i) q^{6} +(-0.938402 + 2.47374i) q^{7} +(2.44440 + 1.17716i) q^{8} +(-1.27452 - 1.59820i) q^{9} +(-1.21761 + 0.586371i) q^{10} +(-0.128892 + 0.161626i) q^{11} +(-0.0325151 + 0.142458i) q^{12} +(-1.07906 + 1.35310i) q^{13} +(1.97772 + 3.33689i) q^{14} +(0.561892 + 0.704590i) q^{15} +(3.85307 - 1.85554i) q^{16} +(1.14223 - 5.00446i) q^{17} -2.99698 q^{18} -3.25172 q^{19} +(-0.0306571 + 0.134318i) q^{20} +(1.87592 - 1.78092i) q^{21} +(0.0674425 + 0.295485i) q^{22} +(0.238377 + 1.04440i) q^{23} +(-1.65379 - 2.07379i) q^{24} +(-2.58767 - 3.24483i) q^{25} +(0.564616 + 2.47374i) q^{26} +(1.09736 + 4.80786i) q^{27} +(0.391666 + 0.0544655i) q^{28} +(1.32490 - 5.80477i) q^{29} +1.32126 q^{30} +8.38984 q^{31} +(0.187751 - 0.822592i) q^{32} +(0.182094 - 0.0876920i) q^{33} +(-4.69222 - 5.88386i) q^{34} +(1.76873 - 1.67915i) q^{35} +(-0.190491 + 0.238868i) q^{36} +(-1.82444 + 7.99340i) q^{37} +(-2.97240 + 3.72727i) q^{38} +(1.52446 - 0.734141i) q^{39} +(-1.55929 - 1.95529i) q^{40} +(10.9727 + 5.28418i) q^{41} +(-0.326584 - 3.77821i) q^{42} +(-8.14530 + 3.92257i) q^{43} +(0.0278377 + 0.0134059i) q^{44} +(0.419299 + 1.83707i) q^{45} +(1.41504 + 0.681446i) q^{46} +(-3.34737 + 4.19747i) q^{47} -4.18105 q^{48} +(-5.23880 - 4.64273i) q^{49} -6.08476 q^{50} +(-3.12898 + 3.92361i) q^{51} +(0.233052 + 0.112232i) q^{52} +(0.184264 + 0.807315i) q^{53} +(6.51409 + 3.13702i) q^{54} +(0.171689 - 0.0826810i) q^{55} +(-5.20583 + 4.94217i) q^{56} +(2.86425 + 1.37935i) q^{57} +(-5.44260 - 6.82480i) q^{58} +(-4.44313 + 2.13970i) q^{59} +(0.0839804 - 0.105308i) q^{60} +(1.96619 - 8.61445i) q^{61} +(7.66916 - 9.61682i) q^{62} +(5.14956 - 1.65309i) q^{63} +(4.56154 + 5.71999i) q^{64} +(1.43735 - 0.692190i) q^{65} +(0.0659359 - 0.288884i) q^{66} +5.82557 q^{67} -0.767203 q^{68} +(0.233052 - 1.02107i) q^{69} +(-0.307922 - 3.56231i) q^{70} +(-2.33108 - 10.2131i) q^{71} +(-1.23411 - 5.40697i) q^{72} +(5.82595 + 7.30552i) q^{73} +(7.49468 + 9.39803i) q^{74} +(0.902897 + 3.95585i) q^{75} +(0.108146 + 0.473817i) q^{76} +(-0.278868 - 0.470517i) q^{77} +(0.552003 - 2.41848i) q^{78} +4.55282 q^{79} -3.94213 q^{80} +(-0.291768 + 1.27832i) q^{81} +(16.0871 - 7.74716i) q^{82} +(-10.0118 - 12.5543i) q^{83} +(-0.321892 - 0.214117i) q^{84} +(-2.95018 + 3.69941i) q^{85} +(-2.94939 + 12.9221i) q^{86} +(-3.62936 + 4.55107i) q^{87} +(-0.505325 + 0.243352i) q^{88} +(-4.72383 - 5.92350i) q^{89} +(2.48902 + 1.19865i) q^{90} +(-2.33463 - 3.93908i) q^{91} +(0.144254 - 0.0694692i) q^{92} +(-7.39013 - 3.55890i) q^{93} +(1.75150 + 7.67381i) q^{94} +(2.70058 + 1.30053i) q^{95} +(-0.514316 + 0.644931i) q^{96} -5.84138 q^{97} +(-10.1105 + 1.76104i) q^{98} +0.422587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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