LMFDB - Embedded newform 280.2.bv.a.213.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(117,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))

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

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

chi := DirichletCharacter("280.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bv (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			213.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.213
Dual form			280.2.bv.a.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(0.633975 + 0.366025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(0.633975 + 0.366025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +(-2.09808 + 2.36603i) q^{10} +(2.36603 + 1.36603i) q^{11} +(-0.267949 - 1.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(3.36603 + 1.63397i) q^{14} +(0.366025 + 1.09808i) q^{15} -4.00000 q^{16} +(-4.09808 + 1.09808i) q^{17} +(3.73205 + 1.00000i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(4.46410 - 0.267949i) q^{20} +(1.13397 - 0.767949i) q^{21} +(-1.00000 - 3.73205i) q^{22} +(-1.50000 + 5.59808i) q^{23} +(-0.732051 + 1.26795i) q^{24} +(-4.96410 + 0.598076i) q^{25} +6.00000i q^{26} +(2.09808 - 2.09808i) q^{27} +(-1.73205 - 5.00000i) q^{28} -2.46410 q^{29} +(0.732051 - 1.46410i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.36603 - 0.366025i) q^{33} +(5.19615 + 3.00000i) q^{34} +(2.26795 + 5.46410i) q^{35} +(-2.73205 - 4.73205i) q^{36} +(0.464102 - 1.73205i) q^{37} +(4.73205 + 1.26795i) q^{38} +(1.90192 + 1.09808i) q^{39} +(-4.73205 - 4.19615i) q^{40} +6.46410i q^{41} +(-1.90192 - 0.366025i) q^{42} +(-0.633975 + 0.633975i) q^{43} +(-2.73205 + 4.73205i) q^{44} +(3.36603 + 5.09808i) q^{45} +(7.09808 - 4.09808i) q^{46} +(2.36603 - 8.83013i) q^{47} +(2.00000 - 0.535898i) q^{48} +(5.50000 - 4.33013i) q^{49} +(5.56218 + 4.36603i) q^{50} +(1.90192 - 1.09808i) q^{51} +(6.00000 - 6.00000i) q^{52} +(-3.00000 - 11.1962i) q^{53} -4.19615 q^{54} +(2.73205 - 5.46410i) q^{55} +(-3.26795 + 6.73205i) q^{56} +(1.26795 - 1.26795i) q^{57} +(2.46410 + 2.46410i) q^{58} +(-4.26795 - 2.46410i) q^{59} +(-2.19615 + 0.732051i) q^{60} +(-1.96410 - 3.40192i) q^{61} +(0.0717968 + 0.267949i) q^{62} +(4.73205 - 5.46410i) q^{63} -8.00000i q^{64} +(-6.29423 + 7.09808i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-7.96410 + 2.13397i) q^{67} +(-2.19615 - 8.19615i) q^{68} -3.00000i q^{69} +(3.19615 - 7.73205i) q^{70} +8.53590 q^{71} +(-2.00000 + 7.46410i) q^{72} +(-2.90192 - 10.8301i) q^{73} +(-2.19615 + 1.26795i) q^{74} +(2.40192 - 0.964102i) q^{75} +(-3.46410 - 6.00000i) q^{76} +(-7.09808 - 1.36603i) q^{77} +(-0.803848 - 3.00000i) q^{78} +(-0.803848 + 0.464102i) q^{79} +(0.535898 + 8.92820i) q^{80} +(3.33013 - 5.76795i) q^{81} +(6.46410 - 6.46410i) q^{82} +(7.56218 + 7.56218i) q^{83} +(1.53590 + 2.26795i) q^{84} +(3.00000 + 9.00000i) q^{85} +1.26795 q^{86} +(1.23205 - 0.330127i) q^{87} +(7.46410 - 2.00000i) q^{88} +(-3.40192 - 5.89230i) q^{89} +(1.73205 - 8.46410i) q^{90} +(10.0981 + 4.90192i) q^{91} +(-11.1962 - 3.00000i) q^{92} +(0.0980762 + 0.0262794i) q^{93} +(-11.1962 + 6.46410i) q^{94} +(4.26795 + 6.46410i) q^{95} +(-2.53590 - 1.46410i) q^{96} +(9.73205 + 9.73205i) q^{97} +(-9.83013 - 1.16987i) q^{98} -7.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} + 2 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 10 q^{14} - 2 q^{15} - 16 q^{16} - 6 q^{17} + 8 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 18 q^{31} + 16 q^{32} - 2 q^{33} + 16 q^{35} - 4 q^{36} - 12 q^{37} + 12 q^{38} + 18 q^{39} - 12 q^{40} - 18 q^{42} - 6 q^{43} - 4 q^{44} + 10 q^{45} + 18 q^{46} + 6 q^{47} + 8 q^{48} + 22 q^{49} - 2 q^{50} + 18 q^{51} + 24 q^{52} - 12 q^{53} + 4 q^{54} + 4 q^{55} - 20 q^{56} + 12 q^{57} - 4 q^{58} - 24 q^{59} + 12 q^{60} + 6 q^{61} + 28 q^{62} + 12 q^{63} + 6 q^{65} + 4 q^{66} - 18 q^{67} + 12 q^{68} - 8 q^{70} + 48 q^{71} - 8 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 18 q^{77} - 24 q^{78} - 24 q^{79} + 16 q^{80} - 4 q^{81} + 12 q^{82} + 6 q^{83} + 20 q^{84} + 12 q^{85} + 12 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 30 q^{91} - 24 q^{92} - 10 q^{93} - 24 q^{94} + 24 q^{95} - 24 q^{96} + 32 q^{97} - 22 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 + 2 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 10 * q^14 - 2 * q^15 - 16 * q^16 - 6 * q^17 + 8 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 - 2 * q^27 + 4 * q^29 - 4 * q^30 - 18 * q^31 + 16 * q^32 - 2 * q^33 + 16 * q^35 - 4 * q^36 - 12 * q^37 + 12 * q^38 + 18 * q^39 - 12 * q^40 - 18 * q^42 - 6 * q^43 - 4 * q^44 + 10 * q^45 + 18 * q^46 + 6 * q^47 + 8 * q^48 + 22 * q^49 - 2 * q^50 + 18 * q^51 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 4 * q^55 - 20 * q^56 + 12 * q^57 - 4 * q^58 - 24 * q^59 + 12 * q^60 + 6 * q^61 + 28 * q^62 + 12 * q^63 + 6 * q^65 + 4 * q^66 - 18 * q^67 + 12 * q^68 - 8 * q^70 + 48 * q^71 - 8 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 18 * q^77 - 24 * q^78 - 24 * q^79 + 16 * q^80 - 4 * q^81 + 12 * q^82 + 6 * q^83 + 20 * q^84 + 12 * q^85 + 12 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 30 * q^91 - 24 * q^92 - 10 * q^93 - 24 * q^94 + 24 * q^95 - 24 * q^96 + 32 * q^97 - 22 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	−0.400251	−	0.916406i	$-0.631077\pi$
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	0.111576	+	0.993756i	$0.464410\pi$
$4$			2.00000i			1.00000i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$	0.633975	+	0.366025i	0.258819	+	0.149429i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−2.36603	+	1.36603i	−0.788675	+	0.455342i
$10$	−2.09808	+	2.36603i	−0.663470	+	0.748203i
$11$	2.36603	+	1.36603i	0.713384	+	0.411872i	0.812313	−	0.583222i	$-0.198208\pi$
$11$	2.36603	+	1.36603i	0.713384	+	0.411872i	−0.0989291	+	0.995094i	$0.531542\pi$
$12$	−0.267949	−	1.00000i	−0.0773503	−	0.288675i
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$	3.36603	+	1.63397i	0.899608	+	0.436698i
$15$	0.366025	+	1.09808i	0.0945074	+	0.283522i
$16$	−4.00000			−1.00000
$17$	−4.09808	+	1.09808i	−0.993929	+	0.266323i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	−4.09808	+	1.09808i	−0.993929	+	0.266323i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	3.73205	+	1.00000i	0.879653	+	0.235702i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	4.46410	−	0.267949i	0.998203	−	0.0599153i
$21$	1.13397	−	0.767949i	0.247454	−	0.167580i
$22$	−1.00000	−	3.73205i	−0.213201	−	0.795676i
$23$	−1.50000	+	5.59808i	−0.312772	+	1.16728i	0.613275	+	0.789870i	$0.289852\pi$
$23$	−1.50000	+	5.59808i	−0.312772	+	1.16728i	−0.926046	+	0.377410i	$0.876815\pi$
$24$	−0.732051	+	1.26795i	−0.149429	+	0.258819i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$			6.00000i			1.17670i
$27$	2.09808	−	2.09808i	0.403775	−	0.403775i
$28$	−1.73205	−	5.00000i	−0.327327	−	0.944911i
$29$	−2.46410			−0.457572			−0.228786	−	0.973477i	$-0.573476\pi$
$29$	−2.46410			−0.457572			−0.228786	+	0.973477i	$0.573476\pi$
$30$	0.732051	−	1.46410i	0.133654	−	0.267307i
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	0.484667	−	0.874699i	$-0.338941\pi$
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	−0.515177	+	0.857084i	$0.672274\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	−1.36603	−	0.366025i	−0.237795	−	0.0637168i
$34$	5.19615	+	3.00000i	0.891133	+	0.514496i
$35$	2.26795	+	5.46410i	0.383353	+	0.923602i
$36$	−2.73205	−	4.73205i	−0.455342	−	0.788675i
$37$	0.464102	−	1.73205i	0.0762978	−	0.284747i	−0.917227	−	0.398366i	$-0.869577\pi$
$37$	0.464102	−	1.73205i	0.0762978	−	0.284747i	0.993524	+	0.113618i	$0.0362441\pi$
$38$	4.73205	+	1.26795i	0.767640	+	0.205689i
$39$	1.90192	+	1.09808i	0.304552	+	0.175833i
$40$	−4.73205	−	4.19615i	−0.748203	−	0.663470i
$41$			6.46410i			1.00952i	0.863259	+	0.504762i	$0.168420\pi$
$41$			6.46410i			1.00952i	−0.863259	+	0.504762i	$0.831580\pi$
$42$	−1.90192	−	0.366025i	−0.293473	−	0.0564789i
$43$	−0.633975	+	0.633975i	−0.0966802	+	0.0966802i	−0.753793	−	0.657112i	$-0.771778\pi$
$43$	−0.633975	+	0.633975i	−0.0966802	+	0.0966802i	0.657112	+	0.753793i	$0.271778\pi$
$44$	−2.73205	+	4.73205i	−0.411872	+	0.713384i
$45$	3.36603	+	5.09808i	0.501777	+	0.759976i
$46$	7.09808	−	4.09808i	1.04655	−	0.604228i
$47$	2.36603	−	8.83013i	0.345120	−	1.28801i	−0.547351	−	0.836903i	$-0.684364\pi$
$47$	2.36603	−	8.83013i	0.345120	−	1.28801i	0.892472	−	0.451103i	$-0.148969\pi$
$48$	2.00000	−	0.535898i	0.288675	−	0.0773503i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	5.56218	+	4.36603i	0.786611	+	0.617449i
$51$	1.90192	−	1.09808i	0.266323	−	0.153761i
$52$	6.00000	−	6.00000i	0.832050	−	0.832050i
$53$	−3.00000	−	11.1962i	−0.412082	−	1.53791i	−0.790610	−	0.612320i	$-0.790236\pi$
$53$	−3.00000	−	11.1962i	−0.412082	−	1.53791i	0.378528	−	0.925590i	$-0.376430\pi$
$54$	−4.19615			−0.571024
$55$	2.73205	−	5.46410i	0.368390	−	0.736779i
$56$	−3.26795	+	6.73205i	−0.436698	+	0.899608i
$57$	1.26795	−	1.26795i	0.167944	−	0.167944i
$58$	2.46410	+	2.46410i	0.323552	+	0.323552i
$59$	−4.26795	−	2.46410i	−0.555640	−	0.320799i	0.195754	−	0.980653i	$-0.437285\pi$
$59$	−4.26795	−	2.46410i	−0.555640	−	0.320799i	−0.751394	+	0.659854i	$0.770618\pi$
$60$	−2.19615	+	0.732051i	−0.283522	+	0.0945074i
$61$	−1.96410	−	3.40192i	−0.251477	−	0.435572i	0.712455	−	0.701717i	$-0.247583\pi$
$61$	−1.96410	−	3.40192i	−0.251477	−	0.435572i	−0.963933	+	0.266146i	$0.914250\pi$
$62$	0.0717968	+	0.267949i	0.00911820	+	0.0340296i
$63$	4.73205	−	5.46410i	0.596182	−	0.688412i
$64$		−	8.00000i		−	1.00000i
$65$	−6.29423	+	7.09808i	−0.780703	+	0.880408i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−7.96410	+	2.13397i	−0.972970	+	0.260706i	−0.710081	−	0.704120i	$-0.751342\pi$
$67$	−7.96410	+	2.13397i	−0.972970	+	0.260706i	−0.262889	+	0.964826i	$0.584675\pi$
$68$	−2.19615	−	8.19615i	−0.266323	−	0.993929i
$69$		−	3.00000i		−	0.361158i
$70$	3.19615	−	7.73205i	0.382013	−	0.924157i
$71$	8.53590			1.01302			0.506512	−	0.862233i	$-0.330934\pi$
$71$	8.53590			1.01302			0.506512	+	0.862233i	$0.330934\pi$
$72$	−2.00000	+	7.46410i	−0.235702	+	0.879653i
$73$	−2.90192	−	10.8301i	−0.339644	−	1.26757i	−0.898745	−	0.438471i	$-0.855520\pi$
$73$	−2.90192	−	10.8301i	−0.339644	−	1.26757i	0.559101	−	0.829100i	$-0.311146\pi$
$74$	−2.19615	+	1.26795i	−0.255298	+	0.147396i
$75$	2.40192	−	0.964102i	0.277350	−	0.111325i
$76$	−3.46410	−	6.00000i	−0.397360	−	0.688247i
$77$	−7.09808	−	1.36603i	−0.808901	−	0.155673i
$78$	−0.803848	−	3.00000i	−0.0910178	−	0.339683i
$79$	−0.803848	+	0.464102i	−0.0904399	+	0.0522155i	−0.544538	−	0.838736i	$-0.683295\pi$
$79$	−0.803848	+	0.464102i	−0.0904399	+	0.0522155i	0.454098	+	0.890952i	$0.349962\pi$
$80$	0.535898	+	8.92820i	0.0599153	+	0.998203i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	6.46410	−	6.46410i	0.713841	−	0.713841i
$83$	7.56218	+	7.56218i	0.830057	+	0.830057i	0.987524	−	0.157467i	$-0.0503329\pi$
$83$	7.56218	+	7.56218i	0.830057	+	0.830057i	−0.157467	+	0.987524i	$0.550333\pi$
$84$	1.53590	+	2.26795i	0.167580	+	0.247454i
$85$	3.00000	+	9.00000i	0.325396	+	0.976187i
$86$	1.26795			0.136726
$87$	1.23205	−	0.330127i	0.132090	−	0.0353933i
$88$	7.46410	−	2.00000i	0.795676	−	0.213201i
$89$	−3.40192	−	5.89230i	−0.360603	−	0.624583i	0.627457	−	0.778651i	$-0.284096\pi$
$89$	−3.40192	−	5.89230i	−0.360603	−	0.624583i	−0.988060	+	0.154068i	$0.950762\pi$
$90$	1.73205	−	8.46410i	0.182574	−	0.892195i
$91$	10.0981	+	4.90192i	1.05857	+	0.513861i
$92$	−11.1962	−	3.00000i	−1.16728	−	0.312772i
$93$	0.0980762	+	0.0262794i	0.0101700	+	0.00272505i
$94$	−11.1962	+	6.46410i	−1.15479	+	0.666721i
$95$	4.26795	+	6.46410i	0.437882	+	0.663203i
$96$	−2.53590	−	1.46410i	−0.258819	−	0.149429i
$97$	9.73205	+	9.73205i	0.988140	+	0.988140i	0.999930	−	0.0117904i	$-0.00375310\pi$
$97$	9.73205	+	9.73205i	0.988140	+	0.988140i	−0.0117904	+	0.999930i	$0.503753\pi$
$98$	−9.83013	−	1.16987i	−0.992993	−	0.118175i
$99$	−7.46410			−0.750170
$100$	−1.19615	−	9.92820i	−0.119615	−	0.992820i
$101$	7.06218	−	12.2321i	0.702713	−	1.21713i	−0.264798	−	0.964304i	$-0.585305\pi$
$101$	7.06218	−	12.2321i	0.702713	−	1.21713i	0.967511	−	0.252831i	$-0.0813615\pi$
$102$	−3.00000	−	0.803848i	−0.297044	−	0.0795928i
$103$	−5.33013	−	1.42820i	−0.525193	−	0.140725i	−0.0135254	−	0.999909i	$-0.504305\pi$
$103$	−5.33013	−	1.42820i	−0.525193	−	0.140725i	−0.511668	+	0.859183i	$0.670972\pi$
$104$	−12.0000			−1.17670
$105$	−1.86603	−	2.42820i	−0.182105	−	0.236968i
$106$	−8.19615	+	14.1962i	−0.796081	+	1.37885i
$107$	−3.33013	+	12.4282i	−0.321936	+	1.20148i	0.595421	+	0.803414i	$0.296985\pi$
$107$	−3.33013	+	12.4282i	−0.321936	+	1.20148i	−0.917357	+	0.398066i	$0.869681\pi$
$108$	4.19615	+	4.19615i	0.403775	+	0.403775i
$109$	−3.86603	+	6.69615i	−0.370298	+	0.641375i	−0.989611	−	0.143769i	$-0.954078\pi$
$109$	−3.86603	+	6.69615i	−0.370298	+	0.641375i	0.619313	+	0.785144i	$0.287411\pi$
$110$	−8.19615	+	2.73205i	−0.781472	+	0.260491i
$111$			0.928203i			0.0881012i
$112$	10.0000	−	3.46410i	0.944911	−	0.327327i
$113$	9.46410	+	9.46410i	0.890308	+	0.890308i	0.994552	−	0.104244i	$-0.0332423\pi$
$113$	9.46410	+	9.46410i	0.890308	+	0.890308i	−0.104244	+	0.994552i	$0.533242\pi$
$114$	−2.53590			−0.237509
$115$	12.6962	+	2.59808i	1.18392	+	0.242272i
$116$		−	4.92820i		−	0.457572i
$117$	11.1962	+	3.00000i	1.03508	+	0.277350i
$118$	1.80385	+	6.73205i	0.166058	+	0.619736i
$119$	9.29423	−	6.29423i	0.852001	−	0.576991i
$120$	2.92820	+	1.46410i	0.267307	+	0.133654i
$121$	−1.76795	−	3.06218i	−0.160723	−	0.278380i
$122$	−1.43782	+	5.36603i	−0.130174	+	0.485817i
$123$	−0.866025	−	3.23205i	−0.0780869	−	0.291424i
$124$	0.196152	−	0.339746i	0.0176150	−	0.0305101i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−10.1962	+	0.732051i	−0.908345	+	0.0652163i
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	−0.999721	−	0.0236286i	$-0.992478\pi$
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	0.0236286	+	0.999721i	$0.492478\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	0.232051	−	0.401924i	0.0204309	−	0.0353874i
$130$	13.3923	−	0.803848i	1.17458	−	0.0705021i
$131$	0.267949	+	0.464102i	0.0234108	+	0.0405487i	0.877493	−	0.479589i	$-0.159214\pi$
$131$	0.267949	+	0.464102i	0.0234108	+	0.0405487i	−0.854083	+	0.520137i	$0.825881\pi$
$132$	0.732051	−	2.73205i	0.0637168	−	0.237795i
$133$	6.00000	−	6.92820i	0.520266	−	0.600751i
$134$	10.0981	+	5.83013i	0.872341	+	0.503646i
$135$	−4.96410	−	4.40192i	−0.427242	−	0.378857i
$136$	−6.00000	+	10.3923i	−0.514496	+	0.891133i
$137$	2.19615	+	8.19615i	0.187630	+	0.700245i	0.994052	+	0.108904i	$0.0347343\pi$
$137$	2.19615	+	8.19615i	0.187630	+	0.700245i	−0.806422	+	0.591340i	$0.798599\pi$
$138$	−3.00000	+	3.00000i	−0.255377	+	0.255377i
$139$		−	4.73205i		−	0.401367i	−0.979656	−	0.200684i	$-0.935684\pi$
$139$		−	4.73205i		−	0.401367i	0.979656	−	0.200684i	$-0.0643163\pi$
$140$	−10.9282	+	4.53590i	−0.923602	+	0.383353i
$141$			4.73205i			0.398511i
$142$	−8.53590	−	8.53590i	−0.716317	−	0.716317i
$143$	−3.00000	−	11.1962i	−0.250873	−	0.936269i
$144$	9.46410	−	5.46410i	0.788675	−	0.455342i
$145$	0.330127	+	5.50000i	0.0274156	+	0.456750i
$146$	−7.92820	+	13.7321i	−0.656143	+	1.13647i
$147$	−2.16987	+	2.90192i	−0.178968	+	0.239347i
$148$	3.46410	+	0.928203i	0.284747	+	0.0762978i
$149$	−2.66987	−	4.62436i	−0.218725	−	0.378842i	0.735694	−	0.677314i	$-0.236856\pi$
$149$	−2.66987	−	4.62436i	−0.218725	−	0.378842i	−0.954418	+	0.298472i	$0.903523\pi$
$150$	−3.36603	−	1.43782i	−0.274835	−	0.117398i
$151$	−12.0981	+	20.9545i	−0.984527	+	1.70525i	−0.340510	+	0.940241i	$0.610600\pi$
$151$	−12.0981	+	20.9545i	−0.984527	+	1.70525i	−0.644018	+	0.765011i	$0.722734\pi$
$152$	−2.53590	+	9.46410i	−0.205689	+	0.767640i
$153$	8.19615	−	8.19615i	0.662620	−	0.662620i
$154$	5.73205	+	8.46410i	0.461902	+	0.682057i
$155$	−0.196152	+	0.392305i	−0.0157553	+	0.0315107i
$156$	−2.19615	+	3.80385i	−0.175833	+	0.304552i
$157$	−2.02628	−	7.56218i	−0.161715	−	0.603527i	−0.998436	−	0.0558992i	$-0.982197\pi$
$157$	−2.02628	−	7.56218i	−0.161715	−	0.603527i	0.836722	−	0.547628i	$-0.184469\pi$
$158$	1.26795	+	0.339746i	0.100873	+	0.0270287i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	8.39230	−	9.46410i	0.663470	−	0.748203i
$161$	−1.09808	−	15.2942i	−0.0865405	−	1.20535i
$162$	−9.09808	+	2.43782i	−0.714812	+	0.191533i
$163$	−20.0263	−	5.36603i	−1.56858	−	0.420300i	−0.633212	−	0.773978i	$-0.718264\pi$
$163$	−20.0263	−	5.36603i	−1.56858	−	0.420300i	−0.935367	+	0.353679i	$0.884931\pi$
$164$	−12.9282			−1.00952
$165$	−0.633975	+	3.09808i	−0.0493549	+	0.241185i
$166$		−	15.1244i		−	1.17388i
$167$	−12.2942	−	12.2942i	−0.951356	−	0.951356i	0.0475146	−	0.998871i	$-0.484870\pi$
$167$	−12.2942	−	12.2942i	−0.951356	−	0.951356i	−0.998871	+	0.0475146i	$0.984870\pi$
$168$	0.732051	−	3.80385i	0.0564789	−	0.293473i
$169$			5.00000i			0.384615i
$170$	6.00000	−	12.0000i	0.460179	−	0.920358i
$171$	4.73205	−	8.19615i	0.361869	−	0.626775i
$172$	−1.26795	−	1.26795i	−0.0966802	−	0.0966802i
$173$	−6.46410	+	24.1244i	−0.491457	+	1.83414i	0.0575778	+	0.998341i	$0.481662\pi$
$173$	−6.46410	+	24.1244i	−0.491457	+	1.83414i	−0.549034	+	0.835800i	$0.685004\pi$
$174$	−1.56218	−	0.901924i	−0.118428	−	0.0683747i
$175$	11.8923	−	5.79423i	0.898974	−	0.438003i
$176$	−9.46410	−	5.46410i	−0.713384	−	0.411872i
$177$	2.46410	+	0.660254i	0.185213	+	0.0496277i
$178$	−2.49038	+	9.29423i	−0.186662	+	0.696632i
$179$	12.0263	−	20.8301i	0.898886	−	1.55692i	0.0699665	−	0.997549i	$-0.477711\pi$
$179$	12.0263	−	20.8301i	0.898886	−	1.55692i	0.828920	−	0.559367i	$-0.188956\pi$
$180$	−10.1962	+	6.73205i	−0.759976	+	0.501777i
$181$	−22.5167			−1.67365			−0.836825	−	0.547470i	$-0.815591\pi$
$181$	−22.5167			−1.67365			−0.836825	+	0.547470i	$0.815591\pi$
$182$	−5.19615	−	15.0000i	−0.385164	−	1.11187i
$183$	1.43782	+	1.43782i	0.106287	+	0.106287i
$184$	8.19615	+	14.1962i	0.604228	+	1.04655i
$185$	−3.92820	−	0.803848i	−0.288807	−	0.0591000i
$186$	−0.0717968	−	0.124356i	−0.00526439	−	0.00911820i
$187$	−11.1962	−	3.00000i	−0.818744	−	0.219382i
$188$	17.6603	+	4.73205i	1.28801	+	0.345120i
$189$	−3.42820	+	7.06218i	−0.249365	+	0.513698i
$190$	2.19615	−	10.7321i	0.159326	−	0.778585i
$191$	10.5622	+	18.2942i	0.764252	+	1.32372i	0.940641	+	0.339403i	$0.110225\pi$
$191$	10.5622	+	18.2942i	0.764252	+	1.32372i	−0.176389	+	0.984321i	$0.556442\pi$
$192$	1.07180	+	4.00000i	0.0773503	+	0.288675i
$193$	−2.09808	+	0.562178i	−0.151023	+	0.0404664i	−0.333538	−	0.942737i	$-0.608243\pi$
$193$	−2.09808	+	0.562178i	−0.151023	+	0.0404664i	0.182516	+	0.983203i	$0.441576\pi$
$194$		−	19.4641i		−	1.39744i
$195$	2.19615	−	4.39230i	0.157270	−	0.314539i
$196$	8.66025	+	11.0000i	0.618590	+	0.785714i
$197$	12.4641	+	12.4641i	0.888030	+	0.888030i	0.994334	−	0.106303i	$-0.0339014\pi$
$197$	12.4641	+	12.4641i	0.888030	+	0.888030i	−0.106303	+	0.994334i	$0.533901\pi$
$198$	7.46410	+	7.46410i	0.530451	+	0.530451i
$199$	1.73205	−	3.00000i	0.122782	−	0.212664i	−0.798082	−	0.602549i	$-0.794152\pi$
$199$	1.73205	−	3.00000i	0.122782	−	0.212664i	0.920864	+	0.389885i	$0.127485\pi$
$200$	−8.73205	+	11.1244i	−0.617449	+	0.786611i
$201$	3.69615	−	2.13397i	0.260706	−	0.150519i
$202$	−19.2942	+	5.16987i	−1.35754	+	0.363751i
$203$	6.16025	−	2.13397i	0.432365	−	0.149776i
$204$	2.19615	+	3.80385i	0.153761	+	0.266323i
$205$	14.4282	−	0.866025i	1.00771	−	0.0604858i
$206$	3.90192	+	6.75833i	0.271860	+	0.470875i
$207$	−4.09808	−	15.2942i	−0.284836	−	1.06302i
$208$	12.0000	+	12.0000i	0.832050	+	0.832050i
$209$	−9.46410			−0.654646
$210$	−0.562178	+	4.29423i	−0.0387940	+	0.296330i
$211$		−	27.4641i		−	1.89071i	−0.326048	−	0.945353i	$-0.605717\pi$
$211$		−	27.4641i		−	1.89071i	0.326048	−	0.945353i	$-0.394283\pi$
$212$	22.3923	−	6.00000i	1.53791	−	0.412082i
$213$	−4.26795	+	1.14359i	−0.292435	+	0.0783577i
$214$	15.7583	−	9.09808i	1.07722	−	0.621932i
$215$	1.50000	+	1.33013i	0.102299	+	0.0907139i
$216$		−	8.39230i		−	0.571024i
$217$	0.509619	+	0.0980762i	0.0345952	+	0.00665785i
$218$	10.5622	−	2.83013i	0.715361	−	0.191680i
$219$	2.90192	+	5.02628i	0.196094	+	0.339644i
$220$	10.9282	+	5.46410i	0.736779	+	0.368390i
$221$	15.5885	+	9.00000i	1.04859	+	0.605406i
$222$	0.928203	−	0.928203i	0.0622969	−	0.0622969i
$223$	−5.92820	+	5.92820i	−0.396982	+	0.396982i	−0.877167	−	0.480185i	$-0.840569\pi$
$223$	−5.92820	+	5.92820i	−0.396982	+	0.396982i	0.480185	+	0.877167i	$0.340569\pi$
$224$	−13.4641	−	6.53590i	−0.899608	−	0.436698i
$225$	10.9282	−	8.19615i	0.728547	−	0.546410i
$226$		−	18.9282i		−	1.25909i
$227$	4.16987	+	15.5622i	0.276764	+	1.03290i	0.954650	+	0.297731i	$0.0962298\pi$
$227$	4.16987	+	15.5622i	0.276764	+	1.03290i	−0.677886	+	0.735167i	$0.737104\pi$
$228$	2.53590	+	2.53590i	0.167944	+	0.167944i
$229$	7.39230	−	4.26795i	0.488497	−	0.282034i	−0.235454	−	0.971886i	$-0.575658\pi$
$229$	7.39230	−	4.26795i	0.488497	−	0.282034i	0.723951	+	0.689852i	$0.242324\pi$
$230$	−10.0981	−	15.2942i	−0.665847	−	1.00847i
$231$	3.73205	−	0.267949i	0.245551	−	0.0176298i
$232$	−4.92820	+	4.92820i	−0.323552	+	0.323552i
$233$	1.90192	−	7.09808i	0.124599	−	0.465010i	−0.875226	−	0.483714i	$-0.839287\pi$
$233$	1.90192	−	7.09808i	0.124599	−	0.465010i	0.999825	+	0.0187040i	$0.00595401\pi$
$234$	−8.19615	−	14.1962i	−0.535799	−	0.928032i
$235$	−20.0263	−	4.09808i	−1.30637	−	0.267329i
$236$	4.92820	−	8.53590i	0.320799	−	0.555640i
$237$	0.339746	−	0.339746i	0.0220689	−	0.0220689i
$238$	−15.5885	−	3.00000i	−1.01045	−	0.194461i
$239$		−	1.26795i		−	0.0820168i	−0.999159	−	0.0410084i	$-0.986943\pi$
$239$		−	1.26795i		−	0.0820168i	0.999159	−	0.0410084i	$-0.0130570\pi$
$240$	−1.46410	−	4.39230i	−0.0945074	−	0.283522i
$241$	−0.339746	−	0.196152i	−0.0218850	−	0.0126353i	0.489018	−	0.872274i	$-0.337355\pi$
$241$	−0.339746	−	0.196152i	−0.0218850	−	0.0126353i	−0.510903	+	0.859639i	$0.670689\pi$
$242$	−1.29423	+	4.83013i	−0.0831962	+	0.310492i
$243$	−3.19615	+	11.9282i	−0.205033	+	0.765195i
$244$	6.80385	−	3.92820i	0.435572	−	0.251477i
$245$	−10.4019	−	11.6962i	−0.664555	−	0.747240i
$246$	−2.36603	+	4.09808i	−0.150852	+	0.261284i
$247$	14.1962	+	3.80385i	0.903280	+	0.242033i
$248$	−0.535898	+	0.143594i	−0.0340296	+	0.00911820i
$249$	−4.79423	−	2.76795i	−0.303822	−	0.175412i
$250$	9.00000	−	13.0000i	0.569210	−	0.822192i
$251$	−2.33975			−0.147683			−0.0738417	−	0.997270i	$-0.523526\pi$
$251$	−2.33975			−0.147683			−0.0738417	+	0.997270i	$0.523526\pi$
$252$	10.9282	+	9.46410i	0.688412	+	0.596182i
$253$	−11.1962	+	11.1962i	−0.703896	+	0.703896i
$254$	22.0000			1.38040
$255$	−2.70577	−	4.09808i	−0.169442	−	0.256631i
$256$	16.0000			1.00000
$257$	−1.85641	+	6.92820i	−0.115799	+	0.432169i	−0.999345	−	0.0361749i	$-0.988483\pi$
$257$	−1.85641	+	6.92820i	−0.115799	+	0.432169i	0.883546	+	0.468344i	$0.155149\pi$
$258$	−0.633975	+	0.169873i	−0.0394695	+	0.0105758i
$259$	0.339746	+	4.73205i	0.0211108	+	0.294035i
$260$	−14.1962	−	12.5885i	−0.880408	−	0.780703i
$261$	5.83013	−	3.36603i	0.360876	−	0.208352i
$262$	0.196152	−	0.732051i	0.0121183	−	0.0452262i
$263$	−20.8923	+	5.59808i	−1.28827	+	0.345192i	−0.837005	−	0.547195i	$-0.815695\pi$
$263$	−20.8923	+	5.59808i	−1.28827	+	0.345192i	−0.451270	+	0.892388i	$0.649029\pi$
$264$	−3.46410	+	2.00000i	−0.213201	+	0.123091i
$265$	−24.5885	+	8.19615i	−1.51046	+	0.503486i
$266$	−12.9282	+	0.928203i	−0.792679	+	0.0569118i
$267$	2.49038	+	2.49038i	0.152409	+	0.152409i
$268$	−4.26795	−	15.9282i	−0.260706	−	0.972970i
$269$	−9.06218	−	5.23205i	−0.552531	−	0.319004i	0.197611	−	0.980280i	$-0.436682\pi$
$269$	−9.06218	−	5.23205i	−0.552531	−	0.319004i	−0.750142	+	0.661277i	$0.770015\pi$
$270$	0.562178	+	9.36603i	0.0342131	+	0.569998i
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	−0.781251	−	0.624218i	$-0.785418\pi$
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	0.149963	+	0.988692i	$0.452085\pi$
$272$	16.3923	−	4.39230i	0.993929	−	0.266323i
$273$	−5.70577	−	1.09808i	−0.345329	−	0.0664586i
$274$	6.00000	−	10.3923i	0.362473	−	0.627822i
$275$	−12.5622	−	5.36603i	−0.757528	−	0.323584i
$276$	6.00000			0.361158
$277$	14.0263	−	3.75833i	0.842757	−	0.225816i	0.188486	−	0.982076i	$-0.439642\pi$
$277$	14.0263	−	3.75833i	0.842757	−	0.225816i	0.654272	+	0.756260i	$0.272975\pi$
$278$	−4.73205	+	4.73205i	−0.283810	+	0.283810i
$279$	0.535898			0.0320834
$280$	15.4641	+	6.39230i	0.924157	+	0.382013i
$281$	24.2487			1.44656			0.723278	−	0.690557i	$-0.242634\pi$
$281$	24.2487			1.44656			0.723278	+	0.690557i	$0.242634\pi$
$282$	4.73205	−	4.73205i	0.281790	−	0.281790i
$283$	−5.36603	+	1.43782i	−0.318977	+	0.0854697i	−0.414755	−	0.909933i	$-0.636133\pi$
$283$	−5.36603	+	1.43782i	−0.318977	+	0.0854697i	0.0957780	+	0.995403i	$0.469466\pi$
$284$			17.0718i			1.01302i
$285$	−3.00000	−	2.66025i	−0.177705	−	0.157580i
$286$	−8.19615	+	14.1962i	−0.484649	+	0.839436i
$287$	−5.59808	−	16.1603i	−0.330444	−	0.953910i
$288$	−14.9282	−	4.00000i	−0.879653	−	0.235702i
$289$	0.866025	−	0.500000i	0.0509427	−	0.0294118i
$290$	5.16987	−	5.83013i	0.303585	−	0.342357i
$291$	−6.16987	−	3.56218i	−0.361684	−	0.208819i
$292$	21.6603	−	5.80385i	1.26757	−	0.339644i
$293$	−6.19615	−	6.19615i	−0.361983	−	0.361983i	0.502560	−	0.864543i	$-0.332392\pi$
$293$	−6.19615	−	6.19615i	−0.361983	−	0.361983i	−0.864543	+	0.502560i	$0.832392\pi$
$294$	5.07180	−	0.732051i	0.295793	−	0.0426941i
$295$	−4.92820	+	9.85641i	−0.286931	+	0.573862i
$296$	−2.53590	−	4.39230i	−0.147396	−	0.255298i
$297$	7.83013	−	2.09808i	0.454350	−	0.121743i
$298$	−1.95448	+	7.29423i	−0.113220	+	0.422543i
$299$	21.2942	−	12.2942i	1.23148	−	0.710994i
$300$	1.92820	+	4.80385i	0.111325	+	0.277350i
$301$	1.03590	−	2.13397i	0.0597082	−	0.123000i
$302$	33.0526	−	8.85641i	1.90196	−	0.509629i
$303$	−1.89230	+	7.06218i	−0.108710	+	0.405712i
$304$	12.0000	−	6.92820i	0.688247	−	0.397360i
$305$	−7.33013	+	4.83975i	−0.419722	+	0.277123i
$306$	−16.3923			−0.937086
$307$	21.7583	−	21.7583i	1.24181	−	1.24181i	0.282565	−	0.959248i	$-0.408815\pi$
$307$	21.7583	−	21.7583i	1.24181	−	1.24181i	0.959248	−	0.282565i	$-0.0911854\pi$
$308$	2.73205	−	14.1962i	0.155673	−	0.808901i
$309$	2.85641			0.162495
$310$	0.588457	−	0.196152i	0.0334221	−	0.0111407i
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	0.202870	−	0.979206i	$-0.434973\pi$
$311$	−9.58846	−	5.53590i	−0.543712	−	0.313912i	−0.746582	+	0.665294i	$0.768306\pi$
$312$	6.00000	−	1.60770i	0.339683	−	0.0910178i
$313$	30.3205	+	8.12436i	1.71382	+	0.459216i	0.976355	−	0.216173i	$-0.0693577\pi$
$313$	30.3205	+	8.12436i	1.71382	+	0.459216i	0.737461	+	0.675389i	$0.236024\pi$
$314$	−5.53590	+	9.58846i	−0.312409	+	0.541108i
$315$	−12.8301	−	9.83013i	−0.722896	−	0.553865i
$316$	−0.928203	−	1.60770i	−0.0522155	−	0.0904399i
$317$	2.63397	−	9.83013i	0.147939	−	0.552115i	−0.851668	−	0.524081i	$-0.824409\pi$
$317$	2.63397	−	9.83013i	0.147939	−	0.552115i	0.999607	−	0.0280336i	$-0.00892455\pi$
$318$	2.19615	−	8.19615i	0.123154	−	0.459617i
$319$	−5.83013	−	3.36603i	−0.326424	−	0.188461i
$320$	−17.8564	+	1.07180i	−0.998203	+	0.0599153i
$321$		−	6.66025i		−	0.371739i
$322$	−14.1962	+	16.3923i	−0.791121	+	0.913507i
$323$	10.3923	−	10.3923i	0.578243	−	0.578243i
$324$	11.5359	+	6.66025i	0.640883	+	0.370014i
$325$	16.6865	+	13.0981i	0.925602	+	0.726551i
$326$	14.6603	+	25.3923i	0.811956	+	1.40635i
$327$	1.03590	−	3.86603i	0.0572853	−	0.213792i
$328$	12.9282	+	12.9282i	0.713841	+	0.713841i
$329$	1.73205	+	24.1244i	0.0954911	+	1.33002i
$330$	3.73205	−	2.46410i	0.205443	−	0.135644i
$331$	−9.29423	+	5.36603i	−0.510857	+	0.294943i	−0.733186	−	0.680028i	$-0.761967\pi$
$331$	−9.29423	+	5.36603i	−0.510857	+	0.294943i	0.222329	+	0.974972i	$0.428634\pi$
$332$	−15.1244	+	15.1244i	−0.830057	+	0.830057i
$333$	1.26795	+	4.73205i	0.0694832	+	0.259315i
$334$			24.5885i			1.34542i
$335$	5.83013	+	17.4904i	0.318534	+	0.955602i
$336$	−4.53590	+	3.07180i	−0.247454	+	0.167580i
$337$	−2.33975	+	2.33975i	−0.127454	+	0.127454i	−0.767956	−	0.640502i	$-0.778726\pi$
$337$	−2.33975	+	2.33975i	−0.127454	+	0.127454i	0.640502	+	0.767956i	$0.278726\pi$
$338$	5.00000	−	5.00000i	0.271964	−	0.271964i
$339$	−6.00000	−	3.46410i	−0.325875	−	0.188144i
$340$	−18.0000	+	6.00000i	−0.976187	+	0.325396i
$341$	−0.267949	−	0.464102i	−0.0145103	−	0.0251325i
$342$	−12.9282	+	3.46410i	−0.699077	+	0.187317i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$			2.53590i			0.136726i
$345$	−6.69615	+	0.401924i	−0.360509	+	0.0216388i
$346$	30.5885	−	17.6603i	1.64445	−	0.949421i
$347$	−18.3564	+	4.91858i	−0.985424	+	0.264043i	−0.715327	−	0.698790i	$-0.753722\pi$
$347$	−18.3564	+	4.91858i	−0.985424	+	0.264043i	−0.270096	+	0.962833i	$0.587056\pi$
$348$	0.660254	+	2.46410i	0.0353933	+	0.132090i
$349$			31.9808i			1.71189i	0.517066	+	0.855945i	$0.327024\pi$
$349$			31.9808i			1.71189i	−0.517066	+	0.855945i	$0.672976\pi$
$350$	−17.6865	−	6.09808i	−0.945385	−	0.325956i
$351$	−12.5885			−0.671922
$352$	4.00000	+	14.9282i	0.213201	+	0.795676i
$353$	−4.60770	−	17.1962i	−0.245243	−	0.915259i	−0.973261	−	0.229701i	$-0.926225\pi$
$353$	−4.60770	−	17.1962i	−0.245243	−	0.915259i	0.728018	−	0.685558i	$-0.240442\pi$
$354$	−1.80385	−	3.12436i	−0.0958734	−	0.166058i
$355$	−1.14359	−	19.0526i	−0.0606956	−	1.01120i
$356$	11.7846	−	6.80385i	0.624583	−	0.360603i
$357$	−3.80385	+	4.39230i	−0.201321	+	0.232465i
$358$	−32.8564	+	8.80385i	−1.73652	+	0.465298i
$359$	−1.09808	+	0.633975i	−0.0579542	+	0.0334599i	−0.528697	−	0.848811i	$-0.677319\pi$
$359$	−1.09808	+	0.633975i	−0.0579542	+	0.0334599i	0.470743	+	0.882270i	$0.343986\pi$
$360$	16.9282	+	3.46410i	0.892195	+	0.182574i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	22.5167	+	22.5167i	1.18345	+	1.18345i
$363$	1.29423	+	1.29423i	0.0679294	+	0.0679294i
$364$	−9.80385	+	20.1962i	−0.513861	+	1.05857i
$365$	−23.7846	+	7.92820i	−1.24494	+	0.414981i
$366$		−	2.87564i		−	0.150312i
$367$	−15.1603	+	4.06218i	−0.791359	+	0.212044i	−0.631787	−	0.775142i	$-0.717678\pi$
$367$	−15.1603	+	4.06218i	−0.791359	+	0.212044i	−0.159572	+	0.987186i	$0.551011\pi$
$368$	6.00000	−	22.3923i	0.312772	−	1.16728i
$369$	−8.83013	−	15.2942i	−0.459678	−	0.796186i
$370$	3.12436	+	4.73205i	0.162428	+	0.246008i
$371$	17.1962	+	25.3923i	0.892780	+	1.31830i
$372$	−0.0525589	+	0.196152i	−0.00272505	+	0.0101700i
$373$	−9.46410	−	2.53590i	−0.490033	−	0.131304i	0.00533769	−	0.999986i	$-0.498301\pi$
$373$	−9.46410	−	2.53590i	−0.490033	−	0.131304i	−0.495370	+	0.868682i	$0.664968\pi$
$374$	8.19615	+	14.1962i	0.423813	+	0.734066i
$375$	−2.47372	−	5.23205i	−0.127742	−	0.270182i
$376$	−12.9282	−	22.3923i	−0.666721	−	1.15479i
$377$	7.39230	+	7.39230i	0.380723	+	0.380723i
$378$	10.4904	−	3.63397i	0.539567	−	0.186911i
$379$	−18.2487			−0.937373			−0.468687	−	0.883364i	$-0.655273\pi$
$379$	−18.2487			−0.937373			−0.468687	+	0.883364i	$0.655273\pi$
$380$	−12.9282	+	8.53590i	−0.663203	+	0.437882i
$381$	4.02628	−	6.97372i	0.206273	−	0.357275i
$382$	7.73205	−	28.8564i	0.395606	−	1.47642i
$383$	4.96410	+	1.33013i	0.253654	+	0.0679663i	0.383405	−	0.923580i	$-0.374751\pi$
$383$	4.96410	+	1.33013i	0.253654	+	0.0679663i	−0.129751	+	0.991547i	$0.541418\pi$
$384$	2.92820	−	5.07180i	0.149429	−	0.258819i
$385$	−2.09808	+	16.0263i	−0.106928	+	0.816775i
$386$	2.66025	+	1.53590i	0.135403	+	0.0781752i
$387$	0.633975	−	2.36603i	0.0322267	−	0.120272i
$388$	−19.4641	+	19.4641i	−0.988140	+	0.988140i
$389$	14.4641	−	25.0526i	0.733359	−	1.27022i	−0.222080	−	0.975028i	$-0.571285\pi$
$389$	14.4641	−	25.0526i	0.733359	−	1.27022i	0.955440	−	0.295187i	$-0.0953819\pi$
$390$	−6.58846	+	2.19615i	−0.333620	+	0.111207i
$391$		−	24.5885i		−	1.24349i
$392$	2.33975	−	19.6603i	0.118175	−	0.992993i
$393$	−0.196152	−	0.196152i	−0.00989458	−	0.00989458i
$394$		−	24.9282i		−	1.25586i
$395$	1.14359	+	1.73205i	0.0575404	+	0.0871489i
$396$		−	14.9282i		−	0.750170i
$397$	−2.83013	−	0.758330i	−0.142040	−	0.0380595i	0.187099	−	0.982341i	$-0.440092\pi$
$397$	−2.83013	−	0.758330i	−0.142040	−	0.0380595i	−0.329139	+	0.944282i	$0.606758\pi$
$398$	−4.73205	+	1.26795i	−0.237196	+	0.0635566i
$399$	−2.07180	+	4.26795i	−0.103720	+	0.213665i
$400$	19.8564	−	2.39230i	0.992820	−	0.119615i
$401$	−12.3564	−	21.4019i	−0.617049	−	1.06876i	−0.990021	−	0.140918i	$-0.954994\pi$
$401$	−12.3564	−	21.4019i	−0.617049	−	1.06876i	0.372972	−	0.927843i	$-0.378339\pi$
$402$	−5.83013	−	1.56218i	−0.290780	−	0.0779143i
$403$	0.215390	+	0.803848i	0.0107294	+	0.0400425i
$404$	24.4641	+	14.1244i	1.21713	+	0.702713i
$405$	−13.3205	−	6.66025i	−0.661901	−	0.330951i
$406$	−8.29423	−	4.02628i	−0.411636	−	0.199821i
$407$	3.46410	−	3.46410i	0.171709	−	0.171709i
$408$	1.60770	−	6.00000i	0.0795928	−	0.297044i
$409$	−4.69615	+	8.13397i	−0.232210	+	0.402199i	−0.958458	−	0.285233i	$-0.907929\pi$
$409$	−4.69615	+	8.13397i	−0.232210	+	0.402199i	0.726248	+	0.687432i	$0.241262\pi$
$410$	−15.2942	−	13.5622i	−0.755328	−	0.669788i
$411$	−2.19615	−	3.80385i	−0.108328	−	0.187630i
$412$	2.85641	−	10.6603i	0.140725	−	0.525193i
$413$	12.8038	+	2.46410i	0.630036	+	0.121251i
$414$	−11.1962	+	19.3923i	−0.550261	+	0.953080i
$415$	15.8660	−	17.8923i	0.778833	−	0.878299i
$416$		−	24.0000i		−	1.17670i
$417$	0.633975	+	2.36603i	0.0310459	+	0.115865i
$418$	9.46410	+	9.46410i	0.462904	+	0.462904i
$419$			18.3923i			0.898523i	0.893400	+	0.449261i	$0.148313\pi$
$419$			18.3923i			0.898523i	−0.893400	+	0.449261i	$0.851687\pi$
$420$	4.85641	−	3.73205i	0.236968	−	0.182105i
$421$			5.87564i			0.286361i	0.989697	+	0.143181i	$0.0457330\pi$
$421$			5.87564i			0.286361i	−0.989697	+	0.143181i	$0.954267\pi$
$422$	−27.4641	+	27.4641i	−1.33693	+	1.33693i
$423$	6.46410	+	24.1244i	0.314295	+	1.17297i
$424$	−28.3923	−	16.3923i	−1.37885	−	0.796081i
$425$	19.6865	−	7.90192i	0.954937	−	0.383300i
$426$	5.41154	+	3.12436i	0.262190	+	0.151376i
$427$	7.85641	+	6.80385i	0.380198	+	0.329261i
$428$	−24.8564	−	6.66025i	−1.20148	−	0.321936i
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$	−0.169873	−	2.83013i	−0.00819200	−	0.136481i
$431$	8.36603	−	14.4904i	0.402977	−	0.697977i	−0.591106	−	0.806594i	$-0.701309\pi$
$431$	8.36603	−	14.4904i	0.402977	−	0.697977i	0.994084	+	0.108616i	$0.0346420\pi$
$432$	−8.39230	+	8.39230i	−0.403775	+	0.403775i
$433$	−4.53590	+	4.53590i	−0.217981	+	0.217981i	−0.807647	−	0.589666i	$-0.799259\pi$
$433$	−4.53590	+	4.53590i	−0.217981	+	0.217981i	0.589666	+	0.807647i	$0.299259\pi$
$434$	−0.411543	−	0.607695i	−0.0197547	−	0.0291703i
$435$	−0.901924	−	2.70577i	−0.0432439	−	0.129732i
$436$	−13.3923	−	7.73205i	−0.641375	−	0.370298i
$437$	−5.19615	−	19.3923i	−0.248566	−	0.927660i
$438$	2.12436	−	7.92820i	0.101506	−	0.378824i
$439$	14.6603	+	25.3923i	0.699696	+	1.21191i	0.968572	+	0.248734i	$0.0800144\pi$
$439$	14.6603	+	25.3923i	0.699696	+	1.21191i	−0.268876	+	0.963175i	$0.586652\pi$
$440$	−5.46410	−	16.3923i	−0.260491	−	0.781472i
$441$	−7.09808	+	17.7583i	−0.338004	+	0.845635i
$442$	−6.58846	−	24.5885i	−0.313381	−	1.16955i
$443$	21.0622	+	5.64359i	1.00069	+	0.268135i	0.721736	−	0.692168i	$-0.243344\pi$
$443$	21.0622	+	5.64359i	1.00069	+	0.268135i	0.278958	+	0.960303i	$0.410011\pi$
$444$	−1.85641			−0.0881012
$445$	−12.6962	+	8.38269i	−0.601855	+	0.397377i
$446$	11.8564			0.561417
$447$	1.95448	+	1.95448i	0.0924439	+	0.0924439i
$448$	6.92820	+	20.0000i	0.327327	+	0.944911i
$449$		−	12.8038i		−	0.604251i	−0.953268	−	0.302125i	$-0.902304\pi$
$449$		−	12.8038i		−	0.604251i	0.953268	−	0.302125i	$-0.0976962\pi$
$450$	−19.1244	−	2.73205i	−0.901531	−	0.128790i
$451$	−8.83013	+	15.2942i	−0.415794	+	0.720177i
$452$	−18.9282	+	18.9282i	−0.890308	+	0.890308i
$453$	3.24167	−	12.0981i	0.152307	−	0.568417i
$454$	11.3923	−	19.7321i	0.534667	−	0.926071i
$455$	9.58846	−	23.1962i	0.449514	−	1.08745i
$456$		−	5.07180i		−	0.237509i
$457$	−0.267949	−	0.0717968i	−0.0125341	−	0.00335851i	0.252547	−	0.967585i	$-0.418732\pi$
$457$	−0.267949	−	0.0717968i	−0.0125341	−	0.00335851i	−0.265081	+	0.964226i	$0.585399\pi$
$458$	−11.6603	−	3.12436i	−0.544848	−	0.145992i
$459$	−6.29423	+	10.9019i	−0.293789	+	0.508858i
$460$	−5.19615	+	25.3923i	−0.242272	+	1.18392i
$461$	−39.8564			−1.85630			−0.928149	−	0.372209i	$-0.878600\pi$
$461$	−39.8564			−1.85630			−0.928149	+	0.372209i	$0.878600\pi$
$462$	−4.00000	−	3.46410i	−0.186097	−	0.161165i
$463$	−7.83013	−	7.83013i	−0.363897	−	0.363897i	0.501349	−	0.865245i	$-0.332837\pi$
$463$	−7.83013	−	7.83013i	−0.363897	−	0.363897i	−0.865245	+	0.501349i	$0.832837\pi$
$464$	9.85641			0.457572
$465$	0.0455173	−	0.222432i	0.00211082	−	0.0103150i
$466$	−9.00000	+	5.19615i	−0.416917	+	0.240707i
$467$	−10.3301	−	2.76795i	−0.478021	−	0.128085i	0.0117598	−	0.999931i	$-0.496257\pi$
$467$	−10.3301	−	2.76795i	−0.478021	−	0.128085i	−0.489781	+	0.871845i	$0.662923\pi$
$468$	−6.00000	+	22.3923i	−0.277350	+	1.03508i
$469$	18.0622	−	12.2321i	0.834034	−	0.564824i
$470$	15.9282	+	24.1244i	0.734713	+	1.11277i
$471$	2.02628	+	3.50962i	0.0933660	+	0.161715i
$472$	−13.4641	+	3.60770i	−0.619736	+	0.166058i
$473$	−2.36603	+	0.633975i	−0.108790	+	0.0291502i
$474$	−0.679492			−0.0312101
$475$	13.8564	−	10.3923i	0.635776	−	0.476832i
$476$	12.5885	+	18.5885i	0.576991	+	0.852001i
$477$	22.3923	+	22.3923i	1.02527	+	1.02527i
$478$	−1.26795	+	1.26795i	−0.0579946	+	0.0579946i
$479$	7.09808	−	12.2942i	0.324319	−	0.561738i	−0.657055	−	0.753843i	$-0.728198\pi$
$479$	7.09808	−	12.2942i	0.324319	−	0.561738i	0.981374	+	0.192105i	$0.0615314\pi$
$480$	−2.92820	+	5.85641i	−0.133654	+	0.267307i
$481$	−6.58846	+	3.80385i	−0.300408	+	0.173441i
$482$	0.143594	+	0.535898i	0.00654051	+	0.0244095i
$483$	2.59808	+	7.50000i	0.118217	+	0.341262i
$484$	6.12436	−	3.53590i	0.278380	−	0.160723i
$485$	20.4186	−	23.0263i	0.927160	−	1.04557i
$486$	15.1244	−	8.73205i	0.686055	−	0.396094i
$487$	0.0262794	+	0.0980762i	0.00119084	+	0.00444426i	0.966519	−	0.256596i	$-0.0826011\pi$
$487$	0.0262794	+	0.0980762i	0.00119084	+	0.00444426i	−0.965328	+	0.261040i	$0.915934\pi$
$488$	−10.7321	−	2.87564i	−0.485817	−	0.130174i
$489$	10.7321			0.485320
$490$	−1.29423	+	22.0981i	−0.0584673	+	0.998289i
$491$			1.80385i			0.0814065i	0.999171	+	0.0407033i	$0.0129598\pi$
$491$			1.80385i			0.0814065i	−0.999171	+	0.0407033i	$0.987040\pi$
$492$	6.46410	−	1.73205i	0.291424	−	0.0780869i
$493$	10.0981	−	2.70577i	0.454794	−	0.121862i
$494$	−10.3923	−	18.0000i	−0.467572	−	0.809858i
$495$	1.00000	+	16.6603i	0.0449467	+	0.748823i
$496$	0.679492	+	0.392305i	0.0305101	+	0.0176150i
$497$	−21.3397	+	7.39230i	−0.957218	+	0.331590i
$498$	2.02628	+	7.56218i	0.0907998	+	0.338869i
$499$	15.7583	+	27.2942i	0.705440	+	1.22186i	0.966533	+	0.256544i	$0.0825838\pi$
$499$	15.7583	+	27.2942i	0.705440	+	1.22186i	−0.261093	+	0.965314i	$0.584083\pi$
$500$	−22.0000	+	4.00000i	−0.983870	+	0.178885i
$501$	7.79423	+	4.50000i	0.348220	+	0.201045i
$502$	2.33975	+	2.33975i	0.104428	+	0.104428i
$503$	13.6865	−	13.6865i	0.610252	−	0.610252i	−0.332759	−	0.943012i	$-0.607980\pi$
$503$	13.6865	−	13.6865i	0.610252	−	0.610252i	0.943012	+	0.332759i	$0.107980\pi$
$504$	−1.46410	−	20.3923i	−0.0652163	−	0.908345i
$505$	−28.2487	−	14.1244i	−1.25705	−	0.628526i
$506$	22.3923			0.995459
$507$	−0.669873	−	2.50000i	−0.0297501	−	0.111029i
$508$	−22.0000	−	22.0000i	−0.976092	−	0.976092i
$509$	−23.4282	+	13.5263i	−1.03844	+	0.599542i	−0.919390	−	0.393347i	$-0.871317\pi$
$509$	−23.4282	+	13.5263i	−1.03844	+	0.599542i	−0.119047	+	0.992889i	$0.537984\pi$
$510$	−1.39230	+	6.80385i	−0.0616523	+	0.301279i
$511$	16.6340	+	24.5622i	0.735844	+	1.08657i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−2.66025	+	9.92820i	−0.117453	+	0.438341i
$514$	8.78461	−	5.07180i	0.387473	−	0.223707i
$515$	−2.47372	+	12.0885i	−0.109005	+	0.532681i
$516$	0.803848	+	0.464102i	0.0353874	+	0.0204309i
$517$	17.6603	−	17.6603i	0.776697	−	0.776697i
$518$	4.39230	−	5.07180i	0.192987	−	0.222842i
$519$		−	12.9282i		−	0.567485i
$520$	1.60770	+	26.7846i	0.0705021	+	1.17458i
$521$	−13.3923	−	7.73205i	−0.586728	−	0.338747i	0.177075	−	0.984197i	$-0.443337\pi$
$521$	−13.3923	−	7.73205i	−0.586728	−	0.338747i	−0.763802	+	0.645450i	$0.776670\pi$
$522$	−9.19615	−	2.46410i	−0.402505	−	0.107851i
$523$	−8.70577	+	32.4904i	−0.380677	+	1.42071i	0.464193	+	0.885734i	$0.346344\pi$
$523$	−8.70577	+	32.4904i	−0.380677	+	1.42071i	−0.844870	+	0.534971i	$0.820322\pi$
$524$	−0.928203	+	0.535898i	−0.0405487	+	0.0234108i
$525$	−5.16987	+	4.49038i	−0.225632	+	0.195976i
$526$	26.4904	+	15.2942i	1.15504	+	0.666860i
$527$	0.803848	+	0.215390i	0.0350162	+	0.00938255i
$528$	5.46410	+	1.46410i	0.237795	+	0.0637168i
$529$	−9.16987	−	5.29423i	−0.398690	−	0.230184i
$530$	32.7846	+	16.3923i	1.42407	+	0.712036i
$531$	13.4641			0.584292
$532$	13.8564	+	12.0000i	0.600751	+	0.520266i
$533$	19.3923	−	19.3923i	0.839974	−	0.839974i
$534$		−	4.98076i		−	0.215539i
$535$	28.1865	+	5.76795i	1.21861	+	0.249370i
$536$	−11.6603	+	20.1962i	−0.503646	+	0.872341i
$537$	−3.22243	+	12.0263i	−0.139058	+	0.518972i
$538$	3.83013	+	14.2942i	0.165129	+	0.616268i
$539$	18.9282	−	2.73205i	0.815295	−	0.117678i
$540$	8.80385	−	9.92820i	0.378857	−	0.427242i
$541$	−13.7942	+	7.96410i	−0.593060	+	0.342403i	−0.766307	−	0.642475i	$-0.777908\pi$
$541$	−13.7942	+	7.96410i	−0.593060	+	0.342403i	0.173246	+	0.984879i	$0.444574\pi$
$542$	16.3923	+	4.39230i	0.704110	+	0.188666i
$543$	11.2583	−	3.01666i	0.483141	−	0.129457i
$544$	−20.7846	−	12.0000i	−0.891133	−	0.514496i
$545$	15.4641	+	7.73205i	0.662409	+	0.331205i
$546$	4.60770	+	6.80385i	0.197191	+	0.291178i
$547$	−11.4904	−	11.4904i	−0.491293	−	0.491293i	0.417420	−	0.908714i	$-0.362934\pi$
$547$	−11.4904	−	11.4904i	−0.491293	−	0.491293i	−0.908714	+	0.417420i	$0.862934\pi$
$548$	−16.3923	+	4.39230i	−0.700245	+	0.187630i
$549$	9.29423	+	5.36603i	0.396668	+	0.229016i
$550$	7.19615	+	17.9282i	0.306845	+	0.764461i
$551$	7.39230	−	4.26795i	0.314923	−	0.181821i
$552$	−6.00000	−	6.00000i	−0.255377	−	0.255377i
$553$	1.60770	−	1.85641i	0.0683662	−	0.0789424i
$554$	−17.7846	−	10.2679i	−0.755596	−	0.436243i
$555$	2.07180	−	0.124356i	0.0879429	−	0.00527860i
$556$	9.46410			0.401367
$557$	−30.7583	+	8.24167i	−1.30327	+	0.349211i	−0.842687	−	0.538404i	$-0.819027\pi$
$557$	−30.7583	+	8.24167i	−1.30327	+	0.349211i	−0.460586	+	0.887615i	$0.652361\pi$
$558$	−0.535898	−	0.535898i	−0.0226864	−	0.0226864i
$559$	3.80385			0.160886
$560$	−9.07180	−	21.8564i	−0.383353	−	0.923602i
$561$	6.00000			0.253320
$562$	−24.2487	−	24.2487i	−1.02287	−	1.02287i
$563$	−5.06218	+	1.35641i	−0.213345	+	0.0571657i	−0.363909	−	0.931435i	$-0.618558\pi$
$563$	−5.06218	+	1.35641i	−0.213345	+	0.0571657i	0.150563	+	0.988600i	$0.451891\pi$
$564$	−9.46410			−0.398511
$565$	19.8564	−	22.3923i	0.835365	−	0.942051i
$566$	6.80385	+	3.92820i	0.285987	+	0.165115i
$567$	−3.33013	+	17.3038i	−0.139852	+	0.726693i
$568$	17.0718	−	17.0718i	0.716317	−	0.716317i
$569$	29.1962	−	16.8564i	1.22397	−	0.706657i	0.258205	−	0.966090i	$-0.416869\pi$
$569$	29.1962	−	16.8564i	1.22397	−	0.706657i	0.965761	+	0.259433i	$0.0835356\pi$
$570$	0.339746	+	5.66025i	0.0142304	+	0.237082i
$571$	26.7846	+	15.4641i	1.12090	+	0.647153i	0.941631	−	0.336647i	$-0.109293\pi$
$571$	26.7846	+	15.4641i	1.12090	+	0.647153i	0.179270	+	0.983800i	$0.442626\pi$
$572$	22.3923	−	6.00000i	0.936269	−	0.250873i
$573$	−7.73205	−	7.73205i	−0.323011	−	0.323011i
$574$	−10.5622	+	21.7583i	−0.440857	+	0.908175i
$575$	4.09808	−	28.6865i	0.170902	−	1.19631i
$576$	10.9282	+	18.9282i	0.455342	+	0.788675i
$577$	35.4186	−	9.49038i	1.47449	−	0.395090i	0.570025	−	0.821627i	$-0.306933\pi$
$577$	35.4186	−	9.49038i	1.47449	−	0.395090i	0.904470	+	0.426538i	$0.140267\pi$
$578$	−1.36603	−	0.366025i	−0.0568192	−	0.0152246i
$579$	0.973721	−	0.562178i	0.0404664	−	0.0233633i
$580$	−11.0000	+	0.660254i	−0.456750	+	0.0274156i
$581$	−25.4545	−	12.3564i	−1.05603	−	0.512630i
$582$	2.60770	+	9.73205i	0.108092	+	0.403406i
$583$	8.19615	−	30.5885i	0.339450	−	1.26684i
$584$	−27.4641	−	15.8564i	−1.13647	−	0.656143i
$585$	5.19615	−	25.3923i	0.214834	−	1.04984i
$586$			12.3923i			0.511921i
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	−0.496543	−	0.868012i	$-0.665397\pi$
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	0.868012	+	0.496543i	$0.165397\pi$
$588$	−5.80385	−	4.33975i	−0.239347	−	0.178968i
$589$	0.679492			0.0279980
$590$	14.7846	−	4.92820i	0.608673	−	0.202891i
$591$	−7.90192	−	4.56218i	−0.325042	−	0.187663i
$592$	−1.85641	+	6.92820i	−0.0762978	+	0.284747i
$593$	−14.1962	−	3.80385i	−0.582966	−	0.156205i	−0.0447296	−	0.998999i	$-0.514243\pi$
$593$	−14.1962	−	3.80385i	−0.582966	−	0.156205i	−0.538237	+	0.842794i	$0.680909\pi$
$594$	−9.92820	−	5.73205i	−0.407359	−	0.235189i
$595$	−15.2942	−	19.9019i	−0.627002	−	0.815899i
$596$	9.24871	−	5.33975i	0.378842	−	0.218725i
$597$	−0.464102	+	1.73205i	−0.0189944	+	0.0708881i
$598$	−33.5885	−	9.00000i	−1.37353	−	0.368037i
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	0.863354	−	0.504598i	$-0.168359\pi$
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	−0.00531761	+	0.999986i	$0.501693\pi$
$600$	2.87564	−	6.73205i	0.117398	−	0.274835i
$601$			7.60770i			0.310324i	0.987889	+	0.155162i	$0.0495900\pi$
$601$			7.60770i			0.310324i	−0.987889	+	0.155162i	$0.950410\pi$
$602$	−3.16987	+	1.09808i	−0.129194	+	0.0447542i
$603$	15.9282	−	15.9282i	0.648647	−	0.648647i
$604$	−41.9090	−	24.1962i	−1.70525	−	0.984527i
$605$	−6.59808	+	4.35641i	−0.268250	+	0.177113i
$606$	8.95448	−	5.16987i	0.363751	−	0.210012i
$607$	2.99038	−	11.1603i	0.121376	−	0.452981i	−0.878309	−	0.478094i	$-0.841328\pi$
$607$	2.99038	−	11.1603i	0.121376	−	0.452981i	0.999685	+	0.0251130i	$0.00799457\pi$
$608$	−18.9282	−	5.07180i	−0.767640	−	0.205689i
$609$	−2.79423	+	1.89230i	−0.113228	+	0.0766801i
$610$	12.1699	+	2.49038i	0.492744	+	0.100833i
$611$	−33.5885	+	19.3923i	−1.35884	+	0.784529i
$612$	16.3923	+	16.3923i	0.662620	+	0.662620i
$613$	−3.63397	−	13.5622i	−0.146775	−	0.547771i	−0.999670	−	0.0256889i	$-0.991822\pi$
$613$	−3.63397	−	13.5622i	−0.146775	−	0.547771i	0.852895	−	0.522082i	$-0.174845\pi$
$614$	−43.5167			−1.75619
$615$	−7.09808	+	2.36603i	−0.286222	+	0.0954074i
$616$	−16.9282	+	11.4641i	−0.682057	+	0.461902i
$617$	12.9282	−	12.9282i	0.520470	−	0.520470i	−0.397243	−	0.917713i	$-0.630033\pi$
$617$	12.9282	−	12.9282i	0.520470	−	0.520470i	0.917713	+	0.397243i	$0.130033\pi$
$618$	−2.85641	−	2.85641i	−0.114902	−	0.114902i
$619$	0.294229	+	0.169873i	0.0118260	+	0.00682777i	0.505901	−	0.862591i	$-0.331160\pi$
$619$	0.294229	+	0.169873i	0.0118260	+	0.00682777i	−0.494075	+	0.869419i	$0.664493\pi$
$620$	−0.784610	−	0.392305i	−0.0315107	−	0.0157553i
$621$	8.59808	+	14.8923i	0.345029	+	0.597608i
$622$	4.05256	+	15.1244i	0.162493	+	0.606431i
$623$	13.6077	+	11.7846i	0.545181	+	0.472140i
$624$	−7.60770	−	4.39230i	−0.304552	−	0.175833i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−22.1962	−	38.4449i	−0.887137	−	1.53657i
$627$	4.73205	−	1.26795i	0.188980	−	0.0506370i
$628$	15.1244	−	4.05256i	0.603527	−	0.161715i
$629$			7.60770i			0.303339i
$630$	3.00000	+	22.6603i	0.119523	+	0.902806i
$631$	−10.7321			−0.427236			−0.213618	−	0.976917i	$-0.568525\pi$
$631$	−10.7321			−0.427236			−0.213618	+	0.976917i	$0.568525\pi$
$632$	−0.679492	+	2.53590i	−0.0270287	+	0.100873i
$633$	3.67949	+	13.7321i	0.146247	+	0.545800i
$634$	−12.4641	+	7.19615i	−0.495013	+	0.285796i
$635$	26.0263	+	23.0788i	1.03282	+	0.915856i
$636$	−10.3923	+	6.00000i	−0.412082	+	0.237915i
$637$	−29.4904	−	3.50962i	−1.16845	−	0.139056i
$638$	2.46410	+	9.19615i	0.0975547	+	0.364079i
$639$	−20.1962	+	11.6603i	−0.798947	+	0.461273i
$640$	18.9282	+	16.7846i	0.748203	+	0.663470i
$641$	7.66987	−	13.2846i	0.302942	−	0.524711i	−0.673859	−	0.738860i	$-0.735365\pi$
$641$	7.66987	−	13.2846i	0.302942	−	0.524711i	0.976801	+	0.214149i	$0.0686979\pi$
$642$	−6.66025	+	6.66025i	−0.262859	+	0.262859i
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	0.861938	−	0.507013i	$-0.169250\pi$
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	−0.507013	+	0.861938i	$0.669250\pi$
$644$	30.5885	−	2.19615i	1.20535	−	0.0865405i
$645$	−0.928203	−	0.464102i	−0.0365480	−	0.0182740i
$646$	−20.7846			−0.817760
$647$	13.9641	−	3.74167i	0.548985	−	0.147100i	0.0263442	−	0.999653i	$-0.491613\pi$
$647$	13.9641	−	3.74167i	0.548985	−	0.147100i	0.522641	+	0.852553i	$0.324947\pi$
$648$	−4.87564	−	18.1962i	−0.191533	−	0.714812i
$649$	−6.73205	−	11.6603i	−0.264256	−	0.457705i
$650$	−3.58846	−	29.7846i	−0.140751	−	1.16825i
$651$	−0.267949	+	0.0192379i	−0.0105018	+	0.000753992i
$652$	10.7321	−	40.0526i	0.420300	−	1.56858i
$653$	31.4186	+	8.41858i	1.22950	+	0.329445i	0.814386	−	0.580323i	$-0.197074\pi$
$653$	31.4186	+	8.41858i	1.22950	+	0.329445i	0.415118	+	0.909768i	$0.363740\pi$
$654$	−4.90192	+	2.83013i	−0.191680	+	0.110667i
$655$	1.00000	−	0.660254i	0.0390732	−	0.0257983i
$656$		−	25.8564i		−	1.00952i
$657$	21.6603	+	21.6603i	0.845047	+	0.845047i
$658$	22.3923	−	25.8564i	0.872943	−	1.00799i
$659$	−4.67949			−0.182287			−0.0911436	−	0.995838i	$-0.529052\pi$
$659$	−4.67949			−0.182287			−0.0911436	+	0.995838i	$0.529052\pi$
$660$	−6.19615	−	1.26795i	−0.241185	−	0.0493549i
$661$	−13.0359	+	22.5788i	−0.507038	+	0.878215i	0.492929	+	0.870069i	$0.335926\pi$
$661$	−13.0359	+	22.5788i	−0.507038	+	0.878215i	−0.999967	+	0.00814557i	$0.997407\pi$
$662$	14.6603	+	3.92820i	0.569787	+	0.152674i
$663$	−9.00000	−	2.41154i	−0.349531	−	0.0936566i
$664$	30.2487			1.17388
$665$	−16.2679	−	12.4641i	−0.630844	−	0.483337i
$666$	3.46410	−	6.00000i	0.134231	−	0.232495i
$667$	3.69615	−	13.7942i	0.143116	−	0.534115i
$668$	24.5885	−	24.5885i	0.951356	−	0.951356i
$669$	2.16987	−	3.75833i	0.0838921	−	0.145305i
$670$	11.6603	−	23.3205i	0.450475	−	0.900950i
$671$		−	10.7321i		−	0.414306i
$672$	7.60770	+	1.46410i	0.293473	+	0.0564789i
$673$	0.196152	+	0.196152i	0.00756112	+	0.00756112i	0.710877	−	0.703316i	$-0.248298\pi$
$673$	0.196152	+	0.196152i	0.00756112	+	0.00756112i	−0.703316	+	0.710877i	$0.748298\pi$
$674$	4.67949			0.180247
$675$	−9.16025	+	11.6699i	−0.352578	+	0.449174i
$676$	−10.0000			−0.384615
$677$	−28.2224	−	7.56218i	−1.08468	−	0.290638i	−0.328166	−	0.944620i	$-0.606431\pi$
$677$	−28.2224	−	7.56218i	−1.08468	−	0.290638i	−0.756510	+	0.653982i	$0.773097\pi$
$678$	2.53590	+	9.46410i	0.0973906	+	0.363467i
$679$	−32.7583	−	15.9019i	−1.25715	−	0.610260i
$680$	24.0000	+	12.0000i	0.920358	+	0.460179i
$681$	−4.16987	−	7.22243i	−0.159790	−	0.276764i
$682$	−0.196152	+	0.732051i	−0.00751106	+	0.0280317i
$683$	1.64359	+	6.13397i	0.0628904	+	0.234710i	0.990215	−	0.139547i	$-0.0445645\pi$
$683$	1.64359	+	6.13397i	0.0628904	+	0.234710i	−0.927325	+	0.374257i	$0.877898\pi$
$684$	16.3923	+	9.46410i	0.626775	+	0.361869i
$685$	18.0000	−	6.00000i	0.687745	−	0.229248i
$686$	25.5885	−	5.58846i	0.976972	−	0.213368i
$687$	−3.12436	+	3.12436i	−0.119202	+	0.119202i
$688$	2.53590	−	2.53590i	0.0966802	−	0.0966802i
$689$	−24.5885	+	42.5885i	−0.936746	+	1.62249i
$690$	7.09808	+	6.29423i	0.270219	+	0.239617i
$691$	−0.758330	−	1.31347i	−0.0288482	−	0.0499666i	0.851241	−	0.524775i	$-0.175851\pi$
$691$	−0.758330	−	1.31347i	−0.0288482	−	0.0499666i	−0.880089	+	0.474809i	$0.842517\pi$
$692$	−48.2487	−	12.9282i	−1.83414	−	0.491457i
$693$	18.6603	−	6.46410i	0.708844	−	0.245551i
$694$	23.2750	+	13.4378i	0.883507	+	0.510093i
$695$	−10.5622	+	0.633975i	−0.400646	+	0.0240480i
$696$	1.80385	−	3.12436i	0.0683747	−	0.118428i
$697$	−7.09808	−	26.4904i	−0.268859	−	1.00339i
$698$	31.9808	−	31.9808i	1.21049	−	1.21049i
$699$			3.80385i			0.143875i
$700$	11.5885	+	23.7846i	0.438003	+	0.898974i
$701$		−	17.9808i		−	0.679124i	−0.940584	−	0.339562i	$-0.889721\pi$
$701$		−	17.9808i		−	0.679124i	0.940584	−	0.339562i	$-0.110279\pi$
$702$	12.5885	+	12.5885i	0.475121	+	0.475121i
$703$	1.60770	+	6.00000i	0.0606354	+	0.226294i
$704$	10.9282	−	18.9282i	0.411872	−	0.713384i
$705$	10.5622	−	0.633975i	0.397795	−	0.0238769i
$706$	−12.5885	+	21.8038i	−0.473773	+	0.820599i
$707$	−7.06218	+	36.6962i	−0.265601	+	1.38010i
$708$	−1.32051	+	4.92820i	−0.0496277	+	0.185213i
$709$	−1.03590	−	1.79423i	−0.0389040	−	0.0673837i	0.845918	−	0.533313i	$-0.179053\pi$
$709$	−1.03590	−	1.79423i	−0.0389040	−	0.0673837i	−0.884822	+	0.465930i	$0.845720\pi$
$710$	−17.9090	+	20.1962i	−0.672111	+	0.757948i
$711$	1.26795	−	2.19615i	0.0475518	−	0.0823622i
$712$	−18.5885	−	4.98076i	−0.696632	−	0.186662i
$713$	0.803848	−	0.803848i	0.0301043	−	0.0301043i
$714$	8.19615	−	0.588457i	0.306733	−	0.0220225i
$715$	−24.5885	+	8.19615i	−0.919556	+	0.306519i
$716$	41.6603	+	24.0526i	1.55692	+	0.898886i
$717$	0.169873	+	0.633975i	0.00634402	+	0.0236762i
$718$	1.73205	+	0.464102i	0.0646396	+	0.0173201i
$719$	−3.63397	−	6.29423i	−0.135524	−	0.234735i	0.790273	−	0.612755i	$-0.209939\pi$
$719$	−3.63397	−	6.29423i	−0.135524	−	0.234735i	−0.925798	+	0.378019i	$0.876605\pi$
$720$	−13.4641	−	20.3923i	−0.501777	−	0.759976i
$721$	14.5622	−	1.04552i	0.542324	−	0.0389371i
$722$	9.56218	−	2.56218i	0.355867	−	0.0953544i
$723$	0.196152	+	0.0525589i	0.00729499	+	0.00195469i
$724$		−	45.0333i		−	1.67365i
$725$	12.2321	−	1.47372i	0.454287	−	0.0547326i
$726$		−	2.58846i		−	0.0960667i
$727$	−1.70577	−	1.70577i	−0.0632636	−	0.0632636i	0.674767	−	0.738031i	$-0.264244\pi$
$727$	−1.70577	−	1.70577i	−0.0632636	−	0.0632636i	−0.738031	+	0.674767i	$0.764244\pi$
$728$	30.0000	−	10.3923i	1.11187	−	0.385164i
$729$			13.5885i			0.503276i
$730$	31.7128	+	15.8564i	1.17374	+	0.586872i
$731$	1.90192	−	3.29423i	0.0703452	−	0.121841i
$732$	−2.87564	+	2.87564i	−0.106287	+	0.106287i
$733$	5.70577	−	21.2942i	0.210747	−	0.786520i	−0.776873	−	0.629657i	$-0.783195\pi$
$733$	5.70577	−	21.2942i	0.210747	−	0.786520i	0.987620	−	0.156863i	$-0.0501381\pi$
$734$	19.2224	+	11.0981i	0.709513	+	0.409637i
$735$	6.76795	+	4.45448i	0.249640	+	0.164306i
$736$	−28.3923	+	16.3923i	−1.04655	+	0.604228i
$737$	−21.7583	−	5.83013i	−0.801478	−	0.214755i
$738$	−6.46410	+	24.1244i	−0.237947	+	0.888030i
$739$	2.83013	−	4.90192i	0.104108	−	0.180320i	−0.809265	−	0.587443i	$-0.800135\pi$
$739$	2.83013	−	4.90192i	0.104108	−	0.180320i	0.913373	+	0.407123i	$0.133468\pi$
$740$	1.60770	−	7.85641i	0.0591000	−	0.288807i
$741$	−7.60770			−0.279476
$742$	8.19615	−	42.5885i	0.300890	−	1.56347i
$743$	6.41858	+	6.41858i	0.235475	+	0.235475i	0.814973	−	0.579498i	$-0.196751\pi$
$743$	6.41858	+	6.41858i	0.235475	+	0.235475i	−0.579498	+	0.814973i	$0.696751\pi$
$744$	0.248711	−	0.143594i	0.00911820	−	0.00526439i
$745$	−9.96410	+	6.57884i	−0.365056	+	0.241030i
$746$	6.92820	+	12.0000i	0.253660	+	0.439351i
$747$	−28.2224	−	7.56218i	−1.03260	−	0.276686i
$748$	6.00000	−	22.3923i	0.219382	−	0.818744i
$749$	−2.43782	−	33.9545i	−0.0890761	−	1.24067i
$750$	−2.75833	+	7.70577i	−0.100720	+	0.281375i
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	0.755510	−	0.655137i	$-0.227389\pi$
$751$	−5.19615	−	9.00000i	−0.189610	−	0.328415i	−0.945120	+	0.326722i	$0.894056\pi$
$752$	−9.46410	+	35.3205i	−0.345120	+	1.28801i
$753$	1.16987	−	0.313467i	0.0426325	−	0.0114234i
$754$		−	14.7846i		−	0.538424i
$755$	48.3923	+	24.1962i	1.76118	+	0.880588i
$756$	−14.1244	−	6.85641i	−0.513698	−	0.249365i
$757$	1.05256	+	1.05256i	0.0382559	+	0.0382559i	0.725976	−	0.687720i	$-0.241388\pi$
$757$	1.05256	+	1.05256i	0.0382559	+	0.0382559i	−0.687720	+	0.725976i	$0.741388\pi$
$758$	18.2487	+	18.2487i	0.662823	+	0.662823i
$759$	4.09808	−	7.09808i	0.148751	−	0.257644i
$760$	21.4641	+	4.39230i	0.778585	+	0.159326i
$761$	−41.1962	+	23.7846i	−1.49336	+	0.862191i	−0.999971	−	0.00761770i	$-0.997575\pi$
$761$	−41.1962	+	23.7846i	−1.49336	+	0.862191i	−0.493388	+	0.869809i	$0.664242\pi$
$762$	−11.0000	+	2.94744i	−0.398488	+	0.106775i
$763$	3.86603	−	20.0885i	0.139960	−	0.727251i
$764$	−36.5885	+	21.1244i	−1.32372	+	0.764252i
$765$	−19.3923	−	17.1962i	−0.701130	−	0.621728i
$766$	−3.63397	−	6.29423i	−0.131301	−	0.227420i
$767$	5.41154	+	20.1962i	0.195399	+	0.729241i
$768$	−8.00000	+	2.14359i	−0.288675	+	0.0773503i
$769$	−46.6410			−1.68192			−0.840959	−	0.541099i	$-0.818008\pi$
$769$	−46.6410			−1.68192			−0.840959	+	0.541099i	$0.818008\pi$
$770$	18.1244	−	13.9282i	0.653156	−	0.501938i
$771$		−	3.71281i		−	0.133714i
$772$	−1.12436	−	4.19615i	−0.0404664	−	0.151023i
$773$	−29.4904	+	7.90192i	−1.06070	+	0.284212i	−0.746665	−	0.665200i	$-0.768346\pi$
$773$	−29.4904	+	7.90192i	−1.06070	+	0.284212i	−0.314030	+	0.949413i	$0.601679\pi$
$774$	−3.00000	+	1.73205i	−0.107833	+	0.0622573i
$775$	0.901924	+	0.385263i	0.0323981	+	0.0138391i
$776$	38.9282			1.39744
$777$	−0.803848	−	2.32051i	−0.0288379	−	0.0832478i
$778$	−39.5167	+	10.5885i	−1.41674	+	0.379615i
$779$	−11.1962	−	19.3923i	−0.401144	−	0.694801i
$780$	8.78461	+	4.39230i	0.314539	+	0.157270i
$781$	20.1962	+	11.6603i	0.722675	+	0.417237i
$782$	−24.5885	+	24.5885i	−0.879281	+	0.879281i
$783$	−5.16987	+	5.16987i	−0.184756	+	0.184756i
$784$	−22.0000	+	17.3205i	−0.785714	+	0.618590i
$785$	−16.6077	+	5.53590i	−0.592754	+	0.197585i
$786$			0.392305i			0.0139931i
$787$	−7.16025	−	26.7224i	−0.255235	−	0.952552i	−0.967959	−	0.251107i	$-0.919205\pi$
$787$	−7.16025	−	26.7224i	−0.255235	−	0.952552i	0.712724	−	0.701445i	$-0.247461\pi$
$788$	−24.9282	+	24.9282i	−0.888030	+	0.888030i
$789$	9.69615	−	5.59808i	0.345192	−	0.199297i
$790$	0.588457	−	2.87564i	0.0209364	−	0.102311i
$791$	−31.8564	−	15.4641i	−1.13268	−	0.549840i
$792$	−14.9282	+	14.9282i	−0.530451	+	0.530451i
$793$	−4.31347	+	16.0981i	−0.153176	+	0.571659i
$794$	2.07180	+	3.58846i	0.0735253	+	0.127350i
$795$	11.1962	−	7.39230i	0.397087	−	0.262178i
$796$	6.00000	+	3.46410i	0.212664	+	0.122782i
$797$	12.9282	−	12.9282i	0.457940	−	0.457940i	−0.440038	−	0.897979i	$-0.645035\pi$
$797$	12.9282	−	12.9282i	0.457940	−	0.457940i	0.897979	+	0.440038i	$0.145035\pi$
$798$	6.33975	−	2.19615i	0.224425	−	0.0777430i
$799$			38.7846i			1.37210i
$800$	−22.2487	−	17.4641i	−0.786611	−	0.617449i
$801$	16.0981	+	9.29423i	0.568798	+	0.328395i
$802$	−9.04552	+	33.7583i	−0.319408	+	1.19205i
$803$	7.92820	−	29.5885i	0.279780	−	1.04415i
$804$	4.26795	+	7.39230i	0.150519	+	0.260706i
$805$	−33.9904	+	4.50000i	−1.19800	+	0.158604i
$806$	0.588457	−	1.01924i	0.0207275	−	0.0359011i
$807$	5.23205	+	1.40192i	0.184177	+	0.0493501i
$808$	−10.3397	−	38.5885i	−0.363751	−	1.35754i
$809$	16.5788	+	9.57180i	0.582881	+	0.336526i	0.762277	−	0.647250i	$-0.224081\pi$
$809$	16.5788	+	9.57180i	0.582881	+	0.336526i	−0.179397	+	0.983777i	$0.557415\pi$
$810$	6.66025	+	19.9808i	0.234017	+	0.702052i
$811$	−47.6603			−1.67358			−0.836789	−	0.547526i	$-0.815570\pi$
$811$	−47.6603			−1.67358			−0.836789	+	0.547526i	$0.815570\pi$
$812$	4.26795	+	12.3205i	0.149776	+	0.432365i
$813$	4.39230	−	4.39230i	0.154045	−	0.154045i
$814$	−6.92820			−0.242833
$815$	−9.29423	+	45.4186i	−0.325563	+	1.59094i
$816$	−7.60770	+	4.39230i	−0.266323	+	0.153761i
$817$	0.803848	−	3.00000i	0.0281231	−	0.104957i
$818$	12.8301	−	3.43782i	0.448595	−	0.120201i
$819$	−30.5885	+	2.19615i	−1.06885	+	0.0767398i
$820$	1.73205	+	28.8564i	0.0604858	+	1.00771i
$821$	−3.92820	+	2.26795i	−0.137095	+	0.0791520i	−0.566979	−	0.823732i	$-0.691888\pi$
$821$	−3.92820	+	2.26795i	−0.137095	+	0.0791520i	0.429884	+	0.902884i	$0.358555\pi$
$822$	−1.60770	+	6.00000i	−0.0560748	+	0.209274i
$823$	12.3301	−	3.30385i	0.429801	−	0.115165i	−0.0374316	−	0.999299i	$-0.511918\pi$
$823$	12.3301	−	3.30385i	0.429801	−	0.115165i	0.467233	+	0.884134i	$0.345251\pi$
$824$	−13.5167	+	7.80385i	−0.470875	+	0.271860i
$825$	7.00000	+	1.00000i	0.243709	+	0.0348155i
$826$	−10.3397	−	15.2679i	−0.359766	−	0.531240i
$827$	26.1506	+	26.1506i	0.909347	+	0.909347i	0.996219	−	0.0868727i	$-0.0276874\pi$
$827$	26.1506	+	26.1506i	0.909347	+	0.909347i	−0.0868727	+	0.996219i	$0.527687\pi$
$828$	30.5885	−	8.19615i	1.06302	−	0.284836i
$829$	−2.19615	−	1.26795i	−0.0762755	−	0.0440377i	0.461377	−	0.887204i	$-0.347356\pi$
$829$	−2.19615	−	1.26795i	−0.0762755	−	0.0440377i	−0.537653	+	0.843166i	$0.680689\pi$
$830$	−33.7583	+	2.02628i	−1.17177	+	0.0703332i
$831$	−6.50962	+	3.75833i	−0.225816	+	0.130375i
$832$	−24.0000	+	24.0000i	−0.832050	+	0.832050i
$833$	−17.7846	+	23.7846i	−0.616200	+	0.824088i
$834$	1.73205	−	3.00000i	0.0599760	−	0.103882i
$835$	−25.7942	+	29.0885i	−0.892646	+	1.00665i
$836$		−	18.9282i		−	0.654646i
$837$	−0.562178	+	0.150635i	−0.0194317	+	0.00520671i
$838$	18.3923	−	18.3923i	0.635352	−	0.635352i
$839$	3.80385			0.131323			0.0656617	−	0.997842i	$-0.479084\pi$
$839$	3.80385			0.131323			0.0656617	+	0.997842i	$0.479084\pi$
$840$	−8.58846	−	1.12436i	−0.296330	−	0.0387940i
$841$	−22.9282			−0.790628
$842$	5.87564	−	5.87564i	0.202488	−	0.202488i
$843$	−12.1244	+	3.24871i	−0.417585	+	0.111892i
$844$	54.9282			1.89071
$845$	11.1603	−	0.669873i	0.383924	−	0.0230443i
$846$	17.6603	−	30.5885i	0.607172	−	1.05165i
$847$	7.07180	+	6.12436i	0.242990	+	0.210435i
$848$	12.0000	+	44.7846i	0.412082	+	1.53791i
$849$	2.49038	−	1.43782i	0.0854697	−	0.0493459i
$850$	−27.5885	−	11.7846i	−0.946276	−	0.404209i
$851$	9.00000	+	5.19615i	0.308516	+	0.178122i
$852$	−2.28719	−	8.53590i	−0.0783577	−	0.292435i
$853$	5.32051	+	5.32051i	0.182171	+	0.182171i	0.792301	−	0.610130i	$-0.208883\pi$
$853$	5.32051	+	5.32051i	0.182171	+	0.182171i	−0.610130	+	0.792301i	$0.708883\pi$
$854$	−1.05256	−	14.6603i	−0.0360178	−	0.501664i
$855$	−18.9282	−	9.46410i	−0.647331	−	0.323665i
$856$	18.1962	+	31.5167i	0.621932	+	1.07722i
$857$	−25.2224	+	6.75833i	−0.861582	+	0.230860i	−0.662444	−	0.749111i	$-0.730481\pi$
$857$	−25.2224	+	6.75833i	−0.861582	+	0.230860i	−0.199138	+	0.979972i	$0.563814\pi$
$858$	2.19615	−	8.19615i	0.0749754	−	0.279812i
$859$	−3.80385	+	2.19615i	−0.129786	+	0.0749318i	−0.563487	−	0.826125i	$-0.690541\pi$
$859$	−3.80385	+	2.19615i	−0.129786	+	0.0749318i	0.433702	+	0.901057i	$0.357207\pi$
$860$	−2.66025	+	3.00000i	−0.0907139	+	0.102299i
$861$	4.96410	+	7.33013i	0.169176	+	0.249810i
$862$	−22.8564	+	6.12436i	−0.778492	+	0.208596i
$863$	−0.741670	+	2.76795i	−0.0252467	+	0.0942221i	−0.977400	−	0.211400i	$-0.932198\pi$
$863$	−0.741670	+	2.76795i	−0.0252467	+	0.0942221i	0.952153	+	0.305622i	$0.0988644\pi$
$864$	16.7846			0.571024
$865$	54.7128	+	11.1962i	1.86029	+	0.380681i
$866$	9.07180			0.308272
$867$	−0.366025	+	0.366025i	−0.0124309	+	0.0124309i
$868$	−0.196152	+	1.01924i	−0.00665785	+	0.0345952i
$869$	−2.53590			−0.0860245
$870$	−1.80385	+	3.60770i	−0.0611562	+	0.122312i
$871$	30.2942	+	17.4904i	1.02648	+	0.592639i
$872$	5.66025	+	21.1244i	0.191680	+	0.715361i
$873$	−36.3205	−	9.73205i	−1.22926	−	0.329380i
$874$	−14.1962	+	24.5885i	−0.480192	+	0.831717i
$875$	−14.5263	−	25.7679i	−0.491078	−	0.871116i
$876$	−10.0526	+	5.80385i	−0.339644	+	0.196094i
$877$	1.39230	−	5.19615i	0.0470148	−	0.175462i	−0.938426	−	0.345480i	$-0.887716\pi$
$877$	1.39230	−	5.19615i	0.0470148	−	0.175462i	0.985441	+	0.170018i	$0.0543827\pi$
$878$	10.7321	−	40.0526i	0.362189	−	1.35171i
$879$	3.92820	+	2.26795i	0.132495	+	0.0764960i
$880$	−10.9282	+	21.8564i	−0.368390	+	0.736779i
$881$		−	21.2487i		−	0.715887i	−0.933743	−	0.357944i	$-0.883478\pi$
$881$		−	21.2487i		−	0.715887i	0.933743	−	0.357944i	$-0.116522\pi$
$882$	24.8564	−	10.6603i	0.836959	−	0.358949i
$883$	33.2487	−	33.2487i	1.11891	−	1.11891i	0.127006	−	0.991902i	$-0.459463\pi$
$883$	33.2487	−	33.2487i	1.11891	−	1.11891i	0.991902	−	0.127006i	$-0.0405368\pi$
$884$	−18.0000	+	31.1769i	−0.605406	+	1.04859i
$885$	1.14359	−	5.58846i	0.0384415	−	0.187854i
$886$	−15.4186	−	26.7058i	−0.517997	−	0.897198i
$887$	9.06218	−	33.8205i	0.304278	−	1.13558i	−0.629287	−	0.777173i	$-0.716653\pi$
$887$	9.06218	−	33.8205i	0.304278	−	1.13558i	0.933565	−	0.358408i	$-0.116680\pi$
$888$	1.85641	+	1.85641i	0.0622969	+	0.0622969i
$889$	17.9737	−	37.0263i	0.602819	−	1.24182i
$890$	21.0788	+	4.31347i	0.706564	+	0.144588i
$891$	15.7583	−	9.09808i	0.527924	−	0.304797i
$892$	−11.8564	−	11.8564i	−0.396982	−	0.396982i
$893$	8.19615	+	30.5885i	0.274274	+	1.02360i
$894$		−	3.90897i		−	0.130735i
$895$	−48.1051	−	24.0526i	−1.60798	−	0.803988i
$896$	13.0718	−	26.9282i	0.436698	−	0.899608i
$897$	−9.00000	+	9.00000i	−0.300501	+	0.300501i
$898$	−12.8038	+	12.8038i	−0.427270	+	0.427270i
$899$	0.418584	+	0.241670i	0.0139606	+	0.00806014i
$900$	16.3923	+	21.8564i	0.546410	+	0.728547i
$901$	24.5885	+	42.5885i	0.819160	+	1.41883i
$902$	24.1244	−	6.46410i	0.803253	−	0.215231i
$903$	−0.232051	+	1.20577i	−0.00772217	+	0.0401256i
$904$	37.8564			1.25909
$905$	3.01666	+	50.2583i	0.100277	+	1.67064i
$906$	−15.3397	+	8.85641i	−0.509629	+	0.294234i
$907$	16.7942	−	4.50000i	0.557643	−	0.149420i	0.0310198	−	0.999519i	$-0.490124\pi$
$907$	16.7942	−	4.50000i	0.557643	−	0.149420i	0.526623	+	0.850099i	$0.323458\pi$
$908$	−31.1244	+	8.33975i	−1.03290	+	0.276764i
$909$			38.5885i			1.27990i
$910$	−32.7846	+	13.6077i	−1.08680	+	0.451091i
$911$	−2.19615			−0.0727618			−0.0363809	−	0.999338i	$-0.511583\pi$
$911$	−2.19615			−0.0727618			−0.0363809	+	0.999338i	$0.511583\pi$
$912$	−5.07180	+	5.07180i	−0.167944	+	0.167944i
$913$	7.56218	+	28.2224i	0.250272	+	0.934026i
$914$	0.196152	+	0.339746i	0.00648815	+	0.0112378i
$915$	3.01666	−	3.40192i	0.0997277	−	0.112464i
$916$	8.53590	+	14.7846i	0.282034	+	0.488497i
$917$	−1.07180	−	0.928203i	−0.0353938	−	0.0306520i
$918$	17.1962	−	4.60770i	0.567558	−	0.152077i
$919$	−39.0000	+	22.5167i	−1.28649	+	0.742756i	−0.978027	−	0.208480i	$-0.933148\pi$
$919$	−39.0000	+	22.5167i	−1.28649	+	0.742756i	−0.308465	+	0.951236i	$0.599815\pi$
$920$	30.5885	−	20.1962i	1.00847	−	0.665847i
$921$	−7.96410	+	13.7942i	−0.262426	+	0.454535i
$922$	39.8564	+	39.8564i	1.31260	+	1.31260i
$923$	−25.6077	−	25.6077i	−0.842888	−	0.842888i
$924$	0.535898	+	7.46410i	0.0176298	+	0.245551i
$925$	−1.26795	+	8.87564i	−0.0416899	+	0.291829i
$926$			15.6603i			0.514628i
$927$	14.5622	−	3.90192i	0.478285	−	0.128156i
$928$	−9.85641	−	9.85641i	−0.323552	−	0.323552i
$929$	13.1603	+	22.7942i	0.431774	+	0.747854i	0.997026	−	0.0770637i	$-0.0245545\pi$
$929$	13.1603	+	22.7942i	0.431774	+	0.747854i	−0.565252	+	0.824918i	$0.691221\pi$
$930$	−0.267949	+	0.176915i	−0.00878640	+	0.00580126i
$931$	−9.00000	+	22.5167i	−0.294963	+	0.737954i
$932$	14.1962	+	3.80385i	0.465010	+	0.124599i
$933$	5.53590	+	1.48334i	0.181237	+	0.0485624i
$934$	7.56218	+	13.0981i	0.247442	+	0.428582i
$935$	−5.19615	+	25.3923i	−0.169932	+	0.830417i
$936$	28.3923	−	16.3923i	0.928032	−	0.535799i
$937$	−20.3923	−	20.3923i	−0.666188	−	0.666188i	0.290644	−	0.956831i	$-0.406131\pi$
$937$	−20.3923	−	20.3923i	−0.666188	−	0.666188i	−0.956831	+	0.290644i	$0.906131\pi$
$938$	−30.2942	−	5.83013i	−0.989142	−	0.190360i
$939$	−16.2487			−0.530257
$940$	8.19615	−	40.0526i	0.267329	−	1.30637i
$941$	6.26795	−	10.8564i	0.204329	−	0.353909i	−0.745590	−	0.666405i	$-0.767832\pi$
$941$	6.26795	−	10.8564i	0.204329	−	0.353909i	0.949919	+	0.312497i	$0.101165\pi$
$942$	1.48334	−	5.53590i	0.0483298	−	0.180369i
$943$	−36.1865	−	9.69615i	−1.17840	−	0.315750i
$944$	17.0718	+	9.85641i	0.555640	+	0.320799i
$945$	16.2224	+	6.70577i	0.527716	+	0.218139i
$946$	3.00000	+	1.73205i	0.0975384	+	0.0563138i
$947$	13.6699	−	51.0167i	0.444211	−	1.65782i	−0.273800	−	0.961787i	$-0.588281\pi$
$947$	13.6699	−	51.0167i	0.444211	−	1.65782i	0.718011	−	0.696032i	$-0.245053\pi$
$948$	0.679492	+	0.679492i	0.0220689	+	0.0220689i
$949$	−23.7846	+	41.1962i	−0.772081	+	1.33728i
$950$	−24.2487	−	3.46410i	−0.786732	−	0.112390i
$951$			5.26795i			0.170825i
$952$	6.00000	−	31.1769i	0.194461	−	1.01045i
$953$	−3.46410	−	3.46410i	−0.112213	−	0.112213i	0.648771	−	0.760984i	$-0.275283\pi$
$953$	−3.46410	−	3.46410i	−0.112213	−	0.112213i	−0.760984	+	0.648771i	$0.775283\pi$
$954$		−	44.7846i		−	1.44996i
$955$	39.4186	−	26.0263i	1.27556	−	0.842191i
$956$	2.53590			0.0820168
$957$	3.36603	+	0.901924i	0.108808	+	0.0291551i
$958$	−19.3923	+	5.19615i	−0.626537	+	0.167880i
$959$	−12.5885	−	18.5885i	−0.406502	−	0.600253i
$960$	8.78461	−	2.92820i	0.283522	−	0.0945074i
$961$	−15.4808	−	26.8135i	−0.499379	−	0.864951i
$962$	10.3923	+	2.78461i	0.335061	+	0.0897794i
$963$	−9.09808	−	33.9545i	−0.293181	−	1.09417i
$964$	0.392305	−	0.679492i	0.0126353	−	0.0218850i
$965$	1.53590	+	4.60770i	0.0494423	+	0.148327i
$966$	4.90192	−	10.0981i	0.157717	−	0.324900i
$967$	−36.4904	+	36.4904i	−1.17345	+	1.17345i	−0.192070	+	0.981381i	$0.561520\pi$
$967$	−36.4904	+	36.4904i	−1.17345	+	1.17345i	−0.981381	+	0.192070i	$0.938480\pi$
$968$	−9.66025	−	2.58846i	−0.310492	−	0.0831962i
$969$	−3.80385	+	6.58846i	−0.122197	+	0.211652i
$970$	−43.4449	+	2.60770i	−1.39493	+	0.0837280i
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	0.659762	−	0.751475i	$-0.270657\pi$
$971$	−10.0000	−	17.3205i	−0.320915	−	0.555842i	−0.980677	+	0.195633i	$0.937324\pi$
$972$	−23.8564	−	6.39230i	−0.765195	−	0.205033i
$973$	4.09808	+	11.8301i	0.131378	+	0.379256i
$974$	0.0717968	−	0.124356i	0.00230052	−	0.00398461i
$975$	−10.0981	−	4.31347i	−0.323397	−	0.138141i
$976$	7.85641	+	13.6077i	0.251477	+	0.435572i
$977$	0.973721	+	3.63397i	0.0311521	+	0.116261i	0.979751	−	0.200219i	$-0.0641655\pi$
$977$	0.973721	+	3.63397i	0.0311521	+	0.116261i	−0.948599	+	0.316481i	$0.897499\pi$
$978$	−10.7321	−	10.7321i	−0.343173	−	0.343173i
$979$		−	18.5885i		−	0.594090i
$980$	23.3923	−	20.8038i	0.747240	−	0.664555i
$981$		−	21.1244i		−	0.674449i
$982$	1.80385	−	1.80385i	0.0575631	−	0.0575631i
$983$	8.76795	+	32.7224i	0.279654	+	1.04368i	0.952658	+	0.304044i	$0.0983371\pi$
$983$	8.76795	+	32.7224i	0.279654	+	1.04368i	−0.673004	+	0.739639i	$0.734996\pi$
$984$	−8.19615	−	4.73205i	−0.261284	−	0.150852i
$985$	26.1506	−	29.4904i	0.833229	−	0.939642i
$986$	−12.8038	−	7.39230i	−0.407758	−	0.235419i
$987$	−4.09808	−	11.8301i	−0.130443	−	0.376557i
$988$	−7.60770	+	28.3923i	−0.242033	+	0.903280i
$989$	−2.59808	−	4.50000i	−0.0826140	−	0.143092i
$990$	15.6603	−	17.6603i	0.497716	−	0.561280i
$991$	18.6865	−	32.3660i	0.593597	−	1.02814i	−0.400146	−	0.916451i	$-0.631041\pi$
$991$	18.6865	−	32.3660i	0.593597	−	1.02814i	0.993743	−	0.111689i	$-0.0356261\pi$
$992$	−0.287187	−	1.07180i	−0.00911820	−	0.0340296i
$993$	3.92820	−	3.92820i	0.124658	−	0.124658i
$994$	28.7321	+	13.9474i	0.911325	+	0.442386i
$995$	−6.92820	−	3.46410i	−0.219639	−	0.109819i
$996$	5.53590	−	9.58846i	0.175412	−	0.303822i
$997$	−0.803848	−	3.00000i	−0.0254581	−	0.0950110i	0.952028	−	0.306011i	$-0.0989945\pi$
$997$	−0.803848	−	3.00000i	−0.0254581	−	0.0950110i	−0.977486	+	0.211000i	$0.932328\pi$
$998$	11.5359	−	43.0526i	0.365162	−	1.36280i
$999$	−2.66025	−	4.60770i	−0.0841667	−	0.145781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bv.a.213.1	yes	4
5.2	odd	4		280.2.bv.d.157.1	yes	4
7.5	odd	6		280.2.bv.c.173.1	yes	4
8.5	even	2		280.2.bv.b.213.1	yes	4
35.12	even	12		280.2.bv.b.117.1	yes	4
40.37	odd	4		280.2.bv.c.157.1	yes	4
56.5	odd	6		280.2.bv.d.173.1	yes	4
280.117	even	12	inner	280.2.bv.a.117.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.a.117.1	✓	4	280.117	even	12	inner
280.2.bv.a.213.1	yes	4	1.1	even	1	trivial
280.2.bv.b.117.1	yes	4	35.12	even	12
280.2.bv.b.213.1	yes	4	8.5	even	2
280.2.bv.c.157.1	yes	4	40.37	odd	4
280.2.bv.c.173.1	yes	4	7.5	odd	6
280.2.bv.d.157.1	yes	4	5.2	odd	4
280.2.bv.d.173.1	yes	4	56.5	odd	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(0.633975 + 0.366025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} +2.00000i q^{4} +(-0.133975 - 2.23205i) q^{5} +(0.633975 + 0.366025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +(-2.09808 + 2.36603i) q^{10} +(2.36603 + 1.36603i) q^{11} +(-0.267949 - 1.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(3.36603 + 1.63397i) q^{14} +(0.366025 + 1.09808i) q^{15} -4.00000 q^{16} +(-4.09808 + 1.09808i) q^{17} +(3.73205 + 1.00000i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(4.46410 - 0.267949i) q^{20} +(1.13397 - 0.767949i) q^{21} +(-1.00000 - 3.73205i) q^{22} +(-1.50000 + 5.59808i) q^{23} +(-0.732051 + 1.26795i) q^{24} +(-4.96410 + 0.598076i) q^{25} +6.00000i q^{26} +(2.09808 - 2.09808i) q^{27} +(-1.73205 - 5.00000i) q^{28} -2.46410 q^{29} +(0.732051 - 1.46410i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.36603 - 0.366025i) q^{33} +(5.19615 + 3.00000i) q^{34} +(2.26795 + 5.46410i) q^{35} +(-2.73205 - 4.73205i) q^{36} +(0.464102 - 1.73205i) q^{37} +(4.73205 + 1.26795i) q^{38} +(1.90192 + 1.09808i) q^{39} +(-4.73205 - 4.19615i) q^{40} +6.46410i q^{41} +(-1.90192 - 0.366025i) q^{42} +(-0.633975 + 0.633975i) q^{43} +(-2.73205 + 4.73205i) q^{44} +(3.36603 + 5.09808i) q^{45} +(7.09808 - 4.09808i) q^{46} +(2.36603 - 8.83013i) q^{47} +(2.00000 - 0.535898i) q^{48} +(5.50000 - 4.33013i) q^{49} +(5.56218 + 4.36603i) q^{50} +(1.90192 - 1.09808i) q^{51} +(6.00000 - 6.00000i) q^{52} +(-3.00000 - 11.1962i) q^{53} -4.19615 q^{54} +(2.73205 - 5.46410i) q^{55} +(-3.26795 + 6.73205i) q^{56} +(1.26795 - 1.26795i) q^{57} +(2.46410 + 2.46410i) q^{58} +(-4.26795 - 2.46410i) q^{59} +(-2.19615 + 0.732051i) q^{60} +(-1.96410 - 3.40192i) q^{61} +(0.0717968 + 0.267949i) q^{62} +(4.73205 - 5.46410i) q^{63} -8.00000i q^{64} +(-6.29423 + 7.09808i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-7.96410 + 2.13397i) q^{67} +(-2.19615 - 8.19615i) q^{68} -3.00000i q^{69} +(3.19615 - 7.73205i) q^{70} +8.53590 q^{71} +(-2.00000 + 7.46410i) q^{72} +(-2.90192 - 10.8301i) q^{73} +(-2.19615 + 1.26795i) q^{74} +(2.40192 - 0.964102i) q^{75} +(-3.46410 - 6.00000i) q^{76} +(-7.09808 - 1.36603i) q^{77} +(-0.803848 - 3.00000i) q^{78} +(-0.803848 + 0.464102i) q^{79} +(0.535898 + 8.92820i) q^{80} +(3.33013 - 5.76795i) q^{81} +(6.46410 - 6.46410i) q^{82} +(7.56218 + 7.56218i) q^{83} +(1.53590 + 2.26795i) q^{84} +(3.00000 + 9.00000i) q^{85} +1.26795 q^{86} +(1.23205 - 0.330127i) q^{87} +(7.46410 - 2.00000i) q^{88} +(-3.40192 - 5.89230i) q^{89} +(1.73205 - 8.46410i) q^{90} +(10.0981 + 4.90192i) q^{91} +(-11.1962 - 3.00000i) q^{92} +(0.0980762 + 0.0262794i) q^{93} +(-11.1962 + 6.46410i) q^{94} +(4.26795 + 6.46410i) q^{95} +(-2.53590 - 1.46410i) q^{96} +(9.73205 + 9.73205i) q^{97} +(-9.83013 - 1.16987i) q^{98} -7.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} + 2 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 10 q^{14} - 2 q^{15} - 16 q^{16} - 6 q^{17} + 8 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 18 q^{31} + 16 q^{32} - 2 q^{33} + 16 q^{35} - 4 q^{36} - 12 q^{37} + 12 q^{38} + 18 q^{39} - 12 q^{40} - 18 q^{42} - 6 q^{43} - 4 q^{44} + 10 q^{45} + 18 q^{46} + 6 q^{47} + 8 q^{48} + 22 q^{49} - 2 q^{50} + 18 q^{51} + 24 q^{52} - 12 q^{53} + 4 q^{54} + 4 q^{55} - 20 q^{56} + 12 q^{57} - 4 q^{58} - 24 q^{59} + 12 q^{60} + 6 q^{61} + 28 q^{62} + 12 q^{63} + 6 q^{65} + 4 q^{66} - 18 q^{67} + 12 q^{68} - 8 q^{70} + 48 q^{71} - 8 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 18 q^{77} - 24 q^{78} - 24 q^{79} + 16 q^{80} - 4 q^{81} + 12 q^{82} + 6 q^{83} + 20 q^{84} + 12 q^{85} + 12 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 30 q^{91} - 24 q^{92} - 10 q^{93} - 24 q^{94} + 24 q^{95} - 24 q^{96} + 32 q^{97} - 22 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 + 2 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 10 * q^14 - 2 * q^15 - 16 * q^16 - 6 * q^17 + 8 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 - 2 * q^27 + 4 * q^29 - 4 * q^30 - 18 * q^31 + 16 * q^32 - 2 * q^33 + 16 * q^35 - 4 * q^36 - 12 * q^37 + 12 * q^38 + 18 * q^39 - 12 * q^40 - 18 * q^42 - 6 * q^43 - 4 * q^44 + 10 * q^45 + 18 * q^46 + 6 * q^47 + 8 * q^48 + 22 * q^49 - 2 * q^50 + 18 * q^51 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 4 * q^55 - 20 * q^56 + 12 * q^57 - 4 * q^58 - 24 * q^59 + 12 * q^60 + 6 * q^61 + 28 * q^62 + 12 * q^63 + 6 * q^65 + 4 * q^66 - 18 * q^67 + 12 * q^68 - 8 * q^70 + 48 * q^71 - 8 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 18 * q^77 - 24 * q^78 - 24 * q^79 + 16 * q^80 - 4 * q^81 + 12 * q^82 + 6 * q^83 + 20 * q^84 + 12 * q^85 + 12 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 30 * q^91 - 24 * q^92 - 10 * q^93 - 24 * q^94 + 24 * q^95 - 24 * q^96 + 32 * q^97 - 22 * q^98 - 16 * q^99

Introduction

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