LMFDB - Embedded newform 70.2.k.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,2,Mod(3,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("70.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.k (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:	$0.558952814149$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
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			47.1
Root			$-1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	70.47
Dual form			70.2.k.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.0749894 + 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.20382 - 0.378409i) q^{5} -0.289737i q^{6} +(0.126334 + 2.64273i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.0749894 + 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.20382 - 0.378409i) q^{5} -0.289737i q^{6} +(0.126334 + 2.64273i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +(-2.03078 + 0.935904i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(0.0749894 + 0.279864i) q^{12} +(-1.42962 - 1.42962i) q^{13} +(-0.806019 - 2.51999i) q^{14} +(-0.0593598 + 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-5.12784 - 1.37400i) q^{17} +(-2.81669 - 0.754730i) q^{18} +(-1.94590 + 3.37040i) q^{19} +(1.71936 - 1.42962i) q^{20} +(-0.749081 - 0.162821i) q^{21} +(3.97801 + 3.97801i) q^{22} +(-0.290892 - 1.08562i) q^{23} +(-0.144868 - 0.250919i) q^{24} +(4.71361 - 1.66789i) q^{25} +(1.75092 + 1.01089i) q^{26} +(-1.21205 + 1.21205i) q^{27} +(1.43078 + 2.22551i) q^{28} -3.15502i q^{29} +(-0.109639 - 0.638527i) q^{30} +(-3.33287 + 1.92423i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.57445 - 0.421872i) q^{33} +5.30873 q^{34} +(1.27845 + 5.77629i) q^{35} +2.91605 q^{36} +(4.86824 - 1.30444i) q^{37} +(1.00727 - 3.75919i) q^{38} +(0.507306 - 0.292893i) q^{39} +(-1.29076 + 1.82591i) q^{40} +7.21050i q^{41} +(0.765697 - 0.0366036i) q^{42} +(1.85669 - 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(6.11719 + 2.25760i) q^{45} +(0.561961 + 0.973344i) q^{46} +(-1.52590 - 5.69475i) q^{47} +(0.204875 + 0.204875i) q^{48} +(-6.96808 + 0.667734i) q^{49} +(-4.12132 + 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(-1.95290 - 0.523277i) q^{52} +(1.33599 + 0.357978i) q^{53} +(0.857049 - 1.48445i) q^{54} +(-8.04270 - 9.67269i) q^{55} +(-1.95803 - 1.77936i) q^{56} +(-0.797333 - 0.797333i) q^{57} +(0.816578 + 3.04751i) q^{58} +(2.73923 + 4.74448i) q^{59} +(0.271166 + 0.588393i) q^{60} +(-3.99172 - 2.30462i) q^{61} +(2.72127 - 2.72127i) q^{62} +(-3.53413 + 6.85809i) q^{63} -1.00000i q^{64} +(-3.69160 - 2.60964i) q^{65} +(-1.41161 + 0.814995i) q^{66} +(0.218698 - 0.816193i) q^{67} +(-5.12784 + 1.37400i) q^{68} +0.325641 q^{69} +(-2.72990 - 5.24858i) q^{70} +4.77710 q^{71} +(-2.81669 + 0.754730i) q^{72} +(1.45256 - 5.42104i) q^{73} +(-4.36475 + 2.51999i) q^{74} +(0.113311 + 1.44425i) q^{75} +3.89180i q^{76} +(12.5202 - 8.04920i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(5.41079 + 3.12392i) q^{79} +(0.774197 - 2.09777i) q^{80} +(4.12576 + 7.14603i) q^{81} +(-1.86622 - 6.96481i) q^{82} +(5.67281 + 5.67281i) q^{83} +(-0.730133 + 0.233533i) q^{84} +(-11.8207 - 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(0.882976 + 0.236593i) q^{87} +(5.43407 + 1.45605i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(-6.49307 - 0.597426i) q^{90} +(3.59749 - 3.95871i) q^{91} +(-0.794732 - 0.794732i) q^{92} +(-0.288594 - 1.07705i) q^{93} +(2.94782 + 5.10577i) q^{94} +(-3.01302 + 8.16409i) q^{95} +(-0.250919 - 0.144868i) q^{96} +(-6.63103 + 6.63103i) q^{97} +(6.55783 - 2.44845i) q^{98} -16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 + 8 * q^7	$ 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35} - 8 q^{36} + 4 q^{37} + 24 q^{38} + 36 q^{42} - 8 q^{43} - 12 q^{45} - 8 q^{46} + 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} - 4 q^{56} + 8 q^{57} - 32 q^{58} + 8 q^{60} - 12 q^{61} - 36 q^{63} - 8 q^{65} + 32 q^{67} - 36 q^{68} - 12 q^{70} + 16 q^{71} - 8 q^{72} - 12 q^{73} - 48 q^{75} + 16 q^{77} + 16 q^{78} - 12 q^{80} - 48 q^{82} + 24 q^{85} + 12 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{91} + 8 q^{92} + 28 q^{93} + 20 q^{95} + 12 q^{96} + 40 q^{98}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.0749894	+	0.279864i	−0.0432952	+	0.161580i	−0.984189	−	0.177122i	$-0.943321\pi$
$3$	−0.0749894	+	0.279864i	−0.0432952	+	0.161580i	0.940894	+	0.338702i	$0.109988\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.20382	−	0.378409i	0.985577	−	0.169230i
$5$	2.20382	−	0.378409i	0.985577	−	0.169230i
$6$		−	0.289737i		−	0.118285i
$7$	0.126334	+	2.64273i	0.0477497	+	0.998859i
$7$	0.126334	+	2.64273i	0.0477497	+	0.998859i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.52538	+	1.45803i	0.841792	+	0.486009i
$10$	−2.03078	+	0.935904i	−0.642190	+	0.295959i
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	−0.882888	−	0.469583i	$-0.844404\pi$
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	0.0347729	−	0.999395i	$-0.488929\pi$
$12$	0.0749894	+	0.279864i	0.0216476	+	0.0807899i
$13$	−1.42962	−	1.42962i	−0.396505	−	0.396505i	0.480493	−	0.876998i	$-0.340458\pi$
$13$	−1.42962	−	1.42962i	−0.396505	−	0.396505i	−0.876998	+	0.480493i	$0.840458\pi$
$14$	−0.806019	−	2.51999i	−0.215418	−	0.673495i
$15$	−0.0593598	+	0.645146i	−0.0153266	+	0.166576i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−5.12784	−	1.37400i	−1.24368	−	0.333244i	−0.423790	−	0.905760i	$-0.639301\pi$
$17$	−5.12784	−	1.37400i	−1.24368	−	0.333244i	−0.819893	+	0.572516i	$0.805967\pi$
$18$	−2.81669	−	0.754730i	−0.663900	−	0.177892i
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	−0.998150	−	0.0608002i	$-0.980635\pi$
$19$	−1.94590	+	3.37040i	−0.446420	+	0.773223i	0.551729	+	0.834023i	$0.313968\pi$
$20$	1.71936	−	1.42962i	0.384460	−	0.319673i
$21$	−0.749081	−	0.162821i	−0.163463	−	0.0355304i
$22$	3.97801	+	3.97801i	0.848115	+	0.848115i
$23$	−0.290892	−	1.08562i	−0.0606552	−	0.226368i	0.928944	−	0.370220i	$-0.120718\pi$
$23$	−0.290892	−	1.08562i	−0.0606552	−	0.226368i	−0.989599	+	0.143852i	$0.954051\pi$
$24$	−0.144868	−	0.250919i	−0.0295711	−	0.0512187i
$25$	4.71361	−	1.66789i	0.942723	−	0.333577i
$26$	1.75092	+	1.01089i	0.343384	+	0.198253i
$27$	−1.21205	+	1.21205i	−0.233259	+	0.233259i
$28$	1.43078	+	2.22551i	0.270391	+	0.420581i
$29$		−	3.15502i		−	0.585872i	−0.956132	−	0.292936i	$-0.905368\pi$
$29$		−	3.15502i		−	0.585872i	0.956132	−	0.292936i	$-0.0946322\pi$
$30$	−0.109639	−	0.638527i	−0.0200172	−	0.116579i
$31$	−3.33287	+	1.92423i	−0.598601	+	0.345602i	−0.768491	−	0.639861i	$-0.778992\pi$
$31$	−3.33287	+	1.92423i	−0.598601	+	0.345602i	0.169890	+	0.985463i	$0.445659\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	1.57445	−	0.421872i	0.274076	−	0.0734386i
$34$	5.30873			0.910440
$35$	1.27845	+	5.77629i	0.216098	+	0.976372i
$36$	2.91605			0.486009
$37$	4.86824	−	1.30444i	0.800334	−	0.214449i	0.164603	−	0.986360i	$-0.447366\pi$
$37$	4.86824	−	1.30444i	0.800334	−	0.214449i	0.635731	+	0.771911i	$0.280699\pi$
$38$	1.00727	−	3.75919i	0.163401	−	0.609822i
$39$	0.507306	−	0.292893i	0.0812340	−	0.0469005i
$40$	−1.29076	+	1.82591i	−0.204087	+	0.288702i
$41$			7.21050i			1.12609i	0.826426	+	0.563046i	$0.190371\pi$
$41$			7.21050i			1.12609i	−0.826426	+	0.563046i	$0.809629\pi$
$42$	0.765697	−	0.0366036i	0.118150	−	0.00564806i
$43$	1.85669	−	1.85669i	0.283143	−	0.283143i	−0.551218	−	0.834361i	$-0.685837\pi$
$43$	1.85669	−	1.85669i	0.283143	−	0.283143i	0.834361	+	0.551218i	$0.185837\pi$
$44$	−4.87205	−	2.81288i	−0.734489	−	0.424058i
$45$	6.11719	+	2.25760i	0.911897	+	0.336543i
$46$	0.561961	+	0.973344i	0.0828566	+	0.143512i
$47$	−1.52590	−	5.69475i	−0.222576	−	0.830665i	−0.983361	−	0.181661i	$-0.941853\pi$
$47$	−1.52590	−	5.69475i	−0.222576	−	0.830665i	0.760785	−	0.649004i	$-0.224814\pi$
$48$	0.204875	+	0.204875i	0.0295711	+	0.0295711i
$49$	−6.96808	+	0.667734i	−0.995440	+	0.0953905i
$50$	−4.12132	+	2.83103i	−0.582843	+	0.400368i
$51$	0.769067	−	1.33206i	0.107691	−	0.186526i
$52$	−1.95290	−	0.523277i	−0.270818	−	0.0725655i
$53$	1.33599	+	0.357978i	0.183512	+	0.0491720i	0.349405	−	0.936972i	$-0.386384\pi$
$53$	1.33599	+	0.357978i	0.183512	+	0.0491720i	−0.165892	+	0.986144i	$0.553050\pi$
$54$	0.857049	−	1.48445i	0.116630	−	0.202008i
$55$	−8.04270	−	9.67269i	−1.08448	−	1.30426i
$56$	−1.95803	−	1.77936i	−0.261652	−	0.237777i
$57$	−0.797333	−	0.797333i	−0.105609	−	0.105609i
$58$	0.816578	+	3.04751i	0.107222	+	0.400158i
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	0.987393	−	0.158286i	$-0.0505968\pi$
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	−0.630776	+	0.775965i	$0.717263\pi$
$60$	0.271166	+	0.588393i	0.0350074	+	0.0759612i
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	0.222193	−	0.975003i	$-0.428678\pi$
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	−0.733281	+	0.679926i	$0.762012\pi$
$62$	2.72127	−	2.72127i	0.345602	−	0.345602i
$63$	−3.53413	+	6.85809i	−0.445259	+	0.864038i
$64$		−	1.00000i		−	0.125000i
$65$	−3.69160	−	2.60964i	−0.457887	−	0.323686i
$66$	−1.41161	+	0.814995i	−0.173758	+	0.100319i
$67$	0.218698	−	0.816193i	0.0267182	−	0.0997138i	−0.951279	−	0.308331i	$-0.900230\pi$
$67$	0.218698	−	0.816193i	0.0267182	−	0.0997138i	0.977997	+	0.208617i	$0.0668963\pi$
$68$	−5.12784	+	1.37400i	−0.621842	+	0.166622i
$69$	0.325641			0.0392026
$70$	−2.72990	−	5.24858i	−0.326286	−	0.627326i
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	−2.81669	+	0.754730i	−0.331950	+	0.0889458i
$73$	1.45256	−	5.42104i	0.170010	−	0.634485i	−0.827338	−	0.561704i	$-0.810146\pi$
$73$	1.45256	−	5.42104i	0.170010	−	0.634485i	0.997348	−	0.0727807i	$-0.0231873\pi$
$74$	−4.36475	+	2.51999i	−0.507391	+	0.292943i
$75$	0.113311	+	1.44425i	0.0130840	+	0.166767i
$76$			3.89180i			0.446420i
$77$	12.5202	−	8.04920i	1.42681	−	0.917291i
$78$	−0.414214	+	0.414214i	−0.0469005	+	0.0469005i
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	0.772481	−	0.635038i	$-0.219016\pi$
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	−0.163719	+	0.986507i	$0.552349\pi$
$80$	0.774197	−	2.09777i	0.0865578	−	0.234537i
$81$	4.12576	+	7.14603i	0.458418	+	0.794003i
$82$	−1.86622	−	6.96481i	−0.206089	−	0.769135i
$83$	5.67281	+	5.67281i	0.622672	+	0.622672i	0.946214	−	0.323542i	$-0.104874\pi$
$83$	5.67281	+	5.67281i	0.622672	+	0.622672i	−0.323542	+	0.946214i	$0.604874\pi$
$84$	−0.730133	+	0.233533i	−0.0796641	+	0.0254806i
$85$	−11.8207	−	1.08763i	−1.28214	−	0.117970i
$86$	−1.31288	+	2.27397i	−0.141571	+	0.245209i
$87$	0.882976	+	0.236593i	0.0946650	+	0.0253654i
$88$	5.43407	+	1.45605i	0.579273	+	0.155216i
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	0.355318	+	0.934746i	$0.384373\pi$
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	−0.987172	+	0.159659i	$0.948961\pi$
$90$	−6.49307	−	0.597426i	−0.684429	−	0.0629742i
$91$	3.59749	−	3.95871i	0.377120	−	0.414986i
$92$	−0.794732	−	0.794732i	−0.0828566	−	0.0828566i
$93$	−0.288594	−	1.07705i	−0.0299258	−	0.111685i
$94$	2.94782	+	5.10577i	0.304044	+	0.526620i
$95$	−3.01302	+	8.16409i	−0.309129	+	0.837618i
$96$	−0.250919	−	0.144868i	−0.0256094	−	0.0147856i
$97$	−6.63103	+	6.63103i	−0.673279	+	0.673279i	−0.958471	−	0.285191i	$-0.907943\pi$
$97$	−6.63103	+	6.63103i	−0.673279	+	0.673279i	0.285191	+	0.958471i	$0.407943\pi$
$98$	6.55783	−	2.44845i	0.662440	−	0.247331i
$99$		−	16.4050i		−	1.64877i
$100$	3.24817	−	3.80124i	0.324817	−	0.380124i
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.394301	−	0.918981i	$-0.370987\pi$
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.993012	+	0.118016i	$0.0376535\pi$
$102$	−0.398099	+	1.48572i	−0.0394176	+	0.147109i
$103$	18.9993	−	5.09084i	1.87206	−	0.501616i	0.872132	−	0.489271i	$-0.162737\pi$
$103$	18.9993	−	5.09084i	1.87206	−	0.501616i	0.999924	−	0.0123445i	$-0.00392947\pi$
$104$	2.02179			0.198253
$105$	−1.71245	−	0.0753683i	−0.167118	−	0.00735519i
$106$	−1.38312			−0.134340
$107$	−2.70557	+	0.724955i	−0.261557	+	0.0700840i	−0.387214	−	0.921990i	$-0.626563\pi$
$107$	−2.70557	+	0.724955i	−0.261557	+	0.0700840i	0.125657	+	0.992074i	$0.459896\pi$
$108$	−0.443641	+	1.65569i	−0.0426894	+	0.159319i
$109$	−5.11895	+	2.95543i	−0.490306	+	0.283078i	−0.724701	−	0.689063i	$-0.758022\pi$
$109$	−5.11895	+	2.95543i	−0.490306	+	0.283078i	0.234395	+	0.972141i	$0.424689\pi$
$110$	10.2721	+	7.26150i	0.979409	+	0.692356i
$111$			1.46027i			0.138602i
$112$	2.35184	+	1.21196i	0.222228	+	0.114519i
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.335697	+	0.941970i	$0.608972\pi$
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.941970	+	0.335697i	$0.891028\pi$
$114$	0.976529	+	0.563800i	0.0914604	+	0.0528047i
$115$	−1.05188	−	2.28244i	−0.0980886	−	0.212839i
$116$	−1.57751	−	2.73232i	−0.146468	−	0.253690i
$117$	−1.52590	−	5.69475i	−0.141070	−	0.526480i
$118$	−3.87385	−	3.87385i	−0.356617	−	0.356617i
$119$	2.98330	−	13.7251i	0.273478	−	1.25818i
$120$	−0.414214	−	0.498161i	−0.0378124	−	0.0454757i
$121$	−10.3246	+	17.8827i	−0.938599	+	1.62570i
$122$	4.45219	+	1.19296i	0.403082	+	0.108006i
$123$	−2.01796	−	0.540712i	−0.181954	−	0.0487543i
$124$	−1.92423	+	3.33287i	−0.172801	+	0.299300i
$125$	9.75680	−	5.45939i	0.872674	−	0.488303i
$126$	1.63871	−	7.53911i	0.145988	−	0.671637i
$127$	4.63487	+	4.63487i	0.411278	+	0.411278i	0.882184	−	0.470906i	$-0.156073\pi$
$127$	4.63487	+	4.63487i	0.411278	+	0.411278i	−0.470906	+	0.882184i	$0.656073\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	0.380390	+	0.658854i	0.0334915	+	0.0580089i
$130$	4.24124	+	1.56526i	0.371981	+	0.137282i
$131$	−6.66437	−	3.84768i	−0.582269	−	0.336173i	0.179766	−	0.983709i	$-0.442466\pi$
$131$	−6.66437	−	3.84768i	−0.582269	−	0.336173i	−0.762035	+	0.647536i	$0.775799\pi$
$132$	1.15258	−	1.15258i	0.100319	−	0.100319i
$133$	−9.15290	−	4.71670i	−0.793657	−	0.408990i
$134$			0.844985i			0.0729956i
$135$	−2.21249	+	3.12979i	−0.190421	+	0.269369i
$136$	4.59749	−	2.65436i	0.394232	−	0.227610i
$137$	−2.28687	+	8.53471i	−0.195380	+	0.729170i	0.796788	+	0.604259i	$0.206531\pi$
$137$	−2.28687	+	8.53471i	−0.195380	+	0.729170i	−0.992168	+	0.124910i	$0.960136\pi$
$138$	−0.314545	+	0.0842822i	−0.0267759	+	0.00717458i
$139$	11.0631			0.938361			0.469180	−	0.883102i	$-0.344549\pi$
$139$	11.0631			0.938361			0.469180	+	0.883102i	$0.344549\pi$
$140$	3.99532	+	4.36319i	0.337666	+	0.368757i
$141$	1.70818			0.143855
$142$	−4.61432	+	1.23640i	−0.387225	+	0.103757i
$143$	−2.94383	+	10.9865i	−0.246176	+	0.918740i
$144$	2.52538	−	1.45803i	0.210448	−	0.121502i
$145$	−1.19389	−	6.95307i	−0.0991468	−	0.577421i
$146$			5.61227i			0.464475i
$147$	0.335657	−	2.00019i	0.0276846	−	0.164973i
$148$	3.56380	−	3.56380i	0.292943	−	0.292943i
$149$	−4.37243	−	2.52443i	−0.358204	−	0.206809i	0.310089	−	0.950708i	$-0.399641\pi$
$149$	−4.37243	−	2.52443i	−0.358204	−	0.206809i	−0.668293	+	0.743899i	$0.732975\pi$
$150$	−0.483248	−	1.36571i	−0.0394571	−	0.111510i
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	−0.998479	−	0.0551270i	$-0.982444\pi$
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	0.451498	−	0.892272i	$-0.350890\pi$
$152$	−1.00727	−	3.75919i	−0.0817006	−	0.304911i
$153$	−10.9464	−	10.9464i	−0.884963	−	0.884963i
$154$	−10.0103	+	11.0154i	−0.806651	+	0.887645i
$155$	−6.61688	+	5.50184i	−0.531481	+	0.441918i
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	−1.06529	−	0.285443i	−0.0850191	−	0.0227808i	0.216059	−	0.976380i	$-0.430680\pi$
$157$	−1.06529	−	0.285443i	−0.0850191	−	0.0227808i	−0.301078	+	0.953600i	$0.597346\pi$
$158$	−6.03495	−	1.61706i	−0.480115	−	0.128646i
$159$	−0.200370	+	0.347052i	−0.0158904	+	0.0275230i
$160$	−0.204875	+	2.22666i	−0.0161968	+	0.176033i
$161$	2.83227	−	0.905902i	0.223214	−	0.0713951i
$162$	−5.83471	−	5.83471i	−0.458418	−	0.458418i
$163$	−3.42705	−	12.7899i	−0.268428	−	1.00179i	−0.960119	−	0.279592i	$-0.909801\pi$
$163$	−3.42705	−	12.7899i	−0.268428	−	1.00179i	0.691691	−	0.722193i	$-0.256866\pi$
$164$	3.60525	+	6.24448i	0.281523	+	0.487612i
$165$	3.31016	−	1.52551i	0.257695	−	0.118761i
$166$	−6.94775	−	4.01128i	−0.539250	−	0.311336i
$167$	−4.70680	+	4.70680i	−0.364223	+	0.364223i	−0.865365	−	0.501142i	$-0.832913\pi$
$167$	−4.70680	+	4.70680i	−0.364223	+	0.364223i	0.501142	+	0.865365i	$0.332913\pi$
$168$	0.644812	−	0.414548i	0.0497483	−	0.0319831i
$169$		−	8.91237i		−	0.685567i
$170$	11.6995	−	2.00887i	0.897308	−	0.154073i
$171$	−9.82827	+	5.67435i	−0.751586	+	0.433929i
$172$	0.679597	−	2.53629i	0.0518188	−	0.193390i
$173$	−6.81421	+	1.82586i	−0.518075	+	0.138818i	−0.508376	−	0.861135i	$-0.669754\pi$
$173$	−6.81421	+	1.82586i	−0.518075	+	0.138818i	−0.00969875	+	0.999953i	$0.503087\pi$
$174$	−0.914124			−0.0692996
$175$	5.00327	+	12.2461i	0.378212	+	0.925719i
$176$	−5.62576			−0.424058
$177$	−1.53322	+	0.410826i	−0.115244	+	0.0308796i
$178$	3.08559	−	11.5156i	0.231275	−	0.863129i
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	−0.426889	−	0.904304i	$-0.640391\pi$
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	0.569706	+	0.821849i	$0.307057\pi$
$180$	6.42644	−	1.10346i	0.478999	−	0.0822470i
$181$		−	4.11867i		−	0.306139i	−0.988215	−	0.153069i	$-0.951084\pi$
$181$		−	4.11867i		−	0.306139i	0.988215	−	0.153069i	$-0.0489158\pi$
$182$	−2.45032	+	4.75492i	−0.181630	+	0.352458i
$183$	0.944318	−	0.944318i	0.0698060	−	0.0698060i
$184$	0.973344	+	0.561961i	0.0717559	+	0.0414283i
$185$	10.2351	−	4.71693i	0.752499	−	0.346796i
$186$	0.557521	+	0.965654i	0.0408794	+	0.0708052i
$187$	7.72980	+	28.8480i	0.565259	+	2.10957i
$188$	−4.16885	−	4.16885i	−0.304044	−	0.304044i
$189$	−3.35625	−	3.05000i	−0.244131	−	0.221855i
$190$	0.797333	−	8.66573i	0.0578446	−	0.628678i
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	−0.366686	−	0.930345i	$-0.619508\pi$
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	0.989045	−	0.147613i	$-0.0471589\pi$
$192$	0.279864	+	0.0749894i	0.0201975	+	0.00541190i
$193$	11.6562	+	3.12327i	0.839032	+	0.224818i	0.652650	−	0.757659i	$-0.273657\pi$
$193$	11.6562	+	3.12327i	0.839032	+	0.224818i	0.186382	+	0.982477i	$0.440324\pi$
$194$	4.68885	−	8.12132i	0.336640	−	0.583077i
$195$	1.00718	−	0.837452i	0.0721254	−	0.0599712i
$196$	−5.70067	+	4.06231i	−0.407190	+	0.290165i
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.999800	+	0.0199932i	$0.00636444\pi$
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.0199932	+	0.999800i	$0.493636\pi$
$198$	4.24593	+	15.8460i	0.301745	+	1.12613i
$199$	−3.76653	−	6.52383i	−0.267002	−	0.462462i	0.701084	−	0.713079i	$-0.252700\pi$
$199$	−3.76653	−	6.52383i	−0.267002	−	0.462462i	−0.968086	+	0.250617i	$0.919367\pi$
$200$	−2.15365	+	4.51240i	−0.152286	+	0.319075i
$201$	0.212023	+	0.122412i	0.0149550	+	0.00863425i
$202$	−11.3839	+	11.3839i	−0.800965	+	0.800965i
$203$	8.33786	−	0.398585i	0.585203	−	0.0279752i
$204$		−	1.53813i		−	0.107691i
$205$	2.72852	+	15.8906i	0.190568	+	1.10985i
$206$	−17.0343	+	9.83476i	−1.18684	+	0.685220i
$207$	0.848257	−	3.16574i	0.0589579	−	0.220034i
$208$	−1.95290	+	0.523277i	−0.135409	+	0.0362827i
$209$	21.8944			1.51446
$210$	1.67361	−	0.370414i	0.115490	−	0.0255610i
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	1.33599	−	0.357978i	0.0917562	−	0.0245860i
$213$	−0.358232	+	1.33694i	−0.0245456	+	0.0916056i
$214$	2.42575	−	1.40051i	0.165821	−	0.0957366i
$215$	3.38922	−	4.79440i	0.231143	−	0.326975i
$216$		−	1.71410i		−	0.116630i
$217$	−5.50629	−	8.56478i	−0.373791	−	0.581415i
$218$	4.17960	−	4.17960i	0.283078	−	0.283078i
$219$	1.40823	+	0.813041i	0.0951593	+	0.0549402i
$220$	−11.8015	−	4.35544i	−0.795659	−	0.293644i
$221$	5.36656	+	9.29516i	0.360994	+	0.625260i
$222$	−0.377945	−	1.41051i	−0.0253660	−	0.0946672i
$223$	1.46027	+	1.46027i	0.0977867	+	0.0977867i	0.754308	−	0.656521i	$-0.227973\pi$
$223$	1.46027	+	1.46027i	0.0977867	+	0.0977867i	−0.656521	+	0.754308i	$0.727973\pi$
$224$	−2.58538	−	0.561961i	−0.172743	−	0.0375476i
$225$	14.3355	+	2.66053i	0.955698	+	0.177369i
$226$	9.60377	−	16.6342i	0.638833	−	1.10649i
$227$	−18.0081	−	4.82525i	−1.19524	−	0.320263i	−0.394283	−	0.918989i	$-0.629007\pi$
$227$	−18.0081	−	4.82525i	−1.19524	−	0.320263i	−0.800954	+	0.598726i	$0.795674\pi$
$228$	−1.08918	−	0.291844i	−0.0721325	−	0.0193278i
$229$	−2.00384	+	3.47074i	−0.132417	+	0.229353i	−0.924608	−	0.380920i	$-0.875607\pi$
$229$	−2.00384	+	3.47074i	−0.132417	+	0.229353i	0.792191	+	0.610274i	$0.208941\pi$
$230$	1.60678	+	1.93242i	0.105948	+	0.127420i
$231$	1.31380	+	4.10755i	0.0864419	+	0.270257i
$232$	2.23093	+	2.23093i	0.146468	+	0.146468i
$233$	−3.55400	−	13.2637i	−0.232830	−	0.868934i	−0.979115	−	0.203307i	$-0.934831\pi$
$233$	−3.55400	−	13.2637i	−0.232830	−	0.868934i	0.746285	−	0.665627i	$-0.231836\pi$
$234$	2.94782	+	5.10577i	0.192705	+	0.333775i
$235$	−5.51775	−	11.9728i	−0.359939	−	0.781017i
$236$	4.74448	+	2.73923i	0.308839	+	0.178308i
$237$	−1.28003	+	1.28003i	−0.0831466	+	0.0831466i
$238$	0.670673	+	14.0296i	0.0434732	+	0.909401i
$239$			19.6621i			1.27183i	0.771758	+	0.635916i	$0.219378\pi$
$239$			19.6621i			1.27183i	−0.771758	+	0.635916i	$0.780622\pi$
$240$	0.529033	+	0.373980i	0.0341489	+	0.0241403i
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	−0.655088	−	0.755552i	$-0.727369\pi$
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	0.326783	+	0.945099i	$0.394035\pi$
$242$	5.34440	−	19.9456i	0.343551	−	1.28215i
$243$	−7.27638	+	1.94970i	−0.466780	+	0.125073i
$244$	−4.60924			−0.295077
$245$	−15.1037	+	4.10834i	−0.964939	+	0.262473i
$246$	2.08915			0.133199
$247$	7.60029	−	2.03649i	0.483595	−	0.129579i
$248$	0.996056	−	3.71733i	0.0632496	−	0.236051i
$249$	−2.01302	+	1.16222i	−0.127570	+	0.0736525i
$250$	−8.01135	+	7.79861i	−0.506682	+	0.493227i
$251$		−	7.09950i		−	0.448116i	−0.974576	−	0.224058i	$-0.928069\pi$
$251$		−	7.09950i		−	0.448116i	0.974576	−	0.224058i	$-0.0719306\pi$
$252$	0.368396	+	7.70635i	0.0232068	+	0.485454i
$253$	−4.47097	+	4.47097i	−0.281088	+	0.281088i
$254$	−5.67653	−	3.27735i	−0.356177	−	0.205639i
$255$	1.19082	−	3.22665i	0.0745720	−	0.202060i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.55891	−	9.54998i	−0.159620	−	0.595711i	−0.998665	−	0.0516491i	$-0.983552\pi$
$257$	−2.55891	−	9.54998i	−0.159620	−	0.595711i	0.839045	−	0.544062i	$-0.183114\pi$
$258$	−0.537952	−	0.537952i	−0.0334915	−	0.0334915i
$259$	4.06231	+	12.7007i	0.252420	+	0.789181i
$260$	−4.50184	−	0.414214i	−0.279192	−	0.0256884i
$261$	4.60010	−	7.96760i	0.284739	−	0.493182i
$262$	7.43314	+	1.99170i	0.459221	+	0.123048i
$263$	−13.2797	−	3.55829i	−0.818861	−	0.219413i	−0.175013	−	0.984566i	$-0.555997\pi$
$263$	−13.2797	−	3.55829i	−0.818861	−	0.219413i	−0.643849	+	0.765153i	$0.722663\pi$
$264$	−0.814995	+	1.41161i	−0.0501595	+	0.0868788i
$265$	3.07974	+	0.283366i	0.189187	+	0.0174071i
$266$	10.0618	+	2.18704i	0.616929	+	0.134096i
$267$	−2.44248	−	2.44248i	−0.149477	−	0.149477i
$268$	−0.218698	−	0.816193i	−0.0133591	−	0.0498569i
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	−0.914296	−	0.405046i	$-0.867255\pi$
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	0.106368	−	0.994327i	$-0.466078\pi$
$270$	1.32705	−	3.59578i	0.0807617	−	0.218832i
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	0.124082	−	0.992272i	$-0.460401\pi$
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	−0.797292	+	0.603594i	$0.793735\pi$
$272$	−3.75384	+	3.75384i	−0.227610	+	0.227610i
$273$	0.838129	+	1.30367i	0.0507259	+	0.0789018i
$274$		−	8.83578i		−	0.533789i
$275$	−21.3849	−	18.2734i	−1.28956	−	1.10193i
$276$	0.282014	−	0.162821i	0.0169752	−	0.00980065i
$277$	5.20313	−	19.4184i	0.312626	−	1.16674i	−0.613554	−	0.789653i	$-0.710261\pi$
$277$	5.20313	−	19.4184i	0.312626	−	1.16674i	0.926180	−	0.377083i	$-0.123073\pi$
$278$	−10.6861	+	2.86334i	−0.640912	+	0.171732i
$279$	−11.2223			−0.671863
$280$	−4.98846	−	3.18046i	−0.298117	−	0.190069i
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	−1.64998	+	0.442111i	−0.0982548	+	0.0263273i
$283$	−7.00563	+	26.1454i	−0.416442	+	1.55418i	0.365489	+	0.930816i	$0.380902\pi$
$283$	−7.00563	+	26.1454i	−0.416442	+	1.55418i	−0.781930	+	0.623366i	$0.785765\pi$
$284$	4.13709	−	2.38855i	0.245491	−	0.141734i
$285$	−2.05889	−	1.45546i	−0.121958	−	0.0862139i
$286$		−	11.3741i		−	0.672564i
$287$	−19.0554	+	0.910931i	−1.12481	+	0.0537706i
$288$	−2.06196	+	2.06196i	−0.121502	+	0.121502i
$289$	9.68442	+	5.59130i	0.569672	+	0.328900i
$290$	2.95279	+	6.40715i	0.173394	+	0.376241i
$291$	−1.35853	−	2.35305i	−0.0796385	−	0.137938i
$292$	−1.45256	−	5.42104i	−0.0850048	−	0.317242i
$293$	17.1191	+	17.1191i	1.00011	+	1.00011i	1.00000		0.000106876i	$3.40197e-5\pi$
$293$	17.1191	+	17.1191i	1.00011	+	1.00011i	0.000106876		1.00000i	$0.499966\pi$
$294$	0.193467	+	2.01891i	0.0112832	+	0.117745i
$295$	7.83211	+	9.41941i	0.456003	+	0.548420i
$296$	−2.51999	+	4.36475i	−0.146471	+	0.253696i
$297$	9.31453	+	2.49582i	0.540484	+	0.144822i
$298$	4.87682	+	1.30674i	0.282506	+	0.0756974i
$299$	−1.13616	+	1.96790i	−0.0657061	+	0.113806i
$300$	0.820253	+	1.19410i	0.0473573	+	0.0689413i
$301$	5.14131	+	4.67218i	0.296340	+	0.269300i
$302$	9.50552	+	9.50552i	0.546981	+	0.546981i
$303$	1.20727	+	4.50559i	0.0693558	+	0.258840i
$304$	1.94590	+	3.37040i	0.111605	+	0.193306i
$305$	−9.66911	−	3.56846i	−0.553652	−	0.204329i
$306$	13.4065	+	7.74027i	0.766401	+	0.442482i
$307$	17.2974	−	17.2974i	0.987217	−	0.987217i	−0.0127019	−	0.999919i	$-0.504043\pi$
$307$	17.2974	−	17.2974i	0.987217	−	0.987217i	0.999919	+	0.0127019i	$0.00404326\pi$
$308$	6.81819	−	13.2309i	0.388502	−	0.753900i
$309$			5.69898i			0.324204i
$310$	4.96744	−	7.02694i	0.282131	−	0.399104i
$311$	−9.51095	+	5.49115i	−0.539316	+	0.311374i	−0.744802	−	0.667286i	$-0.767456\pi$
$311$	−9.51095	+	5.49115i	−0.539316	+	0.311374i	0.205486	+	0.978660i	$0.434123\pi$
$312$	−0.151613	+	0.565826i	−0.00858338	+	0.0320336i
$313$	28.4088	−	7.61212i	1.60576	−	0.430262i	0.658985	−	0.752156i	$-0.270986\pi$
$313$	28.4088	−	7.61212i	1.60576	−	0.430262i	0.946776	+	0.321893i	$0.104319\pi$
$314$	1.10287			0.0622383
$315$	−5.19342	+	16.4513i	−0.292616	+	0.926927i
$316$	6.24784			0.351469
$317$	−4.14766	+	1.11136i	−0.232956	+	0.0624203i	−0.373408	−	0.927667i	$-0.621811\pi$
$317$	−4.14766	+	1.11136i	−0.232956	+	0.0624203i	0.140453	+	0.990087i	$0.455144\pi$
$318$	0.103719	−	0.387086i	0.00581629	−	0.0217067i
$319$	−15.3714	+	8.87468i	−0.860633	+	0.496887i
$320$	−0.378409	−	2.20382i	−0.0211537	−	0.123197i
$321$		−	0.811556i		−	0.0452966i
$322$	−2.50129	+	1.60808i	−0.139392	+	0.0896147i
$323$	14.6092	−	14.6092i	0.812878	−	0.812878i
$324$	7.14603	+	4.12576i	0.397001	+	0.229209i
$325$	−9.12312	−	4.35423i	−0.506060	−	0.241529i
$326$	6.62056	+	11.4671i	0.366679	+	0.635106i
$327$	−0.443251	−	1.65424i	−0.0245119	−	0.0914795i
$328$	−5.09860	−	5.09860i	−0.281523	−	0.281523i
$329$	14.8569	−	4.75200i	0.819089	−	0.261986i
$330$	−2.80253	+	2.33027i	−0.154274	+	0.128277i
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.291863	+	0.956460i	$0.594275\pi$
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.682387	+	0.730991i	$0.739058\pi$
$332$	7.74921	+	2.07639i	0.425293	+	0.113957i
$333$	14.1960	+	3.80382i	0.777939	+	0.208448i
$334$	3.32821	−	5.76463i	0.182112	−	0.315426i
$335$	0.173116	−	1.88150i	0.00945835	−	0.102797i
$336$	−0.515547	+	0.567312i	−0.0281254	+	0.0309494i
$337$	−12.1473	−	12.1473i	−0.661708	−	0.661708i	0.294075	−	0.955782i	$-0.404989\pi$
$337$	−12.1473	−	12.1473i	−0.661708	−	0.661708i	−0.955782	+	0.294075i	$0.904989\pi$
$338$	2.30669	+	8.60869i	0.125468	+	0.468251i
$339$	−2.78257	−	4.81955i	−0.151128	−	0.261762i
$340$	−10.7809	+	4.96846i	−0.584675	+	0.269453i
$341$	18.7499	+	10.8253i	1.01536	+	0.586221i
$342$	8.02475	−	8.02475i	0.433929	−	0.433929i
$343$	−2.64495	−	18.3304i	−0.142814	−	0.989750i
$344$			2.62576i			0.141571i
$345$	0.717654	−	0.123226i	0.0386372	−	0.00663424i
$346$	6.10945	−	3.52729i	0.328446	−	0.189628i
$347$	2.32323	−	8.67040i	0.124717	−	0.465452i	−0.875112	−	0.483920i	$-0.839212\pi$
$347$	2.32323	−	8.67040i	0.124717	−	0.465452i	0.999829	+	0.0184687i	$0.00587911\pi$
$348$	0.882976	−	0.236593i	0.0473325	−	0.0126827i
$349$	−26.0251			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$349$	−26.0251			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$350$	−8.00231	−	10.5339i	−0.427742	−	0.563060i
$351$	3.46554			0.184977
$352$	5.43407	−	1.45605i	0.289637	−	0.0776079i
$353$	2.57944	−	9.62659i	0.137290	−	0.512372i	−0.862688	−	0.505736i	$-0.831221\pi$
$353$	2.57944	−	9.62659i	0.137290	−	0.512372i	0.999978	−	0.00663577i	$-0.00211225\pi$
$354$	1.37465	−	0.793655i	0.0730619	−	0.0421823i
$355$	10.5278	−	1.80770i	0.558760	−	0.0959425i
$356$			11.9218i			0.631855i
$357$	3.61745	+	1.86416i	0.191456	+	0.0986615i
$358$	−1.56012	+	1.56012i	−0.0824550	+	0.0824550i
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	0.740617	−	0.671928i	$-0.234533\pi$
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	−0.211598	+	0.977357i	$0.567867\pi$
$360$	−5.92187	+	2.72915i	−0.312110	+	0.143839i
$361$	1.92693	+	3.33754i	0.101417	+	0.175660i
$362$	1.06599	+	3.97833i	0.0560273	+	0.209097i
$363$	−4.23050	−	4.23050i	−0.222044	−	0.222044i
$364$	1.13616	−	5.22709i	0.0595512	−	0.273974i
$365$	1.14981	−	12.4966i	0.0601840	−	0.654104i
$366$	−0.667734	+	1.15655i	−0.0349030	+	0.0604538i
$367$	16.1256	+	4.32083i	0.841747	+	0.225545i	0.653832	−	0.756640i	$-0.273160\pi$
$367$	16.1256	+	4.32083i	0.841747	+	0.225545i	0.187915	+	0.982185i	$0.439827\pi$
$368$	−1.08562	−	0.290892i	−0.0565921	−	0.0151638i
$369$	−10.5131	+	18.2092i	−0.547290	+	0.947935i
$370$	−8.66551	+	7.20525i	−0.450499	+	0.374583i
$371$	−0.777258	+	3.57589i	−0.0403532	+	0.185651i
$372$	−0.788454	−	0.788454i	−0.0408794	−	0.0408794i
$373$	0.822767	+	3.07061i	0.0426013	+	0.158990i	0.983950	−	0.178446i	$-0.0571070\pi$
$373$	0.822767	+	3.07061i	0.0426013	+	0.158990i	−0.941348	+	0.337436i	$0.890440\pi$
$374$	−14.9328	−	25.8644i	−0.772158	−	1.33742i
$375$	0.796232	+	3.13998i	0.0411172	+	0.162148i
$376$	5.10577	+	2.94782i	0.263310	+	0.152022i
$377$	−4.51047	+	4.51047i	−0.232301	+	0.232301i
$378$	4.03129	+	2.07742i	0.207347	+	0.106851i
$379$			7.15349i			0.367450i	0.982978	+	0.183725i	$0.0588156\pi$
$379$			7.15349i			0.367450i	−0.982978	+	0.183725i	$0.941184\pi$
$380$	1.47269	+	8.57682i	0.0755475	+	0.439982i
$381$	−1.64470	+	0.949568i	−0.0842605	+	0.0486478i
$382$	−4.45229	+	16.6162i	−0.227799	+	0.850158i
$383$	−14.0961	+	3.77704i	−0.720278	+	0.192998i	−0.600296	−	0.799778i	$-0.704950\pi$
$383$	−14.0961	+	3.77704i	−0.720278	+	0.192998i	−0.119982	+	0.992776i	$0.538284\pi$
$384$	−0.289737			−0.0147856
$385$	24.5463	−	22.4767i	1.25099	−	1.14552i
$386$	−12.0674			−0.614214
$387$	7.39595	−	1.98174i	0.375957	−	0.100737i
$388$	−2.42713	+	9.05816i	−0.123219	+	0.459858i
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	−0.357750	−	0.933817i	$-0.616456\pi$
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	0.629834	+	0.776729i	$0.283123\pi$
$390$	−0.756109	+	1.06959i	−0.0382870	+	0.0541609i
$391$			5.96659i			0.301744i
$392$	4.45502	−	5.39934i	0.225012	−	0.272708i
$393$	1.57658	−	1.57658i	0.0795282	−	0.0795282i
$394$	−17.5304	−	10.1212i	−0.883167	−	0.509897i
$395$	13.1065	+	4.83706i	0.659460	+	0.243379i
$396$	−8.20251	−	14.2072i	−0.412191	−	0.713937i
$397$	0.754685	+	2.81652i	0.0378766	+	0.141357i	0.982275	−	0.187447i	$-0.0600212\pi$
$397$	0.754685	+	2.81652i	0.0378766	+	0.141357i	−0.944398	+	0.328804i	$0.893354\pi$
$398$	5.32668	+	5.32668i	0.267002	+	0.267002i
$399$	2.00641	−	2.20787i	0.100446	−	0.110532i
$400$	0.912375	−	4.91605i	0.0456187	−	0.245803i
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	−0.236481	−	0.0633649i	−0.0117946	−	0.00316035i
$403$	7.51565	+	2.01381i	0.374381	+	0.100315i
$404$	8.04960	−	13.9423i	0.400483	−	0.693656i
$405$	11.7965	+	14.1873i	0.586175	+	0.704973i
$406$	−7.95060	+	2.54300i	−0.394581	+	0.126207i
$407$	−20.0491	−	20.0491i	−0.993796	−	0.993796i
$408$	0.398099	+	1.48572i	0.0197088	+	0.0735543i
$409$	17.1791	+	29.7550i	0.849451	+	1.47129i	0.881699	+	0.471812i	$0.156400\pi$
$409$	17.1791	+	29.7550i	0.849451	+	1.47129i	−0.0322484	+	0.999480i	$0.510267\pi$
$410$	−6.74834	−	14.6430i	−0.333277	−	0.723165i
$411$	−2.21707	−	1.28003i	−0.109360	−	0.0631390i
$412$	13.9084	−	13.9084i	0.685220	−	0.685220i
$413$	−12.1923	+	7.83843i	−0.599946	+	0.385704i
$414$			3.27741i			0.161076i
$415$	14.6485	+	10.3552i	0.719065	+	0.508317i
$416$	1.75092	−	1.01089i	0.0858459	−	0.0495631i
$417$	−0.829616	+	3.09617i	−0.0406265	+	0.151620i
$418$	−21.1483	+	5.66668i	−1.03440	+	0.277166i
$419$	−31.1360			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$419$	−31.1360			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$420$	−1.52071	+	0.790953i	−0.0742030	+	0.0385946i
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	−18.9095	+	5.06679i	−0.920501	+	0.246648i
$423$	4.44962	−	16.6062i	0.216348	−	0.807421i
$424$	−1.19782	+	0.691560i	−0.0581711	+	0.0335851i
$425$	−26.4623	+	2.07615i	−1.28361	+	0.100708i
$426$		−	1.38410i		−	0.0670599i
$427$	5.58621	−	10.8402i	0.270336	−	0.524594i
$428$	−1.98061	+	1.98061i	−0.0957366	+	0.0957366i
$429$	−2.85398	−	1.64775i	−0.137792	−	0.0795540i
$430$	−2.03285	+	5.50823i	−0.0980330	+	0.265630i
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	0.987141	−	0.159849i	$-0.0511008\pi$
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	−0.632004	+	0.774965i	$0.717767\pi$
$432$	0.443641	+	1.65569i	0.0213447	+	0.0796595i
$433$	−9.98256	−	9.98256i	−0.479731	−	0.479731i	0.425315	−	0.905046i	$-0.360163\pi$
$433$	−9.98256	−	9.98256i	−0.479731	−	0.479731i	−0.905046	+	0.425315i	$0.860163\pi$
$434$	7.53539	+	6.84781i	0.361710	+	0.328706i
$435$	2.03545	+	0.187281i	0.0975922	+	0.00897944i
$436$	−2.95543	+	5.11895i	−0.141539	+	0.245153i
$437$	4.22504	+	1.13210i	0.202111	+	0.0541555i
$438$	−1.57067	−	0.420861i	−0.0750498	−	0.0201095i
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.113167	−	0.993576i	$-0.463900\pi$
$439$	19.2142	−	33.2800i	0.917046	−	1.58837i	0.803878	−	0.594794i	$-0.202766\pi$
$440$	12.5267	+	1.15258i	0.597186	+	0.0549470i
$441$	−18.5706	−	8.47336i	−0.884314	−	0.403494i
$442$	−7.58946	−	7.58946i	−0.360994	−	0.360994i
$443$	1.48448	+	5.54016i	0.0705299	+	0.263221i	0.992183	−	0.124795i	$-0.0398272\pi$
$443$	1.48448	+	5.54016i	0.0705299	+	0.263221i	−0.921653	+	0.388016i	$0.873161\pi$
$444$	0.730133	+	1.26463i	0.0346506	+	0.0600166i
$445$	−9.22982	+	25.0092i	−0.437536	+	1.18555i
$446$	−1.78845	−	1.03256i	−0.0846857	−	0.0488933i
$447$	1.03438	−	1.03438i	0.0489247	−	0.0489247i
$448$	2.64273	−	0.126334i	0.124857	−	0.00596872i
$449$			7.30267i			0.344635i	0.985042	+	0.172317i	$0.0551254\pi$
$449$			7.30267i			0.344635i	−0.985042	+	0.172317i	$0.944875\pi$
$450$	−14.5356	+	1.14042i	−0.685215	+	0.0537597i
$451$	35.1299	−	20.2823i	1.65420	−	0.955055i
$452$	−4.97128	+	18.5531i	−0.233829	+	0.872663i
$453$	3.76217	−	1.00807i	0.176762	−	0.0473633i
$454$	18.6433			0.874974
$455$	6.43021	−	10.0856i	0.301453	−	0.472820i
$456$	1.12760			0.0528047
$457$	−4.97047	+	1.33183i	−0.232509	+	0.0623006i	−0.373192	−	0.927754i	$-0.621737\pi$
$457$	−4.97047	+	1.33183i	−0.232509	+	0.0623006i	0.140683	+	0.990055i	$0.455070\pi$
$458$	1.03726	−	3.87111i	0.0484680	−	0.180885i
$459$	7.88056	−	4.54984i	0.367833	−	0.212368i
$460$	−2.05218	−	1.45071i	−0.0956833	−	0.0676397i
$461$		−	29.4110i		−	1.36981i	−0.728634	−	0.684903i	$-0.759845\pi$
$461$		−	29.4110i		−	1.36981i	0.728634	−	0.684903i	$-0.240155\pi$
$462$	−2.33215	−	3.62755i	−0.108501	−	0.168769i
$463$	−4.04625	+	4.04625i	−0.188045	+	0.188045i	−0.794851	−	0.606805i	$-0.792451\pi$
$463$	−4.04625	+	4.04625i	−0.188045	+	0.188045i	0.606805	+	0.794851i	$0.292451\pi$
$464$	−2.73232	−	1.57751i	−0.126845	−	0.0732340i
$465$	−1.04357	−	2.26441i	−0.0483945	−	0.105009i
$466$	6.86580	+	11.8919i	0.318052	+	0.550882i
$467$	4.30747	+	16.0757i	0.199326	+	0.743894i	0.991105	+	0.133086i	$0.0424886\pi$
$467$	4.30747	+	16.0757i	0.199326	+	0.743894i	−0.791779	+	0.610808i	$0.790845\pi$
$468$	−4.16885	−	4.16885i	−0.192705	−	0.192705i
$469$	2.18461	+	0.474848i	0.100876	+	0.0219264i
$470$	8.42852	+	10.1367i	0.388779	+	0.467571i
$471$	0.159770	−	0.276731i	0.00736184	−	0.0127511i
$472$	−5.29178	−	1.41793i	−0.243574	−	0.0652654i
$473$	−14.2686	−	3.82325i	−0.656069	−	0.175793i
$474$	0.905115	−	1.56771i	0.0415733	−	0.0720071i
$475$	−3.55078	+	19.1323i	−0.162921	+	0.877851i
$476$	−4.27894	−	13.3779i	−0.196125	−	0.613176i
$477$	2.85194	+	2.85194i	0.130581	+	0.130581i
$478$	−5.08891	−	18.9921i	−0.232762	−	0.868678i
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	0.986526	−	0.163607i	$-0.0523128\pi$
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	−0.634950	+	0.772553i	$0.718979\pi$
$480$	−0.607800	−	0.224313i	−0.0277421	−	0.0102385i
$481$	−8.82459	−	5.09488i	−0.402367	−	0.232306i
$482$	4.16141	−	4.16141i	0.189547	−	0.189547i
$483$	0.0411396	+	0.860583i	0.00187191	+	0.0391579i
$484$			20.6492i			0.938599i
$485$	−12.1043	+	17.1228i	−0.549629	+	0.777507i
$486$	6.52383	−	3.76653i	0.295927	−	0.170853i
$487$	−9.31541	+	34.7656i	−0.422122	+	1.57538i	0.348007	+	0.937492i	$0.386858\pi$
$487$	−9.31541	+	34.7656i	−0.422122	+	1.57538i	−0.770129	+	0.637888i	$0.779808\pi$
$488$	4.45219	−	1.19296i	0.201541	−	0.0540028i
$489$	3.83644			0.173490
$490$	13.5257	−	7.87748i	0.611030	−	0.355868i
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	−2.01796	+	0.540712i	−0.0909768	+	0.0243772i
$493$	−4.33499	+	16.1784i	−0.195238	+	0.728639i
$494$	−6.81423	+	3.93420i	−0.306587	+	0.177008i
$495$	−6.20780	−	36.1536i	−0.279020	−	1.62499i
$496$			3.84846i			0.172801i
$497$	0.603509	+	12.6246i	0.0270711	+	0.566290i
$498$	1.64362	−	1.64362i	0.0736525	−	0.0736525i
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.258630	−	0.965976i	$-0.583271\pi$
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.965875	+	0.259008i	$0.916604\pi$
$500$	5.71994	−	9.60637i	0.255803	−	0.429610i
$501$	−0.964305	−	1.67023i	−0.0430820	−	0.0746202i
$502$	1.83749	+	6.85759i	0.0820110	+	0.306069i
$503$	16.9777	+	16.9777i	0.756997	+	0.756997i	0.975775	−	0.218778i	$-0.0702070\pi$
$503$	16.9777	+	16.9777i	0.756997	+	0.756997i	−0.218778	+	0.975775i	$0.570207\pi$
$504$	−2.35039	−	7.34841i	−0.104695	−	0.327324i
$505$	27.6803	−	23.0157i	1.23176	−	1.02419i
$506$	3.16146	−	5.47580i	0.140544	−	0.243429i
$507$	2.49426	+	0.668334i	0.110774	+	0.0296817i
$508$	6.33135	+	1.69648i	0.280908	+	0.0752691i
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	−0.522848	−	0.852426i	$-0.675130\pi$
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	0.999647	+	0.0265865i	$0.00846373\pi$
$510$	−0.315125	+	3.42491i	−0.0139540	+	0.151657i
$511$	14.5099	+	3.15388i	0.641879	+	0.139519i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.72657	−	6.44363i	−0.0762297	−	0.284493i
$514$	4.94343	+	8.56228i	0.218045	+	0.377666i
$515$	39.9445	−	18.4088i	1.76017	−	0.811188i
$516$	0.658854	+	0.380390i	0.0290044	+	0.0167457i
$517$	−23.4529	+	23.4529i	−1.03146	+	1.03146i
$518$	−7.21107	−	11.2165i	−0.316836	−	0.492825i
$519$		−	2.04397i		−	0.0897205i
$520$	4.45565	−	0.765062i	0.195393	−	0.0335502i
$521$	11.4657	−	6.61973i	0.502322	−	0.290016i	−0.227350	−	0.973813i	$-0.573006\pi$
$521$	11.4657	−	6.61973i	0.502322	−	0.290016i	0.729672	+	0.683798i	$0.239673\pi$
$522$	−2.38118	+	8.88670i	−0.104222	+	0.388960i
$523$	−26.0126	+	6.97006i	−1.13745	+	0.304779i	−0.777926	−	0.628356i	$-0.783728\pi$
$523$	−26.0126	+	6.97006i	−1.13745	+	0.304779i	−0.359526	+	0.933135i	$0.617062\pi$
$524$	−7.69535			−0.336173
$525$	−3.80244	+	0.481908i	−0.165952	+	0.0210322i
$526$	13.7482			0.599448
$527$	19.7343	−	5.28779i	0.859640	−	0.230340i
$528$	0.421872	−	1.57445i	0.0183596	−	0.0685191i
$529$	18.8246	−	10.8684i	0.818462	−	0.472539i
$530$	−3.04814	+	0.523384i	−0.132403	+	0.0227344i
$531$			15.9755i			0.693276i
$532$	−10.2850	+	0.491667i	−0.445911	+	0.0213165i
$533$	10.3083	−	10.3083i	0.446501	−	0.446501i
$534$	2.99141	+	1.72709i	0.129451	+	0.0747386i
$535$	−5.68825	+	2.62148i	−0.245924	+	0.113336i
$536$	0.422492	+	0.731778i	0.0182489	+	0.0316080i
$537$	0.165453	+	0.617477i	0.00713980	+	0.0266461i
$538$	18.7398	+	18.7398i	0.807928	+	0.807928i
$539$	22.8536	+	32.0706i	0.984374	+	1.38138i
$540$	−0.351176	+	3.81672i	−0.0151122	+	0.164245i
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$	12.3608	+	3.31208i	0.530943	+	0.142266i
$543$	1.15267	+	0.308857i	0.0494658	+	0.0132543i
$544$	2.65436	−	4.59749i	0.113805	−	0.197116i
$545$	−10.1629	+	8.45027i	−0.435329	+	0.361970i
$546$	−1.14699	−	1.04233i	−0.0490864	−	0.0446075i
$547$	−30.9149	−	30.9149i	−1.32182	−	1.32182i	−0.912298	−	0.409527i	$-0.865694\pi$
$547$	−30.9149	−	30.9149i	−1.32182	−	1.32182i	−0.409527	−	0.912298i	$-0.634306\pi$
$548$	2.28687	+	8.53471i	0.0976902	+	0.364585i
$549$	−6.72040	−	11.6401i	−0.286820	−	0.496786i
$550$	25.3857	+	12.1159i	1.08245	+	0.516625i
$551$	10.6337	+	6.13935i	0.453009	+	0.261545i
$552$	−0.230263	+	0.230263i	−0.00980065	+	0.00980065i
$553$	−7.57212	+	14.6939i	−0.321999	+	0.624850i
$554$			20.1034i			0.854110i
$555$	0.552577	+	3.21816i	0.0234556	+	0.136603i
$556$	9.58094	−	5.53156i	0.406322	−	0.234590i
$557$	−6.83277	+	25.5003i	−0.289514	+	1.08048i	0.655963	+	0.754793i	$0.272263\pi$
$557$	−6.83277	+	25.5003i	−0.289514	+	1.08048i	−0.945477	+	0.325688i	$0.894404\pi$
$558$	10.8399	−	2.90455i	0.458891	−	0.122959i
$559$	−5.30873			−0.224535
$560$	5.64164	+	1.78098i	0.238403	+	0.0752600i
$561$	−8.65318			−0.365337
$562$	13.6677	−	3.66224i	0.576536	−	0.154482i
$563$	5.22648	−	19.5055i	0.220270	−	0.822058i	−0.763975	−	0.645246i	$-0.776755\pi$
$563$	5.22648	−	19.5055i	0.220270	−	0.822058i	0.984245	−	0.176812i	$-0.0565784\pi$
$564$	1.47933	−	0.854092i	0.0622911	−	0.0359638i
$565$	−24.7923	+	35.0712i	−1.04302	+	1.47546i
$566$		−	27.0677i		−	1.13774i
$567$	−18.3638	+	11.8061i	−0.771208	+	0.495808i
$568$	−3.37792	+	3.37792i	−0.141734	+	0.141734i
$569$	21.4890	+	12.4067i	0.900867	+	0.520116i	0.877481	−	0.479611i	$-0.159222\pi$
$569$	21.4890	+	12.4067i	0.900867	+	0.520116i	0.0233856	+	0.999727i	$0.492555\pi$
$570$	2.36544	+	0.872983i	0.0990773	+	0.0365653i
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	0.814116	−	0.580703i	$-0.197222\pi$
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$572$	2.94383	+	10.9865i	0.123088	+	0.459370i
$573$	3.52433	+	3.52433i	0.147231	+	0.147231i
$574$	18.1704	−	5.81180i	0.758417	−	0.242580i
$575$	−3.18185	−	4.63204i	−0.132692	−	0.193169i
$576$	1.45803	−	2.52538i	0.0607511	−	0.105224i
$577$	−19.1065	−	5.11957i	−0.795414	−	0.213131i	−0.161845	−	0.986816i	$-0.551744\pi$
$577$	−19.1065	−	5.11957i	−0.795414	−	0.213131i	−0.633570	+	0.773686i	$0.718411\pi$
$578$	−10.8016	−	2.89427i	−0.449286	−	0.120386i
$579$	−1.74818	+	3.02794i	−0.0726520	+	0.125837i
$580$	−4.51047	−	5.42460i	−0.187287	−	0.225244i
$581$	−14.2751	+	15.7084i	−0.592229	+	0.651694i
$582$	1.92125	+	1.92125i	0.0796385	+	0.0796385i
$583$	−2.01390	−	7.51596i	−0.0834071	−	0.311279i
$584$	2.80614	+	4.86037i	0.116119	+	0.201124i
$585$	−5.51775	−	11.9728i	−0.228131	−	0.495013i
$586$	−20.9665	−	12.1050i	−0.866118	−	0.500053i
$587$	19.3782	−	19.3782i	0.799824	−	0.799824i	−0.183244	−	0.983068i	$-0.558660\pi$
$587$	19.3782	−	19.3782i	0.799824	−	0.799824i	0.983068	+	0.183244i	$0.0586597\pi$
$588$	−0.709407	−	1.90004i	−0.0292555	−	0.0783565i
$589$		−	14.9775i		−	0.617136i
$590$	−10.0032	−	7.07136i	−0.411823	−	0.291123i
$591$	−5.07919	+	2.93247i	−0.208930	+	0.120626i
$592$	1.30444	−	4.86824i	0.0536122	−	0.200083i
$593$	3.12741	−	0.837988i	0.128428	−	0.0344121i	−0.194033	−	0.980995i	$-0.562157\pi$
$593$	3.12741	−	0.837988i	0.128428	−	0.0344121i	0.322460	+	0.946583i	$0.395490\pi$
$594$	−9.64311			−0.395661
$595$	1.38094	−	31.3765i	0.0566131	−	1.28631i
$596$	−5.04885			−0.206809
$597$	2.10824	−	0.564900i	0.0862844	−	0.0231198i
$598$	0.588122	−	2.19490i	0.0240501	−	0.0897562i
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	−0.355543	−	0.934660i	$-0.615704\pi$
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	0.631668	+	0.775239i	$0.282371\pi$
$600$	−1.10136	−	0.941113i	−0.0449628	−	0.0384208i
$601$		−	31.7170i		−	1.29377i	−0.762590	−	0.646883i	$-0.776072\pi$
$601$		−	31.7170i		−	1.29377i	0.762590	−	0.646883i	$-0.223928\pi$
$602$	−6.17537	−	3.18231i	−0.251689	−	0.129701i
$603$	1.74233	−	1.74233i	0.0709530	−	0.0709530i
$604$	−11.6418	−	6.72142i	−0.473699	−	0.273491i
$605$	−15.9865	+	43.3171i	−0.649945	+	1.76109i
$606$	−2.33227	−	4.03960i	−0.0947418	−	0.164098i
$607$	0.199219	+	0.743495i	0.00808604	+	0.0301775i	0.969851	−	0.243699i	$-0.0783608\pi$
$607$	0.199219	+	0.743495i	0.00808604	+	0.0301775i	−0.961765	+	0.273876i	$0.911694\pi$
$608$	−2.75192	−	2.75192i	−0.111605	−	0.111605i
$609$	−0.513702	+	2.36336i	−0.0208162	+	0.0957682i
$610$	10.2632	+	0.944318i	0.415546	+	0.0382343i
$611$	−5.95987	+	10.3228i	−0.241110	+	0.417615i
$612$	−14.9530	−	4.00666i	−0.604441	−	0.161960i
$613$	−33.8086	−	9.05898i	−1.36552	−	0.365889i	−0.499676	−	0.866212i	$-0.666548\pi$
$613$	−33.8086	−	9.05898i	−1.36552	−	0.365889i	−0.865839	+	0.500323i	$0.833214\pi$
$614$	−12.2311	+	21.1850i	−0.493609	+	0.854955i
$615$	−4.65183	−	0.428014i	−0.187580	−	0.0172592i
$616$	−3.16146	+	14.5447i	−0.127379	+	0.586024i
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	0.992159	−	0.124980i	$-0.0398866\pi$
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	−0.124980	+	0.992159i	$0.539887\pi$
$618$	−1.47501	−	5.50479i	−0.0593334	−	0.221435i
$619$	−21.6707	−	37.5348i	−0.871021	−	1.50865i	−0.860942	−	0.508703i	$-0.830125\pi$
$619$	−21.6707	−	37.5348i	−0.871021	−	1.50865i	−0.0100783	−	0.999949i	$-0.503208\pi$
$620$	−2.97947	+	8.07317i	−0.119658	+	0.324226i
$621$	1.66841	+	0.963256i	0.0669509	+	0.0386541i
$622$	7.76566	−	7.76566i	0.311374	−	0.311374i
$623$	−28.0382	−	14.4487i	−1.12333	−	0.578876i
$624$		−	0.585786i		−	0.0234502i
$625$	19.4363	−	15.7235i	0.777452	−	0.628942i
$626$	−25.4707	+	14.7055i	−1.01801	+	0.587749i
$627$	−1.64184	+	6.12745i	−0.0655690	+	0.244707i
$628$	−1.06529	+	0.285443i	−0.0425096	+	0.0113904i
$629$	−26.7559			−1.06683
$630$	0.758543	−	17.2349i	0.0302211	−	0.686655i
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	−6.03495	+	1.61706i	−0.240058	+	0.0643232i
$633$	−1.46804	+	5.47879i	−0.0583492	+	0.217762i
$634$	3.71869	−	2.14699i	0.147688	−	0.0852677i
$635$	11.9683	+	8.46052i	0.474946	+	0.335746i
$636$			0.400741i			0.0158904i
$637$	10.9163	+	9.00710i	0.432520	+	0.356874i
$638$	12.5507	−	12.5507i	0.496887	−	0.496887i
$639$	12.0640	+	6.96513i	0.477243	+	0.275536i
$640$	0.935904	+	2.03078i	0.0369949	+	0.0802738i
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	0.519233	−	0.854633i	$-0.326218\pi$
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	−0.999750	+	0.0223521i	$0.992885\pi$
$642$	0.210046	+	0.783903i	0.00828986	+	0.0309382i
$643$	−6.21713	−	6.21713i	−0.245180	−	0.245180i	0.573809	−	0.818989i	$-0.305465\pi$
$643$	−6.21713	−	6.21713i	−0.245180	−	0.245180i	−0.818989	+	0.573809i	$0.805465\pi$
$644$	1.99986	−	2.20067i	0.0788057	−	0.0867184i
$645$	1.08763	+	1.30805i	0.0428252	+	0.0515045i
$646$	−10.3303	+	17.8925i	−0.406439	+	0.703973i
$647$	19.9243	+	5.33869i	0.783304	+	0.209886i	0.628241	−	0.778019i	$-0.283775\pi$
$647$	19.9243	+	5.33869i	0.783304	+	0.209886i	0.155063	+	0.987905i	$0.450442\pi$
$648$	−7.97036	−	2.13565i	−0.313105	−	0.0838963i
$649$	15.4102	−	26.6913i	0.604905	−	1.04773i
$650$	9.93921	+	1.84463i	0.389848	+	0.0723523i
$651$	2.80989	−	0.898745i	0.110128	−	0.0352246i
$652$	−9.36288	−	9.36288i	−0.366679	−	0.366679i
$653$	6.76544	+	25.2490i	0.264752	+	0.988069i	0.962402	+	0.271630i	$0.0875625\pi$
$653$	6.76544	+	25.2490i	0.264752	+	0.988069i	−0.697650	+	0.716439i	$0.745771\pi$
$654$	0.856296	+	1.48315i	0.0334838	+	0.0579957i
$655$	−16.1430	−	5.95772i	−0.630761	−	0.232787i
$656$	6.24448	+	3.60525i	0.243806	+	0.140761i
$657$	11.5723	−	11.5723i	0.451478	−	0.451478i
$658$	−13.1208	+	8.43533i	−0.511502	+	0.328844i
$659$			24.2448i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$659$			24.2448i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$660$	2.10392	−	2.97621i	0.0818951	−	0.115849i
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	−0.166583	−	0.986027i	$-0.553273\pi$
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	0.770633	+	0.637279i	$0.219940\pi$
$662$	9.17510	−	34.2419i	0.356600	−	1.33085i
$663$	−3.00382	+	0.804871i	−0.116659	+	0.0312586i
$664$	−8.02257			−0.311336
$665$	−21.9562	−	6.93121i	−0.851423	−	0.268781i
$666$	−14.6968			−0.569491
$667$	−3.42516	+	0.917769i	−0.132623	+	0.0355362i
$668$	−1.72281	+	6.42961i	−0.0666574	+	0.248769i
$669$	−0.518181	+	0.299172i	−0.0200340	+	0.0115667i
$670$	0.319750	+	1.86219i	0.0123530	+	0.0719427i
$671$			25.9305i			1.00104i
$672$	0.351149	−	0.681415i	0.0135459	−	0.0262862i
$673$	−4.85386	+	4.85386i	−0.187103	+	0.187103i	−0.794442	−	0.607340i	$-0.792237\pi$
$673$	−4.85386	+	4.85386i	−0.187103	+	0.187103i	0.607340	+	0.794442i	$0.292237\pi$
$674$	14.8774	+	8.58946i	0.573056	+	0.330854i
$675$	−3.69158	+	7.73470i	−0.142089	+	0.297709i
$676$	−4.45619	−	7.71834i	−0.171392	−	0.296859i
$677$	−4.78306	−	17.8506i	−0.183828	−	0.686055i	−0.994878	−	0.101079i	$-0.967771\pi$
$677$	−4.78306	−	17.8506i	−0.183828	−	0.686055i	0.811051	−	0.584976i	$-0.198896\pi$
$678$	3.93514	+	3.93514i	0.151128	+	0.151128i
$679$	−18.3618	−	16.6863i	−0.704660	−	0.640362i
$680$	9.12760	−	7.58946i	0.350027	−	0.291043i
$681$	2.70083	−	4.67797i	0.103496	−	0.179260i
$682$	−20.9128	−	5.60357i	−0.800793	−	0.214572i
$683$	25.8878	+	6.93661i	0.990569	+	0.265422i	0.717489	−	0.696569i	$-0.245291\pi$
$683$	25.8878	+	6.93661i	0.990569	+	0.265422i	0.273079	+	0.961992i	$0.411958\pi$
$684$	−5.67435	+	9.82827i	−0.216964	+	0.375793i
$685$	−1.81023	+	19.6743i	−0.0691653	+	0.751717i
$686$	7.29908	+	17.0213i	0.278680	+	0.649875i
$687$	−0.821071	−	0.821071i	−0.0313258	−	0.0313258i
$688$	−0.679597	−	2.53629i	−0.0259094	−	0.0966951i
$689$	−1.39819	−	2.42173i	−0.0532667	−	0.0922606i
$690$	−0.661307	+	0.304769i	−0.0251755	+	0.0116024i
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.895492	−	0.445077i	$-0.146824\pi$
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.0622976	+	0.998058i	$0.480157\pi$
$692$	−4.98835	+	4.98835i	−0.189628	+	0.189628i
$693$	43.3541	−	2.07251i	1.64689	−	0.0787281i
$694$			8.97626i			0.340734i
$695$	24.3811	−	4.18638i	0.924827	−	0.158798i
$696$	−0.791655	+	0.457062i	−0.0300076	+	0.0173249i
$697$	9.90723	−	36.9743i	0.375263	−	1.40050i
$698$	25.1383	−	6.73580i	0.951500	−	0.254954i
$699$	3.97855			0.150483
$700$	10.4560	+	8.10381i	0.395200	+	0.306295i
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	−3.34746	+	0.896949i	−0.126342	+	0.0338531i
$703$	−5.07663	+	18.9462i	−0.191469	+	0.714571i
$704$	−4.87205	+	2.81288i	−0.183622	+	0.106014i
$705$	3.76452	−	0.646392i	0.141780	−	0.0243445i
$706$			9.96618i			0.375082i
$707$	23.0343	+	35.8289i	0.866295	+	1.34748i
$708$	−1.12240	+	1.12240i	−0.0421823	+	0.0421823i
$709$	−27.1994	−	15.7036i	−1.02150	−	0.589760i	−0.106958	−	0.994263i	$-0.534111\pi$
$709$	−27.1994	−	15.7036i	−1.02150	−	0.589760i	−0.914537	+	0.404503i	$0.867445\pi$
$710$	−9.70125	+	4.47091i	−0.364081	+	0.167790i
$711$	9.10952	+	15.7781i	0.341634	+	0.591727i
$712$	−3.08559	−	11.5156i	−0.115637	−	0.431565i
$713$	3.05850	+	3.05850i	0.114542	+	0.114542i
$714$	−3.97667	−	0.864371i	−0.148823	−	0.0323483i
$715$	−2.33027	+	25.3263i	−0.0871470	+	0.947149i
$716$	1.10317	−	1.91075i	0.0412275	−	0.0714081i
$717$	−5.50271	−	1.47445i	−0.205502	−	0.0550642i
$718$	−11.1797	−	2.99560i	−0.417224	−	0.111795i
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	−0.949001	−	0.315273i	$-0.897904\pi$
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	0.747535	+	0.664222i	$0.231237\pi$
$720$	5.01373	−	4.16885i	0.186851	−	0.155364i
$721$	15.8540	+	49.5669i	0.590434	+	1.84597i
$722$	−2.72509	−	2.72509i	−0.101417	−	0.101417i
$723$	−0.441322	−	1.64704i	−0.0164129	−	0.0612539i
$724$	−2.05934	−	3.56688i	−0.0765347	−	0.132562i
$725$	−5.26221	−	14.8715i	−0.195433	−	0.552315i
$726$	5.18128	+	2.99141i	0.192295	+	0.111022i
$727$	33.6108	−	33.6108i	1.24656	−	1.24656i	0.289326	−	0.957231i	$-0.406569\pi$
$727$	33.6108	−	33.6108i	1.24656	−	1.24656i	0.957231	−	0.289326i	$-0.0934311\pi$
$728$	0.255420	+	5.34305i	0.00946651	+	0.198026i
$729$			22.5720i			0.835998i
$730$	2.12373	+	12.3684i	0.0786029	+	0.457776i
$731$	−12.0719	+	6.96972i	−0.446496	+	0.257785i
$732$	0.345644	−	1.28996i	0.0127754	−	0.0476784i
$733$	24.8800	−	6.66658i	0.918964	−	0.246236i	0.231822	−	0.972758i	$-0.425531\pi$
$733$	24.8800	−	6.66658i	0.918964	−	0.246236i	0.687143	+	0.726523i	$0.258865\pi$
$734$	−16.6944			−0.616202
$735$	−0.0171620	−	4.53507i	−0.000633031	−	0.167278i
$736$	1.12392			0.0414283
$737$	−4.59170	+	1.23034i	−0.169138	+	0.0453203i
$738$	5.44198	−	20.3098i	0.200322	−	0.747613i
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	−0.294392	−	0.955685i	$-0.595117\pi$
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	0.680451	+	0.732793i	$0.261784\pi$
$740$	6.50539	−	9.20253i	0.239143	−	0.338292i
$741$			2.27977i			0.0837493i
$742$	−0.174735	−	3.65522i	−0.00641472	−	0.134187i
$743$	23.2618	−	23.2618i	0.853393	−	0.853393i	−0.137157	−	0.990549i	$-0.543796\pi$
$743$	23.2618	−	23.2618i	0.853393	−	0.853393i	0.990549	+	0.137157i	$0.0437964\pi$
$744$	0.965654	+	0.557521i	0.0354026	+	0.0204397i
$745$	−10.5913	−	3.90881i	−0.388036	−	0.143208i
$746$	−1.58946	−	2.75303i	−0.0581944	−	0.100796i
$747$	6.05487	+	22.5971i	0.221536	+	0.826784i
$748$	21.1182	+	21.1182i	0.772158	+	0.772158i
$749$	−2.25767	−	7.05851i	−0.0824934	−	0.257912i
$750$	−1.58179	−	2.82690i	−0.0577587	−	0.103224i
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	−0.964903	−	0.262607i	$-0.915418\pi$
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	0.709875	+	0.704327i	$0.248751\pi$
$752$	−5.69475	−	1.52590i	−0.207666	−	0.0556440i
$753$	1.98690	+	0.532387i	0.0724065	+	0.0194013i
$754$	3.18939	−	5.52418i	0.116151	−	0.201179i
$755$	−19.2181	−	23.1130i	−0.699420	−	0.841169i
$756$	−4.43160	−	0.963256i	−0.161176	−	0.0350333i
$757$	17.5547	+	17.5547i	0.638036	+	0.638036i	0.950071	−	0.312035i	$-0.101010\pi$
$757$	17.5547	+	17.5547i	0.638036	+	0.638036i	−0.312035	+	0.950071i	$0.601010\pi$
$758$	−1.85146	−	6.90974i	−0.0672481	−	0.250973i
$759$	−0.915990	−	1.58654i	−0.0332483	−	0.0575878i
$760$	−3.64236	−	7.90341i	−0.132122	−	0.286687i
$761$	18.9372	+	10.9334i	0.686471	+	0.396334i	0.802289	−	0.596936i	$-0.203615\pi$
$761$	18.9372	+	10.9334i	0.686471	+	0.396334i	−0.115817	+	0.993271i	$0.536949\pi$
$762$	1.34289	−	1.34289i	0.0486478	−	0.0486478i
$763$	−8.45710	−	13.1546i	−0.306168	−	0.476230i
$764$		−	17.2023i		−	0.622359i
$765$	−28.2660	−	19.9816i	−1.02196	−	0.722437i
$766$	12.6382	−	7.29669i	0.456638	−	0.263640i
$767$	2.86675	−	10.6989i	0.103512	−	0.386313i
$768$	0.279864	−	0.0749894i	0.0100987	−	0.00270595i
$769$	31.0506			1.11971			0.559857	−	0.828589i	$-0.310856\pi$
$769$	31.0506			1.11971			0.559857	+	0.828589i	$0.310856\pi$
$770$	−17.8925	+	28.0639i	−0.644800	+	1.01135i
$771$	2.86459			0.103166
$772$	11.6562	−	3.12327i	0.419516	−	0.112409i
$773$	−1.57065	+	5.86173i	−0.0564922	+	0.210832i	−0.988402	−	0.151857i	$-0.951475\pi$
$773$	−1.57065	+	5.86173i	−0.0564922	+	0.210832i	0.931910	+	0.362689i	$0.118141\pi$
$774$	−6.63103	+	3.82843i	−0.238347	+	0.137610i
$775$	−12.5004	+	14.6289i	−0.449029	+	0.525487i
$776$		−	9.37769i		−	0.336640i
$777$	−3.85909	+	0.184481i	−0.138444	+	0.00661822i
$778$	−4.38160	+	4.38160i	−0.157088	+	0.157088i
$779$	−24.3023	−	14.0309i	−0.870720	−	0.502710i
$780$	0.453514	−	1.22884i	0.0162384	−	0.0439996i
$781$	−13.4374	−	23.2743i	−0.480828	−	0.832819i
$782$	−1.54427	−	5.76329i	−0.0552229	−	0.206095i
$783$	3.82404	+	3.82404i	0.136660	+	0.136660i
$784$	−2.90577	+	6.36840i	−0.103777	+	0.227443i
$785$	−2.45571	−	0.225950i	−0.0876481	−	0.00806449i
$786$	−1.11481	+	1.93091i	−0.0397641	+	0.0688734i
$787$	−21.5993	−	5.78752i	−0.769932	−	0.206303i	−0.147591	−	0.989049i	$-0.547152\pi$
$787$	−21.5993	−	5.78752i	−0.769932	−	0.206303i	−0.622342	+	0.782746i	$0.713818\pi$
$788$	19.5526	+	5.23910i	0.696532	+	0.186635i
$789$	1.99167	−	3.44968i	0.0709055	−	0.122812i
$790$	−13.9118	−	1.28003i	−0.494961	−	0.0455413i
$791$	−37.6089	−	34.1772i	−1.33722	−	1.21520i
$792$	11.6001	+	11.6001i	0.412191	+	0.412191i
$793$	2.41191	+	9.00138i	0.0856495	+	0.319648i
$794$	−1.45794	−	2.52523i	−0.0517403	−	0.0896169i
$795$	−0.310252	+	0.840660i	−0.0110035	+	0.0298151i
$796$	−6.52383	−	3.76653i	−0.231231	−	0.133501i
$797$	16.5528	−	16.5528i	0.586330	−	0.586330i	−0.350305	−	0.936636i	$-0.613922\pi$
$797$	16.5528	−	16.5528i	0.586330	−	0.586330i	0.936636	+	0.350305i	$0.113922\pi$
$798$	−1.36660	+	2.65193i	−0.0483772	+	0.0938774i
$799$			31.2984i			1.10726i
$800$	0.391082	+	4.98468i	0.0138268	+	0.176235i
$801$	−30.1070	+	17.3823i	−1.06378	+	0.614174i
$802$	−5.16876	+	19.2901i	−0.182515	+	0.681156i
$803$	−30.4975	+	8.17177i	−1.07623	+	0.288376i
$804$	0.244823			0.00863425
$805$	5.89899	−	3.06820i	0.207912	−	0.108140i
$806$	−7.78078			−0.274066
$807$	7.41697	−	1.98737i	0.261090	−	0.0699588i
$808$	−4.16678	+	15.5506i	−0.146587	+	0.547069i
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	−0.449219	−	0.893422i	$-0.648298\pi$
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	0.549117	+	0.835746i	$0.314964\pi$
$810$	−15.0665	−	10.6507i	−0.529384	−	0.374228i
$811$			17.8693i			0.627476i	0.949510	+	0.313738i	$0.101581\pi$
$811$			17.8693i			0.627476i	−0.949510	+	0.313738i	$0.898419\pi$
$812$	7.02151	−	4.51412i	0.246407	−	0.158414i
$813$	2.62176	−	2.62176i	0.0919491	−	0.0919491i
$814$	24.5550	+	14.1768i	0.860653	+	0.496898i
$815$	−12.3924	−	26.8898i	−0.434088	−	0.941910i
$816$	−0.769067	−	1.33206i	−0.0269227	−	0.0466316i
$817$	2.64486	+	9.87074i	0.0925318	+	0.345333i
$818$	−24.2949	−	24.2949i	−0.849451	−	0.849451i
$819$	14.8569	−	4.75200i	0.519143	−	0.166048i
$820$	10.3083	+	12.3974i	0.359981	+	0.432937i
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	−0.744312	−	0.667832i	$-0.767222\pi$
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	0.950516	+	0.310677i	$0.100556\pi$
$822$	2.47282	+	0.662590i	0.0862495	+	0.0231105i
$823$	−34.0995	−	9.13692i	−1.18863	−	0.318493i	−0.390287	−	0.920693i	$-0.627624\pi$
$823$	−34.0995	−	9.13692i	−1.18863	−	0.318493i	−0.798345	+	0.602200i	$0.794291\pi$
$824$	−9.83476	+	17.0343i	−0.342610	+	0.593418i
$825$	6.71771	−	4.61455i	0.233881	−	0.160658i
$826$	9.74816	−	10.7270i	0.339182	−	0.373239i
$827$	−17.2835	−	17.2835i	−0.601005	−	0.601005i	0.339574	−	0.940579i	$-0.389717\pi$
$827$	−17.2835	−	17.2835i	−0.601005	−	0.601005i	−0.940579	+	0.339574i	$0.889717\pi$
$828$	−0.848257	−	3.16574i	−0.0294790	−	0.110017i
$829$	17.2877	+	29.9431i	0.600426	+	1.03997i	0.992756	+	0.120144i	$0.0383357\pi$
$829$	17.2877	+	29.9431i	0.600426	+	1.03997i	−0.392330	+	0.919824i	$0.628331\pi$
$830$	−16.8295	−	6.21104i	−0.584159	−	0.215589i
$831$	5.04433	+	2.91234i	0.174986	+	0.101028i
$832$	−1.42962	+	1.42962i	−0.0495631	+	0.0495631i
$833$	36.6487	+	6.15011i	1.26980	+	0.213089i
$834$		−	3.20539i		−	0.110994i
$835$	−8.59183	+	12.1540i	−0.297332	+	0.420607i
$836$	18.9611	−	10.9472i	0.655782	−	0.378616i
$837$	1.70734	−	6.37187i	0.0590142	−	0.220244i
$838$	30.0751	−	8.05859i	1.03893	−	0.278379i
$839$	−50.1328			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$839$	−50.1328			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$840$	1.26418	−	1.15759i	0.0436183	−	0.0399407i
$841$	19.0459			0.656754
$842$	32.5254	−	8.71515i	1.12090	−	0.300344i
$843$	1.06109	−	3.96003i	0.0365458	−	0.136391i
$844$	16.9538	−	9.78829i	0.583575	−	0.336927i
$845$	−3.37252	−	19.6412i	−0.116018	−	0.675679i
$846$			17.1920i			0.591073i
$847$	−48.5636	−	25.0259i	−1.66866	−	0.859901i
$848$	0.978013	−	0.978013i	0.0335851	−	0.0335851i
$849$	−6.79181	−	3.92125i	−0.233094	−	0.134577i
$850$	25.0233	−	8.85436i	0.858292	−	0.303702i
$851$	−2.83227	−	4.90563i	−0.0970888	−	0.168163i
$852$	0.358232	+	1.33694i	0.0122728	+	0.0458028i
$853$	−2.37500	−	2.37500i	−0.0813183	−	0.0813183i	0.665278	−	0.746596i	$-0.268313\pi$
$853$	−2.37500	−	2.37500i	−0.0813183	−	0.0813183i	−0.746596	+	0.665278i	$0.768313\pi$
$854$	−2.59021	+	11.9167i	−0.0886352	+	0.407779i
$855$	−19.5125	+	16.2243i	−0.667312	+	0.554860i
$856$	1.40051	−	2.42575i	0.0478683	−	0.0829103i
$857$	−40.5097	−	10.8545i	−1.38378	−	0.370784i	−0.511290	−	0.859408i	$-0.670832\pi$
$857$	−40.5097	−	10.8545i	−1.38378	−	0.370784i	−0.872494	+	0.488624i	$0.837499\pi$
$858$	3.18320	+	0.852937i	0.108673	+	0.0291188i
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	−0.885430	−	0.464774i	$-0.846136\pi$
$859$	−1.17847	+	2.04117i	−0.0402090	+	0.0696440i	0.845221	+	0.534418i	$0.179469\pi$
$860$	0.537952	−	5.84668i	0.0183440	−	0.199370i
$861$	1.17402	−	5.40125i	0.0400105	−	0.184074i
$862$	−10.4268	−	10.4268i	−0.355137	−	0.355137i
$863$	12.5138	+	46.7022i	0.425975	+	1.58976i	0.761784	+	0.647831i	$0.224324\pi$
$863$	12.5138	+	46.7022i	0.425975	+	1.58976i	−0.335808	+	0.941930i	$0.609009\pi$
$864$	−0.857049	−	1.48445i	−0.0291574	−	0.0505021i
$865$	−14.3263	+	6.60242i	−0.487110	+	0.224489i
$866$	12.2261	+	7.05873i	0.415459	+	0.239865i
$867$	−2.29104	+	2.29104i	−0.0778076	+	0.0778076i
$868$	−9.05097	−	4.66418i	−0.307210	−	0.158312i
$869$		−	35.1489i		−	1.19234i
$870$	−2.01456	+	0.345913i	−0.0683000	+	0.0117275i
$871$	−1.47950	+	0.854190i	−0.0501310	+	0.0289431i
$872$	1.52984	−	5.70944i	0.0518069	−	0.193346i
$873$	−26.4141	+	7.07763i	−0.893980	+	0.239541i
$874$	−4.37408			−0.147955
$875$	15.6603	+	25.0949i	0.529416	+	0.848363i
$876$	1.62608			0.0549402
$877$	13.3115	−	3.56681i	0.449498	−	0.120443i	−0.0269665	−	0.999636i	$-0.508585\pi$
$877$	13.3115	−	3.56681i	0.449498	−	0.120443i	0.476465	+	0.879194i	$0.341918\pi$
$878$	−9.94602	+	37.1191i	−0.335662	+	1.25271i
$879$	−6.07477	+	3.50727i	−0.204897	+	0.118297i
$880$	−12.3981	+	2.12884i	−0.417941	+	0.0717631i
$881$			3.32542i			0.112036i	0.998430	+	0.0560181i	$0.0178405\pi$
$881$			3.32542i			0.112036i	−0.998430	+	0.0560181i	$0.982160\pi$
$882$	20.1309	+	3.37822i	0.677842	+	0.113751i
$883$	−36.8930	+	36.8930i	−1.24155	+	1.24155i	−0.282191	+	0.959358i	$0.591061\pi$
$883$	−36.8930	+	36.8930i	−1.24155	+	1.24155i	−0.959358	+	0.282191i	$0.908939\pi$
$884$	9.29516	+	5.36656i	0.312630	+	0.180497i
$885$	−3.22348	+	1.48557i	−0.108356	+	0.0499369i
$886$	−2.86780	−	4.96718i	−0.0963456	−	0.166876i
$887$	−9.27107	−	34.6001i	−0.311292	−	1.16176i	−0.927392	−	0.374090i	$-0.877955\pi$
$887$	−9.27107	−	34.6001i	−0.311292	−	1.16176i	0.616101	−	0.787668i	$-0.288711\pi$
$888$	−1.03256	−	1.03256i	−0.0346506	−	0.0346506i
$889$	−11.6632	+	12.8343i	−0.391170	+	0.430447i
$890$	2.44248	−	26.5458i	0.0818721	−	0.889819i
$891$	23.2105	−	40.2018i	0.777582	−	1.34681i
$892$	1.99476	+	0.534495i	0.0667895	+	0.0178962i
$893$	22.1628	+	5.93852i	0.741651	+	0.198725i
$894$	−0.731419	+	1.26686i	−0.0244623	+	0.0423700i
$895$	3.79349	−	3.15423i	0.126803	−	0.105434i
$896$	−2.51999	+	0.806019i	−0.0841869	+	0.0269272i
$897$	−0.465543	−	0.465543i	−0.0155440	−	0.0155440i
$898$	−1.89007	−	7.05384i	−0.0630725	−	0.235390i
$899$	6.07098	+	10.5152i	0.202479	+	0.350703i
$900$	13.7451	−	4.86365i	0.458172	−	0.162122i
$901$	−6.35888	−	3.67130i	−0.211845	−	0.122309i
$902$	−28.6835	+	28.6835i	−0.955055	+	0.955055i
$903$	−1.69312	+	1.08850i	−0.0563435	+	0.0362232i
$904$		−	19.2075i		−	0.638833i
$905$	−1.55854	−	9.07680i	−0.0518077	−	0.301723i
$906$	−3.37307	+	1.94744i	−0.112063	+	0.0646994i
$907$	−4.46661	+	16.6696i	−0.148312	+	0.553506i	0.851274	+	0.524721i	$0.175830\pi$
$907$	−4.46661	+	16.6696i	−0.148312	+	0.553506i	−0.999586	+	0.0287849i	$0.990836\pi$
$908$	−18.0081	+	4.82525i	−0.597618	+	0.160131i
$909$	46.9461			1.55710
$910$	−3.60076	+	11.4062i	−0.119364	+	0.378112i
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	−1.08918	+	0.291844i	−0.0360663	+	0.00966392i
$913$	11.6813	−	43.5952i	0.386594	−	1.44279i
$914$	4.45641	−	2.57291i	0.147405	−	0.0851042i
$915$	1.72377	−	2.43844i	0.0569859	−	0.0806124i
$916$			4.00767i			0.132417i
$917$	9.32645	−	18.0982i	0.307986	−	0.597657i
$918$	−6.43445	+	6.43445i	−0.212368	+	0.212368i
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	0.586098	−	0.810240i	$-0.300663\pi$
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	−0.408640	+	0.912696i	$0.633997\pi$
$920$	2.35772	+	0.870136i	0.0777318	+	0.0286875i
$921$	3.54381	+	6.13806i	0.116773	+	0.202256i
$922$	7.61212	+	28.4088i	0.250692	+	0.935595i
$923$	−6.82943	−	6.82943i	−0.224794	−	0.224794i
$924$	3.19156	+	2.90034i	0.104995	+	0.0954143i
$925$	20.7713	−	14.2683i	0.682958	−	0.469139i
$926$	2.86113	−	4.95563i	0.0940226	−	0.162852i
$927$	55.4029	+	14.8452i	1.81967	+	0.487579i
$928$	3.04751	+	0.816578i	0.100039	+	0.0268055i
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	−0.864467	−	0.502689i	$-0.832344\pi$
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	0.867575	+	0.497306i	$0.165677\pi$
$930$	1.59409	+	1.91715i	0.0522721	+	0.0628660i
$931$	11.3087	−	24.7846i	0.370627	−	0.812281i
$932$	−9.70971	−	9.70971i	−0.318052	−	0.318052i
$933$	−0.823556	−	3.07355i	−0.0269620	−	0.100624i
$934$	−8.32139	−	14.4131i	−0.272284	−	0.471610i
$935$	27.9514	+	60.6507i	0.914108	+	1.98349i
$936$	5.10577	+	2.94782i	0.166887	+	0.0963525i
$937$	−34.2022	+	34.2022i	−1.11734	+	1.11734i	−0.125208	+	0.992131i	$0.539960\pi$
$937$	−34.2022	+	34.2022i	−1.11734	+	1.11734i	−0.992131	+	0.125208i	$0.960040\pi$
$938$	−2.23307	+	0.106750i	−0.0729123	+	0.00348552i
$939$			8.52144i			0.278087i
$940$	−10.7649	−	7.60984i	−0.351112	−	0.248206i
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	−0.742667	−	0.669660i	$-0.766440\pi$
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	0.208609	+	0.977999i	$0.433106\pi$
$942$	−0.0827033	+	0.308653i	−0.00269462	+	0.0100565i
$943$	7.82790	−	2.09748i	0.254911	−	0.0683033i
$944$	5.47845			0.178308
$945$	−8.55071	−	5.45161i	−0.278155	−	0.177341i
$946$	14.7719			0.480276
$947$	−45.5435	+	12.2033i	−1.47996	+	0.396555i	−0.906335	−	0.422560i	$-0.861131\pi$
$947$	−45.5435	+	12.2033i	−1.47996	+	0.396555i	−0.573629	+	0.819115i	$0.694465\pi$
$948$	−0.468522	+	1.74855i	−0.0152169	+	0.0567902i
$949$	−9.82664	+	5.67341i	−0.318986	+	0.184167i
$950$	−1.52201	−	19.3994i	−0.0493806	−	0.629400i
$951$		−	1.24412i		−	0.0403434i
$952$	7.59560	+	11.8146i	0.246175	+	0.382914i
$953$	18.8431	−	18.8431i	0.610389	−	0.610389i	−0.332658	−	0.943047i	$-0.607946\pi$
$953$	18.8431	−	18.8431i	0.610389	−	0.610389i	0.943047	+	0.332658i	$0.107946\pi$
$954$	−3.49290	−	2.01662i	−0.113087	−	0.0652906i
$955$	13.3180	−	36.0865i	0.430960	−	1.16773i
$956$	9.83103	+	17.0278i	0.317958	+	0.550720i
$957$	−1.33101	−	4.96741i	−0.0430256	−	0.160574i
$958$	−10.8818	−	10.8818i	−0.351575	−	0.351575i
$959$	−22.8439	−	4.96536i	−0.737667	−	0.160340i
$960$	0.645146	+	0.0593598i	0.0208220	+	0.00191583i
$961$	−8.09467	+	14.0204i	−0.261118	+	0.452270i
$962$	9.84255	+	2.63730i	0.317337	+	0.0850301i
$963$	−7.88958	−	2.11401i	−0.254238	−	0.0681229i
$964$	−2.94256	+	5.09667i	−0.0947735	+	0.164153i
$965$	26.8700	+	2.47231i	0.864976	+	0.0795863i
$966$	−0.262473	−	0.820612i	−0.00844493	−	0.0264028i
$967$	27.3703	+	27.3703i	0.880169	+	0.880169i	0.993551	−	0.113383i	$-0.0361687\pi$
$967$	27.3703	+	27.3703i	0.880169	+	0.880169i	−0.113383	+	0.993551i	$0.536169\pi$
$968$	−5.34440	−	19.9456i	−0.171776	−	0.641075i
$969$	2.99306	+	5.18413i	0.0961509	+	0.166538i
$970$	7.26018	−	19.6722i	0.233110	−	0.631636i
$971$	−27.8750	−	16.0936i	−0.894550	−	0.516469i	−0.0191221	−	0.999817i	$-0.506087\pi$
$971$	−27.8750	−	16.0936i	−0.894550	−	0.516469i	−0.875428	+	0.483348i	$0.839420\pi$
$972$	−5.32668	+	5.32668i	−0.170853	+	0.170853i
$973$	1.39765	+	29.2369i	0.0448065	+	0.937291i
$974$		−	35.9920i		−	1.15326i
$975$	1.90273	−	2.22671i	0.0609362	−	0.0713119i
$976$	−3.99172	+	2.30462i	−0.127772	+	0.0737691i
$977$	−6.02479	+	22.4848i	−0.192750	+	0.719353i	0.800088	+	0.599883i	$0.204786\pi$
$977$	−6.02479	+	22.4848i	−0.192750	+	0.719353i	−0.992838	+	0.119470i	$0.961881\pi$
$978$	−3.70572	+	0.992944i	−0.118496	+	0.0317508i
$979$	67.0692			2.14354
$980$	−11.0260	+	11.1098i	−0.352213	+	0.354889i
$981$	−17.2364			−0.550314
$982$	14.7616	−	3.95535i	0.471060	−	0.126220i
$983$	14.7630	−	55.0964i	0.470868	−	1.75730i	−0.165793	−	0.986160i	$-0.553019\pi$
$983$	14.7630	−	55.0964i	0.470868	−	1.75730i	0.636662	−	0.771143i	$-0.280315\pi$
$984$	1.80926	−	1.04457i	0.0576770	−	0.0332998i
$985$	36.9606	+	26.1279i	1.17766	+	0.832505i
$986$		−	16.7491i		−	0.533401i
$987$	0.215802	+	4.51427i	0.00686904	+	0.143691i
$988$	5.56380	−	5.56380i	0.177008	−	0.177008i
$989$	−2.55577	−	1.47557i	−0.0812687	−	0.0469205i
$990$	15.3535	+	33.3150i	0.487967	+	1.05882i
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.808478	+	0.588526i	$0.200292\pi$
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.105440	+	0.994426i	$0.466375\pi$
$992$	−0.996056	−	3.71733i	−0.0316248	−	0.118025i
$993$	−7.26279	−	7.26279i	−0.230478	−	0.230478i
$994$	−3.85043	−	12.0382i	−0.122128	−	0.381829i
$995$	−10.7694	−	12.9520i	−0.341414	−	0.410607i
$996$	−1.16222	+	2.01302i	−0.0368262	+	0.0637849i
$997$	23.4284	+	6.27762i	0.741985	+	0.198814i	0.609960	−	0.792432i	$-0.291185\pi$
$997$	23.4284	+	6.27762i	0.741985	+	0.198814i	0.132025	+	0.991246i	$0.457852\pi$
$998$	30.5087	+	8.17479i	0.965737	+	0.258768i
$999$	−4.31951	+	7.48160i	−0.136663	+	0.236707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.k.a.47.1	yes	16
3.2	odd	2		630.2.bv.c.397.3		16
4.3	odd	2		560.2.ci.c.257.3		16
5.2	odd	4		350.2.o.c.243.2		16
5.3	odd	4	inner	70.2.k.a.33.3	yes	16
5.4	even	2		350.2.o.c.257.4		16
7.2	even	3		490.2.g.c.97.6		16
7.3	odd	6	inner	70.2.k.a.17.3	yes	16
7.4	even	3		490.2.l.c.227.4		16
7.5	odd	6		490.2.g.c.97.7		16
7.6	odd	2		490.2.l.c.117.2		16
15.8	even	4		630.2.bv.c.523.1		16
20.3	even	4		560.2.ci.c.33.3		16
21.17	even	6		630.2.bv.c.577.1		16
28.3	even	6		560.2.ci.c.17.3		16
35.3	even	12	inner	70.2.k.a.3.1	✓	16
35.13	even	4		490.2.l.c.313.4		16
35.17	even	12		350.2.o.c.143.4		16
35.18	odd	12		490.2.l.c.423.2		16
35.23	odd	12		490.2.g.c.293.7		16
35.24	odd	6		350.2.o.c.157.2		16
35.33	even	12		490.2.g.c.293.6		16
105.38	odd	12		630.2.bv.c.73.3		16
140.3	odd	12		560.2.ci.c.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	35.3	even	12	inner
70.2.k.a.17.3	yes	16	7.3	odd	6	inner
70.2.k.a.33.3	yes	16	5.3	odd	4	inner
70.2.k.a.47.1	yes	16	1.1	even	1	trivial
350.2.o.c.143.4		16	35.17	even	12
350.2.o.c.157.2		16	35.24	odd	6
350.2.o.c.243.2		16	5.2	odd	4
350.2.o.c.257.4		16	5.4	even	2
490.2.g.c.97.6		16	7.2	even	3
490.2.g.c.97.7		16	7.5	odd	6
490.2.g.c.293.6		16	35.33	even	12
490.2.g.c.293.7		16	35.23	odd	12
490.2.l.c.117.2		16	7.6	odd	2
490.2.l.c.227.4		16	7.4	even	3
490.2.l.c.313.4		16	35.13	even	4
490.2.l.c.423.2		16	35.18	odd	12
560.2.ci.c.17.3		16	28.3	even	6
560.2.ci.c.33.3		16	20.3	even	4
560.2.ci.c.257.3		16	4.3	odd	2
560.2.ci.c.353.3		16	140.3	odd	12
630.2.bv.c.73.3		16	105.38	odd	12
630.2.bv.c.397.3		16	3.2	odd	2
630.2.bv.c.523.1		16	15.8	even	4
630.2.bv.c.577.1		16	21.17	even	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.0749894 + 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.20382 - 0.378409i) q^{5} -0.289737i q^{6} +(0.126334 + 2.64273i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.0749894 + 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.20382 - 0.378409i) q^{5} -0.289737i q^{6} +(0.126334 + 2.64273i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +(-2.03078 + 0.935904i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(0.0749894 + 0.279864i) q^{12} +(-1.42962 - 1.42962i) q^{13} +(-0.806019 - 2.51999i) q^{14} +(-0.0593598 + 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-5.12784 - 1.37400i) q^{17} +(-2.81669 - 0.754730i) q^{18} +(-1.94590 + 3.37040i) q^{19} +(1.71936 - 1.42962i) q^{20} +(-0.749081 - 0.162821i) q^{21} +(3.97801 + 3.97801i) q^{22} +(-0.290892 - 1.08562i) q^{23} +(-0.144868 - 0.250919i) q^{24} +(4.71361 - 1.66789i) q^{25} +(1.75092 + 1.01089i) q^{26} +(-1.21205 + 1.21205i) q^{27} +(1.43078 + 2.22551i) q^{28} -3.15502i q^{29} +(-0.109639 - 0.638527i) q^{30} +(-3.33287 + 1.92423i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.57445 - 0.421872i) q^{33} +5.30873 q^{34} +(1.27845 + 5.77629i) q^{35} +2.91605 q^{36} +(4.86824 - 1.30444i) q^{37} +(1.00727 - 3.75919i) q^{38} +(0.507306 - 0.292893i) q^{39} +(-1.29076 + 1.82591i) q^{40} +7.21050i q^{41} +(0.765697 - 0.0366036i) q^{42} +(1.85669 - 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(6.11719 + 2.25760i) q^{45} +(0.561961 + 0.973344i) q^{46} +(-1.52590 - 5.69475i) q^{47} +(0.204875 + 0.204875i) q^{48} +(-6.96808 + 0.667734i) q^{49} +(-4.12132 + 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(-1.95290 - 0.523277i) q^{52} +(1.33599 + 0.357978i) q^{53} +(0.857049 - 1.48445i) q^{54} +(-8.04270 - 9.67269i) q^{55} +(-1.95803 - 1.77936i) q^{56} +(-0.797333 - 0.797333i) q^{57} +(0.816578 + 3.04751i) q^{58} +(2.73923 + 4.74448i) q^{59} +(0.271166 + 0.588393i) q^{60} +(-3.99172 - 2.30462i) q^{61} +(2.72127 - 2.72127i) q^{62} +(-3.53413 + 6.85809i) q^{63} -1.00000i q^{64} +(-3.69160 - 2.60964i) q^{65} +(-1.41161 + 0.814995i) q^{66} +(0.218698 - 0.816193i) q^{67} +(-5.12784 + 1.37400i) q^{68} +0.325641 q^{69} +(-2.72990 - 5.24858i) q^{70} +4.77710 q^{71} +(-2.81669 + 0.754730i) q^{72} +(1.45256 - 5.42104i) q^{73} +(-4.36475 + 2.51999i) q^{74} +(0.113311 + 1.44425i) q^{75} +3.89180i q^{76} +(12.5202 - 8.04920i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(5.41079 + 3.12392i) q^{79} +(0.774197 - 2.09777i) q^{80} +(4.12576 + 7.14603i) q^{81} +(-1.86622 - 6.96481i) q^{82} +(5.67281 + 5.67281i) q^{83} +(-0.730133 + 0.233533i) q^{84} +(-11.8207 - 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(0.882976 + 0.236593i) q^{87} +(5.43407 + 1.45605i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(-6.49307 - 0.597426i) q^{90} +(3.59749 - 3.95871i) q^{91} +(-0.794732 - 0.794732i) q^{92} +(-0.288594 - 1.07705i) q^{93} +(2.94782 + 5.10577i) q^{94} +(-3.01302 + 8.16409i) q^{95} +(-0.250919 - 0.144868i) q^{96} +(-6.63103 + 6.63103i) q^{97} +(6.55783 - 2.44845i) q^{98} -16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 + 8 * q^7	\( 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35} - 8 q^{36} + 4 q^{37} + 24 q^{38} + 36 q^{42} - 8 q^{43} - 12 q^{45} - 8 q^{46} + 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} - 4 q^{56} + 8 q^{57} - 32 q^{58} + 8 q^{60} - 12 q^{61} - 36 q^{63} - 8 q^{65} + 32 q^{67} - 36 q^{68} - 12 q^{70} + 16 q^{71} - 8 q^{72} - 12 q^{73} - 48 q^{75} + 16 q^{77} + 16 q^{78} - 12 q^{80} - 48 q^{82} + 24 q^{85} + 12 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{91} + 8 q^{92} + 28 q^{93} + 20 q^{95} + 12 q^{96} + 40 q^{98}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

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