LMFDB - Embedded newform 70.2.k.a.47.2

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			47.2
Root			$0.144868 + 1.25092i$ of defining polynomial
Character	$\chi$	$=$	70.47
Dual form			70.2.k.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.523277 - 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.03078 - 0.935904i) q^{5} +2.02179i q^{6} +(1.83959 - 1.90155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.523277 - 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.03078 - 0.935904i) q^{5} +2.02179i q^{6} +(1.83959 - 1.90155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +(2.20382 + 0.378409i) q^{10} +(2.01999 + 3.49872i) q^{11} +(-0.523277 - 1.95290i) q^{12} +(0.204875 + 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(-2.89039 + 3.47617i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.97024 - 0.527924i) q^{17} +(1.05057 + 0.281498i) q^{18} +(-3.10166 + 5.37224i) q^{19} +(-2.22666 + 0.204875i) q^{20} +(-2.75092 - 4.58757i) q^{21} +(-2.85669 - 2.85669i) q^{22} +(1.17456 + 4.38350i) q^{23} +(1.01089 + 1.75092i) q^{24} +(3.24817 + 3.80124i) q^{25} +(-0.250919 - 0.144868i) q^{26} +(2.73397 - 2.73397i) q^{27} +(0.642357 - 2.56659i) q^{28} -7.15869i q^{29} +(1.89220 - 4.10581i) q^{30} +(6.33287 - 3.65628i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(7.88965 - 2.11403i) q^{33} +2.03974 q^{34} +(-5.51548 + 2.13996i) q^{35} -1.08763 q^{36} +(-4.46814 + 1.19723i) q^{37} +(1.60554 - 5.99195i) q^{38} +(0.507306 - 0.292893i) q^{39} +(2.09777 - 0.774197i) q^{40} +2.58745i q^{41} +(3.84454 + 3.71926i) q^{42} +(-4.97801 + 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(1.40386 + 1.98590i) q^{45} +(-2.26907 - 3.93014i) q^{46} +(-0.0815604 - 0.304388i) q^{47} +(-1.42962 - 1.42962i) q^{48} +(-0.231803 - 6.99616i) q^{49} +(-4.12132 - 2.83103i) q^{50} +(-2.06196 + 3.57142i) q^{51} +(0.279864 + 0.0749894i) q^{52} +(-8.00039 - 2.14370i) q^{53} +(-1.93321 + 3.34841i) q^{54} +(-0.827689 - 8.99566i) q^{55} +(0.0438127 + 2.64539i) q^{56} +(8.86840 + 8.86840i) q^{57} +(1.85281 + 6.91477i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-0.765062 + 4.45565i) q^{60} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 + 5.17076i) q^{62} +(-2.76682 + 0.790700i) q^{63} -1.00000i q^{64} +(-0.224313 - 0.607800i) q^{65} +(-7.07367 + 4.08398i) q^{66} +(-0.817530 + 3.05106i) q^{67} +(-1.97024 + 0.527924i) q^{68} +9.17514 q^{69} +(4.77369 - 3.49455i) q^{70} +7.12240 q^{71} +(1.05057 - 0.281498i) q^{72} +(-2.98311 + 11.1331i) q^{73} +(4.00603 - 2.31288i) q^{74} +(9.12312 - 4.35423i) q^{75} +6.20333i q^{76} +(10.3690 + 2.59511i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(-4.39618 - 2.53813i) q^{79} +(-1.82591 + 1.29076i) q^{80} +(-5.53997 - 9.59552i) q^{81} +(-0.669683 - 2.49929i) q^{82} +(-3.85372 - 3.85372i) q^{83} +(-4.67615 - 2.59749i) q^{84} +(3.50704 + 2.91605i) q^{85} +(3.51999 - 6.09680i) q^{86} +(-13.9802 - 3.74598i) q^{87} +(-3.90231 - 1.04562i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(-1.87002 - 1.55489i) q^{90} +(0.766467 - 0.0126942i) q^{91} +(3.20895 + 3.20895i) q^{92} +(-3.82650 - 14.2807i) q^{93} +(0.157563 + 0.272906i) q^{94} +(11.3267 - 8.00700i) q^{95} +(1.75092 + 1.01089i) q^{96} +(-6.63103 + 6.63103i) q^{97} +(2.03464 + 6.69778i) q^{98} -4.39398i 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
$3$	0.523277	−	1.95290i	0.302114	−	1.12751i	−0.633287	−	0.773917i	$-0.718295\pi$
$3$	0.523277	−	1.95290i	0.302114	−	1.12751i	0.935401	−	0.353588i	$-0.115039\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.03078	−	0.935904i	−0.908194	−	0.418549i
$5$	−2.03078	−	0.935904i	−0.908194	−	0.418549i
$6$			2.02179i			0.825391i
$7$	1.83959	−	1.90155i	0.695300	−	0.718719i
$7$	1.83959	−	1.90155i	0.695300	−	0.718719i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.941911	−	0.543813i	−0.313970	−	0.181271i
$10$	2.20382	+	0.378409i	0.696908	+	0.119663i
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	0.991397	+	0.130886i	$0.0417820\pi$
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	−0.382349	+	0.924018i	$0.624885\pi$
$12$	−0.523277	−	1.95290i	−0.151057	−	0.563753i
$13$	0.204875	+	0.204875i	0.0568221	+	0.0568221i	0.734947	−	0.678125i	$-0.237207\pi$
$13$	0.204875	+	0.204875i	0.0568221	+	0.0568221i	−0.678125	+	0.734947i	$0.737207\pi$
$14$	−1.28475	+	2.31288i	−0.343364	+	0.618143i
$15$	−2.89039	+	3.47617i	−0.746295	+	0.897544i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.97024	−	0.527924i	−0.477853	−	0.128040i	0.0118498	−	0.999930i	$-0.496228\pi$
$17$	−1.97024	−	0.527924i	−0.477853	−	0.128040i	−0.489703	+	0.871890i	$0.662895\pi$
$18$	1.05057	+	0.281498i	0.247621	+	0.0663498i
$19$	−3.10166	+	5.37224i	−0.711571	+	1.23248i	0.252697	+	0.967545i	$0.418682\pi$
$19$	−3.10166	+	5.37224i	−0.711571	+	1.23248i	−0.964267	+	0.264931i	$0.914651\pi$
$20$	−2.22666	+	0.204875i	−0.497897	+	0.0458114i
$21$	−2.75092	−	4.58757i	−0.600300	−	1.00109i
$22$	−2.85669	−	2.85669i	−0.609049	−	0.609049i
$23$	1.17456	+	4.38350i	0.244912	+	0.914023i	0.973428	+	0.228994i	$0.0735437\pi$
$23$	1.17456	+	4.38350i	0.244912	+	0.914023i	−0.728516	+	0.685029i	$0.759790\pi$
$24$	1.01089	+	1.75092i	0.206348	+	0.357405i
$25$	3.24817	+	3.80124i	0.649633	+	0.760248i
$26$	−0.250919	−	0.144868i	−0.0492094	−	0.0284110i
$27$	2.73397	−	2.73397i	0.526152	−	0.526152i
$28$	0.642357	−	2.56659i	0.121394	−	0.485040i
$29$		−	7.15869i		−	1.32934i	−0.747139	−	0.664668i	$-0.768573\pi$
$29$		−	7.15869i		−	1.32934i	0.747139	−	0.664668i	$-0.231427\pi$
$30$	1.89220	−	4.10581i	0.345467	−	0.749616i
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.191627	−	0.981468i	$-0.438624\pi$
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.945790	+	0.324780i	$0.105290\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	7.88965	−	2.11403i	1.37341	−	0.368005i
$34$	2.03974			0.349813
$35$	−5.51548	+	2.13996i	−0.932287	+	0.361719i
$36$	−1.08763			−0.181271
$37$	−4.46814	+	1.19723i	−0.734558	+	0.196824i	−0.606658	−	0.794963i	$-0.707490\pi$
$37$	−4.46814	+	1.19723i	−0.734558	+	0.196824i	−0.127900	+	0.991787i	$0.540824\pi$
$38$	1.60554	−	5.99195i	0.260453	−	0.972023i
$39$	0.507306	−	0.292893i	0.0812340	−	0.0469005i
$40$	2.09777	−	0.774197i	0.331686	−	0.122411i
$41$			2.58745i			0.404093i	0.979376	+	0.202046i	$0.0647591\pi$
$41$			2.58745i			0.404093i	−0.979376	+	0.202046i	$0.935241\pi$
$42$	3.84454	+	3.71926i	0.593225	+	0.573895i
$43$	−4.97801	+	4.97801i	−0.759140	+	0.759140i	−0.976166	−	0.217026i	$-0.930364\pi$
$43$	−4.97801	+	4.97801i	−0.759140	+	0.759140i	0.217026	+	0.976166i	$0.430364\pi$
$44$	3.49872	+	2.01999i	0.527452	+	0.304524i
$45$	1.40386	+	1.98590i	0.209275	+	0.296041i
$46$	−2.26907	−	3.93014i	−0.334556	−	0.579468i
$47$	−0.0815604	−	0.304388i	−0.0118968	−	0.0443995i	0.959722	−	0.280950i	$-0.0906497\pi$
$47$	−0.0815604	−	0.304388i	−0.0118968	−	0.0443995i	−0.971619	+	0.236551i	$0.923983\pi$
$48$	−1.42962	−	1.42962i	−0.206348	−	0.206348i
$49$	−0.231803	−	6.99616i	−0.0331148	−	0.999452i
$50$	−4.12132	−	2.83103i	−0.582843	−	0.400368i
$51$	−2.06196	+	3.57142i	−0.288732	+	0.500099i
$52$	0.279864	+	0.0749894i	0.0388102	+	0.0103992i
$53$	−8.00039	−	2.14370i	−1.09894	−	0.294460i	−0.336606	−	0.941646i	$-0.609279\pi$
$53$	−8.00039	−	2.14370i	−1.09894	−	0.294460i	−0.762332	+	0.647186i	$0.775946\pi$
$54$	−1.93321	+	3.34841i	−0.263076	+	0.455661i
$55$	−0.827689	−	8.99566i	−0.111606	−	1.21297i
$56$	0.0438127	+	2.64539i	0.00585472	+	0.353505i
$57$	8.86840	+	8.86840i	1.17465	+	1.17465i
$58$	1.85281	+	6.91477i	0.243285	+	0.907953i
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	0.892523	−	0.451002i	$-0.148933\pi$
$59$	0.427702	+	0.740802i	0.0556821	+	0.0964442i	−0.836841	+	0.547446i	$0.815600\pi$
$60$	−0.765062	+	4.45565i	−0.0987691	+	0.575222i
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	0.0645484	−	0.997915i	$-0.479439\pi$
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	−0.831945	+	0.554858i	$0.812773\pi$
$62$	−5.17076	+	5.17076i	−0.656688	+	0.656688i
$63$	−2.76682	+	0.790700i	−0.348587	+	0.0996189i
$64$		−	1.00000i		−	0.125000i
$65$	−0.224313	−	0.607800i	−0.0278226	−	0.0753883i
$66$	−7.07367	+	4.08398i	−0.870708	+	0.502704i
$67$	−0.817530	+	3.05106i	−0.0998772	+	0.372747i	−0.997714	−	0.0675822i	$-0.978472\pi$
$67$	−0.817530	+	3.05106i	−0.0998772	+	0.372747i	0.897837	+	0.440329i	$0.145138\pi$
$68$	−1.97024	+	0.527924i	−0.238926	+	0.0640201i
$69$	9.17514			1.10456
$70$	4.77369	−	3.49455i	0.570565	−	0.417679i
$71$	7.12240			0.845273			0.422637	−	0.906299i	$-0.361105\pi$
$71$	7.12240			0.845273			0.422637	+	0.906299i	$0.361105\pi$
$72$	1.05057	−	0.281498i	0.123810	−	0.0331749i
$73$	−2.98311	+	11.1331i	−0.349147	+	1.30303i	0.538545	+	0.842597i	$0.318974\pi$
$73$	−2.98311	+	11.1331i	−0.349147	+	1.30303i	−0.887692	+	0.460438i	$0.847693\pi$
$74$	4.00603	−	2.31288i	0.465691	−	0.268867i
$75$	9.12312	−	4.35423i	1.05345	−	0.502783i
$76$			6.20333i			0.711571i
$77$	10.3690	+	2.59511i	1.18165	+	0.295740i
$78$	−0.414214	+	0.414214i	−0.0469005	+	0.0469005i
$79$	−4.39618	−	2.53813i	−0.494609	−	0.285562i	0.231876	−	0.972745i	$-0.425514\pi$
$79$	−4.39618	−	2.53813i	−0.494609	−	0.285562i	−0.726484	+	0.687183i	$0.758847\pi$
$80$	−1.82591	+	1.29076i	−0.204143	+	0.144311i
$81$	−5.53997	−	9.59552i	−0.615553	−	1.06617i
$82$	−0.669683	−	2.49929i	−0.0739541	−	0.276000i
$83$	−3.85372	−	3.85372i	−0.423001	−	0.423001i	0.463235	−	0.886236i	$-0.346689\pi$
$83$	−3.85372	−	3.85372i	−0.423001	−	0.423001i	−0.886236	+	0.463235i	$0.846689\pi$
$84$	−4.67615	−	2.59749i	−0.510210	−	0.283410i
$85$	3.50704	+	2.91605i	0.380392	+	0.316290i
$86$	3.51999	−	6.09680i	0.379570	−	0.657434i
$87$	−13.9802	−	3.74598i	−1.49883	−	0.401611i
$88$	−3.90231	−	1.04562i	−0.415988	−	0.111464i
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	−0.935883	−	0.352310i	$-0.885396\pi$
$89$	−1.53615	+	2.66069i	−0.162832	+	0.282033i	0.773051	+	0.634343i	$0.218729\pi$
$90$	−1.87002	−	1.55489i	−0.197117	−	0.163900i
$91$	0.766467	−	0.0126942i	0.0803475	−	0.00133071i
$92$	3.20895	+	3.20895i	0.334556	+	0.334556i
$93$	−3.82650	−	14.2807i	−0.396789	−	1.48084i
$94$	0.157563	+	0.272906i	0.0162513	+	0.0281481i
$95$	11.3267	−	8.00700i	1.16210	−	0.821501i
$96$	1.75092	+	1.01089i	0.178702	+	0.103174i
$97$	−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	$0.407943\pi$
$98$	2.03464	+	6.69778i	0.205530	+	0.676578i
$99$		−	4.39398i		−	0.441611i
$100$	4.71361	+	1.66789i	0.471361	+	0.166789i
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	−0.861364	−	0.507989i	$-0.830389\pi$
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	0.00924966	+	0.999957i	$0.497056\pi$
$102$	1.06735	−	3.98340i	0.105683	−	0.394416i
$103$	4.13612	−	1.10827i	0.407544	−	0.109201i	−0.0492221	−	0.998788i	$-0.515674\pi$
$103$	4.13612	−	1.10827i	0.407544	−	0.109201i	0.456766	+	0.889587i	$0.349008\pi$
$104$	−0.289737			−0.0284110
$105$	1.29299	+	11.8910i	0.126183	+	1.16044i
$106$	8.28261			0.804479
$107$	14.3653	−	3.84918i	1.38875	−	0.372114i	0.514457	−	0.857516i	$-0.327993\pi$
$107$	14.3653	−	3.84918i	1.38875	−	0.372114i	0.874291	+	0.485402i	$0.161327\pi$
$108$	1.00070	−	3.73467i	0.0962926	−	0.359369i
$109$	−11.4586	+	6.61564i	−1.09754	+	0.633664i	−0.935573	−	0.353133i	$-0.885116\pi$
$109$	−11.4586	+	6.61564i	−1.09754	+	0.633664i	−0.161964	+	0.986797i	$0.551783\pi$
$110$	3.12773	+	8.47492i	0.298218	+	0.808052i
$111$			9.35230i			0.887681i
$112$	−0.726997	−	2.54391i	−0.0686947	−	0.240377i
$113$	9.75336	−	9.75336i	0.917519	−	0.917519i	−0.0793296	−	0.996848i	$-0.525278\pi$
$113$	9.75336	−	9.75336i	0.917519	−	0.917519i	0.996848	+	0.0793296i	$0.0252780\pi$
$114$	−10.8615	−	6.27091i	−1.01728	−	0.587324i
$115$	1.71727	−	10.0012i	0.160136	−	0.932618i
$116$	−3.57935	−	6.19961i	−0.332334	−	0.575619i
$117$	−0.0815604	−	0.304388i	−0.00754026	−	0.0281406i
$118$	−0.604862	−	0.604862i	−0.0556821	−	0.0556821i
$119$	−4.62831	+	2.77535i	−0.424276	+	0.254416i
$120$	−0.414214	−	4.50184i	−0.0378124	−	0.410960i
$121$	−2.66069	+	4.60846i	−0.241881	+	0.418951i
$122$	6.68495	+	1.79123i	0.605227	+	0.162170i
$123$	5.05303	+	1.35396i	0.455617	+	0.122082i
$124$	3.65628	−	6.33287i	0.328344	−	0.568708i
$125$	−3.03873	−	10.7595i	−0.271792	−	0.962356i
$126$	2.46790	−	1.47986i	0.219858	−	0.131837i
$127$	−2.19984	−	2.19984i	−0.195204	−	0.195204i	0.602736	−	0.797940i	$-0.294077\pi$
$127$	−2.19984	−	2.19984i	−0.195204	−	0.195204i	−0.797940	+	0.602736i	$0.794077\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	7.11667	+	12.3264i	0.626587	+	1.08528i
$130$	0.373980	+	0.529033i	0.0328002	+	0.0463993i
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	0.197773	−	0.980248i	$-0.436629\pi$
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	−0.750033	+	0.661400i	$0.769963\pi$
$132$	5.77563	−	5.77563i	0.502704	−	0.502704i
$133$	4.50980	+	15.7807i	0.391049	+	1.36836i
$134$		−	3.15869i		−	0.272870i
$135$	−8.11083	+	2.99337i	−0.698069	+	0.257628i
$136$	1.76647	−	1.01987i	0.151473	−	0.0874531i
$137$	1.85804	−	6.93431i	0.158743	−	0.592438i	−0.840012	−	0.542567i	$-0.817452\pi$
$137$	1.85804	−	6.93431i	0.158743	−	0.592438i	0.998756	−	0.0498710i	$-0.0158810\pi$
$138$	−8.86251	+	2.37470i	−0.754427	+	0.202148i
$139$	12.4172			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$139$	12.4172			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$140$	−3.70657	+	4.61100i	−0.313262	+	0.389701i
$141$	−0.637116			−0.0536549
$142$	−6.87971	+	1.84341i	−0.577332	+	0.154696i
$143$	−0.302955	+	1.13064i	−0.0253344	+	0.0945492i
$144$	−0.941911	+	0.543813i	−0.0784926	+	0.0453177i
$145$	−6.69985	+	14.5378i	−0.556392	+	1.20730i
$146$		−	11.5259i		−	0.953887i
$147$	−13.7841	−	3.20824i	−1.13689	−	0.264611i
$148$	−3.27091	+	3.27091i	−0.268867	+	0.268867i
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.946637	+	0.322302i	$0.104457\pi$
$149$	20.7399	+	11.9742i	1.69908	+	0.980963i	0.752440	+	0.658661i	$0.228877\pi$
$150$	−7.68530	+	6.56710i	−0.627502	+	0.536202i
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	0.929065	−	0.369916i	$-0.120613\pi$
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	−0.784889	+	0.619636i	$0.787280\pi$
$152$	−1.60554	−	5.99195i	−0.130226	−	0.486012i
$153$	1.56870	+	1.56870i	0.126822	+	0.126822i
$154$	−10.6873	+	0.177002i	−0.861207	+	0.0142632i
$155$	−16.2826	+	1.49816i	−1.30785	+	0.120335i
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	−5.91389	−	1.58462i	−0.471980	−	0.126467i	0.0149859	−	0.999888i	$-0.495230\pi$
$157$	−5.91389	−	1.58462i	−0.471980	−	0.126467i	−0.486966	+	0.873421i	$0.661896\pi$
$158$	4.90330	+	1.31384i	0.390086	+	0.104523i
$159$	−8.37284	+	14.5022i	−0.664010	+	1.15010i
$160$	1.42962	−	1.71936i	0.113021	−	0.135927i
$161$	10.4962	+	5.83037i	0.827213	+	0.459498i
$162$	7.83471	+	7.83471i	0.615553	+	0.615553i
$163$	−4.28549	−	15.9937i	−0.335666	−	1.25272i	−0.903146	−	0.429334i	$-0.858748\pi$
$163$	−4.28549	−	15.9937i	−0.335666	−	1.25272i	0.567480	−	0.823387i	$-0.307918\pi$
$164$	1.29373	+	2.24080i	0.101023	+	0.174977i
$165$	−18.0007	−	3.09083i	−1.40135	−	0.240621i
$166$	4.71983	+	2.72499i	0.366329	+	0.211500i
$167$	−10.2873	+	10.2873i	−0.796056	+	0.796056i	−0.982471	−	0.186415i	$-0.940313\pi$
$167$	−10.2873	+	10.2873i	−0.796056	+	0.796056i	0.186415	+	0.982471i	$0.440313\pi$
$168$	5.18910	+	1.29871i	0.400348	+	0.100198i
$169$		−	12.9161i		−	0.993543i
$170$	−4.14227	−	1.90900i	−0.317698	−	0.146414i
$171$	5.84298	−	3.37345i	0.446824	−	0.257974i
$172$	−1.82208	+	6.80009i	−0.138932	+	0.518502i
$173$	7.50720	−	2.01155i	0.570762	−	0.152935i	0.0381159	−	0.999273i	$-0.487864\pi$
$173$	7.50720	−	2.01155i	0.570762	−	0.152935i	0.532646	+	0.846338i	$0.321198\pi$
$174$	14.4734			1.09722
$175$	13.2036	+	0.816171i	0.998095	+	0.0616967i
$176$	4.03997			0.304524
$177$	1.67052	−	0.447613i	0.125564	−	0.0336447i
$178$	0.795171	−	2.96762i	0.0596006	−	0.222432i
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	−0.369676	−	0.929161i	$-0.620531\pi$
$179$	3.34695	−	1.93236i	0.250163	−	0.144431i	0.619839	+	0.784729i	$0.287198\pi$
$180$	2.20873	+	1.01791i	0.164629	+	0.0758708i
$181$		−	6.99107i		−	0.519642i	−0.965657	−	0.259821i	$-0.916336\pi$
$181$		−	6.99107i		−	0.519642i	0.965657	−	0.259821i	$-0.0836636\pi$
$182$	−0.737064	+	0.210638i	−0.0546348	+	0.0156135i
$183$	−9.89407	+	9.89407i	−0.731390	+	0.731390i
$184$	−3.93014	−	2.26907i	−0.289734	−	0.167278i
$185$	10.1943	+	1.75043i	0.749502	+	0.128694i
$186$	7.39223	+	12.8037i	0.542024	+	0.938814i
$187$	−2.13280	−	7.95971i	−0.155966	−	0.582071i
$188$	−0.222827	−	0.222827i	−0.0162513	−	0.0162513i
$189$	−0.169398	−	10.2282i	−0.0123219	−	0.743990i
$190$	−8.86840	+	10.6657i	−0.643381	+	0.773774i
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	−0.935543	−	0.353214i	$-0.885089\pi$
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	0.773664	+	0.633597i	$0.218422\pi$
$192$	−1.95290	−	0.523277i	−0.140938	−	0.0377643i
$193$	19.3907	+	5.19573i	1.39577	+	0.373997i	0.876825	−	0.480809i	$-0.159657\pi$
$193$	19.3907	+	5.19573i	1.39577	+	0.373997i	0.518949	+	0.854805i	$0.326324\pi$
$194$	4.68885	−	8.12132i	0.336640	−	0.583077i
$195$	−1.30435	+	0.120013i	−0.0934064	+	0.00859431i
$196$	−3.69883	−	5.94295i	−0.264202	−	0.424497i
$197$	−7.84901	−	7.84901i	−0.559219	−	0.559219i	0.369866	−	0.929085i	$-0.379404\pi$
$197$	−7.84901	−	7.84901i	−0.559219	−	0.559219i	−0.929085	+	0.369866i	$0.879404\pi$
$198$	1.13725	+	4.24426i	0.0808205	+	0.301626i
$199$	−5.40103	−	9.35485i	−0.382869	−	0.663148i	0.608602	−	0.793475i	$-0.291730\pi$
$199$	−5.40103	−	9.35485i	−0.382869	−	0.663148i	−0.991471	+	0.130327i	$0.958397\pi$
$200$	−4.98468	−	0.391082i	−0.352470	−	0.0276537i
$201$	5.53062	+	3.19310i	0.390100	+	0.225224i
$202$	6.99218	−	6.99218i	0.491968	−	0.491968i
$203$	−13.6126	−	13.1691i	−0.955419	−	0.924288i
$204$			4.12392i			0.288732i
$205$	2.42161	−	5.25456i	0.169133	−	0.366995i
$206$	−3.70835	+	2.14101i	−0.258373	+	0.149172i
$207$	1.27748	−	4.76761i	0.0887908	−	0.331372i
$208$	0.279864	−	0.0749894i	0.0194051	−	0.00519958i
$209$	−25.0613			−1.73353
$210$	−4.32654	−	11.1511i	−0.298560	−	0.769502i
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	−8.00039	+	2.14370i	−0.549469	+	0.147230i
$213$	3.72699	−	13.9093i	0.255369	−	0.953050i
$214$	−12.8796	+	7.43604i	−0.880431	+	0.508317i
$215$	14.7682	−	5.45032i	1.00718	−	0.371709i
$216$			3.86642i			0.263076i
$217$	4.69728	−	18.7683i	0.318872	−	1.27408i
$218$	9.35593	−	9.35593i	0.633664	−	0.633664i
$219$	20.1809	+	11.6514i	1.36370	+	0.787330i
$220$	−5.21463	−	7.37662i	−0.351570	−	0.497332i
$221$	−0.295494	−	0.511811i	−0.0198771	−	0.0344281i
$222$	−2.42055	−	9.03363i	−0.162457	−	0.606298i
$223$	9.35230	+	9.35230i	0.626277	+	0.626277i	0.947129	−	0.320853i	$-0.103969\pi$
$223$	9.35230	+	9.35230i	0.626277	+	0.626277i	−0.320853	+	0.947129i	$0.603969\pi$
$224$	1.36064	+	2.26907i	0.0909114	+	0.151608i
$225$	−0.992322	−	5.34682i	−0.0661548	−	0.356455i
$226$	−6.89667	+	11.9454i	−0.458759	+	0.794595i
$227$	15.6420	+	4.19127i	1.03820	+	0.278184i	0.737367	−	0.675493i	$-0.236069\pi$
$227$	15.6420	+	4.19127i	1.03820	+	0.278184i	0.300832	+	0.953677i	$0.402736\pi$
$228$	12.1145	+	3.24606i	0.802300	+	0.214976i
$229$	5.88820	−	10.1987i	0.389103	−	0.673947i	−0.603226	−	0.797570i	$-0.706118\pi$
$229$	5.88820	−	10.1987i	0.389103	−	0.673947i	0.992329	+	0.123624i	$0.0394515\pi$
$230$	0.929750	+	10.1049i	0.0613059	+	0.666297i
$231$	10.4938	−	18.8915i	0.690442	−	1.24297i
$232$	5.06196	+	5.06196i	0.332334	+	0.332334i
$233$	−1.48154	−	5.52920i	−0.0970591	−	0.362230i	0.900264	−	0.435343i	$-0.143373\pi$
$233$	−1.48154	−	5.52920i	−0.0970591	−	0.362230i	−0.997324	+	0.0731138i	$0.976706\pi$
$234$	0.157563	+	0.272906i	0.0103002	+	0.0178405i
$235$	−0.119246	+	0.694478i	−0.00777876	+	0.0453028i
$236$	0.740802	+	0.427702i	0.0482221	+	0.0278410i
$237$	−7.25713	+	7.25713i	−0.471402	+	0.471402i
$238$	3.75229	−	3.87867i	0.243225	−	0.251417i
$239$			8.33794i			0.539337i	0.962953	+	0.269668i	$0.0869141\pi$
$239$			8.33794i			0.539337i	−0.962953	+	0.269668i	$0.913086\pi$
$240$	1.56526	+	4.24124i	0.101037	+	0.273771i
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	−0.415031	−	0.909807i	$-0.636229\pi$
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	0.580401	+	0.814331i	$0.302896\pi$
$242$	1.37728	−	5.14006i	0.0885347	−	0.330416i
$243$	−10.4340	+	2.79578i	−0.669340	+	0.179349i
$244$	−6.92077			−0.443057
$245$	−6.07700	+	14.4246i	−0.388245	+	0.921556i
$246$	−5.23128			−0.333535
$247$	−1.73609	+	0.465184i	−0.110465	+	0.0295989i
$248$	−1.89263	+	7.06340i	−0.120182	+	0.448526i
$249$	−9.54248	+	5.50936i	−0.604730	+	0.349141i
$250$	5.71994	+	9.60637i	0.361761	+	0.607560i
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$	−2.00079	+	2.06818i	−0.126038	+	0.130283i
$253$	−12.9641	+	12.9641i	−0.815043	+	0.815043i
$254$	2.69424	+	1.55552i	0.169052	+	0.0976020i
$255$	7.52990	−	5.32298i	0.471541	−	0.333338i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50754	−	5.62621i	−0.0940377	−	0.350954i	0.902834	−	0.429989i	$-0.141483\pi$
$257$	−1.50754	−	5.62621i	−0.0940377	−	0.350954i	−0.996872	+	0.0790355i	$0.974816\pi$
$258$	−10.0645	−	10.0645i	−0.626587	−	0.626587i
$259$	−5.94295	+	10.6988i	−0.369277	+	0.664793i
$260$	−0.498161	−	0.414214i	−0.0308946	−	0.0256884i
$261$	−3.89299	+	6.74285i	−0.240970	+	0.417372i
$262$	7.05006	+	1.88906i	0.435554	+	0.116706i
$263$	−1.67793	−	0.449601i	−0.103466	−	0.0277236i	0.206715	−	0.978401i	$-0.433723\pi$
$263$	−1.67793	−	0.449601i	−0.103466	−	0.0277236i	−0.310180	+	0.950678i	$0.600389\pi$
$264$	−4.08398	+	7.07367i	−0.251352	+	0.435354i
$265$	14.2408	+	11.8410i	0.874803	+	0.727386i
$266$	−8.44048	−	14.0758i	−0.517519	−	0.863041i
$267$	4.39223	+	4.39223i	0.268800	+	0.268800i
$268$	0.817530	+	3.05106i	0.0499386	+	0.186373i
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	0.802577	−	0.596549i	$-0.203462\pi$
$269$	−1.89169	−	3.27650i	−0.115338	−	0.199772i	−0.917915	+	0.396777i	$0.870128\pi$
$270$	7.05972	−	4.99061i	0.429641	−	0.303719i
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.177032	−	0.984205i	$-0.556649\pi$
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.940862	+	0.338789i	$0.889983\pi$
$272$	−1.44231	+	1.44231i	−0.0874531	+	0.0874531i
$273$	0.376284	−	1.50347i	0.0227737	−	0.0909943i
$274$			7.17893i			0.433695i
$275$	−6.73822	+	19.0429i	−0.406330	+	1.14833i
$276$	7.94591	−	4.58757i	0.478287	−	0.276139i
$277$	−1.26567	+	4.72353i	−0.0760465	+	0.283810i	−0.993469	−	0.114106i	$-0.963600\pi$
$277$	−1.26567	+	4.72353i	−0.0760465	+	0.283810i	0.917422	+	0.397916i	$0.130266\pi$
$278$	−11.9941	+	3.21380i	−0.719356	+	0.192751i
$279$	−7.95333			−0.476153
$280$	2.38686	−	5.41322i	0.142642	−	0.323502i
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$	0.615407	−	0.164898i	0.0366470	−	0.00981952i
$283$	−2.92041	+	10.8991i	−0.173601	+	0.647886i	0.823185	+	0.567773i	$0.192195\pi$
$283$	−2.92041	+	10.8991i	−0.173601	+	0.647886i	−0.996786	+	0.0801133i	$0.974472\pi$
$284$	6.16818	−	3.56120i	0.366014	−	0.211318i
$285$	−9.70983	−	26.3098i	−0.575161	−	1.55846i
$286$		−	1.17053i		−	0.0692148i
$287$	4.92018	+	4.75986i	0.290429	+	0.280966i
$288$	0.769067	−	0.769067i	0.0453177	−	0.0453177i
$289$	−11.1193	−	6.41973i	−0.654076	−	0.377631i
$290$	2.70891	−	15.7764i	0.159073	−	0.926425i
$291$	9.47985	+	16.4196i	0.555719	+	0.962533i
$292$	2.98311	+	11.1331i	0.174573	+	0.651517i
$293$	−7.23407	−	7.23407i	−0.422619	−	0.422619i	0.463485	−	0.886105i	$-0.346599\pi$
$293$	−7.23407	−	7.23407i	−0.422619	−	0.422619i	−0.886105	+	0.463485i	$0.846599\pi$
$294$	14.1448	−	0.468657i	0.824939	−	0.0273326i
$295$	−0.175251	−	1.90470i	−0.0102035	−	0.110896i
$296$	2.31288	−	4.00603i	0.134433	−	0.232846i
$297$	15.0880	+	4.04281i	0.875493	+	0.234588i
$298$	−23.1323	−	6.19829i	−1.34002	−	0.359057i
$299$	−0.657432	+	1.13871i	−0.0380203	+	0.0658531i
$300$	5.72374	−	8.33243i	0.330460	−	0.481073i
$301$	0.308440	+	18.6235i	0.0177782	+	1.07344i
$302$	−2.50552	−	2.50552i	−0.144176	−	0.144176i
$303$	5.17439	+	19.3111i	0.297261	+	1.10939i
$304$	3.10166	+	5.37224i	0.177893	+	0.308119i
$305$	8.93304	+	12.6367i	0.511504	+	0.723575i
$306$	−1.92125	−	1.10924i	−0.109831	−	0.0634108i
$307$	−1.07859	+	1.07859i	−0.0615584	+	0.0615584i	−0.737216	−	0.675657i	$-0.763860\pi$
$307$	−1.07859	+	1.07859i	−0.0615584	+	0.0615584i	0.675657	+	0.737216i	$0.263860\pi$
$308$	10.2773	−	2.93705i	0.585605	−	0.167354i
$309$		−	8.65735i		−	0.492500i
$310$	15.3400	−	5.66136i	0.871256	−	0.321544i
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	−0.717420	−	0.696641i	$-0.754677\pi$
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	0.244599	+	0.969624i	$0.421344\pi$
$312$	−0.151613	+	0.565826i	−0.00858338	+	0.0320336i
$313$	2.92361	−	0.783378i	0.165252	−	0.0442791i	−0.175244	−	0.984525i	$-0.556072\pi$
$313$	2.92361	−	0.783378i	0.165252	−	0.0442791i	0.340496	+	0.940246i	$0.389405\pi$
$314$	6.12251			0.345513
$315$	6.35883	+	0.983739i	0.358280	+	0.0554274i
$316$	−5.07627			−0.285562
$317$	−1.88227	+	0.504353i	−0.105719	+	0.0283273i	−0.311291	−	0.950315i	$-0.600761\pi$
$317$	−1.88227	+	0.504353i	−0.105719	+	0.0283273i	0.205572	+	0.978642i	$0.434095\pi$
$318$	4.33410	−	16.1751i	0.243044	−	0.907054i
$319$	25.0463	−	14.4605i	1.40232	−	0.809631i
$320$	−0.935904	+	2.03078i	−0.0523186	+	0.113524i
$321$		−	30.0682i		−	1.67824i
$322$	−11.6475	−	2.91510i	−0.649091	−	0.162452i
$323$	8.94715	−	8.94715i	0.497833	−	0.497833i
$324$	−9.59552	−	5.53997i	−0.533084	−	0.307776i
$325$	−0.113311	+	1.44425i	−0.00628535	+	0.0801124i
$326$	8.27894	+	14.3395i	0.458528	+	0.794194i
$327$	6.92363	+	25.8393i	0.382878	+	1.42892i
$328$	−1.82961	−	1.82961i	−0.101023	−	0.101023i
$329$	−0.728847	−	0.404858i	−0.0401826	−	0.0223205i
$330$	18.1873	−	1.67341i	1.00118	−	0.0921183i
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	−0.129365	−	0.991597i	$-0.541294\pi$
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	0.923431	−	0.383765i	$-0.125373\pi$
$332$	−5.26428	−	1.41056i	−0.288915	−	0.0774145i
$333$	4.85966	+	1.30214i	0.266308	+	0.0713570i
$334$	7.27423	−	12.5993i	0.398028	−	0.689405i
$335$	4.51573	−	5.43092i	0.246721	−	0.296723i
$336$	−5.34841	+	0.0885800i	−0.291780	+	0.00483244i
$337$	−0.823226	−	0.823226i	−0.0448440	−	0.0448440i	0.684329	−	0.729173i	$-0.260095\pi$
$337$	−0.823226	−	0.823226i	−0.0448440	−	0.0448440i	−0.729173	+	0.684329i	$0.760095\pi$
$338$	3.34292	+	12.4759i	0.181831	+	0.678602i
$339$	−13.9436	−	24.1510i	−0.757312	−	1.31170i
$340$	4.49521	+	0.771855i	0.243787	+	0.0418597i
$341$	25.5846	+	14.7713i	1.38548	+	0.799910i
$342$	−4.77078	+	4.77078i	−0.257974	+	0.257974i
$343$	−13.7300	−	12.4293i	−0.741350	−	0.671119i
$344$		−	7.03997i		−	0.379570i
$345$	−18.6327	−	8.58706i	−1.00315	−	0.462312i
$346$	−6.73077	+	3.88601i	−0.361849	+	0.208913i
$347$	−4.32336	+	16.1350i	−0.232090	+	0.866172i	0.747349	+	0.664432i	$0.231326\pi$
$347$	−4.32336	+	16.1350i	−0.232090	+	0.866172i	−0.979439	+	0.201740i	$0.935340\pi$
$348$	−13.9802	+	3.74598i	−0.749417	+	0.200806i
$349$	36.7146			1.96529			0.982644	−	0.185503i	$-0.0593916\pi$
$349$	36.7146			1.96529			0.982644	+	0.185503i	$0.0593916\pi$
$350$	−12.9649	+	2.62897i	−0.693003	+	0.140524i
$351$	1.12024			0.0597942
$352$	−3.90231	+	1.04562i	−0.207994	+	0.0557318i
$353$	−3.69356	+	13.7845i	−0.196588	+	0.733677i	0.795262	+	0.606266i	$0.207333\pi$
$353$	−3.69356	+	13.7845i	−0.196588	+	0.733677i	−0.991850	+	0.127411i	$0.959333\pi$
$354$	−1.49774	+	0.864723i	−0.0796042	+	0.0459595i
$355$	−14.4640	−	6.66588i	−0.767672	−	0.353788i
$356$			3.07230i			0.162832i
$357$	2.99808	+	10.4909i	0.158675	+	0.555236i
$358$	−2.73277	+	2.73277i	−0.144431	+	0.144431i
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.269435	−	0.963019i	$-0.586837\pi$
$359$	−23.4596	−	13.5444i	−1.23815	−	0.714847i	−0.968716	+	0.248172i	$0.920170\pi$
$360$	−2.39693	−	0.411567i	−0.126329	−	0.0216915i
$361$	−9.74064	−	16.8713i	−0.512665	−	0.887962i
$362$	1.80942	+	6.75285i	0.0951011	+	0.354922i
$363$	7.60756	+	7.60756i	0.399293	+	0.399293i
$364$	0.657432	−	0.394227i	0.0344588	−	0.0206631i
$365$	16.4776	−	19.8171i	0.862477	−	1.03727i
$366$	6.99616	−	12.1177i	0.365695	−	0.633403i
$367$	21.8990	+	5.86782i	1.14312	+	0.306298i	0.780204	−	0.625525i	$-0.215115\pi$
$367$	21.8990	+	5.86782i	1.14312	+	0.306298i	0.362914	+	0.931823i	$0.381782\pi$
$368$	4.38350	+	1.17456i	0.228506	+	0.0612279i
$369$	1.40709	−	2.43715i	0.0732502	−	0.126873i
$370$	−10.3000	+	0.947702i	−0.535472	+	0.0492687i
$371$	−18.7938	+	11.2696i	−0.975726	+	0.585090i
$372$	−10.4542	−	10.4542i	−0.542024	−	0.542024i
$373$	−3.32215	−	12.3984i	−0.172014	−	0.641966i	−0.997041	−	0.0768720i	$-0.975507\pi$
$373$	−3.32215	−	12.3984i	−0.172014	−	0.641966i	0.825027	−	0.565094i	$-0.191160\pi$
$374$	4.12025	+	7.13648i	0.213053	+	0.369019i
$375$	−22.6022	+	0.304135i	−1.16717	+	0.0157055i
$376$	0.272906	+	0.157563i	0.0140741	+	0.00812567i
$377$	1.46664	−	1.46664i	0.0755356	−	0.0755356i
$378$	2.81087	+	9.83581i	0.144576	+	0.505900i
$379$			14.4739i			0.743476i	0.928338	+	0.371738i	$0.121238\pi$
$379$			14.4739i			0.743476i	−0.928338	+	0.371738i	$0.878762\pi$
$380$	5.80572	−	12.5976i	0.297827	−	0.646244i
$381$	−5.44718	+	3.14493i	−0.279068	+	0.161120i
$382$	1.15807	−	4.32196i	0.0592518	−	0.221131i
$383$	1.69189	−	0.453341i	0.0864517	−	0.0231647i	−0.215334	−	0.976540i	$-0.569084\pi$
$383$	1.69189	−	0.453341i	0.0864517	−	0.0231647i	0.301786	+	0.953376i	$0.402417\pi$
$384$	2.02179			0.103174
$385$	−18.6283	−	14.9744i	−0.949387	−	0.763168i
$386$	−20.0747			−1.02178
$387$	7.39595	−	1.98174i	0.375957	−	0.100737i
$388$	−2.42713	+	9.05816i	−0.123219	+	0.459858i
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	−0.559839	−	0.828601i	$-0.689137\pi$
$389$	−2.40954	+	1.39115i	−0.122169	+	0.0705341i	0.437670	+	0.899135i	$0.355804\pi$
$390$	1.22884	−	0.453514i	0.0622249	−	0.0229646i
$391$		−	9.25661i		−	0.468127i
$392$	5.11094	+	4.78312i	0.258142	+	0.241584i
$393$	−10.4344	+	10.4344i	−0.526348	+	0.526348i
$394$	9.61304	+	5.55009i	0.484298	+	0.279610i
$395$	6.55224	+	9.26881i	0.329679	+	0.466364i
$396$	−2.19699	−	3.80530i	−0.110403	−	0.191223i
$397$	10.2668	+	38.3163i	0.515277	+	1.92304i	0.349791	+	0.936828i	$0.386253\pi$
$397$	10.2668	+	38.3163i	0.515277	+	1.92304i	0.165486	+	0.986212i	$0.447081\pi$
$398$	7.63821	+	7.63821i	0.382869	+	0.382869i
$399$	33.1780	−	0.549491i	1.66098	−	0.0275089i
$400$	4.91605	−	0.912375i	0.245803	−	0.0456187i
$401$	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	$0.000499221\pi$
$402$	−6.16860	−	1.65287i	−0.307662	−	0.0824378i
$403$	2.04653	+	0.548365i	0.101945	+	0.0273160i
$404$	−4.94422	+	8.56364i	−0.245984	+	0.426057i
$405$	2.27000	+	24.6713i	0.112797	+	1.22593i
$406$	16.5572	+	9.19714i	0.821720	+	0.456446i
$407$	−13.2144	−	13.2144i	−0.655012	−	0.655012i
$408$	−1.06735	−	3.98340i	−0.0528417	−	0.197208i
$409$	−7.65280	−	13.2550i	−0.378407	−	0.655419i	0.612424	−	0.790529i	$-0.290195\pi$
$409$	−7.65280	−	13.2550i	−0.378407	−	0.655419i	−0.990831	+	0.135110i	$0.956861\pi$
$410$	−0.979116	+	5.70228i	−0.0483551	+	0.281615i
$411$	−12.5697	−	7.25713i	−0.620019	−	0.357968i
$412$	3.02785	−	3.02785i	0.149172	−	0.149172i
$413$	2.19547	+	0.549475i	0.108032	+	0.0270379i
$414$			4.93579i			0.242581i
$415$	4.21936	+	11.4328i	0.207120	+	0.561214i
$416$	−0.250919	+	0.144868i	−0.0123023	+	0.00710276i
$417$	6.49762	−	24.2495i	0.318190	−	1.18750i
$418$	24.2073	−	6.48634i	1.18402	−	0.317257i
$419$	−27.7027			−1.35337			−0.676684	−	0.736274i	$-0.736584\pi$
$419$	−27.7027			−1.35337			−0.676684	+	0.736274i	$0.736584\pi$
$420$	7.06525	+	9.65138i	0.344749	+	0.470939i
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	−7.30776	+	1.95811i	−0.355736	+	0.0953192i
$423$	−0.0887072	+	0.331060i	−0.00431309	+	0.0160967i
$424$	7.17295	−	4.14131i	0.348349	−	0.201120i
$425$	−4.39289	−	9.20413i	−0.213087	−	0.446466i
$426$			14.4000i			0.697681i
$427$	−17.6058	+	5.03138i	−0.852005	+	0.243485i
$428$	10.5161	−	10.5161i	0.508317	−	0.508317i
$429$	2.04950	+	1.18328i	0.0989509	+	0.0571293i
$430$	−12.8544	+	9.08690i	−0.619892	+	0.438209i
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	−0.995929	−	0.0901384i	$-0.971269\pi$
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	0.419902	−	0.907569i	$-0.362064\pi$
$432$	−1.00070	−	3.73467i	−0.0481463	−	0.179684i
$433$	−13.2515	−	13.2515i	−0.636829	−	0.636829i	0.312943	−	0.949772i	$-0.398685\pi$
$433$	−13.2515	−	13.2515i	−0.636829	−	0.636829i	−0.949772	+	0.312943i	$0.898685\pi$
$434$	0.320383	+	19.3446i	0.0153789	+	0.928569i
$435$	24.8849	+	20.6914i	1.19314	+	0.992077i
$436$	−6.61564	+	11.4586i	−0.316832	+	0.548769i
$437$	−27.1923	−	7.28615i	−1.30078	−	0.348544i
$438$	−22.5088	−	6.03122i	−1.07551	−	0.288183i
$439$	−7.05383	+	12.2176i	−0.336661	+	0.583114i	−0.983802	−	0.179256i	$-0.942631\pi$
$439$	−7.05383	+	12.2176i	−0.336661	+	0.583114i	0.647141	+	0.762370i	$0.275964\pi$
$440$	6.94616	+	5.77563i	0.331145	+	0.275342i
$441$	−3.58626	+	6.71582i	−0.170774	+	0.319801i
$442$	0.417892	+	0.417892i	0.0198771	+	0.0198771i
$443$	5.45161	+	20.3457i	0.259014	+	0.966652i	0.965813	+	0.259238i	$0.0834715\pi$
$443$	5.45161	+	20.3457i	0.259014	+	0.966652i	−0.706800	+	0.707414i	$0.749862\pi$
$444$	4.67615	+	8.09933i	0.221920	+	0.384377i
$445$	5.60975	−	3.96560i	0.265928	−	0.187988i
$446$	−11.4542	−	6.61308i	−0.542371	−	0.313138i
$447$	34.2370	−	34.2370i	1.61936	−	1.61936i
$448$	−1.90155	−	1.83959i	−0.0898399	−	0.0869125i
$449$			31.3247i			1.47831i	0.673538	+	0.739153i	$0.264774\pi$
$449$			31.3247i			1.47831i	−0.673538	+	0.739153i	$0.735226\pi$
$450$	2.34237	+	4.90780i	0.110420	+	0.231356i
$451$	−9.05278	+	5.22662i	−0.426279	+	0.246112i
$452$	3.56998	−	13.3233i	0.167918	−	0.626677i
$453$	6.91977	−	1.85415i	0.325119	−	0.0871154i
$454$	−16.1938			−0.760014
$455$	−1.56841	−	0.691560i	−0.0735281	−	0.0324209i
$456$	−12.5418			−0.587324
$457$	2.76404	−	0.740622i	0.129296	−	0.0346448i	−0.193591	−	0.981082i	$-0.562013\pi$
$457$	2.76404	−	0.740622i	0.129296	−	0.0346448i	0.322887	+	0.946438i	$0.395347\pi$
$458$	−3.04796	+	11.3751i	−0.142422	+	0.531525i
$459$	−6.82989	+	3.94324i	−0.318792	+	0.184055i
$460$	−3.51341	−	9.51994i	−0.163814	−	0.443870i
$461$		−	3.02674i		−	0.140969i	−0.997513	−	0.0704846i	$-0.977545\pi$
$461$		−	3.02674i		−	0.140969i	0.997513	−	0.0704846i	$-0.0224546\pi$
$462$	−5.24675	+	20.9638i	−0.244101	+	0.975325i
$463$	19.2889	−	19.2889i	0.896431	−	0.896431i	−0.0986876	−	0.995118i	$-0.531464\pi$
$463$	19.2889	−	19.2889i	0.896431	−	0.896431i	0.995118	+	0.0986876i	$0.0314644\pi$
$464$	−6.19961	−	3.57935i	−0.287810	−	0.166167i
$465$	−5.59457	+	32.5822i	−0.259442	+	1.51096i
$466$	2.86212	+	4.95734i	0.132585	+	0.229644i
$467$	−6.50385	−	24.2727i	−0.300962	−	1.12321i	−0.936366	−	0.351026i	$-0.885833\pi$
$467$	−6.50385	−	24.2727i	−0.300962	−	1.12321i	0.635403	−	0.772180i	$-0.280834\pi$
$468$	−0.222827	−	0.222827i	−0.0103002	−	0.0103002i
$469$	4.29784	+	7.16729i	0.198456	+	0.330955i
$470$	−0.0645612	−	0.701677i	−0.00297799	−	0.0323660i
$471$	−6.18921	+	10.7200i	−0.285184	+	0.493953i
$472$	−0.826257	−	0.221395i	−0.0380316	−	0.0101905i
$473$	−27.4722	−	7.36115i	−1.26317	−	0.338466i
$474$	5.13157	−	8.88814i	0.235701	−	0.408246i
$475$	−30.4959	+	5.65976i	−1.39925	+	0.259688i
$476$	−2.62056	+	4.71767i	−0.120113	+	0.216234i
$477$	6.36989	+	6.36989i	0.291657	+	0.291657i
$478$	−2.15802	−	8.05384i	−0.0987055	−	0.368374i
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	0.755704	−	0.654913i	$-0.227295\pi$
$479$	−4.14346	−	7.17668i	−0.189319	−	0.327911i	−0.945024	+	0.327002i	$0.893961\pi$
$480$	−2.60964	−	3.69160i	−0.119113	−	0.168498i
$481$	−1.16069	−	0.670127i	−0.0529231	−	0.0305551i
$482$	−2.09613	+	2.09613i	−0.0954763	+	0.0954763i
$483$	16.8785	−	17.4470i	0.767999	−	0.793867i
$484$			5.32139i			0.241881i
$485$	19.6722	−	7.26018i	0.893269	−	0.329668i
$486$	9.35485	−	5.40103i	0.424345	−	0.244996i
$487$	2.76375	−	10.3144i	0.125237	−	0.467392i	−0.874611	−	0.484826i	$-0.838883\pi$
$487$	2.76375	−	10.3144i	0.125237	−	0.467392i	0.999848	+	0.0174340i	$0.00554969\pi$
$488$	6.68495	−	1.79123i	0.302613	−	0.0810850i
$489$	−33.4765			−1.51386
$490$	2.13656	−	15.5060i	0.0965198	−	0.700488i
$491$	25.7259			1.16100			0.580498	−	0.814262i	$-0.302858\pi$
$491$	25.7259			1.16100			0.580498	+	0.814262i	$0.302858\pi$
$492$	5.05303	−	1.35396i	0.227808	−	0.0610411i
$493$	−3.77924	+	14.1043i	−0.170209	+	0.635227i
$494$	1.55654	−	0.898666i	0.0700319	−	0.0404329i
$495$	−4.11234	+	8.92322i	−0.184836	+	0.401069i
$496$		−	7.31256i		−	0.328344i
$497$	13.1023	−	13.5436i	0.587719	−	0.607514i
$498$	7.79141	−	7.79141i	0.349141	−	0.349141i
$499$	−12.6429	−	7.29940i	−0.565975	−	0.326766i	0.189565	−	0.981868i	$-0.439292\pi$
$499$	−12.6429	−	7.29940i	−0.565975	−	0.326766i	−0.755540	+	0.655102i	$0.772626\pi$
$500$	−8.01135	−	7.79861i	−0.358278	−	0.348764i
$501$	14.7069	+	25.4732i	0.657058	+	1.13806i
$502$	−4.18770	−	15.6287i	−0.186906	−	0.697543i
$503$	13.9891	+	13.9891i	0.623744	+	0.623744i	0.946487	−	0.322743i	$-0.104605\pi$
$503$	13.9891	+	13.9891i	0.623744	+	0.623744i	−0.322743	+	0.946487i	$0.604605\pi$
$504$	1.39733	−	2.51555i	0.0622419	−	0.112051i
$505$	22.0182	−	2.02589i	0.979798	−	0.0901510i
$506$	9.16697	−	15.8777i	0.407522	−	0.705848i
$507$	−25.2237	−	6.75868i	−1.12022	−	0.300163i
$508$	−3.00504	−	0.805197i	−0.133327	−	0.0357248i
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	−0.832621	−	0.553843i	$-0.813161\pi$
$509$	1.42883	−	2.47481i	0.0633319	−	0.109694i	0.895953	+	0.444149i	$0.146494\pi$
$510$	−5.89564	+	7.09049i	−0.261063	+	0.313972i
$511$	15.6825	+	26.1530i	0.693754	+	1.15694i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	6.20768	+	23.1674i	0.274076	+	1.02287i
$514$	2.91234	+	5.04433i	0.128458	+	0.222496i
$515$	−9.43680	−	1.62036i	−0.415835	−	0.0714015i
$516$	12.3264	+	7.11667i	0.542641	+	0.313294i
$517$	0.900216	−	0.900216i	0.0395914	−	0.0395914i
$518$	2.97139	−	11.8724i	0.130555	−	0.521644i
$519$		−	15.7134i		−	0.689741i
$520$	0.588393	+	0.271166i	0.0258027	+	0.0118914i
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.153595	−	0.988134i	$-0.450915\pi$
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.932547	+	0.361049i	$0.117581\pi$
$522$	2.01516	−	7.52068i	0.0882011	−	0.329171i
$523$	30.5069	−	8.17429i	1.33397	−	0.357437i	0.479777	−	0.877390i	$-0.340717\pi$
$523$	30.5069	−	8.17429i	1.33397	−	0.357437i	0.854195	+	0.519954i	$0.174051\pi$
$524$	−7.29876			−0.318848
$525$	8.50302	−	25.3581i	0.371102	−	1.10672i
$526$	1.73712			0.0757422
$527$	−14.4075	+	3.86048i	−0.627600	+	0.168165i
$528$	2.11403	−	7.88965i	0.0920012	−	0.343353i
$529$	2.08308	−	1.20267i	0.0905687	−	0.0522899i
$530$	−16.8202	−	7.75174i	−0.730623	−	0.336714i
$531$		−	0.930359i		−	0.0403742i
$532$	11.7960	+	11.4116i	0.511419	+	0.494755i
$533$	−0.530105	+	0.530105i	−0.0229614	+	0.0229614i
$534$	−5.37936	−	3.10577i	−0.232788	−	0.134400i
$535$	−32.7753	−	5.62772i	−1.41700	−	0.243308i
$536$	−1.57935	−	2.73551i	−0.0682174	−	0.118156i
$537$	−2.02232	−	7.54741i	−0.0872696	−	0.325695i
$538$	2.67525	+	2.67525i	0.115338	+	0.115338i
$539$	24.0094	−	14.9432i	1.03416	−	0.643648i
$540$	−5.52750	+	6.64775i	−0.237866	+	0.286073i
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	0.127262	+	0.991869i	$0.459381\pi$
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	−0.922615	+	0.385722i	$0.873952\pi$
$542$	20.5257	+	5.49985i	0.881655	+	0.236239i
$543$	−13.6528	−	3.65827i	−0.585899	−	0.156991i
$544$	1.01987	−	1.76647i	0.0437266	−	0.0757366i
$545$	29.4616	−	2.71076i	1.26200	−	0.116116i
$546$	0.0256649	+	1.54963i	0.00109836	+	0.0663182i
$547$	−20.0765	−	20.0765i	−0.858409	−	0.858409i	0.132742	−	0.991151i	$-0.457622\pi$
$547$	−20.0765	−	20.0765i	−0.858409	−	0.858409i	−0.991151	+	0.132742i	$0.957622\pi$
$548$	−1.85804	−	6.93431i	−0.0793717	−	0.296219i
$549$	3.76360	+	6.51875i	0.160627	+	0.278213i
$550$	1.57996	−	20.1380i	0.0673697	−	0.858687i
$551$	38.4582	+	22.2039i	1.63838	+	0.945916i
$552$	−6.48781	+	6.48781i	−0.276139	+	0.276139i
$553$	−12.9136	+	3.69043i	−0.549141	+	0.156933i
$554$		−	4.89016i		−	0.207763i
$555$	8.75286	−	18.9925i	0.371538	−	0.806187i
$556$	10.7536	−	6.20859i	0.456054	−	0.263303i
$557$	−6.65499	+	24.8367i	−0.281981	+	1.05237i	0.669037	+	0.743229i	$0.266707\pi$
$557$	−6.65499	+	24.8367i	−0.281981	+	1.05237i	−0.951017	+	0.309137i	$0.899960\pi$
$558$	7.68233	−	2.05847i	0.325219	−	0.0871421i
$559$	−2.03974			−0.0862718
$560$	−0.904483	+	5.84653i	−0.0382214	+	0.247061i
$561$	−16.6605			−0.703408
$562$	28.4732	−	7.62937i	1.20107	−	0.321825i
$563$	1.38907	−	5.18407i	0.0585422	−	0.218482i	−0.930458	−	0.366400i	$-0.880590\pi$
$563$	1.38907	−	5.18407i	0.0585422	−	0.218482i	0.989000	+	0.147917i	$0.0472569\pi$
$564$	−0.551759	+	0.318558i	−0.0232332	+	0.0134137i
$565$	−28.9352	+	10.6788i	−1.21731	+	0.449258i
$566$		−	11.2836i		−	0.474286i
$567$	−28.4377	−	7.11728i	−1.19427	−	0.298898i
$568$	−5.03630	+	5.03630i	−0.211318	+	0.211318i
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.885483	−	0.464672i	$-0.153828\pi$
$569$	22.0839	+	12.7502i	0.925806	+	0.534514i	0.0403234	+	0.999187i	$0.487161\pi$
$570$	16.1884	+	22.9002i	0.678059	+	0.959184i
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	0.650263	−	0.759709i	$-0.274659\pi$
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	−0.983059	+	0.183290i	$0.941325\pi$
$572$	0.302955	+	1.13064i	0.0126672	+	0.0472746i
$573$	6.39672	+	6.39672i	0.267227	+	0.267227i
$574$	−5.98447	−	3.32424i	−0.249787	−	0.138751i
$575$	−12.8476	+	18.7031i	−0.535781	+	0.779973i
$576$	−0.543813	+	0.941911i	−0.0226589	+	0.0392463i
$577$	−22.2641	−	5.96565i	−0.926867	−	0.248353i	−0.236349	−	0.971668i	$-0.575951\pi$
$577$	−22.2641	−	5.96565i	−0.926867	−	0.248353i	−0.690518	+	0.723315i	$0.742617\pi$
$578$	12.4020	+	3.32310i	0.515854	+	0.138223i
$579$	20.2934	−	35.1493i	0.843366	−	1.46075i
$580$	1.46664	+	15.9400i	0.0608988	+	0.661872i
$581$	−14.4173	+	0.238779i	−0.598132	+	0.00990621i
$582$	−13.4065	−	13.4065i	−0.555719	−	0.555719i
$583$	−8.66048	−	32.3214i	−0.358681	−	1.33861i
$584$	−5.76293	−	9.98169i	−0.238472	−	0.413045i
$585$	−0.119246	+	0.694478i	−0.00493022	+	0.0287131i
$586$	8.85989	+	5.11526i	0.365999	+	0.211310i
$587$	28.2277	−	28.2277i	1.16508	−	1.16508i	0.181734	−	0.983348i	$-0.441829\pi$
$587$	28.2277	−	28.2277i	1.16508	−	1.16508i	0.983348	−	0.181734i	$-0.0581711\pi$
$588$	−13.5415	+	4.11362i	−0.558441	+	0.169643i
$589$			45.3622i			1.86912i
$590$	0.662251	+	1.79444i	0.0272644	+	0.0738758i
$591$	−19.4355	+	11.2211i	−0.799471	+	0.461575i
$592$	−1.19723	+	4.46814i	−0.0492060	+	0.183639i
$593$	−34.2220	+	9.16977i	−1.40533	+	0.376557i	−0.880256	−	0.474499i	$-0.842629\pi$
$593$	−34.2220	+	9.16977i	−1.40533	+	0.376557i	−0.525075	+	0.851056i	$0.675963\pi$
$594$	−15.6202			−0.640905
$595$	11.9965	−	1.30447i	0.491811	−	0.0534782i
$596$	23.9483			0.980963
$597$	−21.0953	+	5.65247i	−0.863373	+	0.231340i
$598$	0.340312	−	1.27006i	0.0139164	−	0.0519367i
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	−0.172775	−	0.984961i	$-0.555273\pi$
$599$	14.5339	−	8.39115i	0.593839	−	0.342853i	0.766614	+	0.642108i	$0.221940\pi$
$600$	−3.37211	+	9.52993i	−0.137666	+	0.389058i
$601$		−	1.73528i		−	0.0707833i	−0.999374	−	0.0353917i	$-0.988732\pi$
$601$		−	1.73528i		−	0.0707833i	0.999374	−	0.0353917i	$-0.0112679\pi$
$602$	−5.11804	−	17.9091i	−0.208596	−	0.729919i
$603$	2.42925	−	2.42925i	0.0989266	−	0.0989266i
$604$	3.06862	+	1.77167i	0.124860	+	0.0720881i
$605$	9.71637	−	6.86862i	0.395027	−	0.279249i
$606$	−9.99616	−	17.3139i	−0.406066	−	0.703327i
$607$	10.2070	+	38.0930i	0.414288	+	1.54615i	0.786257	+	0.617900i	$0.212016\pi$
$607$	10.2070	+	38.0930i	0.414288	+	1.54615i	−0.371968	+	0.928245i	$0.621317\pi$
$608$	−4.38642	−	4.38642i	−0.177893	−	0.177893i
$609$	−32.8410	+	19.6930i	−1.33079	+	0.798000i
$610$	−11.8993	−	9.89407i	−0.481787	−	0.400599i
$611$	0.0456517	−	0.0790711i	0.00184687	−	0.00319887i
$612$	2.14288	+	0.574183i	0.0866208	+	0.0232100i
$613$	−0.330293	−	0.0885018i	−0.0133404	−	0.00357455i	0.252143	−	0.967690i	$-0.418865\pi$
$613$	−0.330293	−	0.0885018i	−0.0133404	−	0.00357455i	−0.265483	+	0.964116i	$0.585531\pi$
$614$	0.762678	−	1.32100i	0.0307792	−	0.0533111i
$615$	−8.99444	−	7.47875i	−0.362691	−	0.301572i
$616$	−9.16697	+	5.49694i	−0.369348	+	0.221478i
$617$	11.1876	+	11.1876i	0.450397	+	0.450397i	0.895486	−	0.445089i	$-0.146828\pi$
$617$	11.1876	+	11.1876i	0.450397	+	0.450397i	−0.445089	+	0.895486i	$0.646828\pi$
$618$	2.24069	+	8.36236i	0.0901337	+	0.336383i
$619$	18.2682	+	31.6414i	0.734260	+	1.27178i	0.955047	+	0.296454i	$0.0958042\pi$
$619$	18.2682	+	31.6414i	0.734260	+	1.27178i	−0.220787	+	0.975322i	$0.570862\pi$
$620$	−13.3521	+	9.43875i	−0.536232	+	0.379069i
$621$	15.1956	+	8.77316i	0.609777	+	0.352055i
$622$	6.80819	−	6.80819i	0.272984	−	0.272984i
$623$	2.23356	+	7.81566i	0.0894855	+	0.313128i
$624$		−	0.585786i		−	0.0234502i
$625$	−3.89884	+	24.6941i	−0.155953	+	0.987764i
$626$	−2.62123	+	1.51337i	−0.104766	+	0.0604864i
$627$	−13.1140	+	48.9421i	−0.523723	+	1.95456i
$628$	−5.91389	+	1.58462i	−0.235990	+	0.0632333i
$629$	9.43535			0.376212
$630$	−6.39677	+	0.695569i	−0.254854	+	0.0277121i
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	4.90330	−	1.31384i	0.195043	−	0.0522616i
$633$	3.95888	−	14.7747i	0.157351	−	0.587243i
$634$	1.68760	−	0.974335i	0.0670231	−	0.0386958i
$635$	2.40856	+	6.52623i	0.0955807	+	0.258986i
$636$			16.7457i			0.664010i
$637$	1.38585	−	1.48083i	0.0549093	−	0.0586726i
$638$	−20.4502	+	20.4502i	−0.809631	+	0.809631i
$639$	−6.70867	−	3.87325i	−0.265391	−	0.153223i
$640$	0.378409	−	2.20382i	0.0149579	−	0.0871135i
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	0.972129	−	0.234445i	$-0.0753272\pi$
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	−0.689100	+	0.724666i	$0.741994\pi$
$642$	7.78222	+	29.0436i	0.307140	+	1.14626i
$643$	7.65201	+	7.65201i	0.301766	+	0.301766i	0.841704	−	0.539939i	$-0.181553\pi$
$643$	7.65201	+	7.65201i	0.301766	+	0.301766i	−0.539939	+	0.841704i	$0.681553\pi$
$644$	12.0051	−	0.198828i	0.473068	−	0.00783492i
$645$	−2.91605	−	31.6928i	−0.114819	−	1.24790i
$646$	−6.32659	+	10.9580i	−0.248916	+	0.431136i
$647$	31.2468	+	8.37254i	1.22844	+	0.329159i	0.813971	−	0.580906i	$-0.197302\pi$
$647$	31.2468	+	8.37254i	1.22844	+	0.329159i	0.414466	+	0.910065i	$0.363968\pi$
$648$	10.7024	+	2.86770i	0.420430	+	0.112654i
$649$	−1.72791	+	2.99282i	−0.0678262	+	0.117478i
$650$	−0.264349	−	1.42436i	−0.0103686	−	0.0558681i
$651$	−34.1947	−	18.9943i	−1.34019	−	0.744447i
$652$	−11.7082	−	11.7082i	−0.458528	−	0.458528i
$653$	−0.132578	−	0.494788i	−0.00518818	−	0.0193625i	0.963283	−	0.268487i	$-0.0865237\pi$
$653$	−0.132578	−	0.494788i	−0.00518818	−	0.0193625i	−0.968471	+	0.249125i	$0.919857\pi$
$654$	−13.3754	−	23.1669i	−0.523020	−	0.905898i
$655$	9.42093	+	13.3269i	0.368106	+	0.520724i
$656$	2.24080	+	1.29373i	0.0874886	+	0.0505116i
$657$	8.86417	−	8.86417i	0.345824	−	0.345824i
$658$	0.808797	+	0.202423i	0.0315302	+	0.00789127i
$659$			19.5542i			0.761723i	0.924632	+	0.380862i	$0.124373\pi$
$659$			19.5542i			0.761723i	−0.924632	+	0.380862i	$0.875627\pi$
$660$	−17.1345	+	6.32361i	−0.666959	+	0.246146i
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.339388	−	0.940647i	$-0.389780\pi$
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.984318	+	0.176405i	$0.0564468\pi$
$662$	−7.47819	+	27.9090i	−0.290648	+	1.08471i
$663$	−1.15414	+	0.309250i	−0.0448230	+	0.0120103i
$664$	5.44998			0.211500
$665$	5.61080	−	36.2679i	0.217578	−	1.40641i
$666$	−5.03109			−0.194951
$667$	31.3801	−	8.40828i	1.21504	−	0.325570i
$668$	−3.76542	+	14.0527i	−0.145688	+	0.543716i
$669$	23.1579	−	13.3702i	0.895337	−	0.516923i
$670$	−2.95623	+	6.41462i	−0.114209	+	0.247819i
$671$		−	27.9597i		−	1.07937i
$672$	5.14324	−	1.46983i	0.198405	−	0.0567000i
$673$	18.4813	−	18.4813i	0.712401	−	0.712401i	−0.254636	−	0.967037i	$-0.581956\pi$
$673$	18.4813	−	18.4813i	0.712401	−	0.712401i	0.967037	+	0.254636i	$0.0819556\pi$
$674$	1.00824	+	0.582108i	0.0388360	+	0.0224220i
$675$	19.2729	+	1.51208i	0.741812	+	0.0582002i
$676$	−6.45803	−	11.1856i	−0.248386	−	0.430217i
$677$	−10.6631	−	39.7951i	−0.409815	−	1.52945i	−0.794999	−	0.606611i	$-0.792528\pi$
$677$	−10.6631	−	39.7951i	−0.409815	−	1.52945i	0.385183	−	0.922840i	$-0.374138\pi$
$678$	19.7192	+	19.7192i	0.757312	+	0.757312i
$679$	0.410862	+	24.8076i	0.0157674	+	0.952030i
$680$	−4.54181	+	0.417892i	−0.174171	+	0.0160254i
$681$	16.3702	−	28.3541i	0.627309	−	1.08653i
$682$	−28.5359	−	7.64618i	−1.09270	−	0.292787i
$683$	8.81689	+	2.36248i	0.337369	+	0.0903978i	0.423526	−	0.905884i	$-0.360792\pi$
$683$	8.81689	+	2.36248i	0.337369	+	0.0903978i	−0.0861573	+	0.996282i	$0.527459\pi$
$684$	3.37345	−	5.84298i	0.128987	−	0.223412i
$685$	−10.2631	+	12.3431i	−0.392134	+	0.471607i
$686$	16.4791	+	8.45219i	0.629175	+	0.322706i
$687$	−16.8358	−	16.8358i	−0.642325	−	0.642325i
$688$	1.82208	+	6.80009i	0.0694661	+	0.259251i
$689$	−1.19989	−	2.07827i	−0.0457121	−	0.0791758i
$690$	20.2203	+	3.47195i	0.769775	+	0.132175i
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.991940	−	0.126712i	$-0.959558\pi$
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.605706	−	0.795689i	$-0.707109\pi$
$692$	5.49565	−	5.49565i	0.208913	−	0.208913i
$693$	−8.35538	−	8.08313i	−0.317395	−	0.307053i
$694$		−	16.7042i		−	0.634082i
$695$	−25.2166	−	11.6213i	−0.956520	−	0.440821i
$696$	12.5343	−	7.23668i	0.475111	−	0.274306i
$697$	1.36598	−	5.09790i	0.0517401	−	0.193097i
$698$	−35.4636	+	9.50244i	−1.34232	+	0.359673i
$699$	−11.5732			−0.437739
$700$	11.8427	−	5.89495i	0.447612	−	0.222808i
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$	−1.08207	+	0.289940i	−0.0408402	+	0.0109431i
$703$	7.42684	−	27.7173i	0.280109	−	1.04538i
$704$	3.49872	−	2.01999i	0.131863	−	0.0761311i
$705$	1.29385	+	0.596280i	0.0487290	+	0.0224572i
$706$		−	14.2708i		−	0.537089i
$707$	−6.35191	+	25.3796i	−0.238888	+	0.954496i
$708$	1.22290	−	1.22290i	0.0459595	−	0.0459595i
$709$	−12.7354	−	7.35277i	−0.478287	−	0.276139i	0.241416	−	0.970422i	$-0.422388\pi$
$709$	−12.7354	−	7.35277i	−0.478287	−	0.276139i	−0.719702	+	0.694283i	$0.755722\pi$
$710$	15.6965	+	2.69518i	0.589078	+	0.101148i
$711$	2.76054	+	4.78140i	0.103528	+	0.179316i
$712$	−0.795171	−	2.96762i	−0.0298003	−	0.111216i
$713$	23.4656	+	23.4656i	0.878795	+	0.878795i
$714$	−5.61116	−	9.35745i	−0.209992	−	0.350194i
$715$	1.67341	−	2.01256i	0.0625821	−	0.0752654i
$716$	1.93236	−	3.34695i	0.0722157	−	0.125081i
$717$	16.2831	+	4.36306i	0.608105	+	0.162941i
$718$	26.1658	+	7.01110i	0.976499	+	0.261652i
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	−0.559831	−	0.828607i	$-0.689134\pi$
$719$	11.7360	−	20.3273i	0.437679	−	0.758082i	0.997510	+	0.0705247i	$0.0224674\pi$
$720$	2.42177	−	0.222827i	0.0902542	−	0.00830428i
$721$	5.50134	−	9.90382i	0.204881	−	0.368837i
$722$	13.7753	+	13.7753i	0.512665	+	0.512665i
$723$	−1.55119	−	5.78913i	−0.0576895	−	0.215300i
$724$	−3.49553	−	6.05444i	−0.129911	−	0.225012i
$725$	27.2119	−	23.2526i	1.01062	−	0.863581i
$726$	−9.31732	−	5.37936i	−0.345798	−	0.199647i
$727$	−14.1380	+	14.1380i	−0.524349	+	0.524349i	−0.918882	−	0.394533i	$-0.870907\pi$
$727$	−14.1380	+	14.1380i	−0.524349	+	0.524349i	0.394533	+	0.918882i	$0.370907\pi$
$728$	−0.532998	+	0.550950i	−0.0197542	+	0.0204196i
$729$		−	11.4004i		−	0.422236i
$730$	−10.7871	+	23.4065i	−0.399249	+	0.866315i
$731$	12.4359	−	7.17986i	0.459958	−	0.265557i
$732$	−3.62148	+	13.5155i	−0.133854	+	0.499549i
$733$	−26.7908	+	7.17859i	−0.989543	+	0.265147i	−0.717058	−	0.697013i	$-0.754512\pi$
$733$	−26.7908	+	7.17859i	−0.989543	+	0.265147i	−0.272484	+	0.962160i	$0.587845\pi$
$734$	−22.6715			−0.836821
$735$	24.9899	+	19.4158i	0.921765	+	0.716164i
$736$	−4.53813			−0.167278
$737$	−12.3262	+	3.30280i	−0.454042	+	0.121660i
$738$	−0.728364	+	2.71829i	−0.0268114	+	0.100062i
$739$	−11.7451	+	6.78102i	−0.432050	+	0.249444i	−0.700219	−	0.713928i	$-0.746915\pi$
$739$	−11.7451	+	6.78102i	−0.432050	+	0.249444i	0.268170	+	0.963372i	$0.413581\pi$
$740$	9.70376	−	3.58125i	0.356717	−	0.131649i
$741$			3.63383i			0.133492i
$742$	15.2366	−	15.7498i	0.559354	−	0.578194i
$743$	13.5961	−	13.5961i	0.498791	−	0.498791i	−0.412270	−	0.911062i	$-0.635264\pi$
$743$	13.5961	−	13.5961i	0.498791	−	0.498791i	0.911062	+	0.412270i	$0.135264\pi$
$744$	12.8037	+	7.39223i	0.469407	+	0.271012i
$745$	−30.9115	−	43.7275i	−1.13251	−	1.60205i
$746$	6.41789	+	11.1161i	0.234976	+	0.406990i
$747$	1.53416	+	5.72557i	0.0561320	+	0.209488i
$748$	−5.82691	−	5.82691i	−0.213053	−	0.213053i
$749$	19.1069	−	34.3973i	0.698152	−	1.25685i
$750$	21.7534	−	6.14366i	0.794320	−	0.224335i
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	0.125182	+	0.992134i	$0.460049\pi$
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	−0.921804	+	0.387656i	$0.873285\pi$
$752$	−0.304388	−	0.0815604i	−0.0110999	−	0.00297420i
$753$	31.5979	+	8.46663i	1.15149	+	0.308541i
$754$	−1.03707	+	1.79626i	−0.0377678	+	0.0654158i
$755$	−0.725941	−	7.88981i	−0.0264197	−	0.287140i
$756$	−5.26079	−	8.77316i	−0.191333	−	0.319077i
$757$	7.88896	+	7.88896i	0.286729	+	0.286729i	0.835785	−	0.549056i	$-0.185013\pi$
$757$	7.88896	+	7.88896i	0.286729	+	0.286729i	−0.549056	+	0.835785i	$0.685013\pi$
$758$	−3.74613	−	13.9807i	−0.136065	−	0.507803i
$759$	18.5337	+	32.1013i	0.672730	+	1.16520i
$760$	−2.34739	+	13.6710i	−0.0851489	+	0.495899i
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	0.468700	−	0.883357i	$-0.344722\pi$
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	−0.530660	+	0.847585i	$0.678056\pi$
$762$	4.44761	−	4.44761i	0.161120	−	0.161120i
$763$	−8.49921	+	33.9593i	−0.307692	+	1.22941i
$764$			4.47442i			0.161879i
$765$	−1.71753	−	4.65384i	−0.0620976	−	0.168260i
$766$	−1.51691	+	0.875788i	−0.0548082	+	0.0316435i
$767$	−0.0641463	+	0.239397i	−0.00231619	+	0.00864413i
$768$	−1.95290	+	0.523277i	−0.0704691	+	0.0188821i
$769$	−17.4914			−0.630756			−0.315378	−	0.948966i	$-0.602131\pi$
$769$	−17.4914			−0.630756			−0.315378	+	0.948966i	$0.602131\pi$
$770$	21.8693	+	9.64284i	0.788113	+	0.347504i
$771$	−11.7763			−0.424112
$772$	19.3907	−	5.19573i	0.697887	−	0.186998i
$773$	11.5736	−	43.1933i	0.416274	−	1.55355i	−0.365997	−	0.930616i	$-0.619272\pi$
$773$	11.5736	−	43.1933i	0.416274	−	1.55355i	0.782271	−	0.622939i	$-0.214061\pi$
$774$	−6.63103	+	3.82843i	−0.238347	+	0.137610i
$775$	34.4686	+	12.1965i	1.23815	+	0.438112i
$776$		−	9.37769i		−	0.336640i
$777$	17.7839	+	17.2044i	0.637994	+	0.617205i
$778$	1.96738	−	1.96738i	0.0705341	−	0.0705341i
$779$	−13.9004	−	8.02542i	−0.498035	−	0.287540i
$780$	−1.06959	+	0.756109i	−0.0382976	+	0.0270730i
$781$	14.3871	+	24.9193i	0.514813	+	0.891682i
$782$	2.39579	+	8.94120i	0.0856732	+	0.319737i
$783$	−19.5716	−	19.5716i	−0.699433	−	0.699433i
$784$	−6.17475	−	3.29733i	−0.220527	−	0.117762i
$785$	10.5268	+	8.75286i	0.375717	+	0.312403i
$786$	7.37827	−	12.7795i	0.263174	−	0.455831i
$787$	25.0643	+	6.71595i	0.893445	+	0.239398i	0.676199	−	0.736719i	$-0.263626\pi$
$787$	25.0643	+	6.71595i	0.893445	+	0.239398i	0.217246	+	0.976117i	$0.430293\pi$
$788$	−10.7220	−	2.87294i	−0.381954	−	0.102344i
$789$	−1.75605	+	3.04156i	−0.0625170	+	0.108283i
$790$	−8.72792	−	7.25713i	−0.310525	−	0.258197i
$791$	−0.604323	−	36.4887i	−0.0214873	−	1.29739i
$792$	3.10701	+	3.10701i	0.110403	+	0.110403i
$793$	−0.518984	−	1.93688i	−0.0184297	−	0.0687805i
$794$	−19.8340	−	34.3535i	−0.703881	−	1.21916i
$795$	30.5761	−	21.6146i	1.08442	−	0.766592i
$796$	−9.35485	−	5.40103i	−0.331574	−	0.191434i
$797$	−37.3374	+	37.3374i	−1.32256	+	1.32256i	−0.410861	+	0.911698i	$0.634772\pi$
$797$	−37.3374	+	37.3374i	−1.32256	+	1.32256i	−0.911698	+	0.410861i	$0.865228\pi$
$798$	−31.9052	+	9.11786i	−1.12943	+	0.322769i
$799$			0.642773i			0.0227397i
$800$	−4.51240	+	2.15365i	−0.159538	+	0.0761432i
$801$	2.89384	−	1.67076i	0.102249	−	0.0590333i
$802$	−5.16876	+	19.2901i	−0.182515	+	0.681156i
$803$	−44.9776	+	12.0517i	−1.58722	+	0.425295i
$804$	6.38621			0.225224
$805$	−15.8588	−	21.6636i	−0.558948	−	0.763543i
$806$	−2.11872			−0.0746287
$807$	−7.38854	+	1.97975i	−0.260089	+	0.0696906i
$808$	2.55932	−	9.55150i	0.0900364	−	0.336021i
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	−0.724036	−	0.689762i	$-0.757715\pi$
$809$	−13.9001	+	8.02525i	−0.488703	+	0.282153i	0.235333	+	0.971915i	$0.424382\pi$
$810$	−8.57806	−	23.2431i	−0.301402	−	0.816680i
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$	−18.3734	−	4.59844i	−0.644781	−	0.161374i
$813$	−30.3791	+	30.3791i	−1.06544	+	1.06544i
$814$	16.1842	+	9.34397i	0.567257	+	0.327506i
$815$	−6.26564	+	36.4905i	−0.219476	+	1.27821i
$816$	2.06196	+	3.57142i	0.0721831	+	0.125025i
$817$	−11.3030	−	42.1832i	−0.395440	−	1.47580i
$818$	10.8227	+	10.8227i	0.378407	+	0.378407i
$819$	−0.728847	−	0.404858i	−0.0254680	−	0.0141469i
$820$	−0.530105	−	5.76139i	−0.0185121	−	0.201196i
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	−0.999351	−	0.0360337i	$-0.988528\pi$
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	0.530881	+	0.847446i	$0.321861\pi$
$822$	14.0197	+	3.75657i	0.488993	+	0.131025i
$823$	−27.0285	−	7.24225i	−0.942153	−	0.252449i	−0.245124	−	0.969492i	$-0.578829\pi$
$823$	−27.0285	−	7.24225i	−0.942153	−	0.252449i	−0.697029	+	0.717043i	$0.745495\pi$
$824$	−2.14101	+	3.70835i	−0.0745858	+	0.129186i
$825$	33.6628	+	23.1237i	1.17199	+	0.805066i
$826$	−2.26288	+	0.0374776i	−0.0787355	+	0.00130401i
$827$	16.8901	+	16.8901i	0.587325	+	0.587325i	0.936906	−	0.349581i	$-0.113676\pi$
$827$	16.8901	+	16.8901i	0.587325	+	0.587325i	−0.349581	+	0.936906i	$0.613676\pi$
$828$	−1.27748	−	4.76761i	−0.0443954	−	0.165686i
$829$	7.08412	+	12.2701i	0.246042	+	0.426157i	0.962424	−	0.271551i	$-0.0875367\pi$
$829$	7.08412	+	12.2701i	0.246042	+	0.426157i	−0.716382	+	0.697708i	$0.754203\pi$
$830$	−7.03461	−	9.95118i	−0.244175	−	0.345410i
$831$	8.56228	+	4.94343i	0.297022	+	0.171486i
$832$	0.204875	−	0.204875i	0.00710276	−	0.00710276i
$833$	−3.23673	+	13.9065i	−0.112146	+	0.481831i
$834$			25.1049i			0.869311i
$835$	30.5192	−	11.2634i	1.05616	−	0.389785i
$836$	−21.7037	+	12.5306i	−0.750638	+	0.433381i
$837$	7.31770	−	27.3100i	0.252937	−	0.943972i
$838$	26.7588	−	7.17000i	0.924367	−	0.247683i
$839$	18.1874			0.627900			0.313950	−	0.949439i	$-0.398348\pi$
$839$	18.1874			0.627900			0.313950	+	0.949439i	$0.398348\pi$
$840$	−9.32247	−	7.49390i	−0.321656	−	0.258564i
$841$	−22.2469			−0.767134
$842$	−31.8909	+	8.54515i	−1.09903	+	0.294485i
$843$	−15.4250	+	57.5667i	−0.531264	+	1.98270i
$844$	6.55196	−	3.78278i	0.225528	−	0.130209i
$845$	−12.0882	+	26.2297i	−0.415846	+	0.902329i
$846$		−	0.342738i		−	0.0117836i
$847$	3.86863	+	13.5371i	0.132928	+	0.465141i
$848$	−5.85669	+	5.85669i	−0.201120	+	0.201120i
$849$	19.7567	+	11.4065i	0.678048	+	0.391471i
$850$	6.62541	+	7.75354i	0.227250	+	0.265944i
$851$	−10.4962	−	18.1799i	−0.359804	−	0.623198i
$852$	−3.72699	−	13.9093i	−0.127685	−	0.476525i
$853$	−17.4820	−	17.4820i	−0.598574	−	0.598574i	0.341359	−	0.939933i	$-0.389113\pi$
$853$	−17.4820	−	17.4820i	−0.598574	−	0.598574i	−0.939933	+	0.341359i	$0.889113\pi$
$854$	15.7037	−	9.41665i	0.537369	−	0.322231i
$855$	−15.0231	+	1.38227i	−0.513778	+	0.0472726i
$856$	−7.43604	+	12.8796i	−0.254159	+	0.440216i
$857$	−25.2634	−	6.76932i	−0.862982	−	0.231235i	−0.199932	−	0.979810i	$-0.564072\pi$
$857$	−25.2634	−	6.76932i	−0.862982	−	0.231235i	−0.663051	+	0.748574i	$0.730739\pi$
$858$	−2.28592	−	0.612511i	−0.0780401	−	0.0209108i
$859$	24.4126	−	42.2838i	0.832946	−	1.44271i	−0.0627455	−	0.998030i	$-0.519986\pi$
$859$	24.4126	−	42.2838i	0.832946	−	1.44271i	0.895692	−	0.444676i	$-0.146681\pi$
$860$	10.0645	−	12.1042i	0.343196	−	0.412751i
$861$	11.8701	−	7.11788i	0.404533	−	0.242577i
$862$	16.9121	+	16.9121i	0.576027	+	0.576027i
$863$	3.97256	+	14.8258i	0.135228	+	0.504676i	0.999997	+	0.00250685i	$0.000797956\pi$
$863$	3.97256	+	14.8258i	0.135228	+	0.504676i	−0.864769	+	0.502169i	$0.832535\pi$
$864$	1.93321	+	3.34841i	0.0657691	+	0.113915i
$865$	−17.1281	−	2.94100i	−0.582373	−	0.0999971i
$866$	16.2298	+	9.37026i	0.551510	+	0.318414i
$867$	−18.3555	+	18.3555i	−0.623387	+	0.623387i
$868$	−5.31621	−	18.6025i	−0.180444	−	0.631410i
$869$		−	20.5080i		−	0.695686i
$870$	−29.3923	−	13.5457i	−0.996491	−	0.459242i
$871$	−0.792578	+	0.457595i	−0.0268555	+	0.0155050i
$872$	3.42451	−	12.7804i	0.115968	−	0.432800i
$873$	9.85188	−	2.63980i	0.333436	−	0.0893438i
$874$	28.1515			0.952240
$875$	−26.0497	−	14.0147i	−0.880641	−	0.473784i
$876$	23.3028			0.787330
$877$	38.1169	−	10.2134i	1.28712	−	0.344882i	0.450552	−	0.892750i	$-0.351227\pi$
$877$	38.1169	−	10.2134i	1.28712	−	0.344882i	0.836565	+	0.547868i	$0.184560\pi$
$878$	3.65133	−	13.6270i	0.123227	−	0.459888i
$879$	−17.9128	+	10.3420i	−0.604185	+	0.348826i
$880$	−8.20431	−	3.78103i	−0.276567	−	0.127458i
$881$			52.5926i			1.77189i	0.463791	+	0.885945i	$0.346489\pi$
$881$			52.5926i			1.77189i	−0.463791	+	0.885945i	$0.653511\pi$
$882$	1.72588	−	7.41518i	0.0581135	−	0.249682i
$883$	13.0940	−	13.0940i	0.440649	−	0.440649i	−0.451581	−	0.892230i	$-0.649140\pi$
$883$	13.0940	−	13.0940i	0.440649	−	0.440649i	0.892230	+	0.451581i	$0.149140\pi$
$884$	−0.511811	−	0.295494i	−0.0172141	−	0.00993854i
$885$	−3.81138	−	0.654437i	−0.128118	−	0.0219987i
$886$	−10.5317	−	18.2414i	−0.353819	−	0.612833i
$887$	9.56553	+	35.6990i	0.321179	+	1.19866i	0.918098	+	0.396354i	$0.129725\pi$
$887$	9.56553	+	35.6990i	0.321179	+	1.19866i	−0.596919	+	0.802302i	$0.703609\pi$
$888$	−6.61308	−	6.61308i	−0.221920	−	0.221920i
$889$	−8.22991	+	0.136303i	−0.276022	+	0.00457146i
$890$	−4.39223	+	5.28239i	−0.147228	+	0.177066i
$891$	22.3813	−	38.7656i	0.749803	−	1.29870i
$892$	12.7755	+	3.42318i	0.427755	+	0.114617i
$893$	1.88822	+	0.505946i	0.0631867	+	0.0169308i
$894$	−24.2092	+	41.9316i	−0.809678	+	1.40240i
$895$	−8.60543	+	0.791785i	−0.287648	+	0.0264664i
$896$	2.31288	+	1.28475i	0.0772679	+	0.0429205i
$897$	1.87976	+	1.87976i	0.0627633	+	0.0627633i
$898$	−8.10744	−	30.2574i	−0.270549	−	1.00970i
$899$	−26.1742	−	45.3351i	−0.872959	−	1.51201i
$900$	−3.53279	−	4.13432i	−0.117760	−	0.137811i
$901$	14.6310	+	8.44719i	0.487428	+	0.281417i
$902$	7.39156	−	7.39156i	0.246112	−	0.246112i
$903$	36.5311	+	9.14288i	1.21568	+	0.304256i
$904$			13.7933i			0.458759i
$905$	−6.54297	+	14.1974i	−0.217496	+	0.471936i
$906$	−6.20410	+	3.58194i	−0.206117	+	0.119002i
$907$	−4.28883	+	16.0061i	−0.142408	+	0.531474i	0.857449	+	0.514569i	$0.172048\pi$
$907$	−4.28883	+	16.0061i	−0.142408	+	0.531474i	−0.999857	+	0.0169054i	$0.994619\pi$
$908$	15.6420	−	4.19127i	0.519099	−	0.139092i
$909$	10.7549			0.356718
$910$	1.69396	+	0.262062i	0.0561541	+	0.00868727i
$911$	−1.46770			−0.0486270			−0.0243135	−	0.999704i	$-0.507740\pi$
$911$	−1.46770			−0.0486270			−0.0243135	+	0.999704i	$0.507740\pi$
$912$	12.1145	−	3.24606i	0.401150	−	0.107488i
$913$	5.69862	−	21.2676i	0.188597	−	0.703853i
$914$	−2.47817	+	1.43077i	−0.0819705	+	0.0473257i
$915$	29.3526	−	10.8328i	0.970367	−	0.358122i
$916$		−	11.7764i		−	0.389103i
$917$	−18.5674	+	5.30617i	−0.613149	+	0.175225i
$918$	5.57658	−	5.57658i	0.184055	−	0.184055i
$919$	24.1523	+	13.9443i	0.796710	+	0.459981i	0.842319	−	0.538979i	$-0.181190\pi$
$919$	24.1523	+	13.9443i	0.796710	+	0.459981i	−0.0456096	+	0.998959i	$0.514523\pi$
$920$	5.85763	+	8.28622i	0.193120	+	0.273189i
$921$	1.54197	+	2.67078i	0.0508098	+	0.0880051i
$922$	0.783378	+	2.92361i	0.0257992	+	0.0962838i
$923$	1.45920	+	1.45920i	0.0480302	+	0.0480302i
$924$	−0.357861	−	21.6075i	−0.0117728	−	0.710833i
$925$	−19.0642	−	13.0957i	−0.626828	−	0.430582i
$926$	−13.6393	+	23.6240i	−0.448215	+	0.776332i
$927$	−4.49855	−	1.20538i	−0.147752	−	0.0395900i
$928$	6.91477	+	1.85281i	0.226988	+	0.0608213i
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	0.452368	+	0.891831i	$0.350579\pi$
$929$	−16.6468	+	28.8331i	−0.546164	+	0.945984i	−0.998533	+	0.0541530i	$0.982754\pi$
$930$	−3.02896	−	32.9200i	−0.0993236	−	1.07949i
$931$	38.3040	+	20.4544i	1.25536	+	0.670367i
$932$	−4.04765	−	4.04765i	−0.132585	−	0.132585i
$933$	5.03824	+	18.8030i	0.164944	+	0.615581i
$934$	12.5645	+	21.7623i	0.411122	+	0.712084i
$935$	−3.11828	+	18.1605i	−0.101979	+	0.593913i
$936$	0.272906	+	0.157563i	0.00892023	+	0.00515009i
$937$	25.6651	−	25.6651i	0.838442	−	0.838442i	−0.150212	−	0.988654i	$-0.547996\pi$
$937$	25.6651	−	25.6651i	0.838442	−	0.838442i	0.988654	+	0.150212i	$0.0479957\pi$
$938$	−6.00642	−	5.81071i	−0.196117	−	0.189726i
$939$		−	6.11942i		−	0.199700i
$940$	0.243969	+	0.661059i	0.00795739	+	0.0215614i
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	−0.802475	−	0.596686i	$-0.796484\pi$
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	0.115508	+	0.993307i	$0.463151\pi$
$942$	3.20377	−	11.9566i	0.104384	−	0.389568i
$943$	−11.3421	+	3.03911i	−0.369350	+	0.0989670i
$944$	0.855404			0.0278410
$945$	−9.22858	+	20.9297i	−0.300206	+	0.680845i
$946$	28.4413			0.924707
$947$	2.07680	−	0.556477i	0.0674869	−	0.0180831i	−0.224918	−	0.974378i	$-0.572211\pi$
$947$	2.07680	−	0.556477i	0.0674869	−	0.0180831i	0.292405	+	0.956295i	$0.405545\pi$
$948$	−2.65630	+	9.91343i	−0.0862725	+	0.321973i
$949$	−2.89206	+	1.66973i	−0.0938804	+	0.0542019i
$950$	27.9919	−	13.3598i	0.908178	−	0.433450i
$951$			3.93980i			0.127757i
$952$	1.31024	−	5.23517i	0.0424652	−	0.169673i
$953$	−13.1863	+	13.1863i	−0.427146	+	0.427146i	−0.887655	−	0.460509i	$-0.847667\pi$
$953$	−13.1863	+	13.1863i	−0.427146	+	0.427146i	0.460509	+	0.887655i	$0.347667\pi$
$954$	−7.80149	−	4.50419i	−0.252582	−	0.145829i
$955$	8.16989	−	5.77540i	0.264371	−	0.186887i
$956$	4.16897	+	7.22087i	0.134834	+	0.233540i
$957$	−15.1337	−	56.4796i	−0.489202	−	1.82573i
$958$	5.85973	+	5.85973i	0.189319	+	0.189319i
$959$	−9.76792	−	16.2895i	−0.315423	−	0.526015i
$960$	3.47617	+	2.89039i	0.112193	+	0.0932869i
$961$	11.2368	−	19.4627i	0.362477	−	0.627829i
$962$	1.29459	+	0.346883i	0.0417391	+	0.0111840i
$963$	−15.6241	−	4.18646i	−0.503479	−	0.134907i
$964$	1.48219	−	2.56723i	0.0477381	−	0.0826849i
$965$	−34.5156	−	28.6993i	−1.11110	−	0.923862i
$966$	−11.7878	+	21.2210i	−0.379266	+	0.682775i
$967$	−27.7931	−	27.7931i	−0.893766	−	0.893766i	0.101109	−	0.994875i	$-0.467761\pi$
$967$	−27.7931	−	27.7931i	−0.893766	−	0.893766i	−0.994875	+	0.101109i	$0.967761\pi$
$968$	−1.37728	−	5.14006i	−0.0442673	−	0.165208i
$969$	−12.7910	−	22.1547i	−0.410907	−	0.711711i
$970$	−17.1228	+	12.1043i	−0.549780	+	0.388647i
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	0.681467	−	0.731849i	$-0.261342\pi$
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	−0.293067	+	0.956092i	$0.594676\pi$
$972$	−7.63821	+	7.63821i	−0.244996	+	0.244996i
$973$	22.8425	−	23.6119i	0.732298	−	0.756963i
$974$			10.6783i			0.342155i
$975$	2.76117	+	0.977025i	0.0884282	+	0.0312899i
$976$	−5.99356	+	3.46038i	−0.191849	+	0.110764i
$977$	2.16089	−	8.06456i	0.0691331	−	0.258008i	−0.922706	−	0.385505i	$-0.874027\pi$
$977$	2.16089	−	8.06456i	0.0691331	−	0.258008i	0.991839	+	0.127496i	$0.0406941\pi$
$978$	32.3358	−	8.66436i	1.03399	−	0.277056i
$979$	−12.4120			−0.396690
$980$	1.94949	+	15.5306i	0.0622740	+	0.496107i
$981$	14.3907			0.459459
$982$	−24.8494	+	6.65836i	−0.792975	+	0.212477i
$983$	−6.30383	+	23.5262i	−0.201061	+	0.750370i	0.789553	+	0.613682i	$0.210312\pi$
$983$	−6.30383	+	23.5262i	−0.201061	+	0.750370i	−0.990614	+	0.136688i	$0.956354\pi$
$984$	−4.53043	+	2.61564i	−0.144425	+	0.0833836i
$985$	8.59372	+	23.2856i	0.273819	+	0.741940i
$986$		−	14.6019i		−	0.465018i
$987$	−1.17203	+	1.21151i	−0.0373062	+	0.0385628i
$988$	−1.27091	+	1.27091i	−0.0404329	+	0.0404329i
$989$	−27.6681	−	15.9742i	−0.879794	−	0.507949i
$990$	1.66272	−	9.68352i	0.0528447	−	0.307762i
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	0.693637	−	0.720324i	$-0.256007\pi$
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	−0.970638	+	0.240545i	$0.922674\pi$
$992$	1.89263	+	7.06340i	0.0600911	+	0.224263i
$993$	−41.3067	−	41.3067i	−1.31083	−	1.31083i
$994$	−9.15051	+	16.4733i	−0.290237	+	0.522500i
$995$	2.21307	+	24.0525i	0.0701590	+	0.762516i
$996$	−5.50936	+	9.54248i	−0.174571	+	0.302365i
$997$	25.2781	+	6.77324i	0.800565	+	0.214511i	0.635832	−	0.771827i	$-0.280657\pi$
$997$	25.2781	+	6.77324i	0.800565	+	0.214511i	0.164733	+	0.986338i	$0.447324\pi$
$998$	14.1014	+	3.77845i	0.446371	+	0.119605i
$999$	−8.94255	+	15.4890i	−0.282930	+	0.490049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.k.a.47.2	yes	16
3.2	odd	2		630.2.bv.c.397.4		16
4.3	odd	2		560.2.ci.c.257.1		16
5.2	odd	4		350.2.o.c.243.1		16
5.3	odd	4	inner	70.2.k.a.33.4	yes	16
5.4	even	2		350.2.o.c.257.3		16
7.2	even	3		490.2.g.c.97.8		16
7.3	odd	6	inner	70.2.k.a.17.4	yes	16
7.4	even	3		490.2.l.c.227.3		16
7.5	odd	6		490.2.g.c.97.5		16
7.6	odd	2		490.2.l.c.117.1		16
15.8	even	4		630.2.bv.c.523.2		16
20.3	even	4		560.2.ci.c.33.1		16
21.17	even	6		630.2.bv.c.577.2		16
28.3	even	6		560.2.ci.c.17.1		16
35.3	even	12	inner	70.2.k.a.3.2	✓	16
35.13	even	4		490.2.l.c.313.3		16
35.17	even	12		350.2.o.c.143.3		16
35.18	odd	12		490.2.l.c.423.1		16
35.23	odd	12		490.2.g.c.293.5		16
35.24	odd	6		350.2.o.c.157.1		16
35.33	even	12		490.2.g.c.293.8		16
105.38	odd	12		630.2.bv.c.73.4		16
140.3	odd	12		560.2.ci.c.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	35.3	even	12	inner
70.2.k.a.17.4	yes	16	7.3	odd	6	inner
70.2.k.a.33.4	yes	16	5.3	odd	4	inner
70.2.k.a.47.2	yes	16	1.1	even	1	trivial
350.2.o.c.143.3		16	35.17	even	12
350.2.o.c.157.1		16	35.24	odd	6
350.2.o.c.243.1		16	5.2	odd	4
350.2.o.c.257.3		16	5.4	even	2
490.2.g.c.97.5		16	7.5	odd	6
490.2.g.c.97.8		16	7.2	even	3
490.2.g.c.293.5		16	35.23	odd	12
490.2.g.c.293.8		16	35.33	even	12
490.2.l.c.117.1		16	7.6	odd	2
490.2.l.c.227.3		16	7.4	even	3
490.2.l.c.313.3		16	35.13	even	4
490.2.l.c.423.1		16	35.18	odd	12
560.2.ci.c.17.1		16	28.3	even	6
560.2.ci.c.33.1		16	20.3	even	4
560.2.ci.c.257.1		16	4.3	odd	2
560.2.ci.c.353.1		16	140.3	odd	12
630.2.bv.c.73.4		16	105.38	odd	12
630.2.bv.c.397.4		16	3.2	odd	2
630.2.bv.c.523.2		16	15.8	even	4
630.2.bv.c.577.2		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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.523277 - 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.03078 - 0.935904i) q^{5} +2.02179i q^{6} +(1.83959 - 1.90155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.523277 - 1.95290i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.03078 - 0.935904i) q^{5} +2.02179i q^{6} +(1.83959 - 1.90155i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.941911 - 0.543813i) q^{9} +(2.20382 + 0.378409i) q^{10} +(2.01999 + 3.49872i) q^{11} +(-0.523277 - 1.95290i) q^{12} +(0.204875 + 0.204875i) q^{13} +(-1.28475 + 2.31288i) q^{14} +(-2.89039 + 3.47617i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.97024 - 0.527924i) q^{17} +(1.05057 + 0.281498i) q^{18} +(-3.10166 + 5.37224i) q^{19} +(-2.22666 + 0.204875i) q^{20} +(-2.75092 - 4.58757i) q^{21} +(-2.85669 - 2.85669i) q^{22} +(1.17456 + 4.38350i) q^{23} +(1.01089 + 1.75092i) q^{24} +(3.24817 + 3.80124i) q^{25} +(-0.250919 - 0.144868i) q^{26} +(2.73397 - 2.73397i) q^{27} +(0.642357 - 2.56659i) q^{28} -7.15869i q^{29} +(1.89220 - 4.10581i) q^{30} +(6.33287 - 3.65628i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(7.88965 - 2.11403i) q^{33} +2.03974 q^{34} +(-5.51548 + 2.13996i) q^{35} -1.08763 q^{36} +(-4.46814 + 1.19723i) q^{37} +(1.60554 - 5.99195i) q^{38} +(0.507306 - 0.292893i) q^{39} +(2.09777 - 0.774197i) q^{40} +2.58745i q^{41} +(3.84454 + 3.71926i) q^{42} +(-4.97801 + 4.97801i) q^{43} +(3.49872 + 2.01999i) q^{44} +(1.40386 + 1.98590i) q^{45} +(-2.26907 - 3.93014i) q^{46} +(-0.0815604 - 0.304388i) q^{47} +(-1.42962 - 1.42962i) q^{48} +(-0.231803 - 6.99616i) q^{49} +(-4.12132 - 2.83103i) q^{50} +(-2.06196 + 3.57142i) q^{51} +(0.279864 + 0.0749894i) q^{52} +(-8.00039 - 2.14370i) q^{53} +(-1.93321 + 3.34841i) q^{54} +(-0.827689 - 8.99566i) q^{55} +(0.0438127 + 2.64539i) q^{56} +(8.86840 + 8.86840i) q^{57} +(1.85281 + 6.91477i) q^{58} +(0.427702 + 0.740802i) q^{59} +(-0.765062 + 4.45565i) q^{60} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 + 5.17076i) q^{62} +(-2.76682 + 0.790700i) q^{63} -1.00000i q^{64} +(-0.224313 - 0.607800i) q^{65} +(-7.07367 + 4.08398i) q^{66} +(-0.817530 + 3.05106i) q^{67} +(-1.97024 + 0.527924i) q^{68} +9.17514 q^{69} +(4.77369 - 3.49455i) q^{70} +7.12240 q^{71} +(1.05057 - 0.281498i) q^{72} +(-2.98311 + 11.1331i) q^{73} +(4.00603 - 2.31288i) q^{74} +(9.12312 - 4.35423i) q^{75} +6.20333i q^{76} +(10.3690 + 2.59511i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(-4.39618 - 2.53813i) q^{79} +(-1.82591 + 1.29076i) q^{80} +(-5.53997 - 9.59552i) q^{81} +(-0.669683 - 2.49929i) q^{82} +(-3.85372 - 3.85372i) q^{83} +(-4.67615 - 2.59749i) q^{84} +(3.50704 + 2.91605i) q^{85} +(3.51999 - 6.09680i) q^{86} +(-13.9802 - 3.74598i) q^{87} +(-3.90231 - 1.04562i) q^{88} +(-1.53615 + 2.66069i) q^{89} +(-1.87002 - 1.55489i) q^{90} +(0.766467 - 0.0126942i) q^{91} +(3.20895 + 3.20895i) q^{92} +(-3.82650 - 14.2807i) q^{93} +(0.157563 + 0.272906i) q^{94} +(11.3267 - 8.00700i) q^{95} +(1.75092 + 1.01089i) q^{96} +(-6.63103 + 6.63103i) q^{97} +(2.03464 + 6.69778i) q^{98} -4.39398i 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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