LMFDB - Embedded newform 70.2.k.a.17.3

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			17.3
Root			$1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	70.17
Dual form			70.2.k.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.279864 + 0.0749894i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(2.64273 + 0.126334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52538 + 1.45803i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.279864 + 0.0749894i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(2.64273 + 0.126334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52538 + 1.45803i) q^{9} +(-1.82591 - 1.29076i) q^{10} +(-2.81288 + 4.87205i) q^{11} +(0.279864 + 0.0749894i) 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} +(-1.37400 - 5.12784i) q^{17} +(0.754730 + 2.81669i) 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} +(1.08562 + 0.290892i) q^{23} +(0.144868 - 0.250919i) q^{24} +(-3.80124 - 3.24817i) q^{25} +(1.75092 - 1.01089i) q^{26} +(1.21205 - 1.21205i) q^{27} +(-2.22551 - 1.43078i) q^{28} -3.15502i q^{29} +(0.607800 + 0.224313i) q^{30} +(-3.33287 - 1.92423i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.421872 - 1.57445i) q^{33} -5.30873 q^{34} +(2.31101 - 5.44603i) q^{35} +2.91605 q^{36} +(-1.30444 + 4.86824i) q^{37} +(3.75919 - 1.00727i) q^{38} +(-0.507306 - 0.292893i) q^{39} +(0.935904 + 2.03078i) q^{40} -7.21050i q^{41} +(-0.0366036 + 0.765697i) q^{42} +(1.85669 - 1.85669i) q^{43} +(4.87205 - 2.81288i) q^{44} +(1.10346 + 6.42644i) q^{45} +(0.561961 - 0.973344i) q^{46} +(-5.69475 - 1.52590i) 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} +(-0.523277 - 1.95290i) q^{52} +(-0.357978 - 1.33599i) 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} +(-3.04751 - 0.816578i) q^{58} +(-2.73923 + 4.74448i) q^{59} +(0.373980 - 0.529033i) q^{60} +(-3.99172 + 2.30462i) q^{61} +(-2.72127 + 2.72127i) q^{62} +(-6.85809 + 3.53413i) q^{63} -1.00000i q^{64} +(4.10581 - 1.89220i) q^{65} +(-1.41161 - 0.814995i) q^{66} +(-0.816193 + 0.218698i) q^{67} +(-1.37400 + 5.12784i) q^{68} -0.325641 q^{69} +(-4.66232 - 3.64180i) q^{70} +4.77710 q^{71} +(0.754730 - 2.81669i) q^{72} +(5.42104 - 1.45256i) q^{73} +(4.36475 + 2.51999i) q^{74} +(1.30741 + 0.623993i) q^{75} -3.89180i q^{76} +(-8.04920 + 12.5202i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(-5.41079 + 3.12392i) q^{79} +(2.20382 - 0.378409i) q^{80} +(4.12576 - 7.14603i) q^{81} +(-6.96481 - 1.86622i) 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} +(0.236593 + 0.882976i) q^{87} +(-1.45605 - 5.43407i) 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} +(1.07705 + 0.288594i) q^{93} +(-2.94782 + 5.10577i) q^{94} +(8.57682 - 1.47269i) q^{95} +(-0.250919 + 0.144868i) q^{96} +(6.63103 - 6.63103i) q^{97} +(2.44845 - 6.55783i) 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 $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.279864	+	0.0749894i	−0.161580	+	0.0432952i	−0.338702	−	0.940894i	$-0.609988\pi$
$3$	−0.279864	+	0.0749894i	−0.161580	+	0.0432952i	0.177122	+	0.984189i	$0.443321\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.774197	−	2.09777i	0.346231	−	0.938149i
$5$	0.774197	−	2.09777i	0.346231	−	0.938149i
$6$			0.289737i			0.118285i
$7$	2.64273	+	0.126334i	0.998859	+	0.0477497i
$7$	2.64273	+	0.126334i	0.998859	+	0.0477497i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.52538	+	1.45803i	−0.841792	+	0.486009i
$10$	−1.82591	−	1.29076i	−0.577403	−	0.408174i
$11$	−2.81288	+	4.87205i	−0.848115	+	1.46898i	0.0347729	+	0.999395i	$0.488929\pi$
$11$	−2.81288	+	4.87205i	−0.848115	+	1.46898i	−0.882888	+	0.469583i	$0.844404\pi$
$12$	0.279864	+	0.0749894i	0.0807899	+	0.0216476i
$13$	1.42962	+	1.42962i	0.396505	+	0.396505i	0.876998	−	0.480493i	$-0.159542\pi$
$13$	1.42962	+	1.42962i	0.396505	+	0.396505i	−0.480493	+	0.876998i	$0.659542\pi$
$14$	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
$17$	−1.37400	−	5.12784i	−0.333244	−	1.24368i	−0.905760	−	0.423790i	$-0.860699\pi$
$17$	−1.37400	−	5.12784i	−0.333244	−	1.24368i	0.572516	−	0.819893i	$-0.305967\pi$
$18$	0.754730	+	2.81669i	0.177892	+	0.663900i
$19$	1.94590	+	3.37040i	0.446420	+	0.773223i	0.998150	−	0.0608002i	$-0.0193652\pi$
$19$	1.94590	+	3.37040i	0.446420	+	0.773223i	−0.551729	+	0.834023i	$0.686032\pi$
$20$	−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
$23$	1.08562	+	0.290892i	0.226368	+	0.0606552i	0.370220	−	0.928944i	$-0.379282\pi$
$23$	1.08562	+	0.290892i	0.226368	+	0.0606552i	−0.143852	+	0.989599i	$0.545949\pi$
$24$	0.144868	−	0.250919i	0.0295711	−	0.0512187i
$25$	−3.80124	−	3.24817i	−0.760248	−	0.649633i
$26$	1.75092	−	1.01089i	0.343384	−	0.198253i
$27$	1.21205	−	1.21205i	0.233259	−	0.233259i
$28$	−2.22551	−	1.43078i	−0.420581	−	0.270391i
$29$		−	3.15502i		−	0.585872i	−0.956132	−	0.292936i	$-0.905368\pi$
$29$		−	3.15502i		−	0.585872i	0.956132	−	0.292936i	$-0.0946322\pi$
$30$	0.607800	+	0.224313i	0.110969	+	0.0409538i
$31$	−3.33287	−	1.92423i	−0.598601	−	0.345602i	0.169890	−	0.985463i	$-0.445659\pi$
$31$	−3.33287	−	1.92423i	−0.598601	−	0.345602i	−0.768491	+	0.639861i	$0.778992\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	0.421872	−	1.57445i	0.0734386	−	0.274076i
$34$	−5.30873			−0.910440
$35$	2.31101	−	5.44603i	0.390633	−	0.920547i
$36$	2.91605			0.486009
$37$	−1.30444	+	4.86824i	−0.214449	+	0.800334i	0.771911	+	0.635731i	$0.219301\pi$
$37$	−1.30444	+	4.86824i	−0.214449	+	0.800334i	−0.986360	+	0.164603i	$0.947366\pi$
$38$	3.75919	−	1.00727i	0.609822	−	0.163401i
$39$	−0.507306	−	0.292893i	−0.0812340	−	0.0469005i
$40$	0.935904	+	2.03078i	0.147979	+	0.321095i
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$	−0.0366036	+	0.765697i	−0.00564806	+	0.118150i
$43$	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
$45$	1.10346	+	6.42644i	0.164494	+	0.957998i
$46$	0.561961	−	0.973344i	0.0828566	−	0.143512i
$47$	−5.69475	−	1.52590i	−0.830665	−	0.222576i	−0.181661	−	0.983361i	$-0.558147\pi$
$47$	−5.69475	−	1.52590i	−0.830665	−	0.222576i	−0.649004	+	0.760785i	$0.724814\pi$
$48$	−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
$52$	−0.523277	−	1.95290i	−0.0725655	−	0.270818i
$53$	−0.357978	−	1.33599i	−0.0491720	−	0.183512i	0.936972	−	0.349405i	$-0.113616\pi$
$53$	−0.357978	−	1.33599i	−0.0491720	−	0.183512i	−0.986144	+	0.165892i	$0.946950\pi$
$54$	−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
$58$	−3.04751	−	0.816578i	−0.400158	−	0.107222i
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	−0.987393	−	0.158286i	$-0.949403\pi$
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	0.630776	+	0.775965i	$0.282737\pi$
$60$	0.373980	−	0.529033i	0.0482806	−	0.0682979i
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	−0.733281	−	0.679926i	$-0.762012\pi$
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	0.222193	+	0.975003i	$0.428678\pi$
$62$	−2.72127	+	2.72127i	−0.345602	+	0.345602i
$63$	−6.85809	+	3.53413i	−0.864038	+	0.445259i
$64$		−	1.00000i		−	0.125000i
$65$	4.10581	−	1.89220i	0.509264	−	0.234699i
$66$	−1.41161	−	0.814995i	−0.173758	−	0.100319i
$67$	−0.816193	+	0.218698i	−0.0997138	+	0.0267182i	−0.308331	−	0.951279i	$-0.599770\pi$
$67$	−0.816193	+	0.218698i	−0.0997138	+	0.0267182i	0.208617	+	0.977997i	$0.433104\pi$
$68$	−1.37400	+	5.12784i	−0.166622	+	0.621842i
$69$	−0.325641			−0.0392026
$70$	−4.66232	−	3.64180i	−0.557254	−	0.435279i
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	0.754730	−	2.81669i	0.0889458	−	0.331950i
$73$	5.42104	−	1.45256i	0.634485	−	0.170010i	0.0727807	−	0.997348i	$-0.476813\pi$
$73$	5.42104	−	1.45256i	0.634485	−	0.170010i	0.561704	+	0.827338i	$0.310146\pi$
$74$	4.36475	+	2.51999i	0.507391	+	0.292943i
$75$	1.30741	+	0.623993i	0.150967	+	0.0720525i
$76$		−	3.89180i		−	0.446420i
$77$	−8.04920	+	12.5202i	−0.917291	+	1.42681i
$78$	−0.414214	+	0.414214i	−0.0469005	+	0.0469005i
$79$	−5.41079	+	3.12392i	−0.608761	+	0.351469i	−0.772481	−	0.635038i	$-0.780984\pi$
$79$	−5.41079	+	3.12392i	−0.608761	+	0.351469i	0.163719	+	0.986507i	$0.447651\pi$
$80$	2.20382	−	0.378409i	0.246394	−	0.0423074i
$81$	4.12576	−	7.14603i	0.458418	−	0.794003i
$82$	−6.96481	−	1.86622i	−0.769135	−	0.206089i
$83$	−5.67281	−	5.67281i	−0.622672	−	0.622672i	0.323542	−	0.946214i	$-0.395126\pi$
$83$	−5.67281	−	5.67281i	−0.622672	−	0.622672i	−0.946214	+	0.323542i	$0.895126\pi$
$84$	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
$87$	0.236593	+	0.882976i	0.0253654	+	0.0946650i
$88$	−1.45605	−	5.43407i	−0.155216	−	0.579273i
$89$	5.96090	+	10.3246i	0.631855	+	1.09440i	0.987172	+	0.159659i	$0.0510393\pi$
$89$	5.96090	+	10.3246i	0.631855	+	1.09440i	−0.355318	+	0.934746i	$0.615627\pi$
$90$	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
$93$	1.07705	+	0.288594i	0.111685	+	0.0299258i
$94$	−2.94782	+	5.10577i	−0.304044	+	0.526620i
$95$	8.57682	−	1.47269i	0.879963	−	0.151095i
$96$	−0.250919	+	0.144868i	−0.0256094	+	0.0147856i
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	−0.285191	−	0.958471i	$-0.592057\pi$
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	0.958471	+	0.285191i	$0.0920572\pi$
$98$	2.44845	−	6.55783i	0.247331	−	0.662440i
$99$		−	16.4050i		−	1.64877i
$100$	1.66789	+	4.71361i	0.166789	+	0.471361i
$101$	13.9423	+	8.04960i	1.38731	+	0.800965i	0.993012	−	0.118016i	$-0.0376535\pi$
$101$	13.9423	+	8.04960i	1.38731	+	0.800965i	0.394301	+	0.918981i	$0.370987\pi$
$102$	1.48572	−	0.398099i	0.147109	−	0.0394176i
$103$	5.09084	−	18.9993i	0.501616	−	1.87206i	0.0123445	−	0.999924i	$-0.496071\pi$
$103$	5.09084	−	18.9993i	0.501616	−	1.87206i	0.489271	−	0.872132i	$-0.337263\pi$
$104$	−2.02179			−0.198253
$105$	−0.238376	+	1.69745i	−0.0232631	+	0.165654i
$106$	−1.38312			−0.134340
$107$	0.724955	−	2.70557i	0.0700840	−	0.261557i	−0.921990	−	0.387214i	$-0.873437\pi$
$107$	0.724955	−	2.70557i	0.0700840	−	0.261557i	0.992074	+	0.125657i	$0.0401040\pi$
$108$	−1.65569	+	0.443641i	−0.159319	+	0.0426894i
$109$	5.11895	+	2.95543i	0.490306	+	0.283078i	0.724701	−	0.689063i	$-0.241978\pi$
$109$	5.11895	+	2.95543i	0.490306	+	0.283078i	−0.234395	+	0.972141i	$0.575311\pi$
$110$	11.4247	−	5.26517i	1.08930	−	0.502015i
$111$		−	1.46027i		−	0.138602i
$112$	1.21196	+	2.35184i	0.114519	+	0.222228i
$113$	−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
$115$	1.45071	−	2.05218i	0.135279	−	0.191367i
$116$	−1.57751	+	2.73232i	−0.146468	+	0.253690i
$117$	−5.69475	−	1.52590i	−0.526480	−	0.141070i
$118$	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
$122$	1.19296	+	4.45219i	0.108006	+	0.403082i
$123$	0.540712	+	2.01796i	0.0487543	+	0.181954i
$124$	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	$0.656073\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−0.380390	+	0.658854i	−0.0334915	+	0.0580089i
$130$	−0.765062	−	4.45565i	−0.0671004	−	0.390786i
$131$	−6.66437	+	3.84768i	−0.582269	+	0.336173i	−0.762035	−	0.647536i	$-0.775799\pi$
$131$	−6.66437	+	3.84768i	−0.582269	+	0.336173i	0.179766	+	0.983709i	$0.442466\pi$
$132$	−1.15258	+	1.15258i	−0.100319	+	0.100319i
$133$	4.71670	+	9.15290i	0.408990	+	0.793657i
$134$			0.844985i			0.0729956i
$135$	−1.60423	−	3.48096i	−0.138070	−	0.299594i
$136$	4.59749	+	2.65436i	0.394232	+	0.227610i
$137$	8.53471	−	2.28687i	0.729170	−	0.195380i	0.124910	−	0.992168i	$-0.460136\pi$
$137$	8.53471	−	2.28687i	0.729170	−	0.195380i	0.604259	+	0.796788i	$0.293469\pi$
$138$	−0.0842822	+	0.314545i	−0.00717458	+	0.0267759i
$139$	−11.0631			−0.938361			−0.469180	−	0.883102i	$-0.655451\pi$
$139$	−11.0631			−0.938361			−0.469180	+	0.883102i	$0.655451\pi$
$140$	−4.72441	+	3.56089i	−0.399286	+	0.300950i
$141$	1.70818			0.143855
$142$	1.23640	−	4.61432i	0.103757	−	0.387225i
$143$	−10.9865	+	2.94383i	−0.918740	+	0.246176i
$144$	−2.52538	−	1.45803i	−0.210448	−	0.121502i
$145$	−6.61848	−	2.44260i	−0.549635	−	0.202847i
$146$		−	5.61227i		−	0.464475i
$147$	−2.00019	+	0.335657i	−0.164973	+	0.0276846i
$148$	3.56380	−	3.56380i	0.292943	−	0.292943i
$149$	4.37243	−	2.52443i	0.358204	−	0.206809i	−0.310089	−	0.950708i	$-0.600359\pi$
$149$	4.37243	−	2.52443i	0.358204	−	0.206809i	0.668293	+	0.743899i	$0.267025\pi$
$150$	0.941113	−	1.10136i	0.0768416	−	0.0899256i
$151$	−6.72142	+	11.6418i	−0.546981	+	0.947399i	0.451498	+	0.892272i	$0.350890\pi$
$151$	−6.72142	+	11.6418i	−0.546981	+	0.947399i	−0.998479	+	0.0551270i	$0.982444\pi$
$152$	−3.75919	−	1.00727i	−0.304911	−	0.0817006i
$153$	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
$157$	−0.285443	−	1.06529i	−0.0227808	−	0.0850191i	0.953600	−	0.301078i	$-0.0973464\pi$
$157$	−0.285443	−	1.06529i	−0.0227808	−	0.0850191i	−0.976380	+	0.216059i	$0.930680\pi$
$158$	1.61706	+	6.03495i	0.128646	+	0.480115i
$159$	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
$163$	12.7899	+	3.42705i	1.00179	+	0.268428i	0.722193	−	0.691691i	$-0.243134\pi$
$163$	12.7899	+	3.42705i	1.00179	+	0.268428i	0.279592	+	0.960119i	$0.409801\pi$
$164$	−3.60525	+	6.24448i	−0.281523	+	0.487612i
$165$	−2.97621	−	2.10392i	−0.231698	−	0.163790i
$166$	−6.94775	+	4.01128i	−0.539250	+	0.311336i
$167$	4.70680	−	4.70680i	0.364223	−	0.364223i	−0.501142	−	0.865365i	$-0.667087\pi$
$167$	4.70680	−	4.70680i	0.364223	−	0.364223i	0.865365	+	0.501142i	$0.167087\pi$
$168$	0.414548	−	0.644812i	0.0319831	−	0.0497483i
$169$		−	8.91237i		−	0.685567i
$170$	−4.11000	+	11.1365i	−0.315223	+	0.854128i
$171$	−9.82827	−	5.67435i	−0.751586	−	0.433929i
$172$	−2.53629	+	0.679597i	−0.193390	+	0.0518188i
$173$	−1.82586	+	6.81421i	−0.138818	+	0.518075i	0.861135	+	0.508376i	$0.169754\pi$
$173$	−1.82586	+	6.81421i	−0.138818	+	0.518075i	−0.999953	+	0.00969875i	$0.996913\pi$
$174$	0.914124			0.0692996
$175$	−9.63531	−	9.06426i	−0.728361	−	0.685194i
$176$	−5.62576			−0.424058
$177$	0.410826	−	1.53322i	0.0308796	−	0.115244i
$178$	11.5156	−	3.08559i	0.863129	−	0.231275i
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	0.426889	−	0.904304i	$-0.359609\pi$
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	−0.569706	+	0.821849i	$0.692943\pi$
$180$	2.25760	−	6.11719i	0.168271	−	0.455949i
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$	4.75492	−	2.45032i	0.352458	−	0.181630i
$183$	0.944318	−	0.944318i	0.0698060	−	0.0698060i
$184$	−0.973344	+	0.561961i	−0.0717559	+	0.0414283i
$185$	9.20253	+	6.50539i	0.676584	+	0.478286i
$186$	0.557521	−	0.965654i	0.0408794	−	0.0708052i
$187$	28.8480	+	7.72980i	2.10957	+	0.565259i
$188$	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	0.989045	+	0.147613i	$0.0471589\pi$
$191$	8.60117	+	14.8977i	0.622359	+	1.07796i	−0.366686	+	0.930345i	$0.619508\pi$
$192$	0.0749894	+	0.279864i	0.00541190	+	0.0201975i
$193$	−3.12327	−	11.6562i	−0.224818	−	0.839032i	−0.982477	−	0.186382i	$-0.940324\pi$
$193$	−3.12327	−	11.6562i	−0.224818	−	0.839032i	0.757659	−	0.652650i	$-0.226343\pi$
$194$	−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	$0.493636\pi$
$198$	−15.8460	−	4.24593i	−1.12613	−	0.301745i
$199$	3.76653	−	6.52383i	0.267002	−	0.462462i	−0.701084	−	0.713079i	$-0.747300\pi$
$199$	3.76653	−	6.52383i	0.267002	−	0.462462i	0.968086	+	0.250617i	$0.0806335\pi$
$200$	4.98468	−	0.391082i	0.352470	−	0.0276537i
$201$	0.212023	−	0.122412i	0.0149550	−	0.00863425i
$202$	11.3839	−	11.3839i	0.800965	−	0.800965i
$203$	0.398585	−	8.33786i	0.0279752	−	0.585203i
$204$		−	1.53813i		−	0.107691i
$205$	−15.1259	−	5.58235i	−1.05644	−	0.389888i
$206$	−17.0343	−	9.83476i	−1.18684	−	0.685220i
$207$	−3.16574	+	0.848257i	−0.220034	+	0.0589579i
$208$	−0.523277	+	1.95290i	−0.0362827	+	0.135409i
$209$	−21.8944			−1.51446
$210$	1.57791	+	0.669586i	0.108886	+	0.0462058i
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	−0.357978	+	1.33599i	−0.0245860	+	0.0917562i
$213$	−1.33694	+	0.358232i	−0.0916056	+	0.0245456i
$214$	−2.42575	−	1.40051i	−0.165821	−	0.0957366i
$215$	−2.45746	−	5.33235i	−0.167597	−	0.363663i
$216$			1.71410i			0.116630i
$217$	−8.56478	−	5.50629i	−0.581415	−	0.373791i
$218$	4.17960	−	4.17960i	0.283078	−	0.283078i
$219$	−1.40823	+	0.813041i	−0.0951593	+	0.0549402i
$220$	−2.12884	−	12.3981i	−0.143526	−	0.835883i
$221$	5.36656	−	9.29516i	0.360994	−	0.625260i
$222$	−1.41051	−	0.377945i	−0.0946672	−	0.0253660i
$223$	−1.46027	−	1.46027i	−0.0977867	−	0.0977867i	0.656521	−	0.754308i	$-0.272027\pi$
$223$	−1.46027	−	1.46027i	−0.0977867	−	0.0977867i	−0.754308	+	0.656521i	$0.772027\pi$
$224$	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
$227$	−4.82525	−	18.0081i	−0.320263	−	1.19524i	−0.918989	−	0.394283i	$-0.870993\pi$
$227$	−4.82525	−	18.0081i	−0.320263	−	1.19524i	0.598726	−	0.800954i	$-0.295674\pi$
$228$	0.291844	+	1.08918i	0.0193278	+	0.0721325i
$229$	2.00384	+	3.47074i	0.132417	+	0.229353i	0.924608	−	0.380920i	$-0.124393\pi$
$229$	2.00384	+	3.47074i	0.132417	+	0.229353i	−0.792191	+	0.610274i	$0.791059\pi$
$230$	−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
$233$	13.2637	+	3.55400i	0.868934	+	0.232830i	0.665627	−	0.746285i	$-0.268164\pi$
$233$	13.2637	+	3.55400i	0.868934	+	0.232830i	0.203307	+	0.979115i	$0.434831\pi$
$234$	−2.94782	+	5.10577i	−0.192705	+	0.333775i
$235$	−7.60984	+	10.7649i	−0.496412	+	0.702225i
$236$	4.74448	−	2.73923i	0.308839	−	0.178308i
$237$	1.28003	−	1.28003i	0.0831466	−	0.0831466i
$238$	−14.0296	−	0.670673i	−0.909401	−	0.0434732i
$239$			19.6621i			1.27183i	0.771758	+	0.635916i	$0.219378\pi$
$239$			19.6621i			1.27183i	−0.771758	+	0.635916i	$0.780622\pi$
$240$	−0.588393	+	0.271166i	−0.0379806	+	0.0175037i
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	0.326783	−	0.945099i	$-0.394035\pi$
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	−0.655088	+	0.755552i	$0.727369\pi$
$242$	−19.9456	+	5.34440i	−1.28215	+	0.343551i
$243$	−1.94970	+	7.27638i	−0.125073	+	0.466780i
$244$	4.60924			0.295077
$245$	6.79541	−	14.1004i	0.434143	−	0.900844i
$246$	2.08915			0.133199
$247$	−2.03649	+	7.60029i	−0.129579	+	0.483595i
$248$	3.71733	−	0.996056i	0.236051	−	0.0632496i
$249$	2.01302	+	1.16222i	0.127570	+	0.0736525i
$250$	2.74812	+	10.8373i	0.173806	+	0.685413i
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$	7.70635	+	0.368396i	0.485454	+	0.0232068i
$253$	−4.47097	+	4.47097i	−0.281088	+	0.281088i
$254$	5.67653	−	3.27735i	0.356177	−	0.205639i
$255$	3.38977	−	0.582044i	0.212275	−	0.0364490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.54998	−	2.55891i	−0.595711	−	0.159620i	−0.0516491	−	0.998665i	$-0.516448\pi$
$257$	−9.54998	−	2.55891i	−0.595711	−	0.159620i	−0.544062	+	0.839045i	$0.683114\pi$
$258$	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
$262$	1.99170	+	7.43314i	0.123048	+	0.459221i
$263$	3.55829	+	13.2797i	0.219413	+	0.818861i	0.984566	+	0.175013i	$0.0559967\pi$
$263$	3.55829	+	13.2797i	0.219413	+	0.818861i	−0.765153	+	0.643849i	$0.777337\pi$
$264$	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
$268$	0.816193	+	0.218698i	0.0498569	+	0.0133591i
$269$	13.2510	−	22.9514i	0.807928	−	1.39937i	−0.106368	−	0.994327i	$-0.533922\pi$
$269$	13.2510	−	22.9514i	0.807928	−	1.39937i	0.914296	−	0.405046i	$-0.132745\pi$
$270$	−3.77756	+	0.648630i	−0.229895	+	0.0394744i
$271$	−11.0824	+	6.39844i	−0.673209	+	0.388678i	−0.797292	−	0.603594i	$-0.793735\pi$
$271$	−11.0824	+	6.39844i	−0.673209	+	0.388678i	0.124082	+	0.992272i	$0.460401\pi$
$272$	3.75384	−	3.75384i	0.227610	−	0.227610i
$273$	−1.30367	−	0.838129i	−0.0789018	−	0.0507259i
$274$		−	8.83578i		−	0.533789i
$275$	26.5177	−	9.38313i	1.59908	−	0.565824i
$276$	0.282014	+	0.162821i	0.0169752	+	0.00980065i
$277$	−19.4184	+	5.20313i	−1.16674	+	0.312626i	−0.789653	−	0.613554i	$-0.789739\pi$
$277$	−19.4184	+	5.20313i	−1.16674	+	0.312626i	−0.377083	+	0.926180i	$0.623073\pi$
$278$	−2.86334	+	10.6861i	−0.171732	+	0.640912i
$279$	11.2223			0.671863
$280$	2.21679	+	5.48506i	0.132478	+	0.327795i
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	0.442111	−	1.64998i	0.0263273	−	0.0982548i
$283$	−26.1454	+	7.00563i	−1.55418	+	0.416442i	−0.930816	−	0.365489i	$-0.880902\pi$
$283$	−26.1454	+	7.00563i	−1.55418	+	0.416442i	−0.623366	+	0.781930i	$0.714235\pi$
$284$	−4.13709	−	2.38855i	−0.245491	−	0.141734i
$285$	−2.28991	+	1.05532i	−0.135643	+	0.0625121i
$286$			11.3741i			0.672564i
$287$	0.910931	−	19.0554i	0.0537706	−	1.12481i
$288$	−2.06196	+	2.06196i	−0.121502	+	0.121502i
$289$	−9.68442	+	5.59130i	−0.569672	+	0.328900i
$290$	−4.07236	+	5.76077i	−0.239137	+	0.338284i
$291$	−1.35853	+	2.35305i	−0.0796385	+	0.137938i
$292$	−5.42104	−	1.45256i	−0.317242	−	0.0850048i
$293$	−17.1191	−	17.1191i	−1.00011	−	1.00011i	−1.00000		0.000106876i	$-0.999966\pi$
$293$	−17.1191	−	17.1191i	−1.00011	−	1.00011i	−0.000106876	−	1.00000i	$-0.500034\pi$
$294$	−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
$297$	2.49582	+	9.31453i	0.144822	+	0.540484i
$298$	−1.30674	−	4.87682i	−0.0756974	−	0.282506i
$299$	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
$303$	−4.50559	−	1.20727i	−0.258840	−	0.0693558i
$304$	−1.94590	+	3.37040i	−0.111605	+	0.193306i
$305$	1.74418	+	10.1579i	0.0998713	+	0.581641i
$306$	13.4065	−	7.74027i	0.766401	−	0.442482i
$307$	−17.2974	+	17.2974i	−0.987217	+	0.987217i	−0.999919	−	0.0127019i	$-0.995957\pi$
$307$	−17.2974	+	17.2974i	−0.987217	+	0.987217i	0.0127019	+	0.999919i	$0.495957\pi$
$308$	13.2309	−	6.81819i	0.753900	−	0.388502i
$309$			5.69898i			0.324204i
$310$	3.60179	+	7.81540i	0.204568	+	0.443885i
$311$	−9.51095	−	5.49115i	−0.539316	−	0.311374i	0.205486	−	0.978660i	$-0.434123\pi$
$311$	−9.51095	−	5.49115i	−0.539316	−	0.311374i	−0.744802	+	0.667286i	$0.767456\pi$
$312$	0.565826	−	0.151613i	0.0320336	−	0.00858338i
$313$	7.61212	−	28.4088i	0.430262	−	1.60576i	−0.321893	−	0.946776i	$-0.604319\pi$
$313$	7.61212	−	28.4088i	0.430262	−	1.60576i	0.752156	−	0.658985i	$-0.229014\pi$
$314$	−1.10287			−0.0622383
$315$	2.10427	+	17.1228i	0.118562	+	0.964760i
$316$	6.24784			0.351469
$317$	1.11136	−	4.14766i	0.0624203	−	0.232956i	−0.927667	−	0.373408i	$-0.878189\pi$
$317$	1.11136	−	4.14766i	0.0624203	−	0.232956i	0.990087	+	0.140453i	$0.0448558\pi$
$318$	0.387086	−	0.103719i	0.0217067	−	0.00581629i
$319$	15.3714	+	8.87468i	0.860633	+	0.496887i
$320$	−2.09777	−	0.774197i	−0.117269	−	0.0432789i
$321$			0.811556i			0.0452966i
$322$	1.60808	−	2.50129i	0.0896147	−	0.139392i
$323$	14.6092	−	14.6092i	0.812878	−	0.812878i
$324$	−7.14603	+	4.12576i	−0.397001	+	0.229209i
$325$	−0.790684	−	10.0780i	−0.0438593	−	0.559025i
$326$	6.62056	−	11.4671i	0.366679	−	0.635106i
$327$	−1.65424	−	0.443251i	−0.0914795	−	0.0245119i
$328$	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	−0.682387	−	0.730991i	$-0.739058\pi$
$331$	−17.7249	−	30.7005i	−0.974250	−	1.68745i	−0.291863	−	0.956460i	$-0.594275\pi$
$332$	2.07639	+	7.74921i	0.113957	+	0.425293i
$333$	−3.80382	−	14.1960i	−0.208448	−	0.777939i
$334$	−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	$0.904989\pi$
$338$	−8.60869	−	2.30669i	−0.468251	−	0.125468i
$339$	2.78257	−	4.81955i	0.151128	−	0.261762i
$340$	9.69326	+	6.85229i	0.525691	+	0.371617i
$341$	18.7499	−	10.8253i	1.01536	−	0.586221i
$342$	−8.02475	+	8.02475i	−0.433929	+	0.433929i
$343$	18.3304	+	2.64495i	0.989750	+	0.142814i
$344$			2.62576i			0.141571i
$345$	−0.252110	+	0.683119i	−0.0135732	+	0.0367779i
$346$	6.10945	+	3.52729i	0.328446	+	0.189628i
$347$	−8.67040	+	2.32323i	−0.465452	+	0.124717i	−0.483920	−	0.875112i	$-0.660788\pi$
$347$	−8.67040	+	2.32323i	−0.465452	+	0.124717i	0.0184687	+	0.999829i	$0.494121\pi$
$348$	0.236593	−	0.882976i	0.0126827	−	0.0473325i
$349$	26.0251			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$349$	26.0251			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$350$	−11.2492	+	6.96099i	−0.601295	+	0.372081i
$351$	3.46554			0.184977
$352$	−1.45605	+	5.43407i	−0.0776079	+	0.289637i
$353$	9.62659	−	2.57944i	0.512372	−	0.137290i	0.00663577	−	0.999978i	$-0.497888\pi$
$353$	9.62659	−	2.57944i	0.512372	−	0.137290i	0.505736	+	0.862688i	$0.331221\pi$
$354$	−1.37465	−	0.793655i	−0.0730619	−	0.0421823i
$355$	3.69841	−	10.0212i	0.196291	−	0.531872i
$356$		−	11.9218i		−	0.631855i
$357$	1.86416	+	3.61745i	0.0986615	+	0.191456i
$358$	−1.56012	+	1.56012i	−0.0824550	+	0.0824550i
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	−0.740617	−	0.671928i	$-0.765467\pi$
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	0.211598	+	0.977357i	$0.432133\pi$
$360$	−5.32445	−	3.76392i	−0.280623	−	0.198376i
$361$	1.92693	−	3.33754i	0.101417	−	0.175660i
$362$	3.97833	+	1.06599i	0.209097	+	0.0560273i
$363$	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
$367$	4.32083	+	16.1256i	0.225545	+	0.841747i	0.982185	+	0.187915i	$0.0601730\pi$
$367$	4.32083	+	16.1256i	0.225545	+	0.841747i	−0.756640	+	0.653832i	$0.773160\pi$
$368$	0.290892	+	1.08562i	0.0151638	+	0.0565921i
$369$	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
$373$	−3.07061	−	0.822767i	−0.158990	−	0.0426013i	0.178446	−	0.983950i	$-0.442893\pi$
$373$	−3.07061	−	0.822767i	−0.158990	−	0.0426013i	−0.337436	+	0.941348i	$0.609560\pi$
$374$	14.9328	−	25.8644i	0.772158	−	1.33742i
$375$	2.32118	−	2.25954i	0.119865	−	0.116682i
$376$	5.10577	−	2.94782i	0.263310	−	0.152022i
$377$	4.51047	−	4.51047i	0.232301	−	0.232301i
$378$	−2.07742	−	4.03129i	−0.106851	−	0.207347i
$379$			7.15349i			0.367450i	0.982978	+	0.183725i	$0.0588156\pi$
$379$			7.15349i			0.367450i	−0.982978	+	0.183725i	$0.941184\pi$
$380$	−8.16409	−	3.01302i	−0.418809	−	0.154565i
$381$	−1.64470	−	0.949568i	−0.0842605	−	0.0486478i
$382$	16.6162	−	4.45229i	0.850158	−	0.227799i
$383$	−3.77704	+	14.0961i	−0.192998	+	0.720278i	0.799778	+	0.600296i	$0.204950\pi$
$383$	−3.77704	+	14.0961i	−0.192998	+	0.720278i	−0.992776	+	0.119982i	$0.961716\pi$
$384$	0.289737			0.0147856
$385$	20.0327	+	26.5784i	1.02096	+	1.35456i
$386$	−12.0674			−0.614214
$387$	−1.98174	+	7.39595i	−0.100737	+	0.375957i
$388$	−9.05816	+	2.42713i	−0.459858	+	0.123219i
$389$	−5.36634	−	3.09826i	−0.272084	−	0.157088i	0.357750	−	0.933817i	$-0.383544\pi$
$389$	−5.36634	−	3.09826i	−0.272084	−	0.157088i	−0.629834	+	0.776729i	$0.716877\pi$
$390$	0.548240	+	1.18961i	0.0277612	+	0.0602380i
$391$		−	5.96659i		−	0.301744i
$392$	−5.39934	+	4.45502i	−0.272708	+	0.225012i
$393$	1.57658	−	1.57658i	0.0795282	−	0.0795282i
$394$	17.5304	−	10.1212i	0.883167	−	0.509897i
$395$	2.36424	+	13.7691i	0.118958	+	0.692798i
$396$	−8.20251	+	14.2072i	−0.412191	+	0.713937i
$397$	2.81652	+	0.754685i	0.141357	+	0.0378766i	0.328804	−	0.944398i	$-0.393354\pi$
$397$	2.81652	+	0.754685i	0.141357	+	0.0378766i	−0.187447	+	0.982275i	$0.560021\pi$
$398$	−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	0.999999	−	0.00156835i	$-0.000499221\pi$
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	−0.501358	+	0.865240i	$0.667166\pi$
$402$	−0.0633649	−	0.236481i	−0.00316035	−	0.0117946i
$403$	−2.01381	−	7.51565i	−0.100315	−	0.374381i
$404$	−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
$408$	−1.48572	−	0.398099i	−0.0735543	−	0.0197088i
$409$	−17.1791	+	29.7550i	−0.849451	+	1.47129i	0.0322484	+	0.999480i	$0.489733\pi$
$409$	−17.1791	+	29.7550i	−0.849451	+	1.47129i	−0.881699	+	0.471812i	$0.843600\pi$
$410$	−9.30702	+	13.1657i	−0.459641	+	0.650209i
$411$	−2.21707	+	1.28003i	−0.109360	+	0.0631390i
$412$	−13.9084	+	13.9084i	−0.685220	+	0.685220i
$413$	−7.83843	+	12.1923i	−0.385704	+	0.599946i
$414$			3.27741i			0.161076i
$415$	−16.2921	+	7.50836i	−0.799748	+	0.368571i
$416$	1.75092	+	1.01089i	0.0858459	+	0.0495631i
$417$	3.09617	−	0.829616i	0.151620	−	0.0406265i
$418$	−5.66668	+	21.1483i	−0.277166	+	1.03440i
$419$	31.1360			1.52109			0.760547	−	0.649283i	$-0.224931\pi$
$419$	31.1360			1.52109			0.760547	+	0.649283i	$0.224931\pi$
$420$	1.05516	−	1.35085i	0.0514868	−	0.0659146i
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	5.06679	−	18.9095i	0.246648	−	0.920501i
$423$	16.6062	−	4.44962i	0.807421	−	0.216348i
$424$	1.19782	+	0.691560i	0.0581711	+	0.0335851i
$425$	−11.4332	+	23.9551i	−0.554590	+	1.16199i
$426$			1.38410i			0.0670599i
$427$	−10.8402	+	5.58621i	−0.524594	+	0.270336i
$428$	−1.98061	+	1.98061i	−0.0957366	+	0.0957366i
$429$	2.85398	−	1.64775i	0.137792	−	0.0795540i
$430$	−5.78669	+	0.993610i	−0.279059	+	0.0479162i
$431$	7.37284	−	12.7701i	0.355137	−	0.615116i	−0.632004	−	0.774965i	$-0.717767\pi$
$431$	7.37284	−	12.7701i	0.355137	−	0.615116i	0.987141	+	0.159849i	$0.0511008\pi$
$432$	1.65569	+	0.443641i	0.0796595	+	0.0213447i
$433$	9.98256	+	9.98256i	0.479731	+	0.479731i	0.905046	−	0.425315i	$-0.139837\pi$
$433$	9.98256	+	9.98256i	0.479731	+	0.479731i	−0.425315	+	0.905046i	$0.639837\pi$
$434$	−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
$437$	1.13210	+	4.22504i	0.0541555	+	0.202111i
$438$	0.420861	+	1.57067i	0.0201095	+	0.0750498i
$439$	−19.2142	−	33.2800i	−0.917046	−	1.58837i	−0.803878	−	0.594794i	$-0.797234\pi$
$439$	−19.2142	−	33.2800i	−0.917046	−	1.58837i	−0.113167	−	0.993576i	$-0.536100\pi$
$440$	−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
$443$	−5.54016	−	1.48448i	−0.263221	−	0.0705299i	0.124795	−	0.992183i	$-0.460173\pi$
$443$	−5.54016	−	1.48448i	−0.263221	−	0.0705299i	−0.388016	+	0.921653i	$0.626839\pi$
$444$	−0.730133	+	1.26463i	−0.0346506	+	0.0600166i
$445$	26.2735	−	4.51132i	1.24548	−	0.213857i
$446$	−1.78845	+	1.03256i	−0.0846857	+	0.0488933i
$447$	−1.03438	+	1.03438i	−0.0489247	+	0.0489247i
$448$	0.126334	−	2.64273i	0.00596872	−	0.124857i
$449$			7.30267i			0.344635i	0.985042	+	0.172317i	$0.0551254\pi$
$449$			7.30267i			0.344635i	−0.985042	+	0.172317i	$0.944875\pi$
$450$	6.28017	−	13.1584i	0.296050	−	0.620293i
$451$	35.1299	+	20.2823i	1.65420	+	0.955055i
$452$	18.5531	−	4.97128i	0.872663	−	0.233829i
$453$	1.00807	−	3.76217i	0.0473633	−	0.176762i
$454$	−18.6433			−0.874974
$455$	11.0896	−	4.48188i	0.519889	−	0.210114i
$456$	1.12760			0.0528047
$457$	1.33183	−	4.97047i	0.0623006	−	0.232509i	−0.927754	−	0.373192i	$-0.878263\pi$
$457$	1.33183	−	4.97047i	0.0623006	−	0.232509i	0.990055	+	0.140683i	$0.0449299\pi$
$458$	3.87111	−	1.03726i	0.180885	−	0.0484680i
$459$	−7.88056	−	4.54984i	−0.367833	−	0.212368i
$460$	−2.28244	+	1.05188i	−0.106419	+	0.0490443i
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$	−3.62755	−	2.33215i	−0.168769	−	0.108501i
$463$	−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
$465$	1.43925	−	2.03596i	0.0667436	−	0.0944156i
$466$	6.86580	−	11.8919i	0.318052	−	0.550882i
$467$	16.0757	+	4.30747i	0.743894	+	0.199326i	0.610808	−	0.791779i	$-0.290845\pi$
$467$	16.0757	+	4.30747i	0.743894	+	0.199326i	0.133086	+	0.991105i	$0.457511\pi$
$468$	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
$472$	−1.41793	−	5.29178i	−0.0652654	−	0.243574i
$473$	3.82325	+	14.2686i	0.175793	+	0.656069i
$474$	−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
$478$	18.9921	+	5.08891i	0.868678	+	0.232762i
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	−0.986526	−	0.163607i	$-0.947687\pi$
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	0.634950	+	0.772553i	$0.281021\pi$
$480$	0.109639	+	0.638527i	0.00500431	+	0.0291446i
$481$	−8.82459	+	5.09488i	−0.402367	+	0.232306i
$482$	−4.16141	+	4.16141i	−0.189547	+	0.189547i
$483$	−0.860583	−	0.0411396i	−0.0391579	−	0.00187191i
$484$			20.6492i			0.938599i
$485$	−8.77662	−	19.0441i	−0.398526	−	0.864747i
$486$	6.52383	+	3.76653i	0.295927	+	0.170853i
$487$	34.7656	−	9.31541i	1.57538	−	0.422122i	0.637888	−	0.770129i	$-0.279808\pi$
$487$	34.7656	−	9.31541i	1.57538	−	0.422122i	0.937492	+	0.348007i	$0.113142\pi$
$488$	1.19296	−	4.45219i	0.0540028	−	0.201541i
$489$	−3.83644			−0.173490
$490$	−11.8612	−	10.2133i	−0.535834	−	0.461391i
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	0.540712	−	2.01796i	0.0243772	−	0.0909768i
$493$	−16.1784	+	4.33499i	−0.728639	+	0.195238i
$494$	6.81423	+	3.93420i	0.306587	+	0.177008i
$495$	−34.4139	−	12.7007i	−1.54679	−	0.570854i
$496$		−	3.84846i		−	0.172801i
$497$	12.6246	+	0.603509i	0.566290	+	0.0270711i
$498$	1.64362	−	1.64362i	0.0736525	−	0.0736525i
$499$	27.3534	−	15.7925i	1.22451	−	0.706969i	0.258630	−	0.965976i	$-0.416729\pi$
$499$	27.3534	−	15.7925i	1.22451	−	0.706969i	0.965875	+	0.259008i	$0.0833955\pi$
$500$	11.1793	+	0.150429i	0.499955	+	0.00672739i
$501$	−0.964305	+	1.67023i	−0.0430820	+	0.0746202i
$502$	6.85759	+	1.83749i	0.306069	+	0.0820110i
$503$	−16.9777	−	16.9777i	−0.756997	−	0.756997i	0.218778	−	0.975775i	$-0.429793\pi$
$503$	−16.9777	−	16.9777i	−0.756997	−	0.756997i	−0.975775	+	0.218778i	$0.929793\pi$
$504$	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
$507$	0.668334	+	2.49426i	0.0296817	+	0.110774i
$508$	−1.69648	−	6.33135i	−0.0752691	−	0.280908i
$509$	−10.7571	−	18.6318i	−0.476799	−	0.825840i	0.522848	−	0.852426i	$-0.324870\pi$
$509$	−10.7571	−	18.6318i	−0.476799	−	0.825840i	−0.999647	+	0.0265865i	$0.991536\pi$
$510$	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
$513$	6.44363	+	1.72657i	0.284493	+	0.0762297i
$514$	−4.94343	+	8.56228i	−0.218045	+	0.377666i
$515$	−35.9147	−	25.3886i	−1.58259	−	1.11875i
$516$	0.658854	−	0.380390i	0.0290044	−	0.0167457i
$517$	23.4529	−	23.4529i	1.03146	−	1.03146i
$518$	11.2165	+	7.21107i	0.492825	+	0.316836i
$519$		−	2.04397i		−	0.0897205i
$520$	−1.56526	+	4.24124i	−0.0686412	+	0.185991i
$521$	11.4657	+	6.61973i	0.502322	+	0.290016i	0.729672	−	0.683798i	$-0.239673\pi$
$521$	11.4657	+	6.61973i	0.502322	+	0.290016i	−0.227350	+	0.973813i	$0.573006\pi$
$522$	8.88670	−	2.38118i	0.388960	−	0.104222i
$523$	−6.97006	+	26.0126i	−0.304779	+	1.13745i	0.628356	+	0.777926i	$0.283728\pi$
$523$	−6.97006	+	26.0126i	−0.304779	+	1.13745i	−0.933135	+	0.359526i	$0.882938\pi$
$524$	7.69535			0.336173
$525$	3.37630	+	1.81422i	0.147354	+	0.0791789i
$526$	13.7482			0.599448
$527$	−5.28779	+	19.7343i	−0.230340	+	0.859640i
$528$	1.57445	−	0.421872i	0.0685191	−	0.0183596i
$529$	−18.8246	−	10.8684i	−0.818462	−	0.472539i
$530$	−1.07081	+	2.90146i	−0.0465129	+	0.126031i
$531$		−	15.9755i		−	0.693276i
$532$	0.491667	−	10.2850i	0.0213165	−	0.445911i
$533$	10.3083	−	10.3083i	0.446501	−	0.446501i
$534$	−2.99141	+	1.72709i	−0.129451	+	0.0747386i
$535$	−5.11439	−	3.61543i	−0.221114	−	0.156309i
$536$	0.422492	−	0.731778i	0.0182489	−	0.0316080i
$537$	0.617477	+	0.165453i	0.0266461	+	0.00713980i
$538$	−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	0.961724	−	0.274020i	$-0.0883536\pi$
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$542$	3.31208	+	12.3608i	0.142266	+	0.530943i
$543$	−0.308857	−	1.15267i	−0.0132543	−	0.0494658i
$544$	−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	$-0.634306\pi$
$548$	−8.53471	−	2.28687i	−0.364585	−	0.0976902i
$549$	6.72040	−	11.6401i	0.286820	−	0.496786i
$550$	−2.20013	−	28.0426i	−0.0938140	−	1.19574i
$551$	10.6337	−	6.13935i	0.453009	−	0.261545i
$552$	0.230263	−	0.230263i	0.00980065	−	0.00980065i
$553$	−14.6939	+	7.57212i	−0.624850	+	0.321999i
$554$			20.1034i			0.854110i
$555$	−3.06330	−	1.13053i	−0.130030	−	0.0479885i
$556$	9.58094	+	5.53156i	0.406322	+	0.234590i
$557$	25.5003	−	6.83277i	1.08048	−	0.289514i	0.325688	−	0.945477i	$-0.394404\pi$
$557$	25.5003	−	6.83277i	1.08048	−	0.289514i	0.754793	+	0.655963i	$0.227737\pi$
$558$	2.90455	−	10.8399i	0.122959	−	0.458891i
$559$	5.30873			0.224535
$560$	5.87191	−	0.721617i	0.248133	−	0.0304939i
$561$	−8.65318			−0.365337
$562$	−3.66224	+	13.6677i	−0.154482	+	0.576536i
$563$	19.5055	−	5.22648i	0.822058	−	0.220270i	0.176812	−	0.984245i	$-0.443422\pi$
$563$	19.5055	−	5.22648i	0.822058	−	0.220270i	0.645246	+	0.763975i	$0.276755\pi$
$564$	−1.47933	−	0.854092i	−0.0622911	−	0.0359638i
$565$	17.9764	+	39.0064i	0.756274	+	1.64101i
$566$			27.0677i			1.13774i
$567$	11.8061	−	18.3638i	0.495808	−	0.771208i
$568$	−3.37792	+	3.37792i	−0.141734	+	0.141734i
$569$	−21.4890	+	12.4067i	−0.900867	+	0.520116i	−0.877481	−	0.479611i	$-0.840778\pi$
$569$	−21.4890	+	12.4067i	−0.900867	+	0.520116i	−0.0233856	+	0.999727i	$0.507445\pi$
$570$	0.426693	+	2.48502i	0.0178722	+	0.104086i
$571$	−2.29029	+	3.96690i	−0.0958458	+	0.166010i	−0.909961	−	0.414693i	$-0.863889\pi$
$571$	−2.29029	+	3.96690i	−0.0958458	+	0.166010i	0.814116	+	0.580703i	$0.197222\pi$
$572$	10.9865	+	2.94383i	0.459370	+	0.123088i
$573$	−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
$577$	−5.11957	−	19.1065i	−0.213131	−	0.795414i	−0.986816	−	0.161845i	$-0.948256\pi$
$577$	−5.11957	−	19.1065i	−0.213131	−	0.795414i	0.773686	−	0.633570i	$-0.218411\pi$
$578$	2.89427	+	10.8016i	0.120386	+	0.449286i
$579$	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
$583$	7.51596	+	2.01390i	0.311279	+	0.0834071i
$584$	−2.80614	+	4.86037i	−0.116119	+	0.201124i
$585$	−7.60984	+	10.7649i	−0.314628	+	0.445074i
$586$	−20.9665	+	12.1050i	−0.866118	+	0.500053i
$587$	−19.3782	+	19.3782i	−0.799824	+	0.799824i	−0.983068	−	0.183244i	$-0.941340\pi$
$587$	−19.3782	+	19.3782i	−0.799824	+	0.799824i	0.183244	+	0.983068i	$0.441340\pi$
$588$	1.90004	+	0.709407i	0.0783565	+	0.0292555i
$589$		−	14.9775i		−	0.617136i
$590$	11.1256	−	5.12731i	0.458032	−	0.211088i
$591$	−5.07919	−	2.93247i	−0.208930	−	0.120626i
$592$	−4.86824	+	1.30444i	−0.200083	+	0.0536122i
$593$	0.837988	−	3.12741i	0.0344121	−	0.128428i	−0.946583	−	0.322460i	$-0.895490\pi$
$593$	0.837988	−	3.12741i	0.0344121	−	0.128428i	0.980995	+	0.194033i	$0.0621568\pi$
$594$	9.64311			0.395661
$595$	−31.1017	−	4.36767i	−1.27504	−	0.179057i
$596$	−5.04885			−0.206809
$597$	−0.564900	+	2.10824i	−0.0231198	+	0.0862844i
$598$	2.19490	−	0.588122i	0.0897562	−	0.0240501i
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	0.355543	−	0.934660i	$-0.384296\pi$
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	−0.631668	+	0.775239i	$0.717629\pi$
$600$	−1.36571	+	0.483248i	−0.0557548	+	0.0197285i
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$	−3.18231	−	6.17537i	−0.129701	−	0.251689i
$603$	1.74233	−	1.74233i	0.0709530	−	0.0709530i
$604$	11.6418	−	6.72142i	0.473699	−	0.273491i
$605$	−45.5070	+	7.81383i	−1.85012	+	0.317677i
$606$	−2.33227	+	4.03960i	−0.0947418	+	0.164098i
$607$	0.743495	+	0.199219i	0.0301775	+	0.00808604i	0.273876	−	0.961765i	$-0.411694\pi$
$607$	0.743495	+	0.199219i	0.0301775	+	0.00808604i	−0.243699	+	0.969851i	$0.578361\pi$
$608$	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
$612$	−4.00666	−	14.9530i	−0.161960	−	0.604441i
$613$	9.05898	+	33.8086i	0.365889	+	1.36552i	0.866212	+	0.499676i	$0.166548\pi$
$613$	9.05898	+	33.8086i	0.365889	+	1.36552i	−0.500323	+	0.865839i	$0.666786\pi$
$614$	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	$0.539887\pi$
$618$	5.50479	+	1.47501i	0.221435	+	0.0593334i
$619$	21.6707	−	37.5348i	0.871021	−	1.50865i	0.0100783	−	0.999949i	$-0.496792\pi$
$619$	21.6707	−	37.5348i	0.871021	−	1.50865i	0.860942	−	0.508703i	$-0.169875\pi$
$620$	8.48131	−	1.45629i	0.340617	−	0.0584861i
$621$	1.66841	−	0.963256i	0.0669509	−	0.0386541i
$622$	−7.76566	+	7.76566i	−0.311374	+	0.311374i
$623$	14.4487	+	28.0382i	0.578876	+	1.12333i
$624$		−	0.585786i		−	0.0234502i
$625$	3.89884	+	24.6941i	0.155953	+	0.987764i
$626$	−25.4707	−	14.7055i	−1.01801	−	0.587749i
$627$	6.12745	−	1.64184i	0.244707	−	0.0655690i
$628$	−0.285443	+	1.06529i	−0.0113904	+	0.0425096i
$629$	26.7559			1.06683
$630$	17.0840	+	2.39913i	0.680641	+	0.0955837i
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	1.61706	−	6.03495i	0.0643232	−	0.240058i
$633$	−5.47879	+	1.46804i	−0.217762	+	0.0583492i
$634$	−3.71869	−	2.14699i	−0.147688	−	0.0852677i
$635$	13.3112	−	6.13457i	0.528237	−	0.243443i
$636$		−	0.400741i		−	0.0158904i
$637$	9.00710	+	10.9163i	0.356874	+	0.432520i
$638$	12.5507	−	12.5507i	0.496887	−	0.496887i
$639$	−12.0640	+	6.96513i	−0.477243	+	0.275536i
$640$	−1.29076	+	1.82591i	−0.0510217	+	0.0721754i
$641$	−12.1657	+	21.0717i	−0.480518	+	0.832281i	−0.999750	−	0.0223521i	$-0.992885\pi$
$641$	−12.1657	+	21.0717i	−0.480518	+	0.832281i	0.519233	+	0.854633i	$0.326218\pi$
$642$	0.783903	+	0.210046i	0.0309382	+	0.00828986i
$643$	6.21713	+	6.21713i	0.245180	+	0.245180i	0.818989	−	0.573809i	$-0.194535\pi$
$643$	6.21713	+	6.21713i	0.245180	+	0.245180i	−0.573809	+	0.818989i	$0.694535\pi$
$644$	−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
$647$	5.33869	+	19.9243i	0.209886	+	0.783304i	0.987905	+	0.155063i	$0.0495581\pi$
$647$	5.33869	+	19.9243i	0.209886	+	0.783304i	−0.778019	+	0.628241i	$0.783775\pi$
$648$	2.13565	+	7.97036i	0.0838963	+	0.313105i
$649$	−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
$653$	−25.2490	−	6.76544i	−0.988069	−	0.264752i	−0.271630	−	0.962402i	$-0.587563\pi$
$653$	−25.2490	−	6.76544i	−0.988069	−	0.264752i	−0.716439	+	0.697650i	$0.754229\pi$
$654$	−0.856296	+	1.48315i	−0.0334838	+	0.0579957i
$655$	2.91199	+	16.9591i	0.113781	+	0.662649i
$656$	6.24448	−	3.60525i	0.243806	−	0.140761i
$657$	−11.5723	+	11.5723i	−0.451478	+	0.451478i
$658$	−8.43533	+	13.1208i	−0.328844	+	0.511502i
$659$			24.2448i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$659$			24.2448i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$660$	1.52551	+	3.31016i	0.0593806	+	0.128848i
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	0.770633	−	0.637279i	$-0.219940\pi$
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	−0.166583	+	0.986027i	$0.553273\pi$
$662$	−34.2419	+	9.17510i	−1.33085	+	0.356600i
$663$	−0.804871	+	3.00382i	−0.0312586	+	0.116659i
$664$	8.02257			0.311336
$665$	22.8523	−	2.80839i	0.886174	−	0.108905i
$666$	−14.6968			−0.569491
$667$	0.917769	−	3.42516i	0.0355362	−	0.132623i
$668$	−6.42961	+	1.72281i	−0.248769	+	0.0666574i
$669$	0.518181	+	0.299172i	0.0200340	+	0.0115667i
$670$	1.77258	+	0.654184i	0.0684807	+	0.0252733i
$671$		−	25.9305i		−	1.00104i
$672$	−0.681415	+	0.351149i	−0.0262862	+	0.0135459i
$673$	−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
$675$	−8.54424	+	0.670353i	−0.328868	+	0.0258019i
$676$	−4.45619	+	7.71834i	−0.171392	+	0.296859i
$677$	−17.8506	−	4.78306i	−0.686055	−	0.183828i	−0.101079	−	0.994878i	$-0.532229\pi$
$677$	−17.8506	−	4.78306i	−0.686055	−	0.183828i	−0.584976	+	0.811051i	$0.698896\pi$
$678$	−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
$682$	−5.60357	−	20.9128i	−0.214572	−	0.800793i
$683$	−6.93661	−	25.8878i	−0.265422	−	0.990569i	−0.961992	−	0.273079i	$-0.911958\pi$
$683$	−6.93661	−	25.8878i	−0.265422	−	0.990569i	0.696569	−	0.717489i	$-0.254709\pi$
$684$	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
$688$	2.53629	+	0.679597i	0.0966951	+	0.0259094i
$689$	1.39819	−	2.42173i	0.0532667	−	0.0922606i
$690$	0.594591	+	0.420324i	0.0226357	+	0.0160015i
$691$	25.1773	−	14.5361i	0.957790	−	0.552980i	0.0622976	−	0.998058i	$-0.480157\pi$
$691$	25.1773	−	14.5361i	0.957790	−	0.552980i	0.895492	+	0.445077i	$0.146824\pi$
$692$	4.98835	−	4.98835i	0.189628	−	0.189628i
$693$	2.07251	−	43.3541i	0.0787281	−	1.64689i
$694$			8.97626i			0.340734i
$695$	−8.56502	+	23.2078i	−0.324890	+	0.880323i
$696$	−0.791655	−	0.457062i	−0.0300076	−	0.0173249i
$697$	−36.9743	+	9.90723i	−1.40050	+	0.375263i
$698$	6.73580	−	25.1383i	0.254954	−	0.951500i
$699$	−3.97855			−0.150483
$700$	3.81229	+	12.6675i	0.144091	+	0.478788i
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	0.896949	−	3.34746i	0.0338531	−	0.126342i
$703$	−18.9462	+	5.07663i	−0.714571	+	0.191469i
$704$	4.87205	+	2.81288i	0.183622	+	0.106014i
$705$	1.32247	−	3.58337i	0.0498071	−	0.134957i
$706$		−	9.96618i		−	0.375082i
$707$	35.8289	+	23.0343i	1.34748	+	0.866295i
$708$	−1.12240	+	1.12240i	−0.0421823	+	0.0421823i
$709$	27.1994	−	15.7036i	1.02150	−	0.589760i	0.106958	−	0.994263i	$-0.465889\pi$
$709$	27.1994	−	15.7036i	1.02150	−	0.589760i	0.914537	+	0.404503i	$0.132555\pi$
$710$	−8.72254	−	6.16608i	−0.327351	−	0.231409i
$711$	9.10952	−	15.7781i	0.341634	−	0.591727i
$712$	−11.5156	−	3.08559i	−0.431565	−	0.115637i
$713$	−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
$717$	−1.47445	−	5.50271i	−0.0550642	−	0.205502i
$718$	2.99560	+	11.1797i	0.111795	+	0.417224i
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	0.949001	−	0.315273i	$-0.102096\pi$
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	−0.747535	+	0.664222i	$0.768763\pi$
$720$	−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
$723$	1.64704	+	0.441322i	0.0612539	+	0.0164129i
$724$	2.05934	−	3.56688i	0.0765347	−	0.132562i
$725$	−10.2480	+	11.9930i	−0.380602	+	0.445408i
$726$	5.18128	−	2.99141i	0.192295	−	0.111022i
$727$	−33.6108	+	33.6108i	−1.24656	+	1.24656i	−0.289326	+	0.957231i	$0.593431\pi$
$727$	−33.6108	+	33.6108i	−1.24656	+	1.24656i	−0.957231	+	0.289326i	$0.906569\pi$
$728$	−5.34305	−	0.255420i	−0.198026	−	0.00946651i
$729$			22.5720i			0.835998i
$730$	−11.7732	−	4.34500i	−0.435747	−	0.160816i
$731$	−12.0719	−	6.96972i	−0.446496	−	0.257785i
$732$	−1.28996	+	0.345644i	−0.0476784	+	0.0127754i
$733$	6.66658	−	24.8800i	0.246236	−	0.918964i	−0.726523	−	0.687143i	$-0.758865\pi$
$733$	6.66658	−	24.8800i	0.246236	−	0.918964i	0.972758	−	0.231822i	$-0.0744686\pi$
$734$	16.6944			0.616202
$735$	−0.844410	+	4.45579i	−0.0311465	+	0.164354i
$736$	1.12392			0.0414283
$737$	1.23034	−	4.59170i	0.0453203	−	0.169138i
$738$	20.3098	−	5.44198i	0.747613	−	0.200322i
$739$	−10.4948	−	6.05920i	−0.386059	−	0.222891i	0.294392	−	0.955685i	$-0.404883\pi$
$739$	−10.4948	−	6.05920i	−0.386059	−	0.222891i	−0.680451	+	0.732793i	$0.738216\pi$
$740$	−4.71693	−	10.2351i	−0.173398	−	0.376250i
$741$		−	2.27977i		−	0.0837493i
$742$	−3.65522	−	0.174735i	−0.134187	−	0.00641472i
$743$	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
$745$	−1.91053	−	11.1267i	−0.0699964	−	0.407652i
$746$	−1.58946	+	2.75303i	−0.0581944	+	0.100796i
$747$	22.5971	+	6.05487i	0.826784	+	0.221536i
$748$	−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	0.709875	−	0.704327i	$-0.248751\pi$
$751$	−6.98887	−	12.1051i	−0.255028	−	0.441721i	−0.964903	+	0.262607i	$0.915418\pi$
$752$	−1.52590	−	5.69475i	−0.0556440	−	0.207666i
$753$	−0.532387	−	1.98690i	−0.0194013	−	0.0724065i
$754$	−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	$0.601010\pi$
$758$	6.90974	+	1.85146i	0.250973	+	0.0672481i
$759$	0.915990	−	1.58654i	0.0332483	−	0.0575878i
$760$	−5.02338	+	7.10608i	−0.182217	+	0.257765i
$761$	18.9372	−	10.9334i	0.686471	−	0.396334i	−0.115817	−	0.993271i	$-0.536949\pi$
$761$	18.9372	−	10.9334i	0.686471	−	0.396334i	0.802289	+	0.596936i	$0.203615\pi$
$762$	−1.34289	+	1.34289i	−0.0486478	+	0.0486478i
$763$	13.1546	+	8.45710i	0.476230	+	0.306168i
$764$		−	17.2023i		−	0.622359i
$765$	31.4376	−	14.4883i	1.13663	−	0.523826i
$766$	12.6382	+	7.29669i	0.456638	+	0.263640i
$767$	−10.6989	+	2.86675i	−0.386313	+	0.103512i
$768$	0.0749894	−	0.279864i	0.00270595	−	0.0100987i
$769$	−31.0506			−1.11971			−0.559857	−	0.828589i	$-0.689144\pi$
$769$	−31.0506			−1.11971			−0.559857	+	0.828589i	$0.689144\pi$
$770$	30.8576	−	12.4711i	1.11203	−	0.449428i
$771$	2.86459			0.103166
$772$	−3.12327	+	11.6562i	−0.112409	+	0.419516i
$773$	−5.86173	+	1.57065i	−0.210832	+	0.0564922i	−0.362689	−	0.931910i	$-0.618141\pi$
$773$	−5.86173	+	1.57065i	−0.210832	+	0.0564922i	0.151857	+	0.988402i	$0.451475\pi$
$774$	6.63103	+	3.82843i	0.238347	+	0.137610i
$775$	6.41880	+	18.1402i	0.230570	+	0.651614i
$776$			9.37769i			0.336640i
$777$	0.184481	−	3.85909i	0.00661822	−	0.138444i
$778$	−4.38160	+	4.38160i	−0.157088	+	0.157088i
$779$	24.3023	−	14.0309i	0.870720	−	0.502710i
$780$	1.29097	−	0.221667i	0.0462240	−	0.00793694i
$781$	−13.4374	+	23.2743i	−0.480828	+	0.832819i
$782$	−5.76329	−	1.54427i	−0.206095	−	0.0552229i
$783$	−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
$787$	−5.78752	−	21.5993i	−0.206303	−	0.769932i	−0.989049	−	0.147591i	$-0.952848\pi$
$787$	−5.78752	−	21.5993i	−0.206303	−	0.769932i	0.782746	−	0.622342i	$-0.213818\pi$
$788$	−5.23910	−	19.5526i	−0.186635	−	0.696532i
$789$	−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
$793$	−9.00138	−	2.41191i	−0.319648	−	0.0856495i
$794$	1.45794	−	2.52523i	0.0517403	−	0.0896169i
$795$	0.883159	−	0.151644i	0.0313224	−	0.00537825i
$796$	−6.52383	+	3.76653i	−0.231231	+	0.133501i
$797$	−16.5528	+	16.5528i	−0.586330	+	0.586330i	−0.936636	−	0.350305i	$-0.886078\pi$
$797$	−16.5528	+	16.5528i	−0.586330	+	0.586330i	0.350305	+	0.936636i	$0.386078\pi$
$798$	−2.65193	+	1.36660i	−0.0938774	+	0.0483772i
$799$			31.2984i			1.10726i
$800$	−4.51240	−	2.15365i	−0.159538	−	0.0761432i
$801$	−30.1070	−	17.3823i	−1.06378	−	0.614174i
$802$	19.2901	−	5.16876i	0.681156	−	0.182515i
$803$	−8.17177	+	30.4975i	−0.288376	+	1.07623i
$804$	−0.244823			−0.00863425
$805$	4.09310	−	5.24008i	0.144263	−	0.184689i
$806$	−7.78078			−0.274066
$807$	−1.98737	+	7.41697i	−0.0699588	+	0.261090i
$808$	−15.5506	+	4.16678i	−0.547069	+	0.146587i
$809$	−2.84139	−	1.64048i	−0.0998980	−	0.0576762i	0.449219	−	0.893422i	$-0.351702\pi$
$809$	−2.84139	−	1.64048i	−0.0998980	−	0.0576762i	−0.549117	+	0.835746i	$0.685036\pi$
$810$	−16.7571	+	7.72263i	−0.588783	+	0.271346i
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$	−4.51412	+	7.02151i	−0.158414	+	0.246407i
$813$	2.62176	−	2.62176i	0.0919491	−	0.0919491i
$814$	−24.5550	+	14.1768i	−0.860653	+	0.496898i
$815$	17.0911	−	24.1771i	0.598674	−	0.846886i
$816$	−0.769067	+	1.33206i	−0.0269227	+	0.0466316i
$817$	9.87074	+	2.64486i	0.345333	+	0.0925318i
$818$	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	0.950516	−	0.310677i	$-0.100556\pi$
$821$	5.90837	+	10.2336i	0.206204	+	0.357155i	−0.744312	+	0.667832i	$0.767222\pi$
$822$	0.662590	+	2.47282i	0.0231105	+	0.0862495i
$823$	9.13692	+	34.0995i	0.318493	+	1.18863i	0.920693	+	0.390287i	$0.127624\pi$
$823$	9.13692	+	34.0995i	0.318493	+	1.18863i	−0.602200	+	0.798345i	$0.705709\pi$
$824$	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	$0.889717\pi$
$828$	3.16574	+	0.848257i	0.110017	+	0.0294790i
$829$	−17.2877	+	29.9431i	−0.600426	+	1.03997i	0.392330	+	0.919824i	$0.371669\pi$
$829$	−17.2877	+	29.9431i	−0.600426	+	1.03997i	−0.992756	+	0.120144i	$0.961664\pi$
$830$	3.03581	+	17.6803i	0.105374	+	0.613691i
$831$	5.04433	−	2.91234i	0.174986	−	0.101028i
$832$	1.42962	−	1.42962i	0.0495631	−	0.0495631i
$833$	−6.15011	−	36.6487i	−0.213089	−	1.26980i
$834$		−	3.20539i		−	0.110994i
$835$	−6.22977	−	13.5177i	−0.215590	−	0.467801i
$836$	18.9611	+	10.9472i	0.655782	+	0.378616i
$837$	−6.37187	+	1.70734i	−0.220244	+	0.0590142i
$838$	8.05859	−	30.0751i	0.278379	−	1.03893i
$839$	50.1328			1.73078			0.865388	−	0.501102i	$-0.167072\pi$
$839$	50.1328			1.73078			0.865388	+	0.501102i	$0.167072\pi$
$840$	−1.03172	−	1.36884i	−0.0355978	−	0.0472293i
$841$	19.0459			0.656754
$842$	−8.71515	+	32.5254i	−0.300344	+	1.12090i
$843$	3.96003	−	1.06109i	0.136391	−	0.0365458i
$844$	−16.9538	−	9.78829i	−0.583575	−	0.336927i
$845$	−18.6961	−	6.89993i	−0.643164	−	0.237365i
$846$		−	17.1920i		−	0.591073i
$847$	−25.0259	−	48.5636i	−0.859901	−	1.66866i
$848$	0.978013	−	0.978013i	0.0335851	−	0.0335851i
$849$	6.79181	−	3.92125i	0.233094	−	0.134577i
$850$	20.1797	+	17.2436i	0.692160	+	0.591452i
$851$	−2.83227	+	4.90563i	−0.0970888	+	0.168163i
$852$	1.33694	+	0.358232i	0.0458028	+	0.0122728i
$853$	2.37500	+	2.37500i	0.0813183	+	0.0813183i	0.746596	−	0.665278i	$-0.231687\pi$
$853$	2.37500	+	2.37500i	0.0813183	+	0.0813183i	−0.665278	+	0.746596i	$0.731687\pi$
$854$	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
$857$	−10.8545	−	40.5097i	−0.370784	−	1.38378i	−0.859408	−	0.511290i	$-0.829168\pi$
$857$	−10.8545	−	40.5097i	−0.370784	−	1.38378i	0.488624	−	0.872494i	$-0.337499\pi$
$858$	−0.852937	−	3.18320i	−0.0291188	−	0.108673i
$859$	1.17847	+	2.04117i	0.0402090	+	0.0696440i	0.885430	−	0.464774i	$-0.153864\pi$
$859$	1.17847	+	2.04117i	0.0402090	+	0.0696440i	−0.845221	+	0.534418i	$0.820531\pi$
$860$	−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
$863$	−46.7022	−	12.5138i	−1.58976	−	0.425975i	−0.647831	−	0.761784i	$-0.724324\pi$
$863$	−46.7022	−	12.5138i	−1.58976	−	0.425975i	−0.941930	+	0.335808i	$0.890991\pi$
$864$	0.857049	−	1.48445i	0.0291574	−	0.0505021i
$865$	12.8810	+	9.10577i	0.437968	+	0.309605i
$866$	12.2261	−	7.05873i	0.415459	−	0.239865i
$867$	2.29104	−	2.29104i	0.0778076	−	0.0778076i
$868$	4.66418	+	9.05097i	0.158312	+	0.307210i
$869$		−	35.1489i		−	1.19234i
$870$	0.707712	−	1.91762i	0.0239937	−	0.0650133i
$871$	−1.47950	−	0.854190i	−0.0501310	−	0.0289431i
$872$	−5.70944	+	1.52984i	−0.193346	+	0.0518069i
$873$	−7.07763	+	26.4141i	−0.239541	+	0.893980i
$874$	4.37408			0.147955
$875$	−26.4743	+	13.1951i	−0.894995	+	0.446076i
$876$	1.62608			0.0549402
$877$	−3.56681	+	13.3115i	−0.120443	+	0.449498i	−0.999636	−	0.0269665i	$-0.991415\pi$
$877$	−3.56681	+	13.3115i	−0.120443	+	0.449498i	0.879194	+	0.476465i	$0.158082\pi$
$878$	−37.1191	+	9.94602i	−1.25271	+	0.335662i
$879$	6.07477	+	3.50727i	0.204897	+	0.118297i
$880$	−4.35544	+	11.8015i	−0.146822	+	0.397829i
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$	3.37822	+	20.1309i	0.113751	+	0.677842i
$883$	−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
$885$	−2.89828	−	2.04883i	−0.0974247	−	0.0688708i
$886$	−2.86780	+	4.96718i	−0.0963456	+	0.166876i
$887$	−34.6001	−	9.27107i	−1.16176	−	0.311292i	−0.374090	−	0.927392i	$-0.622045\pi$
$887$	−34.6001	−	9.27107i	−1.16176	−	0.311292i	−0.787668	+	0.616101i	$0.788711\pi$
$888$	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
$892$	0.534495	+	1.99476i	0.0178962	+	0.0667895i
$893$	−5.93852	−	22.1628i	−0.198725	−	0.741651i
$894$	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
$898$	7.05384	+	1.89007i	0.235390	+	0.0630725i
$899$	−6.07098	+	10.5152i	−0.202479	+	0.350703i
$900$	−11.0846	−	9.47182i	−0.369487	−	0.315727i
$901$	−6.35888	+	3.67130i	−0.211845	+	0.122309i
$902$	28.6835	−	28.6835i	0.955055	−	0.955055i
$903$	−1.08850	+	1.69312i	−0.0362232	+	0.0563435i
$904$		−	19.2075i		−	0.638833i
$905$	8.64001	+	3.18866i	0.287204	+	0.105995i
$906$	−3.37307	−	1.94744i	−0.112063	−	0.0646994i
$907$	16.6696	−	4.46661i	0.553506	−	0.148312i	0.0287849	−	0.999586i	$-0.490836\pi$
$907$	16.6696	−	4.46661i	0.553506	−	0.148312i	0.524721	+	0.851274i	$0.324170\pi$
$908$	−4.82525	+	18.0081i	−0.160131	+	0.597618i
$909$	−46.9461			−1.55710
$910$	−1.45896	−	11.8717i	−0.0483639	−	0.393545i
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	0.291844	−	1.08918i	0.00966392	−	0.0360663i
$913$	43.5952	−	11.6813i	1.44279	−	0.386594i
$914$	−4.45641	−	2.57291i	−0.147405	−	0.0851042i
$915$	−1.24987	−	2.71205i	−0.0413194	−	0.0896575i
$916$		−	4.00767i		−	0.132417i
$917$	−18.0982	+	9.32645i	−0.597657	+	0.307986i
$918$	−6.43445	+	6.43445i	−0.212368	+	0.212368i
$919$	−5.37964	+	3.10593i	−0.177458	+	0.102455i	−0.586098	−	0.810240i	$-0.699337\pi$
$919$	−5.37964	+	3.10593i	−0.177458	+	0.102455i	0.408640	+	0.912696i	$0.366003\pi$
$920$	0.425302	+	2.47692i	0.0140218	+	0.0816615i
$921$	3.54381	−	6.13806i	0.116773	−	0.202256i
$922$	28.4088	+	7.61212i	0.935595	+	0.250692i
$923$	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
$927$	14.8452	+	55.4029i	0.487579	+	1.81967i
$928$	−0.816578	−	3.04751i	−0.0268055	−	0.100039i
$929$	−0.0947297	−	0.164077i	−0.00310798	−	0.00538318i	0.864467	−	0.502689i	$-0.167656\pi$
$929$	−0.0947297	−	0.164077i	−0.00310798	−	0.00538318i	−0.867575	+	0.497306i	$0.834323\pi$
$930$	−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
$933$	3.07355	+	0.823556i	0.100624	+	0.0269620i
$934$	8.32139	−	14.4131i	0.272284	−	0.471610i
$935$	38.5493	−	54.5319i	1.26070	−	1.78338i
$936$	5.10577	−	2.94782i	0.166887	−	0.0963525i
$937$	34.2022	−	34.2022i	1.11734	−	1.11734i	0.125208	−	0.992131i	$-0.460040\pi$
$937$	34.2022	−	34.2022i	1.11734	−	1.11734i	0.992131	−	0.125208i	$-0.0399598\pi$
$938$	−0.106750	+	2.23307i	−0.00348552	+	0.0729123i
$939$			8.52144i			0.278087i
$940$	11.9728	−	5.51775i	0.390509	−	0.179969i
$941$	−16.3826	−	9.45851i	−0.534058	−	0.308339i	0.208609	−	0.977999i	$-0.433106\pi$
$941$	−16.3826	−	9.45851i	−0.534058	−	0.308339i	−0.742667	+	0.669660i	$0.766440\pi$
$942$	0.308653	−	0.0827033i	0.0100565	−	0.00269462i
$943$	2.09748	−	7.82790i	0.0683033	−	0.254911i
$944$	−5.47845			−0.178308
$945$	−3.79979	−	9.40193i	−0.123607	−	0.305845i
$946$	14.7719			0.480276
$947$	12.2033	−	45.5435i	0.396555	−	1.47996i	−0.422560	−	0.906335i	$-0.638869\pi$
$947$	12.2033	−	45.5435i	0.396555	−	1.47996i	0.819115	−	0.573629i	$-0.194465\pi$
$948$	−1.74855	+	0.468522i	−0.0567902	+	0.0152169i
$949$	9.82664	+	5.67341i	0.318986	+	0.184167i
$950$	−17.5614	−	8.38160i	−0.569767	−	0.271935i
$951$			1.24412i			0.0403434i
$952$	11.8146	+	7.59560i	0.382914	+	0.246175i
$953$	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
$955$	37.9108	−	6.50952i	1.22677	−	0.210643i
$956$	9.83103	−	17.0278i	0.317958	−	0.550720i
$957$	−4.96741	−	1.33101i	−0.160574	−	0.0430256i
$958$	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
$962$	2.63730	+	9.84255i	0.0850301	+	0.317337i
$963$	2.11401	+	7.88958i	0.0681229	+	0.254238i
$964$	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	$0.536169\pi$
$968$	19.9456	+	5.34440i	0.641075	+	0.171776i
$969$	−2.99306	+	5.18413i	−0.0961509	+	0.166538i
$970$	−20.6667	+	3.54860i	−0.663568	+	0.113939i
$971$	−27.8750	+	16.0936i	−0.894550	+	0.516469i	−0.875428	−	0.483348i	$-0.839420\pi$
$971$	−27.8750	+	16.0936i	−0.894550	+	0.516469i	−0.0191221	+	0.999817i	$0.506087\pi$
$972$	5.32668	−	5.32668i	0.170853	−	0.170853i
$973$	−29.2369	−	1.39765i	−0.937291	−	0.0448065i
$974$		−	35.9920i		−	1.15326i
$975$	0.977025	+	2.76117i	0.0312899	+	0.0884282i
$976$	−3.99172	−	2.30462i	−0.127772	−	0.0737691i
$977$	22.4848	−	6.02479i	0.719353	−	0.192750i	0.119470	−	0.992838i	$-0.461881\pi$
$977$	22.4848	−	6.02479i	0.719353	−	0.192750i	0.599883	+	0.800088i	$0.295214\pi$
$978$	−0.992944	+	3.70572i	−0.0317508	+	0.118496i
$979$	−67.0692			−2.14354
$980$	−12.9352	+	8.81363i	−0.413200	+	0.281541i
$981$	−17.2364			−0.550314
$982$	−3.95535	+	14.7616i	−0.126220	+	0.471060i
$983$	55.0964	−	14.7630i	1.75730	−	0.470868i	0.771143	−	0.636662i	$-0.219685\pi$
$983$	55.0964	−	14.7630i	1.75730	−	0.470868i	0.986160	+	0.165793i	$0.0530185\pi$
$984$	−1.80926	−	1.04457i	−0.0576770	−	0.0332998i
$985$	41.1078	−	18.9449i	1.30980	−	0.603634i
$986$			16.7491i			0.533401i
$987$	4.51427	+	0.215802i	0.143691	+	0.00686904i
$988$	5.56380	−	5.56380i	0.177008	−	0.177008i
$989$	2.55577	−	1.47557i	0.0812687	−	0.0469205i
$990$	−21.1749	+	29.9541i	−0.672983	+	0.952002i
$991$	28.7703	−	49.8316i	0.913918	−	1.58295i	0.105440	−	0.994426i	$-0.466375\pi$
$991$	28.7703	−	49.8316i	0.913918	−	1.58295i	0.808478	−	0.588526i	$-0.200292\pi$
$992$	−3.71733	−	0.996056i	−0.118025	−	0.0316248i
$993$	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
$997$	6.27762	+	23.4284i	0.198814	+	0.741985i	0.991246	+	0.132025i	$0.0421479\pi$
$997$	6.27762	+	23.4284i	0.198814	+	0.741985i	−0.792432	+	0.609960i	$0.791185\pi$
$998$	−8.17479	−	30.5087i	−0.258768	−	0.965737i
$999$	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.17.3	yes	16
3.2	odd	2		630.2.bv.c.577.1		16
4.3	odd	2		560.2.ci.c.17.3		16
5.2	odd	4		350.2.o.c.143.4		16
5.3	odd	4	inner	70.2.k.a.3.1	✓	16
5.4	even	2		350.2.o.c.157.2		16
7.2	even	3		490.2.l.c.117.2		16
7.3	odd	6		490.2.g.c.97.6		16
7.4	even	3		490.2.g.c.97.7		16
7.5	odd	6	inner	70.2.k.a.47.1	yes	16
7.6	odd	2		490.2.l.c.227.4		16
15.8	even	4		630.2.bv.c.73.3		16
20.3	even	4		560.2.ci.c.353.3		16
21.5	even	6		630.2.bv.c.397.3		16
28.19	even	6		560.2.ci.c.257.3		16
35.3	even	12		490.2.g.c.293.7		16
35.12	even	12		350.2.o.c.243.2		16
35.13	even	4		490.2.l.c.423.2		16
35.18	odd	12		490.2.g.c.293.6		16
35.19	odd	6		350.2.o.c.257.4		16
35.23	odd	12		490.2.l.c.313.4		16
35.33	even	12	inner	70.2.k.a.33.3	yes	16
105.68	odd	12		630.2.bv.c.523.1		16
140.103	odd	12		560.2.ci.c.33.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	5.3	odd	4	inner
70.2.k.a.17.3	yes	16	1.1	even	1	trivial
70.2.k.a.33.3	yes	16	35.33	even	12	inner
70.2.k.a.47.1	yes	16	7.5	odd	6	inner
350.2.o.c.143.4		16	5.2	odd	4
350.2.o.c.157.2		16	5.4	even	2
350.2.o.c.243.2		16	35.12	even	12
350.2.o.c.257.4		16	35.19	odd	6
490.2.g.c.97.6		16	7.3	odd	6
490.2.g.c.97.7		16	7.4	even	3
490.2.g.c.293.6		16	35.18	odd	12
490.2.g.c.293.7		16	35.3	even	12
490.2.l.c.117.2		16	7.2	even	3
490.2.l.c.227.4		16	7.6	odd	2
490.2.l.c.313.4		16	35.23	odd	12
490.2.l.c.423.2		16	35.13	even	4
560.2.ci.c.17.3		16	4.3	odd	2
560.2.ci.c.33.3		16	140.103	odd	12
560.2.ci.c.257.3		16	28.19	even	6
560.2.ci.c.353.3		16	20.3	even	4
630.2.bv.c.73.3		16	15.8	even	4
630.2.bv.c.397.3		16	21.5	even	6
630.2.bv.c.523.1		16	105.68	odd	12
630.2.bv.c.577.1		16	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.279864 + 0.0749894i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(2.64273 + 0.126334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52538 + 1.45803i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.279864 + 0.0749894i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.774197 - 2.09777i) q^{5} +0.289737i q^{6} +(2.64273 + 0.126334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52538 + 1.45803i) q^{9} +(-1.82591 - 1.29076i) q^{10} +(-2.81288 + 4.87205i) q^{11} +(0.279864 + 0.0749894i) 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} +(-1.37400 - 5.12784i) q^{17} +(0.754730 + 2.81669i) 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} +(1.08562 + 0.290892i) q^{23} +(0.144868 - 0.250919i) q^{24} +(-3.80124 - 3.24817i) q^{25} +(1.75092 - 1.01089i) q^{26} +(1.21205 - 1.21205i) q^{27} +(-2.22551 - 1.43078i) q^{28} -3.15502i q^{29} +(0.607800 + 0.224313i) q^{30} +(-3.33287 - 1.92423i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.421872 - 1.57445i) q^{33} -5.30873 q^{34} +(2.31101 - 5.44603i) q^{35} +2.91605 q^{36} +(-1.30444 + 4.86824i) q^{37} +(3.75919 - 1.00727i) q^{38} +(-0.507306 - 0.292893i) q^{39} +(0.935904 + 2.03078i) q^{40} -7.21050i q^{41} +(-0.0366036 + 0.765697i) q^{42} +(1.85669 - 1.85669i) q^{43} +(4.87205 - 2.81288i) q^{44} +(1.10346 + 6.42644i) q^{45} +(0.561961 - 0.973344i) q^{46} +(-5.69475 - 1.52590i) 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} +(-0.523277 - 1.95290i) q^{52} +(-0.357978 - 1.33599i) 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} +(-3.04751 - 0.816578i) q^{58} +(-2.73923 + 4.74448i) q^{59} +(0.373980 - 0.529033i) q^{60} +(-3.99172 + 2.30462i) q^{61} +(-2.72127 + 2.72127i) q^{62} +(-6.85809 + 3.53413i) q^{63} -1.00000i q^{64} +(4.10581 - 1.89220i) q^{65} +(-1.41161 - 0.814995i) q^{66} +(-0.816193 + 0.218698i) q^{67} +(-1.37400 + 5.12784i) q^{68} -0.325641 q^{69} +(-4.66232 - 3.64180i) q^{70} +4.77710 q^{71} +(0.754730 - 2.81669i) q^{72} +(5.42104 - 1.45256i) q^{73} +(4.36475 + 2.51999i) q^{74} +(1.30741 + 0.623993i) q^{75} -3.89180i q^{76} +(-8.04920 + 12.5202i) q^{77} +(-0.414214 + 0.414214i) q^{78} +(-5.41079 + 3.12392i) q^{79} +(2.20382 - 0.378409i) q^{80} +(4.12576 - 7.14603i) q^{81} +(-6.96481 - 1.86622i) 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} +(0.236593 + 0.882976i) q^{87} +(-1.45605 - 5.43407i) 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} +(1.07705 + 0.288594i) q^{93} +(-2.94782 + 5.10577i) q^{94} +(8.57682 - 1.47269i) q^{95} +(-0.250919 + 0.144868i) q^{96} +(6.63103 - 6.63103i) q^{97} +(2.44845 - 6.55783i) 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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