LMFDB - Embedded newform 39.2.k.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,2,Mod(2,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("39.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	39.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:	$0.311416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
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			11.1
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	39.11
Dual form			39.2.k.b.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})$	\(q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(-1.96410 + 1.13397i) q^{10} +(-1.06488 + 3.97420i) q^{11} +(0.285334 - 0.366025i) q^{12} +(3.59808 + 0.232051i) q^{13} -2.12976i q^{14} +(-1.57203 - 2.08148i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(2.51954 - 4.36397i) q^{17} +(3.87762 + 2.31853i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(0.389774 - 0.104440i) q^{20} +(2.43091 - 0.301143i) q^{21} +(3.09808 - 5.36603i) q^{22} +(3.60523 - 2.72284i) q^{24} +2.73205i q^{25} +(-5.14352 - 1.73999i) q^{26} +(-2.09808 + 4.75374i) q^{27} +(-0.0980762 + 0.366025i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(1.47546 + 3.64058i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(0.389774 + 1.45466i) q^{32} +(6.56283 + 2.77739i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(1.84443 + 1.06488i) q^{35} +(-0.559647 - 0.577032i) q^{36} +(-5.23205 - 1.40192i) q^{37} +5.81863 q^{38} +(1.25874 - 6.11683i) q^{39} +3.92820 q^{40} +(5.42885 + 1.45466i) q^{41} +(-3.65351 - 0.509445i) q^{42} +(1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(-3.94672 + 2.19886i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(-7.16590 + 2.90422i) q^{48} +(4.33013 - 2.50000i) q^{49} +(1.06488 - 3.97420i) q^{50} +(-6.88351 - 5.36603i) q^{51} +(0.803848 + 0.535898i) q^{52} -0.779548i q^{53} +(4.90487 - 6.09729i) q^{54} +(3.09808 + 5.36603i) q^{55} +(-1.84443 + 3.19465i) q^{56} +(0.822738 + 6.64136i) q^{57} +(10.4282 - 2.79423i) q^{58} +(-2.90931 + 0.779548i) q^{59} +(-0.0859264 - 0.693622i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.62398 + 4.54486i) q^{62} +(0.0648824 - 4.24214i) q^{63} +6.66025i q^{64} +(4.07863 - 3.58442i) q^{65} +(-8.46410 - 6.59817i) q^{66} +(-1.53590 + 5.73205i) q^{67} +(1.16932 - 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(-0.779548 - 2.90931i) q^{71} +(-3.80853 - 6.83591i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(4.68671 + 0.653513i) q^{75} +(-1.00000 - 0.267949i) q^{76} -5.81863 q^{77} +(-4.21522 + 8.40726i) q^{78} +2.00000 q^{79} +(-6.49373 - 1.73999i) q^{80} +(7.65296 + 4.73626i) q^{81} +(-7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(0.604440 + 0.255799i) q^{84} +(-1.96410 - 7.33013i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(4.66384 + 11.5076i) q^{87} +(-9.29423 + 5.36603i) q^{88} +(-2.41510 + 9.01327i) q^{89} +(6.59817 - 1.66025i) q^{90} +(1.00000 + 5.00000i) q^{91} +(-4.81647 + 3.63763i) q^{93} +(4.53590 + 7.85641i) q^{94} +(-2.90931 + 5.03908i) q^{95} +(2.58863 - 0.320682i) q^{96} +(1.63397 - 0.437822i) q^{97} +(-7.27328 + 1.94887i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9	$ 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{10} + 8 q^{13} - 14 q^{15} - 4 q^{16} + 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{22} + 18 q^{24} + 4 q^{27} + 20 q^{28} + 18 q^{30} + 8 q^{31} + 16 q^{33} - 36 q^{34} - 36 q^{36} - 28 q^{37} - 14 q^{39} - 24 q^{40} - 16 q^{42} + 36 q^{43} - 20 q^{45} - 14 q^{48} + 48 q^{52} + 46 q^{54} + 4 q^{55} + 16 q^{57} + 28 q^{58} + 44 q^{60} + 28 q^{61} - 8 q^{63} - 40 q^{66} - 40 q^{67} - 32 q^{70} + 12 q^{72} - 28 q^{73} + 12 q^{75} - 8 q^{76} - 80 q^{78} + 16 q^{79} + 4 q^{81} - 24 q^{82} + 4 q^{84} + 12 q^{85} - 34 q^{87} - 12 q^{88} + 8 q^{91} + 4 q^{93} + 64 q^{94} + 16 q^{96} + 20 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^10 + 8 * q^13 - 14 * q^15 - 4 * q^16 + 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^22 + 18 * q^24 + 4 * q^27 + 20 * q^28 + 18 * q^30 + 8 * q^31 + 16 * q^33 - 36 * q^34 - 36 * q^36 - 28 * q^37 - 14 * q^39 - 24 * q^40 - 16 * q^42 + 36 * q^43 - 20 * q^45 - 14 * q^48 + 48 * q^52 + 46 * q^54 + 4 * q^55 + 16 * q^57 + 28 * q^58 + 44 * q^60 + 28 * q^61 - 8 * q^63 - 40 * q^66 - 40 * q^67 - 32 * q^70 + 12 * q^72 - 28 * q^73 + 12 * q^75 - 8 * q^76 - 80 * q^78 + 16 * q^79 + 4 * q^81 - 24 * q^82 + 4 * q^84 + 12 * q^85 - 34 * q^87 - 12 * q^88 + 8 * q^91 + 4 * q^93 + 64 * q^94 + 16 * q^96 + 20 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.45466	−	0.389774i	−1.02860	−	0.275612i	−0.295217	−	0.955430i	$-0.595392\pi$
$2$	−1.45466	−	0.389774i	−1.02860	−	0.275612i	−0.733380	+	0.679818i	$0.762059\pi$
$3$	0.239203	−	1.71545i	0.138104	−	0.990418i
$3$	0.239203	−	1.71545i	0.138104	−	0.990418i
$4$	0.232051	+	0.133975i	0.116025	+	0.0669873i
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	−0.427694	−	0.903924i	$-0.640674\pi$
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	0.903924	+	0.427694i	$0.140674\pi$
$6$	−1.01660	+	2.40216i	−0.415024	+	0.980678i
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	0.999962	+	0.00875026i	$0.00278533\pi$
$7$	0.366025	+	1.36603i	0.138345	+	0.516309i	−0.861617	+	0.507559i	$0.830548\pi$
$8$	1.84443	+	1.84443i	0.652105	+	0.652105i
$9$	−2.88556	−	0.820682i	−0.961855	−	0.273561i
$10$	−1.96410	+	1.13397i	−0.621103	+	0.358594i
$11$	−1.06488	+	3.97420i	−0.321074	+	1.19826i	0.597126	+	0.802148i	$0.296309\pi$
$11$	−1.06488	+	3.97420i	−0.321074	+	1.19826i	−0.918200	+	0.396117i	$0.870357\pi$
$12$	0.285334	−	0.366025i	0.0823689	−	0.105662i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$14$		−	2.12976i		−	0.569204i
$15$	−1.57203	−	2.08148i	−0.405897	−	0.537436i
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	2.51954	−	4.36397i	0.611078	−	1.05842i	−0.379981	−	0.924994i	$-0.624070\pi$
$17$	2.51954	−	4.36397i	0.611078	−	1.05842i	0.991059	−	0.133424i	$-0.0425971\pi$
$18$	3.87762	+	2.31853i	0.913965	+	0.546482i
$19$	−3.73205	+	1.00000i	−0.856191	+	0.229416i	−0.660107	−	0.751171i	$-0.729489\pi$
$19$	−3.73205	+	1.00000i	−0.856191	+	0.229416i	−0.196084	+	0.980587i	$0.562823\pi$
$20$	0.389774	−	0.104440i	0.0871561	−	0.0233534i
$21$	2.43091	−	0.301143i	0.530468	−	0.0657148i
$22$	3.09808	−	5.36603i	0.660512	−	1.14404i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	3.60523	−	2.72284i	0.735914	−	0.555798i
$25$			2.73205i			0.546410i
$26$	−5.14352	−	1.73999i	−1.00873	−	0.341240i
$27$	−2.09808	+	4.75374i	−0.403775	+	0.914858i
$28$	−0.0980762	+	0.366025i	−0.0185347	+	0.0691723i
$29$	−6.20840	+	3.58442i	−1.15287	+	0.665610i	−0.949585	−	0.313509i	$-0.898495\pi$
$29$	−6.20840	+	3.58442i	−1.15287	+	0.665610i	−0.203286	+	0.979119i	$0.565162\pi$
$30$	1.47546	+	3.64058i	0.269381	+	0.664675i
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	0.450308	−	0.892873i	$-0.351314\pi$
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	−0.892873	+	0.450308i	$0.851314\pi$
$32$	0.389774	+	1.45466i	0.0689030	+	0.257149i
$33$	6.56283	+	2.77739i	1.14244	+	0.483482i
$34$	−5.36603	+	5.36603i	−0.920266	+	0.920266i
$35$	1.84443	+	1.06488i	0.311766	+	0.179998i
$36$	−0.559647	−	0.577032i	−0.0932745	−	0.0961720i
$37$	−5.23205	−	1.40192i	−0.860144	−	0.230475i	−0.198323	−	0.980137i	$-0.563549\pi$
$37$	−5.23205	−	1.40192i	−0.860144	−	0.230475i	−0.661821	+	0.749662i	$0.730216\pi$
$38$	5.81863			0.943906
$39$	1.25874	−	6.11683i	0.201560	−	0.979476i
$40$	3.92820			0.621103
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.656483	−	0.754341i	$-0.272043\pi$
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.191361	+	0.981520i	$0.438710\pi$
$42$	−3.65351	−	0.509445i	−0.563749	−	0.0786091i
$43$	1.90192	+	1.09808i	0.290041	+	0.167455i	0.637960	−	0.770069i	$-0.279778\pi$
$43$	1.90192	+	1.09808i	0.290041	+	0.167455i	−0.347920	+	0.937524i	$0.613112\pi$
$44$	−0.779548	+	0.779548i	−0.117521	+	0.117521i
$45$	−3.94672	+	2.19886i	−0.588342	+	0.327786i
$46$		0			0
$47$	−4.25953	−	4.25953i	−0.621316	−	0.621316i	0.324552	−	0.945868i	$-0.394787\pi$
$47$	−4.25953	−	4.25953i	−0.621316	−	0.621316i	−0.945868	+	0.324552i	$0.894787\pi$
$48$	−7.16590	+	2.90422i	−1.03431	+	0.419188i
$49$	4.33013	−	2.50000i	0.618590	−	0.357143i
$50$	1.06488	−	3.97420i	0.150597	−	0.562036i
$51$	−6.88351	−	5.36603i	−0.963884	−	0.751394i
$52$	0.803848	+	0.535898i	0.111474	+	0.0743157i
$53$		−	0.779548i		−	0.107079i	−0.998566	−	0.0535396i	$-0.982950\pi$
$53$		−	0.779548i		−	0.107079i	0.998566	−	0.0535396i	$-0.0170503\pi$
$54$	4.90487	−	6.09729i	0.667468	−	0.829736i
$55$	3.09808	+	5.36603i	0.417745	+	0.723555i
$56$	−1.84443	+	3.19465i	−0.246472	+	0.426903i
$57$	0.822738	+	6.64136i	0.108974	+	0.879670i
$58$	10.4282	−	2.79423i	1.36929	−	0.366900i
$59$	−2.90931	+	0.779548i	−0.378760	+	0.101489i	−0.443176	−	0.896435i	$-0.646148\pi$
$59$	−2.90931	+	0.779548i	−0.378760	+	0.101489i	0.0644157	+	0.997923i	$0.479482\pi$
$60$	−0.0859264	−	0.693622i	−0.0110931	−	0.0895462i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	2.62398	+	4.54486i	0.333246	+	0.577198i
$63$	0.0648824	−	4.24214i	0.00817442	−	0.534460i
$64$			6.66025i			0.832532i
$65$	4.07863	−	3.58442i	0.505892	−	0.444593i
$66$	−8.46410	−	6.59817i	−1.04186	−	0.812179i
$67$	−1.53590	+	5.73205i	−0.187640	+	0.700281i	0.806410	+	0.591357i	$0.201407\pi$
$67$	−1.53590	+	5.73205i	−0.187640	+	0.700281i	−0.994050	+	0.108925i	$0.965259\pi$
$68$	1.16932	−	0.675108i	0.141801	−	0.0818689i
$69$		0			0
$70$	−2.26795	−	2.26795i	−0.271072	−	0.271072i
$71$	−0.779548	−	2.90931i	−0.0925153	−	0.345272i	0.904116	−	0.427288i	$-0.140531\pi$
$71$	−0.779548	−	2.90931i	−0.0925153	−	0.345272i	−0.996631	+	0.0820158i	$0.973864\pi$
$72$	−3.80853	−	6.83591i	−0.448840	−	0.805620i
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	−0.757915	−	0.652353i	$-0.773782\pi$
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	0.652353	+	0.757915i	$0.273782\pi$
$74$	7.06440	+	4.07863i	0.821220	+	0.474132i
$75$	4.68671	+	0.653513i	0.541174	+	0.0754612i
$76$	−1.00000	−	0.267949i	−0.114708	−	0.0307359i
$77$	−5.81863			−0.663094
$78$	−4.21522	+	8.40726i	−0.477279	+	0.951934i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	−6.49373	−	1.73999i	−0.726022	−	0.194537i
$81$	7.65296	+	4.73626i	0.850329	+	0.526251i
$82$	−7.33013	−	4.23205i	−0.809477	−	0.467352i
$83$	2.90931	−	2.90931i	0.319339	−	0.319339i	−0.529174	−	0.848513i	$-0.677498\pi$
$83$	2.90931	−	2.90931i	0.319339	−	0.319339i	0.848513	+	0.529174i	$0.177498\pi$
$84$	0.604440	+	0.255799i	0.0659498	+	0.0279100i
$85$	−1.96410	−	7.33013i	−0.213037	−	0.795064i
$86$	−2.33864	−	2.33864i	−0.252182	−	0.252182i
$87$	4.66384	+	11.5076i	0.500017	+	1.23375i
$88$	−9.29423	+	5.36603i	−0.990768	+	0.572020i
$89$	−2.41510	+	9.01327i	−0.256000	+	0.955405i	0.711531	+	0.702654i	$0.248002\pi$
$89$	−2.41510	+	9.01327i	−0.256000	+	0.955405i	−0.967531	+	0.252751i	$0.918665\pi$
$90$	6.59817	−	1.66025i	0.695509	−	0.175006i
$91$	1.00000	+	5.00000i	0.104828	+	0.524142i
$92$		0			0
$93$	−4.81647	+	3.63763i	−0.499445	+	0.377205i
$94$	4.53590	+	7.85641i	0.467842	+	0.810326i
$95$	−2.90931	+	5.03908i	−0.298489	+	0.516998i
$96$	2.58863	−	0.320682i	0.264201	−	0.0327295i
$97$	1.63397	−	0.437822i	0.165905	−	0.0444541i	−0.174910	−	0.984584i	$-0.555964\pi$
$97$	1.63397	−	0.437822i	0.165905	−	0.0444541i	0.340815	+	0.940130i	$0.389297\pi$
$98$	−7.27328	+	1.94887i	−0.734712	+	0.196866i
$99$	6.33434	−	10.5939i	0.636625	−	1.06472i
$100$	−0.366025	+	0.633975i	−0.0366025	+	0.0633975i
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	0.676229	−	0.736692i	$-0.263613\pi$
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	−0.976108	+	0.217285i	$0.930280\pi$
$102$	7.92160	+	10.4887i	0.784356	+	1.03854i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	6.20840	+	7.06440i	0.608784	+	0.692722i
$105$	2.26795	−	2.90931i	0.221329	−	0.283920i
$106$	−0.303848	+	1.13397i	−0.0295123	+	0.110141i
$107$	16.4675	−	9.50749i	1.59197	−	0.919123i	0.598999	−	0.800749i	$-0.295565\pi$
$107$	16.4675	−	9.50749i	1.59197	−	0.919123i	0.992969	−	0.118374i	$-0.0377682\pi$
$108$	−1.12374	+	0.822021i	−0.108132	+	0.0790990i
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.949156	−	0.314806i	$-0.898060\pi$
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.314806	−	0.949156i	$-0.601940\pi$
$110$	−2.41510	−	9.01327i	−0.230271	−	0.859382i
$111$	−3.65646	+	8.64000i	−0.347055	+	0.820072i
$112$	4.46410	−	4.46410i	0.421818	−	0.421818i
$113$	−8.90883	−	5.14352i	−0.838073	−	0.483861i	0.0185360	−	0.999828i	$-0.494099\pi$
$113$	−8.90883	−	5.14352i	−0.838073	−	0.483861i	−0.856609	+	0.515967i	$0.827433\pi$
$114$	1.39183	−	9.98158i	0.130357	−	0.934861i
$115$		0			0
$116$	−1.92089			−0.178350
$117$	−10.1920	−	3.62247i	−0.942254	−	0.334898i
$118$	4.53590			0.417563
$119$	6.88351	+	1.84443i	0.631010	+	0.169079i
$120$	0.939636	−	6.73865i	0.0857767	−	0.615152i
$121$	−5.13397	−	2.96410i	−0.466725	−	0.269464i
$122$	−7.45418	+	7.45418i	−0.674869	+	0.674869i
$123$	3.79399	−	8.96499i	0.342093	−	0.808346i
$124$	−0.241670	−	0.901924i	−0.0217026	−	0.0809951i
$125$	8.23373	+	8.23373i	0.736447	+	0.736447i
$126$	−1.74786	+	6.14557i	−0.155712	+	0.547491i
$127$	7.90192	−	4.56218i	0.701182	−	0.404828i	−0.106605	−	0.994301i	$-0.533998\pi$
$127$	7.90192	−	4.56218i	0.701182	−	0.404828i	0.807788	+	0.589474i	$0.200665\pi$
$128$	3.37554	−	12.5977i	0.298359	−	1.11349i
$129$	2.33864	−	3.00000i	0.205906	−	0.264135i
$130$	−7.33013	+	3.62436i	−0.642895	+	0.317877i
$131$			7.94839i			0.694454i	0.937781	+	0.347227i	$0.112877\pi$
$131$			7.94839i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$132$	1.15081	+	1.52375i	0.100165	+	0.132625i
$133$	−2.73205	−	4.73205i	−0.236899	−	0.410321i
$134$	4.46841	−	7.73951i	0.386012	−	0.668592i
$135$	2.82797	+	7.29638i	0.243393	+	0.627973i
$136$	12.6962	−	3.40192i	1.08869	−	0.291713i
$137$	6.49373	−	1.73999i	0.554797	−	0.148657i	0.0294822	−	0.999565i	$-0.490614\pi$
$137$	6.49373	−	1.73999i	0.554797	−	0.148657i	0.525315	+	0.850908i	$0.323948\pi$
$138$		0			0
$139$	−9.19615	+	15.9282i	−0.780007	+	1.35101i	0.151929	+	0.988391i	$0.451451\pi$
$139$	−9.19615	+	15.9282i	−0.780007	+	1.35101i	−0.931937	+	0.362621i	$0.881882\pi$
$140$	0.285334	+	0.494214i	0.0241152	+	0.0417687i
$141$	−8.32592	+	6.28814i	−0.701169	+	0.529557i
$142$			4.53590i			0.380644i
$143$	−4.75374	+	14.0524i	−0.397528	+	1.17512i
$144$	3.26795	+	12.9875i	0.272329	+	1.08229i
$145$	−2.79423	+	10.4282i	−0.232048	+	0.866015i
$146$	1.66354	−	0.960443i	0.137675	−	0.0794868i
$147$	−3.25286	−	8.02614i	−0.268291	−	0.661985i
$148$	−1.02628	−	1.02628i	−0.0843597	−	0.0843597i
$149$	2.23420	+	8.33816i	0.183033	+	0.683089i	0.995043	+	0.0994454i	$0.0317068\pi$
$149$	2.23420	+	8.33816i	0.183033	+	0.683089i	−0.812010	+	0.583644i	$0.801626\pi$
$150$	−6.56283	−	2.77739i	−0.535853	−	0.226773i
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	−0.684965	−	0.728576i	$-0.740183\pi$
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	0.728576	+	0.684965i	$0.240183\pi$
$152$	−8.72794	−	5.03908i	−0.707929	−	0.408723i
$153$	−10.8517	+	10.5248i	−0.877310	+	0.850878i
$154$	8.46410	+	2.26795i	0.682057	+	0.182757i
$155$	−5.24796			−0.421526
$156$	1.11159	−	1.25078i	0.0889985	−	0.100142i
$157$	−4.80385			−0.383389			−0.191694	−	0.981455i	$-0.561398\pi$
$157$	−4.80385			−0.383389			−0.191694	+	0.981455i	$0.561398\pi$
$158$	−2.90931	−	0.779548i	−0.231453	−	0.0620175i
$159$	−1.33728	−	0.186470i	−0.106053	−	0.0147880i
$160$	1.96410	+	1.13397i	0.155276	+	0.0896486i
$161$		0			0
$162$	−9.28636	−	9.87256i	−0.729605	−	0.775661i
$163$	−1.07180	−	4.00000i	−0.0839496	−	0.313304i	0.911164	−	0.412045i	$-0.135185\pi$
$163$	−1.07180	−	4.00000i	−0.0839496	−	0.313304i	−0.995113	+	0.0987406i	$0.968519\pi$
$164$	1.06488	+	1.06488i	0.0831533	+	0.0831533i
$165$	9.94624	−	4.03104i	0.774313	−	0.313816i
$166$	−5.36603	+	3.09808i	−0.416484	+	0.240457i
$167$	3.47998	−	12.9875i	0.269289	−	1.00500i	−0.690283	−	0.723539i	$-0.742514\pi$
$167$	3.47998	−	12.9875i	0.269289	−	1.00500i	0.959573	−	0.281461i	$-0.0908192\pi$
$168$	5.03908	+	3.92820i	0.388773	+	0.303067i
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$			11.4284i			0.876516i
$171$	11.5898	+	0.177262i	0.886291	+	0.0135556i
$172$	0.294229	+	0.509619i	0.0224347	+	0.0388581i
$173$	−8.72794	+	15.1172i	−0.663573	+	1.14934i	0.316097	+	0.948727i	$0.397627\pi$
$173$	−8.72794	+	15.1172i	−0.663573	+	1.14934i	−0.979670	+	0.200615i	$0.935706\pi$
$174$	−2.29892	−	18.5575i	−0.174281	−	1.40684i
$175$	−3.73205	+	1.00000i	−0.282117	+	0.0755929i
$176$	17.7412	−	4.75374i	1.33729	−	0.358327i
$177$	0.641364	+	5.17726i	0.0482078	+	0.389147i
$178$	7.02628	−	12.1699i	0.526642	−	0.912171i
$179$	−13.2728	−	22.9892i	−0.992056	−	1.71829i	−0.604972	−	0.796247i	$-0.706816\pi$
$179$	−13.2728	−	22.9892i	−0.992056	−	1.71829i	−0.387084	−	0.922045i	$-0.626518\pi$
$180$	−1.21043	−	0.0185132i	−0.0902201	−	0.00137989i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	0.494214	−	7.66306i	0.0366336	−	0.568024i
$183$	−9.56218	−	7.45418i	−0.706857	−	0.551029i
$184$		0			0
$185$	−7.06440	+	4.07863i	−0.519385	+	0.299867i
$186$	8.42417	−	3.41417i	0.617690	−	0.250339i
$187$	14.6603	+	14.6603i	1.07206	+	1.07206i
$188$	−0.417759	−	1.55910i	−0.0304682	−	0.113709i
$189$	−7.26168	−	1.12603i	−0.528210	−	0.0819070i
$190$	6.19615	−	6.19615i	0.449516	−	0.449516i
$191$	4.18307	+	2.41510i	0.302677	+	0.174750i	0.643645	−	0.765324i	$-0.277421\pi$
$191$	4.18307	+	2.41510i	0.302677	+	0.174750i	−0.340968	+	0.940075i	$0.610755\pi$
$192$	11.4254	+	1.59315i	0.824554	+	0.114976i
$193$	0.133975	+	0.0358984i	0.00964370	+	0.00258402i	0.263638	−	0.964622i	$-0.415078\pi$
$193$	0.133975	+	0.0358984i	0.00964370	+	0.00258402i	−0.253994	+	0.967206i	$0.581744\pi$
$194$	−2.54752			−0.182902
$195$	−5.17329	−	7.85411i	−0.370467	−	0.562445i
$196$	1.33975			0.0956961
$197$	−3.97420	−	1.06488i	−0.283150	−	0.0758697i	0.114449	−	0.993429i	$-0.463490\pi$
$197$	−3.97420	−	1.06488i	−0.283150	−	0.0758697i	−0.397599	+	0.917559i	$0.630156\pi$
$198$	−13.3435	+	12.9415i	−0.948281	+	0.919711i
$199$	11.1962	+	6.46410i	0.793674	+	0.458228i	0.841254	−	0.540639i	$-0.181818\pi$
$199$	11.1962	+	6.46410i	0.793674	+	0.458228i	−0.0475802	+	0.998867i	$0.515151\pi$
$200$	−5.03908	+	5.03908i	−0.356317	+	0.356317i
$201$	9.46568	+	4.00588i	0.667657	+	0.282553i
$202$	2.34936	+	8.76795i	0.165301	+	0.616911i
$203$	−7.16884	−	7.16884i	−0.503154	−	0.503154i
$204$	−0.878413	−	2.16741i	−0.0615012	−	0.151749i
$205$	7.33013	−	4.23205i	0.511958	−	0.295579i
$206$	−2.70043	+	10.0782i	−0.188148	+	0.702178i
$207$		0			0
$208$	−7.13397	−	14.4282i	−0.494652	−	1.00042i
$209$		−	15.8968i		−	1.09960i
$210$	−4.43306	+	3.34806i	−0.305910	+	0.231038i
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$	0.104440	−	0.180895i	0.00717294	−	0.0124239i
$213$	−5.17726	+	0.641364i	−0.354740	+	0.0439455i
$214$	−27.6603	+	7.41154i	−1.89082	+	0.506643i
$215$	3.19465	−	0.856003i	0.217873	−	0.0583789i
$216$	−12.6377	+	4.89819i	−0.859887	+	0.333280i
$217$	2.46410	−	4.26795i	0.167274	−	0.289727i
$218$	14.0524	+	24.3394i	0.951745	+	1.64847i
$219$	1.33147	+	1.76295i	0.0899722	+	0.119129i
$220$			1.66025i			0.111934i
$221$	10.0782	−	15.1172i	0.677930	−	1.01690i
$222$	8.68653	−	11.1430i	0.583002	−	0.747872i
$223$	6.70577	−	25.0263i	0.449052	−	1.67588i	−0.255960	−	0.966687i	$-0.582391\pi$
$223$	6.70577	−	25.0263i	0.449052	−	1.67588i	0.705011	−	0.709196i	$-0.250942\pi$
$224$	−1.84443	+	1.06488i	−0.123236	+	0.0711505i
$225$	2.24214	−	7.88351i	0.149476	−	0.525567i
$226$	10.9545	+	10.9545i	0.728681	+	0.728681i
$227$	5.24796	+	19.5856i	0.348319	+	1.29994i	0.888686	+	0.458515i	$0.151619\pi$
$227$	5.24796	+	19.5856i	0.348319	+	1.29994i	−0.540367	+	0.841429i	$0.681715\pi$
$228$	−0.698857	+	1.65136i	−0.0462829	+	0.109364i
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	−0.997914	−	0.0645507i	$-0.979439\pi$
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	0.0645507	+	0.997914i	$0.479439\pi$
$230$		0			0
$231$	−1.39183	+	9.98158i	−0.0915757	+	0.656740i
$232$	−18.0622	−	4.83975i	−1.18584	−	0.317745i
$233$	17.4559			1.14357			0.571786	−	0.820403i	$-0.306251\pi$
$233$	17.4559			1.14357			0.571786	+	0.820403i	$0.306251\pi$
$234$	13.4140	+	9.24205i	0.876899	+	0.604172i
$235$	−9.07180			−0.591779
$236$	−0.779548	−	0.208879i	−0.0507443	−	0.0135969i
$237$	0.478405	−	3.43091i	0.0310757	−	0.222861i
$238$	−9.29423	−	5.36603i	−0.602455	−	0.347828i
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	−0.460737	−	0.887537i	$-0.652415\pi$
$239$	6.59817	−	6.59817i	0.426800	−	0.426800i	0.887537	+	0.460737i	$0.152415\pi$
$240$	−4.53819	+	10.7235i	−0.292939	+	0.692198i
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	0.974518	+	0.224309i	$0.0720123\pi$
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	−0.731803	+	0.681516i	$0.761321\pi$
$242$	6.31284	+	6.31284i	0.405805	+	0.405805i
$243$	9.95544	−	11.9954i	0.638642	−	0.769504i
$244$	1.62436	−	0.937822i	0.103989	−	0.0600379i
$245$	1.94887	−	7.27328i	0.124509	−	0.464673i
$246$	−9.01327	+	11.5622i	−0.574665	+	0.737178i
$247$	−13.6603	+	2.73205i	−0.869181	+	0.173836i
$248$		−	9.08973i		−	0.577198i
$249$	−4.29488	−	5.68671i	−0.272177	−	0.360380i
$250$	−8.76795	−	15.1865i	−0.554534	−	0.960481i
$251$	0.494214	−	0.856003i	0.0311945	−	0.0540304i	−0.850007	−	0.526772i	$-0.823402\pi$
$251$	0.494214	−	0.856003i	0.0311945	−	0.0540304i	0.881201	+	0.472741i	$0.156736\pi$
$252$	0.583396	−	0.975700i	0.0367505	−	0.0614634i
$253$		0			0
$254$	−13.2728	+	3.55644i	−0.832810	+	0.223151i
$255$	−13.0443	+	1.61594i	−0.816867	+	0.101194i
$256$	−3.16025	+	5.47372i	−0.197516	+	0.342108i
$257$	10.7533	+	18.6252i	0.670770	+	1.16181i	0.977686	+	0.210071i	$0.0673696\pi$
$257$	10.7533	+	18.6252i	0.670770	+	1.16181i	−0.306916	+	0.951737i	$0.599297\pi$
$258$	−4.57125	+	3.45243i	−0.284593	+	0.214939i
$259$		−	7.66025i		−	0.475985i
$260$	1.42667	−	0.285334i	0.0884784	−	0.0176957i
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$	3.09808	−	11.5622i	0.191400	−	0.714314i
$263$	−19.3003	+	11.1430i	−1.19011	+	0.687109i	−0.958331	−	0.285660i	$-0.907787\pi$
$263$	−19.3003	+	11.1430i	−1.19011	+	0.687109i	−0.231777	+	0.972769i	$0.574454\pi$
$264$	6.98197	+	17.2274i	0.429710	+	1.06027i
$265$	−0.830127	−	0.830127i	−0.0509943	−	0.0509943i
$266$	2.12976	+	7.94839i	0.130584	+	0.487347i
$267$	14.8842	+	6.29899i	0.910896	+	0.385492i
$268$	−1.12436	+	1.12436i	−0.0686810	+	0.0686810i
$269$	−12.4168	−	7.16884i	−0.757066	−	0.437092i	0.0711756	−	0.997464i	$-0.477325\pi$
$269$	−12.4168	−	7.16884i	−0.757066	−	0.437092i	−0.828241	+	0.560372i	$0.810658\pi$
$270$	−1.26979	−	11.7160i	−0.0772769	−	0.713013i
$271$	7.46410	+	2.00000i	0.453412	+	0.121491i	0.478295	−	0.878199i	$-0.341255\pi$
$271$	7.46410	+	2.00000i	0.453412	+	0.121491i	−0.0248835	+	0.999690i	$0.507921\pi$
$272$	−22.4950			−1.36396
$273$	8.81647	−	0.519441i	0.533597	−	0.0314380i
$274$	−10.1244			−0.611635
$275$	−10.8577	−	2.90931i	−0.654744	−	0.175438i
$276$		0			0
$277$	23.8923	+	13.7942i	1.43555	+	0.828815i	0.997536	−	0.0701536i	$-0.0223490\pi$
$277$	23.8923	+	13.7942i	1.43555	+	0.828815i	0.438013	+	0.898969i	$0.355682\pi$
$278$	19.5856	−	19.5856i	1.17467	−	1.17467i
$279$	5.08808	+	9.13257i	0.304615	+	0.546752i
$280$	1.43782	+	5.36603i	0.0859263	+	0.320681i
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	0.245655	−	0.969357i	$-0.420997\pi$
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	−0.969357	+	0.245655i	$0.920997\pi$
$282$	14.5623	−	5.90185i	0.867172	−	0.351450i
$283$	−5.70577	+	3.29423i	−0.339173	+	0.195822i	−0.659906	−	0.751348i	$-0.729404\pi$
$283$	−5.70577	+	3.29423i	−0.339173	+	0.195822i	0.320733	+	0.947170i	$0.396071\pi$
$284$	0.208879	−	0.779548i	0.0123947	−	0.0462577i
$285$	7.94839	+	6.19615i	0.470822	+	0.367028i
$286$	12.3923	−	18.5885i	0.732772	−	1.09916i
$287$			7.94839i			0.469179i
$288$	0.0690922	−	4.51739i	0.00407129	−	0.266189i
$289$	−4.19615	−	7.26795i	−0.246832	−	0.427526i
$290$	8.12929	−	14.0803i	0.477368	−	0.826826i
$291$	−0.360213	−	2.90774i	−0.0211161	−	0.170455i
$292$	−0.330127	+	0.0884573i	−0.0193192	+	0.00517657i
$293$	−1.73999	+	0.466229i	−0.101651	+	0.0272374i	−0.309286	−	0.950969i	$-0.600090\pi$
$293$	−1.73999	+	0.466229i	−0.101651	+	0.0272374i	0.207635	+	0.978206i	$0.433423\pi$
$294$	1.60341	+	12.9432i	0.0935127	+	0.754860i
$295$	−2.26795	+	3.92820i	−0.132045	+	0.228709i
$296$	−7.06440	−	12.2359i	−0.410610	−	0.711198i
$297$	−16.6581	−	13.4003i	−0.966601	−	0.777567i
$298$		−	13.0000i		−	0.753070i
$299$		0			0
$300$	1.00000	+	0.779548i	0.0577350	+	0.0450072i
$301$	−0.803848	+	3.00000i	−0.0463330	+	0.172917i
$302$	−0.988427	+	0.570669i	−0.0568776	+	0.0328383i
$303$	−9.67552	+	3.92132i	−0.555844	+	0.225274i
$304$	12.1962	+	12.1962i	0.699497	+	0.699497i
$305$	−2.72842	−	10.1826i	−0.156229	−	0.583054i
$306$	19.8878	−	11.0802i	1.13691	−	0.633414i
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	−0.425829	−	0.904803i	$-0.640018\pi$
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	0.904803	+	0.425829i	$0.140018\pi$
$308$	−1.35022	−	0.779548i	−0.0769357	−	0.0444189i
$309$	−11.8850	−	1.65724i	−0.676115	−	0.0942773i
$310$	7.63397	+	2.04552i	0.433581	+	0.116178i
$311$	10.0782			0.571480			0.285740	−	0.958307i	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$	13.6037	−	8.96040i	0.770159	−	0.507283i
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	6.98795	+	1.87241i	0.394353	+	0.105666i
$315$	−4.44829	−	4.58648i	−0.250633	−	0.258419i
$316$	0.464102	+	0.267949i	0.0261078	+	0.0150733i
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	−0.949960	−	0.312373i	$-0.898876\pi$
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	0.312373	+	0.949960i	$0.398876\pi$
$318$	1.87260	+	0.792486i	0.105010	+	0.0444404i
$319$	−7.63397	−	28.4904i	−0.427421	−	1.59516i
$320$	7.09239	+	7.09239i	0.396477	+	0.396477i
$321$	−12.3706	−	30.5234i	−0.690460	−	1.70365i
$322$		0			0
$323$	−5.03908	+	18.8061i	−0.280382	+	1.04640i
$324$	1.14134	+	2.12436i	0.0634076	+	0.118020i
$325$	−0.633975	+	9.83013i	−0.0351666	+	0.545277i
$326$			6.23638i			0.345401i
$327$	−25.7939	+	19.4808i	−1.42641	+	1.07729i
$328$	7.33013	+	12.6962i	0.404739	+	0.701028i
$329$	4.25953	−	7.37772i	0.234835	−	0.406747i
$330$	−16.0396	+	1.98699i	−0.882948	+	0.109380i
$331$	−33.0526	+	8.85641i	−1.81673	+	0.486792i	−0.996376	−	0.0850595i	$-0.972892\pi$
$331$	−33.0526	+	8.85641i	−1.81673	+	0.486792i	−0.820357	+	0.571852i	$0.806225\pi$
$332$	1.06488	−	0.285334i	0.0584430	−	0.0156598i
$333$	13.9469	+	8.33919i	0.764285	+	0.456985i
$334$	−10.1244	+	17.5359i	−0.553980	+	0.959522i
$335$	4.46841	+	7.73951i	0.244135	+	0.422855i
$336$	−6.59014	−	8.72579i	−0.359521	−	0.476031i
$337$			18.4641i			1.00580i	0.864344	+	0.502902i	$0.167734\pi$
$337$			18.4641i			1.00580i	−0.864344	+	0.502902i	$0.832266\pi$
$338$	−18.1030	−	7.45418i	−0.984673	−	0.405454i
$339$	−10.9545	+	14.0524i	−0.594966	+	0.763219i
$340$	0.526279	−	1.96410i	0.0285415	−	0.106518i
$341$	12.4168	−	7.16884i	0.672407	−	0.388215i
$342$	−16.7900	−	4.77524i	−0.907900	−	0.258215i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	1.48264	+	5.53329i	0.0799386	+	0.298335i
$345$		0			0
$346$	18.5885	−	18.5885i	0.999322	−	0.999322i
$347$	17.8177	+	10.2870i	0.956502	+	0.552237i	0.895095	−	0.445876i	$-0.147108\pi$
$347$	17.8177	+	10.2870i	0.956502	+	0.552237i	0.0614076	+	0.998113i	$0.480441\pi$
$348$	−0.459481	+	3.29519i	−0.0246308	+	0.176641i
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.903454	−	0.428684i	$-0.141023\pi$
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.568072	+	0.822979i	$0.307689\pi$
$350$	5.81863			0.311019
$351$	−8.65215	+	16.6175i	−0.461818	+	0.886975i
$352$	−6.19615			−0.330256
$353$	13.6626	+	3.66088i	0.727186	+	0.194849i	0.603376	−	0.797457i	$-0.293822\pi$
$353$	13.6626	+	3.66088i	0.727186	+	0.194849i	0.123810	+	0.992306i	$0.460489\pi$
$354$	1.08500	−	7.78112i	0.0576670	−	0.413562i
$355$	−3.92820	−	2.26795i	−0.208487	−	0.120370i
$356$	−1.76798	+	1.76798i	−0.0937025	+	0.0937025i
$357$	4.81059	−	11.3671i	0.254603	−	0.601613i
$358$	10.3468	+	38.6147i	0.546845	+	2.04085i
$359$	18.2354	+	18.2354i	0.962429	+	0.962429i	0.999319	−	0.0368904i	$-0.0117452\pi$
$359$	18.2354	+	18.2354i	0.962429	+	0.962429i	−0.0368904	+	0.999319i	$0.511745\pi$
$360$	−11.3351	−	3.22381i	−0.597411	−	0.169909i
$361$	−3.52628	+	2.03590i	−0.185594	+	0.107153i
$362$	−1.16932	+	4.36397i	−0.0614582	+	0.229365i
$363$	−6.31284	+	8.09808i	−0.331338	+	0.425039i
$364$	−0.437822	+	1.29423i	−0.0229481	+	0.0678360i
$365$			1.92089i			0.100544i
$366$	11.0042	+	14.5704i	0.575201	+	0.761605i
$367$	−15.1962	−	26.3205i	−0.793233	−	1.37392i	−0.923955	−	0.382500i	$-0.875063\pi$
$367$	−15.1962	−	26.3205i	−0.793233	−	1.37392i	0.130723	−	0.991419i	$-0.458270\pi$
$368$		0			0
$369$	−14.4715	−	8.65286i	−0.753356	−	0.450450i
$370$	11.8660	−	3.17949i	0.616885	−	0.165294i
$371$	1.06488	−	0.285334i	0.0552859	−	0.0148138i
$372$	−1.60502	+	0.198831i	−0.0832162	+	0.0103089i
$373$	−5.79423	+	10.0359i	−0.300014	+	0.519639i	−0.976139	−	0.217148i	$-0.930325\pi$
$373$	−5.79423	+	10.0359i	−0.300014	+	0.519639i	0.676125	+	0.736787i	$0.263658\pi$
$374$	−15.6114	−	27.0398i	−0.807249	−	1.39820i
$375$	16.0941	−	12.1550i	0.831096	−	0.627684i
$376$		−	15.7128i		−	0.810326i
$377$	−23.1701	+	11.4564i	−1.19332	+	0.590032i
$378$	10.1244	+	4.46841i	0.520741	+	0.229830i
$379$	3.83013	−	14.2942i	0.196740	−	0.734245i	−0.795069	−	0.606519i	$-0.792565\pi$
$379$	3.83013	−	14.2942i	0.196740	−	0.734245i	0.991809	−	0.127726i	$-0.0407679\pi$
$380$	−1.35022	+	0.779548i	−0.0692647	+	0.0399900i
$381$	−5.93605	−	14.6467i	−0.304113	−	0.750372i
$382$	−5.14359	−	5.14359i	−0.263169	−	0.263169i
$383$	−8.51906	−	31.7936i	−0.435304	−	1.62458i	−0.740339	−	0.672234i	$-0.765335\pi$
$383$	−8.51906	−	31.7936i	−0.435304	−	1.62458i	0.305035	−	0.952341i	$-0.401332\pi$
$384$	−20.8033	−	8.80399i	−1.06162	−	0.449277i
$385$	−6.19615	+	6.19615i	−0.315785	+	0.315785i
$386$	−0.180895	−	0.104440i	−0.00920730	−	0.00531584i
$387$	−4.58695	−	4.72944i	−0.233168	−	0.240411i
$388$	0.437822	+	0.117314i	0.0222271	+	0.00595572i
$389$	22.4950			1.14054			0.570270	−	0.821457i	$-0.306839\pi$
$389$	22.4950			1.14054			0.570270	+	0.821457i	$0.306839\pi$
$390$	4.46403	+	13.4415i	0.226045	+	0.680634i
$391$		0			0
$392$	12.5977	+	3.37554i	0.636280	+	0.170491i
$393$	13.6351	+	1.90128i	0.687800	+	0.0959066i
$394$	5.36603	+	3.09808i	0.270336	+	0.156079i
$395$	2.12976	−	2.12976i	0.107160	−	0.107160i
$396$	2.88920	−	1.60968i	0.145188	−	0.0808892i
$397$	−3.56218	−	13.2942i	−0.178781	−	0.667218i	−0.995877	−	0.0907168i	$-0.971084\pi$
$397$	−3.56218	−	13.2942i	−0.178781	−	0.667218i	0.817096	−	0.576501i	$-0.195582\pi$
$398$	−13.7670	−	13.7670i	−0.690078	−	0.690078i
$399$	−8.77113	+	3.55479i	−0.439106	+	0.177962i
$400$	10.5622	−	6.09808i	0.528109	−	0.304904i
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	0.837594	+	0.546294i	$0.183962\pi$
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	−0.998524	+	0.0543073i	$0.982705\pi$
$402$	−12.2079	−	9.51666i	−0.608876	−	0.474648i
$403$	−8.29423	−	9.43782i	−0.413165	−	0.470131i
$404$		−	1.61507i		−	0.0803525i
$405$	13.1931	−	3.10594i	0.655569	−	0.154336i
$406$	7.63397	+	13.2224i	0.378868	+	0.656218i
$407$	11.1430	−	19.3003i	0.552340	−	0.956681i
$408$	−2.79889	−	22.5934i	−0.138566	−	1.11854i
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.543236	−	0.839580i	$-0.317199\pi$
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.890246	+	0.455480i	$0.150532\pi$
$410$	−12.3124	+	3.29909i	−0.608064	+	0.162930i
$411$	−1.43156	−	11.5559i	−0.0706135	−	0.570011i
$412$	0.928203	−	1.60770i	0.0457293	−	0.0792055i
$413$	−2.12976	−	3.68886i	−0.104799	−	0.181517i
$414$		0			0
$415$		−	6.19615i		−	0.304157i
$416$	1.06488	+	5.32441i	0.0522102	+	0.261051i
$417$	25.1244	+	19.5856i	1.23034	+	0.959113i
$418$	−6.19615	+	23.1244i	−0.303064	+	1.13105i
$419$	−8.23373	+	4.75374i	−0.402244	+	0.232236i	−0.687452	−	0.726230i	$-0.741271\pi$
$419$	−8.23373	+	4.75374i	−0.402244	+	0.232236i	0.285208	+	0.958466i	$0.407937\pi$
$420$	0.916053	−	0.371261i	0.0446988	−	0.0181157i
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	0.490067	−	0.871685i	$-0.336972\pi$
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	−0.871685	+	0.490067i	$0.836972\pi$
$422$	−0.703093	−	2.62398i	−0.0342260	−	0.127733i
$423$	8.79543	+	15.7869i	0.427648	+	0.767584i
$424$	1.43782	−	1.43782i	0.0698268	−	0.0698268i
$425$	11.9226	+	6.88351i	0.578330	+	0.333899i
$426$	7.78112	+	1.08500i	0.376997	+	0.0525683i
$427$	9.56218	+	2.56218i	0.462746	+	0.123992i
$428$	5.09505			0.246278
$429$	22.9691	+	11.5162i	1.10896	+	0.556007i
$430$	−4.98076			−0.240194
$431$	−36.5473	−	9.79282i	−1.76042	−	0.471704i	−0.773622	−	0.633648i	$-0.781557\pi$
$431$	−36.5473	−	9.79282i	−1.76042	−	0.471704i	−0.986800	+	0.161944i	$0.948224\pi$
$432$	23.0611	−	2.49938i	1.10953	−	0.120252i
$433$	−26.8923	−	15.5263i	−1.29236	−	0.746145i	−0.313289	−	0.949658i	$-0.601431\pi$
$433$	−26.8923	−	15.5263i	−1.29236	−	0.746145i	−0.979072	+	0.203512i	$0.934764\pi$
$434$	−5.24796	+	5.24796i	−0.251910	+	0.251910i
$435$	17.2207	+	7.28782i	0.825670	+	0.349424i
$436$	−1.29423	−	4.83013i	−0.0619823	−	0.231321i
$437$		0			0
$438$	−1.24967	−	3.08346i	−0.0597117	−	0.147333i
$439$	1.09808	−	0.633975i	0.0524083	−	0.0302580i	−0.473567	−	0.880758i	$-0.657034\pi$
$439$	1.09808	−	0.633975i	0.0524083	−	0.0302580i	0.525975	+	0.850500i	$0.323700\pi$
$440$	−4.18307	+	15.6114i	−0.199420	+	0.744247i
$441$	−14.5466	+	3.66025i	−0.692694	+	0.174298i
$442$	−20.5526	+	18.0622i	−0.977586	+	0.859130i
$443$		−	11.2195i		−	0.533054i	−0.963827	−	0.266527i	$-0.914124\pi$
$443$		−	11.2195i		−	0.533054i	0.963827	−	0.266527i	$-0.0858762\pi$
$444$	−2.00602	+	1.51505i	−0.0952017	+	0.0719009i
$445$	7.02628	+	12.1699i	0.333078	+	0.576907i
$446$	−19.5092	+	33.7909i	−0.923787	+	1.60005i
$447$	14.8382	−	1.83816i	0.701821	−	0.0869422i
$448$	−9.09808	+	2.43782i	−0.429844	+	0.115176i
$449$	−19.8710	+	5.32441i	−0.937769	+	0.251275i	−0.695165	−	0.718851i	$-0.744669\pi$
$449$	−19.8710	+	5.32441i	−0.937769	+	0.251275i	−0.242605	+	0.970125i	$0.578002\pi$
$450$	−6.33434	+	10.5939i	−0.298603	+	0.499400i
$451$	−11.5622	+	20.0263i	−0.544442	+	0.943001i
$452$	−1.37820	−	2.38711i	−0.0648251	−	0.112280i
$453$	−0.791121	−	1.04750i	−0.0371701	−	0.0492157i
$454$		−	30.5359i		−	1.43312i
$455$	6.38929	+	4.25953i	0.299535	+	0.199690i
$456$	−10.7321	+	13.7670i	−0.502574	+	0.644700i
$457$	−1.00962	+	3.76795i	−0.0472280	+	0.176257i	−0.985511	−	0.169611i	$-0.945749\pi$
$457$	−1.00962	+	3.76795i	−0.0472280	+	0.176257i	0.938283	+	0.345868i	$0.112416\pi$
$458$	26.0514	−	15.0408i	1.21730	−	0.702809i
$459$	15.4590	+	21.1332i	0.721565	+	0.986412i
$460$		0			0
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	−0.967302	−	0.253628i	$-0.918376\pi$
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	0.710894	−	0.703299i	$-0.248290\pi$
$462$	5.91520	−	13.9773i	0.275200	−	0.650282i
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.0740918	−	0.997251i	$-0.476394\pi$
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.997251	−	0.0740918i	$-0.0236058\pi$
$464$	27.7149	+	16.0012i	1.28663	+	0.742838i
$465$	−1.25532	+	9.00263i	−0.0582143	+	0.417487i
$466$	−25.3923	−	6.80385i	−1.17628	−	0.315182i
$467$	−19.1679			−0.886984			−0.443492	−	0.896278i	$-0.646261\pi$
$467$	−19.1679			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$468$	−1.87975	−	2.20607i	−0.0868916	−	0.101976i
$469$	−8.39230			−0.387521
$470$	13.1963	+	3.53595i	0.608702	+	0.163101i
$471$	−1.14909	+	8.24078i	−0.0529474	+	0.379715i
$472$	−6.80385	−	3.92820i	−0.313172	−	0.180810i
$473$	−6.38929	+	6.38929i	−0.293780	+	0.293780i
$474$	−2.03319	+	4.80432i	−0.0933877	+	0.220670i
$475$	−2.73205	−	10.1962i	−0.125355	−	0.467832i
$476$	1.35022	+	1.35022i	0.0618871	+	0.0618871i
$477$	−0.639761	+	2.24944i	−0.0292926	+	0.102995i
$478$	−12.1699	+	7.02628i	−0.556637	+	0.321375i
$479$	5.32441	−	19.8710i	0.243279	−	0.907928i	−0.730962	−	0.682418i	$-0.760928\pi$
$479$	5.32441	−	19.8710i	0.243279	−	0.907928i	0.974241	−	0.225510i	$-0.0724049\pi$
$480$	2.41510	−	3.09808i	0.110234	−	0.141407i
$481$	−18.5000	−	6.25833i	−0.843527	−	0.285355i
$482$		−	21.9243i		−	0.998624i
$483$		0			0
$484$	−0.794229	−	1.37564i	−0.0361013	−	0.0625293i
$485$	1.27376	−	2.20622i	0.0578385	−	0.100179i
$486$	−19.1572	+	13.5688i	−0.868990	+	0.615492i
$487$	5.56218	−	1.49038i	0.252046	−	0.0675356i	−0.130584	−	0.991437i	$-0.541685\pi$
$487$	5.56218	−	1.49038i	0.252046	−	0.0675356i	0.382630	+	0.923902i	$0.375018\pi$
$488$	17.6368	−	4.72576i	0.798379	−	0.213925i
$489$	−7.11819	+	0.881808i	−0.321896	+	0.0398767i
$490$	−5.66987	+	9.82051i	−0.256139	+	0.443645i
$491$	14.2612	+	24.7012i	0.643600	+	1.11475i	0.984623	+	0.174693i	$0.0558934\pi$
$491$	14.2612	+	24.7012i	0.643600	+	1.11475i	−0.341023	+	0.940055i	$0.610773\pi$
$492$	2.08148	−	1.57203i	0.0938403	−	0.0708728i
$493$			36.1244i			1.62696i
$494$	20.9359	+	1.35022i	0.941949	+	0.0607491i
$495$	−4.53590	−	18.0265i	−0.203873	−	0.810233i
$496$	−4.02628	+	15.0263i	−0.180785	+	0.674700i
$497$	3.68886	−	2.12976i	0.165468	−	0.0955330i
$498$	4.03104	+	9.94624i	0.180635	+	0.445702i
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	0.649798	−	0.760107i	$-0.274853\pi$
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	−0.760107	+	0.649798i	$0.774853\pi$
$500$	0.807533	+	3.01375i	0.0361140	+	0.134779i
$501$	−21.4470	−	9.07638i	−0.958181	−	0.405503i
$502$	−1.05256	+	1.05256i	−0.0469780	+	0.0469780i
$503$	−2.83286	−	1.63555i	−0.126311	−	0.0729256i	0.435513	−	0.900182i	$-0.356567\pi$
$503$	−2.83286	−	1.63555i	−0.126311	−	0.0729256i	−0.561824	+	0.827257i	$0.689900\pi$
$504$	7.94401	−	7.70467i	0.353854	−	0.343193i
$505$	−8.76795	−	2.34936i	−0.390169	−	0.104545i
$506$		0			0
$507$	5.94846	−	21.7167i	0.264180	−	0.964473i
$508$	2.44486			0.108473
$509$	14.1568	+	3.79330i	0.627489	+	0.168135i	0.558530	−	0.829484i	$-0.311366\pi$
$509$	14.1568	+	3.79330i	0.627489	+	0.168135i	0.0689588	+	0.997620i	$0.478032\pi$
$510$	19.6048	+	2.73370i	0.868117	+	0.121050i
$511$	−1.56218	−	0.901924i	−0.0691067	−	0.0398988i
$512$	−11.7137	+	11.7137i	−0.517678	+	0.517678i
$513$	3.07638	−	19.8393i	0.135826	−	0.875926i
$514$	−8.38269	−	31.2846i	−0.369744	−	1.37990i
$515$	−7.37772	−	7.37772i	−0.325101	−	0.325101i
$516$	0.944608	−	0.382834i	0.0415841	−	0.0168533i
$517$	21.4641	−	12.3923i	0.943990	−	0.545013i
$518$	−2.98577	+	11.1430i	−0.131187	+	0.489597i
$519$	23.8452	+	18.5885i	1.04669	+	0.815943i
$520$	14.1340	+	0.911543i	0.619816	+	0.0399738i
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$	−32.3844	−	0.495311i	−1.41743	−	0.0216792i
$523$	19.4904	+	33.7583i	0.852255	+	1.47615i	0.879169	+	0.476511i	$0.158099\pi$
$523$	19.4904	+	33.7583i	0.852255	+	1.47615i	−0.0269137	+	0.999638i	$0.508568\pi$
$524$	−1.06488	+	1.84443i	−0.0465196	+	0.0805743i
$525$	0.822738	+	6.64136i	0.0359072	+	0.289853i
$526$	32.4186	−	8.68653i	1.41352	−	0.378751i
$527$	−16.9617	+	4.54486i	−0.738862	+	0.197977i
$528$	−3.91108	−	31.5713i	−0.170208	−	1.37397i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	0.883988	+	1.53111i	0.0383980	+	0.0665072i
$531$	9.03477	+	0.138184i	0.392076	+	0.00599669i
$532$		−	1.46410i		−	0.0634769i
$533$	19.1959	+	6.49373i	0.831465	+	0.281275i
$534$	−19.1962	−	14.9643i	−0.830699	−	0.647570i
$535$	7.41154	−	27.6603i	0.320429	−	1.19586i
$536$	−13.4052	+	7.73951i	−0.579018	+	0.334296i
$537$	−42.6117	+	17.2698i	−1.83883	+	0.745247i
$538$	15.2679	+	15.2679i	0.658248	+	0.658248i
$539$	5.32441	+	19.8710i	0.229339	+	0.855904i
$540$	−0.321296	+	2.07201i	−0.0138264	+	0.0891650i
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	−0.925118	−	0.379681i	$-0.876034\pi$
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$542$	−10.0782	−	5.81863i	−0.432894	−	0.249931i
$543$	−5.14636	−	0.717608i	−0.220852	−	0.0307955i
$544$	7.33013	+	1.96410i	0.314277	+	0.0842102i
$545$	−28.1047			−1.20387
$546$	−13.0274	−	2.68082i	−0.557521	−	0.114729i
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	1.73999	+	0.466229i	0.0743287	+	0.0199163i
$549$	−15.0746	+	14.6204i	−0.643368	+	0.623984i
$550$	14.6603	+	8.46410i	0.625115	+	0.360911i
$551$	19.5856	−	19.5856i	0.834376	−	0.834376i
$552$		0			0
$553$	0.732051	+	2.73205i	0.0311300	+	0.116179i
$554$	−29.3785	−	29.3785i	−1.24817	−	1.24817i
$555$	5.30689	+	13.0943i	0.225265	+	0.555821i
$556$	−4.26795	+	2.46410i	−0.181001	+	0.104501i
$557$	6.62616	−	24.7292i	0.280759	−	1.04781i	−0.671123	−	0.741346i	$-0.734188\pi$
$557$	6.62616	−	24.7292i	0.280759	−	1.04781i	0.951883	−	0.306462i	$-0.0991454\pi$
$558$	−3.84177	−	15.2679i	−0.162635	−	0.646344i
$559$	6.58846	+	4.39230i	0.278662	+	0.185775i
$560$		−	9.50749i		−	0.401765i
$561$	28.6558	−	21.6422i	1.20985	−	0.913735i
$562$	12.9186	+	22.3756i	0.544938	+	0.943860i
$563$	5.03908	−	8.72794i	0.212372	−	0.367839i	−0.740085	−	0.672514i	$-0.765215\pi$
$563$	5.03908	−	8.72794i	0.212372	−	0.367839i	0.952456	+	0.304675i	$0.0985479\pi$
$564$	−2.77449	+	0.343706i	−0.116827	+	0.0144726i
$565$	−14.9641	+	4.00962i	−0.629544	+	0.168686i
$566$	9.58394	−	2.56801i	0.402843	−	0.107941i
$567$	−3.66867	+	12.1877i	−0.154070	+	0.511837i
$568$	3.92820	−	6.80385i	0.164824	−	0.285483i
$569$	1.35022	+	2.33864i	0.0566040	+	0.0980411i	0.892939	−	0.450178i	$-0.148639\pi$
$569$	1.35022	+	2.33864i	0.0566040	+	0.0980411i	−0.836335	+	0.548219i	$0.815306\pi$
$570$	−9.14708	−	12.1113i	−0.383129	−	0.507289i
$571$		−	1.94744i		−	0.0814979i	−0.999169	−	0.0407489i	$-0.987026\pi$
$571$		−	1.94744i		−	0.0814979i	0.999169	−	0.0407489i	$-0.0129744\pi$
$572$	−2.98577	+	2.62398i	−0.124841	+	0.109714i
$573$	5.14359	−	6.59817i	0.214877	−	0.275643i
$574$	3.09808	−	11.5622i	0.129311	−	0.482596i
$575$		0			0
$576$	5.46595	−	19.2186i	0.227748	−	0.800775i
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	0.0618016	−	0.998088i	$-0.480315\pi$
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	−0.998088	+	0.0618016i	$0.980315\pi$
$578$	3.27110	+	12.2079i	0.136060	+	0.507783i
$579$	0.0936291	−	0.221240i	0.00389109	−	0.00919443i
$580$	−2.04552	+	2.04552i	−0.0849355	+	0.0849355i
$581$	5.03908	+	2.90931i	0.209056	+	0.120699i
$582$	−0.609374	+	4.37016i	−0.0252594	+	0.181149i
$583$	3.09808	+	0.830127i	0.128309	+	0.0343803i
$584$	−3.32707			−0.137675
$585$	−14.7108	+	6.99582i	−0.608218	+	0.289241i
$586$	2.71281			0.112065
$587$	18.0265	+	4.83020i	0.744035	+	0.199364i	0.610871	−	0.791730i	$-0.290819\pi$
$587$	18.0265	+	4.83020i	0.744035	+	0.199364i	0.133164	+	0.991094i	$0.457486\pi$
$588$	0.320471	−	2.29827i	0.0132160	−	0.0947792i
$589$	11.6603	+	6.73205i	0.480452	+	0.277389i
$590$	4.83020	−	4.83020i	0.198856	−	0.198856i
$591$	−2.77739	+	6.56283i	−0.114247	+	0.269959i
$592$	6.25833	+	23.3564i	0.257216	+	0.959942i
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	0.887119	−	0.461541i	$-0.152703\pi$
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	−0.461541	+	0.887119i	$0.652703\pi$
$594$	19.0087	+	25.9858i	0.779937	+	1.06621i
$595$	9.29423	−	5.36603i	0.381026	−	0.219986i
$596$	−0.598653	+	2.23420i	−0.0245218	+	0.0915166i
$597$	13.7670	−	17.6603i	0.563446	−	0.722786i
$598$		0			0
$599$			20.7270i			0.846881i	0.905924	+	0.423441i	$0.139178\pi$
$599$			20.7270i			0.846881i	−0.905924	+	0.423441i	$0.860822\pi$
$600$	7.43895	+	9.84967i	0.303694	+	0.402111i
$601$	−11.7942	−	20.4282i	−0.481097	−	0.833284i	0.518668	−	0.854976i	$-0.326428\pi$
$601$	−11.7942	−	20.4282i	−0.481097	−	0.833284i	−0.999765	+	0.0216919i	$0.993095\pi$
$602$	2.33864	−	4.05065i	0.0953160	−	0.165092i
$603$	9.13612	−	15.2797i	0.372052	−	0.622238i
$604$	0.196152	−	0.0525589i	0.00798133	−	0.00213859i
$605$	−8.62350	+	2.31066i	−0.350595	+	0.0939417i
$606$	15.6030	−	1.93291i	0.633828	−	0.0785192i
$607$	0.0980762	−	0.169873i	0.00398079	−	0.00689493i	−0.864028	−	0.503444i	$-0.832066\pi$
$607$	0.0980762	−	0.169873i	0.00398079	−	0.00689493i	0.868009	+	0.496549i	$0.165400\pi$
$608$	−2.90931	−	5.03908i	−0.117988	−	0.204362i
$609$	−14.0126	+	10.5830i	−0.567820	+	0.428845i
$610$			15.8756i			0.642786i
$611$	−14.3377	−	16.3145i	−0.580041	−	0.660016i
$612$	−3.92820	+	0.988427i	−0.158788	+	0.0399548i
$613$	−11.3564	+	42.3827i	−0.458681	+	1.71182i	0.218354	+	0.975870i	$0.429931\pi$
$613$	−11.3564	+	42.3827i	−0.458681	+	1.71182i	−0.677035	+	0.735951i	$0.736735\pi$
$614$	−15.4790	+	8.93682i	−0.624683	+	0.360661i
$615$	−5.50650	−	13.5868i	−0.222044	−	0.547873i
$616$	−10.7321	−	10.7321i	−0.432407	−	0.432407i
$617$	−4.78173	−	17.8457i	−0.192505	−	0.718439i	−0.992899	−	0.118964i	$-0.962043\pi$
$617$	−4.78173	−	17.8457i	−0.192505	−	0.718439i	0.800393	−	0.599475i	$-0.204624\pi$
$618$	16.6427	+	7.04319i	0.669466	+	0.283319i
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.327778	+	0.944755i	$0.606300\pi$
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.944755	+	0.327778i	$0.893700\pi$
$620$	−1.21779	−	0.703093i	−0.0489077	−	0.0282369i
$621$		0			0
$622$	−14.6603	−	3.92820i	−0.587823	−	0.157507i
$623$	−13.1963			−0.528701
$624$	−26.4574	+	8.78674i	−1.05914	+	0.351751i
$625$	3.87564			0.155026
$626$	−2.90931	−	0.779548i	−0.116280	−	0.0311570i
$627$	−27.2702	−	3.80255i	−1.08907	−	0.151859i
$628$	−1.11474	−	0.643594i	−0.0444828	−	0.0256822i
$629$	−19.3003	+	19.3003i	−0.769554	+	0.769554i
$630$	4.68305	+	8.40558i	0.186577	+	0.334886i
$631$	5.73205	+	21.3923i	0.228189	+	0.851614i	0.981102	+	0.193493i	$0.0619818\pi$
$631$	5.73205	+	21.3923i	0.228189	+	0.851614i	−0.752912	+	0.658121i	$0.771352\pi$
$632$	3.68886	+	3.68886i	0.146735	+	0.146735i
$633$	2.89559	−	1.17353i	0.115089	−	0.0466437i
$634$	20.9378	−	12.0885i	0.831547	−	0.480094i
$635$	3.55644	−	13.2728i	0.141133	−	0.526715i
$636$	−0.285334	−	0.222432i	−0.0113142	−	0.00882000i
$637$	16.1603	−	7.99038i	0.640293	−	0.316590i
$638$			44.4192i			1.75857i
$639$	−0.138184	+	9.03477i	−0.00546649	+	0.357410i
$640$	−9.82051	−	17.0096i	−0.388190	−	0.672364i
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.0626345	+	0.998037i	$0.519950\pi$
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.833008	+	0.553261i	$0.813383\pi$
$642$	6.09776	+	49.2228i	0.240659	+	1.94267i
$643$	7.00000	−	1.87564i	0.276053	−	0.0739682i	−0.118136	−	0.992997i	$-0.537692\pi$
$643$	7.00000	−	1.87564i	0.276053	−	0.0739682i	0.394190	+	0.919029i	$0.371025\pi$
$644$		0			0
$645$	−0.704266	−	5.68503i	−0.0277305	−	0.223848i
$646$	14.6603	−	25.3923i	0.576800	−	0.999047i
$647$	8.23373	+	14.2612i	0.323701	+	0.560667i	0.981249	−	0.192746i	$-0.0617394\pi$
$647$	8.23373	+	14.2612i	0.323701	+	0.560667i	−0.657547	+	0.753413i	$0.728406\pi$
$648$	5.37965	+	22.8511i	0.211333	+	0.897674i
$649$		−	12.3923i		−	0.486441i
$650$	4.75374	−	14.0524i	0.186457	−	0.551179i
$651$	−6.73205	−	5.24796i	−0.263850	−	0.205684i
$652$	0.287187	−	1.07180i	0.0112471	−	0.0419748i
$653$	8.36615	−	4.83020i	0.327393	−	0.189020i	−0.327290	−	0.944924i	$-0.606135\pi$
$653$	8.36615	−	4.83020i	0.327393	−	0.189020i	0.654683	+	0.755904i	$0.272802\pi$
$654$	45.1145	−	18.2841i	1.76411	−	0.714966i
$655$	8.46410	+	8.46410i	0.330720	+	0.330720i
$656$	−6.49373	−	24.2349i	−0.253538	−	0.946216i
$657$	3.34275	−	1.86237i	0.130413	−	0.0726578i
$658$	−9.07180	+	9.07180i	−0.353655	+	0.353655i
$659$	−23.4834	−	13.5581i	−0.914783	−	0.528150i	−0.0328158	−	0.999461i	$-0.510447\pi$
$659$	−23.4834	−	13.5581i	−0.914783	−	0.528150i	−0.881967	+	0.471311i	$0.843781\pi$
$660$	2.84809	+	0.397137i	0.110862	+	0.0154585i
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	0.437470	−	0.899233i	$-0.355874\pi$
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	−0.0707559	+	0.997494i	$0.522541\pi$
$662$	51.5321			2.00285
$663$	−23.5222	−	20.9047i	−0.913526	−	0.811871i
$664$	10.7321			0.416484
$665$	−7.94839	−	2.12976i	−0.308225	−	0.0825887i
$666$	−17.0375	−	17.5668i	−0.660191	−	0.680699i
$667$		0			0
$668$	2.54752	−	2.54752i	0.0985666	−	0.0985666i
$669$	−41.3274	−	17.4898i	−1.59781	−	0.676194i
$670$	−3.48334	−	13.0000i	−0.134573	−	0.502234i
$671$	20.3652	+	20.3652i	0.786189	+	0.786189i
$672$	1.38556	+	3.41876i	0.0534493	+	0.131881i
$673$	−36.9904	+	21.3564i	−1.42587	+	0.823229i	−0.996792	−	0.0800364i	$-0.974496\pi$
$673$	−36.9904	+	21.3564i	−1.42587	+	0.823229i	−0.429082	+	0.903265i	$0.641163\pi$
$674$	7.19683	−	26.8589i	0.277211	−	1.03457i
$675$	−12.9875	−	5.73205i	−0.499888	−	0.220627i
$676$	2.76795	+	2.11474i	0.106460	+	0.0813360i
$677$			9.66040i			0.371279i	0.982618	+	0.185640i	$0.0594357\pi$
$677$			9.66040i			0.371279i	−0.982618	+	0.185640i	$0.940564\pi$
$678$	21.4123	−	16.1716i	0.822333	−	0.621065i
$679$	1.19615	+	2.07180i	0.0459041	+	0.0795083i
$680$	9.89726	−	17.1426i	0.379543	−	0.657387i
$681$	34.8536	−	4.31769i	1.33559	−	0.165454i
$682$	−20.8564	+	5.58846i	−0.798633	+	0.213993i
$683$	45.2752	−	12.1315i	1.73241	−	0.464198i	0.751673	−	0.659536i	$-0.229247\pi$
$683$	45.2752	−	12.1315i	1.73241	−	0.464198i	0.980736	+	0.195338i	$0.0625804\pi$
$684$	2.66566	+	1.59387i	0.101924	+	0.0609430i
$685$	5.06218	−	8.76795i	0.193416	−	0.335006i
$686$	−12.7786	−	22.1332i	−0.487889	−	0.845048i
$687$	20.8511	+	27.6083i	0.795519	+	1.05332i
$688$		−	9.80385i		−	0.373768i
$689$	0.180895	−	2.80487i	0.00689154	−	0.106857i
$690$		0			0
$691$	4.88269	−	18.2224i	0.185746	−	0.693214i	−0.808723	−	0.588189i	$-0.799841\pi$
$691$	4.88269	−	18.2224i	0.185746	−	0.693214i	0.994470	−	0.105025i	$-0.0334922\pi$
$692$	−4.05065	+	2.33864i	−0.153983	+	0.0889019i
$693$	16.7900	+	4.77524i	0.637800	+	0.181396i
$694$	−21.9090	−	21.9090i	−0.831653	−	0.831653i
$695$	7.16884	+	26.7545i	0.271930	+	1.01486i
$696$	−12.6229	+	29.8272i	−0.478469	+	1.13060i
$697$	20.0263	−	20.0263i	0.758549	−	0.758549i
$698$	−37.1180	−	21.4301i	−1.40494	−	0.811140i
$699$	4.17549	−	29.9448i	0.157932	−	1.13261i
$700$	−1.00000	−	0.267949i	−0.0377964	−	0.0101275i
$701$	12.7786			0.482641			0.241320	−	0.970446i	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$	19.0630	−	20.8003i	0.719485	−	0.785058i
$703$	20.9282			0.789322
$704$	−26.4692	−	7.09239i	−0.997594	−	0.267304i
$705$	−2.17000	+	15.5622i	−0.0817268	+	0.586108i
$706$	−18.4474	−	10.6506i	−0.694279	−	0.400842i
$707$	6.02751	−	6.02751i	0.226688	−	0.226688i
$708$	−0.544793	+	1.28731i	−0.0204746	+	0.0483802i
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	0.885196	−	0.465219i	$-0.154024\pi$
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	−0.999211	+	0.0397068i	$0.987358\pi$
$710$	4.83020	+	4.83020i	0.181274	+	0.181274i
$711$	−5.77113	−	1.64136i	−0.216434	−	0.0615559i
$712$	−21.0788	+	12.1699i	−0.789963	+	0.456085i
$713$		0			0
$714$	−11.4284	+	14.6603i	−0.427696	+	0.548646i
$715$	9.90192	+	20.0263i	0.370311	+	0.748940i
$716$		−	7.11287i		−	0.265821i
$717$	−9.74056	−	12.8972i	−0.363768	−	0.481653i
$718$	−19.4186	−	33.6340i	−0.724695	−	1.25521i
$719$	3.68886	−	6.38929i	0.137571	−	0.238280i	−0.789005	−	0.614386i	$-0.789404\pi$
$719$	3.68886	−	6.38929i	0.137571	−	0.238280i	0.926577	+	0.376106i	$0.122737\pi$
$720$	17.3101	+	10.3501i	0.645110	+	0.385727i
$721$	9.46410	−	2.53590i	0.352462	−	0.0944418i
$722$	5.92307	−	1.58708i	0.220434	−	0.0590650i
$723$	25.0243	−	3.10003i	0.930665	−	0.115292i
$724$	0.401924	−	0.696152i	0.0149374	−	0.0258723i
$725$	−9.79282	−	16.9617i	−0.363696	−	0.629940i
$726$	12.3394	−	9.31934i	0.457959	−	0.345873i
$727$			19.5167i			0.723833i	0.932211	+	0.361916i	$0.117877\pi$
$727$			19.5167i			0.723833i	−0.932211	+	0.361916i	$0.882123\pi$
$728$	−7.37772	+	11.0666i	−0.273437	+	0.410155i
$729$	−18.1962	−	19.9474i	−0.673932	−	0.738794i
$730$	0.748711	−	2.79423i	0.0277110	−	0.103419i
$731$	9.58394	−	5.53329i	0.354475	−	0.204656i
$732$	−1.22024	−	3.01084i	−0.0451014	−	0.111284i
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	0.570773	−	0.821108i	$-0.306644\pi$
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	−0.821108	+	0.570773i	$0.806644\pi$
$734$	11.8461	+	44.2104i	0.437249	+	1.63183i
$735$	−12.0108	−	5.08298i	−0.443025	−	0.187489i
$736$		0			0
$737$	−21.1447	−	12.2079i	−0.778876	−	0.449685i
$738$	17.6784	+	18.2276i	0.650750	+	0.670966i
$739$	−11.1244	−	2.98076i	−0.409216	−	0.109649i	0.0483378	−	0.998831i	$-0.484608\pi$
$739$	−11.1244	−	2.98076i	−0.409216	−	0.109649i	−0.457554	+	0.889182i	$0.651274\pi$
$740$	−2.18573			−0.0803492
$741$	1.41914	+	24.0870i	0.0521334	+	0.884860i
$742$	−1.66025			−0.0609498
$743$	−8.51906	−	2.28268i	−0.312534	−	0.0837432i	0.0991426	−	0.995073i	$-0.468390\pi$
$743$	−8.51906	−	2.28268i	−0.312534	−	0.0837432i	−0.411677	+	0.911330i	$0.635057\pi$
$744$	−15.5930	−	2.17429i	−0.571667	−	0.0797132i
$745$	11.2583	+	6.50000i	0.412473	+	0.238142i
$746$	12.3403	−	12.3403i	0.451812	−	0.451812i
$747$	−10.7826	+	6.00739i	−0.394516	+	0.219799i
$748$	1.43782	+	5.36603i	0.0525720	+	0.196201i
$749$	19.0150	+	19.0150i	0.694792	+	0.694792i
$750$	−28.1491	+	11.4084i	−1.02786	+	0.416574i
$751$	−29.2750	+	16.9019i	−1.06826	+	0.616760i	−0.927705	−	0.373313i	$-0.878222\pi$
$751$	−29.2750	+	16.9019i	−1.06826	+	0.616760i	−0.140554	+	0.990073i	$0.544888\pi$
$752$	−6.95996	+	25.9749i	−0.253804	+	0.947208i
$753$	−1.35022	−	1.05256i	−0.0492046	−	0.0383574i
$754$	38.1699	−	7.63397i	1.39006	−	0.278013i
$755$		−	1.14134i		−	0.0415375i
$756$	−1.53422	−	1.23418i	−0.0557990	−	0.0448866i
$757$	−8.39230	−	14.5359i	−0.305024	−	0.528316i	0.672243	−	0.740331i	$-0.265331\pi$
$757$	−8.39230	−	14.5359i	−0.305024	−	0.528316i	−0.977267	+	0.212014i	$0.931998\pi$
$758$	−11.1430	+	19.3003i	−0.404733	+	0.701019i
$759$		0			0
$760$	−14.6603	+	3.92820i	−0.531783	+	0.142491i
$761$	17.7412	−	4.75374i	0.643118	−	0.172323i	0.0775029	−	0.996992i	$-0.475305\pi$
$761$	17.7412	−	4.75374i	0.643118	−	0.172323i	0.565616	+	0.824669i	$0.308639\pi$
$762$	2.92602	+	23.6196i	0.105998	+	0.855647i
$763$	13.1962	−	22.8564i	0.477733	−	0.827457i
$764$	0.647124	+	1.12085i	0.0234121	+	0.0405510i
$765$	−0.348161	+	22.7635i	−0.0125878	+	0.823014i
$766$			49.5692i			1.79101i
$767$	−10.6488	+	2.12976i	−0.384507	+	0.0769014i
$768$	8.63397	+	6.73060i	0.311552	+	0.242870i
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	0.438694	+	0.898636i	$0.355441\pi$
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	−0.829238	+	0.558895i	$0.811225\pi$
$770$	11.4284	−	6.59817i	0.411850	−	0.237782i
$771$	34.5229	−	13.9915i	1.24331	−	0.503893i
$772$	0.0262794	+	0.0262794i	0.000945818	+	0.000945818i
$773$	11.1430	+	41.5864i	0.400787	+	1.49576i	0.811695	+	0.584081i	$0.198545\pi$
$773$	11.1430	+	41.5864i	0.400787	+	1.49576i	−0.410908	+	0.911677i	$0.634788\pi$
$774$	4.82903	+	8.66759i	0.173576	+	0.311550i
$775$	6.73205	−	6.73205i	0.241822	−	0.241822i
$776$	3.82129	+	2.20622i	0.137176	+	0.0791987i
$777$	−13.1408	−	1.83235i	−0.471424	−	0.0657353i
$778$	−32.7224	−	8.76795i	−1.17316	−	0.314346i
$779$	−21.7154			−0.778035
$780$	−0.148214	−	2.51564i	−0.00530693	−	0.0900745i
$781$	12.3923			0.443432
$782$		0			0
$783$	−4.01372	−	37.0335i	−0.143439	−	1.32347i
$784$	−19.3301	−	11.1603i	−0.690362	−	0.398581i
$785$	−5.11553	+	5.11553i	−0.182581	+	0.182581i
$786$	−19.0933	−	8.08031i	−0.681036	−	0.288215i
$787$	4.29423	+	16.0263i	0.153073	+	0.571275i	0.999263	+	0.0383938i	$0.0122241\pi$
$787$	4.29423	+	16.0263i	0.153073	+	0.571275i	−0.846190	+	0.532881i	$0.821109\pi$
$788$	−0.779548	−	0.779548i	−0.0277702	−	0.0277702i
$789$	14.4987	+	35.7742i	0.516167	+	1.27360i
$790$	−3.92820	+	2.26795i	−0.139759	+	0.0806900i
$791$	3.76532	−	14.0524i	0.133879	−	0.499644i
$792$	31.2229	−	7.85641i	1.10946	−	0.279165i
$793$	14.0000	−	21.0000i	0.497155	−	0.745732i
$794$			20.7270i			0.735573i
$795$	−1.62261	+	1.22548i	−0.0575482	+	0.0434632i
$796$	1.73205	+	3.00000i	0.0613909	+	0.106332i
$797$	20.1563	−	34.9118i	0.713973	−	1.23664i	−0.249381	−	0.968405i	$-0.580227\pi$
$797$	20.1563	−	34.9118i	0.713973	−	1.23664i	0.963354	−	0.268232i	$-0.0864395\pi$
$798$	14.1445	−	1.75224i	0.500711	−	0.0620286i
$799$	−29.3205	+	7.85641i	−1.03729	+	0.277940i
$800$	−3.97420	+	1.06488i	−0.140509	+	0.0376493i
$801$	14.3660	−	24.0264i	0.507596	−	0.848929i
$802$	9.37564	−	16.2391i	0.331066	−	0.573422i
$803$	−2.62398	−	4.54486i	−0.0925982	−	0.160385i
$804$	1.65983	+	2.19773i	0.0585377	+	0.0775079i
$805$		0			0
$806$	8.38664	+	16.9617i	0.295407	+	0.597449i
$807$	−15.2679	+	19.5856i	−0.537457	+	0.689447i
$808$	4.06922	−	15.1865i	0.143155	−	0.534260i
$809$	24.0261	−	13.8715i	0.844712	−	0.487694i	−0.0141514	−	0.999900i	$-0.504505\pi$
$809$	24.0261	−	13.8715i	0.844712	−	0.487694i	0.858863	+	0.512205i	$0.171171\pi$
$810$	−20.4020	−	0.624232i	−0.716853	−	0.0219333i
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	−0.703093	−	2.62398i	−0.0246737	−	0.0920836i
$813$	5.21634	−	12.3259i	0.182945	−	0.432289i
$814$	−23.7321	+	23.7321i	−0.831808	+	0.831808i
$815$	−5.40087	−	3.11819i	−0.189184	−	0.109226i
$816$	−5.38085	+	38.5891i	−0.188367	+	1.35089i
$817$	−8.19615	−	2.19615i	−0.286747	−	0.0768336i
$818$	−45.1988			−1.58034
$819$	1.21785	−	15.2485i	0.0425549	−	0.532826i
$820$	2.26795			0.0792002
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.554873	−	0.831935i	$-0.687233\pi$
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.896502	+	0.443040i	$0.853900\pi$
$822$	−2.42177	+	17.3679i	−0.0844690	+	0.605774i
$823$	−7.39230	−	4.26795i	−0.257680	−	0.148771i	0.365596	−	0.930774i	$-0.380865\pi$
$823$	−7.39230	−	4.26795i	−0.257680	−	0.148771i	−0.623276	+	0.782002i	$0.714199\pi$
$824$	12.7786	−	12.7786i	0.445163	−	0.445163i
$825$	−7.58798	+	17.9300i	−0.264180	+	0.624242i
$826$	1.66025	+	6.19615i	0.0577676	+	0.215592i
$827$	−31.7936	−	31.7936i	−1.10557	−	1.10557i	−0.993726	−	0.111845i	$-0.964324\pi$
$827$	−31.7936	−	31.7936i	−1.10557	−	1.10557i	−0.111845	−	0.993726i	$-0.535676\pi$
$828$		0			0
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.449167	−	0.893448i	$-0.351721\pi$
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.998332	+	0.0577338i	$0.0183875\pi$
$830$	−2.41510	+	9.01327i	−0.0838293	+	0.312855i
$831$	29.3785	−	37.6865i	1.01913	−	1.30733i
$832$	−1.54552	+	23.9641i	−0.0535812	+	0.830806i
$833$		−	25.1954i		−	0.872968i
$834$	−28.9133	−	38.2832i	−1.00119	−	1.32564i
$835$	−10.1244	−	17.5359i	−0.350368	−	0.606855i
$836$	2.12976	−	3.68886i	0.0736595	−	0.127582i
$837$	16.8836	−	6.54383i	0.583582	−	0.226188i
$838$	13.8301	−	3.70577i	0.477754	−	0.128014i
$839$	−9.79282	+	2.62398i	−0.338086	+	0.0905898i	−0.423868	−	0.905724i	$-0.639328\pi$
$839$	−9.79282	+	2.62398i	−0.338086	+	0.0905898i	0.0857819	+	0.996314i	$0.472661\pi$
$840$	9.54910	−	1.18295i	0.329475	−	0.0408157i
$841$	11.1962	−	19.3923i	0.386074	−	0.668700i
$842$	8.33816	+	14.4421i	0.287352	+	0.497708i
$843$	−23.7128	+	17.9091i	−0.816714	+	0.616822i
$844$			0.483340i			0.0166372i
$845$	15.5070	−	11.9506i	0.533457	−	0.411112i
$846$	−6.64102	−	26.3927i	−0.228323	−	0.907400i
$847$	2.16987	−	8.09808i	0.0745577	−	0.278253i
$848$	−3.01375	+	1.73999i	−0.103493	+	0.0597515i
$849$	4.28626	+	10.5760i	0.147104	+	0.362967i
$850$	−14.6603	−	14.6603i	−0.502843	−	0.502843i
$851$		0			0
$852$	−1.28731	−	0.544793i	−0.0441027	−	0.0186643i
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	−0.977364	−	0.211566i	$-0.932144\pi$
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	0.211566	+	0.977364i	$0.432144\pi$
$854$	−12.9110	−	7.45418i	−0.441806	−	0.255077i
$855$	12.5305	−	12.1530i	0.428534	−	0.415623i
$856$	47.9090	+	12.8372i	1.63749	+	0.438765i
$857$	3.32707			0.113651			0.0568253	−	0.998384i	$-0.481902\pi$
$857$	3.32707			0.113651			0.0568253	+	0.998384i	$0.481902\pi$
$858$	−28.9234	−	25.7048i	−0.987428	−	0.877549i
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$	0.856003	+	0.229365i	0.0291895	+	0.00782129i
$861$	13.6351	+	1.90128i	0.464683	+	0.0647953i
$862$	49.3468	+	28.4904i	1.68076	+	0.970386i
$863$	−18.2354	+	18.2354i	−0.620741	+	0.620741i	−0.945721	−	0.324980i	$-0.894642\pi$
$863$	−18.2354	+	18.2354i	−0.620741	+	0.620741i	0.324980	+	0.945721i	$0.394642\pi$
$864$	−7.73284	−	1.19909i	−0.263077	−	0.0407940i
$865$	6.80385	+	25.3923i	0.231338	+	0.863364i
$866$	33.0673	+	33.0673i	1.12367	+	1.12367i
$867$	−13.4716	+	5.45979i	−0.457518	+	0.185424i
$868$	1.14359	−	0.660254i	0.0388161	−	0.0224105i
$869$	−2.12976	+	7.94839i	−0.0722473	+	0.269631i
$870$	−22.2096	−	17.3135i	−0.752977	−	0.586981i
$871$	−6.85641	+	20.2679i	−0.232320	+	0.686753i
$872$		−	48.6788i		−	1.64847i
$873$	−5.07425	−	0.0776093i	−0.171737	−	0.00262668i
$874$		0			0
$875$	−8.23373	+	14.2612i	−0.278351	+	0.482118i
$876$	0.0727771	+	0.587477i	0.00245891	+	0.0198490i
$877$	28.9904	−	7.76795i	0.978936	−	0.262305i	0.266339	−	0.963879i	$-0.414186\pi$
$877$	28.9904	−	7.76795i	0.978936	−	0.262305i	0.712596	+	0.701574i	$0.247519\pi$
$878$	−1.84443	+	0.494214i	−0.0622465	+	0.0166789i
$879$	0.383584	+	3.09640i	0.0129380	+	0.104439i
$880$	13.8301	−	23.9545i	0.466213	−	0.807505i
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	0.993176	−	0.116625i	$-0.0372076\pi$
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	−0.597588	+	0.801803i	$0.703874\pi$
$882$	22.5869	+	0.345461i	0.760541	+	0.0116323i
$883$		−	33.3731i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$883$		−	33.3731i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$884$	4.36397	−	2.15775i	0.146776	−	0.0725730i
$885$	6.19615	+	4.83020i	0.208281	+	0.162365i
$886$	−4.37307	+	16.3205i	−0.146916	+	0.548298i
$887$	−21.8683	+	12.6257i	−0.734266	+	0.423929i	−0.819981	−	0.572391i	$-0.806016\pi$
$887$	−21.8683	+	12.6257i	−0.734266	+	0.423929i	0.0857146	+	0.996320i	$0.472683\pi$
$888$	−22.6800	+	9.19180i	−0.761089	+	0.308457i
$889$	9.12436	+	9.12436i	0.306021	+	0.306021i
$890$	−5.47732	−	20.4416i	−0.183600	−	0.685206i
$891$	−26.9723	+	25.3708i	−0.903607	+	0.849954i
$892$	4.90897	−	4.90897i	0.164364	−	0.164364i
$893$	20.1563	+	11.6373i	0.674505	+	0.389426i
$894$	−22.3009	−	3.10963i	−0.745854	−	0.104002i
$895$	−38.6147	−	10.3468i	−1.29075	−	0.345855i
$896$	18.4443			0.616181
$897$		0			0
$898$	30.9808			1.03384
$899$	24.1305	+	6.46575i	0.804797	+	0.215645i
$900$	1.57648	−	1.52898i	0.0525494	−	0.0509661i
$901$	−3.40192	−	1.96410i	−0.113335	−	0.0654337i
$902$	24.6247	−	24.6247i	0.819913	−	0.819913i
$903$	4.95408	+	2.09657i	0.164861	+	0.0697695i
$904$	−6.94486	−	25.9186i	−0.230983	−	0.862039i
$905$	−3.19465	−	3.19465i	−0.106194	−	0.106194i
$906$	0.742522	+	1.83211i	0.0246686	+	0.0608677i
$907$	−15.0000	+	8.66025i	−0.498067	+	0.287559i	−0.727915	−	0.685668i	$-0.759510\pi$
$907$	−15.0000	+	8.66025i	−0.498067	+	0.287559i	0.229848	+	0.973227i	$0.426177\pi$
$908$	−1.40619	+	5.24796i	−0.0466659	+	0.174160i
$909$	4.41244	+	17.5359i	0.146351	+	0.581629i
$910$	−7.63397	−	8.68653i	−0.253064	−	0.287956i
$911$			1.55910i			0.0516552i	0.999666	+	0.0258276i	$0.00822209\pi$
$911$			1.55910i			0.0516552i	−0.999666	+	0.0258276i	$0.991778\pi$
$912$	23.8393	−	18.0046i	0.789398	−	0.596191i
$913$	8.46410	+	14.6603i	0.280121	+	0.485184i
$914$	2.93730	−	5.08755i	0.0971572	−	0.168281i
$915$	−18.1204	+	2.24477i	−0.599043	+	0.0742099i
$916$	−5.16987	+	1.38526i	−0.170817	+	0.0457704i
$917$	−10.8577	+	2.90931i	−0.358553	+	0.0960740i
$918$	−14.2504	−	36.7670i	−0.470333	−	1.21349i
$919$	−6.70577	+	11.6147i	−0.221203	+	0.383135i	−0.955174	−	0.296046i	$-0.904332\pi$
$919$	−6.70577	+	11.6147i	−0.221203	+	0.383135i	0.733971	+	0.679181i	$0.237665\pi$
$920$		0			0
$921$	−12.3892	−	16.4041i	−0.408236	−	0.540533i
$922$			32.0333i			1.05496i
$923$	−2.12976	−	10.6488i	−0.0701021	−	0.350510i
$924$	−1.66025	+	2.12976i	−0.0546183	+	0.0700641i
$925$	3.83013	−	14.2942i	0.125934	−	0.469991i
$926$	−42.5188	+	24.5483i	−1.39726	+	0.806706i
$927$	−5.68585	+	19.9918i	−0.186748	+	0.656616i
$928$	−7.63397	−	7.63397i	−0.250597	−	0.250597i
$929$	−5.27594	−	19.6901i	−0.173098	−	0.646011i	−0.996868	−	0.0790861i	$-0.974800\pi$
$929$	−5.27594	−	19.6901i	−0.173098	−	0.646011i	0.823770	−	0.566924i	$-0.191867\pi$
$930$	5.33506	−	12.6064i	0.174943	−	0.413381i
$931$	−13.6603	+	13.6603i	−0.447697	+	0.447697i
$932$	4.05065	+	2.33864i	0.132683	+	0.0766048i
$933$	2.41072	−	17.2886i	0.0789234	−	0.566004i
$934$	27.8827	+	7.47114i	0.912349	+	0.244463i
$935$	31.2229			1.02110
$936$	−12.1171	−	25.4799i	−0.396060	−	0.832837i
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	12.2079	+	3.27110i	0.398603	+	0.106805i
$939$	0.478405	−	3.43091i	0.0156122	−	0.111963i
$940$	−2.10512	−	1.21539i	−0.0686614	−	0.0396417i
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	−0.840285	−	0.542144i	$-0.817613\pi$
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	0.542144	+	0.840285i	$0.317613\pi$
$942$	4.88358	−	11.5396i	0.159116	−	0.375981i
$943$		0			0
$944$	9.50749	+	9.50749i	0.309442	+	0.309442i
$945$	−8.93193	+	6.53374i	−0.290556	+	0.212543i
$946$	11.7846	−	6.80385i	0.383151	−	0.221212i
$947$	−2.77689	+	10.3635i	−0.0902368	+	0.336768i	−0.996254	−	0.0864720i	$-0.972441\pi$
$947$	−2.77689	+	10.3635i	−0.0902368	+	0.336768i	0.906018	+	0.423240i	$0.139107\pi$
$948$	0.570669	−	0.732051i	0.0185345	−	0.0237759i
$949$	−3.45448	+	3.03590i	−0.112137	+	0.0985494i
$950$			15.8968i			0.515760i
$951$	16.7583	+	22.1891i	0.543425	+	0.719531i
$952$	9.29423	+	16.0981i	0.301228	+	0.521742i
$953$	−0.988427	+	1.71201i	−0.0320183	+	0.0554573i	−0.881591	−	0.472015i	$-0.843527\pi$
$953$	−0.988427	+	1.71201i	−0.0320183	+	0.0554573i	0.849572	+	0.527472i	$0.176860\pi$
$954$	1.80740	−	3.02279i	0.0585169	−	0.0978666i
$955$	7.02628	−	1.88269i	0.227365	−	0.0609223i
$956$	2.41510	−	0.647124i	0.0781099	−	0.0209295i
$957$	−50.7000	+	6.28076i	−1.63890	+	0.203028i
$958$	−15.4904	+	26.8301i	−0.500471	+	0.866842i
$959$	4.75374	+	8.23373i	0.153506	+	0.265881i
$960$	13.8632	−	10.4701i	0.447432	−	0.337923i
$961$		−	18.8564i		−	0.608271i
$962$	24.4718	+	16.3145i	0.789003	+	0.526002i
$963$	−55.3205	+	13.9199i	−1.78268	+	0.448563i
$964$	−1.00962	+	3.76795i	−0.0325176	+	0.121357i
$965$	0.180895	−	0.104440i	0.00582321	−	0.00336203i
$966$		0			0
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	0.0992599	−	0.995062i	$-0.468352\pi$
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	−0.995062	+	0.0992599i	$0.968352\pi$
$968$	−4.00218	−	14.9363i	−0.128635	−	0.480072i
$969$	31.0556	+	13.1428i	0.997651	+	0.422207i
$970$	−2.71281	+	2.71281i	−0.0871032	+	0.0871032i
$971$	41.4335	+	23.9216i	1.32966	+	0.767682i	0.985247	−	0.171136i	$-0.0547436\pi$
$971$	41.4335	+	23.9216i	1.32966	+	0.767682i	0.344416	+	0.938817i	$0.388077\pi$
$972$	3.91725	−	1.44976i	0.125646	−	0.0465011i
$973$	−25.1244	−	6.73205i	−0.805450	−	0.215820i
$974$	−8.67197			−0.277868
$975$	16.7115	+	3.43895i	0.535196	+	0.110134i
$976$	−31.2487			−1.00025
$977$	22.8847	+	6.13194i	0.732147	+	0.196178i	0.605585	−	0.795780i	$-0.292939\pi$
$977$	22.8847	+	6.13194i	0.732147	+	0.196178i	0.126562	+	0.991959i	$0.459606\pi$
$978$	10.6982	+	1.49176i	0.342092	+	0.0477012i
$979$	−33.2487	−	19.1962i	−1.06263	−	0.613512i
$980$	1.42667	−	1.42667i	0.0455734	−	0.0455734i
$981$	27.2485	+	48.9082i	0.869978	+	1.56152i
$982$	−11.1173	−	41.4904i	−0.354768	−	1.32401i
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	0.0285990	−	0.999591i	$-0.490895\pi$
$983$	−30.4433	−	30.4433i	−0.970992	−	0.970992i	−0.999591	+	0.0285990i	$0.990895\pi$
$984$	23.5330	−	9.53754i	0.750206	−	0.304046i
$985$	−5.36603	+	3.09808i	−0.170976	+	0.0987129i
$986$	14.0803	−	52.5485i	0.448409	−	1.67349i
$987$	−11.6373	−	9.07180i	−0.370418	−	0.288758i
$988$	−3.53590	−	1.19615i	−0.112492	−	0.0380547i
$989$		0			0
$990$	−0.428106	+	27.9904i	−0.0136061	+	0.889594i
$991$	28.7846	+	49.8564i	0.914373	+	1.58374i	0.807816	+	0.589434i	$0.200649\pi$
$991$	28.7846	+	49.8564i	0.914373	+	1.58374i	0.106557	+	0.994307i	$0.466017\pi$
$992$	2.62398	−	4.54486i	0.0833114	−	0.144300i
$993$	7.28650	+	58.8186i	0.231230	+	1.86655i
$994$	−6.19615	+	1.66025i	−0.196530	+	0.0526601i
$995$	18.8061	−	5.03908i	0.596193	−	0.159750i
$996$	−0.234755	−	1.89501i	−0.00743851	−	0.0600457i
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$	2.62398	+	4.54486i	0.0830606	+	0.143865i
$999$	17.6416	−	21.9305i	0.558156	−	0.693850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.2.k.b.11.1	✓	8
3.2	odd	2	inner	39.2.k.b.11.2	yes	8
4.3	odd	2		624.2.cn.c.401.1		8
5.2	odd	4		975.2.bp.e.674.2		8
5.3	odd	4		975.2.bp.f.674.1		8
5.4	even	2		975.2.bo.d.401.2		8
12.11	even	2		624.2.cn.c.401.2		8
13.2	odd	12		507.2.f.f.239.2		8
13.3	even	3		507.2.f.f.437.3		8
13.4	even	6		507.2.k.f.488.1		8
13.5	odd	4		507.2.k.e.80.1		8
13.6	odd	12	inner	39.2.k.b.32.2	yes	8
13.7	odd	12		507.2.k.d.188.1		8
13.8	odd	4		507.2.k.f.80.2		8
13.9	even	3		507.2.k.e.488.2		8
13.10	even	6		507.2.f.e.437.2		8
13.11	odd	12		507.2.f.e.239.3		8
13.12	even	2		507.2.k.d.89.2		8
15.2	even	4		975.2.bp.e.674.1		8
15.8	even	4		975.2.bp.f.674.2		8
15.14	odd	2		975.2.bo.d.401.1		8
39.2	even	12		507.2.f.f.239.3		8
39.5	even	4		507.2.k.e.80.2		8
39.8	even	4		507.2.k.f.80.1		8
39.11	even	12		507.2.f.e.239.2		8
39.17	odd	6		507.2.k.f.488.2		8
39.20	even	12		507.2.k.d.188.2		8
39.23	odd	6		507.2.f.e.437.3		8
39.29	odd	6		507.2.f.f.437.2		8
39.32	even	12	inner	39.2.k.b.32.1	yes	8
39.35	odd	6		507.2.k.e.488.1		8
39.38	odd	2		507.2.k.d.89.1		8
52.19	even	12		624.2.cn.c.305.2		8
65.19	odd	12		975.2.bo.d.851.1		8
65.32	even	12		975.2.bp.f.149.2		8
65.58	even	12		975.2.bp.e.149.1		8
156.71	odd	12		624.2.cn.c.305.1		8
195.32	odd	12		975.2.bp.f.149.1		8
195.149	even	12		975.2.bo.d.851.2		8
195.188	odd	12		975.2.bp.e.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	1.1	even	1	trivial
39.2.k.b.11.2	yes	8	3.2	odd	2	inner
39.2.k.b.32.1	yes	8	39.32	even	12	inner
39.2.k.b.32.2	yes	8	13.6	odd	12	inner
507.2.f.e.239.2		8	39.11	even	12
507.2.f.e.239.3		8	13.11	odd	12
507.2.f.e.437.2		8	13.10	even	6
507.2.f.e.437.3		8	39.23	odd	6
507.2.f.f.239.2		8	13.2	odd	12
507.2.f.f.239.3		8	39.2	even	12
507.2.f.f.437.2		8	39.29	odd	6
507.2.f.f.437.3		8	13.3	even	3
507.2.k.d.89.1		8	39.38	odd	2
507.2.k.d.89.2		8	13.12	even	2
507.2.k.d.188.1		8	13.7	odd	12
507.2.k.d.188.2		8	39.20	even	12
507.2.k.e.80.1		8	13.5	odd	4
507.2.k.e.80.2		8	39.5	even	4
507.2.k.e.488.1		8	39.35	odd	6
507.2.k.e.488.2		8	13.9	even	3
507.2.k.f.80.1		8	39.8	even	4
507.2.k.f.80.2		8	13.8	odd	4
507.2.k.f.488.1		8	13.4	even	6
507.2.k.f.488.2		8	39.17	odd	6
624.2.cn.c.305.1		8	156.71	odd	12
624.2.cn.c.305.2		8	52.19	even	12
624.2.cn.c.401.1		8	4.3	odd	2
624.2.cn.c.401.2		8	12.11	even	2
975.2.bo.d.401.1		8	15.14	odd	2
975.2.bo.d.401.2		8	5.4	even	2
975.2.bo.d.851.1		8	65.19	odd	12
975.2.bo.d.851.2		8	195.149	even	12
975.2.bp.e.149.1		8	65.58	even	12
975.2.bp.e.149.2		8	195.188	odd	12
975.2.bp.e.674.1		8	15.2	even	4
975.2.bp.e.674.2		8	5.2	odd	4
975.2.bp.f.149.1		8	195.32	odd	12
975.2.bp.f.149.2		8	65.32	even	12
975.2.bp.f.674.1		8	5.3	odd	4
975.2.bp.f.674.2		8	15.8	even	4

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	39.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})\)	\(q+(-1.45466 - 0.389774i) q^{2} +(0.239203 - 1.71545i) q^{3} +(0.232051 + 0.133975i) q^{4} +(1.06488 - 1.06488i) q^{5} +(-1.01660 + 2.40216i) q^{6} +(0.366025 + 1.36603i) q^{7} +(1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(-1.96410 + 1.13397i) q^{10} +(-1.06488 + 3.97420i) q^{11} +(0.285334 - 0.366025i) q^{12} +(3.59808 + 0.232051i) q^{13} -2.12976i q^{14} +(-1.57203 - 2.08148i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(2.51954 - 4.36397i) q^{17} +(3.87762 + 2.31853i) q^{18} +(-3.73205 + 1.00000i) q^{19} +(0.389774 - 0.104440i) q^{20} +(2.43091 - 0.301143i) q^{21} +(3.09808 - 5.36603i) q^{22} +(3.60523 - 2.72284i) q^{24} +2.73205i q^{25} +(-5.14352 - 1.73999i) q^{26} +(-2.09808 + 4.75374i) q^{27} +(-0.0980762 + 0.366025i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(1.47546 + 3.64058i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(0.389774 + 1.45466i) q^{32} +(6.56283 + 2.77739i) q^{33} +(-5.36603 + 5.36603i) q^{34} +(1.84443 + 1.06488i) q^{35} +(-0.559647 - 0.577032i) q^{36} +(-5.23205 - 1.40192i) q^{37} +5.81863 q^{38} +(1.25874 - 6.11683i) q^{39} +3.92820 q^{40} +(5.42885 + 1.45466i) q^{41} +(-3.65351 - 0.509445i) q^{42} +(1.90192 + 1.09808i) q^{43} +(-0.779548 + 0.779548i) q^{44} +(-3.94672 + 2.19886i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(-7.16590 + 2.90422i) q^{48} +(4.33013 - 2.50000i) q^{49} +(1.06488 - 3.97420i) q^{50} +(-6.88351 - 5.36603i) q^{51} +(0.803848 + 0.535898i) q^{52} -0.779548i q^{53} +(4.90487 - 6.09729i) q^{54} +(3.09808 + 5.36603i) q^{55} +(-1.84443 + 3.19465i) q^{56} +(0.822738 + 6.64136i) q^{57} +(10.4282 - 2.79423i) q^{58} +(-2.90931 + 0.779548i) q^{59} +(-0.0859264 - 0.693622i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.62398 + 4.54486i) q^{62} +(0.0648824 - 4.24214i) q^{63} +6.66025i q^{64} +(4.07863 - 3.58442i) q^{65} +(-8.46410 - 6.59817i) q^{66} +(-1.53590 + 5.73205i) q^{67} +(1.16932 - 0.675108i) q^{68} +(-2.26795 - 2.26795i) q^{70} +(-0.779548 - 2.90931i) q^{71} +(-3.80853 - 6.83591i) q^{72} +(-0.901924 + 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(4.68671 + 0.653513i) q^{75} +(-1.00000 - 0.267949i) q^{76} -5.81863 q^{77} +(-4.21522 + 8.40726i) q^{78} +2.00000 q^{79} +(-6.49373 - 1.73999i) q^{80} +(7.65296 + 4.73626i) q^{81} +(-7.33013 - 4.23205i) q^{82} +(2.90931 - 2.90931i) q^{83} +(0.604440 + 0.255799i) q^{84} +(-1.96410 - 7.33013i) q^{85} +(-2.33864 - 2.33864i) q^{86} +(4.66384 + 11.5076i) q^{87} +(-9.29423 + 5.36603i) q^{88} +(-2.41510 + 9.01327i) q^{89} +(6.59817 - 1.66025i) q^{90} +(1.00000 + 5.00000i) q^{91} +(-4.81647 + 3.63763i) q^{93} +(4.53590 + 7.85641i) q^{94} +(-2.90931 + 5.03908i) q^{95} +(2.58863 - 0.320682i) q^{96} +(1.63397 - 0.437822i) q^{97} +(-7.27328 + 1.94887i) q^{98} +(6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9	\( 8 q - 2 q^{3} - 12 q^{4} - 2 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{10} + 8 q^{13} - 14 q^{15} - 4 q^{16} + 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{22} + 18 q^{24} + 4 q^{27} + 20 q^{28} + 18 q^{30} + 8 q^{31} + 16 q^{33} - 36 q^{34} - 36 q^{36} - 28 q^{37} - 14 q^{39} - 24 q^{40} - 16 q^{42} + 36 q^{43} - 20 q^{45} - 14 q^{48} + 48 q^{52} + 46 q^{54} + 4 q^{55} + 16 q^{57} + 28 q^{58} + 44 q^{60} + 28 q^{61} - 8 q^{63} - 40 q^{66} - 40 q^{67} - 32 q^{70} + 12 q^{72} - 28 q^{73} + 12 q^{75} - 8 q^{76} - 80 q^{78} + 16 q^{79} + 4 q^{81} - 24 q^{82} + 4 q^{84} + 12 q^{85} - 34 q^{87} - 12 q^{88} + 8 q^{91} + 4 q^{93} + 64 q^{94} + 16 q^{96} + 20 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 12 * q^4 - 2 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^10 + 8 * q^13 - 14 * q^15 - 4 * q^16 + 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^22 + 18 * q^24 + 4 * q^27 + 20 * q^28 + 18 * q^30 + 8 * q^31 + 16 * q^33 - 36 * q^34 - 36 * q^36 - 28 * q^37 - 14 * q^39 - 24 * q^40 - 16 * q^42 + 36 * q^43 - 20 * q^45 - 14 * q^48 + 48 * q^52 + 46 * q^54 + 4 * q^55 + 16 * q^57 + 28 * q^58 + 44 * q^60 + 28 * q^61 - 8 * q^63 - 40 * q^66 - 40 * q^67 - 32 * q^70 + 12 * q^72 - 28 * q^73 + 12 * q^75 - 8 * q^76 - 80 * q^78 + 16 * q^79 + 4 * q^81 - 24 * q^82 + 4 * q^84 + 12 * q^85 - 34 * q^87 - 12 * q^88 + 8 * q^91 + 4 * q^93 + 64 * q^94 + 16 * q^96 + 20 * q^97 + 40 * q^99

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