LMFDB - Embedded newform 390.2.bd.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (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:	$3.11416567883$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.4
Root			$0.339278 + 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	390.37
Dual form			390.2.bd.b.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.64991 + 1.50924i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.56046 + 2.70280i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.64991 + 1.50924i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.56046 + 2.70280i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.18348 - 0.482081i) q^{10} +(0.628610 + 0.168435i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.13115 + 1.78771i) q^{13} -3.12092i q^{14} +(1.20307 + 1.88484i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0226346 - 0.0844736i) q^{17} -1.00000 q^{18} +(0.264302 + 0.986389i) q^{19} +(2.13199 - 0.674247i) q^{20} +(-2.20683 + 2.20683i) q^{21} +(-0.628610 + 0.168435i) q^{22} +(0.611240 - 2.28118i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(0.444415 + 4.98021i) q^{25} +(1.81780 - 3.11378i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.56046 + 2.70280i) q^{28} +(7.96403 - 4.59804i) q^{29} +(-1.98431 - 1.03078i) q^{30} +(-1.40560 - 1.40560i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.563596 + 0.325392i) q^{33} +(0.0618390 + 0.0618390i) q^{34} +(-6.65378 + 2.10427i) q^{35} +(0.866025 - 0.500000i) q^{36} +(3.80043 + 6.58253i) q^{37} +(-0.722087 - 0.722087i) q^{38} +(-3.48715 + 0.916397i) q^{39} +(-1.50924 + 1.64991i) q^{40} +(-0.901032 + 3.36270i) q^{41} +(0.807754 - 3.01458i) q^{42} +(-9.73152 + 2.60755i) q^{43} +(0.460174 - 0.460174i) q^{44} +(0.674247 + 2.13199i) q^{45} +(0.611240 + 2.28118i) q^{46} +4.74221 q^{47} +(-0.258819 - 0.965926i) q^{48} +(-1.37008 - 2.37305i) q^{49} +(-2.87498 - 4.09078i) q^{50} -0.0874535i q^{51} +(-0.0173697 + 3.60551i) q^{52} +(6.10974 - 6.10974i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(0.782942 + 1.22662i) q^{55} +(-2.70280 - 1.56046i) q^{56} +1.02119i q^{57} +(-4.59804 + 7.96403i) q^{58} +(-12.7884 + 3.42665i) q^{59} +(2.23385 - 0.0994727i) q^{60} +(3.40217 - 5.89274i) q^{61} +(1.92008 + 0.514484i) q^{62} +(-2.70280 + 1.56046i) q^{63} -1.00000 q^{64} +(-7.86420 - 1.77607i) q^{65} -0.650785 q^{66} +(9.39213 - 5.42255i) q^{67} +(-0.0844736 - 0.0226346i) q^{68} +(1.18083 - 2.04525i) q^{69} +(4.71021 - 5.14925i) q^{70} +(13.0079 - 3.48547i) q^{71} +(-0.500000 + 0.866025i) q^{72} +2.45159i q^{73} +(-6.58253 - 3.80043i) q^{74} +(-0.859701 + 4.92554i) q^{75} +(0.986389 + 0.264302i) q^{76} +(-1.43617 + 1.43617i) q^{77} +(2.56176 - 2.53720i) q^{78} -10.4433i q^{79} +(0.482081 - 2.18348i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.901032 - 3.36270i) q^{82} +1.51346 q^{83} +(0.807754 + 3.01458i) q^{84} +(0.0901454 - 0.173535i) q^{85} +(7.12397 - 7.12397i) q^{86} +(8.88272 - 2.38012i) q^{87} +(-0.168435 + 0.628610i) q^{88} +(4.84513 - 18.0823i) q^{89} +(-1.64991 - 1.50924i) q^{90} +(0.0542094 - 11.2525i) q^{91} +(-1.66994 - 1.66994i) q^{92} +(-0.993907 - 1.72150i) q^{93} +(-4.10687 + 2.37110i) q^{94} +(-1.05262 + 2.02635i) q^{95} +(0.707107 + 0.707107i) q^{96} +(4.43146 + 2.55851i) q^{97} +(2.37305 + 1.37008i) q^{98} +(0.460174 + 0.460174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	$ 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.64991	+	1.50924i	0.737863	+	0.674951i
$5$	1.64991	+	1.50924i	0.737863	+	0.674951i
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	−1.56046	+	2.70280i	−0.589799	+	1.02156i	0.404459	+	0.914556i	$0.367460\pi$
$7$	−1.56046	+	2.70280i	−0.589799	+	1.02156i	−0.994258	+	0.107006i	$0.965874\pi$
$8$			1.00000i			0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−2.18348	−	0.482081i	−0.690478	−	0.152447i
$11$	0.628610	+	0.168435i	0.189533	+	0.0507852i	0.352337	−	0.935873i	$-0.385387\pi$
$11$	0.628610	+	0.168435i	0.189533	+	0.0507852i	−0.162804	+	0.986658i	$0.552054\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.13115	+	1.78771i	−0.868424	+	0.495822i
$13$	−3.13115	+	1.78771i	−0.868424	+	0.495822i
$14$		−	3.12092i		−	0.834102i
$15$	1.20307	+	1.88484i	0.310632	+	0.486663i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0226346	−	0.0844736i	−0.00548970	−	0.0204879i	0.963127	−	0.269048i	$-0.0867092\pi$
$17$	−0.0226346	−	0.0844736i	−0.00548970	−	0.0204879i	−0.968616	+	0.248561i	$0.920042\pi$
$18$	−1.00000			−0.235702
$19$	0.264302	+	0.986389i	0.0606351	+	0.226293i	0.989594	−	0.143891i	$-0.0459614\pi$
$19$	0.264302	+	0.986389i	0.0606351	+	0.226293i	−0.928959	+	0.370184i	$0.879295\pi$
$20$	2.13199	−	0.674247i	0.476728	−	0.150766i
$21$	−2.20683	+	2.20683i	−0.481569	+	0.481569i
$22$	−0.628610	+	0.168435i	−0.134020	+	0.0359106i
$23$	0.611240	−	2.28118i	0.127452	−	0.475659i	−0.872463	−	0.488680i	$-0.837478\pi$
$23$	0.611240	−	2.28118i	0.127452	−	0.475659i	0.999915	+	0.0130217i	$0.00414507\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	0.444415	+	4.98021i	0.0888830	+	0.996042i
$26$	1.81780	−	3.11378i	0.356499	−	0.610662i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.56046	+	2.70280i	0.294899	+	0.510781i
$29$	7.96403	−	4.59804i	1.47888	−	0.853834i	0.479169	−	0.877723i	$-0.340938\pi$
$29$	7.96403	−	4.59804i	1.47888	−	0.853834i	0.999715	+	0.0238887i	$0.00760474\pi$
$30$	−1.98431	−	1.03078i	−0.362284	−	0.188194i
$31$	−1.40560	−	1.40560i	−0.252453	−	0.252453i	0.569523	−	0.821975i	$-0.307128\pi$
$31$	−1.40560	−	1.40560i	−0.252453	−	0.252453i	−0.821975	+	0.569523i	$0.807128\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.563596	+	0.325392i	0.0981095	+	0.0566435i
$34$	0.0618390	+	0.0618390i	0.0106053	+	0.0106053i
$35$	−6.65378	+	2.10427i	−1.12469	+	0.355687i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	3.80043	+	6.58253i	0.624786	+	1.08216i	0.988582	+	0.150683i	$0.0481473\pi$
$37$	3.80043	+	6.58253i	0.624786	+	1.08216i	−0.363796	+	0.931479i	$0.618519\pi$
$38$	−0.722087	−	0.722087i	−0.117138	−	0.117138i
$39$	−3.48715	+	0.916397i	−0.558391	+	0.146741i
$40$	−1.50924	+	1.64991i	−0.238631	+	0.260874i
$41$	−0.901032	+	3.36270i	−0.140718	+	0.525165i	0.859191	+	0.511655i	$0.170967\pi$
$41$	−0.901032	+	3.36270i	−0.140718	+	0.525165i	−0.999909	+	0.0135103i	$0.995699\pi$
$42$	0.807754	−	3.01458i	0.124639	−	0.465160i
$43$	−9.73152	+	2.60755i	−1.48404	+	0.397648i	−0.907721	−	0.419575i	$-0.862179\pi$
$43$	−9.73152	+	2.60755i	−1.48404	+	0.397648i	−0.576322	+	0.817223i	$0.695513\pi$
$44$	0.460174	−	0.460174i	0.0693739	−	0.0693739i
$45$	0.674247	+	2.13199i	0.100511	+	0.317819i
$46$	0.611240	+	2.28118i	0.0901224	+	0.336341i
$47$	4.74221			0.691722			0.345861	−	0.938286i	$-0.387587\pi$
$47$	4.74221			0.691722			0.345861	+	0.938286i	$0.387587\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	−1.37008	−	2.37305i	−0.195726	−	0.339007i
$50$	−2.87498	−	4.09078i	−0.406584	−	0.578524i
$51$		−	0.0874535i		−	0.0122459i
$52$	−0.0173697	+	3.60551i	−0.00240874	+	0.499994i
$53$	6.10974	−	6.10974i	0.839237	−	0.839237i	−0.149521	−	0.988758i	$-0.547773\pi$
$53$	6.10974	−	6.10974i	0.839237	−	0.839237i	0.988758	+	0.149521i	$0.0477733\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	0.782942	+	1.22662i	0.105572	+	0.165398i
$56$	−2.70280	−	1.56046i	−0.361177	−	0.208525i
$57$			1.02119i			0.135259i
$58$	−4.59804	+	7.96403i	−0.603752	+	1.04573i
$59$	−12.7884	+	3.42665i	−1.66491	+	0.446112i	−0.963732	−	0.266872i	$-0.914010\pi$
$59$	−12.7884	+	3.42665i	−1.66491	+	0.446112i	−0.701181	+	0.712984i	$0.747343\pi$
$60$	2.23385	−	0.0994727i	0.288389	−	0.0128419i
$61$	3.40217	−	5.89274i	0.435604	−	0.754488i	−0.561741	−	0.827313i	$-0.689868\pi$
$61$	3.40217	−	5.89274i	0.435604	−	0.754488i	0.997345	+	0.0728252i	$0.0232015\pi$
$62$	1.92008	+	0.514484i	0.243851	+	0.0653395i
$63$	−2.70280	+	1.56046i	−0.340521	+	0.196600i
$64$	−1.00000			−0.125000
$65$	−7.86420	−	1.77607i	−0.975433	−	0.220295i
$66$	−0.650785			−0.0801061
$67$	9.39213	−	5.42255i	1.14743	−	0.662470i	0.199172	−	0.979965i	$-0.436175\pi$
$67$	9.39213	−	5.42255i	1.14743	−	0.662470i	0.948260	+	0.317495i	$0.102842\pi$
$68$	−0.0844736	−	0.0226346i	−0.0102439	−	0.00274485i
$69$	1.18083	−	2.04525i	0.142155	−	0.246219i
$70$	4.71021	−	5.14925i	0.562978	−	0.615453i
$71$	13.0079	−	3.48547i	1.54376	−	0.413649i	0.616281	−	0.787526i	$-0.288639\pi$
$71$	13.0079	−	3.48547i	1.54376	−	0.413649i	0.927478	+	0.373878i	$0.121972\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$			2.45159i			0.286937i	0.989655	+	0.143469i	$0.0458256\pi$
$73$			2.45159i			0.286937i	−0.989655	+	0.143469i	$0.954174\pi$
$74$	−6.58253	−	3.80043i	−0.765204	−	0.441791i
$75$	−0.859701	+	4.92554i	−0.0992697	+	0.568752i
$76$	0.986389	+	0.264302i	0.113147	+	0.0303175i
$77$	−1.43617	+	1.43617i	−0.163667	+	0.163667i
$78$	2.56176	−	2.53720i	0.290062	−	0.287281i
$79$		−	10.4433i		−	1.17496i	−0.809239	−	0.587480i	$-0.800120\pi$
$79$		−	10.4433i		−	1.17496i	0.809239	−	0.587480i	$-0.199880\pi$
$80$	0.482081	−	2.18348i	0.0538983	−	0.244121i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.901032	−	3.36270i	−0.0995023	−	0.371348i
$83$	1.51346			0.166124			0.0830620	−	0.996544i	$-0.473530\pi$
$83$	1.51346			0.166124			0.0830620	+	0.996544i	$0.473530\pi$
$84$	0.807754	+	3.01458i	0.0881332	+	0.328918i
$85$	0.0901454	−	0.173535i	0.00977764	−	0.0188225i
$86$	7.12397	−	7.12397i	0.768197	−	0.768197i
$87$	8.88272	−	2.38012i	0.952328	−	0.255176i
$88$	−0.168435	+	0.628610i	−0.0179553	+	0.0670100i
$89$	4.84513	−	18.0823i	0.513583	−	1.91672i	0.136116	−	0.990693i	$-0.456538\pi$
$89$	4.84513	−	18.0823i	0.513583	−	1.91672i	0.377466	−	0.926023i	$-0.376795\pi$
$90$	−1.64991	−	1.50924i	−0.173916	−	0.159087i
$91$	0.0542094	−	11.2525i	0.00568268	−	1.17958i
$92$	−1.66994	−	1.66994i	−0.174103	−	0.174103i
$93$	−0.993907	−	1.72150i	−0.103063	−	0.178511i
$94$	−4.10687	+	2.37110i	−0.423592	+	0.244561i
$95$	−1.05262	+	2.02635i	−0.107996	+	0.207899i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	4.43146	+	2.55851i	0.449947	+	0.259777i	0.707808	−	0.706405i	$-0.249684\pi$
$97$	4.43146	+	2.55851i	0.449947	+	0.259777i	−0.257861	+	0.966182i	$0.583018\pi$
$98$	2.37305	+	1.37008i	0.239714	+	0.138399i
$99$	0.460174	+	0.460174i	0.0462493	+	0.0462493i
$100$	4.53520	+	2.10523i	0.453520	+	0.210523i
$101$	3.59747	−	2.07700i	0.357961	−	0.206669i	−0.310225	−	0.950663i	$-0.600404\pi$
$101$	3.59747	−	2.07700i	0.357961	−	0.206669i	0.668186	+	0.743994i	$0.267071\pi$
$102$	0.0437267	+	0.0757369i	0.00432959	+	0.00749908i
$103$	−8.89096	−	8.89096i	−0.876052	−	0.876052i	0.117071	−	0.993124i	$-0.462649\pi$
$103$	−8.89096	−	8.89096i	−0.876052	−	0.876052i	−0.993124	+	0.117071i	$0.962649\pi$
$104$	−1.78771	−	3.13115i	−0.175300	−	0.307034i
$105$	−6.97169	+	0.310447i	−0.680367	+	0.0302965i
$106$	−2.23632	+	8.34606i	−0.217211	+	0.810641i
$107$	−0.860303	+	3.21069i	−0.0831686	+	0.310389i	−0.994961	−	0.100262i	$-0.968032\pi$
$107$	−0.860303	+	3.21069i	−0.0831686	+	0.310389i	0.911792	+	0.410651i	$0.134699\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	8.53927	−	8.53927i	0.817914	−	0.817914i	−0.167891	−	0.985805i	$-0.553696\pi$
$109$	8.53927	−	8.53927i	0.817914	−	0.817914i	0.985805	+	0.167891i	$0.0536958\pi$
$110$	−1.29136	−	0.670817i	−0.123126	−	0.0639599i
$111$	1.96725	+	7.34186i	0.186723	+	0.696859i
$112$	3.12092			0.294899
$113$	1.76817	+	6.59892i	0.166336	+	0.620774i	0.997866	+	0.0652944i	$0.0207986\pi$
$113$	1.76817	+	6.59892i	0.166336	+	0.620774i	−0.831530	+	0.555480i	$0.812535\pi$
$114$	−0.510593	−	0.884372i	−0.0478214	−	0.0828291i
$115$	4.45133	−	2.84124i	0.415089	−	0.264947i
$116$		−	9.19607i		−	0.853834i
$117$	−3.60551	−	0.0173697i	−0.333329	−	0.00160583i
$118$	9.36178	−	9.36178i	0.861822	−	0.861822i
$119$	0.263636	+	0.0706409i	0.0241674	+	0.00647564i
$120$	−1.88484	+	1.20307i	−0.172061	+	0.109825i
$121$	−9.15950	−	5.28824i	−0.832682	−	0.480749i
$122$			6.80435i			0.616037i
$123$	−1.74066	+	3.01491i	−0.156950	+	0.271845i
$124$	−1.92008	+	0.514484i	−0.172428	+	0.0462020i
$125$	−6.78307	+	8.88763i	−0.606696	+	0.794934i
$126$	1.56046	−	2.70280i	0.139017	−	0.240784i
$127$	5.79169	+	1.55188i	0.513930	+	0.137707i	0.506457	−	0.862265i	$-0.330955\pi$
$127$	5.79169	+	1.55188i	0.513930	+	0.137707i	0.00747241	+	0.999972i	$0.497621\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.0748			−0.887038
$130$	7.69863	−	2.39397i	0.675214	−	0.209965i
$131$	−4.63651			−0.405094			−0.202547	−	0.979273i	$-0.564922\pi$
$131$	−4.63651			−0.405094			−0.202547	+	0.979273i	$0.564922\pi$
$132$	0.563596	−	0.325392i	0.0490547	−	0.0283218i
$133$	−3.07844	−	0.824867i	−0.266935	−	0.0715250i
$134$	−5.42255	+	9.39213i	−0.468437	+	0.811357i
$135$	0.0994727	+	2.23385i	0.00856125	+	0.192260i
$136$	0.0844736	−	0.0226346i	0.00724355	−	0.00194090i
$137$	5.30261	−	9.18440i	0.453033	−	0.784676i	−0.545540	−	0.838085i	$-0.683675\pi$
$137$	5.30261	−	9.18440i	0.453033	−	0.784676i	0.998573	+	0.0534088i	$0.0170086\pi$
$138$			2.36165i			0.201037i
$139$	−14.2433	−	8.22339i	−1.20810	−	0.697499i	−0.245759	−	0.969331i	$-0.579037\pi$
$139$	−14.2433	−	8.22339i	−1.20810	−	0.697499i	−0.962345	+	0.271832i	$0.912371\pi$
$140$	−1.50454	+	6.81448i	−0.127157	+	0.575929i
$141$	4.58062	+	1.22737i	0.385758	+	0.103364i
$142$	−9.52248	+	9.52248i	−0.799108	+	0.799108i
$143$	−2.26938	+	0.596377i	−0.189775	+	0.0498715i
$144$		−	1.00000i		−	0.0833333i
$145$	20.0795	+	4.43325i	1.66751	+	0.368161i
$146$	−1.22580	−	2.12314i	−0.101448	−	0.175712i
$147$	−0.709205	−	2.64679i	−0.0584943	−	0.218304i
$148$	7.60086			0.624786
$149$	3.53174	+	13.1806i	0.289331	+	1.07980i	0.945616	+	0.325286i	$0.105461\pi$
$149$	3.53174	+	13.1806i	0.289331	+	1.07980i	−0.656284	+	0.754514i	$0.727873\pi$
$150$	−1.71825	−	4.69549i	−0.140294	−	0.383385i
$151$	−11.3033	+	11.3033i	−0.919852	+	0.919852i	−0.997018	−	0.0771662i	$-0.975413\pi$
$151$	−11.3033	+	11.3033i	−0.919852	+	0.919852i	0.0771662	+	0.997018i	$0.475413\pi$
$152$	−0.986389	+	0.264302i	−0.0800067	+	0.0214377i
$153$	0.0226346	−	0.0844736i	0.00182990	−	0.00682928i
$154$	0.525674	−	1.96184i	0.0423600	−	0.158090i
$155$	−0.197733	−	4.44049i	−0.0158823	−	0.356668i
$156$	−0.949952	+	3.47816i	−0.0760571	+	0.278476i
$157$	2.26173	+	2.26173i	0.180506	+	0.180506i	0.791576	−	0.611070i	$-0.209261\pi$
$157$	2.26173	+	2.26173i	0.180506	+	0.180506i	−0.611070	+	0.791576i	$0.709261\pi$
$158$	5.22163	+	9.04413i	0.415411	+	0.719513i
$159$	7.48287	−	4.32024i	0.593430	−	0.342617i
$160$	0.674247	+	2.13199i	0.0533039	+	0.168549i
$161$	5.21175	+	5.21175i	0.410743	+	0.410743i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−13.7097	−	7.91529i	−1.07383	−	0.619973i	−0.144601	−	0.989490i	$-0.546190\pi$
$163$	−13.7097	−	7.91529i	−1.07383	−	0.619973i	−0.929224	+	0.369517i	$0.879523\pi$
$164$	2.46166	+	2.46166i	0.192224	+	0.192224i
$165$	0.438790	+	1.38747i	0.0341597	+	0.108014i
$166$	−1.31070	+	0.756731i	−0.101730	+	0.0587337i
$167$	−8.97024	−	15.5369i	−0.694138	−	1.20228i	−0.970470	−	0.241221i	$-0.922452\pi$
$167$	−8.97024	−	15.5369i	−0.694138	−	1.20228i	0.276332	−	0.961062i	$-0.410881\pi$
$168$	−2.20683	−	2.20683i	−0.170260	−	0.170260i
$169$	6.60817	−	11.1952i	0.508321	−	0.861168i
$170$	0.00869924	+	0.195358i	0.000667201	+	0.0149833i
$171$	−0.264302	+	0.986389i	−0.0202117	+	0.0754311i
$172$	−2.60755	+	9.73152i	−0.198824	+	0.742021i
$173$	0.317409	−	0.0850494i	0.0241321	−	0.00646619i	−0.246733	−	0.969084i	$-0.579357\pi$
$173$	0.317409	−	0.0850494i	0.0241321	−	0.00646619i	0.270865	+	0.962617i	$0.412690\pi$
$174$	−6.50261	+	6.50261i	−0.492961	+	0.492961i
$175$	−14.1540	−	6.57026i	−1.06994	−	0.496665i
$176$	−0.168435	−	0.628610i	−0.0126963	−	0.0473832i
$177$	−13.2396			−0.995147
$178$	4.84513	+	18.0823i	0.363158	+	1.35532i
$179$	10.9575	+	18.9789i	0.819001	+	1.41855i	0.906419	+	0.422380i	$0.138805\pi$
$179$	10.9575	+	18.9789i	0.819001	+	1.41855i	−0.0874180	+	0.996172i	$0.527862\pi$
$180$	2.18348	+	0.482081i	0.162747	+	0.0359322i
$181$		−	6.11180i		−	0.454286i	−0.973861	−	0.227143i	$-0.927061\pi$
$181$		−	6.11180i		−	0.454286i	0.973861	−	0.227143i	$-0.0729385\pi$
$182$	5.57931	+	9.77207i	0.413566	+	0.724354i
$183$	4.81140	−	4.81140i	0.355669	−	0.355669i
$184$	2.28118	+	0.611240i	0.168171	+	0.0450612i
$185$	−3.66423	+	16.5963i	−0.269399	+	1.22019i
$186$	1.72150	+	0.993907i	0.126226	+	0.0728768i
$187$		−	0.0569134i		−	0.00416192i
$188$	2.37110	−	4.10687i	0.172931	−	0.299525i
$189$	−3.01458	+	0.807754i	−0.219278	+	0.0587555i
$190$	−0.101580	−	2.28118i	−0.00736939	−	0.165494i
$191$	−2.41078	+	4.17559i	−0.174438	+	0.302135i	−0.939966	−	0.341267i	$-0.889144\pi$
$191$	−2.41078	+	4.17559i	−0.174438	+	0.302135i	0.765529	+	0.643401i	$0.222477\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−2.65297	+	1.53169i	−0.190965	+	0.110254i	−0.592434	−	0.805619i	$-0.701833\pi$
$193$	−2.65297	+	1.53169i	−0.190965	+	0.110254i	0.401469	+	0.915872i	$0.368500\pi$
$194$	−5.11701			−0.367380
$195$	−7.13655	−	3.75096i	−0.511059	−	0.268612i
$196$	−2.74016			−0.195726
$197$	−1.78952	+	1.03318i	−0.127498	+	0.0736108i	−0.562392	−	0.826871i	$-0.690119\pi$
$197$	−1.78952	+	1.03318i	−0.127498	+	0.0736108i	0.434895	+	0.900481i	$0.356786\pi$
$198$	−0.628610	−	0.168435i	−0.0446733	−	0.0119702i
$199$	−2.09521	+	3.62902i	−0.148526	+	0.257254i	−0.930683	−	0.365827i	$-0.880786\pi$
$199$	−2.09521	+	3.62902i	−0.148526	+	0.257254i	0.782157	+	0.623081i	$0.214119\pi$
$200$	−4.98021	+	0.444415i	−0.352154	+	0.0314249i
$201$	10.4756	−	2.80692i	0.738889	−	0.197985i
$202$	−2.07700	+	3.59747i	−0.146137	+	0.253117i
$203$			28.7002i			2.01436i
$204$	−0.0757369	−	0.0437267i	−0.00530265	−	0.00306148i
$205$	−6.56172	+	4.18828i	−0.458291	+	0.292522i
$206$	12.1453	+	3.25432i	0.846202	+	0.226739i
$207$	1.66994	−	1.66994i	0.116069	−	0.116069i
$208$	3.11378	+	1.81780i	0.215902	+	0.126042i
$209$			0.664572i			0.0459694i
$210$	5.88243	−	3.75470i	0.405927	−	0.259099i
$211$	6.34508	+	10.9900i	0.436813	+	0.756583i	0.997442	−	0.0714847i	$-0.0227737\pi$
$211$	6.34508	+	10.9900i	0.436813	+	0.756583i	−0.560628	+	0.828068i	$0.689440\pi$
$212$	−2.23632	−	8.34606i	−0.153591	−	0.573210i
$213$	13.4668			0.922731
$214$	−0.860303	−	3.21069i	−0.0588091	−	0.219478i
$215$	−19.9916	−	10.3849i	−1.36341	−	0.708246i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	5.99242	−	1.60567i	0.406792	−	0.109000i
$218$	−3.12559	+	11.6649i	−0.211692	+	0.790044i
$219$	−0.634519	+	2.36806i	−0.0428768	+	0.160018i
$220$	1.45376	−	0.0647353i	0.0980124	−	0.00436445i
$221$	0.221887	+	0.224035i	0.0149257	+	0.0150702i
$222$	−5.37462	−	5.37462i	−0.360721	−	0.360721i
$223$	7.16344	+	12.4074i	0.479699	+	0.830863i	0.999729	−	0.0232849i	$-0.00741247\pi$
$223$	7.16344	+	12.4074i	0.479699	+	0.830863i	−0.520030	+	0.854148i	$0.674079\pi$
$224$	−2.70280	+	1.56046i	−0.180588	+	0.104263i
$225$	−2.10523	+	4.53520i	−0.140349	+	0.302346i
$226$	−4.83074	−	4.83074i	−0.321336	−	0.321336i
$227$	−14.7394	−	8.50979i	−0.978288	−	0.564815i	−0.0765352	−	0.997067i	$-0.524386\pi$
$227$	−14.7394	−	8.50979i	−0.978288	−	0.564815i	−0.901753	+	0.432252i	$0.857719\pi$
$228$	0.884372	+	0.510593i	0.0585690	+	0.0338148i
$229$	11.8234	+	11.8234i	0.781309	+	0.781309i	0.980052	−	0.198742i	$-0.0636857\pi$
$229$	11.8234	+	11.8234i	0.781309	+	0.781309i	−0.198742	+	0.980052i	$0.563686\pi$
$230$	−2.43434	+	4.68625i	−0.160516	+	0.309002i
$231$	−1.75894	+	1.01552i	−0.115730	+	0.0668166i
$232$	4.59804	+	7.96403i	0.301876	+	0.522864i
$233$	1.14372	+	1.14372i	0.0749275	+	0.0749275i	0.743577	−	0.668650i	$-0.233127\pi$
$233$	1.14372	+	1.14372i	0.0749275	+	0.0749275i	−0.668650	+	0.743577i	$0.733127\pi$
$234$	3.13115	−	1.78771i	0.204690	−	0.116866i
$235$	7.82423	+	7.15711i	0.510396	+	0.466878i
$236$	−3.42665	+	12.7884i	−0.223056	+	0.832456i
$237$	2.70292	−	10.0874i	0.175573	−	0.655248i
$238$	−0.263636	+	0.0706409i	−0.0170890	+	0.00457897i
$239$	−0.186214	+	0.186214i	−0.0120452	+	0.0120452i	−0.713104	−	0.701059i	$-0.752711\pi$
$239$	−0.186214	+	0.186214i	−0.0120452	+	0.0120452i	0.701059	+	0.713104i	$0.252711\pi$
$240$	1.03078	−	1.98431i	0.0665366	−	0.128087i
$241$	6.98567	+	26.0709i	0.449987	+	1.67937i	0.702423	+	0.711759i	$0.252101\pi$
$241$	6.98567	+	26.0709i	0.449987	+	1.67937i	−0.252437	+	0.967613i	$0.581232\pi$
$242$	10.5765			0.679882
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−3.40217	−	5.89274i	−0.217802	−	0.377244i
$245$	1.32098	−	5.98309i	0.0843942	−	0.382246i
$246$		−	3.48132i		−	0.221961i
$247$	−2.59095	−	2.61603i	−0.164858	−	0.166454i
$248$	1.40560	−	1.40560i	0.0892555	−	0.0892555i
$249$	1.46189	+	0.391713i	0.0926436	+	0.0248238i
$250$	1.43049	−	11.0884i	0.0904722	−	0.701295i
$251$	−1.82325	−	1.05266i	−0.115083	−	0.0664430i	0.441354	−	0.897333i	$-0.354498\pi$
$251$	−1.82325	−	1.05266i	−0.115083	−	0.0664430i	−0.556436	+	0.830890i	$0.687832\pi$
$252$			3.12092i			0.196600i
$253$	0.768463	−	1.33102i	0.0483128	−	0.0836803i
$254$	−5.79169	+	1.55188i	−0.363403	+	0.0973736i
$255$	0.131988	−	0.144291i	0.00826541	−	0.00903582i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.1229	−	2.98037i	−0.693827	−	0.185910i	−0.105363	−	0.994434i	$-0.533600\pi$
$257$	−11.1229	−	2.98037i	−0.693827	−	0.185910i	−0.588464	+	0.808523i	$0.700267\pi$
$258$	8.72504	−	5.03741i	0.543197	−	0.313615i
$259$	−23.7217			−1.47399
$260$	−5.47022	+	5.92256i	−0.339249	+	0.367301i
$261$	9.19607			0.569223
$262$	4.01534	−	2.31825i	0.248068	−	0.143222i
$263$	0.721608	+	0.193354i	0.0444963	+	0.0119227i	0.280999	−	0.959708i	$-0.409334\pi$
$263$	0.721608	+	0.193354i	0.0444963	+	0.0119227i	−0.236502	+	0.971631i	$0.576001\pi$
$264$	−0.325392	+	0.563596i	−0.0200265	+	0.0346869i
$265$	19.3016	−	0.859491i	1.18569	−	0.0527981i
$266$	3.07844	−	0.824867i	0.188752	−	0.0505758i
$267$	9.36007	−	16.2121i	0.572827	−	0.992165i
$268$		−	10.8451i		−	0.662470i
$269$	13.5976	+	7.85055i	0.829058	+	0.478657i	0.853530	−	0.521044i	$-0.174457\pi$
$269$	13.5976	+	7.85055i	0.829058	+	0.478657i	−0.0244723	+	0.999701i	$0.507791\pi$
$270$	−1.20307	−	1.88484i	−0.0732167	−	0.114708i
$271$	−8.22569	−	2.20407i	−0.499675	−	0.133888i	0.000173978	−	1.00000i	$-0.499945\pi$
$271$	−8.22569	−	2.20407i	−0.499675	−	0.133888i	−0.499849	+	0.866112i	$0.666611\pi$
$272$	−0.0618390	+	0.0618390i	−0.00374954	+	0.00374954i
$273$	2.96473	−	10.8551i	0.179433	−	0.656978i
$274$			10.6052i			0.640685i
$275$	−0.559480	+	3.20546i	−0.0337379	+	0.193297i
$276$	−1.18083	−	2.04525i	−0.0710773	−	0.123110i
$277$	1.02469	+	3.82420i	0.0615677	+	0.229774i	0.989853	−	0.142095i	$-0.0453838\pi$
$277$	1.02469	+	3.82420i	0.0615677	+	0.229774i	−0.928285	+	0.371869i	$0.878717\pi$
$278$	16.4468			0.986413
$279$	−0.514484	−	1.92008i	−0.0308014	−	0.114952i
$280$	−2.10427	−	6.65378i	−0.125754	−	0.397640i
$281$	−16.6714	+	16.6714i	−0.994534	+	0.994534i	−0.999985	−	0.00545067i	$-0.998265\pi$
$281$	−16.6714	+	16.6714i	−0.994534	+	0.994534i	0.00545067	+	0.999985i	$0.498265\pi$
$282$	−4.58062	+	1.22737i	−0.272772	+	0.0730891i
$283$	8.00692	−	29.8822i	0.475962	−	1.77631i	−0.141743	−	0.989903i	$-0.545271\pi$
$283$	8.00692	−	29.8822i	0.475962	−	1.77631i	0.617705	−	0.786410i	$-0.288063\pi$
$284$	3.48547	−	13.0079i	0.206824	−	0.771879i
$285$	−1.54121	+	1.68487i	−0.0912934	+	0.0998028i
$286$	1.66716	−	1.65117i	0.0985810	−	0.0976357i
$287$	−7.68266	−	7.68266i	−0.453493	−	0.453493i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	14.7158	−	8.49618i	0.865636	−	0.499775i
$290$	−19.6060	+	6.20043i	−1.15130	+	0.364102i
$291$	3.61828	+	3.61828i	0.212107	+	0.212107i
$292$	2.12314	+	1.22580i	0.124247	+	0.0717343i
$293$	−17.6162	−	10.1707i	−1.02915	−	0.594178i	−0.112407	−	0.993662i	$-0.535856\pi$
$293$	−17.6162	−	10.1707i	−1.02915	−	0.594178i	−0.916740	+	0.399484i	$0.869189\pi$
$294$	1.93758	+	1.93758i	0.113002	+	0.113002i
$295$	−26.2714	−	13.6471i	−1.52958	−	0.794565i
$296$	−6.58253	+	3.80043i	−0.382602	+	0.220895i
$297$	0.325392	+	0.563596i	0.0188812	+	0.0327032i
$298$	−9.64889	−	9.64889i	−0.558945	−	0.558945i
$299$	2.16421	+	8.23543i	0.125159	+	0.476267i
$300$	3.83579	+	3.20729i	0.221459	+	0.185173i
$301$	8.13797	−	30.3713i	0.469065	−	1.75057i
$302$	4.13731	−	15.4406i	0.238075	−	0.888509i
$303$	4.01245	−	1.07513i	0.230509	−	0.0617648i
$304$	0.722087	−	0.722087i	0.0414145	−	0.0414145i
$305$	14.5068	−	4.58781i	0.830658	−	0.262697i
$306$	0.0226346	+	0.0844736i	0.00129394	+	0.00482903i
$307$	14.2902			0.815585			0.407792	−	0.913075i	$-0.366299\pi$
$307$	14.2902			0.815585			0.407792	+	0.913075i	$0.366299\pi$
$308$	0.525674	+	1.96184i	0.0299531	+	0.111786i
$309$	−6.28686	−	10.8892i	−0.357647	−	0.619463i
$310$	2.39149	+	3.74671i	0.135827	+	0.212799i
$311$		−	24.6571i		−	1.39818i	−0.715034	−	0.699089i	$-0.753589\pi$
$311$		−	24.6571i		−	1.39818i	0.715034	−	0.699089i	$-0.246411\pi$
$312$	−0.916397	−	3.48715i	−0.0518807	−	0.197421i
$313$	3.71347	−	3.71347i	0.209898	−	0.209898i	−0.594326	−	0.804224i	$-0.702581\pi$
$313$	3.71347	−	3.71347i	0.209898	−	0.209898i	0.804224	+	0.594326i	$0.202581\pi$
$314$	−3.08959	−	0.827852i	−0.174355	−	0.0467184i
$315$	−6.81448	−	1.50454i	−0.383953	−	0.0847710i
$316$	−9.04413	−	5.22163i	−0.508772	−	0.293740i
$317$		−	10.2414i		−	0.575212i	−0.957749	−	0.287606i	$-0.907141\pi$
$317$		−	10.2414i		−	0.575212i	0.957749	−	0.287606i	$-0.0928593\pi$
$318$	−4.32024	+	7.48287i	−0.242267	+	0.419619i
$319$	5.78074	−	1.54894i	0.323659	−	0.0867243i
$320$	−1.64991	−	1.50924i	−0.0922329	−	0.0843688i
$321$	−1.66198	+	2.87863i	−0.0927625	+	0.160669i
$322$	−7.11938	−	1.90763i	−0.396748	−	0.106308i
$323$	0.0773414	−	0.0446531i	0.00430339	−	0.00248457i
$324$	1.00000			0.0555556
$325$	−10.2947	−	14.7993i	−0.571048	−	0.820917i
$326$	15.8306			0.876775
$327$	10.4584	−	6.03818i	0.578353	−	0.333912i
$328$	−3.36270	−	0.901032i	−0.185674	−	0.0497512i
$329$	−7.40003	+	12.8172i	−0.407977	+	0.706637i
$330$	−1.07374	−	0.982187i	−0.0591073	−	0.0540676i
$331$	−22.3557	+	5.99019i	−1.22878	+	0.329251i	−0.814105	−	0.580718i	$-0.802772\pi$
$331$	−22.3557	+	5.99019i	−1.22878	+	0.329251i	−0.414676	+	0.909969i	$0.636105\pi$
$332$	0.756731	−	1.31070i	0.0415310	−	0.0719338i
$333$			7.60086i			0.416524i
$334$	15.5369	+	8.97024i	0.850142	+	0.490830i
$335$	23.6801	+	5.22822i	1.29378	+	0.285648i
$336$	3.01458	+	0.807754i	0.164459	+	0.0440666i
$337$	−18.6883	+	18.6883i	−1.01801	+	1.01801i	−0.0181791	+	0.999835i	$0.505787\pi$
$337$	−18.6883	+	18.6883i	−1.01801	+	1.01801i	−0.999835	+	0.0181791i	$0.994213\pi$
$338$	−0.125253	+	12.9994i	−0.00681286	+	0.707074i
$339$			6.83170i			0.371047i
$340$	−0.105213	−	0.164836i	−0.00570597	−	0.00893947i
$341$	−0.646819	−	1.12032i	−0.0350272	−	0.0606690i
$342$	−0.264302	−	0.986389i	−0.0142918	−	0.0533378i
$343$	−13.2946			−0.717843
$344$	−2.60755	−	9.73152i	−0.140590	−	0.524688i
$345$	5.03502	−	1.59234i	0.271076	−	0.0857285i
$346$	−0.232359	+	0.232359i	−0.0124917	+	0.0124917i
$347$	19.1265	−	5.12493i	1.02676	−	0.275121i	0.294146	−	0.955761i	$-0.404965\pi$
$347$	19.1265	−	5.12493i	1.02676	−	0.275121i	0.732618	+	0.680640i	$0.238298\pi$
$348$	2.38012	−	8.88272i	0.127588	−	0.476164i
$349$	−0.0805064	+	0.300454i	−0.00430941	+	0.0160829i	−0.968047	−	0.250769i	$-0.919317\pi$
$349$	−0.0805064	+	0.300454i	−0.00430941	+	0.0160829i	0.963738	+	0.266852i	$0.0859833\pi$
$350$	15.5429	−	1.38699i	0.830800	−	0.0741375i
$351$	−3.47816	−	0.949952i	−0.185650	−	0.0507047i
$352$	0.460174	+	0.460174i	0.0245274	+	0.0245274i
$353$	−14.8449	−	25.7121i	−0.790114	−	1.36852i	−0.925896	−	0.377779i	$-0.876688\pi$
$353$	−14.8449	−	25.7121i	−0.790114	−	1.36852i	0.135782	−	0.990739i	$-0.456645\pi$
$354$	11.4658	−	6.61978i	0.609400	−	0.351837i
$355$	26.7223	+	13.8813i	1.41827	+	0.736745i
$356$	−13.2371	−	13.2371i	−0.701567	−	0.701567i
$357$	0.236369	+	0.136468i	0.0125100	+	0.00722264i
$358$	−18.9789	−	10.9575i	−1.00307	−	0.579121i
$359$	24.4058	+	24.4058i	1.28809	+	1.28809i	0.935946	+	0.352143i	$0.114547\pi$
$359$	24.4058	+	24.4058i	1.28809	+	1.28809i	0.352143	+	0.935946i	$0.385453\pi$
$360$	−2.13199	+	0.674247i	−0.112366	+	0.0355360i
$361$	15.5514	−	8.97859i	0.818493	−	0.472557i
$362$	3.05590	+	5.29297i	0.160614	+	0.278192i
$363$	−7.47870	−	7.47870i	−0.392530	−	0.392530i
$364$	−9.71786	−	5.67320i	−0.509354	−	0.297357i
$365$	−3.70003	+	4.04491i	−0.193669	+	0.211720i
$366$	−1.76110	+	6.57250i	−0.0920539	+	0.343550i
$367$	−7.97094	+	29.7480i	−0.416080	+	1.55283i	0.366584	+	0.930385i	$0.380527\pi$
$367$	−7.97094	+	29.7480i	−0.416080	+	1.55283i	−0.782663	+	0.622445i	$0.786139\pi$
$368$	−2.28118	+	0.611240i	−0.118915	+	0.0318631i
$369$	−2.46166	+	2.46166i	−0.128149	+	0.128149i
$370$	−5.12486	−	16.2050i	−0.266429	−	0.842456i
$371$	6.97938	+	26.0474i	0.362351	+	1.35231i
$372$	−1.98781			−0.103063
$373$	0.470335	+	1.75531i	0.0243530	+	0.0908867i	0.977033	−	0.213089i	$-0.0683525\pi$
$373$	0.470335	+	1.75531i	0.0243530	+	0.0908867i	−0.952680	+	0.303976i	$0.901686\pi$
$374$	0.0284567	+	0.0492884i	0.00147146	+	0.00254864i
$375$	−8.85223	+	6.82921i	−0.457127	+	0.352659i
$376$			4.74221i			0.244561i
$377$	−16.7166	+	28.6345i	−0.860948	+	1.47475i
$378$	2.20683	−	2.20683i	0.113507	−	0.113507i
$379$	−6.00997	−	1.61037i	−0.308712	−	0.0827190i	0.101137	−	0.994872i	$-0.467752\pi$
$379$	−6.00997	−	1.61037i	−0.308712	−	0.0827190i	−0.409849	+	0.912153i	$0.634419\pi$
$380$	1.22856	+	1.92477i	0.0630238	+	0.0987386i
$381$	5.19269	+	2.99800i	0.266030	+	0.153592i
$382$		−	4.82155i		−	0.246692i
$383$	−0.531011	+	0.919738i	−0.0271334	+	0.0469964i	−0.879273	−	0.476318i	$-0.841971\pi$
$383$	−0.531011	+	0.919738i	−0.0271334	+	0.0469964i	0.852140	+	0.523314i	$0.175305\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	−4.53707	+	0.202034i	−0.231230	+	0.0102966i
$386$	1.53169	−	2.65297i	0.0779611	−	0.135033i
$387$	−9.73152	−	2.60755i	−0.494681	−	0.132549i
$388$	4.43146	−	2.55851i	0.224974	−	0.129889i
$389$	32.8035			1.66320			0.831602	−	0.555372i	$-0.187424\pi$
$389$	32.8035			1.66320			0.831602	+	0.555372i	$0.187424\pi$
$390$	8.05591	−	0.319849i	0.407927	−	0.0161962i
$391$	−0.206535			−0.0104449
$392$	2.37305	−	1.37008i	0.119857	−	0.0691995i
$393$	−4.47852	−	1.20002i	−0.225912	−	0.0605329i
$394$	1.03318	−	1.78952i	0.0520507	−	0.0901545i
$395$	15.7614	−	17.2305i	0.793040	−	0.866959i
$396$	0.628610	−	0.168435i	0.0315888	−	0.00846420i
$397$	18.6981	−	32.3861i	0.938431	−	1.62541i	0.170031	−	0.985439i	$-0.445613\pi$
$397$	18.6981	−	32.3861i	0.938431	−	1.62541i	0.768399	−	0.639971i	$-0.221054\pi$
$398$		−	4.19043i		−	0.210047i
$399$	−2.76006	−	1.59352i	−0.138176	−	0.0797758i
$400$	4.09078	−	2.87498i	0.204539	−	0.143749i
$401$	−0.873330	−	0.234008i	−0.0436120	−	0.0116858i	0.236947	−	0.971523i	$-0.423853\pi$
$401$	−0.873330	−	0.234008i	−0.0436120	−	0.0116858i	−0.280559	+	0.959837i	$0.590520\pi$
$402$	−7.66865	+	7.66865i	−0.382477	+	0.382477i
$403$	6.91393	+	1.88833i	0.344408	+	0.0940643i
$404$		−	4.15400i		−	0.206669i
$405$	−0.482081	+	2.18348i	−0.0239548	+	0.108498i
$406$	−14.3501	−	24.8551i	−0.712184	−	1.23354i
$407$	1.28025	+	4.77797i	0.0634598	+	0.236835i
$408$	0.0874535			0.00432959
$409$	6.85691	+	25.5903i	0.339052	+	1.26536i	0.899409	+	0.437109i	$0.143998\pi$
$409$	6.85691	+	25.5903i	0.339052	+	1.26536i	−0.560356	+	0.828252i	$0.689336\pi$
$410$	3.58848	−	6.90802i	0.177222	−	0.341163i
$411$	7.49903	−	7.49903i	0.369900	−	0.369900i
$412$	−12.1453	+	3.25432i	−0.598355	+	0.160329i
$413$	10.6943	−	39.9117i	0.526233	−	1.96393i
$414$	−0.611240	+	2.28118i	−0.0300408	+	0.112114i
$415$	2.49708	+	2.28417i	0.122577	+	0.112126i
$416$	−3.60551	−	0.0173697i	−0.176775	−	0.000851617i
$417$	−11.6296	−	11.6296i	−0.569506	−	0.569506i
$418$	−0.332286	−	0.575536i	−0.0162526	−	0.0281504i
$419$	−9.10788	+	5.25844i	−0.444949	+	0.256891i	−0.705695	−	0.708516i	$-0.749365\pi$
$419$	−9.10788	+	5.25844i	−0.444949	+	0.256891i	0.260746	+	0.965408i	$0.416032\pi$
$420$	−3.21699	+	6.19288i	−0.156973	+	0.302182i
$421$	2.06316	+	2.06316i	0.100552	+	0.100552i	0.755593	−	0.655041i	$-0.227349\pi$
$421$	2.06316	+	2.06316i	0.100552	+	0.100552i	−0.655041	+	0.755593i	$0.727349\pi$
$422$	−10.9900	−	6.34508i	−0.534985	−	0.308874i
$423$	4.10687	+	2.37110i	0.199683	+	0.115287i
$424$	6.10974	+	6.10974i	0.296715	+	0.296715i
$425$	0.410637	−	0.150267i	0.0199188	−	0.00728900i
$426$	−11.6626	+	6.73341i	−0.565055	+	0.326235i
$427$	10.6179	+	18.3908i	0.513837	+	0.889992i
$428$	2.35039	+	2.35039i	0.113610	+	0.113610i
$429$	−2.34641	−	0.0113039i	−0.113286	−	0.000545758i
$430$	22.5057	−	1.00217i	1.08532	−	0.0483289i
$431$	−4.66334	+	17.4038i	−0.224625	+	0.838313i	0.757929	+	0.652337i	$0.226211\pi$
$431$	−4.66334	+	17.4038i	−0.224625	+	0.838313i	−0.982554	+	0.185976i	$0.940455\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−34.0900	+	9.13438i	−1.63826	+	0.438970i	−0.956292	−	0.292413i	$-0.905542\pi$
$433$	−34.0900	+	9.13438i	−1.63826	+	0.438970i	−0.681967	+	0.731383i	$0.738875\pi$
$434$	−4.38676	+	4.38676i	−0.210571	+	0.210571i
$435$	18.2479	+	9.47914i	0.874918	+	0.454490i
$436$	−3.12559	−	11.6649i	−0.149689	−	0.558646i
$437$	2.41168			0.115366
$438$	−0.634519	−	2.36806i	−0.0303185	−	0.113150i
$439$	2.75416	+	4.77035i	0.131449	+	0.227677i	0.924235	−	0.381823i	$-0.124704\pi$
$439$	2.75416	+	4.77035i	0.131449	+	0.227677i	−0.792786	+	0.609500i	$0.791370\pi$
$440$	−1.22662	+	0.782942i	−0.0584770	+	0.0373253i
$441$		−	2.74016i		−	0.130484i
$442$	−0.304177	−	0.0830766i	−0.0144682	−	0.00395155i
$443$	1.58762	−	1.58762i	0.0754302	−	0.0754302i	−0.668385	−	0.743815i	$-0.733014\pi$
$443$	1.58762	−	1.58762i	0.0754302	−	0.0754302i	0.743815	+	0.668385i	$0.233014\pi$
$444$	7.34186	+	1.96725i	0.348429	+	0.0933614i
$445$	35.2844	−	22.5217i	1.67264	−	1.06763i
$446$	−12.4074	−	7.16344i	−0.587509	−	0.339199i
$447$			13.6456i			0.645415i
$448$	1.56046	−	2.70280i	0.0737249	−	0.127695i
$449$	−27.8644	+	7.46623i	−1.31500	+	0.352353i	−0.847103	−	0.531429i	$-0.821655\pi$
$449$	−27.8644	+	7.46623i	−1.31500	+	0.352353i	−0.467898	+	0.883782i	$0.654989\pi$
$450$	−0.444415	−	4.98021i	−0.0209499	−	0.234769i
$451$	−1.13279	+	1.96206i	−0.0533412	+	0.0923897i
$452$	6.59892	+	1.76817i	0.310387	+	0.0831679i
$453$	−13.8437	+	7.99266i	−0.650434	+	0.375528i
$454$	17.0196			0.798769
$455$	17.0721	−	18.4838i	0.800354	−	0.866536i
$456$	−1.02119			−0.0478214
$457$	−34.7545	+	20.0655i	−1.62575	+	0.938627i	−0.640407	+	0.768036i	$0.721234\pi$
$457$	−34.7545	+	20.0655i	−1.62575	+	0.938627i	−0.985342	+	0.170591i	$0.945432\pi$
$458$	−16.1510	−	4.32765i	−0.754687	−	0.202218i
$459$	0.0437267	−	0.0757369i	0.00204099	−	0.00353510i
$460$	−0.234920	−	5.27558i	−0.0109532	−	0.245975i
$461$	−16.2685	+	4.35912i	−0.757698	+	0.203025i	−0.616930	−	0.787018i	$-0.711624\pi$
$461$	−16.2685	+	4.35912i	−0.757698	+	0.203025i	−0.140768	+	0.990043i	$0.544957\pi$
$462$	1.01552	−	1.75894i	0.0472465	−	0.0818333i
$463$			38.5945i			1.79364i	0.442399	+	0.896818i	$0.354128\pi$
$463$			38.5945i			1.79364i	−0.442399	+	0.896818i	$0.645872\pi$
$464$	−7.96403	−	4.59804i	−0.369721	−	0.213458i
$465$	0.958287	−	4.34036i	0.0444395	−	0.201279i
$466$	−1.56235	−	0.418630i	−0.0723744	−	0.0193927i
$467$	15.2256	−	15.2256i	0.704556	−	0.704556i	−0.260829	−	0.965385i	$-0.583996\pi$
$467$	15.2256	−	15.2256i	0.704556	−	0.704556i	0.965385	+	0.260829i	$0.0839959\pi$
$468$	−1.81780	+	3.11378i	−0.0840277	+	0.143934i
$469$			33.8467i			1.56290i
$470$	−10.3545	−	2.28613i	−0.477619	−	0.105451i
$471$	1.59929	+	2.77005i	0.0736913	+	0.127637i
$472$	−3.42665	−	12.7884i	−0.157724	−	0.588635i
$473$	−6.55653			−0.301470
$474$	2.70292	+	10.0874i	0.124149	+	0.463331i
$475$	−4.79497	+	1.75465i	−0.220008	+	0.0805087i
$476$	0.192995	−	0.192995i	0.00884589	−	0.00884589i
$477$	8.34606	−	2.23632i	0.382140	−	0.102394i
$478$	0.0681589	−	0.254373i	0.00311752	−	0.0116347i
$479$	3.98679	−	14.8789i	0.182161	−	0.679835i	−0.813059	−	0.582181i	$-0.802200\pi$
$479$	3.98679	−	14.8789i	0.182161	−	0.679835i	0.995220	−	0.0976537i	$-0.0311338\pi$
$480$	0.0994727	+	2.23385i	0.00454029	+	0.101961i
$481$	−23.6674	−	13.8168i	−1.07914	−	0.629992i
$482$	−19.0852	−	19.0852i	−0.869307	−	0.869307i
$483$	3.68526	+	6.38306i	0.167685	+	0.290439i
$484$	−9.15950	+	5.28824i	−0.416341	+	0.240375i
$485$	3.45013	+	10.9094i	0.156662	+	0.495372i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−16.3277	−	9.42678i	−0.739877	−	0.427168i	0.0821477	−	0.996620i	$-0.473822\pi$
$487$	−16.3277	−	9.42678i	−0.739877	−	0.427168i	−0.822025	+	0.569452i	$0.807155\pi$
$488$	5.89274	+	3.40217i	0.266752	+	0.154009i
$489$	−11.1939	−	11.1939i	−0.506206	−	0.506206i
$490$	1.84754	+	5.84200i	0.0834636	+	0.263915i
$491$	−4.22759	+	2.44080i	−0.190789	+	0.110152i	−0.592352	−	0.805680i	$-0.701800\pi$
$491$	−4.22759	+	2.44080i	−0.190789	+	0.110152i	0.401563	+	0.915831i	$0.368467\pi$
$492$	1.74066	+	3.01491i	0.0784750	+	0.135923i
$493$	−0.568676	−	0.568676i	−0.0256119	−	0.0256119i
$494$	3.55184	+	0.970077i	0.159805	+	0.0436458i
$495$	0.0647353	+	1.45376i	0.00290964	+	0.0653416i
$496$	−0.514484	+	1.92008i	−0.0231010	+	0.0862142i
$497$	−10.8779	+	40.5968i	−0.487939	+	1.82101i
$498$	−1.46189	+	0.391713i	−0.0655090	+	0.0175531i
$499$	6.12464	−	6.12464i	0.274176	−	0.274176i	−0.556603	−	0.830779i	$-0.687895\pi$
$499$	6.12464	−	6.12464i	0.274176	−	0.274176i	0.830779	+	0.556603i	$0.187895\pi$
$500$	4.30538	+	10.3181i	0.192543	+	0.461441i
$501$	−4.64334	−	17.3292i	−0.207449	−	0.774211i
$502$	2.10531			0.0939646
$503$	−6.55326	−	24.4571i	−0.292196	−	1.09049i	−0.943419	−	0.331603i	$-0.892411\pi$
$503$	−6.55326	−	24.4571i	−0.292196	−	1.09049i	0.651223	−	0.758886i	$-0.274256\pi$
$504$	−1.56046	−	2.70280i	−0.0695085	−	0.120392i
$505$	9.07018	+	2.00256i	0.403618	+	0.0891129i
$506$			1.53693i			0.0683247i
$507$	9.28053	−	9.10339i	0.412163	−	0.404296i
$508$	4.23981	−	4.23981i	0.188111	−	0.188111i
$509$	−11.3870	−	3.05113i	−0.504719	−	0.135239i	−0.00252998	−	0.999997i	$-0.500805\pi$
$509$	−11.3870	−	3.05113i	−0.504719	−	0.135239i	−0.502189	+	0.864758i	$0.667472\pi$
$510$	−0.0421596	+	0.190953i	−0.00186686	+	0.00845555i
$511$	−6.62616	−	3.82562i	−0.293124	−	0.169235i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.510593	+	0.884372i	−0.0225432	+	0.0390460i
$514$	11.1229	−	2.98037i	0.490610	−	0.131458i
$515$	−1.25074	−	28.0879i	−0.0551143	−	1.23770i
$516$	−5.03741	+	8.72504i	−0.221759	+	0.384099i
$517$	2.98100	+	0.798756i	0.131104	+	0.0351293i
$518$	20.5436	−	11.8608i	0.902633	−	0.521135i
$519$	0.328606			0.0144242
$520$	1.77607	−	7.86420i	0.0778860	−	0.344868i
$521$	7.65452			0.335351			0.167675	−	0.985842i	$-0.446374\pi$
$521$	7.65452			0.335351			0.167675	+	0.985842i	$0.446374\pi$
$522$	−7.96403	+	4.59804i	−0.348576	+	0.201251i
$523$	28.4783	+	7.63073i	1.24527	+	0.333669i	0.820507	−	0.571636i	$-0.193691\pi$
$523$	28.4783	+	7.63073i	1.24527	+	0.333669i	0.424762	+	0.905305i	$0.360358\pi$
$524$	−2.31825	+	4.01534i	−0.101273	+	0.175411i
$525$	−11.9712	−	10.0097i	−0.522466	−	0.436860i
$526$	−0.721608	+	0.193354i	−0.0314636	+	0.00843065i
$527$	−0.0869206	+	0.150551i	−0.00378632	+	0.00655810i
$528$		−	0.650785i		−	0.0283218i
$529$	15.0884	+	8.71130i	0.656018	+	0.378752i
$530$	−16.2859	+	10.3951i	−0.707414	+	0.451535i
$531$	−12.7884	−	3.42665i	−0.554971	−	0.148704i
$532$	−2.25358	+	2.25358i	−0.0977050	+	0.0977050i
$533$	−3.19027	−	12.1399i	−0.138186	−	0.525837i
$534$			18.7201i			0.810100i
$535$	−6.26512	+	3.99896i	−0.270865	+	0.172890i
$536$	5.42255	+	9.39213i	0.234219	+	0.405678i
$537$	5.67201	+	21.1682i	0.244765	+	0.913477i
$538$	−15.7011			−0.676923
$539$	−0.461540	−	1.72249i	−0.0198799	−	0.0741929i
$540$	1.98431	+	1.03078i	0.0853911	+	0.0443578i
$541$	−7.28454	+	7.28454i	−0.313187	+	0.313187i	−0.846143	−	0.532956i	$-0.821081\pi$
$541$	−7.28454	+	7.28454i	−0.313187	+	0.313187i	0.532956	+	0.846143i	$0.321081\pi$
$542$	8.22569	−	2.20407i	0.353324	−	0.0946728i
$543$	1.58185	−	5.90354i	0.0678837	−	0.253345i
$544$	0.0226346	−	0.0844736i	0.000970452	−	0.00362178i
$545$	26.9768	−	1.20127i	1.15556	−	0.0514567i
$546$	2.86000	+	10.8831i	0.122397	+	0.465755i
$547$	−8.12503	−	8.12503i	−0.347401	−	0.347401i	0.511739	−	0.859141i	$-0.329001\pi$
$547$	−8.12503	−	8.12503i	−0.347401	−	0.347401i	−0.859141	+	0.511739i	$0.829001\pi$
$548$	−5.30261	−	9.18440i	−0.226516	−	0.392338i
$549$	5.89274	−	3.40217i	0.251496	−	0.145201i
$550$	−1.11821	−	3.05575i	−0.0476805	−	0.130298i
$551$	6.64036	+	6.64036i	0.282889	+	0.282889i
$552$	2.04525	+	1.18083i	0.0870516	+	0.0502593i
$553$	28.2260	+	16.2963i	1.20029	+	0.692990i
$554$	−2.79951	−	2.79951i	−0.118940	−	0.118940i
$555$	−7.83482	+	15.0825i	−0.332570	+	0.640215i
$556$	−14.2433	+	8.22339i	−0.604052	+	0.348750i
$557$	−9.06907	−	15.7081i	−0.384269	−	0.665573i	0.607399	−	0.794397i	$-0.292213\pi$
$557$	−9.06907	−	15.7081i	−0.384269	−	0.665573i	−0.991667	+	0.128824i	$0.958880\pi$
$558$	1.40560	+	1.40560i	0.0595037	+	0.0595037i
$559$	25.8093	−	25.5618i	1.09162	−	1.08115i
$560$	5.14925	+	4.71021i	0.217595	+	0.199043i
$561$	0.0147303	−	0.0549741i	0.000621912	−	0.00232101i
$562$	6.10217	−	22.7736i	0.257404	−	0.960647i
$563$	33.7469	−	9.04247i	1.42226	−	0.381094i	0.535978	−	0.844232i	$-0.319943\pi$
$563$	33.7469	−	9.04247i	1.42226	−	0.381094i	0.886286	+	0.463138i	$0.153276\pi$
$564$	3.35325	−	3.35325i	0.141197	−	0.141197i
$565$	−7.04199	+	13.5562i	−0.296259	+	0.570315i
$566$	8.00692	+	29.8822i	0.336556	+	1.25604i
$567$	−3.12092			−0.131066
$568$	3.48547	+	13.0079i	0.146247	+	0.545801i
$569$	−12.2319	−	21.1863i	−0.512790	−	0.888178i	−0.999890	−	0.0148316i	$-0.995279\pi$
$569$	−12.2319	−	21.1863i	−0.512790	−	0.888178i	0.487100	−	0.873346i	$-0.338055\pi$
$570$	0.492294	−	2.22974i	0.0206199	−	0.0933936i
$571$			22.5270i			0.942727i	0.881939	+	0.471364i	$0.156238\pi$
$571$			22.5270i			0.942727i	−0.881939	+	0.471364i	$0.843762\pi$
$572$	−0.618214	+	2.26353i	−0.0258488	+	0.0946431i
$573$	−3.40935	+	3.40935i	−0.142428	+	0.142428i
$574$	10.4947	+	2.81205i	0.438041	+	0.117373i
$575$	11.6324	+	2.03031i	0.485104	+	0.0846699i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$			32.1391i			1.33797i	0.743276	+	0.668985i	$0.233271\pi$
$577$			32.1391i			1.33797i	−0.743276	+	0.668985i	$0.766729\pi$
$578$	−8.49618	+	14.7158i	−0.353394	+	0.612097i
$579$	−2.95900	+	0.792862i	−0.122972	+	0.0329502i
$580$	13.8790	−	15.1727i	0.576296	−	0.630012i
$581$	−2.36170	+	4.09058i	−0.0979798	+	0.169706i
$582$	−4.94266	−	1.32438i	−0.204880	−	0.0548973i
$583$	4.86974	−	2.81154i	0.201684	−	0.116442i
$584$	−2.45159			−0.101448
$585$	−5.92256	−	5.47022i	−0.244868	−	0.226166i
$586$	20.3414			0.840295
$587$	−17.2872	+	9.98075i	−0.713517	+	0.411950i	−0.812362	−	0.583153i	$-0.801819\pi$
$587$	−17.2872	+	9.98075i	−0.713517	+	0.411950i	0.0988446	+	0.995103i	$0.468485\pi$
$588$	−2.64679	−	0.709205i	−0.109152	−	0.0292471i
$589$	1.01496	−	1.75797i	0.0418208	−	0.0724358i
$590$	29.5753	−	1.31698i	1.21759	−	0.0542190i
$591$	−1.99594	+	0.534812i	−0.0821022	+	0.0219992i
$592$	3.80043	−	6.58253i	0.156197	−	0.270540i
$593$		−	4.57405i		−	0.187834i	−0.995580	−	0.0939169i	$-0.970061\pi$
$593$		−	4.57405i		−	0.187834i	0.995580	−	0.0939169i	$-0.0299388\pi$
$594$	−0.563596	−	0.325392i	−0.0231246	−	0.0133510i
$595$	0.328361	+	0.514439i	0.0134615	+	0.0210900i
$596$	13.1806	+	3.53174i	0.539900	+	0.144666i
$597$	−2.96308	+	2.96308i	−0.121271	+	0.121271i
$598$	−5.99197	−	6.04999i	−0.245030	−	0.247402i
$599$		−	26.5385i		−	1.08433i	−0.840271	−	0.542167i	$-0.817604\pi$
$599$		−	26.5385i		−	1.08433i	0.840271	−	0.542167i	$-0.182396\pi$
$600$	−4.92554	−	0.859701i	−0.201084	−	0.0350972i
$601$	13.3672	+	23.1528i	0.545261	+	0.944420i	0.998590	+	0.0530772i	$0.0169029\pi$
$601$	13.3672	+	23.1528i	0.545261	+	0.944420i	−0.453329	+	0.891343i	$0.649764\pi$
$602$	8.13797	+	30.3713i	0.331679	+	1.23784i
$603$	10.8451			0.441647
$604$	4.13731	+	15.4406i	0.168345	+	0.628271i
$605$	−7.13116	−	22.5490i	−0.289923	−	0.916746i
$606$	−2.93732	+	2.93732i	−0.119320	+	0.119320i
$607$	11.7486	−	3.14802i	0.476860	−	0.127774i	−0.0123802	−	0.999923i	$-0.503941\pi$
$607$	11.7486	−	3.14802i	0.476860	−	0.127774i	0.489240	+	0.872149i	$0.337274\pi$
$608$	−0.264302	+	0.986389i	−0.0107189	+	0.0400034i
$609$	−7.42817	+	27.7223i	−0.301005	+	1.12336i
$610$	−10.2694	+	11.2266i	−0.415795	+	0.454551i
$611$	−14.8486	+	8.47771i	−0.600708	+	0.342971i
$612$	−0.0618390	−	0.0618390i	−0.00249969	−	0.00249969i
$613$	10.0821	+	17.4627i	0.407212	+	0.705311i	0.994576	−	0.104011i	$-0.0331678\pi$
$613$	10.0821	+	17.4627i	0.407212	+	0.705311i	−0.587364	+	0.809323i	$0.699834\pi$
$614$	−12.3757	+	7.14510i	−0.499442	+	0.288353i
$615$	−7.42214	+	2.34727i	−0.299290	+	0.0946511i
$616$	−1.43617	−	1.43617i	−0.0578649	−	0.0578649i
$617$	−32.6028	−	18.8232i	−1.31254	−	0.757794i	−0.330023	−	0.943973i	$-0.607056\pi$
$617$	−32.6028	−	18.8232i	−1.31254	−	0.757794i	−0.982516	+	0.186179i	$0.940390\pi$
$618$	10.8892	+	6.28686i	0.438026	+	0.252895i
$619$	−27.2529	−	27.2529i	−1.09539	−	1.09539i	−0.994943	−	0.100442i	$-0.967974\pi$
$619$	−27.2529	−	27.2529i	−1.09539	−	1.09539i	−0.100442	−	0.994943i	$-0.532026\pi$
$620$	−3.94444	−	2.04900i	−0.158413	−	0.0822899i
$621$	2.04525	−	1.18083i	0.0820730	−	0.0473849i
$622$	12.3286	+	21.3537i	0.494331	+	0.856206i
$623$	41.3121	+	41.3121i	1.65513	+	1.65513i
$624$	2.53720	+	2.56176i	0.101569	+	0.102553i
$625$	−24.6050	+	4.42656i	−0.984200	+	0.177062i
$626$	−1.35922	+	5.07269i	−0.0543255	+	0.202745i
$627$	−0.172004	+	0.641927i	−0.00686917	+	0.0256361i
$628$	3.08959	−	0.827852i	0.123288	−	0.0330349i
$629$	0.470029	−	0.470029i	0.0187413	−	0.0187413i
$630$	6.65378	−	2.10427i	0.265093	−	0.0838363i
$631$	2.11491	+	7.89297i	0.0841934	+	0.314214i	0.995160	−	0.0982656i	$-0.0313295\pi$
$631$	2.11491	+	7.89297i	0.0841934	+	0.314214i	−0.910967	+	0.412480i	$0.864663\pi$
$632$	10.4433			0.415411
$633$	3.28446	+	12.2578i	0.130545	+	0.487202i
$634$	5.12068	+	8.86927i	0.203368	+	0.352244i
$635$	7.21363	+	11.3015i	0.286264	+	0.448486i
$636$		−	8.64047i		−	0.342617i
$637$	8.53225	+	4.98105i	0.338060	+	0.197357i
$638$	−4.23180	+	4.23180i	−0.167538	+	0.167538i
$639$	13.0079	+	3.48547i	0.514586	+	0.137883i
$640$	2.18348	+	0.482081i	0.0863097	+	0.0190559i
$641$	−15.0450	−	8.68624i	−0.594242	−	0.343086i	0.172531	−	0.985004i	$-0.444805\pi$
$641$	−15.0450	−	8.68624i	−0.594242	−	0.343086i	−0.766773	+	0.641918i	$0.778139\pi$
$642$		−	3.32395i		−	0.131186i
$643$	10.3157	−	17.8672i	0.406810	−	0.704615i	−0.587721	−	0.809064i	$-0.699975\pi$
$643$	10.3157	−	17.8672i	0.406810	−	0.704615i	0.994530	+	0.104449i	$0.0333079\pi$
$644$	7.11938	−	1.90763i	0.280543	−	0.0751713i
$645$	−16.6225	−	15.2053i	−0.654512	−	0.598707i
$646$	−0.0446531	+	0.0773414i	−0.00175685	+	0.00304296i
$647$	18.1785	+	4.87092i	0.714671	+	0.191496i	0.597793	−	0.801651i	$-0.296045\pi$
$647$	18.1785	+	4.87092i	0.714671	+	0.191496i	0.116878	+	0.993146i	$0.462711\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−8.61610			−0.338212
$650$	16.3151	+	7.66920i	0.639932	+	0.300811i
$651$	6.20381			0.243147
$652$	−13.7097	+	7.91529i	−0.536913	+	0.309987i
$653$	−39.8876	−	10.6879i	−1.56092	−	0.418248i	−0.627967	−	0.778240i	$-0.716113\pi$
$653$	−39.8876	−	10.6879i	−1.56092	−	0.418248i	−0.932956	+	0.359992i	$0.882780\pi$
$654$	−6.03818	+	10.4584i	−0.236111	+	0.408957i
$655$	−7.64983	−	6.99759i	−0.298904	−	0.273418i
$656$	3.36270	−	0.901032i	0.131291	−	0.0351794i
$657$	−1.22580	+	2.12314i	−0.0478229	+	0.0828317i
$658$		−	14.8001i		−	0.576967i
$659$	11.0082	+	6.35559i	0.428819	+	0.247579i	0.698843	−	0.715275i	$-0.253698\pi$
$659$	11.0082	+	6.35559i	0.428819	+	0.247579i	−0.270025	+	0.962853i	$0.587032\pi$
$660$	1.42098	+	0.313731i	0.0553115	+	0.0122120i
$661$	−35.9999	−	9.64615i	−1.40023	−	0.375192i	−0.521805	−	0.853065i	$-0.674741\pi$
$661$	−35.9999	−	9.64615i	−1.40023	−	0.375192i	−0.878429	+	0.477873i	$0.841408\pi$
$662$	16.3655	−	16.3655i	0.636064	−	0.636064i
$663$	0.156342	+	0.273830i	0.00607181	+	0.0106347i
$664$			1.51346i			0.0587337i
$665$	−3.83424	−	6.00706i	−0.148686	−	0.232944i
$666$	−3.80043	−	6.58253i	−0.147264	−	0.255068i
$667$	−5.62101	−	20.9779i	−0.217646	−	0.812267i
$668$	−17.9405			−0.694138
$669$	3.70807	+	13.8387i	0.143362	+	0.535035i
$670$	−23.1217	+	7.31228i	−0.893268	+	0.282498i
$671$	3.13119	−	3.13119i	0.120878	−	0.120878i
$672$	−3.01458	+	0.807754i	−0.116290	+	0.0311598i
$673$	−3.37878	+	12.6098i	−0.130242	+	0.486071i	−0.999972	−	0.00745690i	$-0.997626\pi$
$673$	−3.37878	+	12.6098i	−0.130242	+	0.486071i	0.869730	+	0.493528i	$0.164293\pi$
$674$	6.84037	−	25.5286i	0.263481	−	0.983326i
$675$	−3.20729	+	3.83579i	−0.123449	+	0.147640i
$676$	−6.39123	−	11.3204i	−0.245816	−	0.435401i
$677$	−30.3858	−	30.3858i	−1.16782	−	1.16782i	−0.982719	−	0.185101i	$-0.940739\pi$
$677$	−30.3858	−	30.3858i	−1.16782	−	1.16782i	−0.185101	−	0.982719i	$-0.559261\pi$
$678$	−3.41585	−	5.91643i	−0.131185	−	0.227219i
$679$	−13.8303	+	7.98490i	−0.530757	+	0.306432i
$680$	0.173535	+	0.0901454i	0.00665476	+	0.00345692i
$681$	−12.0347	−	12.0347i	−0.461169	−	0.461169i
$682$	1.12032	+	0.646819i	0.0428994	+	0.0247680i
$683$	20.2358	+	11.6831i	0.774302	+	0.447043i	0.834407	−	0.551149i	$-0.185810\pi$
$683$	20.2358	+	11.6831i	0.774302	+	0.447043i	−0.0601053	+	0.998192i	$0.519144\pi$
$684$	0.722087	+	0.722087i	0.0276097	+	0.0276097i
$685$	22.6103	−	7.15055i	0.863894	−	0.273208i
$686$	11.5135	−	6.64732i	0.439587	−	0.253796i
$687$	8.36038	+	14.4806i	0.318968	+	0.552469i
$688$	7.12397	+	7.12397i	0.271599	+	0.271599i
$689$	−8.20804	+	30.0529i	−0.312701	+	1.14493i
$690$	−3.56429	+	3.89651i	−0.135690	+	0.148338i
$691$	10.4146	−	38.8677i	0.396189	−	1.47860i	−0.423557	−	0.905869i	$-0.639219\pi$
$691$	10.4146	−	38.8677i	0.396189	−	1.47860i	0.819746	−	0.572727i	$-0.194115\pi$
$692$	0.0850494	−	0.317409i	0.00323309	−	0.0120661i
$693$	−1.96184	+	0.525674i	−0.0745242	+	0.0199687i
$694$	−14.0016	+	14.0016i	−0.531492	+	0.531492i
$695$	−11.0892	−	35.0644i	−0.420637	−	1.33007i
$696$	2.38012	+	8.88272i	0.0902182	+	0.336699i
$697$	0.304454			0.0115320
$698$	−0.0805064	−	0.300454i	−0.00304721	−	0.0113724i
$699$	0.808731	+	1.40076i	0.0305890	+	0.0529817i
$700$	−12.7670	+	8.97259i	−0.482548	+	0.339132i
$701$		−	38.5740i		−	1.45692i	−0.685087	−	0.728461i	$-0.740236\pi$
$701$		−	38.5740i		−	1.45692i	0.685087	−	0.728461i	$-0.259764\pi$
$702$	3.48715	−	0.916397i	0.131614	−	0.0345872i
$703$	−5.48848	+	5.48848i	−0.207002	+	0.207002i
$704$	−0.628610	−	0.168435i	−0.0236916	−	0.00634815i
$705$	5.70522	+	8.93830i	0.214871	+	0.336636i
$706$	25.7121	+	14.8449i	0.967688	+	0.558695i
$707$			12.9643i			0.487573i
$708$	−6.61978	+	11.4658i	−0.248787	+	0.430911i
$709$	21.1704	−	5.67258i	0.795070	−	0.213038i	0.161652	−	0.986848i	$-0.448318\pi$
$709$	21.1704	−	5.67258i	0.795070	−	0.213038i	0.633418	+	0.773810i	$0.281651\pi$
$710$	−30.0829	+	1.33958i	−1.12899	+	0.0502736i
$711$	5.22163	−	9.04413i	0.195827	−	0.339182i
$712$	18.0823	+	4.84513i	0.677662	+	0.181579i
$713$	−4.06557	+	2.34726i	−0.152257	+	0.0879056i
$714$	−0.272936			−0.0102144
$715$	−4.64436	−	2.44107i	−0.173689	−	0.0912907i
$716$	21.9150			0.819001
$717$	−0.228064	+	0.131673i	−0.00851721	+	0.00491742i
$718$	−33.3389	−	8.93314i	−1.24420	−	0.333382i
$719$	−6.82948	+	11.8290i	−0.254697	+	0.441147i	−0.964813	−	0.262937i	$-0.915309\pi$
$719$	−6.82948	+	11.8290i	−0.254697	+	0.441147i	0.710116	+	0.704084i	$0.248642\pi$
$720$	1.50924	−	1.64991i	0.0562459	−	0.0614886i
$721$	37.9045	−	10.1565i	1.41164	−	0.378247i
$722$	−8.97859	+	15.5514i	−0.334149	+	0.578762i
$723$			26.9906i			1.00379i
$724$	−5.29297	−	3.05590i	−0.196712	−	0.113572i
$725$	26.4385	+	37.6191i	0.981902	+	1.39714i
$726$	10.2161	+	2.73739i	0.379155	+	0.101594i
$727$	−25.9287	+	25.9287i	−0.961642	+	0.961642i	−0.999291	−	0.0376492i	$-0.988013\pi$
$727$	−25.9287	+	25.9287i	−0.961642	+	0.961642i	0.0376492	+	0.999291i	$0.488013\pi$
$728$	11.2525	+	0.0542094i	0.417046	+	0.00200913i
$729$			1.00000i			0.0370370i
$730$	1.18187	−	5.35301i	0.0437428	−	0.198124i
$731$	0.440539	+	0.763035i	0.0162939	+	0.0282219i
$732$	−1.76110	−	6.57250i	−0.0650920	−	0.242926i
$733$	−47.7941			−1.76532			−0.882658	−	0.470015i	$-0.844248\pi$
$733$	−47.7941			−1.76532			−0.882658	+	0.470015i	$0.844248\pi$
$734$	−7.97094	−	29.7480i	−0.294213	−	1.09802i
$735$	2.82450	−	5.43733i	0.104183	−	0.200559i
$736$	1.66994	−	1.66994i	0.0615548	−	0.0615548i
$737$	6.81734	−	1.82670i	0.251120	−	0.0672874i
$738$	0.901032	−	3.36270i	0.0331674	−	0.123783i
$739$	8.68070	−	32.3968i	0.319325	−	1.19174i	−0.600571	−	0.799572i	$-0.705060\pi$
$739$	8.68070	−	32.3968i	0.319325	−	1.19174i	0.919895	−	0.392164i	$-0.128273\pi$
$740$	12.5407	+	11.4715i	0.461007	+	0.421700i
$741$	−1.82559	−	3.19748i	−0.0670645	−	0.117462i
$742$	−19.0680	−	19.0680i	−0.700009	−	0.700009i
$743$	−1.89901	−	3.28918i	−0.0696680	−	0.120668i	0.829087	−	0.559119i	$-0.188861\pi$
$743$	−1.89901	−	3.28918i	−0.0696680	−	0.120668i	−0.898755	+	0.438451i	$0.855527\pi$
$744$	1.72150	−	0.993907i	0.0631132	−	0.0364384i
$745$	−14.0656	+	27.0771i	−0.515325	+	0.992028i
$746$	−1.28498	−	1.28498i	−0.0470464	−	0.0470464i
$747$	1.31070	+	0.756731i	0.0479559	+	0.0276873i
$748$	−0.0492884	−	0.0284567i	−0.00180216	−	0.00104048i
$749$	−7.33539	−	7.33539i	−0.268029	−	0.268029i
$750$	4.25165	−	10.3404i	0.155248	−	0.377577i
$751$	−10.6172	+	6.12985i	−0.387428	+	0.223681i	−0.681045	−	0.732242i	$-0.738474\pi$
$751$	−10.6172	+	6.12985i	−0.387428	+	0.223681i	0.293617	+	0.955923i	$0.405141\pi$
$752$	−2.37110	−	4.10687i	−0.0864653	−	0.149762i
$753$	−1.48868	−	1.48868i	−0.0542505	−	0.0542505i
$754$	0.159733	−	33.1565i	0.00581712	−	1.20749i
$755$	−35.7089	+	1.59010i	−1.29958	+	0.0578698i
$756$	−0.807754	+	3.01458i	−0.0293777	+	0.109639i
$757$	0.220783	−	0.823974i	0.00802450	−	0.0299478i	−0.961798	−	0.273762i	$-0.911732\pi$
$757$	0.220783	−	0.823974i	0.00802450	−	0.0299478i	0.969822	+	0.243814i	$0.0783987\pi$
$758$	6.00997	−	1.61037i	0.218292	−	0.0584912i
$759$	1.08677	−	1.08677i	0.0394473	−	0.0394473i
$760$	−2.02635	−	1.05262i	−0.0735034	−	0.0381825i
$761$	3.67773	+	13.7255i	0.133318	+	0.497548i	0.999999	−	0.00131382i	$-0.000418203\pi$
$761$	3.67773	+	13.7255i	0.133318	+	0.497548i	−0.866682	+	0.498862i	$0.833752\pi$
$762$	−5.99600			−0.217212
$763$	9.75473	+	36.4051i	0.353145	+	1.31795i
$764$	2.41078	+	4.17559i	0.0872188	+	0.151067i
$765$	0.164836	−	0.105213i	0.00595965	−	0.00380398i
$766$		−	1.06202i

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.64991 + 1.50924i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.56046 + 2.70280i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.64991 + 1.50924i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-1.56046 + 2.70280i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.18348 - 0.482081i) q^{10} +(0.628610 + 0.168435i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.13115 + 1.78771i) q^{13} -3.12092i q^{14} +(1.20307 + 1.88484i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0226346 - 0.0844736i) q^{17} -1.00000 q^{18} +(0.264302 + 0.986389i) q^{19} +(2.13199 - 0.674247i) q^{20} +(-2.20683 + 2.20683i) q^{21} +(-0.628610 + 0.168435i) q^{22} +(0.611240 - 2.28118i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(0.444415 + 4.98021i) q^{25} +(1.81780 - 3.11378i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.56046 + 2.70280i) q^{28} +(7.96403 - 4.59804i) q^{29} +(-1.98431 - 1.03078i) q^{30} +(-1.40560 - 1.40560i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.563596 + 0.325392i) q^{33} +(0.0618390 + 0.0618390i) q^{34} +(-6.65378 + 2.10427i) q^{35} +(0.866025 - 0.500000i) q^{36} +(3.80043 + 6.58253i) q^{37} +(-0.722087 - 0.722087i) q^{38} +(-3.48715 + 0.916397i) q^{39} +(-1.50924 + 1.64991i) q^{40} +(-0.901032 + 3.36270i) q^{41} +(0.807754 - 3.01458i) q^{42} +(-9.73152 + 2.60755i) q^{43} +(0.460174 - 0.460174i) q^{44} +(0.674247 + 2.13199i) q^{45} +(0.611240 + 2.28118i) q^{46} +4.74221 q^{47} +(-0.258819 - 0.965926i) q^{48} +(-1.37008 - 2.37305i) q^{49} +(-2.87498 - 4.09078i) q^{50} -0.0874535i q^{51} +(-0.0173697 + 3.60551i) q^{52} +(6.10974 - 6.10974i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(0.782942 + 1.22662i) q^{55} +(-2.70280 - 1.56046i) q^{56} +1.02119i q^{57} +(-4.59804 + 7.96403i) q^{58} +(-12.7884 + 3.42665i) q^{59} +(2.23385 - 0.0994727i) q^{60} +(3.40217 - 5.89274i) q^{61} +(1.92008 + 0.514484i) q^{62} +(-2.70280 + 1.56046i) q^{63} -1.00000 q^{64} +(-7.86420 - 1.77607i) q^{65} -0.650785 q^{66} +(9.39213 - 5.42255i) q^{67} +(-0.0844736 - 0.0226346i) q^{68} +(1.18083 - 2.04525i) q^{69} +(4.71021 - 5.14925i) q^{70} +(13.0079 - 3.48547i) q^{71} +(-0.500000 + 0.866025i) q^{72} +2.45159i q^{73} +(-6.58253 - 3.80043i) q^{74} +(-0.859701 + 4.92554i) q^{75} +(0.986389 + 0.264302i) q^{76} +(-1.43617 + 1.43617i) q^{77} +(2.56176 - 2.53720i) q^{78} -10.4433i q^{79} +(0.482081 - 2.18348i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.901032 - 3.36270i) q^{82} +1.51346 q^{83} +(0.807754 + 3.01458i) q^{84} +(0.0901454 - 0.173535i) q^{85} +(7.12397 - 7.12397i) q^{86} +(8.88272 - 2.38012i) q^{87} +(-0.168435 + 0.628610i) q^{88} +(4.84513 - 18.0823i) q^{89} +(-1.64991 - 1.50924i) q^{90} +(0.0542094 - 11.2525i) q^{91} +(-1.66994 - 1.66994i) q^{92} +(-0.993907 - 1.72150i) q^{93} +(-4.10687 + 2.37110i) q^{94} +(-1.05262 + 2.02635i) q^{95} +(0.707107 + 0.707107i) q^{96} +(4.43146 + 2.55851i) q^{97} +(2.37305 + 1.37008i) q^{98} +(0.460174 + 0.460174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7	\( 16 q + 8 q^{4} + 4 q^{5} + 4 q^{7} + 12 q^{11} - 8 q^{13} + 12 q^{15} - 8 q^{16} + 16 q^{17} - 16 q^{18} + 4 q^{19} - 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{25} + 4 q^{26} - 4 q^{28} + 48 q^{29} - 8 q^{30} + 16 q^{31} + 20 q^{34} + 12 q^{35} + 20 q^{37} - 4 q^{38} - 4 q^{39} - 12 q^{41} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 64 q^{47} + 4 q^{49} + 16 q^{50} - 16 q^{52} + 32 q^{53} - 44 q^{55} - 24 q^{56} - 12 q^{58} - 4 q^{59} + 12 q^{60} + 4 q^{61} - 20 q^{62} - 24 q^{63} - 16 q^{64} - 8 q^{65} + 32 q^{66} - 36 q^{67} - 4 q^{68} - 4 q^{69} - 36 q^{71} - 8 q^{72} - 12 q^{74} + 8 q^{76} - 4 q^{77} - 12 q^{78} - 8 q^{80} + 8 q^{81} - 12 q^{82} + 24 q^{83} - 52 q^{85} + 16 q^{86} - 12 q^{87} + 24 q^{89} - 4 q^{90} - 8 q^{92} - 36 q^{94} - 44 q^{95} + 60 q^{97} + 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 + 4 * q^7 + 12 * q^11 - 8 * q^13 + 12 * q^15 - 8 * q^16 + 16 * q^17 - 16 * q^18 + 4 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^25 + 4 * q^26 - 4 * q^28 + 48 * q^29 - 8 * q^30 + 16 * q^31 + 20 * q^34 + 12 * q^35 + 20 * q^37 - 4 * q^38 - 4 * q^39 - 12 * q^41 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 64 * q^47 + 4 * q^49 + 16 * q^50 - 16 * q^52 + 32 * q^53 - 44 * q^55 - 24 * q^56 - 12 * q^58 - 4 * q^59 + 12 * q^60 + 4 * q^61 - 20 * q^62 - 24 * q^63 - 16 * q^64 - 8 * q^65 + 32 * q^66 - 36 * q^67 - 4 * q^68 - 4 * q^69 - 36 * q^71 - 8 * q^72 - 12 * q^74 + 8 * q^76 - 4 * q^77 - 12 * q^78 - 8 * q^80 + 8 * q^81 - 12 * q^82 + 24 * q^83 - 52 * q^85 + 16 * q^86 - 12 * q^87 + 24 * q^89 - 4 * q^90 - 8 * q^92 - 36 * q^94 - 44 * q^95 + 60 * q^97 + 12 * q^99

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