LMFDB - Embedded newform 8034.2.a.bd.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

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:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$16$
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} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.771393$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.771393 q^{5} +1.00000 q^{6} -0.402524 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.771393 q^{5} +1.00000 q^{6} -0.402524 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.771393 q^{10} +3.35736 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.402524 q^{14} +0.771393 q^{15} +1.00000 q^{16} +2.85461 q^{17} +1.00000 q^{18} -3.72414 q^{19} +0.771393 q^{20} -0.402524 q^{21} +3.35736 q^{22} +5.56453 q^{23} +1.00000 q^{24} -4.40495 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.402524 q^{28} -2.56453 q^{29} +0.771393 q^{30} +6.92926 q^{31} +1.00000 q^{32} +3.35736 q^{33} +2.85461 q^{34} -0.310504 q^{35} +1.00000 q^{36} +11.5017 q^{37} -3.72414 q^{38} -1.00000 q^{39} +0.771393 q^{40} -11.1278 q^{41} -0.402524 q^{42} +5.68649 q^{43} +3.35736 q^{44} +0.771393 q^{45} +5.56453 q^{46} +9.60242 q^{47} +1.00000 q^{48} -6.83797 q^{49} -4.40495 q^{50} +2.85461 q^{51} -1.00000 q^{52} +2.39720 q^{53} +1.00000 q^{54} +2.58984 q^{55} -0.402524 q^{56} -3.72414 q^{57} -2.56453 q^{58} -0.522868 q^{59} +0.771393 q^{60} -0.0978037 q^{61} +6.92926 q^{62} -0.402524 q^{63} +1.00000 q^{64} -0.771393 q^{65} +3.35736 q^{66} -12.3133 q^{67} +2.85461 q^{68} +5.56453 q^{69} -0.310504 q^{70} -12.9321 q^{71} +1.00000 q^{72} +10.8718 q^{73} +11.5017 q^{74} -4.40495 q^{75} -3.72414 q^{76} -1.35142 q^{77} -1.00000 q^{78} +16.1740 q^{79} +0.771393 q^{80} +1.00000 q^{81} -11.1278 q^{82} +6.81663 q^{83} -0.402524 q^{84} +2.20202 q^{85} +5.68649 q^{86} -2.56453 q^{87} +3.35736 q^{88} -3.52882 q^{89} +0.771393 q^{90} +0.402524 q^{91} +5.56453 q^{92} +6.92926 q^{93} +9.60242 q^{94} -2.87277 q^{95} +1.00000 q^{96} -7.64481 q^{97} -6.83797 q^{98} +3.35736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.771393	0.344977	0.172489	−	0.985011i	$-0.444819\pi$
$5$	0.771393	0.344977	0.172489	+	0.985011i	$0.444819\pi$
$6$	1.00000	0.408248
$7$	−0.402524	−0.152140	−0.0760699	−	0.997102i	$-0.524237\pi$
$7$	−0.402524	−0.152140	−0.0760699	+	0.997102i	$0.524237\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.771393	0.243936
$11$	3.35736	1.01228	0.506141	−	0.862451i	$-0.331071\pi$
$11$	3.35736	1.01228	0.506141	+	0.862451i	$0.331071\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.402524	−0.107579
$15$	0.771393	0.199173
$16$	1.00000	0.250000
$17$	2.85461	0.692344	0.346172	−	0.938171i	$-0.387481\pi$
$17$	2.85461	0.692344	0.346172	+	0.938171i	$0.387481\pi$
$18$	1.00000	0.235702
$19$	−3.72414	−0.854375	−0.427188	−	0.904163i	$-0.640496\pi$
$19$	−3.72414	−0.854375	−0.427188	+	0.904163i	$0.640496\pi$
$20$	0.771393	0.172489
$21$	−0.402524	−0.0878380
$22$	3.35736	0.715792
$23$	5.56453	1.16028	0.580142	−	0.814515i	$-0.302997\pi$
$23$	5.56453	1.16028	0.580142	+	0.814515i	$0.302997\pi$
$24$	1.00000	0.204124
$25$	−4.40495	−0.880991
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−0.402524	−0.0760699
$29$	−2.56453	−0.476222	−0.238111	−	0.971238i	$-0.576528\pi$
$29$	−2.56453	−0.476222	−0.238111	+	0.971238i	$0.576528\pi$
$30$	0.771393	0.140836
$31$	6.92926	1.24453	0.622266	−	0.782806i	$-0.286212\pi$
$31$	6.92926	1.24453	0.622266	+	0.782806i	$0.286212\pi$
$32$	1.00000	0.176777
$33$	3.35736	0.584441
$34$	2.85461	0.489561
$35$	−0.310504	−0.0524848
$36$	1.00000	0.166667
$37$	11.5017	1.89087	0.945435	−	0.325811i	$-0.105637\pi$
$37$	11.5017	1.89087	0.945435	+	0.325811i	$0.105637\pi$
$38$	−3.72414	−0.604135
$39$	−1.00000	−0.160128
$40$	0.771393	0.121968
$41$	−11.1278	−1.73787	−0.868933	−	0.494929i	$-0.835194\pi$
$41$	−11.1278	−1.73787	−0.868933	+	0.494929i	$0.835194\pi$
$42$	−0.402524	−0.0621108
$43$	5.68649	0.867181	0.433591	−	0.901110i	$-0.357246\pi$
$43$	5.68649	0.867181	0.433591	+	0.901110i	$0.357246\pi$
$44$	3.35736	0.506141
$45$	0.771393	0.114992
$46$	5.56453	0.820445
$47$	9.60242	1.40066	0.700329	−	0.713820i	$-0.253037\pi$
$47$	9.60242	1.40066	0.700329	+	0.713820i	$0.253037\pi$
$48$	1.00000	0.144338
$49$	−6.83797	−0.976853
$50$	−4.40495	−0.622954
$51$	2.85461	0.399725
$52$	−1.00000	−0.138675
$53$	2.39720	0.329280	0.164640	−	0.986354i	$-0.447354\pi$
$53$	2.39720	0.329280	0.164640	+	0.986354i	$0.447354\pi$
$54$	1.00000	0.136083
$55$	2.58984	0.349215
$56$	−0.402524	−0.0537895
$57$	−3.72414	−0.493274
$58$	−2.56453	−0.336740
$59$	−0.522868	−0.0680716	−0.0340358	−	0.999421i	$-0.510836\pi$
$59$	−0.522868	−0.0680716	−0.0340358	+	0.999421i	$0.510836\pi$
$60$	0.771393	0.0995864
$61$	−0.0978037	−0.0125225	−0.00626124	−	0.999980i	$-0.501993\pi$
$61$	−0.0978037	−0.0125225	−0.00626124	+	0.999980i	$0.501993\pi$
$62$	6.92926	0.880017
$63$	−0.402524	−0.0507133
$64$	1.00000	0.125000
$65$	−0.771393	−0.0956795
$66$	3.35736	0.413263
$67$	−12.3133	−1.50430	−0.752152	−	0.658989i	$-0.770984\pi$
$67$	−12.3133	−1.50430	−0.752152	+	0.658989i	$0.770984\pi$
$68$	2.85461	0.346172
$69$	5.56453	0.669890
$70$	−0.310504	−0.0371124
$71$	−12.9321	−1.53476	−0.767381	−	0.641192i	$-0.778440\pi$
$71$	−12.9321	−1.53476	−0.767381	+	0.641192i	$0.778440\pi$
$72$	1.00000	0.117851
$73$	10.8718	1.27244	0.636222	−	0.771506i	$-0.280496\pi$
$73$	10.8718	1.27244	0.636222	+	0.771506i	$0.280496\pi$
$74$	11.5017	1.33705
$75$	−4.40495	−0.508640
$76$	−3.72414	−0.427188
$77$	−1.35142	−0.154008
$78$	−1.00000	−0.113228
$79$	16.1740	1.81972	0.909858	−	0.414920i	$-0.136190\pi$
$79$	16.1740	1.81972	0.909858	+	0.414920i	$0.136190\pi$
$80$	0.771393	0.0862444
$81$	1.00000	0.111111
$82$	−11.1278	−1.22886
$83$	6.81663	0.748222	0.374111	−	0.927384i	$-0.377948\pi$
$83$	6.81663	0.748222	0.374111	+	0.927384i	$0.377948\pi$
$84$	−0.402524	−0.0439190
$85$	2.20202	0.238843
$86$	5.68649	0.613190
$87$	−2.56453	−0.274947
$88$	3.35736	0.357896
$89$	−3.52882	−0.374054	−0.187027	−	0.982355i	$-0.559885\pi$
$89$	−3.52882	−0.374054	−0.187027	+	0.982355i	$0.559885\pi$
$90$	0.771393	0.0813120
$91$	0.402524	0.0421960
$92$	5.56453	0.580142
$93$	6.92926	0.718531
$94$	9.60242	0.990414
$95$	−2.87277	−0.294740
$96$	1.00000	0.102062
$97$	−7.64481	−0.776213	−0.388106	−	0.921615i	$-0.626871\pi$
$97$	−7.64481	−0.776213	−0.388106	+	0.921615i	$0.626871\pi$
$98$	−6.83797	−0.690740
$99$	3.35736	0.337427
$100$	−4.40495	−0.440495
$101$	−8.43758	−0.839570	−0.419785	−	0.907624i	$-0.637895\pi$
$101$	−8.43758	−0.839570	−0.419785	+	0.907624i	$0.637895\pi$
$102$	2.85461	0.282648
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.310504	−0.0303021
$106$	2.39720	0.232836
$107$	18.1722	1.75677	0.878387	−	0.477950i	$-0.158620\pi$
$107$	18.1722	1.75677	0.878387	+	0.477950i	$0.158620\pi$
$108$	1.00000	0.0962250
$109$	15.9210	1.52496	0.762480	−	0.647012i	$-0.223982\pi$
$109$	15.9210	1.52496	0.762480	+	0.647012i	$0.223982\pi$
$110$	2.58984	0.246932
$111$	11.5017	1.09169
$112$	−0.402524	−0.0380349
$113$	−1.58953	−0.149530	−0.0747651	−	0.997201i	$-0.523821\pi$
$113$	−1.58953	−0.149530	−0.0747651	+	0.997201i	$0.523821\pi$
$114$	−3.72414	−0.348797
$115$	4.29244	0.400272
$116$	−2.56453	−0.238111
$117$	−1.00000	−0.0924500
$118$	−0.522868	−0.0481339
$119$	−1.14905	−0.105333
$120$	0.771393	0.0704182
$121$	0.271871	0.0247155
$122$	−0.0978037	−0.00885473
$123$	−11.1278	−1.00336
$124$	6.92926	0.622266
$125$	−7.25491	−0.648899
$126$	−0.402524	−0.0358597
$127$	16.5317	1.46695	0.733476	−	0.679715i	$-0.237897\pi$
$127$	16.5317	1.46695	0.733476	+	0.679715i	$0.237897\pi$
$128$	1.00000	0.0883883
$129$	5.68649	0.500667
$130$	−0.771393	−0.0676556
$131$	−17.2657	−1.50851	−0.754253	−	0.656583i	$-0.772001\pi$
$131$	−17.2657	−1.50851	−0.754253	+	0.656583i	$0.772001\pi$
$132$	3.35736	0.292221
$133$	1.49905	0.129984
$134$	−12.3133	−1.06370
$135$	0.771393	0.0663909
$136$	2.85461	0.244781
$137$	16.6312	1.42090	0.710450	−	0.703747i	$-0.248491\pi$
$137$	16.6312	1.42090	0.710450	+	0.703747i	$0.248491\pi$
$138$	5.56453	0.473684
$139$	6.23877	0.529166	0.264583	−	0.964363i	$-0.414766\pi$
$139$	6.23877	0.529166	0.264583	+	0.964363i	$0.414766\pi$
$140$	−0.310504	−0.0262424
$141$	9.60242	0.808670
$142$	−12.9321	−1.08524
$143$	−3.35736	−0.280757
$144$	1.00000	0.0833333
$145$	−1.97826	−0.164286
$146$	10.8718	0.899754
$147$	−6.83797	−0.563987
$148$	11.5017	0.945435
$149$	−4.30045	−0.352306	−0.176153	−	0.984363i	$-0.556365\pi$
$149$	−4.30045	−0.352306	−0.176153	+	0.984363i	$0.556365\pi$
$150$	−4.40495	−0.359663
$151$	9.02108	0.734125	0.367063	−	0.930196i	$-0.380363\pi$
$151$	9.02108	0.734125	0.367063	+	0.930196i	$0.380363\pi$
$152$	−3.72414	−0.302067
$153$	2.85461	0.230781
$154$	−1.35142	−0.108900
$155$	5.34518	0.429336
$156$	−1.00000	−0.0800641
$157$	−17.8257	−1.42264	−0.711322	−	0.702866i	$-0.751903\pi$
$157$	−17.8257	−1.42264	−0.711322	+	0.702866i	$0.751903\pi$
$158$	16.1740	1.28673
$159$	2.39720	0.190110
$160$	0.771393	0.0609840
$161$	−2.23986	−0.176525
$162$	1.00000	0.0785674
$163$	14.3933	1.12737	0.563685	−	0.825990i	$-0.309383\pi$
$163$	14.3933	1.12737	0.563685	+	0.825990i	$0.309383\pi$
$164$	−11.1278	−0.868933
$165$	2.58984	0.201619
$166$	6.81663	0.529073
$167$	−8.53020	−0.660086	−0.330043	−	0.943966i	$-0.607063\pi$
$167$	−8.53020	−0.660086	−0.330043	+	0.943966i	$0.607063\pi$
$168$	−0.402524	−0.0310554
$169$	1.00000	0.0769231
$170$	2.20202	0.168887
$171$	−3.72414	−0.284792
$172$	5.68649	0.433591
$173$	0.467602	0.0355511	0.0177756	−	0.999842i	$-0.494342\pi$
$173$	0.467602	0.0355511	0.0177756	+	0.999842i	$0.494342\pi$
$174$	−2.56453	−0.194417
$175$	1.77310	0.134034
$176$	3.35736	0.253071
$177$	−0.522868	−0.0393011
$178$	−3.52882	−0.264496
$179$	−21.5173	−1.60828	−0.804138	−	0.594443i	$-0.797373\pi$
$179$	−21.5173	−1.60828	−0.804138	+	0.594443i	$0.797373\pi$
$180$	0.771393	0.0574962
$181$	6.66087	0.495099	0.247549	−	0.968875i	$-0.420375\pi$
$181$	6.66087	0.495099	0.247549	+	0.968875i	$0.420375\pi$
$182$	0.402524	0.0298371
$183$	−0.0978037	−0.00722986
$184$	5.56453	0.410222
$185$	8.87234	0.652307
$186$	6.92926	0.508078
$187$	9.58394	0.700847
$188$	9.60242	0.700329
$189$	−0.402524	−0.0292793
$190$	−2.87277	−0.208413
$191$	−7.82053	−0.565874	−0.282937	−	0.959138i	$-0.591309\pi$
$191$	−7.82053	−0.565874	−0.282937	+	0.959138i	$0.591309\pi$
$192$	1.00000	0.0721688
$193$	−19.0780	−1.37326	−0.686632	−	0.727006i	$-0.740911\pi$
$193$	−19.0780	−1.37326	−0.686632	+	0.727006i	$0.740911\pi$
$194$	−7.64481	−0.548865
$195$	−0.771393	−0.0552406
$196$	−6.83797	−0.488427
$197$	10.1609	0.723932	0.361966	−	0.932191i	$-0.382106\pi$
$197$	10.1609	0.723932	0.361966	+	0.932191i	$0.382106\pi$
$198$	3.35736	0.238597
$199$	2.80558	0.198882	0.0994412	−	0.995043i	$-0.468294\pi$
$199$	2.80558	0.198882	0.0994412	+	0.995043i	$0.468294\pi$
$200$	−4.40495	−0.311477
$201$	−12.3133	−0.868511
$202$	−8.43758	−0.593666
$203$	1.03229	0.0724523
$204$	2.85461	0.199862
$205$	−8.58389	−0.599525
$206$	1.00000	0.0696733
$207$	5.56453	0.386761
$208$	−1.00000	−0.0693375
$209$	−12.5033	−0.864869
$210$	−0.310504	−0.0214268
$211$	−4.27406	−0.294239	−0.147119	−	0.989119i	$-0.547000\pi$
$211$	−4.27406	−0.294239	−0.147119	+	0.989119i	$0.547000\pi$
$212$	2.39720	0.164640
$213$	−12.9321	−0.886095
$214$	18.1722	1.24223
$215$	4.38652	0.299158
$216$	1.00000	0.0680414
$217$	−2.78919	−0.189343
$218$	15.9210	1.07831
$219$	10.8718	0.734646
$220$	2.58984	0.174607
$221$	−2.85461	−0.192022
$222$	11.5017	0.771945
$223$	24.4874	1.63980	0.819899	−	0.572508i	$-0.194029\pi$
$223$	24.4874	1.63980	0.819899	+	0.572508i	$0.194029\pi$
$224$	−0.402524	−0.0268948
$225$	−4.40495	−0.293664
$226$	−1.58953	−0.105734
$227$	−8.77108	−0.582157	−0.291078	−	0.956699i	$-0.594014\pi$
$227$	−8.77108	−0.582157	−0.291078	+	0.956699i	$0.594014\pi$
$228$	−3.72414	−0.246637
$229$	−29.3151	−1.93720	−0.968598	−	0.248632i	$-0.920019\pi$
$229$	−29.3151	−1.93720	−0.968598	+	0.248632i	$0.920019\pi$
$230$	4.29244	0.283035
$231$	−1.35142	−0.0889168
$232$	−2.56453	−0.168370
$233$	−4.88223	−0.319846	−0.159923	−	0.987130i	$-0.551125\pi$
$233$	−4.88223	−0.319846	−0.159923	+	0.987130i	$0.551125\pi$
$234$	−1.00000	−0.0653720
$235$	7.40724	0.483195
$236$	−0.522868	−0.0340358
$237$	16.1740	1.05061
$238$	−1.14905	−0.0744817
$239$	−4.81232	−0.311283	−0.155642	−	0.987814i	$-0.549745\pi$
$239$	−4.81232	−0.311283	−0.155642	+	0.987814i	$0.549745\pi$
$240$	0.771393	0.0497932
$241$	1.82780	0.117739	0.0588696	−	0.998266i	$-0.481250\pi$
$241$	1.82780	0.117739	0.0588696	+	0.998266i	$0.481250\pi$
$242$	0.271871	0.0174765
$243$	1.00000	0.0641500
$244$	−0.0978037	−0.00626124
$245$	−5.27477	−0.336992
$246$	−11.1278	−0.709481
$247$	3.72414	0.236961
$248$	6.92926	0.440009
$249$	6.81663	0.431986
$250$	−7.25491	−0.458841
$251$	20.0894	1.26803	0.634016	−	0.773320i	$-0.281405\pi$
$251$	20.0894	1.26803	0.634016	+	0.773320i	$0.281405\pi$
$252$	−0.402524	−0.0253566
$253$	18.6821	1.17454
$254$	16.5317	1.03729
$255$	2.20202	0.137896
$256$	1.00000	0.0625000
$257$	19.7037	1.22908	0.614542	−	0.788884i	$-0.289341\pi$
$257$	19.7037	1.22908	0.614542	+	0.788884i	$0.289341\pi$
$258$	5.68649	0.354025
$259$	−4.62972	−0.287677
$260$	−0.771393	−0.0478398
$261$	−2.56453	−0.158741
$262$	−17.2657	−1.06668
$263$	−23.1100	−1.42502	−0.712511	−	0.701661i	$-0.752442\pi$
$263$	−23.1100	−1.42502	−0.712511	+	0.701661i	$0.752442\pi$
$264$	3.35736	0.206631
$265$	1.84918	0.113594
$266$	1.49905	0.0919129
$267$	−3.52882	−0.215960
$268$	−12.3133	−0.752152
$269$	18.8960	1.15211	0.576056	−	0.817410i	$-0.304591\pi$
$269$	18.8960	1.15211	0.576056	+	0.817410i	$0.304591\pi$
$270$	0.771393	0.0469455
$271$	−27.6901	−1.68205	−0.841027	−	0.540993i	$-0.818048\pi$
$271$	−27.6901	−1.68205	−0.841027	+	0.540993i	$0.818048\pi$
$272$	2.85461	0.173086
$273$	0.402524	0.0243619
$274$	16.6312	1.00473
$275$	−14.7890	−0.891811
$276$	5.56453	0.334945
$277$	7.72449	0.464120	0.232060	−	0.972701i	$-0.425453\pi$
$277$	7.72449	0.464120	0.232060	+	0.972701i	$0.425453\pi$
$278$	6.23877	0.374177
$279$	6.92926	0.414844
$280$	−0.310504	−0.0185562
$281$	17.2366	1.02825	0.514124	−	0.857716i	$-0.328117\pi$
$281$	17.2366	1.02825	0.514124	+	0.857716i	$0.328117\pi$
$282$	9.60242	0.571816
$283$	1.02992	0.0612223	0.0306111	−	0.999531i	$-0.490255\pi$
$283$	1.02992	0.0612223	0.0306111	+	0.999531i	$0.490255\pi$
$284$	−12.9321	−0.767381
$285$	−2.87277	−0.170168
$286$	−3.35736	−0.198525
$287$	4.47920	0.264399
$288$	1.00000	0.0589256
$289$	−8.85122	−0.520660
$290$	−1.97826	−0.116168
$291$	−7.64481	−0.448147
$292$	10.8718	0.636222
$293$	23.5939	1.37837	0.689186	−	0.724585i	$-0.257968\pi$
$293$	23.5939	1.37837	0.689186	+	0.724585i	$0.257968\pi$
$294$	−6.83797	−0.398799
$295$	−0.403336	−0.0234831
$296$	11.5017	0.668524
$297$	3.35736	0.194814
$298$	−4.30045	−0.249118
$299$	−5.56453	−0.321805
$300$	−4.40495	−0.254320
$301$	−2.28895	−0.131933
$302$	9.02108	0.519105
$303$	−8.43758	−0.484726
$304$	−3.72414	−0.213594
$305$	−0.0754451	−0.00431997
$306$	2.85461	0.163187
$307$	−33.2668	−1.89864	−0.949318	−	0.314318i	$-0.898224\pi$
$307$	−33.2668	−1.89864	−0.949318	+	0.314318i	$0.898224\pi$
$308$	−1.35142	−0.0770042
$309$	1.00000	0.0568880
$310$	5.34518	0.303586
$311$	19.9637	1.13204	0.566020	−	0.824391i	$-0.308482\pi$
$311$	19.9637	1.13204	0.566020	+	0.824391i	$0.308482\pi$
$312$	−1.00000	−0.0566139
$313$	−32.6475	−1.84535	−0.922674	−	0.385581i	$-0.874001\pi$
$313$	−32.6475	−1.84535	−0.922674	+	0.385581i	$0.874001\pi$
$314$	−17.8257	−1.00596
$315$	−0.310504	−0.0174949
$316$	16.1740	0.909858
$317$	24.3086	1.36531	0.682654	−	0.730742i	$-0.260826\pi$
$317$	24.3086	1.36531	0.682654	+	0.730742i	$0.260826\pi$
$318$	2.39720	0.134428
$319$	−8.61006	−0.482071
$320$	0.771393	0.0431222
$321$	18.1722	1.01427
$322$	−2.23986	−0.124822
$323$	−10.6309	−0.591521
$324$	1.00000	0.0555556
$325$	4.40495	0.244343
$326$	14.3933	0.797171
$327$	15.9210	0.880436
$328$	−11.1278	−0.614429
$329$	−3.86521	−0.213096
$330$	2.58984	0.142566
$331$	13.2108	0.726133	0.363067	−	0.931763i	$-0.381730\pi$
$331$	13.2108	0.726133	0.363067	+	0.931763i	$0.381730\pi$
$332$	6.81663	0.374111
$333$	11.5017	0.630290
$334$	−8.53020	−0.466752
$335$	−9.49837	−0.518951
$336$	−0.402524	−0.0219595
$337$	7.56201	0.411929	0.205965	−	0.978559i	$-0.433967\pi$
$337$	7.56201	0.411929	0.205965	+	0.978559i	$0.433967\pi$
$338$	1.00000	0.0543928
$339$	−1.58953	−0.0863313
$340$	2.20202	0.119421
$341$	23.2640	1.25982
$342$	−3.72414	−0.201378
$343$	5.57012	0.300758
$344$	5.68649	0.306595
$345$	4.29244	0.231097
$346$	0.467602	0.0251385
$347$	9.34550	0.501693	0.250846	−	0.968027i	$-0.419291\pi$
$347$	9.34550	0.501693	0.250846	+	0.968027i	$0.419291\pi$
$348$	−2.56453	−0.137473
$349$	2.56548	0.137327	0.0686634	−	0.997640i	$-0.478127\pi$
$349$	2.56548	0.137327	0.0686634	+	0.997640i	$0.478127\pi$
$350$	1.77310	0.0947762
$351$	−1.00000	−0.0533761
$352$	3.35736	0.178948
$353$	5.01608	0.266979	0.133490	−	0.991050i	$-0.457382\pi$
$353$	5.01608	0.266979	0.133490	+	0.991050i	$0.457382\pi$
$354$	−0.522868	−0.0277901
$355$	−9.97575	−0.529458
$356$	−3.52882	−0.187027
$357$	−1.14905	−0.0608141
$358$	−21.5173	−1.13722
$359$	−3.88039	−0.204799	−0.102400	−	0.994743i	$-0.532652\pi$
$359$	−3.88039	−0.204799	−0.102400	+	0.994743i	$0.532652\pi$
$360$	0.771393	0.0406560
$361$	−5.13082	−0.270043
$362$	6.66087	0.350088
$363$	0.271871	0.0142695
$364$	0.402524	0.0210980
$365$	8.38640	0.438964
$366$	−0.0978037	−0.00511228
$367$	1.49498	0.0780372	0.0390186	−	0.999238i	$-0.487577\pi$
$367$	1.49498	0.0780372	0.0390186	+	0.999238i	$0.487577\pi$
$368$	5.56453	0.290071
$369$	−11.1278	−0.579289
$370$	8.87234	0.461251
$371$	−0.964929	−0.0500966
$372$	6.92926	0.359266
$373$	8.12123	0.420502	0.210251	−	0.977647i	$-0.432572\pi$
$373$	8.12123	0.420502	0.210251	+	0.977647i	$0.432572\pi$
$374$	9.58394	0.495574
$375$	−7.25491	−0.374642
$376$	9.60242	0.495207
$377$	2.56453	0.132080
$378$	−0.402524	−0.0207036
$379$	−31.6411	−1.62529	−0.812647	−	0.582756i	$-0.801974\pi$
$379$	−31.6411	−1.62529	−0.812647	+	0.582756i	$0.801974\pi$
$380$	−2.87277	−0.147370
$381$	16.5317	0.846945
$382$	−7.82053	−0.400133
$383$	12.5504	0.641296	0.320648	−	0.947198i	$-0.396099\pi$
$383$	12.5504	0.641296	0.320648	+	0.947198i	$0.396099\pi$
$384$	1.00000	0.0510310
$385$	−1.04247	−0.0531294
$386$	−19.0780	−0.971044
$387$	5.68649	0.289060
$388$	−7.64481	−0.388106
$389$	−32.9392	−1.67008	−0.835042	−	0.550186i	$-0.814557\pi$
$389$	−32.9392	−1.67008	−0.835042	+	0.550186i	$0.814557\pi$
$390$	−0.771393	−0.0390610
$391$	15.8845	0.803316
$392$	−6.83797	−0.345370
$393$	−17.2657	−0.870937
$394$	10.1609	0.511897
$395$	12.4765	0.627761
$396$	3.35736	0.168714
$397$	−26.8250	−1.34631	−0.673155	−	0.739502i	$-0.735061\pi$
$397$	−26.8250	−1.34631	−0.673155	+	0.739502i	$0.735061\pi$
$398$	2.80558	0.140631
$399$	1.49905	0.0750466
$400$	−4.40495	−0.220248
$401$	6.91974	0.345555	0.172778	−	0.984961i	$-0.444726\pi$
$401$	6.91974	0.345555	0.172778	+	0.984961i	$0.444726\pi$
$402$	−12.3133	−0.614130
$403$	−6.92926	−0.345171
$404$	−8.43758	−0.419785
$405$	0.771393	0.0383308
$406$	1.03229	0.0512315
$407$	38.6154	1.91409
$408$	2.85461	0.141324
$409$	16.5757	0.819615	0.409807	−	0.912172i	$-0.365596\pi$
$409$	16.5757	0.819615	0.409807	+	0.912172i	$0.365596\pi$
$410$	−8.58389	−0.423928
$411$	16.6312	0.820357
$412$	1.00000	0.0492665
$413$	0.210467	0.0103564
$414$	5.56453	0.273482
$415$	5.25830	0.258120
$416$	−1.00000	−0.0490290
$417$	6.23877	0.305514
$418$	−12.5033	−0.611555
$419$	26.4338	1.29137	0.645687	−	0.763602i	$-0.276571\pi$
$419$	26.4338	1.29137	0.645687	+	0.763602i	$0.276571\pi$
$420$	−0.310504	−0.0151511
$421$	0.719679	0.0350750	0.0175375	−	0.999846i	$-0.494417\pi$
$421$	0.719679	0.0350750	0.0175375	+	0.999846i	$0.494417\pi$
$422$	−4.27406	−0.208058
$423$	9.60242	0.466886
$424$	2.39720	0.116418
$425$	−12.5744	−0.609948
$426$	−12.9321	−0.626564
$427$	0.0393684	0.00190517
$428$	18.1722	0.878387
$429$	−3.35736	−0.162095
$430$	4.38652	0.211537
$431$	−26.7745	−1.28968	−0.644842	−	0.764316i	$-0.723077\pi$
$431$	−26.7745	−1.28968	−0.644842	+	0.764316i	$0.723077\pi$
$432$	1.00000	0.0481125
$433$	26.4211	1.26972	0.634858	−	0.772628i	$-0.281058\pi$
$433$	26.4211	1.26972	0.634858	+	0.772628i	$0.281058\pi$
$434$	−2.78919	−0.133886
$435$	−1.97826	−0.0948504
$436$	15.9210	0.762480
$437$	−20.7231	−0.991318
$438$	10.8718	0.519473
$439$	−28.4512	−1.35790	−0.678950	−	0.734184i	$-0.737565\pi$
$439$	−28.4512	−1.35790	−0.678950	+	0.734184i	$0.737565\pi$
$440$	2.58984	0.123466
$441$	−6.83797	−0.325618
$442$	−2.85461	−0.135780
$443$	−16.8823	−0.802100	−0.401050	−	0.916056i	$-0.631355\pi$
$443$	−16.8823	−0.802100	−0.401050	+	0.916056i	$0.631355\pi$
$444$	11.5017	0.545847
$445$	−2.72211	−0.129040
$446$	24.4874	1.15951
$447$	−4.30045	−0.203404
$448$	−0.402524	−0.0190175
$449$	−1.15814	−0.0546562	−0.0273281	−	0.999627i	$-0.508700\pi$
$449$	−1.15814	−0.0546562	−0.0273281	+	0.999627i	$0.508700\pi$
$450$	−4.40495	−0.207651
$451$	−37.3600	−1.75921
$452$	−1.58953	−0.0747651
$453$	9.02108	0.423847
$454$	−8.77108	−0.411647
$455$	0.310504	0.0145567
$456$	−3.72414	−0.174399
$457$	21.7990	1.01971	0.509857	−	0.860259i	$-0.329698\pi$
$457$	21.7990	1.01971	0.509857	+	0.860259i	$0.329698\pi$
$458$	−29.3151	−1.36980
$459$	2.85461	0.133242
$460$	4.29244	0.200136
$461$	−3.69683	−0.172179	−0.0860894	−	0.996287i	$-0.527437\pi$
$461$	−3.69683	−0.172179	−0.0860894	+	0.996287i	$0.527437\pi$
$462$	−1.35142	−0.0628737
$463$	−13.8870	−0.645383	−0.322692	−	0.946504i	$-0.604588\pi$
$463$	−13.8870	−0.645383	−0.322692	+	0.946504i	$0.604588\pi$
$464$	−2.56453	−0.119055
$465$	5.34518	0.247877
$466$	−4.88223	−0.226165
$467$	19.3950	0.897494	0.448747	−	0.893659i	$-0.351870\pi$
$467$	19.3950	0.897494	0.448747	+	0.893659i	$0.351870\pi$
$468$	−1.00000	−0.0462250
$469$	4.95639	0.228865
$470$	7.40724	0.341671
$471$	−17.8257	−0.821364
$472$	−0.522868	−0.0240669
$473$	19.0916	0.877833
$474$	16.1740	0.742896
$475$	16.4046	0.752697
$476$	−1.14905	−0.0526665
$477$	2.39720	0.109760
$478$	−4.81232	−0.220111
$479$	−27.4774	−1.25548	−0.627738	−	0.778425i	$-0.716019\pi$
$479$	−27.4774	−1.25548	−0.627738	+	0.778425i	$0.716019\pi$
$480$	0.771393	0.0352091
$481$	−11.5017	−0.524433
$482$	1.82780	0.0832541
$483$	−2.23986	−0.101917
$484$	0.271871	0.0123578
$485$	−5.89715	−0.267776
$486$	1.00000	0.0453609
$487$	5.39111	0.244294	0.122147	−	0.992512i	$-0.461022\pi$
$487$	5.39111	0.244294	0.122147	+	0.992512i	$0.461022\pi$
$488$	−0.0978037	−0.00442737
$489$	14.3933	0.650887
$490$	−5.27477	−0.238290
$491$	17.4945	0.789516	0.394758	−	0.918785i	$-0.370829\pi$
$491$	17.4945	0.789516	0.394758	+	0.918785i	$0.370829\pi$
$492$	−11.1278	−0.501679
$493$	−7.32073	−0.329709
$494$	3.72414	0.167557
$495$	2.58984	0.116405
$496$	6.92926	0.311133
$497$	5.20549	0.233498
$498$	6.81663	0.305460
$499$	−36.5626	−1.63677	−0.818383	−	0.574674i	$-0.805129\pi$
$499$	−36.5626	−1.63677	−0.818383	+	0.574674i	$0.805129\pi$
$500$	−7.25491	−0.324450
$501$	−8.53020	−0.381101
$502$	20.0894	0.896634
$503$	29.9793	1.33671	0.668356	−	0.743842i	$-0.266998\pi$
$503$	29.9793	1.33671	0.668356	+	0.743842i	$0.266998\pi$
$504$	−0.402524	−0.0179298
$505$	−6.50869	−0.289633
$506$	18.6821	0.830522
$507$	1.00000	0.0444116
$508$	16.5317	0.733476
$509$	−41.5615	−1.84218	−0.921090	−	0.389350i	$-0.872700\pi$
$509$	−41.5615	−1.84218	−0.921090	+	0.389350i	$0.872700\pi$
$510$	2.20202	0.0975072
$511$	−4.37615	−0.193589
$512$	1.00000	0.0441942
$513$	−3.72414	−0.164425
$514$	19.7037	0.869094
$515$	0.771393	0.0339916
$516$	5.68649	0.250334
$517$	32.2388	1.41786
$518$	−4.62972	−0.203418
$519$	0.467602	0.0205255
$520$	−0.771393	−0.0338278
$521$	−24.2873	−1.06405	−0.532023	−	0.846730i	$-0.678568\pi$
$521$	−24.2873	−1.06405	−0.532023	+	0.846730i	$0.678568\pi$
$522$	−2.56453	−0.112247
$523$	−14.5995	−0.638393	−0.319197	−	0.947689i	$-0.603413\pi$
$523$	−14.5995	−0.638393	−0.319197	+	0.947689i	$0.603413\pi$
$524$	−17.2657	−0.754253
$525$	1.77310	0.0773844
$526$	−23.1100	−1.00764
$527$	19.7803	0.861644
$528$	3.35736	0.146110
$529$	7.96397	0.346260
$530$	1.84918	0.0803233
$531$	−0.522868	−0.0226905
$532$	1.49905	0.0649922
$533$	11.1278	0.481997
$534$	−3.52882	−0.152707
$535$	14.0179	0.606047
$536$	−12.3133	−0.531852
$537$	−21.5173	−0.928538
$538$	18.8960	0.814666
$539$	−22.9575	−0.988852
$540$	0.771393	0.0331955
$541$	16.1431	0.694047	0.347023	−	0.937856i	$-0.387192\pi$
$541$	16.1431	0.694047	0.347023	+	0.937856i	$0.387192\pi$
$542$	−27.6901	−1.18939
$543$	6.66087	0.285845
$544$	2.85461	0.122390
$545$	12.2814	0.526077
$546$	0.402524	0.0172264
$547$	21.2076	0.906773	0.453386	−	0.891314i	$-0.350216\pi$
$547$	21.2076	0.906773	0.453386	+	0.891314i	$0.350216\pi$
$548$	16.6312	0.710450
$549$	−0.0978037	−0.00417416
$550$	−14.7890	−0.630606
$551$	9.55067	0.406872
$552$	5.56453	0.236842
$553$	−6.51042	−0.276851
$554$	7.72449	0.328182
$555$	8.87234	0.376610
$556$	6.23877	0.264583
$557$	13.6757	0.579460	0.289730	−	0.957108i	$-0.406435\pi$
$557$	13.6757	0.579460	0.289730	+	0.957108i	$0.406435\pi$
$558$	6.92926	0.293339
$559$	−5.68649	−0.240513
$560$	−0.310504	−0.0131212
$561$	9.58394	0.404634
$562$	17.2366	0.727081
$563$	−26.5422	−1.11862	−0.559309	−	0.828959i	$-0.688934\pi$
$563$	−26.5422	−1.11862	−0.559309	+	0.828959i	$0.688934\pi$
$564$	9.60242	0.404335
$565$	−1.22615	−0.0515845
$566$	1.02992	0.0432907
$567$	−0.402524	−0.0169044
$568$	−12.9321	−0.542620
$569$	−3.77157	−0.158112	−0.0790562	−	0.996870i	$-0.525191\pi$
$569$	−3.77157	−0.158112	−0.0790562	+	0.996870i	$0.525191\pi$
$570$	−2.87277	−0.120327
$571$	−3.49122	−0.146103	−0.0730515	−	0.997328i	$-0.523274\pi$
$571$	−3.49122	−0.146103	−0.0730515	+	0.997328i	$0.523274\pi$
$572$	−3.35736	−0.140378
$573$	−7.82053	−0.326708
$574$	4.47920	0.186958
$575$	−24.5115	−1.02220
$576$	1.00000	0.0416667
$577$	−27.1025	−1.12829	−0.564145	−	0.825676i	$-0.690794\pi$
$577$	−27.1025	−1.12829	−0.564145	+	0.825676i	$0.690794\pi$
$578$	−8.85122	−0.368162
$579$	−19.0780	−0.792854
$580$	−1.97826	−0.0821429
$581$	−2.74386	−0.113834
$582$	−7.64481	−0.316887
$583$	8.04825	0.333325
$584$	10.8718	0.449877
$585$	−0.771393	−0.0318932
$586$	23.5939	0.974656
$587$	26.4415	1.09136	0.545679	−	0.837994i	$-0.316272\pi$
$587$	26.4415	1.09136	0.545679	+	0.837994i	$0.316272\pi$
$588$	−6.83797	−0.281993
$589$	−25.8055	−1.06330
$590$	−0.403336	−0.0166051
$591$	10.1609	0.417962
$592$	11.5017	0.472718
$593$	7.90679	0.324693	0.162347	−	0.986734i	$-0.448094\pi$
$593$	7.90679	0.324693	0.162347	+	0.986734i	$0.448094\pi$
$594$	3.35736	0.137754
$595$	−0.886367	−0.0363375
$596$	−4.30045	−0.176153
$597$	2.80558	0.114825
$598$	−5.56453	−0.227550
$599$	−31.7165	−1.29590	−0.647951	−	0.761682i	$-0.724374\pi$
$599$	−31.7165	−1.29590	−0.647951	+	0.761682i	$0.724374\pi$
$600$	−4.40495	−0.179831
$601$	−36.0341	−1.46986	−0.734931	−	0.678142i	$-0.762785\pi$
$601$	−36.0341	−1.46986	−0.734931	+	0.678142i	$0.762785\pi$
$602$	−2.28895	−0.0932906
$603$	−12.3133	−0.501435
$604$	9.02108	0.367063
$605$	0.209719	0.00852630
$606$	−8.43758	−0.342753
$607$	1.23799	0.0502483	0.0251242	−	0.999684i	$-0.492002\pi$
$607$	1.23799	0.0502483	0.0251242	+	0.999684i	$0.492002\pi$
$608$	−3.72414	−0.151034
$609$	1.03229	0.0418303
$610$	−0.0754451	−0.00305468
$611$	−9.60242	−0.388472
$612$	2.85461	0.115391
$613$	−12.5665	−0.507557	−0.253779	−	0.967262i	$-0.581673\pi$
$613$	−12.5665	−0.507557	−0.253779	+	0.967262i	$0.581673\pi$
$614$	−33.2668	−1.34254
$615$	−8.58389	−0.346136
$616$	−1.35142	−0.0544502
$617$	30.5504	1.22991	0.614957	−	0.788561i	$-0.289173\pi$
$617$	30.5504	1.22991	0.614957	+	0.788561i	$0.289173\pi$
$618$	1.00000	0.0402259
$619$	15.5322	0.624292	0.312146	−	0.950034i	$-0.398952\pi$
$619$	15.5322	0.624292	0.312146	+	0.950034i	$0.398952\pi$
$620$	5.34518	0.214668
$621$	5.56453	0.223297
$622$	19.9637	0.800473
$623$	1.42044	0.0569085
$624$	−1.00000	−0.0400320
$625$	16.4284	0.657135
$626$	−32.6475	−1.30486
$627$	−12.5033	−0.499332
$628$	−17.8257	−0.711322
$629$	32.8329	1.30913
$630$	−0.310504	−0.0123708
$631$	−1.11244	−0.0442857	−0.0221429	−	0.999755i	$-0.507049\pi$
$631$	−1.11244	−0.0442857	−0.0221429	+	0.999755i	$0.507049\pi$
$632$	16.1740	0.643367
$633$	−4.27406	−0.169879
$634$	24.3086	0.965418
$635$	12.7524	0.506065
$636$	2.39720	0.0950550
$637$	6.83797	0.270930
$638$	−8.61006	−0.340876
$639$	−12.9321	−0.511587
$640$	0.771393	0.0304920
$641$	31.3416	1.23792	0.618960	−	0.785422i	$-0.287554\pi$
$641$	31.3416	1.23792	0.618960	+	0.785422i	$0.287554\pi$
$642$	18.1722	0.717200
$643$	4.90261	0.193340	0.0966700	−	0.995316i	$-0.469181\pi$
$643$	4.90261	0.193340	0.0966700	+	0.995316i	$0.469181\pi$
$644$	−2.23986	−0.0882627
$645$	4.38652	0.172719
$646$	−10.6309	−0.418269
$647$	−45.6755	−1.79569	−0.897844	−	0.440314i	$-0.854867\pi$
$647$	−45.6755	−1.79569	−0.897844	+	0.440314i	$0.854867\pi$
$648$	1.00000	0.0392837
$649$	−1.75545	−0.0689076
$650$	4.40495	0.172776
$651$	−2.78919	−0.109317
$652$	14.3933	0.563685
$653$	−36.2253	−1.41761	−0.708803	−	0.705407i	$-0.750764\pi$
$653$	−36.2253	−1.41761	−0.708803	+	0.705407i	$0.750764\pi$
$654$	15.9210	0.622562
$655$	−13.3186	−0.520401
$656$	−11.1278	−0.434467
$657$	10.8718	0.424148
$658$	−3.86521	−0.150681
$659$	−39.6812	−1.54576	−0.772880	−	0.634552i	$-0.781184\pi$
$659$	−39.6812	−1.54576	−0.772880	+	0.634552i	$0.781184\pi$
$660$	2.58984	0.100810
$661$	41.1597	1.60093	0.800463	−	0.599382i	$-0.204587\pi$
$661$	41.1597	1.60093	0.800463	+	0.599382i	$0.204587\pi$
$662$	13.2108	0.513454
$663$	−2.85461	−0.110864
$664$	6.81663	0.264537
$665$	1.15636	0.0448417
$666$	11.5017	0.445682
$667$	−14.2704	−0.552553
$668$	−8.53020	−0.330043
$669$	24.4874	0.946738
$670$	−9.49837	−0.366954
$671$	−0.328362	−0.0126763
$672$	−0.402524	−0.0155277
$673$	−18.2563	−0.703729	−0.351865	−	0.936051i	$-0.614452\pi$
$673$	−18.2563	−0.703729	−0.351865	+	0.936051i	$0.614452\pi$
$674$	7.56201	0.291278
$675$	−4.40495	−0.169547
$676$	1.00000	0.0384615
$677$	−24.7377	−0.950748	−0.475374	−	0.879784i	$-0.657687\pi$
$677$	−24.7377	−0.950748	−0.475374	+	0.879784i	$0.657687\pi$
$678$	−1.58953	−0.0610454
$679$	3.07722	0.118093
$680$	2.20202	0.0844437
$681$	−8.77108	−0.336108
$682$	23.2640	0.890826
$683$	13.3735	0.511722	0.255861	−	0.966714i	$-0.417641\pi$
$683$	13.3735	0.511722	0.255861	+	0.966714i	$0.417641\pi$
$684$	−3.72414	−0.142396
$685$	12.8292	0.490179
$686$	5.57012	0.212668
$687$	−29.3151	−1.11844
$688$	5.68649	0.216795
$689$	−2.39720	−0.0913259
$690$	4.29244	0.163410
$691$	−37.9948	−1.44539	−0.722695	−	0.691167i	$-0.757097\pi$
$691$	−37.9948	−1.44539	−0.722695	+	0.691167i	$0.757097\pi$
$692$	0.467602	0.0177756
$693$	−1.35142	−0.0513361
$694$	9.34550	0.354750
$695$	4.81255	0.182550
$696$	−2.56453	−0.0972083
$697$	−31.7654	−1.20320
$698$	2.56548	0.0971047
$699$	−4.88223	−0.184663
$700$	1.77310	0.0670169
$701$	−1.03427	−0.0390638	−0.0195319	−	0.999809i	$-0.506218\pi$
$701$	−1.03427	−0.0390638	−0.0195319	+	0.999809i	$0.506218\pi$
$702$	−1.00000	−0.0377426
$703$	−42.8339	−1.61551
$704$	3.35736	0.126535
$705$	7.40724	0.278973
$706$	5.01608	0.188783
$707$	3.39633	0.127732
$708$	−0.522868	−0.0196506
$709$	−33.3036	−1.25074	−0.625372	−	0.780327i	$-0.715053\pi$
$709$	−33.3036	−1.25074	−0.625372	+	0.780327i	$0.715053\pi$
$710$	−9.97575	−0.374383
$711$	16.1740	0.606572
$712$	−3.52882	−0.132248
$713$	38.5581	1.44401
$714$	−1.14905	−0.0430020
$715$	−2.58984	−0.0968547
$716$	−21.5173	−0.804138
$717$	−4.81232	−0.179720
$718$	−3.88039	−0.144815
$719$	−22.6380	−0.844254	−0.422127	−	0.906537i	$-0.638716\pi$
$719$	−22.6380	−0.844254	−0.422127	+	0.906537i	$0.638716\pi$
$720$	0.771393	0.0287481
$721$	−0.402524	−0.0149908
$722$	−5.13082	−0.190949
$723$	1.82780	0.0679767
$724$	6.66087	0.247549
$725$	11.2966	0.419547
$726$	0.271871	0.0100901
$727$	31.2001	1.15715	0.578574	−	0.815630i	$-0.303609\pi$
$727$	31.2001	1.15715	0.578574	+	0.815630i	$0.303609\pi$
$728$	0.402524	0.0149185
$729$	1.00000	0.0370370
$730$	8.38640	0.310395
$731$	16.2327	0.600388
$732$	−0.0978037	−0.00361493
$733$	30.0034	1.10820	0.554100	−	0.832450i	$-0.313062\pi$
$733$	30.0034	1.10820	0.554100	+	0.832450i	$0.313062\pi$
$734$	1.49498	0.0551806
$735$	−5.27477	−0.194563
$736$	5.56453	0.205111
$737$	−41.3401	−1.52278
$738$	−11.1278	−0.409619
$739$	20.4959	0.753955	0.376978	−	0.926222i	$-0.376963\pi$
$739$	20.4959	0.753955	0.376978	+	0.926222i	$0.376963\pi$
$740$	8.87234	0.326154
$741$	3.72414	0.136810
$742$	−0.964929	−0.0354237
$743$	−7.54725	−0.276882	−0.138441	−	0.990371i	$-0.544209\pi$
$743$	−7.54725	−0.276882	−0.138441	+	0.990371i	$0.544209\pi$
$744$	6.92926	0.254039
$745$	−3.31733	−0.121538
$746$	8.12123	0.297340
$747$	6.81663	0.249407
$748$	9.58394	0.350424
$749$	−7.31475	−0.267275
$750$	−7.25491	−0.264912
$751$	−4.16846	−0.152109	−0.0760546	−	0.997104i	$-0.524232\pi$
$751$	−4.16846	−0.152109	−0.0760546	+	0.997104i	$0.524232\pi$
$752$	9.60242	0.350164
$753$	20.0894	0.732099
$754$	2.56453	0.0933948
$755$	6.95880	0.253257
$756$	−0.402524	−0.0146397
$757$	51.1642	1.85959	0.929797	−	0.368074i	$-0.119983\pi$
$757$	51.1642	1.85959	0.929797	+	0.368074i	$0.119983\pi$
$758$	−31.6411	−1.14926
$759$	18.6821	0.678118
$760$	−2.87277	−0.104206
$761$	43.7583	1.58624	0.793119	−	0.609067i	$-0.208456\pi$
$761$	43.7583	1.58624	0.793119	+	0.609067i	$0.208456\pi$
$762$	16.5317	0.598881
$763$	−6.40861	−0.232007
$764$	−7.82053	−0.282937
$765$	2.20202	0.0796143
$766$	12.5504	0.453465
$767$	0.522868	0.0188797
$768$	1.00000	0.0360844
$769$	−5.22329	−0.188357	−0.0941783	−	0.995555i	$-0.530022\pi$
$769$	−5.22329	−0.188357	−0.0941783	+	0.995555i	$0.530022\pi$
$770$	−1.04247	−0.0375682
$771$	19.7037	0.709613
$772$	−19.0780	−0.686632
$773$	−13.8179	−0.496994	−0.248497	−	0.968633i	$-0.579937\pi$
$773$	−13.8179	−0.496994	−0.248497	+	0.968633i	$0.579937\pi$
$774$	5.68649	0.204397
$775$	−30.5231	−1.09642
$776$	−7.64481	−0.274433
$777$	−4.62972	−0.166090
$778$	−32.9392	−1.18093
$779$	41.4413	1.48479
$780$	−0.771393	−0.0276203
$781$	−43.4178	−1.55361
$782$	15.8845	0.568030
$783$	−2.56453	−0.0916489
$784$	−6.83797	−0.244213
$785$	−13.7506	−0.490780
$786$	−17.2657	−0.615845
$787$	28.5703	1.01842	0.509211	−	0.860642i	$-0.329937\pi$
$787$	28.5703	1.01842	0.509211	+	0.860642i	$0.329937\pi$
$788$	10.1609	0.361966
$789$	−23.1100	−0.822737
$790$	12.4765	0.443894
$791$	0.639823	0.0227495
$792$	3.35736	0.119299
$793$	0.0978037	0.00347311
$794$	−26.8250	−0.951985
$795$	1.84918	0.0655837
$796$	2.80558	0.0994412
$797$	−31.3536	−1.11060	−0.555301	−	0.831650i	$-0.687397\pi$
$797$	−31.3536	−1.11060	−0.555301	+	0.831650i	$0.687397\pi$
$798$	1.49905	0.0530659
$799$	27.4111	0.969737
$800$	−4.40495	−0.155739
$801$	−3.52882	−0.124685
$802$	6.91974	0.244344
$803$	36.5004	1.28807
$804$	−12.3133	−0.434255
$805$	−1.72781	−0.0608973
$806$	−6.92926	−0.244073
$807$	18.8960	0.665172
$808$	−8.43758	−0.296833
$809$	0.958842	0.0337111	0.0168555	−	0.999858i	$-0.494634\pi$
$809$	0.958842	0.0337111	0.0168555	+	0.999858i	$0.494634\pi$
$810$	0.771393	0.0271040
$811$	12.2298	0.429447	0.214723	−	0.976675i	$-0.431115\pi$
$811$	12.2298	0.429447	0.214723	+	0.976675i	$0.431115\pi$
$812$	1.03229	0.0362261
$813$	−27.6901	−0.971134
$814$	38.6154	1.35347
$815$	11.1029	0.388917
$816$	2.85461	0.0999312
$817$	−21.1773	−0.740898
$818$	16.5757	0.579555
$819$	0.402524	0.0140653
$820$	−8.58389	−0.299762
$821$	3.52527	0.123033	0.0615164	−	0.998106i	$-0.480406\pi$
$821$	3.52527	0.123033	0.0615164	+	0.998106i	$0.480406\pi$
$822$	16.6312	0.580080
$823$	−48.9058	−1.70475	−0.852375	−	0.522931i	$-0.824839\pi$
$823$	−48.9058	−1.70475	−0.852375	+	0.522931i	$0.824839\pi$
$824$	1.00000	0.0348367
$825$	−14.7890	−0.514887
$826$	0.210467	0.00732308
$827$	8.09266	0.281410	0.140705	−	0.990052i	$-0.455063\pi$
$827$	8.09266	0.281410	0.140705	+	0.990052i	$0.455063\pi$
$828$	5.56453	0.193381
$829$	−44.4215	−1.54282	−0.771412	−	0.636336i	$-0.780449\pi$
$829$	−44.4215	−1.54282	−0.771412	+	0.636336i	$0.780449\pi$
$830$	5.25830	0.182518
$831$	7.72449	0.267960
$832$	−1.00000	−0.0346688
$833$	−19.5197	−0.676319
$834$	6.23877	0.216031
$835$	−6.58013	−0.227715
$836$	−12.5033	−0.432434
$837$	6.92926	0.239510
$838$	26.4338	0.913139
$839$	−32.9630	−1.13801	−0.569004	−	0.822335i	$-0.692671\pi$
$839$	−32.9630	−1.13801	−0.569004	+	0.822335i	$0.692671\pi$
$840$	−0.310504	−0.0107134
$841$	−22.4232	−0.773213
$842$	0.719679	0.0248018
$843$	17.2366	0.593659
$844$	−4.27406	−0.147119
$845$	0.771393	0.0265367
$846$	9.60242	0.330138
$847$	−0.109435	−0.00376022
$848$	2.39720	0.0823201
$849$	1.02992	0.0353467
$850$	−12.5744	−0.431299
$851$	64.0016	2.19395
$852$	−12.9321	−0.443048
$853$	−45.6826	−1.56414	−0.782071	−	0.623190i	$-0.785837\pi$
$853$	−45.6826	−1.56414	−0.782071	+	0.623190i	$0.785837\pi$
$854$	0.0393684	0.00134716
$855$	−2.87277	−0.0982467
$856$	18.1722	0.621113
$857$	−17.2933	−0.590727	−0.295364	−	0.955385i	$-0.595441\pi$
$857$	−17.2933	−0.590727	−0.295364	+	0.955385i	$0.595441\pi$
$858$	−3.35736	−0.114618
$859$	−2.87018	−0.0979293	−0.0489647	−	0.998801i	$-0.515592\pi$
$859$	−2.87018	−0.0979293	−0.0489647	+	0.998801i	$0.515592\pi$
$860$	4.38652	0.149579
$861$	4.47920	0.152651
$862$	−26.7745	−0.911944
$863$	−49.6836	−1.69125	−0.845625	−	0.533778i	$-0.820772\pi$
$863$	−49.6836	−1.69125	−0.845625	+	0.533778i	$0.820772\pi$
$864$	1.00000	0.0340207
$865$	0.360705	0.0122643
$866$	26.4211	0.897825
$867$	−8.85122	−0.300603
$868$	−2.78919	−0.0946714
$869$	54.3019	1.84207
$870$	−1.97826	−0.0670694
$871$	12.3133	0.417219
$872$	15.9210	0.539155
$873$	−7.64481	−0.258738
$874$	−20.7231	−0.700968
$875$	2.92028	0.0987234
$876$	10.8718	0.367323
$877$	−26.7588	−0.903580	−0.451790	−	0.892124i	$-0.649214\pi$
$877$	−26.7588	−0.903580	−0.451790	+	0.892124i	$0.649214\pi$
$878$	−28.4512	−0.960181
$879$	23.5939	0.795803
$880$	2.58984	0.0873036
$881$	−28.2382	−0.951369	−0.475684	−	0.879616i	$-0.657800\pi$
$881$	−28.2382	−0.951369	−0.475684	+	0.879616i	$0.657800\pi$
$882$	−6.83797	−0.230247
$883$	26.0302	0.875985	0.437993	−	0.898979i	$-0.355690\pi$
$883$	26.0302	0.875985	0.437993	+	0.898979i	$0.355690\pi$
$884$	−2.85461	−0.0960108
$885$	−0.403336	−0.0135580
$886$	−16.8823	−0.567171
$887$	−6.65754	−0.223538	−0.111769	−	0.993734i	$-0.535652\pi$
$887$	−6.65754	−0.223538	−0.111769	+	0.993734i	$0.535652\pi$
$888$	11.5017	0.385972
$889$	−6.65441	−0.223182
$890$	−2.72211	−0.0912453
$891$	3.35736	0.112476
$892$	24.4874	0.819899
$893$	−35.7607	−1.19669
$894$	−4.30045	−0.143828
$895$	−16.5983	−0.554819
$896$	−0.402524	−0.0134474
$897$	−5.56453	−0.185794
$898$	−1.15814	−0.0386478
$899$	−17.7703	−0.592673
$900$	−4.40495	−0.146832
$901$	6.84305	0.227975
$902$	−37.3600	−1.24395
$903$	−2.28895	−0.0761714
$904$	−1.58953	−0.0528669
$905$	5.13815	0.170798
$906$	9.02108	0.299705
$907$	−9.79208	−0.325141	−0.162570	−	0.986697i	$-0.551978\pi$
$907$	−9.79208	−0.325141	−0.162570	+	0.986697i	$0.551978\pi$
$908$	−8.77108	−0.291078
$909$	−8.43758	−0.279857
$910$	0.310504	0.0102931
$911$	24.9278	0.825896	0.412948	−	0.910755i	$-0.364499\pi$
$911$	24.9278	0.825896	0.412948	+	0.910755i	$0.364499\pi$
$912$	−3.72414	−0.123318
$913$	22.8859	0.757412
$914$	21.7990	0.721046
$915$	−0.0754451	−0.00249414
$916$	−29.3151	−0.968598
$917$	6.94984	0.229504
$918$	2.85461	0.0942161
$919$	14.6145	0.482087	0.241044	−	0.970514i	$-0.422510\pi$
$919$	14.6145	0.482087	0.241044	+	0.970514i	$0.422510\pi$
$920$	4.29244	0.141517
$921$	−33.2668	−1.09618
$922$	−3.69683	−0.121749
$923$	12.9321	0.425666
$924$	−1.35142	−0.0444584
$925$	−50.6645	−1.66584
$926$	−13.8870	−0.456355
$927$	1.00000	0.0328443
$928$	−2.56453	−0.0841849
$929$	−6.58891	−0.216175	−0.108088	−	0.994141i	$-0.534473\pi$
$929$	−6.58891	−0.216175	−0.108088	+	0.994141i	$0.534473\pi$
$930$	5.34518	0.175275
$931$	25.4655	0.834599
$932$	−4.88223	−0.159923
$933$	19.9637	0.653584
$934$	19.3950	0.634624
$935$	7.39299	0.241777
$936$	−1.00000	−0.0326860
$937$	−42.2684	−1.38085	−0.690423	−	0.723405i	$-0.742576\pi$
$937$	−42.2684	−1.38085	−0.690423	+	0.723405i	$0.742576\pi$
$938$	4.95639	0.161832
$939$	−32.6475	−1.06541
$940$	7.40724	0.241598
$941$	13.5333	0.441172	0.220586	−	0.975368i	$-0.429203\pi$
$941$	13.5333	0.441172	0.220586	+	0.975368i	$0.429203\pi$
$942$	−17.8257	−0.580792
$943$	−61.9208	−2.01642
$944$	−0.522868	−0.0170179
$945$	−0.310504	−0.0101007
$946$	19.0916	0.620721
$947$	8.86498	0.288073	0.144037	−	0.989572i	$-0.453992\pi$
$947$	8.86498	0.288073	0.144037	+	0.989572i	$0.453992\pi$
$948$	16.1740	0.525307
$949$	−10.8718	−0.352913
$950$	16.4046	0.532237
$951$	24.3086	0.788261
$952$	−1.14905	−0.0372409
$953$	22.5401	0.730144	0.365072	−	0.930979i	$-0.381044\pi$
$953$	22.5401	0.730144	0.365072	+	0.930979i	$0.381044\pi$
$954$	2.39720	0.0776121
$955$	−6.03270	−0.195214
$956$	−4.81232	−0.155642
$957$	−8.61006	−0.278324
$958$	−27.4774	−0.887755
$959$	−6.69447	−0.216176
$960$	0.771393	0.0248966
$961$	17.0147	0.548861
$962$	−11.5017	−0.370830
$963$	18.1722	0.585591
$964$	1.82780	0.0588696
$965$	−14.7166	−0.473745
$966$	−2.23986	−0.0720662
$967$	−43.4779	−1.39815	−0.699077	−	0.715046i	$-0.746406\pi$
$967$	−43.4779	−1.39815	−0.699077	+	0.715046i	$0.746406\pi$
$968$	0.271871	0.00873826
$969$	−10.6309	−0.341515
$970$	−5.89715	−0.189346
$971$	51.3693	1.64852	0.824259	−	0.566213i	$-0.191592\pi$
$971$	51.3693	1.64852	0.824259	+	0.566213i	$0.191592\pi$
$972$	1.00000	0.0320750
$973$	−2.51126	−0.0805072
$974$	5.39111	0.172742
$975$	4.40495	0.141071
$976$	−0.0978037	−0.00313062
$977$	39.9036	1.27663	0.638315	−	0.769775i	$-0.279632\pi$
$977$	39.9036	1.27663	0.638315	+	0.769775i	$0.279632\pi$
$978$	14.3933	0.460247
$979$	−11.8475	−0.378649
$980$	−5.27477	−0.168496
$981$	15.9210	0.508320
$982$	17.4945	0.558272
$983$	−8.92889	−0.284787	−0.142394	−	0.989810i	$-0.545480\pi$
$983$	−8.92889	−0.284787	−0.142394	+	0.989810i	$0.545480\pi$
$984$	−11.1278	−0.354741
$985$	7.83802	0.249740
$986$	−7.32073	−0.233140
$987$	−3.86521	−0.123031
$988$	3.72414	0.118481
$989$	31.6426	1.00618
$990$	2.58984	0.0823107
$991$	−58.4877	−1.85792	−0.928962	−	0.370176i	$-0.879297\pi$
$991$	−58.4877	−1.85792	−0.928962	+	0.370176i	$0.879297\pi$
$992$	6.92926	0.220004
$993$	13.2108	0.419233
$994$	5.20549	0.165108
$995$	2.16421	0.0686099
$996$	6.81663	0.215993
$997$	40.4440	1.28087	0.640437	−	0.768011i	$-0.278753\pi$
$997$	40.4440	1.28087	0.640437	+	0.768011i	$0.278753\pi$
$998$	−36.5626	−1.15737
$999$	11.5017	0.363898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.8	✓	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.771393 q^{5} +1.00000 q^{6} -0.402524 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.771393 q^{5} +1.00000 q^{6} -0.402524 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.771393 q^{10} +3.35736 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.402524 q^{14} +0.771393 q^{15} +1.00000 q^{16} +2.85461 q^{17} +1.00000 q^{18} -3.72414 q^{19} +0.771393 q^{20} -0.402524 q^{21} +3.35736 q^{22} +5.56453 q^{23} +1.00000 q^{24} -4.40495 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.402524 q^{28} -2.56453 q^{29} +0.771393 q^{30} +6.92926 q^{31} +1.00000 q^{32} +3.35736 q^{33} +2.85461 q^{34} -0.310504 q^{35} +1.00000 q^{36} +11.5017 q^{37} -3.72414 q^{38} -1.00000 q^{39} +0.771393 q^{40} -11.1278 q^{41} -0.402524 q^{42} +5.68649 q^{43} +3.35736 q^{44} +0.771393 q^{45} +5.56453 q^{46} +9.60242 q^{47} +1.00000 q^{48} -6.83797 q^{49} -4.40495 q^{50} +2.85461 q^{51} -1.00000 q^{52} +2.39720 q^{53} +1.00000 q^{54} +2.58984 q^{55} -0.402524 q^{56} -3.72414 q^{57} -2.56453 q^{58} -0.522868 q^{59} +0.771393 q^{60} -0.0978037 q^{61} +6.92926 q^{62} -0.402524 q^{63} +1.00000 q^{64} -0.771393 q^{65} +3.35736 q^{66} -12.3133 q^{67} +2.85461 q^{68} +5.56453 q^{69} -0.310504 q^{70} -12.9321 q^{71} +1.00000 q^{72} +10.8718 q^{73} +11.5017 q^{74} -4.40495 q^{75} -3.72414 q^{76} -1.35142 q^{77} -1.00000 q^{78} +16.1740 q^{79} +0.771393 q^{80} +1.00000 q^{81} -11.1278 q^{82} +6.81663 q^{83} -0.402524 q^{84} +2.20202 q^{85} +5.68649 q^{86} -2.56453 q^{87} +3.35736 q^{88} -3.52882 q^{89} +0.771393 q^{90} +0.402524 q^{91} +5.56453 q^{92} +6.92926 q^{93} +9.60242 q^{94} -2.87277 q^{95} +1.00000 q^{96} -7.64481 q^{97} -6.83797 q^{98} +3.35736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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