LMFDB - Embedded newform 8034.2.a.w.1.6

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 $ x^12 - 6x^11 - 8x^10 + 94x^9 - 7x^8 - 580x^7 + 180x^6 + 1787x^5 - 308x^4 - 2790x^3 - 352x^2 + 1768*x + 768
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.10048$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.18783 q^{5} -1.00000 q^{6} +0.107097 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.18783 q^{5} -1.00000 q^{6} +0.107097 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.18783 q^{10} +0.456412 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.107097 q^{14} -1.18783 q^{15} +1.00000 q^{16} -3.46810 q^{17} -1.00000 q^{18} -0.368926 q^{19} -1.18783 q^{20} +0.107097 q^{21} -0.456412 q^{22} +5.15956 q^{23} -1.00000 q^{24} -3.58905 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.107097 q^{28} -3.44062 q^{29} +1.18783 q^{30} +0.0661943 q^{31} -1.00000 q^{32} +0.456412 q^{33} +3.46810 q^{34} -0.127214 q^{35} +1.00000 q^{36} +4.66735 q^{37} +0.368926 q^{38} +1.00000 q^{39} +1.18783 q^{40} +0.724266 q^{41} -0.107097 q^{42} +3.85350 q^{43} +0.456412 q^{44} -1.18783 q^{45} -5.15956 q^{46} -11.5878 q^{47} +1.00000 q^{48} -6.98853 q^{49} +3.58905 q^{50} -3.46810 q^{51} +1.00000 q^{52} -7.67799 q^{53} -1.00000 q^{54} -0.542142 q^{55} -0.107097 q^{56} -0.368926 q^{57} +3.44062 q^{58} +4.84255 q^{59} -1.18783 q^{60} +6.69692 q^{61} -0.0661943 q^{62} +0.107097 q^{63} +1.00000 q^{64} -1.18783 q^{65} -0.456412 q^{66} +2.46560 q^{67} -3.46810 q^{68} +5.15956 q^{69} +0.127214 q^{70} +6.86345 q^{71} -1.00000 q^{72} -7.04406 q^{73} -4.66735 q^{74} -3.58905 q^{75} -0.368926 q^{76} +0.0488806 q^{77} -1.00000 q^{78} +0.265300 q^{79} -1.18783 q^{80} +1.00000 q^{81} -0.724266 q^{82} +0.324525 q^{83} +0.107097 q^{84} +4.11953 q^{85} -3.85350 q^{86} -3.44062 q^{87} -0.456412 q^{88} -4.77088 q^{89} +1.18783 q^{90} +0.107097 q^{91} +5.15956 q^{92} +0.0661943 q^{93} +11.5878 q^{94} +0.438223 q^{95} -1.00000 q^{96} +3.46515 q^{97} +6.98853 q^{98} +0.456412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * 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
$5$	−1.18783	−0.531216	−0.265608	−	0.964081i	$-0.585573\pi$
$5$	−1.18783	−0.531216	−0.265608	+	0.964081i	$0.585573\pi$
$6$	−1.00000	−0.408248
$7$	0.107097	0.0404790	0.0202395	−	0.999795i	$-0.493557\pi$
$7$	0.107097	0.0404790	0.0202395	+	0.999795i	$0.493557\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.18783	0.375626
$11$	0.456412	0.137613	0.0688067	−	0.997630i	$-0.478081\pi$
$11$	0.456412	0.137613	0.0688067	+	0.997630i	$0.478081\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.107097	−0.0286230
$15$	−1.18783	−0.306698
$16$	1.00000	0.250000
$17$	−3.46810	−0.841138	−0.420569	−	0.907261i	$-0.638170\pi$
$17$	−3.46810	−0.841138	−0.420569	+	0.907261i	$0.638170\pi$
$18$	−1.00000	−0.235702
$19$	−0.368926	−0.0846375	−0.0423187	−	0.999104i	$-0.513475\pi$
$19$	−0.368926	−0.0846375	−0.0423187	+	0.999104i	$0.513475\pi$
$20$	−1.18783	−0.265608
$21$	0.107097	0.0233706
$22$	−0.456412	−0.0973074
$23$	5.15956	1.07584	0.537922	−	0.842995i	$-0.319210\pi$
$23$	5.15956	1.07584	0.537922	+	0.842995i	$0.319210\pi$
$24$	−1.00000	−0.204124
$25$	−3.58905	−0.717810
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0.107097	0.0202395
$29$	−3.44062	−0.638907	−0.319453	−	0.947602i	$-0.603499\pi$
$29$	−3.44062	−0.638907	−0.319453	+	0.947602i	$0.603499\pi$
$30$	1.18783	0.216868
$31$	0.0661943	0.0118888	0.00594442	−	0.999982i	$-0.498108\pi$
$31$	0.0661943	0.0118888	0.00594442	+	0.999982i	$0.498108\pi$
$32$	−1.00000	−0.176777
$33$	0.456412	0.0794511
$34$	3.46810	0.594775
$35$	−0.127214	−0.0215031
$36$	1.00000	0.166667
$37$	4.66735	0.767308	0.383654	−	0.923477i	$-0.374666\pi$
$37$	4.66735	0.767308	0.383654	+	0.923477i	$0.374666\pi$
$38$	0.368926	0.0598477
$39$	1.00000	0.160128
$40$	1.18783	0.187813
$41$	0.724266	0.113111	0.0565556	−	0.998399i	$-0.481988\pi$
$41$	0.724266	0.113111	0.0565556	+	0.998399i	$0.481988\pi$
$42$	−0.107097	−0.0165255
$43$	3.85350	0.587653	0.293826	−	0.955859i	$-0.405071\pi$
$43$	3.85350	0.587653	0.293826	+	0.955859i	$0.405071\pi$
$44$	0.456412	0.0688067
$45$	−1.18783	−0.177072
$46$	−5.15956	−0.760736
$47$	−11.5878	−1.69025	−0.845127	−	0.534565i	$-0.820475\pi$
$47$	−11.5878	−1.69025	−0.845127	+	0.534565i	$0.820475\pi$
$48$	1.00000	0.144338
$49$	−6.98853	−0.998361
$50$	3.58905	0.507568
$51$	−3.46810	−0.485631
$52$	1.00000	0.138675
$53$	−7.67799	−1.05465	−0.527326	−	0.849663i	$-0.676806\pi$
$53$	−7.67799	−1.05465	−0.527326	+	0.849663i	$0.676806\pi$
$54$	−1.00000	−0.136083
$55$	−0.542142	−0.0731024
$56$	−0.107097	−0.0143115
$57$	−0.368926	−0.0488655
$58$	3.44062	0.451775
$59$	4.84255	0.630447	0.315223	−	0.949018i	$-0.397921\pi$
$59$	4.84255	0.630447	0.315223	+	0.949018i	$0.397921\pi$
$60$	−1.18783	−0.153349
$61$	6.69692	0.857452	0.428726	−	0.903435i	$-0.358963\pi$
$61$	6.69692	0.857452	0.428726	+	0.903435i	$0.358963\pi$
$62$	−0.0661943	−0.00840668
$63$	0.107097	0.0134930
$64$	1.00000	0.125000
$65$	−1.18783	−0.147333
$66$	−0.456412	−0.0561804
$67$	2.46560	0.301222	0.150611	−	0.988593i	$-0.451876\pi$
$67$	2.46560	0.301222	0.150611	+	0.988593i	$0.451876\pi$
$68$	−3.46810	−0.420569
$69$	5.15956	0.621139
$70$	0.127214	0.0152050
$71$	6.86345	0.814541	0.407271	−	0.913308i	$-0.366481\pi$
$71$	6.86345	0.814541	0.407271	+	0.913308i	$0.366481\pi$
$72$	−1.00000	−0.117851
$73$	−7.04406	−0.824445	−0.412222	−	0.911083i	$-0.635247\pi$
$73$	−7.04406	−0.824445	−0.412222	+	0.911083i	$0.635247\pi$
$74$	−4.66735	−0.542569
$75$	−3.58905	−0.414428
$76$	−0.368926	−0.0423187
$77$	0.0488806	0.00557046
$78$	−1.00000	−0.113228
$79$	0.265300	0.0298486	0.0149243	−	0.999889i	$-0.495249\pi$
$79$	0.265300	0.0298486	0.0149243	+	0.999889i	$0.495249\pi$
$80$	−1.18783	−0.132804
$81$	1.00000	0.111111
$82$	−0.724266	−0.0799818
$83$	0.324525	0.0356213	0.0178106	−	0.999841i	$-0.494330\pi$
$83$	0.324525	0.0356213	0.0178106	+	0.999841i	$0.494330\pi$
$84$	0.107097	0.0116853
$85$	4.11953	0.446826
$86$	−3.85350	−0.415533
$87$	−3.44062	−0.368873
$88$	−0.456412	−0.0486537
$89$	−4.77088	−0.505713	−0.252856	−	0.967504i	$-0.581370\pi$
$89$	−4.77088	−0.505713	−0.252856	+	0.967504i	$0.581370\pi$
$90$	1.18783	0.125209
$91$	0.107097	0.0112269
$92$	5.15956	0.537922
$93$	0.0661943	0.00686403
$94$	11.5878	1.19519
$95$	0.438223	0.0449608
$96$	−1.00000	−0.102062
$97$	3.46515	0.351833	0.175916	−	0.984405i	$-0.443711\pi$
$97$	3.46515	0.351833	0.175916	+	0.984405i	$0.443711\pi$
$98$	6.98853	0.705948
$99$	0.456412	0.0458711
$100$	−3.58905	−0.358905
$101$	−9.70265	−0.965450	−0.482725	−	0.875772i	$-0.660353\pi$
$101$	−9.70265	−0.965450	−0.482725	+	0.875772i	$0.660353\pi$
$102$	3.46810	0.343393
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.127214	−0.0124148
$106$	7.67799	0.745752
$107$	−10.1786	−0.984006	−0.492003	−	0.870593i	$-0.663735\pi$
$107$	−10.1786	−0.984006	−0.492003	+	0.870593i	$0.663735\pi$
$108$	1.00000	0.0962250
$109$	−6.55701	−0.628047	−0.314024	−	0.949415i	$-0.601677\pi$
$109$	−6.55701	−0.628047	−0.314024	+	0.949415i	$0.601677\pi$
$110$	0.542142	0.0516912
$111$	4.66735	0.443006
$112$	0.107097	0.0101198
$113$	−5.75203	−0.541105	−0.270553	−	0.962705i	$-0.587206\pi$
$113$	−5.75203	−0.541105	−0.270553	+	0.962705i	$0.587206\pi$
$114$	0.368926	0.0345531
$115$	−6.12871	−0.571505
$116$	−3.44062	−0.319453
$117$	1.00000	0.0924500
$118$	−4.84255	−0.445793
$119$	−0.371425	−0.0340485
$120$	1.18783	0.108434
$121$	−10.7917	−0.981063
$122$	−6.69692	−0.606310
$123$	0.724266	0.0653048
$124$	0.0661943	0.00594442
$125$	10.2024	0.912528
$126$	−0.107097	−0.00954100
$127$	6.20597	0.550690	0.275345	−	0.961345i	$-0.411208\pi$
$127$	6.20597	0.550690	0.275345	+	0.961345i	$0.411208\pi$
$128$	−1.00000	−0.0883883
$129$	3.85350	0.339281
$130$	1.18783	0.104180
$131$	−4.57249	−0.399500	−0.199750	−	0.979847i	$-0.564013\pi$
$131$	−4.57249	−0.399500	−0.199750	+	0.979847i	$0.564013\pi$
$132$	0.456412	0.0397256
$133$	−0.0395111	−0.00342605
$134$	−2.46560	−0.212996
$135$	−1.18783	−0.102233
$136$	3.46810	0.297387
$137$	6.01069	0.513528	0.256764	−	0.966474i	$-0.417344\pi$
$137$	6.01069	0.513528	0.256764	+	0.966474i	$0.417344\pi$
$138$	−5.15956	−0.439211
$139$	−4.90383	−0.415937	−0.207969	−	0.978136i	$-0.566685\pi$
$139$	−4.90383	−0.415937	−0.207969	+	0.978136i	$0.566685\pi$
$140$	−0.127214	−0.0107516
$141$	−11.5878	−0.975869
$142$	−6.86345	−0.575968
$143$	0.456412	0.0381671
$144$	1.00000	0.0833333
$145$	4.08688	0.339397
$146$	7.04406	0.582971
$147$	−6.98853	−0.576404
$148$	4.66735	0.383654
$149$	−20.4378	−1.67433	−0.837164	−	0.546952i	$-0.815788\pi$
$149$	−20.4378	−1.67433	−0.837164	+	0.546952i	$0.815788\pi$
$150$	3.58905	0.293045
$151$	11.0469	0.898987	0.449494	−	0.893284i	$-0.351604\pi$
$151$	11.0469	0.898987	0.449494	+	0.893284i	$0.351604\pi$
$152$	0.368926	0.0299239
$153$	−3.46810	−0.280379
$154$	−0.0488806	−0.00393891
$155$	−0.0786279	−0.00631554
$156$	1.00000	0.0800641
$157$	−7.83563	−0.625351	−0.312676	−	0.949860i	$-0.601225\pi$
$157$	−7.83563	−0.625351	−0.312676	+	0.949860i	$0.601225\pi$
$158$	−0.265300	−0.0211061
$159$	−7.67799	−0.608904
$160$	1.18783	0.0939066
$161$	0.552576	0.0435491
$162$	−1.00000	−0.0785674
$163$	18.6201	1.45844	0.729221	−	0.684279i	$-0.239883\pi$
$163$	18.6201	1.45844	0.729221	+	0.684279i	$0.239883\pi$
$164$	0.724266	0.0565556
$165$	−0.542142	−0.0422057
$166$	−0.324525	−0.0251880
$167$	−5.85397	−0.452994	−0.226497	−	0.974012i	$-0.572727\pi$
$167$	−5.85397	−0.452994	−0.226497	+	0.974012i	$0.572727\pi$
$168$	−0.107097	−0.00826275
$169$	1.00000	0.0769231
$170$	−4.11953	−0.315954
$171$	−0.368926	−0.0282125
$172$	3.85350	0.293826
$173$	16.2765	1.23748	0.618740	−	0.785596i	$-0.287644\pi$
$173$	16.2765	1.23748	0.618740	+	0.785596i	$0.287644\pi$
$174$	3.44062	0.260833
$175$	−0.384378	−0.0290563
$176$	0.456412	0.0344033
$177$	4.84255	0.363989
$178$	4.77088	0.357593
$179$	−26.4246	−1.97507	−0.987533	−	0.157415i	$-0.949684\pi$
$179$	−26.4246	−1.97507	−0.987533	+	0.157415i	$0.949684\pi$
$180$	−1.18783	−0.0885360
$181$	2.44713	0.181894	0.0909468	−	0.995856i	$-0.471011\pi$
$181$	2.44713	0.181894	0.0909468	+	0.995856i	$0.471011\pi$
$182$	−0.107097	−0.00793859
$183$	6.69692	0.495050
$184$	−5.15956	−0.380368
$185$	−5.54404	−0.407606
$186$	−0.0661943	−0.00485360
$187$	−1.58288	−0.115752
$188$	−11.5878	−0.845127
$189$	0.107097	0.00779020
$190$	−0.438223	−0.0317921
$191$	9.01356	0.652198	0.326099	−	0.945336i	$-0.394266\pi$
$191$	9.01356	0.652198	0.326099	+	0.945336i	$0.394266\pi$
$192$	1.00000	0.0721688
$193$	−14.1229	−1.01659	−0.508293	−	0.861184i	$-0.669723\pi$
$193$	−14.1229	−1.01659	−0.508293	+	0.861184i	$0.669723\pi$
$194$	−3.46515	−0.248783
$195$	−1.18783	−0.0850626
$196$	−6.98853	−0.499181
$197$	1.74941	0.124640	0.0623201	−	0.998056i	$-0.480150\pi$
$197$	1.74941	0.124640	0.0623201	+	0.998056i	$0.480150\pi$
$198$	−0.456412	−0.0324358
$199$	18.2966	1.29701	0.648507	−	0.761209i	$-0.275394\pi$
$199$	18.2966	1.29701	0.648507	+	0.761209i	$0.275394\pi$
$200$	3.58905	0.253784
$201$	2.46560	0.173910
$202$	9.70265	0.682676
$203$	−0.368481	−0.0258623
$204$	−3.46810	−0.242816
$205$	−0.860308	−0.0600865
$206$	1.00000	0.0696733
$207$	5.15956	0.358615
$208$	1.00000	0.0693375
$209$	−0.168382	−0.0116473
$210$	0.127214	0.00877861
$211$	11.2374	0.773617	0.386808	−	0.922160i	$-0.373578\pi$
$211$	11.2374	0.773617	0.386808	+	0.922160i	$0.373578\pi$
$212$	−7.67799	−0.527326
$213$	6.86345	0.470276
$214$	10.1786	0.695797
$215$	−4.57732	−0.312170
$216$	−1.00000	−0.0680414
$217$	0.00708924	0.000481249 0
$218$	6.55701	0.444096
$219$	−7.04406	−0.475993
$220$	−0.542142	−0.0365512
$221$	−3.46810	−0.233290
$222$	−4.66735	−0.313252
$223$	1.37443	0.0920386	0.0460193	−	0.998941i	$-0.485346\pi$
$223$	1.37443	0.0920386	0.0460193	+	0.998941i	$0.485346\pi$
$224$	−0.107097	−0.00715575
$225$	−3.58905	−0.239270
$226$	5.75203	0.382619
$227$	−4.63666	−0.307746	−0.153873	−	0.988091i	$-0.549175\pi$
$227$	−4.63666	−0.307746	−0.153873	+	0.988091i	$0.549175\pi$
$228$	−0.368926	−0.0244327
$229$	−12.1523	−0.803049	−0.401524	−	0.915848i	$-0.631520\pi$
$229$	−12.1523	−0.803049	−0.401524	+	0.915848i	$0.631520\pi$
$230$	6.12871	0.404115
$231$	0.0488806	0.00321611
$232$	3.44062	0.225888
$233$	−14.8168	−0.970682	−0.485341	−	0.874325i	$-0.661305\pi$
$233$	−14.8168	−0.970682	−0.485341	+	0.874325i	$0.661305\pi$
$234$	−1.00000	−0.0653720
$235$	13.7644	0.897890
$236$	4.84255	0.315223
$237$	0.265300	0.0172331
$238$	0.371425	0.0240759
$239$	7.26585	0.469989	0.234994	−	0.971997i	$-0.424493\pi$
$239$	7.26585	0.469989	0.234994	+	0.971997i	$0.424493\pi$
$240$	−1.18783	−0.0766744
$241$	0.440354	0.0283657	0.0141829	−	0.999899i	$-0.495485\pi$
$241$	0.440354	0.0283657	0.0141829	+	0.999899i	$0.495485\pi$
$242$	10.7917	0.693716
$243$	1.00000	0.0641500
$244$	6.69692	0.428726
$245$	8.30122	0.530345
$246$	−0.724266	−0.0461775
$247$	−0.368926	−0.0234742
$248$	−0.0661943	−0.00420334
$249$	0.324525	0.0205660
$250$	−10.2024	−0.645254
$251$	−26.3082	−1.66056	−0.830280	−	0.557346i	$-0.811820\pi$
$251$	−26.3082	−1.66056	−0.830280	+	0.557346i	$0.811820\pi$
$252$	0.107097	0.00674651
$253$	2.35489	0.148050
$254$	−6.20597	−0.389397
$255$	4.11953	0.257975
$256$	1.00000	0.0625000
$257$	21.8953	1.36579	0.682895	−	0.730517i	$-0.260721\pi$
$257$	21.8953	1.36579	0.682895	+	0.730517i	$0.260721\pi$
$258$	−3.85350	−0.239908
$259$	0.499862	0.0310599
$260$	−1.18783	−0.0736664
$261$	−3.44062	−0.212969
$262$	4.57249	0.282489
$263$	−24.7060	−1.52344	−0.761719	−	0.647908i	$-0.775644\pi$
$263$	−24.7060	−1.52344	−0.761719	+	0.647908i	$0.775644\pi$
$264$	−0.456412	−0.0280902
$265$	9.12018	0.560248
$266$	0.0395111	0.00242258
$267$	−4.77088	−0.291973
$268$	2.46560	0.150611
$269$	−23.3163	−1.42162	−0.710811	−	0.703383i	$-0.751672\pi$
$269$	−23.3163	−1.42162	−0.710811	+	0.703383i	$0.751672\pi$
$270$	1.18783	0.0722893
$271$	3.22302	0.195784	0.0978922	−	0.995197i	$-0.468790\pi$
$271$	3.22302	0.195784	0.0978922	+	0.995197i	$0.468790\pi$
$272$	−3.46810	−0.210285
$273$	0.107097	0.00648183
$274$	−6.01069	−0.363119
$275$	−1.63808	−0.0987802
$276$	5.15956	0.310569
$277$	−17.0469	−1.02425	−0.512125	−	0.858911i	$-0.671142\pi$
$277$	−17.0469	−1.02425	−0.512125	+	0.858911i	$0.671142\pi$
$278$	4.90383	0.294112
$279$	0.0661943	0.00396295
$280$	0.127214	0.00760250
$281$	18.5875	1.10884	0.554418	−	0.832238i	$-0.312941\pi$
$281$	18.5875	1.10884	0.554418	+	0.832238i	$0.312941\pi$
$282$	11.5878	0.690044
$283$	−31.2994	−1.86056	−0.930279	−	0.366852i	$-0.880436\pi$
$283$	−31.2994	−1.86056	−0.930279	+	0.366852i	$0.880436\pi$
$284$	6.86345	0.407271
$285$	0.438223	0.0259581
$286$	−0.456412	−0.0269882
$287$	0.0775670	0.00457864
$288$	−1.00000	−0.0589256
$289$	−4.97227	−0.292486
$290$	−4.08688	−0.239990
$291$	3.46515	0.203131
$292$	−7.04406	−0.412222
$293$	−9.83799	−0.574742	−0.287371	−	0.957819i	$-0.592781\pi$
$293$	−9.83799	−0.574742	−0.287371	+	0.957819i	$0.592781\pi$
$294$	6.98853	0.407579
$295$	−5.75215	−0.334903
$296$	−4.66735	−0.271284
$297$	0.456412	0.0264837
$298$	20.4378	1.18393
$299$	5.15956	0.298385
$300$	−3.58905	−0.207214
$301$	0.412700	0.0237876
$302$	−11.0469	−0.635680
$303$	−9.70265	−0.557403
$304$	−0.368926	−0.0211594
$305$	−7.95483	−0.455492
$306$	3.46810	0.198258
$307$	27.2497	1.55523	0.777613	−	0.628744i	$-0.216431\pi$
$307$	27.2497	1.55523	0.777613	+	0.628744i	$0.216431\pi$
$308$	0.0488806	0.00278523
$309$	−1.00000	−0.0568880
$310$	0.0786279	0.00446576
$311$	−13.5283	−0.767119	−0.383559	−	0.923516i	$-0.625302\pi$
$311$	−13.5283	−0.767119	−0.383559	+	0.923516i	$0.625302\pi$
$312$	−1.00000	−0.0566139
$313$	31.8819	1.80207	0.901035	−	0.433745i	$-0.142808\pi$
$313$	31.8819	1.80207	0.901035	+	0.433745i	$0.142808\pi$
$314$	7.83563	0.442190
$315$	−0.127214	−0.00716770
$316$	0.265300	0.0149243
$317$	−20.7024	−1.16276	−0.581382	−	0.813631i	$-0.697488\pi$
$317$	−20.7024	−1.16276	−0.581382	+	0.813631i	$0.697488\pi$
$318$	7.67799	0.430560
$319$	−1.57034	−0.0879221
$320$	−1.18783	−0.0664020
$321$	−10.1786	−0.568116
$322$	−0.552576	−0.0307939
$323$	1.27947	0.0711918
$324$	1.00000	0.0555556
$325$	−3.58905	−0.199085
$326$	−18.6201	−1.03127
$327$	−6.55701	−0.362603
$328$	−0.724266	−0.0399909
$329$	−1.24102	−0.0684199
$330$	0.542142	0.0298439
$331$	−7.09103	−0.389758	−0.194879	−	0.980827i	$-0.562431\pi$
$331$	−7.09103	−0.389758	−0.194879	+	0.980827i	$0.562431\pi$
$332$	0.324525	0.0178106
$333$	4.66735	0.255769
$334$	5.85397	0.320315
$335$	−2.92873	−0.160014
$336$	0.107097	0.00584265
$337$	−31.5584	−1.71910	−0.859549	−	0.511054i	$-0.829255\pi$
$337$	−31.5584	−1.71910	−0.859549	+	0.511054i	$0.829255\pi$
$338$	−1.00000	−0.0543928
$339$	−5.75203	−0.312407
$340$	4.11953	0.223413
$341$	0.0302119	0.00163606
$342$	0.368926	0.0199492
$343$	−1.49814	−0.0808918
$344$	−3.85350	−0.207767
$345$	−6.12871	−0.329959
$346$	−16.2765	−0.875030
$347$	22.8790	1.22821	0.614104	−	0.789225i	$-0.289517\pi$
$347$	22.8790	1.22821	0.614104	+	0.789225i	$0.289517\pi$
$348$	−3.44062	−0.184436
$349$	−6.93530	−0.371238	−0.185619	−	0.982622i	$-0.559429\pi$
$349$	−6.93530	−0.371238	−0.185619	+	0.982622i	$0.559429\pi$
$350$	0.384378	0.0205459
$351$	1.00000	0.0533761
$352$	−0.456412	−0.0243268
$353$	−26.6699	−1.41950	−0.709748	−	0.704456i	$-0.751191\pi$
$353$	−26.6699	−1.41950	−0.709748	+	0.704456i	$0.751191\pi$
$354$	−4.84255	−0.257379
$355$	−8.15264	−0.432697
$356$	−4.77088	−0.252856
$357$	−0.371425	−0.0196579
$358$	26.4246	1.39658
$359$	−15.3548	−0.810397	−0.405198	−	0.914229i	$-0.632798\pi$
$359$	−15.3548	−0.810397	−0.405198	+	0.914229i	$0.632798\pi$
$360$	1.18783	0.0626044
$361$	−18.8639	−0.992836
$362$	−2.44713	−0.128618
$363$	−10.7917	−0.566417
$364$	0.107097	0.00561343
$365$	8.36718	0.437958
$366$	−6.69692	−0.350053
$367$	12.6547	0.660571	0.330285	−	0.943881i	$-0.392855\pi$
$367$	12.6547	0.660571	0.330285	+	0.943881i	$0.392855\pi$
$368$	5.15956	0.268961
$369$	0.724266	0.0377038
$370$	5.54404	0.288221
$371$	−0.822293	−0.0426913
$372$	0.0661943	0.00343201
$373$	−5.12658	−0.265444	−0.132722	−	0.991153i	$-0.542372\pi$
$373$	−5.12658	−0.265444	−0.132722	+	0.991153i	$0.542372\pi$
$374$	1.58288	0.0818489
$375$	10.2024	0.526848
$376$	11.5878	0.597595
$377$	−3.44062	−0.177201
$378$	−0.107097	−0.00550850
$379$	−15.8405	−0.813674	−0.406837	−	0.913501i	$-0.633368\pi$
$379$	−15.8405	−0.813674	−0.406837	+	0.913501i	$0.633368\pi$
$380$	0.438223	0.0224804
$381$	6.20597	0.317941
$382$	−9.01356	−0.461174
$383$	−34.9706	−1.78691	−0.893457	−	0.449149i	$-0.851727\pi$
$383$	−34.9706	−1.78691	−0.893457	+	0.449149i	$0.851727\pi$
$384$	−1.00000	−0.0510310
$385$	−0.0580620	−0.00295912
$386$	14.1229	0.718834
$387$	3.85350	0.195884
$388$	3.46515	0.175916
$389$	−33.1833	−1.68246	−0.841229	−	0.540678i	$-0.818168\pi$
$389$	−33.1833	−1.68246	−0.841229	+	0.540678i	$0.818168\pi$
$390$	1.18783	0.0601483
$391$	−17.8939	−0.904933
$392$	6.98853	0.352974
$393$	−4.57249	−0.230652
$394$	−1.74941	−0.0881339
$395$	−0.315133	−0.0158560
$396$	0.456412	0.0229356
$397$	−21.0514	−1.05654	−0.528270	−	0.849077i	$-0.677159\pi$
$397$	−21.0514	−1.05654	−0.528270	+	0.849077i	$0.677159\pi$
$398$	−18.2966	−0.917127
$399$	−0.0395111	−0.00197803
$400$	−3.58905	−0.179452
$401$	20.3736	1.01741	0.508703	−	0.860942i	$-0.330125\pi$
$401$	20.3736	1.01741	0.508703	+	0.860942i	$0.330125\pi$
$402$	−2.46560	−0.122973
$403$	0.0661943	0.00329737
$404$	−9.70265	−0.482725
$405$	−1.18783	−0.0590240
$406$	0.368481	0.0182874
$407$	2.13024	0.105592
$408$	3.46810	0.171697
$409$	32.4487	1.60448	0.802242	−	0.596999i	$-0.203640\pi$
$409$	32.4487	1.60448	0.802242	+	0.596999i	$0.203640\pi$
$410$	0.860308	0.0424876
$411$	6.01069	0.296485
$412$	−1.00000	−0.0492665
$413$	0.518625	0.0255199
$414$	−5.15956	−0.253579
$415$	−0.385482	−0.0189226
$416$	−1.00000	−0.0490290
$417$	−4.90383	−0.240141
$418$	0.168382	0.00823585
$419$	−36.4708	−1.78172	−0.890858	−	0.454281i	$-0.849896\pi$
$419$	−36.4708	−1.78172	−0.890858	+	0.454281i	$0.849896\pi$
$420$	−0.127214	−0.00620741
$421$	33.3994	1.62779	0.813893	−	0.581015i	$-0.197344\pi$
$421$	33.3994	1.62779	0.813893	+	0.581015i	$0.197344\pi$
$422$	−11.2374	−0.547030
$423$	−11.5878	−0.563418
$424$	7.67799	0.372876
$425$	12.4472	0.603777
$426$	−6.86345	−0.332535
$427$	0.717223	0.0347088
$428$	−10.1786	−0.492003
$429$	0.456412	0.0220358
$430$	4.57732	0.220738
$431$	15.1652	0.730481	0.365241	−	0.930913i	$-0.380987\pi$
$431$	15.1652	0.730481	0.365241	+	0.930913i	$0.380987\pi$
$432$	1.00000	0.0481125
$433$	−1.62897	−0.0782834	−0.0391417	−	0.999234i	$-0.512462\pi$
$433$	−1.62897	−0.0782834	−0.0391417	+	0.999234i	$0.512462\pi$
$434$	−0.00708924	−0.000340294 0
$435$	4.08688	0.195951
$436$	−6.55701	−0.314024
$437$	−1.90350	−0.0910567
$438$	7.04406	0.336578
$439$	1.42189	0.0678629	0.0339314	−	0.999424i	$-0.489197\pi$
$439$	1.42189	0.0678629	0.0339314	+	0.999424i	$0.489197\pi$
$440$	0.542142	0.0258456
$441$	−6.98853	−0.332787
$442$	3.46810	0.164961
$443$	−11.0750	−0.526190	−0.263095	−	0.964770i	$-0.584743\pi$
$443$	−11.0750	−0.526190	−0.263095	+	0.964770i	$0.584743\pi$
$444$	4.66735	0.221503
$445$	5.66702	0.268642
$446$	−1.37443	−0.0650811
$447$	−20.4378	−0.966674
$448$	0.107097	0.00505988
$449$	40.1535	1.89496	0.947480	−	0.319816i	$-0.103621\pi$
$449$	40.1535	1.89496	0.947480	+	0.319816i	$0.103621\pi$
$450$	3.58905	0.169189
$451$	0.330564	0.0155656
$452$	−5.75203	−0.270553
$453$	11.0469	0.519030
$454$	4.63666	0.217609
$455$	−0.127214	−0.00596389
$456$	0.368926	0.0172766
$457$	−7.61902	−0.356403	−0.178201	−	0.983994i	$-0.557028\pi$
$457$	−7.61902	−0.356403	−0.178201	+	0.983994i	$0.557028\pi$
$458$	12.1523	0.567841
$459$	−3.46810	−0.161877
$460$	−6.12871	−0.285753
$461$	−19.5827	−0.912057	−0.456029	−	0.889965i	$-0.650729\pi$
$461$	−19.5827	−0.912057	−0.456029	+	0.889965i	$0.650729\pi$
$462$	−0.0488806	−0.00227413
$463$	16.2709	0.756173	0.378087	−	0.925770i	$-0.376582\pi$
$463$	16.2709	0.756173	0.378087	+	0.925770i	$0.376582\pi$
$464$	−3.44062	−0.159727
$465$	−0.0786279	−0.00364628
$466$	14.8168	0.686376
$467$	23.5047	1.08767	0.543834	−	0.839193i	$-0.316972\pi$
$467$	23.5047	1.08767	0.543834	+	0.839193i	$0.316972\pi$
$468$	1.00000	0.0462250
$469$	0.264060	0.0121932
$470$	−13.7644	−0.634904
$471$	−7.83563	−0.361047
$472$	−4.84255	−0.222897
$473$	1.75878	0.0808689
$474$	−0.265300	−0.0121856
$475$	1.32409	0.0607536
$476$	−0.371425	−0.0170242
$477$	−7.67799	−0.351551
$478$	−7.26585	−0.332332
$479$	30.9214	1.41283	0.706417	−	0.707796i	$-0.250310\pi$
$479$	30.9214	1.41283	0.706417	+	0.707796i	$0.250310\pi$
$480$	1.18783	0.0542170
$481$	4.66735	0.212813
$482$	−0.440354	−0.0200576
$483$	0.552576	0.0251431
$484$	−10.7917	−0.490531
$485$	−4.11603	−0.186899
$486$	−1.00000	−0.0453609
$487$	−21.0594	−0.954291	−0.477145	−	0.878824i	$-0.658328\pi$
$487$	−21.0594	−0.954291	−0.477145	+	0.878824i	$0.658328\pi$
$488$	−6.69692	−0.303155
$489$	18.6201	0.842031
$490$	−8.30122	−0.375011
$491$	−11.0866	−0.500333	−0.250166	−	0.968203i	$-0.580485\pi$
$491$	−11.0866	−0.500333	−0.250166	+	0.968203i	$0.580485\pi$
$492$	0.724266	0.0326524
$493$	11.9324	0.537409
$494$	0.368926	0.0165988
$495$	−0.542142	−0.0243675
$496$	0.0661943	0.00297221
$497$	0.735058	0.0329719
$498$	−0.324525	−0.0145423
$499$	−17.8682	−0.799889	−0.399944	−	0.916539i	$-0.630971\pi$
$499$	−17.8682	−0.799889	−0.399944	+	0.916539i	$0.630971\pi$
$500$	10.2024	0.456264
$501$	−5.85397	−0.261536
$502$	26.3082	1.17419
$503$	35.9018	1.60078	0.800391	−	0.599478i	$-0.204625\pi$
$503$	35.9018	1.60078	0.800391	+	0.599478i	$0.204625\pi$
$504$	−0.107097	−0.00477050
$505$	11.5251	0.512862
$506$	−2.35489	−0.104687
$507$	1.00000	0.0444116
$508$	6.20597	0.275345
$509$	8.78750	0.389499	0.194750	−	0.980853i	$-0.437611\pi$
$509$	8.78750	0.389499	0.194750	+	0.980853i	$0.437611\pi$
$510$	−4.11953	−0.182416
$511$	−0.754401	−0.0333727
$512$	−1.00000	−0.0441942
$513$	−0.368926	−0.0162885
$514$	−21.8953	−0.965759
$515$	1.18783	0.0523422
$516$	3.85350	0.169641
$517$	−5.28881	−0.232602
$518$	−0.499862	−0.0219627
$519$	16.2765	0.714459
$520$	1.18783	0.0520900
$521$	33.1245	1.45121	0.725606	−	0.688110i	$-0.241559\pi$
$521$	33.1245	1.45121	0.725606	+	0.688110i	$0.241559\pi$
$522$	3.44062	0.150592
$523$	3.48372	0.152332	0.0761662	−	0.997095i	$-0.475732\pi$
$523$	3.48372	0.152332	0.0761662	+	0.997095i	$0.475732\pi$
$524$	−4.57249	−0.199750
$525$	−0.384378	−0.0167756
$526$	24.7060	1.07723
$527$	−0.229569	−0.0100002
$528$	0.456412	0.0198628
$529$	3.62110	0.157439
$530$	−9.12018	−0.396155
$531$	4.84255	0.210149
$532$	−0.0395111	−0.00171302
$533$	0.724266	0.0313714
$534$	4.77088	0.206456
$535$	12.0905	0.522720
$536$	−2.46560	−0.106498
$537$	−26.4246	−1.14030
$538$	23.3163	1.00524
$539$	−3.18965	−0.137388
$540$	−1.18783	−0.0511163
$541$	−28.6991	−1.23387	−0.616936	−	0.787013i	$-0.711626\pi$
$541$	−28.6991	−1.23387	−0.616936	+	0.787013i	$0.711626\pi$
$542$	−3.22302	−0.138440
$543$	2.44713	0.105016
$544$	3.46810	0.148694
$545$	7.78864	0.333629
$546$	−0.107097	−0.00458335
$547$	15.6681	0.669920	0.334960	−	0.942232i	$-0.391277\pi$
$547$	15.6681	0.669920	0.334960	+	0.942232i	$0.391277\pi$
$548$	6.01069	0.256764
$549$	6.69692	0.285817
$550$	1.63808	0.0698482
$551$	1.26933	0.0540755
$552$	−5.15956	−0.219606
$553$	0.0284130	0.00120824
$554$	17.0469	0.724254
$555$	−5.54404	−0.235332
$556$	−4.90383	−0.207969
$557$	−30.3738	−1.28698	−0.643489	−	0.765456i	$-0.722514\pi$
$557$	−30.3738	−1.28698	−0.643489	+	0.765456i	$0.722514\pi$
$558$	−0.0661943	−0.00280223
$559$	3.85350	0.162986
$560$	−0.127214	−0.00537578
$561$	−1.58288	−0.0668294
$562$	−18.5875	−0.784066
$563$	2.56468	0.108088	0.0540442	−	0.998539i	$-0.482789\pi$
$563$	2.56468	0.108088	0.0540442	+	0.998539i	$0.482789\pi$
$564$	−11.5878	−0.487934
$565$	6.83246	0.287444
$566$	31.2994	1.31561
$567$	0.107097	0.00449767
$568$	−6.86345	−0.287984
$569$	−31.4569	−1.31874	−0.659371	−	0.751818i	$-0.729177\pi$
$569$	−31.4569	−1.31874	−0.659371	+	0.751818i	$0.729177\pi$
$570$	−0.438223	−0.0183552
$571$	29.6702	1.24166	0.620830	−	0.783945i	$-0.286796\pi$
$571$	29.6702	1.24166	0.620830	+	0.783945i	$0.286796\pi$
$572$	0.456412	0.0190835
$573$	9.01356	0.376547
$574$	−0.0775670	−0.00323759
$575$	−18.5179	−0.772251
$576$	1.00000	0.0416667
$577$	−14.8406	−0.617821	−0.308911	−	0.951091i	$-0.599964\pi$
$577$	−14.8406	−0.617821	−0.308911	+	0.951091i	$0.599964\pi$
$578$	4.97227	0.206819
$579$	−14.1229	−0.586926
$580$	4.08688	0.169699
$581$	0.0347558	0.00144192
$582$	−3.46515	−0.143635
$583$	−3.50433	−0.145134
$584$	7.04406	0.291485
$585$	−1.18783	−0.0491109
$586$	9.83799	0.406404
$587$	39.7071	1.63889	0.819445	−	0.573158i	$-0.194282\pi$
$587$	39.7071	1.63889	0.819445	+	0.573158i	$0.194282\pi$
$588$	−6.98853	−0.288202
$589$	−0.0244208	−0.00100624
$590$	5.75215	0.236812
$591$	1.74941	0.0719610
$592$	4.66735	0.191827
$593$	−22.7522	−0.934321	−0.467160	−	0.884173i	$-0.654723\pi$
$593$	−22.7522	−0.934321	−0.467160	+	0.884173i	$0.654723\pi$
$594$	−0.456412	−0.0187268
$595$	0.441191	0.0180871
$596$	−20.4378	−0.837164
$597$	18.2966	0.748831
$598$	−5.15956	−0.210990
$599$	−37.4816	−1.53145	−0.765727	−	0.643165i	$-0.777621\pi$
$599$	−37.4816	−1.53145	−0.765727	+	0.643165i	$0.777621\pi$
$600$	3.58905	0.146522
$601$	−21.9244	−0.894315	−0.447158	−	0.894455i	$-0.647564\pi$
$601$	−21.9244	−0.894315	−0.447158	+	0.894455i	$0.647564\pi$
$602$	−0.412700	−0.0168204
$603$	2.46560	0.100407
$604$	11.0469	0.449494
$605$	12.8187	0.521156
$606$	9.70265	0.394143
$607$	−21.6305	−0.877954	−0.438977	−	0.898498i	$-0.644659\pi$
$607$	−21.6305	−0.877954	−0.438977	+	0.898498i	$0.644659\pi$
$608$	0.368926	0.0149619
$609$	−0.368481	−0.0149316
$610$	7.95483	0.322082
$611$	−11.5878	−0.468792
$612$	−3.46810	−0.140190
$613$	−16.8235	−0.679496	−0.339748	−	0.940516i	$-0.610342\pi$
$613$	−16.8235	−0.679496	−0.339748	+	0.940516i	$0.610342\pi$
$614$	−27.2497	−1.09971
$615$	−0.860308	−0.0346910
$616$	−0.0488806	−0.00196945
$617$	−20.9447	−0.843204	−0.421602	−	0.906781i	$-0.638532\pi$
$617$	−20.9447	−0.843204	−0.421602	+	0.906781i	$0.638532\pi$
$618$	1.00000	0.0402259
$619$	−18.8028	−0.755748	−0.377874	−	0.925857i	$-0.623345\pi$
$619$	−18.8028	−0.755748	−0.377874	+	0.925857i	$0.623345\pi$
$620$	−0.0786279	−0.00315777
$621$	5.15956	0.207046
$622$	13.5283	0.542435
$623$	−0.510950	−0.0204708
$624$	1.00000	0.0400320
$625$	5.82652	0.233061
$626$	−31.8819	−1.27426
$627$	−0.168382	−0.00672454
$628$	−7.83563	−0.312676
$629$	−16.1869	−0.645412
$630$	0.127214	0.00506833
$631$	−33.1528	−1.31979	−0.659896	−	0.751357i	$-0.729400\pi$
$631$	−33.1528	−1.31979	−0.659896	+	0.751357i	$0.729400\pi$
$632$	−0.265300	−0.0105531
$633$	11.2374	0.446648
$634$	20.7024	0.822198
$635$	−7.37166	−0.292535
$636$	−7.67799	−0.304452
$637$	−6.98853	−0.276896
$638$	1.57034	0.0621703
$639$	6.86345	0.271514
$640$	1.18783	0.0469533
$641$	33.1896	1.31091	0.655456	−	0.755233i	$-0.272476\pi$
$641$	33.1896	1.31091	0.655456	+	0.755233i	$0.272476\pi$
$642$	10.1786	0.401719
$643$	−23.2804	−0.918089	−0.459045	−	0.888413i	$-0.651808\pi$
$643$	−23.2804	−0.918089	−0.459045	+	0.888413i	$0.651808\pi$
$644$	0.552576	0.0217746
$645$	−4.57732	−0.180232
$646$	−1.27947	−0.0503402
$647$	5.02505	0.197555	0.0987776	−	0.995110i	$-0.468507\pi$
$647$	5.02505	0.197555	0.0987776	+	0.995110i	$0.468507\pi$
$648$	−1.00000	−0.0392837
$649$	2.21020	0.0867579
$650$	3.58905	0.140774
$651$	0.00708924	0.000277849 0
$652$	18.6201	0.729221
$653$	47.7700	1.86938	0.934692	−	0.355460i	$-0.115676\pi$
$653$	47.7700	1.86938	0.934692	+	0.355460i	$0.115676\pi$
$654$	6.55701	0.256399
$655$	5.43136	0.212221
$656$	0.724266	0.0282778
$657$	−7.04406	−0.274815
$658$	1.24102	0.0483802
$659$	−43.9098	−1.71048	−0.855241	−	0.518231i	$-0.826591\pi$
$659$	−43.9098	−1.71048	−0.855241	+	0.518231i	$0.826591\pi$
$660$	−0.542142	−0.0211028
$661$	21.7286	0.845145	0.422572	−	0.906329i	$-0.361127\pi$
$661$	21.7286	0.845145	0.422572	+	0.906329i	$0.361127\pi$
$662$	7.09103	0.275601
$663$	−3.46810	−0.134690
$664$	−0.324525	−0.0125940
$665$	0.0469326	0.00181997
$666$	−4.66735	−0.180856
$667$	−17.7521	−0.687363
$668$	−5.85397	−0.226497
$669$	1.37443	0.0531385
$670$	2.92873	0.113147
$671$	3.05655	0.117997
$672$	−0.107097	−0.00413138
$673$	−48.7646	−1.87974	−0.939869	−	0.341536i	$-0.889053\pi$
$673$	−48.7646	−1.87974	−0.939869	+	0.341536i	$0.889053\pi$
$674$	31.5584	1.21559
$675$	−3.58905	−0.138143
$676$	1.00000	0.0384615
$677$	−27.9698	−1.07497	−0.537483	−	0.843275i	$-0.680625\pi$
$677$	−27.9698	−1.07497	−0.537483	+	0.843275i	$0.680625\pi$
$678$	5.75203	0.220905
$679$	0.371109	0.0142419
$680$	−4.11953	−0.157977
$681$	−4.63666	−0.177677
$682$	−0.0302119	−0.00115687
$683$	−14.1838	−0.542728	−0.271364	−	0.962477i	$-0.587475\pi$
$683$	−14.1838	−0.542728	−0.271364	+	0.962477i	$0.587475\pi$
$684$	−0.368926	−0.0141062
$685$	−7.13970	−0.272794
$686$	1.49814	0.0571991
$687$	−12.1523	−0.463641
$688$	3.85350	0.146913
$689$	−7.67799	−0.292508
$690$	6.12871	0.233316
$691$	8.76863	0.333574	0.166787	−	0.985993i	$-0.446661\pi$
$691$	8.76863	0.333574	0.166787	+	0.985993i	$0.446661\pi$
$692$	16.2765	0.618740
$693$	0.0488806	0.00185682
$694$	−22.8790	−0.868475
$695$	5.82494	0.220952
$696$	3.44062	0.130416
$697$	−2.51183	−0.0951422
$698$	6.93530	0.262505
$699$	−14.8168	−0.560424
$700$	−0.384378	−0.0145281
$701$	−32.7726	−1.23780	−0.618901	−	0.785469i	$-0.712422\pi$
$701$	−32.7726	−1.23780	−0.618901	+	0.785469i	$0.712422\pi$
$702$	−1.00000	−0.0377426
$703$	−1.72191	−0.0649430
$704$	0.456412	0.0172017
$705$	13.7644	0.518397
$706$	26.6699	1.00373
$707$	−1.03913	−0.0390805
$708$	4.84255	0.181994
$709$	25.5291	0.958764	0.479382	−	0.877606i	$-0.340861\pi$
$709$	25.5291	0.958764	0.479382	+	0.877606i	$0.340861\pi$
$710$	8.15264	0.305963
$711$	0.265300	0.00994953
$712$	4.77088	0.178796
$713$	0.341534	0.0127905
$714$	0.371425	0.0139002
$715$	−0.542142	−0.0202750
$716$	−26.4246	−0.987533
$717$	7.26585	0.271348
$718$	15.3548	0.573037
$719$	−3.14371	−0.117240	−0.0586202	−	0.998280i	$-0.518670\pi$
$719$	−3.14371	−0.117240	−0.0586202	+	0.998280i	$0.518670\pi$
$720$	−1.18783	−0.0442680
$721$	−0.107097	−0.00398852
$722$	18.8639	0.702041
$723$	0.440354	0.0163770
$724$	2.44713	0.0909468
$725$	12.3485	0.458613
$726$	10.7917	0.400517
$727$	−39.5438	−1.46660	−0.733300	−	0.679905i	$-0.762021\pi$
$727$	−39.5438	−1.46660	−0.733300	+	0.679905i	$0.762021\pi$
$728$	−0.107097	−0.00396930
$729$	1.00000	0.0370370
$730$	−8.36718	−0.309683
$731$	−13.3643	−0.494297
$732$	6.69692	0.247525
$733$	52.9505	1.95577	0.977885	−	0.209141i	$-0.0670669\pi$
$733$	52.9505	1.95577	0.977885	+	0.209141i	$0.0670669\pi$
$734$	−12.6547	−0.467094
$735$	8.30122	0.306195
$736$	−5.15956	−0.190184
$737$	1.12533	0.0414521
$738$	−0.724266	−0.0266606
$739$	44.1961	1.62578	0.812891	−	0.582416i	$-0.197893\pi$
$739$	44.1961	1.62578	0.812891	+	0.582416i	$0.197893\pi$
$740$	−5.54404	−0.203803
$741$	−0.368926	−0.0135528
$742$	0.822293	0.0301873
$743$	−12.6310	−0.463388	−0.231694	−	0.972789i	$-0.574427\pi$
$743$	−12.6310	−0.463388	−0.231694	+	0.972789i	$0.574427\pi$
$744$	−0.0661943	−0.00242680
$745$	24.2767	0.889429
$746$	5.12658	0.187697
$747$	0.324525	0.0118738
$748$	−1.58288	−0.0578759
$749$	−1.09011	−0.0398316
$750$	−10.2024	−0.372538
$751$	10.2830	0.375232	0.187616	−	0.982242i	$-0.439924\pi$
$751$	10.2830	0.375232	0.187616	+	0.982242i	$0.439924\pi$
$752$	−11.5878	−0.422564
$753$	−26.3082	−0.958725
$754$	3.44062	0.125300
$755$	−13.1219	−0.477556
$756$	0.107097	0.00389510
$757$	25.5769	0.929609	0.464805	−	0.885413i	$-0.346125\pi$
$757$	25.5769	0.929609	0.464805	+	0.885413i	$0.346125\pi$
$758$	15.8405	0.575354
$759$	2.35489	0.0854770
$760$	−0.438223	−0.0158960
$761$	38.5641	1.39795	0.698974	−	0.715147i	$-0.253640\pi$
$761$	38.5641	1.39795	0.698974	+	0.715147i	$0.253640\pi$
$762$	−6.20597	−0.224818
$763$	−0.702239	−0.0254228
$764$	9.01356	0.326099
$765$	4.11953	0.148942
$766$	34.9706	1.26354
$767$	4.84255	0.174854
$768$	1.00000	0.0360844
$769$	−7.99743	−0.288395	−0.144197	−	0.989549i	$-0.546060\pi$
$769$	−7.99743	−0.288395	−0.144197	+	0.989549i	$0.546060\pi$
$770$	0.0580620	0.00209241
$771$	21.8953	0.788539
$772$	−14.1229	−0.508293
$773$	35.3627	1.27191	0.635953	−	0.771727i	$-0.280607\pi$
$773$	35.3627	1.27191	0.635953	+	0.771727i	$0.280607\pi$
$774$	−3.85350	−0.138511
$775$	−0.237575	−0.00853393
$776$	−3.46515	−0.124392
$777$	0.499862	0.0179324
$778$	33.1833	1.18968
$779$	−0.267201	−0.00957346
$780$	−1.18783	−0.0425313
$781$	3.13256	0.112092
$782$	17.8939	0.639884
$783$	−3.44062	−0.122958
$784$	−6.98853	−0.249590
$785$	9.30743	0.332196
$786$	4.57249	0.163095
$787$	54.0602	1.92704	0.963518	−	0.267642i	$-0.0862445\pi$
$787$	54.0602	1.92704	0.963518	+	0.267642i	$0.0862445\pi$
$788$	1.74941	0.0623201
$789$	−24.7060	−0.879557
$790$	0.315133	0.0112119
$791$	−0.616028	−0.0219034
$792$	−0.456412	−0.0162179
$793$	6.69692	0.237814
$794$	21.0514	0.747086
$795$	9.12018	0.323459
$796$	18.2966	0.648507
$797$	6.52244	0.231037	0.115518	−	0.993305i	$-0.463147\pi$
$797$	6.52244	0.231037	0.115518	+	0.993305i	$0.463147\pi$
$798$	0.0395111	0.00139868
$799$	40.1877	1.42174
$800$	3.58905	0.126892
$801$	−4.77088	−0.168571
$802$	−20.3736	−0.719415
$803$	−3.21499	−0.113455
$804$	2.46560	0.0869552
$805$	−0.656369	−0.0231340
$806$	−0.0661943	−0.00233159
$807$	−23.3163	−0.820773
$808$	9.70265	0.341338
$809$	7.00356	0.246232	0.123116	−	0.992392i	$-0.460711\pi$
$809$	7.00356	0.246232	0.123116	+	0.992392i	$0.460711\pi$
$810$	1.18783	0.0417363
$811$	17.6302	0.619080	0.309540	−	0.950886i	$-0.399825\pi$
$811$	17.6302	0.619080	0.309540	+	0.950886i	$0.399825\pi$
$812$	−0.368481	−0.0129312
$813$	3.22302	0.113036
$814$	−2.13024	−0.0746647
$815$	−22.1176	−0.774747
$816$	−3.46810	−0.121408
$817$	−1.42166	−0.0497374
$818$	−32.4487	−1.13454
$819$	0.107097	0.00374229
$820$	−0.860308	−0.0300433
$821$	−3.77869	−0.131877	−0.0659386	−	0.997824i	$-0.521004\pi$
$821$	−3.77869	−0.131877	−0.0659386	+	0.997824i	$0.521004\pi$
$822$	−6.01069	−0.209647
$823$	−1.72699	−0.0601990	−0.0300995	−	0.999547i	$-0.509582\pi$
$823$	−1.72699	−0.0601990	−0.0300995	+	0.999547i	$0.509582\pi$
$824$	1.00000	0.0348367
$825$	−1.63808	−0.0570308
$826$	−0.518625	−0.0180453
$827$	−12.1844	−0.423692	−0.211846	−	0.977303i	$-0.567948\pi$
$827$	−12.1844	−0.423692	−0.211846	+	0.977303i	$0.567948\pi$
$828$	5.15956	0.179307
$829$	21.8809	0.759955	0.379977	−	0.924996i	$-0.375932\pi$
$829$	21.8809	0.759955	0.379977	+	0.924996i	$0.375932\pi$
$830$	0.385482	0.0133803
$831$	−17.0469	−0.591351
$832$	1.00000	0.0346688
$833$	24.2369	0.839760
$834$	4.90383	0.169806
$835$	6.95355	0.240638
$836$	−0.168382	−0.00582363
$837$	0.0661943	0.00228801
$838$	36.4708	1.25986
$839$	−38.0183	−1.31254	−0.656269	−	0.754527i	$-0.727866\pi$
$839$	−38.0183	−1.31254	−0.656269	+	0.754527i	$0.727866\pi$
$840$	0.127214	0.00438930
$841$	−17.1622	−0.591798
$842$	−33.3994	−1.15102
$843$	18.5875	0.640187
$844$	11.2374	0.386808
$845$	−1.18783	−0.0408628
$846$	11.5878	0.398397
$847$	−1.15576	−0.0397125
$848$	−7.67799	−0.263663
$849$	−31.2994	−1.07419
$850$	−12.4472	−0.426935
$851$	24.0815	0.825504
$852$	6.86345	0.235138
$853$	−27.6896	−0.948075	−0.474037	−	0.880505i	$-0.657204\pi$
$853$	−27.6896	−0.948075	−0.474037	+	0.880505i	$0.657204\pi$
$854$	−0.717223	−0.0245429
$855$	0.438223	0.0149869
$856$	10.1786	0.347899
$857$	−18.4397	−0.629889	−0.314945	−	0.949110i	$-0.601986\pi$
$857$	−18.4397	−0.629889	−0.314945	+	0.949110i	$0.601986\pi$
$858$	−0.456412	−0.0155816
$859$	−39.0274	−1.33160	−0.665800	−	0.746131i	$-0.731909\pi$
$859$	−39.0274	−1.33160	−0.665800	+	0.746131i	$0.731909\pi$
$860$	−4.57732	−0.156085
$861$	0.0775670	0.00264348
$862$	−15.1652	−0.516528
$863$	30.3765	1.03403	0.517013	−	0.855977i	$-0.327044\pi$
$863$	30.3765	1.03403	0.517013	+	0.855977i	$0.327044\pi$
$864$	−1.00000	−0.0340207
$865$	−19.3338	−0.657368
$866$	1.62897	0.0553547
$867$	−4.97227	−0.168867
$868$	0.00708924	0.000240625 0
$869$	0.121086	0.00410757
$870$	−4.08688	−0.138558
$871$	2.46560	0.0835438
$872$	6.55701	0.222048
$873$	3.46515	0.117278
$874$	1.90350	0.0643868
$875$	1.09265	0.0369382
$876$	−7.04406	−0.237997
$877$	−30.7986	−1.04000	−0.519998	−	0.854168i	$-0.674067\pi$
$877$	−30.7986	−1.04000	−0.519998	+	0.854168i	$0.674067\pi$
$878$	−1.42189	−0.0479863
$879$	−9.83799	−0.331827
$880$	−0.542142	−0.0182756
$881$	−8.55855	−0.288345	−0.144172	−	0.989553i	$-0.546052\pi$
$881$	−8.55855	−0.288345	−0.144172	+	0.989553i	$0.546052\pi$
$882$	6.98853	0.235316
$883$	−27.6244	−0.929635	−0.464818	−	0.885406i	$-0.653880\pi$
$883$	−27.6244	−0.929635	−0.464818	+	0.885406i	$0.653880\pi$
$884$	−3.46810	−0.116645
$885$	−5.75215	−0.193356
$886$	11.0750	0.372072
$887$	11.4518	0.384515	0.192258	−	0.981344i	$-0.438419\pi$
$887$	11.4518	0.384515	0.192258	+	0.981344i	$0.438419\pi$
$888$	−4.66735	−0.156626
$889$	0.664643	0.0222914
$890$	−5.66702	−0.189959
$891$	0.456412	0.0152904
$892$	1.37443	0.0460193
$893$	4.27504	0.143059
$894$	20.4378	0.683541
$895$	31.3880	1.04919
$896$	−0.107097	−0.00357788
$897$	5.15956	0.172273
$898$	−40.1535	−1.33994
$899$	−0.227749	−0.00759586
$900$	−3.58905	−0.119635
$901$	26.6280	0.887109
$902$	−0.330564	−0.0110066
$903$	0.412700	0.0137338
$904$	5.75203	0.191310
$905$	−2.90678	−0.0966247
$906$	−11.0469	−0.367010
$907$	30.9403	1.02736	0.513678	−	0.857983i	$-0.328283\pi$
$907$	30.9403	1.02736	0.513678	+	0.857983i	$0.328283\pi$
$908$	−4.63666	−0.153873
$909$	−9.70265	−0.321817
$910$	0.127214	0.00421711
$911$	−18.7957	−0.622731	−0.311365	−	0.950290i	$-0.600786\pi$
$911$	−18.7957	−0.622731	−0.311365	+	0.950290i	$0.600786\pi$
$912$	−0.368926	−0.0122164
$913$	0.148117	0.00490196
$914$	7.61902	0.252015
$915$	−7.95483	−0.262978
$916$	−12.1523	−0.401524
$917$	−0.489702	−0.0161714
$918$	3.46810	0.114464
$919$	−45.6953	−1.50735	−0.753675	−	0.657248i	$-0.771721\pi$
$919$	−45.6953	−1.50735	−0.753675	+	0.657248i	$0.771721\pi$
$920$	6.12871	0.202058
$921$	27.2497	0.897910
$922$	19.5827	0.644922
$923$	6.86345	0.225913
$924$	0.0488806	0.00160805
$925$	−16.7514	−0.550781
$926$	−16.2709	−0.534695
$927$	−1.00000	−0.0328443
$928$	3.44062	0.112944
$929$	−8.51591	−0.279398	−0.139699	−	0.990194i	$-0.544613\pi$
$929$	−8.51591	−0.279398	−0.139699	+	0.990194i	$0.544613\pi$
$930$	0.0786279	0.00257831
$931$	2.57825	0.0844988
$932$	−14.8168	−0.485341
$933$	−13.5283	−0.442896
$934$	−23.5047	−0.769098
$935$	1.88020	0.0614892
$936$	−1.00000	−0.0326860
$937$	−22.2829	−0.727951	−0.363976	−	0.931409i	$-0.618581\pi$
$937$	−22.2829	−0.727951	−0.363976	+	0.931409i	$0.618581\pi$
$938$	−0.264060	−0.00862187
$939$	31.8819	1.04043
$940$	13.7644	0.448945
$941$	−58.3034	−1.90064	−0.950318	−	0.311281i	$-0.899242\pi$
$941$	−58.3034	−1.90064	−0.950318	+	0.311281i	$0.899242\pi$
$942$	7.83563	0.255299
$943$	3.73690	0.121690
$944$	4.84255	0.157612
$945$	−0.127214	−0.00413827
$946$	−1.75878	−0.0571829
$947$	54.0157	1.75527	0.877637	−	0.479325i	$-0.159118\pi$
$947$	54.0157	1.75527	0.877637	+	0.479325i	$0.159118\pi$
$948$	0.265300	0.00861655
$949$	−7.04406	−0.228660
$950$	−1.32409	−0.0429593
$951$	−20.7024	−0.671322
$952$	0.371425	0.0120380
$953$	−52.8072	−1.71059	−0.855296	−	0.518139i	$-0.826625\pi$
$953$	−52.8072	−1.71059	−0.855296	+	0.518139i	$0.826625\pi$
$954$	7.67799	0.248584
$955$	−10.7066	−0.346458
$956$	7.26585	0.234994
$957$	−1.57034	−0.0507618
$958$	−30.9214	−0.999025
$959$	0.643730	0.0207871
$960$	−1.18783	−0.0383372
$961$	−30.9956	−0.999859
$962$	−4.66735	−0.150482
$963$	−10.1786	−0.328002
$964$	0.440354	0.0141829
$965$	16.7756	0.540026
$966$	−0.552576	−0.0177789
$967$	51.2680	1.64867	0.824333	−	0.566105i	$-0.191550\pi$
$967$	51.2680	1.64867	0.824333	+	0.566105i	$0.191550\pi$
$968$	10.7917	0.346858
$969$	1.27947	0.0411026
$970$	4.11603	0.132158
$971$	−3.19475	−0.102524	−0.0512621	−	0.998685i	$-0.516324\pi$
$971$	−3.19475	−0.102524	−0.0512621	+	0.998685i	$0.516324\pi$
$972$	1.00000	0.0320750
$973$	−0.525188	−0.0168367
$974$	21.0594	0.674785
$975$	−3.58905	−0.114942
$976$	6.69692	0.214363
$977$	36.6736	1.17329	0.586646	−	0.809843i	$-0.300448\pi$
$977$	36.6736	1.17329	0.586646	+	0.809843i	$0.300448\pi$
$978$	−18.6201	−0.595406
$979$	−2.17749	−0.0695928
$980$	8.30122	0.265173
$981$	−6.55701	−0.209349
$982$	11.0866	0.353789
$983$	−49.2075	−1.56948	−0.784739	−	0.619827i	$-0.787203\pi$
$983$	−49.2075	−1.56948	−0.784739	+	0.619827i	$0.787203\pi$
$984$	−0.724266	−0.0230887
$985$	−2.07801	−0.0662108
$986$	−11.9324	−0.380005
$987$	−1.24102	−0.0395022
$988$	−0.368926	−0.0117371
$989$	19.8824	0.632222
$990$	0.542142	0.0172304
$991$	49.6099	1.57591	0.787956	−	0.615732i	$-0.211140\pi$
$991$	49.6099	1.57591	0.787956	+	0.615732i	$0.211140\pi$
$992$	−0.0661943	−0.00210167
$993$	−7.09103	−0.225027
$994$	−0.735058	−0.0233146
$995$	−21.7334	−0.688994
$996$	0.324525	0.0102830
$997$	14.7221	0.466252	0.233126	−	0.972446i	$-0.425104\pi$
$997$	14.7221	0.466252	0.233126	+	0.972446i	$0.425104\pi$
$998$	17.8682	0.565607
$999$	4.66735	0.147669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.6	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.18783 q^{5} -1.00000 q^{6} +0.107097 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.18783 q^{5} -1.00000 q^{6} +0.107097 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.18783 q^{10} +0.456412 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.107097 q^{14} -1.18783 q^{15} +1.00000 q^{16} -3.46810 q^{17} -1.00000 q^{18} -0.368926 q^{19} -1.18783 q^{20} +0.107097 q^{21} -0.456412 q^{22} +5.15956 q^{23} -1.00000 q^{24} -3.58905 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.107097 q^{28} -3.44062 q^{29} +1.18783 q^{30} +0.0661943 q^{31} -1.00000 q^{32} +0.456412 q^{33} +3.46810 q^{34} -0.127214 q^{35} +1.00000 q^{36} +4.66735 q^{37} +0.368926 q^{38} +1.00000 q^{39} +1.18783 q^{40} +0.724266 q^{41} -0.107097 q^{42} +3.85350 q^{43} +0.456412 q^{44} -1.18783 q^{45} -5.15956 q^{46} -11.5878 q^{47} +1.00000 q^{48} -6.98853 q^{49} +3.58905 q^{50} -3.46810 q^{51} +1.00000 q^{52} -7.67799 q^{53} -1.00000 q^{54} -0.542142 q^{55} -0.107097 q^{56} -0.368926 q^{57} +3.44062 q^{58} +4.84255 q^{59} -1.18783 q^{60} +6.69692 q^{61} -0.0661943 q^{62} +0.107097 q^{63} +1.00000 q^{64} -1.18783 q^{65} -0.456412 q^{66} +2.46560 q^{67} -3.46810 q^{68} +5.15956 q^{69} +0.127214 q^{70} +6.86345 q^{71} -1.00000 q^{72} -7.04406 q^{73} -4.66735 q^{74} -3.58905 q^{75} -0.368926 q^{76} +0.0488806 q^{77} -1.00000 q^{78} +0.265300 q^{79} -1.18783 q^{80} +1.00000 q^{81} -0.724266 q^{82} +0.324525 q^{83} +0.107097 q^{84} +4.11953 q^{85} -3.85350 q^{86} -3.44062 q^{87} -0.456412 q^{88} -4.77088 q^{89} +1.18783 q^{90} +0.107097 q^{91} +5.15956 q^{92} +0.0661943 q^{93} +11.5878 q^{94} +0.438223 q^{95} -1.00000 q^{96} +3.46515 q^{97} +6.98853 q^{98} +0.456412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

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