LMFDB - Embedded newform 8034.2.a.bd.1.3

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			1.3
Root			$-2.68392$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.68392 q^{5} +1.00000 q^{6} -4.10513 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.68392 q^{5} +1.00000 q^{6} -4.10513 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.68392 q^{10} +3.10838 q^{11} +1.00000 q^{12} -1.00000 q^{13} -4.10513 q^{14} -2.68392 q^{15} +1.00000 q^{16} -3.53430 q^{17} +1.00000 q^{18} -6.07479 q^{19} -2.68392 q^{20} -4.10513 q^{21} +3.10838 q^{22} -5.39970 q^{23} +1.00000 q^{24} +2.20340 q^{25} -1.00000 q^{26} +1.00000 q^{27} -4.10513 q^{28} +4.59519 q^{29} -2.68392 q^{30} +7.13492 q^{31} +1.00000 q^{32} +3.10838 q^{33} -3.53430 q^{34} +11.0178 q^{35} +1.00000 q^{36} +1.27443 q^{37} -6.07479 q^{38} -1.00000 q^{39} -2.68392 q^{40} +5.54812 q^{41} -4.10513 q^{42} +12.2627 q^{43} +3.10838 q^{44} -2.68392 q^{45} -5.39970 q^{46} -11.8700 q^{47} +1.00000 q^{48} +9.85206 q^{49} +2.20340 q^{50} -3.53430 q^{51} -1.00000 q^{52} -1.77020 q^{53} +1.00000 q^{54} -8.34262 q^{55} -4.10513 q^{56} -6.07479 q^{57} +4.59519 q^{58} +14.4851 q^{59} -2.68392 q^{60} -12.7107 q^{61} +7.13492 q^{62} -4.10513 q^{63} +1.00000 q^{64} +2.68392 q^{65} +3.10838 q^{66} +5.38738 q^{67} -3.53430 q^{68} -5.39970 q^{69} +11.0178 q^{70} +10.8499 q^{71} +1.00000 q^{72} +0.969543 q^{73} +1.27443 q^{74} +2.20340 q^{75} -6.07479 q^{76} -12.7603 q^{77} -1.00000 q^{78} +2.83725 q^{79} -2.68392 q^{80} +1.00000 q^{81} +5.54812 q^{82} -13.3988 q^{83} -4.10513 q^{84} +9.48576 q^{85} +12.2627 q^{86} +4.59519 q^{87} +3.10838 q^{88} -2.79808 q^{89} -2.68392 q^{90} +4.10513 q^{91} -5.39970 q^{92} +7.13492 q^{93} -11.8700 q^{94} +16.3042 q^{95} +1.00000 q^{96} +15.4478 q^{97} +9.85206 q^{98} +3.10838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.68392	−1.20028	−0.600142	−	0.799894i	$-0.704889\pi$
$5$	−2.68392	−1.20028	−0.600142	+	0.799894i	$0.704889\pi$
$6$	1.00000	0.408248
$7$	−4.10513	−1.55159	−0.775796	−	0.630984i	$-0.782651\pi$
$7$	−4.10513	−1.55159	−0.775796	+	0.630984i	$0.782651\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.68392	−0.848729
$11$	3.10838	0.937211	0.468605	−	0.883408i	$-0.344757\pi$
$11$	3.10838	0.937211	0.468605	+	0.883408i	$0.344757\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.10513	−1.09714
$15$	−2.68392	−0.692984
$16$	1.00000	0.250000
$17$	−3.53430	−0.857193	−0.428597	−	0.903496i	$-0.640992\pi$
$17$	−3.53430	−0.857193	−0.428597	+	0.903496i	$0.640992\pi$
$18$	1.00000	0.235702
$19$	−6.07479	−1.39365	−0.696827	−	0.717239i	$-0.745405\pi$
$19$	−6.07479	−1.39365	−0.696827	+	0.717239i	$0.745405\pi$
$20$	−2.68392	−0.600142
$21$	−4.10513	−0.895812
$22$	3.10838	0.662708
$23$	−5.39970	−1.12592	−0.562958	−	0.826486i	$-0.690337\pi$
$23$	−5.39970	−1.12592	−0.562958	+	0.826486i	$0.690337\pi$
$24$	1.00000	0.204124
$25$	2.20340	0.440681
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−4.10513	−0.775796
$29$	4.59519	0.853306	0.426653	−	0.904415i	$-0.359693\pi$
$29$	4.59519	0.853306	0.426653	+	0.904415i	$0.359693\pi$
$30$	−2.68392	−0.490014
$31$	7.13492	1.28147	0.640734	−	0.767763i	$-0.278630\pi$
$31$	7.13492	1.28147	0.640734	+	0.767763i	$0.278630\pi$
$32$	1.00000	0.176777
$33$	3.10838	0.541099
$34$	−3.53430	−0.606127
$35$	11.0178	1.86235
$36$	1.00000	0.166667
$37$	1.27443	0.209515	0.104758	−	0.994498i	$-0.466593\pi$
$37$	1.27443	0.209515	0.104758	+	0.994498i	$0.466593\pi$
$38$	−6.07479	−0.985462
$39$	−1.00000	−0.160128
$40$	−2.68392	−0.424364
$41$	5.54812	0.866471	0.433235	−	0.901281i	$-0.357372\pi$
$41$	5.54812	0.866471	0.433235	+	0.901281i	$0.357372\pi$
$42$	−4.10513	−0.633435
$43$	12.2627	1.87004	0.935022	−	0.354589i	$-0.115379\pi$
$43$	12.2627	1.87004	0.935022	+	0.354589i	$0.115379\pi$
$44$	3.10838	0.468605
$45$	−2.68392	−0.400095
$46$	−5.39970	−0.796142
$47$	−11.8700	−1.73142	−0.865709	−	0.500547i	$-0.833132\pi$
$47$	−11.8700	−1.73142	−0.865709	+	0.500547i	$0.833132\pi$
$48$	1.00000	0.144338
$49$	9.85206	1.40744
$50$	2.20340	0.311609
$51$	−3.53430	−0.494901
$52$	−1.00000	−0.138675
$53$	−1.77020	−0.243155	−0.121578	−	0.992582i	$-0.538795\pi$
$53$	−1.77020	−0.243155	−0.121578	+	0.992582i	$0.538795\pi$
$54$	1.00000	0.136083
$55$	−8.34262	−1.12492
$56$	−4.10513	−0.548571
$57$	−6.07479	−0.804626
$58$	4.59519	0.603379
$59$	14.4851	1.88579	0.942897	−	0.333085i	$-0.108090\pi$
$59$	14.4851	1.88579	0.942897	+	0.333085i	$0.108090\pi$
$60$	−2.68392	−0.346492
$61$	−12.7107	−1.62744	−0.813718	−	0.581260i	$-0.802560\pi$
$61$	−12.7107	−1.62744	−0.813718	+	0.581260i	$0.802560\pi$
$62$	7.13492	0.906135
$63$	−4.10513	−0.517197
$64$	1.00000	0.125000
$65$	2.68392	0.332899
$66$	3.10838	0.382615
$67$	5.38738	0.658173	0.329086	−	0.944300i	$-0.393259\pi$
$67$	5.38738	0.658173	0.329086	+	0.944300i	$0.393259\pi$
$68$	−3.53430	−0.428597
$69$	−5.39970	−0.650047
$70$	11.0178	1.31688
$71$	10.8499	1.28764	0.643822	−	0.765175i	$-0.277348\pi$
$71$	10.8499	1.28764	0.643822	+	0.765175i	$0.277348\pi$
$72$	1.00000	0.117851
$73$	0.969543	0.113476	0.0567382	−	0.998389i	$-0.481930\pi$
$73$	0.969543	0.113476	0.0567382	+	0.998389i	$0.481930\pi$
$74$	1.27443	0.148150
$75$	2.20340	0.254427
$76$	−6.07479	−0.696827
$77$	−12.7603	−1.45417
$78$	−1.00000	−0.113228
$79$	2.83725	0.319216	0.159608	−	0.987180i	$-0.448977\pi$
$79$	2.83725	0.319216	0.159608	+	0.987180i	$0.448977\pi$
$80$	−2.68392	−0.300071
$81$	1.00000	0.111111
$82$	5.54812	0.612687
$83$	−13.3988	−1.47071	−0.735353	−	0.677684i	$-0.762984\pi$
$83$	−13.3988	−1.47071	−0.735353	+	0.677684i	$0.762984\pi$
$84$	−4.10513	−0.447906
$85$	9.48576	1.02888
$86$	12.2627	1.32232
$87$	4.59519	0.492656
$88$	3.10838	0.331354
$89$	−2.79808	−0.296596	−0.148298	−	0.988943i	$-0.547379\pi$
$89$	−2.79808	−0.296596	−0.148298	+	0.988943i	$0.547379\pi$
$90$	−2.68392	−0.282910
$91$	4.10513	0.430334
$92$	−5.39970	−0.562958
$93$	7.13492	0.739856
$94$	−11.8700	−1.22430
$95$	16.3042	1.67278
$96$	1.00000	0.102062
$97$	15.4478	1.56849	0.784243	−	0.620454i	$-0.213052\pi$
$97$	15.4478	1.56849	0.784243	+	0.620454i	$0.213052\pi$
$98$	9.85206	0.995209
$99$	3.10838	0.312404
$100$	2.20340	0.220340
$101$	16.0658	1.59861	0.799305	−	0.600926i	$-0.205201\pi$
$101$	16.0658	1.59861	0.799305	+	0.600926i	$0.205201\pi$
$102$	−3.53430	−0.349948
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	11.0178	1.07523
$106$	−1.77020	−0.171937
$107$	14.0680	1.36001	0.680005	−	0.733208i	$-0.261978\pi$
$107$	14.0680	1.36001	0.680005	+	0.733208i	$0.261978\pi$
$108$	1.00000	0.0962250
$109$	−4.16954	−0.399370	−0.199685	−	0.979860i	$-0.563992\pi$
$109$	−4.16954	−0.399370	−0.199685	+	0.979860i	$0.563992\pi$
$110$	−8.34262	−0.795438
$111$	1.27443	0.120964
$112$	−4.10513	−0.387898
$113$	−8.78688	−0.826600	−0.413300	−	0.910595i	$-0.635624\pi$
$113$	−8.78688	−0.826600	−0.413300	+	0.910595i	$0.635624\pi$
$114$	−6.07479	−0.568957
$115$	14.4923	1.35142
$116$	4.59519	0.426653
$117$	−1.00000	−0.0924500
$118$	14.4851	1.33346
$119$	14.5087	1.33001
$120$	−2.68392	−0.245007
$121$	−1.33800	−0.121636
$122$	−12.7107	−1.15077
$123$	5.54812	0.500257
$124$	7.13492	0.640734
$125$	7.50583	0.671341
$126$	−4.10513	−0.365714
$127$	2.42086	0.214817	0.107408	−	0.994215i	$-0.465745\pi$
$127$	2.42086	0.214817	0.107408	+	0.994215i	$0.465745\pi$
$128$	1.00000	0.0883883
$129$	12.2627	1.07967
$130$	2.68392	0.235395
$131$	−21.1012	−1.84362	−0.921811	−	0.387640i	$-0.873290\pi$
$131$	−21.1012	−1.84362	−0.921811	+	0.387640i	$0.873290\pi$
$132$	3.10838	0.270549
$133$	24.9378	2.16238
$134$	5.38738	0.465399
$135$	−2.68392	−0.230995
$136$	−3.53430	−0.303064
$137$	19.6454	1.67842	0.839212	−	0.543805i	$-0.183017\pi$
$137$	19.6454	1.67842	0.839212	+	0.543805i	$0.183017\pi$
$138$	−5.39970	−0.459653
$139$	−3.48184	−0.295326	−0.147663	−	0.989038i	$-0.547175\pi$
$139$	−3.48184	−0.295326	−0.147663	+	0.989038i	$0.547175\pi$
$140$	11.0178	0.931175
$141$	−11.8700	−0.999635
$142$	10.8499	0.910502
$143$	−3.10838	−0.259935
$144$	1.00000	0.0833333
$145$	−12.3331	−1.02421
$146$	0.969543	0.0802400
$147$	9.85206	0.812584
$148$	1.27443	0.104758
$149$	16.4553	1.34807	0.674035	−	0.738699i	$-0.264560\pi$
$149$	16.4553	1.34807	0.674035	+	0.738699i	$0.264560\pi$
$150$	2.20340	0.179907
$151$	16.7678	1.36455	0.682274	−	0.731097i	$-0.260991\pi$
$151$	16.7678	1.36455	0.682274	+	0.731097i	$0.260991\pi$
$152$	−6.07479	−0.492731
$153$	−3.53430	−0.285731
$154$	−12.7603	−1.02825
$155$	−19.1495	−1.53813
$156$	−1.00000	−0.0800641
$157$	−6.95977	−0.555450	−0.277725	−	0.960661i	$-0.589580\pi$
$157$	−6.95977	−0.555450	−0.277725	+	0.960661i	$0.589580\pi$
$158$	2.83725	0.225720
$159$	−1.77020	−0.140386
$160$	−2.68392	−0.212182
$161$	22.1664	1.74696
$162$	1.00000	0.0785674
$163$	3.70093	0.289879	0.144939	−	0.989441i	$-0.453701\pi$
$163$	3.70093	0.289879	0.144939	+	0.989441i	$0.453701\pi$
$164$	5.54812	0.433235
$165$	−8.34262	−0.649472
$166$	−13.3988	−1.03995
$167$	−0.0839211	−0.00649401	−0.00324700	−	0.999995i	$-0.501034\pi$
$167$	−0.0839211	−0.00649401	−0.00324700	+	0.999995i	$0.501034\pi$
$168$	−4.10513	−0.316717
$169$	1.00000	0.0769231
$170$	9.48576	0.727525
$171$	−6.07479	−0.464551
$172$	12.2627	0.935022
$173$	−6.63833	−0.504703	−0.252352	−	0.967636i	$-0.581204\pi$
$173$	−6.63833	−0.504703	−0.252352	+	0.967636i	$0.581204\pi$
$174$	4.59519	0.348361
$175$	−9.04526	−0.683757
$176$	3.10838	0.234303
$177$	14.4851	1.08876
$178$	−2.79808	−0.209725
$179$	9.47767	0.708394	0.354197	−	0.935171i	$-0.384754\pi$
$179$	9.47767	0.708394	0.354197	+	0.935171i	$0.384754\pi$
$180$	−2.68392	−0.200047
$181$	−4.38227	−0.325731	−0.162866	−	0.986648i	$-0.552074\pi$
$181$	−4.38227	−0.325731	−0.162866	+	0.986648i	$0.552074\pi$
$182$	4.10513	0.304292
$183$	−12.7107	−0.939601
$184$	−5.39970	−0.398071
$185$	−3.42047	−0.251478
$186$	7.13492	0.523158
$187$	−10.9859	−0.803371
$188$	−11.8700	−0.865709
$189$	−4.10513	−0.298604
$190$	16.3042	1.18283
$191$	−17.7967	−1.28772	−0.643860	−	0.765143i	$-0.722668\pi$
$191$	−17.7967	−1.28772	−0.643860	+	0.765143i	$0.722668\pi$
$192$	1.00000	0.0721688
$193$	5.17454	0.372472	0.186236	−	0.982505i	$-0.440371\pi$
$193$	5.17454	0.372472	0.186236	+	0.982505i	$0.440371\pi$
$194$	15.4478	1.10909
$195$	2.68392	0.192199
$196$	9.85206	0.703719
$197$	17.4369	1.24233	0.621163	−	0.783681i	$-0.286660\pi$
$197$	17.4369	1.24233	0.621163	+	0.783681i	$0.286660\pi$
$198$	3.10838	0.220903
$199$	15.1980	1.07736	0.538678	−	0.842512i	$-0.318924\pi$
$199$	15.1980	1.07736	0.538678	+	0.842512i	$0.318924\pi$
$200$	2.20340	0.155804
$201$	5.38738	0.379996
$202$	16.0658	1.13039
$203$	−18.8639	−1.32398
$204$	−3.53430	−0.247450
$205$	−14.8907	−1.04001
$206$	1.00000	0.0696733
$207$	−5.39970	−0.375305
$208$	−1.00000	−0.0693375
$209$	−18.8827	−1.30615
$210$	11.0178	0.760301
$211$	0.0655512	0.00451273	0.00225636	−	0.999997i	$-0.499282\pi$
$211$	0.0655512	0.00451273	0.00225636	+	0.999997i	$0.499282\pi$
$212$	−1.77020	−0.121578
$213$	10.8499	0.743421
$214$	14.0680	0.961672
$215$	−32.9121	−2.24458
$216$	1.00000	0.0680414
$217$	−29.2897	−1.98832
$218$	−4.16954	−0.282397
$219$	0.969543	0.0655157
$220$	−8.34262	−0.562459
$221$	3.53430	0.237743
$222$	1.27443	0.0855343
$223$	−14.5960	−0.977420	−0.488710	−	0.872446i	$-0.662532\pi$
$223$	−14.5960	−0.977420	−0.488710	+	0.872446i	$0.662532\pi$
$224$	−4.10513	−0.274285
$225$	2.20340	0.146894
$226$	−8.78688	−0.584495
$227$	−6.52314	−0.432956	−0.216478	−	0.976287i	$-0.569457\pi$
$227$	−6.52314	−0.432956	−0.216478	+	0.976287i	$0.569457\pi$
$228$	−6.07479	−0.402313
$229$	17.4135	1.15072	0.575359	−	0.817901i	$-0.304862\pi$
$229$	17.4135	1.15072	0.575359	+	0.817901i	$0.304862\pi$
$230$	14.4923	0.955597
$231$	−12.7603	−0.839565
$232$	4.59519	0.301689
$233$	−0.400509	−0.0262382	−0.0131191	−	0.999914i	$-0.504176\pi$
$233$	−0.400509	−0.0262382	−0.0131191	+	0.999914i	$0.504176\pi$
$234$	−1.00000	−0.0653720
$235$	31.8581	2.07819
$236$	14.4851	0.942897
$237$	2.83725	0.184299
$238$	14.5087	0.940462
$239$	−3.16608	−0.204797	−0.102398	−	0.994743i	$-0.532652\pi$
$239$	−3.16608	−0.204797	−0.102398	+	0.994743i	$0.532652\pi$
$240$	−2.68392	−0.173246
$241$	24.8592	1.60132	0.800662	−	0.599116i	$-0.204481\pi$
$241$	24.8592	1.60132	0.800662	+	0.599116i	$0.204481\pi$
$242$	−1.33800	−0.0860098
$243$	1.00000	0.0641500
$244$	−12.7107	−0.813718
$245$	−26.4421	−1.68932
$246$	5.54812	0.353735
$247$	6.07479	0.386530
$248$	7.13492	0.453068
$249$	−13.3988	−0.849113
$250$	7.50583	0.474710
$251$	−4.91104	−0.309982	−0.154991	−	0.987916i	$-0.549535\pi$
$251$	−4.91104	−0.309982	−0.154991	+	0.987916i	$0.549535\pi$
$252$	−4.10513	−0.258599
$253$	−16.7843	−1.05522
$254$	2.42086	0.151898
$255$	9.48576	0.594021
$256$	1.00000	0.0625000
$257$	13.3052	0.829955	0.414978	−	0.909832i	$-0.363789\pi$
$257$	13.3052	0.829955	0.414978	+	0.909832i	$0.363789\pi$
$258$	12.2627	0.763442
$259$	−5.23171	−0.325082
$260$	2.68392	0.166449
$261$	4.59519	0.284435
$262$	−21.1012	−1.30364
$263$	−11.3427	−0.699420	−0.349710	−	0.936858i	$-0.613720\pi$
$263$	−11.3427	−0.699420	−0.349710	+	0.936858i	$0.613720\pi$
$264$	3.10838	0.191307
$265$	4.75106	0.291855
$266$	24.9378	1.52903
$267$	−2.79808	−0.171240
$268$	5.38738	0.329086
$269$	−24.0058	−1.46366	−0.731830	−	0.681487i	$-0.761333\pi$
$269$	−24.0058	−1.46366	−0.731830	+	0.681487i	$0.761333\pi$
$270$	−2.68392	−0.163338
$271$	−2.53740	−0.154136	−0.0770679	−	0.997026i	$-0.524556\pi$
$271$	−2.53740	−0.154136	−0.0770679	+	0.997026i	$0.524556\pi$
$272$	−3.53430	−0.214298
$273$	4.10513	0.248454
$274$	19.6454	1.18682
$275$	6.84901	0.413011
$276$	−5.39970	−0.325024
$277$	−20.2852	−1.21882	−0.609408	−	0.792856i	$-0.708593\pi$
$277$	−20.2852	−1.21882	−0.609408	+	0.792856i	$0.708593\pi$
$278$	−3.48184	−0.208827
$279$	7.13492	0.427156
$280$	11.0178	0.658440
$281$	13.3071	0.793836	0.396918	−	0.917854i	$-0.370080\pi$
$281$	13.3071	0.793836	0.396918	+	0.917854i	$0.370080\pi$
$282$	−11.8700	−0.706849
$283$	13.6787	0.813114	0.406557	−	0.913625i	$-0.366729\pi$
$283$	13.6787	0.813114	0.406557	+	0.913625i	$0.366729\pi$
$284$	10.8499	0.643822
$285$	16.3042	0.965780
$286$	−3.10838	−0.183802
$287$	−22.7757	−1.34441
$288$	1.00000	0.0589256
$289$	−4.50874	−0.265220
$290$	−12.3331	−0.724225
$291$	15.4478	0.905566
$292$	0.969543	0.0567382
$293$	−13.9945	−0.817570	−0.408785	−	0.912631i	$-0.634047\pi$
$293$	−13.9945	−0.817570	−0.408785	+	0.912631i	$0.634047\pi$
$294$	9.85206	0.574584
$295$	−38.8767	−2.26349
$296$	1.27443	0.0740749
$297$	3.10838	0.180366
$298$	16.4553	0.953229
$299$	5.39970	0.312273
$300$	2.20340	0.127214
$301$	−50.3399	−2.90155
$302$	16.7678	0.964881
$303$	16.0658	0.922958
$304$	−6.07479	−0.348413
$305$	34.1144	1.95338
$306$	−3.53430	−0.202042
$307$	19.3243	1.10290	0.551449	−	0.834209i	$-0.314075\pi$
$307$	19.3243	1.10290	0.551449	+	0.834209i	$0.314075\pi$
$308$	−12.7603	−0.727084
$309$	1.00000	0.0568880
$310$	−19.1495	−1.08762
$311$	24.9134	1.41271	0.706356	−	0.707857i	$-0.250338\pi$
$311$	24.9134	1.41271	0.706356	+	0.707857i	$0.250338\pi$
$312$	−1.00000	−0.0566139
$313$	−13.4884	−0.762410	−0.381205	−	0.924491i	$-0.624491\pi$
$313$	−13.4884	−0.762410	−0.381205	+	0.924491i	$0.624491\pi$
$314$	−6.95977	−0.392763
$315$	11.0178	0.620783
$316$	2.83725	0.159608
$317$	16.2318	0.911671	0.455836	−	0.890064i	$-0.349341\pi$
$317$	16.2318	0.911671	0.455836	+	0.890064i	$0.349341\pi$
$318$	−1.77020	−0.0992677
$319$	14.2836	0.799728
$320$	−2.68392	−0.150035
$321$	14.0680	0.785202
$322$	22.1664	1.23529
$323$	21.4701	1.19463
$324$	1.00000	0.0555556
$325$	−2.20340	−0.122223
$326$	3.70093	0.204975
$327$	−4.16954	−0.230576
$328$	5.54812	0.306344
$329$	48.7279	2.68645
$330$	−8.34262	−0.459246
$331$	14.2585	0.783717	0.391858	−	0.920026i	$-0.371832\pi$
$331$	14.2585	0.783717	0.391858	+	0.920026i	$0.371832\pi$
$332$	−13.3988	−0.735353
$333$	1.27443	0.0698385
$334$	−0.0839211	−0.00459196
$335$	−14.4593	−0.789994
$336$	−4.10513	−0.223953
$337$	6.44173	0.350903	0.175452	−	0.984488i	$-0.443861\pi$
$337$	6.44173	0.350903	0.175452	+	0.984488i	$0.443861\pi$
$338$	1.00000	0.0543928
$339$	−8.78688	−0.477238
$340$	9.48576	0.514438
$341$	22.1780	1.20101
$342$	−6.07479	−0.328487
$343$	−11.7081	−0.632177
$344$	12.2627	0.661161
$345$	14.4923	0.780241
$346$	−6.63833	−0.356879
$347$	10.0037	0.537025	0.268512	−	0.963276i	$-0.413468\pi$
$347$	10.0037	0.537025	0.268512	+	0.963276i	$0.413468\pi$
$348$	4.59519	0.246328
$349$	9.69220	0.518812	0.259406	−	0.965768i	$-0.416473\pi$
$349$	9.69220	0.518812	0.259406	+	0.965768i	$0.416473\pi$
$350$	−9.04526	−0.483489
$351$	−1.00000	−0.0533761
$352$	3.10838	0.165677
$353$	−29.7621	−1.58408	−0.792039	−	0.610470i	$-0.790981\pi$
$353$	−29.7621	−1.58408	−0.792039	+	0.610470i	$0.790981\pi$
$354$	14.4851	0.769872
$355$	−29.1202	−1.54554
$356$	−2.79808	−0.148298
$357$	14.5087	0.767884
$358$	9.47767	0.500910
$359$	19.8579	1.04806	0.524029	−	0.851700i	$-0.324428\pi$
$359$	19.8579	1.04806	0.524029	+	0.851700i	$0.324428\pi$
$360$	−2.68392	−0.141455
$361$	17.9031	0.942270
$362$	−4.38227	−0.230327
$363$	−1.33800	−0.0702267
$364$	4.10513	0.215167
$365$	−2.60217	−0.136204
$366$	−12.7107	−0.664398
$367$	7.43956	0.388342	0.194171	−	0.980968i	$-0.437798\pi$
$367$	7.43956	0.388342	0.194171	+	0.980968i	$0.437798\pi$
$368$	−5.39970	−0.281479
$369$	5.54812	0.288824
$370$	−3.42047	−0.177822
$371$	7.26688	0.377278
$372$	7.13492	0.369928
$373$	12.8013	0.662827	0.331414	−	0.943486i	$-0.392474\pi$
$373$	12.8013	0.662827	0.331414	+	0.943486i	$0.392474\pi$
$374$	−10.9859	−0.568069
$375$	7.50583	0.387599
$376$	−11.8700	−0.612149
$377$	−4.59519	−0.236665
$378$	−4.10513	−0.211145
$379$	−18.5501	−0.952855	−0.476427	−	0.879214i	$-0.658068\pi$
$379$	−18.5501	−0.952855	−0.476427	+	0.879214i	$0.658068\pi$
$380$	16.3042	0.836390
$381$	2.42086	0.124025
$382$	−17.7967	−0.910556
$383$	14.6050	0.746279	0.373139	−	0.927775i	$-0.378281\pi$
$383$	14.6050	0.746279	0.373139	+	0.927775i	$0.378281\pi$
$384$	1.00000	0.0510310
$385$	34.2475	1.74541
$386$	5.17454	0.263377
$387$	12.2627	0.623348
$388$	15.4478	0.784243
$389$	−19.1968	−0.973317	−0.486659	−	0.873592i	$-0.661784\pi$
$389$	−19.1968	−0.973317	−0.486659	+	0.873592i	$0.661784\pi$
$390$	2.68392	0.135905
$391$	19.0841	0.965127
$392$	9.85206	0.497604
$393$	−21.1012	−1.06442
$394$	17.4369	0.878457
$395$	−7.61494	−0.383149
$396$	3.10838	0.156202
$397$	−3.94946	−0.198218	−0.0991090	−	0.995077i	$-0.531599\pi$
$397$	−3.94946	−0.198218	−0.0991090	+	0.995077i	$0.531599\pi$
$398$	15.1980	0.761806
$399$	24.9378	1.24845
$400$	2.20340	0.110170
$401$	−5.34664	−0.266998	−0.133499	−	0.991049i	$-0.542621\pi$
$401$	−5.34664	−0.266998	−0.133499	+	0.991049i	$0.542621\pi$
$402$	5.38738	0.268698
$403$	−7.13492	−0.355416
$404$	16.0658	0.799305
$405$	−2.68392	−0.133365
$406$	−18.8639	−0.936197
$407$	3.96141	0.196360
$408$	−3.53430	−0.174974
$409$	21.3253	1.05447	0.527234	−	0.849720i	$-0.323229\pi$
$409$	21.3253	1.05447	0.527234	+	0.849720i	$0.323229\pi$
$410$	−14.8907	−0.735398
$411$	19.6454	0.969038
$412$	1.00000	0.0492665
$413$	−59.4630	−2.92598
$414$	−5.39970	−0.265381
$415$	35.9612	1.76526
$416$	−1.00000	−0.0490290
$417$	−3.48184	−0.170507
$418$	−18.8827	−0.923585
$419$	27.5951	1.34811	0.674054	−	0.738682i	$-0.264551\pi$
$419$	27.5951	1.34811	0.674054	+	0.738682i	$0.264551\pi$
$420$	11.0178	0.537614
$421$	−25.3216	−1.23410	−0.617050	−	0.786924i	$-0.711672\pi$
$421$	−25.3216	−1.23410	−0.617050	+	0.786924i	$0.711672\pi$
$422$	0.0655512	0.00319098
$423$	−11.8700	−0.577139
$424$	−1.77020	−0.0859684
$425$	−7.78749	−0.377749
$426$	10.8499	0.525678
$427$	52.1790	2.52512
$428$	14.0680	0.680005
$429$	−3.10838	−0.150074
$430$	−32.9121	−1.58716
$431$	32.5753	1.56910	0.784549	−	0.620067i	$-0.212895\pi$
$431$	32.5753	1.56910	0.784549	+	0.620067i	$0.212895\pi$
$432$	1.00000	0.0481125
$433$	−0.749354	−0.0360117	−0.0180058	−	0.999838i	$-0.505732\pi$
$433$	−0.749354	−0.0360117	−0.0180058	+	0.999838i	$0.505732\pi$
$434$	−29.2897	−1.40595
$435$	−12.3331	−0.591328
$436$	−4.16954	−0.199685
$437$	32.8021	1.56914
$438$	0.969543	0.0463266
$439$	−32.4041	−1.54657	−0.773283	−	0.634062i	$-0.781387\pi$
$439$	−32.4041	−1.54657	−0.773283	+	0.634062i	$0.781387\pi$
$440$	−8.34262	−0.397719
$441$	9.85206	0.469146
$442$	3.53430	0.168109
$443$	6.22508	0.295762	0.147881	−	0.989005i	$-0.452755\pi$
$443$	6.22508	0.295762	0.147881	+	0.989005i	$0.452755\pi$
$444$	1.27443	0.0604819
$445$	7.50982	0.355999
$446$	−14.5960	−0.691140
$447$	16.4553	0.778309
$448$	−4.10513	−0.193949
$449$	34.9716	1.65041	0.825207	−	0.564831i	$-0.191059\pi$
$449$	34.9716	1.65041	0.825207	+	0.564831i	$0.191059\pi$
$450$	2.20340	0.103870
$451$	17.2456	0.812065
$452$	−8.78688	−0.413300
$453$	16.7678	0.787822
$454$	−6.52314	−0.306146
$455$	−11.0178	−0.516523
$456$	−6.07479	−0.284478
$457$	1.92567	0.0900792	0.0450396	−	0.998985i	$-0.485659\pi$
$457$	1.92567	0.0900792	0.0450396	+	0.998985i	$0.485659\pi$
$458$	17.4135	0.813681
$459$	−3.53430	−0.164967
$460$	14.4923	0.675709
$461$	3.42069	0.159317	0.0796587	−	0.996822i	$-0.474617\pi$
$461$	3.42069	0.159317	0.0796587	+	0.996822i	$0.474617\pi$
$462$	−12.7603	−0.593662
$463$	−26.6684	−1.23938	−0.619692	−	0.784845i	$-0.712742\pi$
$463$	−26.6684	−1.23938	−0.619692	+	0.784845i	$0.712742\pi$
$464$	4.59519	0.213327
$465$	−19.1495	−0.888038
$466$	−0.400509	−0.0185532
$467$	−9.33445	−0.431947	−0.215973	−	0.976399i	$-0.569292\pi$
$467$	−9.33445	−0.431947	−0.215973	+	0.976399i	$0.569292\pi$
$468$	−1.00000	−0.0462250
$469$	−22.1159	−1.02122
$470$	31.8581	1.46950
$471$	−6.95977	−0.320689
$472$	14.4851	0.666729
$473$	38.1171	1.75263
$474$	2.83725	0.130319
$475$	−13.3852	−0.614157
$476$	14.5087	0.665007
$477$	−1.77020	−0.0810518
$478$	−3.16608	−0.144813
$479$	8.87237	0.405389	0.202695	−	0.979242i	$-0.435030\pi$
$479$	8.87237	0.405389	0.202695	+	0.979242i	$0.435030\pi$
$480$	−2.68392	−0.122503
$481$	−1.27443	−0.0581091
$482$	24.8592	1.13231
$483$	22.1664	1.00861
$484$	−1.33800	−0.0608181
$485$	−41.4606	−1.88263
$486$	1.00000	0.0453609
$487$	−17.2088	−0.779806	−0.389903	−	0.920856i	$-0.627492\pi$
$487$	−17.2088	−0.779806	−0.389903	+	0.920856i	$0.627492\pi$
$488$	−12.7107	−0.575385
$489$	3.70093	0.167362
$490$	−26.4421	−1.19453
$491$	−27.1279	−1.22426	−0.612132	−	0.790756i	$-0.709688\pi$
$491$	−27.1279	−1.22426	−0.612132	+	0.790756i	$0.709688\pi$
$492$	5.54812	0.250128
$493$	−16.2408	−0.731448
$494$	6.07479	0.273318
$495$	−8.34262	−0.374973
$496$	7.13492	0.320367
$497$	−44.5401	−1.99790
$498$	−13.3988	−0.600413
$499$	−27.6628	−1.23836	−0.619179	−	0.785250i	$-0.712535\pi$
$499$	−27.6628	−1.23836	−0.619179	+	0.785250i	$0.712535\pi$
$500$	7.50583	0.335671
$501$	−0.0839211	−0.00374932
$502$	−4.91104	−0.219190
$503$	−30.5714	−1.36311	−0.681555	−	0.731767i	$-0.738696\pi$
$503$	−30.5714	−1.36311	−0.681555	+	0.731767i	$0.738696\pi$
$504$	−4.10513	−0.182857
$505$	−43.1193	−1.91879
$506$	−16.7843	−0.746153
$507$	1.00000	0.0444116
$508$	2.42086	0.107408
$509$	27.7489	1.22995	0.614975	−	0.788546i	$-0.289166\pi$
$509$	27.7489	1.22995	0.614975	+	0.788546i	$0.289166\pi$
$510$	9.48576	0.420036
$511$	−3.98010	−0.176069
$512$	1.00000	0.0441942
$513$	−6.07479	−0.268209
$514$	13.3052	0.586867
$515$	−2.68392	−0.118267
$516$	12.2627	0.539835
$517$	−36.8964	−1.62270
$518$	−5.23171	−0.229868
$519$	−6.63833	−0.291390
$520$	2.68392	0.117698
$521$	6.99599	0.306500	0.153250	−	0.988187i	$-0.451026\pi$
$521$	6.99599	0.306500	0.153250	+	0.988187i	$0.451026\pi$
$522$	4.59519	0.201126
$523$	3.84684	0.168211	0.0841053	−	0.996457i	$-0.473197\pi$
$523$	3.84684	0.168211	0.0841053	+	0.996457i	$0.473197\pi$
$524$	−21.1012	−0.921811
$525$	−9.04526	−0.394767
$526$	−11.3427	−0.494564
$527$	−25.2169	−1.09847
$528$	3.10838	0.135275
$529$	6.15675	0.267685
$530$	4.75106	0.206373
$531$	14.4851	0.628598
$532$	24.9378	1.08119
$533$	−5.54812	−0.240316
$534$	−2.79808	−0.121085
$535$	−37.7574	−1.63240
$536$	5.38738	0.232699
$537$	9.47767	0.408992
$538$	−24.0058	−1.03496
$539$	30.6239	1.31907
$540$	−2.68392	−0.115497
$541$	8.63614	0.371297	0.185648	−	0.982616i	$-0.440561\pi$
$541$	8.63614	0.371297	0.185648	+	0.982616i	$0.440561\pi$
$542$	−2.53740	−0.108990
$543$	−4.38227	−0.188061
$544$	−3.53430	−0.151532
$545$	11.1907	0.479357
$546$	4.10513	0.175683
$547$	−0.554575	−0.0237119	−0.0118560	−	0.999930i	$-0.503774\pi$
$547$	−0.554575	−0.0237119	−0.0118560	+	0.999930i	$0.503774\pi$
$548$	19.6454	0.839212
$549$	−12.7107	−0.542479
$550$	6.84901	0.292043
$551$	−27.9149	−1.18921
$552$	−5.39970	−0.229826
$553$	−11.6473	−0.495292
$554$	−20.2852	−0.861834
$555$	−3.42047	−0.145191
$556$	−3.48184	−0.147663
$557$	−9.48915	−0.402068	−0.201034	−	0.979584i	$-0.564430\pi$
$557$	−9.48915	−0.402068	−0.201034	+	0.979584i	$0.564430\pi$
$558$	7.13492	0.302045
$559$	−12.2627	−0.518657
$560$	11.0178	0.465588
$561$	−10.9859	−0.463826
$562$	13.3071	0.561327
$563$	32.7274	1.37930	0.689648	−	0.724145i	$-0.257765\pi$
$563$	32.7274	1.37930	0.689648	+	0.724145i	$0.257765\pi$
$564$	−11.8700	−0.499817
$565$	23.5832	0.992155
$566$	13.6787	0.574958
$567$	−4.10513	−0.172399
$568$	10.8499	0.455251
$569$	29.1797	1.22328	0.611638	−	0.791138i	$-0.290511\pi$
$569$	29.1797	1.22328	0.611638	+	0.791138i	$0.290511\pi$
$570$	16.3042	0.682909
$571$	5.30733	0.222105	0.111053	−	0.993815i	$-0.464578\pi$
$571$	5.30733	0.222105	0.111053	+	0.993815i	$0.464578\pi$
$572$	−3.10838	−0.129968
$573$	−17.7967	−0.743466
$574$	−22.7757	−0.950640
$575$	−11.8977	−0.496169
$576$	1.00000	0.0416667
$577$	36.6408	1.52538	0.762688	−	0.646766i	$-0.223879\pi$
$577$	36.6408	1.52538	0.762688	+	0.646766i	$0.223879\pi$
$578$	−4.50874	−0.187539
$579$	5.17454	0.215047
$580$	−12.3331	−0.512105
$581$	55.0036	2.28194
$582$	15.4478	0.640332
$583$	−5.50244	−0.227888
$584$	0.969543	0.0401200
$585$	2.68392	0.110966
$586$	−13.9945	−0.578109
$587$	25.5044	1.05268	0.526339	−	0.850275i	$-0.323564\pi$
$587$	25.5044	1.05268	0.526339	+	0.850275i	$0.323564\pi$
$588$	9.85206	0.406292
$589$	−43.3432	−1.78592
$590$	−38.8767	−1.60053
$591$	17.4369	0.717257
$592$	1.27443	0.0523788
$593$	18.0072	0.739465	0.369733	−	0.929138i	$-0.379449\pi$
$593$	18.0072	0.739465	0.369733	+	0.929138i	$0.379449\pi$
$594$	3.10838	0.127538
$595$	−38.9402	−1.59639
$596$	16.4553	0.674035
$597$	15.1980	0.622012
$598$	5.39970	0.220810
$599$	−19.7389	−0.806509	−0.403254	−	0.915088i	$-0.632121\pi$
$599$	−19.7389	−0.806509	−0.403254	+	0.915088i	$0.632121\pi$
$600$	2.20340	0.0899536
$601$	14.7368	0.601126	0.300563	−	0.953762i	$-0.402825\pi$
$601$	14.7368	0.601126	0.300563	+	0.953762i	$0.402825\pi$
$602$	−50.3399	−2.05170
$603$	5.38738	0.219391
$604$	16.7678	0.682274
$605$	3.59108	0.145998
$606$	16.0658	0.652630
$607$	16.5880	0.673285	0.336643	−	0.941632i	$-0.390709\pi$
$607$	16.5880	0.673285	0.336643	+	0.941632i	$0.390709\pi$
$608$	−6.07479	−0.246365
$609$	−18.8639	−0.764402
$610$	34.1144	1.38125
$611$	11.8700	0.480209
$612$	−3.53430	−0.142866
$613$	−41.5875	−1.67970	−0.839852	−	0.542816i	$-0.817358\pi$
$613$	−41.5875	−1.67970	−0.839852	+	0.542816i	$0.817358\pi$
$614$	19.3243	0.779866
$615$	−14.8907	−0.600450
$616$	−12.7603	−0.514126
$617$	−24.0822	−0.969514	−0.484757	−	0.874649i	$-0.661092\pi$
$617$	−24.0822	−0.969514	−0.484757	+	0.874649i	$0.661092\pi$
$618$	1.00000	0.0402259
$619$	−42.1801	−1.69536	−0.847681	−	0.530507i	$-0.822002\pi$
$619$	−42.1801	−1.69536	−0.847681	+	0.530507i	$0.822002\pi$
$620$	−19.1495	−0.769063
$621$	−5.39970	−0.216682
$622$	24.9134	0.998938
$623$	11.4865	0.460196
$624$	−1.00000	−0.0400320
$625$	−31.1620	−1.24648
$626$	−13.4884	−0.539105
$627$	−18.8827	−0.754104
$628$	−6.95977	−0.277725
$629$	−4.50422	−0.179595
$630$	11.0178	0.438960
$631$	−12.8199	−0.510354	−0.255177	−	0.966894i	$-0.582134\pi$
$631$	−12.8199	−0.510354	−0.255177	+	0.966894i	$0.582134\pi$
$632$	2.83725	0.112860
$633$	0.0655512	0.00260543
$634$	16.2318	0.644649
$635$	−6.49739	−0.257841
$636$	−1.77020	−0.0701929
$637$	−9.85206	−0.390353
$638$	14.2836	0.565493
$639$	10.8499	0.429215
$640$	−2.68392	−0.106091
$641$	15.6391	0.617705	0.308853	−	0.951110i	$-0.400055\pi$
$641$	15.6391	0.617705	0.308853	+	0.951110i	$0.400055\pi$
$642$	14.0680	0.555221
$643$	−37.4707	−1.47770	−0.738849	−	0.673871i	$-0.764630\pi$
$643$	−37.4707	−1.47770	−0.738849	+	0.673871i	$0.764630\pi$
$644$	22.1664	0.873480
$645$	−32.9121	−1.29591
$646$	21.4701	0.844731
$647$	21.5863	0.848647	0.424323	−	0.905511i	$-0.360512\pi$
$647$	21.5863	0.848647	0.424323	+	0.905511i	$0.360512\pi$
$648$	1.00000	0.0392837
$649$	45.0250	1.76739
$650$	−2.20340	−0.0864247
$651$	−29.2897	−1.14796
$652$	3.70093	0.144939
$653$	−8.31343	−0.325329	−0.162665	−	0.986681i	$-0.552009\pi$
$653$	−8.31343	−0.325329	−0.162665	+	0.986681i	$0.552009\pi$
$654$	−4.16954	−0.163042
$655$	56.6339	2.21287
$656$	5.54812	0.216618
$657$	0.969543	0.0378255
$658$	48.7279	1.89961
$659$	13.6487	0.531677	0.265838	−	0.964018i	$-0.414351\pi$
$659$	13.6487	0.531677	0.265838	+	0.964018i	$0.414351\pi$
$660$	−8.34262	−0.324736
$661$	−41.6412	−1.61965	−0.809827	−	0.586669i	$-0.800439\pi$
$661$	−41.6412	−1.61965	−0.809827	+	0.586669i	$0.800439\pi$
$662$	14.2585	0.554171
$663$	3.53430	0.137261
$664$	−13.3988	−0.519973
$665$	−66.9310	−2.59547
$666$	1.27443	0.0493832
$667$	−24.8127	−0.960750
$668$	−0.0839211	−0.00324700
$669$	−14.5960	−0.564314
$670$	−14.4593	−0.558610
$671$	−39.5096	−1.52525
$672$	−4.10513	−0.158359
$673$	9.88987	0.381227	0.190613	−	0.981665i	$-0.438952\pi$
$673$	9.88987	0.381227	0.190613	+	0.981665i	$0.438952\pi$
$674$	6.44173	0.248126
$675$	2.20340	0.0848091
$676$	1.00000	0.0384615
$677$	7.35979	0.282860	0.141430	−	0.989948i	$-0.454830\pi$
$677$	7.35979	0.282860	0.141430	+	0.989948i	$0.454830\pi$
$678$	−8.78688	−0.337458
$679$	−63.4152	−2.43365
$680$	9.48576	0.363762
$681$	−6.52314	−0.249967
$682$	22.1780	0.849240
$683$	22.8459	0.874175	0.437088	−	0.899419i	$-0.356010\pi$
$683$	22.8459	0.874175	0.437088	+	0.899419i	$0.356010\pi$
$684$	−6.07479	−0.232276
$685$	−52.7267	−2.01458
$686$	−11.7081	−0.447016
$687$	17.4135	0.664368
$688$	12.2627	0.467511
$689$	1.77020	0.0674392
$690$	14.4923	0.551714
$691$	−10.2576	−0.390218	−0.195109	−	0.980782i	$-0.562506\pi$
$691$	−10.2576	−0.390218	−0.195109	+	0.980782i	$0.562506\pi$
$692$	−6.63833	−0.252352
$693$	−12.7603	−0.484723
$694$	10.0037	0.379734
$695$	9.34498	0.354475
$696$	4.59519	0.174180
$697$	−19.6087	−0.742733
$698$	9.69220	0.366855
$699$	−0.400509	−0.0151486
$700$	−9.04526	−0.341879
$701$	41.0797	1.55156	0.775780	−	0.631004i	$-0.217357\pi$
$701$	41.0797	1.55156	0.775780	+	0.631004i	$0.217357\pi$
$702$	−1.00000	−0.0377426
$703$	−7.74191	−0.291992
$704$	3.10838	0.117151
$705$	31.8581	1.19985
$706$	−29.7621	−1.12011
$707$	−65.9523	−2.48039
$708$	14.4851	0.544382
$709$	−16.9877	−0.637987	−0.318994	−	0.947757i	$-0.603345\pi$
$709$	−16.9877	−0.637987	−0.318994	+	0.947757i	$0.603345\pi$
$710$	−29.1202	−1.09286
$711$	2.83725	0.106405
$712$	−2.79808	−0.104863
$713$	−38.5264	−1.44283
$714$	14.5087	0.542976
$715$	8.34262	0.311996
$716$	9.47767	0.354197
$717$	−3.16608	−0.118240
$718$	19.8579	0.741089
$719$	−35.4433	−1.32181	−0.660907	−	0.750468i	$-0.729828\pi$
$719$	−35.4433	−1.32181	−0.660907	+	0.750468i	$0.729828\pi$
$720$	−2.68392	−0.100024
$721$	−4.10513	−0.152883
$722$	17.9031	0.666286
$723$	24.8592	0.924525
$724$	−4.38227	−0.162866
$725$	10.1251	0.376036
$726$	−1.33800	−0.0496578
$727$	27.4141	1.01673	0.508365	−	0.861141i	$-0.330250\pi$
$727$	27.4141	1.01673	0.508365	+	0.861141i	$0.330250\pi$
$728$	4.10513	0.152146
$729$	1.00000	0.0370370
$730$	−2.60217	−0.0963107
$731$	−43.3400	−1.60299
$732$	−12.7107	−0.469800
$733$	−40.4313	−1.49336	−0.746681	−	0.665182i	$-0.768354\pi$
$733$	−40.4313	−1.49336	−0.746681	+	0.665182i	$0.768354\pi$
$734$	7.43956	0.274599
$735$	−26.4421	−0.975332
$736$	−5.39970	−0.199036
$737$	16.7460	0.616847
$738$	5.54812	0.204229
$739$	−7.46287	−0.274526	−0.137263	−	0.990535i	$-0.543831\pi$
$739$	−7.46287	−0.274526	−0.137263	+	0.990535i	$0.543831\pi$
$740$	−3.42047	−0.125739
$741$	6.07479	0.223163
$742$	7.26688	0.266776
$743$	9.69030	0.355502	0.177751	−	0.984075i	$-0.443118\pi$
$743$	9.69030	0.355502	0.177751	+	0.984075i	$0.443118\pi$
$744$	7.13492	0.261579
$745$	−44.1646	−1.61807
$746$	12.8013	0.468690
$747$	−13.3988	−0.490235
$748$	−10.9859	−0.401685
$749$	−57.7511	−2.11018
$750$	7.50583	0.274074
$751$	17.8295	0.650606	0.325303	−	0.945610i	$-0.394534\pi$
$751$	17.8295	0.650606	0.325303	+	0.945610i	$0.394534\pi$
$752$	−11.8700	−0.432855
$753$	−4.91104	−0.178968
$754$	−4.59519	−0.167347
$755$	−45.0035	−1.63784
$756$	−4.10513	−0.149302
$757$	−6.27713	−0.228146	−0.114073	−	0.993472i	$-0.536390\pi$
$757$	−6.27713	−0.228146	−0.114073	+	0.993472i	$0.536390\pi$
$758$	−18.5501	−0.673770
$759$	−16.7843	−0.609231
$760$	16.3042	0.591417
$761$	46.8864	1.69963	0.849815	−	0.527080i	$-0.176713\pi$
$761$	46.8864	1.69963	0.849815	+	0.527080i	$0.176713\pi$
$762$	2.42086	0.0876986
$763$	17.1165	0.619659
$764$	−17.7967	−0.643860
$765$	9.48576	0.342958
$766$	14.6050	0.527699
$767$	−14.4851	−0.523025
$768$	1.00000	0.0360844
$769$	−20.3080	−0.732326	−0.366163	−	0.930551i	$-0.619329\pi$
$769$	−20.3080	−0.732326	−0.366163	+	0.930551i	$0.619329\pi$
$770$	34.2475	1.23419
$771$	13.3052	0.479175
$772$	5.17454	0.186236
$773$	−46.2142	−1.66221	−0.831104	−	0.556117i	$-0.812291\pi$
$773$	−46.2142	−1.66221	−0.831104	+	0.556117i	$0.812291\pi$
$774$	12.2627	0.440774
$775$	15.7211	0.564719
$776$	15.4478	0.554544
$777$	−5.23171	−0.187686
$778$	−19.1968	−0.688239
$779$	−33.7037	−1.20756
$780$	2.68392	0.0960996
$781$	33.7255	1.20679
$782$	19.0841	0.682448
$783$	4.59519	0.164219
$784$	9.85206	0.351859
$785$	18.6794	0.666698
$786$	−21.1012	−0.752656
$787$	−25.8204	−0.920396	−0.460198	−	0.887816i	$-0.652222\pi$
$787$	−25.8204	−0.920396	−0.460198	+	0.887816i	$0.652222\pi$
$788$	17.4369	0.621163
$789$	−11.3427	−0.403810
$790$	−7.61494	−0.270928
$791$	36.0713	1.28255
$792$	3.10838	0.110451
$793$	12.7107	0.451370
$794$	−3.94946	−0.140161
$795$	4.75106	0.168503
$796$	15.1980	0.538678
$797$	31.7529	1.12474	0.562372	−	0.826884i	$-0.309889\pi$
$797$	31.7529	1.12474	0.562372	+	0.826884i	$0.309889\pi$
$798$	24.9378	0.882789
$799$	41.9521	1.48416
$800$	2.20340	0.0779021
$801$	−2.79808	−0.0988654
$802$	−5.34664	−0.188796
$803$	3.01371	0.106351
$804$	5.38738	0.189998
$805$	−59.4929	−2.09685
$806$	−7.13492	−0.251317
$807$	−24.0058	−0.845044
$808$	16.0658	0.565194
$809$	−23.5046	−0.826378	−0.413189	−	0.910645i	$-0.635585\pi$
$809$	−23.5046	−0.826378	−0.413189	+	0.910645i	$0.635585\pi$
$810$	−2.68392	−0.0943032
$811$	−25.3708	−0.890888	−0.445444	−	0.895310i	$-0.646954\pi$
$811$	−25.3708	−0.890888	−0.445444	+	0.895310i	$0.646954\pi$
$812$	−18.8639	−0.661991
$813$	−2.53740	−0.0889904
$814$	3.96141	0.138848
$815$	−9.93297	−0.347937
$816$	−3.53430	−0.123725
$817$	−74.4934	−2.60619
$818$	21.3253	0.745621
$819$	4.10513	0.143445
$820$	−14.8907	−0.520005
$821$	50.9937	1.77969	0.889845	−	0.456262i	$-0.150812\pi$
$821$	50.9937	1.77969	0.889845	+	0.456262i	$0.150812\pi$
$822$	19.6454	0.685213
$823$	−4.73228	−0.164957	−0.0824785	−	0.996593i	$-0.526284\pi$
$823$	−4.73228	−0.164957	−0.0824785	+	0.996593i	$0.526284\pi$
$824$	1.00000	0.0348367
$825$	6.84901	0.238452
$826$	−59.4630	−2.06898
$827$	44.5145	1.54792	0.773960	−	0.633235i	$-0.218273\pi$
$827$	44.5145	1.54792	0.773960	+	0.633235i	$0.218273\pi$
$828$	−5.39970	−0.187653
$829$	16.1272	0.560121	0.280060	−	0.959982i	$-0.409645\pi$
$829$	16.1272	0.560121	0.280060	+	0.959982i	$0.409645\pi$
$830$	35.9612	1.24823
$831$	−20.2852	−0.703684
$832$	−1.00000	−0.0346688
$833$	−34.8201	−1.20645
$834$	−3.48184	−0.120566
$835$	0.225237	0.00779465
$836$	−18.8827	−0.653073
$837$	7.13492	0.246619
$838$	27.5951	0.953257
$839$	23.5306	0.812366	0.406183	−	0.913792i	$-0.366860\pi$
$839$	23.5306	0.812366	0.406183	+	0.913792i	$0.366860\pi$
$840$	11.0178	0.380151
$841$	−7.88419	−0.271869
$842$	−25.3216	−0.872640
$843$	13.3071	0.458321
$844$	0.0655512	0.00225636
$845$	−2.68392	−0.0923295
$846$	−11.8700	−0.408099
$847$	5.49265	0.188730
$848$	−1.77020	−0.0607888
$849$	13.6787	0.469452
$850$	−7.78749	−0.267109
$851$	−6.88155	−0.235897
$852$	10.8499	0.371711
$853$	−22.0398	−0.754627	−0.377314	−	0.926086i	$-0.623152\pi$
$853$	−22.0398	−0.754627	−0.377314	+	0.926086i	$0.623152\pi$
$854$	52.1790	1.78553
$855$	16.3042	0.557593
$856$	14.0680	0.480836
$857$	48.2535	1.64831	0.824154	−	0.566366i	$-0.191651\pi$
$857$	48.2535	1.64831	0.824154	+	0.566366i	$0.191651\pi$
$858$	−3.10838	−0.106118
$859$	−5.35274	−0.182633	−0.0913166	−	0.995822i	$-0.529108\pi$
$859$	−5.35274	−0.182633	−0.0913166	+	0.995822i	$0.529108\pi$
$860$	−32.9121	−1.12229
$861$	−22.7757	−0.776195
$862$	32.5753	1.10952
$863$	−0.318073	−0.0108273	−0.00541367	−	0.999985i	$-0.501723\pi$
$863$	−0.318073	−0.0108273	−0.00541367	+	0.999985i	$0.501723\pi$
$864$	1.00000	0.0340207
$865$	17.8167	0.605787
$866$	−0.749354	−0.0254641
$867$	−4.50874	−0.153125
$868$	−29.2897	−0.994158
$869$	8.81924	0.299172
$870$	−12.3331	−0.418132
$871$	−5.38738	−0.182544
$872$	−4.16954	−0.141199
$873$	15.4478	0.522829
$874$	32.8021	1.10955
$875$	−30.8124	−1.04165
$876$	0.969543	0.0327578
$877$	18.0243	0.608636	0.304318	−	0.952571i	$-0.401571\pi$
$877$	18.0243	0.608636	0.304318	+	0.952571i	$0.401571\pi$
$878$	−32.4041	−1.09359
$879$	−13.9945	−0.472024
$880$	−8.34262	−0.281230
$881$	−41.4583	−1.39677	−0.698383	−	0.715724i	$-0.746097\pi$
$881$	−41.4583	−1.39677	−0.698383	+	0.715724i	$0.746097\pi$
$882$	9.85206	0.331736
$883$	−28.0010	−0.942310	−0.471155	−	0.882051i	$-0.656163\pi$
$883$	−28.0010	−0.942310	−0.471155	+	0.882051i	$0.656163\pi$
$884$	3.53430	0.118871
$885$	−38.8767	−1.30683
$886$	6.22508	0.209136
$887$	38.6353	1.29724	0.648622	−	0.761110i	$-0.275345\pi$
$887$	38.6353	1.29724	0.648622	+	0.761110i	$0.275345\pi$
$888$	1.27443	0.0427671
$889$	−9.93795	−0.333308
$890$	7.50982	0.251730
$891$	3.10838	0.104135
$892$	−14.5960	−0.488710
$893$	72.1079	2.41300
$894$	16.4553	0.550347
$895$	−25.4373	−0.850274
$896$	−4.10513	−0.137143
$897$	5.39970	0.180291
$898$	34.9716	1.16702
$899$	32.7863	1.09349
$900$	2.20340	0.0734468
$901$	6.25641	0.208431
$902$	17.2456	0.574217
$903$	−50.3399	−1.67521
$904$	−8.78688	−0.292247
$905$	11.7616	0.390970
$906$	16.7678	0.557074
$907$	29.7133	0.986614	0.493307	−	0.869855i	$-0.335788\pi$
$907$	29.7133	0.986614	0.493307	+	0.869855i	$0.335788\pi$
$908$	−6.52314	−0.216478
$909$	16.0658	0.532870
$910$	−11.0178	−0.365237
$911$	−31.3531	−1.03877	−0.519387	−	0.854539i	$-0.673839\pi$
$911$	−31.3531	−1.03877	−0.519387	+	0.854539i	$0.673839\pi$
$912$	−6.07479	−0.201157
$913$	−41.6484	−1.37836
$914$	1.92567	0.0636956
$915$	34.1144	1.12779
$916$	17.4135	0.575359
$917$	86.6232	2.86055
$918$	−3.53430	−0.116649
$919$	−17.2995	−0.570658	−0.285329	−	0.958430i	$-0.592103\pi$
$919$	−17.2995	−0.570658	−0.285329	+	0.958430i	$0.592103\pi$
$920$	14.4923	0.477798
$921$	19.3243	0.636758
$922$	3.42069	0.112654
$923$	−10.8499	−0.357128
$924$	−12.7603	−0.419782
$925$	2.80809	0.0923294
$926$	−26.6684	−0.876377
$927$	1.00000	0.0328443
$928$	4.59519	0.150845
$929$	33.6991	1.10563	0.552816	−	0.833304i	$-0.313553\pi$
$929$	33.6991	1.10563	0.552816	+	0.833304i	$0.313553\pi$
$930$	−19.1495	−0.627937
$931$	−59.8493	−1.96148
$932$	−0.400509	−0.0131191
$933$	24.9134	0.815630
$934$	−9.33445	−0.305432
$935$	29.4853	0.964273
$936$	−1.00000	−0.0326860
$937$	−16.5649	−0.541152	−0.270576	−	0.962699i	$-0.587214\pi$
$937$	−16.5649	−0.541152	−0.270576	+	0.962699i	$0.587214\pi$
$938$	−22.1159	−0.722109
$939$	−13.4884	−0.440178
$940$	31.8581	1.03910
$941$	24.5051	0.798844	0.399422	−	0.916767i	$-0.369211\pi$
$941$	24.5051	0.798844	0.399422	+	0.916767i	$0.369211\pi$
$942$	−6.95977	−0.226762
$943$	−29.9582	−0.975572
$944$	14.4851	0.471448
$945$	11.0178	0.358410
$946$	38.1171	1.23929
$947$	−45.2359	−1.46997	−0.734985	−	0.678083i	$-0.762811\pi$
$947$	−45.2359	−1.46997	−0.734985	+	0.678083i	$0.762811\pi$
$948$	2.83725	0.0921496
$949$	−0.969543	−0.0314727
$950$	−13.3852	−0.434274
$951$	16.2318	0.526353
$952$	14.5087	0.470231
$953$	21.4795	0.695789	0.347895	−	0.937534i	$-0.386897\pi$
$953$	21.4795	0.695789	0.347895	+	0.937534i	$0.386897\pi$
$954$	−1.77020	−0.0573123
$955$	47.7647	1.54563
$956$	−3.16608	−0.102398
$957$	14.2836	0.461723
$958$	8.87237	0.286653
$959$	−80.6470	−2.60423
$960$	−2.68392	−0.0866230
$961$	19.9070	0.642163
$962$	−1.27443	−0.0410893
$963$	14.0680	0.453336
$964$	24.8592	0.800662
$965$	−13.8880	−0.447072
$966$	22.1664	0.713194
$967$	−11.7550	−0.378014	−0.189007	−	0.981976i	$-0.560527\pi$
$967$	−11.7550	−0.378014	−0.189007	+	0.981976i	$0.560527\pi$
$968$	−1.33800	−0.0430049
$969$	21.4701	0.689720
$970$	−41.4606	−1.33122
$971$	40.8437	1.31074	0.655369	−	0.755309i	$-0.272513\pi$
$971$	40.8437	1.31074	0.655369	+	0.755309i	$0.272513\pi$
$972$	1.00000	0.0320750
$973$	14.2934	0.458226
$974$	−17.2088	−0.551406
$975$	−2.20340	−0.0705654
$976$	−12.7107	−0.406859
$977$	−2.26384	−0.0724266	−0.0362133	−	0.999344i	$-0.511530\pi$
$977$	−2.26384	−0.0724266	−0.0362133	+	0.999344i	$0.511530\pi$
$978$	3.70093	0.118343
$979$	−8.69749	−0.277973
$980$	−26.4421	−0.844662
$981$	−4.16954	−0.133123
$982$	−27.1279	−0.865685
$983$	−10.0885	−0.321772	−0.160886	−	0.986973i	$-0.551435\pi$
$983$	−10.0885	−0.321772	−0.160886	+	0.986973i	$0.551435\pi$
$984$	5.54812	0.176868
$985$	−46.7991	−1.49114
$986$	−16.2408	−0.517212
$987$	48.7279	1.55103
$988$	6.07479	0.193265
$989$	−66.2149	−2.10551
$990$	−8.34262	−0.265146
$991$	11.4985	0.365262	0.182631	−	0.983182i	$-0.441539\pi$
$991$	11.4985	0.365262	0.182631	+	0.983182i	$0.441539\pi$
$992$	7.13492	0.226534
$993$	14.2585	0.452479
$994$	−44.5401	−1.41273
$995$	−40.7901	−1.29313
$996$	−13.3988	−0.424556
$997$	30.2423	0.957782	0.478891	−	0.877874i	$-0.341039\pi$
$997$	30.2423	0.957782	0.478891	+	0.877874i	$0.341039\pi$
$998$	−27.6628	−0.875652
$999$	1.27443	0.0403213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.68392 q^{5} +1.00000 q^{6} -4.10513 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.68392 q^{5} +1.00000 q^{6} -4.10513 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.68392 q^{10} +3.10838 q^{11} +1.00000 q^{12} -1.00000 q^{13} -4.10513 q^{14} -2.68392 q^{15} +1.00000 q^{16} -3.53430 q^{17} +1.00000 q^{18} -6.07479 q^{19} -2.68392 q^{20} -4.10513 q^{21} +3.10838 q^{22} -5.39970 q^{23} +1.00000 q^{24} +2.20340 q^{25} -1.00000 q^{26} +1.00000 q^{27} -4.10513 q^{28} +4.59519 q^{29} -2.68392 q^{30} +7.13492 q^{31} +1.00000 q^{32} +3.10838 q^{33} -3.53430 q^{34} +11.0178 q^{35} +1.00000 q^{36} +1.27443 q^{37} -6.07479 q^{38} -1.00000 q^{39} -2.68392 q^{40} +5.54812 q^{41} -4.10513 q^{42} +12.2627 q^{43} +3.10838 q^{44} -2.68392 q^{45} -5.39970 q^{46} -11.8700 q^{47} +1.00000 q^{48} +9.85206 q^{49} +2.20340 q^{50} -3.53430 q^{51} -1.00000 q^{52} -1.77020 q^{53} +1.00000 q^{54} -8.34262 q^{55} -4.10513 q^{56} -6.07479 q^{57} +4.59519 q^{58} +14.4851 q^{59} -2.68392 q^{60} -12.7107 q^{61} +7.13492 q^{62} -4.10513 q^{63} +1.00000 q^{64} +2.68392 q^{65} +3.10838 q^{66} +5.38738 q^{67} -3.53430 q^{68} -5.39970 q^{69} +11.0178 q^{70} +10.8499 q^{71} +1.00000 q^{72} +0.969543 q^{73} +1.27443 q^{74} +2.20340 q^{75} -6.07479 q^{76} -12.7603 q^{77} -1.00000 q^{78} +2.83725 q^{79} -2.68392 q^{80} +1.00000 q^{81} +5.54812 q^{82} -13.3988 q^{83} -4.10513 q^{84} +9.48576 q^{85} +12.2627 q^{86} +4.59519 q^{87} +3.10838 q^{88} -2.79808 q^{89} -2.68392 q^{90} +4.10513 q^{91} -5.39970 q^{92} +7.13492 q^{93} -11.8700 q^{94} +16.3042 q^{95} +1.00000 q^{96} +15.4478 q^{97} +9.85206 q^{98} +3.10838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 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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