LMFDB - Embedded newform 8030.2.a.be.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 24 x^{13} + 64 x^{12} + 237 x^{11} - 524 x^{10} - 1225 x^{9} + 2074 x^{8} + \cdots - 52 $ x^15 - 3x^14 - 24x^13 + 64x^12 + 237x^11 - 524x^10 - 1225x^9 + 2074x^8 + 3463x^7 - 4142x^6 - 5157x^5 + 3892x^4 + 3622x^3 - 1239x^2 - 907x - 52
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			1.13
Root			$2.77411$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.77411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77411 q^{6} +0.220732 q^{7} -1.00000 q^{8} +4.69567 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.77411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77411 q^{6} +0.220732 q^{7} -1.00000 q^{8} +4.69567 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.77411 q^{12} +4.47056 q^{13} -0.220732 q^{14} +2.77411 q^{15} +1.00000 q^{16} +7.05278 q^{17} -4.69567 q^{18} +2.09840 q^{19} +1.00000 q^{20} +0.612335 q^{21} +1.00000 q^{22} +3.13953 q^{23} -2.77411 q^{24} +1.00000 q^{25} -4.47056 q^{26} +4.70398 q^{27} +0.220732 q^{28} -4.96810 q^{29} -2.77411 q^{30} +2.21544 q^{31} -1.00000 q^{32} -2.77411 q^{33} -7.05278 q^{34} +0.220732 q^{35} +4.69567 q^{36} +9.82073 q^{37} -2.09840 q^{38} +12.4018 q^{39} -1.00000 q^{40} +3.42054 q^{41} -0.612335 q^{42} -4.58747 q^{43} -1.00000 q^{44} +4.69567 q^{45} -3.13953 q^{46} -10.7913 q^{47} +2.77411 q^{48} -6.95128 q^{49} -1.00000 q^{50} +19.5652 q^{51} +4.47056 q^{52} +1.71971 q^{53} -4.70398 q^{54} -1.00000 q^{55} -0.220732 q^{56} +5.82118 q^{57} +4.96810 q^{58} -8.27399 q^{59} +2.77411 q^{60} +10.7994 q^{61} -2.21544 q^{62} +1.03649 q^{63} +1.00000 q^{64} +4.47056 q^{65} +2.77411 q^{66} -6.64960 q^{67} +7.05278 q^{68} +8.70939 q^{69} -0.220732 q^{70} +9.58936 q^{71} -4.69567 q^{72} -1.00000 q^{73} -9.82073 q^{74} +2.77411 q^{75} +2.09840 q^{76} -0.220732 q^{77} -12.4018 q^{78} +9.77028 q^{79} +1.00000 q^{80} -1.03767 q^{81} -3.42054 q^{82} -7.32705 q^{83} +0.612335 q^{84} +7.05278 q^{85} +4.58747 q^{86} -13.7820 q^{87} +1.00000 q^{88} +8.46053 q^{89} -4.69567 q^{90} +0.986797 q^{91} +3.13953 q^{92} +6.14588 q^{93} +10.7913 q^{94} +2.09840 q^{95} -2.77411 q^{96} -13.7604 q^{97} +6.95128 q^{98} -4.69567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * 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
$3$	2.77411	1.60163	0.800816	−	0.598911i	$-0.204399\pi$
$3$	2.77411	1.60163	0.800816	+	0.598911i	$0.204399\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.77411	−1.13252
$7$	0.220732	0.0834289	0.0417145	−	0.999130i	$-0.486718\pi$
$7$	0.220732	0.0834289	0.0417145	+	0.999130i	$0.486718\pi$
$8$	−1.00000	−0.353553
$9$	4.69567	1.56522
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.77411	0.800816
$13$	4.47056	1.23991	0.619955	−	0.784637i	$-0.287151\pi$
$13$	4.47056	1.23991	0.619955	+	0.784637i	$0.287151\pi$
$14$	−0.220732	−0.0589932
$15$	2.77411	0.716272
$16$	1.00000	0.250000
$17$	7.05278	1.71055	0.855275	−	0.518175i	$-0.173388\pi$
$17$	7.05278	1.71055	0.855275	+	0.518175i	$0.173388\pi$
$18$	−4.69567	−1.10678
$19$	2.09840	0.481405	0.240703	−	0.970599i	$-0.422622\pi$
$19$	2.09840	0.481405	0.240703	+	0.970599i	$0.422622\pi$
$20$	1.00000	0.223607
$21$	0.612335	0.133622
$22$	1.00000	0.213201
$23$	3.13953	0.654637	0.327318	−	0.944914i	$-0.393855\pi$
$23$	3.13953	0.654637	0.327318	+	0.944914i	$0.393855\pi$
$24$	−2.77411	−0.566262
$25$	1.00000	0.200000
$26$	−4.47056	−0.876749
$27$	4.70398	0.905282
$28$	0.220732	0.0417145
$29$	−4.96810	−0.922552	−0.461276	−	0.887257i	$-0.652608\pi$
$29$	−4.96810	−0.922552	−0.461276	+	0.887257i	$0.652608\pi$
$30$	−2.77411	−0.506480
$31$	2.21544	0.397905	0.198953	−	0.980009i	$-0.436246\pi$
$31$	2.21544	0.397905	0.198953	+	0.980009i	$0.436246\pi$
$32$	−1.00000	−0.176777
$33$	−2.77411	−0.482910
$34$	−7.05278	−1.20954
$35$	0.220732	0.0373105
$36$	4.69567	0.782612
$37$	9.82073	1.61452	0.807259	−	0.590197i	$-0.200950\pi$
$37$	9.82073	1.61452	0.807259	+	0.590197i	$0.200950\pi$
$38$	−2.09840	−0.340405
$39$	12.4018	1.98588
$40$	−1.00000	−0.158114
$41$	3.42054	0.534199	0.267100	−	0.963669i	$-0.413935\pi$
$41$	3.42054	0.534199	0.267100	+	0.963669i	$0.413935\pi$
$42$	−0.612335	−0.0944853
$43$	−4.58747	−0.699582	−0.349791	−	0.936828i	$-0.613747\pi$
$43$	−4.58747	−0.699582	−0.349791	+	0.936828i	$0.613747\pi$
$44$	−1.00000	−0.150756
$45$	4.69567	0.699990
$46$	−3.13953	−0.462898
$47$	−10.7913	−1.57407	−0.787036	−	0.616907i	$-0.788385\pi$
$47$	−10.7913	−1.57407	−0.787036	+	0.616907i	$0.788385\pi$
$48$	2.77411	0.400408
$49$	−6.95128	−0.993040
$50$	−1.00000	−0.141421
$51$	19.5652	2.73967
$52$	4.47056	0.619955
$53$	1.71971	0.236221	0.118110	−	0.993000i	$-0.462316\pi$
$53$	1.71971	0.236221	0.118110	+	0.993000i	$0.462316\pi$
$54$	−4.70398	−0.640131
$55$	−1.00000	−0.134840
$56$	−0.220732	−0.0294966
$57$	5.82118	0.771034
$58$	4.96810	0.652343
$59$	−8.27399	−1.07718	−0.538591	−	0.842567i	$-0.681043\pi$
$59$	−8.27399	−1.07718	−0.538591	+	0.842567i	$0.681043\pi$
$60$	2.77411	0.358136
$61$	10.7994	1.38272	0.691359	−	0.722512i	$-0.257012\pi$
$61$	10.7994	1.38272	0.691359	+	0.722512i	$0.257012\pi$
$62$	−2.21544	−0.281362
$63$	1.03649	0.130585
$64$	1.00000	0.125000
$65$	4.47056	0.554505
$66$	2.77411	0.341469
$67$	−6.64960	−0.812378	−0.406189	−	0.913789i	$-0.633143\pi$
$67$	−6.64960	−0.812378	−0.406189	+	0.913789i	$0.633143\pi$
$68$	7.05278	0.855275
$69$	8.70939	1.04849
$70$	−0.220732	−0.0263825
$71$	9.58936	1.13805	0.569024	−	0.822321i	$-0.307321\pi$
$71$	9.58936	1.13805	0.569024	+	0.822321i	$0.307321\pi$
$72$	−4.69567	−0.553391
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−9.82073	−1.14164
$75$	2.77411	0.320326
$76$	2.09840	0.240703
$77$	−0.220732	−0.0251548
$78$	−12.4018	−1.40423
$79$	9.77028	1.09924	0.549621	−	0.835414i	$-0.314772\pi$
$79$	9.77028	1.09924	0.549621	+	0.835414i	$0.314772\pi$
$80$	1.00000	0.111803
$81$	−1.03767	−0.115296
$82$	−3.42054	−0.377736
$83$	−7.32705	−0.804249	−0.402124	−	0.915585i	$-0.631728\pi$
$83$	−7.32705	−0.804249	−0.402124	+	0.915585i	$0.631728\pi$
$84$	0.612335	0.0668112
$85$	7.05278	0.764981
$86$	4.58747	0.494679
$87$	−13.7820	−1.47759
$88$	1.00000	0.106600
$89$	8.46053	0.896815	0.448407	−	0.893829i	$-0.351991\pi$
$89$	8.46053	0.896815	0.448407	+	0.893829i	$0.351991\pi$
$90$	−4.69567	−0.494968
$91$	0.986797	0.103444
$92$	3.13953	0.327318
$93$	6.14588	0.637298
$94$	10.7913	1.11304
$95$	2.09840	0.215291
$96$	−2.77411	−0.283131
$97$	−13.7604	−1.39716	−0.698581	−	0.715531i	$-0.746185\pi$
$97$	−13.7604	−1.39716	−0.698581	+	0.715531i	$0.746185\pi$
$98$	6.95128	0.702185
$99$	−4.69567	−0.471933
$100$	1.00000	0.100000
$101$	−11.8957	−1.18367	−0.591835	−	0.806059i	$-0.701596\pi$
$101$	−11.8957	−1.18367	−0.591835	+	0.806059i	$0.701596\pi$
$102$	−19.5652	−1.93724
$103$	−9.66533	−0.952354	−0.476177	−	0.879350i	$-0.657978\pi$
$103$	−9.66533	−0.952354	−0.476177	+	0.879350i	$0.657978\pi$
$104$	−4.47056	−0.438375
$105$	0.612335	0.0597578
$106$	−1.71971	−0.167033
$107$	−7.47499	−0.722635	−0.361317	−	0.932443i	$-0.617673\pi$
$107$	−7.47499	−0.722635	−0.361317	+	0.932443i	$0.617673\pi$
$108$	4.70398	0.452641
$109$	15.0298	1.43959	0.719795	−	0.694187i	$-0.244236\pi$
$109$	15.0298	1.43959	0.719795	+	0.694187i	$0.244236\pi$
$110$	1.00000	0.0953463
$111$	27.2438	2.58586
$112$	0.220732	0.0208572
$113$	−8.03178	−0.755567	−0.377783	−	0.925894i	$-0.623314\pi$
$113$	−8.03178	−0.755567	−0.377783	+	0.925894i	$0.623314\pi$
$114$	−5.82118	−0.545203
$115$	3.13953	0.292763
$116$	−4.96810	−0.461276
$117$	20.9923	1.94074
$118$	8.27399	0.761683
$119$	1.55677	0.142709
$120$	−2.77411	−0.253240
$121$	1.00000	0.0909091
$122$	−10.7994	−0.977729
$123$	9.48896	0.855590
$124$	2.21544	0.198953
$125$	1.00000	0.0894427
$126$	−1.03649	−0.0923375
$127$	−0.862450	−0.0765301	−0.0382650	−	0.999268i	$-0.512183\pi$
$127$	−0.862450	−0.0765301	−0.0382650	+	0.999268i	$0.512183\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7261	−1.12047
$130$	−4.47056	−0.392094
$131$	−15.1168	−1.32076	−0.660380	−	0.750931i	$-0.729605\pi$
$131$	−15.1168	−1.32076	−0.660380	+	0.750931i	$0.729605\pi$
$132$	−2.77411	−0.241455
$133$	0.463183	0.0401631
$134$	6.64960	0.574438
$135$	4.70398	0.404854
$136$	−7.05278	−0.604771
$137$	11.5697	0.988466	0.494233	−	0.869330i	$-0.335449\pi$
$137$	11.5697	0.988466	0.494233	+	0.869330i	$0.335449\pi$
$138$	−8.70939	−0.741392
$139$	17.1257	1.45258	0.726290	−	0.687388i	$-0.241243\pi$
$139$	17.1257	1.45258	0.726290	+	0.687388i	$0.241243\pi$
$140$	0.220732	0.0186553
$141$	−29.9362	−2.52108
$142$	−9.58936	−0.804721
$143$	−4.47056	−0.373847
$144$	4.69567	0.391306
$145$	−4.96810	−0.412578
$146$	1.00000	0.0827606
$147$	−19.2836	−1.59048
$148$	9.82073	0.807259
$149$	−3.49472	−0.286299	−0.143149	−	0.989701i	$-0.545723\pi$
$149$	−3.49472	−0.286299	−0.143149	+	0.989701i	$0.545723\pi$
$150$	−2.77411	−0.226505
$151$	−11.5004	−0.935890	−0.467945	−	0.883758i	$-0.655006\pi$
$151$	−11.5004	−0.935890	−0.467945	+	0.883758i	$0.655006\pi$
$152$	−2.09840	−0.170202
$153$	33.1175	2.67739
$154$	0.220732	0.0177871
$155$	2.21544	0.177949
$156$	12.4018	0.992940
$157$	−15.4987	−1.23693	−0.618467	−	0.785811i	$-0.712246\pi$
$157$	−15.4987	−1.23693	−0.618467	+	0.785811i	$0.712246\pi$
$158$	−9.77028	−0.777282
$159$	4.77067	0.378338
$160$	−1.00000	−0.0790569
$161$	0.692995	0.0546156
$162$	1.03767	0.0815268
$163$	−13.1935	−1.03340	−0.516698	−	0.856168i	$-0.672839\pi$
$163$	−13.1935	−1.03340	−0.516698	+	0.856168i	$0.672839\pi$
$164$	3.42054	0.267100
$165$	−2.77411	−0.215964
$166$	7.32705	0.568690
$167$	11.2095	0.867415	0.433707	−	0.901054i	$-0.357205\pi$
$167$	11.2095	0.867415	0.433707	+	0.901054i	$0.357205\pi$
$168$	−0.612335	−0.0472427
$169$	6.98592	0.537378
$170$	−7.05278	−0.540923
$171$	9.85338	0.753507
$172$	−4.58747	−0.349791
$173$	14.3086	1.08786	0.543931	−	0.839130i	$-0.316935\pi$
$173$	14.3086	1.08786	0.543931	+	0.839130i	$0.316935\pi$
$174$	13.7820	1.04481
$175$	0.220732	0.0166858
$176$	−1.00000	−0.0753778
$177$	−22.9529	−1.72525
$178$	−8.46053	−0.634144
$179$	18.6496	1.39393	0.696967	−	0.717103i	$-0.254532\pi$
$179$	18.6496	1.39393	0.696967	+	0.717103i	$0.254532\pi$
$180$	4.69567	0.349995
$181$	−15.9811	−1.18787	−0.593933	−	0.804514i	$-0.702426\pi$
$181$	−15.9811	−1.18787	−0.593933	+	0.804514i	$0.702426\pi$
$182$	−0.986797	−0.0731462
$183$	29.9586	2.21460
$184$	−3.13953	−0.231449
$185$	9.82073	0.722035
$186$	−6.14588	−0.450638
$187$	−7.05278	−0.515750
$188$	−10.7913	−0.787036
$189$	1.03832	0.0755267
$190$	−2.09840	−0.152234
$191$	−12.9296	−0.935556	−0.467778	−	0.883846i	$-0.654945\pi$
$191$	−12.9296	−0.935556	−0.467778	+	0.883846i	$0.654945\pi$
$192$	2.77411	0.200204
$193$	19.1631	1.37939	0.689695	−	0.724100i	$-0.257744\pi$
$193$	19.1631	1.37939	0.689695	+	0.724100i	$0.257744\pi$
$194$	13.7604	0.987942
$195$	12.4018	0.888113
$196$	−6.95128	−0.496520
$197$	−12.4063	−0.883909	−0.441955	−	0.897037i	$-0.645715\pi$
$197$	−12.4063	−0.883909	−0.441955	+	0.897037i	$0.645715\pi$
$198$	4.69567	0.333707
$199$	−8.83892	−0.626575	−0.313287	−	0.949658i	$-0.601430\pi$
$199$	−8.83892	−0.626575	−0.313287	+	0.949658i	$0.601430\pi$
$200$	−1.00000	−0.0707107
$201$	−18.4467	−1.30113
$202$	11.8957	0.836981
$203$	−1.09662	−0.0769675
$204$	19.5652	1.36984
$205$	3.42054	0.238901
$206$	9.66533	0.673416
$207$	14.7422	1.02465
$208$	4.47056	0.309978
$209$	−2.09840	−0.145149
$210$	−0.612335	−0.0422551
$211$	9.96023	0.685691	0.342845	−	0.939392i	$-0.388609\pi$
$211$	9.96023	0.685691	0.342845	+	0.939392i	$0.388609\pi$
$212$	1.71971	0.118110
$213$	26.6019	1.82273
$214$	7.47499	0.510980
$215$	−4.58747	−0.312863
$216$	−4.70398	−0.320065
$217$	0.489020	0.0331968
$218$	−15.0298	−1.01794
$219$	−2.77411	−0.187457
$220$	−1.00000	−0.0674200
$221$	31.5299	2.12093
$222$	−27.2438	−1.82848
$223$	5.78490	0.387386	0.193693	−	0.981062i	$-0.437953\pi$
$223$	5.78490	0.387386	0.193693	+	0.981062i	$0.437953\pi$
$224$	−0.220732	−0.0147483
$225$	4.69567	0.313045
$226$	8.03178	0.534266
$227$	9.94740	0.660232	0.330116	−	0.943940i	$-0.392912\pi$
$227$	9.94740	0.660232	0.330116	+	0.943940i	$0.392912\pi$
$228$	5.82118	0.385517
$229$	4.50535	0.297722	0.148861	−	0.988858i	$-0.452439\pi$
$229$	4.50535	0.297722	0.148861	+	0.988858i	$0.452439\pi$
$230$	−3.13953	−0.207014
$231$	−0.612335	−0.0402887
$232$	4.96810	0.326171
$233$	11.3387	0.742824	0.371412	−	0.928468i	$-0.378874\pi$
$233$	11.3387	0.742824	0.371412	+	0.928468i	$0.378874\pi$
$234$	−20.9923	−1.37231
$235$	−10.7913	−0.703946
$236$	−8.27399	−0.538591
$237$	27.1038	1.76058
$238$	−1.55677	−0.100911
$239$	−9.89094	−0.639792	−0.319896	−	0.947453i	$-0.603648\pi$
$239$	−9.89094	−0.639792	−0.319896	+	0.947453i	$0.603648\pi$
$240$	2.77411	0.179068
$241$	20.4791	1.31918	0.659588	−	0.751627i	$-0.270731\pi$
$241$	20.4791	1.31918	0.659588	+	0.751627i	$0.270731\pi$
$242$	−1.00000	−0.0642824
$243$	−16.9905	−1.08994
$244$	10.7994	0.691359
$245$	−6.95128	−0.444101
$246$	−9.48896	−0.604994
$247$	9.38101	0.596899
$248$	−2.21544	−0.140681
$249$	−20.3260	−1.28811
$250$	−1.00000	−0.0632456
$251$	3.64187	0.229873	0.114936	−	0.993373i	$-0.463334\pi$
$251$	3.64187	0.229873	0.114936	+	0.993373i	$0.463334\pi$
$252$	1.03649	0.0652925
$253$	−3.13953	−0.197380
$254$	0.862450	0.0541149
$255$	19.5652	1.22522
$256$	1.00000	0.0625000
$257$	−8.41691	−0.525032	−0.262516	−	0.964928i	$-0.584552\pi$
$257$	−8.41691	−0.525032	−0.262516	+	0.964928i	$0.584552\pi$
$258$	12.7261	0.792294
$259$	2.16775	0.134698
$260$	4.47056	0.277252
$261$	−23.3286	−1.44400
$262$	15.1168	0.933919
$263$	−4.19115	−0.258437	−0.129219	−	0.991616i	$-0.541247\pi$
$263$	−4.19115	−0.258437	−0.129219	+	0.991616i	$0.541247\pi$
$264$	2.77411	0.170735
$265$	1.71971	0.105641
$266$	−0.463183	−0.0283996
$267$	23.4704	1.43637
$268$	−6.64960	−0.406189
$269$	14.0337	0.855653	0.427826	−	0.903861i	$-0.359279\pi$
$269$	14.0337	0.855653	0.427826	+	0.903861i	$0.359279\pi$
$270$	−4.70398	−0.286275
$271$	−11.3600	−0.690072	−0.345036	−	0.938589i	$-0.612133\pi$
$271$	−11.3600	−0.690072	−0.345036	+	0.938589i	$0.612133\pi$
$272$	7.05278	0.427637
$273$	2.73748	0.165680
$274$	−11.5697	−0.698951
$275$	−1.00000	−0.0603023
$276$	8.70939	0.524244
$277$	−10.1038	−0.607076	−0.303538	−	0.952819i	$-0.598168\pi$
$277$	−10.1038	−0.607076	−0.303538	+	0.952819i	$0.598168\pi$
$278$	−17.1257	−1.02713
$279$	10.4030	0.622811
$280$	−0.220732	−0.0131913
$281$	−19.2882	−1.15064	−0.575318	−	0.817930i	$-0.695122\pi$
$281$	−19.2882	−1.15064	−0.575318	+	0.817930i	$0.695122\pi$
$282$	29.9362	1.78268
$283$	2.93485	0.174459	0.0872293	−	0.996188i	$-0.472199\pi$
$283$	2.93485	0.174459	0.0872293	+	0.996188i	$0.472199\pi$
$284$	9.58936	0.569024
$285$	5.82118	0.344817
$286$	4.47056	0.264350
$287$	0.755024	0.0445677
$288$	−4.69567	−0.276695
$289$	32.7417	1.92598
$290$	4.96810	0.291737
$291$	−38.1730	−2.23774
$292$	−1.00000	−0.0585206
$293$	12.5541	0.733421	0.366710	−	0.930335i	$-0.380484\pi$
$293$	12.5541	0.733421	0.366710	+	0.930335i	$0.380484\pi$
$294$	19.2836	1.12464
$295$	−8.27399	−0.481730
$296$	−9.82073	−0.570818
$297$	−4.70398	−0.272953
$298$	3.49472	0.202444
$299$	14.0355	0.811691
$300$	2.77411	0.160163
$301$	−1.01260	−0.0583654
$302$	11.5004	0.661774
$303$	−33.0001	−1.89580
$304$	2.09840	0.120351
$305$	10.7994	0.618370
$306$	−33.1175	−1.89320
$307$	21.8410	1.24653	0.623265	−	0.782011i	$-0.285806\pi$
$307$	21.8410	1.24653	0.623265	+	0.782011i	$0.285806\pi$
$308$	−0.220732	−0.0125774
$309$	−26.8127	−1.52532
$310$	−2.21544	−0.125829
$311$	1.93875	0.109936	0.0549682	−	0.998488i	$-0.482494\pi$
$311$	1.93875	0.109936	0.0549682	+	0.998488i	$0.482494\pi$
$312$	−12.4018	−0.702115
$313$	17.9450	1.01431	0.507155	−	0.861855i	$-0.330697\pi$
$313$	17.9450	1.01431	0.507155	+	0.861855i	$0.330697\pi$
$314$	15.4987	0.874644
$315$	1.03649	0.0583994
$316$	9.77028	0.549621
$317$	−9.48399	−0.532674	−0.266337	−	0.963880i	$-0.585813\pi$
$317$	−9.48399	−0.532674	−0.266337	+	0.963880i	$0.585813\pi$
$318$	−4.77067	−0.267526
$319$	4.96810	0.278160
$320$	1.00000	0.0559017
$321$	−20.7364	−1.15740
$322$	−0.692995	−0.0386191
$323$	14.7995	0.823467
$324$	−1.03767	−0.0576481
$325$	4.47056	0.247982
$326$	13.1935	0.730721
$327$	41.6942	2.30569
$328$	−3.42054	−0.188868
$329$	−2.38199	−0.131323
$330$	2.77411	0.152710
$331$	4.56249	0.250777	0.125389	−	0.992108i	$-0.459982\pi$
$331$	4.56249	0.250777	0.125389	+	0.992108i	$0.459982\pi$
$332$	−7.32705	−0.402124
$333$	46.1150	2.52708
$334$	−11.2095	−0.613355
$335$	−6.64960	−0.363307
$336$	0.612335	0.0334056
$337$	17.3500	0.945113	0.472557	−	0.881300i	$-0.343331\pi$
$337$	17.3500	0.945113	0.472557	+	0.881300i	$0.343331\pi$
$338$	−6.98592	−0.379984
$339$	−22.2810	−1.21014
$340$	7.05278	0.382491
$341$	−2.21544	−0.119973
$342$	−9.85338	−0.532810
$343$	−3.07950	−0.166277
$344$	4.58747	0.247340
$345$	8.70939	0.468898
$346$	−14.3086	−0.769235
$347$	13.3519	0.716768	0.358384	−	0.933574i	$-0.383328\pi$
$347$	13.3519	0.716768	0.358384	+	0.933574i	$0.383328\pi$
$348$	−13.7820	−0.738795
$349$	30.3732	1.62584	0.812921	−	0.582375i	$-0.197876\pi$
$349$	30.3732	1.62584	0.812921	+	0.582375i	$0.197876\pi$
$350$	−0.220732	−0.0117986
$351$	21.0294	1.12247
$352$	1.00000	0.0533002
$353$	27.4178	1.45930	0.729650	−	0.683820i	$-0.239683\pi$
$353$	27.4178	1.45930	0.729650	+	0.683820i	$0.239683\pi$
$354$	22.9529	1.21994
$355$	9.58936	0.508950
$356$	8.46053	0.448407
$357$	4.31866	0.228568
$358$	−18.6496	−0.985660
$359$	−23.3057	−1.23003	−0.615015	−	0.788516i	$-0.710850\pi$
$359$	−23.3057	−1.23003	−0.615015	+	0.788516i	$0.710850\pi$
$360$	−4.69567	−0.247484
$361$	−14.5967	−0.768249
$362$	15.9811	0.839949
$363$	2.77411	0.145603
$364$	0.986797	0.0517222
$365$	−1.00000	−0.0523424
$366$	−29.9586	−1.56596
$367$	−35.4566	−1.85082	−0.925410	−	0.378968i	$-0.876279\pi$
$367$	−35.4566	−1.85082	−0.925410	+	0.378968i	$0.876279\pi$
$368$	3.13953	0.163659
$369$	16.0618	0.836142
$370$	−9.82073	−0.510556
$371$	0.379596	0.0197076
$372$	6.14588	0.318649
$373$	10.5887	0.548263	0.274132	−	0.961692i	$-0.411610\pi$
$373$	10.5887	0.548263	0.274132	+	0.961692i	$0.411610\pi$
$374$	7.05278	0.364690
$375$	2.77411	0.143254
$376$	10.7913	0.556518
$377$	−22.2102	−1.14388
$378$	−1.03832	−0.0534054
$379$	−22.7762	−1.16994	−0.584968	−	0.811056i	$-0.698893\pi$
$379$	−22.7762	−1.16994	−0.584968	+	0.811056i	$0.698893\pi$
$380$	2.09840	0.107645
$381$	−2.39253	−0.122573
$382$	12.9296	0.661538
$383$	0.753549	0.0385046	0.0192523	−	0.999815i	$-0.493871\pi$
$383$	0.753549	0.0385046	0.0192523	+	0.999815i	$0.493871\pi$
$384$	−2.77411	−0.141566
$385$	−0.220732	−0.0112496
$386$	−19.1631	−0.975377
$387$	−21.5412	−1.09500
$388$	−13.7604	−0.698581
$389$	34.0304	1.72541	0.862705	−	0.505708i	$-0.168769\pi$
$389$	34.0304	1.72541	0.862705	+	0.505708i	$0.168769\pi$
$390$	−12.4018	−0.627991
$391$	22.1424	1.11979
$392$	6.95128	0.351093
$393$	−41.9356	−2.11537
$394$	12.4063	0.625018
$395$	9.77028	0.491596
$396$	−4.69567	−0.235967
$397$	−4.86512	−0.244173	−0.122087	−	0.992519i	$-0.538959\pi$
$397$	−4.86512	−0.244173	−0.122087	+	0.992519i	$0.538959\pi$
$398$	8.83892	0.443055
$399$	1.28492	0.0643265
$400$	1.00000	0.0500000
$401$	−25.1032	−1.25359	−0.626796	−	0.779183i	$-0.715634\pi$
$401$	−25.1032	−1.25359	−0.626796	+	0.779183i	$0.715634\pi$
$402$	18.4467	0.920038
$403$	9.90428	0.493367
$404$	−11.8957	−0.591835
$405$	−1.03767	−0.0515621
$406$	1.09662	0.0544243
$407$	−9.82073	−0.486796
$408$	−19.5652	−0.968620
$409$	13.6642	0.675650	0.337825	−	0.941209i	$-0.390309\pi$
$409$	13.6642	0.675650	0.337825	+	0.941209i	$0.390309\pi$
$410$	−3.42054	−0.168929
$411$	32.0956	1.58316
$412$	−9.66533	−0.476177
$413$	−1.82634	−0.0898681
$414$	−14.7422	−0.724540
$415$	−7.32705	−0.359671
$416$	−4.47056	−0.219187
$417$	47.5085	2.32650
$418$	2.09840	0.102636
$419$	−3.05514	−0.149254	−0.0746268	−	0.997212i	$-0.523777\pi$
$419$	−3.05514	−0.149254	−0.0746268	+	0.997212i	$0.523777\pi$
$420$	0.612335	0.0298789
$421$	29.8384	1.45424	0.727118	−	0.686513i	$-0.240859\pi$
$421$	29.8384	1.45424	0.727118	+	0.686513i	$0.240859\pi$
$422$	−9.96023	−0.484857
$423$	−50.6724	−2.46378
$424$	−1.71971	−0.0835166
$425$	7.05278	0.342110
$426$	−26.6019	−1.28887
$427$	2.38377	0.115359
$428$	−7.47499	−0.361317
$429$	−12.4018	−0.598765
$430$	4.58747	0.221227
$431$	−26.8077	−1.29128	−0.645640	−	0.763642i	$-0.723409\pi$
$431$	−26.8077	−1.29128	−0.645640	+	0.763642i	$0.723409\pi$
$432$	4.70398	0.226320
$433$	26.9535	1.29530	0.647651	−	0.761937i	$-0.275752\pi$
$433$	26.9535	1.29530	0.647651	+	0.761937i	$0.275752\pi$
$434$	−0.489020	−0.0234737
$435$	−13.7820	−0.660798
$436$	15.0298	0.719795
$437$	6.58797	0.315145
$438$	2.77411	0.132552
$439$	14.2280	0.679064	0.339532	−	0.940594i	$-0.389731\pi$
$439$	14.2280	0.679064	0.339532	+	0.940594i	$0.389731\pi$
$440$	1.00000	0.0476731
$441$	−32.6409	−1.55433
$442$	−31.5299	−1.49972
$443$	−29.7698	−1.41441	−0.707203	−	0.707011i	$-0.750043\pi$
$443$	−29.7698	−1.41441	−0.707203	+	0.707011i	$0.750043\pi$
$444$	27.2438	1.29293
$445$	8.46053	0.401068
$446$	−5.78490	−0.273923
$447$	−9.69473	−0.458545
$448$	0.220732	0.0104286
$449$	−6.00435	−0.283363	−0.141681	−	0.989912i	$-0.545251\pi$
$449$	−6.00435	−0.283363	−0.141681	+	0.989912i	$0.545251\pi$
$450$	−4.69567	−0.221356
$451$	−3.42054	−0.161067
$452$	−8.03178	−0.377783
$453$	−31.9034	−1.49895
$454$	−9.94740	−0.466855
$455$	0.986797	0.0462617
$456$	−5.82118	−0.272602
$457$	−2.03065	−0.0949897	−0.0474949	−	0.998871i	$-0.515124\pi$
$457$	−2.03065	−0.0949897	−0.0474949	+	0.998871i	$0.515124\pi$
$458$	−4.50535	−0.210521
$459$	33.1761	1.54853
$460$	3.13953	0.146381
$461$	−22.0998	−1.02929	−0.514646	−	0.857403i	$-0.672077\pi$
$461$	−22.0998	−1.02929	−0.514646	+	0.857403i	$0.672077\pi$
$462$	0.612335	0.0284884
$463$	4.56372	0.212094	0.106047	−	0.994361i	$-0.466181\pi$
$463$	4.56372	0.212094	0.106047	+	0.994361i	$0.466181\pi$
$464$	−4.96810	−0.230638
$465$	6.14588	0.285008
$466$	−11.3387	−0.525256
$467$	−19.2765	−0.892012	−0.446006	−	0.895030i	$-0.647154\pi$
$467$	−19.2765	−0.892012	−0.446006	+	0.895030i	$0.647154\pi$
$468$	20.9923	0.970369
$469$	−1.46778	−0.0677758
$470$	10.7913	0.497765
$471$	−42.9951	−1.98111
$472$	8.27399	0.380841
$473$	4.58747	0.210932
$474$	−27.1038	−1.24492
$475$	2.09840	0.0962810
$476$	1.55677	0.0713547
$477$	8.07521	0.369738
$478$	9.89094	0.452401
$479$	−23.6578	−1.08095	−0.540477	−	0.841359i	$-0.681756\pi$
$479$	−23.6578	−1.08095	−0.540477	+	0.841359i	$0.681756\pi$
$480$	−2.77411	−0.126620
$481$	43.9042	2.00186
$482$	−20.4791	−0.932799
$483$	1.92244	0.0874742
$484$	1.00000	0.0454545
$485$	−13.7604	−0.624830
$486$	16.9905	0.770707
$487$	−4.23735	−0.192012	−0.0960062	−	0.995381i	$-0.530607\pi$
$487$	−4.23735	−0.192012	−0.0960062	+	0.995381i	$0.530607\pi$
$488$	−10.7994	−0.488864
$489$	−36.6002	−1.65512
$490$	6.95128	0.314027
$491$	31.8989	1.43958	0.719789	−	0.694192i	$-0.244238\pi$
$491$	31.8989	1.43958	0.719789	+	0.694192i	$0.244238\pi$
$492$	9.48896	0.427795
$493$	−35.0389	−1.57807
$494$	−9.38101	−0.422071
$495$	−4.69567	−0.211055
$496$	2.21544	0.0994764
$497$	2.11668	0.0949460
$498$	20.3260	0.910831
$499$	−15.7596	−0.705494	−0.352747	−	0.935719i	$-0.614752\pi$
$499$	−15.7596	−0.705494	−0.352747	+	0.935719i	$0.614752\pi$
$500$	1.00000	0.0447214
$501$	31.0963	1.38928
$502$	−3.64187	−0.162545
$503$	22.2130	0.990429	0.495214	−	0.868771i	$-0.335089\pi$
$503$	22.2130	0.990429	0.495214	+	0.868771i	$0.335089\pi$
$504$	−1.03649	−0.0461688
$505$	−11.8957	−0.529354
$506$	3.13953	0.139569
$507$	19.3797	0.860682
$508$	−0.862450	−0.0382650
$509$	−27.3977	−1.21438	−0.607191	−	0.794556i	$-0.707704\pi$
$509$	−27.3977	−1.21438	−0.607191	+	0.794556i	$0.707704\pi$
$510$	−19.5652	−0.866360
$511$	−0.220732	−0.00976462
$512$	−1.00000	−0.0441942
$513$	9.87082	0.435807
$514$	8.41691	0.371254
$515$	−9.66533	−0.425905
$516$	−12.7261	−0.560236
$517$	10.7913	0.474600
$518$	−2.16775	−0.0952455
$519$	39.6936	1.74236
$520$	−4.47056	−0.196047
$521$	28.0321	1.22811	0.614055	−	0.789263i	$-0.289537\pi$
$521$	28.0321	1.22811	0.614055	+	0.789263i	$0.289537\pi$
$522$	23.3286	1.02106
$523$	29.6093	1.29473	0.647363	−	0.762182i	$-0.275872\pi$
$523$	29.6093	1.29473	0.647363	+	0.762182i	$0.275872\pi$
$524$	−15.1168	−0.660380
$525$	0.612335	0.0267245
$526$	4.19115	0.182743
$527$	15.6250	0.680637
$528$	−2.77411	−0.120728
$529$	−13.1434	−0.571451
$530$	−1.71971	−0.0746995
$531$	−38.8520	−1.68603
$532$	0.463183	0.0200816
$533$	15.2917	0.662359
$534$	−23.4704	−1.01566
$535$	−7.47499	−0.323172
$536$	6.64960	0.287219
$537$	51.7359	2.23257
$538$	−14.0337	−0.605038
$539$	6.95128	0.299413
$540$	4.70398	0.202427
$541$	−33.4832	−1.43955	−0.719777	−	0.694206i	$-0.755756\pi$
$541$	−33.4832	−1.43955	−0.719777	+	0.694206i	$0.755756\pi$
$542$	11.3600	0.487954
$543$	−44.3333	−1.90253
$544$	−7.05278	−0.302385
$545$	15.0298	0.643804
$546$	−2.73748	−0.117153
$547$	−28.8617	−1.23404	−0.617019	−	0.786948i	$-0.711660\pi$
$547$	−28.8617	−1.23404	−0.617019	+	0.786948i	$0.711660\pi$
$548$	11.5697	0.494233
$549$	50.7103	2.16426
$550$	1.00000	0.0426401
$551$	−10.4250	−0.444121
$552$	−8.70939	−0.370696
$553$	2.15662	0.0917086
$554$	10.1038	0.429267
$555$	27.2438	1.15643
$556$	17.1257	0.726290
$557$	−27.0959	−1.14809	−0.574045	−	0.818824i	$-0.694627\pi$
$557$	−27.0959	−1.14809	−0.574045	+	0.818824i	$0.694627\pi$
$558$	−10.4030	−0.440394
$559$	−20.5085	−0.867419
$560$	0.220732	0.00932764
$561$	−19.5652	−0.826042
$562$	19.2882	0.813623
$563$	−6.74596	−0.284308	−0.142154	−	0.989845i	$-0.545403\pi$
$563$	−6.74596	−0.284308	−0.142154	+	0.989845i	$0.545403\pi$
$564$	−29.9362	−1.26054
$565$	−8.03178	−0.337900
$566$	−2.93485	−0.123361
$567$	−0.229046	−0.00961905
$568$	−9.58936	−0.402360
$569$	17.0421	0.714443	0.357222	−	0.934020i	$-0.383724\pi$
$569$	17.0421	0.714443	0.357222	+	0.934020i	$0.383724\pi$
$570$	−5.82118	−0.243822
$571$	−22.0928	−0.924555	−0.462277	−	0.886735i	$-0.652968\pi$
$571$	−22.0928	−0.924555	−0.462277	+	0.886735i	$0.652968\pi$
$572$	−4.47056	−0.186924
$573$	−35.8682	−1.49842
$574$	−0.755024	−0.0315141
$575$	3.13953	0.130927
$576$	4.69567	0.195653
$577$	−26.7798	−1.11486	−0.557429	−	0.830224i	$-0.688212\pi$
$577$	−26.7798	−1.11486	−0.557429	+	0.830224i	$0.688212\pi$
$578$	−32.7417	−1.36187
$579$	53.1605	2.20928
$580$	−4.96810	−0.206289
$581$	−1.61732	−0.0670976
$582$	38.1730	1.58232
$583$	−1.71971	−0.0712232
$584$	1.00000	0.0413803
$585$	20.9923	0.867925
$586$	−12.5541	−0.518607
$587$	−9.81643	−0.405167	−0.202584	−	0.979265i	$-0.564934\pi$
$587$	−9.81643	−0.405167	−0.202584	+	0.979265i	$0.564934\pi$
$588$	−19.2836	−0.795242
$589$	4.64888	0.191554
$590$	8.27399	0.340635
$591$	−34.4163	−1.41570
$592$	9.82073	0.403630
$593$	−20.9547	−0.860505	−0.430252	−	0.902709i	$-0.641575\pi$
$593$	−20.9547	−0.860505	−0.430252	+	0.902709i	$0.641575\pi$
$594$	4.70398	0.193007
$595$	1.55677	0.0638215
$596$	−3.49472	−0.143149
$597$	−24.5201	−1.00354
$598$	−14.0355	−0.573952
$599$	13.3363	0.544905	0.272453	−	0.962169i	$-0.412165\pi$
$599$	13.3363	0.544905	0.272453	+	0.962169i	$0.412165\pi$
$600$	−2.77411	−0.113252
$601$	−3.21037	−0.130954	−0.0654769	−	0.997854i	$-0.520857\pi$
$601$	−3.21037	−0.130954	−0.0654769	+	0.997854i	$0.520857\pi$
$602$	1.01260	0.0412706
$603$	−31.2244	−1.27155
$604$	−11.5004	−0.467945
$605$	1.00000	0.0406558
$606$	33.0001	1.34054
$607$	44.6851	1.81371	0.906855	−	0.421442i	$-0.138476\pi$
$607$	44.6851	1.81371	0.906855	+	0.421442i	$0.138476\pi$
$608$	−2.09840	−0.0851012
$609$	−3.04214	−0.123274
$610$	−10.7994	−0.437254
$611$	−48.2431	−1.95171
$612$	33.1175	1.33870
$613$	−28.4082	−1.14740	−0.573698	−	0.819067i	$-0.694492\pi$
$613$	−28.4082	−1.14740	−0.573698	+	0.819067i	$0.694492\pi$
$614$	−21.8410	−0.881430
$615$	9.48896	0.382632
$616$	0.220732	0.00889355
$617$	−0.739791	−0.0297829	−0.0148914	−	0.999889i	$-0.504740\pi$
$617$	−0.739791	−0.0297829	−0.0148914	+	0.999889i	$0.504740\pi$
$618$	26.8127	1.07856
$619$	−15.8194	−0.635837	−0.317918	−	0.948118i	$-0.602984\pi$
$619$	−15.8194	−0.635837	−0.317918	+	0.948118i	$0.602984\pi$
$620$	2.21544	0.0889744
$621$	14.7683	0.592631
$622$	−1.93875	−0.0777367
$623$	1.86751	0.0748203
$624$	12.4018	0.496470
$625$	1.00000	0.0400000
$626$	−17.9450	−0.717226
$627$	−5.82118	−0.232475
$628$	−15.4987	−0.618467
$629$	69.2634	2.76171
$630$	−1.03649	−0.0412946
$631$	8.97564	0.357314	0.178657	−	0.983911i	$-0.442825\pi$
$631$	8.97564	0.357314	0.178657	+	0.983911i	$0.442825\pi$
$632$	−9.77028	−0.388641
$633$	27.6308	1.09822
$634$	9.48399	0.376657
$635$	−0.862450	−0.0342253
$636$	4.77067	0.189169
$637$	−31.0761	−1.23128
$638$	−4.96810	−0.196689
$639$	45.0285	1.78130
$640$	−1.00000	−0.0395285
$641$	4.86604	0.192197	0.0960985	−	0.995372i	$-0.469364\pi$
$641$	4.86604	0.192197	0.0960985	+	0.995372i	$0.469364\pi$
$642$	20.7364	0.818402
$643$	21.8068	0.859977	0.429988	−	0.902834i	$-0.358518\pi$
$643$	21.8068	0.859977	0.429988	+	0.902834i	$0.358518\pi$
$644$	0.692995	0.0273078
$645$	−12.7261	−0.501091
$646$	−14.7995	−0.582279
$647$	37.4480	1.47223	0.736116	−	0.676856i	$-0.236658\pi$
$647$	37.4480	1.47223	0.736116	+	0.676856i	$0.236658\pi$
$648$	1.03767	0.0407634
$649$	8.27399	0.324783
$650$	−4.47056	−0.175350
$651$	1.35659	0.0531691
$652$	−13.1935	−0.516698
$653$	23.3417	0.913432	0.456716	−	0.889613i	$-0.349026\pi$
$653$	23.3417	0.913432	0.456716	+	0.889613i	$0.349026\pi$
$654$	−41.6942	−1.63037
$655$	−15.1168	−0.590662
$656$	3.42054	0.133550
$657$	−4.69567	−0.183196
$658$	2.38199	0.0928595
$659$	−26.3403	−1.02607	−0.513036	−	0.858367i	$-0.671479\pi$
$659$	−26.3403	−1.02607	−0.513036	+	0.858367i	$0.671479\pi$
$660$	−2.77411	−0.107982
$661$	−14.9739	−0.582416	−0.291208	−	0.956660i	$-0.594057\pi$
$661$	−14.9739	−0.582416	−0.291208	+	0.956660i	$0.594057\pi$
$662$	−4.56249	−0.177326
$663$	87.4673	3.39695
$664$	7.32705	0.284345
$665$	0.463183	0.0179615
$666$	−46.1150	−1.78692
$667$	−15.5975	−0.603937
$668$	11.2095	0.433707
$669$	16.0479	0.620449
$670$	6.64960	0.256896
$671$	−10.7994	−0.416905
$672$	−0.612335	−0.0236213
$673$	39.2310	1.51225	0.756123	−	0.654430i	$-0.227091\pi$
$673$	39.2310	1.51225	0.756123	+	0.654430i	$0.227091\pi$
$674$	−17.3500	−0.668296
$675$	4.70398	0.181056
$676$	6.98592	0.268689
$677$	−20.7350	−0.796910	−0.398455	−	0.917188i	$-0.630454\pi$
$677$	−20.7350	−0.796910	−0.398455	+	0.917188i	$0.630454\pi$
$678$	22.2810	0.855698
$679$	−3.03737	−0.116564
$680$	−7.05278	−0.270462
$681$	27.5952	1.05745
$682$	2.21544	0.0848337
$683$	40.3238	1.54295	0.771474	−	0.636261i	$-0.219520\pi$
$683$	40.3238	1.54295	0.771474	+	0.636261i	$0.219520\pi$
$684$	9.85338	0.376754
$685$	11.5697	0.442055
$686$	3.07950	0.117576
$687$	12.4983	0.476841
$688$	−4.58747	−0.174896
$689$	7.68808	0.292892
$690$	−8.70939	−0.331561
$691$	−5.66207	−0.215395	−0.107698	−	0.994184i	$-0.534348\pi$
$691$	−5.66207	−0.215395	−0.107698	+	0.994184i	$0.534348\pi$
$692$	14.3086	0.543931
$693$	−1.03649	−0.0393729
$694$	−13.3519	−0.506831
$695$	17.1257	0.649614
$696$	13.7820	0.522407
$697$	24.1243	0.913774
$698$	−30.3732	−1.14964
$699$	31.4548	1.18973
$700$	0.220732	0.00834289
$701$	−22.6887	−0.856939	−0.428469	−	0.903556i	$-0.640947\pi$
$701$	−22.6887	−0.856939	−0.428469	+	0.903556i	$0.640947\pi$
$702$	−21.0294	−0.793705
$703$	20.6078	0.777237
$704$	−1.00000	−0.0376889
$705$	−29.9362	−1.12746
$706$	−27.4178	−1.03188
$707$	−2.62577	−0.0987524
$708$	−22.9529	−0.862625
$709$	−43.8150	−1.64551	−0.822753	−	0.568400i	$-0.807563\pi$
$709$	−43.8150	−1.64551	−0.822753	+	0.568400i	$0.807563\pi$
$710$	−9.58936	−0.359882
$711$	45.8781	1.72056
$712$	−8.46053	−0.317072
$713$	6.95545	0.260484
$714$	−4.31866	−0.161622
$715$	−4.47056	−0.167190
$716$	18.6496	0.696967
$717$	−27.4385	−1.02471
$718$	23.3057	0.869762
$719$	7.08924	0.264384	0.132192	−	0.991224i	$-0.457798\pi$
$719$	7.08924	0.264384	0.132192	+	0.991224i	$0.457798\pi$
$720$	4.69567	0.174997
$721$	−2.13345	−0.0794538
$722$	14.5967	0.543234
$723$	56.8113	2.11284
$724$	−15.9811	−0.593933
$725$	−4.96810	−0.184510
$726$	−2.77411	−0.102957
$727$	34.1679	1.26722	0.633609	−	0.773653i	$-0.281573\pi$
$727$	34.1679	1.26722	0.633609	+	0.773653i	$0.281573\pi$
$728$	−0.986797	−0.0365731
$729$	−44.0206	−1.63039
$730$	1.00000	0.0370117
$731$	−32.3544	−1.19667
$732$	29.9586	1.10730
$733$	−29.3780	−1.08510	−0.542551	−	0.840023i	$-0.682541\pi$
$733$	−29.3780	−1.08510	−0.542551	+	0.840023i	$0.682541\pi$
$734$	35.4566	1.30873
$735$	−19.2836	−0.711286
$736$	−3.13953	−0.115725
$737$	6.64960	0.244941
$738$	−16.0618	−0.591241
$739$	−3.73043	−0.137226	−0.0686130	−	0.997643i	$-0.521857\pi$
$739$	−3.73043	−0.137226	−0.0686130	+	0.997643i	$0.521857\pi$
$740$	9.82073	0.361017
$741$	26.0239	0.956013
$742$	−0.379596	−0.0139354
$743$	−46.2766	−1.69772	−0.848862	−	0.528614i	$-0.822712\pi$
$743$	−46.2766	−1.69772	−0.848862	+	0.528614i	$0.822712\pi$
$744$	−6.14588	−0.225319
$745$	−3.49472	−0.128037
$746$	−10.5887	−0.387681
$747$	−34.4055	−1.25883
$748$	−7.05278	−0.257875
$749$	−1.64997	−0.0602887
$750$	−2.77411	−0.101296
$751$	−39.1289	−1.42783	−0.713916	−	0.700231i	$-0.753080\pi$
$751$	−39.1289	−1.42783	−0.713916	+	0.700231i	$0.753080\pi$
$752$	−10.7913	−0.393518
$753$	10.1029	0.368172
$754$	22.2102	0.808847
$755$	−11.5004	−0.418543
$756$	1.03832	0.0377633
$757$	39.9056	1.45039	0.725197	−	0.688541i	$-0.241748\pi$
$757$	39.9056	1.45039	0.725197	+	0.688541i	$0.241748\pi$
$758$	22.7762	0.827270
$759$	−8.70939	−0.316131
$760$	−2.09840	−0.0761168
$761$	−26.1152	−0.946674	−0.473337	−	0.880881i	$-0.656951\pi$
$761$	−26.1152	−0.946674	−0.473337	+	0.880881i	$0.656951\pi$
$762$	2.39253	0.0866722
$763$	3.31755	0.120103
$764$	−12.9296	−0.467778
$765$	33.1175	1.19737
$766$	−0.753549	−0.0272268
$767$	−36.9894	−1.33561
$768$	2.77411	0.100102
$769$	41.4170	1.49353	0.746767	−	0.665086i	$-0.231605\pi$
$769$	41.4170	1.49353	0.746767	+	0.665086i	$0.231605\pi$
$770$	0.220732	0.00795464
$771$	−23.3494	−0.840908
$772$	19.1631	0.689695
$773$	−38.3018	−1.37762	−0.688810	−	0.724942i	$-0.741866\pi$
$773$	−38.3018	−1.37762	−0.688810	+	0.724942i	$0.741866\pi$
$774$	21.5412	0.774284
$775$	2.21544	0.0795811
$776$	13.7604	0.493971
$777$	6.01358	0.215736
$778$	−34.0304	−1.22005
$779$	7.17765	0.257166
$780$	12.4018	0.444056
$781$	−9.58936	−0.343134
$782$	−22.1424	−0.791810
$783$	−23.3698	−0.835170
$784$	−6.95128	−0.248260
$785$	−15.4987	−0.553173
$786$	41.9356	1.49579
$787$	20.6742	0.736955	0.368477	−	0.929637i	$-0.379879\pi$
$787$	20.6742	0.736955	0.368477	+	0.929637i	$0.379879\pi$
$788$	−12.4063	−0.441955
$789$	−11.6267	−0.413922
$790$	−9.77028	−0.347611
$791$	−1.77287	−0.0630361
$792$	4.69567	0.166854
$793$	48.2792	1.71445
$794$	4.86512	0.172657
$795$	4.77067	0.169198
$796$	−8.83892	−0.313287
$797$	−49.2543	−1.74468	−0.872338	−	0.488903i	$-0.837397\pi$
$797$	−49.2543	−1.74468	−0.872338	+	0.488903i	$0.837397\pi$
$798$	−1.28492	−0.0454857
$799$	−76.1086	−2.69253
$800$	−1.00000	−0.0353553
$801$	39.7279	1.40372
$802$	25.1032	0.886424
$803$	1.00000	0.0352892
$804$	−18.4467	−0.650565
$805$	0.692995	0.0244249
$806$	−9.90428	−0.348863
$807$	38.9311	1.37044
$808$	11.8957	0.418491
$809$	0.286020	0.0100559	0.00502797	−	0.999987i	$-0.498400\pi$
$809$	0.286020	0.0100559	0.00502797	+	0.999987i	$0.498400\pi$
$810$	1.03767	0.0364599
$811$	11.8611	0.416501	0.208250	−	0.978076i	$-0.433223\pi$
$811$	11.8611	0.416501	0.208250	+	0.978076i	$0.433223\pi$
$812$	−1.09662	−0.0384838
$813$	−31.5139	−1.10524
$814$	9.82073	0.344216
$815$	−13.1935	−0.462149
$816$	19.5652	0.684918
$817$	−9.62632	−0.336782
$818$	−13.6642	−0.477756
$819$	4.63368	0.161914
$820$	3.42054	0.119451
$821$	−25.9110	−0.904299	−0.452149	−	0.891942i	$-0.649343\pi$
$821$	−25.9110	−0.904299	−0.452149	+	0.891942i	$0.649343\pi$
$822$	−32.0956	−1.11946
$823$	−52.6400	−1.83491	−0.917457	−	0.397834i	$-0.869762\pi$
$823$	−52.6400	−1.83491	−0.917457	+	0.397834i	$0.869762\pi$
$824$	9.66533	0.336708
$825$	−2.77411	−0.0965820
$826$	1.82634	0.0635464
$827$	2.59851	0.0903590	0.0451795	−	0.998979i	$-0.485614\pi$
$827$	2.59851	0.0903590	0.0451795	+	0.998979i	$0.485614\pi$
$828$	14.7422	0.512327
$829$	−18.1164	−0.629208	−0.314604	−	0.949223i	$-0.601872\pi$
$829$	−18.1164	−0.629208	−0.314604	+	0.949223i	$0.601872\pi$
$830$	7.32705	0.254326
$831$	−28.0289	−0.972312
$832$	4.47056	0.154989
$833$	−49.0258	−1.69864
$834$	−47.5085	−1.64508
$835$	11.2095	0.387920
$836$	−2.09840	−0.0725745
$837$	10.4214	0.360217
$838$	3.05514	0.105538
$839$	4.43492	0.153110	0.0765552	−	0.997065i	$-0.475608\pi$
$839$	4.43492	0.153110	0.0765552	+	0.997065i	$0.475608\pi$
$840$	−0.612335	−0.0211276
$841$	−4.31802	−0.148897
$842$	−29.8384	−1.02830
$843$	−53.5075	−1.84290
$844$	9.96023	0.342845
$845$	6.98592	0.240323
$846$	50.6724	1.74215
$847$	0.220732	0.00758445
$848$	1.71971	0.0590552
$849$	8.14158	0.279418
$850$	−7.05278	−0.241908
$851$	30.8325	1.05692
$852$	26.6019	0.911366
$853$	−49.0660	−1.67999	−0.839994	−	0.542596i	$-0.817442\pi$
$853$	−49.0660	−1.67999	−0.839994	+	0.542596i	$0.817442\pi$
$854$	−2.38377	−0.0815709
$855$	9.85338	0.336979
$856$	7.47499	0.255490
$857$	−8.31906	−0.284174	−0.142087	−	0.989854i	$-0.545381\pi$
$857$	−8.31906	−0.284174	−0.142087	+	0.989854i	$0.545381\pi$
$858$	12.4018	0.423391
$859$	54.7806	1.86909	0.934545	−	0.355845i	$-0.115807\pi$
$859$	54.7806	1.86909	0.934545	+	0.355845i	$0.115807\pi$
$860$	−4.58747	−0.156431
$861$	2.09452	0.0713810
$862$	26.8077	0.913073
$863$	−37.4394	−1.27445	−0.637226	−	0.770677i	$-0.719918\pi$
$863$	−37.4394	−1.27445	−0.637226	+	0.770677i	$0.719918\pi$
$864$	−4.70398	−0.160033
$865$	14.3086	0.486507
$866$	−26.9535	−0.915917
$867$	90.8289	3.08471
$868$	0.489020	0.0165984
$869$	−9.77028	−0.331434
$870$	13.7820	0.467255
$871$	−29.7274	−1.00728
$872$	−15.0298	−0.508972
$873$	−64.6146	−2.18687
$874$	−6.58797	−0.222842
$875$	0.220732	0.00746211
$876$	−2.77411	−0.0937284
$877$	18.9759	0.640770	0.320385	−	0.947287i	$-0.396188\pi$
$877$	18.9759	0.640770	0.320385	+	0.947287i	$0.396188\pi$
$878$	−14.2280	−0.480171
$879$	34.8265	1.17467
$880$	−1.00000	−0.0337100
$881$	30.8665	1.03992	0.519960	−	0.854191i	$-0.325947\pi$
$881$	30.8665	1.03992	0.519960	+	0.854191i	$0.325947\pi$
$882$	32.6409	1.09908
$883$	5.42075	0.182423	0.0912114	−	0.995832i	$-0.470926\pi$
$883$	5.42075	0.182423	0.0912114	+	0.995832i	$0.470926\pi$
$884$	31.5299	1.06046
$885$	−22.9529	−0.771555
$886$	29.7698	1.00014
$887$	−16.7723	−0.563160	−0.281580	−	0.959538i	$-0.590858\pi$
$887$	−16.7723	−0.563160	−0.281580	+	0.959538i	$0.590858\pi$
$888$	−27.2438	−0.914241
$889$	−0.190370	−0.00638482
$890$	−8.46053	−0.283598
$891$	1.03767	0.0347631
$892$	5.78490	0.193693
$893$	−22.6444	−0.757766
$894$	9.69473	0.324240
$895$	18.6496	0.623386
$896$	−0.220732	−0.00737414
$897$	38.9359	1.30003
$898$	6.00435	0.200368
$899$	−11.0065	−0.367089
$900$	4.69567	0.156522
$901$	12.1287	0.404067
$902$	3.42054	0.113892
$903$	−2.80907	−0.0934798
$904$	8.03178	0.267133
$905$	−15.9811	−0.531230
$906$	31.9034	1.05992
$907$	−3.38297	−0.112330	−0.0561648	−	0.998422i	$-0.517887\pi$
$907$	−3.38297	−0.112330	−0.0561648	+	0.998422i	$0.517887\pi$
$908$	9.94740	0.330116
$909$	−55.8585	−1.85271
$910$	−0.986797	−0.0327120
$911$	−33.3721	−1.10567	−0.552833	−	0.833292i	$-0.686453\pi$
$911$	−33.3721	−1.10567	−0.552833	+	0.833292i	$0.686453\pi$
$912$	5.82118	0.192758
$913$	7.32705	0.242490
$914$	2.03065	0.0671679
$915$	29.9586	0.990401
$916$	4.50535	0.148861
$917$	−3.33676	−0.110190
$918$	−33.1761	−1.09498
$919$	34.4038	1.13488	0.567439	−	0.823416i	$-0.307934\pi$
$919$	34.4038	1.13488	0.567439	+	0.823416i	$0.307934\pi$
$920$	−3.13953	−0.103507
$921$	60.5892	1.99648
$922$	22.0998	0.727820
$923$	42.8698	1.41108
$924$	−0.612335	−0.0201443
$925$	9.82073	0.322904
$926$	−4.56372	−0.149973
$927$	−45.3853	−1.49065
$928$	4.96810	0.163086
$929$	−28.5795	−0.937662	−0.468831	−	0.883288i	$-0.655325\pi$
$929$	−28.5795	−0.937662	−0.468831	+	0.883288i	$0.655325\pi$
$930$	−6.14588	−0.201531
$931$	−14.5865	−0.478054
$932$	11.3387	0.371412
$933$	5.37830	0.176077
$934$	19.2765	0.630748
$935$	−7.05278	−0.230650
$936$	−20.9923	−0.686155
$937$	−19.9846	−0.652868	−0.326434	−	0.945220i	$-0.605847\pi$
$937$	−19.9846	−0.652868	−0.326434	+	0.945220i	$0.605847\pi$
$938$	1.46778	0.0479247
$939$	49.7813	1.62455
$940$	−10.7913	−0.351973
$941$	17.2407	0.562031	0.281015	−	0.959703i	$-0.409329\pi$
$941$	17.2407	0.562031	0.281015	+	0.959703i	$0.409329\pi$
$942$	42.9951	1.40086
$943$	10.7389	0.349706
$944$	−8.27399	−0.269296
$945$	1.03832	0.0337766
$946$	−4.58747	−0.149151
$947$	20.0248	0.650719	0.325359	−	0.945590i	$-0.394515\pi$
$947$	20.0248	0.650719	0.325359	+	0.945590i	$0.394515\pi$
$948$	27.1038	0.880291
$949$	−4.47056	−0.145121
$950$	−2.09840	−0.0680810
$951$	−26.3096	−0.853147
$952$	−1.55677	−0.0504554
$953$	25.3672	0.821726	0.410863	−	0.911697i	$-0.365228\pi$
$953$	25.3672	0.821726	0.410863	+	0.911697i	$0.365228\pi$
$954$	−8.07521	−0.261444
$955$	−12.9296	−0.418394
$956$	−9.89094	−0.319896
$957$	13.7820	0.445510
$958$	23.6578	0.764350
$959$	2.55380	0.0824666
$960$	2.77411	0.0895339
$961$	−26.0918	−0.841671
$962$	−43.9042	−1.41553
$963$	−35.1001	−1.13109
$964$	20.4791	0.659588
$965$	19.1631	0.616882
$966$	−1.92244	−0.0618536
$967$	40.8932	1.31504	0.657519	−	0.753438i	$-0.271606\pi$
$967$	40.8932	1.31504	0.657519	+	0.753438i	$0.271606\pi$
$968$	−1.00000	−0.0321412
$969$	41.0555	1.31889
$970$	13.7604	0.441821
$971$	30.2275	0.970047	0.485024	−	0.874501i	$-0.338811\pi$
$971$	30.2275	0.970047	0.485024	+	0.874501i	$0.338811\pi$
$972$	−16.9905	−0.544972
$973$	3.78019	0.121187
$974$	4.23735	0.135773
$975$	12.4018	0.397176
$976$	10.7994	0.345679
$977$	14.1443	0.452516	0.226258	−	0.974067i	$-0.427351\pi$
$977$	14.1443	0.452516	0.226258	+	0.974067i	$0.427351\pi$
$978$	36.6002	1.17035
$979$	−8.46053	−0.270400
$980$	−6.95128	−0.222050
$981$	70.5749	2.25328
$982$	−31.8989	−1.01794
$983$	12.4158	0.396004	0.198002	−	0.980202i	$-0.436555\pi$
$983$	12.4158	0.396004	0.198002	+	0.980202i	$0.436555\pi$
$984$	−9.48896	−0.302497
$985$	−12.4063	−0.395296
$986$	35.0389	1.11587
$987$	−6.60788	−0.210331
$988$	9.38101	0.298450
$989$	−14.4025	−0.457972
$990$	4.69567	0.149238
$991$	49.3494	1.56764	0.783818	−	0.620991i	$-0.213270\pi$
$991$	49.3494	1.56764	0.783818	+	0.620991i	$0.213270\pi$
$992$	−2.21544	−0.0703404
$993$	12.6568	0.401653
$994$	−2.11668	−0.0671370
$995$	−8.83892	−0.280213
$996$	−20.3260	−0.644055
$997$	−28.0920	−0.889683	−0.444842	−	0.895609i	$-0.646740\pi$
$997$	−28.0920	−0.889683	−0.444842	+	0.895609i	$0.646740\pi$
$998$	15.7596	0.498860
$999$	46.1966	1.46159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.be.1.13	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.be.1.13	✓	15	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.77411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77411 q^{6} +0.220732 q^{7} -1.00000 q^{8} +4.69567 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.77411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.77411 q^{6} +0.220732 q^{7} -1.00000 q^{8} +4.69567 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.77411 q^{12} +4.47056 q^{13} -0.220732 q^{14} +2.77411 q^{15} +1.00000 q^{16} +7.05278 q^{17} -4.69567 q^{18} +2.09840 q^{19} +1.00000 q^{20} +0.612335 q^{21} +1.00000 q^{22} +3.13953 q^{23} -2.77411 q^{24} +1.00000 q^{25} -4.47056 q^{26} +4.70398 q^{27} +0.220732 q^{28} -4.96810 q^{29} -2.77411 q^{30} +2.21544 q^{31} -1.00000 q^{32} -2.77411 q^{33} -7.05278 q^{34} +0.220732 q^{35} +4.69567 q^{36} +9.82073 q^{37} -2.09840 q^{38} +12.4018 q^{39} -1.00000 q^{40} +3.42054 q^{41} -0.612335 q^{42} -4.58747 q^{43} -1.00000 q^{44} +4.69567 q^{45} -3.13953 q^{46} -10.7913 q^{47} +2.77411 q^{48} -6.95128 q^{49} -1.00000 q^{50} +19.5652 q^{51} +4.47056 q^{52} +1.71971 q^{53} -4.70398 q^{54} -1.00000 q^{55} -0.220732 q^{56} +5.82118 q^{57} +4.96810 q^{58} -8.27399 q^{59} +2.77411 q^{60} +10.7994 q^{61} -2.21544 q^{62} +1.03649 q^{63} +1.00000 q^{64} +4.47056 q^{65} +2.77411 q^{66} -6.64960 q^{67} +7.05278 q^{68} +8.70939 q^{69} -0.220732 q^{70} +9.58936 q^{71} -4.69567 q^{72} -1.00000 q^{73} -9.82073 q^{74} +2.77411 q^{75} +2.09840 q^{76} -0.220732 q^{77} -12.4018 q^{78} +9.77028 q^{79} +1.00000 q^{80} -1.03767 q^{81} -3.42054 q^{82} -7.32705 q^{83} +0.612335 q^{84} +7.05278 q^{85} +4.58747 q^{86} -13.7820 q^{87} +1.00000 q^{88} +8.46053 q^{89} -4.69567 q^{90} +0.986797 q^{91} +3.13953 q^{92} +6.14588 q^{93} +10.7913 q^{94} +2.09840 q^{95} -2.77411 q^{96} -13.7604 q^{97} +6.95128 q^{98} -4.69567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * q^99

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