LMFDB - Embedded newform 6042.2.a.bg.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 34 x^{10} + 169 x^{9} + 453 x^{8} - 2095 x^{7} - 3056 x^{6} + 11545 x^{5} + \cdots + 7848 $ x^12 - 5x^11 - 34x^10 + 169x^9 + 453x^8 - 2095x^7 - 3056x^6 + 11545x^5 + 11014x^4 - 26766x^3 - 19370x^2 + 18296*x + 7848
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$4.43811$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.43811 q^{5} +1.00000 q^{6} +3.55047 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.43811 q^{5} +1.00000 q^{6} +3.55047 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.43811 q^{10} -5.05487 q^{11} +1.00000 q^{12} +2.90730 q^{13} +3.55047 q^{14} +4.43811 q^{15} +1.00000 q^{16} +7.34657 q^{17} +1.00000 q^{18} -1.00000 q^{19} +4.43811 q^{20} +3.55047 q^{21} -5.05487 q^{22} -7.19632 q^{23} +1.00000 q^{24} +14.6968 q^{25} +2.90730 q^{26} +1.00000 q^{27} +3.55047 q^{28} -9.18051 q^{29} +4.43811 q^{30} +4.24687 q^{31} +1.00000 q^{32} -5.05487 q^{33} +7.34657 q^{34} +15.7574 q^{35} +1.00000 q^{36} +0.355008 q^{37} -1.00000 q^{38} +2.90730 q^{39} +4.43811 q^{40} -6.18349 q^{41} +3.55047 q^{42} -8.74555 q^{43} -5.05487 q^{44} +4.43811 q^{45} -7.19632 q^{46} -2.77732 q^{47} +1.00000 q^{48} +5.60581 q^{49} +14.6968 q^{50} +7.34657 q^{51} +2.90730 q^{52} +1.00000 q^{53} +1.00000 q^{54} -22.4341 q^{55} +3.55047 q^{56} -1.00000 q^{57} -9.18051 q^{58} -6.25953 q^{59} +4.43811 q^{60} +5.17609 q^{61} +4.24687 q^{62} +3.55047 q^{63} +1.00000 q^{64} +12.9029 q^{65} -5.05487 q^{66} -11.4722 q^{67} +7.34657 q^{68} -7.19632 q^{69} +15.7574 q^{70} -13.9767 q^{71} +1.00000 q^{72} +7.09489 q^{73} +0.355008 q^{74} +14.6968 q^{75} -1.00000 q^{76} -17.9472 q^{77} +2.90730 q^{78} +5.57821 q^{79} +4.43811 q^{80} +1.00000 q^{81} -6.18349 q^{82} +3.36853 q^{83} +3.55047 q^{84} +32.6049 q^{85} -8.74555 q^{86} -9.18051 q^{87} -5.05487 q^{88} -11.0277 q^{89} +4.43811 q^{90} +10.3223 q^{91} -7.19632 q^{92} +4.24687 q^{93} -2.77732 q^{94} -4.43811 q^{95} +1.00000 q^{96} +4.68706 q^{97} +5.60581 q^{98} -5.05487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * 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
$5$	4.43811	1.98478	0.992392	−	0.123118i	$-0.0392893\pi$
$5$	4.43811	1.98478	0.992392	+	0.123118i	$0.0392893\pi$
$6$	1.00000	0.408248
$7$	3.55047	1.34195	0.670975	−	0.741480i	$-0.265876\pi$
$7$	3.55047	1.34195	0.670975	+	0.741480i	$0.265876\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.43811	1.40345
$11$	−5.05487	−1.52410	−0.762051	−	0.647517i	$-0.775807\pi$
$11$	−5.05487	−1.52410	−0.762051	+	0.647517i	$0.775807\pi$
$12$	1.00000	0.288675
$13$	2.90730	0.806340	0.403170	−	0.915125i	$-0.367908\pi$
$13$	2.90730	0.806340	0.403170	+	0.915125i	$0.367908\pi$
$14$	3.55047	0.948902
$15$	4.43811	1.14592
$16$	1.00000	0.250000
$17$	7.34657	1.78180	0.890902	−	0.454196i	$-0.150073\pi$
$17$	7.34657	1.78180	0.890902	+	0.454196i	$0.150073\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.43811	0.992392
$21$	3.55047	0.774775
$22$	−5.05487	−1.07770
$23$	−7.19632	−1.50054	−0.750268	−	0.661134i	$-0.770076\pi$
$23$	−7.19632	−1.50054	−0.750268	+	0.661134i	$0.770076\pi$
$24$	1.00000	0.204124
$25$	14.6968	2.93937
$26$	2.90730	0.570169
$27$	1.00000	0.192450
$28$	3.55047	0.670975
$29$	−9.18051	−1.70478	−0.852389	−	0.522908i	$-0.824847\pi$
$29$	−9.18051	−1.70478	−0.852389	+	0.522908i	$0.824847\pi$
$30$	4.43811	0.810285
$31$	4.24687	0.762760	0.381380	−	0.924418i	$-0.375449\pi$
$31$	4.24687	0.762760	0.381380	+	0.924418i	$0.375449\pi$
$32$	1.00000	0.176777
$33$	−5.05487	−0.879941
$34$	7.34657	1.25993
$35$	15.7574	2.66348
$36$	1.00000	0.166667
$37$	0.355008	0.0583630	0.0291815	−	0.999574i	$-0.490710\pi$
$37$	0.355008	0.0583630	0.0291815	+	0.999574i	$0.490710\pi$
$38$	−1.00000	−0.162221
$39$	2.90730	0.465541
$40$	4.43811	0.701727
$41$	−6.18349	−0.965699	−0.482849	−	0.875703i	$-0.660398\pi$
$41$	−6.18349	−0.965699	−0.482849	+	0.875703i	$0.660398\pi$
$42$	3.55047	0.547849
$43$	−8.74555	−1.33368	−0.666842	−	0.745199i	$-0.732355\pi$
$43$	−8.74555	−1.33368	−0.666842	+	0.745199i	$0.732355\pi$
$44$	−5.05487	−0.762051
$45$	4.43811	0.661595
$46$	−7.19632	−1.06104
$47$	−2.77732	−0.405114	−0.202557	−	0.979270i	$-0.564925\pi$
$47$	−2.77732	−0.405114	−0.202557	+	0.979270i	$0.564925\pi$
$48$	1.00000	0.144338
$49$	5.60581	0.800830
$50$	14.6968	2.07845
$51$	7.34657	1.02872
$52$	2.90730	0.403170
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−22.4341	−3.02501
$56$	3.55047	0.474451
$57$	−1.00000	−0.132453
$58$	−9.18051	−1.20546
$59$	−6.25953	−0.814921	−0.407461	−	0.913223i	$-0.633586\pi$
$59$	−6.25953	−0.814921	−0.407461	+	0.913223i	$0.633586\pi$
$60$	4.43811	0.572958
$61$	5.17609	0.662730	0.331365	−	0.943503i	$-0.392491\pi$
$61$	5.17609	0.662730	0.331365	+	0.943503i	$0.392491\pi$
$62$	4.24687	0.539352
$63$	3.55047	0.447317
$64$	1.00000	0.125000
$65$	12.9029	1.60041
$66$	−5.05487	−0.622212
$67$	−11.4722	−1.40155	−0.700773	−	0.713384i	$-0.747162\pi$
$67$	−11.4722	−1.40155	−0.700773	+	0.713384i	$0.747162\pi$
$68$	7.34657	0.890902
$69$	−7.19632	−0.866335
$70$	15.7574	1.88337
$71$	−13.9767	−1.65873	−0.829365	−	0.558708i	$-0.811297\pi$
$71$	−13.9767	−1.65873	−0.829365	+	0.558708i	$0.811297\pi$
$72$	1.00000	0.117851
$73$	7.09489	0.830394	0.415197	−	0.909731i	$-0.363713\pi$
$73$	7.09489	0.830394	0.415197	+	0.909731i	$0.363713\pi$
$74$	0.355008	0.0412689
$75$	14.6968	1.69704
$76$	−1.00000	−0.114708
$77$	−17.9472	−2.04527
$78$	2.90730	0.329187
$79$	5.57821	0.627598	0.313799	−	0.949489i	$-0.398398\pi$
$79$	5.57821	0.627598	0.313799	+	0.949489i	$0.398398\pi$
$80$	4.43811	0.496196
$81$	1.00000	0.111111
$82$	−6.18349	−0.682852
$83$	3.36853	0.369745	0.184872	−	0.982763i	$-0.440813\pi$
$83$	3.36853	0.369745	0.184872	+	0.982763i	$0.440813\pi$
$84$	3.55047	0.387388
$85$	32.6049	3.53650
$86$	−8.74555	−0.943057
$87$	−9.18051	−0.984254
$88$	−5.05487	−0.538851
$89$	−11.0277	−1.16893	−0.584465	−	0.811419i	$-0.698695\pi$
$89$	−11.0277	−1.16893	−0.584465	+	0.811419i	$0.698695\pi$
$90$	4.43811	0.467818
$91$	10.3223	1.08207
$92$	−7.19632	−0.750268
$93$	4.24687	0.440379
$94$	−2.77732	−0.286459
$95$	−4.43811	−0.455341
$96$	1.00000	0.102062
$97$	4.68706	0.475899	0.237950	−	0.971278i	$-0.423525\pi$
$97$	4.68706	0.475899	0.237950	+	0.971278i	$0.423525\pi$
$98$	5.60581	0.566272
$99$	−5.05487	−0.508034
$100$	14.6968	1.46968
$101$	−6.69483	−0.666161	−0.333080	−	0.942898i	$-0.608088\pi$
$101$	−6.69483	−0.666161	−0.333080	+	0.942898i	$0.608088\pi$
$102$	7.34657	0.727418
$103$	7.55917	0.744827	0.372413	−	0.928067i	$-0.378530\pi$
$103$	7.55917	0.744827	0.372413	+	0.928067i	$0.378530\pi$
$104$	2.90730	0.285084
$105$	15.7574	1.53776
$106$	1.00000	0.0971286
$107$	3.59225	0.347276	0.173638	−	0.984810i	$-0.444448\pi$
$107$	3.59225	0.347276	0.173638	+	0.984810i	$0.444448\pi$
$108$	1.00000	0.0962250
$109$	2.07153	0.198417	0.0992083	−	0.995067i	$-0.468369\pi$
$109$	2.07153	0.198417	0.0992083	+	0.995067i	$0.468369\pi$
$110$	−22.4341	−2.13901
$111$	0.355008	0.0336959
$112$	3.55047	0.335487
$113$	−4.34282	−0.408538	−0.204269	−	0.978915i	$-0.565482\pi$
$113$	−4.34282	−0.408538	−0.204269	+	0.978915i	$0.565482\pi$
$114$	−1.00000	−0.0936586
$115$	−31.9381	−2.97824
$116$	−9.18051	−0.852389
$117$	2.90730	0.268780
$118$	−6.25953	−0.576236
$119$	26.0837	2.39109
$120$	4.43811	0.405142
$121$	14.5518	1.32289
$122$	5.17609	0.468621
$123$	−6.18349	−0.557546
$124$	4.24687	0.381380
$125$	43.0357	3.84923
$126$	3.55047	0.316301
$127$	−1.71521	−0.152200	−0.0761001	−	0.997100i	$-0.524247\pi$
$127$	−1.71521	−0.152200	−0.0761001	+	0.997100i	$0.524247\pi$
$128$	1.00000	0.0883883
$129$	−8.74555	−0.770003
$130$	12.9029	1.13166
$131$	−2.25176	−0.196737	−0.0983685	−	0.995150i	$-0.531362\pi$
$131$	−2.25176	−0.196737	−0.0983685	+	0.995150i	$0.531362\pi$
$132$	−5.05487	−0.439970
$133$	−3.55047	−0.307864
$134$	−11.4722	−0.991043
$135$	4.43811	0.381972
$136$	7.34657	0.629963
$137$	−10.1792	−0.869670	−0.434835	−	0.900510i	$-0.643193\pi$
$137$	−10.1792	−0.869670	−0.434835	+	0.900510i	$0.643193\pi$
$138$	−7.19632	−0.612591
$139$	−7.34551	−0.623038	−0.311519	−	0.950240i	$-0.600838\pi$
$139$	−7.34551	−0.623038	−0.311519	+	0.950240i	$0.600838\pi$
$140$	15.7574	1.33174
$141$	−2.77732	−0.233893
$142$	−13.9767	−1.17290
$143$	−14.6960	−1.22894
$144$	1.00000	0.0833333
$145$	−40.7441	−3.38362
$146$	7.09489	0.587178
$147$	5.60581	0.462359
$148$	0.355008	0.0291815
$149$	−19.5671	−1.60300	−0.801499	−	0.597996i	$-0.795964\pi$
$149$	−19.5671	−1.60300	−0.801499	+	0.597996i	$0.795964\pi$
$150$	14.6968	1.19999
$151$	−5.34007	−0.434569	−0.217284	−	0.976108i	$-0.569720\pi$
$151$	−5.34007	−0.434569	−0.217284	+	0.976108i	$0.569720\pi$
$152$	−1.00000	−0.0811107
$153$	7.34657	0.593935
$154$	−17.9472	−1.44622
$155$	18.8481	1.51391
$156$	2.90730	0.232770
$157$	13.7256	1.09542	0.547712	−	0.836667i	$-0.315499\pi$
$157$	13.7256	1.09542	0.547712	+	0.836667i	$0.315499\pi$
$158$	5.57821	0.443779
$159$	1.00000	0.0793052
$160$	4.43811	0.350864
$161$	−25.5503	−2.01364
$162$	1.00000	0.0785674
$163$	−0.415020	−0.0325069	−0.0162535	−	0.999868i	$-0.505174\pi$
$163$	−0.415020	−0.0325069	−0.0162535	+	0.999868i	$0.505174\pi$
$164$	−6.18349	−0.482849
$165$	−22.4341	−1.74649
$166$	3.36853	0.261449
$167$	18.1847	1.40717	0.703587	−	0.710609i	$-0.251580\pi$
$167$	18.1847	1.40717	0.703587	+	0.710609i	$0.251580\pi$
$168$	3.55047	0.273924
$169$	−4.54760	−0.349815
$170$	32.6049	2.50068
$171$	−1.00000	−0.0764719
$172$	−8.74555	−0.666842
$173$	22.8701	1.73879	0.869393	−	0.494122i	$-0.164510\pi$
$173$	22.8701	1.73879	0.869393	+	0.494122i	$0.164510\pi$
$174$	−9.18051	−0.695973
$175$	52.1806	3.94448
$176$	−5.05487	−0.381025
$177$	−6.25953	−0.470495
$178$	−11.0277	−0.826558
$179$	12.2452	0.915247	0.457623	−	0.889146i	$-0.348701\pi$
$179$	12.2452	0.915247	0.457623	+	0.889146i	$0.348701\pi$
$180$	4.43811	0.330797
$181$	1.55964	0.115927	0.0579635	−	0.998319i	$-0.481539\pi$
$181$	1.55964	0.115927	0.0579635	+	0.998319i	$0.481539\pi$
$182$	10.3223	0.765138
$183$	5.17609	0.382628
$184$	−7.19632	−0.530520
$185$	1.57557	0.115838
$186$	4.24687	0.311395
$187$	−37.1360	−2.71565
$188$	−2.77732	−0.202557
$189$	3.55047	0.258258
$190$	−4.43811	−0.321974
$191$	−6.41410	−0.464108	−0.232054	−	0.972703i	$-0.574545\pi$
$191$	−6.41410	−0.464108	−0.232054	+	0.972703i	$0.574545\pi$
$192$	1.00000	0.0721688
$193$	−1.57347	−0.113261	−0.0566305	−	0.998395i	$-0.518036\pi$
$193$	−1.57347	−0.113261	−0.0566305	+	0.998395i	$0.518036\pi$
$194$	4.68706	0.336511
$195$	12.9029	0.923998
$196$	5.60581	0.400415
$197$	−10.9229	−0.778224	−0.389112	−	0.921191i	$-0.627218\pi$
$197$	−10.9229	−0.778224	−0.389112	+	0.921191i	$0.627218\pi$
$198$	−5.05487	−0.359234
$199$	4.10828	0.291228	0.145614	−	0.989341i	$-0.453484\pi$
$199$	4.10828	0.291228	0.145614	+	0.989341i	$0.453484\pi$
$200$	14.6968	1.03922
$201$	−11.4722	−0.809183
$202$	−6.69483	−0.471047
$203$	−32.5951	−2.28773
$204$	7.34657	0.514362
$205$	−27.4430	−1.91670
$206$	7.55917	0.526672
$207$	−7.19632	−0.500179
$208$	2.90730	0.201585
$209$	5.05487	0.349653
$210$	15.7574	1.08736
$211$	−20.6173	−1.41936	−0.709678	−	0.704527i	$-0.751159\pi$
$211$	−20.6173	−1.41936	−0.709678	+	0.704527i	$0.751159\pi$
$212$	1.00000	0.0686803
$213$	−13.9767	−0.957668
$214$	3.59225	0.245561
$215$	−38.8137	−2.64708
$216$	1.00000	0.0680414
$217$	15.0784	1.02359
$218$	2.07153	0.140302
$219$	7.09489	0.479428
$220$	−22.4341	−1.51251
$221$	21.3587	1.43674
$222$	0.355008	0.0238266
$223$	−17.6221	−1.18007	−0.590033	−	0.807379i	$-0.700885\pi$
$223$	−17.6221	−1.18007	−0.590033	+	0.807379i	$0.700885\pi$
$224$	3.55047	0.237225
$225$	14.6968	0.979789
$226$	−4.34282	−0.288880
$227$	3.51574	0.233348	0.116674	−	0.993170i	$-0.462777\pi$
$227$	3.51574	0.233348	0.116674	+	0.993170i	$0.462777\pi$
$228$	−1.00000	−0.0662266
$229$	15.9273	1.05251	0.526253	−	0.850328i	$-0.323597\pi$
$229$	15.9273	1.05251	0.526253	+	0.850328i	$0.323597\pi$
$230$	−31.9381	−2.10593
$231$	−17.9472	−1.18084
$232$	−9.18051	−0.602730
$233$	28.3834	1.85946	0.929728	−	0.368247i	$-0.120042\pi$
$233$	28.3834	1.85946	0.929728	+	0.368247i	$0.120042\pi$
$234$	2.90730	0.190056
$235$	−12.3261	−0.804065
$236$	−6.25953	−0.407461
$237$	5.57821	0.362344
$238$	26.0837	1.69076
$239$	−14.5338	−0.940111	−0.470056	−	0.882637i	$-0.655766\pi$
$239$	−14.5338	−0.940111	−0.470056	+	0.882637i	$0.655766\pi$
$240$	4.43811	0.286479
$241$	−23.3650	−1.50508	−0.752538	−	0.658549i	$-0.771170\pi$
$241$	−23.3650	−1.50508	−0.752538	+	0.658549i	$0.771170\pi$
$242$	14.5518	0.935422
$243$	1.00000	0.0641500
$244$	5.17609	0.331365
$245$	24.8792	1.58947
$246$	−6.18349	−0.394245
$247$	−2.90730	−0.184987
$248$	4.24687	0.269676
$249$	3.36853	0.213472
$250$	43.0357	2.72181
$251$	26.2871	1.65923	0.829614	−	0.558338i	$-0.188561\pi$
$251$	26.2871	1.65923	0.829614	+	0.558338i	$0.188561\pi$
$252$	3.55047	0.223658
$253$	36.3765	2.28697
$254$	−1.71521	−0.107622
$255$	32.6049	2.04180
$256$	1.00000	0.0625000
$257$	9.47081	0.590773	0.295386	−	0.955378i	$-0.404552\pi$
$257$	9.47081	0.590773	0.295386	+	0.955378i	$0.404552\pi$
$258$	−8.74555	−0.544474
$259$	1.26045	0.0783203
$260$	12.9029	0.800206
$261$	−9.18051	−0.568260
$262$	−2.25176	−0.139114
$263$	4.66372	0.287577	0.143789	−	0.989608i	$-0.454071\pi$
$263$	4.66372	0.287577	0.143789	+	0.989608i	$0.454071\pi$
$264$	−5.05487	−0.311106
$265$	4.43811	0.272631
$266$	−3.55047	−0.217693
$267$	−11.0277	−0.674882
$268$	−11.4722	−0.700773
$269$	8.03131	0.489678	0.244839	−	0.969564i	$-0.421265\pi$
$269$	8.03131	0.489678	0.244839	+	0.969564i	$0.421265\pi$
$270$	4.43811	0.270095
$271$	28.2062	1.71340	0.856702	−	0.515812i	$-0.172510\pi$
$271$	28.2062	1.71340	0.856702	+	0.515812i	$0.172510\pi$
$272$	7.34657	0.445451
$273$	10.3223	0.624732
$274$	−10.1792	−0.614950
$275$	−74.2907	−4.47990
$276$	−7.19632	−0.433168
$277$	−1.53718	−0.0923601	−0.0461801	−	0.998933i	$-0.514705\pi$
$277$	−1.53718	−0.0923601	−0.0461801	+	0.998933i	$0.514705\pi$
$278$	−7.34551	−0.440554
$279$	4.24687	0.254253
$280$	15.7574	0.941683
$281$	−14.7283	−0.878615	−0.439307	−	0.898337i	$-0.644776\pi$
$281$	−14.7283	−0.878615	−0.439307	+	0.898337i	$0.644776\pi$
$282$	−2.77732	−0.165387
$283$	3.53385	0.210065	0.105033	−	0.994469i	$-0.466505\pi$
$283$	3.53385	0.210065	0.105033	+	0.994469i	$0.466505\pi$
$284$	−13.9767	−0.829365
$285$	−4.43811	−0.262891
$286$	−14.6960	−0.868995
$287$	−21.9543	−1.29592
$288$	1.00000	0.0589256
$289$	36.9720	2.17483
$290$	−40.7441	−2.39258
$291$	4.68706	0.274760
$292$	7.09489	0.415197
$293$	−19.6125	−1.14577	−0.572887	−	0.819634i	$-0.694177\pi$
$293$	−19.6125	−1.14577	−0.572887	+	0.819634i	$0.694177\pi$
$294$	5.60581	0.326937
$295$	−27.7805	−1.61744
$296$	0.355008	0.0206344
$297$	−5.05487	−0.293314
$298$	−19.5671	−1.13349
$299$	−20.9219	−1.20994
$300$	14.6968	0.848522
$301$	−31.0508	−1.78974
$302$	−5.34007	−0.307286
$303$	−6.69483	−0.384608
$304$	−1.00000	−0.0573539
$305$	22.9721	1.31538
$306$	7.34657	0.419975
$307$	−33.4526	−1.90924	−0.954622	−	0.297821i	$-0.903740\pi$
$307$	−33.4526	−1.90924	−0.954622	+	0.297821i	$0.903740\pi$
$308$	−17.9472	−1.02263
$309$	7.55917	0.430026
$310$	18.8481	1.07050
$311$	−18.0889	−1.02573	−0.512864	−	0.858470i	$-0.671416\pi$
$311$	−18.0889	−1.02573	−0.512864	+	0.858470i	$0.671416\pi$
$312$	2.90730	0.164594
$313$	19.8568	1.12238	0.561188	−	0.827689i	$-0.310345\pi$
$313$	19.8568	1.12238	0.561188	+	0.827689i	$0.310345\pi$
$314$	13.7256	0.774582
$315$	15.7574	0.887827
$316$	5.57821	0.313799
$317$	3.41721	0.191930	0.0959649	−	0.995385i	$-0.469406\pi$
$317$	3.41721	0.191930	0.0959649	+	0.995385i	$0.469406\pi$
$318$	1.00000	0.0560772
$319$	46.4063	2.59826
$320$	4.43811	0.248098
$321$	3.59225	0.200500
$322$	−25.5503	−1.42386
$323$	−7.34657	−0.408774
$324$	1.00000	0.0555556
$325$	42.7281	2.37013
$326$	−0.415020	−0.0229859
$327$	2.07153	0.114556
$328$	−6.18349	−0.341426
$329$	−9.86079	−0.543643
$330$	−22.4341	−1.23496
$331$	17.3483	0.953550	0.476775	−	0.879025i	$-0.341806\pi$
$331$	17.3483	0.953550	0.476775	+	0.879025i	$0.341806\pi$
$332$	3.36853	0.184872
$333$	0.355008	0.0194543
$334$	18.1847	0.995023
$335$	−50.9147	−2.78177
$336$	3.55047	0.193694
$337$	−8.93743	−0.486853	−0.243427	−	0.969919i	$-0.578271\pi$
$337$	−8.93743	−0.486853	−0.243427	+	0.969919i	$0.578271\pi$
$338$	−4.54760	−0.247357
$339$	−4.34282	−0.235870
$340$	32.6049	1.76825
$341$	−21.4674	−1.16252
$342$	−1.00000	−0.0540738
$343$	−4.95003	−0.267277
$344$	−8.74555	−0.471529
$345$	−31.9381	−1.71949
$346$	22.8701	1.22951
$347$	7.24227	0.388786	0.194393	−	0.980924i	$-0.437726\pi$
$347$	7.24227	0.388786	0.194393	+	0.980924i	$0.437726\pi$
$348$	−9.18051	−0.492127
$349$	−28.1717	−1.50800	−0.753998	−	0.656876i	$-0.771877\pi$
$349$	−28.1717	−1.50800	−0.753998	+	0.656876i	$0.771877\pi$
$350$	52.1806	2.78917
$351$	2.90730	0.155180
$352$	−5.05487	−0.269426
$353$	25.0532	1.33345	0.666725	−	0.745304i	$-0.267696\pi$
$353$	25.0532	1.33345	0.666725	+	0.745304i	$0.267696\pi$
$354$	−6.25953	−0.332690
$355$	−62.0302	−3.29222
$356$	−11.0277	−0.584465
$357$	26.0837	1.38050
$358$	12.2452	0.647177
$359$	11.9198	0.629102	0.314551	−	0.949241i	$-0.398146\pi$
$359$	11.9198	0.629102	0.314551	+	0.949241i	$0.398146\pi$
$360$	4.43811	0.233909
$361$	1.00000	0.0526316
$362$	1.55964	0.0819728
$363$	14.5518	0.763769
$364$	10.3223	0.541034
$365$	31.4879	1.64815
$366$	5.17609	0.270559
$367$	18.1504	0.947445	0.473722	−	0.880674i	$-0.342910\pi$
$367$	18.1504	0.947445	0.473722	+	0.880674i	$0.342910\pi$
$368$	−7.19632	−0.375134
$369$	−6.18349	−0.321900
$370$	1.57557	0.0819098
$371$	3.55047	0.184331
$372$	4.24687	0.220190
$373$	−6.84048	−0.354187	−0.177093	−	0.984194i	$-0.556669\pi$
$373$	−6.84048	−0.354187	−0.177093	+	0.984194i	$0.556669\pi$
$374$	−37.1360	−1.92026
$375$	43.0357	2.22235
$376$	−2.77732	−0.143230
$377$	−26.6905	−1.37463
$378$	3.55047	0.182616
$379$	12.3073	0.632185	0.316092	−	0.948728i	$-0.397629\pi$
$379$	12.3073	0.632185	0.316092	+	0.948728i	$0.397629\pi$
$380$	−4.43811	−0.227670
$381$	−1.71521	−0.0878729
$382$	−6.41410	−0.328174
$383$	24.8482	1.26968	0.634841	−	0.772643i	$-0.281066\pi$
$383$	24.8482	1.26968	0.634841	+	0.772643i	$0.281066\pi$
$384$	1.00000	0.0510310
$385$	−79.6515	−4.05942
$386$	−1.57347	−0.0800877
$387$	−8.74555	−0.444561
$388$	4.68706	0.237950
$389$	14.3279	0.726452	0.363226	−	0.931701i	$-0.381675\pi$
$389$	14.3279	0.726452	0.363226	+	0.931701i	$0.381675\pi$
$390$	12.9029	0.653365
$391$	−52.8682	−2.67366
$392$	5.60581	0.283136
$393$	−2.25176	−0.113586
$394$	−10.9229	−0.550287
$395$	24.7567	1.24565
$396$	−5.05487	−0.254017
$397$	−26.4749	−1.32874	−0.664370	−	0.747404i	$-0.731300\pi$
$397$	−26.4749	−1.32874	−0.664370	+	0.747404i	$0.731300\pi$
$398$	4.10828	0.205930
$399$	−3.55047	−0.177746
$400$	14.6968	0.734842
$401$	−4.59991	−0.229708	−0.114854	−	0.993382i	$-0.536640\pi$
$401$	−4.59991	−0.229708	−0.114854	+	0.993382i	$0.536640\pi$
$402$	−11.4722	−0.572179
$403$	12.3469	0.615044
$404$	−6.69483	−0.333080
$405$	4.43811	0.220532
$406$	−32.5951	−1.61767
$407$	−1.79452	−0.0889512
$408$	7.34657	0.363709
$409$	0.757877	0.0374746	0.0187373	−	0.999824i	$-0.494035\pi$
$409$	0.757877	0.0374746	0.0187373	+	0.999824i	$0.494035\pi$
$410$	−27.4430	−1.35531
$411$	−10.1792	−0.502104
$412$	7.55917	0.372413
$413$	−22.2242	−1.09358
$414$	−7.19632	−0.353680
$415$	14.9499	0.733863
$416$	2.90730	0.142542
$417$	−7.34551	−0.359711
$418$	5.05487	0.247242
$419$	−20.4144	−0.997307	−0.498654	−	0.866801i	$-0.666172\pi$
$419$	−20.4144	−0.997307	−0.498654	+	0.866801i	$0.666172\pi$
$420$	15.7574	0.768881
$421$	27.0157	1.31666	0.658332	−	0.752727i	$-0.271262\pi$
$421$	27.0157	1.31666	0.658332	+	0.752727i	$0.271262\pi$
$422$	−20.6173	−1.00364
$423$	−2.77732	−0.135038
$424$	1.00000	0.0485643
$425$	107.971	5.23738
$426$	−13.9767	−0.677173
$427$	18.3775	0.889351
$428$	3.59225	0.173638
$429$	−14.6960	−0.709532
$430$	−38.8137	−1.87177
$431$	−6.32139	−0.304490	−0.152245	−	0.988343i	$-0.548650\pi$
$431$	−6.32139	−0.304490	−0.152245	+	0.988343i	$0.548650\pi$
$432$	1.00000	0.0481125
$433$	−4.42744	−0.212769	−0.106385	−	0.994325i	$-0.533927\pi$
$433$	−4.42744	−0.212769	−0.106385	+	0.994325i	$0.533927\pi$
$434$	15.0784	0.723784
$435$	−40.7441	−1.95353
$436$	2.07153	0.0992083
$437$	7.19632	0.344247
$438$	7.09489	0.339007
$439$	34.1010	1.62755	0.813775	−	0.581180i	$-0.197409\pi$
$439$	34.1010	1.62755	0.813775	+	0.581180i	$0.197409\pi$
$440$	−22.4341	−1.06950
$441$	5.60581	0.266943
$442$	21.3587	1.01593
$443$	10.2239	0.485751	0.242876	−	0.970057i	$-0.421909\pi$
$443$	10.2239	0.485751	0.242876	+	0.970057i	$0.421909\pi$
$444$	0.355008	0.0168480
$445$	−48.9420	−2.32007
$446$	−17.6221	−0.834432
$447$	−19.5671	−0.925491
$448$	3.55047	0.167744
$449$	28.1595	1.32893	0.664465	−	0.747319i	$-0.268659\pi$
$449$	28.1595	1.32893	0.664465	+	0.747319i	$0.268659\pi$
$450$	14.6968	0.692816
$451$	31.2568	1.47182
$452$	−4.34282	−0.204269
$453$	−5.34007	−0.250898
$454$	3.51574	0.165002
$455$	45.8114	2.14767
$456$	−1.00000	−0.0468293
$457$	−3.03542	−0.141991	−0.0709954	−	0.997477i	$-0.522618\pi$
$457$	−3.03542	−0.141991	−0.0709954	+	0.997477i	$0.522618\pi$
$458$	15.9273	0.744234
$459$	7.34657	0.342908
$460$	−31.9381	−1.48912
$461$	−20.8103	−0.969230	−0.484615	−	0.874727i	$-0.661040\pi$
$461$	−20.8103	−0.969230	−0.484615	+	0.874727i	$0.661040\pi$
$462$	−17.9472	−0.834977
$463$	12.1958	0.566786	0.283393	−	0.959004i	$-0.408540\pi$
$463$	12.1958	0.566786	0.283393	+	0.959004i	$0.408540\pi$
$464$	−9.18051	−0.426195
$465$	18.8481	0.874058
$466$	28.3834	1.31483
$467$	−6.94880	−0.321552	−0.160776	−	0.986991i	$-0.551400\pi$
$467$	−6.94880	−0.321552	−0.160776	+	0.986991i	$0.551400\pi$
$468$	2.90730	0.134390
$469$	−40.7315	−1.88081
$470$	−12.3261	−0.568560
$471$	13.7256	0.632443
$472$	−6.25953	−0.288118
$473$	44.2077	2.03267
$474$	5.57821	0.256216
$475$	−14.6968	−0.674337
$476$	26.0837	1.19555
$477$	1.00000	0.0457869
$478$	−14.5338	−0.664759
$479$	25.2918	1.15561	0.577805	−	0.816175i	$-0.303909\pi$
$479$	25.2918	1.15561	0.577805	+	0.816175i	$0.303909\pi$
$480$	4.43811	0.202571
$481$	1.03212	0.0470605
$482$	−23.3650	−1.06425
$483$	−25.5503	−1.16258
$484$	14.5518	0.661443
$485$	20.8017	0.944557
$486$	1.00000	0.0453609
$487$	−42.9490	−1.94621	−0.973103	−	0.230369i	$-0.926007\pi$
$487$	−42.9490	−1.94621	−0.973103	+	0.230369i	$0.926007\pi$
$488$	5.17609	0.234311
$489$	−0.415020	−0.0187679
$490$	24.8792	1.12393
$491$	44.1739	1.99354	0.996771	−	0.0802948i	$-0.0255862\pi$
$491$	44.1739	1.99354	0.996771	+	0.0802948i	$0.0255862\pi$
$492$	−6.18349	−0.278773
$493$	−67.4452	−3.03758
$494$	−2.90730	−0.130806
$495$	−22.4341	−1.00834
$496$	4.24687	0.190690
$497$	−49.6238	−2.22593
$498$	3.36853	0.150948
$499$	−4.61034	−0.206387	−0.103194	−	0.994661i	$-0.532906\pi$
$499$	−4.61034	−0.206387	−0.103194	+	0.994661i	$0.532906\pi$
$500$	43.0357	1.92461
$501$	18.1847	0.812433
$502$	26.2871	1.17325
$503$	13.3293	0.594324	0.297162	−	0.954827i	$-0.403960\pi$
$503$	13.3293	0.594324	0.297162	+	0.954827i	$0.403960\pi$
$504$	3.55047	0.158150
$505$	−29.7124	−1.32218
$506$	36.3765	1.61713
$507$	−4.54760	−0.201966
$508$	−1.71521	−0.0761001
$509$	2.37105	0.105095	0.0525474	−	0.998618i	$-0.483266\pi$
$509$	2.37105	0.105095	0.0525474	+	0.998618i	$0.483266\pi$
$510$	32.6049	1.44377
$511$	25.1902	1.11435
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	9.47081	0.417740
$515$	33.5484	1.47832
$516$	−8.74555	−0.385002
$517$	14.0390	0.617436
$518$	1.26045	0.0553808
$519$	22.8701	1.00389
$520$	12.9029	0.565831
$521$	−22.7464	−0.996537	−0.498268	−	0.867023i	$-0.666031\pi$
$521$	−22.7464	−0.996537	−0.498268	+	0.867023i	$0.666031\pi$
$522$	−9.18051	−0.401820
$523$	19.6803	0.860560	0.430280	−	0.902696i	$-0.358415\pi$
$523$	19.6803	0.860560	0.430280	+	0.902696i	$0.358415\pi$
$524$	−2.25176	−0.0983685
$525$	52.1806	2.27735
$526$	4.66372	0.203348
$527$	31.1999	1.35909
$528$	−5.05487	−0.219985
$529$	28.7870	1.25161
$530$	4.43811	0.192779
$531$	−6.25953	−0.271640
$532$	−3.55047	−0.153932
$533$	−17.9773	−0.778682
$534$	−11.0277	−0.477213
$535$	15.9428	0.689267
$536$	−11.4722	−0.495522
$537$	12.2452	0.528418
$538$	8.03131	0.346254
$539$	−28.3367	−1.22055
$540$	4.43811	0.190986
$541$	9.74879	0.419133	0.209567	−	0.977794i	$-0.432795\pi$
$541$	9.74879	0.419133	0.209567	+	0.977794i	$0.432795\pi$
$542$	28.2062	1.21156
$543$	1.55964	0.0669305
$544$	7.34657	0.314981
$545$	9.19368	0.393814
$546$	10.3223	0.441753
$547$	34.1956	1.46210	0.731050	−	0.682324i	$-0.239031\pi$
$547$	34.1956	1.46210	0.731050	+	0.682324i	$0.239031\pi$
$548$	−10.1792	−0.434835
$549$	5.17609	0.220910
$550$	−74.2907	−3.16776
$551$	9.18051	0.391103
$552$	−7.19632	−0.306296
$553$	19.8053	0.842205
$554$	−1.53718	−0.0653085
$555$	1.57557	0.0668791
$556$	−7.34551	−0.311519
$557$	9.61675	0.407475	0.203737	−	0.979026i	$-0.434691\pi$
$557$	9.61675	0.407475	0.203737	+	0.979026i	$0.434691\pi$
$558$	4.24687	0.179784
$559$	−25.4260	−1.07540
$560$	15.7574	0.665870
$561$	−37.1360	−1.56788
$562$	−14.7283	−0.621275
$563$	−8.42488	−0.355066	−0.177533	−	0.984115i	$-0.556812\pi$
$563$	−8.42488	−0.355066	−0.177533	+	0.984115i	$0.556812\pi$
$564$	−2.77732	−0.116946
$565$	−19.2739	−0.810860
$566$	3.53385	0.148539
$567$	3.55047	0.149106
$568$	−13.9767	−0.586449
$569$	34.8404	1.46059	0.730293	−	0.683134i	$-0.239384\pi$
$569$	34.8404	1.46059	0.730293	+	0.683134i	$0.239384\pi$
$570$	−4.43811	−0.185892
$571$	28.0866	1.17539	0.587694	−	0.809083i	$-0.300036\pi$
$571$	28.0866	1.17539	0.587694	+	0.809083i	$0.300036\pi$
$572$	−14.6960	−0.614472
$573$	−6.41410	−0.267953
$574$	−21.9543	−0.916353
$575$	−105.763	−4.41063
$576$	1.00000	0.0416667
$577$	7.09135	0.295217	0.147608	−	0.989046i	$-0.452843\pi$
$577$	7.09135	0.295217	0.147608	+	0.989046i	$0.452843\pi$
$578$	36.9720	1.53783
$579$	−1.57347	−0.0653913
$580$	−40.7441	−1.69181
$581$	11.9599	0.496179
$582$	4.68706	0.194285
$583$	−5.05487	−0.209351
$584$	7.09489	0.293589
$585$	12.9029	0.533470
$586$	−19.6125	−0.810185
$587$	−10.6573	−0.439875	−0.219937	−	0.975514i	$-0.570585\pi$
$587$	−10.6573	−0.439875	−0.219937	+	0.975514i	$0.570585\pi$
$588$	5.60581	0.231180
$589$	−4.24687	−0.174989
$590$	−27.7805	−1.14370
$591$	−10.9229	−0.449308
$592$	0.355008	0.0145908
$593$	42.2655	1.73564	0.867819	−	0.496881i	$-0.165521\pi$
$593$	42.2655	1.73564	0.867819	+	0.496881i	$0.165521\pi$
$594$	−5.05487	−0.207404
$595$	115.763	4.74580
$596$	−19.5671	−0.801499
$597$	4.10828	0.168141
$598$	−20.9219	−0.855559
$599$	35.3647	1.44496	0.722482	−	0.691390i	$-0.243001\pi$
$599$	35.3647	1.44496	0.722482	+	0.691390i	$0.243001\pi$
$600$	14.6968	0.599996
$601$	28.0203	1.14297	0.571486	−	0.820612i	$-0.306367\pi$
$601$	28.0203	1.14297	0.571486	+	0.820612i	$0.306367\pi$
$602$	−31.0508	−1.26554
$603$	−11.4722	−0.467182
$604$	−5.34007	−0.217284
$605$	64.5823	2.62564
$606$	−6.69483	−0.271959
$607$	−13.9384	−0.565743	−0.282872	−	0.959158i	$-0.591287\pi$
$607$	−13.9384	−0.565743	−0.282872	+	0.959158i	$0.591287\pi$
$608$	−1.00000	−0.0405554
$609$	−32.5951	−1.32082
$610$	22.9721	0.930112
$611$	−8.07452	−0.326660
$612$	7.34657	0.296967
$613$	40.9619	1.65444	0.827219	−	0.561880i	$-0.189922\pi$
$613$	40.9619	1.65444	0.827219	+	0.561880i	$0.189922\pi$
$614$	−33.4526	−1.35004
$615$	−27.4430	−1.10661
$616$	−17.9472	−0.723112
$617$	−31.9033	−1.28438	−0.642188	−	0.766547i	$-0.721973\pi$
$617$	−31.9033	−1.28438	−0.642188	+	0.766547i	$0.721973\pi$
$618$	7.55917	0.304074
$619$	18.7230	0.752540	0.376270	−	0.926510i	$-0.377206\pi$
$619$	18.7230	0.752540	0.376270	+	0.926510i	$0.377206\pi$
$620$	18.8481	0.756957
$621$	−7.19632	−0.288778
$622$	−18.0889	−0.725299
$623$	−39.1533	−1.56864
$624$	2.90730	0.116385
$625$	117.513	4.70052
$626$	19.8568	0.793639
$627$	5.05487	0.201872
$628$	13.7256	0.547712
$629$	2.60809	0.103991
$630$	15.7574	0.627788
$631$	29.5960	1.17820	0.589100	−	0.808060i	$-0.299482\pi$
$631$	29.5960	1.17820	0.589100	+	0.808060i	$0.299482\pi$
$632$	5.57821	0.221889
$633$	−20.6173	−0.819465
$634$	3.41721	0.135715
$635$	−7.61229	−0.302085
$636$	1.00000	0.0396526
$637$	16.2978	0.645741
$638$	46.4063	1.83724
$639$	−13.9767	−0.552910
$640$	4.43811	0.175432
$641$	24.9031	0.983613	0.491807	−	0.870704i	$-0.336337\pi$
$641$	24.9031	0.983613	0.491807	+	0.870704i	$0.336337\pi$
$642$	3.59225	0.141775
$643$	−17.9686	−0.708614	−0.354307	−	0.935129i	$-0.615283\pi$
$643$	−17.9686	−0.708614	−0.354307	+	0.935129i	$0.615283\pi$
$644$	−25.5503	−1.00682
$645$	−38.8137	−1.52829
$646$	−7.34657	−0.289047
$647$	33.2028	1.30534	0.652668	−	0.757644i	$-0.273649\pi$
$647$	33.2028	1.30534	0.652668	+	0.757644i	$0.273649\pi$
$648$	1.00000	0.0392837
$649$	31.6411	1.24202
$650$	42.7281	1.67594
$651$	15.0784	0.590967
$652$	−0.415020	−0.0162535
$653$	−23.9566	−0.937493	−0.468747	−	0.883333i	$-0.655294\pi$
$653$	−23.9566	−0.937493	−0.468747	+	0.883333i	$0.655294\pi$
$654$	2.07153	0.0810032
$655$	−9.99356	−0.390481
$656$	−6.18349	−0.241425
$657$	7.09489	0.276798
$658$	−9.86079	−0.384414
$659$	24.1310	0.940009	0.470004	−	0.882664i	$-0.344252\pi$
$659$	24.1310	0.940009	0.470004	+	0.882664i	$0.344252\pi$
$660$	−22.4341	−0.873246
$661$	−15.9982	−0.622256	−0.311128	−	0.950368i	$-0.600707\pi$
$661$	−15.9982	−0.622256	−0.311128	+	0.950368i	$0.600707\pi$
$662$	17.3483	0.674262
$663$	21.3587	0.829502
$664$	3.36853	0.130725
$665$	−15.7574	−0.611044
$666$	0.355008	0.0137563
$667$	66.0659	2.55808
$668$	18.1847	0.703587
$669$	−17.6221	−0.681311
$670$	−50.9147	−1.96701
$671$	−26.1645	−1.01007
$672$	3.55047	0.136962
$673$	−0.958934	−0.0369642	−0.0184821	−	0.999829i	$-0.505883\pi$
$673$	−0.958934	−0.0369642	−0.0184821	+	0.999829i	$0.505883\pi$
$674$	−8.93743	−0.344257
$675$	14.6968	0.565682
$676$	−4.54760	−0.174908
$677$	−23.6848	−0.910280	−0.455140	−	0.890420i	$-0.650411\pi$
$677$	−23.6848	−0.910280	−0.455140	+	0.890420i	$0.650411\pi$
$678$	−4.34282	−0.166785
$679$	16.6413	0.638633
$680$	32.6049	1.25034
$681$	3.51574	0.134724
$682$	−21.4674	−0.822028
$683$	3.36066	0.128592	0.0642960	−	0.997931i	$-0.479520\pi$
$683$	3.36066	0.128592	0.0642960	+	0.997931i	$0.479520\pi$
$684$	−1.00000	−0.0382360
$685$	−45.1766	−1.72611
$686$	−4.95003	−0.188993
$687$	15.9273	0.607664
$688$	−8.74555	−0.333421
$689$	2.90730	0.110759
$690$	−31.9381	−1.21586
$691$	−39.3558	−1.49717	−0.748583	−	0.663041i	$-0.769265\pi$
$691$	−39.3558	−1.49717	−0.748583	+	0.663041i	$0.769265\pi$
$692$	22.8701	0.869393
$693$	−17.9472	−0.681756
$694$	7.24227	0.274913
$695$	−32.6002	−1.23660
$696$	−9.18051	−0.347986
$697$	−45.4274	−1.72069
$698$	−28.1717	−1.06631
$699$	28.3834	1.07356
$700$	52.1806	1.97224
$701$	−27.2797	−1.03034	−0.515169	−	0.857088i	$-0.672271\pi$
$701$	−27.2797	−1.03034	−0.515169	+	0.857088i	$0.672271\pi$
$702$	2.90730	0.109729
$703$	−0.355008	−0.0133894
$704$	−5.05487	−0.190513
$705$	−12.3261	−0.464227
$706$	25.0532	0.942891
$707$	−23.7698	−0.893954
$708$	−6.25953	−0.235247
$709$	23.7985	0.893773	0.446886	−	0.894591i	$-0.352533\pi$
$709$	23.7985	0.893773	0.446886	+	0.894591i	$0.352533\pi$
$710$	−62.0302	−2.32795
$711$	5.57821	0.209199
$712$	−11.0277	−0.413279
$713$	−30.5618	−1.14455
$714$	26.0837	0.976159
$715$	−65.2227	−2.43919
$716$	12.2452	0.457623
$717$	−14.5338	−0.542773
$718$	11.9198	0.444842
$719$	41.5686	1.55025	0.775123	−	0.631811i	$-0.217688\pi$
$719$	41.5686	1.55025	0.775123	+	0.631811i	$0.217688\pi$
$720$	4.43811	0.165399
$721$	26.8386	0.999520
$722$	1.00000	0.0372161
$723$	−23.3650	−0.868956
$724$	1.55964	0.0579635
$725$	−134.925	−5.01097
$726$	14.5518	0.540066
$727$	−14.6454	−0.543168	−0.271584	−	0.962415i	$-0.587547\pi$
$727$	−14.6454	−0.543168	−0.271584	+	0.962415i	$0.587547\pi$
$728$	10.3223	0.382569
$729$	1.00000	0.0370370
$730$	31.4879	1.16542
$731$	−64.2498	−2.37636
$732$	5.17609	0.191314
$733$	−4.93892	−0.182423	−0.0912115	−	0.995832i	$-0.529074\pi$
$733$	−4.93892	−0.182423	−0.0912115	+	0.995832i	$0.529074\pi$
$734$	18.1504	0.669945
$735$	24.8792	0.917683
$736$	−7.19632	−0.265260
$737$	57.9903	2.13610
$738$	−6.18349	−0.227617
$739$	20.8218	0.765944	0.382972	−	0.923760i	$-0.374901\pi$
$739$	20.8218	0.765944	0.382972	+	0.923760i	$0.374901\pi$
$740$	1.57557	0.0579190
$741$	−2.90730	−0.106802
$742$	3.55047	0.130342
$743$	−34.7964	−1.27656	−0.638279	−	0.769805i	$-0.720353\pi$
$743$	−34.7964	−1.27656	−0.638279	+	0.769805i	$0.720353\pi$
$744$	4.24687	0.155698
$745$	−86.8409	−3.18160
$746$	−6.84048	−0.250448
$747$	3.36853	0.123248
$748$	−37.1360	−1.35783
$749$	12.7541	0.466026
$750$	43.0357	1.57144
$751$	−12.1006	−0.441556	−0.220778	−	0.975324i	$-0.570860\pi$
$751$	−12.1006	−0.441556	−0.220778	+	0.975324i	$0.570860\pi$
$752$	−2.77732	−0.101279
$753$	26.2871	0.957955
$754$	−26.6905	−0.972011
$755$	−23.6998	−0.862525
$756$	3.55047	0.129129
$757$	−42.5534	−1.54663	−0.773315	−	0.634022i	$-0.781403\pi$
$757$	−42.5534	−1.54663	−0.773315	+	0.634022i	$0.781403\pi$
$758$	12.3073	0.447022
$759$	36.3765	1.32038
$760$	−4.43811	−0.160987
$761$	−9.15688	−0.331937	−0.165968	−	0.986131i	$-0.553075\pi$
$761$	−9.15688	−0.331937	−0.165968	+	0.986131i	$0.553075\pi$
$762$	−1.71521	−0.0621355
$763$	7.35490	0.266265
$764$	−6.41410	−0.232054
$765$	32.6049	1.17883
$766$	24.8482	0.897800
$767$	−18.1983	−0.657104
$768$	1.00000	0.0360844
$769$	−37.8907	−1.36637	−0.683187	−	0.730244i	$-0.739407\pi$
$769$	−37.8907	−1.36637	−0.683187	+	0.730244i	$0.739407\pi$
$770$	−79.6515	−2.87044
$771$	9.47081	0.341083
$772$	−1.57347	−0.0566305
$773$	−21.1732	−0.761546	−0.380773	−	0.924669i	$-0.624342\pi$
$773$	−21.1732	−0.761546	−0.380773	+	0.924669i	$0.624342\pi$
$774$	−8.74555	−0.314352
$775$	62.4155	2.24203
$776$	4.68706	0.168256
$777$	1.26045	0.0452182
$778$	14.3279	0.513679
$779$	6.18349	0.221546
$780$	12.9029	0.461999
$781$	70.6505	2.52807
$782$	−52.8682	−1.89056
$783$	−9.18051	−0.328085
$784$	5.60581	0.200207
$785$	60.9158	2.17418
$786$	−2.25176	−0.0803176
$787$	−25.7934	−0.919435	−0.459718	−	0.888065i	$-0.652049\pi$
$787$	−25.7934	−0.919435	−0.459718	+	0.888065i	$0.652049\pi$
$788$	−10.9229	−0.389112
$789$	4.66372	0.166033
$790$	24.7567	0.880805
$791$	−15.4190	−0.548238
$792$	−5.05487	−0.179617
$793$	15.0484	0.534386
$794$	−26.4749	−0.939561
$795$	4.43811	0.157404
$796$	4.10828	0.145614
$797$	−15.5296	−0.550086	−0.275043	−	0.961432i	$-0.588692\pi$
$797$	−15.5296	−0.550086	−0.275043	+	0.961432i	$0.588692\pi$
$798$	−3.55047	−0.125685
$799$	−20.4038	−0.721834
$800$	14.6968	0.519612
$801$	−11.0277	−0.389643
$802$	−4.59991	−0.162428
$803$	−35.8638	−1.26561
$804$	−11.4722	−0.404592
$805$	−113.395	−3.99665
$806$	12.3469	0.434902
$807$	8.03131	0.282716
$808$	−6.69483	−0.235523
$809$	28.5814	1.00487	0.502435	−	0.864615i	$-0.332438\pi$
$809$	28.5814	1.00487	0.502435	+	0.864615i	$0.332438\pi$
$810$	4.43811	0.155939
$811$	41.8303	1.46886	0.734430	−	0.678685i	$-0.237450\pi$
$811$	41.8303	1.46886	0.734430	+	0.678685i	$0.237450\pi$
$812$	−32.5951	−1.14386
$813$	28.2062	0.989234
$814$	−1.79452	−0.0628980
$815$	−1.84191	−0.0645192
$816$	7.34657	0.257181
$817$	8.74555	0.305968
$818$	0.757877	0.0264985
$819$	10.3223	0.360689
$820$	−27.4430	−0.958352
$821$	−56.7432	−1.98035	−0.990176	−	0.139827i	$-0.955345\pi$
$821$	−56.7432	−1.98035	−0.990176	+	0.139827i	$0.955345\pi$
$822$	−10.1792	−0.355041
$823$	7.05067	0.245771	0.122885	−	0.992421i	$-0.460785\pi$
$823$	7.05067	0.245771	0.122885	+	0.992421i	$0.460785\pi$
$824$	7.55917	0.263336
$825$	−74.2907	−2.58647
$826$	−22.2242	−0.773280
$827$	3.73187	0.129770	0.0648850	−	0.997893i	$-0.479332\pi$
$827$	3.73187	0.129770	0.0648850	+	0.997893i	$0.479332\pi$
$828$	−7.19632	−0.250089
$829$	−39.7300	−1.37988	−0.689939	−	0.723867i	$-0.742363\pi$
$829$	−39.7300	−1.37988	−0.689939	+	0.723867i	$0.742363\pi$
$830$	14.9499	0.518920
$831$	−1.53718	−0.0533241
$832$	2.90730	0.100793
$833$	41.1834	1.42692
$834$	−7.34551	−0.254354
$835$	80.7057	2.79294
$836$	5.05487	0.174826
$837$	4.24687	0.146793
$838$	−20.4144	−0.705203
$839$	22.3262	0.770786	0.385393	−	0.922752i	$-0.374066\pi$
$839$	22.3262	0.770786	0.385393	+	0.922752i	$0.374066\pi$
$840$	15.7574	0.543681
$841$	55.2818	1.90627
$842$	27.0157	0.931023
$843$	−14.7283	−0.507269
$844$	−20.6173	−0.709678
$845$	−20.1828	−0.694308
$846$	−2.77732	−0.0954864
$847$	51.6655	1.77525
$848$	1.00000	0.0343401
$849$	3.53385	0.121281
$850$	107.971	3.70339
$851$	−2.55475	−0.0875758
$852$	−13.9767	−0.478834
$853$	−55.0612	−1.88526	−0.942629	−	0.333842i	$-0.891655\pi$
$853$	−55.0612	−1.88526	−0.942629	+	0.333842i	$0.891655\pi$
$854$	18.3775	0.628866
$855$	−4.43811	−0.151780
$856$	3.59225	0.122780
$857$	−23.6203	−0.806856	−0.403428	−	0.915011i	$-0.632181\pi$
$857$	−23.6203	−0.806856	−0.403428	+	0.915011i	$0.632181\pi$
$858$	−14.6960	−0.501715
$859$	−17.3191	−0.590920	−0.295460	−	0.955355i	$-0.595473\pi$
$859$	−17.3191	−0.590920	−0.295460	+	0.955355i	$0.595473\pi$
$860$	−38.8137	−1.32354
$861$	−21.9543	−0.748199
$862$	−6.32139	−0.215307
$863$	−48.9803	−1.66731	−0.833654	−	0.552287i	$-0.813755\pi$
$863$	−48.9803	−1.66731	−0.833654	+	0.552287i	$0.813755\pi$
$864$	1.00000	0.0340207
$865$	101.500	3.45111
$866$	−4.42744	−0.150451
$867$	36.9720	1.25564
$868$	15.0784	0.511793
$869$	−28.1972	−0.956523
$870$	−40.7441	−1.38136
$871$	−33.3530	−1.13012
$872$	2.07153	0.0701509
$873$	4.68706	0.158633
$874$	7.19632	0.243419
$875$	152.797	5.16547
$876$	7.09489	0.239714
$877$	−1.47428	−0.0497828	−0.0248914	−	0.999690i	$-0.507924\pi$
$877$	−1.47428	−0.0497828	−0.0248914	+	0.999690i	$0.507924\pi$
$878$	34.1010	1.15085
$879$	−19.6125	−0.661513
$880$	−22.4341	−0.756253
$881$	2.65533	0.0894602	0.0447301	−	0.998999i	$-0.485757\pi$
$881$	2.65533	0.0894602	0.0447301	+	0.998999i	$0.485757\pi$
$882$	5.60581	0.188757
$883$	−22.1296	−0.744719	−0.372360	−	0.928089i	$-0.621451\pi$
$883$	−22.1296	−0.744719	−0.372360	+	0.928089i	$0.621451\pi$
$884$	21.3587	0.718370
$885$	−27.7805	−0.933831
$886$	10.2239	0.343478
$887$	−19.0822	−0.640716	−0.320358	−	0.947296i	$-0.603803\pi$
$887$	−19.0822	−0.640716	−0.320358	+	0.947296i	$0.603803\pi$
$888$	0.355008	0.0119133
$889$	−6.08979	−0.204245
$890$	−48.9420	−1.64054
$891$	−5.05487	−0.169345
$892$	−17.6221	−0.590033
$893$	2.77732	0.0929396
$894$	−19.5671	−0.654421
$895$	54.3454	1.81657
$896$	3.55047	0.118613
$897$	−20.9219	−0.698561
$898$	28.1595	0.939696
$899$	−38.9884	−1.30034
$900$	14.6968	0.489895
$901$	7.34657	0.244750
$902$	31.2568	1.04074
$903$	−31.0508	−1.03331
$904$	−4.34282	−0.144440
$905$	6.92185	0.230090
$906$	−5.34007	−0.177412
$907$	52.4922	1.74298	0.871488	−	0.490416i	$-0.163155\pi$
$907$	52.4922	1.74298	0.871488	+	0.490416i	$0.163155\pi$
$908$	3.51574	0.116674
$909$	−6.69483	−0.222054
$910$	45.8114	1.51863
$911$	−32.4962	−1.07665	−0.538324	−	0.842738i	$-0.680942\pi$
$911$	−32.4962	−1.07665	−0.538324	+	0.842738i	$0.680942\pi$
$912$	−1.00000	−0.0331133
$913$	−17.0275	−0.563529
$914$	−3.03542	−0.100403
$915$	22.9721	0.759433
$916$	15.9273	0.526253
$917$	−7.99479	−0.264011
$918$	7.34657	0.242473
$919$	−51.6187	−1.70275	−0.851373	−	0.524561i	$-0.824229\pi$
$919$	−51.6187	−1.70275	−0.851373	+	0.524561i	$0.824229\pi$
$920$	−31.9381	−1.05297
$921$	−33.4526	−1.10230
$922$	−20.8103	−0.685349
$923$	−40.6345	−1.33750
$924$	−17.9472	−0.590418
$925$	5.21750	0.171550
$926$	12.1958	0.400778
$927$	7.55917	0.248276
$928$	−9.18051	−0.301365
$929$	2.44736	0.0802952	0.0401476	−	0.999194i	$-0.487217\pi$
$929$	2.44736	0.0802952	0.0401476	+	0.999194i	$0.487217\pi$
$930$	18.8481	0.618052
$931$	−5.60581	−0.183723
$932$	28.3834	0.929728
$933$	−18.0889	−0.592205
$934$	−6.94880	−0.227372
$935$	−164.814	−5.38998
$936$	2.90730	0.0950281
$937$	−50.9592	−1.66477	−0.832383	−	0.554201i	$-0.813024\pi$
$937$	−50.9592	−1.66477	−0.832383	+	0.554201i	$0.813024\pi$
$938$	−40.7315	−1.32993
$939$	19.8568	0.648004
$940$	−12.3261	−0.402032
$941$	−43.3890	−1.41444	−0.707220	−	0.706993i	$-0.750051\pi$
$941$	−43.3890	−1.41444	−0.707220	+	0.706993i	$0.750051\pi$
$942$	13.7256	0.447205
$943$	44.4984	1.44907
$944$	−6.25953	−0.203730
$945$	15.7574	0.512587
$946$	44.2077	1.43732
$947$	−3.91283	−0.127150	−0.0635749	−	0.997977i	$-0.520250\pi$
$947$	−3.91283	−0.127150	−0.0635749	+	0.997977i	$0.520250\pi$
$948$	5.57821	0.181172
$949$	20.6270	0.669580
$950$	−14.6968	−0.476828
$951$	3.41721	0.110811
$952$	26.0837	0.845379
$953$	−40.7882	−1.32126	−0.660630	−	0.750712i	$-0.729711\pi$
$953$	−40.7882	−1.32126	−0.660630	+	0.750712i	$0.729711\pi$
$954$	1.00000	0.0323762
$955$	−28.4665	−0.921155
$956$	−14.5338	−0.470056
$957$	46.4063	1.50010
$958$	25.2918	0.817140
$959$	−36.1410	−1.16705
$960$	4.43811	0.143239
$961$	−12.9641	−0.418198
$962$	1.03212	0.0332768
$963$	3.59225	0.115759
$964$	−23.3650	−0.752538
$965$	−6.98325	−0.224799
$966$	−25.5503	−0.822067
$967$	58.4243	1.87880	0.939400	−	0.342823i	$-0.111383\pi$
$967$	58.4243	1.87880	0.939400	+	0.342823i	$0.111383\pi$
$968$	14.5518	0.467711
$969$	−7.34657	−0.236006
$970$	20.8017	0.667903
$971$	30.6235	0.982754	0.491377	−	0.870947i	$-0.336494\pi$
$971$	30.6235	0.982754	0.491377	+	0.870947i	$0.336494\pi$
$972$	1.00000	0.0320750
$973$	−26.0800	−0.836086
$974$	−42.9490	−1.37618
$975$	42.7281	1.36840
$976$	5.17609	0.165683
$977$	−44.1037	−1.41100	−0.705501	−	0.708709i	$-0.749278\pi$
$977$	−44.1037	−1.41100	−0.705501	+	0.708709i	$0.749278\pi$
$978$	−0.415020	−0.0132709
$979$	55.7434	1.78157
$980$	24.8792	0.794737
$981$	2.07153	0.0661389
$982$	44.1739	1.40965
$983$	−25.8126	−0.823293	−0.411647	−	0.911344i	$-0.635046\pi$
$983$	−25.8126	−0.823293	−0.411647	+	0.911344i	$0.635046\pi$
$984$	−6.18349	−0.197122
$985$	−48.4770	−1.54461
$986$	−67.4452	−2.14789
$987$	−9.86079	−0.313873
$988$	−2.90730	−0.0924936
$989$	62.9358	2.00124
$990$	−22.4341	−0.713002
$991$	33.2474	1.05614	0.528069	−	0.849202i	$-0.322916\pi$
$991$	33.2474	1.05614	0.528069	+	0.849202i	$0.322916\pi$
$992$	4.24687	0.134838
$993$	17.3483	0.550533
$994$	−49.6238	−1.57397
$995$	18.2330	0.578025
$996$	3.36853	0.106736
$997$	−1.56813	−0.0496630	−0.0248315	−	0.999692i	$-0.507905\pi$
$997$	−1.56813	−0.0496630	−0.0248315	+	0.999692i	$0.507905\pi$
$998$	−4.61034	−0.145938
$999$	0.355008	0.0112320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bg.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bg.1.12	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.43811 q^{5} +1.00000 q^{6} +3.55047 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.43811 q^{5} +1.00000 q^{6} +3.55047 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.43811 q^{10} -5.05487 q^{11} +1.00000 q^{12} +2.90730 q^{13} +3.55047 q^{14} +4.43811 q^{15} +1.00000 q^{16} +7.34657 q^{17} +1.00000 q^{18} -1.00000 q^{19} +4.43811 q^{20} +3.55047 q^{21} -5.05487 q^{22} -7.19632 q^{23} +1.00000 q^{24} +14.6968 q^{25} +2.90730 q^{26} +1.00000 q^{27} +3.55047 q^{28} -9.18051 q^{29} +4.43811 q^{30} +4.24687 q^{31} +1.00000 q^{32} -5.05487 q^{33} +7.34657 q^{34} +15.7574 q^{35} +1.00000 q^{36} +0.355008 q^{37} -1.00000 q^{38} +2.90730 q^{39} +4.43811 q^{40} -6.18349 q^{41} +3.55047 q^{42} -8.74555 q^{43} -5.05487 q^{44} +4.43811 q^{45} -7.19632 q^{46} -2.77732 q^{47} +1.00000 q^{48} +5.60581 q^{49} +14.6968 q^{50} +7.34657 q^{51} +2.90730 q^{52} +1.00000 q^{53} +1.00000 q^{54} -22.4341 q^{55} +3.55047 q^{56} -1.00000 q^{57} -9.18051 q^{58} -6.25953 q^{59} +4.43811 q^{60} +5.17609 q^{61} +4.24687 q^{62} +3.55047 q^{63} +1.00000 q^{64} +12.9029 q^{65} -5.05487 q^{66} -11.4722 q^{67} +7.34657 q^{68} -7.19632 q^{69} +15.7574 q^{70} -13.9767 q^{71} +1.00000 q^{72} +7.09489 q^{73} +0.355008 q^{74} +14.6968 q^{75} -1.00000 q^{76} -17.9472 q^{77} +2.90730 q^{78} +5.57821 q^{79} +4.43811 q^{80} +1.00000 q^{81} -6.18349 q^{82} +3.36853 q^{83} +3.55047 q^{84} +32.6049 q^{85} -8.74555 q^{86} -9.18051 q^{87} -5.05487 q^{88} -11.0277 q^{89} +4.43811 q^{90} +10.3223 q^{91} -7.19632 q^{92} +4.24687 q^{93} -2.77732 q^{94} -4.43811 q^{95} +1.00000 q^{96} +4.68706 q^{97} +5.60581 q^{98} -5.05487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * q^99

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