LMFDB - Embedded newform 6034.2.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.42043$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.42043 q^{3} +1.00000 q^{4} -4.18942 q^{5} -1.42043 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.982389 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.42043 q^{3} +1.00000 q^{4} -4.18942 q^{5} -1.42043 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.982389 q^{9} -4.18942 q^{10} -2.90402 q^{11} -1.42043 q^{12} +0.795551 q^{13} -1.00000 q^{14} +5.95077 q^{15} +1.00000 q^{16} -1.40491 q^{17} -0.982389 q^{18} +5.53709 q^{19} -4.18942 q^{20} +1.42043 q^{21} -2.90402 q^{22} +7.61037 q^{23} -1.42043 q^{24} +12.5513 q^{25} +0.795551 q^{26} +5.65669 q^{27} -1.00000 q^{28} +1.05285 q^{29} +5.95077 q^{30} +3.96610 q^{31} +1.00000 q^{32} +4.12494 q^{33} -1.40491 q^{34} +4.18942 q^{35} -0.982389 q^{36} -4.58701 q^{37} +5.53709 q^{38} -1.13002 q^{39} -4.18942 q^{40} -5.80656 q^{41} +1.42043 q^{42} +2.10200 q^{43} -2.90402 q^{44} +4.11565 q^{45} +7.61037 q^{46} -9.67572 q^{47} -1.42043 q^{48} +1.00000 q^{49} +12.5513 q^{50} +1.99557 q^{51} +0.795551 q^{52} +8.61726 q^{53} +5.65669 q^{54} +12.1662 q^{55} -1.00000 q^{56} -7.86503 q^{57} +1.05285 q^{58} -8.46584 q^{59} +5.95077 q^{60} +13.0600 q^{61} +3.96610 q^{62} +0.982389 q^{63} +1.00000 q^{64} -3.33290 q^{65} +4.12494 q^{66} -5.27877 q^{67} -1.40491 q^{68} -10.8100 q^{69} +4.18942 q^{70} -13.7670 q^{71} -0.982389 q^{72} +6.96523 q^{73} -4.58701 q^{74} -17.8282 q^{75} +5.53709 q^{76} +2.90402 q^{77} -1.13002 q^{78} +7.77424 q^{79} -4.18942 q^{80} -5.08774 q^{81} -5.80656 q^{82} -14.4334 q^{83} +1.42043 q^{84} +5.88575 q^{85} +2.10200 q^{86} -1.49549 q^{87} -2.90402 q^{88} -0.471590 q^{89} +4.11565 q^{90} -0.795551 q^{91} +7.61037 q^{92} -5.63356 q^{93} -9.67572 q^{94} -23.1972 q^{95} -1.42043 q^{96} -5.30191 q^{97} +1.00000 q^{98} +2.85287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	−1.42043	−0.820083	−0.410042	−	0.912067i	$-0.634486\pi$
$3$	−1.42043	−0.820083	−0.410042	+	0.912067i	$0.634486\pi$
$4$	1.00000	0.500000
$5$	−4.18942	−1.87357	−0.936784	−	0.349908i	$-0.886213\pi$
$5$	−4.18942	−1.87357	−0.936784	+	0.349908i	$0.886213\pi$
$6$	−1.42043	−0.579887
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−0.982389	−0.327463
$10$	−4.18942	−1.32481
$11$	−2.90402	−0.875594	−0.437797	−	0.899074i	$-0.644241\pi$
$11$	−2.90402	−0.875594	−0.437797	+	0.899074i	$0.644241\pi$
$12$	−1.42043	−0.410042
$13$	0.795551	0.220646	0.110323	−	0.993896i	$-0.464811\pi$
$13$	0.795551	0.220646	0.110323	+	0.993896i	$0.464811\pi$
$14$	−1.00000	−0.267261
$15$	5.95077	1.53648
$16$	1.00000	0.250000
$17$	−1.40491	−0.340740	−0.170370	−	0.985380i	$-0.554496\pi$
$17$	−1.40491	−0.340740	−0.170370	+	0.985380i	$0.554496\pi$
$18$	−0.982389	−0.231551
$19$	5.53709	1.27030	0.635148	−	0.772390i	$-0.280939\pi$
$19$	5.53709	1.27030	0.635148	+	0.772390i	$0.280939\pi$
$20$	−4.18942	−0.936784
$21$	1.42043	0.309962
$22$	−2.90402	−0.619138
$23$	7.61037	1.58687	0.793436	−	0.608654i	$-0.208290\pi$
$23$	7.61037	1.58687	0.793436	+	0.608654i	$0.208290\pi$
$24$	−1.42043	−0.289943
$25$	12.5513	2.51026
$26$	0.795551	0.156020
$27$	5.65669	1.08863
$28$	−1.00000	−0.188982
$29$	1.05285	0.195509	0.0977543	−	0.995211i	$-0.468834\pi$
$29$	1.05285	0.195509	0.0977543	+	0.995211i	$0.468834\pi$
$30$	5.95077	1.08646
$31$	3.96610	0.712333	0.356166	−	0.934423i	$-0.384084\pi$
$31$	3.96610	0.712333	0.356166	+	0.934423i	$0.384084\pi$
$32$	1.00000	0.176777
$33$	4.12494	0.718060
$34$	−1.40491	−0.240940
$35$	4.18942	0.708142
$36$	−0.982389	−0.163732
$37$	−4.58701	−0.754099	−0.377050	−	0.926193i	$-0.623061\pi$
$37$	−4.58701	−0.754099	−0.377050	+	0.926193i	$0.623061\pi$
$38$	5.53709	0.898235
$39$	−1.13002	−0.180948
$40$	−4.18942	−0.662406
$41$	−5.80656	−0.906833	−0.453416	−	0.891299i	$-0.649795\pi$
$41$	−5.80656	−0.906833	−0.453416	+	0.891299i	$0.649795\pi$
$42$	1.42043	0.219177
$43$	2.10200	0.320552	0.160276	−	0.987072i	$-0.448762\pi$
$43$	2.10200	0.320552	0.160276	+	0.987072i	$0.448762\pi$
$44$	−2.90402	−0.437797
$45$	4.11565	0.613524
$46$	7.61037	1.12209
$47$	−9.67572	−1.41135	−0.705675	−	0.708536i	$-0.749356\pi$
$47$	−9.67572	−1.41135	−0.705675	+	0.708536i	$0.749356\pi$
$48$	−1.42043	−0.205021
$49$	1.00000	0.142857
$50$	12.5513	1.77502
$51$	1.99557	0.279435
$52$	0.795551	0.110323
$53$	8.61726	1.18367	0.591836	−	0.806058i	$-0.298403\pi$
$53$	8.61726	1.18367	0.591836	+	0.806058i	$0.298403\pi$
$54$	5.65669	0.769778
$55$	12.1662	1.64048
$56$	−1.00000	−0.133631
$57$	−7.86503	−1.04175
$58$	1.05285	0.138245
$59$	−8.46584	−1.10216	−0.551079	−	0.834453i	$-0.685784\pi$
$59$	−8.46584	−1.10216	−0.551079	+	0.834453i	$0.685784\pi$
$60$	5.95077	0.768241
$61$	13.0600	1.67216	0.836078	−	0.548611i	$-0.184843\pi$
$61$	13.0600	1.67216	0.836078	+	0.548611i	$0.184843\pi$
$62$	3.96610	0.503695
$63$	0.982389	0.123769
$64$	1.00000	0.125000
$65$	−3.33290	−0.413396
$66$	4.12494	0.507745
$67$	−5.27877	−0.644904	−0.322452	−	0.946586i	$-0.604507\pi$
$67$	−5.27877	−0.644904	−0.322452	+	0.946586i	$0.604507\pi$
$68$	−1.40491	−0.170370
$69$	−10.8100	−1.30137
$70$	4.18942	0.500732
$71$	−13.7670	−1.63384	−0.816922	−	0.576749i	$-0.804321\pi$
$71$	−13.7670	−1.63384	−0.816922	+	0.576749i	$0.804321\pi$
$72$	−0.982389	−0.115776
$73$	6.96523	0.815219	0.407609	−	0.913156i	$-0.366363\pi$
$73$	6.96523	0.815219	0.407609	+	0.913156i	$0.366363\pi$
$74$	−4.58701	−0.533229
$75$	−17.8282	−2.05862
$76$	5.53709	0.635148
$77$	2.90402	0.330943
$78$	−1.13002	−0.127950
$79$	7.77424	0.874671	0.437335	−	0.899298i	$-0.355922\pi$
$79$	7.77424	0.874671	0.437335	+	0.899298i	$0.355922\pi$
$80$	−4.18942	−0.468392
$81$	−5.08774	−0.565305
$82$	−5.80656	−0.641228
$83$	−14.4334	−1.58427	−0.792136	−	0.610345i	$-0.791031\pi$
$83$	−14.4334	−1.58427	−0.792136	+	0.610345i	$0.791031\pi$
$84$	1.42043	0.154981
$85$	5.88575	0.638400
$86$	2.10200	0.226665
$87$	−1.49549	−0.160333
$88$	−2.90402	−0.309569
$89$	−0.471590	−0.0499885	−0.0249942	−	0.999688i	$-0.507957\pi$
$89$	−0.471590	−0.0499885	−0.0249942	+	0.999688i	$0.507957\pi$
$90$	4.11565	0.433827
$91$	−0.795551	−0.0833965
$92$	7.61037	0.793436
$93$	−5.63356	−0.584172
$94$	−9.67572	−0.997974
$95$	−23.1972	−2.37999
$96$	−1.42043	−0.144972
$97$	−5.30191	−0.538328	−0.269164	−	0.963094i	$-0.586747\pi$
$97$	−5.30191	−0.538328	−0.269164	+	0.963094i	$0.586747\pi$
$98$	1.00000	0.101015
$99$	2.85287	0.286725
$100$	12.5513	1.25513
$101$	−11.6176	−1.15600	−0.577999	−	0.816037i	$-0.696166\pi$
$101$	−11.6176	−1.15600	−0.577999	+	0.816037i	$0.696166\pi$
$102$	1.99557	0.197591
$103$	−6.30990	−0.621733	−0.310866	−	0.950454i	$-0.600619\pi$
$103$	−6.30990	−0.621733	−0.310866	+	0.950454i	$0.600619\pi$
$104$	0.795551	0.0780102
$105$	−5.95077	−0.580736
$106$	8.61726	0.836983
$107$	8.87533	0.858011	0.429005	−	0.903302i	$-0.358864\pi$
$107$	8.87533	0.858011	0.429005	+	0.903302i	$0.358864\pi$
$108$	5.65669	0.544315
$109$	14.9587	1.43279	0.716393	−	0.697697i	$-0.245792\pi$
$109$	14.9587	1.43279	0.716393	+	0.697697i	$0.245792\pi$
$110$	12.1662	1.16000
$111$	6.51551	0.618424
$112$	−1.00000	−0.0944911
$113$	12.0505	1.13361	0.566807	−	0.823851i	$-0.308179\pi$
$113$	12.0505	1.13361	0.566807	+	0.823851i	$0.308179\pi$
$114$	−7.86503	−0.736628
$115$	−31.8831	−2.97311
$116$	1.05285	0.0977543
$117$	−0.781541	−0.0722535
$118$	−8.46584	−0.779344
$119$	1.40491	0.128788
$120$	5.95077	0.543228
$121$	−2.56669	−0.233336
$122$	13.0600	1.18239
$123$	8.24780	0.743679
$124$	3.96610	0.356166
$125$	−31.6355	−2.82957
$126$	0.982389	0.0875182
$127$	−15.7992	−1.40196	−0.700978	−	0.713183i	$-0.747253\pi$
$127$	−15.7992	−1.40196	−0.700978	+	0.713183i	$0.747253\pi$
$128$	1.00000	0.0883883
$129$	−2.98574	−0.262879
$130$	−3.33290	−0.292315
$131$	−5.58964	−0.488369	−0.244184	−	0.969729i	$-0.578520\pi$
$131$	−5.58964	−0.488369	−0.244184	+	0.969729i	$0.578520\pi$
$132$	4.12494	0.359030
$133$	−5.53709	−0.480127
$134$	−5.27877	−0.456016
$135$	−23.6983	−2.03962
$136$	−1.40491	−0.120470
$137$	−3.59583	−0.307213	−0.153606	−	0.988132i	$-0.549089\pi$
$137$	−3.59583	−0.307213	−0.153606	+	0.988132i	$0.549089\pi$
$138$	−10.8100	−0.920206
$139$	−16.8358	−1.42799	−0.713995	−	0.700151i	$-0.753116\pi$
$139$	−16.8358	−1.42799	−0.713995	+	0.700151i	$0.753116\pi$
$140$	4.18942	0.354071
$141$	13.7436	1.15742
$142$	−13.7670	−1.15530
$143$	−2.31029	−0.193196
$144$	−0.982389	−0.0818658
$145$	−4.41082	−0.366299
$146$	6.96523	0.576447
$147$	−1.42043	−0.117155
$148$	−4.58701	−0.377050
$149$	−4.46874	−0.366093	−0.183047	−	0.983104i	$-0.558596\pi$
$149$	−4.46874	−0.366093	−0.183047	+	0.983104i	$0.558596\pi$
$150$	−17.8282	−1.45566
$151$	18.2268	1.48327	0.741637	−	0.670801i	$-0.234050\pi$
$151$	18.2268	1.48327	0.741637	+	0.670801i	$0.234050\pi$
$152$	5.53709	0.449118
$153$	1.38017	0.111580
$154$	2.90402	0.234012
$155$	−16.6157	−1.33460
$156$	−1.13002	−0.0904742
$157$	−7.56052	−0.603395	−0.301698	−	0.953404i	$-0.597553\pi$
$157$	−7.56052	−0.603395	−0.301698	+	0.953404i	$0.597553\pi$
$158$	7.77424	0.618486
$159$	−12.2402	−0.970710
$160$	−4.18942	−0.331203
$161$	−7.61037	−0.599781
$162$	−5.08774	−0.399731
$163$	8.25454	0.646546	0.323273	−	0.946306i	$-0.395217\pi$
$163$	8.25454	0.646546	0.323273	+	0.946306i	$0.395217\pi$
$164$	−5.80656	−0.453416
$165$	−17.2811	−1.34533
$166$	−14.4334	−1.12025
$167$	−12.1672	−0.941528	−0.470764	−	0.882259i	$-0.656022\pi$
$167$	−12.1672	−0.941528	−0.470764	+	0.882259i	$0.656022\pi$
$168$	1.42043	0.109588
$169$	−12.3671	−0.951315
$170$	5.88575	0.451417
$171$	−5.43958	−0.415975
$172$	2.10200	0.160276
$173$	−8.47824	−0.644589	−0.322294	−	0.946639i	$-0.604454\pi$
$173$	−8.47824	−0.644589	−0.322294	+	0.946639i	$0.604454\pi$
$174$	−1.49549	−0.113373
$175$	−12.5513	−0.948788
$176$	−2.90402	−0.218898
$177$	12.0251	0.903862
$178$	−0.471590	−0.0353472
$179$	19.7432	1.47568	0.737839	−	0.674976i	$-0.235846\pi$
$179$	19.7432	1.47568	0.737839	+	0.674976i	$0.235846\pi$
$180$	4.11565	0.306762
$181$	−9.89576	−0.735546	−0.367773	−	0.929916i	$-0.619880\pi$
$181$	−9.89576	−0.735546	−0.367773	+	0.929916i	$0.619880\pi$
$182$	−0.795551	−0.0589702
$183$	−18.5507	−1.37131
$184$	7.61037	0.561044
$185$	19.2169	1.41286
$186$	−5.63356	−0.413072
$187$	4.07987	0.298350
$188$	−9.67572	−0.705675
$189$	−5.65669	−0.411464
$190$	−23.1972	−1.68290
$191$	8.28616	0.599566	0.299783	−	0.954007i	$-0.403086\pi$
$191$	8.28616	0.599566	0.299783	+	0.954007i	$0.403086\pi$
$192$	−1.42043	−0.102510
$193$	8.48558	0.610805	0.305403	−	0.952223i	$-0.401209\pi$
$193$	8.48558	0.610805	0.305403	+	0.952223i	$0.401209\pi$
$194$	−5.30191	−0.380655
$195$	4.73414	0.339019
$196$	1.00000	0.0714286
$197$	−9.02646	−0.643109	−0.321554	−	0.946891i	$-0.604205\pi$
$197$	−9.02646	−0.643109	−0.321554	+	0.946891i	$0.604205\pi$
$198$	2.85287	0.202745
$199$	−5.75920	−0.408259	−0.204130	−	0.978944i	$-0.565436\pi$
$199$	−5.75920	−0.408259	−0.204130	+	0.978944i	$0.565436\pi$
$200$	12.5513	0.887510
$201$	7.49810	0.528875
$202$	−11.6176	−0.817414
$203$	−1.05285	−0.0738953
$204$	1.99557	0.139718
$205$	24.3262	1.69901
$206$	−6.30990	−0.439631
$207$	−7.47634	−0.519642
$208$	0.795551	0.0551616
$209$	−16.0798	−1.11226
$210$	−5.95077	−0.410642
$211$	2.65728	0.182935	0.0914673	−	0.995808i	$-0.470844\pi$
$211$	2.65728	0.182935	0.0914673	+	0.995808i	$0.470844\pi$
$212$	8.61726	0.591836
$213$	19.5550	1.33989
$214$	8.87533	0.606705
$215$	−8.80617	−0.600576
$216$	5.65669	0.384889
$217$	−3.96610	−0.269237
$218$	14.9587	1.01313
$219$	−9.89360	−0.668547
$220$	12.1662	0.820242
$221$	−1.11768	−0.0751830
$222$	6.51551	0.437292
$223$	16.2716	1.08962	0.544812	−	0.838558i	$-0.316601\pi$
$223$	16.2716	1.08962	0.544812	+	0.838558i	$0.316601\pi$
$224$	−1.00000	−0.0668153
$225$	−12.3302	−0.822016
$226$	12.0505	0.801586
$227$	16.0171	1.06309	0.531545	−	0.847030i	$-0.321612\pi$
$227$	16.0171	1.06309	0.531545	+	0.847030i	$0.321612\pi$
$228$	−7.86503	−0.520874
$229$	−22.4425	−1.48304	−0.741520	−	0.670931i	$-0.765895\pi$
$229$	−22.4425	−1.48304	−0.741520	+	0.670931i	$0.765895\pi$
$230$	−31.8831	−2.10231
$231$	−4.12494	−0.271401
$232$	1.05285	0.0691227
$233$	28.4884	1.86633	0.933167	−	0.359443i	$-0.117033\pi$
$233$	28.4884	1.86633	0.933167	+	0.359443i	$0.117033\pi$
$234$	−0.781541	−0.0510909
$235$	40.5357	2.64426
$236$	−8.46584	−0.551079
$237$	−11.0427	−0.717303
$238$	1.40491	0.0910666
$239$	10.9588	0.708865	0.354432	−	0.935082i	$-0.384674\pi$
$239$	10.9588	0.708865	0.354432	+	0.935082i	$0.384674\pi$
$240$	5.95077	0.384121
$241$	30.3573	1.95549	0.977743	−	0.209807i	$-0.0672835\pi$
$241$	30.3573	1.95549	0.977743	+	0.209807i	$0.0672835\pi$
$242$	−2.56669	−0.164993
$243$	−9.74331	−0.625033
$244$	13.0600	0.836078
$245$	−4.18942	−0.267653
$246$	8.24780	0.525860
$247$	4.40504	0.280286
$248$	3.96610	0.251848
$249$	20.5016	1.29924
$250$	−31.6355	−2.00081
$251$	5.00983	0.316217	0.158109	−	0.987422i	$-0.449460\pi$
$251$	5.00983	0.316217	0.158109	+	0.987422i	$0.449460\pi$
$252$	0.982389	0.0618847
$253$	−22.1006	−1.38945
$254$	−15.7992	−0.991333
$255$	−8.36028	−0.523541
$256$	1.00000	0.0625000
$257$	24.3975	1.52187	0.760936	−	0.648826i	$-0.224740\pi$
$257$	24.3975	1.52187	0.760936	+	0.648826i	$0.224740\pi$
$258$	−2.98574	−0.185884
$259$	4.58701	0.285023
$260$	−3.33290	−0.206698
$261$	−1.03430	−0.0640218
$262$	−5.58964	−0.345329
$263$	12.0593	0.743608	0.371804	−	0.928311i	$-0.378739\pi$
$263$	12.0593	0.743608	0.371804	+	0.928311i	$0.378739\pi$
$264$	4.12494	0.253872
$265$	−36.1014	−2.21769
$266$	−5.53709	−0.339501
$267$	0.669859	0.0409947
$268$	−5.27877	−0.322452
$269$	9.30339	0.567238	0.283619	−	0.958937i	$-0.408465\pi$
$269$	9.30339	0.567238	0.283619	+	0.958937i	$0.408465\pi$
$270$	−23.6983	−1.44223
$271$	−19.7891	−1.20210	−0.601050	−	0.799212i	$-0.705251\pi$
$271$	−19.7891	−1.20210	−0.601050	+	0.799212i	$0.705251\pi$
$272$	−1.40491	−0.0851850
$273$	1.13002	0.0683921
$274$	−3.59583	−0.217232
$275$	−36.4491	−2.19796
$276$	−10.8100	−0.650684
$277$	−13.1518	−0.790214	−0.395107	−	0.918635i	$-0.629292\pi$
$277$	−13.1518	−0.790214	−0.395107	+	0.918635i	$0.629292\pi$
$278$	−16.8358	−1.00974
$279$	−3.89626	−0.233263
$280$	4.18942	0.250366
$281$	10.1091	0.603061	0.301530	−	0.953457i	$-0.402503\pi$
$281$	10.1091	0.603061	0.301530	+	0.953457i	$0.402503\pi$
$282$	13.7436	0.818422
$283$	−3.66000	−0.217564	−0.108782	−	0.994066i	$-0.534695\pi$
$283$	−3.66000	−0.217564	−0.108782	+	0.994066i	$0.534695\pi$
$284$	−13.7670	−0.816922
$285$	32.9500	1.95179
$286$	−2.31029	−0.136611
$287$	5.80656	0.342751
$288$	−0.982389	−0.0578878
$289$	−15.0262	−0.883896
$290$	−4.41082	−0.259012
$291$	7.53098	0.441474
$292$	6.96523	0.407609
$293$	−19.7082	−1.15137	−0.575683	−	0.817673i	$-0.695264\pi$
$293$	−19.7082	−1.15137	−0.575683	+	0.817673i	$0.695264\pi$
$294$	−1.42043	−0.0828409
$295$	35.4670	2.06497
$296$	−4.58701	−0.266614
$297$	−16.4271	−0.953198
$298$	−4.46874	−0.258867
$299$	6.05444	0.350137
$300$	−17.8282	−1.02931
$301$	−2.10200	−0.121157
$302$	18.2268	1.04883
$303$	16.5020	0.948015
$304$	5.53709	0.317574
$305$	−54.7137	−3.13290
$306$	1.38017	0.0788988
$307$	−5.79590	−0.330789	−0.165395	−	0.986227i	$-0.552890\pi$
$307$	−5.79590	−0.330789	−0.165395	+	0.986227i	$0.552890\pi$
$308$	2.90402	0.165472
$309$	8.96274	0.509873
$310$	−16.6157	−0.943708
$311$	32.3672	1.83538	0.917688	−	0.397302i	$-0.130053\pi$
$311$	32.3672	1.83538	0.917688	+	0.397302i	$0.130053\pi$
$312$	−1.13002	−0.0639749
$313$	0.383732	0.0216898	0.0108449	−	0.999941i	$-0.496548\pi$
$313$	0.383732	0.0216898	0.0108449	+	0.999941i	$0.496548\pi$
$314$	−7.56052	−0.426665
$315$	−4.11565	−0.231890
$316$	7.77424	0.437335
$317$	−10.9766	−0.616510	−0.308255	−	0.951304i	$-0.599745\pi$
$317$	−10.9766	−0.616510	−0.308255	+	0.951304i	$0.599745\pi$
$318$	−12.2402	−0.686396
$319$	−3.05748	−0.171186
$320$	−4.18942	−0.234196
$321$	−12.6068	−0.703640
$322$	−7.61037	−0.424109
$323$	−7.77910	−0.432841
$324$	−5.08774	−0.282652
$325$	9.98519	0.553879
$326$	8.25454	0.457177
$327$	−21.2478	−1.17500
$328$	−5.80656	−0.320614
$329$	9.67572	0.533440
$330$	−17.2811	−0.951295
$331$	4.59344	0.252479	0.126239	−	0.992000i	$-0.459709\pi$
$331$	4.59344	0.252479	0.126239	+	0.992000i	$0.459709\pi$
$332$	−14.4334	−0.792136
$333$	4.50623	0.246940
$334$	−12.1672	−0.665761
$335$	22.1150	1.20827
$336$	1.42043	0.0774906
$337$	10.1707	0.554036	0.277018	−	0.960865i	$-0.410654\pi$
$337$	10.1707	0.554036	0.277018	+	0.960865i	$0.410654\pi$
$338$	−12.3671	−0.672681
$339$	−17.1168	−0.929658
$340$	5.88575	0.319200
$341$	−11.5176	−0.623714
$342$	−5.43958	−0.294139
$343$	−1.00000	−0.0539949
$344$	2.10200	0.113332
$345$	45.2876	2.43820
$346$	−8.47824	−0.455793
$347$	−28.6356	−1.53724	−0.768619	−	0.639707i	$-0.779056\pi$
$347$	−28.6356	−1.53724	−0.768619	+	0.639707i	$0.779056\pi$
$348$	−1.49549	−0.0801667
$349$	−8.41578	−0.450486	−0.225243	−	0.974303i	$-0.572318\pi$
$349$	−8.41578	−0.450486	−0.225243	+	0.974303i	$0.572318\pi$
$350$	−12.5513	−0.670894
$351$	4.50019	0.240202
$352$	−2.90402	−0.154785
$353$	1.67383	0.0890891	0.0445445	−	0.999007i	$-0.485816\pi$
$353$	1.67383	0.0890891	0.0445445	+	0.999007i	$0.485816\pi$
$354$	12.0251	0.639127
$355$	57.6758	3.06112
$356$	−0.471590	−0.0249942
$357$	−1.99557	−0.105617
$358$	19.7432	1.04346
$359$	−26.3319	−1.38975	−0.694873	−	0.719132i	$-0.744539\pi$
$359$	−26.3319	−1.38975	−0.694873	+	0.719132i	$0.744539\pi$
$360$	4.11565	0.216914
$361$	11.6594	0.613652
$362$	−9.89576	−0.520109
$363$	3.64580	0.191355
$364$	−0.795551	−0.0416982
$365$	−29.1803	−1.52737
$366$	−18.5507	−0.969661
$367$	−9.02038	−0.470860	−0.235430	−	0.971891i	$-0.575650\pi$
$367$	−9.02038	−0.470860	−0.235430	+	0.971891i	$0.575650\pi$
$368$	7.61037	0.396718
$369$	5.70431	0.296954
$370$	19.2169	0.999040
$371$	−8.61726	−0.447386
$372$	−5.63356	−0.292086
$373$	−7.40614	−0.383475	−0.191738	−	0.981446i	$-0.561412\pi$
$373$	−7.40614	−0.383475	−0.191738	+	0.981446i	$0.561412\pi$
$374$	4.07987	0.210965
$375$	44.9359	2.32048
$376$	−9.67572	−0.498987
$377$	0.837593	0.0431382
$378$	−5.65669	−0.290949
$379$	−8.44103	−0.433587	−0.216793	−	0.976218i	$-0.569560\pi$
$379$	−8.44103	−0.433587	−0.216793	+	0.976218i	$0.569560\pi$
$380$	−23.1972	−1.18999
$381$	22.4417	1.14972
$382$	8.28616	0.423957
$383$	−12.9405	−0.661227	−0.330613	−	0.943766i	$-0.607256\pi$
$383$	−12.9405	−0.661227	−0.330613	+	0.943766i	$0.607256\pi$
$384$	−1.42043	−0.0724858
$385$	−12.1662	−0.620045
$386$	8.48558	0.431905
$387$	−2.06498	−0.104969
$388$	−5.30191	−0.269164
$389$	−18.0004	−0.912659	−0.456329	−	0.889811i	$-0.650836\pi$
$389$	−18.0004	−0.912659	−0.456329	+	0.889811i	$0.650836\pi$
$390$	4.73414	0.239723
$391$	−10.6919	−0.540711
$392$	1.00000	0.0505076
$393$	7.93967	0.400503
$394$	−9.02646	−0.454747
$395$	−32.5696	−1.63876
$396$	2.85287	0.143362
$397$	−9.00451	−0.451923	−0.225962	−	0.974136i	$-0.572552\pi$
$397$	−9.00451	−0.451923	−0.225962	+	0.974136i	$0.572552\pi$
$398$	−5.75920	−0.288683
$399$	7.86503	0.393744
$400$	12.5513	0.627564
$401$	−23.9040	−1.19371	−0.596855	−	0.802349i	$-0.703583\pi$
$401$	−23.9040	−1.19371	−0.596855	+	0.802349i	$0.703583\pi$
$402$	7.49810	0.373971
$403$	3.15524	0.157174
$404$	−11.6176	−0.577999
$405$	21.3147	1.05914
$406$	−1.05285	−0.0522519
$407$	13.3207	0.660285
$408$	1.99557	0.0987953
$409$	24.7746	1.22502	0.612512	−	0.790461i	$-0.290159\pi$
$409$	24.7746	1.22502	0.612512	+	0.790461i	$0.290159\pi$
$410$	24.3262	1.20138
$411$	5.10761	0.251940
$412$	−6.30990	−0.310866
$413$	8.46584	0.416577
$414$	−7.47634	−0.367442
$415$	60.4677	2.96824
$416$	0.795551	0.0390051
$417$	23.9139	1.17107
$418$	−16.0798	−0.786489
$419$	8.81396	0.430590	0.215295	−	0.976549i	$-0.430929\pi$
$419$	8.81396	0.430590	0.215295	+	0.976549i	$0.430929\pi$
$420$	−5.95077	−0.290368
$421$	−22.2244	−1.08315	−0.541574	−	0.840653i	$-0.682172\pi$
$421$	−22.2244	−1.08315	−0.541574	+	0.840653i	$0.682172\pi$
$422$	2.65728	0.129354
$423$	9.50532	0.462165
$424$	8.61726	0.418491
$425$	−17.6334	−0.855345
$426$	19.5550	0.947444
$427$	−13.0600	−0.632015
$428$	8.87533	0.429005
$429$	3.28160	0.158437
$430$	−8.80617	−0.424671
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.65669	0.272158
$433$	−30.9731	−1.48847	−0.744236	−	0.667916i	$-0.767186\pi$
$433$	−30.9731	−1.48847	−0.744236	+	0.667916i	$0.767186\pi$
$434$	−3.96610	−0.190379
$435$	6.26524	0.300395
$436$	14.9587	0.716393
$437$	42.1393	2.01580
$438$	−9.89360	−0.472734
$439$	13.3840	0.638783	0.319392	−	0.947623i	$-0.396521\pi$
$439$	13.3840	0.638783	0.319392	+	0.947623i	$0.396521\pi$
$440$	12.1662	0.579999
$441$	−0.982389	−0.0467804
$442$	−1.11768	−0.0531624
$443$	−20.3069	−0.964812	−0.482406	−	0.875948i	$-0.660237\pi$
$443$	−20.3069	−0.964812	−0.482406	+	0.875948i	$0.660237\pi$
$444$	6.51551	0.309212
$445$	1.97569	0.0936568
$446$	16.2716	0.770481
$447$	6.34751	0.300227
$448$	−1.00000	−0.0472456
$449$	−34.7231	−1.63868	−0.819341	−	0.573306i	$-0.805661\pi$
$449$	−34.7231	−1.63868	−0.819341	+	0.573306i	$0.805661\pi$
$450$	−12.3302	−0.581253
$451$	16.8624	0.794017
$452$	12.0505	0.566807
$453$	−25.8898	−1.21641
$454$	16.0171	0.751719
$455$	3.33290	0.156249
$456$	−7.86503	−0.368314
$457$	−23.9406	−1.11989	−0.559947	−	0.828528i	$-0.689179\pi$
$457$	−23.9406	−1.11989	−0.559947	+	0.828528i	$0.689179\pi$
$458$	−22.4425	−1.04867
$459$	−7.94712	−0.370940
$460$	−31.8831	−1.48656
$461$	−21.1707	−0.986017	−0.493008	−	0.870025i	$-0.664103\pi$
$461$	−21.1707	−0.986017	−0.493008	+	0.870025i	$0.664103\pi$
$462$	−4.12494	−0.191910
$463$	28.0842	1.30518	0.652591	−	0.757710i	$-0.273682\pi$
$463$	28.0842	1.30518	0.652591	+	0.757710i	$0.273682\pi$
$464$	1.05285	0.0488771
$465$	23.6014	1.09449
$466$	28.4884	1.31970
$467$	−14.2553	−0.659659	−0.329829	−	0.944041i	$-0.606991\pi$
$467$	−14.2553	−0.659659	−0.329829	+	0.944041i	$0.606991\pi$
$468$	−0.781541	−0.0361268
$469$	5.27877	0.243751
$470$	40.5357	1.86977
$471$	10.7392	0.494834
$472$	−8.46584	−0.389672
$473$	−6.10424	−0.280673
$474$	−11.0427	−0.507210
$475$	69.4976	3.18877
$476$	1.40491	0.0643938
$477$	−8.46551	−0.387609
$478$	10.9588	0.501243
$479$	−17.3273	−0.791703	−0.395851	−	0.918315i	$-0.629550\pi$
$479$	−17.3273	−0.791703	−0.395851	+	0.918315i	$0.629550\pi$
$480$	5.95077	0.271614
$481$	−3.64920	−0.166389
$482$	30.3573	1.38274
$483$	10.8100	0.491871
$484$	−2.56669	−0.116668
$485$	22.2120	1.00859
$486$	−9.74331	−0.441965
$487$	−8.66941	−0.392849	−0.196424	−	0.980519i	$-0.562933\pi$
$487$	−8.66941	−0.392849	−0.196424	+	0.980519i	$0.562933\pi$
$488$	13.0600	0.591196
$489$	−11.7250	−0.530221
$490$	−4.18942	−0.189259
$491$	−17.0421	−0.769101	−0.384551	−	0.923104i	$-0.625644\pi$
$491$	−17.0421	−0.769101	−0.384551	+	0.923104i	$0.625644\pi$
$492$	8.24780	0.371839
$493$	−1.47915	−0.0666176
$494$	4.40504	0.198192
$495$	−11.9519	−0.537198
$496$	3.96610	0.178083
$497$	13.7670	0.617535
$498$	20.5016	0.918698
$499$	−43.9309	−1.96662	−0.983309	−	0.181945i	$-0.941761\pi$
$499$	−43.9309	−1.96662	−0.983309	+	0.181945i	$0.941761\pi$
$500$	−31.6355	−1.41478
$501$	17.2826	0.772132
$502$	5.00983	0.223599
$503$	−14.1742	−0.631996	−0.315998	−	0.948760i	$-0.602339\pi$
$503$	−14.1742	−0.631996	−0.315998	+	0.948760i	$0.602339\pi$
$504$	0.982389	0.0437591
$505$	48.6712	2.16584
$506$	−22.1006	−0.982493
$507$	17.5666	0.780158
$508$	−15.7992	−0.700978
$509$	39.5691	1.75387	0.876935	−	0.480609i	$-0.159584\pi$
$509$	39.5691	1.75387	0.876935	+	0.480609i	$0.159584\pi$
$510$	−8.36028	−0.370199
$511$	−6.96523	−0.308124
$512$	1.00000	0.0441942
$513$	31.3216	1.38288
$514$	24.3975	1.07613
$515$	26.4348	1.16486
$516$	−2.98574	−0.131440
$517$	28.0984	1.23577
$518$	4.58701	0.201542
$519$	12.0427	0.528617
$520$	−3.33290	−0.146157
$521$	−10.0572	−0.440615	−0.220308	−	0.975430i	$-0.570706\pi$
$521$	−10.0572	−0.440615	−0.220308	+	0.975430i	$0.570706\pi$
$522$	−1.03430	−0.0452703
$523$	−30.8316	−1.34817	−0.674087	−	0.738652i	$-0.735463\pi$
$523$	−30.8316	−1.34817	−0.674087	+	0.738652i	$0.735463\pi$
$524$	−5.58964	−0.244184
$525$	17.8282	0.778085
$526$	12.0593	0.525810
$527$	−5.57201	−0.242720
$528$	4.12494	0.179515
$529$	34.9177	1.51816
$530$	−36.1014	−1.56814
$531$	8.31675	0.360916
$532$	−5.53709	−0.240063
$533$	−4.61942	−0.200089
$534$	0.669859	0.0289876
$535$	−37.1825	−1.60754
$536$	−5.27877	−0.228008
$537$	−28.0438	−1.21018
$538$	9.30339	0.401098
$539$	−2.90402	−0.125085
$540$	−23.6983	−1.01981
$541$	−18.1370	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$541$	−18.1370	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$542$	−19.7891	−0.850013
$543$	14.0562	0.603209
$544$	−1.40491	−0.0602349
$545$	−62.6685	−2.68442
$546$	1.13002	0.0483605
$547$	−17.1323	−0.732523	−0.366261	−	0.930512i	$-0.619362\pi$
$547$	−17.1323	−0.732523	−0.366261	+	0.930512i	$0.619362\pi$
$548$	−3.59583	−0.153606
$549$	−12.8300	−0.547569
$550$	−36.4491	−1.55420
$551$	5.82970	0.248354
$552$	−10.8100	−0.460103
$553$	−7.77424	−0.330594
$554$	−13.1518	−0.558766
$555$	−27.2962	−1.15866
$556$	−16.8358	−0.713995
$557$	5.37042	0.227552	0.113776	−	0.993506i	$-0.463705\pi$
$557$	5.37042	0.227552	0.113776	+	0.993506i	$0.463705\pi$
$558$	−3.89626	−0.164942
$559$	1.67225	0.0707286
$560$	4.18942	0.177036
$561$	−5.79516	−0.244672
$562$	10.1091	0.426428
$563$	−1.87765	−0.0791335	−0.0395667	−	0.999217i	$-0.512598\pi$
$563$	−1.87765	−0.0791335	−0.0395667	+	0.999217i	$0.512598\pi$
$564$	13.7436	0.578712
$565$	−50.4846	−2.12390
$566$	−3.66000	−0.153841
$567$	5.08774	0.213665
$568$	−13.7670	−0.577651
$569$	−15.3943	−0.645364	−0.322682	−	0.946507i	$-0.604584\pi$
$569$	−15.3943	−0.645364	−0.322682	+	0.946507i	$0.604584\pi$
$570$	32.9500	1.38012
$571$	−30.2496	−1.26591	−0.632954	−	0.774189i	$-0.718158\pi$
$571$	−30.2496	−1.26591	−0.632954	+	0.774189i	$0.718158\pi$
$572$	−2.31029	−0.0965982
$573$	−11.7699	−0.491694
$574$	5.80656	0.242361
$575$	95.5199	3.98345
$576$	−0.982389	−0.0409329
$577$	−29.9676	−1.24757	−0.623785	−	0.781596i	$-0.714406\pi$
$577$	−29.9676	−1.24757	−0.623785	+	0.781596i	$0.714406\pi$
$578$	−15.0262	−0.625009
$579$	−12.0531	−0.500911
$580$	−4.41082	−0.183149
$581$	14.4334	0.598798
$582$	7.53098	0.312169
$583$	−25.0247	−1.03642
$584$	6.96523	0.288223
$585$	3.27421	0.135372
$586$	−19.7082	−0.814139
$587$	13.5283	0.558371	0.279185	−	0.960237i	$-0.409936\pi$
$587$	13.5283	0.558371	0.279185	+	0.960237i	$0.409936\pi$
$588$	−1.42043	−0.0585774
$589$	21.9607	0.904874
$590$	35.4670	1.46015
$591$	12.8214	0.527403
$592$	−4.58701	−0.188525
$593$	14.9665	0.614599	0.307299	−	0.951613i	$-0.400575\pi$
$593$	14.9665	0.614599	0.307299	+	0.951613i	$0.400575\pi$
$594$	−16.4271	−0.674013
$595$	−5.88575	−0.241292
$596$	−4.46874	−0.183047
$597$	8.18053	0.334807
$598$	6.05444	0.247584
$599$	19.5637	0.799352	0.399676	−	0.916657i	$-0.369123\pi$
$599$	19.5637	0.799352	0.399676	+	0.916657i	$0.369123\pi$
$600$	−17.8282	−0.727832
$601$	−18.5373	−0.756153	−0.378076	−	0.925774i	$-0.623414\pi$
$601$	−18.5373	−0.756153	−0.378076	+	0.925774i	$0.623414\pi$
$602$	−2.10200	−0.0856712
$603$	5.18580	0.211182
$604$	18.2268	0.741637
$605$	10.7530	0.437171
$606$	16.5020	0.670348
$607$	−27.3763	−1.11117	−0.555585	−	0.831460i	$-0.687506\pi$
$607$	−27.3763	−1.11117	−0.555585	+	0.831460i	$0.687506\pi$
$608$	5.53709	0.224559
$609$	1.49549	0.0606003
$610$	−54.7137	−2.21529
$611$	−7.69753	−0.311409
$612$	1.38017	0.0557899
$613$	2.44605	0.0987950	0.0493975	−	0.998779i	$-0.484270\pi$
$613$	2.44605	0.0987950	0.0493975	+	0.998779i	$0.484270\pi$
$614$	−5.79590	−0.233903
$615$	−34.5535	−1.39333
$616$	2.90402	0.117006
$617$	−15.4927	−0.623713	−0.311857	−	0.950129i	$-0.600951\pi$
$617$	−15.4927	−0.623713	−0.311857	+	0.950129i	$0.600951\pi$
$618$	8.96274	0.360534
$619$	3.60774	0.145007	0.0725036	−	0.997368i	$-0.476901\pi$
$619$	3.60774	0.145007	0.0725036	+	0.997368i	$0.476901\pi$
$620$	−16.6157	−0.667302
$621$	43.0495	1.72752
$622$	32.3672	1.29781
$623$	0.471590	0.0188939
$624$	−1.13002	−0.0452371
$625$	69.7783	2.79113
$626$	0.383732	0.0153370
$627$	22.8402	0.912149
$628$	−7.56052	−0.301698
$629$	6.44432	0.256952
$630$	−4.11565	−0.163971
$631$	38.8911	1.54823	0.774115	−	0.633045i	$-0.218195\pi$
$631$	38.8911	1.54823	0.774115	+	0.633045i	$0.218195\pi$
$632$	7.77424	0.309243
$633$	−3.77447	−0.150022
$634$	−10.9766	−0.435938
$635$	66.1897	2.62666
$636$	−12.2402	−0.485355
$637$	0.795551	0.0315209
$638$	−3.05748	−0.121047
$639$	13.5246	0.535023
$640$	−4.18942	−0.165602
$641$	−37.4668	−1.47985	−0.739924	−	0.672690i	$-0.765139\pi$
$641$	−37.4668	−1.47985	−0.739924	+	0.672690i	$0.765139\pi$
$642$	−12.6068	−0.497549
$643$	−8.70836	−0.343424	−0.171712	−	0.985147i	$-0.554930\pi$
$643$	−8.70836	−0.343424	−0.171712	+	0.985147i	$0.554930\pi$
$644$	−7.61037	−0.299891
$645$	12.5085	0.492523
$646$	−7.77910	−0.306065
$647$	5.03350	0.197887	0.0989436	−	0.995093i	$-0.468454\pi$
$647$	5.03350	0.197887	0.0989436	+	0.995093i	$0.468454\pi$
$648$	−5.08774	−0.199865
$649$	24.5849	0.965043
$650$	9.98519	0.391651
$651$	5.63356	0.220796
$652$	8.25454	0.323273
$653$	5.51141	0.215678	0.107839	−	0.994168i	$-0.465607\pi$
$653$	5.51141	0.215678	0.107839	+	0.994168i	$0.465607\pi$
$654$	−21.2478	−0.830854
$655$	23.4174	0.914992
$656$	−5.80656	−0.226708
$657$	−6.84257	−0.266954
$658$	9.67572	0.377199
$659$	−28.3934	−1.10605	−0.553025	−	0.833165i	$-0.686526\pi$
$659$	−28.3934	−1.10605	−0.553025	+	0.833165i	$0.686526\pi$
$660$	−17.2811	−0.672667
$661$	−22.6014	−0.879093	−0.439547	−	0.898220i	$-0.644861\pi$
$661$	−22.6014	−0.879093	−0.439547	+	0.898220i	$0.644861\pi$
$662$	4.59344	0.178529
$663$	1.58758	0.0616564
$664$	−14.4334	−0.560125
$665$	23.1972	0.899550
$666$	4.50623	0.174613
$667$	8.01255	0.310247
$668$	−12.1672	−0.470764
$669$	−23.1126	−0.893583
$670$	22.1150	0.854377
$671$	−37.9263	−1.46413
$672$	1.42043	0.0547941
$673$	28.1544	1.08527	0.542637	−	0.839968i	$-0.317426\pi$
$673$	28.1544	1.08527	0.542637	+	0.839968i	$0.317426\pi$
$674$	10.1707	0.391762
$675$	70.9987	2.73274
$676$	−12.3671	−0.475658
$677$	35.7255	1.37304	0.686521	−	0.727110i	$-0.259137\pi$
$677$	35.7255	1.37304	0.686521	+	0.727110i	$0.259137\pi$
$678$	−17.1168	−0.657367
$679$	5.30191	0.203469
$680$	5.88575	0.225708
$681$	−22.7511	−0.871823
$682$	−11.5176	−0.441033
$683$	−28.3095	−1.08323	−0.541617	−	0.840626i	$-0.682188\pi$
$683$	−28.3095	−1.08323	−0.541617	+	0.840626i	$0.682188\pi$
$684$	−5.43958	−0.207988
$685$	15.0645	0.575584
$686$	−1.00000	−0.0381802
$687$	31.8779	1.21622
$688$	2.10200	0.0801380
$689$	6.85548	0.261173
$690$	45.2876	1.72407
$691$	13.7658	0.523675	0.261838	−	0.965112i	$-0.415671\pi$
$691$	13.7658	0.523675	0.261838	+	0.965112i	$0.415671\pi$
$692$	−8.47824	−0.322294
$693$	−2.85287	−0.108372
$694$	−28.6356	−1.08699
$695$	70.5321	2.67544
$696$	−1.49549	−0.0566864
$697$	8.15768	0.308994
$698$	−8.41578	−0.318542
$699$	−40.4656	−1.53055
$700$	−12.5513	−0.474394
$701$	−44.6470	−1.68629	−0.843147	−	0.537683i	$-0.819300\pi$
$701$	−44.6470	−1.68629	−0.843147	+	0.537683i	$0.819300\pi$
$702$	4.50019	0.169849
$703$	−25.3987	−0.957929
$704$	−2.90402	−0.109449
$705$	−57.5780	−2.16851
$706$	1.67383	0.0629955
$707$	11.6176	0.436926
$708$	12.0251	0.451931
$709$	17.7218	0.665558	0.332779	−	0.943005i	$-0.392014\pi$
$709$	17.7218	0.665558	0.332779	+	0.943005i	$0.392014\pi$
$710$	57.6758	2.16454
$711$	−7.63733	−0.286422
$712$	−0.471590	−0.0176736
$713$	30.1835	1.13038
$714$	−1.99557	−0.0746822
$715$	9.67880	0.361967
$716$	19.7432	0.737839
$717$	−15.5661	−0.581328
$718$	−26.3319	−0.982699
$719$	34.5605	1.28889	0.644444	−	0.764651i	$-0.277089\pi$
$719$	34.5605	1.28889	0.644444	+	0.764651i	$0.277089\pi$
$720$	4.11565	0.153381
$721$	6.30990	0.234993
$722$	11.6594	0.433918
$723$	−43.1203	−1.60366
$724$	−9.89576	−0.367773
$725$	13.2146	0.490777
$726$	3.64580	0.135308
$727$	27.8674	1.03354	0.516772	−	0.856123i	$-0.327133\pi$
$727$	27.8674	1.03354	0.516772	+	0.856123i	$0.327133\pi$
$728$	−0.795551	−0.0294851
$729$	29.1029	1.07788
$730$	−29.1803	−1.08001
$731$	−2.95312	−0.109225
$732$	−18.5507	−0.685654
$733$	−18.7690	−0.693248	−0.346624	−	0.938004i	$-0.612672\pi$
$733$	−18.7690	−0.693248	−0.346624	+	0.938004i	$0.612672\pi$
$734$	−9.02038	−0.332948
$735$	5.95077	0.219497
$736$	7.61037	0.280522
$737$	15.3296	0.564674
$738$	5.70431	0.209978
$739$	−17.6933	−0.650860	−0.325430	−	0.945566i	$-0.605509\pi$
$739$	−17.6933	−0.650860	−0.325430	+	0.945566i	$0.605509\pi$
$740$	19.2169	0.706428
$741$	−6.25704	−0.229858
$742$	−8.61726	−0.316350
$743$	41.6015	1.52621	0.763105	−	0.646274i	$-0.223674\pi$
$743$	41.6015	1.52621	0.763105	+	0.646274i	$0.223674\pi$
$744$	−5.63356	−0.206536
$745$	18.7214	0.685901
$746$	−7.40614	−0.271158
$747$	14.1792	0.518791
$748$	4.07987	0.149175
$749$	−8.87533	−0.324298
$750$	44.9359	1.64083
$751$	44.8403	1.63624	0.818122	−	0.575044i	$-0.195015\pi$
$751$	44.8403	1.63624	0.818122	+	0.575044i	$0.195015\pi$
$752$	−9.67572	−0.352837
$753$	−7.11609	−0.259325
$754$	0.837593	0.0305033
$755$	−76.3597	−2.77901
$756$	−5.65669	−0.205732
$757$	−30.1582	−1.09612	−0.548060	−	0.836439i	$-0.684633\pi$
$757$	−30.1582	−1.09612	−0.548060	+	0.836439i	$0.684633\pi$
$758$	−8.44103	−0.306592
$759$	31.3923	1.13947
$760$	−23.1972	−0.841452
$761$	−14.3418	−0.519891	−0.259946	−	0.965623i	$-0.583705\pi$
$761$	−14.3418	−0.519891	−0.259946	+	0.965623i	$0.583705\pi$
$762$	22.4417	0.812976
$763$	−14.9587	−0.541542
$764$	8.28616	0.299783
$765$	−5.78210	−0.209052
$766$	−12.9405	−0.467558
$767$	−6.73501	−0.243187
$768$	−1.42043	−0.0512552
$769$	12.6554	0.456365	0.228182	−	0.973618i	$-0.426722\pi$
$769$	12.6554	0.456365	0.228182	+	0.973618i	$0.426722\pi$
$770$	−12.1662	−0.438438
$771$	−34.6548	−1.24806
$772$	8.48558	0.305403
$773$	15.8593	0.570420	0.285210	−	0.958465i	$-0.407937\pi$
$773$	15.8593	0.570420	0.285210	+	0.958465i	$0.407937\pi$
$774$	−2.06498	−0.0742243
$775$	49.7797	1.78814
$776$	−5.30191	−0.190328
$777$	−6.51551	−0.233742
$778$	−18.0004	−0.645347
$779$	−32.1515	−1.15195
$780$	4.73414	0.169510
$781$	39.9796	1.43058
$782$	−10.6919	−0.382340
$783$	5.95562	0.212837
$784$	1.00000	0.0357143
$785$	31.6742	1.13050
$786$	7.93967	0.283198
$787$	−11.5326	−0.411091	−0.205546	−	0.978648i	$-0.565897\pi$
$787$	−11.5326	−0.411091	−0.205546	+	0.978648i	$0.565897\pi$
$788$	−9.02646	−0.321554
$789$	−17.1293	−0.609820
$790$	−32.5696	−1.15877
$791$	−12.0505	−0.428466
$792$	2.85287	0.101372
$793$	10.3899	0.368955
$794$	−9.00451	−0.319558
$795$	51.2793	1.81869
$796$	−5.75920	−0.204130
$797$	−5.48806	−0.194397	−0.0971986	−	0.995265i	$-0.530988\pi$
$797$	−5.48806	−0.194397	−0.0971986	+	0.995265i	$0.530988\pi$
$798$	7.86503	0.278419
$799$	13.5935	0.480903
$800$	12.5513	0.443755
$801$	0.463285	0.0163694
$802$	−23.9040	−0.844081
$803$	−20.2271	−0.713800
$804$	7.49810	0.264438
$805$	31.8831	1.12373
$806$	3.15524	0.111139
$807$	−13.2148	−0.465182
$808$	−11.6176	−0.408707
$809$	−9.45395	−0.332383	−0.166192	−	0.986093i	$-0.553147\pi$
$809$	−9.45395	−0.332383	−0.166192	+	0.986093i	$0.553147\pi$
$810$	21.3147	0.748923
$811$	17.6311	0.619111	0.309555	−	0.950881i	$-0.399820\pi$
$811$	17.6311	0.619111	0.309555	+	0.950881i	$0.399820\pi$
$812$	−1.05285	−0.0369476
$813$	28.1089	0.985822
$814$	13.3207	0.466892
$815$	−34.5818	−1.21135
$816$	1.99557	0.0698588
$817$	11.6390	0.407196
$818$	24.7746	0.866223
$819$	0.781541	0.0273093
$820$	24.3262	0.849507
$821$	−23.8491	−0.832341	−0.416170	−	0.909287i	$-0.636628\pi$
$821$	−23.8491	−0.832341	−0.416170	+	0.909287i	$0.636628\pi$
$822$	5.10761	0.178149
$823$	−12.8595	−0.448254	−0.224127	−	0.974560i	$-0.571953\pi$
$823$	−12.8595	−0.448254	−0.224127	+	0.974560i	$0.571953\pi$
$824$	−6.30990	−0.219816
$825$	51.7733	1.80251
$826$	8.46584	0.294564
$827$	28.1895	0.980245	0.490123	−	0.871654i	$-0.336952\pi$
$827$	28.1895	0.980245	0.490123	+	0.871654i	$0.336952\pi$
$828$	−7.47634	−0.259821
$829$	−0.387066	−0.0134434	−0.00672168	−	0.999977i	$-0.502140\pi$
$829$	−0.387066	−0.0134434	−0.00672168	+	0.999977i	$0.502140\pi$
$830$	60.4677	2.09886
$831$	18.6811	0.648041
$832$	0.795551	0.0275808
$833$	−1.40491	−0.0486771
$834$	23.9139	0.828072
$835$	50.9737	1.76402
$836$	−16.0798	−0.556132
$837$	22.4350	0.775467
$838$	8.81396	0.304473
$839$	18.0993	0.624856	0.312428	−	0.949941i	$-0.398858\pi$
$839$	18.0993	0.624856	0.312428	+	0.949941i	$0.398858\pi$
$840$	−5.95077	−0.205321
$841$	−27.8915	−0.961776
$842$	−22.2244	−0.765902
$843$	−14.3593	−0.494560
$844$	2.65728	0.0914673
$845$	51.8110	1.78235
$846$	9.50532	0.326800
$847$	2.56669	0.0881927
$848$	8.61726	0.295918
$849$	5.19875	0.178421
$850$	−17.6334	−0.604820
$851$	−34.9088	−1.19666
$852$	19.5550	0.669944
$853$	−7.21737	−0.247118	−0.123559	−	0.992337i	$-0.539431\pi$
$853$	−7.21737	−0.247118	−0.123559	+	0.992337i	$0.539431\pi$
$854$	−13.0600	−0.446902
$855$	22.7887	0.779357
$856$	8.87533	0.303353
$857$	52.5943	1.79659	0.898293	−	0.439398i	$-0.144808\pi$
$857$	52.5943	1.79659	0.898293	+	0.439398i	$0.144808\pi$
$858$	3.28160	0.112032
$859$	−18.1880	−0.620568	−0.310284	−	0.950644i	$-0.600424\pi$
$859$	−18.1880	−0.620568	−0.310284	+	0.950644i	$0.600424\pi$
$860$	−8.80617	−0.300288
$861$	−8.24780	−0.281084
$862$	1.00000	0.0340601
$863$	−54.4038	−1.85193	−0.925964	−	0.377613i	$-0.876745\pi$
$863$	−54.4038	−1.85193	−0.925964	+	0.377613i	$0.876745\pi$
$864$	5.65669	0.192445
$865$	35.5190	1.20768
$866$	−30.9731	−1.05251
$867$	21.3437	0.724869
$868$	−3.96610	−0.134618
$869$	−22.5765	−0.765856
$870$	6.26524	0.212412
$871$	−4.19953	−0.142296
$872$	14.9587	0.506567
$873$	5.20854	0.176282
$874$	42.1393	1.42538
$875$	31.6355	1.06948
$876$	−9.89360	−0.334274
$877$	−45.0226	−1.52031	−0.760153	−	0.649744i	$-0.774876\pi$
$877$	−45.0226	−1.52031	−0.760153	+	0.649744i	$0.774876\pi$
$878$	13.3840	0.451688
$879$	27.9941	0.944217
$880$	12.1662	0.410121
$881$	19.9411	0.671834	0.335917	−	0.941892i	$-0.390954\pi$
$881$	19.9411	0.671834	0.335917	+	0.941892i	$0.390954\pi$
$882$	−0.982389	−0.0330788
$883$	54.2914	1.82705	0.913525	−	0.406783i	$-0.133349\pi$
$883$	54.2914	1.82705	0.913525	+	0.406783i	$0.133349\pi$
$884$	−1.11768	−0.0375915
$885$	−50.3783	−1.69345
$886$	−20.3069	−0.682225
$887$	25.2180	0.846737	0.423369	−	0.905958i	$-0.360848\pi$
$887$	25.2180	0.846737	0.423369	+	0.905958i	$0.360848\pi$
$888$	6.51551	0.218646
$889$	15.7992	0.529890
$890$	1.97569	0.0662253
$891$	14.7749	0.494977
$892$	16.2716	0.544812
$893$	−53.5754	−1.79283
$894$	6.34751	0.212293
$895$	−82.7128	−2.76478
$896$	−1.00000	−0.0334077
$897$	−8.59989	−0.287142
$898$	−34.7231	−1.15872
$899$	4.17569	0.139267
$900$	−12.3302	−0.411008
$901$	−12.1065	−0.403325
$902$	16.8624	0.561455
$903$	2.98574	0.0993591
$904$	12.0505	0.400793
$905$	41.4575	1.37809
$906$	−25.8898	−0.860131
$907$	49.6029	1.64704	0.823518	−	0.567290i	$-0.192008\pi$
$907$	49.6029	1.64704	0.823518	+	0.567290i	$0.192008\pi$
$908$	16.0171	0.531545
$909$	11.4130	0.378547
$910$	3.33290	0.110485
$911$	−6.22170	−0.206134	−0.103067	−	0.994674i	$-0.532866\pi$
$911$	−6.22170	−0.206134	−0.103067	+	0.994674i	$0.532866\pi$
$912$	−7.86503	−0.260437
$913$	41.9148	1.38718
$914$	−23.9406	−0.791885
$915$	77.7168	2.56924
$916$	−22.4425	−0.741520
$917$	5.58964	0.184586
$918$	−7.94712	−0.262294
$919$	12.8605	0.424227	0.212114	−	0.977245i	$-0.431965\pi$
$919$	12.8605	0.424227	0.212114	+	0.977245i	$0.431965\pi$
$920$	−31.8831	−1.05115
$921$	8.23264	0.271275
$922$	−21.1707	−0.697219
$923$	−10.9524	−0.360501
$924$	−4.12494	−0.135701
$925$	−57.5728	−1.89298
$926$	28.0842	0.922904
$927$	6.19877	0.203594
$928$	1.05285	0.0345614
$929$	−27.9643	−0.917478	−0.458739	−	0.888571i	$-0.651699\pi$
$929$	−27.9643	−0.917478	−0.458739	+	0.888571i	$0.651699\pi$
$930$	23.6014	0.773919
$931$	5.53709	0.181471
$932$	28.4884	0.933167
$933$	−45.9752	−1.50516
$934$	−14.2553	−0.466449
$935$	−17.0923	−0.558979
$936$	−0.781541	−0.0255455
$937$	−2.61195	−0.0853286	−0.0426643	−	0.999089i	$-0.513585\pi$
$937$	−2.61195	−0.0853286	−0.0426643	+	0.999089i	$0.513585\pi$
$938$	5.27877	0.172358
$939$	−0.545062	−0.0177874
$940$	40.5357	1.32213
$941$	2.83645	0.0924656	0.0462328	−	0.998931i	$-0.485278\pi$
$941$	2.83645	0.0924656	0.0462328	+	0.998931i	$0.485278\pi$
$942$	10.7392	0.349901
$943$	−44.1901	−1.43903
$944$	−8.46584	−0.275540
$945$	23.6983	0.770905
$946$	−6.10424	−0.198466
$947$	32.7242	1.06339	0.531697	−	0.846935i	$-0.321555\pi$
$947$	32.7242	1.06339	0.531697	+	0.846935i	$0.321555\pi$
$948$	−11.0427	−0.358652
$949$	5.54120	0.179875
$950$	69.4976	2.25480
$951$	15.5915	0.505589
$952$	1.40491	0.0455333
$953$	27.8318	0.901561	0.450781	−	0.892635i	$-0.351146\pi$
$953$	27.8318	0.901561	0.450781	+	0.892635i	$0.351146\pi$
$954$	−8.46551	−0.274081
$955$	−34.7143	−1.12333
$956$	10.9588	0.354432
$957$	4.34293	0.140387
$958$	−17.3273	−0.559818
$959$	3.59583	0.116115
$960$	5.95077	0.192060
$961$	−15.2700	−0.492582
$962$	−3.64920	−0.117655
$963$	−8.71903	−0.280967
$964$	30.3573	0.977743
$965$	−35.5497	−1.14439
$966$	10.8100	0.347805
$967$	−33.4858	−1.07683	−0.538416	−	0.842679i	$-0.680977\pi$
$967$	−33.4858	−1.07683	−0.538416	+	0.842679i	$0.680977\pi$
$968$	−2.56669	−0.0824967
$969$	11.0496	0.354966
$970$	22.2120	0.713183
$971$	−46.3524	−1.48752	−0.743760	−	0.668447i	$-0.766960\pi$
$971$	−46.3524	−1.48752	−0.743760	+	0.668447i	$0.766960\pi$
$972$	−9.74331	−0.312517
$973$	16.8358	0.539729
$974$	−8.66941	−0.277786
$975$	−14.1832	−0.454227
$976$	13.0600	0.418039
$977$	−56.6111	−1.81115	−0.905576	−	0.424185i	$-0.860561\pi$
$977$	−56.6111	−1.81115	−0.905576	+	0.424185i	$0.860561\pi$
$978$	−11.7250	−0.374923
$979$	1.36951	0.0437696
$980$	−4.18942	−0.133826
$981$	−14.6953	−0.469185
$982$	−17.0421	−0.543837
$983$	13.3687	0.426397	0.213198	−	0.977009i	$-0.431612\pi$
$983$	13.3687	0.426397	0.213198	+	0.977009i	$0.431612\pi$
$984$	8.24780	0.262930
$985$	37.8157	1.20491
$986$	−1.47915	−0.0471058
$987$	−13.7436	−0.437465
$988$	4.40504	0.140143
$989$	15.9970	0.508675
$990$	−11.9519	−0.379856
$991$	39.3319	1.24942	0.624709	−	0.780857i	$-0.285218\pi$
$991$	39.3319	1.24942	0.624709	+	0.780857i	$0.285218\pi$
$992$	3.96610	0.125924
$993$	−6.52465	−0.207053
$994$	13.7670	0.436663
$995$	24.1278	0.764901
$996$	20.5016	0.649618
$997$	−25.7633	−0.815931	−0.407965	−	0.912997i	$-0.633762\pi$
$997$	−25.7633	−0.815931	−0.407965	+	0.912997i	$0.633762\pi$
$998$	−43.9309	−1.39061
$999$	−25.9473	−0.820936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.7	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.42043 q^{3} +1.00000 q^{4} -4.18942 q^{5} -1.42043 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.982389 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.42043 q^{3} +1.00000 q^{4} -4.18942 q^{5} -1.42043 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.982389 q^{9} -4.18942 q^{10} -2.90402 q^{11} -1.42043 q^{12} +0.795551 q^{13} -1.00000 q^{14} +5.95077 q^{15} +1.00000 q^{16} -1.40491 q^{17} -0.982389 q^{18} +5.53709 q^{19} -4.18942 q^{20} +1.42043 q^{21} -2.90402 q^{22} +7.61037 q^{23} -1.42043 q^{24} +12.5513 q^{25} +0.795551 q^{26} +5.65669 q^{27} -1.00000 q^{28} +1.05285 q^{29} +5.95077 q^{30} +3.96610 q^{31} +1.00000 q^{32} +4.12494 q^{33} -1.40491 q^{34} +4.18942 q^{35} -0.982389 q^{36} -4.58701 q^{37} +5.53709 q^{38} -1.13002 q^{39} -4.18942 q^{40} -5.80656 q^{41} +1.42043 q^{42} +2.10200 q^{43} -2.90402 q^{44} +4.11565 q^{45} +7.61037 q^{46} -9.67572 q^{47} -1.42043 q^{48} +1.00000 q^{49} +12.5513 q^{50} +1.99557 q^{51} +0.795551 q^{52} +8.61726 q^{53} +5.65669 q^{54} +12.1662 q^{55} -1.00000 q^{56} -7.86503 q^{57} +1.05285 q^{58} -8.46584 q^{59} +5.95077 q^{60} +13.0600 q^{61} +3.96610 q^{62} +0.982389 q^{63} +1.00000 q^{64} -3.33290 q^{65} +4.12494 q^{66} -5.27877 q^{67} -1.40491 q^{68} -10.8100 q^{69} +4.18942 q^{70} -13.7670 q^{71} -0.982389 q^{72} +6.96523 q^{73} -4.58701 q^{74} -17.8282 q^{75} +5.53709 q^{76} +2.90402 q^{77} -1.13002 q^{78} +7.77424 q^{79} -4.18942 q^{80} -5.08774 q^{81} -5.80656 q^{82} -14.4334 q^{83} +1.42043 q^{84} +5.88575 q^{85} +2.10200 q^{86} -1.49549 q^{87} -2.90402 q^{88} -0.471590 q^{89} +4.11565 q^{90} -0.795551 q^{91} +7.61037 q^{92} -5.63356 q^{93} -9.67572 q^{94} -23.1972 q^{95} -1.42043 q^{96} -5.30191 q^{97} +1.00000 q^{98} +2.85287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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