LMFDB - Embedded newform 6015.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60633 q^{2} +1.00000 q^{3} +4.79297 q^{4} -1.00000 q^{5} -2.60633 q^{6} -3.84306 q^{7} -7.27940 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60633 q^{2} +1.00000 q^{3} +4.79297 q^{4} -1.00000 q^{5} -2.60633 q^{6} -3.84306 q^{7} -7.27940 q^{8} +1.00000 q^{9} +2.60633 q^{10} +1.93515 q^{11} +4.79297 q^{12} -2.50925 q^{13} +10.0163 q^{14} -1.00000 q^{15} +9.38661 q^{16} -5.96605 q^{17} -2.60633 q^{18} +0.0654556 q^{19} -4.79297 q^{20} -3.84306 q^{21} -5.04364 q^{22} +8.51674 q^{23} -7.27940 q^{24} +1.00000 q^{25} +6.53995 q^{26} +1.00000 q^{27} -18.4197 q^{28} -1.45014 q^{29} +2.60633 q^{30} -1.78409 q^{31} -9.90581 q^{32} +1.93515 q^{33} +15.5495 q^{34} +3.84306 q^{35} +4.79297 q^{36} +3.57930 q^{37} -0.170599 q^{38} -2.50925 q^{39} +7.27940 q^{40} +9.75108 q^{41} +10.0163 q^{42} +0.475605 q^{43} +9.27510 q^{44} -1.00000 q^{45} -22.1974 q^{46} +1.15362 q^{47} +9.38661 q^{48} +7.76913 q^{49} -2.60633 q^{50} -5.96605 q^{51} -12.0268 q^{52} +0.959226 q^{53} -2.60633 q^{54} -1.93515 q^{55} +27.9752 q^{56} +0.0654556 q^{57} +3.77954 q^{58} -5.91543 q^{59} -4.79297 q^{60} -5.37399 q^{61} +4.64992 q^{62} -3.84306 q^{63} +7.04462 q^{64} +2.50925 q^{65} -5.04364 q^{66} -9.36533 q^{67} -28.5951 q^{68} +8.51674 q^{69} -10.0163 q^{70} +14.2696 q^{71} -7.27940 q^{72} -7.18305 q^{73} -9.32884 q^{74} +1.00000 q^{75} +0.313727 q^{76} -7.43689 q^{77} +6.53995 q^{78} +2.26974 q^{79} -9.38661 q^{80} +1.00000 q^{81} -25.4146 q^{82} +2.50489 q^{83} -18.4197 q^{84} +5.96605 q^{85} -1.23958 q^{86} -1.45014 q^{87} -14.0867 q^{88} +14.4146 q^{89} +2.60633 q^{90} +9.64322 q^{91} +40.8204 q^{92} -1.78409 q^{93} -3.00671 q^{94} -0.0654556 q^{95} -9.90581 q^{96} +15.1589 q^{97} -20.2489 q^{98} +1.93515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - 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 $

$2$	−2.60633	−1.84296	−0.921478	−	0.388431i	$-0.873017\pi$
$2$	−2.60633	−1.84296	−0.921478	+	0.388431i	$0.873017\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.79297	2.39648
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.60633	−1.06403
$7$	−3.84306	−1.45254	−0.726271	−	0.687409i	$-0.758748\pi$
$7$	−3.84306	−1.45254	−0.726271	+	0.687409i	$0.758748\pi$
$8$	−7.27940	−2.57366
$9$	1.00000	0.333333
$10$	2.60633	0.824195
$11$	1.93515	0.583469	0.291734	−	0.956499i	$-0.405768\pi$
$11$	1.93515	0.583469	0.291734	+	0.956499i	$0.405768\pi$
$12$	4.79297	1.38361
$13$	−2.50925	−0.695942	−0.347971	−	0.937505i	$-0.613129\pi$
$13$	−2.50925	−0.695942	−0.347971	+	0.937505i	$0.613129\pi$
$14$	10.0163	2.67697
$15$	−1.00000	−0.258199
$16$	9.38661	2.34665
$17$	−5.96605	−1.44698	−0.723490	−	0.690335i	$-0.757463\pi$
$17$	−5.96605	−1.44698	−0.723490	+	0.690335i	$0.757463\pi$
$18$	−2.60633	−0.614318
$19$	0.0654556	0.0150165	0.00750827	−	0.999972i	$-0.497610\pi$
$19$	0.0654556	0.0150165	0.00750827	+	0.999972i	$0.497610\pi$
$20$	−4.79297	−1.07174
$21$	−3.84306	−0.838625
$22$	−5.04364	−1.07531
$23$	8.51674	1.77586	0.887931	−	0.459976i	$-0.152142\pi$
$23$	8.51674	1.77586	0.887931	+	0.459976i	$0.152142\pi$
$24$	−7.27940	−1.48590
$25$	1.00000	0.200000
$26$	6.53995	1.28259
$27$	1.00000	0.192450
$28$	−18.4197	−3.48099
$29$	−1.45014	−0.269284	−0.134642	−	0.990894i	$-0.542988\pi$
$29$	−1.45014	−0.269284	−0.134642	+	0.990894i	$0.542988\pi$
$30$	2.60633	0.475849
$31$	−1.78409	−0.320431	−0.160216	−	0.987082i	$-0.551219\pi$
$31$	−1.78409	−0.320431	−0.160216	+	0.987082i	$0.551219\pi$
$32$	−9.90581	−1.75112
$33$	1.93515	0.336866
$34$	15.5495	2.66672
$35$	3.84306	0.649596
$36$	4.79297	0.798828
$37$	3.57930	0.588433	0.294216	−	0.955739i	$-0.404941\pi$
$37$	3.57930	0.588433	0.294216	+	0.955739i	$0.404941\pi$
$38$	−0.170599	−0.0276748
$39$	−2.50925	−0.401802
$40$	7.27940	1.15097
$41$	9.75108	1.52286	0.761432	−	0.648245i	$-0.224497\pi$
$41$	9.75108	1.52286	0.761432	+	0.648245i	$0.224497\pi$
$42$	10.0163	1.54555
$43$	0.475605	0.0725291	0.0362645	−	0.999342i	$-0.488454\pi$
$43$	0.475605	0.0725291	0.0362645	+	0.999342i	$0.488454\pi$
$44$	9.27510	1.39827
$45$	−1.00000	−0.149071
$46$	−22.1974	−3.27283
$47$	1.15362	0.168273	0.0841363	−	0.996454i	$-0.473187\pi$
$47$	1.15362	0.168273	0.0841363	+	0.996454i	$0.473187\pi$
$48$	9.38661	1.35484
$49$	7.76913	1.10988
$50$	−2.60633	−0.368591
$51$	−5.96605	−0.835414
$52$	−12.0268	−1.66781
$53$	0.959226	0.131760	0.0658799	−	0.997828i	$-0.479015\pi$
$53$	0.959226	0.131760	0.0658799	+	0.997828i	$0.479015\pi$
$54$	−2.60633	−0.354677
$55$	−1.93515	−0.260935
$56$	27.9752	3.73834
$57$	0.0654556	0.00866980
$58$	3.77954	0.496278
$59$	−5.91543	−0.770124	−0.385062	−	0.922891i	$-0.625820\pi$
$59$	−5.91543	−0.770124	−0.385062	+	0.922891i	$0.625820\pi$
$60$	−4.79297	−0.618770
$61$	−5.37399	−0.688069	−0.344034	−	0.938957i	$-0.611794\pi$
$61$	−5.37399	−0.688069	−0.344034	+	0.938957i	$0.611794\pi$
$62$	4.64992	0.590540
$63$	−3.84306	−0.484180
$64$	7.04462	0.880578
$65$	2.50925	0.311235
$66$	−5.04364	−0.620829
$67$	−9.36533	−1.14416	−0.572079	−	0.820199i	$-0.693863\pi$
$67$	−9.36533	−1.14416	−0.572079	+	0.820199i	$0.693863\pi$
$68$	−28.5951	−3.46766
$69$	8.51674	1.02529
$70$	−10.0163	−1.19718
$71$	14.2696	1.69349	0.846747	−	0.531995i	$-0.178558\pi$
$71$	14.2696	1.69349	0.846747	+	0.531995i	$0.178558\pi$
$72$	−7.27940	−0.857886
$73$	−7.18305	−0.840712	−0.420356	−	0.907359i	$-0.638095\pi$
$73$	−7.18305	−0.840712	−0.420356	+	0.907359i	$0.638095\pi$
$74$	−9.32884	−1.08446
$75$	1.00000	0.115470
$76$	0.313727	0.0359869
$77$	−7.43689	−0.847513
$78$	6.53995	0.740503
$79$	2.26974	0.255366	0.127683	−	0.991815i	$-0.459246\pi$
$79$	2.26974	0.255366	0.127683	+	0.991815i	$0.459246\pi$
$80$	−9.38661	−1.04945
$81$	1.00000	0.111111
$82$	−25.4146	−2.80657
$83$	2.50489	0.274948	0.137474	−	0.990505i	$-0.456102\pi$
$83$	2.50489	0.274948	0.137474	+	0.990505i	$0.456102\pi$
$84$	−18.4197	−2.00975
$85$	5.96605	0.647109
$86$	−1.23958	−0.133668
$87$	−1.45014	−0.155471
$88$	−14.0867	−1.50165
$89$	14.4146	1.52794	0.763970	−	0.645252i	$-0.223247\pi$
$89$	14.4146	1.52794	0.763970	+	0.645252i	$0.223247\pi$
$90$	2.60633	0.274732
$91$	9.64322	1.01088
$92$	40.8204	4.25583
$93$	−1.78409	−0.185001
$94$	−3.00671	−0.310119
$95$	−0.0654556	−0.00671560
$96$	−9.90581	−1.01101
$97$	15.1589	1.53915	0.769576	−	0.638555i	$-0.220468\pi$
$97$	15.1589	1.53915	0.769576	+	0.638555i	$0.220468\pi$
$98$	−20.2489	−2.04545
$99$	1.93515	0.194490
$100$	4.79297	0.479297
$101$	10.2341	1.01833	0.509166	−	0.860669i	$-0.329954\pi$
$101$	10.2341	1.01833	0.509166	+	0.860669i	$0.329954\pi$
$102$	15.5495	1.53963
$103$	−3.21066	−0.316356	−0.158178	−	0.987411i	$-0.550562\pi$
$103$	−3.21066	−0.316356	−0.158178	+	0.987411i	$0.550562\pi$
$104$	18.2659	1.79112
$105$	3.84306	0.375044
$106$	−2.50006	−0.242828
$107$	11.7398	1.13493	0.567466	−	0.823397i	$-0.307924\pi$
$107$	11.7398	1.13493	0.567466	+	0.823397i	$0.307924\pi$
$108$	4.79297	0.461204
$109$	14.6839	1.40646	0.703231	−	0.710962i	$-0.251740\pi$
$109$	14.6839	1.40646	0.703231	+	0.710962i	$0.251740\pi$
$110$	5.04364	0.480892
$111$	3.57930	0.339732
$112$	−36.0733	−3.40861
$113$	−19.0971	−1.79651	−0.898253	−	0.439478i	$-0.855163\pi$
$113$	−19.0971	−1.79651	−0.898253	+	0.439478i	$0.855163\pi$
$114$	−0.170599	−0.0159781
$115$	−8.51674	−0.794190
$116$	−6.95047	−0.645335
$117$	−2.50925	−0.231981
$118$	15.4176	1.41930
$119$	22.9279	2.10180
$120$	7.27940	0.664516
$121$	−7.25520	−0.659564
$122$	14.0064	1.26808
$123$	9.75108	0.879226
$124$	−8.55106	−0.767908
$125$	−1.00000	−0.0894427
$126$	10.0163	0.892323
$127$	−4.08721	−0.362682	−0.181341	−	0.983420i	$-0.558044\pi$
$127$	−4.08721	−0.362682	−0.181341	+	0.983420i	$0.558044\pi$
$128$	1.45099	0.128251
$129$	0.475605	0.0418747
$130$	−6.53995	−0.573591
$131$	−17.9905	−1.57183	−0.785917	−	0.618332i	$-0.787809\pi$
$131$	−17.9905	−1.57183	−0.785917	+	0.618332i	$0.787809\pi$
$132$	9.27510	0.807294
$133$	−0.251550	−0.0218121
$134$	24.4092	2.10863
$135$	−1.00000	−0.0860663
$136$	43.4293	3.72403
$137$	−12.9510	−1.10648	−0.553240	−	0.833022i	$-0.686609\pi$
$137$	−12.9510	−1.10648	−0.553240	+	0.833022i	$0.686609\pi$
$138$	−22.1974	−1.88957
$139$	−1.66531	−0.141250	−0.0706250	−	0.997503i	$-0.522499\pi$
$139$	−1.66531	−0.141250	−0.0706250	+	0.997503i	$0.522499\pi$
$140$	18.4197	1.55675
$141$	1.15362	0.0971522
$142$	−37.1914	−3.12104
$143$	−4.85578	−0.406060
$144$	9.38661	0.782217
$145$	1.45014	0.120427
$146$	18.7214	1.54940
$147$	7.76913	0.640787
$148$	17.1555	1.41017
$149$	7.07251	0.579403	0.289701	−	0.957117i	$-0.406444\pi$
$149$	7.07251	0.579403	0.289701	+	0.957117i	$0.406444\pi$
$150$	−2.60633	−0.212806
$151$	−16.2264	−1.32048	−0.660241	−	0.751053i	$-0.729546\pi$
$151$	−16.2264	−1.32048	−0.660241	+	0.751053i	$0.729546\pi$
$152$	−0.476478	−0.0386474
$153$	−5.96605	−0.482326
$154$	19.3830	1.56193
$155$	1.78409	0.143301
$156$	−12.0268	−0.962912
$157$	−24.1159	−1.92466	−0.962331	−	0.271881i	$-0.912354\pi$
$157$	−24.1159	−1.92466	−0.962331	+	0.271881i	$0.912354\pi$
$158$	−5.91571	−0.470628
$159$	0.959226	0.0760716
$160$	9.90581	0.783123
$161$	−32.7303	−2.57951
$162$	−2.60633	−0.204773
$163$	−8.15755	−0.638949	−0.319474	−	0.947595i	$-0.603506\pi$
$163$	−8.15755	−0.638949	−0.319474	+	0.947595i	$0.603506\pi$
$164$	46.7366	3.64952
$165$	−1.93515	−0.150651
$166$	−6.52858	−0.506716
$167$	−2.28832	−0.177076	−0.0885378	−	0.996073i	$-0.528219\pi$
$167$	−2.28832	−0.177076	−0.0885378	+	0.996073i	$0.528219\pi$
$168$	27.9752	2.15833
$169$	−6.70365	−0.515665
$170$	−15.5495	−1.19259
$171$	0.0654556	0.00500551
$172$	2.27956	0.173815
$173$	−6.24740	−0.474981	−0.237490	−	0.971390i	$-0.576325\pi$
$173$	−6.24740	−0.474981	−0.237490	+	0.971390i	$0.576325\pi$
$174$	3.77954	0.286526
$175$	−3.84306	−0.290508
$176$	18.1645	1.36920
$177$	−5.91543	−0.444631
$178$	−37.5691	−2.81593
$179$	11.9312	0.891778	0.445889	−	0.895088i	$-0.352888\pi$
$179$	11.9312	0.891778	0.445889	+	0.895088i	$0.352888\pi$
$180$	−4.79297	−0.357247
$181$	−15.2857	−1.13617	−0.568087	−	0.822969i	$-0.692316\pi$
$181$	−15.2857	−1.13617	−0.568087	+	0.822969i	$0.692316\pi$
$182$	−25.1334	−1.86301
$183$	−5.37399	−0.397257
$184$	−61.9968	−4.57046
$185$	−3.57930	−0.263155
$186$	4.64992	0.340949
$187$	−11.5452	−0.844267
$188$	5.52926	0.403263
$189$	−3.84306	−0.279542
$190$	0.170599	0.0123766
$191$	−24.4899	−1.77203	−0.886015	−	0.463656i	$-0.846537\pi$
$191$	−24.4899	−1.77203	−0.886015	+	0.463656i	$0.846537\pi$
$192$	7.04462	0.508402
$193$	16.5769	1.19323	0.596617	−	0.802526i	$-0.296511\pi$
$193$	16.5769	1.19323	0.596617	+	0.802526i	$0.296511\pi$
$194$	−39.5091	−2.83659
$195$	2.50925	0.179691
$196$	37.2372	2.65980
$197$	−3.66465	−0.261095	−0.130548	−	0.991442i	$-0.541674\pi$
$197$	−3.66465	−0.261095	−0.130548	+	0.991442i	$0.541674\pi$
$198$	−5.04364	−0.358436
$199$	10.8807	0.771315	0.385657	−	0.922642i	$-0.373975\pi$
$199$	10.8807	0.771315	0.385657	+	0.922642i	$0.373975\pi$
$200$	−7.27940	−0.514732
$201$	−9.36533	−0.660579
$202$	−26.6735	−1.87674
$203$	5.57297	0.391146
$204$	−28.5951	−2.00206
$205$	−9.75108	−0.681045
$206$	8.36804	0.583029
$207$	8.51674	0.591954
$208$	−23.5534	−1.63313
$209$	0.126666	0.00876169
$210$	−10.0163	−0.691190
$211$	−24.3631	−1.67722	−0.838612	−	0.544729i	$-0.816632\pi$
$211$	−24.3631	−1.67722	−0.838612	+	0.544729i	$0.816632\pi$
$212$	4.59754	0.315760
$213$	14.2696	0.977740
$214$	−30.5979	−2.09163
$215$	−0.475605	−0.0324360
$216$	−7.27940	−0.495301
$217$	6.85635	0.465439
$218$	−38.2711	−2.59204
$219$	−7.18305	−0.485386
$220$	−9.27510	−0.625327
$221$	14.9703	1.00701
$222$	−9.32884	−0.626110
$223$	6.62122	0.443390	0.221695	−	0.975116i	$-0.428841\pi$
$223$	6.62122	0.443390	0.221695	+	0.975116i	$0.428841\pi$
$224$	38.0687	2.54357
$225$	1.00000	0.0666667
$226$	49.7735	3.31088
$227$	12.8092	0.850175	0.425087	−	0.905152i	$-0.360243\pi$
$227$	12.8092	0.850175	0.425087	+	0.905152i	$0.360243\pi$
$228$	0.313727	0.0207770
$229$	20.6079	1.36181	0.680903	−	0.732373i	$-0.261587\pi$
$229$	20.6079	1.36181	0.680903	+	0.732373i	$0.261587\pi$
$230$	22.1974	1.46366
$231$	−7.43689	−0.489312
$232$	10.5561	0.693045
$233$	9.54079	0.625038	0.312519	−	0.949911i	$-0.398827\pi$
$233$	9.54079	0.625038	0.312519	+	0.949911i	$0.398827\pi$
$234$	6.53995	0.427530
$235$	−1.15362	−0.0752538
$236$	−28.3525	−1.84559
$237$	2.26974	0.147436
$238$	−59.7577	−3.87352
$239$	−8.18806	−0.529642	−0.264821	−	0.964298i	$-0.585313\pi$
$239$	−8.18806	−0.529642	−0.264821	+	0.964298i	$0.585313\pi$
$240$	−9.38661	−0.605903
$241$	−1.50395	−0.0968782	−0.0484391	−	0.998826i	$-0.515425\pi$
$241$	−1.50395	−0.0968782	−0.0484391	+	0.998826i	$0.515425\pi$
$242$	18.9095	1.21555
$243$	1.00000	0.0641500
$244$	−25.7574	−1.64895
$245$	−7.76913	−0.496351
$246$	−25.4146	−1.62037
$247$	−0.164245	−0.0104506
$248$	12.9871	0.824680
$249$	2.50489	0.158741
$250$	2.60633	0.164839
$251$	17.5437	1.10735	0.553673	−	0.832734i	$-0.313226\pi$
$251$	17.5437	1.10735	0.553673	+	0.832734i	$0.313226\pi$
$252$	−18.4197	−1.16033
$253$	16.4811	1.03616
$254$	10.6526	0.668406
$255$	5.96605	0.373608
$256$	−17.8710	−1.11694
$257$	0.856052	0.0533991	0.0266995	−	0.999644i	$-0.491500\pi$
$257$	0.856052	0.0533991	0.0266995	+	0.999644i	$0.491500\pi$
$258$	−1.23958	−0.0771731
$259$	−13.7555	−0.854723
$260$	12.0268	0.745869
$261$	−1.45014	−0.0897613
$262$	46.8891	2.89682
$263$	−16.8124	−1.03670	−0.518349	−	0.855169i	$-0.673453\pi$
$263$	−16.8124	−1.03670	−0.518349	+	0.855169i	$0.673453\pi$
$264$	−14.0867	−0.866978
$265$	−0.959226	−0.0589248
$266$	0.655623	0.0401988
$267$	14.4146	0.882157
$268$	−44.8877	−2.74195
$269$	−3.06604	−0.186940	−0.0934698	−	0.995622i	$-0.529796\pi$
$269$	−3.06604	−0.186940	−0.0934698	+	0.995622i	$0.529796\pi$
$270$	2.60633	0.158616
$271$	−28.4015	−1.72527	−0.862634	−	0.505828i	$-0.831187\pi$
$271$	−28.4015	−1.72527	−0.862634	+	0.505828i	$0.831187\pi$
$272$	−56.0010	−3.39556
$273$	9.64322	0.583634
$274$	33.7546	2.03919
$275$	1.93515	0.116694
$276$	40.8204	2.45710
$277$	12.2000	0.733027	0.366514	−	0.930413i	$-0.380551\pi$
$277$	12.2000	0.733027	0.366514	+	0.930413i	$0.380551\pi$
$278$	4.34036	0.260318
$279$	−1.78409	−0.106810
$280$	−27.9752	−1.67184
$281$	−22.4653	−1.34017	−0.670083	−	0.742286i	$-0.733742\pi$
$281$	−22.4653	−1.34017	−0.670083	+	0.742286i	$0.733742\pi$
$282$	−3.00671	−0.179047
$283$	−22.2870	−1.32483	−0.662413	−	0.749139i	$-0.730468\pi$
$283$	−22.2870	−1.32483	−0.662413	+	0.749139i	$0.730468\pi$
$284$	68.3939	4.05843
$285$	−0.0654556	−0.00387725
$286$	12.6558	0.748351
$287$	−37.4740	−2.21202
$288$	−9.90581	−0.583706
$289$	18.5937	1.09375
$290$	−3.77954	−0.221942
$291$	15.1589	0.888630
$292$	−34.4281	−2.01475
$293$	14.2686	0.833582	0.416791	−	0.909002i	$-0.363155\pi$
$293$	14.2686	0.833582	0.416791	+	0.909002i	$0.363155\pi$
$294$	−20.2489	−1.18094
$295$	5.91543	0.344410
$296$	−26.0551	−1.51442
$297$	1.93515	0.112289
$298$	−18.4333	−1.06781
$299$	−21.3707	−1.23590
$300$	4.79297	0.276722
$301$	−1.82778	−0.105351
$302$	42.2913	2.43359
$303$	10.2341	0.587934
$304$	0.614406	0.0352386
$305$	5.37399	0.307714
$306$	15.5495	0.888906
$307$	−20.5991	−1.17565	−0.587826	−	0.808988i	$-0.700016\pi$
$307$	−20.5991	−1.17565	−0.587826	+	0.808988i	$0.700016\pi$
$308$	−35.6448	−2.03105
$309$	−3.21066	−0.182648
$310$	−4.64992	−0.264098
$311$	−10.5821	−0.600058	−0.300029	−	0.953930i	$-0.596996\pi$
$311$	−10.5821	−0.600058	−0.300029	+	0.953930i	$0.596996\pi$
$312$	18.2659	1.03410
$313$	−22.8760	−1.29303	−0.646514	−	0.762902i	$-0.723774\pi$
$313$	−22.8760	−1.29303	−0.646514	+	0.762902i	$0.723774\pi$
$314$	62.8542	3.54707
$315$	3.84306	0.216532
$316$	10.8788	0.611981
$317$	20.6518	1.15992	0.579961	−	0.814644i	$-0.303068\pi$
$317$	20.6518	1.15992	0.579961	+	0.814644i	$0.303068\pi$
$318$	−2.50006	−0.140197
$319$	−2.80623	−0.157119
$320$	−7.04462	−0.393806
$321$	11.7398	0.655253
$322$	85.3062	4.75393
$323$	−0.390511	−0.0217286
$324$	4.79297	0.266276
$325$	−2.50925	−0.139188
$326$	21.2613	1.17755
$327$	14.6839	0.812021
$328$	−70.9821	−3.91933
$329$	−4.43343	−0.244423
$330$	5.04364	0.277643
$331$	3.13660	0.172403	0.0862017	−	0.996278i	$-0.472527\pi$
$331$	3.13660	0.172403	0.0862017	+	0.996278i	$0.472527\pi$
$332$	12.0059	0.658908
$333$	3.57930	0.196144
$334$	5.96412	0.326342
$335$	9.36533	0.511683
$336$	−36.0733	−1.96796
$337$	0.147719	0.00804679	0.00402339	−	0.999992i	$-0.498719\pi$
$337$	0.147719	0.00804679	0.00402339	+	0.999992i	$0.498719\pi$
$338$	17.4719	0.950348
$339$	−19.0971	−1.03721
$340$	28.5951	1.55079
$341$	−3.45247	−0.186962
$342$	−0.170599	−0.00922494
$343$	−2.95581	−0.159599
$344$	−3.46212	−0.186665
$345$	−8.51674	−0.458526
$346$	16.2828	0.875368
$347$	−11.8489	−0.636080	−0.318040	−	0.948077i	$-0.603025\pi$
$347$	−11.8489	−0.636080	−0.318040	+	0.948077i	$0.603025\pi$
$348$	−6.95047	−0.372584
$349$	25.0260	1.33961	0.669805	−	0.742537i	$-0.266378\pi$
$349$	25.0260	1.33961	0.669805	+	0.742537i	$0.266378\pi$
$350$	10.0163	0.535394
$351$	−2.50925	−0.133934
$352$	−19.1692	−1.02172
$353$	12.9841	0.691076	0.345538	−	0.938405i	$-0.387696\pi$
$353$	12.9841	0.691076	0.345538	+	0.938405i	$0.387696\pi$
$354$	15.4176	0.819436
$355$	−14.2696	−0.757354
$356$	69.0885	3.66168
$357$	22.9279	1.21347
$358$	−31.0966	−1.64351
$359$	−22.5611	−1.19073	−0.595364	−	0.803456i	$-0.702992\pi$
$359$	−22.5611	−1.19073	−0.595364	+	0.803456i	$0.702992\pi$
$360$	7.27940	0.383658
$361$	−18.9957	−0.999775
$362$	39.8395	2.09392
$363$	−7.25520	−0.380799
$364$	46.2196	2.42257
$365$	7.18305	0.375978
$366$	14.0064	0.732126
$367$	20.7479	1.08303	0.541517	−	0.840690i	$-0.317850\pi$
$367$	20.7479	1.08303	0.541517	+	0.840690i	$0.317850\pi$
$368$	79.9433	4.16733
$369$	9.75108	0.507621
$370$	9.32884	0.484983
$371$	−3.68637	−0.191387
$372$	−8.55106	−0.443352
$373$	−23.9694	−1.24109	−0.620544	−	0.784172i	$-0.713088\pi$
$373$	−23.9694	−1.24109	−0.620544	+	0.784172i	$0.713088\pi$
$374$	30.0906	1.55595
$375$	−1.00000	−0.0516398
$376$	−8.39766	−0.433076
$377$	3.63877	0.187406
$378$	10.0163	0.515183
$379$	1.58055	0.0811876	0.0405938	−	0.999176i	$-0.487075\pi$
$379$	1.58055	0.0811876	0.0405938	+	0.999176i	$0.487075\pi$
$380$	−0.313727	−0.0160938
$381$	−4.08721	−0.209394
$382$	63.8289	3.26577
$383$	5.90402	0.301681	0.150841	−	0.988558i	$-0.451802\pi$
$383$	5.90402	0.301681	0.150841	+	0.988558i	$0.451802\pi$
$384$	1.45099	0.0740457
$385$	7.43689	0.379019
$386$	−43.2050	−2.19908
$387$	0.475605	0.0241764
$388$	72.6561	3.68855
$389$	−18.6510	−0.945643	−0.472822	−	0.881158i	$-0.656765\pi$
$389$	−18.6510	−0.945643	−0.472822	+	0.881158i	$0.656765\pi$
$390$	−6.53995	−0.331163
$391$	−50.8113	−2.56964
$392$	−56.5546	−2.85644
$393$	−17.9905	−0.907499
$394$	9.55129	0.481187
$395$	−2.26974	−0.114203
$396$	9.27510	0.466091
$397$	12.7114	0.637965	0.318982	−	0.947761i	$-0.396659\pi$
$397$	12.7114	0.637965	0.318982	+	0.947761i	$0.396659\pi$
$398$	−28.3588	−1.42150
$399$	−0.251550	−0.0125932
$400$	9.38661	0.469330
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	24.4092	1.21742
$403$	4.47672	0.223001
$404$	49.0517	2.44042
$405$	−1.00000	−0.0496904
$406$	−14.5250	−0.720865
$407$	6.92647	0.343332
$408$	43.4293	2.15007
$409$	−1.78228	−0.0881279	−0.0440640	−	0.999029i	$-0.514031\pi$
$409$	−1.78228	−0.0881279	−0.0440640	+	0.999029i	$0.514031\pi$
$410$	25.4146	1.25514
$411$	−12.9510	−0.638826
$412$	−15.3886	−0.758141
$413$	22.7334	1.11864
$414$	−22.1974	−1.09094
$415$	−2.50489	−0.122960
$416$	24.8562	1.21868
$417$	−1.66531	−0.0815507
$418$	−0.330134	−0.0161474
$419$	−19.4553	−0.950452	−0.475226	−	0.879864i	$-0.657634\pi$
$419$	−19.4553	−0.950452	−0.475226	+	0.879864i	$0.657634\pi$
$420$	18.4197	0.898788
$421$	33.2216	1.61912	0.809561	−	0.587036i	$-0.199705\pi$
$421$	33.2216	1.61912	0.809561	+	0.587036i	$0.199705\pi$
$422$	63.4983	3.09105
$423$	1.15362	0.0560909
$424$	−6.98259	−0.339105
$425$	−5.96605	−0.289396
$426$	−37.1914	−1.80193
$427$	20.6526	0.999448
$428$	56.2686	2.71984
$429$	−4.85578	−0.234439
$430$	1.23958	0.0597781
$431$	16.4984	0.794699	0.397349	−	0.917667i	$-0.369930\pi$
$431$	16.4984	0.794699	0.397349	+	0.917667i	$0.369930\pi$
$432$	9.38661	0.451613
$433$	−19.2974	−0.927374	−0.463687	−	0.885999i	$-0.653474\pi$
$433$	−19.2974	−0.927374	−0.463687	+	0.885999i	$0.653474\pi$
$434$	−17.8699	−0.857784
$435$	1.45014	0.0695288
$436$	70.3794	3.37056
$437$	0.557468	0.0266673
$438$	18.7214	0.894544
$439$	6.13743	0.292924	0.146462	−	0.989216i	$-0.453211\pi$
$439$	6.13743	0.292924	0.146462	+	0.989216i	$0.453211\pi$
$440$	14.0867	0.671558
$441$	7.76913	0.369958
$442$	−39.0176	−1.85588
$443$	24.1198	1.14596	0.572982	−	0.819568i	$-0.305786\pi$
$443$	24.1198	1.14596	0.572982	+	0.819568i	$0.305786\pi$
$444$	17.1555	0.814162
$445$	−14.4146	−0.683316
$446$	−17.2571	−0.817147
$447$	7.07251	0.334518
$448$	−27.0729	−1.27908
$449$	15.9861	0.754429	0.377215	−	0.926126i	$-0.376882\pi$
$449$	15.9861	0.754429	0.377215	+	0.926126i	$0.376882\pi$
$450$	−2.60633	−0.122864
$451$	18.8698	0.888544
$452$	−91.5319	−4.30530
$453$	−16.2264	−0.762381
$454$	−33.3850	−1.56683
$455$	−9.64322	−0.452081
$456$	−0.476478	−0.0223131
$457$	−36.4816	−1.70654	−0.853270	−	0.521470i	$-0.825384\pi$
$457$	−36.4816	−1.70654	−0.853270	+	0.521470i	$0.825384\pi$
$458$	−53.7110	−2.50975
$459$	−5.96605	−0.278471
$460$	−40.8204	−1.90326
$461$	−29.3612	−1.36749	−0.683743	−	0.729723i	$-0.739649\pi$
$461$	−29.3612	−1.36749	−0.683743	+	0.729723i	$0.739649\pi$
$462$	19.3830	0.901779
$463$	−7.33663	−0.340962	−0.170481	−	0.985361i	$-0.554532\pi$
$463$	−7.33663	−0.340962	−0.170481	+	0.985361i	$0.554532\pi$
$464$	−13.6119	−0.631916
$465$	1.78409	0.0827350
$466$	−24.8665	−1.15192
$467$	−21.3542	−0.988154	−0.494077	−	0.869418i	$-0.664494\pi$
$467$	−21.3542	−0.988154	−0.494077	+	0.869418i	$0.664494\pi$
$468$	−12.0268	−0.555938
$469$	35.9915	1.66194
$470$	3.00671	0.138689
$471$	−24.1159	−1.11120
$472$	43.0608	1.98204
$473$	0.920365	0.0423184
$474$	−5.91571	−0.271717
$475$	0.0654556	0.00300331
$476$	109.893	5.03692
$477$	0.959226	0.0439200
$478$	21.3408	0.976106
$479$	−0.206523	−0.00943626	−0.00471813	−	0.999989i	$-0.501502\pi$
$479$	−0.206523	−0.00943626	−0.00471813	+	0.999989i	$0.501502\pi$
$480$	9.90581	0.452136
$481$	−8.98136	−0.409515
$482$	3.91980	0.178542
$483$	−32.7303	−1.48928
$484$	−34.7740	−1.58063
$485$	−15.1589	−0.688330
$486$	−2.60633	−0.118226
$487$	32.3989	1.46813	0.734066	−	0.679078i	$-0.237620\pi$
$487$	32.3989	1.46813	0.734066	+	0.679078i	$0.237620\pi$
$488$	39.1194	1.77085
$489$	−8.15755	−0.368897
$490$	20.2489	0.914753
$491$	5.17530	0.233558	0.116779	−	0.993158i	$-0.462743\pi$
$491$	5.17530	0.233558	0.116779	+	0.993158i	$0.462743\pi$
$492$	46.7366	2.10705
$493$	8.65160	0.389648
$494$	0.428076	0.0192601
$495$	−1.93515	−0.0869784
$496$	−16.7465	−0.751940
$497$	−54.8391	−2.45987
$498$	−6.52858	−0.292553
$499$	−15.0487	−0.673671	−0.336836	−	0.941563i	$-0.609357\pi$
$499$	−15.0487	−0.673671	−0.336836	+	0.941563i	$0.609357\pi$
$500$	−4.79297	−0.214348
$501$	−2.28832	−0.102235
$502$	−45.7246	−2.04079
$503$	−9.77639	−0.435908	−0.217954	−	0.975959i	$-0.569938\pi$
$503$	−9.77639	−0.435908	−0.217954	+	0.975959i	$0.569938\pi$
$504$	27.9752	1.24611
$505$	−10.2341	−0.455412
$506$	−42.9553	−1.90960
$507$	−6.70365	−0.297719
$508$	−19.5899	−0.869161
$509$	−9.03852	−0.400625	−0.200313	−	0.979732i	$-0.564196\pi$
$509$	−9.03852	−0.400625	−0.200313	+	0.979732i	$0.564196\pi$
$510$	−15.5495	−0.688544
$511$	27.6049	1.22117
$512$	43.6758	1.93022
$513$	0.0654556	0.00288993
$514$	−2.23116	−0.0984121
$515$	3.21066	0.141478
$516$	2.27956	0.100352
$517$	2.23242	0.0981818
$518$	35.8513	1.57522
$519$	−6.24740	−0.274230
$520$	−18.2659	−0.801011
$521$	−24.3074	−1.06493	−0.532463	−	0.846454i	$-0.678733\pi$
$521$	−24.3074	−1.06493	−0.532463	+	0.846454i	$0.678733\pi$
$522$	3.77954	0.165426
$523$	10.2546	0.448402	0.224201	−	0.974543i	$-0.428023\pi$
$523$	10.2546	0.448402	0.224201	+	0.974543i	$0.428023\pi$
$524$	−86.2277	−3.76687
$525$	−3.84306	−0.167725
$526$	43.8187	1.91059
$527$	10.6439	0.463657
$528$	18.1645	0.790507
$529$	49.5348	2.15369
$530$	2.50006	0.108596
$531$	−5.91543	−0.256708
$532$	−1.20567	−0.0522725
$533$	−24.4679	−1.05982
$534$	−37.5691	−1.62578
$535$	−11.7398	−0.507557
$536$	68.1740	2.94467
$537$	11.9312	0.514868
$538$	7.99111	0.344521
$539$	15.0344	0.647578
$540$	−4.79297	−0.206257
$541$	13.5442	0.582310	0.291155	−	0.956676i	$-0.405961\pi$
$541$	13.5442	0.582310	0.291155	+	0.956676i	$0.405961\pi$
$542$	74.0238	3.17959
$543$	−15.2857	−0.655970
$544$	59.0986	2.53383
$545$	−14.6839	−0.628989
$546$	−25.1334	−1.07561
$547$	−5.72046	−0.244589	−0.122295	−	0.992494i	$-0.539025\pi$
$547$	−5.72046	−0.244589	−0.122295	+	0.992494i	$0.539025\pi$
$548$	−62.0738	−2.65166
$549$	−5.37399	−0.229356
$550$	−5.04364	−0.215061
$551$	−0.0949197	−0.00404371
$552$	−61.9968	−2.63876
$553$	−8.72277	−0.370930
$554$	−31.7973	−1.35094
$555$	−3.57930	−0.151933
$556$	−7.98179	−0.338503
$557$	−15.0310	−0.636886	−0.318443	−	0.947942i	$-0.603160\pi$
$557$	−15.0310	−0.636886	−0.318443	+	0.947942i	$0.603160\pi$
$558$	4.64992	0.196847
$559$	−1.19341	−0.0504760
$560$	36.0733	1.52438
$561$	−11.5452	−0.487438
$562$	58.5520	2.46987
$563$	4.36257	0.183860	0.0919302	−	0.995765i	$-0.470696\pi$
$563$	4.36257	0.183860	0.0919302	+	0.995765i	$0.470696\pi$
$564$	5.52926	0.232824
$565$	19.0971	0.803422
$566$	58.0874	2.44160
$567$	−3.84306	−0.161393
$568$	−103.874	−4.35848
$569$	−11.0387	−0.462765	−0.231383	−	0.972863i	$-0.574325\pi$
$569$	−11.0387	−0.462765	−0.231383	+	0.972863i	$0.574325\pi$
$570$	0.170599	0.00714561
$571$	13.5181	0.565713	0.282857	−	0.959162i	$-0.408718\pi$
$571$	13.5181	0.565713	0.282857	+	0.959162i	$0.408718\pi$
$572$	−23.2736	−0.973117
$573$	−24.4899	−1.02308
$574$	97.6698	4.07666
$575$	8.51674	0.355172
$576$	7.04462	0.293526
$577$	12.7423	0.530470	0.265235	−	0.964184i	$-0.414550\pi$
$577$	12.7423	0.530470	0.265235	+	0.964184i	$0.414550\pi$
$578$	−48.4614	−2.01573
$579$	16.5769	0.688914
$580$	6.95047	0.288603
$581$	−9.62646	−0.399373
$582$	−39.5091	−1.63770
$583$	1.85624	0.0768778
$584$	52.2883	2.16371
$585$	2.50925	0.103745
$586$	−37.1888	−1.53625
$587$	1.56734	0.0646911	0.0323456	−	0.999477i	$-0.489702\pi$
$587$	1.56734	0.0646911	0.0323456	+	0.999477i	$0.489702\pi$
$588$	37.2372	1.53564
$589$	−0.116778	−0.00481177
$590$	−15.4176	−0.634732
$591$	−3.66465	−0.150743
$592$	33.5975	1.38085
$593$	25.7337	1.05676	0.528378	−	0.849009i	$-0.322800\pi$
$593$	25.7337	1.05676	0.528378	+	0.849009i	$0.322800\pi$
$594$	−5.04364	−0.206943
$595$	−22.9279	−0.939952
$596$	33.8983	1.38853
$597$	10.8807	0.445319
$598$	55.6990	2.27770
$599$	−42.8369	−1.75027	−0.875134	−	0.483880i	$-0.839227\pi$
$599$	−42.8369	−1.75027	−0.875134	+	0.483880i	$0.839227\pi$
$600$	−7.27940	−0.297180
$601$	−19.3952	−0.791146	−0.395573	−	0.918434i	$-0.629454\pi$
$601$	−19.3952	−0.791146	−0.395573	+	0.918434i	$0.629454\pi$
$602$	4.76380	0.194158
$603$	−9.36533	−0.381386
$604$	−77.7725	−3.16452
$605$	7.25520	0.294966
$606$	−26.6735	−1.08354
$607$	22.8987	0.929429	0.464715	−	0.885461i	$-0.346157\pi$
$607$	22.8987	0.929429	0.464715	+	0.885461i	$0.346157\pi$
$608$	−0.648391	−0.0262957
$609$	5.57297	0.225828
$610$	−14.0064	−0.567102
$611$	−2.89472	−0.117108
$612$	−28.5951	−1.15589
$613$	−31.0067	−1.25235	−0.626175	−	0.779682i	$-0.715381\pi$
$613$	−31.0067	−1.25235	−0.626175	+	0.779682i	$0.715381\pi$
$614$	53.6880	2.16667
$615$	−9.75108	−0.393202
$616$	54.1361	2.18121
$617$	−7.55031	−0.303964	−0.151982	−	0.988383i	$-0.548566\pi$
$617$	−7.55031	−0.303964	−0.151982	+	0.988383i	$0.548566\pi$
$618$	8.36804	0.336612
$619$	−20.3614	−0.818395	−0.409197	−	0.912446i	$-0.634191\pi$
$619$	−20.3614	−0.818395	−0.409197	+	0.912446i	$0.634191\pi$
$620$	8.55106	0.343419
$621$	8.51674	0.341765
$622$	27.5806	1.10588
$623$	−55.3961	−2.21940
$624$	−23.5534	−0.942890
$625$	1.00000	0.0400000
$626$	59.6224	2.38299
$627$	0.126666	0.00505856
$628$	−115.587	−4.61242
$629$	−21.3543	−0.851450
$630$	−10.0163	−0.399059
$631$	−19.9627	−0.794703	−0.397352	−	0.917666i	$-0.630071\pi$
$631$	−19.9627	−0.794703	−0.397352	+	0.917666i	$0.630071\pi$
$632$	−16.5224	−0.657225
$633$	−24.3631	−0.968346
$634$	−53.8255	−2.13769
$635$	4.08721	0.162196
$636$	4.59754	0.182304
$637$	−19.4947	−0.772409
$638$	7.31398	0.289563
$639$	14.2696	0.564498
$640$	−1.45099	−0.0573555
$641$	−2.80539	−0.110806	−0.0554032	−	0.998464i	$-0.517644\pi$
$641$	−2.80539	−0.110806	−0.0554032	+	0.998464i	$0.517644\pi$
$642$	−30.5979	−1.20760
$643$	15.2014	0.599486	0.299743	−	0.954020i	$-0.403099\pi$
$643$	15.2014	0.599486	0.299743	+	0.954020i	$0.403099\pi$
$644$	−156.876	−6.18176
$645$	−0.475605	−0.0187269
$646$	1.01780	0.0400449
$647$	27.9212	1.09770	0.548848	−	0.835922i	$-0.315067\pi$
$647$	27.9212	1.09770	0.548848	+	0.835922i	$0.315067\pi$
$648$	−7.27940	−0.285962
$649$	−11.4472	−0.449343
$650$	6.53995	0.256518
$651$	6.85635	0.268722
$652$	−39.0989	−1.53123
$653$	18.5588	0.726262	0.363131	−	0.931738i	$-0.381708\pi$
$653$	18.5588	0.726262	0.363131	+	0.931738i	$0.381708\pi$
$654$	−38.2711	−1.49652
$655$	17.9905	0.702945
$656$	91.5296	3.57363
$657$	−7.18305	−0.280237
$658$	11.5550	0.450460
$659$	44.8275	1.74623	0.873116	−	0.487513i	$-0.162096\pi$
$659$	44.8275	1.74623	0.873116	+	0.487513i	$0.162096\pi$
$660$	−9.27510	−0.361033
$661$	−3.80429	−0.147970	−0.0739849	−	0.997259i	$-0.523572\pi$
$661$	−3.80429	−0.147970	−0.0739849	+	0.997259i	$0.523572\pi$
$662$	−8.17503	−0.317732
$663$	14.9703	0.581399
$664$	−18.2341	−0.707621
$665$	0.251550	0.00975469
$666$	−9.32884	−0.361485
$667$	−12.3505	−0.478211
$668$	−10.9678	−0.424359
$669$	6.62122	0.255991
$670$	−24.4092	−0.943008
$671$	−10.3995	−0.401467
$672$	38.0687	1.46853
$673$	−22.5514	−0.869293	−0.434646	−	0.900601i	$-0.643127\pi$
$673$	−22.5514	−0.869293	−0.434646	+	0.900601i	$0.643127\pi$
$674$	−0.385006	−0.0148299
$675$	1.00000	0.0384900
$676$	−32.1304	−1.23578
$677$	−38.2016	−1.46821	−0.734103	−	0.679038i	$-0.762397\pi$
$677$	−38.2016	−1.46821	−0.734103	+	0.679038i	$0.762397\pi$
$678$	49.7735	1.91154
$679$	−58.2565	−2.23568
$680$	−43.4293	−1.66544
$681$	12.8092	0.490849
$682$	8.99828	0.344562
$683$	−16.3399	−0.625228	−0.312614	−	0.949880i	$-0.601205\pi$
$683$	−16.3399	−0.625228	−0.312614	+	0.949880i	$0.601205\pi$
$684$	0.313727	0.0119956
$685$	12.9510	0.494833
$686$	7.70381	0.294133
$687$	20.6079	0.786239
$688$	4.46432	0.170200
$689$	−2.40694	−0.0916972
$690$	22.1974	0.845042
$691$	41.2600	1.56960	0.784801	−	0.619747i	$-0.212765\pi$
$691$	41.2600	1.56960	0.784801	+	0.619747i	$0.212765\pi$
$692$	−29.9436	−1.13828
$693$	−7.43689	−0.282504
$694$	30.8821	1.17227
$695$	1.66531	0.0631689
$696$	10.5561	0.400130
$697$	−58.1754	−2.20355
$698$	−65.2260	−2.46884
$699$	9.54079	0.360866
$700$	−18.4197	−0.696198
$701$	9.10616	0.343935	0.171967	−	0.985103i	$-0.444988\pi$
$701$	9.10616	0.343935	0.171967	+	0.985103i	$0.444988\pi$
$702$	6.53995	0.246834
$703$	0.234285	0.00883622
$704$	13.6324	0.513790
$705$	−1.15362	−0.0434478
$706$	−33.8410	−1.27362
$707$	−39.3303	−1.47917
$708$	−28.3525	−1.06555
$709$	47.3561	1.77850	0.889248	−	0.457426i	$-0.151228\pi$
$709$	47.3561	1.77850	0.889248	+	0.457426i	$0.151228\pi$
$710$	37.1914	1.39577
$711$	2.26974	0.0851221
$712$	−104.929	−3.93240
$713$	−15.1946	−0.569042
$714$	−59.7577	−2.23638
$715$	4.85578	0.181596
$716$	57.1857	2.13713
$717$	−8.18806	−0.305789
$718$	58.8017	2.19446
$719$	36.2971	1.35365	0.676827	−	0.736142i	$-0.263354\pi$
$719$	36.2971	1.35365	0.676827	+	0.736142i	$0.263354\pi$
$720$	−9.38661	−0.349818
$721$	12.3388	0.459519
$722$	49.5091	1.84254
$723$	−1.50395	−0.0559326
$724$	−73.2637	−2.72282
$725$	−1.45014	−0.0538568
$726$	18.9095	0.701796
$727$	−28.5906	−1.06037	−0.530183	−	0.847883i	$-0.677877\pi$
$727$	−28.5906	−1.06037	−0.530183	+	0.847883i	$0.677877\pi$
$728$	−70.1969	−2.60167
$729$	1.00000	0.0370370
$730$	−18.7214	−0.692911
$731$	−2.83748	−0.104948
$732$	−25.7574	−0.952019
$733$	−10.1880	−0.376301	−0.188150	−	0.982140i	$-0.560249\pi$
$733$	−10.1880	−0.376301	−0.188150	+	0.982140i	$0.560249\pi$
$734$	−54.0760	−1.99598
$735$	−7.76913	−0.286569
$736$	−84.3652	−3.10974
$737$	−18.1233	−0.667580
$738$	−25.4146	−0.935523
$739$	−44.1287	−1.62330	−0.811651	−	0.584143i	$-0.801431\pi$
$739$	−44.1287	−1.62330	−0.811651	+	0.584143i	$0.801431\pi$
$740$	−17.1555	−0.630647
$741$	−0.164245	−0.00603368
$742$	9.60790	0.352717
$743$	−39.2417	−1.43964	−0.719819	−	0.694161i	$-0.755775\pi$
$743$	−39.2417	−1.43964	−0.719819	+	0.694161i	$0.755775\pi$
$744$	12.9871	0.476129
$745$	−7.07251	−0.259117
$746$	62.4722	2.28727
$747$	2.50489	0.0916493
$748$	−55.3357	−2.02327
$749$	−45.1169	−1.64853
$750$	2.60633	0.0951698
$751$	17.3964	0.634804	0.317402	−	0.948291i	$-0.397190\pi$
$751$	17.3964	0.634804	0.317402	+	0.948291i	$0.397190\pi$
$752$	10.8286	0.394877
$753$	17.5437	0.639327
$754$	−9.48383	−0.345381
$755$	16.2264	0.590538
$756$	−18.4197	−0.669917
$757$	−40.7339	−1.48050	−0.740249	−	0.672333i	$-0.765292\pi$
$757$	−40.7339	−1.48050	−0.740249	+	0.672333i	$0.765292\pi$
$758$	−4.11945	−0.149625
$759$	16.4811	0.598228
$760$	0.476478	0.0172837
$761$	−18.0580	−0.654602	−0.327301	−	0.944920i	$-0.606139\pi$
$761$	−18.0580	−0.654602	−0.327301	+	0.944920i	$0.606139\pi$
$762$	10.6526	0.385904
$763$	−56.4311	−2.04294
$764$	−117.380	−4.24664
$765$	5.96605	0.215703
$766$	−15.3878	−0.555985
$767$	14.8433	0.535961
$768$	−17.8710	−0.644865
$769$	−42.8106	−1.54379	−0.771896	−	0.635749i	$-0.780691\pi$
$769$	−42.8106	−1.54379	−0.771896	+	0.635749i	$0.780691\pi$
$770$	−19.3830	−0.698515
$771$	0.856052	0.0308300
$772$	79.4527	2.85957
$773$	−40.9506	−1.47289	−0.736446	−	0.676497i	$-0.763497\pi$
$773$	−40.9506	−1.47289	−0.736446	+	0.676497i	$0.763497\pi$
$774$	−1.23958	−0.0445559
$775$	−1.78409	−0.0640862
$776$	−110.348	−3.96125
$777$	−13.7555	−0.493474
$778$	48.6107	1.74278
$779$	0.638263	0.0228681
$780$	12.0268	0.430628
$781$	27.6139	0.988102
$782$	132.431	4.73572
$783$	−1.45014	−0.0518237
$784$	72.9258	2.60449
$785$	24.1159	0.860735
$786$	46.8891	1.67248
$787$	−38.7202	−1.38023	−0.690113	−	0.723702i	$-0.742439\pi$
$787$	−38.7202	−1.38023	−0.690113	+	0.723702i	$0.742439\pi$
$788$	−17.5645	−0.625711
$789$	−16.8124	−0.598538
$790$	5.91571	0.210471
$791$	73.3914	2.60950
$792$	−14.0867	−0.500550
$793$	13.4847	0.478856
$794$	−33.1300	−1.17574
$795$	−0.959226	−0.0340202
$796$	52.1510	1.84844
$797$	19.2445	0.681676	0.340838	−	0.940122i	$-0.389289\pi$
$797$	19.2445	0.681676	0.340838	+	0.940122i	$0.389289\pi$
$798$	0.655623	0.0232088
$799$	−6.88255	−0.243487
$800$	−9.90581	−0.350223
$801$	14.4146	0.509313
$802$	−2.60633	−0.0920328
$803$	−13.9003	−0.490530
$804$	−44.8877	−1.58307
$805$	32.7303	1.15359
$806$	−11.6678	−0.410982
$807$	−3.06604	−0.107930
$808$	−74.4982	−2.62084
$809$	−10.3361	−0.363397	−0.181698	−	0.983354i	$-0.558159\pi$
$809$	−10.3361	−0.363397	−0.181698	+	0.983354i	$0.558159\pi$
$810$	2.60633	0.0915772
$811$	−37.3063	−1.31000	−0.655000	−	0.755629i	$-0.727331\pi$
$811$	−37.3063	−1.31000	−0.655000	+	0.755629i	$0.727331\pi$
$812$	26.7111	0.937375
$813$	−28.4015	−0.996084
$814$	−18.0527	−0.632746
$815$	8.15755	0.285747
$816$	−56.0010	−1.96043
$817$	0.0311310	0.00108914
$818$	4.64521	0.162416
$819$	9.64322	0.336961
$820$	−46.7366	−1.63211
$821$	−55.0789	−1.92227	−0.961134	−	0.276082i	$-0.910964\pi$
$821$	−55.0789	−1.92227	−0.961134	+	0.276082i	$0.910964\pi$
$822$	33.7546	1.17733
$823$	−0.840933	−0.0293131	−0.0146565	−	0.999893i	$-0.504665\pi$
$823$	−0.840933	−0.0293131	−0.0146565	+	0.999893i	$0.504665\pi$
$824$	23.3717	0.814191
$825$	1.93515	0.0673732
$826$	−59.2508	−2.06160
$827$	−0.719069	−0.0250045	−0.0125022	−	0.999922i	$-0.503980\pi$
$827$	−0.719069	−0.0250045	−0.0125022	+	0.999922i	$0.503980\pi$
$828$	40.8204	1.41861
$829$	13.0569	0.453485	0.226743	−	0.973955i	$-0.427192\pi$
$829$	13.0569	0.453485	0.226743	+	0.973955i	$0.427192\pi$
$830$	6.52858	0.226610
$831$	12.2000	0.423213
$832$	−17.6768	−0.612831
$833$	−46.3510	−1.60597
$834$	4.34036	0.150294
$835$	2.28832	0.0791906
$836$	0.607107	0.0209972
$837$	−1.78409	−0.0616670
$838$	50.7069	1.75164
$839$	−55.6847	−1.92245	−0.961224	−	0.275768i	$-0.911068\pi$
$839$	−55.6847	−1.92245	−0.961224	+	0.275768i	$0.911068\pi$
$840$	−27.9752	−0.965236
$841$	−26.8971	−0.927486
$842$	−86.5865	−2.98397
$843$	−22.4653	−0.773745
$844$	−116.771	−4.01944
$845$	6.70365	0.230612
$846$	−3.00671	−0.103373
$847$	27.8822	0.958044
$848$	9.00388	0.309195
$849$	−22.2870	−0.764889
$850$	15.5495	0.533344
$851$	30.4839	1.04498
$852$	68.3939	2.34314
$853$	21.5369	0.737408	0.368704	−	0.929547i	$-0.379802\pi$
$853$	21.5369	0.737408	0.368704	+	0.929547i	$0.379802\pi$
$854$	−53.8275	−1.84194
$855$	−0.0654556	−0.00223853
$856$	−85.4589	−2.92092
$857$	−6.40199	−0.218688	−0.109344	−	0.994004i	$-0.534875\pi$
$857$	−6.40199	−0.218688	−0.109344	+	0.994004i	$0.534875\pi$
$858$	12.6558	0.432061
$859$	−2.68335	−0.0915549	−0.0457774	−	0.998952i	$-0.514577\pi$
$859$	−2.68335	−0.0915549	−0.0457774	+	0.998952i	$0.514577\pi$
$860$	−2.27956	−0.0777323
$861$	−37.4740	−1.27711
$862$	−43.0002	−1.46459
$863$	1.45640	0.0495765	0.0247883	−	0.999693i	$-0.492109\pi$
$863$	1.45640	0.0495765	0.0247883	+	0.999693i	$0.492109\pi$
$864$	−9.90581	−0.337003
$865$	6.24740	0.212418
$866$	50.2954	1.70911
$867$	18.5937	0.631476
$868$	32.8623	1.11542
$869$	4.39229	0.148998
$870$	−3.77954	−0.128139
$871$	23.5000	0.796267
$872$	−106.890	−3.61975
$873$	15.1589	0.513051
$874$	−1.45295	−0.0491467
$875$	3.84306	0.129919
$876$	−34.4281	−1.16322
$877$	9.64097	0.325553	0.162776	−	0.986663i	$-0.447955\pi$
$877$	9.64097	0.325553	0.162776	+	0.986663i	$0.447955\pi$
$878$	−15.9962	−0.539845
$879$	14.2686	0.481269
$880$	−18.1645	−0.612324
$881$	13.5865	0.457742	0.228871	−	0.973457i	$-0.426497\pi$
$881$	13.5865	0.457742	0.228871	+	0.973457i	$0.426497\pi$
$882$	−20.2489	−0.681817
$883$	13.1850	0.443710	0.221855	−	0.975080i	$-0.428789\pi$
$883$	13.1850	0.443710	0.221855	+	0.975080i	$0.428789\pi$
$884$	71.7523	2.41329
$885$	5.91543	0.198845
$886$	−62.8641	−2.11196
$887$	41.1145	1.38049	0.690245	−	0.723576i	$-0.257503\pi$
$887$	41.1145	1.38049	0.690245	+	0.723576i	$0.257503\pi$
$888$	−26.0551	−0.874353
$889$	15.7074	0.526810
$890$	37.5691	1.25932
$891$	1.93515	0.0648299
$892$	31.7353	1.06258
$893$	0.0755108	0.00252687
$894$	−18.4333	−0.616502
$895$	−11.9312	−0.398815
$896$	−5.57626	−0.186290
$897$	−21.3707	−0.713545
$898$	−41.6650	−1.39038
$899$	2.58717	0.0862870
$900$	4.79297	0.159766
$901$	−5.72279	−0.190654
$902$	−49.1809	−1.63755
$903$	−1.82778	−0.0608247
$904$	139.016	4.62359
$905$	15.2857	0.508112
$906$	42.2913	1.40503
$907$	12.0746	0.400932	0.200466	−	0.979701i	$-0.435754\pi$
$907$	12.0746	0.400932	0.200466	+	0.979701i	$0.435754\pi$
$908$	61.3940	2.03743
$909$	10.2341	0.339444
$910$	25.1334	0.833165
$911$	−1.22737	−0.0406644	−0.0203322	−	0.999793i	$-0.506472\pi$
$911$	−1.22737	−0.0406644	−0.0203322	+	0.999793i	$0.506472\pi$
$912$	0.614406	0.0203450
$913$	4.84734	0.160423
$914$	95.0833	3.14508
$915$	5.37399	0.177659
$916$	98.7729	3.26355
$917$	69.1385	2.28315
$918$	15.5495	0.513210
$919$	9.73587	0.321157	0.160578	−	0.987023i	$-0.448664\pi$
$919$	9.73587	0.321157	0.160578	+	0.987023i	$0.448664\pi$
$920$	61.9968	2.04397
$921$	−20.5991	−0.678763
$922$	76.5249	2.52021
$923$	−35.8061	−1.17857
$924$	−35.6448	−1.17263
$925$	3.57930	0.117687
$926$	19.1217	0.628378
$927$	−3.21066	−0.105452
$928$	14.3648	0.471548
$929$	−31.7685	−1.04229	−0.521146	−	0.853468i	$-0.674495\pi$
$929$	−31.7685	−1.04229	−0.521146	+	0.853468i	$0.674495\pi$
$930$	−4.64992	−0.152477
$931$	0.508533	0.0166665
$932$	45.7287	1.49789
$933$	−10.5821	−0.346444
$934$	55.6561	1.82112
$935$	11.5452	0.377568
$936$	18.2659	0.597039
$937$	30.3705	0.992161	0.496081	−	0.868277i	$-0.334772\pi$
$937$	30.3705	0.992161	0.496081	+	0.868277i	$0.334772\pi$
$938$	−93.8059	−3.06287
$939$	−22.8760	−0.746530
$940$	−5.52926	−0.180345
$941$	−35.8965	−1.17019	−0.585097	−	0.810964i	$-0.698943\pi$
$941$	−35.8965	−1.17019	−0.585097	+	0.810964i	$0.698943\pi$
$942$	62.8542	2.04790
$943$	83.0474	2.70440
$944$	−55.5259	−1.80721
$945$	3.84306	0.125015
$946$	−2.39878	−0.0779910
$947$	−31.4614	−1.02236	−0.511179	−	0.859474i	$-0.670791\pi$
$947$	−31.4614	−1.02236	−0.511179	+	0.859474i	$0.670791\pi$
$948$	10.8788	0.353327
$949$	18.0241	0.585087
$950$	−0.170599	−0.00553496
$951$	20.6518	0.669682
$952$	−166.901	−5.40931
$953$	3.68655	0.119419	0.0597095	−	0.998216i	$-0.480983\pi$
$953$	3.68655	0.119419	0.0597095	+	0.998216i	$0.480983\pi$
$954$	−2.50006	−0.0809425
$955$	24.4899	0.792476
$956$	−39.2451	−1.26928
$957$	−2.80623	−0.0907126
$958$	0.538267	0.0173906
$959$	49.7716	1.60721
$960$	−7.04462	−0.227364
$961$	−27.8170	−0.897324
$962$	23.4084	0.754718
$963$	11.7398	0.378310
$964$	−7.20840	−0.232167
$965$	−16.5769	−0.533631
$966$	85.3062	2.74468
$967$	−38.2881	−1.23126	−0.615631	−	0.788034i	$-0.711099\pi$
$967$	−38.2881	−1.23126	−0.615631	+	0.788034i	$0.711099\pi$
$968$	52.8136	1.69749
$969$	−0.390511	−0.0125450
$970$	39.5091	1.26856
$971$	−32.7324	−1.05043	−0.525216	−	0.850969i	$-0.676015\pi$
$971$	−32.7324	−1.05043	−0.525216	+	0.850969i	$0.676015\pi$
$972$	4.79297	0.153735
$973$	6.39990	0.205171
$974$	−84.4422	−2.70570
$975$	−2.50925	−0.0803604
$976$	−50.4435	−1.61466
$977$	−41.3402	−1.32259	−0.661295	−	0.750126i	$-0.729993\pi$
$977$	−41.3402	−1.32259	−0.661295	+	0.750126i	$0.729993\pi$
$978$	21.2613	0.679861
$979$	27.8943	0.891506
$980$	−37.2372	−1.18950
$981$	14.6839	0.468820
$982$	−13.4886	−0.430437
$983$	−25.3085	−0.807217	−0.403608	−	0.914932i	$-0.632244\pi$
$983$	−25.3085	−0.807217	−0.403608	+	0.914932i	$0.632244\pi$
$984$	−70.9821	−2.26283
$985$	3.66465	0.116765
$986$	−22.5489	−0.718105
$987$	−4.43343	−0.141118
$988$	−0.787220	−0.0250448
$989$	4.05060	0.128802
$990$	5.04364	0.160297
$991$	5.59841	0.177839	0.0889196	−	0.996039i	$-0.471659\pi$
$991$	5.59841	0.177839	0.0889196	+	0.996039i	$0.471659\pi$
$992$	17.6728	0.561112
$993$	3.13660	0.0995371
$994$	142.929	4.53343
$995$	−10.8807	−0.344942
$996$	12.0059	0.380421
$997$	55.9914	1.77327	0.886634	−	0.462473i	$-0.153038\pi$
$997$	55.9914	1.77327	0.886634	+	0.462473i	$0.153038\pi$
$998$	39.2219	1.24155
$999$	3.57930	0.113244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.1	✓	28	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60633 q^{2} +1.00000 q^{3} +4.79297 q^{4} -1.00000 q^{5} -2.60633 q^{6} -3.84306 q^{7} -7.27940 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60633 q^{2} +1.00000 q^{3} +4.79297 q^{4} -1.00000 q^{5} -2.60633 q^{6} -3.84306 q^{7} -7.27940 q^{8} +1.00000 q^{9} +2.60633 q^{10} +1.93515 q^{11} +4.79297 q^{12} -2.50925 q^{13} +10.0163 q^{14} -1.00000 q^{15} +9.38661 q^{16} -5.96605 q^{17} -2.60633 q^{18} +0.0654556 q^{19} -4.79297 q^{20} -3.84306 q^{21} -5.04364 q^{22} +8.51674 q^{23} -7.27940 q^{24} +1.00000 q^{25} +6.53995 q^{26} +1.00000 q^{27} -18.4197 q^{28} -1.45014 q^{29} +2.60633 q^{30} -1.78409 q^{31} -9.90581 q^{32} +1.93515 q^{33} +15.5495 q^{34} +3.84306 q^{35} +4.79297 q^{36} +3.57930 q^{37} -0.170599 q^{38} -2.50925 q^{39} +7.27940 q^{40} +9.75108 q^{41} +10.0163 q^{42} +0.475605 q^{43} +9.27510 q^{44} -1.00000 q^{45} -22.1974 q^{46} +1.15362 q^{47} +9.38661 q^{48} +7.76913 q^{49} -2.60633 q^{50} -5.96605 q^{51} -12.0268 q^{52} +0.959226 q^{53} -2.60633 q^{54} -1.93515 q^{55} +27.9752 q^{56} +0.0654556 q^{57} +3.77954 q^{58} -5.91543 q^{59} -4.79297 q^{60} -5.37399 q^{61} +4.64992 q^{62} -3.84306 q^{63} +7.04462 q^{64} +2.50925 q^{65} -5.04364 q^{66} -9.36533 q^{67} -28.5951 q^{68} +8.51674 q^{69} -10.0163 q^{70} +14.2696 q^{71} -7.27940 q^{72} -7.18305 q^{73} -9.32884 q^{74} +1.00000 q^{75} +0.313727 q^{76} -7.43689 q^{77} +6.53995 q^{78} +2.26974 q^{79} -9.38661 q^{80} +1.00000 q^{81} -25.4146 q^{82} +2.50489 q^{83} -18.4197 q^{84} +5.96605 q^{85} -1.23958 q^{86} -1.45014 q^{87} -14.0867 q^{88} +14.4146 q^{89} +2.60633 q^{90} +9.64322 q^{91} +40.8204 q^{92} -1.78409 q^{93} -3.00671 q^{94} -0.0654556 q^{95} -9.90581 q^{96} +15.1589 q^{97} -20.2489 q^{98} +1.93515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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