LMFDB - Embedded newform 4009.2.a.c.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.104818 q^{2} -2.14601 q^{3} -1.98901 q^{4} -2.02584 q^{5} +0.224941 q^{6} +4.19485 q^{7} +0.418121 q^{8} +1.60536 q^{9} +O(q^{10})$	\(q-0.104818 q^{2} -2.14601 q^{3} -1.98901 q^{4} -2.02584 q^{5} +0.224941 q^{6} +4.19485 q^{7} +0.418121 q^{8} +1.60536 q^{9} +0.212345 q^{10} -1.59389 q^{11} +4.26844 q^{12} -3.24500 q^{13} -0.439697 q^{14} +4.34747 q^{15} +3.93420 q^{16} -1.35352 q^{17} -0.168271 q^{18} +1.00000 q^{19} +4.02942 q^{20} -9.00220 q^{21} +0.167069 q^{22} -7.02820 q^{23} -0.897293 q^{24} -0.895984 q^{25} +0.340135 q^{26} +2.99290 q^{27} -8.34362 q^{28} -0.379718 q^{29} -0.455694 q^{30} +9.57198 q^{31} -1.24862 q^{32} +3.42051 q^{33} +0.141874 q^{34} -8.49809 q^{35} -3.19309 q^{36} +11.1332 q^{37} -0.104818 q^{38} +6.96381 q^{39} -0.847046 q^{40} -9.35069 q^{41} +0.943595 q^{42} +0.0600120 q^{43} +3.17027 q^{44} -3.25221 q^{45} +0.736684 q^{46} -3.84467 q^{47} -8.44284 q^{48} +10.5968 q^{49} +0.0939155 q^{50} +2.90467 q^{51} +6.45435 q^{52} +1.41735 q^{53} -0.313711 q^{54} +3.22896 q^{55} +1.75396 q^{56} -2.14601 q^{57} +0.0398014 q^{58} +1.17130 q^{59} -8.64717 q^{60} +2.94005 q^{61} -1.00332 q^{62} +6.73427 q^{63} -7.73752 q^{64} +6.57384 q^{65} -0.358531 q^{66} +14.7543 q^{67} +2.69217 q^{68} +15.0826 q^{69} +0.890755 q^{70} +8.17988 q^{71} +0.671237 q^{72} +11.3045 q^{73} -1.16696 q^{74} +1.92279 q^{75} -1.98901 q^{76} -6.68614 q^{77} -0.729934 q^{78} +6.24187 q^{79} -7.97005 q^{80} -11.2389 q^{81} +0.980122 q^{82} -5.62691 q^{83} +17.9055 q^{84} +2.74201 q^{85} -0.00629035 q^{86} +0.814879 q^{87} -0.666439 q^{88} -3.51252 q^{89} +0.340891 q^{90} -13.6123 q^{91} +13.9792 q^{92} -20.5416 q^{93} +0.402991 q^{94} -2.02584 q^{95} +2.67955 q^{96} -12.6552 q^{97} -1.11074 q^{98} -2.55877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−0.104818	−0.0741177	−0.0370588	−	0.999313i	$-0.511799\pi$
$2$	−0.104818	−0.0741177	−0.0370588	+	0.999313i	$0.511799\pi$
$3$	−2.14601	−1.23900	−0.619500	−	0.784997i	$-0.712665\pi$
$3$	−2.14601	−1.23900	−0.619500	+	0.784997i	$0.712665\pi$
$4$	−1.98901	−0.994507
$5$	−2.02584	−0.905982	−0.452991	−	0.891515i	$-0.649643\pi$
$5$	−2.02584	−0.905982	−0.452991	+	0.891515i	$0.649643\pi$
$6$	0.224941	0.0918318
$7$	4.19485	1.58551	0.792753	−	0.609543i	$-0.208647\pi$
$7$	4.19485	1.58551	0.792753	+	0.609543i	$0.208647\pi$
$8$	0.418121	0.147828
$9$	1.60536	0.535121
$10$	0.212345	0.0671493
$11$	−1.59389	−0.480576	−0.240288	−	0.970702i	$-0.577242\pi$
$11$	−1.59389	−0.480576	−0.240288	+	0.970702i	$0.577242\pi$
$12$	4.26844	1.23219
$13$	−3.24500	−0.900001	−0.450000	−	0.893028i	$-0.648576\pi$
$13$	−3.24500	−0.900001	−0.450000	+	0.893028i	$0.648576\pi$
$14$	−0.439697	−0.117514
$15$	4.34747	1.12251
$16$	3.93420	0.983550
$17$	−1.35352	−0.328277	−0.164138	−	0.986437i	$-0.552484\pi$
$17$	−1.35352	−0.328277	−0.164138	+	0.986437i	$0.552484\pi$
$18$	−0.168271	−0.0396620
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	4.02942	0.901005
$21$	−9.00220	−1.96444
$22$	0.167069	0.0356192
$23$	−7.02820	−1.46548	−0.732741	−	0.680508i	$-0.761759\pi$
$23$	−7.02820	−1.46548	−0.732741	+	0.680508i	$0.761759\pi$
$24$	−0.897293	−0.183159
$25$	−0.895984	−0.179197
$26$	0.340135	0.0667060
$27$	2.99290	0.575985
$28$	−8.34362	−1.57680
$29$	−0.379718	−0.0705118	−0.0352559	−	0.999378i	$-0.511225\pi$
$29$	−0.379718	−0.0705118	−0.0352559	+	0.999378i	$0.511225\pi$
$30$	−0.455694	−0.0831980
$31$	9.57198	1.71918	0.859589	−	0.510986i	$-0.170719\pi$
$31$	9.57198	1.71918	0.859589	+	0.510986i	$0.170719\pi$
$32$	−1.24862	−0.220727
$33$	3.42051	0.595434
$34$	0.141874	0.0243311
$35$	−8.49809	−1.43644
$36$	−3.19309	−0.532182
$37$	11.1332	1.83028	0.915140	−	0.403136i	$-0.132080\pi$
$37$	11.1332	1.83028	0.915140	+	0.403136i	$0.132080\pi$
$38$	−0.104818	−0.0170038
$39$	6.96381	1.11510
$40$	−0.847046	−0.133930
$41$	−9.35069	−1.46033	−0.730166	−	0.683270i	$-0.760557\pi$
$41$	−9.35069	−1.46033	−0.730166	+	0.683270i	$0.760557\pi$
$42$	0.943595	0.145600
$43$	0.0600120	0.00915175	0.00457587	−	0.999990i	$-0.498543\pi$
$43$	0.0600120	0.00915175	0.00457587	+	0.999990i	$0.498543\pi$
$44$	3.17027	0.477936
$45$	−3.25221	−0.484810
$46$	0.736684	0.108618
$47$	−3.84467	−0.560802	−0.280401	−	0.959883i	$-0.590468\pi$
$47$	−3.84467	−0.560802	−0.280401	+	0.959883i	$0.590468\pi$
$48$	−8.44284	−1.21862
$49$	10.5968	1.51383
$50$	0.0939155	0.0132817
$51$	2.90467	0.406735
$52$	6.45435	0.895057
$53$	1.41735	0.194688	0.0973442	−	0.995251i	$-0.468965\pi$
$53$	1.41735	0.194688	0.0973442	+	0.995251i	$0.468965\pi$
$54$	−0.313711	−0.0426906
$55$	3.22896	0.435393
$56$	1.75396	0.234382
$57$	−2.14601	−0.284246
$58$	0.0398014	0.00522617
$59$	1.17130	0.152491	0.0762454	−	0.997089i	$-0.475707\pi$
$59$	1.17130	0.152491	0.0762454	+	0.997089i	$0.475707\pi$
$60$	−8.64717	−1.11635
$61$	2.94005	0.376435	0.188218	−	0.982127i	$-0.439729\pi$
$61$	2.94005	0.376435	0.188218	+	0.982127i	$0.439729\pi$
$62$	−1.00332	−0.127422
$63$	6.73427	0.848438
$64$	−7.73752	−0.967190
$65$	6.57384	0.815385
$66$	−0.358531	−0.0441322
$67$	14.7543	1.80252	0.901260	−	0.433278i	$-0.142643\pi$
$67$	14.7543	1.80252	0.901260	+	0.433278i	$0.142643\pi$
$68$	2.69217	0.326474
$69$	15.0826	1.81573
$70$	0.890755	0.106466
$71$	8.17988	0.970773	0.485387	−	0.874300i	$-0.338679\pi$
$71$	8.17988	0.970773	0.485387	+	0.874300i	$0.338679\pi$
$72$	0.671237	0.0791060
$73$	11.3045	1.32309	0.661547	−	0.749904i	$-0.269900\pi$
$73$	11.3045	1.32309	0.661547	+	0.749904i	$0.269900\pi$
$74$	−1.16696	−0.135656
$75$	1.92279	0.222025
$76$	−1.98901	−0.228155
$77$	−6.68614	−0.761956
$78$	−0.729934	−0.0826487
$79$	6.24187	0.702265	0.351133	−	0.936326i	$-0.385797\pi$
$79$	6.24187	0.702265	0.351133	+	0.936326i	$0.385797\pi$
$80$	−7.97005	−0.891078
$81$	−11.2389	−1.24877
$82$	0.980122	0.108236
$83$	−5.62691	−0.617634	−0.308817	−	0.951121i	$-0.599933\pi$
$83$	−5.62691	−0.617634	−0.308817	+	0.951121i	$0.599933\pi$
$84$	17.9055	1.95365
$85$	2.74201	0.297413
$86$	−0.00629035	−0.000678306 0
$87$	0.814879	0.0873642
$88$	−0.666439	−0.0710427
$89$	−3.51252	−0.372326	−0.186163	−	0.982519i	$-0.559605\pi$
$89$	−3.51252	−0.372326	−0.186163	+	0.982519i	$0.559605\pi$
$90$	0.340891	0.0359330
$91$	−13.6123	−1.42696
$92$	13.9792	1.45743
$93$	−20.5416	−2.13006
$94$	0.402991	0.0415654
$95$	−2.02584	−0.207847
$96$	2.67955	0.273480
$97$	−12.6552	−1.28494	−0.642472	−	0.766309i	$-0.722091\pi$
$97$	−12.6552	−1.28494	−0.642472	+	0.766309i	$0.722091\pi$
$98$	−1.11074	−0.112201
$99$	−2.55877	−0.257167
$100$	1.78212	0.178212
$101$	6.72982	0.669643	0.334821	−	0.942282i	$-0.391324\pi$
$101$	6.72982	0.669643	0.334821	+	0.942282i	$0.391324\pi$
$102$	−0.304462	−0.0301463
$103$	2.31452	0.228057	0.114028	−	0.993477i	$-0.463625\pi$
$103$	2.31452	0.228057	0.114028	+	0.993477i	$0.463625\pi$
$104$	−1.35680	−0.133046
$105$	18.2370	1.77975
$106$	−0.148564	−0.0144299
$107$	12.6660	1.22447	0.612236	−	0.790675i	$-0.290270\pi$
$107$	12.6660	1.22447	0.612236	+	0.790675i	$0.290270\pi$
$108$	−5.95292	−0.572820
$109$	−6.59633	−0.631814	−0.315907	−	0.948790i	$-0.602309\pi$
$109$	−6.59633	−0.631814	−0.315907	+	0.948790i	$0.602309\pi$
$110$	−0.338454	−0.0322703
$111$	−23.8919	−2.26772
$112$	16.5034	1.55942
$113$	−7.76282	−0.730265	−0.365132	−	0.930956i	$-0.618976\pi$
$113$	−7.76282	−0.730265	−0.365132	+	0.930956i	$0.618976\pi$
$114$	0.224941	0.0210677
$115$	14.2380	1.32770
$116$	0.755264	0.0701245
$117$	−5.20941	−0.481610
$118$	−0.122774	−0.0113023
$119$	−5.67782	−0.520485
$120$	1.81777	0.165939
$121$	−8.45951	−0.769047
$122$	−0.308171	−0.0279005
$123$	20.0667	1.80935
$124$	−19.0388	−1.70973
$125$	11.9443	1.06833
$126$	−0.705874	−0.0628843
$127$	14.9600	1.32749	0.663744	−	0.747960i	$-0.268966\pi$
$127$	14.9600	1.32749	0.663744	+	0.747960i	$0.268966\pi$
$128$	3.30827	0.292413
$129$	−0.128786	−0.0113390
$130$	−0.689058	−0.0604344
$131$	6.08718	0.531840	0.265920	−	0.963995i	$-0.414324\pi$
$131$	6.08718	0.531840	0.265920	+	0.963995i	$0.414324\pi$
$132$	−6.80343	−0.592163
$133$	4.19485	0.363740
$134$	−1.54652	−0.133599
$135$	−6.06314	−0.521832
$136$	−0.565936	−0.0485286
$137$	−13.4287	−1.14729	−0.573645	−	0.819104i	$-0.694471\pi$
$137$	−13.4287	−1.14729	−0.573645	+	0.819104i	$0.694471\pi$
$138$	−1.58093	−0.134578
$139$	16.0120	1.35812	0.679060	−	0.734083i	$-0.262388\pi$
$139$	16.0120	1.35812	0.679060	+	0.734083i	$0.262388\pi$
$140$	16.9028	1.42855
$141$	8.25070	0.694834
$142$	−0.857400	−0.0719514
$143$	5.17217	0.432519
$144$	6.31582	0.526319
$145$	0.769246	0.0638824
$146$	−1.18492	−0.0980647
$147$	−22.7408	−1.87563
$148$	−22.1440	−1.82023
$149$	−13.3227	−1.09144	−0.545720	−	0.837968i	$-0.683744\pi$
$149$	−13.3227	−1.09144	−0.545720	+	0.837968i	$0.683744\pi$
$150$	−0.201544	−0.0164560
$151$	−21.3593	−1.73820	−0.869099	−	0.494638i	$-0.835300\pi$
$151$	−21.3593	−1.73820	−0.869099	+	0.494638i	$0.835300\pi$
$152$	0.418121	0.0339141
$153$	−2.17289	−0.175668
$154$	0.700829	0.0564744
$155$	−19.3913	−1.55754
$156$	−13.8511	−1.10898
$157$	−14.6518	−1.16934	−0.584671	−	0.811270i	$-0.698776\pi$
$157$	−14.6518	−1.16934	−0.584671	+	0.811270i	$0.698776\pi$
$158$	−0.654262	−0.0520503
$159$	−3.04166	−0.241219
$160$	2.52950	0.199974
$161$	−29.4823	−2.32353
$162$	1.17804	0.0925557
$163$	−22.1842	−1.73760	−0.868802	−	0.495160i	$-0.835110\pi$
$163$	−22.1842	−1.73760	−0.868802	+	0.495160i	$0.835110\pi$
$164$	18.5986	1.45231
$165$	−6.92939	−0.539452
$166$	0.589803	0.0457776
$167$	−6.02943	−0.466571	−0.233286	−	0.972408i	$-0.574948\pi$
$167$	−6.02943	−0.466571	−0.233286	+	0.972408i	$0.574948\pi$
$168$	−3.76401	−0.290400
$169$	−2.46998	−0.189998
$170$	−0.287413	−0.0220436
$171$	1.60536	0.122765
$172$	−0.119365	−0.00910147
$173$	16.3272	1.24133	0.620667	−	0.784074i	$-0.286862\pi$
$173$	16.3272	1.24133	0.620667	+	0.784074i	$0.286862\pi$
$174$	−0.0854141	−0.00647523
$175$	−3.75852	−0.284118
$176$	−6.27068	−0.472670
$177$	−2.51363	−0.188936
$178$	0.368176	0.0275959
$179$	−20.7125	−1.54812	−0.774061	−	0.633111i	$-0.781777\pi$
$179$	−20.7125	−1.54812	−0.774061	+	0.633111i	$0.781777\pi$
$180$	6.46868	0.482147
$181$	−12.0211	−0.893521	−0.446760	−	0.894654i	$-0.647422\pi$
$181$	−12.0211	−0.893521	−0.446760	+	0.894654i	$0.647422\pi$
$182$	1.42682	0.105763
$183$	−6.30939	−0.466403
$184$	−2.93864	−0.216639
$185$	−22.5540	−1.65820
$186$	2.15313	0.157875
$187$	2.15736	0.157762
$188$	7.64709	0.557722
$189$	12.5548	0.913227
$190$	0.212345	0.0154051
$191$	5.21234	0.377152	0.188576	−	0.982059i	$-0.439613\pi$
$191$	5.21234	0.377152	0.188576	+	0.982059i	$0.439613\pi$
$192$	16.6048	1.19835
$193$	−6.70278	−0.482476	−0.241238	−	0.970466i	$-0.577554\pi$
$193$	−6.70278	−0.482476	−0.241238	+	0.970466i	$0.577554\pi$
$194$	1.32650	0.0952371
$195$	−14.1075	−1.01026
$196$	−21.0772	−1.50551
$197$	23.2541	1.65679	0.828394	−	0.560145i	$-0.189255\pi$
$197$	23.2541	1.65679	0.828394	+	0.560145i	$0.189255\pi$
$198$	0.268206	0.0190606
$199$	19.8742	1.40885	0.704423	−	0.709780i	$-0.251206\pi$
$199$	19.8742	1.40885	0.704423	+	0.709780i	$0.251206\pi$
$200$	−0.374630	−0.0264903
$201$	−31.6628	−2.23332
$202$	−0.705408	−0.0496324
$203$	−1.59286	−0.111797
$204$	−5.77743	−0.404501
$205$	18.9430	1.32303
$206$	−0.242604	−0.0169030
$207$	−11.2828	−0.784211
$208$	−12.7665	−0.885196
$209$	−1.59389	−0.110252
$210$	−1.91157	−0.131911
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−2.81913	−0.193619
$213$	−17.5541	−1.20279
$214$	−1.32763	−0.0907550
$215$	−0.121575	−0.00829132
$216$	1.25140	0.0851468
$217$	40.1531	2.72577
$218$	0.691415	0.0468286
$219$	−24.2596	−1.63931
$220$	−6.42245	−0.433001
$221$	4.39217	0.295449
$222$	2.50431	0.168078
$223$	−28.6773	−1.92037	−0.960187	−	0.279357i	$-0.909879\pi$
$223$	−28.6773	−1.92037	−0.960187	+	0.279357i	$0.909879\pi$
$224$	−5.23777	−0.349963
$225$	−1.43838	−0.0958921
$226$	0.813685	0.0541255
$227$	0.887065	0.0588765	0.0294383	−	0.999567i	$-0.490628\pi$
$227$	0.887065	0.0588765	0.0294383	+	0.999567i	$0.490628\pi$
$228$	4.26844	0.282685
$229$	−9.48748	−0.626950	−0.313475	−	0.949596i	$-0.601493\pi$
$229$	−9.48748	−0.626950	−0.313475	+	0.949596i	$0.601493\pi$
$230$	−1.49240	−0.0984060
$231$	14.3485	0.944064
$232$	−0.158768	−0.0104236
$233$	0.0686974	0.00450052	0.00225026	−	0.999997i	$-0.499284\pi$
$233$	0.0686974	0.00450052	0.00225026	+	0.999997i	$0.499284\pi$
$234$	0.546041	0.0356958
$235$	7.78867	0.508077
$236$	−2.32974	−0.151653
$237$	−13.3951	−0.870107
$238$	0.595139	0.0385771
$239$	−19.0525	−1.23241	−0.616203	−	0.787588i	$-0.711330\pi$
$239$	−19.0525	−1.23241	−0.616203	+	0.787588i	$0.711330\pi$
$240$	17.1038	1.10405
$241$	−18.6228	−1.19960	−0.599801	−	0.800149i	$-0.704754\pi$
$241$	−18.6228	−1.19960	−0.599801	+	0.800149i	$0.704754\pi$
$242$	0.886711	0.0570000
$243$	15.1401	0.971237
$244$	−5.84781	−0.374367
$245$	−21.4674	−1.37150
$246$	−2.10335	−0.134105
$247$	−3.24500	−0.206474
$248$	4.00225	0.254143
$249$	12.0754	0.765249
$250$	−1.25198	−0.0791822
$251$	31.3940	1.98157	0.990786	−	0.135435i	$-0.0432433\pi$
$251$	31.3940	1.98157	0.990786	+	0.135435i	$0.0432433\pi$
$252$	−13.3945	−0.843777
$253$	11.2022	0.704275
$254$	−1.56808	−0.0983904
$255$	−5.88439	−0.368495
$256$	15.1283	0.945517
$257$	−28.9211	−1.80405	−0.902024	−	0.431687i	$-0.857919\pi$
$257$	−28.9211	−1.80405	−0.902024	+	0.431687i	$0.857919\pi$
$258$	0.0134992	0.000840422 0
$259$	46.7020	2.90192
$260$	−13.0755	−0.810905
$261$	−0.609586	−0.0377324
$262$	−0.638048	−0.0394187
$263$	1.87413	0.115564	0.0577820	−	0.998329i	$-0.481597\pi$
$263$	1.87413	0.115564	0.0577820	+	0.998329i	$0.481597\pi$
$264$	1.43019	0.0880219
$265$	−2.87133	−0.176384
$266$	−0.439697	−0.0269596
$267$	7.53790	0.461312
$268$	−29.3464	−1.79262
$269$	21.7550	1.32643	0.663214	−	0.748430i	$-0.269192\pi$
$269$	21.7550	1.32643	0.663214	+	0.748430i	$0.269192\pi$
$270$	0.635527	0.0386769
$271$	−1.28883	−0.0782910	−0.0391455	−	0.999234i	$-0.512464\pi$
$271$	−1.28883	−0.0782910	−0.0391455	+	0.999234i	$0.512464\pi$
$272$	−5.32502	−0.322877
$273$	29.2121	1.76800
$274$	1.40757	0.0850345
$275$	1.42810	0.0861177
$276$	−29.9995	−1.80576
$277$	−5.48098	−0.329320	−0.164660	−	0.986350i	$-0.552653\pi$
$277$	−5.48098	−0.329320	−0.164660	+	0.986350i	$0.552653\pi$
$278$	−1.67835	−0.100661
$279$	15.3665	0.919969
$280$	−3.55323	−0.212346
$281$	−27.6823	−1.65139	−0.825693	−	0.564120i	$-0.809216\pi$
$281$	−27.6823	−1.65139	−0.825693	+	0.564120i	$0.809216\pi$
$282$	−0.864824	−0.0514995
$283$	−18.2870	−1.08705	−0.543524	−	0.839394i	$-0.682910\pi$
$283$	−18.2870	−1.08705	−0.543524	+	0.839394i	$0.682910\pi$
$284$	−16.2699	−0.965440
$285$	4.34747	0.257522
$286$	−0.542138	−0.0320573
$287$	−39.2248	−2.31536
$288$	−2.00449	−0.118116
$289$	−15.1680	−0.892234
$290$	−0.0806311	−0.00473482
$291$	27.1583	1.59205
$292$	−22.4848	−1.31583
$293$	−18.3827	−1.07393	−0.536964	−	0.843605i	$-0.680429\pi$
$293$	−18.3827	−1.07393	−0.536964	+	0.843605i	$0.680429\pi$
$294$	2.38366	0.139018
$295$	−2.37287	−0.138154
$296$	4.65501	0.270567
$297$	−4.77036	−0.276804
$298$	1.39646	0.0808950
$299$	22.8065	1.31893
$300$	−3.82446	−0.220805
$301$	0.251742	0.0145101
$302$	2.23885	0.128831
$303$	−14.4423	−0.829687
$304$	3.93420	0.225642
$305$	−5.95607	−0.341044
$306$	0.227759	0.0130201
$307$	−8.07174	−0.460679	−0.230339	−	0.973110i	$-0.573984\pi$
$307$	−8.07174	−0.460679	−0.230339	+	0.973110i	$0.573984\pi$
$308$	13.2988	0.757770
$309$	−4.96699	−0.282562
$310$	2.03256	0.115442
$311$	11.9783	0.679226	0.339613	−	0.940565i	$-0.389704\pi$
$311$	11.9783	0.679226	0.339613	+	0.940565i	$0.389704\pi$
$312$	2.91172	0.164843
$313$	8.01599	0.453091	0.226545	−	0.974001i	$-0.427257\pi$
$313$	8.01599	0.453091	0.226545	+	0.974001i	$0.427257\pi$
$314$	1.53578	0.0866689
$315$	−13.6425	−0.768670
$316$	−12.4152	−0.698407
$317$	−25.9699	−1.45862	−0.729308	−	0.684186i	$-0.760158\pi$
$317$	−25.9699	−1.45862	−0.729308	+	0.684186i	$0.760158\pi$
$318$	0.318821	0.0178786
$319$	0.605229	0.0338863
$320$	15.6750	0.876257
$321$	−27.1815	−1.51712
$322$	3.09028	0.172215
$323$	−1.35352	−0.0753119
$324$	22.3543	1.24191
$325$	2.90747	0.161277
$326$	2.32531	0.128787
$327$	14.1558	0.782817
$328$	−3.90972	−0.215878
$329$	−16.1278	−0.889155
$330$	0.726326	0.0399829
$331$	−24.9819	−1.37313	−0.686565	−	0.727068i	$-0.740882\pi$
$331$	−24.9819	−1.37313	−0.686565	+	0.727068i	$0.740882\pi$
$332$	11.1920	0.614241
$333$	17.8728	0.979422
$334$	0.631994	0.0345812
$335$	−29.8897	−1.63305
$336$	−35.4165	−1.93213
$337$	16.8009	0.915206	0.457603	−	0.889157i	$-0.348708\pi$
$337$	16.8009	0.915206	0.457603	+	0.889157i	$0.348708\pi$
$338$	0.258899	0.0140822
$339$	16.6591	0.904798
$340$	−5.45390	−0.295779
$341$	−15.2567	−0.826196
$342$	−0.168271	−0.00909908
$343$	15.0880	0.814677
$344$	0.0250923	0.00135289
$345$	−30.5549	−1.64502
$346$	−1.71139	−0.0920048
$347$	26.2227	1.40771	0.703855	−	0.710344i	$-0.251461\pi$
$347$	26.2227	1.40771	0.703855	+	0.710344i	$0.251461\pi$
$348$	−1.62080	−0.0868842
$349$	10.7960	0.577894	0.288947	−	0.957345i	$-0.406695\pi$
$349$	10.7960	0.577894	0.288947	+	0.957345i	$0.406695\pi$
$350$	0.393962	0.0210581
$351$	−9.71197	−0.518387
$352$	1.99016	0.106076
$353$	5.23431	0.278594	0.139297	−	0.990251i	$-0.455516\pi$
$353$	5.23431	0.278594	0.139297	+	0.990251i	$0.455516\pi$
$354$	0.263474	0.0140035
$355$	−16.5711	−0.879503
$356$	6.98644	0.370281
$357$	12.1847	0.644881
$358$	2.17104	0.114743
$359$	19.3704	1.02233	0.511166	−	0.859482i	$-0.329214\pi$
$359$	19.3704	1.02233	0.511166	+	0.859482i	$0.329214\pi$
$360$	−1.35982	−0.0716686
$361$	1.00000	0.0526316
$362$	1.26003	0.0662257
$363$	18.1542	0.952849
$364$	27.0750	1.41912
$365$	−22.9011	−1.19870
$366$	0.661339	0.0345687
$367$	−17.6557	−0.921621	−0.460810	−	0.887499i	$-0.652441\pi$
$367$	−17.6557	−0.921621	−0.460810	+	0.887499i	$0.652441\pi$
$368$	−27.6503	−1.44137
$369$	−15.0113	−0.781455
$370$	2.36407	0.122902
$371$	5.94559	0.308680
$372$	40.8575	2.11836
$373$	24.1465	1.25026	0.625129	−	0.780522i	$-0.285046\pi$
$373$	24.1465	1.25026	0.625129	+	0.780522i	$0.285046\pi$
$374$	−0.226131	−0.0116930
$375$	−25.6326	−1.32366
$376$	−1.60754	−0.0829024
$377$	1.23218	0.0634607
$378$	−1.31597	−0.0676862
$379$	−19.3373	−0.993291	−0.496645	−	0.867954i	$-0.665435\pi$
$379$	−19.3373	−0.993291	−0.496645	+	0.867954i	$0.665435\pi$
$380$	4.02942	0.206705
$381$	−32.1044	−1.64476
$382$	−0.546348	−0.0279536
$383$	−31.6196	−1.61569	−0.807844	−	0.589396i	$-0.799366\pi$
$383$	−31.6196	−1.61569	−0.807844	+	0.589396i	$0.799366\pi$
$384$	−7.09958	−0.362299
$385$	13.5450	0.690318
$386$	0.702573	0.0357600
$387$	0.0963412	0.00489730
$388$	25.1714	1.27789
$389$	8.01364	0.406308	0.203154	−	0.979147i	$-0.434881\pi$
$389$	8.01364	0.406308	0.203154	+	0.979147i	$0.434881\pi$
$390$	1.47873	0.0748782
$391$	9.51281	0.481084
$392$	4.43075	0.223786
$393$	−13.0632	−0.658950
$394$	−2.43746	−0.122797
$395$	−12.6450	−0.636240
$396$	5.08944	0.255754
$397$	−0.435255	−0.0218448	−0.0109224	−	0.999940i	$-0.503477\pi$
$397$	−0.435255	−0.0218448	−0.0109224	+	0.999940i	$0.503477\pi$
$398$	−2.08318	−0.104420
$399$	−9.00220	−0.450674
$400$	−3.52498	−0.176249
$401$	−7.01538	−0.350331	−0.175166	−	0.984539i	$-0.556046\pi$
$401$	−7.01538	−0.350331	−0.175166	+	0.984539i	$0.556046\pi$
$402$	3.31884	0.165529
$403$	−31.0611	−1.54726
$404$	−13.3857	−0.665964
$405$	22.7682	1.13136
$406$	0.166961	0.00828613
$407$	−17.7450	−0.879589
$408$	1.21450	0.0601269
$409$	4.26476	0.210879	0.105439	−	0.994426i	$-0.466375\pi$
$409$	4.26476	0.210879	0.105439	+	0.994426i	$0.466375\pi$
$410$	−1.98557	−0.0980602
$411$	28.8181	1.42149
$412$	−4.60362	−0.226804
$413$	4.91345	0.241775
$414$	1.18265	0.0581239
$415$	11.3992	0.559565
$416$	4.05177	0.198654
$417$	−34.3619	−1.68271
$418$	0.167069	0.00817160
$419$	26.4892	1.29408	0.647041	−	0.762456i	$-0.276006\pi$
$419$	26.4892	1.29408	0.647041	+	0.762456i	$0.276006\pi$
$420$	−36.2736	−1.76997
$421$	13.6485	0.665189	0.332595	−	0.943070i	$-0.392076\pi$
$421$	13.6485	0.665189	0.332595	+	0.943070i	$0.392076\pi$
$422$	−0.104818	−0.00510247
$423$	−6.17209	−0.300097
$424$	0.592626	0.0287804
$425$	1.21273	0.0588262
$426$	1.83999	0.0891479
$427$	12.3331	0.596840
$428$	−25.1929	−1.21775
$429$	−11.0995	−0.535891
$430$	0.0127432	0.000614533 0
$431$	−8.76629	−0.422257	−0.211129	−	0.977458i	$-0.567714\pi$
$431$	−8.76629	−0.422257	−0.211129	+	0.977458i	$0.567714\pi$
$432$	11.7747	0.566510
$433$	−20.7606	−0.997690	−0.498845	−	0.866691i	$-0.666242\pi$
$433$	−20.7606	−0.997690	−0.498845	+	0.866691i	$0.666242\pi$
$434$	−4.20877	−0.202028
$435$	−1.65081	−0.0791504
$436$	13.1202	0.628343
$437$	−7.02820	−0.336204
$438$	2.54285	0.121502
$439$	13.9646	0.666494	0.333247	−	0.942840i	$-0.391856\pi$
$439$	13.9646	0.666494	0.333247	+	0.942840i	$0.391856\pi$
$440$	1.35010	0.0643634
$441$	17.0117	0.810082
$442$	−0.460380	−0.0218980
$443$	−31.2626	−1.48533	−0.742666	−	0.669662i	$-0.766439\pi$
$443$	−31.2626	−1.48533	−0.742666	+	0.669662i	$0.766439\pi$
$444$	47.5213	2.25526
$445$	7.11578	0.337321
$446$	3.00590	0.142334
$447$	28.5907	1.35229
$448$	−32.4578	−1.53349
$449$	−4.50263	−0.212492	−0.106246	−	0.994340i	$-0.533883\pi$
$449$	−4.50263	−0.212492	−0.106246	+	0.994340i	$0.533883\pi$
$450$	0.150769	0.00710730
$451$	14.9040	0.701800
$452$	15.4404	0.726253
$453$	45.8374	2.15363
$454$	−0.0929805	−0.00436379
$455$	27.5763	1.29280
$456$	−0.897293	−0.0420196
$457$	1.88189	0.0880310	0.0440155	−	0.999031i	$-0.485985\pi$
$457$	1.88189	0.0880310	0.0440155	+	0.999031i	$0.485985\pi$
$458$	0.994461	0.0464681
$459$	−4.05096	−0.189082
$460$	−28.3196	−1.32041
$461$	6.97200	0.324719	0.162359	−	0.986732i	$-0.448090\pi$
$461$	6.97200	0.324719	0.162359	+	0.986732i	$0.448090\pi$
$462$	−1.50399	−0.0699718
$463$	38.6895	1.79805	0.899026	−	0.437895i	$-0.144276\pi$
$463$	38.6895	1.79805	0.899026	+	0.437895i	$0.144276\pi$
$464$	−1.49389	−0.0693519
$465$	41.6139	1.92980
$466$	−0.00720074	−0.000333568 0
$467$	−30.4129	−1.40734	−0.703671	−	0.710526i	$-0.748457\pi$
$467$	−30.4129	−1.40734	−0.703671	+	0.710526i	$0.748457\pi$
$468$	10.3616	0.478964
$469$	61.8920	2.85791
$470$	−0.816395	−0.0376575
$471$	31.4430	1.44882
$472$	0.489747	0.0225424
$473$	−0.0956526	−0.00439811
$474$	1.40405	0.0644903
$475$	−0.895984	−0.0411106
$476$	11.2933	0.517626
$477$	2.27537	0.104182
$478$	1.99705	0.0913430
$479$	23.9873	1.09601	0.548005	−	0.836475i	$-0.315387\pi$
$479$	23.9873	1.09601	0.548005	+	0.836475i	$0.315387\pi$
$480$	−5.42833	−0.247768
$481$	−36.1271	−1.64725
$482$	1.95201	0.0889117
$483$	63.2693	2.87885
$484$	16.8261	0.764822
$485$	25.6374	1.16414
$486$	−1.58696	−0.0719859
$487$	1.47670	0.0669155	0.0334577	−	0.999440i	$-0.489348\pi$
$487$	1.47670	0.0669155	0.0334577	+	0.999440i	$0.489348\pi$
$488$	1.22930	0.0556478
$489$	47.6076	2.15289
$490$	2.25017	0.101652
$491$	−7.85922	−0.354681	−0.177341	−	0.984150i	$-0.556749\pi$
$491$	−7.85922	−0.354681	−0.177341	+	0.984150i	$0.556749\pi$
$492$	−39.9129	−1.79941
$493$	0.513956	0.0231474
$494$	0.340135	0.0153034
$495$	5.18366	0.232988
$496$	37.6581	1.69090
$497$	34.3134	1.53917
$498$	−1.26572	−0.0567185
$499$	−20.0454	−0.897354	−0.448677	−	0.893694i	$-0.648105\pi$
$499$	−20.0454	−0.897354	−0.448677	+	0.893694i	$0.648105\pi$
$500$	−23.7574	−1.06246
$501$	12.9392	0.578082
$502$	−3.29066	−0.146870
$503$	−22.8211	−1.01754	−0.508771	−	0.860902i	$-0.669900\pi$
$503$	−22.8211	−1.01754	−0.508771	+	0.860902i	$0.669900\pi$
$504$	2.81574	0.125423
$505$	−13.6335	−0.606684
$506$	−1.17419	−0.0521992
$507$	5.30060	0.235408
$508$	−29.7557	−1.32020
$509$	−20.2637	−0.898174	−0.449087	−	0.893488i	$-0.648251\pi$
$509$	−20.2637	−0.898174	−0.449087	+	0.893488i	$0.648251\pi$
$510$	0.616791	0.0273120
$511$	47.4208	2.09777
$512$	−8.20226	−0.362492
$513$	2.99290	0.132140
$514$	3.03146	0.133712
$515$	−4.68885	−0.206615
$516$	0.256158	0.0112767
$517$	6.12798	0.269508
$518$	−4.89522	−0.215084
$519$	−35.0384	−1.53801
$520$	2.74866	0.120537
$521$	40.4346	1.77147	0.885736	−	0.464189i	$-0.153654\pi$
$521$	40.4346	1.77147	0.885736	+	0.464189i	$0.153654\pi$
$522$	0.0638957	0.00279664
$523$	1.98595	0.0868396	0.0434198	−	0.999057i	$-0.486175\pi$
$523$	1.98595	0.0868396	0.0434198	+	0.999057i	$0.486175\pi$
$524$	−12.1075	−0.528918
$525$	8.06583	0.352022
$526$	−0.196443	−0.00856534
$527$	−12.9559	−0.564367
$528$	13.4570	0.585639
$529$	26.3956	1.14764
$530$	0.300967	0.0130732
$531$	1.88037	0.0816011
$532$	−8.34362	−0.361742
$533$	30.3430	1.31430
$534$	−0.790109	−0.0341914
$535$	−25.6593	−1.10935
$536$	6.16907	0.266463
$537$	44.4492	1.91812
$538$	−2.28032	−0.0983117
$539$	−16.8901	−0.727509
$540$	12.0597	0.518965
$541$	18.5863	0.799089	0.399544	−	0.916714i	$-0.369168\pi$
$541$	18.5863	0.799089	0.399544	+	0.916714i	$0.369168\pi$
$542$	0.135093	0.00580275
$543$	25.7974	1.10707
$544$	1.69003	0.0724595
$545$	13.3631	0.572412
$546$	−3.06197	−0.131040
$547$	11.2551	0.481234	0.240617	−	0.970620i	$-0.422650\pi$
$547$	11.2551	0.481234	0.240617	+	0.970620i	$0.422650\pi$
$548$	26.7098	1.14099
$549$	4.71986	0.201439
$550$	−0.149691	−0.00638284
$551$	−0.379718	−0.0161765
$552$	6.30636	0.268416
$553$	26.1837	1.11345
$554$	0.574506	0.0244084
$555$	48.4011	2.05451
$556$	−31.8481	−1.35066
$557$	41.0627	1.73988	0.869942	−	0.493154i	$-0.164156\pi$
$557$	41.0627	1.73988	0.869942	+	0.493154i	$0.164156\pi$
$558$	−1.61069	−0.0681860
$559$	−0.194739	−0.00823658
$560$	−33.4332	−1.41281
$561$	−4.62972	−0.195467
$562$	2.90161	0.122397
$563$	18.5422	0.781460	0.390730	−	0.920505i	$-0.372223\pi$
$563$	18.5422	0.781460	0.390730	+	0.920505i	$0.372223\pi$
$564$	−16.4108	−0.691017
$565$	15.7262	0.661607
$566$	1.91681	0.0805695
$567$	−47.1455	−1.97993
$568$	3.42018	0.143508
$569$	−43.9762	−1.84358	−0.921788	−	0.387694i	$-0.873272\pi$
$569$	−43.9762	−1.84358	−0.921788	+	0.387694i	$0.873272\pi$
$570$	−0.455694	−0.0190869
$571$	−26.0321	−1.08941	−0.544704	−	0.838628i	$-0.683358\pi$
$571$	−26.0321	−1.08941	−0.544704	+	0.838628i	$0.683358\pi$
$572$	−10.2875	−0.430143
$573$	−11.1857	−0.467291
$574$	4.11147	0.171609
$575$	6.29716	0.262610
$576$	−12.4215	−0.517564
$577$	−0.692983	−0.0288493	−0.0144246	−	0.999896i	$-0.504592\pi$
$577$	−0.692983	−0.0288493	−0.0144246	+	0.999896i	$0.504592\pi$
$578$	1.58988	0.0661303
$579$	14.3842	0.597788
$580$	−1.53004	−0.0635315
$581$	−23.6041	−0.979262
$582$	−2.84668	−0.117999
$583$	−2.25911	−0.0935626
$584$	4.72666	0.195591
$585$	10.5534	0.436330
$586$	1.92684	0.0795970
$587$	29.0470	1.19890	0.599449	−	0.800413i	$-0.295386\pi$
$587$	29.0470	1.19890	0.599449	+	0.800413i	$0.295386\pi$
$588$	45.2318	1.86533
$589$	9.57198	0.394407
$590$	0.248720	0.0102396
$591$	−49.9036	−2.05276
$592$	43.8001	1.80017
$593$	18.1786	0.746504	0.373252	−	0.927730i	$-0.378243\pi$
$593$	18.1786	0.746504	0.373252	+	0.927730i	$0.378243\pi$
$594$	0.500021	0.0205161
$595$	11.5023	0.471550
$596$	26.4991	1.08544
$597$	−42.6503	−1.74556
$598$	−2.39054	−0.0977564
$599$	18.0108	0.735901	0.367950	−	0.929845i	$-0.380060\pi$
$599$	18.0108	0.735901	0.367950	+	0.929845i	$0.380060\pi$
$600$	0.803960	0.0328215
$601$	−11.9507	−0.487478	−0.243739	−	0.969841i	$-0.578374\pi$
$601$	−11.9507	−0.487478	−0.243739	+	0.969841i	$0.578374\pi$
$602$	−0.0263871	−0.00107546
$603$	23.6860	0.964568
$604$	42.4840	1.72865
$605$	17.1376	0.696742
$606$	1.51381	0.0614945
$607$	−26.0414	−1.05699	−0.528494	−	0.848937i	$-0.677243\pi$
$607$	−26.0414	−1.05699	−0.528494	+	0.848937i	$0.677243\pi$
$608$	−1.24862	−0.0506382
$609$	3.41830	0.138516
$610$	0.624305	0.0252774
$611$	12.4759	0.504723
$612$	4.32191	0.174703
$613$	−22.1670	−0.895316	−0.447658	−	0.894205i	$-0.647742\pi$
$613$	−22.1670	−0.895316	−0.447658	+	0.894205i	$0.647742\pi$
$614$	0.846065	0.0341444
$615$	−40.6518	−1.63924
$616$	−2.79562	−0.112639
$617$	−23.7461	−0.955983	−0.477992	−	0.878364i	$-0.658635\pi$
$617$	−23.7461	−0.955983	−0.477992	+	0.878364i	$0.658635\pi$
$618$	0.520631	0.0209429
$619$	−18.4188	−0.740314	−0.370157	−	0.928969i	$-0.620696\pi$
$619$	−18.4188	−0.740314	−0.370157	+	0.928969i	$0.620696\pi$
$620$	38.5695	1.54899
$621$	−21.0347	−0.844095
$622$	−1.25554	−0.0503427
$623$	−14.7345	−0.590325
$624$	27.3970	1.09676
$625$	−19.7173	−0.788692
$626$	−0.840222	−0.0335820
$627$	3.42051	0.136602
$628$	29.1427	1.16292
$629$	−15.0690	−0.600839
$630$	1.42999	0.0569720
$631$	14.0929	0.561031	0.280515	−	0.959850i	$-0.409495\pi$
$631$	14.0929	0.561031	0.280515	+	0.959850i	$0.409495\pi$
$632$	2.60986	0.103815
$633$	−2.14601	−0.0852963
$634$	2.72212	0.108109
$635$	−30.3066	−1.20268
$636$	6.04990	0.239894
$637$	−34.3866	−1.36245
$638$	−0.0634390	−0.00251157
$639$	13.1317	0.519481
$640$	−6.70202	−0.264920
$641$	20.1571	0.796158	0.398079	−	0.917351i	$-0.369677\pi$
$641$	20.1571	0.796158	0.398079	+	0.917351i	$0.369677\pi$
$642$	2.84911	0.112445
$643$	21.6134	0.852348	0.426174	−	0.904641i	$-0.359861\pi$
$643$	21.6134	0.852348	0.426174	+	0.904641i	$0.359861\pi$
$644$	58.6406	2.31076
$645$	0.260900	0.0102729
$646$	0.141874	0.00558194
$647$	0.0177580	0.000698137 0	0.000349069	−	1.00000i	$-0.499889\pi$
$647$	0.0177580	0.000698137 0	0.000349069		1.00000i	$0.499889\pi$
$648$	−4.69922	−0.184603
$649$	−1.86693	−0.0732834
$650$	−0.304756	−0.0119535
$651$	−86.1689	−3.37723
$652$	44.1247	1.72806
$653$	−21.8829	−0.856343	−0.428172	−	0.903697i	$-0.640842\pi$
$653$	−21.8829	−0.856343	−0.428172	+	0.903697i	$0.640842\pi$
$654$	−1.48379	−0.0580206
$655$	−12.3316	−0.481837
$656$	−36.7875	−1.43631
$657$	18.1479	0.708016
$658$	1.69049	0.0659021
$659$	25.1819	0.980946	0.490473	−	0.871456i	$-0.336824\pi$
$659$	25.1819	0.980946	0.490473	+	0.871456i	$0.336824\pi$
$660$	13.7826	0.536489
$661$	−37.9744	−1.47703	−0.738516	−	0.674236i	$-0.764473\pi$
$661$	−37.9744	−1.47703	−0.738516	+	0.674236i	$0.764473\pi$
$662$	2.61856	0.101773
$663$	−9.42565	−0.366062
$664$	−2.35273	−0.0913037
$665$	−8.49809	−0.329542
$666$	−1.87339	−0.0725925
$667$	2.66873	0.103334
$668$	11.9926	0.464008
$669$	61.5418	2.37934
$670$	3.13299	0.121038
$671$	−4.68612	−0.180906
$672$	11.2403	0.433605
$673$	42.8041	1.64998	0.824989	−	0.565149i	$-0.191181\pi$
$673$	42.8041	1.64998	0.824989	+	0.565149i	$0.191181\pi$
$674$	−1.76105	−0.0678329
$675$	−2.68159	−0.103215
$676$	4.91282	0.188955
$677$	−33.3817	−1.28296	−0.641482	−	0.767138i	$-0.721680\pi$
$677$	−33.3817	−1.28296	−0.641482	+	0.767138i	$0.721680\pi$
$678$	−1.74618	−0.0670615
$679$	−53.0868	−2.03729
$680$	1.14649	0.0439660
$681$	−1.90365	−0.0729480
$682$	1.59918	0.0612357
$683$	−19.3627	−0.740894	−0.370447	−	0.928854i	$-0.620795\pi$
$683$	−19.3627	−0.740894	−0.370447	+	0.928854i	$0.620795\pi$
$684$	−3.19309	−0.122091
$685$	27.2043	1.03942
$686$	−1.58150	−0.0603820
$687$	20.3602	0.776792
$688$	0.236099	0.00900120
$689$	−4.59931	−0.175220
$690$	3.20271	0.121925
$691$	−0.785969	−0.0298997	−0.0149498	−	0.999888i	$-0.504759\pi$
$691$	−0.785969	−0.0298997	−0.0149498	+	0.999888i	$0.504759\pi$
$692$	−32.4750	−1.23452
$693$	−10.7337	−0.407739
$694$	−2.74862	−0.104336
$695$	−32.4377	−1.23043
$696$	0.340718	0.0129149
$697$	12.6563	0.479393
$698$	−1.13161	−0.0428322
$699$	−0.147425	−0.00557614
$700$	7.47575	0.282557
$701$	45.4134	1.71524	0.857620	−	0.514284i	$-0.171942\pi$
$701$	45.4134	1.71524	0.857620	+	0.514284i	$0.171942\pi$
$702$	1.01799	0.0384216
$703$	11.1332	0.419895
$704$	12.3328	0.464808
$705$	−16.7146	−0.629507
$706$	−0.548651	−0.0206488
$707$	28.2306	1.06172
$708$	4.99965	0.187898
$709$	−10.1528	−0.381297	−0.190649	−	0.981658i	$-0.561059\pi$
$709$	−10.1528	−0.381297	−0.190649	+	0.981658i	$0.561059\pi$
$710$	1.73695	0.0651867
$711$	10.0205	0.375797
$712$	−1.46866	−0.0550403
$713$	−67.2738	−2.51942
$714$	−1.27717	−0.0477971
$715$	−10.4780	−0.391854
$716$	41.1973	1.53962
$717$	40.8869	1.52695
$718$	−2.03038	−0.0757729
$719$	−21.8393	−0.814469	−0.407235	−	0.913324i	$-0.633507\pi$
$719$	−21.8393	−0.814469	−0.407235	+	0.913324i	$0.633507\pi$
$720$	−12.7948	−0.476835
$721$	9.70908	0.361585
$722$	−0.104818	−0.00390093
$723$	39.9648	1.48631
$724$	23.9101	0.888612
$725$	0.340221	0.0126355
$726$	−1.90289	−0.0706230
$727$	7.02411	0.260510	0.130255	−	0.991481i	$-0.458420\pi$
$727$	7.02411	0.260510	0.130255	+	0.991481i	$0.458420\pi$
$728$	−5.69159	−0.210944
$729$	1.22589	0.0454032
$730$	2.40046	0.0888448
$731$	−0.0812275	−0.00300431
$732$	12.5495	0.463841
$733$	25.8187	0.953634	0.476817	−	0.879002i	$-0.341790\pi$
$733$	25.8187	0.953634	0.476817	+	0.879002i	$0.341790\pi$
$734$	1.85064	0.0683084
$735$	46.0692	1.69929
$736$	8.77554	0.323471
$737$	−23.5167	−0.866248
$738$	1.57345	0.0579196
$739$	−33.7260	−1.24063	−0.620315	−	0.784352i	$-0.712995\pi$
$739$	−33.7260	−1.24063	−0.620315	+	0.784352i	$0.712995\pi$
$740$	44.8601	1.64909
$741$	6.96381	0.255822
$742$	−0.623206	−0.0228786
$743$	19.0662	0.699472	0.349736	−	0.936848i	$-0.386271\pi$
$743$	19.0662	0.699472	0.349736	+	0.936848i	$0.386271\pi$
$744$	−8.58887	−0.314883
$745$	26.9897	0.988825
$746$	−2.53099	−0.0926662
$747$	−9.03325	−0.330509
$748$	−4.29102	−0.156895
$749$	53.1322	1.94141
$750$	2.68676	0.0981068
$751$	−30.5660	−1.11537	−0.557684	−	0.830053i	$-0.688310\pi$
$751$	−30.5660	−1.11537	−0.557684	+	0.830053i	$0.688310\pi$
$752$	−15.1257	−0.551577
$753$	−67.3719	−2.45517
$754$	−0.129155	−0.00470356
$755$	43.2705	1.57478
$756$	−24.9716	−0.908210
$757$	−6.15479	−0.223700	−0.111850	−	0.993725i	$-0.535678\pi$
$757$	−6.15479	−0.223700	−0.111850	+	0.993725i	$0.535678\pi$
$758$	2.02690	0.0736204
$759$	−24.0400	−0.872597
$760$	−0.847046	−0.0307256
$761$	−48.9498	−1.77443	−0.887215	−	0.461356i	$-0.847363\pi$
$761$	−48.9498	−1.77443	−0.887215	+	0.461356i	$0.847363\pi$
$762$	3.36513	0.121906
$763$	−27.6706	−1.00174
$764$	−10.3674	−0.375080
$765$	4.40193	0.159152
$766$	3.31431	0.119751
$767$	−3.80088	−0.137242
$768$	−32.4654	−1.17150
$769$	−44.8606	−1.61771	−0.808857	−	0.588005i	$-0.799914\pi$
$769$	−44.8606	−1.61771	−0.808857	+	0.588005i	$0.799914\pi$
$770$	−1.41977	−0.0511648
$771$	62.0650	2.23521
$772$	13.3319	0.479826
$773$	−0.790557	−0.0284343	−0.0142172	−	0.999899i	$-0.504526\pi$
$773$	−0.790557	−0.0284343	−0.0142172	+	0.999899i	$0.504526\pi$
$774$	−0.0100983	−0.000362976 0
$775$	−8.57634	−0.308071
$776$	−5.29142	−0.189951
$777$	−100.223	−3.59548
$778$	−0.839975	−0.0301146
$779$	−9.35069	−0.335023
$780$	28.0601	1.00471
$781$	−13.0378	−0.466530
$782$	−0.997116	−0.0356568
$783$	−1.13646	−0.0406137
$784$	41.6899	1.48893
$785$	29.6822	1.05940
$786$	1.36926	0.0488398
$787$	−28.8625	−1.02884	−0.514418	−	0.857539i	$-0.671992\pi$
$787$	−28.8625	−1.02884	−0.514418	+	0.857539i	$0.671992\pi$
$788$	−46.2528	−1.64769
$789$	−4.02191	−0.143184
$790$	1.32543	0.0471566
$791$	−32.5639	−1.15784
$792$	−1.06988	−0.0380165
$793$	−9.54047	−0.338792
$794$	0.0456226	0.00161909
$795$	6.16190	0.218540
$796$	−39.5301	−1.40111
$797$	−7.28376	−0.258004	−0.129002	−	0.991644i	$-0.541177\pi$
$797$	−7.28376	−0.258004	−0.129002	+	0.991644i	$0.541177\pi$
$798$	0.943595	0.0334029
$799$	5.20384	0.184098
$800$	1.11874	0.0395535
$801$	−5.63887	−0.199240
$802$	0.735340	0.0259657
$803$	−18.0182	−0.635847
$804$	62.9778	2.22106
$805$	59.7263	2.10508
$806$	3.25577	0.114679
$807$	−46.6865	−1.64344
$808$	2.81388	0.0989921
$809$	−14.3444	−0.504322	−0.252161	−	0.967685i	$-0.581141\pi$
$809$	−14.3444	−0.504322	−0.252161	+	0.967685i	$0.581141\pi$
$810$	−2.38652	−0.0838538
$811$	−31.3748	−1.10172	−0.550859	−	0.834598i	$-0.685700\pi$
$811$	−31.3748	−1.10172	−0.550859	+	0.834598i	$0.685700\pi$
$812$	3.16822	0.111183
$813$	2.76585	0.0970026
$814$	1.86000	0.0651931
$815$	44.9417	1.57424
$816$	11.4276	0.400044
$817$	0.0600120	0.00209955
$818$	−0.447025	−0.0156299
$819$	−21.8527	−0.763595
$820$	−37.6778	−1.31577
$821$	−5.42568	−0.189358	−0.0946788	−	0.995508i	$-0.530182\pi$
$821$	−5.42568	−0.189358	−0.0946788	+	0.995508i	$0.530182\pi$
$822$	−3.02066	−0.105358
$823$	−48.8156	−1.70160	−0.850802	−	0.525487i	$-0.823883\pi$
$823$	−48.8156	−1.70160	−0.850802	+	0.525487i	$0.823883\pi$
$824$	0.967751	0.0337132
$825$	−3.06472	−0.106700
$826$	−0.515019	−0.0179198
$827$	−28.2217	−0.981365	−0.490682	−	0.871339i	$-0.663252\pi$
$827$	−28.2217	−0.981365	−0.490682	+	0.871339i	$0.663252\pi$
$828$	22.4417	0.779903
$829$	0.238104	0.00826969	0.00413485	−	0.999991i	$-0.498684\pi$
$829$	0.238104	0.00826969	0.00413485	+	0.999991i	$0.498684\pi$
$830$	−1.19485	−0.0414737
$831$	11.7622	0.408027
$832$	25.1083	0.870472
$833$	−14.3430	−0.496955
$834$	3.60176	0.124719
$835$	12.2146	0.422705
$836$	3.17027	0.109646
$837$	28.6480	0.990220
$838$	−2.77655	−0.0959143
$839$	−33.7112	−1.16384	−0.581920	−	0.813246i	$-0.697698\pi$
$839$	−33.7112	−1.16384	−0.581920	+	0.813246i	$0.697698\pi$
$840$	7.62528	0.263097
$841$	−28.8558	−0.995028
$842$	−1.43062	−0.0493023
$843$	59.4065	2.04607
$844$	−1.98901	−0.0684647
$845$	5.00378	0.172135
$846$	0.646948	0.0222425
$847$	−35.4864	−1.21933
$848$	5.57615	0.191486
$849$	39.2441	1.34685
$850$	−0.127116	−0.00436006
$851$	−78.2461	−2.68224
$852$	34.9154	1.19618
$853$	36.7974	1.25992	0.629960	−	0.776627i	$-0.283071\pi$
$853$	36.7974	1.25992	0.629960	+	0.776627i	$0.283071\pi$
$854$	−1.29273	−0.0442364
$855$	−3.25221	−0.111223
$856$	5.29594	0.181011
$857$	14.5178	0.495918	0.247959	−	0.968771i	$-0.420240\pi$
$857$	14.5178	0.495918	0.247959	+	0.968771i	$0.420240\pi$
$858$	1.16343	0.0397190
$859$	−23.7874	−0.811616	−0.405808	−	0.913958i	$-0.633010\pi$
$859$	−23.7874	−0.811616	−0.405808	+	0.913958i	$0.633010\pi$
$860$	0.241813	0.00824577
$861$	84.1768	2.86874
$862$	0.918867	0.0312967
$863$	−24.7565	−0.842721	−0.421361	−	0.906893i	$-0.638447\pi$
$863$	−24.7565	−0.842721	−0.421361	+	0.906893i	$0.638447\pi$
$864$	−3.73699	−0.127135
$865$	−33.0763	−1.12463
$866$	2.17609	0.0739465
$867$	32.5507	1.10548
$868$	−79.8650	−2.71079
$869$	−9.94885	−0.337492
$870$	0.173035	0.00586644
$871$	−47.8776	−1.62227
$872$	−2.75807	−0.0933999
$873$	−20.3163	−0.687601
$874$	0.736684	0.0249187
$875$	50.1046	1.69384
$876$	48.2527	1.63031
$877$	−22.1504	−0.747966	−0.373983	−	0.927436i	$-0.622008\pi$
$877$	−22.1504	−0.747966	−0.373983	+	0.927436i	$0.622008\pi$
$878$	−1.46374	−0.0493990
$879$	39.4495	1.33060
$880$	12.7034	0.428231
$881$	35.5554	1.19789	0.598945	−	0.800790i	$-0.295587\pi$
$881$	35.5554	1.19789	0.598945	+	0.800790i	$0.295587\pi$
$882$	−1.78314	−0.0600414
$883$	−46.1275	−1.55232	−0.776158	−	0.630539i	$-0.782834\pi$
$883$	−46.1275	−1.55232	−0.776158	+	0.630539i	$0.782834\pi$
$884$	−8.73609	−0.293826
$885$	5.09221	0.171173
$886$	3.27689	0.110089
$887$	41.0746	1.37915	0.689575	−	0.724215i	$-0.257797\pi$
$887$	41.0746	1.37915	0.689575	+	0.724215i	$0.257797\pi$
$888$	−9.98971	−0.335233
$889$	62.7552	2.10474
$890$	−0.745864	−0.0250014
$891$	17.9136	0.600127
$892$	57.0395	1.90983
$893$	−3.84467	−0.128657
$894$	−2.99683	−0.100229
$895$	41.9601	1.40257
$896$	13.8777	0.463622
$897$	−48.9430	−1.63416
$898$	0.471957	0.0157494
$899$	−3.63465	−0.121222
$900$	2.86096	0.0953653
$901$	−1.91842	−0.0639117
$902$	−1.56221	−0.0520158
$903$	−0.540240	−0.0179781
$904$	−3.24580	−0.107954
$905$	24.3528	0.809514
$906$	−4.80459	−0.159622
$907$	−53.4659	−1.77531	−0.887653	−	0.460513i	$-0.847665\pi$
$907$	−53.4659	−1.77531	−0.887653	+	0.460513i	$0.847665\pi$
$908$	−1.76438	−0.0585531
$909$	10.8038	0.358340
$910$	−2.89050	−0.0958191
$911$	14.8166	0.490896	0.245448	−	0.969410i	$-0.421065\pi$
$911$	14.8166	0.490896	0.245448	+	0.969410i	$0.421065\pi$
$912$	−8.44284	−0.279570
$913$	8.96868	0.296820
$914$	−0.197256	−0.00652465
$915$	12.7818	0.422553
$916$	18.8707	0.623506
$917$	25.5348	0.843235
$918$	0.424614	0.0140144
$919$	−13.9455	−0.460019	−0.230009	−	0.973188i	$-0.573876\pi$
$919$	−13.9455	−0.460019	−0.230009	+	0.973188i	$0.573876\pi$
$920$	5.95321	0.196271
$921$	17.3220	0.570781
$922$	−0.730793	−0.0240674
$923$	−26.5437	−0.873697
$924$	−28.5394	−0.938877
$925$	−9.97513	−0.327980
$926$	−4.05536	−0.133267
$927$	3.71565	0.122038
$928$	0.474123	0.0155638
$929$	−33.8233	−1.10971	−0.554853	−	0.831948i	$-0.687226\pi$
$929$	−33.8233	−1.10971	−0.554853	+	0.831948i	$0.687226\pi$
$930$	−4.36189	−0.143032
$931$	10.5968	0.347296
$932$	−0.136640	−0.00447579
$933$	−25.7055	−0.841562
$934$	3.18783	0.104309
$935$	−4.37047	−0.142930
$936$	−2.17816	−0.0711955
$937$	25.0844	0.819472	0.409736	−	0.912204i	$-0.365621\pi$
$937$	25.0844	0.819472	0.409736	+	0.912204i	$0.365621\pi$
$938$	−6.48741	−0.211821
$939$	−17.2024	−0.561380
$940$	−15.4918	−0.505286
$941$	22.8643	0.745354	0.372677	−	0.927961i	$-0.378440\pi$
$941$	22.8643	0.745354	0.372677	+	0.927961i	$0.378440\pi$
$942$	−3.29580	−0.107383
$943$	65.7185	2.14009
$944$	4.60814	0.149982
$945$	−25.4340	−0.827367
$946$	0.0100261	0.000325978 0
$947$	41.0948	1.33540	0.667700	−	0.744430i	$-0.267279\pi$
$947$	41.0948	1.33540	0.667700	+	0.744430i	$0.267279\pi$
$948$	26.6431	0.865327
$949$	−36.6832	−1.19079
$950$	0.0939155	0.00304702
$951$	55.7317	1.80722
$952$	−2.37402	−0.0769423
$953$	37.9671	1.22987	0.614937	−	0.788576i	$-0.289181\pi$
$953$	37.9671	1.22987	0.614937	+	0.788576i	$0.289181\pi$
$954$	−0.238500	−0.00772173
$955$	−10.5594	−0.341693
$956$	37.8957	1.22564
$957$	−1.29883	−0.0419851
$958$	−2.51431	−0.0812337
$959$	−56.3314	−1.81904
$960$	−33.6386	−1.08568
$961$	60.6228	1.95557
$962$	3.78678	0.122091
$963$	20.3336	0.655241
$964$	37.0410	1.19301
$965$	13.5787	0.437115
$966$	−6.63178	−0.213374
$967$	−42.4518	−1.36516	−0.682579	−	0.730812i	$-0.739142\pi$
$967$	−42.4518	−1.36516	−0.682579	+	0.730812i	$0.739142\pi$
$968$	−3.53710	−0.113687
$969$	2.90467	0.0933114
$970$	−2.68727	−0.0862830
$971$	−57.8003	−1.85490	−0.927451	−	0.373946i	$-0.878005\pi$
$971$	−57.8003	−1.85490	−0.927451	+	0.373946i	$0.878005\pi$
$972$	−30.1138	−0.965902
$973$	67.1680	2.15331
$974$	−0.154785	−0.00495962
$975$	−6.23946	−0.199823
$976$	11.5668	0.370243
$977$	53.0193	1.69624	0.848118	−	0.529807i	$-0.177735\pi$
$977$	53.0193	1.69624	0.848118	+	0.529807i	$0.177735\pi$
$978$	−4.99015	−0.159567
$979$	5.59856	0.178931
$980$	42.6989	1.36397
$981$	−10.5895	−0.338097
$982$	0.823789	0.0262882
$983$	−30.4481	−0.971142	−0.485571	−	0.874197i	$-0.661388\pi$
$983$	−30.4481	−0.971142	−0.485571	+	0.874197i	$0.661388\pi$
$984$	8.39031	0.267473
$985$	−47.1091	−1.50102
$986$	−0.0538719	−0.00171563
$987$	34.6105	1.10166
$988$	6.45435	0.205340
$989$	−0.421777	−0.0134117
$990$	−0.543342	−0.0172685
$991$	36.7894	1.16865	0.584326	−	0.811519i	$-0.301359\pi$
$991$	36.7894	1.16865	0.584326	+	0.811519i	$0.301359\pi$
$992$	−11.9518	−0.379468
$993$	53.6115	1.70131
$994$	−3.59667	−0.114079
$995$	−40.2620	−1.27639
$996$	−24.0182	−0.761045
$997$	−22.1846	−0.702594	−0.351297	−	0.936264i	$-0.614259\pi$
$997$	−22.1846	−0.702594	−0.351297	+	0.936264i	$0.614259\pi$
$998$	2.10112	0.0665098
$999$	33.3205	1.05421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.39	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.39	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-0.104818 q^{2} -2.14601 q^{3} -1.98901 q^{4} -2.02584 q^{5} +0.224941 q^{6} +4.19485 q^{7} +0.418121 q^{8} +1.60536 q^{9} +O(q^{10})\)	\(q-0.104818 q^{2} -2.14601 q^{3} -1.98901 q^{4} -2.02584 q^{5} +0.224941 q^{6} +4.19485 q^{7} +0.418121 q^{8} +1.60536 q^{9} +0.212345 q^{10} -1.59389 q^{11} +4.26844 q^{12} -3.24500 q^{13} -0.439697 q^{14} +4.34747 q^{15} +3.93420 q^{16} -1.35352 q^{17} -0.168271 q^{18} +1.00000 q^{19} +4.02942 q^{20} -9.00220 q^{21} +0.167069 q^{22} -7.02820 q^{23} -0.897293 q^{24} -0.895984 q^{25} +0.340135 q^{26} +2.99290 q^{27} -8.34362 q^{28} -0.379718 q^{29} -0.455694 q^{30} +9.57198 q^{31} -1.24862 q^{32} +3.42051 q^{33} +0.141874 q^{34} -8.49809 q^{35} -3.19309 q^{36} +11.1332 q^{37} -0.104818 q^{38} +6.96381 q^{39} -0.847046 q^{40} -9.35069 q^{41} +0.943595 q^{42} +0.0600120 q^{43} +3.17027 q^{44} -3.25221 q^{45} +0.736684 q^{46} -3.84467 q^{47} -8.44284 q^{48} +10.5968 q^{49} +0.0939155 q^{50} +2.90467 q^{51} +6.45435 q^{52} +1.41735 q^{53} -0.313711 q^{54} +3.22896 q^{55} +1.75396 q^{56} -2.14601 q^{57} +0.0398014 q^{58} +1.17130 q^{59} -8.64717 q^{60} +2.94005 q^{61} -1.00332 q^{62} +6.73427 q^{63} -7.73752 q^{64} +6.57384 q^{65} -0.358531 q^{66} +14.7543 q^{67} +2.69217 q^{68} +15.0826 q^{69} +0.890755 q^{70} +8.17988 q^{71} +0.671237 q^{72} +11.3045 q^{73} -1.16696 q^{74} +1.92279 q^{75} -1.98901 q^{76} -6.68614 q^{77} -0.729934 q^{78} +6.24187 q^{79} -7.97005 q^{80} -11.2389 q^{81} +0.980122 q^{82} -5.62691 q^{83} +17.9055 q^{84} +2.74201 q^{85} -0.00629035 q^{86} +0.814879 q^{87} -0.666439 q^{88} -3.51252 q^{89} +0.340891 q^{90} -13.6123 q^{91} +13.9792 q^{92} -20.5416 q^{93} +0.402991 q^{94} -2.02584 q^{95} +2.67955 q^{96} -12.6552 q^{97} -1.11074 q^{98} -2.55877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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