LMFDB - Embedded newform 6034.2.a.r.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.630504 q^{3} +1.00000 q^{4} +3.47508 q^{5} +0.630504 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.60246 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.630504 q^{3} +1.00000 q^{4} +3.47508 q^{5} +0.630504 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.60246 q^{9} +3.47508 q^{10} -2.00134 q^{11} +0.630504 q^{12} -1.94354 q^{13} -1.00000 q^{14} +2.19106 q^{15} +1.00000 q^{16} +3.57012 q^{17} -2.60246 q^{18} +7.18148 q^{19} +3.47508 q^{20} -0.630504 q^{21} -2.00134 q^{22} -3.84295 q^{23} +0.630504 q^{24} +7.07621 q^{25} -1.94354 q^{26} -3.53238 q^{27} -1.00000 q^{28} +7.36856 q^{29} +2.19106 q^{30} -2.56880 q^{31} +1.00000 q^{32} -1.26185 q^{33} +3.57012 q^{34} -3.47508 q^{35} -2.60246 q^{36} +8.12244 q^{37} +7.18148 q^{38} -1.22541 q^{39} +3.47508 q^{40} +6.82774 q^{41} -0.630504 q^{42} +5.87176 q^{43} -2.00134 q^{44} -9.04378 q^{45} -3.84295 q^{46} +6.49291 q^{47} +0.630504 q^{48} +1.00000 q^{49} +7.07621 q^{50} +2.25098 q^{51} -1.94354 q^{52} -4.20825 q^{53} -3.53238 q^{54} -6.95483 q^{55} -1.00000 q^{56} +4.52796 q^{57} +7.36856 q^{58} -10.5051 q^{59} +2.19106 q^{60} -5.84659 q^{61} -2.56880 q^{62} +2.60246 q^{63} +1.00000 q^{64} -6.75397 q^{65} -1.26185 q^{66} +2.15091 q^{67} +3.57012 q^{68} -2.42299 q^{69} -3.47508 q^{70} -0.416734 q^{71} -2.60246 q^{72} +15.2122 q^{73} +8.12244 q^{74} +4.46158 q^{75} +7.18148 q^{76} +2.00134 q^{77} -1.22541 q^{78} -11.7696 q^{79} +3.47508 q^{80} +5.58021 q^{81} +6.82774 q^{82} +11.5955 q^{83} -0.630504 q^{84} +12.4065 q^{85} +5.87176 q^{86} +4.64591 q^{87} -2.00134 q^{88} -1.88276 q^{89} -9.04378 q^{90} +1.94354 q^{91} -3.84295 q^{92} -1.61964 q^{93} +6.49291 q^{94} +24.9563 q^{95} +0.630504 q^{96} -7.27408 q^{97} +1.00000 q^{98} +5.20842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.630504	0.364022	0.182011	−	0.983297i	$-0.441739\pi$
$3$	0.630504	0.364022	0.182011	+	0.983297i	$0.441739\pi$
$4$	1.00000	0.500000
$5$	3.47508	1.55411	0.777053	−	0.629436i	$-0.216714\pi$
$5$	3.47508	1.55411	0.777053	+	0.629436i	$0.216714\pi$
$6$	0.630504	0.257402
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.60246	−0.867488
$10$	3.47508	1.09892
$11$	−2.00134	−0.603427	−0.301713	−	0.953399i	$-0.597559\pi$
$11$	−2.00134	−0.603427	−0.301713	+	0.953399i	$0.597559\pi$
$12$	0.630504	0.182011
$13$	−1.94354	−0.539041	−0.269521	−	0.962995i	$-0.586865\pi$
$13$	−1.94354	−0.539041	−0.269521	+	0.962995i	$0.586865\pi$
$14$	−1.00000	−0.267261
$15$	2.19106	0.565728
$16$	1.00000	0.250000
$17$	3.57012	0.865882	0.432941	−	0.901422i	$-0.357476\pi$
$17$	3.57012	0.865882	0.432941	+	0.901422i	$0.357476\pi$
$18$	−2.60246	−0.613407
$19$	7.18148	1.64755	0.823773	−	0.566920i	$-0.191865\pi$
$19$	7.18148	1.64755	0.823773	+	0.566920i	$0.191865\pi$
$20$	3.47508	0.777053
$21$	−0.630504	−0.137587
$22$	−2.00134	−0.426687
$23$	−3.84295	−0.801310	−0.400655	−	0.916229i	$-0.631217\pi$
$23$	−3.84295	−0.801310	−0.400655	+	0.916229i	$0.631217\pi$
$24$	0.630504	0.128701
$25$	7.07621	1.41524
$26$	−1.94354	−0.381160
$27$	−3.53238	−0.679806
$28$	−1.00000	−0.188982
$29$	7.36856	1.36831	0.684154	−	0.729338i	$-0.260172\pi$
$29$	7.36856	1.36831	0.684154	+	0.729338i	$0.260172\pi$
$30$	2.19106	0.400030
$31$	−2.56880	−0.461371	−0.230685	−	0.973028i	$-0.574097\pi$
$31$	−2.56880	−0.461371	−0.230685	+	0.973028i	$0.574097\pi$
$32$	1.00000	0.176777
$33$	−1.26185	−0.219661
$34$	3.57012	0.612271
$35$	−3.47508	−0.587397
$36$	−2.60246	−0.433744
$37$	8.12244	1.33532	0.667660	−	0.744466i	$-0.267296\pi$
$37$	8.12244	1.33532	0.667660	+	0.744466i	$0.267296\pi$
$38$	7.18148	1.16499
$39$	−1.22541	−0.196223
$40$	3.47508	0.549459
$41$	6.82774	1.06631	0.533157	−	0.846016i	$-0.321005\pi$
$41$	6.82774	1.06631	0.533157	+	0.846016i	$0.321005\pi$
$42$	−0.630504	−0.0972889
$43$	5.87176	0.895435	0.447718	−	0.894175i	$-0.352237\pi$
$43$	5.87176	0.895435	0.447718	+	0.894175i	$0.352237\pi$
$44$	−2.00134	−0.301713
$45$	−9.04378	−1.34817
$46$	−3.84295	−0.566612
$47$	6.49291	0.947088	0.473544	−	0.880770i	$-0.342974\pi$
$47$	6.49291	0.947088	0.473544	+	0.880770i	$0.342974\pi$
$48$	0.630504	0.0910054
$49$	1.00000	0.142857
$50$	7.07621	1.00073
$51$	2.25098	0.315200
$52$	−1.94354	−0.269521
$53$	−4.20825	−0.578047	−0.289024	−	0.957322i	$-0.593331\pi$
$53$	−4.20825	−0.578047	−0.289024	+	0.957322i	$0.593331\pi$
$54$	−3.53238	−0.480696
$55$	−6.95483	−0.937789
$56$	−1.00000	−0.133631
$57$	4.52796	0.599742
$58$	7.36856	0.967539
$59$	−10.5051	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$59$	−10.5051	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$60$	2.19106	0.282864
$61$	−5.84659	−0.748579	−0.374290	−	0.927312i	$-0.622113\pi$
$61$	−5.84659	−0.748579	−0.374290	+	0.927312i	$0.622113\pi$
$62$	−2.56880	−0.326238
$63$	2.60246	0.327880
$64$	1.00000	0.125000
$65$	−6.75397	−0.837727
$66$	−1.26185	−0.155323
$67$	2.15091	0.262775	0.131388	−	0.991331i	$-0.458057\pi$
$67$	2.15091	0.262775	0.131388	+	0.991331i	$0.458057\pi$
$68$	3.57012	0.432941
$69$	−2.42299	−0.291694
$70$	−3.47508	−0.415352
$71$	−0.416734	−0.0494572	−0.0247286	−	0.999694i	$-0.507872\pi$
$71$	−0.416734	−0.0494572	−0.0247286	+	0.999694i	$0.507872\pi$
$72$	−2.60246	−0.306703
$73$	15.2122	1.78045	0.890225	−	0.455520i	$-0.150547\pi$
$73$	15.2122	1.78045	0.890225	+	0.455520i	$0.150547\pi$
$74$	8.12244	0.944214
$75$	4.46158	0.515179
$76$	7.18148	0.823773
$77$	2.00134	0.228074
$78$	−1.22541	−0.138750
$79$	−11.7696	−1.32418	−0.662092	−	0.749423i	$-0.730331\pi$
$79$	−11.7696	−1.32418	−0.662092	+	0.749423i	$0.730331\pi$
$80$	3.47508	0.388526
$81$	5.58021	0.620024
$82$	6.82774	0.753998
$83$	11.5955	1.27277	0.636386	−	0.771371i	$-0.280429\pi$
$83$	11.5955	1.27277	0.636386	+	0.771371i	$0.280429\pi$
$84$	−0.630504	−0.0687937
$85$	12.4065	1.34567
$86$	5.87176	0.633168
$87$	4.64591	0.498094
$88$	−2.00134	−0.213344
$89$	−1.88276	−0.199572	−0.0997858	−	0.995009i	$-0.531816\pi$
$89$	−1.88276	−0.199572	−0.0997858	+	0.995009i	$0.531816\pi$
$90$	−9.04378	−0.953299
$91$	1.94354	0.203738
$92$	−3.84295	−0.400655
$93$	−1.61964	−0.167949
$94$	6.49291	0.669692
$95$	24.9563	2.56046
$96$	0.630504	0.0643506
$97$	−7.27408	−0.738571	−0.369285	−	0.929316i	$-0.620397\pi$
$97$	−7.27408	−0.738571	−0.369285	+	0.929316i	$0.620397\pi$
$98$	1.00000	0.101015
$99$	5.20842	0.523466
$100$	7.07621	0.707621
$101$	2.21496	0.220397	0.110199	−	0.993910i	$-0.464851\pi$
$101$	2.21496	0.220397	0.110199	+	0.993910i	$0.464851\pi$
$102$	2.25098	0.222880
$103$	−9.13637	−0.900234	−0.450117	−	0.892970i	$-0.648618\pi$
$103$	−9.13637	−0.900234	−0.450117	+	0.892970i	$0.648618\pi$
$104$	−1.94354	−0.190580
$105$	−2.19106	−0.213825
$106$	−4.20825	−0.408741
$107$	10.9322	1.05686	0.528429	−	0.848977i	$-0.322781\pi$
$107$	10.9322	1.05686	0.528429	+	0.848977i	$0.322781\pi$
$108$	−3.53238	−0.339903
$109$	16.1935	1.55106	0.775529	−	0.631312i	$-0.217483\pi$
$109$	16.1935	1.55106	0.775529	+	0.631312i	$0.217483\pi$
$110$	−6.95483	−0.663117
$111$	5.12123	0.486086
$112$	−1.00000	−0.0944911
$113$	20.8192	1.95851	0.979255	−	0.202632i	$-0.0649494\pi$
$113$	20.8192	1.95851	0.979255	+	0.202632i	$0.0649494\pi$
$114$	4.52796	0.424082
$115$	−13.3546	−1.24532
$116$	7.36856	0.684154
$117$	5.05800	0.467612
$118$	−10.5051	−0.967075
$119$	−3.57012	−0.327273
$120$	2.19106	0.200015
$121$	−6.99464	−0.635876
$122$	−5.84659	−0.529325
$123$	4.30492	0.388162
$124$	−2.56880	−0.230685
$125$	7.21502	0.645331
$126$	2.60246	0.231846
$127$	5.21553	0.462803	0.231402	−	0.972858i	$-0.425669\pi$
$127$	5.21553	0.462803	0.231402	+	0.972858i	$0.425669\pi$
$128$	1.00000	0.0883883
$129$	3.70217	0.325958
$130$	−6.75397	−0.592362
$131$	7.33057	0.640475	0.320237	−	0.947337i	$-0.396237\pi$
$131$	7.33057	0.640475	0.320237	+	0.947337i	$0.396237\pi$
$132$	−1.26185	−0.109830
$133$	−7.18148	−0.622714
$134$	2.15091	0.185810
$135$	−12.2753	−1.05649
$136$	3.57012	0.306136
$137$	−10.2852	−0.878721	−0.439360	−	0.898311i	$-0.644795\pi$
$137$	−10.2852	−0.878721	−0.439360	+	0.898311i	$0.644795\pi$
$138$	−2.42299	−0.206259
$139$	0.701577	0.0595070	0.0297535	−	0.999557i	$-0.490528\pi$
$139$	0.701577	0.0595070	0.0297535	+	0.999557i	$0.490528\pi$
$140$	−3.47508	−0.293698
$141$	4.09381	0.344761
$142$	−0.416734	−0.0349715
$143$	3.88969	0.325272
$144$	−2.60246	−0.216872
$145$	25.6064	2.12649
$146$	15.2122	1.25897
$147$	0.630504	0.0520031
$148$	8.12244	0.667660
$149$	5.25699	0.430669	0.215335	−	0.976540i	$-0.430916\pi$
$149$	5.25699	0.430669	0.215335	+	0.976540i	$0.430916\pi$
$150$	4.46158	0.364287
$151$	−4.81087	−0.391503	−0.195752	−	0.980654i	$-0.562715\pi$
$151$	−4.81087	−0.391503	−0.195752	+	0.980654i	$0.562715\pi$
$152$	7.18148	0.582495
$153$	−9.29112	−0.751143
$154$	2.00134	0.161273
$155$	−8.92681	−0.717019
$156$	−1.22541	−0.0981114
$157$	−10.3910	−0.829292	−0.414646	−	0.909983i	$-0.636095\pi$
$157$	−10.3910	−0.829292	−0.414646	+	0.909983i	$0.636095\pi$
$158$	−11.7696	−0.936339
$159$	−2.65332	−0.210422
$160$	3.47508	0.274730
$161$	3.84295	0.302867
$162$	5.58021	0.438423
$163$	−6.49894	−0.509036	−0.254518	−	0.967068i	$-0.581917\pi$
$163$	−6.49894	−0.509036	−0.254518	+	0.967068i	$0.581917\pi$
$164$	6.82774	0.533157
$165$	−4.38505	−0.341376
$166$	11.5955	0.899985
$167$	−24.5649	−1.90089	−0.950446	−	0.310889i	$-0.899373\pi$
$167$	−24.5649	−1.90089	−0.950446	+	0.310889i	$0.899373\pi$
$168$	−0.630504	−0.0486445
$169$	−9.22265	−0.709434
$170$	12.4065	0.951534
$171$	−18.6896	−1.42923
$172$	5.87176	0.447718
$173$	−3.81521	−0.290065	−0.145032	−	0.989427i	$-0.546329\pi$
$173$	−3.81521	−0.290065	−0.145032	+	0.989427i	$0.546329\pi$
$174$	4.64591	0.352205
$175$	−7.07621	−0.534912
$176$	−2.00134	−0.150857
$177$	−6.62352	−0.497854
$178$	−1.88276	−0.141118
$179$	0.477868	0.0357175	0.0178588	−	0.999841i	$-0.494315\pi$
$179$	0.477868	0.0357175	0.0178588	+	0.999841i	$0.494315\pi$
$180$	−9.04378	−0.674084
$181$	−7.88450	−0.586050	−0.293025	−	0.956105i	$-0.594662\pi$
$181$	−7.88450	−0.586050	−0.293025	+	0.956105i	$0.594662\pi$
$182$	1.94354	0.144065
$183$	−3.68630	−0.272499
$184$	−3.84295	−0.283306
$185$	28.2262	2.07523
$186$	−1.61964	−0.118758
$187$	−7.14503	−0.522497
$188$	6.49291	0.473544
$189$	3.53238	0.256943
$190$	24.9563	1.81052
$191$	−4.31033	−0.311885	−0.155942	−	0.987766i	$-0.549841\pi$
$191$	−4.31033	−0.311885	−0.155942	+	0.987766i	$0.549841\pi$
$192$	0.630504	0.0455027
$193$	26.8130	1.93004	0.965021	−	0.262173i	$-0.0844391\pi$
$193$	26.8130	1.93004	0.965021	+	0.262173i	$0.0844391\pi$
$194$	−7.27408	−0.522248
$195$	−4.25841	−0.304951
$196$	1.00000	0.0714286
$197$	2.20342	0.156987	0.0784935	−	0.996915i	$-0.474989\pi$
$197$	2.20342	0.156987	0.0784935	+	0.996915i	$0.474989\pi$
$198$	5.20842	0.370146
$199$	6.68182	0.473662	0.236831	−	0.971551i	$-0.423891\pi$
$199$	6.68182	0.473662	0.236831	+	0.971551i	$0.423891\pi$
$200$	7.07621	0.500364
$201$	1.35616	0.0956560
$202$	2.21496	0.155844
$203$	−7.36856	−0.517171
$204$	2.25098	0.157600
$205$	23.7270	1.65717
$206$	−9.13637	−0.636561
$207$	10.0011	0.695127
$208$	−1.94354	−0.134760
$209$	−14.3726	−0.994173
$210$	−2.19106	−0.151197
$211$	3.49669	0.240722	0.120361	−	0.992730i	$-0.461595\pi$
$211$	3.49669	0.240722	0.120361	+	0.992730i	$0.461595\pi$
$212$	−4.20825	−0.289024
$213$	−0.262752	−0.0180035
$214$	10.9322	0.747312
$215$	20.4049	1.39160
$216$	−3.53238	−0.240348
$217$	2.56880	0.174382
$218$	16.1935	1.09676
$219$	9.59134	0.648123
$220$	−6.95483	−0.468894
$221$	−6.93868	−0.466746
$222$	5.12123	0.343714
$223$	−1.26988	−0.0850376	−0.0425188	−	0.999096i	$-0.513538\pi$
$223$	−1.26988	−0.0850376	−0.0425188	+	0.999096i	$0.513538\pi$
$224$	−1.00000	−0.0668153
$225$	−18.4156	−1.22771
$226$	20.8192	1.38488
$227$	8.86542	0.588418	0.294209	−	0.955741i	$-0.404944\pi$
$227$	8.86542	0.588418	0.294209	+	0.955741i	$0.404944\pi$
$228$	4.52796	0.299871
$229$	−19.8736	−1.31329	−0.656644	−	0.754201i	$-0.728025\pi$
$229$	−19.8736	−1.31329	−0.656644	+	0.754201i	$0.728025\pi$
$230$	−13.3546	−0.880574
$231$	1.26185	0.0830239
$232$	7.36856	0.483770
$233$	−3.32615	−0.217903	−0.108952	−	0.994047i	$-0.534749\pi$
$233$	−3.32615	−0.217903	−0.108952	+	0.994047i	$0.534749\pi$
$234$	5.05800	0.330652
$235$	22.5634	1.47187
$236$	−10.5051	−0.683825
$237$	−7.42078	−0.482032
$238$	−3.57012	−0.231417
$239$	0.262382	0.0169721	0.00848603	−	0.999964i	$-0.497299\pi$
$239$	0.262382	0.0169721	0.00848603	+	0.999964i	$0.497299\pi$
$240$	2.19106	0.141432
$241$	0.702442	0.0452483	0.0226241	−	0.999744i	$-0.492798\pi$
$241$	0.702442	0.0452483	0.0226241	+	0.999744i	$0.492798\pi$
$242$	−6.99464	−0.449632
$243$	14.1155	0.905509
$244$	−5.84659	−0.374290
$245$	3.47508	0.222015
$246$	4.30492	0.274472
$247$	−13.9575	−0.888095
$248$	−2.56880	−0.163119
$249$	7.31101	0.463316
$250$	7.21502	0.456318
$251$	−18.2076	−1.14926	−0.574628	−	0.818415i	$-0.694853\pi$
$251$	−18.2076	−1.14926	−0.574628	+	0.818415i	$0.694853\pi$
$252$	2.60246	0.163940
$253$	7.69105	0.483532
$254$	5.21553	0.327251
$255$	7.82234	0.489854
$256$	1.00000	0.0625000
$257$	−8.15400	−0.508632	−0.254316	−	0.967121i	$-0.581850\pi$
$257$	−8.15400	−0.508632	−0.254316	+	0.967121i	$0.581850\pi$
$258$	3.70217	0.230487
$259$	−8.12244	−0.504704
$260$	−6.75397	−0.418863
$261$	−19.1764	−1.18699
$262$	7.33057	0.452884
$263$	−4.80245	−0.296132	−0.148066	−	0.988978i	$-0.547305\pi$
$263$	−4.80245	−0.296132	−0.148066	+	0.988978i	$0.547305\pi$
$264$	−1.26185	−0.0776617
$265$	−14.6240	−0.898346
$266$	−7.18148	−0.440325
$267$	−1.18709	−0.0726484
$268$	2.15091	0.131388
$269$	−32.0871	−1.95639	−0.978194	−	0.207694i	$-0.933404\pi$
$269$	−32.0871	−1.95639	−0.978194	+	0.207694i	$0.933404\pi$
$270$	−12.2753	−0.747052
$271$	16.2153	0.985011	0.492506	−	0.870309i	$-0.336081\pi$
$271$	16.2153	0.985011	0.492506	+	0.870309i	$0.336081\pi$
$272$	3.57012	0.216471
$273$	1.22541	0.0741653
$274$	−10.2852	−0.621349
$275$	−14.1619	−0.853995
$276$	−2.42299	−0.145847
$277$	−7.95336	−0.477871	−0.238936	−	0.971035i	$-0.576798\pi$
$277$	−7.95336	−0.477871	−0.238936	+	0.971035i	$0.576798\pi$
$278$	0.701577	0.0420778
$279$	6.68522	0.400234
$280$	−3.47508	−0.207676
$281$	−27.0581	−1.61415	−0.807076	−	0.590448i	$-0.798951\pi$
$281$	−27.0581	−1.61415	−0.807076	+	0.590448i	$0.798951\pi$
$282$	4.09381	0.243783
$283$	8.16938	0.485619	0.242810	−	0.970074i	$-0.421931\pi$
$283$	8.16938	0.485619	0.242810	+	0.970074i	$0.421931\pi$
$284$	−0.416734	−0.0247286
$285$	15.7350	0.932063
$286$	3.88969	0.230002
$287$	−6.82774	−0.403029
$288$	−2.60246	−0.153352
$289$	−4.25422	−0.250248
$290$	25.6064	1.50366
$291$	−4.58634	−0.268856
$292$	15.2122	0.890225
$293$	18.8946	1.10384	0.551918	−	0.833898i	$-0.313896\pi$
$293$	18.8946	1.10384	0.551918	+	0.833898i	$0.313896\pi$
$294$	0.630504	0.0367718
$295$	−36.5062	−2.12547
$296$	8.12244	0.472107
$297$	7.06949	0.410213
$298$	5.25699	0.304529
$299$	7.46893	0.431939
$300$	4.46158	0.257590
$301$	−5.87176	−0.338443
$302$	−4.81087	−0.276834
$303$	1.39654	0.0802293
$304$	7.18148	0.411886
$305$	−20.3174	−1.16337
$306$	−9.29112	−0.531138
$307$	−15.6033	−0.890525	−0.445263	−	0.895400i	$-0.646890\pi$
$307$	−15.6033	−0.890525	−0.445263	+	0.895400i	$0.646890\pi$
$308$	2.00134	0.114037
$309$	−5.76052	−0.327705
$310$	−8.92681	−0.507009
$311$	−6.13362	−0.347806	−0.173903	−	0.984763i	$-0.555638\pi$
$311$	−6.13362	−0.347806	−0.173903	+	0.984763i	$0.555638\pi$
$312$	−1.22541	−0.0693752
$313$	−2.47466	−0.139876	−0.0699380	−	0.997551i	$-0.522280\pi$
$313$	−2.47466	−0.139876	−0.0699380	+	0.997551i	$0.522280\pi$
$314$	−10.3910	−0.586398
$315$	9.04378	0.509560
$316$	−11.7696	−0.662092
$317$	−15.1055	−0.848410	−0.424205	−	0.905566i	$-0.639446\pi$
$317$	−15.1055	−0.848410	−0.424205	+	0.905566i	$0.639446\pi$
$318$	−2.65332	−0.148791
$319$	−14.7470	−0.825673
$320$	3.47508	0.194263
$321$	6.89282	0.384720
$322$	3.84295	0.214159
$323$	25.6388	1.42658
$324$	5.58021	0.310012
$325$	−13.7529	−0.762874
$326$	−6.49894	−0.359943
$327$	10.2101	0.564619
$328$	6.82774	0.376999
$329$	−6.49291	−0.357966
$330$	−4.38505	−0.241389
$331$	3.34377	0.183790	0.0918950	−	0.995769i	$-0.470708\pi$
$331$	3.34377	0.183790	0.0918950	+	0.995769i	$0.470708\pi$
$332$	11.5955	0.636386
$333$	−21.1383	−1.15837
$334$	−24.5649	−1.34413
$335$	7.47459	0.408381
$336$	−0.630504	−0.0343968
$337$	15.1165	0.823449	0.411724	−	0.911308i	$-0.364927\pi$
$337$	15.1165	0.823449	0.411724	+	0.911308i	$0.364927\pi$
$338$	−9.22265	−0.501646
$339$	13.1266	0.712940
$340$	12.4065	0.672836
$341$	5.14105	0.278404
$342$	−18.6896	−1.01062
$343$	−1.00000	−0.0539949
$344$	5.87176	0.316584
$345$	−8.42011	−0.453324
$346$	−3.81521	−0.205107
$347$	−12.0466	−0.646696	−0.323348	−	0.946280i	$-0.604808\pi$
$347$	−12.0466	−0.646696	−0.323348	+	0.946280i	$0.604808\pi$
$348$	4.64591	0.249047
$349$	−21.3969	−1.14535	−0.572676	−	0.819782i	$-0.694095\pi$
$349$	−21.3969	−1.14535	−0.572676	+	0.819782i	$0.694095\pi$
$350$	−7.07621	−0.378240
$351$	6.86532	0.366444
$352$	−2.00134	−0.106672
$353$	−11.9249	−0.634698	−0.317349	−	0.948309i	$-0.602793\pi$
$353$	−11.9249	−0.634698	−0.317349	+	0.948309i	$0.602793\pi$
$354$	−6.62352	−0.352036
$355$	−1.44819	−0.0768617
$356$	−1.88276	−0.0997858
$357$	−2.25098	−0.119134
$358$	0.477868	0.0252561
$359$	−10.1564	−0.536032	−0.268016	−	0.963414i	$-0.586368\pi$
$359$	−10.1564	−0.536032	−0.268016	+	0.963414i	$0.586368\pi$
$360$	−9.04378	−0.476649
$361$	32.5737	1.71441
$362$	−7.88450	−0.414400
$363$	−4.41015	−0.231473
$364$	1.94354	0.101869
$365$	52.8636	2.76701
$366$	−3.68630	−0.192686
$367$	−12.2879	−0.641424	−0.320712	−	0.947177i	$-0.603922\pi$
$367$	−12.2879	−0.641424	−0.320712	+	0.947177i	$0.603922\pi$
$368$	−3.84295	−0.200327
$369$	−17.7690	−0.925015
$370$	28.2262	1.46741
$371$	4.20825	0.218481
$372$	−1.61964	−0.0839745
$373$	−28.8059	−1.49151	−0.745757	−	0.666218i	$-0.767912\pi$
$373$	−28.8059	−1.49151	−0.745757	+	0.666218i	$0.767912\pi$
$374$	−7.14503	−0.369461
$375$	4.54910	0.234915
$376$	6.49291	0.334846
$377$	−14.3211	−0.737574
$378$	3.53238	0.181686
$379$	−13.2997	−0.683161	−0.341580	−	0.939853i	$-0.610962\pi$
$379$	−13.2997	−0.683161	−0.341580	+	0.939853i	$0.610962\pi$
$380$	24.9563	1.28023
$381$	3.28841	0.168470
$382$	−4.31033	−0.220536
$383$	−11.0934	−0.566848	−0.283424	−	0.958995i	$-0.591470\pi$
$383$	−11.0934	−0.566848	−0.283424	+	0.958995i	$0.591470\pi$
$384$	0.630504	0.0321753
$385$	6.95483	0.354451
$386$	26.8130	1.36475
$387$	−15.2810	−0.776779
$388$	−7.27408	−0.369285
$389$	31.3233	1.58816	0.794078	−	0.607816i	$-0.207954\pi$
$389$	31.3233	1.58816	0.794078	+	0.607816i	$0.207954\pi$
$390$	−4.25841	−0.215633
$391$	−13.7198	−0.693840
$392$	1.00000	0.0505076
$393$	4.62195	0.233147
$394$	2.20342	0.111007
$395$	−40.9004	−2.05792
$396$	5.20842	0.261733
$397$	−10.5491	−0.529446	−0.264723	−	0.964325i	$-0.585280\pi$
$397$	−10.5491	−0.529446	−0.264723	+	0.964325i	$0.585280\pi$
$398$	6.68182	0.334929
$399$	−4.52796	−0.226681
$400$	7.07621	0.353811
$401$	−14.1971	−0.708972	−0.354486	−	0.935061i	$-0.615344\pi$
$401$	−14.1971	−0.708972	−0.354486	+	0.935061i	$0.615344\pi$
$402$	1.35616	0.0676390
$403$	4.99258	0.248698
$404$	2.21496	0.110199
$405$	19.3917	0.963582
$406$	−7.36856	−0.365695
$407$	−16.2558	−0.805768
$408$	2.25098	0.111440
$409$	25.6365	1.26764	0.633822	−	0.773479i	$-0.281485\pi$
$409$	25.6365	1.26764	0.633822	+	0.773479i	$0.281485\pi$
$410$	23.7270	1.17179
$411$	−6.48484	−0.319874
$412$	−9.13637	−0.450117
$413$	10.5051	0.516923
$414$	10.0011	0.491529
$415$	40.2953	1.97802
$416$	−1.94354	−0.0952900
$417$	0.442347	0.0216618
$418$	−14.3726	−0.702987
$419$	18.7274	0.914894	0.457447	−	0.889237i	$-0.348764\pi$
$419$	18.7274	0.914894	0.457447	+	0.889237i	$0.348764\pi$
$420$	−2.19106	−0.106913
$421$	−4.97162	−0.242302	−0.121151	−	0.992634i	$-0.538659\pi$
$421$	−4.97162	−0.242302	−0.121151	+	0.992634i	$0.538659\pi$
$422$	3.49669	0.170216
$423$	−16.8976	−0.821588
$424$	−4.20825	−0.204371
$425$	25.2630	1.22543
$426$	−0.262752	−0.0127304
$427$	5.84659	0.282936
$428$	10.9322	0.528429
$429$	2.45246	0.118406
$430$	20.4049	0.984010
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−3.53238	−0.169952
$433$	20.7144	0.995471	0.497736	−	0.867329i	$-0.334165\pi$
$433$	20.7144	0.995471	0.497736	+	0.867329i	$0.334165\pi$
$434$	2.56880	0.123307
$435$	16.1449	0.774090
$436$	16.1935	0.775529
$437$	−27.5981	−1.32019
$438$	9.59134	0.458292
$439$	8.79904	0.419955	0.209978	−	0.977706i	$-0.432661\pi$
$439$	8.79904	0.419955	0.209978	+	0.977706i	$0.432661\pi$
$440$	−6.95483	−0.331558
$441$	−2.60246	−0.123927
$442$	−6.93868	−0.330039
$443$	−40.2301	−1.91139	−0.955694	−	0.294361i	$-0.904893\pi$
$443$	−40.2301	−1.91139	−0.955694	+	0.294361i	$0.904893\pi$
$444$	5.12123	0.243043
$445$	−6.54273	−0.310155
$446$	−1.26988	−0.0601306
$447$	3.31455	0.156773
$448$	−1.00000	−0.0472456
$449$	27.7863	1.31132	0.655659	−	0.755057i	$-0.272391\pi$
$449$	27.7863	1.31132	0.655659	+	0.755057i	$0.272391\pi$
$450$	−18.4156	−0.868120
$451$	−13.6646	−0.643443
$452$	20.8192	0.979255
$453$	−3.03327	−0.142516
$454$	8.86542	0.416075
$455$	6.75397	0.316631
$456$	4.52796	0.212041
$457$	−22.8475	−1.06876	−0.534381	−	0.845244i	$-0.679455\pi$
$457$	−22.8475	−1.06876	−0.534381	+	0.845244i	$0.679455\pi$
$458$	−19.8736	−0.928635
$459$	−12.6110	−0.588632
$460$	−13.3546	−0.622660
$461$	22.4577	1.04596	0.522981	−	0.852344i	$-0.324820\pi$
$461$	22.4577	1.04596	0.522981	+	0.852344i	$0.324820\pi$
$462$	1.26185	0.0587067
$463$	23.5686	1.09532	0.547662	−	0.836700i	$-0.315518\pi$
$463$	23.5686	1.09532	0.547662	+	0.836700i	$0.315518\pi$
$464$	7.36856	0.342077
$465$	−5.62839	−0.261010
$466$	−3.32615	−0.154081
$467$	−18.1600	−0.840344	−0.420172	−	0.907444i	$-0.638030\pi$
$467$	−18.1600	−0.840344	−0.420172	+	0.907444i	$0.638030\pi$
$468$	5.05800	0.233806
$469$	−2.15091	−0.0993198
$470$	22.5634	1.04077
$471$	−6.55157	−0.301880
$472$	−10.5051	−0.483537
$473$	−11.7514	−0.540330
$474$	−7.42078	−0.340848
$475$	50.8177	2.33168
$476$	−3.57012	−0.163636
$477$	10.9518	0.501449
$478$	0.262382	0.0120011
$479$	18.6288	0.851173	0.425586	−	0.904918i	$-0.360068\pi$
$479$	18.6288	0.851173	0.425586	+	0.904918i	$0.360068\pi$
$480$	2.19106	0.100008
$481$	−15.7863	−0.719793
$482$	0.702442	0.0319954
$483$	2.42299	0.110250
$484$	−6.99464	−0.317938
$485$	−25.2780	−1.14782
$486$	14.1155	0.640291
$487$	−32.2560	−1.46166	−0.730830	−	0.682560i	$-0.760867\pi$
$487$	−32.2560	−1.46166	−0.730830	+	0.682560i	$0.760867\pi$
$488$	−5.84659	−0.264663
$489$	−4.09761	−0.185300
$490$	3.47508	0.156988
$491$	−20.6599	−0.932370	−0.466185	−	0.884687i	$-0.654372\pi$
$491$	−20.6599	−0.932370	−0.466185	+	0.884687i	$0.654372\pi$
$492$	4.30492	0.194081
$493$	26.3067	1.18479
$494$	−13.9575	−0.627978
$495$	18.0997	0.813521
$496$	−2.56880	−0.115343
$497$	0.416734	0.0186931
$498$	7.31101	0.327614
$499$	32.1780	1.44048	0.720242	−	0.693723i	$-0.244031\pi$
$499$	32.1780	1.44048	0.720242	+	0.693723i	$0.244031\pi$
$500$	7.21502	0.322666
$501$	−15.4883	−0.691966
$502$	−18.2076	−0.812647
$503$	−1.38704	−0.0618450	−0.0309225	−	0.999522i	$-0.509845\pi$
$503$	−1.38704	−0.0618450	−0.0309225	+	0.999522i	$0.509845\pi$
$504$	2.60246	0.115923
$505$	7.69718	0.342520
$506$	7.69105	0.341909
$507$	−5.81492	−0.258250
$508$	5.21553	0.231402
$509$	−6.93649	−0.307454	−0.153727	−	0.988113i	$-0.549128\pi$
$509$	−6.93649	−0.307454	−0.153727	+	0.988113i	$0.549128\pi$
$510$	7.82234	0.346379
$511$	−15.2122	−0.672947
$512$	1.00000	0.0441942
$513$	−25.3677	−1.12001
$514$	−8.15400	−0.359657
$515$	−31.7497	−1.39906
$516$	3.70217	0.162979
$517$	−12.9945	−0.571498
$518$	−8.12244	−0.356879
$519$	−2.40551	−0.105590
$520$	−6.75397	−0.296181
$521$	34.5470	1.51353	0.756767	−	0.653685i	$-0.226778\pi$
$521$	34.5470	1.51353	0.756767	+	0.653685i	$0.226778\pi$
$522$	−19.1764	−0.839329
$523$	15.7049	0.686727	0.343363	−	0.939203i	$-0.388434\pi$
$523$	15.7049	0.686727	0.343363	+	0.939203i	$0.388434\pi$
$524$	7.33057	0.320237
$525$	−4.46158	−0.194719
$526$	−4.80245	−0.209397
$527$	−9.17095	−0.399493
$528$	−1.26185	−0.0549151
$529$	−8.23175	−0.357902
$530$	−14.6240	−0.635227
$531$	27.3392	1.18642
$532$	−7.18148	−0.311357
$533$	−13.2700	−0.574788
$534$	−1.18709	−0.0513702
$535$	37.9904	1.64247
$536$	2.15091	0.0929052
$537$	0.301298	0.0130020
$538$	−32.0871	−1.38338
$539$	−2.00134	−0.0862038
$540$	−12.2753	−0.528245
$541$	33.5995	1.44456	0.722279	−	0.691602i	$-0.243095\pi$
$541$	33.5995	1.44456	0.722279	+	0.691602i	$0.243095\pi$
$542$	16.2153	0.696508
$543$	−4.97121	−0.213335
$544$	3.57012	0.153068
$545$	56.2739	2.41051
$546$	1.22541	0.0524428
$547$	−4.50240	−0.192509	−0.0962544	−	0.995357i	$-0.530686\pi$
$547$	−4.50240	−0.192509	−0.0962544	+	0.995357i	$0.530686\pi$
$548$	−10.2852	−0.439360
$549$	15.2155	0.649384
$550$	−14.1619	−0.603866
$551$	52.9172	2.25435
$552$	−2.42299	−0.103130
$553$	11.7696	0.500494
$554$	−7.95336	−0.337906
$555$	17.7967	0.755428
$556$	0.701577	0.0297535
$557$	27.7354	1.17519	0.587594	−	0.809156i	$-0.300075\pi$
$557$	27.7354	1.17519	0.587594	+	0.809156i	$0.300075\pi$
$558$	6.68522	0.283008
$559$	−11.4120	−0.482677
$560$	−3.47508	−0.146849
$561$	−4.50497	−0.190200
$562$	−27.0581	−1.14138
$563$	5.18264	0.218422	0.109211	−	0.994019i	$-0.465168\pi$
$563$	5.18264	0.218422	0.109211	+	0.994019i	$0.465168\pi$
$564$	4.09381	0.172380
$565$	72.3486	3.04373
$566$	8.16938	0.343385
$567$	−5.58021	−0.234347
$568$	−0.416734	−0.0174858
$569$	9.23898	0.387318	0.193659	−	0.981069i	$-0.437964\pi$
$569$	9.23898	0.387318	0.193659	+	0.981069i	$0.437964\pi$
$570$	15.7350	0.659068
$571$	25.8857	1.08328	0.541641	−	0.840610i	$-0.317803\pi$
$571$	25.8857	1.08328	0.541641	+	0.840610i	$0.317803\pi$
$572$	3.88969	0.162636
$573$	−2.71768	−0.113533
$574$	−6.82774	−0.284985
$575$	−27.1935	−1.13405
$576$	−2.60246	−0.108436
$577$	7.92820	0.330055	0.165028	−	0.986289i	$-0.447229\pi$
$577$	7.92820	0.330055	0.165028	+	0.986289i	$0.447229\pi$
$578$	−4.25422	−0.176952
$579$	16.9057	0.702577
$580$	25.6064	1.06325
$581$	−11.5955	−0.481062
$582$	−4.58634	−0.190110
$583$	8.42214	0.348809
$584$	15.2122	0.629484
$585$	17.5770	0.726718
$586$	18.8946	0.780530
$587$	−1.77583	−0.0732965	−0.0366482	−	0.999328i	$-0.511668\pi$
$587$	−1.77583	−0.0732965	−0.0366482	+	0.999328i	$0.511668\pi$
$588$	0.630504	0.0260016
$589$	−18.4478	−0.760129
$590$	−36.5062	−1.50294
$591$	1.38926	0.0571467
$592$	8.12244	0.333830
$593$	−33.3061	−1.36772	−0.683859	−	0.729614i	$-0.739700\pi$
$593$	−33.3061	−1.36772	−0.683859	+	0.729614i	$0.739700\pi$
$594$	7.06949	0.290065
$595$	−12.4065	−0.508616
$596$	5.25699	0.215335
$597$	4.21292	0.172423
$598$	7.46893	0.305427
$599$	−44.2814	−1.80929	−0.904645	−	0.426167i	$-0.859864\pi$
$599$	−44.2814	−1.80929	−0.904645	+	0.426167i	$0.859864\pi$
$600$	4.46158	0.182143
$601$	24.9400	1.01733	0.508663	−	0.860966i	$-0.330140\pi$
$601$	24.9400	1.01733	0.508663	+	0.860966i	$0.330140\pi$
$602$	−5.87176	−0.239315
$603$	−5.59767	−0.227955
$604$	−4.81087	−0.195752
$605$	−24.3070	−0.988218
$606$	1.39654	0.0567307
$607$	−25.2545	−1.02505	−0.512525	−	0.858673i	$-0.671290\pi$
$607$	−25.2545	−1.02505	−0.512525	+	0.858673i	$0.671290\pi$
$608$	7.18148	0.291248
$609$	−4.64591	−0.188262
$610$	−20.3174	−0.822627
$611$	−12.6192	−0.510520
$612$	−9.29112	−0.375571
$613$	−13.1460	−0.530961	−0.265480	−	0.964116i	$-0.585531\pi$
$613$	−13.1460	−0.530961	−0.265480	+	0.964116i	$0.585531\pi$
$614$	−15.6033	−0.629697
$615$	14.9600	0.603244
$616$	2.00134	0.0806363
$617$	0.237778	0.00957259	0.00478629	−	0.999989i	$-0.498476\pi$
$617$	0.237778	0.00957259	0.00478629	+	0.999989i	$0.498476\pi$
$618$	−5.76052	−0.231722
$619$	−7.60297	−0.305589	−0.152795	−	0.988258i	$-0.548827\pi$
$619$	−7.60297	−0.305589	−0.152795	+	0.988258i	$0.548827\pi$
$620$	−8.92681	−0.358509
$621$	13.5747	0.544736
$622$	−6.13362	−0.245936
$623$	1.88276	0.0754310
$624$	−1.22541	−0.0490557
$625$	−10.3083	−0.412331
$626$	−2.47466	−0.0989072
$627$	−9.06198	−0.361901
$628$	−10.3910	−0.414646
$629$	28.9981	1.15623
$630$	9.04378	0.360313
$631$	−24.2955	−0.967189	−0.483594	−	0.875292i	$-0.660669\pi$
$631$	−24.2955	−0.967189	−0.483594	+	0.875292i	$0.660669\pi$
$632$	−11.7696	−0.468170
$633$	2.20468	0.0876282
$634$	−15.1055	−0.599917
$635$	18.1244	0.719245
$636$	−2.65332	−0.105211
$637$	−1.94354	−0.0770059
$638$	−14.7470	−0.583839
$639$	1.08454	0.0429035
$640$	3.47508	0.137365
$641$	1.05443	0.0416475	0.0208237	−	0.999783i	$-0.493371\pi$
$641$	1.05443	0.0416475	0.0208237	+	0.999783i	$0.493371\pi$
$642$	6.89282	0.272038
$643$	31.7901	1.25368	0.626840	−	0.779148i	$-0.284348\pi$
$643$	31.7901	1.25368	0.626840	+	0.779148i	$0.284348\pi$
$644$	3.84295	0.151433
$645$	12.8654	0.506573
$646$	25.6388	1.00874
$647$	24.0131	0.944053	0.472026	−	0.881584i	$-0.343523\pi$
$647$	24.0131	0.944053	0.472026	+	0.881584i	$0.343523\pi$
$648$	5.58021	0.219212
$649$	21.0243	0.825277
$650$	−13.7529	−0.539434
$651$	1.61964	0.0634788
$652$	−6.49894	−0.254518
$653$	15.5990	0.610436	0.305218	−	0.952283i	$-0.401271\pi$
$653$	15.5990	0.610436	0.305218	+	0.952283i	$0.401271\pi$
$654$	10.2101	0.399246
$655$	25.4743	0.995365
$656$	6.82774	0.266579
$657$	−39.5891	−1.54452
$658$	−6.49291	−0.253120
$659$	−9.88409	−0.385029	−0.192515	−	0.981294i	$-0.561664\pi$
$659$	−9.88409	−0.385029	−0.192515	+	0.981294i	$0.561664\pi$
$660$	−4.38505	−0.170688
$661$	−30.8794	−1.20107	−0.600534	−	0.799599i	$-0.705045\pi$
$661$	−30.8794	−1.20107	−0.600534	+	0.799599i	$0.705045\pi$
$662$	3.34377	0.129959
$663$	−4.37487	−0.169906
$664$	11.5955	0.449993
$665$	−24.9563	−0.967762
$666$	−21.1383	−0.819094
$667$	−28.3170	−1.09644
$668$	−24.5649	−0.950446
$669$	−0.800666	−0.0309555
$670$	7.47459	0.288769
$671$	11.7010	0.451713
$672$	−0.630504	−0.0243222
$673$	−0.990291	−0.0381729	−0.0190865	−	0.999818i	$-0.506076\pi$
$673$	−0.990291	−0.0381729	−0.0190865	+	0.999818i	$0.506076\pi$
$674$	15.1165	0.582266
$675$	−24.9959	−0.962091
$676$	−9.22265	−0.354717
$677$	32.1670	1.23628	0.618139	−	0.786069i	$-0.287887\pi$
$677$	32.1670	1.23628	0.618139	+	0.786069i	$0.287887\pi$
$678$	13.1266	0.504125
$679$	7.27408	0.279153
$680$	12.4065	0.475767
$681$	5.58968	0.214197
$682$	5.14105	0.196861
$683$	−34.9493	−1.33730	−0.668649	−	0.743578i	$-0.733127\pi$
$683$	−34.9493	−1.33730	−0.668649	+	0.743578i	$0.733127\pi$
$684$	−18.6896	−0.714613
$685$	−35.7418	−1.36562
$686$	−1.00000	−0.0381802
$687$	−12.5304	−0.478065
$688$	5.87176	0.223859
$689$	8.17890	0.311591
$690$	−8.42011	−0.320548
$691$	−27.4448	−1.04405	−0.522025	−	0.852930i	$-0.674823\pi$
$691$	−27.4448	−1.04405	−0.522025	+	0.852930i	$0.674823\pi$
$692$	−3.81521	−0.145032
$693$	−5.20842	−0.197851
$694$	−12.0466	−0.457283
$695$	2.43804	0.0924801
$696$	4.64591	0.176103
$697$	24.3759	0.923303
$698$	−21.3969	−0.809886
$699$	−2.09715	−0.0793215
$700$	−7.07621	−0.267456
$701$	−3.12648	−0.118085	−0.0590427	−	0.998255i	$-0.518805\pi$
$701$	−3.12648	−0.118085	−0.0590427	+	0.998255i	$0.518805\pi$
$702$	6.86532	0.259115
$703$	58.3311	2.20000
$704$	−2.00134	−0.0754284
$705$	14.2263	0.535794
$706$	−11.9249	−0.448799
$707$	−2.21496	−0.0833022
$708$	−6.62352	−0.248927
$709$	44.7571	1.68089	0.840444	−	0.541898i	$-0.182294\pi$
$709$	44.7571	1.68089	0.840444	+	0.541898i	$0.182294\pi$
$710$	−1.44819	−0.0543494
$711$	30.6300	1.14871
$712$	−1.88276	−0.0705592
$713$	9.87178	0.369701
$714$	−2.25098	−0.0842407
$715$	13.5170	0.505507
$716$	0.477868	0.0178588
$717$	0.165433	0.00617820
$718$	−10.1564	−0.379032
$719$	−44.2587	−1.65057	−0.825286	−	0.564716i	$-0.808986\pi$
$719$	−44.2587	−1.65057	−0.825286	+	0.564716i	$0.808986\pi$
$720$	−9.04378	−0.337042
$721$	9.13637	0.340256
$722$	32.5737	1.21227
$723$	0.442893	0.0164714
$724$	−7.88450	−0.293025
$725$	52.1415	1.93649
$726$	−4.41015	−0.163676
$727$	−0.505605	−0.0187519	−0.00937593	−	0.999956i	$-0.502984\pi$
$727$	−0.505605	−0.0187519	−0.00937593	+	0.999956i	$0.502984\pi$
$728$	1.94354	0.0720324
$729$	−7.84077	−0.290399
$730$	52.8636	1.95657
$731$	20.9629	0.775341
$732$	−3.68630	−0.136250
$733$	−31.4192	−1.16050	−0.580248	−	0.814440i	$-0.697044\pi$
$733$	−31.4192	−1.16050	−0.580248	+	0.814440i	$0.697044\pi$
$734$	−12.2879	−0.453556
$735$	2.19106	0.0808183
$736$	−3.84295	−0.141653
$737$	−4.30470	−0.158566
$738$	−17.7690	−0.654085
$739$	−28.9124	−1.06356	−0.531780	−	0.846883i	$-0.678477\pi$
$739$	−28.9124	−1.06356	−0.531780	+	0.846883i	$0.678477\pi$
$740$	28.2262	1.03761
$741$	−8.80027	−0.323286
$742$	4.20825	0.154490
$743$	−48.2148	−1.76883	−0.884414	−	0.466703i	$-0.845442\pi$
$743$	−48.2148	−1.76883	−0.884414	+	0.466703i	$0.845442\pi$
$744$	−1.61964	−0.0593789
$745$	18.2685	0.669305
$746$	−28.8059	−1.05466
$747$	−30.1769	−1.10411
$748$	−7.14503	−0.261248
$749$	−10.9322	−0.399455
$750$	4.54910	0.166110
$751$	19.2494	0.702420	0.351210	−	0.936297i	$-0.385770\pi$
$751$	19.2494	0.702420	0.351210	+	0.936297i	$0.385770\pi$
$752$	6.49291	0.236772
$753$	−11.4800	−0.418354
$754$	−14.3211	−0.521544
$755$	−16.7182	−0.608437
$756$	3.53238	0.128471
$757$	16.9029	0.614348	0.307174	−	0.951653i	$-0.400617\pi$
$757$	16.9029	0.614348	0.307174	+	0.951653i	$0.400617\pi$
$758$	−13.2997	−0.483068
$759$	4.84924	0.176016
$760$	24.9563	0.905259
$761$	34.9162	1.26571	0.632856	−	0.774270i	$-0.281883\pi$
$761$	34.9162	1.26571	0.632856	+	0.774270i	$0.281883\pi$
$762$	3.28841	0.119127
$763$	−16.1935	−0.586245
$764$	−4.31033	−0.155942
$765$	−32.2874	−1.16735
$766$	−11.0934	−0.400822
$767$	20.4171	0.737220
$768$	0.630504	0.0227514
$769$	−16.5016	−0.595062	−0.297531	−	0.954712i	$-0.596163\pi$
$769$	−16.5016	−0.595062	−0.297531	+	0.954712i	$0.596163\pi$
$770$	6.95483	0.250635
$771$	−5.14113	−0.185153
$772$	26.8130	0.965021
$773$	−7.13914	−0.256777	−0.128389	−	0.991724i	$-0.540980\pi$
$773$	−7.13914	−0.256777	−0.128389	+	0.991724i	$0.540980\pi$
$774$	−15.2810	−0.549266
$775$	−18.1774	−0.652952
$776$	−7.27408	−0.261124
$777$	−5.12123	−0.183723
$778$	31.3233	1.12300
$779$	49.0333	1.75680
$780$	−4.25841	−0.152475
$781$	0.834026	0.0298438
$782$	−13.7198	−0.490619
$783$	−26.0285	−0.930184
$784$	1.00000	0.0357143
$785$	−36.1096	−1.28881
$786$	4.62195	0.164860
$787$	18.7696	0.669064	0.334532	−	0.942384i	$-0.391422\pi$
$787$	18.7696	0.669064	0.334532	+	0.942384i	$0.391422\pi$
$788$	2.20342	0.0784935
$789$	−3.02796	−0.107798
$790$	−40.9004	−1.45517
$791$	−20.8192	−0.740247
$792$	5.20842	0.185073
$793$	11.3631	0.403515
$794$	−10.5491	−0.374375
$795$	−9.22051	−0.327018
$796$	6.68182	0.236831
$797$	44.1788	1.56490	0.782448	−	0.622716i	$-0.213971\pi$
$797$	44.1788	1.56490	0.782448	+	0.622716i	$0.213971\pi$
$798$	−4.52796	−0.160288
$799$	23.1805	0.820067
$800$	7.07621	0.250182
$801$	4.89980	0.173126
$802$	−14.1971	−0.501319
$803$	−30.4447	−1.07437
$804$	1.35616	0.0478280
$805$	13.3546	0.470687
$806$	4.99258	0.175856
$807$	−20.2311	−0.712168
$808$	2.21496	0.0779221
$809$	−7.44698	−0.261822	−0.130911	−	0.991394i	$-0.541790\pi$
$809$	−7.44698	−0.261822	−0.130911	+	0.991394i	$0.541790\pi$
$810$	19.3917	0.681355
$811$	23.9946	0.842564	0.421282	−	0.906930i	$-0.361580\pi$
$811$	23.9946	0.842564	0.421282	+	0.906930i	$0.361580\pi$
$812$	−7.36856	−0.258586
$813$	10.2238	0.358565
$814$	−16.2558	−0.569764
$815$	−22.5844	−0.791096
$816$	2.25098	0.0788000
$817$	42.1680	1.47527
$818$	25.6365	0.896360
$819$	−5.05800	−0.176741
$820$	23.7270	0.828583
$821$	−49.7845	−1.73749	−0.868746	−	0.495257i	$-0.835074\pi$
$821$	−49.7845	−1.73749	−0.868746	+	0.495257i	$0.835074\pi$
$822$	−6.48484	−0.226185
$823$	39.1106	1.36331	0.681655	−	0.731674i	$-0.261260\pi$
$823$	39.1106	1.36331	0.681655	+	0.731674i	$0.261260\pi$
$824$	−9.13637	−0.318281
$825$	−8.92915	−0.310873
$826$	10.5051	0.365520
$827$	−18.8726	−0.656266	−0.328133	−	0.944632i	$-0.606419\pi$
$827$	−18.8726	−0.656266	−0.328133	+	0.944632i	$0.606419\pi$
$828$	10.0011	0.347563
$829$	26.9900	0.937401	0.468700	−	0.883357i	$-0.344722\pi$
$829$	26.9900	0.937401	0.468700	+	0.883357i	$0.344722\pi$
$830$	40.2953	1.39867
$831$	−5.01463	−0.173955
$832$	−1.94354	−0.0673802
$833$	3.57012	0.123697
$834$	0.442347	0.0153172
$835$	−85.3653	−2.95419
$836$	−14.3726	−0.497087
$837$	9.07399	0.313643
$838$	18.7274	0.646928
$839$	−14.2837	−0.493127	−0.246564	−	0.969127i	$-0.579301\pi$
$839$	−14.2837	−0.493127	−0.246564	+	0.969127i	$0.579301\pi$
$840$	−2.19106	−0.0755986
$841$	25.2957	0.872264
$842$	−4.97162	−0.171333
$843$	−17.0603	−0.587587
$844$	3.49669	0.120361
$845$	−32.0495	−1.10254
$846$	−16.8976	−0.580950
$847$	6.99464	0.240339
$848$	−4.20825	−0.144512
$849$	5.15083	0.176776
$850$	25.2630	0.866512
$851$	−31.2141	−1.07001
$852$	−0.262752	−0.00900175
$853$	−24.1508	−0.826909	−0.413455	−	0.910525i	$-0.635678\pi$
$853$	−24.1508	−0.826909	−0.413455	+	0.910525i	$0.635678\pi$
$854$	5.84659	0.200066
$855$	−64.9478	−2.22117
$856$	10.9322	0.373656
$857$	44.8388	1.53166	0.765832	−	0.643041i	$-0.222328\pi$
$857$	44.8388	1.53166	0.765832	+	0.643041i	$0.222328\pi$
$858$	2.45246	0.0837258
$859$	−4.08558	−0.139398	−0.0696992	−	0.997568i	$-0.522204\pi$
$859$	−4.08558	−0.139398	−0.0696992	+	0.997568i	$0.522204\pi$
$860$	20.4049	0.695800
$861$	−4.30492	−0.146711
$862$	−1.00000	−0.0340601
$863$	−31.3845	−1.06834	−0.534171	−	0.845377i	$-0.679376\pi$
$863$	−31.3845	−1.06834	−0.534171	+	0.845377i	$0.679376\pi$
$864$	−3.53238	−0.120174
$865$	−13.2582	−0.450791
$866$	20.7144	0.703905
$867$	−2.68230	−0.0910957
$868$	2.56880	0.0871909
$869$	23.5550	0.799048
$870$	16.1449	0.547364
$871$	−4.18038	−0.141647
$872$	16.1935	0.548382
$873$	18.9305	0.640701
$874$	−27.5981	−0.933518
$875$	−7.21502	−0.243912
$876$	9.59134	0.324061
$877$	35.7468	1.20708	0.603541	−	0.797332i	$-0.293756\pi$
$877$	35.7468	1.20708	0.603541	+	0.797332i	$0.293756\pi$
$878$	8.79904	0.296953
$879$	11.9131	0.401820
$880$	−6.95483	−0.234447
$881$	8.07152	0.271937	0.135968	−	0.990713i	$-0.456585\pi$
$881$	8.07152	0.271937	0.135968	+	0.990713i	$0.456585\pi$
$882$	−2.60246	−0.0876295
$883$	−18.4219	−0.619946	−0.309973	−	0.950745i	$-0.600320\pi$
$883$	−18.4219	−0.619946	−0.309973	+	0.950745i	$0.600320\pi$
$884$	−6.93868	−0.233373
$885$	−23.0173	−0.773718
$886$	−40.2301	−1.35156
$887$	32.2052	1.08135	0.540673	−	0.841233i	$-0.318170\pi$
$887$	32.2052	1.08135	0.540673	+	0.841233i	$0.318170\pi$
$888$	5.12123	0.171857
$889$	−5.21553	−0.174923
$890$	−6.54273	−0.219313
$891$	−11.1679	−0.374139
$892$	−1.26988	−0.0425188
$893$	46.6287	1.56037
$894$	3.31455	0.110855
$895$	1.66063	0.0555088
$896$	−1.00000	−0.0334077
$897$	4.70919	0.157235
$898$	27.7863	0.927242
$899$	−18.9284	−0.631297
$900$	−18.4156	−0.613853
$901$	−15.0240	−0.500521
$902$	−13.6646	−0.454983
$903$	−3.70217	−0.123200
$904$	20.8192	0.692438
$905$	−27.3993	−0.910783
$906$	−3.03327	−0.100774
$907$	−29.9310	−0.993842	−0.496921	−	0.867796i	$-0.665536\pi$
$907$	−29.9310	−0.993842	−0.496921	+	0.867796i	$0.665536\pi$
$908$	8.86542	0.294209
$909$	−5.76436	−0.191192
$910$	6.75397	0.223892
$911$	6.40874	0.212331	0.106165	−	0.994348i	$-0.466143\pi$
$911$	6.40874	0.212331	0.106165	+	0.994348i	$0.466143\pi$
$912$	4.52796	0.149936
$913$	−23.2065	−0.768024
$914$	−22.8475	−0.755729
$915$	−12.8102	−0.423492
$916$	−19.8736	−0.656644
$917$	−7.33057	−0.242077
$918$	−12.6110	−0.416226
$919$	0.423005	0.0139536	0.00697682	−	0.999976i	$-0.497779\pi$
$919$	0.423005	0.0139536	0.00697682	+	0.999976i	$0.497779\pi$
$920$	−13.3546	−0.440287
$921$	−9.83792	−0.324171
$922$	22.4577	0.739607
$923$	0.809940	0.0266595
$924$	1.26185	0.0415119
$925$	57.4761	1.88980
$926$	23.5686	0.774511
$927$	23.7771	0.780942
$928$	7.36856	0.241885
$929$	33.7387	1.10693	0.553465	−	0.832872i	$-0.313305\pi$
$929$	33.7387	1.10693	0.553465	+	0.832872i	$0.313305\pi$
$930$	−5.62839	−0.184562
$931$	7.18148	0.235364
$932$	−3.32615	−0.108952
$933$	−3.86727	−0.126609
$934$	−18.1600	−0.594213
$935$	−24.8296	−0.812015
$936$	5.05800	0.165326
$937$	−13.6808	−0.446932	−0.223466	−	0.974712i	$-0.571737\pi$
$937$	−13.6808	−0.446932	−0.223466	+	0.974712i	$0.571737\pi$
$938$	−2.15091	−0.0702297
$939$	−1.56028	−0.0509179
$940$	22.5634	0.735937
$941$	−18.0103	−0.587119	−0.293559	−	0.955941i	$-0.594840\pi$
$941$	−18.0103	−0.587119	−0.293559	+	0.955941i	$0.594840\pi$
$942$	−6.55157	−0.213462
$943$	−26.2387	−0.854448
$944$	−10.5051	−0.341912
$945$	12.2753	0.399316
$946$	−11.7514	−0.382071
$947$	20.5479	0.667718	0.333859	−	0.942623i	$-0.391649\pi$
$947$	20.5479	0.667718	0.333859	+	0.942623i	$0.391649\pi$
$948$	−7.42078	−0.241016
$949$	−29.5655	−0.959737
$950$	50.8177	1.64874
$951$	−9.52409	−0.308840
$952$	−3.57012	−0.115708
$953$	41.3888	1.34071	0.670357	−	0.742038i	$-0.266141\pi$
$953$	41.3888	1.34071	0.670357	+	0.742038i	$0.266141\pi$
$954$	10.9518	0.354578
$955$	−14.9788	−0.484702
$956$	0.262382	0.00848603
$957$	−9.29804	−0.300563
$958$	18.6288	0.601870
$959$	10.2852	0.332125
$960$	2.19106	0.0707160
$961$	−24.4012	−0.787137
$962$	−15.7863	−0.508970
$963$	−28.4507	−0.916813
$964$	0.702442	0.0226241
$965$	93.1774	2.99949
$966$	2.42299	0.0779586
$967$	56.7825	1.82600	0.913002	−	0.407956i	$-0.133758\pi$
$967$	56.7825	1.82600	0.913002	+	0.407956i	$0.133758\pi$
$968$	−6.99464	−0.224816
$969$	16.1654	0.519306
$970$	−25.2780	−0.811629
$971$	−9.67375	−0.310445	−0.155223	−	0.987880i	$-0.549610\pi$
$971$	−9.67375	−0.310445	−0.155223	+	0.987880i	$0.549610\pi$
$972$	14.1155	0.452754
$973$	−0.701577	−0.0224915
$974$	−32.2560	−1.03355
$975$	−8.67127	−0.277703
$976$	−5.84659	−0.187145
$977$	−45.1986	−1.44603	−0.723016	−	0.690831i	$-0.757245\pi$
$977$	−45.1986	−1.44603	−0.723016	+	0.690831i	$0.757245\pi$
$978$	−4.09761	−0.131027
$979$	3.76803	0.120427
$980$	3.47508	0.111008
$981$	−42.1431	−1.34552
$982$	−20.6599	−0.659285
$983$	−2.49396	−0.0795449	−0.0397725	−	0.999209i	$-0.512663\pi$
$983$	−2.49396	−0.0795449	−0.0397725	+	0.999209i	$0.512663\pi$
$984$	4.30492	0.137236
$985$	7.65706	0.243974
$986$	26.3067	0.837775
$987$	−4.09381	−0.130307
$988$	−13.9575	−0.444048
$989$	−22.5649	−0.717521
$990$	18.0997	0.575246
$991$	31.4794	0.999977	0.499989	−	0.866032i	$-0.333337\pi$
$991$	31.4794	0.999977	0.499989	+	0.866032i	$0.333337\pi$
$992$	−2.56880	−0.0815596
$993$	2.10826	0.0669036
$994$	0.416734	0.0132180
$995$	23.2199	0.736120
$996$	7.31101	0.231658
$997$	−4.78122	−0.151423	−0.0757114	−	0.997130i	$-0.524123\pi$
$997$	−4.78122	−0.151423	−0.0757114	+	0.997130i	$0.524123\pi$
$998$	32.1780	1.01858
$999$	−28.6915	−0.907759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.17	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.17	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.630504 q^{3} +1.00000 q^{4} +3.47508 q^{5} +0.630504 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.60246 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.630504 q^{3} +1.00000 q^{4} +3.47508 q^{5} +0.630504 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.60246 q^{9} +3.47508 q^{10} -2.00134 q^{11} +0.630504 q^{12} -1.94354 q^{13} -1.00000 q^{14} +2.19106 q^{15} +1.00000 q^{16} +3.57012 q^{17} -2.60246 q^{18} +7.18148 q^{19} +3.47508 q^{20} -0.630504 q^{21} -2.00134 q^{22} -3.84295 q^{23} +0.630504 q^{24} +7.07621 q^{25} -1.94354 q^{26} -3.53238 q^{27} -1.00000 q^{28} +7.36856 q^{29} +2.19106 q^{30} -2.56880 q^{31} +1.00000 q^{32} -1.26185 q^{33} +3.57012 q^{34} -3.47508 q^{35} -2.60246 q^{36} +8.12244 q^{37} +7.18148 q^{38} -1.22541 q^{39} +3.47508 q^{40} +6.82774 q^{41} -0.630504 q^{42} +5.87176 q^{43} -2.00134 q^{44} -9.04378 q^{45} -3.84295 q^{46} +6.49291 q^{47} +0.630504 q^{48} +1.00000 q^{49} +7.07621 q^{50} +2.25098 q^{51} -1.94354 q^{52} -4.20825 q^{53} -3.53238 q^{54} -6.95483 q^{55} -1.00000 q^{56} +4.52796 q^{57} +7.36856 q^{58} -10.5051 q^{59} +2.19106 q^{60} -5.84659 q^{61} -2.56880 q^{62} +2.60246 q^{63} +1.00000 q^{64} -6.75397 q^{65} -1.26185 q^{66} +2.15091 q^{67} +3.57012 q^{68} -2.42299 q^{69} -3.47508 q^{70} -0.416734 q^{71} -2.60246 q^{72} +15.2122 q^{73} +8.12244 q^{74} +4.46158 q^{75} +7.18148 q^{76} +2.00134 q^{77} -1.22541 q^{78} -11.7696 q^{79} +3.47508 q^{80} +5.58021 q^{81} +6.82774 q^{82} +11.5955 q^{83} -0.630504 q^{84} +12.4065 q^{85} +5.87176 q^{86} +4.64591 q^{87} -2.00134 q^{88} -1.88276 q^{89} -9.04378 q^{90} +1.94354 q^{91} -3.84295 q^{92} -1.61964 q^{93} +6.49291 q^{94} +24.9563 q^{95} +0.630504 q^{96} -7.27408 q^{97} +1.00000 q^{98} +5.20842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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