LMFDB - Embedded newform 6035.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.619688 q^{2} -2.94210 q^{3} -1.61599 q^{4} +1.00000 q^{5} +1.82319 q^{6} -1.69113 q^{7} +2.24078 q^{8} +5.65598 q^{9} +O(q^{10})$	\(q-0.619688 q^{2} -2.94210 q^{3} -1.61599 q^{4} +1.00000 q^{5} +1.82319 q^{6} -1.69113 q^{7} +2.24078 q^{8} +5.65598 q^{9} -0.619688 q^{10} +3.40791 q^{11} +4.75440 q^{12} +1.18568 q^{13} +1.04797 q^{14} -2.94210 q^{15} +1.84339 q^{16} -1.00000 q^{17} -3.50494 q^{18} -6.17895 q^{19} -1.61599 q^{20} +4.97548 q^{21} -2.11184 q^{22} +5.44934 q^{23} -6.59262 q^{24} +1.00000 q^{25} -0.734754 q^{26} -7.81416 q^{27} +2.73285 q^{28} -5.01979 q^{29} +1.82319 q^{30} -4.56846 q^{31} -5.62389 q^{32} -10.0264 q^{33} +0.619688 q^{34} -1.69113 q^{35} -9.13998 q^{36} +0.419235 q^{37} +3.82902 q^{38} -3.48840 q^{39} +2.24078 q^{40} +2.18812 q^{41} -3.08325 q^{42} +5.78424 q^{43} -5.50714 q^{44} +5.65598 q^{45} -3.37689 q^{46} -5.29382 q^{47} -5.42343 q^{48} -4.14008 q^{49} -0.619688 q^{50} +2.94210 q^{51} -1.91605 q^{52} -0.0781118 q^{53} +4.84234 q^{54} +3.40791 q^{55} -3.78946 q^{56} +18.1791 q^{57} +3.11071 q^{58} +6.33168 q^{59} +4.75440 q^{60} -12.7973 q^{61} +2.83102 q^{62} -9.56500 q^{63} -0.201711 q^{64} +1.18568 q^{65} +6.21326 q^{66} +6.41093 q^{67} +1.61599 q^{68} -16.0325 q^{69} +1.04797 q^{70} +1.00000 q^{71} +12.6738 q^{72} -6.00110 q^{73} -0.259795 q^{74} -2.94210 q^{75} +9.98510 q^{76} -5.76322 q^{77} +2.16172 q^{78} +13.9554 q^{79} +1.84339 q^{80} +6.02214 q^{81} -1.35595 q^{82} -1.66407 q^{83} -8.04031 q^{84} -1.00000 q^{85} -3.58443 q^{86} +14.7687 q^{87} +7.63639 q^{88} -15.1223 q^{89} -3.50494 q^{90} -2.00515 q^{91} -8.80607 q^{92} +13.4409 q^{93} +3.28052 q^{94} -6.17895 q^{95} +16.5461 q^{96} +2.18586 q^{97} +2.56556 q^{98} +19.2751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * 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 $

$2$	−0.619688	−0.438186	−0.219093	−	0.975704i	$-0.570310\pi$
$2$	−0.619688	−0.438186	−0.219093	+	0.975704i	$0.570310\pi$
$3$	−2.94210	−1.69862	−0.849312	−	0.527891i	$-0.822983\pi$
$3$	−2.94210	−1.69862	−0.849312	+	0.527891i	$0.822983\pi$
$4$	−1.61599	−0.807993
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.82319	0.744313
$7$	−1.69113	−0.639187	−0.319594	−	0.947555i	$-0.603546\pi$
$7$	−1.69113	−0.639187	−0.319594	+	0.947555i	$0.603546\pi$
$8$	2.24078	0.792237
$9$	5.65598	1.88533
$10$	−0.619688	−0.195963
$11$	3.40791	1.02752	0.513762	−	0.857933i	$-0.328251\pi$
$11$	3.40791	1.02752	0.513762	+	0.857933i	$0.328251\pi$
$12$	4.75440	1.37248
$13$	1.18568	0.328849	0.164425	−	0.986390i	$-0.447423\pi$
$13$	1.18568	0.328849	0.164425	+	0.986390i	$0.447423\pi$
$14$	1.04797	0.280083
$15$	−2.94210	−0.759648
$16$	1.84339	0.460846
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.50494	−0.826123
$19$	−6.17895	−1.41755	−0.708774	−	0.705435i	$-0.750751\pi$
$19$	−6.17895	−1.41755	−0.708774	+	0.705435i	$0.750751\pi$
$20$	−1.61599	−0.361346
$21$	4.97548	1.08574
$22$	−2.11184	−0.450246
$23$	5.44934	1.13627	0.568133	−	0.822937i	$-0.307666\pi$
$23$	5.44934	1.13627	0.568133	+	0.822937i	$0.307666\pi$
$24$	−6.59262	−1.34571
$25$	1.00000	0.200000
$26$	−0.734754	−0.144097
$27$	−7.81416	−1.50384
$28$	2.73285	0.516459
$29$	−5.01979	−0.932152	−0.466076	−	0.884745i	$-0.654333\pi$
$29$	−5.01979	−0.932152	−0.466076	+	0.884745i	$0.654333\pi$
$30$	1.82319	0.332867
$31$	−4.56846	−0.820520	−0.410260	−	0.911969i	$-0.634562\pi$
$31$	−4.56846	−0.820520	−0.410260	+	0.911969i	$0.634562\pi$
$32$	−5.62389	−0.994173
$33$	−10.0264	−1.74538
$34$	0.619688	0.106276
$35$	−1.69113	−0.285853
$36$	−9.13998	−1.52333
$37$	0.419235	0.0689219	0.0344609	−	0.999406i	$-0.489029\pi$
$37$	0.419235	0.0689219	0.0344609	+	0.999406i	$0.489029\pi$
$38$	3.82902	0.621149
$39$	−3.48840	−0.558591
$40$	2.24078	0.354299
$41$	2.18812	0.341727	0.170863	−	0.985295i	$-0.445344\pi$
$41$	2.18812	0.341727	0.170863	+	0.985295i	$0.445344\pi$
$42$	−3.08325	−0.475756
$43$	5.78424	0.882089	0.441044	−	0.897485i	$-0.354608\pi$
$43$	5.78424	0.882089	0.441044	+	0.897485i	$0.354608\pi$
$44$	−5.50714	−0.830232
$45$	5.65598	0.843143
$46$	−3.37689	−0.497896
$47$	−5.29382	−0.772182	−0.386091	−	0.922461i	$-0.626175\pi$
$47$	−5.29382	−0.772182	−0.386091	+	0.922461i	$0.626175\pi$
$48$	−5.42343	−0.782805
$49$	−4.14008	−0.591439
$50$	−0.619688	−0.0876371
$51$	2.94210	0.411977
$52$	−1.91605	−0.265708
$53$	−0.0781118	−0.0107295	−0.00536474	−	0.999986i	$-0.501708\pi$
$53$	−0.0781118	−0.0107295	−0.00536474	+	0.999986i	$0.501708\pi$
$54$	4.84234	0.658959
$55$	3.40791	0.459523
$56$	−3.78946	−0.506388
$57$	18.1791	2.40788
$58$	3.11071	0.408456
$59$	6.33168	0.824315	0.412157	−	0.911113i	$-0.364775\pi$
$59$	6.33168	0.824315	0.412157	+	0.911113i	$0.364775\pi$
$60$	4.75440	0.613790
$61$	−12.7973	−1.63853	−0.819265	−	0.573414i	$-0.805619\pi$
$61$	−12.7973	−1.63853	−0.819265	+	0.573414i	$0.805619\pi$
$62$	2.83102	0.359540
$63$	−9.56500	−1.20508
$64$	−0.201711	−0.0252139
$65$	1.18568	0.147066
$66$	6.21326	0.764799
$67$	6.41093	0.783220	0.391610	−	0.920131i	$-0.371918\pi$
$67$	6.41093	0.783220	0.391610	+	0.920131i	$0.371918\pi$
$68$	1.61599	0.195967
$69$	−16.0325	−1.93009
$70$	1.04797	0.125257
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	12.6738	1.49362
$73$	−6.00110	−0.702375	−0.351188	−	0.936305i	$-0.614222\pi$
$73$	−6.00110	−0.702375	−0.351188	+	0.936305i	$0.614222\pi$
$74$	−0.259795	−0.0302006
$75$	−2.94210	−0.339725
$76$	9.98510	1.14537
$77$	−5.76322	−0.656780
$78$	2.16172	0.244767
$79$	13.9554	1.57010	0.785051	−	0.619431i	$-0.212637\pi$
$79$	13.9554	1.57010	0.785051	+	0.619431i	$0.212637\pi$
$80$	1.84339	0.206097
$81$	6.02214	0.669127
$82$	−1.35595	−0.149740
$83$	−1.66407	−0.182655	−0.0913276	−	0.995821i	$-0.529111\pi$
$83$	−1.66407	−0.182655	−0.0913276	+	0.995821i	$0.529111\pi$
$84$	−8.04031	−0.877270
$85$	−1.00000	−0.108465
$86$	−3.58443	−0.386519
$87$	14.7687	1.58338
$88$	7.63639	0.814042
$89$	−15.1223	−1.60296	−0.801478	−	0.598025i	$-0.795953\pi$
$89$	−15.1223	−1.60296	−0.801478	+	0.598025i	$0.795953\pi$
$90$	−3.50494	−0.369453
$91$	−2.00515	−0.210196
$92$	−8.80607	−0.918096
$93$	13.4409	1.39376
$94$	3.28052	0.338359
$95$	−6.17895	−0.633947
$96$	16.5461	1.68873
$97$	2.18586	0.221940	0.110970	−	0.993824i	$-0.464604\pi$
$97$	2.18586	0.221940	0.110970	+	0.993824i	$0.464604\pi$
$98$	2.56556	0.259160
$99$	19.2751	1.93722
$100$	−1.61599	−0.161599
$101$	15.7097	1.56318	0.781589	−	0.623794i	$-0.214410\pi$
$101$	15.7097	1.56318	0.781589	+	0.623794i	$0.214410\pi$
$102$	−1.82319	−0.180522
$103$	15.4096	1.51836	0.759179	−	0.650882i	$-0.225601\pi$
$103$	15.4096	1.51836	0.759179	+	0.650882i	$0.225601\pi$
$104$	2.65686	0.260526
$105$	4.97548	0.485558
$106$	0.0484050	0.00470151
$107$	14.0273	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$107$	14.0273	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$108$	12.6276	1.21509
$109$	−2.07944	−0.199174	−0.0995872	−	0.995029i	$-0.531752\pi$
$109$	−2.07944	−0.199174	−0.0995872	+	0.995029i	$0.531752\pi$
$110$	−2.11184	−0.201356
$111$	−1.23343	−0.117072
$112$	−3.11741	−0.294567
$113$	0.435459	0.0409645	0.0204823	−	0.999790i	$-0.493480\pi$
$113$	0.435459	0.0409645	0.0204823	+	0.999790i	$0.493480\pi$
$114$	−11.2654	−1.05510
$115$	5.44934	0.508154
$116$	8.11192	0.753172
$117$	6.70619	0.619988
$118$	−3.92367	−0.361203
$119$	1.69113	0.155026
$120$	−6.59262	−0.601821
$121$	0.613854	0.0558049
$122$	7.93036	0.717981
$123$	−6.43767	−0.580465
$124$	7.38257	0.662975
$125$	1.00000	0.0894427
$126$	5.92732	0.528047
$127$	13.1329	1.16536	0.582679	−	0.812702i	$-0.302004\pi$
$127$	13.1329	1.16536	0.582679	+	0.812702i	$0.302004\pi$
$128$	11.3728	1.00522
$129$	−17.0178	−1.49834
$130$	−0.734754	−0.0644422
$131$	−3.71720	−0.324773	−0.162386	−	0.986727i	$-0.551919\pi$
$131$	−3.71720	−0.324773	−0.162386	+	0.986727i	$0.551919\pi$
$132$	16.2026	1.41025
$133$	10.4494	0.906079
$134$	−3.97278	−0.343196
$135$	−7.81416	−0.672536
$136$	−2.24078	−0.192146
$137$	−15.9301	−1.36100	−0.680498	−	0.732750i	$-0.738237\pi$
$137$	−15.9301	−1.36100	−0.680498	+	0.732750i	$0.738237\pi$
$138$	9.93517	0.845738
$139$	−4.74946	−0.402844	−0.201422	−	0.979505i	$-0.564556\pi$
$139$	−4.74946	−0.402844	−0.201422	+	0.979505i	$0.564556\pi$
$140$	2.73285	0.230968
$141$	15.5750	1.31165
$142$	−0.619688	−0.0520031
$143$	4.04070	0.337900
$144$	10.4261	0.868846
$145$	−5.01979	−0.416871
$146$	3.71881	0.307771
$147$	12.1805	1.00463
$148$	−0.677479	−0.0556884
$149$	−6.53933	−0.535723	−0.267862	−	0.963457i	$-0.586317\pi$
$149$	−6.53933	−0.535723	−0.267862	+	0.963457i	$0.586317\pi$
$150$	1.82319	0.148863
$151$	10.0086	0.814486	0.407243	−	0.913320i	$-0.366490\pi$
$151$	10.0086	0.814486	0.407243	+	0.913320i	$0.366490\pi$
$152$	−13.8457	−1.12303
$153$	−5.65598	−0.457259
$154$	3.57140	0.287792
$155$	−4.56846	−0.366948
$156$	5.63721	0.451338
$157$	4.85279	0.387295	0.193647	−	0.981071i	$-0.437968\pi$
$157$	4.85279	0.387295	0.193647	+	0.981071i	$0.437968\pi$
$158$	−8.64798	−0.687996
$159$	0.229813	0.0182254
$160$	−5.62389	−0.444608
$161$	−9.21555	−0.726287
$162$	−3.73185	−0.293202
$163$	19.1915	1.50320	0.751598	−	0.659621i	$-0.229283\pi$
$163$	19.1915	1.50320	0.751598	+	0.659621i	$0.229283\pi$
$164$	−3.53597	−0.276113
$165$	−10.0264	−0.780556
$166$	1.03120	0.0800369
$167$	−4.15982	−0.321897	−0.160948	−	0.986963i	$-0.551455\pi$
$167$	−4.15982	−0.321897	−0.160948	+	0.986963i	$0.551455\pi$
$168$	11.1490	0.860163
$169$	−11.5942	−0.891858
$170$	0.619688	0.0475279
$171$	−34.9480	−2.67254
$172$	−9.34726	−0.712722
$173$	0.620865	0.0472035	0.0236017	−	0.999721i	$-0.492487\pi$
$173$	0.620865	0.0472035	0.0236017	+	0.999721i	$0.492487\pi$
$174$	−9.15202	−0.693813
$175$	−1.69113	−0.127837
$176$	6.28209	0.473531
$177$	−18.6285	−1.40020
$178$	9.37108	0.702392
$179$	−13.5679	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$179$	−13.5679	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$180$	−9.13998	−0.681254
$181$	−5.90637	−0.439017	−0.219508	−	0.975611i	$-0.570445\pi$
$181$	−5.90637	−0.439017	−0.219508	+	0.975611i	$0.570445\pi$
$182$	1.24256	0.0921050
$183$	37.6511	2.78325
$184$	12.2108	0.900192
$185$	0.419235	0.0308228
$186$	−8.32916	−0.610724
$187$	−3.40791	−0.249211
$188$	8.55474	0.623918
$189$	13.2148	0.961233
$190$	3.82902	0.277786
$191$	1.56313	0.113104	0.0565521	−	0.998400i	$-0.481989\pi$
$191$	1.56313	0.113104	0.0565521	+	0.998400i	$0.481989\pi$
$192$	0.593456	0.0428290
$193$	7.75400	0.558145	0.279072	−	0.960270i	$-0.409973\pi$
$193$	7.75400	0.558145	0.279072	+	0.960270i	$0.409973\pi$
$194$	−1.35455	−0.0972510
$195$	−3.48840	−0.249810
$196$	6.69031	0.477879
$197$	16.2084	1.15480	0.577401	−	0.816461i	$-0.304067\pi$
$197$	16.2084	1.15480	0.577401	+	0.816461i	$0.304067\pi$
$198$	−11.9445	−0.848861
$199$	6.01963	0.426720	0.213360	−	0.976974i	$-0.431559\pi$
$199$	6.01963	0.426720	0.213360	+	0.976974i	$0.431559\pi$
$200$	2.24078	0.158447
$201$	−18.8616	−1.33040
$202$	−9.73514	−0.684962
$203$	8.48913	0.595820
$204$	−4.75440	−0.332875
$205$	2.18812	0.152825
$206$	−9.54917	−0.665323
$207$	30.8214	2.14223
$208$	2.18567	0.151549
$209$	−21.0573	−1.45656
$210$	−3.08325	−0.212764
$211$	−9.56262	−0.658318	−0.329159	−	0.944275i	$-0.606765\pi$
$211$	−9.56262	−0.658318	−0.329159	+	0.944275i	$0.606765\pi$
$212$	0.126228	0.00866935
$213$	−2.94210	−0.201590
$214$	−8.69257	−0.594212
$215$	5.78424	0.394482
$216$	−17.5098	−1.19139
$217$	7.72587	0.524466
$218$	1.28861	0.0872754
$219$	17.6558	1.19307
$220$	−5.50714	−0.371291
$221$	−1.18568	−0.0797577
$222$	0.764345	0.0512994
$223$	−9.76369	−0.653825	−0.326912	−	0.945055i	$-0.606008\pi$
$223$	−9.76369	−0.653825	−0.326912	+	0.945055i	$0.606008\pi$
$224$	9.51074	0.635463
$225$	5.65598	0.377065
$226$	−0.269849	−0.0179501
$227$	−15.9709	−1.06003	−0.530013	−	0.847989i	$-0.677813\pi$
$227$	−15.9709	−1.06003	−0.530013	+	0.847989i	$0.677813\pi$
$228$	−29.3772	−1.94555
$229$	11.9190	0.787632	0.393816	−	0.919189i	$-0.371155\pi$
$229$	11.9190	0.787632	0.393816	+	0.919189i	$0.371155\pi$
$230$	−3.37689	−0.222666
$231$	16.9560	1.11562
$232$	−11.2483	−0.738485
$233$	5.73078	0.375436	0.187718	−	0.982223i	$-0.439891\pi$
$233$	5.73078	0.375436	0.187718	+	0.982223i	$0.439891\pi$
$234$	−4.15575	−0.271670
$235$	−5.29382	−0.345330
$236$	−10.2319	−0.666041
$237$	−41.0582	−2.66701
$238$	−1.04797	−0.0679301
$239$	6.93201	0.448395	0.224197	−	0.974544i	$-0.428024\pi$
$239$	6.93201	0.448395	0.224197	+	0.974544i	$0.428024\pi$
$240$	−5.42343	−0.350081
$241$	−15.0583	−0.969988	−0.484994	−	0.874517i	$-0.661178\pi$
$241$	−15.0583	−0.969988	−0.484994	+	0.874517i	$0.661178\pi$
$242$	−0.380398	−0.0244529
$243$	5.72471	0.367240
$244$	20.6803	1.32392
$245$	−4.14008	−0.264500
$246$	3.98935	0.254352
$247$	−7.32627	−0.466160
$248$	−10.2369	−0.650046
$249$	4.89586	0.310263
$250$	−0.619688	−0.0391925
$251$	1.39295	0.0879225	0.0439613	−	0.999033i	$-0.486002\pi$
$251$	1.39295	0.0879225	0.0439613	+	0.999033i	$0.486002\pi$
$252$	15.4569	0.973694
$253$	18.5709	1.16754
$254$	−8.13832	−0.510644
$255$	2.94210	0.184242
$256$	−6.64416	−0.415260
$257$	−18.4588	−1.15143	−0.575714	−	0.817651i	$-0.695276\pi$
$257$	−18.4588	−1.15143	−0.575714	+	0.817651i	$0.695276\pi$
$258$	10.5458	0.656550
$259$	−0.708982	−0.0440540
$260$	−1.91605	−0.118828
$261$	−28.3918	−1.75741
$262$	2.30350	0.142311
$263$	3.82961	0.236144	0.118072	−	0.993005i	$-0.462329\pi$
$263$	3.82961	0.236144	0.118072	+	0.993005i	$0.462329\pi$
$264$	−22.4671	−1.38275
$265$	−0.0781118	−0.00479837
$266$	−6.47538	−0.397031
$267$	44.4912	2.72282
$268$	−10.3600	−0.632836
$269$	1.82617	0.111344	0.0556718	−	0.998449i	$-0.482270\pi$
$269$	1.82617	0.111344	0.0556718	+	0.998449i	$0.482270\pi$
$270$	4.84234	0.294696
$271$	5.41491	0.328932	0.164466	−	0.986383i	$-0.447410\pi$
$271$	5.41491	0.328932	0.164466	+	0.986383i	$0.447410\pi$
$272$	−1.84339	−0.111772
$273$	5.89935	0.357045
$274$	9.87167	0.596369
$275$	3.40791	0.205505
$276$	25.9084	1.55950
$277$	−15.3061	−0.919657	−0.459828	−	0.888008i	$-0.652089\pi$
$277$	−15.3061	−0.919657	−0.459828	+	0.888008i	$0.652089\pi$
$278$	2.94319	0.176521
$279$	−25.8391	−1.54695
$280$	−3.78946	−0.226464
$281$	−1.78123	−0.106259	−0.0531296	−	0.998588i	$-0.516920\pi$
$281$	−1.78123	−0.106259	−0.0531296	+	0.998588i	$0.516920\pi$
$282$	−9.65162	−0.574745
$283$	6.72333	0.399661	0.199830	−	0.979831i	$-0.435961\pi$
$283$	6.72333	0.399661	0.199830	+	0.979831i	$0.435961\pi$
$284$	−1.61599	−0.0958912
$285$	18.1791	1.07684
$286$	−2.50397	−0.148063
$287$	−3.70039	−0.218427
$288$	−31.8086	−1.87434
$289$	1.00000	0.0588235
$290$	3.11071	0.182667
$291$	−6.43102	−0.376993
$292$	9.69769	0.567514
$293$	−12.2975	−0.718428	−0.359214	−	0.933255i	$-0.616955\pi$
$293$	−12.2975	−0.718428	−0.359214	+	0.933255i	$0.616955\pi$
$294$	−7.54813	−0.440216
$295$	6.33168	0.368645
$296$	0.939416	0.0546024
$297$	−26.6300	−1.54523
$298$	4.05235	0.234746
$299$	6.46119	0.373660
$300$	4.75440	0.274495
$301$	−9.78191	−0.563820
$302$	−6.20219	−0.356896
$303$	−46.2197	−2.65525
$304$	−11.3902	−0.653272
$305$	−12.7973	−0.732773
$306$	3.50494	0.200364
$307$	−17.7393	−1.01244	−0.506218	−	0.862406i	$-0.668957\pi$
$307$	−17.7393	−1.01244	−0.506218	+	0.862406i	$0.668957\pi$
$308$	9.31329	0.530674
$309$	−45.3368	−2.57912
$310$	2.83102	0.160791
$311$	−33.5273	−1.90116	−0.950578	−	0.310485i	$-0.899509\pi$
$311$	−33.5273	−1.90116	−0.950578	+	0.310485i	$0.899509\pi$
$312$	−7.81676	−0.442537
$313$	22.6899	1.28251	0.641256	−	0.767327i	$-0.278414\pi$
$313$	22.6899	1.28251	0.641256	+	0.767327i	$0.278414\pi$
$314$	−3.00722	−0.169707
$315$	−9.56500	−0.538927
$316$	−22.5517	−1.26863
$317$	−22.5235	−1.26505	−0.632523	−	0.774542i	$-0.717981\pi$
$317$	−22.5235	−1.26505	−0.632523	+	0.774542i	$0.717981\pi$
$318$	−0.142413	−0.00798610
$319$	−17.1070	−0.957808
$320$	−0.201711	−0.0112760
$321$	−41.2698	−2.30346
$322$	5.71077	0.318249
$323$	6.17895	0.343806
$324$	−9.73170	−0.540650
$325$	1.18568	0.0657699
$326$	−11.8928	−0.658679
$327$	6.11794	0.338323
$328$	4.90310	0.270728
$329$	8.95254	0.493569
$330$	6.21326	0.342029
$331$	9.52217	0.523386	0.261693	−	0.965151i	$-0.415719\pi$
$331$	9.52217	0.523386	0.261693	+	0.965151i	$0.415719\pi$
$332$	2.68911	0.147584
$333$	2.37119	0.129940
$334$	2.57779	0.141051
$335$	6.41093	0.350266
$336$	9.17174	0.500359
$337$	−5.15976	−0.281070	−0.140535	−	0.990076i	$-0.544882\pi$
$337$	−5.15976	−0.281070	−0.140535	+	0.990076i	$0.544882\pi$
$338$	7.18476	0.390800
$339$	−1.28116	−0.0695833
$340$	1.61599	0.0876392
$341$	−15.5689	−0.843104
$342$	21.6569	1.17107
$343$	18.8393	1.01723
$344$	12.9612	0.698823
$345$	−16.0325	−0.863163
$346$	−0.384743	−0.0206839
$347$	−26.5923	−1.42755	−0.713776	−	0.700374i	$-0.753016\pi$
$347$	−26.5923	−1.42755	−0.713776	+	0.700374i	$0.753016\pi$
$348$	−23.8661	−1.27936
$349$	−18.3261	−0.980976	−0.490488	−	0.871448i	$-0.663181\pi$
$349$	−18.3261	−0.980976	−0.490488	+	0.871448i	$0.663181\pi$
$350$	1.04797	0.0560166
$351$	−9.26512	−0.494535
$352$	−19.1657	−1.02154
$353$	−16.1839	−0.861381	−0.430691	−	0.902500i	$-0.641730\pi$
$353$	−16.1839	−0.861381	−0.430691	+	0.902500i	$0.641730\pi$
$354$	11.5438	0.613548
$355$	1.00000	0.0530745
$356$	24.4374	1.29518
$357$	−4.97548	−0.263331
$358$	8.40790	0.444371
$359$	32.8302	1.73271	0.866355	−	0.499429i	$-0.166457\pi$
$359$	32.8302	1.73271	0.866355	+	0.499429i	$0.166457\pi$
$360$	12.6738	0.667969
$361$	19.1794	1.00944
$362$	3.66011	0.192371
$363$	−1.80602	−0.0947916
$364$	3.24029	0.169837
$365$	−6.00110	−0.314112
$366$	−23.3319	−1.21958
$367$	26.1395	1.36447	0.682235	−	0.731133i	$-0.261008\pi$
$367$	26.1395	1.36447	0.682235	+	0.731133i	$0.261008\pi$
$368$	10.0452	0.523644
$369$	12.3759	0.644266
$370$	−0.259795	−0.0135061
$371$	0.132097	0.00685815
$372$	−21.7203	−1.12615
$373$	17.3008	0.895803	0.447901	−	0.894083i	$-0.352172\pi$
$373$	17.3008	0.895803	0.447901	+	0.894083i	$0.352172\pi$
$374$	2.11184	0.109201
$375$	−2.94210	−0.151930
$376$	−11.8623	−0.611751
$377$	−5.95188	−0.306537
$378$	−8.18904	−0.421199
$379$	−22.7378	−1.16796	−0.583980	−	0.811768i	$-0.698505\pi$
$379$	−22.7378	−1.16796	−0.583980	+	0.811768i	$0.698505\pi$
$380$	9.98510	0.512225
$381$	−38.6384	−1.97951
$382$	−0.968654	−0.0495607
$383$	−14.8254	−0.757544	−0.378772	−	0.925490i	$-0.623654\pi$
$383$	−14.8254	−0.757544	−0.378772	+	0.925490i	$0.623654\pi$
$384$	−33.4599	−1.70749
$385$	−5.76322	−0.293721
$386$	−4.80506	−0.244571
$387$	32.7155	1.66302
$388$	−3.53232	−0.179326
$389$	−19.4401	−0.985650	−0.492825	−	0.870128i	$-0.664036\pi$
$389$	−19.4401	−0.985650	−0.492825	+	0.870128i	$0.664036\pi$
$390$	2.16172	0.109463
$391$	−5.44934	−0.275585
$392$	−9.27702	−0.468560
$393$	10.9364	0.551667
$394$	−10.0442	−0.506017
$395$	13.9554	0.702171
$396$	−31.1482	−1.56526
$397$	−15.4299	−0.774403	−0.387202	−	0.921995i	$-0.626558\pi$
$397$	−15.4299	−0.774403	−0.387202	+	0.921995i	$0.626558\pi$
$398$	−3.73030	−0.186983
$399$	−30.7433	−1.53909
$400$	1.84339	0.0921693
$401$	38.3978	1.91750	0.958748	−	0.284258i	$-0.0917474\pi$
$401$	38.3978	1.91750	0.958748	+	0.284258i	$0.0917474\pi$
$402$	11.6883	0.582961
$403$	−5.41675	−0.269827
$404$	−25.3867	−1.26304
$405$	6.02214	0.299243
$406$	−5.26061	−0.261080
$407$	1.42872	0.0708189
$408$	6.59262	0.326383
$409$	4.13237	0.204332	0.102166	−	0.994767i	$-0.467423\pi$
$409$	4.13237	0.204332	0.102166	+	0.994767i	$0.467423\pi$
$410$	−1.35595	−0.0669656
$411$	46.8679	2.31182
$412$	−24.9018	−1.22682
$413$	−10.7077	−0.526892
$414$	−19.0996	−0.938696
$415$	−1.66407	−0.0816859
$416$	−6.66815	−0.326933
$417$	13.9734	0.684281
$418$	13.0490	0.638246
$419$	16.5889	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$419$	16.5889	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$420$	−8.04031	−0.392327
$421$	0.683243	0.0332992	0.0166496	−	0.999861i	$-0.494700\pi$
$421$	0.683243	0.0332992	0.0166496	+	0.999861i	$0.494700\pi$
$422$	5.92584	0.288465
$423$	−29.9417	−1.45582
$424$	−0.175032	−0.00850030
$425$	−1.00000	−0.0485071
$426$	1.82319	0.0883337
$427$	21.6420	1.04733
$428$	−22.6680	−1.09570
$429$	−11.8882	−0.573966
$430$	−3.58443	−0.172856
$431$	−31.7198	−1.52789	−0.763944	−	0.645282i	$-0.776740\pi$
$431$	−31.7198	−1.52789	−0.763944	+	0.645282i	$0.776740\pi$
$432$	−14.4045	−0.693037
$433$	4.46044	0.214355	0.107178	−	0.994240i	$-0.465819\pi$
$433$	4.46044	0.214355	0.107178	+	0.994240i	$0.465819\pi$
$434$	−4.78763	−0.229814
$435$	14.7687	0.708107
$436$	3.36035	0.160932
$437$	−33.6712	−1.61071
$438$	−10.9411	−0.522787
$439$	−16.3159	−0.778717	−0.389358	−	0.921086i	$-0.627303\pi$
$439$	−16.3159	−0.778717	−0.389358	+	0.921086i	$0.627303\pi$
$440$	7.63639	0.364051
$441$	−23.4162	−1.11506
$442$	0.734754	0.0349487
$443$	−32.4622	−1.54232	−0.771162	−	0.636639i	$-0.780324\pi$
$443$	−32.4622	−1.54232	−0.771162	+	0.636639i	$0.780324\pi$
$444$	1.99321	0.0945937
$445$	−15.1223	−0.716864
$446$	6.05044	0.286497
$447$	19.2394	0.909992
$448$	0.341121	0.0161164
$449$	10.2024	0.481480	0.240740	−	0.970590i	$-0.422610\pi$
$449$	10.2024	0.481480	0.240740	+	0.970590i	$0.422610\pi$
$450$	−3.50494	−0.165225
$451$	7.45691	0.351132
$452$	−0.703695	−0.0330990
$453$	−29.4463	−1.38351
$454$	9.89698	0.464488
$455$	−2.00515	−0.0940027
$456$	40.7355	1.90761
$457$	10.2264	0.478373	0.239186	−	0.970974i	$-0.423119\pi$
$457$	10.2264	0.478373	0.239186	+	0.970974i	$0.423119\pi$
$458$	−7.38609	−0.345129
$459$	7.81416	0.364734
$460$	−8.80607	−0.410585
$461$	−10.2257	−0.476256	−0.238128	−	0.971234i	$-0.576534\pi$
$461$	−10.2257	−0.476256	−0.238128	+	0.971234i	$0.576534\pi$
$462$	−10.5074	−0.488850
$463$	11.0521	0.513634	0.256817	−	0.966460i	$-0.417326\pi$
$463$	11.0521	0.513634	0.256817	+	0.966460i	$0.417326\pi$
$464$	−9.25341	−0.429579
$465$	13.4409	0.623307
$466$	−3.55130	−0.164511
$467$	25.6707	1.18790	0.593949	−	0.804502i	$-0.297568\pi$
$467$	25.6707	1.18790	0.593949	+	0.804502i	$0.297568\pi$
$468$	−10.8371	−0.500946
$469$	−10.8417	−0.500624
$470$	3.28052	0.151319
$471$	−14.2774	−0.657868
$472$	14.1879	0.653053
$473$	19.7122	0.906367
$474$	25.4433	1.16865
$475$	−6.17895	−0.283510
$476$	−2.73285	−0.125260
$477$	−0.441799	−0.0202286
$478$	−4.29569	−0.196480
$479$	19.5405	0.892828	0.446414	−	0.894827i	$-0.352701\pi$
$479$	19.5405	0.892828	0.446414	+	0.894827i	$0.352701\pi$
$480$	16.5461	0.755222
$481$	0.497080	0.0226649
$482$	9.33143	0.425035
$483$	27.1131	1.23369
$484$	−0.991980	−0.0450900
$485$	2.18586	0.0992546
$486$	−3.54754	−0.160919
$487$	−17.0088	−0.770740	−0.385370	−	0.922762i	$-0.625926\pi$
$487$	−17.0088	−0.770740	−0.385370	+	0.922762i	$0.625926\pi$
$488$	−28.6761	−1.29810
$489$	−56.4635	−2.55337
$490$	2.56556	0.115900
$491$	−33.0347	−1.49084	−0.745418	−	0.666597i	$-0.767750\pi$
$491$	−33.0347	−1.49084	−0.745418	+	0.666597i	$0.767750\pi$
$492$	10.4032	0.469012
$493$	5.01979	0.226080
$494$	4.54001	0.204265
$495$	19.2751	0.866350
$496$	−8.42144	−0.378134
$497$	−1.69113	−0.0758576
$498$	−3.03391	−0.135953
$499$	−22.9016	−1.02521	−0.512607	−	0.858623i	$-0.671320\pi$
$499$	−22.9016	−1.02521	−0.512607	+	0.858623i	$0.671320\pi$
$500$	−1.61599	−0.0722691
$501$	12.2386	0.546782
$502$	−0.863198	−0.0385264
$503$	−0.698234	−0.0311327	−0.0155664	−	0.999879i	$-0.504955\pi$
$503$	−0.698234	−0.0311327	−0.0155664	+	0.999879i	$0.504955\pi$
$504$	−21.4331	−0.954706
$505$	15.7097	0.699074
$506$	−11.5082	−0.511600
$507$	34.1112	1.51493
$508$	−21.2226	−0.941602
$509$	24.6253	1.09150	0.545748	−	0.837949i	$-0.316246\pi$
$509$	24.6253	1.09150	0.545748	+	0.837949i	$0.316246\pi$
$510$	−1.82319	−0.0807321
$511$	10.1486	0.448949
$512$	−18.6283	−0.823261
$513$	48.2833	2.13176
$514$	11.4387	0.504540
$515$	15.4096	0.679030
$516$	27.5006	1.21065
$517$	−18.0409	−0.793436
$518$	0.439348	0.0193038
$519$	−1.82665	−0.0801810
$520$	2.65686	0.116511
$521$	35.2365	1.54374	0.771869	−	0.635781i	$-0.219322\pi$
$521$	35.2365	1.54374	0.771869	+	0.635781i	$0.219322\pi$
$522$	17.5941	0.770072
$523$	4.15374	0.181631	0.0908153	−	0.995868i	$-0.471053\pi$
$523$	4.15374	0.181631	0.0908153	+	0.995868i	$0.471053\pi$
$524$	6.00694	0.262414
$525$	4.97548	0.217148
$526$	−2.37317	−0.103475
$527$	4.56846	0.199005
$528$	−18.4826	−0.804351
$529$	6.69534	0.291102
$530$	0.0484050	0.00210258
$531$	35.8119	1.55410
$532$	−16.8861	−0.732106
$533$	2.59441	0.112377
$534$	−27.5707	−1.19310
$535$	14.0273	0.606454
$536$	14.3655	0.620495
$537$	39.9183	1.72260
$538$	−1.13166	−0.0487892
$539$	−14.1090	−0.607718
$540$	12.6276	0.543404
$541$	15.4608	0.664713	0.332356	−	0.943154i	$-0.392156\pi$
$541$	15.4608	0.664713	0.332356	+	0.943154i	$0.392156\pi$
$542$	−3.35556	−0.144133
$543$	17.3771	0.745725
$544$	5.62389	0.241122
$545$	−2.07944	−0.0890735
$546$	−3.65575	−0.156452
$547$	−20.8658	−0.892158	−0.446079	−	0.894994i	$-0.647180\pi$
$547$	−20.8658	−0.892158	−0.446079	+	0.894994i	$0.647180\pi$
$548$	25.7428	1.09968
$549$	−72.3814	−3.08916
$550$	−2.11184	−0.0900492
$551$	31.0170	1.32137
$552$	−35.9255	−1.52909
$553$	−23.6004	−1.00359
$554$	9.48503	0.402981
$555$	−1.23343	−0.0523564
$556$	7.67507	0.325495
$557$	21.1398	0.895722	0.447861	−	0.894103i	$-0.352186\pi$
$557$	21.1398	0.895722	0.447861	+	0.894103i	$0.352186\pi$
$558$	16.0122	0.677850
$559$	6.85828	0.290074
$560$	−3.11741	−0.131734
$561$	10.0264	0.423316
$562$	1.10381	0.0465613
$563$	2.95262	0.124438	0.0622190	−	0.998063i	$-0.480182\pi$
$563$	2.95262	0.124438	0.0622190	+	0.998063i	$0.480182\pi$
$564$	−25.1689	−1.05980
$565$	0.435459	0.0183199
$566$	−4.16637	−0.175126
$567$	−10.1842	−0.427698
$568$	2.24078	0.0940212
$569$	−30.0002	−1.25767	−0.628836	−	0.777538i	$-0.716468\pi$
$569$	−30.0002	−1.25767	−0.628836	+	0.777538i	$0.716468\pi$
$570$	−11.2654	−0.471855
$571$	34.7676	1.45498	0.727490	−	0.686118i	$-0.240687\pi$
$571$	34.7676	1.45498	0.727490	+	0.686118i	$0.240687\pi$
$572$	−6.52972	−0.273021
$573$	−4.59890	−0.192122
$574$	2.29309	0.0957118
$575$	5.44934	0.227253
$576$	−1.14088	−0.0475365
$577$	2.13985	0.0890833	0.0445416	−	0.999008i	$-0.485817\pi$
$577$	2.13985	0.0890833	0.0445416	+	0.999008i	$0.485817\pi$
$578$	−0.619688	−0.0257756
$579$	−22.8131	−0.948079
$580$	8.11192	0.336829
$581$	2.81416	0.116751
$582$	3.98523	0.165193
$583$	−0.266198	−0.0110248
$584$	−13.4472	−0.556447
$585$	6.70619	0.277267
$586$	7.62062	0.314805
$587$	−26.4463	−1.09156	−0.545778	−	0.837930i	$-0.683766\pi$
$587$	−26.4463	−1.09156	−0.545778	+	0.837930i	$0.683766\pi$
$588$	−19.6836	−0.811737
$589$	28.2283	1.16313
$590$	−3.92367	−0.161535
$591$	−47.6868	−1.96157
$592$	0.772812	0.0317624
$593$	−7.19401	−0.295423	−0.147711	−	0.989031i	$-0.547191\pi$
$593$	−7.19401	−0.295423	−0.147711	+	0.989031i	$0.547191\pi$
$594$	16.5023	0.677096
$595$	1.69113	0.0693296
$596$	10.5675	0.432861
$597$	−17.7104	−0.724838
$598$	−4.00392	−0.163733
$599$	−23.9525	−0.978674	−0.489337	−	0.872095i	$-0.662761\pi$
$599$	−23.9525	−0.978674	−0.489337	+	0.872095i	$0.662761\pi$
$600$	−6.59262	−0.269143
$601$	1.38118	0.0563396	0.0281698	−	0.999603i	$-0.491032\pi$
$601$	1.38118	0.0563396	0.0281698	+	0.999603i	$0.491032\pi$
$602$	6.06173	0.247058
$603$	36.2601	1.47662
$604$	−16.1737	−0.658099
$605$	0.613854	0.0249567
$606$	28.6418	1.16349
$607$	−17.7689	−0.721219	−0.360609	−	0.932717i	$-0.617431\pi$
$607$	−17.7689	−0.721219	−0.360609	+	0.932717i	$0.617431\pi$
$608$	34.7498	1.40929
$609$	−24.9759	−1.01207
$610$	7.93036	0.321091
$611$	−6.27679	−0.253932
$612$	9.13998	0.369462
$613$	3.68478	0.148827	0.0744134	−	0.997227i	$-0.476292\pi$
$613$	3.68478	0.148827	0.0744134	+	0.997227i	$0.476292\pi$
$614$	10.9928	0.443635
$615$	−6.43767	−0.259592
$616$	−12.9141	−0.520326
$617$	−8.36001	−0.336562	−0.168281	−	0.985739i	$-0.553822\pi$
$617$	−8.36001	−0.336562	−0.168281	+	0.985739i	$0.553822\pi$
$618$	28.0947	1.13013
$619$	−11.7386	−0.471813	−0.235907	−	0.971776i	$-0.575806\pi$
$619$	−11.7386	−0.471813	−0.235907	+	0.971776i	$0.575806\pi$
$620$	7.38257	0.296491
$621$	−42.5820	−1.70876
$622$	20.7764	0.833060
$623$	25.5737	1.02459
$624$	−6.43047	−0.257425
$625$	1.00000	0.0400000
$626$	−14.0607	−0.561978
$627$	61.9528	2.47416
$628$	−7.84204	−0.312931
$629$	−0.419235	−0.0167160
$630$	5.92732	0.236150
$631$	−7.79756	−0.310416	−0.155208	−	0.987882i	$-0.549605\pi$
$631$	−7.79756	−0.310416	−0.155208	+	0.987882i	$0.549605\pi$
$632$	31.2710	1.24389
$633$	28.1342	1.11823
$634$	13.9575	0.554325
$635$	13.1329	0.521164
$636$	−0.371375	−0.0147260
$637$	−4.90882	−0.194494
$638$	10.6010	0.419698
$639$	5.65598	0.223747
$640$	11.3728	0.449549
$641$	9.76678	0.385765	0.192882	−	0.981222i	$-0.438216\pi$
$641$	9.76678	0.385765	0.192882	+	0.981222i	$0.438216\pi$
$642$	25.5744	1.00934
$643$	2.93211	0.115631	0.0578156	−	0.998327i	$-0.481586\pi$
$643$	2.93211	0.115631	0.0578156	+	0.998327i	$0.481586\pi$
$644$	14.8922	0.586835
$645$	−17.0178	−0.670077
$646$	−3.82902	−0.150651
$647$	20.1165	0.790859	0.395430	−	0.918496i	$-0.370596\pi$
$647$	20.1165	0.790859	0.395430	+	0.918496i	$0.370596\pi$
$648$	13.4943	0.530107
$649$	21.5778	0.847003
$650$	−0.734754	−0.0288194
$651$	−22.7303	−0.890871
$652$	−31.0133	−1.21457
$653$	12.7933	0.500639	0.250319	−	0.968163i	$-0.419464\pi$
$653$	12.7933	0.500639	0.250319	+	0.968163i	$0.419464\pi$
$654$	−3.79121	−0.148248
$655$	−3.71720	−0.145243
$656$	4.03355	0.157483
$657$	−33.9421	−1.32421
$658$	−5.54778	−0.216275
$659$	−32.1246	−1.25140	−0.625698	−	0.780066i	$-0.715186\pi$
$659$	−32.1246	−1.25140	−0.625698	+	0.780066i	$0.715186\pi$
$660$	16.2026	0.630684
$661$	−23.8968	−0.929479	−0.464740	−	0.885447i	$-0.653852\pi$
$661$	−23.8968	−0.929479	−0.464740	+	0.885447i	$0.653852\pi$
$662$	−5.90078	−0.229340
$663$	3.48840	0.135478
$664$	−3.72882	−0.144706
$665$	10.4494	0.405211
$666$	−1.46940	−0.0569379
$667$	−27.3546	−1.05917
$668$	6.72222	0.260090
$669$	28.7258	1.11060
$670$	−3.97278	−0.153482
$671$	−43.6122	−1.68363
$672$	−27.9816	−1.07941
$673$	−12.8999	−0.497256	−0.248628	−	0.968599i	$-0.579980\pi$
$673$	−12.8999	−0.497256	−0.248628	+	0.968599i	$0.579980\pi$
$674$	3.19745	0.123161
$675$	−7.81416	−0.300767
$676$	18.7360	0.720615
$677$	−33.5097	−1.28788	−0.643941	−	0.765075i	$-0.722702\pi$
$677$	−33.5097	−1.28788	−0.643941	+	0.765075i	$0.722702\pi$
$678$	0.793923	0.0304904
$679$	−3.69657	−0.141861
$680$	−2.24078	−0.0859301
$681$	46.9881	1.80059
$682$	9.64787	0.369436
$683$	1.57572	0.0602932	0.0301466	−	0.999545i	$-0.490403\pi$
$683$	1.57572	0.0602932	0.0301466	+	0.999545i	$0.490403\pi$
$684$	56.4755	2.15939
$685$	−15.9301	−0.608656
$686$	−11.6745	−0.445735
$687$	−35.0671	−1.33789
$688$	10.6626	0.406507
$689$	−0.0926159	−0.00352838
$690$	9.93517	0.378226
$691$	−2.93774	−0.111757	−0.0558785	−	0.998438i	$-0.517796\pi$
$691$	−2.93774	−0.111757	−0.0558785	+	0.998438i	$0.517796\pi$
$692$	−1.00331	−0.0381401
$693$	−32.5967	−1.23824
$694$	16.4790	0.625533
$695$	−4.74946	−0.180157
$696$	33.0936	1.25441
$697$	−2.18812	−0.0828809
$698$	11.3565	0.429849
$699$	−16.8606	−0.637725
$700$	2.73285	0.103292
$701$	−33.3864	−1.26099	−0.630494	−	0.776194i	$-0.717148\pi$
$701$	−33.3864	−1.26099	−0.630494	+	0.776194i	$0.717148\pi$
$702$	5.74148	0.216698
$703$	−2.59043	−0.0977001
$704$	−0.687415	−0.0259079
$705$	15.5750	0.586587
$706$	10.0290	0.377445
$707$	−26.5672	−0.999163
$708$	30.1034	1.13135
$709$	46.0078	1.72786	0.863929	−	0.503613i	$-0.167996\pi$
$709$	46.0078	1.72786	0.863929	+	0.503613i	$0.167996\pi$
$710$	−0.619688	−0.0232565
$711$	78.9313	2.96015
$712$	−33.8857	−1.26992
$713$	−24.8951	−0.932330
$714$	3.08325	0.115388
$715$	4.04070	0.151114
$716$	21.9256	0.819399
$717$	−20.3947	−0.761654
$718$	−20.3445	−0.759249
$719$	−34.0759	−1.27081	−0.635407	−	0.772177i	$-0.719168\pi$
$719$	−34.0759	−1.27081	−0.635407	+	0.772177i	$0.719168\pi$
$720$	10.4261	0.388560
$721$	−26.0597	−0.970515
$722$	−11.8853	−0.442324
$723$	44.3030	1.64765
$724$	9.54461	0.354723
$725$	−5.01979	−0.186430
$726$	1.11917	0.0415363
$727$	−30.3506	−1.12564	−0.562822	−	0.826578i	$-0.690284\pi$
$727$	−30.3506	−1.12564	−0.562822	+	0.826578i	$0.690284\pi$
$728$	−4.49310	−0.166525
$729$	−34.9091	−1.29293
$730$	3.71881	0.137639
$731$	−5.78424	−0.213938
$732$	−60.8437	−2.24885
$733$	33.7215	1.24553	0.622767	−	0.782408i	$-0.286009\pi$
$733$	33.7215	1.24553	0.622767	+	0.782408i	$0.286009\pi$
$734$	−16.1983	−0.597891
$735$	12.1805	0.449286
$736$	−30.6465	−1.12965
$737$	21.8479	0.804777
$738$	−7.66923	−0.282308
$739$	−26.7568	−0.984265	−0.492132	−	0.870520i	$-0.663782\pi$
$739$	−26.7568	−0.984265	−0.492132	+	0.870520i	$0.663782\pi$
$740$	−0.677479	−0.0249046
$741$	21.5547	0.791830
$742$	−0.0818592	−0.00300515
$743$	10.5693	0.387750	0.193875	−	0.981026i	$-0.437894\pi$
$743$	10.5693	0.387750	0.193875	+	0.981026i	$0.437894\pi$
$744$	30.1181	1.10418
$745$	−6.53933	−0.239583
$746$	−10.7211	−0.392528
$747$	−9.41193	−0.344364
$748$	5.50714	0.201361
$749$	−23.7220	−0.866784
$750$	1.82319	0.0665734
$751$	13.3437	0.486918	0.243459	−	0.969911i	$-0.421718\pi$
$751$	13.3437	0.486918	0.243459	+	0.969911i	$0.421718\pi$
$752$	−9.75854	−0.355858
$753$	−4.09822	−0.149347
$754$	3.68831	0.134320
$755$	10.0086	0.364249
$756$	−21.3549	−0.776670
$757$	28.6619	1.04174	0.520868	−	0.853638i	$-0.325609\pi$
$757$	28.6619	1.04174	0.520868	+	0.853638i	$0.325609\pi$
$758$	14.0903	0.511784
$759$	−54.6374	−1.98321
$760$	−13.8457	−0.502236
$761$	−10.4763	−0.379766	−0.189883	−	0.981807i	$-0.560811\pi$
$761$	−10.4763	−0.379766	−0.189883	+	0.981807i	$0.560811\pi$
$762$	23.9438	0.867392
$763$	3.51661	0.127310
$764$	−2.52600	−0.0913875
$765$	−5.65598	−0.204492
$766$	9.18714	0.331945
$767$	7.50737	0.271075
$768$	19.5478	0.705370
$769$	−39.8301	−1.43631	−0.718155	−	0.695883i	$-0.755013\pi$
$769$	−39.8301	−1.43631	−0.718155	+	0.695883i	$0.755013\pi$
$770$	3.57140	0.128704
$771$	54.3077	1.95584
$772$	−12.5304	−0.450977
$773$	−18.2439	−0.656187	−0.328094	−	0.944645i	$-0.606406\pi$
$773$	−18.2439	−0.656187	−0.328094	+	0.944645i	$0.606406\pi$
$774$	−20.2734	−0.728713
$775$	−4.56846	−0.164104
$776$	4.89803	0.175829
$777$	2.08590	0.0748312
$778$	12.0468	0.431898
$779$	−13.5203	−0.484414
$780$	5.63721	0.201845
$781$	3.40791	0.121945
$782$	3.37689	0.120757
$783$	39.2255	1.40180
$784$	−7.63176	−0.272563
$785$	4.85279	0.173203
$786$	−6.77714	−0.241733
$787$	−36.8514	−1.31361	−0.656805	−	0.754060i	$-0.728093\pi$
$787$	−36.8514	−1.31361	−0.656805	+	0.754060i	$0.728093\pi$
$788$	−26.1926	−0.933071
$789$	−11.2671	−0.401120
$790$	−8.64798	−0.307681
$791$	−0.736418	−0.0261840
$792$	43.1913	1.53473
$793$	−15.1736	−0.538830
$794$	9.56171	0.339332
$795$	0.229813	0.00815063
$796$	−9.72765	−0.344787
$797$	−17.6290	−0.624450	−0.312225	−	0.950008i	$-0.601074\pi$
$797$	−17.6290	−0.624450	−0.312225	+	0.950008i	$0.601074\pi$
$798$	19.0512	0.674407
$799$	5.29382	0.187282
$800$	−5.62389	−0.198835
$801$	−85.5311	−3.02209
$802$	−23.7947	−0.840219
$803$	−20.4512	−0.721707
$804$	30.4801	1.07495
$805$	−9.21555	−0.324806
$806$	3.35669	0.118235
$807$	−5.37278	−0.189131
$808$	35.2021	1.23841
$809$	28.6409	1.00696	0.503479	−	0.864007i	$-0.332053\pi$
$809$	28.6409	1.00696	0.503479	+	0.864007i	$0.332053\pi$
$810$	−3.73185	−0.131124
$811$	−16.9097	−0.593780	−0.296890	−	0.954912i	$-0.595949\pi$
$811$	−16.9097	−0.593780	−0.296890	+	0.954912i	$0.595949\pi$
$812$	−13.7183	−0.481418
$813$	−15.9312	−0.558733
$814$	−0.885359	−0.0310318
$815$	19.1915	0.672250
$816$	5.42343	0.189858
$817$	−35.7405	−1.25040
$818$	−2.56078	−0.0895356
$819$	−11.3411	−0.396289
$820$	−3.53597	−0.123481
$821$	38.4903	1.34332	0.671661	−	0.740858i	$-0.265581\pi$
$821$	38.4903	1.34332	0.671661	+	0.740858i	$0.265581\pi$
$822$	−29.0435	−1.01301
$823$	42.7207	1.48915	0.744574	−	0.667540i	$-0.232653\pi$
$823$	42.7207	1.48915	0.744574	+	0.667540i	$0.232653\pi$
$824$	34.5297	1.20290
$825$	−10.0264	−0.349075
$826$	6.63544	0.230876
$827$	−23.0065	−0.800015	−0.400007	−	0.916512i	$-0.630992\pi$
$827$	−23.0065	−0.800015	−0.400007	+	0.916512i	$0.630992\pi$
$828$	−49.8069	−1.73091
$829$	−33.2049	−1.15326	−0.576628	−	0.817007i	$-0.695632\pi$
$829$	−33.2049	−1.15326	−0.576628	+	0.817007i	$0.695632\pi$
$830$	1.03120	0.0357936
$831$	45.0323	1.56215
$832$	−0.239166	−0.00829158
$833$	4.14008	0.143445
$834$	−8.65916	−0.299842
$835$	−4.15982	−0.143957
$836$	34.0283	1.17689
$837$	35.6987	1.23393
$838$	−10.2800	−0.355115
$839$	22.4702	0.775757	0.387878	−	0.921711i	$-0.373208\pi$
$839$	22.4702	0.775757	0.387878	+	0.921711i	$0.373208\pi$
$840$	11.1490	0.384677
$841$	−3.80169	−0.131093
$842$	−0.423398	−0.0145912
$843$	5.24056	0.180495
$844$	15.4531	0.531916
$845$	−11.5942	−0.398851
$846$	18.5545	0.637917
$847$	−1.03811	−0.0356698
$848$	−0.143990	−0.00494465
$849$	−19.7807	−0.678873
$850$	0.619688	0.0212551
$851$	2.28456	0.0783136
$852$	4.75440	0.162883
$853$	−57.3642	−1.96411	−0.982057	−	0.188585i	$-0.939610\pi$
$853$	−57.3642	−1.96411	−0.982057	+	0.188585i	$0.939610\pi$
$854$	−13.4113	−0.458924
$855$	−34.9480	−1.19520
$856$	31.4322	1.07433
$857$	34.7311	1.18639	0.593195	−	0.805059i	$-0.297866\pi$
$857$	34.7311	1.18639	0.593195	+	0.805059i	$0.297866\pi$
$858$	7.36695	0.251504
$859$	−43.5337	−1.48535	−0.742676	−	0.669651i	$-0.766444\pi$
$859$	−43.5337	−1.48535	−0.742676	+	0.669651i	$0.766444\pi$
$860$	−9.34726	−0.318739
$861$	10.8869	0.371026
$862$	19.6564	0.669499
$863$	−50.0654	−1.70424	−0.852122	−	0.523343i	$-0.824685\pi$
$863$	−50.0654	−1.70424	−0.852122	+	0.523343i	$0.824685\pi$
$864$	43.9460	1.49507
$865$	0.620865	0.0211100
$866$	−2.76408	−0.0939274
$867$	−2.94210	−0.0999191
$868$	−12.4849	−0.423765
$869$	47.5587	1.61332
$870$	−9.15202	−0.310283
$871$	7.60133	0.257561
$872$	−4.65958	−0.157793
$873$	12.3632	0.418429
$874$	20.8657	0.705791
$875$	−1.69113	−0.0571707
$876$	−28.5316	−0.963994
$877$	−8.68880	−0.293400	−0.146700	−	0.989181i	$-0.546865\pi$
$877$	−8.68880	−0.293400	−0.146700	+	0.989181i	$0.546865\pi$
$878$	10.1108	0.341223
$879$	36.1805	1.22034
$880$	6.28209	0.211769
$881$	−55.8872	−1.88289	−0.941444	−	0.337171i	$-0.890530\pi$
$881$	−55.8872	−1.88289	−0.941444	+	0.337171i	$0.890530\pi$
$882$	14.5107	0.488602
$883$	−54.1497	−1.82228	−0.911141	−	0.412094i	$-0.864798\pi$
$883$	−54.1497	−1.82228	−0.911141	+	0.412094i	$0.864798\pi$
$884$	1.91605	0.0644437
$885$	−18.6285	−0.626189
$886$	20.1164	0.675824
$887$	43.9383	1.47530	0.737651	−	0.675182i	$-0.235935\pi$
$887$	43.9383	1.47530	0.737651	+	0.675182i	$0.235935\pi$
$888$	−2.76386	−0.0927491
$889$	−22.2095	−0.744883
$890$	9.37108	0.314119
$891$	20.5229	0.687544
$892$	15.7780	0.528286
$893$	32.7102	1.09461
$894$	−11.9224	−0.398746
$895$	−13.5679	−0.453526
$896$	−19.2329	−0.642525
$897$	−19.0095	−0.634709
$898$	−6.32229	−0.210978
$899$	22.9327	0.764849
$900$	−9.13998	−0.304666
$901$	0.0781118	0.00260228
$902$	−4.62096	−0.153861
$903$	28.7794	0.957719
$904$	0.975769	0.0324536
$905$	−5.90637	−0.196334
$906$	18.2475	0.606232
$907$	9.84772	0.326988	0.163494	−	0.986544i	$-0.447724\pi$
$907$	9.84772	0.326988	0.163494	+	0.986544i	$0.447724\pi$
$908$	25.8088	0.856494
$909$	88.8539	2.94710
$910$	1.24256	0.0411906
$911$	40.5503	1.34349	0.671746	−	0.740782i	$-0.265545\pi$
$911$	40.5503	1.34349	0.671746	+	0.740782i	$0.265545\pi$
$912$	33.5111	1.10966
$913$	−5.67099	−0.187683
$914$	−6.33721	−0.209616
$915$	37.6511	1.24471
$916$	−19.2610	−0.636402
$917$	6.28627	0.207591
$918$	−4.84234	−0.159821
$919$	−53.6856	−1.77093	−0.885463	−	0.464710i	$-0.846158\pi$
$919$	−53.6856	−1.77093	−0.885463	+	0.464710i	$0.846158\pi$
$920$	12.2108	0.402578
$921$	52.1909	1.71975
$922$	6.33672	0.208689
$923$	1.18568	0.0390272
$924$	−27.4007	−0.901416
$925$	0.419235	0.0137844
$926$	−6.84885	−0.225067
$927$	87.1566	2.86260
$928$	28.2308	0.926720
$929$	4.38659	0.143919	0.0719597	−	0.997408i	$-0.477075\pi$
$929$	4.38659	0.143919	0.0719597	+	0.997408i	$0.477075\pi$
$930$	−8.32916	−0.273124
$931$	25.5813	0.838394
$932$	−9.26087	−0.303350
$933$	98.6407	3.22935
$934$	−15.9078	−0.520520
$935$	−3.40791	−0.111451
$936$	15.0271	0.491177
$937$	49.1717	1.60637	0.803185	−	0.595729i	$-0.203137\pi$
$937$	49.1717	1.60637	0.803185	+	0.595729i	$0.203137\pi$
$938$	6.71849	0.219366
$939$	−66.7562	−2.17851
$940$	8.55474	0.279025
$941$	−31.7610	−1.03538	−0.517689	−	0.855569i	$-0.673208\pi$
$941$	−31.7610	−1.03538	−0.517689	+	0.855569i	$0.673208\pi$
$942$	8.84754	0.288268
$943$	11.9238	0.388293
$944$	11.6717	0.379883
$945$	13.2148	0.429876
$946$	−12.2154	−0.397157
$947$	43.6881	1.41967	0.709836	−	0.704367i	$-0.248769\pi$
$947$	43.6881	1.41967	0.709836	+	0.704367i	$0.248769\pi$
$948$	66.3494	2.15493
$949$	−7.11540	−0.230976
$950$	3.82902	0.124230
$951$	66.2665	2.14884
$952$	3.78946	0.122817
$953$	3.76199	0.121863	0.0609314	−	0.998142i	$-0.480593\pi$
$953$	3.76199	0.121863	0.0609314	+	0.998142i	$0.480593\pi$
$954$	0.273777	0.00886387
$955$	1.56313	0.0505818
$956$	−11.2020	−0.362300
$957$	50.3306	1.62696
$958$	−12.1090	−0.391224
$959$	26.9398	0.869932
$960$	0.593456	0.0191537
$961$	−10.1291	−0.326747
$962$	−0.308035	−0.00993144
$963$	79.3382	2.55664
$964$	24.3340	0.783744
$965$	7.75400	0.249610
$966$	−16.8017	−0.540585
$967$	11.7037	0.376365	0.188182	−	0.982134i	$-0.439740\pi$
$967$	11.7037	0.376365	0.188182	+	0.982134i	$0.439740\pi$
$968$	1.37551	0.0442107
$969$	−18.1791	−0.583997
$970$	−1.35455	−0.0434920
$971$	17.1970	0.551878	0.275939	−	0.961175i	$-0.411011\pi$
$971$	17.1970	0.551878	0.275939	+	0.961175i	$0.411011\pi$
$972$	−9.25106	−0.296728
$973$	8.03197	0.257493
$974$	10.5401	0.337727
$975$	−3.48840	−0.111718
$976$	−23.5904	−0.755111
$977$	13.3083	0.425770	0.212885	−	0.977077i	$-0.431714\pi$
$977$	13.3083	0.425770	0.212885	+	0.977077i	$0.431714\pi$
$978$	34.9898	1.11885
$979$	−51.5353	−1.64707
$980$	6.69031	0.213714
$981$	−11.7613	−0.375509
$982$	20.4712	0.653263
$983$	−22.9876	−0.733190	−0.366595	−	0.930381i	$-0.619477\pi$
$983$	−22.9876	−0.733190	−0.366595	+	0.930381i	$0.619477\pi$
$984$	−14.4254	−0.459866
$985$	16.2084	0.516443
$986$	−3.11071	−0.0990650
$987$	−26.3393	−0.838389
$988$	11.8392	0.376654
$989$	31.5203	1.00229
$990$	−11.9445	−0.379622
$991$	−19.6558	−0.624387	−0.312194	−	0.950018i	$-0.601064\pi$
$991$	−19.6558	−0.624387	−0.312194	+	0.950018i	$0.601064\pi$
$992$	25.6925	0.815739
$993$	−28.0152	−0.889036
$994$	1.04797	0.0332397
$995$	6.01963	0.190835
$996$	−7.91164	−0.250690
$997$	18.0402	0.571338	0.285669	−	0.958328i	$-0.407784\pi$
$997$	18.0402	0.571338	0.285669	+	0.958328i	$0.407784\pi$
$998$	14.1918	0.449234
$999$	−3.27597	−0.103647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.15	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-0.619688 q^{2} -2.94210 q^{3} -1.61599 q^{4} +1.00000 q^{5} +1.82319 q^{6} -1.69113 q^{7} +2.24078 q^{8} +5.65598 q^{9} +O(q^{10})\)	\(q-0.619688 q^{2} -2.94210 q^{3} -1.61599 q^{4} +1.00000 q^{5} +1.82319 q^{6} -1.69113 q^{7} +2.24078 q^{8} +5.65598 q^{9} -0.619688 q^{10} +3.40791 q^{11} +4.75440 q^{12} +1.18568 q^{13} +1.04797 q^{14} -2.94210 q^{15} +1.84339 q^{16} -1.00000 q^{17} -3.50494 q^{18} -6.17895 q^{19} -1.61599 q^{20} +4.97548 q^{21} -2.11184 q^{22} +5.44934 q^{23} -6.59262 q^{24} +1.00000 q^{25} -0.734754 q^{26} -7.81416 q^{27} +2.73285 q^{28} -5.01979 q^{29} +1.82319 q^{30} -4.56846 q^{31} -5.62389 q^{32} -10.0264 q^{33} +0.619688 q^{34} -1.69113 q^{35} -9.13998 q^{36} +0.419235 q^{37} +3.82902 q^{38} -3.48840 q^{39} +2.24078 q^{40} +2.18812 q^{41} -3.08325 q^{42} +5.78424 q^{43} -5.50714 q^{44} +5.65598 q^{45} -3.37689 q^{46} -5.29382 q^{47} -5.42343 q^{48} -4.14008 q^{49} -0.619688 q^{50} +2.94210 q^{51} -1.91605 q^{52} -0.0781118 q^{53} +4.84234 q^{54} +3.40791 q^{55} -3.78946 q^{56} +18.1791 q^{57} +3.11071 q^{58} +6.33168 q^{59} +4.75440 q^{60} -12.7973 q^{61} +2.83102 q^{62} -9.56500 q^{63} -0.201711 q^{64} +1.18568 q^{65} +6.21326 q^{66} +6.41093 q^{67} +1.61599 q^{68} -16.0325 q^{69} +1.04797 q^{70} +1.00000 q^{71} +12.6738 q^{72} -6.00110 q^{73} -0.259795 q^{74} -2.94210 q^{75} +9.98510 q^{76} -5.76322 q^{77} +2.16172 q^{78} +13.9554 q^{79} +1.84339 q^{80} +6.02214 q^{81} -1.35595 q^{82} -1.66407 q^{83} -8.04031 q^{84} -1.00000 q^{85} -3.58443 q^{86} +14.7687 q^{87} +7.63639 q^{88} -15.1223 q^{89} -3.50494 q^{90} -2.00515 q^{91} -8.80607 q^{92} +13.4409 q^{93} +3.28052 q^{94} -6.17895 q^{95} +16.5461 q^{96} +2.18586 q^{97} +2.56556 q^{98} +19.2751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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