LMFDB - Embedded newform 6035.2.a.b.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.85242 q^{2} +0.130041 q^{3} +1.43148 q^{4} +1.00000 q^{5} -0.240891 q^{6} +2.44217 q^{7} +1.05315 q^{8} -2.98309 q^{9} +O(q^{10})$	\(q-1.85242 q^{2} +0.130041 q^{3} +1.43148 q^{4} +1.00000 q^{5} -0.240891 q^{6} +2.44217 q^{7} +1.05315 q^{8} -2.98309 q^{9} -1.85242 q^{10} +0.379418 q^{11} +0.186150 q^{12} +1.02133 q^{13} -4.52393 q^{14} +0.130041 q^{15} -4.81383 q^{16} -1.00000 q^{17} +5.52595 q^{18} +0.879320 q^{19} +1.43148 q^{20} +0.317581 q^{21} -0.702843 q^{22} -5.33854 q^{23} +0.136952 q^{24} +1.00000 q^{25} -1.89195 q^{26} -0.778046 q^{27} +3.49591 q^{28} +3.70355 q^{29} -0.240891 q^{30} -1.47371 q^{31} +6.81096 q^{32} +0.0493398 q^{33} +1.85242 q^{34} +2.44217 q^{35} -4.27022 q^{36} -3.07854 q^{37} -1.62887 q^{38} +0.132815 q^{39} +1.05315 q^{40} +1.90992 q^{41} -0.588295 q^{42} +4.84610 q^{43} +0.543128 q^{44} -2.98309 q^{45} +9.88925 q^{46} +0.747547 q^{47} -0.625994 q^{48} -1.03582 q^{49} -1.85242 q^{50} -0.130041 q^{51} +1.46202 q^{52} -10.2068 q^{53} +1.44127 q^{54} +0.379418 q^{55} +2.57196 q^{56} +0.114347 q^{57} -6.86055 q^{58} +4.48576 q^{59} +0.186150 q^{60} +1.43294 q^{61} +2.72994 q^{62} -7.28520 q^{63} -2.98914 q^{64} +1.02133 q^{65} -0.0913983 q^{66} -13.4544 q^{67} -1.43148 q^{68} -0.694228 q^{69} -4.52393 q^{70} +1.00000 q^{71} -3.14163 q^{72} -11.7712 q^{73} +5.70275 q^{74} +0.130041 q^{75} +1.25873 q^{76} +0.926602 q^{77} -0.246030 q^{78} -6.16503 q^{79} -4.81383 q^{80} +8.84809 q^{81} -3.53798 q^{82} +0.447396 q^{83} +0.454610 q^{84} -1.00000 q^{85} -8.97704 q^{86} +0.481613 q^{87} +0.399582 q^{88} +6.11177 q^{89} +5.52595 q^{90} +2.49427 q^{91} -7.64200 q^{92} -0.191643 q^{93} -1.38477 q^{94} +0.879320 q^{95} +0.885703 q^{96} +5.92443 q^{97} +1.91879 q^{98} -1.13184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.85242	−1.30986	−0.654931	−	0.755689i	$-0.727302\pi$
$2$	−1.85242	−1.30986	−0.654931	+	0.755689i	$0.727302\pi$
$3$	0.130041	0.0750791	0.0375395	−	0.999295i	$-0.488048\pi$
$3$	0.130041	0.0750791	0.0375395	+	0.999295i	$0.488048\pi$
$4$	1.43148	0.715739
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.240891	−0.0983433
$7$	2.44217	0.923052	0.461526	−	0.887127i	$-0.347302\pi$
$7$	2.44217	0.923052	0.461526	+	0.887127i	$0.347302\pi$
$8$	1.05315	0.372343
$9$	−2.98309	−0.994363
$10$	−1.85242	−0.585788
$11$	0.379418	0.114399	0.0571994	−	0.998363i	$-0.481783\pi$
$11$	0.379418	0.114399	0.0571994	+	0.998363i	$0.481783\pi$
$12$	0.186150	0.0537370
$13$	1.02133	0.283267	0.141634	−	0.989919i	$-0.454765\pi$
$13$	1.02133	0.283267	0.141634	+	0.989919i	$0.454765\pi$
$14$	−4.52393	−1.20907
$15$	0.130041	0.0335764
$16$	−4.81383	−1.20346
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.52595	1.30248
$19$	0.879320	0.201730	0.100865	−	0.994900i	$-0.467839\pi$
$19$	0.879320	0.201730	0.100865	+	0.994900i	$0.467839\pi$
$20$	1.43148	0.320088
$21$	0.317581	0.0693019
$22$	−0.702843	−0.149847
$23$	−5.33854	−1.11316	−0.556581	−	0.830793i	$-0.687887\pi$
$23$	−5.33854	−1.11316	−0.556581	+	0.830793i	$0.687887\pi$
$24$	0.136952	0.0279552
$25$	1.00000	0.200000
$26$	−1.89195	−0.371041
$27$	−0.778046	−0.149735
$28$	3.49591	0.660664
$29$	3.70355	0.687732	0.343866	−	0.939019i	$-0.388263\pi$
$29$	3.70355	0.687732	0.343866	+	0.939019i	$0.388263\pi$
$30$	−0.240891	−0.0439804
$31$	−1.47371	−0.264686	−0.132343	−	0.991204i	$-0.542250\pi$
$31$	−1.47371	−0.264686	−0.132343	+	0.991204i	$0.542250\pi$
$32$	6.81096	1.20402
$33$	0.0493398	0.00858896
$34$	1.85242	0.317688
$35$	2.44217	0.412801
$36$	−4.27022	−0.711704
$37$	−3.07854	−0.506108	−0.253054	−	0.967452i	$-0.581435\pi$
$37$	−3.07854	−0.506108	−0.253054	+	0.967452i	$0.581435\pi$
$38$	−1.62887	−0.264238
$39$	0.132815	0.0212675
$40$	1.05315	0.166517
$41$	1.90992	0.298279	0.149140	−	0.988816i	$-0.452350\pi$
$41$	1.90992	0.298279	0.149140	+	0.988816i	$0.452350\pi$
$42$	−0.588295	−0.0907759
$43$	4.84610	0.739023	0.369512	−	0.929226i	$-0.379525\pi$
$43$	4.84610	0.739023	0.369512	+	0.929226i	$0.379525\pi$
$44$	0.543128	0.0818797
$45$	−2.98309	−0.444693
$46$	9.88925	1.45809
$47$	0.747547	0.109041	0.0545205	−	0.998513i	$-0.482637\pi$
$47$	0.747547	0.109041	0.0545205	+	0.998513i	$0.482637\pi$
$48$	−0.625994	−0.0903544
$49$	−1.03582	−0.147975
$50$	−1.85242	−0.261972
$51$	−0.130041	−0.0182094
$52$	1.46202	0.202745
$53$	−10.2068	−1.40201	−0.701005	−	0.713156i	$-0.747265\pi$
$53$	−10.2068	−1.40201	−0.701005	+	0.713156i	$0.747265\pi$
$54$	1.44127	0.196132
$55$	0.379418	0.0511607
$56$	2.57196	0.343692
$57$	0.114347	0.0151457
$58$	−6.86055	−0.900834
$59$	4.48576	0.583997	0.291998	−	0.956419i	$-0.405680\pi$
$59$	4.48576	0.583997	0.291998	+	0.956419i	$0.405680\pi$
$60$	0.186150	0.0240319
$61$	1.43294	0.183469	0.0917345	−	0.995784i	$-0.470759\pi$
$61$	1.43294	0.183469	0.0917345	+	0.995784i	$0.470759\pi$
$62$	2.72994	0.346703
$63$	−7.28520	−0.917849
$64$	−2.98914	−0.373642
$65$	1.02133	0.126681
$66$	−0.0913983	−0.0112504
$67$	−13.4544	−1.64372	−0.821861	−	0.569688i	$-0.807064\pi$
$67$	−13.4544	−1.64372	−0.821861	+	0.569688i	$0.807064\pi$
$68$	−1.43148	−0.173592
$69$	−0.694228	−0.0835752
$70$	−4.52393	−0.540713
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−3.14163	−0.370244
$73$	−11.7712	−1.37771	−0.688856	−	0.724898i	$-0.741887\pi$
$73$	−11.7712	−1.37771	−0.688856	+	0.724898i	$0.741887\pi$
$74$	5.70275	0.662932
$75$	0.130041	0.0150158
$76$	1.25873	0.144386
$77$	0.926602	0.105596
$78$	−0.246030	−0.0278574
$79$	−6.16503	−0.693620	−0.346810	−	0.937935i	$-0.612735\pi$
$79$	−6.16503	−0.693620	−0.346810	+	0.937935i	$0.612735\pi$
$80$	−4.81383	−0.538202
$81$	8.84809	0.983121
$82$	−3.53798	−0.390705
$83$	0.447396	0.0491080	0.0245540	−	0.999699i	$-0.492183\pi$
$83$	0.447396	0.0491080	0.0245540	+	0.999699i	$0.492183\pi$
$84$	0.454610	0.0496021
$85$	−1.00000	−0.108465
$86$	−8.97704	−0.968019
$87$	0.481613	0.0516343
$88$	0.399582	0.0425956
$89$	6.11177	0.647846	0.323923	−	0.946083i	$-0.394998\pi$
$89$	6.11177	0.647846	0.323923	+	0.946083i	$0.394998\pi$
$90$	5.52595	0.582486
$91$	2.49427	0.261470
$92$	−7.64200	−0.796734
$93$	−0.191643	−0.0198724
$94$	−1.38477	−0.142829
$95$	0.879320	0.0902163
$96$	0.885703	0.0903967
$97$	5.92443	0.601535	0.300767	−	0.953698i	$-0.402757\pi$
$97$	5.92443	0.601535	0.300767	+	0.953698i	$0.402757\pi$
$98$	1.91879	0.193827
$99$	−1.13184	−0.113754
$100$	1.43148	0.143148
$101$	−5.12790	−0.510245	−0.255122	−	0.966909i	$-0.582116\pi$
$101$	−5.12790	−0.510245	−0.255122	+	0.966909i	$0.582116\pi$
$102$	0.240891	0.0238517
$103$	−12.1296	−1.19517	−0.597583	−	0.801807i	$-0.703872\pi$
$103$	−12.1296	−1.19517	−0.597583	+	0.801807i	$0.703872\pi$
$104$	1.07561	0.105473
$105$	0.317581	0.0309928
$106$	18.9073	1.83644
$107$	2.90735	0.281064	0.140532	−	0.990076i	$-0.455119\pi$
$107$	2.90735	0.281064	0.140532	+	0.990076i	$0.455119\pi$
$108$	−1.11375	−0.107171
$109$	−7.50047	−0.718415	−0.359207	−	0.933258i	$-0.616953\pi$
$109$	−7.50047	−0.718415	−0.359207	+	0.933258i	$0.616953\pi$
$110$	−0.702843	−0.0670135
$111$	−0.400335	−0.0379981
$112$	−11.7562	−1.11085
$113$	−8.52650	−0.802106	−0.401053	−	0.916055i	$-0.631356\pi$
$113$	−8.52650	−0.802106	−0.401053	+	0.916055i	$0.631356\pi$
$114$	−0.211820	−0.0198388
$115$	−5.33854	−0.497822
$116$	5.30155	0.492236
$117$	−3.04673	−0.281671
$118$	−8.30954	−0.764955
$119$	−2.44217	−0.223873
$120$	0.136952	0.0125019
$121$	−10.8560	−0.986913
$122$	−2.65441	−0.240319
$123$	0.248367	0.0223945
$124$	−2.10958	−0.189446
$125$	1.00000	0.0894427
$126$	13.4953	1.20226
$127$	−4.42502	−0.392657	−0.196329	−	0.980538i	$-0.562902\pi$
$127$	−4.42502	−0.392657	−0.196329	+	0.980538i	$0.562902\pi$
$128$	−8.08477	−0.714599
$129$	0.630191	0.0554852
$130$	−1.89195	−0.165935
$131$	−16.0569	−1.40290	−0.701448	−	0.712721i	$-0.747463\pi$
$131$	−16.0569	−1.40290	−0.701448	+	0.712721i	$0.747463\pi$
$132$	0.0706288	0.00614745
$133$	2.14745	0.186207
$134$	24.9234	2.15305
$135$	−0.778046	−0.0669635
$136$	−1.05315	−0.0903065
$137$	16.4448	1.40497	0.702485	−	0.711699i	$-0.252074\pi$
$137$	16.4448	1.40497	0.702485	+	0.711699i	$0.252074\pi$
$138$	1.28601	0.109472
$139$	−1.57382	−0.133489	−0.0667447	−	0.997770i	$-0.521261\pi$
$139$	−1.57382	−0.133489	−0.0667447	+	0.997770i	$0.521261\pi$
$140$	3.49591	0.295458
$141$	0.0972116	0.00818669
$142$	−1.85242	−0.155452
$143$	0.387513	0.0324055
$144$	14.3601	1.19667
$145$	3.70355	0.307563
$146$	21.8052	1.80461
$147$	−0.134699	−0.0111098
$148$	−4.40685	−0.362241
$149$	−23.4844	−1.92392	−0.961959	−	0.273196i	$-0.911919\pi$
$149$	−23.4844	−1.92392	−0.961959	+	0.273196i	$0.911919\pi$
$150$	−0.240891	−0.0196687
$151$	16.6829	1.35764	0.678818	−	0.734307i	$-0.262493\pi$
$151$	16.6829	1.35764	0.678818	+	0.734307i	$0.262493\pi$
$152$	0.926052	0.0751127
$153$	2.98309	0.241168
$154$	−1.71646	−0.138316
$155$	−1.47371	−0.118371
$156$	0.190122	0.0152219
$157$	22.1432	1.76722	0.883609	−	0.468225i	$-0.155106\pi$
$157$	22.1432	1.76722	0.883609	+	0.468225i	$0.155106\pi$
$158$	11.4203	0.908547
$159$	−1.32730	−0.105262
$160$	6.81096	0.538454
$161$	−13.0376	−1.02751
$162$	−16.3904	−1.28775
$163$	20.3504	1.59397	0.796983	−	0.604001i	$-0.206428\pi$
$163$	20.3504	1.59397	0.796983	+	0.604001i	$0.206428\pi$
$164$	2.73401	0.213490
$165$	0.0493398	0.00384110
$166$	−0.828767	−0.0643248
$167$	17.6984	1.36954	0.684770	−	0.728759i	$-0.259902\pi$
$167$	17.6984	1.36954	0.684770	+	0.728759i	$0.259902\pi$
$168$	0.334459	0.0258041
$169$	−11.9569	−0.919760
$170$	1.85242	0.142074
$171$	−2.62309	−0.200593
$172$	6.93708	0.528948
$173$	18.7224	1.42344	0.711719	−	0.702464i	$-0.247917\pi$
$173$	18.7224	1.42344	0.711719	+	0.702464i	$0.247917\pi$
$174$	−0.892151	−0.0676338
$175$	2.44217	0.184610
$176$	−1.82645	−0.137674
$177$	0.583332	0.0438459
$178$	−11.3216	−0.848589
$179$	−15.8515	−1.18480	−0.592398	−	0.805646i	$-0.701819\pi$
$179$	−15.8515	−1.18480	−0.592398	+	0.805646i	$0.701819\pi$
$180$	−4.27022	−0.318284
$181$	−13.8999	−1.03317	−0.516587	−	0.856235i	$-0.672798\pi$
$181$	−13.8999	−1.03317	−0.516587	+	0.856235i	$0.672798\pi$
$182$	−4.62045	−0.342490
$183$	0.186340	0.0137747
$184$	−5.62226	−0.414479
$185$	−3.07854	−0.226338
$186$	0.355003	0.0260301
$187$	−0.379418	−0.0277458
$188$	1.07010	0.0780448
$189$	−1.90012	−0.138213
$190$	−1.62887	−0.118171
$191$	−8.01173	−0.579708	−0.289854	−	0.957071i	$-0.593607\pi$
$191$	−8.01173	−0.579708	−0.289854	+	0.957071i	$0.593607\pi$
$192$	−0.388710	−0.0280527
$193$	2.03848	0.146733	0.0733663	−	0.997305i	$-0.476626\pi$
$193$	2.03848	0.146733	0.0733663	+	0.997305i	$0.476626\pi$
$194$	−10.9746	−0.787928
$195$	0.132815	0.00951109
$196$	−1.48276	−0.105911
$197$	−12.6113	−0.898521	−0.449260	−	0.893401i	$-0.648312\pi$
$197$	−12.6113	−0.898521	−0.449260	+	0.893401i	$0.648312\pi$
$198$	2.09664	0.149002
$199$	−18.4060	−1.30477	−0.652383	−	0.757890i	$-0.726231\pi$
$199$	−18.4060	−1.30477	−0.652383	+	0.757890i	$0.726231\pi$
$200$	1.05315	0.0744686
$201$	−1.74963	−0.123409
$202$	9.49904	0.668350
$203$	9.04469	0.634813
$204$	−0.186150	−0.0130331
$205$	1.90992	0.133395
$206$	22.4692	1.56550
$207$	15.9253	1.10689
$208$	−4.91653	−0.340900
$209$	0.333630	0.0230777
$210$	−0.588295	−0.0405962
$211$	−19.1582	−1.31891	−0.659454	−	0.751745i	$-0.729212\pi$
$211$	−19.1582	−1.31891	−0.659454	+	0.751745i	$0.729212\pi$
$212$	−14.6108	−1.00347
$213$	0.130041	0.00891025
$214$	−5.38564	−0.368155
$215$	4.84610	0.330501
$216$	−0.819395	−0.0557528
$217$	−3.59905	−0.244319
$218$	13.8941	0.941025
$219$	−1.53073	−0.103437
$220$	0.543128	0.0366177
$221$	−1.02133	−0.0687024
$222$	0.741591	0.0497723
$223$	−24.0045	−1.60746	−0.803729	−	0.594996i	$-0.797154\pi$
$223$	−24.0045	−1.60746	−0.803729	+	0.594996i	$0.797154\pi$
$224$	16.6335	1.11137
$225$	−2.98309	−0.198873
$226$	15.7947	1.05065
$227$	−5.38935	−0.357703	−0.178852	−	0.983876i	$-0.557238\pi$
$227$	−5.38935	−0.357703	−0.178852	+	0.983876i	$0.557238\pi$
$228$	0.163686	0.0108404
$229$	15.9404	1.05337	0.526686	−	0.850060i	$-0.323434\pi$
$229$	15.9404	1.05337	0.526686	+	0.850060i	$0.323434\pi$
$230$	9.88925	0.652078
$231$	0.120496	0.00792806
$232$	3.90038	0.256072
$233$	10.9470	0.717162	0.358581	−	0.933499i	$-0.383261\pi$
$233$	10.9470	0.717162	0.358581	+	0.933499i	$0.383261\pi$
$234$	5.64384	0.368950
$235$	0.747547	0.0487646
$236$	6.42127	0.417989
$237$	−0.801706	−0.0520764
$238$	4.52393	0.293243
$239$	−4.80384	−0.310735	−0.155367	−	0.987857i	$-0.549656\pi$
$239$	−4.80384	−0.310735	−0.155367	+	0.987857i	$0.549656\pi$
$240$	−0.625994	−0.0404077
$241$	11.9967	0.772775	0.386387	−	0.922337i	$-0.373723\pi$
$241$	11.9967	0.772775	0.386387	+	0.922337i	$0.373723\pi$
$242$	20.1100	1.29272
$243$	3.48475	0.223547
$244$	2.05122	0.131316
$245$	−1.03582	−0.0661764
$246$	−0.460082	−0.0293338
$247$	0.898080	0.0571435
$248$	−1.55203	−0.0985542
$249$	0.0581797	0.00368699
$250$	−1.85242	−0.117158
$251$	15.6753	0.989416	0.494708	−	0.869059i	$-0.335275\pi$
$251$	15.6753	0.989416	0.494708	+	0.869059i	$0.335275\pi$
$252$	−10.4286	−0.656940
$253$	−2.02554	−0.127345
$254$	8.19702	0.514327
$255$	−0.130041	−0.00814347
$256$	20.9547	1.30967
$257$	1.16358	0.0725823	0.0362912	−	0.999341i	$-0.488446\pi$
$257$	1.16358	0.0725823	0.0362912	+	0.999341i	$0.488446\pi$
$258$	−1.16738	−0.0726780
$259$	−7.51829	−0.467164
$260$	1.46202	0.0906705
$261$	−11.0480	−0.683855
$262$	29.7442	1.83760
$263$	18.1369	1.11837	0.559185	−	0.829043i	$-0.311114\pi$
$263$	18.1369	1.11837	0.559185	+	0.829043i	$0.311114\pi$
$264$	0.0519620	0.00319804
$265$	−10.2068	−0.626998
$266$	−3.97798	−0.243906
$267$	0.794779	0.0486397
$268$	−19.2597	−1.17648
$269$	15.0080	0.915054	0.457527	−	0.889196i	$-0.348735\pi$
$269$	15.0080	0.915054	0.457527	+	0.889196i	$0.348735\pi$
$270$	1.44127	0.0877130
$271$	−17.2872	−1.05013	−0.525063	−	0.851064i	$-0.675958\pi$
$271$	−17.2872	−1.05013	−0.525063	+	0.851064i	$0.675958\pi$
$272$	4.81383	0.291881
$273$	0.324357	0.0196310
$274$	−30.4627	−1.84032
$275$	0.379418	0.0228798
$276$	−0.993772	−0.0598180
$277$	−16.4364	−0.987568	−0.493784	−	0.869585i	$-0.664387\pi$
$277$	−16.4364	−0.987568	−0.493784	+	0.869585i	$0.664387\pi$
$278$	2.91538	0.174853
$279$	4.39621	0.263194
$280$	2.57196	0.153704
$281$	13.4244	0.800832	0.400416	−	0.916333i	$-0.368866\pi$
$281$	13.4244	0.800832	0.400416	+	0.916333i	$0.368866\pi$
$282$	−0.180077	−0.0107234
$283$	−15.5213	−0.922646	−0.461323	−	0.887232i	$-0.652625\pi$
$283$	−15.5213	−0.922646	−0.461323	+	0.887232i	$0.652625\pi$
$284$	1.43148	0.0849425
$285$	0.114347	0.00677336
$286$	−0.717838	−0.0424467
$287$	4.66434	0.275327
$288$	−20.3177	−1.19723
$289$	1.00000	0.0588235
$290$	−6.86055	−0.402865
$291$	0.770418	0.0451627
$292$	−16.8502	−0.986082
$293$	13.2854	0.776142	0.388071	−	0.921629i	$-0.373141\pi$
$293$	13.2854	0.776142	0.388071	+	0.921629i	$0.373141\pi$
$294$	0.249520	0.0145523
$295$	4.48576	0.261171
$296$	−3.24215	−0.188446
$297$	−0.295205	−0.0171295
$298$	43.5031	2.52007
$299$	−5.45244	−0.315323
$300$	0.186150	0.0107474
$301$	11.8350	0.682157
$302$	−30.9038	−1.77832
$303$	−0.666836	−0.0383087
$304$	−4.23289	−0.242773
$305$	1.43294	0.0820498
$306$	−5.52595	−0.315897
$307$	25.0788	1.43132	0.715660	−	0.698449i	$-0.246126\pi$
$307$	25.0788	1.43132	0.715660	+	0.698449i	$0.246126\pi$
$308$	1.32641	0.0755792
$309$	−1.57734	−0.0897319
$310$	2.72994	0.155050
$311$	10.1823	0.577388	0.288694	−	0.957421i	$-0.406779\pi$
$311$	10.1823	0.577388	0.288694	+	0.957421i	$0.406779\pi$
$312$	0.139874	0.00791879
$313$	22.1503	1.25201	0.626004	−	0.779820i	$-0.284689\pi$
$313$	22.1503	1.25201	0.626004	+	0.779820i	$0.284689\pi$
$314$	−41.0186	−2.31481
$315$	−7.28520	−0.410475
$316$	−8.82510	−0.496451
$317$	−16.3069	−0.915886	−0.457943	−	0.888982i	$-0.651414\pi$
$317$	−16.3069	−0.915886	−0.457943	+	0.888982i	$0.651414\pi$
$318$	2.45872	0.137878
$319$	1.40519	0.0786758
$320$	−2.98914	−0.167098
$321$	0.378074	0.0211020
$322$	24.1512	1.34589
$323$	−0.879320	−0.0489267
$324$	12.6658	0.703658
$325$	1.02133	0.0566535
$326$	−37.6976	−2.08788
$327$	−0.975367	−0.0539379
$328$	2.01142	0.111062
$329$	1.82563	0.100650
$330$	−0.0913983	−0.00503131
$331$	20.1923	1.10987	0.554935	−	0.831893i	$-0.312743\pi$
$331$	20.1923	1.10987	0.554935	+	0.831893i	$0.312743\pi$
$332$	0.640437	0.0351485
$333$	9.18355	0.503255
$334$	−32.7849	−1.79391
$335$	−13.4544	−0.735095
$336$	−1.52878	−0.0834019
$337$	8.08077	0.440188	0.220094	−	0.975479i	$-0.429364\pi$
$337$	8.08077	0.440188	0.220094	+	0.975479i	$0.429364\pi$
$338$	22.1492	1.20476
$339$	−1.10879	−0.0602214
$340$	−1.43148	−0.0776328
$341$	−0.559153	−0.0302798
$342$	4.85908	0.262749
$343$	−19.6248	−1.05964
$344$	5.10365	0.275170
$345$	−0.694228	−0.0373760
$346$	−34.6818	−1.86451
$347$	5.32859	0.286054	0.143027	−	0.989719i	$-0.454317\pi$
$347$	5.32859	0.286054	0.143027	+	0.989719i	$0.454317\pi$
$348$	0.689418	0.0369567
$349$	−10.8727	−0.582005	−0.291002	−	0.956722i	$-0.593989\pi$
$349$	−10.8727	−0.582005	−0.291002	+	0.956722i	$0.593989\pi$
$350$	−4.52393	−0.241814
$351$	−0.794645	−0.0424150
$352$	2.58420	0.137738
$353$	−23.4362	−1.24738	−0.623692	−	0.781670i	$-0.714368\pi$
$353$	−23.4362	−1.24738	−0.623692	+	0.781670i	$0.714368\pi$
$354$	−1.08058	−0.0574321
$355$	1.00000	0.0530745
$356$	8.74886	0.463689
$357$	−0.317581	−0.0168082
$358$	29.3637	1.55192
$359$	−27.9358	−1.47439	−0.737196	−	0.675679i	$-0.763851\pi$
$359$	−27.9358	−1.47439	−0.737196	+	0.675679i	$0.763851\pi$
$360$	−3.14163	−0.165578
$361$	−18.2268	−0.959305
$362$	25.7486	1.35332
$363$	−1.41173	−0.0740965
$364$	3.57049	0.187145
$365$	−11.7712	−0.616132
$366$	−0.345182	−0.0180429
$367$	20.5400	1.07218	0.536090	−	0.844161i	$-0.319901\pi$
$367$	20.5400	1.07218	0.536090	+	0.844161i	$0.319901\pi$
$368$	25.6988	1.33964
$369$	−5.69746	−0.296598
$370$	5.70275	0.296472
$371$	−24.9267	−1.29413
$372$	−0.274332	−0.0142235
$373$	−20.0090	−1.03603	−0.518013	−	0.855373i	$-0.673328\pi$
$373$	−20.0090	−1.03603	−0.518013	+	0.855373i	$0.673328\pi$
$374$	0.702843	0.0363432
$375$	0.130041	0.00671528
$376$	0.787276	0.0406007
$377$	3.78257	0.194812
$378$	3.51982	0.181040
$379$	28.8673	1.48282	0.741408	−	0.671055i	$-0.234158\pi$
$379$	28.8673	1.48282	0.741408	+	0.671055i	$0.234158\pi$
$380$	1.25873	0.0645713
$381$	−0.575433	−0.0294803
$382$	14.8411	0.759338
$383$	−20.9643	−1.07122	−0.535612	−	0.844464i	$-0.679919\pi$
$383$	−20.9643	−1.07122	−0.535612	+	0.844464i	$0.679919\pi$
$384$	−1.05135	−0.0536515
$385$	0.926602	0.0472240
$386$	−3.77612	−0.192200
$387$	−14.4563	−0.734858
$388$	8.48069	0.430542
$389$	14.7680	0.748770	0.374385	−	0.927273i	$-0.377854\pi$
$389$	14.7680	0.748770	0.374385	+	0.927273i	$0.377854\pi$
$390$	−0.246030	−0.0124582
$391$	5.33854	0.269982
$392$	−1.09087	−0.0550974
$393$	−2.08805	−0.105328
$394$	23.3616	1.17694
$395$	−6.16503	−0.310196
$396$	−1.62020	−0.0814181
$397$	−24.6028	−1.23478	−0.617390	−	0.786657i	$-0.711810\pi$
$397$	−24.6028	−1.23478	−0.617390	+	0.786657i	$0.711810\pi$
$398$	34.0957	1.70906
$399$	0.279255	0.0139803
$400$	−4.81383	−0.240691
$401$	−14.6755	−0.732860	−0.366430	−	0.930446i	$-0.619420\pi$
$401$	−14.6755	−0.732860	−0.366430	+	0.930446i	$0.619420\pi$
$402$	3.24105	0.161649
$403$	−1.50515	−0.0749770
$404$	−7.34047	−0.365202
$405$	8.84809	0.439665
$406$	−16.7546	−0.831517
$407$	−1.16805	−0.0578982
$408$	−0.136952	−0.00678013
$409$	−31.9586	−1.58025	−0.790126	−	0.612945i	$-0.789985\pi$
$409$	−31.9586	−1.58025	−0.790126	+	0.612945i	$0.789985\pi$
$410$	−3.53798	−0.174729
$411$	2.13849	0.105484
$412$	−17.3633	−0.855426
$413$	10.9550	0.539059
$414$	−29.5005	−1.44987
$415$	0.447396	0.0219618
$416$	6.95627	0.341059
$417$	−0.204660	−0.0100223
$418$	−0.618024	−0.0302285
$419$	17.9651	0.877653	0.438827	−	0.898572i	$-0.355394\pi$
$419$	17.9651	0.877653	0.438827	+	0.898572i	$0.355394\pi$
$420$	0.454610	0.0221827
$421$	−8.64484	−0.421324	−0.210662	−	0.977559i	$-0.567562\pi$
$421$	−8.64484	−0.421324	−0.210662	+	0.977559i	$0.567562\pi$
$422$	35.4892	1.72759
$423$	−2.23000	−0.108426
$424$	−10.7492	−0.522029
$425$	−1.00000	−0.0485071
$426$	−0.240891	−0.0116712
$427$	3.49947	0.169351
$428$	4.16180	0.201168
$429$	0.0503925	0.00243297
$430$	−8.97704	−0.432911
$431$	−39.5185	−1.90354	−0.951769	−	0.306816i	$-0.900736\pi$
$431$	−39.5185	−1.90354	−0.951769	+	0.306816i	$0.900736\pi$
$432$	3.74538	0.180200
$433$	−6.75940	−0.324836	−0.162418	−	0.986722i	$-0.551929\pi$
$433$	−6.75940	−0.324836	−0.162418	+	0.986722i	$0.551929\pi$
$434$	6.66697	0.320025
$435$	0.481613	0.0230916
$436$	−10.7368	−0.514197
$437$	−4.69428	−0.224558
$438$	2.83557	0.135489
$439$	−28.2110	−1.34644	−0.673219	−	0.739443i	$-0.735089\pi$
$439$	−28.2110	−1.34644	−0.673219	+	0.739443i	$0.735089\pi$
$440$	0.399582	0.0190493
$441$	3.08996	0.147141
$442$	1.89195	0.0899907
$443$	−29.5141	−1.40225	−0.701127	−	0.713036i	$-0.747320\pi$
$443$	−29.5141	−1.40225	−0.701127	+	0.713036i	$0.747320\pi$
$444$	−0.573071	−0.0271967
$445$	6.11177	0.289726
$446$	44.4665	2.10555
$447$	−3.05393	−0.144446
$448$	−7.29997	−0.344891
$449$	8.78587	0.414631	0.207315	−	0.978274i	$-0.433527\pi$
$449$	8.78587	0.414631	0.207315	+	0.978274i	$0.433527\pi$
$450$	5.52595	0.260496
$451$	0.724658	0.0341228
$452$	−12.2055	−0.574098
$453$	2.16946	0.101930
$454$	9.98336	0.468542
$455$	2.49427	0.116933
$456$	0.120425	0.00563939
$457$	−9.75158	−0.456160	−0.228080	−	0.973642i	$-0.573245\pi$
$457$	−9.75158	−0.456160	−0.228080	+	0.973642i	$0.573245\pi$
$458$	−29.5284	−1.37977
$459$	0.778046	0.0363161
$460$	−7.64200	−0.356310
$461$	24.7489	1.15267	0.576337	−	0.817212i	$-0.304482\pi$
$461$	24.7489	1.15267	0.576337	+	0.817212i	$0.304482\pi$
$462$	−0.223210	−0.0103847
$463$	−34.3548	−1.59660	−0.798301	−	0.602259i	$-0.794267\pi$
$463$	−34.3548	−1.59660	−0.798301	+	0.602259i	$0.794267\pi$
$464$	−17.8283	−0.827656
$465$	−0.191643	−0.00888721
$466$	−20.2785	−0.939383
$467$	4.75605	0.220084	0.110042	−	0.993927i	$-0.464902\pi$
$467$	4.75605	0.220084	0.110042	+	0.993927i	$0.464902\pi$
$468$	−4.36133	−0.201602
$469$	−32.8580	−1.51724
$470$	−1.38477	−0.0638749
$471$	2.87952	0.132681
$472$	4.72416	0.217447
$473$	1.83870	0.0845434
$474$	1.48510	0.0682129
$475$	0.879320	0.0403460
$476$	−3.49591	−0.160235
$477$	30.4478	1.39411
$478$	8.89875	0.407019
$479$	2.73706	0.125059	0.0625296	−	0.998043i	$-0.480083\pi$
$479$	2.73706	0.125059	0.0625296	+	0.998043i	$0.480083\pi$
$480$	0.885703	0.0404266
$481$	−3.14421	−0.143364
$482$	−22.2230	−1.01223
$483$	−1.69542	−0.0771443
$484$	−15.5402	−0.706372
$485$	5.92443	0.269015
$486$	−6.45524	−0.292815
$487$	33.9850	1.54001	0.770004	−	0.638039i	$-0.220254\pi$
$487$	33.9850	1.54001	0.770004	+	0.638039i	$0.220254\pi$
$488$	1.50909	0.0683134
$489$	2.64638	0.119674
$490$	1.91879	0.0866819
$491$	31.4300	1.41842	0.709208	−	0.705000i	$-0.249053\pi$
$491$	31.4300	1.41842	0.709208	+	0.705000i	$0.249053\pi$
$492$	0.355532	0.0160286
$493$	−3.70355	−0.166800
$494$	−1.66363	−0.0748500
$495$	−1.13184	−0.0508723
$496$	7.09419	0.318539
$497$	2.44217	0.109546
$498$	−0.107773	−0.00482944
$499$	23.4869	1.05142	0.525708	−	0.850665i	$-0.323800\pi$
$499$	23.4869	1.05142	0.525708	+	0.850665i	$0.323800\pi$
$500$	1.43148	0.0640176
$501$	2.30151	0.102824
$502$	−29.0373	−1.29600
$503$	−31.0704	−1.38536	−0.692681	−	0.721244i	$-0.743571\pi$
$503$	−31.0704	−1.38536	−0.692681	+	0.721244i	$0.743571\pi$
$504$	−7.67238	−0.341755
$505$	−5.12790	−0.228188
$506$	3.75216	0.166804
$507$	−1.55488	−0.0690547
$508$	−6.33432	−0.281040
$509$	−19.6476	−0.870866	−0.435433	−	0.900221i	$-0.643405\pi$
$509$	−19.6476	−0.870866	−0.435433	+	0.900221i	$0.643405\pi$
$510$	0.240891	0.0106668
$511$	−28.7472	−1.27170
$512$	−22.6475	−1.00089
$513$	−0.684151	−0.0302060
$514$	−2.15545	−0.0950728
$515$	−12.1296	−0.534494
$516$	0.902104	0.0397129
$517$	0.283633	0.0124742
$518$	13.9271	0.611921
$519$	2.43468	0.106870
$520$	1.07561	0.0471688
$521$	14.4520	0.633153	0.316576	−	0.948567i	$-0.397467\pi$
$521$	14.4520	0.633153	0.316576	+	0.948567i	$0.397467\pi$
$522$	20.4656	0.895756
$523$	13.3474	0.583643	0.291822	−	0.956473i	$-0.405739\pi$
$523$	13.3474	0.583643	0.291822	+	0.956473i	$0.405739\pi$
$524$	−22.9851	−1.00411
$525$	0.317581	0.0138604
$526$	−33.5972	−1.46491
$527$	1.47371	0.0641959
$528$	−0.237513	−0.0103364
$529$	5.50002	0.239131
$530$	18.9073	0.821281
$531$	−13.3814	−0.580705
$532$	3.07402	0.133276
$533$	1.95067	0.0844928
$534$	−1.47227	−0.0637113
$535$	2.90735	0.125696
$536$	−14.1695	−0.612029
$537$	−2.06134	−0.0889534
$538$	−27.8012	−1.19859
$539$	−0.393010	−0.0169282
$540$	−1.11375	−0.0479284
$541$	−42.2136	−1.81491	−0.907453	−	0.420154i	$-0.861976\pi$
$541$	−42.2136	−1.81491	−0.907453	+	0.420154i	$0.861976\pi$
$542$	32.0233	1.37552
$543$	−1.80756	−0.0775697
$544$	−6.81096	−0.292018
$545$	−7.50047	−0.321285
$546$	−0.600846	−0.0257139
$547$	−21.3155	−0.911386	−0.455693	−	0.890137i	$-0.650608\pi$
$547$	−21.3155	−0.911386	−0.455693	+	0.890137i	$0.650608\pi$
$548$	23.5403	1.00559
$549$	−4.27458	−0.182435
$550$	−0.702843	−0.0299693
$551$	3.25661	0.138736
$552$	−0.731123	−0.0311187
$553$	−15.0560	−0.640248
$554$	30.4472	1.29358
$555$	−0.400335	−0.0169933
$556$	−2.25288	−0.0955435
$557$	12.8961	0.546426	0.273213	−	0.961953i	$-0.411914\pi$
$557$	12.8961	0.546426	0.273213	+	0.961953i	$0.411914\pi$
$558$	−8.14365	−0.344748
$559$	4.94949	0.209341
$560$	−11.7562	−0.496789
$561$	−0.0493398	−0.00208313
$562$	−24.8677	−1.04898
$563$	−29.8807	−1.25932	−0.629662	−	0.776870i	$-0.716806\pi$
$563$	−29.8807	−1.25932	−0.629662	+	0.776870i	$0.716806\pi$
$564$	0.139156	0.00585953
$565$	−8.52650	−0.358713
$566$	28.7521	1.20854
$567$	21.6085	0.907472
$568$	1.05315	0.0441890
$569$	−35.5371	−1.48979	−0.744896	−	0.667181i	$-0.767501\pi$
$569$	−35.5371	−1.48979	−0.744896	+	0.667181i	$0.767501\pi$
$570$	−0.211820	−0.00887217
$571$	6.52768	0.273175	0.136587	−	0.990628i	$-0.456387\pi$
$571$	6.52768	0.273175	0.136587	+	0.990628i	$0.456387\pi$
$572$	0.554716	0.0231938
$573$	−1.04185	−0.0435240
$574$	−8.64034	−0.360641
$575$	−5.33854	−0.222633
$576$	8.91687	0.371536
$577$	16.3074	0.678887	0.339443	−	0.940626i	$-0.389761\pi$
$577$	16.3074	0.678887	0.339443	+	0.940626i	$0.389761\pi$
$578$	−1.85242	−0.0770507
$579$	0.265085	0.0110166
$580$	5.30155	0.220135
$581$	1.09261	0.0453293
$582$	−1.42714	−0.0591569
$583$	−3.87264	−0.160388
$584$	−12.3968	−0.512982
$585$	−3.04673	−0.125967
$586$	−24.6102	−1.01664
$587$	40.4615	1.67002	0.835011	−	0.550232i	$-0.185461\pi$
$587$	40.4615	1.67002	0.835011	+	0.550232i	$0.185461\pi$
$588$	−0.192819	−0.00795173
$589$	−1.29586	−0.0533951
$590$	−8.30954	−0.342098
$591$	−1.63999	−0.0674601
$592$	14.8195	0.609079
$593$	−19.3171	−0.793256	−0.396628	−	0.917979i	$-0.629820\pi$
$593$	−19.3171	−0.793256	−0.396628	+	0.917979i	$0.629820\pi$
$594$	0.546844	0.0224373
$595$	−2.44217	−0.100119
$596$	−33.6174	−1.37702
$597$	−2.39353	−0.0979606
$598$	10.1002	0.413029
$599$	16.7610	0.684835	0.342418	−	0.939548i	$-0.388754\pi$
$599$	16.7610	0.684835	0.342418	+	0.939548i	$0.388754\pi$
$600$	0.136952	0.00559104
$601$	6.39421	0.260825	0.130413	−	0.991460i	$-0.458370\pi$
$601$	6.39421	0.260825	0.130413	+	0.991460i	$0.458370\pi$
$602$	−21.9234	−0.893532
$603$	40.1358	1.63446
$604$	23.8812	0.971713
$605$	−10.8560	−0.441361
$606$	1.23526	0.0501791
$607$	6.03586	0.244988	0.122494	−	0.992469i	$-0.460911\pi$
$607$	6.03586	0.244988	0.122494	+	0.992469i	$0.460911\pi$
$608$	5.98901	0.242887
$609$	1.17618	0.0476611
$610$	−2.65441	−0.107474
$611$	0.763496	0.0308877
$612$	4.27022	0.172614
$613$	−43.4884	−1.75648	−0.878240	−	0.478220i	$-0.841282\pi$
$613$	−43.4884	−1.75648	−0.878240	+	0.478220i	$0.841282\pi$
$614$	−46.4565	−1.87483
$615$	0.248367	0.0100151
$616$	0.975847	0.0393180
$617$	17.0943	0.688193	0.344096	−	0.938934i	$-0.388185\pi$
$617$	17.0943	0.688193	0.344096	+	0.938934i	$0.388185\pi$
$618$	2.92191	0.117536
$619$	−41.2047	−1.65616	−0.828078	−	0.560613i	$-0.810566\pi$
$619$	−41.2047	−1.65616	−0.828078	+	0.560613i	$0.810566\pi$
$620$	−2.10958	−0.0847229
$621$	4.15363	0.166679
$622$	−18.8620	−0.756298
$623$	14.9260	0.597996
$624$	−0.639349	−0.0255945
$625$	1.00000	0.0400000
$626$	−41.0317	−1.63996
$627$	0.0433855	0.00173265
$628$	31.6975	1.26487
$629$	3.07854	0.122749
$630$	13.4953	0.537665
$631$	−40.5431	−1.61399	−0.806997	−	0.590555i	$-0.798909\pi$
$631$	−40.5431	−1.61399	−0.806997	+	0.590555i	$0.798909\pi$
$632$	−6.49268	−0.258265
$633$	−2.49135	−0.0990224
$634$	30.2073	1.19968
$635$	−4.42502	−0.175602
$636$	−1.90000	−0.0753398
$637$	−1.05792	−0.0419164
$638$	−2.60302	−0.103054
$639$	−2.98309	−0.118009
$640$	−8.08477	−0.319579
$641$	−21.2272	−0.838426	−0.419213	−	0.907888i	$-0.637694\pi$
$641$	−21.2272	−0.838426	−0.419213	+	0.907888i	$0.637694\pi$
$642$	−0.700353	−0.0276407
$643$	36.8685	1.45395	0.726976	−	0.686663i	$-0.240925\pi$
$643$	36.8685	1.45395	0.726976	+	0.686663i	$0.240925\pi$
$644$	−18.6630	−0.735427
$645$	0.630191	0.0248137
$646$	1.62887	0.0640872
$647$	−2.52969	−0.0994523	−0.0497262	−	0.998763i	$-0.515835\pi$
$647$	−2.52969	−0.0994523	−0.0497262	+	0.998763i	$0.515835\pi$
$648$	9.31833	0.366058
$649$	1.70198	0.0668085
$650$	−1.89195	−0.0742082
$651$	−0.468023	−0.0183433
$652$	29.1311	1.14086
$653$	−38.5363	−1.50804	−0.754021	−	0.656850i	$-0.771888\pi$
$653$	−38.5363	−1.50804	−0.754021	+	0.656850i	$0.771888\pi$
$654$	1.80679	0.0706513
$655$	−16.0569	−0.627394
$656$	−9.19402	−0.358966
$657$	35.1145	1.36995
$658$	−3.38185	−0.131838
$659$	8.16132	0.317920	0.158960	−	0.987285i	$-0.449186\pi$
$659$	8.16132	0.317920	0.158960	+	0.987285i	$0.449186\pi$
$660$	0.0706288	0.00274922
$661$	−23.5892	−0.917514	−0.458757	−	0.888562i	$-0.651705\pi$
$661$	−23.5892	−0.917514	−0.458757	+	0.888562i	$0.651705\pi$
$662$	−37.4048	−1.45378
$663$	−0.132815	−0.00515811
$664$	0.471173	0.0182850
$665$	2.14745	0.0832743
$666$	−17.0118	−0.659195
$667$	−19.7716	−0.765558
$668$	25.3348	0.980233
$669$	−3.12156	−0.120686
$670$	24.9234	0.962873
$671$	0.543683	0.0209886
$672$	2.16303	0.0834408
$673$	−47.3916	−1.82681	−0.913407	−	0.407048i	$-0.866558\pi$
$673$	−47.3916	−1.82681	−0.913407	+	0.407048i	$0.866558\pi$
$674$	−14.9690	−0.576585
$675$	−0.778046	−0.0299470
$676$	−17.1160	−0.658308
$677$	46.6493	1.79288	0.896439	−	0.443168i	$-0.146145\pi$
$677$	46.6493	1.79288	0.896439	+	0.443168i	$0.146145\pi$
$678$	2.05396	0.0788817
$679$	14.4684	0.555248
$680$	−1.05315	−0.0403863
$681$	−0.700835	−0.0268560
$682$	1.03579	0.0396624
$683$	32.5810	1.24668	0.623338	−	0.781953i	$-0.285776\pi$
$683$	32.5810	1.24668	0.623338	+	0.781953i	$0.285776\pi$
$684$	−3.75489	−0.143572
$685$	16.4448	0.628322
$686$	36.3535	1.38798
$687$	2.07290	0.0790862
$688$	−23.3283	−0.889383
$689$	−10.4245	−0.397144
$690$	1.28601	0.0489574
$691$	−43.0423	−1.63741	−0.818704	−	0.574216i	$-0.805307\pi$
$691$	−43.0423	−1.63741	−0.818704	+	0.574216i	$0.805307\pi$
$692$	26.8007	1.01881
$693$	−2.76414	−0.105001
$694$	−9.87081	−0.374691
$695$	−1.57382	−0.0596983
$696$	0.507208	0.0192257
$697$	−1.90992	−0.0723434
$698$	20.1409	0.762346
$699$	1.42356	0.0538439
$700$	3.49591	0.132133
$701$	26.0528	0.983999	0.492000	−	0.870595i	$-0.336266\pi$
$701$	26.0528	0.983999	0.492000	+	0.870595i	$0.336266\pi$
$702$	1.47202	0.0555578
$703$	−2.70702	−0.102097
$704$	−1.13413	−0.0427443
$705$	0.0972116	0.00366120
$706$	43.4138	1.63390
$707$	−12.5232	−0.470982
$708$	0.835027	0.0313822
$709$	−29.3525	−1.10236	−0.551178	−	0.834387i	$-0.685822\pi$
$709$	−29.3525	−1.10236	−0.551178	+	0.834387i	$0.685822\pi$
$710$	−1.85242	−0.0695203
$711$	18.3908	0.689711
$712$	6.43658	0.241221
$713$	7.86747	0.294639
$714$	0.588295	0.0220164
$715$	0.387513	0.0144922
$716$	−22.6910	−0.848004
$717$	−0.624695	−0.0233297
$718$	51.7489	1.93125
$719$	−4.64261	−0.173140	−0.0865701	−	0.996246i	$-0.527591\pi$
$719$	−4.64261	−0.173140	−0.0865701	+	0.996246i	$0.527591\pi$
$720$	14.3601	0.535168
$721$	−29.6225	−1.10320
$722$	33.7638	1.25656
$723$	1.56006	0.0580192
$724$	−19.8974	−0.739482
$725$	3.70355	0.137546
$726$	2.61512	0.0970562
$727$	−11.0387	−0.409404	−0.204702	−	0.978824i	$-0.565623\pi$
$727$	−11.0387	−0.409404	−0.204702	+	0.978824i	$0.565623\pi$
$728$	2.62683	0.0973567
$729$	−26.0911	−0.966337
$730$	21.8052	0.807048
$731$	−4.84610	−0.179239
$732$	0.266742	0.00985907
$733$	45.6165	1.68489	0.842443	−	0.538786i	$-0.181117\pi$
$733$	45.6165	1.68489	0.842443	+	0.538786i	$0.181117\pi$
$734$	−38.0488	−1.40441
$735$	−0.134699	−0.00496846
$736$	−36.3606	−1.34027
$737$	−5.10486	−0.188040
$738$	10.5541	0.388502
$739$	−41.5564	−1.52868	−0.764339	−	0.644815i	$-0.776934\pi$
$739$	−41.5564	−1.52868	−0.764339	+	0.644815i	$0.776934\pi$
$740$	−4.40685	−0.161999
$741$	0.116787	0.00429028
$742$	46.1748	1.69513
$743$	14.8016	0.543018	0.271509	−	0.962436i	$-0.412477\pi$
$743$	14.8016	0.543018	0.271509	+	0.962436i	$0.412477\pi$
$744$	−0.201828	−0.00739936
$745$	−23.4844	−0.860402
$746$	37.0651	1.35705
$747$	−1.33462	−0.0488312
$748$	−0.543128	−0.0198587
$749$	7.10023	0.259437
$750$	−0.240891	−0.00879609
$751$	−25.0204	−0.913008	−0.456504	−	0.889721i	$-0.650899\pi$
$751$	−25.0204	−0.913008	−0.456504	+	0.889721i	$0.650899\pi$
$752$	−3.59856	−0.131226
$753$	2.03843	0.0742845
$754$	−7.00692	−0.255177
$755$	16.6829	0.607153
$756$	−2.71997	−0.0989245
$757$	41.8236	1.52010	0.760052	−	0.649862i	$-0.225173\pi$
$757$	41.8236	1.52010	0.760052	+	0.649862i	$0.225173\pi$
$758$	−53.4746	−1.94228
$759$	−0.263403	−0.00956091
$760$	0.926052	0.0335914
$761$	37.4712	1.35833	0.679165	−	0.733985i	$-0.262342\pi$
$761$	37.4712	1.35833	0.679165	+	0.733985i	$0.262342\pi$
$762$	1.06595	0.0386152
$763$	−18.3174	−0.663134
$764$	−11.4686	−0.414920
$765$	2.98309	0.107854
$766$	38.8347	1.40315
$767$	4.58147	0.165427
$768$	2.72497	0.0983288
$769$	9.24133	0.333251	0.166625	−	0.986020i	$-0.446713\pi$
$769$	9.24133	0.333251	0.166625	+	0.986020i	$0.446713\pi$
$770$	−1.71646	−0.0618569
$771$	0.151313	0.00544942
$772$	2.91803	0.105022
$773$	−13.0525	−0.469467	−0.234734	−	0.972060i	$-0.575422\pi$
$773$	−13.0525	−0.469467	−0.234734	+	0.972060i	$0.575422\pi$
$774$	26.7793	0.962562
$775$	−1.47371	−0.0529373
$776$	6.23929	0.223977
$777$	−0.977685	−0.0350743
$778$	−27.3567	−0.980785
$779$	1.67943	0.0601718
$780$	0.190122	0.00680746
$781$	0.379418	0.0135766
$782$	−9.88925	−0.353639
$783$	−2.88153	−0.102978
$784$	4.98628	0.178081
$785$	22.1432	0.790324
$786$	3.86795	0.137965
$787$	−54.2473	−1.93371	−0.966853	−	0.255333i	$-0.917815\pi$
$787$	−54.2473	−1.93371	−0.966853	+	0.255333i	$0.917815\pi$
$788$	−18.0528	−0.643106
$789$	2.35854	0.0839661
$790$	11.4203	0.406315
$791$	−20.8231	−0.740386
$792$	−1.19199	−0.0423555
$793$	1.46351	0.0519708
$794$	45.5749	1.61739
$795$	−1.32730	−0.0470744
$796$	−26.3477	−0.933871
$797$	6.23122	0.220721	0.110361	−	0.993892i	$-0.464799\pi$
$797$	6.23122	0.220721	0.110361	+	0.993892i	$0.464799\pi$
$798$	−0.517300	−0.0183122
$799$	−0.747547	−0.0264463
$800$	6.81096	0.240804
$801$	−18.2320	−0.644194
$802$	27.1853	0.959945
$803$	−4.46620	−0.157609
$804$	−2.50455	−0.0883287
$805$	−13.0376	−0.459515
$806$	2.78818	0.0982095
$807$	1.95165	0.0687014
$808$	−5.40042	−0.189986
$809$	−28.4378	−0.999819	−0.499909	−	0.866078i	$-0.666633\pi$
$809$	−28.4378	−0.999819	−0.499909	+	0.866078i	$0.666633\pi$
$810$	−16.3904	−0.575901
$811$	−26.2021	−0.920080	−0.460040	−	0.887898i	$-0.652165\pi$
$811$	−26.2021	−0.920080	−0.460040	+	0.887898i	$0.652165\pi$
$812$	12.9473	0.454360
$813$	−2.24805	−0.0788424
$814$	2.16373	0.0758386
$815$	20.3504	0.712844
$816$	0.625994	0.0219142
$817$	4.26127	0.149083
$818$	59.2009	2.06991
$819$	−7.44063	−0.259997
$820$	2.73401	0.0954757
$821$	37.6372	1.31355	0.656775	−	0.754087i	$-0.271920\pi$
$821$	37.6372	1.31355	0.656775	+	0.754087i	$0.271920\pi$
$822$	−3.96139	−0.138169
$823$	−50.1781	−1.74910	−0.874550	−	0.484936i	$-0.838843\pi$
$823$	−50.1781	−1.74910	−0.874550	+	0.484936i	$0.838843\pi$
$824$	−12.7742	−0.445012
$825$	0.0493398	0.00171779
$826$	−20.2933	−0.706093
$827$	−24.7373	−0.860201	−0.430101	−	0.902781i	$-0.641522\pi$
$827$	−24.7373	−0.860201	−0.430101	+	0.902781i	$0.641522\pi$
$828$	22.7968	0.792243
$829$	−2.69577	−0.0936278	−0.0468139	−	0.998904i	$-0.514907\pi$
$829$	−2.69577	−0.0936278	−0.0468139	+	0.998904i	$0.514907\pi$
$830$	−0.828767	−0.0287669
$831$	−2.13740	−0.0741457
$832$	−3.05291	−0.105841
$833$	1.03582	0.0358892
$834$	0.379118	0.0131278
$835$	17.6984	0.612477
$836$	0.477584	0.0165176
$837$	1.14661	0.0396328
$838$	−33.2790	−1.14960
$839$	−12.2443	−0.422721	−0.211360	−	0.977408i	$-0.567789\pi$
$839$	−12.2443	−0.422721	−0.211360	+	0.977408i	$0.567789\pi$
$840$	0.334459	0.0115399
$841$	−15.2837	−0.527025
$842$	16.0139	0.551876
$843$	1.74572	0.0601257
$844$	−27.4246	−0.943993
$845$	−11.9569	−0.411329
$846$	4.13091	0.142023
$847$	−26.5123	−0.910972
$848$	49.1337	1.68726
$849$	−2.01840	−0.0692714
$850$	1.85242	0.0635376
$851$	16.4349	0.563381
$852$	0.186150	0.00637741
$853$	24.8718	0.851594	0.425797	−	0.904819i	$-0.359994\pi$
$853$	24.8718	0.851594	0.425797	+	0.904819i	$0.359994\pi$
$854$	−6.48251	−0.221827
$855$	−2.62309	−0.0897078
$856$	3.06186	0.104652
$857$	17.3151	0.591472	0.295736	−	0.955270i	$-0.404435\pi$
$857$	17.3151	0.591472	0.295736	+	0.955270i	$0.404435\pi$
$858$	−0.0933483	−0.00318686
$859$	−29.9364	−1.02142	−0.510708	−	0.859754i	$-0.670617\pi$
$859$	−29.9364	−1.02142	−0.510708	+	0.859754i	$0.670617\pi$
$860$	6.93708	0.236553
$861$	0.606555	0.0206713
$862$	73.2050	2.49337
$863$	9.43534	0.321183	0.160591	−	0.987021i	$-0.448660\pi$
$863$	9.43534	0.321183	0.160591	+	0.987021i	$0.448660\pi$
$864$	−5.29924	−0.180284
$865$	18.7224	0.636581
$866$	12.5213	0.425490
$867$	0.130041	0.00441642
$868$	−5.15196	−0.174869
$869$	−2.33912	−0.0793494
$870$	−0.892151	−0.0302468
$871$	−13.7415	−0.465613
$872$	−7.89909	−0.267497
$873$	−17.6731	−0.598144
$874$	8.69581	0.294140
$875$	2.44217	0.0825603
$876$	−2.19121	−0.0740341
$877$	12.4643	0.420888	0.210444	−	0.977606i	$-0.432509\pi$
$877$	12.4643	0.420888	0.210444	+	0.977606i	$0.432509\pi$
$878$	52.2588	1.76365
$879$	1.72765	0.0582721
$880$	−1.82645	−0.0615697
$881$	48.1795	1.62321	0.811604	−	0.584208i	$-0.198595\pi$
$881$	48.1795	1.62321	0.811604	+	0.584208i	$0.198595\pi$
$882$	−5.72391	−0.192734
$883$	−0.236257	−0.00795069	−0.00397534	−	0.999992i	$-0.501265\pi$
$883$	−0.236257	−0.00795069	−0.00397534	+	0.999992i	$0.501265\pi$
$884$	−1.46202	−0.0491730
$885$	0.583332	0.0196085
$886$	54.6726	1.83676
$887$	0.0890747	0.00299084	0.00149542	−	0.999999i	$-0.499524\pi$
$887$	0.0890747	0.00299084	0.00149542	+	0.999999i	$0.499524\pi$
$888$	−0.421611	−0.0141483
$889$	−10.8066	−0.362443
$890$	−11.3216	−0.379501
$891$	3.35713	0.112468
$892$	−34.3618	−1.15052
$893$	0.657333	0.0219968
$894$	5.65718	0.189204
$895$	−15.8515	−0.529857
$896$	−19.7443	−0.659612
$897$	−0.709039	−0.0236741
$898$	−16.2752	−0.543109
$899$	−5.45796	−0.182033
$900$	−4.27022	−0.142341
$901$	10.2068	0.340037
$902$	−1.34237	−0.0446962
$903$	1.53903	0.0512157
$904$	−8.97965	−0.298659
$905$	−13.8999	−0.462049
$906$	−4.01876	−0.133514
$907$	0.258258	0.00857530	0.00428765	−	0.999991i	$-0.498635\pi$
$907$	0.258258	0.00857530	0.00428765	+	0.999991i	$0.498635\pi$
$908$	−7.71473	−0.256022
$909$	15.2970	0.507369
$910$	−4.62045	−0.153166
$911$	13.9979	0.463772	0.231886	−	0.972743i	$-0.425510\pi$
$911$	13.9979	0.463772	0.231886	+	0.972743i	$0.425510\pi$
$912$	−0.550449	−0.0182272
$913$	0.169750	0.00561790
$914$	18.0641	0.597506
$915$	0.186340	0.00616023
$916$	22.8183	0.753939
$917$	−39.2136	−1.29495
$918$	−1.44127	−0.0475690
$919$	35.4076	1.16799	0.583995	−	0.811757i	$-0.301489\pi$
$919$	35.4076	1.16799	0.583995	+	0.811757i	$0.301489\pi$
$920$	−5.62226	−0.185360
$921$	3.26126	0.107462
$922$	−45.8456	−1.50984
$923$	1.02133	0.0336176
$924$	0.172487	0.00567442
$925$	−3.07854	−0.101222
$926$	63.6396	2.09133
$927$	36.1837	1.18843
$928$	25.2247	0.828043
$929$	−36.4788	−1.19683	−0.598415	−	0.801186i	$-0.704203\pi$
$929$	−36.4788	−1.19683	−0.598415	+	0.801186i	$0.704203\pi$
$930$	0.355003	0.0116410
$931$	−0.910821	−0.0298509
$932$	15.6704	0.513301
$933$	1.32412	0.0433497
$934$	−8.81022	−0.288279
$935$	−0.379418	−0.0124083
$936$	−3.20865	−0.104878
$937$	−16.1837	−0.528697	−0.264349	−	0.964427i	$-0.585157\pi$
$937$	−16.1837	−0.528697	−0.264349	+	0.964427i	$0.585157\pi$
$938$	60.8670	1.98738
$939$	2.88044	0.0939997
$940$	1.07010	0.0349027
$941$	−30.0169	−0.978522	−0.489261	−	0.872138i	$-0.662733\pi$
$941$	−30.0169	−0.978522	−0.489261	+	0.872138i	$0.662733\pi$
$942$	−5.33409	−0.173794
$943$	−10.1962	−0.332033
$944$	−21.5937	−0.702815
$945$	−1.90012	−0.0618108
$946$	−3.40605	−0.110740
$947$	−2.65441	−0.0862569	−0.0431284	−	0.999070i	$-0.513732\pi$
$947$	−2.65441	−0.0862569	−0.0431284	+	0.999070i	$0.513732\pi$
$948$	−1.14762	−0.0372731
$949$	−12.0223	−0.390261
$950$	−1.62887	−0.0528476
$951$	−2.12056	−0.0687639
$952$	−2.57196	−0.0833576
$953$	−44.7025	−1.44806	−0.724028	−	0.689771i	$-0.757711\pi$
$953$	−44.7025	−1.44806	−0.724028	+	0.689771i	$0.757711\pi$
$954$	−56.4022	−1.82609
$955$	−8.01173	−0.259254
$956$	−6.87659	−0.222405
$957$	0.182733	0.00590690
$958$	−5.07019	−0.163810
$959$	40.1608	1.29686
$960$	−0.388710	−0.0125456
$961$	−28.8282	−0.929941
$962$	5.82442	0.187787
$963$	−8.67288	−0.279480
$964$	17.1730	0.553105
$965$	2.03848	0.0656208
$966$	3.14064	0.101048
$967$	11.0304	0.354713	0.177357	−	0.984147i	$-0.443245\pi$
$967$	11.0304	0.354713	0.177357	+	0.984147i	$0.443245\pi$
$968$	−11.4330	−0.367470
$969$	−0.114347	−0.00367337
$970$	−10.9746	−0.352372
$971$	46.4743	1.49143	0.745716	−	0.666264i	$-0.232107\pi$
$971$	46.4743	1.49143	0.745716	+	0.666264i	$0.232107\pi$
$972$	4.98834	0.160001
$973$	−3.84352	−0.123218
$974$	−62.9547	−2.01720
$975$	0.132815	0.00425349
$976$	−6.89792	−0.220797
$977$	59.1630	1.89279	0.946396	−	0.323008i	$-0.104694\pi$
$977$	59.1630	1.89279	0.946396	+	0.323008i	$0.104694\pi$
$978$	−4.90222	−0.156756
$979$	2.31892	0.0741129
$980$	−1.48276	−0.0473650
$981$	22.3746	0.714365
$982$	−58.2217	−1.85793
$983$	−49.7510	−1.58681	−0.793405	−	0.608693i	$-0.791694\pi$
$983$	−49.7510	−1.58681	−0.793405	+	0.608693i	$0.791694\pi$
$984$	0.261567	0.00833846
$985$	−12.6113	−0.401831
$986$	6.86055	0.218484
$987$	0.237407	0.00755675
$988$	1.28558	0.0408998
$989$	−25.8711	−0.822653
$990$	2.09664	0.0666357
$991$	10.6005	0.336735	0.168367	−	0.985724i	$-0.446151\pi$
$991$	10.6005	0.336735	0.168367	+	0.985724i	$0.446151\pi$
$992$	−10.0374	−0.318687
$993$	2.62583	0.0833281
$994$	−4.52393	−0.143490
$995$	−18.4060	−0.583509
$996$	0.0832829	0.00263892
$997$	22.0041	0.696876	0.348438	−	0.937332i	$-0.386712\pi$
$997$	22.0041	0.696876	0.348438	+	0.937332i	$0.386712\pi$
$998$	−43.5076	−1.37721
$999$	2.39524	0.0757821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.85242 q^{2} +0.130041 q^{3} +1.43148 q^{4} +1.00000 q^{5} -0.240891 q^{6} +2.44217 q^{7} +1.05315 q^{8} -2.98309 q^{9} +O(q^{10})\)	\(q-1.85242 q^{2} +0.130041 q^{3} +1.43148 q^{4} +1.00000 q^{5} -0.240891 q^{6} +2.44217 q^{7} +1.05315 q^{8} -2.98309 q^{9} -1.85242 q^{10} +0.379418 q^{11} +0.186150 q^{12} +1.02133 q^{13} -4.52393 q^{14} +0.130041 q^{15} -4.81383 q^{16} -1.00000 q^{17} +5.52595 q^{18} +0.879320 q^{19} +1.43148 q^{20} +0.317581 q^{21} -0.702843 q^{22} -5.33854 q^{23} +0.136952 q^{24} +1.00000 q^{25} -1.89195 q^{26} -0.778046 q^{27} +3.49591 q^{28} +3.70355 q^{29} -0.240891 q^{30} -1.47371 q^{31} +6.81096 q^{32} +0.0493398 q^{33} +1.85242 q^{34} +2.44217 q^{35} -4.27022 q^{36} -3.07854 q^{37} -1.62887 q^{38} +0.132815 q^{39} +1.05315 q^{40} +1.90992 q^{41} -0.588295 q^{42} +4.84610 q^{43} +0.543128 q^{44} -2.98309 q^{45} +9.88925 q^{46} +0.747547 q^{47} -0.625994 q^{48} -1.03582 q^{49} -1.85242 q^{50} -0.130041 q^{51} +1.46202 q^{52} -10.2068 q^{53} +1.44127 q^{54} +0.379418 q^{55} +2.57196 q^{56} +0.114347 q^{57} -6.86055 q^{58} +4.48576 q^{59} +0.186150 q^{60} +1.43294 q^{61} +2.72994 q^{62} -7.28520 q^{63} -2.98914 q^{64} +1.02133 q^{65} -0.0913983 q^{66} -13.4544 q^{67} -1.43148 q^{68} -0.694228 q^{69} -4.52393 q^{70} +1.00000 q^{71} -3.14163 q^{72} -11.7712 q^{73} +5.70275 q^{74} +0.130041 q^{75} +1.25873 q^{76} +0.926602 q^{77} -0.246030 q^{78} -6.16503 q^{79} -4.81383 q^{80} +8.84809 q^{81} -3.53798 q^{82} +0.447396 q^{83} +0.454610 q^{84} -1.00000 q^{85} -8.97704 q^{86} +0.481613 q^{87} +0.399582 q^{88} +6.11177 q^{89} +5.52595 q^{90} +2.49427 q^{91} -7.64200 q^{92} -0.191643 q^{93} -1.38477 q^{94} +0.879320 q^{95} +0.885703 q^{96} +5.92443 q^{97} +1.91879 q^{98} -1.13184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 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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