LMFDB - Embedded newform 6033.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.97726 q^{2} -1.00000 q^{3} +1.90954 q^{4} +3.20847 q^{5} +1.97726 q^{6} -2.72854 q^{7} +0.178858 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.97726 q^{2} -1.00000 q^{3} +1.90954 q^{4} +3.20847 q^{5} +1.97726 q^{6} -2.72854 q^{7} +0.178858 q^{8} +1.00000 q^{9} -6.34396 q^{10} -3.53141 q^{11} -1.90954 q^{12} -4.67993 q^{13} +5.39502 q^{14} -3.20847 q^{15} -4.17273 q^{16} -2.19725 q^{17} -1.97726 q^{18} +3.80206 q^{19} +6.12670 q^{20} +2.72854 q^{21} +6.98249 q^{22} -5.67988 q^{23} -0.178858 q^{24} +5.29425 q^{25} +9.25342 q^{26} -1.00000 q^{27} -5.21026 q^{28} -2.88969 q^{29} +6.34396 q^{30} -4.70992 q^{31} +7.89285 q^{32} +3.53141 q^{33} +4.34453 q^{34} -8.75443 q^{35} +1.90954 q^{36} -4.39063 q^{37} -7.51764 q^{38} +4.67993 q^{39} +0.573861 q^{40} -12.4274 q^{41} -5.39502 q^{42} +6.82026 q^{43} -6.74337 q^{44} +3.20847 q^{45} +11.2306 q^{46} +4.19563 q^{47} +4.17273 q^{48} +0.444933 q^{49} -10.4681 q^{50} +2.19725 q^{51} -8.93653 q^{52} -10.4226 q^{53} +1.97726 q^{54} -11.3304 q^{55} -0.488023 q^{56} -3.80206 q^{57} +5.71366 q^{58} -11.3145 q^{59} -6.12670 q^{60} -10.6972 q^{61} +9.31272 q^{62} -2.72854 q^{63} -7.26071 q^{64} -15.0154 q^{65} -6.98249 q^{66} +3.49968 q^{67} -4.19574 q^{68} +5.67988 q^{69} +17.3097 q^{70} +11.7358 q^{71} +0.178858 q^{72} +6.36021 q^{73} +8.68140 q^{74} -5.29425 q^{75} +7.26019 q^{76} +9.63558 q^{77} -9.25342 q^{78} +9.11059 q^{79} -13.3881 q^{80} +1.00000 q^{81} +24.5721 q^{82} +15.4776 q^{83} +5.21026 q^{84} -7.04980 q^{85} -13.4854 q^{86} +2.88969 q^{87} -0.631622 q^{88} +12.4164 q^{89} -6.34396 q^{90} +12.7694 q^{91} -10.8460 q^{92} +4.70992 q^{93} -8.29583 q^{94} +12.1988 q^{95} -7.89285 q^{96} +13.4550 q^{97} -0.879746 q^{98} -3.53141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−1.97726	−1.39813	−0.699066	−	0.715058i	$-0.746400\pi$
$2$	−1.97726	−1.39813	−0.699066	+	0.715058i	$0.746400\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.90954	0.954771
$5$	3.20847	1.43487	0.717435	−	0.696626i	$-0.245316\pi$
$5$	3.20847	1.43487	0.717435	+	0.696626i	$0.245316\pi$
$6$	1.97726	0.807211
$7$	−2.72854	−1.03129	−0.515646	−	0.856802i	$-0.672448\pi$
$7$	−2.72854	−1.03129	−0.515646	+	0.856802i	$0.672448\pi$
$8$	0.178858	0.0632360
$9$	1.00000	0.333333
$10$	−6.34396	−2.00614
$11$	−3.53141	−1.06476	−0.532379	−	0.846506i	$-0.678702\pi$
$11$	−3.53141	−1.06476	−0.532379	+	0.846506i	$0.678702\pi$
$12$	−1.90954	−0.551237
$13$	−4.67993	−1.29798	−0.648990	−	0.760797i	$-0.724808\pi$
$13$	−4.67993	−1.29798	−0.648990	+	0.760797i	$0.724808\pi$
$14$	5.39502	1.44188
$15$	−3.20847	−0.828422
$16$	−4.17273	−1.04318
$17$	−2.19725	−0.532912	−0.266456	−	0.963847i	$-0.585853\pi$
$17$	−2.19725	−0.532912	−0.266456	+	0.963847i	$0.585853\pi$
$18$	−1.97726	−0.466044
$19$	3.80206	0.872252	0.436126	−	0.899886i	$-0.356350\pi$
$19$	3.80206	0.872252	0.436126	+	0.899886i	$0.356350\pi$
$20$	6.12670	1.36997
$21$	2.72854	0.595416
$22$	6.98249	1.48867
$23$	−5.67988	−1.18434	−0.592169	−	0.805814i	$-0.701728\pi$
$23$	−5.67988	−1.18434	−0.592169	+	0.805814i	$0.701728\pi$
$24$	−0.178858	−0.0365093
$25$	5.29425	1.05885
$26$	9.25342	1.81475
$27$	−1.00000	−0.192450
$28$	−5.21026	−0.984647
$29$	−2.88969	−0.536602	−0.268301	−	0.963335i	$-0.586462\pi$
$29$	−2.88969	−0.536602	−0.268301	+	0.963335i	$0.586462\pi$
$30$	6.34396	1.15824
$31$	−4.70992	−0.845926	−0.422963	−	0.906147i	$-0.639010\pi$
$31$	−4.70992	−0.845926	−0.422963	+	0.906147i	$0.639010\pi$
$32$	7.89285	1.39527
$33$	3.53141	0.614739
$34$	4.34453	0.745080
$35$	−8.75443	−1.47977
$36$	1.90954	0.318257
$37$	−4.39063	−0.721815	−0.360907	−	0.932602i	$-0.617533\pi$
$37$	−4.39063	−0.721815	−0.360907	+	0.932602i	$0.617533\pi$
$38$	−7.51764	−1.21952
$39$	4.67993	0.749389
$40$	0.573861	0.0907354
$41$	−12.4274	−1.94083	−0.970416	−	0.241440i	$-0.922380\pi$
$41$	−12.4274	−1.94083	−0.970416	+	0.241440i	$0.922380\pi$
$42$	−5.39502	−0.832470
$43$	6.82026	1.04008	0.520040	−	0.854142i	$-0.325917\pi$
$43$	6.82026	1.04008	0.520040	+	0.854142i	$0.325917\pi$
$44$	−6.74337	−1.01660
$45$	3.20847	0.478290
$46$	11.2306	1.65586
$47$	4.19563	0.611995	0.305998	−	0.952032i	$-0.401010\pi$
$47$	4.19563	0.611995	0.305998	+	0.952032i	$0.401010\pi$
$48$	4.17273	0.602282
$49$	0.444933	0.0635618
$50$	−10.4681	−1.48041
$51$	2.19725	0.307677
$52$	−8.93653	−1.23927
$53$	−10.4226	−1.43165	−0.715827	−	0.698278i	$-0.753950\pi$
$53$	−10.4226	−1.43165	−0.715827	+	0.698278i	$0.753950\pi$
$54$	1.97726	0.269070
$55$	−11.3304	−1.52779
$56$	−0.488023	−0.0652148
$57$	−3.80206	−0.503595
$58$	5.71366	0.750240
$59$	−11.3145	−1.47302	−0.736510	−	0.676426i	$-0.763528\pi$
$59$	−11.3145	−1.47302	−0.736510	+	0.676426i	$0.763528\pi$
$60$	−6.12670	−0.790954
$61$	−10.6972	−1.36964	−0.684819	−	0.728713i	$-0.740119\pi$
$61$	−10.6972	−1.36964	−0.684819	+	0.728713i	$0.740119\pi$
$62$	9.31272	1.18272
$63$	−2.72854	−0.343764
$64$	−7.26071	−0.907589
$65$	−15.0154	−1.86243
$66$	−6.98249	−0.859486
$67$	3.49968	0.427554	0.213777	−	0.976883i	$-0.431423\pi$
$67$	3.49968	0.427554	0.213777	+	0.976883i	$0.431423\pi$
$68$	−4.19574	−0.508809
$69$	5.67988	0.683778
$70$	17.3097	2.06891
$71$	11.7358	1.39278	0.696392	−	0.717662i	$-0.254788\pi$
$71$	11.7358	1.39278	0.696392	+	0.717662i	$0.254788\pi$
$72$	0.178858	0.0210787
$73$	6.36021	0.744407	0.372203	−	0.928151i	$-0.378602\pi$
$73$	6.36021	0.744407	0.372203	+	0.928151i	$0.378602\pi$
$74$	8.68140	1.00919
$75$	−5.29425	−0.611328
$76$	7.26019	0.832801
$77$	9.63558	1.09808
$78$	−9.25342	−1.04774
$79$	9.11059	1.02502	0.512510	−	0.858681i	$-0.328716\pi$
$79$	9.11059	1.02502	0.512510	+	0.858681i	$0.328716\pi$
$80$	−13.3881	−1.49683
$81$	1.00000	0.111111
$82$	24.5721	2.71354
$83$	15.4776	1.69888	0.849441	−	0.527683i	$-0.176939\pi$
$83$	15.4776	1.69888	0.849441	+	0.527683i	$0.176939\pi$
$84$	5.21026	0.568486
$85$	−7.04980	−0.764659
$86$	−13.4854	−1.45417
$87$	2.88969	0.309807
$88$	−0.631622	−0.0673311
$89$	12.4164	1.31614	0.658070	−	0.752957i	$-0.271373\pi$
$89$	12.4164	1.31614	0.658070	+	0.752957i	$0.271373\pi$
$90$	−6.34396	−0.668712
$91$	12.7694	1.33860
$92$	−10.8460	−1.13077
$93$	4.70992	0.488396
$94$	−8.29583	−0.855649
$95$	12.1988	1.25157
$96$	−7.89285	−0.805560
$97$	13.4550	1.36615	0.683074	−	0.730350i	$-0.260643\pi$
$97$	13.4550	1.36615	0.683074	+	0.730350i	$0.260643\pi$
$98$	−0.879746	−0.0888678
$99$	−3.53141	−0.354920
$100$	10.1096	1.01096
$101$	4.52230	0.449986	0.224993	−	0.974360i	$-0.427764\pi$
$101$	4.52230	0.449986	0.224993	+	0.974360i	$0.427764\pi$
$102$	−4.34453	−0.430172
$103$	3.18000	0.313335	0.156668	−	0.987651i	$-0.449925\pi$
$103$	3.18000	0.313335	0.156668	+	0.987651i	$0.449925\pi$
$104$	−0.837045	−0.0820791
$105$	8.75443	0.854345
$106$	20.6081	2.00164
$107$	−9.83638	−0.950919	−0.475460	−	0.879738i	$-0.657718\pi$
$107$	−9.83638	−0.950919	−0.475460	+	0.879738i	$0.657718\pi$
$108$	−1.90954	−0.183746
$109$	−18.7484	−1.79577	−0.897885	−	0.440230i	$-0.854897\pi$
$109$	−18.7484	−1.79577	−0.897885	+	0.440230i	$0.854897\pi$
$110$	22.4031	2.13605
$111$	4.39063	0.416740
$112$	11.3855	1.07583
$113$	12.2691	1.15418	0.577092	−	0.816679i	$-0.304187\pi$
$113$	12.2691	1.15418	0.577092	+	0.816679i	$0.304187\pi$
$114$	7.51764	0.704092
$115$	−18.2237	−1.69937
$116$	−5.51798	−0.512332
$117$	−4.67993	−0.432660
$118$	22.3716	2.05948
$119$	5.99529	0.549587
$120$	−0.573861	−0.0523861
$121$	1.47083	0.133712
$122$	21.1511	1.91493
$123$	12.4274	1.12054
$124$	−8.99379	−0.807666
$125$	0.944102	0.0844431
$126$	5.39502	0.480627
$127$	−4.08926	−0.362863	−0.181432	−	0.983404i	$-0.558073\pi$
$127$	−4.08926	−0.362863	−0.181432	+	0.983404i	$0.558073\pi$
$128$	−1.42940	−0.126343
$129$	−6.82026	−0.600491
$130$	29.6893	2.60392
$131$	14.4729	1.26450	0.632252	−	0.774763i	$-0.282131\pi$
$131$	14.4729	1.26450	0.632252	+	0.774763i	$0.282131\pi$
$132$	6.74337	0.586935
$133$	−10.3741	−0.899546
$134$	−6.91976	−0.597776
$135$	−3.20847	−0.276141
$136$	−0.392997	−0.0336992
$137$	12.1294	1.03628	0.518142	−	0.855294i	$-0.326624\pi$
$137$	12.1294	1.03628	0.518142	+	0.855294i	$0.326624\pi$
$138$	−11.2306	−0.956011
$139$	−6.94245	−0.588851	−0.294426	−	0.955674i	$-0.595128\pi$
$139$	−6.94245	−0.588851	−0.294426	+	0.955674i	$0.595128\pi$
$140$	−16.7170	−1.41284
$141$	−4.19563	−0.353335
$142$	−23.2047	−1.94729
$143$	16.5267	1.38204
$144$	−4.17273	−0.347728
$145$	−9.27147	−0.769954
$146$	−12.5758	−1.04078
$147$	−0.444933	−0.0366974
$148$	−8.38409	−0.689168
$149$	−1.21246	−0.0993284	−0.0496642	−	0.998766i	$-0.515815\pi$
$149$	−1.21246	−0.0993284	−0.0496642	+	0.998766i	$0.515815\pi$
$150$	10.4681	0.854716
$151$	11.1177	0.904748	0.452374	−	0.891828i	$-0.350577\pi$
$151$	11.1177	0.904748	0.452374	+	0.891828i	$0.350577\pi$
$152$	0.680030	0.0551577
$153$	−2.19725	−0.177637
$154$	−19.0520	−1.53526
$155$	−15.1116	−1.21379
$156$	8.93653	0.715495
$157$	18.7206	1.49407	0.747033	−	0.664786i	$-0.231477\pi$
$157$	18.7206	1.49407	0.747033	+	0.664786i	$0.231477\pi$
$158$	−18.0140	−1.43311
$159$	10.4226	0.826566
$160$	25.3239	2.00203
$161$	15.4978	1.22140
$162$	−1.97726	−0.155348
$163$	−8.14446	−0.637923	−0.318962	−	0.947768i	$-0.603334\pi$
$163$	−8.14446	−0.637923	−0.318962	+	0.947768i	$0.603334\pi$
$164$	−23.7306	−1.85305
$165$	11.3304	0.882070
$166$	−30.6031	−2.37526
$167$	18.9892	1.46943	0.734713	−	0.678378i	$-0.237317\pi$
$167$	18.9892	1.46943	0.734713	+	0.678378i	$0.237317\pi$
$168$	0.488023	0.0376518
$169$	8.90176	0.684751
$170$	13.9393	1.06909
$171$	3.80206	0.290751
$172$	13.0236	0.993039
$173$	7.34640	0.558536	0.279268	−	0.960213i	$-0.409908\pi$
$173$	7.34640	0.558536	0.279268	+	0.960213i	$0.409908\pi$
$174$	−5.71366	−0.433151
$175$	−14.4456	−1.09198
$176$	14.7356	1.11074
$177$	11.3145	0.850449
$178$	−24.5505	−1.84014
$179$	−12.8612	−0.961295	−0.480647	−	0.876914i	$-0.659598\pi$
$179$	−12.8612	−0.961295	−0.480647	+	0.876914i	$0.659598\pi$
$180$	6.12670	0.456657
$181$	−14.3233	−1.06464	−0.532321	−	0.846543i	$-0.678680\pi$
$181$	−14.3233	−1.06464	−0.532321	+	0.846543i	$0.678680\pi$
$182$	−25.2483	−1.87153
$183$	10.6972	0.790761
$184$	−1.01590	−0.0748928
$185$	−14.0872	−1.03571
$186$	−9.31272	−0.682841
$187$	7.75938	0.567422
$188$	8.01173	0.584315
$189$	2.72854	0.198472
$190$	−24.1201	−1.74986
$191$	−2.78355	−0.201411	−0.100705	−	0.994916i	$-0.532110\pi$
$191$	−2.78355	−0.201411	−0.100705	+	0.994916i	$0.532110\pi$
$192$	7.26071	0.523997
$193$	−10.9664	−0.789381	−0.394690	−	0.918814i	$-0.629148\pi$
$193$	−10.9664	−0.789381	−0.394690	+	0.918814i	$0.629148\pi$
$194$	−26.6040	−1.91005
$195$	15.0154	1.07528
$196$	0.849618	0.0606870
$197$	13.0910	0.932692	0.466346	−	0.884602i	$-0.345570\pi$
$197$	13.0910	0.932692	0.466346	+	0.884602i	$0.345570\pi$
$198$	6.98249	0.496224
$199$	−18.4409	−1.30724	−0.653622	−	0.756821i	$-0.726751\pi$
$199$	−18.4409	−1.30724	−0.653622	+	0.756821i	$0.726751\pi$
$200$	0.946922	0.0669575
$201$	−3.49968	−0.246848
$202$	−8.94175	−0.629139
$203$	7.88464	0.553393
$204$	4.19574	0.293761
$205$	−39.8728	−2.78484
$206$	−6.28768	−0.438084
$207$	−5.67988	−0.394779
$208$	19.5281	1.35403
$209$	−13.4266	−0.928738
$210$	−17.3097	−1.19449
$211$	−3.34004	−0.229938	−0.114969	−	0.993369i	$-0.536677\pi$
$211$	−3.34004	−0.229938	−0.114969	+	0.993369i	$0.536677\pi$
$212$	−19.9024	−1.36690
$213$	−11.7358	−0.804124
$214$	19.4491	1.32951
$215$	21.8826	1.49238
$216$	−0.178858	−0.0121698
$217$	12.8512	0.872397
$218$	37.0704	2.51072
$219$	−6.36021	−0.429783
$220$	−21.6359	−1.45869
$221$	10.2830	0.691708
$222$	−8.68140	−0.582657
$223$	22.1755	1.48498	0.742490	−	0.669857i	$-0.233645\pi$
$223$	22.1755	1.48498	0.742490	+	0.669857i	$0.233645\pi$
$224$	−21.5359	−1.43893
$225$	5.29425	0.352950
$226$	−24.2593	−1.61370
$227$	3.19271	0.211907	0.105954	−	0.994371i	$-0.466210\pi$
$227$	3.19271	0.211907	0.105954	+	0.994371i	$0.466210\pi$
$228$	−7.26019	−0.480818
$229$	−11.8301	−0.781757	−0.390879	−	0.920442i	$-0.627829\pi$
$229$	−11.8301	−0.781757	−0.390879	+	0.920442i	$0.627829\pi$
$230$	36.0329	2.37594
$231$	−9.63558	−0.633975
$232$	−0.516846	−0.0339326
$233$	−11.6889	−0.765764	−0.382882	−	0.923797i	$-0.625068\pi$
$233$	−11.6889	−0.765764	−0.382882	+	0.923797i	$0.625068\pi$
$234$	9.25342	0.604915
$235$	13.4615	0.878133
$236$	−21.6055	−1.40640
$237$	−9.11059	−0.591796
$238$	−11.8542	−0.768395
$239$	20.6990	1.33890	0.669452	−	0.742855i	$-0.266529\pi$
$239$	20.6990	1.33890	0.669452	+	0.742855i	$0.266529\pi$
$240$	13.3881	0.864196
$241$	12.9797	0.836093	0.418046	−	0.908426i	$-0.362715\pi$
$241$	12.9797	0.836093	0.418046	+	0.908426i	$0.362715\pi$
$242$	−2.90820	−0.186946
$243$	−1.00000	−0.0641500
$244$	−20.4268	−1.30769
$245$	1.42755	0.0912029
$246$	−24.5721	−1.56666
$247$	−17.7934	−1.13217
$248$	−0.842409	−0.0534930
$249$	−15.4776	−0.980850
$250$	−1.86673	−0.118062
$251$	2.14699	0.135516	0.0677582	−	0.997702i	$-0.478415\pi$
$251$	2.14699	0.135516	0.0677582	+	0.997702i	$0.478415\pi$
$252$	−5.21026	−0.328216
$253$	20.0580	1.26103
$254$	8.08552	0.507331
$255$	7.04980	0.441476
$256$	17.3477	1.08423
$257$	−7.34450	−0.458137	−0.229069	−	0.973410i	$-0.573568\pi$
$257$	−7.34450	−0.458137	−0.229069	+	0.973410i	$0.573568\pi$
$258$	13.4854	0.839565
$259$	11.9800	0.744401
$260$	−28.6725	−1.77820
$261$	−2.88969	−0.178867
$262$	−28.6166	−1.76794
$263$	1.47708	0.0910809	0.0455404	−	0.998962i	$-0.485499\pi$
$263$	1.47708	0.0910809	0.0455404	+	0.998962i	$0.485499\pi$
$264$	0.631622	0.0388736
$265$	−33.4405	−2.05424
$266$	20.5122	1.25768
$267$	−12.4164	−0.759874
$268$	6.68278	0.408216
$269$	−9.02054	−0.549992	−0.274996	−	0.961445i	$-0.588677\pi$
$269$	−9.02054	−0.549992	−0.274996	+	0.961445i	$0.588677\pi$
$270$	6.34396	0.386081
$271$	10.1668	0.617586	0.308793	−	0.951129i	$-0.400075\pi$
$271$	10.1668	0.617586	0.308793	+	0.951129i	$0.400075\pi$
$272$	9.16854	0.555924
$273$	−12.7694	−0.772838
$274$	−23.9829	−1.44886
$275$	−18.6962	−1.12742
$276$	10.8460	0.652851
$277$	0.360925	0.0216859	0.0108429	−	0.999941i	$-0.496549\pi$
$277$	0.360925	0.0216859	0.0108429	+	0.999941i	$0.496549\pi$
$278$	13.7270	0.823291
$279$	−4.70992	−0.281975
$280$	−1.56580	−0.0935747
$281$	−1.12092	−0.0668682	−0.0334341	−	0.999441i	$-0.510644\pi$
$281$	−1.12092	−0.0668682	−0.0334341	+	0.999441i	$0.510644\pi$
$282$	8.29583	0.494009
$283$	−25.9783	−1.54425	−0.772124	−	0.635472i	$-0.780806\pi$
$283$	−25.9783	−1.54425	−0.772124	+	0.635472i	$0.780806\pi$
$284$	22.4100	1.32979
$285$	−12.1988	−0.722593
$286$	−32.6776	−1.93227
$287$	33.9086	2.00156
$288$	7.89285	0.465090
$289$	−12.1721	−0.716005
$290$	18.3321	1.07650
$291$	−13.4550	−0.788745
$292$	12.1451	0.710738
$293$	7.08154	0.413708	0.206854	−	0.978372i	$-0.433677\pi$
$293$	7.08154	0.413708	0.206854	+	0.978372i	$0.433677\pi$
$294$	0.879746	0.0513078
$295$	−36.3021	−2.11359
$296$	−0.785301	−0.0456447
$297$	3.53141	0.204913
$298$	2.39734	0.138874
$299$	26.5815	1.53725
$300$	−10.1096	−0.583678
$301$	−18.6094	−1.07263
$302$	−21.9826	−1.26496
$303$	−4.52230	−0.259800
$304$	−15.8650	−0.909919
$305$	−34.3216	−1.96525
$306$	4.34453	0.248360
$307$	−4.33340	−0.247320	−0.123660	−	0.992325i	$-0.539463\pi$
$307$	−4.33340	−0.247320	−0.123660	+	0.992325i	$0.539463\pi$
$308$	18.3996	1.04841
$309$	−3.18000	−0.180904
$310$	29.8795	1.69704
$311$	−16.9811	−0.962912	−0.481456	−	0.876470i	$-0.659892\pi$
$311$	−16.9811	−0.962912	−0.481456	+	0.876470i	$0.659892\pi$
$312$	0.837045	0.0473884
$313$	−12.1375	−0.686054	−0.343027	−	0.939326i	$-0.611452\pi$
$313$	−12.1375	−0.686054	−0.343027	+	0.939326i	$0.611452\pi$
$314$	−37.0154	−2.08890
$315$	−8.75443	−0.493256
$316$	17.3970	0.978660
$317$	−12.0359	−0.676002	−0.338001	−	0.941146i	$-0.609751\pi$
$317$	−12.0359	−0.676002	−0.338001	+	0.941146i	$0.609751\pi$
$318$	−20.6081	−1.15565
$319$	10.2047	0.571352
$320$	−23.2957	−1.30227
$321$	9.83638	0.549013
$322$	−30.6431	−1.70767
$323$	−8.35408	−0.464833
$324$	1.90954	0.106086
$325$	−24.7767	−1.37437
$326$	16.1037	0.891901
$327$	18.7484	1.03679
$328$	−2.22274	−0.122730
$329$	−11.4479	−0.631145
$330$	−22.4031	−1.23325
$331$	8.13170	0.446958	0.223479	−	0.974709i	$-0.428259\pi$
$331$	8.13170	0.446958	0.223479	+	0.974709i	$0.428259\pi$
$332$	29.5550	1.62204
$333$	−4.39063	−0.240605
$334$	−37.5465	−2.05445
$335$	11.2286	0.613484
$336$	−11.3855	−0.621128
$337$	11.1755	0.608769	0.304384	−	0.952549i	$-0.401549\pi$
$337$	11.1755	0.608769	0.304384	+	0.952549i	$0.401549\pi$
$338$	−17.6011	−0.957372
$339$	−12.2691	−0.666369
$340$	−13.4619	−0.730074
$341$	16.6326	0.900708
$342$	−7.51764	−0.406508
$343$	17.8858	0.965741
$344$	1.21986	0.0657705
$345$	18.2237	0.981132
$346$	−14.5257	−0.780907
$347$	19.8404	1.06509	0.532544	−	0.846402i	$-0.321236\pi$
$347$	19.8404	1.06509	0.532544	+	0.846402i	$0.321236\pi$
$348$	5.51798	0.295795
$349$	20.7490	1.11067	0.555334	−	0.831627i	$-0.312590\pi$
$349$	20.7490	1.11067	0.555334	+	0.831627i	$0.312590\pi$
$350$	28.5626	1.52674
$351$	4.67993	0.249796
$352$	−27.8728	−1.48563
$353$	−1.73897	−0.0925562	−0.0462781	−	0.998929i	$-0.514736\pi$
$353$	−1.73897	−0.0925562	−0.0462781	+	0.998929i	$0.514736\pi$
$354$	−22.3716	−1.18904
$355$	37.6539	1.99846
$356$	23.7097	1.25661
$357$	−5.99529	−0.317304
$358$	25.4300	1.34402
$359$	16.1188	0.850716	0.425358	−	0.905025i	$-0.360148\pi$
$359$	16.1188	0.850716	0.425358	+	0.905025i	$0.360148\pi$
$360$	0.573861	0.0302451
$361$	−4.54436	−0.239177
$362$	28.3208	1.48851
$363$	−1.47083	−0.0771985
$364$	24.3837	1.27805
$365$	20.4065	1.06813
$366$	−21.1511	−1.10559
$367$	21.9163	1.14402	0.572010	−	0.820247i	$-0.306164\pi$
$367$	21.9163	1.14402	0.572010	+	0.820247i	$0.306164\pi$
$368$	23.7006	1.23548
$369$	−12.4274	−0.646944
$370$	27.8540	1.44806
$371$	28.4385	1.47645
$372$	8.99379	0.466306
$373$	26.9229	1.39402	0.697008	−	0.717064i	$-0.254514\pi$
$373$	26.9229	1.39402	0.697008	+	0.717064i	$0.254514\pi$
$374$	−15.3423	−0.793331
$375$	−0.944102	−0.0487532
$376$	0.750423	0.0387001
$377$	13.5236	0.696498
$378$	−5.39502	−0.277490
$379$	−9.93932	−0.510548	−0.255274	−	0.966869i	$-0.582166\pi$
$379$	−9.93932	−0.510548	−0.255274	+	0.966869i	$0.582166\pi$
$380$	23.2941	1.19496
$381$	4.08926	0.209499
$382$	5.50380	0.281599
$383$	−16.5837	−0.847388	−0.423694	−	0.905805i	$-0.639267\pi$
$383$	−16.5837	−0.847388	−0.423694	+	0.905805i	$0.639267\pi$
$384$	1.42940	0.0729440
$385$	30.9154	1.57560
$386$	21.6834	1.10366
$387$	6.82026	0.346693
$388$	25.6929	1.30436
$389$	11.8172	0.599155	0.299577	−	0.954072i	$-0.403154\pi$
$389$	11.8172	0.599155	0.299577	+	0.954072i	$0.403154\pi$
$390$	−29.6893	−1.50338
$391$	12.4801	0.631147
$392$	0.0795800	0.00401940
$393$	−14.4729	−0.730061
$394$	−25.8842	−1.30403
$395$	29.2310	1.47077
$396$	−6.74337	−0.338867
$397$	−28.5549	−1.43313	−0.716566	−	0.697520i	$-0.754287\pi$
$397$	−28.5549	−1.43313	−0.716566	+	0.697520i	$0.754287\pi$
$398$	36.4625	1.82770
$399$	10.3741	0.519353
$400$	−22.0915	−1.10458
$401$	−11.1919	−0.558896	−0.279448	−	0.960161i	$-0.590152\pi$
$401$	−11.1919	−0.558896	−0.279448	+	0.960161i	$0.590152\pi$
$402$	6.91976	0.345126
$403$	22.0421	1.09800
$404$	8.63553	0.429634
$405$	3.20847	0.159430
$406$	−15.5899	−0.773716
$407$	15.5051	0.768559
$408$	0.392997	0.0194562
$409$	−26.4354	−1.30715	−0.653574	−	0.756862i	$-0.726731\pi$
$409$	−26.4354	−1.30715	−0.653574	+	0.756862i	$0.726731\pi$
$410$	78.8388	3.89357
$411$	−12.1294	−0.598299
$412$	6.07235	0.299163
$413$	30.8720	1.51911
$414$	11.2306	0.551953
$415$	49.6592	2.43768
$416$	−36.9380	−1.81103
$417$	6.94245	0.339973
$418$	26.5478	1.29850
$419$	−7.82780	−0.382413	−0.191206	−	0.981550i	$-0.561240\pi$
$419$	−7.82780	−0.382413	−0.191206	+	0.981550i	$0.561240\pi$
$420$	16.7170	0.815704
$421$	5.59275	0.272574	0.136287	−	0.990669i	$-0.456483\pi$
$421$	5.59275	0.272574	0.136287	+	0.990669i	$0.456483\pi$
$422$	6.60411	0.321483
$423$	4.19563	0.203998
$424$	−1.86417	−0.0905321
$425$	−11.6328	−0.564274
$426$	23.2047	1.12427
$427$	29.1878	1.41250
$428$	−18.7830	−0.907910
$429$	−16.5267	−0.797919
$430$	−43.2675	−2.08654
$431$	−34.5706	−1.66521	−0.832603	−	0.553870i	$-0.813151\pi$
$431$	−34.5706	−1.66521	−0.832603	+	0.553870i	$0.813151\pi$
$432$	4.17273	0.200761
$433$	5.32865	0.256078	0.128039	−	0.991769i	$-0.459132\pi$
$433$	5.32865	0.256078	0.128039	+	0.991769i	$0.459132\pi$
$434$	−25.4101	−1.21972
$435$	9.27147	0.444533
$436$	−35.8008	−1.71455
$437$	−21.5952	−1.03304
$438$	12.5758	0.600894
$439$	−22.6504	−1.08105	−0.540523	−	0.841329i	$-0.681774\pi$
$439$	−22.6504	−1.08105	−0.540523	+	0.841329i	$0.681774\pi$
$440$	−2.02654	−0.0966114
$441$	0.444933	0.0211873
$442$	−20.3321	−0.967099
$443$	−34.2200	−1.62584	−0.812919	−	0.582376i	$-0.802123\pi$
$443$	−34.2200	−1.62584	−0.812919	+	0.582376i	$0.802123\pi$
$444$	8.38409	0.397891
$445$	39.8377	1.88849
$446$	−43.8466	−2.07620
$447$	1.21246	0.0573473
$448$	19.8111	0.935989
$449$	−24.4435	−1.15356	−0.576779	−	0.816900i	$-0.695691\pi$
$449$	−24.4435	−1.15356	−0.576779	+	0.816900i	$0.695691\pi$
$450$	−10.4681	−0.493471
$451$	43.8861	2.06652
$452$	23.4285	1.10198
$453$	−11.1177	−0.522357
$454$	−6.31280	−0.296274
$455$	40.9701	1.92071
$456$	−0.680030	−0.0318453
$457$	−2.81615	−0.131734	−0.0658669	−	0.997828i	$-0.520981\pi$
$457$	−2.81615	−0.131734	−0.0658669	+	0.997828i	$0.520981\pi$
$458$	23.3912	1.09300
$459$	2.19725	0.102559
$460$	−34.7989	−1.62251
$461$	30.3479	1.41344	0.706721	−	0.707492i	$-0.250173\pi$
$461$	30.3479	1.41344	0.706721	+	0.707492i	$0.250173\pi$
$462$	19.0520	0.886380
$463$	−18.1922	−0.845464	−0.422732	−	0.906255i	$-0.638929\pi$
$463$	−18.1922	−0.845464	−0.422732	+	0.906255i	$0.638929\pi$
$464$	12.0579	0.559774
$465$	15.1116	0.700784
$466$	23.1119	1.07064
$467$	41.8134	1.93489	0.967447	−	0.253075i	$-0.0814420\pi$
$467$	41.8134	1.93489	0.967447	+	0.253075i	$0.0814420\pi$
$468$	−8.93653	−0.413091
$469$	−9.54901	−0.440932
$470$	−26.6169	−1.22775
$471$	−18.7206	−0.862600
$472$	−2.02369	−0.0931479
$473$	−24.0851	−1.10743
$474$	18.0140	0.827409
$475$	20.1291	0.923585
$476$	11.4483	0.524730
$477$	−10.4226	−0.477218
$478$	−40.9272	−1.87196
$479$	38.6784	1.76726	0.883630	−	0.468186i	$-0.155092\pi$
$479$	38.6784	1.76726	0.883630	+	0.468186i	$0.155092\pi$
$480$	−25.3239	−1.15587
$481$	20.5478	0.936901
$482$	−25.6641	−1.16897
$483$	−15.4978	−0.705174
$484$	2.80861	0.127664
$485$	43.1699	1.96024
$486$	1.97726	0.0896902
$487$	6.26622	0.283949	0.141975	−	0.989870i	$-0.454655\pi$
$487$	6.26622	0.283949	0.141975	+	0.989870i	$0.454655\pi$
$488$	−1.91329	−0.0866104
$489$	8.14446	0.368305
$490$	−2.82263	−0.127514
$491$	30.4966	1.37629	0.688145	−	0.725573i	$-0.258425\pi$
$491$	30.4966	1.37629	0.688145	+	0.725573i	$0.258425\pi$
$492$	23.7306	1.06986
$493$	6.34937	0.285961
$494$	35.1821	1.58292
$495$	−11.3304	−0.509263
$496$	19.6532	0.882456
$497$	−32.0216	−1.43637
$498$	30.6031	1.37136
$499$	27.2834	1.22137	0.610686	−	0.791873i	$-0.290894\pi$
$499$	27.2834	1.22137	0.610686	+	0.791873i	$0.290894\pi$
$500$	1.80280	0.0806238
$501$	−18.9892	−0.848374
$502$	−4.24514	−0.189470
$503$	22.9149	1.02173	0.510864	−	0.859662i	$-0.329326\pi$
$503$	22.9149	1.02173	0.510864	+	0.859662i	$0.329326\pi$
$504$	−0.488023	−0.0217383
$505$	14.5097	0.645671
$506$	−39.6597	−1.76309
$507$	−8.90176	−0.395341
$508$	−7.80862	−0.346451
$509$	−31.7901	−1.40907	−0.704537	−	0.709667i	$-0.748845\pi$
$509$	−31.7901	−1.40907	−0.704537	+	0.709667i	$0.748845\pi$
$510$	−13.9393	−0.617241
$511$	−17.3541	−0.767700
$512$	−31.4421	−1.38956
$513$	−3.80206	−0.167865
$514$	14.5220	0.640536
$515$	10.2029	0.449595
$516$	−13.0236	−0.573331
$517$	−14.8165	−0.651627
$518$	−23.6875	−1.04077
$519$	−7.34640	−0.322471
$520$	−2.68563	−0.117773
$521$	31.7790	1.39226	0.696132	−	0.717914i	$-0.254903\pi$
$521$	31.7790	1.39226	0.696132	+	0.717914i	$0.254903\pi$
$522$	5.71366	0.250080
$523$	−20.4250	−0.893124	−0.446562	−	0.894753i	$-0.647352\pi$
$523$	−20.4250	−0.893124	−0.446562	+	0.894753i	$0.647352\pi$
$524$	27.6366	1.20731
$525$	14.4456	0.630457
$526$	−2.92057	−0.127343
$527$	10.3489	0.450804
$528$	−14.7356	−0.641285
$529$	9.26107	0.402655
$530$	66.1205	2.87209
$531$	−11.3145	−0.491007
$532$	−19.8097	−0.858860
$533$	58.1593	2.51916
$534$	24.5505	1.06240
$535$	−31.5597	−1.36444
$536$	0.625947	0.0270368
$537$	12.8612	0.555004
$538$	17.8359	0.768961
$539$	−1.57124	−0.0676780
$540$	−6.12670	−0.263651
$541$	−8.37332	−0.359997	−0.179999	−	0.983667i	$-0.557609\pi$
$541$	−8.37332	−0.359997	−0.179999	+	0.983667i	$0.557609\pi$
$542$	−20.1023	−0.863467
$543$	14.3233	0.614671
$544$	−17.3426	−0.743556
$545$	−60.1536	−2.57670
$546$	25.2483	1.08053
$547$	11.8370	0.506112	0.253056	−	0.967452i	$-0.418564\pi$
$547$	11.8370	0.506112	0.253056	+	0.967452i	$0.418564\pi$
$548$	23.1616	0.989414
$549$	−10.6972	−0.456546
$550$	36.9671	1.57628
$551$	−10.9868	−0.468052
$552$	1.01590	0.0432394
$553$	−24.8586	−1.05710
$554$	−0.713641	−0.0303197
$555$	14.0872	0.597967
$556$	−13.2569	−0.562218
$557$	26.5512	1.12501	0.562505	−	0.826794i	$-0.309838\pi$
$557$	26.5512	1.12501	0.562505	+	0.826794i	$0.309838\pi$
$558$	9.31272	0.394239
$559$	−31.9184	−1.35000
$560$	36.5299	1.54367
$561$	−7.75938	−0.327601
$562$	2.21634	0.0934905
$563$	−14.5205	−0.611968	−0.305984	−	0.952037i	$-0.598985\pi$
$563$	−14.5205	−0.611968	−0.305984	+	0.952037i	$0.598985\pi$
$564$	−8.01173	−0.337355
$565$	39.3651	1.65610
$566$	51.3657	2.15906
$567$	−2.72854	−0.114588
$568$	2.09905	0.0880741
$569$	38.5275	1.61516	0.807579	−	0.589760i	$-0.200778\pi$
$569$	38.5275	1.61516	0.807579	+	0.589760i	$0.200778\pi$
$570$	24.1201	1.01028
$571$	8.07698	0.338011	0.169005	−	0.985615i	$-0.445944\pi$
$571$	8.07698	0.338011	0.169005	+	0.985615i	$0.445944\pi$
$572$	31.5585	1.31953
$573$	2.78355	0.116285
$574$	−67.0460	−2.79845
$575$	−30.0707	−1.25404
$576$	−7.26071	−0.302530
$577$	−9.36834	−0.390009	−0.195005	−	0.980802i	$-0.562472\pi$
$577$	−9.36834	−0.390009	−0.195005	+	0.980802i	$0.562472\pi$
$578$	24.0673	1.00107
$579$	10.9664	0.455749
$580$	−17.7043	−0.735130
$581$	−42.2311	−1.75204
$582$	26.6040	1.10277
$583$	36.8064	1.52437
$584$	1.13758	0.0470733
$585$	−15.0154	−0.620810
$586$	−14.0020	−0.578418
$587$	14.4404	0.596017	0.298009	−	0.954563i	$-0.403678\pi$
$587$	14.4404	0.596017	0.298009	+	0.954563i	$0.403678\pi$
$588$	−0.849618	−0.0350376
$589$	−17.9074	−0.737861
$590$	71.7786	2.95508
$591$	−13.0910	−0.538490
$592$	18.3209	0.752985
$593$	15.7109	0.645168	0.322584	−	0.946541i	$-0.395448\pi$
$593$	15.7109	0.645168	0.322584	+	0.946541i	$0.395448\pi$
$594$	−6.98249	−0.286495
$595$	19.2357	0.788586
$596$	−2.31524	−0.0948358
$597$	18.4409	0.754737
$598$	−52.5584	−2.14927
$599$	6.41778	0.262223	0.131112	−	0.991368i	$-0.458145\pi$
$599$	6.41778	0.262223	0.131112	+	0.991368i	$0.458145\pi$
$600$	−0.946922	−0.0386579
$601$	−32.9628	−1.34458	−0.672291	−	0.740287i	$-0.734689\pi$
$601$	−32.9628	−1.34458	−0.672291	+	0.740287i	$0.734689\pi$
$602$	36.7955	1.49967
$603$	3.49968	0.142518
$604$	21.2298	0.863827
$605$	4.71910	0.191859
$606$	8.94175	0.363234
$607$	−38.9655	−1.58156	−0.790780	−	0.612101i	$-0.790325\pi$
$607$	−38.9655	−1.58156	−0.790780	+	0.612101i	$0.790325\pi$
$608$	30.0091	1.21703
$609$	−7.88464	−0.319502
$610$	67.8627	2.74768
$611$	−19.6352	−0.794357
$612$	−4.19574	−0.169603
$613$	−37.1259	−1.49950	−0.749750	−	0.661722i	$-0.769826\pi$
$613$	−37.1259	−1.49950	−0.749750	+	0.661722i	$0.769826\pi$
$614$	8.56824	0.345786
$615$	39.8728	1.60783
$616$	1.72341	0.0694380
$617$	−6.53709	−0.263173	−0.131587	−	0.991305i	$-0.542007\pi$
$617$	−6.53709	−0.263173	−0.131587	+	0.991305i	$0.542007\pi$
$618$	6.28768	0.252928
$619$	−12.6955	−0.510275	−0.255137	−	0.966905i	$-0.582121\pi$
$619$	−12.6955	−0.510275	−0.255137	+	0.966905i	$0.582121\pi$
$620$	−28.8563	−1.15890
$621$	5.67988	0.227926
$622$	33.5760	1.34628
$623$	−33.8787	−1.35732
$624$	−19.5281	−0.781750
$625$	−23.4421	−0.937686
$626$	23.9990	0.959193
$627$	13.4266	0.536207
$628$	35.7478	1.42649
$629$	9.64731	0.384663
$630$	17.3097	0.689637
$631$	18.6314	0.741703	0.370852	−	0.928692i	$-0.379066\pi$
$631$	18.6314	0.741703	0.370852	+	0.928692i	$0.379066\pi$
$632$	1.62951	0.0648182
$633$	3.34004	0.132755
$634$	23.7980	0.945139
$635$	−13.1203	−0.520662
$636$	19.9024	0.789181
$637$	−2.08225	−0.0825019
$638$	−20.1772	−0.798825
$639$	11.7358	0.464261
$640$	−4.58619	−0.181285
$641$	−24.2143	−0.956409	−0.478205	−	0.878248i	$-0.658712\pi$
$641$	−24.2143	−0.956409	−0.478205	+	0.878248i	$0.658712\pi$
$642$	−19.4491	−0.767593
$643$	−21.4439	−0.845666	−0.422833	−	0.906208i	$-0.638964\pi$
$643$	−21.4439	−0.845666	−0.422833	+	0.906208i	$0.638964\pi$
$644$	29.5937	1.16615
$645$	−21.8826	−0.861626
$646$	16.5181	0.649898
$647$	40.3998	1.58828	0.794141	−	0.607734i	$-0.207921\pi$
$647$	40.3998	1.58828	0.794141	+	0.607734i	$0.207921\pi$
$648$	0.178858	0.00702622
$649$	39.9560	1.56841
$650$	48.9900	1.92154
$651$	−12.8512	−0.503678
$652$	−15.5522	−0.609071
$653$	−5.73034	−0.224246	−0.112123	−	0.993694i	$-0.535765\pi$
$653$	−5.73034	−0.224246	−0.112123	+	0.993694i	$0.535765\pi$
$654$	−37.0704	−1.44957
$655$	46.4358	1.81440
$656$	51.8562	2.02464
$657$	6.36021	0.248136
$658$	22.6355	0.882424
$659$	21.2631	0.828292	0.414146	−	0.910210i	$-0.364080\pi$
$659$	21.2631	0.828292	0.414146	+	0.910210i	$0.364080\pi$
$660$	21.6359	0.842175
$661$	27.2168	1.05861	0.529305	−	0.848432i	$-0.322453\pi$
$661$	27.2168	1.05861	0.529305	+	0.848432i	$0.322453\pi$
$662$	−16.0784	−0.624907
$663$	−10.2830	−0.399358
$664$	2.76829	0.107431
$665$	−33.2848	−1.29073
$666$	8.68140	0.336397
$667$	16.4131	0.635518
$668$	36.2606	1.40297
$669$	−22.1755	−0.857354
$670$	−22.2018	−0.857731
$671$	37.7762	1.45833
$672$	21.5359	0.830767
$673$	22.1283	0.852984	0.426492	−	0.904491i	$-0.359749\pi$
$673$	22.1283	0.852984	0.426492	+	0.904491i	$0.359749\pi$
$674$	−22.0968	−0.851139
$675$	−5.29425	−0.203776
$676$	16.9983	0.653781
$677$	15.3508	0.589980	0.294990	−	0.955500i	$-0.404684\pi$
$677$	15.3508	0.589980	0.294990	+	0.955500i	$0.404684\pi$
$678$	24.2593	0.931671
$679$	−36.7125	−1.40890
$680$	−1.26092	−0.0483540
$681$	−3.19271	−0.122345
$682$	−32.8870	−1.25931
$683$	−3.60191	−0.137823	−0.0689116	−	0.997623i	$-0.521953\pi$
$683$	−3.60191	−0.137823	−0.0689116	+	0.997623i	$0.521953\pi$
$684$	7.26019	0.277600
$685$	38.9168	1.48693
$686$	−35.3647	−1.35023
$687$	11.8301	0.451348
$688$	−28.4591	−1.08499
$689$	48.7770	1.85826
$690$	−36.0329	−1.37175
$691$	−21.4198	−0.814848	−0.407424	−	0.913239i	$-0.633573\pi$
$691$	−21.4198	−0.814848	−0.407424	+	0.913239i	$0.633573\pi$
$692$	14.0283	0.533274
$693$	9.63558	0.366026
$694$	−39.2296	−1.48913
$695$	−22.2746	−0.844925
$696$	0.516846	0.0195910
$697$	27.3061	1.03429
$698$	−41.0261	−1.55286
$699$	11.6889	0.442114
$700$	−27.5845	−1.04259
$701$	−2.67122	−0.100891	−0.0504453	−	0.998727i	$-0.516064\pi$
$701$	−2.67122	−0.100891	−0.0504453	+	0.998727i	$0.516064\pi$
$702$	−9.25342	−0.349248
$703$	−16.6934	−0.629604
$704$	25.6405	0.966363
$705$	−13.4615	−0.506990
$706$	3.43839	0.129406
$707$	−12.3393	−0.464067
$708$	21.6055	0.811984
$709$	15.9424	0.598731	0.299365	−	0.954139i	$-0.403225\pi$
$709$	15.9424	0.598731	0.299365	+	0.954139i	$0.403225\pi$
$710$	−74.4514	−2.79411
$711$	9.11059	0.341674
$712$	2.22078	0.0832274
$713$	26.7518	1.00186
$714$	11.8542	0.443633
$715$	53.0255	1.98304
$716$	−24.5591	−0.917816
$717$	−20.6990	−0.773017
$718$	−31.8709	−1.18941
$719$	9.49053	0.353937	0.176969	−	0.984216i	$-0.443371\pi$
$719$	9.49053	0.353937	0.176969	+	0.984216i	$0.443371\pi$
$720$	−13.3881	−0.498944
$721$	−8.67677	−0.323140
$722$	8.98536	0.334400
$723$	−12.9797	−0.482718
$724$	−27.3509	−1.01649
$725$	−15.2988	−0.568181
$726$	2.90820	0.107934
$727$	10.1223	0.375415	0.187708	−	0.982225i	$-0.439894\pi$
$727$	10.1223	0.375415	0.187708	+	0.982225i	$0.439894\pi$
$728$	2.28391	0.0846474
$729$	1.00000	0.0370370
$730$	−40.3489	−1.49338
$731$	−14.9858	−0.554271
$732$	20.4268	0.754995
$733$	23.3755	0.863395	0.431697	−	0.902019i	$-0.357915\pi$
$733$	23.3755	0.863395	0.431697	+	0.902019i	$0.357915\pi$
$734$	−43.3341	−1.59949
$735$	−1.42755	−0.0526560
$736$	−44.8304	−1.65247
$737$	−12.3588	−0.455242
$738$	24.5721	0.904512
$739$	16.2094	0.596271	0.298135	−	0.954524i	$-0.403635\pi$
$739$	16.2094	0.596271	0.298135	+	0.954524i	$0.403635\pi$
$740$	−26.9001	−0.988866
$741$	17.7934	0.653656
$742$	−56.2302	−2.06427
$743$	21.6481	0.794193	0.397096	−	0.917777i	$-0.370018\pi$
$743$	21.6481	0.794193	0.397096	+	0.917777i	$0.370018\pi$
$744$	0.842409	0.0308842
$745$	−3.89013	−0.142523
$746$	−53.2335	−1.94902
$747$	15.4776	0.566294
$748$	14.8169	0.541759
$749$	26.8390	0.980675
$750$	1.86673	0.0681634
$751$	19.8253	0.723436	0.361718	−	0.932287i	$-0.382190\pi$
$751$	19.8253	0.723436	0.361718	+	0.932287i	$0.382190\pi$
$752$	−17.5072	−0.638423
$753$	−2.14699	−0.0782405
$754$	−26.7395	−0.973796
$755$	35.6709	1.29820
$756$	5.21026	0.189495
$757$	34.2346	1.24428	0.622139	−	0.782907i	$-0.286264\pi$
$757$	34.2346	1.24428	0.622139	+	0.782907i	$0.286264\pi$
$758$	19.6526	0.713814
$759$	−20.0580	−0.728058
$760$	2.18185	0.0791442
$761$	−2.35806	−0.0854796	−0.0427398	−	0.999086i	$-0.513609\pi$
$761$	−2.35806	−0.0854796	−0.0427398	+	0.999086i	$0.513609\pi$
$762$	−8.08552	−0.292908
$763$	51.1557	1.85196
$764$	−5.31531	−0.192301
$765$	−7.04980	−0.254886
$766$	32.7902	1.18476
$767$	52.9510	1.91195
$768$	−17.3477	−0.625982
$769$	5.61720	0.202561	0.101281	−	0.994858i	$-0.467706\pi$
$769$	5.61720	0.202561	0.101281	+	0.994858i	$0.467706\pi$
$770$	−61.1278	−2.20289
$771$	7.34450	0.264506
$772$	−20.9409	−0.753678
$773$	−5.86659	−0.211007	−0.105503	−	0.994419i	$-0.533645\pi$
$773$	−5.86659	−0.211007	−0.105503	+	0.994419i	$0.533645\pi$
$774$	−13.4854	−0.484723
$775$	−24.9355	−0.895710
$776$	2.40654	0.0863897
$777$	−11.9800	−0.429780
$778$	−23.3656	−0.837697
$779$	−47.2496	−1.69289
$780$	28.6725	1.02664
$781$	−41.4439	−1.48298
$782$	−24.6764	−0.882427
$783$	2.88969	0.103269
$784$	−1.85659	−0.0663066
$785$	60.0644	2.14379
$786$	28.6166	1.02072
$787$	−29.6328	−1.05629	−0.528147	−	0.849153i	$-0.677113\pi$
$787$	−29.6328	−1.05629	−0.528147	+	0.849153i	$0.677113\pi$
$788$	24.9977	0.890507
$789$	−1.47708	−0.0525856
$790$	−57.7972	−2.05633
$791$	−33.4769	−1.19030
$792$	−0.631622	−0.0224437
$793$	50.0622	1.77776
$794$	56.4604	2.00371
$795$	33.4405	1.18601
$796$	−35.2137	−1.24812
$797$	5.22687	0.185145	0.0925726	−	0.995706i	$-0.470491\pi$
$797$	5.22687	0.185145	0.0925726	+	0.995706i	$0.470491\pi$
$798$	−20.5122	−0.726124
$799$	−9.21884	−0.326139
$800$	41.7867	1.47738
$801$	12.4164	0.438713
$802$	22.1292	0.781411
$803$	−22.4605	−0.792614
$804$	−6.68278	−0.235684
$805$	49.7241	1.75255
$806$	−43.5829	−1.53514
$807$	9.02054	0.317538
$808$	0.808852	0.0284553
$809$	−18.6870	−0.657001	−0.328501	−	0.944504i	$-0.606543\pi$
$809$	−18.6870	−0.657001	−0.328501	+	0.944504i	$0.606543\pi$
$810$	−6.34396	−0.222904
$811$	52.4296	1.84105	0.920525	−	0.390683i	$-0.127761\pi$
$811$	52.4296	1.84105	0.920525	+	0.390683i	$0.127761\pi$
$812$	15.0560	0.528364
$813$	−10.1668	−0.356564
$814$	−30.6575	−1.07455
$815$	−26.1312	−0.915337
$816$	−9.16854	−0.320963
$817$	25.9310	0.907212
$818$	52.2696	1.82757
$819$	12.7694	0.446198
$820$	−76.1389	−2.65888
$821$	−21.6939	−0.757122	−0.378561	−	0.925576i	$-0.623581\pi$
$821$	−21.6939	−0.757122	−0.378561	+	0.925576i	$0.623581\pi$
$822$	23.9829	0.836501
$823$	23.7450	0.827697	0.413848	−	0.910346i	$-0.364184\pi$
$823$	23.7450	0.827697	0.413848	+	0.910346i	$0.364184\pi$
$824$	0.568771	0.0198141
$825$	18.6962	0.650917
$826$	−61.0419	−2.12392
$827$	−21.6844	−0.754041	−0.377021	−	0.926205i	$-0.623051\pi$
$827$	−21.6844	−0.754041	−0.377021	+	0.926205i	$0.623051\pi$
$828$	−10.8460	−0.376924
$829$	−12.1385	−0.421588	−0.210794	−	0.977531i	$-0.567605\pi$
$829$	−12.1385	−0.421588	−0.210794	+	0.977531i	$0.567605\pi$
$830$	−98.1890	−3.40819
$831$	−0.360925	−0.0125204
$832$	33.9796	1.17803
$833$	−0.977629	−0.0338728
$834$	−13.7270	−0.475328
$835$	60.9261	2.10844
$836$	−25.6387	−0.886732
$837$	4.70992	0.162799
$838$	15.4776	0.534664
$839$	37.0766	1.28003	0.640013	−	0.768364i	$-0.278929\pi$
$839$	37.0766	1.28003	0.640013	+	0.768364i	$0.278929\pi$
$840$	1.56580	0.0540254
$841$	−20.6497	−0.712058
$842$	−11.0583	−0.381094
$843$	1.12092	0.0386064
$844$	−6.37794	−0.219538
$845$	28.5610	0.982529
$846$	−8.29583	−0.285216
$847$	−4.01321	−0.137896
$848$	43.4907	1.49348
$849$	25.9783	0.891572
$850$	23.0010	0.788929
$851$	24.9383	0.854872
$852$	−22.4100	−0.767754
$853$	13.4294	0.459813	0.229907	−	0.973213i	$-0.426158\pi$
$853$	13.4294	0.459813	0.229907	+	0.973213i	$0.426158\pi$
$854$	−57.7117	−1.97485
$855$	12.1988	0.417189
$856$	−1.75932	−0.0601323
$857$	−39.5297	−1.35031	−0.675154	−	0.737677i	$-0.735923\pi$
$857$	−39.5297	−1.35031	−0.675154	+	0.737677i	$0.735923\pi$
$858$	32.6776	1.11559
$859$	−25.8541	−0.882131	−0.441065	−	0.897475i	$-0.645399\pi$
$859$	−25.8541	−0.882131	−0.441065	+	0.897475i	$0.645399\pi$
$860$	41.7857	1.42488
$861$	−33.9086	−1.15560
$862$	68.3549	2.32818
$863$	39.7910	1.35450	0.677250	−	0.735753i	$-0.263172\pi$
$863$	39.7910	1.35450	0.677250	+	0.735753i	$0.263172\pi$
$864$	−7.89285	−0.268520
$865$	23.5707	0.801427
$866$	−10.5361	−0.358031
$867$	12.1721	0.413386
$868$	24.5399	0.832939
$869$	−32.1732	−1.09140
$870$	−18.3321	−0.621516
$871$	−16.3783	−0.554956
$872$	−3.35331	−0.113557
$873$	13.4550	0.455382
$874$	42.6993	1.44433
$875$	−2.57602	−0.0870854
$876$	−12.1451	−0.410345
$877$	38.4219	1.29742	0.648708	−	0.761037i	$-0.275310\pi$
$877$	38.4219	1.29742	0.648708	+	0.761037i	$0.275310\pi$
$878$	44.7857	1.51144
$879$	−7.08154	−0.238855
$880$	47.2787	1.59377
$881$	−41.0407	−1.38269	−0.691347	−	0.722522i	$-0.742983\pi$
$881$	−41.0407	−1.38269	−0.691347	+	0.722522i	$0.742983\pi$
$882$	−0.879746	−0.0296226
$883$	−12.6523	−0.425785	−0.212892	−	0.977076i	$-0.568288\pi$
$883$	−12.6523	−0.425785	−0.212892	+	0.977076i	$0.568288\pi$
$884$	19.6358	0.660423
$885$	36.3021	1.22028
$886$	67.6616	2.27314
$887$	−35.9148	−1.20590	−0.602951	−	0.797778i	$-0.706008\pi$
$887$	−35.9148	−1.20590	−0.602951	+	0.797778i	$0.706008\pi$
$888$	0.785301	0.0263530
$889$	11.1577	0.374218
$890$	−78.7694	−2.64036
$891$	−3.53141	−0.118307
$892$	42.3450	1.41782
$893$	15.9520	0.533814
$894$	−2.39734	−0.0801790
$895$	−41.2649	−1.37933
$896$	3.90019	0.130296
$897$	−26.5815	−0.887529
$898$	48.3310	1.61283
$899$	13.6102	0.453926
$900$	10.1096	0.336987
$901$	22.9011	0.762945
$902$	−86.7741	−2.88926
$903$	18.6094	0.619281
$904$	2.19444	0.0729860
$905$	−45.9558	−1.52762
$906$	21.9826	0.730323
$907$	−5.74606	−0.190795	−0.0953974	−	0.995439i	$-0.530412\pi$
$907$	−5.74606	−0.190795	−0.0953974	+	0.995439i	$0.530412\pi$
$908$	6.09661	0.202323
$909$	4.52230	0.149995
$910$	−81.0084	−2.68540
$911$	45.5934	1.51058	0.755289	−	0.655392i	$-0.227497\pi$
$911$	45.5934	1.51058	0.755289	+	0.655392i	$0.227497\pi$
$912$	15.8650	0.525342
$913$	−54.6575	−1.80890
$914$	5.56825	0.184181
$915$	34.3216	1.13464
$916$	−22.5901	−0.746399
$917$	−39.4899	−1.30407
$918$	−4.34453	−0.143391
$919$	−16.1294	−0.532059	−0.266030	−	0.963965i	$-0.585712\pi$
$919$	−16.1294	−0.532059	−0.266030	+	0.963965i	$0.585712\pi$
$920$	−3.25946	−0.107461
$921$	4.33340	0.142790
$922$	−60.0056	−1.97618
$923$	−54.9227	−1.80780
$924$	−18.3996	−0.605301
$925$	−23.2451	−0.764294
$926$	35.9707	1.18207
$927$	3.18000	0.104445
$928$	−22.8079	−0.748705
$929$	−34.5314	−1.13294	−0.566469	−	0.824083i	$-0.691691\pi$
$929$	−34.5314	−1.13294	−0.566469	+	0.824083i	$0.691691\pi$
$930$	−29.8795	−0.979788
$931$	1.69166	0.0554419
$932$	−22.3204	−0.731129
$933$	16.9811	0.555937
$934$	−82.6758	−2.70523
$935$	24.8957	0.814177
$936$	−0.837045	−0.0273597
$937$	−42.1607	−1.37733	−0.688665	−	0.725079i	$-0.741803\pi$
$937$	−42.1607	−1.37733	−0.688665	+	0.725079i	$0.741803\pi$
$938$	18.8808	0.616481
$939$	12.1375	0.396093
$940$	25.7053	0.838416
$941$	29.3856	0.957944	0.478972	−	0.877830i	$-0.341009\pi$
$941$	29.3856	0.957944	0.478972	+	0.877830i	$0.341009\pi$
$942$	37.0154	1.20603
$943$	70.5861	2.29860
$944$	47.2123	1.53663
$945$	8.75443	0.284782
$946$	47.6225	1.54834
$947$	42.8251	1.39163	0.695815	−	0.718221i	$-0.255043\pi$
$947$	42.8251	1.39163	0.695815	+	0.718221i	$0.255043\pi$
$948$	−17.3970	−0.565030
$949$	−29.7654	−0.966225
$950$	−39.8003	−1.29129
$951$	12.0359	0.390290
$952$	1.07231	0.0347537
$953$	49.2491	1.59534	0.797668	−	0.603097i	$-0.206067\pi$
$953$	49.2491	1.59534	0.797668	+	0.603097i	$0.206067\pi$
$954$	20.6081	0.667213
$955$	−8.93094	−0.288998
$956$	39.5255	1.27835
$957$	−10.2047	−0.329870
$958$	−76.4770	−2.47086
$959$	−33.0956	−1.06871
$960$	23.2957	0.751867
$961$	−8.81666	−0.284409
$962$	−40.6283	−1.30991
$963$	−9.83638	−0.316973
$964$	24.7852	0.798277
$965$	−35.1854	−1.13266
$966$	30.6431	0.985926
$967$	25.6025	0.823321	0.411661	−	0.911337i	$-0.364949\pi$
$967$	25.6025	0.823321	0.411661	+	0.911337i	$0.364949\pi$
$968$	0.263070	0.00845539
$969$	8.35408	0.268372
$970$	−85.3579	−2.74068
$971$	48.1078	1.54385	0.771927	−	0.635712i	$-0.219293\pi$
$971$	48.1078	1.54385	0.771927	+	0.635712i	$0.219293\pi$
$972$	−1.90954	−0.0612486
$973$	18.9428	0.607277
$974$	−12.3899	−0.396998
$975$	24.7767	0.793491
$976$	44.6366	1.42878
$977$	−12.4227	−0.397436	−0.198718	−	0.980057i	$-0.563678\pi$
$977$	−12.4227	−0.397436	−0.198718	+	0.980057i	$0.563678\pi$
$978$	−16.1037	−0.514939
$979$	−43.8475	−1.40137
$980$	2.72597	0.0870779
$981$	−18.7484	−0.598590
$982$	−60.2995	−1.92423
$983$	−1.12513	−0.0358859	−0.0179430	−	0.999839i	$-0.505712\pi$
$983$	−1.12513	−0.0358859	−0.0179430	+	0.999839i	$0.505712\pi$
$984$	2.22274	0.0708585
$985$	42.0019	1.33829
$986$	−12.5543	−0.399812
$987$	11.4479	0.364392
$988$	−33.9772	−1.08096
$989$	−38.7383	−1.23181
$990$	22.4031	0.712017
$991$	−2.12301	−0.0674397	−0.0337198	−	0.999431i	$-0.510735\pi$
$991$	−2.12301	−0.0674397	−0.0337198	+	0.999431i	$0.510735\pi$
$992$	−37.1747	−1.18030
$993$	−8.13170	−0.258052
$994$	63.3149	2.00823
$995$	−59.1671	−1.87572
$996$	−29.5550	−0.936488
$997$	−41.9655	−1.32906	−0.664531	−	0.747261i	$-0.731369\pi$
$997$	−41.9655	−1.32906	−0.664531	+	0.747261i	$0.731369\pi$
$998$	−53.9462	−1.70764
$999$	4.39063	0.138913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.14	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.14	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.97726 q^{2} -1.00000 q^{3} +1.90954 q^{4} +3.20847 q^{5} +1.97726 q^{6} -2.72854 q^{7} +0.178858 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.97726 q^{2} -1.00000 q^{3} +1.90954 q^{4} +3.20847 q^{5} +1.97726 q^{6} -2.72854 q^{7} +0.178858 q^{8} +1.00000 q^{9} -6.34396 q^{10} -3.53141 q^{11} -1.90954 q^{12} -4.67993 q^{13} +5.39502 q^{14} -3.20847 q^{15} -4.17273 q^{16} -2.19725 q^{17} -1.97726 q^{18} +3.80206 q^{19} +6.12670 q^{20} +2.72854 q^{21} +6.98249 q^{22} -5.67988 q^{23} -0.178858 q^{24} +5.29425 q^{25} +9.25342 q^{26} -1.00000 q^{27} -5.21026 q^{28} -2.88969 q^{29} +6.34396 q^{30} -4.70992 q^{31} +7.89285 q^{32} +3.53141 q^{33} +4.34453 q^{34} -8.75443 q^{35} +1.90954 q^{36} -4.39063 q^{37} -7.51764 q^{38} +4.67993 q^{39} +0.573861 q^{40} -12.4274 q^{41} -5.39502 q^{42} +6.82026 q^{43} -6.74337 q^{44} +3.20847 q^{45} +11.2306 q^{46} +4.19563 q^{47} +4.17273 q^{48} +0.444933 q^{49} -10.4681 q^{50} +2.19725 q^{51} -8.93653 q^{52} -10.4226 q^{53} +1.97726 q^{54} -11.3304 q^{55} -0.488023 q^{56} -3.80206 q^{57} +5.71366 q^{58} -11.3145 q^{59} -6.12670 q^{60} -10.6972 q^{61} +9.31272 q^{62} -2.72854 q^{63} -7.26071 q^{64} -15.0154 q^{65} -6.98249 q^{66} +3.49968 q^{67} -4.19574 q^{68} +5.67988 q^{69} +17.3097 q^{70} +11.7358 q^{71} +0.178858 q^{72} +6.36021 q^{73} +8.68140 q^{74} -5.29425 q^{75} +7.26019 q^{76} +9.63558 q^{77} -9.25342 q^{78} +9.11059 q^{79} -13.3881 q^{80} +1.00000 q^{81} +24.5721 q^{82} +15.4776 q^{83} +5.21026 q^{84} -7.04980 q^{85} -13.4854 q^{86} +2.88969 q^{87} -0.631622 q^{88} +12.4164 q^{89} -6.34396 q^{90} +12.7694 q^{91} -10.8460 q^{92} +4.70992 q^{93} -8.29583 q^{94} +12.1988 q^{95} -7.89285 q^{96} +13.4550 q^{97} -0.879746 q^{98} -3.53141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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