LMFDB - Embedded newform 6015.2.a.i.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09711 q^{2} +1.00000 q^{3} +2.39785 q^{4} +1.00000 q^{5} +2.09711 q^{6} -1.39590 q^{7} +0.834334 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.09711 q^{2} +1.00000 q^{3} +2.39785 q^{4} +1.00000 q^{5} +2.09711 q^{6} -1.39590 q^{7} +0.834334 q^{8} +1.00000 q^{9} +2.09711 q^{10} +3.33655 q^{11} +2.39785 q^{12} +5.70684 q^{13} -2.92736 q^{14} +1.00000 q^{15} -3.04601 q^{16} -2.75237 q^{17} +2.09711 q^{18} -3.13429 q^{19} +2.39785 q^{20} -1.39590 q^{21} +6.99711 q^{22} +6.71527 q^{23} +0.834334 q^{24} +1.00000 q^{25} +11.9678 q^{26} +1.00000 q^{27} -3.34717 q^{28} +3.04198 q^{29} +2.09711 q^{30} +9.55939 q^{31} -8.05648 q^{32} +3.33655 q^{33} -5.77202 q^{34} -1.39590 q^{35} +2.39785 q^{36} -3.65290 q^{37} -6.57293 q^{38} +5.70684 q^{39} +0.834334 q^{40} +3.99625 q^{41} -2.92736 q^{42} +1.58466 q^{43} +8.00056 q^{44} +1.00000 q^{45} +14.0826 q^{46} -10.8980 q^{47} -3.04601 q^{48} -5.05145 q^{49} +2.09711 q^{50} -2.75237 q^{51} +13.6841 q^{52} -5.35865 q^{53} +2.09711 q^{54} +3.33655 q^{55} -1.16465 q^{56} -3.13429 q^{57} +6.37936 q^{58} -3.37253 q^{59} +2.39785 q^{60} +12.1004 q^{61} +20.0470 q^{62} -1.39590 q^{63} -10.8033 q^{64} +5.70684 q^{65} +6.99711 q^{66} +3.88303 q^{67} -6.59978 q^{68} +6.71527 q^{69} -2.92736 q^{70} +11.4524 q^{71} +0.834334 q^{72} -10.1807 q^{73} -7.66052 q^{74} +1.00000 q^{75} -7.51555 q^{76} -4.65751 q^{77} +11.9678 q^{78} +2.46612 q^{79} -3.04601 q^{80} +1.00000 q^{81} +8.38056 q^{82} +5.54255 q^{83} -3.34717 q^{84} -2.75237 q^{85} +3.32319 q^{86} +3.04198 q^{87} +2.78380 q^{88} +14.6937 q^{89} +2.09711 q^{90} -7.96619 q^{91} +16.1022 q^{92} +9.55939 q^{93} -22.8542 q^{94} -3.13429 q^{95} -8.05648 q^{96} -13.5057 q^{97} -10.5934 q^{98} +3.33655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	2.09711	1.48288	0.741439	−	0.671021i	$-0.234144\pi$
$2$	2.09711	1.48288	0.741439	+	0.671021i	$0.234144\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.39785	1.19893
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.09711	0.856140
$7$	−1.39590	−0.527602	−0.263801	−	0.964577i	$-0.584976\pi$
$7$	−1.39590	−0.527602	−0.263801	+	0.964577i	$0.584976\pi$
$8$	0.834334	0.294982
$9$	1.00000	0.333333
$10$	2.09711	0.663163
$11$	3.33655	1.00601	0.503005	−	0.864284i	$-0.332228\pi$
$11$	3.33655	1.00601	0.503005	+	0.864284i	$0.332228\pi$
$12$	2.39785	0.692200
$13$	5.70684	1.58279	0.791396	−	0.611304i	$-0.209355\pi$
$13$	5.70684	1.58279	0.791396	+	0.611304i	$0.209355\pi$
$14$	−2.92736	−0.782369
$15$	1.00000	0.258199
$16$	−3.04601	−0.761504
$17$	−2.75237	−0.667549	−0.333774	−	0.942653i	$-0.608322\pi$
$17$	−2.75237	−0.667549	−0.333774	+	0.942653i	$0.608322\pi$
$18$	2.09711	0.494292
$19$	−3.13429	−0.719055	−0.359527	−	0.933135i	$-0.617062\pi$
$19$	−3.13429	−0.719055	−0.359527	+	0.933135i	$0.617062\pi$
$20$	2.39785	0.536176
$21$	−1.39590	−0.304611
$22$	6.99711	1.49179
$23$	6.71527	1.40023	0.700115	−	0.714030i	$-0.253132\pi$
$23$	6.71527	1.40023	0.700115	+	0.714030i	$0.253132\pi$
$24$	0.834334	0.170308
$25$	1.00000	0.200000
$26$	11.9678	2.34709
$27$	1.00000	0.192450
$28$	−3.34717	−0.632555
$29$	3.04198	0.564882	0.282441	−	0.959285i	$-0.408856\pi$
$29$	3.04198	0.564882	0.282441	+	0.959285i	$0.408856\pi$
$30$	2.09711	0.382877
$31$	9.55939	1.71692	0.858458	−	0.512884i	$-0.171423\pi$
$31$	9.55939	1.71692	0.858458	+	0.512884i	$0.171423\pi$
$32$	−8.05648	−1.42420
$33$	3.33655	0.580820
$34$	−5.77202	−0.989893
$35$	−1.39590	−0.235951
$36$	2.39785	0.399642
$37$	−3.65290	−0.600533	−0.300267	−	0.953855i	$-0.597076\pi$
$37$	−3.65290	−0.600533	−0.300267	+	0.953855i	$0.597076\pi$
$38$	−6.57293	−1.06627
$39$	5.70684	0.913825
$40$	0.834334	0.131920
$41$	3.99625	0.624109	0.312055	−	0.950064i	$-0.398983\pi$
$41$	3.99625	0.624109	0.312055	+	0.950064i	$0.398983\pi$
$42$	−2.92736	−0.451701
$43$	1.58466	0.241658	0.120829	−	0.992673i	$-0.461445\pi$
$43$	1.58466	0.241658	0.120829	+	0.992673i	$0.461445\pi$
$44$	8.00056	1.20613
$45$	1.00000	0.149071
$46$	14.0826	2.07637
$47$	−10.8980	−1.58963	−0.794817	−	0.606849i	$-0.792433\pi$
$47$	−10.8980	−1.58963	−0.794817	+	0.606849i	$0.792433\pi$
$48$	−3.04601	−0.439654
$49$	−5.05145	−0.721636
$50$	2.09711	0.296575
$51$	−2.75237	−0.385409
$52$	13.6841	1.89765
$53$	−5.35865	−0.736067	−0.368033	−	0.929813i	$-0.619969\pi$
$53$	−5.35865	−0.736067	−0.368033	+	0.929813i	$0.619969\pi$
$54$	2.09711	0.285380
$55$	3.33655	0.449901
$56$	−1.16465	−0.155633
$57$	−3.13429	−0.415147
$58$	6.37936	0.837651
$59$	−3.37253	−0.439066	−0.219533	−	0.975605i	$-0.570453\pi$
$59$	−3.37253	−0.439066	−0.219533	+	0.975605i	$0.570453\pi$
$60$	2.39785	0.309561
$61$	12.1004	1.54930	0.774648	−	0.632393i	$-0.217927\pi$
$61$	12.1004	1.54930	0.774648	+	0.632393i	$0.217927\pi$
$62$	20.0470	2.54598
$63$	−1.39590	−0.175867
$64$	−10.8033	−1.35041
$65$	5.70684	0.707846
$66$	6.99711	0.861284
$67$	3.88303	0.474387	0.237194	−	0.971462i	$-0.423772\pi$
$67$	3.88303	0.474387	0.237194	+	0.971462i	$0.423772\pi$
$68$	−6.59978	−0.800341
$69$	6.71527	0.808424
$70$	−2.92736	−0.349886
$71$	11.4524	1.35914	0.679572	−	0.733608i	$-0.262165\pi$
$71$	11.4524	1.35914	0.679572	+	0.733608i	$0.262165\pi$
$72$	0.834334	0.0983272
$73$	−10.1807	−1.19156	−0.595778	−	0.803149i	$-0.703156\pi$
$73$	−10.1807	−1.19156	−0.595778	+	0.803149i	$0.703156\pi$
$74$	−7.66052	−0.890517
$75$	1.00000	0.115470
$76$	−7.51555	−0.862093
$77$	−4.65751	−0.530772
$78$	11.9678	1.35509
$79$	2.46612	0.277460	0.138730	−	0.990330i	$-0.455698\pi$
$79$	2.46612	0.277460	0.138730	+	0.990330i	$0.455698\pi$
$80$	−3.04601	−0.340555
$81$	1.00000	0.111111
$82$	8.38056	0.925478
$83$	5.54255	0.608374	0.304187	−	0.952612i	$-0.401615\pi$
$83$	5.54255	0.608374	0.304187	+	0.952612i	$0.401615\pi$
$84$	−3.34717	−0.365206
$85$	−2.75237	−0.298537
$86$	3.32319	0.358349
$87$	3.04198	0.326135
$88$	2.78380	0.296754
$89$	14.6937	1.55753	0.778765	−	0.627316i	$-0.215846\pi$
$89$	14.6937	1.55753	0.778765	+	0.627316i	$0.215846\pi$
$90$	2.09711	0.221054
$91$	−7.96619	−0.835084
$92$	16.1022	1.67877
$93$	9.55939	0.991262
$94$	−22.8542	−2.35723
$95$	−3.13429	−0.321571
$96$	−8.05648	−0.822261
$97$	−13.5057	−1.37130	−0.685648	−	0.727933i	$-0.740481\pi$
$97$	−13.5057	−1.37130	−0.685648	+	0.727933i	$0.740481\pi$
$98$	−10.5934	−1.07010
$99$	3.33655	0.335336
$100$	2.39785	0.239785
$101$	8.12577	0.808544	0.404272	−	0.914639i	$-0.367525\pi$
$101$	8.12577	0.808544	0.404272	+	0.914639i	$0.367525\pi$
$102$	−5.77202	−0.571515
$103$	8.60867	0.848238	0.424119	−	0.905607i	$-0.360584\pi$
$103$	8.60867	0.848238	0.424119	+	0.905607i	$0.360584\pi$
$104$	4.76141	0.466894
$105$	−1.39590	−0.136226
$106$	−11.2376	−1.09150
$107$	−4.05643	−0.392150	−0.196075	−	0.980589i	$-0.562820\pi$
$107$	−4.05643	−0.392150	−0.196075	+	0.980589i	$0.562820\pi$
$108$	2.39785	0.230733
$109$	4.49829	0.430858	0.215429	−	0.976520i	$-0.430885\pi$
$109$	4.49829	0.430858	0.215429	+	0.976520i	$0.430885\pi$
$110$	6.99711	0.667148
$111$	−3.65290	−0.346718
$112$	4.25194	0.401771
$113$	0.304920	0.0286845	0.0143422	−	0.999897i	$-0.495435\pi$
$113$	0.304920	0.0286845	0.0143422	+	0.999897i	$0.495435\pi$
$114$	−6.57293	−0.615611
$115$	6.71527	0.626202
$116$	7.29422	0.677251
$117$	5.70684	0.527597
$118$	−7.07255	−0.651081
$119$	3.84205	0.352200
$120$	0.834334	0.0761639
$121$	0.132597	0.0120543
$122$	25.3758	2.29742
$123$	3.99625	0.360330
$124$	22.9220	2.05845
$125$	1.00000	0.0894427
$126$	−2.92736	−0.260790
$127$	15.3911	1.36574	0.682871	−	0.730539i	$-0.260731\pi$
$127$	15.3911	1.36574	0.682871	+	0.730539i	$0.260731\pi$
$128$	−6.54261	−0.578290
$129$	1.58466	0.139521
$130$	11.9678	1.04965
$131$	−11.1367	−0.973020	−0.486510	−	0.873675i	$-0.661730\pi$
$131$	−11.1367	−0.973020	−0.486510	+	0.873675i	$0.661730\pi$
$132$	8.00056	0.696359
$133$	4.37516	0.379375
$134$	8.14312	0.703458
$135$	1.00000	0.0860663
$136$	−2.29640	−0.196915
$137$	−13.9497	−1.19180	−0.595900	−	0.803059i	$-0.703204\pi$
$137$	−13.9497	−1.19180	−0.595900	+	0.803059i	$0.703204\pi$
$138$	14.0826	1.19879
$139$	−3.93585	−0.333835	−0.166917	−	0.985971i	$-0.553381\pi$
$139$	−3.93585	−0.333835	−0.166917	+	0.985971i	$0.553381\pi$
$140$	−3.34717	−0.282887
$141$	−10.8980	−0.917776
$142$	24.0168	2.01544
$143$	19.0412	1.59230
$144$	−3.04601	−0.253835
$145$	3.04198	0.252623
$146$	−21.3499	−1.76693
$147$	−5.05145	−0.416637
$148$	−8.75911	−0.719995
$149$	6.59923	0.540630	0.270315	−	0.962772i	$-0.412872\pi$
$149$	6.59923	0.540630	0.270315	+	0.962772i	$0.412872\pi$
$150$	2.09711	0.171228
$151$	3.22161	0.262171	0.131086	−	0.991371i	$-0.458154\pi$
$151$	3.22161	0.262171	0.131086	+	0.991371i	$0.458154\pi$
$152$	−2.61504	−0.212108
$153$	−2.75237	−0.222516
$154$	−9.76729	−0.787070
$155$	9.55939	0.767828
$156$	13.6841	1.09561
$157$	0.441707	0.0352520	0.0176260	−	0.999845i	$-0.494389\pi$
$157$	0.441707	0.0352520	0.0176260	+	0.999845i	$0.494389\pi$
$158$	5.17170	0.411439
$159$	−5.35865	−0.424968
$160$	−8.05648	−0.636921
$161$	−9.37387	−0.738765
$162$	2.09711	0.164764
$163$	−11.1651	−0.874518	−0.437259	−	0.899336i	$-0.644051\pi$
$163$	−11.1651	−0.874518	−0.437259	+	0.899336i	$0.644051\pi$
$164$	9.58241	0.748260
$165$	3.33655	0.259750
$166$	11.6233	0.902143
$167$	13.2465	1.02505	0.512523	−	0.858674i	$-0.328711\pi$
$167$	13.2465	1.02505	0.512523	+	0.858674i	$0.328711\pi$
$168$	−1.16465	−0.0898547
$169$	19.5680	1.50523
$170$	−5.77202	−0.442694
$171$	−3.13429	−0.239685
$172$	3.79977	0.289729
$173$	−11.5841	−0.880725	−0.440363	−	0.897820i	$-0.645150\pi$
$173$	−11.5841	−0.880725	−0.440363	+	0.897820i	$0.645150\pi$
$174$	6.37936	0.483618
$175$	−1.39590	−0.105520
$176$	−10.1632	−0.766080
$177$	−3.37253	−0.253495
$178$	30.8143	2.30963
$179$	−23.3077	−1.74210	−0.871051	−	0.491193i	$-0.836561\pi$
$179$	−23.3077	−1.74210	−0.871051	+	0.491193i	$0.836561\pi$
$180$	2.39785	0.178725
$181$	3.58388	0.266388	0.133194	−	0.991090i	$-0.457477\pi$
$181$	3.58388	0.266388	0.133194	+	0.991090i	$0.457477\pi$
$182$	−16.7059	−1.23833
$183$	12.1004	0.894487
$184$	5.60278	0.413042
$185$	−3.65290	−0.268567
$186$	20.0470	1.46992
$187$	−9.18345	−0.671560
$188$	−26.1317	−1.90585
$189$	−1.39590	−0.101537
$190$	−6.57293	−0.476851
$191$	5.19149	0.375643	0.187821	−	0.982203i	$-0.439857\pi$
$191$	5.19149	0.375643	0.187821	+	0.982203i	$0.439857\pi$
$192$	−10.8033	−0.779658
$193$	0.641238	0.0461573	0.0230787	−	0.999734i	$-0.492653\pi$
$193$	0.641238	0.0461573	0.0230787	+	0.999734i	$0.492653\pi$
$194$	−28.3229	−2.03346
$195$	5.70684	0.408675
$196$	−12.1126	−0.865188
$197$	14.0954	1.00426	0.502130	−	0.864792i	$-0.332550\pi$
$197$	14.0954	1.00426	0.502130	+	0.864792i	$0.332550\pi$
$198$	6.99711	0.497263
$199$	−2.14277	−0.151897	−0.0759483	−	0.997112i	$-0.524198\pi$
$199$	−2.14277	−0.151897	−0.0759483	+	0.997112i	$0.524198\pi$
$200$	0.834334	0.0589963
$201$	3.88303	0.273888
$202$	17.0406	1.19897
$203$	−4.24632	−0.298033
$204$	−6.59978	−0.462077
$205$	3.99625	0.279110
$206$	18.0533	1.25783
$207$	6.71527	0.466744
$208$	−17.3831	−1.20530
$209$	−10.4577	−0.723376
$210$	−2.92736	−0.202007
$211$	−26.2605	−1.80785	−0.903925	−	0.427691i	$-0.859327\pi$
$211$	−26.2605	−1.80785	−0.903925	+	0.427691i	$0.859327\pi$
$212$	−12.8492	−0.882489
$213$	11.4524	0.784703
$214$	−8.50676	−0.581510
$215$	1.58466	0.108073
$216$	0.834334	0.0567692
$217$	−13.3440	−0.905849
$218$	9.43338	0.638909
$219$	−10.1807	−0.687946
$220$	8.00056	0.539398
$221$	−15.7073	−1.05659
$222$	−7.66052	−0.514140
$223$	12.6771	0.848919	0.424459	−	0.905447i	$-0.360464\pi$
$223$	12.6771	0.848919	0.424459	+	0.905447i	$0.360464\pi$
$224$	11.2461	0.751410
$225$	1.00000	0.0666667
$226$	0.639450	0.0425355
$227$	−8.60664	−0.571243	−0.285621	−	0.958343i	$-0.592200\pi$
$227$	−8.60664	−0.571243	−0.285621	+	0.958343i	$0.592200\pi$
$228$	−7.51555	−0.497730
$229$	−5.30237	−0.350391	−0.175195	−	0.984534i	$-0.556056\pi$
$229$	−5.30237	−0.350391	−0.175195	+	0.984534i	$0.556056\pi$
$230$	14.0826	0.928581
$231$	−4.65751	−0.306442
$232$	2.53803	0.166630
$233$	7.58016	0.496593	0.248297	−	0.968684i	$-0.420129\pi$
$233$	7.58016	0.496593	0.248297	+	0.968684i	$0.420129\pi$
$234$	11.9678	0.782362
$235$	−10.8980	−0.710906
$236$	−8.08683	−0.526408
$237$	2.46612	0.160191
$238$	8.05718	0.522270
$239$	−28.3853	−1.83609	−0.918045	−	0.396476i	$-0.870233\pi$
$239$	−28.3853	−1.83609	−0.918045	+	0.396476i	$0.870233\pi$
$240$	−3.04601	−0.196619
$241$	−3.46393	−0.223131	−0.111566	−	0.993757i	$-0.535587\pi$
$241$	−3.46393	−0.223131	−0.111566	+	0.993757i	$0.535587\pi$
$242$	0.278071	0.0178751
$243$	1.00000	0.0641500
$244$	29.0149	1.85749
$245$	−5.05145	−0.322725
$246$	8.38056	0.534325
$247$	−17.8869	−1.13811
$248$	7.97572	0.506459
$249$	5.54255	0.351245
$250$	2.09711	0.132633
$251$	16.3374	1.03121	0.515603	−	0.856828i	$-0.327568\pi$
$251$	16.3374	1.03121	0.515603	+	0.856828i	$0.327568\pi$
$252$	−3.34717	−0.210852
$253$	22.4059	1.40865
$254$	32.2768	2.02523
$255$	−2.75237	−0.172360
$256$	7.88598	0.492874
$257$	11.8715	0.740526	0.370263	−	0.928927i	$-0.379268\pi$
$257$	11.8715	0.740526	0.370263	+	0.928927i	$0.379268\pi$
$258$	3.32319	0.206893
$259$	5.09910	0.316843
$260$	13.6841	0.848654
$261$	3.04198	0.188294
$262$	−23.3549	−1.44287
$263$	−4.04816	−0.249620	−0.124810	−	0.992181i	$-0.539832\pi$
$263$	−4.04816	−0.249620	−0.124810	+	0.992181i	$0.539832\pi$
$264$	2.78380	0.171331
$265$	−5.35865	−0.329179
$266$	9.17518	0.562566
$267$	14.6937	0.899240
$268$	9.31092	0.568755
$269$	−19.3313	−1.17865	−0.589324	−	0.807897i	$-0.700606\pi$
$269$	−19.3313	−1.17865	−0.589324	+	0.807897i	$0.700606\pi$
$270$	2.09711	0.127626
$271$	−12.4957	−0.759061	−0.379531	−	0.925179i	$-0.623915\pi$
$271$	−12.4957	−0.759061	−0.379531	+	0.925179i	$0.623915\pi$
$272$	8.38377	0.508341
$273$	−7.96619	−0.482136
$274$	−29.2539	−1.76729
$275$	3.33655	0.201202
$276$	16.1022	0.969239
$277$	−13.1877	−0.792370	−0.396185	−	0.918171i	$-0.629666\pi$
$277$	−13.1877	−0.792370	−0.396185	+	0.918171i	$0.629666\pi$
$278$	−8.25390	−0.495036
$279$	9.55939	0.572305
$280$	−1.16465	−0.0696011
$281$	−21.5168	−1.28359	−0.641793	−	0.766878i	$-0.721809\pi$
$281$	−21.5168	−1.28359	−0.641793	+	0.766878i	$0.721809\pi$
$282$	−22.8542	−1.36095
$283$	−26.5022	−1.57539	−0.787695	−	0.616065i	$-0.788726\pi$
$283$	−26.5022	−1.57539	−0.787695	+	0.616065i	$0.788726\pi$
$284$	27.4610	1.62951
$285$	−3.13429	−0.185659
$286$	39.9313	2.36119
$287$	−5.57838	−0.329281
$288$	−8.05648	−0.474733
$289$	−9.42444	−0.554379
$290$	6.37936	0.374609
$291$	−13.5057	−0.791718
$292$	−24.4117	−1.42859
$293$	−24.7095	−1.44355	−0.721773	−	0.692130i	$-0.756672\pi$
$293$	−24.7095	−1.44355	−0.721773	+	0.692130i	$0.756672\pi$
$294$	−10.5934	−0.617821
$295$	−3.37253	−0.196356
$296$	−3.04774	−0.177146
$297$	3.33655	0.193607
$298$	13.8393	0.801688
$299$	38.3230	2.21627
$300$	2.39785	0.138440
$301$	−2.21203	−0.127499
$302$	6.75606	0.388768
$303$	8.12577	0.466813
$304$	9.54709	0.547563
$305$	12.1004	0.692866
$306$	−5.77202	−0.329964
$307$	−27.9043	−1.59258	−0.796292	−	0.604913i	$-0.793208\pi$
$307$	−27.9043	−1.59258	−0.796292	+	0.604913i	$0.793208\pi$
$308$	−11.1680	−0.636356
$309$	8.60867	0.489730
$310$	20.0470	1.13860
$311$	−1.34723	−0.0763945	−0.0381973	−	0.999270i	$-0.512162\pi$
$311$	−1.34723	−0.0763945	−0.0381973	+	0.999270i	$0.512162\pi$
$312$	4.76141	0.269562
$313$	15.4100	0.871025	0.435512	−	0.900183i	$-0.356567\pi$
$313$	15.4100	0.871025	0.435512	+	0.900183i	$0.356567\pi$
$314$	0.926305	0.0522744
$315$	−1.39590	−0.0786503
$316$	5.91338	0.332653
$317$	6.82789	0.383492	0.191746	−	0.981445i	$-0.438585\pi$
$317$	6.82789	0.383492	0.191746	+	0.981445i	$0.438585\pi$
$318$	−11.2376	−0.630176
$319$	10.1497	0.568277
$320$	−10.8033	−0.603921
$321$	−4.05643	−0.226408
$322$	−19.6580	−1.09550
$323$	8.62673	0.480004
$324$	2.39785	0.133214
$325$	5.70684	0.316558
$326$	−23.4144	−1.29680
$327$	4.49829	0.248756
$328$	3.33421	0.184101
$329$	15.2125	0.838694
$330$	6.99711	0.385178
$331$	10.8909	0.598617	0.299309	−	0.954156i	$-0.403244\pi$
$331$	10.8909	0.598617	0.299309	+	0.954156i	$0.403244\pi$
$332$	13.2902	0.729394
$333$	−3.65290	−0.200178
$334$	27.7793	1.52002
$335$	3.88303	0.212152
$336$	4.25194	0.231963
$337$	5.88288	0.320461	0.160231	−	0.987080i	$-0.448776\pi$
$337$	5.88288	0.320461	0.160231	+	0.987080i	$0.448776\pi$
$338$	41.0361	2.23207
$339$	0.304920	0.0165610
$340$	−6.59978	−0.357923
$341$	31.8954	1.72723
$342$	−6.57293	−0.355423
$343$	16.8227	0.908339
$344$	1.32213	0.0712846
$345$	6.71527	0.361538
$346$	−24.2931	−1.30601
$347$	7.41352	0.397978	0.198989	−	0.980002i	$-0.436234\pi$
$347$	7.41352	0.397978	0.198989	+	0.980002i	$0.436234\pi$
$348$	7.29422	0.391011
$349$	33.6062	1.79890	0.899449	−	0.437025i	$-0.143968\pi$
$349$	33.6062	1.79890	0.899449	+	0.437025i	$0.143968\pi$
$350$	−2.92736	−0.156474
$351$	5.70684	0.304608
$352$	−26.8809	−1.43276
$353$	−8.23214	−0.438153	−0.219076	−	0.975708i	$-0.570304\pi$
$353$	−8.23214	−0.438153	−0.219076	+	0.975708i	$0.570304\pi$
$354$	−7.07255	−0.375902
$355$	11.4524	0.607828
$356$	35.2333	1.86736
$357$	3.84205	0.203343
$358$	−48.8788	−2.58332
$359$	7.65528	0.404030	0.202015	−	0.979382i	$-0.435251\pi$
$359$	7.65528	0.404030	0.202015	+	0.979382i	$0.435251\pi$
$360$	0.834334	0.0439733
$361$	−9.17624	−0.482960
$362$	7.51577	0.395020
$363$	0.132597	0.00695956
$364$	−19.1017	−1.00120
$365$	−10.1807	−0.532880
$366$	25.3758	1.32641
$367$	−6.81601	−0.355793	−0.177896	−	0.984049i	$-0.556929\pi$
$367$	−6.81601	−0.355793	−0.177896	+	0.984049i	$0.556929\pi$
$368$	−20.4548	−1.06628
$369$	3.99625	0.208036
$370$	−7.66052	−0.398251
$371$	7.48015	0.388350
$372$	22.9220	1.18845
$373$	−8.75838	−0.453492	−0.226746	−	0.973954i	$-0.572809\pi$
$373$	−8.75838	−0.453492	−0.226746	+	0.973954i	$0.572809\pi$
$374$	−19.2587	−0.995841
$375$	1.00000	0.0516398
$376$	−9.09256	−0.468913
$377$	17.3601	0.894091
$378$	−2.92736	−0.150567
$379$	−1.33462	−0.0685548	−0.0342774	−	0.999412i	$-0.510913\pi$
$379$	−1.33462	−0.0685548	−0.0342774	+	0.999412i	$0.510913\pi$
$380$	−7.51555	−0.385540
$381$	15.3911	0.788511
$382$	10.8871	0.557032
$383$	12.1623	0.621466	0.310733	−	0.950497i	$-0.399425\pi$
$383$	12.1623	0.621466	0.310733	+	0.950497i	$0.399425\pi$
$384$	−6.54261	−0.333876
$385$	−4.65751	−0.237369
$386$	1.34474	0.0684457
$387$	1.58466	0.0805526
$388$	−32.3846	−1.64408
$389$	−1.04794	−0.0531329	−0.0265664	−	0.999647i	$-0.508457\pi$
$389$	−1.04794	−0.0531329	−0.0265664	+	0.999647i	$0.508457\pi$
$390$	11.9678	0.606015
$391$	−18.4829	−0.934722
$392$	−4.21460	−0.212869
$393$	−11.1367	−0.561774
$394$	29.5596	1.48919
$395$	2.46612	0.124084
$396$	8.00056	0.402043
$397$	−21.1845	−1.06322	−0.531610	−	0.846989i	$-0.678413\pi$
$397$	−21.1845	−1.06322	−0.531610	+	0.846989i	$0.678413\pi$
$398$	−4.49360	−0.225244
$399$	4.37516	0.219032
$400$	−3.04601	−0.152301
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	8.14312	0.406142
$403$	54.5538	2.71752
$404$	19.4844	0.969384
$405$	1.00000	0.0496904
$406$	−8.90497	−0.441946
$407$	−12.1881	−0.604142
$408$	−2.29640	−0.113689
$409$	3.32899	0.164608	0.0823040	−	0.996607i	$-0.473772\pi$
$409$	3.32899	0.164608	0.0823040	+	0.996607i	$0.473772\pi$
$410$	8.38056	0.413886
$411$	−13.9497	−0.688086
$412$	20.6423	1.01697
$413$	4.70773	0.231652
$414$	14.0826	0.692124
$415$	5.54255	0.272073
$416$	−45.9770	−2.25421
$417$	−3.93585	−0.192740
$418$	−21.9309	−1.07268
$419$	−7.95723	−0.388736	−0.194368	−	0.980929i	$-0.562266\pi$
$419$	−7.95723	−0.388736	−0.194368	+	0.980929i	$0.562266\pi$
$420$	−3.34717	−0.163325
$421$	−20.9015	−1.01868	−0.509339	−	0.860566i	$-0.670110\pi$
$421$	−20.9015	−1.01868	−0.509339	+	0.860566i	$0.670110\pi$
$422$	−55.0711	−2.68082
$423$	−10.8980	−0.529878
$424$	−4.47090	−0.217126
$425$	−2.75237	−0.133510
$426$	24.0168	1.16362
$427$	−16.8910	−0.817412
$428$	−9.72671	−0.470158
$429$	19.0412	0.919316
$430$	3.32319	0.160258
$431$	−21.3269	−1.02728	−0.513639	−	0.858006i	$-0.671703\pi$
$431$	−21.3269	−1.02728	−0.513639	+	0.858006i	$0.671703\pi$
$432$	−3.04601	−0.146551
$433$	−14.3313	−0.688721	−0.344360	−	0.938838i	$-0.611904\pi$
$433$	−14.3313	−0.688721	−0.344360	+	0.938838i	$0.611904\pi$
$434$	−27.9837	−1.34326
$435$	3.04198	0.145852
$436$	10.7862	0.516566
$437$	−21.0476	−1.00684
$438$	−21.3499	−1.02014
$439$	23.4195	1.11775	0.558877	−	0.829251i	$-0.311233\pi$
$439$	23.4195	1.11775	0.558877	+	0.829251i	$0.311233\pi$
$440$	2.78380	0.132712
$441$	−5.05145	−0.240545
$442$	−32.9400	−1.56679
$443$	15.7700	0.749253	0.374627	−	0.927176i	$-0.377771\pi$
$443$	15.7700	0.749253	0.374627	+	0.927176i	$0.377771\pi$
$444$	−8.75911	−0.415689
$445$	14.6937	0.696549
$446$	26.5851	1.25884
$447$	6.59923	0.312133
$448$	15.0803	0.712478
$449$	−21.1739	−0.999259	−0.499629	−	0.866239i	$-0.666530\pi$
$449$	−21.1739	−0.999259	−0.499629	+	0.866239i	$0.666530\pi$
$450$	2.09711	0.0988585
$451$	13.3337	0.627860
$452$	0.731153	0.0343905
$453$	3.22161	0.151365
$454$	−18.0490	−0.847083
$455$	−7.96619	−0.373461
$456$	−2.61504	−0.122461
$457$	0.101559	0.00475071	0.00237536	−	0.999997i	$-0.499244\pi$
$457$	0.101559	0.00475071	0.00237536	+	0.999997i	$0.499244\pi$
$458$	−11.1196	−0.519586
$459$	−2.75237	−0.128470
$460$	16.1022	0.750770
$461$	23.0787	1.07488	0.537441	−	0.843302i	$-0.319391\pi$
$461$	23.0787	1.07488	0.537441	+	0.843302i	$0.319391\pi$
$462$	−9.76729	−0.454415
$463$	−23.7359	−1.10310	−0.551550	−	0.834142i	$-0.685963\pi$
$463$	−23.7359	−1.10310	−0.551550	+	0.834142i	$0.685963\pi$
$464$	−9.26593	−0.430160
$465$	9.55939	0.443306
$466$	15.8964	0.736387
$467$	−14.0303	−0.649244	−0.324622	−	0.945844i	$-0.605237\pi$
$467$	−14.0303	−0.649244	−0.324622	+	0.945844i	$0.605237\pi$
$468$	13.6841	0.632550
$469$	−5.42033	−0.250288
$470$	−22.8542	−1.05419
$471$	0.441707	0.0203528
$472$	−2.81382	−0.129516
$473$	5.28729	0.243110
$474$	5.17170	0.237544
$475$	−3.13429	−0.143811
$476$	9.21266	0.422262
$477$	−5.35865	−0.245356
$478$	−59.5269	−2.72270
$479$	−32.0396	−1.46393	−0.731963	−	0.681344i	$-0.761396\pi$
$479$	−32.0396	−1.46393	−0.731963	+	0.681344i	$0.761396\pi$
$480$	−8.05648	−0.367726
$481$	−20.8465	−0.950519
$482$	−7.26422	−0.330876
$483$	−9.37387	−0.426526
$484$	0.317949	0.0144522
$485$	−13.5057	−0.613262
$486$	2.09711	0.0951266
$487$	−7.89835	−0.357908	−0.178954	−	0.983857i	$-0.557271\pi$
$487$	−7.89835	−0.357908	−0.178954	+	0.983857i	$0.557271\pi$
$488$	10.0958	0.457014
$489$	−11.1651	−0.504903
$490$	−10.5934	−0.478562
$491$	12.4824	0.563324	0.281662	−	0.959514i	$-0.409114\pi$
$491$	12.4824	0.563324	0.281662	+	0.959514i	$0.409114\pi$
$492$	9.58241	0.432008
$493$	−8.37268	−0.377086
$494$	−37.5106	−1.68768
$495$	3.33655	0.149967
$496$	−29.1180	−1.30744
$497$	−15.9864	−0.717088
$498$	11.6233	0.520853
$499$	14.5124	0.649665	0.324832	−	0.945772i	$-0.394692\pi$
$499$	14.5124	0.649665	0.324832	+	0.945772i	$0.394692\pi$
$500$	2.39785	0.107235
$501$	13.2465	0.591810
$502$	34.2612	1.52915
$503$	−41.2987	−1.84142	−0.920710	−	0.390248i	$-0.872389\pi$
$503$	−41.2987	−1.84142	−0.920710	+	0.390248i	$0.872389\pi$
$504$	−1.16465	−0.0518776
$505$	8.12577	0.361592
$506$	46.9875	2.08885
$507$	19.5680	0.869044
$508$	36.9056	1.63742
$509$	0.00842759	0.000373546 0	0.000186773	−	1.00000i	$-0.499941\pi$
$509$	0.00842759	0.000373546 0	0.000186773		1.00000i	$0.499941\pi$
$510$	−5.77202	−0.255589
$511$	14.2112	0.628668
$512$	29.6229	1.30916
$513$	−3.13429	−0.138382
$514$	24.8958	1.09811
$515$	8.60867	0.379343
$516$	3.79977	0.167275
$517$	−36.3617	−1.59919
$518$	10.6933	0.469839
$519$	−11.5841	−0.508487
$520$	4.76141	0.208802
$521$	19.0170	0.833150	0.416575	−	0.909101i	$-0.363230\pi$
$521$	19.0170	0.833150	0.416575	+	0.909101i	$0.363230\pi$
$522$	6.37936	0.279217
$523$	−11.1789	−0.488819	−0.244410	−	0.969672i	$-0.578594\pi$
$523$	−11.1789	−0.488819	−0.244410	+	0.969672i	$0.578594\pi$
$524$	−26.7042	−1.16658
$525$	−1.39590	−0.0609222
$526$	−8.48942	−0.370156
$527$	−26.3110	−1.14613
$528$	−10.1632	−0.442296
$529$	22.0949	0.960646
$530$	−11.2376	−0.488132
$531$	−3.37253	−0.146355
$532$	10.4910	0.454842
$533$	22.8059	0.987835
$534$	30.8143	1.33346
$535$	−4.05643	−0.175375
$536$	3.23974	0.139936
$537$	−23.3077	−1.00580
$538$	−40.5397	−1.74779
$539$	−16.8544	−0.725972
$540$	2.39785	0.103187
$541$	−27.1688	−1.16808	−0.584038	−	0.811726i	$-0.698528\pi$
$541$	−27.1688	−1.16808	−0.584038	+	0.811726i	$0.698528\pi$
$542$	−26.2049	−1.12559
$543$	3.58388	0.153799
$544$	22.1744	0.950722
$545$	4.49829	0.192686
$546$	−16.7059	−0.714949
$547$	−30.5223	−1.30504	−0.652519	−	0.757773i	$-0.726288\pi$
$547$	−30.5223	−1.30504	−0.652519	+	0.757773i	$0.726288\pi$
$548$	−33.4492	−1.42888
$549$	12.1004	0.516432
$550$	6.99711	0.298358
$551$	−9.53445	−0.406181
$552$	5.60278	0.238470
$553$	−3.44246	−0.146388
$554$	−27.6559	−1.17499
$555$	−3.65290	−0.155057
$556$	−9.43759	−0.400243
$557$	11.8973	0.504106	0.252053	−	0.967713i	$-0.418894\pi$
$557$	11.8973	0.504106	0.252053	+	0.967713i	$0.418894\pi$
$558$	20.0470	0.848659
$559$	9.04337	0.382494
$560$	4.25194	0.179677
$561$	−9.18345	−0.387725
$562$	−45.1231	−1.90340
$563$	−28.0362	−1.18159	−0.590793	−	0.806823i	$-0.701185\pi$
$563$	−28.0362	−1.18159	−0.590793	+	0.806823i	$0.701185\pi$
$564$	−26.1317	−1.10034
$565$	0.304920	0.0128281
$566$	−55.5778	−2.33611
$567$	−1.39590	−0.0586224
$568$	9.55509	0.400923
$569$	35.5126	1.48877	0.744383	−	0.667752i	$-0.232744\pi$
$569$	35.5126	1.48877	0.744383	+	0.667752i	$0.232744\pi$
$570$	−6.57293	−0.275310
$571$	−10.0707	−0.421444	−0.210722	−	0.977546i	$-0.567581\pi$
$571$	−10.0707	−0.421444	−0.210722	+	0.977546i	$0.567581\pi$
$572$	45.6579	1.90905
$573$	5.19149	0.216877
$574$	−11.6985	−0.488284
$575$	6.71527	0.280046
$576$	−10.8033	−0.450136
$577$	−9.83168	−0.409298	−0.204649	−	0.978835i	$-0.565605\pi$
$577$	−9.83168	−0.409298	−0.204649	+	0.978835i	$0.565605\pi$
$578$	−19.7640	−0.822076
$579$	0.641238	0.0266490
$580$	7.29422	0.302876
$581$	−7.73686	−0.320979
$582$	−28.3229	−1.17402
$583$	−17.8794	−0.740490
$584$	−8.49408	−0.351487
$585$	5.70684	0.235949
$586$	−51.8185	−2.14060
$587$	−41.2013	−1.70056	−0.850279	−	0.526332i	$-0.823567\pi$
$587$	−41.2013	−1.70056	−0.850279	+	0.526332i	$0.823567\pi$
$588$	−12.1126	−0.499516
$589$	−29.9619	−1.23456
$590$	−7.07255	−0.291172
$591$	14.0954	0.579809
$592$	11.1268	0.457308
$593$	1.43546	0.0589472	0.0294736	−	0.999566i	$-0.490617\pi$
$593$	1.43546	0.0589472	0.0294736	+	0.999566i	$0.490617\pi$
$594$	6.99711	0.287095
$595$	3.84205	0.157509
$596$	15.8240	0.648175
$597$	−2.14277	−0.0876976
$598$	80.3673	3.28646
$599$	−38.9136	−1.58997	−0.794984	−	0.606630i	$-0.792521\pi$
$599$	−38.9136	−1.58997	−0.794984	+	0.606630i	$0.792521\pi$
$600$	0.834334	0.0340615
$601$	23.5287	0.959756	0.479878	−	0.877335i	$-0.340681\pi$
$601$	23.5287	0.959756	0.479878	+	0.877335i	$0.340681\pi$
$602$	−4.63885	−0.189065
$603$	3.88303	0.158129
$604$	7.72495	0.314324
$605$	0.132597	0.00539085
$606$	17.0406	0.692227
$607$	−6.60251	−0.267988	−0.133994	−	0.990982i	$-0.542780\pi$
$607$	−6.60251	−0.267988	−0.133994	+	0.990982i	$0.542780\pi$
$608$	25.2513	1.02408
$609$	−4.24632	−0.172069
$610$	25.3758	1.02744
$611$	−62.1930	−2.51606
$612$	−6.59978	−0.266780
$613$	36.6943	1.48207	0.741035	−	0.671467i	$-0.234335\pi$
$613$	36.6943	1.48207	0.741035	+	0.671467i	$0.234335\pi$
$614$	−58.5183	−2.36161
$615$	3.99625	0.161144
$616$	−3.88592	−0.156568
$617$	41.6107	1.67518	0.837591	−	0.546298i	$-0.183963\pi$
$617$	41.6107	1.67518	0.837591	+	0.546298i	$0.183963\pi$
$618$	18.0533	0.726210
$619$	−25.9001	−1.04101	−0.520507	−	0.853857i	$-0.674257\pi$
$619$	−25.9001	−1.04101	−0.520507	+	0.853857i	$0.674257\pi$
$620$	22.9220	0.920569
$621$	6.71527	0.269475
$622$	−2.82529	−0.113284
$623$	−20.5110	−0.821756
$624$	−17.3831	−0.695881
$625$	1.00000	0.0400000
$626$	32.3164	1.29162
$627$	−10.4577	−0.417641
$628$	1.05915	0.0422645
$629$	10.0542	0.400885
$630$	−2.92736	−0.116629
$631$	−19.8681	−0.790936	−0.395468	−	0.918480i	$-0.629418\pi$
$631$	−19.8681	−0.790936	−0.395468	+	0.918480i	$0.629418\pi$
$632$	2.05756	0.0818455
$633$	−26.2605	−1.04376
$634$	14.3188	0.568672
$635$	15.3911	0.610778
$636$	−12.8492	−0.509505
$637$	−28.8278	−1.14220
$638$	21.2851	0.842684
$639$	11.4524	0.453048
$640$	−6.54261	−0.258619
$641$	−25.9062	−1.02323	−0.511617	−	0.859214i	$-0.670953\pi$
$641$	−25.9062	−1.02323	−0.511617	+	0.859214i	$0.670953\pi$
$642$	−8.50676	−0.335735
$643$	26.4860	1.04451	0.522253	−	0.852790i	$-0.325092\pi$
$643$	26.4860	1.04451	0.522253	+	0.852790i	$0.325092\pi$
$644$	−22.4771	−0.885724
$645$	1.58466	0.0623957
$646$	18.0912	0.711787
$647$	−2.50961	−0.0986628	−0.0493314	−	0.998782i	$-0.515709\pi$
$647$	−2.50961	−0.0986628	−0.0493314	+	0.998782i	$0.515709\pi$
$648$	0.834334	0.0327757
$649$	−11.2526	−0.441705
$650$	11.9678	0.469417
$651$	−13.3440	−0.522992
$652$	−26.7722	−1.04848
$653$	−17.3139	−0.677544	−0.338772	−	0.940869i	$-0.610012\pi$
$653$	−17.3139	−0.677544	−0.338772	+	0.940869i	$0.610012\pi$
$654$	9.43338	0.368875
$655$	−11.1367	−0.435148
$656$	−12.1726	−0.475262
$657$	−10.1807	−0.397186
$658$	31.9023	1.24368
$659$	36.9865	1.44079	0.720395	−	0.693564i	$-0.243960\pi$
$659$	36.9865	1.44079	0.720395	+	0.693564i	$0.243960\pi$
$660$	8.00056	0.311421
$661$	−5.26136	−0.204643	−0.102322	−	0.994751i	$-0.532627\pi$
$661$	−5.26136	−0.204643	−0.102322	+	0.994751i	$0.532627\pi$
$662$	22.8393	0.887676
$663$	−15.7073	−0.610023
$664$	4.62434	0.179459
$665$	4.37516	0.169662
$666$	−7.66052	−0.296839
$667$	20.4277	0.790965
$668$	31.7631	1.22895
$669$	12.6771	0.490123
$670$	8.14312	0.314596
$671$	40.3736	1.55861
$672$	11.2461	0.433827
$673$	19.1975	0.740008	0.370004	−	0.929030i	$-0.379356\pi$
$673$	19.1975	0.740008	0.370004	+	0.929030i	$0.379356\pi$
$674$	12.3370	0.475205
$675$	1.00000	0.0384900
$676$	46.9211	1.80466
$677$	26.6961	1.02601	0.513007	−	0.858384i	$-0.328531\pi$
$677$	26.6961	1.02601	0.513007	+	0.858384i	$0.328531\pi$
$678$	0.639450	0.0245579
$679$	18.8527	0.723499
$680$	−2.29640	−0.0880629
$681$	−8.60664	−0.329807
$682$	66.8880	2.56128
$683$	35.6661	1.36472	0.682362	−	0.731014i	$-0.260953\pi$
$683$	35.6661	1.36472	0.682362	+	0.731014i	$0.260953\pi$
$684$	−7.51555	−0.287364
$685$	−13.9497	−0.532989
$686$	35.2789	1.34695
$687$	−5.30237	−0.202298
$688$	−4.82688	−0.184023
$689$	−30.5809	−1.16504
$690$	14.0826	0.536117
$691$	27.5580	1.04835	0.524177	−	0.851609i	$-0.324373\pi$
$691$	27.5580	1.04835	0.524177	+	0.851609i	$0.324373\pi$
$692$	−27.7770	−1.05592
$693$	−4.65751	−0.176924
$694$	15.5469	0.590153
$695$	−3.93585	−0.149295
$696$	2.53803	0.0962038
$697$	−10.9992	−0.416623
$698$	70.4757	2.66755
$699$	7.58016	0.286708
$700$	−3.34717	−0.126511
$701$	−23.1371	−0.873875	−0.436937	−	0.899492i	$-0.643937\pi$
$701$	−23.1371	−0.873875	−0.436937	+	0.899492i	$0.643937\pi$
$702$	11.9678	0.451697
$703$	11.4492	0.431816
$704$	−36.0457	−1.35852
$705$	−10.8980	−0.410442
$706$	−17.2637	−0.649727
$707$	−11.3428	−0.426590
$708$	−8.08683	−0.303922
$709$	36.7364	1.37966	0.689832	−	0.723970i	$-0.257685\pi$
$709$	36.7364	1.37966	0.689832	+	0.723970i	$0.257685\pi$
$710$	24.0168	0.901334
$711$	2.46612	0.0924866
$712$	12.2595	0.459443
$713$	64.1939	2.40408
$714$	8.05718	0.301532
$715$	19.0412	0.712099
$716$	−55.8885	−2.08865
$717$	−28.3853	−1.06007
$718$	16.0539	0.599128
$719$	−50.5705	−1.88596	−0.942981	−	0.332847i	$-0.891991\pi$
$719$	−50.5705	−1.88596	−0.942981	+	0.332847i	$0.891991\pi$
$720$	−3.04601	−0.113518
$721$	−12.0169	−0.447532
$722$	−19.2435	−0.716170
$723$	−3.46393	−0.128825
$724$	8.59361	0.319379
$725$	3.04198	0.112976
$726$	0.278071	0.0103202
$727$	44.1830	1.63866	0.819328	−	0.573325i	$-0.194347\pi$
$727$	44.1830	1.63866	0.819328	+	0.573325i	$0.194347\pi$
$728$	−6.64647	−0.246334
$729$	1.00000	0.0370370
$730$	−21.3499	−0.790196
$731$	−4.36156	−0.161318
$732$	29.0149	1.07242
$733$	7.67333	0.283421	0.141711	−	0.989908i	$-0.454740\pi$
$733$	7.67333	0.283421	0.141711	+	0.989908i	$0.454740\pi$
$734$	−14.2939	−0.527597
$735$	−5.05145	−0.186326
$736$	−54.1015	−1.99421
$737$	12.9559	0.477238
$738$	8.38056	0.308493
$739$	22.9435	0.843992	0.421996	−	0.906598i	$-0.361330\pi$
$739$	22.9435	0.843992	0.421996	+	0.906598i	$0.361330\pi$
$740$	−8.75911	−0.321991
$741$	−17.8869	−0.657090
$742$	15.6867	0.575876
$743$	20.6230	0.756583	0.378291	−	0.925687i	$-0.376512\pi$
$743$	20.6230	0.756583	0.378291	+	0.925687i	$0.376512\pi$
$744$	7.97572	0.292404
$745$	6.59923	0.241777
$746$	−18.3672	−0.672473
$747$	5.54255	0.202791
$748$	−22.0205	−0.805150
$749$	5.66239	0.206899
$750$	2.09711	0.0765755
$751$	6.69702	0.244378	0.122189	−	0.992507i	$-0.461009\pi$
$751$	6.69702	0.244378	0.122189	+	0.992507i	$0.461009\pi$
$752$	33.1954	1.21051
$753$	16.3374	0.595367
$754$	36.4060	1.32583
$755$	3.22161	0.117247
$756$	−3.34717	−0.121735
$757$	−0.959666	−0.0348797	−0.0174398	−	0.999848i	$-0.505552\pi$
$757$	−0.959666	−0.0348797	−0.0174398	+	0.999848i	$0.505552\pi$
$758$	−2.79884	−0.101658
$759$	22.4059	0.813282
$760$	−2.61504	−0.0948576
$761$	−7.45117	−0.270105	−0.135052	−	0.990838i	$-0.543120\pi$
$761$	−7.45117	−0.270105	−0.135052	+	0.990838i	$0.543120\pi$
$762$	32.2768	1.16927
$763$	−6.27918	−0.227322
$764$	12.4484	0.450368
$765$	−2.75237	−0.0995123
$766$	25.5057	0.921559
$767$	−19.2465	−0.694950
$768$	7.88598	0.284561
$769$	−8.80888	−0.317656	−0.158828	−	0.987306i	$-0.550772\pi$
$769$	−8.80888	−0.317656	−0.158828	+	0.987306i	$0.550772\pi$
$770$	−9.76729	−0.351989
$771$	11.8715	0.427543
$772$	1.53759	0.0553392
$773$	37.3979	1.34511	0.672555	−	0.740047i	$-0.265197\pi$
$773$	37.3979	1.34511	0.672555	+	0.740047i	$0.265197\pi$
$774$	3.32319	0.119450
$775$	9.55939	0.343383
$776$	−11.2683	−0.404507
$777$	5.09910	0.182929
$778$	−2.19765	−0.0787895
$779$	−12.5254	−0.448769
$780$	13.6841	0.489971
$781$	38.2114	1.36731
$782$	−38.7607	−1.38608
$783$	3.04198	0.108712
$784$	15.3868	0.549529
$785$	0.441707	0.0157652
$786$	−23.3549	−0.833041
$787$	−21.4879	−0.765961	−0.382981	−	0.923756i	$-0.625102\pi$
$787$	−21.4879	−0.765961	−0.382981	+	0.923756i	$0.625102\pi$
$788$	33.7988	1.20403
$789$	−4.04816	−0.144118
$790$	5.17170	0.184001
$791$	−0.425639	−0.0151340
$792$	2.78380	0.0989181
$793$	69.0549	2.45221
$794$	−44.4261	−1.57662
$795$	−5.35865	−0.190052
$796$	−5.13803	−0.182113
$797$	−15.4712	−0.548018	−0.274009	−	0.961727i	$-0.588350\pi$
$797$	−15.4712	−0.548018	−0.274009	+	0.961727i	$0.588350\pi$
$798$	9.17518	0.324798
$799$	29.9953	1.06116
$800$	−8.05648	−0.284840
$801$	14.6937	0.519177
$802$	2.09711	0.0740514
$803$	−33.9684	−1.19872
$804$	9.31092	0.328371
$805$	−9.37387	−0.330386
$806$	114.405	4.02975
$807$	−19.3313	−0.680493
$808$	6.77960	0.238506
$809$	10.9084	0.383517	0.191759	−	0.981442i	$-0.438581\pi$
$809$	10.9084	0.383517	0.191759	+	0.981442i	$0.438581\pi$
$810$	2.09711	0.0736848
$811$	−33.3266	−1.17025	−0.585127	−	0.810942i	$-0.698955\pi$
$811$	−33.3266	−1.17025	−0.585127	+	0.810942i	$0.698955\pi$
$812$	−10.1820	−0.357319
$813$	−12.4957	−0.438244
$814$	−25.5597	−0.895868
$815$	−11.1651	−0.391096
$816$	8.38377	0.293491
$817$	−4.96677	−0.173765
$818$	6.98124	0.244093
$819$	−7.96619	−0.278361
$820$	9.58241	0.334632
$821$	2.54763	0.0889129	0.0444565	−	0.999011i	$-0.485844\pi$
$821$	2.54763	0.0889129	0.0444565	+	0.999011i	$0.485844\pi$
$822$	−29.2539	−1.02035
$823$	−39.5919	−1.38009	−0.690044	−	0.723768i	$-0.742409\pi$
$823$	−39.5919	−1.38009	−0.690044	+	0.723768i	$0.742409\pi$
$824$	7.18251	0.250214
$825$	3.33655	0.116164
$826$	9.87261	0.343512
$827$	−39.1630	−1.36183	−0.680916	−	0.732362i	$-0.738418\pi$
$827$	−39.1630	−1.36183	−0.680916	+	0.732362i	$0.738418\pi$
$828$	16.1022	0.559591
$829$	44.8079	1.55624	0.778122	−	0.628113i	$-0.216173\pi$
$829$	44.8079	1.55624	0.778122	+	0.628113i	$0.216173\pi$
$830$	11.6233	0.403451
$831$	−13.1877	−0.457475
$832$	−61.6524	−2.13741
$833$	13.9035	0.481727
$834$	−8.25390	−0.285809
$835$	13.2465	0.458414
$836$	−25.0761	−0.867273
$837$	9.55939	0.330421
$838$	−16.6872	−0.576448
$839$	−35.4443	−1.22367	−0.611836	−	0.790984i	$-0.709569\pi$
$839$	−35.4443	−1.22367	−0.611836	+	0.790984i	$0.709569\pi$
$840$	−1.16465	−0.0401842
$841$	−19.7463	−0.680908
$842$	−43.8327	−1.51057
$843$	−21.5168	−0.741079
$844$	−62.9688	−2.16748
$845$	19.5680	0.673159
$846$	−22.8542	−0.785744
$847$	−0.185093	−0.00635988
$848$	16.3225	0.560517
$849$	−26.5022	−0.909552
$850$	−5.77202	−0.197979
$851$	−24.5302	−0.840885
$852$	27.4610	0.940800
$853$	−0.653428	−0.0223729	−0.0111865	−	0.999937i	$-0.503561\pi$
$853$	−0.653428	−0.0223729	−0.0111865	+	0.999937i	$0.503561\pi$
$854$	−35.4222	−1.21212
$855$	−3.13429	−0.107190
$856$	−3.38442	−0.115677
$857$	54.1358	1.84924	0.924621	−	0.380888i	$-0.124382\pi$
$857$	54.1358	1.84924	0.924621	+	0.380888i	$0.124382\pi$
$858$	39.9313	1.36323
$859$	13.6621	0.466146	0.233073	−	0.972459i	$-0.425122\pi$
$859$	13.6621	0.466146	0.233073	+	0.972459i	$0.425122\pi$
$860$	3.79977	0.129571
$861$	−5.57838	−0.190111
$862$	−44.7247	−1.52333
$863$	20.9020	0.711511	0.355756	−	0.934579i	$-0.384224\pi$
$863$	20.9020	0.711511	0.355756	+	0.934579i	$0.384224\pi$
$864$	−8.05648	−0.274087
$865$	−11.5841	−0.393872
$866$	−30.0543	−1.02129
$867$	−9.42444	−0.320071
$868$	−31.9969	−1.08604
$869$	8.22833	0.279127
$870$	6.37936	0.216281
$871$	22.1598	0.750856
$872$	3.75307	0.127095
$873$	−13.5057	−0.457099
$874$	−44.1390	−1.49302
$875$	−1.39590	−0.0471902
$876$	−24.4117	−0.824795
$877$	−33.2548	−1.12294	−0.561468	−	0.827499i	$-0.689763\pi$
$877$	−33.2548	−1.12294	−0.561468	+	0.827499i	$0.689763\pi$
$878$	49.1132	1.65749
$879$	−24.7095	−0.833431
$880$	−10.1632	−0.342601
$881$	1.06617	0.0359202	0.0179601	−	0.999839i	$-0.494283\pi$
$881$	1.06617	0.0359202	0.0179601	+	0.999839i	$0.494283\pi$
$882$	−10.5934	−0.356699
$883$	−55.0147	−1.85139	−0.925696	−	0.378268i	$-0.876520\pi$
$883$	−55.0147	−1.85139	−0.925696	+	0.378268i	$0.876520\pi$
$884$	−37.6639	−1.26677
$885$	−3.37253	−0.113366
$886$	33.0713	1.11105
$887$	24.5046	0.822783	0.411392	−	0.911459i	$-0.365043\pi$
$887$	24.5046	0.822783	0.411392	+	0.911459i	$0.365043\pi$
$888$	−3.04774	−0.102275
$889$	−21.4845	−0.720568
$890$	30.8143	1.03290
$891$	3.33655	0.111779
$892$	30.3977	1.01779
$893$	34.1574	1.14303
$894$	13.8393	0.462855
$895$	−23.3077	−0.779092
$896$	9.13285	0.305107
$897$	38.3230	1.27957
$898$	−44.4039	−1.48178
$899$	29.0795	0.969855
$900$	2.39785	0.0799283
$901$	14.7490	0.491360
$902$	27.9622	0.931039
$903$	−2.21203	−0.0736116
$904$	0.254405	0.00846139
$905$	3.58388	0.119132
$906$	6.75606	0.224455
$907$	−9.67801	−0.321353	−0.160676	−	0.987007i	$-0.551368\pi$
$907$	−9.67801	−0.321353	−0.160676	+	0.987007i	$0.551368\pi$
$908$	−20.6374	−0.684877
$909$	8.12577	0.269515
$910$	−16.7059	−0.553797
$911$	−14.8226	−0.491095	−0.245547	−	0.969385i	$-0.578968\pi$
$911$	−14.8226	−0.491095	−0.245547	+	0.969385i	$0.578968\pi$
$912$	9.54709	0.316136
$913$	18.4930	0.612029
$914$	0.212979	0.00704472
$915$	12.1004	0.400027
$916$	−12.7143	−0.420092
$917$	15.5458	0.513368
$918$	−5.77202	−0.190505
$919$	44.0830	1.45417	0.727083	−	0.686550i	$-0.240876\pi$
$919$	44.0830	1.45417	0.727083	+	0.686550i	$0.240876\pi$
$920$	5.60278	0.184718
$921$	−27.9043	−0.919478
$922$	48.3984	1.59392
$923$	65.3567	2.15124
$924$	−11.1680	−0.367401
$925$	−3.65290	−0.120107
$926$	−49.7766	−1.63576
$927$	8.60867	0.282746
$928$	−24.5077	−0.804504
$929$	−3.36327	−0.110345	−0.0551727	−	0.998477i	$-0.517571\pi$
$929$	−3.36327	−0.110345	−0.0551727	+	0.998477i	$0.517571\pi$
$930$	20.0470	0.657368
$931$	15.8327	0.518896
$932$	18.1761	0.595378
$933$	−1.34723	−0.0441064
$934$	−29.4230	−0.962749
$935$	−9.18345	−0.300331
$936$	4.76141	0.155631
$937$	22.2610	0.727237	0.363618	−	0.931548i	$-0.381541\pi$
$937$	22.2610	0.727237	0.363618	+	0.931548i	$0.381541\pi$
$938$	−11.3670	−0.371146
$939$	15.4100	0.502886
$940$	−26.1317	−0.852323
$941$	−35.6318	−1.16156	−0.580782	−	0.814059i	$-0.697253\pi$
$941$	−35.6318	−1.16156	−0.580782	+	0.814059i	$0.697253\pi$
$942$	0.926305	0.0301807
$943$	26.8359	0.873897
$944$	10.2728	0.334351
$945$	−1.39590	−0.0454088
$946$	11.0880	0.360502
$947$	2.09751	0.0681600	0.0340800	−	0.999419i	$-0.489150\pi$
$947$	2.09751	0.0681600	0.0340800	+	0.999419i	$0.489150\pi$
$948$	5.91338	0.192058
$949$	−58.0994	−1.88599
$950$	−6.57293	−0.213254
$951$	6.82789	0.221409
$952$	3.20555	0.103893
$953$	−33.0609	−1.07095	−0.535474	−	0.844552i	$-0.679867\pi$
$953$	−33.0609	−1.07095	−0.535474	+	0.844552i	$0.679867\pi$
$954$	−11.2376	−0.363832
$955$	5.19149	0.167993
$956$	−68.0636	−2.20133
$957$	10.1497	0.328095
$958$	−67.1904	−2.17082
$959$	19.4724	0.628796
$960$	−10.8033	−0.348674
$961$	60.3818	1.94780
$962$	−43.7173	−1.40950
$963$	−4.05643	−0.130717
$964$	−8.30598	−0.267517
$965$	0.641238	0.0206422
$966$	−19.6580	−0.632486
$967$	22.8577	0.735054	0.367527	−	0.930013i	$-0.380205\pi$
$967$	22.8577	0.735054	0.367527	+	0.930013i	$0.380205\pi$
$968$	0.110631	0.00355580
$969$	8.62673	0.277131
$970$	−28.3229	−0.909393
$971$	8.59550	0.275843	0.137921	−	0.990443i	$-0.455958\pi$
$971$	8.59550	0.275843	0.137921	+	0.990443i	$0.455958\pi$
$972$	2.39785	0.0769111
$973$	5.49407	0.176132
$974$	−16.5637	−0.530734
$975$	5.70684	0.182765
$976$	−36.8580	−1.17979
$977$	24.9409	0.797931	0.398965	−	0.916966i	$-0.369369\pi$
$977$	24.9409	0.797931	0.398965	+	0.916966i	$0.369369\pi$
$978$	−23.4144	−0.748709
$979$	49.0264	1.56689
$980$	−12.1126	−0.386924
$981$	4.49829	0.143619
$982$	26.1769	0.835340
$983$	−37.3587	−1.19156	−0.595779	−	0.803148i	$-0.703157\pi$
$983$	−37.3587	−1.19156	−0.595779	+	0.803148i	$0.703157\pi$
$984$	3.33421	0.106291
$985$	14.0954	0.449118
$986$	−17.5584	−0.559173
$987$	15.2125	0.484220
$988$	−42.8900	−1.36451
$989$	10.6414	0.338377
$990$	6.99711	0.222383
$991$	52.4164	1.66506	0.832532	−	0.553977i	$-0.186891\pi$
$991$	52.4164	1.66506	0.832532	+	0.553977i	$0.186891\pi$
$992$	−77.0150	−2.44523
$993$	10.8909	0.345612
$994$	−33.5251	−1.06335
$995$	−2.14277	−0.0679302
$996$	13.2902	0.421116
$997$	31.7128	1.00435	0.502177	−	0.864765i	$-0.332532\pi$
$997$	31.7128	1.00435	0.502177	+	0.864765i	$0.332532\pi$
$998$	30.4340	0.963373
$999$	−3.65290	−0.115573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.34	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.34	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09711 q^{2} +1.00000 q^{3} +2.39785 q^{4} +1.00000 q^{5} +2.09711 q^{6} -1.39590 q^{7} +0.834334 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.09711 q^{2} +1.00000 q^{3} +2.39785 q^{4} +1.00000 q^{5} +2.09711 q^{6} -1.39590 q^{7} +0.834334 q^{8} +1.00000 q^{9} +2.09711 q^{10} +3.33655 q^{11} +2.39785 q^{12} +5.70684 q^{13} -2.92736 q^{14} +1.00000 q^{15} -3.04601 q^{16} -2.75237 q^{17} +2.09711 q^{18} -3.13429 q^{19} +2.39785 q^{20} -1.39590 q^{21} +6.99711 q^{22} +6.71527 q^{23} +0.834334 q^{24} +1.00000 q^{25} +11.9678 q^{26} +1.00000 q^{27} -3.34717 q^{28} +3.04198 q^{29} +2.09711 q^{30} +9.55939 q^{31} -8.05648 q^{32} +3.33655 q^{33} -5.77202 q^{34} -1.39590 q^{35} +2.39785 q^{36} -3.65290 q^{37} -6.57293 q^{38} +5.70684 q^{39} +0.834334 q^{40} +3.99625 q^{41} -2.92736 q^{42} +1.58466 q^{43} +8.00056 q^{44} +1.00000 q^{45} +14.0826 q^{46} -10.8980 q^{47} -3.04601 q^{48} -5.05145 q^{49} +2.09711 q^{50} -2.75237 q^{51} +13.6841 q^{52} -5.35865 q^{53} +2.09711 q^{54} +3.33655 q^{55} -1.16465 q^{56} -3.13429 q^{57} +6.37936 q^{58} -3.37253 q^{59} +2.39785 q^{60} +12.1004 q^{61} +20.0470 q^{62} -1.39590 q^{63} -10.8033 q^{64} +5.70684 q^{65} +6.99711 q^{66} +3.88303 q^{67} -6.59978 q^{68} +6.71527 q^{69} -2.92736 q^{70} +11.4524 q^{71} +0.834334 q^{72} -10.1807 q^{73} -7.66052 q^{74} +1.00000 q^{75} -7.51555 q^{76} -4.65751 q^{77} +11.9678 q^{78} +2.46612 q^{79} -3.04601 q^{80} +1.00000 q^{81} +8.38056 q^{82} +5.54255 q^{83} -3.34717 q^{84} -2.75237 q^{85} +3.32319 q^{86} +3.04198 q^{87} +2.78380 q^{88} +14.6937 q^{89} +2.09711 q^{90} -7.96619 q^{91} +16.1022 q^{92} +9.55939 q^{93} -22.8542 q^{94} -3.13429 q^{95} -8.05648 q^{96} -13.5057 q^{97} -10.5934 q^{98} +3.33655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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