LMFDB - Embedded newform 8035.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42522 q^{2} -2.38106 q^{3} +3.88170 q^{4} +1.00000 q^{5} +5.77461 q^{6} +1.76614 q^{7} -4.56353 q^{8} +2.66946 q^{9} +O(q^{10})$	\(q-2.42522 q^{2} -2.38106 q^{3} +3.88170 q^{4} +1.00000 q^{5} +5.77461 q^{6} +1.76614 q^{7} -4.56353 q^{8} +2.66946 q^{9} -2.42522 q^{10} -2.72831 q^{11} -9.24257 q^{12} +5.55591 q^{13} -4.28328 q^{14} -2.38106 q^{15} +3.30418 q^{16} +0.659133 q^{17} -6.47404 q^{18} +2.98235 q^{19} +3.88170 q^{20} -4.20529 q^{21} +6.61676 q^{22} -7.86230 q^{23} +10.8661 q^{24} +1.00000 q^{25} -13.4743 q^{26} +0.787030 q^{27} +6.85562 q^{28} -1.80900 q^{29} +5.77461 q^{30} +7.09146 q^{31} +1.11369 q^{32} +6.49628 q^{33} -1.59854 q^{34} +1.76614 q^{35} +10.3620 q^{36} -0.284830 q^{37} -7.23285 q^{38} -13.2290 q^{39} -4.56353 q^{40} -12.6745 q^{41} +10.1988 q^{42} +5.75244 q^{43} -10.5905 q^{44} +2.66946 q^{45} +19.0678 q^{46} -5.69256 q^{47} -7.86747 q^{48} -3.88075 q^{49} -2.42522 q^{50} -1.56944 q^{51} +21.5663 q^{52} +9.15858 q^{53} -1.90872 q^{54} -2.72831 q^{55} -8.05984 q^{56} -7.10116 q^{57} +4.38723 q^{58} +9.67733 q^{59} -9.24257 q^{60} +2.54672 q^{61} -17.1984 q^{62} +4.71465 q^{63} -9.30932 q^{64} +5.55591 q^{65} -15.7549 q^{66} -0.447707 q^{67} +2.55856 q^{68} +18.7206 q^{69} -4.28328 q^{70} +2.80398 q^{71} -12.1822 q^{72} -5.14118 q^{73} +0.690776 q^{74} -2.38106 q^{75} +11.5766 q^{76} -4.81858 q^{77} +32.0832 q^{78} -7.12150 q^{79} +3.30418 q^{80} -9.88236 q^{81} +30.7386 q^{82} +3.25377 q^{83} -16.3237 q^{84} +0.659133 q^{85} -13.9509 q^{86} +4.30735 q^{87} +12.4507 q^{88} -11.8772 q^{89} -6.47404 q^{90} +9.81251 q^{91} -30.5191 q^{92} -16.8852 q^{93} +13.8057 q^{94} +2.98235 q^{95} -2.65177 q^{96} +6.76833 q^{97} +9.41167 q^{98} -7.28312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) $ 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * 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 $

$2$	−2.42522	−1.71489	−0.857445	−	0.514575i	$-0.827950\pi$
$2$	−2.42522	−1.71489	−0.857445	+	0.514575i	$0.827950\pi$
$3$	−2.38106	−1.37471	−0.687354	−	0.726323i	$-0.741228\pi$
$3$	−2.38106	−1.37471	−0.687354	+	0.726323i	$0.741228\pi$
$4$	3.88170	1.94085
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.77461	2.35747
$7$	1.76614	0.667538	0.333769	−	0.942655i	$-0.391679\pi$
$7$	1.76614	0.667538	0.333769	+	0.942655i	$0.391679\pi$
$8$	−4.56353	−1.61345
$9$	2.66946	0.889821
$10$	−2.42522	−0.766922
$11$	−2.72831	−0.822616	−0.411308	−	0.911496i	$-0.634928\pi$
$11$	−2.72831	−0.822616	−0.411308	+	0.911496i	$0.634928\pi$
$12$	−9.24257	−2.66810
$13$	5.55591	1.54093	0.770466	−	0.637482i	$-0.220024\pi$
$13$	5.55591	1.54093	0.770466	+	0.637482i	$0.220024\pi$
$14$	−4.28328	−1.14475
$15$	−2.38106	−0.614788
$16$	3.30418	0.826046
$17$	0.659133	0.159863	0.0799316	−	0.996800i	$-0.474530\pi$
$17$	0.659133	0.159863	0.0799316	+	0.996800i	$0.474530\pi$
$18$	−6.47404	−1.52595
$19$	2.98235	0.684197	0.342099	−	0.939664i	$-0.388862\pi$
$19$	2.98235	0.684197	0.342099	+	0.939664i	$0.388862\pi$
$20$	3.88170	0.867974
$21$	−4.20529	−0.917670
$22$	6.61676	1.41070
$23$	−7.86230	−1.63940	−0.819702	−	0.572791i	$-0.805861\pi$
$23$	−7.86230	−1.63940	−0.819702	+	0.572791i	$0.805861\pi$
$24$	10.8661	2.21803
$25$	1.00000	0.200000
$26$	−13.4743	−2.64253
$27$	0.787030	0.151464
$28$	6.85562	1.29559
$29$	−1.80900	−0.335923	−0.167962	−	0.985794i	$-0.553719\pi$
$29$	−1.80900	−0.335923	−0.167962	+	0.985794i	$0.553719\pi$
$30$	5.77461	1.05429
$31$	7.09146	1.27366	0.636832	−	0.771003i	$-0.280245\pi$
$31$	7.09146	1.27366	0.636832	+	0.771003i	$0.280245\pi$
$32$	1.11369	0.196875
$33$	6.49628	1.13086
$34$	−1.59854	−0.274148
$35$	1.76614	0.298532
$36$	10.3620	1.72701
$37$	−0.284830	−0.0468258	−0.0234129	−	0.999726i	$-0.507453\pi$
$37$	−0.284830	−0.0468258	−0.0234129	+	0.999726i	$0.507453\pi$
$38$	−7.23285	−1.17332
$39$	−13.2290	−2.11833
$40$	−4.56353	−0.721558
$41$	−12.6745	−1.97943	−0.989715	−	0.143051i	$-0.954309\pi$
$41$	−12.6745	−1.97943	−0.989715	+	0.143051i	$0.954309\pi$
$42$	10.1988	1.57370
$43$	5.75244	0.877239	0.438619	−	0.898673i	$-0.355468\pi$
$43$	5.75244	0.877239	0.438619	+	0.898673i	$0.355468\pi$
$44$	−10.5905	−1.59657
$45$	2.66946	0.397940
$46$	19.0678	2.81140
$47$	−5.69256	−0.830345	−0.415172	−	0.909743i	$-0.636279\pi$
$47$	−5.69256	−0.830345	−0.415172	+	0.909743i	$0.636279\pi$
$48$	−7.86747	−1.13557
$49$	−3.88075	−0.554393
$50$	−2.42522	−0.342978
$51$	−1.56944	−0.219765
$52$	21.5663	2.99071
$53$	9.15858	1.25803	0.629014	−	0.777394i	$-0.283459\pi$
$53$	9.15858	1.25803	0.629014	+	0.777394i	$0.283459\pi$
$54$	−1.90872	−0.259744
$55$	−2.72831	−0.367885
$56$	−8.05984	−1.07704
$57$	−7.10116	−0.940571
$58$	4.38723	0.576072
$59$	9.67733	1.25988	0.629941	−	0.776643i	$-0.283079\pi$
$59$	9.67733	1.25988	0.629941	+	0.776643i	$0.283079\pi$
$60$	−9.24257	−1.19321
$61$	2.54672	0.326074	0.163037	−	0.986620i	$-0.447871\pi$
$61$	2.54672	0.326074	0.163037	+	0.986620i	$0.447871\pi$
$62$	−17.1984	−2.18419
$63$	4.71465	0.593990
$64$	−9.30932	−1.16366
$65$	5.55591	0.689125
$66$	−15.7549	−1.93930
$67$	−0.447707	−0.0546961	−0.0273480	−	0.999626i	$-0.508706\pi$
$67$	−0.447707	−0.0546961	−0.0273480	+	0.999626i	$0.508706\pi$
$68$	2.55856	0.310270
$69$	18.7206	2.25370
$70$	−4.28328	−0.511950
$71$	2.80398	0.332771	0.166386	−	0.986061i	$-0.446790\pi$
$71$	2.80398	0.332771	0.166386	+	0.986061i	$0.446790\pi$
$72$	−12.1822	−1.43568
$73$	−5.14118	−0.601730	−0.300865	−	0.953667i	$-0.597275\pi$
$73$	−5.14118	−0.601730	−0.300865	+	0.953667i	$0.597275\pi$
$74$	0.690776	0.0803011
$75$	−2.38106	−0.274942
$76$	11.5766	1.32792
$77$	−4.81858	−0.549128
$78$	32.0832	3.63270
$79$	−7.12150	−0.801232	−0.400616	−	0.916246i	$-0.631204\pi$
$79$	−7.12150	−0.801232	−0.400616	+	0.916246i	$0.631204\pi$
$80$	3.30418	0.369419
$81$	−9.88236	−1.09804
$82$	30.7386	3.39451
$83$	3.25377	0.357148	0.178574	−	0.983927i	$-0.442852\pi$
$83$	3.25377	0.357148	0.178574	+	0.983927i	$0.442852\pi$
$84$	−16.3237	−1.78106
$85$	0.659133	0.0714930
$86$	−13.9509	−1.50437
$87$	4.30735	0.461797
$88$	12.4507	1.32725
$89$	−11.8772	−1.25898	−0.629490	−	0.777009i	$-0.716736\pi$
$89$	−11.8772	−1.25898	−0.629490	+	0.777009i	$0.716736\pi$
$90$	−6.47404	−0.682424
$91$	9.81251	1.02863
$92$	−30.5191	−3.18183
$93$	−16.8852	−1.75092
$94$	13.8057	1.42395
$95$	2.98235	0.305982
$96$	−2.65177	−0.270645
$97$	6.76833	0.687220	0.343610	−	0.939112i	$-0.388350\pi$
$97$	6.76833	0.687220	0.343610	+	0.939112i	$0.388350\pi$
$98$	9.41167	0.950723
$99$	−7.28312	−0.731981
$100$	3.88170	0.388170
$101$	−9.59186	−0.954425	−0.477213	−	0.878788i	$-0.658353\pi$
$101$	−9.59186	−0.954425	−0.477213	+	0.878788i	$0.658353\pi$
$102$	3.80623	0.376873
$103$	8.56487	0.843922	0.421961	−	0.906614i	$-0.361342\pi$
$103$	8.56487	0.843922	0.421961	+	0.906614i	$0.361342\pi$
$104$	−25.3546	−2.48622
$105$	−4.20529	−0.410394
$106$	−22.2116	−2.15738
$107$	4.03065	0.389658	0.194829	−	0.980837i	$-0.437585\pi$
$107$	4.03065	0.389658	0.194829	+	0.980837i	$0.437585\pi$
$108$	3.05501	0.293969
$109$	−12.0383	−1.15306	−0.576530	−	0.817076i	$-0.695593\pi$
$109$	−12.0383	−1.15306	−0.576530	+	0.817076i	$0.695593\pi$
$110$	6.61676	0.630883
$111$	0.678199	0.0643718
$112$	5.83565	0.551417
$113$	−17.7652	−1.67121	−0.835607	−	0.549328i	$-0.814884\pi$
$113$	−17.7652	−1.67121	−0.835607	+	0.549328i	$0.814884\pi$
$114$	17.2219	1.61298
$115$	−7.86230	−0.733163
$116$	−7.02200	−0.651977
$117$	14.8313	1.37115
$118$	−23.4697	−2.16056
$119$	1.16412	0.106715
$120$	10.8661	0.991931
$121$	−3.55632	−0.323302
$122$	−6.17636	−0.559182
$123$	30.1789	2.72114
$124$	27.5269	2.47199
$125$	1.00000	0.0894427
$126$	−11.4341	−1.01863
$127$	−2.80674	−0.249058	−0.124529	−	0.992216i	$-0.539742\pi$
$127$	−2.80674	−0.249058	−0.124529	+	0.992216i	$0.539742\pi$
$128$	20.3498	1.79868
$129$	−13.6969	−1.20595
$130$	−13.4743	−1.18177
$131$	−17.7156	−1.54782	−0.773910	−	0.633296i	$-0.781702\pi$
$131$	−17.7156	−1.54782	−0.773910	+	0.633296i	$0.781702\pi$
$132$	25.2166	2.19482
$133$	5.26724	0.456728
$134$	1.08579	0.0937978
$135$	0.787030	0.0677367
$136$	−3.00798	−0.257932
$137$	−12.9633	−1.10753	−0.553766	−	0.832673i	$-0.686810\pi$
$137$	−12.9633	−1.10753	−0.553766	+	0.832673i	$0.686810\pi$
$138$	−45.4017	−3.86485
$139$	−13.3761	−1.13455	−0.567275	−	0.823528i	$-0.692002\pi$
$139$	−13.3761	−1.13455	−0.567275	+	0.823528i	$0.692002\pi$
$140$	6.85562	0.579406
$141$	13.5543	1.14148
$142$	−6.80027	−0.570666
$143$	−15.1582	−1.26760
$144$	8.82040	0.735033
$145$	−1.80900	−0.150230
$146$	12.4685	1.03190
$147$	9.24031	0.762128
$148$	−1.10562	−0.0908818
$149$	9.81194	0.803826	0.401913	−	0.915678i	$-0.368345\pi$
$149$	9.81194	0.803826	0.401913	+	0.915678i	$0.368345\pi$
$150$	5.77461	0.471495
$151$	−20.2312	−1.64639	−0.823194	−	0.567760i	$-0.807810\pi$
$151$	−20.2312	−1.64639	−0.823194	+	0.567760i	$0.807810\pi$
$152$	−13.6100	−1.10392
$153$	1.75953	0.142250
$154$	11.6861	0.941694
$155$	7.09146	0.569600
$156$	−51.3508	−4.11136
$157$	4.13669	0.330144	0.165072	−	0.986282i	$-0.447214\pi$
$157$	4.13669	0.330144	0.165072	+	0.986282i	$0.447214\pi$
$158$	17.2712	1.37402
$159$	−21.8072	−1.72942
$160$	1.11369	0.0880451
$161$	−13.8859	−1.09436
$162$	23.9669	1.88302
$163$	2.95278	0.231280	0.115640	−	0.993291i	$-0.463108\pi$
$163$	2.95278	0.231280	0.115640	+	0.993291i	$0.463108\pi$
$164$	−49.1987	−3.84178
$165$	6.49628	0.505735
$166$	−7.89111	−0.612469
$167$	−2.07099	−0.160258	−0.0801292	−	0.996784i	$-0.525533\pi$
$167$	−2.07099	−0.160258	−0.0801292	+	0.996784i	$0.525533\pi$
$168$	19.1910	1.48062
$169$	17.8681	1.37447
$170$	−1.59854	−0.122603
$171$	7.96126	0.608813
$172$	22.3292	1.70259
$173$	19.2923	1.46677	0.733385	−	0.679814i	$-0.237940\pi$
$173$	19.2923	1.46677	0.733385	+	0.679814i	$0.237940\pi$
$174$	−10.4463	−0.791930
$175$	1.76614	0.133508
$176$	−9.01484	−0.679519
$177$	−23.0423	−1.73197
$178$	28.8048	2.15901
$179$	10.2689	0.767537	0.383769	−	0.923429i	$-0.374626\pi$
$179$	10.2689	0.767537	0.383769	+	0.923429i	$0.374626\pi$
$180$	10.3620	0.772342
$181$	−13.9021	−1.03333	−0.516666	−	0.856187i	$-0.672827\pi$
$181$	−13.9021	−1.03333	−0.516666	+	0.856187i	$0.672827\pi$
$182$	−23.7975	−1.76399
$183$	−6.06391	−0.448257
$184$	35.8799	2.64510
$185$	−0.284830	−0.0209411
$186$	40.9504	3.00263
$187$	−1.79832	−0.131506
$188$	−22.0968	−1.61157
$189$	1.39000	0.101108
$190$	−7.23285	−0.524726
$191$	−26.7768	−1.93750	−0.968750	−	0.248039i	$-0.920214\pi$
$191$	−26.7768	−1.93750	−0.968750	+	0.248039i	$0.920214\pi$
$192$	22.1661	1.59970
$193$	−23.9446	−1.72357	−0.861786	−	0.507272i	$-0.830654\pi$
$193$	−23.9446	−1.72357	−0.861786	+	0.507272i	$0.830654\pi$
$194$	−16.4147	−1.17851
$195$	−13.2290	−0.947346
$196$	−15.0639	−1.07599
$197$	−1.35289	−0.0963891	−0.0481945	−	0.998838i	$-0.515347\pi$
$197$	−1.35289	−0.0963891	−0.0481945	+	0.998838i	$0.515347\pi$
$198$	17.6632	1.25527
$199$	2.79719	0.198288	0.0991438	−	0.995073i	$-0.468390\pi$
$199$	2.79719	0.198288	0.0991438	+	0.995073i	$0.468390\pi$
$200$	−4.56353	−0.322691
$201$	1.06602	0.0751911
$202$	23.2624	1.63674
$203$	−3.19495	−0.224242
$204$	−6.09208	−0.426531
$205$	−12.6745	−0.885228
$206$	−20.7717	−1.44723
$207$	−20.9881	−1.45878
$208$	18.3577	1.27288
$209$	−8.13676	−0.562832
$210$	10.1988	0.703781
$211$	23.8147	1.63947	0.819737	−	0.572740i	$-0.194120\pi$
$211$	23.8147	1.63947	0.819737	+	0.572740i	$0.194120\pi$
$212$	35.5508	2.44164
$213$	−6.67646	−0.457463
$214$	−9.77522	−0.668220
$215$	5.75244	0.392313
$216$	−3.59164	−0.244380
$217$	12.5245	0.850219
$218$	29.1955	1.97737
$219$	12.2415	0.827203
$220$	−10.5905	−0.714010
$221$	3.66208	0.246338
$222$	−1.64478	−0.110391
$223$	16.9829	1.13726	0.568629	−	0.822594i	$-0.307474\pi$
$223$	16.9829	1.13726	0.568629	+	0.822594i	$0.307474\pi$
$224$	1.96694	0.131421
$225$	2.66946	0.177964
$226$	43.0846	2.86595
$227$	−3.51410	−0.233239	−0.116620	−	0.993177i	$-0.537206\pi$
$227$	−3.51410	−0.233239	−0.116620	+	0.993177i	$0.537206\pi$
$228$	−27.5645	−1.82551
$229$	−2.01078	−0.132876	−0.0664380	−	0.997791i	$-0.521163\pi$
$229$	−2.01078	−0.132876	−0.0664380	+	0.997791i	$0.521163\pi$
$230$	19.0678	1.25729
$231$	11.4733	0.754890
$232$	8.25545	0.541997
$233$	13.9785	0.915763	0.457881	−	0.889013i	$-0.348608\pi$
$233$	13.9785	0.915763	0.457881	+	0.889013i	$0.348608\pi$
$234$	−35.9691	−2.35138
$235$	−5.69256	−0.371341
$236$	37.5645	2.44524
$237$	16.9568	1.10146
$238$	−2.82325	−0.183004
$239$	5.38562	0.348367	0.174184	−	0.984713i	$-0.444271\pi$
$239$	5.38562	0.348367	0.174184	+	0.984713i	$0.444271\pi$
$240$	−7.86747	−0.507843
$241$	−10.5039	−0.676613	−0.338307	−	0.941036i	$-0.609854\pi$
$241$	−10.5039	−0.676613	−0.338307	+	0.941036i	$0.609854\pi$
$242$	8.62487	0.554428
$243$	21.1694	1.35802
$244$	9.88561	0.632861
$245$	−3.88075	−0.247932
$246$	−73.1905	−4.66645
$247$	16.5696	1.05430
$248$	−32.3621	−2.05500
$249$	−7.74743	−0.490974
$250$	−2.42522	−0.153384
$251$	17.0893	1.07867	0.539333	−	0.842093i	$-0.318677\pi$
$251$	17.0893	1.07867	0.539333	+	0.842093i	$0.318677\pi$
$252$	18.3008	1.15284
$253$	21.4508	1.34860
$254$	6.80696	0.427107
$255$	−1.56944	−0.0982820
$256$	−30.7341	−1.92088
$257$	−1.69780	−0.105906	−0.0529530	−	0.998597i	$-0.516863\pi$
$257$	−1.69780	−0.105906	−0.0529530	+	0.998597i	$0.516863\pi$
$258$	33.2181	2.06807
$259$	−0.503050	−0.0312580
$260$	21.5663	1.33749
$261$	−4.82907	−0.298912
$262$	42.9643	2.65434
$263$	17.3008	1.06681	0.533407	−	0.845859i	$-0.320911\pi$
$263$	17.3008	1.06681	0.533407	+	0.845859i	$0.320911\pi$
$264$	−29.6460	−1.82458
$265$	9.15858	0.562607
$266$	−12.7742	−0.783238
$267$	28.2804	1.73073
$268$	−1.73786	−0.106157
$269$	−18.7756	−1.14477	−0.572383	−	0.819986i	$-0.693981\pi$
$269$	−18.7756	−1.14477	−0.572383	+	0.819986i	$0.693981\pi$
$270$	−1.90872	−0.116161
$271$	11.8179	0.717888	0.358944	−	0.933359i	$-0.383137\pi$
$271$	11.8179	0.717888	0.358944	+	0.933359i	$0.383137\pi$
$272$	2.17790	0.132054
$273$	−23.3642	−1.41407
$274$	31.4389	1.89929
$275$	−2.72831	−0.164523
$276$	72.6679	4.37409
$277$	−7.04446	−0.423260	−0.211630	−	0.977350i	$-0.567877\pi$
$277$	−7.04446	−0.423260	−0.211630	+	0.977350i	$0.567877\pi$
$278$	32.4401	1.94563
$279$	18.9304	1.13333
$280$	−8.05984	−0.481668
$281$	22.0222	1.31373	0.656867	−	0.754006i	$-0.271881\pi$
$281$	22.0222	1.31373	0.656867	+	0.754006i	$0.271881\pi$
$282$	−32.8723	−1.95751
$283$	−25.2349	−1.50006	−0.750030	−	0.661404i	$-0.769961\pi$
$283$	−25.2349	−1.50006	−0.750030	+	0.661404i	$0.769961\pi$
$284$	10.8842	0.645859
$285$	−7.10116	−0.420636
$286$	36.7621	2.17379
$287$	−22.3850	−1.32135
$288$	2.97296	0.175183
$289$	−16.5655	−0.974444
$290$	4.38723	0.257627
$291$	−16.1158	−0.944726
$292$	−19.9565	−1.16787
$293$	0.486994	0.0284505	0.0142252	−	0.999899i	$-0.495472\pi$
$293$	0.486994	0.0284505	0.0142252	+	0.999899i	$0.495472\pi$
$294$	−22.4098	−1.30697
$295$	9.67733	0.563436
$296$	1.29983	0.0755512
$297$	−2.14726	−0.124597
$298$	−23.7961	−1.37847
$299$	−43.6822	−2.52621
$300$	−9.24257	−0.533620
$301$	10.1596	0.585590
$302$	49.0650	2.82337
$303$	22.8388	1.31206
$304$	9.85422	0.565178
$305$	2.54672	0.145825
$306$	−4.26725	−0.243943
$307$	0.0327294	0.00186797	0.000933983	−	1.00000i	$-0.499703\pi$
$307$	0.0327294	0.00186797	0.000933983		1.00000i	$0.499703\pi$
$308$	−18.7043	−1.06577
$309$	−20.3935	−1.16015
$310$	−17.1984	−0.976801
$311$	33.2783	1.88704	0.943519	−	0.331317i	$-0.107493\pi$
$311$	33.2783	1.88704	0.943519	+	0.331317i	$0.107493\pi$
$312$	60.3708	3.41783
$313$	0.406480	0.0229756	0.0114878	−	0.999934i	$-0.496343\pi$
$313$	0.406480	0.0229756	0.0114878	+	0.999934i	$0.496343\pi$
$314$	−10.0324	−0.566160
$315$	4.71465	0.265640
$316$	−27.6435	−1.55507
$317$	−1.51878	−0.0853030	−0.0426515	−	0.999090i	$-0.513581\pi$
$317$	−1.51878	−0.0853030	−0.0426515	+	0.999090i	$0.513581\pi$
$318$	52.8872	2.96577
$319$	4.93552	0.276336
$320$	−9.30932	−0.520407
$321$	−9.59723	−0.535665
$322$	33.6764	1.87671
$323$	1.96576	0.109378
$324$	−38.3603	−2.13113
$325$	5.55591	0.308186
$326$	−7.16115	−0.396619
$327$	28.6639	1.58512
$328$	57.8407	3.19372
$329$	−10.0539	−0.554287
$330$	−15.7549	−0.867280
$331$	2.07255	0.113918	0.0569589	−	0.998377i	$-0.481860\pi$
$331$	2.07255	0.113918	0.0569589	+	0.998377i	$0.481860\pi$
$332$	12.6302	0.693170
$333$	−0.760344	−0.0416666
$334$	5.02262	0.274826
$335$	−0.447707	−0.0244608
$336$	−13.8951	−0.758037
$337$	4.36869	0.237978	0.118989	−	0.992896i	$-0.462035\pi$
$337$	4.36869	0.237978	0.118989	+	0.992896i	$0.462035\pi$
$338$	−43.3341	−2.35706
$339$	42.3002	2.29743
$340$	2.55856	0.138757
$341$	−19.3477	−1.04774
$342$	−19.3078	−1.04405
$343$	−19.2169	−1.03762
$344$	−26.2515	−1.41538
$345$	18.7206	1.00789
$346$	−46.7882	−2.51535
$347$	19.8722	1.06679	0.533396	−	0.845865i	$-0.320915\pi$
$347$	19.8722	1.06679	0.533396	+	0.845865i	$0.320915\pi$
$348$	16.7198	0.896277
$349$	31.4701	1.68456	0.842279	−	0.539042i	$-0.181214\pi$
$349$	31.4701	1.68456	0.842279	+	0.539042i	$0.181214\pi$
$350$	−4.28328	−0.228951
$351$	4.37266	0.233395
$352$	−3.03850	−0.161952
$353$	14.5136	0.772480	0.386240	−	0.922398i	$-0.373774\pi$
$353$	14.5136	0.772480	0.386240	+	0.922398i	$0.373774\pi$
$354$	55.8828	2.97014
$355$	2.80398	0.148820
$356$	−46.1037	−2.44349
$357$	−2.77185	−0.146702
$358$	−24.9045	−1.31624
$359$	9.37639	0.494867	0.247433	−	0.968905i	$-0.420413\pi$
$359$	9.37639	0.494867	0.247433	+	0.968905i	$0.420413\pi$
$360$	−12.1822	−0.642058
$361$	−10.1056	−0.531874
$362$	33.7156	1.77205
$363$	8.46783	0.444446
$364$	38.0892	1.99642
$365$	−5.14118	−0.269102
$366$	14.7063	0.768711
$367$	6.69667	0.349563	0.174782	−	0.984607i	$-0.444078\pi$
$367$	6.69667	0.349563	0.174782	+	0.984607i	$0.444078\pi$
$368$	−25.9785	−1.35422
$369$	−33.8342	−1.76134
$370$	0.690776	0.0359117
$371$	16.1753	0.839782
$372$	−65.5433	−3.39826
$373$	−20.0272	−1.03697	−0.518485	−	0.855087i	$-0.673504\pi$
$373$	−20.0272	−1.03697	−0.518485	+	0.855087i	$0.673504\pi$
$374$	4.36132	0.225519
$375$	−2.38106	−0.122958
$376$	25.9782	1.33972
$377$	−10.0507	−0.517635
$378$	−3.37107	−0.173389
$379$	−25.5586	−1.31286	−0.656429	−	0.754387i	$-0.727934\pi$
$379$	−25.5586	−1.31286	−0.656429	+	0.754387i	$0.727934\pi$
$380$	11.5766	0.593865
$381$	6.68302	0.342381
$382$	64.9396	3.32260
$383$	31.0919	1.58872	0.794362	−	0.607445i	$-0.207805\pi$
$383$	31.0919	1.58872	0.794362	+	0.607445i	$0.207805\pi$
$384$	−48.4541	−2.47266
$385$	−4.81858	−0.245577
$386$	58.0710	2.95574
$387$	15.3559	0.780585
$388$	26.2726	1.33379
$389$	−11.1603	−0.565850	−0.282925	−	0.959142i	$-0.591305\pi$
$389$	−11.1603	−0.565850	−0.282925	+	0.959142i	$0.591305\pi$
$390$	32.0832	1.62459
$391$	−5.18230	−0.262080
$392$	17.7099	0.894487
$393$	42.1820	2.12780
$394$	3.28105	0.165297
$395$	−7.12150	−0.358322
$396$	−28.2709	−1.42067
$397$	−35.5322	−1.78331	−0.891655	−	0.452715i	$-0.850456\pi$
$397$	−35.5322	−1.78331	−0.891655	+	0.452715i	$0.850456\pi$
$398$	−6.78381	−0.340042
$399$	−12.5416	−0.627867
$400$	3.30418	0.165209
$401$	−4.66527	−0.232973	−0.116486	−	0.993192i	$-0.537163\pi$
$401$	−4.66527	−0.232973	−0.116486	+	0.993192i	$0.537163\pi$
$402$	−2.58533	−0.128945
$403$	39.3995	1.96263
$404$	−37.2327	−1.85240
$405$	−9.88236	−0.491058
$406$	7.74847	0.384550
$407$	0.777105	0.0385197
$408$	7.16218	0.354581
$409$	−23.4616	−1.16010	−0.580050	−	0.814581i	$-0.696967\pi$
$409$	−23.4616	−1.16010	−0.580050	+	0.814581i	$0.696967\pi$
$410$	30.7386	1.51807
$411$	30.8665	1.52253
$412$	33.2462	1.63792
$413$	17.0915	0.841019
$414$	50.9008	2.50164
$415$	3.25377	0.159721
$416$	6.18757	0.303370
$417$	31.8495	1.55967
$418$	19.7335	0.965195
$419$	13.1535	0.642590	0.321295	−	0.946979i	$-0.395882\pi$
$419$	13.1535	0.642590	0.321295	+	0.946979i	$0.395882\pi$
$420$	−16.3237	−0.796514
$421$	8.25026	0.402093	0.201047	−	0.979582i	$-0.435566\pi$
$421$	8.25026	0.402093	0.201047	+	0.979582i	$0.435566\pi$
$422$	−57.7560	−2.81152
$423$	−15.1961	−0.738858
$424$	−41.7955	−2.02977
$425$	0.659133	0.0319726
$426$	16.1919	0.784499
$427$	4.49787	0.217667
$428$	15.6458	0.756267
$429$	36.0927	1.74257
$430$	−13.9509	−0.672774
$431$	26.7642	1.28918	0.644592	−	0.764527i	$-0.277027\pi$
$431$	26.7642	1.28918	0.644592	+	0.764527i	$0.277027\pi$
$432$	2.60049	0.125116
$433$	−17.1009	−0.821814	−0.410907	−	0.911677i	$-0.634788\pi$
$433$	−17.1009	−0.821814	−0.410907	+	0.911677i	$0.634788\pi$
$434$	−30.3747	−1.45803
$435$	4.30735	0.206522
$436$	−46.7290	−2.23791
$437$	−23.4481	−1.12167
$438$	−29.6883	−1.41856
$439$	−2.38399	−0.113781	−0.0568907	−	0.998380i	$-0.518119\pi$
$439$	−2.38399	−0.113781	−0.0568907	+	0.998380i	$0.518119\pi$
$440$	12.4507	0.593566
$441$	−10.3595	−0.493310
$442$	−8.88136	−0.422443
$443$	29.1311	1.38406	0.692030	−	0.721869i	$-0.256717\pi$
$443$	29.1311	1.38406	0.692030	+	0.721869i	$0.256717\pi$
$444$	2.63256	0.124936
$445$	−11.8772	−0.563033
$446$	−41.1873	−1.95027
$447$	−23.3629	−1.10503
$448$	−16.4416	−0.776791
$449$	6.23425	0.294213	0.147106	−	0.989121i	$-0.453004\pi$
$449$	6.23425	0.294213	0.147106	+	0.989121i	$0.453004\pi$
$450$	−6.47404	−0.305189
$451$	34.5801	1.62831
$452$	−68.9593	−3.24357
$453$	48.1717	2.26330
$454$	8.52248	0.399980
$455$	9.81251	0.460017
$456$	32.4064	1.51757
$457$	−10.0381	−0.469562	−0.234781	−	0.972048i	$-0.575437\pi$
$457$	−10.0381	−0.469562	−0.234781	+	0.972048i	$0.575437\pi$
$458$	4.87658	0.227868
$459$	0.518757	0.0242135
$460$	−30.5191	−1.42296
$461$	−19.0634	−0.887869	−0.443934	−	0.896059i	$-0.646418\pi$
$461$	−19.0634	−0.887869	−0.443934	+	0.896059i	$0.646418\pi$
$462$	−27.8254	−1.29455
$463$	−33.1209	−1.53926	−0.769630	−	0.638490i	$-0.779560\pi$
$463$	−33.1209	−1.53926	−0.769630	+	0.638490i	$0.779560\pi$
$464$	−5.97728	−0.277488
$465$	−16.8852	−0.783033
$466$	−33.9010	−1.57043
$467$	−27.2318	−1.26014	−0.630070	−	0.776538i	$-0.716974\pi$
$467$	−27.2318	−1.26014	−0.630070	+	0.776538i	$0.716974\pi$
$468$	57.5706	2.66120
$469$	−0.790713	−0.0365117
$470$	13.8057	0.636810
$471$	−9.84972	−0.453851
$472$	−44.1628	−2.03276
$473$	−15.6944	−0.721631
$474$	−41.1239	−1.88888
$475$	2.98235	0.136839
$476$	4.51877	0.207117
$477$	24.4485	1.11942
$478$	−13.0613	−0.597411
$479$	−40.9387	−1.87054	−0.935269	−	0.353938i	$-0.884842\pi$
$479$	−40.9387	−1.87054	−0.935269	+	0.353938i	$0.884842\pi$
$480$	−2.65177	−0.121036
$481$	−1.58249	−0.0721553
$482$	25.4742	1.16032
$483$	33.0633	1.50443
$484$	−13.8046	−0.627481
$485$	6.76833	0.307334
$486$	−51.3405	−2.32885
$487$	35.8552	1.62475	0.812377	−	0.583132i	$-0.198173\pi$
$487$	35.8552	1.62475	0.812377	+	0.583132i	$0.198173\pi$
$488$	−11.6221	−0.526106
$489$	−7.03076	−0.317942
$490$	9.41167	0.425176
$491$	14.1824	0.640042	0.320021	−	0.947410i	$-0.396310\pi$
$491$	14.1824	0.640042	0.320021	+	0.947410i	$0.396310\pi$
$492$	117.145	5.28132
$493$	−1.19237	−0.0537018
$494$	−40.1850	−1.80801
$495$	−7.28312	−0.327352
$496$	23.4315	1.05210
$497$	4.95222	0.222138
$498$	18.7892	0.841966
$499$	7.71370	0.345313	0.172656	−	0.984982i	$-0.444765\pi$
$499$	7.71370	0.345313	0.172656	+	0.984982i	$0.444765\pi$
$500$	3.88170	0.173595
$501$	4.93117	0.220308
$502$	−41.4453	−1.84979
$503$	19.6008	0.873957	0.436979	−	0.899472i	$-0.356049\pi$
$503$	19.6008	0.873957	0.436979	+	0.899472i	$0.356049\pi$
$504$	−21.5154	−0.958374
$505$	−9.59186	−0.426832
$506$	−52.0229	−2.31270
$507$	−42.5451	−1.88949
$508$	−10.8949	−0.483383
$509$	−1.11743	−0.0495293	−0.0247647	−	0.999693i	$-0.507884\pi$
$509$	−1.11743	−0.0495293	−0.0247647	+	0.999693i	$0.507884\pi$
$510$	3.80623	0.168543
$511$	−9.08005	−0.401678
$512$	33.8374	1.49541
$513$	2.34719	0.103631
$514$	4.11755	0.181617
$515$	8.56487	0.377413
$516$	−53.1673	−2.34056
$517$	15.5311	0.683055
$518$	1.22001	0.0536041
$519$	−45.9363	−2.01638
$520$	−25.3546	−1.11187
$521$	−12.0763	−0.529072	−0.264536	−	0.964376i	$-0.585219\pi$
$521$	−12.0763	−0.529072	−0.264536	+	0.964376i	$0.585219\pi$
$522$	11.7116	0.512601
$523$	2.91181	0.127324	0.0636622	−	0.997972i	$-0.479722\pi$
$523$	2.91181	0.127324	0.0636622	+	0.997972i	$0.479722\pi$
$524$	−68.7667	−3.00409
$525$	−4.20529	−0.183534
$526$	−41.9583	−1.82947
$527$	4.67422	0.203612
$528$	21.4649	0.934140
$529$	38.8158	1.68764
$530$	−22.2116	−0.964810
$531$	25.8333	1.12107
$532$	20.4458	0.886440
$533$	−70.4186	−3.05017
$534$	−68.5861	−2.96801
$535$	4.03065	0.174260
$536$	2.04313	0.0882496
$537$	−24.4510	−1.05514
$538$	45.5349	1.96315
$539$	10.5879	0.456053
$540$	3.05501	0.131467
$541$	25.8160	1.10991	0.554957	−	0.831879i	$-0.312735\pi$
$541$	25.8160	1.10991	0.554957	+	0.831879i	$0.312735\pi$
$542$	−28.6611	−1.23110
$543$	33.1017	1.42053
$544$	0.734071	0.0314730
$545$	−12.0383	−0.515664
$546$	56.6634	2.42497
$547$	14.3003	0.611438	0.305719	−	0.952122i	$-0.401103\pi$
$547$	14.3003	0.611438	0.305719	+	0.952122i	$0.401103\pi$
$548$	−50.3197	−2.14955
$549$	6.79838	0.290148
$550$	6.61676	0.282139
$551$	−5.39507	−0.229838
$552$	−85.4323	−3.63624
$553$	−12.5776	−0.534853
$554$	17.0844	0.725845
$555$	0.678199	0.0287879
$556$	−51.9222	−2.20199
$557$	37.2945	1.58022	0.790108	−	0.612967i	$-0.210024\pi$
$557$	37.2945	1.58022	0.790108	+	0.612967i	$0.210024\pi$
$558$	−45.9104	−1.94354
$559$	31.9600	1.35176
$560$	5.83565	0.246601
$561$	4.28191	0.180782
$562$	−53.4087	−2.25291
$563$	−7.88998	−0.332523	−0.166262	−	0.986082i	$-0.553170\pi$
$563$	−7.88998	−0.332523	−0.166262	+	0.986082i	$0.553170\pi$
$564$	52.6138	2.21544
$565$	−17.7652	−0.747389
$566$	61.2002	2.57244
$567$	−17.4536	−0.732983
$568$	−12.7961	−0.536911
$569$	9.23350	0.387089	0.193544	−	0.981092i	$-0.438002\pi$
$569$	9.23350	0.387089	0.193544	+	0.981092i	$0.438002\pi$
$570$	17.2219	0.721345
$571$	43.9276	1.83831	0.919157	−	0.393890i	$-0.128871\pi$
$571$	43.9276	1.83831	0.919157	+	0.393890i	$0.128871\pi$
$572$	−58.8397	−2.46021
$573$	63.7572	2.66350
$574$	54.2886	2.26596
$575$	−7.86230	−0.327881
$576$	−24.8509	−1.03545
$577$	28.3287	1.17934	0.589669	−	0.807645i	$-0.299258\pi$
$577$	28.3287	1.17934	0.589669	+	0.807645i	$0.299258\pi$
$578$	40.1751	1.67106
$579$	57.0137	2.36941
$580$	−7.02200	−0.291573
$581$	5.74661	0.238410
$582$	39.0844	1.62010
$583$	−24.9874	−1.03487
$584$	23.4620	0.970863
$585$	14.8313	0.613198
$586$	−1.18107	−0.0487894
$587$	−32.2546	−1.33129	−0.665646	−	0.746268i	$-0.731844\pi$
$587$	−32.2546	−1.33129	−0.665646	+	0.746268i	$0.731844\pi$
$588$	35.8681	1.47918
$589$	21.1492	0.871437
$590$	−23.4697	−0.966231
$591$	3.22131	0.132507
$592$	−0.941131	−0.0386803
$593$	−24.2932	−0.997603	−0.498802	−	0.866716i	$-0.666226\pi$
$593$	−24.2932	−0.997603	−0.498802	+	0.866716i	$0.666226\pi$
$594$	5.20758	0.213670
$595$	1.16412	0.0477243
$596$	38.0870	1.56010
$597$	−6.66029	−0.272588
$598$	105.939	4.33217
$599$	9.13089	0.373078	0.186539	−	0.982448i	$-0.440273\pi$
$599$	9.13089	0.373078	0.186539	+	0.982448i	$0.440273\pi$
$600$	10.8661	0.443605
$601$	5.10815	0.208366	0.104183	−	0.994558i	$-0.466777\pi$
$601$	5.10815	0.208366	0.104183	+	0.994558i	$0.466777\pi$
$602$	−24.6393	−1.00422
$603$	−1.19514	−0.0486697
$604$	−78.5312	−3.19539
$605$	−3.55632	−0.144585
$606$	−55.3892	−2.25003
$607$	−41.2262	−1.67332	−0.836660	−	0.547722i	$-0.815495\pi$
$607$	−41.2262	−1.67332	−0.836660	+	0.547722i	$0.815495\pi$
$608$	3.32141	0.134701
$609$	7.60739	0.308267
$610$	−6.17636	−0.250074
$611$	−31.6273	−1.27950
$612$	6.82997	0.276085
$613$	−2.72502	−0.110063	−0.0550313	−	0.998485i	$-0.517526\pi$
$613$	−2.72502	−0.110063	−0.0550313	+	0.998485i	$0.517526\pi$
$614$	−0.0793761	−0.00320336
$615$	30.1789	1.21693
$616$	21.9897	0.885992
$617$	−14.3045	−0.575877	−0.287939	−	0.957649i	$-0.592970\pi$
$617$	−14.3045	−0.575877	−0.287939	+	0.957649i	$0.592970\pi$
$618$	49.4587	1.98952
$619$	−13.8964	−0.558542	−0.279271	−	0.960212i	$-0.590093\pi$
$619$	−13.8964	−0.558542	−0.279271	+	0.960212i	$0.590093\pi$
$620$	27.5269	1.10551
$621$	−6.18787	−0.248310
$622$	−80.7072	−3.23606
$623$	−20.9768	−0.840417
$624$	−43.7109	−1.74984
$625$	1.00000	0.0400000
$626$	−0.985805	−0.0394007
$627$	19.3742	0.773729
$628$	16.0574	0.640759
$629$	−0.187741	−0.00748572
$630$	−11.4341	−0.455544
$631$	0.590790	0.0235190	0.0117595	−	0.999931i	$-0.496257\pi$
$631$	0.590790	0.0235190	0.0117595	+	0.999931i	$0.496257\pi$
$632$	32.4992	1.29275
$633$	−56.7044	−2.25380
$634$	3.68337	0.146285
$635$	−2.80674	−0.111382
$636$	−84.6488	−3.35654
$637$	−21.5611	−0.854281
$638$	−11.9697	−0.473886
$639$	7.48512	0.296107
$640$	20.3498	0.804395
$641$	16.9543	0.669655	0.334827	−	0.942279i	$-0.391322\pi$
$641$	16.9543	0.669655	0.334827	+	0.942279i	$0.391322\pi$
$642$	23.2754	0.918607
$643$	−11.0627	−0.436269	−0.218135	−	0.975919i	$-0.569997\pi$
$643$	−11.0627	−0.436269	−0.218135	+	0.975919i	$0.569997\pi$
$644$	−53.9010	−2.12400
$645$	−13.6969	−0.539316
$646$	−4.76741	−0.187571
$647$	−25.9893	−1.02175	−0.510873	−	0.859656i	$-0.670678\pi$
$647$	−25.9893	−1.02175	−0.510873	+	0.859656i	$0.670678\pi$
$648$	45.0985	1.77164
$649$	−26.4028	−1.03640
$650$	−13.4743	−0.528506
$651$	−29.8217	−1.16880
$652$	11.4618	0.448879
$653$	−26.0273	−1.01853	−0.509263	−	0.860611i	$-0.670082\pi$
$653$	−26.0273	−1.01853	−0.509263	+	0.860611i	$0.670082\pi$
$654$	−69.5164	−2.71831
$655$	−17.7156	−0.692206
$656$	−41.8790	−1.63510
$657$	−13.7242	−0.535432
$658$	24.3828	0.950541
$659$	−33.9747	−1.32347	−0.661734	−	0.749739i	$-0.730179\pi$
$659$	−33.9747	−1.32347	−0.661734	+	0.749739i	$0.730179\pi$
$660$	25.2166	0.981555
$661$	5.30314	0.206268	0.103134	−	0.994667i	$-0.467113\pi$
$661$	5.30314	0.206268	0.103134	+	0.994667i	$0.467113\pi$
$662$	−5.02640	−0.195357
$663$	−8.71965	−0.338643
$664$	−14.8487	−0.576241
$665$	5.26724	0.204255
$666$	1.84400	0.0714536
$667$	14.2229	0.550714
$668$	−8.03897	−0.311037
$669$	−40.4374	−1.56340
$670$	1.08579	0.0419477
$671$	−6.94825	−0.268234
$672$	−4.68340	−0.180666
$673$	−29.2933	−1.12917	−0.564587	−	0.825374i	$-0.690964\pi$
$673$	−29.2933	−1.12917	−0.564587	+	0.825374i	$0.690964\pi$
$674$	−10.5950	−0.408105
$675$	0.787030	0.0302928
$676$	69.3585	2.66764
$677$	13.6537	0.524753	0.262376	−	0.964966i	$-0.415494\pi$
$677$	13.6537	0.524753	0.262376	+	0.964966i	$0.415494\pi$
$678$	−102.587	−3.93984
$679$	11.9538	0.458746
$680$	−3.00798	−0.115351
$681$	8.36731	0.320636
$682$	46.9225	1.79675
$683$	−27.4721	−1.05119	−0.525595	−	0.850735i	$-0.676157\pi$
$683$	−27.4721	−1.05119	−0.525595	+	0.850735i	$0.676157\pi$
$684$	30.9032	1.18161
$685$	−12.9633	−0.495303
$686$	46.6053	1.77940
$687$	4.78779	0.182666
$688$	19.0071	0.724640
$689$	50.8842	1.93853
$690$	−45.4017	−1.72841
$691$	−36.2662	−1.37963	−0.689816	−	0.723985i	$-0.742308\pi$
$691$	−36.2662	−1.37963	−0.689816	+	0.723985i	$0.742308\pi$
$692$	74.8870	2.84678
$693$	−12.8630	−0.488626
$694$	−48.1944	−1.82943
$695$	−13.3761	−0.507386
$696$	−19.6567	−0.745087
$697$	−8.35421	−0.316438
$698$	−76.3220	−2.88883
$699$	−33.2837	−1.25891
$700$	6.85562	0.259118
$701$	6.72525	0.254009	0.127005	−	0.991902i	$-0.459464\pi$
$701$	6.72525	0.254009	0.127005	+	0.991902i	$0.459464\pi$
$702$	−10.6047	−0.400248
$703$	−0.849462	−0.0320381
$704$	25.3987	0.957250
$705$	13.5543	0.510486
$706$	−35.1986	−1.32472
$707$	−16.9406	−0.637115
$708$	−89.4434	−3.36149
$709$	11.2352	0.421946	0.210973	−	0.977492i	$-0.432337\pi$
$709$	11.2352	0.421946	0.210973	+	0.977492i	$0.432337\pi$
$710$	−6.80027	−0.255210
$711$	−19.0106	−0.712953
$712$	54.2020	2.03131
$713$	−55.7552	−2.08805
$714$	6.72234	0.251577
$715$	−15.1582	−0.566886
$716$	39.8609	1.48967
$717$	−12.8235	−0.478903
$718$	−22.7398	−0.848643
$719$	−34.1899	−1.27507	−0.637533	−	0.770423i	$-0.720045\pi$
$719$	−34.1899	−1.27507	−0.637533	+	0.770423i	$0.720045\pi$
$720$	8.82040	0.328717
$721$	15.1268	0.563350
$722$	24.5083	0.912106
$723$	25.0104	0.930145
$724$	−53.9636	−2.00554
$725$	−1.80900	−0.0671847
$726$	−20.5364	−0.762176
$727$	−0.497927	−0.0184671	−0.00923355	−	0.999957i	$-0.502939\pi$
$727$	−0.497927	−0.0184671	−0.00923355	+	0.999957i	$0.502939\pi$
$728$	−44.7797	−1.65965
$729$	−20.7587	−0.768840
$730$	12.4685	0.461480
$731$	3.79162	0.140238
$732$	−23.5383	−0.869999
$733$	−43.7013	−1.61415	−0.807073	−	0.590452i	$-0.798949\pi$
$733$	−43.7013	−1.61415	−0.807073	+	0.590452i	$0.798949\pi$
$734$	−16.2409	−0.599463
$735$	9.24031	0.340834
$736$	−8.75618	−0.322757
$737$	1.22148	0.0449939
$738$	82.0555	3.02050
$739$	−4.77405	−0.175616	−0.0878081	−	0.996137i	$-0.527986\pi$
$739$	−4.77405	−0.175616	−0.0878081	+	0.996137i	$0.527986\pi$
$740$	−1.10562	−0.0406436
$741$	−39.4533	−1.44935
$742$	−39.2288	−1.44013
$743$	21.7357	0.797407	0.398704	−	0.917080i	$-0.369460\pi$
$743$	21.7357	0.797407	0.398704	+	0.917080i	$0.369460\pi$
$744$	77.0563	2.82502
$745$	9.81194	0.359482
$746$	48.5704	1.77829
$747$	8.68582	0.317797
$748$	−6.98053	−0.255234
$749$	7.11869	0.260111
$750$	5.77461	0.210859
$751$	30.1918	1.10172	0.550858	−	0.834599i	$-0.314301\pi$
$751$	30.1918	1.10172	0.550858	+	0.834599i	$0.314301\pi$
$752$	−18.8093	−0.685903
$753$	−40.6906	−1.48285
$754$	24.3751	0.887687
$755$	−20.2312	−0.736287
$756$	5.39558	0.196235
$757$	−12.5272	−0.455310	−0.227655	−	0.973742i	$-0.573106\pi$
$757$	−12.5272	−0.455310	−0.227655	+	0.973742i	$0.573106\pi$
$758$	61.9853	2.25141
$759$	−51.0757	−1.85393
$760$	−13.6100	−0.493688
$761$	−15.7609	−0.571334	−0.285667	−	0.958329i	$-0.592215\pi$
$761$	−15.7609	−0.571334	−0.285667	+	0.958329i	$0.592215\pi$
$762$	−16.2078	−0.587147
$763$	−21.2613	−0.769711
$764$	−103.939	−3.76040
$765$	1.75953	0.0636160
$766$	−75.4048	−2.72449
$767$	53.7664	1.94139
$768$	73.1797	2.64065
$769$	41.8909	1.51062	0.755312	−	0.655365i	$-0.227485\pi$
$769$	41.8909	1.51062	0.755312	+	0.655365i	$0.227485\pi$
$770$	11.6861	0.421138
$771$	4.04258	0.145590
$772$	−92.9458	−3.34519
$773$	−37.3719	−1.34418	−0.672088	−	0.740472i	$-0.734602\pi$
$773$	−37.3719	−1.34418	−0.672088	+	0.740472i	$0.734602\pi$
$774$	−37.2415	−1.33862
$775$	7.09146	0.254733
$776$	−30.8875	−1.10880
$777$	1.19779	0.0429706
$778$	27.0662	0.970371
$779$	−37.7999	−1.35432
$780$	−51.3508	−1.83866
$781$	−7.65013	−0.273743
$782$	12.5682	0.449439
$783$	−1.42374	−0.0508803
$784$	−12.8227	−0.457954
$785$	4.13669	0.147645
$786$	−102.301	−3.64894
$787$	−34.4921	−1.22951	−0.614755	−	0.788718i	$-0.710745\pi$
$787$	−34.4921	−1.22951	−0.614755	+	0.788718i	$0.710745\pi$
$788$	−5.25149	−0.187077
$789$	−41.1943	−1.46656
$790$	17.2712	0.614483
$791$	−31.3759	−1.11560
$792$	33.2368	1.18102
$793$	14.1493	0.502458
$794$	86.1735	3.05818
$795$	−21.8072	−0.773420
$796$	10.8579	0.384846
$797$	−16.1804	−0.573138	−0.286569	−	0.958060i	$-0.592515\pi$
$797$	−16.1804	−0.573138	−0.286569	+	0.958060i	$0.592515\pi$
$798$	30.4162	1.07672
$799$	−3.75215	−0.132742
$800$	1.11369	0.0393749
$801$	−31.7057	−1.12027
$802$	11.3143	0.399522
$803$	14.0267	0.494993
$804$	4.13796	0.145935
$805$	−13.8859	−0.489415
$806$	−95.5525	−3.36569
$807$	44.7058	1.57372
$808$	43.7728	1.53992
$809$	30.2825	1.06468	0.532339	−	0.846531i	$-0.321313\pi$
$809$	30.2825	1.06468	0.532339	+	0.846531i	$0.321313\pi$
$810$	23.9669	0.842111
$811$	−49.1785	−1.72689	−0.863446	−	0.504442i	$-0.831698\pi$
$811$	−49.1785	−1.72689	−0.863446	+	0.504442i	$0.831698\pi$
$812$	−12.4018	−0.435219
$813$	−28.1392	−0.986886
$814$	−1.88465	−0.0660570
$815$	2.95278	0.103431
$816$	−5.18571	−0.181536
$817$	17.1558	0.600204
$818$	56.8995	1.98945
$819$	26.1941	0.915297
$820$	−49.1987	−1.71809
$821$	−20.3071	−0.708724	−0.354362	−	0.935108i	$-0.615302\pi$
$821$	−20.3071	−0.708724	−0.354362	+	0.935108i	$0.615302\pi$
$822$	−74.8581	−2.61097
$823$	−10.9751	−0.382569	−0.191285	−	0.981535i	$-0.561265\pi$
$823$	−10.9751	−0.382569	−0.191285	+	0.981535i	$0.561265\pi$
$824$	−39.0861	−1.36163
$825$	6.49628	0.226171
$826$	−41.4507	−1.44226
$827$	−25.7680	−0.896042	−0.448021	−	0.894023i	$-0.647871\pi$
$827$	−25.7680	−0.896042	−0.448021	+	0.894023i	$0.647871\pi$
$828$	−81.4696	−2.83126
$829$	−35.6480	−1.23811	−0.619053	−	0.785349i	$-0.712483\pi$
$829$	−35.6480	−1.23811	−0.619053	+	0.785349i	$0.712483\pi$
$830$	−7.89111	−0.273905
$831$	16.7733	0.581859
$832$	−51.7217	−1.79313
$833$	−2.55793	−0.0886270
$834$	−77.2420	−2.67467
$835$	−2.07099	−0.0716697
$836$	−31.5845	−1.09237
$837$	5.58119	0.192914
$838$	−31.9001	−1.10197
$839$	41.3250	1.42670	0.713349	−	0.700809i	$-0.247177\pi$
$839$	41.3250	1.42670	0.713349	+	0.700809i	$0.247177\pi$
$840$	19.1910	0.662152
$841$	−25.7275	−0.887155
$842$	−20.0087	−0.689546
$843$	−52.4363	−1.80600
$844$	92.4416	3.18197
$845$	17.8681	0.614681
$846$	36.8538	1.26706
$847$	−6.28097	−0.215817
$848$	30.2616	1.03919
$849$	60.0859	2.06214
$850$	−1.59854	−0.0548296
$851$	2.23942	0.0767664
$852$	−25.9160	−0.887867
$853$	−25.6890	−0.879574	−0.439787	−	0.898102i	$-0.644946\pi$
$853$	−25.6890	−0.879574	−0.439787	+	0.898102i	$0.644946\pi$
$854$	−10.9083	−0.373275
$855$	7.96126	0.272269
$856$	−18.3940	−0.628694
$857$	10.3291	0.352837	0.176418	−	0.984315i	$-0.443549\pi$
$857$	10.3291	0.352837	0.176418	+	0.984315i	$0.443549\pi$
$858$	−87.5328	−2.98832
$859$	−23.0836	−0.787602	−0.393801	−	0.919196i	$-0.628840\pi$
$859$	−23.0836	−0.787602	−0.393801	+	0.919196i	$0.628840\pi$
$860$	22.3292	0.761421
$861$	53.3001	1.81646
$862$	−64.9090	−2.21081
$863$	−29.1450	−0.992108	−0.496054	−	0.868292i	$-0.665218\pi$
$863$	−29.1450	−0.992108	−0.496054	+	0.868292i	$0.665218\pi$
$864$	0.876508	0.0298194
$865$	19.2923	0.655959
$866$	41.4733	1.40932
$867$	39.4436	1.33958
$868$	48.6164	1.65015
$869$	19.4297	0.659106
$870$	−10.4463	−0.354162
$871$	−2.48742	−0.0842829
$872$	54.9372	1.86041
$873$	18.0678	0.611503
$874$	56.8668	1.92355
$875$	1.76614	0.0597064
$876$	47.5177	1.60548
$877$	35.2718	1.19105	0.595523	−	0.803338i	$-0.296945\pi$
$877$	35.2718	1.19105	0.595523	+	0.803338i	$0.296945\pi$
$878$	5.78169	0.195123
$879$	−1.15956	−0.0391111
$880$	−9.01484	−0.303890
$881$	−15.3942	−0.518645	−0.259323	−	0.965791i	$-0.583499\pi$
$881$	−15.3942	−0.518645	−0.259323	+	0.965791i	$0.583499\pi$
$882$	25.1241	0.845973
$883$	−14.8922	−0.501162	−0.250581	−	0.968096i	$-0.580622\pi$
$883$	−14.8922	−0.501162	−0.250581	+	0.968096i	$0.580622\pi$
$884$	14.2151	0.478105
$885$	−23.0423	−0.774560
$886$	−70.6493	−2.37351
$887$	11.4510	0.384487	0.192243	−	0.981347i	$-0.438424\pi$
$887$	11.4510	0.384487	0.192243	+	0.981347i	$0.438424\pi$
$888$	−3.09498	−0.103861
$889$	−4.95709	−0.166255
$890$	28.8048	0.965540
$891$	26.9621	0.903265
$892$	65.9225	2.20725
$893$	−16.9772	−0.568119
$894$	56.6601	1.89500
$895$	10.2689	0.343253
$896$	35.9405	1.20069
$897$	104.010	3.47280
$898$	−15.1194	−0.504542
$899$	−12.8285	−0.427854
$900$	10.3620	0.345402
$901$	6.03672	0.201112
$902$	−83.8643	−2.79238
$903$	−24.1907	−0.805016
$904$	81.0723	2.69642
$905$	−13.9021	−0.462120
$906$	−116.827	−3.88131
$907$	47.0098	1.56094	0.780468	−	0.625196i	$-0.214981\pi$
$907$	47.0098	1.56094	0.780468	+	0.625196i	$0.214981\pi$
$908$	−13.6407	−0.452682
$909$	−25.6051	−0.849268
$910$	−23.7975	−0.788880
$911$	−53.1106	−1.75963	−0.879816	−	0.475314i	$-0.842334\pi$
$911$	−53.1106	−1.75963	−0.879816	+	0.475314i	$0.842334\pi$
$912$	−23.4635	−0.776955
$913$	−8.87729	−0.293796
$914$	24.3446	0.805248
$915$	−6.06391	−0.200467
$916$	−7.80524	−0.257892
$917$	−31.2883	−1.03323
$918$	−1.25810	−0.0415235
$919$	0.00856049	0.000282385 0	0.000141192	−	1.00000i	$-0.499955\pi$
$919$	0.00856049	0.000282385 0	0.000141192		1.00000i	$0.499955\pi$
$920$	35.8799	1.18292
$921$	−0.0779308	−0.00256791
$922$	46.2328	1.52260
$923$	15.5787	0.512778
$924$	44.5360	1.46513
$925$	−0.284830	−0.00936516
$926$	80.3256	2.63966
$927$	22.8636	0.750939
$928$	−2.01467	−0.0661348
$929$	−13.7246	−0.450288	−0.225144	−	0.974326i	$-0.572285\pi$
$929$	−13.7246	−0.450288	−0.225144	+	0.974326i	$0.572285\pi$
$930$	40.9504	1.34282
$931$	−11.5737	−0.379314
$932$	54.2604	1.77736
$933$	−79.2377	−2.59413
$934$	66.0433	2.16100
$935$	−1.79832	−0.0588113
$936$	−67.6831	−2.21229
$937$	4.13889	0.135211	0.0676057	−	0.997712i	$-0.478464\pi$
$937$	4.13889	0.135211	0.0676057	+	0.997712i	$0.478464\pi$
$938$	1.91765	0.0626136
$939$	−0.967855	−0.0315848
$940$	−22.0968	−0.720718
$941$	29.5575	0.963548	0.481774	−	0.876295i	$-0.339993\pi$
$941$	29.5575	0.963548	0.481774	+	0.876295i	$0.339993\pi$
$942$	23.8877	0.778305
$943$	99.6511	3.24509
$944$	31.9757	1.04072
$945$	1.39000	0.0452169
$946$	38.0625	1.23752
$947$	21.2716	0.691233	0.345617	−	0.938376i	$-0.387670\pi$
$947$	21.2716	0.691233	0.345617	+	0.938376i	$0.387670\pi$
$948$	65.8210	2.13777
$949$	−28.5639	−0.927224
$950$	−7.23285	−0.234665
$951$	3.61630	0.117267
$952$	−5.31251	−0.172179
$953$	−48.7408	−1.57887	−0.789435	−	0.613835i	$-0.789626\pi$
$953$	−48.7408	−1.57887	−0.789435	+	0.613835i	$0.789626\pi$
$954$	−59.2930	−1.91968
$955$	−26.7768	−0.866476
$956$	20.9054	0.676128
$957$	−11.7518	−0.379881
$958$	99.2855	3.20777
$959$	−22.8950	−0.739319
$960$	22.1661	0.715407
$961$	19.2888	0.622220
$962$	3.83789	0.123738
$963$	10.7597	0.346726
$964$	−40.7728	−1.31320
$965$	−23.9446	−0.770805
$966$	−80.1858	−2.57993
$967$	−4.56961	−0.146949	−0.0734744	−	0.997297i	$-0.523409\pi$
$967$	−4.56961	−0.146949	−0.0734744	+	0.997297i	$0.523409\pi$
$968$	16.2294	0.521633
$969$	−4.68061	−0.150363
$970$	−16.4147	−0.527044
$971$	−11.4737	−0.368208	−0.184104	−	0.982907i	$-0.558938\pi$
$971$	−11.4737	−0.368208	−0.184104	+	0.982907i	$0.558938\pi$
$972$	82.1733	2.63571
$973$	−23.6242	−0.757356
$974$	−86.9568	−2.78628
$975$	−13.2290	−0.423666
$976$	8.41484	0.269352
$977$	33.2548	1.06392	0.531958	−	0.846771i	$-0.321457\pi$
$977$	33.2548	1.06392	0.531958	+	0.846771i	$0.321457\pi$
$978$	17.0511	0.545235
$979$	32.4047	1.03566
$980$	−15.0639	−0.481198
$981$	−32.1358	−1.02602
$982$	−34.3954	−1.09760
$983$	−15.7629	−0.502760	−0.251380	−	0.967888i	$-0.580884\pi$
$983$	−15.7629	−0.502760	−0.251380	+	0.967888i	$0.580884\pi$
$984$	−137.722	−4.39043
$985$	−1.35289	−0.0431065
$986$	2.89177	0.0920927
$987$	23.9389	0.761982
$988$	64.3183	2.04624
$989$	−45.2274	−1.43815
$990$	17.6632	0.561373
$991$	−51.6725	−1.64143	−0.820716	−	0.571337i	$-0.806425\pi$
$991$	−51.6725	−1.64143	−0.820716	+	0.571337i	$0.806425\pi$
$992$	7.89770	0.250752
$993$	−4.93488	−0.156604
$994$	−12.0102	−0.380942
$995$	2.79719	0.0886769
$996$	−30.0732	−0.952906
$997$	56.5089	1.78966	0.894828	−	0.446412i	$-0.147298\pi$
$997$	56.5089	1.78966	0.894828	+	0.446412i	$0.147298\pi$
$998$	−18.7074	−0.592173
$999$	−0.224170	−0.00709242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.b.1.12	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.b.1.12	✓	114	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42522 q^{2} -2.38106 q^{3} +3.88170 q^{4} +1.00000 q^{5} +5.77461 q^{6} +1.76614 q^{7} -4.56353 q^{8} +2.66946 q^{9} +O(q^{10})\)	\(q-2.42522 q^{2} -2.38106 q^{3} +3.88170 q^{4} +1.00000 q^{5} +5.77461 q^{6} +1.76614 q^{7} -4.56353 q^{8} +2.66946 q^{9} -2.42522 q^{10} -2.72831 q^{11} -9.24257 q^{12} +5.55591 q^{13} -4.28328 q^{14} -2.38106 q^{15} +3.30418 q^{16} +0.659133 q^{17} -6.47404 q^{18} +2.98235 q^{19} +3.88170 q^{20} -4.20529 q^{21} +6.61676 q^{22} -7.86230 q^{23} +10.8661 q^{24} +1.00000 q^{25} -13.4743 q^{26} +0.787030 q^{27} +6.85562 q^{28} -1.80900 q^{29} +5.77461 q^{30} +7.09146 q^{31} +1.11369 q^{32} +6.49628 q^{33} -1.59854 q^{34} +1.76614 q^{35} +10.3620 q^{36} -0.284830 q^{37} -7.23285 q^{38} -13.2290 q^{39} -4.56353 q^{40} -12.6745 q^{41} +10.1988 q^{42} +5.75244 q^{43} -10.5905 q^{44} +2.66946 q^{45} +19.0678 q^{46} -5.69256 q^{47} -7.86747 q^{48} -3.88075 q^{49} -2.42522 q^{50} -1.56944 q^{51} +21.5663 q^{52} +9.15858 q^{53} -1.90872 q^{54} -2.72831 q^{55} -8.05984 q^{56} -7.10116 q^{57} +4.38723 q^{58} +9.67733 q^{59} -9.24257 q^{60} +2.54672 q^{61} -17.1984 q^{62} +4.71465 q^{63} -9.30932 q^{64} +5.55591 q^{65} -15.7549 q^{66} -0.447707 q^{67} +2.55856 q^{68} +18.7206 q^{69} -4.28328 q^{70} +2.80398 q^{71} -12.1822 q^{72} -5.14118 q^{73} +0.690776 q^{74} -2.38106 q^{75} +11.5766 q^{76} -4.81858 q^{77} +32.0832 q^{78} -7.12150 q^{79} +3.30418 q^{80} -9.88236 q^{81} +30.7386 q^{82} +3.25377 q^{83} -16.3237 q^{84} +0.659133 q^{85} -13.9509 q^{86} +4.30735 q^{87} +12.4507 q^{88} -11.8772 q^{89} -6.47404 q^{90} +9.81251 q^{91} -30.5191 q^{92} -16.8852 q^{93} +13.8057 q^{94} +2.98235 q^{95} -2.65177 q^{96} +6.76833 q^{97} +9.41167 q^{98} -7.28312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * q^99

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