LMFDB - Embedded newform 8035.2.a.c.1.17

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:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.09243 q^{2} -1.43223 q^{3} +2.37828 q^{4} -1.00000 q^{5} +2.99685 q^{6} -1.24970 q^{7} -0.791531 q^{8} -0.948714 q^{9} +O(q^{10})$	\(q-2.09243 q^{2} -1.43223 q^{3} +2.37828 q^{4} -1.00000 q^{5} +2.99685 q^{6} -1.24970 q^{7} -0.791531 q^{8} -0.948714 q^{9} +2.09243 q^{10} +2.93180 q^{11} -3.40625 q^{12} -2.32991 q^{13} +2.61492 q^{14} +1.43223 q^{15} -3.10034 q^{16} +2.74135 q^{17} +1.98512 q^{18} -6.72100 q^{19} -2.37828 q^{20} +1.78986 q^{21} -6.13460 q^{22} -9.08546 q^{23} +1.13366 q^{24} +1.00000 q^{25} +4.87519 q^{26} +5.65547 q^{27} -2.97214 q^{28} -9.80823 q^{29} -2.99685 q^{30} +0.937775 q^{31} +8.07032 q^{32} -4.19902 q^{33} -5.73609 q^{34} +1.24970 q^{35} -2.25631 q^{36} +1.97884 q^{37} +14.0632 q^{38} +3.33697 q^{39} +0.791531 q^{40} -7.03396 q^{41} -3.74516 q^{42} -3.12709 q^{43} +6.97265 q^{44} +0.948714 q^{45} +19.0107 q^{46} -6.51664 q^{47} +4.44040 q^{48} -5.43825 q^{49} -2.09243 q^{50} -3.92624 q^{51} -5.54119 q^{52} +1.59351 q^{53} -11.8337 q^{54} -2.93180 q^{55} +0.989176 q^{56} +9.62602 q^{57} +20.5231 q^{58} -8.81278 q^{59} +3.40625 q^{60} +0.187223 q^{61} -1.96223 q^{62} +1.18561 q^{63} -10.6859 q^{64} +2.32991 q^{65} +8.78617 q^{66} -3.91562 q^{67} +6.51970 q^{68} +13.0125 q^{69} -2.61492 q^{70} +3.70108 q^{71} +0.750937 q^{72} +4.37612 q^{73} -4.14060 q^{74} -1.43223 q^{75} -15.9844 q^{76} -3.66387 q^{77} -6.98240 q^{78} +12.4634 q^{79} +3.10034 q^{80} -5.25380 q^{81} +14.7181 q^{82} -0.231146 q^{83} +4.25679 q^{84} -2.74135 q^{85} +6.54324 q^{86} +14.0477 q^{87} -2.32061 q^{88} -17.1881 q^{89} -1.98512 q^{90} +2.91169 q^{91} -21.6078 q^{92} -1.34311 q^{93} +13.6357 q^{94} +6.72100 q^{95} -11.5586 q^{96} -0.112329 q^{97} +11.3792 q^{98} -2.78144 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.09243	−1.47957	−0.739787	−	0.672841i	$-0.765074\pi$
$2$	−2.09243	−1.47957	−0.739787	+	0.672841i	$0.765074\pi$
$3$	−1.43223	−0.826899	−0.413450	−	0.910527i	$-0.635676\pi$
$3$	−1.43223	−0.826899	−0.413450	+	0.910527i	$0.635676\pi$
$4$	2.37828	1.18914
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.99685	1.22346
$7$	−1.24970	−0.472342	−0.236171	−	0.971711i	$-0.575893\pi$
$7$	−1.24970	−0.472342	−0.236171	+	0.971711i	$0.575893\pi$
$8$	−0.791531	−0.279849
$9$	−0.948714	−0.316238
$10$	2.09243	0.661686
$11$	2.93180	0.883971	0.441986	−	0.897022i	$-0.354274\pi$
$11$	2.93180	0.883971	0.441986	+	0.897022i	$0.354274\pi$
$12$	−3.40625	−0.983300
$13$	−2.32991	−0.646202	−0.323101	−	0.946365i	$-0.604725\pi$
$13$	−2.32991	−0.646202	−0.323101	+	0.946365i	$0.604725\pi$
$14$	2.61492	0.698866
$15$	1.43223	0.369800
$16$	−3.10034	−0.775084
$17$	2.74135	0.664875	0.332437	−	0.943125i	$-0.392129\pi$
$17$	2.74135	0.664875	0.332437	+	0.943125i	$0.392129\pi$
$18$	1.98512	0.467898
$19$	−6.72100	−1.54190	−0.770951	−	0.636894i	$-0.780219\pi$
$19$	−6.72100	−1.54190	−0.770951	+	0.636894i	$0.780219\pi$
$20$	−2.37828	−0.531800
$21$	1.78986	0.390579
$22$	−6.13460	−1.30790
$23$	−9.08546	−1.89445	−0.947224	−	0.320572i	$-0.896125\pi$
$23$	−9.08546	−1.89445	−0.947224	+	0.320572i	$0.896125\pi$
$24$	1.13366	0.231406
$25$	1.00000	0.200000
$26$	4.87519	0.956104
$27$	5.65547	1.08840
$28$	−2.97214	−0.561682
$29$	−9.80823	−1.82134	−0.910672	−	0.413131i	$-0.864435\pi$
$29$	−9.80823	−1.82134	−0.910672	+	0.413131i	$0.864435\pi$
$30$	−2.99685	−0.547147
$31$	0.937775	0.168429	0.0842147	−	0.996448i	$-0.473162\pi$
$31$	0.937775	0.168429	0.0842147	+	0.996448i	$0.473162\pi$
$32$	8.07032	1.42664
$33$	−4.19902	−0.730955
$34$	−5.73609	−0.983732
$35$	1.24970	0.211238
$36$	−2.25631	−0.376052
$37$	1.97884	0.325320	0.162660	−	0.986682i	$-0.447993\pi$
$37$	1.97884	0.325320	0.162660	+	0.986682i	$0.447993\pi$
$38$	14.0632	2.28136
$39$	3.33697	0.534344
$40$	0.791531	0.125152
$41$	−7.03396	−1.09852	−0.549260	−	0.835652i	$-0.685090\pi$
$41$	−7.03396	−1.09852	−0.549260	+	0.835652i	$0.685090\pi$
$42$	−3.74516	−0.577891
$43$	−3.12709	−0.476877	−0.238439	−	0.971158i	$-0.576636\pi$
$43$	−3.12709	−0.476877	−0.238439	+	0.971158i	$0.576636\pi$
$44$	6.97265	1.05117
$45$	0.948714	0.141426
$46$	19.0107	2.80298
$47$	−6.51664	−0.950550	−0.475275	−	0.879837i	$-0.657651\pi$
$47$	−6.51664	−0.950550	−0.475275	+	0.879837i	$0.657651\pi$
$48$	4.44040	0.640917
$49$	−5.43825	−0.776893
$50$	−2.09243	−0.295915
$51$	−3.92624	−0.549784
$52$	−5.54119	−0.768425
$53$	1.59351	0.218886	0.109443	−	0.993993i	$-0.465093\pi$
$53$	1.59351	0.218886	0.109443	+	0.993993i	$0.465093\pi$
$54$	−11.8337	−1.61036
$55$	−2.93180	−0.395324
$56$	0.989176	0.132184
$57$	9.62602	1.27500
$58$	20.5231	2.69481
$59$	−8.81278	−1.14733	−0.573663	−	0.819091i	$-0.694478\pi$
$59$	−8.81278	−1.14733	−0.573663	+	0.819091i	$0.694478\pi$
$60$	3.40625	0.439745
$61$	0.187223	0.0239715	0.0119858	−	0.999928i	$-0.496185\pi$
$61$	0.187223	0.0239715	0.0119858	+	0.999928i	$0.496185\pi$
$62$	−1.96223	−0.249204
$63$	1.18561	0.149373
$64$	−10.6859	−1.33574
$65$	2.32991	0.288990
$66$	8.78617	1.08150
$67$	−3.91562	−0.478369	−0.239184	−	0.970974i	$-0.576880\pi$
$67$	−3.91562	−0.478369	−0.239184	+	0.970974i	$0.576880\pi$
$68$	6.51970	0.790630
$69$	13.0125	1.56652
$70$	−2.61492	−0.312542
$71$	3.70108	0.439237	0.219618	−	0.975586i	$-0.429519\pi$
$71$	3.70108	0.439237	0.219618	+	0.975586i	$0.429519\pi$
$72$	0.750937	0.0884987
$73$	4.37612	0.512186	0.256093	−	0.966652i	$-0.417565\pi$
$73$	4.37612	0.512186	0.256093	+	0.966652i	$0.417565\pi$
$74$	−4.14060	−0.481335
$75$	−1.43223	−0.165380
$76$	−15.9844	−1.83354
$77$	−3.66387	−0.417537
$78$	−6.98240	−0.790601
$79$	12.4634	1.40224	0.701122	−	0.713041i	$-0.252683\pi$
$79$	12.4634	1.40224	0.701122	+	0.713041i	$0.252683\pi$
$80$	3.10034	0.346628
$81$	−5.25380	−0.583756
$82$	14.7181	1.62534
$83$	−0.231146	−0.0253715	−0.0126858	−	0.999920i	$-0.504038\pi$
$83$	−0.231146	−0.0253715	−0.0126858	+	0.999920i	$0.504038\pi$
$84$	4.25679	0.464454
$85$	−2.74135	−0.297341
$86$	6.54324	0.705576
$87$	14.0477	1.50607
$88$	−2.32061	−0.247378
$89$	−17.1881	−1.82193	−0.910967	−	0.412479i	$-0.864663\pi$
$89$	−17.1881	−1.82193	−0.910967	+	0.412479i	$0.864663\pi$
$90$	−1.98512	−0.209250
$91$	2.91169	0.305228
$92$	−21.6078	−2.25277
$93$	−1.34311	−0.139274
$94$	13.6357	1.40641
$95$	6.72100	0.689560
$96$	−11.5586	−1.17969
$97$	−0.112329	−0.0114053	−0.00570264	−	0.999984i	$-0.501815\pi$
$97$	−0.112329	−0.0114053	−0.00570264	+	0.999984i	$0.501815\pi$
$98$	11.3792	1.14947
$99$	−2.78144	−0.279545
$100$	2.37828	0.237828
$101$	1.01386	0.100883	0.0504413	−	0.998727i	$-0.483937\pi$
$101$	1.01386	0.100883	0.0504413	+	0.998727i	$0.483937\pi$
$102$	8.21541	0.813447
$103$	11.4052	1.12379	0.561893	−	0.827210i	$-0.310073\pi$
$103$	11.4052	1.12379	0.561893	+	0.827210i	$0.310073\pi$
$104$	1.84420	0.180839
$105$	−1.78986	−0.174672
$106$	−3.33432	−0.323858
$107$	−5.42982	−0.524920	−0.262460	−	0.964943i	$-0.584534\pi$
$107$	−5.42982	−0.524920	−0.262460	+	0.964943i	$0.584534\pi$
$108$	13.4503	1.29426
$109$	−17.7002	−1.69537	−0.847686	−	0.530498i	$-0.822005\pi$
$109$	−17.7002	−1.69537	−0.847686	+	0.530498i	$0.822005\pi$
$110$	6.13460	0.584911
$111$	−2.83416	−0.269007
$112$	3.87449	0.366105
$113$	2.67072	0.251240	0.125620	−	0.992078i	$-0.459908\pi$
$113$	2.67072	0.251240	0.125620	+	0.992078i	$0.459908\pi$
$114$	−20.1418	−1.88645
$115$	9.08546	0.847223
$116$	−23.3267	−2.16583
$117$	2.21042	0.204354
$118$	18.4402	1.69756
$119$	−3.42586	−0.314048
$120$	−1.13366	−0.103488
$121$	−2.40454	−0.218595
$122$	−0.391753	−0.0354676
$123$	10.0743	0.908365
$124$	2.23029	0.200286
$125$	−1.00000	−0.0894427
$126$	−2.48081	−0.221008
$127$	−10.3338	−0.916979	−0.458489	−	0.888700i	$-0.651609\pi$
$127$	−10.3338	−0.916979	−0.458489	+	0.888700i	$0.651609\pi$
$128$	6.21898	0.549686
$129$	4.47872	0.394329
$130$	−4.87519	−0.427583
$131$	4.24578	0.370956	0.185478	−	0.982648i	$-0.440617\pi$
$131$	4.24578	0.370956	0.185478	+	0.982648i	$0.440617\pi$
$132$	−9.98645	−0.869209
$133$	8.39923	0.728306
$134$	8.19318	0.707783
$135$	−5.65547	−0.486745
$136$	−2.16986	−0.186064
$137$	2.26108	0.193177	0.0965885	−	0.995324i	$-0.469207\pi$
$137$	2.26108	0.193177	0.0965885	+	0.995324i	$0.469207\pi$
$138$	−27.2277	−2.31778
$139$	−7.70009	−0.653113	−0.326557	−	0.945178i	$-0.605888\pi$
$139$	−7.70009	−0.653113	−0.326557	+	0.945178i	$0.605888\pi$
$140$	2.97214	0.251192
$141$	9.33334	0.786009
$142$	−7.74426	−0.649884
$143$	−6.83084	−0.571224
$144$	2.94133	0.245111
$145$	9.80823	0.814529
$146$	−9.15674	−0.757817
$147$	7.78883	0.642412
$148$	4.70625	0.386851
$149$	9.14412	0.749116	0.374558	−	0.927204i	$-0.377795\pi$
$149$	9.14412	0.749116	0.374558	+	0.927204i	$0.377795\pi$
$150$	2.99685	0.244692
$151$	−20.2965	−1.65171	−0.825854	−	0.563885i	$-0.809306\pi$
$151$	−20.2965	−1.65171	−0.825854	+	0.563885i	$0.809306\pi$
$152$	5.31988	0.431499
$153$	−2.60076	−0.210259
$154$	7.66641	0.617777
$155$	−0.937775	−0.0753239
$156$	7.93627	0.635410
$157$	6.68384	0.533428	0.266714	−	0.963776i	$-0.414062\pi$
$157$	6.68384	0.533428	0.266714	+	0.963776i	$0.414062\pi$
$158$	−26.0789	−2.07473
$159$	−2.28228	−0.180996
$160$	−8.07032	−0.638014
$161$	11.3541	0.894828
$162$	10.9932	0.863710
$163$	−14.4947	−1.13531	−0.567656	−	0.823266i	$-0.692150\pi$
$163$	−14.4947	−1.13531	−0.567656	+	0.823266i	$0.692150\pi$
$164$	−16.7287	−1.30630
$165$	4.19902	0.326893
$166$	0.483657	0.0375391
$167$	−2.03391	−0.157389	−0.0786945	−	0.996899i	$-0.525075\pi$
$167$	−2.03391	−0.157389	−0.0786945	+	0.996899i	$0.525075\pi$
$168$	−1.41673	−0.109303
$169$	−7.57150	−0.582423
$170$	5.73609	0.439938
$171$	6.37630	0.487608
$172$	−7.43711	−0.567074
$173$	0.243310	0.0184985	0.00924926	−	0.999957i	$-0.497056\pi$
$173$	0.243310	0.0184985	0.00924926	+	0.999957i	$0.497056\pi$
$174$	−29.3938	−2.22834
$175$	−1.24970	−0.0944684
$176$	−9.08957	−0.685152
$177$	12.6219	0.948723
$178$	35.9650	2.69569
$179$	−11.0799	−0.828151	−0.414076	−	0.910243i	$-0.635895\pi$
$179$	−11.0799	−0.828151	−0.414076	+	0.910243i	$0.635895\pi$
$180$	2.25631	0.168175
$181$	−4.18528	−0.311089	−0.155545	−	0.987829i	$-0.549713\pi$
$181$	−4.18528	−0.311089	−0.155545	+	0.987829i	$0.549713\pi$
$182$	−6.09253	−0.451608
$183$	−0.268147	−0.0198220
$184$	7.19142	0.530159
$185$	−1.97884	−0.145487
$186$	2.81037	0.206066
$187$	8.03709	0.587730
$188$	−15.4984	−1.13034
$189$	−7.06764	−0.514095
$190$	−14.0632	−1.02025
$191$	−10.6658	−0.771753	−0.385876	−	0.922550i	$-0.626101\pi$
$191$	−10.6658	−0.771753	−0.385876	+	0.922550i	$0.626101\pi$
$192$	15.3047	1.10452
$193$	−6.15101	−0.442759	−0.221380	−	0.975188i	$-0.571056\pi$
$193$	−6.15101	−0.442759	−0.221380	+	0.975188i	$0.571056\pi$
$194$	0.235041	0.0168750
$195$	−3.33697	−0.238966
$196$	−12.9337	−0.923835
$197$	−1.45650	−0.103771	−0.0518855	−	0.998653i	$-0.516523\pi$
$197$	−1.45650	−0.103771	−0.0518855	+	0.998653i	$0.516523\pi$
$198$	5.81998	0.413608
$199$	−4.34884	−0.308281	−0.154141	−	0.988049i	$-0.549261\pi$
$199$	−4.34884	−0.308281	−0.154141	+	0.988049i	$0.549261\pi$
$200$	−0.791531	−0.0559697
$201$	5.60807	0.395563
$202$	−2.12143	−0.149263
$203$	12.2574	0.860297
$204$	−9.33772	−0.653771
$205$	7.03396	0.491273
$206$	−23.8646	−1.66273
$207$	8.61950	0.599097
$208$	7.22352	0.500861
$209$	−19.7046	−1.36300
$210$	3.74516	0.258441
$211$	−5.22628	−0.359792	−0.179896	−	0.983686i	$-0.557576\pi$
$211$	−5.22628	−0.359792	−0.179896	+	0.983686i	$0.557576\pi$
$212$	3.78982	0.260286
$213$	−5.30080	−0.363205
$214$	11.3615	0.776659
$215$	3.12709	0.213266
$216$	−4.47648	−0.304586
$217$	−1.17194	−0.0795563
$218$	37.0365	2.50843
$219$	−6.26761	−0.423526
$220$	−6.97265	−0.470096
$221$	−6.38711	−0.429643
$222$	5.93029	0.398015
$223$	−23.6207	−1.58176	−0.790879	−	0.611973i	$-0.790376\pi$
$223$	−23.6207	−1.58176	−0.790879	+	0.611973i	$0.790376\pi$
$224$	−10.0855	−0.673864
$225$	−0.948714	−0.0632476
$226$	−5.58831	−0.371729
$227$	14.5342	0.964666	0.482333	−	0.875988i	$-0.339790\pi$
$227$	14.5342	0.964666	0.482333	+	0.875988i	$0.339790\pi$
$228$	22.8934	1.51615
$229$	15.0708	0.995905	0.497952	−	0.867204i	$-0.334085\pi$
$229$	15.0708	0.995905	0.497952	+	0.867204i	$0.334085\pi$
$230$	−19.0107	−1.25353
$231$	5.24751	0.345261
$232$	7.76352	0.509700
$233$	−7.54479	−0.494276	−0.247138	−	0.968980i	$-0.579490\pi$
$233$	−7.54479	−0.494276	−0.247138	+	0.968980i	$0.579490\pi$
$234$	−4.62516	−0.302356
$235$	6.51664	0.425099
$236$	−20.9593	−1.36433
$237$	−17.8505	−1.15951
$238$	7.16839	0.464658
$239$	−2.48425	−0.160693	−0.0803463	−	0.996767i	$-0.525603\pi$
$239$	−2.48425	−0.160693	−0.0803463	+	0.996767i	$0.525603\pi$
$240$	−4.44040	−0.286627
$241$	−12.5411	−0.807841	−0.403921	−	0.914794i	$-0.632353\pi$
$241$	−12.5411	−0.807841	−0.403921	+	0.914794i	$0.632353\pi$
$242$	5.03134	0.323427
$243$	−9.44176	−0.605689
$244$	0.445270	0.0285055
$245$	5.43825	0.347437
$246$	−21.0797	−1.34399
$247$	15.6593	0.996380
$248$	−0.742278	−0.0471347
$249$	0.331054	0.0209797
$250$	2.09243	0.132337
$251$	−6.83247	−0.431262	−0.215631	−	0.976475i	$-0.569181\pi$
$251$	−6.83247	−0.431262	−0.215631	+	0.976475i	$0.569181\pi$
$252$	2.81971	0.177625
$253$	−26.6368	−1.67464
$254$	21.6229	1.35674
$255$	3.92624	0.245871
$256$	8.35905	0.522441
$257$	22.3377	1.39339	0.696695	−	0.717368i	$-0.254653\pi$
$257$	22.3377	1.39339	0.696695	+	0.717368i	$0.254653\pi$
$258$	−9.37143	−0.583440
$259$	−2.47296	−0.153662
$260$	5.54119	0.343650
$261$	9.30521	0.575978
$262$	−8.88402	−0.548857
$263$	9.87688	0.609034	0.304517	−	0.952507i	$-0.401505\pi$
$263$	9.87688	0.609034	0.304517	+	0.952507i	$0.401505\pi$
$264$	3.32365	0.204557
$265$	−1.59351	−0.0978887
$266$	−17.5748	−1.07758
$267$	24.6173	1.50656
$268$	−9.31245	−0.568848
$269$	21.6830	1.32203	0.661017	−	0.750371i	$-0.270125\pi$
$269$	21.6830	1.32203	0.661017	+	0.750371i	$0.270125\pi$
$270$	11.8337	0.720176
$271$	−12.0148	−0.729846	−0.364923	−	0.931038i	$-0.618905\pi$
$271$	−12.0148	−0.729846	−0.364923	+	0.931038i	$0.618905\pi$
$272$	−8.49911	−0.515334
$273$	−4.17022	−0.252393
$274$	−4.73116	−0.285820
$275$	2.93180	0.176794
$276$	30.9473	1.86281
$277$	−17.5372	−1.05371	−0.526855	−	0.849955i	$-0.676629\pi$
$277$	−17.5372	−1.05371	−0.526855	+	0.849955i	$0.676629\pi$
$278$	16.1119	0.966330
$279$	−0.889680	−0.0532638
$280$	−0.989176	−0.0591146
$281$	−8.62324	−0.514419	−0.257210	−	0.966356i	$-0.582803\pi$
$281$	−8.62324	−0.514419	−0.257210	+	0.966356i	$0.582803\pi$
$282$	−19.5294	−1.16296
$283$	−16.0719	−0.955377	−0.477689	−	0.878529i	$-0.658525\pi$
$283$	−16.0719	−0.955377	−0.477689	+	0.878529i	$0.658525\pi$
$284$	8.80220	0.522315
$285$	−9.62602	−0.570196
$286$	14.2931	0.845168
$287$	8.79034	0.518877
$288$	−7.65642	−0.451159
$289$	−9.48501	−0.557942
$290$	−20.5231	−1.20516
$291$	0.160881	0.00943101
$292$	10.4076	0.609061
$293$	4.35908	0.254660	0.127330	−	0.991860i	$-0.459359\pi$
$293$	4.35908	0.254660	0.127330	+	0.991860i	$0.459359\pi$
$294$	−16.2976	−0.950496
$295$	8.81278	0.513100
$296$	−1.56632	−0.0910402
$297$	16.5807	0.962111
$298$	−19.1335	−1.10837
$299$	21.1683	1.22420
$300$	−3.40625	−0.196660
$301$	3.90793	0.225249
$302$	42.4691	2.44382
$303$	−1.45208	−0.0834197
$304$	20.8374	1.19510
$305$	−0.187223	−0.0107204
$306$	5.44191	0.311093
$307$	15.9140	0.908259	0.454129	−	0.890936i	$-0.349950\pi$
$307$	15.9140	0.908259	0.454129	+	0.890936i	$0.349950\pi$
$308$	−8.71372	−0.496510
$309$	−16.3349	−0.929258
$310$	1.96223	0.111447
$311$	7.42629	0.421106	0.210553	−	0.977582i	$-0.432474\pi$
$311$	7.42629	0.421106	0.210553	+	0.977582i	$0.432474\pi$
$312$	−2.64132	−0.149535
$313$	3.52479	0.199233	0.0996165	−	0.995026i	$-0.468238\pi$
$313$	3.52479	0.199233	0.0996165	+	0.995026i	$0.468238\pi$
$314$	−13.9855	−0.789247
$315$	−1.18561	−0.0668014
$316$	29.6415	1.66747
$317$	−25.0742	−1.40830	−0.704152	−	0.710049i	$-0.748673\pi$
$317$	−25.0742	−1.40830	−0.704152	+	0.710049i	$0.748673\pi$
$318$	4.77552	0.267798
$319$	−28.7558	−1.61002
$320$	10.6859	0.597362
$321$	7.77676	0.434056
$322$	−23.7577	−1.32396
$323$	−18.4246	−1.02517
$324$	−12.4950	−0.694168
$325$	−2.32991	−0.129240
$326$	30.3292	1.67978
$327$	25.3508	1.40190
$328$	5.56760	0.307419
$329$	8.14385	0.448985
$330$	−8.78617	−0.483663
$331$	13.8838	0.763124	0.381562	−	0.924343i	$-0.375386\pi$
$331$	13.8838	0.763124	0.381562	+	0.924343i	$0.375386\pi$
$332$	−0.549730	−0.0301703
$333$	−1.87736	−0.102878
$334$	4.25583	0.232869
$335$	3.91562	0.213933
$336$	−5.54917	−0.302732
$337$	13.9544	0.760147	0.380074	−	0.924956i	$-0.375899\pi$
$337$	13.9544	0.760147	0.380074	+	0.924956i	$0.375899\pi$
$338$	15.8429	0.861739
$339$	−3.82509	−0.207750
$340$	−6.51970	−0.353580
$341$	2.74937	0.148887
$342$	−13.3420	−0.721452
$343$	15.5441	0.839301
$344$	2.47519	0.133453
$345$	−13.0125	−0.700568
$346$	−0.509110	−0.0273699
$347$	14.9187	0.800880	0.400440	−	0.916323i	$-0.368857\pi$
$347$	14.9187	0.800880	0.400440	+	0.916323i	$0.368857\pi$
$348$	33.4093	1.79093
$349$	−35.3858	−1.89416	−0.947078	−	0.321003i	$-0.895980\pi$
$349$	−35.3858	−1.89416	−0.947078	+	0.321003i	$0.895980\pi$
$350$	2.61492	0.139773
$351$	−13.1768	−0.703323
$352$	23.6606	1.26111
$353$	−11.1277	−0.592270	−0.296135	−	0.955146i	$-0.595698\pi$
$353$	−11.1277	−0.592270	−0.296135	+	0.955146i	$0.595698\pi$
$354$	−26.4106	−1.40371
$355$	−3.70108	−0.196433
$356$	−40.8781	−2.16654
$357$	4.90663	0.259686
$358$	23.1840	1.22531
$359$	−16.5211	−0.871949	−0.435974	−	0.899959i	$-0.643596\pi$
$359$	−16.5211	−0.871949	−0.435974	+	0.899959i	$0.643596\pi$
$360$	−0.750937	−0.0395778
$361$	26.1718	1.37746
$362$	8.75742	0.460280
$363$	3.44386	0.180756
$364$	6.92483	0.362960
$365$	−4.37612	−0.229056
$366$	0.561081	0.0293282
$367$	−35.6046	−1.85854	−0.929272	−	0.369397i	$-0.879564\pi$
$367$	−35.6046	−1.85854	−0.929272	+	0.369397i	$0.879564\pi$
$368$	28.1680	1.46836
$369$	6.67322	0.347394
$370$	4.14060	0.215259
$371$	−1.99141	−0.103389
$372$	−3.19430	−0.165617
$373$	−1.19768	−0.0620134	−0.0310067	−	0.999519i	$-0.509871\pi$
$373$	−1.19768	−0.0620134	−0.0310067	+	0.999519i	$0.509871\pi$
$374$	−16.8171	−0.869591
$375$	1.43223	0.0739601
$376$	5.15813	0.266010
$377$	22.8523	1.17696
$378$	14.7886	0.760642
$379$	−6.15015	−0.315912	−0.157956	−	0.987446i	$-0.550490\pi$
$379$	−6.15015	−0.315912	−0.157956	+	0.987446i	$0.550490\pi$
$380$	15.9844	0.819984
$381$	14.8004	0.758249
$382$	22.3176	1.14187
$383$	16.8321	0.860079	0.430040	−	0.902810i	$-0.358500\pi$
$383$	16.8321	0.860079	0.430040	+	0.902810i	$0.358500\pi$
$384$	−8.90702	−0.454534
$385$	3.66387	0.186728
$386$	12.8706	0.655095
$387$	2.96672	0.150807
$388$	−0.267150	−0.0135625
$389$	−1.71276	−0.0868402	−0.0434201	−	0.999057i	$-0.513825\pi$
$389$	−1.71276	−0.0868402	−0.0434201	+	0.999057i	$0.513825\pi$
$390$	6.98240	0.353568
$391$	−24.9064	−1.25957
$392$	4.30454	0.217412
$393$	−6.08094	−0.306743
$394$	3.04762	0.153537
$395$	−12.4634	−0.627103
$396$	−6.61505	−0.332419
$397$	7.93073	0.398032	0.199016	−	0.979996i	$-0.436225\pi$
$397$	7.93073	0.398032	0.199016	+	0.979996i	$0.436225\pi$
$398$	9.09967	0.456125
$399$	−12.0296	−0.602235
$400$	−3.10034	−0.155017
$401$	18.2776	0.912739	0.456370	−	0.889790i	$-0.349149\pi$
$401$	18.2776	0.912739	0.456370	+	0.889790i	$0.349149\pi$
$402$	−11.7345	−0.585265
$403$	−2.18494	−0.108839
$404$	2.41124	0.119964
$405$	5.25380	0.261063
$406$	−25.6477	−1.27287
$407$	5.80157	0.287573
$408$	3.10774	0.153856
$409$	14.4955	0.716758	0.358379	−	0.933576i	$-0.383330\pi$
$409$	14.4955	0.716758	0.358379	+	0.933576i	$0.383330\pi$
$410$	−14.7181	−0.726875
$411$	−3.23839	−0.159738
$412$	27.1248	1.33634
$413$	11.0133	0.541931
$414$	−18.0357	−0.886408
$415$	0.231146	0.0113465
$416$	−18.8031	−0.921900
$417$	11.0283	0.540059
$418$	41.2306	2.01666
$419$	−25.3125	−1.23660	−0.618299	−	0.785943i	$-0.712178\pi$
$419$	−25.3125	−1.23660	−0.618299	+	0.785943i	$0.712178\pi$
$420$	−4.25679	−0.207710
$421$	−13.8149	−0.673298	−0.336649	−	0.941630i	$-0.609294\pi$
$421$	−13.8149	−0.673298	−0.336649	+	0.941630i	$0.609294\pi$
$422$	10.9356	0.532339
$423$	6.18243	0.300600
$424$	−1.26131	−0.0612548
$425$	2.74135	0.132975
$426$	11.0916	0.537388
$427$	−0.233973	−0.0113228
$428$	−12.9136	−0.624205
$429$	9.78335	0.472344
$430$	−6.54324	−0.315543
$431$	−25.3792	−1.22247	−0.611236	−	0.791449i	$-0.709327\pi$
$431$	−25.3792	−1.22247	−0.611236	+	0.791449i	$0.709327\pi$
$432$	−17.5339	−0.843599
$433$	−34.0914	−1.63833	−0.819164	−	0.573559i	$-0.805562\pi$
$433$	−34.0914	−1.63833	−0.819164	+	0.573559i	$0.805562\pi$
$434$	2.45220	0.117710
$435$	−14.0477	−0.673534
$436$	−42.0961	−2.01604
$437$	61.0633	2.92105
$438$	13.1146	0.626638
$439$	−32.9824	−1.57416	−0.787082	−	0.616849i	$-0.788409\pi$
$439$	−32.9824	−1.57416	−0.787082	+	0.616849i	$0.788409\pi$
$440$	2.32061	0.110631
$441$	5.15934	0.245683
$442$	13.3646	0.635689
$443$	−36.2376	−1.72170	−0.860849	−	0.508860i	$-0.830067\pi$
$443$	−36.2376	−1.72170	−0.860849	+	0.508860i	$0.830067\pi$
$444$	−6.74043	−0.319887
$445$	17.1881	0.814794
$446$	49.4247	2.34033
$447$	−13.0965	−0.619443
$448$	13.3542	0.630927
$449$	−2.72457	−0.128580	−0.0642901	−	0.997931i	$-0.520478\pi$
$449$	−2.72457	−0.128580	−0.0642901	+	0.997931i	$0.520478\pi$
$450$	1.98512	0.0935795
$451$	−20.6222	−0.971060
$452$	6.35173	0.298760
$453$	29.0693	1.36580
$454$	−30.4118	−1.42730
$455$	−2.91169	−0.136502
$456$	−7.61929	−0.356806
$457$	−14.6840	−0.686889	−0.343444	−	0.939173i	$-0.611594\pi$
$457$	−14.6840	−0.686889	−0.343444	+	0.939173i	$0.611594\pi$
$458$	−31.5346	−1.47352
$459$	15.5036	0.723647
$460$	21.6078	1.00747
$461$	−3.43661	−0.160059	−0.0800295	−	0.996792i	$-0.525501\pi$
$461$	−3.43661	−0.160059	−0.0800295	+	0.996792i	$0.525501\pi$
$462$	−10.9801	−0.510839
$463$	−2.52870	−0.117518	−0.0587592	−	0.998272i	$-0.518714\pi$
$463$	−2.52870	−0.117518	−0.0587592	+	0.998272i	$0.518714\pi$
$464$	30.4088	1.41169
$465$	1.34311	0.0622853
$466$	15.7870	0.731318
$467$	−7.51925	−0.347949	−0.173975	−	0.984750i	$-0.555661\pi$
$467$	−7.51925	−0.347949	−0.173975	+	0.984750i	$0.555661\pi$
$468$	5.25701	0.243005
$469$	4.89335	0.225954
$470$	−13.6357	−0.628966
$471$	−9.57280	−0.441091
$472$	6.97559	0.321078
$473$	−9.16802	−0.421546
$474$	37.3510	1.71559
$475$	−6.72100	−0.308380
$476$	−8.14767	−0.373448
$477$	−1.51179	−0.0692200
$478$	5.19813	0.237757
$479$	6.48522	0.296317	0.148159	−	0.988964i	$-0.452665\pi$
$479$	6.48522	0.296317	0.148159	+	0.988964i	$0.452665\pi$
$480$	11.5586	0.527574
$481$	−4.61053	−0.210222
$482$	26.2414	1.19526
$483$	−16.2617	−0.739932
$484$	−5.71868	−0.259940
$485$	0.112329	0.00510059
$486$	19.7563	0.896162
$487$	0.724656	0.0328373	0.0164186	−	0.999865i	$-0.494774\pi$
$487$	0.724656	0.0328373	0.0164186	+	0.999865i	$0.494774\pi$
$488$	−0.148193	−0.00670839
$489$	20.7597	0.938788
$490$	−11.3792	−0.514059
$491$	−16.7316	−0.755089	−0.377544	−	0.925992i	$-0.623231\pi$
$491$	−16.7316	−0.755089	−0.377544	+	0.925992i	$0.623231\pi$
$492$	23.9594	1.08017
$493$	−26.8878	−1.21097
$494$	−32.7661	−1.47422
$495$	2.78144	0.125016
$496$	−2.90742	−0.130547
$497$	−4.62524	−0.207470
$498$	−0.692709	−0.0310410
$499$	4.67468	0.209268	0.104634	−	0.994511i	$-0.466633\pi$
$499$	4.67468	0.209268	0.104634	+	0.994511i	$0.466633\pi$
$500$	−2.37828	−0.106360
$501$	2.91304	0.130145
$502$	14.2965	0.638084
$503$	3.54365	0.158003	0.0790017	−	0.996874i	$-0.474827\pi$
$503$	3.54365	0.158003	0.0790017	+	0.996874i	$0.474827\pi$
$504$	−0.938445	−0.0418017
$505$	−1.01386	−0.0451160
$506$	55.7357	2.47775
$507$	10.8441	0.481605
$508$	−24.5768	−1.09042
$509$	−5.40481	−0.239564	−0.119782	−	0.992800i	$-0.538220\pi$
$509$	−5.40481	−0.239564	−0.119782	+	0.992800i	$0.538220\pi$
$510$	−8.21541	−0.363784
$511$	−5.46883	−0.241927
$512$	−29.9287	−1.32268
$513$	−38.0104	−1.67820
$514$	−46.7403	−2.06162
$515$	−11.4052	−0.502573
$516$	10.6517	0.468913
$517$	−19.1055	−0.840259
$518$	5.17451	0.227355
$519$	−0.348476	−0.0152964
$520$	−1.84420	−0.0808735
$521$	20.8485	0.913389	0.456695	−	0.889624i	$-0.349033\pi$
$521$	20.8485	0.913389	0.456695	+	0.889624i	$0.349033\pi$
$522$	−19.4705	−0.852202
$523$	−6.80055	−0.297367	−0.148684	−	0.988885i	$-0.547504\pi$
$523$	−6.80055	−0.297367	−0.148684	+	0.988885i	$0.547504\pi$
$524$	10.0977	0.441119
$525$	1.78986	0.0781159
$526$	−20.6667	−0.901112
$527$	2.57077	0.111984
$528$	13.0184	0.566552
$529$	59.5455	2.58893
$530$	3.33432	0.144834
$531$	8.36081	0.362828
$532$	19.9757	0.866058
$533$	16.3885	0.709866
$534$	−51.5101	−2.22906
$535$	5.42982	0.234752
$536$	3.09933	0.133871
$537$	15.8690	0.684797
$538$	−45.3702	−1.95605
$539$	−15.9439	−0.686751
$540$	−13.4503	−0.578809
$541$	−29.4268	−1.26516	−0.632578	−	0.774497i	$-0.718003\pi$
$541$	−29.4268	−1.26516	−0.632578	+	0.774497i	$0.718003\pi$
$542$	25.1401	1.07986
$543$	5.99429	0.257240
$544$	22.1235	0.948539
$545$	17.7002	0.758193
$546$	8.72591	0.373434
$547$	2.53767	0.108503	0.0542514	−	0.998527i	$-0.482723\pi$
$547$	2.53767	0.108503	0.0542514	+	0.998527i	$0.482723\pi$
$548$	5.37748	0.229715
$549$	−0.177621	−0.00758070
$550$	−6.13460	−0.261580
$551$	65.9211	2.80833
$552$	−10.2998	−0.438388
$553$	−15.5755	−0.662339
$554$	36.6955	1.55904
$555$	2.83416	0.120303
$556$	−18.3130	−0.776644
$557$	38.4904	1.63089	0.815444	−	0.578835i	$-0.196493\pi$
$557$	38.4904	1.63089	0.815444	+	0.578835i	$0.196493\pi$
$558$	1.86160	0.0788077
$559$	7.28586	0.308159
$560$	−3.87449	−0.163727
$561$	−11.5110	−0.485994
$562$	18.0436	0.761122
$563$	11.3208	0.477115	0.238557	−	0.971128i	$-0.423326\pi$
$563$	11.3208	0.477115	0.238557	+	0.971128i	$0.423326\pi$
$564$	22.1973	0.934676
$565$	−2.67072	−0.112358
$566$	33.6295	1.41355
$567$	6.56567	0.275732
$568$	−2.92952	−0.122920
$569$	35.5921	1.49210	0.746049	−	0.665891i	$-0.231948\pi$
$569$	35.5921	1.49210	0.746049	+	0.665891i	$0.231948\pi$
$570$	20.1418	0.843648
$571$	5.18043	0.216794	0.108397	−	0.994108i	$-0.465428\pi$
$571$	5.18043	0.216794	0.108397	+	0.994108i	$0.465428\pi$
$572$	−16.2457	−0.679266
$573$	15.2759	0.638162
$574$	−18.3932	−0.767718
$575$	−9.08546	−0.378890
$576$	10.1379	0.422412
$577$	−37.7248	−1.57050	−0.785252	−	0.619177i	$-0.787467\pi$
$577$	−37.7248	−1.57050	−0.785252	+	0.619177i	$0.787467\pi$
$578$	19.8468	0.825516
$579$	8.80966	0.366117
$580$	23.3267	0.968591
$581$	0.288863	0.0119841
$582$	−0.336633	−0.0139539
$583$	4.67186	0.193489
$584$	−3.46383	−0.143334
$585$	−2.21042	−0.0913897
$586$	−9.12110	−0.376789
$587$	35.6340	1.47077	0.735387	−	0.677648i	$-0.237000\pi$
$587$	35.6340	1.47077	0.735387	+	0.677648i	$0.237000\pi$
$588$	18.5240	0.763919
$589$	−6.30278	−0.259702
$590$	−18.4402	−0.759170
$591$	2.08604	0.0858082
$592$	−6.13508	−0.252150
$593$	−4.03395	−0.165654	−0.0828272	−	0.996564i	$-0.526395\pi$
$593$	−4.03395	−0.165654	−0.0828272	+	0.996564i	$0.526395\pi$
$594$	−34.6941	−1.42351
$595$	3.42586	0.140447
$596$	21.7473	0.890804
$597$	6.22855	0.254917
$598$	−44.2933	−1.81129
$599$	16.6826	0.681632	0.340816	−	0.940130i	$-0.389297\pi$
$599$	16.6826	0.681632	0.340816	+	0.940130i	$0.389297\pi$
$600$	1.13366	0.0462813
$601$	−27.1774	−1.10859	−0.554294	−	0.832321i	$-0.687012\pi$
$601$	−27.1774	−1.10859	−0.554294	+	0.832321i	$0.687012\pi$
$602$	−8.17709	−0.333273
$603$	3.71480	0.151278
$604$	−48.2709	−1.96411
$605$	2.40454	0.0977585
$606$	3.03838	0.123426
$607$	19.9999	0.811770	0.405885	−	0.913924i	$-0.366963\pi$
$607$	19.9999	0.811770	0.405885	+	0.913924i	$0.366963\pi$
$608$	−54.2406	−2.19975
$609$	−17.5554	−0.711379
$610$	0.391753	0.0158616
$611$	15.1832	0.614247
$612$	−6.18533	−0.250027
$613$	22.9543	0.927117	0.463559	−	0.886066i	$-0.346572\pi$
$613$	22.9543	0.927117	0.463559	+	0.886066i	$0.346572\pi$
$614$	−33.2990	−1.34384
$615$	−10.0743	−0.406233
$616$	2.90007	0.116847
$617$	−40.6127	−1.63501	−0.817503	−	0.575924i	$-0.804643\pi$
$617$	−40.6127	−1.63501	−0.817503	+	0.575924i	$0.804643\pi$
$618$	34.1796	1.37491
$619$	41.9803	1.68733	0.843665	−	0.536870i	$-0.180393\pi$
$619$	41.9803	1.68733	0.843665	+	0.536870i	$0.180393\pi$
$620$	−2.23029	−0.0895708
$621$	−51.3825	−2.06191
$622$	−15.5390	−0.623058
$623$	21.4800	0.860576
$624$	−10.3457	−0.414161
$625$	1.00000	0.0400000
$626$	−7.37540	−0.294780
$627$	28.2216	1.12706
$628$	15.8961	0.634322
$629$	5.42470	0.216297
$630$	2.48081	0.0988377
$631$	32.1747	1.28085	0.640427	−	0.768019i	$-0.278757\pi$
$631$	32.1747	1.28085	0.640427	+	0.768019i	$0.278757\pi$
$632$	−9.86519	−0.392416
$633$	7.48523	0.297511
$634$	52.4660	2.08369
$635$	10.3338	0.410085
$636$	−5.42790	−0.215230
$637$	12.6707	0.502030
$638$	60.1696	2.38214
$639$	−3.51126	−0.138903
$640$	−6.21898	−0.245827
$641$	47.2146	1.86487	0.932433	−	0.361343i	$-0.117682\pi$
$641$	47.2146	1.86487	0.932433	+	0.361343i	$0.117682\pi$
$642$	−16.2724	−0.642219
$643$	42.6776	1.68304	0.841520	−	0.540226i	$-0.181661\pi$
$643$	42.6776	1.68304	0.841520	+	0.540226i	$0.181661\pi$
$644$	27.0032	1.06408
$645$	−4.47872	−0.176349
$646$	38.5523	1.51682
$647$	16.3264	0.641858	0.320929	−	0.947103i	$-0.396005\pi$
$647$	16.3264	0.641858	0.320929	+	0.947103i	$0.396005\pi$
$648$	4.15855	0.163363
$649$	−25.8373	−1.01420
$650$	4.87519	0.191221
$651$	1.67849	0.0657850
$652$	−34.4725	−1.35005
$653$	−17.1444	−0.670912	−0.335456	−	0.942056i	$-0.608890\pi$
$653$	−17.1444	−0.670912	−0.335456	+	0.942056i	$0.608890\pi$
$654$	−53.0449	−2.07422
$655$	−4.24578	−0.165896
$656$	21.8077	0.851446
$657$	−4.15168	−0.161973
$658$	−17.0405	−0.664307
$659$	37.5872	1.46419	0.732094	−	0.681204i	$-0.238543\pi$
$659$	37.5872	1.46419	0.732094	+	0.681204i	$0.238543\pi$
$660$	9.98645	0.388722
$661$	−21.6516	−0.842149	−0.421074	−	0.907026i	$-0.638347\pi$
$661$	−21.6516	−0.842149	−0.421074	+	0.907026i	$0.638347\pi$
$662$	−29.0510	−1.12910
$663$	9.14781	0.355272
$664$	0.182959	0.00710019
$665$	−8.39923	−0.325708
$666$	3.92824	0.152216
$667$	89.1123	3.45044
$668$	−4.83722	−0.187158
$669$	33.8303	1.30795
$670$	−8.19318	−0.316530
$671$	0.548902	0.0211901
$672$	14.4447	0.557218
$673$	12.3278	0.475203	0.237602	−	0.971363i	$-0.423639\pi$
$673$	12.3278	0.475203	0.237602	+	0.971363i	$0.423639\pi$
$674$	−29.1988	−1.12469
$675$	5.65547	0.217679
$676$	−18.0072	−0.692584
$677$	−31.1892	−1.19870	−0.599349	−	0.800488i	$-0.704574\pi$
$677$	−31.1892	−1.19870	−0.599349	+	0.800488i	$0.704574\pi$
$678$	8.00375	0.307382
$679$	0.140377	0.00538719
$680$	2.16986	0.0832104
$681$	−20.8163	−0.797681
$682$	−5.75288	−0.220289
$683$	19.8633	0.760048	0.380024	−	0.924977i	$-0.375916\pi$
$683$	19.8633	0.760048	0.380024	+	0.924977i	$0.375916\pi$
$684$	15.1646	0.579835
$685$	−2.26108	−0.0863914
$686$	−32.5250	−1.24181
$687$	−21.5848	−0.823513
$688$	9.69505	0.369620
$689$	−3.71275	−0.141444
$690$	27.2277	1.03654
$691$	−38.9159	−1.48043	−0.740216	−	0.672370i	$-0.765277\pi$
$691$	−38.9159	−1.48043	−0.740216	+	0.672370i	$0.765277\pi$
$692$	0.578660	0.0219974
$693$	3.47597	0.132041
$694$	−31.2165	−1.18496
$695$	7.70009	0.292081
$696$	−11.1192	−0.421471
$697$	−19.2825	−0.730378
$698$	74.0424	2.80255
$699$	10.8059	0.408716
$700$	−2.97214	−0.112336
$701$	19.7973	0.747732	0.373866	−	0.927483i	$-0.378032\pi$
$701$	19.7973	0.747732	0.373866	+	0.927483i	$0.378032\pi$
$702$	27.5715	1.04062
$703$	−13.2998	−0.501611
$704$	−31.3290	−1.18076
$705$	−9.33334	−0.351514
$706$	23.2841	0.876308
$707$	−1.26702	−0.0476511
$708$	30.0185	1.12817
$709$	25.3590	0.952377	0.476189	−	0.879343i	$-0.342018\pi$
$709$	25.3590	0.952377	0.476189	+	0.879343i	$0.342018\pi$
$710$	7.74426	0.290637
$711$	−11.8242	−0.443443
$712$	13.6049	0.509865
$713$	−8.52012	−0.319081
$714$	−10.2668	−0.384225
$715$	6.83084	0.255459
$716$	−26.3511	−0.984789
$717$	3.55802	0.132877
$718$	34.5693	1.29011
$719$	−34.1974	−1.27535	−0.637675	−	0.770306i	$-0.720104\pi$
$719$	−34.1974	−1.27535	−0.637675	+	0.770306i	$0.720104\pi$
$720$	−2.94133	−0.109617
$721$	−14.2531	−0.530812
$722$	−54.7628	−2.03806
$723$	17.9617	0.668003
$724$	−9.95378	−0.369929
$725$	−9.80823	−0.364269
$726$	−7.20605	−0.267442
$727$	−12.9315	−0.479601	−0.239801	−	0.970822i	$-0.577082\pi$
$727$	−12.9315	−0.479601	−0.239801	+	0.970822i	$0.577082\pi$
$728$	−2.30470	−0.0854177
$729$	29.2842	1.08460
$730$	9.15674	0.338906
$731$	−8.57245	−0.317064
$732$	−0.637730	−0.0235712
$733$	30.4437	1.12446	0.562232	−	0.826980i	$-0.309943\pi$
$733$	30.4437	1.12446	0.562232	+	0.826980i	$0.309943\pi$
$734$	74.5002	2.74985
$735$	−7.78883	−0.287295
$736$	−73.3225	−2.70270
$737$	−11.4798	−0.422864
$738$	−13.9633	−0.513995
$739$	36.4543	1.34099	0.670496	−	0.741913i	$-0.266081\pi$
$739$	36.4543	1.34099	0.670496	+	0.741913i	$0.266081\pi$
$740$	−4.70625	−0.173005
$741$	−22.4278	−0.823906
$742$	4.16690	0.152972
$743$	22.3423	0.819660	0.409830	−	0.912162i	$-0.365588\pi$
$743$	22.3423	0.819660	0.409830	+	0.912162i	$0.365588\pi$
$744$	1.06311	0.0389757
$745$	−9.14412	−0.335015
$746$	2.50606	0.0917534
$747$	0.219291	0.00802345
$748$	19.1145	0.698894
$749$	6.78565	0.247942
$750$	−2.99685	−0.109429
$751$	4.29257	0.156638	0.0783190	−	0.996928i	$-0.475045\pi$
$751$	4.29257	0.156638	0.0783190	+	0.996928i	$0.475045\pi$
$752$	20.2038	0.736757
$753$	9.78567	0.356610
$754$	−47.8170	−1.74139
$755$	20.2965	0.738666
$756$	−16.8088	−0.611332
$757$	4.95028	0.179921	0.0899605	−	0.995945i	$-0.471326\pi$
$757$	4.95028	0.179921	0.0899605	+	0.995945i	$0.471326\pi$
$758$	12.8688	0.467416
$759$	38.1500	1.38476
$760$	−5.31988	−0.192972
$761$	39.3216	1.42541	0.712704	−	0.701465i	$-0.247470\pi$
$761$	39.3216	1.42541	0.712704	+	0.701465i	$0.247470\pi$
$762$	−30.9689	−1.12189
$763$	22.1199	0.800796
$764$	−25.3664	−0.917723
$765$	2.60076	0.0940305
$766$	−35.2200	−1.27255
$767$	20.5330	0.741405
$768$	−11.9721	−0.432006
$769$	2.33229	0.0841046	0.0420523	−	0.999115i	$-0.486610\pi$
$769$	2.33229	0.0841046	0.0420523	+	0.999115i	$0.486610\pi$
$770$	−7.66641	−0.276278
$771$	−31.9928	−1.15219
$772$	−14.6288	−0.526503
$773$	24.5047	0.881372	0.440686	−	0.897661i	$-0.354735\pi$
$773$	24.5047	0.881372	0.440686	+	0.897661i	$0.354735\pi$
$774$	−6.20766	−0.223130
$775$	0.937775	0.0336859
$776$	0.0889119	0.00319175
$777$	3.54185	0.127063
$778$	3.58383	0.128487
$779$	47.2752	1.69381
$780$	−7.93627	−0.284164
$781$	10.8508	0.388273
$782$	52.1150	1.86363
$783$	−55.4702	−1.98234
$784$	16.8604	0.602158
$785$	−6.68384	−0.238556
$786$	12.7240	0.453849
$787$	2.14827	0.0765776	0.0382888	−	0.999267i	$-0.487809\pi$
$787$	2.14827	0.0765776	0.0382888	+	0.999267i	$0.487809\pi$
$788$	−3.46396	−0.123398
$789$	−14.1460	−0.503610
$790$	26.0789	0.927845
$791$	−3.33760	−0.118671
$792$	2.20160	0.0782303
$793$	−0.436214	−0.0154904
$794$	−16.5945	−0.588918
$795$	2.28228	0.0809440
$796$	−10.3428	−0.366590
$797$	24.0265	0.851064	0.425532	−	0.904943i	$-0.360087\pi$
$797$	24.0265	0.851064	0.425532	+	0.904943i	$0.360087\pi$
$798$	25.1712	0.891052
$799$	−17.8644	−0.631997
$800$	8.07032	0.285329
$801$	16.3066	0.576165
$802$	−38.2447	−1.35047
$803$	12.8299	0.452758
$804$	13.3376	0.470380
$805$	−11.3541	−0.400179
$806$	4.57183	0.161036
$807$	−31.0550	−1.09319
$808$	−0.802499	−0.0282318
$809$	13.0098	0.457401	0.228700	−	0.973497i	$-0.426552\pi$
$809$	13.0098	0.457401	0.228700	+	0.973497i	$0.426552\pi$
$810$	−10.9932	−0.386263
$811$	−55.3424	−1.94334	−0.971668	−	0.236351i	$-0.924048\pi$
$811$	−55.3424	−1.94334	−0.971668	+	0.236351i	$0.924048\pi$
$812$	29.1514	1.02301
$813$	17.2079	0.603509
$814$	−12.1394	−0.425486
$815$	14.4947	0.507727
$816$	12.1727	0.426129
$817$	21.0172	0.735298
$818$	−30.3310	−1.06050
$819$	−2.76236	−0.0965248
$820$	16.7287	0.584193
$821$	32.6778	1.14046	0.570231	−	0.821484i	$-0.306854\pi$
$821$	32.6778	1.14046	0.570231	+	0.821484i	$0.306854\pi$
$822$	6.77611	0.236344
$823$	23.9793	0.835865	0.417932	−	0.908478i	$-0.362755\pi$
$823$	23.9793	0.835865	0.417932	+	0.908478i	$0.362755\pi$
$824$	−9.02756	−0.314490
$825$	−4.19902	−0.146191
$826$	−23.0447	−0.801827
$827$	−20.8184	−0.723926	−0.361963	−	0.932193i	$-0.617893\pi$
$827$	−20.8184	−0.723926	−0.361963	+	0.932193i	$0.617893\pi$
$828$	20.4996	0.712410
$829$	16.3352	0.567345	0.283673	−	0.958921i	$-0.408447\pi$
$829$	16.3352	0.567345	0.283673	+	0.958921i	$0.408447\pi$
$830$	−0.483657	−0.0167880
$831$	25.1173	0.871311
$832$	24.8973	0.863159
$833$	−14.9081	−0.516536
$834$	−23.0760	−0.799057
$835$	2.03391	0.0703865
$836$	−46.8632	−1.62080
$837$	5.30356	0.183318
$838$	52.9648	1.82964
$839$	−24.3705	−0.841363	−0.420681	−	0.907208i	$-0.638209\pi$
$839$	−24.3705	−0.841363	−0.420681	+	0.907208i	$0.638209\pi$
$840$	1.41673	0.0488818
$841$	67.2015	2.31729
$842$	28.9068	0.996195
$843$	12.3505	0.425373
$844$	−12.4296	−0.427843
$845$	7.57150	0.260468
$846$	−12.9363	−0.444760
$847$	3.00495	0.103251
$848$	−4.94043	−0.169655
$849$	23.0187	0.790001
$850$	−5.73609	−0.196746
$851$	−17.9787	−0.616301
$852$	−12.6068	−0.431902
$853$	5.22998	0.179071	0.0895355	−	0.995984i	$-0.471462\pi$
$853$	5.22998	0.179071	0.0895355	+	0.995984i	$0.471462\pi$
$854$	0.489574	0.0167529
$855$	−6.37630	−0.218065
$856$	4.29787	0.146898
$857$	−17.3336	−0.592106	−0.296053	−	0.955172i	$-0.595670\pi$
$857$	−17.3336	−0.592106	−0.296053	+	0.955172i	$0.595670\pi$
$858$	−20.4710	−0.698869
$859$	19.7167	0.672724	0.336362	−	0.941733i	$-0.390803\pi$
$859$	19.7167	0.672724	0.336362	+	0.941733i	$0.390803\pi$
$860$	7.43711	0.253603
$861$	−12.5898	−0.429059
$862$	53.1042	1.80874
$863$	15.6182	0.531649	0.265825	−	0.964021i	$-0.414356\pi$
$863$	15.6182	0.531649	0.265825	+	0.964021i	$0.414356\pi$
$864$	45.6414	1.55275
$865$	−0.243310	−0.00827279
$866$	71.3340	2.42403
$867$	13.5847	0.461361
$868$	−2.78720	−0.0946037
$869$	36.5403	1.23954
$870$	29.3938	0.996543
$871$	9.12305	0.309123
$872$	14.0103	0.474447
$873$	0.106568	0.00360678
$874$	−127.771	−4.32192
$875$	1.24970	0.0422476
$876$	−14.9061	−0.503632
$877$	34.3011	1.15827	0.579133	−	0.815233i	$-0.303391\pi$
$877$	34.3011	1.15827	0.579133	+	0.815233i	$0.303391\pi$
$878$	69.0135	2.32909
$879$	−6.24321	−0.210578
$880$	9.08957	0.306409
$881$	−27.7685	−0.935545	−0.467772	−	0.883849i	$-0.654943\pi$
$881$	−27.7685	−0.935545	−0.467772	+	0.883849i	$0.654943\pi$
$882$	−10.7956	−0.363506
$883$	−41.4932	−1.39636	−0.698179	−	0.715923i	$-0.746006\pi$
$883$	−41.4932	−1.39636	−0.698179	+	0.715923i	$0.746006\pi$
$884$	−15.1903	−0.510906
$885$	−12.6219	−0.424282
$886$	75.8247	2.54738
$887$	15.3559	0.515599	0.257800	−	0.966198i	$-0.417003\pi$
$887$	15.3559	0.515599	0.257800	+	0.966198i	$0.417003\pi$
$888$	2.24333	0.0752811
$889$	12.9142	0.433128
$890$	−35.9650	−1.20555
$891$	−15.4031	−0.516023
$892$	−56.1766	−1.88093
$893$	43.7983	1.46566
$894$	27.4036	0.916512
$895$	11.0799	0.370360
$896$	−7.77186	−0.259640
$897$	−30.3179	−1.01229
$898$	5.70098	0.190244
$899$	−9.19792	−0.306768
$900$	−2.25631	−0.0752103
$901$	4.36837	0.145532
$902$	43.1505	1.43676
$903$	−5.59706	−0.186258
$904$	−2.11396	−0.0703092
$905$	4.18528	0.139123
$906$	−60.8256	−2.02080
$907$	−55.7310	−1.85052	−0.925259	−	0.379336i	$-0.876152\pi$
$907$	−55.7310	−1.85052	−0.925259	+	0.379336i	$0.876152\pi$
$908$	34.5663	1.14712
$909$	−0.961860	−0.0319029
$910$	6.09253	0.201965
$911$	19.0775	0.632066	0.316033	−	0.948748i	$-0.397649\pi$
$911$	19.0775	0.632066	0.316033	+	0.948748i	$0.397649\pi$
$912$	−29.8439	−0.988231
$913$	−0.677673	−0.0224277
$914$	30.7253	1.01630
$915$	0.268147	0.00886468
$916$	35.8426	1.18427
$917$	−5.30596	−0.175218
$918$	−32.4403	−1.07069
$919$	−23.9946	−0.791508	−0.395754	−	0.918357i	$-0.629517\pi$
$919$	−23.9946	−0.791508	−0.395754	+	0.918357i	$0.629517\pi$
$920$	−7.19142	−0.237094
$921$	−22.7925	−0.751038
$922$	7.19089	0.236819
$923$	−8.62319	−0.283836
$924$	12.4801	0.410564
$925$	1.97884	0.0650639
$926$	5.29113	0.173877
$927$	−10.8203	−0.355384
$928$	−79.1555	−2.59841
$929$	4.19374	0.137592	0.0687961	−	0.997631i	$-0.478084\pi$
$929$	4.19374	0.137592	0.0687961	+	0.997631i	$0.478084\pi$
$930$	−2.81037	−0.0921557
$931$	36.5505	1.19789
$932$	−17.9436	−0.587764
$933$	−10.6362	−0.348212
$934$	15.7335	0.514817
$935$	−8.03709	−0.262841
$936$	−1.74962	−0.0571880
$937$	23.6577	0.772862	0.386431	−	0.922318i	$-0.373708\pi$
$937$	23.6577	0.772862	0.386431	+	0.922318i	$0.373708\pi$
$938$	−10.2390	−0.334316
$939$	−5.04832	−0.164746
$940$	15.4984	0.505503
$941$	−10.6186	−0.346155	−0.173077	−	0.984908i	$-0.555371\pi$
$941$	−10.6186	−0.346155	−0.173077	+	0.984908i	$0.555371\pi$
$942$	20.0305	0.652628
$943$	63.9067	2.08109
$944$	27.3226	0.889275
$945$	7.06764	0.229910
$946$	19.1835	0.623709
$947$	54.9495	1.78562	0.892810	−	0.450434i	$-0.148731\pi$
$947$	54.9495	1.78562	0.892810	+	0.450434i	$0.148731\pi$
$948$	−42.4535	−1.37883
$949$	−10.1960	−0.330975
$950$	14.0632	0.456272
$951$	35.9120	1.16453
$952$	2.71168	0.0878860
$953$	14.5741	0.472101	0.236050	−	0.971741i	$-0.424147\pi$
$953$	14.5741	0.472101	0.236050	+	0.971741i	$0.424147\pi$
$954$	3.16332	0.102416
$955$	10.6658	0.345138
$956$	−5.90824	−0.191086
$957$	41.1849	1.33132
$958$	−13.5699	−0.438424
$959$	−2.82567	−0.0912456
$960$	−15.3047	−0.493958
$961$	−30.1206	−0.971632
$962$	9.64724	0.311039
$963$	5.15135	0.166000
$964$	−29.8262	−0.960637
$965$	6.15101	0.198008
$966$	34.0265	1.09479
$967$	45.0244	1.44789	0.723944	−	0.689859i	$-0.242328\pi$
$967$	45.0244	1.44789	0.723944	+	0.689859i	$0.242328\pi$
$968$	1.90327	0.0611734
$969$	26.3883	0.847714
$970$	−0.235041	−0.00754671
$971$	13.6406	0.437746	0.218873	−	0.975753i	$-0.429762\pi$
$971$	13.6406	0.437746	0.218873	+	0.975753i	$0.429762\pi$
$972$	−22.4552	−0.720250
$973$	9.62281	0.308493
$974$	−1.51630	−0.0485852
$975$	3.33697	0.106869
$976$	−0.580456	−0.0185799
$977$	13.6845	0.437806	0.218903	−	0.975747i	$-0.429752\pi$
$977$	13.6845	0.437806	0.218903	+	0.975747i	$0.429752\pi$
$978$	−43.4384	−1.38901
$979$	−50.3921	−1.61054
$980$	12.9337	0.413152
$981$	16.7924	0.536141
$982$	35.0099	1.11721
$983$	9.07103	0.289321	0.144660	−	0.989481i	$-0.453791\pi$
$983$	9.07103	0.289321	0.144660	+	0.989481i	$0.453791\pi$
$984$	−7.97409	−0.254205
$985$	1.45650	0.0464078
$986$	56.2609	1.79171
$987$	−11.6639	−0.371265
$988$	37.2423	1.18484
$989$	28.4111	0.903420
$990$	−5.81998	−0.184971
$991$	53.9126	1.71259	0.856296	−	0.516486i	$-0.172760\pi$
$991$	53.9126	1.71259	0.856296	+	0.516486i	$0.172760\pi$
$992$	7.56814	0.240289
$993$	−19.8848	−0.631026
$994$	9.67800	0.306968
$995$	4.34884	0.137868
$996$	0.787340	0.0249478
$997$	−4.46648	−0.141455	−0.0707274	−	0.997496i	$-0.522532\pi$
$997$	−4.46648	−0.141455	−0.0707274	+	0.997496i	$0.522532\pi$
$998$	−9.78147	−0.309627
$999$	11.1913	0.354077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.17	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.17	✓	127	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)

\(f(q)\)	\(=\)	\(q-2.09243 q^{2} -1.43223 q^{3} +2.37828 q^{4} -1.00000 q^{5} +2.99685 q^{6} -1.24970 q^{7} -0.791531 q^{8} -0.948714 q^{9} +O(q^{10})\)	\(q-2.09243 q^{2} -1.43223 q^{3} +2.37828 q^{4} -1.00000 q^{5} +2.99685 q^{6} -1.24970 q^{7} -0.791531 q^{8} -0.948714 q^{9} +2.09243 q^{10} +2.93180 q^{11} -3.40625 q^{12} -2.32991 q^{13} +2.61492 q^{14} +1.43223 q^{15} -3.10034 q^{16} +2.74135 q^{17} +1.98512 q^{18} -6.72100 q^{19} -2.37828 q^{20} +1.78986 q^{21} -6.13460 q^{22} -9.08546 q^{23} +1.13366 q^{24} +1.00000 q^{25} +4.87519 q^{26} +5.65547 q^{27} -2.97214 q^{28} -9.80823 q^{29} -2.99685 q^{30} +0.937775 q^{31} +8.07032 q^{32} -4.19902 q^{33} -5.73609 q^{34} +1.24970 q^{35} -2.25631 q^{36} +1.97884 q^{37} +14.0632 q^{38} +3.33697 q^{39} +0.791531 q^{40} -7.03396 q^{41} -3.74516 q^{42} -3.12709 q^{43} +6.97265 q^{44} +0.948714 q^{45} +19.0107 q^{46} -6.51664 q^{47} +4.44040 q^{48} -5.43825 q^{49} -2.09243 q^{50} -3.92624 q^{51} -5.54119 q^{52} +1.59351 q^{53} -11.8337 q^{54} -2.93180 q^{55} +0.989176 q^{56} +9.62602 q^{57} +20.5231 q^{58} -8.81278 q^{59} +3.40625 q^{60} +0.187223 q^{61} -1.96223 q^{62} +1.18561 q^{63} -10.6859 q^{64} +2.32991 q^{65} +8.78617 q^{66} -3.91562 q^{67} +6.51970 q^{68} +13.0125 q^{69} -2.61492 q^{70} +3.70108 q^{71} +0.750937 q^{72} +4.37612 q^{73} -4.14060 q^{74} -1.43223 q^{75} -15.9844 q^{76} -3.66387 q^{77} -6.98240 q^{78} +12.4634 q^{79} +3.10034 q^{80} -5.25380 q^{81} +14.7181 q^{82} -0.231146 q^{83} +4.25679 q^{84} -2.74135 q^{85} +6.54324 q^{86} +14.0477 q^{87} -2.32061 q^{88} -17.1881 q^{89} -1.98512 q^{90} +2.91169 q^{91} -21.6078 q^{92} -1.34311 q^{93} +13.6357 q^{94} +6.72100 q^{95} -11.5586 q^{96} -0.112329 q^{97} +11.3792 q^{98} -2.78144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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