LMFDB - Embedded newform 8035.2.a.e.1.13

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:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} +O(q^{10})$	\(q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} -2.41868 q^{10} -4.56961 q^{11} +12.3534 q^{12} +3.08185 q^{13} +5.02812 q^{14} +3.20867 q^{15} +3.12259 q^{16} +3.05404 q^{17} -17.6456 q^{18} -0.524240 q^{19} +3.85002 q^{20} -6.67040 q^{21} +11.0524 q^{22} +7.45230 q^{23} -14.3575 q^{24} +1.00000 q^{25} -7.45401 q^{26} +13.7830 q^{27} -8.00367 q^{28} +2.84809 q^{29} -7.76074 q^{30} -6.26218 q^{31} +1.39665 q^{32} -14.6624 q^{33} -7.38676 q^{34} -2.07887 q^{35} +28.0880 q^{36} +5.05829 q^{37} +1.26797 q^{38} +9.88864 q^{39} -4.47460 q^{40} +1.86903 q^{41} +16.1336 q^{42} +7.79340 q^{43} -17.5931 q^{44} +7.29555 q^{45} -18.0247 q^{46} +2.35402 q^{47} +10.0194 q^{48} -2.67831 q^{49} -2.41868 q^{50} +9.79941 q^{51} +11.8652 q^{52} -7.65213 q^{53} -33.3367 q^{54} -4.56961 q^{55} +9.30210 q^{56} -1.68211 q^{57} -6.88861 q^{58} -1.36729 q^{59} +12.3534 q^{60} +4.00882 q^{61} +15.1462 q^{62} -15.1665 q^{63} -9.62322 q^{64} +3.08185 q^{65} +35.4636 q^{66} +3.62849 q^{67} +11.7581 q^{68} +23.9120 q^{69} +5.02812 q^{70} -9.13799 q^{71} -32.6447 q^{72} +16.3476 q^{73} -12.2344 q^{74} +3.20867 q^{75} -2.01833 q^{76} +9.49961 q^{77} -23.9175 q^{78} +2.32344 q^{79} +3.12259 q^{80} +22.3384 q^{81} -4.52059 q^{82} -6.26732 q^{83} -25.6811 q^{84} +3.05404 q^{85} -18.8497 q^{86} +9.13856 q^{87} +20.4472 q^{88} +6.63886 q^{89} -17.6456 q^{90} -6.40676 q^{91} +28.6915 q^{92} -20.0933 q^{93} -5.69363 q^{94} -0.524240 q^{95} +4.48137 q^{96} -6.71316 q^{97} +6.47797 q^{98} -33.3378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.41868	−1.71027	−0.855133	−	0.518409i	$-0.826524\pi$
$2$	−2.41868	−1.71027	−0.855133	+	0.518409i	$0.826524\pi$
$3$	3.20867	1.85253	0.926263	−	0.376878i	$-0.123002\pi$
$3$	3.20867	1.85253	0.926263	+	0.376878i	$0.123002\pi$
$4$	3.85002	1.92501
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.76074	−3.16831
$7$	−2.07887	−0.785738	−0.392869	−	0.919594i	$-0.628517\pi$
$7$	−2.07887	−0.785738	−0.392869	+	0.919594i	$0.628517\pi$
$8$	−4.47460	−1.58201
$9$	7.29555	2.43185
$10$	−2.41868	−0.764854
$11$	−4.56961	−1.37779	−0.688894	−	0.724862i	$-0.741904\pi$
$11$	−4.56961	−1.37779	−0.688894	+	0.724862i	$0.741904\pi$
$12$	12.3534	3.56613
$13$	3.08185	0.854752	0.427376	−	0.904074i	$-0.359438\pi$
$13$	3.08185	0.854752	0.427376	+	0.904074i	$0.359438\pi$
$14$	5.02812	1.34382
$15$	3.20867	0.828475
$16$	3.12259	0.780648
$17$	3.05404	0.740714	0.370357	−	0.928889i	$-0.379235\pi$
$17$	3.05404	0.740714	0.370357	+	0.928889i	$0.379235\pi$
$18$	−17.6456	−4.15911
$19$	−0.524240	−0.120269	−0.0601345	−	0.998190i	$-0.519153\pi$
$19$	−0.524240	−0.120269	−0.0601345	+	0.998190i	$0.519153\pi$
$20$	3.85002	0.860890
$21$	−6.67040	−1.45560
$22$	11.0524	2.35638
$23$	7.45230	1.55391	0.776956	−	0.629555i	$-0.216763\pi$
$23$	7.45230	1.55391	0.776956	+	0.629555i	$0.216763\pi$
$24$	−14.3575	−2.93071
$25$	1.00000	0.200000
$26$	−7.45401	−1.46185
$27$	13.7830	2.65254
$28$	−8.00367	−1.51255
$29$	2.84809	0.528876	0.264438	−	0.964403i	$-0.414814\pi$
$29$	2.84809	0.528876	0.264438	+	0.964403i	$0.414814\pi$
$30$	−7.76074	−1.41691
$31$	−6.26218	−1.12472	−0.562360	−	0.826892i	$-0.690107\pi$
$31$	−6.26218	−1.12472	−0.562360	+	0.826892i	$0.690107\pi$
$32$	1.39665	0.246894
$33$	−14.6624	−2.55239
$34$	−7.38676	−1.26682
$35$	−2.07887	−0.351393
$36$	28.0880	4.68133
$37$	5.05829	0.831577	0.415789	−	0.909461i	$-0.363506\pi$
$37$	5.05829	0.831577	0.415789	+	0.909461i	$0.363506\pi$
$38$	1.26797	0.205692
$39$	9.88864	1.58345
$40$	−4.47460	−0.707496
$41$	1.86903	0.291894	0.145947	−	0.989292i	$-0.453377\pi$
$41$	1.86903	0.291894	0.145947	+	0.989292i	$0.453377\pi$
$42$	16.1336	2.48946
$43$	7.79340	1.18848	0.594241	−	0.804287i	$-0.297452\pi$
$43$	7.79340	1.18848	0.594241	+	0.804287i	$0.297452\pi$
$44$	−17.5931	−2.65225
$45$	7.29555	1.08756
$46$	−18.0247	−2.65760
$47$	2.35402	0.343370	0.171685	−	0.985152i	$-0.445079\pi$
$47$	2.35402	0.343370	0.171685	+	0.985152i	$0.445079\pi$
$48$	10.0194	1.44617
$49$	−2.67831	−0.382616
$50$	−2.41868	−0.342053
$51$	9.79941	1.37219
$52$	11.8652	1.64540
$53$	−7.65213	−1.05110	−0.525551	−	0.850762i	$-0.676141\pi$
$53$	−7.65213	−1.05110	−0.525551	+	0.850762i	$0.676141\pi$
$54$	−33.3367	−4.53655
$55$	−4.56961	−0.616166
$56$	9.30210	1.24304
$57$	−1.68211	−0.222801
$58$	−6.88861	−0.904519
$59$	−1.36729	−0.178006	−0.0890032	−	0.996031i	$-0.528368\pi$
$59$	−1.36729	−0.178006	−0.0890032	+	0.996031i	$0.528368\pi$
$60$	12.3534	1.59482
$61$	4.00882	0.513277	0.256638	−	0.966507i	$-0.417385\pi$
$61$	4.00882	0.513277	0.256638	+	0.966507i	$0.417385\pi$
$62$	15.1462	1.92357
$63$	−15.1665	−1.91080
$64$	−9.62322	−1.20290
$65$	3.08185	0.382257
$66$	35.4636	4.36526
$67$	3.62849	0.443291	0.221646	−	0.975127i	$-0.428857\pi$
$67$	3.62849	0.443291	0.221646	+	0.975127i	$0.428857\pi$
$68$	11.7581	1.42588
$69$	23.9120	2.87866
$70$	5.02812	0.600975
$71$	−9.13799	−1.08448	−0.542240	−	0.840224i	$-0.682424\pi$
$71$	−9.13799	−1.08448	−0.542240	+	0.840224i	$0.682424\pi$
$72$	−32.6447	−3.84721
$73$	16.3476	1.91334	0.956669	−	0.291178i	$-0.0940473\pi$
$73$	16.3476	1.91334	0.956669	+	0.291178i	$0.0940473\pi$
$74$	−12.2344	−1.42222
$75$	3.20867	0.370505
$76$	−2.01833	−0.231519
$77$	9.49961	1.08258
$78$	−23.9175	−2.70812
$79$	2.32344	0.261407	0.130704	−	0.991421i	$-0.458276\pi$
$79$	2.32344	0.261407	0.130704	+	0.991421i	$0.458276\pi$
$80$	3.12259	0.349116
$81$	22.3384	2.48205
$82$	−4.52059	−0.499215
$83$	−6.26732	−0.687928	−0.343964	−	0.938983i	$-0.611770\pi$
$83$	−6.26732	−0.687928	−0.343964	+	0.938983i	$0.611770\pi$
$84$	−25.6811	−2.80204
$85$	3.05404	0.331258
$86$	−18.8497	−2.03262
$87$	9.13856	0.979757
$88$	20.4472	2.17967
$89$	6.63886	0.703717	0.351859	−	0.936053i	$-0.385550\pi$
$89$	6.63886	0.703717	0.351859	+	0.936053i	$0.385550\pi$
$90$	−17.6456	−1.86001
$91$	−6.40676	−0.671611
$92$	28.6915	2.99129
$93$	−20.0933	−2.08357
$94$	−5.69363	−0.587254
$95$	−0.524240	−0.0537859
$96$	4.48137	0.457378
$97$	−6.71316	−0.681618	−0.340809	−	0.940133i	$-0.610701\pi$
$97$	−6.71316	−0.681618	−0.340809	+	0.940133i	$0.610701\pi$
$98$	6.47797	0.654374
$99$	−33.3378	−3.35058
$100$	3.85002	0.385002
$101$	11.0639	1.10090	0.550450	−	0.834868i	$-0.314456\pi$
$101$	11.0639	1.10090	0.550450	+	0.834868i	$0.314456\pi$
$102$	−23.7017	−2.34681
$103$	−7.09138	−0.698734	−0.349367	−	0.936986i	$-0.613603\pi$
$103$	−7.09138	−0.698734	−0.349367	+	0.936986i	$0.613603\pi$
$104$	−13.7900	−1.35222
$105$	−6.67040	−0.650964
$106$	18.5081	1.79766
$107$	9.34656	0.903566	0.451783	−	0.892128i	$-0.350788\pi$
$107$	9.34656	0.903566	0.451783	+	0.892128i	$0.350788\pi$
$108$	53.0648	5.10616
$109$	−11.6573	−1.11657	−0.558284	−	0.829650i	$-0.688540\pi$
$109$	−11.6573	−1.11657	−0.558284	+	0.829650i	$0.688540\pi$
$110$	11.0524	1.05381
$111$	16.2304	1.54052
$112$	−6.49145	−0.613385
$113$	−17.3684	−1.63388	−0.816939	−	0.576724i	$-0.804331\pi$
$113$	−17.3684	−1.63388	−0.816939	+	0.576724i	$0.804331\pi$
$114$	4.06849	0.381049
$115$	7.45230	0.694930
$116$	10.9652	1.01809
$117$	22.4838	2.07863
$118$	3.30704	0.304438
$119$	−6.34895	−0.582008
$120$	−14.3575	−1.31065
$121$	9.88133	0.898302
$122$	−9.69606	−0.877840
$123$	5.99710	0.540740
$124$	−24.1095	−2.16510
$125$	1.00000	0.0894427
$126$	36.6829	3.26797
$127$	3.99446	0.354451	0.177225	−	0.984170i	$-0.443288\pi$
$127$	3.99446	0.354451	0.177225	+	0.984170i	$0.443288\pi$
$128$	20.4822	1.81039
$129$	25.0064	2.20169
$130$	−7.45401	−0.653760
$131$	3.18872	0.278600	0.139300	−	0.990250i	$-0.455515\pi$
$131$	3.18872	0.278600	0.139300	+	0.990250i	$0.455515\pi$
$132$	−56.4503	−4.91337
$133$	1.08983	0.0944999
$134$	−8.77617	−0.758145
$135$	13.7830	1.18625
$136$	−13.6656	−1.17182
$137$	−14.4679	−1.23608	−0.618038	−	0.786148i	$-0.712072\pi$
$137$	−14.4679	−1.23608	−0.618038	+	0.786148i	$0.712072\pi$
$138$	−57.8354	−4.92327
$139$	−4.85721	−0.411983	−0.205991	−	0.978554i	$-0.566042\pi$
$139$	−4.85721	−0.411983	−0.205991	+	0.978554i	$0.566042\pi$
$140$	−8.00367	−0.676434
$141$	7.55329	0.636101
$142$	22.1019	1.85475
$143$	−14.0829	−1.17767
$144$	22.7810	1.89842
$145$	2.84809	0.236521
$146$	−39.5395	−3.27232
$147$	−8.59380	−0.708805
$148$	19.4745	1.60079
$149$	7.53589	0.617365	0.308682	−	0.951165i	$-0.400112\pi$
$149$	7.53589	0.617365	0.308682	+	0.951165i	$0.400112\pi$
$150$	−7.76074	−0.633662
$151$	2.85900	0.232662	0.116331	−	0.993210i	$-0.462887\pi$
$151$	2.85900	0.232662	0.116331	+	0.993210i	$0.462887\pi$
$152$	2.34576	0.190267
$153$	22.2809	1.80131
$154$	−22.9765	−1.85150
$155$	−6.26218	−0.502990
$156$	38.0714	3.04815
$157$	−18.2262	−1.45461	−0.727305	−	0.686314i	$-0.759228\pi$
$157$	−18.2262	−1.45461	−0.727305	+	0.686314i	$0.759228\pi$
$158$	−5.61966	−0.447076
$159$	−24.5532	−1.94719
$160$	1.39665	0.110415
$161$	−15.4923	−1.22097
$162$	−54.0295	−4.24496
$163$	−7.16288	−0.561040	−0.280520	−	0.959848i	$-0.590507\pi$
$163$	−7.16288	−0.561040	−0.280520	+	0.959848i	$0.590507\pi$
$164$	7.19580	0.561897
$165$	−14.6624	−1.14146
$166$	15.1587	1.17654
$167$	−6.18720	−0.478780	−0.239390	−	0.970923i	$-0.576947\pi$
$167$	−6.18720	−0.478780	−0.239390	+	0.970923i	$0.576947\pi$
$168$	29.8473	2.30277
$169$	−3.50220	−0.269400
$170$	−7.38676	−0.566538
$171$	−3.82462	−0.292476
$172$	30.0047	2.28784
$173$	7.49442	0.569790	0.284895	−	0.958559i	$-0.408041\pi$
$173$	7.49442	0.569790	0.284895	+	0.958559i	$0.408041\pi$
$174$	−22.1033	−1.67564
$175$	−2.07887	−0.157148
$176$	−14.2690	−1.07557
$177$	−4.38719	−0.329761
$178$	−16.0573	−1.20354
$179$	21.6911	1.62127	0.810634	−	0.585553i	$-0.199123\pi$
$179$	21.6911	1.62127	0.810634	+	0.585553i	$0.199123\pi$
$180$	28.0880	2.09356
$181$	9.80379	0.728710	0.364355	−	0.931260i	$-0.381289\pi$
$181$	9.80379	0.728710	0.364355	+	0.931260i	$0.381289\pi$
$182$	15.4959	1.14863
$183$	12.8630	0.950859
$184$	−33.3460	−2.45830
$185$	5.05829	0.371893
$186$	48.5992	3.56346
$187$	−13.9558	−1.02055
$188$	9.06303	0.660990
$189$	−28.6530	−2.08420
$190$	1.26797	0.0919882
$191$	23.0035	1.66447	0.832237	−	0.554420i	$-0.187060\pi$
$191$	23.0035	1.66447	0.832237	+	0.554420i	$0.187060\pi$
$192$	−30.8777	−2.22841
$193$	−22.9828	−1.65434	−0.827168	−	0.561954i	$-0.810050\pi$
$193$	−22.9828	−1.65434	−0.827168	+	0.561954i	$0.810050\pi$
$194$	16.2370	1.16575
$195$	9.88864	0.708140
$196$	−10.3115	−0.736538
$197$	17.1115	1.21914	0.609570	−	0.792732i	$-0.291342\pi$
$197$	17.1115	1.21914	0.609570	+	0.792732i	$0.291342\pi$
$198$	80.6336	5.73038
$199$	7.00526	0.496590	0.248295	−	0.968685i	$-0.420130\pi$
$199$	7.00526	0.496590	0.248295	+	0.968685i	$0.420130\pi$
$200$	−4.47460	−0.316402
$201$	11.6426	0.821208
$202$	−26.7601	−1.88283
$203$	−5.92079	−0.415558
$204$	37.7279	2.64148
$205$	1.86903	0.130539
$206$	17.1518	1.19502
$207$	54.3686	3.77888
$208$	9.62336	0.667260
$209$	2.39557	0.165705
$210$	16.1336	1.11332
$211$	−14.2337	−0.979887	−0.489944	−	0.871754i	$-0.662983\pi$
$211$	−14.2337	−0.979887	−0.489944	+	0.871754i	$0.662983\pi$
$212$	−29.4608	−2.02338
$213$	−29.3208	−2.00903
$214$	−22.6064	−1.54534
$215$	7.79340	0.531506
$216$	−61.6734	−4.19634
$217$	13.0182	0.883736
$218$	28.1953	1.90963
$219$	52.4539	3.54451
$220$	−17.5931	−1.18612
$221$	9.41211	0.633127
$222$	−39.2561	−2.63470
$223$	−5.36588	−0.359326	−0.179663	−	0.983728i	$-0.557501\pi$
$223$	−5.36588	−0.359326	−0.179663	+	0.983728i	$0.557501\pi$
$224$	−2.90344	−0.193994
$225$	7.29555	0.486370
$226$	42.0085	2.79436
$227$	14.3492	0.952392	0.476196	−	0.879339i	$-0.342015\pi$
$227$	14.3492	0.952392	0.476196	+	0.879339i	$0.342015\pi$
$228$	−6.47616	−0.428894
$229$	17.9188	1.18411	0.592054	−	0.805899i	$-0.298317\pi$
$229$	17.9188	1.18411	0.592054	+	0.805899i	$0.298317\pi$
$230$	−18.0247	−1.18852
$231$	30.4811	2.00551
$232$	−12.7440	−0.836687
$233$	5.33613	0.349582	0.174791	−	0.984606i	$-0.444075\pi$
$233$	5.33613	0.349582	0.174791	+	0.984606i	$0.444075\pi$
$234$	−54.3811	−3.55501
$235$	2.35402	0.153560
$236$	−5.26410	−0.342664
$237$	7.45515	0.484264
$238$	15.3561	0.995387
$239$	−6.48503	−0.419482	−0.209741	−	0.977757i	$-0.567262\pi$
$239$	−6.48503	−0.419482	−0.209741	+	0.977757i	$0.567262\pi$
$240$	10.0194	0.646747
$241$	20.2686	1.30561	0.652807	−	0.757524i	$-0.273591\pi$
$241$	20.2686	1.30561	0.652807	+	0.757524i	$0.273591\pi$
$242$	−23.8998	−1.53634
$243$	30.3276	1.94552
$244$	15.4340	0.988062
$245$	−2.67831	−0.171111
$246$	−14.5051	−0.924809
$247$	−1.61563	−0.102800
$248$	28.0207	1.77932
$249$	−20.1098	−1.27440
$250$	−2.41868	−0.152971
$251$	−5.24465	−0.331039	−0.165520	−	0.986207i	$-0.552930\pi$
$251$	−5.24465	−0.331039	−0.165520	+	0.986207i	$0.552930\pi$
$252$	−58.3912	−3.67830
$253$	−34.0541	−2.14096
$254$	−9.66131	−0.606205
$255$	9.79941	0.613663
$256$	−30.2935	−1.89334
$257$	18.1737	1.13365	0.566823	−	0.823839i	$-0.308172\pi$
$257$	18.1737	1.13365	0.566823	+	0.823839i	$0.308172\pi$
$258$	−60.4826	−3.76548
$259$	−10.5155	−0.653402
$260$	11.8652	0.735847
$261$	20.7784	1.28615
$262$	−7.71249	−0.476479
$263$	11.5009	0.709176	0.354588	−	0.935023i	$-0.384621\pi$
$263$	11.5009	0.709176	0.354588	+	0.935023i	$0.384621\pi$
$264$	65.6082	4.03790
$265$	−7.65213	−0.470067
$266$	−2.63594	−0.161620
$267$	21.3019	1.30365
$268$	13.9698	0.853339
$269$	6.68235	0.407430	0.203715	−	0.979030i	$-0.434698\pi$
$269$	6.68235	0.407430	0.203715	+	0.979030i	$0.434698\pi$
$270$	−33.3367	−2.02881
$271$	3.76727	0.228845	0.114423	−	0.993432i	$-0.463498\pi$
$271$	3.76727	0.228845	0.114423	+	0.993432i	$0.463498\pi$
$272$	9.53653	0.578237
$273$	−20.5572	−1.24418
$274$	34.9933	2.11402
$275$	−4.56961	−0.275558
$276$	92.0614	5.54144
$277$	−10.4187	−0.626001	−0.313001	−	0.949753i	$-0.601334\pi$
$277$	−10.4187	−0.626001	−0.313001	+	0.949753i	$0.601334\pi$
$278$	11.7480	0.704600
$279$	−45.6861	−2.73515
$280$	9.30210	0.555907
$281$	27.4287	1.63626	0.818129	−	0.575035i	$-0.195012\pi$
$281$	27.4287	1.63626	0.818129	+	0.575035i	$0.195012\pi$
$282$	−18.2690	−1.08790
$283$	21.2660	1.26413	0.632067	−	0.774913i	$-0.282207\pi$
$283$	21.2660	1.26413	0.632067	+	0.774913i	$0.282207\pi$
$284$	−35.1814	−2.08763
$285$	−1.68211	−0.0996398
$286$	34.0619	2.01412
$287$	−3.88547	−0.229352
$288$	10.1893	0.600411
$289$	−7.67282	−0.451342
$290$	−6.88861	−0.404513
$291$	−21.5403	−1.26272
$292$	62.9384	3.68319
$293$	2.12681	0.124250	0.0621248	−	0.998068i	$-0.480212\pi$
$293$	2.12681	0.124250	0.0621248	+	0.998068i	$0.480212\pi$
$294$	20.7857	1.21224
$295$	−1.36729	−0.0796069
$296$	−22.6338	−1.31556
$297$	−62.9829	−3.65464
$298$	−18.2269	−1.05586
$299$	22.9669	1.32821
$300$	12.3534	0.713225
$301$	−16.2014	−0.933836
$302$	−6.91501	−0.397914
$303$	35.5004	2.03945
$304$	−1.63699	−0.0938877
$305$	4.00882	0.229544
$306$	−53.8905	−3.08071
$307$	32.5608	1.85834	0.929170	−	0.369652i	$-0.120523\pi$
$307$	32.5608	1.85834	0.929170	+	0.369652i	$0.120523\pi$
$308$	36.5737	2.08398
$309$	−22.7539	−1.29442
$310$	15.1462	0.860247
$311$	28.2988	1.60468	0.802339	−	0.596868i	$-0.203589\pi$
$311$	28.2988	1.60468	0.802339	+	0.596868i	$0.203589\pi$
$312$	−44.2477	−2.50503
$313$	20.3450	1.14997	0.574983	−	0.818165i	$-0.305009\pi$
$313$	20.3450	1.14997	0.574983	+	0.818165i	$0.305009\pi$
$314$	44.0834	2.48777
$315$	−15.1665	−0.854535
$316$	8.94528	0.503211
$317$	23.1495	1.30021	0.650104	−	0.759846i	$-0.274725\pi$
$317$	23.1495	1.30021	0.650104	+	0.759846i	$0.274725\pi$
$318$	59.3862	3.33022
$319$	−13.0146	−0.728680
$320$	−9.62322	−0.537954
$321$	29.9900	1.67388
$322$	37.4710	2.08818
$323$	−1.60105	−0.0890850
$324$	86.0033	4.77796
$325$	3.08185	0.170950
$326$	17.3247	0.959528
$327$	−37.4044	−2.06847
$328$	−8.36316	−0.461778
$329$	−4.89371	−0.269799
$330$	35.4636	1.95221
$331$	−16.2276	−0.891947	−0.445974	−	0.895046i	$-0.647142\pi$
$331$	−16.2276	−0.891947	−0.445974	+	0.895046i	$0.647142\pi$
$332$	−24.1293	−1.32427
$333$	36.9030	2.02227
$334$	14.9649	0.818841
$335$	3.62849	0.198246
$336$	−20.8289	−1.13631
$337$	−7.54943	−0.411244	−0.205622	−	0.978632i	$-0.565922\pi$
$337$	−7.54943	−0.411244	−0.205622	+	0.978632i	$0.565922\pi$
$338$	8.47070	0.460745
$339$	−55.7293	−3.02680
$340$	11.7581	0.637673
$341$	28.6157	1.54963
$342$	9.25054	0.500212
$343$	20.1199	1.08637
$344$	−34.8723	−1.88019
$345$	23.9120	1.28738
$346$	−18.1266	−0.974492
$347$	7.01011	0.376323	0.188161	−	0.982138i	$-0.439747\pi$
$347$	7.01011	0.376323	0.188161	+	0.982138i	$0.439747\pi$
$348$	35.1836	1.88604
$349$	25.3886	1.35902	0.679509	−	0.733667i	$-0.262193\pi$
$349$	25.3886	1.35902	0.679509	+	0.733667i	$0.262193\pi$
$350$	5.02812	0.268764
$351$	42.4772	2.26726
$352$	−6.38213	−0.340168
$353$	−2.32093	−0.123531	−0.0617654	−	0.998091i	$-0.519673\pi$
$353$	−2.32093	−0.123531	−0.0617654	+	0.998091i	$0.519673\pi$
$354$	10.6112	0.563979
$355$	−9.13799	−0.484994
$356$	25.5597	1.35466
$357$	−20.3717	−1.07818
$358$	−52.4638	−2.77280
$359$	31.2488	1.64925	0.824625	−	0.565680i	$-0.191386\pi$
$359$	31.2488	1.64925	0.824625	+	0.565680i	$0.191386\pi$
$360$	−32.6447	−1.72052
$361$	−18.7252	−0.985535
$362$	−23.7122	−1.24629
$363$	31.7059	1.66413
$364$	−24.6661	−1.29286
$365$	16.3476	0.855671
$366$	−31.1114	−1.62622
$367$	−10.4243	−0.544143	−0.272071	−	0.962277i	$-0.587709\pi$
$367$	−10.4243	−0.544143	−0.272071	+	0.962277i	$0.587709\pi$
$368$	23.2705	1.21306
$369$	13.6356	0.709842
$370$	−12.2344	−0.636035
$371$	15.9078	0.825890
$372$	−77.3593	−4.01090
$373$	−20.1508	−1.04337	−0.521683	−	0.853139i	$-0.674696\pi$
$373$	−20.1508	−1.04337	−0.521683	+	0.853139i	$0.674696\pi$
$374$	33.7546	1.74541
$375$	3.20867	0.165695
$376$	−10.5333	−0.543214
$377$	8.77737	0.452058
$378$	69.3026	3.56454
$379$	20.6357	1.05999	0.529994	−	0.848002i	$-0.322194\pi$
$379$	20.6357	1.05999	0.529994	+	0.848002i	$0.322194\pi$
$380$	−2.01833	−0.103538
$381$	12.8169	0.656629
$382$	−55.6381	−2.84669
$383$	1.81219	0.0925987	0.0462994	−	0.998928i	$-0.485257\pi$
$383$	1.81219	0.0925987	0.0462994	+	0.998928i	$0.485257\pi$
$384$	65.7206	3.35379
$385$	9.49961	0.484145
$386$	55.5880	2.82935
$387$	56.8572	2.89021
$388$	−25.8458	−1.31212
$389$	−0.775387	−0.0393137	−0.0196568	−	0.999807i	$-0.506257\pi$
$389$	−0.775387	−0.0393137	−0.0196568	+	0.999807i	$0.506257\pi$
$390$	−23.9175	−1.21111
$391$	22.7596	1.15100
$392$	11.9844	0.605301
$393$	10.2315	0.516113
$394$	−41.3871	−2.08505
$395$	2.32344	0.116905
$396$	−128.351	−6.44989
$397$	−29.1485	−1.46292	−0.731460	−	0.681885i	$-0.761161\pi$
$397$	−29.1485	−1.46292	−0.731460	+	0.681885i	$0.761161\pi$
$398$	−16.9435	−0.849300
$399$	3.49689	0.175064
$400$	3.12259	0.156130
$401$	−2.92900	−0.146267	−0.0731336	−	0.997322i	$-0.523300\pi$
$401$	−2.92900	−0.146267	−0.0731336	+	0.997322i	$0.523300\pi$
$402$	−28.1598	−1.40448
$403$	−19.2991	−0.961357
$404$	42.5962	2.11924
$405$	22.3384	1.11001
$406$	14.3205	0.710715
$407$	−23.1144	−1.14574
$408$	−43.8484	−2.17082
$409$	12.5090	0.618532	0.309266	−	0.950976i	$-0.399917\pi$
$409$	12.5090	0.618532	0.309266	+	0.950976i	$0.399917\pi$
$410$	−4.52059	−0.223256
$411$	−46.4227	−2.28986
$412$	−27.3019	−1.34507
$413$	2.84242	0.139866
$414$	−131.500	−6.46289
$415$	−6.26732	−0.307651
$416$	4.30425	0.211033
$417$	−15.5852	−0.763209
$418$	−5.79413	−0.283400
$419$	21.2780	1.03950	0.519750	−	0.854318i	$-0.326025\pi$
$419$	21.2780	1.03950	0.519750	+	0.854318i	$0.326025\pi$
$420$	−25.6811	−1.25311
$421$	24.7633	1.20689	0.603445	−	0.797405i	$-0.293794\pi$
$421$	24.7633	1.20689	0.603445	+	0.797405i	$0.293794\pi$
$422$	34.4267	1.67587
$423$	17.1739	0.835024
$424$	34.2402	1.66285
$425$	3.05404	0.148143
$426$	70.9176	3.43597
$427$	−8.33381	−0.403301
$428$	35.9844	1.73937
$429$	−45.1872	−2.18166
$430$	−18.8497	−0.909016
$431$	−13.1762	−0.634674	−0.317337	−	0.948313i	$-0.602789\pi$
$431$	−13.1762	−0.634674	−0.317337	+	0.948313i	$0.602789\pi$
$432$	43.0387	2.07070
$433$	32.2915	1.55183	0.775916	−	0.630836i	$-0.217288\pi$
$433$	32.2915	1.55183	0.775916	+	0.630836i	$0.217288\pi$
$434$	−31.4870	−1.51142
$435$	9.13856	0.438160
$436$	−44.8808	−2.14940
$437$	−3.90679	−0.186887
$438$	−126.869	−6.06205
$439$	7.69188	0.367114	0.183557	−	0.983009i	$-0.441239\pi$
$439$	7.69188	0.367114	0.183557	+	0.983009i	$0.441239\pi$
$440$	20.4472	0.974780
$441$	−19.5397	−0.930464
$442$	−22.7649	−1.08281
$443$	−7.75332	−0.368371	−0.184186	−	0.982891i	$-0.558965\pi$
$443$	−7.75332	−0.368371	−0.184186	+	0.982891i	$0.558965\pi$
$444$	62.4872	2.96551
$445$	6.63886	0.314712
$446$	12.9783	0.614542
$447$	24.1802	1.14368
$448$	20.0054	0.945167
$449$	−33.3073	−1.57187	−0.785935	−	0.618310i	$-0.787818\pi$
$449$	−33.3073	−1.57187	−0.785935	+	0.618310i	$0.787818\pi$
$450$	−17.6456	−0.831822
$451$	−8.54074	−0.402168
$452$	−66.8684	−3.14523
$453$	9.17358	0.431012
$454$	−34.7062	−1.62884
$455$	−6.40676	−0.300354
$456$	7.52678	0.352474
$457$	8.52564	0.398813	0.199406	−	0.979917i	$-0.436099\pi$
$457$	8.52564	0.398813	0.199406	+	0.979917i	$0.436099\pi$
$458$	−43.3398	−2.02514
$459$	42.0939	1.96478
$460$	28.6915	1.33775
$461$	−6.52883	−0.304078	−0.152039	−	0.988375i	$-0.548584\pi$
$461$	−6.52883	−0.304078	−0.152039	+	0.988375i	$0.548584\pi$
$462$	−73.7241	−3.42995
$463$	−39.4131	−1.83168	−0.915841	−	0.401541i	$-0.868475\pi$
$463$	−39.4131	−1.83168	−0.915841	+	0.401541i	$0.868475\pi$
$464$	8.89340	0.412866
$465$	−20.0933	−0.931802
$466$	−12.9064	−0.597877
$467$	8.60565	0.398222	0.199111	−	0.979977i	$-0.436195\pi$
$467$	8.60565	0.398222	0.199111	+	0.979977i	$0.436195\pi$
$468$	86.5630	4.00138
$469$	−7.54316	−0.348311
$470$	−5.69363	−0.262628
$471$	−58.4819	−2.69470
$472$	6.11809	0.281608
$473$	−35.6128	−1.63748
$474$	−18.0316	−0.828220
$475$	−0.524240	−0.0240538
$476$	−24.4436	−1.12037
$477$	−55.8265	−2.55612
$478$	15.6852	0.717425
$479$	−2.29903	−0.105045	−0.0525226	−	0.998620i	$-0.516726\pi$
$479$	−2.29903	−0.105045	−0.0525226	+	0.998620i	$0.516726\pi$
$480$	4.48137	0.204546
$481$	15.5889	0.710792
$482$	−49.0232	−2.23295
$483$	−49.7098	−2.26187
$484$	38.0433	1.72924
$485$	−6.71316	−0.304829
$486$	−73.3528	−3.32735
$487$	26.9406	1.22080	0.610398	−	0.792095i	$-0.291010\pi$
$487$	26.9406	1.22080	0.610398	+	0.792095i	$0.291010\pi$
$488$	−17.9379	−0.812009
$489$	−22.9833	−1.03934
$490$	6.47797	0.292645
$491$	−40.1734	−1.81300	−0.906501	−	0.422205i	$-0.861256\pi$
$491$	−40.1734	−1.81300	−0.906501	+	0.422205i	$0.861256\pi$
$492$	23.0889	1.04093
$493$	8.69818	0.391746
$494$	3.90769	0.175815
$495$	−33.3378	−1.49842
$496$	−19.5542	−0.878010
$497$	18.9967	0.852117
$498$	48.6391	2.17957
$499$	−23.0032	−1.02977	−0.514883	−	0.857261i	$-0.672165\pi$
$499$	−23.0032	−1.02977	−0.514883	+	0.857261i	$0.672165\pi$
$500$	3.85002	0.172178
$501$	−19.8527	−0.886952
$502$	12.6851	0.566165
$503$	−13.6086	−0.606778	−0.303389	−	0.952867i	$-0.598118\pi$
$503$	−13.6086	−0.606778	−0.303389	+	0.952867i	$0.598118\pi$
$504$	67.8639	3.02290
$505$	11.0639	0.492338
$506$	82.3660	3.66161
$507$	−11.2374	−0.499070
$508$	15.3787	0.682320
$509$	−4.84045	−0.214549	−0.107275	−	0.994229i	$-0.534212\pi$
$509$	−4.84045	−0.214549	−0.107275	+	0.994229i	$0.534212\pi$
$510$	−23.7017	−1.04953
$511$	−33.9844	−1.50338
$512$	32.3058	1.42773
$513$	−7.22561	−0.319018
$514$	−43.9565	−1.93884
$515$	−7.09138	−0.312483
$516$	96.2752	4.23828
$517$	−10.7570	−0.473091
$518$	25.4337	1.11749
$519$	24.0471	1.05555
$520$	−13.7900	−0.604733
$521$	30.2522	1.32537	0.662686	−	0.748897i	$-0.269416\pi$
$521$	30.2522	1.32537	0.662686	+	0.748897i	$0.269416\pi$
$522$	−50.2562	−2.19965
$523$	14.2555	0.623350	0.311675	−	0.950189i	$-0.399110\pi$
$523$	14.2555	0.623350	0.311675	+	0.950189i	$0.399110\pi$
$524$	12.2766	0.536306
$525$	−6.67040	−0.291120
$526$	−27.8170	−1.21288
$527$	−19.1250	−0.833097
$528$	−45.7845	−1.99252
$529$	32.5367	1.41464
$530$	18.5081	0.803939
$531$	−9.97516	−0.432885
$532$	4.19585	0.181913
$533$	5.76007	0.249496
$534$	−51.5225	−2.22959
$535$	9.34656	0.404087
$536$	−16.2360	−0.701290
$537$	69.5995	3.00344
$538$	−16.1625	−0.696814
$539$	12.2388	0.527163
$540$	53.0648	2.28355
$541$	−36.9524	−1.58871	−0.794354	−	0.607456i	$-0.792190\pi$
$541$	−36.9524	−1.58871	−0.794354	+	0.607456i	$0.792190\pi$
$542$	−9.11182	−0.391386
$543$	31.4571	1.34995
$544$	4.26542	0.182878
$545$	−11.6573	−0.499344
$546$	49.7212	2.12787
$547$	−30.3372	−1.29713	−0.648563	−	0.761161i	$-0.724630\pi$
$547$	−30.3372	−1.29713	−0.648563	+	0.761161i	$0.724630\pi$
$548$	−55.7017	−2.37946
$549$	29.2466	1.24821
$550$	11.0524	0.471277
$551$	−1.49308	−0.0636074
$552$	−106.996	−4.55407
$553$	−4.83012	−0.205398
$554$	25.1996	1.07063
$555$	16.2304	0.688941
$556$	−18.7003	−0.793070
$557$	−3.80562	−0.161249	−0.0806247	−	0.996745i	$-0.525692\pi$
$557$	−3.80562	−0.161249	−0.0806247	+	0.996745i	$0.525692\pi$
$558$	110.500	4.67784
$559$	24.0181	1.01586
$560$	−6.49145	−0.274314
$561$	−44.7795	−1.89059
$562$	−66.3412	−2.79843
$563$	−40.8938	−1.72347	−0.861735	−	0.507359i	$-0.830622\pi$
$563$	−40.8938	−1.72347	−0.861735	+	0.507359i	$0.830622\pi$
$564$	29.0803	1.22450
$565$	−17.3684	−0.730692
$566$	−51.4358	−2.16201
$567$	−46.4387	−1.95024
$568$	40.8888	1.71566
$569$	7.97790	0.334451	0.167225	−	0.985919i	$-0.446519\pi$
$569$	7.97790	0.334451	0.167225	+	0.985919i	$0.446519\pi$
$570$	4.06849	0.170410
$571$	−41.2854	−1.72774	−0.863870	−	0.503714i	$-0.831966\pi$
$571$	−41.2854	−1.72774	−0.863870	+	0.503714i	$0.831966\pi$
$572$	−54.2192	−2.26702
$573$	73.8105	3.08348
$574$	9.39771	0.392253
$575$	7.45230	0.310782
$576$	−70.2067	−2.92528
$577$	21.5844	0.898571	0.449285	−	0.893388i	$-0.351679\pi$
$577$	21.5844	0.898571	0.449285	+	0.893388i	$0.351679\pi$
$578$	18.5581	0.771915
$579$	−73.7441	−3.06470
$580$	10.9652	0.455304
$581$	13.0289	0.540531
$582$	52.0991	2.15958
$583$	34.9673	1.44820
$584$	−73.1488	−3.02692
$585$	22.4838	0.929591
$586$	−5.14407	−0.212500
$587$	−14.4554	−0.596639	−0.298319	−	0.954466i	$-0.596426\pi$
$587$	−14.4554	−0.596639	−0.298319	+	0.954466i	$0.596426\pi$
$588$	−33.0863	−1.36446
$589$	3.28289	0.135269
$590$	3.30704	0.136149
$591$	54.9050	2.25849
$592$	15.7950	0.649169
$593$	23.3477	0.958776	0.479388	−	0.877603i	$-0.340859\pi$
$593$	23.3477	0.958776	0.479388	+	0.877603i	$0.340859\pi$
$594$	152.336	6.25041
$595$	−6.34895	−0.260282
$596$	29.0133	1.18843
$597$	22.4775	0.919945
$598$	−55.5495	−2.27159
$599$	2.35020	0.0960266	0.0480133	−	0.998847i	$-0.484711\pi$
$599$	2.35020	0.0960266	0.0480133	+	0.998847i	$0.484711\pi$
$600$	−14.3575	−0.586142
$601$	30.9849	1.26390	0.631950	−	0.775009i	$-0.282255\pi$
$601$	30.9849	1.26390	0.631950	+	0.775009i	$0.282255\pi$
$602$	39.1861	1.59711
$603$	26.4719	1.07802
$604$	11.0072	0.447876
$605$	9.88133	0.401733
$606$	−85.8642	−3.48799
$607$	−36.8369	−1.49516	−0.747582	−	0.664169i	$-0.768785\pi$
$607$	−36.8369	−1.49516	−0.747582	+	0.664169i	$0.768785\pi$
$608$	−0.732178	−0.0296937
$609$	−18.9979	−0.769832
$610$	−9.69606	−0.392582
$611$	7.25475	0.293496
$612$	85.7820	3.46753
$613$	−9.13529	−0.368971	−0.184485	−	0.982835i	$-0.559062\pi$
$613$	−9.13529	−0.368971	−0.184485	+	0.982835i	$0.559062\pi$
$614$	−78.7541	−3.17826
$615$	5.99710	0.241826
$616$	−42.5069	−1.71265
$617$	22.8004	0.917908	0.458954	−	0.888460i	$-0.348224\pi$
$617$	22.8004	0.917908	0.458954	+	0.888460i	$0.348224\pi$
$618$	55.0344	2.21381
$619$	−31.3972	−1.26196	−0.630980	−	0.775799i	$-0.717347\pi$
$619$	−31.3972	−1.26196	−0.630980	+	0.775799i	$0.717347\pi$
$620$	−24.1095	−0.968260
$621$	102.715	4.12181
$622$	−68.4458	−2.74443
$623$	−13.8013	−0.552938
$624$	30.8782	1.23612
$625$	1.00000	0.0400000
$626$	−49.2080	−1.96675
$627$	7.68660	0.306973
$628$	−70.1712	−2.80014
$629$	15.4482	0.615961
$630$	36.6829	1.46148
$631$	24.9187	0.991996	0.495998	−	0.868324i	$-0.334802\pi$
$631$	24.9187	0.991996	0.495998	+	0.868324i	$0.334802\pi$
$632$	−10.3965	−0.413549
$633$	−45.6712	−1.81527
$634$	−55.9913	−2.22370
$635$	3.99446	0.158515
$636$	−94.5300	−3.74836
$637$	−8.25415	−0.327041
$638$	31.4782	1.24624
$639$	−66.6667	−2.63729
$640$	20.4822	0.809630
$641$	−45.3830	−1.79252	−0.896260	−	0.443529i	$-0.853726\pi$
$641$	−45.3830	−1.79252	−0.896260	+	0.443529i	$0.853726\pi$
$642$	−72.5363	−2.86278
$643$	17.3675	0.684907	0.342454	−	0.939535i	$-0.388742\pi$
$643$	17.3675	0.684907	0.342454	+	0.939535i	$0.388742\pi$
$644$	−59.6458	−2.35037
$645$	25.0064	0.984628
$646$	3.87244	0.152359
$647$	13.6988	0.538556	0.269278	−	0.963062i	$-0.413215\pi$
$647$	13.6988	0.538556	0.269278	+	0.963062i	$0.413215\pi$
$648$	−99.9555	−3.92662
$649$	6.24799	0.245255
$650$	−7.45401	−0.292370
$651$	41.7712	1.63714
$652$	−27.5772	−1.08001
$653$	34.1028	1.33455	0.667273	−	0.744813i	$-0.267462\pi$
$653$	34.1028	1.33455	0.667273	+	0.744813i	$0.267462\pi$
$654$	90.4694	3.53763
$655$	3.18872	0.124594
$656$	5.83622	0.227866
$657$	119.265	4.65295
$658$	11.8363	0.461428
$659$	−42.3915	−1.65134	−0.825669	−	0.564155i	$-0.809202\pi$
$659$	−42.3915	−1.65134	−0.825669	+	0.564155i	$0.809202\pi$
$660$	−56.4503	−2.19733
$661$	−0.955563	−0.0371671	−0.0185836	−	0.999827i	$-0.505916\pi$
$661$	−0.955563	−0.0371671	−0.0185836	+	0.999827i	$0.505916\pi$
$662$	39.2493	1.52547
$663$	30.2003	1.17288
$664$	28.0438	1.08831
$665$	1.08983	0.0422616
$666$	−89.2566	−3.45862
$667$	21.2248	0.821827
$668$	−23.8208	−0.921656
$669$	−17.2173	−0.665660
$670$	−8.77617	−0.339053
$671$	−18.3187	−0.707187
$672$	−9.31618	−0.359380
$673$	−3.53237	−0.136163	−0.0680814	−	0.997680i	$-0.521688\pi$
$673$	−3.53237	−0.136163	−0.0680814	+	0.997680i	$0.521688\pi$
$674$	18.2597	0.703336
$675$	13.7830	0.530508
$676$	−13.4835	−0.518597
$677$	33.5824	1.29068	0.645339	−	0.763896i	$-0.276716\pi$
$677$	33.5824	1.29068	0.645339	+	0.763896i	$0.276716\pi$
$678$	134.791	5.17663
$679$	13.9558	0.535573
$680$	−13.6656	−0.524052
$681$	46.0419	1.76433
$682$	−69.2123	−2.65027
$683$	−17.6851	−0.676702	−0.338351	−	0.941020i	$-0.609869\pi$
$683$	−17.6851	−0.676702	−0.338351	+	0.941020i	$0.609869\pi$
$684$	−14.7249	−0.563019
$685$	−14.4679	−0.552790
$686$	−48.6637	−1.85799
$687$	57.4955	2.19359
$688$	24.3356	0.927786
$689$	−23.5827	−0.898430
$690$	−57.8354	−2.20175
$691$	−26.3266	−1.00151	−0.500755	−	0.865589i	$-0.666944\pi$
$691$	−26.3266	−1.00151	−0.500755	+	0.865589i	$0.666944\pi$
$692$	28.8536	1.09685
$693$	69.3049	2.63268
$694$	−16.9552	−0.643611
$695$	−4.85721	−0.184244
$696$	−40.8914	−1.54998
$697$	5.70810	0.216210
$698$	−61.4068	−2.32428
$699$	17.1219	0.647609
$700$	−8.00367	−0.302510
$701$	−5.22791	−0.197455	−0.0987277	−	0.995114i	$-0.531477\pi$
$701$	−5.22791	−0.197455	−0.0987277	+	0.995114i	$0.531477\pi$
$702$	−102.739	−3.87762
$703$	−2.65176	−0.100013
$704$	43.9744	1.65735
$705$	7.55329	0.284473
$706$	5.61359	0.211270
$707$	−23.0004	−0.865019
$708$	−16.8908	−0.634793
$709$	12.3423	0.463525	0.231763	−	0.972772i	$-0.425551\pi$
$709$	12.3423	0.463525	0.231763	+	0.972772i	$0.425551\pi$
$710$	22.1019	0.829469
$711$	16.9508	0.635704
$712$	−29.7062	−1.11329
$713$	−46.6676	−1.74772
$714$	49.2726	1.84398
$715$	−14.0829	−0.526669
$716$	83.5111	3.12095
$717$	−20.8083	−0.777101
$718$	−75.5809	−2.82065
$719$	1.13009	0.0421452	0.0210726	−	0.999778i	$-0.493292\pi$
$719$	1.13009	0.0421452	0.0210726	+	0.999778i	$0.493292\pi$
$720$	22.7810	0.848999
$721$	14.7420	0.549022
$722$	45.2902	1.68553
$723$	65.0351	2.41868
$724$	37.7447	1.40277
$725$	2.84809	0.105775
$726$	−76.6864	−2.84610
$727$	−41.5701	−1.54175	−0.770875	−	0.636986i	$-0.780181\pi$
$727$	−41.5701	−1.54175	−0.770875	+	0.636986i	$0.780181\pi$
$728$	28.6677	1.06249
$729$	30.2960	1.12207
$730$	−39.5395	−1.46342
$731$	23.8014	0.880326
$732$	49.5227	1.83041
$733$	−6.40419	−0.236544	−0.118272	−	0.992981i	$-0.537735\pi$
$733$	−6.40419	−0.236544	−0.118272	+	0.992981i	$0.537735\pi$
$734$	25.2130	0.930628
$735$	−8.59380	−0.316987
$736$	10.4082	0.383652
$737$	−16.5808	−0.610761
$738$	−32.9802	−1.21402
$739$	−15.5457	−0.571858	−0.285929	−	0.958251i	$-0.592302\pi$
$739$	−15.5457	−0.571858	−0.285929	+	0.958251i	$0.592302\pi$
$740$	19.4745	0.715896
$741$	−5.18402	−0.190440
$742$	−38.4758	−1.41249
$743$	−14.8375	−0.544335	−0.272167	−	0.962250i	$-0.587740\pi$
$743$	−14.8375	−0.544335	−0.272167	+	0.962250i	$0.587740\pi$
$744$	89.9092	3.29623
$745$	7.53589	0.276094
$746$	48.7382	1.78443
$747$	−45.7236	−1.67294
$748$	−53.7300	−1.96456
$749$	−19.4303	−0.709967
$750$	−7.76074	−0.283382
$751$	−50.5683	−1.84526	−0.922631	−	0.385683i	$-0.873966\pi$
$751$	−50.5683	−1.84526	−0.922631	+	0.385683i	$0.873966\pi$
$752$	7.35066	0.268051
$753$	−16.8283	−0.613259
$754$	−21.2297	−0.773139
$755$	2.85900	0.104050
$756$	−110.315	−4.01211
$757$	−10.1071	−0.367348	−0.183674	−	0.982987i	$-0.558799\pi$
$757$	−10.1071	−0.367348	−0.183674	+	0.982987i	$0.558799\pi$
$758$	−49.9113	−1.81286
$759$	−109.268	−3.96619
$760$	2.34576	0.0850898
$761$	51.5532	1.86880	0.934400	−	0.356224i	$-0.115936\pi$
$761$	51.5532	1.86880	0.934400	+	0.356224i	$0.115936\pi$
$762$	−31.0000	−1.12301
$763$	24.2340	0.877330
$764$	88.5638	3.20412
$765$	22.2809	0.805569
$766$	−4.38312	−0.158368
$767$	−4.21379	−0.152151
$768$	−97.2017	−3.50746
$769$	−27.7346	−1.00013	−0.500067	−	0.865987i	$-0.666691\pi$
$769$	−27.7346	−1.00013	−0.500067	+	0.865987i	$0.666691\pi$
$770$	−22.9765	−0.828017
$771$	58.3135	2.10011
$772$	−88.4841	−3.18461
$773$	16.3729	0.588892	0.294446	−	0.955668i	$-0.404865\pi$
$773$	16.3729	0.588892	0.294446	+	0.955668i	$0.404865\pi$
$774$	−137.519	−4.94303
$775$	−6.26218	−0.224944
$776$	30.0387	1.07833
$777$	−33.7408	−1.21044
$778$	1.87541	0.0672368
$779$	−0.979821	−0.0351057
$780$	38.0714	1.36318
$781$	41.7571	1.49418
$782$	−55.0483	−1.96852
$783$	39.2552	1.40287
$784$	−8.36326	−0.298688
$785$	−18.2262	−0.650522
$786$	−24.7468	−0.882690
$787$	−26.9931	−0.962200	−0.481100	−	0.876666i	$-0.659763\pi$
$787$	−26.9931	−0.962200	−0.481100	+	0.876666i	$0.659763\pi$
$788$	65.8794	2.34685
$789$	36.9026	1.31377
$790$	−5.61966	−0.199938
$791$	36.1065	1.28380
$792$	149.173	5.30064
$793$	12.3546	0.438724
$794$	70.5008	2.50198
$795$	−24.5532	−0.870811
$796$	26.9704	0.955939
$797$	25.8694	0.916343	0.458171	−	0.888864i	$-0.348505\pi$
$797$	25.8694	0.916343	0.458171	+	0.888864i	$0.348505\pi$
$798$	−8.45786	−0.299405
$799$	7.18929	0.254339
$800$	1.39665	0.0493789
$801$	48.4341	1.71134
$802$	7.08431	0.250156
$803$	−74.7020	−2.63618
$804$	44.8243	1.58083
$805$	−15.4923	−0.546033
$806$	46.6784	1.64417
$807$	21.4415	0.754775
$808$	−49.5066	−1.74163
$809$	3.11806	0.109625	0.0548126	−	0.998497i	$-0.482544\pi$
$809$	3.11806	0.109625	0.0548126	+	0.998497i	$0.482544\pi$
$810$	−54.0295	−1.89840
$811$	18.9745	0.666285	0.333143	−	0.942876i	$-0.391891\pi$
$811$	18.9745	0.666285	0.333143	+	0.942876i	$0.391891\pi$
$812$	−22.7951	−0.799953
$813$	12.0879	0.423942
$814$	55.9063	1.95952
$815$	−7.16288	−0.250905
$816$	30.5996	1.07120
$817$	−4.08561	−0.142938
$818$	−30.2554	−1.05785
$819$	−46.7409	−1.63326
$820$	7.19580	0.251288
$821$	−24.6619	−0.860708	−0.430354	−	0.902660i	$-0.641611\pi$
$821$	−24.6619	−0.860708	−0.430354	+	0.902660i	$0.641611\pi$
$822$	112.282	3.91628
$823$	−51.5756	−1.79781	−0.898906	−	0.438142i	$-0.855637\pi$
$823$	−51.5756	−1.79781	−0.898906	+	0.438142i	$0.855637\pi$
$824$	31.7311	1.10540
$825$	−14.6624	−0.510478
$826$	−6.87491	−0.239209
$827$	−10.6889	−0.371691	−0.185846	−	0.982579i	$-0.559502\pi$
$827$	−10.6889	−0.371691	−0.185846	+	0.982579i	$0.559502\pi$
$828$	209.320	7.27438
$829$	−33.0486	−1.14783	−0.573913	−	0.818916i	$-0.694575\pi$
$829$	−33.0486	−1.14783	−0.573913	+	0.818916i	$0.694575\pi$
$830$	15.1587	0.526165
$831$	−33.4303	−1.15968
$832$	−29.6573	−1.02818
$833$	−8.17967	−0.283409
$834$	37.6955	1.30529
$835$	−6.18720	−0.214117
$836$	9.22299	0.318984
$837$	−86.3116	−2.98337
$838$	−51.4648	−1.77782
$839$	10.6417	0.367392	0.183696	−	0.982983i	$-0.441194\pi$
$839$	10.6417	0.367392	0.183696	+	0.982983i	$0.441194\pi$
$840$	29.8473	1.02983
$841$	−20.8884	−0.720290
$842$	−59.8945	−2.06410
$843$	88.0095	3.03121
$844$	−54.7999	−1.88629
$845$	−3.50220	−0.120479
$846$	−41.5382	−1.42811
$847$	−20.5420	−0.705830
$848$	−23.8945	−0.820540
$849$	68.2357	2.34184
$850$	−7.38676	−0.253364
$851$	37.6959	1.29220
$852$	−112.885	−3.86739
$853$	−17.5451	−0.600732	−0.300366	−	0.953824i	$-0.597109\pi$
$853$	−17.5451	−0.600732	−0.300366	+	0.953824i	$0.597109\pi$
$854$	20.1568	0.689752
$855$	−3.82462	−0.130799
$856$	−41.8221	−1.42945
$857$	−23.0552	−0.787551	−0.393775	−	0.919207i	$-0.628831\pi$
$857$	−23.0552	−0.787551	−0.393775	+	0.919207i	$0.628831\pi$
$858$	109.293	3.73122
$859$	−38.8993	−1.32723	−0.663614	−	0.748075i	$-0.730978\pi$
$859$	−38.8993	−1.32723	−0.663614	+	0.748075i	$0.730978\pi$
$860$	30.0047	1.02315
$861$	−12.4672	−0.424880
$862$	31.8690	1.08546
$863$	41.6221	1.41683	0.708416	−	0.705795i	$-0.249410\pi$
$863$	41.6221	1.41683	0.708416	+	0.705795i	$0.249410\pi$
$864$	19.2500	0.654898
$865$	7.49442	0.254818
$866$	−78.1029	−2.65404
$867$	−24.6195	−0.836123
$868$	50.1204	1.70120
$869$	−10.6172	−0.360164
$870$	−22.1033	−0.749371
$871$	11.1825	0.378904
$872$	52.1618	1.76642
$873$	−48.9762	−1.65759
$874$	9.44929	0.319627
$875$	−2.07887	−0.0702786
$876$	201.948	6.82320
$877$	−39.4937	−1.33361	−0.666803	−	0.745234i	$-0.732338\pi$
$877$	−39.4937	−1.33361	−0.666803	+	0.745234i	$0.732338\pi$
$878$	−18.6042	−0.627862
$879$	6.82423	0.230175
$880$	−14.2690	−0.481008
$881$	−32.6211	−1.09903	−0.549517	−	0.835483i	$-0.685188\pi$
$881$	−32.6211	−1.09903	−0.549517	+	0.835483i	$0.685188\pi$
$882$	47.2604	1.59134
$883$	−28.8237	−0.969995	−0.484998	−	0.874515i	$-0.661180\pi$
$883$	−28.8237	−0.969995	−0.484998	+	0.874515i	$0.661180\pi$
$884$	36.2368	1.21877
$885$	−4.38719	−0.147474
$886$	18.7528	0.630013
$887$	25.2813	0.848864	0.424432	−	0.905460i	$-0.360474\pi$
$887$	25.2813	0.848864	0.424432	+	0.905460i	$0.360474\pi$
$888$	−72.6244	−2.43711
$889$	−8.30395	−0.278505
$890$	−16.0573	−0.538241
$891$	−102.078	−3.41974
$892$	−20.6587	−0.691705
$893$	−1.23407	−0.0412967
$894$	−58.4841	−1.95600
$895$	21.6911	0.725053
$896$	−42.5798	−1.42249
$897$	73.6931	2.46054
$898$	80.5597	2.68831
$899$	−17.8352	−0.594838
$900$	28.0880	0.936267
$901$	−23.3699	−0.778566
$902$	20.6573	0.687814
$903$	−51.9851	−1.72996
$904$	77.7164	2.58481
$905$	9.80379	0.325889
$906$	−22.1880	−0.737146
$907$	53.1095	1.76347	0.881737	−	0.471742i	$-0.156375\pi$
$907$	53.1095	1.76347	0.881737	+	0.471742i	$0.156375\pi$
$908$	55.2448	1.83336
$909$	80.7174	2.67723
$910$	15.4959	0.513684
$911$	25.6482	0.849761	0.424881	−	0.905249i	$-0.360316\pi$
$911$	25.6482	0.849761	0.424881	+	0.905249i	$0.360316\pi$
$912$	−5.25255	−0.173929
$913$	28.6392	0.947820
$914$	−20.6208	−0.682076
$915$	12.8630	0.425237
$916$	68.9876	2.27942
$917$	−6.62892	−0.218906
$918$	−101.812	−3.36029
$919$	1.15059	0.0379544	0.0189772	−	0.999820i	$-0.493959\pi$
$919$	1.15059	0.0379544	0.0189772	+	0.999820i	$0.493959\pi$
$920$	−33.3460	−1.09939
$921$	104.477	3.44262
$922$	15.7912	0.520054
$923$	−28.1619	−0.926961
$924$	117.353	3.86062
$925$	5.05829	0.166315
$926$	95.3277	3.13266
$927$	−51.7355	−1.69922
$928$	3.97777	0.130577
$929$	44.0573	1.44547	0.722737	−	0.691123i	$-0.242884\pi$
$929$	44.0573	1.44547	0.722737	+	0.691123i	$0.242884\pi$
$930$	48.5992	1.59363
$931$	1.40408	0.0460168
$932$	20.5442	0.672948
$933$	90.8015	2.97271
$934$	−20.8143	−0.681065
$935$	−13.9558	−0.456403
$936$	−100.606	−3.28841
$937$	51.6634	1.68777	0.843885	−	0.536524i	$-0.180263\pi$
$937$	51.6634	1.68777	0.843885	+	0.536524i	$0.180263\pi$
$938$	18.2445	0.595704
$939$	65.2803	2.13034
$940$	9.06303	0.295604
$941$	−1.85595	−0.0605021	−0.0302510	−	0.999542i	$-0.509631\pi$
$941$	−1.85595	−0.0605021	−0.0302510	+	0.999542i	$0.509631\pi$
$942$	141.449	4.60866
$943$	13.9286	0.453577
$944$	−4.26950	−0.138960
$945$	−28.6530	−0.932084
$946$	86.1360	2.80052
$947$	−22.1760	−0.720622	−0.360311	−	0.932832i	$-0.617329\pi$
$947$	−22.1760	−0.720622	−0.360311	+	0.932832i	$0.617329\pi$
$948$	28.7024	0.932212
$949$	50.3807	1.63543
$950$	1.26797	0.0411384
$951$	74.2792	2.40867
$952$	28.4090	0.920741
$953$	44.7958	1.45108	0.725540	−	0.688180i	$-0.241590\pi$
$953$	44.7958	1.45108	0.725540	+	0.688180i	$0.241590\pi$
$954$	135.027	4.37165
$955$	23.0035	0.744375
$956$	−24.9675	−0.807506
$957$	−41.7596	−1.34990
$958$	5.56061	0.179655
$959$	30.0769	0.971233
$960$	−30.8777	−0.996574
$961$	8.21488	0.264996
$962$	−37.7045	−1.21564
$963$	68.1884	2.19734
$964$	78.0343	2.51332
$965$	−22.9828	−0.739842
$966$	120.232	3.86840
$967$	36.9652	1.18872	0.594361	−	0.804199i	$-0.297405\pi$
$967$	36.9652	1.18872	0.594361	+	0.804199i	$0.297405\pi$
$968$	−44.2150	−1.42112
$969$	−5.13725	−0.165032
$970$	16.2370	0.521338
$971$	−45.0408	−1.44543	−0.722715	−	0.691146i	$-0.757106\pi$
$971$	−45.0408	−1.44543	−0.722715	+	0.691146i	$0.757106\pi$
$972$	116.762	3.74514
$973$	10.0975	0.323711
$974$	−65.1608	−2.08789
$975$	9.88864	0.316690
$976$	12.5179	0.400688
$977$	23.5274	0.752709	0.376354	−	0.926476i	$-0.377178\pi$
$977$	23.5274	0.752709	0.376354	+	0.926476i	$0.377178\pi$
$978$	55.5893	1.77755
$979$	−30.3370	−0.969574
$980$	−10.3115	−0.329390
$981$	−85.0465	−2.71533
$982$	97.1667	3.10071
$983$	−33.5789	−1.07100	−0.535501	−	0.844535i	$-0.679877\pi$
$983$	−33.5789	−1.07100	−0.535501	+	0.844535i	$0.679877\pi$
$984$	−26.8346	−0.855456
$985$	17.1115	0.545216
$986$	−21.0381	−0.669990
$987$	−15.7023	−0.499809
$988$	−6.22020	−0.197891
$989$	58.0787	1.84680
$990$	80.6336	2.56270
$991$	−6.92238	−0.219897	−0.109948	−	0.993937i	$-0.535069\pi$
$991$	−6.92238	−0.219897	−0.109948	+	0.993937i	$0.535069\pi$
$992$	−8.74605	−0.277687
$993$	−52.0689	−1.65236
$994$	−45.9469	−1.45735
$995$	7.00526	0.222082
$996$	−77.4229	−2.45324
$997$	42.5962	1.34904	0.674518	−	0.738258i	$-0.264351\pi$
$997$	42.5962	1.34904	0.674518	+	0.738258i	$0.264351\pi$
$998$	55.6374	1.76117
$999$	69.7184	2.20579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.13	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.13	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} +O(q^{10})\)	\(q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} -2.41868 q^{10} -4.56961 q^{11} +12.3534 q^{12} +3.08185 q^{13} +5.02812 q^{14} +3.20867 q^{15} +3.12259 q^{16} +3.05404 q^{17} -17.6456 q^{18} -0.524240 q^{19} +3.85002 q^{20} -6.67040 q^{21} +11.0524 q^{22} +7.45230 q^{23} -14.3575 q^{24} +1.00000 q^{25} -7.45401 q^{26} +13.7830 q^{27} -8.00367 q^{28} +2.84809 q^{29} -7.76074 q^{30} -6.26218 q^{31} +1.39665 q^{32} -14.6624 q^{33} -7.38676 q^{34} -2.07887 q^{35} +28.0880 q^{36} +5.05829 q^{37} +1.26797 q^{38} +9.88864 q^{39} -4.47460 q^{40} +1.86903 q^{41} +16.1336 q^{42} +7.79340 q^{43} -17.5931 q^{44} +7.29555 q^{45} -18.0247 q^{46} +2.35402 q^{47} +10.0194 q^{48} -2.67831 q^{49} -2.41868 q^{50} +9.79941 q^{51} +11.8652 q^{52} -7.65213 q^{53} -33.3367 q^{54} -4.56961 q^{55} +9.30210 q^{56} -1.68211 q^{57} -6.88861 q^{58} -1.36729 q^{59} +12.3534 q^{60} +4.00882 q^{61} +15.1462 q^{62} -15.1665 q^{63} -9.62322 q^{64} +3.08185 q^{65} +35.4636 q^{66} +3.62849 q^{67} +11.7581 q^{68} +23.9120 q^{69} +5.02812 q^{70} -9.13799 q^{71} -32.6447 q^{72} +16.3476 q^{73} -12.2344 q^{74} +3.20867 q^{75} -2.01833 q^{76} +9.49961 q^{77} -23.9175 q^{78} +2.32344 q^{79} +3.12259 q^{80} +22.3384 q^{81} -4.52059 q^{82} -6.26732 q^{83} -25.6811 q^{84} +3.05404 q^{85} -18.8497 q^{86} +9.13856 q^{87} +20.4472 q^{88} +6.63886 q^{89} -17.6456 q^{90} -6.40676 q^{91} +28.6915 q^{92} -20.0933 q^{93} -5.69363 q^{94} -0.524240 q^{95} +4.48137 q^{96} -6.71316 q^{97} +6.47797 q^{98} -33.3378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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