LMFDB - Embedded newform 8035.2.a.e.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.59020 q^{2} -1.81242 q^{3} +4.70914 q^{4} +1.00000 q^{5} +4.69454 q^{6} +3.39615 q^{7} -7.01723 q^{8} +0.284882 q^{9} +O(q^{10})$	\(q-2.59020 q^{2} -1.81242 q^{3} +4.70914 q^{4} +1.00000 q^{5} +4.69454 q^{6} +3.39615 q^{7} -7.01723 q^{8} +0.284882 q^{9} -2.59020 q^{10} -1.32471 q^{11} -8.53497 q^{12} -3.86304 q^{13} -8.79671 q^{14} -1.81242 q^{15} +8.75774 q^{16} +3.76805 q^{17} -0.737903 q^{18} +6.58689 q^{19} +4.70914 q^{20} -6.15527 q^{21} +3.43126 q^{22} +7.28957 q^{23} +12.7182 q^{24} +1.00000 q^{25} +10.0061 q^{26} +4.92095 q^{27} +15.9930 q^{28} +8.62813 q^{29} +4.69454 q^{30} +6.81479 q^{31} -8.64987 q^{32} +2.40093 q^{33} -9.76000 q^{34} +3.39615 q^{35} +1.34155 q^{36} +5.89626 q^{37} -17.0614 q^{38} +7.00147 q^{39} -7.01723 q^{40} +2.60937 q^{41} +15.9434 q^{42} -4.42923 q^{43} -6.23824 q^{44} +0.284882 q^{45} -18.8815 q^{46} +9.03366 q^{47} -15.8727 q^{48} +4.53384 q^{49} -2.59020 q^{50} -6.82930 q^{51} -18.1916 q^{52} +0.850156 q^{53} -12.7462 q^{54} -1.32471 q^{55} -23.8316 q^{56} -11.9382 q^{57} -22.3486 q^{58} +11.0464 q^{59} -8.53497 q^{60} +11.4790 q^{61} -17.6517 q^{62} +0.967503 q^{63} +4.88941 q^{64} -3.86304 q^{65} -6.21890 q^{66} -1.35486 q^{67} +17.7443 q^{68} -13.2118 q^{69} -8.79671 q^{70} +13.3330 q^{71} -1.99908 q^{72} -14.0983 q^{73} -15.2725 q^{74} -1.81242 q^{75} +31.0186 q^{76} -4.49891 q^{77} -18.1352 q^{78} -3.18348 q^{79} +8.75774 q^{80} -9.77349 q^{81} -6.75879 q^{82} +2.46109 q^{83} -28.9860 q^{84} +3.76805 q^{85} +11.4726 q^{86} -15.6378 q^{87} +9.29578 q^{88} +7.25621 q^{89} -0.737903 q^{90} -13.1195 q^{91} +34.3277 q^{92} -12.3513 q^{93} -23.3990 q^{94} +6.58689 q^{95} +15.6772 q^{96} -4.36597 q^{97} -11.7436 q^{98} -0.377386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59020	−1.83155	−0.915774	−	0.401693i	$-0.868422\pi$
$2$	−2.59020	−1.83155	−0.915774	+	0.401693i	$0.868422\pi$
$3$	−1.81242	−1.04640	−0.523202	−	0.852209i	$-0.675263\pi$
$3$	−1.81242	−1.04640	−0.523202	+	0.852209i	$0.675263\pi$
$4$	4.70914	2.35457
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.69454	1.91654
$7$	3.39615	1.28362	0.641812	−	0.766862i	$-0.278183\pi$
$7$	3.39615	1.28362	0.641812	+	0.766862i	$0.278183\pi$
$8$	−7.01723	−2.48096
$9$	0.284882	0.0949608
$10$	−2.59020	−0.819094
$11$	−1.32471	−0.399415	−0.199707	−	0.979856i	$-0.563999\pi$
$11$	−1.32471	−0.399415	−0.199707	+	0.979856i	$0.563999\pi$
$12$	−8.53497	−2.46383
$13$	−3.86304	−1.07142	−0.535708	−	0.844404i	$-0.679955\pi$
$13$	−3.86304	−1.07142	−0.535708	+	0.844404i	$0.679955\pi$
$14$	−8.79671	−2.35102
$15$	−1.81242	−0.467966
$16$	8.75774	2.18944
$17$	3.76805	0.913885	0.456943	−	0.889496i	$-0.348944\pi$
$17$	3.76805	0.913885	0.456943	+	0.889496i	$0.348944\pi$
$18$	−0.737903	−0.173925
$19$	6.58689	1.51114	0.755568	−	0.655070i	$-0.227361\pi$
$19$	6.58689	1.51114	0.755568	+	0.655070i	$0.227361\pi$
$20$	4.70914	1.05300
$21$	−6.15527	−1.34319
$22$	3.43126	0.731547
$23$	7.28957	1.51998	0.759991	−	0.649934i	$-0.225203\pi$
$23$	7.28957	1.51998	0.759991	+	0.649934i	$0.225203\pi$
$24$	12.7182	2.59609
$25$	1.00000	0.200000
$26$	10.0061	1.96235
$27$	4.92095	0.947036
$28$	15.9930	3.02239
$29$	8.62813	1.60220	0.801102	−	0.598528i	$-0.204247\pi$
$29$	8.62813	1.60220	0.801102	+	0.598528i	$0.204247\pi$
$30$	4.69454	0.857103
$31$	6.81479	1.22397	0.611986	−	0.790869i	$-0.290371\pi$
$31$	6.81479	1.22397	0.611986	+	0.790869i	$0.290371\pi$
$32$	−8.64987	−1.52909
$33$	2.40093	0.417949
$34$	−9.76000	−1.67383
$35$	3.39615	0.574054
$36$	1.34155	0.223592
$37$	5.89626	0.969339	0.484669	−	0.874697i	$-0.338940\pi$
$37$	5.89626	0.969339	0.484669	+	0.874697i	$0.338940\pi$
$38$	−17.0614	−2.76772
$39$	7.00147	1.12113
$40$	−7.01723	−1.10952
$41$	2.60937	0.407515	0.203757	−	0.979021i	$-0.434685\pi$
$41$	2.60937	0.407515	0.203757	+	0.979021i	$0.434685\pi$
$42$	15.9434	2.46012
$43$	−4.42923	−0.675451	−0.337726	−	0.941245i	$-0.609658\pi$
$43$	−4.42923	−0.675451	−0.337726	+	0.941245i	$0.609658\pi$
$44$	−6.23824	−0.940450
$45$	0.284882	0.0424677
$46$	−18.8815	−2.78392
$47$	9.03366	1.31769	0.658847	−	0.752277i	$-0.271044\pi$
$47$	9.03366	1.31769	0.658847	+	0.752277i	$0.271044\pi$
$48$	−15.8727	−2.29103
$49$	4.53384	0.647692
$50$	−2.59020	−0.366310
$51$	−6.82930	−0.956293
$52$	−18.1916	−2.52272
$53$	0.850156	0.116778	0.0583890	−	0.998294i	$-0.481404\pi$
$53$	0.850156	0.116778	0.0583890	+	0.998294i	$0.481404\pi$
$54$	−12.7462	−1.73454
$55$	−1.32471	−0.178624
$56$	−23.8316	−3.18463
$57$	−11.9382	−1.58126
$58$	−22.3486	−2.93451
$59$	11.0464	1.43812	0.719061	−	0.694946i	$-0.244572\pi$
$59$	11.0464	1.43812	0.719061	+	0.694946i	$0.244572\pi$
$60$	−8.53497	−1.10186
$61$	11.4790	1.46973	0.734867	−	0.678211i	$-0.237245\pi$
$61$	11.4790	1.46973	0.734867	+	0.678211i	$0.237245\pi$
$62$	−17.6517	−2.24176
$63$	0.967503	0.121894
$64$	4.88941	0.611176
$65$	−3.86304	−0.479151
$66$	−6.21890	−0.765494
$67$	−1.35486	−0.165522	−0.0827610	−	0.996569i	$-0.526374\pi$
$67$	−1.35486	−0.165522	−0.0827610	+	0.996569i	$0.526374\pi$
$68$	17.7443	2.15181
$69$	−13.2118	−1.59051
$70$	−8.79671	−1.05141
$71$	13.3330	1.58234	0.791168	−	0.611599i	$-0.209473\pi$
$71$	13.3330	1.58234	0.791168	+	0.611599i	$0.209473\pi$
$72$	−1.99908	−0.235594
$73$	−14.0983	−1.65008	−0.825038	−	0.565078i	$-0.808846\pi$
$73$	−14.0983	−1.65008	−0.825038	+	0.565078i	$0.808846\pi$
$74$	−15.2725	−1.77539
$75$	−1.81242	−0.209281
$76$	31.0186	3.55808
$77$	−4.49891	−0.512698
$78$	−18.1352	−2.05341
$79$	−3.18348	−0.358170	−0.179085	−	0.983834i	$-0.557314\pi$
$79$	−3.18348	−0.358170	−0.179085	+	0.983834i	$0.557314\pi$
$80$	8.75774	0.979146
$81$	−9.77349	−1.08594
$82$	−6.75879	−0.746383
$83$	2.46109	0.270139	0.135070	−	0.990836i	$-0.456874\pi$
$83$	2.46109	0.270139	0.135070	+	0.990836i	$0.456874\pi$
$84$	−28.9860	−3.16264
$85$	3.76805	0.408702
$86$	11.4726	1.23712
$87$	−15.6378	−1.67655
$88$	9.29578	0.990933
$89$	7.25621	0.769157	0.384578	−	0.923092i	$-0.374347\pi$
$89$	7.25621	0.769157	0.384578	+	0.923092i	$0.374347\pi$
$90$	−0.737903	−0.0777818
$91$	−13.1195	−1.37529
$92$	34.3277	3.57891
$93$	−12.3513	−1.28077
$94$	−23.3990	−2.41342
$95$	6.58689	0.675801
$96$	15.6772	1.60005
$97$	−4.36597	−0.443297	−0.221648	−	0.975127i	$-0.571144\pi$
$97$	−4.36597	−0.443297	−0.221648	+	0.975127i	$0.571144\pi$
$98$	−11.7436	−1.18628
$99$	−0.377386	−0.0379287
$100$	4.70914	0.470914
$101$	4.48412	0.446186	0.223093	−	0.974797i	$-0.428385\pi$
$101$	4.48412	0.446186	0.223093	+	0.974797i	$0.428385\pi$
$102$	17.6893	1.75150
$103$	−18.0840	−1.78187	−0.890935	−	0.454130i	$-0.849950\pi$
$103$	−18.0840	−1.78187	−0.890935	+	0.454130i	$0.849950\pi$
$104$	27.1078	2.65814
$105$	−6.15527	−0.600693
$106$	−2.20208	−0.213885
$107$	0.142024	0.0137300	0.00686499	−	0.999976i	$-0.497815\pi$
$107$	0.142024	0.0137300	0.00686499	+	0.999976i	$0.497815\pi$
$108$	23.1734	2.22987
$109$	9.08459	0.870146	0.435073	−	0.900395i	$-0.356723\pi$
$109$	9.08459	0.870146	0.435073	+	0.900395i	$0.356723\pi$
$110$	3.43126	0.327158
$111$	−10.6865	−1.01432
$112$	29.7426	2.81041
$113$	−3.36861	−0.316892	−0.158446	−	0.987368i	$-0.550648\pi$
$113$	−3.36861	−0.316892	−0.158446	+	0.987368i	$0.550648\pi$
$114$	30.9224	2.89615
$115$	7.28957	0.679756
$116$	40.6311	3.77250
$117$	−1.10051	−0.101742
$118$	−28.6125	−2.63399
$119$	12.7969	1.17309
$120$	12.7182	1.16101
$121$	−9.24515	−0.840468
$122$	−29.7329	−2.69189
$123$	−4.72928	−0.426425
$124$	32.0918	2.88193
$125$	1.00000	0.0894427
$126$	−2.50603	−0.223255
$127$	5.01415	0.444934	0.222467	−	0.974940i	$-0.428589\pi$
$127$	5.01415	0.444934	0.222467	+	0.974940i	$0.428589\pi$
$128$	4.63518	0.409696
$129$	8.02765	0.706795
$130$	10.0061	0.877589
$131$	−19.4581	−1.70006	−0.850032	−	0.526730i	$-0.823418\pi$
$131$	−19.4581	−1.70006	−0.850032	+	0.526730i	$0.823418\pi$
$132$	11.3063	0.984091
$133$	22.3701	1.93973
$134$	3.50935	0.303162
$135$	4.92095	0.423528
$136$	−26.4412	−2.26732
$137$	4.80858	0.410825	0.205412	−	0.978676i	$-0.434146\pi$
$137$	4.80858	0.410825	0.205412	+	0.978676i	$0.434146\pi$
$138$	34.2212	2.91310
$139$	17.3714	1.47342	0.736710	−	0.676209i	$-0.236379\pi$
$139$	17.3714	1.47342	0.736710	+	0.676209i	$0.236379\pi$
$140$	15.9930	1.35165
$141$	−16.3728	−1.37884
$142$	−34.5352	−2.89813
$143$	5.11740	0.427939
$144$	2.49493	0.207911
$145$	8.62813	0.716527
$146$	36.5173	3.02219
$147$	−8.21724	−0.677747
$148$	27.7663	2.28238
$149$	17.4498	1.42954	0.714772	−	0.699358i	$-0.246531\pi$
$149$	17.4498	1.42954	0.714772	+	0.699358i	$0.246531\pi$
$150$	4.69454	0.383308
$151$	19.5516	1.59109	0.795543	−	0.605897i	$-0.207186\pi$
$151$	19.5516	1.59109	0.795543	+	0.605897i	$0.207186\pi$
$152$	−46.2217	−3.74907
$153$	1.07345	0.0867833
$154$	11.6531	0.939032
$155$	6.81479	0.547377
$156$	32.9709	2.63979
$157$	−17.3445	−1.38425	−0.692123	−	0.721780i	$-0.743324\pi$
$157$	−17.3445	−1.38425	−0.692123	+	0.721780i	$0.743324\pi$
$158$	8.24586	0.656005
$159$	−1.54084	−0.122197
$160$	−8.64987	−0.683832
$161$	24.7565	1.95109
$162$	25.3153	1.98896
$163$	−4.17029	−0.326642	−0.163321	−	0.986573i	$-0.552221\pi$
$163$	−4.17029	−0.326642	−0.163321	+	0.986573i	$0.552221\pi$
$164$	12.2879	0.959522
$165$	2.40093	0.186912
$166$	−6.37471	−0.494774
$167$	13.3766	1.03512	0.517558	−	0.855648i	$-0.326841\pi$
$167$	13.3766	1.03512	0.517558	+	0.855648i	$0.326841\pi$
$168$	43.1929	3.33240
$169$	1.92310	0.147930
$170$	−9.76000	−0.748558
$171$	1.87649	0.143499
$172$	−20.8579	−1.59040
$173$	−17.5692	−1.33576	−0.667881	−	0.744268i	$-0.732799\pi$
$173$	−17.5692	−1.33576	−0.667881	+	0.744268i	$0.732799\pi$
$174$	40.5051	3.07069
$175$	3.39615	0.256725
$176$	−11.6015	−0.874493
$177$	−20.0208	−1.50486
$178$	−18.7950	−1.40875
$179$	−8.67362	−0.648297	−0.324148	−	0.946006i	$-0.605078\pi$
$179$	−8.67362	−0.648297	−0.324148	+	0.946006i	$0.605078\pi$
$180$	1.34155	0.0999933
$181$	2.28975	0.170196	0.0850980	−	0.996373i	$-0.472880\pi$
$181$	2.28975	0.170196	0.0850980	+	0.996373i	$0.472880\pi$
$182$	33.9821	2.51892
$183$	−20.8048	−1.53794
$184$	−51.1526	−3.77102
$185$	5.89626	0.433501
$186$	31.9923	2.34579
$187$	−4.99156	−0.365019
$188$	42.5408	3.10261
$189$	16.7123	1.21564
$190$	−17.0614	−1.23776
$191$	−11.7395	−0.849439	−0.424719	−	0.905325i	$-0.639627\pi$
$191$	−11.7395	−0.849439	−0.424719	+	0.905325i	$0.639627\pi$
$192$	−8.86169	−0.639537
$193$	−25.8016	−1.85724	−0.928620	−	0.371033i	$-0.879004\pi$
$193$	−25.8016	−1.85724	−0.928620	+	0.371033i	$0.879004\pi$
$194$	11.3087	0.811920
$195$	7.00147	0.501386
$196$	21.3505	1.52504
$197$	12.0201	0.856394	0.428197	−	0.903685i	$-0.359149\pi$
$197$	12.0201	0.856394	0.428197	+	0.903685i	$0.359149\pi$
$198$	0.977506	0.0694683
$199$	−5.30959	−0.376387	−0.188193	−	0.982132i	$-0.560263\pi$
$199$	−5.30959	−0.376387	−0.188193	+	0.982132i	$0.560263\pi$
$200$	−7.01723	−0.496193
$201$	2.45557	0.173203
$202$	−11.6148	−0.817212
$203$	29.3024	2.05663
$204$	−32.1601	−2.25166
$205$	2.60937	0.182246
$206$	46.8412	3.26358
$207$	2.07667	0.144339
$208$	−33.8315	−2.34579
$209$	−8.72571	−0.603570
$210$	15.9434	1.10020
$211$	7.84093	0.539792	0.269896	−	0.962890i	$-0.413011\pi$
$211$	7.84093	0.539792	0.269896	+	0.962890i	$0.413011\pi$
$212$	4.00351	0.274962
$213$	−24.1651	−1.65576
$214$	−0.367871	−0.0251471
$215$	−4.42923	−0.302071
$216$	−34.5314	−2.34956
$217$	23.1440	1.57112
$218$	−23.5309	−1.59372
$219$	25.5520	1.72665
$220$	−6.23824	−0.420582
$221$	−14.5561	−0.979151
$222$	27.6802	1.85778
$223$	5.17734	0.346700	0.173350	−	0.984860i	$-0.444541\pi$
$223$	5.17734	0.346700	0.173350	+	0.984860i	$0.444541\pi$
$224$	−29.3763	−1.96278
$225$	0.284882	0.0189922
$226$	8.72537	0.580403
$227$	22.4006	1.48678	0.743391	−	0.668857i	$-0.233216\pi$
$227$	22.4006	1.48678	0.743391	+	0.668857i	$0.233216\pi$
$228$	−56.2189	−3.72319
$229$	−8.94754	−0.591270	−0.295635	−	0.955301i	$-0.595531\pi$
$229$	−8.94754	−0.591270	−0.295635	+	0.955301i	$0.595531\pi$
$230$	−18.8815	−1.24501
$231$	8.15393	0.536489
$232$	−60.5456	−3.97501
$233$	−27.8092	−1.82184	−0.910921	−	0.412582i	$-0.864627\pi$
$233$	−27.8092	−1.82184	−0.910921	+	0.412582i	$0.864627\pi$
$234$	2.85055	0.186346
$235$	9.03366	0.589291
$236$	52.0192	3.38616
$237$	5.76982	0.374790
$238$	−33.1464	−2.14856
$239$	−6.12700	−0.396323	−0.198161	−	0.980169i	$-0.563497\pi$
$239$	−6.12700	−0.396323	−0.198161	+	0.980169i	$0.563497\pi$
$240$	−15.8727	−1.02458
$241$	−15.2461	−0.982084	−0.491042	−	0.871136i	$-0.663384\pi$
$241$	−15.2461	−0.982084	−0.491042	+	0.871136i	$0.663384\pi$
$242$	23.9468	1.53936
$243$	2.95087	0.189299
$244$	54.0562	3.46059
$245$	4.53384	0.289656
$246$	12.2498	0.781018
$247$	−25.4454	−1.61905
$248$	−47.8209	−3.03663
$249$	−4.46053	−0.282675
$250$	−2.59020	−0.163819
$251$	−15.7528	−0.994307	−0.497153	−	0.867663i	$-0.665621\pi$
$251$	−15.7528	−0.994307	−0.497153	+	0.867663i	$0.665621\pi$
$252$	4.55611	0.287008
$253$	−9.65656	−0.607103
$254$	−12.9876	−0.814918
$255$	−6.82930	−0.427667
$256$	−21.7849	−1.36155
$257$	10.9656	0.684018	0.342009	−	0.939697i	$-0.388893\pi$
$257$	10.9656	0.684018	0.342009	+	0.939697i	$0.388893\pi$
$258$	−20.7932	−1.29453
$259$	20.0246	1.24427
$260$	−18.1916	−1.12820
$261$	2.45800	0.152147
$262$	50.4005	3.11375
$263$	−19.7992	−1.22087	−0.610435	−	0.792066i	$-0.709005\pi$
$263$	−19.7992	−1.22087	−0.610435	+	0.792066i	$0.709005\pi$
$264$	−16.8479	−1.03692
$265$	0.850156	0.0522247
$266$	−57.9430	−3.55271
$267$	−13.1513	−0.804849
$268$	−6.38021	−0.389733
$269$	−24.9416	−1.52072	−0.760358	−	0.649504i	$-0.774977\pi$
$269$	−24.9416	−1.52072	−0.760358	+	0.649504i	$0.774977\pi$
$270$	−12.7462	−0.775711
$271$	−6.58375	−0.399934	−0.199967	−	0.979803i	$-0.564084\pi$
$271$	−6.58375	−0.399934	−0.199967	+	0.979803i	$0.564084\pi$
$272$	32.9996	2.00089
$273$	23.7781	1.43911
$274$	−12.4552	−0.752445
$275$	−1.32471	−0.0798829
$276$	−62.2163	−3.74498
$277$	−7.17253	−0.430955	−0.215478	−	0.976509i	$-0.569131\pi$
$277$	−7.17253	−0.430955	−0.215478	+	0.976509i	$0.569131\pi$
$278$	−44.9953	−2.69864
$279$	1.94141	0.116229
$280$	−23.8316	−1.42421
$281$	2.12600	0.126827	0.0634133	−	0.997987i	$-0.479801\pi$
$281$	2.12600	0.126827	0.0634133	+	0.997987i	$0.479801\pi$
$282$	42.4089	2.52541
$283$	16.7610	0.996337	0.498168	−	0.867080i	$-0.334006\pi$
$283$	16.7610	0.996337	0.498168	+	0.867080i	$0.334006\pi$
$284$	62.7870	3.72572
$285$	−11.9382	−0.707160
$286$	−13.2551	−0.783791
$287$	8.86180	0.523096
$288$	−2.46419	−0.145204
$289$	−2.80183	−0.164813
$290$	−22.3486	−1.31235
$291$	7.91298	0.463867
$292$	−66.3907	−3.88522
$293$	−15.2160	−0.888926	−0.444463	−	0.895797i	$-0.646605\pi$
$293$	−15.2160	−0.888926	−0.444463	+	0.895797i	$0.646605\pi$
$294$	21.2843	1.24133
$295$	11.0464	0.643148
$296$	−41.3754	−2.40489
$297$	−6.51882	−0.378260
$298$	−45.1985	−2.61828
$299$	−28.1599	−1.62853
$300$	−8.53497	−0.492767
$301$	−15.0423	−0.867026
$302$	−50.6426	−2.91415
$303$	−8.12712	−0.466891
$304$	57.6863	3.30854
$305$	11.4790	0.657285
$306$	−2.78045	−0.158948
$307$	22.7998	1.30125	0.650626	−	0.759398i	$-0.274507\pi$
$307$	22.7998	1.30125	0.650626	+	0.759398i	$0.274507\pi$
$308$	−21.1860	−1.20718
$309$	32.7759	1.86456
$310$	−17.6517	−1.00255
$311$	31.4060	1.78087	0.890436	−	0.455108i	$-0.150400\pi$
$311$	31.4060	1.78087	0.890436	+	0.455108i	$0.150400\pi$
$312$	−49.1309	−2.78149
$313$	16.8328	0.951444	0.475722	−	0.879596i	$-0.342187\pi$
$313$	16.8328	0.951444	0.475722	+	0.879596i	$0.342187\pi$
$314$	44.9259	2.53531
$315$	0.967503	0.0545126
$316$	−14.9915	−0.843336
$317$	0.279917	0.0157217	0.00786086	−	0.999969i	$-0.497498\pi$
$317$	0.279917	0.0157217	0.00786086	+	0.999969i	$0.497498\pi$
$318$	3.99110	0.223810
$319$	−11.4298	−0.639944
$320$	4.88941	0.273326
$321$	−0.257408	−0.0143671
$322$	−64.1243	−3.57351
$323$	24.8197	1.38101
$324$	−46.0248	−2.55693
$325$	−3.86304	−0.214283
$326$	10.8019	0.598261
$327$	−16.4651	−0.910524
$328$	−18.3105	−1.01103
$329$	30.6797	1.69143
$330$	−6.21890	−0.342339
$331$	−3.04772	−0.167518	−0.0837588	−	0.996486i	$-0.526693\pi$
$331$	−3.04772	−0.167518	−0.0837588	+	0.996486i	$0.526693\pi$
$332$	11.5896	0.636063
$333$	1.67974	0.0920491
$334$	−34.6482	−1.89586
$335$	−1.35486	−0.0740237
$336$	−53.9063	−2.94083
$337$	34.1747	1.86161	0.930807	−	0.365512i	$-0.119106\pi$
$337$	34.1747	1.86161	0.930807	+	0.365512i	$0.119106\pi$
$338$	−4.98120	−0.270942
$339$	6.10535	0.331597
$340$	17.7443	0.962318
$341$	−9.02760	−0.488872
$342$	−4.86048	−0.262825
$343$	−8.37545	−0.452232
$344$	31.0809	1.67577
$345$	−13.2118	−0.711300
$346$	45.5078	2.44651
$347$	0.248874	0.0133603	0.00668013	−	0.999978i	$-0.497874\pi$
$347$	0.248874	0.0133603	0.00668013	+	0.999978i	$0.497874\pi$
$348$	−73.6408	−3.94756
$349$	−35.1882	−1.88358	−0.941791	−	0.336198i	$-0.890859\pi$
$349$	−35.1882	−1.88358	−0.941791	+	0.336198i	$0.890859\pi$
$350$	−8.79671	−0.470204
$351$	−19.0098	−1.01467
$352$	11.4586	0.610743
$353$	−6.95343	−0.370093	−0.185047	−	0.982730i	$-0.559244\pi$
$353$	−6.95343	−0.370093	−0.185047	+	0.982730i	$0.559244\pi$
$354$	51.8580	2.75622
$355$	13.3330	0.707642
$356$	34.1705	1.81104
$357$	−23.1933	−1.22752
$358$	22.4664	1.18739
$359$	−12.0994	−0.638583	−0.319292	−	0.947657i	$-0.603445\pi$
$359$	−12.0994	−0.638583	−0.319292	+	0.947657i	$0.603445\pi$
$360$	−1.99908	−0.105361
$361$	24.3871	1.28353
$362$	−5.93092	−0.311722
$363$	16.7561	0.879469
$364$	−61.7815	−3.23823
$365$	−14.0983	−0.737936
$366$	53.8886	2.81680
$367$	−11.5433	−0.602556	−0.301278	−	0.953536i	$-0.597413\pi$
$367$	−11.5433	−0.602556	−0.301278	+	0.953536i	$0.597413\pi$
$368$	63.8402	3.32790
$369$	0.743362	0.0386979
$370$	−15.2725	−0.793979
$371$	2.88726	0.149899
$372$	−58.1640	−3.01566
$373$	−5.98838	−0.310066	−0.155033	−	0.987909i	$-0.549548\pi$
$373$	−5.98838	−0.310066	−0.155033	+	0.987909i	$0.549548\pi$
$374$	12.9292	0.668550
$375$	−1.81242	−0.0935932
$376$	−63.3913	−3.26915
$377$	−33.3308	−1.71663
$378$	−43.2882	−2.22650
$379$	19.8025	1.01719	0.508594	−	0.861007i	$-0.330166\pi$
$379$	19.8025	1.01719	0.508594	+	0.861007i	$0.330166\pi$
$380$	31.0186	1.59122
$381$	−9.08776	−0.465580
$382$	30.4076	1.55579
$383$	34.4967	1.76270	0.881349	−	0.472466i	$-0.156636\pi$
$383$	34.4967	1.76270	0.881349	+	0.472466i	$0.156636\pi$
$384$	−8.40091	−0.428707
$385$	−4.49891	−0.229286
$386$	66.8313	3.40163
$387$	−1.26181	−0.0641414
$388$	−20.5600	−1.04377
$389$	27.5347	1.39606	0.698032	−	0.716066i	$-0.254059\pi$
$389$	27.5347	1.39606	0.698032	+	0.716066i	$0.254059\pi$
$390$	−18.1352	−0.918313
$391$	27.4675	1.38909
$392$	−31.8150	−1.60690
$393$	35.2664	1.77895
$394$	−31.1344	−1.56853
$395$	−3.18348	−0.160178
$396$	−1.77716	−0.0893059
$397$	−2.20360	−0.110595	−0.0552977	−	0.998470i	$-0.517611\pi$
$397$	−2.20360	−0.110595	−0.0552977	+	0.998470i	$0.517611\pi$
$398$	13.7529	0.689371
$399$	−40.5441	−2.02974
$400$	8.75774	0.437887
$401$	22.9951	1.14832	0.574159	−	0.818743i	$-0.305329\pi$
$401$	22.9951	1.14832	0.574159	+	0.818743i	$0.305329\pi$
$402$	−6.36043	−0.317229
$403$	−26.3258	−1.31138
$404$	21.1163	1.05058
$405$	−9.77349	−0.485649
$406$	−75.8992	−3.76681
$407$	−7.81082	−0.387168
$408$	47.9227	2.37253
$409$	37.3641	1.84753	0.923767	−	0.382956i	$-0.125094\pi$
$409$	37.3641	1.84753	0.923767	+	0.382956i	$0.125094\pi$
$410$	−6.75879	−0.333793
$411$	−8.71518	−0.429888
$412$	−85.1602	−4.19554
$413$	37.5154	1.84601
$414$	−5.37900	−0.264363
$415$	2.46109	0.120810
$416$	33.4148	1.63830
$417$	−31.4843	−1.54179
$418$	22.6013	1.10547
$419$	−18.5700	−0.907205	−0.453603	−	0.891204i	$-0.649861\pi$
$419$	−18.5700	−0.907205	−0.453603	+	0.891204i	$0.649861\pi$
$420$	−28.9860	−1.41437
$421$	−21.8681	−1.06579	−0.532894	−	0.846182i	$-0.678895\pi$
$421$	−21.8681	−1.06579	−0.532894	+	0.846182i	$0.678895\pi$
$422$	−20.3096	−0.988655
$423$	2.57353	0.125129
$424$	−5.96574	−0.289722
$425$	3.76805	0.182777
$426$	62.5924	3.03261
$427$	38.9844	1.88659
$428$	0.668812	0.0323282
$429$	−9.27491	−0.447797
$430$	11.4726	0.553258
$431$	−13.4451	−0.647626	−0.323813	−	0.946121i	$-0.604965\pi$
$431$	−13.4451	−0.647626	−0.323813	+	0.946121i	$0.604965\pi$
$432$	43.0964	2.07348
$433$	−10.6563	−0.512110	−0.256055	−	0.966662i	$-0.582423\pi$
$433$	−10.6563	−0.512110	−0.256055	+	0.966662i	$0.582423\pi$
$434$	−59.9477	−2.87758
$435$	−15.6378	−0.749777
$436$	42.7806	2.04882
$437$	48.0156	2.29690
$438$	−66.1849	−3.16243
$439$	−22.8873	−1.09235	−0.546174	−	0.837671i	$-0.683916\pi$
$439$	−22.8873	−1.09235	−0.546174	+	0.837671i	$0.683916\pi$
$440$	9.29578	0.443159
$441$	1.29161	0.0615053
$442$	37.7033	1.79336
$443$	−16.9165	−0.803726	−0.401863	−	0.915700i	$-0.631637\pi$
$443$	−16.9165	−0.803726	−0.401863	+	0.915700i	$0.631637\pi$
$444$	−50.3244	−2.38829
$445$	7.25621	0.343977
$446$	−13.4104	−0.634999
$447$	−31.6265	−1.49588
$448$	16.6052	0.784521
$449$	4.83364	0.228114	0.114057	−	0.993474i	$-0.463615\pi$
$449$	4.83364	0.228114	0.114057	+	0.993474i	$0.463615\pi$
$450$	−0.737903	−0.0347851
$451$	−3.45665	−0.162767
$452$	−15.8633	−0.746145
$453$	−35.4358	−1.66492
$454$	−58.0222	−2.72311
$455$	−13.1195	−0.615050
$456$	83.7733	3.92305
$457$	−32.9070	−1.53932	−0.769662	−	0.638451i	$-0.779576\pi$
$457$	−32.9070	−1.53932	−0.769662	+	0.638451i	$0.779576\pi$
$458$	23.1759	1.08294
$459$	18.5424	0.865483
$460$	34.3277	1.60053
$461$	−13.8105	−0.643220	−0.321610	−	0.946872i	$-0.604224\pi$
$461$	−13.8105	−0.643220	−0.321610	+	0.946872i	$0.604224\pi$
$462$	−21.1203	−0.982607
$463$	−19.6237	−0.911992	−0.455996	−	0.889982i	$-0.650717\pi$
$463$	−19.6237	−0.911992	−0.455996	+	0.889982i	$0.650717\pi$
$464$	75.5630	3.50792
$465$	−12.3513	−0.572777
$466$	72.0314	3.33679
$467$	−29.0152	−1.34266	−0.671331	−	0.741157i	$-0.734277\pi$
$467$	−29.0152	−1.34266	−0.671331	+	0.741157i	$0.734277\pi$
$468$	−5.18247	−0.239560
$469$	−4.60129	−0.212468
$470$	−23.3990	−1.07932
$471$	31.4357	1.44848
$472$	−77.5153	−3.56793
$473$	5.86744	0.269785
$474$	−14.9450	−0.686446
$475$	6.58689	0.302227
$476$	60.2622	2.76211
$477$	0.242194	0.0110893
$478$	15.8702	0.725884
$479$	−6.77108	−0.309379	−0.154689	−	0.987963i	$-0.549438\pi$
$479$	−6.77108	−0.309379	−0.154689	+	0.987963i	$0.549438\pi$
$480$	15.6772	0.715564
$481$	−22.7775	−1.03856
$482$	39.4903	1.79874
$483$	−44.8693	−2.04162
$484$	−43.5367	−1.97894
$485$	−4.36597	−0.198248
$486$	−7.64336	−0.346710
$487$	−11.6567	−0.528216	−0.264108	−	0.964493i	$-0.585078\pi$
$487$	−11.6567	−0.528216	−0.264108	+	0.964493i	$0.585078\pi$
$488$	−80.5507	−3.64636
$489$	7.55833	0.341799
$490$	−11.7436	−0.530520
$491$	10.4262	0.470528	0.235264	−	0.971932i	$-0.424405\pi$
$491$	10.4262	0.470528	0.235264	+	0.971932i	$0.424405\pi$
$492$	−22.2709	−1.00405
$493$	32.5112	1.46423
$494$	65.9088	2.96538
$495$	−0.377386	−0.0169622
$496$	59.6822	2.67981
$497$	45.2809	2.03112
$498$	11.5537	0.517733
$499$	−1.03251	−0.0462214	−0.0231107	−	0.999733i	$-0.507357\pi$
$499$	−1.03251	−0.0462214	−0.0231107	+	0.999733i	$0.507357\pi$
$500$	4.70914	0.210599
$501$	−24.2441	−1.08315
$502$	40.8029	1.82112
$503$	3.07118	0.136937	0.0684685	−	0.997653i	$-0.478189\pi$
$503$	3.07118	0.136937	0.0684685	+	0.997653i	$0.478189\pi$
$504$	−6.78919	−0.302415
$505$	4.48412	0.199541
$506$	25.0124	1.11194
$507$	−3.48547	−0.154795
$508$	23.6123	1.04763
$509$	−1.93778	−0.0858907	−0.0429453	−	0.999077i	$-0.513674\pi$
$509$	−1.93778	−0.0858907	−0.0429453	+	0.999077i	$0.513674\pi$
$510$	17.6893	0.783294
$511$	−47.8798	−2.11808
$512$	47.1568	2.08406
$513$	32.4137	1.43110
$514$	−28.4032	−1.25281
$515$	−18.0840	−0.796877
$516$	37.8033	1.66420
$517$	−11.9670	−0.526307
$518$	−51.8677	−2.27894
$519$	31.8429	1.39775
$520$	27.1078	1.18876
$521$	−40.2414	−1.76301	−0.881503	−	0.472178i	$-0.843468\pi$
$521$	−40.2414	−1.76301	−0.881503	+	0.472178i	$0.843468\pi$
$522$	−6.36672	−0.278664
$523$	25.6942	1.12353	0.561765	−	0.827297i	$-0.310122\pi$
$523$	25.6942	1.12353	0.561765	+	0.827297i	$0.310122\pi$
$524$	−91.6311	−4.00292
$525$	−6.15527	−0.268638
$526$	51.2839	2.23608
$527$	25.6784	1.11857
$528$	21.0268	0.915072
$529$	30.1379	1.31034
$530$	−2.20208	−0.0956521
$531$	3.14693	0.136565
$532$	105.344	4.56724
$533$	−10.0801	−0.436617
$534$	34.0646	1.47412
$535$	0.142024	0.00614024
$536$	9.50733	0.410654
$537$	15.7203	0.678380
$538$	64.6038	2.78527
$539$	−6.00602	−0.258697
$540$	23.1734	0.997226
$541$	31.4635	1.35272	0.676361	−	0.736570i	$-0.263556\pi$
$541$	31.4635	1.35272	0.676361	+	0.736570i	$0.263556\pi$
$542$	17.0532	0.732499
$543$	−4.15000	−0.178094
$544$	−32.5931	−1.39742
$545$	9.08459	0.389141
$546$	−61.5900	−2.63581
$547$	26.9061	1.15042	0.575210	−	0.818006i	$-0.304920\pi$
$547$	26.9061	1.15042	0.575210	+	0.818006i	$0.304920\pi$
$548$	22.6443	0.967316
$549$	3.27016	0.139567
$550$	3.43126	0.146309
$551$	56.8326	2.42115
$552$	92.7102	3.94601
$553$	−10.8116	−0.459755
$554$	18.5783	0.789316
$555$	−10.6865	−0.453617
$556$	81.8042	3.46927
$557$	−40.4446	−1.71369	−0.856846	−	0.515572i	$-0.827580\pi$
$557$	−40.4446	−1.71369	−0.856846	+	0.515572i	$0.827580\pi$
$558$	−5.02865	−0.212880
$559$	17.1103	0.723689
$560$	29.7426	1.25686
$561$	9.04683	0.381957
$562$	−5.50677	−0.232289
$563$	−12.8532	−0.541697	−0.270849	−	0.962622i	$-0.587304\pi$
$563$	−12.8532	−0.541697	−0.270849	+	0.962622i	$0.587304\pi$
$564$	−77.1020	−3.24658
$565$	−3.36861	−0.141718
$566$	−43.4143	−1.82484
$567$	−33.1922	−1.39394
$568$	−93.5607	−3.92572
$569$	6.90463	0.289457	0.144729	−	0.989471i	$-0.453769\pi$
$569$	6.90463	0.289457	0.144729	+	0.989471i	$0.453769\pi$
$570$	30.9224	1.29520
$571$	−33.8435	−1.41631	−0.708154	−	0.706058i	$-0.750472\pi$
$571$	−33.8435	−1.41631	−0.708154	+	0.706058i	$0.750472\pi$
$572$	24.0986	1.00761
$573$	21.2769	0.888856
$574$	−22.9539	−0.958075
$575$	7.28957	0.303996
$576$	1.39291	0.0580378
$577$	0.868174	0.0361426	0.0180713	−	0.999837i	$-0.494247\pi$
$577$	0.868174	0.0361426	0.0180713	+	0.999837i	$0.494247\pi$
$578$	7.25729	0.301864
$579$	46.7634	1.94342
$580$	40.6311	1.68711
$581$	8.35822	0.346758
$582$	−20.4962	−0.849596
$583$	−1.12621	−0.0466428
$584$	98.9306	4.09378
$585$	−1.10051	−0.0455006
$586$	39.4124	1.62811
$587$	18.6255	0.768757	0.384379	−	0.923175i	$-0.374416\pi$
$587$	18.6255	0.768757	0.384379	+	0.923175i	$0.374416\pi$
$588$	−38.6962	−1.59580
$589$	44.8883	1.84959
$590$	−28.6125	−1.17796
$591$	−21.7855	−0.896134
$592$	51.6379	2.12230
$593$	22.3707	0.918656	0.459328	−	0.888267i	$-0.348090\pi$
$593$	22.3707	0.918656	0.459328	+	0.888267i	$0.348090\pi$
$594$	16.8850	0.692802
$595$	12.7969	0.524620
$596$	82.1736	3.36596
$597$	9.62323	0.393852
$598$	72.9399	2.98273
$599$	−24.3762	−0.995985	−0.497993	−	0.867181i	$-0.665929\pi$
$599$	−24.3762	−0.995985	−0.497993	+	0.867181i	$0.665929\pi$
$600$	12.7182	0.519218
$601$	12.2157	0.498288	0.249144	−	0.968466i	$-0.419851\pi$
$601$	12.2157	0.498288	0.249144	+	0.968466i	$0.419851\pi$
$602$	38.9627	1.58800
$603$	−0.385974	−0.0157181
$604$	92.0712	3.74633
$605$	−9.24515	−0.375869
$606$	21.0509	0.855134
$607$	−37.4271	−1.51912	−0.759560	−	0.650438i	$-0.774585\pi$
$607$	−37.4271	−1.51912	−0.759560	+	0.650438i	$0.774585\pi$
$608$	−56.9757	−2.31067
$609$	−53.1085	−2.15206
$610$	−29.7329	−1.20385
$611$	−34.8974	−1.41180
$612$	5.05503	0.204337
$613$	28.5154	1.15173	0.575863	−	0.817547i	$-0.304666\pi$
$613$	28.5154	1.15173	0.575863	+	0.817547i	$0.304666\pi$
$614$	−59.0560	−2.38331
$615$	−4.72928	−0.190703
$616$	31.5699	1.27199
$617$	−13.7692	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$617$	−13.7692	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$618$	−84.8962	−3.41503
$619$	22.6537	0.910531	0.455265	−	0.890356i	$-0.349544\pi$
$619$	22.6537	0.910531	0.455265	+	0.890356i	$0.349544\pi$
$620$	32.0918	1.28884
$621$	35.8716	1.43948
$622$	−81.3479	−3.26175
$623$	24.6432	0.987309
$624$	61.3171	2.45465
$625$	1.00000	0.0400000
$626$	−43.6002	−1.74262
$627$	15.8147	0.631578
$628$	−81.6780	−3.25931
$629$	22.2174	0.885865
$630$	−2.50603	−0.0998426
$631$	−36.2838	−1.44444	−0.722218	−	0.691666i	$-0.756877\pi$
$631$	−36.2838	−1.44444	−0.722218	+	0.691666i	$0.756877\pi$
$632$	22.3392	0.888606
$633$	−14.2111	−0.564840
$634$	−0.725042	−0.0287951
$635$	5.01415	0.198980
$636$	−7.25605	−0.287721
$637$	−17.5144	−0.693947
$638$	29.6054	1.17209
$639$	3.79834	0.150260
$640$	4.63518	0.183221
$641$	−33.5998	−1.32711	−0.663557	−	0.748126i	$-0.730954\pi$
$641$	−33.5998	−1.32711	−0.663557	+	0.748126i	$0.730954\pi$
$642$	0.666738	0.0263141
$643$	−2.31227	−0.0911869	−0.0455935	−	0.998960i	$-0.514518\pi$
$643$	−2.31227	−0.0911869	−0.0455935	+	0.998960i	$0.514518\pi$
$644$	116.582	4.59397
$645$	8.02765	0.316088
$646$	−64.2880	−2.52938
$647$	−27.6768	−1.08809	−0.544044	−	0.839057i	$-0.683107\pi$
$647$	−27.6768	−1.08809	−0.544044	+	0.839057i	$0.683107\pi$
$648$	68.5828	2.69419
$649$	−14.6333	−0.574407
$650$	10.0061	0.392470
$651$	−41.9468	−1.64403
$652$	−19.6385	−0.769102
$653$	42.5956	1.66689	0.833447	−	0.552600i	$-0.186364\pi$
$653$	42.5956	1.66689	0.833447	+	0.552600i	$0.186364\pi$
$654$	42.6480	1.66767
$655$	−19.4581	−0.760292
$656$	22.8522	0.892227
$657$	−4.01634	−0.156692
$658$	−79.4665	−3.09793
$659$	−42.0494	−1.63801	−0.819005	−	0.573786i	$-0.805474\pi$
$659$	−42.0494	−1.63801	−0.819005	+	0.573786i	$0.805474\pi$
$660$	11.3063	0.440099
$661$	−20.6057	−0.801469	−0.400735	−	0.916194i	$-0.631245\pi$
$661$	−20.6057	−0.801469	−0.400735	+	0.916194i	$0.631245\pi$
$662$	7.89420	0.306817
$663$	26.3819	1.02459
$664$	−17.2700	−0.670206
$665$	22.3701	0.867474
$666$	−4.35086	−0.168593
$667$	62.8954	2.43532
$668$	62.9925	2.43725
$669$	−9.38354	−0.362789
$670$	3.50935	0.135578
$671$	−15.2063	−0.587033
$672$	53.2422	2.05386
$673$	−35.2427	−1.35851	−0.679253	−	0.733904i	$-0.737696\pi$
$673$	−35.2427	−1.35851	−0.679253	+	0.733904i	$0.737696\pi$
$674$	−88.5193	−3.40964
$675$	4.92095	0.189407
$676$	9.05613	0.348313
$677$	5.10569	0.196227	0.0981137	−	0.995175i	$-0.468719\pi$
$677$	5.10569	0.196227	0.0981137	+	0.995175i	$0.468719\pi$
$678$	−15.8141	−0.607336
$679$	−14.8275	−0.569026
$680$	−26.4412	−1.01398
$681$	−40.5995	−1.55577
$682$	23.3833	0.895393
$683$	−9.01076	−0.344787	−0.172394	−	0.985028i	$-0.555150\pi$
$683$	−9.01076	−0.344787	−0.172394	+	0.985028i	$0.555150\pi$
$684$	8.83665	0.337878
$685$	4.80858	0.183726
$686$	21.6941	0.828285
$687$	16.2167	0.618707
$688$	−38.7901	−1.47886
$689$	−3.28419	−0.125118
$690$	34.2212	1.30278
$691$	26.2076	0.996984	0.498492	−	0.866894i	$-0.333887\pi$
$691$	26.2076	0.996984	0.498492	+	0.866894i	$0.333887\pi$
$692$	−82.7359	−3.14515
$693$	−1.28166	−0.0486862
$694$	−0.644634	−0.0244700
$695$	17.3714	0.658933
$696$	109.734	4.15947
$697$	9.83222	0.372422
$698$	91.1446	3.44987
$699$	50.4021	1.90638
$700$	15.9930	0.604477
$701$	29.3166	1.10727	0.553637	−	0.832758i	$-0.313240\pi$
$701$	29.3166	1.10727	0.553637	+	0.832758i	$0.313240\pi$
$702$	49.2393	1.85842
$703$	38.8380	1.46480
$704$	−6.47704	−0.244113
$705$	−16.3728	−0.616636
$706$	18.0108	0.677844
$707$	15.2287	0.572736
$708$	−94.2809	−3.54329
$709$	−1.26901	−0.0476586	−0.0238293	−	0.999716i	$-0.507586\pi$
$709$	−1.26901	−0.0476586	−0.0238293	+	0.999716i	$0.507586\pi$
$710$	−34.5352	−1.29608
$711$	−0.906918	−0.0340121
$712$	−50.9185	−1.90825
$713$	49.6769	1.86041
$714$	60.0754	2.24827
$715$	5.11740	0.191380
$716$	−40.8453	−1.52646
$717$	11.1047	0.414714
$718$	31.3399	1.16960
$719$	−50.5572	−1.88547	−0.942733	−	0.333549i	$-0.891754\pi$
$719$	−50.5572	−1.88547	−0.942733	+	0.333549i	$0.891754\pi$
$720$	2.49493	0.0929804
$721$	−61.4160	−2.28725
$722$	−63.1675	−2.35085
$723$	27.6323	1.02766
$724$	10.7828	0.400739
$725$	8.62813	0.320441
$726$	−43.4018	−1.61079
$727$	−36.2039	−1.34273	−0.671364	−	0.741128i	$-0.734291\pi$
$727$	−36.2039	−1.34273	−0.671364	+	0.741128i	$0.734291\pi$
$728$	92.0623	3.41206
$729$	23.9722	0.887860
$730$	36.5173	1.35157
$731$	−16.6895	−0.617285
$732$	−97.9728	−3.62118
$733$	15.8588	0.585759	0.292880	−	0.956149i	$-0.405386\pi$
$733$	15.8588	0.585759	0.292880	+	0.956149i	$0.405386\pi$
$734$	29.8995	1.10361
$735$	−8.21724	−0.303098
$736$	−63.0539	−2.32420
$737$	1.79479	0.0661119
$738$	−1.92546	−0.0708771
$739$	−52.1297	−1.91762	−0.958811	−	0.284044i	$-0.908324\pi$
$739$	−52.1297	−1.91762	−0.958811	+	0.284044i	$0.908324\pi$
$740$	27.7663	1.02071
$741$	46.1179	1.69418
$742$	−7.47858	−0.274547
$743$	41.8970	1.53705	0.768526	−	0.639819i	$-0.220991\pi$
$743$	41.8970	1.53705	0.768526	+	0.639819i	$0.220991\pi$
$744$	86.6718	3.17754
$745$	17.4498	0.639311
$746$	15.5111	0.567902
$747$	0.701120	0.0256526
$748$	−23.5060	−0.859464
$749$	0.482335	0.0176241
$750$	4.69454	0.171421
$751$	3.76648	0.137441	0.0687204	−	0.997636i	$-0.478108\pi$
$751$	3.76648	0.137441	0.0687204	+	0.997636i	$0.478108\pi$
$752$	79.1145	2.88501
$753$	28.5507	1.04045
$754$	86.3336	3.14408
$755$	19.5516	0.711555
$756$	78.7005	2.86231
$757$	28.0916	1.02101	0.510503	−	0.859876i	$-0.329459\pi$
$757$	28.0916	1.02101	0.510503	+	0.859876i	$0.329459\pi$
$758$	−51.2925	−1.86303
$759$	17.5018	0.635275
$760$	−46.2217	−1.67664
$761$	16.9941	0.616036	0.308018	−	0.951380i	$-0.400334\pi$
$761$	16.9941	0.616036	0.308018	+	0.951380i	$0.400334\pi$
$762$	23.5391	0.852733
$763$	30.8526	1.11694
$764$	−55.2829	−2.00006
$765$	1.07345	0.0388107
$766$	−89.3533	−3.22847
$767$	−42.6728	−1.54083
$768$	39.4834	1.42474
$769$	−40.5957	−1.46392	−0.731959	−	0.681349i	$-0.761394\pi$
$769$	−40.5957	−1.46392	−0.731959	+	0.681349i	$0.761394\pi$
$770$	11.6531	0.419948
$771$	−19.8744	−0.715759
$772$	−121.503	−4.37300
$773$	44.7423	1.60927	0.804634	−	0.593771i	$-0.202361\pi$
$773$	44.7423	1.60927	0.804634	+	0.593771i	$0.202361\pi$
$774$	3.26834	0.117478
$775$	6.81479	0.244794
$776$	30.6370	1.09980
$777$	−36.2930	−1.30201
$778$	−71.3204	−2.55696
$779$	17.1876	0.615810
$780$	32.9709	1.18055
$781$	−17.6623	−0.632008
$782$	−71.1462	−2.54418
$783$	42.4586	1.51735
$784$	39.7062	1.41808
$785$	−17.3445	−0.619054
$786$	−91.3471	−3.25824
$787$	37.5204	1.33746	0.668729	−	0.743507i	$-0.266839\pi$
$787$	37.5204	1.33746	0.668729	+	0.743507i	$0.266839\pi$
$788$	56.6042	2.01644
$789$	35.8845	1.27752
$790$	8.24586	0.293374
$791$	−11.4403	−0.406770
$792$	2.64820	0.0940998
$793$	−44.3438	−1.57470
$794$	5.70776	0.202561
$795$	−1.54084	−0.0546481
$796$	−25.0036	−0.886230
$797$	−16.1211	−0.571039	−0.285520	−	0.958373i	$-0.592166\pi$
$797$	−16.1211	−0.571039	−0.285520	+	0.958373i	$0.592166\pi$
$798$	105.017	3.71757
$799$	34.0393	1.20422
$800$	−8.64987	−0.305819
$801$	2.06717	0.0730397
$802$	−59.5619	−2.10320
$803$	18.6761	0.659064
$804$	11.5636	0.407818
$805$	24.7565	0.872552
$806$	68.1892	2.40186
$807$	45.2048	1.59128
$808$	−31.4661	−1.10697
$809$	40.0168	1.40692	0.703459	−	0.710736i	$-0.251638\pi$
$809$	40.0168	1.40692	0.703459	+	0.710736i	$0.251638\pi$
$810$	25.3153	0.889489
$811$	16.1245	0.566206	0.283103	−	0.959089i	$-0.408636\pi$
$811$	16.1245	0.566206	0.283103	+	0.959089i	$0.408636\pi$
$812$	137.989	4.84248
$813$	11.9325	0.418493
$814$	20.2316	0.709117
$815$	−4.17029	−0.146079
$816$	−59.8093	−2.09374
$817$	−29.1749	−1.02070
$818$	−96.7804	−3.38385
$819$	−3.73751	−0.130599
$820$	12.2879	0.429111
$821$	−32.2379	−1.12511	−0.562555	−	0.826760i	$-0.690181\pi$
$821$	−32.2379	−1.12511	−0.562555	+	0.826760i	$0.690181\pi$
$822$	22.5741	0.787362
$823$	−31.3986	−1.09449	−0.547244	−	0.836973i	$-0.684323\pi$
$823$	−31.3986	−1.09449	−0.547244	+	0.836973i	$0.684323\pi$
$824$	126.900	4.42076
$825$	2.40093	0.0835898
$826$	−97.1723	−3.38106
$827$	−35.8683	−1.24726	−0.623631	−	0.781719i	$-0.714343\pi$
$827$	−35.8683	−1.24726	−0.623631	+	0.781719i	$0.714343\pi$
$828$	9.77934	0.339856
$829$	29.7801	1.03431	0.517153	−	0.855893i	$-0.326992\pi$
$829$	29.7801	1.03431	0.517153	+	0.855893i	$0.326992\pi$
$830$	−6.37471	−0.221269
$831$	12.9997	0.450953
$832$	−18.8880	−0.654824
$833$	17.0837	0.591916
$834$	81.5506	2.82387
$835$	13.3766	0.462918
$836$	−41.0906	−1.42115
$837$	33.5352	1.15915
$838$	48.1001	1.66159
$839$	−0.647770	−0.0223635	−0.0111817	−	0.999937i	$-0.503559\pi$
$839$	−0.647770	−0.0223635	−0.0111817	+	0.999937i	$0.503559\pi$
$840$	43.1929	1.49030
$841$	45.4447	1.56706
$842$	56.6429	1.95204
$843$	−3.85322	−0.132712
$844$	36.9240	1.27098
$845$	1.92310	0.0661565
$846$	−6.66596	−0.229180
$847$	−31.3979	−1.07885
$848$	7.44545	0.255678
$849$	−30.3780	−1.04257
$850$	−9.76000	−0.334765
$851$	42.9812	1.47338
$852$	−113.797	−3.89861
$853$	−7.16623	−0.245367	−0.122684	−	0.992446i	$-0.539150\pi$
$853$	−7.16623	−0.245367	−0.122684	+	0.992446i	$0.539150\pi$
$854$	−100.977	−3.45538
$855$	1.87649	0.0641745
$856$	−0.996615	−0.0340636
$857$	−18.5761	−0.634546	−0.317273	−	0.948334i	$-0.602767\pi$
$857$	−18.5761	−0.634546	−0.317273	+	0.948334i	$0.602767\pi$
$858$	24.0239	0.820162
$859$	20.2596	0.691248	0.345624	−	0.938373i	$-0.387667\pi$
$859$	20.2596	0.691248	0.345624	+	0.938373i	$0.387667\pi$
$860$	−20.8579	−0.711248
$861$	−16.0613	−0.547369
$862$	34.8254	1.18616
$863$	−40.3671	−1.37411	−0.687056	−	0.726605i	$-0.741097\pi$
$863$	−40.3671	−1.37411	−0.687056	+	0.726605i	$0.741097\pi$
$864$	−42.5655	−1.44811
$865$	−17.5692	−0.597371
$866$	27.6020	0.937954
$867$	5.07810	0.172461
$868$	108.989	3.69932
$869$	4.21718	0.143058
$870$	40.5051	1.37325
$871$	5.23386	0.177343
$872$	−63.7486	−2.15880
$873$	−1.24379	−0.0420958
$874$	−124.370	−4.20688
$875$	3.39615	0.114811
$876$	120.328	4.06551
$877$	11.0694	0.373786	0.186893	−	0.982380i	$-0.440158\pi$
$877$	11.0694	0.373786	0.186893	+	0.982380i	$0.440158\pi$
$878$	59.2826	2.00069
$879$	27.5778	0.930175
$880$	−11.6015	−0.391085
$881$	39.7284	1.33848	0.669241	−	0.743045i	$-0.266619\pi$
$881$	39.7284	1.33848	0.669241	+	0.743045i	$0.266619\pi$
$882$	−3.34553	−0.112650
$883$	−38.1221	−1.28291	−0.641455	−	0.767160i	$-0.721669\pi$
$883$	−38.1221	−1.28291	−0.641455	+	0.767160i	$0.721669\pi$
$884$	−68.5469	−2.30548
$885$	−20.0208	−0.672993
$886$	43.8171	1.47206
$887$	21.3100	0.715521	0.357760	−	0.933813i	$-0.383540\pi$
$887$	21.3100	0.715521	0.357760	+	0.933813i	$0.383540\pi$
$888$	74.9897	2.51649
$889$	17.0288	0.571128
$890$	−18.7950	−0.630012
$891$	12.9470	0.433742
$892$	24.3808	0.816331
$893$	59.5037	1.99122
$894$	81.9189	2.73978
$895$	−8.67362	−0.289927
$896$	15.7418	0.525895
$897$	51.0378	1.70410
$898$	−12.5201	−0.417801
$899$	58.7989	1.96105
$900$	1.34155	0.0447184
$901$	3.20343	0.106722
$902$	8.95342	0.298116
$903$	27.2631	0.907259
$904$	23.6383	0.786198
$905$	2.28975	0.0761140
$906$	91.7858	3.04938
$907$	−42.8511	−1.42285	−0.711423	−	0.702764i	$-0.751949\pi$
$907$	−42.8511	−1.42285	−0.711423	+	0.702764i	$0.751949\pi$
$908$	105.488	3.50074
$909$	1.27745	0.0423702
$910$	33.9821	1.12650
$911$	20.5782	0.681785	0.340892	−	0.940102i	$-0.389271\pi$
$911$	20.5782	0.681785	0.340892	+	0.940102i	$0.389271\pi$
$912$	−104.552	−3.46206
$913$	−3.26022	−0.107898
$914$	85.2358	2.81935
$915$	−20.8048	−0.687785
$916$	−42.1353	−1.39219
$917$	−66.0827	−2.18224
$918$	−48.0284	−1.58517
$919$	−0.606079	−0.0199927	−0.00999635	−	0.999950i	$-0.503182\pi$
$919$	−0.606079	−0.0199927	−0.00999635	+	0.999950i	$0.503182\pi$
$920$	−51.1526	−1.68645
$921$	−41.3229	−1.36163
$922$	35.7720	1.17809
$923$	−51.5059	−1.69534
$924$	38.3980	1.26320
$925$	5.89626	0.193868
$926$	50.8294	1.67036
$927$	−5.15181	−0.169208
$928$	−74.6322	−2.44992
$929$	17.3701	0.569895	0.284947	−	0.958543i	$-0.408024\pi$
$929$	17.3701	0.569895	0.284947	+	0.958543i	$0.408024\pi$
$930$	31.9923	1.04907
$931$	29.8639	0.978750
$932$	−130.958	−4.28966
$933$	−56.9210	−1.86351
$934$	75.1552	2.45915
$935$	−4.99156	−0.163242
$936$	7.72254	0.252419
$937$	9.22360	0.301322	0.150661	−	0.988586i	$-0.451860\pi$
$937$	9.22360	0.301322	0.150661	+	0.988586i	$0.451860\pi$
$938$	11.9183	0.389146
$939$	−30.5081	−0.995594
$940$	42.5408	1.38753
$941$	−23.8738	−0.778265	−0.389133	−	0.921182i	$-0.627225\pi$
$941$	−23.8738	−0.778265	−0.389133	+	0.921182i	$0.627225\pi$
$942$	−81.4248	−2.65296
$943$	19.0212	0.619415
$944$	96.7418	3.14868
$945$	16.7123	0.543650
$946$	−15.1978	−0.494125
$947$	20.8721	0.678251	0.339126	−	0.940741i	$-0.389869\pi$
$947$	20.8721	0.678251	0.339126	+	0.940741i	$0.389869\pi$
$948$	27.1709	0.882470
$949$	54.4621	1.76792
$950$	−17.0614	−0.553544
$951$	−0.507329	−0.0164513
$952$	−89.7984	−2.91038
$953$	−19.1648	−0.620810	−0.310405	−	0.950604i	$-0.600465\pi$
$953$	−19.1648	−0.620810	−0.310405	+	0.950604i	$0.600465\pi$
$954$	−0.627332	−0.0203106
$955$	−11.7395	−0.379881
$956$	−28.8529	−0.933170
$957$	20.7156	0.669639
$958$	17.5385	0.566642
$959$	16.3307	0.527344
$960$	−8.86169	−0.286010
$961$	15.4413	0.498107
$962$	58.9983	1.90218
$963$	0.0404601	0.00130381
$964$	−71.7958	−2.31239
$965$	−25.8016	−0.830583
$966$	116.220	3.73933
$967$	−45.6857	−1.46915	−0.734577	−	0.678526i	$-0.762619\pi$
$967$	−45.6857	−1.46915	−0.734577	+	0.678526i	$0.762619\pi$
$968$	64.8753	2.08517
$969$	−44.9838	−1.44509
$970$	11.3087	0.363101
$971$	0.256015	0.00821593	0.00410796	−	0.999992i	$-0.498692\pi$
$971$	0.256015	0.00821593	0.00410796	+	0.999992i	$0.498692\pi$
$972$	13.8961	0.445717
$973$	58.9957	1.89132
$974$	30.1933	0.967454
$975$	7.00147	0.224227
$976$	100.530	3.21789
$977$	−48.2134	−1.54248	−0.771242	−	0.636542i	$-0.780364\pi$
$977$	−48.2134	−1.54248	−0.771242	+	0.636542i	$0.780364\pi$
$978$	−19.5776	−0.626022
$979$	−9.61236	−0.307212
$980$	21.3505	0.682017
$981$	2.58804	0.0826297
$982$	−27.0060	−0.861795
$983$	43.8001	1.39701	0.698503	−	0.715607i	$-0.253850\pi$
$983$	43.8001	1.39701	0.698503	+	0.715607i	$0.253850\pi$
$984$	33.1864	1.05794
$985$	12.0201	0.382991
$986$	−84.2106	−2.68181
$987$	−55.6046	−1.76991
$988$	−119.826	−3.81218
$989$	−32.2872	−1.02667
$990$	0.977506	0.0310672
$991$	22.7807	0.723652	0.361826	−	0.932246i	$-0.382154\pi$
$991$	22.7807	0.723652	0.361826	+	0.932246i	$0.382154\pi$
$992$	−58.9470	−1.87157
$993$	5.52376	0.175291
$994$	−117.287	−3.72010
$995$	−5.30959	−0.168325
$996$	−21.0053	−0.665578
$997$	−23.5871	−0.747012	−0.373506	−	0.927628i	$-0.621844\pi$
$997$	−23.5871	−0.747012	−0.373506	+	0.927628i	$0.621844\pi$
$998$	2.67441	0.0846568
$999$	29.0152	0.917999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.8	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.59020 q^{2} -1.81242 q^{3} +4.70914 q^{4} +1.00000 q^{5} +4.69454 q^{6} +3.39615 q^{7} -7.01723 q^{8} +0.284882 q^{9} +O(q^{10})\)	\(q-2.59020 q^{2} -1.81242 q^{3} +4.70914 q^{4} +1.00000 q^{5} +4.69454 q^{6} +3.39615 q^{7} -7.01723 q^{8} +0.284882 q^{9} -2.59020 q^{10} -1.32471 q^{11} -8.53497 q^{12} -3.86304 q^{13} -8.79671 q^{14} -1.81242 q^{15} +8.75774 q^{16} +3.76805 q^{17} -0.737903 q^{18} +6.58689 q^{19} +4.70914 q^{20} -6.15527 q^{21} +3.43126 q^{22} +7.28957 q^{23} +12.7182 q^{24} +1.00000 q^{25} +10.0061 q^{26} +4.92095 q^{27} +15.9930 q^{28} +8.62813 q^{29} +4.69454 q^{30} +6.81479 q^{31} -8.64987 q^{32} +2.40093 q^{33} -9.76000 q^{34} +3.39615 q^{35} +1.34155 q^{36} +5.89626 q^{37} -17.0614 q^{38} +7.00147 q^{39} -7.01723 q^{40} +2.60937 q^{41} +15.9434 q^{42} -4.42923 q^{43} -6.23824 q^{44} +0.284882 q^{45} -18.8815 q^{46} +9.03366 q^{47} -15.8727 q^{48} +4.53384 q^{49} -2.59020 q^{50} -6.82930 q^{51} -18.1916 q^{52} +0.850156 q^{53} -12.7462 q^{54} -1.32471 q^{55} -23.8316 q^{56} -11.9382 q^{57} -22.3486 q^{58} +11.0464 q^{59} -8.53497 q^{60} +11.4790 q^{61} -17.6517 q^{62} +0.967503 q^{63} +4.88941 q^{64} -3.86304 q^{65} -6.21890 q^{66} -1.35486 q^{67} +17.7443 q^{68} -13.2118 q^{69} -8.79671 q^{70} +13.3330 q^{71} -1.99908 q^{72} -14.0983 q^{73} -15.2725 q^{74} -1.81242 q^{75} +31.0186 q^{76} -4.49891 q^{77} -18.1352 q^{78} -3.18348 q^{79} +8.75774 q^{80} -9.77349 q^{81} -6.75879 q^{82} +2.46109 q^{83} -28.9860 q^{84} +3.76805 q^{85} +11.4726 q^{86} -15.6378 q^{87} +9.29578 q^{88} +7.25621 q^{89} -0.737903 q^{90} -13.1195 q^{91} +34.3277 q^{92} -12.3513 q^{93} -23.3990 q^{94} +6.58689 q^{95} +15.6772 q^{96} -4.36597 q^{97} -11.7436 q^{98} -0.377386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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