LMFDB - Embedded newform 8015.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76326 q^{2} +3.03127 q^{3} +5.63562 q^{4} +1.00000 q^{5} -8.37621 q^{6} +1.00000 q^{7} -10.0462 q^{8} +6.18862 q^{9} +O(q^{10})$	\(q-2.76326 q^{2} +3.03127 q^{3} +5.63562 q^{4} +1.00000 q^{5} -8.37621 q^{6} +1.00000 q^{7} -10.0462 q^{8} +6.18862 q^{9} -2.76326 q^{10} +0.604546 q^{11} +17.0831 q^{12} -4.59820 q^{13} -2.76326 q^{14} +3.03127 q^{15} +16.4890 q^{16} +7.38462 q^{17} -17.1008 q^{18} -0.698229 q^{19} +5.63562 q^{20} +3.03127 q^{21} -1.67052 q^{22} -5.10832 q^{23} -30.4527 q^{24} +1.00000 q^{25} +12.7060 q^{26} +9.66556 q^{27} +5.63562 q^{28} +2.36541 q^{29} -8.37621 q^{30} +8.12219 q^{31} -25.4711 q^{32} +1.83254 q^{33} -20.4056 q^{34} +1.00000 q^{35} +34.8767 q^{36} +5.76350 q^{37} +1.92939 q^{38} -13.9384 q^{39} -10.0462 q^{40} +1.14332 q^{41} -8.37621 q^{42} -3.53783 q^{43} +3.40699 q^{44} +6.18862 q^{45} +14.1156 q^{46} +5.14899 q^{47} +49.9827 q^{48} +1.00000 q^{49} -2.76326 q^{50} +22.3848 q^{51} -25.9137 q^{52} -12.4625 q^{53} -26.7085 q^{54} +0.604546 q^{55} -10.0462 q^{56} -2.11652 q^{57} -6.53626 q^{58} +5.71904 q^{59} +17.0831 q^{60} +1.37880 q^{61} -22.4438 q^{62} +6.18862 q^{63} +37.4054 q^{64} -4.59820 q^{65} -5.06380 q^{66} +7.80564 q^{67} +41.6169 q^{68} -15.4847 q^{69} -2.76326 q^{70} +7.81712 q^{71} -62.1720 q^{72} -3.54404 q^{73} -15.9261 q^{74} +3.03127 q^{75} -3.93496 q^{76} +0.604546 q^{77} +38.5155 q^{78} +13.4653 q^{79} +16.4890 q^{80} +10.7331 q^{81} -3.15929 q^{82} +10.4127 q^{83} +17.0831 q^{84} +7.38462 q^{85} +9.77595 q^{86} +7.17021 q^{87} -6.07338 q^{88} -9.53288 q^{89} -17.1008 q^{90} -4.59820 q^{91} -28.7886 q^{92} +24.6206 q^{93} -14.2280 q^{94} -0.698229 q^{95} -77.2099 q^{96} +14.3025 q^{97} -2.76326 q^{98} +3.74130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.76326	−1.95392	−0.976961	−	0.213417i	$-0.931541\pi$
$2$	−2.76326	−1.95392	−0.976961	+	0.213417i	$0.931541\pi$
$3$	3.03127	1.75011	0.875053	−	0.484027i	$-0.160826\pi$
$3$	3.03127	1.75011	0.875053	+	0.484027i	$0.160826\pi$
$4$	5.63562	2.81781
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−8.37621	−3.41957
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.0462	−3.55186
$9$	6.18862	2.06287
$10$	−2.76326	−0.873821
$11$	0.604546	0.182277	0.0911387	−	0.995838i	$-0.470949\pi$
$11$	0.604546	0.182277	0.0911387	+	0.995838i	$0.470949\pi$
$12$	17.0831	4.93147
$13$	−4.59820	−1.27531	−0.637656	−	0.770322i	$-0.720096\pi$
$13$	−4.59820	−1.27531	−0.637656	+	0.770322i	$0.720096\pi$
$14$	−2.76326	−0.738513
$15$	3.03127	0.782671
$16$	16.4890	4.12225
$17$	7.38462	1.79103	0.895516	−	0.445028i	$-0.146806\pi$
$17$	7.38462	1.79103	0.895516	+	0.445028i	$0.146806\pi$
$18$	−17.1008	−4.03069
$19$	−0.698229	−0.160185	−0.0800924	−	0.996787i	$-0.525522\pi$
$19$	−0.698229	−0.160185	−0.0800924	+	0.996787i	$0.525522\pi$
$20$	5.63562	1.26016
$21$	3.03127	0.661478
$22$	−1.67052	−0.356156
$23$	−5.10832	−1.06516	−0.532579	−	0.846380i	$-0.678777\pi$
$23$	−5.10832	−1.06516	−0.532579	+	0.846380i	$0.678777\pi$
$24$	−30.4527	−6.21614
$25$	1.00000	0.200000
$26$	12.7060	2.49186
$27$	9.66556	1.86014
$28$	5.63562	1.06503
$29$	2.36541	0.439246	0.219623	−	0.975585i	$-0.429517\pi$
$29$	2.36541	0.439246	0.219623	+	0.975585i	$0.429517\pi$
$30$	−8.37621	−1.52928
$31$	8.12219	1.45879	0.729394	−	0.684093i	$-0.239802\pi$
$31$	8.12219	1.45879	0.729394	+	0.684093i	$0.239802\pi$
$32$	−25.4711	−4.50270
$33$	1.83254	0.319005
$34$	−20.4056	−3.49954
$35$	1.00000	0.169031
$36$	34.8767	5.81279
$37$	5.76350	0.947513	0.473756	−	0.880656i	$-0.342898\pi$
$37$	5.76350	0.947513	0.473756	+	0.880656i	$0.342898\pi$
$38$	1.92939	0.312989
$39$	−13.9384	−2.23193
$40$	−10.0462	−1.58844
$41$	1.14332	0.178556	0.0892781	−	0.996007i	$-0.471544\pi$
$41$	1.14332	0.178556	0.0892781	+	0.996007i	$0.471544\pi$
$42$	−8.37621	−1.29248
$43$	−3.53783	−0.539514	−0.269757	−	0.962928i	$-0.586943\pi$
$43$	−3.53783	−0.539514	−0.269757	+	0.962928i	$0.586943\pi$
$44$	3.40699	0.513624
$45$	6.18862	0.922544
$46$	14.1156	2.08124
$47$	5.14899	0.751057	0.375528	−	0.926811i	$-0.377461\pi$
$47$	5.14899	0.751057	0.375528	+	0.926811i	$0.377461\pi$
$48$	49.9827	7.21438
$49$	1.00000	0.142857
$50$	−2.76326	−0.390784
$51$	22.3848	3.13450
$52$	−25.9137	−3.59359
$53$	−12.4625	−1.71186	−0.855929	−	0.517093i	$-0.827014\pi$
$53$	−12.4625	−1.71186	−0.855929	+	0.517093i	$0.827014\pi$
$54$	−26.7085	−3.63457
$55$	0.604546	0.0815170
$56$	−10.0462	−1.34248
$57$	−2.11652	−0.280340
$58$	−6.53626	−0.858253
$59$	5.71904	0.744555	0.372278	−	0.928121i	$-0.378577\pi$
$59$	5.71904	0.744555	0.372278	+	0.928121i	$0.378577\pi$
$60$	17.0831	2.20542
$61$	1.37880	0.176538	0.0882689	−	0.996097i	$-0.471867\pi$
$61$	1.37880	0.176538	0.0882689	+	0.996097i	$0.471867\pi$
$62$	−22.4438	−2.85036
$63$	6.18862	0.779692
$64$	37.4054	4.67567
$65$	−4.59820	−0.570336
$66$	−5.06380	−0.623311
$67$	7.80564	0.953610	0.476805	−	0.879009i	$-0.341795\pi$
$67$	7.80564	0.953610	0.476805	+	0.879009i	$0.341795\pi$
$68$	41.6169	5.04679
$69$	−15.4847	−1.86414
$70$	−2.76326	−0.330273
$71$	7.81712	0.927721	0.463861	−	0.885908i	$-0.346464\pi$
$71$	7.81712	0.927721	0.463861	+	0.885908i	$0.346464\pi$
$72$	−62.1720	−7.32704
$73$	−3.54404	−0.414799	−0.207400	−	0.978256i	$-0.566500\pi$
$73$	−3.54404	−0.414799	−0.207400	+	0.978256i	$0.566500\pi$
$74$	−15.9261	−1.85137
$75$	3.03127	0.350021
$76$	−3.93496	−0.451371
$77$	0.604546	0.0688944
$78$	38.5155	4.36102
$79$	13.4653	1.51496	0.757480	−	0.652859i	$-0.226430\pi$
$79$	13.4653	1.51496	0.757480	+	0.652859i	$0.226430\pi$
$80$	16.4890	1.84353
$81$	10.7331	1.19257
$82$	−3.15929	−0.348885
$83$	10.4127	1.14294	0.571470	−	0.820623i	$-0.306373\pi$
$83$	10.4127	1.14294	0.571470	+	0.820623i	$0.306373\pi$
$84$	17.0831	1.86392
$85$	7.38462	0.800974
$86$	9.77595	1.05417
$87$	7.17021	0.768727
$88$	−6.07338	−0.647425
$89$	−9.53288	−1.01048	−0.505242	−	0.862978i	$-0.668597\pi$
$89$	−9.53288	−1.01048	−0.505242	+	0.862978i	$0.668597\pi$
$90$	−17.1008	−1.80258
$91$	−4.59820	−0.482022
$92$	−28.7886	−3.00142
$93$	24.6206	2.55304
$94$	−14.2280	−1.46751
$95$	−0.698229	−0.0716368
$96$	−77.2099	−7.88020
$97$	14.3025	1.45220	0.726099	−	0.687590i	$-0.241331\pi$
$97$	14.3025	1.45220	0.726099	+	0.687590i	$0.241331\pi$
$98$	−2.76326	−0.279132
$99$	3.74130	0.376015
$100$	5.63562	0.563562
$101$	−8.04020	−0.800030	−0.400015	−	0.916509i	$-0.630995\pi$
$101$	−8.04020	−0.800030	−0.400015	+	0.916509i	$0.630995\pi$
$102$	−61.8551	−6.12457
$103$	−5.64984	−0.556695	−0.278347	−	0.960480i	$-0.589787\pi$
$103$	−5.64984	−0.556695	−0.278347	+	0.960480i	$0.589787\pi$
$104$	46.1944	4.52973
$105$	3.03127	0.295822
$106$	34.4372	3.34484
$107$	−8.74537	−0.845447	−0.422724	−	0.906259i	$-0.638926\pi$
$107$	−8.74537	−0.845447	−0.422724	+	0.906259i	$0.638926\pi$
$108$	54.4715	5.24152
$109$	−11.7056	−1.12119	−0.560595	−	0.828090i	$-0.689428\pi$
$109$	−11.7056	−1.12119	−0.560595	+	0.828090i	$0.689428\pi$
$110$	−1.67052	−0.159278
$111$	17.4707	1.65825
$112$	16.4890	1.55807
$113$	−12.1743	−1.14526	−0.572629	−	0.819815i	$-0.694076\pi$
$113$	−12.1743	−1.14526	−0.572629	+	0.819815i	$0.694076\pi$
$114$	5.84851	0.547763
$115$	−5.10832	−0.476353
$116$	13.3306	1.23771
$117$	−28.4565	−2.63080
$118$	−15.8032	−1.45480
$119$	7.38462	0.676947
$120$	−30.4527	−2.77994
$121$	−10.6345	−0.966775
$122$	−3.81000	−0.344941
$123$	3.46571	0.312492
$124$	45.7736	4.11059
$125$	1.00000	0.0894427
$126$	−17.1008	−1.52346
$127$	7.82763	0.694590	0.347295	−	0.937756i	$-0.387100\pi$
$127$	7.82763	0.694590	0.347295	+	0.937756i	$0.387100\pi$
$128$	−52.4187	−4.63320
$129$	−10.7241	−0.944206
$130$	12.7060	1.11439
$131$	−0.348766	−0.0304719	−0.0152359	−	0.999884i	$-0.504850\pi$
$131$	−0.348766	−0.0304719	−0.0152359	+	0.999884i	$0.504850\pi$
$132$	10.3275	0.898896
$133$	−0.698229	−0.0605442
$134$	−21.5690	−1.86328
$135$	9.66556	0.831879
$136$	−74.1873	−6.36151
$137$	−7.22669	−0.617418	−0.308709	−	0.951157i	$-0.599897\pi$
$137$	−7.22669	−0.617418	−0.308709	+	0.951157i	$0.599897\pi$
$138$	42.7883	3.64238
$139$	10.3060	0.874141	0.437071	−	0.899427i	$-0.356016\pi$
$139$	10.3060	0.874141	0.437071	+	0.899427i	$0.356016\pi$
$140$	5.63562	0.476297
$141$	15.6080	1.31443
$142$	−21.6008	−1.81270
$143$	−2.77982	−0.232461
$144$	102.044	8.50368
$145$	2.36541	0.196437
$146$	9.79313	0.810485
$147$	3.03127	0.250015
$148$	32.4809	2.66991
$149$	−7.19812	−0.589693	−0.294846	−	0.955545i	$-0.595268\pi$
$149$	−7.19812	−0.589693	−0.294846	+	0.955545i	$0.595268\pi$
$150$	−8.37621	−0.683914
$151$	−16.8236	−1.36908	−0.684542	−	0.728973i	$-0.739998\pi$
$151$	−16.8236	−1.36908	−0.684542	+	0.728973i	$0.739998\pi$
$152$	7.01454	0.568955
$153$	45.7006	3.69467
$154$	−1.67052	−0.134614
$155$	8.12219	0.652390
$156$	−78.5516	−6.28916
$157$	−16.4529	−1.31308	−0.656541	−	0.754290i	$-0.727981\pi$
$157$	−16.4529	−1.31308	−0.656541	+	0.754290i	$0.727981\pi$
$158$	−37.2080	−2.96011
$159$	−37.7773	−2.99593
$160$	−25.4711	−2.01367
$161$	−5.10832	−0.402592
$162$	−29.6584	−2.33019
$163$	14.1717	1.11001	0.555005	−	0.831847i	$-0.312716\pi$
$163$	14.1717	1.11001	0.555005	+	0.831847i	$0.312716\pi$
$164$	6.44331	0.503138
$165$	1.83254	0.142663
$166$	−28.7730	−2.23322
$167$	15.4929	1.19888	0.599439	−	0.800420i	$-0.295390\pi$
$167$	15.4929	1.19888	0.599439	+	0.800420i	$0.295390\pi$
$168$	−30.4527	−2.34948
$169$	8.14344	0.626418
$170$	−20.4056	−1.56504
$171$	−4.32107	−0.330441
$172$	−19.9379	−1.52025
$173$	−19.3540	−1.47146	−0.735730	−	0.677275i	$-0.763161\pi$
$173$	−19.3540	−1.47146	−0.735730	+	0.677275i	$0.763161\pi$
$174$	−19.8132	−1.50203
$175$	1.00000	0.0755929
$176$	9.96837	0.751394
$177$	17.3360	1.30305
$178$	26.3419	1.97441
$179$	14.4374	1.07910	0.539551	−	0.841953i	$-0.318594\pi$
$179$	14.4374	1.07910	0.539551	+	0.841953i	$0.318594\pi$
$180$	34.8767	2.59956
$181$	24.9874	1.85730	0.928649	−	0.370960i	$-0.120971\pi$
$181$	24.9874	1.85730	0.928649	+	0.370960i	$0.120971\pi$
$182$	12.7060	0.941834
$183$	4.17953	0.308960
$184$	51.3191	3.78330
$185$	5.76350	0.423741
$186$	−68.0332	−4.98843
$187$	4.46434	0.326465
$188$	29.0178	2.11634
$189$	9.66556	0.703066
$190$	1.92939	0.139973
$191$	6.15653	0.445471	0.222736	−	0.974879i	$-0.428501\pi$
$191$	6.15653	0.445471	0.222736	+	0.974879i	$0.428501\pi$
$192$	113.386	8.18292
$193$	6.58298	0.473853	0.236927	−	0.971528i	$-0.423860\pi$
$193$	6.58298	0.473853	0.236927	+	0.971528i	$0.423860\pi$
$194$	−39.5216	−2.83748
$195$	−13.9384	−0.998149
$196$	5.63562	0.402545
$197$	−5.31216	−0.378476	−0.189238	−	0.981931i	$-0.560602\pi$
$197$	−5.31216	−0.378476	−0.189238	+	0.981931i	$0.560602\pi$
$198$	−10.3382	−0.734704
$199$	20.9254	1.48336	0.741682	−	0.670751i	$-0.234028\pi$
$199$	20.9254	1.48336	0.741682	+	0.670751i	$0.234028\pi$
$200$	−10.0462	−0.710373
$201$	23.6610	1.66892
$202$	22.2172	1.56320
$203$	2.36541	0.166019
$204$	126.152	8.83243
$205$	1.14332	0.0798528
$206$	15.6120	1.08774
$207$	−31.6134	−2.19728
$208$	−75.8198	−5.25716
$209$	−0.422112	−0.0291981
$210$	−8.37621	−0.578013
$211$	−17.8823	−1.23107	−0.615534	−	0.788110i	$-0.711060\pi$
$211$	−17.8823	−1.23107	−0.615534	+	0.788110i	$0.711060\pi$
$212$	−70.2341	−4.82369
$213$	23.6958	1.62361
$214$	24.1658	1.65194
$215$	−3.53783	−0.241278
$216$	−97.1021	−6.60696
$217$	8.12219	0.551370
$218$	32.3456	2.19072
$219$	−10.7430	−0.725942
$220$	3.40699	0.229700
$221$	−33.9559	−2.28412
$222$	−48.2762	−3.24009
$223$	−3.17994	−0.212944	−0.106472	−	0.994316i	$-0.533955\pi$
$223$	−3.17994	−0.212944	−0.106472	+	0.994316i	$0.533955\pi$
$224$	−25.4711	−1.70186
$225$	6.18862	0.412574
$226$	33.6407	2.23774
$227$	−13.4163	−0.890474	−0.445237	−	0.895413i	$-0.646880\pi$
$227$	−13.4163	−0.890474	−0.445237	+	0.895413i	$0.646880\pi$
$228$	−11.9279	−0.789947
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	14.1156	0.930757
$231$	1.83254	0.120573
$232$	−23.7634	−1.56014
$233$	−16.7949	−1.10027	−0.550136	−	0.835075i	$-0.685424\pi$
$233$	−16.7949	−1.10027	−0.550136	+	0.835075i	$0.685424\pi$
$234$	78.6328	5.14039
$235$	5.14899	0.335883
$236$	32.2303	2.09802
$237$	40.8169	2.65134
$238$	−20.4056	−1.32270
$239$	−11.9165	−0.770816	−0.385408	−	0.922746i	$-0.625939\pi$
$239$	−11.9165	−0.770816	−0.385408	+	0.922746i	$0.625939\pi$
$240$	49.9827	3.22637
$241$	20.0909	1.29417	0.647084	−	0.762418i	$-0.275988\pi$
$241$	20.0909	1.29417	0.647084	+	0.762418i	$0.275988\pi$
$242$	29.3860	1.88900
$243$	3.53831	0.226982
$244$	7.77042	0.497450
$245$	1.00000	0.0638877
$246$	−9.57667	−0.610586
$247$	3.21060	0.204285
$248$	−81.5971	−5.18142
$249$	31.5637	2.00027
$250$	−2.76326	−0.174764
$251$	−12.9876	−0.819768	−0.409884	−	0.912138i	$-0.634431\pi$
$251$	−12.9876	−0.819768	−0.409884	+	0.912138i	$0.634431\pi$
$252$	34.8767	2.19703
$253$	−3.08821	−0.194154
$254$	−21.6298	−1.35717
$255$	22.3848	1.40179
$256$	70.0359	4.37724
$257$	21.3437	1.33139	0.665693	−	0.746226i	$-0.268136\pi$
$257$	21.3437	1.33139	0.665693	+	0.746226i	$0.268136\pi$
$258$	29.6336	1.84491
$259$	5.76350	0.358126
$260$	−25.9137	−1.60710
$261$	14.6386	0.906108
$262$	0.963733	0.0595396
$263$	−8.43909	−0.520377	−0.260188	−	0.965558i	$-0.583785\pi$
$263$	−8.43909	−0.520377	−0.260188	+	0.965558i	$0.583785\pi$
$264$	−18.4101	−1.13306
$265$	−12.4625	−0.765566
$266$	1.92939	0.118299
$267$	−28.8968	−1.76845
$268$	43.9896	2.68709
$269$	27.3040	1.66475	0.832376	−	0.554211i	$-0.186980\pi$
$269$	27.3040	1.66475	0.832376	+	0.554211i	$0.186980\pi$
$270$	−26.7085	−1.62543
$271$	15.4972	0.941387	0.470693	−	0.882297i	$-0.344004\pi$
$271$	15.4972	0.941387	0.470693	+	0.882297i	$0.344004\pi$
$272$	121.765	7.38309
$273$	−13.9384	−0.843590
$274$	19.9693	1.20639
$275$	0.604546	0.0364555
$276$	−87.2660	−5.25280
$277$	15.7414	0.945806	0.472903	−	0.881114i	$-0.343206\pi$
$277$	15.7414	0.945806	0.472903	+	0.881114i	$0.343206\pi$
$278$	−28.4781	−1.70800
$279$	50.2651	3.00929
$280$	−10.0462	−0.600375
$281$	8.94010	0.533322	0.266661	−	0.963790i	$-0.414080\pi$
$281$	8.94010	0.533322	0.266661	+	0.963790i	$0.414080\pi$
$282$	−43.1290	−2.56829
$283$	−7.38504	−0.438995	−0.219497	−	0.975613i	$-0.570442\pi$
$283$	−7.38504	−0.438995	−0.219497	+	0.975613i	$0.570442\pi$
$284$	44.0543	2.61414
$285$	−2.11652	−0.125372
$286$	7.68138	0.454210
$287$	1.14332	0.0674879
$288$	−157.631	−9.28849
$289$	37.5326	2.20780
$290$	−6.53626	−0.383822
$291$	43.3548	2.54150
$292$	−19.9729	−1.16883
$293$	8.32979	0.486632	0.243316	−	0.969947i	$-0.421765\pi$
$293$	8.32979	0.486632	0.243316	+	0.969947i	$0.421765\pi$
$294$	−8.37621	−0.488510
$295$	5.71904	0.332975
$296$	−57.9012	−3.36544
$297$	5.84328	0.339061
$298$	19.8903	1.15221
$299$	23.4891	1.35841
$300$	17.0831	0.986294
$301$	−3.53783	−0.203917
$302$	46.4880	2.67508
$303$	−24.3720	−1.40014
$304$	−11.5131	−0.660323
$305$	1.37880	0.0789501
$306$	−126.283	−7.21910
$307$	26.6433	1.52061	0.760307	−	0.649564i	$-0.225049\pi$
$307$	26.6433	1.52061	0.760307	+	0.649564i	$0.225049\pi$
$308$	3.40699	0.194132
$309$	−17.1262	−0.974275
$310$	−22.4438	−1.27472
$311$	27.5599	1.56278	0.781388	−	0.624045i	$-0.214512\pi$
$311$	27.5599	1.56278	0.781388	+	0.624045i	$0.214512\pi$
$312$	140.028	7.92751
$313$	17.3834	0.982571	0.491285	−	0.870999i	$-0.336527\pi$
$313$	17.3834	0.982571	0.491285	+	0.870999i	$0.336527\pi$
$314$	45.4636	2.56566
$315$	6.18862	0.348689
$316$	75.8851	4.26887
$317$	4.90688	0.275598	0.137799	−	0.990460i	$-0.455997\pi$
$317$	4.90688	0.275598	0.137799	+	0.990460i	$0.455997\pi$
$318$	104.389	5.85382
$319$	1.43000	0.0800647
$320$	37.4054	2.09102
$321$	−26.5096	−1.47962
$322$	14.1156	0.786633
$323$	−5.15616	−0.286896
$324$	60.4878	3.36043
$325$	−4.59820	−0.255062
$326$	−39.1600	−2.16887
$327$	−35.4828	−1.96220
$328$	−11.4860	−0.634208
$329$	5.14899	0.283873
$330$	−5.06380	−0.278753
$331$	12.0226	0.660822	0.330411	−	0.943837i	$-0.392813\pi$
$331$	12.0226	0.660822	0.330411	+	0.943837i	$0.392813\pi$
$332$	58.6820	3.22059
$333$	35.6681	1.95460
$334$	−42.8110	−2.34252
$335$	7.80564	0.426467
$336$	49.9827	2.72678
$337$	−7.04635	−0.383839	−0.191920	−	0.981411i	$-0.561471\pi$
$337$	−7.04635	−0.383839	−0.191920	+	0.981411i	$0.561471\pi$
$338$	−22.5025	−1.22397
$339$	−36.9035	−2.00432
$340$	41.6169	2.25700
$341$	4.91024	0.265904
$342$	11.9403	0.645655
$343$	1.00000	0.0539949
$344$	35.5417	1.91628
$345$	−15.4847	−0.833669
$346$	53.4803	2.87512
$347$	30.9268	1.66024	0.830120	−	0.557585i	$-0.188272\pi$
$347$	30.9268	1.66024	0.830120	+	0.557585i	$0.188272\pi$
$348$	40.4086	2.16613
$349$	7.60816	0.407256	0.203628	−	0.979048i	$-0.434727\pi$
$349$	7.60816	0.407256	0.203628	+	0.979048i	$0.434727\pi$
$350$	−2.76326	−0.147703
$351$	−44.4442	−2.37226
$352$	−15.3985	−0.820741
$353$	8.45196	0.449852	0.224926	−	0.974376i	$-0.427786\pi$
$353$	8.45196	0.449852	0.224926	+	0.974376i	$0.427786\pi$
$354$	−47.9038	−2.54606
$355$	7.81712	0.414890
$356$	−53.7237	−2.84735
$357$	22.3848	1.18473
$358$	−39.8943	−2.10848
$359$	12.7087	0.670740	0.335370	−	0.942087i	$-0.391139\pi$
$359$	12.7087	0.670740	0.335370	+	0.942087i	$0.391139\pi$
$360$	−62.1720	−3.27675
$361$	−18.5125	−0.974341
$362$	−69.0467	−3.62902
$363$	−32.2361	−1.69196
$364$	−25.9137	−1.35825
$365$	−3.54404	−0.185504
$366$	−11.5491	−0.603684
$367$	−36.8623	−1.92420	−0.962099	−	0.272700i	$-0.912083\pi$
$367$	−36.8623	−1.92420	−0.962099	+	0.272700i	$0.912083\pi$
$368$	−84.2312	−4.39085
$369$	7.07556	0.368339
$370$	−15.9261	−0.827956
$371$	−12.4625	−0.647021
$372$	138.752	7.19398
$373$	−27.1832	−1.40749	−0.703746	−	0.710451i	$-0.748491\pi$
$373$	−27.1832	−1.40749	−0.703746	+	0.710451i	$0.748491\pi$
$374$	−12.3362	−0.637887
$375$	3.03127	0.156534
$376$	−51.7277	−2.66765
$377$	−10.8766	−0.560175
$378$	−26.7085	−1.37374
$379$	9.04852	0.464791	0.232396	−	0.972621i	$-0.425344\pi$
$379$	9.04852	0.464791	0.232396	+	0.972621i	$0.425344\pi$
$380$	−3.93496	−0.201859
$381$	23.7277	1.21561
$382$	−17.0121	−0.870416
$383$	9.55973	0.488479	0.244240	−	0.969715i	$-0.421462\pi$
$383$	9.55973	0.488479	0.244240	+	0.969715i	$0.421462\pi$
$384$	−158.895	−8.10859
$385$	0.604546	0.0308105
$386$	−18.1905	−0.925872
$387$	−21.8942	−1.11295
$388$	80.6035	4.09202
$389$	−25.5098	−1.29340	−0.646699	−	0.762745i	$-0.723851\pi$
$389$	−25.5098	−1.29340	−0.646699	+	0.762745i	$0.723851\pi$
$390$	38.5155	1.95031
$391$	−37.7230	−1.90773
$392$	−10.0462	−0.507409
$393$	−1.05721	−0.0533290
$394$	14.6789	0.739512
$395$	13.4653	0.677511
$396$	21.0846	1.05954
$397$	31.0943	1.56058	0.780290	−	0.625418i	$-0.215071\pi$
$397$	31.0943	1.56058	0.780290	+	0.625418i	$0.215071\pi$
$398$	−57.8225	−2.89838
$399$	−2.11652	−0.105959
$400$	16.4890	0.824451
$401$	−2.21720	−0.110722	−0.0553609	−	0.998466i	$-0.517631\pi$
$401$	−2.21720	−0.110722	−0.0553609	+	0.998466i	$0.517631\pi$
$402$	−65.3816	−3.26094
$403$	−37.3475	−1.86041
$404$	−45.3116	−2.25433
$405$	10.7331	0.533333
$406$	−6.53626	−0.324389
$407$	3.48430	0.172710
$408$	−224.882	−11.1333
$409$	32.5136	1.60770	0.803848	−	0.594834i	$-0.202782\pi$
$409$	32.5136	1.60770	0.803848	+	0.594834i	$0.202782\pi$
$410$	−3.15929	−0.156026
$411$	−21.9061	−1.08055
$412$	−31.8404	−1.56866
$413$	5.71904	0.281415
$414$	87.3562	4.29332
$415$	10.4127	0.511139
$416$	117.121	5.74234
$417$	31.2402	1.52984
$418$	1.16641	0.0570508
$419$	−27.9395	−1.36493	−0.682466	−	0.730917i	$-0.739092\pi$
$419$	−27.9395	−1.36493	−0.682466	+	0.730917i	$0.739092\pi$
$420$	17.0831	0.833571
$421$	21.0911	1.02792	0.513958	−	0.857815i	$-0.328179\pi$
$421$	21.0911	1.02792	0.513958	+	0.857815i	$0.328179\pi$
$422$	49.4135	2.40541
$423$	31.8651	1.54933
$424$	125.201	6.08029
$425$	7.38462	0.358207
$426$	−65.4778	−3.17241
$427$	1.37880	0.0667250
$428$	−49.2856	−2.38231
$429$	−8.42640	−0.406831
$430$	9.77595	0.471438
$431$	−27.9233	−1.34502	−0.672510	−	0.740088i	$-0.734784\pi$
$431$	−27.9233	−1.34502	−0.672510	+	0.740088i	$0.734784\pi$
$432$	159.376	7.66796
$433$	3.12073	0.149973	0.0749864	−	0.997185i	$-0.476109\pi$
$433$	3.12073	0.149973	0.0749864	+	0.997185i	$0.476109\pi$
$434$	−22.4438	−1.07733
$435$	7.17021	0.343785
$436$	−65.9682	−3.15930
$437$	3.56678	0.170622
$438$	29.6856	1.41844
$439$	−29.2869	−1.39779	−0.698894	−	0.715225i	$-0.746324\pi$
$439$	−29.2869	−1.39779	−0.698894	+	0.715225i	$0.746324\pi$
$440$	−6.07338	−0.289537
$441$	6.18862	0.294696
$442$	93.8292	4.46300
$443$	24.7197	1.17447	0.587233	−	0.809418i	$-0.300217\pi$
$443$	24.7197	1.17447	0.587233	+	0.809418i	$0.300217\pi$
$444$	98.4585	4.67263
$445$	−9.53288	−0.451902
$446$	8.78700	0.416077
$447$	−21.8195	−1.03203
$448$	37.4054	1.76724
$449$	−4.07783	−0.192445	−0.0962223	−	0.995360i	$-0.530676\pi$
$449$	−4.07783	−0.192445	−0.0962223	+	0.995360i	$0.530676\pi$
$450$	−17.1008	−0.806138
$451$	0.691188	0.0325468
$452$	−68.6095	−3.22712
$453$	−50.9969	−2.39604
$454$	37.0729	1.73992
$455$	−4.59820	−0.215567
$456$	21.2630	0.995731
$457$	−21.6644	−1.01342	−0.506709	−	0.862117i	$-0.669138\pi$
$457$	−21.6644	−1.01342	−0.506709	+	0.862117i	$0.669138\pi$
$458$	−2.76326	−0.129119
$459$	71.3765	3.33157
$460$	−28.7886	−1.34227
$461$	−40.4903	−1.88582	−0.942910	−	0.333047i	$-0.891923\pi$
$461$	−40.4903	−1.88582	−0.942910	+	0.333047i	$0.891923\pi$
$462$	−5.06380	−0.235589
$463$	21.4774	0.998140	0.499070	−	0.866562i	$-0.333675\pi$
$463$	21.4774	0.998140	0.499070	+	0.866562i	$0.333675\pi$
$464$	39.0033	1.81068
$465$	24.6206	1.14175
$466$	46.4088	2.14985
$467$	−42.0796	−1.94721	−0.973606	−	0.228236i	$-0.926704\pi$
$467$	−42.0796	−1.94721	−0.973606	+	0.228236i	$0.926704\pi$
$468$	−160.370	−7.41311
$469$	7.80564	0.360431
$470$	−14.2280	−0.656289
$471$	−49.8732	−2.29803
$472$	−57.4545	−2.64456
$473$	−2.13878	−0.0983412
$474$	−112.788	−5.18051
$475$	−0.698229	−0.0320370
$476$	41.6169	1.90751
$477$	−77.1257	−3.53134
$478$	32.9285	1.50612
$479$	−24.6188	−1.12486	−0.562432	−	0.826844i	$-0.690134\pi$
$479$	−24.6188	−1.12486	−0.562432	+	0.826844i	$0.690134\pi$
$480$	−77.2099	−3.52413
$481$	−26.5017	−1.20837
$482$	−55.5164	−2.52870
$483$	−15.4847	−0.704579
$484$	−59.9322	−2.72419
$485$	14.3025	0.649443
$486$	−9.77727	−0.443506
$487$	−22.6328	−1.02559	−0.512794	−	0.858512i	$-0.671390\pi$
$487$	−22.6328	−1.02559	−0.512794	+	0.858512i	$0.671390\pi$
$488$	−13.8517	−0.627038
$489$	42.9581	1.94263
$490$	−2.76326	−0.124832
$491$	−0.788358	−0.0355781	−0.0177890	−	0.999842i	$-0.505663\pi$
$491$	−0.788358	−0.0355781	−0.0177890	+	0.999842i	$0.505663\pi$
$492$	19.5314	0.880545
$493$	17.4677	0.786704
$494$	−8.87173	−0.399158
$495$	3.74130	0.168159
$496$	133.927	6.01350
$497$	7.81712	0.350646
$498$	−87.2188	−3.90837
$499$	0.0729536	0.00326585	0.00163293	−	0.999999i	$-0.499480\pi$
$499$	0.0729536	0.00326585	0.00163293	+	0.999999i	$0.499480\pi$
$500$	5.63562	0.252033
$501$	46.9633	2.09817
$502$	35.8881	1.60176
$503$	−9.13274	−0.407209	−0.203604	−	0.979053i	$-0.565266\pi$
$503$	−9.13274	−0.407209	−0.203604	+	0.979053i	$0.565266\pi$
$504$	−62.1720	−2.76936
$505$	−8.04020	−0.357784
$506$	8.53355	0.379362
$507$	24.6850	1.09630
$508$	44.1136	1.95722
$509$	4.59319	0.203590	0.101795	−	0.994805i	$-0.467541\pi$
$509$	4.59319	0.203590	0.101795	+	0.994805i	$0.467541\pi$
$510$	−61.8551	−2.73899
$511$	−3.54404	−0.156779
$512$	−88.6902	−3.91959
$513$	−6.74878	−0.297966
$514$	−58.9784	−2.60143
$515$	−5.64984	−0.248962
$516$	−60.4371	−2.66060
$517$	3.11280	0.136901
$518$	−15.9261	−0.699751
$519$	−58.6673	−2.57521
$520$	46.1944	2.02576
$521$	−15.0237	−0.658200	−0.329100	−	0.944295i	$-0.606745\pi$
$521$	−15.0237	−0.658200	−0.329100	+	0.944295i	$0.606745\pi$
$522$	−40.4504	−1.77047
$523$	34.5781	1.51200	0.755998	−	0.654574i	$-0.227152\pi$
$523$	34.5781	1.51200	0.755998	+	0.654574i	$0.227152\pi$
$524$	−1.96552	−0.0858640
$525$	3.03127	0.132296
$526$	23.3194	1.01678
$527$	59.9793	2.61274
$528$	30.2169	1.31502
$529$	3.09492	0.134562
$530$	34.4372	1.49586
$531$	35.3929	1.53592
$532$	−3.93496	−0.170602
$533$	−5.25720	−0.227715
$534$	79.8494	3.45542
$535$	−8.74537	−0.378095
$536$	−78.4169	−3.38709
$537$	43.7637	1.88854
$538$	−75.4481	−3.25280
$539$	0.604546	0.0260396
$540$	54.4715	2.34408
$541$	−6.98639	−0.300368	−0.150184	−	0.988658i	$-0.547987\pi$
$541$	−6.98639	−0.300368	−0.150184	+	0.988658i	$0.547987\pi$
$542$	−42.8228	−1.83940
$543$	75.7436	3.25047
$544$	−188.095	−8.06449
$545$	−11.7056	−0.501411
$546$	38.5155	1.64831
$547$	17.2283	0.736629	0.368315	−	0.929701i	$-0.379935\pi$
$547$	17.2283	0.736629	0.368315	+	0.929701i	$0.379935\pi$
$548$	−40.7269	−1.73977
$549$	8.53289	0.364175
$550$	−1.67052	−0.0712312
$551$	−1.65160	−0.0703605
$552$	155.562	6.62117
$553$	13.4653	0.572601
$554$	−43.4975	−1.84803
$555$	17.4707	0.741591
$556$	58.0806	2.46317
$557$	−35.5282	−1.50538	−0.752690	−	0.658375i	$-0.771244\pi$
$557$	−35.5282	−1.50538	−0.752690	+	0.658375i	$0.771244\pi$
$558$	−138.896	−5.87993
$559$	16.2676	0.688048
$560$	16.4890	0.696788
$561$	13.5326	0.571348
$562$	−24.7039	−1.04207
$563$	12.7410	0.536969	0.268484	−	0.963284i	$-0.413477\pi$
$563$	12.7410	0.536969	0.268484	+	0.963284i	$0.413477\pi$
$564$	87.9607	3.70381
$565$	−12.1743	−0.512175
$566$	20.4068	0.857762
$567$	10.7331	0.450748
$568$	−78.5322	−3.29514
$569$	32.4830	1.36176	0.680879	−	0.732396i	$-0.261598\pi$
$569$	32.4830	1.36176	0.680879	+	0.732396i	$0.261598\pi$
$570$	5.84851	0.244967
$571$	19.9633	0.835440	0.417720	−	0.908576i	$-0.362829\pi$
$571$	19.9633	0.835440	0.417720	+	0.908576i	$0.362829\pi$
$572$	−15.6660	−0.655030
$573$	18.6621	0.779622
$574$	−3.15929	−0.131866
$575$	−5.10832	−0.213032
$576$	231.488	9.64531
$577$	−14.3133	−0.595871	−0.297936	−	0.954586i	$-0.596298\pi$
$577$	−14.3133	−0.595871	−0.297936	+	0.954586i	$0.596298\pi$
$578$	−103.712	−4.31387
$579$	19.9548	0.829293
$580$	13.3306	0.553522
$581$	10.4127	0.431991
$582$	−119.801	−4.96590
$583$	−7.53416	−0.312033
$584$	35.6041	1.47331
$585$	−28.4565	−1.17653
$586$	−23.0174	−0.950840
$587$	38.9266	1.60667	0.803337	−	0.595525i	$-0.203056\pi$
$587$	38.9266	1.60667	0.803337	+	0.595525i	$0.203056\pi$
$588$	17.0831	0.704496
$589$	−5.67115	−0.233676
$590$	−15.8032	−0.650608
$591$	−16.1026	−0.662373
$592$	95.0344	3.90589
$593$	24.0952	0.989471	0.494736	−	0.869044i	$-0.335265\pi$
$593$	24.0952	0.989471	0.494736	+	0.869044i	$0.335265\pi$
$594$	−16.1465	−0.662500
$595$	7.38462	0.302740
$596$	−40.5659	−1.66164
$597$	63.4307	2.59605
$598$	−64.9065	−2.65422
$599$	−33.3193	−1.36139	−0.680694	−	0.732568i	$-0.738322\pi$
$599$	−33.3193	−1.36139	−0.680694	+	0.732568i	$0.738322\pi$
$600$	−30.4527	−1.24323
$601$	28.9048	1.17905	0.589525	−	0.807750i	$-0.299315\pi$
$601$	28.9048	1.17905	0.589525	+	0.807750i	$0.299315\pi$
$602$	9.77595	0.398438
$603$	48.3061	1.96718
$604$	−94.8114	−3.85782
$605$	−10.6345	−0.432355
$606$	67.3464	2.73576
$607$	13.7828	0.559425	0.279712	−	0.960084i	$-0.409761\pi$
$607$	13.7828	0.559425	0.279712	+	0.960084i	$0.409761\pi$
$608$	17.7847	0.721264
$609$	7.17021	0.290552
$610$	−3.81000	−0.154262
$611$	−23.6761	−0.957831
$612$	257.551	10.4109
$613$	−11.9239	−0.481602	−0.240801	−	0.970574i	$-0.577410\pi$
$613$	−11.9239	−0.481602	−0.240801	+	0.970574i	$0.577410\pi$
$614$	−73.6225	−2.97116
$615$	3.46571	0.139751
$616$	−6.07338	−0.244704
$617$	−26.3245	−1.05978	−0.529892	−	0.848065i	$-0.677768\pi$
$617$	−26.3245	−1.05978	−0.529892	+	0.848065i	$0.677768\pi$
$618$	47.3242	1.90366
$619$	−38.6964	−1.55534	−0.777669	−	0.628673i	$-0.783598\pi$
$619$	−38.6964	−1.55534	−0.777669	+	0.628673i	$0.783598\pi$
$620$	45.7736	1.83831
$621$	−49.3748	−1.98134
$622$	−76.1552	−3.05354
$623$	−9.53288	−0.381927
$624$	−229.830	−9.20058
$625$	1.00000	0.0400000
$626$	−48.0350	−1.91987
$627$	−1.27954	−0.0510997
$628$	−92.7222	−3.70002
$629$	42.5612	1.69703
$630$	−17.1008	−0.681311
$631$	9.76803	0.388859	0.194430	−	0.980916i	$-0.437714\pi$
$631$	9.76803	0.388859	0.194430	+	0.980916i	$0.437714\pi$
$632$	−135.275	−5.38093
$633$	−54.2061	−2.15450
$634$	−13.5590	−0.538496
$635$	7.82763	0.310630
$636$	−212.899	−8.44198
$637$	−4.59820	−0.182187
$638$	−3.95147	−0.156440
$639$	48.3771	1.91377
$640$	−52.4187	−2.07203
$641$	−40.7039	−1.60771	−0.803853	−	0.594828i	$-0.797220\pi$
$641$	−40.7039	−1.60771	−0.803853	+	0.594828i	$0.797220\pi$
$642$	73.2530	2.89107
$643$	37.0714	1.46195	0.730976	−	0.682403i	$-0.239065\pi$
$643$	37.0714	1.46195	0.730976	+	0.682403i	$0.239065\pi$
$644$	−28.7886	−1.13443
$645$	−10.7241	−0.422262
$646$	14.2478	0.560573
$647$	−32.5252	−1.27870	−0.639349	−	0.768917i	$-0.720796\pi$
$647$	−32.5252	−1.27870	−0.639349	+	0.768917i	$0.720796\pi$
$648$	−107.827	−4.23584
$649$	3.45742	0.135716
$650$	12.7060	0.498372
$651$	24.6206	0.964957
$652$	79.8661	3.12780
$653$	−40.0501	−1.56728	−0.783641	−	0.621214i	$-0.786640\pi$
$653$	−40.0501	−1.56728	−0.783641	+	0.621214i	$0.786640\pi$
$654$	98.0483	3.83399
$655$	−0.348766	−0.0136274
$656$	18.8522	0.736054
$657$	−21.9327	−0.855677
$658$	−14.2280	−0.554665
$659$	26.8135	1.04450	0.522252	−	0.852791i	$-0.325092\pi$
$659$	26.8135	1.04450	0.522252	+	0.852791i	$0.325092\pi$
$660$	10.3275	0.401999
$661$	19.8049	0.770323	0.385161	−	0.922849i	$-0.374146\pi$
$661$	19.8049	0.770323	0.385161	+	0.922849i	$0.374146\pi$
$662$	−33.2216	−1.29119
$663$	−102.930	−3.99746
$664$	−104.608	−4.05957
$665$	−0.698229	−0.0270762
$666$	−98.5602	−3.81913
$667$	−12.0833	−0.467866
$668$	87.3123	3.37822
$669$	−9.63925	−0.372675
$670$	−21.5690	−0.833284
$671$	0.833551	0.0321789
$672$	−77.2099	−2.97844
$673$	24.1343	0.930310	0.465155	−	0.885229i	$-0.345999\pi$
$673$	24.1343	0.930310	0.465155	+	0.885229i	$0.345999\pi$
$674$	19.4709	0.749992
$675$	9.66556	0.372028
$676$	45.8934	1.76513
$677$	−33.3404	−1.28138	−0.640688	−	0.767801i	$-0.721351\pi$
$677$	−33.3404	−1.28138	−0.640688	+	0.767801i	$0.721351\pi$
$678$	101.974	3.91629
$679$	14.3025	0.548879
$680$	−74.1873	−2.84495
$681$	−40.6686	−1.55842
$682$	−13.5683	−0.519556
$683$	−34.4286	−1.31737	−0.658687	−	0.752417i	$-0.728888\pi$
$683$	−34.4286	−1.31737	−0.658687	+	0.752417i	$0.728888\pi$
$684$	−24.3519	−0.931120
$685$	−7.22669	−0.276118
$686$	−2.76326	−0.105502
$687$	3.03127	0.115650
$688$	−58.3353	−2.22401
$689$	57.3051	2.18315
$690$	42.7883	1.62892
$691$	−20.5014	−0.779909	−0.389954	−	0.920834i	$-0.627509\pi$
$691$	−20.5014	−0.779909	−0.389954	+	0.920834i	$0.627509\pi$
$692$	−109.072	−4.14630
$693$	3.74130	0.142120
$694$	−85.4590	−3.24398
$695$	10.3060	0.390928
$696$	−72.0333	−2.73041
$697$	8.44297	0.319800
$698$	−21.0234	−0.795746
$699$	−50.9100	−1.92559
$700$	5.63562	0.213007
$701$	17.8896	0.675680	0.337840	−	0.941204i	$-0.390304\pi$
$701$	17.8896	0.675680	0.337840	+	0.941204i	$0.390304\pi$
$702$	122.811	4.63520
$703$	−4.02424	−0.151777
$704$	22.6133	0.852270
$705$	15.6080	0.587831
$706$	−23.3550	−0.878976
$707$	−8.04020	−0.302383
$708$	97.6990	3.67175
$709$	2.90442	0.109078	0.0545389	−	0.998512i	$-0.482631\pi$
$709$	2.90442	0.109078	0.0545389	+	0.998512i	$0.482631\pi$
$710$	−21.6008	−0.810662
$711$	83.3313	3.12517
$712$	95.7691	3.58910
$713$	−41.4907	−1.55384
$714$	−61.8551	−2.31487
$715$	−2.77982	−0.103959
$716$	81.3637	3.04071
$717$	−36.1223	−1.34901
$718$	−35.1175	−1.31057
$719$	−1.47523	−0.0550166	−0.0275083	−	0.999622i	$-0.508757\pi$
$719$	−1.47523	−0.0550166	−0.0275083	+	0.999622i	$0.508757\pi$
$720$	102.044	3.80296
$721$	−5.64984	−0.210411
$722$	51.1548	1.90379
$723$	60.9010	2.26493
$724$	140.820	5.23352
$725$	2.36541	0.0878492
$726$	89.0770	3.30596
$727$	7.31796	0.271408	0.135704	−	0.990749i	$-0.456670\pi$
$727$	7.31796	0.271408	0.135704	+	0.990749i	$0.456670\pi$
$728$	46.1944	1.71208
$729$	−21.4738	−0.795325
$730$	9.79313	0.362460
$731$	−26.1255	−0.966287
$732$	23.5543	0.870591
$733$	−35.1647	−1.29884	−0.649418	−	0.760431i	$-0.724988\pi$
$733$	−35.1647	−1.29884	−0.649418	+	0.760431i	$0.724988\pi$
$734$	101.860	3.75973
$735$	3.03127	0.111810
$736$	130.115	4.79609
$737$	4.71887	0.173822
$738$	−19.5516	−0.719705
$739$	−41.7609	−1.53620	−0.768100	−	0.640330i	$-0.778798\pi$
$739$	−41.7609	−1.53620	−0.768100	+	0.640330i	$0.778798\pi$
$740$	32.4809	1.19402
$741$	9.73220	0.357521
$742$	34.4372	1.26423
$743$	−47.3486	−1.73705	−0.868527	−	0.495643i	$-0.834933\pi$
$743$	−47.3486	−1.73705	−0.868527	+	0.495643i	$0.834933\pi$
$744$	−247.343	−9.06804
$745$	−7.19812	−0.263719
$746$	75.1144	2.75013
$747$	64.4401	2.35774
$748$	25.1594	0.919917
$749$	−8.74537	−0.319549
$750$	−8.37621	−0.305856
$751$	6.90912	0.252117	0.126059	−	0.992023i	$-0.459767\pi$
$751$	6.90912	0.252117	0.126059	+	0.992023i	$0.459767\pi$
$752$	84.9017	3.09605
$753$	−39.3689	−1.43468
$754$	30.0550	1.09454
$755$	−16.8236	−0.612273
$756$	54.4715	1.98111
$757$	−0.847804	−0.0308140	−0.0154070	−	0.999881i	$-0.504904\pi$
$757$	−0.847804	−0.0308140	−0.0154070	+	0.999881i	$0.504904\pi$
$758$	−25.0035	−0.908166
$759$	−9.36122	−0.339791
$760$	7.01454	0.254444
$761$	9.43953	0.342183	0.171091	−	0.985255i	$-0.445271\pi$
$761$	9.43953	0.342183	0.171091	+	0.985255i	$0.445271\pi$
$762$	−65.5658	−2.37520
$763$	−11.7056	−0.423770
$764$	34.6959	1.25525
$765$	45.7006	1.65231
$766$	−26.4161	−0.954451
$767$	−26.2973	−0.949540
$768$	212.298	7.66064
$769$	32.5775	1.17477	0.587387	−	0.809306i	$-0.300157\pi$
$769$	32.5775	1.17477	0.587387	+	0.809306i	$0.300157\pi$
$770$	−1.67052	−0.0602014
$771$	64.6987	2.33007
$772$	37.0992	1.33523
$773$	−0.780394	−0.0280688	−0.0140344	−	0.999902i	$-0.504467\pi$
$773$	−0.780394	−0.0280688	−0.0140344	+	0.999902i	$0.504467\pi$
$774$	60.4996	2.17461
$775$	8.12219	0.291758
$776$	−143.686	−5.15801
$777$	17.4707	0.626759
$778$	70.4903	2.52720
$779$	−0.798298	−0.0286020
$780$	−78.5516	−2.81260
$781$	4.72581	0.169103
$782$	104.239	3.72756
$783$	22.8630	0.817059
$784$	16.4890	0.588894
$785$	−16.4529	−0.587228
$786$	2.92134	0.104201
$787$	−38.1403	−1.35956	−0.679778	−	0.733418i	$-0.737924\pi$
$787$	−38.1403	−1.35956	−0.679778	+	0.733418i	$0.737924\pi$
$788$	−29.9373	−1.06647
$789$	−25.5812	−0.910715
$790$	−37.2080	−1.32380
$791$	−12.1743	−0.432867
$792$	−37.5858	−1.33555
$793$	−6.34002	−0.225141
$794$	−85.9219	−3.04925
$795$	−37.7773	−1.33982
$796$	117.928	4.17984
$797$	5.86572	0.207775	0.103887	−	0.994589i	$-0.466872\pi$
$797$	5.86572	0.207775	0.103887	+	0.994589i	$0.466872\pi$
$798$	5.84851	0.207035
$799$	38.0233	1.34517
$800$	−25.4711	−0.900540
$801$	−58.9953	−2.08450
$802$	6.12672	0.216342
$803$	−2.14254	−0.0756085
$804$	133.345	4.70270
$805$	−5.10832	−0.180045
$806$	103.201	3.63510
$807$	82.7658	2.91349
$808$	80.7734	2.84160
$809$	42.4635	1.49294	0.746469	−	0.665421i	$-0.231748\pi$
$809$	42.4635	1.49294	0.746469	+	0.665421i	$0.231748\pi$
$810$	−29.6584	−1.04209
$811$	−1.27862	−0.0448985	−0.0224492	−	0.999748i	$-0.507146\pi$
$811$	−1.27862	−0.0448985	−0.0224492	+	0.999748i	$0.507146\pi$
$812$	13.3306	0.467812
$813$	46.9762	1.64753
$814$	−9.62803	−0.337462
$815$	14.1717	0.496411
$816$	369.103	12.9212
$817$	2.47021	0.0864219
$818$	−89.8438	−3.14131
$819$	−28.4565	−0.994350
$820$	6.44331	0.225010
$821$	34.5442	1.20560	0.602801	−	0.797891i	$-0.294051\pi$
$821$	34.5442	1.20560	0.602801	+	0.797891i	$0.294051\pi$
$822$	60.5323	2.11130
$823$	−9.47441	−0.330257	−0.165129	−	0.986272i	$-0.552804\pi$
$823$	−9.47441	−0.330257	−0.165129	+	0.986272i	$0.552804\pi$
$824$	56.7593	1.97731
$825$	1.83254	0.0638010
$826$	−15.8032	−0.549864
$827$	3.43332	0.119388	0.0596941	−	0.998217i	$-0.480987\pi$
$827$	3.43332	0.119388	0.0596941	+	0.998217i	$0.480987\pi$
$828$	−178.161	−6.19154
$829$	50.0690	1.73897	0.869484	−	0.493962i	$-0.164452\pi$
$829$	50.0690	1.73897	0.869484	+	0.493962i	$0.164452\pi$
$830$	−28.7730	−0.998725
$831$	47.7163	1.65526
$832$	−171.997	−5.96294
$833$	7.38462	0.255862
$834$	−86.3250	−2.98919
$835$	15.4929	0.536155
$836$	−2.37886	−0.0822747
$837$	78.5056	2.71355
$838$	77.2041	2.66697
$839$	−30.9610	−1.06889	−0.534445	−	0.845203i	$-0.679480\pi$
$839$	−30.9610	−1.06889	−0.534445	+	0.845203i	$0.679480\pi$
$840$	−30.4527	−1.05072
$841$	−23.4048	−0.807063
$842$	−58.2802	−2.00847
$843$	27.0999	0.933370
$844$	−100.778	−3.46892
$845$	8.14344	0.280143
$846$	−88.0516	−3.02728
$847$	−10.6345	−0.365407
$848$	−205.495	−7.05671
$849$	−22.3861	−0.768288
$850$	−20.4056	−0.699908
$851$	−29.4418	−1.00925
$852$	133.541	4.57503
$853$	−28.3404	−0.970356	−0.485178	−	0.874416i	$-0.661245\pi$
$853$	−28.3404	−0.970356	−0.485178	+	0.874416i	$0.661245\pi$
$854$	−3.81000	−0.130375
$855$	−4.32107	−0.147778
$856$	87.8577	3.00291
$857$	−41.9486	−1.43294	−0.716468	−	0.697620i	$-0.754242\pi$
$857$	−41.9486	−1.43294	−0.716468	+	0.697620i	$0.754242\pi$
$858$	23.2844	0.794915
$859$	21.1004	0.719935	0.359967	−	0.932965i	$-0.382788\pi$
$859$	21.1004	0.719935	0.359967	+	0.932965i	$0.382788\pi$
$860$	−19.9379	−0.679876
$861$	3.46571	0.118111
$862$	77.1596	2.62806
$863$	34.1021	1.16085	0.580425	−	0.814314i	$-0.302887\pi$
$863$	34.1021	1.16085	0.580425	+	0.814314i	$0.302887\pi$
$864$	−246.193	−8.37565
$865$	−19.3540	−0.658057
$866$	−8.62341	−0.293035
$867$	113.771	3.86388
$868$	45.7736	1.55366
$869$	8.14037	0.276143
$870$	−19.8132	−0.671730
$871$	−35.8919	−1.21615
$872$	117.596	3.98232
$873$	88.5126	2.99570
$874$	−9.85595	−0.333382
$875$	1.00000	0.0338062
$876$	−60.5433	−2.04557
$877$	−13.8235	−0.466786	−0.233393	−	0.972383i	$-0.574983\pi$
$877$	−13.8235	−0.466786	−0.233393	+	0.972383i	$0.574983\pi$
$878$	80.9275	2.73117
$879$	25.2499	0.851657
$880$	9.96837	0.336034
$881$	13.8058	0.465128	0.232564	−	0.972581i	$-0.425289\pi$
$881$	13.8058	0.465128	0.232564	+	0.972581i	$0.425289\pi$
$882$	−17.1008	−0.575813
$883$	−40.0709	−1.34849	−0.674247	−	0.738506i	$-0.735532\pi$
$883$	−40.0709	−1.34849	−0.674247	+	0.738506i	$0.735532\pi$
$884$	−191.363	−6.43623
$885$	17.3360	0.582742
$886$	−68.3069	−2.29482
$887$	−39.8547	−1.33819	−0.669095	−	0.743177i	$-0.733318\pi$
$887$	−39.8547	−1.33819	−0.669095	+	0.743177i	$0.733318\pi$
$888$	−175.514	−5.88987
$889$	7.82763	0.262530
$890$	26.3419	0.882981
$891$	6.48866	0.217378
$892$	−17.9209	−0.600037
$893$	−3.59517	−0.120308
$894$	60.2929	2.01650
$895$	14.4374	0.482589
$896$	−52.4187	−1.75119
$897$	71.2018	2.37736
$898$	11.2681	0.376022
$899$	19.2123	0.640767
$900$	34.8767	1.16256
$901$	−92.0309	−3.06599
$902$	−1.90994	−0.0635939
$903$	−10.7241	−0.356876
$904$	122.305	4.06780
$905$	24.9874	0.830609
$906$	140.918	4.68168
$907$	−33.4081	−1.10930	−0.554650	−	0.832084i	$-0.687148\pi$
$907$	−33.4081	−1.10930	−0.554650	+	0.832084i	$0.687148\pi$
$908$	−75.6094	−2.50919
$909$	−49.7577	−1.65036
$910$	12.7060	0.421201
$911$	27.2508	0.902859	0.451430	−	0.892307i	$-0.350914\pi$
$911$	27.2508	0.902859	0.451430	+	0.892307i	$0.350914\pi$
$912$	−34.8994	−1.15563
$913$	6.29495	0.208332
$914$	59.8645	1.98014
$915$	4.17953	0.138171
$916$	5.63562	0.186206
$917$	−0.348766	−0.0115173
$918$	−197.232	−6.50963
$919$	−35.2017	−1.16120	−0.580599	−	0.814190i	$-0.697181\pi$
$919$	−35.2017	−1.16120	−0.580599	+	0.814190i	$0.697181\pi$
$920$	51.3191	1.69194
$921$	80.7631	2.66124
$922$	111.885	3.68475
$923$	−35.9447	−1.18313
$924$	10.3275	0.339751
$925$	5.76350	0.189503
$926$	−59.3478	−1.95029
$927$	−34.9647	−1.14839
$928$	−60.2497	−1.97779
$929$	23.9838	0.786883	0.393441	−	0.919350i	$-0.371284\pi$
$929$	23.9838	0.786883	0.393441	+	0.919350i	$0.371284\pi$
$930$	−68.0332	−2.23090
$931$	−0.698229	−0.0228835
$932$	−94.6499	−3.10036
$933$	83.5415	2.73503
$934$	116.277	3.80470
$935$	4.46434	0.146000
$936$	285.879	9.34426
$937$	−25.6048	−0.836472	−0.418236	−	0.908338i	$-0.637351\pi$
$937$	−25.6048	−0.836472	−0.418236	+	0.908338i	$0.637351\pi$
$938$	−21.5690	−0.704254
$939$	52.6940	1.71960
$940$	29.0178	0.946455
$941$	13.4178	0.437409	0.218704	−	0.975791i	$-0.429817\pi$
$941$	13.4178	0.437409	0.218704	+	0.975791i	$0.429817\pi$
$942$	137.813	4.49018
$943$	−5.84043	−0.190191
$944$	94.3013	3.06925
$945$	9.66556	0.314421
$946$	5.91001	0.192151
$947$	17.8475	0.579965	0.289982	−	0.957032i	$-0.406351\pi$
$947$	17.8475	0.579965	0.289982	+	0.957032i	$0.406351\pi$
$948$	230.029	7.47098
$949$	16.2962	0.528998
$950$	1.92939	0.0625977
$951$	14.8741	0.482325
$952$	−74.1873	−2.40442
$953$	16.8613	0.546192	0.273096	−	0.961987i	$-0.411952\pi$
$953$	16.8613	0.546192	0.273096	+	0.961987i	$0.411952\pi$
$954$	213.119	6.89997
$955$	6.15653	0.199221
$956$	−67.1571	−2.17202
$957$	4.33472	0.140122
$958$	68.0283	2.19790
$959$	−7.22669	−0.233362
$960$	113.386	3.65952
$961$	34.9700	1.12807
$962$	73.2312	2.36107
$963$	−54.1217	−1.74405
$964$	113.225	3.64672
$965$	6.58298	0.211914
$966$	42.7883	1.37669
$967$	13.3820	0.430337	0.215169	−	0.976577i	$-0.430970\pi$
$967$	13.3820	0.430337	0.215169	+	0.976577i	$0.430970\pi$
$968$	106.836	3.43385
$969$	−15.6297	−0.502099
$970$	−39.5216	−1.26896
$971$	26.9202	0.863909	0.431954	−	0.901895i	$-0.357824\pi$
$971$	26.9202	0.863909	0.431954	+	0.901895i	$0.357824\pi$
$972$	19.9406	0.639594
$973$	10.3060	0.330394
$974$	62.5403	2.00392
$975$	−13.9384	−0.446386
$976$	22.7351	0.727734
$977$	3.69460	0.118201	0.0591004	−	0.998252i	$-0.481177\pi$
$977$	3.69460	0.118201	0.0591004	+	0.998252i	$0.481177\pi$
$978$	−118.705	−3.79576
$979$	−5.76307	−0.184188
$980$	5.63562	0.180023
$981$	−72.4413	−2.31287
$982$	2.17844	0.0695168
$983$	35.0896	1.11918	0.559592	−	0.828769i	$-0.310958\pi$
$983$	35.0896	1.11918	0.559592	+	0.828769i	$0.310958\pi$
$984$	−34.8172	−1.10993
$985$	−5.31216	−0.169260
$986$	−48.2678	−1.53716
$987$	15.6080	0.496807
$988$	18.0937	0.575638
$989$	18.0723	0.574667
$990$	−10.3382	−0.328570
$991$	7.53622	0.239396	0.119698	−	0.992810i	$-0.461807\pi$
$991$	7.53622	0.239396	0.119698	+	0.992810i	$0.461807\pi$
$992$	−206.881	−6.56849
$993$	36.4438	1.15651
$994$	−21.6008	−0.685134
$995$	20.9254	0.663381
$996$	177.881	5.63638
$997$	−15.5113	−0.491248	−0.245624	−	0.969365i	$-0.578993\pi$
$997$	−15.5113	−0.491248	−0.245624	+	0.969365i	$0.578993\pi$
$998$	−0.201590	−0.00638122
$999$	55.7074	1.76250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.2	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.2	✓	73	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76326 q^{2} +3.03127 q^{3} +5.63562 q^{4} +1.00000 q^{5} -8.37621 q^{6} +1.00000 q^{7} -10.0462 q^{8} +6.18862 q^{9} +O(q^{10})\)	\(q-2.76326 q^{2} +3.03127 q^{3} +5.63562 q^{4} +1.00000 q^{5} -8.37621 q^{6} +1.00000 q^{7} -10.0462 q^{8} +6.18862 q^{9} -2.76326 q^{10} +0.604546 q^{11} +17.0831 q^{12} -4.59820 q^{13} -2.76326 q^{14} +3.03127 q^{15} +16.4890 q^{16} +7.38462 q^{17} -17.1008 q^{18} -0.698229 q^{19} +5.63562 q^{20} +3.03127 q^{21} -1.67052 q^{22} -5.10832 q^{23} -30.4527 q^{24} +1.00000 q^{25} +12.7060 q^{26} +9.66556 q^{27} +5.63562 q^{28} +2.36541 q^{29} -8.37621 q^{30} +8.12219 q^{31} -25.4711 q^{32} +1.83254 q^{33} -20.4056 q^{34} +1.00000 q^{35} +34.8767 q^{36} +5.76350 q^{37} +1.92939 q^{38} -13.9384 q^{39} -10.0462 q^{40} +1.14332 q^{41} -8.37621 q^{42} -3.53783 q^{43} +3.40699 q^{44} +6.18862 q^{45} +14.1156 q^{46} +5.14899 q^{47} +49.9827 q^{48} +1.00000 q^{49} -2.76326 q^{50} +22.3848 q^{51} -25.9137 q^{52} -12.4625 q^{53} -26.7085 q^{54} +0.604546 q^{55} -10.0462 q^{56} -2.11652 q^{57} -6.53626 q^{58} +5.71904 q^{59} +17.0831 q^{60} +1.37880 q^{61} -22.4438 q^{62} +6.18862 q^{63} +37.4054 q^{64} -4.59820 q^{65} -5.06380 q^{66} +7.80564 q^{67} +41.6169 q^{68} -15.4847 q^{69} -2.76326 q^{70} +7.81712 q^{71} -62.1720 q^{72} -3.54404 q^{73} -15.9261 q^{74} +3.03127 q^{75} -3.93496 q^{76} +0.604546 q^{77} +38.5155 q^{78} +13.4653 q^{79} +16.4890 q^{80} +10.7331 q^{81} -3.15929 q^{82} +10.4127 q^{83} +17.0831 q^{84} +7.38462 q^{85} +9.77595 q^{86} +7.17021 q^{87} -6.07338 q^{88} -9.53288 q^{89} -17.1008 q^{90} -4.59820 q^{91} -28.7886 q^{92} +24.6206 q^{93} -14.2280 q^{94} -0.698229 q^{95} -77.2099 q^{96} +14.3025 q^{97} -2.76326 q^{98} +3.74130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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