LMFDB - Embedded newform 8035.2.a.e.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.27555 q^{2} +1.50447 q^{3} +3.17814 q^{4} +1.00000 q^{5} -3.42350 q^{6} +2.50382 q^{7} -2.68091 q^{8} -0.736575 q^{9} +O(q^{10})$	\(q-2.27555 q^{2} +1.50447 q^{3} +3.17814 q^{4} +1.00000 q^{5} -3.42350 q^{6} +2.50382 q^{7} -2.68091 q^{8} -0.736575 q^{9} -2.27555 q^{10} -5.24727 q^{11} +4.78141 q^{12} -3.80317 q^{13} -5.69758 q^{14} +1.50447 q^{15} -0.255719 q^{16} -4.81056 q^{17} +1.67612 q^{18} -6.96879 q^{19} +3.17814 q^{20} +3.76692 q^{21} +11.9404 q^{22} +7.29962 q^{23} -4.03335 q^{24} +1.00000 q^{25} +8.65432 q^{26} -5.62156 q^{27} +7.95750 q^{28} +4.20392 q^{29} -3.42350 q^{30} +1.55323 q^{31} +5.94373 q^{32} -7.89435 q^{33} +10.9467 q^{34} +2.50382 q^{35} -2.34094 q^{36} -2.66575 q^{37} +15.8579 q^{38} -5.72175 q^{39} -2.68091 q^{40} -1.82214 q^{41} -8.57183 q^{42} +6.25569 q^{43} -16.6765 q^{44} -0.736575 q^{45} -16.6107 q^{46} +9.31783 q^{47} -0.384720 q^{48} -0.730862 q^{49} -2.27555 q^{50} -7.23733 q^{51} -12.0870 q^{52} +10.0844 q^{53} +12.7921 q^{54} -5.24727 q^{55} -6.71253 q^{56} -10.4843 q^{57} -9.56624 q^{58} -14.1232 q^{59} +4.78141 q^{60} +4.75049 q^{61} -3.53446 q^{62} -1.84426 q^{63} -13.0138 q^{64} -3.80317 q^{65} +17.9640 q^{66} +14.3978 q^{67} -15.2886 q^{68} +10.9820 q^{69} -5.69758 q^{70} -4.86014 q^{71} +1.97469 q^{72} -6.55155 q^{73} +6.06606 q^{74} +1.50447 q^{75} -22.1478 q^{76} -13.1382 q^{77} +13.0201 q^{78} +9.02603 q^{79} -0.255719 q^{80} -6.24773 q^{81} +4.14637 q^{82} -3.79250 q^{83} +11.9718 q^{84} -4.81056 q^{85} -14.2351 q^{86} +6.32467 q^{87} +14.0675 q^{88} -16.5487 q^{89} +1.67612 q^{90} -9.52248 q^{91} +23.1992 q^{92} +2.33679 q^{93} -21.2032 q^{94} -6.96879 q^{95} +8.94215 q^{96} +2.97990 q^{97} +1.66312 q^{98} +3.86501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.27555	−1.60906	−0.804529	−	0.593913i	$-0.797582\pi$
$2$	−2.27555	−1.60906	−0.804529	+	0.593913i	$0.797582\pi$
$3$	1.50447	0.868605	0.434303	−	0.900767i	$-0.356995\pi$
$3$	1.50447	0.868605	0.434303	+	0.900767i	$0.356995\pi$
$4$	3.17814	1.58907
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.42350	−1.39764
$7$	2.50382	0.946357	0.473178	−	0.880967i	$-0.343107\pi$
$7$	2.50382	0.946357	0.473178	+	0.880967i	$0.343107\pi$
$8$	−2.68091	−0.947846
$9$	−0.736575	−0.245525
$10$	−2.27555	−0.719593
$11$	−5.24727	−1.58211	−0.791056	−	0.611744i	$-0.790468\pi$
$11$	−5.24727	−1.58211	−0.791056	+	0.611744i	$0.790468\pi$
$12$	4.78141	1.38027
$13$	−3.80317	−1.05481	−0.527405	−	0.849614i	$-0.676835\pi$
$13$	−3.80317	−1.05481	−0.527405	+	0.849614i	$0.676835\pi$
$14$	−5.69758	−1.52274
$15$	1.50447	0.388452
$16$	−0.255719	−0.0639296
$17$	−4.81056	−1.16673	−0.583366	−	0.812210i	$-0.698264\pi$
$17$	−4.81056	−1.16673	−0.583366	+	0.812210i	$0.698264\pi$
$18$	1.67612	0.395064
$19$	−6.96879	−1.59875	−0.799375	−	0.600832i	$-0.794836\pi$
$19$	−6.96879	−1.59875	−0.799375	+	0.600832i	$0.794836\pi$
$20$	3.17814	0.710653
$21$	3.76692	0.822010
$22$	11.9404	2.54571
$23$	7.29962	1.52208	0.761038	−	0.648707i	$-0.224690\pi$
$23$	7.29962	1.52208	0.761038	+	0.648707i	$0.224690\pi$
$24$	−4.03335	−0.823304
$25$	1.00000	0.200000
$26$	8.65432	1.69725
$27$	−5.62156	−1.08187
$28$	7.95750	1.50383
$29$	4.20392	0.780649	0.390324	−	0.920677i	$-0.372363\pi$
$29$	4.20392	0.780649	0.390324	+	0.920677i	$0.372363\pi$
$30$	−3.42350	−0.625042
$31$	1.55323	0.278969	0.139484	−	0.990224i	$-0.455456\pi$
$31$	1.55323	0.278969	0.139484	+	0.990224i	$0.455456\pi$
$32$	5.94373	1.05071
$33$	−7.89435	−1.37423
$34$	10.9467	1.87734
$35$	2.50382	0.423224
$36$	−2.34094	−0.390156
$37$	−2.66575	−0.438247	−0.219124	−	0.975697i	$-0.570320\pi$
$37$	−2.66575	−0.438247	−0.219124	+	0.975697i	$0.570320\pi$
$38$	15.8579	2.57248
$39$	−5.72175	−0.916214
$40$	−2.68091	−0.423889
$41$	−1.82214	−0.284570	−0.142285	−	0.989826i	$-0.545445\pi$
$41$	−1.82214	−0.284570	−0.142285	+	0.989826i	$0.545445\pi$
$42$	−8.57183	−1.32266
$43$	6.25569	0.953984	0.476992	−	0.878908i	$-0.341727\pi$
$43$	6.25569	0.953984	0.476992	+	0.878908i	$0.341727\pi$
$44$	−16.6765	−2.51408
$45$	−0.736575	−0.109802
$46$	−16.6107	−2.44911
$47$	9.31783	1.35915	0.679573	−	0.733608i	$-0.262165\pi$
$47$	9.31783	1.35915	0.679573	+	0.733608i	$0.262165\pi$
$48$	−0.384720	−0.0555296
$49$	−0.730862	−0.104409
$50$	−2.27555	−0.321812
$51$	−7.23733	−1.01343
$52$	−12.0870	−1.67617
$53$	10.0844	1.38520	0.692599	−	0.721323i	$-0.256466\pi$
$53$	10.0844	1.38520	0.692599	+	0.721323i	$0.256466\pi$
$54$	12.7921	1.74079
$55$	−5.24727	−0.707542
$56$	−6.71253	−0.897000
$57$	−10.4843	−1.38868
$58$	−9.56624	−1.25611
$59$	−14.1232	−1.83869	−0.919343	−	0.393458i	$-0.871279\pi$
$59$	−14.1232	−1.83869	−0.919343	+	0.393458i	$0.871279\pi$
$60$	4.78141	0.617277
$61$	4.75049	0.608237	0.304119	−	0.952634i	$-0.401638\pi$
$61$	4.75049	0.608237	0.304119	+	0.952634i	$0.401638\pi$
$62$	−3.53446	−0.448877
$63$	−1.84426	−0.232354
$64$	−13.0138	−1.62673
$65$	−3.80317	−0.471726
$66$	17.9640	2.21122
$67$	14.3978	1.75897	0.879484	−	0.475928i	$-0.157888\pi$
$67$	14.3978	1.75897	0.879484	+	0.475928i	$0.157888\pi$
$68$	−15.2886	−1.85402
$69$	10.9820	1.32208
$70$	−5.69758	−0.680991
$71$	−4.86014	−0.576793	−0.288396	−	0.957511i	$-0.593122\pi$
$71$	−4.86014	−0.576793	−0.288396	+	0.957511i	$0.593122\pi$
$72$	1.97469	0.232720
$73$	−6.55155	−0.766801	−0.383401	−	0.923582i	$-0.625247\pi$
$73$	−6.55155	−0.766801	−0.383401	+	0.923582i	$0.625247\pi$
$74$	6.06606	0.705165
$75$	1.50447	0.173721
$76$	−22.1478	−2.54052
$77$	−13.1382	−1.49724
$78$	13.0201	1.47424
$79$	9.02603	1.01551	0.507754	−	0.861502i	$-0.330476\pi$
$79$	9.02603	1.01551	0.507754	+	0.861502i	$0.330476\pi$
$80$	−0.255719	−0.0285902
$81$	−6.24773	−0.694192
$82$	4.14637	0.457890
$83$	−3.79250	−0.416281	−0.208141	−	0.978099i	$-0.566741\pi$
$83$	−3.79250	−0.416281	−0.208141	+	0.978099i	$0.566741\pi$
$84$	11.9718	1.30623
$85$	−4.81056	−0.521778
$86$	−14.2351	−1.53502
$87$	6.32467	0.678075
$88$	14.0675	1.49960
$89$	−16.5487	−1.75416	−0.877079	−	0.480347i	$-0.840511\pi$
$89$	−16.5487	−1.75416	−0.877079	+	0.480347i	$0.840511\pi$
$90$	1.67612	0.176678
$91$	−9.52248	−0.998227
$92$	23.1992	2.41868
$93$	2.33679	0.242314
$94$	−21.2032	−2.18694
$95$	−6.96879	−0.714983
$96$	8.94215	0.912654
$97$	2.97990	0.302563	0.151281	−	0.988491i	$-0.451660\pi$
$97$	2.97990	0.302563	0.151281	+	0.988491i	$0.451660\pi$
$98$	1.66312	0.168000
$99$	3.86501	0.388448
$100$	3.17814	0.317814
$101$	13.8701	1.38013	0.690066	−	0.723747i	$-0.257582\pi$
$101$	13.8701	1.38013	0.690066	+	0.723747i	$0.257582\pi$
$102$	16.4689	1.63067
$103$	−11.7824	−1.16095	−0.580476	−	0.814277i	$-0.697134\pi$
$103$	−11.7824	−1.16095	−0.580476	+	0.814277i	$0.697134\pi$
$104$	10.1960	0.999797
$105$	3.76692	0.367614
$106$	−22.9476	−2.22886
$107$	−1.28361	−0.124091	−0.0620454	−	0.998073i	$-0.519762\pi$
$107$	−1.28361	−0.124091	−0.0620454	+	0.998073i	$0.519762\pi$
$108$	−17.8661	−1.71916
$109$	18.6045	1.78198	0.890992	−	0.454018i	$-0.150010\pi$
$109$	18.6045	1.78198	0.890992	+	0.454018i	$0.150010\pi$
$110$	11.9404	1.13848
$111$	−4.01054	−0.380664
$112$	−0.640274	−0.0605002
$113$	11.1810	1.05182	0.525909	−	0.850541i	$-0.323725\pi$
$113$	11.1810	1.05182	0.525909	+	0.850541i	$0.323725\pi$
$114$	23.8576	2.23447
$115$	7.29962	0.680693
$116$	13.3606	1.24050
$117$	2.80132	0.258982
$118$	32.1381	2.95855
$119$	−12.0448	−1.10414
$120$	−4.03335	−0.368193
$121$	16.5338	1.50308
$122$	−10.8100	−0.978690
$123$	−2.74135	−0.247179
$124$	4.93638	0.443300
$125$	1.00000	0.0894427
$126$	4.19670	0.373872
$127$	−0.734058	−0.0651371	−0.0325685	−	0.999470i	$-0.510369\pi$
$127$	−0.734058	−0.0651371	−0.0325685	+	0.999470i	$0.510369\pi$
$128$	17.7262	1.56679
$129$	9.41148	0.828635
$130$	8.65432	0.759034
$131$	14.5580	1.27194	0.635971	−	0.771713i	$-0.280600\pi$
$131$	14.5580	1.27194	0.635971	+	0.771713i	$0.280600\pi$
$132$	−25.0893	−2.18375
$133$	−17.4486	−1.51299
$134$	−32.7629	−2.83028
$135$	−5.62156	−0.483827
$136$	12.8967	1.10588
$137$	16.8803	1.44218	0.721089	−	0.692842i	$-0.243642\pi$
$137$	16.8803	1.44218	0.721089	+	0.692842i	$0.243642\pi$
$138$	−24.9902	−2.12731
$139$	12.6496	1.07292	0.536462	−	0.843925i	$-0.319761\pi$
$139$	12.6496	1.07292	0.536462	+	0.843925i	$0.319761\pi$
$140$	7.95750	0.672531
$141$	14.0184	1.18056
$142$	11.0595	0.928093
$143$	19.9563	1.66883
$144$	0.188356	0.0156963
$145$	4.20392	0.349117
$146$	14.9084	1.23383
$147$	−1.09956	−0.0906901
$148$	−8.47213	−0.696405
$149$	6.26500	0.513249	0.256624	−	0.966511i	$-0.417390\pi$
$149$	6.26500	0.513249	0.256624	+	0.966511i	$0.417390\pi$
$150$	−3.42350	−0.279527
$151$	−4.22092	−0.343493	−0.171747	−	0.985141i	$-0.554941\pi$
$151$	−4.22092	−0.343493	−0.171747	+	0.985141i	$0.554941\pi$
$152$	18.6827	1.51537
$153$	3.54334	0.286462
$154$	29.8968	2.40915
$155$	1.55323	0.124759
$156$	−18.1845	−1.45593
$157$	8.69378	0.693839	0.346919	−	0.937895i	$-0.387228\pi$
$157$	8.69378	0.693839	0.346919	+	0.937895i	$0.387228\pi$
$158$	−20.5392	−1.63401
$159$	15.1716	1.20319
$160$	5.94373	0.469893
$161$	18.2770	1.44043
$162$	14.2170	1.11700
$163$	−12.8601	−1.00728	−0.503642	−	0.863913i	$-0.668007\pi$
$163$	−12.8601	−1.00728	−0.503642	+	0.863913i	$0.668007\pi$
$164$	−5.79100	−0.452201
$165$	−7.89435	−0.614574
$166$	8.63004	0.669821
$167$	7.17778	0.555434	0.277717	−	0.960663i	$-0.410422\pi$
$167$	7.17778	0.555434	0.277717	+	0.960663i	$0.410422\pi$
$168$	−10.0988	−0.779139
$169$	1.46412	0.112625
$170$	10.9467	0.839571
$171$	5.13304	0.392534
$172$	19.8814	1.51595
$173$	8.54652	0.649780	0.324890	−	0.945752i	$-0.394673\pi$
$173$	8.54652	0.649780	0.324890	+	0.945752i	$0.394673\pi$
$174$	−14.3921	−1.09106
$175$	2.50382	0.189271
$176$	1.34182	0.101144
$177$	−21.2479	−1.59709
$178$	37.6574	2.82254
$179$	12.3954	0.926478	0.463239	−	0.886233i	$-0.346687\pi$
$179$	12.3954	0.926478	0.463239	+	0.886233i	$0.346687\pi$
$180$	−2.34094	−0.174483
$181$	−22.3674	−1.66256	−0.831279	−	0.555855i	$-0.812391\pi$
$181$	−22.3674	−1.66256	−0.831279	+	0.555855i	$0.812391\pi$
$182$	21.6689	1.60621
$183$	7.14696	0.528318
$184$	−19.5696	−1.44269
$185$	−2.66575	−0.195990
$186$	−5.31748	−0.389897
$187$	25.2423	1.84590
$188$	29.6133	2.15978
$189$	−14.0754	−1.02383
$190$	15.8579	1.15045
$191$	9.59032	0.693931	0.346965	−	0.937878i	$-0.387212\pi$
$191$	9.59032	0.693931	0.346965	+	0.937878i	$0.387212\pi$
$192$	−19.5789	−1.41298
$193$	−21.0726	−1.51684	−0.758421	−	0.651765i	$-0.774029\pi$
$193$	−21.0726	−1.51684	−0.758421	+	0.651765i	$0.774029\pi$
$194$	−6.78091	−0.486841
$195$	−5.72175	−0.409743
$196$	−2.32278	−0.165913
$197$	−24.4357	−1.74097	−0.870485	−	0.492196i	$-0.836194\pi$
$197$	−24.4357	−1.74097	−0.870485	+	0.492196i	$0.836194\pi$
$198$	−8.79503	−0.625036
$199$	−21.0865	−1.49478	−0.747391	−	0.664384i	$-0.768694\pi$
$199$	−21.0865	−1.49478	−0.747391	+	0.664384i	$0.768694\pi$
$200$	−2.68091	−0.189569
$201$	21.6610	1.52785
$202$	−31.5622	−2.22071
$203$	10.5259	0.738772
$204$	−23.0012	−1.61041
$205$	−1.82214	−0.127264
$206$	26.8114	1.86804
$207$	−5.37672	−0.373708
$208$	0.972542	0.0674336
$209$	36.5671	2.52940
$210$	−8.57183	−0.591513
$211$	23.1396	1.59300	0.796498	−	0.604642i	$-0.206684\pi$
$211$	23.1396	1.59300	0.796498	+	0.604642i	$0.206684\pi$
$212$	32.0496	2.20117
$213$	−7.31193	−0.501005
$214$	2.92091	0.199669
$215$	6.25569	0.426634
$216$	15.0709	1.02545
$217$	3.88902	0.264004
$218$	−42.3354	−2.86732
$219$	−9.85660	−0.666048
$220$	−16.6765	−1.12433
$221$	18.2954	1.23068
$222$	9.12620	0.612510
$223$	24.1681	1.61841	0.809207	−	0.587523i	$-0.199897\pi$
$223$	24.1681	1.61841	0.809207	+	0.587523i	$0.199897\pi$
$224$	14.8820	0.994349
$225$	−0.736575	−0.0491050
$226$	−25.4429	−1.69244
$227$	23.2897	1.54579	0.772895	−	0.634533i	$-0.218808\pi$
$227$	23.2897	1.54579	0.772895	+	0.634533i	$0.218808\pi$
$228$	−33.3206	−2.20671
$229$	−15.2617	−1.00852	−0.504262	−	0.863551i	$-0.668236\pi$
$229$	−15.2617	−1.00852	−0.504262	+	0.863551i	$0.668236\pi$
$230$	−16.6107	−1.09527
$231$	−19.7661	−1.30051
$232$	−11.2703	−0.739934
$233$	14.9388	0.978676	0.489338	−	0.872094i	$-0.337238\pi$
$233$	14.9388	0.978676	0.489338	+	0.872094i	$0.337238\pi$
$234$	−6.37456	−0.416718
$235$	9.31783	0.607828
$236$	−44.8855	−2.92180
$237$	13.5794	0.882075
$238$	27.4085	1.77663
$239$	−18.0666	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$239$	−18.0666	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$240$	−0.384720	−0.0248336
$241$	1.29823	0.0836264	0.0418132	−	0.999125i	$-0.486687\pi$
$241$	1.29823	0.0836264	0.0418132	+	0.999125i	$0.486687\pi$
$242$	−37.6236	−2.41854
$243$	7.46517	0.478891
$244$	15.0977	0.966531
$245$	−0.730862	−0.0466931
$246$	6.23808	0.397725
$247$	26.5035	1.68638
$248$	−4.16408	−0.264419
$249$	−5.70570	−0.361584
$250$	−2.27555	−0.143919
$251$	21.8057	1.37636	0.688182	−	0.725538i	$-0.258409\pi$
$251$	21.8057	1.37636	0.688182	+	0.725538i	$0.258409\pi$
$252$	−5.86130	−0.369227
$253$	−38.3031	−2.40809
$254$	1.67039	0.104809
$255$	−7.23733	−0.453219
$256$	−14.3092	−0.894324
$257$	3.37353	0.210435	0.105217	−	0.994449i	$-0.466446\pi$
$257$	3.37353	0.210435	0.105217	+	0.994449i	$0.466446\pi$
$258$	−21.4163	−1.33332
$259$	−6.67458	−0.414738
$260$	−12.0870	−0.749604
$261$	−3.09651	−0.191669
$262$	−33.1276	−2.04663
$263$	25.2581	1.55748	0.778740	−	0.627346i	$-0.215859\pi$
$263$	25.2581	1.55748	0.778740	+	0.627346i	$0.215859\pi$
$264$	21.1641	1.30256
$265$	10.0844	0.619479
$266$	39.7053	2.43449
$267$	−24.8970	−1.52367
$268$	45.7581	2.79512
$269$	−18.2060	−1.11004	−0.555019	−	0.831837i	$-0.687289\pi$
$269$	−18.2060	−1.11004	−0.555019	+	0.831837i	$0.687289\pi$
$270$	12.7921	0.778505
$271$	7.11004	0.431904	0.215952	−	0.976404i	$-0.430714\pi$
$271$	7.11004	0.431904	0.215952	+	0.976404i	$0.430714\pi$
$272$	1.23015	0.0745887
$273$	−14.3263	−0.867065
$274$	−38.4119	−2.32055
$275$	−5.24727	−0.316422
$276$	34.9025	2.10088
$277$	−11.3819	−0.683873	−0.341937	−	0.939723i	$-0.611083\pi$
$277$	−11.3819	−0.683873	−0.341937	+	0.939723i	$0.611083\pi$
$278$	−28.7848	−1.72640
$279$	−1.14407	−0.0684938
$280$	−6.71253	−0.401151
$281$	−7.36784	−0.439529	−0.219764	−	0.975553i	$-0.570529\pi$
$281$	−7.36784	−0.439529	−0.219764	+	0.975553i	$0.570529\pi$
$282$	−31.8996	−1.89959
$283$	−16.9802	−1.00937	−0.504683	−	0.863305i	$-0.668391\pi$
$283$	−16.9802	−1.00937	−0.504683	+	0.863305i	$0.668391\pi$
$284$	−15.4462	−0.916564
$285$	−10.4843	−0.621038
$286$	−45.4115	−2.68524
$287$	−4.56231	−0.269305
$288$	−4.37800	−0.257976
$289$	6.14144	0.361261
$290$	−9.56624	−0.561749
$291$	4.48316	0.262807
$292$	−20.8217	−1.21850
$293$	25.2249	1.47365	0.736826	−	0.676083i	$-0.236324\pi$
$293$	25.2249	1.47365	0.736826	+	0.676083i	$0.236324\pi$
$294$	2.50210	0.145926
$295$	−14.1232	−0.822285
$296$	7.14665	0.415391
$297$	29.4978	1.71164
$298$	−14.2563	−0.825847
$299$	−27.7617	−1.60550
$300$	4.78141	0.276055
$301$	15.6631	0.902809
$302$	9.60491	0.552701
$303$	20.8672	1.19879
$304$	1.78205	0.102208
$305$	4.75049	0.272012
$306$	−8.06305	−0.460934
$307$	−4.82295	−0.275260	−0.137630	−	0.990484i	$-0.543949\pi$
$307$	−4.82295	−0.275260	−0.137630	+	0.990484i	$0.543949\pi$
$308$	−41.7551	−2.37922
$309$	−17.7262	−1.00841
$310$	−3.53446	−0.200744
$311$	−8.97997	−0.509208	−0.254604	−	0.967045i	$-0.581945\pi$
$311$	−8.97997	−0.509208	−0.254604	+	0.967045i	$0.581945\pi$
$312$	15.3395	0.868429
$313$	21.2719	1.20236	0.601180	−	0.799114i	$-0.294698\pi$
$313$	21.2719	1.20236	0.601180	+	0.799114i	$0.294698\pi$
$314$	−19.7831	−1.11643
$315$	−1.84426	−0.103912
$316$	28.6860	1.61371
$317$	7.44384	0.418088	0.209044	−	0.977906i	$-0.432965\pi$
$317$	7.44384	0.418088	0.209044	+	0.977906i	$0.432965\pi$
$318$	−34.5239	−1.93600
$319$	−22.0591	−1.23507
$320$	−13.0138	−0.727495
$321$	−1.93114	−0.107786
$322$	−41.5902	−2.31773
$323$	33.5238	1.86531
$324$	−19.8561	−1.10312
$325$	−3.80317	−0.210962
$326$	29.2639	1.62078
$327$	27.9898	1.54784
$328$	4.88499	0.269728
$329$	23.3302	1.28624
$330$	17.9640	0.988886
$331$	7.76416	0.426757	0.213378	−	0.976970i	$-0.431553\pi$
$331$	7.76416	0.426757	0.213378	+	0.976970i	$0.431553\pi$
$332$	−12.0531	−0.661499
$333$	1.96353	0.107601
$334$	−16.3334	−0.893725
$335$	14.3978	0.786635
$336$	−0.963272	−0.0525508
$337$	8.30367	0.452330	0.226165	−	0.974089i	$-0.427381\pi$
$337$	8.30367	0.452330	0.226165	+	0.974089i	$0.427381\pi$
$338$	−3.33169	−0.181220
$339$	16.8214	0.913615
$340$	−15.2886	−0.829141
$341$	−8.15022	−0.441359
$342$	−11.6805	−0.631609
$343$	−19.3567	−1.04516
$344$	−16.7710	−0.904229
$345$	10.9820	0.591254
$346$	−19.4481	−1.04553
$347$	34.0457	1.82767	0.913834	−	0.406089i	$-0.133108\pi$
$347$	34.0457	1.82767	0.913834	+	0.406089i	$0.133108\pi$
$348$	20.1007	1.07751
$349$	20.7211	1.10918	0.554589	−	0.832125i	$-0.312876\pi$
$349$	20.7211	1.10918	0.554589	+	0.832125i	$0.312876\pi$
$350$	−5.69758	−0.304549
$351$	21.3798	1.14117
$352$	−31.1883	−1.66234
$353$	4.76457	0.253593	0.126796	−	0.991929i	$-0.459531\pi$
$353$	4.76457	0.253593	0.126796	+	0.991929i	$0.459531\pi$
$354$	48.3507	2.56981
$355$	−4.86014	−0.257950
$356$	−52.5940	−2.78748
$357$	−18.1210	−0.959065
$358$	−28.2064	−1.49076
$359$	14.2631	0.752780	0.376390	−	0.926461i	$-0.377165\pi$
$359$	14.2631	0.752780	0.376390	+	0.926461i	$0.377165\pi$
$360$	1.97469	0.104076
$361$	29.5641	1.55600
$362$	50.8983	2.67515
$363$	24.8746	1.30558
$364$	−30.2637	−1.58625
$365$	−6.55155	−0.342924
$366$	−16.2633	−0.850095
$367$	−21.6388	−1.12954	−0.564769	−	0.825249i	$-0.691035\pi$
$367$	−21.6388	−1.12954	−0.564769	+	0.825249i	$0.691035\pi$
$368$	−1.86665	−0.0973058
$369$	1.34214	0.0698691
$370$	6.06606	0.315360
$371$	25.2496	1.31089
$372$	7.42663	0.385053
$373$	4.14912	0.214833	0.107417	−	0.994214i	$-0.465742\pi$
$373$	4.14912	0.214833	0.107417	+	0.994214i	$0.465742\pi$
$374$	−57.4401	−2.97016
$375$	1.50447	0.0776904
$376$	−24.9803	−1.28826
$377$	−15.9882	−0.823436
$378$	32.0293	1.64741
$379$	−6.72024	−0.345196	−0.172598	−	0.984992i	$-0.555216\pi$
$379$	−6.72024	−0.345196	−0.172598	+	0.984992i	$0.555216\pi$
$380$	−22.1478	−1.13616
$381$	−1.10437	−0.0565784
$382$	−21.8233	−1.11658
$383$	−6.70720	−0.342722	−0.171361	−	0.985208i	$-0.554816\pi$
$383$	−6.70720	−0.342722	−0.171361	+	0.985208i	$0.554816\pi$
$384$	26.6685	1.36092
$385$	−13.1382	−0.669587
$386$	47.9519	2.44069
$387$	−4.60779	−0.234227
$388$	9.47052	0.480793
$389$	6.34437	0.321672	0.160836	−	0.986981i	$-0.448581\pi$
$389$	6.34437	0.321672	0.160836	+	0.986981i	$0.448581\pi$
$390$	13.0201	0.659301
$391$	−35.1152	−1.77585
$392$	1.95938	0.0989635
$393$	21.9021	1.10481
$394$	55.6046	2.80132
$395$	9.02603	0.454149
$396$	12.2835	0.617271
$397$	−14.8646	−0.746034	−0.373017	−	0.927825i	$-0.621677\pi$
$397$	−14.8646	−0.746034	−0.373017	+	0.927825i	$0.621677\pi$
$398$	47.9834	2.40519
$399$	−26.2509	−1.31419
$400$	−0.255719	−0.0127859
$401$	20.4359	1.02052	0.510260	−	0.860020i	$-0.329549\pi$
$401$	20.4359	1.02052	0.510260	+	0.860020i	$0.329549\pi$
$402$	−49.2907	−2.45840
$403$	−5.90721	−0.294259
$404$	44.0812	2.19312
$405$	−6.24773	−0.310452
$406$	−23.9522	−1.18873
$407$	13.9879	0.693356
$408$	19.4026	0.960574
$409$	14.2914	0.706663	0.353332	−	0.935498i	$-0.385049\pi$
$409$	14.2914	0.706663	0.353332	+	0.935498i	$0.385049\pi$
$410$	4.14637	0.204774
$411$	25.3958	1.25268
$412$	−37.4460	−1.84483
$413$	−35.3620	−1.74005
$414$	12.2350	0.601318
$415$	−3.79250	−0.186167
$416$	−22.6050	−1.10830
$417$	19.0309	0.931947
$418$	−83.2104	−4.06995
$419$	−2.01427	−0.0984036	−0.0492018	−	0.998789i	$-0.515668\pi$
$419$	−2.01427	−0.0984036	−0.0492018	+	0.998789i	$0.515668\pi$
$420$	11.9718	0.584164
$421$	−9.92116	−0.483528	−0.241764	−	0.970335i	$-0.577726\pi$
$421$	−9.92116	−0.483528	−0.241764	+	0.970335i	$0.577726\pi$
$422$	−52.6553	−2.56322
$423$	−6.86329	−0.333704
$424$	−27.0354	−1.31295
$425$	−4.81056	−0.233346
$426$	16.6387	0.806147
$427$	11.8944	0.575610
$428$	−4.07947	−0.197189
$429$	30.0236	1.44955
$430$	−14.2351	−0.686480
$431$	30.9377	1.49022	0.745108	−	0.666943i	$-0.232398\pi$
$431$	30.9377	1.49022	0.745108	+	0.666943i	$0.232398\pi$
$432$	1.43754	0.0691635
$433$	1.62121	0.0779104	0.0389552	−	0.999241i	$-0.487597\pi$
$433$	1.62121	0.0779104	0.0389552	+	0.999241i	$0.487597\pi$
$434$	−8.84966	−0.424797
$435$	6.32467	0.303245
$436$	59.1275	2.83170
$437$	−50.8695	−2.43342
$438$	22.4292	1.07171
$439$	3.37600	0.161128	0.0805638	−	0.996749i	$-0.474328\pi$
$439$	3.37600	0.161128	0.0805638	+	0.996749i	$0.474328\pi$
$440$	14.0675	0.670640
$441$	0.538335	0.0256350
$442$	−41.6321	−1.98024
$443$	−3.11412	−0.147956	−0.0739781	−	0.997260i	$-0.523569\pi$
$443$	−3.11412	−0.147956	−0.0739781	+	0.997260i	$0.523569\pi$
$444$	−12.7461	−0.604901
$445$	−16.5487	−0.784483
$446$	−54.9957	−2.60412
$447$	9.42549	0.445810
$448$	−32.5843	−1.53946
$449$	24.2005	1.14209	0.571047	−	0.820917i	$-0.306537\pi$
$449$	24.2005	1.14209	0.571047	+	0.820917i	$0.306537\pi$
$450$	1.67612	0.0790129
$451$	9.56124	0.450221
$452$	35.5347	1.67141
$453$	−6.35023	−0.298360
$454$	−52.9969	−2.48727
$455$	−9.52248	−0.446421
$456$	28.1076	1.31626
$457$	−26.2123	−1.22616	−0.613079	−	0.790022i	$-0.710069\pi$
$457$	−26.2123	−1.22616	−0.613079	+	0.790022i	$0.710069\pi$
$458$	34.7289	1.62278
$459$	27.0428	1.26225
$460$	23.1992	1.08167
$461$	22.2314	1.03542	0.517709	−	0.855557i	$-0.326785\pi$
$461$	22.2314	1.03542	0.517709	+	0.855557i	$0.326785\pi$
$462$	44.9787	2.09260
$463$	−10.6473	−0.494821	−0.247411	−	0.968911i	$-0.579580\pi$
$463$	−10.6473	−0.494821	−0.247411	+	0.968911i	$0.579580\pi$
$464$	−1.07502	−0.0499066
$465$	2.33679	0.108366
$466$	−33.9941	−1.57475
$467$	−36.7629	−1.70119	−0.850593	−	0.525825i	$-0.823757\pi$
$467$	−36.7629	−1.70119	−0.850593	+	0.525825i	$0.823757\pi$
$468$	8.90299	0.411541
$469$	36.0495	1.66461
$470$	−21.2032	−0.978031
$471$	13.0795	0.602672
$472$	37.8631	1.74279
$473$	−32.8253	−1.50931
$474$	−30.9006	−1.41931
$475$	−6.96879	−0.319750
$476$	−38.2800	−1.75456
$477$	−7.42792	−0.340101
$478$	41.1116	1.88040
$479$	27.2857	1.24672	0.623358	−	0.781936i	$-0.285768\pi$
$479$	27.2857	1.24672	0.623358	+	0.781936i	$0.285768\pi$
$480$	8.94215	0.408151
$481$	10.1383	0.462268
$482$	−2.95419	−0.134560
$483$	27.4971	1.25116
$484$	52.5468	2.38849
$485$	2.97990	0.135310
$486$	−16.9874	−0.770563
$487$	−19.0676	−0.864036	−0.432018	−	0.901865i	$-0.642198\pi$
$487$	−19.0676	−0.864036	−0.432018	+	0.901865i	$0.642198\pi$
$488$	−12.7356	−0.576515
$489$	−19.3477	−0.874932
$490$	1.66312	0.0751319
$491$	−0.263944	−0.0119116	−0.00595581	−	0.999982i	$-0.501896\pi$
$491$	−0.263944	−0.0119116	−0.00595581	+	0.999982i	$0.501896\pi$
$492$	−8.71238	−0.392784
$493$	−20.2232	−0.910807
$494$	−60.3102	−2.71348
$495$	3.86501	0.173719
$496$	−0.397190	−0.0178344
$497$	−12.1689	−0.545852
$498$	12.9836	0.581810
$499$	−4.36997	−0.195627	−0.0978133	−	0.995205i	$-0.531185\pi$
$499$	−4.36997	−0.195627	−0.0978133	+	0.995205i	$0.531185\pi$
$500$	3.17814	0.142131
$501$	10.7987	0.482452
$502$	−49.6201	−2.21465
$503$	28.6997	1.27965	0.639827	−	0.768519i	$-0.279006\pi$
$503$	28.6997	1.27965	0.639827	+	0.768519i	$0.279006\pi$
$504$	4.94429	0.220236
$505$	13.8701	0.617213
$506$	87.1606	3.87476
$507$	2.20273	0.0978266
$508$	−2.33294	−0.103507
$509$	−14.7584	−0.654156	−0.327078	−	0.944997i	$-0.606064\pi$
$509$	−14.7584	−0.654156	−0.327078	+	0.944997i	$0.606064\pi$
$510$	16.4689	0.729256
$511$	−16.4039	−0.725668
$512$	−2.89104	−0.127767
$513$	39.1755	1.72964
$514$	−7.67664	−0.338602
$515$	−11.7824	−0.519194
$516$	29.9110	1.31676
$517$	−48.8932	−2.15032
$518$	15.1884	0.667338
$519$	12.8580	0.564402
$520$	10.1960	0.447123
$521$	−31.9970	−1.40182	−0.700908	−	0.713252i	$-0.747222\pi$
$521$	−31.9970	−1.40182	−0.700908	+	0.713252i	$0.747222\pi$
$522$	7.04626	0.308406
$523$	−4.60845	−0.201514	−0.100757	−	0.994911i	$-0.532126\pi$
$523$	−4.60845	−0.201514	−0.100757	+	0.994911i	$0.532126\pi$
$524$	46.2674	2.02120
$525$	3.76692	0.164402
$526$	−57.4761	−2.50608
$527$	−7.47190	−0.325481
$528$	2.01873	0.0878540
$529$	30.2845	1.31672
$530$	−22.9476	−0.996778
$531$	10.4028	0.451443
$532$	−55.4542	−2.40424
$533$	6.92990	0.300167
$534$	56.6544	2.45167
$535$	−1.28361	−0.0554951
$536$	−38.5992	−1.66723
$537$	18.6485	0.804743
$538$	41.4287	1.78612
$539$	3.83503	0.165187
$540$	−17.8661	−0.768834
$541$	27.8353	1.19673	0.598366	−	0.801223i	$-0.295817\pi$
$541$	27.8353	1.19673	0.598366	+	0.801223i	$0.295817\pi$
$542$	−16.1793	−0.694959
$543$	−33.6511	−1.44411
$544$	−28.5926	−1.22590
$545$	18.6045	0.796928
$546$	32.6002	1.39516
$547$	−44.5854	−1.90633	−0.953166	−	0.302448i	$-0.902196\pi$
$547$	−44.5854	−1.90633	−0.953166	+	0.302448i	$0.902196\pi$
$548$	53.6478	2.29172
$549$	−3.49909	−0.149338
$550$	11.9404	0.509142
$551$	−29.2963	−1.24806
$552$	−29.4419	−1.25313
$553$	22.5996	0.961033
$554$	25.9002	1.10039
$555$	−4.01054	−0.170238
$556$	40.2021	1.70495
$557$	9.70433	0.411186	0.205593	−	0.978638i	$-0.434088\pi$
$557$	9.70433	0.411186	0.205593	+	0.978638i	$0.434088\pi$
$558$	2.60340	0.110211
$559$	−23.7915	−1.00627
$560$	−0.640274	−0.0270565
$561$	37.9762	1.60336
$562$	16.7659	0.707227
$563$	31.4912	1.32719	0.663597	−	0.748090i	$-0.269029\pi$
$563$	31.4912	1.32719	0.663597	+	0.748090i	$0.269029\pi$
$564$	44.5523	1.87599
$565$	11.1810	0.470387
$566$	38.6392	1.62413
$567$	−15.6432	−0.656954
$568$	13.0296	0.546711
$569$	−15.3630	−0.644049	−0.322025	−	0.946731i	$-0.604363\pi$
$569$	−15.3630	−0.644049	−0.322025	+	0.946731i	$0.604363\pi$
$570$	23.8576	0.999286
$571$	−11.9601	−0.500517	−0.250258	−	0.968179i	$-0.580516\pi$
$571$	−11.9601	−0.500517	−0.250258	+	0.968179i	$0.580516\pi$
$572$	63.4238	2.65188
$573$	14.4283	0.602752
$574$	10.3818	0.433327
$575$	7.29962	0.304415
$576$	9.58566	0.399403
$577$	12.6390	0.526168	0.263084	−	0.964773i	$-0.415260\pi$
$577$	12.6390	0.526168	0.263084	+	0.964773i	$0.415260\pi$
$578$	−13.9752	−0.581291
$579$	−31.7031	−1.31754
$580$	13.3606	0.554770
$581$	−9.49576	−0.393951
$582$	−10.2017	−0.422872
$583$	−52.9155	−2.19154
$584$	17.5641	0.726809
$585$	2.80132	0.115820
$586$	−57.4005	−2.37119
$587$	−20.0503	−0.827566	−0.413783	−	0.910376i	$-0.635793\pi$
$587$	−20.0503	−0.827566	−0.413783	+	0.910376i	$0.635793\pi$
$588$	−3.49455	−0.144113
$589$	−10.8241	−0.446001
$590$	32.1381	1.32310
$591$	−36.7627	−1.51221
$592$	0.681683	0.0280170
$593$	−10.3794	−0.426230	−0.213115	−	0.977027i	$-0.568361\pi$
$593$	−10.3794	−0.426230	−0.213115	+	0.977027i	$0.568361\pi$
$594$	−67.1239	−2.75413
$595$	−12.0448	−0.493788
$596$	19.9110	0.815587
$597$	−31.7240	−1.29838
$598$	63.1732	2.58335
$599$	−45.6014	−1.86322	−0.931611	−	0.363456i	$-0.881597\pi$
$599$	−45.6014	−1.86322	−0.931611	+	0.363456i	$0.881597\pi$
$600$	−4.03335	−0.164661
$601$	−7.21630	−0.294359	−0.147179	−	0.989110i	$-0.547019\pi$
$601$	−7.21630	−0.294359	−0.147179	+	0.989110i	$0.547019\pi$
$602$	−35.6423	−1.45267
$603$	−10.6051	−0.431871
$604$	−13.4146	−0.545834
$605$	16.5338	0.672196
$606$	−47.4844	−1.92892
$607$	24.9637	1.01325	0.506623	−	0.862168i	$-0.330894\pi$
$607$	24.9637	1.01325	0.506623	+	0.862168i	$0.330894\pi$
$608$	−41.4206	−1.67983
$609$	15.8359	0.641701
$610$	−10.8100	−0.437683
$611$	−35.4373	−1.43364
$612$	11.2612	0.455207
$613$	−41.3282	−1.66923	−0.834616	−	0.550832i	$-0.814310\pi$
$613$	−41.3282	−1.66923	−0.834616	+	0.550832i	$0.814310\pi$
$614$	10.9749	0.442910
$615$	−2.74135	−0.110542
$616$	35.2225	1.41915
$617$	−26.2962	−1.05865	−0.529323	−	0.848420i	$-0.677554\pi$
$617$	−26.2962	−1.05865	−0.529323	+	0.848420i	$0.677554\pi$
$618$	40.3369	1.62259
$619$	−10.1084	−0.406289	−0.203145	−	0.979149i	$-0.565116\pi$
$619$	−10.1084	−0.406289	−0.203145	+	0.979149i	$0.565116\pi$
$620$	4.93638	0.198250
$621$	−41.0352	−1.64669
$622$	20.4344	0.819345
$623$	−41.4350	−1.66006
$624$	1.46316	0.0585732
$625$	1.00000	0.0400000
$626$	−48.4053	−1.93467
$627$	55.0141	2.19705
$628$	27.6300	1.10256
$629$	12.8238	0.511317
$630$	4.19670	0.167201
$631$	24.4124	0.971844	0.485922	−	0.874002i	$-0.338484\pi$
$631$	24.4124	0.971844	0.485922	+	0.874002i	$0.338484\pi$
$632$	−24.1980	−0.962545
$633$	34.8128	1.38368
$634$	−16.9388	−0.672728
$635$	−0.734058	−0.0291302
$636$	48.2176	1.91195
$637$	2.77960	0.110132
$638$	50.1967	1.98730
$639$	3.57986	0.141617
$640$	17.7262	0.700689
$641$	36.7001	1.44957	0.724783	−	0.688977i	$-0.241940\pi$
$641$	36.7001	1.44957	0.724783	+	0.688977i	$0.241940\pi$
$642$	4.39442	0.173434
$643$	−0.957989	−0.0377794	−0.0188897	−	0.999822i	$-0.506013\pi$
$643$	−0.957989	−0.0377794	−0.0188897	+	0.999822i	$0.506013\pi$
$644$	58.0867	2.28894
$645$	9.41148	0.370577
$646$	−76.2851	−3.00140
$647$	−6.76900	−0.266117	−0.133058	−	0.991108i	$-0.542480\pi$
$647$	−6.76900	−0.266117	−0.133058	+	0.991108i	$0.542480\pi$
$648$	16.7496	0.657987
$649$	74.1083	2.90900
$650$	8.65432	0.339450
$651$	5.85090	0.229315
$652$	−40.8713	−1.60064
$653$	9.30651	0.364192	0.182096	−	0.983281i	$-0.441712\pi$
$653$	9.30651	0.364192	0.182096	+	0.983281i	$0.441712\pi$
$654$	−63.6923	−2.49057
$655$	14.5580	0.568829
$656$	0.465954	0.0181925
$657$	4.82571	0.188269
$658$	−53.0891	−2.06963
$659$	27.3110	1.06389	0.531943	−	0.846780i	$-0.321462\pi$
$659$	27.3110	1.06389	0.531943	+	0.846780i	$0.321462\pi$
$660$	−25.0893	−0.976601
$661$	0.661490	0.0257290	0.0128645	−	0.999917i	$-0.495905\pi$
$661$	0.661490	0.0257290	0.0128645	+	0.999917i	$0.495905\pi$
$662$	−17.6677	−0.686676
$663$	27.5248	1.06898
$664$	10.1674	0.394570
$665$	−17.4486	−0.676629
$666$	−4.46811	−0.173136
$667$	30.6870	1.18821
$668$	22.8120	0.882622
$669$	36.3601	1.40576
$670$	−32.7629	−1.26574
$671$	−24.9271	−0.962299
$672$	22.3896	0.863696
$673$	1.58588	0.0611313	0.0305657	−	0.999533i	$-0.490269\pi$
$673$	1.58588	0.0611313	0.0305657	+	0.999533i	$0.490269\pi$
$674$	−18.8954	−0.727825
$675$	−5.62156	−0.216374
$676$	4.65319	0.178969
$677$	18.1146	0.696200	0.348100	−	0.937457i	$-0.386827\pi$
$677$	18.1146	0.696200	0.348100	+	0.937457i	$0.386827\pi$
$678$	−38.2780	−1.47006
$679$	7.46114	0.286332
$680$	12.8967	0.494565
$681$	35.0386	1.34268
$682$	18.5463	0.710173
$683$	9.70328	0.371286	0.185643	−	0.982617i	$-0.440563\pi$
$683$	9.70328	0.371286	0.185643	+	0.982617i	$0.440563\pi$
$684$	16.3135	0.623763
$685$	16.8803	0.644962
$686$	44.0472	1.68173
$687$	−22.9608	−0.876010
$688$	−1.59970	−0.0609878
$689$	−38.3527	−1.46112
$690$	−24.9902	−0.951361
$691$	45.9000	1.74612	0.873059	−	0.487615i	$-0.162133\pi$
$691$	45.9000	1.74612	0.873059	+	0.487615i	$0.162133\pi$
$692$	27.1620	1.03255
$693$	9.67731	0.367610
$694$	−77.4727	−2.94082
$695$	12.6496	0.479826
$696$	−16.9559	−0.642711
$697$	8.76549	0.332017
$698$	−47.1521	−1.78473
$699$	22.4750	0.850083
$700$	7.95750	0.300765
$701$	46.3137	1.74924	0.874621	−	0.484807i	$-0.161110\pi$
$701$	46.3137	1.74924	0.874621	+	0.484807i	$0.161110\pi$
$702$	−48.6508	−1.83620
$703$	18.5771	0.700648
$704$	68.2870	2.57366
$705$	14.0184	0.527963
$706$	−10.8420	−0.408045
$707$	34.7284	1.30610
$708$	−67.5288	−2.53789
$709$	−32.1345	−1.20684	−0.603418	−	0.797425i	$-0.706195\pi$
$709$	−32.1345	−1.20684	−0.603418	+	0.797425i	$0.706195\pi$
$710$	11.0595	0.415056
$711$	−6.64835	−0.249333
$712$	44.3656	1.66267
$713$	11.3380	0.424611
$714$	41.2353	1.54319
$715$	19.9563	0.746322
$716$	39.3944	1.47224
$717$	−27.1807	−1.01508
$718$	−32.4565	−1.21127
$719$	6.24392	0.232859	0.116429	−	0.993199i	$-0.462855\pi$
$719$	6.24392	0.232859	0.116429	+	0.993199i	$0.462855\pi$
$720$	0.188356	0.00701961
$721$	−29.5010	−1.09868
$722$	−67.2746	−2.50370
$723$	1.95315	0.0726383
$724$	−71.0868	−2.64192
$725$	4.20392	0.156130
$726$	−56.6035	−2.10075
$727$	−24.0601	−0.892339	−0.446170	−	0.894948i	$-0.647212\pi$
$727$	−24.0601	−0.892339	−0.446170	+	0.894948i	$0.647212\pi$
$728$	25.5289	0.946165
$729$	29.9743	1.11016
$730$	14.9084	0.551785
$731$	−30.0933	−1.11304
$732$	22.7140	0.839534
$733$	−5.67735	−0.209698	−0.104849	−	0.994488i	$-0.533436\pi$
$733$	−5.67735	−0.209698	−0.104849	+	0.994488i	$0.533436\pi$
$734$	49.2403	1.81749
$735$	−1.09956	−0.0405579
$736$	43.3869	1.59926
$737$	−75.5490	−2.78288
$738$	−3.05411	−0.112423
$739$	−5.58461	−0.205433	−0.102717	−	0.994711i	$-0.532753\pi$
$739$	−5.58461	−0.205433	−0.102717	+	0.994711i	$0.532753\pi$
$740$	−8.47213	−0.311442
$741$	39.8737	1.46480
$742$	−57.4567	−2.10930
$743$	15.0241	0.551181	0.275591	−	0.961275i	$-0.411127\pi$
$743$	15.0241	0.551181	0.275591	+	0.961275i	$0.411127\pi$
$744$	−6.26472	−0.229676
$745$	6.26500	0.229532
$746$	−9.44153	−0.345679
$747$	2.79346	0.102208
$748$	80.2234	2.93326
$749$	−3.21392	−0.117434
$750$	−3.42350	−0.125008
$751$	6.55352	0.239141	0.119571	−	0.992826i	$-0.461848\pi$
$751$	6.55352	0.239141	0.119571	+	0.992826i	$0.461848\pi$
$752$	−2.38274	−0.0868897
$753$	32.8060	1.19552
$754$	36.3821	1.32496
$755$	−4.22092	−0.153615
$756$	−44.7335	−1.62694
$757$	−5.82641	−0.211764	−0.105882	−	0.994379i	$-0.533767\pi$
$757$	−5.82641	−0.211764	−0.105882	+	0.994379i	$0.533767\pi$
$758$	15.2923	0.555440
$759$	−57.6258	−2.09168
$760$	18.6827	0.677694
$761$	−16.9781	−0.615456	−0.307728	−	0.951474i	$-0.599569\pi$
$761$	−16.9781	−0.615456	−0.307728	+	0.951474i	$0.599569\pi$
$762$	2.51304	0.0910380
$763$	46.5823	1.68639
$764$	30.4793	1.10270
$765$	3.54334	0.128110
$766$	15.2626	0.551459
$767$	53.7130	1.93946
$768$	−21.5277	−0.776815
$769$	24.1800	0.871953	0.435977	−	0.899958i	$-0.356403\pi$
$769$	24.1800	0.871953	0.435977	+	0.899958i	$0.356403\pi$
$770$	29.8968	1.07740
$771$	5.07537	0.182785
$772$	−66.9718	−2.41037
$773$	−37.1179	−1.33504	−0.667519	−	0.744593i	$-0.732644\pi$
$773$	−37.1179	−1.33504	−0.667519	+	0.744593i	$0.732644\pi$
$774$	10.4853	0.376885
$775$	1.55323	0.0557937
$776$	−7.98884	−0.286783
$777$	−10.0417	−0.360244
$778$	−14.4369	−0.517589
$779$	12.6981	0.454957
$780$	−18.1845	−0.651110
$781$	25.5025	0.912551
$782$	79.9065	2.85745
$783$	−23.6326	−0.844560
$784$	0.186895	0.00667482
$785$	8.69378	0.310294
$786$	−49.8394	−1.77771
$787$	−43.6677	−1.55659	−0.778293	−	0.627901i	$-0.783914\pi$
$787$	−43.6677	−1.55659	−0.778293	+	0.627901i	$0.783914\pi$
$788$	−77.6599	−2.76652
$789$	38.0000	1.35284
$790$	−20.5392	−0.730752
$791$	27.9952	0.995395
$792$	−10.3618	−0.368189
$793$	−18.0669	−0.641575
$794$	33.8252	1.20041
$795$	15.1716	0.538083
$796$	−67.0158	−2.37531
$797$	4.42656	0.156797	0.0783984	−	0.996922i	$-0.475019\pi$
$797$	4.42656	0.156797	0.0783984	+	0.996922i	$0.475019\pi$
$798$	59.7353	2.11461
$799$	−44.8239	−1.58576
$800$	5.94373	0.210142
$801$	12.1894	0.430690
$802$	−46.5030	−1.64208
$803$	34.3778	1.21317
$804$	68.8416	2.42786
$805$	18.2770	0.644179
$806$	13.4422	0.473480
$807$	−27.3903	−0.964186
$808$	−37.1847	−1.30815
$809$	−34.2476	−1.20408	−0.602040	−	0.798466i	$-0.705645\pi$
$809$	−34.2476	−1.20408	−0.602040	+	0.798466i	$0.705645\pi$
$810$	14.2170	0.499536
$811$	9.05938	0.318118	0.159059	−	0.987269i	$-0.449154\pi$
$811$	9.05938	0.318118	0.159059	+	0.987269i	$0.449154\pi$
$812$	33.4527	1.17396
$813$	10.6968	0.375154
$814$	−31.8303	−1.11565
$815$	−12.8601	−0.450471
$816$	1.85072	0.0647881
$817$	−43.5946	−1.52518
$818$	−32.5208	−1.13706
$819$	7.01402	0.245090
$820$	−5.79100	−0.202231
$821$	9.69965	0.338520	0.169260	−	0.985571i	$-0.445862\pi$
$821$	9.69965	0.338520	0.169260	+	0.985571i	$0.445862\pi$
$822$	−57.7895	−2.01564
$823$	17.9811	0.626783	0.313391	−	0.949624i	$-0.398535\pi$
$823$	17.9811	0.626783	0.313391	+	0.949624i	$0.398535\pi$
$824$	31.5875	1.10040
$825$	−7.89435	−0.274846
$826$	80.4682	2.79985
$827$	−1.06152	−0.0369127	−0.0184563	−	0.999830i	$-0.505875\pi$
$827$	−1.06152	−0.0369127	−0.0184563	+	0.999830i	$0.505875\pi$
$828$	−17.0880	−0.593848
$829$	24.3000	0.843973	0.421986	−	0.906602i	$-0.361333\pi$
$829$	24.3000	0.843973	0.421986	+	0.906602i	$0.361333\pi$
$830$	8.63004	0.299553
$831$	−17.1237	−0.594016
$832$	49.4938	1.71589
$833$	3.51585	0.121817
$834$	−43.3058	−1.49956
$835$	7.17778	0.248397
$836$	116.215	4.01939
$837$	−8.73158	−0.301808
$838$	4.58358	0.158337
$839$	19.8474	0.685207	0.342604	−	0.939480i	$-0.388691\pi$
$839$	19.8474	0.685207	0.342604	+	0.939480i	$0.388691\pi$
$840$	−10.0988	−0.348442
$841$	−11.3270	−0.390588
$842$	22.5761	0.778024
$843$	−11.0847	−0.381777
$844$	73.5408	2.53138
$845$	1.46412	0.0503674
$846$	15.6178	0.536950
$847$	41.3978	1.42245
$848$	−2.57877	−0.0885552
$849$	−25.5461	−0.876740
$850$	10.9467	0.375468
$851$	−19.4590	−0.667046
$852$	−23.2383	−0.796132
$853$	−50.5322	−1.73019	−0.865095	−	0.501608i	$-0.832742\pi$
$853$	−50.5322	−1.73019	−0.865095	+	0.501608i	$0.832742\pi$
$854$	−27.0663	−0.926189
$855$	5.13304	0.175546
$856$	3.44123	0.117619
$857$	37.7693	1.29017	0.645087	−	0.764109i	$-0.276821\pi$
$857$	37.7693	1.29017	0.645087	+	0.764109i	$0.276821\pi$
$858$	−68.3202	−2.33241
$859$	47.6612	1.62618	0.813089	−	0.582139i	$-0.197784\pi$
$859$	47.6612	1.62618	0.813089	+	0.582139i	$0.197784\pi$
$860$	19.8814	0.677951
$861$	−6.86385	−0.233919
$862$	−70.4004	−2.39785
$863$	5.82396	0.198250	0.0991249	−	0.995075i	$-0.468396\pi$
$863$	5.82396	0.198250	0.0991249	+	0.995075i	$0.468396\pi$
$864$	−33.4130	−1.13673
$865$	8.54652	0.290591
$866$	−3.68915	−0.125362
$867$	9.23961	0.313794
$868$	12.3598	0.419520
$869$	−47.3620	−1.60665
$870$	−14.3921	−0.487938
$871$	−54.7573	−1.85538
$872$	−49.8769	−1.68905
$873$	−2.19492	−0.0742867
$874$	115.756	3.91552
$875$	2.50382	0.0846447
$876$	−31.3256	−1.05840
$877$	41.2030	1.39133	0.695664	−	0.718367i	$-0.255110\pi$
$877$	41.2030	1.39133	0.695664	+	0.718367i	$0.255110\pi$
$878$	−7.68226	−0.259264
$879$	37.9500	1.28002
$880$	1.34182	0.0452329
$881$	−43.7348	−1.47346	−0.736731	−	0.676185i	$-0.763632\pi$
$881$	−43.7348	−1.47346	−0.736731	+	0.676185i	$0.763632\pi$
$882$	−1.22501	−0.0412482
$883$	5.26972	0.177340	0.0886701	−	0.996061i	$-0.471738\pi$
$883$	5.26972	0.177340	0.0886701	+	0.996061i	$0.471738\pi$
$884$	58.1452	1.95564
$885$	−21.2479	−0.714241
$886$	7.08634	0.238070
$887$	−16.2680	−0.546227	−0.273113	−	0.961982i	$-0.588053\pi$
$887$	−16.2680	−0.546227	−0.273113	+	0.961982i	$0.588053\pi$
$888$	10.7519	0.360811
$889$	−1.83795	−0.0616429
$890$	37.6574	1.26228
$891$	32.7835	1.09829
$892$	76.8095	2.57177
$893$	−64.9340	−2.17294
$894$	−21.4482	−0.717335
$895$	12.3954	0.414334
$896$	44.3832	1.48274
$897$	−41.7666	−1.39455
$898$	−55.0696	−1.83770
$899$	6.52966	0.217776
$900$	−2.34094	−0.0780313
$901$	−48.5115	−1.61615
$902$	−21.7571	−0.724432
$903$	23.5647	0.784184
$904$	−29.9752	−0.996961
$905$	−22.3674	−0.743519
$906$	14.4503	0.480079
$907$	4.99565	0.165878	0.0829388	−	0.996555i	$-0.473569\pi$
$907$	4.99565	0.165878	0.0829388	+	0.996555i	$0.473569\pi$
$908$	74.0178	2.45637
$909$	−10.2164	−0.338857
$910$	21.6689	0.718317
$911$	−37.7436	−1.25050	−0.625251	−	0.780424i	$-0.715003\pi$
$911$	−37.7436	−1.25050	−0.625251	+	0.780424i	$0.715003\pi$
$912$	2.68104	0.0887780
$913$	19.9003	0.658603
$914$	59.6474	1.97296
$915$	7.14696	0.236271
$916$	−48.5039	−1.60261
$917$	36.4508	1.20371
$918$	−61.5373	−2.03104
$919$	−2.66360	−0.0878640	−0.0439320	−	0.999035i	$-0.513988\pi$
$919$	−2.66360	−0.0878640	−0.0439320	+	0.999035i	$0.513988\pi$
$920$	−19.5696	−0.645192
$921$	−7.25597	−0.239092
$922$	−50.5886	−1.66605
$923$	18.4840	0.608407
$924$	−62.8193	−2.06660
$925$	−2.66575	−0.0876495
$926$	24.2285	0.796196
$927$	8.67861	0.285043
$928$	24.9870	0.820237
$929$	42.7429	1.40235	0.701175	−	0.712989i	$-0.252659\pi$
$929$	42.7429	1.40235	0.701175	+	0.712989i	$0.252659\pi$
$930$	−5.31748	−0.174367
$931$	5.09323	0.166924
$932$	47.4777	1.55518
$933$	−13.5101	−0.442300
$934$	83.6560	2.73731
$935$	25.2423	0.825511
$936$	−7.51010	−0.245475
$937$	−2.15757	−0.0704848	−0.0352424	−	0.999379i	$-0.511220\pi$
$937$	−2.15757	−0.0704848	−0.0352424	+	0.999379i	$0.511220\pi$
$938$	−82.0326	−2.67846
$939$	32.0029	1.04438
$940$	29.6133	0.965881
$941$	12.0300	0.392165	0.196083	−	0.980587i	$-0.437178\pi$
$941$	12.0300	0.392165	0.196083	+	0.980587i	$0.437178\pi$
$942$	−29.7631	−0.969735
$943$	−13.3009	−0.433137
$944$	3.61157	0.117546
$945$	−14.0754	−0.457873
$946$	74.6956	2.42856
$947$	3.89171	0.126464	0.0632318	−	0.997999i	$-0.479859\pi$
$947$	3.89171	0.126464	0.0632318	+	0.997999i	$0.479859\pi$
$948$	43.1571	1.40168
$949$	24.9167	0.808830
$950$	15.8579	0.514497
$951$	11.1990	0.363153
$952$	32.2910	1.04656
$953$	11.9064	0.385685	0.192842	−	0.981230i	$-0.438229\pi$
$953$	11.9064	0.385685	0.192842	+	0.981230i	$0.438229\pi$
$954$	16.9026	0.547242
$955$	9.59032	0.310335
$956$	−57.4183	−1.85704
$957$	−33.1872	−1.07279
$958$	−62.0901	−2.00604
$959$	42.2652	1.36482
$960$	−19.5789	−0.631906
$961$	−28.5875	−0.922177
$962$	−23.0703	−0.743816
$963$	0.945472	0.0304674
$964$	4.12596	0.132888
$965$	−21.0726	−0.678353
$966$	−62.5711	−2.01319
$967$	−4.05346	−0.130351	−0.0651753	−	0.997874i	$-0.520761\pi$
$967$	−4.05346	−0.130351	−0.0651753	+	0.997874i	$0.520761\pi$
$968$	−44.3258	−1.42468
$969$	50.4354	1.62022
$970$	−6.78091	−0.217722
$971$	−35.5755	−1.14167	−0.570836	−	0.821064i	$-0.693381\pi$
$971$	−35.5755	−1.14167	−0.570836	+	0.821064i	$0.693381\pi$
$972$	23.7253	0.760990
$973$	31.6723	1.01537
$974$	43.3893	1.39028
$975$	−5.72175	−0.183243
$976$	−1.21479	−0.0388844
$977$	−2.31298	−0.0739988	−0.0369994	−	0.999315i	$-0.511780\pi$
$977$	−2.31298	−0.0739988	−0.0369994	+	0.999315i	$0.511780\pi$
$978$	44.0266	1.40782
$979$	86.8354	2.77527
$980$	−2.32278	−0.0741985
$981$	−13.7036	−0.437522
$982$	0.600618	0.0191665
$983$	−24.5345	−0.782527	−0.391264	−	0.920279i	$-0.627962\pi$
$983$	−24.5345	−0.782527	−0.391264	+	0.920279i	$0.627962\pi$
$984$	7.34931	0.234287
$985$	−24.4357	−0.778585
$986$	46.0189	1.46554
$987$	35.0996	1.11723
$988$	84.2318	2.67977
$989$	45.6642	1.45204
$990$	−8.79503	−0.279524
$991$	36.3419	1.15444	0.577218	−	0.816590i	$-0.304138\pi$
$991$	36.3419	1.15444	0.577218	+	0.816590i	$0.304138\pi$
$992$	9.23198	0.293116
$993$	11.6809	0.370683
$994$	27.6911	0.878308
$995$	−21.0865	−0.668487
$996$	−18.1335	−0.574582
$997$	43.8370	1.38833	0.694166	−	0.719815i	$-0.255773\pi$
$997$	43.8370	1.38833	0.694166	+	0.719815i	$0.255773\pi$
$998$	9.94409	0.314775
$999$	14.9857	0.474126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.20	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.27555 q^{2} +1.50447 q^{3} +3.17814 q^{4} +1.00000 q^{5} -3.42350 q^{6} +2.50382 q^{7} -2.68091 q^{8} -0.736575 q^{9} +O(q^{10})\)	\(q-2.27555 q^{2} +1.50447 q^{3} +3.17814 q^{4} +1.00000 q^{5} -3.42350 q^{6} +2.50382 q^{7} -2.68091 q^{8} -0.736575 q^{9} -2.27555 q^{10} -5.24727 q^{11} +4.78141 q^{12} -3.80317 q^{13} -5.69758 q^{14} +1.50447 q^{15} -0.255719 q^{16} -4.81056 q^{17} +1.67612 q^{18} -6.96879 q^{19} +3.17814 q^{20} +3.76692 q^{21} +11.9404 q^{22} +7.29962 q^{23} -4.03335 q^{24} +1.00000 q^{25} +8.65432 q^{26} -5.62156 q^{27} +7.95750 q^{28} +4.20392 q^{29} -3.42350 q^{30} +1.55323 q^{31} +5.94373 q^{32} -7.89435 q^{33} +10.9467 q^{34} +2.50382 q^{35} -2.34094 q^{36} -2.66575 q^{37} +15.8579 q^{38} -5.72175 q^{39} -2.68091 q^{40} -1.82214 q^{41} -8.57183 q^{42} +6.25569 q^{43} -16.6765 q^{44} -0.736575 q^{45} -16.6107 q^{46} +9.31783 q^{47} -0.384720 q^{48} -0.730862 q^{49} -2.27555 q^{50} -7.23733 q^{51} -12.0870 q^{52} +10.0844 q^{53} +12.7921 q^{54} -5.24727 q^{55} -6.71253 q^{56} -10.4843 q^{57} -9.56624 q^{58} -14.1232 q^{59} +4.78141 q^{60} +4.75049 q^{61} -3.53446 q^{62} -1.84426 q^{63} -13.0138 q^{64} -3.80317 q^{65} +17.9640 q^{66} +14.3978 q^{67} -15.2886 q^{68} +10.9820 q^{69} -5.69758 q^{70} -4.86014 q^{71} +1.97469 q^{72} -6.55155 q^{73} +6.06606 q^{74} +1.50447 q^{75} -22.1478 q^{76} -13.1382 q^{77} +13.0201 q^{78} +9.02603 q^{79} -0.255719 q^{80} -6.24773 q^{81} +4.14637 q^{82} -3.79250 q^{83} +11.9718 q^{84} -4.81056 q^{85} -14.2351 q^{86} +6.32467 q^{87} +14.0675 q^{88} -16.5487 q^{89} +1.67612 q^{90} -9.52248 q^{91} +23.1992 q^{92} +2.33679 q^{93} -21.2032 q^{94} -6.96879 q^{95} +8.94215 q^{96} +2.97990 q^{97} +1.66312 q^{98} +3.86501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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