LMFDB - Embedded newform 8035.2.a.e.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} +O(q^{10})$	\(q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} -2.52944 q^{10} +0.560693 q^{11} -10.6638 q^{12} -5.31322 q^{13} -0.649984 q^{14} -2.42468 q^{15} +6.54671 q^{16} -6.32354 q^{17} -7.28238 q^{18} +0.712431 q^{19} +4.39805 q^{20} -0.623064 q^{21} -1.41824 q^{22} +6.12771 q^{23} +14.7074 q^{24} +1.00000 q^{25} +13.4394 q^{26} +0.293257 q^{27} +1.13016 q^{28} -5.89093 q^{29} +6.13306 q^{30} +6.98787 q^{31} -4.42808 q^{32} -1.35950 q^{33} +15.9950 q^{34} +0.256968 q^{35} +12.6622 q^{36} -11.9083 q^{37} -1.80205 q^{38} +12.8828 q^{39} -6.06570 q^{40} +0.740184 q^{41} +1.57600 q^{42} -6.63627 q^{43} +2.46595 q^{44} +2.87905 q^{45} -15.4997 q^{46} -10.2422 q^{47} -15.8736 q^{48} -6.93397 q^{49} -2.52944 q^{50} +15.3325 q^{51} -23.3678 q^{52} -2.83729 q^{53} -0.741775 q^{54} +0.560693 q^{55} -1.55869 q^{56} -1.72742 q^{57} +14.9007 q^{58} +2.23817 q^{59} -10.6638 q^{60} -8.91289 q^{61} -17.6754 q^{62} +0.739824 q^{63} -1.89288 q^{64} -5.31322 q^{65} +3.43877 q^{66} -0.700692 q^{67} -27.8112 q^{68} -14.8577 q^{69} -0.649984 q^{70} -12.3380 q^{71} -17.4635 q^{72} +10.8490 q^{73} +30.1212 q^{74} -2.42468 q^{75} +3.13331 q^{76} +0.144080 q^{77} -32.5863 q^{78} +3.82196 q^{79} +6.54671 q^{80} -9.34821 q^{81} -1.87225 q^{82} +4.20223 q^{83} -2.74026 q^{84} -6.32354 q^{85} +16.7860 q^{86} +14.2836 q^{87} -3.40100 q^{88} +2.98034 q^{89} -7.28238 q^{90} -1.36533 q^{91} +26.9500 q^{92} -16.9433 q^{93} +25.9070 q^{94} +0.712431 q^{95} +10.7367 q^{96} +7.51559 q^{97} +17.5390 q^{98} +1.61427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.52944	−1.78858	−0.894291	−	0.447487i	$-0.852319\pi$
$2$	−2.52944	−1.78858	−0.894291	+	0.447487i	$0.852319\pi$
$3$	−2.42468	−1.39989	−0.699944	−	0.714198i	$-0.746792\pi$
$3$	−2.42468	−1.39989	−0.699944	+	0.714198i	$0.746792\pi$
$4$	4.39805	2.19902
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	6.13306	2.50381
$7$	0.256968	0.0971247	0.0485624	−	0.998820i	$-0.484536\pi$
$7$	0.256968	0.0971247	0.0485624	+	0.998820i	$0.484536\pi$
$8$	−6.06570	−2.14455
$9$	2.87905	0.959684
$10$	−2.52944	−0.799878
$11$	0.560693	0.169055	0.0845277	−	0.996421i	$-0.473062\pi$
$11$	0.560693	0.169055	0.0845277	+	0.996421i	$0.473062\pi$
$12$	−10.6638	−3.07838
$13$	−5.31322	−1.47362	−0.736811	−	0.676099i	$-0.763669\pi$
$13$	−5.31322	−1.47362	−0.736811	+	0.676099i	$0.763669\pi$
$14$	−0.649984	−0.173715
$15$	−2.42468	−0.626049
$16$	6.54671	1.63668
$17$	−6.32354	−1.53368	−0.766842	−	0.641836i	$-0.778173\pi$
$17$	−6.32354	−1.53368	−0.766842	+	0.641836i	$0.778173\pi$
$18$	−7.28238	−1.71647
$19$	0.712431	0.163443	0.0817215	−	0.996655i	$-0.473958\pi$
$19$	0.712431	0.163443	0.0817215	+	0.996655i	$0.473958\pi$
$20$	4.39805	0.983433
$21$	−0.623064	−0.135964
$22$	−1.41824	−0.302369
$23$	6.12771	1.27772	0.638858	−	0.769324i	$-0.279407\pi$
$23$	6.12771	1.27772	0.638858	+	0.769324i	$0.279407\pi$
$24$	14.7074	3.00213
$25$	1.00000	0.200000
$26$	13.4394	2.63569
$27$	0.293257	0.0564374
$28$	1.13016	0.213579
$29$	−5.89093	−1.09392	−0.546959	−	0.837159i	$-0.684215\pi$
$29$	−5.89093	−1.09392	−0.546959	+	0.837159i	$0.684215\pi$
$30$	6.13306	1.11974
$31$	6.98787	1.25506	0.627529	−	0.778593i	$-0.284066\pi$
$31$	6.98787	1.25506	0.627529	+	0.778593i	$0.284066\pi$
$32$	−4.42808	−0.782781
$33$	−1.35950	−0.236658
$34$	15.9950	2.74312
$35$	0.256968	0.0434355
$36$	12.6622	2.11037
$37$	−11.9083	−1.95771	−0.978854	−	0.204561i	$-0.934423\pi$
$37$	−11.9083	−1.95771	−0.978854	+	0.204561i	$0.934423\pi$
$38$	−1.80205	−0.292331
$39$	12.8828	2.06290
$40$	−6.06570	−0.959071
$41$	0.740184	0.115597	0.0577987	−	0.998328i	$-0.481592\pi$
$41$	0.740184	0.115597	0.0577987	+	0.998328i	$0.481592\pi$
$42$	1.57600	0.243182
$43$	−6.63627	−1.01202	−0.506011	−	0.862527i	$-0.668880\pi$
$43$	−6.63627	−1.01202	−0.506011	+	0.862527i	$0.668880\pi$
$44$	2.46595	0.371756
$45$	2.87905	0.429184
$46$	−15.4997	−2.28530
$47$	−10.2422	−1.49398	−0.746991	−	0.664834i	$-0.768502\pi$
$47$	−10.2422	−1.49398	−0.746991	+	0.664834i	$0.768502\pi$
$48$	−15.8736	−2.29116
$49$	−6.93397	−0.990567
$50$	−2.52944	−0.357716
$51$	15.3325	2.14698
$52$	−23.3678	−3.24053
$53$	−2.83729	−0.389731	−0.194866	−	0.980830i	$-0.562427\pi$
$53$	−2.83729	−0.389731	−0.194866	+	0.980830i	$0.562427\pi$
$54$	−0.741775	−0.100943
$55$	0.560693	0.0756038
$56$	−1.55869	−0.208289
$57$	−1.72742	−0.228802
$58$	14.9007	1.95656
$59$	2.23817	0.291385	0.145692	−	0.989330i	$-0.453459\pi$
$59$	2.23817	0.291385	0.145692	+	0.989330i	$0.453459\pi$
$60$	−10.6638	−1.37669
$61$	−8.91289	−1.14118	−0.570589	−	0.821236i	$-0.693285\pi$
$61$	−8.91289	−1.14118	−0.570589	+	0.821236i	$0.693285\pi$
$62$	−17.6754	−2.24477
$63$	0.739824	0.0932091
$64$	−1.89288	−0.236609
$65$	−5.31322	−0.659023
$66$	3.43877	0.423283
$67$	−0.700692	−0.0856031	−0.0428016	−	0.999084i	$-0.513628\pi$
$67$	−0.700692	−0.0856031	−0.0428016	+	0.999084i	$0.513628\pi$
$68$	−27.8112	−3.37261
$69$	−14.8577	−1.78866
$70$	−0.649984	−0.0776879
$71$	−12.3380	−1.46425	−0.732125	−	0.681171i	$-0.761471\pi$
$71$	−12.3380	−1.46425	−0.732125	+	0.681171i	$0.761471\pi$
$72$	−17.4635	−2.05809
$73$	10.8490	1.26978	0.634890	−	0.772603i	$-0.281046\pi$
$73$	10.8490	1.26978	0.634890	+	0.772603i	$0.281046\pi$
$74$	30.1212	3.50152
$75$	−2.42468	−0.279977
$76$	3.13331	0.359415
$77$	0.144080	0.0164195
$78$	−32.5863	−3.68967
$79$	3.82196	0.430005	0.215002	−	0.976614i	$-0.431024\pi$
$79$	3.82196	0.430005	0.215002	+	0.976614i	$0.431024\pi$
$80$	6.54671	0.731944
$81$	−9.34821	−1.03869
$82$	−1.87225	−0.206755
$83$	4.20223	0.461255	0.230627	−	0.973042i	$-0.425922\pi$
$83$	4.20223	0.461255	0.230627	+	0.973042i	$0.425922\pi$
$84$	−2.74026	−0.298987
$85$	−6.32354	−0.685884
$86$	16.7860	1.81008
$87$	14.2836	1.53136
$88$	−3.40100	−0.362547
$89$	2.98034	0.315915	0.157958	−	0.987446i	$-0.449509\pi$
$89$	2.98034	0.315915	0.157958	+	0.987446i	$0.449509\pi$
$90$	−7.28238	−0.767630
$91$	−1.36533	−0.143125
$92$	26.9500	2.80973
$93$	−16.9433	−1.75694
$94$	25.9070	2.67211
$95$	0.712431	0.0730939
$96$	10.7367	1.09581
$97$	7.51559	0.763093	0.381546	−	0.924350i	$-0.375392\pi$
$97$	7.51559	0.763093	0.381546	+	0.924350i	$0.375392\pi$
$98$	17.5390	1.77171
$99$	1.61427	0.162240
$100$	4.39805	0.439805
$101$	8.33417	0.829281	0.414640	−	0.909985i	$-0.363907\pi$
$101$	8.33417	0.829281	0.414640	+	0.909985i	$0.363907\pi$
$102$	−38.7827	−3.84006
$103$	−7.14407	−0.703926	−0.351963	−	0.936014i	$-0.614486\pi$
$103$	−7.14407	−0.703926	−0.351963	+	0.936014i	$0.614486\pi$
$104$	32.2284	3.16025
$105$	−0.623064	−0.0608048
$106$	7.17673	0.697066
$107$	11.4466	1.10658	0.553291	−	0.832988i	$-0.313372\pi$
$107$	11.4466	1.10658	0.553291	+	0.832988i	$0.313372\pi$
$108$	1.28976	0.124107
$109$	4.92878	0.472092	0.236046	−	0.971742i	$-0.424148\pi$
$109$	4.92878	0.472092	0.236046	+	0.971742i	$0.424148\pi$
$110$	−1.41824	−0.135224
$111$	28.8737	2.74057
$112$	1.68229	0.158962
$113$	4.70337	0.442456	0.221228	−	0.975222i	$-0.428993\pi$
$113$	4.70337	0.442456	0.221228	+	0.975222i	$0.428993\pi$
$114$	4.36939	0.409230
$115$	6.12771	0.571412
$116$	−25.9086	−2.40555
$117$	−15.2970	−1.41421
$118$	−5.66131	−0.521166
$119$	−1.62495	−0.148959
$120$	14.7074	1.34259
$121$	−10.6856	−0.971420
$122$	22.5446	2.04109
$123$	−1.79471	−0.161823
$124$	30.7330	2.75990
$125$	1.00000	0.0894427
$126$	−1.87134	−0.166712
$127$	2.40934	0.213794	0.106897	−	0.994270i	$-0.465908\pi$
$127$	2.40934	0.213794	0.106897	+	0.994270i	$0.465908\pi$
$128$	13.6441	1.20598
$129$	16.0908	1.41672
$130$	13.4394	1.17872
$131$	−2.66779	−0.233086	−0.116543	−	0.993186i	$-0.537181\pi$
$131$	−2.66779	−0.233086	−0.116543	+	0.993186i	$0.537181\pi$
$132$	−5.97914	−0.520417
$133$	0.183072	0.0158744
$134$	1.77235	0.153108
$135$	0.293257	0.0252396
$136$	38.3567	3.28906
$137$	−15.6485	−1.33694	−0.668469	−	0.743740i	$-0.733050\pi$
$137$	−15.6485	−1.33694	−0.668469	+	0.743740i	$0.733050\pi$
$138$	37.5816	3.19916
$139$	−9.47689	−0.803819	−0.401910	−	0.915679i	$-0.631653\pi$
$139$	−9.47689	−0.803819	−0.401910	+	0.915679i	$0.631653\pi$
$140$	1.13016	0.0955156
$141$	24.8341	2.09141
$142$	31.2081	2.61893
$143$	−2.97908	−0.249123
$144$	18.8483	1.57069
$145$	−5.89093	−0.489215
$146$	−27.4418	−2.27110
$147$	16.8126	1.38668
$148$	−52.3731	−4.30504
$149$	5.41227	0.443391	0.221695	−	0.975116i	$-0.428841\pi$
$149$	5.41227	0.443391	0.221695	+	0.975116i	$0.428841\pi$
$150$	6.13306	0.500762
$151$	−6.02995	−0.490710	−0.245355	−	0.969433i	$-0.578905\pi$
$151$	−6.02995	−0.490710	−0.245355	+	0.969433i	$0.578905\pi$
$152$	−4.32140	−0.350511
$153$	−18.2058	−1.47185
$154$	−0.364441	−0.0293675
$155$	6.98787	0.561279
$156$	56.6593	4.53637
$157$	−14.8601	−1.18596	−0.592982	−	0.805216i	$-0.702049\pi$
$157$	−14.8601	−1.18596	−0.592982	+	0.805216i	$0.702049\pi$
$158$	−9.66741	−0.769098
$159$	6.87950	0.545580
$160$	−4.42808	−0.350070
$161$	1.57463	0.124098
$162$	23.6457	1.85778
$163$	9.87485	0.773458	0.386729	−	0.922193i	$-0.373605\pi$
$163$	9.87485	0.773458	0.386729	+	0.922193i	$0.373605\pi$
$164$	3.25536	0.254201
$165$	−1.35950	−0.105837
$166$	−10.6293	−0.824991
$167$	7.76686	0.601018	0.300509	−	0.953779i	$-0.402843\pi$
$167$	7.76686	0.601018	0.300509	+	0.953779i	$0.402843\pi$
$168$	3.77932	0.291581
$169$	15.2303	1.17156
$170$	15.9950	1.22676
$171$	2.05113	0.156854
$172$	−29.1866	−2.22546
$173$	10.9674	0.833834	0.416917	−	0.908945i	$-0.363111\pi$
$173$	10.9674	0.833834	0.416917	+	0.908945i	$0.363111\pi$
$174$	−36.1294	−2.73897
$175$	0.256968	0.0194249
$176$	3.67070	0.276689
$177$	−5.42684	−0.407906
$178$	−7.53858	−0.565040
$179$	11.0270	0.824200	0.412100	−	0.911139i	$-0.364796\pi$
$179$	11.0270	0.824200	0.412100	+	0.911139i	$0.364796\pi$
$180$	12.6622	0.943785
$181$	14.5274	1.07981	0.539907	−	0.841725i	$-0.318459\pi$
$181$	14.5274	1.07981	0.539907	+	0.841725i	$0.318459\pi$
$182$	3.45350	0.255991
$183$	21.6109	1.59752
$184$	−37.1689	−2.74013
$185$	−11.9083	−0.875514
$186$	42.8570	3.14243
$187$	−3.54557	−0.259277
$188$	−45.0457	−3.28530
$189$	0.0753577	0.00548146
$190$	−1.80205	−0.130734
$191$	−26.8149	−1.94026	−0.970130	−	0.242587i	$-0.922004\pi$
$191$	−26.8149	−1.94026	−0.970130	+	0.242587i	$0.922004\pi$
$192$	4.58961	0.331226
$193$	−3.11703	−0.224369	−0.112185	−	0.993687i	$-0.535785\pi$
$193$	−3.11703	−0.224369	−0.112185	+	0.993687i	$0.535785\pi$
$194$	−19.0102	−1.36485
$195$	12.8828	0.922558
$196$	−30.4959	−2.17828
$197$	−15.1781	−1.08139	−0.540697	−	0.841217i	$-0.681840\pi$
$197$	−15.1781	−1.08139	−0.540697	+	0.841217i	$0.681840\pi$
$198$	−4.08318	−0.290179
$199$	−11.3538	−0.804850	−0.402425	−	0.915453i	$-0.631833\pi$
$199$	−11.3538	−0.804850	−0.402425	+	0.915453i	$0.631833\pi$
$200$	−6.06570	−0.428910
$201$	1.69895	0.119835
$202$	−21.0807	−1.48324
$203$	−1.51378	−0.106247
$204$	67.4332	4.72127
$205$	0.740184	0.0516967
$206$	18.0705	1.25903
$207$	17.6420	1.22620
$208$	−34.7841	−2.41184
$209$	0.399455	0.0276309
$210$	1.57600	0.108754
$211$	11.1800	0.769665	0.384832	−	0.922986i	$-0.374259\pi$
$211$	11.1800	0.769665	0.384832	+	0.922986i	$0.374259\pi$
$212$	−12.4785	−0.857028
$213$	29.9156	2.04978
$214$	−28.9534	−1.97921
$215$	−6.63627	−0.452590
$216$	−1.77881	−0.121033
$217$	1.79566	0.121897
$218$	−12.4670	−0.844375
$219$	−26.3053	−1.77755
$220$	2.46595	0.166255
$221$	33.5983	2.26007
$222$	−73.0342	−4.90173
$223$	−27.4596	−1.83883	−0.919415	−	0.393289i	$-0.871337\pi$
$223$	−27.4596	−1.83883	−0.919415	+	0.393289i	$0.871337\pi$
$224$	−1.13787	−0.0760274
$225$	2.87905	0.191937
$226$	−11.8969	−0.791369
$227$	10.5942	0.703164	0.351582	−	0.936157i	$-0.385644\pi$
$227$	10.5942	0.703164	0.351582	+	0.936157i	$0.385644\pi$
$228$	−7.59725	−0.503140
$229$	−10.6220	−0.701923	−0.350962	−	0.936390i	$-0.614145\pi$
$229$	−10.6220	−0.701923	−0.350962	+	0.936390i	$0.614145\pi$
$230$	−15.4997	−1.02202
$231$	−0.349348	−0.0229854
$232$	35.7326	2.34596
$233$	−6.38347	−0.418195	−0.209097	−	0.977895i	$-0.567053\pi$
$233$	−6.38347	−0.418195	−0.209097	+	0.977895i	$0.567053\pi$
$234$	38.6929	2.52943
$235$	−10.2422	−0.668129
$236$	9.84357	0.640762
$237$	−9.26702	−0.601958
$238$	4.11020	0.266425
$239$	−0.689703	−0.0446132	−0.0223066	−	0.999751i	$-0.507101\pi$
$239$	−0.689703	−0.0446132	−0.0223066	+	0.999751i	$0.507101\pi$
$240$	−15.8736	−1.02464
$241$	−16.4419	−1.05911	−0.529557	−	0.848274i	$-0.677642\pi$
$241$	−16.4419	−1.05911	−0.529557	+	0.848274i	$0.677642\pi$
$242$	27.0286	1.73746
$243$	21.7866	1.39761
$244$	−39.1993	−2.50948
$245$	−6.93397	−0.442995
$246$	4.53960	0.289434
$247$	−3.78530	−0.240853
$248$	−42.3863	−2.69153
$249$	−10.1890	−0.645704
$250$	−2.52944	−0.159976
$251$	13.0815	0.825695	0.412847	−	0.910800i	$-0.364534\pi$
$251$	13.0815	0.825695	0.412847	+	0.910800i	$0.364534\pi$
$252$	3.25378	0.204969
$253$	3.43577	0.216005
$254$	−6.09427	−0.382389
$255$	15.3325	0.960161
$256$	−30.7260	−1.92038
$257$	−8.24367	−0.514226	−0.257113	−	0.966381i	$-0.582771\pi$
$257$	−8.24367	−0.514226	−0.257113	+	0.966381i	$0.582771\pi$
$258$	−40.7007	−2.53391
$259$	−3.06004	−0.190142
$260$	−23.3678	−1.44921
$261$	−16.9603	−1.04982
$262$	6.74800	0.416893
$263$	11.3850	0.702031	0.351015	−	0.936370i	$-0.385836\pi$
$263$	11.3850	0.702031	0.351015	+	0.936370i	$0.385836\pi$
$264$	8.24631	0.507526
$265$	−2.83729	−0.174293
$266$	−0.463069	−0.0283926
$267$	−7.22636	−0.442246
$268$	−3.08167	−0.188243
$269$	23.3969	1.42653	0.713267	−	0.700893i	$-0.247215\pi$
$269$	23.3969	1.42653	0.713267	+	0.700893i	$0.247215\pi$
$270$	−0.741775	−0.0451430
$271$	−2.63333	−0.159964	−0.0799818	−	0.996796i	$-0.525486\pi$
$271$	−2.63333	−0.159964	−0.0799818	+	0.996796i	$0.525486\pi$
$272$	−41.3984	−2.51015
$273$	3.31047	0.200359
$274$	39.5818	2.39122
$275$	0.560693	0.0338111
$276$	−65.3449	−3.93330
$277$	23.2174	1.39500	0.697500	−	0.716585i	$-0.254296\pi$
$277$	23.2174	1.39500	0.697500	+	0.716585i	$0.254296\pi$
$278$	23.9712	1.43770
$279$	20.1184	1.20446
$280$	−1.55869	−0.0931496
$281$	6.70722	0.400119	0.200060	−	0.979784i	$-0.435886\pi$
$281$	6.70722	0.400119	0.200060	+	0.979784i	$0.435886\pi$
$282$	−62.8162	−3.74065
$283$	−27.8629	−1.65628	−0.828139	−	0.560523i	$-0.810600\pi$
$283$	−27.8629	−1.65628	−0.828139	+	0.560523i	$0.810600\pi$
$284$	−54.2630	−3.21992
$285$	−1.72742	−0.102323
$286$	7.53540	0.445578
$287$	0.190204	0.0112274
$288$	−12.7487	−0.751223
$289$	22.9872	1.35219
$290$	14.9007	0.875001
$291$	−18.2229	−1.06824
$292$	47.7144	2.79227
$293$	19.2210	1.12291	0.561453	−	0.827509i	$-0.310243\pi$
$293$	19.2210	1.12291	0.561453	+	0.827509i	$0.310243\pi$
$294$	−42.5265	−2.48019
$295$	2.23817	0.130311
$296$	72.2320	4.19840
$297$	0.164427	0.00954104
$298$	−13.6900	−0.793040
$299$	−32.5579	−1.88287
$300$	−10.6638	−0.615677
$301$	−1.70531	−0.0982924
$302$	15.2524	0.877675
$303$	−20.2077	−1.16090
$304$	4.66408	0.267503
$305$	−8.91289	−0.510351
$306$	46.0504	2.63253
$307$	−5.71845	−0.326369	−0.163185	−	0.986596i	$-0.552177\pi$
$307$	−5.71845	−0.326369	−0.163185	+	0.986596i	$0.552177\pi$
$308$	0.633671	0.0361067
$309$	17.3220	0.985417
$310$	−17.6754	−1.00389
$311$	−19.8674	−1.12657	−0.563287	−	0.826261i	$-0.690464\pi$
$311$	−19.8674	−1.12657	−0.563287	+	0.826261i	$0.690464\pi$
$312$	−78.1434	−4.42400
$313$	−27.7658	−1.56942	−0.784709	−	0.619865i	$-0.787187\pi$
$313$	−27.7658	−1.56942	−0.784709	+	0.619865i	$0.787187\pi$
$314$	37.5876	2.12119
$315$	0.739824	0.0416844
$316$	16.8092	0.945590
$317$	10.5408	0.592031	0.296015	−	0.955183i	$-0.404342\pi$
$317$	10.5408	0.592031	0.296015	+	0.955183i	$0.404342\pi$
$318$	−17.4013	−0.975814
$319$	−3.30300	−0.184933
$320$	−1.89288	−0.105815
$321$	−27.7542	−1.54909
$322$	−3.98291	−0.221959
$323$	−4.50509	−0.250670
$324$	−41.1139	−2.28410
$325$	−5.31322	−0.294724
$326$	−24.9778	−1.38339
$327$	−11.9507	−0.660875
$328$	−4.48974	−0.247904
$329$	−2.63192	−0.145103
$330$	3.43877	0.189298
$331$	23.1138	1.27045	0.635224	−	0.772328i	$-0.280908\pi$
$331$	23.1138	1.27045	0.635224	+	0.772328i	$0.280908\pi$
$332$	18.4816	1.01431
$333$	−34.2845	−1.87878
$334$	−19.6458	−1.07497
$335$	−0.700692	−0.0382829
$336$	−4.07902	−0.222529
$337$	−30.9590	−1.68645	−0.843223	−	0.537564i	$-0.819345\pi$
$337$	−30.9590	−1.68645	−0.843223	+	0.537564i	$0.819345\pi$
$338$	−38.5240	−2.09543
$339$	−11.4042	−0.619389
$340$	−27.8112	−1.50828
$341$	3.91805	0.212174
$342$	−5.18820	−0.280545
$343$	−3.58058	−0.193333
$344$	40.2536	2.17033
$345$	−14.8577	−0.799913
$346$	−27.7413	−1.49138
$347$	19.3837	1.04057	0.520286	−	0.853992i	$-0.325825\pi$
$347$	19.3837	1.04057	0.520286	+	0.853992i	$0.325825\pi$
$348$	62.8199	3.36750
$349$	0.0165295	0.000884806 0	0.000442403	−	1.00000i	$-0.499859\pi$
$349$	0.0165295	0.000884806 0	0.000442403		1.00000i	$0.499859\pi$
$350$	−0.649984	−0.0347431
$351$	−1.55814	−0.0831673
$352$	−2.48279	−0.132333
$353$	−6.58197	−0.350323	−0.175161	−	0.984540i	$-0.556045\pi$
$353$	−6.58197	−0.350323	−0.175161	+	0.984540i	$0.556045\pi$
$354$	13.7268	0.729573
$355$	−12.3380	−0.654832
$356$	13.1077	0.694705
$357$	3.93997	0.208525
$358$	−27.8922	−1.47415
$359$	12.0294	0.634889	0.317444	−	0.948277i	$-0.397175\pi$
$359$	12.0294	0.634889	0.317444	+	0.948277i	$0.397175\pi$
$360$	−17.4635	−0.920406
$361$	−18.4924	−0.973286
$362$	−36.7462	−1.93133
$363$	25.9092	1.35988
$364$	−6.00476	−0.314735
$365$	10.8490	0.567863
$366$	−54.6633	−2.85730
$367$	25.3888	1.32528	0.662641	−	0.748937i	$-0.269435\pi$
$367$	25.3888	1.32528	0.662641	+	0.748937i	$0.269435\pi$
$368$	40.1164	2.09121
$369$	2.13103	0.110937
$370$	30.1212	1.56593
$371$	−0.729092	−0.0378525
$372$	−74.5174	−3.86355
$373$	−24.3993	−1.26335	−0.631673	−	0.775235i	$-0.717632\pi$
$373$	−24.3993	−1.26335	−0.631673	+	0.775235i	$0.717632\pi$
$374$	8.96828	0.463739
$375$	−2.42468	−0.125210
$376$	62.1262	3.20392
$377$	31.2998	1.61202
$378$	−0.190612	−0.00980404
$379$	4.08624	0.209896	0.104948	−	0.994478i	$-0.466532\pi$
$379$	4.08624	0.209896	0.104948	+	0.994478i	$0.466532\pi$
$380$	3.13331	0.160735
$381$	−5.84187	−0.299288
$382$	67.8266	3.47031
$383$	−0.228835	−0.0116929	−0.00584645	−	0.999983i	$-0.501861\pi$
$383$	−0.228835	−0.0116929	−0.00584645	+	0.999983i	$0.501861\pi$
$384$	−33.0824	−1.68823
$385$	0.144080	0.00734300
$386$	7.88434	0.401302
$387$	−19.1062	−0.971222
$388$	33.0539	1.67806
$389$	21.2474	1.07729	0.538644	−	0.842534i	$-0.318937\pi$
$389$	21.2474	1.07729	0.538644	+	0.842534i	$0.318937\pi$
$390$	−32.5863	−1.65007
$391$	−38.7489	−1.95961
$392$	42.0594	2.12432
$393$	6.46853	0.326294
$394$	38.3920	1.93416
$395$	3.82196	0.192304
$396$	7.09961	0.356769
$397$	30.2025	1.51582	0.757910	−	0.652359i	$-0.226220\pi$
$397$	30.2025	1.51582	0.757910	+	0.652359i	$0.226220\pi$
$398$	28.7187	1.43954
$399$	−0.443890	−0.0222223
$400$	6.54671	0.327335
$401$	−5.88318	−0.293792	−0.146896	−	0.989152i	$-0.546928\pi$
$401$	−5.88318	−0.293792	−0.146896	+	0.989152i	$0.546928\pi$
$402$	−4.29738	−0.214334
$403$	−37.1280	−1.84948
$404$	36.6540	1.82361
$405$	−9.34821	−0.464516
$406$	3.82901	0.190031
$407$	−6.67689	−0.330961
$408$	−93.0026	−4.60431
$409$	12.4334	0.614792	0.307396	−	0.951582i	$-0.400542\pi$
$409$	12.4334	0.614792	0.307396	+	0.951582i	$0.400542\pi$
$410$	−1.87225	−0.0924638
$411$	37.9424	1.87156
$412$	−31.4199	−1.54795
$413$	0.575138	0.0283007
$414$	−44.6243	−2.19317
$415$	4.20223	0.206279
$416$	23.5273	1.15352
$417$	22.9784	1.12526
$418$	−1.01040	−0.0494201
$419$	0.268305	0.0131076	0.00655378	−	0.999979i	$-0.497914\pi$
$419$	0.268305	0.0131076	0.00655378	+	0.999979i	$0.497914\pi$
$420$	−2.74026	−0.133711
$421$	9.42360	0.459278	0.229639	−	0.973276i	$-0.426245\pi$
$421$	9.42360	0.459278	0.229639	+	0.973276i	$0.426245\pi$
$422$	−28.2792	−1.37661
$423$	−29.4879	−1.43375
$424$	17.2101	0.835798
$425$	−6.32354	−0.306737
$426$	−75.6696	−3.66621
$427$	−2.29033	−0.110837
$428$	50.3426	2.43340
$429$	7.22331	0.348745
$430$	16.7860	0.809494
$431$	−7.08354	−0.341202	−0.170601	−	0.985340i	$-0.554571\pi$
$431$	−7.08354	−0.341202	−0.170601	+	0.985340i	$0.554571\pi$
$432$	1.91987	0.0923697
$433$	−9.61195	−0.461921	−0.230961	−	0.972963i	$-0.574187\pi$
$433$	−9.61195	−0.461921	−0.230961	+	0.972963i	$0.574187\pi$
$434$	−4.54200	−0.218023
$435$	14.2836	0.684846
$436$	21.6770	1.03814
$437$	4.36558	0.208834
$438$	66.5376	3.17929
$439$	0.649770	0.0310118	0.0155059	−	0.999880i	$-0.495064\pi$
$439$	0.649770	0.0310118	0.0155059	+	0.999880i	$0.495064\pi$
$440$	−3.40100	−0.162136
$441$	−19.9633	−0.950631
$442$	−84.9848	−4.04232
$443$	7.71222	0.366418	0.183209	−	0.983074i	$-0.441351\pi$
$443$	7.71222	0.366418	0.183209	+	0.983074i	$0.441351\pi$
$444$	126.988	6.02658
$445$	2.98034	0.141282
$446$	69.4572	3.28890
$447$	−13.1230	−0.620697
$448$	−0.486408	−0.0229806
$449$	−32.4820	−1.53292	−0.766460	−	0.642292i	$-0.777983\pi$
$449$	−32.4820	−1.53292	−0.766460	+	0.642292i	$0.777983\pi$
$450$	−7.28238	−0.343295
$451$	0.415016	0.0195424
$452$	20.6856	0.972971
$453$	14.6207	0.686939
$454$	−26.7974	−1.25767
$455$	−1.36533	−0.0640075
$456$	10.4780	0.490677
$457$	11.1553	0.521825	0.260912	−	0.965362i	$-0.415977\pi$
$457$	11.1553	0.521825	0.260912	+	0.965362i	$0.415977\pi$
$458$	26.8677	1.25545
$459$	−1.85442	−0.0865571
$460$	26.9500	1.25655
$461$	29.8157	1.38866	0.694328	−	0.719659i	$-0.255702\pi$
$461$	29.8157	1.38866	0.694328	+	0.719659i	$0.255702\pi$
$462$	0.883652	0.0411112
$463$	−7.56499	−0.351575	−0.175787	−	0.984428i	$-0.556247\pi$
$463$	−7.56499	−0.351575	−0.175787	+	0.984428i	$0.556247\pi$
$464$	−38.5662	−1.79039
$465$	−16.9433	−0.785727
$466$	16.1466	0.747976
$467$	−24.9538	−1.15473	−0.577363	−	0.816488i	$-0.695918\pi$
$467$	−24.9538	−1.15473	−0.577363	+	0.816488i	$0.695918\pi$
$468$	−67.2770	−3.10988
$469$	−0.180055	−0.00831418
$470$	25.9070	1.19500
$471$	36.0309	1.66022
$472$	−13.5761	−0.624889
$473$	−3.72091	−0.171088
$474$	23.4403	1.07665
$475$	0.712431	0.0326886
$476$	−7.14659	−0.327563
$477$	−8.16870	−0.374019
$478$	1.74456	0.0797943
$479$	37.2881	1.70374	0.851869	−	0.523756i	$-0.175469\pi$
$479$	37.2881	1.70374	0.851869	+	0.523756i	$0.175469\pi$
$480$	10.7367	0.490059
$481$	63.2712	2.88492
$482$	41.5886	1.89431
$483$	−3.81796	−0.173723
$484$	−46.9959	−2.13618
$485$	7.51559	0.341265
$486$	−55.1078	−2.49974
$487$	−2.90652	−0.131707	−0.0658536	−	0.997829i	$-0.520977\pi$
$487$	−2.90652	−0.131707	−0.0658536	+	0.997829i	$0.520977\pi$
$488$	54.0629	2.44731
$489$	−23.9433	−1.08275
$490$	17.5390	0.792332
$491$	1.75165	0.0790508	0.0395254	−	0.999219i	$-0.487415\pi$
$491$	1.75165	0.0790508	0.0395254	+	0.999219i	$0.487415\pi$
$492$	−7.89320	−0.355853
$493$	37.2515	1.67773
$494$	9.57468	0.430785
$495$	1.61427	0.0725558
$496$	45.7475	2.05412
$497$	−3.17047	−0.142215
$498$	25.7725	1.15489
$499$	−11.0372	−0.494094	−0.247047	−	0.969004i	$-0.579460\pi$
$499$	−11.0372	−0.494094	−0.247047	+	0.969004i	$0.579460\pi$
$500$	4.39805	0.196687
$501$	−18.8321	−0.841357
$502$	−33.0887	−1.47682
$503$	−17.5668	−0.783265	−0.391633	−	0.920122i	$-0.628090\pi$
$503$	−17.5668	−0.783265	−0.391633	+	0.920122i	$0.628090\pi$
$504$	−4.48755	−0.199891
$505$	8.33417	0.370866
$506$	−8.69055	−0.386342
$507$	−36.9285	−1.64005
$508$	10.5964	0.470139
$509$	−35.7059	−1.58264	−0.791318	−	0.611405i	$-0.790605\pi$
$509$	−35.7059	−1.58264	−0.791318	+	0.611405i	$0.790605\pi$
$510$	−38.7827	−1.71733
$511$	2.78784	0.123327
$512$	50.4314	2.22877
$513$	0.208926	0.00922429
$514$	20.8518	0.919734
$515$	−7.14407	−0.314805
$516$	70.7681	3.11539
$517$	−5.74274	−0.252566
$518$	7.74018	0.340084
$519$	−26.5923	−1.16727
$520$	32.2284	1.41331
$521$	−31.5676	−1.38300	−0.691500	−	0.722376i	$-0.743050\pi$
$521$	−31.5676	−1.38300	−0.691500	+	0.722376i	$0.743050\pi$
$522$	42.9000	1.87768
$523$	14.1432	0.618437	0.309219	−	0.950991i	$-0.399933\pi$
$523$	14.1432	0.618437	0.309219	+	0.950991i	$0.399933\pi$
$524$	−11.7331	−0.512561
$525$	−0.623064	−0.0271927
$526$	−28.7977	−1.25564
$527$	−44.1881	−1.92486
$528$	−8.90025	−0.387333
$529$	14.5489	0.632560
$530$	7.17673	0.311737
$531$	6.44381	0.279638
$532$	0.805159	0.0349081
$533$	−3.93276	−0.170347
$534$	18.2786	0.790992
$535$	11.4466	0.494879
$536$	4.25019	0.183580
$537$	−26.7370	−1.15379
$538$	−59.1809	−2.55147
$539$	−3.88783	−0.167461
$540$	1.28976	0.0555023
$541$	−1.17196	−0.0503864	−0.0251932	−	0.999683i	$-0.508020\pi$
$541$	−1.17196	−0.0503864	−0.0251932	+	0.999683i	$0.508020\pi$
$542$	6.66085	0.286108
$543$	−35.2243	−1.51162
$544$	28.0011	1.20054
$545$	4.92878	0.211126
$546$	−8.37363	−0.358358
$547$	−22.0249	−0.941715	−0.470857	−	0.882209i	$-0.656055\pi$
$547$	−22.0249	−0.941715	−0.470857	+	0.882209i	$0.656055\pi$
$548$	−68.8226	−2.93996
$549$	−25.6607	−1.09517
$550$	−1.41824	−0.0604738
$551$	−4.19688	−0.178793
$552$	90.1225	3.83587
$553$	0.982122	0.0417641
$554$	−58.7269	−2.49507
$555$	28.8737	1.22562
$556$	−41.6798	−1.76762
$557$	−19.3907	−0.821610	−0.410805	−	0.911723i	$-0.634752\pi$
$557$	−19.3907	−0.821610	−0.410805	+	0.911723i	$0.634752\pi$
$558$	−50.8883	−2.15427
$559$	35.2599	1.49134
$560$	1.68229	0.0710899
$561$	8.59685	0.362959
$562$	−16.9655	−0.715646
$563$	−0.659476	−0.0277936	−0.0138968	−	0.999903i	$-0.504424\pi$
$563$	−0.659476	−0.0277936	−0.0138968	+	0.999903i	$0.504424\pi$
$564$	109.221	4.59905
$565$	4.70337	0.197872
$566$	70.4774	2.96239
$567$	−2.40219	−0.100883
$568$	74.8385	3.14016
$569$	16.4349	0.688986	0.344493	−	0.938789i	$-0.388051\pi$
$569$	16.4349	0.688986	0.344493	+	0.938789i	$0.388051\pi$
$570$	4.36939	0.183013
$571$	−25.7096	−1.07591	−0.537957	−	0.842973i	$-0.680804\pi$
$571$	−25.7096	−1.07591	−0.537957	+	0.842973i	$0.680804\pi$
$572$	−13.1021	−0.547828
$573$	65.0175	2.71614
$574$	−0.481108	−0.0200811
$575$	6.12771	0.255543
$576$	−5.44969	−0.227070
$577$	−1.71956	−0.0715861	−0.0357930	−	0.999359i	$-0.511396\pi$
$577$	−1.71956	−0.0715861	−0.0357930	+	0.999359i	$0.511396\pi$
$578$	−58.1446	−2.41850
$579$	7.55780	0.314091
$580$	−25.9086	−1.07580
$581$	1.07984	0.0447992
$582$	46.0936	1.91064
$583$	−1.59085	−0.0658862
$584$	−65.8068	−2.72310
$585$	−15.2970	−0.632454
$586$	−48.6184	−2.00841
$587$	31.9336	1.31804	0.659020	−	0.752125i	$-0.270971\pi$
$587$	31.9336	1.31804	0.659020	+	0.752125i	$0.270971\pi$
$588$	73.9427	3.04934
$589$	4.97838	0.205130
$590$	−5.66131	−0.233072
$591$	36.8020	1.51383
$592$	−77.9600	−3.20414
$593$	33.1485	1.36125	0.680624	−	0.732633i	$-0.261709\pi$
$593$	33.1485	1.36125	0.680624	+	0.732633i	$0.261709\pi$
$594$	−0.415908	−0.0170649
$595$	−1.62495	−0.0666163
$596$	23.8034	0.975026
$597$	27.5293	1.12670
$598$	82.3530	3.36767
$599$	41.2813	1.68671	0.843355	−	0.537358i	$-0.180577\pi$
$599$	41.2813	1.68671	0.843355	+	0.537358i	$0.180577\pi$
$600$	14.7074	0.600425
$601$	−42.9948	−1.75380	−0.876898	−	0.480677i	$-0.840391\pi$
$601$	−42.9948	−1.75380	−0.876898	+	0.480677i	$0.840391\pi$
$602$	4.31347	0.175804
$603$	−2.01733	−0.0821520
$604$	−26.5200	−1.07908
$605$	−10.6856	−0.434432
$606$	51.1140	2.07636
$607$	13.2110	0.536216	0.268108	−	0.963389i	$-0.413602\pi$
$607$	13.2110	0.536216	0.268108	+	0.963389i	$0.413602\pi$
$608$	−3.15470	−0.127940
$609$	3.67043	0.148733
$610$	22.5446	0.912804
$611$	54.4191	2.20156
$612$	−80.0700	−3.23664
$613$	−4.08552	−0.165012	−0.0825062	−	0.996591i	$-0.526292\pi$
$613$	−4.08552	−0.165012	−0.0825062	+	0.996591i	$0.526292\pi$
$614$	14.4645	0.583738
$615$	−1.79471	−0.0723696
$616$	−0.873947	−0.0352123
$617$	−8.56336	−0.344748	−0.172374	−	0.985032i	$-0.555144\pi$
$617$	−8.56336	−0.344748	−0.172374	+	0.985032i	$0.555144\pi$
$618$	−43.8150	−1.76250
$619$	13.6141	0.547196	0.273598	−	0.961844i	$-0.411786\pi$
$619$	13.6141	0.547196	0.273598	+	0.961844i	$0.411786\pi$
$620$	30.7330	1.23426
$621$	1.79700	0.0721110
$622$	50.2532	2.01497
$623$	0.765851	0.0306832
$624$	84.3401	3.37631
$625$	1.00000	0.0400000
$626$	70.2319	2.80703
$627$	−0.968550	−0.0386802
$628$	−65.3553	−2.60796
$629$	75.3024	3.00250
$630$	−1.87134	−0.0745559
$631$	−31.6516	−1.26003	−0.630014	−	0.776583i	$-0.716951\pi$
$631$	−31.6516	−1.26003	−0.630014	+	0.776583i	$0.716951\pi$
$632$	−23.1829	−0.922166
$633$	−27.1079	−1.07744
$634$	−26.6623	−1.05890
$635$	2.40934	0.0956118
$636$	30.2564	1.19974
$637$	36.8417	1.45972
$638$	8.35474	0.330767
$639$	−35.5217	−1.40522
$640$	13.6441	0.539329
$641$	−23.7758	−0.939086	−0.469543	−	0.882910i	$-0.655581\pi$
$641$	−23.7758	−0.939086	−0.469543	+	0.882910i	$0.655581\pi$
$642$	70.2026	2.77067
$643$	−16.1474	−0.636791	−0.318395	−	0.947958i	$-0.603144\pi$
$643$	−16.1474	−0.636791	−0.318395	+	0.947958i	$0.603144\pi$
$644$	6.92527	0.272894
$645$	16.0908	0.633575
$646$	11.3953	0.448343
$647$	−36.0772	−1.41834	−0.709170	−	0.705037i	$-0.750930\pi$
$647$	−36.0772	−1.41834	−0.709170	+	0.705037i	$0.750930\pi$
$648$	56.7035	2.22752
$649$	1.25493	0.0492602
$650$	13.4394	0.527138
$651$	−4.35389	−0.170642
$652$	43.4300	1.70085
$653$	−26.9875	−1.05610	−0.528050	−	0.849213i	$-0.677077\pi$
$653$	−26.9875	−1.05610	−0.528050	+	0.849213i	$0.677077\pi$
$654$	30.2285	1.18203
$655$	−2.66779	−0.104239
$656$	4.84577	0.189196
$657$	31.2348	1.21859
$658$	6.65728	0.259528
$659$	12.1382	0.472836	0.236418	−	0.971651i	$-0.424027\pi$
$659$	12.1382	0.472836	0.236418	+	0.971651i	$0.424027\pi$
$660$	−5.97914	−0.232738
$661$	−26.4559	−1.02901	−0.514507	−	0.857486i	$-0.672025\pi$
$661$	−26.4559	−1.02901	−0.514507	+	0.857486i	$0.672025\pi$
$662$	−58.4648	−2.27230
$663$	−81.4651	−3.16384
$664$	−25.4895	−0.989183
$665$	0.183072	0.00709923
$666$	86.7206	3.36035
$667$	−36.0979	−1.39772
$668$	34.1590	1.32165
$669$	66.5806	2.57415
$670$	1.77235	0.0684720
$671$	−4.99740	−0.192922
$672$	2.75898	0.106430
$673$	38.0008	1.46482	0.732412	−	0.680861i	$-0.238394\pi$
$673$	38.0008	1.46482	0.732412	+	0.680861i	$0.238394\pi$
$674$	78.3089	3.01635
$675$	0.293257	0.0112875
$676$	66.9834	2.57628
$677$	−16.8012	−0.645722	−0.322861	−	0.946446i	$-0.604645\pi$
$677$	−16.8012	−0.645722	−0.322861	+	0.946446i	$0.604645\pi$
$678$	28.8461	1.10783
$679$	1.93127	0.0741152
$680$	38.3567	1.47091
$681$	−25.6876	−0.984350
$682$	−9.91045	−0.379491
$683$	−23.6603	−0.905335	−0.452668	−	0.891679i	$-0.649528\pi$
$683$	−23.6603	−0.905335	−0.452668	+	0.891679i	$0.649528\pi$
$684$	9.02095	0.344925
$685$	−15.6485	−0.597897
$686$	9.05685	0.345792
$687$	25.7550	0.982613
$688$	−43.4457	−1.65635
$689$	15.0751	0.574316
$690$	37.5816	1.43071
$691$	−44.5630	−1.69526	−0.847629	−	0.530590i	$-0.821970\pi$
$691$	−44.5630	−1.69526	−0.847629	+	0.530590i	$0.821970\pi$
$692$	48.2350	1.83362
$693$	0.414814	0.0157575
$694$	−49.0298	−1.86115
$695$	−9.47689	−0.359479
$696$	−86.6400	−3.28408
$697$	−4.68059	−0.177290
$698$	−0.0418104	−0.00158255
$699$	15.4778	0.585426
$700$	1.13016	0.0427159
$701$	42.1789	1.59307	0.796537	−	0.604590i	$-0.206663\pi$
$701$	42.1789	1.59307	0.796537	+	0.604590i	$0.206663\pi$
$702$	3.94121	0.148751
$703$	−8.48383	−0.319974
$704$	−1.06132	−0.0400001
$705$	24.8341	0.935305
$706$	16.6487	0.626581
$707$	2.14161	0.0805436
$708$	−23.8675	−0.896995
$709$	−36.1417	−1.35733	−0.678665	−	0.734448i	$-0.737441\pi$
$709$	−36.1417	−1.35733	−0.678665	+	0.734448i	$0.737441\pi$
$710$	31.2081	1.17122
$711$	11.0036	0.412669
$712$	−18.0778	−0.677496
$713$	42.8196	1.60361
$714$	−9.96590	−0.372964
$715$	−2.97908	−0.111411
$716$	48.4974	1.81243
$717$	1.67231	0.0624534
$718$	−30.4277	−1.13555
$719$	−20.6227	−0.769099	−0.384549	−	0.923104i	$-0.625643\pi$
$719$	−20.6227	−0.769099	−0.384549	+	0.923104i	$0.625643\pi$
$720$	18.8483	0.702436
$721$	−1.83580	−0.0683686
$722$	46.7754	1.74080
$723$	39.8662	1.48264
$724$	63.8922	2.37454
$725$	−5.89093	−0.218784
$726$	−65.5356	−2.43225
$727$	−27.4176	−1.01686	−0.508431	−	0.861103i	$-0.669774\pi$
$727$	−27.4176	−1.01686	−0.508431	+	0.861103i	$0.669774\pi$
$728$	8.28166	0.306939
$729$	−24.7808	−0.917809
$730$	−27.4418	−1.01567
$731$	41.9647	1.55212
$732$	95.0456	3.51299
$733$	19.8461	0.733034	0.366517	−	0.930411i	$-0.380550\pi$
$733$	19.8461	0.733034	0.366517	+	0.930411i	$0.380550\pi$
$734$	−64.2192	−2.37038
$735$	16.8126	0.620143
$736$	−27.1340	−1.00017
$737$	−0.392873	−0.0144717
$738$	−5.39030	−0.198420
$739$	22.3901	0.823632	0.411816	−	0.911267i	$-0.364895\pi$
$739$	22.3901	0.823632	0.411816	+	0.911267i	$0.364895\pi$
$740$	−52.3731	−1.92527
$741$	9.17813	0.337167
$742$	1.84419	0.0677023
$743$	39.2243	1.43900	0.719499	−	0.694493i	$-0.244371\pi$
$743$	39.2243	1.43900	0.719499	+	0.694493i	$0.244371\pi$
$744$	102.773	3.76784
$745$	5.41227	0.198290
$746$	61.7164	2.25960
$747$	12.0984	0.442659
$748$	−15.5936	−0.570157
$749$	2.94140	0.107476
$750$	6.13306	0.223948
$751$	−27.7488	−1.01257	−0.506285	−	0.862366i	$-0.668982\pi$
$751$	−27.7488	−1.01257	−0.506285	+	0.862366i	$0.668982\pi$
$752$	−67.0529	−2.44517
$753$	−31.7183	−1.15588
$754$	−79.1708	−2.88323
$755$	−6.02995	−0.219452
$756$	0.331426	0.0120539
$757$	13.3443	0.485008	0.242504	−	0.970150i	$-0.422031\pi$
$757$	13.3443	0.485008	0.242504	+	0.970150i	$0.422031\pi$
$758$	−10.3359	−0.375416
$759$	−8.33062	−0.302382
$760$	−4.32140	−0.156753
$761$	3.62843	0.131530	0.0657652	−	0.997835i	$-0.479051\pi$
$761$	3.62843	0.131530	0.0657652	+	0.997835i	$0.479051\pi$
$762$	14.7766	0.535301
$763$	1.26654	0.0458518
$764$	−117.933	−4.26667
$765$	−18.2058	−0.658232
$766$	0.578823	0.0209137
$767$	−11.8919	−0.429391
$768$	74.5007	2.68831
$769$	7.27894	0.262485	0.131243	−	0.991350i	$-0.458103\pi$
$769$	7.27894	0.262485	0.131243	+	0.991350i	$0.458103\pi$
$770$	−0.364441	−0.0131336
$771$	19.9882	0.719858
$772$	−13.7089	−0.493393
$773$	37.3601	1.34375	0.671875	−	0.740665i	$-0.265489\pi$
$773$	37.3601	1.34375	0.671875	+	0.740665i	$0.265489\pi$
$774$	48.3279	1.73711
$775$	6.98787	0.251012
$776$	−45.5873	−1.63649
$777$	7.41961	0.266177
$778$	−53.7440	−1.92682
$779$	0.527331	0.0188936
$780$	56.6593	2.02873
$781$	−6.91782	−0.247539
$782$	98.0127	3.50493
$783$	−1.72756	−0.0617379
$784$	−45.3947	−1.62124
$785$	−14.8601	−0.530379
$786$	−16.3617	−0.583603
$787$	−5.81874	−0.207416	−0.103708	−	0.994608i	$-0.533071\pi$
$787$	−5.81874	−0.207416	−0.103708	+	0.994608i	$0.533071\pi$
$788$	−66.7539	−2.37801
$789$	−27.6050	−0.982764
$790$	−9.66741	−0.343951
$791$	1.20862	0.0429734
$792$	−9.79165	−0.347931
$793$	47.3561	1.68167
$794$	−76.3953	−2.71117
$795$	6.87950	0.243991
$796$	−49.9346	−1.76988
$797$	32.3175	1.14475	0.572373	−	0.819993i	$-0.306023\pi$
$797$	32.3175	1.14475	0.572373	+	0.819993i	$0.306023\pi$
$798$	1.12279	0.0397464
$799$	64.7671	2.29130
$800$	−4.42808	−0.156556
$801$	8.58055	0.303179
$802$	14.8811	0.525471
$803$	6.08296	0.214663
$804$	7.47206	0.263519
$805$	1.57463	0.0554983
$806$	93.9130	3.30794
$807$	−56.7299	−1.99699
$808$	−50.5526	−1.77843
$809$	−37.6548	−1.32387	−0.661937	−	0.749560i	$-0.730265\pi$
$809$	−37.6548	−1.32387	−0.661937	+	0.749560i	$0.730265\pi$
$810$	23.6457	0.830825
$811$	−3.12197	−0.109627	−0.0548137	−	0.998497i	$-0.517456\pi$
$811$	−3.12197	−0.109627	−0.0548137	+	0.998497i	$0.517456\pi$
$812$	−6.65767	−0.233639
$813$	6.38498	0.223931
$814$	16.8888	0.591950
$815$	9.87485	0.345901
$816$	100.378	3.51392
$817$	−4.72789	−0.165408
$818$	−31.4495	−1.09961
$819$	−3.93085	−0.137355
$820$	3.25536	0.113682
$821$	47.2997	1.65077	0.825386	−	0.564569i	$-0.190958\pi$
$821$	47.2997	1.65077	0.825386	+	0.564569i	$0.190958\pi$
$822$	−95.9730	−3.34744
$823$	16.2203	0.565405	0.282702	−	0.959208i	$-0.408769\pi$
$823$	16.2203	0.565405	0.282702	+	0.959208i	$0.408769\pi$
$824$	43.3338	1.50960
$825$	−1.35950	−0.0473317
$826$	−1.45477	−0.0506181
$827$	41.1812	1.43201	0.716006	−	0.698094i	$-0.245968\pi$
$827$	41.1812	1.43201	0.716006	+	0.698094i	$0.245968\pi$
$828$	77.5904	2.69645
$829$	12.1916	0.423431	0.211716	−	0.977331i	$-0.432095\pi$
$829$	12.1916	0.423431	0.211716	+	0.977331i	$0.432095\pi$
$830$	−10.6293	−0.368947
$831$	−56.2947	−1.95284
$832$	10.0573	0.348673
$833$	43.8472	1.51922
$834$	−58.1224	−2.01261
$835$	7.76686	0.268783
$836$	1.75682	0.0607610
$837$	2.04924	0.0708321
$838$	−0.678660	−0.0234439
$839$	−19.6117	−0.677072	−0.338536	−	0.940953i	$-0.609932\pi$
$839$	−19.6117	−0.677072	−0.338536	+	0.940953i	$0.609932\pi$
$840$	3.77932	0.130399
$841$	5.70307	0.196658
$842$	−23.8364	−0.821456
$843$	−16.2628	−0.560122
$844$	49.1703	1.69251
$845$	15.2303	0.523937
$846$	74.5877	2.56438
$847$	−2.74586	−0.0943489
$848$	−18.5749	−0.637864
$849$	67.5585	2.31860
$850$	15.9950	0.548624
$851$	−72.9705	−2.50140
$852$	131.570	4.50752
$853$	−4.16124	−0.142478	−0.0712391	−	0.997459i	$-0.522695\pi$
$853$	−4.16124	−0.142478	−0.0712391	+	0.997459i	$0.522695\pi$
$854$	5.79323	0.198240
$855$	2.05113	0.0701471
$856$	−69.4315	−2.37312
$857$	1.45006	0.0495330	0.0247665	−	0.999693i	$-0.492116\pi$
$857$	1.45006	0.0495330	0.0247665	+	0.999693i	$0.492116\pi$
$858$	−18.2709	−0.623758
$859$	7.62894	0.260296	0.130148	−	0.991495i	$-0.458455\pi$
$859$	7.62894	0.260296	0.130148	+	0.991495i	$0.458455\pi$
$860$	−29.1866	−0.995256
$861$	−0.461182	−0.0157170
$862$	17.9174	0.610268
$863$	30.8038	1.04857	0.524286	−	0.851542i	$-0.324332\pi$
$863$	30.8038	1.04857	0.524286	+	0.851542i	$0.324332\pi$
$864$	−1.29857	−0.0441781
$865$	10.9674	0.372902
$866$	24.3128	0.826183
$867$	−55.7364	−1.89291
$868$	7.89738	0.268055
$869$	2.14295	0.0726946
$870$	−36.1294	−1.22490
$871$	3.72293	0.126147
$872$	−29.8965	−1.01242
$873$	21.6378	0.732328
$874$	−11.0424	−0.373516
$875$	0.256968	0.00868710
$876$	−115.692	−3.90887
$877$	42.4825	1.43453	0.717267	−	0.696799i	$-0.245393\pi$
$877$	42.4825	1.43453	0.717267	+	0.696799i	$0.245393\pi$
$878$	−1.64355	−0.0554672
$879$	−46.6048	−1.57194
$880$	3.67070	0.123739
$881$	−25.3391	−0.853695	−0.426848	−	0.904324i	$-0.640376\pi$
$881$	−25.3391	−0.853695	−0.426848	+	0.904324i	$0.640376\pi$
$882$	50.4958	1.70028
$883$	50.6192	1.70347	0.851737	−	0.523970i	$-0.175550\pi$
$883$	50.6192	1.70347	0.851737	+	0.523970i	$0.175550\pi$
$884$	147.767	4.96994
$885$	−5.42684	−0.182421
$886$	−19.5076	−0.655369
$887$	42.1374	1.41484	0.707418	−	0.706795i	$-0.249860\pi$
$887$	42.1374	1.41484	0.707418	+	0.706795i	$0.249860\pi$
$888$	−175.139	−5.87729
$889$	0.619123	0.0207647
$890$	−7.53858	−0.252694
$891$	−5.24148	−0.175596
$892$	−120.768	−4.04363
$893$	−7.29688	−0.244181
$894$	33.1938	1.11017
$895$	11.0270	0.368593
$896$	3.50609	0.117130
$897$	78.9423	2.63581
$898$	82.1611	2.74175
$899$	−41.1650	−1.37293
$900$	12.6622	0.422073
$901$	17.9417	0.597725
$902$	−1.04976	−0.0349531
$903$	4.13482	0.137598
$904$	−28.5293	−0.948869
$905$	14.5274	0.482907
$906$	−36.9820	−1.22865
$907$	−19.6576	−0.652721	−0.326360	−	0.945245i	$-0.605822\pi$
$907$	−19.6576	−0.652721	−0.326360	+	0.945245i	$0.605822\pi$
$908$	46.5939	1.54627
$909$	23.9945	0.795848
$910$	3.45350	0.114483
$911$	31.9613	1.05893	0.529463	−	0.848333i	$-0.322393\pi$
$911$	31.9613	1.05893	0.529463	+	0.848333i	$0.322393\pi$
$912$	−11.3089	−0.374475
$913$	2.35616	0.0779775
$914$	−28.2167	−0.933326
$915$	21.6109	0.714433
$916$	−46.7161	−1.54354
$917$	−0.685536	−0.0226384
$918$	4.69064	0.154814
$919$	27.0232	0.891413	0.445707	−	0.895179i	$-0.352952\pi$
$919$	27.0232	0.891413	0.445707	+	0.895179i	$0.352952\pi$
$920$	−37.1689	−1.22542
$921$	13.8654	0.456880
$922$	−75.4169	−2.48372
$923$	65.5544	2.15775
$924$	−1.53645	−0.0505454
$925$	−11.9083	−0.391542
$926$	19.1352	0.628820
$927$	−20.5681	−0.675547
$928$	26.0855	0.856299
$929$	53.0777	1.74142	0.870711	−	0.491795i	$-0.163659\pi$
$929$	53.0777	1.74142	0.870711	+	0.491795i	$0.163659\pi$
$930$	42.8570	1.40534
$931$	−4.93998	−0.161901
$932$	−28.0748	−0.919620
$933$	48.1719	1.57708
$934$	63.1191	2.06532
$935$	−3.54557	−0.115952
$936$	92.7872	3.03285
$937$	39.8321	1.30126	0.650629	−	0.759396i	$-0.274505\pi$
$937$	39.8321	1.30126	0.650629	+	0.759396i	$0.274505\pi$
$938$	0.455438	0.0148706
$939$	67.3231	2.19701
$940$	−45.0457	−1.46923
$941$	19.4679	0.634634	0.317317	−	0.948319i	$-0.397218\pi$
$941$	19.4679	0.634634	0.317317	+	0.948319i	$0.397218\pi$
$942$	−91.1378	−2.96943
$943$	4.53564	0.147701
$944$	14.6526	0.476903
$945$	0.0753577	0.00245138
$946$	9.41181	0.306004
$947$	−22.2190	−0.722020	−0.361010	−	0.932562i	$-0.617568\pi$
$947$	−22.2190	−0.722020	−0.361010	+	0.932562i	$0.617568\pi$
$948$	−40.7568	−1.32372
$949$	−57.6431	−1.87117
$950$	−1.80205	−0.0584662
$951$	−25.5580	−0.828776
$952$	9.85644	0.319449
$953$	34.6986	1.12400	0.561999	−	0.827138i	$-0.310032\pi$
$953$	34.6986	1.12400	0.561999	+	0.827138i	$0.310032\pi$
$954$	20.6622	0.668963
$955$	−26.8149	−0.867710
$956$	−3.03334	−0.0981054
$957$	8.00872	0.258885
$958$	−94.3179	−3.04727
$959$	−4.02115	−0.129850
$960$	4.58961	0.148129
$961$	17.8303	0.575170
$962$	−160.040	−5.15991
$963$	32.9553	1.06197
$964$	−72.3121	−2.32901
$965$	−3.11703	−0.100341
$966$	9.65728	0.310718
$967$	−12.0819	−0.388527	−0.194264	−	0.980949i	$-0.562232\pi$
$967$	−12.0819	−0.388527	−0.194264	+	0.980949i	$0.562232\pi$
$968$	64.8158	2.08326
$969$	10.9234	0.350910
$970$	−19.0102	−0.610381
$971$	−35.3199	−1.13347	−0.566736	−	0.823900i	$-0.691794\pi$
$971$	−35.3199	−1.13347	−0.566736	+	0.823900i	$0.691794\pi$
$972$	95.8185	3.07338
$973$	−2.43526	−0.0780707
$974$	7.35186	0.235569
$975$	12.8828	0.412581
$976$	−58.3501	−1.86774
$977$	47.9789	1.53498	0.767490	−	0.641061i	$-0.221506\pi$
$977$	47.9789	1.53498	0.767490	+	0.641061i	$0.221506\pi$
$978$	60.5631	1.93659
$979$	1.67106	0.0534072
$980$	−30.4959	−0.974156
$981$	14.1902	0.453059
$982$	−4.43068	−0.141389
$983$	52.8181	1.68463	0.842317	−	0.538982i	$-0.181191\pi$
$983$	52.8181	1.68463	0.842317	+	0.538982i	$0.181191\pi$
$984$	10.8862	0.347038
$985$	−15.1781	−0.483614
$986$	−94.2254	−3.00075
$987$	6.38156	0.203127
$988$	−16.6479	−0.529641
$989$	−40.6652	−1.29308
$990$	−4.08318	−0.129772
$991$	17.2468	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$991$	17.2468	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$992$	−30.9428	−0.982436
$993$	−56.0434	−1.77849
$994$	8.01949	0.254363
$995$	−11.3538	−0.359940
$996$	−44.8119	−1.41992
$997$	−0.846695	−0.0268151	−0.0134076	−	0.999910i	$-0.504268\pi$
$997$	−0.846695	−0.0268151	−0.0134076	+	0.999910i	$0.504268\pi$
$998$	27.9179	0.883727
$999$	−3.49219	−0.110488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.11	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} +O(q^{10})\)	\(q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} -2.52944 q^{10} +0.560693 q^{11} -10.6638 q^{12} -5.31322 q^{13} -0.649984 q^{14} -2.42468 q^{15} +6.54671 q^{16} -6.32354 q^{17} -7.28238 q^{18} +0.712431 q^{19} +4.39805 q^{20} -0.623064 q^{21} -1.41824 q^{22} +6.12771 q^{23} +14.7074 q^{24} +1.00000 q^{25} +13.4394 q^{26} +0.293257 q^{27} +1.13016 q^{28} -5.89093 q^{29} +6.13306 q^{30} +6.98787 q^{31} -4.42808 q^{32} -1.35950 q^{33} +15.9950 q^{34} +0.256968 q^{35} +12.6622 q^{36} -11.9083 q^{37} -1.80205 q^{38} +12.8828 q^{39} -6.06570 q^{40} +0.740184 q^{41} +1.57600 q^{42} -6.63627 q^{43} +2.46595 q^{44} +2.87905 q^{45} -15.4997 q^{46} -10.2422 q^{47} -15.8736 q^{48} -6.93397 q^{49} -2.52944 q^{50} +15.3325 q^{51} -23.3678 q^{52} -2.83729 q^{53} -0.741775 q^{54} +0.560693 q^{55} -1.55869 q^{56} -1.72742 q^{57} +14.9007 q^{58} +2.23817 q^{59} -10.6638 q^{60} -8.91289 q^{61} -17.6754 q^{62} +0.739824 q^{63} -1.89288 q^{64} -5.31322 q^{65} +3.43877 q^{66} -0.700692 q^{67} -27.8112 q^{68} -14.8577 q^{69} -0.649984 q^{70} -12.3380 q^{71} -17.4635 q^{72} +10.8490 q^{73} +30.1212 q^{74} -2.42468 q^{75} +3.13331 q^{76} +0.144080 q^{77} -32.5863 q^{78} +3.82196 q^{79} +6.54671 q^{80} -9.34821 q^{81} -1.87225 q^{82} +4.20223 q^{83} -2.74026 q^{84} -6.32354 q^{85} +16.7860 q^{86} +14.2836 q^{87} -3.40100 q^{88} +2.98034 q^{89} -7.28238 q^{90} -1.36533 q^{91} +26.9500 q^{92} -16.9433 q^{93} +25.9070 q^{94} +0.712431 q^{95} +10.7367 q^{96} +7.51559 q^{97} +17.5390 q^{98} +1.61427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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