LMFDB - Embedded newform 8035.2.a.e.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.28006 q^{2} +1.15086 q^{3} +3.19869 q^{4} +1.00000 q^{5} -2.62404 q^{6} -0.851041 q^{7} -2.73309 q^{8} -1.67552 q^{9} +O(q^{10})$	\(q-2.28006 q^{2} +1.15086 q^{3} +3.19869 q^{4} +1.00000 q^{5} -2.62404 q^{6} -0.851041 q^{7} -2.73309 q^{8} -1.67552 q^{9} -2.28006 q^{10} -4.47426 q^{11} +3.68125 q^{12} -5.96077 q^{13} +1.94043 q^{14} +1.15086 q^{15} -0.165768 q^{16} -7.60594 q^{17} +3.82028 q^{18} +3.98204 q^{19} +3.19869 q^{20} -0.979430 q^{21} +10.2016 q^{22} -8.96149 q^{23} -3.14541 q^{24} +1.00000 q^{25} +13.5909 q^{26} -5.38087 q^{27} -2.72221 q^{28} +7.44110 q^{29} -2.62404 q^{30} -4.02401 q^{31} +5.84413 q^{32} -5.14926 q^{33} +17.3420 q^{34} -0.851041 q^{35} -5.35946 q^{36} +6.29845 q^{37} -9.07931 q^{38} -6.86003 q^{39} -2.73309 q^{40} +10.1364 q^{41} +2.23316 q^{42} -5.50881 q^{43} -14.3118 q^{44} -1.67552 q^{45} +20.4328 q^{46} -5.34036 q^{47} -0.190776 q^{48} -6.27573 q^{49} -2.28006 q^{50} -8.75339 q^{51} -19.0667 q^{52} +10.5970 q^{53} +12.2687 q^{54} -4.47426 q^{55} +2.32597 q^{56} +4.58278 q^{57} -16.9662 q^{58} -1.91943 q^{59} +3.68125 q^{60} -10.6988 q^{61} +9.17500 q^{62} +1.42593 q^{63} -12.9935 q^{64} -5.96077 q^{65} +11.7406 q^{66} -1.14548 q^{67} -24.3290 q^{68} -10.3134 q^{69} +1.94043 q^{70} +2.44211 q^{71} +4.57933 q^{72} +0.585835 q^{73} -14.3609 q^{74} +1.15086 q^{75} +12.7373 q^{76} +3.80778 q^{77} +15.6413 q^{78} -8.15531 q^{79} -0.165768 q^{80} -1.16609 q^{81} -23.1116 q^{82} -11.0014 q^{83} -3.13289 q^{84} -7.60594 q^{85} +12.5604 q^{86} +8.56368 q^{87} +12.2286 q^{88} +14.6865 q^{89} +3.82028 q^{90} +5.07286 q^{91} -28.6650 q^{92} -4.63108 q^{93} +12.1764 q^{94} +3.98204 q^{95} +6.72579 q^{96} +10.1915 q^{97} +14.3091 q^{98} +7.49670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.28006	−1.61225	−0.806124	−	0.591746i	$-0.798439\pi$
$2$	−2.28006	−1.61225	−0.806124	+	0.591746i	$0.798439\pi$
$3$	1.15086	0.664450	0.332225	−	0.943200i	$-0.392201\pi$
$3$	1.15086	0.664450	0.332225	+	0.943200i	$0.392201\pi$
$4$	3.19869	1.59934
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.62404	−1.07126
$7$	−0.851041	−0.321663	−0.160832	−	0.986982i	$-0.551418\pi$
$7$	−0.851041	−0.321663	−0.160832	+	0.986982i	$0.551418\pi$
$8$	−2.73309	−0.966292
$9$	−1.67552	−0.558506
$10$	−2.28006	−0.721019
$11$	−4.47426	−1.34904	−0.674521	−	0.738256i	$-0.735650\pi$
$11$	−4.47426	−1.34904	−0.674521	+	0.738256i	$0.735650\pi$
$12$	3.68125	1.06269
$13$	−5.96077	−1.65322	−0.826611	−	0.562774i	$-0.809734\pi$
$13$	−5.96077	−1.65322	−0.826611	+	0.562774i	$0.809734\pi$
$14$	1.94043	0.518601
$15$	1.15086	0.297151
$16$	−0.165768	−0.0414419
$17$	−7.60594	−1.84471	−0.922356	−	0.386342i	$-0.873739\pi$
$17$	−7.60594	−1.84471	−0.922356	+	0.386342i	$0.873739\pi$
$18$	3.82028	0.900450
$19$	3.98204	0.913544	0.456772	−	0.889584i	$-0.349006\pi$
$19$	3.98204	0.913544	0.456772	+	0.889584i	$0.349006\pi$
$20$	3.19869	0.715249
$21$	−0.979430	−0.213729
$22$	10.2016	2.17499
$23$	−8.96149	−1.86860	−0.934300	−	0.356487i	$-0.883974\pi$
$23$	−8.96149	−1.86860	−0.934300	+	0.356487i	$0.883974\pi$
$24$	−3.14541	−0.642053
$25$	1.00000	0.200000
$26$	13.5909	2.66540
$27$	−5.38087	−1.03555
$28$	−2.72221	−0.514450
$29$	7.44110	1.38178	0.690889	−	0.722961i	$-0.257219\pi$
$29$	7.44110	1.38178	0.690889	+	0.722961i	$0.257219\pi$
$30$	−2.62404	−0.479082
$31$	−4.02401	−0.722733	−0.361367	−	0.932424i	$-0.617690\pi$
$31$	−4.02401	−0.722733	−0.361367	+	0.932424i	$0.617690\pi$
$32$	5.84413	1.03311
$33$	−5.14926	−0.896371
$34$	17.3420	2.97413
$35$	−0.851041	−0.143852
$36$	−5.35946	−0.893243
$37$	6.29845	1.03546	0.517730	−	0.855544i	$-0.326777\pi$
$37$	6.29845	1.03546	0.517730	+	0.855544i	$0.326777\pi$
$38$	−9.07931	−1.47286
$39$	−6.86003	−1.09848
$40$	−2.73309	−0.432139
$41$	10.1364	1.58304	0.791518	−	0.611146i	$-0.209291\pi$
$41$	10.1364	1.58304	0.791518	+	0.611146i	$0.209291\pi$
$42$	2.23316	0.344585
$43$	−5.50881	−0.840086	−0.420043	−	0.907504i	$-0.637985\pi$
$43$	−5.50881	−0.840086	−0.420043	+	0.907504i	$0.637985\pi$
$44$	−14.3118	−2.15758
$45$	−1.67552	−0.249771
$46$	20.4328	3.01265
$47$	−5.34036	−0.778971	−0.389486	−	0.921033i	$-0.627347\pi$
$47$	−5.34036	−0.778971	−0.389486	+	0.921033i	$0.627347\pi$
$48$	−0.190776	−0.0275361
$49$	−6.27573	−0.896533
$50$	−2.28006	−0.322450
$51$	−8.75339	−1.22572
$52$	−19.0667	−2.64407
$53$	10.5970	1.45560	0.727802	−	0.685787i	$-0.240542\pi$
$53$	10.5970	1.45560	0.727802	+	0.685787i	$0.240542\pi$
$54$	12.2687	1.66956
$55$	−4.47426	−0.603310
$56$	2.32597	0.310820
$57$	4.58278	0.607005
$58$	−16.9662	−2.22777
$59$	−1.91943	−0.249888	−0.124944	−	0.992164i	$-0.539875\pi$
$59$	−1.91943	−0.249888	−0.124944	+	0.992164i	$0.539875\pi$
$60$	3.68125	0.475247
$61$	−10.6988	−1.36984	−0.684919	−	0.728620i	$-0.740162\pi$
$61$	−10.6988	−1.36984	−0.684919	+	0.728620i	$0.740162\pi$
$62$	9.17500	1.16523
$63$	1.42593	0.179651
$64$	−12.9935	−1.62418
$65$	−5.96077	−0.739343
$66$	11.7406	1.44517
$67$	−1.14548	−0.139942	−0.0699712	−	0.997549i	$-0.522291\pi$
$67$	−1.14548	−0.139942	−0.0699712	+	0.997549i	$0.522291\pi$
$68$	−24.3290	−2.95033
$69$	−10.3134	−1.24159
$70$	1.94043	0.231925
$71$	2.44211	0.289825	0.144913	−	0.989444i	$-0.453710\pi$
$71$	2.44211	0.289825	0.144913	+	0.989444i	$0.453710\pi$
$72$	4.57933	0.539679
$73$	0.585835	0.0685668	0.0342834	−	0.999412i	$-0.489085\pi$
$73$	0.585835	0.0685668	0.0342834	+	0.999412i	$0.489085\pi$
$74$	−14.3609	−1.66942
$75$	1.15086	0.132890
$76$	12.7373	1.46107
$77$	3.80778	0.433937
$78$	15.6413	1.77103
$79$	−8.15531	−0.917544	−0.458772	−	0.888554i	$-0.651710\pi$
$79$	−8.15531	−0.917544	−0.458772	+	0.888554i	$0.651710\pi$
$80$	−0.165768	−0.0185334
$81$	−1.16609	−0.129566
$82$	−23.1116	−2.55225
$83$	−11.0014	−1.20756	−0.603781	−	0.797150i	$-0.706340\pi$
$83$	−11.0014	−1.20756	−0.603781	+	0.797150i	$0.706340\pi$
$84$	−3.13289	−0.341827
$85$	−7.60594	−0.824980
$86$	12.5604	1.35443
$87$	8.56368	0.918123
$88$	12.2286	1.30357
$89$	14.6865	1.55677	0.778383	−	0.627789i	$-0.216040\pi$
$89$	14.6865	1.55677	0.778383	+	0.627789i	$0.216040\pi$
$90$	3.82028	0.402693
$91$	5.07286	0.531780
$92$	−28.6650	−2.98854
$93$	−4.63108	−0.480221
$94$	12.1764	1.25589
$95$	3.98204	0.408549
$96$	6.72579	0.686448
$97$	10.1915	1.03479	0.517394	−	0.855747i	$-0.326902\pi$
$97$	10.1915	1.03479	0.517394	+	0.855747i	$0.326902\pi$
$98$	14.3091	1.44543
$99$	7.49670	0.753447
$100$	3.19869	0.319869
$101$	−1.69842	−0.169000	−0.0844998	−	0.996423i	$-0.526929\pi$
$101$	−1.69842	−0.169000	−0.0844998	+	0.996423i	$0.526929\pi$
$102$	19.9583	1.97616
$103$	−3.19745	−0.315054	−0.157527	−	0.987515i	$-0.550352\pi$
$103$	−3.19745	−0.315054	−0.157527	+	0.987515i	$0.550352\pi$
$104$	16.2913	1.59749
$105$	−0.979430	−0.0955826
$106$	−24.1617	−2.34680
$107$	1.90224	0.183897	0.0919484	−	0.995764i	$-0.470691\pi$
$107$	1.90224	0.183897	0.0919484	+	0.995764i	$0.470691\pi$
$108$	−17.2117	−1.65620
$109$	−18.9596	−1.81600	−0.907998	−	0.418974i	$-0.862390\pi$
$109$	−18.9596	−1.81600	−0.907998	+	0.418974i	$0.862390\pi$
$110$	10.2016	0.972685
$111$	7.24865	0.688012
$112$	0.141075	0.0133303
$113$	−17.2936	−1.62684	−0.813422	−	0.581674i	$-0.802398\pi$
$113$	−17.2936	−1.62684	−0.813422	+	0.581674i	$0.802398\pi$
$114$	−10.4490	−0.978642
$115$	−8.96149	−0.835663
$116$	23.8018	2.20994
$117$	9.98737	0.923333
$118$	4.37641	0.402881
$119$	6.47296	0.593376
$120$	−3.14541	−0.287135
$121$	9.01904	0.819913
$122$	24.3939	2.20852
$123$	11.6656	1.05185
$124$	−12.8716	−1.15590
$125$	1.00000	0.0894427
$126$	−3.25122	−0.289641
$127$	−8.08267	−0.717221	−0.358610	−	0.933487i	$-0.616749\pi$
$127$	−8.08267	−0.717221	−0.358610	+	0.933487i	$0.616749\pi$
$128$	17.9376	1.58548
$129$	−6.33988	−0.558195
$130$	13.5909	1.19200
$131$	2.52746	0.220825	0.110413	−	0.993886i	$-0.464783\pi$
$131$	2.52746	0.220825	0.110413	+	0.993886i	$0.464783\pi$
$132$	−16.4709	−1.43361
$133$	−3.38888	−0.293853
$134$	2.61176	0.225622
$135$	−5.38087	−0.463112
$136$	20.7877	1.78253
$137$	−10.1491	−0.867095	−0.433548	−	0.901131i	$-0.642738\pi$
$137$	−10.1491	−0.867095	−0.433548	+	0.901131i	$0.642738\pi$
$138$	23.5153	2.00176
$139$	−11.4921	−0.974744	−0.487372	−	0.873195i	$-0.662044\pi$
$139$	−11.4921	−0.974744	−0.487372	+	0.873195i	$0.662044\pi$
$140$	−2.72221	−0.230069
$141$	−6.14601	−0.517588
$142$	−5.56817	−0.467270
$143$	26.6701	2.23026
$144$	0.277746	0.0231455
$145$	7.44110	0.617950
$146$	−1.33574	−0.110547
$147$	−7.22250	−0.595702
$148$	20.1468	1.65606
$149$	20.2394	1.65808	0.829040	−	0.559190i	$-0.188888\pi$
$149$	20.2394	1.65808	0.829040	+	0.559190i	$0.188888\pi$
$150$	−2.62404	−0.214252
$151$	17.8074	1.44915	0.724573	−	0.689198i	$-0.242037\pi$
$151$	17.8074	1.44915	0.724573	+	0.689198i	$0.242037\pi$
$152$	−10.8833	−0.882750
$153$	12.7439	1.03028
$154$	−8.68198	−0.699614
$155$	−4.02401	−0.323216
$156$	−21.9431	−1.75685
$157$	−3.64311	−0.290752	−0.145376	−	0.989376i	$-0.546439\pi$
$157$	−3.64311	−0.290752	−0.145376	+	0.989376i	$0.546439\pi$
$158$	18.5946	1.47931
$159$	12.1956	0.967177
$160$	5.84413	0.462019
$161$	7.62659	0.601060
$162$	2.65877	0.208893
$163$	17.2437	1.35063	0.675316	−	0.737528i	$-0.264007\pi$
$163$	17.2437	1.35063	0.675316	+	0.737528i	$0.264007\pi$
$164$	32.4231	2.53182
$165$	−5.14926	−0.400869
$166$	25.0839	1.94689
$167$	−23.1080	−1.78815	−0.894077	−	0.447914i	$-0.852167\pi$
$167$	−23.1080	−1.78815	−0.894077	+	0.447914i	$0.852167\pi$
$168$	2.67687	0.206525
$169$	22.5308	1.73314
$170$	17.3420	1.33007
$171$	−6.67198	−0.510219
$172$	−17.6210	−1.34359
$173$	5.02692	0.382189	0.191095	−	0.981572i	$-0.438796\pi$
$173$	5.02692	0.382189	0.191095	+	0.981572i	$0.438796\pi$
$174$	−19.5257	−1.48024
$175$	−0.851041	−0.0643326
$176$	0.741688	0.0559068
$177$	−2.20899	−0.166038
$178$	−33.4862	−2.50989
$179$	−8.87136	−0.663077	−0.331538	−	0.943442i	$-0.607568\pi$
$179$	−8.87136	−0.663077	−0.331538	+	0.943442i	$0.607568\pi$
$180$	−5.35946	−0.399470
$181$	−0.590912	−0.0439221	−0.0219611	−	0.999759i	$-0.506991\pi$
$181$	−0.590912	−0.0439221	−0.0219611	+	0.999759i	$0.506991\pi$
$182$	−11.5664	−0.857362
$183$	−12.3128	−0.910189
$184$	24.4925	1.80561
$185$	6.29845	0.463072
$186$	10.5592	0.774235
$187$	34.0310	2.48859
$188$	−17.0821	−1.24584
$189$	4.57934	0.333098
$190$	−9.07931	−0.658683
$191$	4.56601	0.330385	0.165192	−	0.986261i	$-0.447176\pi$
$191$	4.56601	0.330385	0.165192	+	0.986261i	$0.447176\pi$
$192$	−14.9537	−1.07919
$193$	15.5989	1.12283	0.561417	−	0.827533i	$-0.310256\pi$
$193$	15.5989	1.12283	0.561417	+	0.827533i	$0.310256\pi$
$194$	−23.2372	−1.66833
$195$	−6.86003	−0.491257
$196$	−20.0741	−1.43386
$197$	19.8507	1.41430	0.707152	−	0.707062i	$-0.249980\pi$
$197$	19.8507	1.41430	0.707152	+	0.707062i	$0.249980\pi$
$198$	−17.0930	−1.21474
$199$	−10.7219	−0.760056	−0.380028	−	0.924975i	$-0.624086\pi$
$199$	−10.7219	−0.760056	−0.380028	+	0.924975i	$0.624086\pi$
$200$	−2.73309	−0.193258
$201$	−1.31829	−0.0929848
$202$	3.87251	0.272469
$203$	−6.33268	−0.444467
$204$	−27.9994	−1.96035
$205$	10.1364	0.707955
$206$	7.29039	0.507945
$207$	15.0151	1.04362
$208$	0.988103	0.0685126
$209$	−17.8167	−1.23241
$210$	2.23316	0.154103
$211$	−9.10373	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$211$	−9.10373	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$212$	33.8964	2.32801
$213$	2.81053	0.192575
$214$	−4.33723	−0.296487
$215$	−5.50881	−0.375698
$216$	14.7064	1.00064
$217$	3.42460	0.232477
$218$	43.2290	2.92784
$219$	0.674216	0.0455593
$220$	−14.3118	−0.964900
$221$	45.3373	3.04972
$222$	−16.5274	−1.10925
$223$	−13.0519	−0.874017	−0.437009	−	0.899457i	$-0.643962\pi$
$223$	−13.0519	−0.874017	−0.437009	+	0.899457i	$0.643962\pi$
$224$	−4.97359	−0.332312
$225$	−1.67552	−0.111701
$226$	39.4305	2.62288
$227$	10.5108	0.697623	0.348812	−	0.937193i	$-0.386585\pi$
$227$	10.5108	0.697623	0.348812	+	0.937193i	$0.386585\pi$
$228$	14.6589	0.970809
$229$	14.6567	0.968543	0.484271	−	0.874918i	$-0.339085\pi$
$229$	14.6567	0.968543	0.484271	+	0.874918i	$0.339085\pi$
$230$	20.4328	1.34730
$231$	4.38223	0.288330
$232$	−20.3372	−1.33520
$233$	−17.9965	−1.17899	−0.589495	−	0.807772i	$-0.700673\pi$
$233$	−17.9965	−1.17899	−0.589495	+	0.807772i	$0.700673\pi$
$234$	−22.7718	−1.48864
$235$	−5.34036	−0.348366
$236$	−6.13964	−0.399657
$237$	−9.38563	−0.609662
$238$	−14.7588	−0.956669
$239$	18.2297	1.17918	0.589592	−	0.807701i	$-0.299288\pi$
$239$	18.2297	1.17918	0.589592	+	0.807701i	$0.299288\pi$
$240$	−0.190776	−0.0123145
$241$	3.14810	0.202787	0.101393	−	0.994846i	$-0.467670\pi$
$241$	3.14810	0.202787	0.101393	+	0.994846i	$0.467670\pi$
$242$	−20.5640	−1.32190
$243$	14.8006	0.949460
$244$	−34.2220	−2.19084
$245$	−6.27573	−0.400942
$246$	−26.5982	−1.69584
$247$	−23.7361	−1.51029
$248$	10.9980	0.698371
$249$	−12.6611	−0.802365
$250$	−2.28006	−0.144204
$251$	−10.8307	−0.683629	−0.341814	−	0.939767i	$-0.611041\pi$
$251$	−10.8307	−0.683629	−0.341814	+	0.939767i	$0.611041\pi$
$252$	4.56111	0.287323
$253$	40.0961	2.52082
$254$	18.4290	1.15634
$255$	−8.75339	−0.548158
$256$	−14.9120	−0.932003
$257$	23.6306	1.47404	0.737018	−	0.675873i	$-0.236233\pi$
$257$	23.6306	1.47404	0.737018	+	0.675873i	$0.236233\pi$
$258$	14.4553	0.899950
$259$	−5.36024	−0.333069
$260$	−19.0667	−1.18246
$261$	−12.4677	−0.771731
$262$	−5.76277	−0.356025
$263$	2.76852	0.170714	0.0853572	−	0.996350i	$-0.472797\pi$
$263$	2.76852	0.170714	0.0853572	+	0.996350i	$0.472797\pi$
$264$	14.0734	0.866156
$265$	10.5970	0.650966
$266$	7.72686	0.473764
$267$	16.9021	1.03439
$268$	−3.66403	−0.223816
$269$	−26.5828	−1.62078	−0.810390	−	0.585891i	$-0.800745\pi$
$269$	−26.5828	−1.62078	−0.810390	+	0.585891i	$0.800745\pi$
$270$	12.2687	0.746651
$271$	6.19227	0.376153	0.188077	−	0.982154i	$-0.439775\pi$
$271$	6.19227	0.376153	0.188077	+	0.982154i	$0.439775\pi$
$272$	1.26082	0.0764484
$273$	5.83816	0.353342
$274$	23.1406	1.39797
$275$	−4.47426	−0.269808
$276$	−32.9895	−1.98573
$277$	6.77737	0.407213	0.203606	−	0.979053i	$-0.434734\pi$
$277$	6.77737	0.407213	0.203606	+	0.979053i	$0.434734\pi$
$278$	26.2026	1.57153
$279$	6.74229	0.403651
$280$	2.32597	0.139003
$281$	24.5927	1.46708	0.733538	−	0.679649i	$-0.237868\pi$
$281$	24.5927	1.46708	0.733538	+	0.679649i	$0.237868\pi$
$282$	14.0133	0.834480
$283$	4.64584	0.276167	0.138083	−	0.990421i	$-0.455906\pi$
$283$	4.64584	0.276167	0.138083	+	0.990421i	$0.455906\pi$
$284$	7.81155	0.463530
$285$	4.58278	0.271461
$286$	−60.8095	−3.59574
$287$	−8.62646	−0.509204
$288$	−9.79194	−0.576996
$289$	40.8503	2.40296
$290$	−16.9662	−0.996289
$291$	11.7290	0.687565
$292$	1.87390	0.109662
$293$	30.2073	1.76473	0.882365	−	0.470566i	$-0.155950\pi$
$293$	30.2073	1.76473	0.882365	+	0.470566i	$0.155950\pi$
$294$	16.4678	0.960419
$295$	−1.91943	−0.111753
$296$	−17.2142	−1.00056
$297$	24.0755	1.39700
$298$	−46.1472	−2.67324
$299$	53.4174	3.08921
$300$	3.68125	0.212537
$301$	4.68822	0.270225
$302$	−40.6020	−2.33638
$303$	−1.95465	−0.112292
$304$	−0.660094	−0.0378590
$305$	−10.6988	−0.612610
$306$	−29.0569	−1.66107
$307$	3.89479	0.222288	0.111144	−	0.993804i	$-0.464549\pi$
$307$	3.89479	0.222288	0.111144	+	0.993804i	$0.464549\pi$
$308$	12.1799	0.694014
$309$	−3.67982	−0.209338
$310$	9.17500	0.521105
$311$	17.0374	0.966100	0.483050	−	0.875593i	$-0.339529\pi$
$311$	17.0374	0.966100	0.483050	+	0.875593i	$0.339529\pi$
$312$	18.7490	1.06146
$313$	−19.1541	−1.08266	−0.541328	−	0.840812i	$-0.682078\pi$
$313$	−19.1541	−1.08266	−0.541328	+	0.840812i	$0.682078\pi$
$314$	8.30653	0.468765
$315$	1.42593	0.0803422
$316$	−26.0863	−1.46747
$317$	8.27307	0.464662	0.232331	−	0.972637i	$-0.425365\pi$
$317$	8.27307	0.464662	0.232331	+	0.972637i	$0.425365\pi$
$318$	−27.8068	−1.55933
$319$	−33.2935	−1.86408
$320$	−12.9935	−0.726356
$321$	2.18922	0.122190
$322$	−17.3891	−0.969058
$323$	−30.2872	−1.68522
$324$	−3.72997	−0.207221
$325$	−5.96077	−0.330644
$326$	−39.3168	−2.17756
$327$	−21.8198	−1.20664
$328$	−27.7036	−1.52967
$329$	4.54486	0.250566
$330$	11.7406	0.646301
$331$	−18.2283	−1.00192	−0.500960	−	0.865470i	$-0.667020\pi$
$331$	−18.2283	−1.00192	−0.500960	+	0.865470i	$0.667020\pi$
$332$	−35.1901	−1.93131
$333$	−10.5532	−0.578310
$334$	52.6878	2.88295
$335$	−1.14548	−0.0625842
$336$	0.162358	0.00885734
$337$	−12.1404	−0.661332	−0.330666	−	0.943748i	$-0.607273\pi$
$337$	−12.1404	−0.661332	−0.330666	+	0.943748i	$0.607273\pi$
$338$	−51.3717	−2.79425
$339$	−19.9025	−1.08096
$340$	−24.3290	−1.31943
$341$	18.0045	0.974997
$342$	15.2125	0.822600
$343$	11.2982	0.610045
$344$	15.0561	0.811768
$345$	−10.3134	−0.555257
$346$	−11.4617	−0.616184
$347$	−8.03659	−0.431427	−0.215713	−	0.976457i	$-0.569208\pi$
$347$	−8.03659	−0.431427	−0.215713	+	0.976457i	$0.569208\pi$
$348$	27.3926	1.46840
$349$	0.856938	0.0458708	0.0229354	−	0.999737i	$-0.492699\pi$
$349$	0.856938	0.0458708	0.0229354	+	0.999737i	$0.492699\pi$
$350$	1.94043	0.103720
$351$	32.0742	1.71199
$352$	−26.1482	−1.39370
$353$	−15.0983	−0.803599	−0.401800	−	0.915728i	$-0.631615\pi$
$353$	−15.0983	−0.803599	−0.401800	+	0.915728i	$0.631615\pi$
$354$	5.03665	0.267695
$355$	2.44211	0.129614
$356$	46.9776	2.48981
$357$	7.44949	0.394269
$358$	20.2273	1.06904
$359$	−16.6800	−0.880335	−0.440167	−	0.897916i	$-0.645081\pi$
$359$	−16.6800	−0.880335	−0.440167	+	0.897916i	$0.645081\pi$
$360$	4.57933	0.241352
$361$	−3.14332	−0.165438
$362$	1.34732	0.0708134
$363$	10.3797	0.544791
$364$	16.2265	0.850500
$365$	0.585835	0.0306640
$366$	28.0740	1.46745
$367$	−1.25576	−0.0655499	−0.0327749	−	0.999463i	$-0.510434\pi$
$367$	−1.25576	−0.0655499	−0.0327749	+	0.999463i	$0.510434\pi$
$368$	1.48553	0.0774384
$369$	−16.9837	−0.884134
$370$	−14.3609	−0.746586
$371$	−9.01844	−0.468214
$372$	−14.8134	−0.768038
$373$	9.23550	0.478196	0.239098	−	0.970995i	$-0.423148\pi$
$373$	9.23550	0.478196	0.239098	+	0.970995i	$0.423148\pi$
$374$	−77.5928	−4.01223
$375$	1.15086	0.0594303
$376$	14.5957	0.752713
$377$	−44.3547	−2.28439
$378$	−10.4412	−0.537037
$379$	5.00757	0.257221	0.128611	−	0.991695i	$-0.458948\pi$
$379$	5.00757	0.257221	0.128611	+	0.991695i	$0.458948\pi$
$380$	12.7373	0.653411
$381$	−9.30204	−0.476558
$382$	−10.4108	−0.532662
$383$	28.3321	1.44770	0.723851	−	0.689957i	$-0.242370\pi$
$383$	28.3321	1.44770	0.723851	+	0.689957i	$0.242370\pi$
$384$	20.6438	1.05347
$385$	3.80778	0.194062
$386$	−35.5665	−1.81029
$387$	9.23010	0.469193
$388$	32.5994	1.65498
$389$	15.4718	0.784450	0.392225	−	0.919869i	$-0.371706\pi$
$389$	15.4718	0.784450	0.392225	+	0.919869i	$0.371706\pi$
$390$	15.6413	0.792028
$391$	68.1606	3.44703
$392$	17.1521	0.866312
$393$	2.90876	0.146728
$394$	−45.2608	−2.28021
$395$	−8.15531	−0.410338
$396$	23.9796	1.20502
$397$	21.9553	1.10190	0.550952	−	0.834537i	$-0.314265\pi$
$397$	21.9553	1.10190	0.550952	+	0.834537i	$0.314265\pi$
$398$	24.4466	1.22540
$399$	−3.90013	−0.195251
$400$	−0.165768	−0.00828838
$401$	6.54841	0.327012	0.163506	−	0.986542i	$-0.447720\pi$
$401$	6.54841	0.327012	0.163506	+	0.986542i	$0.447720\pi$
$402$	3.00578	0.149915
$403$	23.9862	1.19484
$404$	−5.43273	−0.270288
$405$	−1.16609	−0.0579437
$406$	14.4389	0.716591
$407$	−28.1810	−1.39688
$408$	23.9238	1.18440
$409$	2.58117	0.127631	0.0638154	−	0.997962i	$-0.479673\pi$
$409$	2.58117	0.127631	0.0638154	+	0.997962i	$0.479673\pi$
$410$	−23.1116	−1.14140
$411$	−11.6802	−0.576142
$412$	−10.2276	−0.503880
$413$	1.63351	0.0803797
$414$	−34.2354	−1.68258
$415$	−11.0014	−0.540038
$416$	−34.8356	−1.70795
$417$	−13.2258	−0.647669
$418$	40.6232	1.98695
$419$	21.6954	1.05989	0.529944	−	0.848033i	$-0.322213\pi$
$419$	21.6954	1.05989	0.529944	+	0.848033i	$0.322213\pi$
$420$	−3.13289	−0.152869
$421$	−29.7689	−1.45085	−0.725424	−	0.688303i	$-0.758356\pi$
$421$	−29.7689	−1.45085	−0.725424	+	0.688303i	$0.758356\pi$
$422$	20.7571	1.01044
$423$	8.94786	0.435060
$424$	−28.9624	−1.40654
$425$	−7.60594	−0.368942
$426$	−6.40819	−0.310478
$427$	9.10509	0.440626
$428$	6.08468	0.294114
$429$	30.6936	1.48190
$430$	12.5604	0.605718
$431$	5.88079	0.283267	0.141634	−	0.989919i	$-0.454764\pi$
$431$	5.88079	0.283267	0.141634	+	0.989919i	$0.454764\pi$
$432$	0.891975	0.0429152
$433$	−16.9070	−0.812500	−0.406250	−	0.913762i	$-0.633164\pi$
$433$	−16.9070	−0.812500	−0.406250	+	0.913762i	$0.633164\pi$
$434$	−7.80829	−0.374810
$435$	8.56368	0.410597
$436$	−60.6457	−2.90440
$437$	−35.6851	−1.70705
$438$	−1.53725	−0.0734529
$439$	9.13729	0.436099	0.218050	−	0.975938i	$-0.430031\pi$
$439$	9.13729	0.436099	0.218050	+	0.975938i	$0.430031\pi$
$440$	12.2286	0.582973
$441$	10.5151	0.500719
$442$	−103.372	−4.91690
$443$	−29.7050	−1.41132	−0.705662	−	0.708548i	$-0.749350\pi$
$443$	−29.7050	−1.41132	−0.705662	+	0.708548i	$0.749350\pi$
$444$	23.1862	1.10037
$445$	14.6865	0.696207
$446$	29.7591	1.40913
$447$	23.2928	1.10171
$448$	11.0580	0.522440
$449$	−2.64872	−0.125001	−0.0625004	−	0.998045i	$-0.519907\pi$
$449$	−2.64872	−0.125001	−0.0625004	+	0.998045i	$0.519907\pi$
$450$	3.82028	0.180090
$451$	−45.3528	−2.13558
$452$	−55.3168	−2.60188
$453$	20.4939	0.962886
$454$	−23.9652	−1.12474
$455$	5.07286	0.237819
$456$	−12.5251	−0.586544
$457$	1.77245	0.0829115	0.0414558	−	0.999140i	$-0.486800\pi$
$457$	1.77245	0.0829115	0.0414558	+	0.999140i	$0.486800\pi$
$458$	−33.4182	−1.56153
$459$	40.9266	1.91029
$460$	−28.6650	−1.33651
$461$	1.50816	0.0702419	0.0351210	−	0.999383i	$-0.488818\pi$
$461$	1.50816	0.0702419	0.0351210	+	0.999383i	$0.488818\pi$
$462$	−9.99176	−0.464859
$463$	−28.7937	−1.33816	−0.669078	−	0.743192i	$-0.733311\pi$
$463$	−28.7937	−1.33816	−0.669078	+	0.743192i	$0.733311\pi$
$464$	−1.23349	−0.0572635
$465$	−4.63108	−0.214761
$466$	41.0332	1.90082
$467$	−16.4285	−0.760220	−0.380110	−	0.924941i	$-0.624114\pi$
$467$	−16.4285	−0.760220	−0.380110	+	0.924941i	$0.624114\pi$
$468$	31.9465	1.47673
$469$	0.974849	0.0450143
$470$	12.1764	0.561653
$471$	−4.19272	−0.193190
$472$	5.24596	0.241465
$473$	24.6479	1.13331
$474$	21.3998	0.982927
$475$	3.98204	0.182709
$476$	20.7050	0.949012
$477$	−17.7554	−0.812963
$478$	−41.5650	−1.90114
$479$	−9.47171	−0.432773	−0.216387	−	0.976308i	$-0.569427\pi$
$479$	−9.47171	−0.432773	−0.216387	+	0.976308i	$0.569427\pi$
$480$	6.72579	0.306989
$481$	−37.5437	−1.71184
$482$	−7.17786	−0.326943
$483$	8.77716	0.399374
$484$	28.8491	1.31132
$485$	10.1915	0.462771
$486$	−33.7463	−1.53076
$487$	11.0766	0.501929	0.250964	−	0.967996i	$-0.419252\pi$
$487$	11.0766	0.501929	0.250964	+	0.967996i	$0.419252\pi$
$488$	29.2407	1.32366
$489$	19.8451	0.897429
$490$	14.3091	0.646418
$491$	38.8335	1.75253	0.876267	−	0.481826i	$-0.160026\pi$
$491$	38.8335	1.75253	0.876267	+	0.481826i	$0.160026\pi$
$492$	37.3145	1.68227
$493$	−56.5966	−2.54898
$494$	54.1197	2.43496
$495$	7.49670	0.336952
$496$	0.667050	0.0299514
$497$	−2.07834	−0.0932261
$498$	28.8681	1.29361
$499$	2.43635	0.109066	0.0545330	−	0.998512i	$-0.482633\pi$
$499$	2.43635	0.109066	0.0545330	+	0.998512i	$0.482633\pi$
$500$	3.19869	0.143050
$501$	−26.5942	−1.18814
$502$	24.6947	1.10218
$503$	17.7347	0.790752	0.395376	−	0.918519i	$-0.370614\pi$
$503$	17.7347	0.790752	0.395376	+	0.918519i	$0.370614\pi$
$504$	−3.89720	−0.173595
$505$	−1.69842	−0.0755789
$506$	−91.4216	−4.06419
$507$	25.9299	1.15159
$508$	−25.8539	−1.14708
$509$	−32.7436	−1.45134	−0.725668	−	0.688045i	$-0.758469\pi$
$509$	−32.7436	−1.45134	−0.725668	+	0.688045i	$0.758469\pi$
$510$	19.9583	0.883767
$511$	−0.498570	−0.0220554
$512$	−1.87488	−0.0828589
$513$	−21.4269	−0.946020
$514$	−53.8793	−2.37651
$515$	−3.19745	−0.140896
$516$	−20.2793	−0.892747
$517$	23.8942	1.05086
$518$	12.2217	0.536990
$519$	5.78529	0.253946
$520$	16.2913	0.714421
$521$	−1.29770	−0.0568532	−0.0284266	−	0.999596i	$-0.509050\pi$
$521$	−1.29770	−0.0568532	−0.0284266	+	0.999596i	$0.509050\pi$
$522$	28.4271	1.24422
$523$	29.8560	1.30551	0.652755	−	0.757569i	$-0.273613\pi$
$523$	29.8560	1.30551	0.652755	+	0.757569i	$0.273613\pi$
$524$	8.08457	0.353176
$525$	−0.979430	−0.0427458
$526$	−6.31241	−0.275234
$527$	30.6064	1.33323
$528$	0.853581	0.0371473
$529$	57.3083	2.49167
$530$	−24.1617	−1.04952
$531$	3.21603	0.139564
$532$	−10.8400	−0.469973
$533$	−60.4206	−2.61711
$534$	−38.5380	−1.66770
$535$	1.90224	0.0822411
$536$	3.13069	0.135225
$537$	−10.2097	−0.440582
$538$	60.6104	2.61310
$539$	28.0793	1.20946
$540$	−17.2117	−0.740675
$541$	13.7272	0.590180	0.295090	−	0.955470i	$-0.404650\pi$
$541$	13.7272	0.590180	0.295090	+	0.955470i	$0.404650\pi$
$542$	−14.1188	−0.606453
$543$	−0.680058	−0.0291841
$544$	−44.4501	−1.90578
$545$	−18.9596	−0.812138
$546$	−13.3114	−0.569674
$547$	−34.3003	−1.46658	−0.733288	−	0.679918i	$-0.762015\pi$
$547$	−34.3003	−1.46658	−0.733288	+	0.679918i	$0.762015\pi$
$548$	−32.4638	−1.38678
$549$	17.9260	0.765062
$550$	10.2016	0.434998
$551$	29.6308	1.26232
$552$	28.1875	1.19974
$553$	6.94050	0.295140
$554$	−15.4528	−0.656528
$555$	7.24865	0.307688
$556$	−36.7595	−1.55895
$557$	−5.33307	−0.225969	−0.112985	−	0.993597i	$-0.536041\pi$
$557$	−5.33307	−0.225969	−0.112985	+	0.993597i	$0.536041\pi$
$558$	−15.3729	−0.650785
$559$	32.8368	1.38885
$560$	0.141075	0.00596150
$561$	39.1650	1.65355
$562$	−56.0728	−2.36529
$563$	39.5053	1.66495	0.832475	−	0.554062i	$-0.186923\pi$
$563$	39.5053	1.66495	0.832475	+	0.554062i	$0.186923\pi$
$564$	−19.6592	−0.827801
$565$	−17.2936	−0.727546
$566$	−10.5928	−0.445249
$567$	0.992393	0.0416766
$568$	−6.67450	−0.280056
$569$	21.3177	0.893685	0.446842	−	0.894613i	$-0.352548\pi$
$569$	21.3177	0.893685	0.446842	+	0.894613i	$0.352548\pi$
$570$	−10.4490	−0.437662
$571$	−9.95790	−0.416725	−0.208363	−	0.978052i	$-0.566813\pi$
$571$	−9.95790	−0.416725	−0.208363	+	0.978052i	$0.566813\pi$
$572$	85.3093	3.56696
$573$	5.25484	0.219524
$574$	19.6689	0.820963
$575$	−8.96149	−0.373720
$576$	21.7708	0.907115
$577$	10.6056	0.441518	0.220759	−	0.975328i	$-0.429147\pi$
$577$	10.6056	0.441518	0.220759	+	0.975328i	$0.429147\pi$
$578$	−93.1413	−3.87417
$579$	17.9522	0.746068
$580$	23.8018	0.988315
$581$	9.36265	0.388428
$582$	−26.7428	−1.10853
$583$	−47.4136	−1.96367
$584$	−1.60114	−0.0662556
$585$	9.98737	0.412927
$586$	−68.8746	−2.84518
$587$	−18.3736	−0.758361	−0.379180	−	0.925323i	$-0.623794\pi$
$587$	−18.3736	−0.758361	−0.379180	+	0.925323i	$0.623794\pi$
$588$	−23.1025	−0.952732
$589$	−16.0238	−0.660249
$590$	4.37641	0.180174
$591$	22.8454	0.939735
$592$	−1.04408	−0.0429114
$593$	−7.84694	−0.322235	−0.161118	−	0.986935i	$-0.551510\pi$
$593$	−7.84694	−0.322235	−0.161118	+	0.986935i	$0.551510\pi$
$594$	−54.8936	−2.25231
$595$	6.47296	0.265366
$596$	64.7397	2.65184
$597$	−12.3394	−0.505020
$598$	−121.795	−4.98057
$599$	3.43399	0.140309	0.0701545	−	0.997536i	$-0.477651\pi$
$599$	3.43399	0.140309	0.0701545	+	0.997536i	$0.477651\pi$
$600$	−3.14541	−0.128411
$601$	3.77224	0.153873	0.0769365	−	0.997036i	$-0.475486\pi$
$601$	3.77224	0.153873	0.0769365	+	0.997036i	$0.475486\pi$
$602$	−10.6894	−0.435669
$603$	1.91927	0.0781586
$604$	56.9604	2.31768
$605$	9.01904	0.366676
$606$	4.45673	0.181042
$607$	−23.5666	−0.956540	−0.478270	−	0.878213i	$-0.658736\pi$
$607$	−23.5666	−0.956540	−0.478270	+	0.878213i	$0.658736\pi$
$608$	23.2716	0.943788
$609$	−7.28804	−0.295326
$610$	24.3939	0.987679
$611$	31.8327	1.28781
$612$	40.7637	1.64778
$613$	−9.88640	−0.399308	−0.199654	−	0.979866i	$-0.563982\pi$
$613$	−9.88640	−0.399308	−0.199654	+	0.979866i	$0.563982\pi$
$614$	−8.88038	−0.358383
$615$	11.6656	0.470401
$616$	−10.4070	−0.419310
$617$	−33.2682	−1.33933	−0.669664	−	0.742664i	$-0.733562\pi$
$617$	−33.2682	−1.33933	−0.669664	+	0.742664i	$0.733562\pi$
$618$	8.39023	0.337504
$619$	22.3304	0.897534	0.448767	−	0.893649i	$-0.351863\pi$
$619$	22.3304	0.897534	0.448767	+	0.893649i	$0.351863\pi$
$620$	−12.8716	−0.516934
$621$	48.2207	1.93503
$622$	−38.8463	−1.55759
$623$	−12.4988	−0.500754
$624$	1.13717	0.0455232
$625$	1.00000	0.0400000
$626$	43.6726	1.74551
$627$	−20.5046	−0.818874
$628$	−11.6532	−0.465013
$629$	−47.9057	−1.91012
$630$	−3.25122	−0.129532
$631$	4.50741	0.179437	0.0897187	−	0.995967i	$-0.471403\pi$
$631$	4.50741	0.179437	0.0897187	+	0.995967i	$0.471403\pi$
$632$	22.2892	0.886615
$633$	−10.4771	−0.416429
$634$	−18.8631	−0.749151
$635$	−8.08267	−0.320751
$636$	39.0101	1.54685
$637$	37.4082	1.48217
$638$	75.9112	3.00535
$639$	−4.09180	−0.161869
$640$	17.9376	0.709048
$641$	34.4693	1.36146	0.680729	−	0.732536i	$-0.261663\pi$
$641$	34.4693	1.36146	0.680729	+	0.732536i	$0.261663\pi$
$642$	−4.99156	−0.197001
$643$	−2.52205	−0.0994600	−0.0497300	−	0.998763i	$-0.515836\pi$
$643$	−2.52205	−0.0994600	−0.0497300	+	0.998763i	$0.515836\pi$
$644$	24.3951	0.961302
$645$	−6.33988	−0.249633
$646$	69.0567	2.71700
$647$	−6.34952	−0.249626	−0.124813	−	0.992180i	$-0.539833\pi$
$647$	−6.34952	−0.249626	−0.124813	+	0.992180i	$0.539833\pi$
$648$	3.18704	0.125199
$649$	8.58802	0.337109
$650$	13.5909	0.533081
$651$	3.94124	0.154469
$652$	55.1573	2.16013
$653$	48.3184	1.89084	0.945422	−	0.325847i	$-0.105649\pi$
$653$	48.3184	1.89084	0.945422	+	0.325847i	$0.105649\pi$
$654$	49.7506	1.94540
$655$	2.52746	0.0987561
$656$	−1.68028	−0.0656040
$657$	−0.981577	−0.0382950
$658$	−10.3626	−0.403975
$659$	6.11791	0.238320	0.119160	−	0.992875i	$-0.461980\pi$
$659$	6.11791	0.238320	0.119160	+	0.992875i	$0.461980\pi$
$660$	−16.4709	−0.641128
$661$	−25.2321	−0.981416	−0.490708	−	0.871324i	$-0.663262\pi$
$661$	−25.2321	−0.981416	−0.490708	+	0.871324i	$0.663262\pi$
$662$	41.5618	1.61534
$663$	52.1770	2.02639
$664$	30.0678	1.16686
$665$	−3.38888	−0.131415
$666$	24.0619	0.932379
$667$	−66.6834	−2.58199
$668$	−73.9154	−2.85987
$669$	−15.0209	−0.580741
$670$	2.61176	0.100901
$671$	47.8691	1.84797
$672$	−5.72392	−0.220805
$673$	−46.2002	−1.78089	−0.890443	−	0.455094i	$-0.849606\pi$
$673$	−46.2002	−1.78089	−0.890443	+	0.455094i	$0.849606\pi$
$674$	27.6810	1.06623
$675$	−5.38087	−0.207110
$676$	72.0691	2.77189
$677$	−40.3289	−1.54997	−0.774983	−	0.631982i	$-0.782242\pi$
$677$	−40.3289	−1.54997	−0.774983	+	0.631982i	$0.782242\pi$
$678$	45.3790	1.74277
$679$	−8.67336	−0.332853
$680$	20.7877	0.797172
$681$	12.0964	0.463536
$682$	−41.0514	−1.57194
$683$	8.76492	0.335380	0.167690	−	0.985840i	$-0.446369\pi$
$683$	8.76492	0.335380	0.167690	+	0.985840i	$0.446369\pi$
$684$	−21.3416	−0.816016
$685$	−10.1491	−0.387777
$686$	−25.7606	−0.983543
$687$	16.8679	0.643549
$688$	0.913182	0.0348148
$689$	−63.1661	−2.40644
$690$	23.5153	0.895212
$691$	−17.9806	−0.684013	−0.342006	−	0.939698i	$-0.611106\pi$
$691$	−17.9806	−0.684013	−0.342006	+	0.939698i	$0.611106\pi$
$692$	16.0795	0.611252
$693$	−6.38000	−0.242356
$694$	18.3239	0.695567
$695$	−11.4921	−0.435919
$696$	−23.4053	−0.887175
$697$	−77.0966	−2.92024
$698$	−1.95387	−0.0739552
$699$	−20.7115	−0.783380
$700$	−2.72221	−0.102890
$701$	28.5781	1.07938	0.539690	−	0.841864i	$-0.318541\pi$
$701$	28.5781	1.07938	0.539690	+	0.841864i	$0.318541\pi$
$702$	−73.1311	−2.76016
$703$	25.0807	0.945938
$704$	58.1362	2.19109
$705$	−6.14601	−0.231472
$706$	34.4250	1.29560
$707$	1.44543	0.0543609
$708$	−7.06588	−0.265552
$709$	3.08152	0.115729	0.0578644	−	0.998324i	$-0.481571\pi$
$709$	3.08152	0.115729	0.0578644	+	0.998324i	$0.481571\pi$
$710$	−5.56817	−0.208970
$711$	13.6644	0.512453
$712$	−40.1395	−1.50429
$713$	36.0611	1.35050
$714$	−16.9853	−0.635659
$715$	26.6701	0.997404
$716$	−28.3767	−1.06049
$717$	20.9799	0.783510
$718$	38.0314	1.41932
$719$	−37.3606	−1.39331	−0.696657	−	0.717404i	$-0.745330\pi$
$719$	−37.3606	−1.39331	−0.696657	+	0.717404i	$0.745330\pi$
$720$	0.277746	0.0103510
$721$	2.72116	0.101341
$722$	7.16697	0.266727
$723$	3.62303	0.134742
$724$	−1.89014	−0.0702466
$725$	7.44110	0.276356
$726$	−23.6663	−0.878339
$727$	15.8784	0.588897	0.294449	−	0.955667i	$-0.404864\pi$
$727$	15.8784	0.588897	0.294449	+	0.955667i	$0.404864\pi$
$728$	−13.8646	−0.513855
$729$	20.5317	0.760435
$730$	−1.33574	−0.0494380
$731$	41.8997	1.54972
$732$	−39.3848	−1.45571
$733$	−38.2749	−1.41372	−0.706858	−	0.707356i	$-0.749888\pi$
$733$	−38.2749	−1.41372	−0.706858	+	0.707356i	$0.749888\pi$
$734$	2.86320	0.105683
$735$	−7.22250	−0.266406
$736$	−52.3722	−1.93046
$737$	5.12517	0.188788
$738$	38.7238	1.42544
$739$	−42.2068	−1.55260	−0.776301	−	0.630363i	$-0.782906\pi$
$739$	−42.2068	−1.55260	−0.776301	+	0.630363i	$0.782906\pi$
$740$	20.1468	0.740611
$741$	−27.3169	−1.00351
$742$	20.5626	0.754877
$743$	25.9945	0.953647	0.476824	−	0.878999i	$-0.341788\pi$
$743$	25.9945	0.953647	0.476824	+	0.878999i	$0.341788\pi$
$744$	12.6571	0.464033
$745$	20.2394	0.741516
$746$	−21.0575	−0.770971
$747$	18.4331	0.674430
$748$	108.855	3.98012
$749$	−1.61889	−0.0591528
$750$	−2.62404	−0.0958163
$751$	−40.6898	−1.48479	−0.742396	−	0.669961i	$-0.766311\pi$
$751$	−40.6898	−1.48479	−0.742396	+	0.669961i	$0.766311\pi$
$752$	0.885258	0.0322820
$753$	−12.4647	−0.454237
$754$	101.132	3.68300
$755$	17.8074	0.648078
$756$	14.6479	0.532739
$757$	−15.3374	−0.557448	−0.278724	−	0.960371i	$-0.589911\pi$
$757$	−15.3374	−0.557448	−0.278724	+	0.960371i	$0.589911\pi$
$758$	−11.4176	−0.414705
$759$	46.1451	1.67496
$760$	−10.8833	−0.394778
$761$	37.3320	1.35329	0.676643	−	0.736312i	$-0.263434\pi$
$761$	37.3320	1.35329	0.676643	+	0.736312i	$0.263434\pi$
$762$	21.2092	0.768329
$763$	16.1354	0.584139
$764$	14.6052	0.528399
$765$	12.7439	0.460756
$766$	−64.5989	−2.33405
$767$	11.4413	0.413120
$768$	−17.1617	−0.619270
$769$	36.2014	1.30546	0.652728	−	0.757593i	$-0.273625\pi$
$769$	36.2014	1.30546	0.652728	+	0.757593i	$0.273625\pi$
$770$	−8.68198	−0.312877
$771$	27.1956	0.979424
$772$	49.8961	1.79580
$773$	−16.5850	−0.596520	−0.298260	−	0.954485i	$-0.596406\pi$
$773$	−16.5850	−0.596520	−0.298260	+	0.954485i	$0.596406\pi$
$774$	−21.0452	−0.756455
$775$	−4.02401	−0.144547
$776$	−27.8542	−0.999907
$777$	−6.16890	−0.221308
$778$	−35.2766	−1.26473
$779$	40.3635	1.44617
$780$	−21.9431	−0.785689
$781$	−10.9267	−0.390986
$782$	−155.410	−5.55747
$783$	−40.0397	−1.43090
$784$	1.04031	0.0371540
$785$	−3.64311	−0.130028
$786$	−6.63216	−0.236561
$787$	−43.3720	−1.54605	−0.773023	−	0.634378i	$-0.781256\pi$
$787$	−43.3720	−1.54605	−0.773023	+	0.634378i	$0.781256\pi$
$788$	63.4962	2.26196
$789$	3.18619	0.113431
$790$	18.5946	0.661567
$791$	14.7175	0.523295
$792$	−20.4891	−0.728050
$793$	63.7729	2.26464
$794$	−50.0595	−1.77654
$795$	12.1956	0.432535
$796$	−34.2961	−1.21559
$797$	−40.5342	−1.43580	−0.717898	−	0.696148i	$-0.754896\pi$
$797$	−40.5342	−1.43580	−0.717898	+	0.696148i	$0.754896\pi$
$798$	8.89255	0.314793
$799$	40.6184	1.43698
$800$	5.84413	0.206621
$801$	−24.6075	−0.869463
$802$	−14.9308	−0.527225
$803$	−2.62118	−0.0924995
$804$	−4.21679	−0.148715
$805$	7.62659	0.268802
$806$	−54.6901	−1.92638
$807$	−30.5931	−1.07693
$808$	4.64194	0.163303
$809$	18.3441	0.644945	0.322472	−	0.946579i	$-0.395486\pi$
$809$	18.3441	0.644945	0.322472	+	0.946579i	$0.395486\pi$
$810$	2.65877	0.0934196
$811$	39.9941	1.40438	0.702192	−	0.711988i	$-0.252205\pi$
$811$	39.9941	1.40438	0.702192	+	0.711988i	$0.252205\pi$
$812$	−20.2563	−0.710856
$813$	7.12644	0.249935
$814$	64.2544	2.25211
$815$	17.2437	0.604021
$816$	1.45103	0.0507961
$817$	−21.9363	−0.767455
$818$	−5.88524	−0.205773
$819$	−8.49966	−0.297002
$820$	32.4231	1.13226
$821$	0.520721	0.0181733	0.00908664	−	0.999959i	$-0.497108\pi$
$821$	0.520721	0.0181733	0.00908664	+	0.999959i	$0.497108\pi$
$822$	26.6316	0.928883
$823$	50.5973	1.76371	0.881856	−	0.471519i	$-0.156294\pi$
$823$	50.5973	1.76371	0.881856	+	0.471519i	$0.156294\pi$
$824$	8.73890	0.304434
$825$	−5.14926	−0.179274
$826$	−3.72450	−0.129592
$827$	16.0127	0.556817	0.278409	−	0.960463i	$-0.410193\pi$
$827$	16.0127	0.556817	0.278409	+	0.960463i	$0.410193\pi$
$828$	48.0287	1.66911
$829$	14.7812	0.513372	0.256686	−	0.966495i	$-0.417369\pi$
$829$	14.7812	0.513372	0.256686	+	0.966495i	$0.417369\pi$
$830$	25.0839	0.870676
$831$	7.79982	0.270573
$832$	77.4511	2.68513
$833$	47.7328	1.65384
$834$	30.1556	1.04420
$835$	−23.1080	−0.799687
$836$	−56.9901	−1.97105
$837$	21.6527	0.748426
$838$	−49.4668	−1.70880
$839$	−25.0577	−0.865087	−0.432543	−	0.901613i	$-0.642384\pi$
$839$	−25.0577	−0.865087	−0.432543	+	0.901613i	$0.642384\pi$
$840$	2.67687	0.0923607
$841$	26.3700	0.909312
$842$	67.8750	2.33913
$843$	28.3028	0.974799
$844$	−29.1200	−1.00235
$845$	22.5308	0.775084
$846$	−20.4017	−0.701424
$847$	−7.67557	−0.263736
$848$	−1.75663	−0.0603230
$849$	5.34672	0.183499
$850$	17.3420	0.594827
$851$	−56.4436	−1.93486
$852$	8.99002	0.307993
$853$	−26.0015	−0.890276	−0.445138	−	0.895462i	$-0.646845\pi$
$853$	−26.0015	−0.890276	−0.445138	+	0.895462i	$0.646845\pi$
$854$	−20.7602	−0.710399
$855$	−6.67198	−0.228177
$856$	−5.19899	−0.177698
$857$	−23.9697	−0.818791	−0.409395	−	0.912357i	$-0.634260\pi$
$857$	−23.9697	−0.818791	−0.409395	+	0.912357i	$0.634260\pi$
$858$	−69.9833	−2.38919
$859$	42.2242	1.44067	0.720336	−	0.693626i	$-0.243988\pi$
$859$	42.2242	1.44067	0.720336	+	0.693626i	$0.243988\pi$
$860$	−17.6210	−0.600870
$861$	−9.92787	−0.338341
$862$	−13.4086	−0.456697
$863$	10.9708	0.373450	0.186725	−	0.982412i	$-0.440213\pi$
$863$	10.9708	0.373450	0.186725	+	0.982412i	$0.440213\pi$
$864$	−31.4465	−1.06983
$865$	5.02692	0.170920
$866$	38.5491	1.30995
$867$	47.0131	1.59665
$868$	10.9542	0.371810
$869$	36.4890	1.23780
$870$	−19.5257	−0.661985
$871$	6.82794	0.231356
$872$	51.8181	1.75478
$873$	−17.0760	−0.577935
$874$	81.3642	2.75219
$875$	−0.851041	−0.0287704
$876$	2.15661	0.0728650
$877$	−36.0358	−1.21684	−0.608422	−	0.793614i	$-0.708197\pi$
$877$	−36.0358	−1.21684	−0.608422	+	0.793614i	$0.708197\pi$
$878$	−20.8336	−0.703100
$879$	34.7644	1.17258
$880$	0.741688	0.0250023
$881$	−16.6108	−0.559633	−0.279816	−	0.960054i	$-0.590274\pi$
$881$	−16.6108	−0.559633	−0.279816	+	0.960054i	$0.590274\pi$
$882$	−23.9751	−0.807283
$883$	4.52130	0.152154	0.0760769	−	0.997102i	$-0.475761\pi$
$883$	4.52130	0.152154	0.0760769	+	0.997102i	$0.475761\pi$
$884$	145.020	4.87755
$885$	−2.20899	−0.0742545
$886$	67.7292	2.27541
$887$	−27.7457	−0.931608	−0.465804	−	0.884888i	$-0.654235\pi$
$887$	−27.7457	−0.931608	−0.465804	+	0.884888i	$0.654235\pi$
$888$	−19.8112	−0.664820
$889$	6.87868	0.230703
$890$	−33.4862	−1.12246
$891$	5.21741	0.174790
$892$	−41.7488	−1.39785
$893$	−21.2655	−0.711624
$894$	−53.1091	−1.77623
$895$	−8.87136	−0.296537
$896$	−15.2657	−0.509990
$897$	61.4761	2.05263
$898$	6.03925	0.201532
$899$	−29.9431	−0.998657
$900$	−5.35946	−0.178649
$901$	−80.5998	−2.68517
$902$	103.407	3.44309
$903$	5.39550	0.179551
$904$	47.2649	1.57201
$905$	−0.590912	−0.0196426
$906$	−46.7273	−1.55241
$907$	−7.92585	−0.263173	−0.131587	−	0.991305i	$-0.542007\pi$
$907$	−7.92585	−0.263173	−0.131587	+	0.991305i	$0.542007\pi$
$908$	33.6206	1.11574
$909$	2.84574	0.0943872
$910$	−11.5664	−0.383424
$911$	14.6839	0.486498	0.243249	−	0.969964i	$-0.421787\pi$
$911$	14.6839	0.486498	0.243249	+	0.969964i	$0.421787\pi$
$912$	−0.759677	−0.0251554
$913$	49.2232	1.62905
$914$	−4.04129	−0.133674
$915$	−12.3128	−0.407049
$916$	46.8823	1.54903
$917$	−2.15097	−0.0710314
$918$	−93.3153	−3.07986
$919$	20.2561	0.668186	0.334093	−	0.942540i	$-0.391570\pi$
$919$	20.2561	0.668186	0.334093	+	0.942540i	$0.391570\pi$
$920$	24.4925	0.807495
$921$	4.48237	0.147699
$922$	−3.43870	−0.113247
$923$	−14.5569	−0.479145
$924$	14.0174	0.461138
$925$	6.29845	0.207092
$926$	65.6514	2.15744
$927$	5.35738	0.175959
$928$	43.4868	1.42752
$929$	44.5280	1.46092	0.730458	−	0.682958i	$-0.239307\pi$
$929$	44.5280	1.46092	0.730458	+	0.682958i	$0.239307\pi$
$930$	10.5592	0.346248
$931$	−24.9902	−0.819022
$932$	−57.5652	−1.88561
$933$	19.6076	0.641926
$934$	37.4580	1.22566
$935$	34.0310	1.11293
$936$	−27.2964	−0.892209
$937$	−26.6782	−0.871538	−0.435769	−	0.900059i	$-0.643524\pi$
$937$	−26.6782	−0.871538	−0.435769	+	0.900059i	$0.643524\pi$
$938$	−2.22272	−0.0725743
$939$	−22.0438	−0.719371
$940$	−17.0821	−0.557158
$941$	11.0343	0.359708	0.179854	−	0.983693i	$-0.442438\pi$
$941$	11.0343	0.359708	0.179854	+	0.983693i	$0.442438\pi$
$942$	9.55967	0.311471
$943$	−90.8370	−2.95806
$944$	0.318179	0.0103558
$945$	4.57934	0.148966
$946$	−56.1987	−1.82718
$947$	−8.38953	−0.272623	−0.136312	−	0.990666i	$-0.543525\pi$
$947$	−8.38953	−0.272623	−0.136312	+	0.990666i	$0.543525\pi$
$948$	−30.0217	−0.975060
$949$	−3.49203	−0.113356
$950$	−9.07931	−0.294572
$951$	9.52117	0.308745
$952$	−17.6912	−0.573374
$953$	−7.66315	−0.248234	−0.124117	−	0.992268i	$-0.539610\pi$
$953$	−7.66315	−0.248234	−0.124117	+	0.992268i	$0.539610\pi$
$954$	40.4834	1.31070
$955$	4.56601	0.147752
$956$	58.3113	1.88592
$957$	−38.3162	−1.23859
$958$	21.5961	0.697738
$959$	8.63728	0.278912
$960$	−14.9537	−0.482628
$961$	−14.8073	−0.477656
$962$	85.6019	2.75992
$963$	−3.18724	−0.102707
$964$	10.0698	0.324326
$965$	15.5989	0.502147
$966$	−20.0125	−0.643891
$967$	−11.0863	−0.356512	−0.178256	−	0.983984i	$-0.557046\pi$
$967$	−11.0863	−0.356512	−0.178256	+	0.983984i	$0.557046\pi$
$968$	−24.6498	−0.792275
$969$	−34.8564	−1.11975
$970$	−23.2372	−0.746102
$971$	47.7547	1.53252	0.766260	−	0.642530i	$-0.222115\pi$
$971$	47.7547	1.53252	0.766260	+	0.642530i	$0.222115\pi$
$972$	47.3425	1.51851
$973$	9.78021	0.313539
$974$	−25.2554	−0.809234
$975$	−6.86003	−0.219697
$976$	1.77351	0.0567687
$977$	−53.4877	−1.71122	−0.855612	−	0.517617i	$-0.826819\pi$
$977$	−53.4877	−1.71122	−0.855612	+	0.517617i	$0.826819\pi$
$978$	−45.2482	−1.44688
$979$	−65.7113	−2.10014
$980$	−20.0741	−0.641244
$981$	31.7671	1.01424
$982$	−88.5429	−2.82552
$983$	48.3581	1.54238	0.771192	−	0.636603i	$-0.219661\pi$
$983$	48.3581	1.54238	0.771192	+	0.636603i	$0.219661\pi$
$984$	−31.8830	−1.01639
$985$	19.8507	0.632496
$986$	129.044	4.10959
$987$	5.23051	0.166489
$988$	−75.9243	−2.41547
$989$	49.3672	1.56978
$990$	−17.0930	−0.543250
$991$	51.3019	1.62966	0.814829	−	0.579701i	$-0.196831\pi$
$991$	51.3019	1.62966	0.814829	+	0.579701i	$0.196831\pi$
$992$	−23.5168	−0.746661
$993$	−20.9783	−0.665726
$994$	4.73874	0.150304
$995$	−10.7219	−0.339908
$996$	−40.4989	−1.28326
$997$	33.2743	1.05381	0.526903	−	0.849925i	$-0.323353\pi$
$997$	33.2743	1.05381	0.526903	+	0.849925i	$0.323353\pi$
$998$	−5.55503	−0.175841
$999$	−33.8912	−1.07227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.19	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.28006 q^{2} +1.15086 q^{3} +3.19869 q^{4} +1.00000 q^{5} -2.62404 q^{6} -0.851041 q^{7} -2.73309 q^{8} -1.67552 q^{9} +O(q^{10})\)	\(q-2.28006 q^{2} +1.15086 q^{3} +3.19869 q^{4} +1.00000 q^{5} -2.62404 q^{6} -0.851041 q^{7} -2.73309 q^{8} -1.67552 q^{9} -2.28006 q^{10} -4.47426 q^{11} +3.68125 q^{12} -5.96077 q^{13} +1.94043 q^{14} +1.15086 q^{15} -0.165768 q^{16} -7.60594 q^{17} +3.82028 q^{18} +3.98204 q^{19} +3.19869 q^{20} -0.979430 q^{21} +10.2016 q^{22} -8.96149 q^{23} -3.14541 q^{24} +1.00000 q^{25} +13.5909 q^{26} -5.38087 q^{27} -2.72221 q^{28} +7.44110 q^{29} -2.62404 q^{30} -4.02401 q^{31} +5.84413 q^{32} -5.14926 q^{33} +17.3420 q^{34} -0.851041 q^{35} -5.35946 q^{36} +6.29845 q^{37} -9.07931 q^{38} -6.86003 q^{39} -2.73309 q^{40} +10.1364 q^{41} +2.23316 q^{42} -5.50881 q^{43} -14.3118 q^{44} -1.67552 q^{45} +20.4328 q^{46} -5.34036 q^{47} -0.190776 q^{48} -6.27573 q^{49} -2.28006 q^{50} -8.75339 q^{51} -19.0667 q^{52} +10.5970 q^{53} +12.2687 q^{54} -4.47426 q^{55} +2.32597 q^{56} +4.58278 q^{57} -16.9662 q^{58} -1.91943 q^{59} +3.68125 q^{60} -10.6988 q^{61} +9.17500 q^{62} +1.42593 q^{63} -12.9935 q^{64} -5.96077 q^{65} +11.7406 q^{66} -1.14548 q^{67} -24.3290 q^{68} -10.3134 q^{69} +1.94043 q^{70} +2.44211 q^{71} +4.57933 q^{72} +0.585835 q^{73} -14.3609 q^{74} +1.15086 q^{75} +12.7373 q^{76} +3.80778 q^{77} +15.6413 q^{78} -8.15531 q^{79} -0.165768 q^{80} -1.16609 q^{81} -23.1116 q^{82} -11.0014 q^{83} -3.13289 q^{84} -7.60594 q^{85} +12.5604 q^{86} +8.56368 q^{87} +12.2286 q^{88} +14.6865 q^{89} +3.82028 q^{90} +5.07286 q^{91} -28.6650 q^{92} -4.63108 q^{93} +12.1764 q^{94} +3.98204 q^{95} +6.72579 q^{96} +10.1915 q^{97} +14.3091 q^{98} +7.49670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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