LMFDB - Embedded newform 8015.2.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23328 q^{2} +1.54114 q^{3} +2.98754 q^{4} -1.00000 q^{5} -3.44181 q^{6} -1.00000 q^{7} -2.20546 q^{8} -0.624877 q^{9} +O(q^{10})$	\(q-2.23328 q^{2} +1.54114 q^{3} +2.98754 q^{4} -1.00000 q^{5} -3.44181 q^{6} -1.00000 q^{7} -2.20546 q^{8} -0.624877 q^{9} +2.23328 q^{10} -0.380972 q^{11} +4.60423 q^{12} -3.83163 q^{13} +2.23328 q^{14} -1.54114 q^{15} -1.04967 q^{16} -2.25256 q^{17} +1.39553 q^{18} -4.69167 q^{19} -2.98754 q^{20} -1.54114 q^{21} +0.850816 q^{22} +3.81705 q^{23} -3.39893 q^{24} +1.00000 q^{25} +8.55710 q^{26} -5.58646 q^{27} -2.98754 q^{28} -4.90178 q^{29} +3.44181 q^{30} -0.412751 q^{31} +6.75514 q^{32} -0.587132 q^{33} +5.03059 q^{34} +1.00000 q^{35} -1.86685 q^{36} -4.75791 q^{37} +10.4778 q^{38} -5.90509 q^{39} +2.20546 q^{40} +2.15652 q^{41} +3.44181 q^{42} -8.37449 q^{43} -1.13817 q^{44} +0.624877 q^{45} -8.52455 q^{46} +9.23317 q^{47} -1.61770 q^{48} +1.00000 q^{49} -2.23328 q^{50} -3.47151 q^{51} -11.4471 q^{52} -9.56310 q^{53} +12.4761 q^{54} +0.380972 q^{55} +2.20546 q^{56} -7.23054 q^{57} +10.9470 q^{58} -0.910238 q^{59} -4.60423 q^{60} +9.37004 q^{61} +0.921789 q^{62} +0.624877 q^{63} -12.9868 q^{64} +3.83163 q^{65} +1.31123 q^{66} +3.78810 q^{67} -6.72961 q^{68} +5.88262 q^{69} -2.23328 q^{70} -8.71837 q^{71} +1.37814 q^{72} -3.06051 q^{73} +10.6258 q^{74} +1.54114 q^{75} -14.0166 q^{76} +0.380972 q^{77} +13.1877 q^{78} +6.21476 q^{79} +1.04967 q^{80} -6.73490 q^{81} -4.81611 q^{82} -2.30591 q^{83} -4.60423 q^{84} +2.25256 q^{85} +18.7026 q^{86} -7.55434 q^{87} +0.840217 q^{88} -12.4143 q^{89} -1.39553 q^{90} +3.83163 q^{91} +11.4036 q^{92} -0.636109 q^{93} -20.6203 q^{94} +4.69167 q^{95} +10.4106 q^{96} -13.2234 q^{97} -2.23328 q^{98} +0.238060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−2.23328	−1.57917	−0.789584	−	0.613643i	$-0.789704\pi$
$2$	−2.23328	−1.57917	−0.789584	+	0.613643i	$0.789704\pi$
$3$	1.54114	0.889780	0.444890	−	0.895585i	$-0.353243\pi$
$3$	1.54114	0.889780	0.444890	+	0.895585i	$0.353243\pi$
$4$	2.98754	1.49377
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.44181	−1.40511
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.20546	−0.779748
$9$	−0.624877	−0.208292
$10$	2.23328	0.706225
$11$	−0.380972	−0.114867	−0.0574336	−	0.998349i	$-0.518292\pi$
$11$	−0.380972	−0.114867	−0.0574336	+	0.998349i	$0.518292\pi$
$12$	4.60423	1.32913
$13$	−3.83163	−1.06270	−0.531351	−	0.847152i	$-0.678315\pi$
$13$	−3.83163	−1.06270	−0.531351	+	0.847152i	$0.678315\pi$
$14$	2.23328	0.596869
$15$	−1.54114	−0.397922
$16$	−1.04967	−0.262419
$17$	−2.25256	−0.546325	−0.273163	−	0.961968i	$-0.588070\pi$
$17$	−2.25256	−0.546325	−0.273163	+	0.961968i	$0.588070\pi$
$18$	1.39553	0.328929
$19$	−4.69167	−1.07634	−0.538171	−	0.842835i	$-0.680885\pi$
$19$	−4.69167	−1.07634	−0.538171	+	0.842835i	$0.680885\pi$
$20$	−2.98754	−0.668035
$21$	−1.54114	−0.336305
$22$	0.850816	0.181395
$23$	3.81705	0.795910	0.397955	−	0.917405i	$-0.369720\pi$
$23$	3.81705	0.795910	0.397955	+	0.917405i	$0.369720\pi$
$24$	−3.39893	−0.693804
$25$	1.00000	0.200000
$26$	8.55710	1.67818
$27$	−5.58646	−1.07511
$28$	−2.98754	−0.564592
$29$	−4.90178	−0.910237	−0.455118	−	0.890431i	$-0.650403\pi$
$29$	−4.90178	−0.910237	−0.455118	+	0.890431i	$0.650403\pi$
$30$	3.44181	0.628385
$31$	−0.412751	−0.0741323	−0.0370661	−	0.999313i	$-0.511801\pi$
$31$	−0.412751	−0.0741323	−0.0370661	+	0.999313i	$0.511801\pi$
$32$	6.75514	1.19415
$33$	−0.587132	−0.102207
$34$	5.03059	0.862739
$35$	1.00000	0.169031
$36$	−1.86685	−0.311141
$37$	−4.75791	−0.782196	−0.391098	−	0.920349i	$-0.627905\pi$
$37$	−4.75791	−0.782196	−0.391098	+	0.920349i	$0.627905\pi$
$38$	10.4778	1.69973
$39$	−5.90509	−0.945570
$40$	2.20546	0.348714
$41$	2.15652	0.336791	0.168396	−	0.985719i	$-0.446141\pi$
$41$	2.15652	0.336791	0.168396	+	0.985719i	$0.446141\pi$
$42$	3.44181	0.531082
$43$	−8.37449	−1.27710	−0.638549	−	0.769581i	$-0.720465\pi$
$43$	−8.37449	−1.27710	−0.638549	+	0.769581i	$0.720465\pi$
$44$	−1.13817	−0.171585
$45$	0.624877	0.0931512
$46$	−8.52455	−1.25688
$47$	9.23317	1.34680	0.673398	−	0.739280i	$-0.264834\pi$
$47$	9.23317	1.34680	0.673398	+	0.739280i	$0.264834\pi$
$48$	−1.61770	−0.233495
$49$	1.00000	0.142857
$50$	−2.23328	−0.315834
$51$	−3.47151	−0.486109
$52$	−11.4471	−1.58743
$53$	−9.56310	−1.31359	−0.656796	−	0.754068i	$-0.728089\pi$
$53$	−9.56310	−1.31359	−0.656796	+	0.754068i	$0.728089\pi$
$54$	12.4761	1.69779
$55$	0.380972	0.0513702
$56$	2.20546	0.294717
$57$	−7.23054	−0.957708
$58$	10.9470	1.43742
$59$	−0.910238	−0.118503	−0.0592514	−	0.998243i	$-0.518871\pi$
$59$	−0.910238	−0.118503	−0.0592514	+	0.998243i	$0.518871\pi$
$60$	−4.60423	−0.594404
$61$	9.37004	1.19971	0.599855	−	0.800108i	$-0.295225\pi$
$61$	9.37004	1.19971	0.599855	+	0.800108i	$0.295225\pi$
$62$	0.921789	0.117067
$63$	0.624877	0.0787271
$64$	−12.9868	−1.62335
$65$	3.83163	0.475255
$66$	1.31123	0.161401
$67$	3.78810	0.462790	0.231395	−	0.972860i	$-0.425671\pi$
$67$	3.78810	0.462790	0.231395	+	0.972860i	$0.425671\pi$
$68$	−6.72961	−0.816085
$69$	5.88262	0.708185
$70$	−2.23328	−0.266928
$71$	−8.71837	−1.03468	−0.517340	−	0.855780i	$-0.673078\pi$
$71$	−8.71837	−1.03468	−0.517340	+	0.855780i	$0.673078\pi$
$72$	1.37814	0.162415
$73$	−3.06051	−0.358206	−0.179103	−	0.983830i	$-0.557319\pi$
$73$	−3.06051	−0.358206	−0.179103	+	0.983830i	$0.557319\pi$
$74$	10.6258	1.23522
$75$	1.54114	0.177956
$76$	−14.0166	−1.60781
$77$	0.380972	0.0434157
$78$	13.1877	1.49321
$79$	6.21476	0.699216	0.349608	−	0.936896i	$-0.386315\pi$
$79$	6.21476	0.699216	0.349608	+	0.936896i	$0.386315\pi$
$80$	1.04967	0.117357
$81$	−6.73490	−0.748322
$82$	−4.81611	−0.531850
$83$	−2.30591	−0.253106	−0.126553	−	0.991960i	$-0.540391\pi$
$83$	−2.30591	−0.253106	−0.126553	+	0.991960i	$0.540391\pi$
$84$	−4.60423	−0.502363
$85$	2.25256	0.244324
$86$	18.7026	2.01675
$87$	−7.55434	−0.809910
$88$	0.840217	0.0895675
$89$	−12.4143	−1.31591	−0.657955	−	0.753057i	$-0.728578\pi$
$89$	−12.4143	−1.31591	−0.657955	+	0.753057i	$0.728578\pi$
$90$	−1.39553	−0.147101
$91$	3.83163	0.401664
$92$	11.4036	1.18891
$93$	−0.636109	−0.0659614
$94$	−20.6203	−2.12682
$95$	4.69167	0.481355
$96$	10.4106	1.06253
$97$	−13.2234	−1.34263	−0.671315	−	0.741172i	$-0.734270\pi$
$97$	−13.2234	−1.34263	−0.671315	+	0.741172i	$0.734270\pi$
$98$	−2.23328	−0.225595
$99$	0.238060	0.0239260
$100$	2.98754	0.298754
$101$	−3.18741	−0.317159	−0.158579	−	0.987346i	$-0.550691\pi$
$101$	−3.18741	−0.317159	−0.158579	+	0.987346i	$0.550691\pi$
$102$	7.75286	0.767648
$103$	7.80859	0.769403	0.384702	−	0.923041i	$-0.374304\pi$
$103$	7.80859	0.769403	0.384702	+	0.923041i	$0.374304\pi$
$104$	8.45050	0.828639
$105$	1.54114	0.150400
$106$	21.3571	2.07438
$107$	5.06847	0.489988	0.244994	−	0.969525i	$-0.421214\pi$
$107$	5.06847	0.489988	0.244994	+	0.969525i	$0.421214\pi$
$108$	−16.6898	−1.60597
$109$	18.4401	1.76624	0.883122	−	0.469143i	$-0.155437\pi$
$109$	18.4401	1.76624	0.883122	+	0.469143i	$0.155437\pi$
$110$	−0.850816	−0.0811222
$111$	−7.33263	−0.695982
$112$	1.04967	0.0991849
$113$	14.2113	1.33689	0.668446	−	0.743761i	$-0.266960\pi$
$113$	14.2113	1.33689	0.668446	+	0.743761i	$0.266960\pi$
$114$	16.1478	1.51238
$115$	−3.81705	−0.355942
$116$	−14.6443	−1.35969
$117$	2.39429	0.221353
$118$	2.03282	0.187136
$119$	2.25256	0.206492
$120$	3.39893	0.310278
$121$	−10.8549	−0.986806
$122$	−20.9259	−1.89454
$123$	3.32350	0.299670
$124$	−1.23311	−0.110737
$125$	−1.00000	−0.0894427
$126$	−1.39553	−0.124323
$127$	2.02659	0.179831	0.0899153	−	0.995949i	$-0.471340\pi$
$127$	2.02659	0.179831	0.0899153	+	0.995949i	$0.471340\pi$
$128$	15.4928	1.36939
$129$	−12.9063	−1.13634
$130$	−8.55710	−0.750507
$131$	0.716254	0.0625794	0.0312897	−	0.999510i	$-0.490039\pi$
$131$	0.716254	0.0625794	0.0312897	+	0.999510i	$0.490039\pi$
$132$	−1.75408	−0.152673
$133$	4.69167	0.406819
$134$	−8.45990	−0.730824
$135$	5.58646	0.480806
$136$	4.96792	0.425996
$137$	20.0041	1.70907	0.854534	−	0.519395i	$-0.173843\pi$
$137$	20.0041	1.70907	0.854534	+	0.519395i	$0.173843\pi$
$138$	−13.1376	−1.11834
$139$	8.57697	0.727489	0.363745	−	0.931499i	$-0.381498\pi$
$139$	8.57697	0.727489	0.363745	+	0.931499i	$0.381498\pi$
$140$	2.98754	0.252493
$141$	14.2296	1.19835
$142$	19.4706	1.63393
$143$	1.45974	0.122070
$144$	0.655917	0.0546598
$145$	4.90178	0.407070
$146$	6.83498	0.565667
$147$	1.54114	0.127111
$148$	−14.2145	−1.16842
$149$	−20.2101	−1.65568	−0.827840	−	0.560965i	$-0.810430\pi$
$149$	−20.2101	−1.65568	−0.827840	+	0.560965i	$0.810430\pi$
$150$	−3.44181	−0.281022
$151$	8.30709	0.676022	0.338011	−	0.941142i	$-0.390246\pi$
$151$	8.30709	0.676022	0.338011	+	0.941142i	$0.390246\pi$
$152$	10.3473	0.839276
$153$	1.40757	0.113795
$154$	−0.850816	−0.0685607
$155$	0.412751	0.0331530
$156$	−17.6417	−1.41247
$157$	13.4589	1.07414	0.537069	−	0.843538i	$-0.319531\pi$
$157$	13.4589	1.07414	0.537069	+	0.843538i	$0.319531\pi$
$158$	−13.8793	−1.10418
$159$	−14.7381	−1.16881
$160$	−6.75514	−0.534040
$161$	−3.81705	−0.300826
$162$	15.0409	1.18173
$163$	−3.86110	−0.302425	−0.151212	−	0.988501i	$-0.548318\pi$
$163$	−3.86110	−0.302425	−0.151212	+	0.988501i	$0.548318\pi$
$164$	6.44269	0.503089
$165$	0.587132	0.0457081
$166$	5.14973	0.399697
$167$	−6.59998	−0.510722	−0.255361	−	0.966846i	$-0.582194\pi$
$167$	−6.59998	−0.510722	−0.255361	+	0.966846i	$0.582194\pi$
$168$	3.39893	0.262233
$169$	1.68136	0.129335
$170$	−5.03059	−0.385829
$171$	2.93172	0.224194
$172$	−25.0192	−1.90769
$173$	−20.3752	−1.54910	−0.774549	−	0.632514i	$-0.782023\pi$
$173$	−20.3752	−1.54910	−0.774549	+	0.632514i	$0.782023\pi$
$174$	16.8710	1.27898
$175$	−1.00000	−0.0755929
$176$	0.399896	0.0301433
$177$	−1.40281	−0.105441
$178$	27.7245	2.07804
$179$	−10.4006	−0.777375	−0.388688	−	0.921370i	$-0.627071\pi$
$179$	−10.4006	−0.777375	−0.388688	+	0.921370i	$0.627071\pi$
$180$	1.86685	0.139147
$181$	5.23795	0.389334	0.194667	−	0.980869i	$-0.437637\pi$
$181$	5.23795	0.389334	0.194667	+	0.980869i	$0.437637\pi$
$182$	−8.55710	−0.634294
$183$	14.4406	1.06748
$184$	−8.41835	−0.620609
$185$	4.75791	0.349809
$186$	1.42061	0.104164
$187$	0.858160	0.0627549
$188$	27.5845	2.01181
$189$	5.58646	0.406355
$190$	−10.4778	−0.760141
$191$	7.80441	0.564708	0.282354	−	0.959310i	$-0.408885\pi$
$191$	7.80441	0.564708	0.282354	+	0.959310i	$0.408885\pi$
$192$	−20.0145	−1.44442
$193$	17.0029	1.22389	0.611946	−	0.790900i	$-0.290387\pi$
$193$	17.0029	1.22389	0.611946	+	0.790900i	$0.290387\pi$
$194$	29.5315	2.12024
$195$	5.90509	0.422872
$196$	2.98754	0.213396
$197$	−9.63174	−0.686233	−0.343117	−	0.939293i	$-0.611483\pi$
$197$	−9.63174	−0.686233	−0.343117	+	0.939293i	$0.611483\pi$
$198$	−0.531656	−0.0377831
$199$	−8.90697	−0.631399	−0.315699	−	0.948859i	$-0.602239\pi$
$199$	−8.90697	−0.631399	−0.315699	+	0.948859i	$0.602239\pi$
$200$	−2.20546	−0.155950
$201$	5.83801	0.411781
$202$	7.11838	0.500847
$203$	4.90178	0.344037
$204$	−10.3713	−0.726136
$205$	−2.15652	−0.150618
$206$	−17.4388	−1.21502
$207$	−2.38519	−0.165782
$208$	4.02196	0.278873
$209$	1.78739	0.123637
$210$	−3.44181	−0.237507
$211$	7.26557	0.500183	0.250091	−	0.968222i	$-0.419539\pi$
$211$	7.26557	0.500183	0.250091	+	0.968222i	$0.419539\pi$
$212$	−28.5702	−1.96221
$213$	−13.4363	−0.920637
$214$	−11.3193	−0.773773
$215$	8.37449	0.571136
$216$	12.3207	0.838318
$217$	0.412751	0.0280194
$218$	−41.1820	−2.78920
$219$	−4.71669	−0.318724
$220$	1.13817	0.0767353
$221$	8.63096	0.580581
$222$	16.3758	1.09907
$223$	21.9365	1.46898	0.734488	−	0.678622i	$-0.237422\pi$
$223$	21.9365	1.46898	0.734488	+	0.678622i	$0.237422\pi$
$224$	−6.75514	−0.451347
$225$	−0.624877	−0.0416585
$226$	−31.7379	−2.11118
$227$	−24.7687	−1.64396	−0.821980	−	0.569517i	$-0.807130\pi$
$227$	−24.7687	−1.64396	−0.821980	+	0.569517i	$0.807130\pi$
$228$	−21.6015	−1.43060
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.52455	0.562092
$231$	0.587132	0.0386304
$232$	10.8107	0.709755
$233$	24.6662	1.61593	0.807967	−	0.589227i	$-0.200568\pi$
$233$	24.6662	1.61593	0.807967	+	0.589227i	$0.200568\pi$
$234$	−5.34713	−0.349553
$235$	−9.23317	−0.602306
$236$	−2.71937	−0.177016
$237$	9.57784	0.622148
$238$	−5.03059	−0.326085
$239$	17.7292	1.14680	0.573402	−	0.819274i	$-0.305623\pi$
$239$	17.7292	1.14680	0.573402	+	0.819274i	$0.305623\pi$
$240$	1.61770	0.104422
$241$	−9.54025	−0.614542	−0.307271	−	0.951622i	$-0.599416\pi$
$241$	−9.54025	−0.614542	−0.307271	+	0.951622i	$0.599416\pi$
$242$	24.2420	1.55833
$243$	6.37992	0.409272
$244$	27.9934	1.79209
$245$	−1.00000	−0.0638877
$246$	−7.42231	−0.473229
$247$	17.9767	1.14383
$248$	0.910306	0.0578045
$249$	−3.55373	−0.225209
$250$	2.23328	0.141245
$251$	16.6146	1.04871	0.524353	−	0.851501i	$-0.324307\pi$
$251$	16.6146	1.04871	0.524353	+	0.851501i	$0.324307\pi$
$252$	1.86685	0.117600
$253$	−1.45419	−0.0914240
$254$	−4.52594	−0.283983
$255$	3.47151	0.217395
$256$	−8.62629	−0.539143
$257$	17.5157	1.09260	0.546301	−	0.837589i	$-0.316035\pi$
$257$	17.5157	1.09260	0.546301	+	0.837589i	$0.316035\pi$
$258$	28.8234	1.79447
$259$	4.75791	0.295642
$260$	11.4471	0.709922
$261$	3.06301	0.189595
$262$	−1.59960	−0.0988234
$263$	−14.1019	−0.869561	−0.434780	−	0.900537i	$-0.643174\pi$
$263$	−14.1019	−0.869561	−0.434780	+	0.900537i	$0.643174\pi$
$264$	1.29490	0.0796953
$265$	9.56310	0.587457
$266$	−10.4778	−0.642436
$267$	−19.1322	−1.17087
$268$	11.3171	0.691303
$269$	−24.2271	−1.47715	−0.738576	−	0.674170i	$-0.764501\pi$
$269$	−24.2271	−1.47715	−0.738576	+	0.674170i	$0.764501\pi$
$270$	−12.4761	−0.759273
$271$	23.7745	1.44420	0.722100	−	0.691788i	$-0.243177\pi$
$271$	23.7745	1.44420	0.722100	+	0.691788i	$0.243177\pi$
$272$	2.36445	0.143366
$273$	5.90509	0.357392
$274$	−44.6749	−2.69891
$275$	−0.380972	−0.0229734
$276$	17.5746	1.05787
$277$	−17.4180	−1.04654	−0.523272	−	0.852166i	$-0.675289\pi$
$277$	−17.4180	−1.04654	−0.523272	+	0.852166i	$0.675289\pi$
$278$	−19.1548	−1.14883
$279$	0.257919	0.0154412
$280$	−2.20546	−0.131801
$281$	−19.9487	−1.19004	−0.595020	−	0.803711i	$-0.702856\pi$
$281$	−19.9487	−1.19004	−0.595020	+	0.803711i	$0.702856\pi$
$282$	−31.7788	−1.89240
$283$	21.8565	1.29923	0.649617	−	0.760262i	$-0.274929\pi$
$283$	21.8565	1.29923	0.649617	+	0.760262i	$0.274929\pi$
$284$	−26.0465	−1.54558
$285$	7.23054	0.428300
$286$	−3.26001	−0.192768
$287$	−2.15652	−0.127295
$288$	−4.22113	−0.248732
$289$	−11.9260	−0.701529
$290$	−10.9470	−0.642832
$291$	−20.3791	−1.19464
$292$	−9.14341	−0.535077
$293$	20.0155	1.16932	0.584660	−	0.811279i	$-0.301228\pi$
$293$	20.0155	1.16932	0.584660	+	0.811279i	$0.301228\pi$
$294$	−3.44181	−0.200730
$295$	0.910238	0.0529961
$296$	10.4934	0.609916
$297$	2.12828	0.123495
$298$	45.1349	2.61460
$299$	−14.6255	−0.845815
$300$	4.60423	0.265825
$301$	8.37449	0.482698
$302$	−18.5521	−1.06755
$303$	−4.91225	−0.282201
$304$	4.92473	0.282452
$305$	−9.37004	−0.536527
$306$	−3.14350	−0.179702
$307$	9.51221	0.542890	0.271445	−	0.962454i	$-0.412498\pi$
$307$	9.51221	0.542890	0.271445	+	0.962454i	$0.412498\pi$
$308$	1.13817	0.0648532
$309$	12.0342	0.684599
$310$	−0.921789	−0.0523541
$311$	−3.04029	−0.172399	−0.0861996	−	0.996278i	$-0.527472\pi$
$311$	−3.04029	−0.172399	−0.0861996	+	0.996278i	$0.527472\pi$
$312$	13.0234	0.737306
$313$	26.1113	1.47590	0.737948	−	0.674858i	$-0.235795\pi$
$313$	26.1113	1.47590	0.737948	+	0.674858i	$0.235795\pi$
$314$	−30.0575	−1.69624
$315$	−0.624877	−0.0352078
$316$	18.5669	1.04447
$317$	13.1203	0.736909	0.368455	−	0.929646i	$-0.379887\pi$
$317$	13.1203	0.736909	0.368455	+	0.929646i	$0.379887\pi$
$318$	32.9143	1.84574
$319$	1.86744	0.104556
$320$	12.9868	0.725982
$321$	7.81124	0.435981
$322$	8.52455	0.475054
$323$	10.5683	0.588033
$324$	−20.1208	−1.11782
$325$	−3.83163	−0.212540
$326$	8.62292	0.477579
$327$	28.4189	1.57157
$328$	−4.75611	−0.262612
$329$	−9.23317	−0.509041
$330$	−1.31123	−0.0721808
$331$	25.4724	1.40009	0.700044	−	0.714099i	$-0.253163\pi$
$331$	25.4724	1.40009	0.700044	+	0.714099i	$0.253163\pi$
$332$	−6.88899	−0.378083
$333$	2.97311	0.162925
$334$	14.7396	0.806515
$335$	−3.78810	−0.206966
$336$	1.61770	0.0882527
$337$	−6.09729	−0.332141	−0.166070	−	0.986114i	$-0.553108\pi$
$337$	−6.09729	−0.332141	−0.166070	+	0.986114i	$0.553108\pi$
$338$	−3.75495	−0.204242
$339$	21.9017	1.18954
$340$	6.72961	0.364964
$341$	0.157246	0.00851537
$342$	−6.54734	−0.354040
$343$	−1.00000	−0.0539949
$344$	18.4696	0.995815
$345$	−5.88262	−0.316710
$346$	45.5036	2.44629
$347$	−5.46481	−0.293366	−0.146683	−	0.989184i	$-0.546860\pi$
$347$	−5.46481	−0.293366	−0.146683	+	0.989184i	$0.546860\pi$
$348$	−22.5689	−1.20982
$349$	5.83658	0.312425	0.156213	−	0.987723i	$-0.450072\pi$
$349$	5.83658	0.312425	0.156213	+	0.987723i	$0.450072\pi$
$350$	2.23328	0.119374
$351$	21.4052	1.14253
$352$	−2.57352	−0.137169
$353$	36.0809	1.92039	0.960197	−	0.279323i	$-0.0901099\pi$
$353$	36.0809	1.92039	0.960197	+	0.279323i	$0.0901099\pi$
$354$	3.13286	0.166510
$355$	8.71837	0.462723
$356$	−37.0881	−1.96567
$357$	3.47151	0.183732
$358$	23.2274	1.22761
$359$	−30.6301	−1.61660	−0.808299	−	0.588773i	$-0.799611\pi$
$359$	−30.6301	−1.61660	−0.808299	+	0.588773i	$0.799611\pi$
$360$	−1.37814	−0.0726344
$361$	3.01176	0.158514
$362$	−11.6978	−0.614824
$363$	−16.7289	−0.878039
$364$	11.4471	0.599994
$365$	3.06051	0.160194
$366$	−32.2499	−1.68573
$367$	−8.12487	−0.424115	−0.212057	−	0.977257i	$-0.568016\pi$
$367$	−8.12487	−0.424115	−0.212057	+	0.977257i	$0.568016\pi$
$368$	−4.00666	−0.208862
$369$	−1.34756	−0.0701511
$370$	−10.6258	−0.552407
$371$	9.56310	0.496491
$372$	−1.90040	−0.0985312
$373$	−4.82394	−0.249774	−0.124887	−	0.992171i	$-0.539857\pi$
$373$	−4.82394	−0.249774	−0.124887	+	0.992171i	$0.539857\pi$
$374$	−1.91651	−0.0991005
$375$	−1.54114	−0.0795843
$376$	−20.3634	−1.05016
$377$	18.7818	0.967310
$378$	−12.4761	−0.641703
$379$	12.6207	0.648282	0.324141	−	0.946009i	$-0.394925\pi$
$379$	12.6207	0.648282	0.324141	+	0.946009i	$0.394925\pi$
$380$	14.0166	0.719034
$381$	3.12326	0.160010
$382$	−17.4294	−0.891768
$383$	33.0414	1.68834	0.844168	−	0.536079i	$-0.180095\pi$
$383$	33.0414	1.68834	0.844168	+	0.536079i	$0.180095\pi$
$384$	23.8767	1.21845
$385$	−0.380972	−0.0194161
$386$	−37.9721	−1.93273
$387$	5.23303	0.266010
$388$	−39.5054	−2.00558
$389$	−2.33412	−0.118345	−0.0591724	−	0.998248i	$-0.518846\pi$
$389$	−2.33412	−0.118345	−0.0591724	+	0.998248i	$0.518846\pi$
$390$	−13.1877	−0.667786
$391$	−8.59813	−0.434826
$392$	−2.20546	−0.111393
$393$	1.10385	0.0556819
$394$	21.5104	1.08368
$395$	−6.21476	−0.312699
$396$	0.711215	0.0357399
$397$	30.7694	1.54427	0.772135	−	0.635459i	$-0.219189\pi$
$397$	30.7694	1.54427	0.772135	+	0.635459i	$0.219189\pi$
$398$	19.8918	0.997085
$399$	7.23054	0.361980
$400$	−1.04967	−0.0524837
$401$	−14.2027	−0.709249	−0.354625	−	0.935009i	$-0.615391\pi$
$401$	−14.2027	−0.709249	−0.354625	+	0.935009i	$0.615391\pi$
$402$	−13.0379	−0.650272
$403$	1.58151	0.0787805
$404$	−9.52252	−0.473763
$405$	6.73490	0.334660
$406$	−10.9470	−0.543292
$407$	1.81263	0.0898487
$408$	7.65628	0.379042
$409$	−38.7098	−1.91407	−0.957037	−	0.289965i	$-0.906356\pi$
$409$	−38.7098	−1.91407	−0.957037	+	0.289965i	$0.906356\pi$
$410$	4.81611	0.237851
$411$	30.8292	1.52069
$412$	23.3285	1.14931
$413$	0.910238	0.0447899
$414$	5.32679	0.261798
$415$	2.30591	0.113192
$416$	−25.8832	−1.26903
$417$	13.2183	0.647305
$418$	−3.99175	−0.195243
$419$	−19.2477	−0.940312	−0.470156	−	0.882583i	$-0.655802\pi$
$419$	−19.2477	−0.940312	−0.470156	+	0.882583i	$0.655802\pi$
$420$	4.60423	0.224664
$421$	28.1700	1.37292	0.686460	−	0.727167i	$-0.259164\pi$
$421$	28.1700	1.37292	0.686460	+	0.727167i	$0.259164\pi$
$422$	−16.2261	−0.789873
$423$	−5.76960	−0.280527
$424$	21.0910	1.02427
$425$	−2.25256	−0.109265
$426$	30.0069	1.45384
$427$	−9.37004	−0.453448
$428$	15.1423	0.731930
$429$	2.24967	0.108615
$430$	−18.7026	−0.901919
$431$	22.7563	1.09613	0.548065	−	0.836435i	$-0.315364\pi$
$431$	22.7563	1.09613	0.548065	+	0.836435i	$0.315364\pi$
$432$	5.86396	0.282130
$433$	−10.6690	−0.512718	−0.256359	−	0.966582i	$-0.582523\pi$
$433$	−10.6690	−0.512718	−0.256359	+	0.966582i	$0.582523\pi$
$434$	−0.921789	−0.0442473
$435$	7.55434	0.362203
$436$	55.0907	2.63837
$437$	−17.9083	−0.856672
$438$	10.5337	0.503319
$439$	17.9960	0.858901	0.429450	−	0.903090i	$-0.358707\pi$
$439$	17.9960	0.858901	0.429450	+	0.903090i	$0.358707\pi$
$440$	−0.840217	−0.0400558
$441$	−0.624877	−0.0297560
$442$	−19.2753	−0.916835
$443$	6.43490	0.305731	0.152866	−	0.988247i	$-0.451150\pi$
$443$	6.43490	0.305731	0.152866	+	0.988247i	$0.451150\pi$
$444$	−21.9065	−1.03964
$445$	12.4143	0.588493
$446$	−48.9903	−2.31976
$447$	−31.1467	−1.47319
$448$	12.9868	0.613567
$449$	−21.2567	−1.00316	−0.501582	−	0.865110i	$-0.667248\pi$
$449$	−21.2567	−1.00316	−0.501582	+	0.865110i	$0.667248\pi$
$450$	1.39553	0.0657857
$451$	−0.821572	−0.0386863
$452$	42.4570	1.99701
$453$	12.8024	0.601510
$454$	55.3156	2.59609
$455$	−3.83163	−0.179629
$456$	15.9467	0.746771
$457$	6.69014	0.312952	0.156476	−	0.987682i	$-0.449987\pi$
$457$	6.69014	0.312952	0.156476	+	0.987682i	$0.449987\pi$
$458$	−2.23328	−0.104354
$459$	12.5838	0.587362
$460$	−11.4036	−0.531696
$461$	−10.0798	−0.469464	−0.234732	−	0.972060i	$-0.575421\pi$
$461$	−10.0798	−0.469464	−0.234732	+	0.972060i	$0.575421\pi$
$462$	−1.31123	−0.0610039
$463$	1.39149	0.0646678	0.0323339	−	0.999477i	$-0.489706\pi$
$463$	1.39149	0.0646678	0.0323339	+	0.999477i	$0.489706\pi$
$464$	5.14527	0.238863
$465$	0.636109	0.0294988
$466$	−55.0865	−2.55183
$467$	−9.02204	−0.417490	−0.208745	−	0.977970i	$-0.566938\pi$
$467$	−9.02204	−0.417490	−0.208745	+	0.977970i	$0.566938\pi$
$468$	7.15306	0.330650
$469$	−3.78810	−0.174918
$470$	20.6203	0.951142
$471$	20.7421	0.955746
$472$	2.00749	0.0924023
$473$	3.19044	0.146697
$474$	−21.3900	−0.982476
$475$	−4.69167	−0.215269
$476$	6.72961	0.308451
$477$	5.97576	0.273611
$478$	−39.5942	−1.81100
$479$	−27.5480	−1.25870	−0.629351	−	0.777121i	$-0.716679\pi$
$479$	−27.5480	−1.25870	−0.629351	+	0.777121i	$0.716679\pi$
$480$	−10.4106	−0.475178
$481$	18.2306	0.831242
$482$	21.3061	0.970465
$483$	−5.88262	−0.267669
$484$	−32.4294	−1.47406
$485$	13.2234	0.600442
$486$	−14.2482	−0.646309
$487$	−41.1581	−1.86505	−0.932526	−	0.361104i	$-0.882400\pi$
$487$	−41.1581	−1.86505	−0.932526	+	0.361104i	$0.882400\pi$
$488$	−20.6652	−0.935472
$489$	−5.95051	−0.269091
$490$	2.23328	0.100889
$491$	20.5104	0.925621	0.462810	−	0.886457i	$-0.346841\pi$
$491$	20.5104	0.925621	0.462810	+	0.886457i	$0.346841\pi$
$492$	9.92911	0.447639
$493$	11.0415	0.497285
$494$	−40.1471	−1.80630
$495$	−0.238060	−0.0107000
$496$	0.433254	0.0194537
$497$	8.71837	0.391072
$498$	7.93648	0.355642
$499$	−35.1629	−1.57411	−0.787054	−	0.616884i	$-0.788395\pi$
$499$	−35.1629	−1.57411	−0.787054	+	0.616884i	$0.788395\pi$
$500$	−2.98754	−0.133607
$501$	−10.1715	−0.454430
$502$	−37.1051	−1.65608
$503$	−30.7471	−1.37095	−0.685473	−	0.728098i	$-0.740404\pi$
$503$	−30.7471	−1.37095	−0.685473	+	0.728098i	$0.740404\pi$
$504$	−1.37814	−0.0613873
$505$	3.18741	0.141838
$506$	3.24761	0.144374
$507$	2.59122	0.115080
$508$	6.05452	0.268626
$509$	−28.5293	−1.26454	−0.632270	−	0.774748i	$-0.717877\pi$
$509$	−28.5293	−1.26454	−0.632270	+	0.774748i	$0.717877\pi$
$510$	−7.75286	−0.343303
$511$	3.06051	0.135389
$512$	−11.7207	−0.517988
$513$	26.2098	1.15719
$514$	−39.1176	−1.72540
$515$	−7.80859	−0.344088
$516$	−38.5581	−1.69743
$517$	−3.51758	−0.154703
$518$	−10.6258	−0.466869
$519$	−31.4011	−1.37836
$520$	−8.45050	−0.370579
$521$	−15.4156	−0.675368	−0.337684	−	0.941260i	$-0.609643\pi$
$521$	−15.4156	−0.675368	−0.337684	+	0.941260i	$0.609643\pi$
$522$	−6.84055	−0.299403
$523$	0.212709	0.00930113	0.00465056	−	0.999989i	$-0.498520\pi$
$523$	0.212709	0.00930113	0.00465056	+	0.999989i	$0.498520\pi$
$524$	2.13984	0.0934793
$525$	−1.54114	−0.0672610
$526$	31.4935	1.37318
$527$	0.929745	0.0405003
$528$	0.616297	0.0268209
$529$	−8.43012	−0.366527
$530$	−21.3571	−0.927693
$531$	0.568787	0.0246832
$532$	14.0166	0.607695
$533$	−8.26297	−0.357909
$534$	42.7275	1.84900
$535$	−5.06847	−0.219129
$536$	−8.35451	−0.360860
$537$	−16.0288	−0.691693
$538$	54.1059	2.33267
$539$	−0.380972	−0.0164096
$540$	16.6898	0.718213
$541$	11.2131	0.482089	0.241044	−	0.970514i	$-0.422510\pi$
$541$	11.2131	0.482089	0.241044	+	0.970514i	$0.422510\pi$
$542$	−53.0952	−2.28064
$543$	8.07243	0.346421
$544$	−15.2163	−0.652395
$545$	−18.4401	−0.789889
$546$	−13.1877	−0.564382
$547$	−3.37544	−0.144323	−0.0721617	−	0.997393i	$-0.522990\pi$
$547$	−3.37544	−0.144323	−0.0721617	+	0.997393i	$0.522990\pi$
$548$	59.7632	2.55296
$549$	−5.85512	−0.249891
$550$	0.850816	0.0362789
$551$	22.9975	0.979727
$552$	−12.9739	−0.552205
$553$	−6.21476	−0.264279
$554$	38.8992	1.65267
$555$	7.33263	0.311253
$556$	25.6241	1.08670
$557$	−25.7181	−1.08971	−0.544854	−	0.838531i	$-0.683415\pi$
$557$	−25.7181	−1.08971	−0.544854	+	0.838531i	$0.683415\pi$
$558$	−0.576005	−0.0243842
$559$	32.0879	1.35717
$560$	−1.04967	−0.0443568
$561$	1.32255	0.0558380
$562$	44.5510	1.87927
$563$	−18.1389	−0.764463	−0.382231	−	0.924067i	$-0.624844\pi$
$563$	−18.1389	−0.764463	−0.382231	+	0.924067i	$0.624844\pi$
$564$	42.5117	1.79006
$565$	−14.2113	−0.597876
$566$	−48.8117	−2.05171
$567$	6.73490	0.282839
$568$	19.2280	0.806790
$569$	−10.3828	−0.435268	−0.217634	−	0.976030i	$-0.569834\pi$
$569$	−10.3828	−0.435268	−0.217634	+	0.976030i	$0.569834\pi$
$570$	−16.1478	−0.676358
$571$	−3.08998	−0.129312	−0.0646558	−	0.997908i	$-0.520595\pi$
$571$	−3.08998	−0.129312	−0.0646558	+	0.997908i	$0.520595\pi$
$572$	4.36104	0.182344
$573$	12.0277	0.502465
$574$	4.81611	0.201020
$575$	3.81705	0.159182
$576$	8.11513	0.338130
$577$	−18.0913	−0.753150	−0.376575	−	0.926386i	$-0.622898\pi$
$577$	−18.0913	−0.753150	−0.376575	+	0.926386i	$0.622898\pi$
$578$	26.6341	1.10783
$579$	26.2038	1.08899
$580$	14.6443	0.608070
$581$	2.30591	0.0956651
$582$	45.5123	1.88654
$583$	3.64327	0.150889
$584$	6.74983	0.279310
$585$	−2.39429	−0.0989919
$586$	−44.7003	−1.84655
$587$	30.1312	1.24365	0.621823	−	0.783158i	$-0.286392\pi$
$587$	30.1312	1.24365	0.621823	+	0.783158i	$0.286392\pi$
$588$	4.60423	0.189875
$589$	1.93649	0.0797918
$590$	−2.03282	−0.0836897
$591$	−14.8439	−0.610596
$592$	4.99426	0.205263
$593$	32.8192	1.34772	0.673861	−	0.738858i	$-0.264635\pi$
$593$	32.8192	1.34772	0.673861	+	0.738858i	$0.264635\pi$
$594$	−4.75305	−0.195020
$595$	−2.25256	−0.0923458
$596$	−60.3787	−2.47321
$597$	−13.7269	−0.561806
$598$	32.6629	1.33568
$599$	24.8317	1.01460	0.507299	−	0.861770i	$-0.330644\pi$
$599$	24.8317	1.01460	0.507299	+	0.861770i	$0.330644\pi$
$600$	−3.39893	−0.138761
$601$	13.0088	0.530642	0.265321	−	0.964160i	$-0.414522\pi$
$601$	13.0088	0.530642	0.265321	+	0.964160i	$0.414522\pi$
$602$	−18.7026	−0.762261
$603$	−2.36710	−0.0963957
$604$	24.8178	1.00982
$605$	10.8549	0.441313
$606$	10.9704	0.445644
$607$	−14.7777	−0.599807	−0.299904	−	0.953970i	$-0.596954\pi$
$607$	−14.7777	−0.599807	−0.299904	+	0.953970i	$0.596954\pi$
$608$	−31.6929	−1.28532
$609$	7.55434	0.306117
$610$	20.9259	0.847266
$611$	−35.3781	−1.43124
$612$	4.20518	0.169984
$613$	−3.16953	−0.128016	−0.0640080	−	0.997949i	$-0.520388\pi$
$613$	−3.16953	−0.128016	−0.0640080	+	0.997949i	$0.520388\pi$
$614$	−21.2434	−0.857315
$615$	−3.32350	−0.134017
$616$	−0.840217	−0.0338533
$617$	−17.5745	−0.707521	−0.353761	−	0.935336i	$-0.615097\pi$
$617$	−17.5745	−0.707521	−0.353761	+	0.935336i	$0.615097\pi$
$618$	−26.8757	−1.08110
$619$	−23.9026	−0.960727	−0.480364	−	0.877069i	$-0.659495\pi$
$619$	−23.9026	−0.960727	−0.480364	+	0.877069i	$0.659495\pi$
$620$	1.23311	0.0495229
$621$	−21.3238	−0.855694
$622$	6.78983	0.272247
$623$	12.4143	0.497367
$624$	6.19842	0.248135
$625$	1.00000	0.0400000
$626$	−58.3138	−2.33069
$627$	2.75463	0.110009
$628$	40.2091	1.60452
$629$	10.7175	0.427334
$630$	1.39553	0.0555991
$631$	21.1444	0.841744	0.420872	−	0.907120i	$-0.361724\pi$
$631$	21.1444	0.841744	0.420872	+	0.907120i	$0.361724\pi$
$632$	−13.7064	−0.545212
$633$	11.1973	0.445052
$634$	−29.3013	−1.16370
$635$	−2.02659	−0.0804227
$636$	−44.0307	−1.74593
$637$	−3.83163	−0.151815
$638$	−4.17051	−0.165112
$639$	5.44791	0.215516
$640$	−15.4928	−0.612408
$641$	−16.0787	−0.635069	−0.317534	−	0.948247i	$-0.602855\pi$
$641$	−16.0787	−0.635069	−0.317534	+	0.948247i	$0.602855\pi$
$642$	−17.4447	−0.688487
$643$	2.34504	0.0924795	0.0462398	−	0.998930i	$-0.485276\pi$
$643$	2.34504	0.0924795	0.0462398	+	0.998930i	$0.485276\pi$
$644$	−11.4036	−0.449365
$645$	12.9063	0.508185
$646$	−23.6019	−0.928603
$647$	50.3655	1.98007	0.990037	−	0.140808i	$-0.0449700\pi$
$647$	50.3655	1.98007	0.990037	+	0.140808i	$0.0449700\pi$
$648$	14.8535	0.583502
$649$	0.346775	0.0136121
$650$	8.55710	0.335637
$651$	0.636109	0.0249311
$652$	−11.5352	−0.451753
$653$	−40.2477	−1.57501	−0.787506	−	0.616307i	$-0.788628\pi$
$653$	−40.2477	−1.57501	−0.787506	+	0.616307i	$0.788628\pi$
$654$	−63.4674	−2.48177
$655$	−0.716254	−0.0279864
$656$	−2.26364	−0.0883803
$657$	1.91244	0.0746115
$658$	20.6203	0.803862
$659$	28.7884	1.12144	0.560719	−	0.828006i	$-0.310525\pi$
$659$	28.7884	1.12144	0.560719	+	0.828006i	$0.310525\pi$
$660$	1.75408	0.0682775
$661$	14.3056	0.556425	0.278213	−	0.960520i	$-0.410258\pi$
$661$	14.3056	0.556425	0.278213	+	0.960520i	$0.410258\pi$
$662$	−56.8870	−2.21098
$663$	13.3015	0.516589
$664$	5.08558	0.197359
$665$	−4.69167	−0.181935
$666$	−6.63979	−0.257287
$667$	−18.7103	−0.724467
$668$	−19.7177	−0.762901
$669$	33.8073	1.30706
$670$	8.45990	0.326834
$671$	−3.56972	−0.137807
$672$	−10.4106	−0.401599
$673$	22.3913	0.863122	0.431561	−	0.902084i	$-0.357963\pi$
$673$	22.3913	0.863122	0.431561	+	0.902084i	$0.357963\pi$
$674$	13.6170	0.524506
$675$	−5.58646	−0.215023
$676$	5.02313	0.193197
$677$	−40.7403	−1.56578	−0.782889	−	0.622161i	$-0.786255\pi$
$677$	−40.7403	−1.56578	−0.782889	+	0.622161i	$0.786255\pi$
$678$	−48.9127	−1.87848
$679$	13.2234	0.507467
$680$	−4.96792	−0.190511
$681$	−38.1722	−1.46276
$682$	−0.351175	−0.0134472
$683$	28.6458	1.09610	0.548050	−	0.836446i	$-0.315370\pi$
$683$	28.6458	1.09610	0.548050	+	0.836446i	$0.315370\pi$
$684$	8.75863	0.334894
$685$	−20.0041	−0.764319
$686$	2.23328	0.0852671
$687$	1.54114	0.0587983
$688$	8.79049	0.335134
$689$	36.6422	1.39596
$690$	13.1376	0.500138
$691$	11.8958	0.452537	0.226268	−	0.974065i	$-0.427347\pi$
$691$	11.8958	0.452537	0.226268	+	0.974065i	$0.427347\pi$
$692$	−60.8718	−2.31400
$693$	−0.238060	−0.00904316
$694$	12.2045	0.463275
$695$	−8.57697	−0.325343
$696$	16.6608	0.631526
$697$	−4.85768	−0.183998
$698$	−13.0347	−0.493372
$699$	38.0141	1.43783
$700$	−2.98754	−0.112918
$701$	−43.0097	−1.62445	−0.812227	−	0.583341i	$-0.801745\pi$
$701$	−43.0097	−1.62445	−0.812227	+	0.583341i	$0.801745\pi$
$702$	−47.8038	−1.80424
$703$	22.3226	0.841911
$704$	4.94759	0.186469
$705$	−14.2296	−0.535919
$706$	−80.5789	−3.03263
$707$	3.18741	0.119875
$708$	−4.19095	−0.157505
$709$	27.5433	1.03441	0.517205	−	0.855862i	$-0.326972\pi$
$709$	27.5433	1.03441	0.517205	+	0.855862i	$0.326972\pi$
$710$	−19.4706	−0.730717
$711$	−3.88346	−0.145641
$712$	27.3792	1.02608
$713$	−1.57549	−0.0590027
$714$	−7.75286	−0.290144
$715$	−1.45974	−0.0545912
$716$	−31.0722	−1.16122
$717$	27.3232	1.02040
$718$	68.4057	2.55288
$719$	43.9234	1.63807	0.819034	−	0.573745i	$-0.194510\pi$
$719$	43.9234	1.63807	0.819034	+	0.573745i	$0.194510\pi$
$720$	−0.655917	−0.0244446
$721$	−7.80859	−0.290807
$722$	−6.72611	−0.250320
$723$	−14.7029	−0.546807
$724$	15.6486	0.581576
$725$	−4.90178	−0.182047
$726$	37.3603	1.38657
$727$	39.2889	1.45714	0.728571	−	0.684970i	$-0.240185\pi$
$727$	39.2889	1.45714	0.728571	+	0.684970i	$0.240185\pi$
$728$	−8.45050	−0.313196
$729$	30.0371	1.11248
$730$	−6.83498	−0.252974
$731$	18.8640	0.697711
$732$	43.1418	1.59457
$733$	−9.47636	−0.350017	−0.175009	−	0.984567i	$-0.555995\pi$
$733$	−9.47636	−0.350017	−0.175009	+	0.984567i	$0.555995\pi$
$734$	18.1451	0.669748
$735$	−1.54114	−0.0568459
$736$	25.7847	0.950437
$737$	−1.44316	−0.0531595
$738$	3.00948	0.110780
$739$	−14.9002	−0.548114	−0.274057	−	0.961713i	$-0.588366\pi$
$739$	−14.9002	−0.548114	−0.274057	+	0.961713i	$0.588366\pi$
$740$	14.2145	0.522534
$741$	27.7047	1.01776
$742$	−21.3571	−0.784043
$743$	−36.8848	−1.35317	−0.676587	−	0.736363i	$-0.736542\pi$
$743$	−36.8848	−1.35317	−0.676587	+	0.736363i	$0.736542\pi$
$744$	1.40291	0.0514333
$745$	20.2101	0.740442
$746$	10.7732	0.394435
$747$	1.44091	0.0527200
$748$	2.56379	0.0937414
$749$	−5.06847	−0.185198
$750$	3.44181	0.125677
$751$	−0.259560	−0.00947148	−0.00473574	−	0.999989i	$-0.501507\pi$
$751$	−0.259560	−0.00947148	−0.00473574	+	0.999989i	$0.501507\pi$
$752$	−9.69183	−0.353425
$753$	25.6055	0.933117
$754$	−41.9450	−1.52755
$755$	−8.30709	−0.302326
$756$	16.6898	0.607001
$757$	26.7576	0.972521	0.486260	−	0.873814i	$-0.338361\pi$
$757$	26.7576	0.972521	0.486260	+	0.873814i	$0.338361\pi$
$758$	−28.1856	−1.02375
$759$	−2.24111	−0.0813472
$760$	−10.3473	−0.375336
$761$	17.7603	0.643810	0.321905	−	0.946772i	$-0.395677\pi$
$761$	17.7603	0.643810	0.321905	+	0.946772i	$0.395677\pi$
$762$	−6.97512	−0.252682
$763$	−18.4401	−0.667578
$764$	23.3160	0.843544
$765$	−1.40757	−0.0508908
$766$	−73.7907	−2.66617
$767$	3.48769	0.125933
$768$	−13.2943	−0.479719
$769$	47.4772	1.71207	0.856036	−	0.516917i	$-0.172920\pi$
$769$	47.4772	1.71207	0.856036	+	0.516917i	$0.172920\pi$
$770$	0.850816	0.0306613
$771$	26.9943	0.972175
$772$	50.7967	1.82821
$773$	32.7896	1.17936	0.589679	−	0.807638i	$-0.299254\pi$
$773$	32.7896	1.17936	0.589679	+	0.807638i	$0.299254\pi$
$774$	−11.6868	−0.420074
$775$	−0.412751	−0.0148265
$776$	29.1636	1.04691
$777$	7.33263	0.263057
$778$	5.21275	0.186886
$779$	−10.1177	−0.362503
$780$	17.6417	0.631674
$781$	3.32145	0.118851
$782$	19.2020	0.686663
$783$	27.3835	0.978608
$784$	−1.04967	−0.0374884
$785$	−13.4589	−0.480369
$786$	−2.46521	−0.0879310
$787$	5.67269	0.202210	0.101105	−	0.994876i	$-0.467762\pi$
$787$	5.67269	0.202210	0.101105	+	0.994876i	$0.467762\pi$
$788$	−28.7752	−1.02508
$789$	−21.7331	−0.773717
$790$	13.8793	0.493804
$791$	−14.2113	−0.505297
$792$	−0.525032	−0.0186562
$793$	−35.9025	−1.27493
$794$	−68.7166	−2.43866
$795$	14.7381	0.522707
$796$	−26.6100	−0.943165
$797$	31.4624	1.11445	0.557227	−	0.830360i	$-0.311865\pi$
$797$	31.4624	1.11445	0.557227	+	0.830360i	$0.311865\pi$
$798$	−16.1478	−0.571626
$799$	−20.7982	−0.735789
$800$	6.75514	0.238830
$801$	7.75739	0.274094
$802$	31.7186	1.12002
$803$	1.16597	0.0411461
$804$	17.4413	0.615107
$805$	3.81705	0.134533
$806$	−3.53195	−0.124408
$807$	−37.3374	−1.31434
$808$	7.02970	0.247304
$809$	0.372042	0.0130803	0.00654015	−	0.999979i	$-0.497918\pi$
$809$	0.372042	0.0130803	0.00654015	+	0.999979i	$0.497918\pi$
$810$	−15.0409	−0.528484
$811$	13.6360	0.478826	0.239413	−	0.970918i	$-0.423045\pi$
$811$	13.6360	0.478826	0.239413	+	0.970918i	$0.423045\pi$
$812$	14.6443	0.513913
$813$	36.6400	1.28502
$814$	−4.04811	−0.141886
$815$	3.86110	0.135248
$816$	3.64396	0.127564
$817$	39.2904	1.37460
$818$	86.4498	3.02265
$819$	−2.39429	−0.0836634
$820$	−6.44269	−0.224988
$821$	0.536072	0.0187090	0.00935452	−	0.999956i	$-0.497022\pi$
$821$	0.536072	0.0187090	0.00935452	+	0.999956i	$0.497022\pi$
$822$	−68.8504	−2.40143
$823$	−21.3508	−0.744243	−0.372121	−	0.928184i	$-0.621369\pi$
$823$	−21.3508	−0.744243	−0.372121	+	0.928184i	$0.621369\pi$
$824$	−17.2215	−0.599941
$825$	−0.587132	−0.0204413
$826$	−2.03282	−0.0707307
$827$	1.13907	0.0396094	0.0198047	−	0.999804i	$-0.493696\pi$
$827$	1.13907	0.0396094	0.0198047	+	0.999804i	$0.493696\pi$
$828$	−7.12585	−0.247640
$829$	0.933015	0.0324050	0.0162025	−	0.999869i	$-0.494842\pi$
$829$	0.933015	0.0324050	0.0162025	+	0.999869i	$0.494842\pi$
$830$	−5.14973	−0.178750
$831$	−26.8436	−0.931194
$832$	49.7604	1.72513
$833$	−2.25256	−0.0780465
$834$	−29.5203	−1.02220
$835$	6.59998	0.228402
$836$	5.33991	0.184685
$837$	2.30582	0.0797006
$838$	42.9855	1.48491
$839$	23.9276	0.826071	0.413036	−	0.910715i	$-0.364469\pi$
$839$	23.9276	0.826071	0.413036	+	0.910715i	$0.364469\pi$
$840$	−3.39893	−0.117274
$841$	−4.97260	−0.171469
$842$	−62.9114	−2.16807
$843$	−30.7438	−1.05887
$844$	21.7062	0.747159
$845$	−1.68136	−0.0578405
$846$	12.8851	0.443000
$847$	10.8549	0.372977
$848$	10.0381	0.344711
$849$	33.6840	1.15603
$850$	5.03059	0.172548
$851$	−18.1612	−0.622558
$852$	−40.1414	−1.37522
$853$	−38.6365	−1.32289	−0.661444	−	0.749994i	$-0.730056\pi$
$853$	−38.6365	−1.32289	−0.661444	+	0.749994i	$0.730056\pi$
$854$	20.9259	0.716071
$855$	−2.93172	−0.100263
$856$	−11.1783	−0.382067
$857$	33.6508	1.14949	0.574745	−	0.818332i	$-0.305101\pi$
$857$	33.6508	1.14949	0.574745	+	0.818332i	$0.305101\pi$
$858$	−5.02414	−0.171521
$859$	20.3792	0.695330	0.347665	−	0.937619i	$-0.386975\pi$
$859$	20.3792	0.695330	0.347665	+	0.937619i	$0.386975\pi$
$860$	25.0192	0.853146
$861$	−3.32350	−0.113265
$862$	−50.8211	−1.73097
$863$	34.0931	1.16054	0.580271	−	0.814424i	$-0.302947\pi$
$863$	34.0931	1.16054	0.580271	+	0.814424i	$0.302947\pi$
$864$	−37.7373	−1.28385
$865$	20.3752	0.692778
$866$	23.8268	0.809668
$867$	−18.3797	−0.624206
$868$	1.23311	0.0418545
$869$	−2.36765	−0.0803170
$870$	−16.8710	−0.571979
$871$	−14.5146	−0.491808
$872$	−40.6690	−1.37723
$873$	8.26298	0.279660
$874$	39.9944	1.35283
$875$	1.00000	0.0338062
$876$	−14.0913	−0.476101
$877$	28.2374	0.953510	0.476755	−	0.879036i	$-0.341813\pi$
$877$	28.2374	0.953510	0.476755	+	0.879036i	$0.341813\pi$
$878$	−40.1900	−1.35635
$879$	30.8468	1.04044
$880$	−0.399896	−0.0134805
$881$	−45.0761	−1.51865	−0.759326	−	0.650710i	$-0.774471\pi$
$881$	−45.0761	−1.51865	−0.759326	+	0.650710i	$0.774471\pi$
$882$	1.39553	0.0469898
$883$	34.0592	1.14618	0.573092	−	0.819491i	$-0.305744\pi$
$883$	34.0592	1.14618	0.573092	+	0.819491i	$0.305744\pi$
$884$	25.7853	0.867255
$885$	1.40281	0.0471548
$886$	−14.3709	−0.482801
$887$	−16.7922	−0.563828	−0.281914	−	0.959440i	$-0.590969\pi$
$887$	−16.7922	−0.563828	−0.281914	+	0.959440i	$0.590969\pi$
$888$	16.1718	0.542691
$889$	−2.02659	−0.0679696
$890$	−27.7245	−0.929329
$891$	2.56580	0.0859577
$892$	65.5362	2.19431
$893$	−43.3190	−1.44962
$894$	69.5594	2.32641
$895$	10.4006	0.347653
$896$	−15.4928	−0.517579
$897$	−22.5400	−0.752589
$898$	47.4721	1.58416
$899$	2.02321	0.0674779
$900$	−1.86685	−0.0622282
$901$	21.5414	0.717649
$902$	1.83480	0.0610922
$903$	12.9063	0.429495
$904$	−31.3426	−1.04244
$905$	−5.23795	−0.174115
$906$	−28.5914	−0.949886
$907$	31.8896	1.05888	0.529439	−	0.848348i	$-0.322402\pi$
$907$	31.8896	1.05888	0.529439	+	0.848348i	$0.322402\pi$
$908$	−73.9977	−2.45570
$909$	1.99174	0.0660618
$910$	8.55710	0.283665
$911$	46.7294	1.54822	0.774108	−	0.633054i	$-0.218199\pi$
$911$	46.7294	1.54822	0.774108	+	0.633054i	$0.218199\pi$
$912$	7.58971	0.251320
$913$	0.878484	0.0290736
$914$	−14.9410	−0.494203
$915$	−14.4406	−0.477391
$916$	2.98754	0.0987112
$917$	−0.716254	−0.0236528
$918$	−28.1032	−0.927543
$919$	−9.96466	−0.328704	−0.164352	−	0.986402i	$-0.552553\pi$
$919$	−9.96466	−0.328704	−0.164352	+	0.986402i	$0.552553\pi$
$920$	8.41835	0.277545
$921$	14.6597	0.483053
$922$	22.5111	0.741363
$923$	33.4055	1.09956
$924$	1.75408	0.0577050
$925$	−4.75791	−0.156439
$926$	−3.10758	−0.102121
$927$	−4.87941	−0.160261
$928$	−33.1122	−1.08696
$929$	−24.8109	−0.814019	−0.407010	−	0.913424i	$-0.633428\pi$
$929$	−24.8109	−0.814019	−0.407010	+	0.913424i	$0.633428\pi$
$930$	−1.42061	−0.0465836
$931$	−4.69167	−0.153763
$932$	73.6912	2.41384
$933$	−4.68553	−0.153397
$934$	20.1487	0.659287
$935$	−0.858160	−0.0280648
$936$	−5.28052	−0.172599
$937$	12.7167	0.415438	0.207719	−	0.978189i	$-0.433396\pi$
$937$	12.7167	0.415438	0.207719	+	0.978189i	$0.433396\pi$
$938$	8.45990	0.276225
$939$	40.2412	1.31322
$940$	−27.5845	−0.899707
$941$	−31.2644	−1.01919	−0.509595	−	0.860415i	$-0.670205\pi$
$941$	−31.2644	−1.01919	−0.509595	+	0.860415i	$0.670205\pi$
$942$	−46.3230	−1.50928
$943$	8.23154	0.268056
$944$	0.955453	0.0310974
$945$	−5.58646	−0.181727
$946$	−7.12516	−0.231659
$947$	8.72480	0.283518	0.141759	−	0.989901i	$-0.454724\pi$
$947$	8.72480	0.283518	0.141759	+	0.989901i	$0.454724\pi$
$948$	28.6142	0.929347
$949$	11.7267	0.380666
$950$	10.4778	0.339945
$951$	20.2203	0.655687
$952$	−4.96792	−0.161011
$953$	44.2799	1.43437	0.717184	−	0.696884i	$-0.245431\pi$
$953$	44.2799	1.43437	0.717184	+	0.696884i	$0.245431\pi$
$954$	−13.3456	−0.432078
$955$	−7.80441	−0.252545
$956$	52.9666	1.71306
$957$	2.87799	0.0930321
$958$	61.5225	1.98770
$959$	−20.0041	−0.645967
$960$	20.0145	0.645964
$961$	−30.8296	−0.994504
$962$	−40.7139	−1.31267
$963$	−3.16717	−0.102061
$964$	−28.5019	−0.917985
$965$	−17.0029	−0.547341
$966$	13.1376	0.422694
$967$	21.6899	0.697499	0.348749	−	0.937216i	$-0.386606\pi$
$967$	21.6899	0.697499	0.348749	+	0.937216i	$0.386606\pi$
$968$	23.9400	0.769459
$969$	16.2872	0.523220
$970$	−29.5315	−0.948199
$971$	0.927211	0.0297556	0.0148778	−	0.999889i	$-0.495264\pi$
$971$	0.927211	0.0297556	0.0148778	+	0.999889i	$0.495264\pi$
$972$	19.0603	0.611359
$973$	−8.57697	−0.274965
$974$	91.9176	2.94523
$975$	−5.90509	−0.189114
$976$	−9.83549	−0.314826
$977$	30.3914	0.972306	0.486153	−	0.873874i	$-0.338400\pi$
$977$	30.3914	0.972306	0.486153	+	0.873874i	$0.338400\pi$
$978$	13.2892	0.424940
$979$	4.72948	0.151155
$980$	−2.98754	−0.0954335
$981$	−11.5228	−0.367895
$982$	−45.8055	−1.46171
$983$	47.8510	1.52621	0.763104	−	0.646275i	$-0.223674\pi$
$983$	47.8510	1.52621	0.763104	+	0.646275i	$0.223674\pi$
$984$	−7.32985	−0.233667
$985$	9.63174	0.306893
$986$	−24.6588	−0.785297
$987$	−14.2296	−0.452935
$988$	53.7062	1.70862
$989$	−31.9659	−1.01646
$990$	0.531656	0.0168971
$991$	−44.0474	−1.39921	−0.699605	−	0.714529i	$-0.746641\pi$
$991$	−44.0474	−1.39921	−0.699605	+	0.714529i	$0.746641\pi$
$992$	−2.78819	−0.0885251
$993$	39.2566	1.24577
$994$	−19.4706	−0.617569
$995$	8.90697	0.282370
$996$	−10.6169	−0.336410
$997$	−29.6342	−0.938523	−0.469261	−	0.883059i	$-0.655480\pi$
$997$	−29.6342	−0.938523	−0.469261	+	0.883059i	$0.655480\pi$
$998$	78.5287	2.48578
$999$	26.5799	0.840950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.8	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.8	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23328 q^{2} +1.54114 q^{3} +2.98754 q^{4} -1.00000 q^{5} -3.44181 q^{6} -1.00000 q^{7} -2.20546 q^{8} -0.624877 q^{9} +O(q^{10})\)	\(q-2.23328 q^{2} +1.54114 q^{3} +2.98754 q^{4} -1.00000 q^{5} -3.44181 q^{6} -1.00000 q^{7} -2.20546 q^{8} -0.624877 q^{9} +2.23328 q^{10} -0.380972 q^{11} +4.60423 q^{12} -3.83163 q^{13} +2.23328 q^{14} -1.54114 q^{15} -1.04967 q^{16} -2.25256 q^{17} +1.39553 q^{18} -4.69167 q^{19} -2.98754 q^{20} -1.54114 q^{21} +0.850816 q^{22} +3.81705 q^{23} -3.39893 q^{24} +1.00000 q^{25} +8.55710 q^{26} -5.58646 q^{27} -2.98754 q^{28} -4.90178 q^{29} +3.44181 q^{30} -0.412751 q^{31} +6.75514 q^{32} -0.587132 q^{33} +5.03059 q^{34} +1.00000 q^{35} -1.86685 q^{36} -4.75791 q^{37} +10.4778 q^{38} -5.90509 q^{39} +2.20546 q^{40} +2.15652 q^{41} +3.44181 q^{42} -8.37449 q^{43} -1.13817 q^{44} +0.624877 q^{45} -8.52455 q^{46} +9.23317 q^{47} -1.61770 q^{48} +1.00000 q^{49} -2.23328 q^{50} -3.47151 q^{51} -11.4471 q^{52} -9.56310 q^{53} +12.4761 q^{54} +0.380972 q^{55} +2.20546 q^{56} -7.23054 q^{57} +10.9470 q^{58} -0.910238 q^{59} -4.60423 q^{60} +9.37004 q^{61} +0.921789 q^{62} +0.624877 q^{63} -12.9868 q^{64} +3.83163 q^{65} +1.31123 q^{66} +3.78810 q^{67} -6.72961 q^{68} +5.88262 q^{69} -2.23328 q^{70} -8.71837 q^{71} +1.37814 q^{72} -3.06051 q^{73} +10.6258 q^{74} +1.54114 q^{75} -14.0166 q^{76} +0.380972 q^{77} +13.1877 q^{78} +6.21476 q^{79} +1.04967 q^{80} -6.73490 q^{81} -4.81611 q^{82} -2.30591 q^{83} -4.60423 q^{84} +2.25256 q^{85} +18.7026 q^{86} -7.55434 q^{87} +0.840217 q^{88} -12.4143 q^{89} -1.39553 q^{90} +3.83163 q^{91} +11.4036 q^{92} -0.636109 q^{93} -20.6203 q^{94} +4.69167 q^{95} +10.4106 q^{96} -13.2234 q^{97} -2.23328 q^{98} +0.238060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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