LMFDB - Embedded newform 4015.2.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50747 q^{2} -0.655267 q^{3} +0.272451 q^{4} -1.00000 q^{5} +0.987792 q^{6} -1.30717 q^{7} +2.60422 q^{8} -2.57063 q^{9} +O(q^{10})$	\(q-1.50747 q^{2} -0.655267 q^{3} +0.272451 q^{4} -1.00000 q^{5} +0.987792 q^{6} -1.30717 q^{7} +2.60422 q^{8} -2.57063 q^{9} +1.50747 q^{10} -1.00000 q^{11} -0.178528 q^{12} +2.03555 q^{13} +1.97051 q^{14} +0.655267 q^{15} -4.47067 q^{16} +0.00767831 q^{17} +3.87513 q^{18} +2.45380 q^{19} -0.272451 q^{20} +0.856545 q^{21} +1.50747 q^{22} -2.20213 q^{23} -1.70646 q^{24} +1.00000 q^{25} -3.06851 q^{26} +3.65025 q^{27} -0.356140 q^{28} -5.12345 q^{29} -0.987792 q^{30} -3.16581 q^{31} +1.53094 q^{32} +0.655267 q^{33} -0.0115748 q^{34} +1.30717 q^{35} -0.700370 q^{36} +7.40517 q^{37} -3.69901 q^{38} -1.33383 q^{39} -2.60422 q^{40} +5.71836 q^{41} -1.29121 q^{42} -2.78948 q^{43} -0.272451 q^{44} +2.57063 q^{45} +3.31964 q^{46} +7.47011 q^{47} +2.92948 q^{48} -5.29131 q^{49} -1.50747 q^{50} -0.00503134 q^{51} +0.554587 q^{52} -5.37173 q^{53} -5.50262 q^{54} +1.00000 q^{55} -3.40416 q^{56} -1.60789 q^{57} +7.72343 q^{58} +9.19598 q^{59} +0.178528 q^{60} +3.65638 q^{61} +4.77234 q^{62} +3.36024 q^{63} +6.63350 q^{64} -2.03555 q^{65} -0.987792 q^{66} +8.26082 q^{67} +0.00209196 q^{68} +1.44298 q^{69} -1.97051 q^{70} -1.32081 q^{71} -6.69447 q^{72} -1.00000 q^{73} -11.1630 q^{74} -0.655267 q^{75} +0.668540 q^{76} +1.30717 q^{77} +2.01070 q^{78} +9.22995 q^{79} +4.47067 q^{80} +5.31999 q^{81} -8.62024 q^{82} -17.6526 q^{83} +0.233367 q^{84} -0.00767831 q^{85} +4.20504 q^{86} +3.35723 q^{87} -2.60422 q^{88} +7.40421 q^{89} -3.87513 q^{90} -2.66081 q^{91} -0.599973 q^{92} +2.07445 q^{93} -11.2609 q^{94} -2.45380 q^{95} -1.00318 q^{96} +7.13564 q^{97} +7.97646 q^{98} +2.57063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−1.50747	−1.06594	−0.532969	−	0.846135i	$-0.678924\pi$
$2$	−1.50747	−1.06594	−0.532969	+	0.846135i	$0.678924\pi$
$3$	−0.655267	−0.378319	−0.189159	−	0.981946i	$-0.560576\pi$
$3$	−0.655267	−0.378319	−0.189159	+	0.981946i	$0.560576\pi$
$4$	0.272451	0.136226
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.987792	0.403264
$7$	−1.30717	−0.494064	−0.247032	−	0.969007i	$-0.579455\pi$
$7$	−1.30717	−0.494064	−0.247032	+	0.969007i	$0.579455\pi$
$8$	2.60422	0.920731
$9$	−2.57063	−0.856875
$10$	1.50747	0.476702
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.178528	−0.0515367
$13$	2.03555	0.564559	0.282279	−	0.959332i	$-0.408909\pi$
$13$	2.03555	0.564559	0.282279	+	0.959332i	$0.408909\pi$
$14$	1.97051	0.526642
$15$	0.655267	0.169189
$16$	−4.47067	−1.11767
$17$	0.00767831	0.00186226	0.000931131	−	1.00000i	$-0.499704\pi$
$17$	0.00767831	0.00186226	0.000931131		1.00000i	$0.499704\pi$
$18$	3.87513	0.913376
$19$	2.45380	0.562940	0.281470	−	0.959570i	$-0.409178\pi$
$19$	2.45380	0.562940	0.281470	+	0.959570i	$0.409178\pi$
$20$	−0.272451	−0.0609219
$21$	0.856545	0.186914
$22$	1.50747	0.321393
$23$	−2.20213	−0.459176	−0.229588	−	0.973288i	$-0.573738\pi$
$23$	−2.20213	−0.459176	−0.229588	+	0.973288i	$0.573738\pi$
$24$	−1.70646	−0.348329
$25$	1.00000	0.200000
$26$	−3.06851	−0.601785
$27$	3.65025	0.702490
$28$	−0.356140	−0.0673041
$29$	−5.12345	−0.951402	−0.475701	−	0.879607i	$-0.657805\pi$
$29$	−5.12345	−0.951402	−0.475701	+	0.879607i	$0.657805\pi$
$30$	−0.987792	−0.180345
$31$	−3.16581	−0.568596	−0.284298	−	0.958736i	$-0.591760\pi$
$31$	−3.16581	−0.568596	−0.284298	+	0.958736i	$0.591760\pi$
$32$	1.53094	0.270635
$33$	0.655267	0.114067
$34$	−0.0115748	−0.00198506
$35$	1.30717	0.220952
$36$	−0.700370	−0.116728
$37$	7.40517	1.21740	0.608701	−	0.793400i	$-0.291691\pi$
$37$	7.40517	1.21740	0.608701	+	0.793400i	$0.291691\pi$
$38$	−3.69901	−0.600059
$39$	−1.33383	−0.213583
$40$	−2.60422	−0.411763
$41$	5.71836	0.893058	0.446529	−	0.894769i	$-0.352660\pi$
$41$	5.71836	0.893058	0.446529	+	0.894769i	$0.352660\pi$
$42$	−1.29121	−0.199238
$43$	−2.78948	−0.425391	−0.212696	−	0.977119i	$-0.568224\pi$
$43$	−2.78948	−0.425391	−0.212696	+	0.977119i	$0.568224\pi$
$44$	−0.272451	−0.0410736
$45$	2.57063	0.383206
$46$	3.31964	0.489454
$47$	7.47011	1.08963	0.544814	−	0.838557i	$-0.316600\pi$
$47$	7.47011	1.08963	0.544814	+	0.838557i	$0.316600\pi$
$48$	2.92948	0.422835
$49$	−5.29131	−0.755901
$50$	−1.50747	−0.213188
$51$	−0.00503134	−0.000704529 0
$52$	0.554587	0.0769074
$53$	−5.37173	−0.737863	−0.368932	−	0.929457i	$-0.620276\pi$
$53$	−5.37173	−0.737863	−0.368932	+	0.929457i	$0.620276\pi$
$54$	−5.50262	−0.748812
$55$	1.00000	0.134840
$56$	−3.40416	−0.454900
$57$	−1.60789	−0.212971
$58$	7.72343	1.01414
$59$	9.19598	1.19721	0.598607	−	0.801043i	$-0.295721\pi$
$59$	9.19598	1.19721	0.598607	+	0.801043i	$0.295721\pi$
$60$	0.178528	0.0230479
$61$	3.65638	0.468152	0.234076	−	0.972218i	$-0.424794\pi$
$61$	3.65638	0.468152	0.234076	+	0.972218i	$0.424794\pi$
$62$	4.77234	0.606088
$63$	3.36024	0.423351
$64$	6.63350	0.829188
$65$	−2.03555	−0.252478
$66$	−0.987792	−0.121589
$67$	8.26082	1.00922	0.504610	−	0.863348i	$-0.331636\pi$
$67$	8.26082	1.00922	0.504610	+	0.863348i	$0.331636\pi$
$68$	0.00209196	0.000253688 0
$69$	1.44298	0.173715
$70$	−1.97051	−0.235521
$71$	−1.32081	−0.156752	−0.0783758	−	0.996924i	$-0.524973\pi$
$71$	−1.32081	−0.156752	−0.0783758	+	0.996924i	$0.524973\pi$
$72$	−6.69447	−0.788951
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−11.1630	−1.29768
$75$	−0.655267	−0.0756637
$76$	0.668540	0.0766868
$77$	1.30717	0.148966
$78$	2.01070	0.227666
$79$	9.22995	1.03845	0.519225	−	0.854637i	$-0.326220\pi$
$79$	9.22995	1.03845	0.519225	+	0.854637i	$0.326220\pi$
$80$	4.47067	0.499836
$81$	5.31999	0.591110
$82$	−8.62024	−0.951946
$83$	−17.6526	−1.93762	−0.968811	−	0.247801i	$-0.920292\pi$
$83$	−17.6526	−1.93762	−0.968811	+	0.247801i	$0.920292\pi$
$84$	0.233367	0.0254624
$85$	−0.00767831	−0.000832829 0
$86$	4.20504	0.453441
$87$	3.35723	0.359933
$88$	−2.60422	−0.277611
$89$	7.40421	0.784844	0.392422	−	0.919785i	$-0.371637\pi$
$89$	7.40421	0.784844	0.392422	+	0.919785i	$0.371637\pi$
$90$	−3.87513	−0.408474
$91$	−2.66081	−0.278928
$92$	−0.599973	−0.0625515
$93$	2.07445	0.215110
$94$	−11.2609	−1.16148
$95$	−2.45380	−0.251754
$96$	−1.00318	−0.102386
$97$	7.13564	0.724515	0.362257	−	0.932078i	$-0.382006\pi$
$97$	7.13564	0.724515	0.362257	+	0.932078i	$0.382006\pi$
$98$	7.97646	0.805744
$99$	2.57063	0.258358
$100$	0.272451	0.0272451
$101$	19.2109	1.91156	0.955779	−	0.294087i	$-0.0950154\pi$
$101$	19.2109	1.91156	0.955779	+	0.294087i	$0.0950154\pi$
$102$	0.00758457	0.000750984 0
$103$	−3.37846	−0.332890	−0.166445	−	0.986051i	$-0.553229\pi$
$103$	−3.37846	−0.332890	−0.166445	+	0.986051i	$0.553229\pi$
$104$	5.30101	0.519807
$105$	−0.856545	−0.0835903
$106$	8.09769	0.786517
$107$	−4.63582	−0.448162	−0.224081	−	0.974571i	$-0.571938\pi$
$107$	−4.63582	−0.448162	−0.224081	+	0.974571i	$0.571938\pi$
$108$	0.994514	0.0956971
$109$	−12.6426	−1.21094	−0.605469	−	0.795869i	$-0.707015\pi$
$109$	−12.6426	−1.21094	−0.605469	+	0.795869i	$0.707015\pi$
$110$	−1.50747	−0.143731
$111$	−4.85236	−0.460566
$112$	5.84393	0.552199
$113$	−17.2752	−1.62511	−0.812555	−	0.582884i	$-0.801924\pi$
$113$	−17.2752	−1.62511	−0.812555	+	0.582884i	$0.801924\pi$
$114$	2.42384	0.227014
$115$	2.20213	0.205350
$116$	−1.39589	−0.129605
$117$	−5.23263	−0.483756
$118$	−13.8626	−1.27616
$119$	−0.0100369	−0.000920077 0
$120$	1.70646	0.155778
$121$	1.00000	0.0909091
$122$	−5.51187	−0.499021
$123$	−3.74705	−0.337861
$124$	−0.862527	−0.0774573
$125$	−1.00000	−0.0894427
$126$	−5.06545	−0.451266
$127$	−0.954567	−0.0847041	−0.0423520	−	0.999103i	$-0.513485\pi$
$127$	−0.954567	−0.0847041	−0.0423520	+	0.999103i	$0.513485\pi$
$128$	−13.0617	−1.15450
$129$	1.82785	0.160933
$130$	3.06851	0.269127
$131$	12.9885	1.13481	0.567403	−	0.823440i	$-0.307948\pi$
$131$	12.9885	1.13481	0.567403	+	0.823440i	$0.307948\pi$
$132$	0.178528	0.0155389
$133$	−3.20753	−0.278128
$134$	−12.4529	−1.07577
$135$	−3.65025	−0.314163
$136$	0.0199960	0.00171464
$137$	2.47093	0.211106	0.105553	−	0.994414i	$-0.466339\pi$
$137$	2.47093	0.211106	0.105553	+	0.994414i	$0.466339\pi$
$138$	−2.17525	−0.185169
$139$	−4.09005	−0.346914	−0.173457	−	0.984841i	$-0.555494\pi$
$139$	−4.09005	−0.346914	−0.173457	+	0.984841i	$0.555494\pi$
$140$	0.356140	0.0300993
$141$	−4.89491	−0.412226
$142$	1.99108	0.167088
$143$	−2.03555	−0.170221
$144$	11.4924	0.957702
$145$	5.12345	0.425480
$146$	1.50747	0.124759
$147$	3.46722	0.285971
$148$	2.01755	0.165841
$149$	−4.24080	−0.347420	−0.173710	−	0.984797i	$-0.555576\pi$
$149$	−4.24080	−0.347420	−0.173710	+	0.984797i	$0.555576\pi$
$150$	0.987792	0.0806529
$151$	1.88133	0.153101	0.0765503	−	0.997066i	$-0.475609\pi$
$151$	1.88133	0.153101	0.0765503	+	0.997066i	$0.475609\pi$
$152$	6.39023	0.518316
$153$	−0.0197381	−0.00159573
$154$	−1.97051	−0.158788
$155$	3.16581	0.254284
$156$	−0.363402	−0.0290955
$157$	10.7748	0.859921	0.429960	−	0.902848i	$-0.358528\pi$
$157$	10.7748	0.859921	0.429960	+	0.902848i	$0.358528\pi$
$158$	−13.9138	−1.10693
$159$	3.51991	0.279147
$160$	−1.53094	−0.121032
$161$	2.87856	0.226862
$162$	−8.01970	−0.630087
$163$	1.15974	0.0908375	0.0454187	−	0.998968i	$-0.485538\pi$
$163$	1.15974	0.0908375	0.0454187	+	0.998968i	$0.485538\pi$
$164$	1.55797	0.121657
$165$	−0.655267	−0.0510125
$166$	26.6106	2.06539
$167$	−2.33487	−0.180677	−0.0903387	−	0.995911i	$-0.528795\pi$
$167$	−2.33487	−0.180677	−0.0903387	+	0.995911i	$0.528795\pi$
$168$	2.23063	0.172097
$169$	−8.85655	−0.681273
$170$	0.0115748	0.000887745 0
$171$	−6.30780	−0.482369
$172$	−0.759996	−0.0579492
$173$	−6.36995	−0.484299	−0.242149	−	0.970239i	$-0.577852\pi$
$173$	−6.36995	−0.484299	−0.242149	+	0.970239i	$0.577852\pi$
$174$	−5.06091	−0.383666
$175$	−1.30717	−0.0988128
$176$	4.47067	0.336990
$177$	−6.02582	−0.452928
$178$	−11.1616	−0.836596
$179$	5.54701	0.414603	0.207302	−	0.978277i	$-0.433532\pi$
$179$	5.54701	0.414603	0.207302	+	0.978277i	$0.433532\pi$
$180$	0.700370	0.0522025
$181$	0.236835	0.0176038	0.00880190	−	0.999961i	$-0.497198\pi$
$181$	0.236835	0.0176038	0.00880190	+	0.999961i	$0.497198\pi$
$182$	4.01107	0.297320
$183$	−2.39591	−0.177110
$184$	−5.73483	−0.422777
$185$	−7.40517	−0.544439
$186$	−3.12716	−0.229294
$187$	−0.00767831	−0.000561493 0
$188$	2.03524	0.148435
$189$	−4.77149	−0.347075
$190$	3.69901	0.268355
$191$	−0.474014	−0.0342984	−0.0171492	−	0.999853i	$-0.505459\pi$
$191$	−0.474014	−0.0342984	−0.0171492	+	0.999853i	$0.505459\pi$
$192$	−4.34671	−0.313697
$193$	1.85098	0.133237	0.0666183	−	0.997779i	$-0.478779\pi$
$193$	1.85098	0.133237	0.0666183	+	0.997779i	$0.478779\pi$
$194$	−10.7567	−0.772288
$195$	1.33383	0.0955173
$196$	−1.44162	−0.102973
$197$	−12.5582	−0.894733	−0.447367	−	0.894351i	$-0.647638\pi$
$197$	−12.5582	−0.894733	−0.447367	+	0.894351i	$0.647638\pi$
$198$	−3.87513	−0.275393
$199$	4.30112	0.304898	0.152449	−	0.988311i	$-0.451284\pi$
$199$	4.30112	0.304898	0.152449	+	0.988311i	$0.451284\pi$
$200$	2.60422	0.184146
$201$	−5.41304	−0.381806
$202$	−28.9598	−2.03760
$203$	6.69723	0.470053
$204$	−0.00137079	−9.59748e−5 0
$205$	−5.71836	−0.399388
$206$	5.09291	0.354840
$207$	5.66085	0.393456
$208$	−9.10026	−0.630990
$209$	−2.45380	−0.169733
$210$	1.29121	0.0891021
$211$	−15.5596	−1.07116	−0.535582	−	0.844483i	$-0.679908\pi$
$211$	−15.5596	−1.07116	−0.535582	+	0.844483i	$0.679908\pi$
$212$	−1.46353	−0.100516
$213$	0.865485	0.0593020
$214$	6.98834	0.477713
$215$	2.78948	0.190241
$216$	9.50604	0.646804
$217$	4.13825	0.280923
$218$	19.0582	1.29079
$219$	0.655267	0.0442788
$220$	0.272451	0.0183687
$221$	0.0156295	0.00105136
$222$	7.31477	0.490935
$223$	16.8118	1.12580	0.562901	−	0.826524i	$-0.309685\pi$
$223$	16.8118	1.12580	0.562901	+	0.826524i	$0.309685\pi$
$224$	−2.00120	−0.133711
$225$	−2.57063	−0.171375
$226$	26.0417	1.73227
$227$	−18.3034	−1.21484	−0.607419	−	0.794382i	$-0.707795\pi$
$227$	−18.3034	−1.21484	−0.607419	+	0.794382i	$0.707795\pi$
$228$	−0.438072	−0.0290120
$229$	−8.18891	−0.541138	−0.270569	−	0.962701i	$-0.587212\pi$
$229$	−8.18891	−0.541138	−0.270569	+	0.962701i	$0.587212\pi$
$230$	−3.31964	−0.218890
$231$	−0.856545	−0.0563565
$232$	−13.3426	−0.875985
$233$	17.1212	1.12165	0.560824	−	0.827935i	$-0.310484\pi$
$233$	17.1212	1.12165	0.560824	+	0.827935i	$0.310484\pi$
$234$	7.88800	0.515655
$235$	−7.47011	−0.487296
$236$	2.50545	0.163091
$237$	−6.04808	−0.392865
$238$	0.0151302	0.000980746 0
$239$	−4.24176	−0.274377	−0.137188	−	0.990545i	$-0.543807\pi$
$239$	−4.24176	−0.274377	−0.137188	+	0.990545i	$0.543807\pi$
$240$	−2.92948	−0.189097
$241$	15.7386	1.01381	0.506906	−	0.862001i	$-0.330789\pi$
$241$	15.7386	1.01381	0.506906	+	0.862001i	$0.330789\pi$
$242$	−1.50747	−0.0969035
$243$	−14.4368	−0.926118
$244$	0.996185	0.0637742
$245$	5.29131	0.338049
$246$	5.64855	0.360139
$247$	4.99482	0.317813
$248$	−8.24445	−0.523523
$249$	11.5671	0.733038
$250$	1.50747	0.0953405
$251$	−1.85611	−0.117156	−0.0585782	−	0.998283i	$-0.518657\pi$
$251$	−1.85611	−0.117156	−0.0585782	+	0.998283i	$0.518657\pi$
$252$	0.915503	0.0576712
$253$	2.20213	0.138447
$254$	1.43898	0.0902894
$255$	0.00503134	0.000315075 0
$256$	6.42299	0.401437
$257$	0.304229	0.0189773	0.00948863	−	0.999955i	$-0.496980\pi$
$257$	0.304229	0.0189773	0.00948863	+	0.999955i	$0.496980\pi$
$258$	−2.75542	−0.171545
$259$	−9.67982	−0.601475
$260$	−0.554587	−0.0343940
$261$	13.1705	0.815232
$262$	−19.5796	−1.20963
$263$	−27.9135	−1.72122	−0.860609	−	0.509266i	$-0.829917\pi$
$263$	−27.9135	−1.72122	−0.860609	+	0.509266i	$0.829917\pi$
$264$	1.70646	0.105025
$265$	5.37173	0.329982
$266$	4.83524	0.296468
$267$	−4.85173	−0.296921
$268$	2.25067	0.137481
$269$	−10.5144	−0.641073	−0.320536	−	0.947236i	$-0.603863\pi$
$269$	−10.5144	−0.641073	−0.320536	+	0.947236i	$0.603863\pi$
$270$	5.50262	0.334879
$271$	3.22142	0.195688	0.0978438	−	0.995202i	$-0.468805\pi$
$271$	3.22142	0.195688	0.0978438	+	0.995202i	$0.468805\pi$
$272$	−0.0343272	−0.00208139
$273$	1.74354	0.105524
$274$	−3.72484	−0.225026
$275$	−1.00000	−0.0603023
$276$	0.393142	0.0236644
$277$	−23.9399	−1.43841	−0.719204	−	0.694799i	$-0.755493\pi$
$277$	−23.9399	−1.43841	−0.719204	+	0.694799i	$0.755493\pi$
$278$	6.16561	0.369789
$279$	8.13810	0.487215
$280$	3.40416	0.203437
$281$	−19.2929	−1.15092	−0.575459	−	0.817831i	$-0.695176\pi$
$281$	−19.2929	−1.15092	−0.575459	+	0.817831i	$0.695176\pi$
$282$	7.37891	0.439408
$283$	0.347798	0.0206745	0.0103372	−	0.999947i	$-0.496710\pi$
$283$	0.347798	0.0206745	0.0103372	+	0.999947i	$0.496710\pi$
$284$	−0.359857	−0.0213536
$285$	1.60789	0.0952433
$286$	3.06851	0.181445
$287$	−7.47488	−0.441228
$288$	−3.93548	−0.231901
$289$	−16.9999	−0.999997
$290$	−7.72343	−0.453535
$291$	−4.67575	−0.274097
$292$	−0.272451	−0.0159440
$293$	−8.37053	−0.489012	−0.244506	−	0.969648i	$-0.578626\pi$
$293$	−8.37053	−0.489012	−0.244506	+	0.969648i	$0.578626\pi$
$294$	−5.22671	−0.304828
$295$	−9.19598	−0.535411
$296$	19.2847	1.12090
$297$	−3.65025	−0.211809
$298$	6.39286	0.370328
$299$	−4.48254	−0.259232
$300$	−0.178528	−0.0103073
$301$	3.64632	0.210170
$302$	−2.83604	−0.163196
$303$	−12.5883	−0.723178
$304$	−10.9701	−0.629180
$305$	−3.65638	−0.209364
$306$	0.0297544	0.00170095
$307$	5.28274	0.301502	0.150751	−	0.988572i	$-0.451831\pi$
$307$	5.28274	0.301502	0.150751	+	0.988572i	$0.451831\pi$
$308$	0.356140	0.0202930
$309$	2.21379	0.125938
$310$	−4.77234	−0.271051
$311$	−17.9536	−1.01805	−0.509027	−	0.860751i	$-0.669995\pi$
$311$	−17.9536	−1.01805	−0.509027	+	0.860751i	$0.669995\pi$
$312$	−3.47358	−0.196652
$313$	−11.5349	−0.651989	−0.325994	−	0.945372i	$-0.605699\pi$
$313$	−11.5349	−0.651989	−0.325994	+	0.945372i	$0.605699\pi$
$314$	−16.2426	−0.916623
$315$	−3.36024	−0.189328
$316$	2.51471	0.141464
$317$	−31.3524	−1.76093	−0.880464	−	0.474113i	$-0.842769\pi$
$317$	−31.3524	−1.76093	−0.880464	+	0.474113i	$0.842769\pi$
$318$	−5.30615	−0.297554
$319$	5.12345	0.286858
$320$	−6.63350	−0.370824
$321$	3.03770	0.169548
$322$	−4.33933	−0.241821
$323$	0.0188410	0.00104834
$324$	1.44944	0.0805243
$325$	2.03555	0.112912
$326$	−1.74826	−0.0968272
$327$	8.28426	0.458121
$328$	14.8919	0.822266
$329$	−9.76470	−0.538346
$330$	0.987792	0.0543762
$331$	3.92435	0.215702	0.107851	−	0.994167i	$-0.465603\pi$
$331$	3.92435	0.215702	0.107851	+	0.994167i	$0.465603\pi$
$332$	−4.80946	−0.263954
$333$	−19.0359	−1.04316
$334$	3.51973	0.192591
$335$	−8.26082	−0.451337
$336$	−3.82933	−0.208907
$337$	−22.8891	−1.24685	−0.623425	−	0.781883i	$-0.714259\pi$
$337$	−22.8891	−1.24685	−0.623425	+	0.781883i	$0.714259\pi$
$338$	13.3509	0.726196
$339$	11.3198	0.614809
$340$	−0.00209196	−0.000113453 0
$341$	3.16581	0.171438
$342$	9.50878	0.514176
$343$	16.0668	0.867527
$344$	−7.26441	−0.391671
$345$	−1.44298	−0.0776876
$346$	9.60248	0.516233
$347$	−3.75334	−0.201490	−0.100745	−	0.994912i	$-0.532123\pi$
$347$	−3.75334	−0.201490	−0.100745	+	0.994912i	$0.532123\pi$
$348$	0.914681	0.0490321
$349$	1.30066	0.0696226	0.0348113	−	0.999394i	$-0.488917\pi$
$349$	1.30066	0.0696226	0.0348113	+	0.999394i	$0.488917\pi$
$350$	1.97051	0.105328
$351$	7.43024	0.396597
$352$	−1.53094	−0.0815996
$353$	−5.64333	−0.300364	−0.150182	−	0.988658i	$-0.547986\pi$
$353$	−5.64333	−0.300364	−0.150182	+	0.988658i	$0.547986\pi$
$354$	9.08371	0.482794
$355$	1.32081	0.0701014
$356$	2.01728	0.106916
$357$	0.00657682	0.000348082 0
$358$	−8.36193	−0.441942
$359$	32.6083	1.72100	0.860500	−	0.509450i	$-0.170151\pi$
$359$	32.6083	1.72100	0.860500	+	0.509450i	$0.170151\pi$
$360$	6.69447	0.352830
$361$	−12.9789	−0.683099
$362$	−0.357020	−0.0187646
$363$	−0.655267	−0.0343926
$364$	−0.724939	−0.0379971
$365$	1.00000	0.0523424
$366$	3.61174	0.188789
$367$	−34.7125	−1.81198	−0.905989	−	0.423302i	$-0.860871\pi$
$367$	−34.7125	−1.81198	−0.905989	+	0.423302i	$0.860871\pi$
$368$	9.84501	0.513206
$369$	−14.6998	−0.765240
$370$	11.1630	0.580339
$371$	7.02176	0.364552
$372$	0.565186	0.0293035
$373$	5.57297	0.288557	0.144279	−	0.989537i	$-0.453914\pi$
$373$	5.57297	0.288557	0.144279	+	0.989537i	$0.453914\pi$
$374$	0.0115748	0.000598518 0
$375$	0.655267	0.0338378
$376$	19.4538	1.00325
$377$	−10.4290	−0.537122
$378$	7.19286	0.369961
$379$	8.98785	0.461675	0.230837	−	0.972992i	$-0.425853\pi$
$379$	8.98785	0.461675	0.230837	+	0.972992i	$0.425853\pi$
$380$	−0.668540	−0.0342954
$381$	0.625496	0.0320451
$382$	0.714559	0.0365600
$383$	−10.1221	−0.517214	−0.258607	−	0.965983i	$-0.583263\pi$
$383$	−10.1221	−0.517214	−0.258607	+	0.965983i	$0.583263\pi$
$384$	8.55887	0.436768
$385$	−1.30717	−0.0666196
$386$	−2.79029	−0.142022
$387$	7.17070	0.364507
$388$	1.94411	0.0986974
$389$	−32.9779	−1.67205	−0.836024	−	0.548693i	$-0.815126\pi$
$389$	−32.9779	−1.67205	−0.836024	+	0.548693i	$0.815126\pi$
$390$	−2.01070	−0.101816
$391$	−0.0169086	−0.000855106 0
$392$	−13.7797	−0.695981
$393$	−8.51090	−0.429318
$394$	18.9310	0.953731
$395$	−9.22995	−0.464409
$396$	0.700370	0.0351949
$397$	15.3644	0.771115	0.385558	−	0.922684i	$-0.374009\pi$
$397$	15.3644	0.771115	0.385558	+	0.922684i	$0.374009\pi$
$398$	−6.48379	−0.325003
$399$	2.10179	0.105221
$400$	−4.47067	−0.223534
$401$	−3.70334	−0.184936	−0.0924680	−	0.995716i	$-0.529476\pi$
$401$	−3.70334	−0.184936	−0.0924680	+	0.995716i	$0.529476\pi$
$402$	8.15997	0.406982
$403$	−6.44414	−0.321006
$404$	5.23404	0.260403
$405$	−5.31999	−0.264352
$406$	−10.0958	−0.501048
$407$	−7.40517	−0.367061
$408$	−0.0131027	−0.000648681 0
$409$	38.9418	1.92555	0.962773	−	0.270311i	$-0.0871265\pi$
$409$	38.9418	1.92555	0.962773	+	0.270311i	$0.0871265\pi$
$410$	8.62024	0.425723
$411$	−1.61912	−0.0798652
$412$	−0.920465	−0.0453481
$413$	−12.0207	−0.591500
$414$	−8.53354	−0.419401
$415$	17.6526	0.866531
$416$	3.11631	0.152790
$417$	2.68008	0.131244
$418$	3.69901	0.180925
$419$	−5.67218	−0.277104	−0.138552	−	0.990355i	$-0.544245\pi$
$419$	−5.67218	−0.277104	−0.138552	+	0.990355i	$0.544245\pi$
$420$	−0.233367	−0.0113871
$421$	−2.55303	−0.124427	−0.0622136	−	0.998063i	$-0.519816\pi$
$421$	−2.55303	−0.124427	−0.0622136	+	0.998063i	$0.519816\pi$
$422$	23.4555	1.14180
$423$	−19.2029	−0.933675
$424$	−13.9892	−0.679373
$425$	0.00767831	0.000372453 0
$426$	−1.30469	−0.0632123
$427$	−4.77951	−0.231297
$428$	−1.26304	−0.0610511
$429$	1.33383	0.0643977
$430$	−4.20504	−0.202785
$431$	34.8955	1.68086	0.840428	−	0.541923i	$-0.182304\pi$
$431$	34.8955	1.68086	0.840428	+	0.541923i	$0.182304\pi$
$432$	−16.3191	−0.785151
$433$	−22.9783	−1.10427	−0.552134	−	0.833755i	$-0.686186\pi$
$433$	−22.9783	−1.10427	−0.552134	+	0.833755i	$0.686186\pi$
$434$	−6.23826	−0.299446
$435$	−3.35723	−0.160967
$436$	−3.44448	−0.164961
$437$	−5.40358	−0.258488
$438$	−0.987792	−0.0471985
$439$	7.82425	0.373431	0.186715	−	0.982414i	$-0.440216\pi$
$439$	7.82425	0.373431	0.186715	+	0.982414i	$0.440216\pi$
$440$	2.60422	0.124151
$441$	13.6020	0.647713
$442$	−0.0235610	−0.00112068
$443$	18.4235	0.875326	0.437663	−	0.899139i	$-0.355806\pi$
$443$	18.4235	0.875326	0.437663	+	0.899139i	$0.355806\pi$
$444$	−1.32203	−0.0627409
$445$	−7.40421	−0.350993
$446$	−25.3432	−1.20004
$447$	2.77886	0.131435
$448$	−8.67111	−0.409672
$449$	−21.6685	−1.02260	−0.511300	−	0.859402i	$-0.670836\pi$
$449$	−21.6685	−1.02260	−0.511300	+	0.859402i	$0.670836\pi$
$450$	3.87513	0.182675
$451$	−5.71836	−0.269267
$452$	−4.70664	−0.221382
$453$	−1.23277	−0.0579208
$454$	27.5917	1.29494
$455$	2.66081	0.124740
$456$	−4.18731	−0.196089
$457$	9.40010	0.439718	0.219859	−	0.975532i	$-0.429440\pi$
$457$	9.40010	0.439718	0.219859	+	0.975532i	$0.429440\pi$
$458$	12.3445	0.576820
$459$	0.0280277	0.00130822
$460$	0.599973	0.0279739
$461$	−10.2349	−0.476686	−0.238343	−	0.971181i	$-0.576604\pi$
$461$	−10.2349	−0.476686	−0.238343	+	0.971181i	$0.576604\pi$
$462$	1.29121	0.0600726
$463$	−22.4706	−1.04430	−0.522148	−	0.852855i	$-0.674869\pi$
$463$	−22.4706	−1.04430	−0.522148	+	0.852855i	$0.674869\pi$
$464$	22.9053	1.06335
$465$	−2.07445	−0.0962002
$466$	−25.8097	−1.19561
$467$	−6.98172	−0.323075	−0.161538	−	0.986867i	$-0.551645\pi$
$467$	−6.98172	−0.323075	−0.161538	+	0.986867i	$0.551645\pi$
$468$	−1.42564	−0.0659000
$469$	−10.7983	−0.498619
$470$	11.2609	0.519428
$471$	−7.06035	−0.325324
$472$	23.9483	1.10231
$473$	2.78948	0.128260
$474$	9.11727	0.418770
$475$	2.45380	0.112588
$476$	−0.00273455	−0.000125338 0
$477$	13.8087	0.632257
$478$	6.39430	0.292469
$479$	1.11578	0.0509814	0.0254907	−	0.999675i	$-0.491885\pi$
$479$	1.11578	0.0509814	0.0254907	+	0.999675i	$0.491885\pi$
$480$	1.00318	0.0457885
$481$	15.0736	0.687295
$482$	−23.7254	−1.08066
$483$	−1.88622	−0.0858262
$484$	0.272451	0.0123841
$485$	−7.13564	−0.324013
$486$	21.7629	0.987185
$487$	8.33538	0.377712	0.188856	−	0.982005i	$-0.439522\pi$
$487$	8.33538	0.377712	0.188856	+	0.982005i	$0.439522\pi$
$488$	9.52202	0.431042
$489$	−0.759936	−0.0343655
$490$	−7.97646	−0.360340
$491$	−32.6718	−1.47446	−0.737229	−	0.675643i	$-0.763866\pi$
$491$	−32.6718	−1.47446	−0.737229	+	0.675643i	$0.763866\pi$
$492$	−1.02089	−0.0460252
$493$	−0.0393395	−0.00177176
$494$	−7.52952	−0.338769
$495$	−2.57063	−0.115541
$496$	14.1533	0.635501
$497$	1.72653	0.0774453
$498$	−17.4371	−0.781374
$499$	−21.8182	−0.976716	−0.488358	−	0.872643i	$-0.662404\pi$
$499$	−21.8182	−0.976716	−0.488358	+	0.872643i	$0.662404\pi$
$500$	−0.272451	−0.0121844
$501$	1.52996	0.0683536
$502$	2.79802	0.124882
$503$	−41.8375	−1.86544	−0.932721	−	0.360599i	$-0.882572\pi$
$503$	−41.8375	−1.86544	−0.932721	+	0.360599i	$0.882572\pi$
$504$	8.75082	0.389792
$505$	−19.2109	−0.854875
$506$	−3.31964	−0.147576
$507$	5.80341	0.257738
$508$	−0.260073	−0.0115389
$509$	20.1458	0.892945	0.446472	−	0.894797i	$-0.352680\pi$
$509$	20.1458	0.892945	0.446472	+	0.894797i	$0.352680\pi$
$510$	−0.00758457	−0.000335850 0
$511$	1.30717	0.0578258
$512$	16.4409	0.726591
$513$	8.95697	0.395460
$514$	−0.458614	−0.0202286
$515$	3.37846	0.148873
$516$	0.498000	0.0219232
$517$	−7.47011	−0.328535
$518$	14.5920	0.641135
$519$	4.17402	0.183219
$520$	−5.30101	−0.232465
$521$	10.6193	0.465239	0.232619	−	0.972568i	$-0.425270\pi$
$521$	10.6193	0.465239	0.232619	+	0.972568i	$0.425270\pi$
$522$	−19.8540	−0.868988
$523$	−22.1410	−0.968158	−0.484079	−	0.875024i	$-0.660845\pi$
$523$	−22.1410	−0.968158	−0.484079	+	0.875024i	$0.660845\pi$
$524$	3.53872	0.154590
$525$	0.856545	0.0373827
$526$	42.0786	1.83471
$527$	−0.0243080	−0.00105887
$528$	−2.92948	−0.127489
$529$	−18.1506	−0.789157
$530$	−8.09769	−0.351741
$531$	−23.6394	−1.02586
$532$	−0.873896	−0.0378882
$533$	11.6400	0.504184
$534$	7.31382	0.316500
$535$	4.63582	0.200424
$536$	21.5130	0.929219
$537$	−3.63477	−0.156852
$538$	15.8500	0.683344
$539$	5.29131	0.227913
$540$	−0.994514	−0.0427971
$541$	6.66974	0.286754	0.143377	−	0.989668i	$-0.454204\pi$
$541$	6.66974	0.286754	0.143377	+	0.989668i	$0.454204\pi$
$542$	−4.85618	−0.208591
$543$	−0.155190	−0.00665984
$544$	0.0117551	0.000503994 0
$545$	12.6426	0.541548
$546$	−2.62832	−0.112482
$547$	−43.1248	−1.84388	−0.921942	−	0.387328i	$-0.873398\pi$
$547$	−43.1248	−1.84388	−0.921942	+	0.387328i	$0.873398\pi$
$548$	0.673207	0.0287580
$549$	−9.39919	−0.401148
$550$	1.50747	0.0642785
$551$	−12.5719	−0.535582
$552$	3.75785	0.159945
$553$	−12.0651	−0.513061
$554$	36.0885	1.53326
$555$	4.85236	0.205971
$556$	−1.11434	−0.0472585
$557$	14.3791	0.609263	0.304632	−	0.952470i	$-0.401467\pi$
$557$	14.3791	0.609263	0.304632	+	0.952470i	$0.401467\pi$
$558$	−12.2679	−0.519342
$559$	−5.67811	−0.240158
$560$	−5.84393	−0.246951
$561$	0.00503134	0.000212423 0
$562$	29.0834	1.22681
$563$	8.08506	0.340745	0.170372	−	0.985380i	$-0.445503\pi$
$563$	8.08506	0.340745	0.170372	+	0.985380i	$0.445503\pi$
$564$	−1.33363	−0.0561557
$565$	17.2752	0.726772
$566$	−0.524293	−0.0220377
$567$	−6.95413	−0.292046
$568$	−3.43969	−0.144326
$569$	−7.60982	−0.319020	−0.159510	−	0.987196i	$-0.550991\pi$
$569$	−7.60982	−0.319020	−0.159510	+	0.987196i	$0.550991\pi$
$570$	−2.42384	−0.101524
$571$	1.11895	0.0468267	0.0234133	−	0.999726i	$-0.492547\pi$
$571$	1.11895	0.0468267	0.0234133	+	0.999726i	$0.492547\pi$
$572$	−0.554587	−0.0231884
$573$	0.310605	0.0129757
$574$	11.2681	0.470322
$575$	−2.20213	−0.0918352
$576$	−17.0522	−0.710510
$577$	39.7214	1.65362	0.826811	−	0.562480i	$-0.190153\pi$
$577$	39.7214	1.65362	0.826811	+	0.562480i	$0.190153\pi$
$578$	25.6268	1.06594
$579$	−1.21289	−0.0504059
$580$	1.39589	0.0579612
$581$	23.0749	0.957309
$582$	7.04853	0.292171
$583$	5.37173	0.222474
$584$	−2.60422	−0.107763
$585$	5.23263	0.216342
$586$	12.6183	0.521257
$587$	−45.3179	−1.87047	−0.935234	−	0.354030i	$-0.884811\pi$
$587$	−45.3179	−1.87047	−0.935234	+	0.354030i	$0.884811\pi$
$588$	0.944647	0.0389566
$589$	−7.76825	−0.320085
$590$	13.8626	0.570715
$591$	8.22896	0.338494
$592$	−33.1061	−1.36065
$593$	−26.7482	−1.09842	−0.549208	−	0.835686i	$-0.685071\pi$
$593$	−26.7482	−1.09842	−0.549208	+	0.835686i	$0.685071\pi$
$594$	5.50262	0.225775
$595$	0.0100369	0.000411471 0
$596$	−1.15541	−0.0473275
$597$	−2.81838	−0.115349
$598$	6.75727	0.276325
$599$	−10.6120	−0.433593	−0.216796	−	0.976217i	$-0.569561\pi$
$599$	−10.6120	−0.433593	−0.216796	+	0.976217i	$0.569561\pi$
$600$	−1.70646	−0.0696659
$601$	13.2536	0.540627	0.270314	−	0.962772i	$-0.412873\pi$
$601$	13.2536	0.540627	0.270314	+	0.962772i	$0.412873\pi$
$602$	−5.49670	−0.224029
$603$	−21.2355	−0.864775
$604$	0.512571	0.0208562
$605$	−1.00000	−0.0406558
$606$	18.9764	0.770863
$607$	16.4130	0.666183	0.333092	−	0.942895i	$-0.391908\pi$
$607$	16.4130	0.666183	0.333092	+	0.942895i	$0.391908\pi$
$608$	3.75663	0.152351
$609$	−4.38847	−0.177830
$610$	5.51187	0.223169
$611$	15.2058	0.615159
$612$	−0.00537765	−0.000217379 0
$613$	−20.6151	−0.832634	−0.416317	−	0.909220i	$-0.636679\pi$
$613$	−20.6151	−0.832634	−0.416317	+	0.909220i	$0.636679\pi$
$614$	−7.96355	−0.321383
$615$	3.74705	0.151096
$616$	3.40416	0.137157
$617$	−34.6161	−1.39359	−0.696796	−	0.717269i	$-0.745392\pi$
$617$	−34.6161	−1.39359	−0.696796	+	0.717269i	$0.745392\pi$
$618$	−3.33722	−0.134242
$619$	20.0894	0.807463	0.403732	−	0.914878i	$-0.367713\pi$
$619$	20.0894	0.807463	0.403732	+	0.914878i	$0.367713\pi$
$620$	0.862527	0.0346399
$621$	−8.03832	−0.322567
$622$	27.0644	1.08518
$623$	−9.67856	−0.387763
$624$	5.96310	0.238715
$625$	1.00000	0.0400000
$626$	17.3884	0.694980
$627$	1.60789	0.0642130
$628$	2.93560	0.117143
$629$	0.0568592	0.00226712
$630$	5.06545	0.201812
$631$	11.3963	0.453678	0.226839	−	0.973932i	$-0.427161\pi$
$631$	11.3963	0.453678	0.226839	+	0.973932i	$0.427161\pi$
$632$	24.0368	0.956134
$633$	10.1957	0.405241
$634$	47.2627	1.87704
$635$	0.954567	0.0378808
$636$	0.959005	0.0380270
$637$	−10.7707	−0.426751
$638$	−7.72343	−0.305773
$639$	3.39531	0.134317
$640$	13.0617	0.516307
$641$	−36.9978	−1.46132	−0.730662	−	0.682739i	$-0.760789\pi$
$641$	−36.9978	−1.46132	−0.730662	+	0.682739i	$0.760789\pi$
$642$	−4.57923	−0.180728
$643$	25.7117	1.01397	0.506986	−	0.861954i	$-0.330760\pi$
$643$	25.7117	1.01397	0.506986	+	0.861954i	$0.330760\pi$
$644$	0.784267	0.0309044
$645$	−1.82785	−0.0719716
$646$	−0.0284022	−0.00111747
$647$	6.63294	0.260768	0.130384	−	0.991464i	$-0.458379\pi$
$647$	6.63294	0.260768	0.130384	+	0.991464i	$0.458379\pi$
$648$	13.8544	0.544253
$649$	−9.19598	−0.360974
$650$	−3.06851	−0.120357
$651$	−2.71166	−0.106278
$652$	0.315971	0.0123744
$653$	−45.0286	−1.76210	−0.881052	−	0.473019i	$-0.843164\pi$
$653$	−45.0286	−1.76210	−0.881052	+	0.473019i	$0.843164\pi$
$654$	−12.4882	−0.488329
$655$	−12.9885	−0.507501
$656$	−25.5649	−0.998143
$657$	2.57063	0.100290
$658$	14.7199	0.573843
$659$	−22.1259	−0.861904	−0.430952	−	0.902375i	$-0.641822\pi$
$659$	−22.1259	−0.861904	−0.430952	+	0.902375i	$0.641822\pi$
$660$	−0.178528	−0.00694920
$661$	46.6632	1.81499	0.907493	−	0.420067i	$-0.137993\pi$
$661$	46.6632	1.81499	0.907493	+	0.420067i	$0.137993\pi$
$662$	−5.91582	−0.229925
$663$	−0.0102415	−0.000397748 0
$664$	−45.9712	−1.78403
$665$	3.20753	0.124383
$666$	28.6960	1.11195
$667$	11.2825	0.436861
$668$	−0.636137	−0.0246129
$669$	−11.0162	−0.425912
$670$	12.4529	0.481097
$671$	−3.65638	−0.141153
$672$	1.31132	0.0505854
$673$	−3.48291	−0.134256	−0.0671282	−	0.997744i	$-0.521384\pi$
$673$	−3.48291	−0.134256	−0.0671282	+	0.997744i	$0.521384\pi$
$674$	34.5046	1.32907
$675$	3.65025	0.140498
$676$	−2.41298	−0.0928068
$677$	−4.95109	−0.190286	−0.0951429	−	0.995464i	$-0.530331\pi$
$677$	−4.95109	−0.190286	−0.0951429	+	0.995464i	$0.530331\pi$
$678$	−17.0643	−0.655349
$679$	−9.32750	−0.357957
$680$	−0.0199960	−0.000766812 0
$681$	11.9936	0.459596
$682$	−4.77234	−0.182742
$683$	33.7212	1.29031	0.645153	−	0.764053i	$-0.276793\pi$
$683$	33.7212	1.29031	0.645153	+	0.764053i	$0.276793\pi$
$684$	−1.71857	−0.0657110
$685$	−2.47093	−0.0944093
$686$	−24.2202	−0.924731
$687$	5.36592	0.204723
$688$	12.4708	0.475446
$689$	−10.9344	−0.416567
$690$	2.17525	0.0828102
$691$	0.534705	0.0203412	0.0101706	−	0.999948i	$-0.496763\pi$
$691$	0.534705	0.0203412	0.0101706	+	0.999948i	$0.496763\pi$
$692$	−1.73550	−0.0659739
$693$	−3.36024	−0.127645
$694$	5.65803	0.214776
$695$	4.09005	0.155145
$696$	8.74296	0.331401
$697$	0.0439074	0.00166311
$698$	−1.96070	−0.0742135
$699$	−11.2190	−0.424341
$700$	−0.356140	−0.0134608
$701$	4.24353	0.160276	0.0801379	−	0.996784i	$-0.474464\pi$
$701$	4.24353	0.160276	0.0801379	+	0.996784i	$0.474464\pi$
$702$	−11.2008	−0.422748
$703$	18.1708	0.685324
$704$	−6.63350	−0.250009
$705$	4.89491	0.184353
$706$	8.50713	0.320170
$707$	−25.1119	−0.944432
$708$	−1.64174	−0.0617004
$709$	6.52937	0.245216	0.122608	−	0.992455i	$-0.460874\pi$
$709$	6.52937	0.245216	0.122608	+	0.992455i	$0.460874\pi$
$710$	−1.99108	−0.0747239
$711$	−23.7268	−0.889823
$712$	19.2822	0.722630
$713$	6.97152	0.261085
$714$	−0.00991432	−0.000371034 0
$715$	2.03555	0.0761251
$716$	1.51129	0.0564796
$717$	2.77948	0.103802
$718$	−49.1559	−1.83448
$719$	0.288752	0.0107686	0.00538431	−	0.999986i	$-0.498286\pi$
$719$	0.288752	0.0107686	0.00538431	+	0.999986i	$0.498286\pi$
$720$	−11.4924	−0.428297
$721$	4.41622	0.164469
$722$	19.5652	0.728141
$723$	−10.3130	−0.383544
$724$	0.0645260	0.00239809
$725$	−5.12345	−0.190280
$726$	0.987792	0.0366604
$727$	−25.2667	−0.937089	−0.468544	−	0.883440i	$-0.655221\pi$
$727$	−25.2667	−0.937089	−0.468544	+	0.883440i	$0.655221\pi$
$728$	−6.92932	−0.256818
$729$	−6.50005	−0.240742
$730$	−1.50747	−0.0557938
$731$	−0.0214185	−0.000792190 0
$732$	−0.652767	−0.0241270
$733$	17.8716	0.660103	0.330051	−	0.943963i	$-0.392934\pi$
$733$	17.8716	0.660103	0.330051	+	0.943963i	$0.392934\pi$
$734$	52.3279	1.93146
$735$	−3.46722	−0.127890
$736$	−3.37134	−0.124269
$737$	−8.26082	−0.304291
$738$	22.1594	0.815699
$739$	41.5818	1.52961	0.764806	−	0.644260i	$-0.222835\pi$
$739$	41.5818	1.52961	0.764806	+	0.644260i	$0.222835\pi$
$740$	−2.01755	−0.0741665
$741$	−3.27294	−0.120234
$742$	−10.5851	−0.388590
$743$	−19.6130	−0.719531	−0.359766	−	0.933043i	$-0.617143\pi$
$743$	−19.6130	−0.719531	−0.359766	+	0.933043i	$0.617143\pi$
$744$	5.40232	0.198059
$745$	4.24080	0.155371
$746$	−8.40106	−0.307585
$747$	45.3782	1.66030
$748$	−0.00209196	−7.64898e−5 0
$749$	6.05981	0.221421
$750$	−0.987792	−0.0360691
$751$	39.7189	1.44936	0.724681	−	0.689084i	$-0.241987\pi$
$751$	39.7189	1.44936	0.724681	+	0.689084i	$0.241987\pi$
$752$	−33.3964	−1.21784
$753$	1.21625	0.0443225
$754$	15.7214	0.572539
$755$	−1.88133	−0.0684687
$756$	−1.30000	−0.0472805
$757$	52.9809	1.92562	0.962812	−	0.270171i	$-0.0870802\pi$
$757$	52.9809	1.92562	0.962812	+	0.270171i	$0.0870802\pi$
$758$	−13.5489	−0.492117
$759$	−1.44298	−0.0523770
$760$	−6.39023	−0.231798
$761$	41.0431	1.48781	0.743905	−	0.668285i	$-0.232971\pi$
$761$	41.0431	1.48781	0.743905	+	0.668285i	$0.232971\pi$
$762$	−0.942913	−0.0341581
$763$	16.5260	0.598281
$764$	−0.129146	−0.00467232
$765$	0.0197381	0.000713631 0
$766$	15.2587	0.551318
$767$	18.7188	0.675898
$768$	−4.20878	−0.151871
$769$	28.4696	1.02664	0.513319	−	0.858198i	$-0.328416\pi$
$769$	28.4696	1.02664	0.513319	+	0.858198i	$0.328416\pi$
$770$	1.97051	0.0710124
$771$	−0.199351	−0.00717945
$772$	0.504302	0.0181502
$773$	18.0179	0.648060	0.324030	−	0.946047i	$-0.394962\pi$
$773$	18.0179	0.648060	0.324030	+	0.946047i	$0.394962\pi$
$774$	−10.8096	−0.388542
$775$	−3.16581	−0.113719
$776$	18.5828	0.667083
$777$	6.34286	0.227549
$778$	49.7131	1.78230
$779$	14.0317	0.502738
$780$	0.363402	0.0130119
$781$	1.32081	0.0472624
$782$	0.0254892	0.000911491 0
$783$	−18.7019	−0.668350
$784$	23.6557	0.844846
$785$	−10.7748	−0.384568
$786$	12.8299	0.457627
$787$	41.1035	1.46518	0.732590	−	0.680670i	$-0.238311\pi$
$787$	41.1035	1.46518	0.732590	+	0.680670i	$0.238311\pi$
$788$	−3.42149	−0.121886
$789$	18.2908	0.651169
$790$	13.9138	0.495032
$791$	22.5816	0.802909
$792$	6.69447	0.237878
$793$	7.44273	0.264299
$794$	−23.1612	−0.821962
$795$	−3.51991	−0.124838
$796$	1.17184	0.0415349
$797$	−33.9558	−1.20278	−0.601388	−	0.798957i	$-0.705385\pi$
$797$	−33.9558	−1.20278	−0.601388	+	0.798957i	$0.705385\pi$
$798$	−3.16837	−0.112159
$799$	0.0573578	0.00202917
$800$	1.53094	0.0541270
$801$	−19.0334	−0.672514
$802$	5.58266	0.197130
$803$	1.00000	0.0352892
$804$	−1.47479	−0.0520118
$805$	−2.87856	−0.101456
$806$	9.71432	0.342172
$807$	6.88972	0.242530
$808$	50.0294	1.76003
$809$	−26.9406	−0.947182	−0.473591	−	0.880745i	$-0.657042\pi$
$809$	−26.9406	−0.947182	−0.473591	+	0.880745i	$0.657042\pi$
$810$	8.01970	0.281784
$811$	14.1154	0.495660	0.247830	−	0.968804i	$-0.420283\pi$
$811$	14.1154	0.495660	0.247830	+	0.968804i	$0.420283\pi$
$812$	1.82467	0.0640333
$813$	−2.11089	−0.0740322
$814$	11.1630	0.391264
$815$	−1.15974	−0.0406238
$816$	0.0224935	0.000787429 0
$817$	−6.84481	−0.239470
$818$	−58.7033	−2.05251
$819$	6.83993	0.239007
$820$	−1.55797	−0.0544068
$821$	−41.9162	−1.46289	−0.731443	−	0.681903i	$-0.761153\pi$
$821$	−41.9162	−1.46289	−0.731443	+	0.681903i	$0.761153\pi$
$822$	2.44076	0.0851314
$823$	8.33849	0.290662	0.145331	−	0.989383i	$-0.453575\pi$
$823$	8.33849	0.290662	0.145331	+	0.989383i	$0.453575\pi$
$824$	−8.79825	−0.306502
$825$	0.655267	0.0228135
$826$	18.1208	0.630503
$827$	−4.95583	−0.172331	−0.0861655	−	0.996281i	$-0.527461\pi$
$827$	−4.95583	−0.172331	−0.0861655	+	0.996281i	$0.527461\pi$
$828$	1.54231	0.0535988
$829$	12.7174	0.441694	0.220847	−	0.975308i	$-0.429118\pi$
$829$	12.7174	0.441694	0.220847	+	0.975308i	$0.429118\pi$
$830$	−26.6106	−0.923669
$831$	15.6870	0.544177
$832$	13.5028	0.468125
$833$	−0.0406283	−0.00140769
$834$	−4.04012	−0.139898
$835$	2.33487	0.0808014
$836$	−0.668540	−0.0231219
$837$	−11.5560	−0.399433
$838$	8.55061	0.295376
$839$	13.6035	0.469646	0.234823	−	0.972038i	$-0.424549\pi$
$839$	13.6035	0.469646	0.234823	+	0.972038i	$0.424549\pi$
$840$	−2.23063	−0.0769641
$841$	−2.75022	−0.0948351
$842$	3.84861	0.132632
$843$	12.6420	0.435413
$844$	−4.23922	−0.145920
$845$	8.85655	0.304675
$846$	28.9476	0.995240
$847$	−1.30717	−0.0449149
$848$	24.0152	0.824686
$849$	−0.227901	−0.00782153
$850$	−0.0115748	−0.000397012 0
$851$	−16.3072	−0.559002
$852$	0.235802	0.00807845
$853$	−11.3743	−0.389449	−0.194725	−	0.980858i	$-0.562381\pi$
$853$	−11.3743	−0.389449	−0.194725	+	0.980858i	$0.562381\pi$
$854$	7.20495	0.246548
$855$	6.30780	0.215722
$856$	−12.0727	−0.412636
$857$	−16.5144	−0.564122	−0.282061	−	0.959396i	$-0.591018\pi$
$857$	−16.5144	−0.564122	−0.282061	+	0.959396i	$0.591018\pi$
$858$	−2.01070	−0.0686440
$859$	−18.1050	−0.617736	−0.308868	−	0.951105i	$-0.599950\pi$
$859$	−18.1050	−0.617736	−0.308868	+	0.951105i	$0.599950\pi$
$860$	0.759996	0.0259157
$861$	4.89804	0.166925
$862$	−52.6037	−1.79169
$863$	7.47794	0.254552	0.127276	−	0.991867i	$-0.459377\pi$
$863$	7.47794	0.254552	0.127276	+	0.991867i	$0.459377\pi$
$864$	5.58832	0.190119
$865$	6.36995	0.216585
$866$	34.6391	1.17708
$867$	11.1395	0.378317
$868$	1.12747	0.0382688
$869$	−9.22995	−0.313105
$870$	5.06091	0.171581
$871$	16.8153	0.569764
$872$	−32.9240	−1.11495
$873$	−18.3431	−0.620819
$874$	8.14571	0.275533
$875$	1.30717	0.0441904
$876$	0.178528	0.00603191
$877$	−10.6856	−0.360827	−0.180414	−	0.983591i	$-0.557744\pi$
$877$	−10.6856	−0.360827	−0.180414	+	0.983591i	$0.557744\pi$
$878$	−11.7948	−0.398055
$879$	5.48493	0.185002
$880$	−4.47067	−0.150706
$881$	−33.2086	−1.11883	−0.559414	−	0.828889i	$-0.688974\pi$
$881$	−33.2086	−1.11883	−0.559414	+	0.828889i	$0.688974\pi$
$882$	−20.5045	−0.690422
$883$	−55.1670	−1.85652	−0.928259	−	0.371934i	$-0.878695\pi$
$883$	−55.1670	−1.85652	−0.928259	+	0.371934i	$0.878695\pi$
$884$	0.00425829	0.000143222 0
$885$	6.02582	0.202556
$886$	−27.7728	−0.933044
$887$	11.9558	0.401438	0.200719	−	0.979649i	$-0.435672\pi$
$887$	11.9558	0.401438	0.200719	+	0.979649i	$0.435672\pi$
$888$	−12.6366	−0.424057
$889$	1.24778	0.0418492
$890$	11.1616	0.374137
$891$	−5.31999	−0.178226
$892$	4.58040	0.153363
$893$	18.3301	0.613395
$894$	−4.18903	−0.140102
$895$	−5.54701	−0.185416
$896$	17.0738	0.570396
$897$	2.93726	0.0980722
$898$	32.6645	1.09003
$899$	16.2199	0.540963
$900$	−0.700370	−0.0233457
$901$	−0.0412458	−0.00137410
$902$	8.62024	0.287022
$903$	−2.38931	−0.0795114
$904$	−44.9883	−1.49629
$905$	−0.236835	−0.00787266
$906$	1.85836	0.0617400
$907$	6.42486	0.213334	0.106667	−	0.994295i	$-0.465982\pi$
$907$	6.42486	0.213334	0.106667	+	0.994295i	$0.465982\pi$
$908$	−4.98678	−0.165492
$909$	−49.3841	−1.63797
$910$	−4.01107	−0.132966
$911$	22.6397	0.750085	0.375043	−	0.927008i	$-0.377628\pi$
$911$	22.6397	0.750085	0.375043	+	0.927008i	$0.377628\pi$
$912$	7.18836	0.238030
$913$	17.6526	0.584215
$914$	−14.1703	−0.468713
$915$	2.39591	0.0792062
$916$	−2.23108	−0.0737169
$917$	−16.9781	−0.560667
$918$	−0.0422508	−0.00139448
$919$	28.0280	0.924560	0.462280	−	0.886734i	$-0.347032\pi$
$919$	28.0280	0.924560	0.462280	+	0.886734i	$0.347032\pi$
$920$	5.73483	0.189072
$921$	−3.46161	−0.114064
$922$	15.4287	0.508118
$923$	−2.68857	−0.0884955
$924$	−0.233367	−0.00767720
$925$	7.40517	0.243480
$926$	33.8736	1.11315
$927$	8.68475	0.285245
$928$	−7.84372	−0.257483
$929$	−13.8380	−0.454010	−0.227005	−	0.973894i	$-0.572893\pi$
$929$	−13.8380	−0.454010	−0.227005	+	0.973894i	$0.572893\pi$
$930$	3.12716	0.102544
$931$	−12.9838	−0.425527
$932$	4.66470	0.152797
$933$	11.7644	0.385149
$934$	10.5247	0.344379
$935$	0.00767831	0.000251107 0
$936$	−13.6269	−0.445409
$937$	12.3987	0.405049	0.202524	−	0.979277i	$-0.435085\pi$
$937$	12.3987	0.405049	0.202524	+	0.979277i	$0.435085\pi$
$938$	16.2780	0.531497
$939$	7.55841	0.246659
$940$	−2.03524	−0.0663822
$941$	−32.7414	−1.06734	−0.533669	−	0.845694i	$-0.679187\pi$
$941$	−32.7414	−1.06734	−0.533669	+	0.845694i	$0.679187\pi$
$942$	10.6432	0.346775
$943$	−12.5926	−0.410071
$944$	−41.1122	−1.33809
$945$	4.77149	0.155217
$946$	−4.20504	−0.136718
$947$	18.0766	0.587411	0.293705	−	0.955896i	$-0.405112\pi$
$947$	18.0766	0.587411	0.293705	+	0.955896i	$0.405112\pi$
$948$	−1.64781	−0.0535183
$949$	−2.03555	−0.0660766
$950$	−3.69901	−0.120012
$951$	20.5442	0.666192
$952$	−0.0261382	−0.000847143 0
$953$	19.0454	0.616940	0.308470	−	0.951234i	$-0.400183\pi$
$953$	19.0454	0.616940	0.308470	+	0.951234i	$0.400183\pi$
$954$	−20.8161	−0.673947
$955$	0.474014	0.0153387
$956$	−1.15567	−0.0373771
$957$	−3.35723	−0.108524
$958$	−1.68200	−0.0543431
$959$	−3.22992	−0.104300
$960$	4.34671	0.140290
$961$	−20.9777	−0.676699
$962$	−22.7229	−0.732615
$963$	11.9170	0.384019
$964$	4.28800	0.138107
$965$	−1.85098	−0.0595852
$966$	2.84342	0.0914855
$967$	45.6037	1.46652	0.733258	−	0.679950i	$-0.237999\pi$
$967$	45.6037	1.46652	0.733258	+	0.679950i	$0.237999\pi$
$968$	2.60422	0.0837028
$969$	−0.0123459	−0.000396607 0
$970$	10.7567	0.345378
$971$	−42.1493	−1.35264	−0.676318	−	0.736610i	$-0.736425\pi$
$971$	−42.1493	−1.35264	−0.676318	+	0.736610i	$0.736425\pi$
$972$	−3.93331	−0.126161
$973$	5.34639	0.171398
$974$	−12.5653	−0.402618
$975$	−1.33383	−0.0427166
$976$	−16.3465	−0.523238
$977$	34.2822	1.09678	0.548392	−	0.836222i	$-0.315240\pi$
$977$	34.2822	1.09678	0.548392	+	0.836222i	$0.315240\pi$
$978$	1.14558	0.0366315
$979$	−7.40421	−0.236639
$980$	1.44162	0.0460509
$981$	32.4993	1.03762
$982$	49.2516	1.57168
$983$	21.8129	0.695725	0.347862	−	0.937546i	$-0.386908\pi$
$983$	21.8129	0.695725	0.347862	+	0.937546i	$0.386908\pi$
$984$	−9.75815	−0.311079
$985$	12.5582	0.400137
$986$	0.0593029	0.00188859
$987$	6.39849	0.203666
$988$	1.36084	0.0432942
$989$	6.14279	0.195329
$990$	3.87513	0.123160
$991$	21.9106	0.696014	0.348007	−	0.937492i	$-0.386858\pi$
$991$	21.9106	0.696014	0.348007	+	0.937492i	$0.386858\pi$
$992$	−4.84667	−0.153882
$993$	−2.57149	−0.0816039
$994$	−2.60268	−0.0825520
$995$	−4.30112	−0.136355
$996$	3.15148	0.0998585
$997$	52.1511	1.65164	0.825821	−	0.563933i	$-0.190712\pi$
$997$	52.1511	1.65164	0.825821	+	0.563933i	$0.190712\pi$
$998$	32.8901	1.04112
$999$	27.0307	0.855213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.11	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50747 q^{2} -0.655267 q^{3} +0.272451 q^{4} -1.00000 q^{5} +0.987792 q^{6} -1.30717 q^{7} +2.60422 q^{8} -2.57063 q^{9} +O(q^{10})\)	\(q-1.50747 q^{2} -0.655267 q^{3} +0.272451 q^{4} -1.00000 q^{5} +0.987792 q^{6} -1.30717 q^{7} +2.60422 q^{8} -2.57063 q^{9} +1.50747 q^{10} -1.00000 q^{11} -0.178528 q^{12} +2.03555 q^{13} +1.97051 q^{14} +0.655267 q^{15} -4.47067 q^{16} +0.00767831 q^{17} +3.87513 q^{18} +2.45380 q^{19} -0.272451 q^{20} +0.856545 q^{21} +1.50747 q^{22} -2.20213 q^{23} -1.70646 q^{24} +1.00000 q^{25} -3.06851 q^{26} +3.65025 q^{27} -0.356140 q^{28} -5.12345 q^{29} -0.987792 q^{30} -3.16581 q^{31} +1.53094 q^{32} +0.655267 q^{33} -0.0115748 q^{34} +1.30717 q^{35} -0.700370 q^{36} +7.40517 q^{37} -3.69901 q^{38} -1.33383 q^{39} -2.60422 q^{40} +5.71836 q^{41} -1.29121 q^{42} -2.78948 q^{43} -0.272451 q^{44} +2.57063 q^{45} +3.31964 q^{46} +7.47011 q^{47} +2.92948 q^{48} -5.29131 q^{49} -1.50747 q^{50} -0.00503134 q^{51} +0.554587 q^{52} -5.37173 q^{53} -5.50262 q^{54} +1.00000 q^{55} -3.40416 q^{56} -1.60789 q^{57} +7.72343 q^{58} +9.19598 q^{59} +0.178528 q^{60} +3.65638 q^{61} +4.77234 q^{62} +3.36024 q^{63} +6.63350 q^{64} -2.03555 q^{65} -0.987792 q^{66} +8.26082 q^{67} +0.00209196 q^{68} +1.44298 q^{69} -1.97051 q^{70} -1.32081 q^{71} -6.69447 q^{72} -1.00000 q^{73} -11.1630 q^{74} -0.655267 q^{75} +0.668540 q^{76} +1.30717 q^{77} +2.01070 q^{78} +9.22995 q^{79} +4.47067 q^{80} +5.31999 q^{81} -8.62024 q^{82} -17.6526 q^{83} +0.233367 q^{84} -0.00767831 q^{85} +4.20504 q^{86} +3.35723 q^{87} -2.60422 q^{88} +7.40421 q^{89} -3.87513 q^{90} -2.66081 q^{91} -0.599973 q^{92} +2.07445 q^{93} -11.2609 q^{94} -2.45380 q^{95} -1.00318 q^{96} +7.13564 q^{97} +7.97646 q^{98} +2.57063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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