LMFDB - Embedded newform 4015.2.a.h.1.12

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.11064 q^{2} +3.24263 q^{3} -0.766474 q^{4} +1.00000 q^{5} -3.60140 q^{6} +2.31774 q^{7} +3.07256 q^{8} +7.51466 q^{9} +O(q^{10})$	\(q-1.11064 q^{2} +3.24263 q^{3} -0.766474 q^{4} +1.00000 q^{5} -3.60140 q^{6} +2.31774 q^{7} +3.07256 q^{8} +7.51466 q^{9} -1.11064 q^{10} +1.00000 q^{11} -2.48539 q^{12} -0.104355 q^{13} -2.57417 q^{14} +3.24263 q^{15} -1.87957 q^{16} +3.59955 q^{17} -8.34610 q^{18} +3.68931 q^{19} -0.766474 q^{20} +7.51556 q^{21} -1.11064 q^{22} +7.11088 q^{23} +9.96319 q^{24} +1.00000 q^{25} +0.115901 q^{26} +14.6394 q^{27} -1.77648 q^{28} +4.35072 q^{29} -3.60140 q^{30} +0.187969 q^{31} -4.05760 q^{32} +3.24263 q^{33} -3.99781 q^{34} +2.31774 q^{35} -5.75979 q^{36} -2.99014 q^{37} -4.09750 q^{38} -0.338386 q^{39} +3.07256 q^{40} -9.01977 q^{41} -8.34710 q^{42} -5.30348 q^{43} -0.766474 q^{44} +7.51466 q^{45} -7.89764 q^{46} -12.0184 q^{47} -6.09475 q^{48} -1.62810 q^{49} -1.11064 q^{50} +11.6720 q^{51} +0.0799857 q^{52} -12.2860 q^{53} -16.2591 q^{54} +1.00000 q^{55} +7.12139 q^{56} +11.9631 q^{57} -4.83209 q^{58} -4.26462 q^{59} -2.48539 q^{60} -0.802852 q^{61} -0.208766 q^{62} +17.4170 q^{63} +8.26568 q^{64} -0.104355 q^{65} -3.60140 q^{66} +6.84360 q^{67} -2.75896 q^{68} +23.0580 q^{69} -2.57417 q^{70} -8.85756 q^{71} +23.0893 q^{72} +1.00000 q^{73} +3.32098 q^{74} +3.24263 q^{75} -2.82776 q^{76} +2.31774 q^{77} +0.375826 q^{78} -4.89807 q^{79} -1.87957 q^{80} +24.9261 q^{81} +10.0177 q^{82} +8.39151 q^{83} -5.76048 q^{84} +3.59955 q^{85} +5.89027 q^{86} +14.1078 q^{87} +3.07256 q^{88} +2.19724 q^{89} -8.34610 q^{90} -0.241868 q^{91} -5.45030 q^{92} +0.609514 q^{93} +13.3481 q^{94} +3.68931 q^{95} -13.1573 q^{96} -0.769097 q^{97} +1.80824 q^{98} +7.51466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−1.11064	−0.785343	−0.392671	−	0.919679i	$-0.628449\pi$
$2$	−1.11064	−0.785343	−0.392671	+	0.919679i	$0.628449\pi$
$3$	3.24263	1.87213	0.936067	−	0.351821i	$-0.114438\pi$
$3$	3.24263	1.87213	0.936067	+	0.351821i	$0.114438\pi$
$4$	−0.766474	−0.383237
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.60140	−1.47027
$7$	2.31774	0.876021	0.438011	−	0.898970i	$-0.355683\pi$
$7$	2.31774	0.876021	0.438011	+	0.898970i	$0.355683\pi$
$8$	3.07256	1.08631
$9$	7.51466	2.50489
$10$	−1.11064	−0.351216
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.48539	−0.717471
$13$	−0.104355	−0.0289430	−0.0144715	−	0.999895i	$-0.504607\pi$
$13$	−0.104355	−0.0289430	−0.0144715	+	0.999895i	$0.504607\pi$
$14$	−2.57417	−0.687977
$15$	3.24263	0.837244
$16$	−1.87957	−0.469892
$17$	3.59955	0.873019	0.436509	−	0.899700i	$-0.356215\pi$
$17$	3.59955	0.873019	0.436509	+	0.899700i	$0.356215\pi$
$18$	−8.34610	−1.96719
$19$	3.68931	0.846386	0.423193	−	0.906040i	$-0.360909\pi$
$19$	3.68931	0.846386	0.423193	+	0.906040i	$0.360909\pi$
$20$	−0.766474	−0.171389
$21$	7.51556	1.64003
$22$	−1.11064	−0.236790
$23$	7.11088	1.48272	0.741360	−	0.671107i	$-0.234181\pi$
$23$	7.11088	1.48272	0.741360	+	0.671107i	$0.234181\pi$
$24$	9.96319	2.03373
$25$	1.00000	0.200000
$26$	0.115901	0.0227301
$27$	14.6394	2.81735
$28$	−1.77648	−0.335724
$29$	4.35072	0.807908	0.403954	−	0.914779i	$-0.367636\pi$
$29$	4.35072	0.807908	0.403954	+	0.914779i	$0.367636\pi$
$30$	−3.60140	−0.657523
$31$	0.187969	0.0337602	0.0168801	−	0.999858i	$-0.494627\pi$
$31$	0.187969	0.0337602	0.0168801	+	0.999858i	$0.494627\pi$
$32$	−4.05760	−0.717289
$33$	3.24263	0.564470
$34$	−3.99781	−0.685619
$35$	2.31774	0.391769
$36$	−5.75979	−0.959966
$37$	−2.99014	−0.491576	−0.245788	−	0.969324i	$-0.579047\pi$
$37$	−2.99014	−0.491576	−0.245788	+	0.969324i	$0.579047\pi$
$38$	−4.09750	−0.664703
$39$	−0.338386	−0.0541851
$40$	3.07256	0.485815
$41$	−9.01977	−1.40865	−0.704325	−	0.709877i	$-0.748750\pi$
$41$	−9.01977	−1.40865	−0.704325	+	0.709877i	$0.748750\pi$
$42$	−8.34710	−1.28799
$43$	−5.30348	−0.808773	−0.404387	−	0.914588i	$-0.632515\pi$
$43$	−5.30348	−0.808773	−0.404387	+	0.914588i	$0.632515\pi$
$44$	−0.766474	−0.115550
$45$	7.51466	1.12022
$46$	−7.89764	−1.16444
$47$	−12.0184	−1.75306	−0.876532	−	0.481344i	$-0.840149\pi$
$47$	−12.0184	−1.75306	−0.876532	+	0.481344i	$0.840149\pi$
$48$	−6.09475	−0.879701
$49$	−1.62810	−0.232586
$50$	−1.11064	−0.157069
$51$	11.6720	1.63441
$52$	0.0799857	0.0110920
$53$	−12.2860	−1.68762	−0.843808	−	0.536646i	$-0.819691\pi$
$53$	−12.2860	−1.68762	−0.843808	+	0.536646i	$0.819691\pi$
$54$	−16.2591	−2.21258
$55$	1.00000	0.134840
$56$	7.12139	0.951635
$57$	11.9631	1.58455
$58$	−4.83209	−0.634484
$59$	−4.26462	−0.555206	−0.277603	−	0.960696i	$-0.589540\pi$
$59$	−4.26462	−0.555206	−0.277603	+	0.960696i	$0.589540\pi$
$60$	−2.48539	−0.320863
$61$	−0.802852	−0.102795	−0.0513973	−	0.998678i	$-0.516367\pi$
$61$	−0.802852	−0.102795	−0.0513973	+	0.998678i	$0.516367\pi$
$62$	−0.208766	−0.0265133
$63$	17.4170	2.19433
$64$	8.26568	1.03321
$65$	−0.104355	−0.0129437
$66$	−3.60140	−0.443302
$67$	6.84360	0.836079	0.418039	−	0.908429i	$-0.362717\pi$
$67$	6.84360	0.836079	0.418039	+	0.908429i	$0.362717\pi$
$68$	−2.75896	−0.334573
$69$	23.0580	2.77585
$70$	−2.57417	−0.307673
$71$	−8.85756	−1.05120	−0.525600	−	0.850732i	$-0.676159\pi$
$71$	−8.85756	−1.05120	−0.525600	+	0.850732i	$0.676159\pi$
$72$	23.0893	2.72110
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	3.32098	0.386056
$75$	3.24263	0.374427
$76$	−2.82776	−0.324366
$77$	2.31774	0.264130
$78$	0.375826	0.0425539
$79$	−4.89807	−0.551076	−0.275538	−	0.961290i	$-0.588856\pi$
$79$	−4.89807	−0.551076	−0.275538	+	0.961290i	$0.588856\pi$
$80$	−1.87957	−0.210142
$81$	24.9261	2.76957
$82$	10.0177	1.10627
$83$	8.39151	0.921088	0.460544	−	0.887637i	$-0.347654\pi$
$83$	8.39151	0.921088	0.460544	+	0.887637i	$0.347654\pi$
$84$	−5.76048	−0.628520
$85$	3.59955	0.390426
$86$	5.89027	0.635164
$87$	14.1078	1.51251
$88$	3.07256	0.327536
$89$	2.19724	0.232907	0.116454	−	0.993196i	$-0.462847\pi$
$89$	2.19724	0.232907	0.116454	+	0.993196i	$0.462847\pi$
$90$	−8.34610	−0.879756
$91$	−0.241868	−0.0253547
$92$	−5.45030	−0.568233
$93$	0.609514	0.0632037
$94$	13.3481	1.37676
$95$	3.68931	0.378515
$96$	−13.1573	−1.34286
$97$	−0.769097	−0.0780900	−0.0390450	−	0.999237i	$-0.512432\pi$
$97$	−0.769097	−0.0780900	−0.0390450	+	0.999237i	$0.512432\pi$
$98$	1.80824	0.182660
$99$	7.51466	0.755252
$100$	−0.766474	−0.0766474
$101$	−12.0828	−1.20229	−0.601143	−	0.799141i	$-0.705288\pi$
$101$	−12.0828	−1.20229	−0.601143	+	0.799141i	$0.705288\pi$
$102$	−12.9634	−1.28357
$103$	−2.23624	−0.220344	−0.110172	−	0.993913i	$-0.535140\pi$
$103$	−2.23624	−0.220344	−0.110172	+	0.993913i	$0.535140\pi$
$104$	−0.320638	−0.0314412
$105$	7.51556	0.733444
$106$	13.6454	1.32536
$107$	11.7229	1.13330	0.566649	−	0.823959i	$-0.308239\pi$
$107$	11.7229	1.13330	0.566649	+	0.823959i	$0.308239\pi$
$108$	−11.2207	−1.07971
$109$	−6.69712	−0.641468	−0.320734	−	0.947169i	$-0.603930\pi$
$109$	−6.69712	−0.641468	−0.320734	+	0.947169i	$0.603930\pi$
$110$	−1.11064	−0.105896
$111$	−9.69593	−0.920297
$112$	−4.35634	−0.411636
$113$	−10.6623	−1.00302	−0.501511	−	0.865151i	$-0.667222\pi$
$113$	−10.6623	−1.00302	−0.501511	+	0.865151i	$0.667222\pi$
$114$	−13.2867	−1.24441
$115$	7.11088	0.663093
$116$	−3.33471	−0.309620
$117$	−0.784195	−0.0724989
$118$	4.73647	0.436027
$119$	8.34280	0.764783
$120$	9.96319	0.909511
$121$	1.00000	0.0909091
$122$	0.891681	0.0807290
$123$	−29.2478	−2.63718
$124$	−0.144073	−0.0129382
$125$	1.00000	0.0894427
$126$	−19.3440	−1.72330
$127$	−8.78544	−0.779582	−0.389791	−	0.920903i	$-0.627453\pi$
$127$	−8.78544	−0.779582	−0.389791	+	0.920903i	$0.627453\pi$
$128$	−1.06501	−0.0941347
$129$	−17.1972	−1.51413
$130$	0.115901	0.0101652
$131$	1.42501	0.124504	0.0622519	−	0.998060i	$-0.480172\pi$
$131$	1.42501	0.124504	0.0622519	+	0.998060i	$0.480172\pi$
$132$	−2.48539	−0.216326
$133$	8.55084	0.741452
$134$	−7.60079	−0.656608
$135$	14.6394	1.25996
$136$	11.0598	0.948373
$137$	1.06013	0.0905734	0.0452867	−	0.998974i	$-0.485580\pi$
$137$	1.06013	0.0905734	0.0452867	+	0.998974i	$0.485580\pi$
$138$	−25.6091	−2.17999
$139$	3.28018	0.278221	0.139111	−	0.990277i	$-0.455576\pi$
$139$	3.28018	0.278221	0.139111	+	0.990277i	$0.455576\pi$
$140$	−1.77648	−0.150140
$141$	−38.9712	−3.28197
$142$	9.83758	0.825551
$143$	−0.104355	−0.00872663
$144$	−14.1243	−1.17703
$145$	4.35072	0.361307
$146$	−1.11064	−0.0919174
$147$	−5.27934	−0.435433
$148$	2.29187	0.188390
$149$	1.07627	0.0881711	0.0440856	−	0.999028i	$-0.485963\pi$
$149$	1.07627	0.0881711	0.0440856	+	0.999028i	$0.485963\pi$
$150$	−3.60140	−0.294053
$151$	12.7304	1.03599	0.517994	−	0.855384i	$-0.326679\pi$
$151$	12.7304	1.03599	0.517994	+	0.855384i	$0.326679\pi$
$152$	11.3356	0.919442
$153$	27.0494	2.18681
$154$	−2.57417	−0.207433
$155$	0.187969	0.0150980
$156$	0.259364	0.0207657
$157$	16.1169	1.28627	0.643136	−	0.765752i	$-0.277633\pi$
$157$	16.1169	1.28627	0.643136	+	0.765752i	$0.277633\pi$
$158$	5.44000	0.432783
$159$	−39.8391	−3.15944
$160$	−4.05760	−0.320781
$161$	16.4811	1.29889
$162$	−27.6840	−2.17506
$163$	−5.22058	−0.408907	−0.204454	−	0.978876i	$-0.565542\pi$
$163$	−5.22058	−0.408907	−0.204454	+	0.978876i	$0.565542\pi$
$164$	6.91342	0.539847
$165$	3.24263	0.252439
$166$	−9.31997	−0.723370
$167$	1.12152	0.0867855	0.0433928	−	0.999058i	$-0.486183\pi$
$167$	1.12152	0.0867855	0.0433928	+	0.999058i	$0.486183\pi$
$168$	23.0920	1.78159
$169$	−12.9891	−0.999162
$170$	−3.99781	−0.306618
$171$	27.7239	2.12010
$172$	4.06498	0.309952
$173$	−11.1407	−0.847010	−0.423505	−	0.905894i	$-0.639200\pi$
$173$	−11.1407	−0.847010	−0.423505	+	0.905894i	$0.639200\pi$
$174$	−15.6687	−1.18784
$175$	2.31774	0.175204
$176$	−1.87957	−0.141678
$177$	−13.8286	−1.03942
$178$	−2.44035	−0.182912
$179$	5.42469	0.405460	0.202730	−	0.979235i	$-0.435019\pi$
$179$	5.42469	0.405460	0.202730	+	0.979235i	$0.435019\pi$
$180$	−5.75979	−0.429310
$181$	−24.4907	−1.82038	−0.910190	−	0.414191i	$-0.864065\pi$
$181$	−24.4907	−1.82038	−0.910190	+	0.414191i	$0.864065\pi$
$182$	0.268629	0.0199121
$183$	−2.60335	−0.192445
$184$	21.8486	1.61070
$185$	−2.99014	−0.219840
$186$	−0.676952	−0.0496365
$187$	3.59955	0.263225
$188$	9.21179	0.671839
$189$	33.9302	2.46806
$190$	−4.09750	−0.297264
$191$	−5.73400	−0.414898	−0.207449	−	0.978246i	$-0.566516\pi$
$191$	−5.73400	−0.414898	−0.207449	+	0.978246i	$0.566516\pi$
$192$	26.8025	1.93431
$193$	−6.13432	−0.441558	−0.220779	−	0.975324i	$-0.570860\pi$
$193$	−6.13432	−0.441558	−0.220779	+	0.975324i	$0.570860\pi$
$194$	0.854192	0.0613274
$195$	−0.338386	−0.0242323
$196$	1.24790	0.0891357
$197$	21.1772	1.50881	0.754406	−	0.656408i	$-0.227925\pi$
$197$	21.1772	1.50881	0.754406	+	0.656408i	$0.227925\pi$
$198$	−8.34610	−0.593131
$199$	−15.3514	−1.08823	−0.544114	−	0.839011i	$-0.683134\pi$
$199$	−15.3514	−1.08823	−0.544114	+	0.839011i	$0.683134\pi$
$200$	3.07256	0.217263
$201$	22.1913	1.56525
$202$	13.4197	0.944207
$203$	10.0838	0.707745
$204$	−8.94630	−0.626366
$205$	−9.01977	−0.629968
$206$	2.48367	0.173045
$207$	53.4358	3.71405
$208$	0.196143	0.0136001
$209$	3.68931	0.255195
$210$	−8.34710	−0.576004
$211$	−5.00689	−0.344688	−0.172344	−	0.985037i	$-0.555134\pi$
$211$	−5.00689	−0.344688	−0.172344	+	0.985037i	$0.555134\pi$
$212$	9.41692	0.646757
$213$	−28.7218	−1.96799
$214$	−13.0200	−0.890028
$215$	−5.30348	−0.361694
$216$	44.9804	3.06053
$217$	0.435662	0.0295747
$218$	7.43810	0.503772
$219$	3.24263	0.219117
$220$	−0.766474	−0.0516757
$221$	−0.375632	−0.0252678
$222$	10.7687	0.722748
$223$	1.46903	0.0983736	0.0491868	−	0.998790i	$-0.484337\pi$
$223$	1.46903	0.0983736	0.0491868	+	0.998790i	$0.484337\pi$
$224$	−9.40444	−0.628360
$225$	7.51466	0.500977
$226$	11.8420	0.787716
$227$	14.8681	0.986829	0.493414	−	0.869794i	$-0.335749\pi$
$227$	14.8681	0.986829	0.493414	+	0.869794i	$0.335749\pi$
$228$	−9.16939	−0.607258
$229$	−7.39386	−0.488600	−0.244300	−	0.969700i	$-0.578558\pi$
$229$	−7.39386	−0.488600	−0.244300	+	0.969700i	$0.578558\pi$
$230$	−7.89764	−0.520755
$231$	7.51556	0.494488
$232$	13.3678	0.877642
$233$	−9.19061	−0.602097	−0.301048	−	0.953609i	$-0.597337\pi$
$233$	−9.19061	−0.602097	−0.301048	+	0.953609i	$0.597337\pi$
$234$	0.870960	0.0569364
$235$	−12.0184	−0.783994
$236$	3.26872	0.212776
$237$	−15.8826	−1.03169
$238$	−9.26586	−0.600617
$239$	−17.5535	−1.13544	−0.567720	−	0.823222i	$-0.692174\pi$
$239$	−17.5535	−1.13544	−0.567720	+	0.823222i	$0.692174\pi$
$240$	−6.09475	−0.393414
$241$	13.9738	0.900133	0.450066	−	0.892995i	$-0.351400\pi$
$241$	13.9738	0.900133	0.450066	+	0.892995i	$0.351400\pi$
$242$	−1.11064	−0.0713948
$243$	36.9081	2.36766
$244$	0.615366	0.0393947
$245$	−1.62810	−0.104016
$246$	32.4838	2.07109
$247$	−0.384999	−0.0244969
$248$	0.577546	0.0366742
$249$	27.2106	1.72440
$250$	−1.11064	−0.0702432
$251$	−15.8761	−1.00209	−0.501044	−	0.865422i	$-0.667050\pi$
$251$	−15.8761	−1.00209	−0.501044	+	0.865422i	$0.667050\pi$
$252$	−13.3497	−0.840950
$253$	7.11088	0.447057
$254$	9.75748	0.612239
$255$	11.6720	0.730930
$256$	−15.3485	−0.959281
$257$	−10.8144	−0.674583	−0.337291	−	0.941400i	$-0.609511\pi$
$257$	−10.8144	−0.674583	−0.337291	+	0.941400i	$0.609511\pi$
$258$	19.1000	1.18911
$259$	−6.93035	−0.430631
$260$	0.0799857	0.00496050
$261$	32.6942	2.02372
$262$	−1.58268	−0.0977782
$263$	9.71885	0.599290	0.299645	−	0.954051i	$-0.403132\pi$
$263$	9.71885	0.599290	0.299645	+	0.954051i	$0.403132\pi$
$264$	9.96319	0.613192
$265$	−12.2860	−0.754725
$266$	−9.49693	−0.582294
$267$	7.12485	0.436034
$268$	−5.24544	−0.320416
$269$	14.9942	0.914212	0.457106	−	0.889412i	$-0.348886\pi$
$269$	14.9942	0.914212	0.457106	+	0.889412i	$0.348886\pi$
$270$	−16.2591	−0.989498
$271$	17.1807	1.04365	0.521827	−	0.853052i	$-0.325251\pi$
$271$	17.1807	1.04365	0.521827	+	0.853052i	$0.325251\pi$
$272$	−6.76560	−0.410225
$273$	−0.784289	−0.0474673
$274$	−1.17743	−0.0711312
$275$	1.00000	0.0603023
$276$	−17.6733	−1.06381
$277$	21.3363	1.28198	0.640988	−	0.767551i	$-0.278525\pi$
$277$	21.3363	1.28198	0.640988	+	0.767551i	$0.278525\pi$
$278$	−3.64310	−0.218499
$279$	1.41252	0.0845655
$280$	7.12139	0.425584
$281$	5.93349	0.353962	0.176981	−	0.984214i	$-0.443367\pi$
$281$	5.93349	0.353962	0.176981	+	0.984214i	$0.443367\pi$
$282$	43.2831	2.57747
$283$	10.5608	0.627775	0.313888	−	0.949460i	$-0.398368\pi$
$283$	10.5608	0.627775	0.313888	+	0.949460i	$0.398368\pi$
$284$	6.78909	0.402858
$285$	11.9631	0.708631
$286$	0.115901	0.00685340
$287$	−20.9054	−1.23401
$288$	−30.4915	−1.79673
$289$	−4.04325	−0.237838
$290$	−4.83209	−0.283750
$291$	−2.49390	−0.146195
$292$	−0.766474	−0.0448545
$293$	17.5725	1.02660	0.513298	−	0.858211i	$-0.328424\pi$
$293$	17.5725	1.02660	0.513298	+	0.858211i	$0.328424\pi$
$294$	5.86346	0.341964
$295$	−4.26462	−0.248296
$296$	−9.18740	−0.534006
$297$	14.6394	0.849463
$298$	−1.19535	−0.0692445
$299$	−0.742058	−0.0429143
$300$	−2.48539	−0.143494
$301$	−12.2921	−0.708503
$302$	−14.1390	−0.813605
$303$	−39.1802	−2.25084
$304$	−6.93431	−0.397710
$305$	−0.802852	−0.0459712
$306$	−30.0422	−1.71740
$307$	28.5979	1.63217	0.816083	−	0.577935i	$-0.196141\pi$
$307$	28.5979	1.63217	0.816083	+	0.577935i	$0.196141\pi$
$308$	−1.77648	−0.101225
$309$	−7.25132	−0.412513
$310$	−0.208766	−0.0118571
$311$	−7.86587	−0.446033	−0.223016	−	0.974815i	$-0.571590\pi$
$311$	−7.86587	−0.446033	−0.223016	+	0.974815i	$0.571590\pi$
$312$	−1.03971	−0.0588621
$313$	−34.7967	−1.96683	−0.983414	−	0.181375i	$-0.941945\pi$
$313$	−34.7967	−1.96683	−0.983414	+	0.181375i	$0.941945\pi$
$314$	−17.9002	−1.01016
$315$	17.4170	0.981336
$316$	3.75425	0.211193
$317$	13.8673	0.778867	0.389434	−	0.921055i	$-0.372671\pi$
$317$	13.8673	0.778867	0.389434	+	0.921055i	$0.372671\pi$
$318$	44.2469	2.48124
$319$	4.35072	0.243593
$320$	8.26568	0.462065
$321$	38.0132	2.12169
$322$	−18.3046	−1.02008
$323$	13.2799	0.738911
$324$	−19.1052	−1.06140
$325$	−0.104355	−0.00578859
$326$	5.79819	0.321132
$327$	−21.7163	−1.20091
$328$	−27.7138	−1.53024
$329$	−27.8555	−1.53572
$330$	−3.60140	−0.198251
$331$	−0.832550	−0.0457611	−0.0228806	−	0.999738i	$-0.507284\pi$
$331$	−0.832550	−0.0457611	−0.0228806	+	0.999738i	$0.507284\pi$
$332$	−6.43188	−0.352995
$333$	−22.4699	−1.23134
$334$	−1.24560	−0.0681563
$335$	6.84360	0.373906
$336$	−14.1260	−0.770637
$337$	−6.98939	−0.380736	−0.190368	−	0.981713i	$-0.560968\pi$
$337$	−6.98939	−0.380736	−0.190368	+	0.981713i	$0.560968\pi$
$338$	14.4263	0.784685
$339$	−34.5738	−1.87779
$340$	−2.75896	−0.149626
$341$	0.187969	0.0101791
$342$	−30.7913	−1.66501
$343$	−19.9977	−1.07977
$344$	−16.2953	−0.878582
$345$	23.0580	1.24140
$346$	12.3733	0.665193
$347$	17.4871	0.938755	0.469378	−	0.882998i	$-0.344478\pi$
$347$	17.4871	0.938755	0.469378	+	0.882998i	$0.344478\pi$
$348$	−10.8132	−0.579651
$349$	19.0408	1.01923	0.509616	−	0.860402i	$-0.329788\pi$
$349$	19.0408	1.01923	0.509616	+	0.860402i	$0.329788\pi$
$350$	−2.57417	−0.137595
$351$	−1.52770	−0.0815425
$352$	−4.05760	−0.216271
$353$	3.33126	0.177305	0.0886524	−	0.996063i	$-0.471744\pi$
$353$	3.33126	0.177305	0.0886524	+	0.996063i	$0.471744\pi$
$354$	15.3586	0.816301
$355$	−8.85756	−0.470111
$356$	−1.68413	−0.0892587
$357$	27.0526	1.43178
$358$	−6.02489	−0.318425
$359$	35.6412	1.88107	0.940535	−	0.339696i	$-0.110324\pi$
$359$	35.6412	1.88107	0.940535	+	0.339696i	$0.110324\pi$
$360$	23.0893	1.21691
$361$	−5.38899	−0.283631
$362$	27.2004	1.42962
$363$	3.24263	0.170194
$364$	0.185386	0.00971685
$365$	1.00000	0.0523424
$366$	2.89139	0.151136
$367$	31.4974	1.64415	0.822075	−	0.569379i	$-0.192816\pi$
$367$	31.4974	1.64415	0.822075	+	0.569379i	$0.192816\pi$
$368$	−13.3654	−0.696719
$369$	−67.7805	−3.52851
$370$	3.32098	0.172649
$371$	−28.4757	−1.47839
$372$	−0.467177	−0.0242220
$373$	−18.3239	−0.948775	−0.474388	−	0.880316i	$-0.657331\pi$
$373$	−18.3239	−0.948775	−0.474388	+	0.880316i	$0.657331\pi$
$374$	−3.99781	−0.206722
$375$	3.24263	0.167449
$376$	−36.9273	−1.90438
$377$	−0.454021	−0.0233832
$378$	−37.6843	−1.93827
$379$	−26.1585	−1.34367	−0.671835	−	0.740701i	$-0.734494\pi$
$379$	−26.1585	−1.34367	−0.671835	+	0.740701i	$0.734494\pi$
$380$	−2.82776	−0.145061
$381$	−28.4879	−1.45948
$382$	6.36843	0.325837
$383$	21.8437	1.11616	0.558082	−	0.829786i	$-0.311538\pi$
$383$	21.8437	1.11616	0.558082	+	0.829786i	$0.311538\pi$
$384$	−3.45344	−0.176233
$385$	2.31774	0.118123
$386$	6.81304	0.346775
$387$	−39.8538	−2.02588
$388$	0.589493	0.0299270
$389$	21.6212	1.09624	0.548119	−	0.836401i	$-0.315344\pi$
$389$	21.6212	1.09624	0.548119	+	0.836401i	$0.315344\pi$
$390$	0.375826	0.0190307
$391$	25.5959	1.29444
$392$	−5.00245	−0.252662
$393$	4.62079	0.233088
$394$	−23.5203	−1.18493
$395$	−4.89807	−0.246449
$396$	−5.75979	−0.289441
$397$	−23.7727	−1.19312	−0.596560	−	0.802569i	$-0.703466\pi$
$397$	−23.7727	−1.19312	−0.596560	+	0.802569i	$0.703466\pi$
$398$	17.0499	0.854632
$399$	27.7272	1.38810
$400$	−1.87957	−0.0939784
$401$	12.7742	0.637911	0.318955	−	0.947770i	$-0.396668\pi$
$401$	12.7742	0.637911	0.318955	+	0.947770i	$0.396668\pi$
$402$	−24.6466	−1.22926
$403$	−0.0196156	−0.000977121 0
$404$	9.26118	0.460761
$405$	24.9261	1.23859
$406$	−11.1995	−0.555822
$407$	−2.99014	−0.148216
$408$	35.8630	1.77548
$409$	−19.0333	−0.941136	−0.470568	−	0.882364i	$-0.655951\pi$
$409$	−19.0333	−0.941136	−0.470568	+	0.882364i	$0.655951\pi$
$410$	10.0177	0.494741
$411$	3.43763	0.169566
$412$	1.71402	0.0844439
$413$	−9.88426	−0.486373
$414$	−59.3481	−2.91680
$415$	8.39151	0.411923
$416$	0.423432	0.0207605
$417$	10.6364	0.520867
$418$	−4.09750	−0.200415
$419$	−27.3911	−1.33814	−0.669072	−	0.743198i	$-0.733308\pi$
$419$	−27.3911	−1.33814	−0.669072	+	0.743198i	$0.733308\pi$
$420$	−5.76048	−0.281083
$421$	15.2897	0.745176	0.372588	−	0.927997i	$-0.378471\pi$
$421$	15.2897	0.745176	0.372588	+	0.927997i	$0.378471\pi$
$422$	5.56086	0.270699
$423$	−90.3142	−4.39123
$424$	−37.7496	−1.83328
$425$	3.59955	0.174604
$426$	31.8996	1.54554
$427$	−1.86080	−0.0900504
$428$	−8.98533	−0.434322
$429$	−0.338386	−0.0163374
$430$	5.89027	0.284054
$431$	−21.5046	−1.03584	−0.517919	−	0.855430i	$-0.673293\pi$
$431$	−21.5046	−1.03584	−0.517919	+	0.855430i	$0.673293\pi$
$432$	−27.5157	−1.32385
$433$	34.0633	1.63698	0.818489	−	0.574522i	$-0.194812\pi$
$433$	34.0633	1.63698	0.818489	+	0.574522i	$0.194812\pi$
$434$	−0.483865	−0.0232263
$435$	14.1078	0.676416
$436$	5.13317	0.245834
$437$	26.2342	1.25495
$438$	−3.60140	−0.172082
$439$	−22.3758	−1.06794	−0.533968	−	0.845504i	$-0.679300\pi$
$439$	−22.3758	−1.06794	−0.533968	+	0.845504i	$0.679300\pi$
$440$	3.07256	0.146479
$441$	−12.2347	−0.582602
$442$	0.417193	0.0198438
$443$	10.8216	0.514147	0.257074	−	0.966392i	$-0.417242\pi$
$443$	10.8216	0.514147	0.257074	+	0.966392i	$0.417242\pi$
$444$	7.43168	0.352692
$445$	2.19724	0.104159
$446$	−1.63157	−0.0772569
$447$	3.48993	0.165068
$448$	19.1576	0.905114
$449$	34.7691	1.64085	0.820427	−	0.571751i	$-0.193736\pi$
$449$	34.7691	1.64085	0.820427	+	0.571751i	$0.193736\pi$
$450$	−8.34610	−0.393439
$451$	−9.01977	−0.424724
$452$	8.17236	0.384395
$453$	41.2801	1.93951
$454$	−16.5131	−0.774998
$455$	−0.241868	−0.0113389
$456$	36.7573	1.72132
$457$	−19.5949	−0.916612	−0.458306	−	0.888795i	$-0.651544\pi$
$457$	−19.5949	−0.916612	−0.458306	+	0.888795i	$0.651544\pi$
$458$	8.21193	0.383718
$459$	52.6952	2.45960
$460$	−5.45030	−0.254122
$461$	−8.50366	−0.396055	−0.198027	−	0.980196i	$-0.563454\pi$
$461$	−8.50366	−0.396055	−0.198027	+	0.980196i	$0.563454\pi$
$462$	−8.34710	−0.388342
$463$	−1.52409	−0.0708303	−0.0354152	−	0.999373i	$-0.511275\pi$
$463$	−1.52409	−0.0708303	−0.0354152	+	0.999373i	$0.511275\pi$
$464$	−8.17747	−0.379630
$465$	0.609514	0.0282655
$466$	10.2075	0.472852
$467$	−8.67250	−0.401315	−0.200658	−	0.979661i	$-0.564308\pi$
$467$	−8.67250	−0.401315	−0.200658	+	0.979661i	$0.564308\pi$
$468$	0.601065	0.0277843
$469$	15.8617	0.732423
$470$	13.3481	0.615704
$471$	52.2613	2.40807
$472$	−13.1033	−0.603129
$473$	−5.30348	−0.243854
$474$	17.6399	0.810229
$475$	3.68931	0.169277
$476$	−6.39454	−0.293093
$477$	−92.3253	−4.22729
$478$	19.4956	0.891709
$479$	−30.7065	−1.40301	−0.701507	−	0.712662i	$-0.747489\pi$
$479$	−30.7065	−1.40301	−0.701507	+	0.712662i	$0.747489\pi$
$480$	−13.1573	−0.600546
$481$	0.312037	0.0142277
$482$	−15.5199	−0.706912
$483$	53.4422	2.43171
$484$	−0.766474	−0.0348397
$485$	−0.769097	−0.0349229
$486$	−40.9917	−1.85942
$487$	−5.66639	−0.256768	−0.128384	−	0.991725i	$-0.540979\pi$
$487$	−5.66639	−0.256768	−0.128384	+	0.991725i	$0.540979\pi$
$488$	−2.46681	−0.111667
$489$	−16.9284	−0.765529
$490$	1.80824	0.0816880
$491$	27.3569	1.23460	0.617300	−	0.786728i	$-0.288227\pi$
$491$	27.3569	1.23460	0.617300	+	0.786728i	$0.288227\pi$
$492$	22.4177	1.01067
$493$	15.6606	0.705319
$494$	0.427596	0.0192385
$495$	7.51466	0.337759
$496$	−0.353301	−0.0158637
$497$	−20.5295	−0.920873
$498$	−30.2212	−1.35425
$499$	2.61647	0.117129	0.0585647	−	0.998284i	$-0.481348\pi$
$499$	2.61647	0.117129	0.0585647	+	0.998284i	$0.481348\pi$
$500$	−0.766474	−0.0342778
$501$	3.63666	0.162474
$502$	17.6326	0.786982
$503$	14.7349	0.656996	0.328498	−	0.944505i	$-0.393458\pi$
$503$	14.7349	0.656996	0.328498	+	0.944505i	$0.393458\pi$
$504$	53.5148	2.38374
$505$	−12.0828	−0.537679
$506$	−7.89764	−0.351093
$507$	−42.1189	−1.87057
$508$	6.73381	0.298765
$509$	24.3139	1.07769	0.538847	−	0.842404i	$-0.318860\pi$
$509$	24.3139	1.07769	0.538847	+	0.842404i	$0.318860\pi$
$510$	−12.9634	−0.574030
$511$	2.31774	0.102531
$512$	19.1767	0.847499
$513$	54.0092	2.38457
$514$	12.0109	0.529778
$515$	−2.23624	−0.0985407
$516$	13.1812	0.580272
$517$	−12.0184	−0.528568
$518$	7.69714	0.338193
$519$	−36.1251	−1.58572
$520$	−0.320638	−0.0140609
$521$	18.4182	0.806917	0.403459	−	0.914998i	$-0.367808\pi$
$521$	18.4182	0.806917	0.403459	+	0.914998i	$0.367808\pi$
$522$	−36.3115	−1.58931
$523$	9.39261	0.410710	0.205355	−	0.978688i	$-0.434165\pi$
$523$	9.39261	0.410710	0.205355	+	0.978688i	$0.434165\pi$
$524$	−1.09223	−0.0477145
$525$	7.51556	0.328006
$526$	−10.7942	−0.470648
$527$	0.676603	0.0294733
$528$	−6.09475	−0.265240
$529$	27.5646	1.19846
$530$	13.6454	0.592717
$531$	−32.0472	−1.39073
$532$	−6.55400	−0.284152
$533$	0.941261	0.0407705
$534$	−7.91316	−0.342436
$535$	11.7229	0.506827
$536$	21.0274	0.908245
$537$	17.5903	0.759076
$538$	−16.6532	−0.717969
$539$	−1.62810	−0.0701274
$540$	−11.2207	−0.482862
$541$	26.4794	1.13844	0.569220	−	0.822185i	$-0.307245\pi$
$541$	26.4794	1.13844	0.569220	+	0.822185i	$0.307245\pi$
$542$	−19.0816	−0.819625
$543$	−79.4144	−3.40800
$544$	−14.6055	−0.626206
$545$	−6.69712	−0.286873
$546$	0.871064	0.0372781
$547$	23.5934	1.00878	0.504391	−	0.863475i	$-0.331717\pi$
$547$	23.5934	1.00878	0.504391	+	0.863475i	$0.331717\pi$
$548$	−0.812566	−0.0347111
$549$	−6.03316	−0.257489
$550$	−1.11064	−0.0473579
$551$	16.0511	0.683802
$552$	70.8470	3.01545
$553$	−11.3524	−0.482754
$554$	−23.6970	−1.00679
$555$	−9.69593	−0.411569
$556$	−2.51417	−0.106625
$557$	−27.7533	−1.17595	−0.587973	−	0.808881i	$-0.700074\pi$
$557$	−27.7533	−1.17595	−0.587973	+	0.808881i	$0.700074\pi$
$558$	−1.56881	−0.0664129
$559$	0.553447	0.0234083
$560$	−4.35634	−0.184089
$561$	11.6720	0.492793
$562$	−6.58998	−0.277982
$563$	−22.3231	−0.940808	−0.470404	−	0.882451i	$-0.655892\pi$
$563$	−22.3231	−0.940808	−0.470404	+	0.882451i	$0.655892\pi$
$564$	29.8704	1.25777
$565$	−10.6623	−0.448565
$566$	−11.7293	−0.493019
$567$	57.7722	2.42620
$568$	−27.2154	−1.14193
$569$	4.78450	0.200577	0.100288	−	0.994958i	$-0.468023\pi$
$569$	4.78450	0.200577	0.100288	+	0.994958i	$0.468023\pi$
$570$	−13.2867	−0.556518
$571$	17.6031	0.736668	0.368334	−	0.929693i	$-0.379928\pi$
$571$	17.6031	0.736668	0.368334	+	0.929693i	$0.379928\pi$
$572$	0.0799857	0.00334437
$573$	−18.5933	−0.776745
$574$	23.2184	0.969119
$575$	7.11088	0.296544
$576$	62.1137	2.58807
$577$	−19.6879	−0.819616	−0.409808	−	0.912172i	$-0.634404\pi$
$577$	−19.6879	−0.819616	−0.409808	+	0.912172i	$0.634404\pi$
$578$	4.49060	0.186784
$579$	−19.8914	−0.826656
$580$	−3.33471	−0.138466
$581$	19.4493	0.806893
$582$	2.76983	0.114813
$583$	−12.2860	−0.508835
$584$	3.07256	0.127144
$585$	−0.784195	−0.0324225
$586$	−19.5167	−0.806229
$587$	−16.7400	−0.690934	−0.345467	−	0.938431i	$-0.612279\pi$
$587$	−16.7400	−0.690934	−0.345467	+	0.938431i	$0.612279\pi$
$588$	4.04648	0.166874
$589$	0.693476	0.0285742
$590$	4.73647	0.194997
$591$	68.6698	2.82470
$592$	5.62018	0.230988
$593$	−34.5839	−1.42019	−0.710096	−	0.704105i	$-0.751348\pi$
$593$	−34.5839	−1.42019	−0.710096	+	0.704105i	$0.751348\pi$
$594$	−16.2591	−0.667119
$595$	8.34280	0.342021
$596$	−0.824930	−0.0337905
$597$	−49.7788	−2.03731
$598$	0.824161	0.0337024
$599$	1.02128	0.0417283	0.0208642	−	0.999782i	$-0.493358\pi$
$599$	1.02128	0.0417283	0.0208642	+	0.999782i	$0.493358\pi$
$600$	9.96319	0.406745
$601$	36.9998	1.50925	0.754626	−	0.656156i	$-0.227818\pi$
$601$	36.9998	1.50925	0.754626	+	0.656156i	$0.227818\pi$
$602$	13.6521	0.556417
$603$	51.4273	2.09428
$604$	−9.75755	−0.397029
$605$	1.00000	0.0406558
$606$	43.5151	1.76768
$607$	−38.3325	−1.55587	−0.777934	−	0.628346i	$-0.783732\pi$
$607$	−38.3325	−1.55587	−0.777934	+	0.628346i	$0.783732\pi$
$608$	−14.9697	−0.607103
$609$	32.6981	1.32499
$610$	0.891681	0.0361031
$611$	1.25418	0.0507389
$612$	−20.7327	−0.838068
$613$	−7.99889	−0.323072	−0.161536	−	0.986867i	$-0.551645\pi$
$613$	−7.99889	−0.323072	−0.161536	+	0.986867i	$0.551645\pi$
$614$	−31.7620	−1.28181
$615$	−29.2478	−1.17938
$616$	7.12139	0.286929
$617$	8.32067	0.334978	0.167489	−	0.985874i	$-0.446434\pi$
$617$	8.32067	0.334978	0.167489	+	0.985874i	$0.446434\pi$
$618$	8.05362	0.323964
$619$	−3.23706	−0.130108	−0.0650541	−	0.997882i	$-0.520722\pi$
$619$	−3.23706	−0.130108	−0.0650541	+	0.997882i	$0.520722\pi$
$620$	−0.144073	−0.00578613
$621$	104.099	4.17734
$622$	8.73616	0.350288
$623$	5.09263	0.204032
$624$	0.636020	0.0254612
$625$	1.00000	0.0400000
$626$	38.6467	1.54463
$627$	11.9631	0.477759
$628$	−12.3532	−0.492947
$629$	−10.7632	−0.429155
$630$	−19.3440	−0.770685
$631$	−45.7667	−1.82194	−0.910972	−	0.412469i	$-0.864667\pi$
$631$	−45.7667	−1.82194	−0.910972	+	0.412469i	$0.864667\pi$
$632$	−15.0496	−0.598642
$633$	−16.2355	−0.645303
$634$	−15.4016	−0.611677
$635$	−8.78544	−0.348640
$636$	30.5356	1.21082
$637$	0.169901	0.00673174
$638$	−4.83209	−0.191304
$639$	−66.5616	−2.63313
$640$	−1.06501	−0.0420983
$641$	−19.4579	−0.768542	−0.384271	−	0.923220i	$-0.625547\pi$
$641$	−19.4579	−0.768542	−0.384271	+	0.923220i	$0.625547\pi$
$642$	−42.2190	−1.66625
$643$	−22.2063	−0.875732	−0.437866	−	0.899040i	$-0.644266\pi$
$643$	−22.2063	−0.875732	−0.437866	+	0.899040i	$0.644266\pi$
$644$	−12.6324	−0.497785
$645$	−17.1972	−0.677140
$646$	−14.7492	−0.580298
$647$	41.1684	1.61850	0.809249	−	0.587466i	$-0.199874\pi$
$647$	41.1684	1.61850	0.809249	+	0.587466i	$0.199874\pi$
$648$	76.5871	3.00863
$649$	−4.26462	−0.167401
$650$	0.115901	0.00454603
$651$	1.41269	0.0553678
$652$	4.00144	0.156708
$653$	−27.1831	−1.06376	−0.531879	−	0.846820i	$-0.678514\pi$
$653$	−27.1831	−1.06376	−0.531879	+	0.846820i	$0.678514\pi$
$654$	24.1190	0.943129
$655$	1.42501	0.0556798
$656$	16.9533	0.661914
$657$	7.51466	0.293175
$658$	30.9374	1.20607
$659$	−4.05460	−0.157945	−0.0789723	−	0.996877i	$-0.525164\pi$
$659$	−4.05460	−0.157945	−0.0789723	+	0.996877i	$0.525164\pi$
$660$	−2.48539	−0.0967438
$661$	25.5990	0.995686	0.497843	−	0.867267i	$-0.334126\pi$
$661$	25.5990	0.995686	0.497843	+	0.867267i	$0.334126\pi$
$662$	0.924665	0.0359381
$663$	−1.21804	−0.0473046
$664$	25.7835	1.00059
$665$	8.55084	0.331588
$666$	24.9560	0.967026
$667$	30.9374	1.19790
$668$	−0.859613	−0.0332594
$669$	4.76353	0.184169
$670$	−7.60079	−0.293644
$671$	−0.802852	−0.0309938
$672$	−30.4951	−1.17637
$673$	5.15543	0.198727	0.0993637	−	0.995051i	$-0.468319\pi$
$673$	5.15543	0.198727	0.0993637	+	0.995051i	$0.468319\pi$
$674$	7.76271	0.299009
$675$	14.6394	0.563470
$676$	9.95582	0.382916
$677$	30.3026	1.16462	0.582312	−	0.812965i	$-0.302148\pi$
$677$	30.3026	1.16462	0.582312	+	0.812965i	$0.302148\pi$
$678$	38.3991	1.47471
$679$	−1.78256	−0.0684085
$680$	11.0598	0.424125
$681$	48.2117	1.84748
$682$	−0.208766	−0.00799407
$683$	35.3348	1.35205	0.676024	−	0.736879i	$-0.263701\pi$
$683$	35.3348	1.35205	0.676024	+	0.736879i	$0.263701\pi$
$684$	−21.2497	−0.812501
$685$	1.06013	0.0405057
$686$	22.2102	0.847991
$687$	−23.9756	−0.914725
$688$	9.96825	0.380036
$689$	1.28211	0.0488446
$690$	−25.6091	−0.974923
$691$	28.4840	1.08358	0.541791	−	0.840513i	$-0.317746\pi$
$691$	28.4840	1.08358	0.541791	+	0.840513i	$0.317746\pi$
$692$	8.53905	0.324606
$693$	17.4170	0.661617
$694$	−19.4219	−0.737244
$695$	3.28018	0.124424
$696$	43.3470	1.64306
$697$	−32.4671	−1.22978
$698$	−21.1475	−0.800445
$699$	−29.8018	−1.12721
$700$	−1.77648	−0.0671448
$701$	−25.7728	−0.973424	−0.486712	−	0.873562i	$-0.661804\pi$
$701$	−25.7728	−0.973424	−0.486712	+	0.873562i	$0.661804\pi$
$702$	1.69673	0.0640388
$703$	−11.0316	−0.416063
$704$	8.26568	0.311524
$705$	−38.9712	−1.46774
$706$	−3.69983	−0.139245
$707$	−28.0048	−1.05323
$708$	10.5993	0.398345
$709$	37.6115	1.41253	0.706265	−	0.707948i	$-0.250379\pi$
$709$	37.6115	1.41253	0.706265	+	0.707948i	$0.250379\pi$
$710$	9.83758	0.369198
$711$	−36.8073	−1.38038
$712$	6.75117	0.253011
$713$	1.33662	0.0500570
$714$	−30.0458	−1.12444
$715$	−0.104355	−0.00390267
$716$	−4.15789	−0.155387
$717$	−56.9194	−2.12570
$718$	−39.5846	−1.47728
$719$	16.3335	0.609137	0.304568	−	0.952490i	$-0.401488\pi$
$719$	16.3335	0.609137	0.304568	+	0.952490i	$0.401488\pi$
$720$	−14.1243	−0.526382
$721$	−5.18302	−0.193026
$722$	5.98524	0.222747
$723$	45.3119	1.68517
$724$	18.7715	0.697637
$725$	4.35072	0.161582
$726$	−3.60140	−0.133661
$727$	−23.3093	−0.864492	−0.432246	−	0.901756i	$-0.642279\pi$
$727$	−23.3093	−0.864492	−0.432246	+	0.901756i	$0.642279\pi$
$728$	−0.743155	−0.0275431
$729$	44.9011	1.66300
$730$	−1.11064	−0.0411067
$731$	−19.0901	−0.706074
$732$	1.99540	0.0737522
$733$	−50.1884	−1.85375	−0.926875	−	0.375371i	$-0.877515\pi$
$733$	−50.1884	−1.85375	−0.926875	+	0.375371i	$0.877515\pi$
$734$	−34.9823	−1.29122
$735$	−5.27934	−0.194732
$736$	−28.8531	−1.06354
$737$	6.84360	0.252087
$738$	75.2799	2.77109
$739$	39.1895	1.44161	0.720805	−	0.693138i	$-0.243772\pi$
$739$	39.1895	1.44161	0.720805	+	0.693138i	$0.243772\pi$
$740$	2.29187	0.0842507
$741$	−1.24841	−0.0458615
$742$	31.6264	1.16104
$743$	35.4247	1.29961	0.649803	−	0.760102i	$-0.274851\pi$
$743$	35.4247	1.29961	0.649803	+	0.760102i	$0.274851\pi$
$744$	1.87277	0.0686591
$745$	1.07627	0.0394313
$746$	20.3513	0.745114
$747$	63.0594	2.30722
$748$	−2.75896	−0.100878
$749$	27.1707	0.992794
$750$	−3.60140	−0.131505
$751$	18.1970	0.664019	0.332010	−	0.943276i	$-0.392273\pi$
$751$	18.1970	0.664019	0.332010	+	0.943276i	$0.392273\pi$
$752$	22.5894	0.823751
$753$	−51.4802	−1.87604
$754$	0.504254	0.0183639
$755$	12.7304	0.463308
$756$	−26.0066	−0.945852
$757$	8.91458	0.324006	0.162003	−	0.986790i	$-0.448205\pi$
$757$	8.91458	0.324006	0.162003	+	0.986790i	$0.448205\pi$
$758$	29.0527	1.05524
$759$	23.0580	0.836951
$760$	11.3356	0.411187
$761$	20.5297	0.744201	0.372100	−	0.928192i	$-0.378638\pi$
$761$	20.5297	0.744201	0.372100	+	0.928192i	$0.378638\pi$
$762$	31.6399	1.14619
$763$	−15.5222	−0.561940
$764$	4.39497	0.159004
$765$	27.0494	0.977973
$766$	−24.2606	−0.876570
$767$	0.445036	0.0160693
$768$	−49.7695	−1.79590
$769$	37.1119	1.33829	0.669145	−	0.743132i	$-0.266660\pi$
$769$	37.1119	1.33829	0.669145	+	0.743132i	$0.266660\pi$
$770$	−2.57417	−0.0927668
$771$	−35.0671	−1.26291
$772$	4.70180	0.169222
$773$	−46.0364	−1.65581	−0.827907	−	0.560866i	$-0.810468\pi$
$773$	−46.0364	−1.65581	−0.827907	+	0.560866i	$0.810468\pi$
$774$	44.2634	1.59101
$775$	0.187969	0.00675204
$776$	−2.36310	−0.0848303
$777$	−22.4726	−0.806200
$778$	−24.0134	−0.860922
$779$	−33.2767	−1.19226
$780$	0.259364	0.00928673
$781$	−8.85756	−0.316948
$782$	−28.4279	−1.01658
$783$	63.6918	2.27616
$784$	3.06013	0.109291
$785$	16.1169	0.575238
$786$	−5.13204	−0.183054
$787$	−45.1949	−1.61102	−0.805512	−	0.592580i	$-0.798110\pi$
$787$	−45.1949	−1.61102	−0.805512	+	0.592580i	$0.798110\pi$
$788$	−16.2318	−0.578233
$789$	31.5146	1.12195
$790$	5.44000	0.193547
$791$	−24.7123	−0.878669
$792$	23.0893	0.820441
$793$	0.0837819	0.00297518
$794$	26.4030	0.937007
$795$	−39.8391	−1.41295
$796$	11.7664	0.417050
$797$	−46.4228	−1.64438	−0.822191	−	0.569212i	$-0.807248\pi$
$797$	−46.4228	−1.64438	−0.822191	+	0.569212i	$0.807248\pi$
$798$	−30.7950	−1.09013
$799$	−43.2608	−1.53046
$800$	−4.05760	−0.143458
$801$	16.5115	0.583406
$802$	−14.1875	−0.500979
$803$	1.00000	0.0352892
$804$	−17.0090	−0.599863
$805$	16.4811	0.580883
$806$	0.0217859	0.000767375 0
$807$	48.6206	1.71153
$808$	−37.1252	−1.30606
$809$	22.3728	0.786584	0.393292	−	0.919414i	$-0.371336\pi$
$809$	22.3728	0.786584	0.393292	+	0.919414i	$0.371336\pi$
$810$	−27.6840	−0.972717
$811$	49.9496	1.75397	0.876984	−	0.480520i	$-0.159552\pi$
$811$	49.9496	1.75397	0.876984	+	0.480520i	$0.159552\pi$
$812$	−7.72898	−0.271234
$813$	55.7107	1.95386
$814$	3.32098	0.116400
$815$	−5.22058	−0.182869
$816$	−21.9383	−0.767996
$817$	−19.5662	−0.684534
$818$	21.1392	0.739114
$819$	−1.81756	−0.0635106
$820$	6.91342	0.241427
$821$	12.9215	0.450963	0.225482	−	0.974247i	$-0.427604\pi$
$821$	12.9215	0.450963	0.225482	+	0.974247i	$0.427604\pi$
$822$	−3.81797	−0.133167
$823$	−30.8889	−1.07672	−0.538359	−	0.842715i	$-0.680956\pi$
$823$	−30.8889	−1.07672	−0.538359	+	0.842715i	$0.680956\pi$
$824$	−6.87100	−0.239363
$825$	3.24263	0.112894
$826$	10.9779	0.381969
$827$	22.0987	0.768446	0.384223	−	0.923240i	$-0.374469\pi$
$827$	22.0987	0.768446	0.384223	+	0.923240i	$0.374469\pi$
$828$	−40.9572	−1.42336
$829$	−23.1793	−0.805049	−0.402525	−	0.915409i	$-0.631867\pi$
$829$	−23.1793	−0.805049	−0.402525	+	0.915409i	$0.631867\pi$
$830$	−9.31997	−0.323501
$831$	69.1859	2.40003
$832$	−0.862567	−0.0299041
$833$	−5.86044	−0.203052
$834$	−11.8132	−0.409059
$835$	1.12152	0.0388117
$836$	−2.82776	−0.0978002
$837$	2.75175	0.0951143
$838$	30.4217	1.05090
$839$	54.6105	1.88537	0.942683	−	0.333690i	$-0.108294\pi$
$839$	54.6105	1.88537	0.942683	+	0.333690i	$0.108294\pi$
$840$	23.0920	0.796751
$841$	−10.0713	−0.347285
$842$	−16.9814	−0.585218
$843$	19.2401	0.662665
$844$	3.83765	0.132097
$845$	−12.9891	−0.446839
$846$	100.307	3.44862
$847$	2.31774	0.0796383
$848$	23.0924	0.792997
$849$	34.2448	1.17528
$850$	−3.99781	−0.137124
$851$	−21.2625	−0.728870
$852$	22.0145	0.754205
$853$	−44.7750	−1.53307	−0.766534	−	0.642204i	$-0.778020\pi$
$853$	−44.7750	−1.53307	−0.766534	+	0.642204i	$0.778020\pi$
$854$	2.06668	0.0707204
$855$	27.7239	0.948138
$856$	36.0194	1.23112
$857$	53.9241	1.84201	0.921006	−	0.389549i	$-0.127369\pi$
$857$	53.9241	1.84201	0.921006	+	0.389549i	$0.127369\pi$
$858$	0.375826	0.0128305
$859$	14.6892	0.501190	0.250595	−	0.968092i	$-0.419374\pi$
$859$	14.6892	0.501190	0.250595	+	0.968092i	$0.419374\pi$
$860$	4.06498	0.138615
$861$	−67.7886	−2.31023
$862$	23.8839	0.813488
$863$	−13.7763	−0.468952	−0.234476	−	0.972122i	$-0.575337\pi$
$863$	−13.7763	−0.468952	−0.234476	+	0.972122i	$0.575337\pi$
$864$	−59.4007	−2.02085
$865$	−11.1407	−0.378795
$866$	−37.8321	−1.28559
$867$	−13.1108	−0.445265
$868$	−0.333924	−0.0113341
$869$	−4.89807	−0.166156
$870$	−15.6687	−0.531218
$871$	−0.714166	−0.0241986
$872$	−20.5773	−0.696836
$873$	−5.77951	−0.195607
$874$	−29.1368	−0.985568
$875$	2.31774	0.0783537
$876$	−2.48539	−0.0839737
$877$	−12.2557	−0.413844	−0.206922	−	0.978357i	$-0.566345\pi$
$877$	−12.2557	−0.413844	−0.206922	+	0.978357i	$0.566345\pi$
$878$	24.8515	0.838696
$879$	56.9811	1.92192
$880$	−1.87957	−0.0633602
$881$	−37.9263	−1.27777	−0.638885	−	0.769302i	$-0.720604\pi$
$881$	−37.9263	−1.27777	−0.638885	+	0.769302i	$0.720604\pi$
$882$	13.5883	0.457542
$883$	26.3489	0.886710	0.443355	−	0.896346i	$-0.353788\pi$
$883$	26.3489	0.886710	0.443355	+	0.896346i	$0.353788\pi$
$884$	0.287912	0.00968354
$885$	−13.8286	−0.464843
$886$	−12.0189	−0.403782
$887$	5.07689	0.170465	0.0852327	−	0.996361i	$-0.472837\pi$
$887$	5.07689	0.170465	0.0852327	+	0.996361i	$0.472837\pi$
$888$	−29.7913	−0.999732
$889$	−20.3623	−0.682930
$890$	−2.44035	−0.0818007
$891$	24.9261	0.835057
$892$	−1.12597	−0.0377004
$893$	−44.3396	−1.48377
$894$	−3.87607	−0.129635
$895$	5.42469	0.181327
$896$	−2.46842	−0.0824640
$897$	−2.40622	−0.0803414
$898$	−38.6160	−1.28863
$899$	0.817800	0.0272751
$900$	−5.75979	−0.191993
$901$	−44.2241	−1.47332
$902$	10.0177	0.333554
$903$	−39.8586	−1.32641
$904$	−32.7605	−1.08960
$905$	−24.4907	−0.814099
$906$	−45.8474	−1.52318
$907$	−38.5702	−1.28070	−0.640351	−	0.768082i	$-0.721211\pi$
$907$	−38.5702	−1.28070	−0.640351	+	0.768082i	$0.721211\pi$
$908$	−11.3960	−0.378189
$909$	−90.7984	−3.01159
$910$	0.268629	0.00890496
$911$	48.1779	1.59621	0.798103	−	0.602521i	$-0.205837\pi$
$911$	48.1779	1.59621	0.798103	+	0.602521i	$0.205837\pi$
$912$	−22.4854	−0.744567
$913$	8.39151	0.277719
$914$	21.7629	0.719854
$915$	−2.60335	−0.0860642
$916$	5.66720	0.187250
$917$	3.30280	0.109068
$918$	−58.5255	−1.93163
$919$	18.8156	0.620671	0.310335	−	0.950627i	$-0.399559\pi$
$919$	18.8156	0.620671	0.310335	+	0.950627i	$0.399559\pi$
$920$	21.8486	0.720327
$921$	92.7323	3.05563
$922$	9.44452	0.311039
$923$	0.924334	0.0304248
$924$	−5.76048	−0.189506
$925$	−2.99014	−0.0983152
$926$	1.69272	0.0556261
$927$	−16.8046	−0.551936
$928$	−17.6535	−0.579503
$929$	−55.5219	−1.82162	−0.910808	−	0.412830i	$-0.864540\pi$
$929$	−55.5219	−1.82162	−0.910808	+	0.412830i	$0.864540\pi$
$930$	−0.676952	−0.0221981
$931$	−6.00658	−0.196858
$932$	7.04437	0.230746
$933$	−25.5061	−0.835033
$934$	9.63204	0.315170
$935$	3.59955	0.117718
$936$	−2.40949	−0.0787566
$937$	2.30247	0.0752184	0.0376092	−	0.999293i	$-0.488026\pi$
$937$	2.30247	0.0752184	0.0376092	+	0.999293i	$0.488026\pi$
$938$	−17.6166	−0.575203
$939$	−112.833	−3.68217
$940$	9.21179	0.300456
$941$	−53.8253	−1.75465	−0.877327	−	0.479893i	$-0.840676\pi$
$941$	−53.8253	−1.75465	−0.877327	+	0.479893i	$0.840676\pi$
$942$	−58.0436	−1.89116
$943$	−64.1384	−2.08864
$944$	8.01565	0.260887
$945$	33.9302	1.10375
$946$	5.89027	0.191509
$947$	5.47100	0.177784	0.0888918	−	0.996041i	$-0.471667\pi$
$947$	5.47100	0.177784	0.0888918	+	0.996041i	$0.471667\pi$
$948$	12.1736	0.395381
$949$	−0.104355	−0.00338752
$950$	−4.09750	−0.132941
$951$	44.9667	1.45814
$952$	25.6338	0.830795
$953$	−14.2194	−0.460613	−0.230307	−	0.973118i	$-0.573973\pi$
$953$	−14.2194	−0.460613	−0.230307	+	0.973118i	$0.573973\pi$
$954$	102.540	3.31987
$955$	−5.73400	−0.185548
$956$	13.4543	0.435143
$957$	14.1078	0.456039
$958$	34.1039	1.10185
$959$	2.45711	0.0793443
$960$	26.8025	0.865048
$961$	−30.9647	−0.998860
$962$	−0.346562	−0.0111736
$963$	88.0939	2.83879
$964$	−10.7106	−0.344964
$965$	−6.13432	−0.197471
$966$	−59.3552	−1.90972
$967$	−27.1002	−0.871484	−0.435742	−	0.900072i	$-0.643514\pi$
$967$	−27.1002	−0.871484	−0.435742	+	0.900072i	$0.643514\pi$
$968$	3.07256	0.0987559
$969$	43.0617	1.38334
$970$	0.854192	0.0274264
$971$	−28.0582	−0.900431	−0.450215	−	0.892920i	$-0.648653\pi$
$971$	−28.0582	−0.900431	−0.450215	+	0.892920i	$0.648653\pi$
$972$	−28.2891	−0.907375
$973$	7.60258	0.243728
$974$	6.29333	0.201651
$975$	−0.338386	−0.0108370
$976$	1.50902	0.0483024
$977$	−17.0216	−0.544569	−0.272285	−	0.962217i	$-0.587779\pi$
$977$	−17.0216	−0.544569	−0.272285	+	0.962217i	$0.587779\pi$
$978$	18.8014	0.601203
$979$	2.19724	0.0702242
$980$	1.24790	0.0398627
$981$	−50.3266	−1.60680
$982$	−30.3837	−0.969584
$983$	33.1812	1.05832	0.529158	−	0.848523i	$-0.322508\pi$
$983$	33.1812	1.05832	0.529158	+	0.848523i	$0.322508\pi$
$984$	−89.8656	−2.86481
$985$	21.1772	0.674761
$986$	−17.3933	−0.553917
$987$	−90.3250	−2.87508
$988$	0.295092	0.00938813
$989$	−37.7124	−1.19918
$990$	−8.34610	−0.265256
$991$	−59.5509	−1.89170	−0.945848	−	0.324610i	$-0.894767\pi$
$991$	−59.5509	−1.89170	−0.945848	+	0.324610i	$0.894767\pi$
$992$	−0.762702	−0.0242158
$993$	−2.69965	−0.0856709
$994$	22.8009	0.723201
$995$	−15.3514	−0.486671
$996$	−20.8562	−0.660854
$997$	11.7572	0.372355	0.186177	−	0.982516i	$-0.440390\pi$
$997$	11.7572	0.372355	0.186177	+	0.982516i	$0.440390\pi$
$998$	−2.90596	−0.0919866
$999$	−43.7738	−1.38494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.12	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.12	✓	37	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)

\(f(q)\)	\(=\)	\(q-1.11064 q^{2} +3.24263 q^{3} -0.766474 q^{4} +1.00000 q^{5} -3.60140 q^{6} +2.31774 q^{7} +3.07256 q^{8} +7.51466 q^{9} +O(q^{10})\)	\(q-1.11064 q^{2} +3.24263 q^{3} -0.766474 q^{4} +1.00000 q^{5} -3.60140 q^{6} +2.31774 q^{7} +3.07256 q^{8} +7.51466 q^{9} -1.11064 q^{10} +1.00000 q^{11} -2.48539 q^{12} -0.104355 q^{13} -2.57417 q^{14} +3.24263 q^{15} -1.87957 q^{16} +3.59955 q^{17} -8.34610 q^{18} +3.68931 q^{19} -0.766474 q^{20} +7.51556 q^{21} -1.11064 q^{22} +7.11088 q^{23} +9.96319 q^{24} +1.00000 q^{25} +0.115901 q^{26} +14.6394 q^{27} -1.77648 q^{28} +4.35072 q^{29} -3.60140 q^{30} +0.187969 q^{31} -4.05760 q^{32} +3.24263 q^{33} -3.99781 q^{34} +2.31774 q^{35} -5.75979 q^{36} -2.99014 q^{37} -4.09750 q^{38} -0.338386 q^{39} +3.07256 q^{40} -9.01977 q^{41} -8.34710 q^{42} -5.30348 q^{43} -0.766474 q^{44} +7.51466 q^{45} -7.89764 q^{46} -12.0184 q^{47} -6.09475 q^{48} -1.62810 q^{49} -1.11064 q^{50} +11.6720 q^{51} +0.0799857 q^{52} -12.2860 q^{53} -16.2591 q^{54} +1.00000 q^{55} +7.12139 q^{56} +11.9631 q^{57} -4.83209 q^{58} -4.26462 q^{59} -2.48539 q^{60} -0.802852 q^{61} -0.208766 q^{62} +17.4170 q^{63} +8.26568 q^{64} -0.104355 q^{65} -3.60140 q^{66} +6.84360 q^{67} -2.75896 q^{68} +23.0580 q^{69} -2.57417 q^{70} -8.85756 q^{71} +23.0893 q^{72} +1.00000 q^{73} +3.32098 q^{74} +3.24263 q^{75} -2.82776 q^{76} +2.31774 q^{77} +0.375826 q^{78} -4.89807 q^{79} -1.87957 q^{80} +24.9261 q^{81} +10.0177 q^{82} +8.39151 q^{83} -5.76048 q^{84} +3.59955 q^{85} +5.89027 q^{86} +14.1078 q^{87} +3.07256 q^{88} +2.19724 q^{89} -8.34610 q^{90} -0.241868 q^{91} -5.45030 q^{92} +0.609514 q^{93} +13.3481 q^{94} +3.68931 q^{95} -13.1573 q^{96} -0.769097 q^{97} +1.80824 q^{98} +7.51466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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