LMFDB - Embedded newform 8035.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66914 q^{2} -3.32233 q^{3} +5.12432 q^{4} -1.00000 q^{5} +8.86776 q^{6} -1.95943 q^{7} -8.33924 q^{8} +8.03786 q^{9} +O(q^{10})$	\(q-2.66914 q^{2} -3.32233 q^{3} +5.12432 q^{4} -1.00000 q^{5} +8.86776 q^{6} -1.95943 q^{7} -8.33924 q^{8} +8.03786 q^{9} +2.66914 q^{10} -0.642003 q^{11} -17.0247 q^{12} +0.944586 q^{13} +5.22999 q^{14} +3.32233 q^{15} +12.0100 q^{16} -4.40714 q^{17} -21.4542 q^{18} +6.94812 q^{19} -5.12432 q^{20} +6.50986 q^{21} +1.71360 q^{22} +7.48133 q^{23} +27.7057 q^{24} +1.00000 q^{25} -2.52123 q^{26} -16.7374 q^{27} -10.0407 q^{28} -3.93064 q^{29} -8.86776 q^{30} -1.85967 q^{31} -15.3779 q^{32} +2.13294 q^{33} +11.7633 q^{34} +1.95943 q^{35} +41.1886 q^{36} +8.22240 q^{37} -18.5455 q^{38} -3.13822 q^{39} +8.33924 q^{40} -6.27984 q^{41} -17.3757 q^{42} -9.59687 q^{43} -3.28982 q^{44} -8.03786 q^{45} -19.9687 q^{46} +0.518563 q^{47} -39.9011 q^{48} -3.16064 q^{49} -2.66914 q^{50} +14.6420 q^{51} +4.84036 q^{52} +4.41342 q^{53} +44.6746 q^{54} +0.642003 q^{55} +16.3401 q^{56} -23.0840 q^{57} +10.4914 q^{58} +1.70721 q^{59} +17.0247 q^{60} +9.46226 q^{61} +4.96372 q^{62} -15.7496 q^{63} +17.0257 q^{64} -0.944586 q^{65} -5.69313 q^{66} +7.21213 q^{67} -22.5836 q^{68} -24.8554 q^{69} -5.22999 q^{70} -3.55614 q^{71} -67.0297 q^{72} +11.9857 q^{73} -21.9467 q^{74} -3.32233 q^{75} +35.6044 q^{76} +1.25796 q^{77} +8.37637 q^{78} -7.31294 q^{79} -12.0100 q^{80} +31.4937 q^{81} +16.7618 q^{82} -3.13686 q^{83} +33.3586 q^{84} +4.40714 q^{85} +25.6154 q^{86} +13.0589 q^{87} +5.35381 q^{88} -17.0845 q^{89} +21.4542 q^{90} -1.85085 q^{91} +38.3367 q^{92} +6.17843 q^{93} -1.38412 q^{94} -6.94812 q^{95} +51.0903 q^{96} -12.1606 q^{97} +8.43621 q^{98} -5.16033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.66914	−1.88737	−0.943684	−	0.330848i	$-0.892665\pi$
$2$	−2.66914	−1.88737	−0.943684	+	0.330848i	$0.892665\pi$
$3$	−3.32233	−1.91815	−0.959074	−	0.283157i	$-0.908618\pi$
$3$	−3.32233	−1.91815	−0.959074	+	0.283157i	$0.908618\pi$
$4$	5.12432	2.56216
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	8.86776	3.62025
$7$	−1.95943	−0.740594	−0.370297	−	0.928913i	$-0.620744\pi$
$7$	−1.95943	−0.740594	−0.370297	+	0.928913i	$0.620744\pi$
$8$	−8.33924	−2.94837
$9$	8.03786	2.67929
$10$	2.66914	0.844057
$11$	−0.642003	−0.193571	−0.0967855	−	0.995305i	$-0.530856\pi$
$11$	−0.642003	−0.193571	−0.0967855	+	0.995305i	$0.530856\pi$
$12$	−17.0247	−4.91460
$13$	0.944586	0.261981	0.130991	−	0.991384i	$-0.458184\pi$
$13$	0.944586	0.261981	0.130991	+	0.991384i	$0.458184\pi$
$14$	5.22999	1.39777
$15$	3.32233	0.857821
$16$	12.0100	3.00249
$17$	−4.40714	−1.06889	−0.534445	−	0.845203i	$-0.679479\pi$
$17$	−4.40714	−1.06889	−0.534445	+	0.845203i	$0.679479\pi$
$18$	−21.4542	−5.05680
$19$	6.94812	1.59401	0.797005	−	0.603973i	$-0.206417\pi$
$19$	6.94812	1.59401	0.797005	+	0.603973i	$0.206417\pi$
$20$	−5.12432	−1.14583
$21$	6.50986	1.42057
$22$	1.71360	0.365340
$23$	7.48133	1.55997	0.779983	−	0.625801i	$-0.215228\pi$
$23$	7.48133	1.55997	0.779983	+	0.625801i	$0.215228\pi$
$24$	27.7057	5.65540
$25$	1.00000	0.200000
$26$	−2.52123	−0.494455
$27$	−16.7374	−3.22112
$28$	−10.0407	−1.89752
$29$	−3.93064	−0.729901	−0.364951	−	0.931027i	$-0.618914\pi$
$29$	−3.93064	−0.729901	−0.364951	+	0.931027i	$0.618914\pi$
$30$	−8.86776	−1.61902
$31$	−1.85967	−0.334007	−0.167003	−	0.985956i	$-0.553409\pi$
$31$	−1.85967	−0.334007	−0.167003	+	0.985956i	$0.553409\pi$
$32$	−15.3779	−2.71845
$33$	2.13294	0.371298
$34$	11.7633	2.01739
$35$	1.95943	0.331204
$36$	41.1886	6.86476
$37$	8.22240	1.35175	0.675877	−	0.737015i	$-0.263765\pi$
$37$	8.22240	1.35175	0.675877	+	0.737015i	$0.263765\pi$
$38$	−18.5455	−3.00848
$39$	−3.13822	−0.502518
$40$	8.33924	1.31855
$41$	−6.27984	−0.980746	−0.490373	−	0.871513i	$-0.663139\pi$
$41$	−6.27984	−0.980746	−0.490373	+	0.871513i	$0.663139\pi$
$42$	−17.3757	−2.68113
$43$	−9.59687	−1.46351	−0.731755	−	0.681568i	$-0.761298\pi$
$43$	−9.59687	−1.46351	−0.731755	+	0.681568i	$0.761298\pi$
$44$	−3.28982	−0.495960
$45$	−8.03786	−1.19821
$46$	−19.9687	−2.94423
$47$	0.518563	0.0756402	0.0378201	−	0.999285i	$-0.487959\pi$
$47$	0.518563	0.0756402	0.0378201	+	0.999285i	$0.487959\pi$
$48$	−39.9011	−5.75923
$49$	−3.16064	−0.451521
$50$	−2.66914	−0.377474
$51$	14.6420	2.05029
$52$	4.84036	0.671237
$53$	4.41342	0.606230	0.303115	−	0.952954i	$-0.401973\pi$
$53$	4.41342	0.606230	0.303115	+	0.952954i	$0.401973\pi$
$54$	44.6746	6.07944
$55$	0.642003	0.0865676
$56$	16.3401	2.18354
$57$	−23.0840	−3.05754
$58$	10.4914	1.37759
$59$	1.70721	0.222259	0.111130	−	0.993806i	$-0.464553\pi$
$59$	1.70721	0.222259	0.111130	+	0.993806i	$0.464553\pi$
$60$	17.0247	2.19787
$61$	9.46226	1.21152	0.605759	−	0.795648i	$-0.292870\pi$
$61$	9.46226	1.21152	0.605759	+	0.795648i	$0.292870\pi$
$62$	4.96372	0.630393
$63$	−15.7496	−1.98426
$64$	17.0257	2.12821
$65$	−0.944586	−0.117161
$66$	−5.69313	−0.700776
$67$	7.21213	0.881102	0.440551	−	0.897728i	$-0.354783\pi$
$67$	7.21213	0.881102	0.440551	+	0.897728i	$0.354783\pi$
$68$	−22.5836	−2.73866
$69$	−24.8554	−2.99224
$70$	−5.22999	−0.625103
$71$	−3.55614	−0.422037	−0.211018	−	0.977482i	$-0.567678\pi$
$71$	−3.55614	−0.422037	−0.211018	+	0.977482i	$0.567678\pi$
$72$	−67.0297	−7.89952
$73$	11.9857	1.40282	0.701409	−	0.712759i	$-0.252555\pi$
$73$	11.9857	1.40282	0.701409	+	0.712759i	$0.252555\pi$
$74$	−21.9467	−2.55126
$75$	−3.32233	−0.383629
$76$	35.6044	4.08410
$77$	1.25796	0.143358
$78$	8.37637	0.948437
$79$	−7.31294	−0.822770	−0.411385	−	0.911462i	$-0.634955\pi$
$79$	−7.31294	−0.822770	−0.411385	+	0.911462i	$0.634955\pi$
$80$	−12.0100	−1.34276
$81$	31.4937	3.49930
$82$	16.7618	1.85103
$83$	−3.13686	−0.344315	−0.172158	−	0.985069i	$-0.555074\pi$
$83$	−3.13686	−0.344315	−0.172158	+	0.985069i	$0.555074\pi$
$84$	33.3586	3.63972
$85$	4.40714	0.478022
$86$	25.6154	2.76218
$87$	13.0589	1.40006
$88$	5.35381	0.570718
$89$	−17.0845	−1.81095	−0.905476	−	0.424396i	$-0.860486\pi$
$89$	−17.0845	−1.81095	−0.905476	+	0.424396i	$0.860486\pi$
$90$	21.4542	2.26147
$91$	−1.85085	−0.194022
$92$	38.3367	3.99688
$93$	6.17843	0.640674
$94$	−1.38412	−0.142761
$95$	−6.94812	−0.712863
$96$	51.0903	5.21438
$97$	−12.1606	−1.23472	−0.617359	−	0.786681i	$-0.711798\pi$
$97$	−12.1606	−1.23472	−0.617359	+	0.786681i	$0.711798\pi$
$98$	8.43621	0.852186
$99$	−5.16033	−0.518633
$100$	5.12432	0.512432
$101$	1.46049	0.145325	0.0726623	−	0.997357i	$-0.476850\pi$
$101$	1.46049	0.145325	0.0726623	+	0.997357i	$0.476850\pi$
$102$	−39.0815	−3.86965
$103$	7.23080	0.712472	0.356236	−	0.934396i	$-0.384060\pi$
$103$	7.23080	0.712472	0.356236	+	0.934396i	$0.384060\pi$
$104$	−7.87713	−0.772416
$105$	−6.50986	−0.635297
$106$	−11.7800	−1.14418
$107$	−3.79325	−0.366707	−0.183354	−	0.983047i	$-0.558695\pi$
$107$	−3.79325	−0.366707	−0.183354	+	0.983047i	$0.558695\pi$
$108$	−85.7679	−8.25302
$109$	−12.0910	−1.15810	−0.579052	−	0.815291i	$-0.696577\pi$
$109$	−12.0910	−1.15810	−0.579052	+	0.815291i	$0.696577\pi$
$110$	−1.71360	−0.163385
$111$	−27.3175	−2.59286
$112$	−23.5327	−2.22363
$113$	−7.31800	−0.688419	−0.344210	−	0.938893i	$-0.611853\pi$
$113$	−7.31800	−0.688419	−0.344210	+	0.938893i	$0.611853\pi$
$114$	61.6143	5.77071
$115$	−7.48133	−0.697638
$116$	−20.1418	−1.87012
$117$	7.59245	0.701923
$118$	−4.55678	−0.419485
$119$	8.63548	0.791613
$120$	−27.7057	−2.52917
$121$	−10.5878	−0.962530
$122$	−25.2561	−2.28658
$123$	20.8637	1.88122
$124$	−9.52954	−0.855778
$125$	−1.00000	−0.0894427
$126$	42.0379	3.74504
$127$	−0.943795	−0.0837482	−0.0418741	−	0.999123i	$-0.513333\pi$
$127$	−0.943795	−0.0837482	−0.0418741	+	0.999123i	$0.513333\pi$
$128$	−14.6883	−1.29827
$129$	31.8840	2.80723
$130$	2.52123	0.221127
$131$	3.84938	0.336322	0.168161	−	0.985760i	$-0.446217\pi$
$131$	3.84938	0.336322	0.168161	+	0.985760i	$0.446217\pi$
$132$	10.9299	0.951323
$133$	−13.6143	−1.18051
$134$	−19.2502	−1.66296
$135$	16.7374	1.44053
$136$	36.7522	3.15148
$137$	−11.6315	−0.993745	−0.496872	−	0.867824i	$-0.665518\pi$
$137$	−11.6315	−0.993745	−0.496872	+	0.867824i	$0.665518\pi$
$138$	66.3427	5.64746
$139$	4.35997	0.369808	0.184904	−	0.982757i	$-0.440803\pi$
$139$	4.35997	0.369808	0.184904	+	0.982757i	$0.440803\pi$
$140$	10.0407	0.848596
$141$	−1.72284	−0.145089
$142$	9.49185	0.796538
$143$	−0.606427	−0.0507119
$144$	96.5346	8.04455
$145$	3.93064	0.326422
$146$	−31.9915	−2.64763
$147$	10.5007	0.866083
$148$	42.1342	3.46341
$149$	3.37098	0.276162	0.138081	−	0.990421i	$-0.455907\pi$
$149$	3.37098	0.276162	0.138081	+	0.990421i	$0.455907\pi$
$150$	8.86776	0.724050
$151$	18.2693	1.48673	0.743367	−	0.668884i	$-0.233228\pi$
$151$	18.2693	1.48673	0.743367	+	0.668884i	$0.233228\pi$
$152$	−57.9421	−4.69972
$153$	−35.4240	−2.86386
$154$	−3.35767	−0.270568
$155$	1.85967	0.149372
$156$	−16.0813	−1.28753
$157$	−1.84632	−0.147352	−0.0736760	−	0.997282i	$-0.523473\pi$
$157$	−1.84632	−0.147352	−0.0736760	+	0.997282i	$0.523473\pi$
$158$	19.5193	1.55287
$159$	−14.6628	−1.16284
$160$	15.3779	1.21573
$161$	−14.6591	−1.15530
$162$	−84.0610	−6.60446
$163$	−16.2411	−1.27210	−0.636052	−	0.771646i	$-0.719434\pi$
$163$	−16.2411	−1.27210	−0.636052	+	0.771646i	$0.719434\pi$
$164$	−32.1799	−2.51283
$165$	−2.13294	−0.166049
$166$	8.37273	0.649850
$167$	−2.07068	−0.160234	−0.0801171	−	0.996785i	$-0.525529\pi$
$167$	−2.07068	−0.160234	−0.0801171	+	0.996785i	$0.525529\pi$
$168$	−54.2873	−4.18836
$169$	−12.1078	−0.931366
$170$	−11.7633	−0.902203
$171$	55.8481	4.27081
$172$	−49.1774	−3.74974
$173$	14.4483	1.09848	0.549241	−	0.835664i	$-0.314917\pi$
$173$	14.4483	1.09848	0.549241	+	0.835664i	$0.314917\pi$
$174$	−34.8560	−2.64242
$175$	−1.95943	−0.148119
$176$	−7.71044	−0.581196
$177$	−5.67190	−0.426326
$178$	45.6009	3.41793
$179$	−20.9674	−1.56717	−0.783587	−	0.621282i	$-0.786612\pi$
$179$	−20.9674	−1.56717	−0.783587	+	0.621282i	$0.786612\pi$
$180$	−41.1886	−3.07001
$181$	1.65974	0.123367	0.0616837	−	0.998096i	$-0.480353\pi$
$181$	1.65974	0.123367	0.0616837	+	0.998096i	$0.480353\pi$
$182$	4.94017	0.366190
$183$	−31.4367	−2.32387
$184$	−62.3886	−4.59935
$185$	−8.22240	−0.604523
$186$	−16.4911	−1.20919
$187$	2.82940	0.206906
$188$	2.65728	0.193802
$189$	32.7958	2.38554
$190$	18.5455	1.34543
$191$	10.8459	0.784782	0.392391	−	0.919799i	$-0.371648\pi$
$191$	10.8459	0.784782	0.392391	+	0.919799i	$0.371648\pi$
$192$	−56.5650	−4.08222
$193$	−14.6300	−1.05309	−0.526546	−	0.850147i	$-0.676513\pi$
$193$	−14.6300	−1.05309	−0.526546	+	0.850147i	$0.676513\pi$
$194$	32.4583	2.33037
$195$	3.13822	0.224733
$196$	−16.1961	−1.15687
$197$	1.85140	0.131907	0.0659535	−	0.997823i	$-0.478991\pi$
$197$	1.85140	0.131907	0.0659535	+	0.997823i	$0.478991\pi$
$198$	13.7736	0.978851
$199$	27.3071	1.93575	0.967875	−	0.251430i	$-0.0809010\pi$
$199$	27.3071	1.93575	0.967875	+	0.251430i	$0.0809010\pi$
$200$	−8.33924	−0.589673
$201$	−23.9611	−1.69008
$202$	−3.89827	−0.274281
$203$	7.70180	0.540560
$204$	75.0301	5.25316
$205$	6.27984	0.438603
$206$	−19.3000	−1.34470
$207$	60.1339	4.17960
$208$	11.3445	0.786597
$209$	−4.46071	−0.308554
$210$	17.3757	1.19904
$211$	7.49282	0.515827	0.257913	−	0.966168i	$-0.416965\pi$
$211$	7.49282	0.515827	0.257913	+	0.966168i	$0.416965\pi$
$212$	22.6158	1.55326
$213$	11.8147	0.809528
$214$	10.1247	0.692111
$215$	9.59687	0.654501
$216$	139.578	9.49705
$217$	3.64389	0.247363
$218$	32.2725	2.18577
$219$	−39.8204	−2.69081
$220$	3.28982	0.221800
$221$	−4.16293	−0.280029
$222$	72.9143	4.89369
$223$	−4.03442	−0.270165	−0.135082	−	0.990834i	$-0.543130\pi$
$223$	−4.03442	−0.270165	−0.135082	+	0.990834i	$0.543130\pi$
$224$	30.1318	2.01326
$225$	8.03786	0.535858
$226$	19.5328	1.29930
$227$	21.0012	1.39390	0.696951	−	0.717119i	$-0.254540\pi$
$227$	21.0012	1.39390	0.696951	+	0.717119i	$0.254540\pi$
$228$	−118.289	−7.83391
$229$	23.4269	1.54809	0.774046	−	0.633129i	$-0.218230\pi$
$229$	23.4269	1.54809	0.774046	+	0.633129i	$0.218230\pi$
$230$	19.9687	1.31670
$231$	−4.17935	−0.274981
$232$	32.7785	2.15202
$233$	25.3697	1.66202	0.831012	−	0.556255i	$-0.187762\pi$
$233$	25.3697	1.66202	0.831012	+	0.556255i	$0.187762\pi$
$234$	−20.2653	−1.32479
$235$	−0.518563	−0.0338273
$236$	8.74827	0.569464
$237$	24.2960	1.57819
$238$	−23.0493	−1.49406
$239$	−6.05611	−0.391737	−0.195869	−	0.980630i	$-0.562753\pi$
$239$	−6.05611	−0.391737	−0.195869	+	0.980630i	$0.562753\pi$
$240$	39.9011	2.57560
$241$	−21.0434	−1.35552	−0.677762	−	0.735281i	$-0.737050\pi$
$241$	−21.0434	−1.35552	−0.677762	+	0.735281i	$0.737050\pi$
$242$	28.2604	1.81665
$243$	−54.4200	−3.49104
$244$	48.4876	3.10410
$245$	3.16064	0.201926
$246$	−55.6881	−3.55055
$247$	6.56310	0.417600
$248$	15.5082	0.984774
$249$	10.4217	0.660447
$250$	2.66914	0.168811
$251$	12.2753	0.774807	0.387404	−	0.921910i	$-0.373372\pi$
$251$	12.2753	0.774807	0.387404	+	0.921910i	$0.373372\pi$
$252$	−80.7060	−5.08400
$253$	−4.80303	−0.301964
$254$	2.51912	0.158064
$255$	−14.6420	−0.916916
$256$	5.15375	0.322109
$257$	1.90511	0.118837	0.0594186	−	0.998233i	$-0.481075\pi$
$257$	1.90511	0.118837	0.0594186	+	0.998233i	$0.481075\pi$
$258$	−85.1028	−5.29827
$259$	−16.1112	−1.00110
$260$	−4.84036	−0.300186
$261$	−31.5939	−1.95562
$262$	−10.2746	−0.634764
$263$	30.2721	1.86666	0.933328	−	0.359025i	$-0.116891\pi$
$263$	30.2721	1.86666	0.933328	+	0.359025i	$0.116891\pi$
$264$	−17.7871	−1.09472
$265$	−4.41342	−0.271114
$266$	36.3386	2.22806
$267$	56.7603	3.47367
$268$	36.9572	2.25752
$269$	−30.2358	−1.84351	−0.921756	−	0.387771i	$-0.873245\pi$
$269$	−30.2358	−1.84351	−0.921756	+	0.387771i	$0.873245\pi$
$270$	−44.6746	−2.71881
$271$	5.55658	0.337538	0.168769	−	0.985656i	$-0.446021\pi$
$271$	5.55658	0.337538	0.168769	+	0.985656i	$0.446021\pi$
$272$	−52.9297	−3.20933
$273$	6.14912	0.372162
$274$	31.0461	1.87556
$275$	−0.642003	−0.0387142
$276$	−127.367	−7.66660
$277$	−12.4183	−0.746144	−0.373072	−	0.927802i	$-0.621696\pi$
$277$	−12.4183	−0.746144	−0.373072	+	0.927802i	$0.621696\pi$
$278$	−11.6374	−0.697963
$279$	−14.9478	−0.894900
$280$	−16.3401	−0.976510
$281$	11.7540	0.701184	0.350592	−	0.936528i	$-0.385980\pi$
$281$	11.7540	0.701184	0.350592	+	0.936528i	$0.385980\pi$
$282$	4.59849	0.273836
$283$	4.93790	0.293528	0.146764	−	0.989172i	$-0.453114\pi$
$283$	4.93790	0.293528	0.146764	+	0.989172i	$0.453114\pi$
$284$	−18.2228	−1.08132
$285$	23.0840	1.36738
$286$	1.61864	0.0957121
$287$	12.3049	0.726335
$288$	−123.605	−7.28350
$289$	2.42291	0.142524
$290$	−10.4914	−0.616078
$291$	40.4014	2.36837
$292$	61.4184	3.59424
$293$	0.0424106	0.00247765	0.00123883	−	0.999999i	$-0.499606\pi$
$293$	0.0424106	0.00247765	0.00123883	+	0.999999i	$0.499606\pi$
$294$	−28.0279	−1.63462
$295$	−1.70721	−0.0993975
$296$	−68.5685	−3.98547
$297$	10.7455	0.623516
$298$	−8.99763	−0.521219
$299$	7.06676	0.408681
$300$	−17.0247	−0.982919
$301$	18.8044	1.08387
$302$	−48.7633	−2.80601
$303$	−4.85224	−0.278754
$304$	83.4468	4.78600
$305$	−9.46226	−0.541807
$306$	94.5517	5.40516
$307$	16.4563	0.939208	0.469604	−	0.882877i	$-0.344397\pi$
$307$	16.4563	0.939208	0.469604	+	0.882877i	$0.344397\pi$
$308$	6.44617	0.367305
$309$	−24.0231	−1.36663
$310$	−4.96372	−0.281920
$311$	−16.9555	−0.961460	−0.480730	−	0.876869i	$-0.659628\pi$
$311$	−16.9555	−0.961460	−0.480730	+	0.876869i	$0.659628\pi$
$312$	26.1704	1.48161
$313$	22.1312	1.25093	0.625465	−	0.780252i	$-0.284909\pi$
$313$	22.1312	1.25093	0.625465	+	0.780252i	$0.284909\pi$
$314$	4.92808	0.278108
$315$	15.7496	0.887390
$316$	−37.4738	−2.10807
$317$	−14.8072	−0.831657	−0.415828	−	0.909443i	$-0.636508\pi$
$317$	−14.8072	−0.831657	−0.415828	+	0.909443i	$0.636508\pi$
$318$	39.1372	2.19470
$319$	2.52348	0.141288
$320$	−17.0257	−0.951766
$321$	12.6024	0.703398
$322$	39.1273	2.18048
$323$	−30.6214	−1.70382
$324$	161.383	8.96575
$325$	0.944586	0.0523962
$326$	43.3499	2.40093
$327$	40.1701	2.22141
$328$	52.3691	2.89160
$329$	−1.01609	−0.0560186
$330$	5.69313	0.313396
$331$	8.94638	0.491738	0.245869	−	0.969303i	$-0.420927\pi$
$331$	8.94638	0.491738	0.245869	+	0.969303i	$0.420927\pi$
$332$	−16.0743	−0.882190
$333$	66.0905	3.62174
$334$	5.52694	0.302421
$335$	−7.21213	−0.394041
$336$	78.1833	4.26525
$337$	20.7159	1.12847	0.564234	−	0.825615i	$-0.309171\pi$
$337$	20.7159	1.12847	0.564234	+	0.825615i	$0.309171\pi$
$338$	32.3173	1.75783
$339$	24.3128	1.32049
$340$	22.5836	1.22477
$341$	1.19391	0.0646540
$342$	−149.066	−8.06059
$343$	19.9090	1.07499
$344$	80.0306	4.31496
$345$	24.8554	1.33817
$346$	−38.5645	−2.07324
$347$	−30.0321	−1.61221	−0.806104	−	0.591774i	$-0.798428\pi$
$347$	−30.0321	−1.61221	−0.806104	+	0.591774i	$0.798428\pi$
$348$	66.9178	3.58717
$349$	13.4656	0.720797	0.360398	−	0.932798i	$-0.382641\pi$
$349$	13.4656	0.720797	0.360398	+	0.932798i	$0.382641\pi$
$350$	5.22999	0.279555
$351$	−15.8100	−0.843873
$352$	9.87262	0.526212
$353$	0.0373077	0.00198569	0.000992845	−	1.00000i	$-0.499684\pi$
$353$	0.0373077	0.00198569	0.000992845		1.00000i	$0.499684\pi$
$354$	15.1391	0.804635
$355$	3.55614	0.188741
$356$	−87.5463	−4.63995
$357$	−28.6899	−1.51843
$358$	55.9649	2.95783
$359$	−14.3648	−0.758145	−0.379072	−	0.925367i	$-0.623757\pi$
$359$	−14.3648	−0.758145	−0.379072	+	0.925367i	$0.623757\pi$
$360$	67.0297	3.53277
$361$	29.2764	1.54087
$362$	−4.43008	−0.232840
$363$	35.1763	1.84627
$364$	−9.48433	−0.497114
$365$	−11.9857	−0.627359
$366$	83.9090	4.38600
$367$	26.0208	1.35828	0.679139	−	0.734010i	$-0.262354\pi$
$367$	26.0208	1.35828	0.679139	+	0.734010i	$0.262354\pi$
$368$	89.8506	4.68379
$369$	−50.4765	−2.62770
$370$	21.9467	1.14096
$371$	−8.64778	−0.448970
$372$	31.6602	1.64151
$373$	−27.9678	−1.44812	−0.724059	−	0.689738i	$-0.757726\pi$
$373$	−27.9678	−1.44812	−0.724059	+	0.689738i	$0.757726\pi$
$374$	−7.55206	−0.390508
$375$	3.32233	0.171564
$376$	−4.32442	−0.223015
$377$	−3.71283	−0.191220
$378$	−87.5366	−4.50240
$379$	−7.04397	−0.361824	−0.180912	−	0.983499i	$-0.557905\pi$
$379$	−7.04397	−0.361824	−0.180912	+	0.983499i	$0.557905\pi$
$380$	−35.6044	−1.82647
$381$	3.13560	0.160641
$382$	−28.9492	−1.48117
$383$	33.4846	1.71098	0.855491	−	0.517818i	$-0.173255\pi$
$383$	33.4846	1.71098	0.855491	+	0.517818i	$0.173255\pi$
$384$	48.7994	2.49028
$385$	−1.25796	−0.0641114
$386$	39.0496	1.98757
$387$	−77.1384	−3.92116
$388$	−62.3146	−3.16354
$389$	−1.18613	−0.0601392	−0.0300696	−	0.999548i	$-0.509573\pi$
$389$	−1.18613	−0.0601392	−0.0300696	+	0.999548i	$0.509573\pi$
$390$	−8.37637	−0.424154
$391$	−32.9713	−1.66743
$392$	26.3574	1.33125
$393$	−12.7889	−0.645116
$394$	−4.94165	−0.248957
$395$	7.31294	0.367954
$396$	−26.4432	−1.32882
$397$	33.3510	1.67384	0.836920	−	0.547326i	$-0.184354\pi$
$397$	33.3510	1.67384	0.836920	+	0.547326i	$0.184354\pi$
$398$	−72.8866	−3.65347
$399$	45.2313	2.26440
$400$	12.0100	0.600499
$401$	13.0987	0.654119	0.327059	−	0.945004i	$-0.393942\pi$
$401$	13.0987	0.654119	0.327059	+	0.945004i	$0.393942\pi$
$402$	63.9555	3.18981
$403$	−1.75662	−0.0875034
$404$	7.48404	0.372345
$405$	−31.4937	−1.56493
$406$	−20.5572	−1.02024
$407$	−5.27880	−0.261660
$408$	−122.103	−6.04500
$409$	29.3111	1.44934	0.724670	−	0.689096i	$-0.241992\pi$
$409$	29.3111	1.44934	0.724670	+	0.689096i	$0.241992\pi$
$410$	−16.7618	−0.827805
$411$	38.6436	1.90615
$412$	37.0529	1.82547
$413$	−3.34515	−0.164604
$414$	−160.506	−7.88844
$415$	3.13686	0.153982
$416$	−14.5257	−0.712181
$417$	−14.4852	−0.709346
$418$	11.9063	0.582355
$419$	−1.74124	−0.0850651	−0.0425326	−	0.999095i	$-0.513543\pi$
$419$	−1.74124	−0.0850651	−0.0425326	+	0.999095i	$0.513543\pi$
$420$	−33.3586	−1.62773
$421$	4.02454	0.196144	0.0980721	−	0.995179i	$-0.468732\pi$
$421$	4.02454	0.196144	0.0980721	+	0.995179i	$0.468732\pi$
$422$	−19.9994	−0.973555
$423$	4.16814	0.202662
$424$	−36.8046	−1.78739
$425$	−4.40714	−0.213778
$426$	−31.5350	−1.52788
$427$	−18.5406	−0.897243
$428$	−19.4378	−0.939562
$429$	2.01475	0.0972730
$430$	−25.6154	−1.23528
$431$	23.5784	1.13573	0.567866	−	0.823121i	$-0.307769\pi$
$431$	23.5784	1.13573	0.567866	+	0.823121i	$0.307769\pi$
$432$	−201.016	−9.67140
$433$	8.32103	0.399883	0.199941	−	0.979808i	$-0.435925\pi$
$433$	8.32103	0.399883	0.199941	+	0.979808i	$0.435925\pi$
$434$	−9.72605	−0.466865
$435$	−13.0589	−0.626125
$436$	−61.9579	−2.96724
$437$	51.9812	2.48660
$438$	106.286	5.07855
$439$	31.5719	1.50685	0.753423	−	0.657536i	$-0.228401\pi$
$439$	31.5719	1.50685	0.753423	+	0.657536i	$0.228401\pi$
$440$	−5.35381	−0.255233
$441$	−25.4048	−1.20975
$442$	11.1114	0.528517
$443$	−16.7447	−0.795564	−0.397782	−	0.917480i	$-0.630220\pi$
$443$	−16.7447	−0.795564	−0.397782	+	0.917480i	$0.630220\pi$
$444$	−139.983	−6.64332
$445$	17.0845	0.809883
$446$	10.7684	0.509900
$447$	−11.1995	−0.529719
$448$	−33.3606	−1.57614
$449$	26.3664	1.24431	0.622155	−	0.782894i	$-0.286257\pi$
$449$	26.3664	1.24431	0.622155	+	0.782894i	$0.286257\pi$
$450$	−21.4542	−1.01136
$451$	4.03167	0.189844
$452$	−37.4997	−1.76384
$453$	−60.6966	−2.85177
$454$	−56.0553	−2.63081
$455$	1.85085	0.0867691
$456$	192.503	9.01476
$457$	−8.50455	−0.397826	−0.198913	−	0.980017i	$-0.563741\pi$
$457$	−8.50455	−0.397826	−0.198913	+	0.980017i	$0.563741\pi$
$458$	−62.5297	−2.92182
$459$	73.7643	3.44302
$460$	−38.3367	−1.78746
$461$	−19.2327	−0.895755	−0.447877	−	0.894095i	$-0.647820\pi$
$461$	−19.2327	−0.895755	−0.447877	+	0.894095i	$0.647820\pi$
$462$	11.1553	0.518990
$463$	−36.5082	−1.69668	−0.848341	−	0.529450i	$-0.822398\pi$
$463$	−36.5082	−1.69668	−0.848341	+	0.529450i	$0.822398\pi$
$464$	−47.2069	−2.19152
$465$	−6.17843	−0.286518
$466$	−67.7153	−3.13685
$467$	−13.2303	−0.612223	−0.306112	−	0.951996i	$-0.599028\pi$
$467$	−13.2303	−0.612223	−0.306112	+	0.951996i	$0.599028\pi$
$468$	38.9061	1.79844
$469$	−14.1316	−0.652539
$470$	1.38412	0.0638446
$471$	6.13407	0.282643
$472$	−14.2368	−0.655302
$473$	6.16122	0.283293
$474$	−64.8494	−2.97863
$475$	6.94812	0.318802
$476$	44.2509	2.02824
$477$	35.4745	1.62426
$478$	16.1646	0.739352
$479$	28.8235	1.31698	0.658489	−	0.752591i	$-0.271196\pi$
$479$	28.8235	1.31698	0.658489	+	0.752591i	$0.271196\pi$
$480$	−51.0903	−2.33194
$481$	7.76676	0.354134
$482$	56.1678	2.55837
$483$	48.7024	2.21604
$484$	−54.2554	−2.46615
$485$	12.1606	0.552183
$486$	145.255	6.58888
$487$	4.20168	0.190396	0.0951982	−	0.995458i	$-0.469652\pi$
$487$	4.20168	0.190396	0.0951982	+	0.995458i	$0.469652\pi$
$488$	−78.9080	−3.57200
$489$	53.9584	2.44008
$490$	−8.43621	−0.381109
$491$	−29.8752	−1.34825	−0.674124	−	0.738618i	$-0.735479\pi$
$491$	−29.8752	−1.34825	−0.674124	+	0.738618i	$0.735479\pi$
$492$	106.912	4.81997
$493$	17.3229	0.780184
$494$	−17.5178	−0.788165
$495$	5.16033	0.231940
$496$	−22.3346	−1.00285
$497$	6.96801	0.312558
$498$	−27.8169	−1.24651
$499$	17.5246	0.784507	0.392254	−	0.919857i	$-0.371696\pi$
$499$	17.5246	0.784507	0.392254	+	0.919857i	$0.371696\pi$
$500$	−5.12432	−0.229166
$501$	6.87948	0.307353
$502$	−32.7644	−1.46235
$503$	−9.85060	−0.439217	−0.219608	−	0.975588i	$-0.570478\pi$
$503$	−9.85060	−0.439217	−0.219608	+	0.975588i	$0.570478\pi$
$504$	131.340	5.85034
$505$	−1.46049	−0.0649912
$506$	12.8200	0.569917
$507$	40.2259	1.78650
$508$	−4.83630	−0.214576
$509$	26.7467	1.18553	0.592764	−	0.805376i	$-0.298037\pi$
$509$	26.7467	1.18553	0.592764	+	0.805376i	$0.298037\pi$
$510$	39.0815	1.73056
$511$	−23.4851	−1.03892
$512$	15.6205	0.690336
$513$	−116.294	−5.13450
$514$	−5.08500	−0.224290
$515$	−7.23080	−0.318627
$516$	163.383	7.19256
$517$	−0.332919	−0.0146417
$518$	43.0030	1.88945
$519$	−48.0019	−2.10705
$520$	7.87713	0.345435
$521$	−15.9966	−0.700824	−0.350412	−	0.936596i	$-0.613958\pi$
$521$	−15.9966	−0.700824	−0.350412	+	0.936596i	$0.613958\pi$
$522$	84.3287	3.69097
$523$	2.59914	0.113652	0.0568262	−	0.998384i	$-0.481902\pi$
$523$	2.59914	0.113652	0.0568262	+	0.998384i	$0.481902\pi$
$524$	19.7255	0.861711
$525$	6.50986	0.284114
$526$	−80.8004	−3.52307
$527$	8.19583	0.357016
$528$	25.6166	1.11482
$529$	32.9703	1.43349
$530$	11.7800	0.511692
$531$	13.7223	0.595497
$532$	−69.7642	−3.02466
$533$	−5.93185	−0.256937
$534$	−151.501	−6.55610
$535$	3.79325	0.163996
$536$	−60.1437	−2.59781
$537$	69.6605	3.00607
$538$	80.7037	3.47938
$539$	2.02914	0.0874013
$540$	85.7679	3.69086
$541$	−28.2550	−1.21478	−0.607388	−	0.794405i	$-0.707783\pi$
$541$	−28.2550	−1.21478	−0.607388	+	0.794405i	$0.707783\pi$
$542$	−14.8313	−0.637059
$543$	−5.51420	−0.236637
$544$	67.7724	2.90572
$545$	12.0910	0.517920
$546$	−16.4129	−0.702406
$547$	−39.0058	−1.66777	−0.833884	−	0.551939i	$-0.813888\pi$
$547$	−39.0058	−1.66777	−0.833884	+	0.551939i	$0.813888\pi$
$548$	−59.6034	−2.54613
$549$	76.0563	3.24601
$550$	1.71360	0.0730680
$551$	−27.3106	−1.16347
$552$	207.275	8.82223
$553$	14.3292	0.609339
$554$	33.1462	1.40825
$555$	27.3175	1.15956
$556$	22.3419	0.947506
$557$	−46.6827	−1.97801	−0.989006	−	0.147878i	$-0.952756\pi$
$557$	−46.6827	−1.97801	−0.989006	+	0.147878i	$0.952756\pi$
$558$	39.8977	1.68901
$559$	−9.06507	−0.383412
$560$	23.5327	0.994437
$561$	−9.40019	−0.396876
$562$	−31.3731	−1.32339
$563$	−30.0373	−1.26592	−0.632960	−	0.774185i	$-0.718160\pi$
$563$	−30.0373	−1.26592	−0.632960	+	0.774185i	$0.718160\pi$
$564$	−8.82835	−0.371741
$565$	7.31800	0.307870
$566$	−13.1800	−0.553995
$567$	−61.7095	−2.59156
$568$	29.6555	1.24432
$569$	−46.0484	−1.93045	−0.965224	−	0.261425i	$-0.915808\pi$
$569$	−46.0484	−1.93045	−0.965224	+	0.261425i	$0.915808\pi$
$570$	−61.6143	−2.58074
$571$	24.3021	1.01701	0.508507	−	0.861058i	$-0.330198\pi$
$571$	24.3021	1.01701	0.508507	+	0.861058i	$0.330198\pi$
$572$	−3.10752	−0.129932
$573$	−36.0336	−1.50533
$574$	−32.8435	−1.37086
$575$	7.48133	0.311993
$576$	136.850	5.70209
$577$	−18.8486	−0.784677	−0.392339	−	0.919821i	$-0.628334\pi$
$577$	−18.8486	−0.784677	−0.392339	+	0.919821i	$0.628334\pi$
$578$	−6.46709	−0.268996
$579$	48.6057	2.01998
$580$	20.1418	0.836344
$581$	6.14645	0.254998
$582$	−107.837	−4.46999
$583$	−2.83343	−0.117349
$584$	−99.9514	−4.13602
$585$	−7.59245	−0.313909
$586$	−0.113200	−0.00467624
$587$	46.7228	1.92846	0.964229	−	0.265072i	$-0.0853957\pi$
$587$	46.7228	1.92846	0.964229	+	0.265072i	$0.0853957\pi$
$588$	53.8089	2.21904
$589$	−12.9212	−0.532410
$590$	4.55678	0.187600
$591$	−6.15097	−0.253017
$592$	98.7508	4.05863
$593$	−18.6677	−0.766590	−0.383295	−	0.923626i	$-0.625211\pi$
$593$	−18.6677	−0.766590	−0.383295	+	0.923626i	$0.625211\pi$
$594$	−28.6812	−1.17680
$595$	−8.63548	−0.354020
$596$	17.2740	0.707570
$597$	−90.7232	−3.71305
$598$	−18.8622	−0.771332
$599$	24.1280	0.985844	0.492922	−	0.870074i	$-0.335929\pi$
$599$	24.1280	0.985844	0.492922	+	0.870074i	$0.335929\pi$
$600$	27.7057	1.13108
$601$	−9.70101	−0.395713	−0.197856	−	0.980231i	$-0.563398\pi$
$601$	−9.70101	−0.395713	−0.197856	+	0.980231i	$0.563398\pi$
$602$	−50.1915	−2.04565
$603$	57.9701	2.36073
$604$	93.6176	3.80925
$605$	10.5878	0.430457
$606$	12.9513	0.526111
$607$	15.5326	0.630450	0.315225	−	0.949017i	$-0.397920\pi$
$607$	15.5326	0.630450	0.315225	+	0.949017i	$0.397920\pi$
$608$	−106.847	−4.33323
$609$	−25.5879	−1.03687
$610$	25.2561	1.02259
$611$	0.489827	0.0198163
$612$	−181.524	−7.33767
$613$	−24.2290	−0.978599	−0.489300	−	0.872116i	$-0.662748\pi$
$613$	−24.2290	−0.978599	−0.489300	+	0.872116i	$0.662748\pi$
$614$	−43.9241	−1.77263
$615$	−20.8637	−0.841305
$616$	−10.4904	−0.422671
$617$	33.3925	1.34433	0.672166	−	0.740401i	$-0.265364\pi$
$617$	33.3925	1.34433	0.672166	+	0.740401i	$0.265364\pi$
$618$	64.1210	2.57933
$619$	−34.1967	−1.37448	−0.687241	−	0.726430i	$-0.741178\pi$
$619$	−34.1967	−1.37448	−0.687241	+	0.726430i	$0.741178\pi$
$620$	9.52954	0.382715
$621$	−125.218	−5.02484
$622$	45.2567	1.81463
$623$	33.4758	1.34118
$624$	−37.6900	−1.50881
$625$	1.00000	0.0400000
$626$	−59.0714	−2.36097
$627$	14.8200	0.591852
$628$	−9.46110	−0.377539
$629$	−36.2373	−1.44488
$630$	−42.0379	−1.67483
$631$	25.7778	1.02620	0.513100	−	0.858329i	$-0.328497\pi$
$631$	25.7778	1.02620	0.513100	+	0.858329i	$0.328497\pi$
$632$	60.9844	2.42583
$633$	−24.8936	−0.989432
$634$	39.5226	1.56964
$635$	0.943795	0.0374533
$636$	−75.1370	−2.97938
$637$	−2.98550	−0.118290
$638$	−6.73552	−0.266662
$639$	−28.5838	−1.13076
$640$	14.6883	0.580606
$641$	15.9087	0.628358	0.314179	−	0.949364i	$-0.398271\pi$
$641$	15.9087	0.628358	0.314179	+	0.949364i	$0.398271\pi$
$642$	−33.6376	−1.32757
$643$	−21.2458	−0.837854	−0.418927	−	0.908020i	$-0.637594\pi$
$643$	−21.2458	−0.837854	−0.418927	+	0.908020i	$0.637594\pi$
$644$	−75.1180	−2.96006
$645$	−31.8840	−1.25543
$646$	81.7328	3.21573
$647$	−1.83076	−0.0719746	−0.0359873	−	0.999352i	$-0.511458\pi$
$647$	−1.83076	−0.0719746	−0.0359873	+	0.999352i	$0.511458\pi$
$648$	−262.633	−10.3172
$649$	−1.09603	−0.0430230
$650$	−2.52123	−0.0988909
$651$	−12.1062	−0.474479
$652$	−83.2247	−3.25933
$653$	7.06822	0.276601	0.138300	−	0.990390i	$-0.455836\pi$
$653$	7.06822	0.276601	0.138300	+	0.990390i	$0.455836\pi$
$654$	−107.220	−4.19262
$655$	−3.84938	−0.150408
$656$	−75.4207	−2.94469
$657$	96.3392	3.75855
$658$	2.71208	0.105728
$659$	27.2074	1.05985	0.529926	−	0.848044i	$-0.322220\pi$
$659$	27.2074	1.05985	0.529926	+	0.848044i	$0.322220\pi$
$660$	−10.9299	−0.425445
$661$	−6.62769	−0.257787	−0.128894	−	0.991658i	$-0.541143\pi$
$661$	−6.62769	−0.257787	−0.128894	+	0.991658i	$0.541143\pi$
$662$	−23.8792	−0.928090
$663$	13.8306	0.537136
$664$	26.1590	1.01517
$665$	13.6143	0.527942
$666$	−176.405	−6.83555
$667$	−29.4064	−1.13862
$668$	−10.6108	−0.410545
$669$	13.4037	0.518216
$670$	19.2502	0.743700
$671$	−6.07479	−0.234515
$672$	−100.108	−3.86174
$673$	5.13063	0.197771	0.0988856	−	0.995099i	$-0.468472\pi$
$673$	5.13063	0.197771	0.0988856	+	0.995099i	$0.468472\pi$
$674$	−55.2937	−2.12984
$675$	−16.7374	−0.644224
$676$	−62.0440	−2.38631
$677$	−44.2163	−1.69937	−0.849686	−	0.527289i	$-0.823209\pi$
$677$	−44.2163	−1.69937	−0.849686	+	0.527289i	$0.823209\pi$
$678$	−64.8943	−2.49225
$679$	23.8278	0.914425
$680$	−36.7522	−1.40938
$681$	−69.7730	−2.67371
$682$	−3.18672	−0.122026
$683$	−13.2432	−0.506738	−0.253369	−	0.967370i	$-0.581539\pi$
$683$	−13.2432	−0.506738	−0.253369	+	0.967370i	$0.581539\pi$
$684$	286.183	10.9425
$685$	11.6315	0.444416
$686$	−53.1401	−2.02890
$687$	−77.8318	−2.96947
$688$	−115.258	−4.39418
$689$	4.16886	0.158821
$690$	−66.3427	−2.52562
$691$	−15.8204	−0.601835	−0.300918	−	0.953650i	$-0.597293\pi$
$691$	−15.8204	−0.601835	−0.300918	+	0.953650i	$0.597293\pi$
$692$	74.0376	2.81449
$693$	10.1113	0.384096
$694$	80.1600	3.04283
$695$	−4.35997	−0.165383
$696$	−108.901	−4.12788
$697$	27.6762	1.04831
$698$	−35.9416	−1.36041
$699$	−84.2864	−3.18801
$700$	−10.0407	−0.379504
$701$	−3.53650	−0.133572	−0.0667859	−	0.997767i	$-0.521274\pi$
$701$	−3.53650	−0.133572	−0.0667859	+	0.997767i	$0.521274\pi$
$702$	42.1990	1.59270
$703$	57.1302	2.15471
$704$	−10.9305	−0.411960
$705$	1.72284	0.0648857
$706$	−0.0995796	−0.00374773
$707$	−2.86173	−0.107627
$708$	−29.0646	−1.09232
$709$	−26.2866	−0.987213	−0.493607	−	0.869685i	$-0.664322\pi$
$709$	−26.2866	−0.987213	−0.493607	+	0.869685i	$0.664322\pi$
$710$	−9.49185	−0.356223
$711$	−58.7804	−2.20444
$712$	142.472	5.33935
$713$	−13.9128	−0.521039
$714$	76.5774	2.86584
$715$	0.606427	0.0226791
$716$	−107.443	−4.01535
$717$	20.1204	0.751409
$718$	38.3417	1.43090
$719$	31.5866	1.17798	0.588991	−	0.808139i	$-0.299525\pi$
$719$	31.5866	1.17798	0.588991	+	0.808139i	$0.299525\pi$
$720$	−96.5346	−3.59763
$721$	−14.1682	−0.527652
$722$	−78.1429	−2.90818
$723$	69.9131	2.60009
$724$	8.50503	0.316087
$725$	−3.93064	−0.145980
$726$	−93.8904	−3.48460
$727$	21.3305	0.791104	0.395552	−	0.918444i	$-0.370553\pi$
$727$	21.3305	0.791104	0.395552	+	0.918444i	$0.370553\pi$
$728$	15.4347	0.572047
$729$	86.3200	3.19704
$730$	31.9915	1.18406
$731$	42.2948	1.56433
$732$	−161.092	−5.95412
$733$	−1.43517	−0.0530094	−0.0265047	−	0.999649i	$-0.508438\pi$
$733$	−1.43517	−0.0530094	−0.0265047	+	0.999649i	$0.508438\pi$
$734$	−69.4533	−2.56357
$735$	−10.5007	−0.387324
$736$	−115.047	−4.24068
$737$	−4.63021	−0.170556
$738$	134.729	4.95944
$739$	−48.9951	−1.80231	−0.901156	−	0.433494i	$-0.857281\pi$
$739$	−48.9951	−1.80231	−0.901156	+	0.433494i	$0.857281\pi$
$740$	−42.1342	−1.54888
$741$	−21.8048	−0.801019
$742$	23.0821	0.847372
$743$	−1.57359	−0.0577294	−0.0288647	−	0.999583i	$-0.509189\pi$
$743$	−1.57359	−0.0577294	−0.0288647	+	0.999583i	$0.509189\pi$
$744$	−51.5234	−1.88894
$745$	−3.37098	−0.123503
$746$	74.6500	2.73313
$747$	−25.2137	−0.922520
$748$	14.4987	0.530126
$749$	7.43260	0.271581
$750$	−8.86776	−0.323805
$751$	41.2129	1.50388	0.751940	−	0.659231i	$-0.229118\pi$
$751$	41.2129	1.50388	0.751940	+	0.659231i	$0.229118\pi$
$752$	6.22793	0.227109
$753$	−40.7824	−1.48619
$754$	9.91006	0.360903
$755$	−18.2693	−0.664888
$756$	168.056	6.11214
$757$	−5.64453	−0.205154	−0.102577	−	0.994725i	$-0.532709\pi$
$757$	−5.64453	−0.205154	−0.102577	+	0.994725i	$0.532709\pi$
$758$	18.8013	0.682896
$759$	15.9573	0.579212
$760$	57.9421	2.10178
$761$	20.9055	0.757825	0.378913	−	0.925432i	$-0.376298\pi$
$761$	20.9055	0.757825	0.378913	+	0.925432i	$0.376298\pi$
$762$	−8.36935	−0.303189
$763$	23.6914	0.857685
$764$	55.5778	2.01073
$765$	35.4240	1.28076
$766$	−89.3751	−3.22925
$767$	1.61260	0.0582278
$768$	−17.1224	−0.617853
$769$	12.5592	0.452896	0.226448	−	0.974023i	$-0.427289\pi$
$769$	12.5592	0.452896	0.226448	+	0.974023i	$0.427289\pi$
$770$	3.35767	0.121002
$771$	−6.32939	−0.227947
$772$	−74.9688	−2.69819
$773$	0.279575	0.0100556	0.00502781	−	0.999987i	$-0.498400\pi$
$773$	0.279575	0.0100556	0.00502781	+	0.999987i	$0.498400\pi$
$774$	205.893	7.40068
$775$	−1.85967	−0.0668013
$776$	101.410	3.64040
$777$	53.5267	1.92026
$778$	3.16595	0.113505
$779$	−43.6331	−1.56332
$780$	16.0813	0.575801
$781$	2.28305	0.0816941
$782$	88.0051	3.14705
$783$	65.7888	2.35110
$784$	−37.9593	−1.35569
$785$	1.84632	0.0658978
$786$	34.1354	1.21757
$787$	−38.2629	−1.36393	−0.681963	−	0.731387i	$-0.738873\pi$
$787$	−38.2629	−1.36393	−0.681963	+	0.731387i	$0.738873\pi$
$788$	9.48717	0.337966
$789$	−100.574	−3.58052
$790$	−19.5193	−0.694465
$791$	14.3391	0.509839
$792$	43.0332	1.52912
$793$	8.93792	0.317395
$794$	−89.0186	−3.15915
$795$	14.6628	0.520037
$796$	139.930	4.95970
$797$	−12.9873	−0.460034	−0.230017	−	0.973187i	$-0.573878\pi$
$797$	−12.9873	−0.460034	−0.230017	+	0.973187i	$0.573878\pi$
$798$	−120.729	−4.27375
$799$	−2.28538	−0.0808510
$800$	−15.3779	−0.543689
$801$	−137.323	−4.85206
$802$	−34.9623	−1.23456
$803$	−7.69484	−0.271545
$804$	−122.784	−4.33026
$805$	14.6591	0.516666
$806$	4.68866	0.165151
$807$	100.453	3.53613
$808$	−12.1794	−0.428470
$809$	−27.9012	−0.980953	−0.490476	−	0.871454i	$-0.663177\pi$
$809$	−27.9012	−0.980953	−0.490476	+	0.871454i	$0.663177\pi$
$810$	84.0610	2.95360
$811$	−17.4935	−0.614279	−0.307139	−	0.951665i	$-0.599372\pi$
$811$	−17.4935	−0.614279	−0.307139	+	0.951665i	$0.599372\pi$
$812$	39.4665	1.38500
$813$	−18.4608	−0.647448
$814$	14.0899	0.493849
$815$	16.2411	0.568902
$816$	175.850	6.15598
$817$	−66.6803	−2.33285
$818$	−78.2355	−2.73544
$819$	−14.8769	−0.519840
$820$	32.1799	1.12377
$821$	−34.1512	−1.19189	−0.595943	−	0.803027i	$-0.703221\pi$
$821$	−34.1512	−1.19189	−0.595943	+	0.803027i	$0.703221\pi$
$822$	−103.145	−3.59760
$823$	34.7802	1.21236	0.606181	−	0.795327i	$-0.292701\pi$
$823$	34.7802	1.21236	0.606181	+	0.795327i	$0.292701\pi$
$824$	−60.2994	−2.10063
$825$	2.13294	0.0742596
$826$	8.92867	0.310668
$827$	−24.6743	−0.858011	−0.429005	−	0.903302i	$-0.641136\pi$
$827$	−24.6743	−0.858011	−0.429005	+	0.903302i	$0.641136\pi$
$828$	308.145	10.7088
$829$	21.1800	0.735610	0.367805	−	0.929903i	$-0.380109\pi$
$829$	21.1800	0.735610	0.367805	+	0.929903i	$0.380109\pi$
$830$	−8.37273	−0.290622
$831$	41.2577	1.43121
$832$	16.0822	0.557551
$833$	13.9294	0.482626
$834$	38.6632	1.33880
$835$	2.07068	0.0716589
$836$	−22.8581	−0.790564
$837$	31.1261	1.07588
$838$	4.64761	0.160549
$839$	13.6729	0.472041	0.236021	−	0.971748i	$-0.424157\pi$
$839$	13.6729	0.472041	0.236021	+	0.971748i	$0.424157\pi$
$840$	54.2873	1.87309
$841$	−13.5501	−0.467244
$842$	−10.7421	−0.370196
$843$	−39.0506	−1.34497
$844$	38.3956	1.32163
$845$	12.1078	0.416520
$846$	−11.1253	−0.382497
$847$	20.7461	0.712844
$848$	53.0051	1.82020
$849$	−16.4053	−0.563029
$850$	11.7633	0.403477
$851$	61.5145	2.10869
$852$	60.5421	2.07414
$853$	35.4542	1.21393	0.606964	−	0.794730i	$-0.292387\pi$
$853$	35.4542	1.21393	0.606964	+	0.794730i	$0.292387\pi$
$854$	49.4875	1.69343
$855$	−55.8481	−1.90996
$856$	31.6328	1.08119
$857$	−47.5947	−1.62580	−0.812902	−	0.582401i	$-0.802114\pi$
$857$	−47.5947	−1.62580	−0.812902	+	0.582401i	$0.802114\pi$
$858$	−5.37765	−0.183590
$859$	25.9968	0.887001	0.443500	−	0.896274i	$-0.353736\pi$
$859$	25.9968	0.887001	0.443500	+	0.896274i	$0.353736\pi$
$860$	49.1774	1.67694
$861$	−40.8809	−1.39322
$862$	−62.9341	−2.14354
$863$	48.6311	1.65542	0.827712	−	0.561154i	$-0.189642\pi$
$863$	48.6311	1.65542	0.827712	+	0.561154i	$0.189642\pi$
$864$	257.386	8.75644
$865$	−14.4483	−0.491256
$866$	−22.2100	−0.754726
$867$	−8.04971	−0.273382
$868$	18.6724	0.633784
$869$	4.69493	0.159265
$870$	34.8560	1.18173
$871$	6.81248	0.230832
$872$	100.829	3.41451
$873$	−97.7450	−3.30817
$874$	−138.745	−4.69313
$875$	1.95943	0.0662407
$876$	−204.052	−6.89428
$877$	49.5101	1.67184	0.835918	−	0.548855i	$-0.184936\pi$
$877$	49.5101	1.67184	0.835918	+	0.548855i	$0.184936\pi$
$878$	−84.2700	−2.84397
$879$	−0.140902	−0.00475250
$880$	7.71044	0.259919
$881$	−21.7332	−0.732211	−0.366105	−	0.930573i	$-0.619309\pi$
$881$	−21.7332	−0.732211	−0.366105	+	0.930573i	$0.619309\pi$
$882$	67.8091	2.28325
$883$	−25.4916	−0.857860	−0.428930	−	0.903338i	$-0.641109\pi$
$883$	−25.4916	−0.857860	−0.428930	+	0.903338i	$0.641109\pi$
$884$	−21.3321	−0.717478
$885$	5.67190	0.190659
$886$	44.6939	1.50152
$887$	−33.3996	−1.12145	−0.560724	−	0.828003i	$-0.689477\pi$
$887$	−33.3996	−1.12145	−0.560724	+	0.828003i	$0.689477\pi$
$888$	227.807	7.64471
$889$	1.84930	0.0620234
$890$	−45.6009	−1.52855
$891$	−20.2190	−0.677363
$892$	−20.6736	−0.692205
$893$	3.60304	0.120571
$894$	29.8931	0.999774
$895$	20.9674	0.700862
$896$	28.7807	0.961494
$897$	−23.4781	−0.783911
$898$	−70.3758	−2.34847
$899$	7.30969	0.243792
$900$	41.1886	1.37295
$901$	−19.4506	−0.647993
$902$	−10.7611	−0.358306
$903$	−62.4743	−2.07901
$904$	61.0265	2.02971
$905$	−1.65974	−0.0551716
$906$	162.008	5.38235
$907$	−56.4472	−1.87430	−0.937150	−	0.348927i	$-0.886546\pi$
$907$	−56.4472	−1.87430	−0.937150	+	0.348927i	$0.886546\pi$
$908$	107.617	3.57140
$909$	11.7393	0.389367
$910$	−4.94017	−0.163765
$911$	36.5380	1.21056	0.605279	−	0.796013i	$-0.293061\pi$
$911$	36.5380	1.21056	0.605279	+	0.796013i	$0.293061\pi$
$912$	−277.238	−9.18026
$913$	2.01387	0.0666495
$914$	22.6998	0.750844
$915$	31.4367	1.03927
$916$	120.047	3.96646
$917$	−7.54259	−0.249078
$918$	−196.887	−6.49825
$919$	10.5544	0.348158	0.174079	−	0.984732i	$-0.444305\pi$
$919$	10.5544	0.348158	0.174079	+	0.984732i	$0.444305\pi$
$920$	62.3886	2.05689
$921$	−54.6731	−1.80154
$922$	51.3347	1.69062
$923$	−3.35908	−0.110566
$924$	−21.4163	−0.704544
$925$	8.22240	0.270351
$926$	97.4456	3.20226
$927$	58.1202	1.90892
$928$	60.4448	1.98420
$929$	4.69049	0.153890	0.0769449	−	0.997035i	$-0.475483\pi$
$929$	4.69049	0.153890	0.0769449	+	0.997035i	$0.475483\pi$
$930$	16.4911	0.540765
$931$	−21.9606	−0.719728
$932$	130.002	4.25837
$933$	56.3318	1.84422
$934$	35.3134	1.15549
$935$	−2.82940	−0.0925312
$936$	−63.3153	−2.06953
$937$	21.2227	0.693315	0.346657	−	0.937992i	$-0.387317\pi$
$937$	21.2227	0.693315	0.346657	+	0.937992i	$0.387317\pi$
$938$	37.7194	1.23158
$939$	−73.5272	−2.39947
$940$	−2.65728	−0.0866709
$941$	−49.6213	−1.61761	−0.808803	−	0.588079i	$-0.799884\pi$
$941$	−49.6213	−1.61761	−0.808803	+	0.588079i	$0.799884\pi$
$942$	−16.3727	−0.533451
$943$	−46.9816	−1.52993
$944$	20.5035	0.667333
$945$	−32.7958	−1.06685
$946$	−16.4452	−0.534678
$947$	−30.0246	−0.975669	−0.487835	−	0.872936i	$-0.662213\pi$
$947$	−30.0246	−0.975669	−0.487835	+	0.872936i	$0.662213\pi$
$948$	124.500	4.04358
$949$	11.3215	0.367512
$950$	−18.5455	−0.601696
$951$	49.1945	1.59524
$952$	−72.0133	−2.33396
$953$	−51.8574	−1.67983	−0.839913	−	0.542721i	$-0.817394\pi$
$953$	−51.8574	−1.67983	−0.839913	+	0.542721i	$0.817394\pi$
$954$	−94.6864	−3.06559
$955$	−10.8459	−0.350965
$956$	−31.0334	−1.00369
$957$	−8.38383	−0.271011
$958$	−76.9339	−2.48562
$959$	22.7910	0.735961
$960$	56.5650	1.82563
$961$	−27.5416	−0.888440
$962$	−20.7306	−0.668381
$963$	−30.4896	−0.982514
$964$	−107.833	−3.47307
$965$	14.6300	0.470957
$966$	−129.994	−4.18248
$967$	−4.38184	−0.140911	−0.0704553	−	0.997515i	$-0.522445\pi$
$967$	−4.38184	−0.140911	−0.0704553	+	0.997515i	$0.522445\pi$
$968$	88.2945	2.83789
$969$	101.734	3.26818
$970$	−32.4583	−1.04217
$971$	30.0662	0.964869	0.482435	−	0.875932i	$-0.339753\pi$
$971$	30.0662	0.964869	0.482435	+	0.875932i	$0.339753\pi$
$972$	−278.865	−8.94460
$973$	−8.54304	−0.273877
$974$	−11.2149	−0.359348
$975$	−3.13822	−0.100504
$976$	113.641	3.63758
$977$	−35.4888	−1.13539	−0.567694	−	0.823240i	$-0.692164\pi$
$977$	−35.4888	−1.13539	−0.567694	+	0.823240i	$0.692164\pi$
$978$	−144.023	−4.60533
$979$	10.9683	0.350548
$980$	16.1961	0.517367
$981$	−97.1855	−3.10289
$982$	79.7411	2.54464
$983$	−5.73665	−0.182971	−0.0914853	−	0.995806i	$-0.529161\pi$
$983$	−5.73665	−0.182971	−0.0914853	+	0.995806i	$0.529161\pi$
$984$	−173.987	−5.54651
$985$	−1.85140	−0.0589906
$986$	−46.2372	−1.47249
$987$	3.37577	0.107452
$988$	33.6314	1.06996
$989$	−71.7974	−2.28302
$990$	−13.7736	−0.437755
$991$	−27.6388	−0.877976	−0.438988	−	0.898493i	$-0.644663\pi$
$991$	−27.6388	−0.877976	−0.438988	+	0.898493i	$0.644663\pi$
$992$	28.5977	0.907979
$993$	−29.7228	−0.943225
$994$	−18.5986	−0.589911
$995$	−27.3071	−0.865694
$996$	53.4040	1.69217
$997$	−40.3545	−1.27804	−0.639020	−	0.769190i	$-0.720660\pi$
$997$	−40.3545	−1.27804	−0.639020	+	0.769190i	$0.720660\pi$
$998$	−46.7756	−1.48065
$999$	−137.622	−4.35416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.10	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.10	✓	140	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66914 q^{2} -3.32233 q^{3} +5.12432 q^{4} -1.00000 q^{5} +8.86776 q^{6} -1.95943 q^{7} -8.33924 q^{8} +8.03786 q^{9} +O(q^{10})\)	\(q-2.66914 q^{2} -3.32233 q^{3} +5.12432 q^{4} -1.00000 q^{5} +8.86776 q^{6} -1.95943 q^{7} -8.33924 q^{8} +8.03786 q^{9} +2.66914 q^{10} -0.642003 q^{11} -17.0247 q^{12} +0.944586 q^{13} +5.22999 q^{14} +3.32233 q^{15} +12.0100 q^{16} -4.40714 q^{17} -21.4542 q^{18} +6.94812 q^{19} -5.12432 q^{20} +6.50986 q^{21} +1.71360 q^{22} +7.48133 q^{23} +27.7057 q^{24} +1.00000 q^{25} -2.52123 q^{26} -16.7374 q^{27} -10.0407 q^{28} -3.93064 q^{29} -8.86776 q^{30} -1.85967 q^{31} -15.3779 q^{32} +2.13294 q^{33} +11.7633 q^{34} +1.95943 q^{35} +41.1886 q^{36} +8.22240 q^{37} -18.5455 q^{38} -3.13822 q^{39} +8.33924 q^{40} -6.27984 q^{41} -17.3757 q^{42} -9.59687 q^{43} -3.28982 q^{44} -8.03786 q^{45} -19.9687 q^{46} +0.518563 q^{47} -39.9011 q^{48} -3.16064 q^{49} -2.66914 q^{50} +14.6420 q^{51} +4.84036 q^{52} +4.41342 q^{53} +44.6746 q^{54} +0.642003 q^{55} +16.3401 q^{56} -23.0840 q^{57} +10.4914 q^{58} +1.70721 q^{59} +17.0247 q^{60} +9.46226 q^{61} +4.96372 q^{62} -15.7496 q^{63} +17.0257 q^{64} -0.944586 q^{65} -5.69313 q^{66} +7.21213 q^{67} -22.5836 q^{68} -24.8554 q^{69} -5.22999 q^{70} -3.55614 q^{71} -67.0297 q^{72} +11.9857 q^{73} -21.9467 q^{74} -3.32233 q^{75} +35.6044 q^{76} +1.25796 q^{77} +8.37637 q^{78} -7.31294 q^{79} -12.0100 q^{80} +31.4937 q^{81} +16.7618 q^{82} -3.13686 q^{83} +33.3586 q^{84} +4.40714 q^{85} +25.6154 q^{86} +13.0589 q^{87} +5.35381 q^{88} -17.0845 q^{89} +21.4542 q^{90} -1.85085 q^{91} +38.3367 q^{92} +6.17843 q^{93} -1.38412 q^{94} -6.94812 q^{95} +51.0903 q^{96} -12.1606 q^{97} +8.43621 q^{98} -5.16033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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