LMFDB - Embedded newform 8035.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.44538 q^{2} -0.0835630 q^{3} +3.97986 q^{4} -1.00000 q^{5} +0.204343 q^{6} +5.18435 q^{7} -4.84151 q^{8} -2.99302 q^{9} +O(q^{10})$	\(q-2.44538 q^{2} -0.0835630 q^{3} +3.97986 q^{4} -1.00000 q^{5} +0.204343 q^{6} +5.18435 q^{7} -4.84151 q^{8} -2.99302 q^{9} +2.44538 q^{10} -5.05128 q^{11} -0.332569 q^{12} +5.39497 q^{13} -12.6777 q^{14} +0.0835630 q^{15} +3.87959 q^{16} -1.52139 q^{17} +7.31905 q^{18} -4.90382 q^{19} -3.97986 q^{20} -0.433220 q^{21} +12.3523 q^{22} -6.97445 q^{23} +0.404571 q^{24} +1.00000 q^{25} -13.1927 q^{26} +0.500795 q^{27} +20.6330 q^{28} -2.01827 q^{29} -0.204343 q^{30} -5.98869 q^{31} +0.195969 q^{32} +0.422100 q^{33} +3.72037 q^{34} -5.18435 q^{35} -11.9118 q^{36} +7.68246 q^{37} +11.9917 q^{38} -0.450820 q^{39} +4.84151 q^{40} +7.39201 q^{41} +1.05939 q^{42} +1.95084 q^{43} -20.1034 q^{44} +2.99302 q^{45} +17.0551 q^{46} +9.44148 q^{47} -0.324190 q^{48} +19.8775 q^{49} -2.44538 q^{50} +0.127132 q^{51} +21.4713 q^{52} +12.0253 q^{53} -1.22463 q^{54} +5.05128 q^{55} -25.1001 q^{56} +0.409778 q^{57} +4.93543 q^{58} -2.47893 q^{59} +0.332569 q^{60} -5.60578 q^{61} +14.6446 q^{62} -15.5168 q^{63} -8.23840 q^{64} -5.39497 q^{65} -1.03219 q^{66} +1.21720 q^{67} -6.05492 q^{68} +0.582806 q^{69} +12.6777 q^{70} -13.1153 q^{71} +14.4907 q^{72} -12.4890 q^{73} -18.7865 q^{74} -0.0835630 q^{75} -19.5165 q^{76} -26.1876 q^{77} +1.10242 q^{78} +2.83376 q^{79} -3.87959 q^{80} +8.93720 q^{81} -18.0762 q^{82} +16.2685 q^{83} -1.72416 q^{84} +1.52139 q^{85} -4.77055 q^{86} +0.168653 q^{87} +24.4558 q^{88} +9.68757 q^{89} -7.31905 q^{90} +27.9694 q^{91} -27.7574 q^{92} +0.500433 q^{93} -23.0880 q^{94} +4.90382 q^{95} -0.0163758 q^{96} -7.64489 q^{97} -48.6078 q^{98} +15.1186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44538	−1.72914	−0.864571	−	0.502511i	$-0.832410\pi$
$2$	−2.44538	−1.72914	−0.864571	+	0.502511i	$0.832410\pi$
$3$	−0.0835630	−0.0482451	−0.0241226	−	0.999709i	$-0.507679\pi$
$3$	−0.0835630	−0.0482451	−0.0241226	+	0.999709i	$0.507679\pi$
$4$	3.97986	1.98993
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.204343	0.0834227
$7$	5.18435	1.95950	0.979749	−	0.200227i	$-0.0641680\pi$
$7$	5.18435	1.95950	0.979749	+	0.200227i	$0.0641680\pi$
$8$	−4.84151	−1.71173
$9$	−2.99302	−0.997672
$10$	2.44538	0.773296
$11$	−5.05128	−1.52302	−0.761509	−	0.648154i	$-0.775541\pi$
$11$	−5.05128	−1.52302	−0.761509	+	0.648154i	$0.775541\pi$
$12$	−0.332569	−0.0960045
$13$	5.39497	1.49630	0.748148	−	0.663532i	$-0.230943\pi$
$13$	5.39497	1.49630	0.748148	+	0.663532i	$0.230943\pi$
$14$	−12.6777	−3.38825
$15$	0.0835630	0.0215759
$16$	3.87959	0.969897
$17$	−1.52139	−0.368991	−0.184495	−	0.982833i	$-0.559065\pi$
$17$	−1.52139	−0.368991	−0.184495	+	0.982833i	$0.559065\pi$
$18$	7.31905	1.72512
$19$	−4.90382	−1.12501	−0.562506	−	0.826793i	$-0.690163\pi$
$19$	−4.90382	−1.12501	−0.562506	+	0.826793i	$0.690163\pi$
$20$	−3.97986	−0.889925
$21$	−0.433220	−0.0945363
$22$	12.3523	2.63351
$23$	−6.97445	−1.45427	−0.727136	−	0.686493i	$-0.759149\pi$
$23$	−6.97445	−1.45427	−0.727136	+	0.686493i	$0.759149\pi$
$24$	0.404571	0.0825828
$25$	1.00000	0.200000
$26$	−13.1927	−2.58731
$27$	0.500795	0.0963780
$28$	20.6330	3.89927
$29$	−2.01827	−0.374783	−0.187392	−	0.982285i	$-0.560003\pi$
$29$	−2.01827	−0.374783	−0.187392	+	0.982285i	$0.560003\pi$
$30$	−0.204343	−0.0373078
$31$	−5.98869	−1.07560	−0.537801	−	0.843072i	$-0.680745\pi$
$31$	−5.98869	−1.07560	−0.537801	+	0.843072i	$0.680745\pi$
$32$	0.195969	0.0346427
$33$	0.422100	0.0734782
$34$	3.72037	0.638038
$35$	−5.18435	−0.876315
$36$	−11.9118	−1.98530
$37$	7.68246	1.26299	0.631494	−	0.775381i	$-0.282442\pi$
$37$	7.68246	1.26299	0.631494	+	0.775381i	$0.282442\pi$
$38$	11.9917	1.94531
$39$	−0.450820	−0.0721890
$40$	4.84151	0.765510
$41$	7.39201	1.15444	0.577219	−	0.816589i	$-0.304138\pi$
$41$	7.39201	1.15444	0.577219	+	0.816589i	$0.304138\pi$
$42$	1.05939	0.163467
$43$	1.95084	0.297501	0.148751	−	0.988875i	$-0.452475\pi$
$43$	1.95084	0.297501	0.148751	+	0.988875i	$0.452475\pi$
$44$	−20.1034	−3.03070
$45$	2.99302	0.446173
$46$	17.0551	2.51464
$47$	9.44148	1.37718	0.688590	−	0.725151i	$-0.258230\pi$
$47$	9.44148	1.37718	0.688590	+	0.725151i	$0.258230\pi$
$48$	−0.324190	−0.0467928
$49$	19.8775	2.83964
$50$	−2.44538	−0.345828
$51$	0.127132	0.0178020
$52$	21.4713	2.97753
$53$	12.0253	1.65180	0.825902	−	0.563814i	$-0.190667\pi$
$53$	12.0253	1.65180	0.825902	+	0.563814i	$0.190667\pi$
$54$	−1.22463	−0.166651
$55$	5.05128	0.681114
$56$	−25.1001	−3.35414
$57$	0.409778	0.0542764
$58$	4.93543	0.648053
$59$	−2.47893	−0.322729	−0.161364	−	0.986895i	$-0.551589\pi$
$59$	−2.47893	−0.322729	−0.161364	+	0.986895i	$0.551589\pi$
$60$	0.332569	0.0429345
$61$	−5.60578	−0.717747	−0.358873	−	0.933386i	$-0.616839\pi$
$61$	−5.60578	−0.717747	−0.358873	+	0.933386i	$0.616839\pi$
$62$	14.6446	1.85987
$63$	−15.5168	−1.95494
$64$	−8.23840	−1.02980
$65$	−5.39497	−0.669164
$66$	−1.03219	−0.127054
$67$	1.21720	0.148704	0.0743521	−	0.997232i	$-0.476311\pi$
$67$	1.21720	0.148704	0.0743521	+	0.997232i	$0.476311\pi$
$68$	−6.05492	−0.734267
$69$	0.582806	0.0701616
$70$	12.6777	1.51527
$71$	−13.1153	−1.55650	−0.778250	−	0.627955i	$-0.783892\pi$
$71$	−13.1153	−1.55650	−0.778250	+	0.627955i	$0.783892\pi$
$72$	14.4907	1.70775
$73$	−12.4890	−1.46172	−0.730861	−	0.682527i	$-0.760881\pi$
$73$	−12.4890	−1.46172	−0.730861	+	0.682527i	$0.760881\pi$
$74$	−18.7865	−2.18389
$75$	−0.0835630	−0.00964903
$76$	−19.5165	−2.23870
$77$	−26.1876	−2.98435
$78$	1.10242	0.124825
$79$	2.83376	0.318823	0.159412	−	0.987212i	$-0.449040\pi$
$79$	2.83376	0.318823	0.159412	+	0.987212i	$0.449040\pi$
$80$	−3.87959	−0.433751
$81$	8.93720	0.993023
$82$	−18.0762	−1.99619
$83$	16.2685	1.78570	0.892851	−	0.450352i	$-0.148702\pi$
$83$	16.2685	1.78570	0.892851	+	0.450352i	$0.148702\pi$
$84$	−1.72416	−0.188121
$85$	1.52139	0.165018
$86$	−4.77055	−0.514421
$87$	0.168653	0.0180815
$88$	24.4558	2.60700
$89$	9.68757	1.02688	0.513440	−	0.858125i	$-0.328371\pi$
$89$	9.68757	1.02688	0.513440	+	0.858125i	$0.328371\pi$
$90$	−7.31905	−0.771496
$91$	27.9694	2.93199
$92$	−27.7574	−2.89390
$93$	0.500433	0.0518925
$94$	−23.0880	−2.38134
$95$	4.90382	0.503121
$96$	−0.0163758	−0.00167134
$97$	−7.64489	−0.776221	−0.388111	−	0.921613i	$-0.626872\pi$
$97$	−7.64489	−0.776221	−0.388111	+	0.921613i	$0.626872\pi$
$98$	−48.6078	−4.91013
$99$	15.1186	1.51947
$100$	3.97986	0.397986
$101$	−13.3054	−1.32393	−0.661966	−	0.749534i	$-0.730278\pi$
$101$	−13.3054	−1.32393	−0.661966	+	0.749534i	$0.730278\pi$
$102$	−0.310885	−0.0307822
$103$	15.0014	1.47813	0.739064	−	0.673636i	$-0.235268\pi$
$103$	15.0014	1.47813	0.739064	+	0.673636i	$0.235268\pi$
$104$	−26.1198	−2.56126
$105$	0.433220	0.0422779
$106$	−29.4064	−2.85620
$107$	13.5144	1.30649	0.653244	−	0.757147i	$-0.273407\pi$
$107$	13.5144	1.30649	0.653244	+	0.757147i	$0.273407\pi$
$108$	1.99309	0.191786
$109$	−1.58187	−0.151516	−0.0757578	−	0.997126i	$-0.524138\pi$
$109$	−1.58187	−0.151516	−0.0757578	+	0.997126i	$0.524138\pi$
$110$	−12.3523	−1.17774
$111$	−0.641969	−0.0609330
$112$	20.1131	1.90051
$113$	1.37013	0.128891	0.0644453	−	0.997921i	$-0.479472\pi$
$113$	1.37013	0.128891	0.0644453	+	0.997921i	$0.479472\pi$
$114$	−1.00206	−0.0938516
$115$	6.97445	0.650371
$116$	−8.03244	−0.745793
$117$	−16.1472	−1.49281
$118$	6.06191	0.558044
$119$	−7.88740	−0.723037
$120$	−0.404571	−0.0369321
$121$	14.5154	1.31958
$122$	13.7082	1.24109
$123$	−0.617699	−0.0556960
$124$	−23.8342	−2.14037
$125$	−1.00000	−0.0894427
$126$	37.9445	3.38037
$127$	−1.04537	−0.0927617	−0.0463808	−	0.998924i	$-0.514769\pi$
$127$	−1.04537	−0.0927617	−0.0463808	+	0.998924i	$0.514769\pi$
$128$	19.7540	1.74603
$129$	−0.163018	−0.0143530
$130$	13.1927	1.15708
$131$	−11.3416	−0.990920	−0.495460	−	0.868631i	$-0.665000\pi$
$131$	−11.3416	−0.990920	−0.495460	+	0.868631i	$0.665000\pi$
$132$	1.67990	0.146217
$133$	−25.4231	−2.20446
$134$	−2.97650	−0.257131
$135$	−0.500795	−0.0431015
$136$	7.36582	0.631614
$137$	−13.2544	−1.13240	−0.566199	−	0.824269i	$-0.691587\pi$
$137$	−13.2544	−1.13240	−0.566199	+	0.824269i	$0.691587\pi$
$138$	−1.42518	−0.121319
$139$	18.9208	1.60484	0.802419	−	0.596762i	$-0.203546\pi$
$139$	18.9208	1.60484	0.802419	+	0.596762i	$0.203546\pi$
$140$	−20.6330	−1.74381
$141$	−0.788958	−0.0664423
$142$	32.0718	2.69141
$143$	−27.2515	−2.27889
$144$	−11.6117	−0.967640
$145$	2.01827	0.167608
$146$	30.5402	2.52752
$147$	−1.66102	−0.136999
$148$	30.5751	2.51326
$149$	−3.56619	−0.292153	−0.146077	−	0.989273i	$-0.546665\pi$
$149$	−3.56619	−0.292153	−0.146077	+	0.989273i	$0.546665\pi$
$150$	0.204343	0.0166845
$151$	5.40893	0.440173	0.220086	−	0.975480i	$-0.429366\pi$
$151$	5.40893	0.440173	0.220086	+	0.975480i	$0.429366\pi$
$152$	23.7419	1.92572
$153$	4.55354	0.368132
$154$	64.0385	5.16037
$155$	5.98869	0.481024
$156$	−1.79420	−0.143651
$157$	−18.6504	−1.48846	−0.744231	−	0.667922i	$-0.767184\pi$
$157$	−18.6504	−1.48846	−0.744231	+	0.667922i	$0.767184\pi$
$158$	−6.92962	−0.551291
$159$	−1.00487	−0.0796915
$160$	−0.195969	−0.0154927
$161$	−36.1580	−2.84965
$162$	−21.8548	−1.71708
$163$	−12.9146	−1.01155	−0.505777	−	0.862664i	$-0.668794\pi$
$163$	−12.9146	−1.01155	−0.505777	+	0.862664i	$0.668794\pi$
$164$	29.4192	2.29725
$165$	−0.422100	−0.0328605
$166$	−39.7826	−3.08773
$167$	−5.67337	−0.439019	−0.219509	−	0.975610i	$-0.570446\pi$
$167$	−5.67337	−0.439019	−0.219509	+	0.975610i	$0.570446\pi$
$168$	2.09744	0.161821
$169$	16.1057	1.23890
$170$	−3.72037	−0.285339
$171$	14.6772	1.12239
$172$	7.76410	0.592007
$173$	−22.6845	−1.72467	−0.862337	−	0.506335i	$-0.831000\pi$
$173$	−22.6845	−1.72467	−0.862337	+	0.506335i	$0.831000\pi$
$174$	−0.412419	−0.0312654
$175$	5.18435	0.391900
$176$	−19.5969	−1.47717
$177$	0.207147	0.0155701
$178$	−23.6897	−1.77562
$179$	−8.11611	−0.606627	−0.303313	−	0.952891i	$-0.598093\pi$
$179$	−8.11611	−0.606627	−0.303313	+	0.952891i	$0.598093\pi$
$180$	11.9118	0.887853
$181$	9.96334	0.740569	0.370285	−	0.928918i	$-0.379260\pi$
$181$	9.96334	0.740569	0.370285	+	0.928918i	$0.379260\pi$
$182$	−68.3957	−5.06983
$183$	0.468436	0.0346278
$184$	33.7669	2.48933
$185$	−7.68246	−0.564825
$186$	−1.22375	−0.0897296
$187$	7.68496	0.561980
$188$	37.5758	2.74050
$189$	2.59629	0.188853
$190$	−11.9917	−0.869968
$191$	−4.51909	−0.326990	−0.163495	−	0.986544i	$-0.552277\pi$
$191$	−4.51909	−0.326990	−0.163495	+	0.986544i	$0.552277\pi$
$192$	0.688425	0.0496828
$193$	−26.5354	−1.91006	−0.955031	−	0.296506i	$-0.904179\pi$
$193$	−26.5354	−1.91006	−0.955031	+	0.296506i	$0.904179\pi$
$194$	18.6946	1.34220
$195$	0.450820	0.0322839
$196$	79.1096	5.65068
$197$	0.635148	0.0452524	0.0226262	−	0.999744i	$-0.492797\pi$
$197$	0.635148	0.0452524	0.0226262	+	0.999744i	$0.492797\pi$
$198$	−36.9706	−2.62738
$199$	−12.8361	−0.909925	−0.454962	−	0.890511i	$-0.650347\pi$
$199$	−12.8361	−0.909925	−0.454962	+	0.890511i	$0.650347\pi$
$200$	−4.84151	−0.342347
$201$	−0.101713	−0.00717426
$202$	32.5366	2.28927
$203$	−10.4634	−0.734387
$204$	0.505967	0.0354248
$205$	−7.39201	−0.516280
$206$	−36.6839	−2.55589
$207$	20.8746	1.45089
$208$	20.9303	1.45125
$209$	24.7706	1.71341
$210$	−1.05939	−0.0731045
$211$	−12.0024	−0.826280	−0.413140	−	0.910667i	$-0.635568\pi$
$211$	−12.0024	−0.826280	−0.413140	+	0.910667i	$0.635568\pi$
$212$	47.8591	3.28698
$213$	1.09595	0.0750935
$214$	−33.0478	−2.25910
$215$	−1.95084	−0.133046
$216$	−2.42460	−0.164973
$217$	−31.0475	−2.10764
$218$	3.86826	0.261992
$219$	1.04361	0.0705209
$220$	20.1034	1.35537
$221$	−8.20784	−0.552119
$222$	1.56986	0.105362
$223$	−9.26643	−0.620526	−0.310263	−	0.950651i	$-0.600417\pi$
$223$	−9.26643	−0.620526	−0.310263	+	0.950651i	$0.600417\pi$
$224$	1.01597	0.0678824
$225$	−2.99302	−0.199534
$226$	−3.35048	−0.222870
$227$	23.8088	1.58025	0.790124	−	0.612947i	$-0.210016\pi$
$227$	23.8088	1.58025	0.790124	+	0.612947i	$0.210016\pi$
$228$	1.63086	0.108006
$229$	−7.86161	−0.519510	−0.259755	−	0.965675i	$-0.583642\pi$
$229$	−7.86161	−0.519510	−0.259755	+	0.965675i	$0.583642\pi$
$230$	−17.0551	−1.12458
$231$	2.18831	0.143980
$232$	9.77147	0.641529
$233$	−3.17896	−0.208261	−0.104130	−	0.994564i	$-0.533206\pi$
$233$	−3.17896	−0.208261	−0.104130	+	0.994564i	$0.533206\pi$
$234$	39.4861	2.58129
$235$	−9.44148	−0.615894
$236$	−9.86579	−0.642208
$237$	−0.236798	−0.0153817
$238$	19.2877	1.25023
$239$	−12.9523	−0.837813	−0.418907	−	0.908029i	$-0.637587\pi$
$239$	−12.9523	−0.837813	−0.418907	+	0.908029i	$0.637587\pi$
$240$	0.324190	0.0209264
$241$	−18.2519	−1.17571	−0.587853	−	0.808968i	$-0.700027\pi$
$241$	−18.2519	−1.17571	−0.587853	+	0.808968i	$0.700027\pi$
$242$	−35.4957	−2.28175
$243$	−2.24920	−0.144286
$244$	−22.3103	−1.42827
$245$	−19.8775	−1.26992
$246$	1.51051	0.0963063
$247$	−26.4560	−1.68335
$248$	28.9943	1.84114
$249$	−1.35945	−0.0861514
$250$	2.44538	0.154659
$251$	−13.7859	−0.870159	−0.435079	−	0.900392i	$-0.643280\pi$
$251$	−13.7859	−0.870159	−0.435079	+	0.900392i	$0.643280\pi$
$252$	−61.7549	−3.89019
$253$	35.2299	2.21488
$254$	2.55632	0.160398
$255$	−0.127132	−0.00796130
$256$	−31.8293	−1.98933
$257$	10.5552	0.658413	0.329206	−	0.944258i	$-0.393219\pi$
$257$	10.5552	0.658413	0.329206	+	0.944258i	$0.393219\pi$
$258$	0.398641	0.0248183
$259$	39.8285	2.47482
$260$	−21.4713	−1.33159
$261$	6.04071	0.373911
$262$	27.7345	1.71344
$263$	11.4571	0.706473	0.353237	−	0.935534i	$-0.385081\pi$
$263$	11.4571	0.706473	0.353237	+	0.935534i	$0.385081\pi$
$264$	−2.04360	−0.125775
$265$	−12.0253	−0.738709
$266$	62.1690	3.81183
$267$	−0.809522	−0.0495420
$268$	4.84428	0.295911
$269$	−29.0292	−1.76994	−0.884970	−	0.465648i	$-0.845821\pi$
$269$	−29.0292	−1.76994	−0.884970	+	0.465648i	$0.845821\pi$
$270$	1.22463	0.0745287
$271$	16.0566	0.975372	0.487686	−	0.873019i	$-0.337841\pi$
$271$	16.0566	0.975372	0.487686	+	0.873019i	$0.337841\pi$
$272$	−5.90236	−0.357883
$273$	−2.33721	−0.141454
$274$	32.4119	1.95808
$275$	−5.05128	−0.304604
$276$	2.31949	0.139617
$277$	−23.9890	−1.44136	−0.720680	−	0.693268i	$-0.756170\pi$
$277$	−23.9890	−1.44136	−0.720680	+	0.693268i	$0.756170\pi$
$278$	−46.2684	−2.77499
$279$	17.9243	1.07310
$280$	25.1001	1.50002
$281$	13.1477	0.784327	0.392163	−	0.919896i	$-0.371727\pi$
$281$	13.1477	0.784327	0.392163	+	0.919896i	$0.371727\pi$
$282$	1.92930	0.114888
$283$	−0.964557	−0.0573370	−0.0286685	−	0.999589i	$-0.509127\pi$
$283$	−0.964557	−0.0573370	−0.0286685	+	0.999589i	$0.509127\pi$
$284$	−52.1971	−3.09733
$285$	−0.409778	−0.0242731
$286$	66.6402	3.94052
$287$	38.3227	2.26212
$288$	−0.586538	−0.0345621
$289$	−14.6854	−0.863846
$290$	−4.93543	−0.289818
$291$	0.638830	0.0374489
$292$	−49.7043	−2.90873
$293$	11.6012	0.677747	0.338873	−	0.940832i	$-0.389954\pi$
$293$	11.6012	0.677747	0.338873	+	0.940832i	$0.389954\pi$
$294$	4.06182	0.236890
$295$	2.47893	0.144329
$296$	−37.1947	−2.16190
$297$	−2.52965	−0.146785
$298$	8.72067	0.505175
$299$	−37.6269	−2.17602
$300$	−0.332569	−0.0192009
$301$	10.1139	0.582953
$302$	−13.2269	−0.761121
$303$	1.11184	0.0638733
$304$	−19.0248	−1.09115
$305$	5.60578	0.320986
$306$	−11.1351	−0.636552
$307$	4.23669	0.241801	0.120900	−	0.992665i	$-0.461422\pi$
$307$	4.23669	0.241801	0.120900	+	0.992665i	$0.461422\pi$
$308$	−104.223	−5.93866
$309$	−1.25356	−0.0713124
$310$	−14.6446	−0.831758
$311$	−16.4320	−0.931771	−0.465885	−	0.884845i	$-0.654264\pi$
$311$	−16.4320	−0.931771	−0.465885	+	0.884845i	$0.654264\pi$
$312$	2.18265	0.123568
$313$	−3.99895	−0.226034	−0.113017	−	0.993593i	$-0.536051\pi$
$313$	−3.99895	−0.226034	−0.113017	+	0.993593i	$0.536051\pi$
$314$	45.6072	2.57376
$315$	15.5168	0.874275
$316$	11.2780	0.634437
$317$	−20.3368	−1.14223	−0.571114	−	0.820871i	$-0.693489\pi$
$317$	−20.3368	−1.14223	−0.571114	+	0.820871i	$0.693489\pi$
$318$	2.45729	0.137798
$319$	10.1948	0.570801
$320$	8.23840	0.460540
$321$	−1.12931	−0.0630317
$322$	88.4198	4.92744
$323$	7.46061	0.415119
$324$	35.5689	1.97605
$325$	5.39497	0.299259
$326$	31.5812	1.74912
$327$	0.132186	0.00730989
$328$	−35.7885	−1.97609
$329$	48.9479	2.69858
$330$	1.03219	0.0568204
$331$	31.1822	1.71393	0.856965	−	0.515375i	$-0.172347\pi$
$331$	31.1822	1.71393	0.856965	+	0.515375i	$0.172347\pi$
$332$	64.7465	3.55343
$333$	−22.9937	−1.26005
$334$	13.8735	0.759126
$335$	−1.21720	−0.0665026
$336$	−1.68071	−0.0916905
$337$	3.48096	0.189620	0.0948099	−	0.995495i	$-0.469776\pi$
$337$	3.48096	0.189620	0.0948099	+	0.995495i	$0.469776\pi$
$338$	−39.3845	−2.14224
$339$	−0.114492	−0.00621835
$340$	6.05492	0.328374
$341$	30.2506	1.63816
$342$	−35.8913	−1.94078
$343$	66.7612	3.60477
$344$	−9.44504	−0.509242
$345$	−0.582806	−0.0313772
$346$	55.4722	2.98221
$347$	−14.8420	−0.796759	−0.398380	−	0.917221i	$-0.630427\pi$
$347$	−14.8420	−0.796759	−0.398380	+	0.917221i	$0.630427\pi$
$348$	0.671215	0.0359809
$349$	−11.6023	−0.621059	−0.310530	−	0.950564i	$-0.600506\pi$
$349$	−11.6023	−0.621059	−0.310530	+	0.950564i	$0.600506\pi$
$350$	−12.6777	−0.677650
$351$	2.70177	0.144210
$352$	−0.989893	−0.0527615
$353$	4.71296	0.250845	0.125423	−	0.992103i	$-0.459971\pi$
$353$	4.71296	0.250845	0.125423	+	0.992103i	$0.459971\pi$
$354$	−0.506551	−0.0269229
$355$	13.1153	0.696088
$356$	38.5552	2.04342
$357$	0.659095	0.0348830
$358$	19.8470	1.04894
$359$	−24.6884	−1.30300	−0.651502	−	0.758647i	$-0.725861\pi$
$359$	−24.6884	−1.30300	−0.651502	+	0.758647i	$0.725861\pi$
$360$	−14.4907	−0.763728
$361$	5.04743	0.265654
$362$	−24.3641	−1.28055
$363$	−1.21295	−0.0636635
$364$	111.314	5.83446
$365$	12.4890	0.653702
$366$	−1.14550	−0.0598764
$367$	7.62077	0.397801	0.198900	−	0.980020i	$-0.436263\pi$
$367$	7.62077	0.397801	0.198900	+	0.980020i	$0.436263\pi$
$368$	−27.0580	−1.41050
$369$	−22.1244	−1.15175
$370$	18.7865	0.976663
$371$	62.3434	3.23671
$372$	1.99166	0.103263
$373$	12.5985	0.652324	0.326162	−	0.945314i	$-0.394244\pi$
$373$	12.5985	0.652324	0.326162	+	0.945314i	$0.394244\pi$
$374$	−18.7926	−0.971743
$375$	0.0835630	0.00431518
$376$	−45.7110	−2.35737
$377$	−10.8885	−0.560786
$378$	−6.34891	−0.326553
$379$	13.1101	0.673423	0.336712	−	0.941608i	$-0.390685\pi$
$379$	13.1101	0.673423	0.336712	+	0.941608i	$0.390685\pi$
$380$	19.5165	1.00118
$381$	0.0873544	0.00447530
$382$	11.0509	0.565412
$383$	26.7533	1.36703	0.683516	−	0.729936i	$-0.260450\pi$
$383$	26.7533	1.36703	0.683516	+	0.729936i	$0.260450\pi$
$384$	−1.65071	−0.0842373
$385$	26.1876	1.33464
$386$	64.8891	3.30277
$387$	−5.83891	−0.296809
$388$	−30.4256	−1.54463
$389$	−33.5828	−1.70272	−0.851358	−	0.524585i	$-0.824220\pi$
$389$	−33.5828	−1.70272	−0.851358	+	0.524585i	$0.824220\pi$
$390$	−1.10242	−0.0558234
$391$	10.6108	0.536613
$392$	−96.2369	−4.86070
$393$	0.947738	0.0478071
$394$	−1.55318	−0.0782479
$395$	−2.83376	−0.142582
$396$	60.1698	3.02365
$397$	−1.92016	−0.0963699	−0.0481850	−	0.998838i	$-0.515344\pi$
$397$	−1.92016	−0.0963699	−0.0481850	+	0.998838i	$0.515344\pi$
$398$	31.3890	1.57339
$399$	2.12443	0.106355
$400$	3.87959	0.193979
$401$	−3.56595	−0.178075	−0.0890376	−	0.996028i	$-0.528379\pi$
$401$	−3.56595	−0.178075	−0.0890376	+	0.996028i	$0.528379\pi$
$402$	0.248726	0.0124053
$403$	−32.3088	−1.60942
$404$	−52.9535	−2.63454
$405$	−8.93720	−0.444093
$406$	25.5870	1.26986
$407$	−38.8062	−1.92355
$408$	−0.615510	−0.0304723
$409$	15.1798	0.750595	0.375298	−	0.926904i	$-0.377541\pi$
$409$	15.1798	0.750595	0.375298	+	0.926904i	$0.377541\pi$
$410$	18.0762	0.892722
$411$	1.10758	0.0546327
$412$	59.7033	2.94137
$413$	−12.8516	−0.632387
$414$	−51.0463	−2.50879
$415$	−16.2685	−0.798590
$416$	1.05725	0.0518358
$417$	−1.58108	−0.0774256
$418$	−60.5733	−2.96274
$419$	18.2365	0.890913	0.445456	−	0.895304i	$-0.353041\pi$
$419$	18.2365	0.890913	0.445456	+	0.895304i	$0.353041\pi$
$420$	1.72416	0.0841302
$421$	−30.4052	−1.48186	−0.740928	−	0.671584i	$-0.765614\pi$
$421$	−30.4052	−1.48186	−0.740928	+	0.671584i	$0.765614\pi$
$422$	29.3504	1.42876
$423$	−28.2585	−1.37398
$424$	−58.2207	−2.82745
$425$	−1.52139	−0.0737982
$426$	−2.68002	−0.129847
$427$	−29.0623	−1.40642
$428$	53.7856	2.59982
$429$	2.27722	0.109945
$430$	4.77055	0.230056
$431$	−12.1451	−0.585011	−0.292505	−	0.956264i	$-0.594489\pi$
$431$	−12.1451	−0.585011	−0.292505	+	0.956264i	$0.594489\pi$
$432$	1.94288	0.0934767
$433$	23.9264	1.14983	0.574916	−	0.818213i	$-0.305035\pi$
$433$	23.9264	1.14983	0.574916	+	0.818213i	$0.305035\pi$
$434$	75.9227	3.64441
$435$	−0.168653	−0.00808628
$436$	−6.29562	−0.301506
$437$	34.2014	1.63608
$438$	−2.55203	−0.121941
$439$	−5.64509	−0.269426	−0.134713	−	0.990885i	$-0.543011\pi$
$439$	−5.64509	−0.269426	−0.134713	+	0.990885i	$0.543011\pi$
$440$	−24.4558	−1.16589
$441$	−59.4936	−2.83303
$442$	20.0713	0.954693
$443$	−12.3117	−0.584946	−0.292473	−	0.956274i	$-0.594478\pi$
$443$	−12.3117	−0.584946	−0.292473	+	0.956274i	$0.594478\pi$
$444$	−2.55495	−0.121253
$445$	−9.68757	−0.459235
$446$	22.6599	1.07298
$447$	0.298001	0.0140950
$448$	−42.7107	−2.01789
$449$	1.85692	0.0876333	0.0438167	−	0.999040i	$-0.486048\pi$
$449$	1.85692	0.0876333	0.0438167	+	0.999040i	$0.486048\pi$
$450$	7.31905	0.345023
$451$	−37.3391	−1.75823
$452$	5.45292	0.256484
$453$	−0.451987	−0.0212362
$454$	−58.2216	−2.73247
$455$	−27.9694	−1.31123
$456$	−1.98394	−0.0929067
$457$	−15.5159	−0.725801	−0.362901	−	0.931828i	$-0.618214\pi$
$457$	−15.5159	−0.725801	−0.362901	+	0.931828i	$0.618214\pi$
$458$	19.2246	0.898306
$459$	−0.761903	−0.0355626
$460$	27.7574	1.29419
$461$	31.2670	1.45625	0.728124	−	0.685445i	$-0.240392\pi$
$461$	31.2670	1.45625	0.728124	+	0.685445i	$0.240392\pi$
$462$	−5.35125	−0.248963
$463$	−1.42434	−0.0661949	−0.0330974	−	0.999452i	$-0.510537\pi$
$463$	−1.42434	−0.0661949	−0.0330974	+	0.999452i	$0.510537\pi$
$464$	−7.83005	−0.363501
$465$	−0.500433	−0.0232070
$466$	7.77375	0.360112
$467$	20.9494	0.969422	0.484711	−	0.874674i	$-0.338925\pi$
$467$	20.9494	0.969422	0.484711	+	0.874674i	$0.338925\pi$
$468$	−64.2638	−2.97060
$469$	6.31037	0.291386
$470$	23.0880	1.06497
$471$	1.55848	0.0718111
$472$	12.0018	0.552425
$473$	−9.85426	−0.453099
$474$	0.579060	0.0265971
$475$	−4.90382	−0.225003
$476$	−31.3908	−1.43879
$477$	−35.9920	−1.64796
$478$	31.6732	1.44870
$479$	−27.7341	−1.26720	−0.633602	−	0.773659i	$-0.718424\pi$
$479$	−27.7341	−1.26720	−0.633602	+	0.773659i	$0.718424\pi$
$480$	0.0163758	0.000747447 0
$481$	41.4466	1.88980
$482$	44.6326	2.03296
$483$	3.02147	0.137482
$484$	57.7694	2.62588
$485$	7.64489	0.347137
$486$	5.50015	0.249492
$487$	−8.20250	−0.371691	−0.185845	−	0.982579i	$-0.559502\pi$
$487$	−8.20250	−0.371691	−0.185845	+	0.982579i	$0.559502\pi$
$488$	27.1405	1.22859
$489$	1.07919	0.0488025
$490$	48.6078	2.19588
$491$	−15.0146	−0.677599	−0.338799	−	0.940859i	$-0.610021\pi$
$491$	−15.0146	−0.677599	−0.338799	+	0.940859i	$0.610021\pi$
$492$	−2.45836	−0.110831
$493$	3.07057	0.138292
$494$	64.6948	2.91075
$495$	−15.1186	−0.679529
$496$	−23.2337	−1.04322
$497$	−67.9942	−3.04996
$498$	3.32436	0.148968
$499$	−16.9037	−0.756715	−0.378358	−	0.925659i	$-0.623511\pi$
$499$	−16.9037	−0.756715	−0.378358	+	0.925659i	$0.623511\pi$
$500$	−3.97986	−0.177985
$501$	0.474084	0.0211805
$502$	33.7117	1.50463
$503$	16.6974	0.744500	0.372250	−	0.928132i	$-0.378586\pi$
$503$	16.6974	0.744500	0.372250	+	0.928132i	$0.378586\pi$
$504$	75.1250	3.34633
$505$	13.3054	0.592081
$506$	−86.1503	−3.82985
$507$	−1.34584	−0.0597709
$508$	−4.16043	−0.184589
$509$	5.02434	0.222700	0.111350	−	0.993781i	$-0.464483\pi$
$509$	5.02434	0.222700	0.111350	+	0.993781i	$0.464483\pi$
$510$	0.310885	0.0137662
$511$	−64.7471	−2.86424
$512$	38.3264	1.69381
$513$	−2.45581	−0.108426
$514$	−25.8113	−1.13849
$515$	−15.0014	−0.661039
$516$	−0.648791	−0.0285614
$517$	−47.6915	−2.09747
$518$	−97.3957	−4.27932
$519$	1.89559	0.0832071
$520$	26.1198	1.14543
$521$	−7.04663	−0.308719	−0.154359	−	0.988015i	$-0.549331\pi$
$521$	−7.04663	−0.308719	−0.154359	+	0.988015i	$0.549331\pi$
$522$	−14.7718	−0.646545
$523$	−19.8825	−0.869403	−0.434701	−	0.900575i	$-0.643146\pi$
$523$	−19.8825	−0.869403	−0.434701	+	0.900575i	$0.643146\pi$
$524$	−45.1380	−1.97186
$525$	−0.433220	−0.0189073
$526$	−28.0168	−1.22159
$527$	9.11113	0.396887
$528$	1.63758	0.0712663
$529$	25.6429	1.11491
$530$	29.4064	1.27733
$531$	7.41947	0.321978
$532$	−101.180	−4.38673
$533$	39.8797	1.72738
$534$	1.97959	0.0856651
$535$	−13.5144	−0.584279
$536$	−5.89307	−0.254542
$537$	0.678207	0.0292668
$538$	70.9872	3.06048
$539$	−100.407	−4.32482
$540$	−1.99309	−0.0857691
$541$	−31.6555	−1.36098	−0.680488	−	0.732759i	$-0.738232\pi$
$541$	−31.6555	−1.36098	−0.680488	+	0.732759i	$0.738232\pi$
$542$	−39.2645	−1.68656
$543$	−0.832567	−0.0357289
$544$	−0.298145	−0.0127828
$545$	1.58187	0.0677598
$546$	5.71535	0.244594
$547$	15.2963	0.654022	0.327011	−	0.945021i	$-0.393959\pi$
$547$	15.2963	0.654022	0.327011	+	0.945021i	$0.393959\pi$
$548$	−52.7506	−2.25339
$549$	16.7782	0.716076
$550$	12.3523	0.526703
$551$	9.89722	0.421636
$552$	−2.82166	−0.120098
$553$	14.6912	0.624734
$554$	58.6622	2.49232
$555$	0.641969	0.0272501
$556$	75.3020	3.19352
$557$	31.4954	1.33450	0.667251	−	0.744833i	$-0.267471\pi$
$557$	31.4954	1.33450	0.667251	+	0.744833i	$0.267471\pi$
$558$	−43.8316	−1.85554
$559$	10.5248	0.445150
$560$	−20.1131	−0.849935
$561$	−0.642178	−0.0271128
$562$	−32.1511	−1.35621
$563$	12.2524	0.516378	0.258189	−	0.966094i	$-0.416874\pi$
$563$	12.2524	0.516378	0.258189	+	0.966094i	$0.416874\pi$
$564$	−3.13995	−0.132216
$565$	−1.37013	−0.0576417
$566$	2.35870	0.0991438
$567$	46.3336	1.94583
$568$	63.4979	2.66431
$569$	12.1317	0.508586	0.254293	−	0.967127i	$-0.418157\pi$
$569$	12.1317	0.508586	0.254293	+	0.967127i	$0.418157\pi$
$570$	1.00206	0.0419717
$571$	6.02171	0.252001	0.126000	−	0.992030i	$-0.459786\pi$
$571$	6.02171	0.252001	0.126000	+	0.992030i	$0.459786\pi$
$572$	−108.457	−4.53483
$573$	0.377629	0.0157757
$574$	−93.7135	−3.91153
$575$	−6.97445	−0.290855
$576$	24.6577	1.02740
$577$	−45.0658	−1.87611	−0.938057	−	0.346481i	$-0.887377\pi$
$577$	−45.0658	−1.87611	−0.938057	+	0.346481i	$0.887377\pi$
$578$	35.9113	1.49371
$579$	2.21738	0.0921512
$580$	8.03244	0.333529
$581$	84.3416	3.49908
$582$	−1.56218	−0.0647545
$583$	−60.7432	−2.51573
$584$	60.4654	2.50208
$585$	16.1472	0.667606
$586$	−28.3692	−1.17192
$587$	−25.4890	−1.05204	−0.526021	−	0.850471i	$-0.676317\pi$
$587$	−25.4890	−1.05204	−0.526021	+	0.850471i	$0.676317\pi$
$588$	−6.61063	−0.272618
$589$	29.3675	1.21007
$590$	−6.06191	−0.249565
$591$	−0.0530749	−0.00218321
$592$	29.8048	1.22497
$593$	15.4431	0.634171	0.317086	−	0.948397i	$-0.397296\pi$
$593$	15.4431	0.634171	0.317086	+	0.948397i	$0.397296\pi$
$594$	6.18595	0.253813
$595$	7.88740	0.323352
$596$	−14.1929	−0.581366
$597$	1.07262	0.0438994
$598$	92.0120	3.76265
$599$	−13.9641	−0.570558	−0.285279	−	0.958445i	$-0.592086\pi$
$599$	−13.9641	−0.570558	−0.285279	+	0.958445i	$0.592086\pi$
$600$	0.404571	0.0165166
$601$	−5.46107	−0.222762	−0.111381	−	0.993778i	$-0.535527\pi$
$601$	−5.46107	−0.222762	−0.111381	+	0.993778i	$0.535527\pi$
$602$	−24.7322	−1.00801
$603$	−3.64309	−0.148358
$604$	21.5268	0.875914
$605$	−14.5154	−0.590136
$606$	−2.71886	−0.110446
$607$	−30.0254	−1.21869	−0.609346	−	0.792905i	$-0.708568\pi$
$607$	−30.0254	−1.21869	−0.609346	+	0.792905i	$0.708568\pi$
$608$	−0.960996	−0.0389735
$609$	0.874354	0.0354306
$610$	−13.7082	−0.555031
$611$	50.9365	2.06067
$612$	18.1225	0.732558
$613$	−8.01017	−0.323528	−0.161764	−	0.986829i	$-0.551718\pi$
$613$	−8.01017	−0.323528	−0.161764	+	0.986829i	$0.551718\pi$
$614$	−10.3603	−0.418108
$615$	0.617699	0.0249080
$616$	126.787	5.10841
$617$	−35.3157	−1.42176	−0.710878	−	0.703316i	$-0.751702\pi$
$617$	−35.3157	−1.42176	−0.710878	+	0.703316i	$0.751702\pi$
$618$	3.06542	0.123309
$619$	−0.681104	−0.0273759	−0.0136879	−	0.999906i	$-0.504357\pi$
$619$	−0.681104	−0.0273759	−0.0136879	+	0.999906i	$0.504357\pi$
$620$	23.8342	0.957204
$621$	−3.49277	−0.140160
$622$	40.1823	1.61116
$623$	50.2237	2.01217
$624$	−1.74900	−0.0700159
$625$	1.00000	0.0400000
$626$	9.77895	0.390845
$627$	−2.06990	−0.0826639
$628$	−74.2260	−2.96194
$629$	−11.6880	−0.466031
$630$	−37.9445	−1.51175
$631$	−36.2488	−1.44304	−0.721522	−	0.692392i	$-0.756557\pi$
$631$	−36.2488	−1.44304	−0.721522	+	0.692392i	$0.756557\pi$
$632$	−13.7197	−0.545741
$633$	1.00296	0.0398640
$634$	49.7311	1.97507
$635$	1.04537	0.0414843
$636$	−3.99925	−0.158581
$637$	107.238	4.24894
$638$	−24.9302	−0.986997
$639$	39.2543	1.55288
$640$	−19.7540	−0.780847
$641$	17.5307	0.692421	0.346210	−	0.938157i	$-0.387468\pi$
$641$	17.5307	0.692421	0.346210	+	0.938157i	$0.387468\pi$
$642$	2.76158	0.108991
$643$	−20.0249	−0.789706	−0.394853	−	0.918744i	$-0.629205\pi$
$643$	−20.0249	−0.789706	−0.394853	+	0.918744i	$0.629205\pi$
$644$	−143.904	−5.67060
$645$	0.163018	0.00641885
$646$	−18.2440	−0.717800
$647$	22.0017	0.864975	0.432488	−	0.901640i	$-0.357636\pi$
$647$	22.0017	0.864975	0.432488	+	0.901640i	$0.357636\pi$
$648$	−43.2696	−1.69979
$649$	12.5218	0.491522
$650$	−13.1927	−0.517462
$651$	2.59442	0.101683
$652$	−51.3986	−2.01292
$653$	1.32474	0.0518413	0.0259206	−	0.999664i	$-0.491748\pi$
$653$	1.32474	0.0518413	0.0259206	+	0.999664i	$0.491748\pi$
$654$	−0.323244	−0.0126398
$655$	11.3416	0.443153
$656$	28.6780	1.11969
$657$	37.3796	1.45832
$658$	−119.696	−4.66624
$659$	−1.61438	−0.0628874	−0.0314437	−	0.999506i	$-0.510010\pi$
$659$	−1.61438	−0.0628874	−0.0314437	+	0.999506i	$0.510010\pi$
$660$	−1.67990	−0.0653901
$661$	−24.2414	−0.942880	−0.471440	−	0.881898i	$-0.656266\pi$
$661$	−24.2414	−0.942880	−0.471440	+	0.881898i	$0.656266\pi$
$662$	−76.2523	−2.96363
$663$	0.685872	0.0266371
$664$	−78.7642	−3.05664
$665$	25.4231	0.985865
$666$	56.2283	2.17880
$667$	14.0763	0.545037
$668$	−22.5792	−0.873617
$669$	0.774331	0.0299374
$670$	2.97650	0.114992
$671$	28.3164	1.09314
$672$	−0.0848976	−0.00327499
$673$	16.1592	0.622890	0.311445	−	0.950264i	$-0.399187\pi$
$673$	16.1592	0.622890	0.311445	+	0.950264i	$0.399187\pi$
$674$	−8.51225	−0.327880
$675$	0.500795	0.0192756
$676$	64.0985	2.46533
$677$	−35.9970	−1.38348	−0.691738	−	0.722148i	$-0.743155\pi$
$677$	−35.9970	−1.38348	−0.691738	+	0.722148i	$0.743155\pi$
$678$	0.279976	0.0107524
$679$	−39.6338	−1.52100
$680$	−7.36582	−0.282466
$681$	−1.98954	−0.0762393
$682$	−73.9740	−2.83261
$683$	18.2396	0.697917	0.348959	−	0.937138i	$-0.386535\pi$
$683$	18.2396	0.697917	0.348959	+	0.937138i	$0.386535\pi$
$684$	58.4133	2.23349
$685$	13.2544	0.506424
$686$	−163.256	−6.23315
$687$	0.656940	0.0250638
$688$	7.56848	0.288545
$689$	64.8762	2.47159
$690$	1.42518	0.0542557
$691$	−10.4196	−0.396380	−0.198190	−	0.980164i	$-0.563506\pi$
$691$	−10.4196	−0.396380	−0.198190	+	0.980164i	$0.563506\pi$
$692$	−90.2814	−3.43198
$693$	78.3799	2.97741
$694$	36.2942	1.37771
$695$	−18.9208	−0.717705
$696$	−0.816534	−0.0309506
$697$	−11.2461	−0.425977
$698$	28.3721	1.07390
$699$	0.265644	0.0100476
$700$	20.6330	0.779854
$701$	−24.4782	−0.924530	−0.462265	−	0.886742i	$-0.652963\pi$
$701$	−24.4782	−0.924530	−0.462265	+	0.886742i	$0.652963\pi$
$702$	−6.60685	−0.249359
$703$	−37.6734	−1.42088
$704$	41.6144	1.56840
$705$	0.788958	0.0297139
$706$	−11.5250	−0.433747
$707$	−68.9796	−2.59424
$708$	0.824415	0.0309834
$709$	−31.7962	−1.19413	−0.597066	−	0.802192i	$-0.703667\pi$
$709$	−31.7962	−1.19413	−0.597066	+	0.802192i	$0.703667\pi$
$710$	−32.0718	−1.20363
$711$	−8.48151	−0.318081
$712$	−46.9025	−1.75774
$713$	41.7678	1.56422
$714$	−1.61174	−0.0603177
$715$	27.2515	1.01915
$716$	−32.3010	−1.20715
$717$	1.08233	0.0404204
$718$	60.3724	2.25308
$719$	1.94020	0.0723571	0.0361785	−	0.999345i	$-0.488481\pi$
$719$	1.94020	0.0723571	0.0361785	+	0.999345i	$0.488481\pi$
$720$	11.6117	0.432742
$721$	77.7722	2.89639
$722$	−12.3429	−0.459354
$723$	1.52518	0.0567221
$724$	39.6527	1.47368
$725$	−2.01827	−0.0749566
$726$	2.96612	0.110083
$727$	5.39961	0.200260	0.100130	−	0.994974i	$-0.468074\pi$
$727$	5.39961	0.200260	0.100130	+	0.994974i	$0.468074\pi$
$728$	−135.414	−5.01878
$729$	−26.6237	−0.986062
$730$	−30.5402	−1.13034
$731$	−2.96799	−0.109775
$732$	1.86431	0.0689070
$733$	12.8764	0.475602	0.237801	−	0.971314i	$-0.423573\pi$
$733$	12.8764	0.475602	0.237801	+	0.971314i	$0.423573\pi$
$734$	−18.6356	−0.687854
$735$	1.66102	0.0612677
$736$	−1.36677	−0.0503800
$737$	−6.14840	−0.226479
$738$	54.1025	1.99154
$739$	40.0785	1.47431	0.737156	−	0.675723i	$-0.236168\pi$
$739$	40.0785	1.47431	0.737156	+	0.675723i	$0.236168\pi$
$740$	−30.5751	−1.12396
$741$	2.21074	0.0812135
$742$	−152.453	−5.59673
$743$	36.9319	1.35490	0.677451	−	0.735568i	$-0.263085\pi$
$743$	36.9319	1.35490	0.677451	+	0.735568i	$0.263085\pi$
$744$	−2.42285	−0.0888262
$745$	3.56619	0.130655
$746$	−30.8080	−1.12796
$747$	−48.6920	−1.78155
$748$	30.5851	1.11830
$749$	70.0635	2.56006
$750$	−0.204343	−0.00746155
$751$	40.0261	1.46057	0.730286	−	0.683141i	$-0.239387\pi$
$751$	40.0261	1.46057	0.730286	+	0.683141i	$0.239387\pi$
$752$	36.6290	1.33572
$753$	1.15199	0.0419809
$754$	26.6265	0.969679
$755$	−5.40893	−0.196851
$756$	10.3329	0.375804
$757$	−20.5202	−0.745818	−0.372909	−	0.927868i	$-0.621640\pi$
$757$	−20.5202	−0.745818	−0.372909	+	0.927868i	$0.621640\pi$
$758$	−32.0592	−1.16444
$759$	−2.94392	−0.106857
$760$	−23.7419	−0.861209
$761$	6.59682	0.239135	0.119567	−	0.992826i	$-0.461849\pi$
$761$	6.59682	0.239135	0.119567	+	0.992826i	$0.461849\pi$
$762$	−0.213614	−0.00773843
$763$	−8.20096	−0.296895
$764$	−17.9854	−0.650688
$765$	−4.55354	−0.164634
$766$	−65.4220	−2.36379
$767$	−13.3737	−0.482898
$768$	2.65975	0.0959754
$769$	−24.4215	−0.880660	−0.440330	−	0.897836i	$-0.645139\pi$
$769$	−24.4215	−0.880660	−0.440330	+	0.897836i	$0.645139\pi$
$770$	−64.0385	−2.30779
$771$	−0.882021	−0.0317652
$772$	−105.607	−3.80089
$773$	0.961514	0.0345832	0.0172916	−	0.999850i	$-0.494496\pi$
$773$	0.961514	0.0345832	0.0172916	+	0.999850i	$0.494496\pi$
$774$	14.2783	0.513224
$775$	−5.98869	−0.215120
$776$	37.0128	1.32868
$777$	−3.32819	−0.119398
$778$	82.1226	2.94424
$779$	−36.2491	−1.29876
$780$	1.79420	0.0642428
$781$	66.2490	2.37058
$782$	−25.9475	−0.927881
$783$	−1.01074	−0.0361208
$784$	77.1164	2.75416
$785$	18.6504	0.665661
$786$	−2.31758	−0.0826652
$787$	−52.4436	−1.86941	−0.934707	−	0.355420i	$-0.884338\pi$
$787$	−52.4436	−1.86941	−0.934707	+	0.355420i	$0.884338\pi$
$788$	2.52780	0.0900492
$789$	−0.957388	−0.0340839
$790$	6.92962	0.246545
$791$	7.10321	0.252561
$792$	−73.1967	−2.60093
$793$	−30.2430	−1.07396
$794$	4.69551	0.166637
$795$	1.00487	0.0356391
$796$	−51.0858	−1.81069
$797$	21.8505	0.773984	0.386992	−	0.922083i	$-0.373514\pi$
$797$	21.8505	0.773984	0.386992	+	0.922083i	$0.373514\pi$
$798$	−5.19503	−0.183902
$799$	−14.3641	−0.508167
$800$	0.195969	0.00692855
$801$	−28.9951	−1.02449
$802$	8.72010	0.307917
$803$	63.0852	2.22623
$804$	−0.404802	−0.0142763
$805$	36.1580	1.27440
$806$	79.0073	2.78291
$807$	2.42577	0.0853910
$808$	64.4180	2.26622
$809$	−17.5250	−0.616145	−0.308072	−	0.951363i	$-0.599684\pi$
$809$	−17.5250	−0.616145	−0.308072	+	0.951363i	$0.599684\pi$
$810$	21.8548	0.767900
$811$	−16.4349	−0.577108	−0.288554	−	0.957464i	$-0.593174\pi$
$811$	−16.4349	−0.577108	−0.288554	+	0.957464i	$0.593174\pi$
$812$	−41.6429	−1.46138
$813$	−1.34174	−0.0470569
$814$	94.8958	3.32610
$815$	12.9146	0.452380
$816$	0.493219	0.0172661
$817$	−9.56659	−0.334692
$818$	−37.1204	−1.29789
$819$	−83.7129	−2.92517
$820$	−29.4192	−1.02736
$821$	−44.4122	−1.55000	−0.774998	−	0.631964i	$-0.782249\pi$
$821$	−44.4122	−1.55000	−0.774998	+	0.631964i	$0.782249\pi$
$822$	−2.70844	−0.0944677
$823$	23.7294	0.827156	0.413578	−	0.910469i	$-0.364279\pi$
$823$	23.7294	0.827156	0.413578	+	0.910469i	$0.364279\pi$
$824$	−72.6292	−2.53016
$825$	0.422100	0.0146956
$826$	31.4270	1.09349
$827$	−19.3608	−0.673239	−0.336620	−	0.941641i	$-0.609284\pi$
$827$	−19.3608	−0.673239	−0.336620	+	0.941641i	$0.609284\pi$
$828$	83.0782	2.88717
$829$	−22.5766	−0.784117	−0.392058	−	0.919940i	$-0.628237\pi$
$829$	−22.5766	−0.784117	−0.392058	+	0.919940i	$0.628237\pi$
$830$	39.7826	1.38088
$831$	2.00459	0.0695386
$832$	−44.4459	−1.54088
$833$	−30.2413	−1.04780
$834$	3.86632	0.133880
$835$	5.67337	0.196335
$836$	98.5834	3.40958
$837$	−2.99911	−0.103664
$838$	−44.5952	−1.54051
$839$	−2.18911	−0.0755765	−0.0377882	−	0.999286i	$-0.512031\pi$
$839$	−2.18911	−0.0755765	−0.0377882	+	0.999286i	$0.512031\pi$
$840$	−2.09744	−0.0723685
$841$	−24.9266	−0.859538
$842$	74.3520	2.56234
$843$	−1.09866	−0.0378400
$844$	−47.7680	−1.64424
$845$	−16.1057	−0.554053
$846$	69.1027	2.37580
$847$	75.2530	2.58572
$848$	46.6533	1.60208
$849$	0.0806013	0.00276623
$850$	3.72037	0.127608
$851$	−53.5809	−1.83673
$852$	4.36175	0.149431
$853$	−38.3749	−1.31393	−0.656967	−	0.753920i	$-0.728161\pi$
$853$	−38.3749	−1.31393	−0.656967	+	0.753920i	$0.728161\pi$
$854$	71.0683	2.43191
$855$	−14.6772	−0.501950
$856$	−65.4302	−2.23636
$857$	18.3712	0.627547	0.313774	−	0.949498i	$-0.398407\pi$
$857$	18.3712	0.627547	0.313774	+	0.949498i	$0.398407\pi$
$858$	−5.56865	−0.190111
$859$	−37.7002	−1.28632	−0.643158	−	0.765734i	$-0.722376\pi$
$859$	−37.7002	−1.28632	−0.643158	+	0.765734i	$0.722376\pi$
$860$	−7.76410	−0.264753
$861$	−3.20236	−0.109136
$862$	29.6994	1.01157
$863$	31.3300	1.06648	0.533242	−	0.845963i	$-0.320973\pi$
$863$	31.3300	1.06648	0.533242	+	0.845963i	$0.320973\pi$
$864$	0.0981402	0.00333880
$865$	22.6845	0.771297
$866$	−58.5092	−1.98822
$867$	1.22715	0.0416764
$868$	−123.565	−4.19406
$869$	−14.3141	−0.485574
$870$	0.412419	0.0139823
$871$	6.56674	0.222506
$872$	7.65864	0.259354
$873$	22.8813	0.774415
$874$	−83.6353	−2.82901
$875$	−5.18435	−0.175263
$876$	4.15344	0.140332
$877$	13.6414	0.460636	0.230318	−	0.973115i	$-0.426023\pi$
$877$	13.6414	0.460636	0.230318	+	0.973115i	$0.426023\pi$
$878$	13.8044	0.465875
$879$	−0.969427	−0.0326980
$880$	19.5969	0.660611
$881$	−40.0471	−1.34922	−0.674611	−	0.738174i	$-0.735688\pi$
$881$	−40.0471	−1.34922	−0.674611	+	0.738174i	$0.735688\pi$
$882$	145.484	4.89871
$883$	−55.5458	−1.86927	−0.934633	−	0.355613i	$-0.884272\pi$
$883$	−55.5458	−1.86927	−0.934633	+	0.355613i	$0.884272\pi$
$884$	−32.6661	−1.09868
$885$	−0.207147	−0.00696316
$886$	30.1067	1.01145
$887$	45.4524	1.52614	0.763070	−	0.646315i	$-0.223691\pi$
$887$	45.4524	1.52614	0.763070	+	0.646315i	$0.223691\pi$
$888$	3.10810	0.104301
$889$	−5.41957	−0.181766
$890$	23.6897	0.794082
$891$	−45.1443	−1.51239
$892$	−36.8791	−1.23480
$893$	−46.2993	−1.54935
$894$	−0.728726	−0.0243722
$895$	8.11611	0.271292
$896$	102.412	3.42134
$897$	3.14422	0.104982
$898$	−4.54086	−0.151530
$899$	12.0868	0.403117
$900$	−11.9118	−0.397060
$901$	−18.2952	−0.609500
$902$	91.3081	3.04023
$903$	−0.845144	−0.0281246
$904$	−6.63349	−0.220626
$905$	−9.96334	−0.331193
$906$	1.10528	0.0367204
$907$	27.1908	0.902855	0.451428	−	0.892308i	$-0.350915\pi$
$907$	27.1908	0.902855	0.451428	+	0.892308i	$0.350915\pi$
$908$	94.7559	3.14459
$909$	39.8232	1.32085
$910$	68.3957	2.26730
$911$	11.7427	0.389052	0.194526	−	0.980897i	$-0.437683\pi$
$911$	11.7427	0.389052	0.194526	+	0.980897i	$0.437683\pi$
$912$	1.58977	0.0526425
$913$	−82.1768	−2.71966
$914$	37.9421	1.25501
$915$	−0.468436	−0.0154860
$916$	−31.2881	−1.03379
$917$	−58.7988	−1.94171
$918$	1.86314	0.0614928
$919$	1.96516	0.0648246	0.0324123	−	0.999475i	$-0.489681\pi$
$919$	1.96516	0.0648246	0.0324123	+	0.999475i	$0.489681\pi$
$920$	−33.7669	−1.11326
$921$	−0.354031	−0.0116657
$922$	−76.4595	−2.51806
$923$	−70.7566	−2.32898
$924$	8.70919	0.286511
$925$	7.68246	0.252598
$926$	3.48306	0.114460
$927$	−44.8993	−1.47469
$928$	−0.395518	−0.0129835
$929$	−54.6398	−1.79267	−0.896337	−	0.443374i	$-0.853782\pi$
$929$	−54.6398	−1.79267	−0.896337	+	0.443374i	$0.853782\pi$
$930$	1.22375	0.0401283
$931$	−97.4754	−3.19463
$932$	−12.6518	−0.414424
$933$	1.37310	0.0449534
$934$	−51.2292	−1.67627
$935$	−7.68496	−0.251325
$936$	78.1771	2.55530
$937$	−8.57789	−0.280227	−0.140114	−	0.990135i	$-0.544747\pi$
$937$	−8.57789	−0.280227	−0.140114	+	0.990135i	$0.544747\pi$
$938$	−15.4312	−0.503847
$939$	0.334165	0.0109051
$940$	−37.5758	−1.22559
$941$	−13.8681	−0.452088	−0.226044	−	0.974117i	$-0.572579\pi$
$941$	−13.8681	−0.452088	−0.226044	+	0.974117i	$0.572579\pi$
$942$	−3.81107	−0.124172
$943$	−51.5552	−1.67887
$944$	−9.61722	−0.313014
$945$	−2.59629	−0.0844574
$946$	24.0974	0.783473
$947$	−20.0809	−0.652542	−0.326271	−	0.945276i	$-0.605792\pi$
$947$	−20.0809	−0.652542	−0.326271	+	0.945276i	$0.605792\pi$
$948$	−0.942424	−0.0306085
$949$	−67.3775	−2.18717
$950$	11.9917	0.389061
$951$	1.69940	0.0551070
$952$	38.1870	1.23765
$953$	4.76470	0.154344	0.0771718	−	0.997018i	$-0.475411\pi$
$953$	4.76470	0.154344	0.0771718	+	0.997018i	$0.475411\pi$
$954$	88.0139	2.84955
$955$	4.51909	0.146234
$956$	−51.5483	−1.66719
$957$	−0.851912	−0.0275384
$958$	67.8204	2.19118
$959$	−68.7153	−2.21893
$960$	−0.688425	−0.0222188
$961$	4.86447	0.156918
$962$	−101.353	−3.26774
$963$	−40.4489	−1.30345
$964$	−72.6399	−2.33957
$965$	26.5354	0.854206
$966$	−7.38863	−0.237725
$967$	39.2050	1.26075	0.630374	−	0.776292i	$-0.282902\pi$
$967$	39.2050	1.26075	0.630374	+	0.776292i	$0.282902\pi$
$968$	−70.2766	−2.25877
$969$	−0.623431	−0.0200275
$970$	−18.6946	−0.600249
$971$	−40.4945	−1.29953	−0.649765	−	0.760135i	$-0.725133\pi$
$971$	−40.4945	−1.29953	−0.649765	+	0.760135i	$0.725133\pi$
$972$	−8.95152	−0.287120
$973$	98.0917	3.14468
$974$	20.0582	0.642706
$975$	−0.450820	−0.0144378
$976$	−21.7481	−0.696141
$977$	0.929562	0.0297393	0.0148697	−	0.999889i	$-0.495267\pi$
$977$	0.929562	0.0297393	0.0148697	+	0.999889i	$0.495267\pi$
$978$	−2.63902	−0.0843865
$979$	−48.9346	−1.56396
$980$	−79.1096	−2.52706
$981$	4.73456	0.151163
$982$	36.7163	1.17166
$983$	−61.8943	−1.97412	−0.987061	−	0.160346i	$-0.948739\pi$
$983$	−61.8943	−1.97412	−0.987061	+	0.160346i	$0.948739\pi$
$984$	2.99059	0.0953367
$985$	−0.635148	−0.0202375
$986$	−7.50870	−0.239126
$987$	−4.09023	−0.130194
$988$	−105.291	−3.34976
$989$	−13.6061	−0.432648
$990$	36.9706	1.17500
$991$	23.0124	0.731014	0.365507	−	0.930809i	$-0.380896\pi$
$991$	23.0124	0.731014	0.365507	+	0.930809i	$0.380896\pi$
$992$	−1.17360	−0.0372618
$993$	−2.60568	−0.0826888
$994$	166.271	5.27381
$995$	12.8361	0.406931
$996$	−5.41041	−0.171435
$997$	46.4844	1.47218	0.736088	−	0.676886i	$-0.236671\pi$
$997$	46.4844	1.47218	0.736088	+	0.676886i	$0.236671\pi$
$998$	41.3360	1.30847
$999$	3.84733	0.121724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.15	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.44538 q^{2} -0.0835630 q^{3} +3.97986 q^{4} -1.00000 q^{5} +0.204343 q^{6} +5.18435 q^{7} -4.84151 q^{8} -2.99302 q^{9} +O(q^{10})\)	\(q-2.44538 q^{2} -0.0835630 q^{3} +3.97986 q^{4} -1.00000 q^{5} +0.204343 q^{6} +5.18435 q^{7} -4.84151 q^{8} -2.99302 q^{9} +2.44538 q^{10} -5.05128 q^{11} -0.332569 q^{12} +5.39497 q^{13} -12.6777 q^{14} +0.0835630 q^{15} +3.87959 q^{16} -1.52139 q^{17} +7.31905 q^{18} -4.90382 q^{19} -3.97986 q^{20} -0.433220 q^{21} +12.3523 q^{22} -6.97445 q^{23} +0.404571 q^{24} +1.00000 q^{25} -13.1927 q^{26} +0.500795 q^{27} +20.6330 q^{28} -2.01827 q^{29} -0.204343 q^{30} -5.98869 q^{31} +0.195969 q^{32} +0.422100 q^{33} +3.72037 q^{34} -5.18435 q^{35} -11.9118 q^{36} +7.68246 q^{37} +11.9917 q^{38} -0.450820 q^{39} +4.84151 q^{40} +7.39201 q^{41} +1.05939 q^{42} +1.95084 q^{43} -20.1034 q^{44} +2.99302 q^{45} +17.0551 q^{46} +9.44148 q^{47} -0.324190 q^{48} +19.8775 q^{49} -2.44538 q^{50} +0.127132 q^{51} +21.4713 q^{52} +12.0253 q^{53} -1.22463 q^{54} +5.05128 q^{55} -25.1001 q^{56} +0.409778 q^{57} +4.93543 q^{58} -2.47893 q^{59} +0.332569 q^{60} -5.60578 q^{61} +14.6446 q^{62} -15.5168 q^{63} -8.23840 q^{64} -5.39497 q^{65} -1.03219 q^{66} +1.21720 q^{67} -6.05492 q^{68} +0.582806 q^{69} +12.6777 q^{70} -13.1153 q^{71} +14.4907 q^{72} -12.4890 q^{73} -18.7865 q^{74} -0.0835630 q^{75} -19.5165 q^{76} -26.1876 q^{77} +1.10242 q^{78} +2.83376 q^{79} -3.87959 q^{80} +8.93720 q^{81} -18.0762 q^{82} +16.2685 q^{83} -1.72416 q^{84} +1.52139 q^{85} -4.77055 q^{86} +0.168653 q^{87} +24.4558 q^{88} +9.68757 q^{89} -7.31905 q^{90} +27.9694 q^{91} -27.7574 q^{92} +0.500433 q^{93} -23.0880 q^{94} +4.90382 q^{95} -0.0163758 q^{96} -7.64489 q^{97} -48.6078 q^{98} +15.1186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 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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