LMFDB - Embedded newform 8035.2.a.c.1.6

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:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.46463 q^{2} -1.44696 q^{3} +4.07438 q^{4} -1.00000 q^{5} +3.56623 q^{6} +3.47016 q^{7} -5.11258 q^{8} -0.906295 q^{9} +O(q^{10})$	\(q-2.46463 q^{2} -1.44696 q^{3} +4.07438 q^{4} -1.00000 q^{5} +3.56623 q^{6} +3.47016 q^{7} -5.11258 q^{8} -0.906295 q^{9} +2.46463 q^{10} +4.95014 q^{11} -5.89549 q^{12} +3.81090 q^{13} -8.55266 q^{14} +1.44696 q^{15} +4.45184 q^{16} +0.332033 q^{17} +2.23368 q^{18} -3.16342 q^{19} -4.07438 q^{20} -5.02120 q^{21} -12.2003 q^{22} +0.874081 q^{23} +7.39772 q^{24} +1.00000 q^{25} -9.39246 q^{26} +5.65227 q^{27} +14.1388 q^{28} +8.02087 q^{29} -3.56623 q^{30} +4.62404 q^{31} -0.746955 q^{32} -7.16268 q^{33} -0.818338 q^{34} -3.47016 q^{35} -3.69259 q^{36} -11.1794 q^{37} +7.79666 q^{38} -5.51424 q^{39} +5.11258 q^{40} -9.49599 q^{41} +12.3754 q^{42} -8.42399 q^{43} +20.1688 q^{44} +0.906295 q^{45} -2.15428 q^{46} +10.9365 q^{47} -6.44165 q^{48} +5.04204 q^{49} -2.46463 q^{50} -0.480440 q^{51} +15.5271 q^{52} +11.2292 q^{53} -13.9307 q^{54} -4.95014 q^{55} -17.7415 q^{56} +4.57736 q^{57} -19.7684 q^{58} +13.5695 q^{59} +5.89549 q^{60} -2.13129 q^{61} -11.3965 q^{62} -3.14499 q^{63} -7.06271 q^{64} -3.81090 q^{65} +17.6533 q^{66} +1.25354 q^{67} +1.35283 q^{68} -1.26476 q^{69} +8.55266 q^{70} -2.17338 q^{71} +4.63351 q^{72} +16.2303 q^{73} +27.5529 q^{74} -1.44696 q^{75} -12.8890 q^{76} +17.1778 q^{77} +13.5905 q^{78} -3.54748 q^{79} -4.45184 q^{80} -5.45974 q^{81} +23.4041 q^{82} +5.96216 q^{83} -20.4583 q^{84} -0.332033 q^{85} +20.7620 q^{86} -11.6059 q^{87} -25.3080 q^{88} -18.5889 q^{89} -2.23368 q^{90} +13.2245 q^{91} +3.56134 q^{92} -6.69083 q^{93} -26.9544 q^{94} +3.16342 q^{95} +1.08082 q^{96} -0.210354 q^{97} -12.4267 q^{98} -4.48629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.46463	−1.74275	−0.871377	−	0.490614i	$-0.836773\pi$
$2$	−2.46463	−1.74275	−0.871377	+	0.490614i	$0.836773\pi$
$3$	−1.44696	−0.835405	−0.417703	−	0.908584i	$-0.637165\pi$
$3$	−1.44696	−0.835405	−0.417703	+	0.908584i	$0.637165\pi$
$4$	4.07438	2.03719
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.56623	1.45591
$7$	3.47016	1.31160	0.655799	−	0.754935i	$-0.272332\pi$
$7$	3.47016	1.31160	0.655799	+	0.754935i	$0.272332\pi$
$8$	−5.11258	−1.80757
$9$	−0.906295	−0.302098
$10$	2.46463	0.779383
$11$	4.95014	1.49252	0.746262	−	0.665652i	$-0.231846\pi$
$11$	4.95014	1.49252	0.746262	+	0.665652i	$0.231846\pi$
$12$	−5.89549	−1.70188
$13$	3.81090	1.05695	0.528477	−	0.848947i	$-0.322763\pi$
$13$	3.81090	1.05695	0.528477	+	0.848947i	$0.322763\pi$
$14$	−8.55266	−2.28579
$15$	1.44696	0.373605
$16$	4.45184	1.11296
$17$	0.332033	0.0805299	0.0402650	−	0.999189i	$-0.487180\pi$
$17$	0.332033	0.0805299	0.0402650	+	0.999189i	$0.487180\pi$
$18$	2.23368	0.526483
$19$	−3.16342	−0.725739	−0.362870	−	0.931840i	$-0.618203\pi$
$19$	−3.16342	−0.725739	−0.362870	+	0.931840i	$0.618203\pi$
$20$	−4.07438	−0.911060
$21$	−5.02120	−1.09572
$22$	−12.2003	−2.60110
$23$	0.874081	0.182259	0.0911293	−	0.995839i	$-0.470952\pi$
$23$	0.874081	0.182259	0.0911293	+	0.995839i	$0.470952\pi$
$24$	7.39772	1.51005
$25$	1.00000	0.200000
$26$	−9.39246	−1.84201
$27$	5.65227	1.08778
$28$	14.1388	2.67198
$29$	8.02087	1.48944	0.744719	−	0.667378i	$-0.232583\pi$
$29$	8.02087	1.48944	0.744719	+	0.667378i	$0.232583\pi$
$30$	−3.56623	−0.651101
$31$	4.62404	0.830503	0.415251	−	0.909707i	$-0.363694\pi$
$31$	4.62404	0.830503	0.415251	+	0.909707i	$0.363694\pi$
$32$	−0.746955	−0.132044
$33$	−7.16268	−1.24686
$34$	−0.818338	−0.140344
$35$	−3.47016	−0.586565
$36$	−3.69259	−0.615432
$37$	−11.1794	−1.83787	−0.918937	−	0.394404i	$-0.870951\pi$
$37$	−11.1794	−1.83787	−0.918937	+	0.394404i	$0.870951\pi$
$38$	7.79666	1.26479
$39$	−5.51424	−0.882985
$40$	5.11258	0.808370
$41$	−9.49599	−1.48302	−0.741512	−	0.670940i	$-0.765891\pi$
$41$	−9.49599	−1.48302	−0.741512	+	0.670940i	$0.765891\pi$
$42$	12.3754	1.90956
$43$	−8.42399	−1.28465	−0.642323	−	0.766434i	$-0.722029\pi$
$43$	−8.42399	−1.28465	−0.642323	+	0.766434i	$0.722029\pi$
$44$	20.1688	3.04056
$45$	0.906295	0.135102
$46$	−2.15428	−0.317632
$47$	10.9365	1.59526	0.797628	−	0.603150i	$-0.206088\pi$
$47$	10.9365	1.59526	0.797628	+	0.603150i	$0.206088\pi$
$48$	−6.44165	−0.929772
$49$	5.04204	0.720291
$50$	−2.46463	−0.348551
$51$	−0.480440	−0.0672751
$52$	15.5271	2.15322
$53$	11.2292	1.54245	0.771226	−	0.636562i	$-0.219644\pi$
$53$	11.2292	1.54245	0.771226	+	0.636562i	$0.219644\pi$
$54$	−13.9307	−1.89573
$55$	−4.95014	−0.667477
$56$	−17.7415	−2.37081
$57$	4.57736	0.606286
$58$	−19.7684	−2.59572
$59$	13.5695	1.76660	0.883301	−	0.468806i	$-0.155316\pi$
$59$	13.5695	1.76660	0.883301	+	0.468806i	$0.155316\pi$
$60$	5.89549	0.761104
$61$	−2.13129	−0.272883	−0.136442	−	0.990648i	$-0.543567\pi$
$61$	−2.13129	−0.272883	−0.136442	+	0.990648i	$0.543567\pi$
$62$	−11.3965	−1.44736
$63$	−3.14499	−0.396232
$64$	−7.06271	−0.882839
$65$	−3.81090	−0.472684
$66$	17.6533	2.17298
$67$	1.25354	0.153144	0.0765720	−	0.997064i	$-0.475603\pi$
$67$	1.25354	0.153144	0.0765720	+	0.997064i	$0.475603\pi$
$68$	1.35283	0.164055
$69$	−1.26476	−0.152260
$70$	8.55266	1.02224
$71$	−2.17338	−0.257933	−0.128966	−	0.991649i	$-0.541166\pi$
$71$	−2.17338	−0.257933	−0.128966	+	0.991649i	$0.541166\pi$
$72$	4.63351	0.546064
$73$	16.2303	1.89962	0.949808	−	0.312832i	$-0.101278\pi$
$73$	16.2303	1.89962	0.949808	+	0.312832i	$0.101278\pi$
$74$	27.5529	3.20296
$75$	−1.44696	−0.167081
$76$	−12.8890	−1.47847
$77$	17.1778	1.95759
$78$	13.5905	1.53883
$79$	−3.54748	−0.399123	−0.199561	−	0.979885i	$-0.563952\pi$
$79$	−3.54748	−0.399123	−0.199561	+	0.979885i	$0.563952\pi$
$80$	−4.45184	−0.497731
$81$	−5.45974	−0.606638
$82$	23.4041	2.58455
$83$	5.96216	0.654432	0.327216	−	0.944950i	$-0.393890\pi$
$83$	5.96216	0.654432	0.327216	+	0.944950i	$0.393890\pi$
$84$	−20.4583	−2.23218
$85$	−0.332033	−0.0360141
$86$	20.7620	2.23882
$87$	−11.6059	−1.24428
$88$	−25.3080	−2.69784
$89$	−18.5889	−1.97042	−0.985208	−	0.171365i	$-0.945182\pi$
$89$	−18.5889	−1.97042	−0.985208	+	0.171365i	$0.945182\pi$
$90$	−2.23368	−0.235450
$91$	13.2245	1.38630
$92$	3.56134	0.371296
$93$	−6.69083	−0.693806
$94$	−26.9544	−2.78014
$95$	3.16342	0.324561
$96$	1.08082	0.110310
$97$	−0.210354	−0.0213582	−0.0106791	−	0.999943i	$-0.503399\pi$
$97$	−0.210354	−0.0213582	−0.0106791	+	0.999943i	$0.503399\pi$
$98$	−12.4267	−1.25529
$99$	−4.48629	−0.450889
$100$	4.07438	0.407438
$101$	1.73385	0.172524	0.0862621	−	0.996272i	$-0.472508\pi$
$101$	1.73385	0.172524	0.0862621	+	0.996272i	$0.472508\pi$
$102$	1.18411	0.117244
$103$	3.86356	0.380688	0.190344	−	0.981717i	$-0.439040\pi$
$103$	3.86356	0.380688	0.190344	+	0.981717i	$0.439040\pi$
$104$	−19.4836	−1.91052
$105$	5.02120	0.490019
$106$	−27.6758	−2.68811
$107$	8.43893	0.815822	0.407911	−	0.913022i	$-0.366257\pi$
$107$	8.43893	0.815822	0.407911	+	0.913022i	$0.366257\pi$
$108$	23.0295	2.21602
$109$	7.43758	0.712391	0.356196	−	0.934411i	$-0.384074\pi$
$109$	7.43758	0.712391	0.356196	+	0.934411i	$0.384074\pi$
$110$	12.2003	1.16325
$111$	16.1761	1.53537
$112$	15.4486	1.45976
$113$	−7.81173	−0.734866	−0.367433	−	0.930050i	$-0.619763\pi$
$113$	−7.81173	−0.734866	−0.367433	+	0.930050i	$0.619763\pi$
$114$	−11.2815	−1.05661
$115$	−0.874081	−0.0815085
$116$	32.6801	3.03427
$117$	−3.45380	−0.319304
$118$	−33.4438	−3.07875
$119$	1.15221	0.105623
$120$	−7.39772	−0.675317
$121$	13.5039	1.22763
$122$	5.25283	0.475569
$123$	13.7404	1.23893
$124$	18.8401	1.69189
$125$	−1.00000	−0.0894427
$126$	7.75123	0.690535
$127$	20.2949	1.80088	0.900440	−	0.434980i	$-0.143245\pi$
$127$	20.2949	1.80088	0.900440	+	0.434980i	$0.143245\pi$
$128$	18.9009	1.67062
$129$	12.1892	1.07320
$130$	9.39246	0.823773
$131$	10.7768	0.941576	0.470788	−	0.882246i	$-0.343970\pi$
$131$	10.7768	0.941576	0.470788	+	0.882246i	$0.343970\pi$
$132$	−29.1835	−2.54010
$133$	−10.9776	−0.951879
$134$	−3.08950	−0.266892
$135$	−5.65227	−0.486470
$136$	−1.69755	−0.145564
$137$	21.6961	1.85362	0.926811	−	0.375527i	$-0.122538\pi$
$137$	21.6961	1.85362	0.926811	+	0.375527i	$0.122538\pi$
$138$	3.11717	0.265351
$139$	−5.63550	−0.477997	−0.238999	−	0.971020i	$-0.576819\pi$
$139$	−5.63550	−0.477997	−0.238999	+	0.971020i	$0.576819\pi$
$140$	−14.1388	−1.19495
$141$	−15.8248	−1.33268
$142$	5.35657	0.449513
$143$	18.8645	1.57753
$144$	−4.03468	−0.336223
$145$	−8.02087	−0.666097
$146$	−40.0017	−3.31057
$147$	−7.29565	−0.601735
$148$	−45.5490	−3.74410
$149$	−2.58174	−0.211505	−0.105752	−	0.994392i	$-0.533725\pi$
$149$	−2.58174	−0.211505	−0.105752	+	0.994392i	$0.533725\pi$
$150$	3.56623	0.291181
$151$	11.0738	0.901171	0.450586	−	0.892733i	$-0.351215\pi$
$151$	11.0738	0.901171	0.450586	+	0.892733i	$0.351215\pi$
$152$	16.1733	1.31183
$153$	−0.300920	−0.0243280
$154$	−42.3369	−3.41160
$155$	−4.62404	−0.371412
$156$	−22.4671	−1.79881
$157$	3.93592	0.314121	0.157060	−	0.987589i	$-0.449798\pi$
$157$	3.93592	0.314121	0.157060	+	0.987589i	$0.449798\pi$
$158$	8.74321	0.695573
$159$	−16.2483	−1.28857
$160$	0.746955	0.0590520
$161$	3.03321	0.239050
$162$	13.4562	1.05722
$163$	−8.79422	−0.688816	−0.344408	−	0.938820i	$-0.611920\pi$
$163$	−8.79422	−0.688816	−0.344408	+	0.938820i	$0.611920\pi$
$164$	−38.6903	−3.02121
$165$	7.16268	0.557614
$166$	−14.6945	−1.14051
$167$	3.61533	0.279763	0.139881	−	0.990168i	$-0.455328\pi$
$167$	3.61533	0.279763	0.139881	+	0.990168i	$0.455328\pi$
$168$	25.6713	1.98058
$169$	1.52299	0.117153
$170$	0.818338	0.0627637
$171$	2.86700	0.219245
$172$	−34.3226	−2.61707
$173$	−0.379647	−0.0288641	−0.0144320	−	0.999896i	$-0.504594\pi$
$173$	−0.379647	−0.0288641	−0.0144320	+	0.999896i	$0.504594\pi$
$174$	28.6042	2.16848
$175$	3.47016	0.262320
$176$	22.0372	1.66112
$177$	−19.6346	−1.47583
$178$	45.8146	3.43395
$179$	−19.2296	−1.43729	−0.718645	−	0.695377i	$-0.755237\pi$
$179$	−19.2296	−1.43729	−0.718645	+	0.695377i	$0.755237\pi$
$180$	3.69259	0.275230
$181$	−11.5302	−0.857031	−0.428516	−	0.903534i	$-0.640963\pi$
$181$	−11.5302	−0.857031	−0.428516	+	0.903534i	$0.640963\pi$
$182$	−32.5934	−2.41598
$183$	3.08390	0.227968
$184$	−4.46881	−0.329445
$185$	11.1794	0.821922
$186$	16.4904	1.20913
$187$	1.64361	0.120193
$188$	44.5596	3.24984
$189$	19.6143	1.42673
$190$	−7.79666	−0.565629
$191$	23.4550	1.69714	0.848571	−	0.529082i	$-0.177464\pi$
$191$	23.4550	1.69714	0.848571	+	0.529082i	$0.177464\pi$
$192$	10.2195	0.737528
$193$	−4.45000	−0.320318	−0.160159	−	0.987091i	$-0.551201\pi$
$193$	−4.45000	−0.320318	−0.160159	+	0.987091i	$0.551201\pi$
$194$	0.518444	0.0372221
$195$	5.51424	0.394883
$196$	20.5432	1.46737
$197$	−9.66698	−0.688744	−0.344372	−	0.938833i	$-0.611908\pi$
$197$	−9.66698	−0.688744	−0.344372	+	0.938833i	$0.611908\pi$
$198$	11.0570	0.785789
$199$	−15.8914	−1.12651	−0.563256	−	0.826282i	$-0.690452\pi$
$199$	−15.8914	−1.12651	−0.563256	+	0.826282i	$0.690452\pi$
$200$	−5.11258	−0.361514
$201$	−1.81382	−0.127937
$202$	−4.27329	−0.300667
$203$	27.8337	1.95354
$204$	−1.95750	−0.137052
$205$	9.49599	0.663229
$206$	−9.52223	−0.663445
$207$	−0.792175	−0.0550600
$208$	16.9655	1.17635
$209$	−15.6594	−1.08318
$210$	−12.3754	−0.853983
$211$	−7.15264	−0.492408	−0.246204	−	0.969218i	$-0.579183\pi$
$211$	−7.15264	−0.492408	−0.246204	+	0.969218i	$0.579183\pi$
$212$	45.7521	3.14227
$213$	3.14480	0.215478
$214$	−20.7988	−1.42178
$215$	8.42399	0.574511
$216$	−28.8977	−1.96624
$217$	16.0462	1.08929
$218$	−18.3309	−1.24152
$219$	−23.4847	−1.58695
$220$	−20.1688	−1.35978
$221$	1.26535	0.0851165
$222$	−39.8681	−2.67577
$223$	3.75770	0.251634	0.125817	−	0.992053i	$-0.459845\pi$
$223$	3.75770	0.251634	0.125817	+	0.992053i	$0.459845\pi$
$224$	−2.59206	−0.173189
$225$	−0.906295	−0.0604197
$226$	19.2530	1.28069
$227$	−6.79572	−0.451048	−0.225524	−	0.974238i	$-0.572409\pi$
$227$	−6.79572	−0.451048	−0.225524	+	0.974238i	$0.572409\pi$
$228$	18.6499	1.23512
$229$	−15.8142	−1.04503	−0.522517	−	0.852629i	$-0.675007\pi$
$229$	−15.8142	−1.04503	−0.522517	+	0.852629i	$0.675007\pi$
$230$	2.15428	0.142049
$231$	−24.8557	−1.63538
$232$	−41.0074	−2.69226
$233$	0.710666	0.0465573	0.0232787	−	0.999729i	$-0.492590\pi$
$233$	0.710666	0.0465573	0.0232787	+	0.999729i	$0.492590\pi$
$234$	8.51233	0.556469
$235$	−10.9365	−0.713420
$236$	55.2875	3.59891
$237$	5.13308	0.333429
$238$	−2.83977	−0.184075
$239$	−1.93156	−0.124942	−0.0624711	−	0.998047i	$-0.519898\pi$
$239$	−1.93156	−0.124942	−0.0624711	+	0.998047i	$0.519898\pi$
$240$	6.44165	0.415807
$241$	−3.44985	−0.222224	−0.111112	−	0.993808i	$-0.535441\pi$
$241$	−3.44985	−0.222224	−0.111112	+	0.993808i	$0.535441\pi$
$242$	−33.2822	−2.13946
$243$	−9.05675	−0.580991
$244$	−8.68369	−0.555916
$245$	−5.04204	−0.322124
$246$	−33.8648	−2.15914
$247$	−12.0555	−0.767074
$248$	−23.6408	−1.50119
$249$	−8.62703	−0.546716
$250$	2.46463	0.155877
$251$	21.7587	1.37340	0.686700	−	0.726941i	$-0.259059\pi$
$251$	21.7587	1.37340	0.686700	+	0.726941i	$0.259059\pi$
$252$	−12.8139	−0.807200
$253$	4.32683	0.272025
$254$	−50.0193	−3.13849
$255$	0.480440	0.0300864
$256$	−32.4581	−2.02863
$257$	3.44444	0.214858	0.107429	−	0.994213i	$-0.465738\pi$
$257$	3.44444	0.214858	0.107429	+	0.994213i	$0.465738\pi$
$258$	−30.0418	−1.87032
$259$	−38.7942	−2.41055
$260$	−15.5271	−0.962949
$261$	−7.26927	−0.449957
$262$	−26.5609	−1.64094
$263$	12.8294	0.791097	0.395549	−	0.918445i	$-0.370554\pi$
$263$	12.8294	0.791097	0.395549	+	0.918445i	$0.370554\pi$
$264$	36.6198	2.25379
$265$	−11.2292	−0.689805
$266$	27.0557	1.65889
$267$	26.8974	1.64609
$268$	5.10739	0.311984
$269$	22.0358	1.34355	0.671773	−	0.740757i	$-0.265533\pi$
$269$	22.0358	1.34355	0.671773	+	0.740757i	$0.265533\pi$
$270$	13.9307	0.847797
$271$	−29.3608	−1.78354	−0.891769	−	0.452490i	$-0.850536\pi$
$271$	−29.3608	−1.78354	−0.891769	+	0.452490i	$0.850536\pi$
$272$	1.47816	0.0896266
$273$	−19.1353	−1.15812
$274$	−53.4728	−3.23041
$275$	4.95014	0.298505
$276$	−5.15314	−0.310182
$277$	−6.85823	−0.412071	−0.206036	−	0.978544i	$-0.566056\pi$
$277$	−6.85823	−0.412071	−0.206036	+	0.978544i	$0.566056\pi$
$278$	13.8894	0.833031
$279$	−4.19075	−0.250894
$280$	17.7415	1.06026
$281$	26.5188	1.58198	0.790991	−	0.611828i	$-0.209566\pi$
$281$	26.5188	1.58198	0.790991	+	0.611828i	$0.209566\pi$
$282$	39.0021	2.32254
$283$	17.8556	1.06140	0.530702	−	0.847558i	$-0.321928\pi$
$283$	17.8556	1.06140	0.530702	+	0.847558i	$0.321928\pi$
$284$	−8.85519	−0.525459
$285$	−4.57736	−0.271140
$286$	−46.4940	−2.74925
$287$	−32.9526	−1.94513
$288$	0.676962	0.0398903
$289$	−16.8898	−0.993515
$290$	19.7684	1.16084
$291$	0.304375	0.0178428
$292$	66.1286	3.86988
$293$	−10.6531	−0.622360	−0.311180	−	0.950351i	$-0.600724\pi$
$293$	−10.6531	−0.622360	−0.311180	+	0.950351i	$0.600724\pi$
$294$	17.9810	1.04868
$295$	−13.5695	−0.790048
$296$	57.1554	3.32209
$297$	27.9795	1.62354
$298$	6.36303	0.368601
$299$	3.33104	0.192639
$300$	−5.89549	−0.340376
$301$	−29.2326	−1.68494
$302$	−27.2927	−1.57052
$303$	−2.50881	−0.144128
$304$	−14.0831	−0.807719
$305$	2.13129	0.122037
$306$	0.741656	0.0423977
$307$	−5.34562	−0.305090	−0.152545	−	0.988296i	$-0.548747\pi$
$307$	−5.34562	−0.305090	−0.152545	+	0.988296i	$0.548747\pi$
$308$	69.9890	3.98799
$309$	−5.59043	−0.318028
$310$	11.3965	0.647280
$311$	−9.90842	−0.561855	−0.280928	−	0.959729i	$-0.590642\pi$
$311$	−9.90842	−0.561855	−0.280928	+	0.959729i	$0.590642\pi$
$312$	28.1920	1.59606
$313$	−17.0187	−0.961955	−0.480977	−	0.876733i	$-0.659718\pi$
$313$	−17.0187	−0.961955	−0.480977	+	0.876733i	$0.659718\pi$
$314$	−9.70058	−0.547435
$315$	3.14499	0.177200
$316$	−14.4538	−0.813090
$317$	−2.24510	−0.126098	−0.0630488	−	0.998010i	$-0.520082\pi$
$317$	−2.24510	−0.126098	−0.0630488	+	0.998010i	$0.520082\pi$
$318$	40.0459	2.24566
$319$	39.7045	2.22302
$320$	7.06271	0.394818
$321$	−12.2108	−0.681542
$322$	−7.47572	−0.416606
$323$	−1.05036	−0.0584437
$324$	−22.2451	−1.23584
$325$	3.81090	0.211391
$326$	21.6745	1.20044
$327$	−10.7619	−0.595135
$328$	48.5490	2.68067
$329$	37.9515	2.09234
$330$	−17.6533	−0.971784
$331$	26.9512	1.48137	0.740686	−	0.671851i	$-0.234501\pi$
$331$	26.9512	1.48137	0.740686	+	0.671851i	$0.234501\pi$
$332$	24.2921	1.33320
$333$	10.1318	0.555219
$334$	−8.91045	−0.487558
$335$	−1.25354	−0.0684880
$336$	−22.3536	−1.21949
$337$	17.4367	0.949837	0.474918	−	0.880030i	$-0.342478\pi$
$337$	17.4367	0.949837	0.474918	+	0.880030i	$0.342478\pi$
$338$	−3.75360	−0.204169
$339$	11.3033	0.613911
$340$	−1.35283	−0.0733676
$341$	22.8897	1.23955
$342$	−7.06607	−0.382089
$343$	−6.79445	−0.366866
$344$	43.0683	2.32209
$345$	1.26476	0.0680926
$346$	0.935689	0.0503030
$347$	−15.2117	−0.816605	−0.408303	−	0.912847i	$-0.633879\pi$
$347$	−15.2117	−0.816605	−0.408303	+	0.912847i	$0.633879\pi$
$348$	−47.2869	−2.53485
$349$	−24.5355	−1.31336	−0.656678	−	0.754171i	$-0.728039\pi$
$349$	−24.5355	−1.31336	−0.656678	+	0.754171i	$0.728039\pi$
$350$	−8.55266	−0.457159
$351$	21.5403	1.14973
$352$	−3.69754	−0.197079
$353$	−21.6642	−1.15307	−0.576535	−	0.817072i	$-0.695596\pi$
$353$	−21.6642	−1.15307	−0.576535	+	0.817072i	$0.695596\pi$
$354$	48.3920	2.57201
$355$	2.17338	0.115351
$356$	−75.7382	−4.01411
$357$	−1.66721	−0.0882380
$358$	47.3938	2.50484
$359$	−20.6185	−1.08820	−0.544102	−	0.839019i	$-0.683130\pi$
$359$	−20.6185	−1.08820	−0.544102	+	0.839019i	$0.683130\pi$
$360$	−4.63351	−0.244207
$361$	−8.99275	−0.473302
$362$	28.4176	1.49359
$363$	−19.5397	−1.02557
$364$	53.8815	2.82416
$365$	−16.2303	−0.849535
$366$	−7.60065	−0.397293
$367$	32.5247	1.69777	0.848887	−	0.528575i	$-0.177273\pi$
$367$	32.5247	1.69777	0.848887	+	0.528575i	$0.177273\pi$
$368$	3.89127	0.202846
$369$	8.60617	0.448019
$370$	−27.5529	−1.43241
$371$	38.9672	2.02308
$372$	−27.2610	−1.41342
$373$	−32.8742	−1.70216	−0.851081	−	0.525035i	$-0.824052\pi$
$373$	−32.8742	−1.70216	−0.851081	+	0.525035i	$0.824052\pi$
$374$	−4.05089	−0.209467
$375$	1.44696	0.0747209
$376$	−55.9139	−2.88354
$377$	30.5668	1.57427
$378$	−48.3419	−2.48644
$379$	16.9593	0.871139	0.435569	−	0.900155i	$-0.356547\pi$
$379$	16.9593	0.871139	0.435569	+	0.900155i	$0.356547\pi$
$380$	12.8890	0.661192
$381$	−29.3660	−1.50446
$382$	−57.8077	−2.95770
$383$	2.36182	0.120683	0.0603416	−	0.998178i	$-0.480781\pi$
$383$	2.36182	0.120683	0.0603416	+	0.998178i	$0.480781\pi$
$384$	−27.3489	−1.39564
$385$	−17.1778	−0.875462
$386$	10.9676	0.558236
$387$	7.63462	0.388089
$388$	−0.857063	−0.0435108
$389$	−12.2417	−0.620678	−0.310339	−	0.950626i	$-0.600443\pi$
$389$	−12.2417	−0.620678	−0.310339	+	0.950626i	$0.600443\pi$
$390$	−13.5905	−0.688184
$391$	0.290224	0.0146773
$392$	−25.7778	−1.30198
$393$	−15.5937	−0.786597
$394$	23.8255	1.20031
$395$	3.54748	0.178493
$396$	−18.2789	−0.918548
$397$	−18.5527	−0.931133	−0.465567	−	0.885013i	$-0.654149\pi$
$397$	−18.5527	−0.931133	−0.465567	+	0.885013i	$0.654149\pi$
$398$	39.1664	1.96323
$399$	15.8842	0.795204
$400$	4.45184	0.222592
$401$	−10.6960	−0.534133	−0.267067	−	0.963678i	$-0.586054\pi$
$401$	−10.6960	−0.534133	−0.267067	+	0.963678i	$0.586054\pi$
$402$	4.47040	0.222963
$403$	17.6218	0.877804
$404$	7.06436	0.351465
$405$	5.45974	0.271297
$406$	−68.5998	−3.40455
$407$	−55.3394	−2.74307
$408$	2.45629	0.121605
$409$	−10.0329	−0.496097	−0.248048	−	0.968748i	$-0.579789\pi$
$409$	−10.0329	−0.496097	−0.248048	+	0.968748i	$0.579789\pi$
$410$	−23.4041	−1.15584
$411$	−31.3935	−1.54853
$412$	15.7416	0.775534
$413$	47.0885	2.31707
$414$	1.95242	0.0959561
$415$	−5.96216	−0.292671
$416$	−2.84657	−0.139565
$417$	8.15437	0.399321
$418$	38.5946	1.88772
$419$	−29.2235	−1.42766	−0.713831	−	0.700318i	$-0.753042\pi$
$419$	−29.2235	−1.42766	−0.713831	+	0.700318i	$0.753042\pi$
$420$	20.4583	0.998263
$421$	18.8271	0.917575	0.458788	−	0.888546i	$-0.348284\pi$
$421$	18.8271	0.917575	0.458788	+	0.888546i	$0.348284\pi$
$422$	17.6286	0.858147
$423$	−9.91171	−0.481924
$424$	−57.4103	−2.78809
$425$	0.332033	0.0161060
$426$	−7.75076	−0.375526
$427$	−7.39592	−0.357914
$428$	34.3834	1.66199
$429$	−27.2963	−1.31788
$430$	−20.7620	−1.00123
$431$	−21.7473	−1.04753	−0.523765	−	0.851863i	$-0.675473\pi$
$431$	−21.7473	−1.04753	−0.523765	+	0.851863i	$0.675473\pi$
$432$	25.1630	1.21065
$433$	−8.58572	−0.412603	−0.206302	−	0.978488i	$-0.566143\pi$
$433$	−8.58572	−0.412603	−0.206302	+	0.978488i	$0.566143\pi$
$434$	−39.5479	−1.89836
$435$	11.6059	0.556461
$436$	30.3036	1.45128
$437$	−2.76509	−0.132272
$438$	57.8810	2.76566
$439$	28.8030	1.37469	0.687347	−	0.726329i	$-0.258775\pi$
$439$	28.8030	1.37469	0.687347	+	0.726329i	$0.258775\pi$
$440$	25.3080	1.20651
$441$	−4.56957	−0.217599
$442$	−3.11861	−0.148337
$443$	5.49352	0.261005	0.130502	−	0.991448i	$-0.458341\pi$
$443$	5.49352	0.261005	0.130502	+	0.991448i	$0.458341\pi$
$444$	65.9077	3.12784
$445$	18.5889	0.881197
$446$	−9.26133	−0.438536
$447$	3.73569	0.176692
$448$	−24.5088	−1.15793
$449$	−3.52750	−0.166473	−0.0832366	−	0.996530i	$-0.526526\pi$
$449$	−3.52750	−0.166473	−0.0832366	+	0.996530i	$0.526526\pi$
$450$	2.23368	0.105297
$451$	−47.0065	−2.21345
$452$	−31.8280	−1.49706
$453$	−16.0234	−0.752843
$454$	16.7489	0.786065
$455$	−13.2245	−0.619972
$456$	−23.4021	−1.09591
$457$	23.2936	1.08963	0.544815	−	0.838556i	$-0.316600\pi$
$457$	23.2936	1.08963	0.544815	+	0.838556i	$0.316600\pi$
$458$	38.9762	1.82124
$459$	1.87674	0.0875988
$460$	−3.56134	−0.166048
$461$	3.28126	0.152824	0.0764118	−	0.997076i	$-0.475654\pi$
$461$	3.28126	0.152824	0.0764118	+	0.997076i	$0.475654\pi$
$462$	61.2600	2.85007
$463$	30.2317	1.40499	0.702493	−	0.711691i	$-0.252070\pi$
$463$	30.2317	1.40499	0.702493	+	0.711691i	$0.252070\pi$
$464$	35.7076	1.65768
$465$	6.69083	0.310280
$466$	−1.75153	−0.0811379
$467$	26.3341	1.21860	0.609299	−	0.792941i	$-0.291451\pi$
$467$	26.3341	1.21860	0.609299	+	0.792941i	$0.291451\pi$
$468$	−14.0721	−0.650484
$469$	4.34998	0.200863
$470$	26.9544	1.24332
$471$	−5.69514	−0.262418
$472$	−69.3753	−3.19326
$473$	−41.7000	−1.91737
$474$	−12.6511	−0.581085
$475$	−3.16342	−0.145148
$476$	4.69455	0.215174
$477$	−10.1770	−0.465972
$478$	4.76057	0.217743
$479$	1.93982	0.0886326	0.0443163	−	0.999018i	$-0.485889\pi$
$479$	1.93982	0.0886326	0.0443163	+	0.999018i	$0.485889\pi$
$480$	−1.08082	−0.0493323
$481$	−42.6034	−1.94255
$482$	8.50259	0.387282
$483$	−4.38894	−0.199704
$484$	55.0202	2.50092
$485$	0.210354	0.00955169
$486$	22.3215	1.01252
$487$	10.0587	0.455801	0.227901	−	0.973684i	$-0.426814\pi$
$487$	10.0587	0.455801	0.227901	+	0.973684i	$0.426814\pi$
$488$	10.8964	0.493256
$489$	12.7249	0.575441
$490$	12.4267	0.561383
$491$	−35.5939	−1.60633	−0.803165	−	0.595757i	$-0.796852\pi$
$491$	−35.5939	−1.60633	−0.803165	+	0.595757i	$0.796852\pi$
$492$	55.9835	2.52393
$493$	2.66320	0.119944
$494$	29.7123	1.33682
$495$	4.48629	0.201644
$496$	20.5855	0.924316
$497$	−7.54198	−0.338304
$498$	21.2624	0.952791
$499$	20.4842	0.916997	0.458499	−	0.888695i	$-0.348387\pi$
$499$	20.4842	0.916997	0.458499	+	0.888695i	$0.348387\pi$
$500$	−4.07438	−0.182212
$501$	−5.23126	−0.233715
$502$	−53.6272	−2.39350
$503$	10.0095	0.446303	0.223152	−	0.974784i	$-0.428365\pi$
$503$	10.0095	0.446303	0.223152	+	0.974784i	$0.428365\pi$
$504$	16.0790	0.716217
$505$	−1.73385	−0.0771552
$506$	−10.6640	−0.474073
$507$	−2.20371	−0.0978702
$508$	82.6892	3.66874
$509$	−10.6956	−0.474074	−0.237037	−	0.971501i	$-0.576176\pi$
$509$	−10.6956	−0.474074	−0.237037	+	0.971501i	$0.576176\pi$
$510$	−1.18411	−0.0524331
$511$	56.3219	2.49154
$512$	42.1955	1.86479
$513$	−17.8805	−0.789444
$514$	−8.48926	−0.374445
$515$	−3.86356	−0.170249
$516$	49.6635	2.18631
$517$	54.1374	2.38096
$518$	95.6132	4.20100
$519$	0.549336	0.0241132
$520$	19.4836	0.854411
$521$	−8.69949	−0.381132	−0.190566	−	0.981674i	$-0.561032\pi$
$521$	−8.69949	−0.381132	−0.190566	+	0.981674i	$0.561032\pi$
$522$	17.9160	0.784164
$523$	−23.3746	−1.02210	−0.511049	−	0.859552i	$-0.670743\pi$
$523$	−23.3746	−1.02210	−0.511049	+	0.859552i	$0.670743\pi$
$524$	43.9089	1.91817
$525$	−5.02120	−0.219143
$526$	−31.6198	−1.37869
$527$	1.53534	0.0668804
$528$	−31.8871	−1.38771
$529$	−22.2360	−0.966782
$530$	27.6758	1.20216
$531$	−12.2980	−0.533687
$532$	−44.7270	−1.93916
$533$	−36.1883	−1.56749
$534$	−66.2921	−2.86874
$535$	−8.43893	−0.364847
$536$	−6.40881	−0.276819
$537$	27.8246	1.20072
$538$	−54.3100	−2.34147
$539$	24.9588	1.07505
$540$	−23.0295	−0.991032
$541$	−32.3967	−1.39284	−0.696421	−	0.717634i	$-0.745225\pi$
$541$	−32.3967	−1.39284	−0.696421	+	0.717634i	$0.745225\pi$
$542$	72.3633	3.10827
$543$	16.6837	0.715968
$544$	−0.248014	−0.0106335
$545$	−7.43758	−0.318591
$546$	47.1614	2.01832
$547$	34.4514	1.47303	0.736517	−	0.676419i	$-0.236469\pi$
$547$	34.4514	1.47303	0.736517	+	0.676419i	$0.236469\pi$
$548$	88.3982	3.77619
$549$	1.93158	0.0824376
$550$	−12.2003	−0.520221
$551$	−25.3734	−1.08094
$552$	6.46621	0.275220
$553$	−12.3103	−0.523489
$554$	16.9030	0.718139
$555$	−16.1761	−0.686638
$556$	−22.9612	−0.973772
$557$	−24.4384	−1.03549	−0.517743	−	0.855536i	$-0.673228\pi$
$557$	−24.4384	−1.03549	−0.517743	+	0.855536i	$0.673228\pi$
$558$	10.3286	0.437246
$559$	−32.1030	−1.35781
$560$	−15.4486	−0.652823
$561$	−2.37825	−0.100410
$562$	−65.3590	−2.75700
$563$	15.7863	0.665315	0.332657	−	0.943048i	$-0.392055\pi$
$563$	15.7863	0.665315	0.332657	+	0.943048i	$0.392055\pi$
$564$	−64.4761	−2.71493
$565$	7.81173	0.328642
$566$	−44.0074	−1.84977
$567$	−18.9462	−0.795666
$568$	11.1116	0.466232
$569$	15.8789	0.665678	0.332839	−	0.942984i	$-0.391993\pi$
$569$	15.8789	0.665678	0.332839	+	0.942984i	$0.391993\pi$
$570$	11.2815	0.472530
$571$	−35.3126	−1.47779	−0.738893	−	0.673822i	$-0.764651\pi$
$571$	−35.3126	−1.47779	−0.738893	+	0.673822i	$0.764651\pi$
$572$	76.8613	3.21373
$573$	−33.9385	−1.41780
$574$	81.2159	3.38989
$575$	0.874081	0.0364517
$576$	6.40090	0.266704
$577$	−26.5710	−1.10616	−0.553082	−	0.833127i	$-0.686548\pi$
$577$	−26.5710	−1.10616	−0.553082	+	0.833127i	$0.686548\pi$
$578$	41.6269	1.73145
$579$	6.43899	0.267595
$580$	−32.6801	−1.35697
$581$	20.6897	0.858352
$582$	−0.750170	−0.0310956
$583$	55.5862	2.30215
$584$	−82.9789	−3.43369
$585$	3.45380	0.142797
$586$	26.2559	1.08462
$587$	−9.30295	−0.383974	−0.191987	−	0.981397i	$-0.561493\pi$
$587$	−9.30295	−0.383974	−0.191987	+	0.981397i	$0.561493\pi$
$588$	−29.7253	−1.22585
$589$	−14.6278	−0.602729
$590$	33.4438	1.37686
$591$	13.9878	0.575380
$592$	−49.7687	−2.04548
$593$	28.2028	1.15815	0.579075	−	0.815275i	$-0.303414\pi$
$593$	28.2028	1.15815	0.579075	+	0.815275i	$0.303414\pi$
$594$	−68.9591	−2.82943
$595$	−1.15221	−0.0472360
$596$	−10.5190	−0.430876
$597$	22.9943	0.941094
$598$	−8.20977	−0.335722
$599$	−29.2852	−1.19656	−0.598281	−	0.801287i	$-0.704149\pi$
$599$	−29.2852	−1.19656	−0.598281	+	0.801287i	$0.704149\pi$
$600$	7.39772	0.302011
$601$	1.64036	0.0669118	0.0334559	−	0.999440i	$-0.489349\pi$
$601$	1.64036	0.0669118	0.0334559	+	0.999440i	$0.489349\pi$
$602$	72.0475	2.93644
$603$	−1.13607	−0.0462645
$604$	45.1188	1.83586
$605$	−13.5039	−0.549013
$606$	6.18329	0.251179
$607$	44.8881	1.82195	0.910975	−	0.412461i	$-0.135331\pi$
$607$	44.8881	1.82195	0.910975	+	0.412461i	$0.135331\pi$
$608$	2.36294	0.0958297
$609$	−40.2744	−1.63200
$610$	−5.25283	−0.212681
$611$	41.6780	1.68611
$612$	−1.22606	−0.0495607
$613$	−39.8919	−1.61122	−0.805610	−	0.592446i	$-0.798162\pi$
$613$	−39.8919	−1.61122	−0.805610	+	0.592446i	$0.798162\pi$
$614$	13.1749	0.531698
$615$	−13.7404	−0.554065
$616$	−87.8230	−3.53849
$617$	17.3426	0.698189	0.349094	−	0.937088i	$-0.386489\pi$
$617$	17.3426	0.698189	0.349094	+	0.937088i	$0.386489\pi$
$618$	13.7783	0.554245
$619$	16.3777	0.658274	0.329137	−	0.944282i	$-0.393242\pi$
$619$	16.3777	0.658274	0.329137	+	0.944282i	$0.393242\pi$
$620$	−18.8401	−0.756638
$621$	4.94054	0.198257
$622$	24.4206	0.979175
$623$	−64.5064	−2.58439
$624$	−24.5485	−0.982727
$625$	1.00000	0.0400000
$626$	41.9448	1.67645
$627$	22.6586	0.904897
$628$	16.0365	0.639924
$629$	−3.71192	−0.148004
$630$	−7.75123	−0.308816
$631$	40.2882	1.60385	0.801925	−	0.597425i	$-0.203809\pi$
$631$	40.2882	1.60385	0.801925	+	0.597425i	$0.203809\pi$
$632$	18.1368	0.721443
$633$	10.3496	0.411360
$634$	5.53334	0.219757
$635$	−20.2949	−0.805378
$636$	−66.2017	−2.62507
$637$	19.2147	0.761315
$638$	−97.8567	−3.87418
$639$	1.96972	0.0779210
$640$	−18.9009	−0.747122
$641$	8.20058	0.323903	0.161952	−	0.986799i	$-0.448221\pi$
$641$	8.20058	0.323903	0.161952	+	0.986799i	$0.448221\pi$
$642$	30.0951	1.18776
$643$	11.0507	0.435798	0.217899	−	0.975971i	$-0.430080\pi$
$643$	11.0507	0.435798	0.217899	+	0.975971i	$0.430080\pi$
$644$	12.3584	0.486991
$645$	−12.1892	−0.479949
$646$	2.58875	0.101853
$647$	−16.6745	−0.655543	−0.327771	−	0.944757i	$-0.606298\pi$
$647$	−16.6745	−0.655543	−0.327771	+	0.944757i	$0.606298\pi$
$648$	27.9134	1.09654
$649$	67.1711	2.63670
$650$	−9.39246	−0.368402
$651$	−23.2183	−0.909996
$652$	−35.8310	−1.40325
$653$	0.0342515	0.00134037	0.000670183	−	1.00000i	$-0.499787\pi$
$653$	0.0342515	0.00134037	0.000670183		1.00000i	$0.499787\pi$
$654$	26.5241	1.03717
$655$	−10.7768	−0.421085
$656$	−42.2746	−1.65055
$657$	−14.7095	−0.573871
$658$	−93.5363	−3.64643
$659$	16.7454	0.652307	0.326153	−	0.945317i	$-0.394247\pi$
$659$	16.7454	0.652307	0.326153	+	0.945317i	$0.394247\pi$
$660$	29.1835	1.13597
$661$	16.1812	0.629374	0.314687	−	0.949195i	$-0.398100\pi$
$661$	16.1812	0.629374	0.314687	+	0.949195i	$0.398100\pi$
$662$	−66.4247	−2.58167
$663$	−1.83091	−0.0711068
$664$	−30.4820	−1.18293
$665$	10.9776	0.425693
$666$	−24.9711	−0.967610
$667$	7.01089	0.271463
$668$	14.7303	0.569931
$669$	−5.43726	−0.210216
$670$	3.08950	0.119358
$671$	−10.5502	−0.407285
$672$	3.75061	0.144683
$673$	−5.55050	−0.213956	−0.106978	−	0.994261i	$-0.534117\pi$
$673$	−5.55050	−0.213956	−0.106978	+	0.994261i	$0.534117\pi$
$674$	−42.9749	−1.65533
$675$	5.65227	0.217556
$676$	6.20524	0.238663
$677$	25.2057	0.968735	0.484367	−	0.874865i	$-0.339050\pi$
$677$	25.2057	0.968735	0.484367	+	0.874865i	$0.339050\pi$
$678$	−27.8584	−1.06990
$679$	−0.729963	−0.0280134
$680$	1.69755	0.0650980
$681$	9.83316	0.376808
$682$	−56.4145	−2.16022
$683$	−39.7144	−1.51963	−0.759815	−	0.650140i	$-0.774710\pi$
$683$	−39.7144	−1.51963	−0.759815	+	0.650140i	$0.774710\pi$
$684$	11.6812	0.446643
$685$	−21.6961	−0.828965
$686$	16.7458	0.639357
$687$	22.8826	0.873027
$688$	−37.5022	−1.42976
$689$	42.7935	1.63030
$690$	−3.11717	−0.118669
$691$	36.4093	1.38508	0.692538	−	0.721381i	$-0.256492\pi$
$691$	36.4093	1.38508	0.692538	+	0.721381i	$0.256492\pi$
$692$	−1.54683	−0.0588016
$693$	−15.5682	−0.591386
$694$	37.4911	1.42314
$695$	5.63550	0.213767
$696$	59.3362	2.24913
$697$	−3.15299	−0.119428
$698$	60.4708	2.28886
$699$	−1.02831	−0.0388942
$700$	14.1388	0.534396
$701$	7.64619	0.288793	0.144396	−	0.989520i	$-0.453876\pi$
$701$	7.64619	0.288793	0.144396	+	0.989520i	$0.453876\pi$
$702$	−53.0887	−2.00370
$703$	35.3650	1.33382
$704$	−34.9615	−1.31766
$705$	15.8248	0.595995
$706$	53.3942	2.00952
$707$	6.01673	0.226283
$708$	−79.9990	−3.00655
$709$	3.08647	0.115915	0.0579574	−	0.998319i	$-0.481541\pi$
$709$	3.08647	0.115915	0.0579574	+	0.998319i	$0.481541\pi$
$710$	−5.35657	−0.201028
$711$	3.21506	0.120574
$712$	95.0371	3.56167
$713$	4.04179	0.151366
$714$	4.10904	0.153777
$715$	−18.8645	−0.705493
$716$	−78.3489	−2.92803
$717$	2.79490	0.104377
$718$	50.8170	1.89647
$719$	−41.1886	−1.53608	−0.768038	−	0.640404i	$-0.778767\pi$
$719$	−41.1886	−1.53608	−0.768038	+	0.640404i	$0.778767\pi$
$720$	4.03468	0.150364
$721$	13.4072	0.499309
$722$	22.1638	0.824850
$723$	4.99181	0.185647
$724$	−46.9784	−1.74594
$725$	8.02087	0.297888
$726$	48.1581	1.78731
$727$	−0.363441	−0.0134793	−0.00673965	−	0.999977i	$-0.502145\pi$
$727$	−0.363441	−0.0134793	−0.00673965	+	0.999977i	$0.502145\pi$
$728$	−67.6112	−2.50584
$729$	29.4840	1.09200
$730$	40.0017	1.48053
$731$	−2.79705	−0.103452
$732$	12.5650	0.464415
$733$	−4.94681	−0.182715	−0.0913574	−	0.995818i	$-0.529121\pi$
$733$	−4.94681	−0.182715	−0.0913574	+	0.995818i	$0.529121\pi$
$734$	−80.1611	−2.95880
$735$	7.29565	0.269104
$736$	−0.652899	−0.0240662
$737$	6.20519	0.228571
$738$	−21.2110	−0.780787
$739$	12.2061	0.449008	0.224504	−	0.974473i	$-0.427924\pi$
$739$	12.2061	0.449008	0.224504	+	0.974473i	$0.427924\pi$
$740$	45.5490	1.67441
$741$	17.4439	0.640817
$742$	−96.0396	−3.52573
$743$	30.7122	1.12672	0.563360	−	0.826211i	$-0.309508\pi$
$743$	30.7122	1.12672	0.563360	+	0.826211i	$0.309508\pi$
$744$	34.2074	1.25410
$745$	2.58174	0.0945878
$746$	81.0226	2.96645
$747$	−5.40347	−0.197703
$748$	6.69671	0.244856
$749$	29.2845	1.07003
$750$	−3.56623	−0.130220
$751$	−15.7568	−0.574973	−0.287487	−	0.957785i	$-0.592820\pi$
$751$	−15.7568	−0.574973	−0.287487	+	0.957785i	$0.592820\pi$
$752$	48.6876	1.77546
$753$	−31.4841	−1.14735
$754$	−75.3357	−2.74356
$755$	−11.0738	−0.403016
$756$	79.9162	2.90652
$757$	−5.41980	−0.196986	−0.0984930	−	0.995138i	$-0.531402\pi$
$757$	−5.41980	−0.196986	−0.0984930	+	0.995138i	$0.531402\pi$
$758$	−41.7982	−1.51818
$759$	−6.26077	−0.227251
$760$	−16.1733	−0.586666
$761$	−24.8491	−0.900780	−0.450390	−	0.892832i	$-0.648715\pi$
$761$	−24.8491	−0.900780	−0.450390	+	0.892832i	$0.648715\pi$
$762$	72.3762	2.62191
$763$	25.8096	0.934372
$764$	95.5645	3.45740
$765$	0.300920	0.0108798
$766$	−5.82099	−0.210321
$767$	51.7122	1.86722
$768$	46.9658	1.69473
$769$	11.4715	0.413671	0.206836	−	0.978376i	$-0.433683\pi$
$769$	11.4715	0.413671	0.206836	+	0.978376i	$0.433683\pi$
$770$	42.3369	1.52572
$771$	−4.98398	−0.179494
$772$	−18.1310	−0.652550
$773$	−7.28612	−0.262063	−0.131032	−	0.991378i	$-0.541829\pi$
$773$	−7.28612	−0.262063	−0.131032	+	0.991378i	$0.541829\pi$
$774$	−18.8165	−0.676344
$775$	4.62404	0.166101
$776$	1.07545	0.0386065
$777$	56.1338	2.01379
$778$	30.1712	1.08169
$779$	30.0398	1.07629
$780$	22.4671	0.804453
$781$	−10.7585	−0.384971
$782$	−0.715294	−0.0255789
$783$	45.3361	1.62018
$784$	22.4463	0.801655
$785$	−3.93592	−0.140479
$786$	38.4326	1.37085
$787$	0.950418	0.0338787	0.0169394	−	0.999857i	$-0.494608\pi$
$787$	0.950418	0.0338787	0.0169394	+	0.999857i	$0.494608\pi$
$788$	−39.3870	−1.40310
$789$	−18.5637	−0.660887
$790$	−8.74321	−0.311070
$791$	−27.1080	−0.963849
$792$	22.9365	0.815014
$793$	−8.12213	−0.288425
$794$	45.7255	1.62274
$795$	16.2483	0.576267
$796$	−64.7477	−2.29492
$797$	38.1710	1.35209	0.676043	−	0.736862i	$-0.263693\pi$
$797$	38.1710	1.35209	0.676043	+	0.736862i	$0.263693\pi$
$798$	−39.1486	−1.38585
$799$	3.63129	0.128466
$800$	−0.746955	−0.0264088
$801$	16.8470	0.595259
$802$	26.3617	0.930863
$803$	80.3425	2.83523
$804$	−7.39021	−0.260633
$805$	−3.03321	−0.106906
$806$	−43.4311	−1.52980
$807$	−31.8850	−1.12240
$808$	−8.86444	−0.311850
$809$	42.2658	1.48599	0.742993	−	0.669299i	$-0.233406\pi$
$809$	42.2658	1.48599	0.742993	+	0.669299i	$0.233406\pi$
$810$	−13.4562	−0.472804
$811$	−3.13731	−0.110166	−0.0550828	−	0.998482i	$-0.517542\pi$
$811$	−3.13731	−0.110166	−0.0550828	+	0.998482i	$0.517542\pi$
$812$	113.405	3.97975
$813$	42.4840	1.48998
$814$	136.391	4.78050
$815$	8.79422	0.308048
$816$	−2.13884	−0.0748745
$817$	26.6486	0.932318
$818$	24.7274	0.864574
$819$	−11.9853	−0.418799
$820$	38.6903	1.35112
$821$	50.6150	1.76648	0.883238	−	0.468924i	$-0.155358\pi$
$821$	50.6150	1.76648	0.883238	+	0.468924i	$0.155358\pi$
$822$	77.3732	2.69870
$823$	−11.8305	−0.412386	−0.206193	−	0.978511i	$-0.566108\pi$
$823$	−11.8305	−0.412386	−0.206193	+	0.978511i	$0.566108\pi$
$824$	−19.7528	−0.688120
$825$	−7.16268	−0.249373
$826$	−116.056	−4.03809
$827$	22.7513	0.791140	0.395570	−	0.918436i	$-0.370547\pi$
$827$	22.7513	0.791140	0.395570	+	0.918436i	$0.370547\pi$
$828$	−3.22763	−0.112168
$829$	−6.88668	−0.239184	−0.119592	−	0.992823i	$-0.538159\pi$
$829$	−6.88668	−0.239184	−0.119592	+	0.992823i	$0.538159\pi$
$830$	14.6945	0.510053
$831$	9.92362	0.344247
$832$	−26.9153	−0.933121
$833$	1.67413	0.0580050
$834$	−20.0975	−0.695919
$835$	−3.61533	−0.125114
$836$	−63.8025	−2.20665
$837$	26.1363	0.903404
$838$	72.0251	2.48806
$839$	35.4080	1.22242	0.611209	−	0.791469i	$-0.290683\pi$
$839$	35.4080	1.22242	0.611209	+	0.791469i	$0.290683\pi$
$840$	−25.6713	−0.885744
$841$	35.3343	1.21843
$842$	−46.4017	−1.59911
$843$	−38.3718	−1.32160
$844$	−29.1426	−1.00313
$845$	−1.52299	−0.0523924
$846$	24.4287	0.839875
$847$	46.8609	1.61016
$848$	49.9907	1.71669
$849$	−25.8364	−0.886703
$850$	−0.818338	−0.0280688
$851$	−9.77166	−0.334968
$852$	12.8131	0.438971
$853$	42.2979	1.44825	0.724127	−	0.689667i	$-0.242243\pi$
$853$	42.2979	1.44825	0.724127	+	0.689667i	$0.242243\pi$
$854$	18.2282	0.623755
$855$	−2.86700	−0.0980492
$856$	−43.1447	−1.47466
$857$	−0.775099	−0.0264769	−0.0132384	−	0.999912i	$-0.504214\pi$
$857$	−0.775099	−0.0264769	−0.0132384	+	0.999912i	$0.504214\pi$
$858$	67.2752	2.29674
$859$	52.9436	1.80641	0.903206	−	0.429207i	$-0.141207\pi$
$859$	52.9436	1.80641	0.903206	+	0.429207i	$0.141207\pi$
$860$	34.3226	1.17039
$861$	47.6813	1.62497
$862$	53.5989	1.82559
$863$	−50.3040	−1.71237	−0.856185	−	0.516670i	$-0.827171\pi$
$863$	−50.3040	−1.71237	−0.856185	+	0.516670i	$0.827171\pi$
$864$	−4.22199	−0.143635
$865$	0.379647	0.0129084
$866$	21.1606	0.719066
$867$	24.4389	0.829987
$868$	65.3784	2.21909
$869$	−17.5605	−0.595701
$870$	−28.6042	−0.969774
$871$	4.77711	0.161866
$872$	−38.0253	−1.28770
$873$	0.190643	0.00645228
$874$	6.81492	0.230518
$875$	−3.47016	−0.117313
$876$	−95.6857	−3.23292
$877$	−12.1488	−0.410235	−0.205118	−	0.978737i	$-0.565758\pi$
$877$	−12.1488	−0.410235	−0.205118	+	0.978737i	$0.565758\pi$
$878$	−70.9887	−2.39575
$879$	15.4146	0.519923
$880$	−22.0372	−0.742875
$881$	51.0088	1.71853	0.859264	−	0.511532i	$-0.170922\pi$
$881$	51.0088	1.71853	0.859264	+	0.511532i	$0.170922\pi$
$882$	11.2623	0.379221
$883$	2.70114	0.0909006	0.0454503	−	0.998967i	$-0.485528\pi$
$883$	2.70114	0.0909006	0.0454503	+	0.998967i	$0.485528\pi$
$884$	5.15551	0.173399
$885$	19.6346	0.660010
$886$	−13.5395	−0.454867
$887$	−5.60311	−0.188134	−0.0940671	−	0.995566i	$-0.529987\pi$
$887$	−5.60311	−0.188134	−0.0940671	+	0.995566i	$0.529987\pi$
$888$	−82.7018	−2.77529
$889$	70.4266	2.36203
$890$	−45.8146	−1.53571
$891$	−27.0265	−0.905423
$892$	15.3103	0.512627
$893$	−34.5969	−1.15774
$894$	−9.20708	−0.307931
$895$	19.2296	0.642775
$896$	65.5891	2.19118
$897$	−4.81990	−0.160932
$898$	8.69398	0.290122
$899$	37.0889	1.23698
$900$	−3.69259	−0.123086
$901$	3.72848	0.124214
$902$	115.854	3.85750
$903$	42.2985	1.40761
$904$	39.9381	1.32832
$905$	11.5302	0.383276
$906$	39.4916	1.31202
$907$	35.1753	1.16798	0.583988	−	0.811762i	$-0.301491\pi$
$907$	35.1753	1.16798	0.583988	+	0.811762i	$0.301491\pi$
$908$	−27.6884	−0.918871
$909$	−1.57138	−0.0521193
$910$	32.5934	1.08046
$911$	20.7534	0.687592	0.343796	−	0.939044i	$-0.388287\pi$
$911$	20.7534	0.687592	0.343796	+	0.939044i	$0.388287\pi$
$912$	20.3777	0.674772
$913$	29.5135	0.976756
$914$	−57.4101	−1.89896
$915$	−3.08390	−0.101950
$916$	−64.4333	−2.12894
$917$	37.3974	1.23497
$918$	−4.62547	−0.152663
$919$	−21.4710	−0.708264	−0.354132	−	0.935195i	$-0.615224\pi$
$919$	−21.4710	−0.708264	−0.354132	+	0.935195i	$0.615224\pi$
$920$	4.46881	0.147332
$921$	7.73492	0.254874
$922$	−8.08709	−0.266334
$923$	−8.28254	−0.272623
$924$	−101.272	−3.33159
$925$	−11.1794	−0.367575
$926$	−74.5098	−2.44855
$927$	−3.50152	−0.115005
$928$	−5.99123	−0.196672
$929$	13.2786	0.435656	0.217828	−	0.975987i	$-0.430103\pi$
$929$	13.2786	0.435656	0.217828	+	0.975987i	$0.430103\pi$
$930$	−16.4904	−0.540741
$931$	−15.9501	−0.522744
$932$	2.89553	0.0948462
$933$	14.3371	0.469377
$934$	−64.9038	−2.12372
$935$	−1.64361	−0.0537519
$936$	17.6579	0.577165
$937$	20.5594	0.671646	0.335823	−	0.941925i	$-0.390986\pi$
$937$	20.5594	0.671646	0.335823	+	0.941925i	$0.390986\pi$
$938$	−10.7211	−0.350055
$939$	24.6255	0.803622
$940$	−44.5596	−1.45337
$941$	34.6131	1.12836	0.564178	−	0.825653i	$-0.309193\pi$
$941$	34.6131	1.12836	0.564178	+	0.825653i	$0.309193\pi$
$942$	14.0364	0.457330
$943$	−8.30027	−0.270294
$944$	60.4093	1.96616
$945$	−19.6143	−0.638053
$946$	102.775	3.34150
$947$	−26.0938	−0.847935	−0.423968	−	0.905677i	$-0.639363\pi$
$947$	−26.0938	−0.847935	−0.423968	+	0.905677i	$0.639363\pi$
$948$	20.9141	0.679259
$949$	61.8522	2.00781
$950$	7.79666	0.252957
$951$	3.24858	0.105343
$952$	−5.89077	−0.190921
$953$	−19.9508	−0.646271	−0.323135	−	0.946353i	$-0.604737\pi$
$953$	−19.9508	−0.646271	−0.323135	+	0.946353i	$0.604737\pi$
$954$	25.0825	0.812075
$955$	−23.4550	−0.758985
$956$	−7.86991	−0.254531
$957$	−57.4509	−1.85713
$958$	−4.78093	−0.154465
$959$	75.2890	2.43121
$960$	−10.2195	−0.329833
$961$	−9.61821	−0.310265
$962$	105.002	3.38539
$963$	−7.64816	−0.246458
$964$	−14.0560	−0.452713
$965$	4.45000	0.143251
$966$	10.8171	0.348034
$967$	0.483593	0.0155513	0.00777564	−	0.999970i	$-0.497525\pi$
$967$	0.483593	0.0155513	0.00777564	+	0.999970i	$0.497525\pi$
$968$	−69.0400	−2.21903
$969$	1.51984	0.0488242
$970$	−0.518444	−0.0166462
$971$	43.8782	1.40812	0.704060	−	0.710141i	$-0.251369\pi$
$971$	43.8782	1.40812	0.704060	+	0.710141i	$0.251369\pi$
$972$	−36.9007	−1.18359
$973$	−19.5561	−0.626940
$974$	−24.7908	−0.794350
$975$	−5.51424	−0.176597
$976$	−9.48815	−0.303708
$977$	3.69462	0.118201	0.0591007	−	0.998252i	$-0.481177\pi$
$977$	3.69462	0.118201	0.0591007	+	0.998252i	$0.481177\pi$
$978$	−31.3622	−1.00285
$979$	−92.0176	−2.94089
$980$	−20.5432	−0.656228
$981$	−6.74065	−0.215212
$982$	87.7256	2.79944
$983$	17.7834	0.567203	0.283602	−	0.958942i	$-0.408471\pi$
$983$	17.7834	0.567203	0.283602	+	0.958942i	$0.408471\pi$
$984$	−70.2487	−2.23945
$985$	9.66698	0.308016
$986$	−6.56379	−0.209034
$987$	−54.9145	−1.74795
$988$	−49.1188	−1.56268
$989$	−7.36325	−0.234138
$990$	−11.0570	−0.351416
$991$	45.1558	1.43442	0.717211	−	0.696856i	$-0.245418\pi$
$991$	45.1558	1.43442	0.717211	+	0.696856i	$0.245418\pi$
$992$	−3.45395	−0.109663
$993$	−38.9974	−1.23755
$994$	18.5882	0.589581
$995$	15.8914	0.503792
$996$	−35.1498	−1.11376
$997$	14.6024	0.462462	0.231231	−	0.972899i	$-0.425725\pi$
$997$	14.6024	0.462462	0.231231	+	0.972899i	$0.425725\pi$
$998$	−50.4858	−1.59810
$999$	−63.1887	−1.99920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.6	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.6	✓	127	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)

\(f(q)\)	\(=\)	\(q-2.46463 q^{2} -1.44696 q^{3} +4.07438 q^{4} -1.00000 q^{5} +3.56623 q^{6} +3.47016 q^{7} -5.11258 q^{8} -0.906295 q^{9} +O(q^{10})\)	\(q-2.46463 q^{2} -1.44696 q^{3} +4.07438 q^{4} -1.00000 q^{5} +3.56623 q^{6} +3.47016 q^{7} -5.11258 q^{8} -0.906295 q^{9} +2.46463 q^{10} +4.95014 q^{11} -5.89549 q^{12} +3.81090 q^{13} -8.55266 q^{14} +1.44696 q^{15} +4.45184 q^{16} +0.332033 q^{17} +2.23368 q^{18} -3.16342 q^{19} -4.07438 q^{20} -5.02120 q^{21} -12.2003 q^{22} +0.874081 q^{23} +7.39772 q^{24} +1.00000 q^{25} -9.39246 q^{26} +5.65227 q^{27} +14.1388 q^{28} +8.02087 q^{29} -3.56623 q^{30} +4.62404 q^{31} -0.746955 q^{32} -7.16268 q^{33} -0.818338 q^{34} -3.47016 q^{35} -3.69259 q^{36} -11.1794 q^{37} +7.79666 q^{38} -5.51424 q^{39} +5.11258 q^{40} -9.49599 q^{41} +12.3754 q^{42} -8.42399 q^{43} +20.1688 q^{44} +0.906295 q^{45} -2.15428 q^{46} +10.9365 q^{47} -6.44165 q^{48} +5.04204 q^{49} -2.46463 q^{50} -0.480440 q^{51} +15.5271 q^{52} +11.2292 q^{53} -13.9307 q^{54} -4.95014 q^{55} -17.7415 q^{56} +4.57736 q^{57} -19.7684 q^{58} +13.5695 q^{59} +5.89549 q^{60} -2.13129 q^{61} -11.3965 q^{62} -3.14499 q^{63} -7.06271 q^{64} -3.81090 q^{65} +17.6533 q^{66} +1.25354 q^{67} +1.35283 q^{68} -1.26476 q^{69} +8.55266 q^{70} -2.17338 q^{71} +4.63351 q^{72} +16.2303 q^{73} +27.5529 q^{74} -1.44696 q^{75} -12.8890 q^{76} +17.1778 q^{77} +13.5905 q^{78} -3.54748 q^{79} -4.45184 q^{80} -5.45974 q^{81} +23.4041 q^{82} +5.96216 q^{83} -20.4583 q^{84} -0.332033 q^{85} +20.7620 q^{86} -11.6059 q^{87} -25.3080 q^{88} -18.5889 q^{89} -2.23368 q^{90} +13.2245 q^{91} +3.56134 q^{92} -6.69083 q^{93} -26.9544 q^{94} +3.16342 q^{95} +1.08082 q^{96} -0.210354 q^{97} -12.4267 q^{98} -4.48629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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