LMFDB - Embedded newform 8013.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44992 q^{2} -1.00000 q^{3} +4.00213 q^{4} +3.65851 q^{5} +2.44992 q^{6} -1.10640 q^{7} -4.90506 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.44992 q^{2} -1.00000 q^{3} +4.00213 q^{4} +3.65851 q^{5} +2.44992 q^{6} -1.10640 q^{7} -4.90506 q^{8} +1.00000 q^{9} -8.96306 q^{10} +2.74944 q^{11} -4.00213 q^{12} +6.23365 q^{13} +2.71060 q^{14} -3.65851 q^{15} +4.01277 q^{16} -1.62787 q^{17} -2.44992 q^{18} -3.15888 q^{19} +14.6418 q^{20} +1.10640 q^{21} -6.73592 q^{22} +0.431387 q^{23} +4.90506 q^{24} +8.38467 q^{25} -15.2720 q^{26} -1.00000 q^{27} -4.42796 q^{28} -3.61274 q^{29} +8.96306 q^{30} +8.01021 q^{31} -0.0208592 q^{32} -2.74944 q^{33} +3.98815 q^{34} -4.04778 q^{35} +4.00213 q^{36} -10.9354 q^{37} +7.73901 q^{38} -6.23365 q^{39} -17.9452 q^{40} -0.102289 q^{41} -2.71060 q^{42} -2.00930 q^{43} +11.0036 q^{44} +3.65851 q^{45} -1.05686 q^{46} +13.2452 q^{47} -4.01277 q^{48} -5.77588 q^{49} -20.5418 q^{50} +1.62787 q^{51} +24.9479 q^{52} -2.15024 q^{53} +2.44992 q^{54} +10.0588 q^{55} +5.42696 q^{56} +3.15888 q^{57} +8.85093 q^{58} -10.8326 q^{59} -14.6418 q^{60} +10.2920 q^{61} -19.6244 q^{62} -1.10640 q^{63} -7.97443 q^{64} +22.8058 q^{65} +6.73592 q^{66} +10.4438 q^{67} -6.51493 q^{68} -0.431387 q^{69} +9.91674 q^{70} -6.41907 q^{71} -4.90506 q^{72} -1.93529 q^{73} +26.7910 q^{74} -8.38467 q^{75} -12.6422 q^{76} -3.04198 q^{77} +15.2720 q^{78} +2.00174 q^{79} +14.6807 q^{80} +1.00000 q^{81} +0.250599 q^{82} +7.75737 q^{83} +4.42796 q^{84} -5.95556 q^{85} +4.92262 q^{86} +3.61274 q^{87} -13.4862 q^{88} +3.10254 q^{89} -8.96306 q^{90} -6.89692 q^{91} +1.72646 q^{92} -8.01021 q^{93} -32.4498 q^{94} -11.5568 q^{95} +0.0208592 q^{96} +0.193953 q^{97} +14.1505 q^{98} +2.74944 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) $ 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * 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 $

$2$	−2.44992	−1.73236	−0.866179	−	0.499734i	$-0.833431\pi$
$2$	−2.44992	−1.73236	−0.866179	+	0.499734i	$0.833431\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.00213	2.00106
$5$	3.65851	1.63613	0.818067	−	0.575123i	$-0.195046\pi$
$5$	3.65851	1.63613	0.818067	+	0.575123i	$0.195046\pi$
$6$	2.44992	1.00018
$7$	−1.10640	−0.418180	−0.209090	−	0.977896i	$-0.567050\pi$
$7$	−1.10640	−0.418180	−0.209090	+	0.977896i	$0.567050\pi$
$8$	−4.90506	−1.73420
$9$	1.00000	0.333333
$10$	−8.96306	−2.83437
$11$	2.74944	0.828988	0.414494	−	0.910052i	$-0.363959\pi$
$11$	2.74944	0.828988	0.414494	+	0.910052i	$0.363959\pi$
$12$	−4.00213	−1.15531
$13$	6.23365	1.72890	0.864452	−	0.502716i	$-0.167666\pi$
$13$	6.23365	1.72890	0.864452	+	0.502716i	$0.167666\pi$
$14$	2.71060	0.724438
$15$	−3.65851	−0.944622
$16$	4.01277	1.00319
$17$	−1.62787	−0.394816	−0.197408	−	0.980321i	$-0.563252\pi$
$17$	−1.62787	−0.394816	−0.197408	+	0.980321i	$0.563252\pi$
$18$	−2.44992	−0.577453
$19$	−3.15888	−0.724696	−0.362348	−	0.932043i	$-0.618025\pi$
$19$	−3.15888	−0.724696	−0.362348	+	0.932043i	$0.618025\pi$
$20$	14.6418	3.27401
$21$	1.10640	0.241437
$22$	−6.73592	−1.43610
$23$	0.431387	0.0899503	0.0449752	−	0.998988i	$-0.485679\pi$
$23$	0.431387	0.0899503	0.0449752	+	0.998988i	$0.485679\pi$
$24$	4.90506	1.00124
$25$	8.38467	1.67693
$26$	−15.2720	−2.99508
$27$	−1.00000	−0.192450
$28$	−4.42796	−0.836805
$29$	−3.61274	−0.670868	−0.335434	−	0.942064i	$-0.608883\pi$
$29$	−3.61274	−0.670868	−0.335434	+	0.942064i	$0.608883\pi$
$30$	8.96306	1.63642
$31$	8.01021	1.43868	0.719338	−	0.694660i	$-0.244445\pi$
$31$	8.01021	1.43868	0.719338	+	0.694660i	$0.244445\pi$
$32$	−0.0208592	−0.00368743
$33$	−2.74944	−0.478616
$34$	3.98815	0.683962
$35$	−4.04778	−0.684199
$36$	4.00213	0.667021
$37$	−10.9354	−1.79778	−0.898888	−	0.438179i	$-0.855624\pi$
$37$	−10.9354	−1.79778	−0.898888	+	0.438179i	$0.855624\pi$
$38$	7.73901	1.25543
$39$	−6.23365	−0.998183
$40$	−17.9452	−2.83738
$41$	−0.102289	−0.0159748	−0.00798739	−	0.999968i	$-0.502542\pi$
$41$	−0.102289	−0.0159748	−0.00798739	+	0.999968i	$0.502542\pi$
$42$	−2.71060	−0.418254
$43$	−2.00930	−0.306415	−0.153207	−	0.988194i	$-0.548960\pi$
$43$	−2.00930	−0.306415	−0.153207	+	0.988194i	$0.548960\pi$
$44$	11.0036	1.65886
$45$	3.65851	0.545378
$46$	−1.05686	−0.155826
$47$	13.2452	1.93202	0.966008	−	0.258513i	$-0.0832326\pi$
$47$	13.2452	1.93202	0.966008	+	0.258513i	$0.0832326\pi$
$48$	−4.01277	−0.579193
$49$	−5.77588	−0.825125
$50$	−20.5418	−2.90505
$51$	1.62787	0.227947
$52$	24.9479	3.45965
$53$	−2.15024	−0.295358	−0.147679	−	0.989035i	$-0.547180\pi$
$53$	−2.15024	−0.295358	−0.147679	+	0.989035i	$0.547180\pi$
$54$	2.44992	0.333392
$55$	10.0588	1.35633
$56$	5.42696	0.725209
$57$	3.15888	0.418403
$58$	8.85093	1.16218
$59$	−10.8326	−1.41029	−0.705144	−	0.709064i	$-0.749118\pi$
$59$	−10.8326	−1.41029	−0.705144	+	0.709064i	$0.749118\pi$
$60$	−14.6418	−1.89025
$61$	10.2920	1.31776	0.658881	−	0.752247i	$-0.271030\pi$
$61$	10.2920	1.31776	0.658881	+	0.752247i	$0.271030\pi$
$62$	−19.6244	−2.49230
$63$	−1.10640	−0.139393
$64$	−7.97443	−0.996804
$65$	22.8058	2.82872
$66$	6.73592	0.829135
$67$	10.4438	1.27591	0.637956	−	0.770072i	$-0.279780\pi$
$67$	10.4438	1.27591	0.637956	+	0.770072i	$0.279780\pi$
$68$	−6.51493	−0.790052
$69$	−0.431387	−0.0519328
$70$	9.91674	1.18528
$71$	−6.41907	−0.761803	−0.380902	−	0.924616i	$-0.624386\pi$
$71$	−6.41907	−0.761803	−0.380902	+	0.924616i	$0.624386\pi$
$72$	−4.90506	−0.578067
$73$	−1.93529	−0.226508	−0.113254	−	0.993566i	$-0.536127\pi$
$73$	−1.93529	−0.226508	−0.113254	+	0.993566i	$0.536127\pi$
$74$	26.7910	3.11439
$75$	−8.38467	−0.968178
$76$	−12.6422	−1.45016
$77$	−3.04198	−0.346666
$78$	15.2720	1.72921
$79$	2.00174	0.225213	0.112606	−	0.993640i	$-0.464080\pi$
$79$	2.00174	0.225213	0.112606	+	0.993640i	$0.464080\pi$
$80$	14.6807	1.64136
$81$	1.00000	0.111111
$82$	0.250599	0.0276740
$83$	7.75737	0.851482	0.425741	−	0.904845i	$-0.360013\pi$
$83$	7.75737	0.851482	0.425741	+	0.904845i	$0.360013\pi$
$84$	4.42796	0.483130
$85$	−5.95556	−0.645971
$86$	4.92262	0.530820
$87$	3.61274	0.387326
$88$	−13.4862	−1.43763
$89$	3.10254	0.328869	0.164434	−	0.986388i	$-0.447420\pi$
$89$	3.10254	0.328869	0.164434	+	0.986388i	$0.447420\pi$
$90$	−8.96306	−0.944790
$91$	−6.89692	−0.722994
$92$	1.72646	0.179996
$93$	−8.01021	−0.830620
$94$	−32.4498	−3.34694
$95$	−11.5568	−1.18570
$96$	0.0208592	0.00212894
$97$	0.193953	0.0196930	0.00984648	−	0.999952i	$-0.496866\pi$
$97$	0.193953	0.0196930	0.00984648	+	0.999952i	$0.496866\pi$
$98$	14.1505	1.42941
$99$	2.74944	0.276329
$100$	33.5565	3.35565
$101$	−17.2616	−1.71760	−0.858798	−	0.512314i	$-0.828788\pi$
$101$	−17.2616	−1.71760	−0.858798	+	0.512314i	$0.828788\pi$
$102$	−3.98815	−0.394886
$103$	3.96944	0.391121	0.195560	−	0.980692i	$-0.437347\pi$
$103$	3.96944	0.391121	0.195560	+	0.980692i	$0.437347\pi$
$104$	−30.5764	−2.99827
$105$	4.04778	0.395022
$106$	5.26791	0.511665
$107$	8.49726	0.821461	0.410731	−	0.911757i	$-0.365274\pi$
$107$	8.49726	0.821461	0.410731	+	0.911757i	$0.365274\pi$
$108$	−4.00213	−0.385105
$109$	−5.14155	−0.492471	−0.246236	−	0.969210i	$-0.579194\pi$
$109$	−5.14155	−0.492471	−0.246236	+	0.969210i	$0.579194\pi$
$110$	−24.6434	−2.34966
$111$	10.9354	1.03795
$112$	−4.43973	−0.419515
$113$	5.33165	0.501559	0.250780	−	0.968044i	$-0.419313\pi$
$113$	5.33165	0.501559	0.250780	+	0.968044i	$0.419313\pi$
$114$	−7.73901	−0.724825
$115$	1.57823	0.147171
$116$	−14.4586	−1.34245
$117$	6.23365	0.576301
$118$	26.5391	2.44312
$119$	1.80107	0.165104
$120$	17.9452	1.63816
$121$	−3.44058	−0.312780
$122$	−25.2147	−2.28283
$123$	0.102289	0.00922305
$124$	32.0579	2.87888
$125$	12.3828	1.10755
$126$	2.71060	0.241479
$127$	−18.4699	−1.63894	−0.819469	−	0.573124i	$-0.805731\pi$
$127$	−18.4699	−1.63894	−0.819469	+	0.573124i	$0.805731\pi$
$128$	19.5785	1.73051
$129$	2.00930	0.176909
$130$	−55.8726	−4.90035
$131$	19.4134	1.69616	0.848080	−	0.529868i	$-0.177759\pi$
$131$	19.4134	1.69616	0.848080	+	0.529868i	$0.177759\pi$
$132$	−11.0036	−0.957742
$133$	3.49499	0.303054
$134$	−25.5865	−2.21034
$135$	−3.65851	−0.314874
$136$	7.98479	0.684690
$137$	17.6472	1.50770	0.753851	−	0.657046i	$-0.228194\pi$
$137$	17.6472	1.50770	0.753851	+	0.657046i	$0.228194\pi$
$138$	1.05686	0.0899663
$139$	20.2938	1.72130	0.860649	−	0.509199i	$-0.170058\pi$
$139$	20.2938	1.72130	0.860649	+	0.509199i	$0.170058\pi$
$140$	−16.1997	−1.36913
$141$	−13.2452	−1.11545
$142$	15.7262	1.31972
$143$	17.1391	1.43324
$144$	4.01277	0.334397
$145$	−13.2172	−1.09763
$146$	4.74130	0.392393
$147$	5.77588	0.476386
$148$	−43.7650	−3.59746
$149$	14.4468	1.18353	0.591763	−	0.806112i	$-0.298432\pi$
$149$	14.4468	1.18353	0.591763	+	0.806112i	$0.298432\pi$
$150$	20.5418	1.67723
$151$	9.35698	0.761460	0.380730	−	0.924686i	$-0.375673\pi$
$151$	9.35698	0.761460	0.380730	+	0.924686i	$0.375673\pi$
$152$	15.4945	1.25677
$153$	−1.62787	−0.131605
$154$	7.45263	0.600550
$155$	29.3054	2.35387
$156$	−24.9479	−1.99743
$157$	−5.54785	−0.442767	−0.221383	−	0.975187i	$-0.571057\pi$
$157$	−5.54785	−0.442767	−0.221383	+	0.975187i	$0.571057\pi$
$158$	−4.90410	−0.390149
$159$	2.15024	0.170525
$160$	−0.0763137	−0.00603312
$161$	−0.477287	−0.0376155
$162$	−2.44992	−0.192484
$163$	13.2063	1.03439	0.517197	−	0.855866i	$-0.326975\pi$
$163$	13.2063	1.03439	0.517197	+	0.855866i	$0.326975\pi$
$164$	−0.409372	−0.0319666
$165$	−10.0588	−0.783080
$166$	−19.0050	−1.47507
$167$	11.1856	0.865568	0.432784	−	0.901498i	$-0.357531\pi$
$167$	11.1856	0.865568	0.432784	+	0.901498i	$0.357531\pi$
$168$	−5.42696	−0.418699
$169$	25.8584	1.98911
$170$	14.5907	1.11905
$171$	−3.15888	−0.241565
$172$	−8.04146	−0.613156
$173$	1.36205	0.103554	0.0517772	−	0.998659i	$-0.483511\pi$
$173$	1.36205	0.103554	0.0517772	+	0.998659i	$0.483511\pi$
$174$	−8.85093	−0.670987
$175$	−9.27680	−0.701260
$176$	11.0329	0.831634
$177$	10.8326	0.814230
$178$	−7.60099	−0.569718
$179$	19.9024	1.48757	0.743787	−	0.668416i	$-0.233028\pi$
$179$	19.9024	1.48757	0.743787	+	0.668416i	$0.233028\pi$
$180$	14.6418	1.09134
$181$	−16.7493	−1.24496	−0.622482	−	0.782634i	$-0.713876\pi$
$181$	−16.7493	−1.24496	−0.622482	+	0.782634i	$0.713876\pi$
$182$	16.8969	1.25248
$183$	−10.2920	−0.760810
$184$	−2.11598	−0.155992
$185$	−40.0074	−2.94140
$186$	19.6244	1.43893
$187$	−4.47572	−0.327297
$188$	53.0091	3.86609
$189$	1.10640	0.0804788
$190$	28.3132	2.05406
$191$	21.6668	1.56776	0.783879	−	0.620914i	$-0.213238\pi$
$191$	21.6668	1.56776	0.783879	+	0.620914i	$0.213238\pi$
$192$	7.97443	0.575505
$193$	2.15564	0.155166	0.0775832	−	0.996986i	$-0.475280\pi$
$193$	2.15564	0.155166	0.0775832	+	0.996986i	$0.475280\pi$
$194$	−0.475171	−0.0341153
$195$	−22.8058	−1.63316
$196$	−23.1158	−1.65113
$197$	10.6360	0.757787	0.378893	−	0.925440i	$-0.376305\pi$
$197$	10.6360	0.757787	0.378893	+	0.925440i	$0.376305\pi$
$198$	−6.73592	−0.478701
$199$	7.68603	0.544849	0.272424	−	0.962177i	$-0.412175\pi$
$199$	7.68603	0.544849	0.272424	+	0.962177i	$0.412175\pi$
$200$	−41.1273	−2.90814
$201$	−10.4438	−0.736649
$202$	42.2897	2.97549
$203$	3.99713	0.280544
$204$	6.51493	0.456137
$205$	−0.374223	−0.0261369
$206$	−9.72483	−0.677561
$207$	0.431387	0.0299834
$208$	25.0142	1.73442
$209$	−8.68515	−0.600764
$210$	−9.91674	−0.684320
$211$	20.3986	1.40430	0.702150	−	0.712029i	$-0.252224\pi$
$211$	20.3986	1.40430	0.702150	+	0.712029i	$0.252224\pi$
$212$	−8.60552	−0.591029
$213$	6.41907	0.439827
$214$	−20.8176	−1.42307
$215$	−7.35102	−0.501336
$216$	4.90506	0.333747
$217$	−8.86250	−0.601626
$218$	12.5964	0.853136
$219$	1.93529	0.130775
$220$	40.2568	2.71411
$221$	−10.1476	−0.682599
$222$	−26.7910	−1.79809
$223$	−14.2661	−0.955328	−0.477664	−	0.878543i	$-0.658516\pi$
$223$	−14.2661	−0.955328	−0.477664	+	0.878543i	$0.658516\pi$
$224$	0.0230787	0.00154201
$225$	8.38467	0.558978
$226$	−13.0621	−0.868880
$227$	26.4207	1.75360	0.876801	−	0.480854i	$-0.159673\pi$
$227$	26.4207	1.75360	0.876801	+	0.480854i	$0.159673\pi$
$228$	12.6422	0.837252
$229$	−27.0351	−1.78653	−0.893266	−	0.449529i	$-0.851592\pi$
$229$	−27.0351	−1.78653	−0.893266	+	0.449529i	$0.851592\pi$
$230$	−3.86654	−0.254952
$231$	3.04198	0.200148
$232$	17.7207	1.16342
$233$	12.7858	0.837626	0.418813	−	0.908073i	$-0.362446\pi$
$233$	12.7858	0.837626	0.418813	+	0.908073i	$0.362446\pi$
$234$	−15.2720	−0.998360
$235$	48.4578	3.16104
$236$	−43.3536	−2.82208
$237$	−2.00174	−0.130027
$238$	−4.41249	−0.286020
$239$	−0.770718	−0.0498536	−0.0249268	−	0.999689i	$-0.507935\pi$
$239$	−0.770718	−0.0498536	−0.0249268	+	0.999689i	$0.507935\pi$
$240$	−14.6807	−0.947638
$241$	−23.5245	−1.51535	−0.757673	−	0.652635i	$-0.773664\pi$
$241$	−23.5245	−1.51535	−0.757673	+	0.652635i	$0.773664\pi$
$242$	8.42915	0.541846
$243$	−1.00000	−0.0641500
$244$	41.1901	2.63692
$245$	−21.1311	−1.35002
$246$	−0.250599	−0.0159776
$247$	−19.6913	−1.25293
$248$	−39.2905	−2.49495
$249$	−7.75737	−0.491603
$250$	−30.3370	−1.91868
$251$	0.680166	0.0429317	0.0214658	−	0.999770i	$-0.493167\pi$
$251$	0.680166	0.0429317	0.0214658	+	0.999770i	$0.493167\pi$
$252$	−4.42796	−0.278935
$253$	1.18607	0.0745677
$254$	45.2498	2.83923
$255$	5.95556	0.372952
$256$	−32.0169	−2.00106
$257$	−15.6841	−0.978347	−0.489173	−	0.872187i	$-0.662701\pi$
$257$	−15.6841	−0.978347	−0.489173	+	0.872187i	$0.662701\pi$
$258$	−4.92262	−0.306469
$259$	12.0990	0.751794
$260$	91.2719	5.66044
$261$	−3.61274	−0.223623
$262$	−47.5615	−2.93836
$263$	−20.2715	−1.25000	−0.624999	−	0.780626i	$-0.714900\pi$
$263$	−20.2715	−1.25000	−0.624999	+	0.780626i	$0.714900\pi$
$264$	13.4862	0.830016
$265$	−7.86665	−0.483244
$266$	−8.56245	−0.524997
$267$	−3.10254	−0.189872
$268$	41.7974	2.55318
$269$	−12.8933	−0.786120	−0.393060	−	0.919513i	$-0.628583\pi$
$269$	−12.8933	−0.786120	−0.393060	+	0.919513i	$0.628583\pi$
$270$	8.96306	0.545475
$271$	−20.1010	−1.22105	−0.610525	−	0.791997i	$-0.709041\pi$
$271$	−20.1010	−1.22105	−0.610525	+	0.791997i	$0.709041\pi$
$272$	−6.53226	−0.396076
$273$	6.89692	0.417420
$274$	−43.2343	−2.61188
$275$	23.0531	1.39016
$276$	−1.72646	−0.103921
$277$	18.1312	1.08940	0.544700	−	0.838631i	$-0.316643\pi$
$277$	18.1312	1.08940	0.544700	+	0.838631i	$0.316643\pi$
$278$	−49.7183	−2.98190
$279$	8.01021	0.479559
$280$	19.8546	1.18654
$281$	17.9590	1.07135	0.535673	−	0.844426i	$-0.320058\pi$
$281$	17.9590	1.07135	0.535673	+	0.844426i	$0.320058\pi$
$282$	32.4498	1.93236
$283$	5.77310	0.343175	0.171588	−	0.985169i	$-0.445110\pi$
$283$	5.77310	0.343175	0.171588	+	0.985169i	$0.445110\pi$
$284$	−25.6899	−1.52442
$285$	11.5568	0.684564
$286$	−41.9894	−2.48288
$287$	0.113172	0.00668034
$288$	−0.0208592	−0.00122914
$289$	−14.3500	−0.844120
$290$	32.3812	1.90149
$291$	−0.193953	−0.0113697
$292$	−7.74526	−0.453257
$293$	21.0045	1.22710	0.613548	−	0.789658i	$-0.289742\pi$
$293$	21.0045	1.22710	0.613548	+	0.789658i	$0.289742\pi$
$294$	−14.1505	−0.825271
$295$	−39.6312	−2.30742
$296$	53.6390	3.11770
$297$	−2.74944	−0.159539
$298$	−35.3935	−2.05029
$299$	2.68911	0.155515
$300$	−33.5565	−1.93739
$301$	2.22309	0.128137
$302$	−22.9239	−1.31912
$303$	17.2616	0.991655
$304$	−12.6758	−0.727010
$305$	37.6535	2.15603
$306$	3.98815	0.227987
$307$	−9.28384	−0.529857	−0.264928	−	0.964268i	$-0.585348\pi$
$307$	−9.28384	−0.529857	−0.264928	+	0.964268i	$0.585348\pi$
$308$	−12.1744	−0.693701
$309$	−3.96944	−0.225814
$310$	−71.7960	−4.07774
$311$	9.25519	0.524814	0.262407	−	0.964957i	$-0.415484\pi$
$311$	9.25519	0.524814	0.262407	+	0.964957i	$0.415484\pi$
$312$	30.5764	1.73105
$313$	21.3016	1.20404	0.602018	−	0.798483i	$-0.294364\pi$
$313$	21.3016	1.20404	0.602018	+	0.798483i	$0.294364\pi$
$314$	13.5918	0.767030
$315$	−4.04778	−0.228066
$316$	8.01120	0.450665
$317$	1.06036	0.0595557	0.0297779	−	0.999557i	$-0.490520\pi$
$317$	1.06036	0.0595557	0.0297779	+	0.999557i	$0.490520\pi$
$318$	−5.26791	−0.295410
$319$	−9.93300	−0.556141
$320$	−29.1745	−1.63091
$321$	−8.49726	−0.474271
$322$	1.16932	0.0651634
$323$	5.14223	0.286121
$324$	4.00213	0.222340
$325$	52.2671	2.89926
$326$	−32.3543	−1.79194
$327$	5.14155	0.284328
$328$	0.501731	0.0277035
$329$	−14.6545	−0.807931
$330$	24.6434	1.35657
$331$	−31.0616	−1.70730	−0.853649	−	0.520848i	$-0.825616\pi$
$331$	−31.0616	−1.70730	−0.853649	+	0.520848i	$0.825616\pi$
$332$	31.0460	1.70387
$333$	−10.9354	−0.599258
$334$	−27.4039	−1.49947
$335$	38.2087	2.08756
$336$	4.43973	0.242207
$337$	35.7173	1.94564	0.972821	−	0.231557i	$-0.0743818\pi$
$337$	35.7173	1.94564	0.972821	+	0.231557i	$0.0743818\pi$
$338$	−63.3511	−3.44585
$339$	−5.33165	−0.289575
$340$	−23.8349	−1.29263
$341$	22.0236	1.19264
$342$	7.73901	0.418478
$343$	14.1352	0.763231
$344$	9.85572	0.531385
$345$	−1.57823	−0.0849691
$346$	−3.33691	−0.179393
$347$	−16.9642	−0.910686	−0.455343	−	0.890316i	$-0.650483\pi$
$347$	−16.9642	−0.910686	−0.455343	+	0.890316i	$0.650483\pi$
$348$	14.4586	0.775064
$349$	0.873991	0.0467836	0.0233918	−	0.999726i	$-0.492553\pi$
$349$	0.873991	0.0467836	0.0233918	+	0.999726i	$0.492553\pi$
$350$	22.7275	1.21483
$351$	−6.23365	−0.332728
$352$	−0.0573512	−0.00305683
$353$	−4.89558	−0.260565	−0.130283	−	0.991477i	$-0.541588\pi$
$353$	−4.89558	−0.260565	−0.130283	+	0.991477i	$0.541588\pi$
$354$	−26.5391	−1.41054
$355$	−23.4842	−1.24641
$356$	12.4168	0.658087
$357$	−1.80107	−0.0953230
$358$	−48.7593	−2.57701
$359$	−24.4988	−1.29300	−0.646498	−	0.762916i	$-0.723767\pi$
$359$	−24.4988	−1.29300	−0.646498	+	0.762916i	$0.723767\pi$
$360$	−17.9452	−0.945795
$361$	−9.02150	−0.474816
$362$	41.0345	2.15672
$363$	3.44058	0.180583
$364$	−27.6023	−1.44676
$365$	−7.08026	−0.370598
$366$	25.2147	1.31800
$367$	−14.7538	−0.770144	−0.385072	−	0.922886i	$-0.625823\pi$
$367$	−14.7538	−0.770144	−0.385072	+	0.922886i	$0.625823\pi$
$368$	1.73105	0.0902375
$369$	−0.102289	−0.00532493
$370$	98.0150	5.09556
$371$	2.37902	0.123513
$372$	−32.0579	−1.66212
$373$	17.3633	0.899040	0.449520	−	0.893270i	$-0.351595\pi$
$373$	17.3633	0.899040	0.449520	+	0.893270i	$0.351595\pi$
$374$	10.9652	0.566996
$375$	−12.3828	−0.639446
$376$	−64.9686	−3.35050
$377$	−22.5205	−1.15987
$378$	−2.71060	−0.139418
$379$	−23.3484	−1.19933	−0.599664	−	0.800252i	$-0.704699\pi$
$379$	−23.3484	−1.19933	−0.599664	+	0.800252i	$0.704699\pi$
$380$	−46.2517	−2.37266
$381$	18.4699	0.946241
$382$	−53.0821	−2.71592
$383$	4.25961	0.217656	0.108828	−	0.994061i	$-0.465290\pi$
$383$	4.25961	0.217656	0.108828	+	0.994061i	$0.465290\pi$
$384$	−19.5785	−0.999110
$385$	−11.1291	−0.567192
$386$	−5.28116	−0.268804
$387$	−2.00930	−0.102138
$388$	0.776226	0.0394069
$389$	−1.89588	−0.0961252	−0.0480626	−	0.998844i	$-0.515305\pi$
$389$	−1.89588	−0.0961252	−0.0480626	+	0.998844i	$0.515305\pi$
$390$	55.8726	2.82922
$391$	−0.702240	−0.0355138
$392$	28.3310	1.43093
$393$	−19.4134	−0.979278
$394$	−26.0575	−1.31276
$395$	7.32336	0.368478
$396$	11.0036	0.552952
$397$	−37.3284	−1.87346	−0.936728	−	0.350058i	$-0.886162\pi$
$397$	−37.3284	−1.87346	−0.936728	+	0.350058i	$0.886162\pi$
$398$	−18.8302	−0.943873
$399$	−3.49499	−0.174968
$400$	33.6457	1.68229
$401$	−20.5550	−1.02647	−0.513234	−	0.858249i	$-0.671553\pi$
$401$	−20.5550	−1.02647	−0.513234	+	0.858249i	$0.671553\pi$
$402$	25.5865	1.27614
$403$	49.9328	2.48733
$404$	−69.0832	−3.43702
$405$	3.65851	0.181793
$406$	−9.79268	−0.486002
$407$	−30.0663	−1.49033
$408$	−7.98479	−0.395306
$409$	15.5178	0.767305	0.383652	−	0.923478i	$-0.374666\pi$
$409$	15.5178	0.767305	0.383652	+	0.923478i	$0.374666\pi$
$410$	0.916818	0.0452784
$411$	−17.6472	−0.870472
$412$	15.8862	0.782657
$413$	11.9852	0.589755
$414$	−1.05686	−0.0519420
$415$	28.3804	1.39314
$416$	−0.130029	−0.00637521
$417$	−20.2938	−0.993792
$418$	21.2779	1.04074
$419$	10.6050	0.518086	0.259043	−	0.965866i	$-0.416593\pi$
$419$	10.6050	0.518086	0.259043	+	0.965866i	$0.416593\pi$
$420$	16.1997	0.790465
$421$	−38.6131	−1.88189	−0.940945	−	0.338560i	$-0.890060\pi$
$421$	−38.6131	−1.88189	−0.940945	+	0.338560i	$0.890060\pi$
$422$	−49.9751	−2.43275
$423$	13.2452	0.644005
$424$	10.5470	0.512209
$425$	−13.6491	−0.662080
$426$	−15.7262	−0.761938
$427$	−11.3871	−0.551062
$428$	34.0071	1.64380
$429$	−17.1391	−0.827481
$430$	18.0094	0.868493
$431$	−6.02429	−0.290180	−0.145090	−	0.989418i	$-0.546347\pi$
$431$	−6.02429	−0.290180	−0.145090	+	0.989418i	$0.546347\pi$
$432$	−4.01277	−0.193064
$433$	37.9024	1.82147	0.910736	−	0.412990i	$-0.135515\pi$
$433$	37.9024	1.82147	0.910736	+	0.412990i	$0.135515\pi$
$434$	21.7125	1.04223
$435$	13.2172	0.633717
$436$	−20.5771	−0.985466
$437$	−1.36270	−0.0651866
$438$	−4.74130	−0.226548
$439$	18.4621	0.881149	0.440574	−	0.897716i	$-0.354775\pi$
$439$	18.4621	0.881149	0.440574	+	0.897716i	$0.354775\pi$
$440$	−49.3392	−2.35216
$441$	−5.77588	−0.275042
$442$	24.8607	1.18250
$443$	−17.7140	−0.841616	−0.420808	−	0.907150i	$-0.638253\pi$
$443$	−17.7140	−0.841616	−0.420808	+	0.907150i	$0.638253\pi$
$444$	43.7650	2.07700
$445$	11.3507	0.538073
$446$	34.9508	1.65497
$447$	−14.4468	−0.683309
$448$	8.82292	0.416844
$449$	−31.0928	−1.46736	−0.733679	−	0.679496i	$-0.762198\pi$
$449$	−31.0928	−1.46736	−0.733679	+	0.679496i	$0.762198\pi$
$450$	−20.5418	−0.968349
$451$	−0.281236	−0.0132429
$452$	21.3379	1.00365
$453$	−9.35698	−0.439629
$454$	−64.7286	−3.03787
$455$	−25.2324	−1.18291
$456$	−15.4945	−0.725596
$457$	11.4303	0.534688	0.267344	−	0.963601i	$-0.413854\pi$
$457$	11.4303	0.534688	0.267344	+	0.963601i	$0.413854\pi$
$458$	66.2340	3.09491
$459$	1.62787	0.0759823
$460$	6.31628	0.294498
$461$	39.5286	1.84103	0.920515	−	0.390707i	$-0.127769\pi$
$461$	39.5286	1.84103	0.920515	+	0.390707i	$0.127769\pi$
$462$	−7.45263	−0.346728
$463$	−8.21785	−0.381916	−0.190958	−	0.981598i	$-0.561159\pi$
$463$	−8.21785	−0.381916	−0.190958	+	0.981598i	$0.561159\pi$
$464$	−14.4971	−0.673010
$465$	−29.3054	−1.35900
$466$	−31.3242	−1.45107
$467$	−36.8537	−1.70539	−0.852693	−	0.522412i	$-0.825032\pi$
$467$	−36.8537	−1.70539	−0.852693	+	0.522412i	$0.825032\pi$
$468$	24.9479	1.15322
$469$	−11.5550	−0.533562
$470$	−118.718	−5.47604
$471$	5.54785	0.255631
$472$	53.1347	2.44572
$473$	−5.52444	−0.254014
$474$	4.90410	0.225253
$475$	−26.4861	−1.21527
$476$	7.20813	0.330384
$477$	−2.15024	−0.0984525
$478$	1.88820	0.0863643
$479$	6.20601	0.283560	0.141780	−	0.989898i	$-0.454717\pi$
$479$	6.20601	0.283560	0.141780	+	0.989898i	$0.454717\pi$
$480$	0.0763137	0.00348323
$481$	−68.1677	−3.10818
$482$	57.6332	2.62512
$483$	0.477287	0.0217173
$484$	−13.7696	−0.625892
$485$	0.709579	0.0322203
$486$	2.44992	0.111131
$487$	20.9634	0.949944	0.474972	−	0.880001i	$-0.342458\pi$
$487$	20.9634	0.949944	0.474972	+	0.880001i	$0.342458\pi$
$488$	−50.4831	−2.28526
$489$	−13.2063	−0.597208
$490$	51.7695	2.33871
$491$	38.2720	1.72719	0.863595	−	0.504186i	$-0.168207\pi$
$491$	38.2720	1.72719	0.863595	+	0.504186i	$0.168207\pi$
$492$	0.409372	0.0184559
$493$	5.88105	0.264869
$494$	48.2423	2.17052
$495$	10.0588	0.452111
$496$	32.1431	1.44327
$497$	7.10207	0.318571
$498$	19.0050	0.851633
$499$	11.5003	0.514823	0.257412	−	0.966302i	$-0.417130\pi$
$499$	11.5003	0.514823	0.257412	+	0.966302i	$0.417130\pi$
$500$	49.5576	2.21628
$501$	−11.1856	−0.499736
$502$	−1.66635	−0.0743731
$503$	39.1761	1.74677	0.873387	−	0.487027i	$-0.161919\pi$
$503$	39.1761	1.74677	0.873387	+	0.487027i	$0.161919\pi$
$504$	5.42696	0.241736
$505$	−63.1518	−2.81022
$506$	−2.90579	−0.129178
$507$	−25.8584	−1.14841
$508$	−73.9189	−3.27962
$509$	19.8596	0.880263	0.440131	−	0.897933i	$-0.354932\pi$
$509$	19.8596	0.880263	0.440131	+	0.897933i	$0.354932\pi$
$510$	−14.5907	−0.646086
$511$	2.14120	0.0947212
$512$	39.2820	1.73604
$513$	3.15888	0.139468
$514$	38.4248	1.69485
$515$	14.5222	0.639926
$516$	8.04146	0.354006
$517$	36.4170	1.60162
$518$	−29.6416	−1.30238
$519$	−1.36205	−0.0597871
$520$	−111.864	−4.90556
$521$	5.55742	0.243475	0.121737	−	0.992562i	$-0.461153\pi$
$521$	5.55742	0.243475	0.121737	+	0.992562i	$0.461153\pi$
$522$	8.85093	0.387395
$523$	11.3376	0.495759	0.247880	−	0.968791i	$-0.420266\pi$
$523$	11.3376	0.495759	0.247880	+	0.968791i	$0.420266\pi$
$524$	77.6951	3.39412
$525$	9.27680	0.404873
$526$	49.6638	2.16544
$527$	−13.0396	−0.568012
$528$	−11.0329	−0.480144
$529$	−22.8139	−0.991909
$530$	19.2727	0.837152
$531$	−10.8326	−0.470096
$532$	13.9874	0.606430
$533$	−0.637631	−0.0276189
$534$	7.60099	0.328927
$535$	31.0873	1.34402
$536$	−51.2274	−2.21269
$537$	−19.9024	−0.858851
$538$	31.5877	1.36184
$539$	−15.8804	−0.684019
$540$	−14.6418	−0.630083
$541$	−18.3110	−0.787253	−0.393626	−	0.919271i	$-0.628780\pi$
$541$	−18.3110	−0.787253	−0.393626	+	0.919271i	$0.628780\pi$
$542$	49.2459	2.11529
$543$	16.7493	0.718781
$544$	0.0339561	0.00145585
$545$	−18.8104	−0.805749
$546$	−16.8969	−0.723122
$547$	−21.8113	−0.932586	−0.466293	−	0.884630i	$-0.654411\pi$
$547$	−21.8113	−0.932586	−0.466293	+	0.884630i	$0.654411\pi$
$548$	70.6263	3.01701
$549$	10.2920	0.439254
$550$	−56.4784	−2.40825
$551$	11.4122	0.486176
$552$	2.11598	0.0900620
$553$	−2.21472	−0.0941796
$554$	−44.4201	−1.88723
$555$	40.0074	1.69822
$556$	81.2184	3.44443
$557$	6.42087	0.272061	0.136030	−	0.990705i	$-0.456566\pi$
$557$	6.42087	0.272061	0.136030	+	0.990705i	$0.456566\pi$
$558$	−19.6244	−0.830767
$559$	−12.5253	−0.529762
$560$	−16.2428	−0.686383
$561$	4.47572	0.188965
$562$	−43.9982	−1.85595
$563$	17.8804	0.753571	0.376785	−	0.926301i	$-0.377029\pi$
$563$	17.8804	0.753571	0.376785	+	0.926301i	$0.377029\pi$
$564$	−53.0091	−2.23209
$565$	19.5059	0.820618
$566$	−14.1437	−0.594503
$567$	−1.10640	−0.0464645
$568$	31.4859	1.32112
$569$	−38.7887	−1.62611	−0.813054	−	0.582188i	$-0.802197\pi$
$569$	−38.7887	−1.62611	−0.813054	+	0.582188i	$0.802197\pi$
$570$	−28.3132	−1.18591
$571$	−26.8735	−1.12462	−0.562310	−	0.826927i	$-0.690087\pi$
$571$	−26.8735	−1.12462	−0.562310	+	0.826927i	$0.690087\pi$
$572$	68.5927	2.86800
$573$	−21.6668	−0.905145
$574$	−0.277263	−0.0115727
$575$	3.61703	0.150841
$576$	−7.97443	−0.332268
$577$	−42.8795	−1.78510	−0.892548	−	0.450952i	$-0.851085\pi$
$577$	−42.8795	−1.78510	−0.892548	+	0.450952i	$0.851085\pi$
$578$	35.1565	1.46232
$579$	−2.15564	−0.0895854
$580$	−52.8970	−2.19643
$581$	−8.58276	−0.356073
$582$	0.475171	0.0196965
$583$	−5.91194	−0.244848
$584$	9.49270	0.392811
$585$	22.8058	0.942906
$586$	−51.4594	−2.12577
$587$	14.1000	0.581967	0.290984	−	0.956728i	$-0.406017\pi$
$587$	14.1000	0.581967	0.290984	+	0.956728i	$0.406017\pi$
$588$	23.1158	0.953279
$589$	−25.3033	−1.04260
$590$	97.0935	3.99728
$591$	−10.6360	−0.437508
$592$	−43.8814	−1.80351
$593$	8.63020	0.354400	0.177200	−	0.984175i	$-0.443296\pi$
$593$	8.63020	0.354400	0.177200	+	0.984175i	$0.443296\pi$
$594$	6.73592	0.276378
$595$	6.58924	0.270133
$596$	57.8178	2.36831
$597$	−7.68603	−0.314568
$598$	−6.58812	−0.269408
$599$	−27.0236	−1.10415	−0.552077	−	0.833793i	$-0.686165\pi$
$599$	−27.0236	−1.10415	−0.552077	+	0.833793i	$0.686165\pi$
$600$	41.1273	1.67901
$601$	−36.2135	−1.47718	−0.738590	−	0.674155i	$-0.764508\pi$
$601$	−36.2135	−1.47718	−0.738590	+	0.674155i	$0.764508\pi$
$602$	−5.44640	−0.221979
$603$	10.4438	0.425304
$604$	37.4478	1.52373
$605$	−12.5874	−0.511749
$606$	−42.2897	−1.71790
$607$	−11.4516	−0.464805	−0.232402	−	0.972620i	$-0.574659\pi$
$607$	−11.4516	−0.464805	−0.232402	+	0.972620i	$0.574659\pi$
$608$	0.0658918	0.00267226
$609$	−3.99713	−0.161972
$610$	−92.2482	−3.73502
$611$	82.5661	3.34027
$612$	−6.51493	−0.263351
$613$	−18.1429	−0.732784	−0.366392	−	0.930461i	$-0.619407\pi$
$613$	−18.1429	−0.732784	−0.366392	+	0.930461i	$0.619407\pi$
$614$	22.7447	0.917901
$615$	0.374223	0.0150901
$616$	14.9211	0.601189
$617$	12.8732	0.518257	0.259128	−	0.965843i	$-0.416565\pi$
$617$	12.8732	0.518257	0.259128	+	0.965843i	$0.416565\pi$
$618$	9.72483	0.391190
$619$	15.8837	0.638420	0.319210	−	0.947684i	$-0.396583\pi$
$619$	15.8837	0.638420	0.319210	+	0.947684i	$0.396583\pi$
$620$	117.284	4.71023
$621$	−0.431387	−0.0173109
$622$	−22.6745	−0.909165
$623$	−3.43266	−0.137526
$624$	−25.0142	−1.00137
$625$	3.37929	0.135172
$626$	−52.1872	−2.08582
$627$	8.68515	0.346851
$628$	−22.2032	−0.886004
$629$	17.8014	0.709790
$630$	9.91674	0.395092
$631$	3.70818	0.147620	0.0738101	−	0.997272i	$-0.476484\pi$
$631$	3.70818	0.147620	0.0738101	+	0.997272i	$0.476484\pi$
$632$	−9.81863	−0.390564
$633$	−20.3986	−0.810773
$634$	−2.59780	−0.103172
$635$	−67.5722	−2.68152
$636$	8.60552	0.341231
$637$	−36.0048	−1.42656
$638$	24.3351	0.963436
$639$	−6.41907	−0.253934
$640$	71.6280	2.83134
$641$	40.5268	1.60071	0.800356	−	0.599525i	$-0.204644\pi$
$641$	40.5268	1.60071	0.800356	+	0.599525i	$0.204644\pi$
$642$	20.8176	0.821607
$643$	−21.8742	−0.862635	−0.431317	−	0.902200i	$-0.641951\pi$
$643$	−21.8742	−0.862635	−0.431317	+	0.902200i	$0.641951\pi$
$644$	−1.91016	−0.0752709
$645$	7.35102	0.289446
$646$	−12.5981	−0.495665
$647$	36.0200	1.41609	0.708047	−	0.706165i	$-0.249576\pi$
$647$	36.0200	1.41609	0.708047	+	0.706165i	$0.249576\pi$
$648$	−4.90506	−0.192689
$649$	−29.7837	−1.16911
$650$	−128.050	−5.02255
$651$	8.86250	0.347349
$652$	52.8531	2.06989
$653$	25.9871	1.01695	0.508476	−	0.861076i	$-0.330209\pi$
$653$	25.9871	1.01695	0.508476	+	0.861076i	$0.330209\pi$
$654$	−12.5964	−0.492558
$655$	71.0242	2.77514
$656$	−0.410460	−0.0160258
$657$	−1.93529	−0.0755027
$658$	35.9025	1.39963
$659$	−4.65653	−0.181393	−0.0906964	−	0.995879i	$-0.528909\pi$
$659$	−4.65653	−0.181393	−0.0906964	+	0.995879i	$0.528909\pi$
$660$	−40.2568	−1.56699
$661$	34.4461	1.33980	0.669899	−	0.742452i	$-0.266337\pi$
$661$	34.4461	1.33980	0.669899	+	0.742452i	$0.266337\pi$
$662$	76.0985	2.95765
$663$	10.1476	0.394098
$664$	−38.0504	−1.47664
$665$	12.7864	0.495836
$666$	26.7910	1.03813
$667$	−1.55849	−0.0603448
$668$	44.7662	1.73206
$669$	14.2661	0.551559
$670$	−93.6084	−3.61641
$671$	28.2974	1.09241
$672$	−0.0230787	−0.000890280 0
$673$	16.0817	0.619903	0.309952	−	0.950752i	$-0.399687\pi$
$673$	16.0817	0.619903	0.309952	+	0.950752i	$0.399687\pi$
$674$	−87.5046	−3.37055
$675$	−8.38467	−0.322726
$676$	103.489	3.98033
$677$	−32.4927	−1.24880	−0.624399	−	0.781106i	$-0.714656\pi$
$677$	−32.4927	−1.24880	−0.624399	+	0.781106i	$0.714656\pi$
$678$	13.0621	0.501648
$679$	−0.214590	−0.00823521
$680$	29.2124	1.12024
$681$	−26.4207	−1.01244
$682$	−53.9561	−2.06609
$683$	0.852411	0.0326166	0.0163083	−	0.999867i	$-0.494809\pi$
$683$	0.852411	0.0326166	0.0163083	+	0.999867i	$0.494809\pi$
$684$	−12.6422	−0.483388
$685$	64.5623	2.46680
$686$	−34.6303	−1.32219
$687$	27.0351	1.03145
$688$	−8.06284	−0.307393
$689$	−13.4038	−0.510645
$690$	3.86654	0.147197
$691$	−25.1353	−0.956190	−0.478095	−	0.878308i	$-0.658673\pi$
$691$	−25.1353	−0.956190	−0.478095	+	0.878308i	$0.658673\pi$
$692$	5.45108	0.207219
$693$	−3.04198	−0.115555
$694$	41.5610	1.57763
$695$	74.2450	2.81627
$696$	−17.7207	−0.671701
$697$	0.166512	0.00630710
$698$	−2.14121	−0.0810460
$699$	−12.7858	−0.483604
$700$	−37.1269	−1.40327
$701$	10.4987	0.396529	0.198265	−	0.980149i	$-0.436469\pi$
$701$	10.4987	0.396529	0.198265	+	0.980149i	$0.436469\pi$
$702$	15.2720	0.576403
$703$	34.5437	1.30284
$704$	−21.9252	−0.826338
$705$	−48.4578	−1.82502
$706$	11.9938	0.451393
$707$	19.0983	0.718265
$708$	43.3536	1.62933
$709$	−6.08810	−0.228643	−0.114322	−	0.993444i	$-0.536469\pi$
$709$	−6.08810	−0.228643	−0.114322	+	0.993444i	$0.536469\pi$
$710$	57.5345	2.15923
$711$	2.00174	0.0750709
$712$	−15.2182	−0.570324
$713$	3.45550	0.129409
$714$	4.41249	0.165133
$715$	62.7033	2.34497
$716$	79.6519	2.97673
$717$	0.770718	0.0287830
$718$	60.0201	2.23993
$719$	26.7381	0.997164	0.498582	−	0.866843i	$-0.333854\pi$
$719$	26.7381	0.997164	0.498582	+	0.866843i	$0.333854\pi$
$720$	14.6807	0.547119
$721$	−4.39179	−0.163559
$722$	22.1020	0.822551
$723$	23.5245	0.874885
$724$	−67.0328	−2.49125
$725$	−30.2916	−1.12500
$726$	−8.42915	−0.312835
$727$	47.4330	1.75919	0.879596	−	0.475722i	$-0.157813\pi$
$727$	47.4330	1.75919	0.879596	+	0.475722i	$0.157813\pi$
$728$	33.8298	1.25382
$729$	1.00000	0.0370370
$730$	17.3461	0.642008
$731$	3.27087	0.120977
$732$	−41.1901	−1.52243
$733$	25.9697	0.959214	0.479607	−	0.877483i	$-0.340779\pi$
$733$	25.9697	0.959214	0.479607	+	0.877483i	$0.340779\pi$
$734$	36.1458	1.33417
$735$	21.1311	0.779432
$736$	−0.00899840	−0.000331685 0
$737$	28.7146	1.05772
$738$	0.250599	0.00922468
$739$	19.9160	0.732621	0.366310	−	0.930493i	$-0.380621\pi$
$739$	19.9160	0.732621	0.366310	+	0.930493i	$0.380621\pi$
$740$	−160.115	−5.88593
$741$	19.6913	0.723379
$742$	−5.82843	−0.213968
$743$	−9.97010	−0.365767	−0.182884	−	0.983135i	$-0.558543\pi$
$743$	−9.97010	−0.365767	−0.182884	+	0.983135i	$0.558543\pi$
$744$	39.2905	1.44046
$745$	52.8536	1.93641
$746$	−42.5389	−1.55746
$747$	7.75737	0.283827
$748$	−17.9124	−0.654943
$749$	−9.40138	−0.343519
$750$	30.3370	1.10775
$751$	−23.8380	−0.869862	−0.434931	−	0.900464i	$-0.643227\pi$
$751$	−23.8380	−0.869862	−0.434931	+	0.900464i	$0.643227\pi$
$752$	53.1501	1.93818
$753$	−0.680166	−0.0247866
$754$	55.1736	2.00930
$755$	34.2326	1.24585
$756$	4.42796	0.161043
$757$	−32.4256	−1.17853	−0.589265	−	0.807940i	$-0.700583\pi$
$757$	−32.4256	−1.17853	−0.589265	+	0.807940i	$0.700583\pi$
$758$	57.2019	2.07767
$759$	−1.18607	−0.0430517
$760$	56.6867	2.05624
$761$	11.9188	0.432057	0.216029	−	0.976387i	$-0.430690\pi$
$761$	11.9188	0.432057	0.216029	+	0.976387i	$0.430690\pi$
$762$	−45.2498	−1.63923
$763$	5.68862	0.205942
$764$	86.7135	3.13718
$765$	−5.95556	−0.215324
$766$	−10.4357	−0.377058
$767$	−67.5268	−2.43825
$768$	32.0169	1.15531
$769$	34.1784	1.23251	0.616253	−	0.787548i	$-0.288650\pi$
$769$	34.1784	1.23251	0.616253	+	0.787548i	$0.288650\pi$
$770$	27.2655	0.982580
$771$	15.6841	0.564849
$772$	8.62715	0.310498
$773$	42.7287	1.53684	0.768422	−	0.639944i	$-0.221042\pi$
$773$	42.7287	1.53684	0.768422	+	0.639944i	$0.221042\pi$
$774$	4.92262	0.176940
$775$	67.1629	2.41256
$776$	−0.951352	−0.0341516
$777$	−12.0990	−0.434049
$778$	4.64477	0.166523
$779$	0.323117	0.0115769
$780$	−91.2719	−3.26806
$781$	−17.6489	−0.631526
$782$	1.72043	0.0615226
$783$	3.61274	0.129109
$784$	−23.1773	−0.827759
$785$	−20.2968	−0.724425
$786$	47.5615	1.69646
$787$	−8.20823	−0.292592	−0.146296	−	0.989241i	$-0.546735\pi$
$787$	−8.20823	−0.292592	−0.146296	+	0.989241i	$0.546735\pi$
$788$	42.5668	1.51638
$789$	20.2715	0.721686
$790$	−17.9417	−0.638336
$791$	−5.89894	−0.209742
$792$	−13.4862	−0.479210
$793$	64.1570	2.27828
$794$	91.4516	3.24550
$795$	7.86665	0.279001
$796$	30.7605	1.09028
$797$	28.7380	1.01795	0.508976	−	0.860781i	$-0.330024\pi$
$797$	28.7380	1.01795	0.508976	+	0.860781i	$0.330024\pi$
$798$	8.56245	0.303107
$799$	−21.5615	−0.762790
$800$	−0.174898	−0.00618357
$801$	3.10254	0.109623
$802$	50.3582	1.77821
$803$	−5.32095	−0.187772
$804$	−41.7974	−1.47408
$805$	−1.74616	−0.0615439
$806$	−122.332	−4.30895
$807$	12.8933	0.453866
$808$	84.6693	2.97866
$809$	12.7268	0.447449	0.223724	−	0.974652i	$-0.428178\pi$
$809$	12.7268	0.447449	0.223724	+	0.974652i	$0.428178\pi$
$810$	−8.96306	−0.314930
$811$	25.8381	0.907298	0.453649	−	0.891181i	$-0.350122\pi$
$811$	25.8381	0.907298	0.453649	+	0.891181i	$0.350122\pi$
$812$	15.9970	0.561386
$813$	20.1010	0.704973
$814$	73.6603	2.58179
$815$	48.3152	1.69241
$816$	6.53226	0.228675
$817$	6.34712	0.222058
$818$	−38.0174	−1.32925
$819$	−6.89692	−0.240998
$820$	−1.49769	−0.0523016
$821$	−11.9840	−0.418243	−0.209122	−	0.977890i	$-0.567060\pi$
$821$	−11.9840	−0.418243	−0.209122	+	0.977890i	$0.567060\pi$
$822$	43.2343	1.50797
$823$	−10.2547	−0.357455	−0.178728	−	0.983899i	$-0.557198\pi$
$823$	−10.2547	−0.357455	−0.178728	+	0.983899i	$0.557198\pi$
$824$	−19.4703	−0.678282
$825$	−23.0531	−0.802607
$826$	−29.3629	−1.02167
$827$	−5.34405	−0.185831	−0.0929154	−	0.995674i	$-0.529619\pi$
$827$	−5.34405	−0.185831	−0.0929154	+	0.995674i	$0.529619\pi$
$828$	1.72646	0.0599988
$829$	4.32660	0.150269	0.0751346	−	0.997173i	$-0.476061\pi$
$829$	4.32660	0.150269	0.0751346	+	0.997173i	$0.476061\pi$
$830$	−69.5298	−2.41341
$831$	−18.1312	−0.628966
$832$	−49.7098	−1.72338
$833$	9.40236	0.325772
$834$	49.7183	1.72160
$835$	40.9226	1.41618
$836$	−34.7591	−1.20217
$837$	−8.01021	−0.276873
$838$	−25.9813	−0.897510
$839$	−11.1102	−0.383568	−0.191784	−	0.981437i	$-0.561427\pi$
$839$	−11.1102	−0.383568	−0.191784	+	0.981437i	$0.561427\pi$
$840$	−19.8546	−0.685048
$841$	−15.9481	−0.549936
$842$	94.5993	3.26011
$843$	−17.9590	−0.618542
$844$	81.6379	2.81009
$845$	94.6031	3.25445
$846$	−32.4498	−1.11565
$847$	3.80666	0.130798
$848$	−8.62840	−0.296300
$849$	−5.77310	−0.198132
$850$	33.4393	1.14696
$851$	−4.71740	−0.161710
$852$	25.6899	0.880123
$853$	−26.4994	−0.907323	−0.453662	−	0.891174i	$-0.649883\pi$
$853$	−26.4994	−0.907323	−0.453662	+	0.891174i	$0.649883\pi$
$854$	27.8976	0.954636
$855$	−11.5568	−0.395233
$856$	−41.6796	−1.42458
$857$	−14.5652	−0.497537	−0.248768	−	0.968563i	$-0.580026\pi$
$857$	−14.5652	−0.497537	−0.248768	+	0.968563i	$0.580026\pi$
$858$	41.9894	1.43349
$859$	32.9213	1.12326	0.561630	−	0.827389i	$-0.310175\pi$
$859$	32.9213	1.12326	0.561630	+	0.827389i	$0.310175\pi$
$860$	−29.4197	−1.00320
$861$	−0.113172	−0.00385690
$862$	14.7590	0.502695
$863$	−25.4340	−0.865784	−0.432892	−	0.901446i	$-0.642507\pi$
$863$	−25.4340	−0.865784	−0.432892	+	0.901446i	$0.642507\pi$
$864$	0.0208592	0.000709646 0
$865$	4.98305	0.169429
$866$	−92.8579	−3.15544
$867$	14.3500	0.487353
$868$	−35.4689	−1.20389
$869$	5.50365	0.186699
$870$	−32.3812	−1.09782
$871$	65.1030	2.20593
$872$	25.2196	0.854044
$873$	0.193953	0.00656432
$874$	3.33850	0.112927
$875$	−13.7004	−0.463157
$876$	7.74526	0.261688
$877$	54.5919	1.84344	0.921720	−	0.387857i	$-0.126785\pi$
$877$	54.5919	1.84344	0.921720	+	0.387857i	$0.126785\pi$
$878$	−45.2308	−1.52647
$879$	−21.0045	−0.708464
$880$	40.3638	1.36066
$881$	−25.7913	−0.868930	−0.434465	−	0.900689i	$-0.643063\pi$
$881$	−25.7913	−0.868930	−0.434465	+	0.900689i	$0.643063\pi$
$882$	14.1505	0.476471
$883$	24.8148	0.835084	0.417542	−	0.908658i	$-0.362892\pi$
$883$	24.8148	0.835084	0.417542	+	0.908658i	$0.362892\pi$
$884$	−40.6118	−1.36592
$885$	39.6312	1.33219
$886$	43.3979	1.45798
$887$	−52.7157	−1.77002	−0.885011	−	0.465571i	$-0.845849\pi$
$887$	−52.7157	−1.77002	−0.885011	+	0.465571i	$0.845849\pi$
$888$	−53.6390	−1.80001
$889$	20.4351	0.685372
$890$	−27.8083	−0.932135
$891$	2.74944	0.0921097
$892$	−57.0947	−1.91167
$893$	−41.8401	−1.40012
$894$	35.3935	1.18373
$895$	72.8130	2.43387
$896$	−21.6616	−0.723665
$897$	−2.68911	−0.0897869
$898$	76.1749	2.54199
$899$	−28.9388	−0.965162
$900$	33.5565	1.11855
$901$	3.50030	0.116612
$902$	0.689008	0.0229414
$903$	−2.22309	−0.0739797
$904$	−26.1521	−0.869804
$905$	−61.2774	−2.03693
$906$	22.9239	0.761595
$907$	29.7990	0.989461	0.494730	−	0.869046i	$-0.335267\pi$
$907$	29.7990	0.989461	0.494730	+	0.869046i	$0.335267\pi$
$908$	105.739	3.50907
$909$	−17.2616	−0.572532
$910$	61.8175	2.04923
$911$	−47.2631	−1.56590	−0.782948	−	0.622087i	$-0.786285\pi$
$911$	−47.2631	−1.56590	−0.782948	+	0.622087i	$0.786285\pi$
$912$	12.6758	0.419739
$913$	21.3284	0.705868
$914$	−28.0034	−0.926271
$915$	−37.6535	−1.24479
$916$	−108.198	−3.57496
$917$	−21.4791	−0.709301
$918$	−3.98815	−0.131629
$919$	−25.5180	−0.841761	−0.420880	−	0.907116i	$-0.638279\pi$
$919$	−25.5180	−0.841761	−0.420880	+	0.907116i	$0.638279\pi$
$920$	−7.74131	−0.255224
$921$	9.28384	0.305913
$922$	−96.8421	−3.18932
$923$	−40.0142	−1.31708
$924$	12.1744	0.400509
$925$	−91.6900	−3.01475
$926$	20.1331	0.661615
$927$	3.96944	0.130374
$928$	0.0753589	0.00247378
$929$	43.1901	1.41702	0.708510	−	0.705701i	$-0.249368\pi$
$929$	43.1901	1.41702	0.708510	+	0.705701i	$0.249368\pi$
$930$	71.7960	2.35428
$931$	18.2453	0.597965
$932$	51.1704	1.67614
$933$	−9.25519	−0.303001
$934$	90.2888	2.95434
$935$	−16.3745	−0.535502
$936$	−30.5764	−0.999422
$937$	0.736710	0.0240673	0.0120336	−	0.999928i	$-0.496169\pi$
$937$	0.736710	0.0240673	0.0120336	+	0.999928i	$0.496169\pi$
$938$	28.3089	0.924320
$939$	−21.3016	−0.695151
$940$	193.934	6.32543
$941$	−20.1333	−0.656326	−0.328163	−	0.944621i	$-0.606430\pi$
$941$	−20.1333	−0.656326	−0.328163	+	0.944621i	$0.606430\pi$
$942$	−13.5918	−0.442845
$943$	−0.0441259	−0.00143694
$944$	−43.4688	−1.41479
$945$	4.04778	0.131674
$946$	13.5345	0.440043
$947$	−42.7799	−1.39016	−0.695080	−	0.718932i	$-0.744631\pi$
$947$	−42.7799	−1.39016	−0.695080	+	0.718932i	$0.744631\pi$
$948$	−8.01120	−0.260192
$949$	−12.0639	−0.391611
$950$	64.8890	2.10528
$951$	−1.06036	−0.0343845
$952$	−8.83438	−0.286324
$953$	−15.7985	−0.511764	−0.255882	−	0.966708i	$-0.582366\pi$
$953$	−15.7985	−0.511764	−0.255882	+	0.966708i	$0.582366\pi$
$954$	5.26791	0.170555
$955$	79.2683	2.56506
$956$	−3.08451	−0.0997602
$957$	9.93300	0.321088
$958$	−15.2043	−0.491227
$959$	−19.5249	−0.630491
$960$	29.1745	0.941603
$961$	33.1634	1.06979
$962$	167.006	5.38448
$963$	8.49726	0.273820
$964$	−94.1480	−3.03230
$965$	7.88643	0.253873
$966$	−1.16932	−0.0376221
$967$	27.7276	0.891661	0.445830	−	0.895117i	$-0.352908\pi$
$967$	27.7276	0.891661	0.445830	+	0.895117i	$0.352908\pi$
$968$	16.8762	0.542423
$969$	−5.14223	−0.165192
$970$	−1.73841	−0.0558171
$971$	33.6076	1.07852	0.539259	−	0.842140i	$-0.318704\pi$
$971$	33.6076	1.07852	0.539259	+	0.842140i	$0.318704\pi$
$972$	−4.00213	−0.128368
$973$	−22.4531	−0.719813
$974$	−51.3588	−1.64564
$975$	−52.2671	−1.67389
$976$	41.2996	1.32197
$977$	35.1606	1.12489	0.562444	−	0.826835i	$-0.309861\pi$
$977$	35.1606	1.12489	0.562444	+	0.826835i	$0.309861\pi$
$978$	32.3543	1.03458
$979$	8.53026	0.272628
$980$	−84.5693	−2.70147
$981$	−5.14155	−0.164157
$982$	−93.7634	−2.99211
$983$	37.4882	1.19569	0.597844	−	0.801612i	$-0.296024\pi$
$983$	37.4882	1.19569	0.597844	+	0.801612i	$0.296024\pi$
$984$	−0.501731	−0.0159946
$985$	38.9120	1.23984
$986$	−14.4081	−0.458849
$987$	14.6545	0.466459
$988$	−78.8072	−2.50719
$989$	−0.866783	−0.0275621
$990$	−24.6434	−0.783219
$991$	45.6401	1.44980	0.724902	−	0.688852i	$-0.241885\pi$
$991$	45.6401	1.44980	0.724902	+	0.688852i	$0.241885\pi$
$992$	−0.167087	−0.00530501
$993$	31.0616	0.985709
$994$	−17.3995	−0.551879
$995$	28.1194	0.891445
$996$	−31.0460	−0.983730
$997$	26.0362	0.824574	0.412287	−	0.911054i	$-0.364730\pi$
$997$	26.0362	0.824574	0.412287	+	0.911054i	$0.364730\pi$
$998$	−28.1748	−0.891858
$999$	10.9354	0.345982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.7	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.7	✓	106	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44992 q^{2} -1.00000 q^{3} +4.00213 q^{4} +3.65851 q^{5} +2.44992 q^{6} -1.10640 q^{7} -4.90506 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.44992 q^{2} -1.00000 q^{3} +4.00213 q^{4} +3.65851 q^{5} +2.44992 q^{6} -1.10640 q^{7} -4.90506 q^{8} +1.00000 q^{9} -8.96306 q^{10} +2.74944 q^{11} -4.00213 q^{12} +6.23365 q^{13} +2.71060 q^{14} -3.65851 q^{15} +4.01277 q^{16} -1.62787 q^{17} -2.44992 q^{18} -3.15888 q^{19} +14.6418 q^{20} +1.10640 q^{21} -6.73592 q^{22} +0.431387 q^{23} +4.90506 q^{24} +8.38467 q^{25} -15.2720 q^{26} -1.00000 q^{27} -4.42796 q^{28} -3.61274 q^{29} +8.96306 q^{30} +8.01021 q^{31} -0.0208592 q^{32} -2.74944 q^{33} +3.98815 q^{34} -4.04778 q^{35} +4.00213 q^{36} -10.9354 q^{37} +7.73901 q^{38} -6.23365 q^{39} -17.9452 q^{40} -0.102289 q^{41} -2.71060 q^{42} -2.00930 q^{43} +11.0036 q^{44} +3.65851 q^{45} -1.05686 q^{46} +13.2452 q^{47} -4.01277 q^{48} -5.77588 q^{49} -20.5418 q^{50} +1.62787 q^{51} +24.9479 q^{52} -2.15024 q^{53} +2.44992 q^{54} +10.0588 q^{55} +5.42696 q^{56} +3.15888 q^{57} +8.85093 q^{58} -10.8326 q^{59} -14.6418 q^{60} +10.2920 q^{61} -19.6244 q^{62} -1.10640 q^{63} -7.97443 q^{64} +22.8058 q^{65} +6.73592 q^{66} +10.4438 q^{67} -6.51493 q^{68} -0.431387 q^{69} +9.91674 q^{70} -6.41907 q^{71} -4.90506 q^{72} -1.93529 q^{73} +26.7910 q^{74} -8.38467 q^{75} -12.6422 q^{76} -3.04198 q^{77} +15.2720 q^{78} +2.00174 q^{79} +14.6807 q^{80} +1.00000 q^{81} +0.250599 q^{82} +7.75737 q^{83} +4.42796 q^{84} -5.95556 q^{85} +4.92262 q^{86} +3.61274 q^{87} -13.4862 q^{88} +3.10254 q^{89} -8.96306 q^{90} -6.89692 q^{91} +1.72646 q^{92} -8.01021 q^{93} -32.4498 q^{94} -11.5568 q^{95} +0.0208592 q^{96} +0.193953 q^{97} +14.1505 q^{98} +2.74944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

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