LMFDB - Embedded newform 8041.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +O(q^{10})$	\(q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +5.95163 q^{10} +1.00000 q^{11} +3.21663 q^{12} -1.37133 q^{13} +0.531361 q^{14} -6.25770 q^{15} -4.62774 q^{16} -1.00000 q^{17} -1.88293 q^{18} +2.56782 q^{19} -5.04353 q^{20} -0.558688 q^{21} -1.90003 q^{22} -5.56968 q^{23} +1.47987 q^{24} +4.81179 q^{25} +2.60557 q^{26} -4.01348 q^{27} -0.450287 q^{28} -5.48031 q^{29} +11.8898 q^{30} -2.40258 q^{31} +7.31133 q^{32} +1.99775 q^{33} +1.90003 q^{34} +0.875997 q^{35} +1.59563 q^{36} -6.44814 q^{37} -4.87895 q^{38} -2.73957 q^{39} -2.32037 q^{40} +5.16443 q^{41} +1.06153 q^{42} -1.00000 q^{43} +1.61013 q^{44} -3.10418 q^{45} +10.5826 q^{46} +4.29668 q^{47} -9.24506 q^{48} -6.92179 q^{49} -9.14257 q^{50} -1.99775 q^{51} -2.20802 q^{52} +3.96910 q^{53} +7.62575 q^{54} -3.13238 q^{55} -0.207162 q^{56} +5.12986 q^{57} +10.4128 q^{58} -0.143220 q^{59} -10.0757 q^{60} +13.9770 q^{61} +4.56498 q^{62} -0.277141 q^{63} -4.63629 q^{64} +4.29552 q^{65} -3.79579 q^{66} -9.52542 q^{67} -1.61013 q^{68} -11.1268 q^{69} -1.66442 q^{70} +12.7841 q^{71} +0.734099 q^{72} -10.1584 q^{73} +12.2517 q^{74} +9.61275 q^{75} +4.13453 q^{76} -0.279659 q^{77} +5.20528 q^{78} +2.40998 q^{79} +14.4958 q^{80} -10.9909 q^{81} -9.81259 q^{82} -13.6597 q^{83} -0.899560 q^{84} +3.13238 q^{85} +1.90003 q^{86} -10.9483 q^{87} +0.740768 q^{88} +11.1325 q^{89} +5.89804 q^{90} +0.383505 q^{91} -8.96791 q^{92} -4.79974 q^{93} -8.16383 q^{94} -8.04339 q^{95} +14.6062 q^{96} -7.90060 q^{97} +13.1516 q^{98} +0.990997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.90003	−1.34353	−0.671763	−	0.740766i	$-0.734463\pi$
$2$	−1.90003	−1.34353	−0.671763	+	0.740766i	$0.734463\pi$
$3$	1.99775	1.15340	0.576700	−	0.816956i	$-0.304340\pi$
$3$	1.99775	1.15340	0.576700	+	0.816956i	$0.304340\pi$
$4$	1.61013	0.805065
$5$	−3.13238	−1.40084	−0.700421	−	0.713730i	$-0.747004\pi$
$5$	−3.13238	−1.40084	−0.700421	+	0.713730i	$0.747004\pi$
$6$	−3.79579	−1.54962
$7$	−0.279659	−0.105701	−0.0528506	−	0.998602i	$-0.516831\pi$
$7$	−0.279659	−0.105701	−0.0528506	+	0.998602i	$0.516831\pi$
$8$	0.740768	0.261901
$9$	0.990997	0.330332
$10$	5.95163	1.88207
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.21663	0.928562
$13$	−1.37133	−0.380338	−0.190169	−	0.981751i	$-0.560904\pi$
$13$	−1.37133	−0.380338	−0.190169	+	0.981751i	$0.560904\pi$
$14$	0.531361	0.142012
$15$	−6.25770	−1.61573
$16$	−4.62774	−1.15694
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.88293	−0.443810
$19$	2.56782	0.589099	0.294550	−	0.955636i	$-0.404830\pi$
$19$	2.56782	0.589099	0.294550	+	0.955636i	$0.404830\pi$
$20$	−5.04353	−1.12777
$21$	−0.558688	−0.121916
$22$	−1.90003	−0.405089
$23$	−5.56968	−1.16136	−0.580680	−	0.814132i	$-0.697213\pi$
$23$	−5.56968	−1.16136	−0.580680	+	0.814132i	$0.697213\pi$
$24$	1.47987	0.302077
$25$	4.81179	0.962359
$26$	2.60557	0.510995
$27$	−4.01348	−0.772395
$28$	−0.450287	−0.0850962
$29$	−5.48031	−1.01767	−0.508834	−	0.860865i	$-0.669923\pi$
$29$	−5.48031	−1.01767	−0.508834	+	0.860865i	$0.669923\pi$
$30$	11.8898	2.17078
$31$	−2.40258	−0.431516	−0.215758	−	0.976447i	$-0.569222\pi$
$31$	−2.40258	−0.431516	−0.215758	+	0.976447i	$0.569222\pi$
$32$	7.31133	1.29247
$33$	1.99775	0.347763
$34$	1.90003	0.325853
$35$	0.875997	0.148071
$36$	1.59563	0.265939
$37$	−6.44814	−1.06007	−0.530034	−	0.847977i	$-0.677821\pi$
$37$	−6.44814	−1.06007	−0.530034	+	0.847977i	$0.677821\pi$
$38$	−4.87895	−0.791471
$39$	−2.73957	−0.438683
$40$	−2.32037	−0.366882
$41$	5.16443	0.806548	0.403274	−	0.915079i	$-0.367872\pi$
$41$	5.16443	0.806548	0.403274	+	0.915079i	$0.367872\pi$
$42$	1.06153	0.163797
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.61013	0.242736
$45$	−3.10418	−0.462743
$46$	10.5826	1.56032
$47$	4.29668	0.626735	0.313367	−	0.949632i	$-0.398543\pi$
$47$	4.29668	0.626735	0.313367	+	0.949632i	$0.398543\pi$
$48$	−9.24506	−1.33441
$49$	−6.92179	−0.988827
$50$	−9.14257	−1.29295
$51$	−1.99775	−0.279741
$52$	−2.20802	−0.306197
$53$	3.96910	0.545198	0.272599	−	0.962128i	$-0.412117\pi$
$53$	3.96910	0.545198	0.272599	+	0.962128i	$0.412117\pi$
$54$	7.62575	1.03773
$55$	−3.13238	−0.422370
$56$	−0.207162	−0.0276832
$57$	5.12986	0.679467
$58$	10.4128	1.36726
$59$	−0.143220	−0.0186457	−0.00932285	−	0.999957i	$-0.502968\pi$
$59$	−0.143220	−0.0186457	−0.00932285	+	0.999957i	$0.502968\pi$
$60$	−10.0757	−1.30077
$61$	13.9770	1.78957	0.894785	−	0.446496i	$-0.147328\pi$
$61$	13.9770	1.78957	0.894785	+	0.446496i	$0.147328\pi$
$62$	4.56498	0.579753
$63$	−0.277141	−0.0349165
$64$	−4.63629	−0.579537
$65$	4.29552	0.532794
$66$	−3.79579	−0.467229
$67$	−9.52542	−1.16371	−0.581857	−	0.813291i	$-0.697674\pi$
$67$	−9.52542	−1.16371	−0.581857	+	0.813291i	$0.697674\pi$
$68$	−1.61013	−0.195257
$69$	−11.1268	−1.33951
$70$	−1.66442	−0.198937
$71$	12.7841	1.51720	0.758600	−	0.651557i	$-0.225884\pi$
$71$	12.7841	1.51720	0.758600	+	0.651557i	$0.225884\pi$
$72$	0.734099	0.0865144
$73$	−10.1584	−1.18896	−0.594478	−	0.804112i	$-0.702641\pi$
$73$	−10.1584	−1.18896	−0.594478	+	0.804112i	$0.702641\pi$
$74$	12.2517	1.42423
$75$	9.61275	1.10998
$76$	4.13453	0.474263
$77$	−0.279659	−0.0318701
$78$	5.20528	0.589382
$79$	2.40998	0.271143	0.135572	−	0.990768i	$-0.456713\pi$
$79$	2.40998	0.271143	0.135572	+	0.990768i	$0.456713\pi$
$80$	14.4958	1.62068
$81$	−10.9909	−1.22121
$82$	−9.81259	−1.08362
$83$	−13.6597	−1.49934	−0.749671	−	0.661811i	$-0.769788\pi$
$83$	−13.6597	−1.49934	−0.749671	+	0.661811i	$0.769788\pi$
$84$	−0.899560	−0.0981500
$85$	3.13238	0.339754
$86$	1.90003	0.204886
$87$	−10.9483	−1.17378
$88$	0.740768	0.0789661
$89$	11.1325	1.18005	0.590023	−	0.807386i	$-0.299119\pi$
$89$	11.1325	1.18005	0.590023	+	0.807386i	$0.299119\pi$
$90$	5.89804	0.621708
$91$	0.383505	0.0402022
$92$	−8.96791	−0.934969
$93$	−4.79974	−0.497710
$94$	−8.16383	−0.842035
$95$	−8.04339	−0.825235
$96$	14.6062	1.49074
$97$	−7.90060	−0.802184	−0.401092	−	0.916038i	$-0.631369\pi$
$97$	−7.90060	−0.802184	−0.401092	+	0.916038i	$0.631369\pi$
$98$	13.1516	1.32852
$99$	0.990997	0.0995989
$100$	7.74761	0.774761
$101$	9.50281	0.945565	0.472783	−	0.881179i	$-0.343250\pi$
$101$	9.50281	0.945565	0.472783	+	0.881179i	$0.343250\pi$
$102$	3.79579	0.375839
$103$	11.4954	1.13267	0.566336	−	0.824175i	$-0.308361\pi$
$103$	11.4954	1.13267	0.566336	+	0.824175i	$0.308361\pi$
$104$	−1.01584	−0.0996110
$105$	1.75002	0.170785
$106$	−7.54142	−0.732488
$107$	6.70439	0.648138	0.324069	−	0.946033i	$-0.394949\pi$
$107$	6.70439	0.648138	0.324069	+	0.946033i	$0.394949\pi$
$108$	−6.46222	−0.621828
$109$	3.19350	0.305882	0.152941	−	0.988235i	$-0.451126\pi$
$109$	3.19350	0.305882	0.152941	+	0.988235i	$0.451126\pi$
$110$	5.95163	0.567465
$111$	−12.8818	−1.22268
$112$	1.29419	0.122289
$113$	2.62618	0.247050	0.123525	−	0.992341i	$-0.460580\pi$
$113$	2.62618	0.247050	0.123525	+	0.992341i	$0.460580\pi$
$114$	−9.74692	−0.912882
$115$	17.4464	1.62688
$116$	−8.82401	−0.819288
$117$	−1.35898	−0.125638
$118$	0.272123	0.0250510
$119$	0.279659	0.0256363
$120$	−4.63551	−0.423162
$121$	1.00000	0.0909091
$122$	−26.5568	−2.40434
$123$	10.3172	0.930273
$124$	−3.86846	−0.347398
$125$	0.589532	0.0527294
$126$	0.526577	0.0469112
$127$	18.1135	1.60731	0.803657	−	0.595093i	$-0.202885\pi$
$127$	18.1135	1.60731	0.803657	+	0.595093i	$0.202885\pi$
$128$	−5.81355	−0.513850
$129$	−1.99775	−0.175892
$130$	−8.16164	−0.715823
$131$	−0.628464	−0.0549092	−0.0274546	−	0.999623i	$-0.508740\pi$
$131$	−0.628464	−0.0549092	−0.0274546	+	0.999623i	$0.508740\pi$
$132$	3.21663	0.279972
$133$	−0.718115	−0.0622684
$134$	18.0986	1.56348
$135$	12.5717	1.08200
$136$	−0.740768	−0.0635203
$137$	−6.27047	−0.535723	−0.267861	−	0.963457i	$-0.586317\pi$
$137$	−6.27047	−0.535723	−0.267861	+	0.963457i	$0.586317\pi$
$138$	21.1413	1.79967
$139$	12.7449	1.08101	0.540503	−	0.841342i	$-0.318234\pi$
$139$	12.7449	1.08101	0.540503	+	0.841342i	$0.318234\pi$
$140$	1.41047	0.119206
$141$	8.58367	0.722876
$142$	−24.2903	−2.03840
$143$	−1.37133	−0.114676
$144$	−4.58608	−0.382173
$145$	17.1664	1.42559
$146$	19.3014	1.59739
$147$	−13.8280	−1.14051
$148$	−10.3823	−0.853422
$149$	−8.36079	−0.684942	−0.342471	−	0.939528i	$-0.611264\pi$
$149$	−8.36079	−0.684942	−0.342471	+	0.939528i	$0.611264\pi$
$150$	−18.2646	−1.49129
$151$	−11.2795	−0.917915	−0.458958	−	0.888458i	$-0.651777\pi$
$151$	−11.2795	−0.917915	−0.458958	+	0.888458i	$0.651777\pi$
$152$	1.90216	0.154286
$153$	−0.990997	−0.0801173
$154$	0.531361	0.0428183
$155$	7.52578	0.604485
$156$	−4.41106	−0.353168
$157$	−17.8591	−1.42531	−0.712657	−	0.701513i	$-0.752508\pi$
$157$	−17.8591	−1.42531	−0.712657	+	0.701513i	$0.752508\pi$
$158$	−4.57903	−0.364288
$159$	7.92926	0.628831
$160$	−22.9019	−1.81055
$161$	1.55761	0.122757
$162$	20.8831	1.64073
$163$	−13.4824	−1.05602	−0.528010	−	0.849238i	$-0.677062\pi$
$163$	−13.4824	−1.05602	−0.528010	+	0.849238i	$0.677062\pi$
$164$	8.31539	0.649323
$165$	−6.25770	−0.487161
$166$	25.9538	2.01441
$167$	−0.721942	−0.0558656	−0.0279328	−	0.999610i	$-0.508892\pi$
$167$	−0.721942	−0.0558656	−0.0279328	+	0.999610i	$0.508892\pi$
$168$	−0.413858	−0.0319298
$169$	−11.1195	−0.855343
$170$	−5.95163	−0.456469
$171$	2.54470	0.194598
$172$	−1.61013	−0.122771
$173$	−24.9192	−1.89457	−0.947284	−	0.320395i	$-0.896184\pi$
$173$	−24.9192	−1.89457	−0.947284	+	0.320395i	$0.896184\pi$
$174$	20.8021	1.57700
$175$	−1.34566	−0.101722
$176$	−4.62774	−0.348829
$177$	−0.286118	−0.0215060
$178$	−21.1522	−1.58542
$179$	3.50222	0.261768	0.130884	−	0.991398i	$-0.458218\pi$
$179$	3.50222	0.261768	0.130884	+	0.991398i	$0.458218\pi$
$180$	−4.99813	−0.372538
$181$	0.594036	0.0441544	0.0220772	−	0.999756i	$-0.492972\pi$
$181$	0.594036	0.0441544	0.0220772	+	0.999756i	$0.492972\pi$
$182$	−0.728672	−0.0540127
$183$	27.9225	2.06409
$184$	−4.12584	−0.304161
$185$	20.1980	1.48499
$186$	9.11967	0.668687
$187$	−1.00000	−0.0731272
$188$	6.91820	0.504562
$189$	1.12241	0.0816430
$190$	15.2827	1.10873
$191$	−3.71613	−0.268889	−0.134445	−	0.990921i	$-0.542925\pi$
$191$	−3.71613	−0.268889	−0.134445	+	0.990921i	$0.542925\pi$
$192$	−9.26215	−0.668438
$193$	−7.08417	−0.509929	−0.254965	−	0.966950i	$-0.582064\pi$
$193$	−7.08417	−0.509929	−0.254965	+	0.966950i	$0.582064\pi$
$194$	15.0114	1.07776
$195$	8.58137	0.614525
$196$	−11.1450	−0.796070
$197$	20.0268	1.42685	0.713424	−	0.700733i	$-0.247143\pi$
$197$	20.0268	1.42685	0.713424	+	0.700733i	$0.247143\pi$
$198$	−1.88293	−0.133814
$199$	8.38545	0.594429	0.297214	−	0.954811i	$-0.403942\pi$
$199$	8.38545	0.594429	0.297214	+	0.954811i	$0.403942\pi$
$200$	3.56442	0.252043
$201$	−19.0294	−1.34223
$202$	−18.0557	−1.27039
$203$	1.53262	0.107569
$204$	−3.21663	−0.225209
$205$	−16.1769	−1.12985
$206$	−21.8416	−1.52177
$207$	−5.51954	−0.383634
$208$	6.34616	0.440027
$209$	2.56782	0.177620
$210$	−3.32510	−0.229454
$211$	−23.2674	−1.60179	−0.800896	−	0.598803i	$-0.795643\pi$
$211$	−23.2674	−1.60179	−0.800896	+	0.598803i	$0.795643\pi$
$212$	6.39076	0.438919
$213$	25.5395	1.74994
$214$	−12.7386	−0.870791
$215$	3.13238	0.213626
$216$	−2.97306	−0.202291
$217$	0.671902	0.0456117
$218$	−6.06776	−0.410961
$219$	−20.2940	−1.37134
$220$	−5.04353	−0.340035
$221$	1.37133	0.0922456
$222$	24.4758	1.64271
$223$	8.70863	0.583173	0.291586	−	0.956544i	$-0.405817\pi$
$223$	8.70863	0.583173	0.291586	+	0.956544i	$0.405817\pi$
$224$	−2.04468	−0.136616
$225$	4.76847	0.317898
$226$	−4.98982	−0.331918
$227$	−20.6202	−1.36861	−0.684304	−	0.729197i	$-0.739894\pi$
$227$	−20.6202	−1.36861	−0.684304	+	0.729197i	$0.739894\pi$
$228$	8.25974	0.547015
$229$	−4.02643	−0.266074	−0.133037	−	0.991111i	$-0.542473\pi$
$229$	−4.02643	−0.266074	−0.133037	+	0.991111i	$0.542473\pi$
$230$	−33.1487	−2.18576
$231$	−0.558688	−0.0367590
$232$	−4.05964	−0.266528
$233$	3.95740	0.259258	0.129629	−	0.991563i	$-0.458621\pi$
$233$	3.95740	0.259258	0.129629	+	0.991563i	$0.458621\pi$
$234$	2.58211	0.168798
$235$	−13.4588	−0.877956
$236$	−0.230603	−0.0150110
$237$	4.81452	0.312737
$238$	−0.531361	−0.0344430
$239$	17.1361	1.10844	0.554222	−	0.832369i	$-0.313016\pi$
$239$	17.1361	1.10844	0.554222	+	0.832369i	$0.313016\pi$
$240$	28.9590	1.86930
$241$	−0.676038	−0.0435474	−0.0217737	−	0.999763i	$-0.506931\pi$
$241$	−0.676038	−0.0435474	−0.0217737	+	0.999763i	$0.506931\pi$
$242$	−1.90003	−0.122139
$243$	−9.91663	−0.636152
$244$	22.5048	1.44072
$245$	21.6817	1.38519
$246$	−19.6031	−1.24985
$247$	−3.52133	−0.224057
$248$	−1.77975	−0.113014
$249$	−27.2885	−1.72934
$250$	−1.12013	−0.0708433
$251$	29.9133	1.88811	0.944057	−	0.329783i	$-0.106976\pi$
$251$	29.9133	1.88811	0.944057	+	0.329783i	$0.106976\pi$
$252$	−0.446233	−0.0281100
$253$	−5.56968	−0.350163
$254$	−34.4163	−2.15947
$255$	6.25770	0.391873
$256$	20.3185	1.26991
$257$	22.3669	1.39521	0.697605	−	0.716483i	$-0.254249\pi$
$257$	22.3669	1.39521	0.697605	+	0.716483i	$0.254249\pi$
$258$	3.79579	0.236315
$259$	1.80328	0.112050
$260$	6.91635	0.428934
$261$	−5.43097	−0.336169
$262$	1.19410	0.0737720
$263$	−7.61166	−0.469355	−0.234677	−	0.972073i	$-0.575403\pi$
$263$	−7.61166	−0.469355	−0.234677	+	0.972073i	$0.575403\pi$
$264$	1.47987	0.0910796
$265$	−12.4327	−0.763736
$266$	1.36444	0.0836593
$267$	22.2400	1.36107
$268$	−15.3371	−0.936865
$269$	6.21577	0.378982	0.189491	−	0.981882i	$-0.439316\pi$
$269$	6.21577	0.378982	0.189491	+	0.981882i	$0.439316\pi$
$270$	−23.8867	−1.45370
$271$	−26.7843	−1.62703	−0.813514	−	0.581546i	$-0.802448\pi$
$271$	−26.7843	−1.62703	−0.813514	+	0.581546i	$0.802448\pi$
$272$	4.62774	0.280598
$273$	0.766145	0.0463692
$274$	11.9141	0.719758
$275$	4.81179	0.290162
$276$	−17.9156	−1.07839
$277$	13.8827	0.834130	0.417065	−	0.908877i	$-0.363059\pi$
$277$	13.8827	0.834130	0.417065	+	0.908877i	$0.363059\pi$
$278$	−24.2157	−1.45236
$279$	−2.38095	−0.142544
$280$	0.648911	0.0387798
$281$	1.67650	0.100012	0.0500059	−	0.998749i	$-0.484076\pi$
$281$	1.67650	0.100012	0.0500059	+	0.998749i	$0.484076\pi$
$282$	−16.3093	−0.971203
$283$	−5.63197	−0.334786	−0.167393	−	0.985890i	$-0.553535\pi$
$283$	−5.63197	−0.334786	−0.167393	+	0.985890i	$0.553535\pi$
$284$	20.5841	1.22144
$285$	−16.0687	−0.951826
$286$	2.60557	0.154071
$287$	−1.44428	−0.0852530
$288$	7.24551	0.426946
$289$	1.00000	0.0588235
$290$	−32.6167	−1.91532
$291$	−15.7834	−0.925239
$292$	−16.3564	−0.957186
$293$	27.0382	1.57959	0.789794	−	0.613372i	$-0.210187\pi$
$293$	27.0382	1.57959	0.789794	+	0.613372i	$0.210187\pi$
$294$	26.2737	1.53231
$295$	0.448620	0.0261197
$296$	−4.77657	−0.277633
$297$	−4.01348	−0.232886
$298$	15.8858	0.920239
$299$	7.63787	0.441710
$300$	15.4778	0.893610
$301$	0.279659	0.0161193
$302$	21.4315	1.23324
$303$	18.9842	1.09062
$304$	−11.8832	−0.681550
$305$	−43.7812	−2.50691
$306$	1.88293	0.107640
$307$	6.70606	0.382735	0.191368	−	0.981518i	$-0.438708\pi$
$307$	6.70606	0.382735	0.191368	+	0.981518i	$0.438708\pi$
$308$	−0.450287	−0.0256575
$309$	22.9648	1.30642
$310$	−14.2992	−0.812142
$311$	28.3030	1.60492	0.802459	−	0.596708i	$-0.203525\pi$
$311$	28.3030	1.60492	0.802459	+	0.596708i	$0.203525\pi$
$312$	−2.02939	−0.114891
$313$	−4.58151	−0.258962	−0.129481	−	0.991582i	$-0.541331\pi$
$313$	−4.58151	−0.258962	−0.129481	+	0.991582i	$0.541331\pi$
$314$	33.9330	1.91495
$315$	0.868111	0.0489125
$316$	3.88037	0.218288
$317$	0.164102	0.00921687	0.00460844	−	0.999989i	$-0.498533\pi$
$317$	0.164102	0.00921687	0.00460844	+	0.999989i	$0.498533\pi$
$318$	−15.0659	−0.844852
$319$	−5.48031	−0.306838
$320$	14.5226	0.811840
$321$	13.3937	0.747562
$322$	−2.95951	−0.164927
$323$	−2.56782	−0.142878
$324$	−17.6968	−0.983155
$325$	−6.59856	−0.366022
$326$	25.6169	1.41879
$327$	6.37981	0.352805
$328$	3.82564	0.211236
$329$	−1.20160	−0.0662465
$330$	11.8898	0.654515
$331$	−4.40814	−0.242293	−0.121147	−	0.992635i	$-0.538657\pi$
$331$	−4.40814	−0.242293	−0.121147	+	0.992635i	$0.538657\pi$
$332$	−21.9938	−1.20707
$333$	−6.39008	−0.350174
$334$	1.37171	0.0750569
$335$	29.8372	1.63018
$336$	2.58546	0.141049
$337$	28.9901	1.57919	0.789595	−	0.613628i	$-0.210291\pi$
$337$	28.9901	1.57919	0.789595	+	0.613628i	$0.210291\pi$
$338$	21.1273	1.14918
$339$	5.24644	0.284947
$340$	5.04353	0.273524
$341$	−2.40258	−0.130107
$342$	−4.83503	−0.261448
$343$	3.89335	0.210221
$344$	−0.740768	−0.0399395
$345$	34.8534	1.87645
$346$	47.3472	2.54540
$347$	26.4139	1.41797	0.708987	−	0.705221i	$-0.249152\pi$
$347$	26.4139	1.41797	0.708987	+	0.705221i	$0.249152\pi$
$348$	−17.6281	−0.944967
$349$	0.263510	0.0141053	0.00705267	−	0.999975i	$-0.497755\pi$
$349$	0.263510	0.0141053	0.00705267	+	0.999975i	$0.497755\pi$
$350$	2.55680	0.136667
$351$	5.50381	0.293772
$352$	7.31133	0.389695
$353$	−24.6920	−1.31422	−0.657112	−	0.753793i	$-0.728222\pi$
$353$	−24.6920	−1.31422	−0.657112	+	0.753793i	$0.728222\pi$
$354$	0.543634	0.0288938
$355$	−40.0448	−2.12536
$356$	17.9248	0.950013
$357$	0.558688	0.0295689
$358$	−6.65433	−0.351693
$359$	27.8514	1.46994	0.734970	−	0.678099i	$-0.237196\pi$
$359$	27.8514	1.46994	0.734970	+	0.678099i	$0.237196\pi$
$360$	−2.29947	−0.121193
$361$	−12.4063	−0.652962
$362$	−1.12869	−0.0593226
$363$	1.99775	0.104855
$364$	0.617492	0.0323654
$365$	31.8201	1.66554
$366$	−53.0537	−2.77316
$367$	29.9724	1.56454	0.782272	−	0.622937i	$-0.214061\pi$
$367$	29.9724	1.56454	0.782272	+	0.622937i	$0.214061\pi$
$368$	25.7751	1.34362
$369$	5.11793	0.266429
$370$	−38.3769	−1.99512
$371$	−1.10999	−0.0576280
$372$	−7.72821	−0.400689
$373$	2.64767	0.137091	0.0685456	−	0.997648i	$-0.478164\pi$
$373$	2.64767	0.137091	0.0685456	+	0.997648i	$0.478164\pi$
$374$	1.90003	0.0982484
$375$	1.17774	0.0608181
$376$	3.18284	0.164142
$377$	7.51531	0.387058
$378$	−2.13261	−0.109690
$379$	19.7109	1.01248	0.506241	−	0.862392i	$-0.331035\pi$
$379$	19.7109	1.01248	0.506241	+	0.862392i	$0.331035\pi$
$380$	−12.9509	−0.664367
$381$	36.1862	1.85388
$382$	7.06077	0.361260
$383$	25.7703	1.31680	0.658400	−	0.752668i	$-0.271234\pi$
$383$	25.7703	1.31680	0.658400	+	0.752668i	$0.271234\pi$
$384$	−11.6140	−0.592675
$385$	0.875997	0.0446450
$386$	13.4602	0.685104
$387$	−0.990997	−0.0503752
$388$	−12.7210	−0.645810
$389$	−23.4021	−1.18654	−0.593268	−	0.805005i	$-0.702162\pi$
$389$	−23.4021	−1.18654	−0.593268	+	0.805005i	$0.702162\pi$
$390$	−16.3049	−0.825631
$391$	5.56968	0.281671
$392$	−5.12744	−0.258975
$393$	−1.25551	−0.0633323
$394$	−38.0515	−1.91701
$395$	−7.54895	−0.379829
$396$	1.59563	0.0801836
$397$	8.67600	0.435436	0.217718	−	0.976012i	$-0.430139\pi$
$397$	8.67600	0.435436	0.217718	+	0.976012i	$0.430139\pi$
$398$	−15.9326	−0.798631
$399$	−1.43461	−0.0718204
$400$	−22.2677	−1.11339
$401$	8.81082	0.439992	0.219996	−	0.975501i	$-0.429396\pi$
$401$	8.81082	0.439992	0.219996	+	0.975501i	$0.429396\pi$
$402$	36.1565	1.80332
$403$	3.29473	0.164122
$404$	15.3008	0.761241
$405$	34.4277	1.71073
$406$	−2.91202	−0.144521
$407$	−6.44814	−0.319622
$408$	−1.47987	−0.0732644
$409$	2.45455	0.121370	0.0606849	−	0.998157i	$-0.480672\pi$
$409$	2.45455	0.121370	0.0606849	+	0.998157i	$0.480672\pi$
$410$	30.7367	1.51798
$411$	−12.5268	−0.617903
$412$	18.5090	0.911873
$413$	0.0400528	0.00197087
$414$	10.4873	0.515423
$415$	42.7872	2.10034
$416$	−10.0262	−0.491577
$417$	25.4610	1.24683
$418$	−4.87895	−0.238637
$419$	30.4297	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$419$	30.4297	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$420$	2.81776	0.137493
$421$	36.3478	1.77148	0.885742	−	0.464178i	$-0.153650\pi$
$421$	36.3478	1.77148	0.885742	+	0.464178i	$0.153650\pi$
$422$	44.2088	2.15205
$423$	4.25799	0.207031
$424$	2.94018	0.142788
$425$	−4.81179	−0.233406
$426$	−48.5259	−2.35109
$427$	−3.90879	−0.189160
$428$	10.7949	0.521793
$429$	−2.73957	−0.132268
$430$	−5.95163	−0.287013
$431$	9.80739	0.472406	0.236203	−	0.971704i	$-0.424097\pi$
$431$	9.80739	0.472406	0.236203	+	0.971704i	$0.424097\pi$
$432$	18.5734	0.893611
$433$	16.2718	0.781971	0.390986	−	0.920397i	$-0.372134\pi$
$433$	16.2718	0.781971	0.390986	+	0.920397i	$0.372134\pi$
$434$	−1.27664	−0.0612805
$435$	34.2941	1.64428
$436$	5.14195	0.246255
$437$	−14.3020	−0.684156
$438$	38.5593	1.84243
$439$	−13.4609	−0.642452	−0.321226	−	0.947003i	$-0.604095\pi$
$439$	−13.4609	−0.642452	−0.321226	+	0.947003i	$0.604095\pi$
$440$	−2.32037	−0.110619
$441$	−6.85947	−0.326642
$442$	−2.60557	−0.123934
$443$	−40.5473	−1.92646	−0.963230	−	0.268678i	$-0.913413\pi$
$443$	−40.5473	−1.92646	−0.963230	+	0.268678i	$0.913413\pi$
$444$	−20.7413	−0.984338
$445$	−34.8713	−1.65306
$446$	−16.5467	−0.783508
$447$	−16.7027	−0.790013
$448$	1.29658	0.0612577
$449$	34.2317	1.61549	0.807747	−	0.589529i	$-0.200687\pi$
$449$	34.2317	1.61549	0.807747	+	0.589529i	$0.200687\pi$
$450$	−9.06026	−0.427105
$451$	5.16443	0.243183
$452$	4.22848	0.198891
$453$	−22.5337	−1.05872
$454$	39.1790	1.83876
$455$	−1.20128	−0.0563169
$456$	3.80004	0.177953
$457$	25.9727	1.21495	0.607476	−	0.794338i	$-0.292182\pi$
$457$	25.9727	1.21495	0.607476	+	0.794338i	$0.292182\pi$
$458$	7.65036	0.357478
$459$	4.01348	0.187333
$460$	28.0909	1.30974
$461$	24.0311	1.11924	0.559621	−	0.828749i	$-0.310947\pi$
$461$	24.0311	1.11924	0.559621	+	0.828749i	$0.310947\pi$
$462$	1.06153	0.0493867
$463$	26.7137	1.24149	0.620745	−	0.784012i	$-0.286830\pi$
$463$	26.7137	1.24149	0.620745	+	0.784012i	$0.286830\pi$
$464$	25.3615	1.17738
$465$	15.0346	0.697213
$466$	−7.51920	−0.348320
$467$	18.5449	0.858157	0.429079	−	0.903267i	$-0.358838\pi$
$467$	18.5449	0.858157	0.429079	+	0.903267i	$0.358838\pi$
$468$	−2.18814	−0.101147
$469$	2.66387	0.123006
$470$	25.5722	1.17956
$471$	−35.6780	−1.64396
$472$	−0.106093	−0.00488333
$473$	−1.00000	−0.0459800
$474$	−9.14776	−0.420170
$475$	12.3558	0.566925
$476$	0.450287	0.0206389
$477$	3.93336	0.180096
$478$	−32.5592	−1.48923
$479$	−24.3418	−1.11221	−0.556103	−	0.831114i	$-0.687704\pi$
$479$	−24.3418	−1.11221	−0.556103	+	0.831114i	$0.687704\pi$
$480$	−45.7521	−2.08829
$481$	8.84252	0.403184
$482$	1.28450	0.0585072
$483$	3.11172	0.141588
$484$	1.61013	0.0731877
$485$	24.7477	1.12373
$486$	18.8419	0.854688
$487$	−14.3721	−0.651262	−0.325631	−	0.945497i	$-0.605577\pi$
$487$	−14.3721	−0.651262	−0.325631	+	0.945497i	$0.605577\pi$
$488$	10.3537	0.468690
$489$	−26.9343	−1.21801
$490$	−41.1959	−1.86104
$491$	−37.5048	−1.69257	−0.846285	−	0.532731i	$-0.821166\pi$
$491$	−37.5048	−1.69257	−0.846285	+	0.532731i	$0.821166\pi$
$492$	16.6121	0.748930
$493$	5.48031	0.246821
$494$	6.69065	0.301027
$495$	−3.10418	−0.139522
$496$	11.1185	0.499236
$497$	−3.57520	−0.160370
$498$	51.8492	2.32342
$499$	37.0309	1.65773	0.828866	−	0.559447i	$-0.188987\pi$
$499$	37.0309	1.65773	0.828866	+	0.559447i	$0.188987\pi$
$500$	0.949223	0.0424506
$501$	−1.44226	−0.0644353
$502$	−56.8364	−2.53673
$503$	−10.1466	−0.452412	−0.226206	−	0.974079i	$-0.572632\pi$
$503$	−10.1466	−0.452412	−0.226206	+	0.974079i	$0.572632\pi$
$504$	−0.205297	−0.00914466
$505$	−29.7664	−1.32459
$506$	10.5826	0.470453
$507$	−22.2139	−0.986552
$508$	29.1651	1.29399
$509$	11.4821	0.508935	0.254467	−	0.967081i	$-0.418100\pi$
$509$	11.4821	0.508935	0.254467	+	0.967081i	$0.418100\pi$
$510$	−11.8898	−0.526491
$511$	2.84090	0.125674
$512$	−26.9788	−1.19231
$513$	−10.3059	−0.455017
$514$	−42.4979	−1.87450
$515$	−36.0078	−1.58669
$516$	−3.21663	−0.141604
$517$	4.29668	0.188968
$518$	−3.42629	−0.150543
$519$	−49.7822	−2.18520
$520$	3.18199	0.139539
$521$	−29.6638	−1.29960	−0.649798	−	0.760107i	$-0.725147\pi$
$521$	−29.6638	−1.29960	−0.649798	+	0.760107i	$0.725147\pi$
$522$	10.3190	0.451651
$523$	−18.4904	−0.808530	−0.404265	−	0.914642i	$-0.632473\pi$
$523$	−18.4904	−0.808530	−0.404265	+	0.914642i	$0.632473\pi$
$524$	−1.01191	−0.0442054
$525$	−2.68829	−0.117327
$526$	14.4624	0.630591
$527$	2.40258	0.104658
$528$	−9.24506	−0.402340
$529$	8.02138	0.348756
$530$	23.6226	1.02610
$531$	−0.141931	−0.00615927
$532$	−1.15626	−0.0501301
$533$	−7.08213	−0.306761
$534$	−42.2567	−1.82863
$535$	−21.0007	−0.907939
$536$	−7.05612	−0.304778
$537$	6.99655	0.301923
$538$	−11.8102	−0.509173
$539$	−6.92179	−0.298143
$540$	20.2421	0.871083
$541$	39.8199	1.71199	0.855996	−	0.516982i	$-0.172945\pi$
$541$	39.8199	1.71199	0.855996	+	0.516982i	$0.172945\pi$
$542$	50.8910	2.18596
$543$	1.18674	0.0509277
$544$	−7.31133	−0.313471
$545$	−10.0033	−0.428493
$546$	−1.45570	−0.0622983
$547$	−22.4465	−0.959743	−0.479871	−	0.877339i	$-0.659317\pi$
$547$	−22.4465	−0.959743	−0.479871	+	0.877339i	$0.659317\pi$
$548$	−10.0963	−0.431291
$549$	13.8512	0.591153
$550$	−9.14257	−0.389841
$551$	−14.0725	−0.599507
$552$	−8.24240	−0.350820
$553$	−0.673971	−0.0286602
$554$	−26.3776	−1.12068
$555$	40.3505	1.71278
$556$	20.5209	0.870279
$557$	44.2445	1.87470	0.937351	−	0.348387i	$-0.113271\pi$
$557$	44.2445	1.87470	0.937351	+	0.348387i	$0.113271\pi$
$558$	4.52388	0.191511
$559$	1.37133	0.0580011
$560$	−4.05389	−0.171308
$561$	−1.99775	−0.0843450
$562$	−3.18541	−0.134369
$563$	−3.57926	−0.150848	−0.0754240	−	0.997152i	$-0.524031\pi$
$563$	−3.57926	−0.150848	−0.0754240	+	0.997152i	$0.524031\pi$
$564$	13.8208	0.581962
$565$	−8.22618	−0.346078
$566$	10.7009	0.449794
$567$	3.07371	0.129084
$568$	9.47009	0.397356
$569$	−20.4397	−0.856877	−0.428438	−	0.903571i	$-0.640936\pi$
$569$	−20.4397	−0.856877	−0.428438	+	0.903571i	$0.640936\pi$
$570$	30.5310	1.27880
$571$	−16.8035	−0.703206	−0.351603	−	0.936149i	$-0.614363\pi$
$571$	−16.8035	−0.703206	−0.351603	+	0.936149i	$0.614363\pi$
$572$	−2.20802	−0.0923219
$573$	−7.42388	−0.310137
$574$	2.74418	0.114540
$575$	−26.8002	−1.11764
$576$	−4.59455	−0.191440
$577$	−42.8148	−1.78240	−0.891202	−	0.453607i	$-0.850137\pi$
$577$	−42.8148	−1.78240	−0.891202	+	0.453607i	$0.850137\pi$
$578$	−1.90003	−0.0790310
$579$	−14.1524	−0.588153
$580$	27.6401	1.14769
$581$	3.82004	0.158482
$582$	29.9890	1.24308
$583$	3.96910	0.164383
$584$	−7.52505	−0.311389
$585$	4.25685	0.175999
$586$	−51.3735	−2.12222
$587$	−2.15540	−0.0889628	−0.0444814	−	0.999010i	$-0.514164\pi$
$587$	−2.15540	−0.0889628	−0.0444814	+	0.999010i	$0.514164\pi$
$588$	−22.2649	−0.918187
$589$	−6.16939	−0.254205
$590$	−0.852394	−0.0350925
$591$	40.0084	1.64573
$592$	29.8403	1.22643
$593$	−29.3176	−1.20393	−0.601964	−	0.798523i	$-0.705615\pi$
$593$	−29.3176	−1.20393	−0.601964	+	0.798523i	$0.705615\pi$
$594$	7.62575	0.312888
$595$	−0.875997	−0.0359124
$596$	−13.4619	−0.551423
$597$	16.7520	0.685614
$598$	−14.5122	−0.593449
$599$	−18.9069	−0.772515	−0.386258	−	0.922391i	$-0.626232\pi$
$599$	−18.9069	−0.772515	−0.386258	+	0.922391i	$0.626232\pi$
$600$	7.12082	0.290706
$601$	37.3438	1.52329	0.761643	−	0.647997i	$-0.224393\pi$
$601$	37.3438	1.52329	0.761643	+	0.647997i	$0.224393\pi$
$602$	−0.531361	−0.0216567
$603$	−9.43966	−0.384413
$604$	−18.1615	−0.738981
$605$	−3.13238	−0.127349
$606$	−36.0707	−1.46527
$607$	8.78314	0.356497	0.178248	−	0.983986i	$-0.442957\pi$
$607$	8.78314	0.356497	0.178248	+	0.983986i	$0.442957\pi$
$608$	18.7742	0.761395
$609$	3.06178	0.124070
$610$	83.1858	3.36810
$611$	−5.89216	−0.238371
$612$	−1.59563	−0.0644996
$613$	−3.76203	−0.151947	−0.0759735	−	0.997110i	$-0.524206\pi$
$613$	−3.76203	−0.151947	−0.0759735	+	0.997110i	$0.524206\pi$
$614$	−12.7417	−0.514215
$615$	−32.3174	−1.30317
$616$	−0.207162	−0.00834681
$617$	25.6242	1.03159	0.515795	−	0.856712i	$-0.327496\pi$
$617$	25.6242	1.03159	0.515795	+	0.856712i	$0.327496\pi$
$618$	−43.6339	−1.75521
$619$	45.8942	1.84465	0.922323	−	0.386421i	$-0.126289\pi$
$619$	45.8942	1.84465	0.922323	+	0.386421i	$0.126289\pi$
$620$	12.1175	0.486650
$621$	22.3538	0.897028
$622$	−53.7767	−2.15625
$623$	−3.11331	−0.124732
$624$	12.6780	0.507527
$625$	−25.9056	−1.03622
$626$	8.70502	0.347922
$627$	5.12986	0.204867
$628$	−28.7555	−1.14747
$629$	6.44814	0.257104
$630$	−1.64944	−0.0657152
$631$	−2.73597	−0.108917	−0.0544586	−	0.998516i	$-0.517343\pi$
$631$	−2.73597	−0.108917	−0.0544586	+	0.998516i	$0.517343\pi$
$632$	1.78523	0.0710127
$633$	−46.4824	−1.84751
$634$	−0.311799	−0.0123831
$635$	−56.7384	−2.25159
$636$	12.7671	0.506250
$637$	9.49206	0.376089
$638$	10.4128	0.412246
$639$	12.6690	0.501180
$640$	18.2102	0.719823
$641$	18.1921	0.718546	0.359273	−	0.933232i	$-0.383025\pi$
$641$	18.1921	0.718546	0.359273	+	0.933232i	$0.383025\pi$
$642$	−25.4484	−1.00437
$643$	−17.0303	−0.671608	−0.335804	−	0.941932i	$-0.609008\pi$
$643$	−17.0303	−0.671608	−0.335804	+	0.941932i	$0.609008\pi$
$644$	2.50796	0.0988273
$645$	6.25770	0.246397
$646$	4.87895	0.191960
$647$	40.3693	1.58708	0.793541	−	0.608517i	$-0.208235\pi$
$647$	40.3693	1.58708	0.793541	+	0.608517i	$0.208235\pi$
$648$	−8.14172	−0.319837
$649$	−0.143220	−0.00562189
$650$	12.5375	0.491761
$651$	1.34229	0.0526085
$652$	−21.7083	−0.850164
$653$	5.90276	0.230993	0.115496	−	0.993308i	$-0.463154\pi$
$653$	5.90276	0.230993	0.115496	+	0.993308i	$0.463154\pi$
$654$	−12.1219	−0.474002
$655$	1.96859	0.0769191
$656$	−23.8996	−0.933124
$657$	−10.0670	−0.392750
$658$	2.28309	0.0890040
$659$	−42.7007	−1.66338	−0.831692	−	0.555237i	$-0.812628\pi$
$659$	−42.7007	−1.66338	−0.831692	+	0.555237i	$0.812628\pi$
$660$	−10.0757	−0.392196
$661$	26.4725	1.02966	0.514831	−	0.857291i	$-0.327855\pi$
$661$	26.4725	1.02966	0.514831	+	0.857291i	$0.327855\pi$
$662$	8.37561	0.325527
$663$	2.73957	0.106396
$664$	−10.1186	−0.392679
$665$	2.24941	0.0872282
$666$	12.1414	0.470469
$667$	30.5236	1.18188
$668$	−1.16242	−0.0449754
$669$	17.3976	0.672632
$670$	−56.6917	−2.19019
$671$	13.9770	0.539576
$672$	−4.08475	−0.157573
$673$	−44.0528	−1.69811	−0.849055	−	0.528305i	$-0.822828\pi$
$673$	−44.0528	−1.69811	−0.849055	+	0.528305i	$0.822828\pi$
$674$	−55.0821	−2.12168
$675$	−19.3120	−0.743321
$676$	−17.9038	−0.688606
$677$	26.1405	1.00466	0.502330	−	0.864676i	$-0.332476\pi$
$677$	26.1405	1.00466	0.502330	+	0.864676i	$0.332476\pi$
$678$	−9.96841	−0.382834
$679$	2.20947	0.0847917
$680$	2.32037	0.0889820
$681$	−41.1939	−1.57855
$682$	4.56498	0.174802
$683$	1.02576	0.0392496	0.0196248	−	0.999807i	$-0.493753\pi$
$683$	1.02576	0.0392496	0.0196248	+	0.999807i	$0.493753\pi$
$684$	4.09730	0.156664
$685$	19.6415	0.750463
$686$	−7.39750	−0.282438
$687$	−8.04380	−0.306890
$688$	4.62774	0.176431
$689$	−5.44294	−0.207360
$690$	−66.2227	−2.52105
$691$	29.8452	1.13536	0.567682	−	0.823248i	$-0.307840\pi$
$691$	29.8452	1.13536	0.567682	+	0.823248i	$0.307840\pi$
$692$	−40.1230	−1.52525
$693$	−0.277141	−0.0105277
$694$	−50.1874	−1.90509
$695$	−39.9217	−1.51432
$696$	−8.11013	−0.307414
$697$	−5.16443	−0.195617
$698$	−0.500677	−0.0189509
$699$	7.90590	0.299028
$700$	−2.16669	−0.0818931
$701$	−48.2659	−1.82298	−0.911489	−	0.411325i	$-0.865066\pi$
$701$	−48.2659	−1.82298	−0.911489	+	0.411325i	$0.865066\pi$
$702$	−10.4574	−0.394690
$703$	−16.5577	−0.624485
$704$	−4.63629	−0.174737
$705$	−26.8873	−1.01263
$706$	46.9157	1.76570
$707$	−2.65755	−0.0999473
$708$	−0.460687	−0.0173137
$709$	−37.0975	−1.39323	−0.696613	−	0.717447i	$-0.745310\pi$
$709$	−37.0975	−1.39323	−0.696613	+	0.717447i	$0.745310\pi$
$710$	76.0865	2.85547
$711$	2.38828	0.0895674
$712$	8.24662	0.309055
$713$	13.3816	0.501145
$714$	−1.06153	−0.0397266
$715$	4.29552	0.160643
$716$	5.63902	0.210740
$717$	34.2337	1.27848
$718$	−52.9186	−1.97491
$719$	9.31302	0.347317	0.173658	−	0.984806i	$-0.444441\pi$
$719$	9.31302	0.347317	0.173658	+	0.984806i	$0.444441\pi$
$720$	14.3653	0.535364
$721$	−3.21478	−0.119725
$722$	23.5724	0.877272
$723$	−1.35055	−0.0502276
$724$	0.956475	0.0355471
$725$	−26.3701	−0.979362
$726$	−3.79579	−0.140875
$727$	−15.5708	−0.577490	−0.288745	−	0.957406i	$-0.593238\pi$
$727$	−15.5708	−0.577490	−0.288745	+	0.957406i	$0.593238\pi$
$728$	0.284088	0.0105290
$729$	13.1618	0.487475
$730$	−60.4592	−2.23770
$731$	1.00000	0.0369863
$732$	44.9589	1.66173
$733$	−4.38913	−0.162116	−0.0810581	−	0.996709i	$-0.525830\pi$
$733$	−4.38913	−0.162116	−0.0810581	+	0.996709i	$0.525830\pi$
$734$	−56.9485	−2.10201
$735$	43.3145	1.59768
$736$	−40.7218	−1.50103
$737$	−9.52542	−0.350873
$738$	−9.72424	−0.357954
$739$	7.84489	0.288579	0.144290	−	0.989536i	$-0.453910\pi$
$739$	7.84489	0.288579	0.144290	+	0.989536i	$0.453910\pi$
$740$	32.5214	1.19551
$741$	−7.03474	−0.258427
$742$	2.10903	0.0774248
$743$	31.9285	1.17134	0.585672	−	0.810548i	$-0.300831\pi$
$743$	31.9285	1.17134	0.585672	+	0.810548i	$0.300831\pi$
$744$	−3.55550	−0.130351
$745$	26.1892	0.959496
$746$	−5.03066	−0.184186
$747$	−13.5367	−0.495281
$748$	−1.61013	−0.0588721
$749$	−1.87494	−0.0685089
$750$	−2.23774	−0.0817107
$751$	34.5510	1.26078	0.630391	−	0.776278i	$-0.282894\pi$
$751$	34.5510	1.26078	0.630391	+	0.776278i	$0.282894\pi$
$752$	−19.8839	−0.725091
$753$	59.7593	2.17775
$754$	−14.2793	−0.520023
$755$	35.3318	1.28585
$756$	1.80722	0.0657279
$757$	−17.3235	−0.629634	−0.314817	−	0.949152i	$-0.601943\pi$
$757$	−17.3235	−0.629634	−0.314817	+	0.949152i	$0.601943\pi$
$758$	−37.4514	−1.36030
$759$	−11.1268	−0.403878
$760$	−5.95829	−0.216130
$761$	20.2802	0.735156	0.367578	−	0.929993i	$-0.380187\pi$
$761$	20.2802	0.735156	0.367578	+	0.929993i	$0.380187\pi$
$762$	−68.7551	−2.49073
$763$	−0.893092	−0.0323321
$764$	−5.98344	−0.216473
$765$	3.10418	0.112232
$766$	−48.9644	−1.76916
$767$	0.196402	0.00709168
$768$	40.5913	1.46471
$769$	12.8641	0.463893	0.231947	−	0.972729i	$-0.425491\pi$
$769$	12.8641	0.463893	0.231947	+	0.972729i	$0.425491\pi$
$770$	−1.66442	−0.0599817
$771$	44.6835	1.60924
$772$	−11.4064	−0.410526
$773$	32.9580	1.18542	0.592708	−	0.805418i	$-0.298059\pi$
$773$	32.9580	1.18542	0.592708	+	0.805418i	$0.298059\pi$
$774$	1.88293	0.0676804
$775$	−11.5607	−0.415273
$776$	−5.85251	−0.210093
$777$	3.60250	0.129239
$778$	44.4648	1.59414
$779$	13.2613	0.475137
$780$	13.8171	0.494732
$781$	12.7841	0.457453
$782$	−10.5826	−0.378433
$783$	21.9951	0.786042
$784$	32.0323	1.14401
$785$	55.9415	1.99664
$786$	2.38552	0.0850886
$787$	−52.9292	−1.88672	−0.943362	−	0.331766i	$-0.892356\pi$
$787$	−52.9292	−1.88672	−0.943362	+	0.331766i	$0.892356\pi$
$788$	32.2457	1.14870
$789$	−15.2062	−0.541354
$790$	14.3433	0.510311
$791$	−0.734433	−0.0261134
$792$	0.734099	0.0260851
$793$	−19.1671	−0.680643
$794$	−16.4847	−0.585020
$795$	−24.8374	−0.880893
$796$	13.5017	0.478553
$797$	−25.4421	−0.901206	−0.450603	−	0.892724i	$-0.648791\pi$
$797$	−25.4421	−0.901206	−0.450603	+	0.892724i	$0.648791\pi$
$798$	2.72581	0.0964927
$799$	−4.29668	−0.152005
$800$	35.1806	1.24382
$801$	11.0323	0.389807
$802$	−16.7409	−0.591140
$803$	−10.1584	−0.358484
$804$	−30.6398	−1.08058
$805$	−4.87903	−0.171963
$806$	−6.26009	−0.220502
$807$	12.4175	0.437118
$808$	7.03938	0.247644
$809$	9.92790	0.349046	0.174523	−	0.984653i	$-0.444162\pi$
$809$	9.92790	0.349046	0.174523	+	0.984653i	$0.444162\pi$
$810$	−65.4138	−2.29841
$811$	−28.9800	−1.01763	−0.508813	−	0.860877i	$-0.669916\pi$
$811$	−28.9800	−1.01763	−0.508813	+	0.860877i	$0.669916\pi$
$812$	2.46771	0.0865997
$813$	−53.5082	−1.87661
$814$	12.2517	0.429421
$815$	42.2318	1.47932
$816$	9.24506	0.323642
$817$	−2.56782	−0.0898368
$818$	−4.66373	−0.163064
$819$	0.380052	0.0132801
$820$	−26.0470	−0.909599
$821$	29.2870	1.02212	0.511062	−	0.859544i	$-0.329252\pi$
$821$	29.2870	1.02212	0.511062	+	0.859544i	$0.329252\pi$
$822$	23.8014	0.830169
$823$	18.1532	0.632779	0.316390	−	0.948629i	$-0.397529\pi$
$823$	18.1532	0.632779	0.316390	+	0.948629i	$0.397529\pi$
$824$	8.51539	0.296648
$825$	9.61275	0.334673
$826$	−0.0761017	−0.00264792
$827$	48.4707	1.68549	0.842746	−	0.538311i	$-0.180937\pi$
$827$	48.4707	1.68549	0.842746	+	0.538311i	$0.180937\pi$
$828$	−8.88717	−0.308851
$829$	−31.1040	−1.08029	−0.540143	−	0.841573i	$-0.681630\pi$
$829$	−31.1040	−1.08029	−0.540143	+	0.841573i	$0.681630\pi$
$830$	−81.2971	−2.82186
$831$	27.7341	0.962086
$832$	6.35789	0.220420
$833$	6.92179	0.239826
$834$	−48.3768	−1.67515
$835$	2.26140	0.0782588
$836$	4.13453	0.142996
$837$	9.64270	0.333300
$838$	−57.8175	−1.99727
$839$	39.7144	1.37109	0.685546	−	0.728029i	$-0.259563\pi$
$839$	39.7144	1.37109	0.685546	+	0.728029i	$0.259563\pi$
$840$	1.29636	0.0447287
$841$	1.03379	0.0356481
$842$	−69.0621	−2.38004
$843$	3.34923	0.115354
$844$	−37.4635	−1.28955
$845$	34.8303	1.19820
$846$	−8.09033	−0.278151
$847$	−0.279659	−0.00960919
$848$	−18.3680	−0.630759
$849$	−11.2512	−0.386142
$850$	9.14257	0.313588
$851$	35.9141	1.23112
$852$	41.1219	1.40881
$853$	−23.3520	−0.799557	−0.399778	−	0.916612i	$-0.630913\pi$
$853$	−23.3520	−0.799557	−0.399778	+	0.916612i	$0.630913\pi$
$854$	7.42684	0.254141
$855$	−7.97098	−0.272602
$856$	4.96640	0.169748
$857$	57.5931	1.96734	0.983671	−	0.179975i	$-0.0576017\pi$
$857$	57.5931	1.96734	0.983671	+	0.179975i	$0.0576017\pi$
$858$	5.20528	0.177705
$859$	23.9841	0.818326	0.409163	−	0.912461i	$-0.365821\pi$
$859$	23.9841	0.818326	0.409163	+	0.912461i	$0.365821\pi$
$860$	5.04353	0.171983
$861$	−2.88530	−0.0983309
$862$	−18.6344	−0.634690
$863$	28.1685	0.958867	0.479433	−	0.877578i	$-0.340842\pi$
$863$	28.1685	0.958867	0.479433	+	0.877578i	$0.340842\pi$
$864$	−29.3439	−0.998300
$865$	78.0562	2.65399
$866$	−30.9169	−1.05060
$867$	1.99775	0.0678471
$868$	1.08185	0.0367203
$869$	2.40998	0.0817528
$870$	−65.1600	−2.20913
$871$	13.0625	0.442605
$872$	2.36565	0.0801109
$873$	−7.82947	−0.264987
$874$	27.1742	0.919182
$875$	−0.164868	−0.00557355
$876$	−32.6760	−1.10402
$877$	−27.4867	−0.928159	−0.464079	−	0.885794i	$-0.653615\pi$
$877$	−27.4867	−0.928159	−0.464079	+	0.885794i	$0.653615\pi$
$878$	25.5761	0.863152
$879$	54.0155	1.82190
$880$	14.4958	0.488655
$881$	11.4034	0.384190	0.192095	−	0.981376i	$-0.438472\pi$
$881$	11.4034	0.384190	0.192095	+	0.981376i	$0.438472\pi$
$882$	13.0332	0.438852
$883$	−17.3540	−0.584010	−0.292005	−	0.956417i	$-0.594322\pi$
$883$	−17.3540	−0.584010	−0.292005	+	0.956417i	$0.594322\pi$
$884$	2.20802	0.0742637
$885$	0.896230	0.0301264
$886$	77.0412	2.58825
$887$	0.928728	0.0311836	0.0155918	−	0.999878i	$-0.495037\pi$
$887$	0.928728	0.0311836	0.0155918	+	0.999878i	$0.495037\pi$
$888$	−9.54239	−0.320222
$889$	−5.06560	−0.169895
$890$	66.2567	2.22093
$891$	−10.9909	−0.368210
$892$	14.0220	0.469492
$893$	11.0331	0.369209
$894$	31.7358	1.06140
$895$	−10.9703	−0.366696
$896$	1.62581	0.0543145
$897$	15.2585	0.509468
$898$	−65.0414	−2.17046
$899$	13.1669	0.439140
$900$	7.67786	0.255929
$901$	−3.96910	−0.132230
$902$	−9.81259	−0.326723
$903$	0.558688	0.0185920
$904$	1.94539	0.0647026
$905$	−1.86075	−0.0618533
$906$	42.8147	1.42242
$907$	−43.7530	−1.45279	−0.726397	−	0.687276i	$-0.758806\pi$
$907$	−43.7530	−1.45279	−0.726397	+	0.687276i	$0.758806\pi$
$908$	−33.2011	−1.10182
$909$	9.41726	0.312351
$910$	2.28248	0.0756633
$911$	−5.46050	−0.180914	−0.0904572	−	0.995900i	$-0.528833\pi$
$911$	−5.46050	−0.180914	−0.0904572	+	0.995900i	$0.528833\pi$
$912$	−23.7397	−0.786100
$913$	−13.6597	−0.452068
$914$	−49.3490	−1.63232
$915$	−87.4639	−2.89147
$916$	−6.48308	−0.214207
$917$	0.175756	0.00580396
$918$	−7.62575	−0.251687
$919$	−39.0785	−1.28908	−0.644540	−	0.764570i	$-0.722951\pi$
$919$	−39.0785	−1.28908	−0.644540	+	0.764570i	$0.722951\pi$
$920$	12.9237	0.426082
$921$	13.3970	0.441447
$922$	−45.6600	−1.50373
$923$	−17.5313	−0.577049
$924$	−0.899560	−0.0295933
$925$	−31.0271	−1.02016
$926$	−50.7569	−1.66798
$927$	11.3919	0.374158
$928$	−40.0684	−1.31531
$929$	8.30350	0.272429	0.136214	−	0.990679i	$-0.456506\pi$
$929$	8.30350	0.272429	0.136214	+	0.990679i	$0.456506\pi$
$930$	−28.5663	−0.936725
$931$	−17.7739	−0.582517
$932$	6.37193	0.208720
$933$	56.5423	1.85111
$934$	−35.2360	−1.15296
$935$	3.13238	0.102440
$936$	−1.00669	−0.0329047
$937$	49.9655	1.63230	0.816152	−	0.577838i	$-0.196103\pi$
$937$	49.9655	1.63230	0.816152	+	0.577838i	$0.196103\pi$
$938$	−5.06144	−0.165262
$939$	−9.15269	−0.298687
$940$	−21.6704	−0.706811
$941$	23.0537	0.751528	0.375764	−	0.926715i	$-0.377380\pi$
$941$	23.0537	0.751528	0.375764	+	0.926715i	$0.377380\pi$
$942$	67.7895	2.20870
$943$	−28.7642	−0.936692
$944$	0.662787	0.0215719
$945$	−3.51580	−0.114369
$946$	1.90003	0.0617754
$947$	35.5679	1.15580	0.577901	−	0.816107i	$-0.303872\pi$
$947$	35.5679	1.15580	0.577901	+	0.816107i	$0.303872\pi$
$948$	7.75200	0.251773
$949$	13.9306	0.452205
$950$	−23.4765	−0.761679
$951$	0.327834	0.0106307
$952$	0.207162	0.00671417
$953$	7.87901	0.255226	0.127613	−	0.991824i	$-0.459268\pi$
$953$	7.87901	0.255226	0.127613	+	0.991824i	$0.459268\pi$
$954$	−7.47353	−0.241964
$955$	11.6403	0.376672
$956$	27.5914	0.892370
$957$	−10.9483	−0.353908
$958$	46.2503	1.49428
$959$	1.75359	0.0566265
$960$	29.0125	0.936376
$961$	−25.2276	−0.813794
$962$	−16.8011	−0.541689
$963$	6.64403	0.214101
$964$	−1.08851	−0.0350585
$965$	22.1903	0.714331
$966$	−5.91236	−0.190227
$967$	3.79544	0.122053	0.0610265	−	0.998136i	$-0.480563\pi$
$967$	3.79544	0.122053	0.0610265	+	0.998136i	$0.480563\pi$
$968$	0.740768	0.0238092
$969$	−5.12986	−0.164795
$970$	−47.0214	−1.50977
$971$	44.9670	1.44306	0.721529	−	0.692384i	$-0.243439\pi$
$971$	44.9670	1.44306	0.721529	+	0.692384i	$0.243439\pi$
$972$	−15.9671	−0.512144
$973$	−3.56421	−0.114263
$974$	27.3075	0.874989
$975$	−13.1823	−0.422170
$976$	−64.6819	−2.07042
$977$	−3.36134	−0.107539	−0.0537694	−	0.998553i	$-0.517124\pi$
$977$	−3.36134	−0.107539	−0.0537694	+	0.998553i	$0.517124\pi$
$978$	51.1762	1.63643
$979$	11.1325	0.355797
$980$	34.9103	1.11517
$981$	3.16475	0.101043
$982$	71.2605	2.27401
$983$	−33.0578	−1.05438	−0.527190	−	0.849747i	$-0.676754\pi$
$983$	−33.0578	−1.05438	−0.527190	+	0.849747i	$0.676754\pi$
$984$	7.64267	0.243639
$985$	−62.7314	−1.99879
$986$	−10.4128	−0.331610
$987$	−2.40050	−0.0764088
$988$	−5.66980	−0.180380
$989$	5.56968	0.177106
$990$	5.89804	0.187452
$991$	53.9622	1.71417	0.857083	−	0.515178i	$-0.172274\pi$
$991$	53.9622	1.71417	0.857083	+	0.515178i	$0.172274\pi$
$992$	−17.5660	−0.557722
$993$	−8.80635	−0.279461
$994$	6.79300	0.215461
$995$	−26.2664	−0.832701
$996$	−43.9381	−1.39223
$997$	−17.3861	−0.550623	−0.275311	−	0.961355i	$-0.588781\pi$
$997$	−17.3861	−0.550623	−0.275311	+	0.961355i	$0.588781\pi$
$998$	−70.3600	−2.22721
$999$	25.8795	0.818790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.15	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.15	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +O(q^{10})\)	\(q-1.90003 q^{2} +1.99775 q^{3} +1.61013 q^{4} -3.13238 q^{5} -3.79579 q^{6} -0.279659 q^{7} +0.740768 q^{8} +0.990997 q^{9} +5.95163 q^{10} +1.00000 q^{11} +3.21663 q^{12} -1.37133 q^{13} +0.531361 q^{14} -6.25770 q^{15} -4.62774 q^{16} -1.00000 q^{17} -1.88293 q^{18} +2.56782 q^{19} -5.04353 q^{20} -0.558688 q^{21} -1.90003 q^{22} -5.56968 q^{23} +1.47987 q^{24} +4.81179 q^{25} +2.60557 q^{26} -4.01348 q^{27} -0.450287 q^{28} -5.48031 q^{29} +11.8898 q^{30} -2.40258 q^{31} +7.31133 q^{32} +1.99775 q^{33} +1.90003 q^{34} +0.875997 q^{35} +1.59563 q^{36} -6.44814 q^{37} -4.87895 q^{38} -2.73957 q^{39} -2.32037 q^{40} +5.16443 q^{41} +1.06153 q^{42} -1.00000 q^{43} +1.61013 q^{44} -3.10418 q^{45} +10.5826 q^{46} +4.29668 q^{47} -9.24506 q^{48} -6.92179 q^{49} -9.14257 q^{50} -1.99775 q^{51} -2.20802 q^{52} +3.96910 q^{53} +7.62575 q^{54} -3.13238 q^{55} -0.207162 q^{56} +5.12986 q^{57} +10.4128 q^{58} -0.143220 q^{59} -10.0757 q^{60} +13.9770 q^{61} +4.56498 q^{62} -0.277141 q^{63} -4.63629 q^{64} +4.29552 q^{65} -3.79579 q^{66} -9.52542 q^{67} -1.61013 q^{68} -11.1268 q^{69} -1.66442 q^{70} +12.7841 q^{71} +0.734099 q^{72} -10.1584 q^{73} +12.2517 q^{74} +9.61275 q^{75} +4.13453 q^{76} -0.279659 q^{77} +5.20528 q^{78} +2.40998 q^{79} +14.4958 q^{80} -10.9909 q^{81} -9.81259 q^{82} -13.6597 q^{83} -0.899560 q^{84} +3.13238 q^{85} +1.90003 q^{86} -10.9483 q^{87} +0.740768 q^{88} +11.1325 q^{89} +5.89804 q^{90} +0.383505 q^{91} -8.96791 q^{92} -4.79974 q^{93} -8.16383 q^{94} -8.04339 q^{95} +14.6062 q^{96} -7.90060 q^{97} +13.1516 q^{98} +0.990997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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