LMFDB - Embedded newform 6041.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79680 q^{2} +0.970719 q^{3} +1.22848 q^{4} -1.22425 q^{5} -1.74419 q^{6} +1.00000 q^{7} +1.38627 q^{8} -2.05770 q^{9} +O(q^{10})$	\(q-1.79680 q^{2} +0.970719 q^{3} +1.22848 q^{4} -1.22425 q^{5} -1.74419 q^{6} +1.00000 q^{7} +1.38627 q^{8} -2.05770 q^{9} +2.19973 q^{10} -2.12253 q^{11} +1.19251 q^{12} +4.74770 q^{13} -1.79680 q^{14} -1.18840 q^{15} -4.94780 q^{16} +5.05015 q^{17} +3.69728 q^{18} -3.21336 q^{19} -1.50397 q^{20} +0.970719 q^{21} +3.81376 q^{22} +5.40901 q^{23} +1.34568 q^{24} -3.50121 q^{25} -8.53065 q^{26} -4.90961 q^{27} +1.22848 q^{28} -1.89652 q^{29} +2.13532 q^{30} +2.28810 q^{31} +6.11766 q^{32} -2.06038 q^{33} -9.07409 q^{34} -1.22425 q^{35} -2.52785 q^{36} -10.1869 q^{37} +5.77376 q^{38} +4.60868 q^{39} -1.69714 q^{40} -3.86606 q^{41} -1.74419 q^{42} +9.60699 q^{43} -2.60748 q^{44} +2.51915 q^{45} -9.71889 q^{46} -9.74375 q^{47} -4.80292 q^{48} +1.00000 q^{49} +6.29096 q^{50} +4.90228 q^{51} +5.83245 q^{52} -1.91705 q^{53} +8.82157 q^{54} +2.59851 q^{55} +1.38627 q^{56} -3.11927 q^{57} +3.40766 q^{58} +3.93101 q^{59} -1.45993 q^{60} -10.8204 q^{61} -4.11125 q^{62} -2.05770 q^{63} -1.09659 q^{64} -5.81237 q^{65} +3.70209 q^{66} -6.12868 q^{67} +6.20400 q^{68} +5.25063 q^{69} +2.19973 q^{70} +2.43210 q^{71} -2.85252 q^{72} +3.48438 q^{73} +18.3038 q^{74} -3.39869 q^{75} -3.94755 q^{76} -2.12253 q^{77} -8.28087 q^{78} +12.8650 q^{79} +6.05734 q^{80} +1.40726 q^{81} +6.94653 q^{82} +13.8222 q^{83} +1.19251 q^{84} -6.18265 q^{85} -17.2618 q^{86} -1.84099 q^{87} -2.94239 q^{88} -8.39583 q^{89} -4.52639 q^{90} +4.74770 q^{91} +6.64486 q^{92} +2.22110 q^{93} +17.5075 q^{94} +3.93396 q^{95} +5.93853 q^{96} +2.65308 q^{97} -1.79680 q^{98} +4.36754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−1.79680	−1.27053	−0.635264	−	0.772295i	$-0.719109\pi$
$2$	−1.79680	−1.27053	−0.635264	+	0.772295i	$0.719109\pi$
$3$	0.970719	0.560445	0.280223	−	0.959935i	$-0.409592\pi$
$3$	0.970719	0.560445	0.280223	+	0.959935i	$0.409592\pi$
$4$	1.22848	0.614240
$5$	−1.22425	−0.547501	−0.273751	−	0.961801i	$-0.588264\pi$
$5$	−1.22425	−0.547501	−0.273751	+	0.961801i	$0.588264\pi$
$6$	−1.74419	−0.712061
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.38627	0.490119
$9$	−2.05770	−0.685901
$10$	2.19973	0.695616
$11$	−2.12253	−0.639967	−0.319983	−	0.947423i	$-0.603677\pi$
$11$	−2.12253	−0.639967	−0.319983	+	0.947423i	$0.603677\pi$
$12$	1.19251	0.344248
$13$	4.74770	1.31677	0.658387	−	0.752679i	$-0.271239\pi$
$13$	4.74770	1.31677	0.658387	+	0.752679i	$0.271239\pi$
$14$	−1.79680	−0.480214
$15$	−1.18840	−0.306845
$16$	−4.94780	−1.23695
$17$	5.05015	1.22484	0.612420	−	0.790532i	$-0.290196\pi$
$17$	5.05015	1.22484	0.612420	+	0.790532i	$0.290196\pi$
$18$	3.69728	0.871456
$19$	−3.21336	−0.737195	−0.368598	−	0.929589i	$-0.620162\pi$
$19$	−3.21336	−0.737195	−0.368598	+	0.929589i	$0.620162\pi$
$20$	−1.50397	−0.336297
$21$	0.970719	0.211828
$22$	3.81376	0.813095
$23$	5.40901	1.12786	0.563928	−	0.825824i	$-0.309289\pi$
$23$	5.40901	1.12786	0.563928	+	0.825824i	$0.309289\pi$
$24$	1.34568	0.274685
$25$	−3.50121	−0.700242
$26$	−8.53065	−1.67300
$27$	−4.90961	−0.944855
$28$	1.22848	0.232161
$29$	−1.89652	−0.352175	−0.176087	−	0.984375i	$-0.556344\pi$
$29$	−1.89652	−0.352175	−0.176087	+	0.984375i	$0.556344\pi$
$30$	2.13532	0.389854
$31$	2.28810	0.410954	0.205477	−	0.978662i	$-0.434125\pi$
$31$	2.28810	0.410954	0.205477	+	0.978662i	$0.434125\pi$
$32$	6.11766	1.08146
$33$	−2.06038	−0.358666
$34$	−9.07409	−1.55619
$35$	−1.22425	−0.206936
$36$	−2.52785	−0.421308
$37$	−10.1869	−1.67471	−0.837356	−	0.546657i	$-0.815900\pi$
$37$	−10.1869	−1.67471	−0.837356	+	0.546657i	$0.815900\pi$
$38$	5.77376	0.936627
$39$	4.60868	0.737980
$40$	−1.69714	−0.268341
$41$	−3.86606	−0.603778	−0.301889	−	0.953343i	$-0.597617\pi$
$41$	−3.86606	−0.603778	−0.301889	+	0.953343i	$0.597617\pi$
$42$	−1.74419	−0.269134
$43$	9.60699	1.46505	0.732526	−	0.680739i	$-0.238341\pi$
$43$	9.60699	1.46505	0.732526	+	0.680739i	$0.238341\pi$
$44$	−2.60748	−0.393093
$45$	2.51915	0.375532
$46$	−9.71889	−1.43297
$47$	−9.74375	−1.42127	−0.710636	−	0.703560i	$-0.751593\pi$
$47$	−9.74375	−1.42127	−0.710636	+	0.703560i	$0.751593\pi$
$48$	−4.80292	−0.693242
$49$	1.00000	0.142857
$50$	6.29096	0.889677
$51$	4.90228	0.686456
$52$	5.83245	0.808815
$53$	−1.91705	−0.263327	−0.131664	−	0.991294i	$-0.542032\pi$
$53$	−1.91705	−0.263327	−0.131664	+	0.991294i	$0.542032\pi$
$54$	8.82157	1.20046
$55$	2.59851	0.350383
$56$	1.38627	0.185248
$57$	−3.11927	−0.413158
$58$	3.40766	0.447447
$59$	3.93101	0.511774	0.255887	−	0.966707i	$-0.417632\pi$
$59$	3.93101	0.511774	0.255887	+	0.966707i	$0.417632\pi$
$60$	−1.45993	−0.188476
$61$	−10.8204	−1.38540	−0.692702	−	0.721224i	$-0.743580\pi$
$61$	−10.8204	−1.38540	−0.692702	+	0.721224i	$0.743580\pi$
$62$	−4.11125	−0.522129
$63$	−2.05770	−0.259246
$64$	−1.09659	−0.137074
$65$	−5.81237	−0.720936
$66$	3.70209	0.455695
$67$	−6.12868	−0.748737	−0.374369	−	0.927280i	$-0.622141\pi$
$67$	−6.12868	−0.748737	−0.374369	+	0.927280i	$0.622141\pi$
$68$	6.20400	0.752346
$69$	5.25063	0.632102
$70$	2.19973	0.262918
$71$	2.43210	0.288637	0.144318	−	0.989531i	$-0.453901\pi$
$71$	2.43210	0.288637	0.144318	+	0.989531i	$0.453901\pi$
$72$	−2.85252	−0.336173
$73$	3.48438	0.407816	0.203908	−	0.978990i	$-0.434636\pi$
$73$	3.48438	0.407816	0.203908	+	0.978990i	$0.434636\pi$
$74$	18.3038	2.12777
$75$	−3.39869	−0.392447
$76$	−3.94755	−0.452815
$77$	−2.12253	−0.241885
$78$	−8.28087	−0.937624
$79$	12.8650	1.44743	0.723714	−	0.690100i	$-0.242434\pi$
$79$	12.8650	1.44743	0.723714	+	0.690100i	$0.242434\pi$
$80$	6.05734	0.677232
$81$	1.40726	0.156362
$82$	6.94653	0.767116
$83$	13.8222	1.51718	0.758592	−	0.651566i	$-0.225887\pi$
$83$	13.8222	1.51718	0.758592	+	0.651566i	$0.225887\pi$
$84$	1.19251	0.130113
$85$	−6.18265	−0.670602
$86$	−17.2618	−1.86139
$87$	−1.84099	−0.197375
$88$	−2.94239	−0.313660
$89$	−8.39583	−0.889956	−0.444978	−	0.895541i	$-0.646789\pi$
$89$	−8.39583	−0.889956	−0.444978	+	0.895541i	$0.646789\pi$
$90$	−4.52639	−0.477124
$91$	4.74770	0.497694
$92$	6.64486	0.692774
$93$	2.22110	0.230317
$94$	17.5075	1.80577
$95$	3.93396	0.403616
$96$	5.93853	0.606098
$97$	2.65308	0.269380	0.134690	−	0.990888i	$-0.456996\pi$
$97$	2.65308	0.269380	0.134690	+	0.990888i	$0.456996\pi$
$98$	−1.79680	−0.181504
$99$	4.36754	0.438954
$100$	−4.30117	−0.430117
$101$	−3.69046	−0.367215	−0.183607	−	0.983000i	$-0.558778\pi$
$101$	−3.69046	−0.367215	−0.183607	+	0.983000i	$0.558778\pi$
$102$	−8.80839	−0.872161
$103$	18.0536	1.77888	0.889438	−	0.457056i	$-0.151096\pi$
$103$	18.0536	1.77888	0.889438	+	0.457056i	$0.151096\pi$
$104$	6.58157	0.645376
$105$	−1.18840	−0.115976
$106$	3.44455	0.334565
$107$	−19.1085	−1.84729	−0.923646	−	0.383247i	$-0.874806\pi$
$107$	−19.1085	−1.84729	−0.923646	+	0.383247i	$0.874806\pi$
$108$	−6.03136	−0.580368
$109$	−3.89603	−0.373172	−0.186586	−	0.982439i	$-0.559742\pi$
$109$	−3.89603	−0.373172	−0.186586	+	0.982439i	$0.559742\pi$
$110$	−4.66899	−0.445171
$111$	−9.88860	−0.938585
$112$	−4.94780	−0.467523
$113$	−1.94569	−0.183035	−0.0915175	−	0.995803i	$-0.529172\pi$
$113$	−1.94569	−0.183035	−0.0915175	+	0.995803i	$0.529172\pi$
$114$	5.60470	0.524928
$115$	−6.62198	−0.617503
$116$	−2.32983	−0.216320
$117$	−9.76936	−0.903178
$118$	−7.06323	−0.650223
$119$	5.05015	0.462946
$120$	−1.64744	−0.150390
$121$	−6.49487	−0.590442
$122$	19.4420	1.76019
$123$	−3.75286	−0.338384
$124$	2.81088	0.252424
$125$	10.4076	0.930885
$126$	3.69728	0.329380
$127$	−16.5868	−1.47184	−0.735919	−	0.677070i	$-0.763249\pi$
$127$	−16.5868	−1.47184	−0.735919	+	0.677070i	$0.763249\pi$
$128$	−10.2650	−0.907303
$129$	9.32569	0.821082
$130$	10.4437	0.915969
$131$	7.63253	0.666857	0.333428	−	0.942775i	$-0.391794\pi$
$131$	7.63253	0.666857	0.333428	+	0.942775i	$0.391794\pi$
$132$	−2.53114	−0.220307
$133$	−3.21336	−0.278634
$134$	11.0120	0.951291
$135$	6.01059	0.517310
$136$	7.00085	0.600318
$137$	1.19012	0.101679	0.0508393	−	0.998707i	$-0.483810\pi$
$137$	1.19012	0.101679	0.0508393	+	0.998707i	$0.483810\pi$
$138$	−9.43432	−0.803102
$139$	−7.57011	−0.642088	−0.321044	−	0.947064i	$-0.604034\pi$
$139$	−7.57011	−0.642088	−0.321044	+	0.947064i	$0.604034\pi$
$140$	−1.50397	−0.127108
$141$	−9.45845	−0.796545
$142$	−4.36999	−0.366721
$143$	−10.0771	−0.842692
$144$	10.1811	0.848425
$145$	2.32181	0.192816
$146$	−6.26072	−0.518141
$147$	0.970719	0.0800636
$148$	−12.5144	−1.02868
$149$	10.3919	0.851342	0.425671	−	0.904878i	$-0.360038\pi$
$149$	10.3919	0.851342	0.425671	+	0.904878i	$0.360038\pi$
$150$	6.10676	0.498615
$151$	22.3973	1.82267	0.911334	−	0.411667i	$-0.135053\pi$
$151$	22.3973	1.82267	0.911334	+	0.411667i	$0.135053\pi$
$152$	−4.45457	−0.361313
$153$	−10.3917	−0.840120
$154$	3.81376	0.307321
$155$	−2.80120	−0.224998
$156$	5.66167	0.453297
$157$	−20.3914	−1.62741	−0.813705	−	0.581279i	$-0.802553\pi$
$157$	−20.3914	−1.62741	−0.813705	+	0.581279i	$0.802553\pi$
$158$	−23.1158	−1.83900
$159$	−1.86092	−0.147580
$160$	−7.48954	−0.592100
$161$	5.40901	0.426290
$162$	−2.52856	−0.198662
$163$	8.88102	0.695615	0.347807	−	0.937566i	$-0.386926\pi$
$163$	8.88102	0.695615	0.347807	+	0.937566i	$0.386926\pi$
$164$	−4.74938	−0.370864
$165$	2.52242	0.196370
$166$	−24.8357	−1.92762
$167$	6.75339	0.522593	0.261296	−	0.965259i	$-0.415850\pi$
$167$	6.75339	0.522593	0.261296	+	0.965259i	$0.415850\pi$
$168$	1.34568	0.103821
$169$	9.54064	0.733896
$170$	11.1090	0.852018
$171$	6.61214	0.505643
$172$	11.8020	0.899894
$173$	−3.70934	−0.282016	−0.141008	−	0.990008i	$-0.545034\pi$
$173$	−3.70934	−0.282016	−0.141008	+	0.990008i	$0.545034\pi$
$174$	3.30788	0.250770
$175$	−3.50121	−0.264667
$176$	10.5018	0.791607
$177$	3.81591	0.286821
$178$	15.0856	1.13071
$179$	0.722798	0.0540244	0.0270122	−	0.999635i	$-0.491401\pi$
$179$	0.722798	0.0540244	0.0270122	+	0.999635i	$0.491401\pi$
$180$	3.09472	0.230667
$181$	6.55569	0.487280	0.243640	−	0.969866i	$-0.421658\pi$
$181$	6.55569	0.487280	0.243640	+	0.969866i	$0.421658\pi$
$182$	−8.53065	−0.632334
$183$	−10.5035	−0.776443
$184$	7.49833	0.552784
$185$	12.4713	0.916908
$186$	−3.99087	−0.292625
$187$	−10.7191	−0.783857
$188$	−11.9700	−0.873002
$189$	−4.90961	−0.357122
$190$	−7.06852	−0.512805
$191$	−3.87164	−0.280142	−0.140071	−	0.990141i	$-0.544733\pi$
$191$	−3.87164	−0.280142	−0.140071	+	0.990141i	$0.544733\pi$
$192$	−1.06448	−0.0768223
$193$	−24.3258	−1.75101	−0.875504	−	0.483211i	$-0.839470\pi$
$193$	−24.3258	−1.75101	−0.875504	+	0.483211i	$0.839470\pi$
$194$	−4.76705	−0.342254
$195$	−5.64218	−0.404045
$196$	1.22848	0.0877485
$197$	19.4719	1.38731	0.693656	−	0.720306i	$-0.255999\pi$
$197$	19.4719	1.38731	0.693656	+	0.720306i	$0.255999\pi$
$198$	−7.84758	−0.557703
$199$	−20.5743	−1.45847	−0.729237	−	0.684261i	$-0.760125\pi$
$199$	−20.5743	−1.45847	−0.729237	+	0.684261i	$0.760125\pi$
$200$	−4.85361	−0.343202
$201$	−5.94923	−0.419626
$202$	6.63101	0.466556
$203$	−1.89652	−0.133109
$204$	6.02234	0.421648
$205$	4.73303	0.330569
$206$	−32.4387	−2.26011
$207$	−11.1301	−0.773598
$208$	−23.4907	−1.62878
$209$	6.82045	0.471781
$210$	2.13532	0.147351
$211$	−22.2884	−1.53440	−0.767198	−	0.641410i	$-0.778350\pi$
$211$	−22.2884	−1.53440	−0.767198	+	0.641410i	$0.778350\pi$
$212$	−2.35506	−0.161746
$213$	2.36088	0.161765
$214$	34.3342	2.34703
$215$	−11.7614	−0.802119
$216$	−6.80603	−0.463091
$217$	2.28810	0.155326
$218$	7.00037	0.474125
$219$	3.38236	0.228558
$220$	3.19221	0.215219
$221$	23.9766	1.61284
$222$	17.7678	1.19250
$223$	−21.1012	−1.41304	−0.706520	−	0.707693i	$-0.749736\pi$
$223$	−21.1012	−1.41304	−0.706520	+	0.707693i	$0.749736\pi$
$224$	6.11766	0.408753
$225$	7.20445	0.480297
$226$	3.49601	0.232551
$227$	4.12441	0.273747	0.136873	−	0.990589i	$-0.456295\pi$
$227$	4.12441	0.273747	0.136873	+	0.990589i	$0.456295\pi$
$228$	−3.83196	−0.253778
$229$	−6.73280	−0.444916	−0.222458	−	0.974942i	$-0.571408\pi$
$229$	−6.73280	−0.444916	−0.222458	+	0.974942i	$0.571408\pi$
$230$	11.8984	0.784555
$231$	−2.06038	−0.135563
$232$	−2.62908	−0.172607
$233$	4.39445	0.287890	0.143945	−	0.989586i	$-0.454021\pi$
$233$	4.39445	0.287890	0.143945	+	0.989586i	$0.454021\pi$
$234$	17.5536	1.14751
$235$	11.9288	0.778149
$236$	4.82917	0.314352
$237$	12.4883	0.811204
$238$	−9.07409	−0.588186
$239$	−7.59704	−0.491412	−0.245706	−	0.969344i	$-0.579020\pi$
$239$	−7.59704	−0.491412	−0.245706	+	0.969344i	$0.579020\pi$
$240$	5.87998	0.379551
$241$	−26.3646	−1.69829	−0.849146	−	0.528158i	$-0.822883\pi$
$241$	−26.3646	−1.69829	−0.849146	+	0.528158i	$0.822883\pi$
$242$	11.6700	0.750173
$243$	16.0949	1.03249
$244$	−13.2926	−0.850971
$245$	−1.22425	−0.0782145
$246$	6.74313	0.429927
$247$	−15.2561	−0.970720
$248$	3.17191	0.201417
$249$	13.4175	0.850299
$250$	−18.7004	−1.18271
$251$	18.4928	1.16726	0.583628	−	0.812021i	$-0.301633\pi$
$251$	18.4928	1.16726	0.583628	+	0.812021i	$0.301633\pi$
$252$	−2.52785	−0.159239
$253$	−11.4808	−0.721791
$254$	29.8030	1.87001
$255$	−6.00161	−0.375836
$256$	20.6372	1.28983
$257$	−17.0578	−1.06404	−0.532018	−	0.846733i	$-0.678566\pi$
$257$	−17.0578	−1.06404	−0.532018	+	0.846733i	$0.678566\pi$
$258$	−16.7564	−1.04321
$259$	−10.1869	−0.632982
$260$	−7.14038	−0.442828
$261$	3.90247	0.241557
$262$	−13.7141	−0.847260
$263$	−12.1214	−0.747435	−0.373718	−	0.927542i	$-0.621917\pi$
$263$	−12.1214	−0.747435	−0.373718	+	0.927542i	$0.621917\pi$
$264$	−2.85624	−0.175789
$265$	2.34695	0.144172
$266$	5.77376	0.354012
$267$	−8.14999	−0.498772
$268$	−7.52896	−0.459904
$269$	4.79856	0.292573	0.146287	−	0.989242i	$-0.453268\pi$
$269$	4.79856	0.292573	0.146287	+	0.989242i	$0.453268\pi$
$270$	−10.7998	−0.657256
$271$	−22.1288	−1.34423	−0.672114	−	0.740447i	$-0.734614\pi$
$271$	−22.1288	−1.34423	−0.672114	+	0.740447i	$0.734614\pi$
$272$	−24.9871	−1.51507
$273$	4.60868	0.278930
$274$	−2.13840	−0.129185
$275$	7.43142	0.448132
$276$	6.45029	0.388262
$277$	3.26445	0.196142	0.0980710	−	0.995179i	$-0.468733\pi$
$277$	3.26445	0.196142	0.0980710	+	0.995179i	$0.468733\pi$
$278$	13.6019	0.815791
$279$	−4.70823	−0.281874
$280$	−1.69714	−0.101423
$281$	17.7510	1.05894	0.529468	−	0.848330i	$-0.322392\pi$
$281$	17.7510	1.05894	0.529468	+	0.848330i	$0.322392\pi$
$282$	16.9949	1.01203
$283$	17.2297	1.02420	0.512100	−	0.858926i	$-0.328868\pi$
$283$	17.2297	1.02420	0.512100	+	0.858926i	$0.328868\pi$
$284$	2.98778	0.177292
$285$	3.81877	0.226204
$286$	18.1066	1.07066
$287$	−3.86606	−0.228207
$288$	−12.5883	−0.741774
$289$	8.50399	0.500235
$290$	−4.17183	−0.244978
$291$	2.57540	0.150973
$292$	4.28049	0.250497
$293$	−0.225749	−0.0131884	−0.00659419	−	0.999978i	$-0.502099\pi$
$293$	−0.225749	−0.0131884	−0.00659419	+	0.999978i	$0.502099\pi$
$294$	−1.74419	−0.101723
$295$	−4.81254	−0.280197
$296$	−14.1217	−0.820809
$297$	10.4208	0.604676
$298$	−18.6722	−1.08165
$299$	25.6804	1.48513
$300$	−4.17522	−0.241057
$301$	9.60699	0.553738
$302$	−40.2434	−2.31575
$303$	−3.58240	−0.205804
$304$	15.8991	0.911873
$305$	13.2468	0.758511
$306$	18.6718	1.06740
$307$	−21.1003	−1.20426	−0.602130	−	0.798398i	$-0.705681\pi$
$307$	−21.1003	−1.20426	−0.602130	+	0.798398i	$0.705681\pi$
$308$	−2.60748	−0.148575
$309$	17.5250	0.996962
$310$	5.03320	0.285866
$311$	0.407029	0.0230805	0.0115402	−	0.999933i	$-0.496327\pi$
$311$	0.407029	0.0230805	0.0115402	+	0.999933i	$0.496327\pi$
$312$	6.38886	0.361698
$313$	−19.0528	−1.07693	−0.538464	−	0.842648i	$-0.680995\pi$
$313$	−19.0528	−1.07693	−0.538464	+	0.842648i	$0.680995\pi$
$314$	36.6392	2.06767
$315$	2.51915	0.141938
$316$	15.8044	0.889068
$317$	20.8230	1.16954	0.584769	−	0.811200i	$-0.301185\pi$
$317$	20.8230	1.16954	0.584769	+	0.811200i	$0.301185\pi$
$318$	3.34369	0.187505
$319$	4.02542	0.225380
$320$	1.34250	0.0750481
$321$	−18.5490	−1.03531
$322$	−9.71889	−0.541613
$323$	−16.2279	−0.902947
$324$	1.72879	0.0960437
$325$	−16.6227	−0.922061
$326$	−15.9574	−0.883798
$327$	−3.78195	−0.209142
$328$	−5.35939	−0.295923
$329$	−9.74375	−0.537191
$330$	−4.53228	−0.249494
$331$	29.7655	1.63606	0.818030	−	0.575176i	$-0.195067\pi$
$331$	29.7655	1.63606	0.818030	+	0.575176i	$0.195067\pi$
$332$	16.9803	0.931915
$333$	20.9616	1.14869
$334$	−12.1345	−0.663968
$335$	7.50304	0.409935
$336$	−4.80292	−0.262021
$337$	−23.9624	−1.30532	−0.652658	−	0.757653i	$-0.726346\pi$
$337$	−23.9624	−1.30532	−0.652658	+	0.757653i	$0.726346\pi$
$338$	−17.1426	−0.932435
$339$	−1.88872	−0.102581
$340$	−7.59525	−0.411910
$341$	−4.85655	−0.262997
$342$	−11.8807	−0.642434
$343$	1.00000	0.0539949
$344$	13.3178	0.718050
$345$	−6.42809	−0.346077
$346$	6.66494	0.358309
$347$	−18.7157	−1.00471	−0.502356	−	0.864661i	$-0.667533\pi$
$347$	−18.7157	−1.00471	−0.502356	+	0.864661i	$0.667533\pi$
$348$	−2.26161	−0.121235
$349$	−5.31317	−0.284408	−0.142204	−	0.989837i	$-0.545419\pi$
$349$	−5.31317	−0.284408	−0.142204	+	0.989837i	$0.545419\pi$
$350$	6.29096	0.336266
$351$	−23.3094	−1.24416
$352$	−12.9849	−0.692098
$353$	−9.69252	−0.515881	−0.257940	−	0.966161i	$-0.583044\pi$
$353$	−9.69252	−0.515881	−0.257940	+	0.966161i	$0.583044\pi$
$354$	−6.85641	−0.364414
$355$	−2.97750	−0.158029
$356$	−10.3141	−0.546646
$357$	4.90228	0.259456
$358$	−1.29872	−0.0686395
$359$	−26.0521	−1.37498	−0.687488	−	0.726196i	$-0.741286\pi$
$359$	−26.0521	−1.37498	−0.687488	+	0.726196i	$0.741286\pi$
$360$	3.49220	0.184055
$361$	−8.67432	−0.456543
$362$	−11.7792	−0.619103
$363$	−6.30469	−0.330911
$364$	5.83245	0.305703
$365$	−4.26575	−0.223280
$366$	18.8727	0.986492
$367$	−6.53937	−0.341352	−0.170676	−	0.985327i	$-0.554595\pi$
$367$	−6.53937	−0.341352	−0.170676	+	0.985327i	$0.554595\pi$
$368$	−26.7627	−1.39510
$369$	7.95522	0.414132
$370$	−22.4084	−1.16496
$371$	−1.91705	−0.0995284
$372$	2.72858	0.141470
$373$	17.4470	0.903371	0.451685	−	0.892177i	$-0.350823\pi$
$373$	17.4470	0.903371	0.451685	+	0.892177i	$0.350823\pi$
$374$	19.2600	0.995912
$375$	10.1029	0.521710
$376$	−13.5074	−0.696593
$377$	−9.00410	−0.463735
$378$	8.82157	0.453733
$379$	−21.2719	−1.09267	−0.546333	−	0.837568i	$-0.683977\pi$
$379$	−21.2719	−1.09267	−0.546333	+	0.837568i	$0.683977\pi$
$380$	4.83279	0.247917
$381$	−16.1011	−0.824884
$382$	6.95654	0.355928
$383$	15.3959	0.786692	0.393346	−	0.919391i	$-0.371317\pi$
$383$	15.3959	0.786692	0.393346	+	0.919391i	$0.371317\pi$
$384$	−9.96440	−0.508493
$385$	2.59851	0.132432
$386$	43.7085	2.22470
$387$	−19.7683	−1.00488
$388$	3.25926	0.165464
$389$	−4.86069	−0.246447	−0.123223	−	0.992379i	$-0.539323\pi$
$389$	−4.86069	−0.246447	−0.123223	+	0.992379i	$0.539323\pi$
$390$	10.1379	0.513350
$391$	27.3163	1.38144
$392$	1.38627	0.0700170
$393$	7.40904	0.373737
$394$	−34.9870	−1.76262
$395$	−15.7500	−0.792469
$396$	5.36543	0.269623
$397$	−9.06103	−0.454760	−0.227380	−	0.973806i	$-0.573016\pi$
$397$	−9.06103	−0.454760	−0.227380	+	0.973806i	$0.573016\pi$
$398$	36.9679	1.85303
$399$	−3.11927	−0.156159
$400$	17.3233	0.866164
$401$	−4.91064	−0.245226	−0.122613	−	0.992455i	$-0.539127\pi$
$401$	−4.91064	−0.245226	−0.122613	+	0.992455i	$0.539127\pi$
$402$	10.6896	0.533147
$403$	10.8632	0.541134
$404$	−4.53366	−0.225558
$405$	−1.72284	−0.0856084
$406$	3.40766	0.169119
$407$	21.6220	1.07176
$408$	6.79586	0.336445
$409$	−17.7200	−0.876196	−0.438098	−	0.898927i	$-0.644348\pi$
$409$	−17.7200	−0.876196	−0.438098	+	0.898927i	$0.644348\pi$
$410$	−8.50430	−0.419997
$411$	1.15527	0.0569853
$412$	22.1785	1.09266
$413$	3.93101	0.193432
$414$	19.9986	0.982878
$415$	−16.9218	−0.830661
$416$	29.0448	1.42404
$417$	−7.34845	−0.359855
$418$	−12.2550	−0.599410
$419$	−40.1242	−1.96019	−0.980097	−	0.198519i	$-0.936387\pi$
$419$	−40.1242	−1.96019	−0.980097	+	0.198519i	$0.936387\pi$
$420$	−1.45993	−0.0712373
$421$	37.4224	1.82386	0.911928	−	0.410350i	$-0.134594\pi$
$421$	37.4224	1.82386	0.911928	+	0.410350i	$0.134594\pi$
$422$	40.0477	1.94949
$423$	20.0498	0.974853
$424$	−2.65754	−0.129062
$425$	−17.6816	−0.857685
$426$	−4.24203	−0.205527
$427$	−10.8204	−0.523634
$428$	−23.4744	−1.13468
$429$	−9.78207	−0.472283
$430$	21.1328	1.01911
$431$	14.9556	0.720386	0.360193	−	0.932878i	$-0.382711\pi$
$431$	14.9556	0.720386	0.360193	+	0.932878i	$0.382711\pi$
$432$	24.2918	1.16874
$433$	−33.3442	−1.60242	−0.801210	−	0.598383i	$-0.795810\pi$
$433$	−33.3442	−1.60242	−0.801210	+	0.598383i	$0.795810\pi$
$434$	−4.11125	−0.197346
$435$	2.25383	0.108063
$436$	−4.78619	−0.229217
$437$	−17.3811	−0.831451
$438$	−6.07741	−0.290390
$439$	2.69192	0.128478	0.0642392	−	0.997935i	$-0.479538\pi$
$439$	2.69192	0.128478	0.0642392	+	0.997935i	$0.479538\pi$
$440$	3.60222	0.171729
$441$	−2.05770	−0.0979859
$442$	−43.0810	−2.04916
$443$	20.2870	0.963864	0.481932	−	0.876208i	$-0.339935\pi$
$443$	20.2870	0.963864	0.481932	+	0.876208i	$0.339935\pi$
$444$	−12.1479	−0.576516
$445$	10.2786	0.487252
$446$	37.9146	1.79531
$447$	10.0877	0.477130
$448$	−1.09659	−0.0518090
$449$	3.34539	0.157879	0.0789395	−	0.996879i	$-0.474847\pi$
$449$	3.34539	0.157879	0.0789395	+	0.996879i	$0.474847\pi$
$450$	−12.9449	−0.610230
$451$	8.20584	0.386398
$452$	−2.39024	−0.112427
$453$	21.7415	1.02151
$454$	−7.41073	−0.347803
$455$	−5.81237	−0.272488
$456$	−4.32414	−0.202496
$457$	−17.9520	−0.839759	−0.419879	−	0.907580i	$-0.637928\pi$
$457$	−17.9520	−0.839759	−0.419879	+	0.907580i	$0.637928\pi$
$458$	12.0975	0.565278
$459$	−24.7943	−1.15730
$460$	−8.13497	−0.379295
$461$	14.2162	0.662112	0.331056	−	0.943611i	$-0.392595\pi$
$461$	14.2162	0.662112	0.331056	+	0.943611i	$0.392595\pi$
$462$	3.70209	0.172237
$463$	−21.2664	−0.988333	−0.494167	−	0.869367i	$-0.664527\pi$
$463$	−21.2664	−0.988333	−0.494167	+	0.869367i	$0.664527\pi$
$464$	9.38359	0.435622
$465$	−2.71918	−0.126099
$466$	−7.89593	−0.365772
$467$	−33.0681	−1.53021	−0.765104	−	0.643906i	$-0.777313\pi$
$467$	−33.0681	−1.53021	−0.765104	+	0.643906i	$0.777313\pi$
$468$	−12.0015	−0.554767
$469$	−6.12868	−0.282996
$470$	−21.4336	−0.988659
$471$	−19.7943	−0.912073
$472$	5.44943	0.250830
$473$	−20.3911	−0.937585
$474$	−22.4390	−1.03066
$475$	11.2507	0.516215
$476$	6.20400	0.284360
$477$	3.94472	0.180617
$478$	13.6503	0.624352
$479$	18.8130	0.859587	0.429794	−	0.902927i	$-0.358586\pi$
$479$	18.8130	0.859587	0.429794	+	0.902927i	$0.358586\pi$
$480$	−7.27024	−0.331840
$481$	−48.3642	−2.20522
$482$	47.3718	2.15773
$483$	5.25063	0.238912
$484$	−7.97881	−0.362673
$485$	−3.24804	−0.147486
$486$	−28.9192	−1.31180
$487$	−4.42672	−0.200594	−0.100297	−	0.994958i	$-0.531979\pi$
$487$	−4.42672	−0.200594	−0.100297	+	0.994958i	$0.531979\pi$
$488$	−14.9999	−0.679013
$489$	8.62098	0.389854
$490$	2.19973	0.0993737
$491$	35.5436	1.60406	0.802031	−	0.597282i	$-0.203753\pi$
$491$	35.5436	1.60406	0.802031	+	0.597282i	$0.203753\pi$
$492$	−4.61032	−0.207849
$493$	−9.57770	−0.431358
$494$	27.4121	1.23333
$495$	−5.34696	−0.240328
$496$	−11.3210	−0.508330
$497$	2.43210	0.109094
$498$	−24.1085	−1.08033
$499$	−1.03404	−0.0462898	−0.0231449	−	0.999732i	$-0.507368\pi$
$499$	−1.03404	−0.0462898	−0.0231449	+	0.999732i	$0.507368\pi$
$500$	12.7855	0.571787
$501$	6.55564	0.292885
$502$	−33.2278	−1.48303
$503$	−22.3536	−0.996699	−0.498350	−	0.866976i	$-0.666060\pi$
$503$	−22.3536	−0.996699	−0.498350	+	0.866976i	$0.666060\pi$
$504$	−2.85252	−0.127062
$505$	4.51805	0.201051
$506$	20.6286	0.917055
$507$	9.26129	0.411308
$508$	−20.3765	−0.904061
$509$	16.6998	0.740207	0.370104	−	0.928990i	$-0.379322\pi$
$509$	16.6998	0.740207	0.370104	+	0.928990i	$0.379322\pi$
$510$	10.7837	0.477509
$511$	3.48438	0.154140
$512$	−16.5510	−0.731457
$513$	15.7763	0.696543
$514$	30.6494	1.35189
$515$	−22.1022	−0.973937
$516$	11.4564	0.504341
$517$	20.6814	0.909567
$518$	18.3038	0.804221
$519$	−3.60073	−0.158055
$520$	−8.05749	−0.353344
$521$	17.0817	0.748364	0.374182	−	0.927355i	$-0.377923\pi$
$521$	17.0817	0.748364	0.374182	+	0.927355i	$0.377923\pi$
$522$	−7.01195	−0.306905
$523$	−42.3136	−1.85025	−0.925123	−	0.379669i	$-0.876038\pi$
$523$	−42.3136	−1.85025	−0.925123	+	0.379669i	$0.876038\pi$
$524$	9.37640	0.409610
$525$	−3.39869	−0.148331
$526$	21.7796	0.949637
$527$	11.5552	0.503354
$528$	10.1943	0.443652
$529$	6.25739	0.272060
$530$	−4.21700	−0.183175
$531$	−8.08886	−0.351026
$532$	−3.94755	−0.171148
$533$	−18.3549	−0.795039
$534$	14.6439	0.633703
$535$	23.3936	1.01140
$536$	−8.49598	−0.366970
$537$	0.701634	0.0302777
$538$	−8.62204	−0.371722
$539$	−2.12253	−0.0914238
$540$	7.38389	0.317752
$541$	20.1252	0.865250	0.432625	−	0.901574i	$-0.357587\pi$
$541$	20.1252	0.865250	0.432625	+	0.901574i	$0.357587\pi$
$542$	39.7610	1.70788
$543$	6.36373	0.273094
$544$	30.8951	1.32461
$545$	4.76971	0.204312
$546$	−8.28087	−0.354388
$547$	−44.1651	−1.88836	−0.944182	−	0.329426i	$-0.893145\pi$
$547$	−44.1651	−1.88836	−0.944182	+	0.329426i	$0.893145\pi$
$548$	1.46203	0.0624550
$549$	22.2651	0.950251
$550$	−13.3528	−0.569364
$551$	6.09420	0.259621
$552$	7.27877	0.309805
$553$	12.8650	0.547076
$554$	−5.86556	−0.249204
$555$	12.1061	0.513876
$556$	−9.29972	−0.394396
$557$	−4.19444	−0.177724	−0.0888621	−	0.996044i	$-0.528323\pi$
$557$	−4.19444	−0.177724	−0.0888621	+	0.996044i	$0.528323\pi$
$558$	8.45973	0.358129
$559$	45.6111	1.92914
$560$	6.05734	0.255969
$561$	−10.4052	−0.439309
$562$	−31.8949	−1.34541
$563$	−26.2011	−1.10424	−0.552122	−	0.833763i	$-0.686182\pi$
$563$	−26.2011	−1.10424	−0.552122	+	0.833763i	$0.686182\pi$
$564$	−11.6195	−0.489270
$565$	2.38201	0.100212
$566$	−30.9583	−1.30127
$567$	1.40726	0.0590992
$568$	3.37153	0.141466
$569$	5.59349	0.234491	0.117246	−	0.993103i	$-0.462593\pi$
$569$	5.59349	0.234491	0.117246	+	0.993103i	$0.462593\pi$
$570$	−6.86155	−0.287399
$571$	8.35724	0.349739	0.174870	−	0.984592i	$-0.444050\pi$
$571$	8.35724	0.349739	0.174870	+	0.984592i	$0.444050\pi$
$572$	−12.3795	−0.517615
$573$	−3.75827	−0.157004
$574$	6.94653	0.289943
$575$	−18.9381	−0.789773
$576$	2.25646	0.0940191
$577$	38.2563	1.59263	0.796315	−	0.604882i	$-0.206780\pi$
$577$	38.2563	1.59263	0.796315	+	0.604882i	$0.206780\pi$
$578$	−15.2799	−0.635562
$579$	−23.6135	−0.981344
$580$	2.85230	0.118435
$581$	13.8222	0.573442
$582$	−4.62747	−0.191815
$583$	4.06900	0.168521
$584$	4.83028	0.199878
$585$	11.9601	0.494491
$586$	0.405625	0.0167562
$587$	−12.5382	−0.517505	−0.258752	−	0.965944i	$-0.583311\pi$
$587$	−12.5382	−0.517505	−0.258752	+	0.965944i	$0.583311\pi$
$588$	1.19251	0.0491782
$589$	−7.35248	−0.302954
$590$	8.64716	0.355998
$591$	18.9017	0.777512
$592$	50.4026	2.07153
$593$	−39.9884	−1.64213	−0.821063	−	0.570837i	$-0.806619\pi$
$593$	−39.9884	−1.64213	−0.821063	+	0.570837i	$0.806619\pi$
$594$	−18.7241	−0.768257
$595$	−6.18265	−0.253464
$596$	12.7663	0.522928
$597$	−19.9719	−0.817395
$598$	−46.1424	−1.88690
$599$	−33.8936	−1.38486	−0.692428	−	0.721487i	$-0.743459\pi$
$599$	−33.8936	−1.38486	−0.692428	+	0.721487i	$0.743459\pi$
$600$	−4.71149	−0.192346
$601$	−18.2916	−0.746132	−0.373066	−	0.927805i	$-0.621693\pi$
$601$	−18.2916	−0.746132	−0.373066	+	0.927805i	$0.621693\pi$
$602$	−17.2618	−0.703539
$603$	12.6110	0.513560
$604$	27.5147	1.11956
$605$	7.95134	0.323268
$606$	6.43685	0.261479
$607$	−27.8990	−1.13238	−0.566192	−	0.824273i	$-0.691584\pi$
$607$	−27.8990	−1.13238	−0.566192	+	0.824273i	$0.691584\pi$
$608$	−19.6582	−0.797246
$609$	−1.84099	−0.0746006
$610$	−23.8019	−0.963709
$611$	−46.2604	−1.87150
$612$	−12.7660	−0.516035
$613$	17.3055	0.698962	0.349481	−	0.936943i	$-0.386358\pi$
$613$	17.3055	0.698962	0.349481	+	0.936943i	$0.386358\pi$
$614$	37.9130	1.53004
$615$	4.59445	0.185266
$616$	−2.94239	−0.118552
$617$	42.9782	1.73024	0.865118	−	0.501568i	$-0.167243\pi$
$617$	42.9782	1.73024	0.865118	+	0.501568i	$0.167243\pi$
$618$	−31.4889	−1.26667
$619$	19.9479	0.801773	0.400887	−	0.916128i	$-0.368702\pi$
$619$	19.9479	0.801773	0.400887	+	0.916128i	$0.368702\pi$
$620$	−3.44122	−0.138203
$621$	−26.5561	−1.06566
$622$	−0.731348	−0.0293244
$623$	−8.39583	−0.336372
$624$	−22.8028	−0.912844
$625$	4.76453	0.190581
$626$	34.2340	1.36827
$627$	6.62075	0.264407
$628$	−25.0504	−0.999619
$629$	−51.4452	−2.05126
$630$	−4.52639	−0.180336
$631$	−15.7972	−0.628877	−0.314438	−	0.949278i	$-0.601816\pi$
$631$	−15.7972	−0.628877	−0.314438	+	0.949278i	$0.601816\pi$
$632$	17.8343	0.709412
$633$	−21.6358	−0.859945
$634$	−37.4147	−1.48593
$635$	20.3064	0.805833
$636$	−2.28610	−0.0906498
$637$	4.74770	0.188111
$638$	−7.23286	−0.286352
$639$	−5.00454	−0.197976
$640$	12.5669	0.496750
$641$	15.7823	0.623364	0.311682	−	0.950186i	$-0.399108\pi$
$641$	15.7823	0.623364	0.311682	+	0.950186i	$0.399108\pi$
$642$	33.3288	1.31538
$643$	7.28567	0.287319	0.143659	−	0.989627i	$-0.454113\pi$
$643$	7.28567	0.287319	0.143659	+	0.989627i	$0.454113\pi$
$644$	6.64486	0.261844
$645$	−11.4170	−0.449543
$646$	29.1583	1.14722
$647$	12.6737	0.498256	0.249128	−	0.968471i	$-0.419856\pi$
$647$	12.6737	0.498256	0.249128	+	0.968471i	$0.419856\pi$
$648$	1.95083	0.0766359
$649$	−8.34369	−0.327518
$650$	29.8676	1.17150
$651$	2.22110	0.0870518
$652$	10.9101	0.427274
$653$	−5.80016	−0.226978	−0.113489	−	0.993539i	$-0.536203\pi$
$653$	−5.80016	−0.226978	−0.113489	+	0.993539i	$0.536203\pi$
$654$	6.79540	0.265721
$655$	−9.34412	−0.365105
$656$	19.1285	0.746843
$657$	−7.16982	−0.279721
$658$	17.5075	0.682515
$659$	15.6403	0.609258	0.304629	−	0.952471i	$-0.401468\pi$
$659$	15.6403	0.609258	0.304629	+	0.952471i	$0.401468\pi$
$660$	3.09874	0.120618
$661$	−38.9194	−1.51379	−0.756895	−	0.653537i	$-0.773284\pi$
$661$	−38.9194	−1.51379	−0.756895	+	0.653537i	$0.773284\pi$
$662$	−53.4825	−2.07866
$663$	23.2745	0.903908
$664$	19.1613	0.743601
$665$	3.93396	0.152552
$666$	−37.6637	−1.45944
$667$	−10.2583	−0.397202
$668$	8.29640	0.320997
$669$	−20.4833	−0.791932
$670$	−13.4814	−0.520833
$671$	22.9665	0.886613
$672$	5.93853	0.229084
$673$	26.1322	1.00732	0.503661	−	0.863901i	$-0.331986\pi$
$673$	26.1322	1.00732	0.503661	+	0.863901i	$0.331986\pi$
$674$	43.0556	1.65844
$675$	17.1896	0.661627
$676$	11.7205	0.450788
$677$	11.0365	0.424167	0.212084	−	0.977252i	$-0.431975\pi$
$677$	11.0365	0.424167	0.212084	+	0.977252i	$0.431975\pi$
$678$	3.39364	0.130332
$679$	2.65308	0.101816
$680$	−8.57079	−0.328675
$681$	4.00364	0.153420
$682$	8.72624	0.334145
$683$	38.3740	1.46834	0.734171	−	0.678965i	$-0.237571\pi$
$683$	38.3740	1.46834	0.734171	+	0.678965i	$0.237571\pi$
$684$	8.12288	0.310586
$685$	−1.45700	−0.0556692
$686$	−1.79680	−0.0686020
$687$	−6.53566	−0.249351
$688$	−47.5335	−1.81220
$689$	−9.10158	−0.346743
$690$	11.5500	0.439700
$691$	−35.8473	−1.36369	−0.681847	−	0.731495i	$-0.738823\pi$
$691$	−35.8473	−1.36369	−0.681847	+	0.731495i	$0.738823\pi$
$692$	−4.55685	−0.173226
$693$	4.36754	0.165909
$694$	33.6283	1.27651
$695$	9.26771	0.351544
$696$	−2.55210	−0.0967370
$697$	−19.5242	−0.739532
$698$	9.54669	0.361348
$699$	4.26578	0.161347
$700$	−4.30117	−0.162569
$701$	−47.7258	−1.80258	−0.901290	−	0.433216i	$-0.857379\pi$
$701$	−47.7258	−1.80258	−0.901290	+	0.433216i	$0.857379\pi$
$702$	41.8822	1.58074
$703$	32.7341	1.23459
$704$	2.32755	0.0877227
$705$	11.5795	0.436110
$706$	17.4155	0.655441
$707$	−3.69046	−0.138794
$708$	4.68776	0.176177
$709$	−47.5757	−1.78674	−0.893371	−	0.449319i	$-0.851667\pi$
$709$	−47.5757	−1.78674	−0.893371	+	0.449319i	$0.851667\pi$
$710$	5.34996	0.200780
$711$	−26.4724	−0.992793
$712$	−11.6389	−0.436184
$713$	12.3763	0.463498
$714$	−8.80839	−0.329646
$715$	12.3369	0.461375
$716$	0.887942	0.0331839
$717$	−7.37459	−0.275409
$718$	46.8103	1.74694
$719$	−27.2536	−1.01639	−0.508194	−	0.861243i	$-0.669687\pi$
$719$	−27.2536	−1.01639	−0.508194	+	0.861243i	$0.669687\pi$
$720$	−12.4642	−0.464514
$721$	18.0536	0.672352
$722$	15.5860	0.580050
$723$	−25.5926	−0.951800
$724$	8.05352	0.299307
$725$	6.64011	0.246607
$726$	11.3283	0.420431
$727$	0.782465	0.0290200	0.0145100	−	0.999895i	$-0.495381\pi$
$727$	0.782465	0.0290200	0.0145100	+	0.999895i	$0.495381\pi$
$728$	6.58157	0.243929
$729$	11.4018	0.422291
$730$	7.66470	0.283683
$731$	48.5167	1.79446
$732$	−12.9034	−0.476922
$733$	24.0766	0.889289	0.444645	−	0.895707i	$-0.353330\pi$
$733$	24.0766	0.889289	0.444645	+	0.895707i	$0.353330\pi$
$734$	11.7499	0.433697
$735$	−1.18840	−0.0438349
$736$	33.0905	1.21973
$737$	13.0083	0.479167
$738$	−14.2939	−0.526166
$739$	−38.0478	−1.39961	−0.699805	−	0.714334i	$-0.746730\pi$
$739$	−38.0478	−1.39961	−0.699805	+	0.714334i	$0.746730\pi$
$740$	15.3207	0.563201
$741$	−14.8094	−0.544035
$742$	3.44455	0.126454
$743$	−12.6098	−0.462610	−0.231305	−	0.972881i	$-0.574299\pi$
$743$	−12.6098	−0.462610	−0.231305	+	0.972881i	$0.574299\pi$
$744$	3.07904	0.112883
$745$	−12.7223	−0.466111
$746$	−31.3487	−1.14776
$747$	−28.4420	−1.04064
$748$	−13.1682	−0.481476
$749$	−19.1085	−0.698211
$750$	−18.1528	−0.662847
$751$	−15.9884	−0.583426	−0.291713	−	0.956506i	$-0.594225\pi$
$751$	−15.9884	−0.583426	−0.291713	+	0.956506i	$0.594225\pi$
$752$	48.2101	1.75804
$753$	17.9513	0.654183
$754$	16.1785	0.589188
$755$	−27.4199	−0.997914
$756$	−6.03136	−0.219358
$757$	−10.0936	−0.366859	−0.183430	−	0.983033i	$-0.558720\pi$
$757$	−10.0936	−0.366859	−0.183430	+	0.983033i	$0.558720\pi$
$758$	38.2213	1.38826
$759$	−11.1446	−0.404524
$760$	5.45351	0.197820
$761$	−9.13254	−0.331054	−0.165527	−	0.986205i	$-0.552933\pi$
$761$	−9.13254	−0.331054	−0.165527	+	0.986205i	$0.552933\pi$
$762$	28.9304	1.04804
$763$	−3.89603	−0.141046
$764$	−4.75622	−0.172074
$765$	12.7221	0.459967
$766$	−27.6632	−0.999514
$767$	18.6633	0.673891
$768$	20.0330	0.722877
$769$	17.4825	0.630435	0.315218	−	0.949019i	$-0.397923\pi$
$769$	17.4825	0.630435	0.315218	+	0.949019i	$0.397923\pi$
$770$	−4.66899	−0.168259
$771$	−16.5583	−0.596333
$772$	−29.8837	−1.07554
$773$	−24.8257	−0.892920	−0.446460	−	0.894804i	$-0.647315\pi$
$773$	−24.8257	−0.892920	−0.446460	+	0.894804i	$0.647315\pi$
$774$	35.5197	1.27673
$775$	−8.01111	−0.287768
$776$	3.67788	0.132028
$777$	−9.88860	−0.354752
$778$	8.73368	0.313118
$779$	12.4231	0.445102
$780$	−6.93131	−0.248181
$781$	−5.16220	−0.184718
$782$	−49.0818	−1.75516
$783$	9.31117	0.332754
$784$	−4.94780	−0.176707
$785$	24.9642	0.891009
$786$	−13.3125	−0.474843
$787$	5.68843	0.202771	0.101385	−	0.994847i	$-0.467673\pi$
$787$	5.68843	0.202771	0.101385	+	0.994847i	$0.467673\pi$
$788$	23.9208	0.852142
$789$	−11.7664	−0.418897
$790$	28.2996	1.00685
$791$	−1.94569	−0.0691807
$792$	6.05457	0.215140
$793$	−51.3718	−1.82427
$794$	16.2808	0.577785
$795$	2.27823	0.0808005
$796$	−25.2751	−0.895853
$797$	9.67097	0.342563	0.171282	−	0.985222i	$-0.445209\pi$
$797$	9.67097	0.342563	0.171282	+	0.985222i	$0.445209\pi$
$798$	5.60470	0.198404
$799$	−49.2074	−1.74083
$800$	−21.4192	−0.757283
$801$	17.2761	0.610422
$802$	8.82343	0.311566
$803$	−7.39570	−0.260989
$804$	−7.30851	−0.257751
$805$	−6.62198	−0.233394
$806$	−19.5190	−0.687526
$807$	4.65805	0.163971
$808$	−5.11596	−0.179979
$809$	−30.3880	−1.06838	−0.534192	−	0.845363i	$-0.679384\pi$
$809$	−30.3880	−1.06838	−0.534192	+	0.845363i	$0.679384\pi$
$810$	3.09559	0.108768
$811$	22.0516	0.774336	0.387168	−	0.922009i	$-0.373453\pi$
$811$	22.0516	0.774336	0.387168	+	0.922009i	$0.373453\pi$
$812$	−2.32983	−0.0817611
$813$	−21.4809	−0.753366
$814$	−38.8503	−1.36170
$815$	−10.8726	−0.380850
$816$	−24.2555	−0.849111
$817$	−30.8707	−1.08003
$818$	31.8392	1.11323
$819$	−9.76936	−0.341369
$820$	5.81443	0.203049
$821$	−47.5502	−1.65952	−0.829758	−	0.558124i	$-0.811521\pi$
$821$	−47.5502	−1.65952	−0.829758	+	0.558124i	$0.811521\pi$
$822$	−2.07579	−0.0724013
$823$	−19.4470	−0.677881	−0.338940	−	0.940808i	$-0.610069\pi$
$823$	−19.4470	−0.677881	−0.338940	+	0.940808i	$0.610069\pi$
$824$	25.0271	0.871861
$825$	7.21383	0.251153
$826$	−7.06323	−0.245761
$827$	−25.6185	−0.890841	−0.445421	−	0.895321i	$-0.646946\pi$
$827$	−25.6185	−0.890841	−0.445421	+	0.895321i	$0.646946\pi$
$828$	−13.6731	−0.475175
$829$	16.3782	0.568837	0.284419	−	0.958700i	$-0.408199\pi$
$829$	16.3782	0.568837	0.284419	+	0.958700i	$0.408199\pi$
$830$	30.4051	1.05538
$831$	3.16887	0.109927
$832$	−5.20628	−0.180495
$833$	5.05015	0.174977
$834$	13.2037	0.457206
$835$	−8.26784	−0.286120
$836$	8.37879	0.289786
$837$	−11.2337	−0.388292
$838$	72.0950	2.49048
$839$	10.4878	0.362079	0.181039	−	0.983476i	$-0.442054\pi$
$839$	10.4878	0.362079	0.181039	+	0.983476i	$0.442054\pi$
$840$	−1.64744	−0.0568422
$841$	−25.4032	−0.875973
$842$	−67.2404	−2.31726
$843$	17.2312	0.593475
$844$	−27.3808	−0.942487
$845$	−11.6801	−0.401809
$846$	−36.0253	−1.23858
$847$	−6.49487	−0.223166
$848$	9.48518	0.325723
$849$	16.7252	0.574008
$850$	31.7703	1.08971
$851$	−55.1009	−1.88884
$852$	2.90030	0.0993626
$853$	−56.4397	−1.93246	−0.966229	−	0.257684i	$-0.917041\pi$
$853$	−56.4397	−1.93246	−0.966229	+	0.257684i	$0.917041\pi$
$854$	19.4420	0.665291
$855$	−8.09492	−0.276840
$856$	−26.4895	−0.905393
$857$	−9.16696	−0.313137	−0.156569	−	0.987667i	$-0.550043\pi$
$857$	−9.16696	−0.313137	−0.156569	+	0.987667i	$0.550043\pi$
$858$	17.5764	0.600048
$859$	14.6292	0.499143	0.249571	−	0.968356i	$-0.419710\pi$
$859$	14.6292	0.499143	0.249571	+	0.968356i	$0.419710\pi$
$860$	−14.4486	−0.492693
$861$	−3.75286	−0.127897
$862$	−26.8722	−0.915270
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−30.0353	−1.02182
$865$	4.54117	0.154404
$866$	59.9128	2.03592
$867$	8.25499	0.280354
$868$	2.81088	0.0954075
$869$	−27.3064	−0.926306
$870$	−4.04967	−0.137297
$871$	−29.0971	−0.985919
$872$	−5.40093	−0.182899
$873$	−5.45926	−0.184768
$874$	31.2303	1.05638
$875$	10.4076	0.351841
$876$	4.15515	0.140390
$877$	−18.1898	−0.614225	−0.307112	−	0.951673i	$-0.599363\pi$
$877$	−18.1898	−0.614225	−0.307112	+	0.951673i	$0.599363\pi$
$878$	−4.83684	−0.163235
$879$	−0.219139	−0.00739136
$880$	−12.8569	−0.433406
$881$	44.9077	1.51298	0.756489	−	0.654007i	$-0.226913\pi$
$881$	44.9077	1.51298	0.756489	+	0.654007i	$0.226913\pi$
$882$	3.69728	0.124494
$883$	0.983817	0.0331081	0.0165540	−	0.999863i	$-0.494730\pi$
$883$	0.983817	0.0331081	0.0165540	+	0.999863i	$0.494730\pi$
$884$	29.4547	0.990670
$885$	−4.67163	−0.157035
$886$	−36.4516	−1.22462
$887$	−28.0638	−0.942289	−0.471145	−	0.882056i	$-0.656159\pi$
$887$	−28.0638	−0.942289	−0.471145	+	0.882056i	$0.656159\pi$
$888$	−13.7082	−0.460018
$889$	−16.5868	−0.556302
$890$	−18.4686	−0.619067
$891$	−2.98695	−0.100066
$892$	−25.9224	−0.867946
$893$	31.3102	1.04776
$894$	−18.1255	−0.606207
$895$	−0.884885	−0.0295785
$896$	−10.2650	−0.342928
$897$	24.9284	0.832336
$898$	−6.01099	−0.200589
$899$	−4.33942	−0.144728
$900$	8.85052	0.295017
$901$	−9.68139	−0.322534
$902$	−14.7442	−0.490929
$903$	9.32569	0.310340
$904$	−2.69724	−0.0897089
$905$	−8.02580	−0.266787
$906$	−39.0651	−1.29785
$907$	34.5067	1.14578	0.572888	−	0.819634i	$-0.305823\pi$
$907$	34.5067	1.14578	0.572888	+	0.819634i	$0.305823\pi$
$908$	5.06675	0.168146
$909$	7.59388	0.251873
$910$	10.4437	0.346204
$911$	−12.8037	−0.424207	−0.212103	−	0.977247i	$-0.568031\pi$
$911$	−12.8037	−0.424207	−0.212103	+	0.977247i	$0.568031\pi$
$912$	15.4335	0.511055
$913$	−29.3381	−0.970948
$914$	32.2561	1.06694
$915$	12.8590	0.425104
$916$	−8.27111	−0.273285
$917$	7.63253	0.252048
$918$	44.5503	1.47038
$919$	−29.8167	−0.983562	−0.491781	−	0.870719i	$-0.663654\pi$
$919$	−29.8167	−0.983562	−0.491781	+	0.870719i	$0.663654\pi$
$920$	−9.17983	−0.302650
$921$	−20.4825	−0.674921
$922$	−25.5435	−0.841232
$923$	11.5469	0.380070
$924$	−2.53114	−0.0832682
$925$	35.6664	1.17270
$926$	38.2114	1.25570
$927$	−37.1490	−1.22013
$928$	−11.6022	−0.380862
$929$	−19.2363	−0.631124	−0.315562	−	0.948905i	$-0.602193\pi$
$929$	−19.2363	−0.631124	−0.315562	+	0.948905i	$0.602193\pi$
$930$	4.88582	0.160212
$931$	−3.21336	−0.105314
$932$	5.39849	0.176833
$933$	0.395111	0.0129353
$934$	59.4167	1.94417
$935$	13.1228	0.429163
$936$	−13.5429	−0.442664
$937$	21.4367	0.700306	0.350153	−	0.936692i	$-0.386130\pi$
$937$	21.4367	0.700306	0.350153	+	0.936692i	$0.386130\pi$
$938$	11.0120	0.359554
$939$	−18.4949	−0.603559
$940$	14.6543	0.477970
$941$	−22.8791	−0.745838	−0.372919	−	0.927864i	$-0.621643\pi$
$941$	−22.8791	−0.745838	−0.372919	+	0.927864i	$0.621643\pi$
$942$	35.5663	1.15881
$943$	−20.9116	−0.680975
$944$	−19.4498	−0.633039
$945$	6.01059	0.195525
$946$	36.6387	1.19123
$947$	20.3801	0.662264	0.331132	−	0.943584i	$-0.392569\pi$
$947$	20.3801	0.662264	0.331132	+	0.943584i	$0.392569\pi$
$948$	15.3416	0.498274
$949$	16.5428	0.537002
$950$	−20.2151	−0.655866
$951$	20.2133	0.655462
$952$	7.00085	0.226899
$953$	−55.5951	−1.80090	−0.900451	−	0.434957i	$-0.856764\pi$
$953$	−55.5951	−1.80090	−0.900451	+	0.434957i	$0.856764\pi$
$954$	−7.08787	−0.229478
$955$	4.73985	0.153378
$956$	−9.33281	−0.301845
$957$	3.90755	0.126313
$958$	−33.8031	−1.09213
$959$	1.19012	0.0384309
$960$	1.30319	0.0420603
$961$	−25.7646	−0.831116
$962$	86.9007	2.80179
$963$	39.3197	1.26706
$964$	−32.3884	−1.04316
$965$	29.7809	0.958680
$966$	−9.43432	−0.303544
$967$	−8.02633	−0.258109	−0.129055	−	0.991637i	$-0.541194\pi$
$967$	−8.02633	−0.258109	−0.129055	+	0.991637i	$0.541194\pi$
$968$	−9.00361	−0.289387
$969$	−15.7528	−0.506052
$970$	5.83607	0.187385
$971$	8.64244	0.277349	0.138675	−	0.990338i	$-0.455716\pi$
$971$	8.64244	0.277349	0.138675	+	0.990338i	$0.455716\pi$
$972$	19.7722	0.634195
$973$	−7.57011	−0.242687
$974$	7.95392	0.254860
$975$	−16.1360	−0.516765
$976$	53.5369	1.71368
$977$	−13.2147	−0.422777	−0.211389	−	0.977402i	$-0.567799\pi$
$977$	−13.2147	−0.422777	−0.211389	+	0.977402i	$0.567799\pi$
$978$	−15.4901	−0.495320
$979$	17.8204	0.569542
$980$	−1.50397	−0.0480424
$981$	8.01687	0.255959
$982$	−63.8647	−2.03801
$983$	−9.13184	−0.291260	−0.145630	−	0.989339i	$-0.546521\pi$
$983$	−9.13184	−0.291260	−0.145630	+	0.989339i	$0.546521\pi$
$984$	−5.20247	−0.165849
$985$	−23.8384	−0.759556
$986$	17.2092	0.548052
$987$	−9.45845	−0.301066
$988$	−18.7418	−0.596255
$989$	51.9643	1.65237
$990$	9.60740	0.305343
$991$	39.9763	1.26989	0.634945	−	0.772557i	$-0.281023\pi$
$991$	39.9763	1.26989	0.634945	+	0.772557i	$0.281023\pi$
$992$	13.9978	0.444430
$993$	28.8939	0.916921
$994$	−4.36999	−0.138608
$995$	25.1881	0.798517
$996$	16.4831	0.522287
$997$	−13.6739	−0.433057	−0.216528	−	0.976276i	$-0.569473\pi$
$997$	−13.6739	−0.433057	−0.216528	+	0.976276i	$0.569473\pi$
$998$	1.85795	0.0588124
$999$	50.0136	1.58236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.17	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.17	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79680 q^{2} +0.970719 q^{3} +1.22848 q^{4} -1.22425 q^{5} -1.74419 q^{6} +1.00000 q^{7} +1.38627 q^{8} -2.05770 q^{9} +O(q^{10})\)	\(q-1.79680 q^{2} +0.970719 q^{3} +1.22848 q^{4} -1.22425 q^{5} -1.74419 q^{6} +1.00000 q^{7} +1.38627 q^{8} -2.05770 q^{9} +2.19973 q^{10} -2.12253 q^{11} +1.19251 q^{12} +4.74770 q^{13} -1.79680 q^{14} -1.18840 q^{15} -4.94780 q^{16} +5.05015 q^{17} +3.69728 q^{18} -3.21336 q^{19} -1.50397 q^{20} +0.970719 q^{21} +3.81376 q^{22} +5.40901 q^{23} +1.34568 q^{24} -3.50121 q^{25} -8.53065 q^{26} -4.90961 q^{27} +1.22848 q^{28} -1.89652 q^{29} +2.13532 q^{30} +2.28810 q^{31} +6.11766 q^{32} -2.06038 q^{33} -9.07409 q^{34} -1.22425 q^{35} -2.52785 q^{36} -10.1869 q^{37} +5.77376 q^{38} +4.60868 q^{39} -1.69714 q^{40} -3.86606 q^{41} -1.74419 q^{42} +9.60699 q^{43} -2.60748 q^{44} +2.51915 q^{45} -9.71889 q^{46} -9.74375 q^{47} -4.80292 q^{48} +1.00000 q^{49} +6.29096 q^{50} +4.90228 q^{51} +5.83245 q^{52} -1.91705 q^{53} +8.82157 q^{54} +2.59851 q^{55} +1.38627 q^{56} -3.11927 q^{57} +3.40766 q^{58} +3.93101 q^{59} -1.45993 q^{60} -10.8204 q^{61} -4.11125 q^{62} -2.05770 q^{63} -1.09659 q^{64} -5.81237 q^{65} +3.70209 q^{66} -6.12868 q^{67} +6.20400 q^{68} +5.25063 q^{69} +2.19973 q^{70} +2.43210 q^{71} -2.85252 q^{72} +3.48438 q^{73} +18.3038 q^{74} -3.39869 q^{75} -3.94755 q^{76} -2.12253 q^{77} -8.28087 q^{78} +12.8650 q^{79} +6.05734 q^{80} +1.40726 q^{81} +6.94653 q^{82} +13.8222 q^{83} +1.19251 q^{84} -6.18265 q^{85} -17.2618 q^{86} -1.84099 q^{87} -2.94239 q^{88} -8.39583 q^{89} -4.52639 q^{90} +4.74770 q^{91} +6.64486 q^{92} +2.22110 q^{93} +17.5075 q^{94} +3.93396 q^{95} +5.93853 q^{96} +2.65308 q^{97} -1.79680 q^{98} +4.36754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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