LMFDB - Embedded newform 8007.2.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.59198 q^{2} +1.00000 q^{3} +0.534400 q^{4} -1.86457 q^{5} -1.59198 q^{6} +2.61461 q^{7} +2.33321 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59198 q^{2} +1.00000 q^{3} +0.534400 q^{4} -1.86457 q^{5} -1.59198 q^{6} +2.61461 q^{7} +2.33321 q^{8} +1.00000 q^{9} +2.96836 q^{10} +5.68819 q^{11} +0.534400 q^{12} +0.882861 q^{13} -4.16240 q^{14} -1.86457 q^{15} -4.78322 q^{16} -1.00000 q^{17} -1.59198 q^{18} +3.90690 q^{19} -0.996427 q^{20} +2.61461 q^{21} -9.05548 q^{22} +0.633312 q^{23} +2.33321 q^{24} -1.52337 q^{25} -1.40550 q^{26} +1.00000 q^{27} +1.39725 q^{28} +6.93755 q^{29} +2.96836 q^{30} +1.23508 q^{31} +2.94837 q^{32} +5.68819 q^{33} +1.59198 q^{34} -4.87512 q^{35} +0.534400 q^{36} +10.2044 q^{37} -6.21970 q^{38} +0.882861 q^{39} -4.35043 q^{40} +6.57386 q^{41} -4.16240 q^{42} -1.10401 q^{43} +3.03977 q^{44} -1.86457 q^{45} -1.00822 q^{46} +1.82388 q^{47} -4.78322 q^{48} -0.163832 q^{49} +2.42518 q^{50} -1.00000 q^{51} +0.471801 q^{52} +7.50615 q^{53} -1.59198 q^{54} -10.6060 q^{55} +6.10042 q^{56} +3.90690 q^{57} -11.0444 q^{58} -10.9416 q^{59} -0.996427 q^{60} +11.1145 q^{61} -1.96623 q^{62} +2.61461 q^{63} +4.87268 q^{64} -1.64616 q^{65} -9.05548 q^{66} +11.9727 q^{67} -0.534400 q^{68} +0.633312 q^{69} +7.76110 q^{70} +1.98123 q^{71} +2.33321 q^{72} -13.8914 q^{73} -16.2453 q^{74} -1.52337 q^{75} +2.08785 q^{76} +14.8724 q^{77} -1.40550 q^{78} -7.81711 q^{79} +8.91865 q^{80} +1.00000 q^{81} -10.4655 q^{82} -8.23180 q^{83} +1.39725 q^{84} +1.86457 q^{85} +1.75756 q^{86} +6.93755 q^{87} +13.2717 q^{88} +6.76191 q^{89} +2.96836 q^{90} +2.30834 q^{91} +0.338442 q^{92} +1.23508 q^{93} -2.90358 q^{94} -7.28469 q^{95} +2.94837 q^{96} -6.40107 q^{97} +0.260817 q^{98} +5.68819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * 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 $

$2$	−1.59198	−1.12570	−0.562850	−	0.826559i	$-0.690295\pi$
$2$	−1.59198	−1.12570	−0.562850	+	0.826559i	$0.690295\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.534400	0.267200
$5$	−1.86457	−0.833862	−0.416931	−	0.908938i	$-0.636894\pi$
$5$	−1.86457	−0.833862	−0.416931	+	0.908938i	$0.636894\pi$
$6$	−1.59198	−0.649923
$7$	2.61461	0.988228	0.494114	−	0.869397i	$-0.335492\pi$
$7$	2.61461	0.988228	0.494114	+	0.869397i	$0.335492\pi$
$8$	2.33321	0.824913
$9$	1.00000	0.333333
$10$	2.96836	0.938678
$11$	5.68819	1.71505	0.857526	−	0.514440i	$-0.172000\pi$
$11$	5.68819	1.71505	0.857526	+	0.514440i	$0.172000\pi$
$12$	0.534400	0.154268
$13$	0.882861	0.244862	0.122431	−	0.992477i	$-0.460931\pi$
$13$	0.882861	0.244862	0.122431	+	0.992477i	$0.460931\pi$
$14$	−4.16240	−1.11245
$15$	−1.86457	−0.481430
$16$	−4.78322	−1.19580
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.59198	−0.375233
$19$	3.90690	0.896304	0.448152	−	0.893957i	$-0.352082\pi$
$19$	3.90690	0.896304	0.448152	+	0.893957i	$0.352082\pi$
$20$	−0.996427	−0.222808
$21$	2.61461	0.570554
$22$	−9.05548	−1.93063
$23$	0.633312	0.132055	0.0660274	−	0.997818i	$-0.478968\pi$
$23$	0.633312	0.132055	0.0660274	+	0.997818i	$0.478968\pi$
$24$	2.33321	0.476264
$25$	−1.52337	−0.304674
$26$	−1.40550	−0.275641
$27$	1.00000	0.192450
$28$	1.39725	0.264055
$29$	6.93755	1.28827	0.644135	−	0.764912i	$-0.277217\pi$
$29$	6.93755	1.28827	0.644135	+	0.764912i	$0.277217\pi$
$30$	2.96836	0.541946
$31$	1.23508	0.221828	0.110914	−	0.993830i	$-0.464622\pi$
$31$	1.23508	0.221828	0.110914	+	0.993830i	$0.464622\pi$
$32$	2.94837	0.521204
$33$	5.68819	0.990186
$34$	1.59198	0.273022
$35$	−4.87512	−0.824046
$36$	0.534400	0.0890667
$37$	10.2044	1.67760	0.838800	−	0.544440i	$-0.183258\pi$
$37$	10.2044	1.67760	0.838800	+	0.544440i	$0.183258\pi$
$38$	−6.21970	−1.00897
$39$	0.882861	0.141371
$40$	−4.35043	−0.687863
$41$	6.57386	1.02667	0.513333	−	0.858190i	$-0.328411\pi$
$41$	6.57386	1.02667	0.513333	+	0.858190i	$0.328411\pi$
$42$	−4.16240	−0.642272
$43$	−1.10401	−0.168360	−0.0841800	−	0.996451i	$-0.526827\pi$
$43$	−1.10401	−0.168360	−0.0841800	+	0.996451i	$0.526827\pi$
$44$	3.03977	0.458262
$45$	−1.86457	−0.277954
$46$	−1.00822	−0.148654
$47$	1.82388	0.266040	0.133020	−	0.991113i	$-0.457533\pi$
$47$	1.82388	0.266040	0.133020	+	0.991113i	$0.457533\pi$
$48$	−4.78322	−0.690398
$49$	−0.163832	−0.0234045
$50$	2.42518	0.342972
$51$	−1.00000	−0.140028
$52$	0.471801	0.0654270
$53$	7.50615	1.03105	0.515525	−	0.856875i	$-0.327597\pi$
$53$	7.50615	1.03105	0.515525	+	0.856875i	$0.327597\pi$
$54$	−1.59198	−0.216641
$55$	−10.6060	−1.43012
$56$	6.10042	0.815202
$57$	3.90690	0.517481
$58$	−11.0444	−1.45021
$59$	−10.9416	−1.42448	−0.712241	−	0.701935i	$-0.752320\pi$
$59$	−10.9416	−1.42448	−0.712241	+	0.701935i	$0.752320\pi$
$60$	−0.996427	−0.128638
$61$	11.1145	1.42306	0.711532	−	0.702654i	$-0.248002\pi$
$61$	11.1145	1.42306	0.711532	+	0.702654i	$0.248002\pi$
$62$	−1.96623	−0.249711
$63$	2.61461	0.329409
$64$	4.87268	0.609085
$65$	−1.64616	−0.204181
$66$	−9.05548	−1.11465
$67$	11.9727	1.46270	0.731350	−	0.682003i	$-0.238891\pi$
$67$	11.9727	1.46270	0.731350	+	0.682003i	$0.238891\pi$
$68$	−0.534400	−0.0648055
$69$	0.633312	0.0762418
$70$	7.76110	0.927628
$71$	1.98123	0.235129	0.117564	−	0.993065i	$-0.462491\pi$
$71$	1.98123	0.235129	0.117564	+	0.993065i	$0.462491\pi$
$72$	2.33321	0.274971
$73$	−13.8914	−1.62586	−0.812932	−	0.582358i	$-0.802130\pi$
$73$	−13.8914	−1.62586	−0.812932	+	0.582358i	$0.802130\pi$
$74$	−16.2453	−1.88847
$75$	−1.52337	−0.175904
$76$	2.08785	0.239492
$77$	14.8724	1.69486
$78$	−1.40550	−0.159141
$79$	−7.81711	−0.879493	−0.439747	−	0.898122i	$-0.644932\pi$
$79$	−7.81711	−0.879493	−0.439747	+	0.898122i	$0.644932\pi$
$80$	8.91865	0.997135
$81$	1.00000	0.111111
$82$	−10.4655	−1.15572
$83$	−8.23180	−0.903557	−0.451779	−	0.892130i	$-0.649210\pi$
$83$	−8.23180	−0.903557	−0.451779	+	0.892130i	$0.649210\pi$
$84$	1.39725	0.152452
$85$	1.86457	0.202241
$86$	1.75756	0.189523
$87$	6.93755	0.743783
$88$	13.2717	1.41477
$89$	6.76191	0.716761	0.358381	−	0.933576i	$-0.383329\pi$
$89$	6.76191	0.716761	0.358381	+	0.933576i	$0.383329\pi$
$90$	2.96836	0.312893
$91$	2.30834	0.241979
$92$	0.338442	0.0352850
$93$	1.23508	0.128072
$94$	−2.90358	−0.299481
$95$	−7.28469	−0.747394
$96$	2.94837	0.300917
$97$	−6.40107	−0.649930	−0.324965	−	0.945726i	$-0.605353\pi$
$97$	−6.40107	−0.649930	−0.324965	+	0.945726i	$0.605353\pi$
$98$	0.260817	0.0263465
$99$	5.68819	0.571684
$100$	−0.814090	−0.0814090
$101$	3.78079	0.376203	0.188101	−	0.982150i	$-0.439767\pi$
$101$	3.78079	0.376203	0.188101	+	0.982150i	$0.439767\pi$
$102$	1.59198	0.157630
$103$	−9.92957	−0.978390	−0.489195	−	0.872174i	$-0.662709\pi$
$103$	−9.92957	−0.978390	−0.489195	+	0.872174i	$0.662709\pi$
$104$	2.05990	0.201990
$105$	−4.87512	−0.475763
$106$	−11.9496	−1.16065
$107$	1.64970	0.159482	0.0797412	−	0.996816i	$-0.474591\pi$
$107$	1.64970	0.159482	0.0797412	+	0.996816i	$0.474591\pi$
$108$	0.534400	0.0514227
$109$	8.73915	0.837059	0.418530	−	0.908203i	$-0.362546\pi$
$109$	8.73915	0.837059	0.418530	+	0.908203i	$0.362546\pi$
$110$	16.8846	1.60988
$111$	10.2044	0.968563
$112$	−12.5062	−1.18173
$113$	20.8354	1.96003	0.980015	−	0.198924i	$-0.0637446\pi$
$113$	20.8354	1.96003	0.980015	+	0.198924i	$0.0637446\pi$
$114$	−6.21970	−0.582529
$115$	−1.18086	−0.110115
$116$	3.70743	0.344226
$117$	0.882861	0.0816206
$118$	17.4189	1.60354
$119$	−2.61461	−0.239681
$120$	−4.35043	−0.397138
$121$	21.3555	1.94141
$122$	−17.6940	−1.60194
$123$	6.57386	0.592745
$124$	0.660029	0.0592723
$125$	12.1633	1.08792
$126$	−4.16240	−0.370816
$127$	−20.1551	−1.78848	−0.894238	−	0.447592i	$-0.852282\pi$
$127$	−20.1551	−1.78848	−0.894238	+	0.447592i	$0.852282\pi$
$128$	−13.6540	−1.20685
$129$	−1.10401	−0.0972027
$130$	2.62065	0.229846
$131$	−6.55183	−0.572436	−0.286218	−	0.958165i	$-0.592398\pi$
$131$	−6.55183	−0.572436	−0.286218	+	0.958165i	$0.592398\pi$
$132$	3.03977	0.264578
$133$	10.2150	0.885753
$134$	−19.0603	−1.64656
$135$	−1.86457	−0.160477
$136$	−2.33321	−0.200071
$137$	18.9231	1.61671	0.808356	−	0.588694i	$-0.200358\pi$
$137$	18.9231	1.61671	0.808356	+	0.588694i	$0.200358\pi$
$138$	−1.00822	−0.0858254
$139$	−12.7188	−1.07880	−0.539399	−	0.842050i	$-0.681349\pi$
$139$	−12.7188	−1.07880	−0.539399	+	0.842050i	$0.681349\pi$
$140$	−2.60527	−0.220185
$141$	1.82388	0.153598
$142$	−3.15408	−0.264684
$143$	5.02188	0.419951
$144$	−4.78322	−0.398601
$145$	−12.9356	−1.07424
$146$	22.1148	1.83024
$147$	−0.163832	−0.0135126
$148$	5.45325	0.448255
$149$	−11.7795	−0.965016	−0.482508	−	0.875891i	$-0.660274\pi$
$149$	−11.7795	−0.965016	−0.482508	+	0.875891i	$0.660274\pi$
$150$	2.42518	0.198015
$151$	7.85323	0.639087	0.319543	−	0.947572i	$-0.396470\pi$
$151$	7.85323	0.639087	0.319543	+	0.947572i	$0.396470\pi$
$152$	9.11560	0.739372
$153$	−1.00000	−0.0808452
$154$	−23.6765	−1.90791
$155$	−2.30290	−0.184974
$156$	0.471801	0.0377743
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	12.4447	0.990045
$159$	7.50615	0.595277
$160$	−5.49745	−0.434612
$161$	1.65586	0.130500
$162$	−1.59198	−0.125078
$163$	14.6400	1.14669	0.573346	−	0.819313i	$-0.305645\pi$
$163$	14.6400	1.14669	0.573346	+	0.819313i	$0.305645\pi$
$164$	3.51307	0.274325
$165$	−10.6060	−0.825678
$166$	13.1049	1.01713
$167$	−9.78221	−0.756970	−0.378485	−	0.925607i	$-0.623555\pi$
$167$	−9.78221	−0.756970	−0.378485	+	0.925607i	$0.623555\pi$
$168$	6.10042	0.470657
$169$	−12.2206	−0.940043
$170$	−2.96836	−0.227663
$171$	3.90690	0.298768
$172$	−0.589983	−0.0449858
$173$	12.3098	0.935893	0.467947	−	0.883757i	$-0.344994\pi$
$173$	12.3098	0.935893	0.467947	+	0.883757i	$0.344994\pi$
$174$	−11.0444	−0.837277
$175$	−3.98302	−0.301088
$176$	−27.2078	−2.05087
$177$	−10.9416	−0.822425
$178$	−10.7648	−0.806858
$179$	10.9579	0.819029	0.409515	−	0.912304i	$-0.365698\pi$
$179$	10.9579	0.819029	0.409515	+	0.912304i	$0.365698\pi$
$180$	−0.996427	−0.0742693
$181$	−11.0342	−0.820169	−0.410084	−	0.912048i	$-0.634501\pi$
$181$	−11.0342	−0.820169	−0.410084	+	0.912048i	$0.634501\pi$
$182$	−3.67482	−0.272396
$183$	11.1145	0.821606
$184$	1.47765	0.108934
$185$	−19.0269	−1.39889
$186$	−1.96623	−0.144171
$187$	−5.68819	−0.415961
$188$	0.974681	0.0710859
$189$	2.61461	0.190185
$190$	11.5971	0.841341
$191$	−15.0524	−1.08915	−0.544576	−	0.838712i	$-0.683309\pi$
$191$	−15.0524	−1.08915	−0.544576	+	0.838712i	$0.683309\pi$
$192$	4.87268	0.351656
$193$	−9.68339	−0.697026	−0.348513	−	0.937304i	$-0.613313\pi$
$193$	−9.68339	−0.697026	−0.348513	+	0.937304i	$0.613313\pi$
$194$	10.1904	0.731626
$195$	−1.64616	−0.117884
$196$	−0.0875516	−0.00625369
$197$	−21.0075	−1.49672	−0.748360	−	0.663293i	$-0.769158\pi$
$197$	−21.0075	−1.49672	−0.748360	+	0.663293i	$0.769158\pi$
$198$	−9.05548	−0.643545
$199$	−22.1599	−1.57087	−0.785435	−	0.618944i	$-0.787561\pi$
$199$	−22.1599	−1.57087	−0.785435	+	0.618944i	$0.787561\pi$
$200$	−3.55434	−0.251330
$201$	11.9727	0.844490
$202$	−6.01894	−0.423491
$203$	18.1390	1.27311
$204$	−0.534400	−0.0374155
$205$	−12.2574	−0.856097
$206$	15.8077	1.10137
$207$	0.633312	0.0440182
$208$	−4.22292	−0.292807
$209$	22.2232	1.53721
$210$	7.76110	0.535567
$211$	−14.1504	−0.974155	−0.487078	−	0.873359i	$-0.661937\pi$
$211$	−14.1504	−0.974155	−0.487078	+	0.873359i	$0.661937\pi$
$212$	4.01129	0.275496
$213$	1.98123	0.135752
$214$	−2.62629	−0.179529
$215$	2.05851	0.140389
$216$	2.33321	0.158755
$217$	3.22926	0.219216
$218$	−13.9126	−0.942277
$219$	−13.8914	−0.938694
$220$	−5.66786	−0.382127
$221$	−0.882861	−0.0593877
$222$	−16.2453	−1.09031
$223$	6.14262	0.411340	0.205670	−	0.978621i	$-0.434063\pi$
$223$	6.14262	0.411340	0.205670	+	0.978621i	$0.434063\pi$
$224$	7.70884	0.515068
$225$	−1.52337	−0.101558
$226$	−33.1695	−2.20641
$227$	22.7116	1.50742	0.753710	−	0.657207i	$-0.228262\pi$
$227$	22.7116	1.50742	0.753710	+	0.657207i	$0.228262\pi$
$228$	2.08785	0.138271
$229$	−12.2457	−0.809219	−0.404609	−	0.914490i	$-0.632592\pi$
$229$	−12.2457	−0.809219	−0.404609	+	0.914490i	$0.632592\pi$
$230$	1.87990	0.123957
$231$	14.8724	0.978530
$232$	16.1867	1.06271
$233$	−29.5961	−1.93891	−0.969453	−	0.245277i	$-0.921121\pi$
$233$	−29.5961	−1.93891	−0.969453	+	0.245277i	$0.921121\pi$
$234$	−1.40550	−0.0918802
$235$	−3.40075	−0.221841
$236$	−5.84722	−0.380621
$237$	−7.81711	−0.507776
$238$	4.16240	0.269808
$239$	29.2497	1.89201	0.946003	−	0.324158i	$-0.105081\pi$
$239$	29.2497	1.89201	0.946003	+	0.324158i	$0.105081\pi$
$240$	8.91865	0.575696
$241$	−25.3890	−1.63545	−0.817726	−	0.575607i	$-0.804766\pi$
$241$	−25.3890	−1.63545	−0.817726	+	0.575607i	$0.804766\pi$
$242$	−33.9975	−2.18544
$243$	1.00000	0.0641500
$244$	5.93958	0.380243
$245$	0.305476	0.0195161
$246$	−10.4655	−0.667253
$247$	3.44925	0.219470
$248$	2.88170	0.182988
$249$	−8.23180	−0.521669
$250$	−19.3637	−1.22467
$251$	−25.2105	−1.59127	−0.795636	−	0.605775i	$-0.792863\pi$
$251$	−25.2105	−1.59127	−0.795636	+	0.605775i	$0.792863\pi$
$252$	1.39725	0.0880182
$253$	3.60240	0.226481
$254$	32.0865	2.01329
$255$	1.86457	0.116764
$256$	11.9915	0.749467
$257$	−7.98328	−0.497984	−0.248992	−	0.968506i	$-0.580099\pi$
$257$	−7.98328	−0.497984	−0.248992	+	0.968506i	$0.580099\pi$
$258$	1.75756	0.109421
$259$	26.6806	1.65785
$260$	−0.879707	−0.0545571
$261$	6.93755	0.429423
$262$	10.4304	0.644391
$263$	−0.879012	−0.0542022	−0.0271011	−	0.999633i	$-0.508628\pi$
$263$	−0.879012	−0.0542022	−0.0271011	+	0.999633i	$0.508628\pi$
$264$	13.2717	0.816817
$265$	−13.9958	−0.859753
$266$	−16.2621	−0.997092
$267$	6.76191	0.413822
$268$	6.39822	0.390833
$269$	−8.79794	−0.536420	−0.268210	−	0.963360i	$-0.586432\pi$
$269$	−8.79794	−0.536420	−0.268210	+	0.963360i	$0.586432\pi$
$270$	2.96836	0.180649
$271$	−24.5399	−1.49069	−0.745345	−	0.666679i	$-0.767715\pi$
$271$	−24.5399	−1.49069	−0.745345	+	0.666679i	$0.767715\pi$
$272$	4.78322	0.290025
$273$	2.30834	0.139707
$274$	−30.1252	−1.81993
$275$	−8.66522	−0.522533
$276$	0.338442	0.0203718
$277$	5.14656	0.309227	0.154614	−	0.987975i	$-0.450587\pi$
$277$	5.14656	0.309227	0.154614	+	0.987975i	$0.450587\pi$
$278$	20.2481	1.21440
$279$	1.23508	0.0739425
$280$	−11.3747	−0.679766
$281$	9.17757	0.547488	0.273744	−	0.961803i	$-0.411738\pi$
$281$	9.17757	0.547488	0.273744	+	0.961803i	$0.411738\pi$
$282$	−2.90358	−0.172906
$283$	−20.0986	−1.19474	−0.597369	−	0.801966i	$-0.703787\pi$
$283$	−20.0986	−1.19474	−0.597369	+	0.801966i	$0.703787\pi$
$284$	1.05877	0.0628264
$285$	−7.28469	−0.431508
$286$	−7.99473	−0.472738
$287$	17.1881	1.01458
$288$	2.94837	0.173735
$289$	1.00000	0.0588235
$290$	20.5931	1.20927
$291$	−6.40107	−0.375237
$292$	−7.42356	−0.434431
$293$	7.21911	0.421745	0.210872	−	0.977514i	$-0.432370\pi$
$293$	7.21911	0.421745	0.210872	+	0.977514i	$0.432370\pi$
$294$	0.260817	0.0152111
$295$	20.4015	1.18782
$296$	23.8091	1.38387
$297$	5.68819	0.330062
$298$	18.7528	1.08632
$299$	0.559127	0.0323351
$300$	−0.814090	−0.0470015
$301$	−2.88655	−0.166378
$302$	−12.5022	−0.719420
$303$	3.78079	0.217201
$304$	−18.6875	−1.07180
$305$	−20.7237	−1.18664
$306$	1.59198	0.0910074
$307$	16.5973	0.947256	0.473628	−	0.880725i	$-0.342944\pi$
$307$	16.5973	0.947256	0.473628	+	0.880725i	$0.342944\pi$
$308$	7.94779	0.452868
$309$	−9.92957	−0.564874
$310$	3.66617	0.208225
$311$	−7.35916	−0.417300	−0.208650	−	0.977990i	$-0.566907\pi$
$311$	−7.35916	−0.417300	−0.208650	+	0.977990i	$0.566907\pi$
$312$	2.05990	0.116619
$313$	−13.7150	−0.775216	−0.387608	−	0.921824i	$-0.626699\pi$
$313$	−13.7150	−0.775216	−0.387608	+	0.921824i	$0.626699\pi$
$314$	1.59198	0.0898406
$315$	−4.87512	−0.274682
$316$	−4.17746	−0.235001
$317$	30.2223	1.69745	0.848725	−	0.528834i	$-0.177371\pi$
$317$	30.2223	1.69745	0.848725	+	0.528834i	$0.177371\pi$
$318$	−11.9496	−0.670103
$319$	39.4621	2.20945
$320$	−9.08546	−0.507893
$321$	1.64970	0.0920772
$322$	−2.63610	−0.146904
$323$	−3.90690	−0.217386
$324$	0.534400	0.0296889
$325$	−1.34493	−0.0746031
$326$	−23.3066	−1.29083
$327$	8.73915	0.483276
$328$	15.3382	0.846909
$329$	4.76873	0.262908
$330$	16.8846	0.929466
$331$	−0.846452	−0.0465252	−0.0232626	−	0.999729i	$-0.507405\pi$
$331$	−0.846452	−0.0465252	−0.0232626	+	0.999729i	$0.507405\pi$
$332$	−4.39907	−0.241431
$333$	10.2044	0.559200
$334$	15.5731	0.852121
$335$	−22.3240	−1.21969
$336$	−12.5062	−0.682271
$337$	−7.19323	−0.391840	−0.195920	−	0.980620i	$-0.562769\pi$
$337$	−7.19323	−0.391840	−0.195920	+	0.980620i	$0.562769\pi$
$338$	19.4549	1.05821
$339$	20.8354	1.13162
$340$	0.996427	0.0540389
$341$	7.02538	0.380446
$342$	−6.21970	−0.336323
$343$	−18.7306	−1.01136
$344$	−2.57588	−0.138882
$345$	−1.18086	−0.0635752
$346$	−19.5969	−1.05353
$347$	0.383790	0.0206029	0.0103015	−	0.999947i	$-0.496721\pi$
$347$	0.383790	0.0206029	0.0103015	+	0.999947i	$0.496721\pi$
$348$	3.70743	0.198739
$349$	13.9983	0.749313	0.374656	−	0.927164i	$-0.377761\pi$
$349$	13.9983	0.749313	0.374656	+	0.927164i	$0.377761\pi$
$350$	6.34089	0.338935
$351$	0.882861	0.0471236
$352$	16.7709	0.893892
$353$	15.6443	0.832662	0.416331	−	0.909213i	$-0.363316\pi$
$353$	15.6443	0.832662	0.416331	+	0.909213i	$0.363316\pi$
$354$	17.4189	0.925803
$355$	−3.69415	−0.196065
$356$	3.61357	0.191519
$357$	−2.61461	−0.138380
$358$	−17.4447	−0.921981
$359$	28.9166	1.52616	0.763079	−	0.646306i	$-0.223687\pi$
$359$	28.9166	1.52616	0.763079	+	0.646306i	$0.223687\pi$
$360$	−4.35043	−0.229288
$361$	−3.73615	−0.196639
$362$	17.5663	0.923264
$363$	21.3555	1.12087
$364$	1.23357	0.0646569
$365$	25.9015	1.35575
$366$	−17.6940	−0.924882
$367$	12.5761	0.656468	0.328234	−	0.944596i	$-0.393546\pi$
$367$	12.5761	0.656468	0.328234	+	0.944596i	$0.393546\pi$
$368$	−3.02927	−0.157912
$369$	6.57386	0.342222
$370$	30.2905	1.57473
$371$	19.6256	1.01891
$372$	0.660029	0.0342209
$373$	23.3459	1.20881	0.604404	−	0.796678i	$-0.293411\pi$
$373$	23.3459	1.20881	0.604404	+	0.796678i	$0.293411\pi$
$374$	9.05548	0.468248
$375$	12.1633	0.628110
$376$	4.25549	0.219460
$377$	6.12489	0.315448
$378$	−4.16240	−0.214091
$379$	16.4295	0.843927	0.421964	−	0.906613i	$-0.361341\pi$
$379$	16.4295	0.843927	0.421964	+	0.906613i	$0.361341\pi$
$380$	−3.89294	−0.199704
$381$	−20.1551	−1.03258
$382$	23.9631	1.22606
$383$	−33.7205	−1.72304	−0.861519	−	0.507725i	$-0.830487\pi$
$383$	−33.7205	−1.72304	−0.861519	+	0.507725i	$0.830487\pi$
$384$	−13.6540	−0.696776
$385$	−27.7306	−1.41328
$386$	15.4158	0.784642
$387$	−1.10401	−0.0561200
$388$	−3.42073	−0.173661
$389$	−3.75012	−0.190139	−0.0950693	−	0.995471i	$-0.530307\pi$
$389$	−3.75012	−0.190139	−0.0950693	+	0.995471i	$0.530307\pi$
$390$	2.62065	0.132702
$391$	−0.633312	−0.0320280
$392$	−0.382253	−0.0193067
$393$	−6.55183	−0.330496
$394$	33.4435	1.68486
$395$	14.5756	0.733376
$396$	3.03977	0.152754
$397$	−7.54765	−0.378806	−0.189403	−	0.981899i	$-0.560655\pi$
$397$	−7.54765	−0.378806	−0.189403	+	0.981899i	$0.560655\pi$
$398$	35.2781	1.76833
$399$	10.2150	0.511390
$400$	7.28662	0.364331
$401$	22.5261	1.12490	0.562450	−	0.826832i	$-0.309859\pi$
$401$	22.5261	1.12490	0.562450	+	0.826832i	$0.309859\pi$
$402$	−19.0603	−0.950642
$403$	1.09041	0.0543171
$404$	2.02045	0.100521
$405$	−1.86457	−0.0926513
$406$	−28.8769	−1.43313
$407$	58.0448	2.87717
$408$	−2.33321	−0.115511
$409$	30.2932	1.49790	0.748952	−	0.662624i	$-0.230557\pi$
$409$	30.2932	1.49790	0.748952	+	0.662624i	$0.230557\pi$
$410$	19.5136	0.963708
$411$	18.9231	0.933409
$412$	−5.30637	−0.261426
$413$	−28.6081	−1.40771
$414$	−1.00822	−0.0495513
$415$	15.3488	0.753442
$416$	2.60300	0.127623
$417$	−12.7188	−0.622845
$418$	−35.3788	−1.73043
$419$	15.2599	0.745494	0.372747	−	0.927933i	$-0.378416\pi$
$419$	15.2599	0.745494	0.372747	+	0.927933i	$0.378416\pi$
$420$	−2.60527	−0.127124
$421$	−25.6919	−1.25215	−0.626074	−	0.779764i	$-0.715339\pi$
$421$	−25.6919	−1.25215	−0.626074	+	0.779764i	$0.715339\pi$
$422$	22.5272	1.09661
$423$	1.82388	0.0886800
$424$	17.5134	0.850526
$425$	1.52337	0.0738944
$426$	−3.15408	−0.152816
$427$	29.0600	1.40631
$428$	0.881599	0.0426137
$429$	5.02188	0.242459
$430$	−3.27710	−0.158036
$431$	19.7179	0.949779	0.474889	−	0.880046i	$-0.342488\pi$
$431$	19.7179	0.949779	0.474889	+	0.880046i	$0.342488\pi$
$432$	−4.78322	−0.230133
$433$	3.41287	0.164012	0.0820060	−	0.996632i	$-0.473867\pi$
$433$	3.41287	0.164012	0.0820060	+	0.996632i	$0.473867\pi$
$434$	−5.14091	−0.246772
$435$	−12.9356	−0.620212
$436$	4.67020	0.223662
$437$	2.47429	0.118361
$438$	22.1148	1.05669
$439$	−24.5881	−1.17353	−0.586763	−	0.809759i	$-0.699598\pi$
$439$	−24.5881	−1.17353	−0.586763	+	0.809759i	$0.699598\pi$
$440$	−24.7460	−1.17972
$441$	−0.163832	−0.00780150
$442$	1.40550	0.0668527
$443$	2.24748	0.106781	0.0533906	−	0.998574i	$-0.482997\pi$
$443$	2.24748	0.106781	0.0533906	+	0.998574i	$0.482997\pi$
$444$	5.45325	0.258800
$445$	−12.6081	−0.597680
$446$	−9.77892	−0.463045
$447$	−11.7795	−0.557152
$448$	12.7401	0.601915
$449$	−31.5153	−1.48730	−0.743649	−	0.668571i	$-0.766906\pi$
$449$	−31.5153	−1.48730	−0.743649	+	0.668571i	$0.766906\pi$
$450$	2.42518	0.114324
$451$	37.3934	1.76078
$452$	11.1344	0.523720
$453$	7.85323	0.368977
$454$	−36.1564	−1.69690
$455$	−4.30406	−0.201777
$456$	9.11560	0.426877
$457$	−1.72007	−0.0804615	−0.0402308	−	0.999190i	$-0.512809\pi$
$457$	−1.72007	−0.0804615	−0.0402308	+	0.999190i	$0.512809\pi$
$458$	19.4949	0.910937
$459$	−1.00000	−0.0466760
$460$	−0.631050	−0.0294228
$461$	11.8258	0.550784	0.275392	−	0.961332i	$-0.411192\pi$
$461$	11.8258	0.550784	0.275392	+	0.961332i	$0.411192\pi$
$462$	−23.6765	−1.10153
$463$	−6.65263	−0.309174	−0.154587	−	0.987979i	$-0.549405\pi$
$463$	−6.65263	−0.309174	−0.154587	+	0.987979i	$0.549405\pi$
$464$	−33.1838	−1.54052
$465$	−2.30290	−0.106795
$466$	47.1164	2.18263
$467$	20.2494	0.937030	0.468515	−	0.883456i	$-0.344789\pi$
$467$	20.2494	0.937030	0.468515	+	0.883456i	$0.344789\pi$
$468$	0.471801	0.0218090
$469$	31.3039	1.44548
$470$	5.41393	0.249726
$471$	−1.00000	−0.0460776
$472$	−25.5291	−1.17507
$473$	−6.27982	−0.288746
$474$	12.4447	0.571603
$475$	−5.95166	−0.273081
$476$	−1.39725	−0.0640427
$477$	7.50615	0.343683
$478$	−46.5649	−2.12983
$479$	−7.60670	−0.347559	−0.173780	−	0.984785i	$-0.555598\pi$
$479$	−7.60670	−0.347559	−0.173780	+	0.984785i	$0.555598\pi$
$480$	−5.49745	−0.250923
$481$	9.00911	0.410780
$482$	40.4189	1.84103
$483$	1.65586	0.0753444
$484$	11.4124	0.518743
$485$	11.9353	0.541952
$486$	−1.59198	−0.0722137
$487$	16.0569	0.727608	0.363804	−	0.931475i	$-0.381478\pi$
$487$	16.0569	0.727608	0.363804	+	0.931475i	$0.381478\pi$
$488$	25.9324	1.17390
$489$	14.6400	0.662043
$490$	−0.486311	−0.0219693
$491$	36.4790	1.64628	0.823138	−	0.567842i	$-0.192221\pi$
$491$	36.4790	1.64628	0.823138	+	0.567842i	$0.192221\pi$
$492$	3.51307	0.158382
$493$	−6.93755	−0.312451
$494$	−5.49113	−0.247058
$495$	−10.6060	−0.476706
$496$	−5.90767	−0.265262
$497$	5.18014	0.232361
$498$	13.1049	0.587243
$499$	−16.0997	−0.720722	−0.360361	−	0.932813i	$-0.617346\pi$
$499$	−16.0997	−0.720722	−0.360361	+	0.932813i	$0.617346\pi$
$500$	6.50007	0.290692
$501$	−9.78221	−0.437037
$502$	40.1346	1.79130
$503$	−32.8788	−1.46599	−0.732997	−	0.680232i	$-0.761879\pi$
$503$	−32.8788	−1.46599	−0.732997	+	0.680232i	$0.761879\pi$
$504$	6.10042	0.271734
$505$	−7.04955	−0.313701
$506$	−5.73495	−0.254949
$507$	−12.2206	−0.542734
$508$	−10.7709	−0.477881
$509$	15.9097	0.705187	0.352593	−	0.935777i	$-0.385300\pi$
$509$	15.9097	0.705187	0.352593	+	0.935777i	$0.385300\pi$
$510$	−2.96836	−0.131441
$511$	−36.3205	−1.60673
$512$	8.21775	0.363177
$513$	3.90690	0.172494
$514$	12.7092	0.560580
$515$	18.5144	0.815842
$516$	−0.589983	−0.0259726
$517$	10.3746	0.456273
$518$	−42.4750	−1.86624
$519$	12.3098	0.540338
$520$	−3.84083	−0.168431
$521$	4.75619	0.208373	0.104186	−	0.994558i	$-0.466776\pi$
$521$	4.75619	0.208373	0.104186	+	0.994558i	$0.466776\pi$
$522$	−11.0444	−0.483402
$523$	20.1416	0.880731	0.440365	−	0.897819i	$-0.354849\pi$
$523$	20.1416	0.880731	0.440365	+	0.897819i	$0.354849\pi$
$524$	−3.50130	−0.152955
$525$	−3.98302	−0.173833
$526$	1.39937	0.0610154
$527$	−1.23508	−0.0538011
$528$	−27.2078	−1.18407
$529$	−22.5989	−0.982562
$530$	22.2810	0.967824
$531$	−10.9416	−0.474827
$532$	5.45890	0.236673
$533$	5.80381	0.251391
$534$	−10.7648	−0.465840
$535$	−3.07598	−0.132986
$536$	27.9348	1.20660
$537$	10.9579	0.472867
$538$	14.0061	0.603848
$539$	−0.931904	−0.0401400
$540$	−0.996427	−0.0428794
$541$	30.2555	1.30078	0.650392	−	0.759598i	$-0.274604\pi$
$541$	30.2555	1.30078	0.650392	+	0.759598i	$0.274604\pi$
$542$	39.0670	1.67807
$543$	−11.0342	−0.473525
$544$	−2.94837	−0.126410
$545$	−16.2948	−0.697992
$546$	−3.67482	−0.157268
$547$	−2.16566	−0.0925971	−0.0462985	−	0.998928i	$-0.514743\pi$
$547$	−2.16566	−0.0925971	−0.0462985	+	0.998928i	$0.514743\pi$
$548$	10.1125	0.431985
$549$	11.1145	0.474355
$550$	13.7949	0.588215
$551$	27.1043	1.15468
$552$	1.47765	0.0628929
$553$	−20.4387	−0.869140
$554$	−8.19323	−0.348097
$555$	−19.0269	−0.807648
$556$	−6.79695	−0.288255
$557$	35.1574	1.48967	0.744833	−	0.667251i	$-0.232529\pi$
$557$	35.1574	1.48967	0.744833	+	0.667251i	$0.232529\pi$
$558$	−1.96623	−0.0832371
$559$	−0.974688	−0.0412249
$560$	23.3188	0.985398
$561$	−5.68819	−0.240155
$562$	−14.6105	−0.616307
$563$	−4.00305	−0.168709	−0.0843543	−	0.996436i	$-0.526883\pi$
$563$	−4.00305	−0.168709	−0.0843543	+	0.996436i	$0.526883\pi$
$564$	0.974681	0.0410415
$565$	−38.8491	−1.63439
$566$	31.9966	1.34492
$567$	2.61461	0.109803
$568$	4.62262	0.193961
$569$	22.7637	0.954302	0.477151	−	0.878821i	$-0.341669\pi$
$569$	22.7637	0.954302	0.477151	+	0.878821i	$0.341669\pi$
$570$	11.5971	0.485748
$571$	−10.0539	−0.420742	−0.210371	−	0.977622i	$-0.567467\pi$
$571$	−10.0539	−0.420742	−0.210371	+	0.977622i	$0.567467\pi$
$572$	2.68369	0.112211
$573$	−15.0524	−0.628822
$574$	−27.3631	−1.14211
$575$	−0.964770	−0.0402337
$576$	4.87268	0.203028
$577$	27.0188	1.12481	0.562405	−	0.826862i	$-0.309876\pi$
$577$	27.0188	1.12481	0.562405	+	0.826862i	$0.309876\pi$
$578$	−1.59198	−0.0662176
$579$	−9.68339	−0.402428
$580$	−6.91276	−0.287037
$581$	−21.5229	−0.892921
$582$	10.1904	0.422405
$583$	42.6964	1.76830
$584$	−32.4115	−1.34120
$585$	−1.64616	−0.0680603
$586$	−11.4927	−0.474758
$587$	−28.6705	−1.18336	−0.591678	−	0.806174i	$-0.701534\pi$
$587$	−28.6705	−1.18336	−0.591678	+	0.806174i	$0.701534\pi$
$588$	−0.0875516	−0.00361057
$589$	4.82535	0.198825
$590$	−32.4788	−1.33713
$591$	−21.0075	−0.864131
$592$	−48.8101	−2.00608
$593$	−37.7079	−1.54848	−0.774238	−	0.632895i	$-0.781867\pi$
$593$	−37.7079	−1.54848	−0.774238	+	0.632895i	$0.781867\pi$
$594$	−9.05548	−0.371551
$595$	4.87512	0.199861
$596$	−6.29498	−0.257852
$597$	−22.1599	−0.906943
$598$	−0.890119	−0.0363997
$599$	−11.1909	−0.457246	−0.228623	−	0.973515i	$-0.573422\pi$
$599$	−11.1909	−0.457246	−0.228623	+	0.973515i	$0.573422\pi$
$600$	−3.55434	−0.145105
$601$	3.37684	0.137744	0.0688720	−	0.997626i	$-0.478060\pi$
$601$	3.37684	0.137744	0.0688720	+	0.997626i	$0.478060\pi$
$602$	4.59534	0.187292
$603$	11.9727	0.487566
$604$	4.19677	0.170764
$605$	−39.8188	−1.61886
$606$	−6.01894	−0.244503
$607$	−36.5905	−1.48516	−0.742581	−	0.669756i	$-0.766399\pi$
$607$	−36.5905	−1.48516	−0.742581	+	0.669756i	$0.766399\pi$
$608$	11.5190	0.467157
$609$	18.1390	0.735028
$610$	32.9918	1.33580
$611$	1.61023	0.0651430
$612$	−0.534400	−0.0216018
$613$	26.2323	1.05951	0.529757	−	0.848150i	$-0.322283\pi$
$613$	26.2323	1.05951	0.529757	+	0.848150i	$0.322283\pi$
$614$	−26.4225	−1.06633
$615$	−12.2574	−0.494268
$616$	34.7003	1.39811
$617$	15.2364	0.613396	0.306698	−	0.951807i	$-0.400776\pi$
$617$	15.2364	0.613396	0.306698	+	0.951807i	$0.400776\pi$
$618$	15.8077	0.635878
$619$	14.4896	0.582387	0.291193	−	0.956664i	$-0.405948\pi$
$619$	14.4896	0.582387	0.291193	+	0.956664i	$0.405948\pi$
$620$	−1.23067	−0.0494249
$621$	0.633312	0.0254139
$622$	11.7156	0.469754
$623$	17.6797	0.708324
$624$	−4.22292	−0.169052
$625$	−15.0625	−0.602499
$626$	21.8340	0.872661
$627$	22.2232	0.887508
$628$	−0.534400	−0.0213249
$629$	−10.2044	−0.406878
$630$	7.76110	0.309209
$631$	−16.1609	−0.643354	−0.321677	−	0.946850i	$-0.604246\pi$
$631$	−16.1609	−0.643354	−0.321677	+	0.946850i	$0.604246\pi$
$632$	−18.2389	−0.725505
$633$	−14.1504	−0.562429
$634$	−48.1132	−1.91082
$635$	37.5806	1.49134
$636$	4.01129	0.159058
$637$	−0.144641	−0.00573087
$638$	−62.8228	−2.48718
$639$	1.98123	0.0783762
$640$	25.4588	1.00635
$641$	15.1881	0.599896	0.299948	−	0.953956i	$-0.403031\pi$
$641$	15.1881	0.599896	0.299948	+	0.953956i	$0.403031\pi$
$642$	−2.62629	−0.103651
$643$	27.1628	1.07120	0.535599	−	0.844473i	$-0.320086\pi$
$643$	27.1628	1.07120	0.535599	+	0.844473i	$0.320086\pi$
$644$	0.884893	0.0348697
$645$	2.05851	0.0810536
$646$	6.21970	0.244711
$647$	−31.1586	−1.22497	−0.612485	−	0.790483i	$-0.709830\pi$
$647$	−31.1586	−1.22497	−0.612485	+	0.790483i	$0.709830\pi$
$648$	2.33321	0.0916570
$649$	−62.2381	−2.44306
$650$	2.14110	0.0839807
$651$	3.22926	0.126565
$652$	7.82361	0.306396
$653$	−15.0768	−0.590001	−0.295000	−	0.955497i	$-0.595320\pi$
$653$	−15.0768	−0.590001	−0.295000	+	0.955497i	$0.595320\pi$
$654$	−13.9126	−0.544024
$655$	12.2164	0.477332
$656$	−31.4442	−1.22769
$657$	−13.8914	−0.541955
$658$	−7.59172	−0.295956
$659$	18.0964	0.704936	0.352468	−	0.935824i	$-0.385343\pi$
$659$	18.0964	0.704936	0.352468	+	0.935824i	$0.385343\pi$
$660$	−5.66786	−0.220621
$661$	−9.59352	−0.373145	−0.186572	−	0.982441i	$-0.559738\pi$
$661$	−9.59352	−0.373145	−0.186572	+	0.982441i	$0.559738\pi$
$662$	1.34753	0.0523734
$663$	−0.882861	−0.0342875
$664$	−19.2065	−0.745356
$665$	−19.0466	−0.738596
$666$	−16.2453	−0.629491
$667$	4.39363	0.170122
$668$	−5.22762	−0.202263
$669$	6.14262	0.237487
$670$	35.5393	1.37300
$671$	63.2212	2.44063
$672$	7.70884	0.297375
$673$	37.5029	1.44563	0.722816	−	0.691041i	$-0.242848\pi$
$673$	37.5029	1.44563	0.722816	+	0.691041i	$0.242848\pi$
$674$	11.4515	0.441095
$675$	−1.52337	−0.0586346
$676$	−6.53067	−0.251179
$677$	7.77236	0.298716	0.149358	−	0.988783i	$-0.452279\pi$
$677$	7.77236	0.298716	0.149358	+	0.988783i	$0.452279\pi$
$678$	−33.1695	−1.27387
$679$	−16.7363	−0.642280
$680$	4.35043	0.166831
$681$	22.7116	0.870309
$682$	−11.1843	−0.428268
$683$	−6.01871	−0.230300	−0.115150	−	0.993348i	$-0.536735\pi$
$683$	−6.01871	−0.230300	−0.115150	+	0.993348i	$0.536735\pi$
$684$	2.08785	0.0798308
$685$	−35.2835	−1.34811
$686$	29.8187	1.13848
$687$	−12.2457	−0.467203
$688$	5.28072	0.201326
$689$	6.62689	0.252465
$690$	1.87990	0.0715665
$691$	36.7762	1.39903	0.699516	−	0.714617i	$-0.253399\pi$
$691$	36.7762	1.39903	0.699516	+	0.714617i	$0.253399\pi$
$692$	6.57833	0.250071
$693$	14.8724	0.564955
$694$	−0.610986	−0.0231927
$695$	23.7152	0.899569
$696$	16.1867	0.613556
$697$	−6.57386	−0.249003
$698$	−22.2850	−0.843501
$699$	−29.5961	−1.11943
$700$	−2.12853	−0.0804507
$701$	24.4635	0.923975	0.461987	−	0.886887i	$-0.347137\pi$
$701$	24.4635	0.923975	0.461987	+	0.886887i	$0.347137\pi$
$702$	−1.40550	−0.0530471
$703$	39.8677	1.50364
$704$	27.7167	1.04461
$705$	−3.40075	−0.128080
$706$	−24.9054	−0.937328
$707$	9.88528	0.371774
$708$	−5.84722	−0.219752
$709$	−0.216574	−0.00813363	−0.00406681	−	0.999992i	$-0.501295\pi$
$709$	−0.216574	−0.00813363	−0.00406681	+	0.999992i	$0.501295\pi$
$710$	5.88101	0.220710
$711$	−7.81711	−0.293164
$712$	15.7769	0.591266
$713$	0.782194	0.0292934
$714$	4.16240	0.155774
$715$	−9.36365	−0.350181
$716$	5.85588	0.218845
$717$	29.2497	1.09235
$718$	−46.0346	−1.71799
$719$	−28.3334	−1.05666	−0.528330	−	0.849039i	$-0.677181\pi$
$719$	−28.3334	−1.05666	−0.528330	+	0.849039i	$0.677181\pi$
$720$	8.91865	0.332378
$721$	−25.9619	−0.966873
$722$	5.94788	0.221357
$723$	−25.3890	−0.944229
$724$	−5.89670	−0.219149
$725$	−10.5685	−0.392503
$726$	−33.9975	−1.26176
$727$	46.8161	1.73631	0.868156	−	0.496291i	$-0.165305\pi$
$727$	46.8161	1.73631	0.868156	+	0.496291i	$0.165305\pi$
$728$	5.38582	0.199612
$729$	1.00000	0.0370370
$730$	−41.2347	−1.52616
$731$	1.10401	0.0408333
$732$	5.93958	0.219533
$733$	36.9308	1.36407	0.682036	−	0.731319i	$-0.261095\pi$
$733$	36.9308	1.36407	0.682036	+	0.731319i	$0.261095\pi$
$734$	−20.0209	−0.738986
$735$	0.305476	0.0112676
$736$	1.86724	0.0688274
$737$	68.1030	2.50861
$738$	−10.4655	−0.385239
$739$	48.8208	1.79590	0.897951	−	0.440095i	$-0.145055\pi$
$739$	48.8208	1.79590	0.897951	+	0.440095i	$0.145055\pi$
$740$	−10.1680	−0.373783
$741$	3.44925	0.126711
$742$	−31.2436	−1.14699
$743$	2.66464	0.0977561	0.0488780	−	0.998805i	$-0.484435\pi$
$743$	2.66464	0.0977561	0.0488780	+	0.998805i	$0.484435\pi$
$744$	2.88170	0.105648
$745$	21.9638	0.804690
$746$	−37.1663	−1.36075
$747$	−8.23180	−0.301186
$748$	−3.03977	−0.111145
$749$	4.31331	0.157605
$750$	−19.3637	−0.707063
$751$	−26.0935	−0.952164	−0.476082	−	0.879401i	$-0.657943\pi$
$751$	−26.0935	−0.952164	−0.476082	+	0.879401i	$0.657943\pi$
$752$	−8.72401	−0.318132
$753$	−25.2105	−0.918722
$754$	−9.75071	−0.355100
$755$	−14.6429	−0.532910
$756$	1.39725	0.0508173
$757$	13.3873	0.486568	0.243284	−	0.969955i	$-0.421775\pi$
$757$	13.3873	0.486568	0.243284	+	0.969955i	$0.421775\pi$
$758$	−26.1554	−0.950008
$759$	3.60240	0.130759
$760$	−16.9967	−0.616534
$761$	−43.8368	−1.58908	−0.794541	−	0.607211i	$-0.792288\pi$
$761$	−43.8368	−1.58908	−0.794541	+	0.607211i	$0.792288\pi$
$762$	32.0865	1.16237
$763$	22.8495	0.827206
$764$	−8.04399	−0.291021
$765$	1.86457	0.0674137
$766$	53.6824	1.93962
$767$	−9.65996	−0.348801
$768$	11.9915	0.432705
$769$	−8.19146	−0.295391	−0.147696	−	0.989033i	$-0.547186\pi$
$769$	−8.19146	−0.295391	−0.147696	+	0.989033i	$0.547186\pi$
$770$	44.1466	1.59093
$771$	−7.98328	−0.287511
$772$	−5.17480	−0.186245
$773$	−45.9378	−1.65227	−0.826134	−	0.563473i	$-0.809465\pi$
$773$	−45.9378	−1.65227	−0.826134	+	0.563473i	$0.809465\pi$
$774$	1.75756	0.0631743
$775$	−1.88149	−0.0675852
$776$	−14.9350	−0.536136
$777$	26.6806	0.957161
$778$	5.97012	0.214039
$779$	25.6834	0.920204
$780$	−0.879707	−0.0314986
$781$	11.2696	0.403258
$782$	1.00822	0.0360539
$783$	6.93755	0.247928
$784$	0.783642	0.0279872
$785$	1.86457	0.0665494
$786$	10.4304	0.372039
$787$	6.60129	0.235311	0.117655	−	0.993054i	$-0.462462\pi$
$787$	6.60129	0.235311	0.117655	+	0.993054i	$0.462462\pi$
$788$	−11.2264	−0.399924
$789$	−0.879012	−0.0312937
$790$	−23.2040	−0.825561
$791$	54.4764	1.93696
$792$	13.2717	0.471590
$793$	9.81255	0.348454
$794$	12.0157	0.426422
$795$	−13.9958	−0.496379
$796$	−11.8422	−0.419737
$797$	−38.9930	−1.38120	−0.690602	−	0.723235i	$-0.742654\pi$
$797$	−38.9930	−1.38120	−0.690602	+	0.723235i	$0.742654\pi$
$798$	−16.2621	−0.575671
$799$	−1.82388	−0.0645242
$800$	−4.49147	−0.158797
$801$	6.76191	0.238920
$802$	−35.8611	−1.26630
$803$	−79.0168	−2.78844
$804$	6.39822	0.225648
$805$	−3.08747	−0.108819
$806$	−1.73591	−0.0611447
$807$	−8.79794	−0.309702
$808$	8.82136	0.310334
$809$	−30.1450	−1.05984	−0.529921	−	0.848047i	$-0.677779\pi$
$809$	−30.1450	−1.05984	−0.529921	+	0.848047i	$0.677779\pi$
$810$	2.96836	0.104298
$811$	−42.0762	−1.47750	−0.738748	−	0.673982i	$-0.764583\pi$
$811$	−42.0762	−1.47750	−0.738748	+	0.673982i	$0.764583\pi$
$812$	9.69346	0.340174
$813$	−24.5399	−0.860650
$814$	−92.4061	−3.23883
$815$	−27.2973	−0.956183
$816$	4.78322	0.167446
$817$	−4.31326	−0.150902
$818$	−48.2262	−1.68619
$819$	2.30834	0.0806598
$820$	−6.55038	−0.228749
$821$	14.4383	0.503902	0.251951	−	0.967740i	$-0.418928\pi$
$821$	14.4383	0.503902	0.251951	+	0.967740i	$0.418928\pi$
$822$	−30.1252	−1.05074
$823$	−45.2704	−1.57803	−0.789013	−	0.614377i	$-0.789407\pi$
$823$	−45.2704	−1.57803	−0.789013	+	0.614377i	$0.789407\pi$
$824$	−23.1677	−0.807086
$825$	−8.66522	−0.301684
$826$	45.5435	1.58466
$827$	−33.3513	−1.15974	−0.579869	−	0.814710i	$-0.696896\pi$
$827$	−33.3513	−1.15974	−0.579869	+	0.814710i	$0.696896\pi$
$828$	0.338442	0.0117617
$829$	28.3420	0.984358	0.492179	−	0.870494i	$-0.336200\pi$
$829$	28.3420	0.984358	0.492179	+	0.870494i	$0.336200\pi$
$830$	−24.4350	−0.848150
$831$	5.14656	0.178532
$832$	4.30190	0.149142
$833$	0.163832	0.00567643
$834$	20.2481	0.701136
$835$	18.2396	0.631209
$836$	11.8761	0.410742
$837$	1.23508	0.0426907
$838$	−24.2934	−0.839203
$839$	44.6907	1.54289	0.771447	−	0.636294i	$-0.219533\pi$
$839$	44.6907	1.54289	0.771447	+	0.636294i	$0.219533\pi$
$840$	−11.3747	−0.392463
$841$	19.1296	0.659641
$842$	40.9010	1.40954
$843$	9.17757	0.316092
$844$	−7.56199	−0.260294
$845$	22.7861	0.783866
$846$	−2.90358	−0.0998271
$847$	55.8361	1.91855
$848$	−35.9036	−1.23293
$849$	−20.0986	−0.689782
$850$	−2.42518	−0.0831829
$851$	6.46260	0.221535
$852$	1.05877	0.0362728
$853$	49.9449	1.71008	0.855040	−	0.518561i	$-0.173532\pi$
$853$	49.9449	1.71008	0.855040	+	0.518561i	$0.173532\pi$
$854$	−46.2629	−1.58309
$855$	−7.28469	−0.249131
$856$	3.84909	0.131559
$857$	55.1774	1.88483	0.942413	−	0.334453i	$-0.108551\pi$
$857$	55.1774	1.88483	0.942413	+	0.334453i	$0.108551\pi$
$858$	−7.99473	−0.272936
$859$	28.0825	0.958163	0.479081	−	0.877770i	$-0.340970\pi$
$859$	28.0825	0.958163	0.479081	+	0.877770i	$0.340970\pi$
$860$	1.10007	0.0375120
$861$	17.1881	0.585768
$862$	−31.3905	−1.06917
$863$	51.4663	1.75193	0.875966	−	0.482372i	$-0.160225\pi$
$863$	51.4663	1.75193	0.875966	+	0.482372i	$0.160225\pi$
$864$	2.94837	0.100306
$865$	−22.9524	−0.780406
$866$	−5.43322	−0.184628
$867$	1.00000	0.0339618
$868$	1.72572	0.0585746
$869$	−44.4652	−1.50838
$870$	20.5931	0.698173
$871$	10.5702	0.358159
$872$	20.3902	0.690501
$873$	−6.40107	−0.216643
$874$	−3.93901	−0.133239
$875$	31.8022	1.07511
$876$	−7.42356	−0.250819
$877$	−20.4887	−0.691853	−0.345927	−	0.938262i	$-0.612435\pi$
$877$	−20.4887	−0.691853	−0.345927	+	0.938262i	$0.612435\pi$
$878$	39.1438	1.32104
$879$	7.21911	0.243495
$880$	50.7309	1.71014
$881$	−51.1457	−1.72314	−0.861570	−	0.507638i	$-0.830519\pi$
$881$	−51.1457	−1.72314	−0.861570	+	0.507638i	$0.830519\pi$
$882$	0.260817	0.00878215
$883$	−29.1394	−0.980619	−0.490309	−	0.871548i	$-0.663116\pi$
$883$	−29.1394	−0.980619	−0.490309	+	0.871548i	$0.663116\pi$
$884$	−0.471801	−0.0158684
$885$	20.4015	0.685789
$886$	−3.57795	−0.120204
$887$	57.6707	1.93639	0.968196	−	0.250191i	$-0.0804935\pi$
$887$	57.6707	1.93639	0.968196	+	0.250191i	$0.0804935\pi$
$888$	23.8091	0.798980
$889$	−52.6977	−1.76742
$890$	20.0718	0.672808
$891$	5.68819	0.190561
$892$	3.28261	0.109910
$893$	7.12571	0.238453
$894$	18.7528	0.627186
$895$	−20.4317	−0.682957
$896$	−35.6997	−1.19264
$897$	0.559127	0.0186687
$898$	50.1717	1.67425
$899$	8.56845	0.285774
$900$	−0.814090	−0.0271363
$901$	−7.50615	−0.250066
$902$	−59.5295	−1.98211
$903$	−2.88655	−0.0960585
$904$	48.6133	1.61685
$905$	20.5741	0.683907
$906$	−12.5022	−0.415357
$907$	−45.4898	−1.51046	−0.755232	−	0.655457i	$-0.772476\pi$
$907$	−45.4898	−1.51046	−0.755232	+	0.655457i	$0.772476\pi$
$908$	12.1371	0.402783
$909$	3.78079	0.125401
$910$	6.85197	0.227141
$911$	45.8403	1.51876	0.759379	−	0.650649i	$-0.225503\pi$
$911$	45.8403	1.51876	0.759379	+	0.650649i	$0.225503\pi$
$912$	−18.6875	−0.618806
$913$	−46.8240	−1.54965
$914$	2.73832	0.0905755
$915$	−20.7237	−0.685106
$916$	−6.54410	−0.216223
$917$	−17.1305	−0.565697
$918$	1.59198	0.0525432
$919$	−10.8770	−0.358800	−0.179400	−	0.983776i	$-0.557416\pi$
$919$	−10.8770	−0.358800	−0.179400	+	0.983776i	$0.557416\pi$
$920$	−2.75518	−0.0908356
$921$	16.5973	0.546898
$922$	−18.8265	−0.620018
$923$	1.74915	0.0575740
$924$	7.94779	0.261463
$925$	−15.5452	−0.511122
$926$	10.5909	0.348037
$927$	−9.92957	−0.326130
$928$	20.4545	0.671451
$929$	−34.4809	−1.13128	−0.565641	−	0.824652i	$-0.691371\pi$
$929$	−34.4809	−1.13128	−0.565641	+	0.824652i	$0.691371\pi$
$930$	3.66617	0.120219
$931$	−0.640073	−0.0209776
$932$	−15.8162	−0.518076
$933$	−7.35916	−0.240928
$934$	−32.2366	−1.05481
$935$	10.6060	0.346854
$936$	2.05990	0.0673298
$937$	−42.5677	−1.39063	−0.695313	−	0.718707i	$-0.744734\pi$
$937$	−42.5677	−1.39063	−0.695313	+	0.718707i	$0.744734\pi$
$938$	−49.8352	−1.62718
$939$	−13.7150	−0.447571
$940$	−1.81736	−0.0592758
$941$	−17.9455	−0.585007	−0.292503	−	0.956264i	$-0.594488\pi$
$941$	−17.9455	−0.585007	−0.292503	+	0.956264i	$0.594488\pi$
$942$	1.59198	0.0518695
$943$	4.16331	0.135576
$944$	52.3363	1.70340
$945$	−4.87512	−0.158588
$946$	9.99734	0.325042
$947$	40.6172	1.31988	0.659941	−	0.751317i	$-0.270581\pi$
$947$	40.6172	1.31988	0.659941	+	0.751317i	$0.270581\pi$
$948$	−4.17746	−0.135678
$949$	−12.2642	−0.398112
$950$	9.47492	0.307407
$951$	30.2223	0.980024
$952$	−6.10042	−0.197716
$953$	−50.5289	−1.63679	−0.818395	−	0.574655i	$-0.805136\pi$
$953$	−50.5289	−1.63679	−0.818395	+	0.574655i	$0.805136\pi$
$954$	−11.9496	−0.386884
$955$	28.0662	0.908202
$956$	15.6310	0.505544
$957$	39.4621	1.27563
$958$	12.1097	0.391247
$959$	49.4765	1.59768
$960$	−9.08546	−0.293232
$961$	−29.4746	−0.950793
$962$	−14.3423	−0.462415
$963$	1.64970	0.0531608
$964$	−13.5679	−0.436993
$965$	18.0554	0.581223
$966$	−2.63610	−0.0848151
$967$	−4.01788	−0.129206	−0.0646032	−	0.997911i	$-0.520578\pi$
$967$	−4.01788	−0.129206	−0.0646032	+	0.997911i	$0.520578\pi$
$968$	49.8267	1.60149
$969$	−3.90690	−0.125508
$970$	−19.0007	−0.610075
$971$	45.8095	1.47010	0.735049	−	0.678014i	$-0.237159\pi$
$971$	45.8095	1.47010	0.735049	+	0.678014i	$0.237159\pi$
$972$	0.534400	0.0171409
$973$	−33.2548	−1.06610
$974$	−25.5623	−0.819069
$975$	−1.34493	−0.0430721
$976$	−53.1630	−1.70171
$977$	9.19112	0.294050	0.147025	−	0.989133i	$-0.453030\pi$
$977$	9.19112	0.294050	0.147025	+	0.989133i	$0.453030\pi$
$978$	−23.3066	−0.745262
$979$	38.4630	1.22928
$980$	0.163246	0.00521471
$981$	8.73915	0.279020
$982$	−58.0739	−1.85321
$983$	29.8631	0.952485	0.476243	−	0.879314i	$-0.341998\pi$
$983$	29.8631	0.952485	0.476243	+	0.879314i	$0.341998\pi$
$984$	15.3382	0.488963
$985$	39.1699	1.24806
$986$	11.0444	0.351727
$987$	4.76873	0.151790
$988$	1.84328	0.0586425
$989$	−0.699184	−0.0222327
$990$	16.8846	0.536627
$991$	45.3295	1.43994	0.719969	−	0.694006i	$-0.244156\pi$
$991$	45.3295	1.43994	0.719969	+	0.694006i	$0.244156\pi$
$992$	3.64149	0.115617
$993$	−0.846452	−0.0268613
$994$	−8.24667	−0.261569
$995$	41.3186	1.30989
$996$	−4.39907	−0.139390
$997$	36.5132	1.15639	0.578193	−	0.815900i	$-0.303758\pi$
$997$	36.5132	1.15639	0.578193	+	0.815900i	$0.303758\pi$
$998$	25.6304	0.811316
$999$	10.2044	0.322854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.13	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.13	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.59198 q^{2} +1.00000 q^{3} +0.534400 q^{4} -1.86457 q^{5} -1.59198 q^{6} +2.61461 q^{7} +2.33321 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59198 q^{2} +1.00000 q^{3} +0.534400 q^{4} -1.86457 q^{5} -1.59198 q^{6} +2.61461 q^{7} +2.33321 q^{8} +1.00000 q^{9} +2.96836 q^{10} +5.68819 q^{11} +0.534400 q^{12} +0.882861 q^{13} -4.16240 q^{14} -1.86457 q^{15} -4.78322 q^{16} -1.00000 q^{17} -1.59198 q^{18} +3.90690 q^{19} -0.996427 q^{20} +2.61461 q^{21} -9.05548 q^{22} +0.633312 q^{23} +2.33321 q^{24} -1.52337 q^{25} -1.40550 q^{26} +1.00000 q^{27} +1.39725 q^{28} +6.93755 q^{29} +2.96836 q^{30} +1.23508 q^{31} +2.94837 q^{32} +5.68819 q^{33} +1.59198 q^{34} -4.87512 q^{35} +0.534400 q^{36} +10.2044 q^{37} -6.21970 q^{38} +0.882861 q^{39} -4.35043 q^{40} +6.57386 q^{41} -4.16240 q^{42} -1.10401 q^{43} +3.03977 q^{44} -1.86457 q^{45} -1.00822 q^{46} +1.82388 q^{47} -4.78322 q^{48} -0.163832 q^{49} +2.42518 q^{50} -1.00000 q^{51} +0.471801 q^{52} +7.50615 q^{53} -1.59198 q^{54} -10.6060 q^{55} +6.10042 q^{56} +3.90690 q^{57} -11.0444 q^{58} -10.9416 q^{59} -0.996427 q^{60} +11.1145 q^{61} -1.96623 q^{62} +2.61461 q^{63} +4.87268 q^{64} -1.64616 q^{65} -9.05548 q^{66} +11.9727 q^{67} -0.534400 q^{68} +0.633312 q^{69} +7.76110 q^{70} +1.98123 q^{71} +2.33321 q^{72} -13.8914 q^{73} -16.2453 q^{74} -1.52337 q^{75} +2.08785 q^{76} +14.8724 q^{77} -1.40550 q^{78} -7.81711 q^{79} +8.91865 q^{80} +1.00000 q^{81} -10.4655 q^{82} -8.23180 q^{83} +1.39725 q^{84} +1.86457 q^{85} +1.75756 q^{86} +6.93755 q^{87} +13.2717 q^{88} +6.76191 q^{89} +2.96836 q^{90} +2.30834 q^{91} +0.338442 q^{92} +1.23508 q^{93} -2.90358 q^{94} -7.28469 q^{95} +2.94837 q^{96} -6.40107 q^{97} +0.260817 q^{98} +5.68819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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