LMFDB - Embedded newform 8042.2.a.a.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2156933055$
Analytic rank:	$1$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.35217 q^{3} +1.00000 q^{4} -2.04388 q^{5} +2.35217 q^{6} -0.147586 q^{7} +1.00000 q^{8} +2.53271 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.35217 q^{3} +1.00000 q^{4} -2.04388 q^{5} +2.35217 q^{6} -0.147586 q^{7} +1.00000 q^{8} +2.53271 q^{9} -2.04388 q^{10} -0.983281 q^{11} +2.35217 q^{12} -1.04431 q^{13} -0.147586 q^{14} -4.80756 q^{15} +1.00000 q^{16} -6.77049 q^{17} +2.53271 q^{18} +0.536048 q^{19} -2.04388 q^{20} -0.347148 q^{21} -0.983281 q^{22} +6.73379 q^{23} +2.35217 q^{24} -0.822551 q^{25} -1.04431 q^{26} -1.09914 q^{27} -0.147586 q^{28} -10.0452 q^{29} -4.80756 q^{30} +6.15966 q^{31} +1.00000 q^{32} -2.31284 q^{33} -6.77049 q^{34} +0.301649 q^{35} +2.53271 q^{36} -0.603699 q^{37} +0.536048 q^{38} -2.45640 q^{39} -2.04388 q^{40} -4.86271 q^{41} -0.347148 q^{42} -1.58037 q^{43} -0.983281 q^{44} -5.17656 q^{45} +6.73379 q^{46} +1.39700 q^{47} +2.35217 q^{48} -6.97822 q^{49} -0.822551 q^{50} -15.9254 q^{51} -1.04431 q^{52} -9.12303 q^{53} -1.09914 q^{54} +2.00971 q^{55} -0.147586 q^{56} +1.26088 q^{57} -10.0452 q^{58} +2.21254 q^{59} -4.80756 q^{60} -1.35309 q^{61} +6.15966 q^{62} -0.373793 q^{63} +1.00000 q^{64} +2.13445 q^{65} -2.31284 q^{66} -13.5761 q^{67} -6.77049 q^{68} +15.8390 q^{69} +0.301649 q^{70} +1.63818 q^{71} +2.53271 q^{72} +3.52669 q^{73} -0.603699 q^{74} -1.93478 q^{75} +0.536048 q^{76} +0.145119 q^{77} -2.45640 q^{78} -6.03902 q^{79} -2.04388 q^{80} -10.1835 q^{81} -4.86271 q^{82} +7.29711 q^{83} -0.347148 q^{84} +13.8381 q^{85} -1.58037 q^{86} -23.6281 q^{87} -0.983281 q^{88} +6.20980 q^{89} -5.17656 q^{90} +0.154126 q^{91} +6.73379 q^{92} +14.4886 q^{93} +1.39700 q^{94} -1.09562 q^{95} +2.35217 q^{96} +7.54539 q^{97} -6.97822 q^{98} -2.49037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.35217	1.35803	0.679013	−	0.734126i	$-0.262408\pi$
$3$	2.35217	1.35803	0.679013	+	0.734126i	$0.262408\pi$
$4$	1.00000	0.500000
$5$	−2.04388	−0.914051	−0.457026	−	0.889454i	$-0.651085\pi$
$5$	−2.04388	−0.914051	−0.457026	+	0.889454i	$0.651085\pi$
$6$	2.35217	0.960270
$7$	−0.147586	−0.0557824	−0.0278912	−	0.999611i	$-0.508879\pi$
$7$	−0.147586	−0.0557824	−0.0278912	+	0.999611i	$0.508879\pi$
$8$	1.00000	0.353553
$9$	2.53271	0.844237
$10$	−2.04388	−0.646332
$11$	−0.983281	−0.296470	−0.148235	−	0.988952i	$-0.547359\pi$
$11$	−0.983281	−0.296470	−0.148235	+	0.988952i	$0.547359\pi$
$12$	2.35217	0.679013
$13$	−1.04431	−0.289640	−0.144820	−	0.989458i	$-0.546260\pi$
$13$	−1.04431	−0.289640	−0.144820	+	0.989458i	$0.546260\pi$
$14$	−0.147586	−0.0394441
$15$	−4.80756	−1.24131
$16$	1.00000	0.250000
$17$	−6.77049	−1.64208	−0.821042	−	0.570867i	$-0.806607\pi$
$17$	−6.77049	−1.64208	−0.821042	+	0.570867i	$0.806607\pi$
$18$	2.53271	0.596966
$19$	0.536048	0.122978	0.0614890	−	0.998108i	$-0.480415\pi$
$19$	0.536048	0.122978	0.0614890	+	0.998108i	$0.480415\pi$
$20$	−2.04388	−0.457026
$21$	−0.347148	−0.0757540
$22$	−0.983281	−0.209636
$23$	6.73379	1.40409	0.702046	−	0.712132i	$-0.252270\pi$
$23$	6.73379	1.40409	0.702046	+	0.712132i	$0.252270\pi$
$24$	2.35217	0.480135
$25$	−0.822551	−0.164510
$26$	−1.04431	−0.204806
$27$	−1.09914	−0.211530
$28$	−0.147586	−0.0278912
$29$	−10.0452	−1.86535	−0.932675	−	0.360717i	$-0.882532\pi$
$29$	−10.0452	−1.86535	−0.932675	+	0.360717i	$0.882532\pi$
$30$	−4.80756	−0.877736
$31$	6.15966	1.10631	0.553154	−	0.833079i	$-0.313424\pi$
$31$	6.15966	1.10631	0.553154	+	0.833079i	$0.313424\pi$
$32$	1.00000	0.176777
$33$	−2.31284	−0.402615
$34$	−6.77049	−1.16113
$35$	0.301649	0.0509880
$36$	2.53271	0.422119
$37$	−0.603699	−0.0992476	−0.0496238	−	0.998768i	$-0.515802\pi$
$37$	−0.603699	−0.0992476	−0.0496238	+	0.998768i	$0.515802\pi$
$38$	0.536048	0.0869585
$39$	−2.45640	−0.393339
$40$	−2.04388	−0.323166
$41$	−4.86271	−0.759428	−0.379714	−	0.925104i	$-0.623978\pi$
$41$	−4.86271	−0.759428	−0.379714	+	0.925104i	$0.623978\pi$
$42$	−0.347148	−0.0535661
$43$	−1.58037	−0.241005	−0.120502	−	0.992713i	$-0.538451\pi$
$43$	−1.58037	−0.241005	−0.120502	+	0.992713i	$0.538451\pi$
$44$	−0.983281	−0.148235
$45$	−5.17656	−0.771676
$46$	6.73379	0.992843
$47$	1.39700	0.203774	0.101887	−	0.994796i	$-0.467512\pi$
$47$	1.39700	0.203774	0.101887	+	0.994796i	$0.467512\pi$
$48$	2.35217	0.339507
$49$	−6.97822	−0.996888
$50$	−0.822551	−0.116326
$51$	−15.9254	−2.23000
$52$	−1.04431	−0.144820
$53$	−9.12303	−1.25314	−0.626572	−	0.779363i	$-0.715543\pi$
$53$	−9.12303	−1.25314	−0.626572	+	0.779363i	$0.715543\pi$
$54$	−1.09914	−0.149574
$55$	2.00971	0.270989
$56$	−0.147586	−0.0197220
$57$	1.26088	0.167007
$58$	−10.0452	−1.31900
$59$	2.21254	0.288049	0.144024	−	0.989574i	$-0.453996\pi$
$59$	2.21254	0.288049	0.144024	+	0.989574i	$0.453996\pi$
$60$	−4.80756	−0.620653
$61$	−1.35309	−0.173245	−0.0866224	−	0.996241i	$-0.527607\pi$
$61$	−1.35309	−0.173245	−0.0866224	+	0.996241i	$0.527607\pi$
$62$	6.15966	0.782277
$63$	−0.373793	−0.0470936
$64$	1.00000	0.125000
$65$	2.13445	0.264746
$66$	−2.31284	−0.284691
$67$	−13.5761	−1.65858	−0.829290	−	0.558818i	$-0.811255\pi$
$67$	−13.5761	−1.65858	−0.829290	+	0.558818i	$0.811255\pi$
$68$	−6.77049	−0.821042
$69$	15.8390	1.90679
$70$	0.301649	0.0360539
$71$	1.63818	0.194417	0.0972083	−	0.995264i	$-0.469009\pi$
$71$	1.63818	0.194417	0.0972083	+	0.995264i	$0.469009\pi$
$72$	2.53271	0.298483
$73$	3.52669	0.412768	0.206384	−	0.978471i	$-0.433830\pi$
$73$	3.52669	0.412768	0.206384	+	0.978471i	$0.433830\pi$
$74$	−0.603699	−0.0701786
$75$	−1.93478	−0.223409
$76$	0.536048	0.0614890
$77$	0.145119	0.0165378
$78$	−2.45640	−0.278133
$79$	−6.03902	−0.679443	−0.339721	−	0.940526i	$-0.610333\pi$
$79$	−6.03902	−0.679443	−0.339721	+	0.940526i	$0.610333\pi$
$80$	−2.04388	−0.228513
$81$	−10.1835	−1.13150
$82$	−4.86271	−0.536996
$83$	7.29711	0.800962	0.400481	−	0.916305i	$-0.368843\pi$
$83$	7.29711	0.800962	0.400481	+	0.916305i	$0.368843\pi$
$84$	−0.347148	−0.0378770
$85$	13.8381	1.50095
$86$	−1.58037	−0.170416
$87$	−23.6281	−2.53320
$88$	−0.983281	−0.104818
$89$	6.20980	0.658238	0.329119	−	0.944288i	$-0.393248\pi$
$89$	6.20980	0.658238	0.329119	+	0.944288i	$0.393248\pi$
$90$	−5.17656	−0.545657
$91$	0.154126	0.0161568
$92$	6.73379	0.702046
$93$	14.4886	1.50239
$94$	1.39700	0.144090
$95$	−1.09562	−0.112408
$96$	2.35217	0.240068
$97$	7.54539	0.766118	0.383059	−	0.923724i	$-0.374871\pi$
$97$	7.54539	0.766118	0.383059	+	0.923724i	$0.374871\pi$
$98$	−6.97822	−0.704906
$99$	−2.49037	−0.250291
$100$	−0.822551	−0.0822551
$101$	1.72889	0.172031	0.0860153	−	0.996294i	$-0.472587\pi$
$101$	1.72889	0.172031	0.0860153	+	0.996294i	$0.472587\pi$
$102$	−15.9254	−1.57684
$103$	−13.7471	−1.35454	−0.677270	−	0.735735i	$-0.736837\pi$
$103$	−13.7471	−1.35454	−0.677270	+	0.735735i	$0.736837\pi$
$104$	−1.04431	−0.102403
$105$	0.709530	0.0692430
$106$	−9.12303	−0.886107
$107$	0.0922948	0.00892248	0.00446124	−	0.999990i	$-0.498580\pi$
$107$	0.0922948	0.00892248	0.00446124	+	0.999990i	$0.498580\pi$
$108$	−1.09914	−0.105765
$109$	14.3290	1.37247	0.686236	−	0.727379i	$-0.259262\pi$
$109$	14.3290	1.37247	0.686236	+	0.727379i	$0.259262\pi$
$110$	2.00971	0.191618
$111$	−1.42000	−0.134781
$112$	−0.147586	−0.0139456
$113$	8.18627	0.770099	0.385050	−	0.922896i	$-0.374184\pi$
$113$	8.18627	0.770099	0.385050	+	0.922896i	$0.374184\pi$
$114$	1.26088	0.118092
$115$	−13.7631	−1.28341
$116$	−10.0452	−0.932675
$117$	−2.64494	−0.244525
$118$	2.21254	0.203681
$119$	0.999231	0.0915994
$120$	−4.80756	−0.438868
$121$	−10.0332	−0.912105
$122$	−1.35309	−0.122503
$123$	−11.4379	−1.03132
$124$	6.15966	0.553154
$125$	11.9006	1.06442
$126$	−0.373793	−0.0333002
$127$	−16.5995	−1.47297	−0.736483	−	0.676456i	$-0.763515\pi$
$127$	−16.5995	−1.47297	−0.736483	+	0.676456i	$0.763515\pi$
$128$	1.00000	0.0883883
$129$	−3.71731	−0.327291
$130$	2.13445	0.187204
$131$	−9.82613	−0.858513	−0.429256	−	0.903183i	$-0.641224\pi$
$131$	−9.82613	−0.858513	−0.429256	+	0.903183i	$0.641224\pi$
$132$	−2.31284	−0.201307
$133$	−0.0791134	−0.00686000
$134$	−13.5761	−1.17279
$135$	2.24652	0.193350
$136$	−6.77049	−0.580565
$137$	1.91963	0.164005	0.0820026	−	0.996632i	$-0.473868\pi$
$137$	1.91963	0.164005	0.0820026	+	0.996632i	$0.473868\pi$
$138$	15.8390	1.34831
$139$	−18.8158	−1.59593	−0.797967	−	0.602701i	$-0.794091\pi$
$139$	−18.8158	−1.59593	−0.797967	+	0.602701i	$0.794091\pi$
$140$	0.301649	0.0254940
$141$	3.28600	0.276731
$142$	1.63818	0.137473
$143$	1.02685	0.0858697
$144$	2.53271	0.211059
$145$	20.5312	1.70503
$146$	3.52669	0.291871
$147$	−16.4140	−1.35380
$148$	−0.603699	−0.0496238
$149$	11.7412	0.961876	0.480938	−	0.876755i	$-0.340296\pi$
$149$	11.7412	0.961876	0.480938	+	0.876755i	$0.340296\pi$
$150$	−1.93478	−0.157974
$151$	−4.15507	−0.338135	−0.169067	−	0.985605i	$-0.554076\pi$
$151$	−4.15507	−0.338135	−0.169067	+	0.985605i	$0.554076\pi$
$152$	0.536048	0.0434793
$153$	−17.1477	−1.38631
$154$	0.145119	0.0116940
$155$	−12.5896	−1.01122
$156$	−2.45640	−0.196669
$157$	−12.9059	−1.03000	−0.515000	−	0.857190i	$-0.672208\pi$
$157$	−12.9059	−1.03000	−0.515000	+	0.857190i	$0.672208\pi$
$158$	−6.03902	−0.480439
$159$	−21.4589	−1.70180
$160$	−2.04388	−0.161583
$161$	−0.993815	−0.0783236
$162$	−10.1835	−0.800092
$163$	9.41660	0.737565	0.368782	−	0.929516i	$-0.379775\pi$
$163$	9.41660	0.737565	0.368782	+	0.929516i	$0.379775\pi$
$164$	−4.86271	−0.379714
$165$	4.72718	0.368010
$166$	7.29711	0.566366
$167$	5.29129	0.409452	0.204726	−	0.978819i	$-0.434370\pi$
$167$	5.29129	0.409452	0.204726	+	0.978819i	$0.434370\pi$
$168$	−0.347148	−0.0267831
$169$	−11.9094	−0.916109
$170$	13.8381	1.06133
$171$	1.35766	0.103823
$172$	−1.58037	−0.120502
$173$	8.05234	0.612208	0.306104	−	0.951998i	$-0.400974\pi$
$173$	8.05234	0.612208	0.306104	+	0.951998i	$0.400974\pi$
$174$	−23.6281	−1.79124
$175$	0.121397	0.00917677
$176$	−0.983281	−0.0741176
$177$	5.20428	0.391178
$178$	6.20980	0.465444
$179$	−0.488227	−0.0364918	−0.0182459	−	0.999834i	$-0.505808\pi$
$179$	−0.488227	−0.0364918	−0.0182459	+	0.999834i	$0.505808\pi$
$180$	−5.17656	−0.385838
$181$	−13.7844	−1.02458	−0.512292	−	0.858811i	$-0.671204\pi$
$181$	−13.7844	−1.02458	−0.512292	+	0.858811i	$0.671204\pi$
$182$	0.154126	0.0114246
$183$	−3.18269	−0.235271
$184$	6.73379	0.496421
$185$	1.23389	0.0907174
$186$	14.4886	1.06235
$187$	6.65729	0.486829
$188$	1.39700	0.101887
$189$	0.162219	0.0117997
$190$	−1.09562	−0.0794846
$191$	22.4470	1.62421	0.812105	−	0.583511i	$-0.198321\pi$
$191$	22.4470	1.62421	0.812105	+	0.583511i	$0.198321\pi$
$192$	2.35217	0.169753
$193$	2.06579	0.148699	0.0743493	−	0.997232i	$-0.476312\pi$
$193$	2.06579	0.148699	0.0743493	+	0.997232i	$0.476312\pi$
$194$	7.54539	0.541727
$195$	5.02059	0.359532
$196$	−6.97822	−0.498444
$197$	−21.0802	−1.50190	−0.750951	−	0.660358i	$-0.770404\pi$
$197$	−21.0802	−1.50190	−0.750951	+	0.660358i	$0.770404\pi$
$198$	−2.49037	−0.176983
$199$	−11.9861	−0.849672	−0.424836	−	0.905270i	$-0.639668\pi$
$199$	−11.9861	−0.849672	−0.424836	+	0.905270i	$0.639668\pi$
$200$	−0.822551	−0.0581631
$201$	−31.9332	−2.25240
$202$	1.72889	0.121644
$203$	1.48254	0.104054
$204$	−15.9254	−1.11500
$205$	9.93880	0.694156
$206$	−13.7471	−0.957804
$207$	17.0547	1.18539
$208$	−1.04431	−0.0724100
$209$	−0.527086	−0.0364593
$210$	0.709530	0.0489622
$211$	−1.33276	−0.0917511	−0.0458756	−	0.998947i	$-0.514608\pi$
$211$	−1.33276	−0.0917511	−0.0458756	+	0.998947i	$0.514608\pi$
$212$	−9.12303	−0.626572
$213$	3.85329	0.264023
$214$	0.0922948	0.00630914
$215$	3.23010	0.220291
$216$	−1.09914	−0.0747872
$217$	−0.909081	−0.0617124
$218$	14.3290	0.970484
$219$	8.29539	0.560550
$220$	2.00971	0.135495
$221$	7.07050	0.475613
$222$	−1.42000	−0.0953045
$223$	−23.9342	−1.60275	−0.801377	−	0.598160i	$-0.795899\pi$
$223$	−23.9342	−1.60275	−0.801377	+	0.598160i	$0.795899\pi$
$224$	−0.147586	−0.00986102
$225$	−2.08328	−0.138886
$226$	8.18627	0.544542
$227$	12.8422	0.852366	0.426183	−	0.904637i	$-0.359858\pi$
$227$	12.8422	0.852366	0.426183	+	0.904637i	$0.359858\pi$
$228$	1.26088	0.0835037
$229$	24.8304	1.64084	0.820420	−	0.571761i	$-0.193739\pi$
$229$	24.8304	1.64084	0.820420	+	0.571761i	$0.193739\pi$
$230$	−13.7631	−0.907509
$231$	0.341344	0.0224588
$232$	−10.0452	−0.659501
$233$	20.5834	1.34846	0.674232	−	0.738520i	$-0.264475\pi$
$233$	20.5834	1.34846	0.674232	+	0.738520i	$0.264475\pi$
$234$	−2.64494	−0.172905
$235$	−2.85531	−0.186260
$236$	2.21254	0.144024
$237$	−14.2048	−0.922702
$238$	0.999231	0.0647706
$239$	19.3176	1.24955	0.624775	−	0.780805i	$-0.285191\pi$
$239$	19.3176	1.24955	0.624775	+	0.780805i	$0.285191\pi$
$240$	−4.80756	−0.310327
$241$	−3.86987	−0.249280	−0.124640	−	0.992202i	$-0.539778\pi$
$241$	−3.86987	−0.249280	−0.124640	+	0.992202i	$0.539778\pi$
$242$	−10.0332	−0.644956
$243$	−20.6559	−1.32508
$244$	−1.35309	−0.0866224
$245$	14.2626	0.911207
$246$	−11.4379	−0.729256
$247$	−0.559802	−0.0356193
$248$	6.15966	0.391139
$249$	17.1641	1.08773
$250$	11.9006	0.752660
$251$	−13.9390	−0.879820	−0.439910	−	0.898042i	$-0.644990\pi$
$251$	−13.9390	−0.879820	−0.439910	+	0.898042i	$0.644990\pi$
$252$	−0.373793	−0.0235468
$253$	−6.62120	−0.416271
$254$	−16.5995	−1.04154
$255$	32.5495	2.03833
$256$	1.00000	0.0625000
$257$	9.17615	0.572393	0.286196	−	0.958171i	$-0.407609\pi$
$257$	9.17615	0.572393	0.286196	+	0.958171i	$0.407609\pi$
$258$	−3.71731	−0.231430
$259$	0.0890978	0.00553627
$260$	2.13445	0.132373
$261$	−25.4416	−1.57480
$262$	−9.82613	−0.607060
$263$	−21.8343	−1.34636	−0.673180	−	0.739478i	$-0.735072\pi$
$263$	−21.8343	−1.34636	−0.673180	+	0.739478i	$0.735072\pi$
$264$	−2.31284	−0.142346
$265$	18.6464	1.14544
$266$	−0.0791134	−0.00485075
$267$	14.6065	0.893905
$268$	−13.5761	−0.829290
$269$	3.69814	0.225480	0.112740	−	0.993625i	$-0.464037\pi$
$269$	3.69814	0.225480	0.112740	+	0.993625i	$0.464037\pi$
$270$	2.24652	0.136719
$271$	−13.7965	−0.838079	−0.419039	−	0.907968i	$-0.637633\pi$
$271$	−13.7965	−0.838079	−0.419039	+	0.907968i	$0.637633\pi$
$272$	−6.77049	−0.410521
$273$	0.362531	0.0219414
$274$	1.91963	0.115969
$275$	0.808798	0.0487724
$276$	15.8390	0.953397
$277$	−8.53784	−0.512989	−0.256495	−	0.966546i	$-0.582568\pi$
$277$	−8.53784	−0.512989	−0.256495	+	0.966546i	$0.582568\pi$
$278$	−18.8158	−1.12850
$279$	15.6006	0.933985
$280$	0.301649	0.0180270
$281$	10.1782	0.607183	0.303592	−	0.952802i	$-0.401814\pi$
$281$	10.1782	0.607183	0.303592	+	0.952802i	$0.401814\pi$
$282$	3.28600	0.195678
$283$	10.0318	0.596327	0.298164	−	0.954515i	$-0.403626\pi$
$283$	10.0318	0.596327	0.298164	+	0.954515i	$0.403626\pi$
$284$	1.63818	0.0972083
$285$	−2.57708	−0.152653
$286$	1.02685	0.0607190
$287$	0.717669	0.0423627
$288$	2.53271	0.149241
$289$	28.8395	1.69644
$290$	20.5312	1.20564
$291$	17.7481	1.04041
$292$	3.52669	0.206384
$293$	−18.2116	−1.06393	−0.531966	−	0.846766i	$-0.678546\pi$
$293$	−18.2116	−1.06393	−0.531966	+	0.846766i	$0.678546\pi$
$294$	−16.4140	−0.957282
$295$	−4.52218	−0.263291
$296$	−0.603699	−0.0350893
$297$	1.08077	0.0627124
$298$	11.7412	0.680149
$299$	−7.03217	−0.406681
$300$	−1.93478	−0.111705
$301$	0.233242	0.0134438
$302$	−4.15507	−0.239097
$303$	4.06664	0.233622
$304$	0.536048	0.0307445
$305$	2.76555	0.158355
$306$	−17.1477	−0.980268
$307$	16.2641	0.928238	0.464119	−	0.885773i	$-0.346371\pi$
$307$	16.2641	0.928238	0.464119	+	0.885773i	$0.346371\pi$
$308$	0.145119	0.00826891
$309$	−32.3355	−1.83950
$310$	−12.5896	−0.715042
$311$	−5.78644	−0.328119	−0.164060	−	0.986450i	$-0.552459\pi$
$311$	−5.78644	−0.328119	−0.164060	+	0.986450i	$0.552459\pi$
$312$	−2.45640	−0.139066
$313$	−32.6656	−1.84637	−0.923185	−	0.384357i	$-0.874423\pi$
$313$	−32.6656	−1.84637	−0.923185	+	0.384357i	$0.874423\pi$
$314$	−12.9059	−0.728321
$315$	0.763989	0.0430459
$316$	−6.03902	−0.339721
$317$	−1.68458	−0.0946152	−0.0473076	−	0.998880i	$-0.515064\pi$
$317$	−1.68458	−0.0946152	−0.0473076	+	0.998880i	$0.515064\pi$
$318$	−21.4589	−1.20336
$319$	9.87727	0.553021
$320$	−2.04388	−0.114256
$321$	0.217093	0.0121170
$322$	−0.993815	−0.0553831
$323$	−3.62931	−0.201940
$324$	−10.1835	−0.565750
$325$	0.859000	0.0476487
$326$	9.41660	0.521537
$327$	33.7043	1.86385
$328$	−4.86271	−0.268498
$329$	−0.206179	−0.0113670
$330$	4.72718	0.260223
$331$	29.2978	1.61035	0.805176	−	0.593036i	$-0.202071\pi$
$331$	29.2978	1.61035	0.805176	+	0.593036i	$0.202071\pi$
$332$	7.29711	0.400481
$333$	−1.52900	−0.0837885
$334$	5.29129	0.289526
$335$	27.7479	1.51603
$336$	−0.347148	−0.0189385
$337$	−8.83084	−0.481046	−0.240523	−	0.970643i	$-0.577319\pi$
$337$	−8.83084	−0.481046	−0.240523	+	0.970643i	$0.577319\pi$
$338$	−11.9094	−0.647787
$339$	19.2555	1.04582
$340$	13.8381	0.750475
$341$	−6.05667	−0.327987
$342$	1.35766	0.0734136
$343$	2.06299	0.111391
$344$	−1.58037	−0.0852081
$345$	−32.3731	−1.74291
$346$	8.05234	0.432897
$347$	27.9862	1.50238	0.751190	−	0.660086i	$-0.229480\pi$
$347$	27.9862	1.50238	0.751190	+	0.660086i	$0.229480\pi$
$348$	−23.6281	−1.26660
$349$	−14.3709	−0.769256	−0.384628	−	0.923072i	$-0.625670\pi$
$349$	−14.3709	−0.769256	−0.384628	+	0.923072i	$0.625670\pi$
$350$	0.121397	0.00648895
$351$	1.14785	0.0612676
$352$	−0.983281	−0.0524090
$353$	8.22110	0.437565	0.218783	−	0.975774i	$-0.429791\pi$
$353$	8.22110	0.437565	0.218783	+	0.975774i	$0.429791\pi$
$354$	5.20428	0.276604
$355$	−3.34825	−0.177707
$356$	6.20980	0.329119
$357$	2.35036	0.124394
$358$	−0.488227	−0.0258036
$359$	−10.6487	−0.562016	−0.281008	−	0.959705i	$-0.590669\pi$
$359$	−10.6487	−0.562016	−0.281008	+	0.959705i	$0.590669\pi$
$360$	−5.17656	−0.272829
$361$	−18.7127	−0.984876
$362$	−13.7844	−0.724491
$363$	−23.5997	−1.23866
$364$	0.154126	0.00807841
$365$	−7.20814	−0.377291
$366$	−3.18269	−0.166362
$367$	3.01700	0.157486	0.0787430	−	0.996895i	$-0.474909\pi$
$367$	3.01700	0.157486	0.0787430	+	0.996895i	$0.474909\pi$
$368$	6.73379	0.351023
$369$	−12.3158	−0.641137
$370$	1.23389	0.0641469
$371$	1.34643	0.0699034
$372$	14.4886	0.751197
$373$	32.1304	1.66365	0.831825	−	0.555039i	$-0.187297\pi$
$373$	32.1304	1.66365	0.831825	+	0.555039i	$0.187297\pi$
$374$	6.65729	0.344240
$375$	27.9923	1.44551
$376$	1.39700	0.0720450
$377$	10.4903	0.540280
$378$	0.162219	0.00834362
$379$	−15.7017	−0.806544	−0.403272	−	0.915080i	$-0.632127\pi$
$379$	−15.7017	−0.806544	−0.403272	+	0.915080i	$0.632127\pi$
$380$	−1.09562	−0.0562041
$381$	−39.0448	−2.00033
$382$	22.4470	1.14849
$383$	27.9221	1.42675	0.713377	−	0.700780i	$-0.247165\pi$
$383$	27.9221	1.42675	0.713377	+	0.700780i	$0.247165\pi$
$384$	2.35217	0.120034
$385$	−0.296605	−0.0151164
$386$	2.06579	0.105146
$387$	−4.00263	−0.203465
$388$	7.54539	0.383059
$389$	30.9175	1.56758	0.783791	−	0.621025i	$-0.213283\pi$
$389$	30.9175	1.56758	0.783791	+	0.621025i	$0.213283\pi$
$390$	5.02059	0.254228
$391$	−45.5910	−2.30564
$392$	−6.97822	−0.352453
$393$	−23.1127	−1.16588
$394$	−21.0802	−1.06200
$395$	12.3430	0.621046
$396$	−2.49037	−0.125146
$397$	23.0408	1.15638	0.578191	−	0.815901i	$-0.303759\pi$
$397$	23.0408	1.15638	0.578191	+	0.815901i	$0.303759\pi$
$398$	−11.9861	−0.600809
$399$	−0.186088	−0.00931607
$400$	−0.822551	−0.0411275
$401$	2.38670	0.119186	0.0595932	−	0.998223i	$-0.481020\pi$
$401$	2.38670	0.119186	0.0595932	+	0.998223i	$0.481020\pi$
$402$	−31.9332	−1.59268
$403$	−6.43260	−0.320431
$404$	1.72889	0.0860153
$405$	20.8139	1.03425
$406$	1.48254	0.0735771
$407$	0.593606	0.0294239
$408$	−15.9254	−0.788422
$409$	21.0247	1.03960	0.519802	−	0.854287i	$-0.326006\pi$
$409$	21.0247	1.03960	0.519802	+	0.854287i	$0.326006\pi$
$410$	9.93880	0.490842
$411$	4.51530	0.222724
$412$	−13.7471	−0.677270
$413$	−0.326541	−0.0160680
$414$	17.0547	0.838194
$415$	−14.9144	−0.732120
$416$	−1.04431	−0.0512016
$417$	−44.2580	−2.16732
$418$	−0.527086	−0.0257806
$419$	−11.7683	−0.574919	−0.287459	−	0.957793i	$-0.592811\pi$
$419$	−11.7683	−0.574919	−0.287459	+	0.957793i	$0.592811\pi$
$420$	0.709530	0.0346215
$421$	25.6087	1.24809	0.624046	−	0.781387i	$-0.285488\pi$
$421$	25.6087	1.24809	0.624046	+	0.781387i	$0.285488\pi$
$422$	−1.33276	−0.0648779
$423$	3.53821	0.172034
$424$	−9.12303	−0.443053
$425$	5.56907	0.270140
$426$	3.85329	0.186692
$427$	0.199697	0.00966401
$428$	0.0922948	0.00446124
$429$	2.41533	0.116613
$430$	3.23010	0.155769
$431$	−12.0918	−0.582443	−0.291221	−	0.956656i	$-0.594062\pi$
$431$	−12.0918	−0.582443	−0.291221	+	0.956656i	$0.594062\pi$
$432$	−1.09914	−0.0528826
$433$	−19.8841	−0.955567	−0.477784	−	0.878478i	$-0.658560\pi$
$433$	−19.8841	−0.955567	−0.477784	+	0.878478i	$0.658560\pi$
$434$	−0.909081	−0.0436373
$435$	48.2930	2.31547
$436$	14.3290	0.686236
$437$	3.60964	0.172672
$438$	8.29539	0.396369
$439$	−19.4372	−0.927686	−0.463843	−	0.885917i	$-0.653530\pi$
$439$	−19.4372	−0.927686	−0.463843	+	0.885917i	$0.653530\pi$
$440$	2.00971	0.0958091
$441$	−17.6738	−0.841610
$442$	7.07050	0.336310
$443$	26.8246	1.27448	0.637238	−	0.770667i	$-0.280077\pi$
$443$	26.8246	1.27448	0.637238	+	0.770667i	$0.280077\pi$
$444$	−1.42000	−0.0673904
$445$	−12.6921	−0.601663
$446$	−23.9342	−1.13332
$447$	27.6173	1.30625
$448$	−0.147586	−0.00697280
$449$	3.18760	0.150432	0.0752161	−	0.997167i	$-0.476035\pi$
$449$	3.18760	0.150432	0.0752161	+	0.997167i	$0.476035\pi$
$450$	−2.08328	−0.0982069
$451$	4.78141	0.225148
$452$	8.18627	0.385050
$453$	−9.77343	−0.459196
$454$	12.8422	0.602714
$455$	−0.315016	−0.0147682
$456$	1.26088	0.0590460
$457$	7.72817	0.361508	0.180754	−	0.983528i	$-0.442146\pi$
$457$	7.72817	0.361508	0.180754	+	0.983528i	$0.442146\pi$
$458$	24.8304	1.16025
$459$	7.44174	0.347351
$460$	−13.7631	−0.641706
$461$	−13.1283	−0.611446	−0.305723	−	0.952120i	$-0.598898\pi$
$461$	−13.1283	−0.611446	−0.305723	+	0.952120i	$0.598898\pi$
$462$	0.341344	0.0158808
$463$	−40.3865	−1.87692	−0.938459	−	0.345390i	$-0.887747\pi$
$463$	−40.3865	−1.87692	−0.938459	+	0.345390i	$0.887747\pi$
$464$	−10.0452	−0.466338
$465$	−29.6129	−1.37327
$466$	20.5834	0.953508
$467$	19.0177	0.880034	0.440017	−	0.897989i	$-0.354972\pi$
$467$	19.0177	0.880034	0.440017	+	0.897989i	$0.354972\pi$
$468$	−2.64494	−0.122262
$469$	2.00364	0.0925196
$470$	−2.85531	−0.131706
$471$	−30.3568	−1.39877
$472$	2.21254	0.101841
$473$	1.55395	0.0714508
$474$	−14.2048	−0.652449
$475$	−0.440927	−0.0202311
$476$	0.999231	0.0457997
$477$	−23.1060	−1.05795
$478$	19.3176	0.883565
$479$	−10.8032	−0.493612	−0.246806	−	0.969065i	$-0.579381\pi$
$479$	−10.8032	−0.493612	−0.246806	+	0.969065i	$0.579381\pi$
$480$	−4.80756	−0.219434
$481$	0.630450	0.0287461
$482$	−3.86987	−0.176268
$483$	−2.33762	−0.106366
$484$	−10.0332	−0.456053
$485$	−15.4219	−0.700271
$486$	−20.6559	−0.936972
$487$	−9.47649	−0.429421	−0.214710	−	0.976678i	$-0.568881\pi$
$487$	−9.47649	−0.429421	−0.214710	+	0.976678i	$0.568881\pi$
$488$	−1.35309	−0.0612513
$489$	22.1495	1.00163
$490$	14.2626	0.644321
$491$	30.0993	1.35836	0.679181	−	0.733971i	$-0.262335\pi$
$491$	30.0993	1.35836	0.679181	+	0.733971i	$0.262335\pi$
$492$	−11.4379	−0.515662
$493$	68.0111	3.06306
$494$	−0.559802	−0.0251867
$495$	5.09001	0.228779
$496$	6.15966	0.276577
$497$	−0.241774	−0.0108450
$498$	17.1641	0.769140
$499$	1.09865	0.0491823	0.0245911	−	0.999698i	$-0.492172\pi$
$499$	1.09865	0.0491823	0.0245911	+	0.999698i	$0.492172\pi$
$500$	11.9006	0.532211
$501$	12.4460	0.556047
$502$	−13.9390	−0.622127
$503$	−33.8361	−1.50868	−0.754339	−	0.656485i	$-0.772042\pi$
$503$	−33.8361	−1.50868	−0.754339	+	0.656485i	$0.772042\pi$
$504$	−0.373793	−0.0166501
$505$	−3.53364	−0.157245
$506$	−6.62120	−0.294348
$507$	−28.0130	−1.24410
$508$	−16.5995	−0.736483
$509$	−38.3938	−1.70178	−0.850888	−	0.525348i	$-0.823935\pi$
$509$	−38.3938	−1.70178	−0.850888	+	0.525348i	$0.823935\pi$
$510$	32.5495	1.44132
$511$	−0.520492	−0.0230252
$512$	1.00000	0.0441942
$513$	−0.589194	−0.0260136
$514$	9.17615	0.404743
$515$	28.0974	1.23812
$516$	−3.71731	−0.163646
$517$	−1.37365	−0.0604130
$518$	0.0890978	0.00391473
$519$	18.9405	0.831395
$520$	2.13445	0.0936018
$521$	−11.9208	−0.522259	−0.261129	−	0.965304i	$-0.584095\pi$
$521$	−11.9208	−0.522259	−0.261129	+	0.965304i	$0.584095\pi$
$522$	−25.4416	−1.11355
$523$	26.8456	1.17388	0.586938	−	0.809632i	$-0.300333\pi$
$523$	26.8456	1.17388	0.586938	+	0.809632i	$0.300333\pi$
$524$	−9.82613	−0.429256
$525$	0.285547	0.0124623
$526$	−21.8343	−0.952021
$527$	−41.7039	−1.81665
$528$	−2.31284	−0.100654
$529$	22.3439	0.971473
$530$	18.6464	0.809947
$531$	5.60373	0.243181
$532$	−0.0791134	−0.00343000
$533$	5.07819	0.219961
$534$	14.6065	0.632086
$535$	−0.188640	−0.00815560
$536$	−13.5761	−0.586397
$537$	−1.14839	−0.0495569
$538$	3.69814	0.159438
$539$	6.86155	0.295548
$540$	2.24652	0.0966748
$541$	6.61975	0.284605	0.142303	−	0.989823i	$-0.454549\pi$
$541$	6.61975	0.284605	0.142303	+	0.989823i	$0.454549\pi$
$542$	−13.7965	−0.592611
$543$	−32.4232	−1.39141
$544$	−6.77049	−0.290282
$545$	−29.2868	−1.25451
$546$	0.362531	0.0155149
$547$	16.3512	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$547$	16.3512	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$548$	1.91963	0.0820026
$549$	−3.42697	−0.146260
$550$	0.808798	0.0344873
$551$	−5.38472	−0.229397
$552$	15.8390	0.674153
$553$	0.891277	0.0379009
$554$	−8.53784	−0.362738
$555$	2.90232	0.123197
$556$	−18.8158	−0.797967
$557$	−27.0230	−1.14500	−0.572501	−	0.819904i	$-0.694027\pi$
$557$	−27.0230	−1.14500	−0.572501	+	0.819904i	$0.694027\pi$
$558$	15.6006	0.660427
$559$	1.65040	0.0698047
$560$	0.301649	0.0127470
$561$	15.6591	0.661127
$562$	10.1782	0.429343
$563$	−6.20226	−0.261394	−0.130697	−	0.991422i	$-0.541722\pi$
$563$	−6.20226	−0.261394	−0.130697	+	0.991422i	$0.541722\pi$
$564$	3.28600	0.138365
$565$	−16.7318	−0.703910
$566$	10.0318	0.421667
$567$	1.50295	0.0631178
$568$	1.63818	0.0687367
$569$	24.8312	1.04098	0.520489	−	0.853868i	$-0.325750\pi$
$569$	24.8312	1.04098	0.520489	+	0.853868i	$0.325750\pi$
$570$	−2.57708	−0.107942
$571$	−28.0467	−1.17372	−0.586858	−	0.809690i	$-0.699635\pi$
$571$	−28.0467	−1.17372	−0.586858	+	0.809690i	$0.699635\pi$
$572$	1.02685	0.0429348
$573$	52.7993	2.20572
$574$	0.717669	0.0299549
$575$	−5.53888	−0.230987
$576$	2.53271	0.105530
$577$	11.5383	0.480344	0.240172	−	0.970730i	$-0.422796\pi$
$577$	11.5383	0.480344	0.240172	+	0.970730i	$0.422796\pi$
$578$	28.8395	1.19957
$579$	4.85909	0.201937
$580$	20.5312	0.852513
$581$	−1.07695	−0.0446796
$582$	17.7481	0.735680
$583$	8.97050	0.371520
$584$	3.52669	0.145936
$585$	5.40594	0.223508
$586$	−18.2116	−0.752313
$587$	−41.8293	−1.72648	−0.863240	−	0.504793i	$-0.831569\pi$
$587$	−41.8293	−1.72648	−0.863240	+	0.504793i	$0.831569\pi$
$588$	−16.4140	−0.676901
$589$	3.30187	0.136051
$590$	−4.52218	−0.186175
$591$	−49.5842	−2.03962
$592$	−0.603699	−0.0248119
$593$	1.69399	0.0695640	0.0347820	−	0.999395i	$-0.488926\pi$
$593$	1.69399	0.0695640	0.0347820	+	0.999395i	$0.488926\pi$
$594$	1.08077	0.0443444
$595$	−2.04231	−0.0837266
$596$	11.7412	0.480938
$597$	−28.1933	−1.15388
$598$	−7.03217	−0.287567
$599$	−22.1250	−0.904002	−0.452001	−	0.892018i	$-0.649290\pi$
$599$	−22.1250	−0.904002	−0.452001	+	0.892018i	$0.649290\pi$
$600$	−1.93478	−0.0789871
$601$	13.8438	0.564702	0.282351	−	0.959311i	$-0.408886\pi$
$601$	13.8438	0.564702	0.282351	+	0.959311i	$0.408886\pi$
$602$	0.233242	0.00950622
$603$	−34.3842	−1.40023
$604$	−4.15507	−0.169067
$605$	20.5066	0.833711
$606$	4.06664	0.165196
$607$	−33.8897	−1.37554	−0.687770	−	0.725929i	$-0.741410\pi$
$607$	−33.8897	−1.37554	−0.687770	+	0.725929i	$0.741410\pi$
$608$	0.536048	0.0217396
$609$	3.48718	0.141308
$610$	2.76555	0.111974
$611$	−1.45891	−0.0590211
$612$	−17.1477	−0.693154
$613$	23.8737	0.964251	0.482126	−	0.876102i	$-0.339865\pi$
$613$	23.8737	0.964251	0.482126	+	0.876102i	$0.339865\pi$
$614$	16.2641	0.656364
$615$	23.3778	0.942682
$616$	0.145119	0.00584700
$617$	−14.3164	−0.576356	−0.288178	−	0.957577i	$-0.593050\pi$
$617$	−14.3164	−0.576356	−0.288178	+	0.957577i	$0.593050\pi$
$618$	−32.3355	−1.30072
$619$	10.0694	0.404724	0.202362	−	0.979311i	$-0.435138\pi$
$619$	10.0694	0.404724	0.202362	+	0.979311i	$0.435138\pi$
$620$	−12.5896	−0.505611
$621$	−7.40140	−0.297008
$622$	−5.78644	−0.232015
$623$	−0.916482	−0.0367181
$624$	−2.45640	−0.0983347
$625$	−20.2107	−0.808426
$626$	−32.6656	−1.30558
$627$	−1.23980	−0.0495127
$628$	−12.9059	−0.515000
$629$	4.08734	0.162973
$630$	0.763989	0.0304381
$631$	−28.9285	−1.15162	−0.575812	−	0.817582i	$-0.695314\pi$
$631$	−28.9285	−1.15162	−0.575812	+	0.817582i	$0.695314\pi$
$632$	−6.03902	−0.240219
$633$	−3.13489	−0.124601
$634$	−1.68458	−0.0669031
$635$	33.9274	1.34637
$636$	−21.4589	−0.850902
$637$	7.28744	0.288739
$638$	9.87727	0.391045
$639$	4.14905	0.164134
$640$	−2.04388	−0.0807915
$641$	−27.8840	−1.10135	−0.550676	−	0.834719i	$-0.685630\pi$
$641$	−27.8840	−1.10135	−0.550676	+	0.834719i	$0.685630\pi$
$642$	0.217093	0.00856799
$643$	12.3267	0.486119	0.243060	−	0.970011i	$-0.421849\pi$
$643$	12.3267	0.486119	0.243060	+	0.970011i	$0.421849\pi$
$644$	−0.993815	−0.0391618
$645$	7.59774	0.299161
$646$	−3.62931	−0.142793
$647$	33.8709	1.33160	0.665801	−	0.746129i	$-0.268090\pi$
$647$	33.8709	1.33160	0.665801	+	0.746129i	$0.268090\pi$
$648$	−10.1835	−0.400046
$649$	−2.17555	−0.0853979
$650$	0.859000	0.0336927
$651$	−2.13831	−0.0838072
$652$	9.41660	0.368782
$653$	5.10363	0.199720	0.0998601	−	0.995001i	$-0.468160\pi$
$653$	5.10363	0.199720	0.0998601	+	0.995001i	$0.468160\pi$
$654$	33.7043	1.31794
$655$	20.0834	0.784725
$656$	−4.86271	−0.189857
$657$	8.93210	0.348474
$658$	−0.206179	−0.00803769
$659$	23.2091	0.904098	0.452049	−	0.891993i	$-0.350693\pi$
$659$	23.2091	0.904098	0.452049	+	0.891993i	$0.350693\pi$
$660$	4.72718	0.184005
$661$	−10.4319	−0.405756	−0.202878	−	0.979204i	$-0.565029\pi$
$661$	−10.4319	−0.405756	−0.202878	+	0.979204i	$0.565029\pi$
$662$	29.2978	1.13869
$663$	16.6310	0.645896
$664$	7.29711	0.283183
$665$	0.161698	0.00627039
$666$	−1.52900	−0.0592474
$667$	−67.6424	−2.61912
$668$	5.29129	0.204726
$669$	−56.2974	−2.17658
$670$	27.7479	1.07199
$671$	1.33046	0.0513619
$672$	−0.347148	−0.0133915
$673$	32.3869	1.24842	0.624211	−	0.781256i	$-0.285420\pi$
$673$	32.3869	1.24842	0.624211	+	0.781256i	$0.285420\pi$
$674$	−8.83084	−0.340151
$675$	0.904101	0.0347989
$676$	−11.9094	−0.458054
$677$	9.38030	0.360514	0.180257	−	0.983620i	$-0.442307\pi$
$677$	9.38030	0.360514	0.180257	+	0.983620i	$0.442307\pi$
$678$	19.2555	0.739503
$679$	−1.11360	−0.0427359
$680$	13.8381	0.530666
$681$	30.2070	1.15754
$682$	−6.05667	−0.231922
$683$	32.9461	1.26065	0.630324	−	0.776332i	$-0.282922\pi$
$683$	32.9461	1.26065	0.630324	+	0.776332i	$0.282922\pi$
$684$	1.35766	0.0519113
$685$	−3.92350	−0.149909
$686$	2.06299	0.0787655
$687$	58.4054	2.22831
$688$	−1.58037	−0.0602512
$689$	9.52729	0.362961
$690$	−32.3731	−1.23242
$691$	−7.67404	−0.291934	−0.145967	−	0.989289i	$-0.546629\pi$
$691$	−7.67404	−0.291934	−0.145967	+	0.989289i	$0.546629\pi$
$692$	8.05234	0.306104
$693$	0.367544	0.0139618
$694$	27.9862	1.06234
$695$	38.4572	1.45877
$696$	−23.6281	−0.895620
$697$	32.9229	1.24704
$698$	−14.3709	−0.543946
$699$	48.4157	1.83125
$700$	0.121397	0.00458838
$701$	2.66254	0.100563	0.0502813	−	0.998735i	$-0.483988\pi$
$701$	2.66254	0.100563	0.0502813	+	0.998735i	$0.483988\pi$
$702$	1.14785	0.0433228
$703$	−0.323612	−0.0122053
$704$	−0.983281	−0.0370588
$705$	−6.71618	−0.252946
$706$	8.22110	0.309405
$707$	−0.255160	−0.00959628
$708$	5.20428	0.195589
$709$	23.3444	0.876717	0.438358	−	0.898800i	$-0.355560\pi$
$709$	23.3444	0.876717	0.438358	+	0.898800i	$0.355560\pi$
$710$	−3.34825	−0.125658
$711$	−15.2951	−0.573611
$712$	6.20980	0.232722
$713$	41.4778	1.55336
$714$	2.35036	0.0879602
$715$	−2.09876	−0.0784893
$716$	−0.488227	−0.0182459
$717$	45.4383	1.69692
$718$	−10.6487	−0.397406
$719$	33.9561	1.26635	0.633175	−	0.774008i	$-0.281751\pi$
$719$	33.9561	1.26635	0.633175	+	0.774008i	$0.281751\pi$
$720$	−5.17656	−0.192919
$721$	2.02888	0.0755595
$722$	−18.7127	−0.696413
$723$	−9.10260	−0.338530
$724$	−13.7844	−0.512292
$725$	8.26270	0.306869
$726$	−23.5997	−0.875867
$727$	21.2049	0.786446	0.393223	−	0.919443i	$-0.371360\pi$
$727$	21.2049	0.786446	0.393223	+	0.919443i	$0.371360\pi$
$728$	0.154126	0.00571230
$729$	−18.0358	−0.667991
$730$	−7.20814	−0.266785
$731$	10.6999	0.395750
$732$	−3.18269	−0.117636
$733$	32.2241	1.19022	0.595111	−	0.803643i	$-0.297108\pi$
$733$	32.2241	1.19022	0.595111	+	0.803643i	$0.297108\pi$
$734$	3.01700	0.111359
$735$	33.5482	1.23744
$736$	6.73379	0.248211
$737$	13.3491	0.491720
$738$	−12.3158	−0.453352
$739$	29.2492	1.07595	0.537974	−	0.842962i	$-0.319190\pi$
$739$	29.2492	1.07595	0.537974	+	0.842962i	$0.319190\pi$
$740$	1.23389	0.0453587
$741$	−1.31675	−0.0483720
$742$	1.34643	0.0494292
$743$	−19.8389	−0.727818	−0.363909	−	0.931434i	$-0.618558\pi$
$743$	−19.8389	−0.727818	−0.363909	+	0.931434i	$0.618558\pi$
$744$	14.4886	0.531177
$745$	−23.9976	−0.879204
$746$	32.1304	1.17638
$747$	18.4815	0.676202
$748$	6.65729	0.243415
$749$	−0.0136215	−0.000497717 0
$750$	27.9923	1.02213
$751$	−11.5020	−0.419713	−0.209856	−	0.977732i	$-0.567300\pi$
$751$	−11.5020	−0.419713	−0.209856	+	0.977732i	$0.567300\pi$
$752$	1.39700	0.0509435
$753$	−32.7868	−1.19482
$754$	10.4903	0.382036
$755$	8.49247	0.309072
$756$	0.162219	0.00589983
$757$	−33.6035	−1.22134	−0.610671	−	0.791885i	$-0.709100\pi$
$757$	−33.6035	−1.22134	−0.610671	+	0.791885i	$0.709100\pi$
$758$	−15.7017	−0.570313
$759$	−15.5742	−0.565308
$760$	−1.09562	−0.0397423
$761$	−14.1535	−0.513064	−0.256532	−	0.966536i	$-0.582580\pi$
$761$	−14.1535	−0.513064	−0.256532	+	0.966536i	$0.582580\pi$
$762$	−39.0448	−1.41444
$763$	−2.11477	−0.0765597
$764$	22.4470	0.812105
$765$	35.0478	1.26716
$766$	27.9221	1.00887
$767$	−2.31059	−0.0834304
$768$	2.35217	0.0848767
$769$	11.0418	0.398179	0.199089	−	0.979981i	$-0.436202\pi$
$769$	11.0418	0.398179	0.199089	+	0.979981i	$0.436202\pi$
$770$	−0.296605	−0.0106889
$771$	21.5839	0.777325
$772$	2.06579	0.0743493
$773$	15.6849	0.564148	0.282074	−	0.959393i	$-0.408978\pi$
$773$	15.6849	0.564148	0.282074	+	0.959393i	$0.408978\pi$
$774$	−4.00263	−0.143872
$775$	−5.06663	−0.181999
$776$	7.54539	0.270864
$777$	0.209573	0.00751840
$778$	30.9175	1.10845
$779$	−2.60665	−0.0933928
$780$	5.02059	0.179766
$781$	−1.61079	−0.0576388
$782$	−45.5910	−1.63033
$783$	11.0411	0.394578
$784$	−6.97822	−0.249222
$785$	26.3781	0.941474
$786$	−23.1127	−0.824404
$787$	−12.5182	−0.446226	−0.223113	−	0.974793i	$-0.571622\pi$
$787$	−12.5182	−0.446226	−0.223113	+	0.974793i	$0.571622\pi$
$788$	−21.0802	−0.750951
$789$	−51.3580	−1.82839
$790$	12.3430	0.439146
$791$	−1.20818	−0.0429580
$792$	−2.49037	−0.0884913
$793$	1.41304	0.0501786
$794$	23.0408	0.817686
$795$	43.8595	1.55554
$796$	−11.9861	−0.424836
$797$	36.4606	1.29150	0.645749	−	0.763549i	$-0.276545\pi$
$797$	36.4606	1.29150	0.645749	+	0.763549i	$0.276545\pi$
$798$	−0.186088	−0.00658745
$799$	−9.45841	−0.334614
$800$	−0.822551	−0.0290816
$801$	15.7276	0.555709
$802$	2.38670	0.0842775
$803$	−3.46773	−0.122374
$804$	−31.9332	−1.12620
$805$	2.03124	0.0715918
$806$	−6.43260	−0.226579
$807$	8.69867	0.306208
$808$	1.72889	0.0608220
$809$	−6.77277	−0.238118	−0.119059	−	0.992887i	$-0.537988\pi$
$809$	−6.77277	−0.238118	−0.119059	+	0.992887i	$0.537988\pi$
$810$	20.8139	0.731325
$811$	47.8992	1.68197	0.840985	−	0.541058i	$-0.181976\pi$
$811$	47.8992	1.68197	0.840985	+	0.541058i	$0.181976\pi$
$812$	1.48254	0.0520269
$813$	−32.4518	−1.13813
$814$	0.593606	0.0208059
$815$	−19.2464	−0.674172
$816$	−15.9254	−0.557499
$817$	−0.847157	−0.0296383
$818$	21.0247	0.735111
$819$	0.390357	0.0136402
$820$	9.93880	0.347078
$821$	−49.3512	−1.72237	−0.861185	−	0.508292i	$-0.830277\pi$
$821$	−49.3512	−1.72237	−0.861185	+	0.508292i	$0.830277\pi$
$822$	4.51530	0.157489
$823$	0.401125	0.0139823	0.00699117	−	0.999976i	$-0.497775\pi$
$823$	0.401125	0.0139823	0.00699117	+	0.999976i	$0.497775\pi$
$824$	−13.7471	−0.478902
$825$	1.90243	0.0662342
$826$	−0.326541	−0.0113618
$827$	−23.0260	−0.800693	−0.400347	−	0.916364i	$-0.631110\pi$
$827$	−23.0260	−0.800693	−0.400347	+	0.916364i	$0.631110\pi$
$828$	17.0547	0.592693
$829$	−10.9316	−0.379670	−0.189835	−	0.981816i	$-0.560795\pi$
$829$	−10.9316	−0.379670	−0.189835	+	0.981816i	$0.560795\pi$
$830$	−14.9144	−0.517687
$831$	−20.0825	−0.696653
$832$	−1.04431	−0.0362050
$833$	47.2460	1.63698
$834$	−44.2580	−1.53253
$835$	−10.8148	−0.374260
$836$	−0.527086	−0.0182296
$837$	−6.77035	−0.234017
$838$	−11.7683	−0.406529
$839$	37.2850	1.28722	0.643611	−	0.765353i	$-0.277435\pi$
$839$	37.2850	1.28722	0.643611	+	0.765353i	$0.277435\pi$
$840$	0.709530	0.0244811
$841$	71.9065	2.47953
$842$	25.6087	0.882535
$843$	23.9410	0.824571
$844$	−1.33276	−0.0458756
$845$	24.3414	0.837370
$846$	3.53821	0.121646
$847$	1.48076	0.0508794
$848$	−9.12303	−0.313286
$849$	23.5965	0.809829
$850$	5.56907	0.191018
$851$	−4.06518	−0.139353
$852$	3.85329	0.132012
$853$	−36.5643	−1.25194	−0.625969	−	0.779848i	$-0.715296\pi$
$853$	−36.5643	−1.25194	−0.625969	+	0.779848i	$0.715296\pi$
$854$	0.199697	0.00683349
$855$	−2.77489	−0.0948991
$856$	0.0922948	0.00315457
$857$	8.50657	0.290579	0.145289	−	0.989389i	$-0.453589\pi$
$857$	8.50657	0.290579	0.145289	+	0.989389i	$0.453589\pi$
$858$	2.41533	0.0824581
$859$	16.3396	0.557500	0.278750	−	0.960364i	$-0.410080\pi$
$859$	16.3396	0.557500	0.278750	+	0.960364i	$0.410080\pi$
$860$	3.23010	0.110145
$861$	1.68808	0.0575297
$862$	−12.0918	−0.411849
$863$	11.4982	0.391404	0.195702	−	0.980663i	$-0.437301\pi$
$863$	11.4982	0.391404	0.195702	+	0.980663i	$0.437301\pi$
$864$	−1.09914	−0.0373936
$865$	−16.4580	−0.559590
$866$	−19.8841	−0.675688
$867$	67.8355	2.30381
$868$	−0.909081	−0.0308562
$869$	5.93805	0.201435
$870$	48.2930	1.63729
$871$	14.1776	0.480391
$872$	14.3290	0.485242
$873$	19.1103	0.646785
$874$	3.60964	0.122098
$875$	−1.75637	−0.0593760
$876$	8.29539	0.280275
$877$	1.78966	0.0604324	0.0302162	−	0.999543i	$-0.490380\pi$
$877$	1.78966	0.0604324	0.0302162	+	0.999543i	$0.490380\pi$
$878$	−19.4372	−0.655973
$879$	−42.8367	−1.44485
$880$	2.00971	0.0677473
$881$	−20.1470	−0.678769	−0.339384	−	0.940648i	$-0.610219\pi$
$881$	−20.1470	−0.678769	−0.339384	+	0.940648i	$0.610219\pi$
$882$	−17.6738	−0.595108
$883$	19.1300	0.643776	0.321888	−	0.946778i	$-0.395683\pi$
$883$	19.1300	0.643776	0.321888	+	0.946778i	$0.395683\pi$
$884$	7.07050	0.237807
$885$	−10.6369	−0.357557
$886$	26.8246	0.901191
$887$	39.8002	1.33636	0.668180	−	0.744000i	$-0.267074\pi$
$887$	39.8002	1.33636	0.668180	+	0.744000i	$0.267074\pi$
$888$	−1.42000	−0.0476522
$889$	2.44986	0.0821655
$890$	−12.6921	−0.425440
$891$	10.0132	0.335456
$892$	−23.9342	−0.801377
$893$	0.748862	0.0250597
$894$	27.6173	0.923660
$895$	0.997879	0.0333554
$896$	−0.147586	−0.00493051
$897$	−16.5409	−0.552284
$898$	3.18760	0.106372
$899$	−61.8751	−2.06365
$900$	−2.08328	−0.0694428
$901$	61.7674	2.05777
$902$	4.78141	0.159203
$903$	0.548624	0.0182571
$904$	8.18627	0.272271
$905$	28.1736	0.936523
$906$	−9.77343	−0.324701
$907$	−37.2076	−1.23546	−0.617729	−	0.786391i	$-0.711947\pi$
$907$	−37.2076	−1.23546	−0.617729	+	0.786391i	$0.711947\pi$
$908$	12.8422	0.426183
$909$	4.37877	0.145235
$910$	−0.315016	−0.0104427
$911$	23.5323	0.779661	0.389831	−	0.920887i	$-0.372534\pi$
$911$	23.5323	0.779661	0.389831	+	0.920887i	$0.372534\pi$
$912$	1.26088	0.0417518
$913$	−7.17511	−0.237461
$914$	7.72817	0.255625
$915$	6.50504	0.215050
$916$	24.8304	0.820420
$917$	1.45020	0.0478899
$918$	7.44174	0.245614
$919$	32.8786	1.08456	0.542282	−	0.840196i	$-0.317560\pi$
$919$	32.8786	1.08456	0.542282	+	0.840196i	$0.317560\pi$
$920$	−13.7631	−0.453755
$921$	38.2558	1.26057
$922$	−13.1283	−0.432358
$923$	−1.71078	−0.0563108
$924$	0.341344	0.0112294
$925$	0.496573	0.0163272
$926$	−40.3865	−1.32718
$927$	−34.8174	−1.14355
$928$	−10.0452	−0.329751
$929$	21.6819	0.711360	0.355680	−	0.934608i	$-0.384249\pi$
$929$	21.6819	0.711360	0.355680	+	0.934608i	$0.384249\pi$
$930$	−29.6129	−0.971046
$931$	−3.74066	−0.122595
$932$	20.5834	0.674232
$933$	−13.6107	−0.445595
$934$	19.0177	0.622278
$935$	−13.6067	−0.444987
$936$	−2.64494	−0.0864526
$937$	−53.9526	−1.76255	−0.881277	−	0.472600i	$-0.843316\pi$
$937$	−53.9526	−1.76255	−0.881277	+	0.472600i	$0.843316\pi$
$938$	2.00364	0.0654212
$939$	−76.8351	−2.50742
$940$	−2.85531	−0.0931300
$941$	−1.03242	−0.0336559	−0.0168280	−	0.999858i	$-0.505357\pi$
$941$	−1.03242	−0.0336559	−0.0168280	+	0.999858i	$0.505357\pi$
$942$	−30.3568	−0.989079
$943$	−32.7444	−1.06631
$944$	2.21254	0.0720122
$945$	−0.331555	−0.0107855
$946$	1.55395	0.0505233
$947$	−53.9434	−1.75292	−0.876462	−	0.481471i	$-0.840103\pi$
$947$	−53.9434	−1.75292	−0.876462	+	0.481471i	$0.840103\pi$
$948$	−14.2048	−0.461351
$949$	−3.68297	−0.119554
$950$	−0.440927	−0.0143056
$951$	−3.96241	−0.128490
$952$	0.999231	0.0323853
$953$	10.0534	0.325663	0.162831	−	0.986654i	$-0.447937\pi$
$953$	10.0534	0.325663	0.162831	+	0.986654i	$0.447937\pi$
$954$	−23.1060	−0.748084
$955$	−45.8791	−1.48461
$956$	19.3176	0.624775
$957$	23.2330	0.751017
$958$	−10.8032	−0.349036
$959$	−0.283311	−0.00914860
$960$	−4.80756	−0.155163
$961$	6.94137	0.223915
$962$	0.630450	0.0203265
$963$	0.233756	0.00753269
$964$	−3.86987	−0.124640
$965$	−4.22222	−0.135918
$966$	−2.33762	−0.0752118
$967$	−13.2293	−0.425426	−0.212713	−	0.977115i	$-0.568230\pi$
$967$	−13.2293	−0.425426	−0.212713	+	0.977115i	$0.568230\pi$
$968$	−10.0332	−0.322478
$969$	−8.53676	−0.274240
$970$	−15.4219	−0.495167
$971$	−56.5091	−1.81346	−0.906731	−	0.421709i	$-0.861430\pi$
$971$	−56.5091	−1.81346	−0.906731	+	0.421709i	$0.861430\pi$
$972$	−20.6559	−0.662539
$973$	2.77695	0.0890250
$974$	−9.47649	−0.303646
$975$	2.02051	0.0647082
$976$	−1.35309	−0.0433112
$977$	−7.01585	−0.224457	−0.112229	−	0.993682i	$-0.535799\pi$
$977$	−7.01585	−0.224457	−0.112229	+	0.993682i	$0.535799\pi$
$978$	22.1495	0.708261
$979$	−6.10598	−0.195148
$980$	14.2626	0.455604
$981$	36.2913	1.15869
$982$	30.0993	0.960507
$983$	−7.36749	−0.234987	−0.117493	−	0.993074i	$-0.537486\pi$
$983$	−7.36749	−0.234987	−0.117493	+	0.993074i	$0.537486\pi$
$984$	−11.4379	−0.364628
$985$	43.0854	1.37281
$986$	68.0111	2.16591
$987$	−0.484968	−0.0154367
$988$	−0.559802	−0.0178097
$989$	−10.6419	−0.338393
$990$	5.09001	0.161771
$991$	−3.83147	−0.121711	−0.0608553	−	0.998147i	$-0.519383\pi$
$991$	−3.83147	−0.121711	−0.0608553	+	0.998147i	$0.519383\pi$
$992$	6.15966	0.195569
$993$	68.9134	2.18690
$994$	−0.241774	−0.00766859
$995$	24.4981	0.776643
$996$	17.1641	0.543864
$997$	−39.3322	−1.24566	−0.622832	−	0.782356i	$-0.714018\pi$
$997$	−39.3322	−1.24566	−0.622832	+	0.782356i	$0.714018\pi$
$998$	1.09865	0.0347771
$999$	0.663552	0.0209939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.a.1.61	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.a.1.61	✓	67	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.35217 q^{3} +1.00000 q^{4} -2.04388 q^{5} +2.35217 q^{6} -0.147586 q^{7} +1.00000 q^{8} +2.53271 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.35217 q^{3} +1.00000 q^{4} -2.04388 q^{5} +2.35217 q^{6} -0.147586 q^{7} +1.00000 q^{8} +2.53271 q^{9} -2.04388 q^{10} -0.983281 q^{11} +2.35217 q^{12} -1.04431 q^{13} -0.147586 q^{14} -4.80756 q^{15} +1.00000 q^{16} -6.77049 q^{17} +2.53271 q^{18} +0.536048 q^{19} -2.04388 q^{20} -0.347148 q^{21} -0.983281 q^{22} +6.73379 q^{23} +2.35217 q^{24} -0.822551 q^{25} -1.04431 q^{26} -1.09914 q^{27} -0.147586 q^{28} -10.0452 q^{29} -4.80756 q^{30} +6.15966 q^{31} +1.00000 q^{32} -2.31284 q^{33} -6.77049 q^{34} +0.301649 q^{35} +2.53271 q^{36} -0.603699 q^{37} +0.536048 q^{38} -2.45640 q^{39} -2.04388 q^{40} -4.86271 q^{41} -0.347148 q^{42} -1.58037 q^{43} -0.983281 q^{44} -5.17656 q^{45} +6.73379 q^{46} +1.39700 q^{47} +2.35217 q^{48} -6.97822 q^{49} -0.822551 q^{50} -15.9254 q^{51} -1.04431 q^{52} -9.12303 q^{53} -1.09914 q^{54} +2.00971 q^{55} -0.147586 q^{56} +1.26088 q^{57} -10.0452 q^{58} +2.21254 q^{59} -4.80756 q^{60} -1.35309 q^{61} +6.15966 q^{62} -0.373793 q^{63} +1.00000 q^{64} +2.13445 q^{65} -2.31284 q^{66} -13.5761 q^{67} -6.77049 q^{68} +15.8390 q^{69} +0.301649 q^{70} +1.63818 q^{71} +2.53271 q^{72} +3.52669 q^{73} -0.603699 q^{74} -1.93478 q^{75} +0.536048 q^{76} +0.145119 q^{77} -2.45640 q^{78} -6.03902 q^{79} -2.04388 q^{80} -10.1835 q^{81} -4.86271 q^{82} +7.29711 q^{83} -0.347148 q^{84} +13.8381 q^{85} -1.58037 q^{86} -23.6281 q^{87} -0.983281 q^{88} +6.20980 q^{89} -5.17656 q^{90} +0.154126 q^{91} +6.73379 q^{92} +14.4886 q^{93} +1.39700 q^{94} -1.09562 q^{95} +2.35217 q^{96} +7.54539 q^{97} -6.97822 q^{98} -2.49037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * q^99

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