LMFDB - Embedded newform 8041.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} +O(q^{10})$	\(q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} -6.44038 q^{10} -1.00000 q^{11} -2.31207 q^{12} +0.566187 q^{13} +7.00579 q^{14} -10.1734 q^{15} -4.98171 q^{16} +1.00000 q^{17} -7.02125 q^{18} -4.77018 q^{19} +3.29053 q^{20} +11.0666 q^{21} +1.69256 q^{22} -4.27889 q^{23} -5.13725 q^{24} +9.47885 q^{25} -0.958308 q^{26} -3.07012 q^{27} -3.57941 q^{28} +0.147169 q^{29} +17.2192 q^{30} +5.78533 q^{31} +4.58895 q^{32} +2.67363 q^{33} -1.69256 q^{34} -15.7500 q^{35} +3.58731 q^{36} -4.53620 q^{37} +8.07382 q^{38} -1.51378 q^{39} +7.31133 q^{40} -3.65027 q^{41} -18.7309 q^{42} +1.00000 q^{43} -0.864767 q^{44} +15.7847 q^{45} +7.24229 q^{46} +10.5702 q^{47} +13.3193 q^{48} +10.1327 q^{49} -16.0435 q^{50} -2.67363 q^{51} +0.489620 q^{52} +12.0128 q^{53} +5.19637 q^{54} -3.80511 q^{55} -7.95320 q^{56} +12.7537 q^{57} -0.249092 q^{58} -12.3631 q^{59} -8.79767 q^{60} +4.08696 q^{61} -9.79203 q^{62} -17.1705 q^{63} +2.19633 q^{64} +2.15440 q^{65} -4.52529 q^{66} -5.44219 q^{67} +0.864767 q^{68} +11.4402 q^{69} +26.6578 q^{70} +7.93867 q^{71} +7.97075 q^{72} -8.98575 q^{73} +7.67781 q^{74} -25.3429 q^{75} -4.12509 q^{76} +4.13916 q^{77} +2.56216 q^{78} -5.18424 q^{79} -18.9560 q^{80} -4.23653 q^{81} +6.17831 q^{82} +0.350834 q^{83} +9.57002 q^{84} +3.80511 q^{85} -1.69256 q^{86} -0.393475 q^{87} -1.92145 q^{88} +7.41740 q^{89} -26.7166 q^{90} -2.34354 q^{91} -3.70024 q^{92} -15.4678 q^{93} -17.8907 q^{94} -18.1510 q^{95} -12.2692 q^{96} +2.23033 q^{97} -17.1501 q^{98} -4.14830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−1.69256	−1.19682	−0.598411	−	0.801189i	$-0.704201\pi$
$2$	−1.69256	−1.19682	−0.598411	+	0.801189i	$0.704201\pi$
$3$	−2.67363	−1.54362	−0.771810	−	0.635853i	$-0.780649\pi$
$3$	−2.67363	−1.54362	−0.771810	+	0.635853i	$0.780649\pi$
$4$	0.864767	0.432384
$5$	3.80511	1.70170	0.850848	−	0.525412i	$-0.176089\pi$
$5$	3.80511	1.70170	0.850848	+	0.525412i	$0.176089\pi$
$6$	4.52529	1.84744
$7$	−4.13916	−1.56446	−0.782228	−	0.622992i	$-0.785917\pi$
$7$	−4.13916	−1.56446	−0.782228	+	0.622992i	$0.785917\pi$
$8$	1.92145	0.679336
$9$	4.14830	1.38277
$10$	−6.44038	−2.03663
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.31207	−0.667437
$13$	0.566187	0.157032	0.0785161	−	0.996913i	$-0.474982\pi$
$13$	0.566187	0.157032	0.0785161	+	0.996913i	$0.474982\pi$
$14$	7.00579	1.87238
$15$	−10.1734	−2.62677
$16$	−4.98171	−1.24543
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−7.02125	−1.65492
$19$	−4.77018	−1.09435	−0.547177	−	0.837017i	$-0.684297\pi$
$19$	−4.77018	−1.09435	−0.547177	+	0.837017i	$0.684297\pi$
$20$	3.29053	0.735786
$21$	11.0666	2.41493
$22$	1.69256	0.360856
$23$	−4.27889	−0.892210	−0.446105	−	0.894981i	$-0.647189\pi$
$23$	−4.27889	−0.892210	−0.446105	+	0.894981i	$0.647189\pi$
$24$	−5.13725	−1.04864
$25$	9.47885	1.89577
$26$	−0.958308	−0.187940
$27$	−3.07012	−0.590845
$28$	−3.57941	−0.676445
$29$	0.147169	0.0273286	0.0136643	−	0.999907i	$-0.495650\pi$
$29$	0.147169	0.0273286	0.0136643	+	0.999907i	$0.495650\pi$
$30$	17.2192	3.14378
$31$	5.78533	1.03908	0.519538	−	0.854447i	$-0.326104\pi$
$31$	5.78533	1.03908	0.519538	+	0.854447i	$0.326104\pi$
$32$	4.58895	0.811220
$33$	2.67363	0.465419
$34$	−1.69256	−0.290272
$35$	−15.7500	−2.66223
$36$	3.58731	0.597885
$37$	−4.53620	−0.745747	−0.372874	−	0.927882i	$-0.621628\pi$
$37$	−4.53620	−0.745747	−0.372874	+	0.927882i	$0.621628\pi$
$38$	8.07382	1.30975
$39$	−1.51378	−0.242398
$40$	7.31133	1.15602
$41$	−3.65027	−0.570076	−0.285038	−	0.958516i	$-0.592006\pi$
$41$	−3.65027	−0.570076	−0.285038	+	0.958516i	$0.592006\pi$
$42$	−18.7309	−2.89024
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−0.864767	−0.130369
$45$	15.7847	2.35305
$46$	7.24229	1.06782
$47$	10.5702	1.54182	0.770908	−	0.636946i	$-0.219803\pi$
$47$	10.5702	1.54182	0.770908	+	0.636946i	$0.219803\pi$
$48$	13.3193	1.92247
$49$	10.1327	1.44752
$50$	−16.0435	−2.26890
$51$	−2.67363	−0.374383
$52$	0.489620	0.0678981
$53$	12.0128	1.65008	0.825040	−	0.565075i	$-0.191153\pi$
$53$	12.0128	1.65008	0.825040	+	0.565075i	$0.191153\pi$
$54$	5.19637	0.707136
$55$	−3.80511	−0.513081
$56$	−7.95320	−1.06279
$57$	12.7537	1.68927
$58$	−0.249092	−0.0327074
$59$	−12.3631	−1.60953	−0.804766	−	0.593592i	$-0.797709\pi$
$59$	−12.3631	−1.60953	−0.804766	+	0.593592i	$0.797709\pi$
$60$	−8.79767	−1.13577
$61$	4.08696	0.523282	0.261641	−	0.965165i	$-0.415736\pi$
$61$	4.08696	0.523282	0.261641	+	0.965165i	$0.415736\pi$
$62$	−9.79203	−1.24359
$63$	−17.1705	−2.16328
$64$	2.19633	0.274542
$65$	2.15440	0.267221
$66$	−4.52529	−0.557024
$67$	−5.44219	−0.664870	−0.332435	−	0.943126i	$-0.607870\pi$
$67$	−5.44219	−0.664870	−0.332435	+	0.943126i	$0.607870\pi$
$68$	0.864767	0.104868
$69$	11.4402	1.37723
$70$	26.6578	3.18621
$71$	7.93867	0.942147	0.471073	−	0.882094i	$-0.343867\pi$
$71$	7.93867	0.942147	0.471073	+	0.882094i	$0.343867\pi$
$72$	7.97075	0.939362
$73$	−8.98575	−1.05170	−0.525851	−	0.850576i	$-0.676253\pi$
$73$	−8.98575	−1.05170	−0.525851	+	0.850576i	$0.676253\pi$
$74$	7.67781	0.892527
$75$	−25.3429	−2.92635
$76$	−4.12509	−0.473181
$77$	4.13916	0.471701
$78$	2.56216	0.290107
$79$	−5.18424	−0.583272	−0.291636	−	0.956529i	$-0.594200\pi$
$79$	−5.18424	−0.583272	−0.291636	+	0.956529i	$0.594200\pi$
$80$	−18.9560	−2.11934
$81$	−4.23653	−0.470725
$82$	6.17831	0.682280
$83$	0.350834	0.0385091	0.0192545	−	0.999815i	$-0.493871\pi$
$83$	0.350834	0.0385091	0.0192545	+	0.999815i	$0.493871\pi$
$84$	9.57002	1.04417
$85$	3.80511	0.412722
$86$	−1.69256	−0.182514
$87$	−0.393475	−0.0421849
$88$	−1.92145	−0.204827
$89$	7.41740	0.786243	0.393121	−	0.919487i	$-0.371395\pi$
$89$	7.41740	0.786243	0.393121	+	0.919487i	$0.371395\pi$
$90$	−26.7166	−2.81618
$91$	−2.34354	−0.245670
$92$	−3.70024	−0.385777
$93$	−15.4678	−1.60394
$94$	−17.8907	−1.84528
$95$	−18.1510	−1.86226
$96$	−12.2692	−1.25222
$97$	2.23033	0.226456	0.113228	−	0.993569i	$-0.463881\pi$
$97$	2.23033	0.226456	0.113228	+	0.993569i	$0.463881\pi$
$98$	−17.1501	−1.73243
$99$	−4.14830	−0.416919
$100$	8.19700	0.819700
$101$	−10.5697	−1.05173	−0.525863	−	0.850569i	$-0.676258\pi$
$101$	−10.5697	−1.05173	−0.525863	+	0.850569i	$0.676258\pi$
$102$	4.52529	0.448070
$103$	−12.0753	−1.18981	−0.594906	−	0.803795i	$-0.702811\pi$
$103$	−12.0753	−1.18981	−0.594906	+	0.803795i	$0.702811\pi$
$104$	1.08790	0.106678
$105$	42.1095	4.10947
$106$	−20.3323	−1.97485
$107$	9.25700	0.894908	0.447454	−	0.894307i	$-0.352331\pi$
$107$	9.25700	0.894908	0.447454	+	0.894307i	$0.352331\pi$
$108$	−2.65494	−0.255472
$109$	−9.76140	−0.934973	−0.467486	−	0.884000i	$-0.654840\pi$
$109$	−9.76140	−0.934973	−0.467486	+	0.884000i	$0.654840\pi$
$110$	6.44038	0.614066
$111$	12.1281	1.15115
$112$	20.6201	1.94842
$113$	13.2203	1.24366	0.621830	−	0.783152i	$-0.286389\pi$
$113$	13.2203	1.24366	0.621830	+	0.783152i	$0.286389\pi$
$114$	−21.5864	−2.02175
$115$	−16.2816	−1.51827
$116$	0.127267	0.0118164
$117$	2.34871	0.217139
$118$	20.9252	1.92632
$119$	−4.13916	−0.379436
$120$	−19.5478	−1.78446
$121$	1.00000	0.0909091
$122$	−6.91744	−0.626276
$123$	9.75947	0.879982
$124$	5.00297	0.449280
$125$	17.0425	1.52433
$126$	29.0621	2.58906
$127$	−4.82113	−0.427807	−0.213903	−	0.976855i	$-0.568618\pi$
$127$	−4.82113	−0.427807	−0.213903	+	0.976855i	$0.568618\pi$
$128$	−12.8953	−1.13980
$129$	−2.67363	−0.235400
$130$	−3.64646	−0.319816
$131$	14.4913	1.26611	0.633053	−	0.774108i	$-0.281801\pi$
$131$	14.4913	1.26611	0.633053	+	0.774108i	$0.281801\pi$
$132$	2.31207	0.201240
$133$	19.7445	1.71207
$134$	9.21125	0.795731
$135$	−11.6821	−1.00544
$136$	1.92145	0.164763
$137$	21.5445	1.84067	0.920337	−	0.391126i	$-0.127914\pi$
$137$	21.5445	1.84067	0.920337	+	0.391126i	$0.127914\pi$
$138$	−19.3632	−1.64830
$139$	−0.640466	−0.0543236	−0.0271618	−	0.999631i	$-0.508647\pi$
$139$	−0.640466	−0.0543236	−0.0271618	+	0.999631i	$0.508647\pi$
$140$	−13.6200	−1.15110
$141$	−28.2607	−2.37998
$142$	−13.4367	−1.12758
$143$	−0.566187	−0.0473470
$144$	−20.6656	−1.72213
$145$	0.559993	0.0465049
$146$	15.2089	1.25870
$147$	−27.0910	−2.23443
$148$	−3.92276	−0.322449
$149$	−5.74175	−0.470382	−0.235191	−	0.971949i	$-0.575572\pi$
$149$	−5.74175	−0.470382	−0.235191	+	0.971949i	$0.575572\pi$
$150$	42.8945	3.50232
$151$	−13.5127	−1.09964	−0.549822	−	0.835282i	$-0.685305\pi$
$151$	−13.5127	−1.09964	−0.549822	+	0.835282i	$0.685305\pi$
$152$	−9.16566	−0.743434
$153$	4.14830	0.335370
$154$	−7.00579	−0.564542
$155$	22.0138	1.76819
$156$	−1.30906	−0.104809
$157$	6.53418	0.521484	0.260742	−	0.965409i	$-0.416033\pi$
$157$	6.53418	0.521484	0.260742	+	0.965409i	$0.416033\pi$
$158$	8.77464	0.698073
$159$	−32.1177	−2.54710
$160$	17.4615	1.38045
$161$	17.7110	1.39582
$162$	7.17059	0.563375
$163$	−0.906761	−0.0710230	−0.0355115	−	0.999369i	$-0.511306\pi$
$163$	−0.906761	−0.0710230	−0.0355115	+	0.999369i	$0.511306\pi$
$164$	−3.15663	−0.246492
$165$	10.1734	0.792002
$166$	−0.593809	−0.0460885
$167$	6.82474	0.528114	0.264057	−	0.964507i	$-0.414939\pi$
$167$	6.82474	0.528114	0.264057	+	0.964507i	$0.414939\pi$
$168$	21.2639	1.64055
$169$	−12.6794	−0.975341
$170$	−6.44038	−0.493955
$171$	−19.7881	−1.51323
$172$	0.864767	0.0659379
$173$	3.09668	0.235436	0.117718	−	0.993047i	$-0.462442\pi$
$173$	3.09668	0.235436	0.117718	+	0.993047i	$0.462442\pi$
$174$	0.665981	0.0504879
$175$	−39.2345	−2.96585
$176$	4.98171	0.375511
$177$	33.0542	2.48451
$178$	−12.5544	−0.940993
$179$	20.5027	1.53244	0.766222	−	0.642577i	$-0.222135\pi$
$179$	20.5027	1.53244	0.766222	+	0.642577i	$0.222135\pi$
$180$	13.6501	1.01742
$181$	−25.3729	−1.88595	−0.942976	−	0.332861i	$-0.891986\pi$
$181$	−25.3729	−1.88595	−0.942976	+	0.332861i	$0.891986\pi$
$182$	3.96659	0.294023
$183$	−10.9270	−0.807749
$184$	−8.22168	−0.606110
$185$	−17.2607	−1.26904
$186$	26.1803	1.91963
$187$	−1.00000	−0.0731272
$188$	9.14073	0.666656
$189$	12.7077	0.924350
$190$	30.7218	2.22879
$191$	−27.0934	−1.96041	−0.980203	−	0.197994i	$-0.936557\pi$
$191$	−27.0934	−1.96041	−0.980203	+	0.197994i	$0.936557\pi$
$192$	−5.87218	−0.423788
$193$	−12.1107	−0.871747	−0.435874	−	0.900008i	$-0.643561\pi$
$193$	−12.1107	−0.871747	−0.435874	+	0.900008i	$0.643561\pi$
$194$	−3.77497	−0.271027
$195$	−5.76008	−0.412488
$196$	8.76239	0.625885
$197$	10.5715	0.753186	0.376593	−	0.926379i	$-0.377096\pi$
$197$	10.5715	0.753186	0.376593	+	0.926379i	$0.377096\pi$
$198$	7.02125	0.498979
$199$	2.32393	0.164739	0.0823696	−	0.996602i	$-0.473751\pi$
$199$	2.32393	0.164739	0.0823696	+	0.996602i	$0.473751\pi$
$200$	18.2131	1.28786
$201$	14.5504	1.02631
$202$	17.8899	1.25873
$203$	−0.609155	−0.0427543
$204$	−2.31207	−0.161877
$205$	−13.8897	−0.970096
$206$	20.4382	1.42399
$207$	−17.7501	−1.23372
$208$	−2.82058	−0.195572
$209$	4.77018	0.329960
$210$	−71.2730	−4.91831
$211$	−0.312375	−0.0215047	−0.0107524	−	0.999942i	$-0.503423\pi$
$211$	−0.312375	−0.0215047	−0.0107524	+	0.999942i	$0.503423\pi$
$212$	10.3882	0.713467
$213$	−21.2251	−1.45432
$214$	−15.6681	−1.07105
$215$	3.80511	0.259506
$216$	−5.89909	−0.401382
$217$	−23.9464	−1.62559
$218$	16.5218	1.11900
$219$	24.0246	1.62343
$220$	−3.29053	−0.221848
$221$	0.566187	0.0380859
$222$	−20.5276	−1.37772
$223$	−8.77479	−0.587604	−0.293802	−	0.955866i	$-0.594921\pi$
$223$	−8.77479	−0.587604	−0.293802	+	0.955866i	$0.594921\pi$
$224$	−18.9944	−1.26912
$225$	39.3211	2.62140
$226$	−22.3762	−1.48844
$227$	26.6838	1.77107	0.885533	−	0.464577i	$-0.153794\pi$
$227$	26.6838	1.77107	0.885533	+	0.464577i	$0.153794\pi$
$228$	11.0290	0.730411
$229$	4.66016	0.307952	0.153976	−	0.988075i	$-0.450792\pi$
$229$	4.66016	0.307952	0.153976	+	0.988075i	$0.450792\pi$
$230$	27.5577	1.81710
$231$	−11.0666	−0.728128
$232$	0.282778	0.0185653
$233$	16.0876	1.05393	0.526966	−	0.849887i	$-0.323330\pi$
$233$	16.0876	1.05393	0.526966	+	0.849887i	$0.323330\pi$
$234$	−3.97534	−0.259876
$235$	40.2206	2.62370
$236$	−10.6912	−0.695936
$237$	13.8607	0.900351
$238$	7.00579	0.454118
$239$	−22.5661	−1.45968	−0.729839	−	0.683619i	$-0.760405\pi$
$239$	−22.5661	−1.45968	−0.729839	+	0.683619i	$0.760405\pi$
$240$	50.6812	3.27146
$241$	5.46713	0.352169	0.176085	−	0.984375i	$-0.443657\pi$
$241$	5.46713	0.352169	0.176085	+	0.984375i	$0.443657\pi$
$242$	−1.69256	−0.108802
$243$	20.5373	1.31747
$244$	3.53427	0.226259
$245$	38.5558	2.46324
$246$	−16.5185	−1.05318
$247$	−2.70081	−0.171849
$248$	11.1162	0.705882
$249$	−0.938001	−0.0594434
$250$	−28.8455	−1.82435
$251$	15.7966	0.997075	0.498537	−	0.866868i	$-0.333871\pi$
$251$	15.7966	0.997075	0.498537	+	0.866868i	$0.333871\pi$
$252$	−14.8485	−0.935365
$253$	4.27889	0.269011
$254$	8.16007	0.512008
$255$	−10.1734	−0.637086
$256$	17.4335	1.08959
$257$	−13.7929	−0.860375	−0.430188	−	0.902740i	$-0.641553\pi$
$257$	−13.7929	−0.860375	−0.430188	+	0.902740i	$0.641553\pi$
$258$	4.52529	0.281732
$259$	18.7761	1.16669
$260$	1.86306	0.115542
$261$	0.610500	0.0377890
$262$	−24.5274	−1.51530
$263$	11.5605	0.712851	0.356425	−	0.934324i	$-0.383995\pi$
$263$	11.5605	0.712851	0.356425	+	0.934324i	$0.383995\pi$
$264$	5.13725	0.316176
$265$	45.7098	2.80793
$266$	−33.4188	−2.04904
$267$	−19.8314	−1.21366
$268$	−4.70623	−0.287479
$269$	24.4717	1.49206	0.746032	−	0.665910i	$-0.231956\pi$
$269$	24.4717	1.49206	0.746032	+	0.665910i	$0.231956\pi$
$270$	19.7727	1.20333
$271$	−12.8118	−0.778264	−0.389132	−	0.921182i	$-0.627225\pi$
$271$	−12.8118	−0.778264	−0.389132	+	0.921182i	$0.627225\pi$
$272$	−4.98171	−0.302061
$273$	6.26576	0.379221
$274$	−36.4655	−2.20296
$275$	−9.47885	−0.571596
$276$	9.89308	0.595494
$277$	−2.23587	−0.134340	−0.0671701	−	0.997742i	$-0.521397\pi$
$277$	−2.23587	−0.134340	−0.0671701	+	0.997742i	$0.521397\pi$
$278$	1.08403	0.0650157
$279$	23.9993	1.43680
$280$	−30.2628	−1.80855
$281$	13.8679	0.827291	0.413645	−	0.910438i	$-0.364255\pi$
$281$	13.8679	0.827291	0.413645	+	0.910438i	$0.364255\pi$
$282$	47.8330	2.84841
$283$	26.6579	1.58465	0.792324	−	0.610100i	$-0.208871\pi$
$283$	26.6579	1.58465	0.792324	+	0.610100i	$0.208871\pi$
$284$	6.86510	0.407369
$285$	48.5291	2.87462
$286$	0.958308	0.0566659
$287$	15.1090	0.891859
$288$	19.0363	1.12173
$289$	1.00000	0.0588235
$290$	−0.947824	−0.0556581
$291$	−5.96308	−0.349562
$292$	−7.77059	−0.454739
$293$	−5.39173	−0.314988	−0.157494	−	0.987520i	$-0.550342\pi$
$293$	−5.39173	−0.314988	−0.157494	+	0.987520i	$0.550342\pi$
$294$	45.8531	2.67421
$295$	−47.0428	−2.73894
$296$	−8.71610	−0.506613
$297$	3.07012	0.178146
$298$	9.71827	0.562964
$299$	−2.42265	−0.140106
$300$	−21.9157	−1.26531
$301$	−4.13916	−0.238577
$302$	22.8710	1.31608
$303$	28.2595	1.62347
$304$	23.7636	1.36294
$305$	15.5513	0.890467
$306$	−7.02125	−0.401378
$307$	1.22157	0.0697187	0.0348594	−	0.999392i	$-0.488902\pi$
$307$	1.22157	0.0697187	0.0348594	+	0.999392i	$0.488902\pi$
$308$	3.57941	0.203956
$309$	32.2848	1.83662
$310$	−37.2597	−2.11621
$311$	15.3395	0.869826	0.434913	−	0.900473i	$-0.356779\pi$
$311$	15.3395	0.869826	0.434913	+	0.900473i	$0.356779\pi$
$312$	−2.90865	−0.164670
$313$	−17.9688	−1.01566	−0.507829	−	0.861458i	$-0.669552\pi$
$313$	−17.9688	−1.01566	−0.507829	+	0.861458i	$0.669552\pi$
$314$	−11.0595	−0.624124
$315$	−65.3355	−3.68124
$316$	−4.48316	−0.252197
$317$	−22.4926	−1.26331	−0.631655	−	0.775250i	$-0.717624\pi$
$317$	−22.4926	−1.26331	−0.631655	+	0.775250i	$0.717624\pi$
$318$	54.3612	3.04842
$319$	−0.147169	−0.00823987
$320$	8.35728	0.467186
$321$	−24.7498	−1.38140
$322$	−29.9770	−1.67055
$323$	−4.77018	−0.265420
$324$	−3.66361	−0.203534
$325$	5.36680	0.297697
$326$	1.53475	0.0850019
$327$	26.0984	1.44324
$328$	−7.01382	−0.387273
$329$	−43.7516	−2.41210
$330$	−17.2192	−0.947886
$331$	−14.5342	−0.798874	−0.399437	−	0.916761i	$-0.630794\pi$
$331$	−14.5342	−0.798874	−0.399437	+	0.916761i	$0.630794\pi$
$332$	0.303390	0.0166507
$333$	−18.8175	−1.03119
$334$	−11.5513	−0.632059
$335$	−20.7081	−1.13141
$336$	−55.1305	−3.00762
$337$	25.9485	1.41351	0.706753	−	0.707460i	$-0.250159\pi$
$337$	25.9485	1.41351	0.706753	+	0.707460i	$0.250159\pi$
$338$	21.4607	1.16731
$339$	−35.3462	−1.91974
$340$	3.29053	0.178454
$341$	−5.78533	−0.313293
$342$	33.4926	1.81107
$343$	−12.9666	−0.700128
$344$	1.92145	0.103598
$345$	43.5311	2.34363
$346$	−5.24132	−0.281775
$347$	8.43818	0.452985	0.226493	−	0.974013i	$-0.427274\pi$
$347$	8.43818	0.452985	0.226493	+	0.974013i	$0.427274\pi$
$348$	−0.340264	−0.0182401
$349$	11.7398	0.628419	0.314210	−	0.949354i	$-0.398261\pi$
$349$	11.7398	0.628419	0.314210	+	0.949354i	$0.398261\pi$
$350$	66.4068	3.54959
$351$	−1.73826	−0.0927816
$352$	−4.58895	−0.244592
$353$	−13.6394	−0.725950	−0.362975	−	0.931799i	$-0.618239\pi$
$353$	−13.6394	−0.725950	−0.362975	+	0.931799i	$0.618239\pi$
$354$	−55.9463	−2.97351
$355$	30.2075	1.60325
$356$	6.41433	0.339959
$357$	11.0666	0.585706
$358$	−34.7021	−1.83406
$359$	31.3133	1.65265	0.826325	−	0.563193i	$-0.190427\pi$
$359$	31.3133	1.65265	0.826325	+	0.563193i	$0.190427\pi$
$360$	30.3296	1.59851
$361$	3.75458	0.197609
$362$	42.9452	2.25715
$363$	−2.67363	−0.140329
$364$	−2.02662	−0.106224
$365$	−34.1918	−1.78968
$366$	18.4947	0.966732
$367$	21.0313	1.09783	0.548913	−	0.835880i	$-0.315042\pi$
$367$	21.0313	1.09783	0.548913	+	0.835880i	$0.315042\pi$
$368$	21.3162	1.11118
$369$	−15.1424	−0.788282
$370$	29.2149	1.51881
$371$	−49.7227	−2.58148
$372$	−13.3761	−0.693517
$373$	−30.6169	−1.58528	−0.792642	−	0.609687i	$-0.791295\pi$
$373$	−30.6169	−1.58528	−0.792642	+	0.609687i	$0.791295\pi$
$374$	1.69256	0.0875203
$375$	−45.5653	−2.35298
$376$	20.3101	1.04741
$377$	0.0833251	0.00429146
$378$	−21.5086	−1.10628
$379$	26.6445	1.36864	0.684319	−	0.729183i	$-0.260100\pi$
$379$	26.6445	1.36864	0.684319	+	0.729183i	$0.260100\pi$
$380$	−15.6964	−0.805210
$381$	12.8899	0.660371
$382$	45.8572	2.34626
$383$	22.1312	1.13085	0.565426	−	0.824799i	$-0.308712\pi$
$383$	22.1312	1.13085	0.565426	+	0.824799i	$0.308712\pi$
$384$	34.4774	1.75942
$385$	15.7500	0.802692
$386$	20.4981	1.04333
$387$	4.14830	0.210870
$388$	1.92872	0.0979158
$389$	4.91377	0.249138	0.124569	−	0.992211i	$-0.460245\pi$
$389$	4.91377	0.249138	0.124569	+	0.992211i	$0.460245\pi$
$390$	9.74929	0.493675
$391$	−4.27889	−0.216393
$392$	19.4694	0.983354
$393$	−38.7443	−1.95439
$394$	−17.8929	−0.901430
$395$	−19.7266	−0.992552
$396$	−3.58731	−0.180269
$397$	−4.72095	−0.236937	−0.118469	−	0.992958i	$-0.537799\pi$
$397$	−4.72095	−0.236937	−0.118469	+	0.992958i	$0.537799\pi$
$398$	−3.93340	−0.197163
$399$	−52.7896	−2.64278
$400$	−47.2209	−2.36104
$401$	−19.7264	−0.985088	−0.492544	−	0.870287i	$-0.663933\pi$
$401$	−19.7264	−0.985088	−0.492544	+	0.870287i	$0.663933\pi$
$402$	−24.6275	−1.22831
$403$	3.27558	0.163168
$404$	−9.14035	−0.454749
$405$	−16.1204	−0.801031
$406$	1.03103	0.0511693
$407$	4.53620	0.224851
$408$	−5.13725	−0.254332
$409$	26.8469	1.32749	0.663746	−	0.747958i	$-0.268965\pi$
$409$	26.8469	1.32749	0.663746	+	0.747958i	$0.268965\pi$
$410$	23.5091	1.16103
$411$	−57.6021	−2.84130
$412$	−10.4423	−0.514456
$413$	51.1727	2.51804
$414$	30.0432	1.47654
$415$	1.33496	0.0655307
$416$	2.59821	0.127388
$417$	1.71237	0.0838551
$418$	−8.07382	−0.394903
$419$	−13.0780	−0.638902	−0.319451	−	0.947603i	$-0.603499\pi$
$419$	−13.0780	−0.638902	−0.319451	+	0.947603i	$0.603499\pi$
$420$	36.4150	1.77687
$421$	33.2758	1.62176	0.810881	−	0.585211i	$-0.198988\pi$
$421$	33.2758	1.62176	0.810881	+	0.585211i	$0.198988\pi$
$422$	0.528713	0.0257374
$423$	43.8482	2.13197
$424$	23.0819	1.12096
$425$	9.47885	0.459792
$426$	35.9247	1.74056
$427$	−16.9166	−0.818652
$428$	8.00515	0.386944
$429$	1.51378	0.0730858
$430$	−6.44038	−0.310583
$431$	−18.3460	−0.883696	−0.441848	−	0.897090i	$-0.645677\pi$
$431$	−18.3460	−0.883696	−0.441848	+	0.897090i	$0.645677\pi$
$432$	15.2944	0.735854
$433$	−26.5619	−1.27648	−0.638241	−	0.769837i	$-0.720338\pi$
$433$	−26.5619	−1.27648	−0.638241	+	0.769837i	$0.720338\pi$
$434$	40.5308	1.94554
$435$	−1.49721	−0.0717860
$436$	−8.44134	−0.404267
$437$	20.4111	0.976393
$438$	−40.6631	−1.94296
$439$	−2.39358	−0.114239	−0.0571196	−	0.998367i	$-0.518192\pi$
$439$	−2.39358	−0.114239	−0.0571196	+	0.998367i	$0.518192\pi$
$440$	−7.31133	−0.348554
$441$	42.0332	2.00158
$442$	−0.958308	−0.0455820
$443$	−13.3207	−0.632887	−0.316444	−	0.948611i	$-0.602489\pi$
$443$	−13.3207	−0.632887	−0.316444	+	0.948611i	$0.602489\pi$
$444$	10.4880	0.497739
$445$	28.2240	1.33795
$446$	14.8519	0.703257
$447$	15.3513	0.726092
$448$	−9.09097	−0.429508
$449$	7.24666	0.341991	0.170995	−	0.985272i	$-0.445302\pi$
$449$	7.24666	0.341991	0.170995	+	0.985272i	$0.445302\pi$
$450$	−66.5534	−3.13736
$451$	3.65027	0.171884
$452$	11.4325	0.537738
$453$	36.1278	1.69743
$454$	−45.1640	−2.11965
$455$	−8.91743	−0.418055
$456$	24.5056	1.14758
$457$	−20.3899	−0.953798	−0.476899	−	0.878958i	$-0.658239\pi$
$457$	−20.3899	−0.953798	−0.476899	+	0.878958i	$0.658239\pi$
$458$	−7.88761	−0.368564
$459$	−3.07012	−0.143301
$460$	−14.0798	−0.656475
$461$	−37.0798	−1.72698	−0.863488	−	0.504369i	$-0.831725\pi$
$461$	−37.0798	−1.72698	−0.863488	+	0.504369i	$0.831725\pi$
$462$	18.7309	0.871440
$463$	19.2087	0.892705	0.446352	−	0.894857i	$-0.352723\pi$
$463$	19.2087	0.892705	0.446352	+	0.894857i	$0.352723\pi$
$464$	−0.733153	−0.0340358
$465$	−58.8568	−2.72942
$466$	−27.2292	−1.26137
$467$	10.2206	0.472953	0.236476	−	0.971637i	$-0.424007\pi$
$467$	10.2206	0.472953	0.236476	+	0.971637i	$0.424007\pi$
$468$	2.03109	0.0938872
$469$	22.5261	1.04016
$470$	−68.0759	−3.14011
$471$	−17.4700	−0.804974
$472$	−23.7550	−1.09341
$473$	−1.00000	−0.0459800
$474$	−23.4602	−1.07756
$475$	−45.2158	−2.07464
$476$	−3.57941	−0.164062
$477$	49.8325	2.28167
$478$	38.1945	1.74697
$479$	−37.7674	−1.72564	−0.862819	−	0.505513i	$-0.831303\pi$
$479$	−37.7674	−1.72564	−0.862819	+	0.505513i	$0.831303\pi$
$480$	−46.6855	−2.13089
$481$	−2.56834	−0.117106
$482$	−9.25346	−0.421484
$483$	−47.3527	−2.15462
$484$	0.864767	0.0393076
$485$	8.48665	0.385359
$486$	−34.7606	−1.57677
$487$	18.0560	0.818197	0.409098	−	0.912490i	$-0.365843\pi$
$487$	18.0560	0.818197	0.409098	+	0.912490i	$0.365843\pi$
$488$	7.85290	0.355484
$489$	2.42434	0.109633
$490$	−65.2582	−2.94806
$491$	−8.50612	−0.383876	−0.191938	−	0.981407i	$-0.561477\pi$
$491$	−8.50612	−0.383876	−0.191938	+	0.981407i	$0.561477\pi$
$492$	8.43967	0.380490
$493$	0.147169	0.00662815
$494$	4.57130	0.205672
$495$	−15.7847	−0.709470
$496$	−28.8209	−1.29409
$497$	−32.8594	−1.47395
$498$	1.58762	0.0711432
$499$	−30.3669	−1.35941	−0.679704	−	0.733487i	$-0.737892\pi$
$499$	−30.3669	−1.35941	−0.679704	+	0.733487i	$0.737892\pi$
$500$	14.7378	0.659094
$501$	−18.2468	−0.815209
$502$	−26.7368	−1.19332
$503$	−6.93629	−0.309274	−0.154637	−	0.987971i	$-0.549421\pi$
$503$	−6.93629	−0.309274	−0.154637	+	0.987971i	$0.549421\pi$
$504$	−32.9922	−1.46959
$505$	−40.2189	−1.78972
$506$	−7.24229	−0.321959
$507$	33.9001	1.50556
$508$	−4.16916	−0.184977
$509$	−23.2046	−1.02853	−0.514264	−	0.857632i	$-0.671935\pi$
$509$	−23.2046	−1.02853	−0.514264	+	0.857632i	$0.671935\pi$
$510$	17.2192	0.762479
$511$	37.1935	1.64534
$512$	−3.71661	−0.164252
$513$	14.6450	0.646593
$514$	23.3453	1.02972
$515$	−45.9477	−2.02470
$516$	−2.31207	−0.101783
$517$	−10.5702	−0.464875
$518$	−31.7797	−1.39632
$519$	−8.27937	−0.363424
$520$	4.13958	0.181533
$521$	−2.93532	−0.128599	−0.0642994	−	0.997931i	$-0.520481\pi$
$521$	−2.93532	−0.128599	−0.0642994	+	0.997931i	$0.520481\pi$
$522$	−1.03331	−0.0452267
$523$	−35.4971	−1.55218	−0.776091	−	0.630621i	$-0.782800\pi$
$523$	−35.4971	−1.55218	−0.776091	+	0.630621i	$0.782800\pi$
$524$	12.5316	0.547444
$525$	104.898	4.57814
$526$	−19.5669	−0.853156
$527$	5.78533	0.252013
$528$	−13.3193	−0.579646
$529$	−4.69110	−0.203961
$530$	−77.3668	−3.36060
$531$	−51.2856	−2.22561
$532$	17.0744	0.740270
$533$	−2.06674	−0.0895203
$534$	33.5659	1.45254
$535$	35.2239	1.52286
$536$	−10.4569	−0.451670
$537$	−54.8166	−2.36551
$538$	−41.4198	−1.78574
$539$	−10.1327	−0.436444
$540$	−10.1023	−0.434735
$541$	−27.5226	−1.18329	−0.591644	−	0.806199i	$-0.701521\pi$
$541$	−27.5226	−1.18329	−0.591644	+	0.806199i	$0.701521\pi$
$542$	21.6849	0.931444
$543$	67.8377	2.91119
$544$	4.58895	0.196750
$545$	−37.1432	−1.59104
$546$	−10.6052	−0.453860
$547$	−10.3640	−0.443132	−0.221566	−	0.975145i	$-0.571117\pi$
$547$	−10.3640	−0.443132	−0.221566	+	0.975145i	$0.571117\pi$
$548$	18.6310	0.795878
$549$	16.9539	0.723576
$550$	16.0435	0.684099
$551$	−0.702021	−0.0299071
$552$	21.9817	0.935605
$553$	21.4584	0.912504
$554$	3.78435	0.160781
$555$	46.1488	1.95891
$556$	−0.553854	−0.0234887
$557$	11.1230	0.471298	0.235649	−	0.971838i	$-0.424278\pi$
$557$	11.1230	0.471298	0.235649	+	0.971838i	$0.424278\pi$
$558$	−40.6203	−1.71959
$559$	0.566187	0.0239472
$560$	78.4617	3.31561
$561$	2.67363	0.112881
$562$	−23.4723	−0.990120
$563$	−9.52926	−0.401610	−0.200805	−	0.979631i	$-0.564356\pi$
$563$	−9.52926	−0.401610	−0.200805	+	0.979631i	$0.564356\pi$
$564$	−24.4389	−1.02906
$565$	50.3046	2.11633
$566$	−45.1202	−1.89654
$567$	17.5357	0.736429
$568$	15.2538	0.640034
$569$	−8.59452	−0.360301	−0.180151	−	0.983639i	$-0.557658\pi$
$569$	−8.59452	−0.360301	−0.180151	+	0.983639i	$0.557658\pi$
$570$	−82.1386	−3.44041
$571$	−4.01146	−0.167874	−0.0839372	−	0.996471i	$-0.526750\pi$
$571$	−4.01146	−0.167874	−0.0839372	+	0.996471i	$0.526750\pi$
$572$	−0.489620	−0.0204721
$573$	72.4376	3.02612
$574$	−25.5730	−1.06740
$575$	−40.5589	−1.69142
$576$	9.11104	0.379627
$577$	−4.19319	−0.174565	−0.0872825	−	0.996184i	$-0.527818\pi$
$577$	−4.19319	−0.174565	−0.0872825	+	0.996184i	$0.527818\pi$
$578$	−1.69256	−0.0704013
$579$	32.3795	1.34565
$580$	0.484264	0.0201080
$581$	−1.45216	−0.0602457
$582$	10.0929	0.418364
$583$	−12.0128	−0.497518
$584$	−17.2657	−0.714460
$585$	8.93711	0.369504
$586$	9.12584	0.376985
$587$	3.14725	0.129901	0.0649504	−	0.997888i	$-0.479311\pi$
$587$	3.14725	0.129901	0.0649504	+	0.997888i	$0.479311\pi$
$588$	−23.4274	−0.966129
$589$	−27.5970	−1.13712
$590$	79.6228	3.27802
$591$	−28.2642	−1.16263
$592$	22.5981	0.928775
$593$	8.88285	0.364775	0.182388	−	0.983227i	$-0.441617\pi$
$593$	8.88285	0.364775	0.182388	+	0.983227i	$0.441617\pi$
$594$	−5.19637	−0.213210
$595$	−15.7500	−0.645685
$596$	−4.96528	−0.203386
$597$	−6.21333	−0.254295
$598$	4.10049	0.167682
$599$	30.8276	1.25958	0.629790	−	0.776765i	$-0.283141\pi$
$599$	30.8276	1.25958	0.629790	+	0.776765i	$0.283141\pi$
$600$	−48.6952	−1.98797
$601$	−9.05763	−0.369468	−0.184734	−	0.982789i	$-0.559142\pi$
$601$	−9.05763	−0.369468	−0.184734	+	0.982789i	$0.559142\pi$
$602$	7.00579	0.285535
$603$	−22.5758	−0.919359
$604$	−11.6853	−0.475468
$605$	3.80511	0.154700
$606$	−47.8310	−1.94300
$607$	4.48265	0.181945	0.0909725	−	0.995853i	$-0.471002\pi$
$607$	4.48265	0.181945	0.0909725	+	0.995853i	$0.471002\pi$
$608$	−21.8901	−0.887762
$609$	1.62866	0.0659965
$610$	−26.3216	−1.06573
$611$	5.98469	0.242115
$612$	3.58731	0.145008
$613$	−35.2953	−1.42556	−0.712782	−	0.701385i	$-0.752565\pi$
$613$	−35.2953	−1.42556	−0.712782	+	0.701385i	$0.752565\pi$
$614$	−2.06758	−0.0834409
$615$	37.1358	1.49746
$616$	7.95320	0.320444
$617$	−19.5833	−0.788395	−0.394197	−	0.919026i	$-0.628977\pi$
$617$	−19.5833	−0.788395	−0.394197	+	0.919026i	$0.628977\pi$
$618$	−54.6441	−2.19811
$619$	−17.2627	−0.693846	−0.346923	−	0.937894i	$-0.612773\pi$
$619$	−17.2627	−0.693846	−0.346923	+	0.937894i	$0.612773\pi$
$620$	19.0368	0.764537
$621$	13.1367	0.527158
$622$	−25.9631	−1.04103
$623$	−30.7018	−1.23004
$624$	7.54119	0.301889
$625$	17.4543	0.698172
$626$	30.4134	1.21556
$627$	−12.7537	−0.509333
$628$	5.65054	0.225481
$629$	−4.53620	−0.180870
$630$	110.584	4.40579
$631$	−37.2850	−1.48429	−0.742147	−	0.670238i	$-0.766192\pi$
$631$	−37.2850	−1.48429	−0.742147	+	0.670238i	$0.766192\pi$
$632$	−9.96126	−0.396238
$633$	0.835174	0.0331952
$634$	38.0701	1.51196
$635$	−18.3449	−0.727997
$636$	−27.7743	−1.10132
$637$	5.73698	0.227307
$638$	0.249092	0.00986166
$639$	32.9320	1.30277
$640$	−49.0682	−1.93959
$641$	−10.9269	−0.431585	−0.215793	−	0.976439i	$-0.569234\pi$
$641$	−10.9269	−0.431585	−0.215793	+	0.976439i	$0.569234\pi$
$642$	41.8906	1.65329
$643$	−0.342707	−0.0135150	−0.00675752	−	0.999977i	$-0.502151\pi$
$643$	−0.342707	−0.0135150	−0.00675752	+	0.999977i	$0.502151\pi$
$644$	15.3159	0.603531
$645$	−10.1734	−0.400579
$646$	8.07382	0.317660
$647$	−8.30809	−0.326625	−0.163312	−	0.986574i	$-0.552218\pi$
$647$	−8.30809	−0.326625	−0.163312	+	0.986574i	$0.552218\pi$
$648$	−8.14028	−0.319781
$649$	12.3631	0.485292
$650$	−9.08365	−0.356290
$651$	64.0239	2.50929
$652$	−0.784137	−0.0307092
$653$	13.2602	0.518912	0.259456	−	0.965755i	$-0.416457\pi$
$653$	13.2602	0.518912	0.259456	+	0.965755i	$0.416457\pi$
$654$	−44.1731	−1.72731
$655$	55.1408	2.15453
$656$	18.1846	0.709989
$657$	−37.2756	−1.45426
$658$	74.0523	2.88686
$659$	−29.9691	−1.16743	−0.583716	−	0.811958i	$-0.698402\pi$
$659$	−29.9691	−1.16743	−0.583716	+	0.811958i	$0.698402\pi$
$660$	8.79767	0.342449
$661$	17.2139	0.669542	0.334771	−	0.942300i	$-0.391341\pi$
$661$	17.2139	0.669542	0.334771	+	0.942300i	$0.391341\pi$
$662$	24.6001	0.956111
$663$	−1.51378	−0.0587902
$664$	0.674111	0.0261606
$665$	75.1301	2.91342
$666$	31.8498	1.23416
$667$	−0.629719	−0.0243828
$668$	5.90182	0.228348
$669$	23.4605	0.907037
$670$	35.0498	1.35409
$671$	−4.08696	−0.157775
$672$	50.7841	1.95904
$673$	−24.7040	−0.952269	−0.476134	−	0.879372i	$-0.657962\pi$
$673$	−24.7040	−0.952269	−0.476134	+	0.879372i	$0.657962\pi$
$674$	−43.9195	−1.69172
$675$	−29.1012	−1.12011
$676$	−10.9648	−0.421722
$677$	−14.7584	−0.567212	−0.283606	−	0.958941i	$-0.591531\pi$
$677$	−14.7584	−0.567212	−0.283606	+	0.958941i	$0.591531\pi$
$678$	59.8256	2.29759
$679$	−9.23170	−0.354280
$680$	7.31133	0.280377
$681$	−71.3426	−2.73385
$682$	9.79203	0.374956
$683$	39.2451	1.50167	0.750835	−	0.660489i	$-0.229651\pi$
$683$	39.2451	1.50167	0.750835	+	0.660489i	$0.229651\pi$
$684$	−17.1121	−0.654298
$685$	81.9793	3.13227
$686$	21.9467	0.837929
$687$	−12.4595	−0.475361
$688$	−4.98171	−0.189926
$689$	6.80147	0.259116
$690$	−73.6791	−2.80491
$691$	28.5965	1.08786	0.543931	−	0.839130i	$-0.316935\pi$
$691$	28.5965	1.08786	0.543931	+	0.839130i	$0.316935\pi$
$692$	2.67791	0.101799
$693$	17.1705	0.652252
$694$	−14.2822	−0.542143
$695$	−2.43704	−0.0924423
$696$	−0.756043	−0.0286577
$697$	−3.65027	−0.138264
$698$	−19.8704	−0.752106
$699$	−43.0122	−1.62687
$700$	−33.9287	−1.28238
$701$	9.85805	0.372333	0.186167	−	0.982518i	$-0.440394\pi$
$701$	9.85805	0.372333	0.186167	+	0.982518i	$0.440394\pi$
$702$	2.94212	0.111043
$703$	21.6385	0.816111
$704$	−2.19633	−0.0827774
$705$	−107.535	−4.05000
$706$	23.0855	0.868833
$707$	43.7498	1.64538
$708$	28.5842	1.07426
$709$	6.92912	0.260229	0.130114	−	0.991499i	$-0.458466\pi$
$709$	6.92912	0.260229	0.130114	+	0.991499i	$0.458466\pi$
$710$	−51.1281	−1.91880
$711$	−21.5058	−0.806529
$712$	14.2522	0.534123
$713$	−24.7548	−0.927074
$714$	−18.7309	−0.700986
$715$	−2.15440	−0.0805702
$716$	17.7301	0.662603
$717$	60.3333	2.25319
$718$	−52.9996	−1.97793
$719$	−30.4056	−1.13394	−0.566969	−	0.823739i	$-0.691884\pi$
$719$	−30.4056	−1.13394	−0.566969	+	0.823739i	$0.691884\pi$
$720$	−78.6349	−2.93055
$721$	49.9815	1.86141
$722$	−6.35486	−0.236503
$723$	−14.6171	−0.543615
$724$	−21.9416	−0.815455
$725$	1.39499	0.0518087
$726$	4.52529	0.167949
$727$	−38.2251	−1.41769	−0.708845	−	0.705364i	$-0.750783\pi$
$727$	−38.2251	−1.41769	−0.708845	+	0.705364i	$0.750783\pi$
$728$	−4.50300	−0.166892
$729$	−42.1995	−1.56294
$730$	57.8717	2.14193
$731$	1.00000	0.0369863
$732$	−9.44934	−0.349258
$733$	−52.1892	−1.92765	−0.963826	−	0.266533i	$-0.914122\pi$
$733$	−52.1892	−1.92765	−0.963826	+	0.266533i	$0.914122\pi$
$734$	−35.5968	−1.31390
$735$	−103.084	−3.80231
$736$	−19.6356	−0.723779
$737$	5.44219	0.200466
$738$	25.6294	0.943433
$739$	−28.4930	−1.04813	−0.524066	−	0.851678i	$-0.675585\pi$
$739$	−28.4930	−1.04813	−0.524066	+	0.851678i	$0.675585\pi$
$740$	−14.9265	−0.548710
$741$	7.22098	0.265269
$742$	84.1589	3.08957
$743$	−25.8450	−0.948163	−0.474081	−	0.880481i	$-0.657220\pi$
$743$	−25.8450	−0.948163	−0.474081	+	0.880481i	$0.657220\pi$
$744$	−29.7207	−1.08961
$745$	−21.8480	−0.800448
$746$	51.8211	1.89730
$747$	1.45536	0.0532490
$748$	−0.864767	−0.0316190
$749$	−38.3162	−1.40004
$750$	77.1221	2.81610
$751$	−36.4527	−1.33018	−0.665089	−	0.746764i	$-0.731607\pi$
$751$	−36.4527	−1.33018	−0.665089	+	0.746764i	$0.731607\pi$
$752$	−52.6575	−1.92022
$753$	−42.2344	−1.53911
$754$	−0.141033	−0.00513612
$755$	−51.4171	−1.87126
$756$	10.9892	0.399674
$757$	47.0009	1.70828	0.854139	−	0.520045i	$-0.174085\pi$
$757$	47.0009	1.70828	0.854139	+	0.520045i	$0.174085\pi$
$758$	−45.0975	−1.63802
$759$	−11.4402	−0.415252
$760$	−34.8763	−1.26510
$761$	−7.62028	−0.276235	−0.138117	−	0.990416i	$-0.544105\pi$
$761$	−7.62028	−0.276235	−0.138117	+	0.990416i	$0.544105\pi$
$762$	−21.8170	−0.790347
$763$	40.4040	1.46272
$764$	−23.4295	−0.847648
$765$	15.7847	0.570698
$766$	−37.4584	−1.35343
$767$	−6.99981	−0.252748
$768$	−46.6107	−1.68192
$769$	−46.2315	−1.66715	−0.833575	−	0.552406i	$-0.813710\pi$
$769$	−46.2315	−1.66715	−0.833575	+	0.552406i	$0.813710\pi$
$770$	−26.6578	−0.960680
$771$	36.8770	1.32809
$772$	−10.4729	−0.376929
$773$	−2.30865	−0.0830362	−0.0415181	−	0.999138i	$-0.513219\pi$
$773$	−2.30865	−0.0830362	−0.0415181	+	0.999138i	$0.513219\pi$
$774$	−7.02125	−0.252374
$775$	54.8383	1.96985
$776$	4.28547	0.153840
$777$	−50.2003	−1.80092
$778$	−8.31687	−0.298174
$779$	17.4124	0.623865
$780$	−4.98113	−0.178353
$781$	−7.93867	−0.284068
$782$	7.24229	0.258984
$783$	−0.451826	−0.0161469
$784$	−50.4780	−1.80278
$785$	24.8632	0.887407
$786$	65.5771	2.33906
$787$	−32.8877	−1.17232	−0.586161	−	0.810195i	$-0.699361\pi$
$787$	−32.8877	−1.17232	−0.586161	+	0.810195i	$0.699361\pi$
$788$	9.14186	0.325665
$789$	−30.9085	−1.10037
$790$	33.3885	1.18791
$791$	−54.7209	−1.94565
$792$	−7.97075	−0.283228
$793$	2.31399	0.0821721
$794$	7.99049	0.283572
$795$	−122.211	−4.33439
$796$	2.00966	0.0712305
$797$	35.6790	1.26382	0.631908	−	0.775044i	$-0.282272\pi$
$797$	35.6790	1.26382	0.631908	+	0.775044i	$0.282272\pi$
$798$	89.3496	3.16294
$799$	10.5702	0.373945
$800$	43.4980	1.53789
$801$	30.7696	1.08719
$802$	33.3881	1.17898
$803$	8.98575	0.317100
$804$	12.5827	0.443758
$805$	67.3923	2.37527
$806$	−5.54413	−0.195284
$807$	−65.4282	−2.30318
$808$	−20.3092	−0.714475
$809$	49.8219	1.75164	0.875822	−	0.482634i	$-0.160320\pi$
$809$	49.8219	1.75164	0.875822	+	0.482634i	$0.160320\pi$
$810$	27.2849	0.958692
$811$	−12.7746	−0.448577	−0.224288	−	0.974523i	$-0.572006\pi$
$811$	−12.7746	−0.448577	−0.224288	+	0.974523i	$0.572006\pi$
$812$	−0.526778	−0.0184863
$813$	34.2541	1.20135
$814$	−7.67781	−0.269107
$815$	−3.45032	−0.120860
$816$	13.3193	0.466267
$817$	−4.77018	−0.166887
$818$	−45.4400	−1.58877
$819$	−9.72170	−0.339704
$820$	−12.0113	−0.419454
$821$	−19.0499	−0.664848	−0.332424	−	0.943130i	$-0.607866\pi$
$821$	−19.0499	−0.664848	−0.332424	+	0.943130i	$0.607866\pi$
$822$	97.4952	3.40054
$823$	2.10973	0.0735405	0.0367702	−	0.999324i	$-0.488293\pi$
$823$	2.10973	0.0735405	0.0367702	+	0.999324i	$0.488293\pi$
$824$	−23.2021	−0.808282
$825$	25.3429	0.882327
$826$	−86.6129	−3.01365
$827$	−24.6155	−0.855966	−0.427983	−	0.903787i	$-0.640776\pi$
$827$	−24.6155	−0.855966	−0.427983	+	0.903787i	$0.640776\pi$
$828$	−15.3497	−0.533439
$829$	−37.4251	−1.29983	−0.649914	−	0.760008i	$-0.725195\pi$
$829$	−37.4251	−1.29983	−0.649914	+	0.760008i	$0.725195\pi$
$830$	−2.25951	−0.0784286
$831$	5.97788	0.207370
$832$	1.24354	0.0431118
$833$	10.1327	0.351076
$834$	−2.89829	−0.100360
$835$	25.9689	0.898690
$836$	4.12509	0.142669
$837$	−17.7617	−0.613933
$838$	22.1353	0.764653
$839$	32.3519	1.11691	0.558456	−	0.829534i	$-0.311394\pi$
$839$	32.3519	1.11691	0.558456	+	0.829534i	$0.311394\pi$
$840$	80.9115	2.79171
$841$	−28.9783	−0.999253
$842$	−56.3213	−1.94096
$843$	−37.0777	−1.27702
$844$	−0.270131	−0.00929830
$845$	−48.2466	−1.65973
$846$	−74.2157	−2.55159
$847$	−4.13916	−0.142223
$848$	−59.8441	−2.05506
$849$	−71.2734	−2.44610
$850$	−16.0435	−0.550289
$851$	19.4099	0.665363
$852$	−18.3547	−0.628823
$853$	−52.5111	−1.79795	−0.898973	−	0.438004i	$-0.855686\pi$
$853$	−52.5111	−1.79795	−0.898973	+	0.438004i	$0.855686\pi$
$854$	28.6324	0.979780
$855$	−75.2959	−2.57506
$856$	17.7869	0.607943
$857$	42.6252	1.45605	0.728025	−	0.685551i	$-0.240439\pi$
$857$	42.6252	1.45605	0.728025	+	0.685551i	$0.240439\pi$
$858$	−2.56216	−0.0874707
$859$	18.4748	0.630353	0.315176	−	0.949033i	$-0.397936\pi$
$859$	18.4748	0.630353	0.315176	+	0.949033i	$0.397936\pi$
$860$	3.29053	0.112206
$861$	−40.3960	−1.37669
$862$	31.0518	1.05763
$863$	−1.60526	−0.0546437	−0.0273218	−	0.999627i	$-0.508698\pi$
$863$	−1.60526	−0.0546437	−0.0273218	+	0.999627i	$0.508698\pi$
$864$	−14.0886	−0.479305
$865$	11.7832	0.400641
$866$	44.9576	1.52772
$867$	−2.67363	−0.0908012
$868$	−20.7081	−0.702878
$869$	5.18424	0.175863
$870$	2.53413	0.0859150
$871$	−3.08130	−0.104406
$872$	−18.7561	−0.635160
$873$	9.25207	0.313135
$874$	−34.5470	−1.16857
$875$	−70.5416	−2.38474
$876$	20.7757	0.701945
$877$	32.0271	1.08148	0.540740	−	0.841190i	$-0.318144\pi$
$877$	32.0271	1.08148	0.540740	+	0.841190i	$0.318144\pi$
$878$	4.05128	0.136724
$879$	14.4155	0.486223
$880$	18.9560	0.639005
$881$	15.1263	0.509618	0.254809	−	0.966991i	$-0.417987\pi$
$881$	15.1263	0.509618	0.254809	+	0.966991i	$0.417987\pi$
$882$	−71.1439	−2.39554
$883$	−10.0289	−0.337501	−0.168750	−	0.985659i	$-0.553973\pi$
$883$	−10.0289	−0.337501	−0.168750	+	0.985659i	$0.553973\pi$
$884$	0.489620	0.0164677
$885$	125.775	4.22788
$886$	22.5462	0.757454
$887$	1.73491	0.0582526	0.0291263	−	0.999576i	$-0.490728\pi$
$887$	1.73491	0.0582526	0.0291263	+	0.999576i	$0.490728\pi$
$888$	23.3036	0.782018
$889$	19.9555	0.669284
$890$	−47.7709	−1.60128
$891$	4.23653	0.141929
$892$	−7.58816	−0.254070
$893$	−50.4215	−1.68729
$894$	−25.9830	−0.869003
$895$	78.0150	2.60775
$896$	53.3759	1.78316
$897$	6.47728	0.216270
$898$	−12.2654	−0.409302
$899$	0.851420	0.0283965
$900$	34.0036	1.13345
$901$	12.0128	0.400203
$902$	−6.17831	−0.205715
$903$	11.0666	0.368273
$904$	25.4021	0.844863
$905$	−96.5466	−3.20932
$906$	−61.1486	−2.03153
$907$	−12.5807	−0.417735	−0.208868	−	0.977944i	$-0.566978\pi$
$907$	−12.5807	−0.417735	−0.208868	+	0.977944i	$0.566978\pi$
$908$	23.0753	0.765780
$909$	−43.8463	−1.45429
$910$	15.0933	0.500338
$911$	−28.5723	−0.946642	−0.473321	−	0.880890i	$-0.656945\pi$
$911$	−28.5723	−0.946642	−0.473321	+	0.880890i	$0.656945\pi$
$912$	−63.5352	−2.10386
$913$	−0.350834	−0.0116109
$914$	34.5111	1.14153
$915$	−41.5785	−1.37454
$916$	4.02995	0.133153
$917$	−59.9816	−1.98077
$918$	5.19637	0.171506
$919$	−13.9540	−0.460300	−0.230150	−	0.973155i	$-0.573922\pi$
$919$	−13.9540	−0.460300	−0.230150	+	0.973155i	$0.573922\pi$
$920$	−31.2844	−1.03142
$921$	−3.26603	−0.107619
$922$	62.7598	2.06688
$923$	4.49477	0.147947
$924$	−9.57002	−0.314831
$925$	−42.9980	−1.41376
$926$	−32.5119	−1.06841
$927$	−50.0918	−1.64523
$928$	0.675351	0.0221695
$929$	36.2975	1.19088	0.595441	−	0.803399i	$-0.296977\pi$
$929$	36.2975	1.19088	0.595441	+	0.803399i	$0.296977\pi$
$930$	99.6188	3.26663
$931$	−48.3345	−1.58410
$932$	13.9120	0.455703
$933$	−41.0123	−1.34268
$934$	−17.2990	−0.566040
$935$	−3.80511	−0.124440
$936$	4.51294	0.147510
$937$	42.3398	1.38318	0.691590	−	0.722290i	$-0.256910\pi$
$937$	42.3398	1.38318	0.691590	+	0.722290i	$0.256910\pi$
$938$	−38.1269	−1.24489
$939$	48.0420	1.56779
$940$	34.7815	1.13445
$941$	−43.2293	−1.40923	−0.704617	−	0.709587i	$-0.748881\pi$
$941$	−43.2293	−1.40923	−0.704617	+	0.709587i	$0.748881\pi$
$942$	29.5690	0.963411
$943$	15.6191	0.508628
$944$	61.5892	2.00456
$945$	48.3542	1.57296
$946$	1.69256	0.0550299
$947$	−54.3855	−1.76729	−0.883645	−	0.468157i	$-0.844918\pi$
$947$	−54.3855	−1.76729	−0.883645	+	0.468157i	$0.844918\pi$
$948$	11.9863	0.389297
$949$	−5.08762	−0.165151
$950$	76.5305	2.48298
$951$	60.1369	1.95007
$952$	−7.95320	−0.257765
$953$	27.0643	0.876700	0.438350	−	0.898804i	$-0.355563\pi$
$953$	27.0643	0.876700	0.438350	+	0.898804i	$0.355563\pi$
$954$	−84.3446	−2.73076
$955$	−103.093	−3.33602
$956$	−19.5144	−0.631141
$957$	0.393475	0.0127192
$958$	63.9237	2.06528
$959$	−89.1763	−2.87965
$960$	−22.3443	−0.721158
$961$	2.47006	0.0796794
$962$	4.34708	0.140155
$963$	38.4008	1.23745
$964$	4.72780	0.152272
$965$	−46.0825	−1.48345
$966$	80.1474	2.57870
$967$	−19.2720	−0.619745	−0.309873	−	0.950778i	$-0.600286\pi$
$967$	−19.2720	−0.619745	−0.309873	+	0.950778i	$0.600286\pi$
$968$	1.92145	0.0617578
$969$	12.7537	0.409707
$970$	−14.3642	−0.461206
$971$	54.4247	1.74657	0.873286	−	0.487208i	$-0.161985\pi$
$971$	54.4247	1.74657	0.873286	+	0.487208i	$0.161985\pi$
$972$	17.7600	0.569651
$973$	2.65099	0.0849869
$974$	−30.5610	−0.979236
$975$	−14.3488	−0.459531
$976$	−20.3601	−0.651710
$977$	−25.7976	−0.825337	−0.412668	−	0.910881i	$-0.635403\pi$
$977$	−25.7976	−0.825337	−0.412668	+	0.910881i	$0.635403\pi$
$978$	−4.10335	−0.131211
$979$	−7.41740	−0.237061
$980$	33.3418	1.06507
$981$	−40.4932	−1.29285
$982$	14.3971	0.459431
$983$	33.0538	1.05425	0.527126	−	0.849787i	$-0.323270\pi$
$983$	33.0538	1.05425	0.527126	+	0.849787i	$0.323270\pi$
$984$	18.7523	0.597803
$985$	40.2256	1.28169
$986$	−0.249092	−0.00793272
$987$	116.976	3.72337
$988$	−2.33558	−0.0743046
$989$	−4.27889	−0.136061
$990$	26.7166	0.849110
$991$	−10.6244	−0.337495	−0.168748	−	0.985659i	$-0.553972\pi$
$991$	−10.6244	−0.337495	−0.168748	+	0.985659i	$0.553972\pi$
$992$	26.5486	0.842920
$993$	38.8592	1.23316
$994$	55.6166	1.76405
$995$	8.84281	0.280336
$996$	−0.811152	−0.0257023
$997$	−52.3704	−1.65859	−0.829294	−	0.558813i	$-0.811257\pi$
$997$	−52.3704	−1.65859	−0.829294	+	0.558813i	$0.811257\pi$
$998$	51.3978	1.62697
$999$	13.9267	0.440621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.18	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.18	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} +O(q^{10})\)	\(q-1.69256 q^{2} -2.67363 q^{3} +0.864767 q^{4} +3.80511 q^{5} +4.52529 q^{6} -4.13916 q^{7} +1.92145 q^{8} +4.14830 q^{9} -6.44038 q^{10} -1.00000 q^{11} -2.31207 q^{12} +0.566187 q^{13} +7.00579 q^{14} -10.1734 q^{15} -4.98171 q^{16} +1.00000 q^{17} -7.02125 q^{18} -4.77018 q^{19} +3.29053 q^{20} +11.0666 q^{21} +1.69256 q^{22} -4.27889 q^{23} -5.13725 q^{24} +9.47885 q^{25} -0.958308 q^{26} -3.07012 q^{27} -3.57941 q^{28} +0.147169 q^{29} +17.2192 q^{30} +5.78533 q^{31} +4.58895 q^{32} +2.67363 q^{33} -1.69256 q^{34} -15.7500 q^{35} +3.58731 q^{36} -4.53620 q^{37} +8.07382 q^{38} -1.51378 q^{39} +7.31133 q^{40} -3.65027 q^{41} -18.7309 q^{42} +1.00000 q^{43} -0.864767 q^{44} +15.7847 q^{45} +7.24229 q^{46} +10.5702 q^{47} +13.3193 q^{48} +10.1327 q^{49} -16.0435 q^{50} -2.67363 q^{51} +0.489620 q^{52} +12.0128 q^{53} +5.19637 q^{54} -3.80511 q^{55} -7.95320 q^{56} +12.7537 q^{57} -0.249092 q^{58} -12.3631 q^{59} -8.79767 q^{60} +4.08696 q^{61} -9.79203 q^{62} -17.1705 q^{63} +2.19633 q^{64} +2.15440 q^{65} -4.52529 q^{66} -5.44219 q^{67} +0.864767 q^{68} +11.4402 q^{69} +26.6578 q^{70} +7.93867 q^{71} +7.97075 q^{72} -8.98575 q^{73} +7.67781 q^{74} -25.3429 q^{75} -4.12509 q^{76} +4.13916 q^{77} +2.56216 q^{78} -5.18424 q^{79} -18.9560 q^{80} -4.23653 q^{81} +6.17831 q^{82} +0.350834 q^{83} +9.57002 q^{84} +3.80511 q^{85} -1.69256 q^{86} -0.393475 q^{87} -1.92145 q^{88} +7.41740 q^{89} -26.7166 q^{90} -2.34354 q^{91} -3.70024 q^{92} -15.4678 q^{93} -17.8907 q^{94} -18.1510 q^{95} -12.2692 q^{96} +2.23033 q^{97} -17.1501 q^{98} -4.14830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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