LMFDB - Embedded newform 8041.2.a.h.1.5

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:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.63295 q^{2} +1.21952 q^{3} +4.93245 q^{4} -0.402998 q^{5} -3.21093 q^{6} +4.56516 q^{7} -7.72100 q^{8} -1.51278 q^{9} +O(q^{10})$	\(q-2.63295 q^{2} +1.21952 q^{3} +4.93245 q^{4} -0.402998 q^{5} -3.21093 q^{6} +4.56516 q^{7} -7.72100 q^{8} -1.51278 q^{9} +1.06108 q^{10} -1.00000 q^{11} +6.01520 q^{12} -0.0458520 q^{13} -12.0199 q^{14} -0.491463 q^{15} +10.4642 q^{16} -1.00000 q^{17} +3.98308 q^{18} -1.53095 q^{19} -1.98777 q^{20} +5.56729 q^{21} +2.63295 q^{22} -4.42774 q^{23} -9.41589 q^{24} -4.83759 q^{25} +0.120726 q^{26} -5.50341 q^{27} +22.5174 q^{28} -2.03835 q^{29} +1.29400 q^{30} +0.711774 q^{31} -12.1096 q^{32} -1.21952 q^{33} +2.63295 q^{34} -1.83975 q^{35} -7.46171 q^{36} +9.36808 q^{37} +4.03091 q^{38} -0.0559173 q^{39} +3.11155 q^{40} +1.58135 q^{41} -14.6584 q^{42} -1.00000 q^{43} -4.93245 q^{44} +0.609647 q^{45} +11.6580 q^{46} +1.99554 q^{47} +12.7612 q^{48} +13.8407 q^{49} +12.7372 q^{50} -1.21952 q^{51} -0.226163 q^{52} -5.72143 q^{53} +14.4902 q^{54} +0.402998 q^{55} -35.2476 q^{56} -1.86701 q^{57} +5.36689 q^{58} -8.42798 q^{59} -2.42412 q^{60} +9.01994 q^{61} -1.87407 q^{62} -6.90609 q^{63} +10.9558 q^{64} +0.0184783 q^{65} +3.21093 q^{66} +3.99313 q^{67} -4.93245 q^{68} -5.39971 q^{69} +4.84398 q^{70} +3.27222 q^{71} +11.6802 q^{72} +0.449067 q^{73} -24.6657 q^{74} -5.89952 q^{75} -7.55131 q^{76} -4.56516 q^{77} +0.147228 q^{78} -12.4515 q^{79} -4.21703 q^{80} -2.17316 q^{81} -4.16363 q^{82} +3.04881 q^{83} +27.4604 q^{84} +0.402998 q^{85} +2.63295 q^{86} -2.48581 q^{87} +7.72100 q^{88} +13.8354 q^{89} -1.60517 q^{90} -0.209322 q^{91} -21.8396 q^{92} +0.868020 q^{93} -5.25417 q^{94} +0.616968 q^{95} -14.7679 q^{96} +11.4699 q^{97} -36.4420 q^{98} +1.51278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.63295	−1.86178	−0.930890	−	0.365300i	$-0.880966\pi$
$2$	−2.63295	−1.86178	−0.930890	+	0.365300i	$0.880966\pi$
$3$	1.21952	0.704088	0.352044	−	0.935983i	$-0.385487\pi$
$3$	1.21952	0.704088	0.352044	+	0.935983i	$0.385487\pi$
$4$	4.93245	2.46622
$5$	−0.402998	−0.180226	−0.0901131	−	0.995932i	$-0.528723\pi$
$5$	−0.402998	−0.180226	−0.0901131	+	0.995932i	$0.528723\pi$
$6$	−3.21093	−1.31086
$7$	4.56516	1.72547	0.862735	−	0.505657i	$-0.168750\pi$
$7$	4.56516	1.72547	0.862735	+	0.505657i	$0.168750\pi$
$8$	−7.72100	−2.72979
$9$	−1.51278	−0.504260
$10$	1.06108	0.335542
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.01520	1.73644
$13$	−0.0458520	−0.0127171	−0.00635853	−	0.999980i	$-0.502024\pi$
$13$	−0.0458520	−0.0127171	−0.00635853	+	0.999980i	$0.502024\pi$
$14$	−12.0199	−3.21244
$15$	−0.491463	−0.126895
$16$	10.4642	2.61604
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.98308	0.938821
$19$	−1.53095	−0.351223	−0.175612	−	0.984460i	$-0.556190\pi$
$19$	−1.53095	−0.351223	−0.175612	+	0.984460i	$0.556190\pi$
$20$	−1.98777	−0.444478
$21$	5.56729	1.21488
$22$	2.63295	0.561348
$23$	−4.42774	−0.923248	−0.461624	−	0.887076i	$-0.652733\pi$
$23$	−4.42774	−0.923248	−0.461624	+	0.887076i	$0.652733\pi$
$24$	−9.41589	−1.92201
$25$	−4.83759	−0.967519
$26$	0.120726	0.0236764
$27$	−5.50341	−1.05913
$28$	22.5174	4.25540
$29$	−2.03835	−0.378513	−0.189256	−	0.981928i	$-0.560608\pi$
$29$	−2.03835	−0.378513	−0.189256	+	0.981928i	$0.560608\pi$
$30$	1.29400	0.236251
$31$	0.711774	0.127838	0.0639192	−	0.997955i	$-0.479640\pi$
$31$	0.711774	0.127838	0.0639192	+	0.997955i	$0.479640\pi$
$32$	−12.1096	−2.14070
$33$	−1.21952	−0.212291
$34$	2.63295	0.451548
$35$	−1.83975	−0.310975
$36$	−7.46171	−1.24362
$37$	9.36808	1.54010	0.770051	−	0.637982i	$-0.220230\pi$
$37$	9.36808	1.54010	0.770051	+	0.637982i	$0.220230\pi$
$38$	4.03091	0.653900
$39$	−0.0559173	−0.00895393
$40$	3.11155	0.491979
$41$	1.58135	0.246966	0.123483	−	0.992347i	$-0.460594\pi$
$41$	1.58135	0.246966	0.123483	+	0.992347i	$0.460594\pi$
$42$	−14.6584	−2.26184
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.93245	−0.743595
$45$	0.609647	0.0908808
$46$	11.6580	1.71889
$47$	1.99554	0.291079	0.145540	−	0.989352i	$-0.453508\pi$
$47$	1.99554	0.291079	0.145540	+	0.989352i	$0.453508\pi$
$48$	12.7612	1.84192
$49$	13.8407	1.97725
$50$	12.7372	1.80131
$51$	−1.21952	−0.170766
$52$	−0.226163	−0.0313631
$53$	−5.72143	−0.785899	−0.392950	−	0.919560i	$-0.628545\pi$
$53$	−5.72143	−0.785899	−0.392950	+	0.919560i	$0.628545\pi$
$54$	14.4902	1.97187
$55$	0.402998	0.0543402
$56$	−35.2476	−4.71016
$57$	−1.86701	−0.247292
$58$	5.36689	0.704707
$59$	−8.42798	−1.09723	−0.548615	−	0.836075i	$-0.684845\pi$
$59$	−8.42798	−1.09723	−0.548615	+	0.836075i	$0.684845\pi$
$60$	−2.42412	−0.312952
$61$	9.01994	1.15488	0.577442	−	0.816431i	$-0.304051\pi$
$61$	9.01994	1.15488	0.577442	+	0.816431i	$0.304051\pi$
$62$	−1.87407	−0.238007
$63$	−6.90609	−0.870085
$64$	10.9558	1.36947
$65$	0.0184783	0.00229195
$66$	3.21093	0.395238
$67$	3.99313	0.487839	0.243919	−	0.969796i	$-0.421567\pi$
$67$	3.99313	0.487839	0.243919	+	0.969796i	$0.421567\pi$
$68$	−4.93245	−0.598147
$69$	−5.39971	−0.650048
$70$	4.84398	0.578967
$71$	3.27222	0.388341	0.194170	−	0.980968i	$-0.437799\pi$
$71$	3.27222	0.388341	0.194170	+	0.980968i	$0.437799\pi$
$72$	11.6802	1.37652
$73$	0.449067	0.0525594	0.0262797	−	0.999655i	$-0.491634\pi$
$73$	0.449067	0.0525594	0.0262797	+	0.999655i	$0.491634\pi$
$74$	−24.6657	−2.86733
$75$	−5.89952	−0.681218
$76$	−7.55131	−0.866195
$77$	−4.56516	−0.520249
$78$	0.147228	0.0166702
$79$	−12.4515	−1.40090	−0.700451	−	0.713700i	$-0.747018\pi$
$79$	−12.4515	−1.40090	−0.700451	+	0.713700i	$0.747018\pi$
$80$	−4.21703	−0.471479
$81$	−2.17316	−0.241462
$82$	−4.16363	−0.459796
$83$	3.04881	0.334650	0.167325	−	0.985902i	$-0.446487\pi$
$83$	3.04881	0.334650	0.167325	+	0.985902i	$0.446487\pi$
$84$	27.4604	2.99617
$85$	0.402998	0.0437113
$86$	2.63295	0.283919
$87$	−2.48581	−0.266506
$88$	7.72100	0.823062
$89$	13.8354	1.46655	0.733276	−	0.679932i	$-0.237991\pi$
$89$	13.8354	1.46655	0.733276	+	0.679932i	$0.237991\pi$
$90$	−1.60517	−0.169200
$91$	−0.209322	−0.0219429
$92$	−21.8396	−2.27694
$93$	0.868020	0.0900095
$94$	−5.25417	−0.541926
$95$	0.616968	0.0632996
$96$	−14.7679	−1.50724
$97$	11.4699	1.16459	0.582296	−	0.812977i	$-0.302154\pi$
$97$	11.4699	1.16459	0.582296	+	0.812977i	$0.302154\pi$
$98$	−36.4420	−3.68120
$99$	1.51278	0.152040
$100$	−23.8612	−2.38612
$101$	−6.60979	−0.657698	−0.328849	−	0.944382i	$-0.606661\pi$
$101$	−6.60979	−0.657698	−0.328849	+	0.944382i	$0.606661\pi$
$102$	3.21093	0.317930
$103$	−15.6522	−1.54225	−0.771127	−	0.636681i	$-0.780307\pi$
$103$	−15.6522	−1.54225	−0.771127	+	0.636681i	$0.780307\pi$
$104$	0.354023	0.0347148
$105$	−2.24361	−0.218954
$106$	15.0643	1.46317
$107$	−10.5950	−1.02426	−0.512128	−	0.858909i	$-0.671143\pi$
$107$	−10.5950	−1.02426	−0.512128	+	0.858909i	$0.671143\pi$
$108$	−27.1453	−2.61206
$109$	19.1765	1.83677	0.918387	−	0.395684i	$-0.129492\pi$
$109$	19.1765	1.83677	0.918387	+	0.395684i	$0.129492\pi$
$110$	−1.06108	−0.101170
$111$	11.4245	1.08437
$112$	47.7706	4.51389
$113$	−0.210671	−0.0198183	−0.00990915	−	0.999951i	$-0.503154\pi$
$113$	−0.210671	−0.0198183	−0.00990915	+	0.999951i	$0.503154\pi$
$114$	4.91576	0.460403
$115$	1.78437	0.166394
$116$	−10.0541	−0.933497
$117$	0.0693639	0.00641270
$118$	22.1905	2.04280
$119$	−4.56516	−0.418488
$120$	3.79459	0.346397
$121$	1.00000	0.0909091
$122$	−23.7491	−2.15014
$123$	1.92849	0.173886
$124$	3.51079	0.315278
$125$	3.96453	0.354598
$126$	18.1834	1.61991
$127$	−8.87752	−0.787752	−0.393876	−	0.919164i	$-0.628866\pi$
$127$	−8.87752	−0.787752	−0.393876	+	0.919164i	$0.628866\pi$
$128$	−4.62685	−0.408960
$129$	−1.21952	−0.107372
$130$	−0.0486524	−0.00426710
$131$	−10.7608	−0.940172	−0.470086	−	0.882621i	$-0.655777\pi$
$131$	−10.7608	−0.940172	−0.470086	+	0.882621i	$0.655777\pi$
$132$	−6.01520	−0.523556
$133$	−6.98902	−0.606025
$134$	−10.5137	−0.908248
$135$	2.21786	0.190883
$136$	7.72100	0.662071
$137$	21.1968	1.81096	0.905482	−	0.424384i	$-0.139509\pi$
$137$	21.1968	1.81096	0.905482	+	0.424384i	$0.139509\pi$
$138$	14.2172	1.21025
$139$	−5.44790	−0.462085	−0.231042	−	0.972944i	$-0.574214\pi$
$139$	−5.44790	−0.462085	−0.231042	+	0.972944i	$0.574214\pi$
$140$	−9.07448	−0.766934
$141$	2.43359	0.204946
$142$	−8.61560	−0.723005
$143$	0.0458520	0.00383434
$144$	−15.8300	−1.31916
$145$	0.821452	0.0682179
$146$	−1.18237	−0.0978540
$147$	16.8790	1.39216
$148$	46.2076	3.79824
$149$	8.21421	0.672934	0.336467	−	0.941695i	$-0.390768\pi$
$149$	8.21421	0.672934	0.336467	+	0.941695i	$0.390768\pi$
$150$	15.5332	1.26828
$151$	−19.3806	−1.57717	−0.788584	−	0.614926i	$-0.789186\pi$
$151$	−19.3806	−1.57717	−0.788584	+	0.614926i	$0.789186\pi$
$152$	11.8204	0.958764
$153$	1.51278	0.122301
$154$	12.0199	0.968589
$155$	−0.286844	−0.0230398
$156$	−0.275809	−0.0220824
$157$	−2.52570	−0.201573	−0.100787	−	0.994908i	$-0.532136\pi$
$157$	−2.52570	−0.201573	−0.100787	+	0.994908i	$0.532136\pi$
$158$	32.7842	2.60817
$159$	−6.97738	−0.553343
$160$	4.88016	0.385810
$161$	−20.2134	−1.59304
$162$	5.72183	0.449550
$163$	−19.7419	−1.54630	−0.773151	−	0.634222i	$-0.781321\pi$
$163$	−19.7419	−1.54630	−0.773151	+	0.634222i	$0.781321\pi$
$164$	7.79994	0.609073
$165$	0.491463	0.0382603
$166$	−8.02738	−0.623045
$167$	3.45457	0.267323	0.133661	−	0.991027i	$-0.457327\pi$
$167$	3.45457	0.267323	0.133661	+	0.991027i	$0.457327\pi$
$168$	−42.9851	−3.31637
$169$	−12.9979	−0.999838
$170$	−1.06108	−0.0813808
$171$	2.31598	0.177108
$172$	−4.93245	−0.376096
$173$	−20.0487	−1.52428	−0.762138	−	0.647415i	$-0.775850\pi$
$173$	−20.0487	−1.52428	−0.762138	+	0.647415i	$0.775850\pi$
$174$	6.54501	0.496176
$175$	−22.0844	−1.66942
$176$	−10.4642	−0.788765
$177$	−10.2781	−0.772546
$178$	−36.4280	−2.73040
$179$	−8.03852	−0.600827	−0.300413	−	0.953809i	$-0.597125\pi$
$179$	−8.03852	−0.600827	−0.300413	+	0.953809i	$0.597125\pi$
$180$	3.00705	0.224133
$181$	−22.0961	−1.64239	−0.821196	−	0.570646i	$-0.806693\pi$
$181$	−22.0961	−1.64239	−0.821196	+	0.570646i	$0.806693\pi$
$182$	0.551135	0.0408528
$183$	11.0000	0.813141
$184$	34.1866	2.52027
$185$	−3.77532	−0.277567
$186$	−2.28546	−0.167578
$187$	1.00000	0.0731272
$188$	9.84290	0.717867
$189$	−25.1240	−1.82750
$190$	−1.62445	−0.117850
$191$	−0.840027	−0.0607822	−0.0303911	−	0.999538i	$-0.509675\pi$
$191$	−0.840027	−0.0607822	−0.0303911	+	0.999538i	$0.509675\pi$
$192$	13.3608	0.964231
$193$	−14.7574	−1.06226	−0.531129	−	0.847291i	$-0.678232\pi$
$193$	−14.7574	−1.06226	−0.531129	+	0.847291i	$0.678232\pi$
$194$	−30.1997	−2.16822
$195$	0.0225345	0.00161373
$196$	68.2686	4.87633
$197$	−27.1546	−1.93469	−0.967343	−	0.253471i	$-0.918428\pi$
$197$	−27.1546	−1.93469	−0.967343	+	0.253471i	$0.918428\pi$
$198$	−3.98308	−0.283065
$199$	4.62786	0.328061	0.164030	−	0.986455i	$-0.447551\pi$
$199$	4.62786	0.328061	0.164030	+	0.986455i	$0.447551\pi$
$200$	37.3511	2.64112
$201$	4.86969	0.343481
$202$	17.4033	1.22449
$203$	−9.30542	−0.653112
$204$	−6.01520	−0.421148
$205$	−0.637282	−0.0445097
$206$	41.2114	2.87134
$207$	6.69820	0.465557
$208$	−0.479802	−0.0332683
$209$	1.53095	0.105898
$210$	5.90732	0.407644
$211$	7.89079	0.543224	0.271612	−	0.962407i	$-0.412443\pi$
$211$	7.89079	0.543224	0.271612	+	0.962407i	$0.412443\pi$
$212$	−28.2207	−1.93820
$213$	3.99052	0.273426
$214$	27.8961	1.90694
$215$	0.402998	0.0274842
$216$	42.4918	2.89120
$217$	3.24937	0.220581
$218$	−50.4908	−3.41967
$219$	0.547645	0.0370064
$220$	1.98777	0.134015
$221$	0.0458520	0.00308434
$222$	−30.0803	−2.01886
$223$	−8.86793	−0.593841	−0.296920	−	0.954902i	$-0.595960\pi$
$223$	−8.86793	−0.593841	−0.296920	+	0.954902i	$0.595960\pi$
$224$	−55.2824	−3.69371
$225$	7.31821	0.487881
$226$	0.554688	0.0368973
$227$	−15.4597	−1.02610	−0.513049	−	0.858359i	$-0.671484\pi$
$227$	−15.4597	−1.02610	−0.513049	+	0.858359i	$0.671484\pi$
$228$	−9.20895	−0.609878
$229$	1.94649	0.128628	0.0643138	−	0.997930i	$-0.479514\pi$
$229$	1.94649	0.128628	0.0643138	+	0.997930i	$0.479514\pi$
$230$	−4.69817	−0.309788
$231$	−5.56729	−0.366301
$232$	15.7381	1.03326
$233$	−21.9061	−1.43512	−0.717558	−	0.696499i	$-0.754740\pi$
$233$	−21.9061	−1.43512	−0.717558	+	0.696499i	$0.754740\pi$
$234$	−0.182632	−0.0119390
$235$	−0.804199	−0.0524601
$236$	−41.5706	−2.70601
$237$	−15.1848	−0.986359
$238$	12.0199	0.779132
$239$	11.1549	0.721554	0.360777	−	0.932652i	$-0.382512\pi$
$239$	11.1549	0.721554	0.360777	+	0.932652i	$0.382512\pi$
$240$	−5.14274	−0.331963
$241$	−6.27075	−0.403934	−0.201967	−	0.979392i	$-0.564733\pi$
$241$	−6.27075	−0.403934	−0.201967	+	0.979392i	$0.564733\pi$
$242$	−2.63295	−0.169253
$243$	13.8600	0.889121
$244$	44.4904	2.84820
$245$	−5.57778	−0.356352
$246$	−5.07762	−0.323737
$247$	0.0701969	0.00446652
$248$	−5.49561	−0.348972
$249$	3.71807	0.235623
$250$	−10.4384	−0.660184
$251$	−14.1562	−0.893529	−0.446764	−	0.894652i	$-0.647424\pi$
$251$	−14.1562	−0.893529	−0.446764	+	0.894652i	$0.647424\pi$
$252$	−34.0639	−2.14582
$253$	4.42774	0.278370
$254$	23.3741	1.46662
$255$	0.491463	0.0307766
$256$	−9.72930	−0.608081
$257$	12.1440	0.757519	0.378760	−	0.925495i	$-0.376351\pi$
$257$	12.1440	0.757519	0.378760	+	0.925495i	$0.376351\pi$
$258$	3.21093	0.199904
$259$	42.7668	2.65740
$260$	0.0911431	0.00565245
$261$	3.08358	0.190869
$262$	28.3326	1.75039
$263$	−16.7011	−1.02984	−0.514918	−	0.857239i	$-0.672178\pi$
$263$	−16.7011	−1.02984	−0.514918	+	0.857239i	$0.672178\pi$
$264$	9.41589	0.579508
$265$	2.30573	0.141640
$266$	18.4018	1.12828
$267$	16.8725	1.03258
$268$	19.6959	1.20312
$269$	26.2842	1.60257	0.801287	−	0.598280i	$-0.204149\pi$
$269$	26.2842	1.60257	0.801287	+	0.598280i	$0.204149\pi$
$270$	−5.83953	−0.355383
$271$	−27.0583	−1.64367	−0.821836	−	0.569724i	$-0.807050\pi$
$271$	−27.0583	−1.64367	−0.821836	+	0.569724i	$0.807050\pi$
$272$	−10.4642	−0.634482
$273$	−0.255271	−0.0154497
$274$	−55.8102	−3.37162
$275$	4.83759	0.291718
$276$	−26.6338	−1.60317
$277$	27.6865	1.66352	0.831759	−	0.555137i	$-0.187334\pi$
$277$	27.6865	1.66352	0.831759	+	0.555137i	$0.187334\pi$
$278$	14.3441	0.860300
$279$	−1.07676	−0.0644638
$280$	14.2047	0.848895
$281$	−24.3639	−1.45343	−0.726714	−	0.686940i	$-0.758954\pi$
$281$	−24.3639	−1.45343	−0.726714	+	0.686940i	$0.758954\pi$
$282$	−6.40754	−0.381564
$283$	19.1960	1.14109	0.570543	−	0.821268i	$-0.306733\pi$
$283$	19.1960	1.14109	0.570543	+	0.821268i	$0.306733\pi$
$284$	16.1400	0.957735
$285$	0.752403	0.0445685
$286$	−0.120726	−0.00713869
$287$	7.21914	0.426132
$288$	18.3192	1.07947
$289$	1.00000	0.0588235
$290$	−2.16285	−0.127007
$291$	13.9877	0.819976
$292$	2.21500	0.129623
$293$	−1.75302	−0.102412	−0.0512062	−	0.998688i	$-0.516307\pi$
$293$	−1.75302	−0.102412	−0.0512062	+	0.998688i	$0.516307\pi$
$294$	−44.4416	−2.59189
$295$	3.39646	0.197749
$296$	−72.3310	−4.20415
$297$	5.50341	0.319340
$298$	−21.6276	−1.25286
$299$	0.203021	0.0117410
$300$	−29.0991	−1.68004
$301$	−4.56516	−0.263132
$302$	51.0282	2.93634
$303$	−8.06075	−0.463078
$304$	−16.0201	−0.918813
$305$	−3.63502	−0.208140
$306$	−3.98308	−0.227697
$307$	−30.2865	−1.72854	−0.864270	−	0.503028i	$-0.832219\pi$
$307$	−30.2865	−1.72854	−0.864270	+	0.503028i	$0.832219\pi$
$308$	−22.5174	−1.28305
$309$	−19.0881	−1.08588
$310$	0.755246	0.0428951
$311$	−15.0049	−0.850847	−0.425424	−	0.904994i	$-0.639875\pi$
$311$	−15.0049	−0.850847	−0.425424	+	0.904994i	$0.639875\pi$
$312$	0.431737	0.0244423
$313$	−26.0615	−1.47308	−0.736541	−	0.676393i	$-0.763542\pi$
$313$	−26.0615	−1.47308	−0.736541	+	0.676393i	$0.763542\pi$
$314$	6.65007	0.375285
$315$	2.78314	0.156812
$316$	−61.4163	−3.45494
$317$	20.4406	1.14806	0.574029	−	0.818835i	$-0.305380\pi$
$317$	20.4406	1.14806	0.574029	+	0.818835i	$0.305380\pi$
$318$	18.3711	1.03020
$319$	2.03835	0.114126
$320$	−4.41516	−0.246815
$321$	−12.9208	−0.721166
$322$	53.2209	2.96588
$323$	1.53095	0.0851841
$324$	−10.7190	−0.595500
$325$	0.221813	0.0123040
$326$	51.9794	2.87887
$327$	23.3860	1.29325
$328$	−12.2096	−0.674164
$329$	9.10997	0.502249
$330$	−1.29400	−0.0712323
$331$	−24.9468	−1.37120	−0.685600	−	0.727979i	$-0.740460\pi$
$331$	−24.9468	−1.37120	−0.685600	+	0.727979i	$0.740460\pi$
$332$	15.0381	0.825323
$333$	−14.1718	−0.776612
$334$	−9.09572	−0.497696
$335$	−1.60922	−0.0879213
$336$	58.2570	3.17818
$337$	−18.4729	−1.00628	−0.503141	−	0.864205i	$-0.667822\pi$
$337$	−18.4729	−1.00628	−0.503141	+	0.864205i	$0.667822\pi$
$338$	34.2229	1.86148
$339$	−0.256917	−0.0139538
$340$	1.98777	0.107802
$341$	−0.711774	−0.0385447
$342$	−6.09788	−0.329736
$343$	31.2290	1.68621
$344$	7.72100	0.416289
$345$	2.17607	0.117156
$346$	52.7874	2.83787
$347$	−17.0688	−0.916304	−0.458152	−	0.888874i	$-0.651488\pi$
$347$	−17.0688	−0.916304	−0.458152	+	0.888874i	$0.651488\pi$
$348$	−12.2611	−0.657264
$349$	−4.75377	−0.254463	−0.127232	−	0.991873i	$-0.540609\pi$
$349$	−4.75377	−0.254463	−0.127232	+	0.991873i	$0.540609\pi$
$350$	58.1472	3.10810
$351$	0.252342	0.0134690
$352$	12.1096	0.645445
$353$	−12.9550	−0.689526	−0.344763	−	0.938690i	$-0.612041\pi$
$353$	−12.9550	−0.689526	−0.344763	+	0.938690i	$0.612041\pi$
$354$	27.0617	1.43831
$355$	−1.31870	−0.0699892
$356$	68.2425	3.61684
$357$	−5.56729	−0.294652
$358$	21.1650	1.11861
$359$	−3.93365	−0.207610	−0.103805	−	0.994598i	$-0.533102\pi$
$359$	−3.93365	−0.207610	−0.103805	+	0.994598i	$0.533102\pi$
$360$	−4.70709	−0.248085
$361$	−16.6562	−0.876642
$362$	58.1781	3.05777
$363$	1.21952	0.0640080
$364$	−1.03247	−0.0541161
$365$	−0.180973	−0.00947258
$366$	−28.9624	−1.51389
$367$	23.5520	1.22940	0.614702	−	0.788759i	$-0.289276\pi$
$367$	23.5520	1.22940	0.614702	+	0.788759i	$0.289276\pi$
$368$	−46.3326	−2.41525
$369$	−2.39224	−0.124535
$370$	9.94024	0.516768
$371$	−26.1193	−1.35605
$372$	4.28147	0.221984
$373$	−9.47324	−0.490506	−0.245253	−	0.969459i	$-0.578871\pi$
$373$	−9.47324	−0.490506	−0.245253	+	0.969459i	$0.578871\pi$
$374$	−2.63295	−0.136147
$375$	4.83481	0.249669
$376$	−15.4076	−0.794585
$377$	0.0934625	0.00481357
$378$	66.1503	3.40240
$379$	22.9062	1.17661	0.588307	−	0.808637i	$-0.299794\pi$
$379$	22.9062	1.17661	0.588307	+	0.808637i	$0.299794\pi$
$380$	3.04316	0.156111
$381$	−10.8263	−0.554647
$382$	2.21175	0.113163
$383$	−3.16299	−0.161621	−0.0808106	−	0.996729i	$-0.525751\pi$
$383$	−3.16299	−0.161621	−0.0808106	+	0.996729i	$0.525751\pi$
$384$	−5.64252	−0.287944
$385$	1.83975	0.0937625
$386$	38.8555	1.97769
$387$	1.51278	0.0768989
$388$	56.5747	2.87215
$389$	16.3499	0.828972	0.414486	−	0.910056i	$-0.363961\pi$
$389$	16.3499	0.828972	0.414486	+	0.910056i	$0.363961\pi$
$390$	−0.0593324	−0.00300441
$391$	4.42774	0.223921
$392$	−106.864	−5.39746
$393$	−13.1229	−0.661964
$394$	71.4968	3.60196
$395$	5.01793	0.252479
$396$	7.46171	0.374965
$397$	−2.27419	−0.114138	−0.0570692	−	0.998370i	$-0.518176\pi$
$397$	−2.27419	−0.114138	−0.0570692	+	0.998370i	$0.518176\pi$
$398$	−12.1850	−0.610777
$399$	−8.52323	−0.426695
$400$	−50.6213	−2.53107
$401$	3.74432	0.186982	0.0934912	−	0.995620i	$-0.470197\pi$
$401$	3.74432	0.186982	0.0934912	+	0.995620i	$0.470197\pi$
$402$	−12.8217	−0.639487
$403$	−0.0326363	−0.00162573
$404$	−32.6024	−1.62203
$405$	0.875780	0.0435178
$406$	24.5007	1.21595
$407$	−9.36808	−0.464359
$408$	9.41589	0.466156
$409$	−8.75573	−0.432943	−0.216471	−	0.976289i	$-0.569455\pi$
$409$	−8.75573	−0.432943	−0.216471	+	0.976289i	$0.569455\pi$
$410$	1.67794	0.0828673
$411$	25.8498	1.27508
$412$	−77.2035	−3.80354
$413$	−38.4751	−1.89324
$414$	−17.6361	−0.866765
$415$	−1.22866	−0.0603128
$416$	0.555251	0.0272234
$417$	−6.64380	−0.325349
$418$	−4.03091	−0.197158
$419$	−0.491469	−0.0240098	−0.0120049	−	0.999928i	$-0.503821\pi$
$419$	−0.491469	−0.0240098	−0.0120049	+	0.999928i	$0.503821\pi$
$420$	−11.0665	−0.539989
$421$	18.2012	0.887072	0.443536	−	0.896257i	$-0.353724\pi$
$421$	18.2012	0.887072	0.443536	+	0.896257i	$0.353724\pi$
$422$	−20.7761	−1.01136
$423$	−3.01881	−0.146780
$424$	44.1752	2.14534
$425$	4.83759	0.234658
$426$	−10.5069	−0.509059
$427$	41.1775	1.99272
$428$	−52.2592	−2.52604
$429$	0.0559173	0.00269971
$430$	−1.06108	−0.0511696
$431$	−14.7589	−0.710909	−0.355455	−	0.934694i	$-0.615674\pi$
$431$	−14.7589	−0.710909	−0.355455	+	0.934694i	$0.615674\pi$
$432$	−57.5885	−2.77073
$433$	14.7374	0.708234	0.354117	−	0.935201i	$-0.384781\pi$
$433$	14.7374	0.708234	0.354117	+	0.935201i	$0.384781\pi$
$434$	−8.55543	−0.410674
$435$	1.00177	0.0480314
$436$	94.5870	4.52990
$437$	6.77864	0.324266
$438$	−1.44192	−0.0688978
$439$	−0.274469	−0.0130997	−0.00654984	−	0.999979i	$-0.502085\pi$
$439$	−0.274469	−0.0130997	−0.00654984	+	0.999979i	$0.502085\pi$
$440$	−3.11155	−0.148337
$441$	−20.9380	−0.997046
$442$	−0.120726	−0.00574236
$443$	−35.8868	−1.70503	−0.852517	−	0.522700i	$-0.824925\pi$
$443$	−35.8868	−1.70503	−0.852517	+	0.522700i	$0.824925\pi$
$444$	56.3509	2.67430
$445$	−5.57565	−0.264311
$446$	23.3489	1.10560
$447$	10.0174	0.473805
$448$	50.0150	2.36299
$449$	19.4446	0.917647	0.458824	−	0.888527i	$-0.348271\pi$
$449$	19.4446	0.917647	0.458824	+	0.888527i	$0.348271\pi$
$450$	−19.2685	−0.908326
$451$	−1.58135	−0.0744630
$452$	−1.03913	−0.0488764
$453$	−23.6349	−1.11047
$454$	40.7048	1.91037
$455$	0.0843563	0.00395468
$456$	14.4152	0.675055
$457$	−12.5029	−0.584862	−0.292431	−	0.956287i	$-0.594464\pi$
$457$	−12.5029	−0.584862	−0.292431	+	0.956287i	$0.594464\pi$
$458$	−5.12501	−0.239476
$459$	5.50341	0.256877
$460$	8.80132	0.410364
$461$	10.6879	0.497783	0.248891	−	0.968531i	$-0.419934\pi$
$461$	10.6879	0.497783	0.248891	+	0.968531i	$0.419934\pi$
$462$	14.6584	0.681972
$463$	35.4351	1.64681	0.823405	−	0.567454i	$-0.192072\pi$
$463$	35.4351	1.64681	0.823405	+	0.567454i	$0.192072\pi$
$464$	−21.3296	−0.990204
$465$	−0.349811	−0.0162221
$466$	57.6777	2.67187
$467$	−38.4735	−1.78034	−0.890170	−	0.455628i	$-0.849415\pi$
$467$	−38.4735	−1.78034	−0.890170	+	0.455628i	$0.849415\pi$
$468$	0.342134	0.0158152
$469$	18.2293	0.841751
$470$	2.11742	0.0976693
$471$	−3.08014	−0.141925
$472$	65.0724	2.99520
$473$	1.00000	0.0459800
$474$	39.9809	1.83638
$475$	7.40609	0.339815
$476$	−22.5174	−1.03209
$477$	8.65527	0.396297
$478$	−29.3705	−1.34337
$479$	26.8374	1.22623	0.613117	−	0.789992i	$-0.289915\pi$
$479$	26.8374	1.22623	0.613117	+	0.789992i	$0.289915\pi$
$480$	5.95143	0.271644
$481$	−0.429545	−0.0195856
$482$	16.5106	0.752037
$483$	−24.6505	−1.12164
$484$	4.93245	0.224202
$485$	−4.62235	−0.209890
$486$	−36.4928	−1.65535
$487$	31.8156	1.44170	0.720852	−	0.693089i	$-0.243751\pi$
$487$	31.8156	1.44170	0.720852	+	0.693089i	$0.243751\pi$
$488$	−69.6430	−3.15259
$489$	−24.0755	−1.08873
$490$	14.6861	0.663448
$491$	14.3788	0.648904	0.324452	−	0.945902i	$-0.394820\pi$
$491$	14.3788	0.648904	0.324452	+	0.945902i	$0.394820\pi$
$492$	9.51216	0.428841
$493$	2.03835	0.0918028
$494$	−0.184825	−0.00831568
$495$	−0.609647	−0.0274016
$496$	7.44811	0.334430
$497$	14.9382	0.670070
$498$	−9.78952	−0.438679
$499$	−15.1535	−0.678364	−0.339182	−	0.940721i	$-0.610150\pi$
$499$	−15.1535	−0.678364	−0.339182	+	0.940721i	$0.610150\pi$
$500$	19.5548	0.874519
$501$	4.21290	0.188219
$502$	37.2725	1.66355
$503$	−20.2146	−0.901323	−0.450662	−	0.892695i	$-0.648812\pi$
$503$	−20.2146	−0.901323	−0.450662	+	0.892695i	$0.648812\pi$
$504$	53.3219	2.37515
$505$	2.66373	0.118534
$506$	−11.6580	−0.518263
$507$	−15.8512	−0.703974
$508$	−43.7879	−1.94277
$509$	31.9857	1.41774	0.708870	−	0.705340i	$-0.249205\pi$
$509$	31.9857	1.41774	0.708870	+	0.705340i	$0.249205\pi$
$510$	−1.29400	−0.0572992
$511$	2.05007	0.0906896
$512$	34.8705	1.54107
$513$	8.42542	0.371991
$514$	−31.9745	−1.41033
$515$	6.30779	0.277955
$516$	−6.01520	−0.264805
$517$	−1.99554	−0.0877638
$518$	−112.603	−4.94750
$519$	−24.4497	−1.07322
$520$	−0.142671	−0.00625652
$521$	18.5820	0.814094	0.407047	−	0.913407i	$-0.366559\pi$
$521$	18.5820	0.814094	0.407047	+	0.913407i	$0.366559\pi$
$522$	−8.11892	−0.355356
$523$	28.7483	1.25708	0.628538	−	0.777779i	$-0.283654\pi$
$523$	28.7483	1.25708	0.628538	+	0.777779i	$0.283654\pi$
$524$	−53.0769	−2.31867
$525$	−26.9323	−1.17542
$526$	43.9733	1.91733
$527$	−0.711774	−0.0310054
$528$	−12.7612	−0.555360
$529$	−3.39508	−0.147612
$530$	−6.07087	−0.263702
$531$	12.7497	0.553289
$532$	−34.4730	−1.49459
$533$	−0.0725082	−0.00314068
$534$	−44.4246	−1.92244
$535$	4.26976	0.184598
$536$	−30.8310	−1.33170
$537$	−9.80310	−0.423035
$538$	−69.2050	−2.98364
$539$	−13.8407	−0.596162
$540$	10.9395	0.470761
$541$	9.40582	0.404388	0.202194	−	0.979346i	$-0.435193\pi$
$541$	9.40582	0.404388	0.202194	+	0.979346i	$0.435193\pi$
$542$	71.2432	3.06016
$543$	−26.9466	−1.15639
$544$	12.1096	0.519196
$545$	−7.72808	−0.331035
$546$	0.672118	0.0287640
$547$	−21.6486	−0.925625	−0.462813	−	0.886456i	$-0.653160\pi$
$547$	−21.6486	−0.925625	−0.462813	+	0.886456i	$0.653160\pi$
$548$	104.552	4.46625
$549$	−13.6452	−0.582362
$550$	−12.7372	−0.543114
$551$	3.12061	0.132942
$552$	41.6912	1.77449
$553$	−56.8431	−2.41721
$554$	−72.8972	−3.09711
$555$	−4.60406	−0.195432
$556$	−26.8715	−1.13960
$557$	−10.5277	−0.446075	−0.223037	−	0.974810i	$-0.571597\pi$
$557$	−10.5277	−0.446075	−0.223037	+	0.974810i	$0.571597\pi$
$558$	2.83505	0.120017
$559$	0.0458520	0.00193933
$560$	−19.2514	−0.813522
$561$	1.21952	0.0514880
$562$	64.1490	2.70596
$563$	2.54113	0.107096	0.0535479	−	0.998565i	$-0.482947\pi$
$563$	2.54113	0.107096	0.0535479	+	0.998565i	$0.482947\pi$
$564$	12.0036	0.505442
$565$	0.0849002	0.00357178
$566$	−50.5423	−2.12445
$567$	−9.92084	−0.416636
$568$	−25.2648	−1.06009
$569$	10.6734	0.447450	0.223725	−	0.974652i	$-0.428178\pi$
$569$	10.6734	0.447450	0.223725	+	0.974652i	$0.428178\pi$
$570$	−1.98104	−0.0829768
$571$	39.5313	1.65434	0.827168	−	0.561955i	$-0.189951\pi$
$571$	39.5313	1.65434	0.827168	+	0.561955i	$0.189951\pi$
$572$	0.226163	0.00945633
$573$	−1.02443	−0.0427960
$574$	−19.0077	−0.793364
$575$	21.4196	0.893260
$576$	−16.5737	−0.690571
$577$	−24.4096	−1.01619	−0.508093	−	0.861302i	$-0.669649\pi$
$577$	−24.4096	−1.01619	−0.508093	+	0.861302i	$0.669649\pi$
$578$	−2.63295	−0.109516
$579$	−17.9968	−0.747923
$580$	4.05177	0.168241
$581$	13.9183	0.577429
$582$	−36.8291	−1.52661
$583$	5.72143	0.236958
$584$	−3.46725	−0.143476
$585$	−0.0279535	−0.00115574
$586$	4.61561	0.190669
$587$	16.5992	0.685122	0.342561	−	0.939496i	$-0.388706\pi$
$587$	16.5992	0.685122	0.342561	+	0.939496i	$0.388706\pi$
$588$	83.2548	3.43337
$589$	−1.08969	−0.0448998
$590$	−8.94272	−0.368166
$591$	−33.1155	−1.36219
$592$	98.0290	4.02897
$593$	−17.5233	−0.719595	−0.359797	−	0.933030i	$-0.617154\pi$
$593$	−17.5233	−0.719595	−0.359797	+	0.933030i	$0.617154\pi$
$594$	−14.4902	−0.594541
$595$	1.83975	0.0754225
$596$	40.5162	1.65961
$597$	5.64376	0.230984
$598$	−0.534545	−0.0218592
$599$	−38.2523	−1.56295	−0.781474	−	0.623938i	$-0.785532\pi$
$599$	−38.2523	−1.56295	−0.781474	+	0.623938i	$0.785532\pi$
$600$	45.5502	1.85958
$601$	7.65745	0.312354	0.156177	−	0.987729i	$-0.450083\pi$
$601$	7.65745	0.312354	0.156177	+	0.987729i	$0.450083\pi$
$602$	12.0199	0.489893
$603$	−6.04073	−0.245997
$604$	−95.5937	−3.88965
$605$	−0.402998	−0.0163842
$606$	21.2236	0.862149
$607$	15.0477	0.610765	0.305383	−	0.952230i	$-0.401216\pi$
$607$	15.0477	0.610765	0.305383	+	0.952230i	$0.401216\pi$
$608$	18.5392	0.751863
$609$	−11.3481	−0.459849
$610$	9.57083	0.387512
$611$	−0.0914995	−0.00370167
$612$	7.46171	0.301622
$613$	42.4620	1.71502	0.857511	−	0.514465i	$-0.172010\pi$
$613$	42.4620	1.71502	0.857511	+	0.514465i	$0.172010\pi$
$614$	79.7429	3.21816
$615$	−0.777176	−0.0313388
$616$	35.2476	1.42017
$617$	−11.2000	−0.450897	−0.225448	−	0.974255i	$-0.572385\pi$
$617$	−11.2000	−0.450897	−0.225448	+	0.974255i	$0.572385\pi$
$618$	50.2580	2.02168
$619$	−6.64034	−0.266898	−0.133449	−	0.991056i	$-0.542605\pi$
$619$	−6.64034	−0.266898	−0.133449	+	0.991056i	$0.542605\pi$
$620$	−1.41484	−0.0568214
$621$	24.3677	0.977842
$622$	39.5071	1.58409
$623$	63.1609	2.53049
$624$	−0.585127	−0.0234238
$625$	22.5903	0.903611
$626$	68.6186	2.74255
$627$	1.86701	0.0745614
$628$	−12.4579	−0.497125
$629$	−9.36808	−0.373530
$630$	−7.32788	−0.291950
$631$	−0.918019	−0.0365458	−0.0182729	−	0.999833i	$-0.505817\pi$
$631$	−0.918019	−0.0365458	−0.0182729	+	0.999833i	$0.505817\pi$
$632$	96.1380	3.82417
$633$	9.62295	0.382478
$634$	−53.8191	−2.13743
$635$	3.57762	0.141974
$636$	−34.4156	−1.36467
$637$	−0.634625	−0.0251447
$638$	−5.36689	−0.212477
$639$	−4.95014	−0.195825
$640$	1.86461	0.0737053
$641$	25.4717	1.00607	0.503035	−	0.864266i	$-0.332217\pi$
$641$	25.4717	1.00607	0.503035	+	0.864266i	$0.332217\pi$
$642$	34.0198	1.34265
$643$	11.6547	0.459616	0.229808	−	0.973236i	$-0.426190\pi$
$643$	11.6547	0.459616	0.229808	+	0.973236i	$0.426190\pi$
$644$	−99.7014	−3.92879
$645$	0.491463	0.0193513
$646$	−4.03091	−0.158594
$647$	9.96620	0.391812	0.195906	−	0.980623i	$-0.437235\pi$
$647$	9.96620	0.391812	0.195906	+	0.980623i	$0.437235\pi$
$648$	16.7790	0.659141
$649$	8.42798	0.330827
$650$	−0.584024	−0.0229073
$651$	3.96266	0.155309
$652$	−97.3758	−3.81353
$653$	37.9375	1.48461	0.742305	−	0.670063i	$-0.233733\pi$
$653$	37.9375	1.48461	0.742305	+	0.670063i	$0.233733\pi$
$654$	−61.5744	−2.40775
$655$	4.33656	0.169444
$656$	16.5475	0.646072
$657$	−0.679340	−0.0265036
$658$	−23.9861	−0.935077
$659$	−35.0382	−1.36489	−0.682447	−	0.730935i	$-0.739084\pi$
$659$	−35.0382	−1.36489	−0.682447	+	0.730935i	$0.739084\pi$
$660$	2.42412	0.0943586
$661$	−11.3947	−0.443204	−0.221602	−	0.975137i	$-0.571129\pi$
$661$	−11.3947	−0.443204	−0.221602	+	0.975137i	$0.571129\pi$
$662$	65.6838	2.55287
$663$	0.0559173	0.00217165
$664$	−23.5399	−0.913524
$665$	2.81656	0.109222
$666$	37.3138	1.44588
$667$	9.02531	0.349461
$668$	17.0395	0.659277
$669$	−10.8146	−0.418116
$670$	4.23701	0.163690
$671$	−9.01994	−0.348211
$672$	−67.4179	−2.60070
$673$	33.2657	1.28230	0.641150	−	0.767415i	$-0.278458\pi$
$673$	33.2657	1.28230	0.641150	+	0.767415i	$0.278458\pi$
$674$	48.6382	1.87347
$675$	26.6233	1.02473
$676$	−64.1115	−2.46583
$677$	−1.53901	−0.0591490	−0.0295745	−	0.999563i	$-0.509415\pi$
$677$	−1.53901	−0.0591490	−0.0295745	+	0.999563i	$0.509415\pi$
$678$	0.676452	0.0259790
$679$	52.3620	2.00947
$680$	−3.11155	−0.119322
$681$	−18.8534	−0.722464
$682$	1.87407	0.0717618
$683$	3.03721	0.116215	0.0581077	−	0.998310i	$-0.481493\pi$
$683$	3.03721	0.116215	0.0581077	+	0.998310i	$0.481493\pi$
$684$	11.4235	0.436787
$685$	−8.54227	−0.326383
$686$	−82.2246	−3.13935
$687$	2.37377	0.0905651
$688$	−10.4642	−0.398942
$689$	0.262339	0.00999433
$690$	−5.72950	−0.218118
$691$	−25.6353	−0.975211	−0.487606	−	0.873064i	$-0.662130\pi$
$691$	−25.6353	−0.975211	−0.487606	+	0.873064i	$0.662130\pi$
$692$	−98.8893	−3.75921
$693$	6.90609	0.262340
$694$	44.9415	1.70596
$695$	2.19549	0.0832798
$696$	19.1929	0.727505
$697$	−1.58135	−0.0598980
$698$	12.5165	0.473755
$699$	−26.7148	−1.01045
$700$	−108.930	−4.11717
$701$	−8.36769	−0.316043	−0.158022	−	0.987436i	$-0.550512\pi$
$701$	−8.36769	−0.316043	−0.158022	+	0.987436i	$0.550512\pi$
$702$	−0.664406	−0.0250764
$703$	−14.3420	−0.540920
$704$	−10.9558	−0.412912
$705$	−0.980734	−0.0369366
$706$	34.1100	1.28375
$707$	−30.1748	−1.13484
$708$	−50.6960	−1.90527
$709$	−16.1788	−0.607607	−0.303804	−	0.952735i	$-0.598257\pi$
$709$	−16.1788	−0.607607	−0.303804	+	0.952735i	$0.598257\pi$
$710$	3.47207	0.130304
$711$	18.8364	0.706419
$712$	−106.823	−4.00337
$713$	−3.15155	−0.118027
$714$	14.6584	0.548578
$715$	−0.0184783	−0.000691048 0
$716$	−39.6496	−1.48177
$717$	13.6036	0.508037
$718$	10.3571	0.386525
$719$	−3.58293	−0.133621	−0.0668103	−	0.997766i	$-0.521282\pi$
$719$	−3.58293	−0.133621	−0.0668103	+	0.997766i	$0.521282\pi$
$720$	6.37944	0.237748
$721$	−71.4547	−2.66111
$722$	43.8550	1.63212
$723$	−7.64728	−0.284405
$724$	−108.988	−4.05051
$725$	9.86072	0.366218
$726$	−3.21093	−0.119169
$727$	22.2075	0.823632	0.411816	−	0.911267i	$-0.364895\pi$
$727$	22.2075	0.823632	0.411816	+	0.911267i	$0.364895\pi$
$728$	1.61617	0.0598994
$729$	23.4220	0.867482
$730$	0.476494	0.0176359
$731$	1.00000	0.0369863
$732$	54.2568	2.00539
$733$	17.5208	0.647144	0.323572	−	0.946203i	$-0.395116\pi$
$733$	17.5208	0.647144	0.323572	+	0.946203i	$0.395116\pi$
$734$	−62.0113	−2.28888
$735$	−6.80220	−0.250903
$736$	53.6183	1.97640
$737$	−3.99313	−0.147089
$738$	6.29865	0.231857
$739$	−25.4226	−0.935185	−0.467592	−	0.883944i	$-0.654878\pi$
$739$	−25.4226	−0.935185	−0.467592	+	0.883944i	$0.654878\pi$
$740$	−18.6216	−0.684542
$741$	0.0856063	0.00314483
$742$	68.7709	2.52466
$743$	−28.3540	−1.04021	−0.520105	−	0.854103i	$-0.674107\pi$
$743$	−28.3540	−1.04021	−0.520105	+	0.854103i	$0.674107\pi$
$744$	−6.70199	−0.245707
$745$	−3.31031	−0.121280
$746$	24.9426	0.913213
$747$	−4.61218	−0.168751
$748$	4.93245	0.180348
$749$	−48.3678	−1.76732
$750$	−12.7298	−0.464828
$751$	−25.2840	−0.922626	−0.461313	−	0.887237i	$-0.652621\pi$
$751$	−25.2840	−0.922626	−0.461313	+	0.887237i	$0.652621\pi$
$752$	20.8816	0.761475
$753$	−17.2637	−0.629123
$754$	−0.246083	−0.00896180
$755$	7.81033	0.284247
$756$	−123.923	−4.50702
$757$	14.7410	0.535769	0.267885	−	0.963451i	$-0.413675\pi$
$757$	14.7410	0.535769	0.267885	+	0.963451i	$0.413675\pi$
$758$	−60.3111	−2.19060
$759$	5.39971	0.195997
$760$	−4.76361	−0.172794
$761$	24.7436	0.896954	0.448477	−	0.893794i	$-0.351967\pi$
$761$	24.7436	0.896954	0.448477	+	0.893794i	$0.351967\pi$
$762$	28.5051	1.03263
$763$	87.5438	3.16930
$764$	−4.14339	−0.149903
$765$	−0.609647	−0.0220418
$766$	8.32801	0.300903
$767$	0.386439	0.0139535
$768$	−11.8650	−0.428143
$769$	−30.1832	−1.08844	−0.544218	−	0.838944i	$-0.683173\pi$
$769$	−30.1832	−1.08844	−0.544218	+	0.838944i	$0.683173\pi$
$770$	−4.84398	−0.174565
$771$	14.8098	0.533360
$772$	−72.7899	−2.61977
$773$	25.8526	0.929854	0.464927	−	0.885349i	$-0.346081\pi$
$773$	25.8526	0.929854	0.464927	+	0.885349i	$0.346081\pi$
$774$	−3.98308	−0.143169
$775$	−3.44327	−0.123686
$776$	−88.5592	−3.17909
$777$	52.1549	1.87104
$778$	−43.0485	−1.54336
$779$	−2.42097	−0.0867401
$780$	0.111150	0.00397983
$781$	−3.27222	−0.117089
$782$	−11.6580	−0.416891
$783$	11.2179	0.400895
$784$	144.831	5.17255
$785$	1.01785	0.0363288
$786$	34.5520	1.23243
$787$	−50.0849	−1.78534	−0.892668	−	0.450716i	$-0.851169\pi$
$787$	−50.0849	−1.78534	−0.892668	+	0.450716i	$0.851169\pi$
$788$	−133.939	−4.77137
$789$	−20.3673	−0.725096
$790$	−13.2120	−0.470061
$791$	−0.961750	−0.0341959
$792$	−11.6802	−0.415037
$793$	−0.413582	−0.0146867
$794$	5.98785	0.212501
$795$	2.81187	0.0997268
$796$	22.8267	0.809071
$797$	3.58773	0.127084	0.0635420	−	0.997979i	$-0.479760\pi$
$797$	3.58773	0.127084	0.0635420	+	0.997979i	$0.479760\pi$
$798$	22.4413	0.794412
$799$	−1.99554	−0.0705971
$800$	58.5814	2.07117
$801$	−20.9299	−0.739523
$802$	−9.85863	−0.348120
$803$	−0.449067	−0.0158472
$804$	24.0195	0.847102
$805$	8.14595	0.287107
$806$	0.0859298	0.00302675
$807$	32.0540	1.12835
$808$	51.0342	1.79538
$809$	−9.21404	−0.323948	−0.161974	−	0.986795i	$-0.551786\pi$
$809$	−9.21404	−0.323948	−0.161974	+	0.986795i	$0.551786\pi$
$810$	−2.30589	−0.0810206
$811$	−38.1872	−1.34093	−0.670467	−	0.741939i	$-0.733906\pi$
$811$	−38.1872	−1.34093	−0.670467	+	0.741939i	$0.733906\pi$
$812$	−45.8985	−1.61072
$813$	−32.9980	−1.15729
$814$	24.6657	0.864533
$815$	7.95593	0.278684
$816$	−12.7612	−0.446732
$817$	1.53095	0.0535610
$818$	23.0534	0.806044
$819$	0.316658	0.0110649
$820$	−3.14336	−0.109771
$821$	−32.8516	−1.14653	−0.573264	−	0.819371i	$-0.694323\pi$
$821$	−32.8516	−1.14653	−0.573264	+	0.819371i	$0.694323\pi$
$822$	−68.0615	−2.37392
$823$	−28.1154	−0.980040	−0.490020	−	0.871711i	$-0.663011\pi$
$823$	−28.1154	−0.980040	−0.490020	+	0.871711i	$0.663011\pi$
$824$	120.850	4.21003
$825$	5.89952	0.205395
$826$	101.303	3.52479
$827$	−11.9385	−0.415141	−0.207571	−	0.978220i	$-0.566556\pi$
$827$	−11.9385	−0.415141	−0.207571	+	0.978220i	$0.566556\pi$
$828$	33.0385	1.14817
$829$	−24.8819	−0.864185	−0.432093	−	0.901829i	$-0.642225\pi$
$829$	−24.8819	−0.864185	−0.432093	+	0.901829i	$0.642225\pi$
$830$	3.23502	0.112289
$831$	33.7641	1.17126
$832$	−0.502345	−0.0174157
$833$	−13.8407	−0.479553
$834$	17.4928	0.605727
$835$	−1.39218	−0.0481785
$836$	7.55131	0.261168
$837$	−3.91718	−0.135398
$838$	1.29402	0.0447011
$839$	18.3206	0.632498	0.316249	−	0.948676i	$-0.397577\pi$
$839$	18.3206	0.632498	0.316249	+	0.948676i	$0.397577\pi$
$840$	17.3229	0.597697
$841$	−24.8451	−0.856728
$842$	−47.9229	−1.65153
$843$	−29.7122	−1.02334
$844$	38.9209	1.33971
$845$	5.23813	0.180197
$846$	7.94839	0.273271
$847$	4.56516	0.156861
$848$	−59.8700	−2.05594
$849$	23.4099	0.803425
$850$	−12.7372	−0.436881
$851$	−41.4795	−1.42190
$852$	19.6830	0.674330
$853$	34.3596	1.17645	0.588226	−	0.808697i	$-0.299827\pi$
$853$	34.3596	1.17645	0.588226	+	0.808697i	$0.299827\pi$
$854$	−108.418	−3.71000
$855$	−0.933337	−0.0319194
$856$	81.8039	2.79600
$857$	−36.4064	−1.24362	−0.621809	−	0.783169i	$-0.713602\pi$
$857$	−36.4064	−1.24362	−0.621809	+	0.783169i	$0.713602\pi$
$858$	−0.147228	−0.00502627
$859$	−22.6326	−0.772213	−0.386106	−	0.922454i	$-0.626180\pi$
$859$	−22.6326	−0.772213	−0.386106	+	0.922454i	$0.626180\pi$
$860$	1.98777	0.0677823
$861$	8.80386	0.300035
$862$	38.8594	1.32356
$863$	56.7281	1.93105	0.965524	−	0.260316i	$-0.0838267\pi$
$863$	56.7281	1.93105	0.965524	+	0.260316i	$0.0838267\pi$
$864$	66.6442	2.26728
$865$	8.07960	0.274714
$866$	−38.8029	−1.31858
$867$	1.21952	0.0414170
$868$	16.0273	0.544003
$869$	12.4515	0.422388
$870$	−2.63763	−0.0894239
$871$	−0.183093	−0.00620387
$872$	−148.062	−5.01400
$873$	−17.3514	−0.587257
$874$	−17.8478	−0.603712
$875$	18.0987	0.611849
$876$	2.70123	0.0912662
$877$	−21.7431	−0.734214	−0.367107	−	0.930179i	$-0.619652\pi$
$877$	−21.7431	−0.734214	−0.367107	+	0.930179i	$0.619652\pi$
$878$	0.722664	0.0243887
$879$	−2.13783	−0.0721073
$880$	4.21703	0.142156
$881$	15.1103	0.509079	0.254539	−	0.967062i	$-0.418076\pi$
$881$	15.1103	0.509079	0.254539	+	0.967062i	$0.418076\pi$
$882$	55.1287	1.85628
$883$	−16.8121	−0.565771	−0.282885	−	0.959154i	$-0.591292\pi$
$883$	−16.8121	−0.565771	−0.282885	+	0.959154i	$0.591292\pi$
$884$	0.226163	0.00760667
$885$	4.14204	0.139233
$886$	94.4883	3.17440
$887$	−43.7502	−1.46899	−0.734495	−	0.678615i	$-0.762581\pi$
$887$	−43.7502	−1.46899	−0.734495	+	0.678615i	$0.762581\pi$
$888$	−88.2088	−2.96009
$889$	−40.5273	−1.35924
$890$	14.6804	0.492089
$891$	2.17316	0.0728036
$892$	−43.7406	−1.46454
$893$	−3.05506	−0.102234
$894$	−26.3753	−0.882121
$895$	3.23951	0.108285
$896$	−21.1223	−0.705648
$897$	0.247587	0.00826670
$898$	−51.1967	−1.70846
$899$	−1.45085	−0.0483885
$900$	36.0967	1.20322
$901$	5.72143	0.190609
$902$	4.16363	0.138634
$903$	−5.56729	−0.185268
$904$	1.62660	0.0540998
$905$	8.90469	0.296002
$906$	62.2297	2.06744
$907$	30.1889	1.00241	0.501203	−	0.865330i	$-0.332891\pi$
$907$	30.1889	1.00241	0.501203	+	0.865330i	$0.332891\pi$
$908$	−76.2543	−2.53059
$909$	9.99915	0.331651
$910$	−0.222106	−0.00736275
$911$	−23.7849	−0.788030	−0.394015	−	0.919104i	$-0.628914\pi$
$911$	−23.7849	−0.788030	−0.394015	+	0.919104i	$0.628914\pi$
$912$	−19.5367	−0.646925
$913$	−3.04881	−0.100901
$914$	32.9196	1.08888
$915$	−4.43296	−0.146549
$916$	9.60095	0.317224
$917$	−49.1246	−1.62224
$918$	−14.4902	−0.478249
$919$	24.4338	0.805996	0.402998	−	0.915201i	$-0.367968\pi$
$919$	24.4338	0.805996	0.402998	+	0.915201i	$0.367968\pi$
$920$	−13.7771	−0.454219
$921$	−36.9348	−1.21704
$922$	−28.1406	−0.926762
$923$	−0.150038	−0.00493855
$924$	−27.4604	−0.903380
$925$	−45.3190	−1.49008
$926$	−93.2991	−3.06600
$927$	23.6783	0.777697
$928$	24.6837	0.810282
$929$	−16.9476	−0.556032	−0.278016	−	0.960577i	$-0.589677\pi$
$929$	−16.9476	−0.556032	−0.278016	+	0.960577i	$0.589677\pi$
$930$	0.921035	0.0302019
$931$	−21.1894	−0.694454
$932$	−108.051	−3.53932
$933$	−18.2987	−0.599071
$934$	101.299	3.31460
$935$	−0.402998	−0.0131794
$936$	−0.535559	−0.0175053
$937$	−36.2097	−1.18292	−0.591460	−	0.806335i	$-0.701448\pi$
$937$	−36.2097	−1.18292	−0.591460	+	0.806335i	$0.701448\pi$
$938$	−47.9969	−1.56715
$939$	−31.7824	−1.03718
$940$	−3.96667	−0.129378
$941$	−39.6702	−1.29321	−0.646606	−	0.762824i	$-0.723812\pi$
$941$	−39.6702	−1.29321	−0.646606	+	0.762824i	$0.723812\pi$
$942$	8.10987	0.264234
$943$	−7.00183	−0.228011
$944$	−88.1916	−2.87039
$945$	10.1249	0.329363
$946$	−2.63295	−0.0856047
$947$	36.6681	1.19155	0.595777	−	0.803150i	$-0.296844\pi$
$947$	36.6681	1.19155	0.595777	+	0.803150i	$0.296844\pi$
$948$	−74.8983	−2.43258
$949$	−0.0205906	−0.000668400 0
$950$	−19.4999	−0.632660
$951$	24.9276	0.808334
$952$	35.2476	1.14238
$953$	−0.894843	−0.0289868	−0.0144934	−	0.999895i	$-0.504614\pi$
$953$	−0.894843	−0.0289868	−0.0144934	+	0.999895i	$0.504614\pi$
$954$	−22.7889	−0.737819
$955$	0.338529	0.0109545
$956$	55.0212	1.77951
$957$	2.48581	0.0803547
$958$	−70.6617	−2.28298
$959$	96.7669	3.12476
$960$	−5.38437	−0.173780
$961$	−30.4934	−0.983657
$962$	1.13097	0.0364640
$963$	16.0279	0.516491
$964$	−30.9301	−0.996193
$965$	5.94719	0.191447
$966$	64.9038	2.08824
$967$	−8.75215	−0.281450	−0.140725	−	0.990049i	$-0.544943\pi$
$967$	−8.75215	−0.281450	−0.140725	+	0.990049i	$0.544943\pi$
$968$	−7.72100	−0.248162
$969$	1.86701	0.0599771
$970$	12.1704	0.390769
$971$	15.3384	0.492233	0.246117	−	0.969240i	$-0.420845\pi$
$971$	15.3384	0.492233	0.246117	+	0.969240i	$0.420845\pi$
$972$	68.3638	2.19277
$973$	−24.8706	−0.797313
$974$	−83.7691	−2.68414
$975$	0.270505	0.00866309
$976$	94.3860	3.02122
$977$	20.4034	0.652763	0.326381	−	0.945238i	$-0.394171\pi$
$977$	20.4034	0.652763	0.326381	+	0.945238i	$0.394171\pi$
$978$	63.3898	2.02698
$979$	−13.8354	−0.442182
$980$	−27.5121	−0.878843
$981$	−29.0098	−0.926211
$982$	−37.8586	−1.20812
$983$	−29.6041	−0.944223	−0.472112	−	0.881539i	$-0.656508\pi$
$983$	−29.6041	−0.944223	−0.472112	+	0.881539i	$0.656508\pi$
$984$	−14.8899	−0.474671
$985$	10.9433	0.348681
$986$	−5.36689	−0.170917
$987$	11.1098	0.353627
$988$	0.346243	0.0110154
$989$	4.42774	0.140794
$990$	1.60517	0.0510157
$991$	42.8134	1.36001	0.680006	−	0.733207i	$-0.261977\pi$
$991$	42.8134	1.36001	0.680006	+	0.733207i	$0.261977\pi$
$992$	−8.61932	−0.273664
$993$	−30.4230	−0.965446
$994$	−39.3316	−1.24752
$995$	−1.86502	−0.0591251
$996$	18.3392	0.581100
$997$	50.6193	1.60313	0.801564	−	0.597909i	$-0.204002\pi$
$997$	50.6193	1.60313	0.801564	+	0.597909i	$0.204002\pi$
$998$	39.8985	1.26297
$999$	−51.5564	−1.63117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.5	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.5	✓	74	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)

\(f(q)\)	\(=\)	\(q-2.63295 q^{2} +1.21952 q^{3} +4.93245 q^{4} -0.402998 q^{5} -3.21093 q^{6} +4.56516 q^{7} -7.72100 q^{8} -1.51278 q^{9} +O(q^{10})\)	\(q-2.63295 q^{2} +1.21952 q^{3} +4.93245 q^{4} -0.402998 q^{5} -3.21093 q^{6} +4.56516 q^{7} -7.72100 q^{8} -1.51278 q^{9} +1.06108 q^{10} -1.00000 q^{11} +6.01520 q^{12} -0.0458520 q^{13} -12.0199 q^{14} -0.491463 q^{15} +10.4642 q^{16} -1.00000 q^{17} +3.98308 q^{18} -1.53095 q^{19} -1.98777 q^{20} +5.56729 q^{21} +2.63295 q^{22} -4.42774 q^{23} -9.41589 q^{24} -4.83759 q^{25} +0.120726 q^{26} -5.50341 q^{27} +22.5174 q^{28} -2.03835 q^{29} +1.29400 q^{30} +0.711774 q^{31} -12.1096 q^{32} -1.21952 q^{33} +2.63295 q^{34} -1.83975 q^{35} -7.46171 q^{36} +9.36808 q^{37} +4.03091 q^{38} -0.0559173 q^{39} +3.11155 q^{40} +1.58135 q^{41} -14.6584 q^{42} -1.00000 q^{43} -4.93245 q^{44} +0.609647 q^{45} +11.6580 q^{46} +1.99554 q^{47} +12.7612 q^{48} +13.8407 q^{49} +12.7372 q^{50} -1.21952 q^{51} -0.226163 q^{52} -5.72143 q^{53} +14.4902 q^{54} +0.402998 q^{55} -35.2476 q^{56} -1.86701 q^{57} +5.36689 q^{58} -8.42798 q^{59} -2.42412 q^{60} +9.01994 q^{61} -1.87407 q^{62} -6.90609 q^{63} +10.9558 q^{64} +0.0184783 q^{65} +3.21093 q^{66} +3.99313 q^{67} -4.93245 q^{68} -5.39971 q^{69} +4.84398 q^{70} +3.27222 q^{71} +11.6802 q^{72} +0.449067 q^{73} -24.6657 q^{74} -5.89952 q^{75} -7.55131 q^{76} -4.56516 q^{77} +0.147228 q^{78} -12.4515 q^{79} -4.21703 q^{80} -2.17316 q^{81} -4.16363 q^{82} +3.04881 q^{83} +27.4604 q^{84} +0.402998 q^{85} +2.63295 q^{86} -2.48581 q^{87} +7.72100 q^{88} +13.8354 q^{89} -1.60517 q^{90} -0.209322 q^{91} -21.8396 q^{92} +0.868020 q^{93} -5.25417 q^{94} +0.616968 q^{95} -14.7679 q^{96} +11.4699 q^{97} -36.4420 q^{98} +1.51278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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