LMFDB - Embedded newform 8041.2.a.i.1.9

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:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} +O(q^{10})$	\(q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} -7.09957 q^{10} +1.00000 q^{11} -2.29834 q^{12} -2.20765 q^{13} -8.54258 q^{14} -2.13819 q^{15} +0.342136 q^{16} -1.00000 q^{17} +5.80361 q^{18} +1.82863 q^{19} +10.2007 q^{20} -2.57278 q^{21} -2.30463 q^{22} +8.54581 q^{23} +2.09758 q^{24} +4.48993 q^{25} +5.08781 q^{26} +3.83014 q^{27} +12.2740 q^{28} -4.48487 q^{29} +4.92772 q^{30} -3.62000 q^{31} +5.25565 q^{32} -0.694087 q^{33} +2.30463 q^{34} +11.4188 q^{35} -8.33867 q^{36} +10.9777 q^{37} -4.21431 q^{38} +1.53230 q^{39} -9.30971 q^{40} +2.53773 q^{41} +5.92930 q^{42} -1.00000 q^{43} +3.31131 q^{44} -7.75763 q^{45} -19.6949 q^{46} -3.78518 q^{47} -0.237472 q^{48} +6.73968 q^{49} -10.3476 q^{50} +0.694087 q^{51} -7.31021 q^{52} -4.35173 q^{53} -8.82705 q^{54} +3.08057 q^{55} -11.2019 q^{56} -1.26923 q^{57} +10.3360 q^{58} -2.26513 q^{59} -7.08019 q^{60} -5.57300 q^{61} +8.34275 q^{62} -9.33439 q^{63} -12.7966 q^{64} -6.80083 q^{65} +1.59961 q^{66} -4.49231 q^{67} -3.31131 q^{68} -5.93154 q^{69} -26.3160 q^{70} -11.2044 q^{71} +7.61031 q^{72} +6.97097 q^{73} -25.2995 q^{74} -3.11640 q^{75} +6.05515 q^{76} +3.70671 q^{77} -3.53139 q^{78} +7.85595 q^{79} +1.05397 q^{80} +4.89627 q^{81} -5.84851 q^{82} +0.718572 q^{83} -8.51926 q^{84} -3.08057 q^{85} +2.30463 q^{86} +3.11289 q^{87} -3.02207 q^{88} +16.6904 q^{89} +17.8784 q^{90} -8.18312 q^{91} +28.2978 q^{92} +2.51260 q^{93} +8.72342 q^{94} +5.63323 q^{95} -3.64788 q^{96} +5.92488 q^{97} -15.5324 q^{98} -2.51824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−2.30463	−1.62962	−0.814809	−	0.579730i	$-0.803158\pi$
$2$	−2.30463	−1.62962	−0.814809	+	0.579730i	$0.803158\pi$
$3$	−0.694087	−0.400732	−0.200366	−	0.979721i	$-0.564213\pi$
$3$	−0.694087	−0.400732	−0.200366	+	0.979721i	$0.564213\pi$
$4$	3.31131	1.65565
$5$	3.08057	1.37767	0.688837	−	0.724916i	$-0.258122\pi$
$5$	3.08057	1.37767	0.688837	+	0.724916i	$0.258122\pi$
$6$	1.59961	0.653039
$7$	3.70671	1.40100	0.700502	−	0.713651i	$-0.252960\pi$
$7$	3.70671	1.40100	0.700502	+	0.713651i	$0.252960\pi$
$8$	−3.02207	−1.06846
$9$	−2.51824	−0.839414
$10$	−7.09957	−2.24508
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.29834	−0.663472
$13$	−2.20765	−0.612292	−0.306146	−	0.951985i	$-0.599040\pi$
$13$	−2.20765	−0.612292	−0.306146	+	0.951985i	$0.599040\pi$
$14$	−8.54258	−2.28310
$15$	−2.13819	−0.552077
$16$	0.342136	0.0855340
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.80361	1.36792
$19$	1.82863	0.419517	0.209758	−	0.977753i	$-0.432732\pi$
$19$	1.82863	0.419517	0.209758	+	0.977753i	$0.432732\pi$
$20$	10.2007	2.28095
$21$	−2.57278	−0.561426
$22$	−2.30463	−0.491348
$23$	8.54581	1.78193	0.890963	−	0.454076i	$-0.150031\pi$
$23$	8.54581	1.78193	0.890963	+	0.454076i	$0.150031\pi$
$24$	2.09758	0.428167
$25$	4.48993	0.897985
$26$	5.08781	0.997802
$27$	3.83014	0.737111
$28$	12.2740	2.31958
$29$	−4.48487	−0.832819	−0.416410	−	0.909177i	$-0.636712\pi$
$29$	−4.48487	−0.832819	−0.416410	+	0.909177i	$0.636712\pi$
$30$	4.92772	0.899675
$31$	−3.62000	−0.650171	−0.325086	−	0.945685i	$-0.605393\pi$
$31$	−3.62000	−0.650171	−0.325086	+	0.945685i	$0.605393\pi$
$32$	5.25565	0.929076
$33$	−0.694087	−0.120825
$34$	2.30463	0.395240
$35$	11.4188	1.93013
$36$	−8.33867	−1.38978
$37$	10.9777	1.80472	0.902361	−	0.430980i	$-0.141832\pi$
$37$	10.9777	1.80472	0.902361	+	0.430980i	$0.141832\pi$
$38$	−4.21431	−0.683652
$39$	1.53230	0.245365
$40$	−9.30971	−1.47199
$41$	2.53773	0.396326	0.198163	−	0.980169i	$-0.436502\pi$
$41$	2.53773	0.396326	0.198163	+	0.980169i	$0.436502\pi$
$42$	5.92930	0.914910
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	3.31131	0.499198
$45$	−7.75763	−1.15644
$46$	−19.6949	−2.90386
$47$	−3.78518	−0.552125	−0.276062	−	0.961140i	$-0.589030\pi$
$47$	−3.78518	−0.552125	−0.276062	+	0.961140i	$0.589030\pi$
$48$	−0.237472	−0.0342762
$49$	6.73968	0.962811
$50$	−10.3476	−1.46337
$51$	0.694087	0.0971917
$52$	−7.31021	−1.01374
$53$	−4.35173	−0.597756	−0.298878	−	0.954291i	$-0.596612\pi$
$53$	−4.35173	−0.597756	−0.298878	+	0.954291i	$0.596612\pi$
$54$	−8.82705	−1.20121
$55$	3.08057	0.415384
$56$	−11.2019	−1.49692
$57$	−1.26923	−0.168114
$58$	10.3360	1.35718
$59$	−2.26513	−0.294895	−0.147448	−	0.989070i	$-0.547106\pi$
$59$	−2.26513	−0.294895	−0.147448	+	0.989070i	$0.547106\pi$
$60$	−7.08019	−0.914049
$61$	−5.57300	−0.713549	−0.356775	−	0.934190i	$-0.616124\pi$
$61$	−5.57300	−0.713549	−0.356775	+	0.934190i	$0.616124\pi$
$62$	8.34275	1.05953
$63$	−9.33439	−1.17602
$64$	−12.7966	−1.59957
$65$	−6.80083	−0.843539
$66$	1.59961	0.196899
$67$	−4.49231	−0.548823	−0.274412	−	0.961612i	$-0.588483\pi$
$67$	−4.49231	−0.548823	−0.274412	+	0.961612i	$0.588483\pi$
$68$	−3.31131	−0.401555
$69$	−5.93154	−0.714074
$70$	−26.3160	−3.14537
$71$	−11.2044	−1.32972	−0.664860	−	0.746968i	$-0.731509\pi$
$71$	−11.2044	−1.32972	−0.664860	+	0.746968i	$0.731509\pi$
$72$	7.61031	0.896884
$73$	6.97097	0.815891	0.407945	−	0.913006i	$-0.366245\pi$
$73$	6.97097	0.815891	0.407945	+	0.913006i	$0.366245\pi$
$74$	−25.2995	−2.94101
$75$	−3.11640	−0.359851
$76$	6.05515	0.694574
$77$	3.70671	0.422418
$78$	−3.53139	−0.399851
$79$	7.85595	0.883864	0.441932	−	0.897049i	$-0.354293\pi$
$79$	7.85595	0.883864	0.441932	+	0.897049i	$0.354293\pi$
$80$	1.05397	0.117838
$81$	4.89627	0.544030
$82$	−5.84851	−0.645860
$83$	0.718572	0.0788735	0.0394368	−	0.999222i	$-0.487444\pi$
$83$	0.718572	0.0788735	0.0394368	+	0.999222i	$0.487444\pi$
$84$	−8.51926	−0.929527
$85$	−3.08057	−0.334135
$86$	2.30463	0.248514
$87$	3.11289	0.333737
$88$	−3.02207	−0.322154
$89$	16.6904	1.76918	0.884589	−	0.466372i	$-0.154439\pi$
$89$	16.6904	1.76918	0.884589	+	0.466372i	$0.154439\pi$
$90$	17.8784	1.88455
$91$	−8.18312	−0.857824
$92$	28.2978	2.95025
$93$	2.51260	0.260544
$94$	8.72342	0.899753
$95$	5.63323	0.577957
$96$	−3.64788	−0.372310
$97$	5.92488	0.601580	0.300790	−	0.953690i	$-0.402750\pi$
$97$	5.92488	0.601580	0.300790	+	0.953690i	$0.402750\pi$
$98$	−15.5324	−1.56901
$99$	−2.51824	−0.253093
$100$	14.8675	1.48675
$101$	−7.86191	−0.782289	−0.391145	−	0.920329i	$-0.627921\pi$
$101$	−7.86191	−0.782289	−0.391145	+	0.920329i	$0.627921\pi$
$102$	−1.59961	−0.158385
$103$	12.0119	1.18357	0.591785	−	0.806096i	$-0.298424\pi$
$103$	12.0119	1.18357	0.591785	+	0.806096i	$0.298424\pi$
$104$	6.67168	0.654212
$105$	−7.92563	−0.773462
$106$	10.0291	0.974113
$107$	3.10129	0.299813	0.149907	−	0.988700i	$-0.452103\pi$
$107$	3.10129	0.299813	0.149907	+	0.988700i	$0.452103\pi$
$108$	12.6828	1.22040
$109$	10.8009	1.03454	0.517268	−	0.855823i	$-0.326949\pi$
$109$	10.8009	1.03454	0.517268	+	0.855823i	$0.326949\pi$
$110$	−7.09957	−0.676917
$111$	−7.61948	−0.723209
$112$	1.26820	0.119833
$113$	12.9869	1.22171	0.610855	−	0.791743i	$-0.290826\pi$
$113$	12.9869	1.22171	0.610855	+	0.791743i	$0.290826\pi$
$114$	2.92510	0.273961
$115$	26.3260	2.45491
$116$	−14.8508	−1.37886
$117$	5.55940	0.513967
$118$	5.22029	0.480567
$119$	−3.70671	−0.339793
$120$	6.46175	0.589875
$121$	1.00000	0.0909091
$122$	12.8437	1.16281
$123$	−1.76140	−0.158820
$124$	−11.9869	−1.07646
$125$	−1.57132	−0.140543
$126$	21.5123	1.91647
$127$	−16.6906	−1.48106	−0.740528	−	0.672026i	$-0.765424\pi$
$127$	−16.6906	−1.48106	−0.740528	+	0.672026i	$0.765424\pi$
$128$	18.9800	1.67762
$129$	0.694087	0.0611110
$130$	15.6734	1.37465
$131$	2.67425	0.233650	0.116825	−	0.993152i	$-0.462728\pi$
$131$	2.67425	0.233650	0.116825	+	0.993152i	$0.462728\pi$
$132$	−2.29834	−0.200044
$133$	6.77820	0.587744
$134$	10.3531	0.894372
$135$	11.7990	1.01550
$136$	3.02207	0.259141
$137$	15.2558	1.30339	0.651694	−	0.758482i	$-0.274059\pi$
$137$	15.2558	1.30339	0.651694	+	0.758482i	$0.274059\pi$
$138$	13.6700	1.16367
$139$	−6.67475	−0.566145	−0.283072	−	0.959099i	$-0.591354\pi$
$139$	−6.67475	−0.566145	−0.283072	+	0.959099i	$0.591354\pi$
$140$	37.8111	3.19562
$141$	2.62724	0.221254
$142$	25.8220	2.16694
$143$	−2.20765	−0.184613
$144$	−0.861581	−0.0717984
$145$	−13.8160	−1.14735
$146$	−16.0655	−1.32959
$147$	−4.67793	−0.385829
$148$	36.3505	2.98799
$149$	−8.50984	−0.697153	−0.348577	−	0.937280i	$-0.613335\pi$
$149$	−8.50984	−0.697153	−0.348577	+	0.937280i	$0.613335\pi$
$150$	7.18214	0.586419
$151$	12.2971	1.00073	0.500363	−	0.865816i	$-0.333200\pi$
$151$	12.2971	1.00073	0.500363	+	0.865816i	$0.333200\pi$
$152$	−5.52625	−0.448238
$153$	2.51824	0.203588
$154$	−8.54258	−0.688381
$155$	−11.1517	−0.895724
$156$	5.07392	0.406239
$157$	−21.7672	−1.73721	−0.868606	−	0.495504i	$-0.834983\pi$
$157$	−21.7672	−1.73721	−0.868606	+	0.495504i	$0.834983\pi$
$158$	−18.1050	−1.44036
$159$	3.02048	0.239540
$160$	16.1904	1.27996
$161$	31.6768	2.49648
$162$	−11.2841	−0.886561
$163$	−7.99913	−0.626540	−0.313270	−	0.949664i	$-0.601425\pi$
$163$	−7.99913	−0.626540	−0.313270	+	0.949664i	$0.601425\pi$
$164$	8.40319	0.656179
$165$	−2.13819	−0.166458
$166$	−1.65604	−0.128534
$167$	18.3801	1.42229	0.711147	−	0.703043i	$-0.248176\pi$
$167$	18.3801	1.42229	0.711147	+	0.703043i	$0.248176\pi$
$168$	7.77512	0.599864
$169$	−8.12628	−0.625098
$170$	7.09957	0.544512
$171$	−4.60493	−0.352148
$172$	−3.31131	−0.252485
$173$	21.3999	1.62701	0.813503	−	0.581561i	$-0.197558\pi$
$173$	21.3999	1.62701	0.813503	+	0.581561i	$0.197558\pi$
$174$	−7.17406	−0.543864
$175$	16.6428	1.25808
$176$	0.342136	0.0257895
$177$	1.57220	0.118174
$178$	−38.4651	−2.88308
$179$	−15.7639	−1.17825	−0.589124	−	0.808043i	$-0.700527\pi$
$179$	−15.7639	−1.17825	−0.589124	+	0.808043i	$0.700527\pi$
$180$	−25.6879	−1.91466
$181$	24.9670	1.85578	0.927890	−	0.372854i	$-0.121621\pi$
$181$	24.9670	1.85578	0.927890	+	0.372854i	$0.121621\pi$
$182$	18.8590	1.39792
$183$	3.86815	0.285942
$184$	−25.8261	−1.90392
$185$	33.8176	2.48632
$186$	−5.79060	−0.424587
$187$	−1.00000	−0.0731272
$188$	−12.5339	−0.914127
$189$	14.1972	1.03270
$190$	−12.9825	−0.941849
$191$	−11.6340	−0.841807	−0.420903	−	0.907106i	$-0.638287\pi$
$191$	−11.6340	−0.841807	−0.420903	+	0.907106i	$0.638287\pi$
$192$	8.88195	0.640999
$193$	−13.0433	−0.938879	−0.469439	−	0.882965i	$-0.655544\pi$
$193$	−13.0433	−0.938879	−0.469439	+	0.882965i	$0.655544\pi$
$194$	−13.6546	−0.980346
$195$	4.72037	0.338033
$196$	22.3171	1.59408
$197$	26.7822	1.90815	0.954077	−	0.299560i	$-0.0968399\pi$
$197$	26.7822	1.90815	0.954077	+	0.299560i	$0.0968399\pi$
$198$	5.80361	0.412445
$199$	25.7217	1.82336	0.911682	−	0.410896i	$-0.134784\pi$
$199$	25.7217	1.82336	0.911682	+	0.410896i	$0.134784\pi$
$200$	−13.5689	−0.959464
$201$	3.11806	0.219931
$202$	18.1188	1.27483
$203$	−16.6241	−1.16678
$204$	2.29834	0.160916
$205$	7.81765	0.546008
$206$	−27.6830	−1.92877
$207$	−21.5204	−1.49577
$208$	−0.755317	−0.0523718
$209$	1.82863	0.126489
$210$	18.2656	1.26045
$211$	−15.8034	−1.08795	−0.543975	−	0.839101i	$-0.683081\pi$
$211$	−15.8034	−1.08795	−0.543975	+	0.839101i	$0.683081\pi$
$212$	−14.4099	−0.989676
$213$	7.77685	0.532861
$214$	−7.14732	−0.488581
$215$	−3.08057	−0.210093
$216$	−11.5750	−0.787577
$217$	−13.4183	−0.910892
$218$	−24.8920	−1.68590
$219$	−4.83847	−0.326953
$220$	10.2007	0.687732
$221$	2.20765	0.148503
$222$	17.5601	1.17855
$223$	22.3927	1.49953	0.749764	−	0.661705i	$-0.230167\pi$
$223$	22.3927	1.49953	0.749764	+	0.661705i	$0.230167\pi$
$224$	19.4811	1.30164
$225$	−11.3067	−0.753781
$226$	−29.9301	−1.99092
$227$	23.9347	1.58860	0.794299	−	0.607527i	$-0.207838\pi$
$227$	23.9347	1.58860	0.794299	+	0.607527i	$0.207838\pi$
$228$	−4.20281	−0.278338
$229$	−2.34414	−0.154905	−0.0774524	−	0.996996i	$-0.524679\pi$
$229$	−2.34414	−0.154905	−0.0774524	+	0.996996i	$0.524679\pi$
$230$	−60.6716	−4.00057
$231$	−2.57278	−0.169276
$232$	13.5536	0.889837
$233$	8.78772	0.575702	0.287851	−	0.957675i	$-0.407059\pi$
$233$	8.78772	0.575702	0.287851	+	0.957675i	$0.407059\pi$
$234$	−12.8123	−0.837569
$235$	−11.6605	−0.760648
$236$	−7.50055	−0.488244
$237$	−5.45272	−0.354192
$238$	8.54258	0.553733
$239$	−15.8447	−1.02491	−0.512454	−	0.858715i	$-0.671263\pi$
$239$	−15.8447	−1.02491	−0.512454	+	0.858715i	$0.671263\pi$
$240$	−0.731550	−0.0472214
$241$	−15.6352	−1.00715	−0.503574	−	0.863952i	$-0.667982\pi$
$241$	−15.6352	−1.00715	−0.503574	+	0.863952i	$0.667982\pi$
$242$	−2.30463	−0.148147
$243$	−14.8889	−0.955122
$244$	−18.4539	−1.18139
$245$	20.7621	1.32644
$246$	4.05938	0.258817
$247$	−4.03698	−0.256867
$248$	10.9399	0.694684
$249$	−0.498752	−0.0316071
$250$	3.62131	0.229032
$251$	13.4314	0.847784	0.423892	−	0.905713i	$-0.360664\pi$
$251$	13.4314	0.847784	0.423892	+	0.905713i	$0.360664\pi$
$252$	−30.9090	−1.94708
$253$	8.54581	0.537271
$254$	38.4657	2.41355
$255$	2.13819	0.133898
$256$	−18.1488	−1.13430
$257$	11.6332	0.725657	0.362829	−	0.931856i	$-0.381811\pi$
$257$	11.6332	0.725657	0.362829	+	0.931856i	$0.381811\pi$
$258$	−1.59961	−0.0995875
$259$	40.6911	2.52842
$260$	−22.5196	−1.39661
$261$	11.2940	0.699080
$262$	−6.16315	−0.380761
$263$	−21.2984	−1.31332	−0.656659	−	0.754187i	$-0.728031\pi$
$263$	−21.2984	−1.31332	−0.656659	+	0.754187i	$0.728031\pi$
$264$	2.09758	0.129097
$265$	−13.4058	−0.823512
$266$	−15.6212	−0.957798
$267$	−11.5846	−0.708965
$268$	−14.8754	−0.908661
$269$	23.7164	1.44601	0.723007	−	0.690840i	$-0.242759\pi$
$269$	23.7164	1.44601	0.723007	+	0.690840i	$0.242759\pi$
$270$	−27.1924	−1.65487
$271$	18.7128	1.13672	0.568361	−	0.822779i	$-0.307578\pi$
$271$	18.7128	1.13672	0.568361	+	0.822779i	$0.307578\pi$
$272$	−0.342136	−0.0207450
$273$	5.67980	0.343757
$274$	−35.1589	−2.12402
$275$	4.48993	0.270753
$276$	−19.6412	−1.18226
$277$	−14.7870	−0.888464	−0.444232	−	0.895912i	$-0.646523\pi$
$277$	−14.7870	−0.888464	−0.444232	+	0.895912i	$0.646523\pi$
$278$	15.3828	0.922600
$279$	9.11604	0.545763
$280$	−34.5084	−2.06227
$281$	0.848238	0.0506016	0.0253008	−	0.999680i	$-0.491946\pi$
$281$	0.848238	0.0506016	0.0253008	+	0.999680i	$0.491946\pi$
$282$	−6.05482	−0.360559
$283$	4.82669	0.286917	0.143458	−	0.989656i	$-0.454178\pi$
$283$	4.82669	0.286917	0.143458	+	0.989656i	$0.454178\pi$
$284$	−37.1013	−2.20156
$285$	−3.90995	−0.231606
$286$	5.08781	0.300849
$287$	9.40661	0.555254
$288$	−13.2350	−0.779880
$289$	1.00000	0.0588235
$290$	31.8406	1.86975
$291$	−4.11238	−0.241072
$292$	23.0830	1.35083
$293$	−32.7621	−1.91398	−0.956990	−	0.290122i	$-0.906304\pi$
$293$	−32.7621	−1.91398	−0.956990	+	0.290122i	$0.906304\pi$
$294$	10.7809	0.628753
$295$	−6.97791	−0.406270
$296$	−33.1754	−1.92828
$297$	3.83014	0.222247
$298$	19.6120	1.13609
$299$	−18.8662	−1.09106
$300$	−10.3194	−0.595788
$301$	−3.70671	−0.213651
$302$	−28.3403	−1.63080
$303$	5.45685	0.313488
$304$	0.625640	0.0358829
$305$	−17.1680	−0.983038
$306$	−5.80361	−0.331770
$307$	−4.30262	−0.245563	−0.122782	−	0.992434i	$-0.539182\pi$
$307$	−4.30262	−0.245563	−0.122782	+	0.992434i	$0.539182\pi$
$308$	12.2740	0.699378
$309$	−8.33732	−0.474294
$310$	25.7004	1.45969
$311$	−12.4691	−0.707055	−0.353528	−	0.935424i	$-0.615018\pi$
$311$	−12.4691	−0.707055	−0.353528	+	0.935424i	$0.615018\pi$
$312$	−4.63073	−0.262163
$313$	21.5567	1.21846	0.609229	−	0.792994i	$-0.291479\pi$
$313$	21.5567	1.21846	0.609229	+	0.792994i	$0.291479\pi$
$314$	50.1653	2.83099
$315$	−28.7553	−1.62018
$316$	26.0135	1.46337
$317$	13.4095	0.753152	0.376576	−	0.926386i	$-0.377101\pi$
$317$	13.4095	0.753152	0.376576	+	0.926386i	$0.377101\pi$
$318$	−6.96108	−0.390358
$319$	−4.48487	−0.251105
$320$	−39.4208	−2.20369
$321$	−2.15257	−0.120145
$322$	−73.0033	−4.06831
$323$	−1.82863	−0.101748
$324$	16.2131	0.900726
$325$	−9.91219	−0.549829
$326$	18.4350	1.02102
$327$	−7.49676	−0.414572
$328$	−7.66919	−0.423460
$329$	−14.0305	−0.773529
$330$	4.92772	0.271262
$331$	23.4848	1.29084	0.645421	−	0.763827i	$-0.276682\pi$
$331$	23.4848	1.29084	0.645421	+	0.763827i	$0.276682\pi$
$332$	2.37941	0.130587
$333$	−27.6445	−1.51491
$334$	−42.3593	−2.31780
$335$	−13.8389	−0.756099
$336$	−0.880240	−0.0480210
$337$	−8.79842	−0.479280	−0.239640	−	0.970862i	$-0.577029\pi$
$337$	−8.79842	−0.479280	−0.239640	+	0.970862i	$0.577029\pi$
$338$	18.7280	1.01867
$339$	−9.01408	−0.489578
$340$	−10.2007	−0.553212
$341$	−3.62000	−0.196034
$342$	10.6127	0.573867
$343$	−0.964942	−0.0521020
$344$	3.02207	0.162939
$345$	−18.2725	−0.983761
$346$	−49.3188	−2.65140
$347$	−16.2572	−0.872733	−0.436366	−	0.899769i	$-0.643735\pi$
$347$	−16.2572	−0.872733	−0.436366	+	0.899769i	$0.643735\pi$
$348$	10.3077	0.552553
$349$	−30.7187	−1.64434	−0.822168	−	0.569244i	$-0.807236\pi$
$349$	−30.7187	−1.64434	−0.822168	+	0.569244i	$0.807236\pi$
$350$	−38.3555	−2.05019
$351$	−8.45562	−0.451328
$352$	5.25565	0.280127
$353$	−9.43362	−0.502101	−0.251050	−	0.967974i	$-0.580776\pi$
$353$	−9.43362	−0.502101	−0.251050	+	0.967974i	$0.580776\pi$
$354$	−3.62334	−0.192578
$355$	−34.5160	−1.83192
$356$	55.2670	2.92914
$357$	2.57278	0.136166
$358$	36.3299	1.92009
$359$	21.1969	1.11873	0.559366	−	0.828921i	$-0.311045\pi$
$359$	21.1969	1.11873	0.559366	+	0.828921i	$0.311045\pi$
$360$	23.4441	1.23561
$361$	−15.6561	−0.824006
$362$	−57.5395	−3.02421
$363$	−0.694087	−0.0364301
$364$	−27.0968	−1.42026
$365$	21.4746	1.12403
$366$	−8.91464	−0.465976
$367$	5.42407	0.283134	0.141567	−	0.989929i	$-0.454786\pi$
$367$	5.42407	0.283134	0.141567	+	0.989929i	$0.454786\pi$
$368$	2.92383	0.152415
$369$	−6.39061	−0.332682
$370$	−77.9369	−4.05175
$371$	−16.1306	−0.837458
$372$	8.31997	0.431371
$373$	2.21586	0.114733	0.0573664	−	0.998353i	$-0.481730\pi$
$373$	2.21586	0.114733	0.0573664	+	0.998353i	$0.481730\pi$
$374$	2.30463	0.119169
$375$	1.09064	0.0563202
$376$	11.4391	0.589925
$377$	9.90103	0.509929
$378$	−32.7193	−1.68290
$379$	−17.4205	−0.894833	−0.447417	−	0.894326i	$-0.647656\pi$
$379$	−17.4205	−0.894833	−0.447417	+	0.894326i	$0.647656\pi$
$380$	18.6533	0.956896
$381$	11.5848	0.593506
$382$	26.8120	1.37182
$383$	32.1577	1.64318	0.821591	−	0.570078i	$-0.193087\pi$
$383$	32.1577	1.64318	0.821591	+	0.570078i	$0.193087\pi$
$384$	−13.1738	−0.672273
$385$	11.4188	0.581955
$386$	30.0600	1.53001
$387$	2.51824	0.128009
$388$	19.6191	0.996008
$389$	21.7253	1.10151	0.550757	−	0.834666i	$-0.314339\pi$
$389$	21.7253	1.10151	0.550757	+	0.834666i	$0.314339\pi$
$390$	−10.8787	−0.550864
$391$	−8.54581	−0.432180
$392$	−20.3678	−1.02873
$393$	−1.85616	−0.0936311
$394$	−61.7231	−3.10956
$395$	24.2008	1.21768
$396$	−8.33867	−0.419034
$397$	−5.45373	−0.273715	−0.136857	−	0.990591i	$-0.543700\pi$
$397$	−5.45373	−0.273715	−0.136857	+	0.990591i	$0.543700\pi$
$398$	−59.2790	−2.97139
$399$	−4.70466	−0.235528
$400$	1.53616	0.0768082
$401$	38.3657	1.91589	0.957945	−	0.286952i	$-0.0926421\pi$
$401$	38.3657	1.91589	0.957945	+	0.286952i	$0.0926421\pi$
$402$	−7.18596	−0.358403
$403$	7.99170	0.398095
$404$	−26.0332	−1.29520
$405$	15.0833	0.749496
$406$	38.3123	1.90141
$407$	10.9777	0.544144
$408$	−2.09758	−0.103846
$409$	−19.4340	−0.960948	−0.480474	−	0.877009i	$-0.659535\pi$
$409$	−19.4340	−0.960948	−0.480474	+	0.877009i	$0.659535\pi$
$410$	−18.0168	−0.889785
$411$	−10.5888	−0.522309
$412$	39.7751	1.95958
$413$	−8.39619	−0.413149
$414$	49.5966	2.43754
$415$	2.21361	0.108662
$416$	−11.6026	−0.568866
$417$	4.63286	0.226872
$418$	−4.21431	−0.206129
$419$	−25.1553	−1.22892	−0.614458	−	0.788950i	$-0.710625\pi$
$419$	−25.1553	−1.22892	−0.614458	+	0.788950i	$0.710625\pi$
$420$	−26.2442	−1.28059
$421$	−13.0378	−0.635423	−0.317712	−	0.948187i	$-0.602914\pi$
$421$	−13.0378	−0.635423	−0.317712	+	0.948187i	$0.602914\pi$
$422$	36.4209	1.77294
$423$	9.53200	0.463462
$424$	13.1512	0.638680
$425$	−4.48993	−0.217793
$426$	−17.9227	−0.868359
$427$	−20.6575	−0.999685
$428$	10.2693	0.496387
$429$	1.53230	0.0739803
$430$	7.09957	0.342372
$431$	23.3378	1.12414	0.562072	−	0.827088i	$-0.310004\pi$
$431$	23.3378	1.12414	0.562072	+	0.827088i	$0.310004\pi$
$432$	1.31043	0.0630481
$433$	−3.35230	−0.161101	−0.0805506	−	0.996751i	$-0.525668\pi$
$433$	−3.35230	−0.161101	−0.0805506	+	0.996751i	$0.525668\pi$
$434$	30.9241	1.48441
$435$	9.58949	0.459781
$436$	35.7650	1.71283
$437$	15.6271	0.747547
$438$	11.1509	0.532809
$439$	2.66791	0.127333	0.0636663	−	0.997971i	$-0.479721\pi$
$439$	2.66791	0.127333	0.0636663	+	0.997971i	$0.479721\pi$
$440$	−9.30971	−0.443823
$441$	−16.9721	−0.808197
$442$	−5.08781	−0.242003
$443$	10.6111	0.504148	0.252074	−	0.967708i	$-0.418887\pi$
$443$	10.6111	0.504148	0.252074	+	0.967708i	$0.418887\pi$
$444$	−25.2304	−1.19738
$445$	51.4159	2.43735
$446$	−51.6069	−2.44366
$447$	5.90657	0.279371
$448$	−47.4332	−2.24101
$449$	19.8559	0.937057	0.468528	−	0.883449i	$-0.344784\pi$
$449$	19.8559	0.937057	0.468528	+	0.883449i	$0.344784\pi$
$450$	26.0578	1.22838
$451$	2.53773	0.119497
$452$	43.0038	2.02273
$453$	−8.53529	−0.401023
$454$	−55.1604	−2.58881
$455$	−25.2087	−1.18180
$456$	3.83570	0.179623
$457$	−25.5907	−1.19708	−0.598541	−	0.801092i	$-0.704253\pi$
$457$	−25.5907	−1.19708	−0.598541	+	0.801092i	$0.704253\pi$
$458$	5.40236	0.252436
$459$	−3.83014	−0.178776
$460$	87.1734	4.06448
$461$	38.4897	1.79264	0.896322	−	0.443403i	$-0.146229\pi$
$461$	38.4897	1.79264	0.896322	+	0.443403i	$0.146229\pi$
$462$	5.92930	0.275856
$463$	13.7876	0.640765	0.320383	−	0.947288i	$-0.396188\pi$
$463$	13.7876	0.640765	0.320383	+	0.947288i	$0.396188\pi$
$464$	−1.53444	−0.0712344
$465$	7.74023	0.358945
$466$	−20.2524	−0.938175
$467$	1.70939	0.0791010	0.0395505	−	0.999218i	$-0.487407\pi$
$467$	1.70939	0.0791010	0.0395505	+	0.999218i	$0.487407\pi$
$468$	18.4089	0.850951
$469$	−16.6517	−0.768903
$470$	26.8731	1.23957
$471$	15.1083	0.696155
$472$	6.84540	0.315085
$473$	−1.00000	−0.0459800
$474$	12.5665	0.577198
$475$	8.21041	0.376720
$476$	−12.2740	−0.562580
$477$	10.9587	0.501765
$478$	36.5161	1.67021
$479$	30.7191	1.40359	0.701797	−	0.712377i	$-0.252381\pi$
$479$	30.7191	1.40359	0.701797	+	0.712377i	$0.252381\pi$
$480$	−11.2376	−0.512922
$481$	−24.2349	−1.10502
$482$	36.0332	1.64127
$483$	−21.9865	−1.00042
$484$	3.31131	0.150514
$485$	18.2520	0.828781
$486$	34.3133	1.55648
$487$	−35.1720	−1.59379	−0.796897	−	0.604115i	$-0.793527\pi$
$487$	−35.1720	−1.59379	−0.796897	+	0.604115i	$0.793527\pi$
$488$	16.8420	0.762402
$489$	5.55210	0.251075
$490$	−47.8488	−2.16159
$491$	23.7828	1.07330	0.536652	−	0.843803i	$-0.319689\pi$
$491$	23.7828	1.07330	0.536652	+	0.843803i	$0.319689\pi$
$492$	−5.83255	−0.262952
$493$	4.48487	0.201988
$494$	9.30373	0.418595
$495$	−7.75763	−0.348679
$496$	−1.23853	−0.0556117
$497$	−41.5315	−1.86294
$498$	1.14944	0.0515075
$499$	6.70034	0.299948	0.149974	−	0.988690i	$-0.452081\pi$
$499$	6.70034	0.299948	0.149974	+	0.988690i	$0.452081\pi$
$500$	−5.20313	−0.232691
$501$	−12.7574	−0.569958
$502$	−30.9544	−1.38156
$503$	−37.2696	−1.66177	−0.830885	−	0.556443i	$-0.812166\pi$
$503$	−37.2696	−1.66177	−0.830885	+	0.556443i	$0.812166\pi$
$504$	28.2092	1.25654
$505$	−24.2192	−1.07774
$506$	−19.6949	−0.875546
$507$	5.64035	0.250497
$508$	−55.2678	−2.45211
$509$	−27.1425	−1.20307	−0.601536	−	0.798846i	$-0.705444\pi$
$509$	−27.1425	−1.20307	−0.601536	+	0.798846i	$0.705444\pi$
$510$	−4.92772	−0.218203
$511$	25.8394	1.14307
$512$	3.86606	0.170858
$513$	7.00392	0.309230
$514$	−26.8101	−1.18254
$515$	37.0036	1.63057
$516$	2.29834	0.101179
$517$	−3.78518	−0.166472
$518$	−93.7778	−4.12036
$519$	−14.8534	−0.651993
$520$	20.5526	0.901291
$521$	−24.4008	−1.06902	−0.534509	−	0.845163i	$-0.679503\pi$
$521$	−24.4008	−1.06902	−0.534509	+	0.845163i	$0.679503\pi$
$522$	−26.0284	−1.13923
$523$	−17.7438	−0.775880	−0.387940	−	0.921685i	$-0.626813\pi$
$523$	−17.7438	−0.775880	−0.387940	+	0.921685i	$0.626813\pi$
$524$	8.85526	0.386844
$525$	−11.5516	−0.504152
$526$	49.0850	2.14021
$527$	3.62000	0.157690
$528$	−0.237472	−0.0103347
$529$	50.0309	2.17526
$530$	30.8954	1.34201
$531$	5.70416	0.247539
$532$	22.4447	0.973100
$533$	−5.60241	−0.242667
$534$	26.6982	1.15534
$535$	9.55375	0.413045
$536$	13.5761	0.586398
$537$	10.9415	0.472161
$538$	−54.6575	−2.35645
$539$	6.73968	0.290298
$540$	39.0702	1.68131
$541$	3.09173	0.132924	0.0664620	−	0.997789i	$-0.478829\pi$
$541$	3.09173	0.132924	0.0664620	+	0.997789i	$0.478829\pi$
$542$	−43.1260	−1.85242
$543$	−17.3293	−0.743670
$544$	−5.25565	−0.225334
$545$	33.2729	1.42525
$546$	−13.0898	−0.560192
$547$	−16.5702	−0.708489	−0.354245	−	0.935153i	$-0.615262\pi$
$547$	−16.5702	−0.708489	−0.354245	+	0.935153i	$0.615262\pi$
$548$	50.5165	2.15796
$549$	14.0342	0.598963
$550$	−10.3476	−0.441223
$551$	−8.20117	−0.349382
$552$	17.9255	0.762962
$553$	29.1197	1.23830
$554$	34.0785	1.44786
$555$	−23.4724	−0.996346
$556$	−22.1021	−0.937339
$557$	−7.34964	−0.311414	−0.155707	−	0.987803i	$-0.549766\pi$
$557$	−7.34964	−0.311414	−0.155707	+	0.987803i	$0.549766\pi$
$558$	−21.0091	−0.889385
$559$	2.20765	0.0933737
$560$	3.90677	0.165091
$561$	0.694087	0.0293044
$562$	−1.95487	−0.0824613
$563$	27.6376	1.16479	0.582393	−	0.812907i	$-0.302116\pi$
$563$	27.6376	1.16479	0.582393	+	0.812907i	$0.302116\pi$
$564$	8.69961	0.366320
$565$	40.0072	1.68312
$566$	−11.1237	−0.467564
$567$	18.1491	0.762189
$568$	33.8606	1.42076
$569$	31.9126	1.33785	0.668924	−	0.743331i	$-0.266755\pi$
$569$	31.9126	1.33785	0.668924	+	0.743331i	$0.266755\pi$
$570$	9.01098	0.377429
$571$	−37.3063	−1.56122	−0.780611	−	0.625017i	$-0.785092\pi$
$571$	−37.3063	−1.56122	−0.780611	+	0.625017i	$0.785092\pi$
$572$	−7.31021	−0.305655
$573$	8.07501	0.337338
$574$	−21.6787	−0.904852
$575$	38.3701	1.60014
$576$	32.2249	1.34270
$577$	−7.05552	−0.293725	−0.146863	−	0.989157i	$-0.546918\pi$
$577$	−7.05552	−0.293725	−0.146863	+	0.989157i	$0.546918\pi$
$578$	−2.30463	−0.0958599
$579$	9.05321	0.376238
$580$	−45.7489	−1.89962
$581$	2.66354	0.110502
$582$	9.47751	0.392855
$583$	−4.35173	−0.180230
$584$	−21.0668	−0.871750
$585$	17.1261	0.708079
$586$	75.5043	3.11905
$587$	2.03167	0.0838560	0.0419280	−	0.999121i	$-0.486650\pi$
$587$	2.03167	0.0838560	0.0419280	+	0.999121i	$0.486650\pi$
$588$	−15.4900	−0.638799
$589$	−6.61964	−0.272758
$590$	16.0815	0.662064
$591$	−18.5892	−0.764658
$592$	3.75586	0.154365
$593$	27.4258	1.12624	0.563122	−	0.826374i	$-0.309600\pi$
$593$	27.4258	1.12624	0.563122	+	0.826374i	$0.309600\pi$
$594$	−8.82705	−0.362178
$595$	−11.4188	−0.468124
$596$	−28.1787	−1.15424
$597$	−17.8531	−0.730680
$598$	43.4795	1.77801
$599$	31.0388	1.26821	0.634106	−	0.773246i	$-0.281368\pi$
$599$	31.0388	1.26821	0.634106	+	0.773246i	$0.281368\pi$
$600$	9.41799	0.384488
$601$	10.6181	0.433123	0.216561	−	0.976269i	$-0.430516\pi$
$601$	10.6181	0.433123	0.216561	+	0.976269i	$0.430516\pi$
$602$	8.54258	0.348169
$603$	11.3127	0.460690
$604$	40.7196	1.65686
$605$	3.08057	0.125243
$606$	−12.5760	−0.510865
$607$	−8.82037	−0.358008	−0.179004	−	0.983848i	$-0.557287\pi$
$607$	−8.82037	−0.358008	−0.179004	+	0.983848i	$0.557287\pi$
$608$	9.61064	0.389763
$609$	11.5386	0.467567
$610$	39.5659	1.60198
$611$	8.35635	0.338062
$612$	8.33867	0.337071
$613$	−21.0897	−0.851805	−0.425903	−	0.904769i	$-0.640043\pi$
$613$	−21.0897	−0.851805	−0.425903	+	0.904769i	$0.640043\pi$
$614$	9.91593	0.400175
$615$	−5.42613	−0.218803
$616$	−11.2019	−0.451339
$617$	−13.5453	−0.545314	−0.272657	−	0.962111i	$-0.587902\pi$
$617$	−13.5453	−0.545314	−0.272657	+	0.962111i	$0.587902\pi$
$618$	19.2144	0.772917
$619$	10.1383	0.407492	0.203746	−	0.979024i	$-0.434688\pi$
$619$	10.1383	0.407492	0.203746	+	0.979024i	$0.434688\pi$
$620$	−36.9266	−1.48301
$621$	32.7317	1.31348
$622$	28.7365	1.15223
$623$	61.8664	2.47862
$624$	0.524256	0.0209870
$625$	−27.2902	−1.09161
$626$	−49.6802	−1.98562
$627$	−1.26923	−0.0506881
$628$	−72.0778	−2.87622
$629$	−10.9777	−0.437710
$630$	66.2701	2.64027
$631$	−5.70047	−0.226932	−0.113466	−	0.993542i	$-0.536195\pi$
$631$	−5.70047	−0.226932	−0.113466	+	0.993542i	$0.536195\pi$
$632$	−23.7413	−0.944376
$633$	10.9689	0.435976
$634$	−30.9039	−1.22735
$635$	−51.4167	−2.04041
$636$	10.0017	0.396594
$637$	−14.8789	−0.589522
$638$	10.3360	0.409204
$639$	28.2155	1.11619
$640$	58.4694	2.31121
$641$	−19.1348	−0.755779	−0.377889	−	0.925851i	$-0.623350\pi$
$641$	−19.1348	−0.755779	−0.377889	+	0.925851i	$0.623350\pi$
$642$	4.96087	0.195790
$643$	27.0018	1.06485	0.532424	−	0.846478i	$-0.321281\pi$
$643$	27.0018	1.06485	0.532424	+	0.846478i	$0.321281\pi$
$644$	104.892	4.13331
$645$	2.13819	0.0841910
$646$	4.21431	0.165810
$647$	7.42279	0.291820	0.145910	−	0.989298i	$-0.453389\pi$
$647$	7.42279	0.291820	0.145910	+	0.989298i	$0.453389\pi$
$648$	−14.7969	−0.581277
$649$	−2.26513	−0.0889143
$650$	22.8439	0.896011
$651$	9.31346	0.365023
$652$	−26.4876	−1.03733
$653$	−9.70158	−0.379652	−0.189826	−	0.981818i	$-0.560792\pi$
$653$	−9.70158	−0.379652	−0.189826	+	0.981818i	$0.560792\pi$
$654$	17.2772	0.675593
$655$	8.23822	0.321894
$656$	0.868247	0.0338994
$657$	−17.5546	−0.684870
$658$	32.3352	1.26056
$659$	13.1684	0.512966	0.256483	−	0.966549i	$-0.417436\pi$
$659$	13.1684	0.512966	0.256483	+	0.966549i	$0.417436\pi$
$660$	−7.08019	−0.275596
$661$	34.4073	1.33829	0.669144	−	0.743133i	$-0.266661\pi$
$661$	34.4073	1.33829	0.669144	+	0.743133i	$0.266661\pi$
$662$	−54.1237	−2.10358
$663$	−1.53230	−0.0595097
$664$	−2.17158	−0.0842735
$665$	20.8807	0.809720
$666$	63.7103	2.46872
$667$	−38.3269	−1.48402
$668$	60.8621	2.35483
$669$	−15.5425	−0.600908
$670$	31.8935	1.23215
$671$	−5.57300	−0.215143
$672$	−13.5216	−0.521608
$673$	24.1977	0.932753	0.466377	−	0.884586i	$-0.345559\pi$
$673$	24.1977	0.932753	0.466377	+	0.884586i	$0.345559\pi$
$674$	20.2771	0.781044
$675$	17.1971	0.661915
$676$	−26.9086	−1.03495
$677$	−23.6630	−0.909444	−0.454722	−	0.890633i	$-0.650261\pi$
$677$	−23.6630	−0.909444	−0.454722	+	0.890633i	$0.650261\pi$
$678$	20.7741	0.797824
$679$	21.9618	0.842816
$680$	9.30971	0.357011
$681$	−16.6127	−0.636602
$682$	8.34275	0.319460
$683$	−22.1462	−0.847400	−0.423700	−	0.905803i	$-0.639269\pi$
$683$	−22.1462	−0.847400	−0.423700	+	0.905803i	$0.639269\pi$
$684$	−15.2483	−0.583035
$685$	46.9965	1.79564
$686$	2.22383	0.0849063
$687$	1.62703	0.0620753
$688$	−0.342136	−0.0130438
$689$	9.60710	0.366001
$690$	42.1114	1.60315
$691$	−21.5348	−0.819221	−0.409610	−	0.912261i	$-0.634335\pi$
$691$	−21.5348	−0.819221	−0.409610	+	0.912261i	$0.634335\pi$
$692$	70.8617	2.69376
$693$	−9.33439	−0.354584
$694$	37.4668	1.42222
$695$	−20.5620	−0.779963
$696$	−9.40738	−0.356586
$697$	−2.53773	−0.0961232
$698$	70.7953	2.67964
$699$	−6.09944	−0.230702
$700$	55.1095	2.08294
$701$	−5.28937	−0.199777	−0.0998885	−	0.994999i	$-0.531849\pi$
$701$	−5.28937	−0.199777	−0.0998885	+	0.994999i	$0.531849\pi$
$702$	19.4871	0.735491
$703$	20.0742	0.757111
$704$	−12.7966	−0.482289
$705$	8.09342	0.304816
$706$	21.7410	0.818232
$707$	−29.1418	−1.09599
$708$	5.20604	0.195655
$709$	−20.2639	−0.761028	−0.380514	−	0.924775i	$-0.624253\pi$
$709$	−20.2639	−0.761028	−0.380514	+	0.924775i	$0.624253\pi$
$710$	79.5466	2.98533
$711$	−19.7832	−0.741928
$712$	−50.4395	−1.89030
$713$	−30.9358	−1.15856
$714$	−5.92930	−0.221898
$715$	−6.80083	−0.254337
$716$	−52.1990	−1.95077
$717$	10.9976	0.410713
$718$	−48.8510	−1.82310
$719$	−41.7053	−1.55534	−0.777672	−	0.628670i	$-0.783600\pi$
$719$	−41.7053	−1.55534	−0.777672	+	0.628670i	$0.783600\pi$
$720$	−2.65416	−0.0989148
$721$	44.5247	1.65818
$722$	36.0815	1.34281
$723$	10.8522	0.403596
$724$	82.6733	3.07253
$725$	−20.1367	−0.747859
$726$	1.59961	0.0593672
$727$	−25.8932	−0.960326	−0.480163	−	0.877179i	$-0.659423\pi$
$727$	−25.8932	−0.960326	−0.480163	+	0.877179i	$0.659423\pi$
$728$	24.7300	0.916553
$729$	−4.35464	−0.161283
$730$	−49.4909	−1.83174
$731$	1.00000	0.0369863
$732$	12.8086	0.473420
$733$	−36.8943	−1.36272	−0.681362	−	0.731947i	$-0.738612\pi$
$733$	−36.8943	−1.36272	−0.681362	+	0.731947i	$0.738612\pi$
$734$	−12.5005	−0.461401
$735$	−14.4107	−0.531546
$736$	44.9138	1.65554
$737$	−4.49231	−0.165476
$738$	14.7280	0.542144
$739$	−14.4893	−0.532999	−0.266499	−	0.963835i	$-0.585867\pi$
$739$	−14.4893	−0.532999	−0.266499	+	0.963835i	$0.585867\pi$
$740$	111.980	4.11648
$741$	2.80202	0.102935
$742$	37.1750	1.36474
$743$	37.5194	1.37645	0.688226	−	0.725496i	$-0.258390\pi$
$743$	37.5194	1.37645	0.688226	+	0.725496i	$0.258390\pi$
$744$	−7.59325	−0.278382
$745$	−26.2152	−0.960449
$746$	−5.10673	−0.186971
$747$	−1.80954	−0.0662076
$748$	−3.31131	−0.121073
$749$	11.4956	0.420039
$750$	−2.51351	−0.0917803
$751$	−32.2504	−1.17683	−0.588416	−	0.808558i	$-0.700248\pi$
$751$	−32.2504	−1.17683	−0.588416	+	0.808558i	$0.700248\pi$
$752$	−1.29505	−0.0472254
$753$	−9.32259	−0.339734
$754$	−22.8182	−0.830989
$755$	37.8822	1.37867
$756$	47.0113	1.70979
$757$	44.3654	1.61249	0.806244	−	0.591583i	$-0.201497\pi$
$757$	44.3654	1.61249	0.806244	+	0.591583i	$0.201497\pi$
$758$	40.1479	1.45824
$759$	−5.93154	−0.215301
$760$	−17.0240	−0.617526
$761$	16.6548	0.603735	0.301867	−	0.953350i	$-0.402390\pi$
$761$	16.6548	0.603735	0.301867	+	0.953350i	$0.402390\pi$
$762$	−26.6986	−0.967187
$763$	40.0357	1.44939
$764$	−38.5237	−1.39374
$765$	7.75763	0.280478
$766$	−74.1115	−2.67776
$767$	5.00063	0.180562
$768$	12.5968	0.454549
$769$	24.9015	0.897971	0.448985	−	0.893539i	$-0.351786\pi$
$769$	24.9015	0.897971	0.448985	+	0.893539i	$0.351786\pi$
$770$	−26.3160	−0.948364
$771$	−8.07444	−0.290794
$772$	−43.1904	−1.55446
$773$	33.8813	1.21863	0.609313	−	0.792930i	$-0.291445\pi$
$773$	33.8813	1.21863	0.609313	+	0.792930i	$0.291445\pi$
$774$	−5.80361	−0.208606
$775$	−16.2535	−0.583844
$776$	−17.9054	−0.642767
$777$	−28.2432	−1.01322
$778$	−50.0686	−1.79505
$779$	4.64056	0.166265
$780$	15.6306	0.559665
$781$	−11.2044	−0.400926
$782$	19.6949	0.704289
$783$	−17.1777	−0.613881
$784$	2.30589	0.0823531
$785$	−67.0554	−2.39331
$786$	4.27777	0.152583
$787$	0.105538	0.00376202	0.00188101	−	0.999998i	$-0.499401\pi$
$787$	0.105538	0.00376202	0.00188101	+	0.999998i	$0.499401\pi$
$788$	88.6842	3.15924
$789$	14.7830	0.526288
$790$	−55.7739	−1.98435
$791$	48.1388	1.71162
$792$	7.61031	0.270421
$793$	12.3032	0.436901
$794$	12.5688	0.446050
$795$	9.30480	0.330007
$796$	85.1725	3.01886
$797$	10.7265	0.379952	0.189976	−	0.981789i	$-0.439159\pi$
$797$	10.7265	0.379952	0.189976	+	0.981789i	$0.439159\pi$
$798$	10.8425	0.383820
$799$	3.78518	0.133910
$800$	23.5975	0.834296
$801$	−42.0304	−1.48507
$802$	−88.4185	−3.12217
$803$	6.97097	0.246000
$804$	10.3248	0.364129
$805$	97.5828	3.43934
$806$	−18.4179	−0.648742
$807$	−16.4613	−0.579464
$808$	23.7592	0.835847
$809$	−28.6097	−1.00586	−0.502932	−	0.864326i	$-0.667745\pi$
$809$	−28.6097	−1.00586	−0.502932	+	0.864326i	$0.667745\pi$
$810$	−34.7614	−1.22139
$811$	−32.5642	−1.14348	−0.571742	−	0.820433i	$-0.693732\pi$
$811$	−32.5642	−1.14348	−0.571742	+	0.820433i	$0.693732\pi$
$812$	−55.0475	−1.93179
$813$	−12.9883	−0.455520
$814$	−25.2995	−0.886747
$815$	−24.6419	−0.863168
$816$	0.237472	0.00831319
$817$	−1.82863	−0.0639757
$818$	44.7881	1.56598
$819$	20.6071	0.720069
$820$	25.8866	0.904000
$821$	−24.9277	−0.869984	−0.434992	−	0.900434i	$-0.643249\pi$
$821$	−24.9277	−0.869984	−0.434992	+	0.900434i	$0.643249\pi$
$822$	24.4033	0.851164
$823$	44.7510	1.55992	0.779961	−	0.625828i	$-0.215239\pi$
$823$	44.7510	1.55992	0.779961	+	0.625828i	$0.215239\pi$
$824$	−36.3009	−1.26460
$825$	−3.11640	−0.108499
$826$	19.3501	0.673275
$827$	−13.3013	−0.462532	−0.231266	−	0.972891i	$-0.574287\pi$
$827$	−13.3013	−0.462532	−0.231266	+	0.972891i	$0.574287\pi$
$828$	−71.2607	−2.47648
$829$	−35.1222	−1.21985	−0.609923	−	0.792461i	$-0.708800\pi$
$829$	−35.1222	−1.21985	−0.609923	+	0.792461i	$0.708800\pi$
$830$	−5.10155	−0.177077
$831$	10.2635	0.356036
$832$	28.2504	0.979406
$833$	−6.73968	−0.233516
$834$	−10.6770	−0.369715
$835$	56.6212	1.95946
$836$	6.05515	0.209422
$837$	−13.8651	−0.479248
$838$	57.9735	2.00266
$839$	25.7797	0.890013	0.445007	−	0.895527i	$-0.353201\pi$
$839$	25.7797	0.890013	0.445007	+	0.895527i	$0.353201\pi$
$840$	23.9518	0.826416
$841$	−8.88594	−0.306412
$842$	30.0473	1.03550
$843$	−0.588751	−0.0202777
$844$	−52.3298	−1.80127
$845$	−25.0336	−0.861181
$846$	−21.9677	−0.755265
$847$	3.70671	0.127364
$848$	−1.48888	−0.0511284
$849$	−3.35014	−0.114977
$850$	10.3476	0.354920
$851$	93.8134	3.21588
$852$	25.7515	0.882233
$853$	7.06395	0.241865	0.120932	−	0.992661i	$-0.461412\pi$
$853$	7.06395	0.241865	0.120932	+	0.992661i	$0.461412\pi$
$854$	47.6078	1.62910
$855$	−14.1858	−0.485145
$856$	−9.37232	−0.320339
$857$	−26.3846	−0.901281	−0.450640	−	0.892706i	$-0.648804\pi$
$857$	−26.3846	−0.901281	−0.450640	+	0.892706i	$0.648804\pi$
$858$	−3.53139	−0.120560
$859$	43.2579	1.47594	0.737970	−	0.674833i	$-0.235785\pi$
$859$	43.2579	1.47594	0.737970	+	0.674833i	$0.235785\pi$
$860$	−10.2007	−0.347842
$861$	−6.52901	−0.222508
$862$	−53.7850	−1.83193
$863$	−27.6360	−0.940739	−0.470370	−	0.882470i	$-0.655879\pi$
$863$	−27.6360	−0.940739	−0.470370	+	0.882470i	$0.655879\pi$
$864$	20.1299	0.684832
$865$	65.9240	2.24148
$866$	7.72580	0.262533
$867$	−0.694087	−0.0235724
$868$	−44.4320	−1.50812
$869$	7.85595	0.266495
$870$	−22.1002	−0.749267
$871$	9.91746	0.336040
$872$	−32.6410	−1.10537
$873$	−14.9203	−0.504975
$874$	−36.0147	−1.21822
$875$	−5.82443	−0.196902
$876$	−16.0216	−0.541321
$877$	21.9636	0.741657	0.370829	−	0.928701i	$-0.379074\pi$
$877$	21.9636	0.741657	0.370829	+	0.928701i	$0.379074\pi$
$878$	−6.14855	−0.207503
$879$	22.7397	0.766992
$880$	1.05397	0.0355295
$881$	18.5236	0.624077	0.312039	−	0.950069i	$-0.398988\pi$
$881$	18.5236	0.624077	0.312039	+	0.950069i	$0.398988\pi$
$882$	39.1145	1.31705
$883$	41.9748	1.41257	0.706283	−	0.707930i	$-0.250371\pi$
$883$	41.9748	1.41257	0.706283	+	0.707930i	$0.250371\pi$
$884$	7.31021	0.245869
$885$	4.84328	0.162805
$886$	−24.4546	−0.821568
$887$	−14.8914	−0.500004	−0.250002	−	0.968245i	$-0.580431\pi$
$887$	−14.8914	−0.500004	−0.250002	+	0.968245i	$0.580431\pi$
$888$	23.0266	0.772723
$889$	−61.8673	−2.07496
$890$	−118.495	−3.97195
$891$	4.89627	0.164031
$892$	74.1492	2.48270
$893$	−6.92169	−0.231626
$894$	−13.6124	−0.455268
$895$	−48.5618	−1.62324
$896$	70.3535	2.35034
$897$	13.0948	0.437222
$898$	−45.7604	−1.52704
$899$	16.2352	0.541475
$900$	−37.4400	−1.24800
$901$	4.35173	0.144977
$902$	−5.84851	−0.194734
$903$	2.57278	0.0856167
$904$	−39.2475	−1.30535
$905$	76.9125	2.55666
$906$	19.6707	0.653514
$907$	5.27828	0.175262	0.0876312	−	0.996153i	$-0.472070\pi$
$907$	5.27828	0.175262	0.0876312	+	0.996153i	$0.472070\pi$
$908$	79.2550	2.63017
$909$	19.7982	0.656665
$910$	58.0966	1.92588
$911$	41.5392	1.37625	0.688127	−	0.725590i	$-0.258433\pi$
$911$	41.5392	1.37625	0.688127	+	0.725590i	$0.258433\pi$
$912$	−0.434249	−0.0143794
$913$	0.718572	0.0237813
$914$	58.9770	1.95079
$915$	11.9161	0.393934
$916$	−7.76215	−0.256469
$917$	9.91266	0.327345
$918$	8.82705	0.291336
$919$	−15.6250	−0.515422	−0.257711	−	0.966222i	$-0.582968\pi$
$919$	−15.6250	−0.515422	−0.257711	+	0.966222i	$0.582968\pi$
$920$	−79.5590	−2.62298
$921$	2.98639	0.0984050
$922$	−88.7044	−2.92133
$923$	24.7355	0.814177
$924$	−8.51926	−0.280263
$925$	49.2890	1.62061
$926$	−31.7753	−1.04420
$927$	−30.2489	−0.993505
$928$	−23.5709	−0.773753
$929$	−17.8744	−0.586442	−0.293221	−	0.956045i	$-0.594727\pi$
$929$	−17.8744	−0.586442	−0.293221	+	0.956045i	$0.594727\pi$
$930$	−17.8384	−0.584943
$931$	12.3244	0.403915
$932$	29.0988	0.953163
$933$	8.65461	0.283339
$934$	−3.93950	−0.128904
$935$	−3.08057	−0.100745
$936$	−16.8009	−0.549155
$937$	−22.5454	−0.736525	−0.368263	−	0.929722i	$-0.620047\pi$
$937$	−22.5454	−0.736525	−0.368263	+	0.929722i	$0.620047\pi$
$938$	38.3759	1.25302
$939$	−14.9623	−0.488275
$940$	−38.6115	−1.25937
$941$	−1.22495	−0.0399323	−0.0199662	−	0.999801i	$-0.506356\pi$
$941$	−1.22495	−0.0399323	−0.0199662	+	0.999801i	$0.506356\pi$
$942$	−34.8191	−1.13447
$943$	21.6869	0.706224
$944$	−0.774984	−0.0252236
$945$	43.7356	1.42272
$946$	2.30463	0.0749299
$947$	22.6657	0.736537	0.368269	−	0.929719i	$-0.379951\pi$
$947$	22.6657	0.736537	0.368269	+	0.929719i	$0.379951\pi$
$948$	−18.0556	−0.586419
$949$	−15.3895	−0.499564
$950$	−18.9219	−0.613909
$951$	−9.30736	−0.301812
$952$	11.2019	0.363057
$953$	0.756122	0.0244932	0.0122466	−	0.999925i	$-0.496102\pi$
$953$	0.756122	0.0244932	0.0122466	+	0.999925i	$0.496102\pi$
$954$	−25.2557	−0.817684
$955$	−35.8394	−1.15973
$956$	−52.4666	−1.69689
$957$	3.11289	0.100626
$958$	−70.7962	−2.28732
$959$	56.5487	1.82605
$960$	27.3615	0.883088
$961$	−17.8956	−0.577278
$962$	55.8525	1.80076
$963$	−7.80980	−0.251667
$964$	−51.7728	−1.66749
$965$	−40.1809	−1.29347
$966$	50.6707	1.63030
$967$	−15.7627	−0.506893	−0.253447	−	0.967349i	$-0.581564\pi$
$967$	−15.7627	−0.506893	−0.253447	+	0.967349i	$0.581564\pi$
$968$	−3.02207	−0.0971331
$969$	1.26923	0.0407735
$970$	−42.0641	−1.35060
$971$	51.9825	1.66820	0.834099	−	0.551615i	$-0.185988\pi$
$971$	51.9825	1.66820	0.834099	+	0.551615i	$0.185988\pi$
$972$	−49.3016	−1.58135
$973$	−24.7413	−0.793171
$974$	81.0582	2.59727
$975$	6.87993	0.220334
$976$	−1.90672	−0.0610327
$977$	−57.8715	−1.85147	−0.925737	−	0.378167i	$-0.876555\pi$
$977$	−57.8715	−1.85147	−0.925737	+	0.378167i	$0.876555\pi$
$978$	−12.7955	−0.409155
$979$	16.6904	0.533427
$980$	68.7495	2.19612
$981$	−27.1992	−0.868405
$982$	−54.8106	−1.74908
$983$	−5.69178	−0.181540	−0.0907698	−	0.995872i	$-0.528933\pi$
$983$	−5.69178	−0.181540	−0.0907698	+	0.995872i	$0.528933\pi$
$984$	5.32309	0.169694
$985$	82.5046	2.62881
$986$	−10.3360	−0.329164
$987$	9.73843	0.309978
$988$	−13.3677	−0.425282
$989$	−8.54581	−0.271741
$990$	17.8784	0.568214
$991$	58.7428	1.86603	0.933013	−	0.359844i	$-0.117170\pi$
$991$	58.7428	1.86603	0.933013	+	0.359844i	$0.117170\pi$
$992$	−19.0254	−0.604058
$993$	−16.3005	−0.517281
$994$	95.7146	3.03588
$995$	79.2376	2.51200
$996$	−1.65152	−0.0523304
$997$	−4.85531	−0.153769	−0.0768846	−	0.997040i	$-0.524497\pi$
$997$	−4.85531	−0.153769	−0.0768846	+	0.997040i	$0.524497\pi$
$998$	−15.4418	−0.488801
$999$	42.0462	1.33028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.9	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.9	✓	78	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)

\(f(q)\)	\(=\)	\(q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} +O(q^{10})\)	\(q-2.30463 q^{2} -0.694087 q^{3} +3.31131 q^{4} +3.08057 q^{5} +1.59961 q^{6} +3.70671 q^{7} -3.02207 q^{8} -2.51824 q^{9} -7.09957 q^{10} +1.00000 q^{11} -2.29834 q^{12} -2.20765 q^{13} -8.54258 q^{14} -2.13819 q^{15} +0.342136 q^{16} -1.00000 q^{17} +5.80361 q^{18} +1.82863 q^{19} +10.2007 q^{20} -2.57278 q^{21} -2.30463 q^{22} +8.54581 q^{23} +2.09758 q^{24} +4.48993 q^{25} +5.08781 q^{26} +3.83014 q^{27} +12.2740 q^{28} -4.48487 q^{29} +4.92772 q^{30} -3.62000 q^{31} +5.25565 q^{32} -0.694087 q^{33} +2.30463 q^{34} +11.4188 q^{35} -8.33867 q^{36} +10.9777 q^{37} -4.21431 q^{38} +1.53230 q^{39} -9.30971 q^{40} +2.53773 q^{41} +5.92930 q^{42} -1.00000 q^{43} +3.31131 q^{44} -7.75763 q^{45} -19.6949 q^{46} -3.78518 q^{47} -0.237472 q^{48} +6.73968 q^{49} -10.3476 q^{50} +0.694087 q^{51} -7.31021 q^{52} -4.35173 q^{53} -8.82705 q^{54} +3.08057 q^{55} -11.2019 q^{56} -1.26923 q^{57} +10.3360 q^{58} -2.26513 q^{59} -7.08019 q^{60} -5.57300 q^{61} +8.34275 q^{62} -9.33439 q^{63} -12.7966 q^{64} -6.80083 q^{65} +1.59961 q^{66} -4.49231 q^{67} -3.31131 q^{68} -5.93154 q^{69} -26.3160 q^{70} -11.2044 q^{71} +7.61031 q^{72} +6.97097 q^{73} -25.2995 q^{74} -3.11640 q^{75} +6.05515 q^{76} +3.70671 q^{77} -3.53139 q^{78} +7.85595 q^{79} +1.05397 q^{80} +4.89627 q^{81} -5.84851 q^{82} +0.718572 q^{83} -8.51926 q^{84} -3.08057 q^{85} +2.30463 q^{86} +3.11289 q^{87} -3.02207 q^{88} +16.6904 q^{89} +17.8784 q^{90} -8.18312 q^{91} +28.2978 q^{92} +2.51260 q^{93} +8.72342 q^{94} +5.63323 q^{95} -3.64788 q^{96} +5.92488 q^{97} -15.5324 q^{98} -2.51824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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