LMFDB - Embedded newform 8041.2.a.j.1.10

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:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.30649 q^{2} -1.79768 q^{3} +3.31992 q^{4} +3.97246 q^{5} +4.14634 q^{6} +2.36407 q^{7} -3.04439 q^{8} +0.231661 q^{9} +O(q^{10})$	\(q-2.30649 q^{2} -1.79768 q^{3} +3.31992 q^{4} +3.97246 q^{5} +4.14634 q^{6} +2.36407 q^{7} -3.04439 q^{8} +0.231661 q^{9} -9.16247 q^{10} +1.00000 q^{11} -5.96816 q^{12} +5.03650 q^{13} -5.45271 q^{14} -7.14123 q^{15} +0.382023 q^{16} +1.00000 q^{17} -0.534324 q^{18} +4.61118 q^{19} +13.1883 q^{20} -4.24984 q^{21} -2.30649 q^{22} +2.01155 q^{23} +5.47284 q^{24} +10.7805 q^{25} -11.6167 q^{26} +4.97659 q^{27} +7.84851 q^{28} +4.72977 q^{29} +16.4712 q^{30} +2.96757 q^{31} +5.20764 q^{32} -1.79768 q^{33} -2.30649 q^{34} +9.39117 q^{35} +0.769095 q^{36} -2.93712 q^{37} -10.6357 q^{38} -9.05402 q^{39} -12.0937 q^{40} +2.94886 q^{41} +9.80223 q^{42} +1.00000 q^{43} +3.31992 q^{44} +0.920264 q^{45} -4.63962 q^{46} +0.804974 q^{47} -0.686755 q^{48} -1.41119 q^{49} -24.8651 q^{50} -1.79768 q^{51} +16.7208 q^{52} +2.26444 q^{53} -11.4785 q^{54} +3.97246 q^{55} -7.19713 q^{56} -8.28943 q^{57} -10.9092 q^{58} -5.18744 q^{59} -23.7083 q^{60} -3.03068 q^{61} -6.84467 q^{62} +0.547661 q^{63} -12.7754 q^{64} +20.0073 q^{65} +4.14634 q^{66} +9.82283 q^{67} +3.31992 q^{68} -3.61612 q^{69} -21.6607 q^{70} +3.86568 q^{71} -0.705265 q^{72} +4.61176 q^{73} +6.77445 q^{74} -19.3799 q^{75} +15.3087 q^{76} +2.36407 q^{77} +20.8831 q^{78} -12.2298 q^{79} +1.51757 q^{80} -9.64132 q^{81} -6.80154 q^{82} +0.879944 q^{83} -14.1091 q^{84} +3.97246 q^{85} -2.30649 q^{86} -8.50262 q^{87} -3.04439 q^{88} +5.21525 q^{89} -2.12258 q^{90} +11.9066 q^{91} +6.67817 q^{92} -5.33474 q^{93} -1.85667 q^{94} +18.3177 q^{95} -9.36168 q^{96} -5.31064 q^{97} +3.25490 q^{98} +0.231661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * 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 $

$2$	−2.30649	−1.63094	−0.815469	−	0.578801i	$-0.803521\pi$
$2$	−2.30649	−1.63094	−0.815469	+	0.578801i	$0.803521\pi$
$3$	−1.79768	−1.03789	−0.518946	−	0.854807i	$-0.673675\pi$
$3$	−1.79768	−1.03789	−0.518946	+	0.854807i	$0.673675\pi$
$4$	3.31992	1.65996
$5$	3.97246	1.77654	0.888270	−	0.459322i	$-0.151907\pi$
$5$	3.97246	1.77654	0.888270	+	0.459322i	$0.151907\pi$
$6$	4.14634	1.69274
$7$	2.36407	0.893533	0.446767	−	0.894651i	$-0.352575\pi$
$7$	2.36407	0.893533	0.446767	+	0.894651i	$0.352575\pi$
$8$	−3.04439	−1.07635
$9$	0.231661	0.0772202
$10$	−9.16247	−2.89743
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.96816	−1.72286
$13$	5.03650	1.39687	0.698437	−	0.715672i	$-0.253879\pi$
$13$	5.03650	1.39687	0.698437	+	0.715672i	$0.253879\pi$
$14$	−5.45271	−1.45730
$15$	−7.14123	−1.84386
$16$	0.382023	0.0955057
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.534324	−0.125941
$19$	4.61118	1.05788	0.528938	−	0.848660i	$-0.322590\pi$
$19$	4.61118	1.05788	0.528938	+	0.848660i	$0.322590\pi$
$20$	13.1883	2.94898
$21$	−4.24984	−0.927391
$22$	−2.30649	−0.491746
$23$	2.01155	0.419437	0.209718	−	0.977762i	$-0.432745\pi$
$23$	2.01155	0.419437	0.209718	+	0.977762i	$0.432745\pi$
$24$	5.47284	1.11714
$25$	10.7805	2.15609
$26$	−11.6167	−2.27821
$27$	4.97659	0.957746
$28$	7.84851	1.48323
$29$	4.72977	0.878296	0.439148	−	0.898415i	$-0.355280\pi$
$29$	4.72977	0.878296	0.439148	+	0.898415i	$0.355280\pi$
$30$	16.4712	3.00722
$31$	2.96757	0.532991	0.266495	−	0.963836i	$-0.414134\pi$
$31$	2.96757	0.532991	0.266495	+	0.963836i	$0.414134\pi$
$32$	5.20764	0.920589
$33$	−1.79768	−0.312936
$34$	−2.30649	−0.395561
$35$	9.39117	1.58740
$36$	0.769095	0.128182
$37$	−2.93712	−0.482859	−0.241430	−	0.970418i	$-0.577616\pi$
$37$	−2.93712	−0.482859	−0.241430	+	0.970418i	$0.577616\pi$
$38$	−10.6357	−1.72533
$39$	−9.05402	−1.44980
$40$	−12.0937	−1.91218
$41$	2.94886	0.460535	0.230268	−	0.973127i	$-0.426040\pi$
$41$	2.94886	0.460535	0.230268	+	0.973127i	$0.426040\pi$
$42$	9.80223	1.51252
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.31992	0.500497
$45$	0.920264	0.137185
$46$	−4.63962	−0.684075
$47$	0.804974	0.117418	0.0587088	−	0.998275i	$-0.481302\pi$
$47$	0.804974	0.117418	0.0587088	+	0.998275i	$0.481302\pi$
$48$	−0.686755	−0.0991246
$49$	−1.41119	−0.201599
$50$	−24.8651	−3.51646
$51$	−1.79768	−0.251726
$52$	16.7208	2.31875
$53$	2.26444	0.311045	0.155522	−	0.987832i	$-0.450294\pi$
$53$	2.26444	0.311045	0.155522	+	0.987832i	$0.450294\pi$
$54$	−11.4785	−1.56202
$55$	3.97246	0.535647
$56$	−7.19713	−0.961757
$57$	−8.28943	−1.09796
$58$	−10.9092	−1.43245
$59$	−5.18744	−0.675348	−0.337674	−	0.941263i	$-0.609640\pi$
$59$	−5.18744	−0.675348	−0.337674	+	0.941263i	$0.609640\pi$
$60$	−23.7083	−3.06073
$61$	−3.03068	−0.388039	−0.194020	−	0.980998i	$-0.562153\pi$
$61$	−3.03068	−0.388039	−0.194020	+	0.980998i	$0.562153\pi$
$62$	−6.84467	−0.869275
$63$	0.547661	0.0689988
$64$	−12.7754	−1.59693
$65$	20.0073	2.48160
$66$	4.14634	0.510380
$67$	9.82283	1.20005	0.600025	−	0.799981i	$-0.295157\pi$
$67$	9.82283	1.20005	0.600025	+	0.799981i	$0.295157\pi$
$68$	3.31992	0.402599
$69$	−3.61612	−0.435330
$70$	−21.6607	−2.58895
$71$	3.86568	0.458772	0.229386	−	0.973336i	$-0.426328\pi$
$71$	3.86568	0.458772	0.229386	+	0.973336i	$0.426328\pi$
$72$	−0.705265	−0.0831162
$73$	4.61176	0.539766	0.269883	−	0.962893i	$-0.413015\pi$
$73$	4.61176	0.539766	0.269883	+	0.962893i	$0.413015\pi$
$74$	6.77445	0.787514
$75$	−19.3799	−2.23779
$76$	15.3087	1.75603
$77$	2.36407	0.269410
$78$	20.8831	2.36454
$79$	−12.2298	−1.37596	−0.687978	−	0.725732i	$-0.741501\pi$
$79$	−12.2298	−1.37596	−0.687978	+	0.725732i	$0.741501\pi$
$80$	1.51757	0.169670
$81$	−9.64132	−1.07126
$82$	−6.80154	−0.751105
$83$	0.879944	0.0965864	0.0482932	−	0.998833i	$-0.484622\pi$
$83$	0.879944	0.0965864	0.0482932	+	0.998833i	$0.484622\pi$
$84$	−14.1091	−1.53943
$85$	3.97246	0.430874
$86$	−2.30649	−0.248716
$87$	−8.50262	−0.911577
$88$	−3.04439	−0.324533
$89$	5.21525	0.552815	0.276408	−	0.961040i	$-0.410856\pi$
$89$	5.21525	0.552815	0.276408	+	0.961040i	$0.410856\pi$
$90$	−2.12258	−0.223740
$91$	11.9066	1.24815
$92$	6.67817	0.696248
$93$	−5.33474	−0.553187
$94$	−1.85667	−0.191501
$95$	18.3177	1.87936
$96$	−9.36168	−0.955472
$97$	−5.31064	−0.539214	−0.269607	−	0.962970i	$-0.586894\pi$
$97$	−5.31064	−0.539214	−0.269607	+	0.962970i	$0.586894\pi$
$98$	3.25490	0.328795
$99$	0.231661	0.0232828
$100$	35.7903	3.57903
$101$	10.9985	1.09439	0.547194	−	0.837006i	$-0.315696\pi$
$101$	10.9985	1.09439	0.547194	+	0.837006i	$0.315696\pi$
$102$	4.14634	0.410549
$103$	5.30396	0.522614	0.261307	−	0.965256i	$-0.415846\pi$
$103$	5.30396	0.522614	0.261307	+	0.965256i	$0.415846\pi$
$104$	−15.3330	−1.50353
$105$	−16.8823	−1.64755
$106$	−5.22292	−0.507295
$107$	3.18411	0.307819	0.153910	−	0.988085i	$-0.450814\pi$
$107$	3.18411	0.307819	0.153910	+	0.988085i	$0.450814\pi$
$108$	16.5219	1.58982
$109$	−6.03357	−0.577912	−0.288956	−	0.957342i	$-0.593308\pi$
$109$	−6.03357	−0.577912	−0.288956	+	0.957342i	$0.593308\pi$
$110$	−9.16247	−0.873607
$111$	5.28001	0.501156
$112$	0.903127	0.0853375
$113$	−2.87695	−0.270641	−0.135321	−	0.990802i	$-0.543206\pi$
$113$	−2.87695	−0.270641	−0.135321	+	0.990802i	$0.543206\pi$
$114$	19.1195	1.79071
$115$	7.99080	0.745146
$116$	15.7025	1.45794
$117$	1.16676	0.107867
$118$	11.9648	1.10145
$119$	2.36407	0.216714
$120$	21.7407	1.98464
$121$	1.00000	0.0909091
$122$	6.99026	0.632868
$123$	−5.30112	−0.477986
$124$	9.85208	0.884743
$125$	22.9627	2.05385
$126$	−1.26318	−0.112533
$127$	−0.497074	−0.0441082	−0.0220541	−	0.999757i	$-0.507021\pi$
$127$	−0.497074	−0.0441082	−0.0220541	+	0.999757i	$0.507021\pi$
$128$	19.0512	1.68390
$129$	−1.79768	−0.158277
$130$	−46.1468	−4.04734
$131$	15.8516	1.38496	0.692482	−	0.721435i	$-0.256517\pi$
$131$	15.8516	1.38496	0.692482	+	0.721435i	$0.256517\pi$
$132$	−5.96816	−0.519461
$133$	10.9011	0.945247
$134$	−22.6563	−1.95721
$135$	19.7693	1.70147
$136$	−3.04439	−0.261054
$137$	−3.74813	−0.320224	−0.160112	−	0.987099i	$-0.551186\pi$
$137$	−3.74813	−0.320224	−0.160112	+	0.987099i	$0.551186\pi$
$138$	8.34057	0.709996
$139$	9.20379	0.780655	0.390328	−	0.920676i	$-0.372362\pi$
$139$	9.20379	0.780655	0.390328	+	0.920676i	$0.372362\pi$
$140$	31.1779	2.63502
$141$	−1.44709	−0.121867
$142$	−8.91618	−0.748229
$143$	5.03650	0.421173
$144$	0.0884997	0.00737497
$145$	18.7888	1.56033
$146$	−10.6370	−0.880324
$147$	2.53687	0.209238
$148$	−9.75100	−0.801527
$149$	−6.52470	−0.534525	−0.267262	−	0.963624i	$-0.586119\pi$
$149$	−6.52470	−0.534525	−0.267262	+	0.963624i	$0.586119\pi$
$150$	44.6996	3.64970
$151$	6.42473	0.522837	0.261419	−	0.965226i	$-0.415810\pi$
$151$	6.42473	0.522837	0.261419	+	0.965226i	$0.415810\pi$
$152$	−14.0382	−1.13865
$153$	0.231661	0.0187287
$154$	−5.45271	−0.439392
$155$	11.7885	0.946879
$156$	−30.0586	−2.40662
$157$	−14.1635	−1.13037	−0.565184	−	0.824965i	$-0.691195\pi$
$157$	−14.1635	−1.13037	−0.565184	+	0.824965i	$0.691195\pi$
$158$	28.2079	2.24410
$159$	−4.07075	−0.322831
$160$	20.6872	1.63546
$161$	4.75543	0.374781
$162$	22.2376	1.74715
$163$	4.34203	0.340094	0.170047	−	0.985436i	$-0.445608\pi$
$163$	4.34203	0.340094	0.170047	+	0.985436i	$0.445608\pi$
$164$	9.78999	0.764470
$165$	−7.14123	−0.555944
$166$	−2.02959	−0.157526
$167$	7.71459	0.596973	0.298486	−	0.954414i	$-0.403518\pi$
$167$	7.71459	0.596973	0.298486	+	0.954414i	$0.403518\pi$
$168$	12.9382	0.998200
$169$	12.3663	0.951256
$170$	−9.16247	−0.702729
$171$	1.06823	0.0816894
$172$	3.31992	0.253141
$173$	−21.3548	−1.62358	−0.811789	−	0.583952i	$-0.801506\pi$
$173$	−21.3548	−1.62358	−0.811789	+	0.583952i	$0.801506\pi$
$174$	19.6113	1.48673
$175$	25.4858	1.92654
$176$	0.382023	0.0287960
$177$	9.32537	0.700938
$178$	−12.0289	−0.901608
$179$	13.5048	1.00940	0.504698	−	0.863296i	$-0.331604\pi$
$179$	13.5048	1.00940	0.504698	+	0.863296i	$0.331604\pi$
$180$	3.05520	0.227721
$181$	−13.6974	−1.01812	−0.509060	−	0.860731i	$-0.670007\pi$
$181$	−13.6974	−1.01812	−0.509060	+	0.860731i	$0.670007\pi$
$182$	−27.4626	−2.03566
$183$	5.44821	0.402743
$184$	−6.12393	−0.451462
$185$	−11.6676	−0.857819
$186$	12.3045	0.902213
$187$	1.00000	0.0731272
$188$	2.67245	0.194908
$189$	11.7650	0.855778
$190$	−42.2497	−3.06512
$191$	3.65345	0.264354	0.132177	−	0.991226i	$-0.457803\pi$
$191$	3.65345	0.264354	0.132177	+	0.991226i	$0.457803\pi$
$192$	22.9662	1.65744
$193$	14.9246	1.07430	0.537148	−	0.843488i	$-0.319502\pi$
$193$	14.9246	1.07430	0.537148	+	0.843488i	$0.319502\pi$
$194$	12.2490	0.879424
$195$	−35.9668	−2.57564
$196$	−4.68504	−0.334646
$197$	−23.6293	−1.68352	−0.841760	−	0.539851i	$-0.818481\pi$
$197$	−23.6293	−1.68352	−0.841760	+	0.539851i	$0.818481\pi$
$198$	−0.534324	−0.0379728
$199$	19.9392	1.41345	0.706727	−	0.707486i	$-0.250171\pi$
$199$	19.9392	1.41345	0.706727	+	0.707486i	$0.250171\pi$
$200$	−32.8199	−2.32072
$201$	−17.6583	−1.24552
$202$	−25.3679	−1.78488
$203$	11.1815	0.784787
$204$	−5.96816	−0.417855
$205$	11.7143	0.818159
$206$	−12.2335	−0.852351
$207$	0.465997	0.0323890
$208$	1.92406	0.133409
$209$	4.61118	0.318962
$210$	38.9390	2.68705
$211$	−10.3178	−0.710304	−0.355152	−	0.934809i	$-0.615571\pi$
$211$	−10.3178	−0.710304	−0.355152	+	0.934809i	$0.615571\pi$
$212$	7.51776	0.516322
$213$	−6.94927	−0.476156
$214$	−7.34413	−0.502034
$215$	3.97246	0.270920
$216$	−15.1507	−1.03087
$217$	7.01552	0.476245
$218$	13.9164	0.942538
$219$	−8.29048	−0.560219
$220$	13.1883	0.889152
$221$	5.03650	0.338792
$222$	−12.1783	−0.817355
$223$	−24.3295	−1.62922	−0.814610	−	0.580009i	$-0.803049\pi$
$223$	−24.3295	−1.62922	−0.814610	+	0.580009i	$0.803049\pi$
$224$	12.3112	0.822577
$225$	2.49741	0.166494
$226$	6.63568	0.441399
$227$	3.67046	0.243617	0.121809	−	0.992554i	$-0.461131\pi$
$227$	3.67046	0.243617	0.121809	+	0.992554i	$0.461131\pi$
$228$	−27.5202	−1.82257
$229$	−3.79206	−0.250586	−0.125293	−	0.992120i	$-0.539987\pi$
$229$	−3.79206	−0.250586	−0.125293	+	0.992120i	$0.539987\pi$
$230$	−18.4307	−1.21529
$231$	−4.24984	−0.279619
$232$	−14.3992	−0.945357
$233$	−14.4413	−0.946080	−0.473040	−	0.881041i	$-0.656843\pi$
$233$	−14.4413	−0.946080	−0.473040	+	0.881041i	$0.656843\pi$
$234$	−2.69112	−0.175924
$235$	3.19773	0.208597
$236$	−17.2219	−1.12105
$237$	21.9852	1.42809
$238$	−5.45271	−0.353446
$239$	6.58703	0.426080	0.213040	−	0.977043i	$-0.431664\pi$
$239$	6.58703	0.426080	0.213040	+	0.977043i	$0.431664\pi$
$240$	−2.72811	−0.176099
$241$	−15.4574	−0.995699	−0.497850	−	0.867263i	$-0.665877\pi$
$241$	−15.4574	−0.995699	−0.497850	+	0.867263i	$0.665877\pi$
$242$	−2.30649	−0.148267
$243$	2.40224	0.154104
$244$	−10.0616	−0.644130
$245$	−5.60590	−0.358148
$246$	12.2270	0.779566
$247$	23.2242	1.47772
$248$	−9.03441	−0.573686
$249$	−1.58186	−0.100246
$250$	−52.9634	−3.34970
$251$	1.77896	0.112287	0.0561433	−	0.998423i	$-0.482120\pi$
$251$	1.77896	0.112287	0.0561433	+	0.998423i	$0.482120\pi$
$252$	1.81819	0.114535
$253$	2.01155	0.126465
$254$	1.14650	0.0719377
$255$	−7.14123	−0.447201
$256$	−18.3906	−1.14941
$257$	−28.2634	−1.76302	−0.881510	−	0.472165i	$-0.843473\pi$
$257$	−28.2634	−1.76302	−0.881510	+	0.472165i	$0.843473\pi$
$258$	4.14634	0.258140
$259$	−6.94354	−0.431451
$260$	66.4227	4.11936
$261$	1.09570	0.0678223
$262$	−36.5617	−2.25879
$263$	−3.86383	−0.238254	−0.119127	−	0.992879i	$-0.538010\pi$
$263$	−3.86383	−0.238254	−0.119127	+	0.992879i	$0.538010\pi$
$264$	5.47284	0.336830
$265$	8.99541	0.552584
$266$	−25.1434	−1.54164
$267$	−9.37536	−0.573763
$268$	32.6110	1.99203
$269$	18.7882	1.14554	0.572768	−	0.819717i	$-0.305870\pi$
$269$	18.7882	1.14554	0.572768	+	0.819717i	$0.305870\pi$
$270$	−45.5979	−2.77500
$271$	−21.7851	−1.32335	−0.661674	−	0.749791i	$-0.730154\pi$
$271$	−21.7851	−1.32335	−0.661674	+	0.749791i	$0.730154\pi$
$272$	0.382023	0.0231635
$273$	−21.4043	−1.29545
$274$	8.64504	0.522266
$275$	10.7805	0.650087
$276$	−12.0052	−0.722630
$277$	4.44164	0.266872	0.133436	−	0.991057i	$-0.457399\pi$
$277$	4.44164	0.266872	0.133436	+	0.991057i	$0.457399\pi$
$278$	−21.2285	−1.27320
$279$	0.687468	0.0411577
$280$	−28.5903	−1.70860
$281$	−24.5731	−1.46591	−0.732956	−	0.680276i	$-0.761860\pi$
$281$	−24.5731	−1.46591	−0.732956	+	0.680276i	$0.761860\pi$
$282$	3.33770	0.198757
$283$	−11.0069	−0.654294	−0.327147	−	0.944973i	$-0.606087\pi$
$283$	−11.0069	−0.654294	−0.327147	+	0.944973i	$0.606087\pi$
$284$	12.8338	0.761543
$285$	−32.9295	−1.95057
$286$	−11.6167	−0.686908
$287$	6.97131	0.411503
$288$	1.20641	0.0710881
$289$	1.00000	0.0588235
$290$	−43.3364	−2.54480
$291$	9.54684	0.559646
$292$	15.3107	0.895989
$293$	13.3828	0.781834	0.390917	−	0.920426i	$-0.372158\pi$
$293$	13.3828	0.781834	0.390917	+	0.920426i	$0.372158\pi$
$294$	−5.85128	−0.341254
$295$	−20.6069	−1.19978
$296$	8.94172	0.519727
$297$	4.97659	0.288771
$298$	15.0492	0.871776
$299$	10.1312	0.585900
$300$	−64.3396	−3.71465
$301$	2.36407	0.136263
$302$	−14.8186	−0.852715
$303$	−19.7717	−1.13586
$304$	1.76157	0.101033
$305$	−12.0393	−0.689368
$306$	−0.534324	−0.0305453
$307$	7.62337	0.435089	0.217544	−	0.976050i	$-0.430195\pi$
$307$	7.62337	0.435089	0.217544	+	0.976050i	$0.430195\pi$
$308$	7.84851	0.447210
$309$	−9.53482	−0.542417
$310$	−27.1902	−1.54430
$311$	−1.07712	−0.0610777	−0.0305388	−	0.999534i	$-0.509722\pi$
$311$	−1.07712	−0.0610777	−0.0305388	+	0.999534i	$0.509722\pi$
$312$	27.5639	1.56050
$313$	−6.48880	−0.366769	−0.183384	−	0.983041i	$-0.558705\pi$
$313$	−6.48880	−0.366769	−0.183384	+	0.983041i	$0.558705\pi$
$314$	32.6680	1.84356
$315$	2.17556	0.122579
$316$	−40.6018	−2.28403
$317$	8.97582	0.504132	0.252066	−	0.967710i	$-0.418890\pi$
$317$	8.97582	0.504132	0.252066	+	0.967710i	$0.418890\pi$
$318$	9.38916	0.526518
$319$	4.72977	0.264816
$320$	−50.7500	−2.83701
$321$	−5.72402	−0.319483
$322$	−10.9684	−0.611244
$323$	4.61118	0.256573
$324$	−32.0084	−1.77824
$325$	54.2958	3.01179
$326$	−10.0149	−0.554673
$327$	10.8464	0.599810
$328$	−8.97748	−0.495698
$329$	1.90301	0.104916
$330$	16.4712	0.906710
$331$	20.5957	1.13204	0.566022	−	0.824390i	$-0.308482\pi$
$331$	20.5957	1.13204	0.566022	+	0.824390i	$0.308482\pi$
$332$	2.92134	0.160330
$333$	−0.680415	−0.0372865
$334$	−17.7937	−0.973626
$335$	39.0209	2.13194
$336$	−1.62354	−0.0885711
$337$	−30.2896	−1.64998	−0.824991	−	0.565146i	$-0.808820\pi$
$337$	−30.2896	−1.64998	−0.824991	+	0.565146i	$0.808820\pi$
$338$	−28.5229	−1.55144
$339$	5.17185	0.280896
$340$	13.1883	0.715234
$341$	2.96757	0.160703
$342$	−2.46386	−0.133230
$343$	−19.8846	−1.07367
$344$	−3.04439	−0.164142
$345$	−14.3649	−0.773381
$346$	49.2548	2.64795
$347$	−16.3565	−0.878062	−0.439031	−	0.898472i	$-0.644678\pi$
$347$	−16.3565	−0.878062	−0.439031	+	0.898472i	$0.644678\pi$
$348$	−28.2280	−1.51318
$349$	−35.5578	−1.90336	−0.951682	−	0.307086i	$-0.900646\pi$
$349$	−35.5578	−1.90336	−0.951682	+	0.307086i	$0.900646\pi$
$350$	−58.7828	−3.14207
$351$	25.0646	1.33785
$352$	5.20764	0.277568
$353$	12.5560	0.668291	0.334145	−	0.942522i	$-0.391552\pi$
$353$	12.5560	0.668291	0.334145	+	0.942522i	$0.391552\pi$
$354$	−21.5089	−1.14319
$355$	15.3563	0.815027
$356$	17.3142	0.917651
$357$	−4.24984	−0.224925
$358$	−31.1487	−1.64626
$359$	−4.29395	−0.226626	−0.113313	−	0.993559i	$-0.536146\pi$
$359$	−4.29395	−0.226626	−0.113313	+	0.993559i	$0.536146\pi$
$360$	−2.80164	−0.147659
$361$	2.26294	0.119102
$362$	31.5930	1.66049
$363$	−1.79768	−0.0943538
$364$	39.5290	2.07188
$365$	18.3200	0.958915
$366$	−12.5663	−0.656849
$367$	1.24864	0.0651785	0.0325892	−	0.999469i	$-0.489625\pi$
$367$	1.24864	0.0651785	0.0325892	+	0.999469i	$0.489625\pi$
$368$	0.768457	0.0400586
$369$	0.683136	0.0355626
$370$	26.9113	1.39905
$371$	5.35329	0.277929
$372$	−17.7109	−0.918267
$373$	30.4820	1.57830	0.789149	−	0.614202i	$-0.210522\pi$
$373$	30.4820	1.57830	0.789149	+	0.614202i	$0.210522\pi$
$374$	−2.30649	−0.119266
$375$	−41.2797	−2.13167
$376$	−2.45065	−0.126383
$377$	23.8215	1.22687
$378$	−27.1359	−1.39572
$379$	−21.4909	−1.10391	−0.551957	−	0.833873i	$-0.686119\pi$
$379$	−21.4909	−1.10391	−0.551957	+	0.833873i	$0.686119\pi$
$380$	60.8134	3.11966
$381$	0.893581	0.0457795
$382$	−8.42666	−0.431146
$383$	−12.9004	−0.659179	−0.329590	−	0.944124i	$-0.606910\pi$
$383$	−12.9004	−0.659179	−0.329590	+	0.944124i	$0.606910\pi$
$384$	−34.2480	−1.74771
$385$	9.39117	0.478618
$386$	−34.4235	−1.75211
$387$	0.231661	0.0117760
$388$	−17.6309	−0.895073
$389$	−34.4946	−1.74895	−0.874473	−	0.485074i	$-0.838793\pi$
$389$	−34.4946	−1.74895	−0.874473	+	0.485074i	$0.838793\pi$
$390$	82.9572	4.20070
$391$	2.01155	0.101728
$392$	4.29621	0.216991
$393$	−28.4962	−1.43744
$394$	54.5010	2.74572
$395$	−48.5823	−2.44444
$396$	0.769095	0.0386485
$397$	−19.8626	−0.996875	−0.498437	−	0.866926i	$-0.666093\pi$
$397$	−19.8626	−0.996875	−0.498437	+	0.866926i	$0.666093\pi$
$398$	−45.9897	−2.30526
$399$	−19.5968	−0.981065
$400$	4.11839	0.205919
$401$	5.32106	0.265721	0.132860	−	0.991135i	$-0.457584\pi$
$401$	5.32106	0.265721	0.132860	+	0.991135i	$0.457584\pi$
$402$	40.7289	2.03137
$403$	14.9461	0.744520
$404$	36.5140	1.81664
$405$	−38.2998	−1.90313
$406$	−25.7901	−1.27994
$407$	−2.93712	−0.145588
$408$	5.47284	0.270946
$409$	25.3552	1.25373	0.626867	−	0.779126i	$-0.284337\pi$
$409$	25.3552	1.25373	0.626867	+	0.779126i	$0.284337\pi$
$410$	−27.0189	−1.33437
$411$	6.73794	0.332358
$412$	17.6087	0.867518
$413$	−12.2635	−0.603445
$414$	−1.07482	−0.0528245
$415$	3.49555	0.171590
$416$	26.2283	1.28595
$417$	−16.5455	−0.810236
$418$	−10.6357	−0.520207
$419$	−16.0949	−0.786289	−0.393144	−	0.919477i	$-0.628613\pi$
$419$	−16.0949	−0.786289	−0.393144	+	0.919477i	$0.628613\pi$
$420$	−56.0480	−2.73486
$421$	25.1303	1.22477	0.612387	−	0.790558i	$-0.290209\pi$
$421$	25.1303	1.22477	0.612387	+	0.790558i	$0.290209\pi$
$422$	23.7979	1.15846
$423$	0.186481	0.00906701
$424$	−6.89383	−0.334794
$425$	10.7805	0.522930
$426$	16.0285	0.776581
$427$	−7.16474	−0.346726
$428$	10.5710	0.510968
$429$	−9.05402	−0.437132
$430$	−9.16247	−0.441853
$431$	−27.7556	−1.33694	−0.668469	−	0.743740i	$-0.733050\pi$
$431$	−27.7556	−1.33694	−0.668469	+	0.743740i	$0.733050\pi$
$432$	1.90117	0.0914702
$433$	−23.4623	−1.12753	−0.563763	−	0.825937i	$-0.690647\pi$
$433$	−23.4623	−1.12753	−0.563763	+	0.825937i	$0.690647\pi$
$434$	−16.1813	−0.776726
$435$	−33.7764	−1.61945
$436$	−20.0310	−0.959310
$437$	9.27560	0.443712
$438$	19.1219	0.913682
$439$	−14.9357	−0.712842	−0.356421	−	0.934326i	$-0.616003\pi$
$439$	−14.9357	−0.712842	−0.356421	+	0.934326i	$0.616003\pi$
$440$	−12.0937	−0.576545
$441$	−0.326917	−0.0155675
$442$	−11.6167	−0.552548
$443$	−26.4690	−1.25758	−0.628789	−	0.777576i	$-0.716449\pi$
$443$	−26.4690	−1.25758	−0.628789	+	0.777576i	$0.716449\pi$
$444$	17.5292	0.831899
$445$	20.7174	0.982099
$446$	56.1158	2.65716
$447$	11.7293	0.554779
$448$	−30.2020	−1.42691
$449$	−12.1365	−0.572756	−0.286378	−	0.958117i	$-0.592451\pi$
$449$	−12.1365	−0.572756	−0.286378	+	0.958117i	$0.592451\pi$
$450$	−5.76027	−0.271542
$451$	2.94886	0.138857
$452$	−9.55125	−0.449253
$453$	−11.5496	−0.542649
$454$	−8.46591	−0.397325
$455$	47.2986	2.21739
$456$	25.2362	1.18179
$457$	−24.0835	−1.12658	−0.563290	−	0.826259i	$-0.690465\pi$
$457$	−24.0835	−1.12658	−0.563290	+	0.826259i	$0.690465\pi$
$458$	8.74636	0.408691
$459$	4.97659	0.232288
$460$	26.5288	1.23691
$461$	38.0126	1.77042	0.885211	−	0.465189i	$-0.154014\pi$
$461$	38.0126	1.77042	0.885211	+	0.465189i	$0.154014\pi$
$462$	9.80223	0.456041
$463$	−8.42811	−0.391688	−0.195844	−	0.980635i	$-0.562745\pi$
$463$	−8.42811	−0.391688	−0.195844	+	0.980635i	$0.562745\pi$
$464$	1.80688	0.0838823
$465$	−21.1921	−0.982758
$466$	33.3088	1.54300
$467$	7.65618	0.354286	0.177143	−	0.984185i	$-0.443315\pi$
$467$	7.65618	0.354286	0.177143	+	0.984185i	$0.443315\pi$
$468$	3.87355	0.179055
$469$	23.2218	1.07228
$470$	−7.37555	−0.340209
$471$	25.4614	1.17320
$472$	15.7926	0.726912
$473$	1.00000	0.0459800
$474$	−50.7088	−2.32913
$475$	49.7106	2.28088
$476$	7.84851	0.359736
$477$	0.524582	0.0240190
$478$	−15.1930	−0.694910
$479$	−15.8805	−0.725600	−0.362800	−	0.931867i	$-0.618179\pi$
$479$	−15.8805	−0.725600	−0.362800	+	0.931867i	$0.618179\pi$
$480$	−37.1889	−1.69743
$481$	−14.7928	−0.674494
$482$	35.6524	1.62392
$483$	−8.54875	−0.388982
$484$	3.31992	0.150905
$485$	−21.0963	−0.957935
$486$	−5.54075	−0.251334
$487$	9.58877	0.434509	0.217254	−	0.976115i	$-0.430290\pi$
$487$	9.58877	0.434509	0.217254	+	0.976115i	$0.430290\pi$
$488$	9.22657	0.417667
$489$	−7.80559	−0.352981
$490$	12.9300	0.584117
$491$	10.5643	0.476762	0.238381	−	0.971172i	$-0.423383\pi$
$491$	10.5643	0.476762	0.238381	+	0.971172i	$0.423383\pi$
$492$	−17.5993	−0.793437
$493$	4.72977	0.213018
$494$	−53.5665	−2.41007
$495$	0.920264	0.0413628
$496$	1.13368	0.0509036
$497$	9.13873	0.409928
$498$	3.64855	0.163495
$499$	−3.31503	−0.148401	−0.0742006	−	0.997243i	$-0.523641\pi$
$499$	−3.31503	−0.148401	−0.0742006	+	0.997243i	$0.523641\pi$
$500$	76.2344	3.40930
$501$	−13.8684	−0.619593
$502$	−4.10315	−0.183133
$503$	5.41307	0.241357	0.120678	−	0.992692i	$-0.461493\pi$
$503$	5.41307	0.241357	0.120678	+	0.992692i	$0.461493\pi$
$504$	−1.66729	−0.0742671
$505$	43.6910	1.94422
$506$	−4.63962	−0.206256
$507$	−22.2307	−0.987301
$508$	−1.65025	−0.0732178
$509$	22.4941	0.997034	0.498517	−	0.866880i	$-0.333878\pi$
$509$	22.4941	0.997034	0.498517	+	0.866880i	$0.333878\pi$
$510$	16.4712	0.729357
$511$	10.9025	0.482298
$512$	4.31549	0.190719
$513$	22.9479	1.01318
$514$	65.1893	2.87538
$515$	21.0698	0.928445
$516$	−5.96816	−0.262734
$517$	0.804974	0.0354027
$518$	16.0153	0.703670
$519$	38.3892	1.68510
$520$	−60.9100	−2.67108
$521$	25.4152	1.11346	0.556729	−	0.830694i	$-0.312056\pi$
$521$	25.4152	1.11346	0.556729	+	0.830694i	$0.312056\pi$
$522$	−2.52723	−0.110614
$523$	5.89531	0.257784	0.128892	−	0.991659i	$-0.458858\pi$
$523$	5.89531	0.257784	0.128892	+	0.991659i	$0.458858\pi$
$524$	52.6261	2.29898
$525$	−45.8153	−1.99954
$526$	8.91190	0.388577
$527$	2.96757	0.129269
$528$	−0.686755	−0.0298872
$529$	−18.9537	−0.824073
$530$	−20.7479	−0.901230
$531$	−1.20173	−0.0521505
$532$	36.1908	1.56907
$533$	14.8520	0.643310
$534$	21.6242	0.935772
$535$	12.6488	0.546854
$536$	−29.9045	−1.29168
$537$	−24.2773	−1.04764
$538$	−43.3349	−1.86830
$539$	−1.41119	−0.0607843
$540$	65.6326	2.82438
$541$	−29.8660	−1.28404	−0.642020	−	0.766688i	$-0.721904\pi$
$541$	−29.8660	−1.28404	−0.642020	+	0.766688i	$0.721904\pi$
$542$	50.2471	2.15830
$543$	24.6236	1.05670
$544$	5.20764	0.223276
$545$	−23.9682	−1.02668
$546$	49.3689	2.11280
$547$	−36.5808	−1.56408	−0.782041	−	0.623227i	$-0.785821\pi$
$547$	−36.5808	−1.56408	−0.782041	+	0.623227i	$0.785821\pi$
$548$	−12.4435	−0.531559
$549$	−0.702091	−0.0299645
$550$	−24.8651	−1.06025
$551$	21.8098	0.929129
$552$	11.0089	0.468569
$553$	−28.9120	−1.22946
$554$	−10.2446	−0.435252
$555$	20.9746	0.890324
$556$	30.5558	1.29586
$557$	4.75495	0.201474	0.100737	−	0.994913i	$-0.467880\pi$
$557$	4.75495	0.201474	0.100737	+	0.994913i	$0.467880\pi$
$558$	−1.58564	−0.0671256
$559$	5.03650	0.213021
$560$	3.58764	0.151605
$561$	−1.79768	−0.0758982
$562$	56.6778	2.39081
$563$	−28.1317	−1.18561	−0.592805	−	0.805346i	$-0.701980\pi$
$563$	−28.1317	−1.18561	−0.592805	+	0.805346i	$0.701980\pi$
$564$	−4.80421	−0.202294
$565$	−11.4286	−0.480805
$566$	25.3874	1.06711
$567$	−22.7927	−0.957204
$568$	−11.7686	−0.493801
$569$	3.73881	0.156739	0.0783696	−	0.996924i	$-0.475029\pi$
$569$	3.73881	0.156739	0.0783696	+	0.996924i	$0.475029\pi$
$570$	75.9516	3.18126
$571$	−21.4103	−0.895994	−0.447997	−	0.894035i	$-0.647863\pi$
$571$	−21.4103	−0.895994	−0.447997	+	0.894035i	$0.647863\pi$
$572$	16.7208	0.699130
$573$	−6.56774	−0.274371
$574$	−16.0793	−0.671137
$575$	21.6854	0.904345
$576$	−2.95957	−0.123315
$577$	16.2220	0.675330	0.337665	−	0.941266i	$-0.390363\pi$
$577$	16.2220	0.675330	0.337665	+	0.941266i	$0.390363\pi$
$578$	−2.30649	−0.0959375
$579$	−26.8297	−1.11500
$580$	62.3774	2.59008
$581$	2.08025	0.0863032
$582$	−22.0197	−0.912748
$583$	2.26444	0.0937836
$584$	−14.0400	−0.580978
$585$	4.63491	0.191630
$586$	−30.8675	−1.27512
$587$	5.49789	0.226922	0.113461	−	0.993542i	$-0.463806\pi$
$587$	5.49789	0.226922	0.113461	+	0.993542i	$0.463806\pi$
$588$	8.42221	0.347326
$589$	13.6840	0.563838
$590$	47.5298	1.95677
$591$	42.4780	1.74731
$592$	−1.12205	−0.0461158
$593$	−38.6582	−1.58750	−0.793751	−	0.608243i	$-0.791875\pi$
$593$	−38.6582	−1.58750	−0.793751	+	0.608243i	$0.791875\pi$
$594$	−11.4785	−0.470968
$595$	9.39117	0.385000
$596$	−21.6615	−0.887289
$597$	−35.8444	−1.46701
$598$	−23.3675	−0.955567
$599$	−22.5254	−0.920362	−0.460181	−	0.887825i	$-0.652215\pi$
$599$	−22.5254	−0.920362	−0.460181	+	0.887825i	$0.652215\pi$
$600$	58.9998	2.40866
$601$	−33.6816	−1.37390	−0.686951	−	0.726704i	$-0.741051\pi$
$601$	−33.6816	−1.37390	−0.686951	+	0.726704i	$0.741051\pi$
$602$	−5.45271	−0.222236
$603$	2.27556	0.0926682
$604$	21.3296	0.867888
$605$	3.97246	0.161504
$606$	45.6034	1.85251
$607$	−17.1069	−0.694348	−0.347174	−	0.937801i	$-0.612859\pi$
$607$	−17.1069	−0.694348	−0.347174	+	0.937801i	$0.612859\pi$
$608$	24.0133	0.973869
$609$	−20.1008	−0.814524
$610$	27.7686	1.12432
$611$	4.05425	0.164018
$612$	0.769095	0.0310888
$613$	−37.3777	−1.50967	−0.754836	−	0.655914i	$-0.772283\pi$
$613$	−37.3777	−1.50967	−0.754836	+	0.655914i	$0.772283\pi$
$614$	−17.5833	−0.709603
$615$	−21.0585	−0.849161
$616$	−7.19713	−0.289981
$617$	20.4256	0.822305	0.411153	−	0.911567i	$-0.365126\pi$
$617$	20.4256	0.822305	0.411153	+	0.911567i	$0.365126\pi$
$618$	21.9920	0.884649
$619$	−9.59815	−0.385782	−0.192891	−	0.981220i	$-0.561786\pi$
$619$	−9.59815	−0.385782	−0.192891	+	0.981220i	$0.561786\pi$
$620$	39.1370	1.57178
$621$	10.0107	0.401714
$622$	2.48436	0.0996139
$623$	12.3292	0.493959
$624$	−3.45884	−0.138465
$625$	37.3162	1.49265
$626$	14.9664	0.598177
$627$	−8.28943	−0.331048
$628$	−47.0216	−1.87637
$629$	−2.93712	−0.117111
$630$	−5.01793	−0.199919
$631$	−2.81773	−0.112172	−0.0560861	−	0.998426i	$-0.517862\pi$
$631$	−2.81773	−0.112172	−0.0560861	+	0.998426i	$0.517862\pi$
$632$	37.2321	1.48101
$633$	18.5481	0.737219
$634$	−20.7027	−0.822208
$635$	−1.97461	−0.0783600
$636$	−13.5145	−0.535887
$637$	−7.10746	−0.281608
$638$	−10.9092	−0.431899
$639$	0.895527	0.0354265
$640$	75.6802	2.99152
$641$	26.4632	1.04523	0.522616	−	0.852568i	$-0.324956\pi$
$641$	26.4632	1.04523	0.522616	+	0.852568i	$0.324956\pi$
$642$	13.2024	0.521058
$643$	−10.6832	−0.421305	−0.210652	−	0.977561i	$-0.567559\pi$
$643$	−10.6832	−0.421305	−0.210652	+	0.977561i	$0.567559\pi$
$644$	15.7876	0.622120
$645$	−7.14123	−0.281186
$646$	−10.6357	−0.418454
$647$	−27.2263	−1.07038	−0.535188	−	0.844733i	$-0.679759\pi$
$647$	−27.2263	−1.07038	−0.535188	+	0.844733i	$0.679759\pi$
$648$	29.3519	1.15305
$649$	−5.18744	−0.203625
$650$	−125.233	−4.91205
$651$	−12.6117	−0.494291
$652$	14.4152	0.564542
$653$	43.2871	1.69396	0.846978	−	0.531628i	$-0.178420\pi$
$653$	43.2871	1.69396	0.846978	+	0.531628i	$0.178420\pi$
$654$	−25.0173	−0.978253
$655$	62.9701	2.46044
$656$	1.12653	0.0439837
$657$	1.06836	0.0416808
$658$	−4.38929	−0.171112
$659$	39.2963	1.53076	0.765382	−	0.643576i	$-0.222550\pi$
$659$	39.2963	1.53076	0.765382	+	0.643576i	$0.222550\pi$
$660$	−23.7083	−0.922844
$661$	36.7242	1.42840	0.714202	−	0.699940i	$-0.246790\pi$
$661$	36.7242	1.42840	0.714202	+	0.699940i	$0.246790\pi$
$662$	−47.5040	−1.84630
$663$	−9.05402	−0.351629
$664$	−2.67889	−0.103961
$665$	43.3043	1.67927
$666$	1.56937	0.0608120
$667$	9.51416	0.368390
$668$	25.6118	0.990951
$669$	43.7366	1.69096
$670$	−90.0014	−3.47706
$671$	−3.03068	−0.116998
$672$	−22.1316	−0.853746
$673$	−21.6886	−0.836036	−0.418018	−	0.908439i	$-0.637275\pi$
$673$	−21.6886	−0.836036	−0.418018	+	0.908439i	$0.637275\pi$
$674$	69.8629	2.69102
$675$	53.6500	2.06499
$676$	41.0552	1.57905
$677$	7.81484	0.300349	0.150174	−	0.988660i	$-0.452016\pi$
$677$	7.81484	0.300349	0.150174	+	0.988660i	$0.452016\pi$
$678$	−11.9288	−0.458124
$679$	−12.5547	−0.481805
$680$	−12.0937	−0.463773
$681$	−6.59833	−0.252848
$682$	−6.84467	−0.262096
$683$	−6.99262	−0.267565	−0.133783	−	0.991011i	$-0.542712\pi$
$683$	−6.99262	−0.267565	−0.133783	+	0.991011i	$0.542712\pi$
$684$	3.54643	0.135601
$685$	−14.8893	−0.568891
$686$	45.8638	1.75109
$687$	6.81692	0.260082
$688$	0.382023	0.0145645
$689$	11.4049	0.434491
$690$	33.1326	1.26134
$691$	40.5559	1.54282	0.771409	−	0.636340i	$-0.219552\pi$
$691$	40.5559	1.54282	0.771409	+	0.636340i	$0.219552\pi$
$692$	−70.8963	−2.69507
$693$	0.547661	0.0208039
$694$	37.7261	1.43206
$695$	36.5617	1.38687
$696$	25.8853	0.981178
$697$	2.94886	0.111696
$698$	82.0138	3.10427
$699$	25.9608	0.981930
$700$	84.6106	3.19798
$701$	−38.9586	−1.47144	−0.735722	−	0.677283i	$-0.763157\pi$
$701$	−38.9586	−1.47144	−0.735722	+	0.677283i	$0.763157\pi$
$702$	−57.8114	−2.18195
$703$	−13.5436	−0.510805
$704$	−12.7754	−0.481492
$705$	−5.74850	−0.216501
$706$	−28.9604	−1.08994
$707$	26.0011	0.977871
$708$	30.9595	1.16353
$709$	51.8099	1.94576	0.972881	−	0.231307i	$-0.0743000\pi$
$709$	51.8099	1.94576	0.972881	+	0.231307i	$0.0743000\pi$
$710$	−35.4192	−1.32926
$711$	−2.83315	−0.106252
$712$	−15.8772	−0.595024
$713$	5.96940	0.223556
$714$	9.80223	0.366839
$715$	20.0073	0.748231
$716$	44.8348	1.67556
$717$	−11.8414	−0.442225
$718$	9.90397	0.369613
$719$	−1.97125	−0.0735151	−0.0367575	−	0.999324i	$-0.511703\pi$
$719$	−1.97125	−0.0735151	−0.0367575	+	0.999324i	$0.511703\pi$
$720$	0.351562	0.0131019
$721$	12.5389	0.466973
$722$	−5.21945	−0.194248
$723$	27.7875	1.03343
$724$	−45.4743	−1.69004
$725$	50.9892	1.89369
$726$	4.14634	0.153885
$727$	−19.0114	−0.705095	−0.352548	−	0.935794i	$-0.614685\pi$
$727$	−19.0114	−0.705095	−0.352548	+	0.935794i	$0.614685\pi$
$728$	−36.2483	−1.34345
$729$	24.6055	0.911314
$730$	−42.2551	−1.56393
$731$	1.00000	0.0369863
$732$	18.0876	0.668537
$733$	−32.4912	−1.20009	−0.600046	−	0.799966i	$-0.704851\pi$
$733$	−32.4912	−1.20009	−0.600046	+	0.799966i	$0.704851\pi$
$734$	−2.87998	−0.106302
$735$	10.0776	0.371719
$736$	10.4754	0.386129
$737$	9.82283	0.361829
$738$	−1.57565	−0.0580005
$739$	−6.70734	−0.246733	−0.123367	−	0.992361i	$-0.539369\pi$
$739$	−6.70734	−0.246733	−0.123367	+	0.992361i	$0.539369\pi$
$740$	−38.7355	−1.42394
$741$	−41.7497	−1.53371
$742$	−12.3473	−0.453285
$743$	−11.4142	−0.418745	−0.209372	−	0.977836i	$-0.567142\pi$
$743$	−11.4142	−0.418745	−0.209372	+	0.977836i	$0.567142\pi$
$744$	16.2410	0.595424
$745$	−25.9192	−0.949604
$746$	−70.3066	−2.57411
$747$	0.203848	0.00745843
$748$	3.31992	0.121388
$749$	7.52744	0.275047
$750$	95.2114	3.47663
$751$	3.03628	0.110796	0.0553978	−	0.998464i	$-0.482357\pi$
$751$	3.03628	0.110796	0.0553978	+	0.998464i	$0.482357\pi$
$752$	0.307518	0.0112140
$753$	−3.19800	−0.116541
$754$	−54.9441	−2.00095
$755$	25.5220	0.928841
$756$	39.0588	1.42056
$757$	−20.5266	−0.746050	−0.373025	−	0.927821i	$-0.621680\pi$
$757$	−20.5266	−0.746050	−0.373025	+	0.927821i	$0.621680\pi$
$758$	49.5686	1.80041
$759$	−3.61612	−0.131257
$760$	−55.7662	−2.02285
$761$	39.0941	1.41716	0.708579	−	0.705631i	$-0.249337\pi$
$761$	39.0941	1.41716	0.708579	+	0.705631i	$0.249337\pi$
$762$	−2.06104	−0.0746636
$763$	−14.2638	−0.516383
$764$	12.1292	0.438817
$765$	0.920264	0.0332722
$766$	29.7547	1.07508
$767$	−26.1266	−0.943375
$768$	33.0605	1.19297
$769$	−10.5632	−0.380919	−0.190460	−	0.981695i	$-0.560998\pi$
$769$	−10.5632	−0.380919	−0.190460	+	0.981695i	$0.560998\pi$
$770$	−21.6607	−0.780597
$771$	50.8085	1.82982
$772$	49.5484	1.78329
$773$	2.62092	0.0942681	0.0471340	−	0.998889i	$-0.484991\pi$
$773$	2.62092	0.0942681	0.0471340	+	0.998889i	$0.484991\pi$
$774$	−0.534324	−0.0192059
$775$	31.9918	1.14918
$776$	16.1676	0.580384
$777$	12.4823	0.447799
$778$	79.5616	2.85242
$779$	13.5977	0.487189
$780$	−119.407	−4.27545
$781$	3.86568	0.138325
$782$	−4.63962	−0.165913
$783$	23.5381	0.841185
$784$	−0.539107	−0.0192538
$785$	−56.2639	−2.00815
$786$	65.7263	2.34438
$787$	42.1682	1.50314	0.751568	−	0.659656i	$-0.229298\pi$
$787$	42.1682	1.50314	0.751568	+	0.659656i	$0.229298\pi$
$788$	−78.4475	−2.79458
$789$	6.94593	0.247282
$790$	112.055	3.98673
$791$	−6.80131	−0.241827
$792$	−0.705265	−0.0250605
$793$	−15.2640	−0.542042
$794$	45.8130	1.62584
$795$	−16.1709	−0.573523
$796$	66.1966	2.34628
$797$	31.4080	1.11253	0.556263	−	0.831006i	$-0.312235\pi$
$797$	31.4080	1.11253	0.556263	+	0.831006i	$0.312235\pi$
$798$	45.1998	1.60006
$799$	0.804974	0.0284779
$800$	56.1408	1.98488
$801$	1.20817	0.0426885
$802$	−12.2730	−0.433374
$803$	4.61176	0.162745
$804$	−58.6242	−2.06752
$805$	18.8908	0.665813
$806$	−34.4732	−1.21427
$807$	−33.7752	−1.18894
$808$	−33.4835	−1.17795
$809$	20.0924	0.706412	0.353206	−	0.935546i	$-0.385091\pi$
$809$	20.0924	0.706412	0.353206	+	0.935546i	$0.385091\pi$
$810$	88.3383	3.10389
$811$	−1.68860	−0.0592948	−0.0296474	−	0.999560i	$-0.509438\pi$
$811$	−1.68860	−0.0592948	−0.0296474	+	0.999560i	$0.509438\pi$
$812$	37.1216	1.30271
$813$	39.1626	1.37349
$814$	6.77445	0.237444
$815$	17.2486	0.604191
$816$	−0.686755	−0.0240412
$817$	4.61118	0.161325
$818$	−58.4817	−2.04476
$819$	2.75830	0.0963827
$820$	38.8904	1.35811
$821$	8.08410	0.282137	0.141068	−	0.990000i	$-0.454946\pi$
$821$	8.08410	0.282137	0.141068	+	0.990000i	$0.454946\pi$
$822$	−15.5410	−0.542056
$823$	−48.9410	−1.70597	−0.852987	−	0.521931i	$-0.825212\pi$
$823$	−48.9410	−1.70597	−0.852987	+	0.521931i	$0.825212\pi$
$824$	−16.1473	−0.562517
$825$	−19.3799	−0.674720
$826$	28.2856	0.984182
$827$	36.6010	1.27274	0.636371	−	0.771384i	$-0.280435\pi$
$827$	36.6010	1.27274	0.636371	+	0.771384i	$0.280435\pi$
$828$	1.54707	0.0537644
$829$	40.4011	1.40319	0.701594	−	0.712577i	$-0.252472\pi$
$829$	40.4011	1.40319	0.701594	+	0.712577i	$0.252472\pi$
$830$	−8.06246	−0.279852
$831$	−7.98465	−0.276985
$832$	−64.3435	−2.23071
$833$	−1.41119	−0.0488949
$834$	38.1621	1.32144
$835$	30.6459	1.06055
$836$	15.3087	0.529463
$837$	14.7684	0.510470
$838$	37.1229	1.28239
$839$	49.1878	1.69815	0.849076	−	0.528270i	$-0.177159\pi$
$839$	49.1878	1.69815	0.849076	+	0.528270i	$0.177159\pi$
$840$	51.3963	1.77334
$841$	−6.62927	−0.228596
$842$	−57.9629	−1.99753
$843$	44.1747	1.52146
$844$	−34.2541	−1.17908
$845$	49.1248	1.68994
$846$	−0.430117	−0.0147877
$847$	2.36407	0.0812303
$848$	0.865068	0.0297066
$849$	19.7870	0.679087
$850$	−24.8651	−0.852866
$851$	−5.90816	−0.202529
$852$	−23.0710	−0.790400
$853$	−8.59589	−0.294318	−0.147159	−	0.989113i	$-0.547013\pi$
$853$	−8.59589	−0.294318	−0.147159	+	0.989113i	$0.547013\pi$
$854$	16.5254	0.565489
$855$	4.24350	0.145125
$856$	−9.69366	−0.331322
$857$	−6.09109	−0.208068	−0.104034	−	0.994574i	$-0.533175\pi$
$857$	−6.09109	−0.208068	−0.104034	+	0.994574i	$0.533175\pi$
$858$	20.8831	0.712936
$859$	21.3565	0.728676	0.364338	−	0.931267i	$-0.381295\pi$
$859$	21.3565	0.728676	0.364338	+	0.931267i	$0.381295\pi$
$860$	13.1883	0.449716
$861$	−12.5322	−0.427096
$862$	64.0181	2.18046
$863$	37.7200	1.28400	0.642002	−	0.766703i	$-0.278104\pi$
$863$	37.7200	1.28400	0.642002	+	0.766703i	$0.278104\pi$
$864$	25.9163	0.881690
$865$	−84.8313	−2.88435
$866$	54.1157	1.83893
$867$	−1.79768	−0.0610525
$868$	23.2910	0.790547
$869$	−12.2298	−0.414866
$870$	77.9050	2.64123
$871$	49.4727	1.67632
$872$	18.3685	0.622037
$873$	−1.23027	−0.0416382
$874$	−21.3941	−0.723667
$875$	54.2854	1.83518
$876$	−27.5237	−0.929940
$877$	−22.9518	−0.775029	−0.387514	−	0.921864i	$-0.626666\pi$
$877$	−22.9518	−0.775029	−0.387514	+	0.921864i	$0.626666\pi$
$878$	34.4491	1.16260
$879$	−24.0581	−0.811459
$880$	1.51757	0.0511573
$881$	−40.4541	−1.36293	−0.681467	−	0.731849i	$-0.738658\pi$
$881$	−40.4541	−1.36293	−0.681467	+	0.731849i	$0.738658\pi$
$882$	0.754033	0.0253896
$883$	−31.5257	−1.06092	−0.530462	−	0.847708i	$-0.677982\pi$
$883$	−31.5257	−1.06092	−0.530462	+	0.847708i	$0.677982\pi$
$884$	16.7208	0.562380
$885$	37.0447	1.24524
$886$	61.0505	2.05103
$887$	53.9270	1.81069	0.905346	−	0.424676i	$-0.139612\pi$
$887$	53.9270	1.81069	0.905346	+	0.424676i	$0.139612\pi$
$888$	−16.0744	−0.539421
$889$	−1.17512	−0.0394121
$890$	−47.7846	−1.60174
$891$	−9.64132	−0.322996
$892$	−80.7718	−2.70444
$893$	3.71188	0.124213
$894$	−27.0537	−0.904810
$895$	53.6473	1.79323
$896$	45.0383	1.50462
$897$	−18.2126	−0.608101
$898$	27.9927	0.934129
$899$	14.0359	0.468124
$900$	8.29120	0.276373
$901$	2.26444	0.0754395
$902$	−6.80154	−0.226467
$903$	−4.24984	−0.141426
$904$	8.75856	0.291305
$905$	−54.4124	−1.80873
$906$	26.6391	0.885026
$907$	37.3036	1.23865	0.619323	−	0.785136i	$-0.287407\pi$
$907$	37.3036	1.23865	0.619323	+	0.785136i	$0.287407\pi$
$908$	12.1856	0.404395
$909$	2.54791	0.0845088
$910$	−109.094	−3.61643
$911$	−19.4609	−0.644769	−0.322384	−	0.946609i	$-0.604484\pi$
$911$	−19.4609	−0.644769	−0.322384	+	0.946609i	$0.604484\pi$
$912$	−3.16675	−0.104862
$913$	0.879944	0.0291219
$914$	55.5485	1.83738
$915$	21.6428	0.715489
$916$	−12.5893	−0.415963
$917$	37.4743	1.23751
$918$	−11.4785	−0.378847
$919$	−0.333493	−0.0110009	−0.00550046	−	0.999985i	$-0.501751\pi$
$919$	−0.333493	−0.0110009	−0.00550046	+	0.999985i	$0.501751\pi$
$920$	−24.3271	−0.802040
$921$	−13.7044	−0.451575
$922$	−87.6758	−2.88745
$923$	19.4695	0.640847
$924$	−14.1091	−0.464156
$925$	−31.6635	−1.04109
$926$	19.4394	0.638818
$927$	1.22872	0.0403564
$928$	24.6309	0.808550
$929$	−48.7790	−1.60039	−0.800194	−	0.599742i	$-0.795270\pi$
$929$	−48.7790	−1.60039	−0.800194	+	0.599742i	$0.795270\pi$
$930$	48.8794	1.60282
$931$	−6.50725	−0.213266
$932$	−47.9439	−1.57046
$933$	1.93631	0.0633921
$934$	−17.6589	−0.577818
$935$	3.97246	0.129913
$936$	−3.55206	−0.116103
$937$	−13.6133	−0.444726	−0.222363	−	0.974964i	$-0.571377\pi$
$937$	−13.6133	−0.444726	−0.222363	+	0.974964i	$0.571377\pi$
$938$	−53.5610	−1.74883
$939$	11.6648	0.380666
$940$	10.6162	0.346263
$941$	1.09381	0.0356572	0.0178286	−	0.999841i	$-0.494325\pi$
$941$	1.09381	0.0356572	0.0178286	+	0.999841i	$0.494325\pi$
$942$	−58.7267	−1.91342
$943$	5.93178	0.193165
$944$	−1.98172	−0.0644995
$945$	46.7360	1.52032
$946$	−2.30649	−0.0749906
$947$	17.8443	0.579863	0.289931	−	0.957047i	$-0.406368\pi$
$947$	17.8443	0.579863	0.289931	+	0.957047i	$0.406368\pi$
$948$	72.9891	2.37058
$949$	23.2271	0.753984
$950$	−114.657	−3.71998
$951$	−16.1357	−0.523235
$952$	−7.19713	−0.233260
$953$	−28.7536	−0.931420	−0.465710	−	0.884937i	$-0.654201\pi$
$953$	−28.7536	−0.931420	−0.465710	+	0.884937i	$0.654201\pi$
$954$	−1.20995	−0.0391735
$955$	14.5132	0.469636
$956$	21.8684	0.707275
$957$	−8.50262	−0.274851
$958$	36.6284	1.18341
$959$	−8.86082	−0.286131
$960$	91.2323	2.94451
$961$	−22.1936	−0.715921
$962$	34.1195	1.10006
$963$	0.737633	0.0237699
$964$	−51.3173	−1.65282
$965$	59.2874	1.90853
$966$	19.7177	0.634405
$967$	−34.8048	−1.11925	−0.559624	−	0.828747i	$-0.689054\pi$
$967$	−34.8048	−1.11925	−0.559624	+	0.828747i	$0.689054\pi$
$968$	−3.04439	−0.0978503
$969$	−8.28943	−0.266295
$970$	48.6586	1.56233
$971$	−46.7985	−1.50184	−0.750918	−	0.660395i	$-0.770389\pi$
$971$	−46.7985	−1.50184	−0.750918	+	0.660395i	$0.770389\pi$
$972$	7.97524	0.255806
$973$	21.7584	0.697541
$974$	−22.1164	−0.708657
$975$	−97.6067	−3.12592
$976$	−1.15779	−0.0370600
$977$	−3.80196	−0.121635	−0.0608177	−	0.998149i	$-0.519371\pi$
$977$	−3.80196	−0.121635	−0.0608177	+	0.998149i	$0.519371\pi$
$978$	18.0036	0.575690
$979$	5.21525	0.166680
$980$	−18.6111	−0.594511
$981$	−1.39774	−0.0446265
$982$	−24.3666	−0.777570
$983$	−23.6880	−0.755531	−0.377765	−	0.925901i	$-0.623307\pi$
$983$	−23.6880	−0.755531	−0.377765	+	0.925901i	$0.623307\pi$
$984$	16.1387	0.514482
$985$	−93.8667	−2.99084
$986$	−10.9092	−0.347419
$987$	−3.42101	−0.108892
$988$	77.1024	2.45295
$989$	2.01155	0.0639635
$990$	−2.12258	−0.0674601
$991$	14.2183	0.451659	0.225830	−	0.974167i	$-0.427491\pi$
$991$	14.2183	0.451659	0.225830	+	0.974167i	$0.427491\pi$
$992$	15.4540	0.490665
$993$	−37.0246	−1.17494
$994$	−21.0784	−0.668568
$995$	79.2078	2.51106
$996$	−5.25165	−0.166405
$997$	−53.4245	−1.69197	−0.845986	−	0.533206i	$-0.820987\pi$
$997$	−53.4245	−1.69197	−0.845986	+	0.533206i	$0.820987\pi$
$998$	7.64611	0.242033
$999$	−14.6168	−0.462457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.10	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.10	✓	82	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)

\(f(q)\)	\(=\)	\(q-2.30649 q^{2} -1.79768 q^{3} +3.31992 q^{4} +3.97246 q^{5} +4.14634 q^{6} +2.36407 q^{7} -3.04439 q^{8} +0.231661 q^{9} +O(q^{10})\)	\(q-2.30649 q^{2} -1.79768 q^{3} +3.31992 q^{4} +3.97246 q^{5} +4.14634 q^{6} +2.36407 q^{7} -3.04439 q^{8} +0.231661 q^{9} -9.16247 q^{10} +1.00000 q^{11} -5.96816 q^{12} +5.03650 q^{13} -5.45271 q^{14} -7.14123 q^{15} +0.382023 q^{16} +1.00000 q^{17} -0.534324 q^{18} +4.61118 q^{19} +13.1883 q^{20} -4.24984 q^{21} -2.30649 q^{22} +2.01155 q^{23} +5.47284 q^{24} +10.7805 q^{25} -11.6167 q^{26} +4.97659 q^{27} +7.84851 q^{28} +4.72977 q^{29} +16.4712 q^{30} +2.96757 q^{31} +5.20764 q^{32} -1.79768 q^{33} -2.30649 q^{34} +9.39117 q^{35} +0.769095 q^{36} -2.93712 q^{37} -10.6357 q^{38} -9.05402 q^{39} -12.0937 q^{40} +2.94886 q^{41} +9.80223 q^{42} +1.00000 q^{43} +3.31992 q^{44} +0.920264 q^{45} -4.63962 q^{46} +0.804974 q^{47} -0.686755 q^{48} -1.41119 q^{49} -24.8651 q^{50} -1.79768 q^{51} +16.7208 q^{52} +2.26444 q^{53} -11.4785 q^{54} +3.97246 q^{55} -7.19713 q^{56} -8.28943 q^{57} -10.9092 q^{58} -5.18744 q^{59} -23.7083 q^{60} -3.03068 q^{61} -6.84467 q^{62} +0.547661 q^{63} -12.7754 q^{64} +20.0073 q^{65} +4.14634 q^{66} +9.82283 q^{67} +3.31992 q^{68} -3.61612 q^{69} -21.6607 q^{70} +3.86568 q^{71} -0.705265 q^{72} +4.61176 q^{73} +6.77445 q^{74} -19.3799 q^{75} +15.3087 q^{76} +2.36407 q^{77} +20.8831 q^{78} -12.2298 q^{79} +1.51757 q^{80} -9.64132 q^{81} -6.80154 q^{82} +0.879944 q^{83} -14.1091 q^{84} +3.97246 q^{85} -2.30649 q^{86} -8.50262 q^{87} -3.04439 q^{88} +5.21525 q^{89} -2.12258 q^{90} +11.9066 q^{91} +6.67817 q^{92} -5.33474 q^{93} -1.85667 q^{94} +18.3177 q^{95} -9.36168 q^{96} -5.31064 q^{97} +3.25490 q^{98} +0.231661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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