LMFDB - Embedded newform 8002.2.a.d.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.611304 q^{3} +1.00000 q^{4} -0.869294 q^{5} +0.611304 q^{6} +0.772937 q^{7} +1.00000 q^{8} -2.62631 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.611304 q^{3} +1.00000 q^{4} -0.869294 q^{5} +0.611304 q^{6} +0.772937 q^{7} +1.00000 q^{8} -2.62631 q^{9} -0.869294 q^{10} +1.67144 q^{11} +0.611304 q^{12} +3.12877 q^{13} +0.772937 q^{14} -0.531402 q^{15} +1.00000 q^{16} +2.22748 q^{17} -2.62631 q^{18} -6.30025 q^{19} -0.869294 q^{20} +0.472499 q^{21} +1.67144 q^{22} -8.93358 q^{23} +0.611304 q^{24} -4.24433 q^{25} +3.12877 q^{26} -3.43938 q^{27} +0.772937 q^{28} -0.827311 q^{29} -0.531402 q^{30} -2.32006 q^{31} +1.00000 q^{32} +1.02176 q^{33} +2.22748 q^{34} -0.671909 q^{35} -2.62631 q^{36} +7.06551 q^{37} -6.30025 q^{38} +1.91263 q^{39} -0.869294 q^{40} +2.16777 q^{41} +0.472499 q^{42} -0.338873 q^{43} +1.67144 q^{44} +2.28303 q^{45} -8.93358 q^{46} -5.40162 q^{47} +0.611304 q^{48} -6.40257 q^{49} -4.24433 q^{50} +1.36167 q^{51} +3.12877 q^{52} -4.36125 q^{53} -3.43938 q^{54} -1.45297 q^{55} +0.772937 q^{56} -3.85137 q^{57} -0.827311 q^{58} +2.57016 q^{59} -0.531402 q^{60} -5.61001 q^{61} -2.32006 q^{62} -2.02997 q^{63} +1.00000 q^{64} -2.71982 q^{65} +1.02176 q^{66} +12.2317 q^{67} +2.22748 q^{68} -5.46113 q^{69} -0.671909 q^{70} +6.30648 q^{71} -2.62631 q^{72} -15.5606 q^{73} +7.06551 q^{74} -2.59457 q^{75} -6.30025 q^{76} +1.29192 q^{77} +1.91263 q^{78} -8.89115 q^{79} -0.869294 q^{80} +5.77642 q^{81} +2.16777 q^{82} -1.33322 q^{83} +0.472499 q^{84} -1.93634 q^{85} -0.338873 q^{86} -0.505738 q^{87} +1.67144 q^{88} -6.31077 q^{89} +2.28303 q^{90} +2.41834 q^{91} -8.93358 q^{92} -1.41826 q^{93} -5.40162 q^{94} +5.47677 q^{95} +0.611304 q^{96} -5.91946 q^{97} -6.40257 q^{98} -4.38972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.611304	0.352936	0.176468	−	0.984306i	$-0.443533\pi$
$3$	0.611304	0.352936	0.176468	+	0.984306i	$0.443533\pi$
$4$	1.00000	0.500000
$5$	−0.869294	−0.388760	−0.194380	−	0.980926i	$-0.562269\pi$
$5$	−0.869294	−0.388760	−0.194380	+	0.980926i	$0.562269\pi$
$6$	0.611304	0.249564
$7$	0.772937	0.292143	0.146071	−	0.989274i	$-0.453337\pi$
$7$	0.772937	0.292143	0.146071	+	0.989274i	$0.453337\pi$
$8$	1.00000	0.353553
$9$	−2.62631	−0.875436
$10$	−0.869294	−0.274895
$11$	1.67144	0.503958	0.251979	−	0.967733i	$-0.418919\pi$
$11$	1.67144	0.503958	0.251979	+	0.967733i	$0.418919\pi$
$12$	0.611304	0.176468
$13$	3.12877	0.867764	0.433882	−	0.900970i	$-0.357143\pi$
$13$	3.12877	0.867764	0.433882	+	0.900970i	$0.357143\pi$
$14$	0.772937	0.206576
$15$	−0.531402	−0.137207
$16$	1.00000	0.250000
$17$	2.22748	0.540244	0.270122	−	0.962826i	$-0.412936\pi$
$17$	2.22748	0.540244	0.270122	+	0.962826i	$0.412936\pi$
$18$	−2.62631	−0.619027
$19$	−6.30025	−1.44538	−0.722689	−	0.691174i	$-0.757094\pi$
$19$	−6.30025	−1.44538	−0.722689	+	0.691174i	$0.757094\pi$
$20$	−0.869294	−0.194380
$21$	0.472499	0.103108
$22$	1.67144	0.356352
$23$	−8.93358	−1.86278	−0.931390	−	0.364023i	$-0.881403\pi$
$23$	−8.93358	−1.86278	−0.931390	+	0.364023i	$0.881403\pi$
$24$	0.611304	0.124782
$25$	−4.24433	−0.848866
$26$	3.12877	0.613602
$27$	−3.43938	−0.661909
$28$	0.772937	0.146071
$29$	−0.827311	−0.153628	−0.0768139	−	0.997045i	$-0.524475\pi$
$29$	−0.827311	−0.153628	−0.0768139	+	0.997045i	$0.524475\pi$
$30$	−0.531402	−0.0970203
$31$	−2.32006	−0.416695	−0.208348	−	0.978055i	$-0.566809\pi$
$31$	−2.32006	−0.416695	−0.208348	+	0.978055i	$0.566809\pi$
$32$	1.00000	0.176777
$33$	1.02176	0.177865
$34$	2.22748	0.382010
$35$	−0.671909	−0.113573
$36$	−2.62631	−0.437718
$37$	7.06551	1.16156	0.580782	−	0.814059i	$-0.302747\pi$
$37$	7.06551	1.16156	0.580782	+	0.814059i	$0.302747\pi$
$38$	−6.30025	−1.02204
$39$	1.91263	0.306265
$40$	−0.869294	−0.137447
$41$	2.16777	0.338550	0.169275	−	0.985569i	$-0.445857\pi$
$41$	2.16777	0.338550	0.169275	+	0.985569i	$0.445857\pi$
$42$	0.472499	0.0729082
$43$	−0.338873	−0.0516776	−0.0258388	−	0.999666i	$-0.508226\pi$
$43$	−0.338873	−0.0516776	−0.0258388	+	0.999666i	$0.508226\pi$
$44$	1.67144	0.251979
$45$	2.28303	0.340334
$46$	−8.93358	−1.31718
$47$	−5.40162	−0.787907	−0.393953	−	0.919130i	$-0.628893\pi$
$47$	−5.40162	−0.787907	−0.393953	+	0.919130i	$0.628893\pi$
$48$	0.611304	0.0882341
$49$	−6.40257	−0.914653
$50$	−4.24433	−0.600239
$51$	1.36167	0.190672
$52$	3.12877	0.433882
$53$	−4.36125	−0.599064	−0.299532	−	0.954086i	$-0.596830\pi$
$53$	−4.36125	−0.599064	−0.299532	+	0.954086i	$0.596830\pi$
$54$	−3.43938	−0.468041
$55$	−1.45297	−0.195919
$56$	0.772937	0.103288
$57$	−3.85137	−0.510126
$58$	−0.827311	−0.108631
$59$	2.57016	0.334606	0.167303	−	0.985906i	$-0.446494\pi$
$59$	2.57016	0.334606	0.167303	+	0.985906i	$0.446494\pi$
$60$	−0.531402	−0.0686037
$61$	−5.61001	−0.718288	−0.359144	−	0.933282i	$-0.616931\pi$
$61$	−5.61001	−0.718288	−0.359144	+	0.933282i	$0.616931\pi$
$62$	−2.32006	−0.294648
$63$	−2.02997	−0.255752
$64$	1.00000	0.125000
$65$	−2.71982	−0.337352
$66$	1.02176	0.125770
$67$	12.2317	1.49434	0.747168	−	0.664636i	$-0.231413\pi$
$67$	12.2317	1.49434	0.747168	+	0.664636i	$0.231413\pi$
$68$	2.22748	0.270122
$69$	−5.46113	−0.657443
$70$	−0.671909	−0.0803085
$71$	6.30648	0.748441	0.374221	−	0.927340i	$-0.377910\pi$
$71$	6.30648	0.748441	0.374221	+	0.927340i	$0.377910\pi$
$72$	−2.62631	−0.309513
$73$	−15.5606	−1.82123	−0.910614	−	0.413257i	$-0.864391\pi$
$73$	−15.5606	−1.82123	−0.910614	+	0.413257i	$0.864391\pi$
$74$	7.06551	0.821349
$75$	−2.59457	−0.299596
$76$	−6.30025	−0.722689
$77$	1.29192	0.147228
$78$	1.91263	0.216562
$79$	−8.89115	−1.00033	−0.500166	−	0.865930i	$-0.666728\pi$
$79$	−8.89115	−1.00033	−0.500166	+	0.865930i	$0.666728\pi$
$80$	−0.869294	−0.0971900
$81$	5.77642	0.641824
$82$	2.16777	0.239391
$83$	−1.33322	−0.146340	−0.0731702	−	0.997319i	$-0.523312\pi$
$83$	−1.33322	−0.146340	−0.0731702	+	0.997319i	$0.523312\pi$
$84$	0.472499	0.0515539
$85$	−1.93634	−0.210025
$86$	−0.338873	−0.0365416
$87$	−0.505738	−0.0542208
$88$	1.67144	0.178176
$89$	−6.31077	−0.668941	−0.334470	−	0.942406i	$-0.608557\pi$
$89$	−6.31077	−0.668941	−0.334470	+	0.942406i	$0.608557\pi$
$90$	2.28303	0.240653
$91$	2.41834	0.253511
$92$	−8.93358	−0.931390
$93$	−1.41826	−0.147067
$94$	−5.40162	−0.557134
$95$	5.47677	0.561905
$96$	0.611304	0.0623909
$97$	−5.91946	−0.601030	−0.300515	−	0.953777i	$-0.597159\pi$
$97$	−5.91946	−0.601030	−0.300515	+	0.953777i	$0.597159\pi$
$98$	−6.40257	−0.646757
$99$	−4.38972	−0.441183
$100$	−4.24433	−0.424433
$101$	−16.0928	−1.60129	−0.800647	−	0.599136i	$-0.795511\pi$
$101$	−16.0928	−1.60129	−0.800647	+	0.599136i	$0.795511\pi$
$102$	1.36167	0.134825
$103$	0.987807	0.0973315	0.0486658	−	0.998815i	$-0.484503\pi$
$103$	0.987807	0.0973315	0.0486658	+	0.998815i	$0.484503\pi$
$104$	3.12877	0.306801
$105$	−0.410740	−0.0400841
$106$	−4.36125	−0.423602
$107$	8.16510	0.789350	0.394675	−	0.918821i	$-0.370857\pi$
$107$	8.16510	0.789350	0.394675	+	0.918821i	$0.370857\pi$
$108$	−3.43938	−0.330955
$109$	2.03132	0.194565	0.0972827	−	0.995257i	$-0.468985\pi$
$109$	2.03132	0.194565	0.0972827	+	0.995257i	$0.468985\pi$
$110$	−1.45297	−0.138535
$111$	4.31917	0.409958
$112$	0.772937	0.0730356
$113$	9.62883	0.905804	0.452902	−	0.891560i	$-0.350389\pi$
$113$	9.62883	0.905804	0.452902	+	0.891560i	$0.350389\pi$
$114$	−3.85137	−0.360714
$115$	7.76590	0.724174
$116$	−0.827311	−0.0768139
$117$	−8.21711	−0.759672
$118$	2.57016	0.236602
$119$	1.72170	0.157828
$120$	−0.531402	−0.0485102
$121$	−8.20629	−0.746026
$122$	−5.61001	−0.507907
$123$	1.32517	0.119486
$124$	−2.32006	−0.208348
$125$	8.03604	0.718765
$126$	−2.02997	−0.180844
$127$	−5.30494	−0.470737	−0.235368	−	0.971906i	$-0.575630\pi$
$127$	−5.30494	−0.470737	−0.235368	+	0.971906i	$0.575630\pi$
$128$	1.00000	0.0883883
$129$	−0.207154	−0.0182389
$130$	−2.71982	−0.238544
$131$	−9.50668	−0.830602	−0.415301	−	0.909684i	$-0.636324\pi$
$131$	−9.50668	−0.830602	−0.415301	+	0.909684i	$0.636324\pi$
$132$	1.02176	0.0889326
$133$	−4.86970	−0.422256
$134$	12.2317	1.05665
$135$	2.98983	0.257324
$136$	2.22748	0.191005
$137$	7.42404	0.634279	0.317139	−	0.948379i	$-0.397278\pi$
$137$	7.42404	0.634279	0.317139	+	0.948379i	$0.397278\pi$
$138$	−5.46113	−0.464882
$139$	2.41750	0.205050	0.102525	−	0.994730i	$-0.467308\pi$
$139$	2.41750	0.205050	0.102525	+	0.994730i	$0.467308\pi$
$140$	−0.671909	−0.0567867
$141$	−3.30203	−0.278081
$142$	6.30648	0.529228
$143$	5.22955	0.437317
$144$	−2.62631	−0.218859
$145$	0.719177	0.0597244
$146$	−15.5606	−1.28780
$147$	−3.91391	−0.322814
$148$	7.06551	0.580782
$149$	−17.7242	−1.45203	−0.726013	−	0.687681i	$-0.758629\pi$
$149$	−17.7242	−1.45203	−0.726013	+	0.687681i	$0.758629\pi$
$150$	−2.59457	−0.211846
$151$	0.604095	0.0491606	0.0245803	−	0.999698i	$-0.492175\pi$
$151$	0.604095	0.0491606	0.0245803	+	0.999698i	$0.492175\pi$
$152$	−6.30025	−0.511018
$153$	−5.85006	−0.472949
$154$	1.29192	0.104106
$155$	2.01681	0.161994
$156$	1.91263	0.153133
$157$	15.7348	1.25577	0.627885	−	0.778306i	$-0.283921\pi$
$157$	15.7348	1.25577	0.627885	+	0.778306i	$0.283921\pi$
$158$	−8.89115	−0.707342
$159$	−2.66605	−0.211431
$160$	−0.869294	−0.0687237
$161$	−6.90509	−0.544197
$162$	5.77642	0.453838
$163$	1.62611	0.127367	0.0636833	−	0.997970i	$-0.479715\pi$
$163$	1.62611	0.127367	0.0636833	+	0.997970i	$0.479715\pi$
$164$	2.16777	0.169275
$165$	−0.888207	−0.0691468
$166$	−1.33322	−0.103478
$167$	8.60152	0.665606	0.332803	−	0.942996i	$-0.392006\pi$
$167$	8.60152	0.665606	0.332803	+	0.942996i	$0.392006\pi$
$168$	0.472499	0.0364541
$169$	−3.21081	−0.246985
$170$	−1.93634	−0.148510
$171$	16.5464	1.26534
$172$	−0.338873	−0.0258388
$173$	−15.1901	−1.15488	−0.577442	−	0.816432i	$-0.695949\pi$
$173$	−15.1901	−1.15488	−0.577442	+	0.816432i	$0.695949\pi$
$174$	−0.505738	−0.0383399
$175$	−3.28060	−0.247990
$176$	1.67144	0.125990
$177$	1.57115	0.118095
$178$	−6.31077	−0.473012
$179$	6.78133	0.506861	0.253430	−	0.967354i	$-0.418441\pi$
$179$	6.78133	0.506861	0.253430	+	0.967354i	$0.418441\pi$
$180$	2.28303	0.170167
$181$	17.8098	1.32379	0.661897	−	0.749595i	$-0.269752\pi$
$181$	17.8098	1.32379	0.661897	+	0.749595i	$0.269752\pi$
$182$	2.41834	0.179259
$183$	−3.42942	−0.253510
$184$	−8.93358	−0.658592
$185$	−6.14200	−0.451569
$186$	−1.41826	−0.103992
$187$	3.72310	0.272260
$188$	−5.40162	−0.393953
$189$	−2.65842	−0.193372
$190$	5.47677	0.397327
$191$	−8.70307	−0.629732	−0.314866	−	0.949136i	$-0.601960\pi$
$191$	−8.70307	−0.629732	−0.314866	+	0.949136i	$0.601960\pi$
$192$	0.611304	0.0441170
$193$	−0.689269	−0.0496147	−0.0248073	−	0.999692i	$-0.507897\pi$
$193$	−0.689269	−0.0496147	−0.0248073	+	0.999692i	$0.507897\pi$
$194$	−5.91946	−0.424992
$195$	−1.66263	−0.119064
$196$	−6.40257	−0.457326
$197$	−2.23811	−0.159459	−0.0797295	−	0.996817i	$-0.525406\pi$
$197$	−2.23811	−0.159459	−0.0797295	+	0.996817i	$0.525406\pi$
$198$	−4.38972	−0.311964
$199$	−2.43410	−0.172549	−0.0862744	−	0.996271i	$-0.527496\pi$
$199$	−2.43410	−0.172549	−0.0862744	+	0.996271i	$0.527496\pi$
$200$	−4.24433	−0.300119
$201$	7.47726	0.527405
$202$	−16.0928	−1.13229
$203$	−0.639459	−0.0448812
$204$	1.36167	0.0953358
$205$	−1.88443	−0.131614
$206$	0.987807	0.0688238
$207$	23.4623	1.63074
$208$	3.12877	0.216941
$209$	−10.5305	−0.728410
$210$	−0.410740	−0.0283438
$211$	−0.780721	−0.0537471	−0.0268735	−	0.999639i	$-0.508555\pi$
$211$	−0.780721	−0.0537471	−0.0268735	+	0.999639i	$0.508555\pi$
$212$	−4.36125	−0.299532
$213$	3.85517	0.264152
$214$	8.16510	0.558154
$215$	0.294580	0.0200902
$216$	−3.43938	−0.234020
$217$	−1.79326	−0.121734
$218$	2.03132	0.137578
$219$	−9.51224	−0.642778
$220$	−1.45297	−0.0979594
$221$	6.96928	0.468804
$222$	4.31917	0.289884
$223$	14.2711	0.955662	0.477831	−	0.878452i	$-0.341423\pi$
$223$	14.2711	0.955662	0.477831	+	0.878452i	$0.341423\pi$
$224$	0.772937	0.0516440
$225$	11.1469	0.743128
$226$	9.62883	0.640500
$227$	5.19982	0.345124	0.172562	−	0.984999i	$-0.444795\pi$
$227$	5.19982	0.345124	0.172562	+	0.984999i	$0.444795\pi$
$228$	−3.85137	−0.255063
$229$	15.5719	1.02902	0.514511	−	0.857484i	$-0.327974\pi$
$229$	15.5719	1.02902	0.514511	+	0.857484i	$0.327974\pi$
$230$	7.76590	0.512069
$231$	0.789754	0.0519620
$232$	−0.827311	−0.0543157
$233$	−18.2382	−1.19482	−0.597411	−	0.801935i	$-0.703804\pi$
$233$	−18.2382	−1.19482	−0.597411	+	0.801935i	$0.703804\pi$
$234$	−8.21711	−0.537169
$235$	4.69559	0.306307
$236$	2.57016	0.167303
$237$	−5.43519	−0.353053
$238$	1.72170	0.111601
$239$	5.98766	0.387309	0.193655	−	0.981070i	$-0.437966\pi$
$239$	5.98766	0.387309	0.193655	+	0.981070i	$0.437966\pi$
$240$	−0.531402	−0.0343019
$241$	−15.3978	−0.991859	−0.495929	−	0.868363i	$-0.665173\pi$
$241$	−15.3978	−0.991859	−0.495929	+	0.868363i	$0.665173\pi$
$242$	−8.20629	−0.527520
$243$	13.8493	0.888432
$244$	−5.61001	−0.359144
$245$	5.56571	0.355580
$246$	1.32517	0.0844896
$247$	−19.7120	−1.25425
$248$	−2.32006	−0.147324
$249$	−0.815005	−0.0516488
$250$	8.03604	0.508244
$251$	−21.9144	−1.38322	−0.691611	−	0.722270i	$-0.743099\pi$
$251$	−21.9144	−1.38322	−0.691611	+	0.722270i	$0.743099\pi$
$252$	−2.02997	−0.127876
$253$	−14.9319	−0.938763
$254$	−5.30494	−0.332861
$255$	−1.18369	−0.0741255
$256$	1.00000	0.0625000
$257$	0.290836	0.0181419	0.00907094	−	0.999959i	$-0.497113\pi$
$257$	0.290836	0.0181419	0.00907094	+	0.999959i	$0.497113\pi$
$258$	−0.207154	−0.0128969
$259$	5.46119	0.339342
$260$	−2.71982	−0.168676
$261$	2.17277	0.134491
$262$	−9.50668	−0.587325
$263$	−16.0806	−0.991573	−0.495787	−	0.868444i	$-0.665120\pi$
$263$	−16.0806	−0.991573	−0.495787	+	0.868444i	$0.665120\pi$
$264$	1.02176	0.0628848
$265$	3.79121	0.232892
$266$	−4.86970	−0.298580
$267$	−3.85780	−0.236093
$268$	12.2317	0.747168
$269$	16.5293	1.00781	0.503906	−	0.863759i	$-0.331896\pi$
$269$	16.5293	1.00781	0.503906	+	0.863759i	$0.331896\pi$
$270$	2.98983	0.181955
$271$	4.47796	0.272016	0.136008	−	0.990708i	$-0.456573\pi$
$271$	4.47796	0.272016	0.136008	+	0.990708i	$0.456573\pi$
$272$	2.22748	0.135061
$273$	1.47834	0.0894732
$274$	7.42404	0.448503
$275$	−7.09414	−0.427793
$276$	−5.46113	−0.328721
$277$	13.0721	0.785424	0.392712	−	0.919661i	$-0.371537\pi$
$277$	13.0721	0.785424	0.392712	+	0.919661i	$0.371537\pi$
$278$	2.41750	0.144992
$279$	6.09319	0.364790
$280$	−0.671909	−0.0401542
$281$	−5.69941	−0.339998	−0.169999	−	0.985444i	$-0.554377\pi$
$281$	−5.69941	−0.339998	−0.169999	+	0.985444i	$0.554377\pi$
$282$	−3.30203	−0.196633
$283$	−12.5389	−0.745362	−0.372681	−	0.927960i	$-0.621561\pi$
$283$	−12.5389	−0.745362	−0.372681	+	0.927960i	$0.621561\pi$
$284$	6.30648	0.374221
$285$	3.34797	0.198317
$286$	5.22955	0.309230
$287$	1.67555	0.0989047
$288$	−2.62631	−0.154757
$289$	−12.0383	−0.708136
$290$	0.719177	0.0422315
$291$	−3.61859	−0.212125
$292$	−15.5606	−0.910614
$293$	−6.94290	−0.405608	−0.202804	−	0.979219i	$-0.565006\pi$
$293$	−6.94290	−0.405608	−0.202804	+	0.979219i	$0.565006\pi$
$294$	−3.91391	−0.228264
$295$	−2.23422	−0.130081
$296$	7.06551	0.410675
$297$	−5.74872	−0.333575
$298$	−17.7242	−1.02674
$299$	−27.9511	−1.61645
$300$	−2.59457	−0.149798
$301$	−0.261927	−0.0150972
$302$	0.604095	0.0347618
$303$	−9.83759	−0.565155
$304$	−6.30025	−0.361344
$305$	4.87675	0.279242
$306$	−5.85006	−0.334425
$307$	1.76305	0.100623	0.0503113	−	0.998734i	$-0.483979\pi$
$307$	1.76305	0.100623	0.0503113	+	0.998734i	$0.483979\pi$
$308$	1.29192	0.0736138
$309$	0.603850	0.0343518
$310$	2.01681	0.114547
$311$	−2.41207	−0.136776	−0.0683881	−	0.997659i	$-0.521786\pi$
$311$	−2.41207	−0.136776	−0.0683881	+	0.997659i	$0.521786\pi$
$312$	1.91263	0.108281
$313$	−16.6605	−0.941705	−0.470853	−	0.882212i	$-0.656054\pi$
$313$	−16.6605	−0.941705	−0.470853	+	0.882212i	$0.656054\pi$
$314$	15.7348	0.887964
$315$	1.76464	0.0994262
$316$	−8.89115	−0.500166
$317$	9.60468	0.539453	0.269726	−	0.962937i	$-0.413067\pi$
$317$	9.60468	0.539453	0.269726	+	0.962937i	$0.413067\pi$
$318$	−2.66605	−0.149504
$319$	−1.38280	−0.0774220
$320$	−0.869294	−0.0485950
$321$	4.99135	0.278590
$322$	−6.90509	−0.384806
$323$	−14.0337	−0.780856
$324$	5.77642	0.320912
$325$	−13.2795	−0.736615
$326$	1.62611	0.0900618
$327$	1.24175	0.0686692
$328$	2.16777	0.119695
$329$	−4.17511	−0.230181
$330$	−0.888207	−0.0488942
$331$	−21.2126	−1.16595	−0.582976	−	0.812489i	$-0.698112\pi$
$331$	−21.2126	−1.16595	−0.582976	+	0.812489i	$0.698112\pi$
$332$	−1.33322	−0.0731702
$333$	−18.5562	−1.01687
$334$	8.60152	0.470654
$335$	−10.6329	−0.580938
$336$	0.472499	0.0257769
$337$	−26.2859	−1.43189	−0.715943	−	0.698158i	$-0.754003\pi$
$337$	−26.2859	−1.43189	−0.715943	+	0.698158i	$0.754003\pi$
$338$	−3.21081	−0.174645
$339$	5.88614	0.319691
$340$	−1.93634	−0.105013
$341$	−3.87784	−0.209997
$342$	16.5464	0.894727
$343$	−10.3593	−0.559352
$344$	−0.338873	−0.0182708
$345$	4.74732	0.255587
$346$	−15.1901	−0.816626
$347$	14.5989	0.783710	0.391855	−	0.920027i	$-0.371834\pi$
$347$	14.5989	0.783710	0.391855	+	0.920027i	$0.371834\pi$
$348$	−0.505738	−0.0271104
$349$	−17.5336	−0.938554	−0.469277	−	0.883051i	$-0.655486\pi$
$349$	−17.5336	−0.938554	−0.469277	+	0.883051i	$0.655486\pi$
$350$	−3.28060	−0.175355
$351$	−10.7610	−0.574381
$352$	1.67144	0.0890881
$353$	−5.35871	−0.285216	−0.142608	−	0.989779i	$-0.545549\pi$
$353$	−5.35871	−0.285216	−0.142608	+	0.989779i	$0.545549\pi$
$354$	1.57115	0.0835055
$355$	−5.48218	−0.290964
$356$	−6.31077	−0.334470
$357$	1.05248	0.0557033
$358$	6.78133	0.358405
$359$	−29.3033	−1.54657	−0.773283	−	0.634061i	$-0.781387\pi$
$359$	−29.3033	−1.54657	−0.773283	+	0.634061i	$0.781387\pi$
$360$	2.28303	0.120326
$361$	20.6932	1.08912
$362$	17.8098	0.936064
$363$	−5.01653	−0.263300
$364$	2.41834	0.126755
$365$	13.5267	0.708021
$366$	−3.42942	−0.179259
$367$	−16.1469	−0.842862	−0.421431	−	0.906861i	$-0.638472\pi$
$367$	−16.1469	−0.842862	−0.421431	+	0.906861i	$0.638472\pi$
$368$	−8.93358	−0.465695
$369$	−5.69324	−0.296378
$370$	−6.14200	−0.319308
$371$	−3.37097	−0.175012
$372$	−1.41826	−0.0735334
$373$	28.7159	1.48685	0.743426	−	0.668818i	$-0.233200\pi$
$373$	28.7159	1.48685	0.743426	+	0.668818i	$0.233200\pi$
$374$	3.72310	0.192517
$375$	4.91246	0.253678
$376$	−5.40162	−0.278567
$377$	−2.58847	−0.133313
$378$	−2.65842	−0.136735
$379$	26.5570	1.36414	0.682071	−	0.731286i	$-0.261079\pi$
$379$	26.5570	1.36414	0.682071	+	0.731286i	$0.261079\pi$
$380$	5.47677	0.280952
$381$	−3.24293	−0.166140
$382$	−8.70307	−0.445288
$383$	−16.1396	−0.824696	−0.412348	−	0.911026i	$-0.635291\pi$
$383$	−16.1396	−0.824696	−0.412348	+	0.911026i	$0.635291\pi$
$384$	0.611304	0.0311955
$385$	−1.12306	−0.0572362
$386$	−0.689269	−0.0350829
$387$	0.889985	0.0452405
$388$	−5.91946	−0.300515
$389$	−30.4342	−1.54308	−0.771538	−	0.636184i	$-0.780512\pi$
$389$	−30.4342	−1.54308	−0.771538	+	0.636184i	$0.780512\pi$
$390$	−1.66263	−0.0841908
$391$	−19.8994	−1.00636
$392$	−6.40257	−0.323379
$393$	−5.81147	−0.293150
$394$	−2.23811	−0.112755
$395$	7.72902	0.388889
$396$	−4.38972	−0.220592
$397$	9.28035	0.465767	0.232884	−	0.972505i	$-0.425184\pi$
$397$	9.28035	0.465767	0.232884	+	0.972505i	$0.425184\pi$
$398$	−2.43410	−0.122010
$399$	−2.97686	−0.149030
$400$	−4.24433	−0.212216
$401$	28.8875	1.44257	0.721286	−	0.692637i	$-0.243551\pi$
$401$	28.8875	1.44257	0.721286	+	0.692637i	$0.243551\pi$
$402$	7.47726	0.372932
$403$	−7.25893	−0.361593
$404$	−16.0928	−0.800647
$405$	−5.02140	−0.249516
$406$	−0.639459	−0.0317358
$407$	11.8096	0.585379
$408$	1.36167	0.0674126
$409$	−10.3549	−0.512016	−0.256008	−	0.966675i	$-0.582407\pi$
$409$	−10.3549	−0.512016	−0.256008	+	0.966675i	$0.582407\pi$
$410$	−1.88443	−0.0930655
$411$	4.53834	0.223860
$412$	0.987807	0.0486658
$413$	1.98657	0.0977527
$414$	23.4623	1.15311
$415$	1.15896	0.0568913
$416$	3.12877	0.153400
$417$	1.47783	0.0723695
$418$	−10.5305	−0.515063
$419$	14.6192	0.714193	0.357097	−	0.934067i	$-0.383767\pi$
$419$	14.6192	0.714193	0.357097	+	0.934067i	$0.383767\pi$
$420$	−0.410740	−0.0200421
$421$	3.11496	0.151814	0.0759070	−	0.997115i	$-0.475815\pi$
$421$	3.11496	0.151814	0.0759070	+	0.997115i	$0.475815\pi$
$422$	−0.780721	−0.0380049
$423$	14.1863	0.689762
$424$	−4.36125	−0.211801
$425$	−9.45417	−0.458595
$426$	3.85517	0.186784
$427$	−4.33618	−0.209843
$428$	8.16510	0.394675
$429$	3.19684	0.154345
$430$	0.294580	0.0142059
$431$	−18.8149	−0.906283	−0.453141	−	0.891439i	$-0.649697\pi$
$431$	−18.8149	−0.906283	−0.453141	+	0.891439i	$0.649697\pi$
$432$	−3.43938	−0.165477
$433$	3.04398	0.146284	0.0731422	−	0.997322i	$-0.476697\pi$
$433$	3.04398	0.146284	0.0731422	+	0.997322i	$0.476697\pi$
$434$	−1.79326	−0.0860792
$435$	0.439635	0.0210789
$436$	2.03132	0.0972827
$437$	56.2838	2.69242
$438$	−9.51224	−0.454512
$439$	16.6669	0.795466	0.397733	−	0.917501i	$-0.369797\pi$
$439$	16.6669	0.795466	0.397733	+	0.917501i	$0.369797\pi$
$440$	−1.45297	−0.0692677
$441$	16.8151	0.800720
$442$	6.96928	0.331495
$443$	25.4559	1.20945	0.604723	−	0.796436i	$-0.293284\pi$
$443$	25.4559	1.20945	0.604723	+	0.796436i	$0.293284\pi$
$444$	4.31917	0.204979
$445$	5.48591	0.260057
$446$	14.2711	0.675755
$447$	−10.8349	−0.512472
$448$	0.772937	0.0365178
$449$	12.3105	0.580970	0.290485	−	0.956880i	$-0.406183\pi$
$449$	12.3105	0.580970	0.290485	+	0.956880i	$0.406183\pi$
$450$	11.1469	0.525471
$451$	3.62331	0.170615
$452$	9.62883	0.452902
$453$	0.369286	0.0173505
$454$	5.19982	0.244040
$455$	−2.10225	−0.0985549
$456$	−3.85137	−0.180357
$457$	14.0330	0.656435	0.328217	−	0.944602i	$-0.393552\pi$
$457$	14.0330	0.656435	0.328217	+	0.944602i	$0.393552\pi$
$458$	15.5719	0.727628
$459$	−7.66116	−0.357593
$460$	7.76590	0.362087
$461$	−20.1070	−0.936476	−0.468238	−	0.883602i	$-0.655111\pi$
$461$	−20.1070	−0.936476	−0.468238	+	0.883602i	$0.655111\pi$
$462$	0.789754	0.0367427
$463$	−25.1593	−1.16925	−0.584625	−	0.811304i	$-0.698758\pi$
$463$	−25.1593	−1.16925	−0.584625	+	0.811304i	$0.698758\pi$
$464$	−0.827311	−0.0384070
$465$	1.23289	0.0571737
$466$	−18.2382	−0.844866
$467$	−33.3490	−1.54321	−0.771603	−	0.636105i	$-0.780545\pi$
$467$	−33.3490	−1.54321	−0.771603	+	0.636105i	$0.780545\pi$
$468$	−8.21711	−0.379836
$469$	9.45430	0.436559
$470$	4.69559	0.216592
$471$	9.61871	0.443207
$472$	2.57016	0.118301
$473$	−0.566406	−0.0260434
$474$	−5.43519	−0.249647
$475$	26.7403	1.22693
$476$	1.72170	0.0789141
$477$	11.4540	0.524442
$478$	5.98766	0.273869
$479$	−5.96274	−0.272444	−0.136222	−	0.990678i	$-0.543496\pi$
$479$	−5.96274	−0.272444	−0.136222	+	0.990678i	$0.543496\pi$
$480$	−0.531402	−0.0242551
$481$	22.1063	1.00796
$482$	−15.3978	−0.701350
$483$	−4.22111	−0.192067
$484$	−8.20629	−0.373013
$485$	5.14575	0.233656
$486$	13.8493	0.628217
$487$	−28.2516	−1.28020	−0.640101	−	0.768291i	$-0.721107\pi$
$487$	−28.2516	−1.28020	−0.640101	+	0.768291i	$0.721107\pi$
$488$	−5.61001	−0.253953
$489$	0.994046	0.0449523
$490$	5.56571	0.251433
$491$	−1.68569	−0.0760743	−0.0380372	−	0.999276i	$-0.512111\pi$
$491$	−1.68569	−0.0760743	−0.0380372	+	0.999276i	$0.512111\pi$
$492$	1.32517	0.0597432
$493$	−1.84282	−0.0829965
$494$	−19.7120	−0.886886
$495$	3.81595	0.171514
$496$	−2.32006	−0.104174
$497$	4.87451	0.218652
$498$	−0.815005	−0.0365212
$499$	30.5537	1.36777	0.683885	−	0.729589i	$-0.260289\pi$
$499$	30.5537	1.36777	0.683885	+	0.729589i	$0.260289\pi$
$500$	8.03604	0.359382
$501$	5.25814	0.234916
$502$	−21.9144	−0.978086
$503$	−32.4376	−1.44632	−0.723161	−	0.690680i	$-0.757311\pi$
$503$	−32.4376	−1.44632	−0.723161	+	0.690680i	$0.757311\pi$
$504$	−2.02997	−0.0904220
$505$	13.9894	0.622519
$506$	−14.9319	−0.663806
$507$	−1.96278	−0.0871701
$508$	−5.30494	−0.235368
$509$	11.1623	0.494762	0.247381	−	0.968918i	$-0.420430\pi$
$509$	11.1623	0.494762	0.247381	+	0.968918i	$0.420430\pi$
$510$	−1.18369	−0.0524147
$511$	−12.0273	−0.532058
$512$	1.00000	0.0441942
$513$	21.6690	0.956709
$514$	0.290836	0.0128282
$515$	−0.858694	−0.0378386
$516$	−0.207154	−0.00911946
$517$	−9.02848	−0.397072
$518$	5.46119	0.239951
$519$	−9.28578	−0.407601
$520$	−2.71982	−0.119272
$521$	24.7894	1.08604	0.543021	−	0.839719i	$-0.317280\pi$
$521$	24.7894	1.08604	0.543021	+	0.839719i	$0.317280\pi$
$522$	2.17277	0.0950998
$523$	−11.5170	−0.503602	−0.251801	−	0.967779i	$-0.581023\pi$
$523$	−11.5170	−0.503602	−0.251801	+	0.967779i	$0.581023\pi$
$524$	−9.50668	−0.415301
$525$	−2.00544	−0.0875246
$526$	−16.0806	−0.701148
$527$	−5.16789	−0.225117
$528$	1.02176	0.0444663
$529$	56.8088	2.46995
$530$	3.79121	0.164679
$531$	−6.75003	−0.292926
$532$	−4.86970	−0.211128
$533$	6.78246	0.293781
$534$	−3.85780	−0.166943
$535$	−7.09787	−0.306868
$536$	12.2317	0.528327
$537$	4.14545	0.178889
$538$	16.5293	0.712631
$539$	−10.7015	−0.460947
$540$	2.98983	0.128662
$541$	11.6928	0.502714	0.251357	−	0.967894i	$-0.419123\pi$
$541$	11.6928	0.502714	0.251357	+	0.967894i	$0.419123\pi$
$542$	4.47796	0.192345
$543$	10.8872	0.467215
$544$	2.22748	0.0955025
$545$	−1.76582	−0.0756392
$546$	1.47834	0.0632671
$547$	11.4571	0.489870	0.244935	−	0.969539i	$-0.421233\pi$
$547$	11.4571	0.489870	0.244935	+	0.969539i	$0.421233\pi$
$548$	7.42404	0.317139
$549$	14.7336	0.628815
$550$	−7.09414	−0.302495
$551$	5.21227	0.222050
$552$	−5.46113	−0.232441
$553$	−6.87229	−0.292240
$554$	13.0721	0.555379
$555$	−3.75463	−0.159375
$556$	2.41750	0.102525
$557$	5.89436	0.249752	0.124876	−	0.992172i	$-0.460147\pi$
$557$	5.89436	0.249752	0.124876	+	0.992172i	$0.460147\pi$
$558$	6.09319	0.257945
$559$	−1.06025	−0.0448440
$560$	−0.671909	−0.0283933
$561$	2.27595	0.0960905
$562$	−5.69941	−0.240415
$563$	29.0505	1.22433	0.612167	−	0.790729i	$-0.290298\pi$
$563$	29.0505	1.22433	0.612167	+	0.790729i	$0.290298\pi$
$564$	−3.30203	−0.139040
$565$	−8.37028	−0.352140
$566$	−12.5389	−0.527050
$567$	4.46480	0.187504
$568$	6.30648	0.264614
$569$	−29.0772	−1.21898	−0.609489	−	0.792794i	$-0.708625\pi$
$569$	−29.0772	−1.21898	−0.609489	+	0.792794i	$0.708625\pi$
$570$	3.34797	0.140231
$571$	4.90129	0.205113	0.102556	−	0.994727i	$-0.467298\pi$
$571$	4.90129	0.205113	0.102556	+	0.994727i	$0.467298\pi$
$572$	5.22955	0.218658
$573$	−5.32022	−0.222255
$574$	1.67555	0.0699362
$575$	37.9170	1.58125
$576$	−2.62631	−0.109429
$577$	39.3425	1.63785	0.818925	−	0.573901i	$-0.194570\pi$
$577$	39.3425	1.63785	0.818925	+	0.573901i	$0.194570\pi$
$578$	−12.0383	−0.500728
$579$	−0.421353	−0.0175108
$580$	0.719177	0.0298622
$581$	−1.03050	−0.0427523
$582$	−3.61859	−0.149995
$583$	−7.28957	−0.301903
$584$	−15.5606	−0.643902
$585$	7.14308	0.295330
$586$	−6.94290	−0.286809
$587$	44.5552	1.83899	0.919495	−	0.393102i	$-0.128598\pi$
$587$	44.5552	1.83899	0.919495	+	0.393102i	$0.128598\pi$
$588$	−3.91391	−0.161407
$589$	14.6170	0.602282
$590$	−2.23422	−0.0919815
$591$	−1.36817	−0.0562789
$592$	7.06551	0.290391
$593$	33.2660	1.36607	0.683035	−	0.730386i	$-0.260660\pi$
$593$	33.2660	1.36607	0.683035	+	0.730386i	$0.260660\pi$
$594$	−5.74872	−0.235873
$595$	−1.49667	−0.0613573
$596$	−17.7242	−0.726013
$597$	−1.48797	−0.0608988
$598$	−27.9511	−1.14301
$599$	33.6691	1.37568	0.687841	−	0.725861i	$-0.258559\pi$
$599$	33.6691	1.37568	0.687841	+	0.725861i	$0.258559\pi$
$600$	−2.59457	−0.105923
$601$	−35.8907	−1.46401	−0.732007	−	0.681297i	$-0.761416\pi$
$601$	−35.8907	−1.46401	−0.732007	+	0.681297i	$0.761416\pi$
$602$	−0.261927	−0.0106754
$603$	−32.1241	−1.30819
$604$	0.604095	0.0245803
$605$	7.13367	0.290025
$606$	−9.83759	−0.399625
$607$	12.2823	0.498523	0.249262	−	0.968436i	$-0.419812\pi$
$607$	12.2823	0.498523	0.249262	+	0.968436i	$0.419812\pi$
$608$	−6.30025	−0.255509
$609$	−0.390904	−0.0158402
$610$	4.87675	0.197454
$611$	−16.9004	−0.683717
$612$	−5.85006	−0.236474
$613$	5.89193	0.237973	0.118986	−	0.992896i	$-0.462036\pi$
$613$	5.89193	0.237973	0.118986	+	0.992896i	$0.462036\pi$
$614$	1.76305	0.0711510
$615$	−1.15196	−0.0464515
$616$	1.29192	0.0520528
$617$	−20.9205	−0.842226	−0.421113	−	0.907008i	$-0.638360\pi$
$617$	−20.9205	−0.842226	−0.421113	+	0.907008i	$0.638360\pi$
$618$	0.603850	0.0242904
$619$	−4.97926	−0.200134	−0.100067	−	0.994981i	$-0.531906\pi$
$619$	−4.97926	−0.200134	−0.100067	+	0.994981i	$0.531906\pi$
$620$	2.01681	0.0809972
$621$	30.7260	1.23299
$622$	−2.41207	−0.0967154
$623$	−4.87783	−0.195426
$624$	1.91263	0.0765664
$625$	14.2360	0.569439
$626$	−16.6605	−0.665886
$627$	−6.43733	−0.257082
$628$	15.7348	0.627885
$629$	15.7383	0.627527
$630$	1.76464	0.0703049
$631$	2.46799	0.0982489	0.0491245	−	0.998793i	$-0.484357\pi$
$631$	2.46799	0.0982489	0.0491245	+	0.998793i	$0.484357\pi$
$632$	−8.89115	−0.353671
$633$	−0.477258	−0.0189693
$634$	9.60468	0.381451
$635$	4.61155	0.183004
$636$	−2.66605	−0.105716
$637$	−20.0322	−0.793703
$638$	−1.38280	−0.0547456
$639$	−16.5628	−0.655212
$640$	−0.869294	−0.0343618
$641$	−35.2998	−1.39426	−0.697129	−	0.716946i	$-0.745539\pi$
$641$	−35.2998	−1.39426	−0.697129	+	0.716946i	$0.745539\pi$
$642$	4.99135	0.196993
$643$	20.0940	0.792430	0.396215	−	0.918158i	$-0.370323\pi$
$643$	20.0940	0.792430	0.396215	+	0.918158i	$0.370323\pi$
$644$	−6.90509	−0.272099
$645$	0.180078	0.00709056
$646$	−14.0337	−0.552149
$647$	20.8727	0.820590	0.410295	−	0.911953i	$-0.365426\pi$
$647$	20.8727	0.820590	0.410295	+	0.911953i	$0.365426\pi$
$648$	5.77642	0.226919
$649$	4.29586	0.168627
$650$	−13.2795	−0.520866
$651$	−1.09623	−0.0429645
$652$	1.62611	0.0636833
$653$	−25.3802	−0.993204	−0.496602	−	0.867978i	$-0.665419\pi$
$653$	−25.3802	−0.993204	−0.496602	+	0.867978i	$0.665419\pi$
$654$	1.24175	0.0485564
$655$	8.26410	0.322905
$656$	2.16777	0.0846374
$657$	40.8669	1.59437
$658$	−4.17511	−0.162763
$659$	−23.1687	−0.902524	−0.451262	−	0.892391i	$-0.649026\pi$
$659$	−23.1687	−0.902524	−0.451262	+	0.892391i	$0.649026\pi$
$660$	−0.888207	−0.0345734
$661$	−25.9524	−1.00943	−0.504716	−	0.863285i	$-0.668403\pi$
$661$	−25.9524	−1.00943	−0.504716	+	0.863285i	$0.668403\pi$
$662$	−21.2126	−0.824452
$663$	4.26034	0.165458
$664$	−1.33322	−0.0517391
$665$	4.23320	0.164156
$666$	−18.5562	−0.719039
$667$	7.39085	0.286175
$668$	8.60152	0.332803
$669$	8.72396	0.337288
$670$	−10.6329	−0.410785
$671$	−9.37680	−0.361987
$672$	0.472499	0.0182270
$673$	19.8769	0.766197	0.383098	−	0.923708i	$-0.374857\pi$
$673$	19.8769	0.766197	0.383098	+	0.923708i	$0.374857\pi$
$674$	−26.2859	−1.01250
$675$	14.5979	0.561872
$676$	−3.21081	−0.123493
$677$	−9.75565	−0.374940	−0.187470	−	0.982270i	$-0.560029\pi$
$677$	−9.75565	−0.374940	−0.187470	+	0.982270i	$0.560029\pi$
$678$	5.88614	0.226056
$679$	−4.57537	−0.175586
$680$	−1.93634	−0.0742551
$681$	3.17867	0.121807
$682$	−3.87784	−0.148490
$683$	17.5961	0.673296	0.336648	−	0.941630i	$-0.390707\pi$
$683$	17.5961	0.673296	0.336648	+	0.941630i	$0.390707\pi$
$684$	16.5464	0.632668
$685$	−6.45367	−0.246582
$686$	−10.3593	−0.395521
$687$	9.51917	0.363179
$688$	−0.338873	−0.0129194
$689$	−13.6453	−0.519846
$690$	4.74732	0.180728
$691$	33.9434	1.29127	0.645634	−	0.763647i	$-0.276593\pi$
$691$	33.9434	1.29127	0.645634	+	0.763647i	$0.276593\pi$
$692$	−15.1901	−0.577442
$693$	−3.39297	−0.128888
$694$	14.5989	0.554166
$695$	−2.10152	−0.0797151
$696$	−0.505738	−0.0191700
$697$	4.82868	0.182899
$698$	−17.5336	−0.663658
$699$	−11.1491	−0.421696
$700$	−3.28060	−0.123995
$701$	11.0162	0.416078	0.208039	−	0.978121i	$-0.433292\pi$
$701$	11.0162	0.416078	0.208039	+	0.978121i	$0.433292\pi$
$702$	−10.7610	−0.406149
$703$	−44.5145	−1.67890
$704$	1.67144	0.0629948
$705$	2.87043	0.108107
$706$	−5.35871	−0.201678
$707$	−12.4387	−0.467806
$708$	1.57115	0.0590473
$709$	7.27084	0.273062	0.136531	−	0.990636i	$-0.456405\pi$
$709$	7.27084	0.273062	0.136531	+	0.990636i	$0.456405\pi$
$710$	−5.48218	−0.205743
$711$	23.3509	0.875727
$712$	−6.31077	−0.236506
$713$	20.7264	0.776211
$714$	1.05248	0.0393882
$715$	−4.54601	−0.170011
$716$	6.78133	0.253430
$717$	3.66028	0.136695
$718$	−29.3033	−1.09359
$719$	27.1015	1.01071	0.505357	−	0.862910i	$-0.331361\pi$
$719$	27.1015	1.01071	0.505357	+	0.862910i	$0.331361\pi$
$720$	2.28303	0.0850836
$721$	0.763512	0.0284347
$722$	20.6932	0.770121
$723$	−9.41272	−0.350063
$724$	17.8098	0.661897
$725$	3.51138	0.130409
$726$	−5.01653	−0.186181
$727$	46.0059	1.70626	0.853131	−	0.521696i	$-0.174700\pi$
$727$	46.0059	1.70626	0.853131	+	0.521696i	$0.174700\pi$
$728$	2.41834	0.0896296
$729$	−8.86313	−0.328264
$730$	13.5267	0.500646
$731$	−0.754834	−0.0279185
$732$	−3.42942	−0.126755
$733$	14.7938	0.546422	0.273211	−	0.961954i	$-0.411914\pi$
$733$	14.7938	0.546422	0.273211	+	0.961954i	$0.411914\pi$
$734$	−16.1469	−0.595993
$735$	3.40234	0.125497
$736$	−8.93358	−0.329296
$737$	20.4445	0.753082
$738$	−5.69324	−0.209571
$739$	−0.0764120	−0.00281086	−0.00140543	−	0.999999i	$-0.500447\pi$
$739$	−0.0764120	−0.00281086	−0.00140543	+	0.999999i	$0.500447\pi$
$740$	−6.14200	−0.225785
$741$	−12.0500	−0.442669
$742$	−3.37097	−0.123752
$743$	4.63763	0.170138	0.0850691	−	0.996375i	$-0.472889\pi$
$743$	4.63763	0.170138	0.0850691	+	0.996375i	$0.472889\pi$
$744$	−1.41826	−0.0519960
$745$	15.4076	0.564489
$746$	28.7159	1.05136
$747$	3.50146	0.128112
$748$	3.72310	0.136130
$749$	6.31110	0.230603
$750$	4.91246	0.179378
$751$	−48.7564	−1.77915	−0.889573	−	0.456793i	$-0.848998\pi$
$751$	−48.7564	−1.77915	−0.889573	+	0.456793i	$0.848998\pi$
$752$	−5.40162	−0.196977
$753$	−13.3963	−0.488189
$754$	−2.58847	−0.0942664
$755$	−0.525136	−0.0191117
$756$	−2.65842	−0.0966860
$757$	−14.0424	−0.510378	−0.255189	−	0.966891i	$-0.582138\pi$
$757$	−14.0424	−0.510378	−0.255189	+	0.966891i	$0.582138\pi$
$758$	26.5570	0.964595
$759$	−9.12795	−0.331324
$760$	5.47677	0.198663
$761$	6.60839	0.239554	0.119777	−	0.992801i	$-0.461782\pi$
$761$	6.60839	0.239554	0.119777	+	0.992801i	$0.461782\pi$
$762$	−3.24293	−0.117479
$763$	1.57008	0.0568408
$764$	−8.70307	−0.314866
$765$	5.08542	0.183864
$766$	−16.1396	−0.583148
$767$	8.04143	0.290359
$768$	0.611304	0.0220585
$769$	10.9735	0.395715	0.197857	−	0.980231i	$-0.436602\pi$
$769$	10.9735	0.395715	0.197857	+	0.980231i	$0.436602\pi$
$770$	−1.12306	−0.0404721
$771$	0.177789	0.00640293
$772$	−0.689269	−0.0248073
$773$	28.7668	1.03467	0.517335	−	0.855783i	$-0.326924\pi$
$773$	28.7668	1.03467	0.517335	+	0.855783i	$0.326924\pi$
$774$	0.889985	0.0319898
$775$	9.84710	0.353718
$776$	−5.91946	−0.212496
$777$	3.33845	0.119766
$778$	−30.4342	−1.09112
$779$	−13.6575	−0.489332
$780$	−1.66263	−0.0595319
$781$	10.5409	0.377183
$782$	−19.8994	−0.711601
$783$	2.84544	0.101688
$784$	−6.40257	−0.228663
$785$	−13.6781	−0.488193
$786$	−5.81147	−0.207288
$787$	11.2159	0.399805	0.199902	−	0.979816i	$-0.435937\pi$
$787$	11.2159	0.399805	0.199902	+	0.979816i	$0.435937\pi$
$788$	−2.23811	−0.0797295
$789$	−9.83014	−0.349962
$790$	7.72902	0.274986
$791$	7.44248	0.264624
$792$	−4.38972	−0.155982
$793$	−17.5524	−0.623305
$794$	9.28035	0.329347
$795$	2.31758	0.0821960
$796$	−2.43410	−0.0862744
$797$	−36.5525	−1.29476	−0.647378	−	0.762169i	$-0.724135\pi$
$797$	−36.5525	−1.29476	−0.647378	+	0.762169i	$0.724135\pi$
$798$	−2.97686	−0.105380
$799$	−12.0320	−0.425662
$800$	−4.24433	−0.150060
$801$	16.5740	0.585615
$802$	28.8875	1.02005
$803$	−26.0086	−0.917823
$804$	7.47726	0.263703
$805$	6.00255	0.211562
$806$	−7.25893	−0.255685
$807$	10.1044	0.355693
$808$	−16.0928	−0.566143
$809$	−5.74757	−0.202074	−0.101037	−	0.994883i	$-0.532216\pi$
$809$	−5.74757	−0.202074	−0.101037	+	0.994883i	$0.532216\pi$
$810$	−5.02140	−0.176434
$811$	42.8951	1.50625	0.753125	−	0.657877i	$-0.228545\pi$
$811$	42.8951	1.50625	0.753125	+	0.657877i	$0.228545\pi$
$812$	−0.639459	−0.0224406
$813$	2.73739	0.0960045
$814$	11.8096	0.413926
$815$	−1.41357	−0.0495151
$816$	1.36167	0.0476679
$817$	2.13499	0.0746937
$818$	−10.3549	−0.362050
$819$	−6.35130	−0.221933
$820$	−1.88443	−0.0658072
$821$	−9.53222	−0.332677	−0.166338	−	0.986069i	$-0.553194\pi$
$821$	−9.53222	−0.332677	−0.166338	+	0.986069i	$0.553194\pi$
$822$	4.53834	0.158293
$823$	−35.7384	−1.24576	−0.622880	−	0.782317i	$-0.714038\pi$
$823$	−35.7384	−1.24576	−0.622880	+	0.782317i	$0.714038\pi$
$824$	0.987807	0.0344119
$825$	−4.33667	−0.150984
$826$	1.98657	0.0691216
$827$	−25.0647	−0.871586	−0.435793	−	0.900047i	$-0.643532\pi$
$827$	−25.0647	−0.871586	−0.435793	+	0.900047i	$0.643532\pi$
$828$	23.4623	0.815372
$829$	7.40283	0.257111	0.128556	−	0.991702i	$-0.458966\pi$
$829$	7.40283	0.257111	0.128556	+	0.991702i	$0.458966\pi$
$830$	1.15896	0.0402282
$831$	7.99100	0.277205
$832$	3.12877	0.108471
$833$	−14.2616	−0.494136
$834$	1.47783	0.0511730
$835$	−7.47725	−0.258761
$836$	−10.5305	−0.364205
$837$	7.97957	0.275814
$838$	14.6192	0.505011
$839$	4.74666	0.163873	0.0819364	−	0.996638i	$-0.473890\pi$
$839$	4.74666	0.163873	0.0819364	+	0.996638i	$0.473890\pi$
$840$	−0.410740	−0.0141719
$841$	−28.3156	−0.976398
$842$	3.11496	0.107349
$843$	−3.48407	−0.119998
$844$	−0.780721	−0.0268735
$845$	2.79114	0.0960180
$846$	14.1863	0.487735
$847$	−6.34294	−0.217946
$848$	−4.36125	−0.149766
$849$	−7.66509	−0.263065
$850$	−9.45417	−0.324275
$851$	−63.1203	−2.16374
$852$	3.85517	0.132076
$853$	15.7152	0.538078	0.269039	−	0.963129i	$-0.413294\pi$
$853$	15.7152	0.538078	0.269039	+	0.963129i	$0.413294\pi$
$854$	−4.33618	−0.148381
$855$	−14.3837	−0.491912
$856$	8.16510	0.279077
$857$	−16.9704	−0.579696	−0.289848	−	0.957073i	$-0.593605\pi$
$857$	−16.9704	−0.579696	−0.289848	+	0.957073i	$0.593605\pi$
$858$	3.19684	0.109138
$859$	−6.46317	−0.220521	−0.110260	−	0.993903i	$-0.535168\pi$
$859$	−6.46317	−0.220521	−0.110260	+	0.993903i	$0.535168\pi$
$860$	0.294580	0.0100451
$861$	1.02427	0.0349071
$862$	−18.8149	−0.640839
$863$	25.4507	0.866353	0.433177	−	0.901309i	$-0.357393\pi$
$863$	25.4507	0.866353	0.433177	+	0.901309i	$0.357393\pi$
$864$	−3.43938	−0.117010
$865$	13.2047	0.448973
$866$	3.04398	0.103439
$867$	−7.35907	−0.249927
$868$	−1.79326	−0.0608672
$869$	−14.8610	−0.504126
$870$	0.439635	0.0149050
$871$	38.2700	1.29673
$872$	2.03132	0.0687892
$873$	15.5463	0.526163
$874$	56.2838	1.90383
$875$	6.21135	0.209982
$876$	−9.51224	−0.321389
$877$	8.94191	0.301947	0.150973	−	0.988538i	$-0.451759\pi$
$877$	8.94191	0.301947	0.150973	+	0.988538i	$0.451759\pi$
$878$	16.6669	0.562480
$879$	−4.24422	−0.143154
$880$	−1.45297	−0.0489797
$881$	−40.3803	−1.36045	−0.680223	−	0.733005i	$-0.738117\pi$
$881$	−40.3803	−1.36045	−0.680223	+	0.733005i	$0.738117\pi$
$882$	16.8151	0.566194
$883$	50.2961	1.69260	0.846299	−	0.532708i	$-0.178826\pi$
$883$	50.2961	1.69260	0.846299	+	0.532708i	$0.178826\pi$
$884$	6.96928	0.234402
$885$	−1.36579	−0.0459105
$886$	25.4559	0.855208
$887$	6.17802	0.207438	0.103719	−	0.994607i	$-0.466926\pi$
$887$	6.17802	0.207438	0.103719	+	0.994607i	$0.466926\pi$
$888$	4.31917	0.144942
$889$	−4.10038	−0.137522
$890$	5.48591	0.183888
$891$	9.65494	0.323453
$892$	14.2711	0.477831
$893$	34.0316	1.13882
$894$	−10.8349	−0.362373
$895$	−5.89497	−0.197047
$896$	0.772937	0.0258220
$897$	−17.0866	−0.570505
$898$	12.3105	0.410808
$899$	1.91941	0.0640160
$900$	11.1469	0.371564
$901$	−9.71461	−0.323640
$902$	3.62331	0.120643
$903$	−0.160117	−0.00532836
$904$	9.62883	0.320250
$905$	−15.4820	−0.514638
$906$	0.369286	0.0122687
$907$	22.7591	0.755703	0.377852	−	0.925866i	$-0.376663\pi$
$907$	22.7591	0.755703	0.377852	+	0.925866i	$0.376663\pi$
$908$	5.19982	0.172562
$909$	42.2647	1.40183
$910$	−2.10225	−0.0696888
$911$	−0.630238	−0.0208807	−0.0104404	−	0.999945i	$-0.503323\pi$
$911$	−0.630238	−0.0208807	−0.0104404	+	0.999945i	$0.503323\pi$
$912$	−3.85137	−0.127532
$913$	−2.22840	−0.0737494
$914$	14.0330	0.464169
$915$	2.98117	0.0985545
$916$	15.5719	0.514511
$917$	−7.34806	−0.242654
$918$	−7.66116	−0.252856
$919$	−40.6875	−1.34216	−0.671079	−	0.741386i	$-0.734169\pi$
$919$	−40.6875	−1.34216	−0.671079	+	0.741386i	$0.734169\pi$
$920$	7.76590	0.256034
$921$	1.07776	0.0355134
$922$	−20.1070	−0.662189
$923$	19.7315	0.649470
$924$	0.789754	0.0259810
$925$	−29.9884	−0.986011
$926$	−25.1593	−0.826784
$927$	−2.59429	−0.0852075
$928$	−0.827311	−0.0271578
$929$	20.4801	0.671931	0.335966	−	0.941874i	$-0.390937\pi$
$929$	20.4801	0.671931	0.335966	+	0.941874i	$0.390937\pi$
$930$	1.23289	0.0404279
$931$	40.3378	1.32202
$932$	−18.2382	−0.597411
$933$	−1.47451	−0.0482733
$934$	−33.3490	−1.09121
$935$	−3.23647	−0.105844
$936$	−8.21711	−0.268585
$937$	−35.3448	−1.15466	−0.577332	−	0.816510i	$-0.695906\pi$
$937$	−35.3448	−1.15466	−0.577332	+	0.816510i	$0.695906\pi$
$938$	9.45430	0.308694
$939$	−10.1846	−0.332362
$940$	4.69559	0.153153
$941$	−39.6173	−1.29149	−0.645744	−	0.763554i	$-0.723453\pi$
$941$	−39.6173	−1.29149	−0.645744	+	0.763554i	$0.723453\pi$
$942$	9.61871	0.313395
$943$	−19.3660	−0.630643
$944$	2.57016	0.0836515
$945$	2.31095	0.0751753
$946$	−0.566406	−0.0184154
$947$	7.97338	0.259100	0.129550	−	0.991573i	$-0.458647\pi$
$947$	7.97338	0.259100	0.129550	+	0.991573i	$0.458647\pi$
$948$	−5.43519	−0.176527
$949$	−48.6855	−1.58040
$950$	26.7403	0.867571
$951$	5.87138	0.190392
$952$	1.72170	0.0558007
$953$	−42.2547	−1.36877	−0.684383	−	0.729123i	$-0.739928\pi$
$953$	−42.2547	−1.36877	−0.684383	+	0.729123i	$0.739928\pi$
$954$	11.4540	0.370836
$955$	7.56552	0.244815
$956$	5.98766	0.193655
$957$	−0.845311	−0.0273250
$958$	−5.96274	−0.192647
$959$	5.73832	0.185300
$960$	−0.531402	−0.0171509
$961$	−25.6173	−0.826365
$962$	22.1063	0.712737
$963$	−21.4441	−0.691025
$964$	−15.3978	−0.495929
$965$	0.599177	0.0192882
$966$	−4.22111	−0.135812
$967$	41.4516	1.33299	0.666496	−	0.745508i	$-0.267793\pi$
$967$	41.4516	1.33299	0.666496	+	0.745508i	$0.267793\pi$
$968$	−8.20629	−0.263760
$969$	−8.57886	−0.275593
$970$	5.14575	0.165220
$971$	−41.9954	−1.34770	−0.673848	−	0.738870i	$-0.735360\pi$
$971$	−41.9954	−1.34770	−0.673848	+	0.738870i	$0.735360\pi$
$972$	13.8493	0.444216
$973$	1.86858	0.0599038
$974$	−28.2516	−0.905239
$975$	−8.11782	−0.259978
$976$	−5.61001	−0.179572
$977$	13.2701	0.424549	0.212275	−	0.977210i	$-0.431913\pi$
$977$	13.2701	0.424549	0.212275	+	0.977210i	$0.431913\pi$
$978$	0.994046	0.0317861
$979$	−10.5481	−0.337118
$980$	5.56571	0.177790
$981$	−5.33488	−0.170330
$982$	−1.68569	−0.0537927
$983$	33.8490	1.07962	0.539808	−	0.841788i	$-0.318497\pi$
$983$	33.8490	1.07962	0.539808	+	0.841788i	$0.318497\pi$
$984$	1.32517	0.0422448
$985$	1.94558	0.0619913
$986$	−1.84282	−0.0586874
$987$	−2.55226	−0.0812393
$988$	−19.7120	−0.627123
$989$	3.02735	0.0962641
$990$	3.81595	0.121279
$991$	−40.9591	−1.30111	−0.650554	−	0.759460i	$-0.725463\pi$
$991$	−40.9591	−1.30111	−0.650554	+	0.759460i	$0.725463\pi$
$992$	−2.32006	−0.0736620
$993$	−12.9674	−0.411507
$994$	4.87451	0.154610
$995$	2.11595	0.0670801
$996$	−0.815005	−0.0258244
$997$	47.6475	1.50901	0.754506	−	0.656293i	$-0.227876\pi$
$997$	47.6475	1.50901	0.754506	+	0.656293i	$0.227876\pi$
$998$	30.5537	0.967160
$999$	−24.3010	−0.768849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.44	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.44	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.611304 q^{3} +1.00000 q^{4} -0.869294 q^{5} +0.611304 q^{6} +0.772937 q^{7} +1.00000 q^{8} -2.62631 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.611304 q^{3} +1.00000 q^{4} -0.869294 q^{5} +0.611304 q^{6} +0.772937 q^{7} +1.00000 q^{8} -2.62631 q^{9} -0.869294 q^{10} +1.67144 q^{11} +0.611304 q^{12} +3.12877 q^{13} +0.772937 q^{14} -0.531402 q^{15} +1.00000 q^{16} +2.22748 q^{17} -2.62631 q^{18} -6.30025 q^{19} -0.869294 q^{20} +0.472499 q^{21} +1.67144 q^{22} -8.93358 q^{23} +0.611304 q^{24} -4.24433 q^{25} +3.12877 q^{26} -3.43938 q^{27} +0.772937 q^{28} -0.827311 q^{29} -0.531402 q^{30} -2.32006 q^{31} +1.00000 q^{32} +1.02176 q^{33} +2.22748 q^{34} -0.671909 q^{35} -2.62631 q^{36} +7.06551 q^{37} -6.30025 q^{38} +1.91263 q^{39} -0.869294 q^{40} +2.16777 q^{41} +0.472499 q^{42} -0.338873 q^{43} +1.67144 q^{44} +2.28303 q^{45} -8.93358 q^{46} -5.40162 q^{47} +0.611304 q^{48} -6.40257 q^{49} -4.24433 q^{50} +1.36167 q^{51} +3.12877 q^{52} -4.36125 q^{53} -3.43938 q^{54} -1.45297 q^{55} +0.772937 q^{56} -3.85137 q^{57} -0.827311 q^{58} +2.57016 q^{59} -0.531402 q^{60} -5.61001 q^{61} -2.32006 q^{62} -2.02997 q^{63} +1.00000 q^{64} -2.71982 q^{65} +1.02176 q^{66} +12.2317 q^{67} +2.22748 q^{68} -5.46113 q^{69} -0.671909 q^{70} +6.30648 q^{71} -2.62631 q^{72} -15.5606 q^{73} +7.06551 q^{74} -2.59457 q^{75} -6.30025 q^{76} +1.29192 q^{77} +1.91263 q^{78} -8.89115 q^{79} -0.869294 q^{80} +5.77642 q^{81} +2.16777 q^{82} -1.33322 q^{83} +0.472499 q^{84} -1.93634 q^{85} -0.338873 q^{86} -0.505738 q^{87} +1.67144 q^{88} -6.31077 q^{89} +2.28303 q^{90} +2.41834 q^{91} -8.93358 q^{92} -1.41826 q^{93} -5.40162 q^{94} +5.47677 q^{95} +0.611304 q^{96} -5.91946 q^{97} -6.40257 q^{98} -4.38972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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