LMFDB - Embedded newform 4034.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.423572 q^{3} +1.00000 q^{4} -0.487122 q^{5} -0.423572 q^{6} +2.40385 q^{7} +1.00000 q^{8} -2.82059 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.423572 q^{3} +1.00000 q^{4} -0.487122 q^{5} -0.423572 q^{6} +2.40385 q^{7} +1.00000 q^{8} -2.82059 q^{9} -0.487122 q^{10} +1.38245 q^{11} -0.423572 q^{12} -1.29945 q^{13} +2.40385 q^{14} +0.206331 q^{15} +1.00000 q^{16} -2.88437 q^{17} -2.82059 q^{18} +0.654438 q^{19} -0.487122 q^{20} -1.01820 q^{21} +1.38245 q^{22} -8.21328 q^{23} -0.423572 q^{24} -4.76271 q^{25} -1.29945 q^{26} +2.46544 q^{27} +2.40385 q^{28} +4.28186 q^{29} +0.206331 q^{30} -10.7659 q^{31} +1.00000 q^{32} -0.585566 q^{33} -2.88437 q^{34} -1.17097 q^{35} -2.82059 q^{36} -8.21314 q^{37} +0.654438 q^{38} +0.550409 q^{39} -0.487122 q^{40} -0.313899 q^{41} -1.01820 q^{42} +4.40071 q^{43} +1.38245 q^{44} +1.37397 q^{45} -8.21328 q^{46} -5.56192 q^{47} -0.423572 q^{48} -1.22152 q^{49} -4.76271 q^{50} +1.22174 q^{51} -1.29945 q^{52} +8.99732 q^{53} +2.46544 q^{54} -0.673421 q^{55} +2.40385 q^{56} -0.277201 q^{57} +4.28186 q^{58} +0.393777 q^{59} +0.206331 q^{60} +8.49444 q^{61} -10.7659 q^{62} -6.78026 q^{63} +1.00000 q^{64} +0.632989 q^{65} -0.585566 q^{66} +3.95326 q^{67} -2.88437 q^{68} +3.47891 q^{69} -1.17097 q^{70} +0.756879 q^{71} -2.82059 q^{72} -9.00288 q^{73} -8.21314 q^{74} +2.01735 q^{75} +0.654438 q^{76} +3.32320 q^{77} +0.550409 q^{78} +10.9266 q^{79} -0.487122 q^{80} +7.41747 q^{81} -0.313899 q^{82} -10.0973 q^{83} -1.01820 q^{84} +1.40504 q^{85} +4.40071 q^{86} -1.81367 q^{87} +1.38245 q^{88} -12.2322 q^{89} +1.37397 q^{90} -3.12368 q^{91} -8.21328 q^{92} +4.56015 q^{93} -5.56192 q^{94} -0.318791 q^{95} -0.423572 q^{96} +16.8496 q^{97} -1.22152 q^{98} -3.89932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−0.423572	−0.244549	−0.122275	−	0.992496i	$-0.539019\pi$
$3$	−0.423572	−0.244549	−0.122275	+	0.992496i	$0.539019\pi$
$4$	1.00000	0.500000
$5$	−0.487122	−0.217847	−0.108924	−	0.994050i	$-0.534740\pi$
$5$	−0.487122	−0.217847	−0.108924	+	0.994050i	$0.534740\pi$
$6$	−0.423572	−0.172922
$7$	2.40385	0.908569	0.454285	−	0.890857i	$-0.349895\pi$
$7$	2.40385	0.908569	0.454285	+	0.890857i	$0.349895\pi$
$8$	1.00000	0.353553
$9$	−2.82059	−0.940196
$10$	−0.487122	−0.154041
$11$	1.38245	0.416824	0.208412	−	0.978041i	$-0.433171\pi$
$11$	1.38245	0.416824	0.208412	+	0.978041i	$0.433171\pi$
$12$	−0.423572	−0.122275
$13$	−1.29945	−0.360402	−0.180201	−	0.983630i	$-0.557675\pi$
$13$	−1.29945	−0.360402	−0.180201	+	0.983630i	$0.557675\pi$
$14$	2.40385	0.642455
$15$	0.206331	0.0532744
$16$	1.00000	0.250000
$17$	−2.88437	−0.699562	−0.349781	−	0.936832i	$-0.613744\pi$
$17$	−2.88437	−0.699562	−0.349781	+	0.936832i	$0.613744\pi$
$18$	−2.82059	−0.664819
$19$	0.654438	0.150138	0.0750692	−	0.997178i	$-0.476082\pi$
$19$	0.654438	0.150138	0.0750692	+	0.997178i	$0.476082\pi$
$20$	−0.487122	−0.108924
$21$	−1.01820	−0.222190
$22$	1.38245	0.294739
$23$	−8.21328	−1.71259	−0.856293	−	0.516490i	$-0.827238\pi$
$23$	−8.21328	−1.71259	−0.856293	+	0.516490i	$0.827238\pi$
$24$	−0.423572	−0.0864612
$25$	−4.76271	−0.952543
$26$	−1.29945	−0.254843
$27$	2.46544	0.474473
$28$	2.40385	0.454285
$29$	4.28186	0.795121	0.397560	−	0.917576i	$-0.369857\pi$
$29$	4.28186	0.795121	0.397560	+	0.917576i	$0.369857\pi$
$30$	0.206331	0.0376707
$31$	−10.7659	−1.93362	−0.966811	−	0.255494i	$-0.917762\pi$
$31$	−10.7659	−1.93362	−0.966811	+	0.255494i	$0.917762\pi$
$32$	1.00000	0.176777
$33$	−0.585566	−0.101934
$34$	−2.88437	−0.494665
$35$	−1.17097	−0.197929
$36$	−2.82059	−0.470098
$37$	−8.21314	−1.35023	−0.675116	−	0.737712i	$-0.735906\pi$
$37$	−8.21314	−1.35023	−0.675116	+	0.737712i	$0.735906\pi$
$38$	0.654438	0.106164
$39$	0.550409	0.0881360
$40$	−0.487122	−0.0770207
$41$	−0.313899	−0.0490228	−0.0245114	−	0.999700i	$-0.507803\pi$
$41$	−0.313899	−0.0490228	−0.0245114	+	0.999700i	$0.507803\pi$
$42$	−1.01820	−0.157112
$43$	4.40071	0.671102	0.335551	−	0.942022i	$-0.391078\pi$
$43$	4.40071	0.671102	0.335551	+	0.942022i	$0.391078\pi$
$44$	1.38245	0.208412
$45$	1.37397	0.204819
$46$	−8.21328	−1.21098
$47$	−5.56192	−0.811290	−0.405645	−	0.914031i	$-0.632953\pi$
$47$	−5.56192	−0.811290	−0.405645	+	0.914031i	$0.632953\pi$
$48$	−0.423572	−0.0611373
$49$	−1.22152	−0.174502
$50$	−4.76271	−0.673549
$51$	1.22174	0.171077
$52$	−1.29945	−0.180201
$53$	8.99732	1.23588	0.617938	−	0.786227i	$-0.287968\pi$
$53$	8.99732	1.23588	0.617938	+	0.786227i	$0.287968\pi$
$54$	2.46544	0.335503
$55$	−0.673421	−0.0908040
$56$	2.40385	0.321228
$57$	−0.277201	−0.0367162
$58$	4.28186	0.562235
$59$	0.393777	0.0512654	0.0256327	−	0.999671i	$-0.491840\pi$
$59$	0.393777	0.0512654	0.0256327	+	0.999671i	$0.491840\pi$
$60$	0.206331	0.0266372
$61$	8.49444	1.08760	0.543801	−	0.839214i	$-0.316985\pi$
$61$	8.49444	1.08760	0.543801	+	0.839214i	$0.316985\pi$
$62$	−10.7659	−1.36728
$63$	−6.78026	−0.854233
$64$	1.00000	0.125000
$65$	0.632989	0.0785126
$66$	−0.585566	−0.0720782
$67$	3.95326	0.482968	0.241484	−	0.970405i	$-0.422366\pi$
$67$	3.95326	0.482968	0.241484	+	0.970405i	$0.422366\pi$
$68$	−2.88437	−0.349781
$69$	3.47891	0.418812
$70$	−1.17097	−0.139957
$71$	0.756879	0.0898251	0.0449125	−	0.998991i	$-0.485699\pi$
$71$	0.756879	0.0898251	0.0449125	+	0.998991i	$0.485699\pi$
$72$	−2.82059	−0.332409
$73$	−9.00288	−1.05371	−0.526854	−	0.849956i	$-0.676628\pi$
$73$	−9.00288	−1.05371	−0.526854	+	0.849956i	$0.676628\pi$
$74$	−8.21314	−0.954758
$75$	2.01735	0.232943
$76$	0.654438	0.0750692
$77$	3.32320	0.378713
$78$	0.550409	0.0623216
$79$	10.9266	1.22934	0.614671	−	0.788784i	$-0.289289\pi$
$79$	10.9266	1.22934	0.614671	+	0.788784i	$0.289289\pi$
$80$	−0.487122	−0.0544618
$81$	7.41747	0.824164
$82$	−0.313899	−0.0346644
$83$	−10.0973	−1.10832	−0.554160	−	0.832410i	$-0.686961\pi$
$83$	−10.0973	−1.10832	−0.554160	+	0.832410i	$0.686961\pi$
$84$	−1.01820	−0.111095
$85$	1.40504	0.152398
$86$	4.40071	0.474541
$87$	−1.81367	−0.194446
$88$	1.38245	0.147370
$89$	−12.2322	−1.29661	−0.648304	−	0.761382i	$-0.724521\pi$
$89$	−12.2322	−1.29661	−0.648304	+	0.761382i	$0.724521\pi$
$90$	1.37397	0.144829
$91$	−3.12368	−0.327450
$92$	−8.21328	−0.856293
$93$	4.56015	0.472865
$94$	−5.56192	−0.573669
$95$	−0.318791	−0.0327072
$96$	−0.423572	−0.0432306
$97$	16.8496	1.71082	0.855408	−	0.517955i	$-0.173306\pi$
$97$	16.8496	1.71082	0.855408	+	0.517955i	$0.173306\pi$
$98$	−1.22152	−0.123392
$99$	−3.89932	−0.391896
$100$	−4.76271	−0.476271
$101$	−8.18914	−0.814850	−0.407425	−	0.913239i	$-0.633573\pi$
$101$	−8.18914	−0.814850	−0.407425	+	0.913239i	$0.633573\pi$
$102$	1.22174	0.120970
$103$	−17.2804	−1.70269	−0.851345	−	0.524606i	$-0.824213\pi$
$103$	−17.2804	−1.70269	−0.851345	+	0.524606i	$0.824213\pi$
$104$	−1.29945	−0.127421
$105$	0.495988	0.0484035
$106$	8.99732	0.873897
$107$	−5.92372	−0.572668	−0.286334	−	0.958130i	$-0.592437\pi$
$107$	−5.92372	−0.572668	−0.286334	+	0.958130i	$0.592437\pi$
$108$	2.46544	0.237237
$109$	−14.5587	−1.39447	−0.697234	−	0.716843i	$-0.745586\pi$
$109$	−14.5587	−1.39447	−0.697234	+	0.716843i	$0.745586\pi$
$110$	−0.673421	−0.0642081
$111$	3.47885	0.330198
$112$	2.40385	0.227142
$113$	13.2666	1.24801	0.624007	−	0.781419i	$-0.285504\pi$
$113$	13.2666	1.24801	0.624007	+	0.781419i	$0.285504\pi$
$114$	−0.277201	−0.0259623
$115$	4.00086	0.373083
$116$	4.28186	0.397560
$117$	3.66521	0.338848
$118$	0.393777	0.0362501
$119$	−6.93358	−0.635600
$120$	0.206331	0.0188353
$121$	−9.08883	−0.826258
$122$	8.49444	0.769050
$123$	0.132959	0.0119885
$124$	−10.7659	−0.966811
$125$	4.75563	0.425356
$126$	−6.78026	−0.604034
$127$	2.02739	0.179902	0.0899510	−	0.995946i	$-0.471329\pi$
$127$	2.02739	0.179902	0.0899510	+	0.995946i	$0.471329\pi$
$128$	1.00000	0.0883883
$129$	−1.86402	−0.164117
$130$	0.632989	0.0555168
$131$	−1.55630	−0.135975	−0.0679874	−	0.997686i	$-0.521658\pi$
$131$	−1.55630	−0.135975	−0.0679874	+	0.997686i	$0.521658\pi$
$132$	−0.585566	−0.0509670
$133$	1.57317	0.136411
$134$	3.95326	0.341510
$135$	−1.20097	−0.103363
$136$	−2.88437	−0.247332
$137$	−17.9866	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$137$	−17.9866	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$138$	3.47891	0.296145
$139$	−19.2869	−1.63590	−0.817948	−	0.575292i	$-0.804888\pi$
$139$	−19.2869	−1.63590	−0.817948	+	0.575292i	$0.804888\pi$
$140$	−1.17097	−0.0989647
$141$	2.35587	0.198400
$142$	0.756879	0.0635159
$143$	−1.79642	−0.150224
$144$	−2.82059	−0.235049
$145$	−2.08578	−0.173215
$146$	−9.00288	−0.745083
$147$	0.517399	0.0426744
$148$	−8.21314	−0.675116
$149$	5.69382	0.466456	0.233228	−	0.972422i	$-0.425071\pi$
$149$	5.69382	0.466456	0.233228	+	0.972422i	$0.425071\pi$
$150$	2.01735	0.164716
$151$	15.0185	1.22219	0.611093	−	0.791559i	$-0.290730\pi$
$151$	15.0185	1.22219	0.611093	+	0.791559i	$0.290730\pi$
$152$	0.654438	0.0530819
$153$	8.13561	0.657725
$154$	3.32320	0.267791
$155$	5.24433	0.421234
$156$	0.550409	0.0440680
$157$	22.5572	1.80026	0.900129	−	0.435624i	$-0.143472\pi$
$157$	22.5572	1.80026	0.900129	+	0.435624i	$0.143472\pi$
$158$	10.9266	0.869276
$159$	−3.81101	−0.302233
$160$	−0.487122	−0.0385103
$161$	−19.7435	−1.55600
$162$	7.41747	0.582772
$163$	−6.69948	−0.524744	−0.262372	−	0.964967i	$-0.584505\pi$
$163$	−6.69948	−0.524744	−0.262372	+	0.964967i	$0.584505\pi$
$164$	−0.313899	−0.0245114
$165$	0.285242	0.0222060
$166$	−10.0973	−0.783701
$167$	9.77539	0.756442	0.378221	−	0.925715i	$-0.376536\pi$
$167$	9.77539	0.756442	0.378221	+	0.925715i	$0.376536\pi$
$168$	−1.01820	−0.0785560
$169$	−11.3114	−0.870110
$170$	1.40504	0.107761
$171$	−1.84590	−0.141159
$172$	4.40071	0.335551
$173$	6.39981	0.486568	0.243284	−	0.969955i	$-0.421775\pi$
$173$	6.39981	0.486568	0.243284	+	0.969955i	$0.421775\pi$
$174$	−1.81367	−0.137494
$175$	−11.4488	−0.865451
$176$	1.38245	0.104206
$177$	−0.166793	−0.0125369
$178$	−12.2322	−0.916840
$179$	−2.76473	−0.206646	−0.103323	−	0.994648i	$-0.532947\pi$
$179$	−2.76473	−0.206646	−0.103323	+	0.994648i	$0.532947\pi$
$180$	1.37397	0.102410
$181$	−9.51712	−0.707402	−0.353701	−	0.935359i	$-0.615077\pi$
$181$	−9.51712	−0.707402	−0.353701	+	0.935359i	$0.615077\pi$
$182$	−3.12368	−0.231542
$183$	−3.59800	−0.265972
$184$	−8.21328	−0.605491
$185$	4.00080	0.294145
$186$	4.56015	0.334366
$187$	−3.98749	−0.291594
$188$	−5.56192	−0.405645
$189$	5.92653	0.431092
$190$	−0.318791	−0.0231275
$191$	−26.5851	−1.92363	−0.961816	−	0.273698i	$-0.911753\pi$
$191$	−26.5851	−1.92363	−0.961816	+	0.273698i	$0.911753\pi$
$192$	−0.423572	−0.0305686
$193$	6.55798	0.472054	0.236027	−	0.971747i	$-0.424155\pi$
$193$	6.55798	0.472054	0.236027	+	0.971747i	$0.424155\pi$
$194$	16.8496	1.20973
$195$	−0.268116	−0.0192002
$196$	−1.22152	−0.0872512
$197$	3.97806	0.283425	0.141712	−	0.989908i	$-0.454739\pi$
$197$	3.97806	0.283425	0.141712	+	0.989908i	$0.454739\pi$
$198$	−3.89932	−0.277112
$199$	−13.0404	−0.924409	−0.462204	−	0.886773i	$-0.652941\pi$
$199$	−13.0404	−0.924409	−0.462204	+	0.886773i	$0.652941\pi$
$200$	−4.76271	−0.336775
$201$	−1.67449	−0.118109
$202$	−8.18914	−0.576186
$203$	10.2929	0.722422
$204$	1.22174	0.0855386
$205$	0.152907	0.0106795
$206$	−17.2804	−1.20398
$207$	23.1663	1.61017
$208$	−1.29945	−0.0901005
$209$	0.904727	0.0625813
$210$	0.495988	0.0342264
$211$	22.1547	1.52519	0.762597	−	0.646874i	$-0.223924\pi$
$211$	22.1547	1.52519	0.762597	+	0.646874i	$0.223924\pi$
$212$	8.99732	0.617938
$213$	−0.320593	−0.0219666
$214$	−5.92372	−0.404937
$215$	−2.14368	−0.146198
$216$	2.46544	0.167752
$217$	−25.8797	−1.75683
$218$	−14.5587	−0.986038
$219$	3.81336	0.257683
$220$	−0.673421	−0.0454020
$221$	3.74809	0.252124
$222$	3.47885	0.233485
$223$	−27.2023	−1.82160	−0.910800	−	0.412848i	$-0.864534\pi$
$223$	−27.2023	−1.82160	−0.910800	+	0.412848i	$0.864534\pi$
$224$	2.40385	0.160614
$225$	13.4336	0.895576
$226$	13.2666	0.882479
$227$	18.8854	1.25347	0.626735	−	0.779233i	$-0.284391\pi$
$227$	18.8854	1.25347	0.626735	+	0.779233i	$0.284391\pi$
$228$	−0.277201	−0.0183581
$229$	4.97064	0.328469	0.164234	−	0.986421i	$-0.447485\pi$
$229$	4.97064	0.328469	0.164234	+	0.986421i	$0.447485\pi$
$230$	4.00086	0.263809
$231$	−1.40761	−0.0926141
$232$	4.28186	0.281118
$233$	−2.23009	−0.146098	−0.0730490	−	0.997328i	$-0.523273\pi$
$233$	−2.23009	−0.146098	−0.0730490	+	0.997328i	$0.523273\pi$
$234$	3.66521	0.239602
$235$	2.70933	0.176737
$236$	0.393777	0.0256327
$237$	−4.62821	−0.300634
$238$	−6.93358	−0.449437
$239$	−3.30765	−0.213954	−0.106977	−	0.994261i	$-0.534117\pi$
$239$	−3.30765	−0.213954	−0.106977	+	0.994261i	$0.534117\pi$
$240$	0.206331	0.0133186
$241$	−16.5056	−1.06322	−0.531608	−	0.846990i	$-0.678412\pi$
$241$	−16.5056	−1.06322	−0.531608	+	0.846990i	$0.678412\pi$
$242$	−9.08883	−0.584252
$243$	−10.5381	−0.676022
$244$	8.49444	0.543801
$245$	0.595027	0.0380149
$246$	0.132959	0.00847714
$247$	−0.850408	−0.0541102
$248$	−10.7659	−0.683638
$249$	4.27692	0.271039
$250$	4.75563	0.300772
$251$	−5.28350	−0.333492	−0.166746	−	0.986000i	$-0.553326\pi$
$251$	−5.28350	−0.333492	−0.166746	+	0.986000i	$0.553326\pi$
$252$	−6.78026	−0.427116
$253$	−11.3544	−0.713847
$254$	2.02739	0.127210
$255$	−0.595134	−0.0372687
$256$	1.00000	0.0625000
$257$	25.6201	1.59814	0.799068	−	0.601240i	$-0.205326\pi$
$257$	25.6201	1.59814	0.799068	+	0.601240i	$0.205326\pi$
$258$	−1.86402	−0.116049
$259$	−19.7431	−1.22678
$260$	0.632989	0.0392563
$261$	−12.0773	−0.747569
$262$	−1.55630	−0.0961487
$263$	−4.54683	−0.280370	−0.140185	−	0.990125i	$-0.544770\pi$
$263$	−4.54683	−0.280370	−0.140185	+	0.990125i	$0.544770\pi$
$264$	−0.585566	−0.0360391
$265$	−4.38279	−0.269232
$266$	1.57317	0.0964572
$267$	5.18120	0.317084
$268$	3.95326	0.241484
$269$	27.4647	1.67455	0.837275	−	0.546781i	$-0.184147\pi$
$269$	27.4647	1.67455	0.837275	+	0.546781i	$0.184147\pi$
$270$	−1.20097	−0.0730885
$271$	11.0589	0.671782	0.335891	−	0.941901i	$-0.390963\pi$
$271$	11.0589	0.671782	0.335891	+	0.941901i	$0.390963\pi$
$272$	−2.88437	−0.174890
$273$	1.32310	0.0800777
$274$	−17.9866	−1.08661
$275$	−6.58421	−0.397043
$276$	3.47891	0.209406
$277$	−9.96389	−0.598672	−0.299336	−	0.954148i	$-0.596765\pi$
$277$	−9.96389	−0.598672	−0.299336	+	0.954148i	$0.596765\pi$
$278$	−19.2869	−1.15675
$279$	30.3663	1.81798
$280$	−1.17097	−0.0699786
$281$	13.9946	0.834847	0.417423	−	0.908712i	$-0.362933\pi$
$281$	13.9946	0.834847	0.417423	+	0.908712i	$0.362933\pi$
$282$	2.35587	0.140290
$283$	−6.74061	−0.400688	−0.200344	−	0.979726i	$-0.564206\pi$
$283$	−6.74061	−0.400688	−0.200344	+	0.979726i	$0.564206\pi$
$284$	0.756879	0.0449125
$285$	0.135031	0.00799853
$286$	−1.79642	−0.106225
$287$	−0.754566	−0.0445406
$288$	−2.82059	−0.166205
$289$	−8.68042	−0.510613
$290$	−2.08578	−0.122481
$291$	−7.13700	−0.418379
$292$	−9.00288	−0.526854
$293$	30.9651	1.80900	0.904501	−	0.426471i	$-0.140243\pi$
$293$	30.9651	1.80900	0.904501	+	0.426471i	$0.140243\pi$
$294$	0.517399	0.0301754
$295$	−0.191817	−0.0111680
$296$	−8.21314	−0.477379
$297$	3.40834	0.197772
$298$	5.69382	0.329834
$299$	10.6727	0.617220
$300$	2.01735	0.116472
$301$	10.5786	0.609743
$302$	15.0185	0.864216
$303$	3.46869	0.199271
$304$	0.654438	0.0375346
$305$	−4.13782	−0.236931
$306$	8.13561	0.465082
$307$	23.8326	1.36020	0.680099	−	0.733120i	$-0.261937\pi$
$307$	23.8326	1.36020	0.680099	+	0.733120i	$0.261937\pi$
$308$	3.32320	0.189357
$309$	7.31949	0.416391
$310$	5.24433	0.297858
$311$	0.0857955	0.00486502	0.00243251	−	0.999997i	$-0.499226\pi$
$311$	0.0857955	0.00486502	0.00243251	+	0.999997i	$0.499226\pi$
$312$	0.550409	0.0311608
$313$	−20.5342	−1.16066	−0.580332	−	0.814380i	$-0.697077\pi$
$313$	−20.5342	−1.16066	−0.580332	+	0.814380i	$0.697077\pi$
$314$	22.5572	1.27297
$315$	3.30281	0.186092
$316$	10.9266	0.614671
$317$	−21.9701	−1.23396	−0.616981	−	0.786978i	$-0.711645\pi$
$317$	−21.9701	−1.23396	−0.616981	+	0.786978i	$0.711645\pi$
$318$	−3.81101	−0.213711
$319$	5.91945	0.331425
$320$	−0.487122	−0.0272309
$321$	2.50912	0.140045
$322$	−19.7435	−1.10026
$323$	−1.88764	−0.105031
$324$	7.41747	0.412082
$325$	6.18890	0.343298
$326$	−6.69948	−0.371050
$327$	6.16664	0.341016
$328$	−0.313899	−0.0173322
$329$	−13.3700	−0.737113
$330$	0.285242	0.0157020
$331$	2.54722	0.140008	0.0700040	−	0.997547i	$-0.477699\pi$
$331$	2.54722	0.140008	0.0700040	+	0.997547i	$0.477699\pi$
$332$	−10.0973	−0.554160
$333$	23.1659	1.26948
$334$	9.77539	0.534886
$335$	−1.92572	−0.105213
$336$	−1.01820	−0.0555474
$337$	9.68168	0.527395	0.263697	−	0.964605i	$-0.415058\pi$
$337$	9.68168	0.527395	0.263697	+	0.964605i	$0.415058\pi$
$338$	−11.3114	−0.615261
$339$	−5.61934	−0.305201
$340$	1.40504	0.0761989
$341$	−14.8834	−0.805980
$342$	−1.84590	−0.0998148
$343$	−19.7633	−1.06712
$344$	4.40071	0.237270
$345$	−1.69465	−0.0912370
$346$	6.39981	0.344056
$347$	−20.5598	−1.10371	−0.551855	−	0.833940i	$-0.686080\pi$
$347$	−20.5598	−1.10371	−0.551855	+	0.833940i	$0.686080\pi$
$348$	−1.81367	−0.0972230
$349$	−12.5526	−0.671924	−0.335962	−	0.941876i	$-0.609061\pi$
$349$	−12.5526	−0.671924	−0.335962	+	0.941876i	$0.609061\pi$
$350$	−11.4488	−0.611966
$351$	−3.20370	−0.171001
$352$	1.38245	0.0736848
$353$	0.944759	0.0502845	0.0251422	−	0.999684i	$-0.491996\pi$
$353$	0.944759	0.0502845	0.0251422	+	0.999684i	$0.491996\pi$
$354$	−0.166793	−0.00886493
$355$	−0.368692	−0.0195682
$356$	−12.2322	−0.648304
$357$	2.93687	0.155436
$358$	−2.76473	−0.146121
$359$	14.5533	0.768095	0.384047	−	0.923313i	$-0.374530\pi$
$359$	14.5533	0.768095	0.384047	+	0.923313i	$0.374530\pi$
$360$	1.37397	0.0724145
$361$	−18.5717	−0.977458
$362$	−9.51712	−0.500209
$363$	3.84977	0.202061
$364$	−3.12368	−0.163725
$365$	4.38550	0.229547
$366$	−3.59800	−0.188071
$367$	−18.8279	−0.982809	−0.491405	−	0.870931i	$-0.663516\pi$
$367$	−18.8279	−0.982809	−0.491405	+	0.870931i	$0.663516\pi$
$368$	−8.21328	−0.428147
$369$	0.885380	0.0460910
$370$	4.00080	0.207992
$371$	21.6282	1.12288
$372$	4.56015	0.236433
$373$	−30.3593	−1.57194	−0.785972	−	0.618262i	$-0.787837\pi$
$373$	−30.3593	−1.57194	−0.785972	+	0.618262i	$0.787837\pi$
$374$	−3.98749	−0.206188
$375$	−2.01435	−0.104021
$376$	−5.56192	−0.286834
$377$	−5.56405	−0.286563
$378$	5.92653	0.304828
$379$	22.6287	1.16236	0.581179	−	0.813775i	$-0.302591\pi$
$379$	22.6287	1.16236	0.581179	+	0.813775i	$0.302591\pi$
$380$	−0.318791	−0.0163536
$381$	−0.858746	−0.0439949
$382$	−26.5851	−1.36021
$383$	14.6831	0.750273	0.375136	−	0.926970i	$-0.377596\pi$
$383$	14.6831	0.750273	0.375136	+	0.926970i	$0.377596\pi$
$384$	−0.423572	−0.0216153
$385$	−1.61880	−0.0825017
$386$	6.55798	0.333792
$387$	−12.4126	−0.630967
$388$	16.8496	0.855408
$389$	24.9705	1.26605	0.633026	−	0.774130i	$-0.281812\pi$
$389$	24.9705	1.26605	0.633026	+	0.774130i	$0.281812\pi$
$390$	−0.268116	−0.0135766
$391$	23.6901	1.19806
$392$	−1.22152	−0.0616959
$393$	0.659206	0.0332525
$394$	3.97806	0.200412
$395$	−5.32260	−0.267809
$396$	−3.89932	−0.195948
$397$	10.3228	0.518086	0.259043	−	0.965866i	$-0.416593\pi$
$397$	10.3228	0.518086	0.259043	+	0.965866i	$0.416593\pi$
$398$	−13.0404	−0.653656
$399$	−0.666349	−0.0333592
$400$	−4.76271	−0.238136
$401$	−25.3580	−1.26632	−0.633158	−	0.774022i	$-0.718242\pi$
$401$	−25.3580	−1.26632	−0.633158	+	0.774022i	$0.718242\pi$
$402$	−1.67449	−0.0835159
$403$	13.9898	0.696881
$404$	−8.18914	−0.407425
$405$	−3.61321	−0.179542
$406$	10.2929	0.510829
$407$	−11.3542	−0.562809
$408$	1.22174	0.0604849
$409$	5.90920	0.292191	0.146096	−	0.989270i	$-0.453329\pi$
$409$	5.90920	0.292191	0.146096	+	0.989270i	$0.453329\pi$
$410$	0.152907	0.00755154
$411$	7.61862	0.375799
$412$	−17.2804	−0.851345
$413$	0.946580	0.0465781
$414$	23.1663	1.13856
$415$	4.91860	0.241445
$416$	−1.29945	−0.0637107
$417$	8.16939	0.400057
$418$	0.904727	0.0442516
$419$	−30.4294	−1.48657	−0.743286	−	0.668974i	$-0.766734\pi$
$419$	−30.4294	−1.48657	−0.743286	+	0.668974i	$0.766734\pi$
$420$	0.495988	0.0242017
$421$	15.2300	0.742265	0.371133	−	0.928580i	$-0.378970\pi$
$421$	15.2300	0.742265	0.371133	+	0.928580i	$0.378970\pi$
$422$	22.1547	1.07847
$423$	15.6879	0.762771
$424$	8.99732	0.436948
$425$	13.7374	0.666362
$426$	−0.320593	−0.0155328
$427$	20.4193	0.988161
$428$	−5.92372	−0.286334
$429$	0.760913	0.0367372
$430$	−2.14368	−0.103377
$431$	6.07512	0.292628	0.146314	−	0.989238i	$-0.453259\pi$
$431$	6.07512	0.292628	0.146314	+	0.989238i	$0.453259\pi$
$432$	2.46544	0.118618
$433$	10.3216	0.496026	0.248013	−	0.968757i	$-0.420222\pi$
$433$	10.3216	0.496026	0.248013	+	0.968757i	$0.420222\pi$
$434$	−25.8797	−1.24227
$435$	0.883479	0.0423596
$436$	−14.5587	−0.697234
$437$	−5.37508	−0.257125
$438$	3.81336	0.182210
$439$	−13.4776	−0.643251	−0.321626	−	0.946867i	$-0.604229\pi$
$439$	−13.4776	−0.643251	−0.321626	+	0.946867i	$0.604229\pi$
$440$	−0.673421	−0.0321041
$441$	3.44539	0.164066
$442$	3.74809	0.178278
$443$	−18.8787	−0.896955	−0.448478	−	0.893794i	$-0.648034\pi$
$443$	−18.8787	−0.896955	−0.448478	+	0.893794i	$0.648034\pi$
$444$	3.47885	0.165099
$445$	5.95855	0.282463
$446$	−27.2023	−1.28807
$447$	−2.41174	−0.114071
$448$	2.40385	0.113571
$449$	2.22579	0.105041	0.0525207	−	0.998620i	$-0.483274\pi$
$449$	2.22579	0.105041	0.0525207	+	0.998620i	$0.483274\pi$
$450$	13.4336	0.633268
$451$	−0.433950	−0.0204339
$452$	13.2666	0.624007
$453$	−6.36140	−0.298885
$454$	18.8854	0.886337
$455$	1.52161	0.0713342
$456$	−0.277201	−0.0129811
$457$	−26.8389	−1.25547	−0.627736	−	0.778426i	$-0.716018\pi$
$457$	−26.8389	−1.25547	−0.627736	+	0.778426i	$0.716018\pi$
$458$	4.97064	0.232263
$459$	−7.11122	−0.331923
$460$	4.00086	0.186541
$461$	−30.5674	−1.42367	−0.711833	−	0.702348i	$-0.752135\pi$
$461$	−30.5674	−1.42367	−0.711833	+	0.702348i	$0.752135\pi$
$462$	−1.40761	−0.0654880
$463$	18.6703	0.867682	0.433841	−	0.900989i	$-0.357158\pi$
$463$	18.6703	0.867682	0.433841	+	0.900989i	$0.357158\pi$
$464$	4.28186	0.198780
$465$	−2.22135	−0.103013
$466$	−2.23009	−0.103307
$467$	32.9483	1.52467	0.762333	−	0.647185i	$-0.224054\pi$
$467$	32.9483	1.52467	0.762333	+	0.647185i	$0.224054\pi$
$468$	3.66521	0.169424
$469$	9.50304	0.438810
$470$	2.70933	0.124972
$471$	−9.55457	−0.440251
$472$	0.393777	0.0181251
$473$	6.08376	0.279731
$474$	−4.62821	−0.212581
$475$	−3.11690	−0.143013
$476$	−6.93358	−0.317800
$477$	−25.3777	−1.16197
$478$	−3.30765	−0.151288
$479$	20.0398	0.915642	0.457821	−	0.889044i	$-0.348630\pi$
$479$	20.0398	0.915642	0.457821	+	0.889044i	$0.348630\pi$
$480$	0.206331	0.00941767
$481$	10.6726	0.486626
$482$	−16.5056	−0.751808
$483$	8.36277	0.380519
$484$	−9.08883	−0.413129
$485$	−8.20779	−0.372697
$486$	−10.5381	−0.478020
$487$	−18.9345	−0.858006	−0.429003	−	0.903303i	$-0.641135\pi$
$487$	−18.9345	−0.858006	−0.429003	+	0.903303i	$0.641135\pi$
$488$	8.49444	0.384525
$489$	2.83771	0.128326
$490$	0.595027	0.0268806
$491$	−1.35404	−0.0611071	−0.0305535	−	0.999533i	$-0.509727\pi$
$491$	−1.35404	−0.0611071	−0.0305535	+	0.999533i	$0.509727\pi$
$492$	0.132959	0.00599424
$493$	−12.3504	−0.556236
$494$	−0.850408	−0.0382617
$495$	1.89944	0.0853736
$496$	−10.7659	−0.483405
$497$	1.81942	0.0816123
$498$	4.27692	0.191653
$499$	38.2002	1.71008	0.855038	−	0.518566i	$-0.173534\pi$
$499$	38.2002	1.71008	0.855038	+	0.518566i	$0.173534\pi$
$500$	4.75563	0.212678
$501$	−4.14058	−0.184987
$502$	−5.28350	−0.235814
$503$	14.2520	0.635467	0.317734	−	0.948180i	$-0.397078\pi$
$503$	14.2520	0.635467	0.317734	+	0.948180i	$0.397078\pi$
$504$	−6.78026	−0.302017
$505$	3.98911	0.177513
$506$	−11.3544	−0.504766
$507$	4.79120	0.212785
$508$	2.02739	0.0899510
$509$	18.5447	0.821980	0.410990	−	0.911640i	$-0.365183\pi$
$509$	18.5447	0.821980	0.410990	+	0.911640i	$0.365183\pi$
$510$	−0.595134	−0.0263530
$511$	−21.6415	−0.957366
$512$	1.00000	0.0441942
$513$	1.61347	0.0712366
$514$	25.6201	1.13005
$515$	8.41766	0.370927
$516$	−1.86402	−0.0820587
$517$	−7.68908	−0.338165
$518$	−19.7431	−0.867464
$519$	−2.71078	−0.118990
$520$	0.632989	0.0277584
$521$	5.87186	0.257251	0.128626	−	0.991693i	$-0.458943\pi$
$521$	5.87186	0.257251	0.128626	+	0.991693i	$0.458943\pi$
$522$	−12.0773	−0.528611
$523$	34.3254	1.50094	0.750472	−	0.660902i	$-0.229826\pi$
$523$	34.3254	1.50094	0.750472	+	0.660902i	$0.229826\pi$
$524$	−1.55630	−0.0679874
$525$	4.84940	0.211645
$526$	−4.54683	−0.198251
$527$	31.0530	1.35269
$528$	−0.585566	−0.0254835
$529$	44.4579	1.93295
$530$	−4.38279	−0.190376
$531$	−1.11068	−0.0481995
$532$	1.57317	0.0682055
$533$	0.407896	0.0176679
$534$	5.18120	0.224212
$535$	2.88557	0.124754
$536$	3.95326	0.170755
$537$	1.17106	0.0505350
$538$	27.4647	1.18409
$539$	−1.68868	−0.0727368
$540$	−1.20097	−0.0516814
$541$	−31.4902	−1.35387	−0.676936	−	0.736042i	$-0.736692\pi$
$541$	−31.4902	−1.35387	−0.676936	+	0.736042i	$0.736692\pi$
$542$	11.0589	0.475022
$543$	4.03118	0.172995
$544$	−2.88437	−0.123666
$545$	7.09184	0.303781
$546$	1.32310	0.0566235
$547$	5.58889	0.238963	0.119482	−	0.992836i	$-0.461877\pi$
$547$	5.58889	0.238963	0.119482	+	0.992836i	$0.461877\pi$
$548$	−17.9866	−0.768350
$549$	−23.9593	−1.02256
$550$	−6.58421	−0.280752
$551$	2.80221	0.119378
$552$	3.47891	0.148072
$553$	26.2659	1.11694
$554$	−9.96389	−0.423325
$555$	−1.69462	−0.0719328
$556$	−19.2869	−0.817948
$557$	5.18623	0.219748	0.109874	−	0.993946i	$-0.464955\pi$
$557$	5.18623	0.219748	0.109874	+	0.993946i	$0.464955\pi$
$558$	30.3663	1.28551
$559$	−5.71849	−0.241867
$560$	−1.17097	−0.0494823
$561$	1.68899	0.0713091
$562$	13.9946	0.590326
$563$	11.3474	0.478237	0.239118	−	0.970990i	$-0.423142\pi$
$563$	11.3474	0.478237	0.239118	+	0.970990i	$0.423142\pi$
$564$	2.35587	0.0992001
$565$	−6.46243	−0.271877
$566$	−6.74061	−0.283329
$567$	17.8305	0.748810
$568$	0.756879	0.0317580
$569$	19.9578	0.836673	0.418337	−	0.908292i	$-0.362613\pi$
$569$	19.9578	0.836673	0.418337	+	0.908292i	$0.362613\pi$
$570$	0.135031	0.00565581
$571$	23.8226	0.996947	0.498473	−	0.866905i	$-0.333894\pi$
$571$	23.8226	0.996947	0.498473	+	0.866905i	$0.333894\pi$
$572$	−1.79642	−0.0751121
$573$	11.2607	0.470422
$574$	−0.754566	−0.0314950
$575$	39.1175	1.63131
$576$	−2.82059	−0.117524
$577$	−32.6655	−1.35988	−0.679942	−	0.733266i	$-0.737995\pi$
$577$	−32.6655	−1.35988	−0.679942	+	0.733266i	$0.737995\pi$
$578$	−8.68042	−0.361058
$579$	−2.77777	−0.115440
$580$	−2.08578	−0.0866075
$581$	−24.2723	−1.00699
$582$	−7.13700	−0.295838
$583$	12.4383	0.515143
$584$	−9.00288	−0.372542
$585$	−1.78540	−0.0738172
$586$	30.9651	1.27916
$587$	−32.4538	−1.33951	−0.669755	−	0.742582i	$-0.733601\pi$
$587$	−32.4538	−1.33951	−0.669755	+	0.742582i	$0.733601\pi$
$588$	0.517399	0.0213372
$589$	−7.04564	−0.290311
$590$	−0.191817	−0.00789699
$591$	−1.68499	−0.0693113
$592$	−8.21314	−0.337558
$593$	9.52629	0.391198	0.195599	−	0.980684i	$-0.437335\pi$
$593$	9.52629	0.391198	0.195599	+	0.980684i	$0.437335\pi$
$594$	3.40834	0.139846
$595$	3.37750	0.138464
$596$	5.69382	0.233228
$597$	5.52354	0.226063
$598$	10.6727	0.436440
$599$	22.3459	0.913028	0.456514	−	0.889716i	$-0.349098\pi$
$599$	22.3459	0.913028	0.456514	+	0.889716i	$0.349098\pi$
$600$	2.01735	0.0823580
$601$	−37.1680	−1.51611	−0.758057	−	0.652188i	$-0.773851\pi$
$601$	−37.1680	−1.51611	−0.758057	+	0.652188i	$0.773851\pi$
$602$	10.5786	0.431153
$603$	−11.1505	−0.454084
$604$	15.0185	0.611093
$605$	4.42737	0.179998
$606$	3.46869	0.140906
$607$	34.0379	1.38156	0.690778	−	0.723067i	$-0.257268\pi$
$607$	34.0379	1.38156	0.690778	+	0.723067i	$0.257268\pi$
$608$	0.654438	0.0265410
$609$	−4.35979	−0.176668
$610$	−4.13782	−0.167536
$611$	7.22743	0.292391
$612$	8.13561	0.328863
$613$	−16.7046	−0.674694	−0.337347	−	0.941380i	$-0.609529\pi$
$613$	−16.7046	−0.674694	−0.337347	+	0.941380i	$0.609529\pi$
$614$	23.8326	0.961806
$615$	−0.0647671	−0.00261166
$616$	3.32320	0.133895
$617$	47.8658	1.92700	0.963502	−	0.267702i	$-0.0862642\pi$
$617$	47.8658	1.92700	0.963502	+	0.267702i	$0.0862642\pi$
$618$	7.31949	0.294433
$619$	2.54991	0.102490	0.0512448	−	0.998686i	$-0.483681\pi$
$619$	2.54991	0.102490	0.0512448	+	0.998686i	$0.483681\pi$
$620$	5.24433	0.210617
$621$	−20.2493	−0.812576
$622$	0.0857955	0.00344009
$623$	−29.4043	−1.17806
$624$	0.550409	0.0220340
$625$	21.4970	0.859880
$626$	−20.5342	−0.820713
$627$	−0.383217	−0.0153042
$628$	22.5572	0.900129
$629$	23.6897	0.944571
$630$	3.30281	0.131587
$631$	44.7184	1.78021	0.890106	−	0.455754i	$-0.150630\pi$
$631$	44.7184	1.78021	0.890106	+	0.455754i	$0.150630\pi$
$632$	10.9266	0.434638
$633$	−9.38411	−0.372985
$634$	−21.9701	−0.872543
$635$	−0.987586	−0.0391912
$636$	−3.81101	−0.151116
$637$	1.58730	0.0628910
$638$	5.91945	0.234353
$639$	−2.13484	−0.0844531
$640$	−0.487122	−0.0192552
$641$	35.2092	1.39068	0.695340	−	0.718681i	$-0.255254\pi$
$641$	35.2092	1.39068	0.695340	+	0.718681i	$0.255254\pi$
$642$	2.50912	0.0990270
$643$	19.0321	0.750553	0.375276	−	0.926913i	$-0.377548\pi$
$643$	19.0321	0.750553	0.375276	+	0.926913i	$0.377548\pi$
$644$	−19.7435	−0.778002
$645$	0.908002	0.0357525
$646$	−1.88764	−0.0742682
$647$	−2.69643	−0.106008	−0.0530039	−	0.998594i	$-0.516880\pi$
$647$	−2.69643	−0.106008	−0.0530039	+	0.998594i	$0.516880\pi$
$648$	7.41747	0.291386
$649$	0.544377	0.0213686
$650$	6.18890	0.242749
$651$	10.9619	0.429631
$652$	−6.69948	−0.262372
$653$	−41.4605	−1.62247	−0.811237	−	0.584718i	$-0.801205\pi$
$653$	−41.4605	−1.62247	−0.811237	+	0.584718i	$0.801205\pi$
$654$	6.16664	0.241135
$655$	0.758109	0.0296218
$656$	−0.313899	−0.0122557
$657$	25.3934	0.990691
$658$	−13.3700	−0.521217
$659$	28.5503	1.11216	0.556082	−	0.831128i	$-0.312304\pi$
$659$	28.5503	1.11216	0.556082	+	0.831128i	$0.312304\pi$
$660$	0.285242	0.0111030
$661$	−33.3936	−1.29886	−0.649430	−	0.760421i	$-0.724993\pi$
$661$	−33.3936	−1.29886	−0.649430	+	0.760421i	$0.724993\pi$
$662$	2.54722	0.0990006
$663$	−1.58758	−0.0616566
$664$	−10.0973	−0.391850
$665$	−0.766324	−0.0297168
$666$	23.1659	0.897660
$667$	−35.1681	−1.36171
$668$	9.77539	0.378221
$669$	11.5221	0.445471
$670$	−1.92572	−0.0743970
$671$	11.7431	0.453338
$672$	−1.01820	−0.0392780
$673$	−27.4679	−1.05881	−0.529406	−	0.848369i	$-0.677585\pi$
$673$	−27.4679	−1.05881	−0.529406	+	0.848369i	$0.677585\pi$
$674$	9.68168	0.372924
$675$	−11.7422	−0.451956
$676$	−11.3114	−0.435055
$677$	9.97285	0.383288	0.191644	−	0.981465i	$-0.438618\pi$
$677$	9.97285	0.383288	0.191644	+	0.981465i	$0.438618\pi$
$678$	−5.61934	−0.215810
$679$	40.5038	1.55439
$680$	1.40504	0.0538807
$681$	−7.99933	−0.306535
$682$	−14.8834	−0.569914
$683$	33.4102	1.27840	0.639202	−	0.769039i	$-0.279265\pi$
$683$	33.4102	1.27840	0.639202	+	0.769039i	$0.279265\pi$
$684$	−1.84590	−0.0705797
$685$	8.76167	0.334766
$686$	−19.7633	−0.754565
$687$	−2.10542	−0.0803268
$688$	4.40071	0.167776
$689$	−11.6915	−0.445412
$690$	−1.69465	−0.0645143
$691$	−38.0915	−1.44907	−0.724534	−	0.689239i	$-0.757945\pi$
$691$	−38.0915	−1.44907	−0.724534	+	0.689239i	$0.757945\pi$
$692$	6.39981	0.243284
$693$	−9.37337	−0.356065
$694$	−20.5598	−0.780441
$695$	9.39508	0.356376
$696$	−1.81367	−0.0687471
$697$	0.905400	0.0342945
$698$	−12.5526	−0.475122
$699$	0.944602	0.0357281
$700$	−11.4488	−0.432725
$701$	−12.8284	−0.484522	−0.242261	−	0.970211i	$-0.577889\pi$
$701$	−12.8284	−0.484522	−0.242261	+	0.970211i	$0.577889\pi$
$702$	−3.20370	−0.120916
$703$	−5.37499	−0.202722
$704$	1.38245	0.0521030
$705$	−1.14760	−0.0432210
$706$	0.944759	0.0355565
$707$	−19.6855	−0.740348
$708$	−0.166793	−0.00626845
$709$	15.4241	0.579264	0.289632	−	0.957138i	$-0.406467\pi$
$709$	15.4241	0.579264	0.289632	+	0.957138i	$0.406467\pi$
$710$	−0.368692	−0.0138368
$711$	−30.8195	−1.15582
$712$	−12.2322	−0.458420
$713$	88.4237	3.31149
$714$	2.93687	0.109909
$715$	0.875075	0.0327260
$716$	−2.76473	−0.103323
$717$	1.40103	0.0523223
$718$	14.5533	0.543125
$719$	−13.0923	−0.488261	−0.244130	−	0.969742i	$-0.578502\pi$
$719$	−13.0923	−0.488261	−0.244130	+	0.969742i	$0.578502\pi$
$720$	1.37397	0.0512048
$721$	−41.5395	−1.54701
$722$	−18.5717	−0.691168
$723$	6.99129	0.260009
$724$	−9.51712	−0.353701
$725$	−20.3932	−0.757386
$726$	3.84977	0.142878
$727$	−15.9120	−0.590145	−0.295072	−	0.955475i	$-0.595344\pi$
$727$	−15.9120	−0.590145	−0.295072	+	0.955475i	$0.595344\pi$
$728$	−3.12368	−0.115771
$729$	−17.7888	−0.658843
$730$	4.38550	0.162314
$731$	−12.6933	−0.469477
$732$	−3.59800	−0.132986
$733$	8.45503	0.312294	0.156147	−	0.987734i	$-0.450093\pi$
$733$	8.45503	0.312294	0.156147	+	0.987734i	$0.450093\pi$
$734$	−18.8279	−0.694951
$735$	−0.252036	−0.00929650
$736$	−8.21328	−0.302745
$737$	5.46518	0.201313
$738$	0.885380	0.0325913
$739$	19.5251	0.718243	0.359122	−	0.933291i	$-0.383076\pi$
$739$	19.5251	0.718243	0.359122	+	0.933291i	$0.383076\pi$
$740$	4.00080	0.147072
$741$	0.360209	0.0132326
$742$	21.6282	0.793996
$743$	36.0117	1.32114	0.660570	−	0.750765i	$-0.270315\pi$
$743$	36.0117	1.32114	0.660570	+	0.750765i	$0.270315\pi$
$744$	4.56015	0.167183
$745$	−2.77358	−0.101616
$746$	−30.3593	−1.11153
$747$	28.4803	1.04204
$748$	−3.98749	−0.145797
$749$	−14.2397	−0.520308
$750$	−2.01435	−0.0735536
$751$	17.0215	0.621123	0.310561	−	0.950553i	$-0.399483\pi$
$751$	17.0215	0.621123	0.310561	+	0.950553i	$0.399483\pi$
$752$	−5.56192	−0.202822
$753$	2.23794	0.0815551
$754$	−5.56405	−0.202631
$755$	−7.31582	−0.266250
$756$	5.92653	0.215546
$757$	−8.52782	−0.309949	−0.154974	−	0.987918i	$-0.549530\pi$
$757$	−8.52782	−0.309949	−0.154974	+	0.987918i	$0.549530\pi$
$758$	22.6287	0.821912
$759$	4.80942	0.174571
$760$	−0.318791	−0.0115638
$761$	−14.3668	−0.520795	−0.260397	−	0.965502i	$-0.583854\pi$
$761$	−14.3668	−0.520795	−0.260397	+	0.965502i	$0.583854\pi$
$762$	−0.858746	−0.0311091
$763$	−34.9968	−1.26697
$764$	−26.5851	−0.961816
$765$	−3.96303	−0.143284
$766$	14.6831	0.530523
$767$	−0.511693	−0.0184762
$768$	−0.423572	−0.0152843
$769$	−6.08620	−0.219474	−0.109737	−	0.993961i	$-0.535001\pi$
$769$	−6.08620	−0.219474	−0.109737	+	0.993961i	$0.535001\pi$
$770$	−1.61880	−0.0583375
$771$	−10.8519	−0.390823
$772$	6.55798	0.236027
$773$	−16.6883	−0.600236	−0.300118	−	0.953902i	$-0.597026\pi$
$773$	−16.6883	−0.600236	−0.300118	+	0.953902i	$0.597026\pi$
$774$	−12.4126	−0.446161
$775$	51.2751	1.84186
$776$	16.8496	0.604865
$777$	8.36263	0.300008
$778$	24.9705	0.895234
$779$	−0.205427	−0.00736020
$780$	−0.268116	−0.00960010
$781$	1.04635	0.0374412
$782$	23.6901	0.847157
$783$	10.5566	0.377263
$784$	−1.22152	−0.0436256
$785$	−10.9881	−0.392181
$786$	0.659206	0.0235131
$787$	−29.3303	−1.04551	−0.522756	−	0.852482i	$-0.675096\pi$
$787$	−29.3303	−1.04551	−0.522756	+	0.852482i	$0.675096\pi$
$788$	3.97806	0.141712
$789$	1.92591	0.0685641
$790$	−5.32260	−0.189369
$791$	31.8908	1.13391
$792$	−3.89932	−0.138556
$793$	−11.0381	−0.391974
$794$	10.3228	0.366342
$795$	1.85642	0.0658406
$796$	−13.0404	−0.462204
$797$	−7.13508	−0.252737	−0.126369	−	0.991983i	$-0.540332\pi$
$797$	−7.13508	−0.252737	−0.126369	+	0.991983i	$0.540332\pi$
$798$	−0.666349	−0.0235885
$799$	16.0426	0.567547
$800$	−4.76271	−0.168387
$801$	34.5019	1.21906
$802$	−25.3580	−0.895421
$803$	−12.4460	−0.439210
$804$	−1.67449	−0.0590547
$805$	9.61747	0.338971
$806$	13.9898	0.492769
$807$	−11.6333	−0.409510
$808$	−8.18914	−0.288093
$809$	−24.6870	−0.867948	−0.433974	−	0.900925i	$-0.642889\pi$
$809$	−24.6870	−0.867948	−0.433974	+	0.900925i	$0.642889\pi$
$810$	−3.61321	−0.126955
$811$	−4.22066	−0.148207	−0.0741037	−	0.997251i	$-0.523610\pi$
$811$	−4.22066	−0.148207	−0.0741037	+	0.997251i	$0.523610\pi$
$812$	10.2929	0.361211
$813$	−4.68425	−0.164284
$814$	−11.3542	−0.397966
$815$	3.26346	0.114314
$816$	1.22174	0.0427693
$817$	2.87999	0.100758
$818$	5.90920	0.206610
$819$	8.81060	0.307867
$820$	0.152907	0.00533975
$821$	−38.8041	−1.35427	−0.677136	−	0.735858i	$-0.736779\pi$
$821$	−38.8041	−1.35427	−0.677136	+	0.735858i	$0.736779\pi$
$822$	7.61862	0.265730
$823$	2.28375	0.0796064	0.0398032	−	0.999208i	$-0.487327\pi$
$823$	2.28375	0.0796064	0.0398032	+	0.999208i	$0.487327\pi$
$824$	−17.2804	−0.601992
$825$	2.78888	0.0970964
$826$	0.946580	0.0329357
$827$	42.5631	1.48006	0.740032	−	0.672571i	$-0.234810\pi$
$827$	42.5631	1.48006	0.740032	+	0.672571i	$0.234810\pi$
$828$	23.1663	0.805083
$829$	0.0647099	0.00224747	0.00112373	−	0.999999i	$-0.499642\pi$
$829$	0.0647099	0.00224747	0.00112373	+	0.999999i	$0.499642\pi$
$830$	4.91860	0.170727
$831$	4.22042	0.146405
$832$	−1.29945	−0.0450503
$833$	3.52330	0.122075
$834$	8.16939	0.282883
$835$	−4.76180	−0.164789
$836$	0.904727	0.0312906
$837$	−26.5427	−0.917452
$838$	−30.4294	−1.05116
$839$	54.5046	1.88171	0.940853	−	0.338815i	$-0.110026\pi$
$839$	54.5046	1.88171	0.940853	+	0.338815i	$0.110026\pi$
$840$	0.495988	0.0171132
$841$	−10.6657	−0.367783
$842$	15.2300	0.524861
$843$	−5.92771	−0.204161
$844$	22.1547	0.762597
$845$	5.51004	0.189551
$846$	15.6879	0.539361
$847$	−21.8482	−0.750712
$848$	8.99732	0.308969
$849$	2.85513	0.0979878
$850$	13.7374	0.471189
$851$	67.4568	2.31239
$852$	−0.320593	−0.0109833
$853$	20.6397	0.706690	0.353345	−	0.935493i	$-0.385044\pi$
$853$	20.6397	0.706690	0.353345	+	0.935493i	$0.385044\pi$
$854$	20.4193	0.698735
$855$	0.899177	0.0307512
$856$	−5.92372	−0.202469
$857$	35.8205	1.22361	0.611803	−	0.791010i	$-0.290445\pi$
$857$	35.8205	1.22361	0.611803	+	0.791010i	$0.290445\pi$
$858$	0.760913	0.0259771
$859$	−5.99497	−0.204546	−0.102273	−	0.994756i	$-0.532611\pi$
$859$	−5.99497	−0.204546	−0.102273	+	0.994756i	$0.532611\pi$
$860$	−2.14368	−0.0730989
$861$	0.319613	0.0108924
$862$	6.07512	0.206919
$863$	21.1282	0.719211	0.359606	−	0.933104i	$-0.382911\pi$
$863$	21.1282	0.719211	0.359606	+	0.933104i	$0.382911\pi$
$864$	2.46544	0.0838758
$865$	−3.11748	−0.105998
$866$	10.3216	0.350743
$867$	3.67678	0.124870
$868$	−25.8797	−0.878414
$869$	15.1055	0.512419
$870$	0.883479	0.0299527
$871$	−5.13706	−0.174063
$872$	−14.5587	−0.493019
$873$	−47.5257	−1.60850
$874$	−5.37508	−0.181815
$875$	11.4318	0.386466
$876$	3.81336	0.128842
$877$	−32.1630	−1.08607	−0.543034	−	0.839711i	$-0.682725\pi$
$877$	−32.1630	−1.08607	−0.543034	+	0.839711i	$0.682725\pi$
$878$	−13.4776	−0.454847
$879$	−13.1160	−0.442390
$880$	−0.673421	−0.0227010
$881$	11.8744	0.400059	0.200029	−	0.979790i	$-0.435896\pi$
$881$	11.8744	0.400059	0.200029	+	0.979790i	$0.435896\pi$
$882$	3.44539	0.116012
$883$	44.6036	1.50103	0.750515	−	0.660854i	$-0.229806\pi$
$883$	44.6036	1.50103	0.750515	+	0.660854i	$0.229806\pi$
$884$	3.74809	0.126062
$885$	0.0812483	0.00273113
$886$	−18.8787	−0.634243
$887$	18.9436	0.636064	0.318032	−	0.948080i	$-0.396978\pi$
$887$	18.9436	0.636064	0.318032	+	0.948080i	$0.396978\pi$
$888$	3.47885	0.116743
$889$	4.87354	0.163453
$890$	5.95855	0.199731
$891$	10.2543	0.343531
$892$	−27.2023	−0.910800
$893$	−3.63993	−0.121806
$894$	−2.41174	−0.0806606
$895$	1.34676	0.0450172
$896$	2.40385	0.0803069
$897$	−4.52066	−0.150941
$898$	2.22579	0.0742755
$899$	−46.0982	−1.53746
$900$	13.4336	0.447788
$901$	−25.9516	−0.864572
$902$	−0.433950	−0.0144489
$903$	−4.48081	−0.149112
$904$	13.2666	0.441240
$905$	4.63600	0.154106
$906$	−6.36140	−0.211343
$907$	−9.60532	−0.318939	−0.159470	−	0.987203i	$-0.550978\pi$
$907$	−9.60532	−0.318939	−0.159470	+	0.987203i	$0.550978\pi$
$908$	18.8854	0.626735
$909$	23.0982	0.766119
$910$	1.52161	0.0504409
$911$	−29.1899	−0.967104	−0.483552	−	0.875316i	$-0.660654\pi$
$911$	−29.1899	−0.967104	−0.483552	+	0.875316i	$0.660654\pi$
$912$	−0.277201	−0.00917905
$913$	−13.9590	−0.461975
$914$	−26.8389	−0.887752
$915$	1.75266	0.0579413
$916$	4.97064	0.164234
$917$	−3.74111	−0.123542
$918$	−7.11122	−0.234705
$919$	−17.7538	−0.585644	−0.292822	−	0.956167i	$-0.594594\pi$
$919$	−17.7538	−0.585644	−0.292822	+	0.956167i	$0.594594\pi$
$920$	4.00086	0.131905
$921$	−10.0948	−0.332635
$922$	−30.5674	−1.00668
$923$	−0.983525	−0.0323731
$924$	−1.40761	−0.0463070
$925$	39.1168	1.28615
$926$	18.6703	0.613544
$927$	48.7409	1.60086
$928$	4.28186	0.140559
$929$	−23.2601	−0.763138	−0.381569	−	0.924340i	$-0.624616\pi$
$929$	−23.2601	−0.763138	−0.381569	+	0.924340i	$0.624616\pi$
$930$	−2.22135	−0.0728408
$931$	−0.799406	−0.0261995
$932$	−2.23009	−0.0730490
$933$	−0.0363406	−0.00118974
$934$	32.9483	1.07810
$935$	1.94239	0.0635230
$936$	3.66521	0.119801
$937$	39.2108	1.28096	0.640481	−	0.767974i	$-0.278735\pi$
$937$	39.2108	1.28096	0.640481	+	0.767974i	$0.278735\pi$
$938$	9.50304	0.310285
$939$	8.69772	0.283839
$940$	2.70933	0.0883687
$941$	−25.7206	−0.838467	−0.419233	−	0.907878i	$-0.637701\pi$
$941$	−25.7206	−0.838467	−0.419233	+	0.907878i	$0.637701\pi$
$942$	−9.55457	−0.311305
$943$	2.57814	0.0839558
$944$	0.393777	0.0128163
$945$	−2.88694	−0.0939122
$946$	6.08376	0.197800
$947$	33.9661	1.10375	0.551874	−	0.833927i	$-0.313913\pi$
$947$	33.9661	1.10375	0.551874	+	0.833927i	$0.313913\pi$
$948$	−4.62821	−0.150317
$949$	11.6988	0.379758
$950$	−3.11690	−0.101126
$951$	9.30590	0.301765
$952$	−6.93358	−0.224719
$953$	−53.5320	−1.73407	−0.867035	−	0.498247i	$-0.833977\pi$
$953$	−53.5320	−1.73407	−0.867035	+	0.498247i	$0.833977\pi$
$954$	−25.3777	−0.821634
$955$	12.9502	0.419058
$956$	−3.30765	−0.106977
$957$	−2.50731	−0.0810498
$958$	20.0398	0.647457
$959$	−43.2371	−1.39620
$960$	0.206331	0.00665930
$961$	84.9056	2.73889
$962$	10.6726	0.344097
$963$	16.7084	0.538420
$964$	−16.5056	−0.531608
$965$	−3.19453	−0.102836
$966$	8.36277	0.269068
$967$	19.0347	0.612114	0.306057	−	0.952013i	$-0.400990\pi$
$967$	19.0347	0.612114	0.306057	+	0.952013i	$0.400990\pi$
$968$	−9.08883	−0.292126
$969$	0.799550	0.0256852
$970$	−8.20779	−0.263536
$971$	−1.60381	−0.0514686	−0.0257343	−	0.999669i	$-0.508192\pi$
$971$	−1.60381	−0.0514686	−0.0257343	+	0.999669i	$0.508192\pi$
$972$	−10.5381	−0.338011
$973$	−46.3628	−1.48632
$974$	−18.9345	−0.606702
$975$	−2.62144	−0.0839533
$976$	8.49444	0.271900
$977$	−50.1436	−1.60424	−0.802119	−	0.597165i	$-0.796294\pi$
$977$	−50.1436	−1.60424	−0.802119	+	0.597165i	$0.796294\pi$
$978$	2.83771	0.0907399
$979$	−16.9104	−0.540457
$980$	0.595027	0.0190074
$981$	41.0640	1.31107
$982$	−1.35404	−0.0432092
$983$	−21.8946	−0.698330	−0.349165	−	0.937061i	$-0.613535\pi$
$983$	−21.8946	−0.698330	−0.349165	+	0.937061i	$0.613535\pi$
$984$	0.132959	0.00423857
$985$	−1.93780	−0.0617434
$986$	−12.3504	−0.393318
$987$	5.66316	0.180260
$988$	−0.850408	−0.0270551
$989$	−36.1443	−1.14932
$990$	1.89944	0.0603682
$991$	−2.00108	−0.0635665	−0.0317832	−	0.999495i	$-0.510119\pi$
$991$	−2.00108	−0.0635665	−0.0317832	+	0.999495i	$0.510119\pi$
$992$	−10.7659	−0.341819
$993$	−1.07893	−0.0342388
$994$	1.81942	0.0577086
$995$	6.35226	0.201380
$996$	4.27692	0.135519
$997$	−51.3334	−1.62575	−0.812873	−	0.582441i	$-0.802098\pi$
$997$	−51.3334	−1.62575	−0.812873	+	0.582441i	$0.802098\pi$
$998$	38.2002	1.20921
$999$	−20.2490	−0.640649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.16	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.16	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.423572 q^{3} +1.00000 q^{4} -0.487122 q^{5} -0.423572 q^{6} +2.40385 q^{7} +1.00000 q^{8} -2.82059 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.423572 q^{3} +1.00000 q^{4} -0.487122 q^{5} -0.423572 q^{6} +2.40385 q^{7} +1.00000 q^{8} -2.82059 q^{9} -0.487122 q^{10} +1.38245 q^{11} -0.423572 q^{12} -1.29945 q^{13} +2.40385 q^{14} +0.206331 q^{15} +1.00000 q^{16} -2.88437 q^{17} -2.82059 q^{18} +0.654438 q^{19} -0.487122 q^{20} -1.01820 q^{21} +1.38245 q^{22} -8.21328 q^{23} -0.423572 q^{24} -4.76271 q^{25} -1.29945 q^{26} +2.46544 q^{27} +2.40385 q^{28} +4.28186 q^{29} +0.206331 q^{30} -10.7659 q^{31} +1.00000 q^{32} -0.585566 q^{33} -2.88437 q^{34} -1.17097 q^{35} -2.82059 q^{36} -8.21314 q^{37} +0.654438 q^{38} +0.550409 q^{39} -0.487122 q^{40} -0.313899 q^{41} -1.01820 q^{42} +4.40071 q^{43} +1.38245 q^{44} +1.37397 q^{45} -8.21328 q^{46} -5.56192 q^{47} -0.423572 q^{48} -1.22152 q^{49} -4.76271 q^{50} +1.22174 q^{51} -1.29945 q^{52} +8.99732 q^{53} +2.46544 q^{54} -0.673421 q^{55} +2.40385 q^{56} -0.277201 q^{57} +4.28186 q^{58} +0.393777 q^{59} +0.206331 q^{60} +8.49444 q^{61} -10.7659 q^{62} -6.78026 q^{63} +1.00000 q^{64} +0.632989 q^{65} -0.585566 q^{66} +3.95326 q^{67} -2.88437 q^{68} +3.47891 q^{69} -1.17097 q^{70} +0.756879 q^{71} -2.82059 q^{72} -9.00288 q^{73} -8.21314 q^{74} +2.01735 q^{75} +0.654438 q^{76} +3.32320 q^{77} +0.550409 q^{78} +10.9266 q^{79} -0.487122 q^{80} +7.41747 q^{81} -0.313899 q^{82} -10.0973 q^{83} -1.01820 q^{84} +1.40504 q^{85} +4.40071 q^{86} -1.81367 q^{87} +1.38245 q^{88} -12.2322 q^{89} +1.37397 q^{90} -3.12368 q^{91} -8.21328 q^{92} +4.56015 q^{93} -5.56192 q^{94} -0.318791 q^{95} -0.423572 q^{96} +16.8496 q^{97} -1.22152 q^{98} -3.89932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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