LMFDB - Embedded newform 4011.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55639 q^{2} +1.00000 q^{3} +4.53513 q^{4} +0.170446 q^{5} -2.55639 q^{6} -1.00000 q^{7} -6.48077 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.55639 q^{2} +1.00000 q^{3} +4.53513 q^{4} +0.170446 q^{5} -2.55639 q^{6} -1.00000 q^{7} -6.48077 q^{8} +1.00000 q^{9} -0.435725 q^{10} +0.356639 q^{11} +4.53513 q^{12} -1.97147 q^{13} +2.55639 q^{14} +0.170446 q^{15} +7.49712 q^{16} +2.43492 q^{17} -2.55639 q^{18} -7.54758 q^{19} +0.772992 q^{20} -1.00000 q^{21} -0.911708 q^{22} -4.32395 q^{23} -6.48077 q^{24} -4.97095 q^{25} +5.03983 q^{26} +1.00000 q^{27} -4.53513 q^{28} +2.57991 q^{29} -0.435725 q^{30} +2.19863 q^{31} -6.20402 q^{32} +0.356639 q^{33} -6.22459 q^{34} -0.170446 q^{35} +4.53513 q^{36} +4.37448 q^{37} +19.2945 q^{38} -1.97147 q^{39} -1.10462 q^{40} +7.20002 q^{41} +2.55639 q^{42} -4.73213 q^{43} +1.61740 q^{44} +0.170446 q^{45} +11.0537 q^{46} -5.18342 q^{47} +7.49712 q^{48} +1.00000 q^{49} +12.7077 q^{50} +2.43492 q^{51} -8.94085 q^{52} +10.6089 q^{53} -2.55639 q^{54} +0.0607875 q^{55} +6.48077 q^{56} -7.54758 q^{57} -6.59524 q^{58} -5.46720 q^{59} +0.772992 q^{60} -3.72382 q^{61} -5.62055 q^{62} -1.00000 q^{63} +0.865643 q^{64} -0.336028 q^{65} -0.911708 q^{66} +10.9323 q^{67} +11.0427 q^{68} -4.32395 q^{69} +0.435725 q^{70} +3.92384 q^{71} -6.48077 q^{72} -3.78669 q^{73} -11.1829 q^{74} -4.97095 q^{75} -34.2292 q^{76} -0.356639 q^{77} +5.03983 q^{78} -0.543169 q^{79} +1.27785 q^{80} +1.00000 q^{81} -18.4061 q^{82} +10.0822 q^{83} -4.53513 q^{84} +0.415021 q^{85} +12.0972 q^{86} +2.57991 q^{87} -2.31130 q^{88} +18.0683 q^{89} -0.435725 q^{90} +1.97147 q^{91} -19.6097 q^{92} +2.19863 q^{93} +13.2508 q^{94} -1.28645 q^{95} -6.20402 q^{96} +10.1298 q^{97} -2.55639 q^{98} +0.356639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.55639	−1.80764	−0.903820	−	0.427913i	$-0.859249\pi$
$2$	−2.55639	−1.80764	−0.903820	+	0.427913i	$0.859249\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.53513	2.26756
$5$	0.170446	0.0762256	0.0381128	−	0.999273i	$-0.487865\pi$
$5$	0.170446	0.0762256	0.0381128	+	0.999273i	$0.487865\pi$
$6$	−2.55639	−1.04364
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.48077	−2.29130
$9$	1.00000	0.333333
$10$	−0.435725	−0.137788
$11$	0.356639	0.107531	0.0537654	−	0.998554i	$-0.482878\pi$
$11$	0.356639	0.107531	0.0537654	+	0.998554i	$0.482878\pi$
$12$	4.53513	1.30918
$13$	−1.97147	−0.546786	−0.273393	−	0.961902i	$-0.588146\pi$
$13$	−1.97147	−0.546786	−0.273393	+	0.961902i	$0.588146\pi$
$14$	2.55639	0.683224
$15$	0.170446	0.0440089
$16$	7.49712	1.87428
$17$	2.43492	0.590554	0.295277	−	0.955412i	$-0.404588\pi$
$17$	2.43492	0.590554	0.295277	+	0.955412i	$0.404588\pi$
$18$	−2.55639	−0.602547
$19$	−7.54758	−1.73153	−0.865766	−	0.500448i	$-0.833169\pi$
$19$	−7.54758	−1.73153	−0.865766	+	0.500448i	$0.833169\pi$
$20$	0.772992	0.172846
$21$	−1.00000	−0.218218
$22$	−0.911708	−0.194377
$23$	−4.32395	−0.901606	−0.450803	−	0.892624i	$-0.648862\pi$
$23$	−4.32395	−0.901606	−0.450803	+	0.892624i	$0.648862\pi$
$24$	−6.48077	−1.32288
$25$	−4.97095	−0.994190
$26$	5.03983	0.988393
$27$	1.00000	0.192450
$28$	−4.53513	−0.857058
$29$	2.57991	0.479077	0.239538	−	0.970887i	$-0.423004\pi$
$29$	2.57991	0.479077	0.239538	+	0.970887i	$0.423004\pi$
$30$	−0.435725	−0.0795522
$31$	2.19863	0.394886	0.197443	−	0.980314i	$-0.436736\pi$
$31$	2.19863	0.394886	0.197443	+	0.980314i	$0.436736\pi$
$32$	−6.20402	−1.09673
$33$	0.356639	0.0620829
$34$	−6.22459	−1.06751
$35$	−0.170446	−0.0288106
$36$	4.53513	0.755854
$37$	4.37448	0.719159	0.359580	−	0.933114i	$-0.382920\pi$
$37$	4.37448	0.719159	0.359580	+	0.933114i	$0.382920\pi$
$38$	19.2945	3.12999
$39$	−1.97147	−0.315687
$40$	−1.10462	−0.174656
$41$	7.20002	1.12445	0.562227	−	0.826983i	$-0.309945\pi$
$41$	7.20002	1.12445	0.562227	+	0.826983i	$0.309945\pi$
$42$	2.55639	0.394459
$43$	−4.73213	−0.721643	−0.360822	−	0.932635i	$-0.617504\pi$
$43$	−4.73213	−0.721643	−0.360822	+	0.932635i	$0.617504\pi$
$44$	1.61740	0.243833
$45$	0.170446	0.0254085
$46$	11.0537	1.62978
$47$	−5.18342	−0.756080	−0.378040	−	0.925789i	$-0.623402\pi$
$47$	−5.18342	−0.756080	−0.378040	+	0.925789i	$0.623402\pi$
$48$	7.49712	1.08212
$49$	1.00000	0.142857
$50$	12.7077	1.79714
$51$	2.43492	0.340956
$52$	−8.94085	−1.23987
$53$	10.6089	1.45724	0.728621	−	0.684917i	$-0.240161\pi$
$53$	10.6089	1.45724	0.728621	+	0.684917i	$0.240161\pi$
$54$	−2.55639	−0.347881
$55$	0.0607875	0.00819659
$56$	6.48077	0.866029
$57$	−7.54758	−0.999701
$58$	−6.59524	−0.865998
$59$	−5.46720	−0.711769	−0.355885	−	0.934530i	$-0.615820\pi$
$59$	−5.46720	−0.711769	−0.355885	+	0.934530i	$0.615820\pi$
$60$	0.772992	0.0997929
$61$	−3.72382	−0.476786	−0.238393	−	0.971169i	$-0.576621\pi$
$61$	−3.72382	−0.476786	−0.238393	+	0.971169i	$0.576621\pi$
$62$	−5.62055	−0.713811
$63$	−1.00000	−0.125988
$64$	0.865643	0.108205
$65$	−0.336028	−0.0416791
$66$	−0.911708	−0.112224
$67$	10.9323	1.33559	0.667794	−	0.744346i	$-0.267239\pi$
$67$	10.9323	1.33559	0.667794	+	0.744346i	$0.267239\pi$
$68$	11.0427	1.33912
$69$	−4.32395	−0.520542
$70$	0.435725	0.0520791
$71$	3.92384	0.465675	0.232837	−	0.972516i	$-0.425199\pi$
$71$	3.92384	0.465675	0.232837	+	0.972516i	$0.425199\pi$
$72$	−6.48077	−0.763766
$73$	−3.78669	−0.443198	−0.221599	−	0.975138i	$-0.571128\pi$
$73$	−3.78669	−0.443198	−0.221599	+	0.975138i	$0.571128\pi$
$74$	−11.1829	−1.29998
$75$	−4.97095	−0.573996
$76$	−34.2292	−3.92636
$77$	−0.356639	−0.0406428
$78$	5.03983	0.570649
$79$	−0.543169	−0.0611113	−0.0305557	−	0.999533i	$-0.509728\pi$
$79$	−0.543169	−0.0611113	−0.0305557	+	0.999533i	$0.509728\pi$
$80$	1.27785	0.142868
$81$	1.00000	0.111111
$82$	−18.4061	−2.03261
$83$	10.0822	1.10666	0.553330	−	0.832962i	$-0.313357\pi$
$83$	10.0822	1.10666	0.553330	+	0.832962i	$0.313357\pi$
$84$	−4.53513	−0.494823
$85$	0.415021	0.0450153
$86$	12.0972	1.30447
$87$	2.57991	0.276595
$88$	−2.31130	−0.246385
$89$	18.0683	1.91524	0.957620	−	0.288036i	$-0.0930023\pi$
$89$	18.0683	1.91524	0.957620	+	0.288036i	$0.0930023\pi$
$90$	−0.435725	−0.0459295
$91$	1.97147	0.206666
$92$	−19.6097	−2.04445
$93$	2.19863	0.227987
$94$	13.2508	1.36672
$95$	−1.28645	−0.131987
$96$	−6.20402	−0.633195
$97$	10.1298	1.02852	0.514262	−	0.857633i	$-0.328066\pi$
$97$	10.1298	1.02852	0.514262	+	0.857633i	$0.328066\pi$
$98$	−2.55639	−0.258234
$99$	0.356639	0.0358436
$100$	−22.5439	−2.25439
$101$	18.4714	1.83797	0.918987	−	0.394287i	$-0.129008\pi$
$101$	18.4714	1.83797	0.918987	+	0.394287i	$0.129008\pi$
$102$	−6.22459	−0.616327
$103$	−4.56049	−0.449358	−0.224679	−	0.974433i	$-0.572133\pi$
$103$	−4.56049	−0.449358	−0.224679	+	0.974433i	$0.572133\pi$
$104$	12.7766	1.25285
$105$	−0.170446	−0.0166338
$106$	−27.1204	−2.63417
$107$	−15.8873	−1.53588	−0.767941	−	0.640521i	$-0.778718\pi$
$107$	−15.8873	−1.53588	−0.767941	+	0.640521i	$0.778718\pi$
$108$	4.53513	0.436393
$109$	16.8811	1.61692	0.808460	−	0.588551i	$-0.200301\pi$
$109$	16.8811	1.61692	0.808460	+	0.588551i	$0.200301\pi$
$110$	−0.155397	−0.0148165
$111$	4.37448	0.415207
$112$	−7.49712	−0.708411
$113$	9.86605	0.928120	0.464060	−	0.885804i	$-0.346392\pi$
$113$	9.86605	0.928120	0.464060	+	0.885804i	$0.346392\pi$
$114$	19.2945	1.80710
$115$	−0.736998	−0.0687254
$116$	11.7002	1.08634
$117$	−1.97147	−0.182262
$118$	13.9763	1.28662
$119$	−2.43492	−0.223208
$120$	−1.10462	−0.100837
$121$	−10.8728	−0.988437
$122$	9.51952	0.861857
$123$	7.20002	0.649204
$124$	9.97106	0.895428
$125$	−1.69950	−0.152008
$126$	2.55639	0.227741
$127$	10.6387	0.944028	0.472014	−	0.881591i	$-0.343527\pi$
$127$	10.6387	0.944028	0.472014	+	0.881591i	$0.343527\pi$
$128$	10.1951	0.901129
$129$	−4.73213	−0.416641
$130$	0.859017	0.0753408
$131$	21.2694	1.85831	0.929157	−	0.369685i	$-0.120534\pi$
$131$	21.2694	1.85831	0.929157	+	0.369685i	$0.120534\pi$
$132$	1.61740	0.140777
$133$	7.54758	0.654458
$134$	−27.9471	−2.41426
$135$	0.170446	0.0146696
$136$	−15.7801	−1.35314
$137$	10.9640	0.936714	0.468357	−	0.883539i	$-0.344846\pi$
$137$	10.9640	0.936714	0.468357	+	0.883539i	$0.344846\pi$
$138$	11.0537	0.940953
$139$	−1.68009	−0.142504	−0.0712518	−	0.997458i	$-0.522699\pi$
$139$	−1.68009	−0.142504	−0.0712518	+	0.997458i	$0.522699\pi$
$140$	−0.772992	−0.0653298
$141$	−5.18342	−0.436523
$142$	−10.0309	−0.841772
$143$	−0.703101	−0.0587963
$144$	7.49712	0.624760
$145$	0.439734	0.0365179
$146$	9.68025	0.801143
$147$	1.00000	0.0824786
$148$	19.8388	1.63074
$149$	6.80867	0.557788	0.278894	−	0.960322i	$-0.410032\pi$
$149$	6.80867	0.557788	0.278894	+	0.960322i	$0.410032\pi$
$150$	12.7077	1.03758
$151$	8.24529	0.670992	0.335496	−	0.942042i	$-0.391096\pi$
$151$	8.24529	0.670992	0.335496	+	0.942042i	$0.391096\pi$
$152$	48.9141	3.96746
$153$	2.43492	0.196851
$154$	0.911708	0.0734675
$155$	0.374747	0.0301004
$156$	−8.94085	−0.715841
$157$	−12.7434	−1.01703	−0.508517	−	0.861052i	$-0.669806\pi$
$157$	−12.7434	−1.01703	−0.508517	+	0.861052i	$0.669806\pi$
$158$	1.38855	0.110467
$159$	10.6089	0.841339
$160$	−1.05745	−0.0835986
$161$	4.32395	0.340775
$162$	−2.55639	−0.200849
$163$	−0.282120	−0.0220974	−0.0110487	−	0.999939i	$-0.503517\pi$
$163$	−0.282120	−0.0220974	−0.0110487	+	0.999939i	$0.503517\pi$
$164$	32.6530	2.54977
$165$	0.0607875	0.00473230
$166$	−25.7739	−2.00044
$167$	−22.2911	−1.72493	−0.862467	−	0.506113i	$-0.831082\pi$
$167$	−22.2911	−1.72493	−0.862467	+	0.506113i	$0.831082\pi$
$168$	6.48077	0.500002
$169$	−9.11332	−0.701025
$170$	−1.06095	−0.0813715
$171$	−7.54758	−0.577178
$172$	−21.4608	−1.63637
$173$	−17.4903	−1.32976	−0.664880	−	0.746950i	$-0.731517\pi$
$173$	−17.4903	−1.32976	−0.664880	+	0.746950i	$0.731517\pi$
$174$	−6.59524	−0.499984
$175$	4.97095	0.375768
$176$	2.67377	0.201543
$177$	−5.46720	−0.410940
$178$	−46.1897	−3.46206
$179$	15.2695	1.14129	0.570646	−	0.821196i	$-0.306693\pi$
$179$	15.2695	1.14129	0.570646	+	0.821196i	$0.306693\pi$
$180$	0.772992	0.0576155
$181$	7.80321	0.580008	0.290004	−	0.957025i	$-0.406343\pi$
$181$	7.80321	0.580008	0.290004	+	0.957025i	$0.406343\pi$
$182$	−5.03983	−0.373577
$183$	−3.72382	−0.275272
$184$	28.0225	2.06585
$185$	0.745610	0.0548183
$186$	−5.62055	−0.412119
$187$	0.868386	0.0635027
$188$	−23.5075	−1.71446
$189$	−1.00000	−0.0727393
$190$	3.28867	0.238585
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	0.865643	0.0624724
$193$	26.2312	1.88817	0.944083	−	0.329707i	$-0.106950\pi$
$193$	26.2312	1.88817	0.944083	+	0.329707i	$0.106950\pi$
$194$	−25.8957	−1.85920
$195$	−0.336028	−0.0240634
$196$	4.53513	0.323938
$197$	−13.3946	−0.954323	−0.477161	−	0.878816i	$-0.658334\pi$
$197$	−13.3946	−0.954323	−0.477161	+	0.878816i	$0.658334\pi$
$198$	−0.911708	−0.0647923
$199$	22.7169	1.61036	0.805178	−	0.593033i	$-0.202070\pi$
$199$	22.7169	1.61036	0.805178	+	0.593033i	$0.202070\pi$
$200$	32.2156	2.27799
$201$	10.9323	0.771102
$202$	−47.2201	−3.32240
$203$	−2.57991	−0.181074
$204$	11.0427	0.773140
$205$	1.22721	0.0857122
$206$	11.6584	0.812278
$207$	−4.32395	−0.300535
$208$	−14.7803	−1.02483
$209$	−2.69176	−0.186193
$210$	0.435725	0.0300679
$211$	−21.4599	−1.47736	−0.738679	−	0.674057i	$-0.764550\pi$
$211$	−21.4599	−1.47736	−0.738679	+	0.674057i	$0.764550\pi$
$212$	48.1126	3.30439
$213$	3.92384	0.268857
$214$	40.6141	2.77632
$215$	−0.806571	−0.0550077
$216$	−6.48077	−0.440961
$217$	−2.19863	−0.149253
$218$	−43.1548	−2.92281
$219$	−3.78669	−0.255881
$220$	0.275679	0.0185863
$221$	−4.80035	−0.322907
$222$	−11.1829	−0.750545
$223$	−7.75135	−0.519069	−0.259534	−	0.965734i	$-0.583569\pi$
$223$	−7.75135	−0.519069	−0.259534	+	0.965734i	$0.583569\pi$
$224$	6.20402	0.414523
$225$	−4.97095	−0.331397
$226$	−25.2215	−1.67771
$227$	−23.8945	−1.58594	−0.792968	−	0.609263i	$-0.791465\pi$
$227$	−23.8945	−1.58594	−0.792968	+	0.609263i	$0.791465\pi$
$228$	−34.2292	−2.26689
$229$	3.89013	0.257067	0.128534	−	0.991705i	$-0.458973\pi$
$229$	3.89013	0.257067	0.128534	+	0.991705i	$0.458973\pi$
$230$	1.88405	0.124231
$231$	−0.356639	−0.0234651
$232$	−16.7198	−1.09771
$233$	−7.40977	−0.485430	−0.242715	−	0.970098i	$-0.578038\pi$
$233$	−7.40977	−0.485430	−0.242715	+	0.970098i	$0.578038\pi$
$234$	5.03983	0.329464
$235$	−0.883491	−0.0576326
$236$	−24.7945	−1.61398
$237$	−0.543169	−0.0352826
$238$	6.22459	0.403481
$239$	−7.91636	−0.512067	−0.256034	−	0.966668i	$-0.582416\pi$
$239$	−7.91636	−0.512067	−0.256034	+	0.966668i	$0.582416\pi$
$240$	1.27785	0.0824849
$241$	−22.3536	−1.43992	−0.719960	−	0.694015i	$-0.755840\pi$
$241$	−22.3536	−1.43992	−0.719960	+	0.694015i	$0.755840\pi$
$242$	27.7951	1.78674
$243$	1.00000	0.0641500
$244$	−16.8880	−1.08114
$245$	0.170446	0.0108894
$246$	−18.4061	−1.17353
$247$	14.8798	0.946778
$248$	−14.2488	−0.904801
$249$	10.0822	0.638931
$250$	4.34459	0.274776
$251$	13.0184	0.821711	0.410856	−	0.911700i	$-0.365230\pi$
$251$	13.0184	0.821711	0.410856	+	0.911700i	$0.365230\pi$
$252$	−4.53513	−0.285686
$253$	−1.54209	−0.0969503
$254$	−27.1966	−1.70646
$255$	0.415021	0.0259896
$256$	−27.7940	−1.73712
$257$	19.3143	1.20479	0.602397	−	0.798197i	$-0.294212\pi$
$257$	19.3143	1.20479	0.602397	+	0.798197i	$0.294212\pi$
$258$	12.0972	0.753137
$259$	−4.37448	−0.271817
$260$	−1.52393	−0.0945100
$261$	2.57991	0.159692
$262$	−54.3728	−3.35916
$263$	−1.14136	−0.0703790	−0.0351895	−	0.999381i	$-0.511203\pi$
$263$	−1.14136	−0.0703790	−0.0351895	+	0.999381i	$0.511203\pi$
$264$	−2.31130	−0.142250
$265$	1.80824	0.111079
$266$	−19.2945	−1.18302
$267$	18.0683	1.10576
$268$	49.5792	3.02853
$269$	10.6935	0.651993	0.325996	−	0.945371i	$-0.394300\pi$
$269$	10.6935	0.651993	0.325996	+	0.945371i	$0.394300\pi$
$270$	−0.435725	−0.0265174
$271$	18.7364	1.13816	0.569078	−	0.822284i	$-0.307300\pi$
$271$	18.7364	1.13816	0.569078	+	0.822284i	$0.307300\pi$
$272$	18.2549	1.10686
$273$	1.97147	0.119319
$274$	−28.0281	−1.69324
$275$	−1.77283	−0.106906
$276$	−19.6097	−1.18036
$277$	23.4718	1.41028	0.705142	−	0.709066i	$-0.250883\pi$
$277$	23.4718	1.41028	0.705142	+	0.709066i	$0.250883\pi$
$278$	4.29497	0.257595
$279$	2.19863	0.131629
$280$	1.10462	0.0660136
$281$	13.8189	0.824367	0.412184	−	0.911101i	$-0.364766\pi$
$281$	13.8189	0.824367	0.412184	+	0.911101i	$0.364766\pi$
$282$	13.2508	0.789076
$283$	−24.4352	−1.45252	−0.726261	−	0.687419i	$-0.758744\pi$
$283$	−24.4352	−1.45252	−0.726261	+	0.687419i	$0.758744\pi$
$284$	17.7951	1.05595
$285$	−1.28645	−0.0762028
$286$	1.79740	0.106283
$287$	−7.20002	−0.425004
$288$	−6.20402	−0.365575
$289$	−11.0712	−0.651246
$290$	−1.12413	−0.0660112
$291$	10.1298	0.593819
$292$	−17.1731	−1.00498
$293$	−8.37750	−0.489419	−0.244709	−	0.969596i	$-0.578693\pi$
$293$	−8.37750	−0.489419	−0.244709	+	0.969596i	$0.578693\pi$
$294$	−2.55639	−0.149092
$295$	−0.931861	−0.0542550
$296$	−28.3500	−1.64781
$297$	0.356639	0.0206943
$298$	−17.4056	−1.00828
$299$	8.52452	0.492986
$300$	−22.5439	−1.30157
$301$	4.73213	0.272755
$302$	−21.0782	−1.21291
$303$	18.4714	1.06116
$304$	−56.5851	−3.24538
$305$	−0.634708	−0.0363433
$306$	−6.22459	−0.355836
$307$	29.7269	1.69660	0.848302	−	0.529513i	$-0.177625\pi$
$307$	29.7269	1.69660	0.848302	+	0.529513i	$0.177625\pi$
$308$	−1.61740	−0.0921601
$309$	−4.56049	−0.259437
$310$	−0.957999	−0.0544107
$311$	6.92371	0.392607	0.196304	−	0.980543i	$-0.437106\pi$
$311$	6.92371	0.392607	0.196304	+	0.980543i	$0.437106\pi$
$312$	12.7766	0.723333
$313$	13.4960	0.762837	0.381419	−	0.924402i	$-0.375436\pi$
$313$	13.4960	0.762837	0.381419	+	0.924402i	$0.375436\pi$
$314$	32.5771	1.83843
$315$	−0.170446	−0.00960352
$316$	−2.46334	−0.138574
$317$	−10.1749	−0.571481	−0.285740	−	0.958307i	$-0.592239\pi$
$317$	−10.1749	−0.571481	−0.285740	+	0.958307i	$0.592239\pi$
$318$	−27.1204	−1.52084
$319$	0.920095	0.0515154
$320$	0.147545	0.00824802
$321$	−15.8873	−0.886741
$322$	−11.0537	−0.615999
$323$	−18.3777	−1.02256
$324$	4.53513	0.251951
$325$	9.80005	0.543609
$326$	0.721209	0.0399441
$327$	16.8811	0.933530
$328$	−46.6617	−2.57646
$329$	5.18342	0.285771
$330$	−0.155397	−0.00855430
$331$	−12.6785	−0.696873	−0.348437	−	0.937332i	$-0.613287\pi$
$331$	−12.6785	−0.696873	−0.348437	+	0.937332i	$0.613287\pi$
$332$	45.7238	2.50942
$333$	4.37448	0.239720
$334$	56.9846	3.11806
$335$	1.86336	0.101806
$336$	−7.49712	−0.409001
$337$	−12.1422	−0.661430	−0.330715	−	0.943731i	$-0.607290\pi$
$337$	−12.1422	−0.661430	−0.330715	+	0.943731i	$0.607290\pi$
$338$	23.2972	1.26720
$339$	9.86605	0.535850
$340$	1.88217	0.102075
$341$	0.784117	0.0424623
$342$	19.2945	1.04333
$343$	−1.00000	−0.0539949
$344$	30.6679	1.65350
$345$	−0.736998	−0.0396786
$346$	44.7119	2.40373
$347$	−17.7438	−0.952536	−0.476268	−	0.879300i	$-0.658011\pi$
$347$	−17.7438	−0.952536	−0.476268	+	0.879300i	$0.658011\pi$
$348$	11.7002	0.627197
$349$	−8.53010	−0.456606	−0.228303	−	0.973590i	$-0.573318\pi$
$349$	−8.53010	−0.456606	−0.228303	+	0.973590i	$0.573318\pi$
$350$	−12.7077	−0.679254
$351$	−1.97147	−0.105229
$352$	−2.21259	−0.117932
$353$	−19.3712	−1.03103	−0.515513	−	0.856881i	$-0.672399\pi$
$353$	−19.3712	−1.03103	−0.515513	+	0.856881i	$0.672399\pi$
$354$	13.9763	0.742832
$355$	0.668802	0.0354963
$356$	81.9422	4.34293
$357$	−2.43492	−0.128869
$358$	−39.0347	−2.06305
$359$	0.924011	0.0487674	0.0243837	−	0.999703i	$-0.492238\pi$
$359$	0.924011	0.0487674	0.0243837	+	0.999703i	$0.492238\pi$
$360$	−1.10462	−0.0582185
$361$	37.9659	1.99821
$362$	−19.9480	−1.04845
$363$	−10.8728	−0.570674
$364$	8.94085	0.468628
$365$	−0.645424	−0.0337830
$366$	9.51952	0.497593
$367$	−24.6043	−1.28433	−0.642167	−	0.766565i	$-0.721964\pi$
$367$	−24.6043	−1.28433	−0.642167	+	0.766565i	$0.721964\pi$
$368$	−32.4172	−1.68986
$369$	7.20002	0.374818
$370$	−1.90607	−0.0990918
$371$	−10.6089	−0.550786
$372$	9.97106	0.516976
$373$	14.2887	0.739839	0.369919	−	0.929064i	$-0.379385\pi$
$373$	14.2887	0.739839	0.369919	+	0.929064i	$0.379385\pi$
$374$	−2.21993	−0.114790
$375$	−1.69950	−0.0877620
$376$	33.5926	1.73240
$377$	−5.08620	−0.261952
$378$	2.55639	0.131486
$379$	24.8817	1.27809	0.639044	−	0.769170i	$-0.279330\pi$
$379$	24.8817	1.27809	0.639044	+	0.769170i	$0.279330\pi$
$380$	−5.83422	−0.299289
$381$	10.6387	0.545035
$382$	2.55639	0.130796
$383$	30.5035	1.55866	0.779328	−	0.626617i	$-0.215561\pi$
$383$	30.5035	1.55866	0.779328	+	0.626617i	$0.215561\pi$
$384$	10.1951	0.520267
$385$	−0.0607875	−0.00309802
$386$	−67.0573	−3.41313
$387$	−4.73213	−0.240548
$388$	45.9399	2.33224
$389$	−23.3985	−1.18635	−0.593175	−	0.805074i	$-0.702126\pi$
$389$	−23.3985	−1.18635	−0.593175	+	0.805074i	$0.702126\pi$
$390$	0.859017	0.0434980
$391$	−10.5285	−0.532447
$392$	−6.48077	−0.327328
$393$	21.2694	1.07290
$394$	34.2417	1.72507
$395$	−0.0925808	−0.00465825
$396$	1.61740	0.0812776
$397$	5.04880	0.253392	0.126696	−	0.991942i	$-0.459563\pi$
$397$	5.04880	0.253392	0.126696	+	0.991942i	$0.459563\pi$
$398$	−58.0732	−2.91095
$399$	7.54758	0.377851
$400$	−37.2678	−1.86339
$401$	18.6081	0.929242	0.464621	−	0.885510i	$-0.346191\pi$
$401$	18.6081	0.929242	0.464621	+	0.885510i	$0.346191\pi$
$402$	−27.9471	−1.39388
$403$	−4.33452	−0.215918
$404$	83.7702	4.16772
$405$	0.170446	0.00846951
$406$	6.59524	0.327317
$407$	1.56011	0.0773317
$408$	−15.7801	−0.781233
$409$	12.4901	0.617597	0.308799	−	0.951127i	$-0.400073\pi$
$409$	12.4901	0.617597	0.308799	+	0.951127i	$0.400073\pi$
$410$	−3.13723	−0.154937
$411$	10.9640	0.540812
$412$	−20.6824	−1.01895
$413$	5.46720	0.269023
$414$	11.0537	0.543260
$415$	1.71846	0.0843558
$416$	12.2310	0.599674
$417$	−1.68009	−0.0822745
$418$	6.88119	0.336570
$419$	23.9753	1.17127	0.585635	−	0.810575i	$-0.300845\pi$
$419$	23.9753	1.17127	0.585635	+	0.810575i	$0.300845\pi$
$420$	−0.772992	−0.0377182
$421$	14.9847	0.730311	0.365156	−	0.930946i	$-0.381016\pi$
$421$	14.9847	0.730311	0.365156	+	0.930946i	$0.381016\pi$
$422$	54.8598	2.67053
$423$	−5.18342	−0.252027
$424$	−68.7538	−3.33898
$425$	−12.1038	−0.587123
$426$	−10.0309	−0.485997
$427$	3.72382	0.180208
$428$	−72.0508	−3.48271
$429$	−0.703101	−0.0339461
$430$	2.06191	0.0994341
$431$	2.46660	0.118812	0.0594059	−	0.998234i	$-0.481079\pi$
$431$	2.46660	0.118812	0.0594059	+	0.998234i	$0.481079\pi$
$432$	7.49712	0.360705
$433$	−28.6959	−1.37904	−0.689519	−	0.724268i	$-0.742178\pi$
$433$	−28.6959	−1.37904	−0.689519	+	0.724268i	$0.742178\pi$
$434$	5.62055	0.269795
$435$	0.439734	0.0210836
$436$	76.5581	3.66647
$437$	32.6353	1.56116
$438$	9.68025	0.462540
$439$	−29.6914	−1.41709	−0.708546	−	0.705665i	$-0.750648\pi$
$439$	−29.6914	−1.41709	−0.708546	+	0.705665i	$0.750648\pi$
$440$	−0.393950	−0.0187808
$441$	1.00000	0.0476190
$442$	12.2716	0.583699
$443$	33.4663	1.59003	0.795016	−	0.606588i	$-0.207462\pi$
$443$	33.4663	1.59003	0.795016	+	0.606588i	$0.207462\pi$
$444$	19.8388	0.941508
$445$	3.07967	0.145990
$446$	19.8155	0.938289
$447$	6.80867	0.322039
$448$	−0.865643	−0.0408978
$449$	28.3766	1.33917	0.669586	−	0.742734i	$-0.266471\pi$
$449$	28.3766	1.33917	0.669586	+	0.742734i	$0.266471\pi$
$450$	12.7077	0.599046
$451$	2.56781	0.120913
$452$	44.7438	2.10457
$453$	8.24529	0.387397
$454$	61.0837	2.86680
$455$	0.336028	0.0157532
$456$	48.9141	2.29061
$457$	0.579394	0.0271029	0.0135515	−	0.999908i	$-0.495686\pi$
$457$	0.579394	0.0271029	0.0135515	+	0.999908i	$0.495686\pi$
$458$	−9.94470	−0.464685
$459$	2.43492	0.113652
$460$	−3.34238	−0.155839
$461$	15.7158	0.731957	0.365978	−	0.930623i	$-0.380734\pi$
$461$	15.7158	0.731957	0.365978	+	0.930623i	$0.380734\pi$
$462$	0.911708	0.0424165
$463$	39.3457	1.82855	0.914276	−	0.405092i	$-0.132761\pi$
$463$	39.3457	1.82855	0.914276	+	0.405092i	$0.132761\pi$
$464$	19.3419	0.897924
$465$	0.374747	0.0173785
$466$	18.9423	0.877483
$467$	0.961037	0.0444715	0.0222358	−	0.999753i	$-0.492922\pi$
$467$	0.961037	0.0444715	0.0222358	+	0.999753i	$0.492922\pi$
$468$	−8.94085	−0.413291
$469$	−10.9323	−0.504805
$470$	2.25855	0.104179
$471$	−12.7434	−0.587185
$472$	35.4317	1.63088
$473$	−1.68766	−0.0775988
$474$	1.38855	0.0637783
$475$	37.5186	1.72147
$476$	−11.0427	−0.506139
$477$	10.6089	0.485747
$478$	20.2373	0.925633
$479$	12.3988	0.566516	0.283258	−	0.959044i	$-0.408585\pi$
$479$	12.3988	0.566516	0.283258	+	0.959044i	$0.408585\pi$
$480$	−1.05745	−0.0482657
$481$	−8.62413	−0.393226
$482$	57.1445	2.60286
$483$	4.32395	0.196747
$484$	−49.3096	−2.24134
$485$	1.72658	0.0783999
$486$	−2.55639	−0.115960
$487$	−19.0608	−0.863726	−0.431863	−	0.901939i	$-0.642144\pi$
$487$	−19.0608	−0.863726	−0.431863	+	0.901939i	$0.642144\pi$
$488$	24.1332	1.09246
$489$	−0.282120	−0.0127579
$490$	−0.435725	−0.0196841
$491$	−3.58329	−0.161712	−0.0808558	−	0.996726i	$-0.525765\pi$
$491$	−3.58329	−0.161712	−0.0808558	+	0.996726i	$0.525765\pi$
$492$	32.6530	1.47211
$493$	6.28186	0.282921
$494$	−38.0385	−1.71143
$495$	0.0607875	0.00273220
$496$	16.4834	0.740126
$497$	−3.92384	−0.176008
$498$	−25.7739	−1.15496
$499$	11.8198	0.529126	0.264563	−	0.964368i	$-0.414772\pi$
$499$	11.8198	0.529126	0.264563	+	0.964368i	$0.414772\pi$
$500$	−7.70747	−0.344688
$501$	−22.2911	−0.995891
$502$	−33.2800	−1.48536
$503$	−40.3256	−1.79803	−0.899015	−	0.437917i	$-0.855716\pi$
$503$	−40.3256	−1.79803	−0.899015	+	0.437917i	$0.855716\pi$
$504$	6.48077	0.288676
$505$	3.14837	0.140101
$506$	3.94218	0.175251
$507$	−9.11332	−0.404737
$508$	48.2477	2.14064
$509$	−37.6976	−1.67091	−0.835457	−	0.549555i	$-0.814797\pi$
$509$	−37.6976	−1.67091	−0.835457	+	0.549555i	$0.814797\pi$
$510$	−1.06095	−0.0469799
$511$	3.78669	0.167513
$512$	50.6620	2.23896
$513$	−7.54758	−0.333234
$514$	−49.3749	−2.17783
$515$	−0.777315	−0.0342526
$516$	−21.4608	−0.944760
$517$	−1.84861	−0.0813018
$518$	11.1829	0.491347
$519$	−17.4903	−0.767738
$520$	2.17772	0.0954993
$521$	3.43013	0.150277	0.0751384	−	0.997173i	$-0.476060\pi$
$521$	3.43013	0.150277	0.0751384	+	0.997173i	$0.476060\pi$
$522$	−6.59524	−0.288666
$523$	3.63049	0.158750	0.0793750	−	0.996845i	$-0.474708\pi$
$523$	3.63049	0.158750	0.0793750	+	0.996845i	$0.474708\pi$
$524$	96.4593	4.21384
$525$	4.97095	0.216950
$526$	2.91775	0.127220
$527$	5.35348	0.233201
$528$	2.67377	0.116361
$529$	−4.30346	−0.187107
$530$	−4.62256	−0.200791
$531$	−5.46720	−0.237256
$532$	34.2292	1.48402
$533$	−14.1946	−0.614836
$534$	−46.1897	−1.99882
$535$	−2.70792	−0.117073
$536$	−70.8495	−3.06023
$537$	15.2695	0.658925
$538$	−27.3367	−1.17857
$539$	0.356639	0.0153615
$540$	0.772992	0.0332643
$541$	27.9356	1.20104	0.600522	−	0.799608i	$-0.294960\pi$
$541$	27.9356	1.20104	0.600522	+	0.799608i	$0.294960\pi$
$542$	−47.8975	−2.05738
$543$	7.80321	0.334868
$544$	−15.1063	−0.647676
$545$	2.87732	0.123251
$546$	−5.03983	−0.215685
$547$	20.7308	0.886383	0.443192	−	0.896427i	$-0.353846\pi$
$547$	20.7308	0.886383	0.443192	+	0.896427i	$0.353846\pi$
$548$	49.7229	2.12406
$549$	−3.72382	−0.158929
$550$	4.53205	0.193247
$551$	−19.4720	−0.829537
$552$	28.0225	1.19272
$553$	0.543169	0.0230979
$554$	−60.0030	−2.54929
$555$	0.745610	0.0316494
$556$	−7.61944	−0.323136
$557$	0.642124	0.0272077	0.0136038	−	0.999907i	$-0.495670\pi$
$557$	0.642124	0.0272077	0.0136038	+	0.999907i	$0.495670\pi$
$558$	−5.62055	−0.237937
$559$	9.32923	0.394585
$560$	−1.27785	−0.0539991
$561$	0.868386	0.0366633
$562$	−35.3265	−1.49016
$563$	2.19576	0.0925401	0.0462700	−	0.998929i	$-0.485267\pi$
$563$	2.19576	0.0925401	0.0462700	+	0.998929i	$0.485267\pi$
$564$	−23.5075	−0.989843
$565$	1.68163	0.0707465
$566$	62.4659	2.62564
$567$	−1.00000	−0.0419961
$568$	−25.4295	−1.06700
$569$	−3.79051	−0.158906	−0.0794531	−	0.996839i	$-0.525317\pi$
$569$	−3.79051	−0.158906	−0.0794531	+	0.996839i	$0.525317\pi$
$570$	3.28867	0.137747
$571$	−0.412734	−0.0172724	−0.00863619	−	0.999963i	$-0.502749\pi$
$571$	−0.412734	−0.0172724	−0.00863619	+	0.999963i	$0.502749\pi$
$572$	−3.18865	−0.133324
$573$	−1.00000	−0.0417756
$574$	18.4061	0.768254
$575$	21.4941	0.896367
$576$	0.865643	0.0360685
$577$	6.06824	0.252624	0.126312	−	0.991991i	$-0.459686\pi$
$577$	6.06824	0.252624	0.126312	+	0.991991i	$0.459686\pi$
$578$	28.3023	1.17722
$579$	26.2312	1.09013
$580$	1.99425	0.0828066
$581$	−10.0822	−0.418278
$582$	−25.8957	−1.07341
$583$	3.78354	0.156698
$584$	24.5407	1.01550
$585$	−0.336028	−0.0138930
$586$	21.4161	0.884693
$587$	37.7792	1.55931	0.779657	−	0.626207i	$-0.215394\pi$
$587$	37.7792	1.55931	0.779657	+	0.626207i	$0.215394\pi$
$588$	4.53513	0.187025
$589$	−16.5943	−0.683757
$590$	2.38220	0.0980736
$591$	−13.3946	−0.550979
$592$	32.7960	1.34791
$593$	−35.3535	−1.45180	−0.725898	−	0.687803i	$-0.758575\pi$
$593$	−35.3535	−1.45180	−0.725898	+	0.687803i	$0.758575\pi$
$594$	−0.911708	−0.0374078
$595$	−0.415021	−0.0170142
$596$	30.8782	1.26482
$597$	22.7169	0.929740
$598$	−21.7920	−0.891141
$599$	42.4757	1.73551	0.867755	−	0.496993i	$-0.165562\pi$
$599$	42.4757	1.73551	0.867755	+	0.496993i	$0.165562\pi$
$600$	32.2156	1.31520
$601$	−1.74928	−0.0713544	−0.0356772	−	0.999363i	$-0.511359\pi$
$601$	−1.74928	−0.0713544	−0.0356772	+	0.999363i	$0.511359\pi$
$602$	−12.0972	−0.493044
$603$	10.9323	0.445196
$604$	37.3934	1.52152
$605$	−1.85322	−0.0753442
$606$	−47.2201	−1.91819
$607$	32.2709	1.30984	0.654918	−	0.755700i	$-0.272703\pi$
$607$	32.2709	1.30984	0.654918	+	0.755700i	$0.272703\pi$
$608$	46.8253	1.89902
$609$	−2.57991	−0.104543
$610$	1.62256	0.0656956
$611$	10.2189	0.413414
$612$	11.0427	0.446373
$613$	−5.05570	−0.204198	−0.102099	−	0.994774i	$-0.532556\pi$
$613$	−5.05570	−0.204198	−0.102099	+	0.994774i	$0.532556\pi$
$614$	−75.9935	−3.06685
$615$	1.22721	0.0494859
$616$	2.31130	0.0931248
$617$	2.22585	0.0896092	0.0448046	−	0.998996i	$-0.485733\pi$
$617$	2.22585	0.0896092	0.0448046	+	0.998996i	$0.485733\pi$
$618$	11.6584	0.468969
$619$	−15.8952	−0.638880	−0.319440	−	0.947606i	$-0.603495\pi$
$619$	−15.8952	−0.638880	−0.319440	+	0.947606i	$0.603495\pi$
$620$	1.69952	0.0682545
$621$	−4.32395	−0.173514
$622$	−17.6997	−0.709693
$623$	−18.0683	−0.723892
$624$	−14.7803	−0.591686
$625$	24.5651	0.982603
$626$	−34.5010	−1.37894
$627$	−2.69176	−0.107499
$628$	−57.7929	−2.30619
$629$	10.6515	0.424702
$630$	0.435725	0.0173597
$631$	9.89305	0.393836	0.196918	−	0.980420i	$-0.436907\pi$
$631$	9.89305	0.393836	0.196918	+	0.980420i	$0.436907\pi$
$632$	3.52016	0.140024
$633$	−21.4599	−0.852954
$634$	26.0111	1.03303
$635$	1.81331	0.0719591
$636$	48.1126	1.90779
$637$	−1.97147	−0.0781123
$638$	−2.35212	−0.0931214
$639$	3.92384	0.155225
$640$	1.73771	0.0686891
$641$	−8.72757	−0.344718	−0.172359	−	0.985034i	$-0.555139\pi$
$641$	−8.72757	−0.344718	−0.172359	+	0.985034i	$0.555139\pi$
$642$	40.6141	1.60291
$643$	−4.29325	−0.169309	−0.0846547	−	0.996410i	$-0.526979\pi$
$643$	−4.29325	−0.169309	−0.0846547	+	0.996410i	$0.526979\pi$
$644$	19.6097	0.772729
$645$	−0.806571	−0.0317587
$646$	46.9806	1.84843
$647$	1.54908	0.0609004	0.0304502	−	0.999536i	$-0.490306\pi$
$647$	1.54908	0.0609004	0.0304502	+	0.999536i	$0.490306\pi$
$648$	−6.48077	−0.254589
$649$	−1.94982	−0.0765370
$650$	−25.0528	−0.982650
$651$	−2.19863	−0.0861711
$652$	−1.27945	−0.0501072
$653$	−18.6679	−0.730530	−0.365265	−	0.930904i	$-0.619022\pi$
$653$	−18.6679	−0.730530	−0.365265	+	0.930904i	$0.619022\pi$
$654$	−43.1548	−1.68749
$655$	3.62527	0.141651
$656$	53.9794	2.10754
$657$	−3.78669	−0.147733
$658$	−13.2508	−0.516572
$659$	−3.24534	−0.126420	−0.0632102	−	0.998000i	$-0.520134\pi$
$659$	−3.24534	−0.126420	−0.0632102	+	0.998000i	$0.520134\pi$
$660$	0.275679	0.0107308
$661$	47.3045	1.83993	0.919967	−	0.391997i	$-0.128215\pi$
$661$	47.3045	1.83993	0.919967	+	0.391997i	$0.128215\pi$
$662$	32.4112	1.25970
$663$	−4.80035	−0.186430
$664$	−65.3401	−2.53569
$665$	1.28645	0.0498864
$666$	−11.1829	−0.433327
$667$	−11.1554	−0.431938
$668$	−101.093	−3.91140
$669$	−7.75135	−0.299684
$670$	−4.76346	−0.184029
$671$	−1.32806	−0.0512691
$672$	6.20402	0.239325
$673$	−38.6832	−1.49113	−0.745563	−	0.666435i	$-0.767819\pi$
$673$	−38.6832	−1.49113	−0.745563	+	0.666435i	$0.767819\pi$
$674$	31.0403	1.19563
$675$	−4.97095	−0.191332
$676$	−41.3301	−1.58962
$677$	49.9753	1.92071	0.960353	−	0.278788i	$-0.0899326\pi$
$677$	49.9753	1.92071	0.960353	+	0.278788i	$0.0899326\pi$
$678$	−25.2215	−0.968625
$679$	−10.1298	−0.388746
$680$	−2.68965	−0.103144
$681$	−23.8945	−0.915640
$682$	−2.00451	−0.0767566
$683$	27.5400	1.05379	0.526895	−	0.849930i	$-0.323356\pi$
$683$	27.5400	1.05379	0.526895	+	0.849930i	$0.323356\pi$
$684$	−34.2292	−1.30879
$685$	1.86876	0.0714015
$686$	2.55639	0.0976034
$687$	3.89013	0.148418
$688$	−35.4774	−1.35256
$689$	−20.9151	−0.796800
$690$	1.88405	0.0717247
$691$	13.8118	0.525427	0.262714	−	0.964874i	$-0.415383\pi$
$691$	13.8118	0.525427	0.262714	+	0.964874i	$0.415383\pi$
$692$	−79.3206	−3.01532
$693$	−0.356639	−0.0135476
$694$	45.3600	1.72184
$695$	−0.286365	−0.0108624
$696$	−16.7198	−0.633762
$697$	17.5314	0.664051
$698$	21.8063	0.825379
$699$	−7.40977	−0.280263
$700$	22.5439	0.852079
$701$	32.2598	1.21844	0.609218	−	0.793003i	$-0.291483\pi$
$701$	32.2598	1.21844	0.609218	+	0.793003i	$0.291483\pi$
$702$	5.03983	0.190216
$703$	−33.0167	−1.24525
$704$	0.308722	0.0116354
$705$	−0.883491	−0.0332742
$706$	49.5204	1.86373
$707$	−18.4714	−0.694689
$708$	−24.7945	−0.931833
$709$	4.64781	0.174552	0.0872761	−	0.996184i	$-0.472184\pi$
$709$	4.64781	0.174552	0.0872761	+	0.996184i	$0.472184\pi$
$710$	−1.70972	−0.0641646
$711$	−0.543169	−0.0203704
$712$	−117.097	−4.38838
$713$	−9.50676	−0.356031
$714$	6.22459	0.232950
$715$	−0.119841	−0.00448178
$716$	69.2489	2.58795
$717$	−7.91636	−0.295642
$718$	−2.36213	−0.0881540
$719$	12.9904	0.484460	0.242230	−	0.970219i	$-0.422121\pi$
$719$	12.9904	0.484460	0.242230	+	0.970219i	$0.422121\pi$
$720$	1.27785	0.0476227
$721$	4.56049	0.169842
$722$	−97.0556	−3.61204
$723$	−22.3536	−0.831339
$724$	35.3885	1.31520
$725$	−12.8246	−0.476293
$726$	27.7951	1.03157
$727$	−15.4858	−0.574336	−0.287168	−	0.957880i	$-0.592714\pi$
$727$	−15.4858	−0.574336	−0.287168	+	0.957880i	$0.592714\pi$
$728$	−12.7766	−0.473533
$729$	1.00000	0.0370370
$730$	1.64996	0.0610676
$731$	−11.5223	−0.426169
$732$	−16.8880	−0.624198
$733$	−40.2184	−1.48550	−0.742751	−	0.669568i	$-0.766479\pi$
$733$	−40.2184	−1.48550	−0.742751	+	0.669568i	$0.766479\pi$
$734$	62.8981	2.32161
$735$	0.170446	0.00628698
$736$	26.8259	0.988814
$737$	3.89887	0.143617
$738$	−18.4061	−0.677536
$739$	−17.1731	−0.631724	−0.315862	−	0.948805i	$-0.602294\pi$
$739$	−17.1731	−0.631724	−0.315862	+	0.948805i	$0.602294\pi$
$740$	3.38144	0.124304
$741$	14.8798	0.546623
$742$	27.1204	0.995623
$743$	32.5376	1.19369	0.596844	−	0.802357i	$-0.296421\pi$
$743$	32.5376	1.19369	0.596844	+	0.802357i	$0.296421\pi$
$744$	−14.2488	−0.522387
$745$	1.16051	0.0425177
$746$	−36.5274	−1.33736
$747$	10.0822	0.368887
$748$	3.93824	0.143996
$749$	15.8873	0.580509
$750$	4.34459	0.158642
$751$	32.0229	1.16853	0.584265	−	0.811563i	$-0.301383\pi$
$751$	32.0229	1.16853	0.584265	+	0.811563i	$0.301383\pi$
$752$	−38.8607	−1.41711
$753$	13.0184	0.474415
$754$	13.0023	0.473516
$755$	1.40537	0.0511468
$756$	−4.53513	−0.164941
$757$	−3.06211	−0.111294	−0.0556472	−	0.998450i	$-0.517722\pi$
$757$	−3.06211	−0.111294	−0.0556472	+	0.998450i	$0.517722\pi$
$758$	−63.6074	−2.31032
$759$	−1.54209	−0.0559743
$760$	8.33720	0.302422
$761$	17.8095	0.645593	0.322797	−	0.946468i	$-0.395377\pi$
$761$	17.8095	0.645593	0.322797	+	0.946468i	$0.395377\pi$
$762$	−27.1966	−0.985227
$763$	−16.8811	−0.611139
$764$	−4.53513	−0.164075
$765$	0.415021	0.0150051
$766$	−77.9788	−2.81749
$767$	10.7784	0.389186
$768$	−27.7940	−1.00293
$769$	30.5005	1.09988	0.549938	−	0.835205i	$-0.314651\pi$
$769$	30.5005	1.09988	0.549938	+	0.835205i	$0.314651\pi$
$770$	0.155397	0.00560011
$771$	19.3143	0.695588
$772$	118.962	4.28154
$773$	−3.34451	−0.120294	−0.0601468	−	0.998190i	$-0.519157\pi$
$773$	−3.34451	−0.120294	−0.0601468	+	0.998190i	$0.519157\pi$
$774$	12.0972	0.434824
$775$	−10.9293	−0.392591
$776$	−65.6488	−2.35666
$777$	−4.37448	−0.156933
$778$	59.8156	2.14449
$779$	−54.3427	−1.94703
$780$	−1.52393	−0.0545654
$781$	1.39940	0.0500743
$782$	26.9148	0.962472
$783$	2.57991	0.0921983
$784$	7.49712	0.267754
$785$	−2.17206	−0.0775240
$786$	−54.3728	−1.93941
$787$	−28.7589	−1.02514	−0.512572	−	0.858644i	$-0.671307\pi$
$787$	−28.7589	−1.02514	−0.512572	+	0.858644i	$0.671307\pi$
$788$	−60.7460	−2.16399
$789$	−1.14136	−0.0406333
$790$	0.236673	0.00842044
$791$	−9.86605	−0.350796
$792$	−2.31130	−0.0821283
$793$	7.34137	0.260700
$794$	−12.9067	−0.458042
$795$	1.80824	0.0641316
$796$	103.024	3.65159
$797$	−24.0859	−0.853165	−0.426583	−	0.904449i	$-0.640283\pi$
$797$	−24.0859	−0.853165	−0.426583	+	0.904449i	$0.640283\pi$
$798$	−19.2945	−0.683019
$799$	−12.6212	−0.446506
$800$	30.8398	1.09035
$801$	18.0683	0.638413
$802$	−47.5694	−1.67973
$803$	−1.35048	−0.0476574
$804$	49.5792	1.74852
$805$	0.736998	0.0259758
$806$	11.0807	0.390302
$807$	10.6935	0.376428
$808$	−119.709	−4.21135
$809$	−32.4758	−1.14179	−0.570895	−	0.821023i	$-0.693404\pi$
$809$	−32.4758	−1.14179	−0.570895	+	0.821023i	$0.693404\pi$
$810$	−0.435725	−0.0153098
$811$	19.6671	0.690605	0.345303	−	0.938491i	$-0.387776\pi$
$811$	19.6671	0.690605	0.345303	+	0.938491i	$0.387776\pi$
$812$	−11.7002	−0.410597
$813$	18.7364	0.657114
$814$	−3.98824	−0.139788
$815$	−0.0480861	−0.00168438
$816$	18.2549	0.639048
$817$	35.7161	1.24955
$818$	−31.9296	−1.11639
$819$	1.97147	0.0688886
$820$	5.56556	0.194358
$821$	23.0374	0.804011	0.402005	−	0.915637i	$-0.368313\pi$
$821$	23.0374	0.804011	0.402005	+	0.915637i	$0.368313\pi$
$822$	−28.0281	−0.977593
$823$	2.27565	0.0793241	0.0396621	−	0.999213i	$-0.487372\pi$
$823$	2.27565	0.0793241	0.0396621	+	0.999213i	$0.487372\pi$
$824$	29.5555	1.02961
$825$	−1.77283	−0.0617222
$826$	−13.9763	−0.486298
$827$	−27.0678	−0.941241	−0.470620	−	0.882336i	$-0.655970\pi$
$827$	−27.0678	−0.941241	−0.470620	+	0.882336i	$0.655970\pi$
$828$	−19.6097	−0.681483
$829$	14.1513	0.491495	0.245747	−	0.969334i	$-0.420967\pi$
$829$	14.1513	0.491495	0.245747	+	0.969334i	$0.420967\pi$
$830$	−4.39305	−0.152485
$831$	23.4718	0.814228
$832$	−1.70659	−0.0591652
$833$	2.43492	0.0843648
$834$	4.29497	0.148723
$835$	−3.79941	−0.131484
$836$	−12.2075	−0.422204
$837$	2.19863	0.0759958
$838$	−61.2902	−2.11724
$839$	5.71295	0.197233	0.0986164	−	0.995126i	$-0.468558\pi$
$839$	5.71295	0.197233	0.0986164	+	0.995126i	$0.468558\pi$
$840$	1.10462	0.0381130
$841$	−22.3441	−0.770486
$842$	−38.3068	−1.32014
$843$	13.8189	0.475949
$844$	−97.3233	−3.35001
$845$	−1.55333	−0.0534360
$846$	13.2508	0.455573
$847$	10.8728	0.373594
$848$	79.5361	2.73128
$849$	−24.4352	−0.838614
$850$	30.9421	1.06131
$851$	−18.9150	−0.648398
$852$	17.7951	0.609651
$853$	17.0106	0.582431	0.291215	−	0.956658i	$-0.405940\pi$
$853$	17.0106	0.582431	0.291215	+	0.956658i	$0.405940\pi$
$854$	−9.51952	−0.325751
$855$	−1.28645	−0.0439957
$856$	102.962	3.51916
$857$	33.5684	1.14667	0.573337	−	0.819320i	$-0.305649\pi$
$857$	33.5684	1.14667	0.573337	+	0.819320i	$0.305649\pi$
$858$	1.79740	0.0613623
$859$	17.5719	0.599545	0.299772	−	0.954011i	$-0.403089\pi$
$859$	17.5719	0.599545	0.299772	+	0.954011i	$0.403089\pi$
$860$	−3.65790	−0.124733
$861$	−7.20002	−0.245376
$862$	−6.30558	−0.214769
$863$	13.0532	0.444336	0.222168	−	0.975008i	$-0.428687\pi$
$863$	13.0532	0.444336	0.222168	+	0.975008i	$0.428687\pi$
$864$	−6.20402	−0.211065
$865$	−2.98114	−0.101362
$866$	73.3580	2.49280
$867$	−11.0712	−0.375997
$868$	−9.97106	−0.338440
$869$	−0.193715	−0.00657135
$870$	−1.12413	−0.0381116
$871$	−21.5526	−0.730281
$872$	−109.403	−3.70485
$873$	10.1298	0.342841
$874$	−83.4286	−2.82202
$875$	1.69950	0.0574537
$876$	−17.1731	−0.580226
$877$	46.5378	1.57147	0.785736	−	0.618562i	$-0.212285\pi$
$877$	46.5378	1.57147	0.785736	+	0.618562i	$0.212285\pi$
$878$	75.9027	2.56159
$879$	−8.37750	−0.282566
$880$	0.455732	0.0153627
$881$	22.7098	0.765111	0.382556	−	0.923932i	$-0.375044\pi$
$881$	22.7098	0.765111	0.382556	+	0.923932i	$0.375044\pi$
$882$	−2.55639	−0.0860781
$883$	−44.4914	−1.49726	−0.748628	−	0.662990i	$-0.769287\pi$
$883$	−44.4914	−1.49726	−0.748628	+	0.662990i	$0.769287\pi$
$884$	−21.7702	−0.732211
$885$	−0.931861	−0.0313242
$886$	−85.5530	−2.87421
$887$	5.10716	0.171482	0.0857408	−	0.996317i	$-0.472674\pi$
$887$	5.10716	0.171482	0.0857408	+	0.996317i	$0.472674\pi$
$888$	−28.3500	−0.951363
$889$	−10.6387	−0.356809
$890$	−7.87283	−0.263898
$891$	0.356639	0.0119479
$892$	−35.1533	−1.17702
$893$	39.1223	1.30918
$894$	−17.4056	−0.582131
$895$	2.60261	0.0869957
$896$	−10.1951	−0.340595
$897$	8.52452	0.284625
$898$	−72.5415	−2.42074
$899$	5.67226	0.189180
$900$	−22.5439	−0.751463
$901$	25.8317	0.860580
$902$	−6.56432	−0.218568
$903$	4.73213	0.157475
$904$	−63.9396	−2.12660
$905$	1.33002	0.0442115
$906$	−21.0782	−0.700275
$907$	−47.4298	−1.57488	−0.787440	−	0.616391i	$-0.788594\pi$
$907$	−47.4298	−1.57488	−0.787440	+	0.616391i	$0.788594\pi$
$908$	−108.365	−3.59621
$909$	18.4714	0.612658
$910$	−0.859017	−0.0284762
$911$	−43.6463	−1.44607	−0.723033	−	0.690813i	$-0.757253\pi$
$911$	−43.6463	−1.44607	−0.723033	+	0.690813i	$0.757253\pi$
$912$	−56.5851	−1.87372
$913$	3.59569	0.119000
$914$	−1.48116	−0.0489923
$915$	−0.634708	−0.0209828
$916$	17.6423	0.582916
$917$	−21.2694	−0.702377
$918$	−6.22459	−0.205442
$919$	−13.3110	−0.439089	−0.219544	−	0.975603i	$-0.570457\pi$
$919$	−13.3110	−0.439089	−0.219544	+	0.975603i	$0.570457\pi$
$920$	4.77632	0.157470
$921$	29.7269	0.979534
$922$	−40.1757	−1.32311
$923$	−7.73572	−0.254624
$924$	−1.61740	−0.0532087
$925$	−21.7453	−0.714981
$926$	−100.583	−3.30536
$927$	−4.56049	−0.149786
$928$	−16.0058	−0.525416
$929$	−18.5025	−0.607048	−0.303524	−	0.952824i	$-0.598163\pi$
$929$	−18.5025	−0.607048	−0.303524	+	0.952824i	$0.598163\pi$
$930$	−0.957999	−0.0314140
$931$	−7.54758	−0.247362
$932$	−33.6043	−1.10074
$933$	6.92371	0.226672
$934$	−2.45679	−0.0803885
$935$	0.148013	0.00484053
$936$	12.7766	0.417617
$937$	9.96406	0.325512	0.162756	−	0.986666i	$-0.447962\pi$
$937$	9.96406	0.325512	0.162756	+	0.986666i	$0.447962\pi$
$938$	27.9471	0.912506
$939$	13.4960	0.440424
$940$	−4.00675	−0.130686
$941$	−33.9634	−1.10717	−0.553587	−	0.832791i	$-0.686742\pi$
$941$	−33.9634	−1.10717	−0.553587	+	0.832791i	$0.686742\pi$
$942$	32.5771	1.06142
$943$	−31.1325	−1.01381
$944$	−40.9883	−1.33405
$945$	−0.170446	−0.00554460
$946$	4.31432	0.140271
$947$	11.8362	0.384624	0.192312	−	0.981334i	$-0.438401\pi$
$947$	11.8362	0.384624	0.192312	+	0.981334i	$0.438401\pi$
$948$	−2.46334	−0.0800056
$949$	7.46532	0.242335
$950$	−95.9122	−3.11180
$951$	−10.1749	−0.329945
$952$	15.7801	0.511437
$953$	−51.9127	−1.68162	−0.840808	−	0.541333i	$-0.817920\pi$
$953$	−51.9127	−1.68162	−0.840808	+	0.541333i	$0.817920\pi$
$954$	−27.1204	−0.878057
$955$	−0.170446	−0.00551549
$956$	−35.9017	−1.16114
$957$	0.920095	0.0297425
$958$	−31.6962	−1.02406
$959$	−10.9640	−0.354044
$960$	0.147545	0.00476200
$961$	−26.1660	−0.844065
$962$	22.0466	0.710812
$963$	−15.8873	−0.511960
$964$	−101.376	−3.26511
$965$	4.47100	0.143927
$966$	−11.0537	−0.355647
$967$	−54.0376	−1.73773	−0.868867	−	0.495046i	$-0.835151\pi$
$967$	−54.0376	−1.73773	−0.868867	+	0.495046i	$0.835151\pi$
$968$	70.4642	2.26480
$969$	−18.3777	−0.590377
$970$	−4.41381	−0.141719
$971$	−11.5734	−0.371409	−0.185704	−	0.982606i	$-0.559457\pi$
$971$	−11.5734	−0.371409	−0.185704	+	0.982606i	$0.559457\pi$
$972$	4.53513	0.145464
$973$	1.68009	0.0538613
$974$	48.7268	1.56131
$975$	9.80005	0.313853
$976$	−27.9179	−0.893630
$977$	24.2281	0.775126	0.387563	−	0.921843i	$-0.373317\pi$
$977$	24.2281	0.775126	0.387563	+	0.921843i	$0.373317\pi$
$978$	0.721209	0.0230617
$979$	6.44387	0.205947
$980$	0.772992	0.0246923
$981$	16.8811	0.538974
$982$	9.16028	0.292316
$983$	−21.1336	−0.674057	−0.337028	−	0.941494i	$-0.609422\pi$
$983$	−21.1336	−0.674057	−0.337028	+	0.941494i	$0.609422\pi$
$984$	−46.6617	−1.48752
$985$	−2.28304	−0.0727438
$986$	−16.0589	−0.511419
$987$	5.18342	0.164990
$988$	67.4817	2.14688
$989$	20.4615	0.650638
$990$	−0.155397	−0.00493883
$991$	7.41878	0.235665	0.117833	−	0.993033i	$-0.462405\pi$
$991$	7.41878	0.235665	0.117833	+	0.993033i	$0.462405\pi$
$992$	−13.6403	−0.433081
$993$	−12.6785	−0.402340
$994$	10.0309	0.318160
$995$	3.87199	0.122750
$996$	45.7238	1.44882
$997$	0.518017	0.0164058	0.00820288	−	0.999966i	$-0.497389\pi$
$997$	0.518017	0.0164058	0.00820288	+	0.999966i	$0.497389\pi$
$998$	−30.2160	−0.956470
$999$	4.37448	0.138402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.2	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.2	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55639 q^{2} +1.00000 q^{3} +4.53513 q^{4} +0.170446 q^{5} -2.55639 q^{6} -1.00000 q^{7} -6.48077 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.55639 q^{2} +1.00000 q^{3} +4.53513 q^{4} +0.170446 q^{5} -2.55639 q^{6} -1.00000 q^{7} -6.48077 q^{8} +1.00000 q^{9} -0.435725 q^{10} +0.356639 q^{11} +4.53513 q^{12} -1.97147 q^{13} +2.55639 q^{14} +0.170446 q^{15} +7.49712 q^{16} +2.43492 q^{17} -2.55639 q^{18} -7.54758 q^{19} +0.772992 q^{20} -1.00000 q^{21} -0.911708 q^{22} -4.32395 q^{23} -6.48077 q^{24} -4.97095 q^{25} +5.03983 q^{26} +1.00000 q^{27} -4.53513 q^{28} +2.57991 q^{29} -0.435725 q^{30} +2.19863 q^{31} -6.20402 q^{32} +0.356639 q^{33} -6.22459 q^{34} -0.170446 q^{35} +4.53513 q^{36} +4.37448 q^{37} +19.2945 q^{38} -1.97147 q^{39} -1.10462 q^{40} +7.20002 q^{41} +2.55639 q^{42} -4.73213 q^{43} +1.61740 q^{44} +0.170446 q^{45} +11.0537 q^{46} -5.18342 q^{47} +7.49712 q^{48} +1.00000 q^{49} +12.7077 q^{50} +2.43492 q^{51} -8.94085 q^{52} +10.6089 q^{53} -2.55639 q^{54} +0.0607875 q^{55} +6.48077 q^{56} -7.54758 q^{57} -6.59524 q^{58} -5.46720 q^{59} +0.772992 q^{60} -3.72382 q^{61} -5.62055 q^{62} -1.00000 q^{63} +0.865643 q^{64} -0.336028 q^{65} -0.911708 q^{66} +10.9323 q^{67} +11.0427 q^{68} -4.32395 q^{69} +0.435725 q^{70} +3.92384 q^{71} -6.48077 q^{72} -3.78669 q^{73} -11.1829 q^{74} -4.97095 q^{75} -34.2292 q^{76} -0.356639 q^{77} +5.03983 q^{78} -0.543169 q^{79} +1.27785 q^{80} +1.00000 q^{81} -18.4061 q^{82} +10.0822 q^{83} -4.53513 q^{84} +0.415021 q^{85} +12.0972 q^{86} +2.57991 q^{87} -2.31130 q^{88} +18.0683 q^{89} -0.435725 q^{90} +1.97147 q^{91} -19.6097 q^{92} +2.19863 q^{93} +13.2508 q^{94} -1.28645 q^{95} -6.20402 q^{96} +10.1298 q^{97} -2.55639 q^{98} +0.356639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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