LMFDB - Embedded newform 2738.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, 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("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{36})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 9x^{2} - 3 $ x^6 - 6x^4 + 9x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.684040$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -2.61144 q^{5} -0.347296 q^{6} -2.07935 q^{7} -1.00000 q^{8} -2.87939 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -2.61144 q^{5} -0.347296 q^{6} -2.07935 q^{7} -1.00000 q^{8} -2.87939 q^{9} +2.61144 q^{10} -5.99619 q^{11} +0.347296 q^{12} +4.11695 q^{13} +2.07935 q^{14} -0.906942 q^{15} +1.00000 q^{16} +0.962542 q^{17} +2.87939 q^{18} +1.56408 q^{19} -2.61144 q^{20} -0.722150 q^{21} +5.99619 q^{22} -6.37054 q^{23} -0.347296 q^{24} +1.81960 q^{25} -4.11695 q^{26} -2.04189 q^{27} -2.07935 q^{28} -4.05523 q^{29} +0.906942 q^{30} +3.39997 q^{31} -1.00000 q^{32} -2.08246 q^{33} -0.962542 q^{34} +5.43008 q^{35} -2.87939 q^{36} -1.56408 q^{38} +1.42980 q^{39} +2.61144 q^{40} -10.3715 q^{41} +0.722150 q^{42} -3.76932 q^{43} -5.99619 q^{44} +7.51933 q^{45} +6.37054 q^{46} -6.17501 q^{47} +0.347296 q^{48} -2.67632 q^{49} -1.81960 q^{50} +0.334287 q^{51} +4.11695 q^{52} -8.02781 q^{53} +2.04189 q^{54} +15.6587 q^{55} +2.07935 q^{56} +0.543198 q^{57} +4.05523 q^{58} +5.10018 q^{59} -0.906942 q^{60} +9.73135 q^{61} -3.39997 q^{62} +5.98724 q^{63} +1.00000 q^{64} -10.7512 q^{65} +2.08246 q^{66} +10.5537 q^{67} +0.962542 q^{68} -2.21246 q^{69} -5.43008 q^{70} +10.8018 q^{71} +2.87939 q^{72} -3.55293 q^{73} +0.631940 q^{75} +1.56408 q^{76} +12.4682 q^{77} -1.42980 q^{78} -2.54971 q^{79} -2.61144 q^{80} +7.92902 q^{81} +10.3715 q^{82} +6.91602 q^{83} -0.722150 q^{84} -2.51362 q^{85} +3.76932 q^{86} -1.40837 q^{87} +5.99619 q^{88} +16.2636 q^{89} -7.51933 q^{90} -8.56057 q^{91} -6.37054 q^{92} +1.18080 q^{93} +6.17501 q^{94} -4.08449 q^{95} -0.347296 q^{96} -16.3015 q^{97} +2.67632 q^{98} +17.2653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 12 q^{13} - 6 q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} + 12 q^{19} + 6 q^{20} - 12 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} + 18 q^{31} - 6 q^{32} + 6 q^{33} - 12 q^{34} + 24 q^{35} - 6 q^{36} - 12 q^{38} + 6 q^{39} - 6 q^{40} - 12 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} - 6 q^{50} + 24 q^{51} + 12 q^{52} - 24 q^{53} + 6 q^{54} + 36 q^{55} + 24 q^{57} + 6 q^{58} + 12 q^{59} - 6 q^{60} + 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} - 6 q^{66} + 18 q^{67} + 12 q^{68} + 24 q^{69} - 24 q^{70} + 24 q^{71} + 6 q^{72} - 18 q^{75} + 12 q^{76} + 30 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} - 18 q^{81} + 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} - 6 q^{90} + 12 q^{91} - 6 q^{92} - 36 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 12 * q^13 - 6 * q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 + 12 * q^19 + 6 * q^20 - 12 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 + 18 * q^31 - 6 * q^32 + 6 * q^33 - 12 * q^34 + 24 * q^35 - 6 * q^36 - 12 * q^38 + 6 * q^39 - 6 * q^40 - 12 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 - 6 * q^50 + 24 * q^51 + 12 * q^52 - 24 * q^53 + 6 * q^54 + 36 * q^55 + 24 * q^57 + 6 * q^58 + 12 * q^59 - 6 * q^60 + 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 - 6 * q^66 + 18 * q^67 + 12 * q^68 + 24 * q^69 - 24 * q^70 + 24 * q^71 + 6 * q^72 - 18 * q^75 + 12 * q^76 + 30 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 - 18 * q^81 + 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 - 6 * q^90 + 12 * q^91 - 6 * q^92 - 36 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^97 + 12 * q^98 + 12 * 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
$3$	0.347296	0.200512	0.100256	−	0.994962i	$-0.468034\pi$
$3$	0.347296	0.200512	0.100256	+	0.994962i	$0.468034\pi$
$4$	1.00000	0.500000
$5$	−2.61144	−1.16787	−0.583935	−	0.811801i	$-0.698488\pi$
$5$	−2.61144	−1.16787	−0.583935	+	0.811801i	$0.698488\pi$
$6$	−0.347296	−0.141783
$7$	−2.07935	−0.785919	−0.392960	−	0.919556i	$-0.628549\pi$
$7$	−2.07935	−0.785919	−0.392960	+	0.919556i	$0.628549\pi$
$8$	−1.00000	−0.353553
$9$	−2.87939	−0.959795
$10$	2.61144	0.825809
$11$	−5.99619	−1.80792	−0.903960	−	0.427618i	$-0.859353\pi$
$11$	−5.99619	−1.80792	−0.903960	+	0.427618i	$0.859353\pi$
$12$	0.347296	0.100256
$13$	4.11695	1.14184	0.570918	−	0.821007i	$-0.306587\pi$
$13$	4.11695	1.14184	0.570918	+	0.821007i	$0.306587\pi$
$14$	2.07935	0.555729
$15$	−0.906942	−0.234171
$16$	1.00000	0.250000
$17$	0.962542	0.233451	0.116725	−	0.993164i	$-0.462760\pi$
$17$	0.962542	0.233451	0.116725	+	0.993164i	$0.462760\pi$
$18$	2.87939	0.678678
$19$	1.56408	0.358824	0.179412	−	0.983774i	$-0.442581\pi$
$19$	1.56408	0.358824	0.179412	+	0.983774i	$0.442581\pi$
$20$	−2.61144	−0.583935
$21$	−0.722150	−0.157586
$22$	5.99619	1.27839
$23$	−6.37054	−1.32835	−0.664174	−	0.747578i	$-0.731217\pi$
$23$	−6.37054	−1.32835	−0.664174	+	0.747578i	$0.731217\pi$
$24$	−0.347296	−0.0708916
$25$	1.81960	0.363920
$26$	−4.11695	−0.807400
$27$	−2.04189	−0.392962
$28$	−2.07935	−0.392960
$29$	−4.05523	−0.753037	−0.376519	−	0.926409i	$-0.622879\pi$
$29$	−4.05523	−0.753037	−0.376519	+	0.926409i	$0.622879\pi$
$30$	0.906942	0.165584
$31$	3.39997	0.610653	0.305326	−	0.952248i	$-0.401234\pi$
$31$	3.39997	0.610653	0.305326	+	0.952248i	$0.401234\pi$
$32$	−1.00000	−0.176777
$33$	−2.08246	−0.362509
$34$	−0.962542	−0.165075
$35$	5.43008	0.917851
$36$	−2.87939	−0.479898
$37$	0	0
$37$	0	0
$38$	−1.56408	−0.253727
$39$	1.42980	0.228952
$40$	2.61144	0.412904
$41$	−10.3715	−1.61975	−0.809877	−	0.586599i	$-0.800466\pi$
$41$	−10.3715	−1.61975	−0.809877	+	0.586599i	$0.800466\pi$
$42$	0.722150	0.111430
$43$	−3.76932	−0.574816	−0.287408	−	0.957808i	$-0.592794\pi$
$43$	−3.76932	−0.574816	−0.287408	+	0.957808i	$0.592794\pi$
$44$	−5.99619	−0.903960
$45$	7.51933	1.12092
$46$	6.37054	0.939284
$47$	−6.17501	−0.900717	−0.450359	−	0.892848i	$-0.648704\pi$
$47$	−6.17501	−0.900717	−0.450359	+	0.892848i	$0.648704\pi$
$48$	0.347296	0.0501279
$49$	−2.67632	−0.382331
$50$	−1.81960	−0.257330
$51$	0.334287	0.0468096
$52$	4.11695	0.570918
$53$	−8.02781	−1.10270	−0.551352	−	0.834272i	$-0.685888\pi$
$53$	−8.02781	−1.10270	−0.551352	+	0.834272i	$0.685888\pi$
$54$	2.04189	0.277866
$55$	15.6587	2.11141
$56$	2.07935	0.277864
$57$	0.543198	0.0719484
$58$	4.05523	0.532478
$59$	5.10018	0.663987	0.331993	−	0.943282i	$-0.392279\pi$
$59$	5.10018	0.663987	0.331993	+	0.943282i	$0.392279\pi$
$60$	−0.906942	−0.117086
$61$	9.73135	1.24597	0.622986	−	0.782233i	$-0.285919\pi$
$61$	9.73135	1.24597	0.622986	+	0.782233i	$0.285919\pi$
$62$	−3.39997	−0.431797
$63$	5.98724	0.754322
$64$	1.00000	0.125000
$65$	−10.7512	−1.33352
$66$	2.08246	0.256333
$67$	10.5537	1.28934	0.644671	−	0.764460i	$-0.276994\pi$
$67$	10.5537	1.28934	0.644671	+	0.764460i	$0.276994\pi$
$68$	0.962542	0.116725
$69$	−2.21246	−0.266349
$70$	−5.43008	−0.649019
$71$	10.8018	1.28193	0.640966	−	0.767569i	$-0.278534\pi$
$71$	10.8018	1.28193	0.640966	+	0.767569i	$0.278534\pi$
$72$	2.87939	0.339339
$73$	−3.55293	−0.415839	−0.207920	−	0.978146i	$-0.566669\pi$
$73$	−3.55293	−0.415839	−0.207920	+	0.978146i	$0.566669\pi$
$74$	0	0
$75$	0.631940	0.0729701
$76$	1.56408	0.179412
$77$	12.4682	1.42088
$78$	−1.42980	−0.161893
$79$	−2.54971	−0.286865	−0.143433	−	0.989660i	$-0.545814\pi$
$79$	−2.54971	−0.286865	−0.143433	+	0.989660i	$0.545814\pi$
$80$	−2.61144	−0.291967
$81$	7.92902	0.881002
$82$	10.3715	1.14534
$83$	6.91602	0.759132	0.379566	−	0.925165i	$-0.376073\pi$
$83$	6.91602	0.759132	0.379566	+	0.925165i	$0.376073\pi$
$84$	−0.722150	−0.0787930
$85$	−2.51362	−0.272640
$86$	3.76932	0.406457
$87$	−1.40837	−0.150993
$88$	5.99619	0.639196
$89$	16.2636	1.72393	0.861967	−	0.506965i	$-0.169233\pi$
$89$	16.2636	1.72393	0.861967	+	0.506965i	$0.169233\pi$
$90$	−7.51933	−0.792607
$91$	−8.56057	−0.897391
$92$	−6.37054	−0.664174
$93$	1.18080	0.122443
$94$	6.17501	0.636903
$95$	−4.08449	−0.419059
$96$	−0.347296	−0.0354458
$97$	−16.3015	−1.65517	−0.827583	−	0.561344i	$-0.810284\pi$
$97$	−16.3015	−1.65517	−0.827583	+	0.561344i	$0.810284\pi$
$98$	2.67632	0.270349
$99$	17.2653	1.73523
$100$	1.81960	0.181960
$101$	−4.10247	−0.408211	−0.204106	−	0.978949i	$-0.565429\pi$
$101$	−4.10247	−0.408211	−0.204106	+	0.978949i	$0.565429\pi$
$102$	−0.334287	−0.0330994
$103$	10.7993	1.06409	0.532045	−	0.846716i	$-0.321424\pi$
$103$	10.7993	1.06409	0.532045	+	0.846716i	$0.321424\pi$
$104$	−4.11695	−0.403700
$105$	1.88585	0.184040
$106$	8.02781	0.779730
$107$	20.3055	1.96301	0.981505	−	0.191438i	$-0.0613149\pi$
$107$	20.3055	1.96301	0.981505	+	0.191438i	$0.0613149\pi$
$108$	−2.04189	−0.196481
$109$	−6.22982	−0.596708	−0.298354	−	0.954455i	$-0.596438\pi$
$109$	−6.22982	−0.596708	−0.298354	+	0.954455i	$0.596438\pi$
$110$	−15.6587	−1.49300
$111$	0	0
$112$	−2.07935	−0.196480
$113$	6.13197	0.576848	0.288424	−	0.957503i	$-0.406869\pi$
$113$	6.13197	0.576848	0.288424	+	0.957503i	$0.406869\pi$
$114$	−0.543198	−0.0508752
$115$	16.6363	1.55134
$116$	−4.05523	−0.376519
$117$	−11.8543	−1.09593
$118$	−5.10018	−0.469509
$119$	−2.00146	−0.183473
$120$	0.906942	0.0827921
$121$	24.9543	2.26857
$122$	−9.73135	−0.881035
$123$	−3.60198	−0.324780
$124$	3.39997	0.305326
$125$	8.30542	0.742859
$126$	−5.98724	−0.533386
$127$	−6.38115	−0.566235	−0.283118	−	0.959085i	$-0.591369\pi$
$127$	−6.38115	−0.566235	−0.283118	+	0.959085i	$0.591369\pi$
$128$	−1.00000	−0.0883883
$129$	−1.30907	−0.115257
$130$	10.7512	0.942938
$131$	10.4534	0.913315	0.456657	−	0.889643i	$-0.349047\pi$
$131$	10.4534	0.913315	0.456657	+	0.889643i	$0.349047\pi$
$132$	−2.08246	−0.181254
$133$	−3.25226	−0.282007
$134$	−10.5537	−0.911702
$135$	5.33226	0.458928
$136$	−0.962542	−0.0825373
$137$	6.24181	0.533274	0.266637	−	0.963797i	$-0.414088\pi$
$137$	6.24181	0.533274	0.266637	+	0.963797i	$0.414088\pi$
$138$	2.21246	0.188337
$139$	−6.89241	−0.584606	−0.292303	−	0.956326i	$-0.594422\pi$
$139$	−6.89241	−0.584606	−0.292303	+	0.956326i	$0.594422\pi$
$140$	5.43008	0.458926
$141$	−2.14456	−0.180604
$142$	−10.8018	−0.906463
$143$	−24.6860	−2.06435
$144$	−2.87939	−0.239949
$145$	10.5900	0.879449
$146$	3.55293	0.294043
$147$	−0.929475	−0.0766618
$148$	0	0
$149$	3.49508	0.286328	0.143164	−	0.989699i	$-0.454272\pi$
$149$	3.49508	0.286328	0.143164	+	0.989699i	$0.454272\pi$
$150$	−0.631940	−0.0515977
$151$	9.40855	0.765657	0.382828	−	0.923819i	$-0.374950\pi$
$151$	9.40855	0.765657	0.382828	+	0.923819i	$0.374950\pi$
$152$	−1.56408	−0.126863
$153$	−2.77153	−0.224065
$154$	−12.4682	−1.00471
$155$	−8.87880	−0.713163
$156$	1.42980	0.114476
$157$	2.53470	0.202291	0.101146	−	0.994872i	$-0.467749\pi$
$157$	2.53470	0.202291	0.101146	+	0.994872i	$0.467749\pi$
$158$	2.54971	0.202844
$159$	−2.78803	−0.221105
$160$	2.61144	0.206452
$161$	13.2466	1.04398
$162$	−7.92902	−0.622962
$163$	9.37796	0.734539	0.367269	−	0.930115i	$-0.380293\pi$
$163$	9.37796	0.734539	0.367269	+	0.930115i	$0.380293\pi$
$164$	−10.3715	−0.809877
$165$	5.43820	0.423363
$166$	−6.91602	−0.536787
$167$	−10.4225	−0.806515	−0.403257	−	0.915087i	$-0.632122\pi$
$167$	−10.4225	−0.806515	−0.403257	+	0.915087i	$0.632122\pi$
$168$	0.722150	0.0557151
$169$	3.94928	0.303791
$170$	2.51362	0.192786
$171$	−4.50358	−0.344397
$172$	−3.76932	−0.287408
$173$	−2.92981	−0.222749	−0.111374	−	0.993779i	$-0.535525\pi$
$173$	−2.92981	−0.222749	−0.111374	+	0.993779i	$0.535525\pi$
$174$	1.40837	0.106768
$175$	−3.78358	−0.286011
$176$	−5.99619	−0.451980
$177$	1.77127	0.133137
$178$	−16.2636	−1.21900
$179$	8.76703	0.655279	0.327639	−	0.944803i	$-0.393747\pi$
$179$	8.76703	0.655279	0.327639	+	0.944803i	$0.393747\pi$
$180$	7.51933	0.560458
$181$	−26.7562	−1.98878	−0.994388	−	0.105797i	$-0.966261\pi$
$181$	−26.7562	−1.98878	−0.994388	+	0.105797i	$0.966261\pi$
$182$	8.56057	0.634552
$183$	3.37966	0.249832
$184$	6.37054	0.469642
$185$	0	0
$186$	−1.18080	−0.0865802
$187$	−5.77158	−0.422060
$188$	−6.17501	−0.450359
$189$	4.24580	0.308836
$190$	4.08449	0.296320
$191$	1.81758	0.131515	0.0657577	−	0.997836i	$-0.479054\pi$
$191$	1.81758	0.131515	0.0657577	+	0.997836i	$0.479054\pi$
$192$	0.347296	0.0250640
$193$	−1.06505	−0.0766642	−0.0383321	−	0.999265i	$-0.512204\pi$
$193$	−1.06505	−0.0766642	−0.0383321	+	0.999265i	$0.512204\pi$
$194$	16.3015	1.17038
$195$	−3.73384	−0.267386
$196$	−2.67632	−0.191165
$197$	−15.7567	−1.12262	−0.561308	−	0.827607i	$-0.689702\pi$
$197$	−15.7567	−1.12262	−0.561308	+	0.827607i	$0.689702\pi$
$198$	−17.2653	−1.22699
$199$	−20.6371	−1.46292	−0.731461	−	0.681883i	$-0.761161\pi$
$199$	−20.6371	−1.46292	−0.731461	+	0.681883i	$0.761161\pi$
$200$	−1.81960	−0.128665
$201$	3.66527	0.258528
$202$	4.10247	0.288649
$203$	8.43223	0.591826
$204$	0.334287	0.0234048
$205$	27.0845	1.89166
$206$	−10.7993	−0.752426
$207$	18.3432	1.27494
$208$	4.11695	0.285459
$209$	−9.37850	−0.648725
$210$	−1.88585	−0.130136
$211$	6.20140	0.426922	0.213461	−	0.976952i	$-0.431526\pi$
$211$	6.20140	0.426922	0.213461	+	0.976952i	$0.431526\pi$
$212$	−8.02781	−0.551352
$213$	3.75141	0.257042
$214$	−20.3055	−1.38806
$215$	9.84335	0.671311
$216$	2.04189	0.138933
$217$	−7.06972	−0.479924
$218$	6.22982	0.421937
$219$	−1.23392	−0.0833806
$220$	15.6587	1.05571
$221$	3.96274	0.266563
$222$	0	0
$223$	0.839150	0.0561936	0.0280968	−	0.999605i	$-0.491055\pi$
$223$	0.839150	0.0561936	0.0280968	+	0.999605i	$0.491055\pi$
$224$	2.07935	0.138932
$225$	−5.23932	−0.349288
$226$	−6.13197	−0.407893
$227$	−6.52369	−0.432993	−0.216496	−	0.976283i	$-0.569463\pi$
$227$	−6.52369	−0.432993	−0.216496	+	0.976283i	$0.569463\pi$
$228$	0.543198	0.0359742
$229$	6.60414	0.436414	0.218207	−	0.975903i	$-0.429979\pi$
$229$	6.60414	0.436414	0.218207	+	0.975903i	$0.429979\pi$
$230$	−16.6363	−1.09696
$231$	4.33015	0.284903
$232$	4.05523	0.266239
$233$	22.6093	1.48119	0.740594	−	0.671953i	$-0.234544\pi$
$233$	22.6093	1.48119	0.740594	+	0.671953i	$0.234544\pi$
$234$	11.8543	0.774939
$235$	16.1256	1.05192
$236$	5.10018	0.331993
$237$	−0.885507	−0.0575198
$238$	2.00146	0.129735
$239$	17.1474	1.10917	0.554586	−	0.832126i	$-0.312877\pi$
$239$	17.1474	1.10917	0.554586	+	0.832126i	$0.312877\pi$
$240$	−0.906942	−0.0585429
$241$	5.68755	0.366367	0.183184	−	0.983079i	$-0.441360\pi$
$241$	5.68755	0.366367	0.183184	+	0.983079i	$0.441360\pi$
$242$	−24.9543	−1.60412
$243$	8.87939	0.569613
$244$	9.73135	0.622986
$245$	6.98903	0.446513
$246$	3.60198	0.229654
$247$	6.43923	0.409718
$248$	−3.39997	−0.215898
$249$	2.40191	0.152215
$250$	−8.30542	−0.525281
$251$	−25.3490	−1.60001	−0.800006	−	0.599992i	$-0.795170\pi$
$251$	−25.3490	−1.60001	−0.800006	+	0.599992i	$0.795170\pi$
$252$	5.98724	0.377161
$253$	38.1990	2.40155
$254$	6.38115	0.400389
$255$	−0.872970	−0.0546675
$256$	1.00000	0.0625000
$257$	−5.17095	−0.322555	−0.161278	−	0.986909i	$-0.551561\pi$
$257$	−5.17095	−0.322555	−0.161278	+	0.986909i	$0.551561\pi$
$258$	1.30907	0.0814993
$259$	0	0
$260$	−10.7512	−0.666758
$261$	11.6766	0.722761
$262$	−10.4534	−0.645811
$263$	−9.67206	−0.596405	−0.298202	−	0.954503i	$-0.596387\pi$
$263$	−9.67206	−0.596405	−0.298202	+	0.954503i	$0.596387\pi$
$264$	2.08246	0.128166
$265$	20.9641	1.28782
$266$	3.25226	0.199409
$267$	5.64827	0.345669
$268$	10.5537	0.644671
$269$	−23.8765	−1.45578	−0.727889	−	0.685695i	$-0.759498\pi$
$269$	−23.8765	−1.45578	−0.727889	+	0.685695i	$0.759498\pi$
$270$	−5.33226	−0.324511
$271$	18.3088	1.11218	0.556092	−	0.831121i	$-0.312300\pi$
$271$	18.3088	1.11218	0.556092	+	0.831121i	$0.312300\pi$
$272$	0.962542	0.0583627
$273$	−2.97305	−0.179937
$274$	−6.24181	−0.377082
$275$	−10.9107	−0.657937
$276$	−2.21246	−0.133175
$277$	17.7317	1.06539	0.532697	−	0.846306i	$-0.321179\pi$
$277$	17.7317	1.06539	0.532697	+	0.846306i	$0.321179\pi$
$278$	6.89241	0.413379
$279$	−9.78982	−0.586101
$280$	−5.43008	−0.324509
$281$	−15.2484	−0.909643	−0.454822	−	0.890583i	$-0.650297\pi$
$281$	−15.2484	−0.909643	−0.454822	+	0.890583i	$0.650297\pi$
$282$	2.14456	0.127707
$283$	−24.4532	−1.45359	−0.726795	−	0.686854i	$-0.758991\pi$
$283$	−24.4532	−1.45359	−0.726795	+	0.686854i	$0.758991\pi$
$284$	10.8018	0.640966
$285$	−1.41853	−0.0840263
$286$	24.6860	1.45971
$287$	21.5659	1.27300
$288$	2.87939	0.169669
$289$	−16.0735	−0.945501
$290$	−10.5900	−0.621864
$291$	−5.66145	−0.331880
$292$	−3.55293	−0.207920
$293$	12.5725	0.734494	0.367247	−	0.930123i	$-0.380300\pi$
$293$	12.5725	0.734494	0.367247	+	0.930123i	$0.380300\pi$
$294$	0.929475	0.0542081
$295$	−13.3188	−0.775450
$296$	0	0
$297$	12.2436	0.710443
$298$	−3.49508	−0.202464
$299$	−26.2272	−1.51676
$300$	0.631940	0.0364851
$301$	7.83773	0.451759
$302$	−9.40855	−0.541401
$303$	−1.42477	−0.0818511
$304$	1.56408	0.0897060
$305$	−25.4128	−1.45513
$306$	2.77153	0.158438
$307$	−9.40206	−0.536604	−0.268302	−	0.963335i	$-0.586462\pi$
$307$	−9.40206	−0.536604	−0.268302	+	0.963335i	$0.586462\pi$
$308$	12.4682	0.710439
$309$	3.75057	0.213363
$310$	8.87880	0.504282
$311$	16.1014	0.913029	0.456515	−	0.889716i	$-0.349098\pi$
$311$	16.1014	0.913029	0.456515	+	0.889716i	$0.349098\pi$
$312$	−1.42980	−0.0809466
$313$	−0.575960	−0.0325552	−0.0162776	−	0.999868i	$-0.505182\pi$
$313$	−0.575960	−0.0325552	−0.0162776	+	0.999868i	$0.505182\pi$
$314$	−2.53470	−0.143042
$315$	−15.6353	−0.880949
$316$	−2.54971	−0.143433
$317$	−11.7527	−0.660095	−0.330048	−	0.943964i	$-0.607065\pi$
$317$	−11.7527	−0.660095	−0.330048	+	0.943964i	$0.607065\pi$
$318$	2.78803	0.156345
$319$	24.3159	1.36143
$320$	−2.61144	−0.145984
$321$	7.05204	0.393606
$322$	−13.2466	−0.738202
$323$	1.50549	0.0837677
$324$	7.92902	0.440501
$325$	7.49119	0.415537
$326$	−9.37796	−0.519397
$327$	−2.16359	−0.119647
$328$	10.3715	0.572670
$329$	12.8400	0.707891
$330$	−5.43820	−0.299363
$331$	−14.1375	−0.777065	−0.388533	−	0.921435i	$-0.627018\pi$
$331$	−14.1375	−0.777065	−0.388533	+	0.921435i	$0.627018\pi$
$332$	6.91602	0.379566
$333$	0	0
$334$	10.4225	0.570292
$335$	−27.5604	−1.50578
$336$	−0.722150	−0.0393965
$337$	−10.7205	−0.583985	−0.291992	−	0.956421i	$-0.594318\pi$
$337$	−10.7205	−0.583985	−0.291992	+	0.956421i	$0.594318\pi$
$338$	−3.94928	−0.214812
$339$	2.12961	0.115665
$340$	−2.51362	−0.136320
$341$	−20.3869	−1.10401
$342$	4.50358	0.243526
$343$	20.1204	1.08640
$344$	3.76932	0.203228
$345$	5.77771	0.311061
$346$	2.92981	0.157507
$347$	7.05509	0.378737	0.189368	−	0.981906i	$-0.439356\pi$
$347$	7.05509	0.378737	0.189368	+	0.981906i	$0.439356\pi$
$348$	−1.40837	−0.0754964
$349$	25.6456	1.37278	0.686389	−	0.727234i	$-0.259195\pi$
$349$	25.6456	1.37278	0.686389	+	0.727234i	$0.259195\pi$
$350$	3.78358	0.202241
$351$	−8.40636	−0.448698
$352$	5.99619	0.319598
$353$	6.56542	0.349442	0.174721	−	0.984618i	$-0.444098\pi$
$353$	6.56542	0.349442	0.174721	+	0.984618i	$0.444098\pi$
$354$	−1.77127	−0.0941421
$355$	−28.2081	−1.49713
$356$	16.2636	0.861967
$357$	−0.695099	−0.0367886
$358$	−8.76703	−0.463352
$359$	19.8563	1.04797	0.523987	−	0.851726i	$-0.324444\pi$
$359$	19.8563	1.04797	0.523987	+	0.851726i	$0.324444\pi$
$360$	−7.51933	−0.396304
$361$	−16.5537	−0.871245
$362$	26.7562	1.40628
$363$	8.66654	0.454875
$364$	−8.56057	−0.448696
$365$	9.27825	0.485646
$366$	−3.37966	−0.176658
$367$	−21.5993	−1.12747	−0.563737	−	0.825954i	$-0.690637\pi$
$367$	−21.5993	−1.12747	−0.563737	+	0.825954i	$0.690637\pi$
$368$	−6.37054	−0.332087
$369$	29.8635	1.55463
$370$	0	0
$371$	16.6926	0.866637
$372$	1.18080	0.0612215
$373$	31.2808	1.61966	0.809830	−	0.586665i	$-0.199559\pi$
$373$	31.2808	1.61966	0.809830	+	0.586665i	$0.199559\pi$
$374$	5.77158	0.298442
$375$	2.88444	0.148952
$376$	6.17501	0.318452
$377$	−16.6952	−0.859845
$378$	−4.24580	−0.218380
$379$	−20.0599	−1.03041	−0.515205	−	0.857067i	$-0.672284\pi$
$379$	−20.0599	−1.03041	−0.515205	+	0.857067i	$0.672284\pi$
$380$	−4.08449	−0.209530
$381$	−2.21615	−0.113537
$382$	−1.81758	−0.0929954
$383$	16.4991	0.843066	0.421533	−	0.906813i	$-0.361492\pi$
$383$	16.4991	0.843066	0.421533	+	0.906813i	$0.361492\pi$
$384$	−0.347296	−0.0177229
$385$	−32.5598	−1.65940
$386$	1.06505	0.0542098
$387$	10.8533	0.551706
$388$	−16.3015	−0.827583
$389$	0.826432	0.0419017	0.0209509	−	0.999781i	$-0.493331\pi$
$389$	0.826432	0.0419017	0.0209509	+	0.999781i	$0.493331\pi$
$390$	3.73384	0.189070
$391$	−6.13191	−0.310104
$392$	2.67632	0.135174
$393$	3.63041	0.183130
$394$	15.7567	0.793809
$395$	6.65842	0.335021
$396$	17.2653	0.867616
$397$	−9.04903	−0.454158	−0.227079	−	0.973876i	$-0.572918\pi$
$397$	−9.04903	−0.454158	−0.227079	+	0.973876i	$0.572918\pi$
$398$	20.6371	1.03444
$399$	−1.12950	−0.0565456
$400$	1.81960	0.0909799
$401$	−13.1254	−0.655452	−0.327726	−	0.944773i	$-0.606282\pi$
$401$	−13.1254	−0.655452	−0.327726	+	0.944773i	$0.606282\pi$
$402$	−3.66527	−0.182807
$403$	13.9975	0.697265
$404$	−4.10247	−0.204106
$405$	−20.7061	−1.02890
$406$	−8.43223	−0.418484
$407$	0	0
$408$	−0.334287	−0.0165497
$409$	7.90080	0.390669	0.195335	−	0.980737i	$-0.437421\pi$
$409$	7.90080	0.390669	0.195335	+	0.980737i	$0.437421\pi$
$410$	−27.0845	−1.33761
$411$	2.16776	0.106928
$412$	10.7993	0.532045
$413$	−10.6050	−0.521840
$414$	−18.3432	−0.901521
$415$	−18.0607	−0.886567
$416$	−4.11695	−0.201850
$417$	−2.39371	−0.117220
$418$	9.37850	0.458718
$419$	−31.9808	−1.56237	−0.781183	−	0.624302i	$-0.785383\pi$
$419$	−31.9808	−1.56237	−0.781183	+	0.624302i	$0.785383\pi$
$420$	1.88585	0.0920199
$421$	5.61268	0.273545	0.136773	−	0.990602i	$-0.456327\pi$
$421$	5.61268	0.273545	0.136773	+	0.990602i	$0.456327\pi$
$422$	−6.20140	−0.301879
$423$	17.7802	0.864504
$424$	8.02781	0.389865
$425$	1.75144	0.0849573
$426$	−3.75141	−0.181756
$427$	−20.2349	−0.979233
$428$	20.3055	0.981505
$429$	−8.57336	−0.413926
$430$	−9.84335	−0.474688
$431$	19.9521	0.961059	0.480530	−	0.876978i	$-0.340444\pi$
$431$	19.9521	0.961059	0.480530	+	0.876978i	$0.340444\pi$
$432$	−2.04189	−0.0982404
$433$	−15.8209	−0.760305	−0.380152	−	0.924924i	$-0.624128\pi$
$433$	−15.8209	−0.760305	−0.380152	+	0.924924i	$0.624128\pi$
$434$	7.06972	0.339357
$435$	3.67786	0.176340
$436$	−6.22982	−0.298354
$437$	−9.96401	−0.476643
$438$	1.23392	0.0589590
$439$	3.06328	0.146202	0.0731011	−	0.997325i	$-0.476710\pi$
$439$	3.06328	0.146202	0.0731011	+	0.997325i	$0.476710\pi$
$440$	−15.6587	−0.746498
$441$	7.70614	0.366959
$442$	−3.96274	−0.188488
$443$	2.75923	0.131095	0.0655475	−	0.997849i	$-0.479121\pi$
$443$	2.75923	0.131095	0.0655475	+	0.997849i	$0.479121\pi$
$444$	0	0
$445$	−42.4712	−2.01333
$446$	−0.839150	−0.0397349
$447$	1.21383	0.0574121
$448$	−2.07935	−0.0982399
$449$	22.6562	1.06921	0.534607	−	0.845101i	$-0.320460\pi$
$449$	22.6562	1.06921	0.534607	+	0.845101i	$0.320460\pi$
$450$	5.23932	0.246984
$451$	62.1894	2.92839
$452$	6.13197	0.288424
$453$	3.26756	0.153523
$454$	6.52369	0.306172
$455$	22.3554	1.04804
$456$	−0.543198	−0.0254376
$457$	−29.5024	−1.38007	−0.690033	−	0.723778i	$-0.742404\pi$
$457$	−29.5024	−1.38007	−0.690033	+	0.723778i	$0.742404\pi$
$458$	−6.60414	−0.308591
$459$	−1.96540	−0.0917372
$460$	16.6363	0.775669
$461$	−4.07471	−0.189778	−0.0948890	−	0.995488i	$-0.530250\pi$
$461$	−4.07471	−0.189778	−0.0948890	+	0.995488i	$0.530250\pi$
$462$	−4.33015	−0.201457
$463$	−2.94242	−0.136746	−0.0683730	−	0.997660i	$-0.521781\pi$
$463$	−2.94242	−0.136746	−0.0683730	+	0.997660i	$0.521781\pi$
$464$	−4.05523	−0.188259
$465$	−3.08358	−0.142997
$466$	−22.6093	−1.04736
$467$	5.30243	0.245367	0.122684	−	0.992446i	$-0.460850\pi$
$467$	5.30243	0.245367	0.122684	+	0.992446i	$0.460850\pi$
$468$	−11.8543	−0.547965
$469$	−21.9448	−1.01332
$470$	−16.1256	−0.743820
$471$	0.880293	0.0405618
$472$	−5.10018	−0.234755
$473$	22.6016	1.03922
$474$	0.885507	0.0406727
$475$	2.84599	0.130583
$476$	−2.00146	−0.0917367
$477$	23.1152	1.05837
$478$	−17.1474	−0.784303
$479$	17.8668	0.816353	0.408177	−	0.912903i	$-0.366165\pi$
$479$	17.8668	0.816353	0.408177	+	0.912903i	$0.366165\pi$
$480$	0.906942	0.0413961
$481$	0	0
$482$	−5.68755	−0.259061
$483$	4.60048	0.209329
$484$	24.9543	1.13429
$485$	42.5703	1.93302
$486$	−8.87939	−0.402777
$487$	31.2962	1.41817	0.709084	−	0.705124i	$-0.249109\pi$
$487$	31.2962	1.41817	0.709084	+	0.705124i	$0.249109\pi$
$488$	−9.73135	−0.440517
$489$	3.25693	0.147284
$490$	−6.98903	−0.315732
$491$	−13.4580	−0.607351	−0.303676	−	0.952775i	$-0.598214\pi$
$491$	−13.4580	−0.607351	−0.303676	+	0.952775i	$0.598214\pi$
$492$	−3.60198	−0.162390
$493$	−3.90333	−0.175797
$494$	−6.43923	−0.289714
$495$	−45.0873	−2.02653
$496$	3.39997	0.152663
$497$	−22.4606	−1.00750
$498$	−2.40191	−0.107632
$499$	−36.7694	−1.64603	−0.823013	−	0.568022i	$-0.807709\pi$
$499$	−36.7694	−1.64603	−0.823013	+	0.568022i	$0.807709\pi$
$500$	8.30542	0.371429
$501$	−3.61969	−0.161716
$502$	25.3490	1.13138
$503$	6.24594	0.278493	0.139246	−	0.990258i	$-0.455532\pi$
$503$	6.24594	0.278493	0.139246	+	0.990258i	$0.455532\pi$
$504$	−5.98724	−0.266693
$505$	10.7133	0.476738
$506$	−38.1990	−1.69815
$507$	1.37157	0.0609135
$508$	−6.38115	−0.283118
$509$	8.21974	0.364333	0.182167	−	0.983268i	$-0.441689\pi$
$509$	8.21974	0.364333	0.182167	+	0.983268i	$0.441689\pi$
$510$	0.872970	0.0386558
$511$	7.38778	0.326816
$512$	−1.00000	−0.0441942
$513$	−3.19367	−0.141004
$514$	5.17095	0.228081
$515$	−28.2018	−1.24272
$516$	−1.30907	−0.0576287
$517$	37.0265	1.62842
$518$	0	0
$519$	−1.01751	−0.0446638
$520$	10.7512	0.471469
$521$	−22.1901	−0.972164	−0.486082	−	0.873913i	$-0.661574\pi$
$521$	−22.1901	−0.972164	−0.486082	+	0.873913i	$0.661574\pi$
$522$	−11.6766	−0.511069
$523$	13.9547	0.610198	0.305099	−	0.952321i	$-0.401311\pi$
$523$	13.9547	0.610198	0.305099	+	0.952321i	$0.401311\pi$
$524$	10.4534	0.456657
$525$	−1.31402	−0.0573486
$526$	9.67206	0.421722
$527$	3.27261	0.142557
$528$	−2.08246	−0.0906272
$529$	17.5837	0.764511
$530$	−20.9641	−0.910623
$531$	−14.6854	−0.637291
$532$	−3.25226	−0.141003
$533$	−42.6989	−1.84949
$534$	−5.64827	−0.244425
$535$	−53.0266	−2.29254
$536$	−10.5537	−0.455851
$537$	3.04476	0.131391
$538$	23.8765	1.02939
$539$	16.0477	0.691223
$540$	5.33226	0.229464
$541$	24.1770	1.03945	0.519726	−	0.854333i	$-0.326034\pi$
$541$	24.1770	1.03945	0.519726	+	0.854333i	$0.326034\pi$
$542$	−18.3088	−0.786432
$543$	−9.29234	−0.398773
$544$	−0.962542	−0.0412686
$545$	16.2688	0.696878
$546$	2.97305	0.127235
$547$	−37.2254	−1.59164	−0.795822	−	0.605531i	$-0.792961\pi$
$547$	−37.2254	−1.59164	−0.795822	+	0.605531i	$0.792961\pi$
$548$	6.24181	0.266637
$549$	−28.0203	−1.19588
$550$	10.9107	0.465232
$551$	−6.34269	−0.270208
$552$	2.21246	0.0941687
$553$	5.30174	0.225453
$554$	−17.7317	−0.753347
$555$	0	0
$556$	−6.89241	−0.292303
$557$	2.84794	0.120671	0.0603356	−	0.998178i	$-0.480783\pi$
$557$	2.84794	0.120671	0.0603356	+	0.998178i	$0.480783\pi$
$558$	9.78982	0.414436
$559$	−15.5181	−0.656346
$560$	5.43008	0.229463
$561$	−2.00445	−0.0846280
$562$	15.2484	0.643215
$563$	24.8363	1.04672	0.523362	−	0.852111i	$-0.324678\pi$
$563$	24.8363	1.04672	0.523362	+	0.852111i	$0.324678\pi$
$564$	−2.14456	−0.0903021
$565$	−16.0133	−0.673683
$566$	24.4532	1.02784
$567$	−16.4872	−0.692396
$568$	−10.8018	−0.453231
$569$	10.1674	0.426238	0.213119	−	0.977026i	$-0.431638\pi$
$569$	10.1674	0.426238	0.213119	+	0.977026i	$0.431638\pi$
$570$	1.41853	0.0594156
$571$	18.7691	0.785461	0.392731	−	0.919654i	$-0.371530\pi$
$571$	18.7691	0.785461	0.392731	+	0.919654i	$0.371530\pi$
$572$	−24.6860	−1.03217
$573$	0.631238	0.0263704
$574$	−21.5659	−0.900144
$575$	−11.5918	−0.483412
$576$	−2.87939	−0.119974
$577$	−18.8123	−0.783165	−0.391583	−	0.920143i	$-0.628072\pi$
$577$	−18.8123	−0.783165	−0.391583	+	0.920143i	$0.628072\pi$
$578$	16.0735	0.668570
$579$	−0.369889	−0.0153721
$580$	10.5900	0.439725
$581$	−14.3808	−0.596616
$582$	5.66145	0.234675
$583$	48.1363	1.99360
$584$	3.55293	0.147021
$585$	30.9567	1.27990
$586$	−12.5725	−0.519366
$587$	30.7198	1.26794	0.633971	−	0.773357i	$-0.281424\pi$
$587$	30.7198	1.26794	0.633971	+	0.773357i	$0.281424\pi$
$588$	−0.929475	−0.0383309
$589$	5.31781	0.219117
$590$	13.3188	0.548326
$591$	−5.47223	−0.225097
$592$	0	0
$593$	6.18887	0.254147	0.127073	−	0.991893i	$-0.459442\pi$
$593$	6.18887	0.254147	0.127073	+	0.991893i	$0.459442\pi$
$594$	−12.2436	−0.502359
$595$	5.22668	0.214273
$596$	3.49508	0.143164
$597$	−7.16718	−0.293333
$598$	26.2272	1.07251
$599$	−1.05590	−0.0431429	−0.0215715	−	0.999767i	$-0.506867\pi$
$599$	−1.05590	−0.0431429	−0.0215715	+	0.999767i	$0.506867\pi$
$600$	−0.631940	−0.0257988
$601$	−15.5837	−0.635673	−0.317837	−	0.948145i	$-0.602956\pi$
$601$	−15.5837	−0.635673	−0.317837	+	0.948145i	$0.602956\pi$
$602$	−7.83773	−0.319442
$603$	−30.3882	−1.23750
$604$	9.40855	0.382828
$605$	−65.1666	−2.64940
$606$	1.42477	0.0578775
$607$	32.2395	1.30856	0.654281	−	0.756251i	$-0.272971\pi$
$607$	32.2395	1.30856	0.654281	+	0.756251i	$0.272971\pi$
$608$	−1.56408	−0.0634317
$609$	2.92848	0.118668
$610$	25.4128	1.02893
$611$	−25.4222	−1.02847
$612$	−2.77153	−0.112032
$613$	5.57585	0.225207	0.112603	−	0.993640i	$-0.464081\pi$
$613$	5.57585	0.225207	0.112603	+	0.993640i	$0.464081\pi$
$614$	9.40206	0.379436
$615$	9.40634	0.379300
$616$	−12.4682	−0.502357
$617$	−4.05336	−0.163182	−0.0815910	−	0.996666i	$-0.526000\pi$
$617$	−4.05336	−0.163182	−0.0815910	+	0.996666i	$0.526000\pi$
$618$	−3.75057	−0.150870
$619$	7.37410	0.296390	0.148195	−	0.988958i	$-0.452654\pi$
$619$	7.37410	0.296390	0.148195	+	0.988958i	$0.452654\pi$
$620$	−8.87880	−0.356581
$621$	13.0079	0.521990
$622$	−16.1014	−0.645609
$623$	−33.8176	−1.35487
$624$	1.42980	0.0572379
$625$	−30.7871	−1.23148
$626$	0.575960	0.0230200
$627$	−3.25712	−0.130077
$628$	2.53470	0.101146
$629$	0	0
$630$	15.6353	0.622925
$631$	8.37224	0.333294	0.166647	−	0.986017i	$-0.446706\pi$
$631$	8.37224	0.333294	0.166647	+	0.986017i	$0.446706\pi$
$632$	2.54971	0.101422
$633$	2.15372	0.0856028
$634$	11.7527	0.466758
$635$	16.6640	0.661289
$636$	−2.78803	−0.110553
$637$	−11.0183	−0.436559
$638$	−24.3159	−0.962677
$639$	−31.1024	−1.23039
$640$	2.61144	0.103226
$641$	−11.8744	−0.469011	−0.234506	−	0.972115i	$-0.575347\pi$
$641$	−11.8744	−0.469011	−0.234506	+	0.972115i	$0.575347\pi$
$642$	−7.05204	−0.278322
$643$	38.7093	1.52655	0.763273	−	0.646076i	$-0.223591\pi$
$643$	38.7093	1.52655	0.763273	+	0.646076i	$0.223591\pi$
$644$	13.2466	0.521988
$645$	3.41856	0.134606
$646$	−1.50549	−0.0592327
$647$	−17.6502	−0.693900	−0.346950	−	0.937884i	$-0.612783\pi$
$647$	−17.6502	−0.693900	−0.346950	+	0.937884i	$0.612783\pi$
$648$	−7.92902	−0.311481
$649$	−30.5816	−1.20043
$650$	−7.49119	−0.293829
$651$	−2.45529	−0.0962303
$652$	9.37796	0.367269
$653$	−14.7758	−0.578223	−0.289112	−	0.957295i	$-0.593360\pi$
$653$	−14.7758	−0.578223	−0.289112	+	0.957295i	$0.593360\pi$
$654$	2.16359	0.0846032
$655$	−27.2983	−1.06663
$656$	−10.3715	−0.404939
$657$	10.2303	0.399120
$658$	−12.8400	−0.500555
$659$	−6.61870	−0.257828	−0.128914	−	0.991656i	$-0.541149\pi$
$659$	−6.61870	−0.257828	−0.128914	+	0.991656i	$0.541149\pi$
$660$	5.43820	0.211682
$661$	6.32602	0.246054	0.123027	−	0.992403i	$-0.460740\pi$
$661$	6.32602	0.246054	0.123027	+	0.992403i	$0.460740\pi$
$662$	14.1375	0.549468
$663$	1.37624	0.0534489
$664$	−6.91602	−0.268394
$665$	8.49307	0.329347
$666$	0	0
$667$	25.8340	1.00030
$668$	−10.4225	−0.403257
$669$	0.291434	0.0112675
$670$	27.5604	1.06475
$671$	−58.3510	−2.25262
$672$	0.722150	0.0278575
$673$	24.5583	0.946651	0.473326	−	0.880888i	$-0.343053\pi$
$673$	24.5583	0.946651	0.473326	+	0.880888i	$0.343053\pi$
$674$	10.7205	0.412939
$675$	−3.71542	−0.143006
$676$	3.94928	0.151895
$677$	22.4643	0.863374	0.431687	−	0.902024i	$-0.357919\pi$
$677$	22.4643	0.863374	0.431687	+	0.902024i	$0.357919\pi$
$678$	−2.12961	−0.0817873
$679$	33.8964	1.30083
$680$	2.51362	0.0963928
$681$	−2.26566	−0.0868201
$682$	20.3869	0.780653
$683$	−33.0451	−1.26444	−0.632218	−	0.774791i	$-0.717855\pi$
$683$	−33.0451	−1.26444	−0.632218	+	0.774791i	$0.717855\pi$
$684$	−4.50358	−0.172199
$685$	−16.3001	−0.622794
$686$	−20.1204	−0.768201
$687$	2.29359	0.0875060
$688$	−3.76932	−0.143704
$689$	−33.0501	−1.25911
$690$	−5.77771	−0.219954
$691$	−34.9132	−1.32816	−0.664081	−	0.747660i	$-0.731177\pi$
$691$	−34.9132	−1.32816	−0.664081	+	0.747660i	$0.731177\pi$
$692$	−2.92981	−0.111374
$693$	−35.9006	−1.36375
$694$	−7.05509	−0.267807
$695$	17.9991	0.682744
$696$	1.40837	0.0533840
$697$	−9.98299	−0.378133
$698$	−25.6456	−0.970701
$699$	7.85214	0.296995
$700$	−3.78358	−0.143006
$701$	−26.7618	−1.01078	−0.505390	−	0.862891i	$-0.668651\pi$
$701$	−26.7618	−1.01078	−0.505390	+	0.862891i	$0.668651\pi$
$702$	8.40636	0.317277
$703$	0	0
$704$	−5.99619	−0.225990
$705$	5.60037	0.210922
$706$	−6.56542	−0.247093
$707$	8.53047	0.320821
$708$	1.77127	0.0665685
$709$	−6.67084	−0.250529	−0.125264	−	0.992123i	$-0.539978\pi$
$709$	−6.67084	−0.250529	−0.125264	+	0.992123i	$0.539978\pi$
$710$	28.2081	1.05863
$711$	7.34161	0.275332
$712$	−16.2636	−0.609502
$713$	−21.6596	−0.811160
$714$	0.695099	0.0260134
$715$	64.4660	2.41089
$716$	8.76703	0.327639
$717$	5.95523	0.222402
$718$	−19.8563	−0.741029
$719$	47.6245	1.77610	0.888048	−	0.459752i	$-0.152062\pi$
$719$	47.6245	1.77610	0.888048	+	0.459752i	$0.152062\pi$
$720$	7.51933	0.280229
$721$	−22.4556	−0.836289
$722$	16.5537	0.616064
$723$	1.97527	0.0734609
$724$	−26.7562	−0.994388
$725$	−7.37889	−0.274045
$726$	−8.66654	−0.321645
$727$	50.1422	1.85967	0.929836	−	0.367975i	$-0.119949\pi$
$727$	50.1422	1.85967	0.929836	+	0.367975i	$0.119949\pi$
$728$	8.56057	0.317276
$729$	−20.7033	−0.766788
$730$	−9.27825	−0.343404
$731$	−3.62813	−0.134191
$732$	3.37966	0.124916
$733$	−28.1199	−1.03863	−0.519317	−	0.854582i	$-0.673814\pi$
$733$	−28.1199	−1.03863	−0.519317	+	0.854582i	$0.673814\pi$
$734$	21.5993	0.797244
$735$	2.42726	0.0895310
$736$	6.37054	0.234821
$737$	−63.2821	−2.33103
$738$	−29.8635	−1.09929
$739$	−32.3511	−1.19006	−0.595028	−	0.803705i	$-0.702859\pi$
$739$	−32.3511	−1.19006	−0.595028	+	0.803705i	$0.702859\pi$
$740$	0	0
$741$	2.23632	0.0821533
$742$	−16.6926	−0.612805
$743$	−7.50916	−0.275484	−0.137742	−	0.990468i	$-0.543985\pi$
$743$	−7.50916	−0.275484	−0.137742	+	0.990468i	$0.543985\pi$
$744$	−1.18080	−0.0432901
$745$	−9.12717	−0.334394
$746$	−31.2808	−1.14527
$747$	−19.9139	−0.728611
$748$	−5.77158	−0.211030
$749$	−42.2222	−1.54277
$750$	−2.88444	−0.105325
$751$	−14.7417	−0.537933	−0.268966	−	0.963150i	$-0.586682\pi$
$751$	−14.7417	−0.537933	−0.268966	+	0.963150i	$0.586682\pi$
$752$	−6.17501	−0.225179
$753$	−8.80360	−0.320821
$754$	16.6952	0.608002
$755$	−24.5698	−0.894188
$756$	4.24580	0.154418
$757$	22.1085	0.803548	0.401774	−	0.915739i	$-0.368394\pi$
$757$	22.1085	0.803548	0.401774	+	0.915739i	$0.368394\pi$
$758$	20.0599	0.728609
$759$	13.2664	0.481538
$760$	4.08449	0.148160
$761$	−31.8450	−1.15438	−0.577191	−	0.816609i	$-0.695851\pi$
$761$	−31.8450	−1.15438	−0.577191	+	0.816609i	$0.695851\pi$
$762$	2.21615	0.0802826
$763$	12.9540	0.468965
$764$	1.81758	0.0657577
$765$	7.23767	0.261679
$766$	−16.4991	−0.596138
$767$	20.9972	0.758164
$768$	0.347296	0.0125320
$769$	22.6755	0.817699	0.408849	−	0.912602i	$-0.365930\pi$
$769$	22.6755	0.817699	0.408849	+	0.912602i	$0.365930\pi$
$770$	32.5598	1.17337
$771$	−1.79585	−0.0646761
$772$	−1.06505	−0.0383321
$773$	11.8211	0.425176	0.212588	−	0.977142i	$-0.431811\pi$
$773$	11.8211	0.425176	0.212588	+	0.977142i	$0.431811\pi$
$774$	−10.8533	−0.390115
$775$	6.18658	0.222228
$776$	16.3015	0.585189
$777$	0	0
$778$	−0.826432	−0.0296290
$779$	−16.2218	−0.581207
$780$	−3.73384	−0.133693
$781$	−64.7694	−2.31763
$782$	6.13191	0.219277
$783$	8.28033	0.295915
$784$	−2.67632	−0.0955827
$785$	−6.61922	−0.236250
$786$	−3.63041	−0.129493
$787$	8.14589	0.290370	0.145185	−	0.989405i	$-0.453622\pi$
$787$	8.14589	0.290370	0.145185	+	0.989405i	$0.453622\pi$
$788$	−15.7567	−0.561308
$789$	−3.35907	−0.119586
$790$	−6.65842	−0.236896
$791$	−12.7505	−0.453356
$792$	−17.2653	−0.613497
$793$	40.0635	1.42270
$794$	9.04903	0.321138
$795$	7.28076	0.258222
$796$	−20.6371	−0.731461
$797$	−25.0062	−0.885764	−0.442882	−	0.896580i	$-0.646044\pi$
$797$	−25.0062	−0.885764	−0.442882	+	0.896580i	$0.646044\pi$
$798$	1.12950	0.0399838
$799$	−5.94370	−0.210273
$800$	−1.81960	−0.0643325
$801$	−46.8290	−1.65462
$802$	13.1254	0.463475
$803$	21.3041	0.751804
$804$	3.66527	0.129264
$805$	−34.5925	−1.21923
$806$	−13.9975	−0.493041
$807$	−8.29223	−0.291900
$808$	4.10247	0.144325
$809$	7.03209	0.247235	0.123618	−	0.992330i	$-0.460550\pi$
$809$	7.03209	0.247235	0.123618	+	0.992330i	$0.460550\pi$
$810$	20.7061	0.727539
$811$	−8.11062	−0.284802	−0.142401	−	0.989809i	$-0.545482\pi$
$811$	−8.11062	−0.284802	−0.142401	+	0.989809i	$0.545482\pi$
$812$	8.43223	0.295913
$813$	6.35860	0.223006
$814$	0	0
$815$	−24.4899	−0.857845
$816$	0.334287	0.0117024
$817$	−5.89551	−0.206258
$818$	−7.90080	−0.276245
$819$	24.6492	0.861312
$820$	27.0845	0.945831
$821$	−46.0838	−1.60834	−0.804168	−	0.594403i	$-0.797389\pi$
$821$	−46.0838	−1.60834	−0.804168	+	0.594403i	$0.797389\pi$
$822$	−2.16776	−0.0756092
$823$	11.8074	0.411582	0.205791	−	0.978596i	$-0.434023\pi$
$823$	11.8074	0.411582	0.205791	+	0.978596i	$0.434023\pi$
$824$	−10.7993	−0.376213
$825$	−3.78923	−0.131924
$826$	10.6050	0.368996
$827$	28.5160	0.991598	0.495799	−	0.868437i	$-0.334875\pi$
$827$	28.5160	0.991598	0.495799	+	0.868437i	$0.334875\pi$
$828$	18.3432	0.637471
$829$	−0.270509	−0.00939516	−0.00469758	−	0.999989i	$-0.501495\pi$
$829$	−0.270509	−0.00939516	−0.00469758	+	0.999989i	$0.501495\pi$
$830$	18.0607	0.626897
$831$	6.15815	0.213624
$832$	4.11695	0.142730
$833$	−2.57607	−0.0892554
$834$	2.39371	0.0828873
$835$	27.2176	0.941904
$836$	−9.37850	−0.324362
$837$	−6.94236	−0.239963
$838$	31.9808	1.10476
$839$	−23.3584	−0.806421	−0.403211	−	0.915107i	$-0.632106\pi$
$839$	−23.3584	−0.806421	−0.403211	+	0.915107i	$0.632106\pi$
$840$	−1.88585	−0.0650679
$841$	−12.5551	−0.432935
$842$	−5.61268	−0.193426
$843$	−5.29571	−0.182394
$844$	6.20140	0.213461
$845$	−10.3133	−0.354788
$846$	−17.7802	−0.611297
$847$	−51.8887	−1.78292
$848$	−8.02781	−0.275676
$849$	−8.49250	−0.291462
$850$	−1.75144	−0.0600739
$851$	0	0
$852$	3.75141	0.128521
$853$	−19.9857	−0.684298	−0.342149	−	0.939646i	$-0.611155\pi$
$853$	−19.9857	−0.684298	−0.342149	+	0.939646i	$0.611155\pi$
$854$	20.2349	0.692422
$855$	11.7608	0.402211
$856$	−20.3055	−0.694029
$857$	−16.1108	−0.550334	−0.275167	−	0.961396i	$-0.588733\pi$
$857$	−16.1108	−0.550334	−0.275167	+	0.961396i	$0.588733\pi$
$858$	8.57336	0.292690
$859$	3.34038	0.113972	0.0569861	−	0.998375i	$-0.481851\pi$
$859$	3.34038	0.113972	0.0569861	+	0.998375i	$0.481851\pi$
$860$	9.84335	0.335655
$861$	7.48977	0.255251
$862$	−19.9521	−0.679572
$863$	38.7971	1.32067	0.660334	−	0.750972i	$-0.270415\pi$
$863$	38.7971	1.32067	0.660334	+	0.750972i	$0.270415\pi$
$864$	2.04189	0.0694665
$865$	7.65100	0.260142
$866$	15.8209	0.537617
$867$	−5.58227	−0.189584
$868$	−7.06972	−0.239962
$869$	15.2886	0.518629
$870$	−3.67786	−0.124691
$871$	43.4491	1.47222
$872$	6.22982	0.210968
$873$	46.9383	1.58862
$874$	9.96401	0.337038
$875$	−17.2698	−0.583827
$876$	−1.23392	−0.0416903
$877$	−2.84043	−0.0959145	−0.0479573	−	0.998849i	$-0.515271\pi$
$877$	−2.84043	−0.0959145	−0.0479573	+	0.998849i	$0.515271\pi$
$878$	−3.06328	−0.103381
$879$	4.36639	0.147275
$880$	15.6587	0.527854
$881$	50.5342	1.70254	0.851270	−	0.524727i	$-0.175833\pi$
$881$	50.5342	1.70254	0.851270	+	0.524727i	$0.175833\pi$
$882$	−7.70614	−0.259479
$883$	28.6786	0.965111	0.482555	−	0.875865i	$-0.339709\pi$
$883$	28.6786	0.965111	0.482555	+	0.875865i	$0.339709\pi$
$884$	3.96274	0.133281
$885$	−4.62557	−0.155487
$886$	−2.75923	−0.0926981
$887$	14.6784	0.492851	0.246425	−	0.969162i	$-0.420744\pi$
$887$	14.6784	0.492851	0.246425	+	0.969162i	$0.420744\pi$
$888$	0	0
$889$	13.2686	0.445015
$890$	42.4712	1.42364
$891$	−47.5439	−1.59278
$892$	0.839150	0.0280968
$893$	−9.65818	−0.323199
$894$	−1.21383	−0.0405965
$895$	−22.8945	−0.765280
$896$	2.07935	0.0694661
$897$	−9.10860	−0.304127
$898$	−22.6562	−0.756048
$899$	−13.7877	−0.459844
$900$	−5.23932	−0.174644
$901$	−7.72711	−0.257427
$902$	−62.1894	−2.07068
$903$	2.72202	0.0905830
$904$	−6.13197	−0.203946
$905$	69.8722	2.32263
$906$	−3.26756	−0.108557
$907$	44.7815	1.48695	0.743473	−	0.668766i	$-0.233177\pi$
$907$	44.7815	1.48695	0.743473	+	0.668766i	$0.233177\pi$
$908$	−6.52369	−0.216496
$909$	11.8126	0.391799
$910$	−22.3554	−0.741074
$911$	6.65685	0.220551	0.110276	−	0.993901i	$-0.464827\pi$
$911$	6.65685	0.220551	0.110276	+	0.993901i	$0.464827\pi$
$912$	0.543198	0.0179871
$913$	−41.4698	−1.37245
$914$	29.5024	0.975854
$915$	−8.82577	−0.291771
$916$	6.60414	0.218207
$917$	−21.7362	−0.717792
$918$	1.96540	0.0648680
$919$	−44.6670	−1.47343	−0.736715	−	0.676203i	$-0.763624\pi$
$919$	−44.6670	−1.47343	−0.736715	+	0.676203i	$0.763624\pi$
$920$	−16.6363	−0.548481
$921$	−3.26530	−0.107595
$922$	4.07471	0.134193
$923$	44.4703	1.46376
$924$	4.33015	0.142451
$925$	0	0
$926$	2.94242	0.0966941
$927$	−31.0955	−1.02131
$928$	4.05523	0.133119
$929$	−1.63860	−0.0537607	−0.0268803	−	0.999639i	$-0.508557\pi$
$929$	−1.63860	−0.0537607	−0.0268803	+	0.999639i	$0.508557\pi$
$930$	3.08358	0.101114
$931$	−4.18596	−0.137189
$932$	22.6093	0.740594
$933$	5.59197	0.183073
$934$	−5.30243	−0.173501
$935$	15.0721	0.492911
$936$	11.8543	0.387469
$937$	−39.3740	−1.28629	−0.643147	−	0.765743i	$-0.722372\pi$
$937$	−39.3740	−1.28629	−0.643147	+	0.765743i	$0.722372\pi$
$938$	21.9448	0.716524
$939$	−0.200029	−0.00652770
$940$	16.1256	0.525960
$941$	−30.6741	−0.999948	−0.499974	−	0.866040i	$-0.666657\pi$
$941$	−30.6741	−0.999948	−0.499974	+	0.866040i	$0.666657\pi$
$942$	−0.880293	−0.0286815
$943$	66.0720	2.15160
$944$	5.10018	0.165997
$945$	−11.0876	−0.360680
$946$	−22.6016	−0.734841
$947$	−21.9871	−0.714486	−0.357243	−	0.934011i	$-0.616283\pi$
$947$	−21.9871	−0.714486	−0.357243	+	0.934011i	$0.616283\pi$
$948$	−0.885507	−0.0287599
$949$	−14.6272	−0.474820
$950$	−2.84599	−0.0923362
$951$	−4.08166	−0.132357
$952$	2.00146	0.0648677
$953$	−13.7966	−0.446916	−0.223458	−	0.974714i	$-0.571735\pi$
$953$	−13.7966	−0.446916	−0.223458	+	0.974714i	$0.571735\pi$
$954$	−23.1152	−0.748381
$955$	−4.74649	−0.153593
$956$	17.1474	0.554586
$957$	8.44483	0.272983
$958$	−17.8668	−0.577249
$959$	−12.9789	−0.419110
$960$	−0.906942	−0.0292714
$961$	−19.4402	−0.627103
$962$	0	0
$963$	−58.4674	−1.88409
$964$	5.68755	0.183184
$965$	2.78132	0.0895338
$966$	−4.60048	−0.148018
$967$	42.7683	1.37533	0.687667	−	0.726026i	$-0.258635\pi$
$967$	42.7683	1.37533	0.687667	+	0.726026i	$0.258635\pi$
$968$	−24.9543	−0.802062
$969$	0.522851	0.0167964
$970$	−42.5703	−1.36685
$971$	55.7565	1.78931	0.894656	−	0.446755i	$-0.147420\pi$
$971$	55.7565	1.78931	0.894656	+	0.446755i	$0.147420\pi$
$972$	8.87939	0.284806
$973$	14.3317	0.459453
$974$	−31.2962	−1.00280
$975$	2.60166	0.0833200
$976$	9.73135	0.311493
$977$	18.2779	0.584762	0.292381	−	0.956302i	$-0.405552\pi$
$977$	18.2779	0.584762	0.292381	+	0.956302i	$0.405552\pi$
$978$	−3.25693	−0.104145
$979$	−97.5194	−3.11673
$980$	6.98903	0.223256
$981$	17.9380	0.572718
$982$	13.4580	0.429462
$983$	25.1981	0.803694	0.401847	−	0.915707i	$-0.368368\pi$
$983$	25.1981	0.803694	0.401847	+	0.915707i	$0.368368\pi$
$984$	3.60198	0.114827
$985$	41.1475	1.31107
$986$	3.90333	0.124307
$987$	4.45928	0.141940
$988$	6.43923	0.204859
$989$	24.0126	0.763557
$990$	45.0873	1.43297
$991$	−29.7253	−0.944254	−0.472127	−	0.881531i	$-0.656514\pi$
$991$	−29.7253	−0.944254	−0.472127	+	0.881531i	$0.656514\pi$
$992$	−3.39997	−0.107949
$993$	−4.90989	−0.155811
$994$	22.4606	0.712407
$995$	53.8924	1.70850
$996$	2.40191	0.0761074
$997$	8.87844	0.281183	0.140592	−	0.990068i	$-0.455100\pi$
$997$	8.87844	0.281183	0.140592	+	0.990068i	$0.455100\pi$
$998$	36.7694	1.16392
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.r.1.3		6
37.17	odd	36		74.2.h.a.67.1	yes	12
37.24	odd	36		74.2.h.a.21.1	✓	12
37.36	even	2		2738.2.a.s.1.4		6
111.17	even	36		666.2.bj.c.289.2		12
111.98	even	36		666.2.bj.c.613.2		12
148.91	even	36		592.2.bq.b.289.2		12
148.135	even	36		592.2.bq.b.465.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.1	✓	12	37.24	odd	36
74.2.h.a.67.1	yes	12	37.17	odd	36
592.2.bq.b.289.2		12	148.91	even	36
592.2.bq.b.465.2		12	148.135	even	36
666.2.bj.c.289.2		12	111.17	even	36
666.2.bj.c.613.2		12	111.98	even	36
2738.2.a.r.1.3		6	1.1	even	1	trivial
2738.2.a.s.1.4		6	37.36	even	2

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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -2.61144 q^{5} -0.347296 q^{6} -2.07935 q^{7} -1.00000 q^{8} -2.87939 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -2.61144 q^{5} -0.347296 q^{6} -2.07935 q^{7} -1.00000 q^{8} -2.87939 q^{9} +2.61144 q^{10} -5.99619 q^{11} +0.347296 q^{12} +4.11695 q^{13} +2.07935 q^{14} -0.906942 q^{15} +1.00000 q^{16} +0.962542 q^{17} +2.87939 q^{18} +1.56408 q^{19} -2.61144 q^{20} -0.722150 q^{21} +5.99619 q^{22} -6.37054 q^{23} -0.347296 q^{24} +1.81960 q^{25} -4.11695 q^{26} -2.04189 q^{27} -2.07935 q^{28} -4.05523 q^{29} +0.906942 q^{30} +3.39997 q^{31} -1.00000 q^{32} -2.08246 q^{33} -0.962542 q^{34} +5.43008 q^{35} -2.87939 q^{36} -1.56408 q^{38} +1.42980 q^{39} +2.61144 q^{40} -10.3715 q^{41} +0.722150 q^{42} -3.76932 q^{43} -5.99619 q^{44} +7.51933 q^{45} +6.37054 q^{46} -6.17501 q^{47} +0.347296 q^{48} -2.67632 q^{49} -1.81960 q^{50} +0.334287 q^{51} +4.11695 q^{52} -8.02781 q^{53} +2.04189 q^{54} +15.6587 q^{55} +2.07935 q^{56} +0.543198 q^{57} +4.05523 q^{58} +5.10018 q^{59} -0.906942 q^{60} +9.73135 q^{61} -3.39997 q^{62} +5.98724 q^{63} +1.00000 q^{64} -10.7512 q^{65} +2.08246 q^{66} +10.5537 q^{67} +0.962542 q^{68} -2.21246 q^{69} -5.43008 q^{70} +10.8018 q^{71} +2.87939 q^{72} -3.55293 q^{73} +0.631940 q^{75} +1.56408 q^{76} +12.4682 q^{77} -1.42980 q^{78} -2.54971 q^{79} -2.61144 q^{80} +7.92902 q^{81} +10.3715 q^{82} +6.91602 q^{83} -0.722150 q^{84} -2.51362 q^{85} +3.76932 q^{86} -1.40837 q^{87} +5.99619 q^{88} +16.2636 q^{89} -7.51933 q^{90} -8.56057 q^{91} -6.37054 q^{92} +1.18080 q^{93} +6.17501 q^{94} -4.08449 q^{95} -0.347296 q^{96} -16.3015 q^{97} +2.67632 q^{98} +17.2653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 12 q^{13} - 6 q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} + 12 q^{19} + 6 q^{20} - 12 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} + 18 q^{31} - 6 q^{32} + 6 q^{33} - 12 q^{34} + 24 q^{35} - 6 q^{36} - 12 q^{38} + 6 q^{39} - 6 q^{40} - 12 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} - 6 q^{50} + 24 q^{51} + 12 q^{52} - 24 q^{53} + 6 q^{54} + 36 q^{55} + 24 q^{57} + 6 q^{58} + 12 q^{59} - 6 q^{60} + 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} - 6 q^{66} + 18 q^{67} + 12 q^{68} + 24 q^{69} - 24 q^{70} + 24 q^{71} + 6 q^{72} - 18 q^{75} + 12 q^{76} + 30 q^{77} - 6 q^{78} + 12 q^{79} + 6 q^{80} - 18 q^{81} + 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} - 6 q^{90} + 12 q^{91} - 6 q^{92} - 36 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 12 * q^13 - 6 * q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 + 12 * q^19 + 6 * q^20 - 12 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 + 18 * q^31 - 6 * q^32 + 6 * q^33 - 12 * q^34 + 24 * q^35 - 6 * q^36 - 12 * q^38 + 6 * q^39 - 6 * q^40 - 12 * q^41 + 12 * q^42 - 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 - 6 * q^50 + 24 * q^51 + 12 * q^52 - 24 * q^53 + 6 * q^54 + 36 * q^55 + 24 * q^57 + 6 * q^58 + 12 * q^59 - 6 * q^60 + 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 - 6 * q^66 + 18 * q^67 + 12 * q^68 + 24 * q^69 - 24 * q^70 + 24 * q^71 + 6 * q^72 - 18 * q^75 + 12 * q^76 + 30 * q^77 - 6 * q^78 + 12 * q^79 + 6 * q^80 - 18 * q^81 + 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 - 6 * q^90 + 12 * q^91 - 6 * q^92 - 36 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^97 + 12 * q^98 + 12 * q^99

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