LMFDB - Embedded newform 4034.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.39986 q^{3} +1.00000 q^{4} -1.11547 q^{5} +2.39986 q^{6} +2.17590 q^{7} -1.00000 q^{8} +2.75933 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.39986 q^{3} +1.00000 q^{4} -1.11547 q^{5} +2.39986 q^{6} +2.17590 q^{7} -1.00000 q^{8} +2.75933 q^{9} +1.11547 q^{10} -3.08509 q^{11} -2.39986 q^{12} +2.44024 q^{13} -2.17590 q^{14} +2.67697 q^{15} +1.00000 q^{16} +4.89451 q^{17} -2.75933 q^{18} -4.74068 q^{19} -1.11547 q^{20} -5.22187 q^{21} +3.08509 q^{22} -3.76943 q^{23} +2.39986 q^{24} -3.75573 q^{25} -2.44024 q^{26} +0.577565 q^{27} +2.17590 q^{28} +10.2097 q^{29} -2.67697 q^{30} -7.37186 q^{31} -1.00000 q^{32} +7.40380 q^{33} -4.89451 q^{34} -2.42715 q^{35} +2.75933 q^{36} +3.03887 q^{37} +4.74068 q^{38} -5.85624 q^{39} +1.11547 q^{40} +9.67954 q^{41} +5.22187 q^{42} -6.41301 q^{43} -3.08509 q^{44} -3.07795 q^{45} +3.76943 q^{46} -12.2581 q^{47} -2.39986 q^{48} -2.26544 q^{49} +3.75573 q^{50} -11.7461 q^{51} +2.44024 q^{52} -9.19250 q^{53} -0.577565 q^{54} +3.44132 q^{55} -2.17590 q^{56} +11.3770 q^{57} -10.2097 q^{58} +12.8419 q^{59} +2.67697 q^{60} +12.2248 q^{61} +7.37186 q^{62} +6.00405 q^{63} +1.00000 q^{64} -2.72201 q^{65} -7.40380 q^{66} +1.55009 q^{67} +4.89451 q^{68} +9.04611 q^{69} +2.42715 q^{70} +7.01211 q^{71} -2.75933 q^{72} -6.82879 q^{73} -3.03887 q^{74} +9.01323 q^{75} -4.74068 q^{76} -6.71287 q^{77} +5.85624 q^{78} -10.4918 q^{79} -1.11547 q^{80} -9.66408 q^{81} -9.67954 q^{82} +9.20979 q^{83} -5.22187 q^{84} -5.45967 q^{85} +6.41301 q^{86} -24.5020 q^{87} +3.08509 q^{88} +5.85474 q^{89} +3.07795 q^{90} +5.30973 q^{91} -3.76943 q^{92} +17.6914 q^{93} +12.2581 q^{94} +5.28808 q^{95} +2.39986 q^{96} +3.65649 q^{97} +2.26544 q^{98} -8.51280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−2.39986	−1.38556	−0.692780	−	0.721149i	$-0.743614\pi$
$3$	−2.39986	−1.38556	−0.692780	+	0.721149i	$0.743614\pi$
$4$	1.00000	0.500000
$5$	−1.11547	−0.498852	−0.249426	−	0.968394i	$-0.580242\pi$
$5$	−1.11547	−0.498852	−0.249426	+	0.968394i	$0.580242\pi$
$6$	2.39986	0.979739
$7$	2.17590	0.822414	0.411207	−	0.911542i	$-0.365107\pi$
$7$	2.17590	0.822414	0.411207	+	0.911542i	$0.365107\pi$
$8$	−1.00000	−0.353553
$9$	2.75933	0.919778
$10$	1.11547	0.352742
$11$	−3.08509	−0.930191	−0.465095	−	0.885261i	$-0.653980\pi$
$11$	−3.08509	−0.930191	−0.465095	+	0.885261i	$0.653980\pi$
$12$	−2.39986	−0.692780
$13$	2.44024	0.676801	0.338400	−	0.941002i	$-0.390114\pi$
$13$	2.44024	0.676801	0.338400	+	0.941002i	$0.390114\pi$
$14$	−2.17590	−0.581535
$15$	2.67697	0.691190
$16$	1.00000	0.250000
$17$	4.89451	1.18709	0.593547	−	0.804800i	$-0.297727\pi$
$17$	4.89451	1.18709	0.593547	+	0.804800i	$0.297727\pi$
$18$	−2.75933	−0.650381
$19$	−4.74068	−1.08759	−0.543794	−	0.839219i	$-0.683013\pi$
$19$	−4.74068	−1.08759	−0.543794	+	0.839219i	$0.683013\pi$
$20$	−1.11547	−0.249426
$21$	−5.22187	−1.13950
$22$	3.08509	0.657744
$23$	−3.76943	−0.785980	−0.392990	−	0.919543i	$-0.628559\pi$
$23$	−3.76943	−0.785980	−0.392990	+	0.919543i	$0.628559\pi$
$24$	2.39986	0.489870
$25$	−3.75573	−0.751146
$26$	−2.44024	−0.478570
$27$	0.577565	0.111152
$28$	2.17590	0.411207
$29$	10.2097	1.89590	0.947951	−	0.318415i	$-0.103151\pi$
$29$	10.2097	1.89590	0.947951	+	0.318415i	$0.103151\pi$
$30$	−2.67697	−0.488745
$31$	−7.37186	−1.32403	−0.662013	−	0.749493i	$-0.730297\pi$
$31$	−7.37186	−1.32403	−0.662013	+	0.749493i	$0.730297\pi$
$32$	−1.00000	−0.176777
$33$	7.40380	1.28884
$34$	−4.89451	−0.839402
$35$	−2.42715	−0.410263
$36$	2.75933	0.459889
$37$	3.03887	0.499588	0.249794	−	0.968299i	$-0.419637\pi$
$37$	3.03887	0.499588	0.249794	+	0.968299i	$0.419637\pi$
$38$	4.74068	0.769040
$39$	−5.85624	−0.937748
$40$	1.11547	0.176371
$41$	9.67954	1.51169	0.755845	−	0.654750i	$-0.227226\pi$
$41$	9.67954	1.51169	0.755845	+	0.654750i	$0.227226\pi$
$42$	5.22187	0.805752
$43$	−6.41301	−0.977975	−0.488988	−	0.872291i	$-0.662634\pi$
$43$	−6.41301	−0.977975	−0.488988	+	0.872291i	$0.662634\pi$
$44$	−3.08509	−0.465095
$45$	−3.07795	−0.458834
$46$	3.76943	0.555772
$47$	−12.2581	−1.78803	−0.894016	−	0.448035i	$-0.852124\pi$
$47$	−12.2581	−1.78803	−0.894016	+	0.448035i	$0.852124\pi$
$48$	−2.39986	−0.346390
$49$	−2.26544	−0.323635
$50$	3.75573	0.531141
$51$	−11.7461	−1.64479
$52$	2.44024	0.338400
$53$	−9.19250	−1.26269	−0.631344	−	0.775503i	$-0.717496\pi$
$53$	−9.19250	−1.26269	−0.631344	+	0.775503i	$0.717496\pi$
$54$	−0.577565	−0.0785966
$55$	3.44132	0.464028
$56$	−2.17590	−0.290767
$57$	11.3770	1.50692
$58$	−10.2097	−1.34061
$59$	12.8419	1.67188	0.835939	−	0.548822i	$-0.184924\pi$
$59$	12.8419	1.67188	0.835939	+	0.548822i	$0.184924\pi$
$60$	2.67697	0.345595
$61$	12.2248	1.56523	0.782615	−	0.622506i	$-0.213886\pi$
$61$	12.2248	1.56523	0.782615	+	0.622506i	$0.213886\pi$
$62$	7.37186	0.936227
$63$	6.00405	0.756439
$64$	1.00000	0.125000
$65$	−2.72201	−0.337624
$66$	−7.40380	−0.911344
$67$	1.55009	0.189374	0.0946868	−	0.995507i	$-0.469815\pi$
$67$	1.55009	0.189374	0.0946868	+	0.995507i	$0.469815\pi$
$68$	4.89451	0.593547
$69$	9.04611	1.08902
$70$	2.42715	0.290100
$71$	7.01211	0.832184	0.416092	−	0.909323i	$-0.363399\pi$
$71$	7.01211	0.832184	0.416092	+	0.909323i	$0.363399\pi$
$72$	−2.75933	−0.325191
$73$	−6.82879	−0.799250	−0.399625	−	0.916679i	$-0.630860\pi$
$73$	−6.82879	−0.799250	−0.399625	+	0.916679i	$0.630860\pi$
$74$	−3.03887	−0.353262
$75$	9.01323	1.04076
$76$	−4.74068	−0.543794
$77$	−6.71287	−0.765002
$78$	5.85624	0.663088
$79$	−10.4918	−1.18042	−0.590211	−	0.807249i	$-0.700956\pi$
$79$	−10.4918	−1.18042	−0.590211	+	0.807249i	$0.700956\pi$
$80$	−1.11547	−0.124713
$81$	−9.66408	−1.07379
$82$	−9.67954	−1.06893
$83$	9.20979	1.01091	0.505453	−	0.862854i	$-0.331326\pi$
$83$	9.20979	1.01091	0.505453	+	0.862854i	$0.331326\pi$
$84$	−5.22187	−0.569752
$85$	−5.45967	−0.592185
$86$	6.41301	0.691533
$87$	−24.5020	−2.62689
$88$	3.08509	0.328872
$89$	5.85474	0.620601	0.310301	−	0.950638i	$-0.399570\pi$
$89$	5.85474	0.620601	0.310301	+	0.950638i	$0.399570\pi$
$90$	3.07795	0.324444
$91$	5.30973	0.556611
$92$	−3.76943	−0.392990
$93$	17.6914	1.83452
$94$	12.2581	1.26433
$95$	5.28808	0.542546
$96$	2.39986	0.244935
$97$	3.65649	0.371260	0.185630	−	0.982620i	$-0.440567\pi$
$97$	3.65649	0.371260	0.185630	+	0.982620i	$0.440567\pi$
$98$	2.26544	0.228844
$99$	−8.51280	−0.855569
$100$	−3.75573	−0.375573
$101$	−0.191837	−0.0190885	−0.00954426	−	0.999954i	$-0.503038\pi$
$101$	−0.191837	−0.0190885	−0.00954426	+	0.999954i	$0.503038\pi$
$102$	11.7461	1.16304
$103$	0.505272	0.0497859	0.0248929	−	0.999690i	$-0.492076\pi$
$103$	0.505272	0.0497859	0.0248929	+	0.999690i	$0.492076\pi$
$104$	−2.44024	−0.239285
$105$	5.82483	0.568445
$106$	9.19250	0.892855
$107$	13.9912	1.35258	0.676291	−	0.736634i	$-0.263586\pi$
$107$	13.9912	1.35258	0.676291	+	0.736634i	$0.263586\pi$
$108$	0.577565	0.0555762
$109$	0.384757	0.0368531	0.0184265	−	0.999830i	$-0.494134\pi$
$109$	0.384757	0.0368531	0.0184265	+	0.999830i	$0.494134\pi$
$110$	−3.44132	−0.328117
$111$	−7.29288	−0.692209
$112$	2.17590	0.205604
$113$	−4.57147	−0.430047	−0.215024	−	0.976609i	$-0.568983\pi$
$113$	−4.57147	−0.430047	−0.215024	+	0.976609i	$0.568983\pi$
$114$	−11.3770	−1.06555
$115$	4.20468	0.392088
$116$	10.2097	0.947951
$117$	6.73344	0.622507
$118$	−12.8419	−1.18220
$119$	10.6500	0.976283
$120$	−2.67697	−0.244373
$121$	−1.48220	−0.134745
$122$	−12.2248	−1.10678
$123$	−23.2296	−2.09454
$124$	−7.37186	−0.662013
$125$	9.76674	0.873564
$126$	−6.00405	−0.534883
$127$	15.9153	1.41225	0.706125	−	0.708087i	$-0.250442\pi$
$127$	15.9153	1.41225	0.706125	+	0.708087i	$0.250442\pi$
$128$	−1.00000	−0.0883883
$129$	15.3903	1.35504
$130$	2.72201	0.238736
$131$	−6.61371	−0.577842	−0.288921	−	0.957353i	$-0.593297\pi$
$131$	−6.61371	−0.577842	−0.288921	+	0.957353i	$0.593297\pi$
$132$	7.40380	0.644418
$133$	−10.3153	−0.894447
$134$	−1.55009	−0.133907
$135$	−0.644255	−0.0554486
$136$	−4.89451	−0.419701
$137$	15.5118	1.32526	0.662629	−	0.748947i	$-0.269440\pi$
$137$	15.5118	1.32526	0.662629	+	0.748947i	$0.269440\pi$
$138$	−9.04611	−0.770056
$139$	11.7343	0.995289	0.497645	−	0.867381i	$-0.334198\pi$
$139$	11.7343	0.995289	0.497645	+	0.867381i	$0.334198\pi$
$140$	−2.42715	−0.205132
$141$	29.4178	2.47743
$142$	−7.01211	−0.588443
$143$	−7.52837	−0.629554
$144$	2.75933	0.229945
$145$	−11.3886	−0.945776
$146$	6.82879	0.565155
$147$	5.43675	0.448415
$148$	3.03887	0.249794
$149$	−15.9762	−1.30882	−0.654409	−	0.756141i	$-0.727082\pi$
$149$	−15.9762	−1.30882	−0.654409	+	0.756141i	$0.727082\pi$
$150$	−9.01323	−0.735927
$151$	−4.50899	−0.366936	−0.183468	−	0.983026i	$-0.558732\pi$
$151$	−4.50899	−0.366936	−0.183468	+	0.983026i	$0.558732\pi$
$152$	4.74068	0.384520
$153$	13.5056	1.09186
$154$	6.71287	0.540938
$155$	8.22307	0.660493
$156$	−5.85624	−0.468874
$157$	−11.5156	−0.919044	−0.459522	−	0.888166i	$-0.651979\pi$
$157$	−11.5156	−0.919044	−0.459522	+	0.888166i	$0.651979\pi$
$158$	10.4918	0.834685
$159$	22.0607	1.74953
$160$	1.11547	0.0881855
$161$	−8.20191	−0.646401
$162$	9.66408	0.759282
$163$	−13.5787	−1.06357	−0.531785	−	0.846880i	$-0.678478\pi$
$163$	−13.5787	−1.06357	−0.531785	+	0.846880i	$0.678478\pi$
$164$	9.67954	0.755845
$165$	−8.25870	−0.642939
$166$	−9.20979	−0.714818
$167$	12.5466	0.970886	0.485443	−	0.874268i	$-0.338658\pi$
$167$	12.5466	0.970886	0.485443	+	0.874268i	$0.338658\pi$
$168$	5.22187	0.402876
$169$	−7.04523	−0.541941
$170$	5.45967	0.418738
$171$	−13.0811	−1.00034
$172$	−6.41301	−0.488988
$173$	4.85331	0.368990	0.184495	−	0.982833i	$-0.440935\pi$
$173$	4.85331	0.368990	0.184495	+	0.982833i	$0.440935\pi$
$174$	24.5020	1.85749
$175$	−8.17211	−0.617753
$176$	−3.08509	−0.232548
$177$	−30.8189	−2.31649
$178$	−5.85474	−0.438831
$179$	0.0898258	0.00671390	0.00335695	−	0.999994i	$-0.498931\pi$
$179$	0.0898258	0.00671390	0.00335695	+	0.999994i	$0.498931\pi$
$180$	−3.07795	−0.229417
$181$	−15.9809	−1.18785	−0.593926	−	0.804520i	$-0.702423\pi$
$181$	−15.9809	−1.18785	−0.593926	+	0.804520i	$0.702423\pi$
$182$	−5.30973	−0.393583
$183$	−29.3379	−2.16872
$184$	3.76943	0.277886
$185$	−3.38977	−0.249221
$186$	−17.6914	−1.29720
$187$	−15.1000	−1.10422
$188$	−12.2581	−0.894016
$189$	1.25673	0.0914133
$190$	−5.28808	−0.383638
$191$	−19.7638	−1.43006	−0.715029	−	0.699095i	$-0.753586\pi$
$191$	−19.7638	−1.43006	−0.715029	+	0.699095i	$0.753586\pi$
$192$	−2.39986	−0.173195
$193$	−1.80147	−0.129673	−0.0648364	−	0.997896i	$-0.520653\pi$
$193$	−1.80147	−0.129673	−0.0648364	+	0.997896i	$0.520653\pi$
$194$	−3.65649	−0.262521
$195$	6.53245	0.467798
$196$	−2.26544	−0.161817
$197$	−7.23693	−0.515610	−0.257805	−	0.966197i	$-0.582999\pi$
$197$	−7.23693	−0.515610	−0.257805	+	0.966197i	$0.582999\pi$
$198$	8.51280	0.604979
$199$	−11.1295	−0.788948	−0.394474	−	0.918907i	$-0.629073\pi$
$199$	−11.1295	−0.788948	−0.394474	+	0.918907i	$0.629073\pi$
$200$	3.75573	0.265570
$201$	−3.72000	−0.262389
$202$	0.191837	0.0134976
$203$	22.2154	1.55922
$204$	−11.7461	−0.822395
$205$	−10.7972	−0.754111
$206$	−0.505272	−0.0352039
$207$	−10.4011	−0.722927
$208$	2.44024	0.169200
$209$	14.6255	1.01166
$210$	−5.82483	−0.401951
$211$	4.40223	0.303062	0.151531	−	0.988452i	$-0.451580\pi$
$211$	4.40223	0.303062	0.151531	+	0.988452i	$0.451580\pi$
$212$	−9.19250	−0.631344
$213$	−16.8281	−1.15304
$214$	−13.9912	−0.956421
$215$	7.15351	0.487865
$216$	−0.577565	−0.0392983
$217$	−16.0405	−1.08890
$218$	−0.384757	−0.0260591
$219$	16.3882	1.10741
$220$	3.44132	0.232014
$221$	11.9438	0.803426
$222$	7.29288	0.489466
$223$	12.5357	0.839450	0.419725	−	0.907651i	$-0.362126\pi$
$223$	12.5357	0.839450	0.419725	+	0.907651i	$0.362126\pi$
$224$	−2.17590	−0.145384
$225$	−10.3633	−0.690888
$226$	4.57147	0.304089
$227$	1.05018	0.0697031	0.0348516	−	0.999392i	$-0.488904\pi$
$227$	1.05018	0.0697031	0.0348516	+	0.999392i	$0.488904\pi$
$228$	11.3770	0.753459
$229$	−21.6909	−1.43337	−0.716687	−	0.697395i	$-0.754342\pi$
$229$	−21.6909	−1.43337	−0.716687	+	0.697395i	$0.754342\pi$
$230$	−4.20468	−0.277248
$231$	16.1099	1.05996
$232$	−10.2097	−0.670303
$233$	8.60751	0.563897	0.281948	−	0.959430i	$-0.409019\pi$
$233$	8.60751	0.563897	0.281948	+	0.959430i	$0.409019\pi$
$234$	−6.73344	−0.440179
$235$	13.6735	0.891964
$236$	12.8419	0.835939
$237$	25.1789	1.63555
$238$	−10.6500	−0.690336
$239$	6.55061	0.423724	0.211862	−	0.977300i	$-0.432047\pi$
$239$	6.55061	0.423724	0.211862	+	0.977300i	$0.432047\pi$
$240$	2.67697	0.172798
$241$	−7.04481	−0.453796	−0.226898	−	0.973919i	$-0.572858\pi$
$241$	−7.04481	−0.453796	−0.226898	+	0.973919i	$0.572858\pi$
$242$	1.48220	0.0952792
$243$	21.4598	1.37664
$244$	12.2248	0.782615
$245$	2.52703	0.161446
$246$	23.2296	1.48106
$247$	−11.5684	−0.736080
$248$	7.37186	0.468114
$249$	−22.1022	−1.40067
$250$	−9.76674	−0.617703
$251$	−13.9653	−0.881481	−0.440741	−	0.897634i	$-0.645284\pi$
$251$	−13.9653	−0.881481	−0.440741	+	0.897634i	$0.645284\pi$
$252$	6.00405	0.378219
$253$	11.6290	0.731112
$254$	−15.9153	−0.998612
$255$	13.1025	0.820508
$256$	1.00000	0.0625000
$257$	−2.31452	−0.144376	−0.0721878	−	0.997391i	$-0.522998\pi$
$257$	−2.31452	−0.144376	−0.0721878	+	0.997391i	$0.522998\pi$
$258$	−15.3903	−0.958161
$259$	6.61230	0.410868
$260$	−2.72201	−0.168812
$261$	28.1721	1.74381
$262$	6.61371	0.408596
$263$	0.895260	0.0552041	0.0276021	−	0.999619i	$-0.491213\pi$
$263$	0.895260	0.0552041	0.0276021	+	0.999619i	$0.491213\pi$
$264$	−7.40380	−0.455672
$265$	10.2539	0.629895
$266$	10.3153	0.632470
$267$	−14.0506	−0.859881
$268$	1.55009	0.0946868
$269$	−0.172089	−0.0104925	−0.00524624	−	0.999986i	$-0.501670\pi$
$269$	−0.172089	−0.0104925	−0.00524624	+	0.999986i	$0.501670\pi$
$270$	0.644255	0.0392081
$271$	−21.5467	−1.30887	−0.654433	−	0.756120i	$-0.727093\pi$
$271$	−21.5467	−1.30887	−0.654433	+	0.756120i	$0.727093\pi$
$272$	4.89451	0.296773
$273$	−12.7426	−0.771218
$274$	−15.5118	−0.937100
$275$	11.5868	0.698709
$276$	9.04611	0.544512
$277$	22.9593	1.37949	0.689744	−	0.724053i	$-0.257723\pi$
$277$	22.9593	1.37949	0.689744	+	0.724053i	$0.257723\pi$
$278$	−11.7343	−0.703776
$279$	−20.3414	−1.21781
$280$	2.42715	0.145050
$281$	−29.2208	−1.74317	−0.871583	−	0.490249i	$-0.836906\pi$
$281$	−29.2208	−1.74317	−0.871583	+	0.490249i	$0.836906\pi$
$282$	−29.4178	−1.75180
$283$	−26.7992	−1.59304	−0.796522	−	0.604609i	$-0.793329\pi$
$283$	−26.7992	−1.59304	−0.796522	+	0.604609i	$0.793329\pi$
$284$	7.01211	0.416092
$285$	−12.6907	−0.751730
$286$	7.52837	0.445162
$287$	21.0618	1.24324
$288$	−2.75933	−0.162595
$289$	6.95624	0.409191
$290$	11.3886	0.668765
$291$	−8.77507	−0.514403
$292$	−6.82879	−0.399625
$293$	−24.4877	−1.43059	−0.715294	−	0.698824i	$-0.753707\pi$
$293$	−24.4877	−1.43059	−0.715294	+	0.698824i	$0.753707\pi$
$294$	−5.43675	−0.317078
$295$	−14.3248	−0.834021
$296$	−3.03887	−0.176631
$297$	−1.78184	−0.103393
$298$	15.9762	0.925474
$299$	−9.19831	−0.531952
$300$	9.01323	0.520379
$301$	−13.9541	−0.804301
$302$	4.50899	0.259463
$303$	0.460383	0.0264483
$304$	−4.74068	−0.271897
$305$	−13.6364	−0.780819
$306$	−13.5056	−0.772063
$307$	−9.44215	−0.538892	−0.269446	−	0.963015i	$-0.586841\pi$
$307$	−9.44215	−0.538892	−0.269446	+	0.963015i	$0.586841\pi$
$308$	−6.71287	−0.382501
$309$	−1.21258	−0.0689814
$310$	−8.22307	−0.467039
$311$	−13.8748	−0.786770	−0.393385	−	0.919374i	$-0.628696\pi$
$311$	−13.8748	−0.786770	−0.393385	+	0.919374i	$0.628696\pi$
$312$	5.85624	0.331544
$313$	−0.0463070	−0.00261743	−0.00130871	−	0.999999i	$-0.500417\pi$
$313$	−0.0463070	−0.00261743	−0.00130871	+	0.999999i	$0.500417\pi$
$314$	11.5156	0.649862
$315$	−6.69732	−0.377351
$316$	−10.4918	−0.590211
$317$	21.6109	1.21379	0.606894	−	0.794783i	$-0.292415\pi$
$317$	21.6109	1.21379	0.606894	+	0.794783i	$0.292415\pi$
$318$	−22.0607	−1.23710
$319$	−31.4980	−1.76355
$320$	−1.11547	−0.0623566
$321$	−33.5770	−1.87409
$322$	8.20191	0.457075
$323$	−23.2033	−1.29107
$324$	−9.66408	−0.536893
$325$	−9.16488	−0.508376
$326$	13.5787	0.752057
$327$	−0.923364	−0.0510622
$328$	−9.67954	−0.534463
$329$	−26.6725	−1.47050
$330$	8.25870	0.454626
$331$	15.1368	0.831994	0.415997	−	0.909366i	$-0.363433\pi$
$331$	15.1368	0.831994	0.415997	+	0.909366i	$0.363433\pi$
$332$	9.20979	0.505453
$333$	8.38527	0.459510
$334$	−12.5466	−0.686520
$335$	−1.72908	−0.0944695
$336$	−5.22187	−0.284876
$337$	−4.24745	−0.231374	−0.115687	−	0.993286i	$-0.536907\pi$
$337$	−4.24745	−0.231374	−0.115687	+	0.993286i	$0.536907\pi$
$338$	7.04523	0.383210
$339$	10.9709	0.595857
$340$	−5.45967	−0.296092
$341$	22.7429	1.23160
$342$	13.0811	0.707346
$343$	−20.1607	−1.08858
$344$	6.41301	0.345767
$345$	−10.0906	−0.543262
$346$	−4.85331	−0.260915
$347$	−2.41227	−0.129497	−0.0647487	−	0.997902i	$-0.520625\pi$
$347$	−2.41227	−0.129497	−0.0647487	+	0.997902i	$0.520625\pi$
$348$	−24.5020	−1.31344
$349$	−15.3301	−0.820601	−0.410300	−	0.911950i	$-0.634576\pi$
$349$	−15.3301	−0.820601	−0.410300	+	0.911950i	$0.634576\pi$
$350$	8.17211	0.436818
$351$	1.40940	0.0752280
$352$	3.08509	0.164436
$353$	−28.0894	−1.49505	−0.747524	−	0.664235i	$-0.768758\pi$
$353$	−28.0894	−1.49505	−0.747524	+	0.664235i	$0.768758\pi$
$354$	30.8189	1.63800
$355$	−7.82178	−0.415137
$356$	5.85474	0.310301
$357$	−25.5585	−1.35270
$358$	−0.0898258	−0.00474744
$359$	−25.9313	−1.36860	−0.684302	−	0.729199i	$-0.739893\pi$
$359$	−25.9313	−1.36860	−0.684302	+	0.729199i	$0.739893\pi$
$360$	3.07795	0.162222
$361$	3.47408	0.182846
$362$	15.9809	0.839938
$363$	3.55707	0.186698
$364$	5.30973	0.278305
$365$	7.61730	0.398708
$366$	29.3379	1.53352
$367$	−11.4260	−0.596430	−0.298215	−	0.954499i	$-0.596391\pi$
$367$	−11.4260	−0.596430	−0.298215	+	0.954499i	$0.596391\pi$
$368$	−3.76943	−0.196495
$369$	26.7091	1.39042
$370$	3.38977	0.176226
$371$	−20.0020	−1.03845
$372$	17.6914	0.917259
$373$	−9.88851	−0.512008	−0.256004	−	0.966676i	$-0.582406\pi$
$373$	−9.88851	−0.512008	−0.256004	+	0.966676i	$0.582406\pi$
$374$	15.1000	0.780804
$375$	−23.4388	−1.21038
$376$	12.2581	0.632165
$377$	24.9142	1.28315
$378$	−1.25673	−0.0646390
$379$	−14.1178	−0.725183	−0.362591	−	0.931948i	$-0.618108\pi$
$379$	−14.1178	−0.725183	−0.362591	+	0.931948i	$0.618108\pi$
$380$	5.28808	0.271273
$381$	−38.1944	−1.95676
$382$	19.7638	1.01120
$383$	−5.02639	−0.256836	−0.128418	−	0.991720i	$-0.540990\pi$
$383$	−5.02639	−0.256836	−0.128418	+	0.991720i	$0.540990\pi$
$384$	2.39986	0.122467
$385$	7.48799	0.381623
$386$	1.80147	0.0916925
$387$	−17.6956	−0.899520
$388$	3.65649	0.185630
$389$	23.9220	1.21290	0.606448	−	0.795124i	$-0.292594\pi$
$389$	23.9220	1.21290	0.606448	+	0.795124i	$0.292594\pi$
$390$	−6.53245	−0.330783
$391$	−18.4495	−0.933032
$392$	2.26544	0.114422
$393$	15.8720	0.800636
$394$	7.23693	0.364591
$395$	11.7033	0.588857
$396$	−8.51280	−0.427785
$397$	28.6601	1.43841	0.719204	−	0.694799i	$-0.244507\pi$
$397$	28.6601	1.43841	0.719204	+	0.694799i	$0.244507\pi$
$398$	11.1295	0.557870
$399$	24.7552	1.23931
$400$	−3.75573	−0.187787
$401$	4.87950	0.243671	0.121835	−	0.992550i	$-0.461122\pi$
$401$	4.87950	0.243671	0.121835	+	0.992550i	$0.461122\pi$
$402$	3.72000	0.185537
$403$	−17.9891	−0.896101
$404$	−0.191837	−0.00954426
$405$	10.7800	0.535661
$406$	−22.2154	−1.10253
$407$	−9.37521	−0.464712
$408$	11.7461	0.581521
$409$	3.25415	0.160907	0.0804536	−	0.996758i	$-0.474363\pi$
$409$	3.25415	0.160907	0.0804536	+	0.996758i	$0.474363\pi$
$410$	10.7972	0.533237
$411$	−37.2261	−1.83623
$412$	0.505272	0.0248929
$413$	27.9428	1.37498
$414$	10.4011	0.511187
$415$	−10.2732	−0.504293
$416$	−2.44024	−0.119643
$417$	−28.1607	−1.37903
$418$	−14.6255	−0.715354
$419$	−39.6891	−1.93894	−0.969470	−	0.245211i	$-0.921143\pi$
$419$	−39.6891	−1.93894	−0.969470	+	0.245211i	$0.921143\pi$
$420$	5.82483	0.284222
$421$	−8.27486	−0.403292	−0.201646	−	0.979458i	$-0.564629\pi$
$421$	−8.27486	−0.403292	−0.201646	+	0.979458i	$0.564629\pi$
$422$	−4.40223	−0.214297
$423$	−33.8243	−1.64459
$424$	9.19250	0.446427
$425$	−18.3825	−0.891681
$426$	16.8281	0.815323
$427$	26.6001	1.28727
$428$	13.9912	0.676291
$429$	18.0670	0.872285
$430$	−7.15351	−0.344973
$431$	−38.3167	−1.84565	−0.922824	−	0.385221i	$-0.874125\pi$
$431$	−38.3167	−1.84565	−0.922824	+	0.385221i	$0.874125\pi$
$432$	0.577565	0.0277881
$433$	−6.51220	−0.312957	−0.156478	−	0.987681i	$-0.550014\pi$
$433$	−6.51220	−0.312957	−0.156478	+	0.987681i	$0.550014\pi$
$434$	16.0405	0.769967
$435$	27.3312	1.31043
$436$	0.384757	0.0184265
$437$	17.8697	0.854822
$438$	−16.3882	−0.783056
$439$	−15.2546	−0.728061	−0.364030	−	0.931387i	$-0.618600\pi$
$439$	−15.2546	−0.728061	−0.364030	+	0.931387i	$0.618600\pi$
$440$	−3.44132	−0.164059
$441$	−6.25111	−0.297672
$442$	−11.9438	−0.568108
$443$	−16.6014	−0.788755	−0.394378	−	0.918948i	$-0.629040\pi$
$443$	−16.6014	−0.788755	−0.394378	+	0.918948i	$0.629040\pi$
$444$	−7.29288	−0.346105
$445$	−6.53078	−0.309589
$446$	−12.5357	−0.593581
$447$	38.3406	1.81345
$448$	2.17590	0.102802
$449$	−12.8123	−0.604650	−0.302325	−	0.953205i	$-0.597763\pi$
$449$	−12.8123	−0.604650	−0.302325	+	0.953205i	$0.597763\pi$
$450$	10.3633	0.488531
$451$	−29.8623	−1.40616
$452$	−4.57147	−0.215024
$453$	10.8209	0.508413
$454$	−1.05018	−0.0492876
$455$	−5.92283	−0.277667
$456$	−11.3770	−0.532776
$457$	−9.26228	−0.433271	−0.216636	−	0.976253i	$-0.569508\pi$
$457$	−9.26228	−0.433271	−0.216636	+	0.976253i	$0.569508\pi$
$458$	21.6909	1.01355
$459$	2.82690	0.131948
$460$	4.20468	0.196044
$461$	11.5580	0.538310	0.269155	−	0.963097i	$-0.413256\pi$
$461$	11.5580	0.538310	0.269155	+	0.963097i	$0.413256\pi$
$462$	−16.1099	−0.749503
$463$	−26.6963	−1.24068	−0.620340	−	0.784333i	$-0.713006\pi$
$463$	−26.6963	−1.24068	−0.620340	+	0.784333i	$0.713006\pi$
$464$	10.2097	0.473976
$465$	−19.7342	−0.915153
$466$	−8.60751	−0.398735
$467$	16.7744	0.776228	0.388114	−	0.921611i	$-0.373127\pi$
$467$	16.7744	0.776228	0.388114	+	0.921611i	$0.373127\pi$
$468$	6.73344	0.311253
$469$	3.37285	0.155744
$470$	−13.6735	−0.630714
$471$	27.6358	1.27339
$472$	−12.8419	−0.591098
$473$	19.7847	0.909704
$474$	−25.1789	−1.15651
$475$	17.8047	0.816937
$476$	10.6500	0.488141
$477$	−25.3652	−1.16139
$478$	−6.55061	−0.299618
$479$	15.8014	0.721987	0.360993	−	0.932568i	$-0.382438\pi$
$479$	15.8014	0.721987	0.360993	+	0.932568i	$0.382438\pi$
$480$	−2.67697	−0.122186
$481$	7.41558	0.338122
$482$	7.04481	0.320882
$483$	19.6835	0.895628
$484$	−1.48220	−0.0673726
$485$	−4.07870	−0.185204
$486$	−21.4598	−0.973434
$487$	−33.7514	−1.52942	−0.764712	−	0.644373i	$-0.777119\pi$
$487$	−33.7514	−1.52942	−0.764712	+	0.644373i	$0.777119\pi$
$488$	−12.2248	−0.553392
$489$	32.5871	1.47364
$490$	−2.52703	−0.114160
$491$	25.6541	1.15775	0.578876	−	0.815416i	$-0.303492\pi$
$491$	25.6541	1.15775	0.578876	+	0.815416i	$0.303492\pi$
$492$	−23.2296	−1.04727
$493$	49.9717	2.25061
$494$	11.5684	0.520487
$495$	9.49576	0.426803
$496$	−7.37186	−0.331006
$497$	15.2577	0.684400
$498$	22.1022	0.990424
$499$	31.0571	1.39031	0.695153	−	0.718862i	$-0.255337\pi$
$499$	31.0571	1.39031	0.695153	+	0.718862i	$0.255337\pi$
$500$	9.76674	0.436782
$501$	−30.1101	−1.34522
$502$	13.9653	0.623302
$503$	8.43562	0.376126	0.188063	−	0.982157i	$-0.439779\pi$
$503$	8.43562	0.376126	0.188063	+	0.982157i	$0.439779\pi$
$504$	−6.00405	−0.267441
$505$	0.213988	0.00952235
$506$	−11.6290	−0.516974
$507$	16.9076	0.750892
$508$	15.9153	0.706125
$509$	12.5957	0.558294	0.279147	−	0.960248i	$-0.409948\pi$
$509$	12.5957	0.558294	0.279147	+	0.960248i	$0.409948\pi$
$510$	−13.1025	−0.580186
$511$	−14.8588	−0.657314
$512$	−1.00000	−0.0441942
$513$	−2.73805	−0.120888
$514$	2.31452	0.102089
$515$	−0.563614	−0.0248358
$516$	15.3903	0.677522
$517$	37.8175	1.66321
$518$	−6.61230	−0.290528
$519$	−11.6473	−0.511258
$520$	2.72201	0.119368
$521$	−25.1364	−1.10124	−0.550622	−	0.834755i	$-0.685609\pi$
$521$	−25.1364	−1.10124	−0.550622	+	0.834755i	$0.685609\pi$
$522$	−28.1721	−1.23306
$523$	15.8137	0.691487	0.345743	−	0.938329i	$-0.387627\pi$
$523$	15.8137	0.691487	0.345743	+	0.938329i	$0.387627\pi$
$524$	−6.61371	−0.288921
$525$	19.6119	0.855935
$526$	−0.895260	−0.0390352
$527$	−36.0817	−1.57174
$528$	7.40380	0.322209
$529$	−8.79141	−0.382235
$530$	−10.2539	−0.445403
$531$	35.4352	1.53776
$532$	−10.3153	−0.447224
$533$	23.6204	1.02311
$534$	14.0506	0.608028
$535$	−15.6068	−0.674739
$536$	−1.55009	−0.0669537
$537$	−0.215569	−0.00930251
$538$	0.172089	0.00741930
$539$	6.98910	0.301042
$540$	−0.644255	−0.0277243
$541$	−17.4454	−0.750036	−0.375018	−	0.927017i	$-0.622364\pi$
$541$	−17.4454	−0.750036	−0.375018	+	0.927017i	$0.622364\pi$
$542$	21.5467	0.925508
$543$	38.3520	1.64584
$544$	−4.89451	−0.209850
$545$	−0.429185	−0.0183843
$546$	12.7426	0.545333
$547$	−5.98124	−0.255740	−0.127870	−	0.991791i	$-0.540814\pi$
$547$	−5.98124	−0.255740	−0.127870	+	0.991791i	$0.540814\pi$
$548$	15.5118	0.662629
$549$	33.7324	1.43966
$550$	−11.5868	−0.494062
$551$	−48.4012	−2.06196
$552$	−9.04611	−0.385028
$553$	−22.8292	−0.970796
$554$	−22.9593	−0.975446
$555$	8.13497	0.345310
$556$	11.7343	0.497645
$557$	−6.42454	−0.272216	−0.136108	−	0.990694i	$-0.543459\pi$
$557$	−6.42454	−0.272216	−0.136108	+	0.990694i	$0.543459\pi$
$558$	20.3414	0.861121
$559$	−15.6493	−0.661895
$560$	−2.42715	−0.102566
$561$	36.2380	1.52997
$562$	29.2208	1.23260
$563$	−34.3048	−1.44577	−0.722887	−	0.690966i	$-0.757185\pi$
$563$	−34.3048	−1.44577	−0.722887	+	0.690966i	$0.757185\pi$
$564$	29.4178	1.23871
$565$	5.09933	0.214530
$566$	26.7992	1.12645
$567$	−21.0281	−0.883097
$568$	−7.01211	−0.294221
$569$	−22.1850	−0.930044	−0.465022	−	0.885299i	$-0.653954\pi$
$569$	−22.1850	−0.930044	−0.465022	+	0.885299i	$0.653954\pi$
$570$	12.6907	0.531553
$571$	31.0720	1.30032	0.650161	−	0.759797i	$-0.274701\pi$
$571$	31.0720	1.30032	0.650161	+	0.759797i	$0.274701\pi$
$572$	−7.52837	−0.314777
$573$	47.4303	1.98143
$574$	−21.0618	−0.879101
$575$	14.1570	0.590386
$576$	2.75933	0.114972
$577$	19.7780	0.823369	0.411685	−	0.911326i	$-0.364941\pi$
$577$	19.7780	0.823369	0.411685	+	0.911326i	$0.364941\pi$
$578$	−6.95624	−0.289342
$579$	4.32328	0.179669
$580$	−11.3886	−0.472888
$581$	20.0396	0.831383
$582$	8.77507	0.363738
$583$	28.3597	1.17454
$584$	6.82879	0.282577
$585$	−7.51093	−0.310539
$586$	24.4877	1.01158
$587$	−26.3763	−1.08867	−0.544333	−	0.838869i	$-0.683217\pi$
$587$	−26.3763	−1.08867	−0.544333	+	0.838869i	$0.683217\pi$
$588$	5.43675	0.224208
$589$	34.9477	1.43999
$590$	14.3248	0.589742
$591$	17.3676	0.714409
$592$	3.03887	0.124897
$593$	11.2107	0.460370	0.230185	−	0.973147i	$-0.426067\pi$
$593$	11.2107	0.460370	0.230185	+	0.973147i	$0.426067\pi$
$594$	1.78184	0.0731098
$595$	−11.8797	−0.487021
$596$	−15.9762	−0.654409
$597$	26.7092	1.09314
$598$	9.19831	0.376147
$599$	39.8917	1.62993	0.814966	−	0.579509i	$-0.196755\pi$
$599$	39.8917	1.62993	0.814966	+	0.579509i	$0.196755\pi$
$600$	−9.01323	−0.367964
$601$	15.9475	0.650513	0.325256	−	0.945626i	$-0.394549\pi$
$601$	15.9475	0.650513	0.325256	+	0.945626i	$0.394549\pi$
$602$	13.9541	0.568727
$603$	4.27722	0.174182
$604$	−4.50899	−0.183468
$605$	1.65334	0.0672179
$606$	−0.460383	−0.0187018
$607$	−4.43351	−0.179950	−0.0899752	−	0.995944i	$-0.528679\pi$
$607$	−4.43351	−0.179950	−0.0899752	+	0.995944i	$0.528679\pi$
$608$	4.74068	0.192260
$609$	−53.3140	−2.16039
$610$	13.6364	0.552122
$611$	−29.9128	−1.21014
$612$	13.5056	0.545931
$613$	36.7439	1.48407	0.742036	−	0.670360i	$-0.233860\pi$
$613$	36.7439	1.48407	0.742036	+	0.670360i	$0.233860\pi$
$614$	9.44215	0.381054
$615$	25.9118	1.04487
$616$	6.71287	0.270469
$617$	−6.32609	−0.254679	−0.127339	−	0.991859i	$-0.540644\pi$
$617$	−6.32609	−0.254679	−0.127339	+	0.991859i	$0.540644\pi$
$618$	1.21258	0.0487772
$619$	−33.3567	−1.34072	−0.670359	−	0.742037i	$-0.733860\pi$
$619$	−33.3567	−1.34072	−0.670359	+	0.742037i	$0.733860\pi$
$620$	8.22307	0.330247
$621$	−2.17709	−0.0873636
$622$	13.8748	0.556331
$623$	12.7394	0.510392
$624$	−5.85624	−0.234437
$625$	7.88417	0.315367
$626$	0.0463070	0.00185080
$627$	−35.0991	−1.40172
$628$	−11.5156	−0.459522
$629$	14.8738	0.593058
$630$	6.69732	0.266828
$631$	48.2403	1.92042	0.960208	−	0.279287i	$-0.0900981\pi$
$631$	48.2403	1.92042	0.960208	+	0.279287i	$0.0900981\pi$
$632$	10.4918	0.417342
$633$	−10.5647	−0.419911
$634$	−21.6109	−0.858278
$635$	−17.7530	−0.704505
$636$	22.0607	0.874765
$637$	−5.52822	−0.219036
$638$	31.4980	1.24702
$639$	19.3487	0.765424
$640$	1.11547	0.0440927
$641$	−37.7308	−1.49028	−0.745139	−	0.666909i	$-0.767617\pi$
$641$	−37.7308	−1.49028	−0.745139	+	0.666909i	$0.767617\pi$
$642$	33.5770	1.32518
$643$	4.13355	0.163011	0.0815057	−	0.996673i	$-0.474027\pi$
$643$	4.13355	0.163011	0.0815057	+	0.996673i	$0.474027\pi$
$644$	−8.20191	−0.323201
$645$	−17.1674	−0.675967
$646$	23.2033	0.912923
$647$	21.7095	0.853488	0.426744	−	0.904372i	$-0.359661\pi$
$647$	21.7095	0.853488	0.426744	+	0.904372i	$0.359661\pi$
$648$	9.66408	0.379641
$649$	−39.6186	−1.55517
$650$	9.16488	0.359476
$651$	38.4949	1.50873
$652$	−13.5787	−0.531785
$653$	18.9136	0.740146	0.370073	−	0.929003i	$-0.379333\pi$
$653$	18.9136	0.740146	0.370073	+	0.929003i	$0.379333\pi$
$654$	0.923364	0.0361064
$655$	7.37738	0.288258
$656$	9.67954	0.377923
$657$	−18.8429	−0.735132
$658$	26.6725	1.03980
$659$	−2.75660	−0.107382	−0.0536910	−	0.998558i	$-0.517099\pi$
$659$	−2.75660	−0.107382	−0.0536910	+	0.998558i	$0.517099\pi$
$660$	−8.25870	−0.321469
$661$	4.40930	0.171502	0.0857510	−	0.996317i	$-0.472671\pi$
$661$	4.40930	0.171502	0.0857510	+	0.996317i	$0.472671\pi$
$662$	−15.1368	−0.588308
$663$	−28.6634	−1.11320
$664$	−9.20979	−0.357409
$665$	11.5064	0.446197
$666$	−8.38527	−0.324923
$667$	−38.4849	−1.49014
$668$	12.5466	0.485443
$669$	−30.0839	−1.16311
$670$	1.72908	0.0668000
$671$	−37.7148	−1.45596
$672$	5.22187	0.201438
$673$	11.0555	0.426158	0.213079	−	0.977035i	$-0.431651\pi$
$673$	11.0555	0.426158	0.213079	+	0.977035i	$0.431651\pi$
$674$	4.24745	0.163606
$675$	−2.16918	−0.0834917
$676$	−7.04523	−0.270970
$677$	−41.9181	−1.61104	−0.805522	−	0.592566i	$-0.798115\pi$
$677$	−41.9181	−1.61104	−0.805522	+	0.592566i	$0.798115\pi$
$678$	−10.9709	−0.421334
$679$	7.95617	0.305330
$680$	5.45967	0.209369
$681$	−2.52029	−0.0965779
$682$	−22.7429	−0.870870
$683$	48.4854	1.85524	0.927620	−	0.373525i	$-0.121851\pi$
$683$	48.4854	1.85524	0.927620	+	0.373525i	$0.121851\pi$
$684$	−13.0811	−0.500170
$685$	−17.3029	−0.661109
$686$	20.1607	0.769740
$687$	52.0551	1.98603
$688$	−6.41301	−0.244494
$689$	−22.4319	−0.854588
$690$	10.0906	0.384144
$691$	7.97421	0.303353	0.151677	−	0.988430i	$-0.451533\pi$
$691$	7.97421	0.303353	0.151677	+	0.988430i	$0.451533\pi$
$692$	4.85331	0.184495
$693$	−18.5230	−0.703632
$694$	2.41227	0.0915685
$695$	−13.0892	−0.496503
$696$	24.5020	0.928745
$697$	47.3766	1.79452
$698$	15.3301	0.580252
$699$	−20.6568	−0.781313
$700$	−8.17211	−0.308877
$701$	−49.7799	−1.88016	−0.940080	−	0.340954i	$-0.889250\pi$
$701$	−49.7799	−1.88016	−0.940080	+	0.340954i	$0.889250\pi$
$702$	−1.40940	−0.0531942
$703$	−14.4063	−0.543346
$704$	−3.08509	−0.116274
$705$	−32.8146	−1.23587
$706$	28.0894	1.05716
$707$	−0.417419	−0.0156987
$708$	−30.8189	−1.15824
$709$	24.3834	0.915738	0.457869	−	0.889020i	$-0.348613\pi$
$709$	24.3834	0.915738	0.457869	+	0.889020i	$0.348613\pi$
$710$	7.82178	0.293546
$711$	−28.9504	−1.08573
$712$	−5.85474	−0.219416
$713$	27.7877	1.04066
$714$	25.5585	0.956502
$715$	8.39766	0.314055
$716$	0.0898258	0.00335695
$717$	−15.7206	−0.587095
$718$	25.9313	0.967749
$719$	25.7291	0.959535	0.479768	−	0.877396i	$-0.340721\pi$
$719$	25.7291	0.959535	0.479768	+	0.877396i	$0.340721\pi$
$720$	−3.07795	−0.114708
$721$	1.09942	0.0409446
$722$	−3.47408	−0.129292
$723$	16.9066	0.628762
$724$	−15.9809	−0.593926
$725$	−38.3451	−1.42410
$726$	−3.55707	−0.132015
$727$	28.5151	1.05756	0.528782	−	0.848757i	$-0.322649\pi$
$727$	28.5151	1.05756	0.528782	+	0.848757i	$0.322649\pi$
$728$	−5.30973	−0.196792
$729$	−22.5082	−0.833637
$730$	−7.61730	−0.281929
$731$	−31.3886	−1.16095
$732$	−29.3379	−1.08436
$733$	−24.5700	−0.907515	−0.453758	−	0.891125i	$-0.649917\pi$
$733$	−24.5700	−0.907515	−0.453758	+	0.891125i	$0.649917\pi$
$734$	11.4260	0.421740
$735$	−6.06452	−0.223693
$736$	3.76943	0.138943
$737$	−4.78217	−0.176154
$738$	−26.7091	−0.983175
$739$	33.8597	1.24555	0.622775	−	0.782401i	$-0.286005\pi$
$739$	33.8597	1.24555	0.622775	+	0.782401i	$0.286005\pi$
$740$	−3.38977	−0.124610
$741$	27.7626	1.01988
$742$	20.0020	0.734297
$743$	−3.58016	−0.131343	−0.0656716	−	0.997841i	$-0.520919\pi$
$743$	−3.58016	−0.131343	−0.0656716	+	0.997841i	$0.520919\pi$
$744$	−17.6914	−0.648600
$745$	17.8209	0.652907
$746$	9.88851	0.362044
$747$	25.4129	0.929809
$748$	−15.1000	−0.552112
$749$	30.4436	1.11238
$750$	23.4388	0.855865
$751$	−29.5711	−1.07907	−0.539533	−	0.841964i	$-0.681399\pi$
$751$	−29.5711	−1.07907	−0.539533	+	0.841964i	$0.681399\pi$
$752$	−12.2581	−0.447008
$753$	33.5148	1.22135
$754$	−24.9142	−0.907323
$755$	5.02963	0.183047
$756$	1.25673	0.0457066
$757$	40.8057	1.48311	0.741554	−	0.670893i	$-0.234089\pi$
$757$	40.8057	1.48311	0.741554	+	0.670893i	$0.234089\pi$
$758$	14.1178	0.512782
$759$	−27.9081	−1.01300
$760$	−5.28808	−0.191819
$761$	−11.8362	−0.429063	−0.214532	−	0.976717i	$-0.568822\pi$
$761$	−11.8362	−0.429063	−0.214532	+	0.976717i	$0.568822\pi$
$762$	38.1944	1.38364
$763$	0.837195	0.0303085
$764$	−19.7638	−0.715029
$765$	−15.0651	−0.544678
$766$	5.02639	0.181611
$767$	31.3374	1.13153
$768$	−2.39986	−0.0865975
$769$	−38.5674	−1.39078	−0.695388	−	0.718635i	$-0.744767\pi$
$769$	−38.5674	−1.39078	−0.695388	+	0.718635i	$0.744767\pi$
$770$	−7.48799	−0.269848
$771$	5.55452	0.200041
$772$	−1.80147	−0.0648364
$773$	−50.8072	−1.82741	−0.913704	−	0.406379i	$-0.866791\pi$
$773$	−50.8072	−1.82741	−0.913704	+	0.406379i	$0.866791\pi$
$774$	17.6956	0.636057
$775$	27.6867	0.994536
$776$	−3.65649	−0.131260
$777$	−15.8686	−0.569283
$778$	−23.9220	−0.857646
$779$	−45.8876	−1.64410
$780$	6.53245	0.233899
$781$	−21.6330	−0.774090
$782$	18.4495	0.659753
$783$	5.89679	0.210734
$784$	−2.26544	−0.0809087
$785$	12.8453	0.458467
$786$	−15.8720	−0.566135
$787$	−14.4544	−0.515245	−0.257622	−	0.966246i	$-0.582939\pi$
$787$	−14.4544	−0.515245	−0.257622	+	0.966246i	$0.582939\pi$
$788$	−7.23693	−0.257805
$789$	−2.14850	−0.0764887
$790$	−11.7033	−0.416385
$791$	−9.94707	−0.353677
$792$	8.51280	0.302489
$793$	29.8315	1.05935
$794$	−28.6601	−1.01711
$795$	−24.6080	−0.872757
$796$	−11.1295	−0.394474
$797$	−25.1644	−0.891369	−0.445684	−	0.895190i	$-0.647040\pi$
$797$	−25.1644	−0.891369	−0.445684	+	0.895190i	$0.647040\pi$
$798$	−24.7552	−0.876325
$799$	−59.9975	−2.12256
$800$	3.75573	0.132785
$801$	16.1552	0.570816
$802$	−4.87950	−0.172301
$803$	21.0675	0.743455
$804$	−3.72000	−0.131194
$805$	9.14897	0.322459
$806$	17.9891	0.633639
$807$	0.412991	0.0145380
$808$	0.191837	0.00674881
$809$	−26.9931	−0.949027	−0.474513	−	0.880248i	$-0.657376\pi$
$809$	−26.9931	−0.949027	−0.474513	+	0.880248i	$0.657376\pi$
$810$	−10.7800	−0.378770
$811$	29.0890	1.02145	0.510727	−	0.859743i	$-0.329376\pi$
$811$	29.0890	1.02145	0.510727	+	0.859743i	$0.329376\pi$
$812$	22.2154	0.779609
$813$	51.7090	1.81351
$814$	9.37521	0.328601
$815$	15.1467	0.530564
$816$	−11.7461	−0.411197
$817$	30.4021	1.06363
$818$	−3.25415	−0.113779
$819$	14.6513	0.511958
$820$	−10.7972	−0.377055
$821$	36.5009	1.27389	0.636945	−	0.770909i	$-0.280198\pi$
$821$	36.5009	1.27389	0.636945	+	0.770909i	$0.280198\pi$
$822$	37.2261	1.29841
$823$	−3.11125	−0.108451	−0.0542256	−	0.998529i	$-0.517269\pi$
$823$	−3.11125	−0.108451	−0.0542256	+	0.998529i	$0.517269\pi$
$824$	−0.505272	−0.0176020
$825$	−27.8067	−0.968104
$826$	−27.9428	−0.972255
$827$	−13.2201	−0.459709	−0.229854	−	0.973225i	$-0.573825\pi$
$827$	−13.2201	−0.459709	−0.229854	+	0.973225i	$0.573825\pi$
$828$	−10.4011	−0.361464
$829$	50.0567	1.73854	0.869271	−	0.494337i	$-0.164589\pi$
$829$	50.0567	1.73854	0.869271	+	0.494337i	$0.164589\pi$
$830$	10.2732	0.356589
$831$	−55.0991	−1.91137
$832$	2.44024	0.0846001
$833$	−11.0882	−0.384185
$834$	28.1607	0.975124
$835$	−13.9953	−0.484329
$836$	14.6255	0.505832
$837$	−4.25773	−0.147169
$838$	39.6891	1.37104
$839$	−3.83504	−0.132400	−0.0662001	−	0.997806i	$-0.521088\pi$
$839$	−3.83504	−0.132400	−0.0662001	+	0.997806i	$0.521088\pi$
$840$	−5.82483	−0.200976
$841$	75.2390	2.59445
$842$	8.27486	0.285171
$843$	70.1258	2.41526
$844$	4.40223	0.151531
$845$	7.85873	0.270348
$846$	33.8243	1.16290
$847$	−3.22512	−0.110816
$848$	−9.19250	−0.315672
$849$	64.3143	2.20726
$850$	18.3825	0.630513
$851$	−11.4548	−0.392666
$852$	−16.8281	−0.576521
$853$	−34.1418	−1.16899	−0.584496	−	0.811397i	$-0.698708\pi$
$853$	−34.1418	−1.16899	−0.584496	+	0.811397i	$0.698708\pi$
$854$	−26.6001	−0.910235
$855$	14.5916	0.499022
$856$	−13.9912	−0.478210
$857$	5.03986	0.172158	0.0860792	−	0.996288i	$-0.472566\pi$
$857$	5.03986	0.172158	0.0860792	+	0.996288i	$0.472566\pi$
$858$	−18.0670	−0.616799
$859$	−47.8652	−1.63314	−0.816571	−	0.577246i	$-0.804128\pi$
$859$	−47.8652	−1.63314	−0.816571	+	0.577246i	$0.804128\pi$
$860$	7.15351	0.243933
$861$	−50.5453	−1.72258
$862$	38.3167	1.30507
$863$	30.9367	1.05310	0.526549	−	0.850145i	$-0.323486\pi$
$863$	30.9367	1.05310	0.526549	+	0.850145i	$0.323486\pi$
$864$	−0.577565	−0.0196491
$865$	−5.41371	−0.184072
$866$	6.51220	0.221294
$867$	−16.6940	−0.566959
$868$	−16.0405	−0.544449
$869$	32.3683	1.09802
$870$	−27.3312	−0.926614
$871$	3.78259	0.128168
$872$	−0.384757	−0.0130295
$873$	10.0895	0.341477
$874$	−17.8697	−0.604451
$875$	21.2515	0.718431
$876$	16.3882	0.553704
$877$	25.5362	0.862297	0.431149	−	0.902281i	$-0.358108\pi$
$877$	25.5362	0.862297	0.431149	+	0.902281i	$0.358108\pi$
$878$	15.2546	0.514817
$879$	58.7671	1.98217
$880$	3.44132	0.116007
$881$	−27.2693	−0.918725	−0.459363	−	0.888249i	$-0.651922\pi$
$881$	−27.2693	−0.918725	−0.459363	+	0.888249i	$0.651922\pi$
$882$	6.25111	0.210486
$883$	−1.68445	−0.0566864	−0.0283432	−	0.999598i	$-0.509023\pi$
$883$	−1.68445	−0.0566864	−0.0283432	+	0.999598i	$0.509023\pi$
$884$	11.9438	0.401713
$885$	34.3775	1.15559
$886$	16.6014	0.557734
$887$	32.1257	1.07868	0.539338	−	0.842090i	$-0.318675\pi$
$887$	32.1257	1.07868	0.539338	+	0.842090i	$0.318675\pi$
$888$	7.29288	0.244733
$889$	34.6301	1.16146
$890$	6.53078	0.218912
$891$	29.8146	0.998826
$892$	12.5357	0.419725
$893$	58.1119	1.94464
$894$	−38.3406	−1.28230
$895$	−0.100198	−0.00334924
$896$	−2.17590	−0.0726918
$897$	22.0747	0.737052
$898$	12.8123	0.427552
$899$	−75.2648	−2.51022
$900$	−10.3633	−0.345444
$901$	−44.9928	−1.49893
$902$	29.8623	0.994306
$903$	33.4879	1.11441
$904$	4.57147	0.152045
$905$	17.8262	0.592563
$906$	−10.8209	−0.359502
$907$	−17.8293	−0.592011	−0.296006	−	0.955186i	$-0.595655\pi$
$907$	−17.8293	−0.592011	−0.296006	+	0.955186i	$0.595655\pi$
$908$	1.05018	0.0348516
$909$	−0.529343	−0.0175572
$910$	5.92283	0.196340
$911$	−36.2989	−1.20264	−0.601319	−	0.799009i	$-0.705358\pi$
$911$	−36.2989	−1.20264	−0.601319	+	0.799009i	$0.705358\pi$
$912$	11.3770	0.376730
$913$	−28.4131	−0.940335
$914$	9.26228	0.306369
$915$	32.7255	1.08187
$916$	−21.6909	−0.716687
$917$	−14.3908	−0.475226
$918$	−2.82690	−0.0933015
$919$	−30.3322	−1.00057	−0.500284	−	0.865861i	$-0.666771\pi$
$919$	−30.3322	−1.00057	−0.500284	+	0.865861i	$0.666771\pi$
$920$	−4.20468	−0.138624
$921$	22.6599	0.746668
$922$	−11.5580	−0.380643
$923$	17.1112	0.563223
$924$	16.1099	0.529978
$925$	−11.4132	−0.375264
$926$	26.6963	0.877294
$927$	1.39421	0.0457920
$928$	−10.2097	−0.335151
$929$	−7.14366	−0.234376	−0.117188	−	0.993110i	$-0.537388\pi$
$929$	−7.14366	−0.234376	−0.117188	+	0.993110i	$0.537388\pi$
$930$	19.7342	0.647111
$931$	10.7397	0.351981
$932$	8.60751	0.281948
$933$	33.2977	1.09012
$934$	−16.7744	−0.548876
$935$	16.8436	0.550845
$936$	−6.73344	−0.220089
$937$	−31.2391	−1.02054	−0.510269	−	0.860015i	$-0.670454\pi$
$937$	−31.2391	−1.02054	−0.510269	+	0.860015i	$0.670454\pi$
$938$	−3.37285	−0.110127
$939$	0.111130	0.00362660
$940$	13.6735	0.445982
$941$	−47.9745	−1.56392	−0.781962	−	0.623326i	$-0.785781\pi$
$941$	−47.9745	−1.56392	−0.781962	+	0.623326i	$0.785781\pi$
$942$	−27.6358	−0.900423
$943$	−36.4863	−1.18816
$944$	12.8419	0.417970
$945$	−1.40184	−0.0456018
$946$	−19.7847	−0.643258
$947$	39.0875	1.27017	0.635086	−	0.772442i	$-0.280965\pi$
$947$	39.0875	1.27017	0.635086	+	0.772442i	$0.280965\pi$
$948$	25.1789	0.817773
$949$	−16.6639	−0.540933
$950$	−17.8047	−0.577662
$951$	−51.8631	−1.68178
$952$	−10.6500	−0.345168
$953$	−39.7808	−1.28863	−0.644313	−	0.764762i	$-0.722857\pi$
$953$	−39.7808	−1.28863	−0.644313	+	0.764762i	$0.722857\pi$
$954$	25.3652	0.821228
$955$	22.0459	0.713388
$956$	6.55061	0.211862
$957$	75.5909	2.44351
$958$	−15.8014	−0.510522
$959$	33.7521	1.08991
$960$	2.67697	0.0863988
$961$	23.3443	0.753043
$962$	−7.41558	−0.239088
$963$	38.6065	1.24408
$964$	−7.04481	−0.226898
$965$	2.00948	0.0646876
$966$	−19.6835	−0.633305
$967$	−52.3995	−1.68506	−0.842528	−	0.538653i	$-0.818933\pi$
$967$	−52.3995	−1.68506	−0.842528	+	0.538653i	$0.818933\pi$
$968$	1.48220	0.0476396
$969$	55.6848	1.78885
$970$	4.07870	0.130959
$971$	−24.2010	−0.776648	−0.388324	−	0.921523i	$-0.626946\pi$
$971$	−24.2010	−0.776648	−0.388324	+	0.921523i	$0.626946\pi$
$972$	21.4598	0.688322
$973$	25.5327	0.818540
$974$	33.7514	1.08147
$975$	21.9945	0.704386
$976$	12.2248	0.391307
$977$	34.5719	1.10605	0.553027	−	0.833163i	$-0.313473\pi$
$977$	34.5719	1.10605	0.553027	+	0.833163i	$0.313473\pi$
$978$	−32.5871	−1.04202
$979$	−18.0624	−0.577278
$980$	2.52703	0.0807230
$981$	1.06167	0.0338967
$982$	−25.6541	−0.818654
$983$	−0.624849	−0.0199296	−0.00996479	−	0.999950i	$-0.503172\pi$
$983$	−0.624849	−0.0199296	−0.00996479	+	0.999950i	$0.503172\pi$
$984$	23.2296	0.740531
$985$	8.07256	0.257213
$986$	−49.9717	−1.59142
$987$	64.0103	2.03747
$988$	−11.5684	−0.368040
$989$	24.1734	0.768669
$990$	−9.49576	−0.301795
$991$	−18.3251	−0.582115	−0.291057	−	0.956706i	$-0.594007\pi$
$991$	−18.3251	−0.582115	−0.291057	+	0.956706i	$0.594007\pi$
$992$	7.37186	0.234057
$993$	−36.3262	−1.15278
$994$	−15.2577	−0.483944
$995$	12.4146	0.393569
$996$	−22.1022	−0.700335
$997$	12.8911	0.408264	0.204132	−	0.978943i	$-0.434563\pi$
$997$	12.8911	0.408264	0.204132	+	0.978943i	$0.434563\pi$
$998$	−31.0571	−0.983095
$999$	1.75515	0.0555304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.5	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.5	✓	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.39986 q^{3} +1.00000 q^{4} -1.11547 q^{5} +2.39986 q^{6} +2.17590 q^{7} -1.00000 q^{8} +2.75933 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.39986 q^{3} +1.00000 q^{4} -1.11547 q^{5} +2.39986 q^{6} +2.17590 q^{7} -1.00000 q^{8} +2.75933 q^{9} +1.11547 q^{10} -3.08509 q^{11} -2.39986 q^{12} +2.44024 q^{13} -2.17590 q^{14} +2.67697 q^{15} +1.00000 q^{16} +4.89451 q^{17} -2.75933 q^{18} -4.74068 q^{19} -1.11547 q^{20} -5.22187 q^{21} +3.08509 q^{22} -3.76943 q^{23} +2.39986 q^{24} -3.75573 q^{25} -2.44024 q^{26} +0.577565 q^{27} +2.17590 q^{28} +10.2097 q^{29} -2.67697 q^{30} -7.37186 q^{31} -1.00000 q^{32} +7.40380 q^{33} -4.89451 q^{34} -2.42715 q^{35} +2.75933 q^{36} +3.03887 q^{37} +4.74068 q^{38} -5.85624 q^{39} +1.11547 q^{40} +9.67954 q^{41} +5.22187 q^{42} -6.41301 q^{43} -3.08509 q^{44} -3.07795 q^{45} +3.76943 q^{46} -12.2581 q^{47} -2.39986 q^{48} -2.26544 q^{49} +3.75573 q^{50} -11.7461 q^{51} +2.44024 q^{52} -9.19250 q^{53} -0.577565 q^{54} +3.44132 q^{55} -2.17590 q^{56} +11.3770 q^{57} -10.2097 q^{58} +12.8419 q^{59} +2.67697 q^{60} +12.2248 q^{61} +7.37186 q^{62} +6.00405 q^{63} +1.00000 q^{64} -2.72201 q^{65} -7.40380 q^{66} +1.55009 q^{67} +4.89451 q^{68} +9.04611 q^{69} +2.42715 q^{70} +7.01211 q^{71} -2.75933 q^{72} -6.82879 q^{73} -3.03887 q^{74} +9.01323 q^{75} -4.74068 q^{76} -6.71287 q^{77} +5.85624 q^{78} -10.4918 q^{79} -1.11547 q^{80} -9.66408 q^{81} -9.67954 q^{82} +9.20979 q^{83} -5.22187 q^{84} -5.45967 q^{85} +6.41301 q^{86} -24.5020 q^{87} +3.08509 q^{88} +5.85474 q^{89} +3.07795 q^{90} +5.30973 q^{91} -3.76943 q^{92} +17.6914 q^{93} +12.2581 q^{94} +5.28808 q^{95} +2.39986 q^{96} +3.65649 q^{97} +2.26544 q^{98} -8.51280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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