LMFDB - Embedded newform 4007.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51027 q^{2} -1.47560 q^{3} +4.30145 q^{4} -0.0269498 q^{5} +3.70415 q^{6} +2.66833 q^{7} -5.77725 q^{8} -0.822611 q^{9} +O(q^{10})$	\(q-2.51027 q^{2} -1.47560 q^{3} +4.30145 q^{4} -0.0269498 q^{5} +3.70415 q^{6} +2.66833 q^{7} -5.77725 q^{8} -0.822611 q^{9} +0.0676513 q^{10} -2.54459 q^{11} -6.34720 q^{12} -4.66719 q^{13} -6.69822 q^{14} +0.0397671 q^{15} +5.89954 q^{16} +5.31669 q^{17} +2.06498 q^{18} -3.22201 q^{19} -0.115923 q^{20} -3.93738 q^{21} +6.38759 q^{22} -1.00526 q^{23} +8.52489 q^{24} -4.99927 q^{25} +11.7159 q^{26} +5.64064 q^{27} +11.4777 q^{28} +6.05354 q^{29} -0.0998261 q^{30} +7.05805 q^{31} -3.25494 q^{32} +3.75479 q^{33} -13.3463 q^{34} -0.0719110 q^{35} -3.53842 q^{36} -1.01221 q^{37} +8.08812 q^{38} +6.88690 q^{39} +0.155696 q^{40} +5.65268 q^{41} +9.88388 q^{42} -2.44526 q^{43} -10.9454 q^{44} +0.0221692 q^{45} +2.52348 q^{46} -10.0099 q^{47} -8.70535 q^{48} +0.119985 q^{49} +12.5495 q^{50} -7.84530 q^{51} -20.0757 q^{52} +9.53728 q^{53} -14.1595 q^{54} +0.0685762 q^{55} -15.4156 q^{56} +4.75440 q^{57} -15.1960 q^{58} +7.79484 q^{59} +0.171056 q^{60} +0.720735 q^{61} -17.7176 q^{62} -2.19500 q^{63} -3.62830 q^{64} +0.125780 q^{65} -9.42552 q^{66} +5.95035 q^{67} +22.8695 q^{68} +1.48336 q^{69} +0.180516 q^{70} -5.50883 q^{71} +4.75243 q^{72} -10.4037 q^{73} +2.54093 q^{74} +7.37692 q^{75} -13.8593 q^{76} -6.78980 q^{77} -17.2880 q^{78} -8.50548 q^{79} -0.158992 q^{80} -5.85548 q^{81} -14.1897 q^{82} +11.2651 q^{83} -16.9364 q^{84} -0.143284 q^{85} +6.13826 q^{86} -8.93259 q^{87} +14.7007 q^{88} -0.278394 q^{89} -0.0556507 q^{90} -12.4536 q^{91} -4.32408 q^{92} -10.4148 q^{93} +25.1274 q^{94} +0.0868327 q^{95} +4.80299 q^{96} -11.4105 q^{97} -0.301193 q^{98} +2.09321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.51027	−1.77503	−0.887514	−	0.460781i	$-0.847569\pi$
$2$	−2.51027	−1.77503	−0.887514	+	0.460781i	$0.847569\pi$
$3$	−1.47560	−0.851937	−0.425968	−	0.904738i	$-0.640067\pi$
$3$	−1.47560	−0.851937	−0.425968	+	0.904738i	$0.640067\pi$
$4$	4.30145	2.15072
$5$	−0.0269498	−0.0120523	−0.00602616	−	0.999982i	$-0.501918\pi$
$5$	−0.0269498	−0.0120523	−0.00602616	+	0.999982i	$0.501918\pi$
$6$	3.70415	1.51221
$7$	2.66833	1.00853	0.504267	−	0.863548i	$-0.331763\pi$
$7$	2.66833	1.00853	0.504267	+	0.863548i	$0.331763\pi$
$8$	−5.77725	−2.04256
$9$	−0.822611	−0.274204
$10$	0.0676513	0.0213932
$11$	−2.54459	−0.767222	−0.383611	−	0.923495i	$-0.625320\pi$
$11$	−2.54459	−0.767222	−0.383611	+	0.923495i	$0.625320\pi$
$12$	−6.34720	−1.83228
$13$	−4.66719	−1.29445	−0.647223	−	0.762301i	$-0.724070\pi$
$13$	−4.66719	−1.29445	−0.647223	+	0.762301i	$0.724070\pi$
$14$	−6.69822	−1.79018
$15$	0.0397671	0.0102678
$16$	5.89954	1.47489
$17$	5.31669	1.28949	0.644744	−	0.764399i	$-0.276964\pi$
$17$	5.31669	1.28949	0.644744	+	0.764399i	$0.276964\pi$
$18$	2.06498	0.486719
$19$	−3.22201	−0.739181	−0.369590	−	0.929195i	$-0.620502\pi$
$19$	−3.22201	−0.739181	−0.369590	+	0.929195i	$0.620502\pi$
$20$	−0.115923	−0.0259212
$21$	−3.93738	−0.859207
$22$	6.38759	1.36184
$23$	−1.00526	−0.209612	−0.104806	−	0.994493i	$-0.533422\pi$
$23$	−1.00526	−0.209612	−0.104806	+	0.994493i	$0.533422\pi$
$24$	8.52489	1.74014
$25$	−4.99927	−0.999855
$26$	11.7159	2.29768
$27$	5.64064	1.08554
$28$	11.4777	2.16908
$29$	6.05354	1.12411	0.562057	−	0.827098i	$-0.310010\pi$
$29$	6.05354	1.12411	0.562057	+	0.827098i	$0.310010\pi$
$30$	−0.0998261	−0.0182257
$31$	7.05805	1.26766	0.633831	−	0.773471i	$-0.281481\pi$
$31$	7.05805	1.26766	0.633831	+	0.773471i	$0.281481\pi$
$32$	−3.25494	−0.575398
$33$	3.75479	0.653624
$34$	−13.3463	−2.28888
$35$	−0.0719110	−0.0121552
$36$	−3.53842	−0.589736
$37$	−1.01221	−0.166407	−0.0832034	−	0.996533i	$-0.526515\pi$
$37$	−1.01221	−0.166407	−0.0832034	+	0.996533i	$0.526515\pi$
$38$	8.08812	1.31207
$39$	6.88690	1.10279
$40$	0.155696	0.0246177
$41$	5.65268	0.882800	0.441400	−	0.897310i	$-0.354482\pi$
$41$	5.65268	0.882800	0.441400	+	0.897310i	$0.354482\pi$
$42$	9.88388	1.52512
$43$	−2.44526	−0.372899	−0.186450	−	0.982465i	$-0.559698\pi$
$43$	−2.44526	−0.372899	−0.186450	+	0.982465i	$0.559698\pi$
$44$	−10.9454	−1.65008
$45$	0.0221692	0.00330479
$46$	2.52348	0.372067
$47$	−10.0099	−1.46009	−0.730044	−	0.683401i	$-0.760500\pi$
$47$	−10.0099	−1.46009	−0.730044	+	0.683401i	$0.760500\pi$
$48$	−8.70535	−1.25651
$49$	0.119985	0.0171407
$50$	12.5495	1.77477
$51$	−7.84530	−1.09856
$52$	−20.0757	−2.78400
$53$	9.53728	1.31005	0.655023	−	0.755609i	$-0.272659\pi$
$53$	9.53728	1.31005	0.655023	+	0.755609i	$0.272659\pi$
$54$	−14.1595	−1.92687
$55$	0.0685762	0.00924681
$56$	−15.4156	−2.06000
$57$	4.75440	0.629735
$58$	−15.1960	−1.99533
$59$	7.79484	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$59$	7.79484	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$60$	0.171056	0.0220832
$61$	0.720735	0.0922807	0.0461403	−	0.998935i	$-0.485308\pi$
$61$	0.720735	0.0922807	0.0461403	+	0.998935i	$0.485308\pi$
$62$	−17.7176	−2.25014
$63$	−2.19500	−0.276544
$64$	−3.62830	−0.453538
$65$	0.125780	0.0156011
$66$	−9.42552	−1.16020
$67$	5.95035	0.726951	0.363475	−	0.931604i	$-0.381590\pi$
$67$	5.95035	0.726951	0.363475	+	0.931604i	$0.381590\pi$
$68$	22.8695	2.77333
$69$	1.48336	0.178576
$70$	0.180516	0.0215758
$71$	−5.50883	−0.653778	−0.326889	−	0.945063i	$-0.606000\pi$
$71$	−5.50883	−0.653778	−0.326889	+	0.945063i	$0.606000\pi$
$72$	4.75243	0.560079
$73$	−10.4037	−1.21766	−0.608829	−	0.793301i	$-0.708360\pi$
$73$	−10.4037	−1.21766	−0.608829	+	0.793301i	$0.708360\pi$
$74$	2.54093	0.295377
$75$	7.37692	0.851813
$76$	−13.8593	−1.58977
$77$	−6.78980	−0.773769
$78$	−17.2880	−1.95748
$79$	−8.50548	−0.956942	−0.478471	−	0.878103i	$-0.658809\pi$
$79$	−8.50548	−0.956942	−0.478471	+	0.878103i	$0.658809\pi$
$80$	−0.158992	−0.0177758
$81$	−5.85548	−0.650608
$82$	−14.1897	−1.56699
$83$	11.2651	1.23651	0.618253	−	0.785979i	$-0.287841\pi$
$83$	11.2651	1.23651	0.618253	+	0.785979i	$0.287841\pi$
$84$	−16.9364	−1.84792
$85$	−0.143284	−0.0155413
$86$	6.13826	0.661906
$87$	−8.93259	−0.957674
$88$	14.7007	1.56710
$89$	−0.278394	−0.0295097	−0.0147548	−	0.999891i	$-0.504697\pi$
$89$	−0.278394	−0.0295097	−0.0147548	+	0.999891i	$0.504697\pi$
$90$	−0.0556507	−0.00586610
$91$	−12.4536	−1.30549
$92$	−4.32408	−0.450817
$93$	−10.4148	−1.07997
$94$	25.1274	2.59169
$95$	0.0868327	0.00890885
$96$	4.80299	0.490203
$97$	−11.4105	−1.15856	−0.579280	−	0.815129i	$-0.696666\pi$
$97$	−11.4105	−1.15856	−0.579280	+	0.815129i	$0.696666\pi$
$98$	−0.301193	−0.0304251
$99$	2.09321	0.210375
$100$	−21.5041	−2.15041
$101$	2.42278	0.241075	0.120538	−	0.992709i	$-0.461538\pi$
$101$	2.42278	0.241075	0.120538	+	0.992709i	$0.461538\pi$
$102$	19.6938	1.94998
$103$	12.9362	1.27465	0.637323	−	0.770597i	$-0.280042\pi$
$103$	12.9362	1.27465	0.637323	+	0.770597i	$0.280042\pi$
$104$	26.9635	2.64399
$105$	0.106112	0.0103554
$106$	−23.9411	−2.32537
$107$	−14.8815	−1.43865	−0.719326	−	0.694672i	$-0.755549\pi$
$107$	−14.8815	−1.43865	−0.719326	+	0.694672i	$0.755549\pi$
$108$	24.2629	2.33470
$109$	2.61026	0.250017	0.125009	−	0.992156i	$-0.460104\pi$
$109$	2.61026	0.250017	0.125009	+	0.992156i	$0.460104\pi$
$110$	−0.172145	−0.0164133
$111$	1.49362	0.141768
$112$	15.7419	1.48747
$113$	−6.39100	−0.601215	−0.300607	−	0.953748i	$-0.597189\pi$
$113$	−6.39100	−0.601215	−0.300607	+	0.953748i	$0.597189\pi$
$114$	−11.9348	−1.11780
$115$	0.0270917	0.00252631
$116$	26.0390	2.41766
$117$	3.83929	0.354942
$118$	−19.5671	−1.80130
$119$	14.1867	1.30049
$120$	−0.229744	−0.0209727
$121$	−4.52508	−0.411371
$122$	−1.80924	−0.163801
$123$	−8.34108	−0.752090
$124$	30.3598	2.72639
$125$	0.269479	0.0241029
$126$	5.51004	0.490873
$127$	4.50010	0.399319	0.199660	−	0.979865i	$-0.436016\pi$
$127$	4.50010	0.399319	0.199660	+	0.979865i	$0.436016\pi$
$128$	15.6179	1.38044
$129$	3.60822	0.317686
$130$	−0.315742	−0.0276924
$131$	3.46003	0.302304	0.151152	−	0.988511i	$-0.451702\pi$
$131$	3.46003	0.302304	0.151152	+	0.988511i	$0.451702\pi$
$132$	16.1510	1.40576
$133$	−8.59739	−0.745489
$134$	−14.9370	−1.29036
$135$	−0.152014	−0.0130833
$136$	−30.7158	−2.63386
$137$	18.1298	1.54894	0.774468	−	0.632613i	$-0.218018\pi$
$137$	18.1298	1.54894	0.774468	+	0.632613i	$0.218018\pi$
$138$	−3.72364	−0.316977
$139$	18.1267	1.53748	0.768741	−	0.639560i	$-0.220883\pi$
$139$	18.1267	1.53748	0.768741	+	0.639560i	$0.220883\pi$
$140$	−0.309321	−0.0261424
$141$	14.7705	1.24390
$142$	13.8286	1.16047
$143$	11.8761	0.993127
$144$	−4.85303	−0.404419
$145$	−0.163142	−0.0135482
$146$	26.1160	2.16138
$147$	−0.177049	−0.0146028
$148$	−4.35398	−0.357895
$149$	−7.04588	−0.577221	−0.288611	−	0.957447i	$-0.593193\pi$
$149$	−7.04588	−0.577221	−0.288611	+	0.957447i	$0.593193\pi$
$150$	−18.5180	−1.51199
$151$	8.33478	0.678275	0.339137	−	0.940737i	$-0.389865\pi$
$151$	8.33478	0.678275	0.339137	+	0.940737i	$0.389865\pi$
$152$	18.6144	1.50982
$153$	−4.37357	−0.353582
$154$	17.0442	1.37346
$155$	−0.190213	−0.0152783
$156$	29.6236	2.37179
$157$	4.46433	0.356293	0.178146	−	0.984004i	$-0.442990\pi$
$157$	4.46433	0.356293	0.178146	+	0.984004i	$0.442990\pi$
$158$	21.3510	1.69860
$159$	−14.0732	−1.11608
$160$	0.0877202	0.00693489
$161$	−2.68237	−0.211401
$162$	14.6988	1.15485
$163$	−9.90060	−0.775475	−0.387737	−	0.921770i	$-0.626743\pi$
$163$	−9.90060	−0.775475	−0.387737	+	0.921770i	$0.626743\pi$
$164$	24.3147	1.89866
$165$	−0.101191	−0.00787770
$166$	−28.2785	−2.19483
$167$	−21.8663	−1.69206	−0.846032	−	0.533132i	$-0.821015\pi$
$167$	−21.8663	−1.69206	−0.846032	+	0.533132i	$0.821015\pi$
$168$	22.7472	1.75499
$169$	8.78269	0.675592
$170$	0.359681	0.0275863
$171$	2.65047	0.202686
$172$	−10.5182	−0.802003
$173$	−11.0883	−0.843030	−0.421515	−	0.906821i	$-0.638502\pi$
$173$	−11.0883	−0.843030	−0.421515	+	0.906821i	$0.638502\pi$
$174$	22.4232	1.69990
$175$	−13.3397	−1.00839
$176$	−15.0119	−1.13156
$177$	−11.5021	−0.864547
$178$	0.698843	0.0523805
$179$	5.73934	0.428978	0.214489	−	0.976726i	$-0.431191\pi$
$179$	5.73934	0.428978	0.214489	+	0.976726i	$0.431191\pi$
$180$	0.0953598	0.00710770
$181$	−20.8064	−1.54653	−0.773265	−	0.634083i	$-0.781378\pi$
$181$	−20.8064	−1.54653	−0.773265	+	0.634083i	$0.781378\pi$
$182$	31.2619	2.31729
$183$	−1.06351	−0.0786173
$184$	5.80765	0.428146
$185$	0.0272790	0.00200559
$186$	26.1440	1.91697
$187$	−13.5288	−0.989323
$188$	−43.0568	−3.14024
$189$	15.0511	1.09480
$190$	−0.217973	−0.0158135
$191$	19.4735	1.40905	0.704525	−	0.709679i	$-0.251160\pi$
$191$	19.4735	1.40905	0.704525	+	0.709679i	$0.251160\pi$
$192$	5.35392	0.386386
$193$	−19.7535	−1.42189	−0.710944	−	0.703249i	$-0.751732\pi$
$193$	−19.7535	−1.42189	−0.710944	+	0.703249i	$0.751732\pi$
$194$	28.6434	2.05648
$195$	−0.185601	−0.0132911
$196$	0.516107	0.0368648
$197$	23.1001	1.64581	0.822907	−	0.568176i	$-0.192351\pi$
$197$	23.1001	1.64581	0.822907	+	0.568176i	$0.192351\pi$
$198$	−5.25451	−0.373422
$199$	−15.8669	−1.12477	−0.562387	−	0.826874i	$-0.690117\pi$
$199$	−15.8669	−1.12477	−0.562387	+	0.826874i	$0.690117\pi$
$200$	28.8820	2.04227
$201$	−8.78032	−0.619316
$202$	−6.08182	−0.427915
$203$	16.1528	1.13371
$204$	−33.7461	−2.36270
$205$	−0.152339	−0.0106398
$206$	−32.4734	−2.26253
$207$	0.826941	0.0574764
$208$	−27.5343	−1.90916
$209$	8.19869	0.567115
$210$	−0.266369	−0.0183812
$211$	−1.92286	−0.132375	−0.0661876	−	0.997807i	$-0.521084\pi$
$211$	−1.92286	−0.132375	−0.0661876	+	0.997807i	$0.521084\pi$
$212$	41.0241	2.81755
$213$	8.12882	0.556977
$214$	37.3567	2.55365
$215$	0.0658994	0.00449430
$216$	−32.5873	−2.21729
$217$	18.8332	1.27848
$218$	−6.55244	−0.443787
$219$	15.3516	1.03737
$220$	0.294977	0.0198873
$221$	−24.8140	−1.66917
$222$	−3.74938	−0.251642
$223$	−9.12539	−0.611081	−0.305541	−	0.952179i	$-0.598837\pi$
$223$	−9.12539	−0.611081	−0.305541	+	0.952179i	$0.598837\pi$
$224$	−8.68527	−0.580309
$225$	4.11246	0.274164
$226$	16.0431	1.06717
$227$	−6.30892	−0.418738	−0.209369	−	0.977837i	$-0.567141\pi$
$227$	−6.30892	−0.418738	−0.209369	+	0.977837i	$0.567141\pi$
$228$	20.4508	1.35439
$229$	17.5489	1.15966	0.579832	−	0.814736i	$-0.303118\pi$
$229$	17.5489	1.15966	0.579832	+	0.814736i	$0.303118\pi$
$230$	−0.0680074	−0.00448427
$231$	10.0190	0.659202
$232$	−34.9728	−2.29608
$233$	17.0777	1.11880	0.559399	−	0.828899i	$-0.311032\pi$
$233$	17.0777	1.11880	0.559399	+	0.828899i	$0.311032\pi$
$234$	−9.63764	−0.630032
$235$	0.269764	0.0175975
$236$	33.5291	2.18256
$237$	12.5507	0.815254
$238$	−35.6124	−2.30841
$239$	10.7585	0.695908	0.347954	−	0.937512i	$-0.386876\pi$
$239$	10.7585	0.695908	0.347954	+	0.937512i	$0.386876\pi$
$240$	0.234608	0.0151439
$241$	11.2449	0.724348	0.362174	−	0.932110i	$-0.382035\pi$
$241$	11.2449	0.724348	0.362174	+	0.932110i	$0.382035\pi$
$242$	11.3592	0.730195
$243$	−8.28158	−0.531264
$244$	3.10020	0.198470
$245$	−0.00323356	−0.000206585 0
$246$	20.9383	1.33498
$247$	15.0378	0.956830
$248$	−40.7761	−2.58928
$249$	−16.6228	−1.05343
$250$	−0.676464	−0.0427833
$251$	16.0113	1.01062	0.505312	−	0.862937i	$-0.331377\pi$
$251$	16.0113	1.01062	0.505312	+	0.862937i	$0.331377\pi$
$252$	−9.44167	−0.594769
$253$	2.55798	0.160819
$254$	−11.2965	−0.708803
$255$	0.211429	0.0132402
$256$	−31.9485	−1.99678
$257$	−25.7049	−1.60343	−0.801715	−	0.597707i	$-0.796079\pi$
$257$	−25.7049	−1.60343	−0.801715	+	0.597707i	$0.796079\pi$
$258$	−9.05761	−0.563902
$259$	−2.70092	−0.167827
$260$	0.541036	0.0335536
$261$	−4.97971	−0.308236
$262$	−8.68560	−0.536598
$263$	−19.6388	−1.21098	−0.605491	−	0.795852i	$-0.707023\pi$
$263$	−19.6388	−1.21098	−0.605491	+	0.795852i	$0.707023\pi$
$264$	−21.6923	−1.33507
$265$	−0.257028	−0.0157891
$266$	21.5818	1.32326
$267$	0.410797	0.0251404
$268$	25.5951	1.56347
$269$	−11.3937	−0.694685	−0.347343	−	0.937738i	$-0.612916\pi$
$269$	−11.3937	−0.694685	−0.347343	+	0.937738i	$0.612916\pi$
$270$	0.381596	0.0232232
$271$	−30.0407	−1.82484	−0.912422	−	0.409252i	$-0.865790\pi$
$271$	−30.0407	−1.82484	−0.912422	+	0.409252i	$0.865790\pi$
$272$	31.3661	1.90185
$273$	18.3765	1.11220
$274$	−45.5107	−2.74940
$275$	12.7211	0.767110
$276$	6.38061	0.384068
$277$	20.9521	1.25889	0.629445	−	0.777045i	$-0.283282\pi$
$277$	20.9521	1.25889	0.629445	+	0.777045i	$0.283282\pi$
$278$	−45.5028	−2.72907
$279$	−5.80603	−0.347598
$280$	0.415448	0.0248277
$281$	12.5921	0.751182	0.375591	−	0.926786i	$-0.377440\pi$
$281$	12.5921	0.751182	0.375591	+	0.926786i	$0.377440\pi$
$282$	−37.0780	−2.20796
$283$	−29.0888	−1.72915	−0.864574	−	0.502506i	$-0.832411\pi$
$283$	−29.0888	−1.72915	−0.864574	+	0.502506i	$0.832411\pi$
$284$	−23.6959	−1.40609
$285$	−0.128130	−0.00758978
$286$	−29.8121	−1.76283
$287$	15.0832	0.890334
$288$	2.67755	0.157776
$289$	11.2672	0.662778
$290$	0.409530	0.0240484
$291$	16.8373	0.987020
$292$	−44.7508	−2.61885
$293$	−17.8617	−1.04349	−0.521746	−	0.853101i	$-0.674719\pi$
$293$	−17.8617	−1.04349	−0.521746	+	0.853101i	$0.674719\pi$
$294$	0.444440	0.0259203
$295$	−0.210070	−0.0122307
$296$	5.84780	0.339897
$297$	−14.3531	−0.832851
$298$	17.6870	1.02458
$299$	4.69176	0.271331
$300$	31.7314	1.83201
$301$	−6.52477	−0.376081
$302$	−20.9225	−1.20396
$303$	−3.57504	−0.205381
$304$	−19.0084	−1.09021
$305$	−0.0194237	−0.00111220
$306$	10.9788	0.627618
$307$	−3.66712	−0.209294	−0.104647	−	0.994509i	$-0.533371\pi$
$307$	−3.66712	−0.209294	−0.104647	+	0.994509i	$0.533371\pi$
$308$	−29.2059	−1.66416
$309$	−19.0887	−1.08592
$310$	0.477486	0.0271194
$311$	−3.37948	−0.191633	−0.0958164	−	0.995399i	$-0.530546\pi$
$311$	−3.37948	−0.191633	−0.0958164	+	0.995399i	$0.530546\pi$
$312$	−39.7873	−2.25251
$313$	8.91967	0.504170	0.252085	−	0.967705i	$-0.418884\pi$
$313$	8.91967	0.504170	0.252085	+	0.967705i	$0.418884\pi$
$314$	−11.2067	−0.632429
$315$	0.0591548	0.00333300
$316$	−36.5859	−2.05812
$317$	−11.8836	−0.667450	−0.333725	−	0.942670i	$-0.608306\pi$
$317$	−11.8836	−0.667450	−0.333725	+	0.942670i	$0.608306\pi$
$318$	35.3275	1.98107
$319$	−15.4038	−0.862445
$320$	0.0977822	0.00546619
$321$	21.9592	1.22564
$322$	6.73348	0.375242
$323$	−17.1305	−0.953164
$324$	−25.1870	−1.39928
$325$	23.3326	1.29426
$326$	24.8532	1.37649
$327$	−3.85169	−0.212999
$328$	−32.6569	−1.80318
$329$	−26.7096	−1.47255
$330$	0.254016	0.0139831
$331$	−16.2327	−0.892229	−0.446114	−	0.894976i	$-0.647193\pi$
$331$	−16.2327	−0.892229	−0.446114	+	0.894976i	$0.647193\pi$
$332$	48.4563	2.65938
$333$	0.832658	0.0456294
$334$	54.8902	3.00346
$335$	−0.160361	−0.00876145
$336$	−23.2288	−1.26723
$337$	25.0372	1.36386	0.681931	−	0.731416i	$-0.261140\pi$
$337$	25.0372	1.36386	0.681931	+	0.731416i	$0.261140\pi$
$338$	−22.0469	−1.19919
$339$	9.43054	0.512197
$340$	−0.616328	−0.0334251
$341$	−17.9598	−0.972578
$342$	−6.65338	−0.359773
$343$	−18.3582	−0.991247
$344$	14.1269	0.761671
$345$	−0.0399764	−0.00215226
$346$	27.8347	1.49640
$347$	−14.8312	−0.796182	−0.398091	−	0.917346i	$-0.630327\pi$
$347$	−14.8312	−0.796182	−0.398091	+	0.917346i	$0.630327\pi$
$348$	−38.4230	−2.05969
$349$	21.4424	1.14778	0.573892	−	0.818931i	$-0.305433\pi$
$349$	21.4424	1.14778	0.573892	+	0.818931i	$0.305433\pi$
$350$	33.4863	1.78992
$351$	−26.3259	−1.40517
$352$	8.28249	0.441458
$353$	−25.9394	−1.38061	−0.690306	−	0.723517i	$-0.742524\pi$
$353$	−25.9394	−1.38061	−0.690306	+	0.723517i	$0.742524\pi$
$354$	28.8732	1.53460
$355$	0.148462	0.00787955
$356$	−1.19750	−0.0634672
$357$	−20.9338	−1.10794
$358$	−14.4073	−0.761448
$359$	31.9560	1.68657	0.843286	−	0.537466i	$-0.180618\pi$
$359$	31.9560	1.68657	0.843286	+	0.537466i	$0.180618\pi$
$360$	−0.128077	−0.00675026
$361$	−8.61863	−0.453612
$362$	52.2297	2.74513
$363$	6.67720	0.350462
$364$	−53.5685	−2.80775
$365$	0.280377	0.0146756
$366$	2.66971	0.139548
$367$	−18.5096	−0.966191	−0.483095	−	0.875568i	$-0.660488\pi$
$367$	−18.5096	−0.966191	−0.483095	+	0.875568i	$0.660488\pi$
$368$	−5.93059	−0.309154
$369$	−4.64996	−0.242067
$370$	−0.0684775	−0.00355998
$371$	25.4486	1.32123
$372$	−44.7989	−2.32271
$373$	−17.5243	−0.907373	−0.453687	−	0.891161i	$-0.649891\pi$
$373$	−17.5243	−0.907373	−0.453687	+	0.891161i	$0.649891\pi$
$374$	33.9609	1.75608
$375$	−0.397642	−0.0205342
$376$	57.8294	2.98232
$377$	−28.2530	−1.45511
$378$	−37.7822	−1.94331
$379$	1.43101	0.0735060	0.0367530	−	0.999324i	$-0.488299\pi$
$379$	1.43101	0.0735060	0.0367530	+	0.999324i	$0.488299\pi$
$380$	0.373506	0.0191605
$381$	−6.64034	−0.340195
$382$	−48.8836	−2.50110
$383$	−17.2330	−0.880565	−0.440282	−	0.897859i	$-0.645122\pi$
$383$	−17.2330	−0.880565	−0.440282	+	0.897859i	$0.645122\pi$
$384$	−23.0457	−1.17605
$385$	0.182984	0.00932572
$386$	49.5866	2.52389
$387$	2.01150	0.102250
$388$	−49.0816	−2.49174
$389$	17.8047	0.902735	0.451368	−	0.892338i	$-0.350936\pi$
$389$	17.8047	0.902735	0.451368	+	0.892338i	$0.350936\pi$
$390$	0.465908	0.0235922
$391$	−5.34468	−0.270292
$392$	−0.693180	−0.0350109
$393$	−5.10561	−0.257544
$394$	−57.9874	−2.92136
$395$	0.229221	0.0115334
$396$	9.00381	0.452459
$397$	−6.41463	−0.321941	−0.160970	−	0.986959i	$-0.551462\pi$
$397$	−6.41463	−0.321941	−0.160970	+	0.986959i	$0.551462\pi$
$398$	39.8302	1.99651
$399$	12.6863	0.635109
$400$	−29.4934	−1.47467
$401$	−20.4424	−1.02084	−0.510422	−	0.859924i	$-0.670511\pi$
$401$	−20.4424	−1.02084	−0.510422	+	0.859924i	$0.670511\pi$
$402$	22.0410	1.09930
$403$	−32.9413	−1.64092
$404$	10.4214	0.518486
$405$	0.157804	0.00784135
$406$	−40.5480	−2.01236
$407$	2.57566	0.127671
$408$	45.3242	2.24388
$409$	35.7642	1.76842	0.884212	−	0.467086i	$-0.154696\pi$
$409$	35.7642	1.76842	0.884212	+	0.467086i	$0.154696\pi$
$410$	0.382411	0.0188859
$411$	−26.7523	−1.31960
$412$	55.6445	2.74141
$413$	20.7992	1.02346
$414$	−2.07584	−0.102022
$415$	−0.303593	−0.0149028
$416$	15.1915	0.744822
$417$	−26.7476	−1.30984
$418$	−20.5809	−1.00665
$419$	−13.8844	−0.678298	−0.339149	−	0.940733i	$-0.610139\pi$
$419$	−13.8844	−0.678298	−0.339149	+	0.940733i	$0.610139\pi$
$420$	0.456434	0.0222717
$421$	8.99892	0.438580	0.219290	−	0.975660i	$-0.429626\pi$
$421$	8.99892	0.438580	0.219290	+	0.975660i	$0.429626\pi$
$422$	4.82689	0.234970
$423$	8.23422	0.400361
$424$	−55.0992	−2.67586
$425$	−26.5796	−1.28930
$426$	−20.4055	−0.988650
$427$	1.92316	0.0930682
$428$	−64.0121	−3.09414
$429$	−17.5243	−0.846082
$430$	−0.165425	−0.00797751
$431$	−15.9942	−0.770413	−0.385207	−	0.922830i	$-0.625870\pi$
$431$	−15.9942	−0.770413	−0.385207	+	0.922830i	$0.625870\pi$
$432$	33.2772	1.60105
$433$	−7.98316	−0.383646	−0.191823	−	0.981430i	$-0.561440\pi$
$433$	−7.98316	−0.383646	−0.191823	+	0.981430i	$0.561440\pi$
$434$	−47.2764	−2.26934
$435$	0.240732	0.0115422
$436$	11.2279	0.537718
$437$	3.23897	0.154941
$438$	−38.5367	−1.84136
$439$	−6.62890	−0.316380	−0.158190	−	0.987409i	$-0.550566\pi$
$439$	−6.62890	−0.316380	−0.158190	+	0.987409i	$0.550566\pi$
$440$	−0.396181	−0.0188872
$441$	−0.0987007	−0.00470003
$442$	62.2899	2.96283
$443$	1.29844	0.0616907	0.0308454	−	0.999524i	$-0.490180\pi$
$443$	1.29844	0.0616907	0.0308454	+	0.999524i	$0.490180\pi$
$444$	6.42472	0.304904
$445$	0.00750267	0.000355661 0
$446$	22.9072	1.08469
$447$	10.3969	0.491756
$448$	−9.68151	−0.457408
$449$	−30.9324	−1.45979	−0.729894	−	0.683560i	$-0.760431\pi$
$449$	−30.9324	−1.45979	−0.729894	+	0.683560i	$0.760431\pi$
$450$	−10.3234	−0.486649
$451$	−14.3837	−0.677303
$452$	−27.4905	−1.29305
$453$	−12.2988	−0.577847
$454$	15.8371	0.743271
$455$	0.335623	0.0157342
$456$	−27.4673	−1.28627
$457$	−20.6604	−0.966454	−0.483227	−	0.875495i	$-0.660536\pi$
$457$	−20.6604	−0.966454	−0.483227	+	0.875495i	$0.660536\pi$
$458$	−44.0524	−2.05843
$459$	29.9895	1.39979
$460$	0.116533	0.00543340
$461$	−8.64742	−0.402751	−0.201375	−	0.979514i	$-0.564541\pi$
$461$	−8.64742	−0.402751	−0.201375	+	0.979514i	$0.564541\pi$
$462$	−25.1504	−1.17010
$463$	−12.2277	−0.568269	−0.284135	−	0.958784i	$-0.591706\pi$
$463$	−12.2277	−0.568269	−0.284135	+	0.958784i	$0.591706\pi$
$464$	35.7131	1.65794
$465$	0.280678	0.0130161
$466$	−42.8696	−1.98590
$467$	−34.0814	−1.57710	−0.788550	−	0.614971i	$-0.789168\pi$
$467$	−34.0814	−1.57710	−0.788550	+	0.614971i	$0.789168\pi$
$468$	16.5145	0.763382
$469$	15.8775	0.733154
$470$	−0.677179	−0.0312360
$471$	−6.58756	−0.303539
$472$	−45.0327	−2.07280
$473$	6.22218	0.286096
$474$	−31.5055	−1.44710
$475$	16.1077	0.739073
$476$	61.0233	2.79700
$477$	−7.84548	−0.359220
$478$	−27.0067	−1.23526
$479$	23.7116	1.08341	0.541706	−	0.840568i	$-0.317779\pi$
$479$	23.7116	1.08341	0.541706	+	0.840568i	$0.317779\pi$
$480$	−0.129440	−0.00590809
$481$	4.72419	0.215405
$482$	−28.2277	−1.28574
$483$	3.95810	0.180100
$484$	−19.4644	−0.884745
$485$	0.307511	0.0139633
$486$	20.7890	0.943008
$487$	−13.7837	−0.624601	−0.312301	−	0.949983i	$-0.601100\pi$
$487$	−13.7837	−0.624601	−0.312301	+	0.949983i	$0.601100\pi$
$488$	−4.16386	−0.188489
$489$	14.6093	0.660655
$490$	0.00811711	0.000366694 0
$491$	32.5513	1.46902	0.734509	−	0.678599i	$-0.237413\pi$
$491$	32.5513	1.46902	0.734509	+	0.678599i	$0.237413\pi$
$492$	−35.8787	−1.61754
$493$	32.1848	1.44953
$494$	−37.7488	−1.69840
$495$	−0.0564115	−0.00253551
$496$	41.6393	1.86966
$497$	−14.6994	−0.659357
$498$	41.7276	1.86986
$499$	39.1068	1.75066	0.875330	−	0.483527i	$-0.160644\pi$
$499$	39.1068	1.75066	0.875330	+	0.483527i	$0.160644\pi$
$500$	1.15915	0.0518387
$501$	32.2658	1.44153
$502$	−40.1926	−1.79389
$503$	−19.1271	−0.852836	−0.426418	−	0.904526i	$-0.640225\pi$
$503$	−19.1271	−0.852836	−0.426418	+	0.904526i	$0.640225\pi$
$504$	12.6810	0.564859
$505$	−0.0652934	−0.00290552
$506$	−6.42121	−0.285458
$507$	−12.9597	−0.575561
$508$	19.3569	0.858826
$509$	14.0852	0.624314	0.312157	−	0.950030i	$-0.398948\pi$
$509$	14.0852	0.624314	0.312157	+	0.950030i	$0.398948\pi$
$510$	−0.530745	−0.0235018
$511$	−27.7604	−1.22805
$512$	48.9635	2.16390
$513$	−18.1742	−0.802411
$514$	64.5263	2.84613
$515$	−0.348629	−0.0153624
$516$	15.5206	0.683255
$517$	25.4709	1.12021
$518$	6.78003	0.297897
$519$	16.3619	0.718209
$520$	−0.726662	−0.0318662
$521$	−16.8238	−0.737062	−0.368531	−	0.929615i	$-0.620139\pi$
$521$	−16.8238	−0.737062	−0.368531	+	0.929615i	$0.620139\pi$
$522$	12.5004	0.547128
$523$	17.4809	0.764386	0.382193	−	0.924083i	$-0.375169\pi$
$523$	17.4809	0.764386	0.382193	+	0.924083i	$0.375169\pi$
$524$	14.8831	0.650173
$525$	19.6840	0.859082
$526$	49.2987	2.14953
$527$	37.5255	1.63463
$528$	22.1515	0.964021
$529$	−21.9894	−0.956063
$530$	0.645210	0.0280261
$531$	−6.41213	−0.278263
$532$	−36.9812	−1.60334
$533$	−26.3821	−1.14274
$534$	−1.03121	−0.0446249
$535$	0.401055	0.0173391
$536$	−34.3766	−1.48484
$537$	−8.46895	−0.365462
$538$	28.6012	1.23309
$539$	−0.305311	−0.0131507
$540$	−0.653881	−0.0281385
$541$	−32.6820	−1.40511	−0.702555	−	0.711630i	$-0.747957\pi$
$541$	−32.6820	−1.40511	−0.702555	+	0.711630i	$0.747957\pi$
$542$	75.4102	3.23915
$543$	30.7019	1.31755
$544$	−17.3055	−0.741969
$545$	−0.0703460	−0.00301329
$546$	−46.1300	−1.97418
$547$	−19.7584	−0.844808	−0.422404	−	0.906408i	$-0.638814\pi$
$547$	−19.7584	−0.844808	−0.422404	+	0.906408i	$0.638814\pi$
$548$	77.9845	3.33133
$549$	−0.592885	−0.0253037
$550$	−31.9333	−1.36164
$551$	−19.5046	−0.830923
$552$	−8.56976	−0.364753
$553$	−22.6954	−0.965108
$554$	−52.5954	−2.23457
$555$	−0.0402528	−0.00170864
$556$	77.9708	3.30670
$557$	24.9745	1.05820	0.529102	−	0.848558i	$-0.322529\pi$
$557$	24.9745	1.05820	0.529102	+	0.848558i	$0.322529\pi$
$558$	14.5747	0.616996
$559$	11.4125	0.482698
$560$	−0.424242	−0.0179275
$561$	19.9630	0.842840
$562$	−31.6096	−1.33337
$563$	12.9818	0.547117	0.273558	−	0.961855i	$-0.411799\pi$
$563$	12.9818	0.547117	0.273558	+	0.961855i	$0.411799\pi$
$564$	63.5346	2.67529
$565$	0.172236	0.00724604
$566$	73.0206	3.06928
$567$	−15.6243	−0.656161
$568$	31.8259	1.33538
$569$	3.32206	0.139268	0.0696340	−	0.997573i	$-0.477817\pi$
$569$	3.32206	0.139268	0.0696340	+	0.997573i	$0.477817\pi$
$570$	0.321641	0.0134721
$571$	−11.9313	−0.499311	−0.249655	−	0.968335i	$-0.580317\pi$
$571$	−11.9313	−0.499311	−0.249655	+	0.968335i	$0.580317\pi$
$572$	51.0843	2.13594
$573$	−28.7350	−1.20042
$574$	−37.8629	−1.58037
$575$	5.02559	0.209581
$576$	2.98468	0.124362
$577$	−27.7745	−1.15627	−0.578134	−	0.815942i	$-0.696219\pi$
$577$	−27.7745	−1.15627	−0.578134	+	0.815942i	$0.696219\pi$
$578$	−28.2838	−1.17645
$579$	29.1482	1.21136
$580$	−0.701746	−0.0291384
$581$	30.0590	1.24706
$582$	−42.2661	−1.75199
$583$	−24.2684	−1.00510
$584$	60.1046	2.48715
$585$	−0.103468	−0.00427788
$586$	44.8377	1.85223
$587$	−15.0417	−0.620839	−0.310419	−	0.950600i	$-0.600469\pi$
$587$	−15.0417	−0.620839	−0.310419	+	0.950600i	$0.600469\pi$
$588$	−0.761567	−0.0314065
$589$	−22.7411	−0.937032
$590$	0.527331	0.0217099
$591$	−34.0865	−1.40213
$592$	−5.97160	−0.245431
$593$	−32.8038	−1.34709	−0.673545	−	0.739146i	$-0.735229\pi$
$593$	−32.8038	−1.34709	−0.673545	+	0.739146i	$0.735229\pi$
$594$	36.0301	1.47833
$595$	−0.382329	−0.0156740
$596$	−30.3075	−1.24144
$597$	23.4132	0.958237
$598$	−11.7776	−0.481621
$599$	−22.2344	−0.908472	−0.454236	−	0.890881i	$-0.650088\pi$
$599$	−22.2344	−0.908472	−0.454236	+	0.890881i	$0.650088\pi$
$600$	−42.6183	−1.73988
$601$	−48.2179	−1.96685	−0.983426	−	0.181312i	$-0.941965\pi$
$601$	−48.2179	−1.96685	−0.983426	+	0.181312i	$0.941965\pi$
$602$	16.3789	0.667555
$603$	−4.89482	−0.199333
$604$	35.8516	1.45878
$605$	0.121950	0.00495798
$606$	8.97432	0.364557
$607$	0.840739	0.0341246	0.0170623	−	0.999854i	$-0.494569\pi$
$607$	0.840739	0.0341246	0.0170623	+	0.999854i	$0.494569\pi$
$608$	10.4875	0.425323
$609$	−23.8351	−0.965847
$610$	0.0487587	0.00197418
$611$	46.7179	1.89000
$612$	−18.8127	−0.760458
$613$	−16.5518	−0.668521	−0.334260	−	0.942481i	$-0.608486\pi$
$613$	−16.5518	−0.668521	−0.334260	+	0.942481i	$0.608486\pi$
$614$	9.20546	0.371502
$615$	0.224791	0.00906444
$616$	39.2263	1.58047
$617$	2.49491	0.100441	0.0502207	−	0.998738i	$-0.484008\pi$
$617$	2.49491	0.100441	0.0502207	+	0.998738i	$0.484008\pi$
$618$	47.9177	1.92753
$619$	35.0504	1.40879	0.704397	−	0.709806i	$-0.251218\pi$
$619$	35.0504	1.40879	0.704397	+	0.709806i	$0.251218\pi$
$620$	−0.818191	−0.0328594
$621$	−5.67032	−0.227542
$622$	8.48340	0.340153
$623$	−0.742847	−0.0297615
$624$	40.6296	1.62648
$625$	24.9891	0.999564
$626$	−22.3908	−0.894915
$627$	−12.0980	−0.483146
$628$	19.2031	0.766286
$629$	−5.38163	−0.214579
$630$	−0.148495	−0.00591616
$631$	7.14118	0.284286	0.142143	−	0.989846i	$-0.454601\pi$
$631$	7.14118	0.284286	0.142143	+	0.989846i	$0.454601\pi$
$632$	49.1383	1.95462
$633$	2.83737	0.112775
$634$	29.8310	1.18474
$635$	−0.121277	−0.00481273
$636$	−60.5351	−2.40037
$637$	−0.559991	−0.0221877
$638$	38.6676	1.53086
$639$	4.53163	0.179268
$640$	−0.420900	−0.0166375
$641$	−39.3954	−1.55603	−0.778013	−	0.628248i	$-0.783772\pi$
$641$	−39.3954	−1.55603	−0.778013	+	0.628248i	$0.783772\pi$
$642$	−55.1234	−2.17555
$643$	5.01172	0.197643	0.0988215	−	0.995105i	$-0.468493\pi$
$643$	5.01172	0.197643	0.0988215	+	0.995105i	$0.468493\pi$
$644$	−11.5381	−0.454664
$645$	−0.0972410	−0.00382886
$646$	43.0020	1.69189
$647$	42.4392	1.66846	0.834229	−	0.551419i	$-0.185913\pi$
$647$	42.4392	1.66846	0.834229	+	0.551419i	$0.185913\pi$
$648$	33.8285	1.32891
$649$	−19.8347	−0.778578
$650$	−58.5710	−2.29734
$651$	−27.7902	−1.08918
$652$	−42.5869	−1.66783
$653$	−27.9842	−1.09511	−0.547553	−	0.836771i	$-0.684440\pi$
$653$	−27.9842	−1.09511	−0.547553	+	0.836771i	$0.684440\pi$
$654$	9.66877	0.378079
$655$	−0.0932472	−0.00364347
$656$	33.3482	1.30203
$657$	8.55818	0.333887
$658$	67.0482	2.61381
$659$	9.25126	0.360378	0.180189	−	0.983632i	$-0.442329\pi$
$659$	9.25126	0.360378	0.180189	+	0.983632i	$0.442329\pi$
$660$	−0.435267	−0.0169427
$661$	−8.03659	−0.312587	−0.156294	−	0.987711i	$-0.549955\pi$
$661$	−8.03659	−0.312587	−0.156294	+	0.987711i	$0.549955\pi$
$662$	40.7484	1.58373
$663$	36.6155	1.42203
$664$	−65.0813	−2.52565
$665$	0.231698	0.00898488
$666$	−2.09019	−0.0809934
$667$	−6.08540	−0.235628
$668$	−94.0567	−3.63916
$669$	13.4654	0.520603
$670$	0.402549	0.0155518
$671$	−1.83397	−0.0707997
$672$	12.8160	0.494386
$673$	4.19885	0.161854	0.0809269	−	0.996720i	$-0.474212\pi$
$673$	4.19885	0.161854	0.0809269	+	0.996720i	$0.474212\pi$
$674$	−62.8501	−2.42089
$675$	−28.1991	−1.08538
$676$	37.7783	1.45301
$677$	−34.2807	−1.31751	−0.658757	−	0.752356i	$-0.728918\pi$
$677$	−34.2807	−1.31751	−0.658757	+	0.752356i	$0.728918\pi$
$678$	−23.6732	−0.909163
$679$	−30.4470	−1.16845
$680$	0.827787	0.0317442
$681$	9.30942	0.356738
$682$	45.0839	1.72635
$683$	11.7185	0.448396	0.224198	−	0.974544i	$-0.428024\pi$
$683$	11.7185	0.448396	0.224198	+	0.974544i	$0.428024\pi$
$684$	11.4008	0.435922
$685$	−0.488596	−0.0186683
$686$	46.0839	1.75949
$687$	−25.8951	−0.987960
$688$	−14.4259	−0.549984
$689$	−44.5123	−1.69579
$690$	0.100351	0.00382032
$691$	33.0781	1.25835	0.629176	−	0.777263i	$-0.283393\pi$
$691$	33.0781	1.25835	0.629176	+	0.777263i	$0.283393\pi$
$692$	−47.6959	−1.81312
$693$	5.58536	0.212170
$694$	37.2304	1.41325
$695$	−0.488510	−0.0185302
$696$	51.6058	1.95611
$697$	30.0536	1.13836
$698$	−53.8261	−2.03735
$699$	−25.1998	−0.953145
$700$	−57.3800	−2.16876
$701$	−7.92623	−0.299369	−0.149685	−	0.988734i	$-0.547826\pi$
$701$	−7.92623	−0.299369	−0.149685	+	0.988734i	$0.547826\pi$
$702$	66.0852	2.49422
$703$	3.26136	0.123005
$704$	9.23253	0.347964
$705$	−0.398063	−0.0149919
$706$	65.1147	2.45063
$707$	6.46477	0.243133
$708$	−49.4755	−1.85940
$709$	−20.3863	−0.765623	−0.382812	−	0.923826i	$-0.625044\pi$
$709$	−20.3863	−0.765623	−0.382812	+	0.923826i	$0.625044\pi$
$710$	−0.372679	−0.0139864
$711$	6.99671	0.262397
$712$	1.60835	0.0602755
$713$	−7.09519	−0.265717
$714$	52.5496	1.96662
$715$	−0.320058	−0.0119695
$716$	24.6874	0.922613
$717$	−15.8752	−0.592870
$718$	−80.2180	−2.99371
$719$	11.8222	0.440894	0.220447	−	0.975399i	$-0.429248\pi$
$719$	11.8222	0.440894	0.220447	+	0.975399i	$0.429248\pi$
$720$	0.130788	0.00487420
$721$	34.5182	1.28552
$722$	21.6351	0.805174
$723$	−16.5930	−0.617099
$724$	−89.4977	−3.32616
$725$	−30.2633	−1.12395
$726$	−16.7616	−0.622080
$727$	−9.11018	−0.337878	−0.168939	−	0.985627i	$-0.554034\pi$
$727$	−9.11018	−0.337878	−0.168939	+	0.985627i	$0.554034\pi$
$728$	71.9476	2.66655
$729$	29.7867	1.10321
$730$	−0.703822	−0.0260496
$731$	−13.0007	−0.480849
$732$	−4.57465	−0.169084
$733$	9.26626	0.342257	0.171128	−	0.985249i	$-0.445259\pi$
$733$	9.26626	0.342257	0.171128	+	0.985249i	$0.445259\pi$
$734$	46.4639	1.71502
$735$	0.00477144	0.000175997 0
$736$	3.27208	0.120610
$737$	−15.1412	−0.557732
$738$	11.6726	0.429676
$739$	−3.00749	−0.110632	−0.0553161	−	0.998469i	$-0.517617\pi$
$739$	−3.00749	−0.110632	−0.0553161	+	0.998469i	$0.517617\pi$
$740$	0.117339	0.00431347
$741$	−22.1897	−0.815158
$742$	−63.8829	−2.34521
$743$	−18.2252	−0.668618	−0.334309	−	0.942464i	$-0.608503\pi$
$743$	−18.2252	−0.668618	−0.334309	+	0.942464i	$0.608503\pi$
$744$	60.1691	2.20591
$745$	0.189885	0.00695686
$746$	43.9907	1.61061
$747$	−9.26681	−0.339055
$748$	−58.1933	−2.12776
$749$	−39.7089	−1.45093
$750$	0.998188	0.0364487
$751$	−40.8227	−1.48964	−0.744820	−	0.667265i	$-0.767465\pi$
$751$	−40.8227	−1.48964	−0.744820	+	0.667265i	$0.767465\pi$
$752$	−59.0536	−2.15346
$753$	−23.6262	−0.860988
$754$	70.9227	2.58285
$755$	−0.224621	−0.00817479
$756$	64.7414	2.35462
$757$	−35.1246	−1.27662	−0.638312	−	0.769778i	$-0.720367\pi$
$757$	−35.1246	−1.27662	−0.638312	+	0.769778i	$0.720367\pi$
$758$	−3.59222	−0.130475
$759$	−3.77455	−0.137007
$760$	−0.501654	−0.0181969
$761$	−32.9129	−1.19309	−0.596545	−	0.802579i	$-0.703460\pi$
$761$	−32.9129	−1.19309	−0.596545	+	0.802579i	$0.703460\pi$
$762$	16.6690	0.603855
$763$	6.96502	0.252151
$764$	83.7640	3.03048
$765$	0.117867	0.00426149
$766$	43.2594	1.56303
$767$	−36.3800	−1.31361
$768$	47.1432	1.70113
$769$	6.93883	0.250221	0.125110	−	0.992143i	$-0.460072\pi$
$769$	6.93883	0.250221	0.125110	+	0.992143i	$0.460072\pi$
$770$	−0.459339	−0.0165534
$771$	37.9301	1.36602
$772$	−84.9686	−3.05809
$773$	−30.2446	−1.08782	−0.543911	−	0.839143i	$-0.683057\pi$
$773$	−30.2446	−1.08782	−0.543911	+	0.839143i	$0.683057\pi$
$774$	−5.04941	−0.181497
$775$	−35.2851	−1.26748
$776$	65.9212	2.36643
$777$	3.98547	0.142978
$778$	−44.6946	−1.60238
$779$	−18.2130	−0.652549
$780$	−0.798352	−0.0285856
$781$	14.0177	0.501593
$782$	13.4166	0.479776
$783$	34.1458	1.22027
$784$	0.707854	0.0252805
$785$	−0.120313	−0.00429415
$786$	12.8165	0.457148
$787$	24.3925	0.869498	0.434749	−	0.900552i	$-0.356837\pi$
$787$	24.3925	0.869498	0.434749	+	0.900552i	$0.356837\pi$
$788$	99.3638	3.53969
$789$	28.9790	1.03168
$790$	−0.575407	−0.0204721
$791$	−17.0533	−0.606345
$792$	−12.0930	−0.429705
$793$	−3.36381	−0.119452
$794$	16.1024	0.571454
$795$	0.379270	0.0134513
$796$	−68.2506	−2.41908
$797$	−31.9350	−1.13120	−0.565599	−	0.824681i	$-0.691355\pi$
$797$	−31.9350	−1.13120	−0.565599	+	0.824681i	$0.691355\pi$
$798$	−31.8460	−1.12734
$799$	−53.2193	−1.88276
$800$	16.2724	0.575315
$801$	0.229010	0.00809167
$802$	51.3158	1.81202
$803$	26.4731	0.934214
$804$	−37.7681	−1.33198
$805$	0.0722895	0.00254787
$806$	82.6914	2.91268
$807$	16.8125	0.591828
$808$	−13.9970	−0.492412
$809$	−13.0809	−0.459901	−0.229950	−	0.973202i	$-0.573856\pi$
$809$	−13.0809	−0.459901	−0.229950	+	0.973202i	$0.573856\pi$
$810$	−0.396131	−0.0139186
$811$	41.8983	1.47125	0.735624	−	0.677391i	$-0.236889\pi$
$811$	41.8983	1.47125	0.735624	+	0.677391i	$0.236889\pi$
$812$	69.4806	2.43829
$813$	44.3280	1.55465
$814$	−6.46561	−0.226619
$815$	0.266819	0.00934628
$816$	−46.2837	−1.62025
$817$	7.87867	0.275640
$818$	−89.7776	−3.13900
$819$	10.2445	0.357971
$820$	−0.655277	−0.0228833
$821$	−8.81603	−0.307682	−0.153841	−	0.988096i	$-0.549164\pi$
$821$	−8.81603	−0.307682	−0.153841	+	0.988096i	$0.549164\pi$
$822$	67.1555	2.34232
$823$	32.1300	1.11998	0.559990	−	0.828499i	$-0.310805\pi$
$823$	32.1300	1.11998	0.559990	+	0.828499i	$0.310805\pi$
$824$	−74.7358	−2.60355
$825$	−18.7712	−0.653529
$826$	−52.2116	−1.81667
$827$	−16.5459	−0.575356	−0.287678	−	0.957727i	$-0.592883\pi$
$827$	−16.5459	−0.575356	−0.287678	+	0.957727i	$0.592883\pi$
$828$	3.55704	0.123616
$829$	−27.5184	−0.955752	−0.477876	−	0.878427i	$-0.658593\pi$
$829$	−27.5184	−0.955752	−0.477876	+	0.878427i	$0.658593\pi$
$830$	0.762099	0.0264529
$831$	−30.9169	−1.07250
$832$	16.9340	0.587081
$833$	0.637921	0.0221027
$834$	67.1438	2.32500
$835$	0.589293	0.0203933
$836$	35.2662	1.21971
$837$	39.8119	1.37610
$838$	34.8536	1.20400
$839$	−17.1000	−0.590359	−0.295179	−	0.955442i	$-0.595379\pi$
$839$	−17.1000	−0.590359	−0.295179	+	0.955442i	$0.595379\pi$
$840$	−0.613034	−0.0211517
$841$	7.64534	0.263633
$842$	−22.5897	−0.778492
$843$	−18.5809	−0.639959
$844$	−8.27108	−0.284702
$845$	−0.236692	−0.00814245
$846$	−20.6701	−0.710653
$847$	−12.0744	−0.414881
$848$	56.2656	1.93217
$849$	42.9233	1.47312
$850$	66.7219	2.28854
$851$	1.01754	0.0348808
$852$	34.9657	1.19790
$853$	−24.9815	−0.855351	−0.427676	−	0.903932i	$-0.640667\pi$
$853$	−24.9815	−0.855351	−0.427676	+	0.903932i	$0.640667\pi$
$854$	−4.82764	−0.165199
$855$	−0.0714296	−0.00244284
$856$	85.9743	2.93854
$857$	6.32454	0.216042	0.108021	−	0.994149i	$-0.465549\pi$
$857$	6.32454	0.216042	0.108021	+	0.994149i	$0.465549\pi$
$858$	43.9907	1.50182
$859$	44.6477	1.52336	0.761680	−	0.647954i	$-0.224375\pi$
$859$	44.6477	1.52336	0.761680	+	0.647954i	$0.224375\pi$
$860$	0.283463	0.00966600
$861$	−22.2568	−0.758508
$862$	40.1497	1.36751
$863$	33.8143	1.15105	0.575526	−	0.817783i	$-0.304797\pi$
$863$	33.8143	1.15105	0.575526	+	0.817783i	$0.304797\pi$
$864$	−18.3600	−0.624619
$865$	0.298829	0.0101605
$866$	20.0399	0.680983
$867$	−16.6259	−0.564645
$868$	81.0100	2.74966
$869$	21.6429	0.734186
$870$	−0.604301	−0.0204877
$871$	−27.7714	−0.940999
$872$	−15.0801	−0.510676
$873$	9.38640	0.317682
$874$	−8.13069	−0.275025
$875$	0.719058	0.0243086
$876$	66.0342	2.23109
$877$	−14.6392	−0.494330	−0.247165	−	0.968973i	$-0.579499\pi$
$877$	−14.6392	−0.494330	−0.247165	+	0.968973i	$0.579499\pi$
$878$	16.6403	0.561583
$879$	26.3567	0.888989
$880$	0.404568	0.0136380
$881$	10.1670	0.342535	0.171268	−	0.985225i	$-0.445214\pi$
$881$	10.1670	0.342535	0.171268	+	0.985225i	$0.445214\pi$
$882$	0.247765	0.00834269
$883$	28.5414	0.960493	0.480247	−	0.877134i	$-0.340547\pi$
$883$	28.5414	0.960493	0.480247	+	0.877134i	$0.340547\pi$
$884$	−106.736	−3.58993
$885$	0.309978	0.0104198
$886$	−3.25943	−0.109503
$887$	−7.43313	−0.249580	−0.124790	−	0.992183i	$-0.539826\pi$
$887$	−7.43313	−0.249580	−0.124790	+	0.992183i	$0.539826\pi$
$888$	−8.62901	−0.289570
$889$	12.0078	0.402727
$890$	−0.0188337	−0.000631307 0
$891$	14.8998	0.499161
$892$	−39.2524	−1.31427
$893$	32.2519	1.07927
$894$	−26.0990	−0.872880
$895$	−0.154674	−0.00517019
$896$	41.6737	1.39222
$897$	−6.92315	−0.231157
$898$	77.6485	2.59116
$899$	42.7262	1.42500
$900$	17.6895	0.589651
$901$	50.7068	1.68929
$902$	36.1070	1.20223
$903$	9.62793	0.320398
$904$	36.9224	1.22802
$905$	0.560730	0.0186393
$906$	30.8732	1.02569
$907$	36.2192	1.20264	0.601320	−	0.799008i	$-0.294642\pi$
$907$	36.2192	1.20264	0.601320	+	0.799008i	$0.294642\pi$
$908$	−27.1375	−0.900588
$909$	−1.99300	−0.0661038
$910$	−0.842503	−0.0279287
$911$	38.2935	1.26872	0.634360	−	0.773038i	$-0.281264\pi$
$911$	38.2935	1.26872	0.634360	+	0.773038i	$0.281264\pi$
$912$	28.0488	0.928787
$913$	−28.6651	−0.948675
$914$	51.8632	1.71548
$915$	0.0286615	0.000947521 0
$916$	75.4856	2.49411
$917$	9.23250	0.304884
$918$	−75.2818	−2.48467
$919$	−11.2696	−0.371750	−0.185875	−	0.982573i	$-0.559512\pi$
$919$	−11.2696	−0.371750	−0.185875	+	0.982573i	$0.559512\pi$
$920$	−0.156515	−0.00516015
$921$	5.41120	0.178305
$922$	21.7074	0.714894
$923$	25.7108	0.846280
$924$	43.0962	1.41776
$925$	5.06033	0.166383
$926$	30.6948	1.00869
$927$	−10.6415	−0.349513
$928$	−19.7039	−0.646813
$929$	0.394018	0.0129273	0.00646365	−	0.999979i	$-0.497943\pi$
$929$	0.394018	0.0129273	0.00646365	+	0.999979i	$0.497943\pi$
$930$	−0.704577	−0.0231040
$931$	−0.386592	−0.0126700
$932$	73.4588	2.40622
$933$	4.98675	0.163259
$934$	85.5535	2.79940
$935$	0.364598	0.0119236
$936$	−22.1805	−0.724992
$937$	−50.0343	−1.63455	−0.817274	−	0.576249i	$-0.804516\pi$
$937$	−50.0343	−1.63455	−0.817274	+	0.576249i	$0.804516\pi$
$938$	−39.8568	−1.30137
$939$	−13.1618	−0.429521
$940$	1.16037	0.0378472
$941$	20.1417	0.656601	0.328301	−	0.944573i	$-0.393524\pi$
$941$	20.1417	0.656601	0.328301	+	0.944573i	$0.393524\pi$
$942$	16.5365	0.538790
$943$	−5.68243	−0.185045
$944$	45.9860	1.49672
$945$	−0.405624	−0.0131950
$946$	−15.6193	−0.507829
$947$	−13.6663	−0.444094	−0.222047	−	0.975036i	$-0.571274\pi$
$947$	−13.6663	−0.444094	−0.222047	+	0.975036i	$0.571274\pi$
$948$	53.9860	1.75338
$949$	48.5560	1.57619
$950$	−40.4347	−1.31188
$951$	17.5354	0.568625
$952$	−81.9600	−2.65634
$953$	−29.2291	−0.946824	−0.473412	−	0.880841i	$-0.656978\pi$
$953$	−29.2291	−0.946824	−0.473412	+	0.880841i	$0.656978\pi$
$954$	19.6943	0.637625
$955$	−0.524806	−0.0169823
$956$	46.2770	1.49671
$957$	22.7297	0.734748
$958$	−59.5226	−1.92309
$959$	48.3764	1.56215
$960$	−0.144287	−0.00465685
$961$	18.8160	0.606968
$962$	−11.8590	−0.382349
$963$	12.2417	0.394484
$964$	48.3694	1.55787
$965$	0.532353	0.0171371
$966$	−9.93590	−0.319682
$967$	18.4625	0.593715	0.296858	−	0.954922i	$-0.404061\pi$
$967$	18.4625	0.593715	0.296858	+	0.954922i	$0.404061\pi$
$968$	26.1425	0.840252
$969$	25.2777	0.812036
$970$	−0.771935	−0.0247853
$971$	−2.55091	−0.0818627	−0.0409314	−	0.999162i	$-0.513032\pi$
$971$	−2.55091	−0.0818627	−0.0409314	+	0.999162i	$0.513032\pi$
$972$	−35.6228	−1.14260
$973$	48.3679	1.55060
$974$	34.6009	1.10868
$975$	−34.4295	−1.10263
$976$	4.25201	0.136103
$977$	−24.2975	−0.777345	−0.388672	−	0.921376i	$-0.627066\pi$
$977$	−24.2975	−0.777345	−0.388672	+	0.921376i	$0.627066\pi$
$978$	−36.6733	−1.17268
$979$	0.708397	0.0226405
$980$	−0.0139090	−0.000444307 0
$981$	−2.14723	−0.0685557
$982$	−81.7124	−2.60755
$983$	54.5719	1.74057	0.870287	−	0.492545i	$-0.163933\pi$
$983$	54.5719	1.74057	0.870287	+	0.492545i	$0.163933\pi$
$984$	48.1885	1.53619
$985$	−0.622544	−0.0198359
$986$	−80.7925	−2.57296
$987$	39.4126	1.25452
$988$	64.6841	2.05788
$989$	2.45813	0.0781641
$990$	0.141608	0.00450060
$991$	−3.12892	−0.0993933	−0.0496967	−	0.998764i	$-0.515825\pi$
$991$	−3.12892	−0.0993933	−0.0496967	+	0.998764i	$0.515825\pi$
$992$	−22.9736	−0.729411
$993$	23.9529	0.760122
$994$	36.8994	1.17038
$995$	0.427610	0.0135562
$996$	−71.5020	−2.26563
$997$	−39.2772	−1.24392	−0.621961	−	0.783049i	$-0.713664\pi$
$997$	−39.2772	−1.24392	−0.621961	+	0.783049i	$0.713664\pi$
$998$	−98.1685	−3.10747
$999$	−5.70953	−0.180641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.10	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.10	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51027 q^{2} -1.47560 q^{3} +4.30145 q^{4} -0.0269498 q^{5} +3.70415 q^{6} +2.66833 q^{7} -5.77725 q^{8} -0.822611 q^{9} +O(q^{10})\)	\(q-2.51027 q^{2} -1.47560 q^{3} +4.30145 q^{4} -0.0269498 q^{5} +3.70415 q^{6} +2.66833 q^{7} -5.77725 q^{8} -0.822611 q^{9} +0.0676513 q^{10} -2.54459 q^{11} -6.34720 q^{12} -4.66719 q^{13} -6.69822 q^{14} +0.0397671 q^{15} +5.89954 q^{16} +5.31669 q^{17} +2.06498 q^{18} -3.22201 q^{19} -0.115923 q^{20} -3.93738 q^{21} +6.38759 q^{22} -1.00526 q^{23} +8.52489 q^{24} -4.99927 q^{25} +11.7159 q^{26} +5.64064 q^{27} +11.4777 q^{28} +6.05354 q^{29} -0.0998261 q^{30} +7.05805 q^{31} -3.25494 q^{32} +3.75479 q^{33} -13.3463 q^{34} -0.0719110 q^{35} -3.53842 q^{36} -1.01221 q^{37} +8.08812 q^{38} +6.88690 q^{39} +0.155696 q^{40} +5.65268 q^{41} +9.88388 q^{42} -2.44526 q^{43} -10.9454 q^{44} +0.0221692 q^{45} +2.52348 q^{46} -10.0099 q^{47} -8.70535 q^{48} +0.119985 q^{49} +12.5495 q^{50} -7.84530 q^{51} -20.0757 q^{52} +9.53728 q^{53} -14.1595 q^{54} +0.0685762 q^{55} -15.4156 q^{56} +4.75440 q^{57} -15.1960 q^{58} +7.79484 q^{59} +0.171056 q^{60} +0.720735 q^{61} -17.7176 q^{62} -2.19500 q^{63} -3.62830 q^{64} +0.125780 q^{65} -9.42552 q^{66} +5.95035 q^{67} +22.8695 q^{68} +1.48336 q^{69} +0.180516 q^{70} -5.50883 q^{71} +4.75243 q^{72} -10.4037 q^{73} +2.54093 q^{74} +7.37692 q^{75} -13.8593 q^{76} -6.78980 q^{77} -17.2880 q^{78} -8.50548 q^{79} -0.158992 q^{80} -5.85548 q^{81} -14.1897 q^{82} +11.2651 q^{83} -16.9364 q^{84} -0.143284 q^{85} +6.13826 q^{86} -8.93259 q^{87} +14.7007 q^{88} -0.278394 q^{89} -0.0556507 q^{90} -12.4536 q^{91} -4.32408 q^{92} -10.4148 q^{93} +25.1274 q^{94} +0.0868327 q^{95} +4.80299 q^{96} -11.4105 q^{97} -0.301193 q^{98} +2.09321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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