LMFDB - Embedded newform 4009.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$0$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73978 q^{2} +2.70968 q^{3} +1.02684 q^{4} +3.17028 q^{5} -4.71425 q^{6} +1.26105 q^{7} +1.69309 q^{8} +4.34237 q^{9} +O(q^{10})$	\(q-1.73978 q^{2} +2.70968 q^{3} +1.02684 q^{4} +3.17028 q^{5} -4.71425 q^{6} +1.26105 q^{7} +1.69309 q^{8} +4.34237 q^{9} -5.51560 q^{10} +4.40784 q^{11} +2.78240 q^{12} +0.948807 q^{13} -2.19396 q^{14} +8.59046 q^{15} -4.99928 q^{16} +2.50898 q^{17} -7.55478 q^{18} -1.00000 q^{19} +3.25536 q^{20} +3.41705 q^{21} -7.66868 q^{22} -3.45904 q^{23} +4.58774 q^{24} +5.05070 q^{25} -1.65072 q^{26} +3.63741 q^{27} +1.29490 q^{28} -2.48374 q^{29} -14.9455 q^{30} -0.855306 q^{31} +5.31147 q^{32} +11.9438 q^{33} -4.36507 q^{34} +3.99790 q^{35} +4.45891 q^{36} +6.09070 q^{37} +1.73978 q^{38} +2.57096 q^{39} +5.36758 q^{40} -9.91347 q^{41} -5.94492 q^{42} +7.07662 q^{43} +4.52613 q^{44} +13.7666 q^{45} +6.01797 q^{46} +11.5018 q^{47} -13.5465 q^{48} -5.40974 q^{49} -8.78710 q^{50} +6.79853 q^{51} +0.974269 q^{52} +0.584059 q^{53} -6.32829 q^{54} +13.9741 q^{55} +2.13508 q^{56} -2.70968 q^{57} +4.32115 q^{58} -5.11992 q^{59} +8.82099 q^{60} +1.17804 q^{61} +1.48804 q^{62} +5.47597 q^{63} +0.757772 q^{64} +3.00799 q^{65} -20.7797 q^{66} +1.68431 q^{67} +2.57631 q^{68} -9.37289 q^{69} -6.95546 q^{70} -10.0101 q^{71} +7.35203 q^{72} +11.8757 q^{73} -10.5965 q^{74} +13.6858 q^{75} -1.02684 q^{76} +5.55852 q^{77} -4.47291 q^{78} -15.1952 q^{79} -15.8491 q^{80} -3.17091 q^{81} +17.2473 q^{82} -6.03647 q^{83} +3.50876 q^{84} +7.95417 q^{85} -12.3118 q^{86} -6.73013 q^{87} +7.46288 q^{88} +2.68077 q^{89} -23.9508 q^{90} +1.19650 q^{91} -3.55187 q^{92} -2.31761 q^{93} -20.0106 q^{94} -3.17028 q^{95} +14.3924 q^{96} +4.41596 q^{97} +9.41177 q^{98} +19.1405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + 11 q^{2} + 95 q^{4} + 15 q^{5} + 23 q^{6} + 19 q^{7} + 30 q^{8} + 101 q^{9}+O(q^{10}) $ 83 * q + 11 * q^2 + 95 * q^4 + 15 * q^5 + 23 * q^6 + 19 * q^7 + 30 * q^8 + 101 * q^9	\( 83 q + 11 q^{2} + 95 q^{4} + 15 q^{5} + 23 q^{6} + 19 q^{7} + 30 q^{8} + 101 q^{9} + 9 q^{10} + 56 q^{11} - 2 q^{12} - 5 q^{13} + 6 q^{14} + 19 q^{15} + 123 q^{16} + 19 q^{17} + 40 q^{18} - 83 q^{19} + 49 q^{20} + 9 q^{21} + 18 q^{22} + 74 q^{23} + 38 q^{24} + 98 q^{25} + 28 q^{26} + 6 q^{27} + 50 q^{28} + 16 q^{29} + 56 q^{30} + 24 q^{31} + 81 q^{32} + 13 q^{33} + 9 q^{34} + 71 q^{35} + 156 q^{36} - 6 q^{37} - 11 q^{38} + 126 q^{39} + q^{40} - q^{42} + 34 q^{43} + 140 q^{44} + 42 q^{45} + 34 q^{46} + 53 q^{47} + 16 q^{48} + 118 q^{49} + 51 q^{50} + 57 q^{51} + 32 q^{52} + q^{53} + 53 q^{54} + 60 q^{55} - 2 q^{56} - 2 q^{58} + 44 q^{59} - 9 q^{60} + 21 q^{61} + 28 q^{62} + 83 q^{63} + 154 q^{64} + 44 q^{65} + 17 q^{66} + 5 q^{67} + 63 q^{68} - 36 q^{69} - 48 q^{70} + 193 q^{71} + 135 q^{72} + 54 q^{73} + 127 q^{74} + 5 q^{75} - 95 q^{76} + 54 q^{77} + 45 q^{78} + 54 q^{79} + 45 q^{80} + 147 q^{81} - 35 q^{82} + 84 q^{83} + 12 q^{84} + 28 q^{85} + 60 q^{86} + 51 q^{87} + 23 q^{88} - 24 q^{89} + 31 q^{90} + 28 q^{91} + 108 q^{92} + 39 q^{93} - 49 q^{94} - 15 q^{95} + 25 q^{96} - 22 q^{97} - 67 q^{98} + 132 q^{99}+O(q^{100}) \) 83 * q + 11 * q^2 + 95 * q^4 + 15 * q^5 + 23 * q^6 + 19 * q^7 + 30 * q^8 + 101 * q^9 + 9 * q^10 + 56 * q^11 - 2 * q^12 - 5 * q^13 + 6 * q^14 + 19 * q^15 + 123 * q^16 + 19 * q^17 + 40 * q^18 - 83 * q^19 + 49 * q^20 + 9 * q^21 + 18 * q^22 + 74 * q^23 + 38 * q^24 + 98 * q^25 + 28 * q^26 + 6 * q^27 + 50 * q^28 + 16 * q^29 + 56 * q^30 + 24 * q^31 + 81 * q^32 + 13 * q^33 + 9 * q^34 + 71 * q^35 + 156 * q^36 - 6 * q^37 - 11 * q^38 + 126 * q^39 + q^40 - q^42 + 34 * q^43 + 140 * q^44 + 42 * q^45 + 34 * q^46 + 53 * q^47 + 16 * q^48 + 118 * q^49 + 51 * q^50 + 57 * q^51 + 32 * q^52 + q^53 + 53 * q^54 + 60 * q^55 - 2 * q^56 - 2 * q^58 + 44 * q^59 - 9 * q^60 + 21 * q^61 + 28 * q^62 + 83 * q^63 + 154 * q^64 + 44 * q^65 + 17 * q^66 + 5 * q^67 + 63 * q^68 - 36 * q^69 - 48 * q^70 + 193 * q^71 + 135 * q^72 + 54 * q^73 + 127 * q^74 + 5 * q^75 - 95 * q^76 + 54 * q^77 + 45 * q^78 + 54 * q^79 + 45 * q^80 + 147 * q^81 - 35 * q^82 + 84 * q^83 + 12 * q^84 + 28 * q^85 + 60 * q^86 + 51 * q^87 + 23 * q^88 - 24 * q^89 + 31 * q^90 + 28 * q^91 + 108 * q^92 + 39 * q^93 - 49 * q^94 - 15 * q^95 + 25 * q^96 - 22 * q^97 - 67 * q^98 + 132 * 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 $

$2$	−1.73978	−1.23021	−0.615105	−	0.788445i	$-0.710887\pi$
$2$	−1.73978	−1.23021	−0.615105	+	0.788445i	$0.710887\pi$
$3$	2.70968	1.56444	0.782218	−	0.623005i	$-0.214088\pi$
$3$	2.70968	1.56444	0.782218	+	0.623005i	$0.214088\pi$
$4$	1.02684	0.513418
$5$	3.17028	1.41779	0.708897	−	0.705312i	$-0.249193\pi$
$5$	3.17028	1.41779	0.708897	+	0.705312i	$0.249193\pi$
$6$	−4.71425	−1.92458
$7$	1.26105	0.476633	0.238317	−	0.971187i	$-0.423404\pi$
$7$	1.26105	0.476633	0.238317	+	0.971187i	$0.423404\pi$
$8$	1.69309	0.598598
$9$	4.34237	1.44746
$10$	−5.51560	−1.74418
$11$	4.40784	1.32901	0.664507	−	0.747282i	$-0.268642\pi$
$11$	4.40784	1.32901	0.664507	+	0.747282i	$0.268642\pi$
$12$	2.78240	0.803210
$13$	0.948807	0.263152	0.131576	−	0.991306i	$-0.457996\pi$
$13$	0.948807	0.263152	0.131576	+	0.991306i	$0.457996\pi$
$14$	−2.19396	−0.586360
$15$	8.59046	2.21805
$16$	−4.99928	−1.24982
$17$	2.50898	0.608517	0.304258	−	0.952590i	$-0.401591\pi$
$17$	2.50898	0.608517	0.304258	+	0.952590i	$0.401591\pi$
$18$	−7.55478	−1.78068
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.25536	0.727921
$21$	3.41705	0.745662
$22$	−7.66868	−1.63497
$23$	−3.45904	−0.721259	−0.360630	−	0.932709i	$-0.617438\pi$
$23$	−3.45904	−0.721259	−0.360630	+	0.932709i	$0.617438\pi$
$24$	4.58774	0.936468
$25$	5.05070	1.01014
$26$	−1.65072	−0.323732
$27$	3.63741	0.700019
$28$	1.29490	0.244712
$29$	−2.48374	−0.461218	−0.230609	−	0.973046i	$-0.574072\pi$
$29$	−2.48374	−0.461218	−0.230609	+	0.973046i	$0.574072\pi$
$30$	−14.9455	−2.72866
$31$	−0.855306	−0.153617	−0.0768087	−	0.997046i	$-0.524473\pi$
$31$	−0.855306	−0.153617	−0.0768087	+	0.997046i	$0.524473\pi$
$32$	5.31147	0.938944
$33$	11.9438	2.07916
$34$	−4.36507	−0.748604
$35$	3.99790	0.675768
$36$	4.45891	0.743151
$37$	6.09070	1.00131	0.500653	−	0.865648i	$-0.333093\pi$
$37$	6.09070	1.00131	0.500653	+	0.865648i	$0.333093\pi$
$38$	1.73978	0.282230
$39$	2.57096	0.411684
$40$	5.36758	0.848689
$41$	−9.91347	−1.54822	−0.774112	−	0.633049i	$-0.781803\pi$
$41$	−9.91347	−1.54822	−0.774112	+	0.633049i	$0.781803\pi$
$42$	−5.94492	−0.917322
$43$	7.07662	1.07917	0.539587	−	0.841930i	$-0.318580\pi$
$43$	7.07662	1.07917	0.539587	+	0.841930i	$0.318580\pi$
$44$	4.52613	0.682340
$45$	13.7666	2.05220
$46$	6.01797	0.887301
$47$	11.5018	1.67771	0.838855	−	0.544356i	$-0.183226\pi$
$47$	11.5018	1.67771	0.838855	+	0.544356i	$0.183226\pi$
$48$	−13.5465	−1.95526
$49$	−5.40974	−0.772821
$50$	−8.78710	−1.24268
$51$	6.79853	0.951985
$52$	0.974269	0.135107
$53$	0.584059	0.0802267	0.0401133	−	0.999195i	$-0.487228\pi$
$53$	0.584059	0.0802267	0.0401133	+	0.999195i	$0.487228\pi$
$54$	−6.32829	−0.861171
$55$	13.9741	1.88427
$56$	2.13508	0.285312
$57$	−2.70968	−0.358906
$58$	4.32115	0.567395
$59$	−5.11992	−0.666557	−0.333278	−	0.942828i	$-0.608155\pi$
$59$	−5.11992	−0.666557	−0.333278	+	0.942828i	$0.608155\pi$
$60$	8.82099	1.13879
$61$	1.17804	0.150833	0.0754164	−	0.997152i	$-0.475971\pi$
$61$	1.17804	0.150833	0.0754164	+	0.997152i	$0.475971\pi$
$62$	1.48804	0.188982
$63$	5.47597	0.689907
$64$	0.757772	0.0947215
$65$	3.00799	0.373095
$66$	−20.7797	−2.55780
$67$	1.68431	0.205771	0.102885	−	0.994693i	$-0.467192\pi$
$67$	1.68431	0.205771	0.102885	+	0.994693i	$0.467192\pi$
$68$	2.57631	0.312423
$69$	−9.37289	−1.12836
$70$	−6.95546	−0.831337
$71$	−10.0101	−1.18798	−0.593991	−	0.804471i	$-0.702449\pi$
$71$	−10.0101	−1.18798	−0.593991	+	0.804471i	$0.702449\pi$
$72$	7.35203	0.866446
$73$	11.8757	1.38995	0.694974	−	0.719035i	$-0.255416\pi$
$73$	11.8757	1.38995	0.694974	+	0.719035i	$0.255416\pi$
$74$	−10.5965	−1.23182
$75$	13.6858	1.58030
$76$	−1.02684	−0.117786
$77$	5.55852	0.633453
$78$	−4.47291	−0.506458
$79$	−15.1952	−1.70959	−0.854795	−	0.518966i	$-0.826317\pi$
$79$	−15.1952	−1.70959	−0.854795	+	0.518966i	$0.826317\pi$
$80$	−15.8491	−1.77199
$81$	−3.17091	−0.352324
$82$	17.2473	1.90464
$83$	−6.03647	−0.662589	−0.331294	−	0.943527i	$-0.607485\pi$
$83$	−6.03647	−0.662589	−0.331294	+	0.943527i	$0.607485\pi$
$84$	3.50876	0.382837
$85$	7.95417	0.862751
$86$	−12.3118	−1.32761
$87$	−6.73013	−0.721546
$88$	7.46288	0.795545
$89$	2.68077	0.284161	0.142081	−	0.989855i	$-0.454621\pi$
$89$	2.68077	0.284161	0.142081	+	0.989855i	$0.454621\pi$
$90$	−23.9508	−2.52463
$91$	1.19650	0.125427
$92$	−3.55187	−0.370308
$93$	−2.31761	−0.240325
$94$	−20.0106	−2.06394
$95$	−3.17028	−0.325264
$96$	14.3924	1.46892
$97$	4.41596	0.448373	0.224186	−	0.974546i	$-0.428028\pi$
$97$	4.41596	0.448373	0.224186	+	0.974546i	$0.428028\pi$
$98$	9.41177	0.950732
$99$	19.1405	1.92369
$100$	5.18624	0.518624
$101$	2.20644	0.219549	0.109775	−	0.993957i	$-0.464987\pi$
$101$	2.20644	0.219549	0.109775	+	0.993957i	$0.464987\pi$
$102$	−11.8280	−1.17114
$103$	4.37686	0.431265	0.215632	−	0.976475i	$-0.430819\pi$
$103$	4.37686	0.431265	0.215632	+	0.976475i	$0.430819\pi$
$104$	1.60642	0.157522
$105$	10.8330	1.05720
$106$	−1.01613	−0.0986957
$107$	−0.242329	−0.0234268	−0.0117134	−	0.999931i	$-0.503729\pi$
$107$	−0.242329	−0.0234268	−0.0117134	+	0.999931i	$0.503729\pi$
$108$	3.73502	0.359402
$109$	−8.12888	−0.778605	−0.389303	−	0.921110i	$-0.627284\pi$
$109$	−8.12888	−0.778605	−0.389303	+	0.921110i	$0.627284\pi$
$110$	−24.3119	−2.31805
$111$	16.5039	1.56648
$112$	−6.30436	−0.595706
$113$	−0.309253	−0.0290920	−0.0145460	−	0.999894i	$-0.504630\pi$
$113$	−0.309253	−0.0290920	−0.0145460	+	0.999894i	$0.504630\pi$
$114$	4.71425	0.441530
$115$	−10.9661	−1.02260
$116$	−2.55039	−0.236798
$117$	4.12007	0.380901
$118$	8.90753	0.820005
$119$	3.16396	0.290039
$120$	14.5444	1.32772
$121$	8.42907	0.766279
$122$	−2.04954	−0.185556
$123$	−26.8623	−2.42210
$124$	−0.878259	−0.0788700
$125$	0.160718	0.0143751
$126$	−9.52698	−0.848731
$127$	8.66107	0.768546	0.384273	−	0.923220i	$-0.374452\pi$
$127$	8.66107	0.768546	0.384273	+	0.923220i	$0.374452\pi$
$128$	−11.9413	−1.05547
$129$	19.1754	1.68830
$130$	−5.23323	−0.458985
$131$	−10.8064	−0.944162	−0.472081	−	0.881555i	$-0.656497\pi$
$131$	−10.8064	−0.944162	−0.472081	+	0.881555i	$0.656497\pi$
$132$	12.2644	1.06748
$133$	−1.26105	−0.109347
$134$	−2.93033	−0.253142
$135$	11.5316	0.992482
$136$	4.24793	0.364257
$137$	−14.7031	−1.25617	−0.628084	−	0.778146i	$-0.716161\pi$
$137$	−14.7031	−1.25617	−0.628084	+	0.778146i	$0.716161\pi$
$138$	16.3068	1.38812
$139$	20.4514	1.73467	0.867334	−	0.497727i	$-0.165832\pi$
$139$	20.4514	1.73467	0.867334	+	0.497727i	$0.165832\pi$
$140$	4.10519	0.346952
$141$	31.1662	2.62467
$142$	17.4154	1.46147
$143$	4.18219	0.349732
$144$	−21.7087	−1.80906
$145$	−7.87414	−0.653912
$146$	−20.6612	−1.70993
$147$	−14.6587	−1.20903
$148$	6.25415	0.514088
$149$	3.70254	0.303324	0.151662	−	0.988432i	$-0.451538\pi$
$149$	3.70254	0.303324	0.151662	+	0.988432i	$0.451538\pi$
$150$	−23.8102	−1.94410
$151$	−13.3469	−1.08616	−0.543078	−	0.839682i	$-0.682741\pi$
$151$	−13.3469	−1.08616	−0.543078	+	0.839682i	$0.682741\pi$
$152$	−1.69309	−0.137328
$153$	10.8949	0.880802
$154$	−9.67061	−0.779280
$155$	−2.71156	−0.217798
$156$	2.63996	0.211366
$157$	−23.8100	−1.90024	−0.950121	−	0.311882i	$-0.899040\pi$
$157$	−23.8100	−1.90024	−0.950121	+	0.311882i	$0.899040\pi$
$158$	26.4363	2.10316
$159$	1.58261	0.125509
$160$	16.8389	1.33123
$161$	−4.36203	−0.343776
$162$	5.51669	0.433432
$163$	−10.4033	−0.814852	−0.407426	−	0.913238i	$-0.633574\pi$
$163$	−10.4033	−0.814852	−0.407426	+	0.913238i	$0.633574\pi$
$164$	−10.1795	−0.794886
$165$	37.8654	2.94782
$166$	10.5021	0.815124
$167$	6.12543	0.474000	0.237000	−	0.971510i	$-0.423836\pi$
$167$	6.12543	0.474000	0.237000	+	0.971510i	$0.423836\pi$
$168$	5.78538	0.446352
$169$	−12.0998	−0.930751
$170$	−13.8385	−1.06137
$171$	−4.34237	−0.332070
$172$	7.26653	0.554068
$173$	17.9294	1.36315	0.681574	−	0.731749i	$-0.261296\pi$
$173$	17.9294	1.36315	0.681574	+	0.731749i	$0.261296\pi$
$174$	11.7090	0.887653
$175$	6.36920	0.481466
$176$	−22.0360	−1.66103
$177$	−13.8733	−1.04278
$178$	−4.66395	−0.349578
$179$	−5.51931	−0.412533	−0.206266	−	0.978496i	$-0.566131\pi$
$179$	−5.51931	−0.412533	−0.206266	+	0.978496i	$0.566131\pi$
$180$	14.1360	1.05364
$181$	−5.19250	−0.385956	−0.192978	−	0.981203i	$-0.561815\pi$
$181$	−5.19250	−0.385956	−0.192978	+	0.981203i	$0.561815\pi$
$182$	−2.08164	−0.154301
$183$	3.19212	0.235968
$184$	−5.85647	−0.431744
$185$	19.3092	1.41964
$186$	4.03213	0.295650
$187$	11.0592	0.808727
$188$	11.8105	0.861366
$189$	4.58696	0.333652
$190$	5.51560	0.400143
$191$	3.31232	0.239671	0.119835	−	0.992794i	$-0.461763\pi$
$191$	3.31232	0.239671	0.119835	+	0.992794i	$0.461763\pi$
$192$	2.05332	0.148186
$193$	8.45889	0.608884	0.304442	−	0.952531i	$-0.401530\pi$
$193$	8.45889	0.608884	0.304442	+	0.952531i	$0.401530\pi$
$194$	−7.68280	−0.551593
$195$	8.15068	0.583682
$196$	−5.55492	−0.396780
$197$	11.4899	0.818618	0.409309	−	0.912396i	$-0.365770\pi$
$197$	11.4899	0.818618	0.409309	+	0.912396i	$0.365770\pi$
$198$	−33.3003	−2.36655
$199$	−4.79616	−0.339991	−0.169996	−	0.985445i	$-0.554375\pi$
$199$	−4.79616	−0.339991	−0.169996	+	0.985445i	$0.554375\pi$
$200$	8.55129	0.604667
$201$	4.56394	0.321915
$202$	−3.83873	−0.270092
$203$	−3.13212	−0.219832
$204$	6.98098	0.488766
$205$	−31.4285	−2.19506
$206$	−7.61477	−0.530546
$207$	−15.0204	−1.04399
$208$	−4.74335	−0.328892
$209$	−4.40784	−0.304897
$210$	−18.8471	−1.30057
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	0.599733	0.0411898
$213$	−27.1242	−1.85852
$214$	0.421599	0.0288199
$215$	22.4349	1.53005
$216$	6.15846	0.419030
$217$	−1.07859	−0.0732192
$218$	14.1425	0.957849
$219$	32.1794	2.17448
$220$	14.3491	0.967417
$221$	2.38053	0.160132
$222$	−28.7131	−1.92710
$223$	−16.2103	−1.08552	−0.542760	−	0.839888i	$-0.682621\pi$
$223$	−16.2103	−1.08552	−0.542760	+	0.839888i	$0.682621\pi$
$224$	6.69805	0.447532
$225$	21.9320	1.46213
$226$	0.538032	0.0357893
$227$	7.41078	0.491871	0.245936	−	0.969286i	$-0.420905\pi$
$227$	7.41078	0.491871	0.245936	+	0.969286i	$0.420905\pi$
$228$	−2.78240	−0.184269
$229$	13.6195	0.899999	0.450000	−	0.893029i	$-0.351424\pi$
$229$	13.6195	0.899999	0.450000	+	0.893029i	$0.351424\pi$
$230$	19.0787	1.25801
$231$	15.0618	0.990996
$232$	−4.20519	−0.276084
$233$	2.71673	0.177979	0.0889894	−	0.996033i	$-0.471636\pi$
$233$	2.71673	0.177979	0.0889894	+	0.996033i	$0.471636\pi$
$234$	−7.16802	−0.468588
$235$	36.4639	2.37865
$236$	−5.25732	−0.342222
$237$	−41.1741	−2.67454
$238$	−5.50459	−0.356810
$239$	4.24883	0.274834	0.137417	−	0.990513i	$-0.456120\pi$
$239$	4.24883	0.274834	0.137417	+	0.990513i	$0.456120\pi$
$240$	−42.9461	−2.77216
$241$	−10.7122	−0.690036	−0.345018	−	0.938596i	$-0.612127\pi$
$241$	−10.7122	−0.690036	−0.345018	+	0.938596i	$0.612127\pi$
$242$	−14.6647	−0.942684
$243$	−19.5044	−1.25121
$244$	1.20966	0.0774403
$245$	−17.1504	−1.09570
$246$	46.7346	2.97969
$247$	−0.948807	−0.0603711
$248$	−1.44811	−0.0919551
$249$	−16.3569	−1.03658
$250$	−0.279615	−0.0176844
$251$	10.2158	0.644814	0.322407	−	0.946601i	$-0.395508\pi$
$251$	10.2158	0.644814	0.322407	+	0.946601i	$0.395508\pi$
$252$	5.62292	0.354211
$253$	−15.2469	−0.958564
$254$	−15.0684	−0.945473
$255$	21.5533	1.34972
$256$	19.2597	1.20373
$257$	−11.2555	−0.702096	−0.351048	−	0.936357i	$-0.614175\pi$
$257$	−11.2555	−0.702096	−0.351048	+	0.936357i	$0.614175\pi$
$258$	−33.3610	−2.07696
$259$	7.68070	0.477256
$260$	3.08871	0.191554
$261$	−10.7853	−0.667594
$262$	18.8008	1.16152
$263$	−5.55249	−0.342381	−0.171191	−	0.985238i	$-0.554761\pi$
$263$	−5.55249	−0.342381	−0.171191	+	0.985238i	$0.554761\pi$
$264$	20.2220	1.24458
$265$	1.85163	0.113745
$266$	2.19396	0.134520
$267$	7.26403	0.444552
$268$	1.72951	0.105647
$269$	6.71734	0.409563	0.204782	−	0.978808i	$-0.434352\pi$
$269$	6.71734	0.409563	0.204782	+	0.978808i	$0.434352\pi$
$270$	−20.0625	−1.22096
$271$	−13.4199	−0.815199	−0.407600	−	0.913161i	$-0.633634\pi$
$271$	−13.4199	−0.815199	−0.407600	+	0.913161i	$0.633634\pi$
$272$	−12.5431	−0.760536
$273$	3.24212	0.196222
$274$	25.5801	1.54535
$275$	22.2627	1.34249
$276$	−9.62443	−0.579322
$277$	−18.8106	−1.13022	−0.565111	−	0.825015i	$-0.691167\pi$
$277$	−18.8106	−1.13022	−0.565111	+	0.825015i	$0.691167\pi$
$278$	−35.5810	−2.13401
$279$	−3.71406	−0.222355
$280$	6.76880	0.404513
$281$	−25.3639	−1.51308	−0.756541	−	0.653946i	$-0.773112\pi$
$281$	−25.3639	−1.51308	−0.756541	+	0.653946i	$0.773112\pi$
$282$	−54.2223	−3.22889
$283$	12.3882	0.736401	0.368201	−	0.929746i	$-0.379974\pi$
$283$	12.3882	0.736401	0.368201	+	0.929746i	$0.379974\pi$
$284$	−10.2788	−0.609932
$285$	−8.59046	−0.508855
$286$	−7.27609	−0.430244
$287$	−12.5014	−0.737935
$288$	23.0644	1.35908
$289$	−10.7050	−0.629708
$290$	13.6993	0.804450
$291$	11.9658	0.701450
$292$	12.1944	0.713625
$293$	12.6025	0.736245	0.368122	−	0.929777i	$-0.380001\pi$
$293$	12.6025	0.736245	0.368122	+	0.929777i	$0.380001\pi$
$294$	25.5029	1.48736
$295$	−16.2316	−0.945040
$296$	10.3121	0.599379
$297$	16.0331	0.930335
$298$	−6.44160	−0.373152
$299$	−3.28196	−0.189801
$300$	14.0531	0.811353
$301$	8.92400	0.514371
$302$	23.2207	1.33620
$303$	5.97876	0.343471
$304$	4.99928	0.286728
$305$	3.73473	0.213850
$306$	−18.9548	−1.08357
$307$	12.7099	0.725390	0.362695	−	0.931908i	$-0.381857\pi$
$307$	12.7099	0.725390	0.362695	+	0.931908i	$0.381857\pi$
$308$	5.70770	0.325226
$309$	11.8599	0.674686
$310$	4.71752	0.267937
$311$	5.60603	0.317889	0.158944	−	0.987288i	$-0.449191\pi$
$311$	5.60603	0.317889	0.158944	+	0.987288i	$0.449191\pi$
$312$	4.35288	0.246433
$313$	6.20783	0.350887	0.175444	−	0.984489i	$-0.443864\pi$
$313$	6.20783	0.350887	0.175444	+	0.984489i	$0.443864\pi$
$314$	41.4241	2.33770
$315$	17.3604	0.978146
$316$	−15.6030	−0.877735
$317$	−28.0224	−1.57389	−0.786947	−	0.617021i	$-0.788340\pi$
$317$	−28.0224	−1.57389	−0.786947	+	0.617021i	$0.788340\pi$
$318$	−2.75340	−0.154403
$319$	−10.9479	−0.612965
$320$	2.40235	0.134296
$321$	−0.656633	−0.0366497
$322$	7.58898	0.422917
$323$	−2.50898	−0.139603
$324$	−3.25601	−0.180889
$325$	4.79213	0.265820
$326$	18.0995	1.00244
$327$	−22.0267	−1.21808
$328$	−16.7844	−0.926764
$329$	14.5044	0.799652
$330$	−65.8774	−3.62643
$331$	−17.3737	−0.954946	−0.477473	−	0.878646i	$-0.658447\pi$
$331$	−17.3737	−0.954946	−0.477473	+	0.878646i	$0.658447\pi$
$332$	−6.19847	−0.340185
$333$	26.4481	1.44935
$334$	−10.6569	−0.583120
$335$	5.33973	0.291741
$336$	−17.0828	−0.931944
$337$	−7.27344	−0.396209	−0.198105	−	0.980181i	$-0.563479\pi$
$337$	−7.27344	−0.396209	−0.198105	+	0.980181i	$0.563479\pi$
$338$	21.0509	1.14502
$339$	−0.837976	−0.0455126
$340$	8.16763	0.442952
$341$	−3.77005	−0.204160
$342$	7.55478	0.408516
$343$	−15.6494	−0.844986
$344$	11.9814	0.645992
$345$	−29.7147	−1.59979
$346$	−31.1932	−1.67696
$347$	−26.5752	−1.42663	−0.713316	−	0.700842i	$-0.752808\pi$
$347$	−26.5752	−1.42663	−0.713316	+	0.700842i	$0.752808\pi$
$348$	−6.91074	−0.370455
$349$	−5.37801	−0.287878	−0.143939	−	0.989587i	$-0.545977\pi$
$349$	−5.37801	−0.287878	−0.143939	+	0.989587i	$0.545977\pi$
$350$	−11.0810	−0.592305
$351$	3.45119	0.184211
$352$	23.4121	1.24787
$353$	30.7413	1.63619	0.818097	−	0.575080i	$-0.195029\pi$
$353$	30.7413	1.63619	0.818097	+	0.575080i	$0.195029\pi$
$354$	24.1366	1.28284
$355$	−31.7349	−1.68431
$356$	2.75271	0.145893
$357$	8.57331	0.453748
$358$	9.60239	0.507502
$359$	−24.3247	−1.28381	−0.641903	−	0.766786i	$-0.721855\pi$
$359$	−24.3247	−1.28381	−0.641903	+	0.766786i	$0.721855\pi$
$360$	23.3080	1.22844
$361$	1.00000	0.0526316
$362$	9.03381	0.474807
$363$	22.8401	1.19879
$364$	1.22861	0.0643964
$365$	37.6494	1.97066
$366$	−5.55359	−0.290291
$367$	5.21264	0.272098	0.136049	−	0.990702i	$-0.456560\pi$
$367$	5.21264	0.272098	0.136049	+	0.990702i	$0.456560\pi$
$368$	17.2927	0.901444
$369$	−43.0480	−2.24099
$370$	−33.5939	−1.74646
$371$	0.736530	0.0382387
$372$	−2.37980	−0.123387
$373$	−1.17095	−0.0606295	−0.0303148	−	0.999540i	$-0.509651\pi$
$373$	−1.17095	−0.0606295	−0.0303148	+	0.999540i	$0.509651\pi$
$374$	−19.2405	−0.994905
$375$	0.435496	0.0224889
$376$	19.4736	1.00427
$377$	−2.35658	−0.121370
$378$	−7.98031	−0.410463
$379$	2.72661	0.140057	0.0700284	−	0.997545i	$-0.477691\pi$
$379$	2.72661	0.140057	0.0700284	+	0.997545i	$0.477691\pi$
$380$	−3.25536	−0.166997
$381$	23.4687	1.20234
$382$	−5.76270	−0.294846
$383$	10.2187	0.522153	0.261076	−	0.965318i	$-0.415923\pi$
$383$	10.2187	0.522153	0.261076	+	0.965318i	$0.415923\pi$
$384$	−32.3571	−1.65122
$385$	17.6221	0.898105
$386$	−14.7166	−0.749056
$387$	30.7293	1.56206
$388$	4.53447	0.230203
$389$	30.7047	1.55679	0.778394	−	0.627776i	$-0.216034\pi$
$389$	30.7047	1.55679	0.778394	+	0.627776i	$0.216034\pi$
$390$	−14.1804	−0.718052
$391$	−8.67865	−0.438898
$392$	−9.15919	−0.462609
$393$	−29.2820	−1.47708
$394$	−19.9898	−1.00707
$395$	−48.1730	−2.42385
$396$	19.6542	0.987659
$397$	35.4247	1.77791	0.888957	−	0.457990i	$-0.151431\pi$
$397$	35.4247	1.77791	0.888957	+	0.457990i	$0.151431\pi$
$398$	8.34427	0.418261
$399$	−3.41705	−0.171067
$400$	−25.2498	−1.26249
$401$	−15.0355	−0.750836	−0.375418	−	0.926856i	$-0.622501\pi$
$401$	−15.0355	−0.750836	−0.375418	+	0.926856i	$0.622501\pi$
$402$	−7.94025	−0.396024
$403$	−0.811520	−0.0404247
$404$	2.26566	0.112721
$405$	−10.0527	−0.499522
$406$	5.44921	0.270440
$407$	26.8468	1.33075
$408$	11.5105	0.569856
$409$	17.9760	0.888856	0.444428	−	0.895815i	$-0.353407\pi$
$409$	17.9760	0.888856	0.444428	+	0.895815i	$0.353407\pi$
$410$	54.6787	2.70039
$411$	−39.8406	−1.96519
$412$	4.49432	0.221419
$413$	−6.45649	−0.317703
$414$	26.1323	1.28433
$415$	−19.1373	−0.939414
$416$	5.03956	0.247085
$417$	55.4169	2.71378
$418$	7.66868	0.375087
$419$	−8.30039	−0.405501	−0.202750	−	0.979230i	$-0.564988\pi$
$419$	−8.30039	−0.405501	−0.202750	+	0.979230i	$0.564988\pi$
$420$	11.1237	0.542783
$421$	−11.8959	−0.579772	−0.289886	−	0.957061i	$-0.593617\pi$
$421$	−11.8959	−0.579772	−0.289886	+	0.957061i	$0.593617\pi$
$422$	−1.73978	−0.0846912
$423$	49.9451	2.42841
$424$	0.988865	0.0480235
$425$	12.6721	0.614686
$426$	47.1902	2.28637
$427$	1.48557	0.0718920
$428$	−0.248832	−0.0120277
$429$	11.3324	0.547133
$430$	−39.0318	−1.88228
$431$	−0.313409	−0.0150964	−0.00754819	−	0.999972i	$-0.502403\pi$
$431$	−0.313409	−0.0150964	−0.00754819	+	0.999972i	$0.502403\pi$
$432$	−18.1844	−0.874898
$433$	29.4757	1.41651	0.708257	−	0.705955i	$-0.249482\pi$
$433$	29.4757	1.41651	0.708257	+	0.705955i	$0.249482\pi$
$434$	1.87650	0.0900751
$435$	−21.3364	−1.02300
$436$	−8.34703	−0.399750
$437$	3.45904	0.165468
$438$	−55.9852	−2.67507
$439$	23.9847	1.14473	0.572364	−	0.820000i	$-0.306026\pi$
$439$	23.9847	1.14473	0.572364	+	0.820000i	$0.306026\pi$
$440$	23.6594	1.12792
$441$	−23.4911	−1.11863
$442$	−4.14161	−0.196996
$443$	32.5403	1.54604	0.773019	−	0.634383i	$-0.218746\pi$
$443$	32.5403	1.54604	0.773019	+	0.634383i	$0.218746\pi$
$444$	16.9468	0.804258
$445$	8.49880	0.402882
$446$	28.2023	1.33542
$447$	10.0327	0.474530
$448$	0.955591	0.0451474
$449$	2.06953	0.0976670	0.0488335	−	0.998807i	$-0.484450\pi$
$449$	2.06953	0.0976670	0.0488335	+	0.998807i	$0.484450\pi$
$450$	−38.1569	−1.79873
$451$	−43.6970	−2.05761
$452$	−0.317552	−0.0149364
$453$	−36.1659	−1.69922
$454$	−12.8931	−0.605105
$455$	3.79323	0.177829
$456$	−4.58774	−0.214841
$457$	−26.2331	−1.22713	−0.613567	−	0.789642i	$-0.710266\pi$
$457$	−26.2331	−1.22713	−0.613567	+	0.789642i	$0.710266\pi$
$458$	−23.6949	−1.10719
$459$	9.12617	0.425973
$460$	−11.2604	−0.525020
$461$	10.1882	0.474511	0.237256	−	0.971447i	$-0.423752\pi$
$461$	10.1882	0.474511	0.237256	+	0.971447i	$0.423752\pi$
$462$	−26.2043	−1.21913
$463$	12.3343	0.573223	0.286612	−	0.958047i	$-0.407471\pi$
$463$	12.3343	0.573223	0.286612	+	0.958047i	$0.407471\pi$
$464$	12.4169	0.576440
$465$	−7.34747	−0.340731
$466$	−4.72651	−0.218951
$467$	31.6369	1.46398	0.731989	−	0.681316i	$-0.238592\pi$
$467$	31.6369	1.46398	0.731989	+	0.681316i	$0.238592\pi$
$468$	4.23064	0.195561
$469$	2.12400	0.0980773
$470$	−63.4393	−2.92623
$471$	−64.5174	−2.97280
$472$	−8.66849	−0.399000
$473$	31.1926	1.43424
$474$	71.6338	3.29025
$475$	−5.05070	−0.231742
$476$	3.24886	0.148911
$477$	2.53620	0.116125
$478$	−7.39204	−0.338104
$479$	25.9228	1.18444	0.592221	−	0.805775i	$-0.298251\pi$
$479$	25.9228	1.18444	0.592221	+	0.805775i	$0.298251\pi$
$480$	45.6279	2.08262
$481$	5.77890	0.263495
$482$	18.6369	0.848889
$483$	−11.8197	−0.537816
$484$	8.65527	0.393421
$485$	13.9998	0.635700
$486$	33.9333	1.53925
$487$	−8.19711	−0.371446	−0.185723	−	0.982602i	$-0.559463\pi$
$487$	−8.19711	−0.371446	−0.185723	+	0.982602i	$0.559463\pi$
$488$	1.99453	0.0902883
$489$	−28.1897	−1.27478
$490$	29.8380	1.34794
$491$	11.4886	0.518474	0.259237	−	0.965814i	$-0.416529\pi$
$491$	11.4886	0.518474	0.259237	+	0.965814i	$0.416529\pi$
$492$	−27.5832	−1.24355
$493$	−6.23164	−0.280659
$494$	1.65072	0.0742692
$495$	60.6808	2.72740
$496$	4.27591	0.191994
$497$	−12.6233	−0.566232
$498$	28.4574	1.27521
$499$	−13.5458	−0.606395	−0.303198	−	0.952928i	$-0.598054\pi$
$499$	−13.5458	−0.606395	−0.303198	+	0.952928i	$0.598054\pi$
$500$	0.165031	0.00738043
$501$	16.5980	0.741542
$502$	−17.7732	−0.793257
$503$	42.3375	1.88773	0.943867	−	0.330325i	$-0.107158\pi$
$503$	42.3375	1.88773	0.943867	+	0.330325i	$0.107158\pi$
$504$	9.27131	0.412977
$505$	6.99505	0.311276
$506$	26.5262	1.17924
$507$	−32.7865	−1.45610
$508$	8.89350	0.394585
$509$	18.5953	0.824221	0.412110	−	0.911134i	$-0.364792\pi$
$509$	18.5953	0.824221	0.412110	+	0.911134i	$0.364792\pi$
$510$	−37.4980	−1.66044
$511$	14.9759	0.662496
$512$	−9.62504	−0.425371
$513$	−3.63741	−0.160595
$514$	19.5820	0.863726
$515$	13.8759	0.611444
$516$	19.6900	0.866803
$517$	50.6981	2.22970
$518$	−13.3627	−0.587125
$519$	48.5830	2.13256
$520$	5.09279	0.223334
$521$	−3.62282	−0.158719	−0.0793593	−	0.996846i	$-0.525287\pi$
$521$	−3.62282	−0.158719	−0.0793593	+	0.996846i	$0.525287\pi$
$522$	18.7641	0.821281
$523$	44.2036	1.93289	0.966445	−	0.256875i	$-0.0826928\pi$
$523$	44.2036	1.93289	0.966445	+	0.256875i	$0.0826928\pi$
$524$	−11.0964	−0.484750
$525$	17.2585	0.753223
$526$	9.66011	0.421201
$527$	−2.14594	−0.0934788
$528$	−59.7106	−2.59857
$529$	−11.0351	−0.479785
$530$	−3.22143	−0.139930
$531$	−22.2326	−0.964813
$532$	−1.29490	−0.0561409
$533$	−9.40597	−0.407418
$534$	−12.6378	−0.546892
$535$	−0.768250	−0.0332144
$536$	2.85169	0.123174
$537$	−14.9556	−0.645381
$538$	−11.6867	−0.503849
$539$	−23.8453	−1.02709
$540$	11.8411	0.509559
$541$	32.9107	1.41494	0.707472	−	0.706742i	$-0.249836\pi$
$541$	32.9107	1.41494	0.707472	+	0.706742i	$0.249836\pi$
$542$	23.3476	1.00287
$543$	−14.0700	−0.603803
$544$	13.3264	0.571363
$545$	−25.7708	−1.10390
$546$	−5.64058	−0.241395
$547$	−6.34446	−0.271269	−0.135635	−	0.990759i	$-0.543307\pi$
$547$	−6.34446	−0.271269	−0.135635	+	0.990759i	$0.543307\pi$
$548$	−15.0976	−0.644939
$549$	5.11550	0.218324
$550$	−38.7322	−1.65154
$551$	2.48374	0.105811
$552$	−15.8692	−0.675436
$553$	−19.1619	−0.814848
$554$	32.7264	1.39041
$555$	52.3219	2.22094
$556$	21.0003	0.890610
$557$	−7.62508	−0.323085	−0.161542	−	0.986866i	$-0.551647\pi$
$557$	−7.62508	−0.323085	−0.161542	+	0.986866i	$0.551647\pi$
$558$	6.46165	0.273543
$559$	6.71434	0.283986
$560$	−19.9866	−0.844588
$561$	29.9668	1.26520
$562$	44.1276	1.86141
$563$	20.8325	0.877985	0.438993	−	0.898491i	$-0.355335\pi$
$563$	20.8325	0.877985	0.438993	+	0.898491i	$0.355335\pi$
$564$	32.0026	1.34755
$565$	−0.980418	−0.0412465
$566$	−21.5527	−0.905929
$567$	−3.99869	−0.167929
$568$	−16.9481	−0.711124
$569$	−16.9718	−0.711496	−0.355748	−	0.934582i	$-0.615774\pi$
$569$	−16.9718	−0.711496	−0.355748	+	0.934582i	$0.615774\pi$
$570$	14.9455	0.625999
$571$	−4.03833	−0.168999	−0.0844993	−	0.996424i	$-0.526929\pi$
$571$	−4.03833	−0.168999	−0.0844993	+	0.996424i	$0.526929\pi$
$572$	4.29442	0.179559
$573$	8.97532	0.374950
$574$	21.7497	0.907816
$575$	−17.4705	−0.728572
$576$	3.29053	0.137105
$577$	−14.3708	−0.598265	−0.299132	−	0.954212i	$-0.596697\pi$
$577$	−14.3708	−0.598265	−0.299132	+	0.954212i	$0.596697\pi$
$578$	18.6244	0.774673
$579$	22.9209	0.952560
$580$	−8.08546	−0.335730
$581$	−7.61231	−0.315812
$582$	−20.8179	−0.862931
$583$	2.57444	0.106622
$584$	20.1067	0.832021
$585$	13.0618	0.540039
$586$	−21.9255	−0.905736
$587$	−27.9198	−1.15237	−0.576186	−	0.817319i	$-0.695460\pi$
$587$	−27.9198	−1.15237	−0.576186	+	0.817319i	$0.695460\pi$
$588$	−15.0521	−0.620737
$589$	0.855306	0.0352423
$590$	28.2394	1.16260
$591$	31.1338	1.28068
$592$	−30.4491	−1.25145
$593$	−1.21295	−0.0498099	−0.0249050	−	0.999690i	$-0.507928\pi$
$593$	−1.21295	−0.0498099	−0.0249050	+	0.999690i	$0.507928\pi$
$594$	−27.8941	−1.14451
$595$	10.0306	0.411216
$596$	3.80190	0.155732
$597$	−12.9961	−0.531894
$598$	5.70989	0.233495
$599$	17.5329	0.716374	0.358187	−	0.933650i	$-0.383395\pi$
$599$	17.5329	0.716374	0.358187	+	0.933650i	$0.383395\pi$
$600$	23.1713	0.945963
$601$	44.3803	1.81031	0.905154	−	0.425083i	$-0.139755\pi$
$601$	44.3803	1.81031	0.905154	+	0.425083i	$0.139755\pi$
$602$	−15.5258	−0.632784
$603$	7.31389	0.297845
$604$	−13.7051	−0.557653
$605$	26.7225	1.08643
$606$	−10.4017	−0.422541
$607$	1.45572	0.0590857	0.0295428	−	0.999564i	$-0.490595\pi$
$607$	1.45572	0.0590857	0.0295428	+	0.999564i	$0.490595\pi$
$608$	−5.31147	−0.215408
$609$	−8.48706	−0.343913
$610$	−6.49761	−0.263080
$611$	10.9130	0.441492
$612$	11.1873	0.452220
$613$	18.4843	0.746573	0.373287	−	0.927716i	$-0.378231\pi$
$613$	18.4843	0.746573	0.373287	+	0.927716i	$0.378231\pi$
$614$	−22.1124	−0.892383
$615$	−85.1612	−3.43403
$616$	9.41109	0.379184
$617$	−22.0830	−0.889027	−0.444514	−	0.895772i	$-0.646623\pi$
$617$	−22.0830	−0.889027	−0.444514	+	0.895772i	$0.646623\pi$
$618$	−20.6336	−0.830006
$619$	−42.0612	−1.69058	−0.845292	−	0.534305i	$-0.820573\pi$
$619$	−42.0612	−1.69058	−0.845292	+	0.534305i	$0.820573\pi$
$620$	−2.78433	−0.111821
$621$	−12.5819	−0.504895
$622$	−9.75325	−0.391070
$623$	3.38060	0.135441
$624$	−12.8530	−0.514530
$625$	−24.7440	−0.989758
$626$	−10.8003	−0.431665
$627$	−11.9438	−0.476991
$628$	−24.4489	−0.975618
$629$	15.2814	0.609311
$630$	−30.2032	−1.20333
$631$	−28.5349	−1.13596	−0.567978	−	0.823043i	$-0.692274\pi$
$631$	−28.5349	−1.13596	−0.567978	+	0.823043i	$0.692274\pi$
$632$	−25.7268	−1.02336
$633$	2.70968	0.107700
$634$	48.7528	1.93622
$635$	27.4581	1.08964
$636$	1.62509	0.0644388
$637$	−5.13280	−0.203369
$638$	19.0470	0.754077
$639$	−43.4677	−1.71956
$640$	−37.8573	−1.49644
$641$	−38.1184	−1.50558	−0.752792	−	0.658258i	$-0.771293\pi$
$641$	−38.1184	−1.50558	−0.752792	+	0.658258i	$0.771293\pi$
$642$	1.14240	0.0450869
$643$	−28.9132	−1.14022	−0.570112	−	0.821567i	$-0.693100\pi$
$643$	−28.9132	−1.14022	−0.570112	+	0.821567i	$0.693100\pi$
$644$	−4.47909	−0.176501
$645$	60.7914	2.39366
$646$	4.36507	0.171741
$647$	32.4726	1.27663	0.638315	−	0.769776i	$-0.279632\pi$
$647$	32.4726	1.27663	0.638315	+	0.769776i	$0.279632\pi$
$648$	−5.36864	−0.210900
$649$	−22.5678	−0.885863
$650$	−8.33726	−0.327014
$651$	−2.92263	−0.114547
$652$	−10.6825	−0.418360
$653$	17.9517	0.702504	0.351252	−	0.936281i	$-0.385756\pi$
$653$	17.9517	0.702504	0.351252	+	0.936281i	$0.385756\pi$
$654$	38.3216	1.49849
$655$	−34.2595	−1.33863
$656$	49.5602	1.93500
$657$	51.5688	2.01189
$658$	−25.2344	−0.983741
$659$	18.7115	0.728897	0.364448	−	0.931224i	$-0.381258\pi$
$659$	18.7115	0.728897	0.364448	+	0.931224i	$0.381258\pi$
$660$	38.8815	1.51346
$661$	−31.1520	−1.21167	−0.605836	−	0.795590i	$-0.707161\pi$
$661$	−31.1520	−1.21167	−0.605836	+	0.795590i	$0.707161\pi$
$662$	30.2265	1.17478
$663$	6.45049	0.250516
$664$	−10.2203	−0.396624
$665$	−3.99790	−0.155032
$666$	−46.0139	−1.78300
$667$	8.59134	0.332658
$668$	6.28981	0.243360
$669$	−43.9247	−1.69823
$670$	−9.28996	−0.358903
$671$	5.19262	0.200459
$672$	18.1496	0.700135
$673$	0.615587	0.0237291	0.0118646	−	0.999930i	$-0.496223\pi$
$673$	0.615587	0.0237291	0.0118646	+	0.999930i	$0.496223\pi$
$674$	12.6542	0.487421
$675$	18.3714	0.707116
$676$	−12.4245	−0.477865
$677$	−35.0201	−1.34593	−0.672965	−	0.739674i	$-0.734980\pi$
$677$	−35.0201	−1.34593	−0.672965	+	0.739674i	$0.734980\pi$
$678$	1.45789	0.0559901
$679$	5.56876	0.213709
$680$	13.4671	0.516441
$681$	20.0809	0.769500
$682$	6.55907	0.251160
$683$	−10.9402	−0.418614	−0.209307	−	0.977850i	$-0.567121\pi$
$683$	−10.9402	−0.418614	−0.209307	+	0.977850i	$0.567121\pi$
$684$	−4.45891	−0.170491
$685$	−46.6129	−1.78099
$686$	27.2264	1.03951
$687$	36.9044	1.40799
$688$	−35.3780	−1.34877
$689$	0.554159	0.0211118
$690$	51.6971	1.96807
$691$	−0.105093	−0.00399794	−0.00199897	−	0.999998i	$-0.500636\pi$
$691$	−0.105093	−0.00399794	−0.00199897	+	0.999998i	$0.500636\pi$
$692$	18.4106	0.699865
$693$	24.1372	0.916896
$694$	46.2350	1.75506
$695$	64.8368	2.45940
$696$	−11.3947	−0.431916
$697$	−24.8727	−0.942120
$698$	9.35656	0.354151
$699$	7.36147	0.278436
$700$	6.54012	0.247193
$701$	−0.0749785	−0.00283190	−0.00141595	−	0.999999i	$-0.500451\pi$
$701$	−0.0749785	−0.00283190	−0.00141595	+	0.999999i	$0.500451\pi$
$702$	−6.00432	−0.226618
$703$	−6.09070	−0.229715
$704$	3.34014	0.125886
$705$	98.8057	3.72124
$706$	−53.4831	−2.01286
$707$	2.78244	0.104645
$708$	−14.2457	−0.535385
$709$	31.7445	1.19219	0.596094	−	0.802915i	$-0.296719\pi$
$709$	31.7445	1.19219	0.596094	+	0.802915i	$0.296719\pi$
$710$	55.2118	2.07206
$711$	−65.9831	−2.47456
$712$	4.53879	0.170098
$713$	2.95854	0.110798
$714$	−14.9157	−0.558205
$715$	13.2587	0.495848
$716$	−5.66743	−0.211802
$717$	11.5130	0.429960
$718$	42.3196	1.57935
$719$	−42.7343	−1.59372	−0.796860	−	0.604164i	$-0.793507\pi$
$719$	−42.7343	−1.59372	−0.796860	+	0.604164i	$0.793507\pi$
$720$	−68.8229	−2.56488
$721$	5.51945	0.205555
$722$	−1.73978	−0.0647479
$723$	−29.0267	−1.07952
$724$	−5.33185	−0.198157
$725$	−12.5446	−0.465894
$726$	−39.7367	−1.47477
$727$	42.1503	1.56327	0.781634	−	0.623738i	$-0.214387\pi$
$727$	42.1503	1.56327	0.781634	+	0.623738i	$0.214387\pi$
$728$	2.02578	0.0750803
$729$	−43.3379	−1.60511
$730$	−65.5017	−2.42433
$731$	17.7551	0.656696
$732$	3.27778	0.121150
$733$	−15.0516	−0.555945	−0.277972	−	0.960589i	$-0.589662\pi$
$733$	−15.0516	−0.555945	−0.277972	+	0.960589i	$0.589662\pi$
$734$	−9.06885	−0.334737
$735$	−46.4722	−1.71415
$736$	−18.3726	−0.677222
$737$	7.42416	0.273473
$738$	74.8941	2.75689
$739$	−30.8371	−1.13436	−0.567181	−	0.823593i	$-0.691966\pi$
$739$	−30.8371	−1.13436	−0.567181	+	0.823593i	$0.691966\pi$
$740$	19.8274	0.728871
$741$	−2.57096	−0.0944467
$742$	−1.28140	−0.0470417
$743$	26.1979	0.961107	0.480553	−	0.876965i	$-0.340436\pi$
$743$	26.1979	0.961107	0.480553	+	0.876965i	$0.340436\pi$
$744$	−3.92392	−0.143858
$745$	11.7381	0.430050
$746$	2.03720	0.0745871
$747$	−26.2126	−0.959069
$748$	11.3560	0.415215
$749$	−0.305589	−0.0111660
$750$	−0.757667	−0.0276661
$751$	−20.7594	−0.757520	−0.378760	−	0.925495i	$-0.623649\pi$
$751$	−20.7594	−0.757520	−0.378760	+	0.925495i	$0.623649\pi$
$752$	−57.5007	−2.09683
$753$	27.6815	1.00877
$754$	4.09994	0.149311
$755$	−42.3135	−1.53995
$756$	4.71006	0.171303
$757$	−12.9338	−0.470089	−0.235044	−	0.971985i	$-0.575524\pi$
$757$	−12.9338	−0.470089	−0.235044	+	0.971985i	$0.575524\pi$
$758$	−4.74371	−0.172299
$759$	−41.3142	−1.49961
$760$	−5.36758	−0.194703
$761$	31.9623	1.15863	0.579317	−	0.815103i	$-0.303319\pi$
$761$	31.9623	1.15863	0.579317	+	0.815103i	$0.303319\pi$
$762$	−40.8305	−1.47913
$763$	−10.2510	−0.371109
$764$	3.40121	0.123051
$765$	34.5400	1.24880
$766$	−17.7783	−0.642358
$767$	−4.85781	−0.175405
$768$	52.1876	1.88316
$769$	30.1767	1.08820	0.544099	−	0.839021i	$-0.316872\pi$
$769$	30.1767	1.08820	0.544099	+	0.839021i	$0.316872\pi$
$770$	−30.6586	−1.10486
$771$	−30.4987	−1.09838
$772$	8.68589	0.312612
$773$	47.2831	1.70066	0.850328	−	0.526253i	$-0.176404\pi$
$773$	47.2831	1.70066	0.850328	+	0.526253i	$0.176404\pi$
$774$	−53.4623	−1.92166
$775$	−4.31989	−0.155175
$776$	7.47662	0.268395
$777$	20.8123	0.746636
$778$	−53.4194	−1.91518
$779$	9.91347	0.355187
$780$	8.36942	0.299673
$781$	−44.1230	−1.57885
$782$	15.0989	0.539937
$783$	−9.03435	−0.322861
$784$	27.0448	0.965887
$785$	−75.4843	−2.69415
$786$	50.9442	1.81712
$787$	16.2743	0.580118	0.290059	−	0.957009i	$-0.406325\pi$
$787$	16.2743	0.580118	0.290059	+	0.957009i	$0.406325\pi$
$788$	11.7982	0.420293
$789$	−15.0455	−0.535633
$790$	83.8104	2.98184
$791$	−0.389984	−0.0138662
$792$	32.4066	1.15152
$793$	1.11773	0.0396919
$794$	−61.6312	−2.18721
$795$	5.01733	0.177947
$796$	−4.92488	−0.174558
$797$	18.1554	0.643096	0.321548	−	0.946893i	$-0.395797\pi$
$797$	18.1554	0.643096	0.321548	+	0.946893i	$0.395797\pi$
$798$	5.94492	0.210448
$799$	28.8577	1.02091
$800$	26.8266	0.948464
$801$	11.6409	0.411311
$802$	26.1584	0.923686
$803$	52.3463	1.84726
$804$	4.68642	0.165277
$805$	−13.8289	−0.487404
$806$	1.41187	0.0497309
$807$	18.2018	0.640735
$808$	3.73571	0.131422
$809$	42.6976	1.50117	0.750583	−	0.660776i	$-0.229773\pi$
$809$	42.6976	1.50117	0.750583	+	0.660776i	$0.229773\pi$
$810$	17.4895	0.614517
$811$	21.0734	0.739988	0.369994	−	0.929034i	$-0.379360\pi$
$811$	21.0734	0.739988	0.369994	+	0.929034i	$0.379360\pi$
$812$	−3.21618	−0.112866
$813$	−36.3636	−1.27533
$814$	−46.7076	−1.63710
$815$	−32.9815	−1.15529
$816$	−33.9878	−1.18981
$817$	−7.07662	−0.247580
$818$	−31.2743	−1.09348
$819$	5.19563	0.181550
$820$	−32.2719	−1.12698
$821$	15.8373	0.552724	0.276362	−	0.961054i	$-0.410871\pi$
$821$	15.8373	0.552724	0.276362	+	0.961054i	$0.410871\pi$
$822$	69.3139	2.41760
$823$	3.01202	0.104992	0.0524962	−	0.998621i	$-0.483282\pi$
$823$	3.01202	0.104992	0.0524962	+	0.998621i	$0.483282\pi$
$824$	7.41042	0.258154
$825$	60.3247	2.10024
$826$	11.2329	0.390842
$827$	19.6077	0.681826	0.340913	−	0.940095i	$-0.389264\pi$
$827$	19.6077	0.681826	0.340913	+	0.940095i	$0.389264\pi$
$828$	−15.4235	−0.536005
$829$	−24.6923	−0.857599	−0.428800	−	0.903400i	$-0.641063\pi$
$829$	−24.6923	−0.857599	−0.428800	+	0.903400i	$0.641063\pi$
$830$	33.2947	1.15568
$831$	−50.9708	−1.76816
$832$	0.718979	0.0249261
$833$	−13.5729	−0.470274
$834$	−96.4132	−3.33852
$835$	19.4193	0.672034
$836$	−4.52613	−0.156540
$837$	−3.11109	−0.107535
$838$	14.4409	0.498851
$839$	6.88211	0.237597	0.118798	−	0.992918i	$-0.462096\pi$
$839$	6.88211	0.237597	0.118798	+	0.992918i	$0.462096\pi$
$840$	18.3413	0.632835
$841$	−22.8311	−0.787278
$842$	20.6963	0.713242
$843$	−68.7280	−2.36712
$844$	1.02684	0.0353452
$845$	−38.3597	−1.31961
$846$	−86.8935	−2.98746
$847$	10.6295	0.365234
$848$	−2.91987	−0.100269
$849$	33.5680	1.15205
$850$	−22.0466	−0.756194
$851$	−21.0680	−0.722201
$852$	−27.8522	−0.954199
$853$	9.90354	0.339091	0.169545	−	0.985522i	$-0.445770\pi$
$853$	9.90354	0.339091	0.169545	+	0.985522i	$0.445770\pi$
$854$	−2.58457	−0.0884423
$855$	−13.7666	−0.470806
$856$	−0.410284	−0.0140232
$857$	−13.3142	−0.454805	−0.227402	−	0.973801i	$-0.573023\pi$
$857$	−13.3142	−0.454805	−0.227402	+	0.973801i	$0.573023\pi$
$858$	−19.7159	−0.673089
$859$	19.2115	0.655488	0.327744	−	0.944767i	$-0.393712\pi$
$859$	19.2115	0.655488	0.327744	+	0.944767i	$0.393712\pi$
$860$	23.0370	0.785554
$861$	−33.8749	−1.15445
$862$	0.545263	0.0185717
$863$	41.5635	1.41484	0.707419	−	0.706794i	$-0.249859\pi$
$863$	41.5635	1.41484	0.707419	+	0.706794i	$0.249859\pi$
$864$	19.3200	0.657278
$865$	56.8413	1.93266
$866$	−51.2813	−1.74261
$867$	−29.0072	−0.985137
$868$	−1.10753	−0.0375921
$869$	−66.9779	−2.27207
$870$	37.1207	1.25851
$871$	1.59808	0.0541490
$872$	−13.7629	−0.466072
$873$	19.1757	0.649001
$874$	−6.01797	−0.203561
$875$	0.202674	0.00685165
$876$	33.0430	1.11642
$877$	−38.5754	−1.30260	−0.651300	−	0.758820i	$-0.725776\pi$
$877$	−38.5754	−1.30260	−0.651300	+	0.758820i	$0.725776\pi$
$878$	−41.7281	−1.40826
$879$	34.1487	1.15181
$880$	−69.8605	−2.35500
$881$	−11.7504	−0.395882	−0.197941	−	0.980214i	$-0.563426\pi$
$881$	−11.7504	−0.395882	−0.197941	+	0.980214i	$0.563426\pi$
$882$	40.8694	1.37614
$883$	−21.7862	−0.733164	−0.366582	−	0.930386i	$-0.619472\pi$
$883$	−21.7862	−0.733164	−0.366582	+	0.930386i	$0.619472\pi$
$884$	2.44442	0.0822147
$885$	−43.9824	−1.47845
$886$	−56.6131	−1.90195
$887$	27.0607	0.908611	0.454305	−	0.890846i	$-0.349888\pi$
$887$	27.0607	0.908611	0.454305	+	0.890846i	$0.349888\pi$
$888$	27.9425	0.937690
$889$	10.9221	0.366315
$890$	−14.7860	−0.495629
$891$	−13.9769	−0.468243
$892$	−16.6453	−0.557326
$893$	−11.5018	−0.384893
$894$	−17.4547	−0.583772
$895$	−17.4978	−0.584886
$896$	−15.0586	−0.503073
$897$	−8.89306	−0.296931
$898$	−3.60052	−0.120151
$899$	2.12435	0.0708512
$900$	22.5206	0.750686
$901$	1.46539	0.0488193
$902$	76.0232	2.53130
$903$	24.1812	0.804700
$904$	−0.523593	−0.0174144
$905$	−16.4617	−0.547205
$906$	62.9207	2.09040
$907$	5.72177	0.189988	0.0949941	−	0.995478i	$-0.469717\pi$
$907$	5.72177	0.189988	0.0949941	+	0.995478i	$0.469717\pi$
$908$	7.60966	0.252536
$909$	9.58120	0.317788
$910$	−6.59939	−0.218768
$911$	3.51572	0.116481	0.0582405	−	0.998303i	$-0.481451\pi$
$911$	3.51572	0.116481	0.0582405	+	0.998303i	$0.481451\pi$
$912$	13.5465	0.448568
$913$	−26.6078	−0.880590
$914$	45.6399	1.50963
$915$	10.1199	0.334554
$916$	13.9850	0.462076
$917$	−13.6275	−0.450019
$918$	−15.8775	−0.524037
$919$	21.0276	0.693636	0.346818	−	0.937932i	$-0.387262\pi$
$919$	21.0276	0.693636	0.346818	+	0.937932i	$0.387262\pi$
$920$	−18.5667	−0.612125
$921$	34.4397	1.13483
$922$	−17.7252	−0.583749
$923$	−9.49767	−0.312620
$924$	15.4660	0.508795
$925$	30.7623	1.01146
$926$	−21.4590	−0.705186
$927$	19.0060	0.624238
$928$	−13.1923	−0.433058
$929$	20.4667	0.671491	0.335745	−	0.941953i	$-0.391012\pi$
$929$	20.4667	0.671491	0.335745	+	0.941953i	$0.391012\pi$
$930$	12.7830	0.419171
$931$	5.40974	0.177297
$932$	2.78964	0.0913776
$933$	15.1905	0.497316
$934$	−55.0412	−1.80100
$935$	35.0607	1.14661
$936$	6.97566	0.228007
$937$	−19.6679	−0.642523	−0.321262	−	0.946990i	$-0.604107\pi$
$937$	−19.6679	−0.642523	−0.321262	+	0.946990i	$0.604107\pi$
$938$	−3.69530	−0.120656
$939$	16.8212	0.548940
$940$	37.4425	1.22124
$941$	−27.2269	−0.887571	−0.443785	−	0.896133i	$-0.646365\pi$
$941$	−27.2269	−0.887571	−0.443785	+	0.896133i	$0.646365\pi$
$942$	112.246	3.65718
$943$	34.2911	1.11667
$944$	25.5959	0.833076
$945$	14.5420	0.473050
$946$	−54.2683	−1.76442
$947$	−47.3436	−1.53846	−0.769230	−	0.638972i	$-0.779360\pi$
$947$	−47.3436	−1.53846	−0.769230	+	0.638972i	$0.779360\pi$
$948$	−42.2790	−1.37316
$949$	11.2678	0.365767
$950$	8.78710	0.285091
$951$	−75.9317	−2.46226
$952$	5.35687	0.173617
$953$	31.2229	1.01141	0.505704	−	0.862707i	$-0.331233\pi$
$953$	31.2229	1.01141	0.505704	+	0.862707i	$0.331233\pi$
$954$	−4.41244	−0.142858
$955$	10.5010	0.339804
$956$	4.36286	0.141105
$957$	−29.6654	−0.958945
$958$	−45.1000	−1.45711
$959$	−18.5414	−0.598732
$960$	6.50961	0.210097
$961$	−30.2685	−0.976402
$962$	−10.0540	−0.324154
$963$	−1.05228	−0.0339093
$964$	−10.9997	−0.354277
$965$	26.8171	0.863272
$966$	20.5637	0.661627
$967$	−53.1235	−1.70834	−0.854168	−	0.519996i	$-0.825933\pi$
$967$	−53.1235	−1.70834	−0.854168	+	0.519996i	$0.825933\pi$
$968$	14.2712	0.458693
$969$	−6.79853	−0.218400
$970$	−24.3567	−0.782045
$971$	−35.4618	−1.13802	−0.569012	−	0.822329i	$-0.692674\pi$
$971$	−35.4618	−1.13802	−0.569012	+	0.822329i	$0.692674\pi$
$972$	−20.0278	−0.642392
$973$	25.7904	0.826801
$974$	14.2612	0.456957
$975$	12.9852	0.415858
$976$	−5.88936	−0.188514
$977$	−31.2889	−1.00102	−0.500510	−	0.865731i	$-0.666854\pi$
$977$	−31.2889	−1.00102	−0.500510	+	0.865731i	$0.666854\pi$
$978$	49.0439	1.56825
$979$	11.8164	0.377654
$980$	−17.6107	−0.562552
$981$	−35.2986	−1.12700
$982$	−19.9877	−0.637833
$983$	7.06643	0.225384	0.112692	−	0.993630i	$-0.464053\pi$
$983$	7.06643	0.225384	0.112692	+	0.993630i	$0.464053\pi$
$984$	−45.4804	−1.44986
$985$	36.4261	1.16063
$986$	10.8417	0.345269
$987$	39.3022	1.25100
$988$	−0.974269	−0.0309956
$989$	−24.4783	−0.778365
$990$	−105.571	−3.35527
$991$	−46.1500	−1.46600	−0.733002	−	0.680227i	$-0.761881\pi$
$991$	−46.1500	−1.46600	−0.733002	+	0.680227i	$0.761881\pi$
$992$	−4.54293	−0.144238
$993$	−47.0772	−1.49395
$994$	21.9618	0.696585
$995$	−15.2052	−0.482037
$996$	−16.7959	−0.532198
$997$	−30.2256	−0.957255	−0.478628	−	0.878018i	$-0.658866\pi$
$997$	−30.2256	−0.957255	−0.478628	+	0.878018i	$0.658866\pi$
$998$	23.5668	0.745994
$999$	22.1544	0.700933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.f.1.17	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.f.1.17	✓	83	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73978 q^{2} +2.70968 q^{3} +1.02684 q^{4} +3.17028 q^{5} -4.71425 q^{6} +1.26105 q^{7} +1.69309 q^{8} +4.34237 q^{9} +O(q^{10})\)	\(q-1.73978 q^{2} +2.70968 q^{3} +1.02684 q^{4} +3.17028 q^{5} -4.71425 q^{6} +1.26105 q^{7} +1.69309 q^{8} +4.34237 q^{9} -5.51560 q^{10} +4.40784 q^{11} +2.78240 q^{12} +0.948807 q^{13} -2.19396 q^{14} +8.59046 q^{15} -4.99928 q^{16} +2.50898 q^{17} -7.55478 q^{18} -1.00000 q^{19} +3.25536 q^{20} +3.41705 q^{21} -7.66868 q^{22} -3.45904 q^{23} +4.58774 q^{24} +5.05070 q^{25} -1.65072 q^{26} +3.63741 q^{27} +1.29490 q^{28} -2.48374 q^{29} -14.9455 q^{30} -0.855306 q^{31} +5.31147 q^{32} +11.9438 q^{33} -4.36507 q^{34} +3.99790 q^{35} +4.45891 q^{36} +6.09070 q^{37} +1.73978 q^{38} +2.57096 q^{39} +5.36758 q^{40} -9.91347 q^{41} -5.94492 q^{42} +7.07662 q^{43} +4.52613 q^{44} +13.7666 q^{45} +6.01797 q^{46} +11.5018 q^{47} -13.5465 q^{48} -5.40974 q^{49} -8.78710 q^{50} +6.79853 q^{51} +0.974269 q^{52} +0.584059 q^{53} -6.32829 q^{54} +13.9741 q^{55} +2.13508 q^{56} -2.70968 q^{57} +4.32115 q^{58} -5.11992 q^{59} +8.82099 q^{60} +1.17804 q^{61} +1.48804 q^{62} +5.47597 q^{63} +0.757772 q^{64} +3.00799 q^{65} -20.7797 q^{66} +1.68431 q^{67} +2.57631 q^{68} -9.37289 q^{69} -6.95546 q^{70} -10.0101 q^{71} +7.35203 q^{72} +11.8757 q^{73} -10.5965 q^{74} +13.6858 q^{75} -1.02684 q^{76} +5.55852 q^{77} -4.47291 q^{78} -15.1952 q^{79} -15.8491 q^{80} -3.17091 q^{81} +17.2473 q^{82} -6.03647 q^{83} +3.50876 q^{84} +7.95417 q^{85} -12.3118 q^{86} -6.73013 q^{87} +7.46288 q^{88} +2.68077 q^{89} -23.9508 q^{90} +1.19650 q^{91} -3.55187 q^{92} -2.31761 q^{93} -20.0106 q^{94} -3.17028 q^{95} +14.3924 q^{96} +4.41596 q^{97} +9.41177 q^{98} +19.1405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + 11 q^{2} + 95 q^{4} + 15 q^{5} + 23 q^{6} + 19 q^{7} + 30 q^{8} + 101 q^{9}+O(q^{10}) \) 83 * q + 11 * q^2 + 95 * q^4 + 15 * q^5 + 23 * q^6 + 19 * q^7 + 30 * q^8 + 101 * q^9	\( 83 q + 11 q^{2} + 95 q^{4} + 15 q^{5} + 23 q^{6} + 19 q^{7} + 30 q^{8} + 101 q^{9} + 9 q^{10} + 56 q^{11} - 2 q^{12} - 5 q^{13} + 6 q^{14} + 19 q^{15} + 123 q^{16} + 19 q^{17} + 40 q^{18} - 83 q^{19} + 49 q^{20} + 9 q^{21} + 18 q^{22} + 74 q^{23} + 38 q^{24} + 98 q^{25} + 28 q^{26} + 6 q^{27} + 50 q^{28} + 16 q^{29} + 56 q^{30} + 24 q^{31} + 81 q^{32} + 13 q^{33} + 9 q^{34} + 71 q^{35} + 156 q^{36} - 6 q^{37} - 11 q^{38} + 126 q^{39} + q^{40} - q^{42} + 34 q^{43} + 140 q^{44} + 42 q^{45} + 34 q^{46} + 53 q^{47} + 16 q^{48} + 118 q^{49} + 51 q^{50} + 57 q^{51} + 32 q^{52} + q^{53} + 53 q^{54} + 60 q^{55} - 2 q^{56} - 2 q^{58} + 44 q^{59} - 9 q^{60} + 21 q^{61} + 28 q^{62} + 83 q^{63} + 154 q^{64} + 44 q^{65} + 17 q^{66} + 5 q^{67} + 63 q^{68} - 36 q^{69} - 48 q^{70} + 193 q^{71} + 135 q^{72} + 54 q^{73} + 127 q^{74} + 5 q^{75} - 95 q^{76} + 54 q^{77} + 45 q^{78} + 54 q^{79} + 45 q^{80} + 147 q^{81} - 35 q^{82} + 84 q^{83} + 12 q^{84} + 28 q^{85} + 60 q^{86} + 51 q^{87} + 23 q^{88} - 24 q^{89} + 31 q^{90} + 28 q^{91} + 108 q^{92} + 39 q^{93} - 49 q^{94} - 15 q^{95} + 25 q^{96} - 22 q^{97} - 67 q^{98} + 132 q^{99}+O(q^{100}) \) 83 * q + 11 * q^2 + 95 * q^4 + 15 * q^5 + 23 * q^6 + 19 * q^7 + 30 * q^8 + 101 * q^9 + 9 * q^10 + 56 * q^11 - 2 * q^12 - 5 * q^13 + 6 * q^14 + 19 * q^15 + 123 * q^16 + 19 * q^17 + 40 * q^18 - 83 * q^19 + 49 * q^20 + 9 * q^21 + 18 * q^22 + 74 * q^23 + 38 * q^24 + 98 * q^25 + 28 * q^26 + 6 * q^27 + 50 * q^28 + 16 * q^29 + 56 * q^30 + 24 * q^31 + 81 * q^32 + 13 * q^33 + 9 * q^34 + 71 * q^35 + 156 * q^36 - 6 * q^37 - 11 * q^38 + 126 * q^39 + q^40 - q^42 + 34 * q^43 + 140 * q^44 + 42 * q^45 + 34 * q^46 + 53 * q^47 + 16 * q^48 + 118 * q^49 + 51 * q^50 + 57 * q^51 + 32 * q^52 + q^53 + 53 * q^54 + 60 * q^55 - 2 * q^56 - 2 * q^58 + 44 * q^59 - 9 * q^60 + 21 * q^61 + 28 * q^62 + 83 * q^63 + 154 * q^64 + 44 * q^65 + 17 * q^66 + 5 * q^67 + 63 * q^68 - 36 * q^69 - 48 * q^70 + 193 * q^71 + 135 * q^72 + 54 * q^73 + 127 * q^74 + 5 * q^75 - 95 * q^76 + 54 * q^77 + 45 * q^78 + 54 * q^79 + 45 * q^80 + 147 * q^81 - 35 * q^82 + 84 * q^83 + 12 * q^84 + 28 * q^85 + 60 * q^86 + 51 * q^87 + 23 * q^88 - 24 * q^89 + 31 * q^90 + 28 * q^91 + 108 * q^92 + 39 * q^93 - 49 * q^94 - 15 * q^95 + 25 * q^96 - 22 * q^97 - 67 * q^98 + 132 * q^99

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