LMFDB - Embedded newform 2011.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, 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("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$0$
Dimension:	$90$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30849 q^{2} -0.566470 q^{3} +3.32914 q^{4} -0.195371 q^{5} +1.30769 q^{6} +0.321334 q^{7} -3.06830 q^{8} -2.67911 q^{9} +O(q^{10})$	\(q-2.30849 q^{2} -0.566470 q^{3} +3.32914 q^{4} -0.195371 q^{5} +1.30769 q^{6} +0.321334 q^{7} -3.06830 q^{8} -2.67911 q^{9} +0.451012 q^{10} -0.682754 q^{11} -1.88585 q^{12} -5.37242 q^{13} -0.741798 q^{14} +0.110672 q^{15} +0.424875 q^{16} -5.61707 q^{17} +6.18471 q^{18} -5.00509 q^{19} -0.650416 q^{20} -0.182026 q^{21} +1.57613 q^{22} +7.60476 q^{23} +1.73810 q^{24} -4.96183 q^{25} +12.4022 q^{26} +3.21704 q^{27} +1.06977 q^{28} -9.23781 q^{29} -0.255485 q^{30} +7.47333 q^{31} +5.15578 q^{32} +0.386760 q^{33} +12.9670 q^{34} -0.0627794 q^{35} -8.91913 q^{36} -3.35337 q^{37} +11.5542 q^{38} +3.04332 q^{39} +0.599456 q^{40} +7.53217 q^{41} +0.420206 q^{42} +7.23643 q^{43} -2.27298 q^{44} +0.523420 q^{45} -17.5555 q^{46} +0.977337 q^{47} -0.240679 q^{48} -6.89674 q^{49} +11.4543 q^{50} +3.18190 q^{51} -17.8855 q^{52} -8.95168 q^{53} -7.42652 q^{54} +0.133390 q^{55} -0.985951 q^{56} +2.83523 q^{57} +21.3254 q^{58} +2.09272 q^{59} +0.368441 q^{60} +15.1550 q^{61} -17.2521 q^{62} -0.860891 q^{63} -12.7518 q^{64} +1.04961 q^{65} -0.892831 q^{66} +5.57384 q^{67} -18.7000 q^{68} -4.30787 q^{69} +0.144926 q^{70} +2.86789 q^{71} +8.22032 q^{72} -11.2635 q^{73} +7.74122 q^{74} +2.81073 q^{75} -16.6626 q^{76} -0.219392 q^{77} -7.02547 q^{78} -0.709340 q^{79} -0.0830081 q^{80} +6.21498 q^{81} -17.3880 q^{82} +10.3449 q^{83} -0.605990 q^{84} +1.09741 q^{85} -16.7052 q^{86} +5.23294 q^{87} +2.09489 q^{88} +4.90867 q^{89} -1.20831 q^{90} -1.72634 q^{91} +25.3173 q^{92} -4.23341 q^{93} -2.25618 q^{94} +0.977849 q^{95} -2.92059 q^{96} -16.8172 q^{97} +15.9211 q^{98} +1.82917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) $ 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.30849	−1.63235	−0.816175	−	0.577804i	$-0.803910\pi$
$2$	−2.30849	−1.63235	−0.816175	+	0.577804i	$0.803910\pi$
$3$	−0.566470	−0.327051	−0.163526	−	0.986539i	$-0.552287\pi$
$3$	−0.566470	−0.327051	−0.163526	+	0.986539i	$0.552287\pi$
$4$	3.32914	1.66457
$5$	−0.195371	−0.0873725	−0.0436862	−	0.999045i	$-0.513910\pi$
$5$	−0.195371	−0.0873725	−0.0436862	+	0.999045i	$0.513910\pi$
$6$	1.30769	0.533863
$7$	0.321334	0.121453	0.0607265	−	0.998154i	$-0.480658\pi$
$7$	0.321334	0.121453	0.0607265	+	0.998154i	$0.480658\pi$
$8$	−3.06830	−1.08481
$9$	−2.67911	−0.893037
$10$	0.451012	0.142623
$11$	−0.682754	−0.205858	−0.102929	−	0.994689i	$-0.532821\pi$
$11$	−0.682754	−0.205858	−0.102929	+	0.994689i	$0.532821\pi$
$12$	−1.88585	−0.544399
$13$	−5.37242	−1.49004	−0.745021	−	0.667041i	$-0.767561\pi$
$13$	−5.37242	−1.49004	−0.745021	+	0.667041i	$0.767561\pi$
$14$	−0.741798	−0.198254
$15$	0.110672	0.0285753
$16$	0.424875	0.106219
$17$	−5.61707	−1.36234	−0.681169	−	0.732126i	$-0.738528\pi$
$17$	−5.61707	−1.36234	−0.681169	+	0.732126i	$0.738528\pi$
$18$	6.18471	1.45775
$19$	−5.00509	−1.14825	−0.574123	−	0.818769i	$-0.694657\pi$
$19$	−5.00509	−1.14825	−0.574123	+	0.818769i	$0.694657\pi$
$20$	−0.650416	−0.145437
$21$	−0.182026	−0.0397214
$22$	1.57613	0.336033
$23$	7.60476	1.58570	0.792851	−	0.609415i	$-0.208596\pi$
$23$	7.60476	1.58570	0.792851	+	0.609415i	$0.208596\pi$
$24$	1.73810	0.354788
$25$	−4.96183	−0.992366
$26$	12.4022	2.43227
$27$	3.21704	0.619121
$28$	1.06977	0.202167
$29$	−9.23781	−1.71542	−0.857709	−	0.514135i	$-0.828113\pi$
$29$	−9.23781	−1.71542	−0.857709	+	0.514135i	$0.828113\pi$
$30$	−0.255485	−0.0466449
$31$	7.47333	1.34225	0.671124	−	0.741345i	$-0.265812\pi$
$31$	7.47333	1.34225	0.671124	+	0.741345i	$0.265812\pi$
$32$	5.15578	0.911422
$33$	0.386760	0.0673262
$34$	12.9670	2.22381
$35$	−0.0627794	−0.0106117
$36$	−8.91913	−1.48652
$37$	−3.35337	−0.551290	−0.275645	−	0.961260i	$-0.588891\pi$
$37$	−3.35337	−0.551290	−0.275645	+	0.961260i	$0.588891\pi$
$38$	11.5542	1.87434
$39$	3.04332	0.487320
$40$	0.599456	0.0947824
$41$	7.53217	1.17633	0.588164	−	0.808742i	$-0.299851\pi$
$41$	7.53217	1.17633	0.588164	+	0.808742i	$0.299851\pi$
$42$	0.420206	0.0648392
$43$	7.23643	1.10355	0.551773	−	0.833995i	$-0.313952\pi$
$43$	7.23643	1.10355	0.551773	+	0.833995i	$0.313952\pi$
$44$	−2.27298	−0.342665
$45$	0.523420	0.0780269
$46$	−17.5555	−2.58842
$47$	0.977337	0.142559	0.0712797	−	0.997456i	$-0.477292\pi$
$47$	0.977337	0.142559	0.0712797	+	0.997456i	$0.477292\pi$
$48$	−0.240679	−0.0347390
$49$	−6.89674	−0.985249
$50$	11.4543	1.61989
$51$	3.18190	0.445555
$52$	−17.8855	−2.48028
$53$	−8.95168	−1.22961	−0.614804	−	0.788680i	$-0.710765\pi$
$53$	−8.95168	−1.22961	−0.614804	+	0.788680i	$0.710765\pi$
$54$	−7.42652	−1.01062
$55$	0.133390	0.0179863
$56$	−0.985951	−0.131753
$57$	2.83523	0.375536
$58$	21.3254	2.80016
$59$	2.09272	0.272449	0.136224	−	0.990678i	$-0.456503\pi$
$59$	2.09272	0.272449	0.136224	+	0.990678i	$0.456503\pi$
$60$	0.368441	0.0475655
$61$	15.1550	1.94040	0.970199	−	0.242311i	$-0.0779055\pi$
$61$	15.1550	1.94040	0.970199	+	0.242311i	$0.0779055\pi$
$62$	−17.2521	−2.19102
$63$	−0.860891	−0.108462
$64$	−12.7518	−1.59398
$65$	1.04961	0.130189
$66$	−0.892831	−0.109900
$67$	5.57384	0.680953	0.340477	−	0.940253i	$-0.389412\pi$
$67$	5.57384	0.680953	0.340477	+	0.940253i	$0.389412\pi$
$68$	−18.7000	−2.26771
$69$	−4.30787	−0.518606
$70$	0.144926	0.0173219
$71$	2.86789	0.340356	0.170178	−	0.985413i	$-0.445566\pi$
$71$	2.86789	0.340356	0.170178	+	0.985413i	$0.445566\pi$
$72$	8.22032	0.968774
$73$	−11.2635	−1.31829	−0.659145	−	0.752016i	$-0.729082\pi$
$73$	−11.2635	−1.31829	−0.659145	+	0.752016i	$0.729082\pi$
$74$	7.74122	0.899899
$75$	2.81073	0.324555
$76$	−16.6626	−1.91134
$77$	−0.219392	−0.0250021
$78$	−7.02547	−0.795478
$79$	−0.709340	−0.0798069	−0.0399035	−	0.999204i	$-0.512705\pi$
$79$	−0.709340	−0.0798069	−0.0399035	+	0.999204i	$0.512705\pi$
$80$	−0.0830081	−0.00928059
$81$	6.21498	0.690553
$82$	−17.3880	−1.92018
$83$	10.3449	1.13550	0.567752	−	0.823200i	$-0.307813\pi$
$83$	10.3449	1.13550	0.567752	+	0.823200i	$0.307813\pi$
$84$	−0.605990	−0.0661189
$85$	1.09741	0.119031
$86$	−16.7052	−1.80137
$87$	5.23294	0.561030
$88$	2.09489	0.223317
$89$	4.90867	0.520318	0.260159	−	0.965566i	$-0.416225\pi$
$89$	4.90867	0.520318	0.260159	+	0.965566i	$0.416225\pi$
$90$	−1.20831	−0.127367
$91$	−1.72634	−0.180970
$92$	25.3173	2.63951
$93$	−4.23341	−0.438984
$94$	−2.25618	−0.232707
$95$	0.977849	0.100325
$96$	−2.92059	−0.298082
$97$	−16.8172	−1.70753	−0.853765	−	0.520658i	$-0.825687\pi$
$97$	−16.8172	−1.70753	−0.853765	+	0.520658i	$0.825687\pi$
$98$	15.9211	1.60827
$99$	1.82917	0.183839
$100$	−16.5186	−1.65186
$101$	4.73479	0.471129	0.235565	−	0.971859i	$-0.424306\pi$
$101$	4.73479	0.471129	0.235565	+	0.971859i	$0.424306\pi$
$102$	−7.34539	−0.727302
$103$	−14.9328	−1.47138	−0.735688	−	0.677320i	$-0.763141\pi$
$103$	−14.9328	−1.47138	−0.735688	+	0.677320i	$0.763141\pi$
$104$	16.4842	1.61641
$105$	0.0355626	0.00347056
$106$	20.6649	2.00715
$107$	2.14452	0.207319	0.103659	−	0.994613i	$-0.466945\pi$
$107$	2.14452	0.207319	0.103659	+	0.994613i	$0.466945\pi$
$108$	10.7100	1.03057
$109$	5.55899	0.532455	0.266227	−	0.963910i	$-0.414223\pi$
$109$	5.55899	0.532455	0.266227	+	0.963910i	$0.414223\pi$
$110$	−0.307930	−0.0293600
$111$	1.89958	0.180300
$112$	0.136527	0.0129006
$113$	9.86875	0.928374	0.464187	−	0.885737i	$-0.346347\pi$
$113$	9.86875	0.928374	0.464187	+	0.885737i	$0.346347\pi$
$114$	−6.54511	−0.613006
$115$	−1.48575	−0.138547
$116$	−30.7539	−2.85543
$117$	14.3933	1.33066
$118$	−4.83103	−0.444732
$119$	−1.80496	−0.165460
$120$	−0.339574	−0.0309987
$121$	−10.5338	−0.957622
$122$	−34.9852	−3.16741
$123$	−4.26675	−0.384720
$124$	24.8797	2.23426
$125$	1.94625	0.174078
$126$	1.98736	0.177048
$127$	−17.2187	−1.52791	−0.763957	−	0.645267i	$-0.776746\pi$
$127$	−17.2187	−1.52791	−0.763957	+	0.645267i	$0.776746\pi$
$128$	19.1259	1.69051
$129$	−4.09922	−0.360916
$130$	−2.42303	−0.212514
$131$	12.3035	1.07496	0.537479	−	0.843277i	$-0.319377\pi$
$131$	12.3035	1.07496	0.537479	+	0.843277i	$0.319377\pi$
$132$	1.28758	0.112069
$133$	−1.60831	−0.139458
$134$	−12.8672	−1.11155
$135$	−0.628517	−0.0540941
$136$	17.2348	1.47788
$137$	2.76652	0.236360	0.118180	−	0.992992i	$-0.462294\pi$
$137$	2.76652	0.236360	0.118180	+	0.992992i	$0.462294\pi$
$138$	9.94468	0.846547
$139$	1.74002	0.147586	0.0737931	−	0.997274i	$-0.476490\pi$
$139$	1.74002	0.147586	0.0737931	+	0.997274i	$0.476490\pi$
$140$	−0.209001	−0.0176638
$141$	−0.553632	−0.0466242
$142$	−6.62049	−0.555580
$143$	3.66804	0.306737
$144$	−1.13829	−0.0948572
$145$	1.80480	0.149880
$146$	26.0016	2.15191
$147$	3.90680	0.322227
$148$	−11.1638	−0.917660
$149$	5.95675	0.487996	0.243998	−	0.969776i	$-0.421541\pi$
$149$	5.95675	0.487996	0.243998	+	0.969776i	$0.421541\pi$
$150$	−6.48854	−0.529787
$151$	18.8745	1.53598	0.767991	−	0.640460i	$-0.221256\pi$
$151$	18.8745	1.53598	0.767991	+	0.640460i	$0.221256\pi$
$152$	15.3571	1.24563
$153$	15.0487	1.21662
$154$	0.506466	0.0408122
$155$	−1.46007	−0.117276
$156$	10.1316	0.811178
$157$	−9.43744	−0.753189	−0.376595	−	0.926378i	$-0.622905\pi$
$157$	−9.43744	−0.753189	−0.376595	+	0.926378i	$0.622905\pi$
$158$	1.63750	0.130273
$159$	5.07085	0.402145
$160$	−1.00729	−0.0796332
$161$	2.44367	0.192588
$162$	−14.3472	−1.12722
$163$	−17.2919	−1.35440	−0.677202	−	0.735797i	$-0.736808\pi$
$163$	−17.2919	−1.35440	−0.677202	+	0.735797i	$0.736808\pi$
$164$	25.0756	1.95808
$165$	−0.0755615	−0.00588246
$166$	−23.8812	−1.85354
$167$	10.6006	0.820300	0.410150	−	0.912018i	$-0.365476\pi$
$167$	10.6006	0.820300	0.410150	+	0.912018i	$0.365476\pi$
$168$	0.558511	0.0430901
$169$	15.8629	1.22023
$170$	−2.53336	−0.194300
$171$	13.4092	1.02543
$172$	24.0911	1.83693
$173$	4.81552	0.366117	0.183059	−	0.983102i	$-0.441400\pi$
$173$	4.81552	0.366117	0.183059	+	0.983102i	$0.441400\pi$
$174$	−12.0802	−0.915798
$175$	−1.59441	−0.120526
$176$	−0.290085	−0.0218660
$177$	−1.18546	−0.0891048
$178$	−11.3316	−0.849341
$179$	17.0195	1.27210	0.636049	−	0.771648i	$-0.280567\pi$
$179$	17.0195	1.27210	0.636049	+	0.771648i	$0.280567\pi$
$180$	1.74254	0.129881
$181$	2.95111	0.219354	0.109677	−	0.993967i	$-0.465018\pi$
$181$	2.95111	0.219354	0.109677	+	0.993967i	$0.465018\pi$
$182$	3.98525	0.295407
$183$	−8.58484	−0.634610
$184$	−23.3337	−1.72018
$185$	0.655150	0.0481676
$186$	9.77280	0.716576
$187$	3.83508	0.280448
$188$	3.25369	0.237300
$189$	1.03375	0.0751941
$190$	−2.25736	−0.163766
$191$	−7.95303	−0.575461	−0.287731	−	0.957711i	$-0.592901\pi$
$191$	−7.95303	−0.575461	−0.287731	+	0.957711i	$0.592901\pi$
$192$	7.22352	0.521313
$193$	16.4180	1.18179	0.590896	−	0.806748i	$-0.298774\pi$
$193$	16.4180	1.18179	0.590896	+	0.806748i	$0.298774\pi$
$194$	38.8224	2.78729
$195$	−0.594575	−0.0425784
$196$	−22.9602	−1.64001
$197$	10.1981	0.726584	0.363292	−	0.931675i	$-0.381653\pi$
$197$	10.1981	0.726584	0.363292	+	0.931675i	$0.381653\pi$
$198$	−4.22264	−0.300090
$199$	−19.1334	−1.35633	−0.678166	−	0.734909i	$-0.737225\pi$
$199$	−19.1334	−1.35633	−0.678166	+	0.734909i	$0.737225\pi$
$200$	15.2244	1.07653
$201$	−3.15741	−0.222707
$202$	−10.9302	−0.769048
$203$	−2.96843	−0.208343
$204$	10.5930	0.741656
$205$	−1.47157	−0.102779
$206$	34.4724	2.40180
$207$	−20.3740	−1.41609
$208$	−2.28261	−0.158270
$209$	3.41725	0.236376
$210$	−0.0820960	−0.00566516
$211$	13.4268	0.924340	0.462170	−	0.886791i	$-0.347071\pi$
$211$	13.4268	0.924340	0.462170	+	0.886791i	$0.347071\pi$
$212$	−29.8013	−2.04676
$213$	−1.62457	−0.111314
$214$	−4.95061	−0.338417
$215$	−1.41379	−0.0964195
$216$	−9.87086	−0.671627
$217$	2.40144	0.163020
$218$	−12.8329	−0.869153
$219$	6.38042	0.431149
$220$	0.444074	0.0299395
$221$	30.1773	2.02994
$222$	−4.38517	−0.294313
$223$	5.49153	0.367740	0.183870	−	0.982951i	$-0.441137\pi$
$223$	5.49153	0.367740	0.183870	+	0.982951i	$0.441137\pi$
$224$	1.65673	0.110695
$225$	13.2933	0.886220
$226$	−22.7819	−1.51543
$227$	7.69907	0.511005	0.255502	−	0.966808i	$-0.417759\pi$
$227$	7.69907	0.511005	0.255502	+	0.966808i	$0.417759\pi$
$228$	9.43888	0.625105
$229$	−12.9060	−0.852855	−0.426427	−	0.904522i	$-0.640228\pi$
$229$	−12.9060	−0.852855	−0.426427	+	0.904522i	$0.640228\pi$
$230$	3.42984	0.226157
$231$	0.124279	0.00817697
$232$	28.3444	1.86090
$233$	6.65364	0.435895	0.217947	−	0.975961i	$-0.430064\pi$
$233$	6.65364	0.435895	0.217947	+	0.975961i	$0.430064\pi$
$234$	−33.2269	−2.17211
$235$	−0.190943	−0.0124558
$236$	6.96695	0.453510
$237$	0.401819	0.0261010
$238$	4.16673	0.270089
$239$	11.6387	0.752848	0.376424	−	0.926448i	$-0.377154\pi$
$239$	11.6387	0.752848	0.376424	+	0.926448i	$0.377154\pi$
$240$	0.0470216	0.00303523
$241$	17.0581	1.09881	0.549405	−	0.835556i	$-0.314854\pi$
$241$	17.0581	1.09881	0.549405	+	0.835556i	$0.314854\pi$
$242$	24.3173	1.56318
$243$	−13.1717	−0.844967
$244$	50.4530	3.22992
$245$	1.34742	0.0860837
$246$	9.84975	0.627997
$247$	26.8895	1.71094
$248$	−22.9304	−1.45608
$249$	−5.86009	−0.371368
$250$	−4.49290	−0.284156
$251$	4.44961	0.280857	0.140428	−	0.990091i	$-0.455152\pi$
$251$	4.44961	0.280857	0.140428	+	0.990091i	$0.455152\pi$
$252$	−2.86602	−0.180543
$253$	−5.19218	−0.326430
$254$	39.7493	2.49409
$255$	−0.621650	−0.0389292
$256$	−18.6484	−1.16553
$257$	−6.45486	−0.402643	−0.201321	−	0.979525i	$-0.564524\pi$
$257$	−6.45486	−0.402643	−0.201321	+	0.979525i	$0.564524\pi$
$258$	9.46302	0.589142
$259$	−1.07755	−0.0669558
$260$	3.49431	0.216708
$261$	24.7491	1.53193
$262$	−28.4024	−1.75471
$263$	−23.9364	−1.47598	−0.737989	−	0.674812i	$-0.764225\pi$
$263$	−23.9364	−1.47598	−0.737989	+	0.674812i	$0.764225\pi$
$264$	−1.18669	−0.0730360
$265$	1.74890	0.107434
$266$	3.71277	0.227644
$267$	−2.78061	−0.170171
$268$	18.5561	1.13349
$269$	24.1850	1.47459	0.737294	−	0.675572i	$-0.236103\pi$
$269$	24.1850	1.47459	0.737294	+	0.675572i	$0.236103\pi$
$270$	1.45093	0.0883005
$271$	7.58101	0.460514	0.230257	−	0.973130i	$-0.426043\pi$
$271$	7.58101	0.460514	0.230257	+	0.973130i	$0.426043\pi$
$272$	−2.38655	−0.144706
$273$	0.977922	0.0591865
$274$	−6.38650	−0.385823
$275$	3.38771	0.204287
$276$	−14.3415	−0.863255
$277$	19.6143	1.17851	0.589255	−	0.807947i	$-0.299421\pi$
$277$	19.6143	1.17851	0.589255	+	0.807947i	$0.299421\pi$
$278$	−4.01681	−0.240912
$279$	−20.0219	−1.19868
$280$	0.192626	0.0115116
$281$	4.13150	0.246464	0.123232	−	0.992378i	$-0.460674\pi$
$281$	4.13150	0.246464	0.123232	+	0.992378i	$0.460674\pi$
$282$	1.27806	0.0761071
$283$	27.2059	1.61722	0.808610	−	0.588345i	$-0.200220\pi$
$283$	27.2059	1.61722	0.808610	+	0.588345i	$0.200220\pi$
$284$	9.54759	0.566545
$285$	−0.553922	−0.0328115
$286$	−8.46765	−0.500703
$287$	2.42035	0.142869
$288$	−13.8129	−0.813934
$289$	14.5514	0.855966
$290$	−4.16636	−0.244657
$291$	9.52645	0.558450
$292$	−37.4976	−2.19438
$293$	−20.6950	−1.20902	−0.604508	−	0.796599i	$-0.706630\pi$
$293$	−20.6950	−1.20902	−0.604508	+	0.796599i	$0.706630\pi$
$294$	−9.01881	−0.525988
$295$	−0.408856	−0.0238045
$296$	10.2891	0.598044
$297$	−2.19645	−0.127451
$298$	−13.7511	−0.796580
$299$	−40.8560	−2.36276
$300$	9.35729	0.540243
$301$	2.32531	0.134029
$302$	−43.5716	−2.50726
$303$	−2.68211	−0.154083
$304$	−2.12654	−0.121965
$305$	−2.96084	−0.169537
$306$	−34.7399	−1.98595
$307$	28.7540	1.64108	0.820539	−	0.571590i	$-0.193673\pi$
$307$	28.7540	1.64108	0.820539	+	0.571590i	$0.193673\pi$
$308$	−0.730387	−0.0416177
$309$	8.45900	0.481216
$310$	3.37056	0.191435
$311$	−21.9391	−1.24405	−0.622027	−	0.782995i	$-0.713691\pi$
$311$	−21.9391	−1.24405	−0.622027	+	0.782995i	$0.713691\pi$
$312$	−9.33780	−0.528649
$313$	−26.3310	−1.48832	−0.744158	−	0.668003i	$-0.767149\pi$
$313$	−26.3310	−1.48832	−0.744158	+	0.668003i	$0.767149\pi$
$314$	21.7862	1.22947
$315$	0.168193	0.00947660
$316$	−2.36149	−0.132844
$317$	−12.0803	−0.678499	−0.339250	−	0.940696i	$-0.610173\pi$
$317$	−12.0803	−0.678499	−0.339250	+	0.940696i	$0.610173\pi$
$318$	−11.7060	−0.656441
$319$	6.30715	0.353133
$320$	2.49133	0.139270
$321$	−1.21481	−0.0678038
$322$	−5.64120	−0.314372
$323$	28.1139	1.56430
$324$	20.6905	1.14947
$325$	26.6571	1.47867
$326$	39.9182	2.21086
$327$	−3.14900	−0.174140
$328$	−23.1110	−1.27609
$329$	0.314052	0.0173143
$330$	0.174433	0.00960223
$331$	0.676993	0.0372109	0.0186054	−	0.999827i	$-0.494077\pi$
$331$	0.676993	0.0372109	0.0186054	+	0.999827i	$0.494077\pi$
$332$	34.4397	1.89012
$333$	8.98404	0.492323
$334$	−24.4714	−1.33902
$335$	−1.08897	−0.0594966
$336$	−0.0773383	−0.00421915
$337$	−7.31803	−0.398638	−0.199319	−	0.979935i	$-0.563873\pi$
$337$	−7.31803	−0.398638	−0.199319	+	0.979935i	$0.563873\pi$
$338$	−36.6195	−1.99184
$339$	−5.59035	−0.303626
$340$	3.65343	0.198135
$341$	−5.10244	−0.276313
$342$	−30.9550	−1.67386
$343$	−4.46550	−0.241114
$344$	−22.2035	−1.19713
$345$	0.841631	0.0453119
$346$	−11.1166	−0.597632
$347$	−5.49559	−0.295019	−0.147509	−	0.989061i	$-0.547126\pi$
$347$	−5.49559	−0.295019	−0.147509	+	0.989061i	$0.547126\pi$
$348$	17.4212	0.933873
$349$	19.3332	1.03488	0.517441	−	0.855719i	$-0.326885\pi$
$349$	19.3332	1.03488	0.517441	+	0.855719i	$0.326885\pi$
$350$	3.68068	0.196740
$351$	−17.2833	−0.922516
$352$	−3.52013	−0.187624
$353$	−19.8789	−1.05805	−0.529024	−	0.848607i	$-0.677442\pi$
$353$	−19.8789	−1.05805	−0.529024	+	0.848607i	$0.677442\pi$
$354$	2.73663	0.145450
$355$	−0.560301	−0.0297377
$356$	16.3416	0.866104
$357$	1.02245	0.0541140
$358$	−39.2894	−2.07651
$359$	18.9366	0.999437	0.499718	−	0.866188i	$-0.333437\pi$
$359$	18.9366	0.999437	0.499718	+	0.866188i	$0.333437\pi$
$360$	−1.60601	−0.0846442
$361$	6.05095	0.318471
$362$	−6.81262	−0.358063
$363$	5.96710	0.313192
$364$	−5.74724	−0.301237
$365$	2.20055	0.115182
$366$	19.8180	1.03591
$367$	9.50412	0.496111	0.248055	−	0.968746i	$-0.420208\pi$
$367$	9.50412	0.496111	0.248055	+	0.968746i	$0.420208\pi$
$368$	3.23107	0.168431
$369$	−20.1795	−1.05050
$370$	−1.51241	−0.0786264
$371$	−2.87648	−0.149340
$372$	−14.0936	−0.730719
$373$	4.18786	0.216839	0.108420	−	0.994105i	$-0.465421\pi$
$373$	4.18786	0.216839	0.108420	+	0.994105i	$0.465421\pi$
$374$	−8.85324	−0.457790
$375$	−1.10249	−0.0569324
$376$	−2.99876	−0.154649
$377$	49.6294	2.55605
$378$	−2.38640	−0.122743
$379$	4.22306	0.216924	0.108462	−	0.994101i	$-0.465407\pi$
$379$	4.22306	0.216924	0.108462	+	0.994101i	$0.465407\pi$
$380$	3.25539	0.166998
$381$	9.75389	0.499707
$382$	18.3595	0.939354
$383$	−30.6780	−1.56757	−0.783787	−	0.621029i	$-0.786715\pi$
$383$	−30.6780	−1.56757	−0.783787	+	0.621029i	$0.786715\pi$
$384$	−10.8343	−0.552884
$385$	0.0428629	0.00218449
$386$	−37.9008	−1.92910
$387$	−19.3872	−0.985507
$388$	−55.9868	−2.84230
$389$	31.2061	1.58221	0.791106	−	0.611679i	$-0.209506\pi$
$389$	31.2061	1.58221	0.791106	+	0.611679i	$0.209506\pi$
$390$	1.37257	0.0695029
$391$	−42.7165	−2.16026
$392$	21.1613	1.06881
$393$	−6.96953	−0.351566
$394$	−23.5422	−1.18604
$395$	0.138584	0.00697293
$396$	6.08957	0.306013
$397$	14.2862	0.717001	0.358501	−	0.933529i	$-0.383288\pi$
$397$	14.2862	0.717001	0.358501	+	0.933529i	$0.383288\pi$
$398$	44.1693	2.21401
$399$	0.911058	0.0456100
$400$	−2.10816	−0.105408
$401$	−20.5396	−1.02570	−0.512849	−	0.858479i	$-0.671410\pi$
$401$	−20.5396	−1.02570	−0.512849	+	0.858479i	$0.671410\pi$
$402$	7.28886	0.363535
$403$	−40.1499	−2.00001
$404$	15.7628	0.784226
$405$	−1.21423	−0.0603353
$406$	6.85259	0.340088
$407$	2.28952	0.113488
$408$	−9.76302	−0.483341
$409$	−25.0931	−1.24078	−0.620388	−	0.784295i	$-0.713025\pi$
$409$	−25.0931	−1.24078	−0.620388	+	0.784295i	$0.713025\pi$
$410$	3.39710	0.167771
$411$	−1.56715	−0.0773019
$412$	−49.7135	−2.44921
$413$	0.672463	0.0330897
$414$	47.0332	2.31156
$415$	−2.02110	−0.0992117
$416$	−27.6990	−1.35806
$417$	−0.985666	−0.0482683
$418$	−7.88869	−0.385848
$419$	10.5589	0.515838	0.257919	−	0.966166i	$-0.416963\pi$
$419$	10.5589	0.515838	0.257919	+	0.966166i	$0.416963\pi$
$420$	0.118393	0.00577698
$421$	−31.2922	−1.52509	−0.762544	−	0.646936i	$-0.776050\pi$
$421$	−31.2922	−1.52509	−0.762544	+	0.646936i	$0.776050\pi$
$422$	−30.9957	−1.50885
$423$	−2.61840	−0.127311
$424$	27.4664	1.33389
$425$	27.8709	1.35194
$426$	3.75031	0.181703
$427$	4.86982	0.235667
$428$	7.13940	0.345096
$429$	−2.07784	−0.100319
$430$	3.26372	0.157390
$431$	5.35341	0.257865	0.128932	−	0.991653i	$-0.458845\pi$
$431$	5.35341	0.257865	0.128932	+	0.991653i	$0.458845\pi$
$432$	1.36684	0.0657621
$433$	−3.58545	−0.172306	−0.0861530	−	0.996282i	$-0.527457\pi$
$433$	−3.58545	−0.172306	−0.0861530	+	0.996282i	$0.527457\pi$
$434$	−5.54370	−0.266106
$435$	−1.02236	−0.0490186
$436$	18.5066	0.886307
$437$	−38.0625	−1.82078
$438$	−14.7291	−0.703786
$439$	−26.3521	−1.25771	−0.628857	−	0.777521i	$-0.716477\pi$
$439$	−26.3521	−1.25771	−0.628857	+	0.777521i	$0.716477\pi$
$440$	−0.409281	−0.0195117
$441$	18.4772	0.879864
$442$	−69.6640	−3.31358
$443$	−6.57301	−0.312293	−0.156147	−	0.987734i	$-0.549907\pi$
$443$	−6.57301	−0.312293	−0.156147	+	0.987734i	$0.549907\pi$
$444$	6.32396	0.300122
$445$	−0.959010	−0.0454615
$446$	−12.6772	−0.600281
$447$	−3.37432	−0.159600
$448$	−4.09760	−0.193593
$449$	−1.41111	−0.0665944	−0.0332972	−	0.999445i	$-0.510601\pi$
$449$	−1.41111	−0.0665944	−0.0332972	+	0.999445i	$0.510601\pi$
$450$	−30.6875	−1.44662
$451$	−5.14262	−0.242157
$452$	32.8544	1.54534
$453$	−10.6918	−0.502345
$454$	−17.7732	−0.834139
$455$	0.337277	0.0158118
$456$	−8.69935	−0.407384
$457$	−9.74410	−0.455810	−0.227905	−	0.973683i	$-0.573188\pi$
$457$	−9.74410	−0.455810	−0.227905	+	0.973683i	$0.573188\pi$
$458$	29.7935	1.39216
$459$	−18.0704	−0.843452
$460$	−4.94626	−0.230621
$461$	−11.3957	−0.530751	−0.265375	−	0.964145i	$-0.585496\pi$
$461$	−11.3957	−0.530751	−0.265375	+	0.964145i	$0.585496\pi$
$462$	−0.286897	−0.0133477
$463$	−11.2464	−0.522664	−0.261332	−	0.965249i	$-0.584162\pi$
$463$	−11.2464	−0.522664	−0.261332	+	0.965249i	$0.584162\pi$
$464$	−3.92491	−0.182209
$465$	0.827085	0.0383552
$466$	−15.3599	−0.711533
$467$	−26.6275	−1.23217	−0.616087	−	0.787678i	$-0.711283\pi$
$467$	−26.6275	−1.23217	−0.616087	+	0.787678i	$0.711283\pi$
$468$	47.9173	2.21498
$469$	1.79107	0.0827038
$470$	0.440791	0.0203322
$471$	5.34602	0.246332
$472$	−6.42109	−0.295555
$473$	−4.94070	−0.227174
$474$	−0.927597	−0.0426059
$475$	24.8344	1.13948
$476$	−6.00895	−0.275420
$477$	23.9825	1.09809
$478$	−26.8679	−1.22891
$479$	18.9459	0.865658	0.432829	−	0.901476i	$-0.357515\pi$
$479$	18.9459	0.865658	0.432829	+	0.901476i	$0.357515\pi$
$480$	0.570599	0.0260441
$481$	18.0157	0.821445
$482$	−39.3786	−1.79364
$483$	−1.38427	−0.0629863
$484$	−35.0686	−1.59403
$485$	3.28559	0.149191
$486$	30.4068	1.37928
$487$	22.6104	1.02457	0.512287	−	0.858814i	$-0.328798\pi$
$487$	22.6104	1.02457	0.512287	+	0.858814i	$0.328798\pi$
$488$	−46.5000	−2.10496
$489$	9.79533	0.442960
$490$	−3.11051	−0.140519
$491$	37.2841	1.68261	0.841303	−	0.540564i	$-0.181789\pi$
$491$	37.2841	1.68261	0.841303	+	0.540564i	$0.181789\pi$
$492$	−14.2046	−0.640392
$493$	51.8894	2.33698
$494$	−62.0741	−2.79285
$495$	−0.357367	−0.0160625
$496$	3.17523	0.142572
$497$	0.921551	0.0413372
$498$	13.5280	0.606203
$499$	26.7914	1.19935	0.599675	−	0.800244i	$-0.295297\pi$
$499$	26.7914	1.19935	0.599675	+	0.800244i	$0.295297\pi$
$500$	6.47933	0.289765
$501$	−6.00492	−0.268280
$502$	−10.2719	−0.458457
$503$	−15.3630	−0.685002	−0.342501	−	0.939518i	$-0.611274\pi$
$503$	−15.3630	−0.685002	−0.342501	+	0.939518i	$0.611274\pi$
$504$	2.64147	0.117661
$505$	−0.925040	−0.0411637
$506$	11.9861	0.532848
$507$	−8.98587	−0.399077
$508$	−57.3235	−2.54332
$509$	17.8597	0.791617	0.395808	−	0.918333i	$-0.370464\pi$
$509$	17.8597	0.791617	0.395808	+	0.918333i	$0.370464\pi$
$510$	1.43507	0.0635461
$511$	−3.61934	−0.160110
$512$	4.79785	0.212037
$513$	−16.1016	−0.710903
$514$	14.9010	0.657254
$515$	2.91744	0.128558
$516$	−13.6469	−0.600769
$517$	−0.667281	−0.0293470
$518$	2.48752	0.109295
$519$	−2.72785	−0.119739
$520$	−3.22053	−0.141230
$521$	22.7856	0.998256	0.499128	−	0.866528i	$-0.333654\pi$
$521$	22.7856	0.998256	0.499128	+	0.866528i	$0.333654\pi$
$522$	−57.1332	−2.50065
$523$	6.86595	0.300227	0.150113	−	0.988669i	$-0.452036\pi$
$523$	6.86595	0.300227	0.150113	+	0.988669i	$0.452036\pi$
$524$	40.9599	1.78934
$525$	0.903183	0.0394182
$526$	55.2569	2.40931
$527$	−41.9782	−1.82860
$528$	0.164324	0.00715130
$529$	34.8324	1.51445
$530$	−4.03731	−0.175370
$531$	−5.60663	−0.243307
$532$	−5.35428	−0.232137
$533$	−40.4660	−1.75278
$534$	6.41902	0.277778
$535$	−0.418977	−0.0181139
$536$	−17.1022	−0.738703
$537$	−9.64104	−0.416042
$538$	−55.8310	−2.40705
$539$	4.70878	0.202822
$540$	−2.09242	−0.0900433
$541$	−15.2869	−0.657235	−0.328618	−	0.944463i	$-0.606583\pi$
$541$	−15.2869	−0.657235	−0.328618	+	0.944463i	$0.606583\pi$
$542$	−17.5007	−0.751720
$543$	−1.67172	−0.0717402
$544$	−28.9604	−1.24167
$545$	−1.08606	−0.0465219
$546$	−2.25753	−0.0966132
$547$	3.80261	0.162588	0.0812940	−	0.996690i	$-0.474095\pi$
$547$	3.80261	0.162588	0.0812940	+	0.996690i	$0.474095\pi$
$548$	9.21014	0.393438
$549$	−40.6019	−1.73285
$550$	−7.82050	−0.333467
$551$	46.2361	1.96972
$552$	13.2178	0.562588
$553$	−0.227935	−0.00969279
$554$	−45.2795	−1.92374
$555$	−0.371123	−0.0157533
$556$	5.79275	0.245667
$557$	−34.1559	−1.44723	−0.723615	−	0.690203i	$-0.757521\pi$
$557$	−34.1559	−1.44723	−0.723615	+	0.690203i	$0.757521\pi$
$558$	46.2203	1.95666
$559$	−38.8772	−1.64433
$560$	−0.0266734	−0.00112716
$561$	−2.17245	−0.0917211
$562$	−9.53753	−0.402316
$563$	3.28580	0.138480	0.0692401	−	0.997600i	$-0.477943\pi$
$563$	3.28580	0.138480	0.0692401	+	0.997600i	$0.477943\pi$
$564$	−1.84312	−0.0776092
$565$	−1.92807	−0.0811143
$566$	−62.8045	−2.63987
$567$	1.99709	0.0838698
$568$	−8.79954	−0.369220
$569$	−32.7139	−1.37144	−0.685718	−	0.727867i	$-0.740512\pi$
$569$	−32.7139	−1.37144	−0.685718	+	0.727867i	$0.740512\pi$
$570$	1.27872	0.0535599
$571$	4.65776	0.194921	0.0974606	−	0.995239i	$-0.468928\pi$
$571$	4.65776	0.194921	0.0974606	+	0.995239i	$0.468928\pi$
$572$	12.2114	0.510585
$573$	4.50515	0.188205
$574$	−5.58735	−0.233212
$575$	−37.7335	−1.57360
$576$	34.1636	1.42348
$577$	22.6813	0.944236	0.472118	−	0.881535i	$-0.343490\pi$
$577$	22.6813	0.944236	0.472118	+	0.881535i	$0.343490\pi$
$578$	−33.5919	−1.39724
$579$	−9.30029	−0.386507
$580$	6.00842	0.249486
$581$	3.32418	0.137910
$582$	−21.9917	−0.911586
$583$	6.11179	0.253125
$584$	34.5597	1.43009
$585$	−2.81204	−0.116263
$586$	47.7743	1.97354
$587$	36.5398	1.50816	0.754080	−	0.656783i	$-0.228083\pi$
$587$	36.5398	1.50816	0.754080	+	0.656783i	$0.228083\pi$
$588$	13.0063	0.536369
$589$	−37.4047	−1.54123
$590$	0.943842	0.0388573
$591$	−5.77691	−0.237630
$592$	−1.42476	−0.0585573
$593$	21.0255	0.863414	0.431707	−	0.902014i	$-0.357911\pi$
$593$	21.0255	0.863414	0.431707	+	0.902014i	$0.357911\pi$
$594$	5.07049	0.208045
$595$	0.352636	0.0144567
$596$	19.8308	0.812302
$597$	10.8385	0.443590
$598$	94.3158	3.85686
$599$	−0.146092	−0.00596914	−0.00298457	−	0.999996i	$-0.500950\pi$
$599$	−0.146092	−0.00596914	−0.00298457	+	0.999996i	$0.500950\pi$
$600$	−8.62415	−0.352080
$601$	15.8003	0.644508	0.322254	−	0.946653i	$-0.395560\pi$
$601$	15.8003	0.644508	0.322254	+	0.946653i	$0.395560\pi$
$602$	−5.36797	−0.218782
$603$	−14.9329	−0.608117
$604$	62.8357	2.55675
$605$	2.05801	0.0836698
$606$	6.19164	0.251518
$607$	45.5021	1.84687	0.923437	−	0.383751i	$-0.125368\pi$
$607$	45.5021	1.84687	0.923437	+	0.383751i	$0.125368\pi$
$608$	−25.8052	−1.04654
$609$	1.68152	0.0681388
$610$	6.83508	0.276744
$611$	−5.25067	−0.212419
$612$	50.0993	2.02515
$613$	23.7381	0.958774	0.479387	−	0.877604i	$-0.340859\pi$
$613$	23.7381	0.958774	0.479387	+	0.877604i	$0.340859\pi$
$614$	−66.3784	−2.67882
$615$	0.833598	0.0336139
$616$	0.673162	0.0271225
$617$	−45.9319	−1.84915	−0.924574	−	0.381003i	$-0.875579\pi$
$617$	−45.9319	−1.84915	−0.924574	+	0.381003i	$0.875579\pi$
$618$	−19.5275	−0.785513
$619$	−21.3225	−0.857024	−0.428512	−	0.903536i	$-0.640962\pi$
$619$	−21.3225	−0.857024	−0.428512	+	0.903536i	$0.640962\pi$
$620$	−4.86077	−0.195213
$621$	24.4649	0.981741
$622$	50.6464	2.03073
$623$	1.57732	0.0631942
$624$	1.29303	0.0517625
$625$	24.4289	0.977156
$626$	60.7849	2.42945
$627$	−1.93577	−0.0773071
$628$	−31.4185	−1.25374
$629$	18.8361	0.751044
$630$	−0.388272	−0.0154691
$631$	−4.30232	−0.171273	−0.0856364	−	0.996326i	$-0.527292\pi$
$631$	−4.30232	−0.171273	−0.0856364	+	0.996326i	$0.527292\pi$
$632$	2.17647	0.0865752
$633$	−7.60588	−0.302307
$634$	27.8874	1.10755
$635$	3.36404	0.133498
$636$	16.8816	0.669397
$637$	37.0522	1.46806
$638$	−14.5600	−0.576436
$639$	−7.68339	−0.303950
$640$	−3.73665	−0.147704
$641$	21.2997	0.841287	0.420643	−	0.907226i	$-0.361804\pi$
$641$	21.2997	0.841287	0.420643	+	0.907226i	$0.361804\pi$
$642$	2.80437	0.110680
$643$	23.7201	0.935431	0.467716	−	0.883879i	$-0.345077\pi$
$643$	23.7201	0.935431	0.467716	+	0.883879i	$0.345077\pi$
$644$	8.13532	0.320576
$645$	0.800868	0.0315341
$646$	−64.9008	−2.55349
$647$	42.6401	1.67636	0.838178	−	0.545397i	$-0.183621\pi$
$647$	42.6401	1.67636	0.838178	+	0.545397i	$0.183621\pi$
$648$	−19.0694	−0.749117
$649$	−1.42881	−0.0560858
$650$	−61.5376	−2.41370
$651$	−1.36034	−0.0533160
$652$	−57.5670	−2.25450
$653$	−25.0482	−0.980210	−0.490105	−	0.871663i	$-0.663042\pi$
$653$	−25.0482	−0.980210	−0.490105	+	0.871663i	$0.663042\pi$
$654$	7.26944	0.284258
$655$	−2.40373	−0.0939217
$656$	3.20023	0.124948
$657$	30.1761	1.17728
$658$	−0.724987	−0.0282629
$659$	24.8637	0.968553	0.484277	−	0.874915i	$-0.339083\pi$
$659$	24.8637	0.968553	0.484277	+	0.874915i	$0.339083\pi$
$660$	−0.251555	−0.00979175
$661$	−46.0834	−1.79244	−0.896219	−	0.443612i	$-0.853697\pi$
$661$	−46.0834	−1.79244	−0.896219	+	0.443612i	$0.853697\pi$
$662$	−1.56283	−0.0607412
$663$	−17.0945	−0.663895
$664$	−31.7413	−1.23180
$665$	0.314217	0.0121848
$666$	−20.7396	−0.803643
$667$	−70.2514	−2.72014
$668$	35.2909	1.36544
$669$	−3.11079	−0.120270
$670$	2.51387	0.0971192
$671$	−10.3471	−0.399447
$672$	−0.938487	−0.0362029
$673$	−37.8124	−1.45756	−0.728781	−	0.684747i	$-0.759913\pi$
$673$	−37.8124	−1.45756	−0.728781	+	0.684747i	$0.759913\pi$
$674$	16.8936	0.650717
$675$	−15.9624	−0.614394
$676$	52.8099	2.03115
$677$	−41.0039	−1.57591	−0.787953	−	0.615735i	$-0.788859\pi$
$677$	−41.0039	−1.57591	−0.787953	+	0.615735i	$0.788859\pi$
$678$	12.9053	0.495624
$679$	−5.40395	−0.207385
$680$	−3.36719	−0.129126
$681$	−4.36129	−0.167125
$682$	11.7790	0.451039
$683$	18.6865	0.715017	0.357509	−	0.933910i	$-0.383626\pi$
$683$	18.6865	0.715017	0.357509	+	0.933910i	$0.383626\pi$
$684$	44.6411	1.70689
$685$	−0.540498	−0.0206514
$686$	10.3086	0.393583
$687$	7.31088	0.278927
$688$	3.07458	0.117217
$689$	48.0922	1.83217
$690$	−1.94290	−0.0739649
$691$	5.17847	0.196998	0.0984992	−	0.995137i	$-0.468596\pi$
$691$	5.17847	0.196998	0.0984992	+	0.995137i	$0.468596\pi$
$692$	16.0315	0.609427
$693$	0.587777	0.0223278
$694$	12.6865	0.481574
$695$	−0.339948	−0.0128950
$696$	−16.0562	−0.608610
$697$	−42.3087	−1.60256
$698$	−44.6305	−1.68929
$699$	−3.76909	−0.142560
$700$	−5.30800	−0.200623
$701$	−39.3412	−1.48590	−0.742948	−	0.669349i	$-0.766573\pi$
$701$	−39.3412	−1.48590	−0.742948	+	0.669349i	$0.766573\pi$
$702$	39.8984	1.50587
$703$	16.7839	0.633017
$704$	8.70636	0.328133
$705$	0.108164	0.00407367
$706$	45.8903	1.72711
$707$	1.52145	0.0572201
$708$	−3.94657	−0.148321
$709$	−0.322174	−0.0120995	−0.00604975	−	0.999982i	$-0.501926\pi$
$709$	−0.322174	−0.0120995	−0.00604975	+	0.999982i	$0.501926\pi$
$710$	1.29345	0.0485424
$711$	1.90040	0.0712706
$712$	−15.0613	−0.564445
$713$	56.8329	2.12841
$714$	−2.36033	−0.0883330
$715$	−0.716629	−0.0268004
$716$	56.6603	2.11749
$717$	−6.59299	−0.246220
$718$	−43.7150	−1.63143
$719$	−22.5482	−0.840908	−0.420454	−	0.907314i	$-0.638129\pi$
$719$	−22.5482	−0.840908	−0.420454	+	0.907314i	$0.638129\pi$
$720$	0.222388	0.00828791
$721$	−4.79844	−0.178703
$722$	−13.9686	−0.519856
$723$	−9.66291	−0.359368
$724$	9.82465	0.365130
$725$	45.8364	1.70232
$726$	−13.7750	−0.511239
$727$	35.0894	1.30140	0.650698	−	0.759337i	$-0.274477\pi$
$727$	35.0894	1.30140	0.650698	+	0.759337i	$0.274477\pi$
$728$	5.29694	0.196318
$729$	−11.1835	−0.414205
$730$	−5.07996	−0.188018
$731$	−40.6475	−1.50340
$732$	−28.5801	−1.05635
$733$	−3.77067	−0.139273	−0.0696364	−	0.997572i	$-0.522184\pi$
$733$	−3.77067	−0.139273	−0.0696364	+	0.997572i	$0.522184\pi$
$734$	−21.9402	−0.809827
$735$	−0.763274	−0.0281538
$736$	39.2085	1.44524
$737$	−3.80556	−0.140180
$738$	46.5843	1.71479
$739$	−35.6299	−1.31067	−0.655334	−	0.755339i	$-0.727472\pi$
$739$	−35.6299	−1.31067	−0.655334	+	0.755339i	$0.727472\pi$
$740$	2.18108	0.0801782
$741$	−15.2321	−0.559564
$742$	6.64034	0.243774
$743$	16.9846	0.623103	0.311552	−	0.950229i	$-0.399151\pi$
$743$	16.9846	0.623103	0.311552	+	0.950229i	$0.399151\pi$
$744$	12.9894	0.476214
$745$	−1.16377	−0.0426374
$746$	−9.66763	−0.353957
$747$	−27.7152	−1.01405
$748$	12.7675	0.466826
$749$	0.689108	0.0251795
$750$	2.54509	0.0929337
$751$	28.3061	1.03290	0.516452	−	0.856316i	$-0.327252\pi$
$751$	28.3061	1.03290	0.516452	+	0.856316i	$0.327252\pi$
$752$	0.415246	0.0151425
$753$	−2.52057	−0.0918547
$754$	−114.569	−4.17236
$755$	−3.68752	−0.134203
$756$	3.44149	0.125166
$757$	−31.5509	−1.14674	−0.573369	−	0.819297i	$-0.694364\pi$
$757$	−31.5509	−1.14674	−0.573369	+	0.819297i	$0.694364\pi$
$758$	−9.74891	−0.354096
$759$	2.94121	0.106759
$760$	−3.00033	−0.108834
$761$	14.5836	0.528654	0.264327	−	0.964433i	$-0.414850\pi$
$761$	14.5836	0.528654	0.264327	+	0.964433i	$0.414850\pi$
$762$	−22.5168	−0.815697
$763$	1.78630	0.0646683
$764$	−26.4767	−0.957894
$765$	−2.94009	−0.106299
$766$	70.8200	2.55883
$767$	−11.2430	−0.405960
$768$	10.5638	0.381187
$769$	28.1153	1.01386	0.506932	−	0.861986i	$-0.330779\pi$
$769$	28.1153	1.01386	0.506932	+	0.861986i	$0.330779\pi$
$770$	−0.0989486	−0.00356586
$771$	3.65648	0.131685
$772$	54.6577	1.96717
$773$	37.1917	1.33769	0.668847	−	0.743401i	$-0.266788\pi$
$773$	37.1917	1.33769	0.668847	+	0.743401i	$0.266788\pi$
$774$	44.7552	1.60869
$775$	−37.0814	−1.33200
$776$	51.6003	1.85234
$777$	0.610401	0.0218980
$778$	−72.0390	−2.58272
$779$	−37.6992	−1.35071
$780$	−1.97942	−0.0708746
$781$	−1.95806	−0.0700650
$782$	98.6106	3.52631
$783$	−29.7184	−1.06205
$784$	−2.93025	−0.104652
$785$	1.84380	0.0658080
$786$	16.0891	0.573880
$787$	25.8007	0.919697	0.459848	−	0.887997i	$-0.347904\pi$
$787$	25.8007	0.919697	0.459848	+	0.887997i	$0.347904\pi$
$788$	33.9508	1.20945
$789$	13.5592	0.482721
$790$	−0.319921	−0.0113823
$791$	3.17117	0.112754
$792$	−5.61246	−0.199430
$793$	−81.4190	−2.89127
$794$	−32.9795	−1.17040
$795$	−0.990697	−0.0351364
$796$	−63.6978	−2.25771
$797$	27.3230	0.967829	0.483915	−	0.875115i	$-0.339215\pi$
$797$	27.3230	0.967829	0.483915	+	0.875115i	$0.339215\pi$
$798$	−2.10317	−0.0744514
$799$	−5.48977	−0.194214
$800$	−25.5821	−0.904464
$801$	−13.1509	−0.464663
$802$	47.4155	1.67430
$803$	7.69018	0.271381
$804$	−10.5115	−0.370710
$805$	−0.477422	−0.0168269
$806$	92.6857	3.26471
$807$	−13.7001	−0.482266
$808$	−14.5278	−0.511085
$809$	55.2043	1.94088	0.970440	−	0.241344i	$-0.0775881\pi$
$809$	55.2043	1.94088	0.970440	+	0.241344i	$0.0775881\pi$
$810$	2.80303	0.0984884
$811$	14.1298	0.496164	0.248082	−	0.968739i	$-0.420200\pi$
$811$	14.1298	0.496164	0.248082	+	0.968739i	$0.420200\pi$
$812$	−9.88230	−0.346801
$813$	−4.29441	−0.150612
$814$	−5.28535	−0.185251
$815$	3.37833	0.118338
$816$	1.35191	0.0473262
$817$	−36.2190	−1.26714
$818$	57.9273	2.02538
$819$	4.62507	0.161613
$820$	−4.89905	−0.171082
$821$	−30.8385	−1.07627	−0.538136	−	0.842858i	$-0.680871\pi$
$821$	−30.8385	−1.07627	−0.538136	+	0.842858i	$0.680871\pi$
$822$	3.61776	0.126184
$823$	−44.3722	−1.54672	−0.773359	−	0.633968i	$-0.781425\pi$
$823$	−44.3722	−1.54672	−0.773359	+	0.633968i	$0.781425\pi$
$824$	45.8184	1.59616
$825$	−1.91904	−0.0668122
$826$	−1.55238	−0.0540141
$827$	−22.7953	−0.792671	−0.396336	−	0.918106i	$-0.629718\pi$
$827$	−22.7953	−0.792671	−0.396336	+	0.918106i	$0.629718\pi$
$828$	−67.8279	−2.35718
$829$	−5.38083	−0.186884	−0.0934420	−	0.995625i	$-0.529787\pi$
$829$	−5.38083	−0.186884	−0.0934420	+	0.995625i	$0.529787\pi$
$830$	4.66569	0.161948
$831$	−11.1109	−0.385433
$832$	68.5082	2.37510
$833$	38.7395	1.34224
$834$	2.27540	0.0787908
$835$	−2.07105	−0.0716716
$836$	11.3765	0.393464
$837$	24.0420	0.831014
$838$	−24.3752	−0.842029
$839$	18.6847	0.645066	0.322533	−	0.946558i	$-0.395466\pi$
$839$	18.6847	0.645066	0.322533	+	0.946558i	$0.395466\pi$
$840$	−0.109117	−0.00376489
$841$	56.3371	1.94266
$842$	72.2378	2.48948
$843$	−2.34037	−0.0806065
$844$	44.6997	1.53863
$845$	−3.09915	−0.106614
$846$	6.04455	0.207816
$847$	−3.38489	−0.116306
$848$	−3.80334	−0.130607
$849$	−15.4113	−0.528914
$850$	−64.3398	−2.20684
$851$	−25.5016	−0.874182
$852$	−5.40842	−0.185289
$853$	39.8455	1.36428	0.682141	−	0.731221i	$-0.261049\pi$
$853$	39.8455	1.36428	0.682141	+	0.731221i	$0.261049\pi$
$854$	−11.2419	−0.384691
$855$	−2.61977	−0.0895941
$856$	−6.58003	−0.224901
$857$	−14.3158	−0.489019	−0.244510	−	0.969647i	$-0.578627\pi$
$857$	−14.3158	−0.489019	−0.244510	+	0.969647i	$0.578627\pi$
$858$	4.79667	0.163756
$859$	28.1662	0.961019	0.480510	−	0.876989i	$-0.340452\pi$
$859$	28.1662	0.961019	0.480510	+	0.876989i	$0.340452\pi$
$860$	−4.70669	−0.160497
$861$	−1.37105	−0.0467254
$862$	−12.3583	−0.420925
$863$	18.0078	0.612991	0.306496	−	0.951872i	$-0.400844\pi$
$863$	18.0078	0.612991	0.306496	+	0.951872i	$0.400844\pi$
$864$	16.5864	0.564280
$865$	−0.940813	−0.0319886
$866$	8.27699	0.281264
$867$	−8.24294	−0.279945
$868$	7.99471	0.271358
$869$	0.484305	0.0164289
$870$	2.36012	0.0800155
$871$	−29.9450	−1.01465
$872$	−17.0567	−0.577611
$873$	45.0552	1.52489
$874$	87.8671	2.97215
$875$	0.625397	0.0211423
$876$	21.2413	0.717676
$877$	39.1078	1.32058	0.660289	−	0.751012i	$-0.270434\pi$
$877$	39.1078	1.32058	0.660289	+	0.751012i	$0.270434\pi$
$878$	60.8335	2.05303
$879$	11.7231	0.395411
$880$	0.0566741	0.00191048
$881$	−0.696490	−0.0234654	−0.0117327	−	0.999931i	$-0.503735\pi$
$881$	−0.696490	−0.0234654	−0.0117327	+	0.999931i	$0.503735\pi$
$882$	−42.6544	−1.43625
$883$	3.29337	0.110831	0.0554154	−	0.998463i	$-0.482352\pi$
$883$	3.29337	0.110831	0.0554154	+	0.998463i	$0.482352\pi$
$884$	100.464	3.37898
$885$	0.231605	0.00778531
$886$	15.1737	0.509772
$887$	−42.1007	−1.41360	−0.706802	−	0.707412i	$-0.749863\pi$
$887$	−42.1007	−1.41360	−0.706802	+	0.707412i	$0.749863\pi$
$888$	−5.82848	−0.195591
$889$	−5.53297	−0.185570
$890$	2.21387	0.0742090
$891$	−4.24330	−0.142156
$892$	18.2821	0.612129
$893$	−4.89166	−0.163693
$894$	7.78959	0.260523
$895$	−3.32512	−0.111146
$896$	6.14582	0.205317
$897$	23.1437	0.772745
$898$	3.25754	0.108705
$899$	−69.0372	−2.30252
$900$	44.2552	1.47517
$901$	50.2822	1.67514
$902$	11.8717	0.395285
$903$	−1.31722	−0.0438344
$904$	−30.2803	−1.00711
$905$	−0.576561	−0.0191655
$906$	24.6820	0.820003
$907$	9.92883	0.329681	0.164841	−	0.986320i	$-0.447289\pi$
$907$	9.92883	0.329681	0.164841	+	0.986320i	$0.447289\pi$
$908$	25.6312	0.850602
$909$	−12.6850	−0.420736
$910$	−0.778602	−0.0258104
$911$	−20.7239	−0.686615	−0.343307	−	0.939223i	$-0.611547\pi$
$911$	−20.7239	−0.686615	−0.343307	+	0.939223i	$0.611547\pi$
$912$	1.20462	0.0398889
$913$	−7.06304	−0.233753
$914$	22.4942	0.744042
$915$	1.67723	0.0554474
$916$	−42.9659	−1.41963
$917$	3.95352	0.130557
$918$	41.7153	1.37681
$919$	−6.84722	−0.225869	−0.112935	−	0.993602i	$-0.536025\pi$
$919$	−6.84722	−0.225869	−0.112935	+	0.993602i	$0.536025\pi$
$920$	4.55872	0.150297
$921$	−16.2883	−0.536717
$922$	26.3069	0.866371
$923$	−15.4075	−0.507144
$924$	0.413742	0.0136111
$925$	16.6388	0.547082
$926$	25.9622	0.853171
$927$	40.0068	1.31399
$928$	−47.6281	−1.56347
$929$	0.847784	0.0278149	0.0139074	−	0.999903i	$-0.495573\pi$
$929$	0.847784	0.0278149	0.0139074	+	0.999903i	$0.495573\pi$
$930$	−1.90932	−0.0626091
$931$	34.5188	1.13131
$932$	22.1509	0.725576
$933$	12.4279	0.406870
$934$	61.4694	2.01134
$935$	−0.749262	−0.0245035
$936$	−44.1630	−1.44351
$937$	−14.3587	−0.469078	−0.234539	−	0.972107i	$-0.575358\pi$
$937$	−14.3587	−0.469078	−0.234539	+	0.972107i	$0.575358\pi$
$938$	−4.13467	−0.135002
$939$	14.9157	0.486756
$940$	−0.635676	−0.0207335
$941$	4.28701	0.139753	0.0698763	−	0.997556i	$-0.477740\pi$
$941$	4.28701	0.139753	0.0698763	+	0.997556i	$0.477740\pi$
$942$	−12.3412	−0.402100
$943$	57.2804	1.86531
$944$	0.889143	0.0289392
$945$	−0.201964	−0.00656989
$946$	11.4056	0.370827
$947$	31.3072	1.01735	0.508674	−	0.860959i	$-0.330136\pi$
$947$	31.3072	1.01735	0.508674	+	0.860959i	$0.330136\pi$
$948$	1.33771	0.0434468
$949$	60.5121	1.96431
$950$	−57.3301	−1.86003
$951$	6.84315	0.221904
$952$	5.53815	0.179492
$953$	33.4662	1.08408	0.542038	−	0.840354i	$-0.317653\pi$
$953$	33.4662	1.08408	0.542038	+	0.840354i	$0.317653\pi$
$954$	−55.3635	−1.79246
$955$	1.55379	0.0502795
$956$	38.7469	1.25317
$957$	−3.57281	−0.115493
$958$	−43.7364	−1.41306
$959$	0.888980	0.0287067
$960$	−1.41127	−0.0455484
$961$	24.8506	0.801632
$962$	−41.5891	−1.34089
$963$	−5.74541	−0.185143
$964$	56.7888	1.82905
$965$	−3.20759	−0.103256
$966$	3.19557	0.102816
$967$	18.6034	0.598246	0.299123	−	0.954215i	$-0.403306\pi$
$967$	18.6034	0.598246	0.299123	+	0.954215i	$0.403306\pi$
$968$	32.3210	1.03884
$969$	−15.9257	−0.511607
$970$	−7.58477	−0.243532
$971$	−9.11727	−0.292587	−0.146294	−	0.989241i	$-0.546734\pi$
$971$	−9.11727	−0.292587	−0.146294	+	0.989241i	$0.546734\pi$
$972$	−43.8505	−1.40650
$973$	0.559127	0.0179248
$974$	−52.1959	−1.67246
$975$	−15.1004	−0.483600
$976$	6.43897	0.206106
$977$	49.3536	1.57896	0.789481	−	0.613775i	$-0.210350\pi$
$977$	49.3536	1.57896	0.789481	+	0.613775i	$0.210350\pi$
$978$	−22.6124	−0.723066
$979$	−3.35141	−0.107112
$980$	4.48575	0.143292
$981$	−14.8932	−0.475502
$982$	−86.0699	−2.74660
$983$	26.8659	0.856890	0.428445	−	0.903568i	$-0.359062\pi$
$983$	26.8659	0.856890	0.428445	+	0.903568i	$0.359062\pi$
$984$	13.0917	0.417347
$985$	−1.99241	−0.0634834
$986$	−119.786	−3.81477
$987$	−0.177901	−0.00566265
$988$	89.5187	2.84797
$989$	55.0313	1.74989
$990$	0.824980	0.0262196
$991$	25.0525	0.795819	0.397909	−	0.917425i	$-0.369736\pi$
$991$	25.0525	0.795819	0.397909	+	0.917425i	$0.369736\pi$
$992$	38.5308	1.22335
$993$	−0.383496	−0.0121699
$994$	−2.12739	−0.0674768
$995$	3.73811	0.118506
$996$	−19.5090	−0.618167
$997$	−16.9691	−0.537417	−0.268708	−	0.963222i	$-0.586597\pi$
$997$	−16.9691	−0.537417	−0.268708	+	0.963222i	$0.586597\pi$
$998$	−61.8478	−1.95776
$999$	−10.7879	−0.341315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.b.1.10	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.b.1.10	✓	90	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30849 q^{2} -0.566470 q^{3} +3.32914 q^{4} -0.195371 q^{5} +1.30769 q^{6} +0.321334 q^{7} -3.06830 q^{8} -2.67911 q^{9} +O(q^{10})\)	\(q-2.30849 q^{2} -0.566470 q^{3} +3.32914 q^{4} -0.195371 q^{5} +1.30769 q^{6} +0.321334 q^{7} -3.06830 q^{8} -2.67911 q^{9} +0.451012 q^{10} -0.682754 q^{11} -1.88585 q^{12} -5.37242 q^{13} -0.741798 q^{14} +0.110672 q^{15} +0.424875 q^{16} -5.61707 q^{17} +6.18471 q^{18} -5.00509 q^{19} -0.650416 q^{20} -0.182026 q^{21} +1.57613 q^{22} +7.60476 q^{23} +1.73810 q^{24} -4.96183 q^{25} +12.4022 q^{26} +3.21704 q^{27} +1.06977 q^{28} -9.23781 q^{29} -0.255485 q^{30} +7.47333 q^{31} +5.15578 q^{32} +0.386760 q^{33} +12.9670 q^{34} -0.0627794 q^{35} -8.91913 q^{36} -3.35337 q^{37} +11.5542 q^{38} +3.04332 q^{39} +0.599456 q^{40} +7.53217 q^{41} +0.420206 q^{42} +7.23643 q^{43} -2.27298 q^{44} +0.523420 q^{45} -17.5555 q^{46} +0.977337 q^{47} -0.240679 q^{48} -6.89674 q^{49} +11.4543 q^{50} +3.18190 q^{51} -17.8855 q^{52} -8.95168 q^{53} -7.42652 q^{54} +0.133390 q^{55} -0.985951 q^{56} +2.83523 q^{57} +21.3254 q^{58} +2.09272 q^{59} +0.368441 q^{60} +15.1550 q^{61} -17.2521 q^{62} -0.860891 q^{63} -12.7518 q^{64} +1.04961 q^{65} -0.892831 q^{66} +5.57384 q^{67} -18.7000 q^{68} -4.30787 q^{69} +0.144926 q^{70} +2.86789 q^{71} +8.22032 q^{72} -11.2635 q^{73} +7.74122 q^{74} +2.81073 q^{75} -16.6626 q^{76} -0.219392 q^{77} -7.02547 q^{78} -0.709340 q^{79} -0.0830081 q^{80} +6.21498 q^{81} -17.3880 q^{82} +10.3449 q^{83} -0.605990 q^{84} +1.09741 q^{85} -16.7052 q^{86} +5.23294 q^{87} +2.09489 q^{88} +4.90867 q^{89} -1.20831 q^{90} -1.72634 q^{91} +25.3173 q^{92} -4.23341 q^{93} -2.25618 q^{94} +0.977849 q^{95} -2.92059 q^{96} -16.8172 q^{97} +15.9211 q^{98} +1.82917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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