LMFDB - Embedded newform 6019.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44907 q^{2} -1.63543 q^{3} +3.99796 q^{4} -2.35876 q^{5} +4.00528 q^{6} +1.29431 q^{7} -4.89316 q^{8} -0.325384 q^{9} +O(q^{10})$	\(q-2.44907 q^{2} -1.63543 q^{3} +3.99796 q^{4} -2.35876 q^{5} +4.00528 q^{6} +1.29431 q^{7} -4.89316 q^{8} -0.325384 q^{9} +5.77678 q^{10} -3.10658 q^{11} -6.53837 q^{12} +1.00000 q^{13} -3.16986 q^{14} +3.85757 q^{15} +3.98779 q^{16} -5.35303 q^{17} +0.796890 q^{18} +3.10058 q^{19} -9.43023 q^{20} -2.11675 q^{21} +7.60824 q^{22} -6.13216 q^{23} +8.00240 q^{24} +0.563743 q^{25} -2.44907 q^{26} +5.43842 q^{27} +5.17461 q^{28} +6.49780 q^{29} -9.44748 q^{30} -3.73337 q^{31} +0.0199346 q^{32} +5.08058 q^{33} +13.1100 q^{34} -3.05297 q^{35} -1.30087 q^{36} -0.120878 q^{37} -7.59356 q^{38} -1.63543 q^{39} +11.5418 q^{40} +3.91846 q^{41} +5.18407 q^{42} +3.73891 q^{43} -12.4200 q^{44} +0.767502 q^{45} +15.0181 q^{46} +0.392800 q^{47} -6.52173 q^{48} -5.32476 q^{49} -1.38065 q^{50} +8.75448 q^{51} +3.99796 q^{52} +11.5767 q^{53} -13.3191 q^{54} +7.32767 q^{55} -6.33327 q^{56} -5.07077 q^{57} -15.9136 q^{58} -12.7493 q^{59} +15.4224 q^{60} -2.79114 q^{61} +9.14331 q^{62} -0.421148 q^{63} -8.02440 q^{64} -2.35876 q^{65} -12.4427 q^{66} +3.32332 q^{67} -21.4012 q^{68} +10.0287 q^{69} +7.47694 q^{70} +4.97459 q^{71} +1.59216 q^{72} +5.25555 q^{73} +0.296040 q^{74} -0.921960 q^{75} +12.3960 q^{76} -4.02088 q^{77} +4.00528 q^{78} +10.5654 q^{79} -9.40623 q^{80} -7.91797 q^{81} -9.59659 q^{82} +2.80872 q^{83} -8.46268 q^{84} +12.6265 q^{85} -9.15686 q^{86} -10.6267 q^{87} +15.2010 q^{88} -16.3397 q^{89} -1.87967 q^{90} +1.29431 q^{91} -24.5161 q^{92} +6.10565 q^{93} -0.961995 q^{94} -7.31353 q^{95} -0.0326016 q^{96} -0.559897 q^{97} +13.0407 q^{98} +1.01083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.44907	−1.73176	−0.865878	−	0.500254i	$-0.833240\pi$
$2$	−2.44907	−1.73176	−0.865878	+	0.500254i	$0.833240\pi$
$3$	−1.63543	−0.944213	−0.472107	−	0.881541i	$-0.656506\pi$
$3$	−1.63543	−0.944213	−0.472107	+	0.881541i	$0.656506\pi$
$4$	3.99796	1.99898
$5$	−2.35876	−1.05487	−0.527435	−	0.849596i	$-0.676846\pi$
$5$	−2.35876	−1.05487	−0.527435	+	0.849596i	$0.676846\pi$
$6$	4.00528	1.63515
$7$	1.29431	0.489203	0.244602	−	0.969624i	$-0.421343\pi$
$7$	1.29431	0.489203	0.244602	+	0.969624i	$0.421343\pi$
$8$	−4.89316	−1.72999
$9$	−0.325384	−0.108461
$10$	5.77678	1.82678
$11$	−3.10658	−0.936669	−0.468334	−	0.883551i	$-0.655146\pi$
$11$	−3.10658	−0.936669	−0.468334	+	0.883551i	$0.655146\pi$
$12$	−6.53837	−1.88747
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.16986	−0.847181
$15$	3.85757	0.996021
$16$	3.98779	0.996947
$17$	−5.35303	−1.29830	−0.649150	−	0.760660i	$-0.724875\pi$
$17$	−5.35303	−1.29830	−0.649150	+	0.760660i	$0.724875\pi$
$18$	0.796890	0.187829
$19$	3.10058	0.711323	0.355661	−	0.934615i	$-0.384256\pi$
$19$	3.10058	0.711323	0.355661	+	0.934615i	$0.384256\pi$
$20$	−9.43023	−2.10866
$21$	−2.11675	−0.461912
$22$	7.60824	1.62208
$23$	−6.13216	−1.27864	−0.639322	−	0.768939i	$-0.720785\pi$
$23$	−6.13216	−1.27864	−0.639322	+	0.768939i	$0.720785\pi$
$24$	8.00240	1.63348
$25$	0.563743	0.112749
$26$	−2.44907	−0.480303
$27$	5.43842	1.04662
$28$	5.17461	0.977909
$29$	6.49780	1.20661	0.603306	−	0.797510i	$-0.293850\pi$
$29$	6.49780	1.20661	0.603306	+	0.797510i	$0.293850\pi$
$30$	−9.44748	−1.72487
$31$	−3.73337	−0.670533	−0.335267	−	0.942123i	$-0.608826\pi$
$31$	−3.73337	−0.670533	−0.335267	+	0.942123i	$0.608826\pi$
$32$	0.0199346	0.00352398
$33$	5.08058	0.884415
$34$	13.1100	2.24834
$35$	−3.05297	−0.516046
$36$	−1.30087	−0.216812
$37$	−0.120878	−0.0198723	−0.00993613	−	0.999951i	$-0.503163\pi$
$37$	−0.120878	−0.0198723	−0.00993613	+	0.999951i	$0.503163\pi$
$38$	−7.59356	−1.23184
$39$	−1.63543	−0.261878
$40$	11.5418	1.82492
$41$	3.91846	0.611960	0.305980	−	0.952038i	$-0.401016\pi$
$41$	3.91846	0.611960	0.305980	+	0.952038i	$0.401016\pi$
$42$	5.18407	0.799920
$43$	3.73891	0.570178	0.285089	−	0.958501i	$-0.407977\pi$
$43$	3.73891	0.570178	0.285089	+	0.958501i	$0.407977\pi$
$44$	−12.4200	−1.87238
$45$	0.767502	0.114413
$46$	15.0181	2.21430
$47$	0.392800	0.0572957	0.0286479	−	0.999590i	$-0.490880\pi$
$47$	0.392800	0.0572957	0.0286479	+	0.999590i	$0.490880\pi$
$48$	−6.52173	−0.941331
$49$	−5.32476	−0.760680
$50$	−1.38065	−0.195253
$51$	8.75448	1.22587
$52$	3.99796	0.554418
$53$	11.5767	1.59019	0.795094	−	0.606486i	$-0.207421\pi$
$53$	11.5767	1.59019	0.795094	+	0.606486i	$0.207421\pi$
$54$	−13.3191	−1.81250
$55$	7.32767	0.988063
$56$	−6.33327	−0.846319
$57$	−5.07077	−0.671641
$58$	−15.9136	−2.08956
$59$	−12.7493	−1.65981	−0.829906	−	0.557903i	$-0.811606\pi$
$59$	−12.7493	−1.65981	−0.829906	+	0.557903i	$0.811606\pi$
$60$	15.4224	1.99103
$61$	−2.79114	−0.357368	−0.178684	−	0.983906i	$-0.557184\pi$
$61$	−2.79114	−0.357368	−0.178684	+	0.983906i	$0.557184\pi$
$62$	9.14331	1.16120
$63$	−0.421148	−0.0530597
$64$	−8.02440	−1.00305
$65$	−2.35876	−0.292568
$66$	−12.4427	−1.53159
$67$	3.32332	0.406009	0.203004	−	0.979178i	$-0.434929\pi$
$67$	3.32332	0.406009	0.203004	+	0.979178i	$0.434929\pi$
$68$	−21.4012	−2.59528
$69$	10.0287	1.20731
$70$	7.47694	0.893665
$71$	4.97459	0.590376	0.295188	−	0.955439i	$-0.404618\pi$
$71$	4.97459	0.590376	0.295188	+	0.955439i	$0.404618\pi$
$72$	1.59216	0.187637
$73$	5.25555	0.615115	0.307558	−	0.951529i	$-0.400488\pi$
$73$	5.25555	0.615115	0.307558	+	0.951529i	$0.400488\pi$
$74$	0.296040	0.0344139
$75$	−0.921960	−0.106459
$76$	12.3960	1.42192
$77$	−4.02088	−0.458222
$78$	4.00528	0.453508
$79$	10.5654	1.18870	0.594348	−	0.804208i	$-0.297410\pi$
$79$	10.5654	1.18870	0.594348	+	0.804208i	$0.297410\pi$
$80$	−9.40623	−1.05165
$81$	−7.91797	−0.879775
$82$	−9.59659	−1.05977
$83$	2.80872	0.308298	0.154149	−	0.988048i	$-0.450736\pi$
$83$	2.80872	0.308298	0.154149	+	0.988048i	$0.450736\pi$
$84$	−8.46268	−0.923355
$85$	12.6265	1.36954
$86$	−9.15686	−0.987409
$87$	−10.6267	−1.13930
$88$	15.2010	1.62043
$89$	−16.3397	−1.73200	−0.866001	−	0.500043i	$-0.833318\pi$
$89$	−16.3397	−1.73200	−0.866001	+	0.500043i	$0.833318\pi$
$90$	−1.87967	−0.198135
$91$	1.29431	0.135681
$92$	−24.5161	−2.55598
$93$	6.10565	0.633127
$94$	−0.961995	−0.0992223
$95$	−7.31353	−0.750353
$96$	−0.0326016	−0.00332739
$97$	−0.559897	−0.0568489	−0.0284244	−	0.999596i	$-0.509049\pi$
$97$	−0.559897	−0.0568489	−0.0284244	+	0.999596i	$0.509049\pi$
$98$	13.0407	1.31731
$99$	1.01083	0.101592
$100$	2.25382	0.225382
$101$	11.8184	1.17597	0.587986	−	0.808871i	$-0.299921\pi$
$101$	11.8184	1.17597	0.587986	+	0.808871i	$0.299921\pi$
$102$	−21.4404	−2.12291
$103$	9.83480	0.969052	0.484526	−	0.874777i	$-0.338992\pi$
$103$	9.83480	0.969052	0.484526	+	0.874777i	$0.338992\pi$
$104$	−4.89316	−0.479814
$105$	4.99290	0.487257
$106$	−28.3523	−2.75382
$107$	−11.3132	−1.09369	−0.546845	−	0.837234i	$-0.684171\pi$
$107$	−11.3132	−1.09369	−0.546845	+	0.837234i	$0.684171\pi$
$108$	21.7426	2.09218
$109$	1.17861	0.112891	0.0564454	−	0.998406i	$-0.482023\pi$
$109$	1.17861	0.112891	0.0564454	+	0.998406i	$0.482023\pi$
$110$	−17.9460	−1.71108
$111$	0.197687	0.0187637
$112$	5.16144	0.487710
$113$	−16.9796	−1.59730	−0.798651	−	0.601794i	$-0.794453\pi$
$113$	−16.9796	−1.59730	−0.798651	+	0.601794i	$0.794453\pi$
$114$	12.4187	1.16312
$115$	14.4643	1.34880
$116$	25.9780	2.41199
$117$	−0.325384	−0.0300818
$118$	31.2239	2.87439
$119$	−6.92848	−0.635133
$120$	−18.8757	−1.72311
$121$	−1.34917	−0.122652
$122$	6.83570	0.618875
$123$	−6.40834	−0.577821
$124$	−14.9259	−1.34038
$125$	10.4641	0.935934
$126$	1.03142	0.0918864
$127$	−0.395181	−0.0350666	−0.0175333	−	0.999846i	$-0.505581\pi$
$127$	−0.395181	−0.0350666	−0.0175333	+	0.999846i	$0.505581\pi$
$128$	19.6125	1.73351
$129$	−6.11470	−0.538369
$130$	5.77678	0.506657
$131$	8.37009	0.731298	0.365649	−	0.930753i	$-0.380847\pi$
$131$	8.37009	0.731298	0.365649	+	0.930753i	$0.380847\pi$
$132$	20.3120	1.76793
$133$	4.01312	0.347982
$134$	−8.13907	−0.703108
$135$	−12.8279	−1.10405
$136$	26.1932	2.24605
$137$	15.2210	1.30042	0.650209	−	0.759755i	$-0.274681\pi$
$137$	15.2210	1.30042	0.650209	+	0.759755i	$0.274681\pi$
$138$	−24.5610	−2.09077
$139$	12.1282	1.02870	0.514351	−	0.857580i	$-0.328033\pi$
$139$	12.1282	1.02870	0.514351	+	0.857580i	$0.328033\pi$
$140$	−12.2057	−1.03157
$141$	−0.642394	−0.0540994
$142$	−12.1831	−1.02239
$143$	−3.10658	−0.259785
$144$	−1.29756	−0.108130
$145$	−15.3267	−1.27282
$146$	−12.8712	−1.06523
$147$	8.70825	0.718244
$148$	−0.483267	−0.0397243
$149$	−16.0065	−1.31131	−0.655654	−	0.755062i	$-0.727607\pi$
$149$	−16.0065	−1.31131	−0.655654	+	0.755062i	$0.727607\pi$
$150$	2.25795	0.184361
$151$	−3.57785	−0.291161	−0.145581	−	0.989346i	$-0.546505\pi$
$151$	−3.57785	−0.291161	−0.145581	+	0.989346i	$0.546505\pi$
$152$	−15.1717	−1.23058
$153$	1.74179	0.140815
$154$	9.84743	0.793528
$155$	8.80612	0.707325
$156$	−6.53837	−0.523489
$157$	17.0861	1.36362	0.681808	−	0.731531i	$-0.261194\pi$
$157$	17.0861	1.36362	0.681808	+	0.731531i	$0.261194\pi$
$158$	−25.8754	−2.05853
$159$	−18.9329	−1.50148
$160$	−0.0470210	−0.00371734
$161$	−7.93692	−0.625517
$162$	19.3917	1.52356
$163$	13.0974	1.02587	0.512935	−	0.858428i	$-0.328558\pi$
$163$	13.0974	1.02587	0.512935	+	0.858428i	$0.328558\pi$
$164$	15.6658	1.22330
$165$	−11.9839	−0.932942
$166$	−6.87877	−0.533896
$167$	15.9115	1.23127	0.615635	−	0.788031i	$-0.288900\pi$
$167$	15.9115	1.23127	0.615635	+	0.788031i	$0.288900\pi$
$168$	10.3576	0.799106
$169$	1.00000	0.0769231
$170$	−30.9232	−2.37170
$171$	−1.00888	−0.0771510
$172$	14.9480	1.13977
$173$	−25.9469	−1.97270	−0.986352	−	0.164650i	$-0.947351\pi$
$173$	−25.9469	−1.97270	−0.986352	+	0.164650i	$0.947351\pi$
$174$	26.0255	1.97299
$175$	0.729659	0.0551570
$176$	−12.3884	−0.933809
$177$	20.8505	1.56722
$178$	40.0171	2.99941
$179$	10.4726	0.782759	0.391380	−	0.920229i	$-0.371998\pi$
$179$	10.4726	0.782759	0.391380	+	0.920229i	$0.371998\pi$
$180$	3.06845	0.228709
$181$	9.59386	0.713106	0.356553	−	0.934275i	$-0.383952\pi$
$181$	9.59386	0.713106	0.356553	+	0.934275i	$0.383952\pi$
$182$	−3.16986	−0.234966
$183$	4.56469	0.337432
$184$	30.0056	2.21204
$185$	0.285123	0.0209626
$186$	−14.9532	−1.09642
$187$	16.6296	1.21608
$188$	1.57040	0.114533
$189$	7.03900	0.512012
$190$	17.9114	1.29943
$191$	−12.8112	−0.926989	−0.463495	−	0.886100i	$-0.653405\pi$
$191$	−12.8112	−0.926989	−0.463495	+	0.886100i	$0.653405\pi$
$192$	13.1233	0.947093
$193$	−9.37592	−0.674893	−0.337447	−	0.941345i	$-0.609563\pi$
$193$	−9.37592	−0.674893	−0.337447	+	0.941345i	$0.609563\pi$
$194$	1.37123	0.0984484
$195$	3.85757	0.276247
$196$	−21.2882	−1.52059
$197$	16.4783	1.17403	0.587014	−	0.809577i	$-0.300304\pi$
$197$	16.4783	1.17403	0.587014	+	0.809577i	$0.300304\pi$
$198$	−2.47560	−0.175933
$199$	8.67876	0.615221	0.307610	−	0.951512i	$-0.400471\pi$
$199$	8.67876	0.615221	0.307610	+	0.951512i	$0.400471\pi$
$200$	−2.75849	−0.195054
$201$	−5.43505	−0.383359
$202$	−28.9441	−2.03650
$203$	8.41017	0.590278
$204$	35.0001	2.45050
$205$	−9.24269	−0.645538
$206$	−24.0862	−1.67816
$207$	1.99531	0.138683
$208$	3.98779	0.276503
$209$	−9.63221	−0.666274
$210$	−12.2280	−0.843811
$211$	−24.1684	−1.66382	−0.831909	−	0.554912i	$-0.812752\pi$
$211$	−24.1684	−1.66382	−0.831909	+	0.554912i	$0.812752\pi$
$212$	46.2834	3.17876
$213$	−8.13558	−0.557441
$214$	27.7069	1.89400
$215$	−8.81918	−0.601463
$216$	−26.6111	−1.81065
$217$	−4.83214	−0.328027
$218$	−2.88651	−0.195499
$219$	−8.59506	−0.580800
$220$	29.2958	1.97512
$221$	−5.35303	−0.360084
$222$	−0.484151	−0.0324941
$223$	27.2598	1.82545	0.912724	−	0.408576i	$-0.133974\pi$
$223$	27.2598	1.82545	0.912724	+	0.408576i	$0.133974\pi$
$224$	0.0258016	0.00172394
$225$	−0.183433	−0.0122289
$226$	41.5842	2.76614
$227$	−25.8802	−1.71773	−0.858863	−	0.512205i	$-0.828829\pi$
$227$	−25.8802	−1.71773	−0.858863	+	0.512205i	$0.828829\pi$
$228$	−20.2728	−1.34260
$229$	13.1159	0.866721	0.433361	−	0.901221i	$-0.357328\pi$
$229$	13.1159	0.866721	0.433361	+	0.901221i	$0.357328\pi$
$230$	−35.4241	−2.33580
$231$	6.57584	0.432659
$232$	−31.7948	−2.08743
$233$	21.7119	1.42239	0.711197	−	0.702993i	$-0.248153\pi$
$233$	21.7119	1.42239	0.711197	+	0.702993i	$0.248153\pi$
$234$	0.796890	0.0520943
$235$	−0.926520	−0.0604395
$236$	−50.9711	−3.31794
$237$	−17.2789	−1.12238
$238$	16.9684	1.09990
$239$	20.3696	1.31760	0.658801	−	0.752317i	$-0.271064\pi$
$239$	20.3696	1.31760	0.658801	+	0.752317i	$0.271064\pi$
$240$	15.3832	0.992981
$241$	2.58038	0.166217	0.0831083	−	0.996541i	$-0.473515\pi$
$241$	2.58038	0.166217	0.0831083	+	0.996541i	$0.473515\pi$
$242$	3.30422	0.212403
$243$	−3.36600	−0.215929
$244$	−11.1589	−0.714373
$245$	12.5598	0.802418
$246$	15.6945	1.00065
$247$	3.10058	0.197285
$248$	18.2680	1.16002
$249$	−4.59346	−0.291099
$250$	−25.6273	−1.62081
$251$	−18.4208	−1.16271	−0.581354	−	0.813651i	$-0.697477\pi$
$251$	−18.4208	−1.16271	−0.581354	+	0.813651i	$0.697477\pi$
$252$	−1.68373	−0.106065
$253$	19.0500	1.19766
$254$	0.967827	0.0607269
$255$	−20.6497	−1.29313
$256$	−31.9836	−1.99898
$257$	20.2721	1.26454	0.632269	−	0.774749i	$-0.282124\pi$
$257$	20.2721	1.26454	0.632269	+	0.774749i	$0.282124\pi$
$258$	14.9754	0.932325
$259$	−0.156454	−0.00972158
$260$	−9.43023	−0.584838
$261$	−2.11428	−0.130871
$262$	−20.4990	−1.26643
$263$	−25.2304	−1.55578	−0.777888	−	0.628403i	$-0.783709\pi$
$263$	−25.2304	−1.55578	−0.777888	+	0.628403i	$0.783709\pi$
$264$	−24.8601	−1.53003
$265$	−27.3067	−1.67744
$266$	−9.82843	−0.602620
$267$	26.7223	1.63538
$268$	13.2865	0.811604
$269$	18.7977	1.14612	0.573059	−	0.819514i	$-0.305756\pi$
$269$	18.7977	1.14612	0.573059	+	0.819514i	$0.305756\pi$
$270$	31.4165	1.91195
$271$	5.26300	0.319705	0.159852	−	0.987141i	$-0.448898\pi$
$271$	5.26300	0.319705	0.159852	+	0.987141i	$0.448898\pi$
$272$	−21.3467	−1.29434
$273$	−2.11675	−0.128111
$274$	−37.2774	−2.25201
$275$	−1.75131	−0.105608
$276$	40.0943	2.41339
$277$	−4.44723	−0.267208	−0.133604	−	0.991035i	$-0.542655\pi$
$277$	−4.44723	−0.267208	−0.133604	+	0.991035i	$0.542655\pi$
$278$	−29.7029	−1.78146
$279$	1.21478	0.0727270
$280$	14.9387	0.892756
$281$	24.4396	1.45794	0.728971	−	0.684545i	$-0.239999\pi$
$281$	24.4396	1.45794	0.728971	+	0.684545i	$0.239999\pi$
$282$	1.57327	0.0936870
$283$	3.91251	0.232574	0.116287	−	0.993216i	$-0.462901\pi$
$283$	3.91251	0.232574	0.116287	+	0.993216i	$0.462901\pi$
$284$	19.8882	1.18015
$285$	11.9607	0.708493
$286$	7.60824	0.449885
$287$	5.07170	0.299373
$288$	−0.00648641	−0.000382216 0
$289$	11.6549	0.685583
$290$	37.5363	2.20421
$291$	0.915669	0.0536775
$292$	21.0115	1.22960
$293$	8.00654	0.467747	0.233874	−	0.972267i	$-0.424860\pi$
$293$	8.00654	0.467747	0.233874	+	0.972267i	$0.424860\pi$
$294$	−21.3271	−1.24382
$295$	30.0724	1.75089
$296$	0.591477	0.0343789
$297$	−16.8949	−0.980340
$298$	39.2012	2.27087
$299$	−6.13216	−0.354632
$300$	−3.68596	−0.212809
$301$	4.83930	0.278933
$302$	8.76241	0.504220
$303$	−19.3281	−1.11037
$304$	12.3645	0.709151
$305$	6.58362	0.376977
$306$	−4.26577	−0.243858
$307$	−9.02831	−0.515273	−0.257637	−	0.966242i	$-0.582944\pi$
$307$	−9.02831	−0.515273	−0.257637	+	0.966242i	$0.582944\pi$
$308$	−16.0753	−0.915977
$309$	−16.0841	−0.914992
$310$	−21.5669	−1.22491
$311$	−24.1435	−1.36905	−0.684526	−	0.728988i	$-0.739991\pi$
$311$	−24.1435	−1.36905	−0.684526	+	0.728988i	$0.739991\pi$
$312$	8.00240	0.453047
$313$	15.4535	0.873482	0.436741	−	0.899587i	$-0.356133\pi$
$313$	15.4535	0.873482	0.436741	+	0.899587i	$0.356133\pi$
$314$	−41.8450	−2.36145
$315$	0.993387	0.0559710
$316$	42.2399	2.37618
$317$	23.3549	1.31174	0.655870	−	0.754874i	$-0.272302\pi$
$317$	23.3549	1.31174	0.655870	+	0.754874i	$0.272302\pi$
$318$	46.3681	2.60019
$319$	−20.1859	−1.13020
$320$	18.9276	1.05809
$321$	18.5019	1.03268
$322$	19.4381	1.08324
$323$	−16.5975	−0.923511
$324$	−31.6558	−1.75865
$325$	0.563743	0.0312708
$326$	−32.0766	−1.77656
$327$	−1.92754	−0.106593
$328$	−19.1736	−1.05869
$329$	0.508405	0.0280293
$330$	29.3494	1.61563
$331$	14.4786	0.795815	0.397908	−	0.917425i	$-0.369736\pi$
$331$	14.4786	0.795815	0.397908	+	0.917425i	$0.369736\pi$
$332$	11.2292	0.616281
$333$	0.0393319	0.00215537
$334$	−38.9685	−2.13226
$335$	−7.83892	−0.428286
$336$	−8.44114	−0.460502
$337$	−24.0453	−1.30983	−0.654916	−	0.755701i	$-0.727296\pi$
$337$	−24.0453	−1.30983	−0.654916	+	0.755701i	$0.727296\pi$
$338$	−2.44907	−0.133212
$339$	27.7688	1.50819
$340$	50.4803	2.73768
$341$	11.5980	0.628068
$342$	2.47082	0.133607
$343$	−15.9521	−0.861331
$344$	−18.2951	−0.986404
$345$	−23.6552	−1.27356
$346$	63.5458	3.41624
$347$	15.8106	0.848760	0.424380	−	0.905484i	$-0.360492\pi$
$347$	15.8106	0.848760	0.424380	+	0.905484i	$0.360492\pi$
$348$	−42.4850	−2.27744
$349$	−23.4158	−1.25342	−0.626710	−	0.779252i	$-0.715599\pi$
$349$	−23.4158	−1.25342	−0.626710	+	0.779252i	$0.715599\pi$
$350$	−1.78699	−0.0955185
$351$	5.43842	0.290281
$352$	−0.0619285	−0.00330080
$353$	14.7649	0.785855	0.392928	−	0.919569i	$-0.371462\pi$
$353$	14.7649	0.785855	0.392928	+	0.919569i	$0.371462\pi$
$354$	−51.0643	−2.71404
$355$	−11.7339	−0.622769
$356$	−65.3254	−3.46224
$357$	11.3310	0.599701
$358$	−25.6482	−1.35555
$359$	19.3362	1.02052	0.510262	−	0.860019i	$-0.329548\pi$
$359$	19.3362	1.02052	0.510262	+	0.860019i	$0.329548\pi$
$360$	−3.75551	−0.197933
$361$	−9.38637	−0.494020
$362$	−23.4961	−1.23493
$363$	2.20647	0.115810
$364$	5.17461	0.271223
$365$	−12.3966	−0.648866
$366$	−11.1793	−0.584350
$367$	0.130853	0.00683045	0.00341523	−	0.999994i	$-0.498913\pi$
$367$	0.130853	0.00683045	0.00341523	+	0.999994i	$0.498913\pi$
$368$	−24.4537	−1.27474
$369$	−1.27500	−0.0663740
$370$	−0.698287	−0.0363022
$371$	14.9839	0.777926
$372$	24.4102	1.26561
$373$	−18.8071	−0.973797	−0.486899	−	0.873458i	$-0.661872\pi$
$373$	−18.8071	−0.973797	−0.486899	+	0.873458i	$0.661872\pi$
$374$	−40.7271	−2.10595
$375$	−17.1132	−0.883721
$376$	−1.92203	−0.0991212
$377$	6.49780	0.334654
$378$	−17.2390	−0.886680
$379$	1.27153	0.0653143	0.0326571	−	0.999467i	$-0.489603\pi$
$379$	1.27153	0.0653143	0.0326571	+	0.999467i	$0.489603\pi$
$380$	−29.2392	−1.49994
$381$	0.646288	0.0331104
$382$	31.3757	1.60532
$383$	11.6060	0.593040	0.296520	−	0.955027i	$-0.404174\pi$
$383$	11.6060	0.593040	0.296520	+	0.955027i	$0.404174\pi$
$384$	−32.0747	−1.63681
$385$	9.48428	0.483364
$386$	22.9623	1.16875
$387$	−1.21658	−0.0618422
$388$	−2.23845	−0.113640
$389$	26.6687	1.35216	0.676079	−	0.736829i	$-0.263678\pi$
$389$	26.6687	1.35216	0.676079	+	0.736829i	$0.263678\pi$
$390$	−9.44748	−0.478392
$391$	32.8256	1.66006
$392$	26.0549	1.31597
$393$	−13.6887	−0.690501
$394$	−40.3565	−2.03313
$395$	−24.9211	−1.25392
$396$	4.04127	0.203081
$397$	17.8576	0.896245	0.448122	−	0.893972i	$-0.352093\pi$
$397$	17.8576	0.896245	0.448122	+	0.893972i	$0.352093\pi$
$398$	−21.2549	−1.06541
$399$	−6.56316	−0.328569
$400$	2.24809	0.112404
$401$	−12.4570	−0.622071	−0.311036	−	0.950398i	$-0.600676\pi$
$401$	−12.4570	−0.622071	−0.311036	+	0.950398i	$0.600676\pi$
$402$	13.3108	0.663884
$403$	−3.73337	−0.185973
$404$	47.2494	2.35075
$405$	18.6766	0.928047
$406$	−20.5971	−1.02222
$407$	0.375518	0.0186137
$408$	−42.8371	−2.12075
$409$	4.88686	0.241640	0.120820	−	0.992674i	$-0.461448\pi$
$409$	4.88686	0.241640	0.120820	+	0.992674i	$0.461448\pi$
$410$	22.6360	1.11791
$411$	−24.8928	−1.22787
$412$	39.3192	1.93712
$413$	−16.5015	−0.811986
$414$	−4.88665	−0.240166
$415$	−6.62510	−0.325213
$416$	0.0199346	0.000977376 0
$417$	−19.8348	−0.971315
$418$	23.5900	1.15382
$419$	−5.91033	−0.288738	−0.144369	−	0.989524i	$-0.546115\pi$
$419$	−5.91033	−0.288738	−0.144369	+	0.989524i	$0.546115\pi$
$420$	19.9614	0.974018
$421$	−12.6690	−0.617450	−0.308725	−	0.951151i	$-0.599902\pi$
$421$	−12.6690	−0.617450	−0.308725	+	0.951151i	$0.599902\pi$
$422$	59.1901	2.88133
$423$	−0.127811	−0.00621437
$424$	−56.6469	−2.75102
$425$	−3.01773	−0.146382
$426$	19.9246	0.965351
$427$	−3.61260	−0.174826
$428$	−45.2298	−2.18627
$429$	5.08058	0.245293
$430$	21.5988	1.04159
$431$	7.61888	0.366989	0.183494	−	0.983021i	$-0.441259\pi$
$431$	7.61888	0.366989	0.183494	+	0.983021i	$0.441259\pi$
$432$	21.6873	1.04343
$433$	−35.3854	−1.70051	−0.850257	−	0.526368i	$-0.823553\pi$
$433$	−35.3854	−1.70051	−0.850257	+	0.526368i	$0.823553\pi$
$434$	11.8343	0.568063
$435$	25.0657	1.20181
$436$	4.71206	0.225667
$437$	−19.0133	−0.909528
$438$	21.0499	1.00580
$439$	−39.8835	−1.90354	−0.951768	−	0.306820i	$-0.900735\pi$
$439$	−39.8835	−1.90354	−0.951768	+	0.306820i	$0.900735\pi$
$440$	−35.8555	−1.70934
$441$	1.73259	0.0825044
$442$	13.1100	0.623577
$443$	−23.5868	−1.12064	−0.560322	−	0.828275i	$-0.689323\pi$
$443$	−23.5868	−1.12064	−0.560322	+	0.828275i	$0.689323\pi$
$444$	0.790347	0.0375082
$445$	38.5413	1.82703
$446$	−66.7612	−3.16123
$447$	26.1775	1.23815
$448$	−10.3861	−0.490695
$449$	−4.54768	−0.214618	−0.107309	−	0.994226i	$-0.534223\pi$
$449$	−4.54768	−0.214618	−0.107309	+	0.994226i	$0.534223\pi$
$450$	0.449241	0.0211774
$451$	−12.1730	−0.573204
$452$	−67.8837	−3.19298
$453$	5.85130	0.274918
$454$	63.3824	2.97468
$455$	−3.05297	−0.143125
$456$	24.8121	1.16193
$457$	32.8766	1.53790	0.768951	−	0.639308i	$-0.220779\pi$
$457$	32.8766	1.53790	0.768951	+	0.639308i	$0.220779\pi$
$458$	−32.1217	−1.50095
$459$	−29.1120	−1.35883
$460$	57.8277	2.69623
$461$	−5.36293	−0.249776	−0.124888	−	0.992171i	$-0.539857\pi$
$461$	−5.36293	−0.249776	−0.124888	+	0.992171i	$0.539857\pi$
$462$	−16.1047	−0.749260
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	25.9119	1.20293
$465$	−14.4018	−0.667866
$466$	−53.1741	−2.46324
$467$	−9.82791	−0.454781	−0.227391	−	0.973804i	$-0.573019\pi$
$467$	−9.82791	−0.454781	−0.227391	+	0.973804i	$0.573019\pi$
$468$	−1.30087	−0.0601329
$469$	4.30141	0.198621
$470$	2.26912	0.104666
$471$	−27.9430	−1.28754
$472$	62.3842	2.87147
$473$	−11.6152	−0.534068
$474$	42.3172	1.94369
$475$	1.74793	0.0802007
$476$	−27.6998	−1.26962
$477$	−3.76689	−0.172474
$478$	−49.8867	−2.28177
$479$	19.8933	0.908950	0.454475	−	0.890759i	$-0.349827\pi$
$479$	19.8933	0.908950	0.454475	+	0.890759i	$0.349827\pi$
$480$	0.0768994	0.00350996
$481$	−0.120878	−0.00551157
$482$	−6.31953	−0.287847
$483$	12.9802	0.590621
$484$	−5.39393	−0.245179
$485$	1.32066	0.0599681
$486$	8.24358	0.373936
$487$	23.8794	1.08208	0.541040	−	0.840997i	$-0.318031\pi$
$487$	23.8794	1.08208	0.541040	+	0.840997i	$0.318031\pi$
$488$	13.6575	0.618245
$489$	−21.4199	−0.968639
$490$	−30.7599	−1.38959
$491$	−27.8731	−1.25790	−0.628948	−	0.777448i	$-0.716514\pi$
$491$	−27.8731	−1.25790	−0.628948	+	0.777448i	$0.716514\pi$
$492$	−25.6203	−1.15505
$493$	−34.7829	−1.56654
$494$	−7.59356	−0.341651
$495$	−2.38431	−0.107167
$496$	−14.8879	−0.668486
$497$	6.43867	0.288814
$498$	11.2497	0.504112
$499$	−33.4053	−1.49543	−0.747713	−	0.664022i	$-0.768848\pi$
$499$	−33.4053	−1.49543	−0.747713	+	0.664022i	$0.768848\pi$
$500$	41.8349	1.87092
$501$	−26.0221	−1.16258
$502$	45.1138	2.01353
$503$	1.03500	0.0461484	0.0230742	−	0.999734i	$-0.492655\pi$
$503$	1.03500	0.0461484	0.0230742	+	0.999734i	$0.492655\pi$
$504$	2.06075	0.0917929
$505$	−27.8767	−1.24050
$506$	−46.6549	−2.07406
$507$	−1.63543	−0.0726318
$508$	−1.57992	−0.0700975
$509$	1.15535	0.0512100	0.0256050	−	0.999672i	$-0.491849\pi$
$509$	1.15535	0.0512100	0.0256050	+	0.999672i	$0.491849\pi$
$510$	50.5727	2.23939
$511$	6.80231	0.300917
$512$	39.1053	1.72823
$513$	16.8623	0.744488
$514$	−49.6478	−2.18987
$515$	−23.1979	−1.02222
$516$	−24.4464	−1.07619
$517$	−1.22026	−0.0536671
$518$	0.383167	0.0168354
$519$	42.4342	1.86265
$520$	11.5418	0.506141
$521$	−23.5551	−1.03197	−0.515983	−	0.856599i	$-0.672573\pi$
$521$	−23.5551	−1.03197	−0.515983	+	0.856599i	$0.672573\pi$
$522$	5.17803	0.226636
$523$	−39.3238	−1.71951	−0.859755	−	0.510707i	$-0.829384\pi$
$523$	−39.3238	−1.71951	−0.859755	+	0.510707i	$0.829384\pi$
$524$	33.4633	1.46185
$525$	−1.19330	−0.0520800
$526$	61.7912	2.69423
$527$	19.9848	0.870554
$528$	20.2603	0.881715
$529$	14.6033	0.634928
$530$	66.8763	2.90492
$531$	4.14841	0.180026
$532$	16.0443	0.695609
$533$	3.91846	0.169727
$534$	−65.4449	−2.83208
$535$	26.6851	1.15370
$536$	−16.2616	−0.702393
$537$	−17.1272	−0.739092
$538$	−46.0371	−1.98480
$539$	16.5418	0.712505
$540$	−51.2855	−2.20698
$541$	2.88657	0.124103	0.0620517	−	0.998073i	$-0.480236\pi$
$541$	2.88657	0.124103	0.0620517	+	0.998073i	$0.480236\pi$
$542$	−12.8895	−0.553651
$543$	−15.6900	−0.673324
$544$	−0.106711	−0.00457518
$545$	−2.78007	−0.119085
$546$	5.18407	0.221858
$547$	11.8862	0.508219	0.254109	−	0.967175i	$-0.418218\pi$
$547$	11.8862	0.508219	0.254109	+	0.967175i	$0.418218\pi$
$548$	60.8530	2.59951
$549$	0.908191	0.0387607
$550$	4.28909	0.182888
$551$	20.1470	0.858290
$552$	−49.0720	−2.08864
$553$	13.6749	0.581514
$554$	10.8916	0.462740
$555$	−0.466297	−0.0197932
$556$	48.4882	2.05636
$557$	15.6166	0.661698	0.330849	−	0.943684i	$-0.392665\pi$
$557$	15.6166	0.661698	0.330849	+	0.943684i	$0.392665\pi$
$558$	−2.97509	−0.125945
$559$	3.73891	0.158139
$560$	−12.1746	−0.514470
$561$	−27.1965	−1.14824
$562$	−59.8543	−2.52480
$563$	9.90851	0.417594	0.208797	−	0.977959i	$-0.433045\pi$
$563$	9.90851	0.417594	0.208797	+	0.977959i	$0.433045\pi$
$564$	−2.56827	−0.108144
$565$	40.0507	1.68495
$566$	−9.58202	−0.402762
$567$	−10.2483	−0.430389
$568$	−24.3415	−1.02135
$569$	−37.1042	−1.55549	−0.777744	−	0.628581i	$-0.783636\pi$
$569$	−37.1042	−1.55549	−0.777744	+	0.628581i	$0.783636\pi$
$570$	−29.2927	−1.22694
$571$	−24.2951	−1.01672	−0.508359	−	0.861145i	$-0.669748\pi$
$571$	−24.2951	−1.01672	−0.508359	+	0.861145i	$0.669748\pi$
$572$	−12.4200	−0.519306
$573$	20.9518	0.875275
$574$	−12.4210	−0.518441
$575$	−3.45696	−0.144165
$576$	2.61101	0.108792
$577$	−7.17660	−0.298766	−0.149383	−	0.988779i	$-0.547729\pi$
$577$	−7.17660	−0.298766	−0.149383	+	0.988779i	$0.547729\pi$
$578$	−28.5437	−1.18726
$579$	15.3336	0.637243
$580$	−61.2758	−2.54434
$581$	3.63536	0.150820
$582$	−2.24254	−0.0929563
$583$	−35.9641	−1.48948
$584$	−25.7162	−1.06415
$585$	0.767502	0.0317323
$586$	−19.6086	−0.810024
$587$	19.1940	0.792223	0.396111	−	0.918202i	$-0.370359\pi$
$587$	19.1940	0.792223	0.396111	+	0.918202i	$0.370359\pi$
$588$	34.8153	1.43576
$589$	−11.5756	−0.476966
$590$	−73.6496	−3.03211
$591$	−26.9490	−1.10853
$592$	−0.482037	−0.0198116
$593$	1.51860	0.0623614	0.0311807	−	0.999514i	$-0.490073\pi$
$593$	1.51860	0.0623614	0.0311807	+	0.999514i	$0.490073\pi$
$594$	41.3768	1.69771
$595$	16.3426	0.669982
$596$	−63.9936	−2.62128
$597$	−14.1935	−0.580900
$598$	15.0181	0.614136
$599$	−3.51796	−0.143740	−0.0718700	−	0.997414i	$-0.522897\pi$
$599$	−3.51796	−0.143740	−0.0718700	+	0.997414i	$0.522897\pi$
$600$	4.51130	0.184173
$601$	−19.5689	−0.798232	−0.399116	−	0.916901i	$-0.630683\pi$
$601$	−19.5689	−0.798232	−0.399116	+	0.916901i	$0.630683\pi$
$602$	−11.8518	−0.483044
$603$	−1.08136	−0.0440362
$604$	−14.3041	−0.582026
$605$	3.18237	0.129382
$606$	47.3359	1.92289
$607$	−31.7438	−1.28844	−0.644221	−	0.764839i	$-0.722818\pi$
$607$	−31.7438	−1.28844	−0.644221	+	0.764839i	$0.722818\pi$
$608$	0.0618091	0.00250669
$609$	−13.7542	−0.557349
$610$	−16.1238	−0.652832
$611$	0.392800	0.0158910
$612$	6.96361	0.281487
$613$	−26.9442	−1.08826	−0.544132	−	0.838999i	$-0.683141\pi$
$613$	−26.9442	−1.08826	−0.544132	+	0.838999i	$0.683141\pi$
$614$	22.1110	0.892328
$615$	15.1157	0.609525
$616$	19.6748	0.792720
$617$	−28.2009	−1.13532	−0.567662	−	0.823262i	$-0.692152\pi$
$617$	−28.2009	−1.13532	−0.567662	+	0.823262i	$0.692152\pi$
$618$	39.3911	1.58454
$619$	−24.1218	−0.969539	−0.484769	−	0.874642i	$-0.661096\pi$
$619$	−24.1218	−0.969539	−0.484769	+	0.874642i	$0.661096\pi$
$620$	35.2066	1.41393
$621$	−33.3492	−1.33826
$622$	59.1292	2.37087
$623$	−21.1486	−0.847301
$624$	−6.52173	−0.261078
$625$	−27.5009	−1.10004
$626$	−37.8467	−1.51266
$627$	15.7528	0.629105
$628$	68.3094	2.72584
$629$	0.647065	0.0258002
$630$	−2.43288	−0.0969282
$631$	3.60023	0.143323	0.0716614	−	0.997429i	$-0.477170\pi$
$631$	3.60023	0.143323	0.0716614	+	0.997429i	$0.477170\pi$
$632$	−51.6980	−2.05644
$633$	39.5256	1.57100
$634$	−57.1978	−2.27161
$635$	0.932136	0.0369907
$636$	−75.6931	−3.00143
$637$	−5.32476	−0.210975
$638$	49.4368	1.95722
$639$	−1.61865	−0.0640329
$640$	−46.2611	−1.82863
$641$	−0.523643	−0.0206827	−0.0103413	−	0.999947i	$-0.503292\pi$
$641$	−0.523643	−0.0206827	−0.0103413	+	0.999947i	$0.503292\pi$
$642$	−45.3126	−1.78834
$643$	34.9548	1.37848	0.689242	−	0.724531i	$-0.257944\pi$
$643$	34.9548	1.37848	0.689242	+	0.724531i	$0.257944\pi$
$644$	−31.7315	−1.25040
$645$	14.4231	0.567909
$646$	40.6486	1.59930
$647$	−35.2764	−1.38686	−0.693429	−	0.720525i	$-0.743901\pi$
$647$	−35.2764	−1.38686	−0.693429	+	0.720525i	$0.743901\pi$
$648$	38.7439	1.52201
$649$	39.6066	1.55469
$650$	−1.38065	−0.0541535
$651$	7.90261	0.309728
$652$	52.3630	2.05069
$653$	29.7188	1.16299	0.581493	−	0.813552i	$-0.302469\pi$
$653$	29.7188	1.16299	0.581493	+	0.813552i	$0.302469\pi$
$654$	4.72068	0.184593
$655$	−19.7430	−0.771424
$656$	15.6260	0.610092
$657$	−1.71007	−0.0667162
$658$	−1.24512	−0.0485399
$659$	−6.42140	−0.250142	−0.125071	−	0.992148i	$-0.539916\pi$
$659$	−6.42140	−0.250142	−0.125071	+	0.992148i	$0.539916\pi$
$660$	−47.9110	−1.86493
$661$	−51.1701	−1.99028	−0.995142	−	0.0984458i	$-0.968613\pi$
$661$	−51.1701	−1.99028	−0.995142	+	0.0984458i	$0.968613\pi$
$662$	−35.4591	−1.37816
$663$	8.75448	0.339996
$664$	−13.7435	−0.533353
$665$	−9.46598	−0.367075
$666$	−0.0963266	−0.00373258
$667$	−39.8455	−1.54283
$668$	63.6137	2.46129
$669$	−44.5813	−1.72361
$670$	19.1981	0.741687
$671$	8.67088	0.334736
$672$	−0.0421966	−0.00162777
$673$	−11.6882	−0.450545	−0.225273	−	0.974296i	$-0.572327\pi$
$673$	−11.6882	−0.450545	−0.225273	+	0.974296i	$0.572327\pi$
$674$	58.8888	2.26831
$675$	3.06587	0.118005
$676$	3.99796	0.153768
$677$	26.4493	1.01653	0.508265	−	0.861201i	$-0.330287\pi$
$677$	26.4493	1.01653	0.508265	+	0.861201i	$0.330287\pi$
$678$	−68.0079	−2.61183
$679$	−0.724680	−0.0278107
$680$	−61.7835	−2.36929
$681$	42.3251	1.62190
$682$	−28.4044	−1.08766
$683$	−16.1222	−0.616898	−0.308449	−	0.951241i	$-0.599810\pi$
$683$	−16.1222	−0.616898	−0.308449	+	0.951241i	$0.599810\pi$
$684$	−4.03347	−0.154224
$685$	−35.9027	−1.37177
$686$	39.0678	1.49162
$687$	−21.4500	−0.818370
$688$	14.9100	0.568437
$689$	11.5767	0.441039
$690$	57.9335	2.20549
$691$	−6.15100	−0.233995	−0.116998	−	0.993132i	$-0.537327\pi$
$691$	−6.15100	−0.233995	−0.116998	+	0.993132i	$0.537327\pi$
$692$	−103.735	−3.94340
$693$	1.30833	0.0496993
$694$	−38.7214	−1.46985
$695$	−28.6076	−1.08515
$696$	51.9980	1.97098
$697$	−20.9756	−0.794508
$698$	57.3471	2.17062
$699$	−35.5082	−1.34304
$700$	2.91715	0.110258
$701$	−26.6311	−1.00584	−0.502921	−	0.864332i	$-0.667741\pi$
$701$	−26.6311	−1.00584	−0.502921	+	0.864332i	$0.667741\pi$
$702$	−13.3191	−0.502697
$703$	−0.374793	−0.0141356
$704$	24.9284	0.939525
$705$	1.51525	0.0570678
$706$	−36.1603	−1.36091
$707$	15.2966	0.575290
$708$	83.3594	3.13284
$709$	−51.7951	−1.94520	−0.972602	−	0.232475i	$-0.925318\pi$
$709$	−51.7951	−1.94520	−0.972602	+	0.232475i	$0.925318\pi$
$710$	28.7371	1.07848
$711$	−3.43780	−0.128928
$712$	79.9527	2.99635
$713$	22.8936	0.857373
$714$	−27.7505	−1.03854
$715$	7.32767	0.274039
$716$	41.8691	1.56472
$717$	−33.3130	−1.24410
$718$	−47.3557	−1.76730
$719$	−36.9778	−1.37904	−0.689520	−	0.724267i	$-0.742178\pi$
$719$	−36.9778	−1.37904	−0.689520	+	0.724267i	$0.742178\pi$
$720$	3.06064	0.114063
$721$	12.7293	0.474064
$722$	22.9879	0.855522
$723$	−4.22001	−0.156944
$724$	38.3559	1.42549
$725$	3.66309	0.136044
$726$	−5.40380	−0.200554
$727$	5.91361	0.219324	0.109662	−	0.993969i	$-0.465023\pi$
$727$	5.91361	0.219324	0.109662	+	0.993969i	$0.465023\pi$
$728$	−6.33327	−0.234727
$729$	29.2588	1.08366
$730$	30.3601	1.12368
$731$	−20.0145	−0.740262
$732$	18.2495	0.674520
$733$	−21.1990	−0.783005	−0.391502	−	0.920177i	$-0.628045\pi$
$733$	−21.1990	−0.783005	−0.391502	+	0.920177i	$0.628045\pi$
$734$	−0.320468	−0.0118287
$735$	−20.5407	−0.757653
$736$	−0.122242	−0.00450591
$737$	−10.3242	−0.380296
$738$	3.12258	0.114944
$739$	−53.2063	−1.95722	−0.978612	−	0.205713i	$-0.934049\pi$
$739$	−53.2063	−1.95722	−0.978612	+	0.205713i	$0.934049\pi$
$740$	1.13991	0.0419039
$741$	−5.07077	−0.186280
$742$	−36.6967	−1.34718
$743$	48.6346	1.78423	0.892115	−	0.451809i	$-0.149221\pi$
$743$	48.6346	1.78423	0.892115	+	0.451809i	$0.149221\pi$
$744$	−29.8759	−1.09531
$745$	37.7556	1.38326
$746$	46.0601	1.68638
$747$	−0.913914	−0.0334384
$748$	66.4846	2.43092
$749$	−14.6428	−0.535037
$750$	41.9115	1.53039
$751$	18.0701	0.659387	0.329694	−	0.944088i	$-0.393055\pi$
$751$	18.0701	0.659387	0.329694	+	0.944088i	$0.393055\pi$
$752$	1.56640	0.0571208
$753$	30.1258	1.09784
$754$	−15.9136	−0.579539
$755$	8.43928	0.307137
$756$	28.1417	1.02350
$757$	−0.678696	−0.0246676	−0.0123338	−	0.999924i	$-0.503926\pi$
$757$	−0.678696	−0.0246676	−0.0123338	+	0.999924i	$0.503926\pi$
$758$	−3.11408	−0.113108
$759$	−31.1549	−1.13085
$760$	35.7863	1.29811
$761$	9.84141	0.356751	0.178375	−	0.983963i	$-0.442916\pi$
$761$	9.84141	0.356751	0.178375	+	0.983963i	$0.442916\pi$
$762$	−1.58281	−0.0573391
$763$	1.52549	0.0552266
$764$	−51.2189	−1.85303
$765$	−4.10846	−0.148542
$766$	−28.4240	−1.02700
$767$	−12.7493	−0.460349
$768$	52.3068	1.88746
$769$	28.3540	1.02247	0.511236	−	0.859440i	$-0.329188\pi$
$769$	28.3540	1.02247	0.511236	+	0.859440i	$0.329188\pi$
$770$	−23.2277	−0.837068
$771$	−33.1535	−1.19399
$772$	−37.4846	−1.34910
$773$	−20.0758	−0.722075	−0.361037	−	0.932551i	$-0.617577\pi$
$773$	−20.0758	−0.722075	−0.361037	+	0.932551i	$0.617577\pi$
$774$	2.97949	0.107096
$775$	−2.10466	−0.0756017
$776$	2.73966	0.0983482
$777$	0.255869	0.00917924
$778$	−65.3137	−2.34161
$779$	12.1495	0.435301
$780$	15.4224	0.552212
$781$	−15.4540	−0.552986
$782$	−80.3924	−2.87482
$783$	35.3378	1.26287
$784$	−21.2340	−0.758358
$785$	−40.3019	−1.43844
$786$	33.5245	1.19578
$787$	36.7396	1.30963	0.654813	−	0.755791i	$-0.272747\pi$
$787$	36.7396	1.30963	0.654813	+	0.755791i	$0.272747\pi$
$788$	65.8795	2.34686
$789$	41.2625	1.46898
$790$	61.0337	2.17148
$791$	−21.9768	−0.781406
$792$	−4.94616	−0.175754
$793$	−2.79114	−0.0991161
$794$	−43.7345	−1.55208
$795$	44.6581	1.58386
$796$	34.6974	1.22982
$797$	−53.1892	−1.88406	−0.942029	−	0.335533i	$-0.891084\pi$
$797$	−53.1892	−1.88406	−0.942029	+	0.335533i	$0.891084\pi$
$798$	16.0737	0.569001
$799$	−2.10267	−0.0743870
$800$	0.0112380	0.000397324 0
$801$	5.31667	0.187855
$802$	30.5080	1.07728
$803$	−16.3268	−0.576159
$804$	−21.7291	−0.766327
$805$	18.7213	0.659838
$806$	9.14331	0.322059
$807$	−30.7423	−1.08218
$808$	−57.8292	−2.03442
$809$	13.2575	0.466107	0.233054	−	0.972464i	$-0.425128\pi$
$809$	13.2575	0.466107	0.233054	+	0.972464i	$0.425128\pi$
$810$	−45.7404	−1.60715
$811$	−39.1416	−1.37445	−0.687223	−	0.726447i	$-0.741170\pi$
$811$	−39.1416	−1.37445	−0.687223	+	0.726447i	$0.741170\pi$
$812$	33.6236	1.17996
$813$	−8.60725	−0.301869
$814$	−0.919671	−0.0322344
$815$	−30.8937	−1.08216
$816$	34.9110	1.22213
$817$	11.5928	0.405580
$818$	−11.9683	−0.418461
$819$	−0.421148	−0.0147161
$820$	−36.9520	−1.29042
$821$	−45.6261	−1.59236	−0.796181	−	0.605059i	$-0.793150\pi$
$821$	−45.6261	−1.59236	−0.796181	+	0.605059i	$0.793150\pi$
$822$	60.9644	2.12638
$823$	51.9808	1.81194	0.905968	−	0.423345i	$-0.139144\pi$
$823$	51.9808	1.81194	0.905968	+	0.423345i	$0.139144\pi$
$824$	−48.1233	−1.67645
$825$	2.86414	0.0997166
$826$	40.4134	1.40616
$827$	−14.3976	−0.500653	−0.250326	−	0.968161i	$-0.580538\pi$
$827$	−14.3976	−0.500653	−0.250326	+	0.968161i	$0.580538\pi$
$828$	7.97716	0.277226
$829$	9.68498	0.336373	0.168187	−	0.985755i	$-0.446209\pi$
$829$	9.68498	0.336373	0.168187	+	0.985755i	$0.446209\pi$
$830$	16.2254	0.563191
$831$	7.27311	0.252301
$832$	−8.02440	−0.278196
$833$	28.5036	0.987591
$834$	48.5769	1.68208
$835$	−37.5314	−1.29883
$836$	−38.5092	−1.33187
$837$	−20.3036	−0.701796
$838$	14.4748	0.500025
$839$	10.8435	0.374361	0.187180	−	0.982326i	$-0.440065\pi$
$839$	10.8435	0.374361	0.187180	+	0.982326i	$0.440065\pi$
$840$	−24.4311	−0.842952
$841$	13.2214	0.455911
$842$	31.0274	1.06927
$843$	−39.9691	−1.37661
$844$	−96.6242	−3.32594
$845$	−2.35876	−0.0811438
$846$	0.313018	0.0107618
$847$	−1.74625	−0.0600017
$848$	46.1656	1.58533
$849$	−6.39861	−0.219600
$850$	7.39065	0.253497
$851$	0.741244	0.0254095
$852$	−32.5257	−1.11431
$853$	56.3541	1.92953	0.964764	−	0.263115i	$-0.0847500\pi$
$853$	56.3541	1.92953	0.964764	+	0.263115i	$0.0847500\pi$
$854$	8.84752	0.302756
$855$	2.37971	0.0813842
$856$	55.3574	1.89208
$857$	9.51601	0.325061	0.162530	−	0.986704i	$-0.448034\pi$
$857$	9.51601	0.325061	0.162530	+	0.986704i	$0.448034\pi$
$858$	−12.4427	−0.424787
$859$	−35.4821	−1.21063	−0.605317	−	0.795984i	$-0.706954\pi$
$859$	−35.4821	−1.21063	−0.605317	+	0.795984i	$0.706954\pi$
$860$	−35.2587	−1.20231
$861$	−8.29439	−0.282672
$862$	−18.6592	−0.635535
$863$	−7.29535	−0.248337	−0.124168	−	0.992261i	$-0.539626\pi$
$863$	−7.29535	−0.248337	−0.124168	+	0.992261i	$0.539626\pi$
$864$	0.108413	0.00368828
$865$	61.2024	2.08094
$866$	86.6615	2.94488
$867$	−19.0607	−0.647337
$868$	−19.3187	−0.655721
$869$	−32.8221	−1.11341
$870$	−61.3879	−2.08124
$871$	3.32332	0.112607
$872$	−5.76715	−0.195300
$873$	0.182181	0.00616591
$874$	46.5649	1.57508
$875$	13.5437	0.457862
$876$	−34.3627	−1.16101
$877$	28.6608	0.967805	0.483902	−	0.875122i	$-0.339219\pi$
$877$	28.6608	0.967805	0.483902	+	0.875122i	$0.339219\pi$
$878$	97.6776	3.29646
$879$	−13.0941	−0.441653
$880$	29.2212	0.985046
$881$	−16.7224	−0.563393	−0.281696	−	0.959504i	$-0.590897\pi$
$881$	−16.7224	−0.563393	−0.281696	+	0.959504i	$0.590897\pi$
$882$	−4.24325	−0.142878
$883$	44.1094	1.48440	0.742201	−	0.670178i	$-0.233782\pi$
$883$	44.1094	1.48440	0.742201	+	0.670178i	$0.233782\pi$
$884$	−21.4012	−0.719801
$885$	−49.1812	−1.65321
$886$	57.7659	1.94068
$887$	27.0432	0.908021	0.454010	−	0.890996i	$-0.349993\pi$
$887$	27.0432	0.908021	0.454010	+	0.890996i	$0.349993\pi$
$888$	−0.967316	−0.0324610
$889$	−0.511487	−0.0171547
$890$	−94.3906	−3.16398
$891$	24.5978	0.824057
$892$	108.984	3.64904
$893$	1.21791	0.0407558
$894$	−64.1107	−2.14418
$895$	−24.7024	−0.825709
$896$	25.3846	0.848041
$897$	10.0287	0.334848
$898$	11.1376	0.371667
$899$	−24.2587	−0.809073
$900$	−0.733358	−0.0244453
$901$	−61.9706	−2.06454
$902$	29.8126	0.992650
$903$	−7.91432	−0.263372
$904$	83.0837	2.76332
$905$	−22.6296	−0.752233
$906$	−14.3303	−0.476091
$907$	32.4627	1.07791	0.538954	−	0.842335i	$-0.318820\pi$
$907$	32.4627	1.07791	0.538954	+	0.842335i	$0.318820\pi$
$908$	−103.468	−3.43370
$909$	−3.84551	−0.127548
$910$	7.47694	0.247858
$911$	11.3058	0.374578	0.187289	−	0.982305i	$-0.440030\pi$
$911$	11.3058	0.374578	0.187289	+	0.982305i	$0.440030\pi$
$912$	−20.2212	−0.669590
$913$	−8.72552	−0.288773
$914$	−80.5172	−2.66327
$915$	−10.7670	−0.355946
$916$	52.4368	1.73256
$917$	10.8335	0.357754
$918$	71.2974	2.35317
$919$	48.1869	1.58954	0.794770	−	0.606911i	$-0.207591\pi$
$919$	48.1869	1.58954	0.794770	+	0.606911i	$0.207591\pi$
$920$	−70.7761	−2.33342
$921$	14.7651	0.486528
$922$	13.1342	0.432552
$923$	4.97459	0.163741
$924$	26.2900	0.864877
$925$	−0.0681443	−0.00224057
$926$	−2.44907	−0.0804816
$927$	−3.20009	−0.105105
$928$	0.129531	0.00425207
$929$	27.3489	0.897290	0.448645	−	0.893710i	$-0.351907\pi$
$929$	27.3489	0.897290	0.448645	+	0.893710i	$0.351907\pi$
$930$	35.2710	1.15658
$931$	−16.5099	−0.541089
$932$	86.8034	2.84334
$933$	39.4849	1.29268
$934$	24.0693	0.787571
$935$	−39.2252	−1.28280
$936$	1.59216	0.0520413
$937$	−41.3385	−1.35047	−0.675235	−	0.737603i	$-0.735958\pi$
$937$	−41.3385	−1.35047	−0.675235	+	0.737603i	$0.735958\pi$
$938$	−10.5345	−0.343963
$939$	−25.2730	−0.824753
$940$	−3.70419	−0.120817
$941$	−7.37604	−0.240452	−0.120226	−	0.992747i	$-0.538362\pi$
$941$	−7.37604	−0.240452	−0.120226	+	0.992747i	$0.538362\pi$
$942$	68.4344	2.22971
$943$	−24.0286	−0.782478
$944$	−50.8414	−1.65475
$945$	−16.6033	−0.540106
$946$	28.4465	0.924875
$947$	−7.72737	−0.251106	−0.125553	−	0.992087i	$-0.540071\pi$
$947$	−7.72737	−0.251106	−0.125553	+	0.992087i	$0.540071\pi$
$948$	−69.0803	−2.24362
$949$	5.25555	0.170602
$950$	−4.28082	−0.138888
$951$	−38.1951	−1.23856
$952$	33.9022	1.09878
$953$	−13.7746	−0.446203	−0.223102	−	0.974795i	$-0.571618\pi$
$953$	−13.7746	−0.446203	−0.223102	+	0.974795i	$0.571618\pi$
$954$	9.22539	0.298683
$955$	30.2186	0.977852
$956$	81.4371	2.63386
$957$	33.0126	1.06715
$958$	−48.7203	−1.57408
$959$	19.7007	0.636169
$960$	−30.9547	−0.999059
$961$	−17.0619	−0.550385
$962$	0.296040	0.00954471
$963$	3.68114	0.118623
$964$	10.3163	0.332264
$965$	22.1155	0.711924
$966$	−31.7896	−1.02281
$967$	−44.0421	−1.41630	−0.708149	−	0.706063i	$-0.750469\pi$
$967$	−44.0421	−1.41630	−0.708149	+	0.706063i	$0.750469\pi$
$968$	6.60171	0.212187
$969$	27.1440	0.871991
$970$	−3.23440	−0.103850
$971$	−19.4923	−0.625537	−0.312769	−	0.949829i	$-0.601256\pi$
$971$	−19.4923	−0.625537	−0.312769	+	0.949829i	$0.601256\pi$
$972$	−13.4571	−0.431638
$973$	15.6977	0.503245
$974$	−58.4825	−1.87390
$975$	−0.921960	−0.0295263
$976$	−11.1305	−0.356277
$977$	−18.4073	−0.588900	−0.294450	−	0.955667i	$-0.595136\pi$
$977$	−18.4073	−0.588900	−0.294450	+	0.955667i	$0.595136\pi$
$978$	52.4588	1.67745
$979$	50.7605	1.62231
$980$	50.2137	1.60402
$981$	−0.383502	−0.0122443
$982$	68.2633	2.17837
$983$	19.0199	0.606640	0.303320	−	0.952889i	$-0.401905\pi$
$983$	19.0199	0.606640	0.303320	+	0.952889i	$0.401905\pi$
$984$	31.3571	0.999626
$985$	−38.8682	−1.23844
$986$	85.1859	2.71287
$987$	−0.831458	−0.0264656
$988$	12.3960	0.394370
$989$	−22.9276	−0.729054
$990$	5.83934	0.185587
$991$	16.7970	0.533574	0.266787	−	0.963756i	$-0.414038\pi$
$991$	16.7970	0.533574	0.266787	+	0.963756i	$0.414038\pi$
$992$	−0.0744234	−0.00236295
$993$	−23.6787	−0.751419
$994$	−15.7688	−0.500155
$995$	−20.4711	−0.648977
$996$	−18.3645	−0.581901
$997$	−42.5678	−1.34813	−0.674067	−	0.738670i	$-0.735454\pi$
$997$	−42.5678	−1.34813	−0.674067	+	0.738670i	$0.735454\pi$
$998$	81.8121	2.58972
$999$	−0.657386	−0.0207988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.9	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.9	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44907 q^{2} -1.63543 q^{3} +3.99796 q^{4} -2.35876 q^{5} +4.00528 q^{6} +1.29431 q^{7} -4.89316 q^{8} -0.325384 q^{9} +O(q^{10})\)	\(q-2.44907 q^{2} -1.63543 q^{3} +3.99796 q^{4} -2.35876 q^{5} +4.00528 q^{6} +1.29431 q^{7} -4.89316 q^{8} -0.325384 q^{9} +5.77678 q^{10} -3.10658 q^{11} -6.53837 q^{12} +1.00000 q^{13} -3.16986 q^{14} +3.85757 q^{15} +3.98779 q^{16} -5.35303 q^{17} +0.796890 q^{18} +3.10058 q^{19} -9.43023 q^{20} -2.11675 q^{21} +7.60824 q^{22} -6.13216 q^{23} +8.00240 q^{24} +0.563743 q^{25} -2.44907 q^{26} +5.43842 q^{27} +5.17461 q^{28} +6.49780 q^{29} -9.44748 q^{30} -3.73337 q^{31} +0.0199346 q^{32} +5.08058 q^{33} +13.1100 q^{34} -3.05297 q^{35} -1.30087 q^{36} -0.120878 q^{37} -7.59356 q^{38} -1.63543 q^{39} +11.5418 q^{40} +3.91846 q^{41} +5.18407 q^{42} +3.73891 q^{43} -12.4200 q^{44} +0.767502 q^{45} +15.0181 q^{46} +0.392800 q^{47} -6.52173 q^{48} -5.32476 q^{49} -1.38065 q^{50} +8.75448 q^{51} +3.99796 q^{52} +11.5767 q^{53} -13.3191 q^{54} +7.32767 q^{55} -6.33327 q^{56} -5.07077 q^{57} -15.9136 q^{58} -12.7493 q^{59} +15.4224 q^{60} -2.79114 q^{61} +9.14331 q^{62} -0.421148 q^{63} -8.02440 q^{64} -2.35876 q^{65} -12.4427 q^{66} +3.32332 q^{67} -21.4012 q^{68} +10.0287 q^{69} +7.47694 q^{70} +4.97459 q^{71} +1.59216 q^{72} +5.25555 q^{73} +0.296040 q^{74} -0.921960 q^{75} +12.3960 q^{76} -4.02088 q^{77} +4.00528 q^{78} +10.5654 q^{79} -9.40623 q^{80} -7.91797 q^{81} -9.59659 q^{82} +2.80872 q^{83} -8.46268 q^{84} +12.6265 q^{85} -9.15686 q^{86} -10.6267 q^{87} +15.2010 q^{88} -16.3397 q^{89} -1.87967 q^{90} +1.29431 q^{91} -24.5161 q^{92} +6.10565 q^{93} -0.961995 q^{94} -7.31353 q^{95} -0.0326016 q^{96} -0.559897 q^{97} +13.0407 q^{98} +1.01083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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