LMFDB - Embedded newform 6019.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.66557 q^{2} -0.463578 q^{3} +5.10529 q^{4} +3.99027 q^{5} +1.23570 q^{6} -1.40213 q^{7} -8.27737 q^{8} -2.78510 q^{9} +O(q^{10})$	\(q-2.66557 q^{2} -0.463578 q^{3} +5.10529 q^{4} +3.99027 q^{5} +1.23570 q^{6} -1.40213 q^{7} -8.27737 q^{8} -2.78510 q^{9} -10.6364 q^{10} +0.718687 q^{11} -2.36670 q^{12} +1.00000 q^{13} +3.73748 q^{14} -1.84980 q^{15} +11.8534 q^{16} +1.34196 q^{17} +7.42388 q^{18} -0.874120 q^{19} +20.3715 q^{20} +0.649996 q^{21} -1.91571 q^{22} -7.62495 q^{23} +3.83720 q^{24} +10.9223 q^{25} -2.66557 q^{26} +2.68184 q^{27} -7.15827 q^{28} -6.15672 q^{29} +4.93078 q^{30} -4.79738 q^{31} -15.0413 q^{32} -0.333167 q^{33} -3.57711 q^{34} -5.59488 q^{35} -14.2187 q^{36} -4.85010 q^{37} +2.33003 q^{38} -0.463578 q^{39} -33.0289 q^{40} +3.40375 q^{41} -1.73261 q^{42} +10.6532 q^{43} +3.66910 q^{44} -11.1133 q^{45} +20.3249 q^{46} +3.65512 q^{47} -5.49496 q^{48} -5.03403 q^{49} -29.1141 q^{50} -0.622105 q^{51} +5.10529 q^{52} +4.36835 q^{53} -7.14865 q^{54} +2.86775 q^{55} +11.6059 q^{56} +0.405223 q^{57} +16.4112 q^{58} -0.291354 q^{59} -9.44376 q^{60} +7.01380 q^{61} +12.7878 q^{62} +3.90507 q^{63} +16.3869 q^{64} +3.99027 q^{65} +0.888082 q^{66} +7.11883 q^{67} +6.85111 q^{68} +3.53476 q^{69} +14.9136 q^{70} +11.2560 q^{71} +23.0533 q^{72} -6.07042 q^{73} +12.9283 q^{74} -5.06331 q^{75} -4.46263 q^{76} -1.00769 q^{77} +1.23570 q^{78} +0.898302 q^{79} +47.2981 q^{80} +7.11205 q^{81} -9.07294 q^{82} +1.41895 q^{83} +3.31842 q^{84} +5.35480 q^{85} -28.3969 q^{86} +2.85412 q^{87} -5.94884 q^{88} -14.0070 q^{89} +29.6233 q^{90} -1.40213 q^{91} -38.9275 q^{92} +2.22396 q^{93} -9.74300 q^{94} -3.48798 q^{95} +6.97281 q^{96} -9.88324 q^{97} +13.4186 q^{98} -2.00161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66557	−1.88485	−0.942423	−	0.334424i	$-0.891458\pi$
$2$	−2.66557	−1.88485	−0.942423	+	0.334424i	$0.891458\pi$
$3$	−0.463578	−0.267647	−0.133823	−	0.991005i	$-0.542725\pi$
$3$	−0.463578	−0.267647	−0.133823	+	0.991005i	$0.542725\pi$
$4$	5.10529	2.55264
$5$	3.99027	1.78450	0.892252	−	0.451539i	$-0.149125\pi$
$5$	3.99027	1.78450	0.892252	+	0.451539i	$0.149125\pi$
$6$	1.23570	0.504473
$7$	−1.40213	−0.529955	−0.264978	−	0.964255i	$-0.585365\pi$
$7$	−1.40213	−0.529955	−0.264978	+	0.964255i	$0.585365\pi$
$8$	−8.27737	−2.92649
$9$	−2.78510	−0.928365
$10$	−10.6364	−3.36351
$11$	0.718687	0.216692	0.108346	−	0.994113i	$-0.465445\pi$
$11$	0.718687	0.216692	0.108346	+	0.994113i	$0.465445\pi$
$12$	−2.36670	−0.683206
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.73748	0.998884
$15$	−1.84980	−0.477616
$16$	11.8534	2.96334
$17$	1.34196	0.325474	0.162737	−	0.986669i	$-0.447968\pi$
$17$	1.34196	0.325474	0.162737	+	0.986669i	$0.447968\pi$
$18$	7.42388	1.74983
$19$	−0.874120	−0.200537	−0.100268	−	0.994960i	$-0.531970\pi$
$19$	−0.874120	−0.200537	−0.100268	+	0.994960i	$0.531970\pi$
$20$	20.3715	4.55520
$21$	0.649996	0.141841
$22$	−1.91571	−0.408431
$23$	−7.62495	−1.58991	−0.794956	−	0.606667i	$-0.792506\pi$
$23$	−7.62495	−1.58991	−0.794956	+	0.606667i	$0.792506\pi$
$24$	3.83720	0.783266
$25$	10.9223	2.18445
$26$	−2.66557	−0.522762
$27$	2.68184	0.516121
$28$	−7.15827	−1.35279
$29$	−6.15672	−1.14327	−0.571637	−	0.820506i	$-0.693692\pi$
$29$	−6.15672	−1.14327	−0.571637	+	0.820506i	$0.693692\pi$
$30$	4.93078	0.900233
$31$	−4.79738	−0.861634	−0.430817	−	0.902439i	$-0.641775\pi$
$31$	−4.79738	−0.861634	−0.430817	+	0.902439i	$0.641775\pi$
$32$	−15.0413	−2.65895
$33$	−0.333167	−0.0579970
$34$	−3.57711	−0.613468
$35$	−5.59488	−0.945707
$36$	−14.2187	−2.36978
$37$	−4.85010	−0.797352	−0.398676	−	0.917092i	$-0.630530\pi$
$37$	−4.85010	−0.797352	−0.398676	+	0.917092i	$0.630530\pi$
$38$	2.33003	0.377981
$39$	−0.463578	−0.0742318
$40$	−33.0289	−5.22233
$41$	3.40375	0.531576	0.265788	−	0.964031i	$-0.414368\pi$
$41$	3.40375	0.531576	0.265788	+	0.964031i	$0.414368\pi$
$42$	−1.73261	−0.267348
$43$	10.6532	1.62460	0.812300	−	0.583240i	$-0.198215\pi$
$43$	10.6532	1.62460	0.812300	+	0.583240i	$0.198215\pi$
$44$	3.66910	0.553138
$45$	−11.1133	−1.65667
$46$	20.3249	2.99674
$47$	3.65512	0.533154	0.266577	−	0.963814i	$-0.414107\pi$
$47$	3.65512	0.533154	0.266577	+	0.963814i	$0.414107\pi$
$48$	−5.49496	−0.793129
$49$	−5.03403	−0.719147
$50$	−29.1141	−4.11735
$51$	−0.622105	−0.0871121
$52$	5.10529	0.707976
$53$	4.36835	0.600040	0.300020	−	0.953933i	$-0.403007\pi$
$53$	4.36835	0.600040	0.300020	+	0.953933i	$0.403007\pi$
$54$	−7.14865	−0.972808
$55$	2.86775	0.386688
$56$	11.6059	1.55091
$57$	0.405223	0.0536730
$58$	16.4112	2.15490
$59$	−0.291354	−0.0379311	−0.0189655	−	0.999820i	$-0.506037\pi$
$59$	−0.291354	−0.0379311	−0.0189655	+	0.999820i	$0.506037\pi$
$60$	−9.44376	−1.21918
$61$	7.01380	0.898025	0.449012	−	0.893526i	$-0.351776\pi$
$61$	7.01380	0.898025	0.449012	+	0.893526i	$0.351776\pi$
$62$	12.7878	1.62405
$63$	3.90507	0.491992
$64$	16.3869	2.04837
$65$	3.99027	0.494932
$66$	0.888082	0.109315
$67$	7.11883	0.869704	0.434852	−	0.900502i	$-0.356801\pi$
$67$	7.11883	0.869704	0.434852	+	0.900502i	$0.356801\pi$
$68$	6.85111	0.830819
$69$	3.53476	0.425535
$70$	14.9136	1.78251
$71$	11.2560	1.33584	0.667919	−	0.744234i	$-0.267185\pi$
$71$	11.2560	1.33584	0.667919	+	0.744234i	$0.267185\pi$
$72$	23.0533	2.71685
$73$	−6.07042	−0.710488	−0.355244	−	0.934774i	$-0.615602\pi$
$73$	−6.07042	−0.710488	−0.355244	+	0.934774i	$0.615602\pi$
$74$	12.9283	1.50288
$75$	−5.06331	−0.584661
$76$	−4.46263	−0.511899
$77$	−1.00769	−0.114837
$78$	1.23570	0.139916
$79$	0.898302	0.101067	0.0505334	−	0.998722i	$-0.483908\pi$
$79$	0.898302	0.101067	0.0505334	+	0.998722i	$0.483908\pi$
$80$	47.2981	5.28809
$81$	7.11205	0.790227
$82$	−9.07294	−1.00194
$83$	1.41895	0.155750	0.0778751	−	0.996963i	$-0.475186\pi$
$83$	1.41895	0.155750	0.0778751	+	0.996963i	$0.475186\pi$
$84$	3.31842	0.362069
$85$	5.35480	0.580810
$86$	−28.3969	−3.06212
$87$	2.85412	0.305994
$88$	−5.94884	−0.634148
$89$	−14.0070	−1.48474	−0.742371	−	0.669989i	$-0.766299\pi$
$89$	−14.0070	−1.48474	−0.742371	+	0.669989i	$0.766299\pi$
$90$	29.6233	3.12257
$91$	−1.40213	−0.146983
$92$	−38.9275	−4.05848
$93$	2.22396	0.230614
$94$	−9.74300	−1.00491
$95$	−3.48798	−0.357859
$96$	6.97281	0.711659
$97$	−9.88324	−1.00349	−0.501746	−	0.865015i	$-0.667309\pi$
$97$	−9.88324	−1.00349	−0.501746	+	0.865015i	$0.667309\pi$
$98$	13.4186	1.35548
$99$	−2.00161	−0.201170
$100$	55.7612	5.57612
$101$	−15.4361	−1.53595	−0.767974	−	0.640481i	$-0.778735\pi$
$101$	−15.4361	−1.53595	−0.767974	+	0.640481i	$0.778735\pi$
$102$	1.65827	0.164193
$103$	−1.32920	−0.130970	−0.0654851	−	0.997854i	$-0.520859\pi$
$103$	−1.32920	−0.130970	−0.0654851	+	0.997854i	$0.520859\pi$
$104$	−8.27737	−0.811663
$105$	2.59366	0.253115
$106$	−11.6442	−1.13098
$107$	4.55390	0.440242	0.220121	−	0.975473i	$-0.429355\pi$
$107$	4.55390	0.440242	0.220121	+	0.975473i	$0.429355\pi$
$108$	13.6916	1.31747
$109$	−9.61451	−0.920903	−0.460452	−	0.887685i	$-0.652313\pi$
$109$	−9.61451	−0.920903	−0.460452	+	0.887685i	$0.652313\pi$
$110$	−7.64421	−0.728847
$111$	2.24840	0.213409
$112$	−16.6200	−1.57044
$113$	−4.45560	−0.419147	−0.209574	−	0.977793i	$-0.567208\pi$
$113$	−4.45560	−0.419147	−0.209574	+	0.977793i	$0.567208\pi$
$114$	−1.08015	−0.101165
$115$	−30.4256	−2.83720
$116$	−31.4318	−2.91837
$117$	−2.78510	−0.257482
$118$	0.776626	0.0714942
$119$	−1.88161	−0.172487
$120$	15.3115	1.39774
$121$	−10.4835	−0.953044
$122$	−18.6958	−1.69264
$123$	−1.57790	−0.142275
$124$	−24.4920	−2.19944
$125$	23.6314	2.11366
$126$	−10.4092	−0.927329
$127$	17.8936	1.58780	0.793901	−	0.608048i	$-0.208047\pi$
$127$	17.8936	1.58780	0.793901	+	0.608048i	$0.208047\pi$
$128$	−13.5980	−1.20191
$129$	−4.93859	−0.434819
$130$	−10.6364	−0.932871
$131$	5.77752	0.504784	0.252392	−	0.967625i	$-0.418783\pi$
$131$	5.77752	0.504784	0.252392	+	0.967625i	$0.418783\pi$
$132$	−1.70091	−0.148046
$133$	1.22563	0.106276
$134$	−18.9758	−1.63926
$135$	10.7013	0.921019
$136$	−11.1079	−0.952497
$137$	3.81346	0.325806	0.162903	−	0.986642i	$-0.447914\pi$
$137$	3.81346	0.325806	0.162903	+	0.986642i	$0.447914\pi$
$138$	−9.42215	−0.802067
$139$	−10.3352	−0.876623	−0.438312	−	0.898823i	$-0.644423\pi$
$139$	−10.3352	−0.876623	−0.438312	+	0.898823i	$0.644423\pi$
$140$	−28.5634	−2.41405
$141$	−1.69443	−0.142697
$142$	−30.0036	−2.51785
$143$	0.718687	0.0600996
$144$	−33.0128	−2.75106
$145$	−24.5670	−2.04018
$146$	16.1811	1.33916
$147$	2.33366	0.192477
$148$	−24.7611	−2.03535
$149$	−18.9638	−1.55357	−0.776787	−	0.629764i	$-0.783152\pi$
$149$	−18.9638	−1.55357	−0.776787	+	0.629764i	$0.783152\pi$
$150$	13.4966	1.10200
$151$	−6.80891	−0.554101	−0.277051	−	0.960855i	$-0.589357\pi$
$151$	−6.80891	−0.554101	−0.277051	+	0.960855i	$0.589357\pi$
$152$	7.23541	0.586870
$153$	−3.73750	−0.302159
$154$	2.68608	0.216450
$155$	−19.1428	−1.53759
$156$	−2.36670	−0.189487
$157$	−17.5357	−1.39950	−0.699751	−	0.714387i	$-0.746706\pi$
$157$	−17.5357	−1.39950	−0.699751	+	0.714387i	$0.746706\pi$
$158$	−2.39449	−0.190495
$159$	−2.02507	−0.160599
$160$	−60.0188	−4.74490
$161$	10.6912	0.842582
$162$	−18.9577	−1.48946
$163$	−0.808055	−0.0632917	−0.0316459	−	0.999499i	$-0.510075\pi$
$163$	−0.808055	−0.0632917	−0.0316459	+	0.999499i	$0.510075\pi$
$164$	17.3771	1.35692
$165$	−1.32943	−0.103496
$166$	−3.78232	−0.293565
$167$	−3.92423	−0.303666	−0.151833	−	0.988406i	$-0.548518\pi$
$167$	−3.92423	−0.303666	−0.151833	+	0.988406i	$0.548518\pi$
$168$	−5.38026	−0.415096
$169$	1.00000	0.0769231
$170$	−14.2736	−1.09474
$171$	2.43451	0.186172
$172$	54.3877	4.14702
$173$	10.1568	0.772206	0.386103	−	0.922456i	$-0.373821\pi$
$173$	10.1568	0.772206	0.386103	+	0.922456i	$0.373821\pi$
$174$	−7.60787	−0.576751
$175$	−15.3144	−1.15766
$176$	8.51886	0.642133
$177$	0.135065	0.0101521
$178$	37.3368	2.79851
$179$	0.0668596	0.00499732	0.00249866	−	0.999997i	$-0.499205\pi$
$179$	0.0668596	0.00499732	0.00249866	+	0.999997i	$0.499205\pi$
$180$	−56.7365	−4.22889
$181$	11.8401	0.880069	0.440035	−	0.897981i	$-0.354966\pi$
$181$	11.8401	0.880069	0.440035	+	0.897981i	$0.354966\pi$
$182$	3.73748	0.277041
$183$	−3.25144	−0.240353
$184$	63.1145	4.65286
$185$	−19.3532	−1.42288
$186$	−5.92812	−0.434671
$187$	0.964452	0.0705277
$188$	18.6604	1.36095
$189$	−3.76029	−0.273521
$190$	9.29746	0.674508
$191$	−18.1467	−1.31305	−0.656525	−	0.754304i	$-0.727974\pi$
$191$	−18.1467	−1.31305	−0.656525	+	0.754304i	$0.727974\pi$
$192$	−7.59662	−0.548239
$193$	1.68140	0.121030	0.0605149	−	0.998167i	$-0.480726\pi$
$193$	1.68140	0.121030	0.0605149	+	0.998167i	$0.480726\pi$
$194$	26.3445	1.89143
$195$	−1.84980	−0.132467
$196$	−25.7002	−1.83573
$197$	−18.9115	−1.34739	−0.673695	−	0.739010i	$-0.735294\pi$
$197$	−18.9115	−1.34739	−0.673695	+	0.739010i	$0.735294\pi$
$198$	5.33544	0.379174
$199$	−17.6225	−1.24923	−0.624613	−	0.780934i	$-0.714743\pi$
$199$	−17.6225	−1.24923	−0.624613	+	0.780934i	$0.714743\pi$
$200$	−90.4075	−6.39278
$201$	−3.30013	−0.232773
$202$	41.1460	2.89503
$203$	8.63253	0.605885
$204$	−3.17602	−0.222366
$205$	13.5819	0.948599
$206$	3.54309	0.246859
$207$	21.2362	1.47602
$208$	11.8534	0.821883
$209$	−0.628219	−0.0434548
$210$	−6.91359	−0.477083
$211$	−7.16078	−0.492968	−0.246484	−	0.969147i	$-0.579275\pi$
$211$	−7.16078	−0.492968	−0.246484	+	0.969147i	$0.579275\pi$
$212$	22.3017	1.53169
$213$	−5.21802	−0.357533
$214$	−12.1387	−0.829788
$215$	42.5092	2.89910
$216$	−22.1986	−1.51042
$217$	6.72654	0.456628
$218$	25.6282	1.73576
$219$	2.81411	0.190160
$220$	14.6407	0.987076
$221$	1.34196	0.0902703
$222$	−5.99327	−0.402242
$223$	5.24321	0.351111	0.175555	−	0.984470i	$-0.443828\pi$
$223$	5.24321	0.351111	0.175555	+	0.984470i	$0.443828\pi$
$224$	21.0898	1.40912
$225$	−30.4195	−2.02797
$226$	11.8767	0.790028
$227$	10.8453	0.719830	0.359915	−	0.932985i	$-0.382806\pi$
$227$	10.8453	0.719830	0.359915	+	0.932985i	$0.382806\pi$
$228$	2.06878	0.137008
$229$	−2.82912	−0.186953	−0.0934767	−	0.995621i	$-0.529798\pi$
$229$	−2.82912	−0.186953	−0.0934767	+	0.995621i	$0.529798\pi$
$230$	81.1017	5.34769
$231$	0.467144	0.0307358
$232$	50.9615	3.34578
$233$	−10.4297	−0.683273	−0.341636	−	0.939832i	$-0.610981\pi$
$233$	−10.4297	−0.683273	−0.341636	+	0.939832i	$0.610981\pi$
$234$	7.42388	0.485314
$235$	14.5849	0.951416
$236$	−1.48745	−0.0968244
$237$	−0.416433	−0.0270502
$238$	5.01557	0.325111
$239$	−6.56699	−0.424783	−0.212392	−	0.977185i	$-0.568125\pi$
$239$	−6.56699	−0.424783	−0.212392	+	0.977185i	$0.568125\pi$
$240$	−21.9264	−1.41534
$241$	27.8434	1.79355	0.896774	−	0.442488i	$-0.145904\pi$
$241$	27.8434	1.79355	0.896774	+	0.442488i	$0.145904\pi$
$242$	27.9445	1.79634
$243$	−11.3425	−0.727622
$244$	35.8074	2.29234
$245$	−20.0871	−1.28332
$246$	4.20601	0.268166
$247$	−0.874120	−0.0556189
$248$	39.7096	2.52156
$249$	−0.657794	−0.0416860
$250$	−62.9912	−3.98392
$251$	−1.01410	−0.0640093	−0.0320047	−	0.999488i	$-0.510189\pi$
$251$	−1.01410	−0.0640093	−0.0320047	+	0.999488i	$0.510189\pi$
$252$	19.9365	1.25588
$253$	−5.47995	−0.344522
$254$	−47.6967	−2.99276
$255$	−2.48237	−0.155452
$256$	3.47268	0.217042
$257$	−13.2283	−0.825159	−0.412580	−	0.910921i	$-0.635372\pi$
$257$	−13.2283	−0.825159	−0.412580	+	0.910921i	$0.635372\pi$
$258$	13.1642	0.819566
$259$	6.80047	0.422561
$260$	20.3715	1.26338
$261$	17.1471	1.06138
$262$	−15.4004	−0.951440
$263$	−28.4257	−1.75280	−0.876402	−	0.481580i	$-0.840063\pi$
$263$	−28.4257	−1.75280	−0.876402	+	0.481580i	$0.840063\pi$
$264$	2.75775	0.169728
$265$	17.4309	1.07077
$266$	−3.26701	−0.200313
$267$	6.49335	0.397387
$268$	36.3437	2.22004
$269$	−29.1261	−1.77585	−0.887925	−	0.459987i	$-0.847854\pi$
$269$	−29.1261	−1.77585	−0.887925	+	0.459987i	$0.847854\pi$
$270$	−28.5250	−1.73598
$271$	−11.3507	−0.689507	−0.344753	−	0.938693i	$-0.612037\pi$
$271$	−11.3507	−0.689507	−0.344753	+	0.938693i	$0.612037\pi$
$272$	15.9068	0.964491
$273$	0.649996	0.0393396
$274$	−10.1651	−0.614093
$275$	7.84968	0.473354
$276$	18.0459	1.08624
$277$	−32.5941	−1.95839	−0.979194	−	0.202927i	$-0.934955\pi$
$277$	−32.5941	−1.95839	−0.979194	+	0.202927i	$0.934955\pi$
$278$	27.5493	1.65230
$279$	13.3612	0.799911
$280$	46.3109	2.76760
$281$	−23.5319	−1.40380	−0.701898	−	0.712277i	$-0.747664\pi$
$281$	−23.5319	−1.40380	−0.701898	+	0.712277i	$0.747664\pi$
$282$	4.51664	0.268962
$283$	4.75787	0.282826	0.141413	−	0.989951i	$-0.454835\pi$
$283$	4.75787	0.282826	0.141413	+	0.989951i	$0.454835\pi$
$284$	57.4650	3.40992
$285$	1.61695	0.0957797
$286$	−1.91571	−0.113278
$287$	−4.77250	−0.281712
$288$	41.8914	2.46848
$289$	−15.1991	−0.894067
$290$	65.4851	3.84542
$291$	4.58165	0.268581
$292$	−30.9912	−1.81362
$293$	14.3208	0.836630	0.418315	−	0.908302i	$-0.362621\pi$
$293$	14.3208	0.836630	0.418315	+	0.908302i	$0.362621\pi$
$294$	−6.22056	−0.362790
$295$	−1.16258	−0.0676881
$296$	40.1461	2.33344
$297$	1.92740	0.111839
$298$	50.5494	2.92825
$299$	−7.62495	−0.440962
$300$	−25.8497	−1.49243
$301$	−14.9372	−0.860965
$302$	18.1497	1.04440
$303$	7.15583	0.411092
$304$	−10.3613	−0.594260
$305$	27.9869	1.60253
$306$	9.96258	0.569523
$307$	26.3300	1.50273	0.751367	−	0.659885i	$-0.229395\pi$
$307$	26.3300	1.50273	0.751367	+	0.659885i	$0.229395\pi$
$308$	−5.14456	−0.293138
$309$	0.616189	0.0350538
$310$	51.0266	2.89812
$311$	−2.21146	−0.125400	−0.0627002	−	0.998032i	$-0.519971\pi$
$311$	−2.21146	−0.125400	−0.0627002	+	0.998032i	$0.519971\pi$
$312$	3.83720	0.217239
$313$	−13.1694	−0.744377	−0.372188	−	0.928157i	$-0.621392\pi$
$313$	−13.1694	−0.744377	−0.372188	+	0.928157i	$0.621392\pi$
$314$	46.7427	2.63785
$315$	15.5823	0.877961
$316$	4.58609	0.257988
$317$	−20.6697	−1.16092	−0.580462	−	0.814288i	$-0.697128\pi$
$317$	−20.6697	−1.16092	−0.580462	+	0.814288i	$0.697128\pi$
$318$	5.39798	0.302704
$319$	−4.42476	−0.247739
$320$	65.3883	3.65532
$321$	−2.11108	−0.117829
$322$	−28.4981	−1.58814
$323$	−1.17304	−0.0652696
$324$	36.3090	2.01717
$325$	10.9223	0.605858
$326$	2.15393	0.119295
$327$	4.45707	0.246477
$328$	−28.1741	−1.55565
$329$	−5.12496	−0.282548
$330$	3.54369	0.195074
$331$	32.6628	1.79531	0.897656	−	0.440698i	$-0.145269\pi$
$331$	32.6628	1.79531	0.897656	+	0.440698i	$0.145269\pi$
$332$	7.24415	0.397574
$333$	13.5080	0.740234
$334$	10.4603	0.572364
$335$	28.4061	1.55199
$336$	7.70464	0.420323
$337$	21.6497	1.17934	0.589668	−	0.807646i	$-0.299259\pi$
$337$	21.6497	1.17934	0.589668	+	0.807646i	$0.299259\pi$
$338$	−2.66557	−0.144988
$339$	2.06552	0.112183
$340$	27.3378	1.48260
$341$	−3.44781	−0.186709
$342$	−6.48936	−0.350905
$343$	16.8733	0.911071
$344$	−88.1805	−4.75438
$345$	14.1046	0.759368
$346$	−27.0737	−1.45549
$347$	−5.91835	−0.317714	−0.158857	−	0.987302i	$-0.550781\pi$
$347$	−5.91835	−0.317714	−0.158857	+	0.987302i	$0.550781\pi$
$348$	14.5711	0.781093
$349$	1.73786	0.0930253	0.0465127	−	0.998918i	$-0.485189\pi$
$349$	1.73786	0.0930253	0.0465127	+	0.998918i	$0.485189\pi$
$350$	40.8217	2.18201
$351$	2.68184	0.143146
$352$	−10.8100	−0.576174
$353$	−35.6418	−1.89702	−0.948510	−	0.316747i	$-0.897409\pi$
$353$	−35.6418	−1.89702	−0.948510	+	0.316747i	$0.897409\pi$
$354$	−0.360026	−0.0191352
$355$	44.9144	2.38381
$356$	−71.5099	−3.79002
$357$	0.872272	0.0461655
$358$	−0.178219	−0.00941918
$359$	22.0694	1.16478	0.582388	−	0.812911i	$-0.302118\pi$
$359$	22.0694	1.16478	0.582388	+	0.812911i	$0.302118\pi$
$360$	91.9887	4.84823
$361$	−18.2359	−0.959785
$362$	−31.5607	−1.65879
$363$	4.85991	0.255079
$364$	−7.15827	−0.375195
$365$	−24.2226	−1.26787
$366$	8.66695	0.453029
$367$	33.8620	1.76758	0.883790	−	0.467883i	$-0.154983\pi$
$367$	33.8620	1.76758	0.883790	+	0.467883i	$0.154983\pi$
$368$	−90.3813	−4.71145
$369$	−9.47977	−0.493497
$370$	51.5874	2.68190
$371$	−6.12500	−0.317994
$372$	11.3539	0.588674
$373$	−0.296384	−0.0153462	−0.00767310	−	0.999971i	$-0.502442\pi$
$373$	−0.296384	−0.0153462	−0.00767310	+	0.999971i	$0.502442\pi$
$374$	−2.57082	−0.132934
$375$	−10.9550	−0.565713
$376$	−30.2548	−1.56027
$377$	−6.15672	−0.317087
$378$	10.0233	0.515545
$379$	−16.6387	−0.854675	−0.427337	−	0.904092i	$-0.640548\pi$
$379$	−16.6387	−0.854675	−0.427337	+	0.904092i	$0.640548\pi$
$380$	−17.8071	−0.913486
$381$	−8.29508	−0.424970
$382$	48.3714	2.47490
$383$	−14.2755	−0.729443	−0.364722	−	0.931117i	$-0.618836\pi$
$383$	−14.2755	−0.729443	−0.364722	+	0.931117i	$0.618836\pi$
$384$	6.30375	0.321687
$385$	−4.02096	−0.204927
$386$	−4.48189	−0.228122
$387$	−29.6702	−1.50822
$388$	−50.4568	−2.56155
$389$	−32.9810	−1.67220	−0.836102	−	0.548574i	$-0.815171\pi$
$389$	−32.9810	−1.67220	−0.836102	+	0.548574i	$0.815171\pi$
$390$	4.93078	0.249680
$391$	−10.2324	−0.517475
$392$	41.6685	2.10458
$393$	−2.67833	−0.135104
$394$	50.4100	2.53962
$395$	3.58447	0.180354
$396$	−10.2188	−0.513514
$397$	31.5459	1.58324	0.791622	−	0.611011i	$-0.209237\pi$
$397$	31.5459	1.58324	0.791622	+	0.611011i	$0.209237\pi$
$398$	46.9741	2.35460
$399$	−0.568175	−0.0284443
$400$	129.466	6.47328
$401$	−15.0679	−0.752453	−0.376227	−	0.926528i	$-0.622779\pi$
$401$	−15.0679	−0.752453	−0.376227	+	0.926528i	$0.622779\pi$
$402$	8.79674	0.438742
$403$	−4.79738	−0.238974
$404$	−78.8056	−3.92073
$405$	28.3790	1.41016
$406$	−23.0106	−1.14200
$407$	−3.48570	−0.172780
$408$	5.14939	0.254933
$409$	21.4200	1.05915	0.529575	−	0.848263i	$-0.322351\pi$
$409$	21.4200	1.05915	0.529575	+	0.848263i	$0.322351\pi$
$410$	−36.2035	−1.78796
$411$	−1.76783	−0.0872008
$412$	−6.78596	−0.334320
$413$	0.408516	0.0201018
$414$	−56.6067	−2.78207
$415$	5.66200	0.277937
$416$	−15.0413	−0.737460
$417$	4.79118	0.234625
$418$	1.67456	0.0819056
$419$	24.1281	1.17874	0.589368	−	0.807865i	$-0.299377\pi$
$419$	24.1281	1.17874	0.589368	+	0.807865i	$0.299377\pi$
$420$	13.2414	0.646113
$421$	5.84479	0.284857	0.142429	−	0.989805i	$-0.454509\pi$
$421$	5.84479	0.284857	0.142429	+	0.989805i	$0.454509\pi$
$422$	19.0876	0.929169
$423$	−10.1799	−0.494962
$424$	−36.1585	−1.75601
$425$	14.6573	0.710982
$426$	13.9090	0.673894
$427$	−9.83426	−0.475913
$428$	23.2489	1.12378
$429$	−0.333167	−0.0160855
$430$	−113.311	−5.46436
$431$	−20.5257	−0.988690	−0.494345	−	0.869266i	$-0.664592\pi$
$431$	−20.5257	−0.988690	−0.494345	+	0.869266i	$0.664592\pi$
$432$	31.7889	1.52944
$433$	35.6878	1.71504	0.857522	−	0.514447i	$-0.172003\pi$
$433$	35.6878	1.71504	0.857522	+	0.514447i	$0.172003\pi$
$434$	−17.9301	−0.860672
$435$	11.3887	0.546047
$436$	−49.0848	−2.35074
$437$	6.66512	0.318836
$438$	−7.50122	−0.358422
$439$	21.1646	1.01013	0.505065	−	0.863081i	$-0.331468\pi$
$439$	21.1646	1.01013	0.505065	+	0.863081i	$0.331468\pi$
$440$	−23.7375	−1.13164
$441$	14.0203	0.667631
$442$	−3.57711	−0.170146
$443$	−33.9461	−1.61283	−0.806415	−	0.591350i	$-0.798595\pi$
$443$	−33.9461	−1.61283	−0.806415	+	0.591350i	$0.798595\pi$
$444$	11.4787	0.544756
$445$	−55.8919	−2.64953
$446$	−13.9762	−0.661790
$447$	8.79118	0.415809
$448$	−22.9766	−1.08554
$449$	3.55735	0.167882	0.0839410	−	0.996471i	$-0.473249\pi$
$449$	3.55735	0.167882	0.0839410	+	0.996471i	$0.473249\pi$
$450$	81.0855	3.82241
$451$	2.44623	0.115188
$452$	−22.7471	−1.06993
$453$	3.15646	0.148303
$454$	−28.9090	−1.35677
$455$	−5.59488	−0.262292
$456$	−3.35418	−0.157074
$457$	25.1339	1.17572	0.587858	−	0.808964i	$-0.299971\pi$
$457$	25.1339	1.17572	0.587858	+	0.808964i	$0.299971\pi$
$458$	7.54122	0.352378
$459$	3.59894	0.167984
$460$	−155.331	−7.24236
$461$	20.9976	0.977957	0.488979	−	0.872296i	$-0.337370\pi$
$461$	20.9976	0.977957	0.488979	+	0.872296i	$0.337370\pi$
$462$	−1.24521	−0.0579322
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−72.9779	−3.38791
$465$	8.87419	0.411531
$466$	27.8012	1.28786
$467$	−4.66085	−0.215678	−0.107839	−	0.994168i	$-0.534393\pi$
$467$	−4.66085	−0.215678	−0.107839	+	0.994168i	$0.534393\pi$
$468$	−14.2187	−0.657260
$469$	−9.98153	−0.460904
$470$	−38.8772	−1.79327
$471$	8.12917	0.374572
$472$	2.41164	0.111005
$473$	7.65632	0.352038
$474$	1.11003	0.0509855
$475$	−9.54736	−0.438063
$476$	−9.60615	−0.440297
$477$	−12.1663	−0.557056
$478$	17.5048	0.800651
$479$	−10.7372	−0.490597	−0.245299	−	0.969448i	$-0.578886\pi$
$479$	−10.7372	−0.490597	−0.245299	+	0.969448i	$0.578886\pi$
$480$	27.8234	1.26996
$481$	−4.85010	−0.221146
$482$	−74.2186	−3.38056
$483$	−4.95619	−0.225514
$484$	−53.5212	−2.43278
$485$	−39.4368	−1.79073
$486$	30.2343	1.37146
$487$	−36.1706	−1.63904	−0.819522	−	0.573047i	$-0.805761\pi$
$487$	−36.1706	−1.63904	−0.819522	+	0.573047i	$0.805761\pi$
$488$	−58.0558	−2.62806
$489$	0.374596	0.0169398
$490$	53.5438	2.41886
$491$	−10.2801	−0.463933	−0.231966	−	0.972724i	$-0.574516\pi$
$491$	−10.2801	−0.463933	−0.231966	+	0.972724i	$0.574516\pi$
$492$	−8.05564	−0.363176
$493$	−8.26210	−0.372106
$494$	2.33003	0.104833
$495$	−7.98697	−0.358988
$496$	−56.8651	−2.55332
$497$	−15.7823	−0.707935
$498$	1.75340	0.0785717
$499$	16.7805	0.751198	0.375599	−	0.926782i	$-0.377437\pi$
$499$	16.7805	0.751198	0.375599	+	0.926782i	$0.377437\pi$
$500$	120.645	5.39541
$501$	1.81919	0.0812752
$502$	2.70315	0.120648
$503$	−11.7747	−0.525009	−0.262504	−	0.964931i	$-0.584548\pi$
$503$	−11.7747	−0.525009	−0.262504	+	0.964931i	$0.584548\pi$
$504$	−32.3237	−1.43981
$505$	−61.5942	−2.74090
$506$	14.6072	0.649370
$507$	−0.463578	−0.0205882
$508$	91.3520	4.05309
$509$	3.94273	0.174758	0.0873792	−	0.996175i	$-0.472151\pi$
$509$	3.94273	0.174758	0.0873792	+	0.996175i	$0.472151\pi$
$510$	6.61693	0.293003
$511$	8.51151	0.376527
$512$	17.9394	0.792817
$513$	−2.34425	−0.103501
$514$	35.2610	1.55530
$515$	−5.30388	−0.233717
$516$	−25.2129	−1.10994
$517$	2.62689	0.115530
$518$	−18.1272	−0.796462
$519$	−4.70846	−0.206678
$520$	−33.0289	−1.44841
$521$	−5.16417	−0.226246	−0.113123	−	0.993581i	$-0.536085\pi$
$521$	−5.16417	−0.226246	−0.113123	+	0.993581i	$0.536085\pi$
$522$	−45.7068	−2.00053
$523$	2.57975	0.112804	0.0564022	−	0.998408i	$-0.482037\pi$
$523$	2.57975	0.112804	0.0564022	+	0.998408i	$0.482037\pi$
$524$	29.4959	1.28853
$525$	7.09942	0.309844
$526$	75.7708	3.30376
$527$	−6.43791	−0.280440
$528$	−3.94915	−0.171865
$529$	35.1399	1.52782
$530$	−46.4634	−2.01824
$531$	0.811449	0.0352139
$532$	6.25719	0.271284
$533$	3.40375	0.147433
$534$	−17.3085	−0.749012
$535$	18.1713	0.785613
$536$	−58.9252	−2.54518
$537$	−0.0309946	−0.00133752
$538$	77.6378	3.34720
$539$	−3.61789	−0.155834
$540$	54.6330	2.35103
$541$	−30.8481	−1.32626	−0.663131	−	0.748503i	$-0.730773\pi$
$541$	−30.8481	−1.32626	−0.663131	+	0.748503i	$0.730773\pi$
$542$	30.2562	1.29961
$543$	−5.48882	−0.235548
$544$	−20.1849	−0.865420
$545$	−38.3645	−1.64336
$546$	−1.73261	−0.0741490
$547$	20.8054	0.889575	0.444787	−	0.895636i	$-0.353279\pi$
$547$	20.8054	0.889575	0.444787	+	0.895636i	$0.353279\pi$
$548$	19.4688	0.831666
$549$	−19.5341	−0.833695
$550$	−20.9239	−0.892198
$551$	5.38172	0.229269
$552$	−29.2585	−1.24532
$553$	−1.25954	−0.0535609
$554$	86.8819	3.69126
$555$	8.97172	0.380828
$556$	−52.7643	−2.23771
$557$	25.3575	1.07443	0.537216	−	0.843445i	$-0.319476\pi$
$557$	25.3575	1.07443	0.537216	+	0.843445i	$0.319476\pi$
$558$	−35.6151	−1.50771
$559$	10.6532	0.450583
$560$	−66.3181	−2.80245
$561$	−0.447098	−0.0188765
$562$	62.7261	2.64594
$563$	17.3629	0.731759	0.365880	−	0.930662i	$-0.380768\pi$
$563$	17.3629	0.731759	0.365880	+	0.930662i	$0.380768\pi$
$564$	−8.65056	−0.364254
$565$	−17.7790	−0.747970
$566$	−12.6825	−0.533083
$567$	−9.97201	−0.418785
$568$	−93.1698	−3.90932
$569$	0.0131808	0.000552569 0	0.000276285	−	1.00000i	$-0.499912\pi$
$569$	0.0131808	0.000552569 0	0.000276285		1.00000i	$0.499912\pi$
$570$	−4.31009	−0.180530
$571$	29.3884	1.22987	0.614934	−	0.788579i	$-0.289183\pi$
$571$	29.3884	1.22987	0.614934	+	0.788579i	$0.289183\pi$
$572$	3.66910	0.153413
$573$	8.41241	0.351433
$574$	12.7214	0.530983
$575$	−83.2816	−3.47308
$576$	−45.6392	−1.90163
$577$	−12.0463	−0.501495	−0.250748	−	0.968052i	$-0.580676\pi$
$577$	−12.0463	−0.501495	−0.250748	+	0.968052i	$0.580676\pi$
$578$	40.5144	1.68518
$579$	−0.779459	−0.0323932
$580$	−125.421	−5.20784
$581$	−1.98955	−0.0825406
$582$	−12.2127	−0.506234
$583$	3.13948	0.130024
$584$	50.2471	2.07924
$585$	−11.1133	−0.459478
$586$	−38.1731	−1.57692
$587$	−8.60542	−0.355184	−0.177592	−	0.984104i	$-0.556831\pi$
$587$	−8.60542	−0.355184	−0.177592	+	0.984104i	$0.556831\pi$
$588$	11.9140	0.491326
$589$	4.19348	0.172789
$590$	3.09895	0.127582
$591$	8.76695	0.360624
$592$	−57.4900	−2.36283
$593$	−3.54940	−0.145756	−0.0728782	−	0.997341i	$-0.523218\pi$
$593$	−3.54940	−0.145756	−0.0728782	+	0.997341i	$0.523218\pi$
$594$	−5.13764	−0.210800
$595$	−7.50812	−0.307803
$596$	−96.8155	−3.96572
$597$	8.16940	0.334351
$598$	20.3249	0.831146
$599$	−0.937399	−0.0383011	−0.0191506	−	0.999817i	$-0.506096\pi$
$599$	−0.937399	−0.0383011	−0.0191506	+	0.999817i	$0.506096\pi$
$600$	41.9109	1.71101
$601$	−31.0686	−1.26732	−0.633658	−	0.773613i	$-0.718447\pi$
$601$	−31.0686	−1.26732	−0.633658	+	0.773613i	$0.718447\pi$
$602$	39.8162	1.62279
$603$	−19.8266	−0.807403
$604$	−34.7614	−1.41442
$605$	−41.8320	−1.70071
$606$	−19.0744	−0.774844
$607$	−40.9311	−1.66134	−0.830671	−	0.556763i	$-0.812043\pi$
$607$	−40.9311	−1.66134	−0.830671	+	0.556763i	$0.812043\pi$
$608$	13.1479	0.533218
$609$	−4.00185	−0.162163
$610$	−74.6013	−3.02052
$611$	3.65512	0.147870
$612$	−19.0810	−0.771304
$613$	−10.5335	−0.425444	−0.212722	−	0.977113i	$-0.568233\pi$
$613$	−10.5335	−0.425444	−0.212722	+	0.977113i	$0.568233\pi$
$614$	−70.1846	−2.83242
$615$	−6.29625	−0.253889
$616$	8.34104	0.336070
$617$	21.0607	0.847872	0.423936	−	0.905692i	$-0.360648\pi$
$617$	21.0607	0.847872	0.423936	+	0.905692i	$0.360648\pi$
$618$	−1.64250	−0.0660709
$619$	−25.3890	−1.02047	−0.510235	−	0.860035i	$-0.670442\pi$
$619$	−25.3890	−1.02047	−0.510235	+	0.860035i	$0.670442\pi$
$620$	−97.7296	−3.92491
$621$	−20.4489	−0.820586
$622$	5.89481	0.236360
$623$	19.6397	0.786847
$624$	−5.49496	−0.219974
$625$	39.6844	1.58738
$626$	35.1039	1.40304
$627$	0.291228	0.0116305
$628$	−89.5248	−3.57243
$629$	−6.50866	−0.259517
$630$	−41.5357	−1.65482
$631$	−0.173502	−0.00690701	−0.00345351	−	0.999994i	$-0.501099\pi$
$631$	−0.173502	−0.00690701	−0.00345351	+	0.999994i	$0.501099\pi$
$632$	−7.43557	−0.295771
$633$	3.31958	0.131941
$634$	55.0965	2.18816
$635$	71.4003	2.83344
$636$	−10.3386	−0.409951
$637$	−5.03403	−0.199456
$638$	11.7945	0.466949
$639$	−31.3490	−1.24015
$640$	−54.2598	−2.14481
$641$	16.0447	0.633728	0.316864	−	0.948471i	$-0.397370\pi$
$641$	16.0447	0.633728	0.316864	+	0.948471i	$0.397370\pi$
$642$	5.62725	0.222090
$643$	22.3930	0.883092	0.441546	−	0.897239i	$-0.354430\pi$
$643$	22.3930	0.883092	0.441546	+	0.897239i	$0.354430\pi$
$644$	54.5815	2.15081
$645$	−19.7063	−0.775935
$646$	3.12682	0.123023
$647$	−10.5506	−0.414788	−0.207394	−	0.978257i	$-0.566498\pi$
$647$	−10.5506	−0.414788	−0.207394	+	0.978257i	$0.566498\pi$
$648$	−58.8690	−2.31259
$649$	−0.209392	−0.00821937
$650$	−29.1141	−1.14195
$651$	−3.11828	−0.122215
$652$	−4.12535	−0.161561
$653$	20.8810	0.817138	0.408569	−	0.912727i	$-0.366028\pi$
$653$	20.8810	0.817138	0.408569	+	0.912727i	$0.366028\pi$
$654$	−11.8807	−0.464571
$655$	23.0539	0.900789
$656$	40.3459	1.57524
$657$	16.9067	0.659593
$658$	13.6610	0.532559
$659$	−24.1183	−0.939515	−0.469758	−	0.882795i	$-0.655659\pi$
$659$	−24.1183	−0.939515	−0.469758	+	0.882795i	$0.655659\pi$
$660$	−6.78710	−0.264188
$661$	−18.9490	−0.737031	−0.368515	−	0.929622i	$-0.620134\pi$
$661$	−18.9490	−0.737031	−0.368515	+	0.929622i	$0.620134\pi$
$662$	−87.0652	−3.38388
$663$	−0.622105	−0.0241605
$664$	−11.7452	−0.455801
$665$	4.89060	0.189649
$666$	−36.0066	−1.39523
$667$	46.9447	1.81771
$668$	−20.0343	−0.775151
$669$	−2.43063	−0.0939737
$670$	−75.7185	−2.92526
$671$	5.04072	0.194595
$672$	−9.77678	−0.377148
$673$	22.1156	0.852492	0.426246	−	0.904607i	$-0.359836\pi$
$673$	22.1156	0.852492	0.426246	+	0.904607i	$0.359836\pi$
$674$	−57.7089	−2.22287
$675$	29.2918	1.12744
$676$	5.10529	0.196357
$677$	−25.2729	−0.971316	−0.485658	−	0.874149i	$-0.661420\pi$
$677$	−25.2729	−0.971316	−0.485658	+	0.874149i	$0.661420\pi$
$678$	−5.50578	−0.211448
$679$	13.8576	0.531806
$680$	−44.3237	−1.69973
$681$	−5.02765	−0.192660
$682$	9.19040	0.351918
$683$	−2.71554	−0.103907	−0.0519536	−	0.998649i	$-0.516545\pi$
$683$	−2.71554	−0.103907	−0.0519536	+	0.998649i	$0.516545\pi$
$684$	12.4289	0.475229
$685$	15.2167	0.581401
$686$	−44.9770	−1.71723
$687$	1.31152	0.0500375
$688$	126.276	4.81424
$689$	4.36835	0.166421
$690$	−37.5969	−1.43129
$691$	−34.9305	−1.32882	−0.664410	−	0.747368i	$-0.731317\pi$
$691$	−34.9305	−1.32882	−0.664410	+	0.747368i	$0.731317\pi$
$692$	51.8533	1.97117
$693$	2.80652	0.106611
$694$	15.7758	0.598841
$695$	−41.2404	−1.56434
$696$	−23.6246	−0.895488
$697$	4.56771	0.173014
$698$	−4.63239	−0.175338
$699$	4.83498	0.182876
$700$	−78.1845	−2.95510
$701$	11.6205	0.438900	0.219450	−	0.975624i	$-0.429574\pi$
$701$	11.6205	0.438900	0.219450	+	0.975624i	$0.429574\pi$
$702$	−7.14865	−0.269808
$703$	4.23957	0.159898
$704$	11.7771	0.443866
$705$	−6.76125	−0.254643
$706$	95.0058	3.57559
$707$	21.6434	0.813984
$708$	0.689546	0.0259147
$709$	−14.4760	−0.543656	−0.271828	−	0.962346i	$-0.587628\pi$
$709$	−14.4760	−0.543656	−0.271828	+	0.962346i	$0.587628\pi$
$710$	−119.723	−4.49311
$711$	−2.50186	−0.0938269
$712$	115.941	4.34509
$713$	36.5797	1.36992
$714$	−2.32510	−0.0870148
$715$	2.86775	0.107248
$716$	0.341338	0.0127564
$717$	3.04431	0.113692
$718$	−58.8275	−2.19542
$719$	−17.4073	−0.649184	−0.324592	−	0.945854i	$-0.605227\pi$
$719$	−17.4073	−0.649184	−0.324592	+	0.945854i	$0.605227\pi$
$720$	−131.730	−4.90928
$721$	1.86372	0.0694084
$722$	48.6092	1.80905
$723$	−12.9076	−0.480037
$724$	60.4472	2.24650
$725$	−67.2453	−2.49743
$726$	−12.9545	−0.480785
$727$	−10.4314	−0.386879	−0.193440	−	0.981112i	$-0.561964\pi$
$727$	−10.4314	−0.386879	−0.193440	+	0.981112i	$0.561964\pi$
$728$	11.6059	0.430145
$729$	−16.0780	−0.595482
$730$	64.5671	2.38974
$731$	14.2962	0.528765
$732$	−16.5995	−0.613536
$733$	49.2351	1.81854	0.909270	−	0.416206i	$-0.136641\pi$
$733$	49.2351	1.81854	0.909270	+	0.416206i	$0.136641\pi$
$734$	−90.2616	−3.33162
$735$	9.31195	0.343477
$736$	114.689	4.22750
$737$	5.11621	0.188458
$738$	25.2690	0.930165
$739$	8.27488	0.304396	0.152198	−	0.988350i	$-0.451365\pi$
$739$	8.27488	0.304396	0.152198	+	0.988350i	$0.451365\pi$
$740$	−98.8037	−3.63210
$741$	0.405223	0.0148862
$742$	16.3266	0.599370
$743$	−12.0007	−0.440263	−0.220132	−	0.975470i	$-0.570649\pi$
$743$	−12.0007	−0.440263	−0.220132	+	0.975470i	$0.570649\pi$
$744$	−18.4085	−0.674889
$745$	−75.6706	−2.77236
$746$	0.790035	0.0289252
$747$	−3.95191	−0.144593
$748$	4.92380	0.180032
$749$	−6.38515	−0.233308
$750$	29.2013	1.06628
$751$	42.1053	1.53644	0.768222	−	0.640183i	$-0.221142\pi$
$751$	42.1053	1.53644	0.768222	+	0.640183i	$0.221142\pi$
$752$	43.3255	1.57992
$753$	0.470113	0.0171319
$754$	16.4112	0.597661
$755$	−27.1694	−0.988796
$756$	−19.1974	−0.698201
$757$	−30.1452	−1.09564	−0.547822	−	0.836595i	$-0.684543\pi$
$757$	−30.1452	−1.09564	−0.547822	+	0.836595i	$0.684543\pi$
$758$	44.3518	1.61093
$759$	2.54038	0.0922101
$760$	28.8713	1.04727
$761$	33.4928	1.21411	0.607056	−	0.794659i	$-0.292350\pi$
$761$	33.4928	1.21411	0.607056	+	0.794659i	$0.292350\pi$
$762$	22.1111	0.801002
$763$	13.4808	0.488038
$764$	−92.6441	−3.35175
$765$	−14.9136	−0.539203
$766$	38.0524	1.37489
$767$	−0.291354	−0.0105202
$768$	−1.60986	−0.0580907
$769$	−39.4504	−1.42262	−0.711310	−	0.702879i	$-0.751898\pi$
$769$	−39.4504	−1.42262	−0.711310	+	0.702879i	$0.751898\pi$
$770$	10.7182	0.386256
$771$	6.13235	0.220851
$772$	8.58402	0.308946
$773$	1.81004	0.0651025	0.0325512	−	0.999470i	$-0.489637\pi$
$773$	1.81004	0.0651025	0.0325512	+	0.999470i	$0.489637\pi$
$774$	79.0881	2.84276
$775$	−52.3982	−1.88220
$776$	81.8073	2.93671
$777$	−3.15255	−0.113097
$778$	87.9134	3.15185
$779$	−2.97529	−0.106601
$780$	−9.44376	−0.338141
$781$	8.08952	0.289466
$782$	27.2752	0.975361
$783$	−16.5114	−0.590068
$784$	−59.6702	−2.13108
$785$	−69.9722	−2.49742
$786$	7.13928	0.254650
$787$	10.1013	0.360071	0.180036	−	0.983660i	$-0.442379\pi$
$787$	10.1013	0.360071	0.180036	+	0.983660i	$0.442379\pi$
$788$	−96.5487	−3.43940
$789$	13.1775	0.469132
$790$	−9.55466	−0.339940
$791$	6.24733	0.222129
$792$	16.5681	0.588721
$793$	7.01380	0.249067
$794$	−84.0880	−2.98417
$795$	−8.08058	−0.286589
$796$	−89.9679	−3.18883
$797$	16.3150	0.577905	0.288953	−	0.957343i	$-0.406693\pi$
$797$	16.3150	0.577905	0.288953	+	0.957343i	$0.406693\pi$
$798$	1.51451	0.0536131
$799$	4.90504	0.173528
$800$	−164.285	−5.80835
$801$	39.0109	1.37838
$802$	40.1645	1.41826
$803$	−4.36273	−0.153957
$804$	−16.8481	−0.594187
$805$	42.6607	1.50359
$806$	12.7878	0.450430
$807$	13.5022	0.475301
$808$	127.770	4.49494
$809$	20.0520	0.704992	0.352496	−	0.935813i	$-0.385333\pi$
$809$	20.0520	0.704992	0.352496	+	0.935813i	$0.385333\pi$
$810$	−75.6463	−2.65794
$811$	−12.9151	−0.453512	−0.226756	−	0.973952i	$-0.572812\pi$
$811$	−12.9151	−0.453512	−0.226756	+	0.973952i	$0.572812\pi$
$812$	44.0715	1.54661
$813$	5.26194	0.184544
$814$	9.29140	0.325663
$815$	−3.22436	−0.112944
$816$	−7.37404	−0.258143
$817$	−9.31219	−0.325792
$818$	−57.0966	−1.99634
$819$	3.90507	0.136454
$820$	69.3394	2.42144
$821$	−11.0679	−0.386272	−0.193136	−	0.981172i	$-0.561866\pi$
$821$	−11.0679	−0.386272	−0.193136	+	0.981172i	$0.561866\pi$
$822$	4.71229	0.164360
$823$	−48.7324	−1.69870	−0.849352	−	0.527826i	$-0.823007\pi$
$823$	−48.7324	−1.69870	−0.849352	+	0.527826i	$0.823007\pi$
$824$	11.0023	0.383283
$825$	−3.63894	−0.126692
$826$	−1.08893	−0.0378887
$827$	51.8699	1.80369	0.901846	−	0.432058i	$-0.142212\pi$
$827$	51.8699	1.80369	0.901846	+	0.432058i	$0.142212\pi$
$828$	108.417	3.76775
$829$	−7.73193	−0.268541	−0.134270	−	0.990945i	$-0.542869\pi$
$829$	−7.73193	−0.268541	−0.134270	+	0.990945i	$0.542869\pi$
$830$	−15.0925	−0.523867
$831$	15.1099	0.524156
$832$	16.3869	0.568115
$833$	−6.75549	−0.234064
$834$	−12.7713	−0.442232
$835$	−15.6587	−0.541893
$836$	−3.20724	−0.110925
$837$	−12.8658	−0.444707
$838$	−64.3153	−2.22173
$839$	−21.8300	−0.753655	−0.376828	−	0.926283i	$-0.622985\pi$
$839$	−21.8300	−0.753655	−0.376828	+	0.926283i	$0.622985\pi$
$840$	−21.4687	−0.740740
$841$	8.90524	0.307077
$842$	−15.5797	−0.536912
$843$	10.9089	0.375721
$844$	−36.5578	−1.25837
$845$	3.99027	0.137269
$846$	27.1352	0.932927
$847$	14.6992	0.505071
$848$	51.7797	1.77812
$849$	−2.20564	−0.0756974
$850$	−39.0701	−1.34009
$851$	36.9818	1.26772
$852$	−26.6395	−0.912653
$853$	34.5208	1.18197	0.590985	−	0.806682i	$-0.298739\pi$
$853$	34.5208	1.18197	0.590985	+	0.806682i	$0.298739\pi$
$854$	26.2139	0.897022
$855$	9.71435	0.332224
$856$	−37.6943	−1.28836
$857$	−33.3261	−1.13840	−0.569199	−	0.822200i	$-0.692746\pi$
$857$	−33.3261	−1.13840	−0.569199	+	0.822200i	$0.692746\pi$
$858$	0.888082	0.0303186
$859$	21.1132	0.720373	0.360187	−	0.932880i	$-0.382713\pi$
$859$	21.1132	0.720373	0.360187	+	0.932880i	$0.382713\pi$
$860$	217.022	7.40037
$861$	2.21242	0.0753992
$862$	54.7129	1.86353
$863$	−46.9291	−1.59748	−0.798742	−	0.601674i	$-0.794501\pi$
$863$	−46.9291	−1.59748	−0.798742	+	0.601674i	$0.794501\pi$
$864$	−40.3384	−1.37234
$865$	40.5283	1.37800
$866$	−95.1284	−3.23259
$867$	7.04598	0.239294
$868$	34.3409	1.16561
$869$	0.645598	0.0219004
$870$	−30.3574	−1.02921
$871$	7.11883	0.241212
$872$	79.5829	2.69502
$873$	27.5258	0.931607
$874$	−17.7664	−0.600957
$875$	−33.1343	−1.12014
$876$	14.3668	0.485410
$877$	−0.538194	−0.0181735	−0.00908676	−	0.999959i	$-0.502892\pi$
$877$	−0.538194	−0.0181735	−0.00908676	+	0.999959i	$0.502892\pi$
$878$	−56.4158	−1.90394
$879$	−6.63880	−0.223921
$880$	33.9926	1.14589
$881$	−43.4624	−1.46428	−0.732142	−	0.681152i	$-0.761479\pi$
$881$	−43.4624	−1.46428	−0.732142	+	0.681152i	$0.761479\pi$
$882$	−37.3720	−1.25838
$883$	−15.2884	−0.514494	−0.257247	−	0.966346i	$-0.582815\pi$
$883$	−15.2884	−0.514494	−0.257247	+	0.966346i	$0.582815\pi$
$884$	6.85111	0.230428
$885$	0.538947	0.0181165
$886$	90.4859	3.03993
$887$	−19.7006	−0.661480	−0.330740	−	0.943722i	$-0.607298\pi$
$887$	−19.7006	−0.661480	−0.330740	+	0.943722i	$0.607298\pi$
$888$	−18.6108	−0.624538
$889$	−25.0892	−0.841464
$890$	148.984	4.99395
$891$	5.11133	0.171236
$892$	26.7681	0.896261
$893$	−3.19502	−0.106917
$894$	−23.4336	−0.783735
$895$	0.266788	0.00891774
$896$	19.0662	0.636958
$897$	3.53476	0.118022
$898$	−9.48239	−0.316432
$899$	29.5361	0.985085
$900$	−155.300	−5.17668
$901$	5.86217	0.195297
$902$	−6.52061	−0.217112
$903$	6.92455	0.230434
$904$	36.8806	1.22663
$905$	47.2453	1.57049
$906$	−8.41378	−0.279529
$907$	−38.3599	−1.27372	−0.636860	−	0.770980i	$-0.719767\pi$
$907$	−38.3599	−1.27372	−0.636860	+	0.770980i	$0.719767\pi$
$908$	55.3685	1.83747
$909$	42.9910	1.42592
$910$	14.9136	0.494380
$911$	−27.7083	−0.918018	−0.459009	−	0.888432i	$-0.651795\pi$
$911$	−27.7083	−0.918018	−0.459009	+	0.888432i	$0.651795\pi$
$912$	4.80325	0.159052
$913$	1.01978	0.0337498
$914$	−66.9963	−2.21604
$915$	−12.9741	−0.428911
$916$	−14.4435	−0.477225
$917$	−8.10083	−0.267513
$918$	−9.59323	−0.316624
$919$	19.6529	0.648289	0.324144	−	0.946008i	$-0.394924\pi$
$919$	19.6529	0.648289	0.324144	+	0.946008i	$0.394924\pi$
$920$	251.844	8.30305
$921$	−12.2060	−0.402202
$922$	−55.9707	−1.84330
$923$	11.2560	0.370495
$924$	2.38490	0.0784575
$925$	−52.9740	−1.74178
$926$	−2.66557	−0.0875962
$927$	3.70196	0.121588
$928$	92.6051	3.03991
$929$	46.6899	1.53185	0.765924	−	0.642932i	$-0.222282\pi$
$929$	46.6899	1.53185	0.765924	+	0.642932i	$0.222282\pi$
$930$	−23.6548	−0.775671
$931$	4.40035	0.144216
$932$	−53.2466	−1.74415
$933$	1.02518	0.0335630
$934$	12.4238	0.406520
$935$	3.84842	0.125857
$936$	23.0533	0.753519
$937$	15.3240	0.500614	0.250307	−	0.968167i	$-0.419469\pi$
$937$	15.3240	0.500614	0.250307	+	0.968167i	$0.419469\pi$
$938$	26.6065	0.868733
$939$	6.10503	0.199230
$940$	74.4602	2.42862
$941$	−0.932832	−0.0304094	−0.0152047	−	0.999884i	$-0.504840\pi$
$941$	−0.932832	−0.0304094	−0.0152047	+	0.999884i	$0.504840\pi$
$942$	−21.6689	−0.706011
$943$	−25.9534	−0.845159
$944$	−3.45353	−0.112403
$945$	−15.0046	−0.488099
$946$	−20.4085	−0.663537
$947$	18.1887	0.591054	0.295527	−	0.955334i	$-0.404505\pi$
$947$	18.1887	0.591054	0.295527	+	0.955334i	$0.404505\pi$
$948$	−2.12601	−0.0690495
$949$	−6.07042	−0.197054
$950$	25.4492	0.825681
$951$	9.58199	0.310717
$952$	15.5748	0.504781
$953$	7.31931	0.237096	0.118548	−	0.992948i	$-0.462176\pi$
$953$	7.31931	0.237096	0.118548	+	0.992948i	$0.462176\pi$
$954$	32.4301	1.04996
$955$	−72.4103	−2.34314
$956$	−33.5264	−1.08432
$957$	2.05122	0.0663065
$958$	28.6209	0.924700
$959$	−5.34696	−0.172662
$960$	−30.3126	−0.978334
$961$	−7.98519	−0.257587
$962$	12.9283	0.416825
$963$	−12.6830	−0.408705
$964$	142.148	4.57829
$965$	6.70923	0.215978
$966$	13.2111	0.425060
$967$	−31.2574	−1.00517	−0.502586	−	0.864527i	$-0.667618\pi$
$967$	−31.2574	−1.00517	−0.502586	+	0.864527i	$0.667618\pi$
$968$	86.7757	2.78908
$969$	0.543794	0.0174692
$970$	105.122	3.37526
$971$	−21.1856	−0.679879	−0.339940	−	0.940447i	$-0.610407\pi$
$971$	−21.1856	−0.679879	−0.339940	+	0.940447i	$0.610407\pi$
$972$	−57.9067	−1.85736
$973$	14.4913	0.464571
$974$	96.4153	3.08935
$975$	−5.06331	−0.162156
$976$	83.1371	2.66115
$977$	5.20448	0.166506	0.0832531	−	0.996528i	$-0.473469\pi$
$977$	5.20448	0.166506	0.0832531	+	0.996528i	$0.473469\pi$
$978$	−0.998514	−0.0319290
$979$	−10.0667	−0.321732
$980$	−102.551	−3.27586
$981$	26.7773	0.854935
$982$	27.4023	0.874441
$983$	−37.6867	−1.20202	−0.601009	−	0.799242i	$-0.705235\pi$
$983$	−37.6867	−1.20202	−0.601009	+	0.799242i	$0.705235\pi$
$984$	13.0609	0.416365
$985$	−75.4620	−2.40442
$986$	22.0232	0.701363
$987$	2.37582	0.0756230
$988$	−4.46263	−0.141975
$989$	−81.2302	−2.58297
$990$	21.2899	0.676636
$991$	−47.0719	−1.49529	−0.747644	−	0.664099i	$-0.768815\pi$
$991$	−47.0719	−1.49529	−0.747644	+	0.664099i	$0.768815\pi$
$992$	72.1587	2.29104
$993$	−15.1418	−0.480509
$994$	42.0690	1.33435
$995$	−70.3186	−2.22925
$996$	−3.35823	−0.106409
$997$	−36.5156	−1.15646	−0.578230	−	0.815874i	$-0.696256\pi$
$997$	−36.5156	−1.15646	−0.578230	+	0.815874i	$0.696256\pi$
$998$	−44.7297	−1.41589
$999$	−13.0072	−0.411530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.3	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.66557 q^{2} -0.463578 q^{3} +5.10529 q^{4} +3.99027 q^{5} +1.23570 q^{6} -1.40213 q^{7} -8.27737 q^{8} -2.78510 q^{9} +O(q^{10})\)	\(q-2.66557 q^{2} -0.463578 q^{3} +5.10529 q^{4} +3.99027 q^{5} +1.23570 q^{6} -1.40213 q^{7} -8.27737 q^{8} -2.78510 q^{9} -10.6364 q^{10} +0.718687 q^{11} -2.36670 q^{12} +1.00000 q^{13} +3.73748 q^{14} -1.84980 q^{15} +11.8534 q^{16} +1.34196 q^{17} +7.42388 q^{18} -0.874120 q^{19} +20.3715 q^{20} +0.649996 q^{21} -1.91571 q^{22} -7.62495 q^{23} +3.83720 q^{24} +10.9223 q^{25} -2.66557 q^{26} +2.68184 q^{27} -7.15827 q^{28} -6.15672 q^{29} +4.93078 q^{30} -4.79738 q^{31} -15.0413 q^{32} -0.333167 q^{33} -3.57711 q^{34} -5.59488 q^{35} -14.2187 q^{36} -4.85010 q^{37} +2.33003 q^{38} -0.463578 q^{39} -33.0289 q^{40} +3.40375 q^{41} -1.73261 q^{42} +10.6532 q^{43} +3.66910 q^{44} -11.1133 q^{45} +20.3249 q^{46} +3.65512 q^{47} -5.49496 q^{48} -5.03403 q^{49} -29.1141 q^{50} -0.622105 q^{51} +5.10529 q^{52} +4.36835 q^{53} -7.14865 q^{54} +2.86775 q^{55} +11.6059 q^{56} +0.405223 q^{57} +16.4112 q^{58} -0.291354 q^{59} -9.44376 q^{60} +7.01380 q^{61} +12.7878 q^{62} +3.90507 q^{63} +16.3869 q^{64} +3.99027 q^{65} +0.888082 q^{66} +7.11883 q^{67} +6.85111 q^{68} +3.53476 q^{69} +14.9136 q^{70} +11.2560 q^{71} +23.0533 q^{72} -6.07042 q^{73} +12.9283 q^{74} -5.06331 q^{75} -4.46263 q^{76} -1.00769 q^{77} +1.23570 q^{78} +0.898302 q^{79} +47.2981 q^{80} +7.11205 q^{81} -9.07294 q^{82} +1.41895 q^{83} +3.31842 q^{84} +5.35480 q^{85} -28.3969 q^{86} +2.85412 q^{87} -5.94884 q^{88} -14.0070 q^{89} +29.6233 q^{90} -1.40213 q^{91} -38.9275 q^{92} +2.22396 q^{93} -9.74300 q^{94} -3.48798 q^{95} +6.97281 q^{96} -9.88324 q^{97} +13.4186 q^{98} -2.00161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 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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