LMFDB - Embedded newform 6019.2.a.c.1.14

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:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.26345 q^{2} +2.92995 q^{3} +3.12323 q^{4} +0.680242 q^{5} -6.63181 q^{6} -3.22192 q^{7} -2.54237 q^{8} +5.58462 q^{9} +O(q^{10})$	\(q-2.26345 q^{2} +2.92995 q^{3} +3.12323 q^{4} +0.680242 q^{5} -6.63181 q^{6} -3.22192 q^{7} -2.54237 q^{8} +5.58462 q^{9} -1.53970 q^{10} +3.31025 q^{11} +9.15090 q^{12} -1.00000 q^{13} +7.29267 q^{14} +1.99308 q^{15} -0.491910 q^{16} -1.52177 q^{17} -12.6405 q^{18} +1.11243 q^{19} +2.12455 q^{20} -9.44007 q^{21} -7.49260 q^{22} +3.23019 q^{23} -7.44903 q^{24} -4.53727 q^{25} +2.26345 q^{26} +7.57280 q^{27} -10.0628 q^{28} +0.0198701 q^{29} -4.51124 q^{30} -7.73083 q^{31} +6.19816 q^{32} +9.69887 q^{33} +3.44447 q^{34} -2.19169 q^{35} +17.4420 q^{36} -9.89082 q^{37} -2.51793 q^{38} -2.92995 q^{39} -1.72943 q^{40} -5.18027 q^{41} +21.3672 q^{42} +3.84001 q^{43} +10.3387 q^{44} +3.79889 q^{45} -7.31139 q^{46} -9.40407 q^{47} -1.44127 q^{48} +3.38078 q^{49} +10.2699 q^{50} -4.45873 q^{51} -3.12323 q^{52} -6.20709 q^{53} -17.1407 q^{54} +2.25177 q^{55} +8.19132 q^{56} +3.25936 q^{57} -0.0449750 q^{58} -1.12786 q^{59} +6.22483 q^{60} -10.9419 q^{61} +17.4984 q^{62} -17.9932 q^{63} -13.0454 q^{64} -0.680242 q^{65} -21.9530 q^{66} -7.88697 q^{67} -4.75285 q^{68} +9.46431 q^{69} +4.96078 q^{70} -4.66354 q^{71} -14.1982 q^{72} +2.12653 q^{73} +22.3874 q^{74} -13.2940 q^{75} +3.47437 q^{76} -10.6654 q^{77} +6.63181 q^{78} -7.87136 q^{79} -0.334618 q^{80} +5.43410 q^{81} +11.7253 q^{82} +5.81401 q^{83} -29.4835 q^{84} -1.03518 q^{85} -8.69170 q^{86} +0.0582184 q^{87} -8.41589 q^{88} -5.39332 q^{89} -8.59862 q^{90} +3.22192 q^{91} +10.0886 q^{92} -22.6509 q^{93} +21.2857 q^{94} +0.756722 q^{95} +18.1603 q^{96} +4.09432 q^{97} -7.65223 q^{98} +18.4865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.26345	−1.60050	−0.800252	−	0.599664i	$-0.795301\pi$
$2$	−2.26345	−1.60050	−0.800252	+	0.599664i	$0.795301\pi$
$3$	2.92995	1.69161	0.845804	−	0.533493i	$-0.179121\pi$
$3$	2.92995	1.69161	0.845804	+	0.533493i	$0.179121\pi$
$4$	3.12323	1.56161
$5$	0.680242	0.304214	0.152107	−	0.988364i	$-0.451394\pi$
$5$	0.680242	0.304214	0.152107	+	0.988364i	$0.451394\pi$
$6$	−6.63181	−2.70743
$7$	−3.22192	−1.21777	−0.608886	−	0.793258i	$-0.708383\pi$
$7$	−3.22192	−1.21777	−0.608886	+	0.793258i	$0.708383\pi$
$8$	−2.54237	−0.898864
$9$	5.58462	1.86154
$10$	−1.53970	−0.486895
$11$	3.31025	0.998078	0.499039	−	0.866580i	$-0.333686\pi$
$11$	3.31025	0.998078	0.499039	+	0.866580i	$0.333686\pi$
$12$	9.15090	2.64164
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.29267	1.94905
$15$	1.99308	0.514610
$16$	−0.491910	−0.122977
$17$	−1.52177	−0.369085	−0.184542	−	0.982825i	$-0.559080\pi$
$17$	−1.52177	−0.369085	−0.184542	+	0.982825i	$0.559080\pi$
$18$	−12.6405	−2.97940
$19$	1.11243	0.255209	0.127604	−	0.991825i	$-0.459271\pi$
$19$	1.11243	0.255209	0.127604	+	0.991825i	$0.459271\pi$
$20$	2.12455	0.475064
$21$	−9.44007	−2.05999
$22$	−7.49260	−1.59743
$23$	3.23019	0.673542	0.336771	−	0.941587i	$-0.390665\pi$
$23$	3.23019	0.673542	0.336771	+	0.941587i	$0.390665\pi$
$24$	−7.44903	−1.52053
$25$	−4.53727	−0.907454
$26$	2.26345	0.443900
$27$	7.57280	1.45739
$28$	−10.0628	−1.90169
$29$	0.0198701	0.00368978	0.00184489	−	0.999998i	$-0.499413\pi$
$29$	0.0198701	0.00368978	0.00184489	+	0.999998i	$0.499413\pi$
$30$	−4.51124	−0.823636
$31$	−7.73083	−1.38850	−0.694249	−	0.719735i	$-0.744263\pi$
$31$	−7.73083	−1.38850	−0.694249	+	0.719735i	$0.744263\pi$
$32$	6.19816	1.09569
$33$	9.69887	1.68836
$34$	3.44447	0.590721
$35$	−2.19169	−0.370463
$36$	17.4420	2.90700
$37$	−9.89082	−1.62604	−0.813020	−	0.582235i	$-0.802178\pi$
$37$	−9.89082	−1.62604	−0.813020	+	0.582235i	$0.802178\pi$
$38$	−2.51793	−0.408463
$39$	−2.92995	−0.469168
$40$	−1.72943	−0.273447
$41$	−5.18027	−0.809023	−0.404511	−	0.914533i	$-0.632558\pi$
$41$	−5.18027	−0.809023	−0.404511	+	0.914533i	$0.632558\pi$
$42$	21.3672	3.29703
$43$	3.84001	0.585597	0.292798	−	0.956174i	$-0.405414\pi$
$43$	3.84001	0.585597	0.292798	+	0.956174i	$0.405414\pi$
$44$	10.3387	1.55861
$45$	3.79889	0.566306
$46$	−7.31139	−1.07801
$47$	−9.40407	−1.37172	−0.685862	−	0.727731i	$-0.740575\pi$
$47$	−9.40407	−1.37172	−0.685862	+	0.727731i	$0.740575\pi$
$48$	−1.44127	−0.208030
$49$	3.38078	0.482968
$50$	10.2699	1.45238
$51$	−4.45873	−0.624347
$52$	−3.12323	−0.433114
$53$	−6.20709	−0.852609	−0.426305	−	0.904580i	$-0.640185\pi$
$53$	−6.20709	−0.852609	−0.426305	+	0.904580i	$0.640185\pi$
$54$	−17.1407	−2.33255
$55$	2.25177	0.303629
$56$	8.19132	1.09461
$57$	3.25936	0.431713
$58$	−0.0449750	−0.00590551
$59$	−1.12786	−0.146835	−0.0734176	−	0.997301i	$-0.523391\pi$
$59$	−1.12786	−0.146835	−0.0734176	+	0.997301i	$0.523391\pi$
$60$	6.22483	0.803622
$61$	−10.9419	−1.40096	−0.700481	−	0.713671i	$-0.747031\pi$
$61$	−10.9419	−1.40096	−0.700481	+	0.713671i	$0.747031\pi$
$62$	17.4984	2.22230
$63$	−17.9932	−2.26693
$64$	−13.0454	−1.63068
$65$	−0.680242	−0.0843737
$66$	−21.9530	−2.70222
$67$	−7.88697	−0.963546	−0.481773	−	0.876296i	$-0.660007\pi$
$67$	−7.88697	−0.963546	−0.481773	+	0.876296i	$0.660007\pi$
$68$	−4.75285	−0.576367
$69$	9.46431	1.13937
$70$	4.96078	0.592927
$71$	−4.66354	−0.553460	−0.276730	−	0.960948i	$-0.589251\pi$
$71$	−4.66354	−0.553460	−0.276730	+	0.960948i	$0.589251\pi$
$72$	−14.1982	−1.67327
$73$	2.12653	0.248891	0.124446	−	0.992226i	$-0.460285\pi$
$73$	2.12653	0.248891	0.124446	+	0.992226i	$0.460285\pi$
$74$	22.3874	2.60248
$75$	−13.2940	−1.53506
$76$	3.47437	0.398537
$77$	−10.6654	−1.21543
$78$	6.63181	0.750905
$79$	−7.87136	−0.885597	−0.442799	−	0.896621i	$-0.646014\pi$
$79$	−7.87136	−0.885597	−0.442799	+	0.896621i	$0.646014\pi$
$80$	−0.334618	−0.0374114
$81$	5.43410	0.603789
$82$	11.7253	1.29484
$83$	5.81401	0.638170	0.319085	−	0.947726i	$-0.396624\pi$
$83$	5.81401	0.638170	0.319085	+	0.947726i	$0.396624\pi$
$84$	−29.4835	−3.21691
$85$	−1.03518	−0.112281
$86$	−8.69170	−0.937250
$87$	0.0582184	0.00624166
$88$	−8.41589	−0.897137
$89$	−5.39332	−0.571691	−0.285845	−	0.958276i	$-0.592274\pi$
$89$	−5.39332	−0.571691	−0.285845	+	0.958276i	$0.592274\pi$
$90$	−8.59862	−0.906374
$91$	3.22192	0.337749
$92$	10.0886	1.05181
$93$	−22.6509	−2.34879
$94$	21.2857	2.19545
$95$	0.756722	0.0776380
$96$	18.1603	1.85348
$97$	4.09432	0.415715	0.207857	−	0.978159i	$-0.433351\pi$
$97$	4.09432	0.415715	0.207857	+	0.978159i	$0.433351\pi$
$98$	−7.65223	−0.772992
$99$	18.4865	1.85796
$100$	−14.1709	−1.41709
$101$	15.2432	1.51675	0.758377	−	0.651817i	$-0.225993\pi$
$101$	15.2432	1.51675	0.758377	+	0.651817i	$0.225993\pi$
$102$	10.0921	0.999269
$103$	7.63389	0.752190	0.376095	−	0.926581i	$-0.377267\pi$
$103$	7.63389	0.752190	0.376095	+	0.926581i	$0.377267\pi$
$104$	2.54237	0.249300
$105$	−6.42154	−0.626678
$106$	14.0495	1.36460
$107$	−2.30101	−0.222447	−0.111224	−	0.993795i	$-0.535477\pi$
$107$	−2.30101	−0.222447	−0.111224	+	0.993795i	$0.535477\pi$
$108$	23.6516	2.27587
$109$	−5.94139	−0.569082	−0.284541	−	0.958664i	$-0.591841\pi$
$109$	−5.94139	−0.569082	−0.284541	+	0.958664i	$0.591841\pi$
$110$	−5.09678	−0.485959
$111$	−28.9796	−2.75062
$112$	1.58489	0.149758
$113$	14.7339	1.38605	0.693027	−	0.720912i	$-0.256277\pi$
$113$	14.7339	1.38605	0.693027	+	0.720912i	$0.256277\pi$
$114$	−7.37742	−0.690959
$115$	2.19731	0.204901
$116$	0.0620587	0.00576201
$117$	−5.58462	−0.516298
$118$	2.55286	0.235010
$119$	4.90304	0.449461
$120$	−5.06714	−0.462565
$121$	−0.0422420	−0.00384018
$122$	24.7664	2.24224
$123$	−15.1779	−1.36855
$124$	−24.1451	−2.16830
$125$	−6.48766	−0.580274
$126$	40.7268	3.62823
$127$	19.4666	1.72738	0.863689	−	0.504025i	$-0.168148\pi$
$127$	19.4666	1.72738	0.863689	+	0.504025i	$0.168148\pi$
$128$	17.1314	1.51422
$129$	11.2511	0.990600
$130$	1.53970	0.135040
$131$	5.62875	0.491786	0.245893	−	0.969297i	$-0.420919\pi$
$131$	5.62875	0.491786	0.245893	+	0.969297i	$0.420919\pi$
$132$	30.2918	2.63656
$133$	−3.58416	−0.310786
$134$	17.8518	1.54216
$135$	5.15134	0.443357
$136$	3.86892	0.331757
$137$	−3.05008	−0.260586	−0.130293	−	0.991476i	$-0.541592\pi$
$137$	−3.05008	−0.260586	−0.130293	+	0.991476i	$0.541592\pi$
$138$	−21.4220	−1.82356
$139$	11.5692	0.981288	0.490644	−	0.871360i	$-0.336762\pi$
$139$	11.5692	0.981288	0.490644	+	0.871360i	$0.336762\pi$
$140$	−6.84514	−0.578520
$141$	−27.5535	−2.32042
$142$	10.5557	0.885816
$143$	−3.31025	−0.276817
$144$	−2.74713	−0.228927
$145$	0.0135165	0.00112248
$146$	−4.81330	−0.398352
$147$	9.90551	0.816993
$148$	−30.8913	−2.53925
$149$	17.5796	1.44018	0.720090	−	0.693881i	$-0.244101\pi$
$149$	17.5796	1.44018	0.720090	+	0.693881i	$0.244101\pi$
$150$	30.0903	2.45686
$151$	−16.3004	−1.32651	−0.663255	−	0.748394i	$-0.730825\pi$
$151$	−16.3004	−1.32651	−0.663255	+	0.748394i	$0.730825\pi$
$152$	−2.82821	−0.229398
$153$	−8.49853	−0.687065
$154$	24.1406	1.94530
$155$	−5.25884	−0.422400
$156$	−9.15090	−0.732659
$157$	8.12772	0.648663	0.324331	−	0.945944i	$-0.394861\pi$
$157$	8.12772	0.648663	0.324331	+	0.945944i	$0.394861\pi$
$158$	17.8165	1.41740
$159$	−18.1865	−1.44228
$160$	4.21625	0.333324
$161$	−10.4074	−0.820220
$162$	−12.2998	−0.966366
$163$	−13.2504	−1.03785	−0.518927	−	0.854818i	$-0.673668\pi$
$163$	−13.2504	−1.03785	−0.518927	+	0.854818i	$0.673668\pi$
$164$	−16.1792	−1.26338
$165$	6.59759	0.513621
$166$	−13.1597	−1.02139
$167$	−19.2393	−1.48878	−0.744392	−	0.667742i	$-0.767261\pi$
$167$	−19.2393	−1.48878	−0.744392	+	0.667742i	$0.767261\pi$
$168$	24.0002	1.85165
$169$	1.00000	0.0769231
$170$	2.34307	0.179705
$171$	6.21249	0.475081
$172$	11.9932	0.914475
$173$	8.19152	0.622790	0.311395	−	0.950281i	$-0.399204\pi$
$173$	8.19152	0.622790	0.311395	+	0.950281i	$0.399204\pi$
$174$	−0.131775	−0.00998981
$175$	14.6187	1.10507
$176$	−1.62834	−0.122741
$177$	−3.30458	−0.248388
$178$	12.2075	0.914993
$179$	18.3696	1.37301	0.686506	−	0.727124i	$-0.259144\pi$
$179$	18.3696	1.37301	0.686506	+	0.727124i	$0.259144\pi$
$180$	11.8648	0.884350
$181$	12.9027	0.959051	0.479525	−	0.877528i	$-0.340809\pi$
$181$	12.9027	0.959051	0.479525	+	0.877528i	$0.340809\pi$
$182$	−7.29267	−0.540569
$183$	−32.0591	−2.36988
$184$	−8.21235	−0.605423
$185$	−6.72815	−0.494664
$186$	51.2694	3.75925
$187$	−5.03746	−0.368375
$188$	−29.3710	−2.14210
$189$	−24.3990	−1.77476
$190$	−1.71280	−0.124260
$191$	−5.03605	−0.364395	−0.182198	−	0.983262i	$-0.558321\pi$
$191$	−5.03605	−0.364395	−0.182198	+	0.983262i	$0.558321\pi$
$192$	−38.2225	−2.75847
$193$	6.61862	0.476419	0.238210	−	0.971214i	$-0.423440\pi$
$193$	6.61862	0.476419	0.238210	+	0.971214i	$0.423440\pi$
$194$	−9.26730	−0.665353
$195$	−1.99308	−0.142727
$196$	10.5589	0.754209
$197$	−4.22401	−0.300948	−0.150474	−	0.988614i	$-0.548080\pi$
$197$	−4.22401	−0.300948	−0.150474	+	0.988614i	$0.548080\pi$
$198$	−41.8433	−2.97367
$199$	−17.5872	−1.24673	−0.623363	−	0.781932i	$-0.714234\pi$
$199$	−17.5872	−1.24673	−0.623363	+	0.781932i	$0.714234\pi$
$200$	11.5354	0.815678
$201$	−23.1084	−1.62994
$202$	−34.5022	−2.42757
$203$	−0.0640198	−0.00449331
$204$	−13.9256	−0.974988
$205$	−3.52384	−0.246116
$206$	−17.2790	−1.20388
$207$	18.0394	1.25382
$208$	0.491910	0.0341078
$209$	3.68242	0.254718
$210$	14.5349	1.00300
$211$	−27.5650	−1.89765	−0.948826	−	0.315798i	$-0.897728\pi$
$211$	−27.5650	−1.89765	−0.948826	+	0.315798i	$0.897728\pi$
$212$	−19.3861	−1.33145
$213$	−13.6639	−0.936238
$214$	5.20823	0.356028
$215$	2.61214	0.178146
$216$	−19.2529	−1.30999
$217$	24.9081	1.69087
$218$	13.4481	0.910818
$219$	6.23063	0.421027
$220$	7.03280	0.474151
$221$	1.52177	0.102366
$222$	65.5940	4.40238
$223$	−10.3303	−0.691768	−0.345884	−	0.938277i	$-0.612421\pi$
$223$	−10.3303	−0.691768	−0.345884	+	0.938277i	$0.612421\pi$
$224$	−19.9700	−1.33430
$225$	−25.3389	−1.68926
$226$	−33.3496	−2.21838
$227$	−18.1916	−1.20742	−0.603709	−	0.797204i	$-0.706311\pi$
$227$	−18.1916	−1.20742	−0.603709	+	0.797204i	$0.706311\pi$
$228$	10.1797	0.674169
$229$	11.4352	0.755661	0.377831	−	0.925875i	$-0.376670\pi$
$229$	11.4352	0.755661	0.377831	+	0.925875i	$0.376670\pi$
$230$	−4.97352	−0.327944
$231$	−31.2490	−2.05603
$232$	−0.0505171	−0.00331661
$233$	15.2638	0.999965	0.499982	−	0.866036i	$-0.333340\pi$
$233$	15.2638	0.999965	0.499982	+	0.866036i	$0.333340\pi$
$234$	12.6405	0.826337
$235$	−6.39705	−0.417297
$236$	−3.52257	−0.229300
$237$	−23.0627	−1.49808
$238$	−11.0978	−0.719364
$239$	4.99955	0.323394	0.161697	−	0.986840i	$-0.448303\pi$
$239$	4.99955	0.323394	0.161697	+	0.986840i	$0.448303\pi$
$240$	−0.980414	−0.0632855
$241$	8.77763	0.565417	0.282709	−	0.959206i	$-0.408767\pi$
$241$	8.77763	0.565417	0.282709	+	0.959206i	$0.408767\pi$
$242$	0.0956128	0.00614623
$243$	−6.79677	−0.436013
$244$	−34.1739	−2.18776
$245$	2.29975	0.146925
$246$	34.3546	2.19037
$247$	−1.11243	−0.0707822
$248$	19.6546	1.24807
$249$	17.0348	1.07953
$250$	14.6845	0.928730
$251$	−12.4897	−0.788342	−0.394171	−	0.919037i	$-0.628968\pi$
$251$	−12.4897	−0.788342	−0.394171	+	0.919037i	$0.628968\pi$
$252$	−56.1968	−3.54007
$253$	10.6927	0.672247
$254$	−44.0617	−2.76468
$255$	−3.03301	−0.189935
$256$	−12.6853	−0.792833
$257$	−4.48320	−0.279654	−0.139827	−	0.990176i	$-0.544655\pi$
$257$	−4.48320	−0.279654	−0.139827	+	0.990176i	$0.544655\pi$
$258$	−25.4663	−1.58546
$259$	31.8674	1.98015
$260$	−2.12455	−0.131759
$261$	0.110967	0.00686867
$262$	−12.7404	−0.787106
$263$	−10.1282	−0.624533	−0.312267	−	0.949995i	$-0.601088\pi$
$263$	−10.1282	−0.624533	−0.312267	+	0.949995i	$0.601088\pi$
$264$	−24.6581	−1.51760
$265$	−4.22232	−0.259375
$266$	8.11258	0.497414
$267$	−15.8022	−0.967077
$268$	−24.6328	−1.50469
$269$	−31.0037	−1.89033	−0.945164	−	0.326597i	$-0.894098\pi$
$269$	−31.0037	−1.89033	−0.945164	+	0.326597i	$0.894098\pi$
$270$	−11.6598	−0.709595
$271$	3.81442	0.231709	0.115855	−	0.993266i	$-0.463039\pi$
$271$	3.81442	0.231709	0.115855	+	0.993266i	$0.463039\pi$
$272$	0.748576	0.0453891
$273$	9.44007	0.571339
$274$	6.90372	0.417069
$275$	−15.0195	−0.905710
$276$	29.5592	1.77925
$277$	−8.61452	−0.517596	−0.258798	−	0.965931i	$-0.583326\pi$
$277$	−8.61452	−0.517596	−0.258798	+	0.965931i	$0.583326\pi$
$278$	−26.1864	−1.57056
$279$	−43.1737	−2.58474
$280$	5.57208	0.332996
$281$	−22.3342	−1.33234	−0.666172	−	0.745798i	$-0.732068\pi$
$281$	−22.3342	−1.33234	−0.666172	+	0.745798i	$0.732068\pi$
$282$	62.3660	3.71384
$283$	9.83432	0.584590	0.292295	−	0.956328i	$-0.405581\pi$
$283$	9.83432	0.584590	0.292295	+	0.956328i	$0.405581\pi$
$284$	−14.5653	−0.864291
$285$	2.21716	0.131333
$286$	7.49260	0.443047
$287$	16.6904	0.985205
$288$	34.6143	2.03967
$289$	−14.6842	−0.863777
$290$	−0.0305939	−0.00179654
$291$	11.9962	0.703227
$292$	6.64163	0.388672
$293$	0.481581	0.0281343	0.0140671	−	0.999901i	$-0.495522\pi$
$293$	0.481581	0.0281343	0.0140671	+	0.999901i	$0.495522\pi$
$294$	−22.4207	−1.30760
$295$	−0.767219	−0.0446692
$296$	25.1461	1.46159
$297$	25.0679	1.45459
$298$	−39.7907	−2.30501
$299$	−3.23019	−0.186807
$300$	−41.5201	−2.39717
$301$	−12.3722	−0.713123
$302$	36.8953	2.12308
$303$	44.6618	2.56575
$304$	−0.547215	−0.0313849
$305$	−7.44311	−0.426191
$306$	19.2360	1.09965
$307$	31.4914	1.79731	0.898653	−	0.438660i	$-0.144547\pi$
$307$	31.4914	1.79731	0.898653	+	0.438660i	$0.144547\pi$
$308$	−33.3104	−1.89803
$309$	22.3669	1.27241
$310$	11.9031	0.676053
$311$	−8.55557	−0.485142	−0.242571	−	0.970134i	$-0.577991\pi$
$311$	−8.55557	−0.485142	−0.242571	+	0.970134i	$0.577991\pi$
$312$	7.44903	0.421718
$313$	3.07349	0.173724	0.0868620	−	0.996220i	$-0.472316\pi$
$313$	3.07349	0.173724	0.0868620	+	0.996220i	$0.472316\pi$
$314$	−18.3967	−1.03819
$315$	−12.2397	−0.689631
$316$	−24.5840	−1.38296
$317$	−9.56879	−0.537437	−0.268718	−	0.963219i	$-0.586600\pi$
$317$	−9.56879	−0.537437	−0.268718	+	0.963219i	$0.586600\pi$
$318$	41.1642	2.30838
$319$	0.0657749	0.00368269
$320$	−8.87406	−0.496075
$321$	−6.74185	−0.376293
$322$	23.5567	1.31277
$323$	−1.69287	−0.0941936
$324$	16.9719	0.942884
$325$	4.53727	0.251682
$326$	29.9918	1.66109
$327$	−17.4080	−0.962664
$328$	13.1702	0.727201
$329$	30.2992	1.67045
$330$	−14.9333	−0.822053
$331$	3.20415	0.176116	0.0880580	−	0.996115i	$-0.471934\pi$
$331$	3.20415	0.176116	0.0880580	+	0.996115i	$0.471934\pi$
$332$	18.1585	0.996575
$333$	−55.2364	−3.02694
$334$	43.5474	2.38281
$335$	−5.36505	−0.293124
$336$	4.64366	0.253333
$337$	21.3352	1.16220	0.581102	−	0.813831i	$-0.302622\pi$
$337$	21.3352	1.16220	0.581102	+	0.813831i	$0.302622\pi$
$338$	−2.26345	−0.123116
$339$	43.1698	2.34466
$340$	−3.23309	−0.175339
$341$	−25.5910	−1.38583
$342$	−14.0617	−0.760369
$343$	11.6609	0.629627
$344$	−9.76274	−0.526372
$345$	6.43802	0.346612
$346$	−18.5411	−0.996778
$347$	−12.3745	−0.664296	−0.332148	−	0.943227i	$-0.607773\pi$
$347$	−12.3745	−0.664296	−0.332148	+	0.943227i	$0.607773\pi$
$348$	0.181829	0.00974706
$349$	−2.30594	−0.123434	−0.0617171	−	0.998094i	$-0.519658\pi$
$349$	−2.30594	−0.123434	−0.0617171	+	0.998094i	$0.519658\pi$
$350$	−33.0888	−1.76867
$351$	−7.57280	−0.404206
$352$	20.5175	1.09358
$353$	1.40002	0.0745153	0.0372577	−	0.999306i	$-0.488138\pi$
$353$	1.40002	0.0745153	0.0372577	+	0.999306i	$0.488138\pi$
$354$	7.47977	0.397545
$355$	−3.17234	−0.168370
$356$	−16.8446	−0.892760
$357$	14.3657	0.760312
$358$	−41.5789	−2.19751
$359$	−9.27979	−0.489769	−0.244884	−	0.969552i	$-0.578750\pi$
$359$	−9.27979	−0.489769	−0.244884	+	0.969552i	$0.578750\pi$
$360$	−9.65820	−0.509032
$361$	−17.7625	−0.934868
$362$	−29.2047	−1.53496
$363$	−0.123767	−0.00649608
$364$	10.0628	0.527433
$365$	1.44656	0.0757162
$366$	72.5643	3.79300
$367$	4.55669	0.237857	0.118929	−	0.992903i	$-0.462054\pi$
$367$	4.55669	0.237857	0.118929	+	0.992903i	$0.462054\pi$
$368$	−1.58896	−0.0828304
$369$	−28.9298	−1.50603
$370$	15.2289	0.791711
$371$	19.9987	1.03828
$372$	−70.7440	−3.66791
$373$	33.2759	1.72296	0.861480	−	0.507792i	$-0.169538\pi$
$373$	33.2759	1.72296	0.861480	+	0.507792i	$0.169538\pi$
$374$	11.4021	0.589586
$375$	−19.0085	−0.981596
$376$	23.9086	1.23299
$377$	−0.0198701	−0.00102336
$378$	55.2260	2.84052
$379$	−29.2480	−1.50237	−0.751183	−	0.660094i	$-0.770517\pi$
$379$	−29.2480	−1.50237	−0.751183	+	0.660094i	$0.770517\pi$
$380$	2.36341	0.121241
$381$	57.0361	2.92205
$382$	11.3989	0.583216
$383$	0.595444	0.0304258	0.0152129	−	0.999884i	$-0.495157\pi$
$383$	0.595444	0.0304258	0.0152129	+	0.999884i	$0.495157\pi$
$384$	50.1942	2.56146
$385$	−7.25503	−0.369751
$386$	−14.9810	−0.762511
$387$	21.4450	1.09011
$388$	12.7875	0.649186
$389$	−0.417898	−0.0211883	−0.0105941	−	0.999944i	$-0.503372\pi$
$389$	−0.417898	−0.0211883	−0.0105941	+	0.999944i	$0.503372\pi$
$390$	4.51124	0.228436
$391$	−4.91563	−0.248594
$392$	−8.59519	−0.434123
$393$	16.4920	0.831909
$394$	9.56086	0.481669
$395$	−5.35443	−0.269411
$396$	57.7375	2.90142
$397$	−2.78884	−0.139968	−0.0699839	−	0.997548i	$-0.522295\pi$
$397$	−2.78884	−0.139968	−0.0699839	+	0.997548i	$0.522295\pi$
$398$	39.8079	1.99539
$399$	−10.5014	−0.525728
$400$	2.23193	0.111596
$401$	15.7666	0.787346	0.393673	−	0.919250i	$-0.371204\pi$
$401$	15.7666	0.787346	0.393673	+	0.919250i	$0.371204\pi$
$402$	52.3049	2.60873
$403$	7.73083	0.385100
$404$	47.6079	2.36858
$405$	3.69650	0.183681
$406$	0.144906	0.00719156
$407$	−32.7411	−1.62292
$408$	11.3357	0.561203
$409$	23.4720	1.16062	0.580308	−	0.814397i	$-0.302932\pi$
$409$	23.4720	1.16062	0.580308	+	0.814397i	$0.302932\pi$
$410$	7.97605	0.393909
$411$	−8.93659	−0.440809
$412$	23.8424	1.17463
$413$	3.63388	0.178812
$414$	−40.8313	−2.00675
$415$	3.95493	0.194140
$416$	−6.19816	−0.303890
$417$	33.8973	1.65996
$418$	−8.33499	−0.407678
$419$	−9.97494	−0.487308	−0.243654	−	0.969862i	$-0.578346\pi$
$419$	−9.97494	−0.487308	−0.243654	+	0.969862i	$0.578346\pi$
$420$	−20.0559	−0.978629
$421$	7.59287	0.370054	0.185027	−	0.982733i	$-0.440763\pi$
$421$	7.59287	0.370054	0.185027	+	0.982733i	$0.440763\pi$
$422$	62.3921	3.03720
$423$	−52.5181	−2.55352
$424$	15.7807	0.766380
$425$	6.90470	0.334927
$426$	30.9277	1.49845
$427$	35.2538	1.70605
$428$	−7.18658	−0.347376
$429$	−9.69887	−0.468266
$430$	−5.91246	−0.285124
$431$	−2.04736	−0.0986180	−0.0493090	−	0.998784i	$-0.515702\pi$
$431$	−2.04736	−0.0986180	−0.0493090	+	0.998784i	$0.515702\pi$
$432$	−3.72514	−0.179226
$433$	18.4577	0.887023	0.443511	−	0.896269i	$-0.353733\pi$
$433$	18.4577	0.887023	0.443511	+	0.896269i	$0.353733\pi$
$434$	−56.3784	−2.70625
$435$	0.0396026	0.00189880
$436$	−18.5563	−0.888686
$437$	3.59336	0.171894
$438$	−14.1027	−0.673855
$439$	6.53771	0.312028	0.156014	−	0.987755i	$-0.450136\pi$
$439$	6.53771	0.312028	0.156014	+	0.987755i	$0.450136\pi$
$440$	−5.72484	−0.272921
$441$	18.8803	0.899064
$442$	−3.44447	−0.163837
$443$	−7.98030	−0.379155	−0.189578	−	0.981866i	$-0.560712\pi$
$443$	−7.98030	−0.379155	−0.189578	+	0.981866i	$0.560712\pi$
$444$	−90.5099	−4.29541
$445$	−3.66877	−0.173916
$446$	23.3821	1.10718
$447$	51.5075	2.43622
$448$	42.0314	1.98579
$449$	15.9321	0.751883	0.375942	−	0.926643i	$-0.377319\pi$
$449$	15.9321	0.751883	0.375942	+	0.926643i	$0.377319\pi$
$450$	57.3535	2.70367
$451$	−17.1480	−0.807468
$452$	46.0175	2.16448
$453$	−47.7595	−2.24394
$454$	41.1759	1.93248
$455$	2.19169	0.102748
$456$	−8.28652	−0.388052
$457$	26.8148	1.25435	0.627173	−	0.778880i	$-0.284212\pi$
$457$	26.8148	1.25435	0.627173	+	0.778880i	$0.284212\pi$
$458$	−25.8831	−1.20944
$459$	−11.5241	−0.537899
$460$	6.86271	0.319975
$461$	−28.2264	−1.31464	−0.657318	−	0.753614i	$-0.728309\pi$
$461$	−28.2264	−1.31464	−0.657318	+	0.753614i	$0.728309\pi$
$462$	70.7307	3.29069
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−0.00977428	−0.000453760 0
$465$	−15.4081	−0.714535
$466$	−34.5489	−1.60045
$467$	−6.81840	−0.315518	−0.157759	−	0.987478i	$-0.550427\pi$
$467$	−6.81840	−0.315518	−0.157759	+	0.987478i	$0.550427\pi$
$468$	−17.4420	−0.806258
$469$	25.4112	1.17338
$470$	14.4794	0.667886
$471$	23.8138	1.09728
$472$	2.86744	0.131985
$473$	12.7114	0.584471
$474$	52.2014	2.39769
$475$	−5.04739	−0.231590
$476$	15.3133	0.701884
$477$	−34.6642	−1.58717
$478$	−11.3163	−0.517593
$479$	−6.04125	−0.276032	−0.138016	−	0.990430i	$-0.544072\pi$
$479$	−6.04125	−0.276032	−0.138016	+	0.990430i	$0.544072\pi$
$480$	12.3534	0.563853
$481$	9.89082	0.450982
$482$	−19.8678	−0.904952
$483$	−30.4933	−1.38749
$484$	−0.131931	−0.00599688
$485$	2.78513	0.126466
$486$	15.3842	0.697840
$487$	13.3627	0.605522	0.302761	−	0.953067i	$-0.402092\pi$
$487$	13.3627	0.605522	0.302761	+	0.953067i	$0.402092\pi$
$488$	27.8183	1.25927
$489$	−38.8231	−1.75564
$490$	−5.20537	−0.235155
$491$	−24.2079	−1.09249	−0.546243	−	0.837627i	$-0.683942\pi$
$491$	−24.2079	−1.09249	−0.546243	+	0.837627i	$0.683942\pi$
$492$	−47.4042	−2.13715
$493$	−0.0302378	−0.00136184
$494$	2.51793	0.113287
$495$	12.5753	0.565217
$496$	3.80287	0.170754
$497$	15.0256	0.673988
$498$	−38.5574	−1.72780
$499$	−5.66497	−0.253599	−0.126799	−	0.991928i	$-0.540470\pi$
$499$	−5.66497	−0.253599	−0.126799	+	0.991928i	$0.540470\pi$
$500$	−20.2624	−0.906163
$501$	−56.3703	−2.51844
$502$	28.2698	1.26174
$503$	−25.3285	−1.12934	−0.564671	−	0.825316i	$-0.690997\pi$
$503$	−25.3285	−1.12934	−0.564671	+	0.825316i	$0.690997\pi$
$504$	45.7454	2.03766
$505$	10.3691	0.461417
$506$	−24.2025	−1.07593
$507$	2.92995	0.130124
$508$	60.7985	2.69750
$509$	6.13399	0.271884	0.135942	−	0.990717i	$-0.456594\pi$
$509$	6.13399	0.271884	0.135942	+	0.990717i	$0.456594\pi$
$510$	6.86509	0.303991
$511$	−6.85151	−0.303093
$512$	−5.55017	−0.245285
$513$	8.42421	0.371938
$514$	10.1475	0.447588
$515$	5.19290	0.228826
$516$	35.1396	1.54693
$517$	−31.1298	−1.36909
$518$	−72.1305	−3.16923
$519$	24.0008	1.05352
$520$	1.72943	0.0758405
$521$	26.5921	1.16502	0.582510	−	0.812823i	$-0.302071\pi$
$521$	26.5921	1.16502	0.582510	+	0.812823i	$0.302071\pi$
$522$	−0.251168	−0.0109933
$523$	1.77660	0.0776854	0.0388427	−	0.999245i	$-0.487633\pi$
$523$	1.77660	0.0776854	0.0388427	+	0.999245i	$0.487633\pi$
$524$	17.5799	0.767980
$525$	42.8322	1.86935
$526$	22.9248	0.999568
$527$	11.7646	0.512473
$528$	−4.77097	−0.207630
$529$	−12.5659	−0.546342
$530$	9.55704	0.415131
$531$	−6.29868	−0.273339
$532$	−11.1941	−0.485328
$533$	5.18027	0.224383
$534$	35.7675	1.54781
$535$	−1.56525	−0.0676715
$536$	20.0516	0.866097
$537$	53.8222	2.32260
$538$	70.1754	3.02548
$539$	11.1912	0.482040
$540$	16.0888	0.692352
$541$	35.1097	1.50948	0.754741	−	0.656022i	$-0.227762\pi$
$541$	35.1097	1.50948	0.754741	+	0.656022i	$0.227762\pi$
$542$	−8.63376	−0.370852
$543$	37.8043	1.62234
$544$	−9.43220	−0.404402
$545$	−4.04159	−0.173123
$546$	−21.3672	−0.914431
$547$	31.7831	1.35895	0.679474	−	0.733699i	$-0.262208\pi$
$547$	31.7831	1.35895	0.679474	+	0.733699i	$0.262208\pi$
$548$	−9.52609	−0.406934
$549$	−61.1061	−2.60794
$550$	33.9960	1.44959
$551$	0.0221041	0.000941664 0
$552$	−24.0618	−1.02414
$553$	25.3609	1.07846
$554$	19.4986	0.828415
$555$	−19.7132	−0.836777
$556$	36.1333	1.53239
$557$	−13.4753	−0.570968	−0.285484	−	0.958383i	$-0.592154\pi$
$557$	−13.4753	−0.570968	−0.285484	+	0.958383i	$0.592154\pi$
$558$	97.7217	4.13689
$559$	−3.84001	−0.162415
$560$	1.07811	0.0455586
$561$	−14.7595	−0.623147
$562$	50.5524	2.13242
$563$	3.92036	0.165223	0.0826117	−	0.996582i	$-0.473674\pi$
$563$	3.92036	0.165223	0.0826117	+	0.996582i	$0.473674\pi$
$564$	−86.0557	−3.62360
$565$	10.0227	0.421656
$566$	−22.2595	−0.935638
$567$	−17.5082	−0.735277
$568$	11.8565	0.497486
$569$	−8.68954	−0.364284	−0.182142	−	0.983272i	$-0.558303\pi$
$569$	−8.68954	−0.364284	−0.182142	+	0.983272i	$0.558303\pi$
$570$	−5.01844	−0.210199
$571$	−33.5234	−1.40291	−0.701456	−	0.712713i	$-0.747466\pi$
$571$	−33.5234	−1.40291	−0.701456	+	0.712713i	$0.747466\pi$
$572$	−10.3387	−0.432281
$573$	−14.7554	−0.616414
$574$	−37.7780	−1.57682
$575$	−14.6563	−0.611208
$576$	−72.8537	−3.03557
$577$	−9.89383	−0.411885	−0.205943	−	0.978564i	$-0.566026\pi$
$577$	−9.89383	−0.411885	−0.205943	+	0.978564i	$0.566026\pi$
$578$	33.2370	1.38248
$579$	19.3923	0.805914
$580$	0.0422150	0.00175288
$581$	−18.7323	−0.777146
$582$	−27.1527	−1.12552
$583$	−20.5470	−0.850970
$584$	−5.40643	−0.223720
$585$	−3.79889	−0.157065
$586$	−1.09004	−0.0450290
$587$	18.5916	0.767356	0.383678	−	0.923467i	$-0.374657\pi$
$587$	18.5916	0.767356	0.383678	+	0.923467i	$0.374657\pi$
$588$	30.9372	1.27583
$589$	−8.60000	−0.354357
$590$	1.73657	0.0714933
$591$	−12.3762	−0.509087
$592$	4.86539	0.199966
$593$	−7.01602	−0.288113	−0.144057	−	0.989569i	$-0.546015\pi$
$593$	−7.01602	−0.288113	−0.144057	+	0.989569i	$0.546015\pi$
$594$	−56.7400	−2.32807
$595$	3.33525	0.136732
$596$	54.9052	2.24900
$597$	−51.5298	−2.10897
$598$	7.31139	0.298985
$599$	−18.7944	−0.767917	−0.383958	−	0.923350i	$-0.625439\pi$
$599$	−18.7944	−0.767917	−0.383958	+	0.923350i	$0.625439\pi$
$600$	33.7982	1.37981
$601$	−42.5969	−1.73756	−0.868782	−	0.495195i	$-0.835097\pi$
$601$	−42.5969	−1.73756	−0.868782	+	0.495195i	$0.835097\pi$
$602$	28.0040	1.14136
$603$	−44.0457	−1.79368
$604$	−50.9099	−2.07150
$605$	−0.0287348	−0.00116824
$606$	−101.090	−4.10650
$607$	−23.9555	−0.972323	−0.486162	−	0.873869i	$-0.661603\pi$
$607$	−23.9555	−0.972323	−0.486162	+	0.873869i	$0.661603\pi$
$608$	6.89501	0.279630
$609$	−0.187575	−0.00760092
$610$	16.8472	0.682121
$611$	9.40407	0.380448
$612$	−26.5428	−1.07293
$613$	−38.3699	−1.54974	−0.774872	−	0.632118i	$-0.782186\pi$
$613$	−38.3699	−1.54974	−0.774872	+	0.632118i	$0.782186\pi$
$614$	−71.2792	−2.87660
$615$	−10.3247	−0.416331
$616$	27.1153	1.09251
$617$	44.7158	1.80019	0.900095	−	0.435694i	$-0.143497\pi$
$617$	44.7158	1.80019	0.900095	+	0.435694i	$0.143497\pi$
$618$	−50.6265	−2.03650
$619$	4.28944	0.172407	0.0862035	−	0.996278i	$-0.472526\pi$
$619$	4.28944	0.172407	0.0862035	+	0.996278i	$0.472526\pi$
$620$	−16.4245	−0.659625
$621$	24.4616	0.981611
$622$	19.3651	0.776472
$623$	17.3769	0.696189
$624$	1.44127	0.0576970
$625$	18.2732	0.730927
$626$	−6.95671	−0.278046
$627$	10.7893	0.430884
$628$	25.3847	1.01296
$629$	15.0516	0.600146
$630$	27.7041	1.10376
$631$	−26.9827	−1.07416	−0.537081	−	0.843531i	$-0.680473\pi$
$631$	−26.9827	−1.07416	−0.537081	+	0.843531i	$0.680473\pi$
$632$	20.0119	0.796032
$633$	−80.7641	−3.21009
$634$	21.6585	0.860170
$635$	13.2420	0.525492
$636$	−56.8005	−2.25228
$637$	−3.38078	−0.133951
$638$	−0.148879	−0.00589416
$639$	−26.0441	−1.03029
$640$	11.6535	0.460646
$641$	−43.0590	−1.70073	−0.850363	−	0.526196i	$-0.823618\pi$
$641$	−43.0590	−1.70073	−0.850363	+	0.526196i	$0.823618\pi$
$642$	15.2599	0.602259
$643$	−18.5205	−0.730378	−0.365189	−	0.930933i	$-0.618996\pi$
$643$	−18.5205	−0.730378	−0.365189	+	0.930933i	$0.618996\pi$
$644$	−32.5047	−1.28087
$645$	7.65344	0.301354
$646$	3.83173	0.150757
$647$	38.2908	1.50537	0.752683	−	0.658383i	$-0.228759\pi$
$647$	38.2908	1.50537	0.752683	+	0.658383i	$0.228759\pi$
$648$	−13.8155	−0.542724
$649$	−3.73351	−0.146553
$650$	−10.2699	−0.402819
$651$	72.9796	2.86029
$652$	−41.3841	−1.62073
$653$	−41.0021	−1.60454	−0.802268	−	0.596964i	$-0.796374\pi$
$653$	−41.0021	−1.60454	−0.802268	+	0.596964i	$0.796374\pi$
$654$	39.4022	1.54075
$655$	3.82891	0.149608
$656$	2.54823	0.0994915
$657$	11.8759	0.463321
$658$	−68.5808	−2.67356
$659$	28.4933	1.10994	0.554970	−	0.831870i	$-0.312730\pi$
$659$	28.4933	1.10994	0.554970	+	0.831870i	$0.312730\pi$
$660$	20.6058	0.802078
$661$	−5.34830	−0.208025	−0.104012	−	0.994576i	$-0.533168\pi$
$661$	−5.34830	−0.208025	−0.104012	+	0.994576i	$0.533168\pi$
$662$	−7.25245	−0.281874
$663$	4.45873	0.173163
$664$	−14.7814	−0.573628
$665$	−2.43810	−0.0945454
$666$	125.025	4.84463
$667$	0.0641842	0.00248522
$668$	−60.0888	−2.32491
$669$	−30.2673	−1.17020
$670$	12.1435	0.469146
$671$	−36.2203	−1.39827
$672$	−58.5111	−2.25711
$673$	−27.1439	−1.04632	−0.523161	−	0.852234i	$-0.675247\pi$
$673$	−27.1439	−1.04632	−0.523161	+	0.852234i	$0.675247\pi$
$674$	−48.2913	−1.86011
$675$	−34.3599	−1.32251
$676$	3.12323	0.120124
$677$	16.6676	0.640586	0.320293	−	0.947318i	$-0.396219\pi$
$677$	16.6676	0.640586	0.320293	+	0.947318i	$0.396219\pi$
$678$	−97.7128	−3.75264
$679$	−13.1916	−0.506246
$680$	2.63180	0.100925
$681$	−53.3005	−2.04248
$682$	57.9240	2.21802
$683$	24.9502	0.954693	0.477346	−	0.878715i	$-0.341599\pi$
$683$	24.9502	0.954693	0.477346	+	0.878715i	$0.341599\pi$
$684$	19.4030	0.741893
$685$	−2.07479	−0.0792738
$686$	−26.3938	−1.00772
$687$	33.5047	1.27828
$688$	−1.88894	−0.0720152
$689$	6.20709	0.236471
$690$	−14.5722	−0.554753
$691$	37.4324	1.42400	0.711998	−	0.702182i	$-0.247791\pi$
$691$	37.4324	1.42400	0.711998	+	0.702182i	$0.247791\pi$
$692$	25.5840	0.972557
$693$	−59.5620	−2.26257
$694$	28.0090	1.06321
$695$	7.86987	0.298521
$696$	−0.148013	−0.00561041
$697$	7.88321	0.298598
$698$	5.21939	0.197557
$699$	44.7222	1.69155
$700$	45.6576	1.72569
$701$	27.0410	1.02132	0.510662	−	0.859782i	$-0.329400\pi$
$701$	27.0410	1.02132	0.510662	+	0.859782i	$0.329400\pi$
$702$	17.1407	0.646934
$703$	−11.0028	−0.414980
$704$	−43.1836	−1.62754
$705$	−18.7430	−0.705904
$706$	−3.16887	−0.119262
$707$	−49.1123	−1.84706
$708$	−10.3210	−0.387885
$709$	−16.7139	−0.627703	−0.313851	−	0.949472i	$-0.601619\pi$
$709$	−16.7139	−0.627703	−0.313851	+	0.949472i	$0.601619\pi$
$710$	7.18044	0.269477
$711$	−43.9585	−1.64857
$712$	13.7118	0.513872
$713$	−24.9721	−0.935211
$714$	−32.5160	−1.21688
$715$	−2.25177	−0.0842115
$716$	57.3726	2.14411
$717$	14.6484	0.547056
$718$	21.0044	0.783877
$719$	0.727067	0.0271150	0.0135575	−	0.999908i	$-0.495684\pi$
$719$	0.727067	0.0271150	0.0135575	+	0.999908i	$0.495684\pi$
$720$	−1.86871	−0.0696428
$721$	−24.5958	−0.915995
$722$	40.2046	1.49626
$723$	25.7180	0.956464
$724$	40.2981	1.49767
$725$	−0.0901559	−0.00334831
$726$	0.280141	0.0103970
$727$	−29.9195	−1.10965	−0.554826	−	0.831966i	$-0.687215\pi$
$727$	−29.9195	−1.10965	−0.554826	+	0.831966i	$0.687215\pi$
$728$	−8.19132	−0.303591
$729$	−36.2165	−1.34135
$730$	−3.27421	−0.121184
$731$	−5.84364	−0.216135
$732$	−100.128	−3.70083
$733$	31.8668	1.17703	0.588514	−	0.808487i	$-0.299713\pi$
$733$	31.8668	1.17703	0.588514	+	0.808487i	$0.299713\pi$
$734$	−10.3139	−0.380692
$735$	6.73815	0.248540
$736$	20.0212	0.737993
$737$	−26.1078	−0.961694
$738$	65.4814	2.41040
$739$	−4.89026	−0.179891	−0.0899455	−	0.995947i	$-0.528669\pi$
$739$	−4.89026	−0.179891	−0.0899455	+	0.995947i	$0.528669\pi$
$740$	−21.0135	−0.772473
$741$	−3.25936	−0.119736
$742$	−45.2663	−1.66178
$743$	−9.94066	−0.364687	−0.182344	−	0.983235i	$-0.558368\pi$
$743$	−9.94066	−0.364687	−0.182344	+	0.983235i	$0.558368\pi$
$744$	57.5871	2.11125
$745$	11.9584	0.438122
$746$	−75.3184	−2.75760
$747$	32.4690	1.18798
$748$	−15.7331	−0.575260
$749$	7.41368	0.270890
$750$	43.0249	1.57105
$751$	15.9747	0.582925	0.291462	−	0.956582i	$-0.405858\pi$
$751$	15.9747	0.582925	0.291462	+	0.956582i	$0.405858\pi$
$752$	4.62595	0.168691
$753$	−36.5942	−1.33357
$754$	0.0449750	0.00163789
$755$	−11.0882	−0.403542
$756$	−76.2035	−2.77150
$757$	9.47230	0.344277	0.172138	−	0.985073i	$-0.444932\pi$
$757$	9.47230	0.344277	0.172138	+	0.985073i	$0.444932\pi$
$758$	66.2014	2.40454
$759$	31.3292	1.13718
$760$	−1.92387	−0.0697860
$761$	−42.5489	−1.54240	−0.771198	−	0.636595i	$-0.780342\pi$
$761$	−42.5489	−1.54240	−0.771198	+	0.636595i	$0.780342\pi$
$762$	−129.099	−4.67675
$763$	19.1427	0.693012
$764$	−15.7287	−0.569045
$765$	−5.78106	−0.209015
$766$	−1.34776	−0.0486966
$767$	1.12786	0.0407247
$768$	−37.1674	−1.34116
$769$	−21.9542	−0.791687	−0.395844	−	0.918318i	$-0.629548\pi$
$769$	−21.9542	−0.791687	−0.395844	+	0.918318i	$0.629548\pi$
$770$	16.4214	0.591788
$771$	−13.1355	−0.473065
$772$	20.6715	0.743982
$773$	−38.0044	−1.36692	−0.683462	−	0.729986i	$-0.739526\pi$
$773$	−38.0044	−1.36692	−0.683462	+	0.729986i	$0.739526\pi$
$774$	−48.5398	−1.74473
$775$	35.0768	1.26000
$776$	−10.4093	−0.373671
$777$	93.3700	3.34963
$778$	0.945892	0.0339119
$779$	−5.76269	−0.206470
$780$	−6.22483	−0.222885
$781$	−15.4375	−0.552397
$782$	11.1263	0.397875
$783$	0.150472	0.00537744
$784$	−1.66304	−0.0593942
$785$	5.52882	0.197332
$786$	−37.3288	−1.33147
$787$	−7.41197	−0.264208	−0.132104	−	0.991236i	$-0.542173\pi$
$787$	−7.41197	−0.264208	−0.132104	+	0.991236i	$0.542173\pi$
$788$	−13.1925	−0.469965
$789$	−29.6752	−1.05647
$790$	12.1195	0.431193
$791$	−47.4716	−1.68790
$792$	−46.9995	−1.67005
$793$	10.9419	0.388557
$794$	6.31241	0.224019
$795$	−12.3712	−0.438761
$796$	−54.9289	−1.94690
$797$	−20.2593	−0.717623	−0.358811	−	0.933410i	$-0.616818\pi$
$797$	−20.2593	−0.717623	−0.358811	+	0.933410i	$0.616818\pi$
$798$	23.7695	0.841430
$799$	14.3109	0.506282
$800$	−28.1227	−0.994288
$801$	−30.1196	−1.06422
$802$	−35.6870	−1.26015
$803$	7.03935	0.248413
$804$	−72.1729	−2.54534
$805$	−7.07957	−0.249522
$806$	−17.4984	−0.616354
$807$	−90.8393	−3.19769
$808$	−38.7538	−1.36336
$809$	−30.8077	−1.08314	−0.541570	−	0.840655i	$-0.682170\pi$
$809$	−30.8077	−1.08314	−0.541570	+	0.840655i	$0.682170\pi$
$810$	−8.36687	−0.293982
$811$	54.5747	1.91638	0.958189	−	0.286135i	$-0.0923707\pi$
$811$	54.5747	1.91638	0.958189	+	0.286135i	$0.0923707\pi$
$812$	−0.199948	−0.00701681
$813$	11.1761	0.391962
$814$	74.1080	2.59748
$815$	−9.01351	−0.315729
$816$	2.19329	0.0767805
$817$	4.27174	0.149449
$818$	−53.1278	−1.85757
$819$	17.9932	0.628733
$820$	−11.0058	−0.384338
$821$	44.9502	1.56877	0.784386	−	0.620273i	$-0.212978\pi$
$821$	44.9502	1.56877	0.784386	+	0.620273i	$0.212978\pi$
$822$	20.2276	0.705517
$823$	15.1747	0.528956	0.264478	−	0.964392i	$-0.414800\pi$
$823$	15.1747	0.528956	0.264478	+	0.964392i	$0.414800\pi$
$824$	−19.4082	−0.676116
$825$	−44.0064	−1.53211
$826$	−8.22513	−0.286189
$827$	16.7141	0.581206	0.290603	−	0.956844i	$-0.406144\pi$
$827$	16.7141	0.581206	0.290603	+	0.956844i	$0.406144\pi$
$828$	56.3411	1.95799
$829$	8.89578	0.308963	0.154482	−	0.987996i	$-0.450629\pi$
$829$	8.89578	0.308963	0.154482	+	0.987996i	$0.450629\pi$
$830$	−8.95181	−0.310722
$831$	−25.2401	−0.875570
$832$	13.0454	0.452269
$833$	−5.14478	−0.178256
$834$	−76.7249	−2.65677
$835$	−13.0874	−0.452909
$836$	11.5010	0.397771
$837$	−58.5440	−2.02358
$838$	22.5778	0.779938
$839$	51.4877	1.77755	0.888777	−	0.458340i	$-0.151556\pi$
$839$	51.4877	1.77755	0.888777	+	0.458340i	$0.151556\pi$
$840$	16.3259	0.563298
$841$	−28.9996	−0.999986
$842$	−17.1861	−0.592273
$843$	−65.4380	−2.25380
$844$	−86.0917	−2.96340
$845$	0.680242	0.0234010
$846$	118.872	4.08692
$847$	0.136100	0.00467646
$848$	3.05333	0.104852
$849$	28.8141	0.988897
$850$	−15.6285	−0.536052
$851$	−31.9492	−1.09521
$852$	−42.6756	−1.46204
$853$	0.272071	0.00931553	0.00465776	−	0.999989i	$-0.498517\pi$
$853$	0.272071	0.00931553	0.00465776	+	0.999989i	$0.498517\pi$
$854$	−79.7954	−2.73054
$855$	4.22600	0.144526
$856$	5.85003	0.199950
$857$	−35.1209	−1.19971	−0.599853	−	0.800110i	$-0.704774\pi$
$857$	−35.1209	−1.19971	−0.599853	+	0.800110i	$0.704774\pi$
$858$	21.9530	0.749462
$859$	40.4413	1.37984	0.689919	−	0.723886i	$-0.257646\pi$
$859$	40.4413	1.37984	0.689919	+	0.723886i	$0.257646\pi$
$860$	8.15831	0.278196
$861$	48.9022	1.66658
$862$	4.63411	0.157838
$863$	−13.2307	−0.450378	−0.225189	−	0.974315i	$-0.572300\pi$
$863$	−13.2307	−0.450378	−0.225189	+	0.974315i	$0.572300\pi$
$864$	46.9374	1.59684
$865$	5.57222	0.189461
$866$	−41.7783	−1.41968
$867$	−43.0240	−1.46117
$868$	77.7937	2.64049
$869$	−26.0562	−0.883895
$870$	−0.0896387	−0.00303904
$871$	7.88697	0.267240
$872$	15.1052	0.511528
$873$	22.8652	0.773870
$874$	−8.13341	−0.275117
$875$	20.9027	0.706641
$876$	19.4597	0.657481
$877$	16.4901	0.556830	0.278415	−	0.960461i	$-0.410191\pi$
$877$	16.4901	0.556830	0.278415	+	0.960461i	$0.410191\pi$
$878$	−14.7978	−0.499402
$879$	1.41101	0.0475921
$880$	−1.10767	−0.0373395
$881$	−42.5574	−1.43380	−0.716898	−	0.697179i	$-0.754438\pi$
$881$	−42.5574	−1.43380	−0.716898	+	0.697179i	$0.754438\pi$
$882$	−42.7348	−1.43896
$883$	39.9087	1.34304	0.671518	−	0.740989i	$-0.265643\pi$
$883$	39.9087	1.34304	0.671518	+	0.740989i	$0.265643\pi$
$884$	4.75285	0.159856
$885$	−2.24792	−0.0755629
$886$	18.0630	0.606840
$887$	46.3137	1.55506	0.777530	−	0.628845i	$-0.216472\pi$
$887$	46.3137	1.55506	0.777530	+	0.628845i	$0.216472\pi$
$888$	73.6770	2.47244
$889$	−62.7197	−2.10355
$890$	8.30408	0.278353
$891$	17.9882	0.602628
$892$	−32.2638	−1.08027
$893$	−10.4614	−0.350076
$894$	−116.585	−3.89918
$895$	12.4958	0.417689
$896$	−55.1961	−1.84397
$897$	−9.46431	−0.316004
$898$	−36.0616	−1.20339
$899$	−0.153612	−0.00512325
$900$	−79.1392	−2.63797
$901$	9.44579	0.314685
$902$	38.8137	1.29236
$903$	−36.2500	−1.20632
$904$	−37.4592	−1.24587
$905$	8.77697	0.291756
$906$	108.101	3.59143
$907$	−1.75416	−0.0582459	−0.0291230	−	0.999576i	$-0.509271\pi$
$907$	−1.75416	−0.0582459	−0.0291230	+	0.999576i	$0.509271\pi$
$908$	−56.8165	−1.88552
$909$	85.1273	2.82350
$910$	−4.96078	−0.164448
$911$	41.3414	1.36970	0.684851	−	0.728683i	$-0.259867\pi$
$911$	41.3414	1.36970	0.684851	+	0.728683i	$0.259867\pi$
$912$	−1.60331	−0.0530910
$913$	19.2458	0.636944
$914$	−60.6942	−2.00758
$915$	−21.8080	−0.720949
$916$	35.7148	1.18005
$917$	−18.1354	−0.598883
$918$	26.0843	0.860910
$919$	2.02434	0.0667768	0.0333884	−	0.999442i	$-0.489370\pi$
$919$	2.02434	0.0667768	0.0333884	+	0.999442i	$0.489370\pi$
$920$	−5.58639	−0.184178
$921$	92.2681	3.04034
$922$	63.8892	2.10408
$923$	4.66354	0.153502
$924$	−97.5977	−3.21073
$925$	44.8773	1.47556
$926$	2.26345	0.0743817
$927$	42.6324	1.40023
$928$	0.123158	0.00404286
$929$	12.8983	0.423179	0.211590	−	0.977359i	$-0.432136\pi$
$929$	12.8983	0.423179	0.211590	+	0.977359i	$0.432136\pi$
$930$	34.8756	1.14362
$931$	3.76087	0.123258
$932$	47.6723	1.56156
$933$	−25.0674	−0.820670
$934$	15.4331	0.504988
$935$	−3.42669	−0.112065
$936$	14.1982	0.464082
$937$	−2.31855	−0.0757437	−0.0378719	−	0.999283i	$-0.512058\pi$
$937$	−2.31855	−0.0757437	−0.0378719	+	0.999283i	$0.512058\pi$
$938$	−57.5171	−1.87800
$939$	9.00518	0.293873
$940$	−19.9794	−0.651657
$941$	−28.4465	−0.927328	−0.463664	−	0.886011i	$-0.653466\pi$
$941$	−28.4465	−0.927328	−0.463664	+	0.886011i	$0.653466\pi$
$942$	−53.9015	−1.75621
$943$	−16.7333	−0.544911
$944$	0.554806	0.0180574
$945$	−16.5972	−0.539908
$946$	−28.7717	−0.935448
$947$	55.7179	1.81059	0.905294	−	0.424785i	$-0.139650\pi$
$947$	55.7179	1.81059	0.905294	+	0.424785i	$0.139650\pi$
$948$	−72.0300	−2.33943
$949$	−2.12653	−0.0690301
$950$	11.4245	0.370661
$951$	−28.0361	−0.909133
$952$	−12.4653	−0.404004
$953$	35.7883	1.15930	0.579648	−	0.814867i	$-0.303190\pi$
$953$	35.7883	1.15930	0.579648	+	0.814867i	$0.303190\pi$
$954$	78.4609	2.54026
$955$	−3.42573	−0.110854
$956$	15.6147	0.505016
$957$	0.192717	0.00622967
$958$	13.6741	0.441790
$959$	9.82712	0.317334
$960$	−26.0006	−0.839164
$961$	28.7657	0.927925
$962$	−22.3874	−0.721799
$963$	−12.8503	−0.414094
$964$	27.4145	0.882963
$965$	4.50227	0.144933
$966$	69.0201	2.22069
$967$	14.1750	0.455837	0.227918	−	0.973680i	$-0.426808\pi$
$967$	14.1750	0.455837	0.227918	+	0.973680i	$0.426808\pi$
$968$	0.107395	0.00345180
$969$	−4.96002	−0.159339
$970$	−6.30401	−0.202410
$971$	20.7926	0.667267	0.333633	−	0.942703i	$-0.391725\pi$
$971$	20.7926	0.667267	0.333633	+	0.942703i	$0.391725\pi$
$972$	−21.2278	−0.680883
$973$	−37.2751	−1.19499
$974$	−30.2459	−0.969140
$975$	13.2940	0.425748
$976$	5.38241	0.172287
$977$	14.2968	0.457395	0.228697	−	0.973498i	$-0.426553\pi$
$977$	14.2968	0.457395	0.228697	+	0.973498i	$0.426553\pi$
$978$	87.8744	2.80991
$979$	−17.8532	−0.570592
$980$	7.18263	0.229441
$981$	−33.1804	−1.05937
$982$	54.7934	1.74853
$983$	−13.4566	−0.429199	−0.214599	−	0.976702i	$-0.568845\pi$
$983$	−13.4566	−0.429199	−0.214599	+	0.976702i	$0.568845\pi$
$984$	38.5880	1.23014
$985$	−2.87335	−0.0915526
$986$	0.0684418	0.00217963
$987$	88.7751	2.82574
$988$	−3.47437	−0.110534
$989$	12.4040	0.394424
$990$	−28.4636	−0.904632
$991$	−1.60509	−0.0509874	−0.0254937	−	0.999675i	$-0.508116\pi$
$991$	−1.60509	−0.0509874	−0.0254937	+	0.999675i	$0.508116\pi$
$992$	−47.9169	−1.52136
$993$	9.38800	0.297919
$994$	−34.0097	−1.07872
$995$	−11.9636	−0.379271
$996$	53.2034	1.68581
$997$	−60.8447	−1.92697	−0.963486	−	0.267760i	$-0.913716\pi$
$997$	−60.8447	−1.92697	−0.963486	+	0.267760i	$0.913716\pi$
$998$	12.8224	0.405886
$999$	−74.9012	−2.36977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.14	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.14	✓	108	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)

\(f(q)\)	\(=\)	\(q-2.26345 q^{2} +2.92995 q^{3} +3.12323 q^{4} +0.680242 q^{5} -6.63181 q^{6} -3.22192 q^{7} -2.54237 q^{8} +5.58462 q^{9} +O(q^{10})\)	\(q-2.26345 q^{2} +2.92995 q^{3} +3.12323 q^{4} +0.680242 q^{5} -6.63181 q^{6} -3.22192 q^{7} -2.54237 q^{8} +5.58462 q^{9} -1.53970 q^{10} +3.31025 q^{11} +9.15090 q^{12} -1.00000 q^{13} +7.29267 q^{14} +1.99308 q^{15} -0.491910 q^{16} -1.52177 q^{17} -12.6405 q^{18} +1.11243 q^{19} +2.12455 q^{20} -9.44007 q^{21} -7.49260 q^{22} +3.23019 q^{23} -7.44903 q^{24} -4.53727 q^{25} +2.26345 q^{26} +7.57280 q^{27} -10.0628 q^{28} +0.0198701 q^{29} -4.51124 q^{30} -7.73083 q^{31} +6.19816 q^{32} +9.69887 q^{33} +3.44447 q^{34} -2.19169 q^{35} +17.4420 q^{36} -9.89082 q^{37} -2.51793 q^{38} -2.92995 q^{39} -1.72943 q^{40} -5.18027 q^{41} +21.3672 q^{42} +3.84001 q^{43} +10.3387 q^{44} +3.79889 q^{45} -7.31139 q^{46} -9.40407 q^{47} -1.44127 q^{48} +3.38078 q^{49} +10.2699 q^{50} -4.45873 q^{51} -3.12323 q^{52} -6.20709 q^{53} -17.1407 q^{54} +2.25177 q^{55} +8.19132 q^{56} +3.25936 q^{57} -0.0449750 q^{58} -1.12786 q^{59} +6.22483 q^{60} -10.9419 q^{61} +17.4984 q^{62} -17.9932 q^{63} -13.0454 q^{64} -0.680242 q^{65} -21.9530 q^{66} -7.88697 q^{67} -4.75285 q^{68} +9.46431 q^{69} +4.96078 q^{70} -4.66354 q^{71} -14.1982 q^{72} +2.12653 q^{73} +22.3874 q^{74} -13.2940 q^{75} +3.47437 q^{76} -10.6654 q^{77} +6.63181 q^{78} -7.87136 q^{79} -0.334618 q^{80} +5.43410 q^{81} +11.7253 q^{82} +5.81401 q^{83} -29.4835 q^{84} -1.03518 q^{85} -8.69170 q^{86} +0.0582184 q^{87} -8.41589 q^{88} -5.39332 q^{89} -8.59862 q^{90} +3.22192 q^{91} +10.0886 q^{92} -22.6509 q^{93} +21.2857 q^{94} +0.756722 q^{95} +18.1603 q^{96} +4.09432 q^{97} -7.65223 q^{98} +18.4865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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