LMFDB - Embedded newform 6031.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41585 q^{2} +0.542785 q^{3} +3.83634 q^{4} -2.85515 q^{5} -1.31129 q^{6} -2.66009 q^{7} -4.43632 q^{8} -2.70538 q^{9} +O(q^{10})$	\(q-2.41585 q^{2} +0.542785 q^{3} +3.83634 q^{4} -2.85515 q^{5} -1.31129 q^{6} -2.66009 q^{7} -4.43632 q^{8} -2.70538 q^{9} +6.89763 q^{10} -3.66986 q^{11} +2.08231 q^{12} +0.724095 q^{13} +6.42638 q^{14} -1.54974 q^{15} +3.04482 q^{16} -0.159207 q^{17} +6.53581 q^{18} +0.910249 q^{19} -10.9533 q^{20} -1.44386 q^{21} +8.86584 q^{22} -4.35977 q^{23} -2.40797 q^{24} +3.15190 q^{25} -1.74931 q^{26} -3.09680 q^{27} -10.2050 q^{28} +8.10416 q^{29} +3.74393 q^{30} +2.82462 q^{31} +1.51682 q^{32} -1.99195 q^{33} +0.384622 q^{34} +7.59497 q^{35} -10.3788 q^{36} -1.00000 q^{37} -2.19903 q^{38} +0.393028 q^{39} +12.6664 q^{40} +8.15224 q^{41} +3.48815 q^{42} +8.89541 q^{43} -14.0788 q^{44} +7.72429 q^{45} +10.5326 q^{46} -0.0630801 q^{47} +1.65268 q^{48} +0.0760833 q^{49} -7.61453 q^{50} -0.0864155 q^{51} +2.77787 q^{52} -2.28662 q^{53} +7.48140 q^{54} +10.4780 q^{55} +11.8010 q^{56} +0.494070 q^{57} -19.5784 q^{58} -6.65593 q^{59} -5.94531 q^{60} -10.8043 q^{61} -6.82385 q^{62} +7.19657 q^{63} -9.75404 q^{64} -2.06740 q^{65} +4.81225 q^{66} +8.69582 q^{67} -0.610774 q^{68} -2.36642 q^{69} -18.3483 q^{70} -3.38145 q^{71} +12.0020 q^{72} +15.9344 q^{73} +2.41585 q^{74} +1.71081 q^{75} +3.49202 q^{76} +9.76216 q^{77} -0.949497 q^{78} +12.2281 q^{79} -8.69342 q^{80} +6.43526 q^{81} -19.6946 q^{82} +5.60280 q^{83} -5.53913 q^{84} +0.454562 q^{85} -21.4900 q^{86} +4.39882 q^{87} +16.2807 q^{88} -4.82532 q^{89} -18.6607 q^{90} -1.92616 q^{91} -16.7256 q^{92} +1.53316 q^{93} +0.152392 q^{94} -2.59890 q^{95} +0.823305 q^{96} +2.73668 q^{97} -0.183806 q^{98} +9.92839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.41585	−1.70827	−0.854133	−	0.520055i	$-0.825911\pi$
$2$	−2.41585	−1.70827	−0.854133	+	0.520055i	$0.825911\pi$
$3$	0.542785	0.313377	0.156689	−	0.987648i	$-0.449918\pi$
$3$	0.542785	0.313377	0.156689	+	0.987648i	$0.449918\pi$
$4$	3.83634	1.91817
$5$	−2.85515	−1.27686	−0.638432	−	0.769678i	$-0.720417\pi$
$5$	−2.85515	−1.27686	−0.638432	+	0.769678i	$0.720417\pi$
$6$	−1.31129	−0.535331
$7$	−2.66009	−1.00542	−0.502710	−	0.864455i	$-0.667664\pi$
$7$	−2.66009	−1.00542	−0.502710	+	0.864455i	$0.667664\pi$
$8$	−4.43632	−1.56848
$9$	−2.70538	−0.901795
$10$	6.89763	2.18122
$11$	−3.66986	−1.10650	−0.553252	−	0.833014i	$-0.686614\pi$
$11$	−3.66986	−1.10650	−0.553252	+	0.833014i	$0.686614\pi$
$12$	2.08231	0.601111
$13$	0.724095	0.200828	0.100414	−	0.994946i	$-0.467983\pi$
$13$	0.724095	0.200828	0.100414	+	0.994946i	$0.467983\pi$
$14$	6.42638	1.71752
$15$	−1.54974	−0.400140
$16$	3.04482	0.761205
$17$	−0.159207	−0.0386135	−0.0193067	−	0.999814i	$-0.506146\pi$
$17$	−0.159207	−0.0386135	−0.0193067	+	0.999814i	$0.506146\pi$
$18$	6.53581	1.54050
$19$	0.910249	0.208825	0.104413	−	0.994534i	$-0.466704\pi$
$19$	0.910249	0.208825	0.104413	+	0.994534i	$0.466704\pi$
$20$	−10.9533	−2.44924
$21$	−1.44386	−0.315076
$22$	8.86584	1.89020
$23$	−4.35977	−0.909075	−0.454537	−	0.890728i	$-0.650195\pi$
$23$	−4.35977	−0.909075	−0.454537	+	0.890728i	$0.650195\pi$
$24$	−2.40797	−0.491525
$25$	3.15190	0.630380
$26$	−1.74931	−0.343067
$27$	−3.09680	−0.595979
$28$	−10.2050	−1.92857
$29$	8.10416	1.50490	0.752452	−	0.658647i	$-0.228871\pi$
$29$	8.10416	1.50490	0.752452	+	0.658647i	$0.228871\pi$
$30$	3.74393	0.683545
$31$	2.82462	0.507316	0.253658	−	0.967294i	$-0.418366\pi$
$31$	2.82462	0.507316	0.253658	+	0.967294i	$0.418366\pi$
$32$	1.51682	0.268138
$33$	−1.99195	−0.346753
$34$	0.384622	0.0659621
$35$	7.59497	1.28378
$36$	−10.3788	−1.72980
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−2.19903	−0.356729
$39$	0.393028	0.0629348
$40$	12.6664	2.00273
$41$	8.15224	1.27317	0.636583	−	0.771208i	$-0.280347\pi$
$41$	8.15224	1.27317	0.636583	+	0.771208i	$0.280347\pi$
$42$	3.48815	0.538233
$43$	8.89541	1.35654	0.678269	−	0.734814i	$-0.262731\pi$
$43$	8.89541	1.35654	0.678269	+	0.734814i	$0.262731\pi$
$44$	−14.0788	−2.12246
$45$	7.72429	1.15147
$46$	10.5326	1.55294
$47$	−0.0630801	−0.00920118	−0.00460059	−	0.999989i	$-0.501464\pi$
$47$	−0.0630801	−0.00920118	−0.00460059	+	0.999989i	$0.501464\pi$
$48$	1.65268	0.238544
$49$	0.0760833	0.0108690
$50$	−7.61453	−1.07686
$51$	−0.0864155	−0.0121006
$52$	2.77787	0.385222
$53$	−2.28662	−0.314091	−0.157045	−	0.987591i	$-0.550197\pi$
$53$	−2.28662	−0.314091	−0.157045	+	0.987591i	$0.550197\pi$
$54$	7.48140	1.01809
$55$	10.4780	1.41286
$56$	11.8010	1.57698
$57$	0.494070	0.0654411
$58$	−19.5784	−2.57078
$59$	−6.65593	−0.866528	−0.433264	−	0.901267i	$-0.642638\pi$
$59$	−6.65593	−0.866528	−0.433264	+	0.901267i	$0.642638\pi$
$60$	−5.94531	−0.767536
$61$	−10.8043	−1.38334	−0.691672	−	0.722211i	$-0.743126\pi$
$61$	−10.8043	−1.38334	−0.691672	+	0.722211i	$0.743126\pi$
$62$	−6.82385	−0.866630
$63$	7.19657	0.906682
$64$	−9.75404	−1.21925
$65$	−2.06740	−0.256430
$66$	4.81225	0.592347
$67$	8.69582	1.06236	0.531182	−	0.847258i	$-0.321748\pi$
$67$	8.69582	1.06236	0.531182	+	0.847258i	$0.321748\pi$
$68$	−0.610774	−0.0740672
$69$	−2.36642	−0.284883
$70$	−18.3483	−2.19304
$71$	−3.38145	−0.401305	−0.200652	−	0.979663i	$-0.564306\pi$
$71$	−3.38145	−0.401305	−0.200652	+	0.979663i	$0.564306\pi$
$72$	12.0020	1.41444
$73$	15.9344	1.86498	0.932491	−	0.361194i	$-0.117631\pi$
$73$	15.9344	1.86498	0.932491	+	0.361194i	$0.117631\pi$
$74$	2.41585	0.280837
$75$	1.71081	0.197547
$76$	3.49202	0.400563
$77$	9.76216	1.11250
$78$	−0.949497	−0.107509
$79$	12.2281	1.37577	0.687884	−	0.725821i	$-0.258540\pi$
$79$	12.2281	1.37577	0.687884	+	0.725821i	$0.258540\pi$
$80$	−8.69342	−0.971954
$81$	6.43526	0.715028
$82$	−19.6946	−2.17491
$83$	5.60280	0.614988	0.307494	−	0.951550i	$-0.400510\pi$
$83$	5.60280	0.614988	0.307494	+	0.951550i	$0.400510\pi$
$84$	−5.53913	−0.604368
$85$	0.454562	0.0493041
$86$	−21.4900	−2.31733
$87$	4.39882	0.471603
$88$	16.2807	1.73553
$89$	−4.82532	−0.511483	−0.255741	−	0.966745i	$-0.582320\pi$
$89$	−4.82532	−0.511483	−0.255741	+	0.966745i	$0.582320\pi$
$90$	−18.6607	−1.96701
$91$	−1.92616	−0.201916
$92$	−16.7256	−1.74376
$93$	1.53316	0.158981
$94$	0.152392	0.0157181
$95$	−2.59890	−0.266642
$96$	0.823305	0.0840282
$97$	2.73668	0.277867	0.138934	−	0.990302i	$-0.455633\pi$
$97$	2.73668	0.277867	0.138934	+	0.990302i	$0.455633\pi$
$98$	−0.183806	−0.0185672
$99$	9.92839	0.997840
$100$	12.0918	1.20918
$101$	0.0432731	0.00430584	0.00215292	−	0.999998i	$-0.499315\pi$
$101$	0.0432731	0.00430584	0.00215292	+	0.999998i	$0.499315\pi$
$102$	0.208767	0.0206710
$103$	5.96827	0.588071	0.294035	−	0.955795i	$-0.405002\pi$
$103$	5.96827	0.588071	0.294035	+	0.955795i	$0.405002\pi$
$104$	−3.21232	−0.314994
$105$	4.12244	0.402309
$106$	5.52413	0.536551
$107$	−9.90904	−0.957943	−0.478971	−	0.877830i	$-0.658990\pi$
$107$	−9.90904	−0.957943	−0.478971	+	0.877830i	$0.658990\pi$
$108$	−11.8804	−1.14319
$109$	19.0966	1.82913	0.914563	−	0.404442i	$-0.132534\pi$
$109$	19.0966	1.82913	0.914563	+	0.404442i	$0.132534\pi$
$110$	−25.3133	−2.41353
$111$	−0.542785	−0.0515189
$112$	−8.09949	−0.765330
$113$	3.58243	0.337007	0.168503	−	0.985701i	$-0.446107\pi$
$113$	3.58243	0.337007	0.168503	+	0.985701i	$0.446107\pi$
$114$	−1.19360	−0.111791
$115$	12.4478	1.16076
$116$	31.0903	2.88666
$117$	−1.95895	−0.181105
$118$	16.0797	1.48026
$119$	0.423506	0.0388228
$120$	6.87512	0.627610
$121$	2.46788	0.224353
$122$	26.1015	2.36312
$123$	4.42492	0.398981
$124$	10.8362	0.973118
$125$	5.27660	0.471954
$126$	−17.3858	−1.54885
$127$	−0.0874409	−0.00775913	−0.00387956	−	0.999992i	$-0.501235\pi$
$127$	−0.0874409	−0.00775913	−0.00387956	+	0.999992i	$0.501235\pi$
$128$	20.5307	1.81467
$129$	4.82830	0.425108
$130$	4.99453	0.438050
$131$	−0.621469	−0.0542980	−0.0271490	−	0.999631i	$-0.508643\pi$
$131$	−0.621469	−0.0542980	−0.0271490	+	0.999631i	$0.508643\pi$
$132$	−7.64178	−0.665132
$133$	−2.42135	−0.209957
$134$	−21.0078	−1.81480
$135$	8.84183	0.760984
$136$	0.706296	0.0605644
$137$	−19.8931	−1.69958	−0.849791	−	0.527119i	$-0.823272\pi$
$137$	−19.8931	−1.69958	−0.849791	+	0.527119i	$0.823272\pi$
$138$	5.71692	0.486656
$139$	−16.7258	−1.41866	−0.709330	−	0.704877i	$-0.751002\pi$
$139$	−16.7258	−1.41866	−0.709330	+	0.704877i	$0.751002\pi$
$140$	29.1369	2.46252
$141$	−0.0342390	−0.00288344
$142$	8.16909	0.685535
$143$	−2.65733	−0.222217
$144$	−8.23740	−0.686450
$145$	−23.1386	−1.92156
$146$	−38.4952	−3.18588
$147$	0.0412969	0.00340611
$148$	−3.83634	−0.315345
$149$	−12.3658	−1.01304	−0.506521	−	0.862227i	$-0.669069\pi$
$149$	−12.3658	−1.01304	−0.506521	+	0.862227i	$0.669069\pi$
$150$	−4.13305	−0.337462
$151$	14.2175	1.15700	0.578501	−	0.815682i	$-0.303638\pi$
$151$	14.2175	1.15700	0.578501	+	0.815682i	$0.303638\pi$
$152$	−4.03816	−0.327538
$153$	0.430717	0.0348214
$154$	−23.5839	−1.90045
$155$	−8.06471	−0.647773
$156$	1.50779	0.120720
$157$	3.52417	0.281260	0.140630	−	0.990062i	$-0.455087\pi$
$157$	3.52417	0.281260	0.140630	+	0.990062i	$0.455087\pi$
$158$	−29.5413	−2.35018
$159$	−1.24114	−0.0984289
$160$	−4.33074	−0.342375
$161$	11.5974	0.914002
$162$	−15.5466	−1.22146
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	31.2748	2.44215
$165$	5.68731	0.442757
$166$	−13.5355	−1.05056
$167$	−14.4163	−1.11557	−0.557783	−	0.829987i	$-0.688348\pi$
$167$	−14.4163	−1.11557	−0.557783	+	0.829987i	$0.688348\pi$
$168$	6.40542	0.494189
$169$	−12.4757	−0.959668
$170$	−1.09815	−0.0842246
$171$	−2.46257	−0.188318
$172$	34.1258	2.60207
$173$	−17.3350	−1.31796	−0.658978	−	0.752162i	$-0.729011\pi$
$173$	−17.3350	−1.31796	−0.658978	+	0.752162i	$0.729011\pi$
$174$	−10.6269	−0.805623
$175$	−8.38435	−0.633797
$176$	−11.1741	−0.842277
$177$	−3.61274	−0.271550
$178$	11.6573	0.873749
$179$	−3.33433	−0.249220	−0.124610	−	0.992206i	$-0.539768\pi$
$179$	−3.33433	−0.249220	−0.124610	+	0.992206i	$0.539768\pi$
$180$	29.6330	2.20871
$181$	23.3487	1.73550	0.867749	−	0.497002i	$-0.165566\pi$
$181$	23.3487	1.73550	0.867749	+	0.497002i	$0.165566\pi$
$182$	4.65331	0.344926
$183$	−5.86440	−0.433509
$184$	19.3413	1.42586
$185$	2.85515	0.209915
$186$	−3.70389	−0.271582
$187$	0.584269	0.0427260
$188$	−0.241997	−0.0176494
$189$	8.23776	0.599209
$190$	6.27856	0.455495
$191$	8.95674	0.648087	0.324043	−	0.946042i	$-0.394958\pi$
$191$	8.95674	0.648087	0.324043	+	0.946042i	$0.394958\pi$
$192$	−5.29435	−0.382087
$193$	−15.7535	−1.13396	−0.566982	−	0.823731i	$-0.691889\pi$
$193$	−15.7535	−1.13396	−0.566982	+	0.823731i	$0.691889\pi$
$194$	−6.61140	−0.474671
$195$	−1.12215	−0.0803592
$196$	0.291882	0.0208487
$197$	−0.0883265	−0.00629301	−0.00314650	−	0.999995i	$-0.501002\pi$
$197$	−0.0883265	−0.00629301	−0.00314650	+	0.999995i	$0.501002\pi$
$198$	−23.9855	−1.70458
$199$	−21.9523	−1.55615	−0.778077	−	0.628169i	$-0.783805\pi$
$199$	−21.9523	−1.55615	−0.778077	+	0.628169i	$0.783805\pi$
$200$	−13.9829	−0.988737
$201$	4.71996	0.332921
$202$	−0.104541	−0.00735551
$203$	−21.5578	−1.51306
$204$	−0.331519	−0.0232110
$205$	−23.2759	−1.62566
$206$	−14.4184	−1.00458
$207$	11.7949	0.819799
$208$	2.20474	0.152871
$209$	−3.34049	−0.231066
$210$	−9.95919	−0.687250
$211$	21.9527	1.51129	0.755645	−	0.654982i	$-0.227324\pi$
$211$	21.9527	1.51129	0.755645	+	0.654982i	$0.227324\pi$
$212$	−8.77224	−0.602480
$213$	−1.83540	−0.125760
$214$	23.9388	1.63642
$215$	−25.3978	−1.73211
$216$	13.7384	0.934779
$217$	−7.51373	−0.510065
$218$	−46.1347	−3.12463
$219$	8.64896	0.584443
$220$	40.1972	2.71010
$221$	−0.115281	−0.00775466
$222$	1.31129	0.0880079
$223$	20.4948	1.37243	0.686215	−	0.727399i	$-0.259271\pi$
$223$	20.4948	1.37243	0.686215	+	0.727399i	$0.259271\pi$
$224$	−4.03487	−0.269591
$225$	−8.52711	−0.568474
$226$	−8.65462	−0.575697
$227$	10.1382	0.672898	0.336449	−	0.941702i	$-0.390774\pi$
$227$	10.1382	0.672898	0.336449	+	0.941702i	$0.390774\pi$
$228$	1.89542	0.125527
$229$	−28.8963	−1.90952	−0.954761	−	0.297373i	$-0.903889\pi$
$229$	−28.8963	−1.90952	−0.954761	+	0.297373i	$0.903889\pi$
$230$	−30.0721	−1.98289
$231$	5.29876	0.348633
$232$	−35.9527	−2.36041
$233$	27.9280	1.82963	0.914813	−	0.403877i	$-0.132338\pi$
$233$	27.9280	1.82963	0.914813	+	0.403877i	$0.132338\pi$
$234$	4.73254	0.309376
$235$	0.180103	0.0117487
$236$	−25.5344	−1.66215
$237$	6.63723	0.431134
$238$	−1.02313	−0.0663196
$239$	7.02415	0.454354	0.227177	−	0.973853i	$-0.427050\pi$
$239$	7.02415	0.454354	0.227177	+	0.973853i	$0.427050\pi$
$240$	−4.71866	−0.304588
$241$	−12.6712	−0.816223	−0.408112	−	0.912932i	$-0.633813\pi$
$241$	−12.6712	−0.816223	−0.408112	+	0.912932i	$0.633813\pi$
$242$	−5.96204	−0.383254
$243$	12.7834	0.820053
$244$	−41.4488	−2.65349
$245$	−0.217230	−0.0138783
$246$	−10.6899	−0.681566
$247$	0.659106	0.0419379
$248$	−12.5309	−0.795713
$249$	3.04112	0.192723
$250$	−12.7475	−0.806222
$251$	−22.5933	−1.42607	−0.713037	−	0.701127i	$-0.752681\pi$
$251$	−22.5933	−1.42607	−0.713037	+	0.701127i	$0.752681\pi$
$252$	27.6085	1.73917
$253$	15.9997	1.00590
$254$	0.211244	0.0132546
$255$	0.246729	0.0154508
$256$	−30.0910	−1.88069
$257$	−23.9043	−1.49111	−0.745555	−	0.666444i	$-0.767816\pi$
$257$	−23.9043	−1.49111	−0.745555	+	0.666444i	$0.767816\pi$
$258$	−11.6645	−0.726197
$259$	2.66009	0.165290
$260$	−7.93125	−0.491875
$261$	−21.9249	−1.35712
$262$	1.50138	0.0927553
$263$	−9.43281	−0.581652	−0.290826	−	0.956776i	$-0.593930\pi$
$263$	−9.43281	−0.581652	−0.290826	+	0.956776i	$0.593930\pi$
$264$	8.83692	0.543875
$265$	6.52864	0.401051
$266$	5.84961	0.358663
$267$	−2.61911	−0.160287
$268$	33.3601	2.03779
$269$	−15.1812	−0.925615	−0.462807	−	0.886459i	$-0.653158\pi$
$269$	−15.1812	−0.925615	−0.462807	+	0.886459i	$0.653158\pi$
$270$	−21.3606	−1.29996
$271$	1.98177	0.120384	0.0601920	−	0.998187i	$-0.480829\pi$
$271$	1.98177	0.120384	0.0601920	+	0.998187i	$0.480829\pi$
$272$	−0.484758	−0.0293928
$273$	−1.04549	−0.0632759
$274$	48.0588	2.90334
$275$	−11.5670	−0.697519
$276$	−9.07838	−0.546454
$277$	−10.4325	−0.626826	−0.313413	−	0.949617i	$-0.601472\pi$
$277$	−10.4325	−0.626826	−0.313413	+	0.949617i	$0.601472\pi$
$278$	40.4069	2.42345
$279$	−7.64167	−0.457495
$280$	−33.6937	−2.01359
$281$	16.0935	0.960056	0.480028	−	0.877253i	$-0.340627\pi$
$281$	16.0935	0.960056	0.480028	+	0.877253i	$0.340627\pi$
$282$	0.0827163	0.00492568
$283$	22.4234	1.33293	0.666465	−	0.745536i	$-0.267807\pi$
$283$	22.4234	1.33293	0.666465	+	0.745536i	$0.267807\pi$
$284$	−12.9724	−0.769770
$285$	−1.41065	−0.0835594
$286$	6.41971	0.379605
$287$	−21.6857	−1.28007
$288$	−4.10357	−0.241805
$289$	−16.9747	−0.998509
$290$	55.8995	3.28253
$291$	1.48543	0.0870773
$292$	61.1298	3.57735
$293$	18.8010	1.09837	0.549183	−	0.835702i	$-0.314939\pi$
$293$	18.8010	1.09837	0.549183	+	0.835702i	$0.314939\pi$
$294$	−0.0997672	−0.00581854
$295$	19.0037	1.10644
$296$	4.43632	0.257856
$297$	11.3648	0.659454
$298$	29.8738	1.73055
$299$	−3.15689	−0.182567
$300$	6.56323	0.378928
$301$	−23.6626	−1.36389
$302$	−34.3473	−1.97647
$303$	0.0234880	0.00134935
$304$	2.77154	0.158959
$305$	30.8478	1.76634
$306$	−1.04055	−0.0594842
$307$	33.8133	1.92983	0.964914	−	0.262568i	$-0.0845693\pi$
$307$	33.8133	1.92983	0.964914	+	0.262568i	$0.0845693\pi$
$308$	37.4510	2.13397
$309$	3.23949	0.184288
$310$	19.4831	1.10657
$311$	−10.7445	−0.609266	−0.304633	−	0.952470i	$-0.598534\pi$
$311$	−10.7445	−0.609266	−0.304633	+	0.952470i	$0.598534\pi$
$312$	−1.74360	−0.0987118
$313$	−3.06049	−0.172989	−0.0864946	−	0.996252i	$-0.527567\pi$
$313$	−3.06049	−0.172989	−0.0864946	+	0.996252i	$0.527567\pi$
$314$	−8.51388	−0.480466
$315$	−20.5473	−1.15771
$316$	46.9111	2.63896
$317$	12.0284	0.675583	0.337791	−	0.941221i	$-0.390320\pi$
$317$	12.0284	0.675583	0.337791	+	0.941221i	$0.390320\pi$
$318$	2.99841	0.168143
$319$	−29.7411	−1.66518
$320$	27.8493	1.55682
$321$	−5.37848	−0.300197
$322$	−28.0176	−1.56136
$323$	−0.144918	−0.00806348
$324$	24.6878	1.37155
$325$	2.28228	0.126598
$326$	2.41585	0.133802
$327$	10.3654	0.573207
$328$	−36.1660	−1.99693
$329$	0.167799	0.00925105
$330$	−13.7397	−0.756346
$331$	14.1244	0.776345	0.388172	−	0.921587i	$-0.373107\pi$
$331$	14.1244	0.776345	0.388172	+	0.921587i	$0.373107\pi$
$332$	21.4943	1.17965
$333$	2.70538	0.148254
$334$	34.8276	1.90568
$335$	−24.8279	−1.35649
$336$	−4.39629	−0.239837
$337$	0.704735	0.0383893	0.0191947	−	0.999816i	$-0.493890\pi$
$337$	0.704735	0.0383893	0.0191947	+	0.999816i	$0.493890\pi$
$338$	30.1394	1.63937
$339$	1.94449	0.105610
$340$	1.74385	0.0945737
$341$	−10.3659	−0.561348
$342$	5.94921	0.321697
$343$	18.4182	0.994492
$344$	−39.4629	−2.12770
$345$	6.75649	0.363757
$346$	41.8788	2.25142
$347$	−36.4593	−1.95724	−0.978619	−	0.205683i	$-0.934058\pi$
$347$	−36.4593	−1.95724	−0.978619	+	0.205683i	$0.934058\pi$
$348$	16.8754	0.904614
$349$	22.9979	1.23105	0.615525	−	0.788118i	$-0.288944\pi$
$349$	22.9979	1.23105	0.615525	+	0.788118i	$0.288944\pi$
$350$	20.2553	1.08269
$351$	−2.24237	−0.119689
$352$	−5.56650	−0.296696
$353$	−18.1686	−0.967017	−0.483508	−	0.875340i	$-0.660638\pi$
$353$	−18.1686	−0.967017	−0.483508	+	0.875340i	$0.660638\pi$
$354$	8.72784	0.463879
$355$	9.65457	0.512411
$356$	−18.5116	−0.981111
$357$	0.229873	0.0121662
$358$	8.05526	0.425734
$359$	25.7131	1.35709	0.678544	−	0.734560i	$-0.262611\pi$
$359$	25.7131	1.35709	0.678544	+	0.734560i	$0.262611\pi$
$360$	−34.2674	−1.80605
$361$	−18.1714	−0.956392
$362$	−56.4071	−2.96469
$363$	1.33953	0.0703071
$364$	−7.38939	−0.387309
$365$	−45.4952	−2.38133
$366$	14.1675	0.740548
$367$	7.72680	0.403336	0.201668	−	0.979454i	$-0.435364\pi$
$367$	7.72680	0.403336	0.201668	+	0.979454i	$0.435364\pi$
$368$	−13.2747	−0.691992
$369$	−22.0549	−1.14813
$370$	−6.89763	−0.358591
$371$	6.08261	0.315793
$372$	5.88172	0.304953
$373$	5.53936	0.286817	0.143408	−	0.989664i	$-0.454194\pi$
$373$	5.53936	0.286817	0.143408	+	0.989664i	$0.454194\pi$
$374$	−1.41151	−0.0729873
$375$	2.86406	0.147900
$376$	0.279844	0.0144318
$377$	5.86818	0.302227
$378$	−19.9012	−1.02361
$379$	17.2808	0.887655	0.443828	−	0.896112i	$-0.353620\pi$
$379$	17.2808	0.887655	0.443828	+	0.896112i	$0.353620\pi$
$380$	−9.97027	−0.511464
$381$	−0.0474616	−0.00243153
$382$	−21.6381	−1.10710
$383$	6.55373	0.334880	0.167440	−	0.985882i	$-0.446450\pi$
$383$	6.55373	0.334880	0.167440	+	0.985882i	$0.446450\pi$
$384$	11.1437	0.568677
$385$	−27.8725	−1.42051
$386$	38.0582	1.93711
$387$	−24.0655	−1.22332
$388$	10.4988	0.532997
$389$	−24.3176	−1.23295	−0.616476	−	0.787374i	$-0.711440\pi$
$389$	−24.3176	−1.23295	−0.616476	+	0.787374i	$0.711440\pi$
$390$	2.71096	0.137275
$391$	0.694108	0.0351025
$392$	−0.337530	−0.0170479
$393$	−0.337324	−0.0170157
$394$	0.213384	0.0107501
$395$	−34.9131	−1.75667
$396$	38.0886	1.91403
$397$	−10.9383	−0.548978	−0.274489	−	0.961590i	$-0.588509\pi$
$397$	−10.9383	−0.548978	−0.274489	+	0.961590i	$0.588509\pi$
$398$	53.0334	2.65832
$399$	−1.31427	−0.0657958
$400$	9.59697	0.479848
$401$	−4.37246	−0.218350	−0.109175	−	0.994023i	$-0.534821\pi$
$401$	−4.37246	−0.218350	−0.109175	+	0.994023i	$0.534821\pi$
$402$	−11.4027	−0.568716
$403$	2.04529	0.101883
$404$	0.166010	0.00825932
$405$	−18.3736	−0.912994
$406$	52.0804	2.58471
$407$	3.66986	0.181908
$408$	0.383367	0.0189795
$409$	−11.6886	−0.577965	−0.288982	−	0.957334i	$-0.593317\pi$
$409$	−11.6886	−0.577965	−0.288982	+	0.957334i	$0.593317\pi$
$410$	56.2311	2.77706
$411$	−10.7977	−0.532610
$412$	22.8963	1.12802
$413$	17.7054	0.871224
$414$	−28.4946	−1.40043
$415$	−15.9969	−0.785255
$416$	1.09832	0.0538495
$417$	−9.07849	−0.444576
$418$	8.07012	0.394723
$419$	8.91459	0.435506	0.217753	−	0.976004i	$-0.430127\pi$
$419$	8.91459	0.435506	0.217753	+	0.976004i	$0.430127\pi$
$420$	15.8151	0.771696
$421$	22.8835	1.11527	0.557637	−	0.830085i	$-0.311708\pi$
$421$	22.8835	1.11527	0.557637	+	0.830085i	$0.311708\pi$
$422$	−53.0346	−2.58168
$423$	0.170656	0.00829758
$424$	10.1442	0.492644
$425$	−0.501806	−0.0243412
$426$	4.43406	0.214831
$427$	28.7403	1.39084
$428$	−38.0144	−1.83750
$429$	−1.44236	−0.0696377
$430$	61.3572	2.95891
$431$	36.6626	1.76597	0.882987	−	0.469398i	$-0.155529\pi$
$431$	36.6626	1.76597	0.882987	+	0.469398i	$0.155529\pi$
$432$	−9.42919	−0.453662
$433$	7.09275	0.340856	0.170428	−	0.985370i	$-0.445485\pi$
$433$	7.09275	0.340856	0.170428	+	0.985370i	$0.445485\pi$
$434$	18.1521	0.871327
$435$	−12.5593	−0.602172
$436$	73.2612	3.50858
$437$	−3.96848	−0.189838
$438$	−20.8946	−0.998383
$439$	−23.1121	−1.10308	−0.551540	−	0.834148i	$-0.685960\pi$
$439$	−23.1121	−1.10308	−0.551540	+	0.834148i	$0.685960\pi$
$440$	−46.4839	−2.21603
$441$	−0.205835	−0.00980165
$442$	0.278502	0.0132470
$443$	16.4453	0.781340	0.390670	−	0.920531i	$-0.372243\pi$
$443$	16.4453	0.781340	0.390670	+	0.920531i	$0.372243\pi$
$444$	−2.08231	−0.0988220
$445$	13.7770	0.653094
$446$	−49.5123	−2.34447
$447$	−6.71195	−0.317464
$448$	25.9466	1.22586
$449$	6.65102	0.313881	0.156941	−	0.987608i	$-0.449837\pi$
$449$	6.65102	0.313881	0.156941	+	0.987608i	$0.449837\pi$
$450$	20.6002	0.971104
$451$	−29.9176	−1.40876
$452$	13.7434	0.646436
$453$	7.71704	0.362578
$454$	−24.4925	−1.14949
$455$	5.49948	0.257819
$456$	−2.19185	−0.102643
$457$	3.20470	0.149909	0.0749547	−	0.997187i	$-0.476119\pi$
$457$	3.20470	0.149909	0.0749547	+	0.997187i	$0.476119\pi$
$458$	69.8092	3.26197
$459$	0.493033	0.0230128
$460$	47.7540	2.22654
$461$	9.19608	0.428304	0.214152	−	0.976800i	$-0.431301\pi$
$461$	9.19608	0.428304	0.214152	+	0.976800i	$0.431301\pi$
$462$	−12.8010	−0.595557
$463$	−10.4704	−0.486600	−0.243300	−	0.969951i	$-0.578230\pi$
$463$	−10.4704	−0.486600	−0.243300	+	0.969951i	$0.578230\pi$
$464$	24.6757	1.14554
$465$	−4.37741	−0.202997
$466$	−67.4700	−3.12549
$467$	−21.1874	−0.980436	−0.490218	−	0.871600i	$-0.663083\pi$
$467$	−21.1874	−0.980436	−0.490218	+	0.871600i	$0.663083\pi$
$468$	−7.51521	−0.347391
$469$	−23.1317	−1.06812
$470$	−0.435103	−0.0200698
$471$	1.91287	0.0881404
$472$	29.5278	1.35913
$473$	−32.6449	−1.50102
$474$	−16.0346	−0.736492
$475$	2.86902	0.131639
$476$	1.62471	0.0744686
$477$	6.18618	0.283246
$478$	−16.9693	−0.776158
$479$	12.2040	0.557617	0.278808	−	0.960347i	$-0.410061\pi$
$479$	12.2040	0.557617	0.278808	+	0.960347i	$0.410061\pi$
$480$	−2.35066	−0.107293
$481$	−0.724095	−0.0330159
$482$	30.6117	1.39433
$483$	6.29489	0.286427
$484$	9.46763	0.430347
$485$	−7.81363	−0.354799
$486$	−30.8827	−1.40087
$487$	−28.0852	−1.27266	−0.636332	−	0.771416i	$-0.719549\pi$
$487$	−28.0852	−1.27266	−0.636332	+	0.771416i	$0.719549\pi$
$488$	47.9312	2.16974
$489$	−0.542785	−0.0245456
$490$	0.524795	0.0237078
$491$	15.0157	0.677649	0.338825	−	0.940850i	$-0.389971\pi$
$491$	15.0157	0.677649	0.338825	+	0.940850i	$0.389971\pi$
$492$	16.9755	0.765314
$493$	−1.29024	−0.0581096
$494$	−1.59230	−0.0716411
$495$	−28.3471	−1.27411
$496$	8.60044	0.386171
$497$	8.99497	0.403480
$498$	−7.34689	−0.329222
$499$	−43.4437	−1.94481	−0.972404	−	0.233303i	$-0.925047\pi$
$499$	−43.4437	−1.94481	−0.972404	+	0.233303i	$0.925047\pi$
$500$	20.2428	0.905287
$501$	−7.82494	−0.349593
$502$	54.5819	2.43611
$503$	3.49912	0.156018	0.0780091	−	0.996953i	$-0.475144\pi$
$503$	3.49912	0.156018	0.0780091	+	0.996953i	$0.475144\pi$
$504$	−31.9263	−1.42211
$505$	−0.123551	−0.00549796
$506$	−38.6530	−1.71834
$507$	−6.77162	−0.300738
$508$	−0.335453	−0.0148833
$509$	−23.3020	−1.03284	−0.516422	−	0.856334i	$-0.672736\pi$
$509$	−23.3020	−1.03284	−0.516422	+	0.856334i	$0.672736\pi$
$510$	−0.596062	−0.0263941
$511$	−42.3870	−1.87509
$512$	31.6340	1.39804
$513$	−2.81886	−0.124456
$514$	57.7493	2.54721
$515$	−17.0403	−0.750886
$516$	18.5230	0.815429
$517$	0.231495	0.0101812
$518$	−6.42638	−0.282359
$519$	−9.40918	−0.413017
$520$	9.17166	0.402204
$521$	37.4147	1.63917	0.819583	−	0.572961i	$-0.194205\pi$
$521$	37.4147	1.63917	0.819583	+	0.572961i	$0.194205\pi$
$522$	52.9672	2.31831
$523$	8.64613	0.378069	0.189034	−	0.981970i	$-0.439464\pi$
$523$	8.64613	0.378069	0.189034	+	0.981970i	$0.439464\pi$
$524$	−2.38416	−0.104153
$525$	−4.55090	−0.198618
$526$	22.7883	0.993616
$527$	−0.449700	−0.0195892
$528$	−6.06512	−0.263950
$529$	−3.99241	−0.173583
$530$	−15.7722	−0.685102
$531$	18.0068	0.781430
$532$	−9.28910	−0.402734
$533$	5.90300	0.255687
$534$	6.32739	0.273813
$535$	28.2918	1.22316
$536$	−38.5775	−1.66629
$537$	−1.80983	−0.0780998
$538$	36.6756	1.58120
$539$	−0.279215	−0.0120267
$540$	33.9203	1.45970
$541$	−0.811925	−0.0349074	−0.0174537	−	0.999848i	$-0.505556\pi$
$541$	−0.811925	−0.0349074	−0.0174537	+	0.999848i	$0.505556\pi$
$542$	−4.78767	−0.205648
$543$	12.6734	0.543866
$544$	−0.241488	−0.0103537
$545$	−54.5239	−2.33555
$546$	2.52575	0.108092
$547$	−1.96672	−0.0840908	−0.0420454	−	0.999116i	$-0.513387\pi$
$547$	−1.96672	−0.0840908	−0.0420454	+	0.999116i	$0.513387\pi$
$548$	−76.3167	−3.26009
$549$	29.2297	1.24749
$550$	27.9443	1.19155
$551$	7.37680	0.314262
$552$	10.4982	0.446833
$553$	−32.5278	−1.38322
$554$	25.2033	1.07079
$555$	1.54974	0.0657826
$556$	−64.1657	−2.72123
$557$	33.0588	1.40075	0.700374	−	0.713776i	$-0.253017\pi$
$557$	33.0588	1.40075	0.700374	+	0.713776i	$0.253017\pi$
$558$	18.4611	0.781522
$559$	6.44112	0.272430
$560$	23.1253	0.977222
$561$	0.317133	0.0133894
$562$	−38.8794	−1.64003
$563$	−4.98770	−0.210207	−0.105103	−	0.994461i	$-0.533517\pi$
$563$	−4.98770	−0.210207	−0.105103	+	0.994461i	$0.533517\pi$
$564$	−0.131352	−0.00553093
$565$	−10.2284	−0.430312
$566$	−54.1715	−2.27700
$567$	−17.1184	−0.718904
$568$	15.0012	0.629437
$569$	−8.21856	−0.344540	−0.172270	−	0.985050i	$-0.555110\pi$
$569$	−8.21856	−0.344540	−0.172270	+	0.985050i	$0.555110\pi$
$570$	3.40791	0.142742
$571$	−33.2198	−1.39021	−0.695103	−	0.718910i	$-0.744641\pi$
$571$	−33.2198	−1.39021	−0.695103	+	0.718910i	$0.744641\pi$
$572$	−10.1944	−0.426250
$573$	4.86158	0.203096
$574$	52.3895	2.18669
$575$	−13.7416	−0.573063
$576$	26.3884	1.09952
$577$	−13.4520	−0.560014	−0.280007	−	0.959998i	$-0.590337\pi$
$577$	−13.4520	−0.560014	−0.280007	+	0.959998i	$0.590337\pi$
$578$	41.0082	1.70572
$579$	−8.55078	−0.355358
$580$	−88.7676	−3.68587
$581$	−14.9040	−0.618321
$582$	−3.58857	−0.148751
$583$	8.39157	0.347543
$584$	−70.6902	−2.92518
$585$	5.59311	0.231247
$586$	−45.4205	−1.87630
$587$	40.0766	1.65414	0.827069	−	0.562100i	$-0.190007\pi$
$587$	40.0766	1.65414	0.827069	+	0.562100i	$0.190007\pi$
$588$	0.158429	0.00653350
$589$	2.57110	0.105940
$590$	−45.9101	−1.89009
$591$	−0.0479423	−0.00197208
$592$	−3.04482	−0.125141
$593$	19.2101	0.788866	0.394433	−	0.918925i	$-0.370941\pi$
$593$	19.2101	0.788866	0.394433	+	0.918925i	$0.370941\pi$
$594$	−27.4557	−1.12652
$595$	−1.20918	−0.0495714
$596$	−47.4393	−1.94319
$597$	−11.9154	−0.487663
$598$	7.62657	0.311874
$599$	17.7782	0.726396	0.363198	−	0.931712i	$-0.381685\pi$
$599$	17.7782	0.726396	0.363198	+	0.931712i	$0.381685\pi$
$600$	−7.58969	−0.309848
$601$	−11.4584	−0.467398	−0.233699	−	0.972309i	$-0.575083\pi$
$601$	−11.4584	−0.467398	−0.233699	+	0.972309i	$0.575083\pi$
$602$	57.1653	2.32989
$603$	−23.5255	−0.958034
$604$	54.5431	2.21933
$605$	−7.04618	−0.286468
$606$	−0.0567435	−0.00230505
$607$	28.3493	1.15066	0.575331	−	0.817921i	$-0.304873\pi$
$607$	28.3493	1.15066	0.575331	+	0.817921i	$0.304873\pi$
$608$	1.38068	0.0559940
$609$	−11.7013	−0.474159
$610$	−74.5238	−3.01738
$611$	−0.0456760	−0.00184785
$612$	1.65238	0.0667934
$613$	−33.0731	−1.33581	−0.667905	−	0.744247i	$-0.732809\pi$
$613$	−33.0731	−1.33581	−0.667905	+	0.744247i	$0.732809\pi$
$614$	−81.6879	−3.29666
$615$	−12.6338	−0.509445
$616$	−43.3081	−1.74493
$617$	37.9365	1.52727	0.763633	−	0.645650i	$-0.223414\pi$
$617$	37.9365	1.52727	0.763633	+	0.645650i	$0.223414\pi$
$618$	−7.82612	−0.314813
$619$	−7.41733	−0.298128	−0.149064	−	0.988828i	$-0.547626\pi$
$619$	−7.41733	−0.298128	−0.149064	+	0.988828i	$0.547626\pi$
$620$	−30.9390	−1.24254
$621$	13.5013	0.541790
$622$	25.9572	1.04079
$623$	12.8358	0.514255
$624$	1.19670	0.0479063
$625$	−30.8250	−1.23300
$626$	7.39369	0.295511
$627$	−1.81317	−0.0724109
$628$	13.5199	0.539504
$629$	0.159207	0.00634802
$630$	49.6392	1.97767
$631$	−25.5993	−1.01909	−0.509546	−	0.860443i	$-0.670187\pi$
$631$	−25.5993	−1.01909	−0.509546	+	0.860443i	$0.670187\pi$
$632$	−54.2478	−2.15786
$633$	11.9156	0.473604
$634$	−29.0589	−1.15407
$635$	0.249657	0.00990735
$636$	−4.76144	−0.188803
$637$	0.0550915	0.00218281
$638$	71.8502	2.84458
$639$	9.14813	0.361894
$640$	−58.6182	−2.31709
$641$	−34.4016	−1.35878	−0.679391	−	0.733776i	$-0.737756\pi$
$641$	−34.4016	−1.35878	−0.679391	+	0.733776i	$0.737756\pi$
$642$	12.9936	0.512817
$643$	−6.00011	−0.236621	−0.118311	−	0.992977i	$-0.537748\pi$
$643$	−6.00011	−0.236621	−0.118311	+	0.992977i	$0.537748\pi$
$644$	44.4915	1.75321
$645$	−13.7855	−0.542805
$646$	0.350101	0.0137746
$647$	7.58166	0.298066	0.149033	−	0.988832i	$-0.452384\pi$
$647$	7.58166	0.298066	0.149033	+	0.988832i	$0.452384\pi$
$648$	−28.5489	−1.12151
$649$	24.4263	0.958817
$650$	−5.51364	−0.216263
$651$	−4.07834	−0.159843
$652$	−3.83634	−0.150243
$653$	7.61471	0.297986	0.148993	−	0.988838i	$-0.452397\pi$
$653$	7.61471	0.297986	0.148993	+	0.988838i	$0.452397\pi$
$654$	−25.0412	−0.979189
$655$	1.77439	0.0693311
$656$	24.8221	0.969140
$657$	−43.1087	−1.68183
$658$	−0.405377	−0.0158033
$659$	−13.9287	−0.542587	−0.271293	−	0.962497i	$-0.587451\pi$
$659$	−13.9287	−0.542587	−0.271293	+	0.962497i	$0.587451\pi$
$660$	21.8185	0.849282
$661$	12.9654	0.504297	0.252149	−	0.967689i	$-0.418863\pi$
$661$	12.9654	0.504297	0.252149	+	0.967689i	$0.418863\pi$
$662$	−34.1223	−1.32620
$663$	−0.0625730	−0.00243013
$664$	−24.8558	−0.964594
$665$	6.91331	0.268087
$666$	−6.53581	−0.253257
$667$	−35.3323	−1.36807
$668$	−55.3057	−2.13984
$669$	11.1242	0.430088
$670$	59.9805	2.31725
$671$	39.6502	1.53068
$672$	−2.19007	−0.0844836
$673$	45.2528	1.74437	0.872184	−	0.489178i	$-0.162703\pi$
$673$	45.2528	1.74437	0.872184	+	0.489178i	$0.162703\pi$
$674$	−1.70253	−0.0655792
$675$	−9.76080	−0.375694
$676$	−47.8610	−1.84081
$677$	−25.3881	−0.975745	−0.487873	−	0.872915i	$-0.662227\pi$
$677$	−25.3881	−0.975745	−0.487873	+	0.872915i	$0.662227\pi$
$678$	−4.69760	−0.180410
$679$	−7.27981	−0.279373
$680$	−2.01658	−0.0773324
$681$	5.50288	0.210871
$682$	25.0426	0.958930
$683$	−16.5370	−0.632771	−0.316385	−	0.948631i	$-0.602469\pi$
$683$	−16.5370	−0.632771	−0.316385	+	0.948631i	$0.602469\pi$
$684$	−9.44727	−0.361225
$685$	56.7979	2.17013
$686$	−44.4958	−1.69886
$687$	−15.6845	−0.598401
$688$	27.0849	1.03260
$689$	−1.65573	−0.0630782
$690$	−16.3227	−0.621394
$691$	−5.81756	−0.221310	−0.110655	−	0.993859i	$-0.535295\pi$
$691$	−5.81756	−0.221310	−0.110655	+	0.993859i	$0.535295\pi$
$692$	−66.5030	−2.52806
$693$	−26.4104	−1.00325
$694$	88.0802	3.34348
$695$	47.7546	1.81143
$696$	−19.5146	−0.739698
$697$	−1.29790	−0.0491614
$698$	−55.5595	−2.10296
$699$	15.1589	0.573363
$700$	−32.1652	−1.21573
$701$	−40.5387	−1.53112	−0.765562	−	0.643362i	$-0.777539\pi$
$701$	−40.5387	−1.53112	−0.765562	+	0.643362i	$0.777539\pi$
$702$	5.41724	0.204461
$703$	−0.910249	−0.0343307
$704$	35.7960	1.34911
$705$	0.0977575	0.00368176
$706$	43.8926	1.65192
$707$	−0.115110	−0.00432917
$708$	−13.8597	−0.520879
$709$	−17.2719	−0.648659	−0.324329	−	0.945944i	$-0.605139\pi$
$709$	−17.2719	−0.648659	−0.324329	+	0.945944i	$0.605139\pi$
$710$	−23.3240	−0.875334
$711$	−33.0817	−1.24066
$712$	21.4067	0.802249
$713$	−12.3147	−0.461188
$714$	−0.555339	−0.0207830
$715$	7.58708	0.283741
$716$	−12.7916	−0.478046
$717$	3.81260	0.142384
$718$	−62.1192	−2.31827
$719$	−13.2024	−0.492367	−0.246184	−	0.969223i	$-0.579177\pi$
$719$	−13.2024	−0.492367	−0.246184	+	0.969223i	$0.579177\pi$
$720$	23.5191	0.876503
$721$	−15.8761	−0.591258
$722$	43.8995	1.63377
$723$	−6.87774	−0.255786
$724$	89.5737	3.32898
$725$	25.5435	0.948662
$726$	−3.23611	−0.120103
$727$	−4.90916	−0.182071	−0.0910353	−	0.995848i	$-0.529018\pi$
$727$	−4.90916	−0.182071	−0.0910353	+	0.995848i	$0.529018\pi$
$728$	8.54506	0.316701
$729$	−12.3672	−0.458043
$730$	109.910	4.06794
$731$	−1.41622	−0.0523806
$732$	−22.4978	−0.831543
$733$	39.7597	1.46856	0.734279	−	0.678847i	$-0.237520\pi$
$733$	39.7597	1.46856	0.734279	+	0.678847i	$0.237520\pi$
$734$	−18.6668	−0.689005
$735$	−0.117909	−0.00434914
$736$	−6.61296	−0.243757
$737$	−31.9125	−1.17551
$738$	53.2815	1.96132
$739$	−40.8056	−1.50106	−0.750530	−	0.660837i	$-0.770202\pi$
$739$	−40.8056	−1.50106	−0.750530	+	0.660837i	$0.770202\pi$
$740$	10.9533	0.402653
$741$	0.357753	0.0131424
$742$	−14.6947	−0.539459
$743$	−48.4299	−1.77672	−0.888360	−	0.459148i	$-0.848155\pi$
$743$	−48.4299	−1.77672	−0.888360	+	0.459148i	$0.848155\pi$
$744$	−6.80159	−0.249358
$745$	35.3062	1.29352
$746$	−13.3823	−0.489959
$747$	−15.1577	−0.554593
$748$	2.24146	0.0819557
$749$	26.3589	0.963135
$750$	−6.91915	−0.252652
$751$	−47.0348	−1.71632	−0.858161	−	0.513380i	$-0.828393\pi$
$751$	−47.0348	−1.71632	−0.858161	+	0.513380i	$0.828393\pi$
$752$	−0.192068	−0.00700398
$753$	−12.2633	−0.446899
$754$	−14.1766	−0.516283
$755$	−40.5931	−1.47733
$756$	31.6029	1.14938
$757$	24.1299	0.877016	0.438508	−	0.898727i	$-0.355507\pi$
$757$	24.1299	0.877016	0.438508	+	0.898727i	$0.355507\pi$
$758$	−41.7479	−1.51635
$759$	8.68443	0.315225
$760$	11.5296	0.418221
$761$	−4.26693	−0.154676	−0.0773380	−	0.997005i	$-0.524642\pi$
$761$	−4.26693	−0.154676	−0.0773380	+	0.997005i	$0.524642\pi$
$762$	0.114660	0.00415370
$763$	−50.7988	−1.83904
$764$	34.3611	1.24314
$765$	−1.22976	−0.0444622
$766$	−15.8328	−0.572064
$767$	−4.81952	−0.174023
$768$	−16.3329	−0.589364
$769$	−47.5420	−1.71441	−0.857203	−	0.514978i	$-0.827800\pi$
$769$	−47.5420	−1.71441	−0.857203	+	0.514978i	$0.827800\pi$
$770$	67.3358	2.42661
$771$	−12.9749	−0.467280
$772$	−60.4358	−2.17513
$773$	−19.6666	−0.707357	−0.353679	−	0.935367i	$-0.615069\pi$
$773$	−19.6666	−0.707357	−0.353679	+	0.935367i	$0.615069\pi$
$774$	58.1387	2.08975
$775$	8.90291	0.319802
$776$	−12.1408	−0.435829
$777$	1.44386	0.0517981
$778$	58.7477	2.10621
$779$	7.42057	0.265870
$780$	−4.30497	−0.154143
$781$	12.4095	0.444045
$782$	−1.67686	−0.0599644
$783$	−25.0969	−0.896892
$784$	0.231660	0.00827357
$785$	−10.0621	−0.359130
$786$	0.814925	0.0290674
$787$	13.3023	0.474175	0.237088	−	0.971488i	$-0.423807\pi$
$787$	13.3023	0.474175	0.237088	+	0.971488i	$0.423807\pi$
$788$	−0.338851	−0.0120711
$789$	−5.11999	−0.182277
$790$	84.3448	3.00085
$791$	−9.52959	−0.338833
$792$	−44.0455	−1.56509
$793$	−7.82331	−0.277814
$794$	26.4253	0.937800
$795$	3.54365	0.125680
$796$	−84.2163	−2.98497
$797$	−40.4259	−1.43196	−0.715980	−	0.698121i	$-0.754020\pi$
$797$	−40.4259	−1.43196	−0.715980	+	0.698121i	$0.754020\pi$
$798$	3.17508	0.112397
$799$	0.0100428	0.000355290 0
$800$	4.78085	0.169029
$801$	13.0543	0.461253
$802$	10.5632	0.373000
$803$	−58.4771	−2.06361
$804$	18.1074	0.638598
$805$	−33.1123	−1.16706
$806$	−4.94111	−0.174043
$807$	−8.24014	−0.290067
$808$	−0.191973	−0.00675360
$809$	36.2374	1.27404	0.637019	−	0.770848i	$-0.280167\pi$
$809$	36.2374	1.27404	0.637019	+	0.770848i	$0.280167\pi$
$810$	44.3880	1.55964
$811$	−7.18338	−0.252243	−0.126121	−	0.992015i	$-0.540253\pi$
$811$	−7.18338	−0.252243	−0.126121	+	0.992015i	$0.540253\pi$
$812$	−82.7030	−2.90231
$813$	1.07568	0.0377256
$814$	−8.86584	−0.310748
$815$	2.85515	0.100012
$816$	−0.263119	−0.00921102
$817$	8.09704	0.283280
$818$	28.2380	0.987317
$819$	5.21100	0.182087
$820$	−89.2943	−3.11829
$821$	38.2576	1.33520	0.667599	−	0.744521i	$-0.267322\pi$
$821$	38.2576	1.33520	0.667599	+	0.744521i	$0.267322\pi$
$822$	26.0856	0.909840
$823$	22.6423	0.789259	0.394630	−	0.918840i	$-0.370873\pi$
$823$	22.6423	0.789259	0.394630	+	0.918840i	$0.370873\pi$
$824$	−26.4771	−0.922375
$825$	−6.27842	−0.218587
$826$	−42.7735	−1.48828
$827$	−48.2007	−1.67610	−0.838051	−	0.545592i	$-0.816305\pi$
$827$	−48.2007	−1.67610	−0.838051	+	0.545592i	$0.816305\pi$
$828$	45.2490	1.57251
$829$	2.49836	0.0867715	0.0433857	−	0.999058i	$-0.486186\pi$
$829$	2.49836	0.0867715	0.0433857	+	0.999058i	$0.486186\pi$
$830$	38.6461	1.34142
$831$	−5.66259	−0.196433
$832$	−7.06285	−0.244860
$833$	−0.0121130	−0.000419692 0
$834$	21.9323	0.759453
$835$	41.1607	1.42442
$836$	−12.8152	−0.443225
$837$	−8.74726	−0.302350
$838$	−21.5363	−0.743960
$839$	21.0260	0.725898	0.362949	−	0.931809i	$-0.381770\pi$
$839$	21.0260	0.725898	0.362949	+	0.931809i	$0.381770\pi$
$840$	−18.2885	−0.631012
$841$	36.6774	1.26474
$842$	−55.2831	−1.90518
$843$	8.73530	0.300860
$844$	84.2182	2.89891
$845$	35.6200	1.22537
$846$	−0.412280	−0.0141745
$847$	−6.56479	−0.225569
$848$	−6.96233	−0.239087
$849$	12.1711	0.417710
$850$	1.21229	0.0415812
$851$	4.35977	0.149451
$852$	−7.04123	−0.241228
$853$	−26.8478	−0.919250	−0.459625	−	0.888113i	$-0.652016\pi$
$853$	−26.8478	−0.919250	−0.459625	+	0.888113i	$0.652016\pi$
$854$	−69.4324	−2.37593
$855$	7.03103	0.240456
$856$	43.9597	1.50251
$857$	−5.10038	−0.174226	−0.0871128	−	0.996198i	$-0.527764\pi$
$857$	−5.10038	−0.174226	−0.0871128	+	0.996198i	$0.527764\pi$
$858$	3.48452	0.118960
$859$	5.40700	0.184484	0.0922422	−	0.995737i	$-0.470597\pi$
$859$	5.40700	0.184484	0.0922422	+	0.995737i	$0.470597\pi$
$860$	−97.4344	−3.32249
$861$	−11.7707	−0.401144
$862$	−88.5713	−3.01675
$863$	−27.8573	−0.948273	−0.474137	−	0.880451i	$-0.657240\pi$
$863$	−27.8573	−0.948273	−0.474137	+	0.880451i	$0.657240\pi$
$864$	−4.69727	−0.159804
$865$	49.4941	1.68285
$866$	−17.1350	−0.582272
$867$	−9.21359	−0.312910
$868$	−28.8252	−0.978392
$869$	−44.8754	−1.52229
$870$	30.3414	1.02867
$871$	6.29660	0.213352
$872$	−84.7189	−2.86894
$873$	−7.40376	−0.250579
$874$	9.58725	0.324294
$875$	−14.0362	−0.474512
$876$	33.1803	1.12106
$877$	−4.56035	−0.153992	−0.0769960	−	0.997031i	$-0.524533\pi$
$877$	−4.56035	−0.153992	−0.0769960	+	0.997031i	$0.524533\pi$
$878$	55.8354	1.88435
$879$	10.2049	0.344203
$880$	31.9037	1.07547
$881$	−38.1516	−1.28536	−0.642680	−	0.766134i	$-0.722178\pi$
$881$	−38.1516	−1.28536	−0.642680	+	0.766134i	$0.722178\pi$
$882$	0.497266	0.0167438
$883$	1.77232	0.0596432	0.0298216	−	0.999555i	$-0.490506\pi$
$883$	1.77232	0.0596432	0.0298216	+	0.999555i	$0.490506\pi$
$884$	−0.442258	−0.0148747
$885$	10.3149	0.346732
$886$	−39.7294	−1.33474
$887$	−0.141170	−0.00474001	−0.00237000	−	0.999997i	$-0.500754\pi$
$887$	−0.141170	−0.00474001	−0.00237000	+	0.999997i	$0.500754\pi$
$888$	2.40797	0.0808062
$889$	0.232601	0.00780118
$890$	−33.2833	−1.11566
$891$	−23.6165	−0.791182
$892$	78.6248	2.63255
$893$	−0.0574186	−0.00192144
$894$	16.2151	0.542313
$895$	9.52004	0.318220
$896$	−54.6135	−1.82451
$897$	−1.71351	−0.0572125
$898$	−16.0679	−0.536192
$899$	22.8911	0.763462
$900$	−32.7129	−1.09043
$901$	0.364046	0.0121281
$902$	72.2765	2.40654
$903$	−12.8437	−0.427412
$904$	−15.8928	−0.528587
$905$	−66.6643	−2.21600
$906$	−18.6432	−0.619379
$907$	3.67450	0.122010	0.0610048	−	0.998137i	$-0.480569\pi$
$907$	3.67450	0.122010	0.0610048	+	0.998137i	$0.480569\pi$
$908$	38.8937	1.29073
$909$	−0.117070	−0.00388298
$910$	−13.2859	−0.440424
$911$	−23.3609	−0.773980	−0.386990	−	0.922084i	$-0.626485\pi$
$911$	−23.3609	−0.773980	−0.386990	+	0.922084i	$0.626485\pi$
$912$	1.50435	0.0498141
$913$	−20.5615	−0.680487
$914$	−7.74207	−0.256085
$915$	16.7438	0.553532
$916$	−110.856	−3.66279
$917$	1.65316	0.0545923
$918$	−1.19110	−0.0393120
$919$	21.7195	0.716459	0.358230	−	0.933634i	$-0.383381\pi$
$919$	21.7195	0.716459	0.358230	+	0.933634i	$0.383381\pi$
$920$	−55.2225	−1.82063
$921$	18.3534	0.604764
$922$	−22.2164	−0.731657
$923$	−2.44849	−0.0805931
$924$	20.3278	0.668737
$925$	−3.15190	−0.103634
$926$	25.2949	0.831242
$927$	−16.1465	−0.530319
$928$	12.2925	0.403521
$929$	−31.9359	−1.04778	−0.523892	−	0.851785i	$-0.675520\pi$
$929$	−31.9359	−1.04778	−0.523892	+	0.851785i	$0.675520\pi$
$930$	10.5752	0.346773
$931$	0.0692548	0.00226973
$932$	107.141	3.50953
$933$	−5.83196	−0.190930
$934$	51.1856	1.67485
$935$	−1.66818	−0.0545553
$936$	8.69055	0.284060
$937$	4.52674	0.147882	0.0739411	−	0.997263i	$-0.476442\pi$
$937$	4.52674	0.147882	0.0739411	+	0.997263i	$0.476442\pi$
$938$	55.8827	1.82463
$939$	−1.66119	−0.0542109
$940$	0.690938	0.0225359
$941$	−8.63433	−0.281471	−0.140736	−	0.990047i	$-0.544947\pi$
$941$	−8.63433	−0.281471	−0.140736	+	0.990047i	$0.544947\pi$
$942$	−4.62121	−0.150567
$943$	−35.5419	−1.15740
$944$	−20.2661	−0.659605
$945$	−23.5201	−0.765108
$946$	78.8653	2.56413
$947$	54.2692	1.76351	0.881756	−	0.471706i	$-0.156361\pi$
$947$	54.2692	1.76351	0.881756	+	0.471706i	$0.156361\pi$
$948$	25.4627	0.826988
$949$	11.5380	0.374540
$950$	−6.93112	−0.224875
$951$	6.52884	0.211712
$952$	−1.87881	−0.0608926
$953$	22.2861	0.721917	0.360959	−	0.932582i	$-0.382450\pi$
$953$	22.2861	0.721917	0.360959	+	0.932582i	$0.382450\pi$
$954$	−14.9449	−0.483858
$955$	−25.5729	−0.827518
$956$	26.9470	0.871529
$957$	−16.1431	−0.521831
$958$	−29.4831	−0.952557
$959$	52.9175	1.70879
$960$	15.1162	0.487872
$961$	−23.0215	−0.742631
$962$	1.74931	0.0563999
$963$	26.8078	0.863868
$964$	−48.6110	−1.56565
$965$	44.9787	1.44792
$966$	−15.2075	−0.489294
$967$	−14.1692	−0.455650	−0.227825	−	0.973702i	$-0.573161\pi$
$967$	−14.1692	−0.455650	−0.227825	+	0.973702i	$0.573161\pi$
$968$	−10.9483	−0.351892
$969$	−0.0786596	−0.00252691
$970$	18.8766	0.606090
$971$	13.5717	0.435537	0.217768	−	0.976000i	$-0.430122\pi$
$971$	13.5717	0.435537	0.217768	+	0.976000i	$0.430122\pi$
$972$	49.0413	1.57300
$973$	44.4920	1.42635
$974$	67.8498	2.17405
$975$	1.23879	0.0396729
$976$	−32.8970	−1.05301
$977$	23.9829	0.767280	0.383640	−	0.923483i	$-0.374670\pi$
$977$	23.9829	0.767280	0.383640	+	0.923483i	$0.374670\pi$
$978$	1.31129	0.0419304
$979$	17.7083	0.565958
$980$	−0.833367	−0.0266209
$981$	−51.6638	−1.64950
$982$	−36.2757	−1.15760
$983$	−18.9020	−0.602881	−0.301441	−	0.953485i	$-0.597467\pi$
$983$	−18.9020	−0.602881	−0.301441	+	0.953485i	$0.597467\pi$
$984$	−19.6304	−0.625793
$985$	0.252186	0.00803531
$986$	3.11703	0.0992666
$987$	0.0910788	0.00289907
$988$	2.52856	0.0804441
$989$	−38.7819	−1.23319
$990$	68.4823	2.17651
$991$	41.3370	1.31311	0.656556	−	0.754277i	$-0.272012\pi$
$991$	41.3370	1.31311	0.656556	+	0.754277i	$0.272012\pi$
$992$	4.28442	0.136030
$993$	7.66649	0.243289
$994$	−21.7305	−0.689250
$995$	62.6770	1.98700
$996$	11.6668	0.369676
$997$	24.2326	0.767454	0.383727	−	0.923447i	$-0.374640\pi$
$997$	24.2326	0.767454	0.383727	+	0.923447i	$0.374640\pi$
$998$	104.954	3.32225
$999$	3.09680	0.0979784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.11	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.11	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41585 q^{2} +0.542785 q^{3} +3.83634 q^{4} -2.85515 q^{5} -1.31129 q^{6} -2.66009 q^{7} -4.43632 q^{8} -2.70538 q^{9} +O(q^{10})\)	\(q-2.41585 q^{2} +0.542785 q^{3} +3.83634 q^{4} -2.85515 q^{5} -1.31129 q^{6} -2.66009 q^{7} -4.43632 q^{8} -2.70538 q^{9} +6.89763 q^{10} -3.66986 q^{11} +2.08231 q^{12} +0.724095 q^{13} +6.42638 q^{14} -1.54974 q^{15} +3.04482 q^{16} -0.159207 q^{17} +6.53581 q^{18} +0.910249 q^{19} -10.9533 q^{20} -1.44386 q^{21} +8.86584 q^{22} -4.35977 q^{23} -2.40797 q^{24} +3.15190 q^{25} -1.74931 q^{26} -3.09680 q^{27} -10.2050 q^{28} +8.10416 q^{29} +3.74393 q^{30} +2.82462 q^{31} +1.51682 q^{32} -1.99195 q^{33} +0.384622 q^{34} +7.59497 q^{35} -10.3788 q^{36} -1.00000 q^{37} -2.19903 q^{38} +0.393028 q^{39} +12.6664 q^{40} +8.15224 q^{41} +3.48815 q^{42} +8.89541 q^{43} -14.0788 q^{44} +7.72429 q^{45} +10.5326 q^{46} -0.0630801 q^{47} +1.65268 q^{48} +0.0760833 q^{49} -7.61453 q^{50} -0.0864155 q^{51} +2.77787 q^{52} -2.28662 q^{53} +7.48140 q^{54} +10.4780 q^{55} +11.8010 q^{56} +0.494070 q^{57} -19.5784 q^{58} -6.65593 q^{59} -5.94531 q^{60} -10.8043 q^{61} -6.82385 q^{62} +7.19657 q^{63} -9.75404 q^{64} -2.06740 q^{65} +4.81225 q^{66} +8.69582 q^{67} -0.610774 q^{68} -2.36642 q^{69} -18.3483 q^{70} -3.38145 q^{71} +12.0020 q^{72} +15.9344 q^{73} +2.41585 q^{74} +1.71081 q^{75} +3.49202 q^{76} +9.76216 q^{77} -0.949497 q^{78} +12.2281 q^{79} -8.69342 q^{80} +6.43526 q^{81} -19.6946 q^{82} +5.60280 q^{83} -5.53913 q^{84} +0.454562 q^{85} -21.4900 q^{86} +4.39882 q^{87} +16.2807 q^{88} -4.82532 q^{89} -18.6607 q^{90} -1.92616 q^{91} -16.7256 q^{92} +1.53316 q^{93} +0.152392 q^{94} -2.59890 q^{95} +0.823305 q^{96} +2.73668 q^{97} -0.183806 q^{98} +9.92839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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