LMFDB - Embedded newform 6010.2.a.i.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.46035 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.46035 q^{6} -4.07873 q^{7} -1.00000 q^{8} -0.867392 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.46035 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.46035 q^{6} -4.07873 q^{7} -1.00000 q^{8} -0.867392 q^{9} +1.00000 q^{10} -4.37329 q^{11} -1.46035 q^{12} -4.56080 q^{13} +4.07873 q^{14} +1.46035 q^{15} +1.00000 q^{16} +6.05762 q^{17} +0.867392 q^{18} -1.19215 q^{19} -1.00000 q^{20} +5.95635 q^{21} +4.37329 q^{22} -3.78056 q^{23} +1.46035 q^{24} +1.00000 q^{25} +4.56080 q^{26} +5.64773 q^{27} -4.07873 q^{28} +2.15330 q^{29} -1.46035 q^{30} +6.06139 q^{31} -1.00000 q^{32} +6.38652 q^{33} -6.05762 q^{34} +4.07873 q^{35} -0.867392 q^{36} -4.02402 q^{37} +1.19215 q^{38} +6.66034 q^{39} +1.00000 q^{40} +8.29885 q^{41} -5.95635 q^{42} -4.51185 q^{43} -4.37329 q^{44} +0.867392 q^{45} +3.78056 q^{46} +13.0916 q^{47} -1.46035 q^{48} +9.63601 q^{49} -1.00000 q^{50} -8.84622 q^{51} -4.56080 q^{52} +3.35323 q^{53} -5.64773 q^{54} +4.37329 q^{55} +4.07873 q^{56} +1.74095 q^{57} -2.15330 q^{58} +7.74193 q^{59} +1.46035 q^{60} -1.07606 q^{61} -6.06139 q^{62} +3.53785 q^{63} +1.00000 q^{64} +4.56080 q^{65} -6.38652 q^{66} -7.40179 q^{67} +6.05762 q^{68} +5.52092 q^{69} -4.07873 q^{70} +3.09840 q^{71} +0.867392 q^{72} +1.18067 q^{73} +4.02402 q^{74} -1.46035 q^{75} -1.19215 q^{76} +17.8375 q^{77} -6.66034 q^{78} +14.7565 q^{79} -1.00000 q^{80} -5.64546 q^{81} -8.29885 q^{82} -14.1785 q^{83} +5.95635 q^{84} -6.05762 q^{85} +4.51185 q^{86} -3.14456 q^{87} +4.37329 q^{88} +5.08768 q^{89} -0.867392 q^{90} +18.6022 q^{91} -3.78056 q^{92} -8.85173 q^{93} -13.0916 q^{94} +1.19215 q^{95} +1.46035 q^{96} +9.72633 q^{97} -9.63601 q^{98} +3.79336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.46035	−0.843131	−0.421565	−	0.906798i	$-0.638519\pi$
$3$	−1.46035	−0.843131	−0.421565	+	0.906798i	$0.638519\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.46035	0.596183
$7$	−4.07873	−1.54161	−0.770807	−	0.637069i	$-0.780147\pi$
$7$	−4.07873	−1.54161	−0.770807	+	0.637069i	$0.780147\pi$
$8$	−1.00000	−0.353553
$9$	−0.867392	−0.289131
$10$	1.00000	0.316228
$11$	−4.37329	−1.31860	−0.659299	−	0.751881i	$-0.729147\pi$
$11$	−4.37329	−1.31860	−0.659299	+	0.751881i	$0.729147\pi$
$12$	−1.46035	−0.421565
$13$	−4.56080	−1.26494	−0.632469	−	0.774586i	$-0.717958\pi$
$13$	−4.56080	−1.26494	−0.632469	+	0.774586i	$0.717958\pi$
$14$	4.07873	1.09009
$15$	1.46035	0.377060
$16$	1.00000	0.250000
$17$	6.05762	1.46919	0.734595	−	0.678506i	$-0.237372\pi$
$17$	6.05762	1.46919	0.734595	+	0.678506i	$0.237372\pi$
$18$	0.867392	0.204446
$19$	−1.19215	−0.273499	−0.136749	−	0.990606i	$-0.543665\pi$
$19$	−1.19215	−0.273499	−0.136749	+	0.990606i	$0.543665\pi$
$20$	−1.00000	−0.223607
$21$	5.95635	1.29978
$22$	4.37329	0.932389
$23$	−3.78056	−0.788301	−0.394150	−	0.919046i	$-0.628961\pi$
$23$	−3.78056	−0.788301	−0.394150	+	0.919046i	$0.628961\pi$
$24$	1.46035	0.298092
$25$	1.00000	0.200000
$26$	4.56080	0.894446
$27$	5.64773	1.08691
$28$	−4.07873	−0.770807
$29$	2.15330	0.399858	0.199929	−	0.979810i	$-0.435929\pi$
$29$	2.15330	0.399858	0.199929	+	0.979810i	$0.435929\pi$
$30$	−1.46035	−0.266621
$31$	6.06139	1.08866	0.544329	−	0.838872i	$-0.316784\pi$
$31$	6.06139	1.08866	0.544329	+	0.838872i	$0.316784\pi$
$32$	−1.00000	−0.176777
$33$	6.38652	1.11175
$34$	−6.05762	−1.03887
$35$	4.07873	0.689431
$36$	−0.867392	−0.144565
$37$	−4.02402	−0.661545	−0.330772	−	0.943711i	$-0.607309\pi$
$37$	−4.02402	−0.661545	−0.330772	+	0.943711i	$0.607309\pi$
$38$	1.19215	0.193393
$39$	6.66034	1.06651
$40$	1.00000	0.158114
$41$	8.29885	1.29606	0.648031	−	0.761614i	$-0.275593\pi$
$41$	8.29885	1.29606	0.648031	+	0.761614i	$0.275593\pi$
$42$	−5.95635	−0.919085
$43$	−4.51185	−0.688050	−0.344025	−	0.938960i	$-0.611791\pi$
$43$	−4.51185	−0.688050	−0.344025	+	0.938960i	$0.611791\pi$
$44$	−4.37329	−0.659299
$45$	0.867392	0.129303
$46$	3.78056	0.557413
$47$	13.0916	1.90961	0.954807	−	0.297228i	$-0.0960620\pi$
$47$	13.0916	1.90961	0.954807	+	0.297228i	$0.0960620\pi$
$48$	−1.46035	−0.210783
$49$	9.63601	1.37657
$50$	−1.00000	−0.141421
$51$	−8.84622	−1.23872
$52$	−4.56080	−0.632469
$53$	3.35323	0.460601	0.230300	−	0.973120i	$-0.426029\pi$
$53$	3.35323	0.460601	0.230300	+	0.973120i	$0.426029\pi$
$54$	−5.64773	−0.768558
$55$	4.37329	0.589695
$56$	4.07873	0.545043
$57$	1.74095	0.230595
$58$	−2.15330	−0.282742
$59$	7.74193	1.00791	0.503957	−	0.863729i	$-0.331877\pi$
$59$	7.74193	1.00791	0.503957	+	0.863729i	$0.331877\pi$
$60$	1.46035	0.188530
$61$	−1.07606	−0.137775	−0.0688876	−	0.997624i	$-0.521945\pi$
$61$	−1.07606	−0.137775	−0.0688876	+	0.997624i	$0.521945\pi$
$62$	−6.06139	−0.769798
$63$	3.53785	0.445728
$64$	1.00000	0.125000
$65$	4.56080	0.565697
$66$	−6.38652	−0.786126
$67$	−7.40179	−0.904272	−0.452136	−	0.891949i	$-0.649338\pi$
$67$	−7.40179	−0.904272	−0.452136	+	0.891949i	$0.649338\pi$
$68$	6.05762	0.734595
$69$	5.52092	0.664641
$70$	−4.07873	−0.487501
$71$	3.09840	0.367713	0.183856	−	0.982953i	$-0.441142\pi$
$71$	3.09840	0.367713	0.183856	+	0.982953i	$0.441142\pi$
$72$	0.867392	0.102223
$73$	1.18067	0.138187	0.0690933	−	0.997610i	$-0.477989\pi$
$73$	1.18067	0.138187	0.0690933	+	0.997610i	$0.477989\pi$
$74$	4.02402	0.467783
$75$	−1.46035	−0.168626
$76$	−1.19215	−0.136749
$77$	17.8375	2.03277
$78$	−6.66034	−0.754135
$79$	14.7565	1.66023	0.830116	−	0.557591i	$-0.188274\pi$
$79$	14.7565	1.66023	0.830116	+	0.557591i	$0.188274\pi$
$80$	−1.00000	−0.111803
$81$	−5.64546	−0.627273
$82$	−8.29885	−0.916454
$83$	−14.1785	−1.55629	−0.778147	−	0.628082i	$-0.783840\pi$
$83$	−14.1785	−1.55629	−0.778147	+	0.628082i	$0.783840\pi$
$84$	5.95635	0.649891
$85$	−6.05762	−0.657041
$86$	4.51185	0.486525
$87$	−3.14456	−0.337132
$88$	4.37329	0.466195
$89$	5.08768	0.539293	0.269647	−	0.962959i	$-0.413093\pi$
$89$	5.08768	0.539293	0.269647	+	0.962959i	$0.413093\pi$
$90$	−0.867392	−0.0914311
$91$	18.6022	1.95005
$92$	−3.78056	−0.394150
$93$	−8.85173	−0.917881
$94$	−13.0916	−1.35030
$95$	1.19215	0.122312
$96$	1.46035	0.149046
$97$	9.72633	0.987559	0.493780	−	0.869587i	$-0.335615\pi$
$97$	9.72633	0.987559	0.493780	+	0.869587i	$0.335615\pi$
$98$	−9.63601	−0.973384
$99$	3.79336	0.381247
$100$	1.00000	0.100000
$101$	−15.8907	−1.58118	−0.790591	−	0.612344i	$-0.790227\pi$
$101$	−15.8907	−1.58118	−0.790591	+	0.612344i	$0.790227\pi$
$102$	8.84622	0.875906
$103$	−5.17888	−0.510290	−0.255145	−	0.966903i	$-0.582123\pi$
$103$	−5.17888	−0.510290	−0.255145	+	0.966903i	$0.582123\pi$
$104$	4.56080	0.447223
$105$	−5.95635	−0.581280
$106$	−3.35323	−0.325694
$107$	−10.0043	−0.967157	−0.483578	−	0.875301i	$-0.660663\pi$
$107$	−10.0043	−0.967157	−0.483578	+	0.875301i	$0.660663\pi$
$108$	5.64773	0.543453
$109$	−13.0319	−1.24823	−0.624113	−	0.781334i	$-0.714540\pi$
$109$	−13.0319	−1.24823	−0.624113	+	0.781334i	$0.714540\pi$
$110$	−4.37329	−0.416977
$111$	5.87646	0.557769
$112$	−4.07873	−0.385403
$113$	1.50775	0.141837	0.0709187	−	0.997482i	$-0.477407\pi$
$113$	1.50775	0.141837	0.0709187	+	0.997482i	$0.477407\pi$
$114$	−1.74095	−0.163055
$115$	3.78056	0.352539
$116$	2.15330	0.199929
$117$	3.95600	0.365732
$118$	−7.74193	−0.712702
$119$	−24.7074	−2.26492
$120$	−1.46035	−0.133311
$121$	8.12570	0.738700
$122$	1.07606	0.0974217
$123$	−12.1192	−1.09275
$124$	6.06139	0.544329
$125$	−1.00000	−0.0894427
$126$	−3.53785	−0.315177
$127$	−14.2861	−1.26769	−0.633843	−	0.773462i	$-0.718524\pi$
$127$	−14.2861	−1.26769	−0.633843	+	0.773462i	$0.718524\pi$
$128$	−1.00000	−0.0883883
$129$	6.58885	0.580116
$130$	−4.56080	−0.400008
$131$	−16.7954	−1.46742	−0.733712	−	0.679460i	$-0.762214\pi$
$131$	−16.7954	−1.46742	−0.733712	+	0.679460i	$0.762214\pi$
$132$	6.38652	0.555875
$133$	4.86247	0.421629
$134$	7.40179	0.639417
$135$	−5.64773	−0.486079
$136$	−6.05762	−0.519437
$137$	5.22333	0.446259	0.223129	−	0.974789i	$-0.428373\pi$
$137$	5.22333	0.446259	0.223129	+	0.974789i	$0.428373\pi$
$138$	−5.52092	−0.469972
$139$	−0.734667	−0.0623136	−0.0311568	−	0.999515i	$-0.509919\pi$
$139$	−0.734667	−0.0623136	−0.0311568	+	0.999515i	$0.509919\pi$
$140$	4.07873	0.344715
$141$	−19.1183	−1.61005
$142$	−3.09840	−0.260012
$143$	19.9457	1.66794
$144$	−0.867392	−0.0722826
$145$	−2.15330	−0.178822
$146$	−1.18067	−0.0977126
$147$	−14.0719	−1.16063
$148$	−4.02402	−0.330772
$149$	3.35679	0.274999	0.137499	−	0.990502i	$-0.456093\pi$
$149$	3.35679	0.274999	0.137499	+	0.990502i	$0.456093\pi$
$150$	1.46035	0.119237
$151$	16.5540	1.34714	0.673572	−	0.739122i	$-0.264759\pi$
$151$	16.5540	1.34714	0.673572	+	0.739122i	$0.264759\pi$
$152$	1.19215	0.0966964
$153$	−5.25433	−0.424788
$154$	−17.8375	−1.43738
$155$	−6.06139	−0.486863
$156$	6.66034	0.533254
$157$	23.4384	1.87059	0.935296	−	0.353867i	$-0.115133\pi$
$157$	23.4384	1.87059	0.935296	+	0.353867i	$0.115133\pi$
$158$	−14.7565	−1.17396
$159$	−4.89687	−0.388347
$160$	1.00000	0.0790569
$161$	15.4199	1.21526
$162$	5.64546	0.443549
$163$	−23.7311	−1.85876	−0.929382	−	0.369119i	$-0.879659\pi$
$163$	−23.7311	−1.85876	−0.929382	+	0.369119i	$0.879659\pi$
$164$	8.29885	0.648031
$165$	−6.38652	−0.497190
$166$	14.1785	1.10047
$167$	−18.1796	−1.40678	−0.703390	−	0.710804i	$-0.748331\pi$
$167$	−18.1796	−1.40678	−0.703390	+	0.710804i	$0.748331\pi$
$168$	−5.95635	−0.459542
$169$	7.80087	0.600067
$170$	6.05762	0.464598
$171$	1.03406	0.0790768
$172$	−4.51185	−0.344025
$173$	16.0108	1.21728	0.608641	−	0.793446i	$-0.291715\pi$
$173$	16.0108	1.21728	0.608641	+	0.793446i	$0.291715\pi$
$174$	3.14456	0.238389
$175$	−4.07873	−0.308323
$176$	−4.37329	−0.329649
$177$	−11.3059	−0.849803
$178$	−5.08768	−0.381338
$179$	−7.82796	−0.585089	−0.292544	−	0.956252i	$-0.594502\pi$
$179$	−7.82796	−0.585089	−0.292544	+	0.956252i	$0.594502\pi$
$180$	0.867392	0.0646516
$181$	12.8075	0.951975	0.475987	−	0.879452i	$-0.342091\pi$
$181$	12.8075	0.951975	0.475987	+	0.879452i	$0.342091\pi$
$182$	−18.6022	−1.37889
$183$	1.57142	0.116162
$184$	3.78056	0.278706
$185$	4.02402	0.295852
$186$	8.85173	0.649040
$187$	−26.4918	−1.93727
$188$	13.0916	0.954807
$189$	−23.0355	−1.67559
$190$	−1.19215	−0.0864879
$191$	−0.579127	−0.0419042	−0.0209521	−	0.999780i	$-0.506670\pi$
$191$	−0.579127	−0.0419042	−0.0209521	+	0.999780i	$0.506670\pi$
$192$	−1.46035	−0.105391
$193$	1.45505	0.104737	0.0523684	−	0.998628i	$-0.483323\pi$
$193$	1.45505	0.104737	0.0523684	+	0.998628i	$0.483323\pi$
$194$	−9.72633	−0.698310
$195$	−6.66034	−0.476957
$196$	9.63601	0.688287
$197$	−21.9220	−1.56188	−0.780939	−	0.624608i	$-0.785259\pi$
$197$	−21.9220	−1.56188	−0.780939	+	0.624608i	$0.785259\pi$
$198$	−3.79336	−0.269582
$199$	1.26301	0.0895327	0.0447664	−	0.998997i	$-0.485746\pi$
$199$	1.26301	0.0895327	0.0447664	+	0.998997i	$0.485746\pi$
$200$	−1.00000	−0.0707107
$201$	10.8092	0.762420
$202$	15.8907	1.11806
$203$	−8.78272	−0.616426
$204$	−8.84622	−0.619359
$205$	−8.29885	−0.579616
$206$	5.17888	0.360829
$207$	3.27922	0.227922
$208$	−4.56080	−0.316234
$209$	5.21364	0.360635
$210$	5.95635	0.411027
$211$	12.3681	0.851458	0.425729	−	0.904851i	$-0.360018\pi$
$211$	12.3681	0.851458	0.425729	+	0.904851i	$0.360018\pi$
$212$	3.35323	0.230300
$213$	−4.52474	−0.310030
$214$	10.0043	0.683883
$215$	4.51185	0.307705
$216$	−5.64773	−0.384279
$217$	−24.7228	−1.67829
$218$	13.0319	0.882629
$219$	−1.72418	−0.116509
$220$	4.37329	0.294847
$221$	−27.6276	−1.85843
$222$	−5.87646	−0.394402
$223$	13.6651	0.915080	0.457540	−	0.889189i	$-0.348731\pi$
$223$	13.6651	0.915080	0.457540	+	0.889189i	$0.348731\pi$
$224$	4.07873	0.272521
$225$	−0.867392	−0.0578261
$226$	−1.50775	−0.100294
$227$	16.7423	1.11122	0.555612	−	0.831442i	$-0.312484\pi$
$227$	16.7423	1.11122	0.555612	+	0.831442i	$0.312484\pi$
$228$	1.74095	0.115298
$229$	17.6620	1.16714	0.583570	−	0.812063i	$-0.301655\pi$
$229$	17.6620	1.16714	0.583570	+	0.812063i	$0.301655\pi$
$230$	−3.78056	−0.249283
$231$	−26.0489	−1.71389
$232$	−2.15330	−0.141371
$233$	19.9363	1.30607	0.653034	−	0.757328i	$-0.273496\pi$
$233$	19.9363	1.30607	0.653034	+	0.757328i	$0.273496\pi$
$234$	−3.95600	−0.258612
$235$	−13.0916	−0.854005
$236$	7.74193	0.503957
$237$	−21.5495	−1.39979
$238$	24.7074	1.60154
$239$	−2.21606	−0.143345	−0.0716727	−	0.997428i	$-0.522834\pi$
$239$	−2.21606	−0.143345	−0.0716727	+	0.997428i	$0.522834\pi$
$240$	1.46035	0.0942649
$241$	12.6674	0.815978	0.407989	−	0.912987i	$-0.366230\pi$
$241$	12.6674	0.815978	0.407989	+	0.912987i	$0.366230\pi$
$242$	−8.12570	−0.522340
$243$	−8.69887	−0.558033
$244$	−1.07606	−0.0688876
$245$	−9.63601	−0.615622
$246$	12.1192	0.772691
$247$	5.43717	0.345959
$248$	−6.06139	−0.384899
$249$	20.7055	1.31216
$250$	1.00000	0.0632456
$251$	−0.564930	−0.0356581	−0.0178290	−	0.999841i	$-0.505675\pi$
$251$	−0.564930	−0.0356581	−0.0178290	+	0.999841i	$0.505675\pi$
$252$	3.53785	0.222864
$253$	16.5335	1.03945
$254$	14.2861	0.896390
$255$	8.84622	0.553972
$256$	1.00000	0.0625000
$257$	−25.2389	−1.57436	−0.787181	−	0.616722i	$-0.788460\pi$
$257$	−25.2389	−1.57436	−0.787181	+	0.616722i	$0.788460\pi$
$258$	−6.58885	−0.410204
$259$	16.4129	1.01985
$260$	4.56080	0.282849
$261$	−1.86775	−0.115611
$262$	16.7954	1.03763
$263$	−19.7978	−1.22079	−0.610393	−	0.792098i	$-0.708989\pi$
$263$	−19.7978	−1.22079	−0.610393	+	0.792098i	$0.708989\pi$
$264$	−6.38652	−0.393063
$265$	−3.35323	−0.205987
$266$	−4.86247	−0.298137
$267$	−7.42977	−0.454695
$268$	−7.40179	−0.452136
$269$	24.9489	1.52116	0.760580	−	0.649244i	$-0.224915\pi$
$269$	24.9489	1.52116	0.760580	+	0.649244i	$0.224915\pi$
$270$	5.64773	0.343710
$271$	−1.66193	−0.100955	−0.0504776	−	0.998725i	$-0.516074\pi$
$271$	−1.66193	−0.100955	−0.0504776	+	0.998725i	$0.516074\pi$
$272$	6.05762	0.367297
$273$	−27.1657	−1.64414
$274$	−5.22333	−0.315553
$275$	−4.37329	−0.263720
$276$	5.52092	0.332320
$277$	−13.0813	−0.785978	−0.392989	−	0.919543i	$-0.628559\pi$
$277$	−13.0813	−0.785978	−0.392989	+	0.919543i	$0.628559\pi$
$278$	0.734667	0.0440624
$279$	−5.25760	−0.314764
$280$	−4.07873	−0.243751
$281$	8.36795	0.499190	0.249595	−	0.968350i	$-0.419703\pi$
$281$	8.36795	0.499190	0.249595	+	0.968350i	$0.419703\pi$
$282$	19.1183	1.13848
$283$	4.76570	0.283291	0.141646	−	0.989917i	$-0.454761\pi$
$283$	4.76570	0.283291	0.141646	+	0.989917i	$0.454761\pi$
$284$	3.09840	0.183856
$285$	−1.74095	−0.103125
$286$	−19.9457	−1.17941
$287$	−33.8487	−1.99803
$288$	0.867392	0.0511115
$289$	19.6948	1.15852
$290$	2.15330	0.126446
$291$	−14.2038	−0.832642
$292$	1.18067	0.0690933
$293$	1.61747	0.0944934	0.0472467	−	0.998883i	$-0.484955\pi$
$293$	1.61747	0.0944934	0.0472467	+	0.998883i	$0.484955\pi$
$294$	14.0719	0.820690
$295$	−7.74193	−0.450753
$296$	4.02402	0.233891
$297$	−24.6992	−1.43319
$298$	−3.35679	−0.194454
$299$	17.2424	0.997151
$300$	−1.46035	−0.0843131
$301$	18.4026	1.06071
$302$	−16.5540	−0.952574
$303$	23.2059	1.33314
$304$	−1.19215	−0.0683747
$305$	1.07606	0.0616149
$306$	5.25433	0.300370
$307$	32.9754	1.88200	0.941002	−	0.338402i	$-0.109886\pi$
$307$	32.9754	1.88200	0.941002	+	0.338402i	$0.109886\pi$
$308$	17.8375	1.01638
$309$	7.56295	0.430241
$310$	6.06139	0.344264
$311$	−9.54822	−0.541430	−0.270715	−	0.962660i	$-0.587260\pi$
$311$	−9.54822	−0.541430	−0.270715	+	0.962660i	$0.587260\pi$
$312$	−6.66034	−0.377067
$313$	21.2877	1.20325	0.601625	−	0.798779i	$-0.294520\pi$
$313$	21.2877	1.20325	0.601625	+	0.798779i	$0.294520\pi$
$314$	−23.4384	−1.32271
$315$	−3.53785	−0.199335
$316$	14.7565	0.830116
$317$	31.0778	1.74550	0.872752	−	0.488164i	$-0.162333\pi$
$317$	31.0778	1.74550	0.872752	+	0.488164i	$0.162333\pi$
$318$	4.89687	0.274603
$319$	−9.41701	−0.527252
$320$	−1.00000	−0.0559017
$321$	14.6098	0.815439
$322$	−15.4199	−0.859315
$323$	−7.22161	−0.401821
$324$	−5.64546	−0.313636
$325$	−4.56080	−0.252988
$326$	23.7311	1.31434
$327$	19.0310	1.05242
$328$	−8.29885	−0.458227
$329$	−53.3973	−2.94389
$330$	6.38652	0.351566
$331$	30.2910	1.66494	0.832472	−	0.554068i	$-0.186925\pi$
$331$	30.2910	1.66494	0.832472	+	0.554068i	$0.186925\pi$
$332$	−14.1785	−0.778147
$333$	3.49040	0.191273
$334$	18.1796	0.994743
$335$	7.40179	0.404403
$336$	5.95635	0.324946
$337$	−36.0252	−1.96242	−0.981209	−	0.192949i	$-0.938195\pi$
$337$	−36.0252	−1.96242	−0.981209	+	0.192949i	$0.938195\pi$
$338$	−7.80087	−0.424311
$339$	−2.20184	−0.119587
$340$	−6.05762	−0.328521
$341$	−26.5083	−1.43550
$342$	−1.03406	−0.0559158
$343$	−10.7516	−0.580531
$344$	4.51185	0.243262
$345$	−5.52092	−0.297236
$346$	−16.0108	−0.860749
$347$	−23.9106	−1.28359	−0.641795	−	0.766876i	$-0.721810\pi$
$347$	−23.9106	−1.28359	−0.641795	+	0.766876i	$0.721810\pi$
$348$	−3.14456	−0.168566
$349$	0.298287	0.0159670	0.00798348	−	0.999968i	$-0.497459\pi$
$349$	0.298287	0.0159670	0.00798348	+	0.999968i	$0.497459\pi$
$350$	4.07873	0.218017
$351$	−25.7581	−1.37487
$352$	4.37329	0.233097
$353$	22.9843	1.22333	0.611667	−	0.791116i	$-0.290499\pi$
$353$	22.9843	1.22333	0.611667	+	0.791116i	$0.290499\pi$
$354$	11.3059	0.600901
$355$	−3.09840	−0.164446
$356$	5.08768	0.269647
$357$	36.0813	1.90963
$358$	7.82796	0.413720
$359$	−1.38946	−0.0733327	−0.0366664	−	0.999328i	$-0.511674\pi$
$359$	−1.38946	−0.0733327	−0.0366664	+	0.999328i	$0.511674\pi$
$360$	−0.867392	−0.0457156
$361$	−17.5788	−0.925199
$362$	−12.8075	−0.673148
$363$	−11.8663	−0.622821
$364$	18.6022	0.975023
$365$	−1.18067	−0.0617989
$366$	−1.57142	−0.0821392
$367$	20.2620	1.05767	0.528835	−	0.848725i	$-0.322629\pi$
$367$	20.2620	1.05767	0.528835	+	0.848725i	$0.322629\pi$
$368$	−3.78056	−0.197075
$369$	−7.19835	−0.374731
$370$	−4.02402	−0.209199
$371$	−13.6769	−0.710069
$372$	−8.85173	−0.458941
$373$	−12.4631	−0.645316	−0.322658	−	0.946516i	$-0.604576\pi$
$373$	−12.4631	−0.645316	−0.322658	+	0.946516i	$0.604576\pi$
$374$	26.4918	1.36986
$375$	1.46035	0.0754119
$376$	−13.0916	−0.675150
$377$	−9.82076	−0.505795
$378$	23.0355	1.18482
$379$	3.90893	0.200788	0.100394	−	0.994948i	$-0.467990\pi$
$379$	3.90893	0.200788	0.100394	+	0.994948i	$0.467990\pi$
$380$	1.19215	0.0611561
$381$	20.8626	1.06883
$382$	0.579127	0.0296307
$383$	1.32101	0.0675003	0.0337502	−	0.999430i	$-0.489255\pi$
$383$	1.32101	0.0675003	0.0337502	+	0.999430i	$0.489255\pi$
$384$	1.46035	0.0745229
$385$	−17.8375	−0.909082
$386$	−1.45505	−0.0740601
$387$	3.91354	0.198936
$388$	9.72633	0.493780
$389$	29.7501	1.50839	0.754194	−	0.656651i	$-0.228028\pi$
$389$	29.7501	1.50839	0.754194	+	0.656651i	$0.228028\pi$
$390$	6.66034	0.337259
$391$	−22.9012	−1.15816
$392$	−9.63601	−0.486692
$393$	24.5271	1.23723
$394$	21.9220	1.10441
$395$	−14.7565	−0.742478
$396$	3.79336	0.190623
$397$	−30.4454	−1.52801	−0.764006	−	0.645209i	$-0.776770\pi$
$397$	−30.4454	−1.52801	−0.764006	+	0.645209i	$0.776770\pi$
$398$	−1.26301	−0.0633092
$399$	−7.10088	−0.355489
$400$	1.00000	0.0500000
$401$	−24.9080	−1.24385	−0.621924	−	0.783078i	$-0.713649\pi$
$401$	−24.9080	−1.24385	−0.621924	+	0.783078i	$0.713649\pi$
$402$	−10.8092	−0.539112
$403$	−27.6448	−1.37708
$404$	−15.8907	−0.790591
$405$	5.64546	0.280525
$406$	8.78272	0.435879
$407$	17.5982	0.872311
$408$	8.84622	0.437953
$409$	−3.04952	−0.150789	−0.0753945	−	0.997154i	$-0.524022\pi$
$409$	−3.04952	−0.150789	−0.0753945	+	0.997154i	$0.524022\pi$
$410$	8.29885	0.409851
$411$	−7.62786	−0.376255
$412$	−5.17888	−0.255145
$413$	−31.5772	−1.55381
$414$	−3.27922	−0.161165
$415$	14.1785	0.695996
$416$	4.56080	0.223611
$417$	1.07287	0.0525385
$418$	−5.21364	−0.255007
$419$	−15.5285	−0.758618	−0.379309	−	0.925270i	$-0.623838\pi$
$419$	−15.5285	−0.758618	−0.379309	+	0.925270i	$0.623838\pi$
$420$	−5.95635	−0.290640
$421$	10.8273	0.527688	0.263844	−	0.964565i	$-0.415010\pi$
$421$	10.8273	0.527688	0.263844	+	0.964565i	$0.415010\pi$
$422$	−12.3681	−0.602071
$423$	−11.3556	−0.552128
$424$	−3.35323	−0.162847
$425$	6.05762	0.293838
$426$	4.52474	0.219224
$427$	4.38895	0.212396
$428$	−10.0043	−0.483578
$429$	−29.1276	−1.40629
$430$	−4.51185	−0.217581
$431$	11.8924	0.572835	0.286417	−	0.958105i	$-0.407536\pi$
$431$	11.8924	0.572835	0.286417	+	0.958105i	$0.407536\pi$
$432$	5.64773	0.271726
$433$	−3.61159	−0.173562	−0.0867809	−	0.996227i	$-0.527658\pi$
$433$	−3.61159	−0.173562	−0.0867809	+	0.996227i	$0.527658\pi$
$434$	24.7228	1.18673
$435$	3.14456	0.150770
$436$	−13.0319	−0.624113
$437$	4.50700	0.215599
$438$	1.72418	0.0823845
$439$	3.72603	0.177834	0.0889168	−	0.996039i	$-0.471659\pi$
$439$	3.72603	0.177834	0.0889168	+	0.996039i	$0.471659\pi$
$440$	−4.37329	−0.208489
$441$	−8.35820	−0.398009
$442$	27.6276	1.31411
$443$	−5.45526	−0.259187	−0.129594	−	0.991567i	$-0.541367\pi$
$443$	−5.45526	−0.259187	−0.129594	+	0.991567i	$0.541367\pi$
$444$	5.87646	0.278884
$445$	−5.08768	−0.241179
$446$	−13.6651	−0.647060
$447$	−4.90207	−0.231860
$448$	−4.07873	−0.192702
$449$	38.0778	1.79700	0.898501	−	0.438971i	$-0.144657\pi$
$449$	38.0778	1.79700	0.898501	+	0.438971i	$0.144657\pi$
$450$	0.867392	0.0408892
$451$	−36.2933	−1.70898
$452$	1.50775	0.0709187
$453$	−24.1745	−1.13582
$454$	−16.7423	−0.785754
$455$	−18.6022	−0.872087
$456$	−1.74095	−0.0815277
$457$	1.09012	0.0509939	0.0254969	−	0.999675i	$-0.491883\pi$
$457$	1.09012	0.0509939	0.0254969	+	0.999675i	$0.491883\pi$
$458$	−17.6620	−0.825293
$459$	34.2118	1.59687
$460$	3.78056	0.176269
$461$	−2.93067	−0.136495	−0.0682475	−	0.997668i	$-0.521741\pi$
$461$	−2.93067	−0.136495	−0.0682475	+	0.997668i	$0.521741\pi$
$462$	26.0489	1.21190
$463$	−21.1070	−0.980928	−0.490464	−	0.871462i	$-0.663173\pi$
$463$	−21.1070	−0.980928	−0.490464	+	0.871462i	$0.663173\pi$
$464$	2.15330	0.0999644
$465$	8.85173	0.410489
$466$	−19.9363	−0.923530
$467$	−20.8432	−0.964507	−0.482254	−	0.876032i	$-0.660182\pi$
$467$	−20.8432	−0.964507	−0.482254	+	0.876032i	$0.660182\pi$
$468$	3.95600	0.182866
$469$	30.1899	1.39404
$470$	13.0916	0.603873
$471$	−34.2282	−1.57715
$472$	−7.74193	−0.356351
$473$	19.7316	0.907261
$474$	21.5495	0.989803
$475$	−1.19215	−0.0546997
$476$	−24.7074	−1.13246
$477$	−2.90856	−0.133174
$478$	2.21606	0.101360
$479$	20.6725	0.944551	0.472276	−	0.881451i	$-0.343433\pi$
$479$	20.6725	0.944551	0.472276	+	0.881451i	$0.343433\pi$
$480$	−1.46035	−0.0666553
$481$	18.3527	0.836812
$482$	−12.6674	−0.576983
$483$	−22.5183	−1.02462
$484$	8.12570	0.369350
$485$	−9.72633	−0.441650
$486$	8.69887	0.394589
$487$	−2.55476	−0.115767	−0.0578835	−	0.998323i	$-0.518435\pi$
$487$	−2.55476	−0.115767	−0.0578835	+	0.998323i	$0.518435\pi$
$488$	1.07606	0.0487109
$489$	34.6556	1.56718
$490$	9.63601	0.435311
$491$	−9.66796	−0.436309	−0.218155	−	0.975914i	$-0.570004\pi$
$491$	−9.66796	−0.436309	−0.218155	+	0.975914i	$0.570004\pi$
$492$	−12.1192	−0.546375
$493$	13.0439	0.587467
$494$	−5.43717	−0.244630
$495$	−3.79336	−0.170499
$496$	6.06139	0.272165
$497$	−12.6375	−0.566871
$498$	−20.7055	−0.927837
$499$	−18.9611	−0.848817	−0.424408	−	0.905471i	$-0.639518\pi$
$499$	−18.9611	−0.848817	−0.424408	+	0.905471i	$0.639518\pi$
$500$	−1.00000	−0.0447214
$501$	26.5485	1.18610
$502$	0.564930	0.0252141
$503$	−5.89776	−0.262968	−0.131484	−	0.991318i	$-0.541974\pi$
$503$	−5.89776	−0.262968	−0.131484	+	0.991318i	$0.541974\pi$
$504$	−3.53785	−0.157589
$505$	15.8907	0.707126
$506$	−16.5335	−0.735003
$507$	−11.3920	−0.505935
$508$	−14.2861	−0.633843
$509$	39.9121	1.76907	0.884537	−	0.466469i	$-0.154474\pi$
$509$	39.9121	1.76907	0.884537	+	0.466469i	$0.154474\pi$
$510$	−8.84622	−0.391717
$511$	−4.81562	−0.213030
$512$	−1.00000	−0.0441942
$513$	−6.73295	−0.297267
$514$	25.2389	1.11324
$515$	5.17888	0.228209
$516$	6.58885	0.290058
$517$	−57.2536	−2.51801
$518$	−16.4129	−0.721140
$519$	−23.3814	−1.02633
$520$	−4.56080	−0.200004
$521$	−20.2961	−0.889188	−0.444594	−	0.895732i	$-0.646652\pi$
$521$	−20.2961	−0.889188	−0.444594	+	0.895732i	$0.646652\pi$
$522$	1.86775	0.0817494
$523$	−13.2698	−0.580248	−0.290124	−	0.956989i	$-0.593697\pi$
$523$	−13.2698	−0.580248	−0.290124	+	0.956989i	$0.593697\pi$
$524$	−16.7954	−0.733712
$525$	5.95635	0.259956
$526$	19.7978	0.863227
$527$	36.7176	1.59945
$528$	6.38652	0.277938
$529$	−8.70738	−0.378582
$530$	3.35323	0.145655
$531$	−6.71528	−0.291419
$532$	4.86247	0.210815
$533$	−37.8493	−1.63944
$534$	7.42977	0.321518
$535$	10.0043	0.432526
$536$	7.40179	0.319709
$537$	11.4315	0.493306
$538$	−24.9489	−1.07562
$539$	−42.1411	−1.81515
$540$	−5.64773	−0.243039
$541$	−40.9580	−1.76092	−0.880460	−	0.474120i	$-0.842766\pi$
$541$	−40.9580	−1.76092	−0.880460	+	0.474120i	$0.842766\pi$
$542$	1.66193	0.0713861
$543$	−18.7034	−0.802639
$544$	−6.05762	−0.259718
$545$	13.0319	0.558224
$546$	27.1657	1.16258
$547$	−16.3834	−0.700506	−0.350253	−	0.936655i	$-0.613904\pi$
$547$	−16.3834	−0.700506	−0.350253	+	0.936655i	$0.613904\pi$
$548$	5.22333	0.223129
$549$	0.933364	0.0398350
$550$	4.37329	0.186478
$551$	−2.56706	−0.109361
$552$	−5.52092	−0.234986
$553$	−60.1876	−2.55944
$554$	13.0813	0.555770
$555$	−5.87646	−0.249442
$556$	−0.734667	−0.0311568
$557$	−1.33904	−0.0567368	−0.0283684	−	0.999598i	$-0.509031\pi$
$557$	−1.33904	−0.0567368	−0.0283684	+	0.999598i	$0.509031\pi$
$558$	5.25760	0.222572
$559$	20.5776	0.870340
$560$	4.07873	0.172358
$561$	38.6871	1.63337
$562$	−8.36795	−0.352981
$563$	−11.8766	−0.500539	−0.250270	−	0.968176i	$-0.580519\pi$
$563$	−11.8766	−0.500539	−0.250270	+	0.968176i	$0.580519\pi$
$564$	−19.1183	−0.805027
$565$	−1.50775	−0.0634316
$566$	−4.76570	−0.200317
$567$	23.0263	0.967013
$568$	−3.09840	−0.130006
$569$	−26.8824	−1.12697	−0.563485	−	0.826126i	$-0.690540\pi$
$569$	−26.8824	−1.12697	−0.563485	+	0.826126i	$0.690540\pi$
$570$	1.74095	0.0729206
$571$	10.6311	0.444897	0.222448	−	0.974944i	$-0.428595\pi$
$571$	10.6311	0.444897	0.222448	+	0.974944i	$0.428595\pi$
$572$	19.9457	0.833972
$573$	0.845725	0.0353307
$574$	33.8487	1.41282
$575$	−3.78056	−0.157660
$576$	−0.867392	−0.0361413
$577$	2.91838	0.121494	0.0607469	−	0.998153i	$-0.480652\pi$
$577$	2.91838	0.121494	0.0607469	+	0.998153i	$0.480652\pi$
$578$	−19.6948	−0.819195
$579$	−2.12488	−0.0883069
$580$	−2.15330	−0.0894109
$581$	57.8303	2.39921
$582$	14.2038	0.588767
$583$	−14.6646	−0.607347
$584$	−1.18067	−0.0488563
$585$	−3.95600	−0.163560
$586$	−1.61747	−0.0668169
$587$	−3.71617	−0.153383	−0.0766914	−	0.997055i	$-0.524436\pi$
$587$	−3.71617	−0.153383	−0.0766914	+	0.997055i	$0.524436\pi$
$588$	−14.0719	−0.580316
$589$	−7.22611	−0.297747
$590$	7.74193	0.318730
$591$	32.0137	1.31687
$592$	−4.02402	−0.165386
$593$	20.2786	0.832744	0.416372	−	0.909194i	$-0.363301\pi$
$593$	20.2786	0.832744	0.416372	+	0.909194i	$0.363301\pi$
$594$	24.6992	1.01342
$595$	24.7074	1.01290
$596$	3.35679	0.137499
$597$	−1.84444	−0.0754878
$598$	−17.2424	−0.705092
$599$	−14.1006	−0.576134	−0.288067	−	0.957610i	$-0.593013\pi$
$599$	−14.1006	−0.576134	−0.288067	+	0.957610i	$0.593013\pi$
$600$	1.46035	0.0596183
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−18.4026	−0.750034
$603$	6.42025	0.261453
$604$	16.5540	0.673572
$605$	−8.12570	−0.330357
$606$	−23.2059	−0.942675
$607$	31.2337	1.26774	0.633868	−	0.773442i	$-0.281466\pi$
$607$	31.2337	1.26774	0.633868	+	0.773442i	$0.281466\pi$
$608$	1.19215	0.0483482
$609$	12.8258	0.519728
$610$	−1.07606	−0.0435683
$611$	−59.7084	−2.41554
$612$	−5.25433	−0.212394
$613$	6.73351	0.271964	0.135982	−	0.990711i	$-0.456581\pi$
$613$	6.73351	0.271964	0.135982	+	0.990711i	$0.456581\pi$
$614$	−32.9754	−1.33078
$615$	12.1192	0.488692
$616$	−17.8375	−0.718692
$617$	−35.6405	−1.43483	−0.717417	−	0.696644i	$-0.754676\pi$
$617$	−35.6405	−1.43483	−0.717417	+	0.696644i	$0.754676\pi$
$618$	−7.56295	−0.304226
$619$	−41.4850	−1.66742	−0.833712	−	0.552199i	$-0.813789\pi$
$619$	−41.4850	−1.66742	−0.833712	+	0.552199i	$0.813789\pi$
$620$	−6.06139	−0.243431
$621$	−21.3516	−0.856808
$622$	9.54822	0.382849
$623$	−20.7513	−0.831382
$624$	6.66034	0.266627
$625$	1.00000	0.0400000
$626$	−21.2877	−0.850826
$627$	−7.61371	−0.304062
$628$	23.4384	0.935296
$629$	−24.3760	−0.971934
$630$	3.53785	0.140951
$631$	−1.64984	−0.0656789	−0.0328395	−	0.999461i	$-0.510455\pi$
$631$	−1.64984	−0.0656789	−0.0328395	+	0.999461i	$0.510455\pi$
$632$	−14.7565	−0.586981
$633$	−18.0617	−0.717890
$634$	−31.0778	−1.23426
$635$	14.2861	0.566927
$636$	−4.89687	−0.194173
$637$	−43.9479	−1.74128
$638$	9.41701	0.372823
$639$	−2.68753	−0.106317
$640$	1.00000	0.0395285
$641$	−22.6872	−0.896089	−0.448044	−	0.894011i	$-0.647879\pi$
$641$	−22.6872	−0.896089	−0.448044	+	0.894011i	$0.647879\pi$
$642$	−14.6098	−0.576603
$643$	40.4961	1.59701	0.798505	−	0.601988i	$-0.205624\pi$
$643$	40.4961	1.59701	0.798505	+	0.601988i	$0.205624\pi$
$644$	15.4199	0.607628
$645$	−6.58885	−0.259436
$646$	7.22161	0.284131
$647$	21.6123	0.849669	0.424834	−	0.905271i	$-0.360332\pi$
$647$	21.6123	0.849669	0.424834	+	0.905271i	$0.360332\pi$
$648$	5.64546	0.221774
$649$	−33.8577	−1.32903
$650$	4.56080	0.178889
$651$	36.1038	1.41502
$652$	−23.7311	−0.929382
$653$	8.63061	0.337742	0.168871	−	0.985638i	$-0.445988\pi$
$653$	8.63061	0.337742	0.168871	+	0.985638i	$0.445988\pi$
$654$	−19.0310	−0.744172
$655$	16.7954	0.656252
$656$	8.29885	0.324015
$657$	−1.02410	−0.0399540
$658$	53.3973	2.08164
$659$	27.7176	1.07972	0.539862	−	0.841753i	$-0.318476\pi$
$659$	27.7176	1.07972	0.539862	+	0.841753i	$0.318476\pi$
$660$	−6.38652	−0.248595
$661$	46.4102	1.80515	0.902575	−	0.430533i	$-0.141675\pi$
$661$	46.4102	1.80515	0.902575	+	0.430533i	$0.141675\pi$
$662$	−30.2910	−1.17729
$663$	40.3458	1.56690
$664$	14.1785	0.550233
$665$	−4.86247	−0.188558
$666$	−3.49040	−0.135250
$667$	−8.14067	−0.315208
$668$	−18.1796	−0.703390
$669$	−19.9557	−0.771532
$670$	−7.40179	−0.285956
$671$	4.70592	0.181670
$672$	−5.95635	−0.229771
$673$	−5.15214	−0.198600	−0.0993001	−	0.995058i	$-0.531660\pi$
$673$	−5.15214	−0.198600	−0.0993001	+	0.995058i	$0.531660\pi$
$674$	36.0252	1.38764
$675$	5.64773	0.217381
$676$	7.80087	0.300033
$677$	3.74600	0.143970	0.0719852	−	0.997406i	$-0.477067\pi$
$677$	3.74600	0.143970	0.0719852	+	0.997406i	$0.477067\pi$
$678$	2.20184	0.0845611
$679$	−39.6711	−1.52244
$680$	6.05762	0.232299
$681$	−24.4495	−0.936907
$682$	26.5083	1.01505
$683$	−2.27211	−0.0869401	−0.0434700	−	0.999055i	$-0.513841\pi$
$683$	−2.27211	−0.0869401	−0.0434700	+	0.999055i	$0.513841\pi$
$684$	1.03406	0.0395384
$685$	−5.22333	−0.199573
$686$	10.7516	0.410497
$687$	−25.7927	−0.984052
$688$	−4.51185	−0.172013
$689$	−15.2934	−0.582631
$690$	5.52092	0.210178
$691$	−31.5535	−1.20035	−0.600176	−	0.799868i	$-0.704903\pi$
$691$	−31.5535	−1.20035	−0.600176	+	0.799868i	$0.704903\pi$
$692$	16.0108	0.608641
$693$	−15.4721	−0.587736
$694$	23.9106	0.907635
$695$	0.734667	0.0278675
$696$	3.14456	0.119194
$697$	50.2713	1.90416
$698$	−0.298287	−0.0112903
$699$	−29.1138	−1.10119
$700$	−4.07873	−0.154161
$701$	−30.1678	−1.13942	−0.569711	−	0.821845i	$-0.692945\pi$
$701$	−30.1678	−1.13942	−0.569711	+	0.821845i	$0.692945\pi$
$702$	25.7581	0.972178
$703$	4.79724	0.180932
$704$	−4.37329	−0.164825
$705$	19.1183	0.720038
$706$	−22.9843	−0.865027
$707$	64.8138	2.43757
$708$	−11.3059	−0.424901
$709$	42.9079	1.61144	0.805721	−	0.592296i	$-0.201778\pi$
$709$	42.9079	1.61144	0.805721	+	0.592296i	$0.201778\pi$
$710$	3.09840	0.116281
$711$	−12.7996	−0.480024
$712$	−5.08768	−0.190669
$713$	−22.9154	−0.858190
$714$	−36.0813	−1.35031
$715$	−19.9457	−0.745927
$716$	−7.82796	−0.292544
$717$	3.23622	0.120859
$718$	1.38946	0.0518541
$719$	25.7224	0.959282	0.479641	−	0.877465i	$-0.340767\pi$
$719$	25.7224	0.959282	0.479641	+	0.877465i	$0.340767\pi$
$720$	0.867392	0.0323258
$721$	21.1232	0.786670
$722$	17.5788	0.654214
$723$	−18.4987	−0.687976
$724$	12.8075	0.475987
$725$	2.15330	0.0799715
$726$	11.8663	0.440401
$727$	−2.24958	−0.0834324	−0.0417162	−	0.999130i	$-0.513283\pi$
$727$	−2.24958	−0.0834324	−0.0417162	+	0.999130i	$0.513283\pi$
$728$	−18.6022	−0.689445
$729$	29.6397	1.09777
$730$	1.18067	0.0436984
$731$	−27.3311	−1.01088
$732$	1.57142	0.0580812
$733$	29.4211	1.08669	0.543346	−	0.839509i	$-0.317157\pi$
$733$	29.4211	1.08669	0.543346	+	0.839509i	$0.317157\pi$
$734$	−20.2620	−0.747886
$735$	14.0719	0.519050
$736$	3.78056	0.139353
$737$	32.3702	1.19237
$738$	7.19835	0.264975
$739$	−20.6391	−0.759222	−0.379611	−	0.925146i	$-0.623942\pi$
$739$	−20.6391	−0.759222	−0.379611	+	0.925146i	$0.623942\pi$
$740$	4.02402	0.147926
$741$	−7.94014	−0.291688
$742$	13.6769	0.502094
$743$	−29.6520	−1.08782	−0.543912	−	0.839142i	$-0.683058\pi$
$743$	−29.6520	−1.08782	−0.543912	+	0.839142i	$0.683058\pi$
$744$	8.85173	0.324520
$745$	−3.35679	−0.122983
$746$	12.4631	0.456307
$747$	12.2983	0.449972
$748$	−26.4918	−0.968635
$749$	40.8050	1.49098
$750$	−1.46035	−0.0533243
$751$	51.0134	1.86151	0.930753	−	0.365648i	$-0.119152\pi$
$751$	51.0134	1.86151	0.930753	+	0.365648i	$0.119152\pi$
$752$	13.0916	0.477403
$753$	0.824993	0.0300644
$754$	9.82076	0.357651
$755$	−16.5540	−0.602461
$756$	−23.0355	−0.837794
$757$	7.54009	0.274049	0.137025	−	0.990568i	$-0.456246\pi$
$757$	7.54009	0.274049	0.137025	+	0.990568i	$0.456246\pi$
$758$	−3.90893	−0.141979
$759$	−24.1446	−0.876394
$760$	−1.19215	−0.0432439
$761$	−48.0413	−1.74150	−0.870748	−	0.491729i	$-0.836365\pi$
$761$	−48.0413	−1.74150	−0.870748	+	0.491729i	$0.836365\pi$
$762$	−20.8626	−0.755774
$763$	53.1534	1.92428
$764$	−0.579127	−0.0209521
$765$	5.25433	0.189971
$766$	−1.32101	−0.0477299
$767$	−35.3094	−1.27495
$768$	−1.46035	−0.0526957
$769$	−33.3606	−1.20302	−0.601508	−	0.798867i	$-0.705433\pi$
$769$	−33.3606	−1.20302	−0.601508	+	0.798867i	$0.705433\pi$
$770$	17.8375	0.642818
$771$	36.8576	1.32739
$772$	1.45505	0.0523684
$773$	−24.6116	−0.885219	−0.442610	−	0.896714i	$-0.645947\pi$
$773$	−24.6116	−0.885219	−0.442610	+	0.896714i	$0.645947\pi$
$774$	−3.91354	−0.140669
$775$	6.06139	0.217732
$776$	−9.72633	−0.349155
$777$	−23.9685	−0.859864
$778$	−29.7501	−1.06659
$779$	−9.89349	−0.354471
$780$	−6.66034	−0.238478
$781$	−13.5502	−0.484865
$782$	22.9012	0.818945
$783$	12.1613	0.434608
$784$	9.63601	0.344143
$785$	−23.4384	−0.836554
$786$	−24.5271	−0.874854
$787$	26.3218	0.938270	0.469135	−	0.883127i	$-0.344566\pi$
$787$	26.3218	0.938270	0.469135	+	0.883127i	$0.344566\pi$
$788$	−21.9220	−0.780939
$789$	28.9117	1.02928
$790$	14.7565	0.525011
$791$	−6.14971	−0.218659
$792$	−3.79336	−0.134791
$793$	4.90768	0.174277
$794$	30.4454	1.08047
$795$	4.89687	0.173674
$796$	1.26301	0.0447664
$797$	−5.00012	−0.177113	−0.0885566	−	0.996071i	$-0.528225\pi$
$797$	−5.00012	−0.177113	−0.0885566	+	0.996071i	$0.528225\pi$
$798$	7.10088	0.251368
$799$	79.3043	2.80558
$800$	−1.00000	−0.0353553
$801$	−4.41301	−0.155926
$802$	24.9080	0.879534
$803$	−5.16340	−0.182212
$804$	10.8092	0.381210
$805$	−15.4199	−0.543479
$806$	27.6448	0.973746
$807$	−36.4340	−1.28254
$808$	15.8907	0.559032
$809$	21.0753	0.740968	0.370484	−	0.928839i	$-0.379192\pi$
$809$	21.0753	0.740968	0.370484	+	0.928839i	$0.379192\pi$
$810$	−5.64546	−0.198361
$811$	20.0517	0.704111	0.352056	−	0.935979i	$-0.385483\pi$
$811$	20.0517	0.704111	0.352056	+	0.935979i	$0.385483\pi$
$812$	−8.78272	−0.308213
$813$	2.42699	0.0851184
$814$	−17.5982	−0.616817
$815$	23.7311	0.831265
$816$	−8.84622	−0.309680
$817$	5.37881	0.188181
$818$	3.04952	0.106624
$819$	−16.1354	−0.563818
$820$	−8.29885	−0.289808
$821$	−41.5604	−1.45047	−0.725233	−	0.688503i	$-0.758268\pi$
$821$	−41.5604	−1.45047	−0.725233	+	0.688503i	$0.758268\pi$
$822$	7.62786	0.266052
$823$	−38.1015	−1.32813	−0.664067	−	0.747673i	$-0.731171\pi$
$823$	−38.1015	−1.32813	−0.664067	+	0.747673i	$0.731171\pi$
$824$	5.17888	0.180415
$825$	6.38652	0.222350
$826$	31.5772	1.09871
$827$	−9.61636	−0.334394	−0.167197	−	0.985924i	$-0.553472\pi$
$827$	−9.61636	−0.334394	−0.167197	+	0.985924i	$0.553472\pi$
$828$	3.27922	0.113961
$829$	24.4706	0.849899	0.424949	−	0.905217i	$-0.360292\pi$
$829$	24.4706	0.849899	0.424949	+	0.905217i	$0.360292\pi$
$830$	−14.1785	−0.492144
$831$	19.1032	0.662682
$832$	−4.56080	−0.158117
$833$	58.3713	2.02245
$834$	−1.07287	−0.0371504
$835$	18.1796	0.629131
$836$	5.21364	0.180317
$837$	34.2331	1.18327
$838$	15.5285	0.536424
$839$	−26.5778	−0.917567	−0.458784	−	0.888548i	$-0.651715\pi$
$839$	−26.5778	−0.917567	−0.458784	+	0.888548i	$0.651715\pi$
$840$	5.95635	0.205514
$841$	−24.3633	−0.840114
$842$	−10.8273	−0.373132
$843$	−12.2201	−0.420882
$844$	12.3681	0.425729
$845$	−7.80087	−0.268358
$846$	11.3556	0.390413
$847$	−33.1425	−1.13879
$848$	3.35323	0.115150
$849$	−6.95956	−0.238852
$850$	−6.05762	−0.207775
$851$	15.2130	0.521496
$852$	−4.52474	−0.155015
$853$	−13.6126	−0.466087	−0.233043	−	0.972466i	$-0.574868\pi$
$853$	−13.6126	−0.466087	−0.233043	+	0.972466i	$0.574868\pi$
$854$	−4.38895	−0.150187
$855$	−1.03406	−0.0353642
$856$	10.0043	0.341942
$857$	20.1505	0.688327	0.344164	−	0.938910i	$-0.388163\pi$
$857$	20.1505	0.688327	0.344164	+	0.938910i	$0.388163\pi$
$858$	29.1276	0.994401
$859$	12.1219	0.413593	0.206796	−	0.978384i	$-0.433696\pi$
$859$	12.1219	0.413593	0.206796	+	0.978384i	$0.433696\pi$
$860$	4.51185	0.153853
$861$	49.4308	1.68460
$862$	−11.8924	−0.405055
$863$	−33.2359	−1.13136	−0.565681	−	0.824624i	$-0.691387\pi$
$863$	−33.2359	−1.13136	−0.565681	+	0.824624i	$0.691387\pi$
$864$	−5.64773	−0.192140
$865$	−16.0108	−0.544385
$866$	3.61159	0.122727
$867$	−28.7612	−0.976781
$868$	−24.7228	−0.839145
$869$	−64.5344	−2.18918
$870$	−3.14456	−0.106611
$871$	33.7581	1.14385
$872$	13.0319	0.441315
$873$	−8.43654	−0.285534
$874$	−4.50700	−0.152452
$875$	4.07873	0.137886
$876$	−1.72418	−0.0582547
$877$	35.3600	1.19402	0.597011	−	0.802233i	$-0.296355\pi$
$877$	35.3600	1.19402	0.597011	+	0.802233i	$0.296355\pi$
$878$	−3.72603	−0.125747
$879$	−2.36206	−0.0796703
$880$	4.37329	0.147424
$881$	−47.3086	−1.59387	−0.796934	−	0.604066i	$-0.793546\pi$
$881$	−47.3086	−1.59387	−0.796934	+	0.604066i	$0.793546\pi$
$882$	8.35820	0.281435
$883$	12.4041	0.417431	0.208715	−	0.977976i	$-0.433072\pi$
$883$	12.4041	0.417431	0.208715	+	0.977976i	$0.433072\pi$
$884$	−27.6276	−0.929216
$885$	11.3059	0.380043
$886$	5.45526	0.183273
$887$	11.6556	0.391355	0.195678	−	0.980668i	$-0.437309\pi$
$887$	11.6556	0.391355	0.195678	+	0.980668i	$0.437309\pi$
$888$	−5.87646	−0.197201
$889$	58.2691	1.95428
$890$	5.08768	0.170539
$891$	24.6892	0.827121
$892$	13.6651	0.457540
$893$	−15.6072	−0.522277
$894$	4.90207	0.163950
$895$	7.82796	0.261660
$896$	4.07873	0.136261
$897$	−25.1798	−0.840729
$898$	−38.0778	−1.27067
$899$	13.0520	0.435308
$900$	−0.867392	−0.0289131
$901$	20.3126	0.676710
$902$	36.2933	1.20843
$903$	−26.8741	−0.894315
$904$	−1.50775	−0.0501471
$905$	−12.8075	−0.425736
$906$	24.1745	0.803145
$907$	−44.5129	−1.47803	−0.739013	−	0.673691i	$-0.764708\pi$
$907$	−44.5129	−1.47803	−0.739013	+	0.673691i	$0.764708\pi$
$908$	16.7423	0.555612
$909$	13.7835	0.457168
$910$	18.6022	0.616658
$911$	−26.0633	−0.863516	−0.431758	−	0.901989i	$-0.642107\pi$
$911$	−26.0633	−0.863516	−0.431758	+	0.901989i	$0.642107\pi$
$912$	1.74095	0.0576488
$913$	62.0068	2.05213
$914$	−1.09012	−0.0360581
$915$	−1.57142	−0.0519494
$916$	17.6620	0.583570
$917$	68.5040	2.26220
$918$	−34.2118	−1.12916
$919$	13.0835	0.431585	0.215793	−	0.976439i	$-0.430766\pi$
$919$	13.0835	0.431585	0.215793	+	0.976439i	$0.430766\pi$
$920$	−3.78056	−0.124641
$921$	−48.1554	−1.58677
$922$	2.93067	0.0965165
$923$	−14.1312	−0.465133
$924$	−26.0489	−0.856945
$925$	−4.02402	−0.132309
$926$	21.1070	0.693621
$927$	4.49211	0.147540
$928$	−2.15330	−0.0706855
$929$	−34.5568	−1.13377	−0.566886	−	0.823796i	$-0.691852\pi$
$929$	−34.5568	−1.13377	−0.566886	+	0.823796i	$0.691852\pi$
$930$	−8.85173	−0.290260
$931$	−11.4876	−0.376491
$932$	19.9363	0.653034
$933$	13.9437	0.456496
$934$	20.8432	0.682010
$935$	26.4918	0.866373
$936$	−3.95600	−0.129306
$937$	27.2827	0.891286	0.445643	−	0.895211i	$-0.352975\pi$
$937$	27.2827	0.891286	0.445643	+	0.895211i	$0.352975\pi$
$938$	−30.1899	−0.985734
$939$	−31.0873	−1.01450
$940$	−13.0916	−0.427003
$941$	39.6458	1.29242	0.646208	−	0.763161i	$-0.276354\pi$
$941$	39.6458	1.29242	0.646208	+	0.763161i	$0.276354\pi$
$942$	34.2282	1.11522
$943$	−31.3743	−1.02169
$944$	7.74193	0.251978
$945$	23.0355	0.749346
$946$	−19.7316	−0.641531
$947$	8.30873	0.269997	0.134999	−	0.990846i	$-0.456897\pi$
$947$	8.30873	0.269997	0.134999	+	0.990846i	$0.456897\pi$
$948$	−21.5495	−0.699896
$949$	−5.38478	−0.174797
$950$	1.19215	0.0386785
$951$	−45.3843	−1.47169
$952$	24.7074	0.800771
$953$	−20.8440	−0.675202	−0.337601	−	0.941289i	$-0.609615\pi$
$953$	−20.8440	−0.675202	−0.337601	+	0.941289i	$0.609615\pi$
$954$	2.90856	0.0941681
$955$	0.579127	0.0187401
$956$	−2.21606	−0.0716727
$957$	13.7521	0.444542
$958$	−20.6725	−0.667899
$959$	−21.3045	−0.687959
$960$	1.46035	0.0471324
$961$	5.74049	0.185177
$962$	−18.3527	−0.591716
$963$	8.67769	0.279635
$964$	12.6674	0.407989
$965$	−1.45505	−0.0468397
$966$	22.5183	0.724515
$967$	−47.3745	−1.52346	−0.761731	−	0.647894i	$-0.775650\pi$
$967$	−47.3745	−1.52346	−0.761731	+	0.647894i	$0.775650\pi$
$968$	−8.12570	−0.261170
$969$	10.5460	0.338788
$970$	9.72633	0.312294
$971$	−10.5571	−0.338794	−0.169397	−	0.985548i	$-0.554182\pi$
$971$	−10.5571	−0.338794	−0.169397	+	0.985548i	$0.554182\pi$
$972$	−8.69887	−0.279016
$973$	2.99651	0.0960636
$974$	2.55476	0.0818597
$975$	6.66034	0.213302
$976$	−1.07606	−0.0344438
$977$	23.8709	0.763697	0.381848	−	0.924225i	$-0.375288\pi$
$977$	23.8709	0.763697	0.381848	+	0.924225i	$0.375288\pi$
$978$	−34.6556	−1.10816
$979$	−22.2499	−0.711111
$980$	−9.63601	−0.307811
$981$	11.3037	0.360900
$982$	9.66796	0.308517
$983$	1.28339	0.0409337	0.0204668	−	0.999791i	$-0.493485\pi$
$983$	1.28339	0.0409337	0.0204668	+	0.999791i	$0.493485\pi$
$984$	12.1192	0.386345
$985$	21.9220	0.698493
$986$	−13.0439	−0.415402
$987$	77.9784	2.48208
$988$	5.43717	0.172979
$989$	17.0573	0.542390
$990$	3.79336	0.120561
$991$	13.2004	0.419325	0.209662	−	0.977774i	$-0.432763\pi$
$991$	13.2004	0.419325	0.209662	+	0.977774i	$0.432763\pi$
$992$	−6.06139	−0.192449
$993$	−44.2353	−1.40376
$994$	12.6375	0.400838
$995$	−1.26301	−0.0400403
$996$	20.7055	0.656080
$997$	39.7011	1.25735	0.628673	−	0.777669i	$-0.283598\pi$
$997$	39.7011	1.25735	0.628673	+	0.777669i	$0.283598\pi$
$998$	18.9611	0.600204
$999$	−22.7266	−0.719036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.11	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.11	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.46035 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.46035 q^{6} -4.07873 q^{7} -1.00000 q^{8} -0.867392 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.46035 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.46035 q^{6} -4.07873 q^{7} -1.00000 q^{8} -0.867392 q^{9} +1.00000 q^{10} -4.37329 q^{11} -1.46035 q^{12} -4.56080 q^{13} +4.07873 q^{14} +1.46035 q^{15} +1.00000 q^{16} +6.05762 q^{17} +0.867392 q^{18} -1.19215 q^{19} -1.00000 q^{20} +5.95635 q^{21} +4.37329 q^{22} -3.78056 q^{23} +1.46035 q^{24} +1.00000 q^{25} +4.56080 q^{26} +5.64773 q^{27} -4.07873 q^{28} +2.15330 q^{29} -1.46035 q^{30} +6.06139 q^{31} -1.00000 q^{32} +6.38652 q^{33} -6.05762 q^{34} +4.07873 q^{35} -0.867392 q^{36} -4.02402 q^{37} +1.19215 q^{38} +6.66034 q^{39} +1.00000 q^{40} +8.29885 q^{41} -5.95635 q^{42} -4.51185 q^{43} -4.37329 q^{44} +0.867392 q^{45} +3.78056 q^{46} +13.0916 q^{47} -1.46035 q^{48} +9.63601 q^{49} -1.00000 q^{50} -8.84622 q^{51} -4.56080 q^{52} +3.35323 q^{53} -5.64773 q^{54} +4.37329 q^{55} +4.07873 q^{56} +1.74095 q^{57} -2.15330 q^{58} +7.74193 q^{59} +1.46035 q^{60} -1.07606 q^{61} -6.06139 q^{62} +3.53785 q^{63} +1.00000 q^{64} +4.56080 q^{65} -6.38652 q^{66} -7.40179 q^{67} +6.05762 q^{68} +5.52092 q^{69} -4.07873 q^{70} +3.09840 q^{71} +0.867392 q^{72} +1.18067 q^{73} +4.02402 q^{74} -1.46035 q^{75} -1.19215 q^{76} +17.8375 q^{77} -6.66034 q^{78} +14.7565 q^{79} -1.00000 q^{80} -5.64546 q^{81} -8.29885 q^{82} -14.1785 q^{83} +5.95635 q^{84} -6.05762 q^{85} +4.51185 q^{86} -3.14456 q^{87} +4.37329 q^{88} +5.08768 q^{89} -0.867392 q^{90} +18.6022 q^{91} -3.78056 q^{92} -8.85173 q^{93} -13.0916 q^{94} +1.19215 q^{95} +1.46035 q^{96} +9.72633 q^{97} -9.63601 q^{98} +3.79336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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