LMFDB - Embedded newform 8031.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41661 q^{2} -1.00000 q^{3} +3.83999 q^{4} -2.56069 q^{5} +2.41661 q^{6} -0.401342 q^{7} -4.44652 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41661 q^{2} -1.00000 q^{3} +3.83999 q^{4} -2.56069 q^{5} +2.41661 q^{6} -0.401342 q^{7} -4.44652 q^{8} +1.00000 q^{9} +6.18818 q^{10} -4.98936 q^{11} -3.83999 q^{12} -4.84210 q^{13} +0.969887 q^{14} +2.56069 q^{15} +3.06552 q^{16} +5.64723 q^{17} -2.41661 q^{18} -8.63589 q^{19} -9.83302 q^{20} +0.401342 q^{21} +12.0573 q^{22} +5.00262 q^{23} +4.44652 q^{24} +1.55714 q^{25} +11.7015 q^{26} -1.00000 q^{27} -1.54115 q^{28} +7.55890 q^{29} -6.18818 q^{30} -1.66932 q^{31} +1.48489 q^{32} +4.98936 q^{33} -13.6471 q^{34} +1.02771 q^{35} +3.83999 q^{36} +5.90943 q^{37} +20.8695 q^{38} +4.84210 q^{39} +11.3862 q^{40} -0.0918199 q^{41} -0.969887 q^{42} -2.47241 q^{43} -19.1591 q^{44} -2.56069 q^{45} -12.0894 q^{46} -3.90733 q^{47} -3.06552 q^{48} -6.83892 q^{49} -3.76299 q^{50} -5.64723 q^{51} -18.5936 q^{52} -12.3754 q^{53} +2.41661 q^{54} +12.7762 q^{55} +1.78458 q^{56} +8.63589 q^{57} -18.2669 q^{58} -15.0449 q^{59} +9.83302 q^{60} +0.162345 q^{61} +4.03410 q^{62} -0.401342 q^{63} -9.71943 q^{64} +12.3991 q^{65} -12.0573 q^{66} -11.4956 q^{67} +21.6853 q^{68} -5.00262 q^{69} -2.48358 q^{70} +6.11003 q^{71} -4.44652 q^{72} +3.42177 q^{73} -14.2808 q^{74} -1.55714 q^{75} -33.1617 q^{76} +2.00244 q^{77} -11.7015 q^{78} -13.9251 q^{79} -7.84985 q^{80} +1.00000 q^{81} +0.221892 q^{82} -5.39865 q^{83} +1.54115 q^{84} -14.4608 q^{85} +5.97485 q^{86} -7.55890 q^{87} +22.1853 q^{88} -7.36623 q^{89} +6.18818 q^{90} +1.94334 q^{91} +19.2100 q^{92} +1.66932 q^{93} +9.44247 q^{94} +22.1138 q^{95} -1.48489 q^{96} -13.4274 q^{97} +16.5270 q^{98} -4.98936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.41661	−1.70880	−0.854399	−	0.519617i	$-0.826075\pi$
$2$	−2.41661	−1.70880	−0.854399	+	0.519617i	$0.826075\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.83999	1.91999
$5$	−2.56069	−1.14518	−0.572588	−	0.819843i	$-0.694060\pi$
$5$	−2.56069	−1.14518	−0.572588	+	0.819843i	$0.694060\pi$
$6$	2.41661	0.986575
$7$	−0.401342	−0.151693	−0.0758466	−	0.997119i	$-0.524166\pi$
$7$	−0.401342	−0.151693	−0.0758466	+	0.997119i	$0.524166\pi$
$8$	−4.44652	−1.57208
$9$	1.00000	0.333333
$10$	6.18818	1.95687
$11$	−4.98936	−1.50435	−0.752174	−	0.658964i	$-0.770995\pi$
$11$	−4.98936	−1.50435	−0.752174	+	0.658964i	$0.770995\pi$
$12$	−3.83999	−1.10851
$13$	−4.84210	−1.34296	−0.671479	−	0.741024i	$-0.734341\pi$
$13$	−4.84210	−1.34296	−0.671479	+	0.741024i	$0.734341\pi$
$14$	0.969887	0.259213
$15$	2.56069	0.661168
$16$	3.06552	0.766380
$17$	5.64723	1.36965	0.684827	−	0.728706i	$-0.259878\pi$
$17$	5.64723	1.36965	0.684827	+	0.728706i	$0.259878\pi$
$18$	−2.41661	−0.569600
$19$	−8.63589	−1.98121	−0.990605	−	0.136757i	$-0.956332\pi$
$19$	−8.63589	−1.98121	−0.990605	+	0.136757i	$0.956332\pi$
$20$	−9.83302	−2.19873
$21$	0.401342	0.0875801
$22$	12.0573	2.57063
$23$	5.00262	1.04312	0.521559	−	0.853215i	$-0.325351\pi$
$23$	5.00262	1.04312	0.521559	+	0.853215i	$0.325351\pi$
$24$	4.44652	0.907642
$25$	1.55714	0.311428
$26$	11.7015	2.29484
$27$	−1.00000	−0.192450
$28$	−1.54115	−0.291250
$29$	7.55890	1.40365	0.701827	−	0.712348i	$-0.252368\pi$
$29$	7.55890	1.40365	0.701827	+	0.712348i	$0.252368\pi$
$30$	−6.18818	−1.12980
$31$	−1.66932	−0.299819	−0.149910	−	0.988700i	$-0.547898\pi$
$31$	−1.66932	−0.299819	−0.149910	+	0.988700i	$0.547898\pi$
$32$	1.48489	0.262493
$33$	4.98936	0.868536
$34$	−13.6471	−2.34046
$35$	1.02771	0.173715
$36$	3.83999	0.639998
$37$	5.90943	0.971505	0.485753	−	0.874096i	$-0.338546\pi$
$37$	5.90943	0.971505	0.485753	+	0.874096i	$0.338546\pi$
$38$	20.8695	3.38549
$39$	4.84210	0.775357
$40$	11.3862	1.80031
$41$	−0.0918199	−0.0143399	−0.00716993	−	0.999974i	$-0.502282\pi$
$41$	−0.0918199	−0.0143399	−0.00716993	+	0.999974i	$0.502282\pi$
$42$	−0.969887	−0.149657
$43$	−2.47241	−0.377040	−0.188520	−	0.982069i	$-0.560369\pi$
$43$	−2.47241	−0.377040	−0.188520	+	0.982069i	$0.560369\pi$
$44$	−19.1591	−2.88834
$45$	−2.56069	−0.381725
$46$	−12.0894	−1.78248
$47$	−3.90733	−0.569942	−0.284971	−	0.958536i	$-0.591984\pi$
$47$	−3.90733	−0.569942	−0.284971	+	0.958536i	$0.591984\pi$
$48$	−3.06552	−0.442470
$49$	−6.83892	−0.976989
$50$	−3.76299	−0.532167
$51$	−5.64723	−0.790770
$52$	−18.5936	−2.57847
$53$	−12.3754	−1.69989	−0.849946	−	0.526870i	$-0.823365\pi$
$53$	−12.3754	−1.69989	−0.849946	+	0.526870i	$0.823365\pi$
$54$	2.41661	0.328858
$55$	12.7762	1.72274
$56$	1.78458	0.238474
$57$	8.63589	1.14385
$58$	−18.2669	−2.39856
$59$	−15.0449	−1.95868	−0.979338	−	0.202233i	$-0.935180\pi$
$59$	−15.0449	−1.95868	−0.979338	+	0.202233i	$0.935180\pi$
$60$	9.83302	1.26944
$61$	0.162345	0.0207862	0.0103931	−	0.999946i	$-0.496692\pi$
$61$	0.162345	0.0207862	0.0103931	+	0.999946i	$0.496692\pi$
$62$	4.03410	0.512331
$63$	−0.401342	−0.0505644
$64$	−9.71943	−1.21493
$65$	12.3991	1.53792
$66$	−12.0573	−1.48415
$67$	−11.4956	−1.40441	−0.702204	−	0.711976i	$-0.747800\pi$
$67$	−11.4956	−1.40441	−0.702204	+	0.711976i	$0.747800\pi$
$68$	21.6853	2.62973
$69$	−5.00262	−0.602245
$70$	−2.48358	−0.296845
$71$	6.11003	0.725127	0.362564	−	0.931959i	$-0.381902\pi$
$71$	6.11003	0.725127	0.362564	+	0.931959i	$0.381902\pi$
$72$	−4.44652	−0.524028
$73$	3.42177	0.400488	0.200244	−	0.979746i	$-0.435827\pi$
$73$	3.42177	0.400488	0.200244	+	0.979746i	$0.435827\pi$
$74$	−14.2808	−1.66011
$75$	−1.55714	−0.179803
$76$	−33.1617	−3.80391
$77$	2.00244	0.228199
$78$	−11.7015	−1.32493
$79$	−13.9251	−1.56669	−0.783346	−	0.621586i	$-0.786489\pi$
$79$	−13.9251	−1.56669	−0.783346	+	0.621586i	$0.786489\pi$
$80$	−7.84985	−0.877640
$81$	1.00000	0.111111
$82$	0.221892	0.0245039
$83$	−5.39865	−0.592579	−0.296289	−	0.955098i	$-0.595749\pi$
$83$	−5.39865	−0.592579	−0.296289	+	0.955098i	$0.595749\pi$
$84$	1.54115	0.168153
$85$	−14.4608	−1.56849
$86$	5.97485	0.644285
$87$	−7.55890	−0.810399
$88$	22.1853	2.36496
$89$	−7.36623	−0.780819	−0.390409	−	0.920641i	$-0.627667\pi$
$89$	−7.36623	−0.780819	−0.390409	+	0.920641i	$0.627667\pi$
$90$	6.18818	0.652292
$91$	1.94334	0.203717
$92$	19.2100	2.00278
$93$	1.66932	0.173101
$94$	9.44247	0.973916
$95$	22.1138	2.26883
$96$	−1.48489	−0.151551
$97$	−13.4274	−1.36335	−0.681674	−	0.731656i	$-0.738748\pi$
$97$	−13.4274	−1.36335	−0.681674	+	0.731656i	$0.738748\pi$
$98$	16.5270	1.66948
$99$	−4.98936	−0.501449
$100$	5.97939	0.597939
$101$	18.8841	1.87904	0.939518	−	0.342500i	$-0.111274\pi$
$101$	18.8841	1.87904	0.939518	+	0.342500i	$0.111274\pi$
$102$	13.6471	1.35127
$103$	9.90598	0.976065	0.488033	−	0.872825i	$-0.337715\pi$
$103$	9.90598	0.976065	0.488033	+	0.872825i	$0.337715\pi$
$104$	21.5305	2.11124
$105$	−1.02771	−0.100295
$106$	29.9065	2.90477
$107$	−7.24927	−0.700813	−0.350407	−	0.936598i	$-0.613957\pi$
$107$	−7.24927	−0.700813	−0.350407	+	0.936598i	$0.613957\pi$
$108$	−3.83999	−0.369503
$109$	−0.758459	−0.0726472	−0.0363236	−	0.999340i	$-0.511565\pi$
$109$	−0.758459	−0.0726472	−0.0363236	+	0.999340i	$0.511565\pi$
$110$	−30.8751	−2.94382
$111$	−5.90943	−0.560899
$112$	−1.23032	−0.116255
$113$	−16.0677	−1.51152	−0.755760	−	0.654848i	$-0.772732\pi$
$113$	−16.0677	−1.51152	−0.755760	+	0.654848i	$0.772732\pi$
$114$	−20.8695	−1.95461
$115$	−12.8102	−1.19455
$116$	29.0261	2.69500
$117$	−4.84210	−0.447652
$118$	36.3575	3.34698
$119$	−2.26647	−0.207767
$120$	−11.3862	−1.03941
$121$	13.8937	1.26306
$122$	−0.392324	−0.0355194
$123$	0.0918199	0.00827912
$124$	−6.41018	−0.575651
$125$	8.81611	0.788536
$126$	0.969887	0.0864044
$127$	−17.5642	−1.55857	−0.779285	−	0.626669i	$-0.784418\pi$
$127$	−17.5642	−1.55857	−0.779285	+	0.626669i	$0.784418\pi$
$128$	20.5183	1.81358
$129$	2.47241	0.217684
$130$	−29.9638	−2.62800
$131$	−20.4327	−1.78521	−0.892606	−	0.450837i	$-0.851126\pi$
$131$	−20.4327	−1.78521	−0.892606	+	0.450837i	$0.851126\pi$
$132$	19.1591	1.66758
$133$	3.46595	0.300536
$134$	27.7803	2.39985
$135$	2.56069	0.220389
$136$	−25.1105	−2.15321
$137$	6.57865	0.562052	0.281026	−	0.959700i	$-0.409325\pi$
$137$	6.57865	0.562052	0.281026	+	0.959700i	$0.409325\pi$
$138$	12.0894	1.02912
$139$	0.786990	0.0667516	0.0333758	−	0.999443i	$-0.489374\pi$
$139$	0.786990	0.0667516	0.0333758	+	0.999443i	$0.489374\pi$
$140$	3.94641	0.333532
$141$	3.90733	0.329056
$142$	−14.7655	−1.23910
$143$	24.1590	2.02028
$144$	3.06552	0.255460
$145$	−19.3560	−1.60743
$146$	−8.26906	−0.684353
$147$	6.83892	0.564065
$148$	22.6921	1.86528
$149$	14.9119	1.22163	0.610816	−	0.791773i	$-0.290842\pi$
$149$	14.9119	1.22163	0.610816	+	0.791773i	$0.290842\pi$
$150$	3.76299	0.307247
$151$	−19.1410	−1.55768	−0.778838	−	0.627225i	$-0.784191\pi$
$151$	−19.1410	−1.55768	−0.778838	+	0.627225i	$0.784191\pi$
$152$	38.3997	3.11463
$153$	5.64723	0.456551
$154$	−4.83911	−0.389947
$155$	4.27462	0.343346
$156$	18.5936	1.48868
$157$	−2.10917	−0.168330	−0.0841651	−	0.996452i	$-0.526822\pi$
$157$	−2.10917	−0.168330	−0.0841651	+	0.996452i	$0.526822\pi$
$158$	33.6514	2.67716
$159$	12.3754	0.981433
$160$	−3.80234	−0.300601
$161$	−2.00776	−0.158234
$162$	−2.41661	−0.189867
$163$	−8.74975	−0.685333	−0.342667	−	0.939457i	$-0.611330\pi$
$163$	−8.74975	−0.685333	−0.342667	+	0.939457i	$0.611330\pi$
$164$	−0.352587	−0.0275324
$165$	−12.7762	−0.994626
$166$	13.0464	1.01260
$167$	−15.3042	−1.18427	−0.592137	−	0.805837i	$-0.701716\pi$
$167$	−15.3042	−1.18427	−0.592137	+	0.805837i	$0.701716\pi$
$168$	−1.78458	−0.137683
$169$	10.4459	0.803535
$170$	34.9461	2.68024
$171$	−8.63589	−0.660403
$172$	−9.49403	−0.723913
$173$	5.79986	0.440955	0.220478	−	0.975392i	$-0.429238\pi$
$173$	5.79986	0.440955	0.220478	+	0.975392i	$0.429238\pi$
$174$	18.2669	1.38481
$175$	−0.624945	−0.0472414
$176$	−15.2950	−1.15290
$177$	15.0449	1.13084
$178$	17.8013	1.33426
$179$	−20.6795	−1.54566	−0.772830	−	0.634613i	$-0.781160\pi$
$179$	−20.6795	−1.54566	−0.772830	+	0.634613i	$0.781160\pi$
$180$	−9.83302	−0.732910
$181$	−1.92654	−0.143199	−0.0715994	−	0.997433i	$-0.522810\pi$
$181$	−1.92654	−0.143199	−0.0715994	+	0.997433i	$0.522810\pi$
$182$	−4.69629	−0.348112
$183$	−0.162345	−0.0120009
$184$	−22.2443	−1.63987
$185$	−15.1322	−1.11254
$186$	−4.03410	−0.295794
$187$	−28.1761	−2.06044
$188$	−15.0041	−1.09428
$189$	0.401342	0.0291934
$190$	−53.4405	−3.87698
$191$	16.3169	1.18065	0.590325	−	0.807165i	$-0.298999\pi$
$191$	16.3169	1.18065	0.590325	+	0.807165i	$0.298999\pi$
$192$	9.71943	0.701439
$193$	−9.01782	−0.649117	−0.324558	−	0.945866i	$-0.605216\pi$
$193$	−9.01782	−0.649117	−0.324558	+	0.945866i	$0.605216\pi$
$194$	32.4488	2.32969
$195$	−12.3991	−0.887920
$196$	−26.2614	−1.87581
$197$	−24.1827	−1.72295	−0.861474	−	0.507801i	$-0.830458\pi$
$197$	−24.1827	−1.72295	−0.861474	+	0.507801i	$0.830458\pi$
$198$	12.0573	0.856876
$199$	22.2423	1.57672	0.788358	−	0.615217i	$-0.210932\pi$
$199$	22.2423	1.57672	0.788358	+	0.615217i	$0.210932\pi$
$200$	−6.92385	−0.489590
$201$	11.4956	0.810835
$202$	−45.6354	−3.21089
$203$	−3.03371	−0.212925
$204$	−21.6853	−1.51827
$205$	0.235122	0.0164217
$206$	−23.9389	−1.66790
$207$	5.00262	0.347706
$208$	−14.8436	−1.02922
$209$	43.0876	2.98043
$210$	2.48358	0.171383
$211$	−11.2101	−0.771734	−0.385867	−	0.922555i	$-0.626098\pi$
$211$	−11.2101	−0.771734	−0.385867	+	0.922555i	$0.626098\pi$
$212$	−47.5214	−3.26378
$213$	−6.11003	−0.418652
$214$	17.5186	1.19755
$215$	6.33109	0.431777
$216$	4.44652	0.302547
$217$	0.669970	0.0454806
$218$	1.83290	0.124139
$219$	−3.42177	−0.231222
$220$	49.0605	3.30766
$221$	−27.3445	−1.83939
$222$	14.2808	0.958463
$223$	20.1019	1.34613	0.673063	−	0.739585i	$-0.264978\pi$
$223$	20.1019	1.34613	0.673063	+	0.739585i	$0.264978\pi$
$224$	−0.595948	−0.0398185
$225$	1.55714	0.103809
$226$	38.8293	2.58288
$227$	−3.20661	−0.212830	−0.106415	−	0.994322i	$-0.533937\pi$
$227$	−3.20661	−0.212830	−0.106415	+	0.994322i	$0.533937\pi$
$228$	33.1617	2.19619
$229$	−20.6412	−1.36401	−0.682005	−	0.731348i	$-0.738892\pi$
$229$	−20.6412	−1.36401	−0.682005	+	0.731348i	$0.738892\pi$
$230$	30.9571	2.04125
$231$	−2.00244	−0.131751
$232$	−33.6108	−2.20666
$233$	−5.27961	−0.345879	−0.172939	−	0.984932i	$-0.555326\pi$
$233$	−5.27961	−0.345879	−0.172939	+	0.984932i	$0.555326\pi$
$234$	11.7015	0.764948
$235$	10.0055	0.652684
$236$	−57.7721	−3.76064
$237$	13.9251	0.904530
$238$	5.47717	0.355032
$239$	−8.44431	−0.546217	−0.273109	−	0.961983i	$-0.588052\pi$
$239$	−8.44431	−0.546217	−0.273109	+	0.961983i	$0.588052\pi$
$240$	7.84985	0.506706
$241$	−14.8341	−0.955551	−0.477775	−	0.878482i	$-0.658557\pi$
$241$	−14.8341	−0.955551	−0.477775	+	0.878482i	$0.658557\pi$
$242$	−33.5756	−2.15832
$243$	−1.00000	−0.0641500
$244$	0.623403	0.0399093
$245$	17.5124	1.11882
$246$	−0.221892	−0.0141473
$247$	41.8159	2.66068
$248$	7.42269	0.471341
$249$	5.39865	0.342126
$250$	−21.3051	−1.34745
$251$	17.3565	1.09553	0.547767	−	0.836631i	$-0.315478\pi$
$251$	17.3565	1.09553	0.547767	+	0.836631i	$0.315478\pi$
$252$	−1.54115	−0.0970833
$253$	−24.9599	−1.56921
$254$	42.4457	2.66328
$255$	14.4608	0.905571
$256$	−30.1457	−1.88411
$257$	−23.0185	−1.43586	−0.717929	−	0.696117i	$-0.754910\pi$
$257$	−23.0185	−1.43586	−0.717929	+	0.696117i	$0.754910\pi$
$258$	−5.97485	−0.371978
$259$	−2.37171	−0.147371
$260$	47.6125	2.95280
$261$	7.55890	0.467884
$262$	49.3778	3.05057
$263$	−12.9787	−0.800298	−0.400149	−	0.916450i	$-0.631042\pi$
$263$	−12.9787	−0.800298	−0.400149	+	0.916450i	$0.631042\pi$
$264$	−22.1853	−1.36541
$265$	31.6896	1.94667
$266$	−8.37583	−0.513555
$267$	7.36623	0.450806
$268$	−44.1428	−2.69645
$269$	7.02977	0.428613	0.214306	−	0.976767i	$-0.431251\pi$
$269$	7.02977	0.428613	0.214306	+	0.976767i	$0.431251\pi$
$270$	−6.18818	−0.376601
$271$	−28.6918	−1.74290	−0.871451	−	0.490482i	$-0.836821\pi$
$271$	−28.6918	−1.74290	−0.871451	+	0.490482i	$0.836821\pi$
$272$	17.3117	1.04968
$273$	−1.94334	−0.117616
$274$	−15.8980	−0.960433
$275$	−7.76912	−0.468496
$276$	−19.2100	−1.15631
$277$	6.47681	0.389154	0.194577	−	0.980887i	$-0.437667\pi$
$277$	6.47681	0.389154	0.194577	+	0.980887i	$0.437667\pi$
$278$	−1.90184	−0.114065
$279$	−1.66932	−0.0999398
$280$	−4.56975	−0.273095
$281$	6.29451	0.375499	0.187749	−	0.982217i	$-0.439881\pi$
$281$	6.29451	0.375499	0.187749	+	0.982217i	$0.439881\pi$
$282$	−9.44247	−0.562291
$283$	−27.3386	−1.62511	−0.812556	−	0.582883i	$-0.801924\pi$
$283$	−27.3386	−1.62511	−0.812556	+	0.582883i	$0.801924\pi$
$284$	23.4624	1.39224
$285$	−22.1138	−1.30991
$286$	−58.3828	−3.45224
$287$	0.0368512	0.00217526
$288$	1.48489	0.0874978
$289$	14.8912	0.875953
$290$	46.7759	2.74677
$291$	13.4274	0.787129
$292$	13.1395	0.768933
$293$	−1.69511	−0.0990294	−0.0495147	−	0.998773i	$-0.515767\pi$
$293$	−1.69511	−0.0990294	−0.0495147	+	0.998773i	$0.515767\pi$
$294$	−16.5270	−0.963873
$295$	38.5253	2.24303
$296$	−26.2764	−1.52729
$297$	4.98936	0.289512
$298$	−36.0362	−2.08752
$299$	−24.2232	−1.40086
$300$	−5.97939	−0.345220
$301$	0.992284	0.0571943
$302$	46.2564	2.66176
$303$	−18.8841	−1.08486
$304$	−26.4735	−1.51836
$305$	−0.415715	−0.0238038
$306$	−13.6471	−0.780154
$307$	−0.697221	−0.0397925	−0.0198963	−	0.999802i	$-0.506334\pi$
$307$	−0.697221	−0.0397925	−0.0198963	+	0.999802i	$0.506334\pi$
$308$	7.68935	0.438141
$309$	−9.90598	−0.563532
$310$	−10.3301	−0.586709
$311$	9.57651	0.543034	0.271517	−	0.962434i	$-0.412475\pi$
$311$	9.57651	0.543034	0.271517	+	0.962434i	$0.412475\pi$
$312$	−21.5305	−1.21893
$313$	−24.8708	−1.40578	−0.702891	−	0.711298i	$-0.748108\pi$
$313$	−24.8708	−1.40578	−0.702891	+	0.711298i	$0.748108\pi$
$314$	5.09704	0.287643
$315$	1.02771	0.0579051
$316$	−53.4720	−3.00804
$317$	−12.4985	−0.701983	−0.350992	−	0.936379i	$-0.614155\pi$
$317$	−12.4985	−0.701983	−0.350992	+	0.936379i	$0.614155\pi$
$318$	−29.9065	−1.67707
$319$	−37.7141	−2.11158
$320$	24.8885	1.39131
$321$	7.24927	0.404615
$322$	4.85198	0.270390
$323$	−48.7689	−2.71357
$324$	3.83999	0.213333
$325$	−7.53982	−0.418234
$326$	21.1447	1.17110
$327$	0.758459	0.0419429
$328$	0.408279	0.0225434
$329$	1.56818	0.0864563
$330$	30.8751	1.69962
$331$	4.28274	0.235401	0.117700	−	0.993049i	$-0.462448\pi$
$331$	4.28274	0.235401	0.117700	+	0.993049i	$0.462448\pi$
$332$	−20.7307	−1.13775
$333$	5.90943	0.323835
$334$	36.9842	2.02369
$335$	29.4366	1.60829
$336$	1.23032	0.0671196
$337$	−3.02442	−0.164751	−0.0823754	−	0.996601i	$-0.526251\pi$
$337$	−3.02442	−0.164751	−0.0823754	+	0.996601i	$0.526251\pi$
$338$	−25.2437	−1.37308
$339$	16.0677	0.872677
$340$	−55.5293	−3.01150
$341$	8.32886	0.451033
$342$	20.8695	1.12850
$343$	5.55415	0.299896
$344$	10.9936	0.592737
$345$	12.8102	0.689676
$346$	−14.0160	−0.753504
$347$	14.1121	0.757576	0.378788	−	0.925483i	$-0.376341\pi$
$347$	14.1121	0.757576	0.378788	+	0.925483i	$0.376341\pi$
$348$	−29.0261	−1.55596
$349$	29.8426	1.59744	0.798718	−	0.601706i	$-0.205512\pi$
$349$	29.8426	1.59744	0.798718	+	0.601706i	$0.205512\pi$
$350$	1.51025	0.0807261
$351$	4.84210	0.258452
$352$	−7.40863	−0.394882
$353$	21.0991	1.12299	0.561496	−	0.827480i	$-0.310226\pi$
$353$	21.0991	1.12299	0.561496	+	0.827480i	$0.310226\pi$
$354$	−36.3575	−1.93238
$355$	−15.6459	−0.830398
$356$	−28.2862	−1.49917
$357$	2.26647	0.119954
$358$	49.9743	2.64122
$359$	4.06345	0.214461	0.107230	−	0.994234i	$-0.465802\pi$
$359$	4.06345	0.214461	0.107230	+	0.994234i	$0.465802\pi$
$360$	11.3862	0.600104
$361$	55.5786	2.92519
$362$	4.65570	0.244698
$363$	−13.8937	−0.729230
$364$	7.46240	0.391136
$365$	−8.76209	−0.458629
$366$	0.392324	0.0205071
$367$	3.74189	0.195325	0.0976626	−	0.995220i	$-0.468863\pi$
$367$	3.74189	0.195325	0.0976626	+	0.995220i	$0.468863\pi$
$368$	15.3356	0.799425
$369$	−0.0918199	−0.00477995
$370$	36.5687	1.90111
$371$	4.96677	0.257862
$372$	6.41018	0.332352
$373$	−25.7845	−1.33507	−0.667534	−	0.744579i	$-0.732650\pi$
$373$	−25.7845	−1.33507	−0.667534	+	0.744579i	$0.732650\pi$
$374$	68.0904	3.52087
$375$	−8.81611	−0.455262
$376$	17.3740	0.895996
$377$	−36.6010	−1.88505
$378$	−0.969887	−0.0498856
$379$	−2.99548	−0.153867	−0.0769337	−	0.997036i	$-0.524513\pi$
$379$	−2.99548	−0.153867	−0.0769337	+	0.997036i	$0.524513\pi$
$380$	84.9169	4.35614
$381$	17.5642	0.899841
$382$	−39.4316	−2.01749
$383$	7.61907	0.389316	0.194658	−	0.980871i	$-0.437640\pi$
$383$	7.61907	0.389316	0.194658	+	0.980871i	$0.437640\pi$
$384$	−20.5183	−1.04707
$385$	−5.12763	−0.261328
$386$	21.7925	1.10921
$387$	−2.47241	−0.125680
$388$	−51.5611	−2.61762
$389$	−3.11888	−0.158134	−0.0790668	−	0.996869i	$-0.525194\pi$
$389$	−3.11888	−0.158134	−0.0790668	+	0.996869i	$0.525194\pi$
$390$	29.9638	1.51728
$391$	28.2509	1.42871
$392$	30.4094	1.53591
$393$	20.4327	1.03069
$394$	58.4401	2.94417
$395$	35.6578	1.79414
$396$	−19.1591	−0.962780
$397$	29.3495	1.47301	0.736504	−	0.676433i	$-0.236475\pi$
$397$	29.3495	1.47301	0.736504	+	0.676433i	$0.236475\pi$
$398$	−53.7509	−2.69429
$399$	−3.46595	−0.173514
$400$	4.77344	0.238672
$401$	−14.7924	−0.738696	−0.369348	−	0.929291i	$-0.620419\pi$
$401$	−14.7924	−0.738696	−0.369348	+	0.929291i	$0.620419\pi$
$402$	−27.7803	−1.38555
$403$	8.08304	0.402645
$404$	72.5146	3.60773
$405$	−2.56069	−0.127242
$406$	7.33128	0.363845
$407$	−29.4843	−1.46148
$408$	25.1105	1.24316
$409$	21.6125	1.06867	0.534336	−	0.845272i	$-0.320562\pi$
$409$	21.6125	1.06867	0.534336	+	0.845272i	$0.320562\pi$
$410$	−0.568198	−0.0280613
$411$	−6.57865	−0.324501
$412$	38.0388	1.87404
$413$	6.03814	0.297118
$414$	−12.0894	−0.594160
$415$	13.8243	0.678607
$416$	−7.18997	−0.352517
$417$	−0.786990	−0.0385391
$418$	−104.126	−5.09295
$419$	−2.20679	−0.107809	−0.0539045	−	0.998546i	$-0.517167\pi$
$419$	−2.20679	−0.107809	−0.0539045	+	0.998546i	$0.517167\pi$
$420$	−3.94641	−0.192565
$421$	17.8199	0.868487	0.434244	−	0.900795i	$-0.357016\pi$
$421$	17.8199	0.868487	0.434244	+	0.900795i	$0.357016\pi$
$422$	27.0903	1.31874
$423$	−3.90733	−0.189981
$424$	55.0275	2.67237
$425$	8.79351	0.426548
$426$	14.7655	0.715393
$427$	−0.0651559	−0.00315312
$428$	−27.8371	−1.34556
$429$	−24.1590	−1.16641
$430$	−15.2997	−0.737819
$431$	−21.2147	−1.02187	−0.510937	−	0.859618i	$-0.670701\pi$
$431$	−21.2147	−1.02187	−0.510937	+	0.859618i	$0.670701\pi$
$432$	−3.06552	−0.147490
$433$	−15.0290	−0.722247	−0.361123	−	0.932518i	$-0.617607\pi$
$433$	−15.0290	−0.722247	−0.361123	+	0.932518i	$0.617607\pi$
$434$	−1.61905	−0.0777171
$435$	19.3560	0.928050
$436$	−2.91247	−0.139482
$437$	−43.2021	−2.06664
$438$	8.26906	0.395111
$439$	25.6713	1.22523	0.612613	−	0.790383i	$-0.290118\pi$
$439$	25.6713	1.22523	0.612613	+	0.790383i	$0.290118\pi$
$440$	−56.8097	−2.70830
$441$	−6.83892	−0.325663
$442$	66.0808	3.14314
$443$	−21.1947	−1.00699	−0.503495	−	0.863998i	$-0.667953\pi$
$443$	−21.1947	−1.00699	−0.503495	+	0.863998i	$0.667953\pi$
$444$	−22.6921	−1.07692
$445$	18.8626	0.894175
$446$	−48.5785	−2.30026
$447$	−14.9119	−0.705309
$448$	3.90082	0.184296
$449$	−24.1723	−1.14076	−0.570381	−	0.821380i	$-0.693204\pi$
$449$	−24.1723	−1.14076	−0.570381	+	0.821380i	$0.693204\pi$
$450$	−3.76299	−0.177389
$451$	0.458122	0.0215721
$452$	−61.6997	−2.90211
$453$	19.1410	0.899325
$454$	7.74911	0.363684
$455$	−4.97629	−0.233292
$456$	−38.3997	−1.79823
$457$	−23.7157	−1.10937	−0.554687	−	0.832059i	$-0.687162\pi$
$457$	−23.7157	−1.10937	−0.554687	+	0.832059i	$0.687162\pi$
$458$	49.8817	2.33082
$459$	−5.64723	−0.263590
$460$	−49.1909	−2.29354
$461$	35.1913	1.63902	0.819511	−	0.573063i	$-0.194245\pi$
$461$	35.1913	1.63902	0.819511	+	0.573063i	$0.194245\pi$
$462$	4.83911	0.225136
$463$	15.8652	0.737319	0.368660	−	0.929564i	$-0.379817\pi$
$463$	15.8652	0.737319	0.368660	+	0.929564i	$0.379817\pi$
$464$	23.1720	1.07573
$465$	−4.27462	−0.198231
$466$	12.7587	0.591037
$467$	−16.9319	−0.783515	−0.391757	−	0.920069i	$-0.628133\pi$
$467$	−16.9319	−0.783515	−0.391757	+	0.920069i	$0.628133\pi$
$468$	−18.5936	−0.859490
$469$	4.61366	0.213039
$470$	−24.1792	−1.11531
$471$	2.10917	0.0971855
$472$	66.8973	3.07920
$473$	12.3358	0.567199
$474$	−33.6514	−1.54566
$475$	−13.4473	−0.617003
$476$	−8.70322	−0.398912
$477$	−12.3754	−0.566631
$478$	20.4066	0.933375
$479$	−25.1261	−1.14804	−0.574019	−	0.818842i	$-0.694617\pi$
$479$	−25.1261	−1.14804	−0.574019	+	0.818842i	$0.694617\pi$
$480$	3.80234	0.173552
$481$	−28.6141	−1.30469
$482$	35.8483	1.63284
$483$	2.00776	0.0913564
$484$	53.3516	2.42507
$485$	34.3835	1.56127
$486$	2.41661	0.109619
$487$	−26.5781	−1.20437	−0.602184	−	0.798357i	$-0.705703\pi$
$487$	−26.5781	−1.20437	−0.602184	+	0.798357i	$0.705703\pi$
$488$	−0.721871	−0.0326776
$489$	8.74975	0.395677
$490$	−42.3205	−1.91185
$491$	−3.14355	−0.141867	−0.0709333	−	0.997481i	$-0.522598\pi$
$491$	−3.14355	−0.141867	−0.0709333	+	0.997481i	$0.522598\pi$
$492$	0.352587	0.0158958
$493$	42.6869	1.92252
$494$	−101.052	−4.54657
$495$	12.7762	0.574248
$496$	−5.11735	−0.229776
$497$	−2.45221	−0.109997
$498$	−13.0464	−0.584624
$499$	−18.8743	−0.844930	−0.422465	−	0.906379i	$-0.638835\pi$
$499$	−18.8743	−0.844930	−0.422465	+	0.906379i	$0.638835\pi$
$500$	33.8537	1.51398
$501$	15.3042	0.683741
$502$	−41.9439	−1.87205
$503$	12.3649	0.551323	0.275662	−	0.961255i	$-0.411103\pi$
$503$	12.3649	0.551323	0.275662	+	0.961255i	$0.411103\pi$
$504$	1.78458	0.0794914
$505$	−48.3563	−2.15183
$506$	60.3182	2.68147
$507$	−10.4459	−0.463921
$508$	−67.4463	−2.99244
$509$	−33.0976	−1.46703	−0.733513	−	0.679676i	$-0.762121\pi$
$509$	−33.0976	−1.46703	−0.733513	+	0.679676i	$0.762121\pi$
$510$	−34.9461	−1.54744
$511$	−1.37330	−0.0607512
$512$	31.8138	1.40598
$513$	8.63589	0.381284
$514$	55.6268	2.45359
$515$	−25.3662	−1.11777
$516$	9.49403	0.417952
$517$	19.4950	0.857391
$518$	5.73148	0.251827
$519$	−5.79986	−0.254586
$520$	−55.1330	−2.41774
$521$	4.41797	0.193555	0.0967773	−	0.995306i	$-0.469147\pi$
$521$	4.41797	0.193555	0.0967773	+	0.995306i	$0.469147\pi$
$522$	−18.2669	−0.799520
$523$	35.5174	1.55307	0.776534	−	0.630076i	$-0.216976\pi$
$523$	35.5174	1.55307	0.776534	+	0.630076i	$0.216976\pi$
$524$	−78.4613	−3.42760
$525$	0.624945	0.0272749
$526$	31.3643	1.36755
$527$	−9.42705	−0.410649
$528$	15.2950	0.665629
$529$	2.02622	0.0880966
$530$	−76.5812	−3.32648
$531$	−15.0449	−0.652892
$532$	13.3092	0.577027
$533$	0.444601	0.0192578
$534$	−17.8013	−0.770337
$535$	18.5631	0.802554
$536$	51.1153	2.20784
$537$	20.6795	0.892388
$538$	−16.9882	−0.732413
$539$	34.1219	1.46973
$540$	9.83302	0.423146
$541$	−20.4117	−0.877568	−0.438784	−	0.898593i	$-0.644591\pi$
$541$	−20.4117	−0.877568	−0.438784	+	0.898593i	$0.644591\pi$
$542$	69.3368	2.97827
$543$	1.92654	0.0826759
$544$	8.38550	0.359525
$545$	1.94218	0.0831938
$546$	4.69629	0.200983
$547$	−22.4326	−0.959149	−0.479574	−	0.877501i	$-0.659209\pi$
$547$	−22.4326	−0.959149	−0.479574	+	0.877501i	$0.659209\pi$
$548$	25.2619	1.07914
$549$	0.162345	0.00692872
$550$	18.7749	0.800565
$551$	−65.2779	−2.78093
$552$	22.2443	0.946779
$553$	5.58872	0.237656
$554$	−15.6519	−0.664986
$555$	15.1322	0.642328
$556$	3.02203	0.128163
$557$	−12.8955	−0.546401	−0.273201	−	0.961957i	$-0.588082\pi$
$557$	−12.8955	−0.546401	−0.273201	+	0.961957i	$0.588082\pi$
$558$	4.03410	0.170777
$559$	11.9717	0.506348
$560$	3.15048	0.133132
$561$	28.1761	1.18959
$562$	−15.2113	−0.641652
$563$	−29.3553	−1.23718	−0.618588	−	0.785715i	$-0.712295\pi$
$563$	−29.3553	−1.23718	−0.618588	+	0.785715i	$0.712295\pi$
$564$	15.0041	0.631786
$565$	41.1444	1.73096
$566$	66.0667	2.77699
$567$	−0.401342	−0.0168548
$568$	−27.1684	−1.13996
$569$	39.1757	1.64233	0.821165	−	0.570691i	$-0.193325\pi$
$569$	39.1757	1.64233	0.821165	+	0.570691i	$0.193325\pi$
$570$	53.4405	2.23837
$571$	−4.59323	−0.192221	−0.0961104	−	0.995371i	$-0.530640\pi$
$571$	−4.59323	−0.192221	−0.0961104	+	0.995371i	$0.530640\pi$
$572$	92.7702	3.87892
$573$	−16.3169	−0.681649
$574$	−0.0890548	−0.00371708
$575$	7.78977	0.324856
$576$	−9.71943	−0.404976
$577$	0.969139	0.0403458	0.0201729	−	0.999797i	$-0.493578\pi$
$577$	0.969139	0.0403458	0.0201729	+	0.999797i	$0.493578\pi$
$578$	−35.9862	−1.49683
$579$	9.01782	0.374768
$580$	−74.3268	−3.08625
$581$	2.16671	0.0898902
$582$	−32.4488	−1.34505
$583$	61.7453	2.55723
$584$	−15.2150	−0.629600
$585$	12.3991	0.512641
$586$	4.09641	0.169221
$587$	19.2055	0.792695	0.396348	−	0.918100i	$-0.370277\pi$
$587$	19.2055	0.792695	0.396348	+	0.918100i	$0.370277\pi$
$588$	26.2614	1.08300
$589$	14.4161	0.594005
$590$	−93.1004	−3.83288
$591$	24.1827	0.994745
$592$	18.1155	0.744542
$593$	−12.1051	−0.497095	−0.248548	−	0.968620i	$-0.579953\pi$
$593$	−12.1051	−0.497095	−0.248548	+	0.968620i	$0.579953\pi$
$594$	−12.0573	−0.494718
$595$	5.80374	0.237930
$596$	57.2616	2.34552
$597$	−22.2423	−0.910317
$598$	58.5379	2.39379
$599$	−32.3870	−1.32330	−0.661649	−	0.749814i	$-0.730143\pi$
$599$	−32.3870	−1.32330	−0.661649	+	0.749814i	$0.730143\pi$
$600$	6.92385	0.282665
$601$	−0.629851	−0.0256921	−0.0128461	−	0.999917i	$-0.504089\pi$
$601$	−0.629851	−0.0256921	−0.0128461	+	0.999917i	$0.504089\pi$
$602$	−2.39796	−0.0977336
$603$	−11.4956	−0.468136
$604$	−73.5014	−2.99073
$605$	−35.5775	−1.44643
$606$	45.6354	1.85381
$607$	4.58719	0.186188	0.0930942	−	0.995657i	$-0.470324\pi$
$607$	4.58719	0.186188	0.0930942	+	0.995657i	$0.470324\pi$
$608$	−12.8233	−0.520054
$609$	3.03371	0.122932
$610$	1.00462	0.0406759
$611$	18.9197	0.765408
$612$	21.6853	0.876576
$613$	−0.0168585	−0.000680907 0	−0.000340453	−	1.00000i	$-0.500108\pi$
$613$	−0.0168585	−0.000680907 0	−0.000340453		1.00000i	$0.500108\pi$
$614$	1.68491	0.0679974
$615$	−0.235122	−0.00948105
$616$	−8.90390	−0.358748
$617$	8.88512	0.357702	0.178851	−	0.983876i	$-0.442762\pi$
$617$	8.88512	0.357702	0.178851	+	0.983876i	$0.442762\pi$
$618$	23.9389	0.962962
$619$	28.7472	1.15545	0.577723	−	0.816233i	$-0.303941\pi$
$619$	28.7472	1.15545	0.577723	+	0.816233i	$0.303941\pi$
$620$	16.4145	0.659222
$621$	−5.00262	−0.200748
$622$	−23.1427	−0.927936
$623$	2.95638	0.118445
$624$	14.8436	0.594218
$625$	−30.3610	−1.21444
$626$	60.1030	2.40220
$627$	−43.0876	−1.72075
$628$	−8.09919	−0.323193
$629$	33.3719	1.33063
$630$	−2.48358	−0.0989482
$631$	−5.69614	−0.226760	−0.113380	−	0.993552i	$-0.536168\pi$
$631$	−5.69614	−0.226760	−0.113380	+	0.993552i	$0.536168\pi$
$632$	61.9181	2.46297
$633$	11.2101	0.445561
$634$	30.2038	1.19955
$635$	44.9765	1.78484
$636$	47.5214	1.88434
$637$	33.1148	1.31205
$638$	91.1401	3.60827
$639$	6.11003	0.241709
$640$	−52.5409	−2.07686
$641$	−2.47607	−0.0977989	−0.0488994	−	0.998804i	$-0.515571\pi$
$641$	−2.47607	−0.0977989	−0.0488994	+	0.998804i	$0.515571\pi$
$642$	−17.5186	−0.691405
$643$	20.0447	0.790487	0.395243	−	0.918576i	$-0.370660\pi$
$643$	20.0447	0.790487	0.395243	+	0.918576i	$0.370660\pi$
$644$	−7.70979	−0.303808
$645$	−6.33109	−0.249286
$646$	117.855	4.63695
$647$	41.5976	1.63537	0.817684	−	0.575667i	$-0.195258\pi$
$647$	41.5976	1.63537	0.817684	+	0.575667i	$0.195258\pi$
$648$	−4.44652	−0.174676
$649$	75.0643	2.94653
$650$	18.2208	0.714678
$651$	−0.669970	−0.0262582
$652$	−33.5989	−1.31583
$653$	8.73895	0.341982	0.170991	−	0.985273i	$-0.445303\pi$
$653$	8.73895	0.341982	0.170991	+	0.985273i	$0.445303\pi$
$654$	−1.83290	−0.0716719
$655$	52.3218	2.04438
$656$	−0.281476	−0.0109898
$657$	3.42177	0.133496
$658$	−3.78966	−0.147736
$659$	11.3021	0.440267	0.220133	−	0.975470i	$-0.429351\pi$
$659$	11.3021	0.440267	0.220133	+	0.975470i	$0.429351\pi$
$660$	−49.0605	−1.90968
$661$	27.6619	1.07592	0.537961	−	0.842970i	$-0.319195\pi$
$661$	27.6619	1.07592	0.537961	+	0.842970i	$0.319195\pi$
$662$	−10.3497	−0.402252
$663$	27.3445	1.06197
$664$	24.0052	0.931583
$665$	−8.87522	−0.344166
$666$	−14.2808	−0.553369
$667$	37.8143	1.46418
$668$	−58.7679	−2.27380
$669$	−20.1019	−0.777186
$670$	−71.1367	−2.74825
$671$	−0.809998	−0.0312696
$672$	0.595948	0.0229892
$673$	−9.01424	−0.347473	−0.173737	−	0.984792i	$-0.555584\pi$
$673$	−9.01424	−0.347473	−0.173737	+	0.984792i	$0.555584\pi$
$674$	7.30884	0.281526
$675$	−1.55714	−0.0599343
$676$	40.1123	1.54278
$677$	−25.0426	−0.962464	−0.481232	−	0.876593i	$-0.659810\pi$
$677$	−25.0426	−0.962464	−0.481232	+	0.876593i	$0.659810\pi$
$678$	−38.8293	−1.49123
$679$	5.38899	0.206811
$680$	64.3003	2.46580
$681$	3.20661	0.122877
$682$	−20.1276	−0.770724
$683$	38.2601	1.46398	0.731990	−	0.681315i	$-0.238592\pi$
$683$	38.2601	1.46398	0.731990	+	0.681315i	$0.238592\pi$
$684$	−33.1617	−1.26797
$685$	−16.8459	−0.643648
$686$	−13.4222	−0.512461
$687$	20.6412	0.787511
$688$	−7.57923	−0.288956
$689$	59.9229	2.28288
$690$	−30.9571	−1.17852
$691$	−16.9496	−0.644794	−0.322397	−	0.946605i	$-0.604489\pi$
$691$	−16.9496	−0.644794	−0.322397	+	0.946605i	$0.604489\pi$
$692$	22.2714	0.846631
$693$	2.00244	0.0760665
$694$	−34.1033	−1.29454
$695$	−2.01524	−0.0764423
$696$	33.6108	1.27402
$697$	−0.518528	−0.0196406
$698$	−72.1177	−2.72970
$699$	5.27961	0.199693
$700$	−2.39978	−0.0907032
$701$	−25.7032	−0.970798	−0.485399	−	0.874293i	$-0.661326\pi$
$701$	−25.7032	−0.970798	−0.485399	+	0.874293i	$0.661326\pi$
$702$	−11.7015	−0.441643
$703$	−51.0332	−1.92475
$704$	48.4937	1.82768
$705$	−10.0055	−0.376827
$706$	−50.9882	−1.91897
$707$	−7.57898	−0.285037
$708$	57.7721	2.17121
$709$	37.2270	1.39809	0.699044	−	0.715079i	$-0.253609\pi$
$709$	37.2270	1.39809	0.699044	+	0.715079i	$0.253609\pi$
$710$	37.8100	1.41898
$711$	−13.9251	−0.522230
$712$	32.7541	1.22751
$713$	−8.35100	−0.312747
$714$	−5.47717	−0.204978
$715$	−61.8637	−2.31357
$716$	−79.4091	−2.96766
$717$	8.44431	0.315359
$718$	−9.81975	−0.366470
$719$	15.1393	0.564602	0.282301	−	0.959326i	$-0.408902\pi$
$719$	15.1393	0.564602	0.282301	+	0.959326i	$0.408902\pi$
$720$	−7.84985	−0.292547
$721$	−3.97569	−0.148062
$722$	−134.312	−4.99856
$723$	14.8341	0.551687
$724$	−7.39790	−0.274941
$725$	11.7703	0.437136
$726$	33.5756	1.24611
$727$	−49.3848	−1.83158	−0.915790	−	0.401657i	$-0.868435\pi$
$727$	−49.3848	−1.83158	−0.915790	+	0.401657i	$0.868435\pi$
$728$	−8.64111	−0.320261
$729$	1.00000	0.0370370
$730$	21.1745	0.783704
$731$	−13.9623	−0.516414
$732$	−0.623403	−0.0230416
$733$	0.943966	0.0348662	0.0174331	−	0.999848i	$-0.494451\pi$
$733$	0.943966	0.0348662	0.0174331	+	0.999848i	$0.494451\pi$
$734$	−9.04268	−0.333771
$735$	−17.5124	−0.645954
$736$	7.42833	0.273812
$737$	57.3555	2.11272
$738$	0.221892	0.00816797
$739$	−23.4053	−0.860976	−0.430488	−	0.902596i	$-0.641659\pi$
$739$	−23.4053	−0.860976	−0.430488	+	0.902596i	$0.641659\pi$
$740$	−58.1076	−2.13608
$741$	−41.8159	−1.53614
$742$	−12.0027	−0.440634
$743$	28.3685	1.04074	0.520369	−	0.853942i	$-0.325794\pi$
$743$	28.3685	1.04074	0.520369	+	0.853942i	$0.325794\pi$
$744$	−7.42269	−0.272129
$745$	−38.1848	−1.39898
$746$	62.3109	2.28136
$747$	−5.39865	−0.197526
$748$	−108.196	−3.95603
$749$	2.90944	0.106309
$750$	21.3051	0.777951
$751$	8.22747	0.300224	0.150112	−	0.988669i	$-0.452036\pi$
$751$	8.22747	0.300224	0.150112	+	0.988669i	$0.452036\pi$
$752$	−11.9780	−0.436792
$753$	−17.3565	−0.632507
$754$	88.4502	3.22116
$755$	49.0143	1.78381
$756$	1.54115	0.0560511
$757$	−15.0409	−0.546672	−0.273336	−	0.961919i	$-0.588127\pi$
$757$	−15.0409	−0.546672	−0.273336	+	0.961919i	$0.588127\pi$
$758$	7.23889	0.262928
$759$	24.9599	0.905986
$760$	−98.3297	−3.56679
$761$	52.9011	1.91766	0.958832	−	0.283974i	$-0.0916528\pi$
$761$	52.9011	1.91766	0.958832	+	0.283974i	$0.0916528\pi$
$762$	−42.4457	−1.53765
$763$	0.304402	0.0110201
$764$	62.6567	2.26684
$765$	−14.4608	−0.522832
$766$	−18.4123	−0.665263
$767$	72.8488	2.63042
$768$	30.1457	1.08779
$769$	−7.00511	−0.252611	−0.126305	−	0.991991i	$-0.540312\pi$
$769$	−7.00511	−0.252611	−0.126305	+	0.991991i	$0.540312\pi$
$770$	12.3915	0.446558
$771$	23.0185	0.828993
$772$	−34.6283	−1.24630
$773$	−16.6597	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$773$	−16.6597	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$774$	5.97485	0.214762
$775$	−2.59937	−0.0933720
$776$	59.7053	2.14330
$777$	2.37171	0.0850845
$778$	7.53711	0.270219
$779$	0.792946	0.0284103
$780$	−47.6125	−1.70480
$781$	−30.4851	−1.09084
$782$	−68.2714	−2.44138
$783$	−7.55890	−0.270133
$784$	−20.9649	−0.748745
$785$	5.40094	0.192768
$786$	−49.3778	−1.76125
$787$	−39.4462	−1.40611	−0.703053	−	0.711137i	$-0.748180\pi$
$787$	−39.4462	−1.40611	−0.703053	+	0.711137i	$0.748180\pi$
$788$	−92.8614	−3.30805
$789$	12.9787	0.462052
$790$	−86.1708	−3.06582
$791$	6.44864	0.229287
$792$	22.1853	0.788320
$793$	−0.786091	−0.0279149
$794$	−70.9262	−2.51708
$795$	−31.6896	−1.12391
$796$	85.4101	3.02728
$797$	19.1514	0.678378	0.339189	−	0.940718i	$-0.389847\pi$
$797$	19.1514	0.678378	0.339189	+	0.940718i	$0.389847\pi$
$798$	8.37583	0.296501
$799$	−22.0656	−0.780623
$800$	2.31217	0.0817477
$801$	−7.36623	−0.260273
$802$	35.7474	1.26228
$803$	−17.0724	−0.602473
$804$	44.1428	1.55680
$805$	5.14126	0.181206
$806$	−19.5335	−0.688039
$807$	−7.02977	−0.247460
$808$	−83.9684	−2.95400
$809$	14.2159	0.499805	0.249903	−	0.968271i	$-0.419601\pi$
$809$	14.2159	0.499805	0.249903	+	0.968271i	$0.419601\pi$
$810$	6.18818	0.217431
$811$	43.2752	1.51960	0.759799	−	0.650158i	$-0.225297\pi$
$811$	43.2752	1.51960	0.759799	+	0.650158i	$0.225297\pi$
$812$	−11.6494	−0.408814
$813$	28.6918	1.00627
$814$	71.2519	2.49738
$815$	22.4054	0.784827
$816$	−17.3117	−0.606031
$817$	21.3515	0.746994
$818$	−52.2290	−1.82614
$819$	1.94334	0.0679058
$820$	0.902866	0.0315295
$821$	−52.8661	−1.84504	−0.922520	−	0.385949i	$-0.873874\pi$
$821$	−52.8661	−1.84504	−0.922520	+	0.385949i	$0.873874\pi$
$822$	15.8980	0.554506
$823$	33.0985	1.15374	0.576870	−	0.816836i	$-0.304274\pi$
$823$	33.0985	1.15374	0.576870	+	0.816836i	$0.304274\pi$
$824$	−44.0472	−1.53446
$825$	7.76912	0.270486
$826$	−14.5918	−0.507714
$827$	17.4542	0.606941	0.303470	−	0.952841i	$-0.401855\pi$
$827$	17.4542	0.606941	0.303470	+	0.952841i	$0.401855\pi$
$828$	19.2100	0.667594
$829$	8.29924	0.288244	0.144122	−	0.989560i	$-0.453964\pi$
$829$	8.29924	0.288244	0.144122	+	0.989560i	$0.453964\pi$
$830$	−33.4078	−1.15960
$831$	−6.47681	−0.224678
$832$	47.0625	1.63160
$833$	−38.6210	−1.33814
$834$	1.90184	0.0658555
$835$	39.1893	1.35620
$836$	165.456	5.72240
$837$	1.66932	0.0577003
$838$	5.33295	0.184224
$839$	−9.58460	−0.330897	−0.165449	−	0.986218i	$-0.552907\pi$
$839$	−9.58460	−0.330897	−0.165449	+	0.986218i	$0.552907\pi$
$840$	4.56975	0.157671
$841$	28.1370	0.970242
$842$	−43.0636	−1.48407
$843$	−6.29451	−0.216794
$844$	−43.0465	−1.48172
$845$	−26.7488	−0.920188
$846$	9.44247	0.324639
$847$	−5.57613	−0.191598
$848$	−37.9370	−1.30276
$849$	27.3386	0.938259
$850$	−21.2505	−0.728885
$851$	29.5627	1.01340
$852$	−23.4624	−0.803810
$853$	4.98229	0.170590	0.0852952	−	0.996356i	$-0.472817\pi$
$853$	4.98229	0.170590	0.0852952	+	0.996356i	$0.472817\pi$
$854$	0.157456	0.00538804
$855$	22.1138	0.756278
$856$	32.2340	1.10174
$857$	−18.0372	−0.616139	−0.308070	−	0.951364i	$-0.599683\pi$
$857$	−18.0372	−0.616139	−0.308070	+	0.951364i	$0.599683\pi$
$858$	58.3828	1.99315
$859$	−20.9368	−0.714355	−0.357177	−	0.934037i	$-0.616261\pi$
$859$	−20.9368	−0.714355	−0.357177	+	0.934037i	$0.616261\pi$
$860$	24.3113	0.829008
$861$	−0.0368512	−0.00125589
$862$	51.2675	1.74618
$863$	1.62782	0.0554116	0.0277058	−	0.999616i	$-0.491180\pi$
$863$	1.62782	0.0554116	0.0277058	+	0.999616i	$0.491180\pi$
$864$	−1.48489	−0.0505169
$865$	−14.8517	−0.504971
$866$	36.3191	1.23417
$867$	−14.8912	−0.505732
$868$	2.57268	0.0873223
$869$	69.4771	2.35685
$870$	−46.7759	−1.58585
$871$	55.6627	1.88606
$872$	3.37250	0.114207
$873$	−13.4274	−0.454449
$874$	104.402	3.53147
$875$	−3.53828	−0.119616
$876$	−13.1395	−0.443944
$877$	−44.4906	−1.50234	−0.751170	−	0.660109i	$-0.770510\pi$
$877$	−44.4906	−1.50234	−0.751170	+	0.660109i	$0.770510\pi$
$878$	−62.0375	−2.09367
$879$	1.69511	0.0571746
$880$	39.1657	1.32028
$881$	42.5308	1.43290	0.716450	−	0.697639i	$-0.245766\pi$
$881$	42.5308	1.43290	0.716450	+	0.697639i	$0.245766\pi$
$882$	16.5270	0.556493
$883$	13.8164	0.464958	0.232479	−	0.972601i	$-0.425316\pi$
$883$	13.8164	0.464958	0.232479	+	0.972601i	$0.425316\pi$
$884$	−105.002	−3.53161
$885$	−38.5253	−1.29501
$886$	51.2193	1.72074
$887$	−0.838770	−0.0281631	−0.0140816	−	0.999901i	$-0.504482\pi$
$887$	−0.838770	−0.0281631	−0.0140816	+	0.999901i	$0.504482\pi$
$888$	26.2764	0.881779
$889$	7.04926	0.236424
$890$	−45.5836	−1.52796
$891$	−4.98936	−0.167150
$892$	77.1912	2.58455
$893$	33.7432	1.12917
$894$	36.0362	1.20523
$895$	52.9539	1.77005
$896$	−8.23485	−0.275107
$897$	24.2232	0.808789
$898$	58.4150	1.94933
$899$	−12.6183	−0.420842
$900$	5.97939	0.199313
$901$	−69.8867	−2.32826
$902$	−1.10710	−0.0368624
$903$	−0.992284	−0.0330212
$904$	71.4453	2.37624
$905$	4.93328	0.163988
$906$	−46.2564	−1.53677
$907$	−13.1612	−0.437011	−0.218505	−	0.975836i	$-0.570118\pi$
$907$	−13.1612	−0.437011	−0.218505	+	0.975836i	$0.570118\pi$
$908$	−12.3133	−0.408632
$909$	18.8841	0.626345
$910$	12.0257	0.398650
$911$	32.6437	1.08153	0.540766	−	0.841173i	$-0.318134\pi$
$911$	32.6437	1.08153	0.540766	+	0.841173i	$0.318134\pi$
$912$	26.4735	0.876625
$913$	26.9358	0.891445
$914$	57.3115	1.89570
$915$	0.415715	0.0137431
$916$	−79.2620	−2.61889
$917$	8.20051	0.270805
$918$	13.6471	0.450422
$919$	−32.3804	−1.06813	−0.534065	−	0.845444i	$-0.679336\pi$
$919$	−32.3804	−1.06813	−0.534065	+	0.845444i	$0.679336\pi$
$920$	56.9607	1.87794
$921$	0.697221	0.0229742
$922$	−85.0435	−2.80076
$923$	−29.5854	−0.973815
$924$	−7.68935	−0.252961
$925$	9.20181	0.302554
$926$	−38.3400	−1.25993
$927$	9.90598	0.325355
$928$	11.2241	0.368450
$929$	24.4703	0.802845	0.401423	−	0.915893i	$-0.368516\pi$
$929$	24.4703	0.802845	0.401423	+	0.915893i	$0.368516\pi$
$930$	10.3301	0.338737
$931$	59.0602	1.93562
$932$	−20.2736	−0.664084
$933$	−9.57651	−0.313521
$934$	40.9177	1.33887
$935$	72.1502	2.35956
$936$	21.5305	0.703747
$937$	−50.2671	−1.64215	−0.821077	−	0.570817i	$-0.806627\pi$
$937$	−50.2671	−1.64215	−0.821077	+	0.570817i	$0.806627\pi$
$938$	−11.1494	−0.364041
$939$	24.8708	0.811629
$940$	38.4208	1.25315
$941$	−25.1996	−0.821483	−0.410741	−	0.911752i	$-0.634730\pi$
$941$	−25.1996	−0.821483	−0.410741	+	0.911752i	$0.634730\pi$
$942$	−5.09704	−0.166070
$943$	−0.459340	−0.0149582
$944$	−46.1204	−1.50109
$945$	−1.02771	−0.0334315
$946$	−29.8107	−0.969229
$947$	−30.9512	−1.00578	−0.502889	−	0.864351i	$-0.667729\pi$
$947$	−30.9512	−1.00578	−0.502889	+	0.864351i	$0.667729\pi$
$948$	53.4720	1.73669
$949$	−16.5685	−0.537838
$950$	32.4968	1.05433
$951$	12.4985	0.405290
$952$	10.0779	0.326627
$953$	36.1051	1.16956	0.584779	−	0.811193i	$-0.301181\pi$
$953$	36.1051	1.16956	0.584779	+	0.811193i	$0.301181\pi$
$954$	29.9065	0.968258
$955$	−41.7826	−1.35205
$956$	−32.4260	−1.04873
$957$	37.7141	1.21912
$958$	60.7198	1.96177
$959$	−2.64029	−0.0852594
$960$	−24.8885	−0.803271
$961$	−28.2134	−0.910108
$962$	69.1490	2.22945
$963$	−7.24927	−0.233604
$964$	−56.9629	−1.83465
$965$	23.0918	0.743353
$966$	−4.85198	−0.156110
$967$	28.8919	0.929102	0.464551	−	0.885546i	$-0.346216\pi$
$967$	28.8919	0.929102	0.464551	+	0.885546i	$0.346216\pi$
$968$	−61.7787	−1.98564
$969$	48.7689	1.56668
$970$	−83.0913	−2.66790
$971$	29.1342	0.934962	0.467481	−	0.884003i	$-0.345162\pi$
$971$	29.1342	0.934962	0.467481	+	0.884003i	$0.345162\pi$
$972$	−3.83999	−0.123168
$973$	−0.315852	−0.0101258
$974$	64.2288	2.05802
$975$	7.53982	0.241468
$976$	0.497672	0.0159301
$977$	32.4585	1.03844	0.519220	−	0.854641i	$-0.326223\pi$
$977$	32.4585	1.03844	0.519220	+	0.854641i	$0.326223\pi$
$978$	−21.1447	−0.676133
$979$	36.7528	1.17462
$980$	67.2473	2.14813
$981$	−0.758459	−0.0242157
$982$	7.59673	0.242422
$983$	−52.1706	−1.66398	−0.831992	−	0.554788i	$-0.812799\pi$
$983$	−52.1706	−1.66398	−0.831992	+	0.554788i	$0.812799\pi$
$984$	−0.408279	−0.0130155
$985$	61.9245	1.97308
$986$	−103.157	−3.28520
$987$	−1.56818	−0.0499156
$988$	160.572	5.10849
$989$	−12.3685	−0.393297
$990$	−30.8751	−0.981274
$991$	−34.3673	−1.09171	−0.545857	−	0.837878i	$-0.683796\pi$
$991$	−34.3673	−1.09171	−0.545857	+	0.837878i	$0.683796\pi$
$992$	−2.47876	−0.0787006
$993$	−4.28274	−0.135909
$994$	5.92604	0.187962
$995$	−56.9557	−1.80562
$996$	20.7307	0.656879
$997$	19.0828	0.604358	0.302179	−	0.953251i	$-0.402286\pi$
$997$	19.0828	0.604358	0.302179	+	0.953251i	$0.402286\pi$
$998$	45.6117	1.44381
$999$	−5.90943	−0.186966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.10	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.10	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41661 q^{2} -1.00000 q^{3} +3.83999 q^{4} -2.56069 q^{5} +2.41661 q^{6} -0.401342 q^{7} -4.44652 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41661 q^{2} -1.00000 q^{3} +3.83999 q^{4} -2.56069 q^{5} +2.41661 q^{6} -0.401342 q^{7} -4.44652 q^{8} +1.00000 q^{9} +6.18818 q^{10} -4.98936 q^{11} -3.83999 q^{12} -4.84210 q^{13} +0.969887 q^{14} +2.56069 q^{15} +3.06552 q^{16} +5.64723 q^{17} -2.41661 q^{18} -8.63589 q^{19} -9.83302 q^{20} +0.401342 q^{21} +12.0573 q^{22} +5.00262 q^{23} +4.44652 q^{24} +1.55714 q^{25} +11.7015 q^{26} -1.00000 q^{27} -1.54115 q^{28} +7.55890 q^{29} -6.18818 q^{30} -1.66932 q^{31} +1.48489 q^{32} +4.98936 q^{33} -13.6471 q^{34} +1.02771 q^{35} +3.83999 q^{36} +5.90943 q^{37} +20.8695 q^{38} +4.84210 q^{39} +11.3862 q^{40} -0.0918199 q^{41} -0.969887 q^{42} -2.47241 q^{43} -19.1591 q^{44} -2.56069 q^{45} -12.0894 q^{46} -3.90733 q^{47} -3.06552 q^{48} -6.83892 q^{49} -3.76299 q^{50} -5.64723 q^{51} -18.5936 q^{52} -12.3754 q^{53} +2.41661 q^{54} +12.7762 q^{55} +1.78458 q^{56} +8.63589 q^{57} -18.2669 q^{58} -15.0449 q^{59} +9.83302 q^{60} +0.162345 q^{61} +4.03410 q^{62} -0.401342 q^{63} -9.71943 q^{64} +12.3991 q^{65} -12.0573 q^{66} -11.4956 q^{67} +21.6853 q^{68} -5.00262 q^{69} -2.48358 q^{70} +6.11003 q^{71} -4.44652 q^{72} +3.42177 q^{73} -14.2808 q^{74} -1.55714 q^{75} -33.1617 q^{76} +2.00244 q^{77} -11.7015 q^{78} -13.9251 q^{79} -7.84985 q^{80} +1.00000 q^{81} +0.221892 q^{82} -5.39865 q^{83} +1.54115 q^{84} -14.4608 q^{85} +5.97485 q^{86} -7.55890 q^{87} +22.1853 q^{88} -7.36623 q^{89} +6.18818 q^{90} +1.94334 q^{91} +19.2100 q^{92} +1.66932 q^{93} +9.44247 q^{94} +22.1138 q^{95} -1.48489 q^{96} -13.4274 q^{97} +16.5270 q^{98} -4.98936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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