LMFDB - Embedded newform 8031.2.a.d.1.5

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:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.69638 q^{2} +1.00000 q^{3} +5.27048 q^{4} +2.40729 q^{5} -2.69638 q^{6} -4.24108 q^{7} -8.81846 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69638 q^{2} +1.00000 q^{3} +5.27048 q^{4} +2.40729 q^{5} -2.69638 q^{6} -4.24108 q^{7} -8.81846 q^{8} +1.00000 q^{9} -6.49098 q^{10} +3.78017 q^{11} +5.27048 q^{12} +3.64908 q^{13} +11.4356 q^{14} +2.40729 q^{15} +13.2370 q^{16} -5.08369 q^{17} -2.69638 q^{18} +2.16486 q^{19} +12.6876 q^{20} -4.24108 q^{21} -10.1928 q^{22} +1.83889 q^{23} -8.81846 q^{24} +0.795056 q^{25} -9.83932 q^{26} +1.00000 q^{27} -22.3525 q^{28} +9.20544 q^{29} -6.49098 q^{30} -8.00898 q^{31} -18.0550 q^{32} +3.78017 q^{33} +13.7076 q^{34} -10.2095 q^{35} +5.27048 q^{36} -8.98528 q^{37} -5.83729 q^{38} +3.64908 q^{39} -21.2286 q^{40} -0.388888 q^{41} +11.4356 q^{42} +10.0997 q^{43} +19.9233 q^{44} +2.40729 q^{45} -4.95834 q^{46} -13.2980 q^{47} +13.2370 q^{48} +10.9868 q^{49} -2.14377 q^{50} -5.08369 q^{51} +19.2324 q^{52} -7.16363 q^{53} -2.69638 q^{54} +9.09997 q^{55} +37.3998 q^{56} +2.16486 q^{57} -24.8214 q^{58} +6.72465 q^{59} +12.6876 q^{60} +15.5166 q^{61} +21.5953 q^{62} -4.24108 q^{63} +22.2093 q^{64} +8.78441 q^{65} -10.1928 q^{66} +0.322757 q^{67} -26.7935 q^{68} +1.83889 q^{69} +27.5288 q^{70} +10.2835 q^{71} -8.81846 q^{72} +13.7837 q^{73} +24.2278 q^{74} +0.795056 q^{75} +11.4098 q^{76} -16.0320 q^{77} -9.83932 q^{78} +1.45819 q^{79} +31.8653 q^{80} +1.00000 q^{81} +1.04859 q^{82} -4.01818 q^{83} -22.3525 q^{84} -12.2379 q^{85} -27.2327 q^{86} +9.20544 q^{87} -33.3352 q^{88} +12.7037 q^{89} -6.49098 q^{90} -15.4761 q^{91} +9.69182 q^{92} -8.00898 q^{93} +35.8564 q^{94} +5.21145 q^{95} -18.0550 q^{96} +3.54418 q^{97} -29.6246 q^{98} +3.78017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) $ 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * 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 $

$2$	−2.69638	−1.90663	−0.953315	−	0.301977i	$-0.902353\pi$
$2$	−2.69638	−1.90663	−0.953315	+	0.301977i	$0.902353\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.27048	2.63524
$5$	2.40729	1.07657	0.538287	−	0.842762i	$-0.319072\pi$
$5$	2.40729	1.07657	0.538287	+	0.842762i	$0.319072\pi$
$6$	−2.69638	−1.10079
$7$	−4.24108	−1.60298	−0.801489	−	0.598009i	$-0.795959\pi$
$7$	−4.24108	−1.60298	−0.801489	+	0.598009i	$0.795959\pi$
$8$	−8.81846	−3.11780
$9$	1.00000	0.333333
$10$	−6.49098	−2.05263
$11$	3.78017	1.13976	0.569882	−	0.821727i	$-0.306989\pi$
$11$	3.78017	1.13976	0.569882	+	0.821727i	$0.306989\pi$
$12$	5.27048	1.52146
$13$	3.64908	1.01207	0.506037	−	0.862512i	$-0.331110\pi$
$13$	3.64908	1.01207	0.506037	+	0.862512i	$0.331110\pi$
$14$	11.4356	3.05629
$15$	2.40729	0.621560
$16$	13.2370	3.30924
$17$	−5.08369	−1.23297	−0.616487	−	0.787365i	$-0.711445\pi$
$17$	−5.08369	−1.23297	−0.616487	+	0.787365i	$0.711445\pi$
$18$	−2.69638	−0.635543
$19$	2.16486	0.496653	0.248326	−	0.968676i	$-0.420119\pi$
$19$	2.16486	0.496653	0.248326	+	0.968676i	$0.420119\pi$
$20$	12.6876	2.83703
$21$	−4.24108	−0.925480
$22$	−10.1928	−2.17311
$23$	1.83889	0.383435	0.191717	−	0.981450i	$-0.438594\pi$
$23$	1.83889	0.383435	0.191717	+	0.981450i	$0.438594\pi$
$24$	−8.81846	−1.80006
$25$	0.795056	0.159011
$26$	−9.83932	−1.92965
$27$	1.00000	0.192450
$28$	−22.3525	−4.22423
$29$	9.20544	1.70941	0.854703	−	0.519117i	$-0.173739\pi$
$29$	9.20544	1.70941	0.854703	+	0.519117i	$0.173739\pi$
$30$	−6.49098	−1.18509
$31$	−8.00898	−1.43845	−0.719227	−	0.694775i	$-0.755504\pi$
$31$	−8.00898	−1.43845	−0.719227	+	0.694775i	$0.755504\pi$
$32$	−18.0550	−3.19171
$33$	3.78017	0.658043
$34$	13.7076	2.35083
$35$	−10.2095	−1.72572
$36$	5.27048	0.878413
$37$	−8.98528	−1.47717	−0.738586	−	0.674160i	$-0.764506\pi$
$37$	−8.98528	−1.47717	−0.738586	+	0.674160i	$0.764506\pi$
$38$	−5.83729	−0.946933
$39$	3.64908	0.584321
$40$	−21.2286	−3.35654
$41$	−0.388888	−0.0607341	−0.0303670	−	0.999539i	$-0.509668\pi$
$41$	−0.388888	−0.0607341	−0.0303670	+	0.999539i	$0.509668\pi$
$42$	11.4356	1.76455
$43$	10.0997	1.54019	0.770097	−	0.637926i	$-0.220208\pi$
$43$	10.0997	1.54019	0.770097	+	0.637926i	$0.220208\pi$
$44$	19.9233	3.00355
$45$	2.40729	0.358858
$46$	−4.95834	−0.731068
$47$	−13.2980	−1.93971	−0.969853	−	0.243691i	$-0.921642\pi$
$47$	−13.2980	−1.93971	−0.969853	+	0.243691i	$0.921642\pi$
$48$	13.2370	1.91059
$49$	10.9868	1.56954
$50$	−2.14377	−0.303175
$51$	−5.08369	−0.711858
$52$	19.2324	2.66705
$53$	−7.16363	−0.984001	−0.492000	−	0.870595i	$-0.663734\pi$
$53$	−7.16363	−0.984001	−0.492000	+	0.870595i	$0.663734\pi$
$54$	−2.69638	−0.366931
$55$	9.09997	1.22704
$56$	37.3998	4.99776
$57$	2.16486	0.286743
$58$	−24.8214	−3.25921
$59$	6.72465	0.875475	0.437737	−	0.899103i	$-0.355780\pi$
$59$	6.72465	0.875475	0.437737	+	0.899103i	$0.355780\pi$
$60$	12.6876	1.63796
$61$	15.5166	1.98670	0.993351	−	0.115126i	$-0.0367271\pi$
$61$	15.5166	1.98670	0.993351	+	0.115126i	$0.0367271\pi$
$62$	21.5953	2.74260
$63$	−4.24108	−0.534326
$64$	22.2093	2.77617
$65$	8.78441	1.08957
$66$	−10.1928	−1.25464
$67$	0.322757	0.0394310	0.0197155	−	0.999806i	$-0.493724\pi$
$67$	0.322757	0.0394310	0.0197155	+	0.999806i	$0.493724\pi$
$68$	−26.7935	−3.24918
$69$	1.83889	0.221376
$70$	27.5288	3.29032
$71$	10.2835	1.22043	0.610216	−	0.792235i	$-0.291083\pi$
$71$	10.2835	1.22043	0.610216	+	0.792235i	$0.291083\pi$
$72$	−8.81846	−1.03927
$73$	13.7837	1.61326	0.806630	−	0.591057i	$-0.201289\pi$
$73$	13.7837	1.61326	0.806630	+	0.591057i	$0.201289\pi$
$74$	24.2278	2.81642
$75$	0.795056	0.0918051
$76$	11.4098	1.30880
$77$	−16.0320	−1.82702
$78$	−9.83932	−1.11408
$79$	1.45819	0.164059	0.0820297	−	0.996630i	$-0.473860\pi$
$79$	1.45819	0.164059	0.0820297	+	0.996630i	$0.473860\pi$
$80$	31.8653	3.56265
$81$	1.00000	0.111111
$82$	1.04859	0.115797
$83$	−4.01818	−0.441053	−0.220526	−	0.975381i	$-0.570777\pi$
$83$	−4.01818	−0.441053	−0.220526	+	0.975381i	$0.570777\pi$
$84$	−22.3525	−2.43886
$85$	−12.2379	−1.32739
$86$	−27.2327	−2.93658
$87$	9.20544	0.986927
$88$	−33.3352	−3.55355
$89$	12.7037	1.34659	0.673295	−	0.739374i	$-0.264878\pi$
$89$	12.7037	1.34659	0.673295	+	0.739374i	$0.264878\pi$
$90$	−6.49098	−0.684209
$91$	−15.4761	−1.62233
$92$	9.69182	1.01044
$93$	−8.00898	−0.830492
$94$	35.8564	3.69830
$95$	5.21145	0.534683
$96$	−18.0550	−1.84273
$97$	3.54418	0.359857	0.179928	−	0.983680i	$-0.442413\pi$
$97$	3.54418	0.359857	0.179928	+	0.983680i	$0.442413\pi$
$98$	−29.6246	−2.99253
$99$	3.78017	0.379921
$100$	4.19032	0.419032
$101$	−3.23707	−0.322100	−0.161050	−	0.986946i	$-0.551488\pi$
$101$	−3.23707	−0.322100	−0.161050	+	0.986946i	$0.551488\pi$
$102$	13.7076	1.35725
$103$	−5.65405	−0.557110	−0.278555	−	0.960420i	$-0.589856\pi$
$103$	−5.65405	−0.557110	−0.278555	+	0.960420i	$0.589856\pi$
$104$	−32.1793	−3.15544
$105$	−10.2095	−0.996348
$106$	19.3159	1.87613
$107$	−12.6179	−1.21982	−0.609909	−	0.792472i	$-0.708794\pi$
$107$	−12.6179	−1.21982	−0.609909	+	0.792472i	$0.708794\pi$
$108$	5.27048	0.507152
$109$	−6.44380	−0.617204	−0.308602	−	0.951191i	$-0.599861\pi$
$109$	−6.44380	−0.617204	−0.308602	+	0.951191i	$0.599861\pi$
$110$	−24.5370	−2.33951
$111$	−8.98528	−0.852845
$112$	−56.1391	−5.30465
$113$	−0.752924	−0.0708292	−0.0354146	−	0.999373i	$-0.511275\pi$
$113$	−0.752924	−0.0708292	−0.0354146	+	0.999373i	$0.511275\pi$
$114$	−5.83729	−0.546712
$115$	4.42674	0.412796
$116$	48.5171	4.50470
$117$	3.64908	0.337358
$118$	−18.1322	−1.66921
$119$	21.5603	1.97643
$120$	−21.2286	−1.93790
$121$	3.28966	0.299060
$122$	−41.8388	−3.78791
$123$	−0.388888	−0.0350648
$124$	−42.2111	−3.79067
$125$	−10.1225	−0.905387
$126$	11.4356	1.01876
$127$	16.0712	1.42608	0.713042	−	0.701121i	$-0.247317\pi$
$127$	16.0712	1.42608	0.713042	+	0.701121i	$0.247317\pi$
$128$	−23.7747	−2.10141
$129$	10.0997	0.889232
$130$	−23.6861	−2.07741
$131$	−16.5484	−1.44584	−0.722919	−	0.690932i	$-0.757200\pi$
$131$	−16.5484	−1.44584	−0.722919	+	0.690932i	$0.757200\pi$
$132$	19.9233	1.73410
$133$	−9.18135	−0.796124
$134$	−0.870276	−0.0751804
$135$	2.40729	0.207187
$136$	44.8303	3.84416
$137$	15.0841	1.28872	0.644359	−	0.764723i	$-0.277124\pi$
$137$	15.0841	1.28872	0.644359	+	0.764723i	$0.277124\pi$
$138$	−4.95834	−0.422082
$139$	19.0099	1.61240	0.806201	−	0.591642i	$-0.201520\pi$
$139$	19.0099	1.61240	0.806201	+	0.591642i	$0.201520\pi$
$140$	−53.8091	−4.54770
$141$	−13.2980	−1.11989
$142$	−27.7284	−2.32691
$143$	13.7941	1.15352
$144$	13.2370	1.10308
$145$	22.1602	1.84030
$146$	−37.1661	−3.07589
$147$	10.9868	0.906175
$148$	−47.3567	−3.89270
$149$	−3.29712	−0.270110	−0.135055	−	0.990838i	$-0.543121\pi$
$149$	−3.29712	−0.270110	−0.135055	+	0.990838i	$0.543121\pi$
$150$	−2.14377	−0.175038
$151$	5.97685	0.486389	0.243194	−	0.969978i	$-0.421805\pi$
$151$	5.97685	0.486389	0.243194	+	0.969978i	$0.421805\pi$
$152$	−19.0907	−1.54846
$153$	−5.08369	−0.410992
$154$	43.2284	3.48344
$155$	−19.2799	−1.54860
$156$	19.2324	1.53982
$157$	3.32139	0.265076	0.132538	−	0.991178i	$-0.457687\pi$
$157$	3.32139	0.265076	0.132538	+	0.991178i	$0.457687\pi$
$158$	−3.93184	−0.312801
$159$	−7.16363	−0.568113
$160$	−43.4637	−3.43611
$161$	−7.79887	−0.614637
$162$	−2.69638	−0.211848
$163$	−9.69839	−0.759636	−0.379818	−	0.925061i	$-0.624013\pi$
$163$	−9.69839	−0.759636	−0.379818	+	0.925061i	$0.624013\pi$
$164$	−2.04963	−0.160049
$165$	9.09997	0.708431
$166$	10.8345	0.840924
$167$	3.75991	0.290950	0.145475	−	0.989362i	$-0.453529\pi$
$167$	3.75991	0.290950	0.145475	+	0.989362i	$0.453529\pi$
$168$	37.3998	2.88546
$169$	0.315800	0.0242923
$170$	32.9981	2.53084
$171$	2.16486	0.165551
$172$	53.2304	4.05878
$173$	11.2780	0.857452	0.428726	−	0.903434i	$-0.358963\pi$
$173$	11.2780	0.857452	0.428726	+	0.903434i	$0.358963\pi$
$174$	−24.8214	−1.88170
$175$	−3.37190	−0.254891
$176$	50.0380	3.77175
$177$	6.72465	0.505456
$178$	−34.2540	−2.56745
$179$	−6.59508	−0.492939	−0.246470	−	0.969151i	$-0.579271\pi$
$179$	−6.59508	−0.492939	−0.246470	+	0.969151i	$0.579271\pi$
$180$	12.6876	0.945676
$181$	3.79534	0.282105	0.141053	−	0.990002i	$-0.454951\pi$
$181$	3.79534	0.282105	0.141053	+	0.990002i	$0.454951\pi$
$182$	41.7294	3.09319
$183$	15.5166	1.14702
$184$	−16.2162	−1.19547
$185$	−21.6302	−1.59028
$186$	21.5953	1.58344
$187$	−19.2172	−1.40530
$188$	−70.0866	−5.11159
$189$	−4.24108	−0.308493
$190$	−14.0521	−1.01944
$191$	−9.82359	−0.710810	−0.355405	−	0.934712i	$-0.615657\pi$
$191$	−9.82359	−0.710810	−0.355405	+	0.934712i	$0.615657\pi$
$192$	22.2093	1.60282
$193$	19.7889	1.42443	0.712217	−	0.701959i	$-0.247691\pi$
$193$	19.7889	1.42443	0.712217	+	0.701959i	$0.247691\pi$
$194$	−9.55646	−0.686114
$195$	8.78441	0.629064
$196$	57.9056	4.13611
$197$	25.4975	1.81662	0.908311	−	0.418295i	$-0.137372\pi$
$197$	25.4975	1.81662	0.908311	+	0.418295i	$0.137372\pi$
$198$	−10.1928	−0.724369
$199$	7.42383	0.526261	0.263131	−	0.964760i	$-0.415245\pi$
$199$	7.42383	0.526261	0.263131	+	0.964760i	$0.415245\pi$
$200$	−7.01116	−0.495764
$201$	0.322757	0.0227655
$202$	8.72837	0.614126
$203$	−39.0410	−2.74014
$204$	−26.7935	−1.87592
$205$	−0.936167	−0.0653847
$206$	15.2455	1.06220
$207$	1.83889	0.127812
$208$	48.3028	3.34920
$209$	8.18353	0.566067
$210$	27.5288	1.89967
$211$	25.6179	1.76361	0.881804	−	0.471616i	$-0.156329\pi$
$211$	25.6179	1.76361	0.881804	+	0.471616i	$0.156329\pi$
$212$	−37.7558	−2.59308
$213$	10.2835	0.704617
$214$	34.0227	2.32574
$215$	24.3130	1.65813
$216$	−8.81846	−0.600020
$217$	33.9667	2.30581
$218$	17.3750	1.17678
$219$	13.7837	0.931416
$220$	47.9612	3.23354
$221$	−18.5508	−1.24786
$222$	24.2278	1.62606
$223$	3.55287	0.237918	0.118959	−	0.992899i	$-0.462044\pi$
$223$	3.55287	0.237918	0.118959	+	0.992899i	$0.462044\pi$
$224$	76.5729	5.11624
$225$	0.795056	0.0530037
$226$	2.03017	0.135045
$227$	−18.2803	−1.21331	−0.606654	−	0.794966i	$-0.707489\pi$
$227$	−18.2803	−1.21331	−0.606654	+	0.794966i	$0.707489\pi$
$228$	11.4098	0.755635
$229$	−11.8978	−0.786226	−0.393113	−	0.919490i	$-0.628602\pi$
$229$	−11.8978	−0.786226	−0.393113	+	0.919490i	$0.628602\pi$
$230$	−11.9362	−0.787049
$231$	−16.0320	−1.05483
$232$	−81.1778	−5.32958
$233$	3.72331	0.243922	0.121961	−	0.992535i	$-0.461082\pi$
$233$	3.72331	0.243922	0.121961	+	0.992535i	$0.461082\pi$
$234$	−9.83932	−0.643216
$235$	−32.0121	−2.08824
$236$	35.4421	2.30709
$237$	1.45819	0.0947197
$238$	−58.1349	−3.76833
$239$	−25.0528	−1.62053	−0.810266	−	0.586062i	$-0.800678\pi$
$239$	−25.0528	−1.62053	−0.810266	+	0.586062i	$0.800678\pi$
$240$	31.8653	2.05689
$241$	13.1251	0.845463	0.422731	−	0.906255i	$-0.361071\pi$
$241$	13.1251	0.845463	0.422731	+	0.906255i	$0.361071\pi$
$242$	−8.87019	−0.570197
$243$	1.00000	0.0641500
$244$	81.7801	5.23543
$245$	26.4484	1.68973
$246$	1.04859	0.0668557
$247$	7.89975	0.502649
$248$	70.6268	4.48481
$249$	−4.01818	−0.254642
$250$	27.2942	1.72624
$251$	5.81205	0.366854	0.183427	−	0.983033i	$-0.441281\pi$
$251$	5.81205	0.366854	0.183427	+	0.983033i	$0.441281\pi$
$252$	−22.3525	−1.40808
$253$	6.95130	0.437025
$254$	−43.3340	−2.71902
$255$	−12.2379	−0.766368
$256$	19.6872	1.23045
$257$	23.6174	1.47321	0.736607	−	0.676321i	$-0.236427\pi$
$257$	23.6174	1.47321	0.736607	+	0.676321i	$0.236427\pi$
$258$	−27.2327	−1.69544
$259$	38.1073	2.36787
$260$	46.2980	2.87128
$261$	9.20544	0.569802
$262$	44.6208	2.75668
$263$	3.98662	0.245825	0.122913	−	0.992417i	$-0.460777\pi$
$263$	3.98662	0.245825	0.122913	+	0.992417i	$0.460777\pi$
$264$	−33.3352	−2.05164
$265$	−17.2450	−1.05935
$266$	24.7564	1.51791
$267$	12.7037	0.777454
$268$	1.70108	0.103910
$269$	−21.0747	−1.28495	−0.642474	−	0.766307i	$-0.722092\pi$
$269$	−21.0747	−1.28495	−0.642474	+	0.766307i	$0.722092\pi$
$270$	−6.49098	−0.395028
$271$	20.9692	1.27379	0.636894	−	0.770951i	$-0.280219\pi$
$271$	20.9692	1.27379	0.636894	+	0.770951i	$0.280219\pi$
$272$	−67.2926	−4.08022
$273$	−15.4761	−0.936654
$274$	−40.6724	−2.45711
$275$	3.00544	0.181235
$276$	9.69182	0.583379
$277$	22.5421	1.35443	0.677213	−	0.735787i	$-0.263188\pi$
$277$	22.5421	1.35443	0.677213	+	0.735787i	$0.263188\pi$
$278$	−51.2580	−3.07425
$279$	−8.00898	−0.479485
$280$	90.0323	5.38046
$281$	−27.7344	−1.65450	−0.827248	−	0.561836i	$-0.810095\pi$
$281$	−27.7344	−1.65450	−0.827248	+	0.561836i	$0.810095\pi$
$282$	35.8564	2.13522
$283$	−11.1909	−0.665232	−0.332616	−	0.943062i	$-0.607931\pi$
$283$	−11.1909	−0.665232	−0.332616	+	0.943062i	$0.607931\pi$
$284$	54.1992	3.21613
$285$	5.21145	0.308700
$286$	−37.1943	−2.19934
$287$	1.64931	0.0973555
$288$	−18.0550	−1.06390
$289$	8.84386	0.520227
$290$	−59.7523	−3.50878
$291$	3.54418	0.207763
$292$	72.6467	4.25132
$293$	13.1520	0.768349	0.384175	−	0.923260i	$-0.374486\pi$
$293$	13.1520	0.768349	0.384175	+	0.923260i	$0.374486\pi$
$294$	−29.6246	−1.72774
$295$	16.1882	0.942513
$296$	79.2363	4.60552
$297$	3.78017	0.219348
$298$	8.89029	0.515001
$299$	6.71025	0.388064
$300$	4.19032	0.241928
$301$	−42.8338	−2.46890
$302$	−16.1159	−0.927364
$303$	−3.23707	−0.185965
$304$	28.6562	1.64355
$305$	37.3531	2.13883
$306$	13.7076	0.783609
$307$	−25.4465	−1.45231	−0.726155	−	0.687531i	$-0.758694\pi$
$307$	−25.4465	−1.45231	−0.726155	+	0.687531i	$0.758694\pi$
$308$	−84.4963	−4.81462
$309$	−5.65405	−0.321648
$310$	51.9861	2.95261
$311$	19.3542	1.09747	0.548737	−	0.835995i	$-0.315109\pi$
$311$	19.3542	1.09747	0.548737	+	0.835995i	$0.315109\pi$
$312$	−32.1793	−1.82179
$313$	25.3117	1.43070	0.715351	−	0.698765i	$-0.246267\pi$
$313$	25.3117	1.43070	0.715351	+	0.698765i	$0.246267\pi$
$314$	−8.95573	−0.505401
$315$	−10.2095	−0.575242
$316$	7.68537	0.432336
$317$	−24.3648	−1.36847	−0.684233	−	0.729264i	$-0.739863\pi$
$317$	−24.3648	−1.36847	−0.684233	+	0.729264i	$0.739863\pi$
$318$	19.3159	1.08318
$319$	34.7981	1.94832
$320$	53.4643	2.98875
$321$	−12.6179	−0.704262
$322$	21.0287	1.17189
$323$	−11.0055	−0.612361
$324$	5.27048	0.292804
$325$	2.90122	0.160931
$326$	26.1506	1.44835
$327$	−6.44380	−0.356343
$328$	3.42939	0.189356
$329$	56.3977	3.10931
$330$	−24.5370	−1.35072
$331$	−5.61480	−0.308617	−0.154309	−	0.988023i	$-0.549315\pi$
$331$	−5.61480	−0.308617	−0.154309	+	0.988023i	$0.549315\pi$
$332$	−21.1777	−1.16228
$333$	−8.98528	−0.492390
$334$	−10.1381	−0.554735
$335$	0.776970	0.0424504
$336$	−56.1391	−3.06264
$337$	5.91211	0.322053	0.161026	−	0.986950i	$-0.448520\pi$
$337$	5.91211	0.322053	0.161026	+	0.986950i	$0.448520\pi$
$338$	−0.851518	−0.0463165
$339$	−0.752924	−0.0408932
$340$	−64.4997	−3.49799
$341$	−30.2753	−1.63950
$342$	−5.83729	−0.315644
$343$	−16.9083	−0.912961
$344$	−89.0641	−4.80201
$345$	4.42674	0.238328
$346$	−30.4099	−1.63484
$347$	37.1073	1.99202	0.996011	−	0.0892321i	$-0.0284413\pi$
$347$	37.1073	1.99202	0.996011	+	0.0892321i	$0.0284413\pi$
$348$	48.5171	2.60079
$349$	−24.3584	−1.30388	−0.651938	−	0.758272i	$-0.726044\pi$
$349$	−24.3584	−1.30388	−0.651938	+	0.758272i	$0.726044\pi$
$350$	9.09192	0.485984
$351$	3.64908	0.194774
$352$	−68.2510	−3.63779
$353$	−1.54690	−0.0823331	−0.0411666	−	0.999152i	$-0.513107\pi$
$353$	−1.54690	−0.0823331	−0.0411666	+	0.999152i	$0.513107\pi$
$354$	−18.1322	−0.963717
$355$	24.7555	1.31389
$356$	66.9546	3.54859
$357$	21.5603	1.14109
$358$	17.7829	0.939853
$359$	−25.3200	−1.33634	−0.668169	−	0.744009i	$-0.732922\pi$
$359$	−25.3200	−1.33634	−0.668169	+	0.744009i	$0.732922\pi$
$360$	−21.2286	−1.11885
$361$	−14.3134	−0.753336
$362$	−10.2337	−0.537870
$363$	3.28966	0.172663
$364$	−81.5662	−4.27523
$365$	33.1814	1.73679
$366$	−41.8388	−2.18695
$367$	30.8510	1.61041	0.805206	−	0.592995i	$-0.202055\pi$
$367$	30.8510	1.61041	0.805206	+	0.592995i	$0.202055\pi$
$368$	24.3413	1.26888
$369$	−0.388888	−0.0202447
$370$	58.3233	3.03208
$371$	30.3816	1.57733
$372$	−42.2111	−2.18854
$373$	−4.32981	−0.224189	−0.112095	−	0.993698i	$-0.535756\pi$
$373$	−4.32981	−0.224189	−0.112095	+	0.993698i	$0.535756\pi$
$374$	51.8169	2.67939
$375$	−10.1225	−0.522725
$376$	117.267	6.04761
$377$	33.5914	1.73005
$378$	11.4356	0.588183
$379$	13.2619	0.681218	0.340609	−	0.940205i	$-0.389367\pi$
$379$	13.2619	0.681218	0.340609	+	0.940205i	$0.389367\pi$
$380$	27.4668	1.40902
$381$	16.0712	0.823351
$382$	26.4882	1.35525
$383$	−9.94425	−0.508128	−0.254064	−	0.967187i	$-0.581767\pi$
$383$	−9.94425	−0.508128	−0.254064	+	0.967187i	$0.581767\pi$
$384$	−23.7747	−1.21325
$385$	−38.5937	−1.96692
$386$	−53.3584	−2.71587
$387$	10.0997	0.513398
$388$	18.6795	0.948308
$389$	−5.67440	−0.287704	−0.143852	−	0.989599i	$-0.545949\pi$
$389$	−5.67440	−0.287704	−0.143852	+	0.989599i	$0.545949\pi$
$390$	−23.6861	−1.19939
$391$	−9.34833	−0.472765
$392$	−96.8865	−4.89351
$393$	−16.5484	−0.834755
$394$	−68.7510	−3.46363
$395$	3.51029	0.176622
$396$	19.9233	1.00118
$397$	21.6142	1.08479	0.542393	−	0.840125i	$-0.317518\pi$
$397$	21.6142	1.08479	0.542393	+	0.840125i	$0.317518\pi$
$398$	−20.0175	−1.00339
$399$	−9.18135	−0.459642
$400$	10.5241	0.526207
$401$	−9.51413	−0.475113	−0.237557	−	0.971374i	$-0.576347\pi$
$401$	−9.51413	−0.475113	−0.237557	+	0.971374i	$0.576347\pi$
$402$	−0.870276	−0.0434054
$403$	−29.2254	−1.45582
$404$	−17.0609	−0.848811
$405$	2.40729	0.119619
$406$	105.270	5.22444
$407$	−33.9659	−1.68363
$408$	44.8303	2.21943
$409$	−14.3312	−0.708632	−0.354316	−	0.935126i	$-0.615286\pi$
$409$	−14.3312	−0.708632	−0.354316	+	0.935126i	$0.615286\pi$
$410$	2.52426	0.124665
$411$	15.0841	0.744042
$412$	−29.7996	−1.46812
$413$	−28.5198	−1.40337
$414$	−4.95834	−0.243689
$415$	−9.67293	−0.474826
$416$	−65.8843	−3.23024
$417$	19.0099	0.930920
$418$	−22.0659	−1.07928
$419$	−10.6550	−0.520532	−0.260266	−	0.965537i	$-0.583810\pi$
$419$	−10.6550	−0.520532	−0.260266	+	0.965537i	$0.583810\pi$
$420$	−53.8091	−2.62561
$421$	27.0979	1.32067	0.660335	−	0.750971i	$-0.270414\pi$
$421$	27.0979	1.32067	0.660335	+	0.750971i	$0.270414\pi$
$422$	−69.0756	−3.36255
$423$	−13.2980	−0.646569
$424$	63.1722	3.06791
$425$	−4.04181	−0.196057
$426$	−27.7284	−1.34344
$427$	−65.8073	−3.18464
$428$	−66.5023	−3.21451
$429$	13.7941	0.665987
$430$	−65.5572	−3.16145
$431$	−3.71714	−0.179048	−0.0895241	−	0.995985i	$-0.528535\pi$
$431$	−3.71714	−0.179048	−0.0895241	+	0.995985i	$0.528535\pi$
$432$	13.2370	0.636864
$433$	6.71313	0.322612	0.161306	−	0.986904i	$-0.448429\pi$
$433$	6.71313	0.322612	0.161306	+	0.986904i	$0.448429\pi$
$434$	−91.5873	−4.39633
$435$	22.1602	1.06250
$436$	−33.9619	−1.62648
$437$	3.98093	0.190434
$438$	−37.1661	−1.77587
$439$	−29.6953	−1.41728	−0.708639	−	0.705571i	$-0.750690\pi$
$439$	−29.6953	−1.41728	−0.708639	+	0.705571i	$0.750690\pi$
$440$	−80.2477	−3.82566
$441$	10.9868	0.523180
$442$	50.0200	2.37921
$443$	14.5265	0.690173	0.345087	−	0.938571i	$-0.387850\pi$
$443$	14.5265	0.690173	0.345087	+	0.938571i	$0.387850\pi$
$444$	−47.3567	−2.24745
$445$	30.5815	1.44970
$446$	−9.57989	−0.453621
$447$	−3.29712	−0.155948
$448$	−94.1916	−4.45013
$449$	−1.13652	−0.0536358	−0.0268179	−	0.999640i	$-0.508537\pi$
$449$	−1.13652	−0.0536358	−0.0268179	+	0.999640i	$0.508537\pi$
$450$	−2.14377	−0.101058
$451$	−1.47006	−0.0692225
$452$	−3.96827	−0.186652
$453$	5.97685	0.280817
$454$	49.2907	2.31333
$455$	−37.2554	−1.74656
$456$	−19.0907	−0.894005
$457$	26.6627	1.24723	0.623613	−	0.781733i	$-0.285664\pi$
$457$	26.6627	1.24723	0.623613	+	0.781733i	$0.285664\pi$
$458$	32.0809	1.49904
$459$	−5.08369	−0.237286
$460$	23.3310	1.08781
$461$	−29.3055	−1.36489	−0.682446	−	0.730936i	$-0.739084\pi$
$461$	−29.3055	−1.36489	−0.682446	+	0.730936i	$0.739084\pi$
$462$	43.2284	2.01117
$463$	−19.5035	−0.906404	−0.453202	−	0.891408i	$-0.649718\pi$
$463$	−19.5035	−0.906404	−0.453202	+	0.891408i	$0.649718\pi$
$464$	121.852	5.65684
$465$	−19.2799	−0.894086
$466$	−10.0395	−0.465069
$467$	26.4692	1.22485	0.612424	−	0.790529i	$-0.290194\pi$
$467$	26.4692	1.22485	0.612424	+	0.790529i	$0.290194\pi$
$468$	19.2324	0.889018
$469$	−1.36884	−0.0632071
$470$	86.3167	3.98149
$471$	3.32139	0.153042
$472$	−59.3010	−2.72955
$473$	38.1787	1.75546
$474$	−3.93184	−0.180596
$475$	1.72118	0.0789733
$476$	113.633	5.20837
$477$	−7.16363	−0.328000
$478$	67.5520	3.08976
$479$	20.5838	0.940498	0.470249	−	0.882534i	$-0.344164\pi$
$479$	20.5838	0.940498	0.470249	+	0.882534i	$0.344164\pi$
$480$	−43.4637	−1.98384
$481$	−32.7880	−1.49501
$482$	−35.3903	−1.61198
$483$	−7.79887	−0.354861
$484$	17.3381	0.788095
$485$	8.53187	0.387412
$486$	−2.69638	−0.122310
$487$	30.3502	1.37530	0.687650	−	0.726043i	$-0.258643\pi$
$487$	30.3502	1.37530	0.687650	+	0.726043i	$0.258643\pi$
$488$	−136.833	−6.19413
$489$	−9.69839	−0.438576
$490$	−71.3150	−3.22168
$491$	−17.9089	−0.808217	−0.404109	−	0.914711i	$-0.632418\pi$
$491$	−17.9089	−0.808217	−0.404109	+	0.914711i	$0.632418\pi$
$492$	−2.04963	−0.0924042
$493$	−46.7976	−2.10766
$494$	−21.3007	−0.958366
$495$	9.09997	0.409013
$496$	−106.015	−4.76020
$497$	−43.6134	−1.95633
$498$	10.8345	0.485508
$499$	18.6991	0.837089	0.418544	−	0.908196i	$-0.362540\pi$
$499$	18.6991	0.837089	0.418544	+	0.908196i	$0.362540\pi$
$500$	−53.3506	−2.38591
$501$	3.75991	0.167980
$502$	−15.6715	−0.699454
$503$	−7.62158	−0.339829	−0.169915	−	0.985459i	$-0.554349\pi$
$503$	−7.62158	−0.339829	−0.169915	+	0.985459i	$0.554349\pi$
$504$	37.3998	1.66592
$505$	−7.79257	−0.346765
$506$	−18.7434	−0.833244
$507$	0.315800	0.0140252
$508$	84.7027	3.75807
$509$	30.1691	1.33722	0.668610	−	0.743613i	$-0.266889\pi$
$509$	30.1691	1.33722	0.668610	+	0.743613i	$0.266889\pi$
$510$	32.9981	1.46118
$511$	−58.4578	−2.58602
$512$	−5.53464	−0.244599
$513$	2.16486	0.0955809
$514$	−63.6816	−2.80887
$515$	−13.6110	−0.599770
$516$	53.2304	2.34334
$517$	−50.2685	−2.21081
$518$	−102.752	−4.51466
$519$	11.2780	0.495050
$520$	−77.4649	−3.39706
$521$	−30.5891	−1.34013	−0.670066	−	0.742302i	$-0.733734\pi$
$521$	−30.5891	−1.34013	−0.670066	+	0.742302i	$0.733734\pi$
$522$	−24.8214	−1.08640
$523$	4.73592	0.207087	0.103544	−	0.994625i	$-0.466982\pi$
$523$	4.73592	0.207087	0.103544	+	0.994625i	$0.466982\pi$
$524$	−87.2179	−3.81013
$525$	−3.37190	−0.147162
$526$	−10.7494	−0.468698
$527$	40.7151	1.77358
$528$	50.0380	2.17762
$529$	−19.6185	−0.852978
$530$	46.4990	2.01979
$531$	6.72465	0.291825
$532$	−48.3901	−2.09798
$533$	−1.41908	−0.0614674
$534$	−34.2540	−1.48232
$535$	−30.3749	−1.31322
$536$	−2.84622	−0.122938
$537$	−6.59508	−0.284599
$538$	56.8255	2.44992
$539$	41.5319	1.78890
$540$	12.6876	0.545986
$541$	−40.8114	−1.75462	−0.877311	−	0.479923i	$-0.840665\pi$
$541$	−40.8114	−1.75462	−0.877311	+	0.479923i	$0.840665\pi$
$542$	−56.5410	−2.42864
$543$	3.79534	0.162873
$544$	91.7861	3.93530
$545$	−15.5121	−0.664466
$546$	41.7294	1.78585
$547$	13.8735	0.593188	0.296594	−	0.955004i	$-0.404149\pi$
$547$	13.8735	0.593188	0.296594	+	0.955004i	$0.404149\pi$
$548$	79.5002	3.39608
$549$	15.5166	0.662234
$550$	−8.10382	−0.345548
$551$	19.9285	0.848982
$552$	−16.2162	−0.690205
$553$	−6.18431	−0.262984
$554$	−60.7822	−2.58239
$555$	−21.6302	−0.918151
$556$	100.191	4.24906
$557$	20.0195	0.848253	0.424127	−	0.905603i	$-0.360581\pi$
$557$	20.0195	0.848253	0.424127	+	0.905603i	$0.360581\pi$
$558$	21.5953	0.914200
$559$	36.8548	1.55879
$560$	−135.143	−5.71084
$561$	−19.2172	−0.811350
$562$	74.7826	3.15451
$563$	−5.76501	−0.242966	−0.121483	−	0.992593i	$-0.538765\pi$
$563$	−5.76501	−0.242966	−0.121483	+	0.992593i	$0.538765\pi$
$564$	−70.0866	−2.95118
$565$	−1.81251	−0.0762528
$566$	30.1750	1.26835
$567$	−4.24108	−0.178109
$568$	−90.6850	−3.80506
$569$	36.0225	1.51014	0.755070	−	0.655644i	$-0.227603\pi$
$569$	36.0225	1.51014	0.755070	+	0.655644i	$0.227603\pi$
$570$	−14.0521	−0.588576
$571$	23.0928	0.966403	0.483201	−	0.875509i	$-0.339474\pi$
$571$	23.0928	0.966403	0.483201	+	0.875509i	$0.339474\pi$
$572$	72.7017	3.03981
$573$	−9.82359	−0.410387
$574$	−4.44716	−0.185621
$575$	1.46202	0.0609704
$576$	22.2093	0.925388
$577$	−4.51097	−0.187794	−0.0938970	−	0.995582i	$-0.529932\pi$
$577$	−4.51097	−0.187794	−0.0938970	+	0.995582i	$0.529932\pi$
$578$	−23.8464	−0.991881
$579$	19.7889	0.822398
$580$	116.795	4.84964
$581$	17.0414	0.706998
$582$	−9.55646	−0.396128
$583$	−27.0797	−1.12153
$584$	−121.551	−5.02981
$585$	8.78441	0.363191
$586$	−35.4629	−1.46496
$587$	2.64931	0.109349	0.0546744	−	0.998504i	$-0.482588\pi$
$587$	2.64931	0.109349	0.0546744	+	0.998504i	$0.482588\pi$
$588$	57.9056	2.38799
$589$	−17.3383	−0.714413
$590$	−43.6496	−1.79702
$591$	25.4975	1.04883
$592$	−118.938	−4.88832
$593$	−0.765312	−0.0314276	−0.0157138	−	0.999877i	$-0.505002\pi$
$593$	−0.765312	−0.0314276	−0.0157138	+	0.999877i	$0.505002\pi$
$594$	−10.1928	−0.418215
$595$	51.9020	2.12778
$596$	−17.3774	−0.711805
$597$	7.42383	0.303837
$598$	−18.0934	−0.739894
$599$	6.83394	0.279227	0.139614	−	0.990206i	$-0.455414\pi$
$599$	6.83394	0.279227	0.139614	+	0.990206i	$0.455414\pi$
$600$	−7.01116	−0.286230
$601$	28.3293	1.15558	0.577788	−	0.816187i	$-0.303916\pi$
$601$	28.3293	1.15558	0.577788	+	0.816187i	$0.303916\pi$
$602$	115.496	4.70728
$603$	0.322757	0.0131437
$604$	31.5008	1.28175
$605$	7.91918	0.321960
$606$	8.72837	0.354566
$607$	−26.0050	−1.05551	−0.527754	−	0.849397i	$-0.676966\pi$
$607$	−26.0050	−1.05551	−0.527754	+	0.849397i	$0.676966\pi$
$608$	−39.0866	−1.58517
$609$	−39.0410	−1.58202
$610$	−100.718	−4.07796
$611$	−48.5253	−1.96312
$612$	−26.7935	−1.08306
$613$	10.2750	0.415004	0.207502	−	0.978235i	$-0.433467\pi$
$613$	10.2750	0.415004	0.207502	+	0.978235i	$0.433467\pi$
$614$	68.6136	2.76902
$615$	−0.936167	−0.0377499
$616$	141.378	5.69626
$617$	−19.6942	−0.792859	−0.396430	−	0.918065i	$-0.629751\pi$
$617$	−19.6942	−0.792859	−0.396430	+	0.918065i	$0.629751\pi$
$618$	15.2455	0.613264
$619$	35.3070	1.41911	0.709555	−	0.704650i	$-0.248896\pi$
$619$	35.3070	1.41911	0.709555	+	0.704650i	$0.248896\pi$
$620$	−101.615	−4.08094
$621$	1.83889	0.0737920
$622$	−52.1862	−2.09248
$623$	−53.8775	−2.15856
$624$	48.3028	1.93366
$625$	−28.3432	−1.13373
$626$	−68.2500	−2.72782
$627$	8.18353	0.326819
$628$	17.5053	0.698538
$629$	45.6784	1.82132
$630$	27.5288	1.09677
$631$	40.7286	1.62138	0.810691	−	0.585475i	$-0.199092\pi$
$631$	40.7286	1.62138	0.810691	+	0.585475i	$0.199092\pi$
$632$	−12.8590	−0.511504
$633$	25.6179	1.01822
$634$	65.6969	2.60916
$635$	38.6880	1.53529
$636$	−37.7558	−1.49711
$637$	40.0917	1.58849
$638$	−93.8290	−3.71472
$639$	10.2835	0.406811
$640$	−57.2328	−2.26232
$641$	−12.0768	−0.477007	−0.238503	−	0.971142i	$-0.576657\pi$
$641$	−12.0768	−0.477007	−0.238503	+	0.971142i	$0.576657\pi$
$642$	34.0227	1.34277
$643$	4.56691	0.180101	0.0900506	−	0.995937i	$-0.471297\pi$
$643$	4.56691	0.180101	0.0900506	+	0.995937i	$0.471297\pi$
$644$	−41.1038	−1.61972
$645$	24.3130	0.957324
$646$	29.6749	1.16755
$647$	−7.02477	−0.276172	−0.138086	−	0.990420i	$-0.544095\pi$
$647$	−7.02477	−0.276172	−0.138086	+	0.990420i	$0.544095\pi$
$648$	−8.81846	−0.346422
$649$	25.4203	0.997834
$650$	−7.82281	−0.306836
$651$	33.9667	1.33126
$652$	−51.1151	−2.00182
$653$	2.20892	0.0864417	0.0432209	−	0.999066i	$-0.486238\pi$
$653$	2.20892	0.0864417	0.0432209	+	0.999066i	$0.486238\pi$
$654$	17.3750	0.679414
$655$	−39.8368	−1.55655
$656$	−5.14770	−0.200984
$657$	13.7837	0.537753
$658$	−152.070	−5.92830
$659$	24.5617	0.956786	0.478393	−	0.878146i	$-0.341219\pi$
$659$	24.5617	0.956786	0.478393	+	0.878146i	$0.341219\pi$
$660$	47.9612	1.86689
$661$	−8.57577	−0.333559	−0.166779	−	0.985994i	$-0.553337\pi$
$661$	−8.57577	−0.333559	−0.166779	+	0.985994i	$0.553337\pi$
$662$	15.1396	0.588419
$663$	−18.5508	−0.720453
$664$	35.4341	1.37511
$665$	−22.1022	−0.857086
$666$	24.2278	0.938807
$667$	16.9278	0.655446
$668$	19.8165	0.766723
$669$	3.55287	0.137362
$670$	−2.09501	−0.0809373
$671$	58.6555	2.26437
$672$	76.5729	2.95386
$673$	41.6747	1.60644	0.803220	−	0.595683i	$-0.203118\pi$
$673$	41.6747	1.60644	0.803220	+	0.595683i	$0.203118\pi$
$674$	−15.9413	−0.614036
$675$	0.795056	0.0306017
$676$	1.66442	0.0640161
$677$	−8.02350	−0.308368	−0.154184	−	0.988042i	$-0.549275\pi$
$677$	−8.02350	−0.308368	−0.154184	+	0.988042i	$0.549275\pi$
$678$	2.03017	0.0779683
$679$	−15.0312	−0.576843
$680$	107.920	4.13853
$681$	−18.2803	−0.700504
$682$	81.6337	3.12592
$683$	36.3872	1.39232	0.696159	−	0.717887i	$-0.254891\pi$
$683$	36.3872	1.39232	0.696159	+	0.717887i	$0.254891\pi$
$684$	11.4098	0.436266
$685$	36.3118	1.38740
$686$	45.5912	1.74068
$687$	−11.8978	−0.453928
$688$	133.690	5.09688
$689$	−26.1407	−0.995881
$690$	−11.9362	−0.454403
$691$	−12.2041	−0.464267	−0.232133	−	0.972684i	$-0.574571\pi$
$691$	−12.2041	−0.464267	−0.232133	+	0.972684i	$0.574571\pi$
$692$	59.4406	2.25959
$693$	−16.0320	−0.609005
$694$	−100.055	−3.79805
$695$	45.7625	1.73587
$696$	−81.1778	−3.07703
$697$	1.97698	0.0748836
$698$	65.6796	2.48601
$699$	3.72331	0.140829
$700$	−17.7715	−0.671700
$701$	37.8804	1.43072	0.715361	−	0.698755i	$-0.246262\pi$
$701$	37.8804	1.43072	0.715361	+	0.698755i	$0.246262\pi$
$702$	−9.83932	−0.371361
$703$	−19.4519	−0.733641
$704$	83.9549	3.16417
$705$	−32.0121	−1.20564
$706$	4.17103	0.156979
$707$	13.7287	0.516320
$708$	35.4421	1.33200
$709$	−34.5650	−1.29812	−0.649059	−	0.760738i	$-0.724837\pi$
$709$	−34.5650	−1.29812	−0.649059	+	0.760738i	$0.724837\pi$
$710$	−66.7503	−2.50509
$711$	1.45819	0.0546865
$712$	−112.027	−4.19839
$713$	−14.7276	−0.551553
$714$	−58.1349	−2.17564
$715$	33.2065	1.24185
$716$	−34.7592	−1.29901
$717$	−25.0528	−0.935615
$718$	68.2724	2.54790
$719$	−40.4582	−1.50884	−0.754418	−	0.656394i	$-0.772081\pi$
$719$	−40.4582	−1.50884	−0.754418	+	0.656394i	$0.772081\pi$
$720$	31.8653	1.18755
$721$	23.9793	0.893036
$722$	38.5944	1.43633
$723$	13.1251	0.488128
$724$	20.0032	0.743414
$725$	7.31884	0.271815
$726$	−8.87019	−0.329204
$727$	−5.53805	−0.205395	−0.102697	−	0.994713i	$-0.532747\pi$
$727$	−5.53805	−0.205395	−0.102697	+	0.994713i	$0.532747\pi$
$728$	136.475	5.05810
$729$	1.00000	0.0370370
$730$	−89.4697	−3.31142
$731$	−51.3439	−1.89902
$732$	81.7801	3.02268
$733$	−34.6022	−1.27806	−0.639031	−	0.769181i	$-0.720664\pi$
$733$	−34.6022	−1.27806	−0.639031	+	0.769181i	$0.720664\pi$
$734$	−83.1862	−3.07046
$735$	26.4484	0.975564
$736$	−33.2012	−1.22381
$737$	1.22008	0.0449420
$738$	1.04859	0.0385992
$739$	46.6287	1.71526	0.857632	−	0.514265i	$-0.171935\pi$
$739$	46.6287	1.71526	0.857632	+	0.514265i	$0.171935\pi$
$740$	−114.001	−4.19078
$741$	7.89975	0.290205
$742$	−81.9203	−3.00739
$743$	36.9121	1.35417	0.677086	−	0.735904i	$-0.263242\pi$
$743$	36.9121	1.35417	0.677086	+	0.735904i	$0.263242\pi$
$744$	70.6268	2.58930
$745$	−7.93712	−0.290794
$746$	11.6748	0.427446
$747$	−4.01818	−0.147018
$748$	−101.284	−3.70330
$749$	53.5135	1.95534
$750$	27.2942	0.996644
$751$	−29.9158	−1.09164	−0.545821	−	0.837902i	$-0.683782\pi$
$751$	−29.9158	−1.09164	−0.545821	+	0.837902i	$0.683782\pi$
$752$	−176.025	−6.41896
$753$	5.81205	0.211803
$754$	−90.5753	−3.29856
$755$	14.3880	0.523634
$756$	−22.3525	−0.812954
$757$	30.3474	1.10299	0.551497	−	0.834177i	$-0.314057\pi$
$757$	30.3474	1.10299	0.551497	+	0.834177i	$0.314057\pi$
$758$	−35.7591	−1.29883
$759$	6.95130	0.252316
$760$	−45.9569	−1.66703
$761$	32.7873	1.18854	0.594269	−	0.804266i	$-0.297441\pi$
$761$	32.7873	1.18854	0.594269	+	0.804266i	$0.297441\pi$
$762$	−43.3340	−1.56982
$763$	27.3287	0.989365
$764$	−51.7750	−1.87315
$765$	−12.2379	−0.442463
$766$	26.8135	0.968811
$767$	24.5388	0.886045
$768$	19.6872	0.710400
$769$	34.1216	1.23046	0.615228	−	0.788349i	$-0.289064\pi$
$769$	34.1216	1.23046	0.615228	+	0.788349i	$0.289064\pi$
$770$	104.063	3.75018
$771$	23.6174	0.850561
$772$	104.297	3.75373
$773$	−4.59027	−0.165100	−0.0825502	−	0.996587i	$-0.526306\pi$
$773$	−4.59027	−0.165100	−0.0825502	+	0.996587i	$0.526306\pi$
$774$	−27.2327	−0.978861
$775$	−6.36758	−0.228730
$776$	−31.2542	−1.12196
$777$	38.1073	1.36709
$778$	15.3004	0.548544
$779$	−0.841888	−0.0301638
$780$	46.2980	1.65773
$781$	38.8735	1.39100
$782$	25.2067	0.901388
$783$	9.20544	0.328976
$784$	145.432	5.19399
$785$	7.99555	0.285374
$786$	44.6208	1.59157
$787$	4.88275	0.174051	0.0870257	−	0.996206i	$-0.472264\pi$
$787$	4.88275	0.174051	0.0870257	+	0.996206i	$0.472264\pi$
$788$	134.384	4.78723
$789$	3.98662	0.141927
$790$	−9.46509	−0.336753
$791$	3.19321	0.113538
$792$	−33.3352	−1.18452
$793$	56.6215	2.01069
$794$	−58.2802	−2.06829
$795$	−17.2450	−0.611616
$796$	39.1271	1.38682
$797$	15.5455	0.550650	0.275325	−	0.961351i	$-0.411215\pi$
$797$	15.5455	0.550650	0.275325	+	0.961351i	$0.411215\pi$
$798$	24.7564	0.876368
$799$	67.6026	2.39161
$800$	−14.3548	−0.507517
$801$	12.7037	0.448863
$802$	25.6537	0.905865
$803$	52.1047	1.83873
$804$	1.70108	0.0599926
$805$	−18.7742	−0.661703
$806$	78.8029	2.77571
$807$	−21.0747	−0.741866
$808$	28.5459	1.00424
$809$	−19.9792	−0.702430	−0.351215	−	0.936295i	$-0.614231\pi$
$809$	−19.9792	−0.702430	−0.351215	+	0.936295i	$0.614231\pi$
$810$	−6.49098	−0.228070
$811$	−14.3893	−0.505278	−0.252639	−	0.967561i	$-0.581298\pi$
$811$	−14.3893	−0.505278	−0.252639	+	0.967561i	$0.581298\pi$
$812$	−205.765	−7.22093
$813$	20.9692	0.735422
$814$	91.5850	3.21005
$815$	−23.3468	−0.817804
$816$	−67.2926	−2.35571
$817$	21.8645	0.764942
$818$	38.6424	1.35110
$819$	−15.4761	−0.540777
$820$	−4.93405	−0.172304
$821$	−22.0529	−0.769651	−0.384826	−	0.922989i	$-0.625738\pi$
$821$	−22.0529	−0.769651	−0.384826	+	0.922989i	$0.625738\pi$
$822$	−40.6724	−1.41861
$823$	−43.6342	−1.52099	−0.760497	−	0.649341i	$-0.775045\pi$
$823$	−43.6342	−1.52099	−0.760497	+	0.649341i	$0.775045\pi$
$824$	49.8600	1.73696
$825$	3.00544	0.104636
$826$	76.9003	2.67570
$827$	−48.6959	−1.69332	−0.846661	−	0.532132i	$-0.821391\pi$
$827$	−48.6959	−1.69332	−0.846661	+	0.532132i	$0.821391\pi$
$828$	9.69182	0.336814
$829$	5.85969	0.203516	0.101758	−	0.994809i	$-0.467553\pi$
$829$	5.85969	0.203516	0.101758	+	0.994809i	$0.467553\pi$
$830$	26.0819	0.905317
$831$	22.5421	0.781978
$832$	81.0436	2.80968
$833$	−55.8534	−1.93520
$834$	−51.2580	−1.77492
$835$	9.05119	0.313229
$836$	43.1311	1.49172
$837$	−8.00898	−0.276831
$838$	28.7300	0.992463
$839$	1.62901	0.0562395	0.0281198	−	0.999605i	$-0.491048\pi$
$839$	1.62901	0.0562395	0.0281198	+	0.999605i	$0.491048\pi$
$840$	90.0323	3.10641
$841$	55.7401	1.92207
$842$	−73.0662	−2.51803
$843$	−27.7344	−0.955224
$844$	135.018	4.64753
$845$	0.760223	0.0261525
$846$	35.8564	1.23277
$847$	−13.9517	−0.479387
$848$	−94.8249	−3.25630
$849$	−11.1909	−0.384072
$850$	10.8983	0.373808
$851$	−16.5229	−0.566399
$852$	54.1992	1.85683
$853$	−23.8268	−0.815815	−0.407908	−	0.913023i	$-0.633741\pi$
$853$	−23.8268	−0.815815	−0.407908	+	0.913023i	$0.633741\pi$
$854$	177.442	6.07193
$855$	5.21145	0.178228
$856$	111.270	3.80314
$857$	48.3243	1.65073	0.825363	−	0.564603i	$-0.190971\pi$
$857$	48.3243	1.65073	0.825363	+	0.564603i	$0.190971\pi$
$858$	−37.1943	−1.26979
$859$	5.49734	0.187567	0.0937835	−	0.995593i	$-0.470104\pi$
$859$	5.49734	0.187567	0.0937835	+	0.995593i	$0.470104\pi$
$860$	128.141	4.36958
$861$	1.64931	0.0562082
$862$	10.0228	0.341379
$863$	45.0300	1.53284	0.766420	−	0.642340i	$-0.222036\pi$
$863$	45.0300	1.53284	0.766420	+	0.642340i	$0.222036\pi$
$864$	−18.0550	−0.614245
$865$	27.1495	0.923111
$866$	−18.1012	−0.615102
$867$	8.84386	0.300353
$868$	179.021	6.07636
$869$	5.51221	0.186989
$870$	−59.7523	−2.02579
$871$	1.17777	0.0399071
$872$	56.8244	1.92432
$873$	3.54418	0.119952
$874$	−10.7341	−0.363087
$875$	42.9305	1.45132
$876$	72.6467	2.45450
$877$	−24.2914	−0.820263	−0.410131	−	0.912026i	$-0.634517\pi$
$877$	−24.2914	−0.820263	−0.410131	+	0.912026i	$0.634517\pi$
$878$	80.0698	2.70223
$879$	13.1520	0.443607
$880$	120.456	4.06057
$881$	14.3883	0.484755	0.242378	−	0.970182i	$-0.422073\pi$
$881$	14.3883	0.484755	0.242378	+	0.970182i	$0.422073\pi$
$882$	−29.6246	−0.997511
$883$	−41.4707	−1.39560	−0.697800	−	0.716293i	$-0.745838\pi$
$883$	−41.4707	−1.39560	−0.697800	+	0.716293i	$0.745838\pi$
$884$	−97.7715	−3.28841
$885$	16.1882	0.544160
$886$	−39.1689	−1.31591
$887$	−41.2987	−1.38667	−0.693337	−	0.720614i	$-0.743860\pi$
$887$	−41.2987	−1.38667	−0.693337	+	0.720614i	$0.743860\pi$
$888$	79.2363	2.65900
$889$	−68.1591	−2.28598
$890$	−82.4595	−2.76405
$891$	3.78017	0.126640
$892$	18.7253	0.626970
$893$	−28.7882	−0.963360
$894$	8.89029	0.297336
$895$	−15.8763	−0.530685
$896$	100.831	3.36852
$897$	6.71025	0.224049
$898$	3.06450	0.102264
$899$	−73.7261	−2.45890
$900$	4.19032	0.139677
$901$	36.4177	1.21325
$902$	3.96385	0.131982
$903$	−42.8338	−1.42542
$904$	6.63963	0.220831
$905$	9.13648	0.303707
$906$	−16.1159	−0.535414
$907$	8.73429	0.290017	0.145009	−	0.989430i	$-0.453679\pi$
$907$	8.73429	0.290017	0.145009	+	0.989430i	$0.453679\pi$
$908$	−96.3460	−3.19736
$909$	−3.23707	−0.107367
$910$	100.455	3.33004
$911$	−19.1196	−0.633461	−0.316730	−	0.948516i	$-0.602585\pi$
$911$	−19.1196	−0.633461	−0.316730	+	0.948516i	$0.602585\pi$
$912$	28.6562	0.948901
$913$	−15.1894	−0.502695
$914$	−71.8927	−2.37800
$915$	37.3531	1.23485
$916$	−62.7069	−2.07189
$917$	70.1831	2.31765
$918$	13.7076	0.452417
$919$	5.91251	0.195036	0.0975179	−	0.995234i	$-0.468910\pi$
$919$	5.91251	0.195036	0.0975179	+	0.995234i	$0.468910\pi$
$920$	−39.0370	−1.28701
$921$	−25.4465	−0.838491
$922$	79.0187	2.60234
$923$	37.5255	1.23517
$924$	−84.4963	−2.77972
$925$	−7.14380	−0.234887
$926$	52.5888	1.72818
$927$	−5.65405	−0.185703
$928$	−166.204	−5.45593
$929$	44.2874	1.45302	0.726511	−	0.687155i	$-0.241141\pi$
$929$	44.2874	1.45302	0.726511	+	0.687155i	$0.241141\pi$
$930$	51.9861	1.70469
$931$	23.7848	0.779517
$932$	19.6236	0.642793
$933$	19.3542	0.633627
$934$	−71.3711	−2.33533
$935$	−46.2614	−1.51291
$936$	−32.1793	−1.05181
$937$	7.83346	0.255908	0.127954	−	0.991780i	$-0.459159\pi$
$937$	7.83346	0.255908	0.127954	+	0.991780i	$0.459159\pi$
$938$	3.69091	0.120513
$939$	25.3117	0.826016
$940$	−168.719	−5.50300
$941$	−17.5168	−0.571032	−0.285516	−	0.958374i	$-0.592165\pi$
$941$	−17.5168	−0.571032	−0.285516	+	0.958374i	$0.592165\pi$
$942$	−8.95573	−0.291794
$943$	−0.715121	−0.0232876
$944$	89.0140	2.89716
$945$	−10.2095	−0.332116
$946$	−102.944	−3.34701
$947$	−48.4121	−1.57318	−0.786590	−	0.617475i	$-0.788156\pi$
$947$	−48.4121	−1.57318	−0.786590	+	0.617475i	$0.788156\pi$
$948$	7.68537	0.249609
$949$	50.2978	1.63274
$950$	−4.64097	−0.150573
$951$	−24.3648	−0.790084
$952$	−190.129	−6.16211
$953$	30.6311	0.992237	0.496119	−	0.868255i	$-0.334758\pi$
$953$	30.6311	0.992237	0.496119	+	0.868255i	$0.334758\pi$
$954$	19.3159	0.625375
$955$	−23.6483	−0.765240
$956$	−132.040	−4.27049
$957$	34.7981	1.12486
$958$	−55.5018	−1.79318
$959$	−63.9728	−2.06579
$960$	53.4643	1.72555
$961$	33.1437	1.06915
$962$	88.4091	2.85042
$963$	−12.6179	−0.406606
$964$	69.1756	2.22800
$965$	47.6376	1.53351
$966$	21.0287	0.676589
$967$	0.0571391	0.00183747	0.000918734	−	1.00000i	$-0.499708\pi$
$967$	0.0571391	0.00183747	0.000918734		1.00000i	$0.499708\pi$
$968$	−29.0097	−0.932409
$969$	−11.0055	−0.353547
$970$	−23.0052	−0.738652
$971$	−47.7803	−1.53334	−0.766671	−	0.642041i	$-0.778088\pi$
$971$	−47.7803	−1.53334	−0.766671	+	0.642041i	$0.778088\pi$
$972$	5.27048	0.169051
$973$	−80.6227	−2.58464
$974$	−81.8358	−2.62219
$975$	2.90122	0.0929135
$976$	205.393	6.57448
$977$	0.273586	0.00875280	0.00437640	−	0.999990i	$-0.498607\pi$
$977$	0.273586	0.00875280	0.00437640	+	0.999990i	$0.498607\pi$
$978$	26.1506	0.836203
$979$	48.0221	1.53479
$980$	139.396	4.45283
$981$	−6.44380	−0.205735
$982$	48.2892	1.54097
$983$	−31.9783	−1.01995	−0.509975	−	0.860189i	$-0.670345\pi$
$983$	−31.9783	−1.01995	−0.509975	+	0.860189i	$0.670345\pi$
$984$	3.42939	0.109325
$985$	61.3799	1.95573
$986$	126.184	4.01852
$987$	56.3977	1.79516
$988$	41.6355	1.32460
$989$	18.5723	0.590564
$990$	−24.5370	−0.779837
$991$	−38.3986	−1.21977	−0.609886	−	0.792490i	$-0.708785\pi$
$991$	−38.3986	−1.21977	−0.609886	+	0.792490i	$0.708785\pi$
$992$	144.602	4.59113
$993$	−5.61480	−0.178180
$994$	117.598	3.72999
$995$	17.8713	0.566559
$996$	−21.1777	−0.671042
$997$	10.9948	0.348210	0.174105	−	0.984727i	$-0.444297\pi$
$997$	10.9948	0.348210	0.174105	+	0.984727i	$0.444297\pi$
$998$	−50.4200	−1.59602
$999$	−8.98528	−0.284282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.5	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.5	✓	132	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)

\(f(q)\)	\(=\)	\(q-2.69638 q^{2} +1.00000 q^{3} +5.27048 q^{4} +2.40729 q^{5} -2.69638 q^{6} -4.24108 q^{7} -8.81846 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69638 q^{2} +1.00000 q^{3} +5.27048 q^{4} +2.40729 q^{5} -2.69638 q^{6} -4.24108 q^{7} -8.81846 q^{8} +1.00000 q^{9} -6.49098 q^{10} +3.78017 q^{11} +5.27048 q^{12} +3.64908 q^{13} +11.4356 q^{14} +2.40729 q^{15} +13.2370 q^{16} -5.08369 q^{17} -2.69638 q^{18} +2.16486 q^{19} +12.6876 q^{20} -4.24108 q^{21} -10.1928 q^{22} +1.83889 q^{23} -8.81846 q^{24} +0.795056 q^{25} -9.83932 q^{26} +1.00000 q^{27} -22.3525 q^{28} +9.20544 q^{29} -6.49098 q^{30} -8.00898 q^{31} -18.0550 q^{32} +3.78017 q^{33} +13.7076 q^{34} -10.2095 q^{35} +5.27048 q^{36} -8.98528 q^{37} -5.83729 q^{38} +3.64908 q^{39} -21.2286 q^{40} -0.388888 q^{41} +11.4356 q^{42} +10.0997 q^{43} +19.9233 q^{44} +2.40729 q^{45} -4.95834 q^{46} -13.2980 q^{47} +13.2370 q^{48} +10.9868 q^{49} -2.14377 q^{50} -5.08369 q^{51} +19.2324 q^{52} -7.16363 q^{53} -2.69638 q^{54} +9.09997 q^{55} +37.3998 q^{56} +2.16486 q^{57} -24.8214 q^{58} +6.72465 q^{59} +12.6876 q^{60} +15.5166 q^{61} +21.5953 q^{62} -4.24108 q^{63} +22.2093 q^{64} +8.78441 q^{65} -10.1928 q^{66} +0.322757 q^{67} -26.7935 q^{68} +1.83889 q^{69} +27.5288 q^{70} +10.2835 q^{71} -8.81846 q^{72} +13.7837 q^{73} +24.2278 q^{74} +0.795056 q^{75} +11.4098 q^{76} -16.0320 q^{77} -9.83932 q^{78} +1.45819 q^{79} +31.8653 q^{80} +1.00000 q^{81} +1.04859 q^{82} -4.01818 q^{83} -22.3525 q^{84} -12.2379 q^{85} -27.2327 q^{86} +9.20544 q^{87} -33.3352 q^{88} +12.7037 q^{89} -6.49098 q^{90} -15.4761 q^{91} +9.69182 q^{92} -8.00898 q^{93} +35.8564 q^{94} +5.21145 q^{95} -18.0550 q^{96} +3.54418 q^{97} -29.6246 q^{98} +3.78017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * q^99

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